The Brusov–Filatova–Orekhova Theory of Capital Structure: Applications in Corporate Finance, Investments, Taxation and Ratings 303127928X, 9783031279287

Citation preview

Peter Brusov Tatiana Filatova Natali Orekhova

The Brusov–Filatova– Orekhova Theory of Capital Structure Applications in Corporate Finance, Investments, Taxation and Ratings

The Brusov–Filatova–Orekhova Theory of Capital Structure

Peter Brusov • Tatiana Filatova • Natali Orekhova

The Brusov–Filatova– Orekhova Theory of Capital Structure Applications in Corporate Finance, Investments, Taxation and Ratings

Peter Brusov Financial University under the Government of Russian Federation Moscow, Russia

Tatiana Filatova Financial University under the Government of Russian Federation Moscow, Russia

Natali Orekhova Financial University under the Government of Russian Federation Moscow, Russia

ISBN 978-3-031-27928-7 ISBN 978-3-031-27929-4 https://doi.org/10.1007/978-3-031-27929-4

(eBook)

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Dedicated to eternal love, which touched us with its wing and gave us happiness, without which life is meaningless

Preface

The monograph is devoted to a comprehensive and detailed description of the modern theory of capital cost and capital structure—Brusov–Filatova–Orekhova (BFO) theory—and its application to the real economy: corporate finance, investments, taxation, business valuation, and rating. The BFO theory has replaced the world-famous theory of capital cost and capital structure by Nobel laureates Modigliani and Miller (MM theory), which turns out to be outdated, eliminating the main drawback of the MM theory—the eternity of companies and cash flows. The BFO theory is valid for arbitrary age (and to arbitrary lifetime) companies and investment projects of arbitrary duration. Results of the modern BFO theory turn out to be quite different from those of the Modigliani–Miller theory. They show that the latter, via its perpetuity, underestimates the assessment of the weighted average cost of capital and the equity cost of the company and substantially overestimates the assessment of the capitalization of the company. Such an incorrect assessment of key performance indicators of financial activities of companies has led to an underestimation of risks involved, and impossibility, or serious difficulties in adequate managerial decision-making, which was one of the implicit reasons of the global financial crisis of the year 2008. Within the BFO theory a lot of qualitatively new results have been obtained, among them: – Qualitatively new effect in corporate finance, discovered by authors: abnormal dependence of equity cost on leverage, which significantly alters the principles of the company’s dividend policy. – Bankruptcy of the world-famous trade-off theory has been proven. – Mechanism of the formation of the company optimal capital structure has been suggested, which is different from the trade-off theory. – Inflation in both Modigliani–Miller as well as in Brusov–Filatova–Orekhova theories has been taken into account in explicit form; its nontrivial impact on the dependence of equity cost on leverage has been detected.

vii

viii

Preface

– Study of the role of taxes and leverage has been done, which allows the regulator to set the tax on profits rate, and businesses to choose the optimal level of debt financing. – Investigation of the influence of tax on profit rate on the effectiveness of investment projects at different debt levels showed that an increase in tax on profit rate on one side leads to a decrease in the project NPV, but on the other side, it leads to a decrease in the sensitivity of the NPV with respect to leverage level. At high leverage level L, the influence of tax on profit rate change on the effectiveness of investment projects becomes significantly less. – Study of the influence of growth of tax on profit rate on the efficiency of the investment as well has led to two qualitatively new effects in investments: 1. The growth of tax on profit rate changes the nature of the NPV dependence on leverage L at some value t*: there is a transition from diminishing function NPV(L) at t < t* to growing function NPV(L) at t > t*. 2. At high leverage levels, the growth of tax on profit rate leads to the growth of the efficiency of the investments. Discovered effects in investments can be applied in a real economic practice for optimizing the management of investments. The well-established BFO theory allows us to conduct a valid assessment of the core parameters of financial activities of companies, such as weighted average cost of capital and equity capital cost of the company, its capitalization. It allows the management of a company to make adequate decisions, which improves the effectiveness of the company management. More generally, the introduction of the new system of evaluation of the parameters of financial activities of companies into the systems of financial reporting (IFRS, GAAP, etc.) would lead to a lower risk of global financial crisis. A few types of BFO theory are described in the monograph: BFO-1 theory (for arbitrary age companies) is applicable for the most interesting case of companies that reached the age of n-years and continue to exist on the market. BFO-2 theory is related to companies with arbitrary lifetime companies. BFO-2 theory allows us to examine the financial status of the companies which ceased to exist, i.e., of those for which n means not age but a lifetime, i.e., the time of existence. BFO-3 theory is the BFO theory used in rating methodology: rating ratios are incorporated into the BFO theory. Over the past couple of years, the BFO authors have obtained very important results related to the generalization of the two main theories of the capital structure (Brusov–Filatova–Orekhova and Modigliani–Miller) to take into account the current financial practice of the company’s functioning and taking into account the real conditions of their work. The BFO and MM theories have been generalized to the case of variable income, arbitrary frequency of income tax payments, advance payments of income tax, etc.,

Preface

ix

as well as to their combinations. These generalizations significantly expand the applicability of both theories in practice, in particular, in corporate finance, taxation, business valuation, investments, ratings, etc. The second part of the monograph is devoted to assessing the effectiveness of investment projects within the modern investment models. The determination of the optimal leverage level for investments is studied in the monograph from two points of view: owners of equity capital and owners of both equity and debt capital. Corporate management in the modern world is the management of financial flows. The proposed Brusov–Filatova–Orekhova theory allows us to correctly identify a discount rate—basic parameters for discounting of financial flows to arbitrary time moment—and compare financial flows with a view to making literate managerial decisions. The discount rate is a key link to the existing financial system, on which modern finance can be adequately built and the proposed monograph can be of assistance. The third part of the monograph suggests a new approach to the rating methodology: rating of non-financial issuers, as well as project rating (for arbitrary duration investment projects). The key factors of a new approach are (1) the adequate use of discounting of financial flows virtually not used in existing rating methodologies and (2) the incorporation of rating parameters (financial “ratios”) into the modern theory of capital structure (Brusov–Filatova–Orekhova (BFO) theory). This makes it possible to use the powerful tool of this theory, which provides the correct discount rate when discounting financial flows. The interplay between rating ratios and leverage level which can be quite important in rating is discussed. All these create a new base for rating methodologies. A new approach to ratings and rating methodologies allows us to issue more correct ratings of issuers, making the rating methodologies more understandable and transparent. This book changes our understanding of corporate finance, investments, taxation, business valuation, and rating procedures. It shows that the most used principles of financial management should be changed in accordance with BFO theory. Many of discoveries made within this theory still require interpretations and understanding as well as incorporation into real finance and economy. But it is clear now that without a very serious modification of the conceptions of financial management, it is impossible to adequately manage manufacture, company finance state, investments, taxation, business valuation, and rating procedures, as well as finance in general. The monograph is intended for graduate students, postgraduate students, teachers of economic and financial institutions, students of MBA program, scientists, financial analysts, financial directors of companies, managers of insurance companies and rating agencies, officials of regional and federal ministries and departments, and ministers responsible for economic and financial management. Kronburg, Moscow, Russia 25 January 2023

Peter Brusov

Contents

1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Part I 2

1 1 4

Corporate Finance

Capital Structure Theory: Past, Present, Future . . . . . . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Basic Theories of Capital Structure . . . . . . . . . . . . . . . . . . . . . 2.2.1 A Historical Point of View . . . . . . . . . . . . . . . . . . . . 2.2.2 The Empirical (Traditional) Approach . . . . . . . . . . . . 2.2.3 The Modigliani–Miller Theory . . . . . . . . . . . . . . . . . 2.2.3.1 The Modigliani–Miller Theory with Taxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3.2 The Modigliani–Miller Theory with Taxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.4 Modifications of Modigliani–Miller Theory . . . . . . . . 2.2.4.1 Hamada Model . . . . . . . . . . . . . . . . . . . . . 2.2.4.2 The Cost of Capital Under Risky Debt . . . . 2.2.4.3 The Account of Corporate and Individual Taxes (Miller Model) . . . . . . . . . . . . . . . . 2.2.4.4 Alternative Expression for WACC . . . . . . . 2.2.4.5 The Miles–Ezzell Model Versus the Modigliani–Miller Theory . . . . . . . . . . . . . 2.3 Trade-Off Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Static Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Dynamic Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3 Proof of the Bankruptcy of the Trade-Off Theory . . . . 2.4 Accounting for Transaction Costs . . . . . . . . . . . . . . . . . . . . . . 2.5 Accounting for Asymmetries of Information . . . . . . . . . . . . . .

9 9 10 10 11 12 12 13 13 13 14 15 16 16 17 17 18 18 20 20 xi

xii

Contents

2.6 2.7 2.8

3

Signaling Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pecking Order Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Behavioral Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8.1 Manager Investment Autonomy . . . . . . . . . . . . . . . . . 2.8.2 The Equity Market Timing Theory . . . . . . . . . . . . . . 2.8.3 Information Cascades . . . . . . . . . . . . . . . . . . . . . . . . 2.9 Theories of Conflict of Interests . . . . . . . . . . . . . . . . . . . . . . . 2.9.1 Theory of Agency Costs . . . . . . . . . . . . . . . . . . . . . . 2.9.2 Theory of Corporate Control and Costs Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.9.3 Theory of Stakeholders . . . . . . . . . . . . . . . . . . . . . . . 2.10 BFO Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.10.1 Brusov–Filatova–Orekhova Theorem . . . . . . . . . . . . . 2.11 BFO Theory and Modigliani–Miller Theory Under Inflation . . . 2.12 BFO Theory for the Companies Ceased to Exist at the Time Moment n (BFO–2 Theory) . . . . . . . . . . . . . . . . . . . . . . . . . . 2.13 The Modigliani–Miller Theory with Advance Payments of Tax on Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.14 The Modigliani–Miller Theory with Arbitrary Frequency of Payment of Tax on Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.15 Generalization of the Modigliani–Miller Theory for the Case of Variable Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.16 The Generalization of the Brusov–Filatova–Orekhova Theory for the Case of Payments of Tax on Profit with Arbitrary Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.17 Benefits of Advance Payments of Tax on Profit: Consideration Within the Brusov–Filatova–Orekhova (BFO) Theory . . . . . . . 2.18 Influence of Method and Frequency of Profit Tax Payments on Company Financial Indicators . . . . . . . . . . . . . . . . . . . . . . . . 2.19 The Brusov–Filatova–Orekhova (BFO) Theory with Variable Income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.20 Qualitatively New Effects in the Theory of Capital Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.20.1 Golden and Silver Ages of the Company . . . . . . . . . . 2.20.2 Silver Age of the Company . . . . . . . . . . . . . . . . . . . . 2.20.3 Anomalous Dependence of the Company’s Equity Value on Leverage . . . . . . . . . . . . . . . . . . . . . . . . . . 2.21 A Stochastic Extension of the Modigliani–Miller Theory . . . . . 2.22 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21 21 21 21 21 22 22 22

Main Theories of Capital Structure . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 The Traditional Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Modigliani–Miller Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Modigliani–Miller Theory Without Taxes . . . . . . . . . 3.2.2 Modigliani–Miller Theory with Taxes . . . . . . . . . . . .

51 51 52 52 55

22 22 23 24 25 27 28 29 30

31 32 32 33 34 34 37 37 38 39 46

Contents

3.2.3 Main Assumptions of Modigliani–Miller Theory . . . . 3.2.4 Modifications of Modigliani–Miller Theory . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Modern Theory of Capital Cost and Capital Structure: Brusov–Filatova–Orekhova Theory (BFO Theory) . . . . . . . . . . . . . 4.1 Companies with Arbitrary Lifetime. Brusov–Filatova–Orekhova Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Comparison of Modigliani–Miller Results (Perpetuity Company) with Myers Results (1-Year Company) and Brusov–Filatova– Orekhova Ones (Company with Arbitrary Lifetime) . . . . . . . . 4.3 Brusov–Filatova–Orekhova Theorem . . . . . . . . . . . . . . . . . . . 4.4 From Modigliani–Miller to General Theory of Capital Cost and Capital Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xiii

57 58 70 73 74

76 78 83 86 87

5

Bankruptcy of the Famous Trade-Off Theory . . . . . . . . . . . . . . . . . 89 5.1 Optimal Capital Structure of the Company . . . . . . . . . . . . . . . 89 5.2 Absence of the Optimal Capital Structure in Modified Modigliani–Miller Theory (MMM Theory) . . . . . . . . . . . . . . . 92 5.3 Analysis of the Trade-Off Theory Within the Brusov– Filatova–Orekhova Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.4 The Causes of Absence of the Optimum Capital Structure in Trade-Off Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

6

New Mechanism of Formation of the Company Optimal Capital Structure, Different from Suggested by Trade-off Theory . . . . . . . . 6.1 Absence of Suggested Mechanism of Formation of the Company Optimal Capital Structure Within Modified Modigliani–Miller Theory (MMM Theory) . . . . . . . . . . . . . . . 6.2 Formation of the Company Optimal Capital Structure Within Brusov–Filatova–Orekhova (BFO Theory) . . . . . . . . . . . . . . . 6.2.1 Decrease of Debt Cost at Exponential Rate . . . . . . . . . 6.3 Simple Model of Proposed Mechanism . . . . . . . . . . . . . . . . . . 6.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

119

119 121 122 129 132 138

7

The Global Causes of the Global Financial Crisis . . . . . . . . . . . . . . 139 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

8

The Role of Taxing and Leverage in Evaluation of Capital Cost and Capitalization of the Company . . . . . . . . . . . . . . . . . . . . . . . . . 145 8.1 The Role of Taxes in Modigliani–Miller Theory . . . . . . . . . . . 146 8.2 The Role of Taxes in Brusov–Filatova–Orekhova Theory . . . . 148

xiv

Contents

8.2.1

Weighted Average Cost of Capital of the Company WACC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.2 Equity Cost ke of the Company . . . . . . . . . . . . . . . . . 8.2.3 Dependence of WACC and ke on Lifetime of Company . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

10

11

A Qualitatively New Effect in Corporate Finance: Abnormal Dependence of Equity Cost of Company on Leverage . . . . . . . . . . . 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Equity Cost in the Modigliani–Miller Theory . . . . . . . . . . . . . 9.3 Cost of Equity Capital Within Brusov–Filatova–Orekhova Theory (BFO Theory) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.1 Dependence of Cost of Equity ke on Tax on Profit Rate T at Different Fix Leverage Level L . . . . . . . . . . 9.3.2 Dependence of Cost of Equity ke on Leverage Level L (the Share of Debt Capital wd) at Different Fix Tax on Profit Rate T . . . . . . . . . . . . . . . . . . . . . . 9.4 Dependence of the Critical Value of Tax on Profit Rate T on Parameters n, k0, kd of the Company . . . . . . . . . . . . . . . . . . . . 9.5 Practical Value of Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.6 Equity Cost of 1-Year Company . . . . . . . . . . . . . . . . . . . . . . 9.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inflation in Brusov–Filatova–Orekhova Theory and in Its Perpetuity Limit: Modigliani–Miller Theory . . . . . . . . . . . . . . . . . . 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Accounting of Inflation in Modigliani–Miller Theory Without Taxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3 Accounting of Inflation in Modigliani–Miller Theory with Corporate Taxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4 Accounting of Inflation in Brusov–Filatova–Orekhova Theory with Corporate Taxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.1 Generalized Brusov–Filatova–Orekhova Theorem . . . 10.5 Generalized Brusov–Filatova–Orekhova Formula Under Existing of Inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.6 Irregular Inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.8 Inflation Rate for a Few Periods . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

149 152 154 159 161 163 163 164 168 168

170 173 177 178 182 182 185 185 186 190 192 192 194 196 198 202 203

Benefits of Advance Payments of Tax on Profit: Consideration Within Brusov–Filatova–Orekhova (BFO) Theory . . . . . . . . . . . . . 205 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 11.2 Modification of the Brusov–Filatova–Orekhova (BFO) Theory for Companies with Frequent Payments of Tax on Income . . . . 208

Contents

xv

11.2.1 11.2.2 11.2.3

Calculation of the Tax Shield . . . . . . . . . . . . . . . . . . Company Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Weighted Average Cost of Capital, WACC . . . . . 11.2.3.1 Calculation of the Equity Cost . . . . . . . . . . 11.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3.1 Dependence of the Weighted Average Cost of Capital, WACC, Capital Value, V, Equity Cost, ke, on Leverage Level L for 3-Year Company . . . . . . . . . 11.3.2 Dependence of the Weighted Average Cost of Capital, WACC, Capital Value, V, Equity Cost, ke, on Leverage Level L for 6-Year Company . . . . . . . . . 11.4 Comparison of Results for 3-Year and 6-Year Companies . . . . 11.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.6 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

The Generalization of the Brusov–Filatova–Orekhova Theory for the Case of Payments of Tax on Profit with Arbitrary Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1.1 Capital Structure of the Company . . . . . . . . . . . . . . . 12.1.2 The Modigliani–Miller Theory . . . . . . . . . . . . . . . . . 12.2 Some Modifications of Modigliani–Miller Theory . . . . . . . . . . 12.2.1 Hamada Model: Accounting Market Risk . . . . . . . . . . 12.2.2 The Account of Corporate and Individual Taxes (Miller Model) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2.3 More General Case for WACC Formula . . . . . . . . . . 12.2.4 Fiscal Pressure, Financial Liquidity, Financial Solvency, and Financial Leverage . . . . . . . . . . . . . . . 12.2.5 Brusov–Filatova–Orekhova (BFO) Theory . . . . . . . . . 12.2.6 Trade-off Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3 Modification of the Brusov–Filatova–Orekhova (BFO) Theory for Companies with Frequent Payments of Tax on Income . . . . 12.3.1 Calculation of the Tax Shield . . . . . . . . . . . . . . . . . . 12.3.2 Derivation of the Modified BFO Formula for Weighted Average Cost of Capital (WACC) . . . . . . . 12.3.3 Formulas for Capital Value, V, and Equity Cost, ke . . . 12.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.4.1 Dependence of the Weighted Average Cost of Capital, WACC, Capital Value, V, Equity Cost, ke, on Leverage Level L at Different Frequency of Payment of Tax on Profit p for 3-year Company . . . 12.4.1.1 Dependence of The Weighted Average Cost of Capital, WACC, on Leverage Level L at Different Frequency of Payment of Tax on Profit p for 3-year Company . . . .

208 208 209 209 210

210

212 214 215 216 216

217 217 217 219 223 223 223 224 225 225 226 227 228 228 229 230

230

230

xvi

Contents

12.4.1.2

Dependence of the Company Value, on Leverage Level L at Different Frequencies of Payment of Tax on Profit p for 3-year Company . . . . . . . . . . . . . . . . . . . . . . . . . 12.4.1.3 Dependence of the Equity Cost, ke, on Leverage Level L at Different Frequency of Payment of Tax on Profit p for 3-year Company . . . . . . . . . . . . . . . . . . . . . . . . . 12.4.2 Dependence of the Weighted Average Cost of Capital, WACC, Capital Value, V, Equity Cost, ke, on Leverage Level L at Different Frequency of Payment of Tax on Profit p for 6-year Company . . . . . . . . . . . . . . . . . . . 12.4.2.1 Dependence of The Weighted Average Cost of Capital, WACC, on Leverage Level L at Different Frequency of Payment of Tax on Profit p for 6-year Company . . . . . . . . . . . 12.4.2.2 Dependence of the Company Value, V, on Leverage Level L at Different Frequency of Payment of Tax on Profit p for 6-year Company . . . . . . . . . . . . . . . . . . . . . . . . . 12.4.2.3 Dependence of the Equity Cost, ke, on Leverage Level L at Different Frequencies of Payment of Tax on Profit p for 6-year Company . . . . . . . . . . . . . . . . . . . . . . . . . 12.5 The Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Influence of Method and Frequency of Profit Tax Payments on Company Financial Indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.1.1 A Literature Review on the Development of the Capital Cost and Capital Structure Theory . . . . . . . . . 13.2 The Modified Brusov–Filatova–Orekhova (BFO) Theory for the Case of Frequent Advance Profit Tax Payments . . . . . . . . . 13.2.1 The Tax Shield Calculation . . . . . . . . . . . . . . . . . . . . 13.2.2 Derivation of the Modified BFO Formula for the Weighted Average Cost of Capital (WACC) . . . . . . . 13.2.3 Formulae for the Capital Value and Equity Cost . . . . . 13.3 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.3.1 The Impact of the Frequency of Profit Tax Payments on the Dependence of the Weighted Average Cost of Capital, Capital Value, and Equity Cost on the Leverage Level of a Three-Year-Old Company . . . . . . 13.3.2 The Impact of the Frequency of Profit Tax Payments on the Dependence of the Weighted Average Cost of Capital, Capital Value, and Equity Cost on the Leverage Level of a Six-Year-Old Company . . . . . . .

231

232

233

233

234

235 236 238 241 241 242 247 247 248 249 250

250

256

Contents

xvii

13.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 14

Generalization of the Brusov–Filatova–Orekhova Theory for the Case of Variable Income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.1.1 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.1.2 Before the Modigliani and Miller Work . . . . . . . . . . . 14.1.3 Modigliani–Miller Theory . . . . . . . . . . . . . . . . . . . . . 14.1.3.1 Modigliani–Miller Theory Without Taxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.1.3.2 Modigliani–Miller Theory with Taxes . . . . 14.1.4 Unification of Capital Asset Pricing Model (CAPM) with Modigliani–Miller Model . . . . . . . . . . . . . . . . . 14.1.4.1 Miller Model . . . . . . . . . . . . . . . . . . . . . . 14.1.5 Brusov–Filatova–Orekhova (BFO) Theory . . . . . . . . . 14.1.6 Alternate WACC Formula . . . . . . . . . . . . . . . . . . . . . 14.1.7 Trade-off Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.1.8 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . 14.2 Modification of the BFO Theory for the Case of Companies with Variable Incomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.2.1 The Levered Company Value, V . . . . . . . . . . . . . . . . 14.2.2 The Unlevered Company Value, V0 . . . . . . . . . . . . . . 14.2.3 The Tax Shield Value . . . . . . . . . . . . . . . . . . . . . . . . 14.3 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.3.1 Calculations for Two-Year Company . . . . . . . . . . . . . 14.3.1.1 Calculations of Weighted Average Cost of Capital, WACC . . . . . . . . . . . . . . . . . . 14.3.1.2 Calculations of the Discount Rate, WACC-g . . . . . . . . . . . . . . . . . . . . . . . . . 14.3.1.3 Calculations of the Company Value, V . . . . 14.3.1.4 Calculations of the Equity Cost, ke . . . . . . . 14.3.2 Calculations for Four-Year Company . . . . . . . . . . . . . 14.3.2.1 Calculations of Weighted Average Cost of Capital, WACC . . . . . . . . . . . . . . . . . . 14.3.2.2 Calculations of the Discount Rate, WACC-g . . . . . . . . . . . . . . . . . . . . . . . . . 14.3.2.3 Calculations of the Company Value, V . . . . 14.3.2.4 Calculations of the Cost of Equity ke . . . . . 14.3.3 Comparison with the Theory of Modigliani and Miller with Variable Income . . . . . . . . . . . . . . . . . . . 14.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

265 265 265 266 266 266 267 268 268 268 269 270 272 272 272 273 274 275 275 275 277 278 278 279 280 282 282 284 286 287 288

xviii

15

Contents

BFO Theory with Variable Profit in Case of Advance Payments of Tax on Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.1.1 Review of Literature . . . . . . . . . . . . . . . . . . . . . . . . . 15.1.2 The Basis of the Traditional Approach (TA) . . . . . . . . 15.1.3 Modigliani–Miller Theory . . . . . . . . . . . . . . . . . . . . . 15.1.3.1 Modigliani–Miller Theory Without Taxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.1.3.2 Modigliani–Miller Theory with Taxes . . . . 15.1.4 Unification of Capital Asset Pricing Model (CAPM) with Modigliani–Miller Model . . . . . . . . . . . . . . . . . 15.1.5 Miller Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.1.6 Brusov–Filatova–Orekhova (BFO) Theory . . . . . . . . . 15.1.7 Alternative Expression for WACC . . . . . . . . . . . . . . . 15.1.8 Trade-off Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.2 Modification of the Brusov–Filatova–Orekhova (BFO) Theory to the Case of Companies with Variable Incomes and Advance Payments of Tax on Profit . . . . . . . . . . . . . . . . . 15.2.1 The Financially Dependent Company Value, V . . . . . 15.2.2 The Value of a Financially Independent Company, V0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.2.3 The Tax Shield Value . . . . . . . . . . . . . . . . . . . . . . . . 15.3 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.3.1 Five-year Company . . . . . . . . . . . . . . . . . . . . . . . . . 15.3.1.1 Weighted Average Cost of Capital, WACC . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.3.1.2 Calculations of the Discount Rate, WACC-g . . . . . . . . . . . . . . . . . . . . . . . . . 15.3.1.3 Calculations of the Company Value, V . . . . 15.3.1.4 Calculations of the Equity Cost, ke . . . . . . . 15.3.2 Study the Dependence of Financial Indicators on kd . . 15.3.2.1 The Weighted Average Cost of Capital, WACC . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.3.2.2 The Discount Rate, WACC-g . . . . . . . . . . 15.3.2.3 The Company Value, V . . . . . . . . . . . . . . . 15.3.3 Impact of Company Age, n, on Main Financial Indicators of the Company . . . . . . . . . . . . . . . . . . . . 15.3.3.1 WACC(L) . . . . . . . . . . . . . . . . . . . . . . . . 15.3.3.2 Discount Rate WACC-g . . . . . . . . . . . . . . 15.3.3.3 Company Value, V . . . . . . . . . . . . . . . . . . 15.3.3.4 Equity Cost, ke . . . . . . . . . . . . . . . . . . . . . 15.3.3.5 Results Summary . . . . . . . . . . . . . . . . . . . 15.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

291 291 291 292 292 292 293 293 294 294 295 295

296 296 297 297 299 299 299 300 300 301 302 302 302 303 304 305 305 306 307 308 312 315

Contents

16

BFO Theory with Variable Profit: Two Types of Payments of Tax on Profit: Advanced Payments and at the Ends of Periods . . . . 16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.1.1 A Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . 16.1.1.1 Methods and Materials . . . . . . . . . . . . . . . 16.2 The Brusov–Filatova–Orekhova (BFO) Theory Modification to the Case of Companies with Variable Incomes and Advance Payments of Tax on Profit . . . . . . . . . . . . . . . . . . . . 16.2.1 The Value of a Financially Dependent Company, V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.2.2 The Value of a Financially Independent Company, V0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.2.3 The Tax Shield Value, TS . . . . . . . . . . . . . . . . . . . . . 16.3 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.3.1 Calculations of the Equity Cost, ke . . . . . . . . . . . . . . . 16.3.2 Study the Dependence of Financial Indicators on kd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.3.2.1 The Weighted Average Cost of Capital, WACC . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.3.2.2 The Discount Rate, WACC–g . . . . . . . . . . 16.3.2.3 The Company Value, V . . . . . . . . . . . . . . . 16.3.3 Impact of Company Age, n, on Main Financial Indicators of the Company . . . . . . . . . . . . . . . . . . . . 16.3.3.1 WACC(L) . . . . . . . . . . . . . . . . . . . . . . . . 16.3.3.2 Discount Rate WACC–g . . . . . . . . . . . . . . 16.3.3.3 Company Value, V . . . . . . . . . . . . . . . . . . 16.3.3.4 Equity Cost, ke . . . . . . . . . . . . . . . . . . . . . 16.3.3.5 Results Summary . . . . . . . . . . . . . . . . . . . 16.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Part II 17

xix

317 317 318 322

322 322 323 324 326 328 329 329 330 331 332 332 334 335 335 337 339 341

Investments

Investment Models with Debt Repayment at the End of the Project and their Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.1 Investment Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.2 The Effectiveness of the Investment Project from the Perspective of the Equity Holders Only . . . . . . . . . . . . . . . . . 17.2.1 With the Division of Credit and Investment Flows . . . 17.3 Without Flows Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.4 Modigliani–Miller Limit (Perpetuity Projects) . . . . . . . . . . . . . 17.4.1 With Flows Separation . . . . . . . . . . . . . . . . . . . . . . . 17.4.2 Without Flows Separation . . . . . . . . . . . . . . . . . . . . . 17.5 The Effectiveness of the Investment Project from the perspective of the Owners of Equity and Debt . . . . . . . . . . . . .

345 345 346 346 348 349 349 350 351

xx

Contents

17.5.1 With Flows Separation . . . . . . . . . . . . . . . . . . . . . . . 17.5.2 Without Flows Separation . . . . . . . . . . . . . . . . . . . . . 17.6 Modigliani–Miller Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.6.1 With Flows Separation . . . . . . . . . . . . . . . . . . . . . . . 17.6.2 Without Flows Separation . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

19

Investment Models with Uniform Debt Repayment and their Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.1 Investment Models with Uniform Debt Repayment . . . . . . . . . 18.2 The Effectiveness of the Investment Project from the Perspective of the Equity Holders Only . . . . . . . . . . . . . . . . . 18.2.1 With the Division of Credit and Investment Flows . . . 18.2.2 Without Flows Separation . . . . . . . . . . . . . . . . . . . . . 18.3 The Effectiveness of the Investment Project from the Perspective of the Owners of Equity and Debt . . . . . . . . . . . . . 18.3.1 With Flows Separation . . . . . . . . . . . . . . . . . . . . . . . 18.3.1.1 Projects of Arbitrary (Finite) Duration . . . . 18.3.2 Without Flows Separation . . . . . . . . . . . . . . . . . . . . . 18.4 Example of the Application of the Derived Formulas . . . . . . . . 18.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Analysis of the Exploration of Efficiency of Investment Projects of Arbitrary Duration (within Brusov–Filatova– Orekhova Theory) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.1 The Effectiveness of the Investment Project from the Perspective of the Equity Holders Only . . . . . . . . . . . . . . . . . 19.1.1 With the Division of Credit and Investment Flows . . . 19.1.2 Without Flows Separation . . . . . . . . . . . . . . . . . . . . . 19.2 The Effectiveness of the Investment Project from the Perspective of the Owners of Equity and Debt . . . . . . . . . . . . . 19.2.1 With the Division of Credit and Investment Flows . . . 19.2.2 Without Flows Separation . . . . . . . . . . . . . . . . . . . . . 19.3 The Elaboration of Recommendations on the Capital Structure of Investment of Enterprises, Companies, Taking into Account all the Key Financial Parameters of Investment Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.3.1 General Conclusions and Recommendations on the Definition of Capital Structure of Investment of Enterprises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

351 352 353 353 354 355 357 357 359 359 360 361 361 361 361 362 363 364

365 365 365 372 382 382 389

398

398 400

Contents

20

21

22

xxi

Whether it Is Possible to Increase Taxing and Conserve a Good Investment Climate in the Country? . . . . . . . . . . . . . . . . . . . . . . . . 20.1 Influence of Tax on Profit Rates on the Efficiency of the Investment Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.2 Investment Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.3 Borrowings Abroad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.4 Dependence of NPV on Tax on Profit Rates at Different Leverage Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.5 At a Constant Value of Equity Capital (S = Const) . . . . . . . . . 20.6 Without Flows Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.6.1 At a Constant Value of the Total Invested Capital (I = Const) (Fig. 20.13) . . . . . . . . . . . . . . . . . . . . . . 20.6.2 At a Constant Value of Equity Capital (S = Const) . . . 20.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Whether It Is Possible to Increase the Investment Efficiency, Increasing Tax on Profit Rate? An Abnormal Influence of Growth of Tax on Profit Rate on the Efficiency of the Investment . . . . . . . . 21.1 Dependence of NPV on Leverage Level L at Fixed Levels of Tax on Profit Rates t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.1 The Effectiveness of the Investment Project from the Perspective of the Equity Holders Only . . . . . . . . . . . 21.1.2 The Effectiveness of the Investment Project from the Perspective of the Equity and Debt Holders . . . . . 21.2 Dependence of NPV on Tax on Profit Rates at Fixed Leverage Levels L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2.1 The Effectiveness of the Investment Project from the Perspective of the Equity Holders Only . . . . . . . . 21.2.2 The Effectiveness of the Investment Project from the Perspective of the Equity and Debt Holders . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optimizing the Investment Structure of the Telecommunication Sector Company . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 Investment Analysis and Recommendations for Telecommunication Company “Nastcom Plus” . . . . . . . . . . . 22.2.1 The Dependence of NPV on Investment Capital Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2.2 The Dependence of NPV on the Equity Capital Value and Coefficient β . . . . . . . . . . . . . . . . . . . . . 22.3 Effects of Taxation on the Optimal Capital Structure of Companies in the Telecommunication Sector . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

401 401 403 405 408 409 410 412 414 416 417

419 419 419 423 427 430 431 471

. 473 . 473 . 474 . 476 . 482 . 488 . 491 . 499

xxii

23

24

Contents

Innovative Investment Models with Frequent Payments of Tax on Income and of Interest on Debt . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23.1.1 The Literature Review . . . . . . . . . . . . . . . . . . . . . . . 23.1.2 Some Problems Under the Evaluation of the Effectiveness of the Investment Projects . . . . . . . . . . . 23.1.3 The Discount Rates . . . . . . . . . . . . . . . . . . . . . . . . . 23.1.4 The Structure of the Paper . . . . . . . . . . . . . . . . . . . . . 23.2 The Effectiveness of the Investment Project from the Perspective of the Equity Holders Only . . . . . . . . . . . . . . . . . 23.2.1 With Flow Separation . . . . . . . . . . . . . . . . . . . . . . . . 23.2.2 Without Flow Separation . . . . . . . . . . . . . . . . . . . . . 23.3 The Effectiveness of the Investment Project from the Perspective of the Owners of Equity and Debt . . . . . . . . . . . . . 23.3.1 With Flow Separation . . . . . . . . . . . . . . . . . . . . . . . . 23.3.2 Without Flow Separation . . . . . . . . . . . . . . . . . . . . . 23.4 Discount Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23.5 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23.5.1 Numerical Calculation of the Discount Rates . . . . . . . 23.5.1.1 The Long-Term Investment Projects . . . . . . 23.5.1.2 The Arbitrary Duration Investment Projects . . . . . . . . . . . . . . . . . . . . . . . . . . 23.5.2 The Effectiveness of the Long-Term Investment Project from the Perspective of the Owners of Equity Capital . . . . . . . . . . . . . . . . . . . . . . . . . . . 23.5.3 The Effectiveness of the Long-Term Investment Project from the Perspective of the Owners of Equity and Debt . . . . . . . . . . . . . . . . . . . . . . . . . . 23.5.4 The Effectiveness of the Arbitrary Duration Investment Projects from the Perspective of the Owners of Equity Capital . . . . . . . . . . . . . . . . . . . . . 23.5.5 The Effectiveness of the Arbitrary Duration Investment Project from the Perspective of the Owners of Equity and Debt . . . . . . . . . . . . . . . . . . . . 23.5.6 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Role of the Central Bank and Commercial Banks in Creating and Maintaining a Favorable Investment Climate in the Country . 24.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24.2 Investment Models with Debt Repayment at the End of the Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24.2.1 The Effectiveness of the Investment Project from the Perspective of the Equity Holders Only (Without Flows Separation) . . . . . . . . . . . . . . . . . . .

501 501 501 504 505 506 507 508 510 512 512 513 513 514 515 515 515

518

518

520

523 524 526 528

. 529 . 529 . 530

. 531

Contents

xxiii

24.2.1.1

Modigliani–Miller Limit (Long-Term (Perpetuity) Projects . . . . . . . . . . . . . . . . 24.3 Modigliani–Miller Limit (Long-Term (Perpetuity) Projects) . . 24.3.1 The Dependence of the Efficiency of Investments NPV on the Level of Debt Financing L for the Values of Equity Costs k0 = 0.2 . . . . . . . . . . . . . . . 24.3.2 The Dependence of the Efficiency of Investments NPV on the Level of Debt Financing L for the Value of Equity Costs k0 = 0.28 . . . . . . . . . . . . . . . 24.4 Projects of Finite (Arbitrary) Duration . . . . . . . . . . . . . . . . . 24.4.1 The Dependence of the Efficiency of Investments NPV on the Level of Debt Financing L for the Values of Equity Costs k0 = 0.2 . . . . . . . . . . . . . . . 24.4.2 The Dependence of the Efficiency of Investments NPV on the Level of Debt Financing L for the Values of Equity Costs k0 = 0.28 . . . . . . . . . . . . . . 24.5 The Dependence of the Net Present Value, NPV, on the Leverage Level l for Projects of Different Durations . . . . . . . 24.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

26

. 532 . 533

. 533

. 539 . 540

. 541

. 546 . 549 . 550 . 555

The Golden Age of the Company (Three Colors of Company’s Time) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25.1 Dependence of WACC on the Age of the Company n at Different Leverage Levels . . . . . . . . . . . . . . . . . . . . . . . . . 25.2 Dependence of WACC on the Age of the Company n at Different Values of Capital Costs (Equity, k0, and Debt, kd) and Fixed Leverage Levels . . . . . . . . . . . . . . . . . . . . . . . . . . 25.3 Dependence of WACC on the Age of the Company n at Different Values of Debt Capital Cost, kd, and Fixed Equity Cost, k0, and Fixed Leverage Levels . . . . . . . . . . . . . . 25.4 Dependence of WACC on the Age of the Company n at Different Values of Equity Cost, k0, and Fixed Debt Capital Cost, kd, and Fixed Leverage Levels . . . . . . . . . . . . . . 25.5 Dependence of WACC on the Age of the Company n at High Values of Capital Cost (Equity, k0, and Debt, kd) and High Lifetime of the Company . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25.6 Further Investigation of Effect . . . . . . . . . . . . . . . . . . . . . . . . 25.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

557 560

561

566

569

573 581 582 583

A “Golden Age” of the Companies: Conditions of Its Existence . . . 585 26.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586 26.2 Companies Without the “Golden Age” (Large Difference Between k0 and kd Costs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587

xxiv

Contents

26.2.1

Dependence of Weighted Average Cost of Capital, WACC, on the Company Age n at Different Leverage Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26.3 Companies with the “Golden Age” (Small Difference Between k0 and kd Costs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26.4 Companies with Abnormal “Golden Age” (Intermediate Difference Between k0 and kd Costs) . . . . . . . . . . . . . . . . . . . 26.5 Comparing with Results from Previous Chapter . . . . . . . . . . . 26.5.1 Under Change of the Debt Capital Cost, kd . . . . . . . . . 26.5.2 Under Change of the Equity Capital Cost, k0 . . . . . . . 26.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

New Meaningful Effects in Modern Capital Structure Theory . . . . 27.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27.2 Comparision of Modigliani–Miller (MM) and Brusov–Filatova–Orekhova (BFO) Results . . . . . . . . . . . . . . . 27.2.1 The Traditional Approach . . . . . . . . . . . . . . . . . . . . . 27.2.2 Modigliani–Miller Theory . . . . . . . . . . . . . . . . . . . . . 27.3 Comparision of Modigliani–Miller Results (Perpetuity Company) with Myers Results (One Year Company) and Brusov–Filatova–Orekhova Ones (Company of Arbitrary Age) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27.4 Bankruptcy of the Famous Trade-off Theory . . . . . . . . . . . . . . 27.5 The Qualitatively New Effect in Corporate Finance . . . . . . . . . 27.5.1 Perpetuity Modigliani–Miller Limit . . . . . . . . . . . . . . 27.5.2 BFO Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27.6 Mechanism of Formation of the Company Optimal Capital Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27.7 “A Golden Age” of the Company . . . . . . . . . . . . . . . . . . . . . . 27.8 Inflation in MM and BFO Theories . . . . . . . . . . . . . . . . . . . . 27.9 Effects, Connected with Tax Shields, Taxes and Leverage . . . . 27.10 Effects, Connected with the Influence of Tax on Profit Rate on Effectiveness of Investment Projects . . . . . . . . . . . . . . . . . 27.11 Influence of Growth of Tax on Profit Rate . . . . . . . . . . . . . . . 27.12 New Approach to Ratings . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Part III 28

588 590 594 599 599 600 602 604 607 607 609 609 610

612 614 618 618 618 621 622 628 631 632 632 635 636

Ratings and Rating Methodologies of Non-financial Issuers

Rating: New Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28.2 The Closeness of the Rating Agencies . . . . . . . . . . . . . . . . . The Use of Discounting in the Rating . . . . . . . . . . . . . . . . . . 28.3 28.4 Incorporation of Parameters, Using in Ratings, into Perpetuity Limit of Modern Theory of Capital Structure by Brusov– Filatova–Orekhova . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . .

639 639 640 640

. 641

Contents

28.5

29

xxv

Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28.5.1 One-Period Model . . . . . . . . . . . . . . . . . . . . . . . . . . 28.5.2 Multi-Period Model . . . . . . . . . . . . . . . . . . . . . . . . . 28.6 Theory of Incorporation of Parameters, Using in Ratings, into Perpetuity Limit of Modern Theory of Capital Structure by Brusov–Filatova–Orekhova . . . . . . . . . . . . . . . . . . . . . . . . . . 28.6.1 Coverage Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28.6.1.1 Coverage Ratios of Debt . . . . . . . . . . . . . . 28.6.1.2 Coverage Ratios of Interest on the Credit . . 28.6.1.3 Coverage Ratios of Debt and Interest on the Credit (New Ratios) . . . . . . . . . . . . 28.6.2 More Detailed Consideration . . . . . . . . . . . . . . . . . . . 28.6.3 Leverage Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28.6.3.1 Leverage Ratios for Debt . . . . . . . . . . . . . . 28.6.3.2 Leverage Ratios for Interest on Credit . . . . 28.6.3.3 Leverage Ratios for Debt and Interest on Credit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28.7 Equity Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28.8 How to Evaluate the Discount Rate? . . . . . . . . . . . . . . . . . . . . 28.8.1 Using One Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28.8.2 Using a Few Ratios . . . . . . . . . . . . . . . . . . . . . . . . . 28.9 Influence of Leverage Level . . . . . . . . . . . . . . . . . . . . . . . . . . 28.9.1 The Dependence of Equity Cost ke on Leverage Level at Two Coverage Ratio Values ij = 1 and ij = 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28.10 The Dependence of Equity Cost ke on Leverage Level at Two Leverage Ratio Values lj = 1 and lj = 2 . . . . . . . . . . . . . 28.11 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

642 642 642

Rating Methodology: New Look and New Horizons . . . . . . . . . . . . 29.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29.2 The Analysis of Methodological and Systemic Deficiencies in the Existing Credit Rating of Non-financial Issuers . . . . . . . . . 29.2.1 The Closeness of the Rating Agencies . . . . . . . . . . . . 29.2.2 Discounting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29.2.3 Dividend Policy of the Company . . . . . . . . . . . . . . . . 29.2.4 Leverage Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29.2.5 Taxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29.2.6 Account of the Industrial Specifics of the Issuer . . . . . 29.2.7 Neglect of Taking into Account the Particularities of the Issuer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29.2.8 Financial Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29.3 Modification of the BFO Theory for Companies and Corporations of Arbitrary Age for Purposes of Ranking . . . . . .

675 675

643 643 643 644 644 647 650 650 650 651 653 661 661 662 665

665 668 673 673

676 676 677 677 678 678 679 679 679 681

xxvi

Contents

29.4

Coverage Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29.4.1 Coverage Ratios of Debt . . . . . . . . . . . . . . . . . . . . . . 29.4.2 The Coverage Ratio on Interest on the Credit . . . . . . . 29.4.3 Coverage Ratios of Debt and Interest on the Credit (New Ratios) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29.4.4 All Three Coverage Ratios Together . . . . . . . . . . . . . 29.5 Coverage Ratios (Different Capital Cost Values) . . . . . . . . . . . 29.5.1 Coverage Ratios of Debt . . . . . . . . . . . . . . . . . . . . . . 29.5.2 The Coverage Ratio on Interest on the Credit . . . . . . . 29.5.3 Coverage Ratios of Debt and Interest on the Credit (New Ratios) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29.5.4 Analysis and Conclusions . . . . . . . . . . . . . . . . . . . . . 29.6 Leverage Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29.6.1 Leverage Ratios for Debt . . . . . . . . . . . . . . . . . . . . . 29.6.2 Leverage Ratios for Interest on Credit . . . . . . . . . . . . 29.7 Leverage Ratios (Different Capital Costs) . . . . . . . . . . . . . . . . 29.7.1 Leverage Ratios for Debt . . . . . . . . . . . . . . . . . . . . . 29.7.2 Leverage Ratios for Interests on Credit . . . . . . . . . . . 29.7.3 Leverage Ratios for Debt and Interests on Credit . . . . 29.7.4 Analysis and Conclusions . . . . . . . . . . . . . . . . . . . . . 29.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Application of the Modigliani–Miller Theory, Modified for the Case of Advance Payments of Tax on Profit, in Rating Methodologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30.2 Modified Modigliani–Miller Theory . . . . . . . . . . . . . . . . . . . . 30.3 Application of Modified Modigliani–Miller Theory for Rating Needs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30.3.1 Coverage Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30.3.1.1 Coverage Ratios of Debt . . . . . . . . . . . . . . 30.3.1.2 Coverage Ratios of Interest on the Credit . . 30.3.1.3 Coverage Ratios of Debt and Interest on the Credit . . . . . . . . . . . . . . . . . . . . . . 30.3.2 Dependence of WACC on Leverage Ratios of Debt in “Classical” Modigliani–Miller Theory (MM Theory) and Modified Modigliani–Miller Theory (MMM Theory) . . . . . . . . . . . . . . . . . . . . . . 30.3.3 Leverage Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30.3.3.1 Leverage Ratios for Debt . . . . . . . . . . . . . . 30.3.3.2 Leverage Ratios for Interest on Credit . . . . 30.3.3.3 Leverage Ratios for Debt and Interest on Credit . . . . . . . . . . . . . . . . . . . . . . . . .

682 683 684 686 688 689 689 691 693 693 696 696 697 700 700 703 705 707 709 710

711 711 712 714 715 715 716 716

717 720 720 720 721

Contents

xxvii

30.3.3.4

Dependence of WACC on Leverage Ratios of Debt in “Classical” Modigliani–Miller Theory (MM Theory) and Modified Modigliani–Miller Theory (MMM Theory) . . . . . . . . . . . . . . . . . . . . 722 30.4 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725 Part IV 31

Ratings and Rating Methodologies of the Investment Projects

Ratings of the Investment Projects of Arbitrary Durations: New Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Investment Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2.1 The Effectiveness of the Investment Project from the Perspective of the Equity Holders Only (Without Flows Separation) . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Incorporation of Financial Coefficients, Using in Project Rating into Modern Investment Models, Describing the Investment Projects of Arbitrary Duration . . . . . . . . . . . . . . . . 31.3.1 Coverage Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3.1.1 Coverage Ratios of Debt . . . . . . . . . . . . . . 31.3.1.2 Coverage Ratios of Interest on the Credit . . 31.3.1.3 Coverage Ratios of Debt and Interest on the Credit . . . . . . . . . . . . . . . . . . . . . . . . . 31.3.2 Leverage Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3.2.1 Leverage Ratios for Debt . . . . . . . . . . . . . . 31.3.2.2 Leverage Ratios for Interest on Credit . . . . 31.3.2.3 Leverage Ratios for Debt and Interest on Credit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 Results and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4.1 Dependence of NPV/D on Coverage Ratios . . . . . . . . 31.4.1.1 The Dependence of NPV on Coverage Ratio on Debt i1 . . . . . . . . . . . . . . . . . . . . 31.4.1.2 The Dependence of NPV on Leverage Ratio on Debt l1 . . . . . . . . . . . . . . . . . . . . 31.4.1.3 The Dependence of NPV on Coverage Ratio on Debt i1 at Different Values of kd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4.1.4 The Dependence of NPV/NOI on Leverage Ratio on Debt l1 at Different Values of kd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

729 730 731

732

733 734 734 734 734 735 735 735 735 736 736 736 738

741

742 743 746

xxviii

32

33

Contents

Ratings of Investment Projects of Arbitrary Duration with a Uniform Debt Repayment: A New Approach . . . . . . . . . . . . . . . . 32.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Incorporation of Financial Ratios Used in Project Rating into Modern Investment Models with Uniform Repayment of Debt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2.1 Coverage Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2.1.1 Coverage Ratios of Debt . . . . . . . . . . . . . . 32.2.1.2 Coverage Ratios of Interest on the Credit . . 32.2.1.3 Coverage Ratios of Debt and Interest on the Credit (New Parameter) . . . . . . . . . . . . 32.2.2 Leverage Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2.2.1 Leverage Ratios for Debt . . . . . . . . . . . . . . 32.2.2.2 Leverage Ratios for Interest on Credit . . . . 32.2.2.3 Leverage Ratios for Debt and Interest on Credit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2.3 Perpetuity Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2.4 The Study of the Dependence of the Net Present Value of the Project, NPV, on Rating Parameters . . . . 32.2.4.1 Investigation of the Dependence of the Net Present Value of the Project, NPV (in Units of Debt D) on Coverage Ratios . . 32.2.4.2 Study of the Dependence of the Net Present Value of the Project NPV (in Units of Net Operating Income NOI) on Leverage Ratios . . . . . . . . . . . . . . . . . . 32.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

749 749

750 750 750 751 751 752 752 752 753 753 754

754

757 762 763

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 768

About the Authors

Peter Brusov Peter Nickitovich Brusov is Doctor of Physical and Mathematical Science and Professor of the Financial University under the Government of the Russian Federation. He was born September 23, 1949. Education Peter Brusov graduated from two faculties of Rostov-on-Don State University, Physical and Mathematical, and got PhD degree in Leningrad Mathematical Institute named by V.A. Steklov in 1980 and Doctor of Physical and Mathematical Science degree in Dubna (JINR) in 1993. In the area of physics, he has created (together with Victor Popov) the theory of collective properties of superfluids and superconductors and has calculated the whole spectrum of collective excitations in bulk and films of superfluid He3. Peter Brusov has predicted superfluid phases in He3 films, the nontrivial pairing in high temperature superconductors. In the area of finance and economy, Peter Brusov has created (together with Tatiana Filatova and Natali Orekhova) the modern theory of capital cost and capital structure—Brusov–Filatova–Orekhova theory (BFO theory). Employment experience Peter Brusov has been the Head of the Laboratory of high temperature superconductors in Rostov-on-Don State University up to 2004 and is now Professor of the Financial University under the Government of the Russian. Peter Brusov has been Visiting Professor of Northwestern University (USA), Cornell University (USA), Osaka City University (Japan), Chung-Cheng University (Taiwan), and some others. xxix

xxx

About the Authors

Peter Brusov is the author of over 500 research publications, including six monographs and numerous textbooks and papers. His main interest is in the area of finance and economy related to corporate finance, investments, taxation, and rating.

Tatiana Filatova is PhD in Finance and Professor of the Financial University under the Government of the Russian Federation. She was born 23 November 1948. Education Tatiana Filatova graduated from Moscow Financial Institute in 1973 and got her PhD degree in Finance from Moscow Financial Institute in 1978. In the area of finance and economy, Tatiana Filatova has created (together with Peter Brusov and Natali Orekhova) the modern theory of capital cost and capital structure—Brusov–Filatova–Orekhova theory (BFO theory). Employment experience For the past 20 years (from 1998) Tatiana Filatova has been Dean of a few faculties of the Financial University under the Government of the Russian Federation: Financial Management, Management, State and Municipal Government, and some others. Now Tatiana Filatova is Professor of the Financial University under the Government of the Russian Federation. Tatiana Filatova is the author of over 250 research publications, including five monographs and numerous textbooks and papers. Her main interest is in the area of finance and economy related to financial management, corporate finance, investments, taxation, and rating.

Natali Orekhova is a PhD in Physics and Mathematics and Professor of the Financial University under the Government of the Russian Federation. She was born 17 June 1973. Education Natali Orekhova graduated from the Physical Faculty of Rostov-on-Don State University in 1995. She got a PhD degree from Rostov-on-Don State University in 1998. She graduated from the Presidential Program in Management (including Financial Management) in 2007. Natali Orekhova has created (together with Peter Brusov and Tatiana Filatova) the modern theory of

About the Authors

xxxi

capital cost and capital structure—Brusov–Filatova– Orekhova theory (BFO theory). Employment experience Natali Orekhova has been the leading scientist of the Financial University under the Government of the Russian Federation. She was Professor of the Center of Corporate Finance, Investment, Taxation and Rating at the Research Consortium of Universities of the South of Russia. Now she is Professor of the Financial University under the Government of the Russian Federation. Natali Orekhova is the author of over 100 research publications, including three monographs and numerous textbooks and papers. Her main interest is in the area of finance and economy related to corporate finance, investments, taxation, and rating.

Chapter 1

Introduction

Keywords Capital structure · Modigliani–Miller (MM) theory · Brusov–Filatova– Orekhova (BFO) theory · Trade-off theory · Generalized BFO theory

1.1

Introduction

One of the main problems in corporate finance is the problem of cost of capital and the impact of capital structure on its cost and capitalization of the companies. To date, even the question of the existence of an optimal capital structure of the companies (at which the company capitalization is maximal, and weighted average cost of capital is minimal) is open. Numerous theories and models, including the first and the only one until 2008 quantitative theory by Nobel laureates Modigliani and Miller (MM) (Modigliani and Miller 1958, 1963, 1966), not only do not solve the problem but also because of the large number of restrictions (for example, theory of MM) have a weak relationship to the real economy. Herewith the qualitative theories and models, based on the empirical approach, do not allow to carry out the necessary assessment. In the monograph, the foundation of modern corporate finance and investment is laid. It is based on the authors’s works on modifying the theory of capital cost and capital structure by Nobel Prize winners Modigliani and Miller, which led to the actual replacement of this theory by the modern theory by Brusov–Filatova– Orekhova (BFO theory) (Brusov & Filatova 2011; Brusov et al. 2014b; Brusova 2011; Brusov et al. 2020a, b; Brusov et al. 2021a, b; Brusov & Filatova 2021; Brusov & Filatova 2022a, b; Brusov et al. 2012c; Brusov et al. 2013c, d; Brusov et al. 2014c; Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a; Filatova et al. 2008). The authors have moved from the assumption of Modigliani–Miller concerning the perpetuity (infinite time of life) of companies and further elaborated the quantitative theory of valuation of core parameters of financial activities of companies with arbitrary time of life. Results of modern BFO theory (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a; Filatova et al. 2008) turn out to be quite different from ones of Modigliani–Miller theory (Modigliani and Miller 1958, 1963, 1966). They show that later, via its perpetuity, underestimates (often significantly) the assessment of weighted average © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_1

1

2

1 Introduction

cost of capital, the equity cost of the company and substantially overestimates (also often significantly) the assessment of the capitalization of both financially independent company as well as the company, using the debt financing. Such an incorrect assessment of key performance indicators of financial activities of companies has led to an underestimation of risks involved, and impossibility, or serious difficulties in adequate managerial decision-making, which was one of the implicit reasons for global financial crisis of 2008. Within the modern theory of capital cost and capital structure (BFO theory) a study of the role of taxes and leverage has been done, which allows to the regulator to set the tax on profit rate, and businesses to choose the optimal level of debt financing. The qualitatively new effect in corporate finance, discovered by authors, is described: abnormal dependence of equity cost on leverage, which significantly alters the principles of development of the company’s dividend policy (modern principles of which are formulated in monograph). Authors take into account in explicit form the inflation in both Modigliani–Miller as well as Brusov–Filatova– Orekhova theories, with its non-trivial impact detected on the dependence of equity cost on leverage. Established BFO theory (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a; Filatova et al. 2008) allows to conduct a valid assessment of the core parameters of financial activities of companies, such as weighted average cost of capital and equity capital cost of the company, its capitalization. It allows a management of company to make adequate decisions, which improves the effectiveness of the company management. More generally, the introduction of the new system of evaluation of the parameters of financial activities of companies into the systems of financial reporting (IFRS, GAAP, etc.) would lead to a lower risk of global financial crisis, since, as is shown in monograph, a primary cause of the crisis of 2008 was a mortgage crisis in the US, which is associated with overvalued capitalization of mortgage companies by rating agencies, using incorrect MM theory. Within Brusov–Filatova–Orekhova theory analyses of widely known trade-off theory have been made (Brusov et al. 2013a). It is shown that suggestion of risky debt financing (and growing credit rate near the bankruptcy) in opposite to waiting result does not lead to the growth of weighted average cost of capital, WACC, which still decreases with leverage. This means the absence of minimum in the dependence of WACC on leverage as well as the absence of maximum in the dependence of company capitalization on leverage. This means that the optimal capital structure is absent in the famous trade-off theory, and this fact proves the insolvency of famous trade-off theory. Under the condition of proven by authors, insolvency of well-known classical trade-off theory question of finding of new mechanisms of formation of the company’s optimal capital structure, different from one suggested by trade-off theory, becomes very important. A new such mechanism has been developed by authors in the monograph. It is based on the decrease of debt cost with leverage, which is determined by the growth of debt volume. This mechanism is absent in perpetuity Modigliani–Miller theory (Modigliani and Miller 1958, 1963, 1966),

1.1

Introduction

3

even in the modified version, developed by authors, and exists within more general BFO theory. Over the past couple of years, the BFO authors have obtained very important results related to the generalization of the two main theories of the capital structure (Brusov–Filatova–Orekhova and Modigliani–Miller) to take into account the current financial practice of the company’s functioning and taking into account the real conditions of their work (Brusov et al. 2021a, b, 2022a, b, 2023; Brusov and Filatova 2021, 2022a, b, 2023; Filatova et al. 2022). The BFO and MM theories have been generalized to the case of variable income, to arbitrary frequency of income tax payments, to advance payments of income tax, etc., as well as to their combinations. These generalizations significantly expand the applicability of both theories in practice, in particular, in corporate finance, business valuation, investments, ratings, etc. The results on the generalized Modigliani– Miller theory can be found in the monograph (Brusov et al. 2022a, b). The second part of the monograph is devoted to assessing the effectiveness of investment projects (IP). The authors created the modern investment models of evaluation of the efficiency of IP index, using as the discount rate the correct values of weighted average cost of capital as well as the equity cost of the company, obtained in the BFO theory and in its perpetuity limit (MM theory). Since virtually every investment project uses debt financing, one of the most important problems is the determination of the optimal leverage level for investments. The monograph studies this problem from two points of view: from the point of view of owners of equity capital, as well as from the point of view of owners of both equity and debt capital. The study is being conducted without division of cash flows as well as with the division of cash flows on the financial and operating plus investment flows (Brusov et al. 2011c, 2012a). Within the framework of the established models, the evaluation of the effectiveness of investment from the point of view of their optimal capital structure has been made on the example of one of the largest telecommunication companies in Russia. It has been shown that there is an optimum structure of investment capital. But the company has lost from $98 million up to $645 million because the company has worked at leverage levels that were far from optimal values. The procedure proposed by the authors for the evaluation of the efficiency of investment projects will avoid such losses in the future. In monograph the significant attention has been given to the study of taxes and taxation in manufacture and as well in investments. Some recommendations for Regulator concerning taxation (value of tax on profit rates etc.) has been done. Investigation of the influence of tax on profit rate on the effectiveness of investment projects at different debt levels showed that increase of tax on profit rate from one side leads to a decrease of project NPV, but from other side, it leads to a decrease of sensitivity of NPV with respect to leverage level. At high leverage level L, the influence of tax on profit rate change on the effectiveness of investment projects becomes significantly less. Studying the influence of the growth of tax on profit rate on the efficiency of the investment as well has led to two qualitatively new effects in investments:

4

1

Introduction

1. The growth of tax on profit rate changes the nature of the NPV dependence on leverage at some value t*: there is a transition from diminishing function NPV(L ) when t < t* to growing function NPV(L ). 2. At high leverage levels, the growth of tax on profit rate leads to the growth of the efficiency of the investments. Discovered effects in investments can be applied in a real economic practice for optimizing the management of investments. A distinctive feature of the book is the extensive and adequate use of mathematics, which allows the reader to count various financial and economic parameters, including investment ones, up to the quantitative result. Corporate management in the modern world is the management of financial flows. The proposed Brusov–Filatova–Orekhova theory (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a; Filatova et al. 2008) allows to the reader to correctly identify discount rates—basic parameters for discounting of financial flows to arbitrary time moment, compare financial flows with a view to the adoption of literate managerial decisions. The discount rate is a key link of the existing financial system, by pulling on which modern finance can be adequately built, and the proposed monograph can be of assistance in this substantial assistance. The third part of the monograph (Chaps. 24, 28–32) suggests a new approach to rating methodology. Chapters 28–30 are devoted to the rating of non-financial issuers, while Chaps. 31–32 are devoted to long-term and arbitrary duration project rating. The key factors of a new approach are: (1) The adequate use of discounting of financial flows virtually not used in existing rating methodologies, (2) The incorporation of rating parameters (financial “ratios”) into the modern theory of capital structure (Brusov–Filatova–Orekhova (BFO) theory) (Brusov et al. 2018). This makes it possible to use the powerful tool of this theory, which provides the correct discount rate when discounting financial flows. The interplay between rating ratios and leverage level which can be quite important in rating is discussed. All these create a new base for rating methodologies. New approach to ratings and rating methodologies allows to issue more correct ratings of issuers, makes the rating methodologies more understandable and transparent (Brusov et al. 2021c). The monograph is intended for students, postgraduate students, teachers of economic and financial institutions, students of MBA program, scientists, financial analysts, financial directors of company, managers of insurance companies and rating agencies, officials of regional and federal ministries and departments, ministers responsible for economic and financial management.

References Brusov PN, Filatova ТV (2011) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Financ Credit 435:2–8 Brusov P, Filatova T (2021) The Modigliani–Miller theory with arbitrary frequency of payment of tax on profit. Mathematics 9(11):1198

References

5

Brusov P, Filatova T (2022a) Influence of method and frequency of profit tax payments on company financial indicators. Mathematics 10(14):2479. https://doi.org/10.3390/math10142479 Brusov P, Filatova T (2022b) Generalization of the Brusov–Filatova–Orekhova theory for the case of variable income. Mathematics 10(19):3661. https://doi.org/10.3390/math10193661 Brusov P, Filatova T (2023) Capital structure theory: past, present, future. Mathematics 11(3):616. https://doi.org/10.3390/math11030616 Brusov P, Filatova T, Orehova N, Brusova A (2011a) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Appl Financ Econ 21(11): 815–824 Brusov P, Filatova T, Orehova N et al (2011b) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Bus ICT 2:16–21 Brusov P, Filatova T, Orehova N et al (2011c) Influence of debt financing on the effectiveness of the investment project within the Modigliani–Miller theory. Res J Econ Bus ICT (UK) 2:11–15 Brusov P, Filatova T, Orehova N, Brusov PP, Brusova N (2011d) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Bus ICT 2:16–21 Brusov P, Filatova T, Eskindarov M, Orehova N (2012a) Influence of debt financing on the effectiveness of the finite duration investment project. Appl Financ Econ 22(13):1043–1052 Brusov P, Filatova T, Eskindarov M, Orehova N (2012b) Hidden global causes of the global financial crisis. J Rev Glob Econ 1:106–111 Brusov P, Filatova T, Eskindarov M, Orehova N (2012c) Hidden global causes of the global financial crisis. J Rev Global Econ 1:106–111 Brusov P, Filatova P, Orekhova N (2013a) Absence of an optimal capital structure in the famous tradeoff theory! J Rev Glob Econ 2:94–116 Brusov P, Filatova T, Orehova N (2013b) A qualitatively new effect in corporative finance: abnormal dependence of cost of equity of company on leverage. J Rev Glob Econ 2:183–193 Brusov P, Filatova P, Orekhova N (2013c) Absence of an optimal capital structure in the famous tradeoff theory! J Rev Global Econ 2:94–116 Brusov P, Filatova T, Orehova N (2013d) A qualitatively new effect in corporative finance: abnormal dependence of cost of equity of company on leverage. J Rev Global Econ 2:183–193 Brusov P, Filatova P, Orekhova N (2014a) Mechanism of formation of the company optimal capital structure, different from suggested by trade off theory. Cogent Econ Financ 2:1–13. https://doi. org/10.1080/23322039.2014.946150 Brusov P, Filatova T, Orehova N (2014b) Inflation in Brusov–Filatova–Orekhova theory and in its perpetuity limit – Modigliani–Miller theory. J Rev Glob Econ 3:175–185 Brusov P, Filatova T, Orehova N (2014c) Inflation in Brusov–Filatova–Orekhova theory and in its perpetuity limit–Modigliani–Miller theory. J Rev Global Econ 3:175–185 Brusov P, Filatova T, Orehova N, Eskindarov M (2018) Modern corporate finance, investments, taxation and ratings, 2nd edn. Springer, Cham, Switzerland, pp 1–571 Brusov PN, Filatova TV, Orekhova NP, Kulik VL, Chang SI, Lin YCG (2020a) Modification of the Modigliani–Miller theory for the case of advance payments of tax on profit. J Rev Glob Econ 9: 257–267 Brusov PN, Filatova TV, Orekhova NP, Kulik VL, Chang S-I, Lin YCG (2020b) Application of the Modigliani–Miller theory, modified for the case of advance payments of tax on profit, in rating methodologies. J Rev Glob Econ 9:282–292 Brusov P, Filatova T, Chang S-I, Lin G (2021a) Innovative investment models with frequent payments of tax on income and of interest on debt. Mathematics 9(13):1491 Brusov P, Filatova T, Orekhova N, Kulik V, Chang S-I, Lin G (2021b) Generalization of the Modigliani–Miller theory for the case of variable profit. Mathematics 9(11):1286 Brusov P, Filatova T, Orekhova N (2021c) Ratings: critical analysis and new approaches of quantitative and qualitative methodology. Springer Nature Publishing Brusov P, Filatova T, Orekhova N, Kulik V, Chang S-I, Lin G (2022a) The generalization of the Brusov–Filatova–Orekhova theory for the case of payments of tax on profit with arbitrary frequency. Mathematics 10(8):1343. https://doi.org/10.3390/math10081343

6

1

Introduction

Brusov P, Filatova T, Kulik V (2022b) Benefits of advance payments of tax on profit: consideration within the Brusov–Filatova–Orekhova (BFO) theory. Mathematics 10(12):2013. https://doi.org/ 10.3390/math10122013 Brusov P, Filatova T, Kulik V (2023) Two types of payments of tax on profit: advanced payments and at the end of periods: consideration within BFO Theory with variable profit. J Risk Financ Manag 16(3):1–20 Brusova A (2011) А comparison of the three methods of estimation of weighted average cost of capital and equity cost of company. Financ Anal Prob Sol 34(76):36–42 Filatova Т, Orehova N, Brusova А (2008) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Bull FU 48:68–77 Filatova T, Brusov P, Orekhova N (2022) Impact of advance payments of tax on profit on effectiveness of investments. Mathematics 10(4):666. https://doi.org/10.3390/math10040666 Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Modigliani F, Miller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391

Part I

Corporate Finance

Chapter 2

Capital Structure Theory: Past, Present, Future

Keywords Capital structure · Modigliani–Miller (MM) theory · Brusov–Filatova– Orekhova (BFO) theory · Trade-off theory

2.1

Introduction

The capital structure refers to the ratio between the company’s own and borrowed capital. Does the capital structure affect the main parameters of the company, such as the cost of capital, profit, company value, and others, and if so, how? The choice of the optimal capital structure, i.e., a capital structure that minimizes the weighted average cost of capital WACC and maximizes the company’s capitalization, V, is one of the most important tasks solved by the company’s financial manager. Modigliani and Miller (1958) were the first to seriously study (and the first quantitative study) the effect of a company’s capital structure on its performance. Prior to this study, there was an approach (let us call it traditional) based on the analysis of empirical data. The aim of this review was to analyze all existing theories of capital structure (with their advantages and disadvantages) in order to understand all aspects of the problem and make correct management decisions in practice. The role of the capital structure is that the correct determination of the optimal capital structure allows the company’s management to maximize the capitalization of the company and the long-term goal of the functioning of any company. The moment of breakthrough was the theory of Modigliani–Miller, which was the first quantitative theory. However, it had a large number of limitations and is of little use in practice. At present, there are increased requirements for making high-quality management decisions in the fields of financial management and corporate finance. This increases the requirements for financial analytics and the use of mathematical methods in economic analysis. The importance of the problem has led to great interest in it and great efforts by scientists to modify the Modigliani–Miller theory.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_2

9

10

2.2 2.2.1

2

Capital Structure Theory: Past, Present, Future

Basic Theories of Capital Structure A Historical Point of View

From a historical point of view, five stages in the development of the capital structure theory can be distinguished: First (before 1958), the traditional approach, based on practical experience and existed before the appearance of the first quantitative theory by Modigliani and Miller (the second stage) (1958–1963) (Modigliani and Miller 1958, 1963; Miller 1977; Miller and Modigliani 1961, 1966). The third stage (1964–2008 and later) is the numerous attempts by scientists to modify the Modigliani–Miller theory (Acharya et al. 2011; Arrow 1964; Asquith and Mullins 1986; Baumol et al. 1982; Black 1986; Becker 2021; Berk and DeMarzo 2007; Brealey and Myers 1981; Brealey et al. 2014; Bhattacharya 1978; Filatova et al. 2008; Brusov et al. 2012, 2013a, b, 2014a, b, 2018; Brusova 2011; Derrig 1994; Diamond and He 2014; Donaldson 1961; Erel et al. 2015; Fairley 1979; Fama 1996, 1977; Fama and French 2005; Farber et al. 2006; Fernandez 2006; Fisher and McGowan 1983; Frank and Goyal 2003; Gordon and Shapiro 1956; Graham and Leary 2011; Hamada 1969; Harris and Pringle 1985; Hausman and Myers 2002; Healy et al. 2002; Hirshleifer 1965, 1966; Jensen 1986; Jin and Myers 2006; Kaplan and Ruback 1995; Myers 2015; Keynes 1936; Kolbe et al. 1993; Lambrecht and Myers 2007, 2008, 2012, 2015; Lemmon et al. 2008; Lemmon and Zender 2010; Lintner 1956, 1965; Majd and Myers 1987; DeMarzo 1988; Merton and Perold 1993; Miles and Ezzell 1980; Morck et al. 2000; Mullins 1976; Myers 1967, 1968a, b, 1972, 1973a, b, 1974, 1984a, b, 1988, 1989, 1999, 2000, 2001; Myers and Cohn 1987; Myers et al. 1976, 1984, 1985; Myers and Howe 1997; Myers and Majd 1990; Myers and Majluf 1984; Myers and Pogue 1974; Myers and Rajan 1998; Myers and Read 2001, 2014; Myers and Shyam-Sunder 1996; Myers and Turnbull 1977; Robichek and Myers 1965, 1966a, b, c; Rosenbaum and Pearl 2013; Sethi et al. 1991; Schwartz 1959; Sharpe 1965; Shleifer and Summers 1988; ShyamSunder and Myers 1999; Skinner 2008; Solomon and Laya 1967; Van Horne 1966; Williams 1938). The fourth stage (2008–2019) is the appearance of the Brusov– Filatova–Orekhova (BFO) theory, which removed the main restriction of the Modigliani–Miller (MM) theory associated with the infinite lifetime of a company (Filatova et al. 2008; Brusov et al. 2012, 2013a, b, 2014a, b, 2018; Brusova 2011). Additionally, finally, the fifth stage (2019 up to now), which began a couple of years ago and is associated with the adaptation of the two main theories of the capital structure (Brusov–Filatova–Orekhova and Modigliani–Miller) to the established financial practice of the company’s functioning by taking into account the real conditions of their work (Brusov et al. 2020a, b, 2021a, b; Brusov and Filatova 2021; Brusov et al. 2022a, b; Brusov and Filatova 2022a, b; Filatova et al. 2022). One of the most important assumptions of the Modigliani–Miller theory is that all financial flows and all companies exist in perpetuity. This limitation was lifted by Brusov–Filatova–Orekhova in 2008 (Filatova et al. 2008), who created the BFO (Brusov–Filatova–Orekhova) theory—a modern theory of capital cost and capital

2.2

Basic Theories of Capital Structure

11

Fig. 2.1 The historical development of the theory of capital structure from the empirical traditional approach (TA) to the general theory of capital structure, BFO (Brusov–Filatova–Orekhova), through the perpetuity Modigliani–Miller theory

Fig. 2.2 Only two results for the capital structure of the company were known before the BFO theory: Modigliani–Miller (MM) for perpetual companies and Myers for 1-year companies, while the newly created BFO theory filled the entire interval between n = 1 and n = 1

structure for companies of arbitrary age (BFO–1 theory) and for companies of arbitrary lifetime (BFO–2 theory) (Brusov et al. 2018). Figure 2.1 shows the historical development of the theory of capital structure from the empirical traditional approach to the general theory of capital structure, BFO, through the perpetuity Modigliani–Miller theory. One-year companies were studied by Steve Myers (2001), who showed that the weighted average cost of capital WACC is greater in this case than in the perpetual Modigliani–Miller case, and the value of company V is therefore less. Only two results for the capital structure of the company were known by 2008, when the BFO theory appeared: Modigliani–Miller for perpetual companies and Myers for 1-year companies (see Fig. 2.2). The created BFO theory filled the entire interval between t = 1 and t = 1. This expands capital structure theory for companies of arbitrary ages and/or arbitrary lifetimes. Many new meaningful effects have been discovered in the BFO theory.

2.2.2

The Empirical (Traditional) Approach

In the traditional approach, based on practical experience and existing before the advent of the first quantitative theory of Modigliani and Miller, the weighted average cost of capital WACC and the associated capitalization of the company, V = CF/ WACC, depend on the capital structure and the level of debt load, L. The cost of debt is always lower than the cost of equity, because the former has less risk due to the fact that the claims of creditors are satisfied before the claims of shareholders in the event of bankruptcy. As a result, an increase in the share of cheaper borrowed capital in the total capital structure to the limit that does not cause a violation of financial

12

2 Capital Structure Theory: Past, Present, Future

stability and an increase in the risk of bankruptcy leads to a decrease in the weighted average cost of capital (WACC). The return required by investors (equal to the cost of equity) is growing; however, its growth did not offset the benefits of using cheaper borrowed capital. Therefore, the traditional approach welcomes the increase in leverage L = D/S and the associated increase in the value of the company V = CF/WACC. The empirical, traditional approach existed until the appearance of the first quantitative theory by Modigliani and Miller (1958). Based on existing practical experience traditional approach, the competition between the advantages of debt financing at a low leverage level and its disadvantages at a high leverage level forms the optimal capital structure, defined as the leverage level, at which WACC is minimal and company value, V, is maximum.

2.2.3

The Modigliani–Miller Theory

2.2.3.1

The Modigliani–Miller Theory with Taxes

There are two versions of the Modigliani–Miller theory: without taxes and with taxes. For without taxes, the following expressions for V, WACC, and ke are applicable. V = V0 =

EBIT k0

ð2:1Þ

where V0 stands for the unlevered company value, EBIT stands for earnings before interest and taxes, and k0 stands for the equity cost at zero leverage level L. From (2.1), one gets the weighted average cost of capital WACC: WACC = k0

ð2:2Þ

WACC = k0 = ke we þ kd wd :

ð2:3Þ

From the expression for WACC

and according to (2.1), one gets the equity cost, ke, ke =

k ðS þ DÞ k0 D w D - kd = k 0 þ ðk0- kd Þ = k0 þ ðk 0- k d ÞL ð2:4Þ - kd d = 0 S S we we S

Here, D stands for debt capital value; S stands for equity capital value; kd and wd stand for the cost and share of the company’s debt capital; ke and we stand for the equity capital cost and share. It is seen from (2.4), that the equity increases linearly with the leverage level.

2.2

Basic Theories of Capital Structure

2.2.3.2

13

The Modigliani–Miller Theory with Taxes

Within the framework of the Modigliani–Miller theory with taxes (Modigliani and Miller 1958, 1963; Miller 1977; Miller and Modigliani 1961, 1966), the following expression was postulated for the value of a company using borrowed funds, V, V = V0 þ D  t

ð2:5Þ

The expression for WACC immediately follows from (2.5). WACC = k0  ð1- wd t Þ

ð2:6Þ

The following formula for the cost of equity ke can be obtained from (2.6) within the framework of the Modigliani–Miller theory with taxes. k e = k0 þ L  ðk0- k d Þð1- t Þ

ð2:7Þ

The two, Formulas (2.7) (MM with taxes) and (2.4) (MM without taxes), differ by the multiplier (1-t), called the tax corrector. It is less than one unit, thus, the ke (L ) curve slope decreases with the accounting of taxes.

2.2.4

Modifications of Modigliani–Miller Theory

Since the creation of Modigliani–Miller theory, numerous attempts have been made to improve and develop this theory. We will discuss some of these modifications below. One of them is the Hamada model.

2.2.4.1

Hamada Model

The Modigliani–Miller theory, with the accounting of taxes has been united with CAPM (capital asset pricing model) in 1961 by Hamada (1969). For the cost of equity of a leveraged company, the below formula has been derived. k e = kF þ ðkM- kF ÞbU þ ðkM- kF ÞbU

D ð1- T Þ, S

ð2:8Þ

Here, bU is the β–coefficient of the unlevered company. The first term represents risk-free profitability kF, the second term is business risk premium, (kM - kF)bU, and the third term is financial risk premium ðk M- k F ÞbU DS ð1- T Þ. In the case of an unlevered company (D = 0), the financial risk (the third term) is zero, and its shareholders receive only a business risk premium. Equating CAPM formula to the right side of (2.8), one gets:

14

2

Capital Structure Theory: Past, Present, Future

kF þ ðkM- kF ÞbU = k F þ ðkM- kF ÞbU þ ðk M- k F ÞbU

D ð1- T Þ S

ð2:9Þ

or
 D b = bU 1 þ ð1- T Þ : S

ð2:10Þ

Below are the formulas for the equity cost, ke, debt cost, kd, and WACC in the CAPM model and (in parenthesis) in the Modigliani–Miller theory (Modigliani and Miller 1958, 1963; Miller 1977; Miller and Modigliani 1961, 1966). The equity cost for an unlevered company:   k e = kF þ k M - k F βU , ðke= k0 Þ:

ð2:11Þ

The equity cost and the debt cost for a levered company:   ke = k F þ k M - kF βe , ðk e= k0 þ ð1- T Þðk0- kd ÞLÞ:   k d = k F þ k M - kF βd , ðkd= kF ; βd = 0Þ:

ð2:12Þ

The weighted average cost of capital WACC WACC = ke we þ kd wd ð1- T Þ,

2.2.4.2

ðWACC= k0 ð1- Twd ÞÞ:

ð2:13Þ

The Cost of Capital Under Risky Debt

In the Modigliani–Miller theory, there are two asset types: risky equity and risk-free debt). However, assuming about the risk of bankruptcy of the company and the ability to nonpayment of debt may change the situation with debt. It has been shown by Stiglitz (1969) and Rubinstein (1973) that the assumption concerning risky debt does not change the company’s value with respect to the Modigliani and Miller results under free-of-risk debt (Modigliani and Miller 1958, 1963; Miller 1977; Miller and Modigliani 1961, 1966). However, the debt cost is changed from a constant value kd = kF to a variable one. As Hsia (1981), based on the models of pricing options, Modigliani–Miller and CAPM, has shown in the formula for the net discount profit, a term, reflecting tax shield should be discounted at the rate: k 0d = kF þ ðk0- k F ÞN ð- d1 Þ

1 , wd

ð2:14Þ

2.2

Basic Theories of Capital Structure

15

where d1 =

- ln wd þ kF t 1 pffi pffi kF þ σ t, 2 σ t

ð2:15Þ

N(-d1)—cumulative normal distribution of probability of random value d1 and t—a moment of payment a credit.

2.2.4.3

The Account of Corporate and Individual Taxes (Miller Model)

Modigliani and Miller considered only corporate taxes, but they did not take into account the individual taxes of investors. Miller (1977) has developed the model with an account of the corporate and individual taxes and studied the impact of leverage on the company’s value. The model is described by the following formula for levered company value: VL = VU þ

  ð1 - T C Þð1 - T S Þ I ð1 - T d Þ : 1kd ð1 - T d Þ

ð2:16Þ

Here, the first term is the unlevered company’s value VU =

EBITð1 - T C Þð1 - T S Þ : k0

ð2:17Þ

where TS stands for the tax on income of an individual investor from his ownership by the corporation stock rate, TC stands for the tax rate on corporate income, TD stands for the tax rate on interest income from the provision of investor–individuals of credits to other investors and companies. The Miller model estimates the value of a levered company, accounting for corporate tax, as well as tax on individuals. The second term is the Miller formula.  1-

 ð1 - T C Þð1 - T S Þ D, ð1 - T d Þ

ð2:18Þ

represents the gains from the use of debt capital. This term replaces the tax shield in the Modigliani–Miller model with corporate taxes: V L = V U þ TD:

ð2:19Þ

16

2.2.4.4

2

Capital Structure Theory: Past, Present, Future

Alternative Expression for WACC

Alternative formula for the WACC, different from Modigliani–Miller, one has been derived in (Farber et al. 2006; Fernandez 2006) from the WACC definition and the balance identity (see Berk and De Marzo 2007): WACC = k0 ð1- wd T Þ - k d twd þ kTS twd

ð2:20Þ

where k0, kd, and kTS are the expected returns on the unlevered company, the debt, and the tax shield, respectively. Some additional conditions are required for Eq. (2.20) to have practical applicability. If the WACC is constant over time, as stated in Farber et al. (2006), the levered company capitalization is found by discounting with the WACC of the unlevered company. In textbooks (Berk and DeMarzo 2007; Brealey and Myers 1981; Brealey et al. 2014), formulas for the special cases, where the WACC is constant, could be found. In 1963, Modigliani and Miller assume that the debt value D is constant. Then, as the expected after-tax cash flow of the unlevered firm is fixed, V0 is constant as well. By assumption, kTS = kD and the value of the tax shield is TS = tD. Thus, the capitalization of the company V is a constant, and the alternative Formula (2.20) becomes a formula for a constant WACC: WACC = k 0 ð1- wd T Þ

ð2:21Þ

Since the debt kd and the tax shield kTS have a debt nature, it seems reasonable that the expected returns are equal, as suggested by the “classical” Modigliani– Miller (MM) theory, which has been modified by Brusov et al. for cases of practical meaning.

2.2.4.5

The Miles–Ezzell Model Versus the Modigliani–Miller Theory

Denis M. Becker (2021) discussed the differences between the Modigliani–Miller theory (Modigliani and Miller 1958, 1963; Miller 1977; Miller and Modigliani 1961, 1966) and the Miles–Ezzell model (Miles and Ezzell 1980), which deal with the stochasticity of free cash flows. The Modigliani–Miller theory considers a stationary process, while in the Miles–Ezzell model the process is stochastic. The author conducts a numerical experiment that allows you to determine the values and discount rates using a risk-neutral approach. He analyzes three formulas: Modigliani–Miller theory (Modigliani and Miller 1958, 1963; Miller 1977; Miller and Modigliani 1961, 1966),

2.3

Trade-Off Theory

17

WACC = k0  ð1- wd t Þ

ð2:22Þ

Miles–Ezzell model (Miles and Ezzell 1980), WACC = k0 - t  wd  kf 

1 þ k0 1 þ kf

ð2:23Þ

Cooper and Nyborg (2018) WACC = k0 - kf  wd t

ð2:24Þ

where kf stands for the risk-free rate, which equals the required return of the debt holders. The author shows that in the Miles–Ezzell model, all cash flows and the values depend on the path, in contrast to the Modigliani–Miller theory. Additionally, in the Miles–Ezzell model, all discount rates are time-independent, with the exception of the discount rate used to discount tax shields, which depends on the duration of the cash flows. Conversely, in the Modigliani–Miller theory, all discount rates change over time except for the constant tax shield discount rate. This affects the applicability of the well-known formula for annuities and the development of models for estimating both finite and perpetual cash flows. In this paper, Becker (2021) raises the issue of paying the debt body together with the payment of interest on the debt. Regarding this issue, we would like to note that in both classical MM and BFO theories, the body of the debt is not paid. In the framework of the Modigliani–Miller theory, such an account is fundamentally impossible, while in the BFO theory, it can be conducted and was conducted in the framework of the BFO-2 theory, where the amount of debt D decreases with time. This decrease in the value of debt D results in a decrease in the tax shield (see BFO-2 theory).

2.3

Trade-Off Theory

For decades, one of the main theories of capital structure was the trade-off theory. There are two modifications of the trade-off theory: static and dynamic (Brennan and Schwartz 1978, 1984; Leland 1994; Kane et al. 1984).

2.3.1

Static Theory

The static trade-off theory accounts for income tax and the cost of bankruptcy. Within this theory, the optimal capital structure is formed by the balancing act

18

2 Capital Structure Theory: Past, Present, Future

between the benefits of debt financing at a low leverage level (from the tax shield from interest deduction) and the disadvantages of debt financing at a high leverage level (from the increased financial distress and expected bankruptcy costs). The tax shield benefit is equal to the product of the corporate income tax rate and the market value of debt, and the expected bankruptcy costs are equal to the product of the probability of bankruptcy and the estimated bankruptcy costs. The static version of the trade-off theory does not take into account the costs of adapting the capital structure to the optimal one, the economic behavior of managers, owners, and other participants in an economic process, as well as a number of other factors.

2.3.2

Dynamic Theory

The dynamic version of trade-off theory suggests that the costs of adjusting the capital structure are high, and therefore, companies will only change their capital structure if the benefits outweigh the costs. Therefore, there is an optimal range that varies on the outside of each lever but remains the same on the inside. Companies try to adjust their leverage when it reaches the edge of the optimal range. Depending on the type of adaptation costs, companies reach the target ratio faster or slower. Proportional changes involve a small adjustment, while fixed changes imply significant costs. In the dynamic version of the trade-off theory, a company’s capital structure decision in the current period depends on the expected company income in the next period. As it has been shown within BFO theory (Brusov et al. 2013a), under increased financial distress costs and bankruptcy risk, the optimal capital structure is absent. This means that the trade-off theory does not work in either the static or dynamic versions.

2.3.3

Proof of the Bankruptcy of the Trade-Off Theory

Brusov et al. (2013a) tested whether assumptions about risky debt financing (and about rising lending rates in the run-up to bankruptcy) did not lead to an increase in the weighted average cost of capital, WACC. They used the following model: k 0 = 24%;

kd =

0:07;

at L ≤ 2

0:07 þ 0:1ðL - 2Þ;

at L > 2

:

ð2:25Þ

and showed that under the above conditions, WACC still decreases with leverage (Fig. 2.3).

2.3

Trade-Off Theory

19

WACC(L)

0.3000 0.2500 0.2000 0.1500 0.1000 0.0500 0.0000 0

1

2

3

4

5

6

7

8

9

10

11

Fig. 2.3 Dependence of WACC on L

Ke(L)

0.8000 0.7000 0.6000 0.5000 0.4000 0.3000 0.2000 0.1000 0.0000 0

1

2

3

4

5

6

7

Fig. 2.4 Dependence of equity cost ke on L

This means there is no minimum for WACC with leverage changes, and no maximum for company capitalization with leverage changes. Thus, this means that there is no optimal capital structure in the famous theory of trade-offs. This fact has been explained by Brusov et al. (2013a). The explanation to this fact has been done within the Brusov–Filatova–Orekhova theory by studying the dependence of the equity cost ke on leverage. The explanation for this fact is as follows: The dependence of the cost of equity, ke, on the level of leverage undergoes significant changes when the growth in the cost of debt capital, kd, with the level of leverage is included (Figs. 2.4 and 2.5). The linear growth of the cost of equity ke at a low level of leverage is replaced by its fall, starting from a certain value L0. The value of L0 sometimes correlates exactly with the initial growth point kd with leverage level, but sometimes it takes values much higher. The rate of decline in the cost of equity ke with leverage increases with an increase in the growth rate of the cost of debt kd, as well as when moving from linear to quadratic growth and exponential growth. Thus, we come to the conclusion that the

20

2

Capital Structure Theory: Past, Present, Future

n=5

0.5 0.4

Kd

Kd

0.3

Wacc

0.2 0.1 0 0

2

4

Ke

Wacc

Ke 6

8

L Fig. 2.5 Dependence of equity cost ke, debt cost kd, and WACC on leverage L

increase in the cost of debt capital kd with leverage leads to the decrease in equity cost ke with leverage, starting with some value, L0. This is the cause of the absence of weighted average capital cost growth with leverage at all its values. The conclusions made are independent of the rate of growth of kd with leverage. Thus, this means that there is no optimal capital structure in the famous theory of trade-offs. This paradoxical conclusion explains the absence of an optimal capital structure in the famous trade-off theory. This means that the competition between the benefits of leverage and the cost of financial hardship (or the cost of bankruptcy) is not balanced, and the hope that trade-off theory gives us an optimal capital structure is unfortunately not realized. Mechanism of the formation of the company’s optimal capital structure, different from suggested by the trade-off theory, has been developed by Brusov et al. (2014a).

2.4

Accounting for Transaction Costs

If the cost of changing the capital structure to its optimal value is high, the company may decide not to change the capital structure and maintain the current capital structure. The company may decide that it is more cost-effective not to change the capital structure, even if it is not optimal, for a certain period of time. Due to this, the actual and target capital structure may differ.

2.5

Accounting for Asymmetries of Information

In real financial markets, information is asymmetric (company managers have more reliable information than investors and creditors), and the rationality of economic entities is limited.

2.8

Behavioral Theories

2.6

21

Signaling Theory

Information asymmetry can be reduced based on certain signals for lenders and investors related to the behavior of managers in the capital market. It should take into account the previous company development and the current and projected profitability of the activity (Myers 1984a, b).

2.7

Pecking Order Theory

The pecking order theory (Myers 1984a, b), Fama and French (2005) describes a preferred sequence of funding types for raising capital. That is, companies first use financing from retained earnings (internal equity), the second source is debt, and the last source is the issuance of new shares of common stock (external equity). Empirical data on the leverage level of non-financial companies, combined with the decision-making process of top management and the board of directors, indicate a greater commitment to the pecking order theory. Note that this theory contradicts both MM and BFO theories, which underline the importance of debt financing.

2.8 2.8.1

Behavioral Theories Manager Investment Autonomy

Company managers implement those decisions that, from their point of view, will be positively perceived by investors and, accordingly, will positively affect the market value of companies: when the market value of the company’s shares and the degree of consensus between the expectations of managers and investors is high, the company conducts an additional share issue, and in the opposite situation, it uses debt instruments. Thus, the company capital structure is more influenced by investors, whose expectations are taken into account by company managers.

2.8.2

The Equity Market Timing Theory

The level of leverage is determined by market dynamics. Equity market timing theory means that a company should issue shares at a high price and repurchase them at a low price. The idea is to take advantage of the temporary fluctuations in the value of equity relative to the value of other forms of capital.

22

2.8.3

2

Capital Structure Theory: Past, Present, Future

Information Cascades

To save costs and avoid mistakes, the company’s capital structure can be formed not on the basis of calculations of the optimal capital structure (this is a non-trivial task and its correct solution could be found within the framework of the BFO theory) or depending on the available sources of financing of the company, but borrowed from other companies, having successful, proven managers (heads of companies), as well as using (following the majority) the most popular methods of managing the capital structure, or even simply by copying of the capital structure of successful companies in a similar industry.

2.9 2.9.1

Theories of Conflict of Interests Theory of Agency Costs

The company’s management may make decisions that are contrary to the interests of shareholders or creditors, respectively; expenses are necessary to control its actions. For solving the agency problem, the correct choice of the compensation package (the agent’s share in the property, bonuses, and stock options) is needed, which allows you to link the manager’s profit with the dynamics of equity capital and ensure the motivation of managers for the preservation and growth of equity capital (Jensen 1986).

2.9.2

Theory of Corporate Control and Costs Monitoring

In the presence of information asymmetry, creditors providing capital are interested in the possibility of self-control over the effectiveness of its use and return. Monitoring costs are usually passed on to company owners by being included in the loan rate. The level of monitoring costs depends on the scale of the business; therefore, with the increase in the scale of the business, the company’s weighted average capital cost increases, and the company’s market value decreases.

2.9.3

Theory of Stakeholders

Stakeholder theory is a theory that defines and models the groups that are the stakeholders of a company. The diversity and intersection of the interests of stakeholders, their different assessments of acceptable risk, give rise to conditions for a

2.10

BFO Theory

23

conflict of their interests, that is, they make adjustments to the process of capital structure optimization.

2.10

BFO Theory

The restriction associated with the infinite life of companies and the eternity of cash flows within the framework of the MM theory was removed in 2008 by Brusov, Filatova, and Orekhova (Filatova et al. 2008), who created the modern theory of the cost of capital and capital structure—the BFO theory, which is valid both for companies of arbitrary age, as well as for companies with an arbitrary lifetime. A generalization of the assessment of the tax shield TS and the value of the company: without leverage V0 and with leverage V was required to modify the theory of MM (see the formulas below): TS = kd DT

n X

ð1 þ k d Þ - t = DT ½1- ð1 þ kd Þ - n :

ð2:26Þ

t=1

V 0 = CF½1- ð1 þ k0 Þ - n =k0 ;

V = CF½1- ð1 þ WACCÞ - n =WACC:

1 - ð1 þ k 0 Þ - n 1 - ð1 þ WACCÞ - n : = WACC k 0 ½1 - ωd T ð1 - ð1 þ kd Þ - n Þ

ð2:27Þ ð2:28Þ

D stands for the debt capital Here, S stands for the equity capital value, wd = DþS S share, k e , we = DþS stands for the equity cost and the equity capital share, and L = D/ S stands for the value of financial leverage; D stands for the debt capital value. For a 1-year company Steve Myers in 2001 derived a formula, which could be obtained easily from Formula (2.28) by substituting n = 1.

WACC = k0 -

ð1 þ k0 Þk d wd T 1 þ kd

By substituting n = 1 we arrive to the Modigliani–Miller formula for WACC (Modigliani and Miller 1963): WACC = k0  ð1- wd t Þ Dependence of WACC on leverage level for n = 1, n = 3, and n = 1 see in Fig. 2.6. The methods and the conclusions of the Brusov–Filatova–Orekhova (BFO) theory are well–known in the scientific literature. In a number of works, the BFO theory is used in practical calculations.

24

2

Capital Structure Theory: Past, Present, Future

Fig. 2.6 Dependence of WACC on leverage level for n = 1, n = 3, and n = 1

2.10.1 Brusov–Filatova–Orekhova Theorem Case of Absence of Corporate Taxes Modigliani–Miller theory in case of absence of corporate taxes provides the following results for dependence of WACC and equity cost ke on leverage: V 0 = V L;

CF=k 0 = CF=WACC,

and thus WACC = k 0 :

ð2:29Þ

WACC = we  ke þ wd  kd

ð2:30Þ

L k0 k WACC - wd  kd 1 þ L d ke = = 1 we 1þL = k0 þ Lðk 0 - k d Þ:

ð2:31Þ

and thus,

For the finite lifetime (finite age) companies, the Modigliani–Miller theorem about equality of value of financially independent and financially dependent companies (V0 = VL) has the following view: V 0 = V L; CF 

½ 1 - ð1 þ k 0 Þ k0

-n



= CF 

½1 - ð1 þ WACCÞ - n  : WACC

ð2:32Þ

Using this relation, we have proven an important Brusov–Filatova–Orekhova theorem:

2.11

BFO Theory and Modigliani–Miller Theory Under Inflation

25

Under the absence of corporate taxes, the equity cost of the company, ke, as well as its weighted average cost of capital, WACC, does not depend on the lifetime (age) of the company and is equal, respectively, to ke = k 0 þ Lðk0- kd Þ;

2.11

WACC = k0 :

ð2:33Þ

BFO Theory and Modigliani–Miller Theory Under Inflation

The influence of inflation on the cost of raising capital and the company value has been studied within modern theory of capital cost and capital structure Brusov– Filatova–Orekhova theory (BFO theory) (Brusov et al. 2014b) and within its perpetuity limit Modigliani–Miller theory. For the first time, it was shown by the direct incorporation of inflation into both theories that inflation not only increases the cost of raising capital (the equity cost and the weighted average cost of capital), but that it also changes their dependence on leverage. In particular, it increases the growth rate of equity costs with leverage. The company’s value decreases under inflation (Fig. 2.7). 1 - ð1 þ WACC Þ - n WACC 1 - ½ð1 þ k0 Þð1 þ αÞ - n = : ðk0 ð1 þ αÞ þ αÞ  ½1 - ωd T ð1 - ðð1 þ kd Þð1 þ αÞÞ - n Þ

ð2:34Þ

Formula (2.34) is the generalized Brusov–Filatova–Orekhova formula under inflation. Here, WACC = WACC  (1 + α) + α. In the Modigliani–Miller theory, WACC = ðk0 ð1 þ αÞ þ αÞ  ð1- wd t Þ   ke = k 0 þ Lð1 - T Þ k 0 - kd = ½k 0 ð1 þ αÞ þ α þ Lð1 - T Þðk0 - kd Þð1 þ αÞ:

ð2:35Þ

The modified equation for the weighted average cost of capital WACC, applicable to companies of arbitrary age under inflation, was derived in the framework of the modern theory of cost and capital structure—the theory of Brusov–Filatova– Orekhova (BFO theory). The modified BFO equation allows investigation of the dependence of the weighted average cost of capital, WACC, (see Fig. 2.8) and the cost of equity, ke, on the level of financial leverage, L, on the income tax rate, t, on

26

2

Capital Structure Theory: Past, Present, Future

Fig. 2.7 Dependence of the equity cost and the weighted average cost of capital on leverage in the Modigliani–Miller theory without taxing under inflation. It is seen that the growing rate of equity costs increases with leverage. Axis y means capital costs–CC

Fig. 2.8 Dependence of the weighted average cost of capital WACC on debt fraction wd at different inflation rate α (1, α = 3%; 2, α = 5%; 3, α = 7%; and 4, α = 9%) for a 5-year company

WACC 0.35

WACC(wd), k0=20%, kd=12%, T=20%

0.30 0.25

4 3 2 1

0.20 0.15 0.10 0.05

Wd

0.00 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

1.1

2.12

BFO Theory for the Companies Ceased to Exist at the Time Moment n. . .

27

the age of the company, n, on the cost of equity, k0, and the cost of debt, kd, for various inflation rates α. Using the modified BFO equation, authors analyzed the dependence of the weighted average cost of capital WACC on the share of debt wd at various income taxes t, as well as the inflation rate α. It was shown that WACC decreases with an increase in leverage level L (or the share of debt, wd), and the faster it decreases, the higher the income tax rate t. The distance between the lines, corresponding to different values of the income tax rate at the same step (10%), increases with the growth of the inflation rate α. The area of change (with a change in the income tax rate t) of the weighted average cost of capital WACC increases with the inflation rate α, as well as with the age of the company n.

2.12

BFO Theory for the Companies Ceased to Exist at the Time Moment n (BFO–2 Theory)

The MM theory is only applicable to perpetual companies. As follows from the derivation of the BFO formula, the developed methodology is applied to companies of arbitrary age n (which have reached the age of n-years and continue to operate in the market). In other words, the BFO is applicable to the most interesting practical cases and allows you to analyze the financial condition of operating companies. However, the BFO theory also allows us to consider the financial condition of companies that have ceased to exist, i.e., those for where n does not mean age, but lifetime, i.e., the time of existence. There can be many schemes for terminating a company: bankruptcy, merger, takeover, etc. Below we will consider one of these schemes. When the value of debt capital D becomes equal to zero at the time of the termination of the company n, in this case, the BFO theory requires minimal updates, as shown below (Brusov et al., 2018). From the formula for the company’s capitalization, it is easy to obtain an estimate of the “residual capitalization” of the company, discounted to the time moment k: Vk =

n X t = kþ1

h i CF CF - ðn - kÞ = 1ð 1 þ WACC Þ : WACC ð1 þ WACCÞt

ð2:36Þ

Substituting V k = wd D,

ð2:37Þ

one gets the expression for the tax shield for n years, subject to the termination of the company’s activities at time moment n:

28

2

Capital Structure Theory: Past, Present, Future

n n - ðn - kþ1Þ X tk d wd CF X 1 - ð1 þ WACCÞ Vk -1 = = k WACC k = 1 ð1 þ kd Þk k = 1 ð1 þ k d Þ ð2:38Þ   -n ð1 þ kd Þ - n - ð1 þ WACCÞ - n tk d wd 1 - ð1 þ k d Þ : = WACC kd WACC - k d

TSn = tk d wd

Substituting this formula into the equation, V L = V 0 þ ðTSÞn

ð2:39Þ

we arrive at the following equation (which determines the BFO–2 theory) 1 - ð1 þ WACCÞ - n 1 - ð1 þ k0 Þ - n tk w þ d d = WACC k0 WACC   1 - ð1 þ kd Þ - n ð1 þ kd Þ - n - ð1 þ WACCÞ - n ,  kd WACC - kd

ð2:40Þ

hence, it is possible to find WACC for companies with an arbitrary lifetime n, under the condition that the company ceases to operate at a time moment n.

2.13

The Modigliani–Miller Theory with Advance Payments of Tax on Profit

The first serious study (and first quantitative study) of influence of capital structure of the company on its indicators of activities was the work by Nobel Prize Winners Modigliani and Miller. Their theory has a lot of limitations. One of the most important and serious assumptions of the Modigliani–Miller theory is that all financial flows as well as all companies are in perpetuity. This limitation was lifted by Brusov–Filatova–Orekhova in 2008 (Filatova et al. 2008), who created the BFO theory—a modern theory of capital cost and capital structure for companies of arbitrary age. Despite the fact that the Modigliani–Miller theory is currently a particular case of the general theory of capital cost and capital structure—Brusov– Filatova–Orekhova (BFO) theory—is still widely used in the West. Brusov et al. (Brusov et al. 2020a, b, 2021a, b, 2022a, b; Brusov and Filatova 2021, 2022a, b; Filatova et al. 2022) discuss another limitation of the Modigliani– Miller theory: the method of paying income tax. The Modigliani–Miller theory accounts for these payments as immediate annuities, while in practice these payments are often made in advance and therefore must be accounted for annuities due. The authors generalized the Modigliani–Miller theory to the case of advance payments on income tax, which is widely used in practice. This generalization leads to a serious change in all the main provisions of Modigliani and Miller. These changes are as follows: When WACC begins to depend on the cost of debt kd, WACC turns

2.14

The Modigliani–Miller Theory with Arbitrary Frequency of Payment of. . .

29

out to be lower than in the case of the classical Modigliani–Miller theory, and the value of the company becomes higher. The formula for WACC has the following form: WACC = k0 ð1- wd t ð1 þ kd ÞÞ

ð2:41Þ

Although the dependence of the cost of equity ke on the level of leverage L remains linear, the angle of inclination relative to the L axis turns out to be smaller: this may lead to a modification of the company’s dividend policy. Correct accounting for the method of paying income tax shows that the shortcomings of the Modigliani–Miller theory are more serious than everyone expected: the underestimation of WACC is indeed greater, as is the overestimation of the company’s capitalization. This means that the systematic risks arising from the use of the modified Modigliani–Miller theory (the MMM theory) (more correct than the “classical” theory) are in practice higher than it was supposed by the “classical” version of this theory.

2.14

The Modigliani–Miller Theory with Arbitrary Frequency of Payment of Tax on Profit

One of the conditions for the real functioning of companies is the payment of income tax with an arbitrary frequency (monthly, quarterly, every 6 months or annually). The return is not required more than once a year, but companies may be required to file estimated taxes based on profits earned. The authors of Brusov and Filatova (2021) generalized the Modigliani–Miller theory to the case of paying income tax with arbitrary periodicity. The formula for WACC has the following form (Brusov et al. 2021a, b, 2022a): WACC = k 0 

1-

1 k d wd t Þ p ð1 þ k d Þ1=p - 1

ð2:42Þ

and for company value V=

WACC  k0  1 - kd pwd t

ð2:43Þ

1 Þ 1 ð1þkd Þ =p - 1

They showed that the frequency of income tax payment affects all the main financial indicators of the company and leads to a number of important consequences. Theoretically, the authors derived all the main formulas of the modified Modigliani–Miller theory and used them to obtain all the main financial indicators of the company at arbitrary frequencies of income tax payment. They showed that:

30

2 Capital Structure Theory: Past, Present, Future

(1) all Modigliani–Miller theorems, assertions, and formulas have been changed; (2) all major financial indicators, such as the weighted average cost of capital (WACC), the value of the company, V and the cost of equity, ke, depend on the frequency of income tax payments; (3) in the case of paying tax on profit more than once a year (with p ≠ 1), as is the case in practice, WACC, company value, V and equity value, as well as equity cost ke start to depend on the cost of debt, kd, and in the usual (classical) Modigliani–Miller theory, all these quantities do not depend on kd; (4) the results obtained allow the company to choose the number of tax on profit payments per year (of course, within the framework of the current tax legislation): more frequent tax on profit payments are beneficial to both parties, the company and the tax regulator.

2.15

Generalization of the Modigliani–Miller Theory for the Case of Variable Profit

In Brusov et al. (2021b), for the first time, the world-famous theory of Nobel laureates Modigliani and Miller was generalized to the case of variable income, which significantly expands the applicability of the theory in practice, in particular, in corporate finance, business valuation, investments, ratings, etc. The following formulas for WACC and company value have been obtained WACC - g = ðk0- gÞ  ð1- wd t Þ V=

CF CF = WACC - g ðk 0 - gÞ  ð1 - wd t Þ

ð2:44Þ ð2:45Þ

It was shown that all the theorems, assertions, and formulas of Modigliani and Miller have been essentially changed. The authors obtained the following results: (1) WACC and k0 are no longer the discount rates as it takes place in case of classical Modigliani–Miller theory with constant profit. The role of discount rate for leverage company passes from the weighted average cost of capital, WACC, to WACC - g (where g is growing rate), for a financially independent company from k0 to k0 - g. The real discount rates WACC - g and k0 - g decrease with g, while WACC grows with g. This decrease leads to an increase in company value with g. (2) The slope of the equity cost ke(L) grows with g. Via the fact, that the economically justified value of dividends is equal to equity cost this will modify the company’s dividend policy. (3) It has been discovered the qualitatively new effect in corporate finance: the slope of the curve ke(L) at rate g < g* turns out to be negative. This effect significantly alters the company’s dividend policy principles.

2.16

2.16

The Generalization of the Brusov–Filatova–Orekhova Theory for the. . .

31

The Generalization of the Brusov–Filatova–Orekhova Theory for the Case of Payments of Tax on Profit with Arbitrary Frequency

The Brusov–Filatova–Orekhova (BFO) theory and its limit of eternity, the Modigliani–Miller theory—both the main theories of the cost of capital and capital structure—consider income tax payments once a year. These payments in the real economy are made more frequently (every 6 months, quarter, month, etc.). In Brusov et al. (2021a, b) and Brusov and Filatova (2021), the Modigliani–Miller theory was generalized by Brusov et al., for the case of paying income tax with arbitrary periodicity. In Brusov et al. (2022a, b) and Brusov and Filatova (2022a), for the first time, authors generalized the theory of Brusov–Filatova–Orekhova (BFO) to this case. Taking into account one of the features of the real functioning of companies—frequent payments of income tax—the authors brought the BFO theory closer to economic practice. Authors derived modified BFO formula 1 - ð1 þ WACCÞ - n = WACC

1 - ð1 þ k 0 Þ - n  -n k0  1 - kd pwd t ½1 - ð1þk1=pd -Þ 1 Þ

ð2:46Þ

ð1þk d Þ

and showed that: (1) All BFO formulas change; (2) all major financial parameters of a company, such as company capitalization, V, weighted average cost of capital, WACC, cost of equity, ke, etc. depend on the frequency of tax on profit payments. The cost of raising capital WACC decreases with the frequency of tax on profit payments and the company value, V increases with the frequency of tax on profit payments. A qualitatively new anomalous effect takes place at some age of the company, n, and at some frequency of income tax payments p: the cost of equity ke(L ) decreases with leverage level L. Since the economically justified amount of dividends is equal to the cost of equity, this fundamentally changes the company’s dividend policy. More frequent income tax payments are beneficial to both parties—the company and the tax regulator: the company, because it increases the value of the company, and the tax regulator, because it benefits from earlier payments due to the time value of money.

32

2.17

2

Capital Structure Theory: Past, Present, Future

Benefits of Advance Payments of Tax on Profit: Consideration Within the Brusov–Filatova–Orekhova (BFO) Theory

Both theories of capital structure—the Brusov–Filatova–Orekhova (BFO) and its limit of eternity, the theory of Modigliani–Miller—consider the case of paying tax on profit at the end of the year. However, in practice, companies could make these payments in advance. In Brusov et al. (2020b), the Modigliani–Miller theory was modified for the case of advance payments of tax on profit, and the results turned out to be completely different from the results of the usual Modigliani–Miller theory. In Brusov et al. (2022a, b), the Brusov–Filatova–Orekhova (BFO) theory was modified for the first time for advance payments on income tax. The impact of such a transition to advance payments is much more significant than in the theory of MM and even leads to a qualitatively new effect in the cost of equity dependence on leverage. The authors derived a modified BFO formula for WACC: 1 - ð1 þ k 0 Þ - n 1 - ð1 þ WACCÞ - n  = 1 WACC k0  1 - wd t ½1 - ð1 þ kd Þ - n ð1 þ kd Þ =p Þ

ð2:47Þ

It is concluded that the tax shield and the way it is formed (payments at the end of the year or in advance) have very important consequences, changing all the company’s financial indicators, such as the company’s value and capital raising costs, and also significantly changing the company’s dividend policy.

2.18

Influence of Method and Frequency of Profit Tax Payments on Company Financial Indicators

In practice, income tax payments may (1) be made in advance and (2) more frequently than once a year. In Brusov et al. (2022a, b) and Brusov and Filatova (2022a), the simultaneous influence of these two factors on the company’s financial performance was studied. To this end, the Brusov–Filatova–Orekhova (BFO) theory was first generalized to the case of advance payments of income tax with an arbitrary periodicity. The authors derived the following modified BFO formula for WACC: 1 - ð1 þ WACCÞ - n = WACC

1 - ð1 þ k 0 Þ - n  -n  dÞ k0  1 - kd pwd t  ½1 - ð1=p1þk -1 ð1þkd Þ

ð2:48Þ 1

Þð1þkd Þ =p Þ

It is concluded that all financial indicators of the company, such as the weighted average cost of capital (WACC) and the cost of equity (ke), the value of the company (V ) depend on the frequency of income tax payment. WACC increased with the

2.19

The Brusov–Filatova–Orekhova (BFO) Theory with Variable Income

33

frequency of payments, and the value of the company decreased. This meant that infrequent payments could be beneficial to the company in the case of advance income tax payments. The slope of the cost of equity, ke(L ), increased with the frequency of payments. Depending on the age of the company, ke(L) either increased for some payment frequencies or decreased with L for all payment frequencies. The authors compared these results with their results for income tax payments at the end of the periods (see Formula (2.47)) and found a huge difference: while in the latter case, WACC decreased with payment frequency, and the company capitalization increased with payment frequency, the value of WACC in this case remains bigger, and the company capitalization remains lower than in the case of advance income tax payments of any frequency. The importance of advance income tax payments has been underlined by this fact. The authors developed the recommendations to the regulator to increase the practice of advance payments of income tax due to the benefits of this for both parties: the companies and the state. A new effect—the decrease in equity cost with the level of leverage (L )—has been discovered.

2.19

The Brusov–Filatova–Orekhova (BFO) Theory with Variable Income

Two main theories of capital structure—Brusov–Filatova–Orekhova (BFO) and Modigliani–Miller consider the case of constant profit. However, in practice, the company’s income, of course, is variable. Both theories have recently been generalized to the case of variable income (Brusov and Filatova 2022b), which significantly expands the applicability of both theories of capital structure in practice. The following generalized BFO formula for WACC has been discovered: 1-




1þg 1þWACC

n

WACC - g

=

1-




1þg 1þk 0

n

ðk0 - gÞ  ð1 - wd t ½1 - ð1 þ k d Þ - n Þ

ð2:49Þ

In the theory of Brusov–Filatova–Orekhova (BFO) (Brusov et al. 2022b), generalized to the case of variable income, income tax payments are made at the end of periods, while in practice these payments can also be made in advance. In Brusov et al.’s (Brusov and Filatova 2022b) work, the authors considered two modifications of the Brusov–Filatova–Orekhova (BFO) theory with variable income: (1) with the payment of income tax at the end of the periods and (2) with advance payments of income tax. For these two cases, BFO formulas were derived for the weighted average cost of capital, WACC, for the value of the company, V, and within these formulas, a comprehensive analysis of the dependence of WACC, of the discount rate, WACC–g (here g is the growth rate), company capitalization, V, the cost of equity, ke, on debt financing at different values of the growth rate, g, at different values of the cost of debt capital, kd, and at different values of the age of the company, n. The

34

2 Capital Structure Theory: Past, Present, Future

results for cases (1) and (2) are compared, which allows us to conclude that case (2) is always preferable for both the company and the regulator. This makes it possible to develop recommendations for both parties to expand the practice of advance income tax payments within the framework of real economic practice. Brusov et al. emphasized an important observation. If in the classical versions of the Brusov–Filatova–Orekhova (BFO) theory and its perpetual limit—the theory of Nobel laureates Modigliani and Miller—the case of constant profit was considered, and where the gap between these two theories is huge (many qualitative effects that take place in the first theory, missing in the second), when taking into account variable profit, some effects of the BFO theory also take place in the Modigliani– Miller theory. This means that taking into account some effects that are present in economic practice (for example, variable income) brings both theories closer, and even the Modigliani–Miller theory, with all its many limitations, becomes more applicable in economic practice. However, it should be remembered that the Modigliani–Miller theory is only true for perpetual companies, while the BFO theory is valid for companies of any age, and from this point of view, they never coincide.

2.20

Qualitatively New Effects in the Theory of Capital Structure

Two qualitatively new effects in the theory of capital structure. Among the many new effects discovered in the framework of the BFO theory, we will describe only two new ones qualitatively: 1. Golden and silver ages of the company 2. Anomalous dependence of the cost of equity on the leverage level

2.20.1

Golden and Silver Ages of the Company

To determine the minimum cost of raising capital depending on the age of the company, Brusov et al. (2018) studied the dependence of the cost of raising capital on the age of the company, n, at different levels of leverage, L, at different values of capital costs. The authors used the Brusov–Filatova–Orekhova theory (Filatova et al. 2008; Brusov et al. 2018). It was shown for the first time that the value of WACC in the Modigliani–Miller theory is not minimal, and the value of the company is not maximal, contrary to the opinion of all financiers: it turned out that at a certain age of the company, the value of WACC is lower than in the eternal Modigliani–Miller theory, and the value of company V is greater than the value of company V in the Modigliani–Miller theory.

2.20

Qualitatively New Effects in the Theory of Capital Structure

35

Fig. 2.9 Two types of dependences of WACC, and company value, V, on the company age n

Authors discovered two types of WACC dependences on the age of company n: monotonic decreases with n and WACC decreases with passage through the minimum, followed by a limited growth (Brusov et al. 2018) (Fig. 2.9). The latter type of dependence of WACC on the age of company n allows the companies to take advantage of the benefits given at a certain stage of their development. Moreover, since capital costs, ke and kd, affect the company’s golden age by changing it (for example, changing the value of dividend payments to reflect the cost of equity, etc.), the company can postpone or extend its golden age, at which the cost of raising capital is minimal (and less than its perpetual limit), and the value of companies is maximum (above their perpetual value). 1–1′—monotonic decrease in WACC, and company value, V, increases with the company age n; 2–2’—WACC decreasing with n, passage through minimum (at n0), followed by a limited growth and increase in V with the passage through a maximum (at n0) and then a limited decreasing. It has been shown that the existence of the company “golden age” depends not on the capital cost values, but on the difference between equity k0 and debt kd costs. The effect of the company “golden age” takes place at small enough difference between k0 and kd costs, while at this difference the high value effect is absent: curve WACC (n) monotonic decreases with company age n. Curve WACC(L ) for perpetuity limit is the lowest one for the companies without the “golden age” (Fig. 2.10), while for the companies with the “golden age,” curve WACC(L ) for perpetuity limit (n = 1) lies between curves WACC(L ) for 1 year (n = 1) and 3 years (n = 3) companies (Figs. 2.6 and 2.11).

36

2

Capital Structure Theory: Past, Present, Future

Fig. 2.10 The dependence of WACC on leverage level, L, at different company ages n (n = 1, 3, and 49)

WACC(L) 0.21000000 0.20000000

WACC

0.19000000 0.18000000 0.17000000 0.16000000 0.15000000 0.14000000

0

1

2

3

WACC(n=1)

4

5

6

WACC(n=3)

7

8

9

10 L

WACC(n=45)

Fig. 2.11 The dependence of WACC on the leverage level, L, at different company ages n (n = 1, 3, and 45)

2.20

Qualitatively New Effects in the Theory of Capital Structure

37

WACC

K0 2 K0(1-wd t) 1

n0

n1

n

Fig. 2.12 Dependence of WACC on company age n: company “golden age” (curve 1) and company “silver age” (curve 2) under the existence of the “Kulik” effect, where n0 is the company “golden (silver) age” and n1 is the company age of local maximum in the dependence of WACC(n)

2.20.2

Silver Age of the Company

In Fig. 2.12 the effect of “Silver Age of the Company” is shown.

2.20.3

Anomalous Dependence of the Company’s Equity Value on Leverage

Brusov et al. (2013b) found a qualitatively new effect in the capital structure: a decrease in the cost of equity at a leverage level L (Fig. 2.13). This effect is absent in the perpetual Modigliani–Miller limit, but appears in companies of finite age at an income tax rate exceeding a certain value T*. For some values of the cost of equity and the cost of debt, this effect exists at the tax on income values existing in financial practice. This ensures the practical significance of the discovered effect. Accounting for this effect is important when changing tax legislation and can significantly change the company’s dividend policy.

38

2

Ke

Capital Structure Theory: Past, Present, Future

Ke(L), at fix T

0.4000 0.3000

1

0.2000

2

0.1000

3

0.0000

4 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 1010.5

-0.1000

5

-0.2000 6 -0.3000

L

Fig. 2.13 Dependence of equity cost, ke, on leverage level L at different tax on income rate T. (n = 5, k0 = 10 % , kd = 8%) (1—T = 0; 2—T = 0.2; 3—T = 0.4; 4—T = 0.6; 5—T = 0.8; 6— T = 1)

2.21

A Stochastic Extension of the Modigliani–Miller Theory

A stochastic extension of the Modigliani–Miller theory has been conducted in a few papers. Demarzo (1988) showed that the Modigliani–Miller theory is correct in a multiperiod stochastic economy with incomplete markets. In the model the author developed, companies could trade securities, and stock prices and dividends became completely interdependent. Several corporate control mechanisms were considered, including maximizing the value of the company and shareholder voting. It is shown that equilibrium companies have no incentive to trade securities and that the set of equilibrium distributions does not change as a result of such trading. Sethi et al. (1991) studied the company value valuation problem under a partial equilibrium, a time-dependent discount rate, and a general stochastic environment in a discrete-time setting. The time path of the share price and the company value are obtained upon the assumption of risk neutrality.

2.22

2.22

Conclusions

39

Conclusions

The chapter analyzes all the main existing theories of capital structure, including Modigliani–Miller and BFO. Various modifications of these two and other theories, including the latest ones, related to the conditions of the real functioning of companies and developed in recent years are discussed in detail. The generalization of the Modigliani–Miller theory for cases of practical interest led to a much more significant change in the Modigliani–Miller theory than in all previous modifications studied over the previous decades. Obtained results showed that under such a generalization there is some convergence of the Modigliani–Miller theory and the BFO theory. The former theory began to have some new properties similar to those of the BFO theory, which were not there in the classical Modigliani– Miller theory. Between the properties of the former and those of the BFO theory, there was a huge gap. Most of the innovative effects existing in the BFO theory are absent in the classical Modigliani–Miller theory. All the above means that the considered effects, such as the variable income of the company, the frequent payment of income tax, advance payment of income tax, and the combinations of these conditions and others, are more important than the effects studied earlier and have much less influence on the Modigliani–Miller theory. Taking these effects into account leads to some convergence between the Modigliani–Miller theory and the BFO theory. At the same time, one must understand that the Modigliani–Miller theory remains perpetual and will never describe a company of arbitrary age, which is extremely important for the practical application of the theory. Despite the great progress associated with the described generalization of both theories during the last couple of years, there are still some limitations that dictate the direction of further research. If we talk about the two main theories of the structure of capital: Modigliani– Miller and BFO, then one of the limitations is that the BFO theory and the MM theory were generalized to the case of a variable company income, but with a constant growth rate g. The directions for further research are as follows: 1. Generalization of the BFO theory and the MM theory to the case of a company’s variable-in-time income 2. Generalization of the BFO theory to the stochastic case and to the case of a company’s variable-in-time income 3. Further generalization of the BFO theory and MM theory on the conditions for the practical functioning of the company 4. Study the dependence of the effects of the “golden and silver age of the company” on the growth rate of income in the case of a company’s variable income, on the frequency of income tax payment, on the advance payment of income tax, and on a combination of these conditions

40

2

Capital Structure Theory: Past, Present, Future

5. Develop a methodology for determining the financial parameters of a company in the event of a drop in income, in the event of an increase in the company’s income, as well as in the case of alternating growth and falling income The practical significance of the capital structure theory is as follows: – Analysts can evaluate the company’s financial indicators for companies of arbitrary age – Allows for taking into account the conditions of the company’s real functioning – Allows to take into account the anomalous effects discovered in the BFO theory (such as “Golden age,” “abnormal dependence of equity cost with leverage,” etc.), which allow for making nonstandard effective management decisions – Allows the regulator to improve tax policy – Allows for the correct determination of the discount rate, which is extremely important in business valuation – Allows us to correctly determine the effectiveness of investments through the correct determination of the discount rate – Allows to correctly issue ratings of non-financial issuers, financial issuers, and investment projects In conclusion, we present in Table 2.1 a classification and summary of the main theories of capital structures of company. Table 2.1 The main theories of the company’s capital structure: classification and summary Theory Traditional theory

Modigliani–Miller theory (ММ)

Without taxes

With taxes

Main thesis Before appearance of the first quantitative theory of capital structures (Modigliani– Miller theory) in 1958 (Modigliani and Miller 1958, 1963; Miller 1977; Miller and Modigliani 1961, 1966) empirical theory existed. Weighted average cost of capital, WACC, and company value, V, depends on capital structures of company. Within the based on existing practical experience traditional approach the competition between the advantages of debt financing at a low leverage level and its disadvantages at a high leverage level forms the optimal capital structure, defined as the leverage level, at which WACC is minimal and company value, V, is maximum. Under many constraints, Modigliani and Miller concluded that the cost of raising capital and capitalization of a company do not depend on the company’s capital structure at all. Under corporate taxation, the weighted average cost of capital WACC decreases with the level of leverage, the cost of equity (continued)

2.22

Conclusions

41

Table 2.1 (continued) Theory

Brusov–Filatova– Orekhova theory (BFO–1)

Main thesis

For arbitrary age Without inflation

For arbitrary age With inflation

For arbitrary age With increased financial distress costs and risk of bankruptcy For arbitrary lifetime

ke increases linearly with the level of leverage, and the value of company V increases continuously with the level of leverage. In 2008 Brusov–Filatova–Orekhova (BFO) theory (Filatova et al. 2008) has replaced the famous Modigliani and Miller theory (Modigliani and Miller 1958, 1963; Miller 1977; Miller and Modigliani 1961, 1966). The authors have moved from the assumption of Modigliani–Miller concerning the perpetuity (infinite time of life) of companies and elaborated the quantitative theory of valuation of main indicators of financial activities of arbitrary age companies. Results of modern BFO theory turn out to be quite different from that of Modigliani– Miller theory. It shows that later, via its perpetuity, underestimates the valuation of cost of raising capital the company and substantially overestimates the valuation of the company value. Such an incorrect valuation of main financial parameters of companies has led to an underestimation of risks involved, and impossibility, or serious difficulties in adequate managerial decision-making, which was one of the implicit reasons of 2008 global financial crisis. In the BFO theory, in investments at certain values of return–on–investment, there is an optimum investment structure. As well a new mechanism of formation of the company optimal capital structure, different from suggested by trade-off theory has been developed. Inflation has a twofold effect on costs of raising capital: (1) increases the equity cost and the weighted average cost of capital, (2) changes their dependence on leverage, increasing, in particular, the rate of growth of the cost of equity with leverage. The company value decreases under accounting of inflation. In Brusov–Filatova–Orekhova (BFO) theory, with increased financial costs and bankruptcy risk, there is no optimal capital structure, which means that the trade-off theory does NOT work. In the Modigliani–Miller theory (in the limit of eternity), the lifetime of a company and (continued)

2 Capital Structure Theory: Past, Present, Future

42 Table 2.1 (continued) Theory Brusov–Filatova– Orekhova theory (BFO–2)

Brusov–Filatova– Orekhova theory (BFO–3)

Main thesis

For rating needs

the age of a company mean the same thing: they are both infinite. When moving to a company with a finite age, the terms “company lifetime” and “company age” become different, and they should be distinguished when generalizing the Modigliani–Miller theory to a finite n. Thus Brusov et al. have developed two kinds of finite n–theories: BFO–1 and BFO–2. BFO–1 theory is related to companies with arbitrary age and BFO–2 theory is related to companies with arbitrary lifetime companies. In other words, BFO–1 is applicable to most interesting cases of companies that reached the age of n–years and continue to exist on the market, and allows to analyze the financial condition of the operating companies. BFO–2 theory allows examine the financial status of the companies which ceased to exist, i.e., of those for which n means not age, but a lifetime, i.e., the time of existence. In real economy, there are a lot of schemes of termination of activities of the company: bankruptcy, merger, acquisition, etc. One of those schemes, when the value of the debt capital D becomes zero at the time of termination of activity of company n, is considered in Brusov et al. (2018), where as well where the results of BFO-1 and BFO-2 are also compared. A new approach to rating methodology (for non-financial issuers and for long-term project rating), within both BFO and MM theories has been developed be Brusov et al. (2018, 2020b). The key factors of a new approach are: (1) The adequate use of discounting of financial flows virtually not used in existing rating methodologies, (2) The incorporation of rating parameters (financial “ratios”) into these theories. This, on the one hand, allows use of the powerful tools of these theories in the rating, and on the other hand, it ensures the correct discount rates when discounting of financial flows. The interplay between rating ratios and leverage level which is quite important in rating. This creates a new base for rating methodologies, which allows to issue more correct ratings of issuers, makes the rating (continued)

2.22

Conclusions

43

Table 2.1 (continued) Theory

Trade-off theory

Main thesis

Static

Dynamic

methodologies more understandable and transparent. During decades one of the main theory of capital structure was the trade-off theory. There are two modifications of trade-off theory: static and dynamic. Static The static trade-off theory accounts the income tax and cost of bankruptcy. Within this theory the optimal capital structure is formed by the balancing act between the benefits of debt financing at low leverage level (from the tax shield from interest deduction) and the disadvantage of debt financing at high leverage level (from the increased financial distress and expected bankruptcy costs). The tax shield benefit is equal to the product of corporate income tax rate and the market value of debt and the expected bankruptcy costs are equal to the product of probability of bankruptcy and the estimated bankruptcy costs. The static version of the trade-off theory does not take into account the costs of adapting of the capital structure to the optimal one, economic behavior of managers, owners, and other participants of economical process, as well as a number of other factors. As it has been shown in BFO theory, the optimal capital structure is absent in tradeoff theory The dynamic version of trade-off theory suggests that the costs of adjusting the capital structure are high, and therefore companies will only change their capital structure if the benefits outweigh the costs. Therefore, there is an optimal range that varies on the outside of each lever but remains the same on the inside. Companies try to adjust their leverage when it reaches the edge of the optimal range. Depending on the type of adaptation costs, companies reach the target ratio faster or slower. Proportional changes involve a small adjustment, while fixed changes imply significant costs. In the dynamic version of the trade-off theory, company capital structure decision in (continued)

44

2

Capital Structure Theory: Past, Present, Future

Table 2.1 (continued) Theory

Accounting of transaction cost

Accounting of asymmetry of information

Signaling theory

Pecking order theory

Main thesis current period depends on the waiting company income in the next period. As it has been shown within BFO theory (Brusov et al. 2013a), under increased financial distress costs and bankruptcy risk, the optimal capital structure is absent. This means that the trade-off theory does NOT work in either the static or dynamic version. In BFO theory, with increased financial distress costs and risk of bankruptcy, the optimal capital structure is absent, which means that trade-off theory does NOT work: in static version as well as in dynamic one If the cost of changing the capital structure to its optimal value is high, the company may decide not to change the capital structure and maintain the current capital structure. The company may decide that it is more cost-effective not to change the capital structure, even if it is not optimal, for a certain period of time. Because of this, the actual and target capital structure may differ. In real financial markets, information is asymmetric (company managers have more reliable information than investors and creditors), and the rationality of economic entities is limited. Information asymmetry can be reduced based on certain signals for lenders and investors related to the behavior of managers in the capital market. It should take into account the previous company development and the current and projected profitability of the activity. The pecking order theory describes a preferred sequence of funding types for raising capital. That is, companies first use financing from retained earnings (internal equity), the second source is debt, and the last source is the issuance of new shares of common stock (external equity). Empirical data on the leverage level of non-financial companies, combined with the decisionmaking process of top management and the board of directors, indicate a greater commitment to pecking order theory. Note that (continued)

2.22

Conclusions

45

Table 2.1 (continued) Theory

Theories of conflict of interests

Main thesis

Theory of agency costs

Theory of corporate control and costs monitoring

Theory of stakeholders

Behavioral theories

Manager investment autonomy

this theory contradicts both MM and BFO theory, which underlines the quite importance of debt financing. The company management may make decisions that are contrary to the interests of shareholders or creditors, respectively; expenses are necessary to control its actions. For solving the agency problem the correct choice of compensation package (the agent’s share in the property, bonus, stock options) is needed, which allows you to link the manager’s profit with the dynamics of equity capital and ensure the motivation of managers for preservation and growth of equity capital. In the presence of information asymmetry, creditors providing capital are interested in the possibility of self-control of the effectiveness of its use and return. Monitoring costs are usually passed on to company owners by being included in the loan rate. The level of monitoring costs depends on the scale of the business; therefore, with the increase in the scale of the business, the company weighted average capital cost increases, and the company market value decreases. Stakeholder theory is a theory that defines and models the groups that are the stakeholders of a company. The diversity and intersection of interests of stakeholders, their different assessments of acceptable risk give rise to conditions for a conflict of their interests, that is, they make adjustments to the process of capital structure optimizing. Company managers implement those decisions that, from their point of view, will be positively perceived by investors and, accordingly, will positively affect the market value of companies: when the market value of the company’s shares and the degree of consensus between the expectations of managers and investors is high, the company conducts an additional share issue, and in the opposite situation uses debt instruments. Thus, the company capital structure is more influenced by investors, (continued)

46

2

Capital Structure Theory: Past, Present, Future

Table 2.1 (continued) Theory

Main thesis

The equity market timing theory

Information cascades

whose expectations are taken into account by company managers. The level of leverage is determined by market dynamics. Equity market timing theory means that a company should issue shares at a high price and repurchase them at a low price. The idea is to take advantage of the temporary fluctuations in the value of equity relative to the value of other forms of capital. To save costs and avoid mistakes, the company’s capital structure can be formed not on the basis of calculations of the optimal capital structure (this is a non-trivial task and its correct solution could be found within the framework of the BFO theory) or depending on the available sources of financing of the company, but borrowed from other companies, having successful, proven managers (heads of companies), as well as using (following the majority) the most popular methods of managing the capital structure, or even simply by copying of the capital structure of successful companies in a similar industry.

References Acharya V, Myers SC, Rajan R (2011) The internal governance of firms. J Financ 66:689–720 Arrow KJ (1964) The role of securities in the optimal allocation of risk-bearing. Rev Econ Stud 31: 91–96 Asquith P, Mullins DW (1986) Equity issues and offering dilution. J Financ Econ 15:61–89 Baumol W, Panzar JG, Willig RD (1982) Contestable markets and the theory of industry structure. Harcourt College Pub, New York, NY, USA Becker DM (2021) The difference between Modigliani–Miller and Miles–Ezzell and its consequences for the valuation of annuities. Cogent Econ Financ 9:1. https://doi.org/10.1080/ 23322039.2020.1862446 Berk J, DeMarzo P (2007) Corporate finance. Pearson–Addison Wesley, Boston, MA, USA Bhattacharya S (1978) Project valuation with mean-reacting cash flows. J Financ 33:1317–1331 Black F (1986) Noise. J Financ 41:529–543 Brealey RA, Myers SC (1981) Principles of corporate finance, 1st edn. McGraw-Hill, New York, NY, USA Brealey RA, Myers SC, Allen F (2014) Principles of corporate finance, 11th edn. McGraw-Hill, New York, NY, USA Brennan M, Schwartz E (1978) Corporate income taxes, valuation, and the problem of optimal capital structure. J Bus 51:103–114 Brennan M, Schwartz E (1984) Optimal financial policy and firm valuation. J Financ 39:593–607

References

47

Brusov P, Filatova T (2021) The Modigliani–Miller theory with arbitrary frequency of payment of tax on profit. Mathematics 9:1198 Brusov P, Filatova T (2022a) Influence of method and frequency of profit tax payments on company financial indicators. Mathematics 10:2479. https://doi.org/10.3390/math10142479 Brusov P, Filatova T (2022b) Generalization of the Brusov–Filatova–Orekhova theory for the case of variable income. Mathematics 10:3661. https://doi.org/10.3390/math10193661 Brusov P, Filatova T, Eskindarov M, Orehova N (2012) Hidden global causes of the global financial crisis. J Rev Glob Econ 1:106–111 Brusov P, Filatova P, Orekhova N (2013a) Absence of an optimal capital structure in the famous tradeoff theory! J Rev Glob Econ 2:94–116 Brusov P, Filatova T, Orehova N (2013b) A qualitatively new effect in corporative finance: abnormal dependence of cost of equity of company on leverage. J Rev Glob Econ 2:183–193 Brusov P, Filatova P, Orekhova N (2014a) Mechanism of formation of the company optimal capital structure. Different from suggested by trade off theory. Cogent Econ Financ 2:1–13. https://doi. org/10.1080/23322039.2014.946150 Brusov P, Filatova T, Orehova N (2014b) Inflation in Brusov–Filatova–Orekhova theory and in its perpetuity limit–Modigliani–Miller theory. J Rev Glob Econ 3:175–185 Brusov P, Filatova T, Orehova N, Eskindarov M (2018) Modern corporate finance, investments, taxation and ratings, 2nd edn. Springer, Cham, Switzerland, pp 1–571 Brusov PN, Filatova TV, Orekhova NP, Kulik VL, Chang SI, Lin YCG (2020a) Modification of the Modigliani–Miller theory for the case of advance payments of tax on profit. J Rev Glob Econ 9: 257–267 Brusov P, Filatova T, Orekhova N, Kulik V, Chang S-I, Lin Y (2020b) Application of the Modigliani–Miller theory, modified for the case of advance payments of tax on profit, in rating methodologies. J Rev Glob Econ 9:282–292 Brusov P, Filatova T, Chang S-I, Lin G (2021a) Innovative investment models with frequent payments of tax on income and of interest on debt. Mathematics 9:1491 Brusov P, Filatova T, Orekhova N, Kulik V, Chang S-I, Lin G (2021b) Generalization of the Modigliani–Miller theory for the case of variable profit. Mathematics 9:1286 Brusov P, Filatova T, Orekhova N, Kulik V, Chang SI, Lin G (2022a) The generalization of the Brusov–Filatova–Orekhova theory for the case of payments of tax on profit with arbitrary frequency. Mathematics 10:1343. https://doi.org/10.3390/math10081343 Brusov P, Brusov T, Kulik V (2022b) Benefits of advance payments of tax on profit: consideration within the Brusov–Filatova–Orekhova (BFO) theory. Mathematics 10:2013. https://doi.org/10. 3390/math10122013 Brusova A (2011) А comparison of the three methods of estimation of weighted average cost of capital and equity cost of company. Financ Anal Prob Sol 34:36–42 Cooper I, Nyborg KG (2018) Consistent valuation of project finance and LBO’s using the flow-toequity method. Eur Financ Manag 24(1):34–52. ISSN 1468-036X DeMarzo PM (1988) An extension of the Modigliani-Miller theorem to stochastic economies with incomplete markets and fully interdependent securities. J Econ Theory 45:353–369 Derrig R (1994) Theoretical considerations of the effect of federal income taxes on investment income in property-liability ratemaking. J Risk Insur 61:691–709 Diamond DA, He Z (2014) A theory of debt maturity: the long and short of debt overhang. J Financ 69:719–762 Donaldson G (1961) Debt capacity: a study of corporate debt policy and the determination of debt capacity. Division of Research, Graduate School of Business Administration, Harvard University, Boston, MA, USA Erel I, Myers SC, Read JA Jr (2015) A theory of risk capital. J Financ Econ 118:620–635. https:// doi.org/10.1016/j.jfineco.2014.10.006 Fairley WB (1979) Investment income and profit margins in property-liability insurance. Bell J Econ 10:191–210

48

2

Capital Structure Theory: Past, Present, Future

Fama EF (1977) Risk adjusted discount rates and capital budgeting under uncertainty. J Financ Econ 5:3–24 Fama EF (1996) Discounting under uncertainty. J Bus 69:415–429 Fama EF, French K (2005) Financing decisions: who issues stock? J Financ Econ 76:549–582. Federal Power Commission et al., v. Hope Natural Gas Co., 320 U.S. 591 (1944) Farber A, Gillet R, Szafarz A (2006) A general formula for the WACC. Int J Bus 11:211–218 Fernandez P (2006) A general formula for the WACC: a comment. Int J Bus 11:219 Filatova Т, Orehova N, Brusova А (2008) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Bull FU 48:68–77 Filatova T, Brusov P, Orekhova N (2022) Impact of advance payments of tax on profit on effectiveness of investments. Mathematics 10:666. https://doi.org/10.3390/math10040666 Fisher FM, McGowan JJ (1983) On the misuse of accounting rates of return to infer monopoly profits. Am Econ Rev 73:82–97 Frank MZ, Goyal VK (2003) Testing the pecking order theory of capital structure. J Financ Econ 67:217–248 Gordon MJ, Shapiro E (1956) Capital equipment analysis: the required rate of profit. Manag Sci 3: 102–110 Graham JR, Leary MT (2011) A review of empirical capital structure research and directions for the future. Annu Rev Financ Econ 3:309–345 Hamada R (1969) Portfolio analysis, market equilibrium, and corporate finance. J Financ 24:13–31 Harris R, Pringle J (1985) Risk–adjusted discount rates—extension form the average–risk case. J Financ Res 8:237–244 Hausman J, Myers SC (2002) Regulating U.S. railroads: the effects of sunk costs and asymmetric risk. J Regul Econ 22:287–310 Healy P, Howe C, Myers SC (2002) R&D accounting the tradeoff between relevance objectivity: a pharmaceutical industry simulation. J Account Res 40:677–710 Hirshleifer J (1965) Investment decision under uncertainty: choice-theoretic approaches. Q J Econ 79:509–536 Hirshleifer J (1966) Investment decision under certainty: applications of the state-preference approach. Q J Econ 80:252–277 Hsia С (1981) Coherence of the modern theories of finance. Financ Rev 16(1):27–42 Jensen MC (1986) Agency costs of free cash flow, corporate finance and takeovers. Am Econ Rev 76:323–329 Jin L, Myers SC (2006) R2 around the world: new theory and new tests. J Financ Econ 79:257–292 Kane A, Marcus A, McDonald R (1984) How big is the tax advantage to debt? J Financ 39:841–853 Kaplan S, Ruback R (1995) The valuation of cash flow forecasts: an empirical analysis. J Financ 50: 1059–1093 Keynes JM (1936) The general theory of employment, interest and money. Macmillan, New York, NY, USA Kolbe AL, Tye WB, Myers SC (1993) Regulatory risk: economic principles and applications to natural gas pipelines and other industries. Springer, New York, NY, USA Lambrecht B, Myers SC (2007) A theory of takeovers and disinvestment. J Financ 62:809–845 Lambrecht B, Myers SC (2008) Debt and managerial rents in a real-options model of the firm. J Financ Econ 89:209–231 Lambrecht B, Myers SC (2012) A Lintner model of dividends and managerial rents. J Financ 67: 1761–1810 Lambrecht B, Myers SC (2015) The dynamics of investment, payout and debt. Work. Pap.; Massachusetts Institute of Technology, Cambridge, MA, USA Leland H (1994) Corporate debt value, bond covenants, and optimal capital structure. J Financ 49(4):1213–1252 Lemmon ML, Zender J (2010) Debt capacity and tests of capital structure theories. J Financ Quant Anal 45:1161–1187

References

49

Lemmon ML, Roberts MR, Zender J (2008) Back to the beginning: persistence and the crosssection of corporate capital structure. J Financ 63:1575–1608 Lintner J (1956) Distribution of incomes of corporations between dividends, retained earnings and taxes. Am Econ Rev 46:97–113 Lintner J (1965) Optimal dividends and corporate growth under uncertainty. Q J Econ 77:59–95 Majd S, Myers SC (1987) Tax asymmetries and corporate income tax reform. In: Feldstein M (ed) The effects of taxation on capital accumulation. Univ. Chic. Press, Chicago, IL, USA, pp 343–373 Merton RC, Perold AF (1993) Theory of risk capital in financial firms. J Appl Corp Financ 6:16–32 Miles J, Ezzell R (1980) The weighted average cost of capital, perfect capital markets and project life: a clarification. J Financ Quant Anal 15:719–730 Miller MH (1977) Debt and taxes. J Financ 32:261–276 Miller MH, Modigliani F (1961) Dividend policy, growth and the valuation of shares. J Bus 34: 411–433 Miller MH, Modigliani F (1966) Some estimates of the cost of capital to the electric utility industry, 1954–1957. Am Econ Rev 56:333–391 Modigliani F, Miller MH (1958) The cost of capital, corporation finance and the theory of investment. Am Econ Rev 48:261–296 Modigliani F, Miller MH (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:433–443 Morck R, Yeung BY, Yu W (2000) The information content on stock markets: why do emerging markets have synchronous stock price movements? J Financ Econ 58:215–260 Mullins DW Jr (1976) Communications satellite corp. Case study 276195. Harvard Bus. Sch, Cambridge, MA, USA Myers SC (1967) Effects of uncertainty on the valuation of securities and the financial decisions of the firm. Ph.D. Thesis, Stanford University, Stanford, CA, USA Myers SC (1968a) A time-state-preference model of security valuation. J Financ Quant Anal 3:1–33 Myers SC (1968b) Procedures for capital budgeting under uncertainty. Ind Manag Rev 9:1–20 Myers SC (1972) Application of finance theory to public utility rates cases. Bell J Econ 3:58–97 Myers SC (1973a) A simple model of firm behavior under regulation and uncertainty. Bell J Econ 4: 304–315 Myers SC (1973b) On public utility regulation under uncertainty. In: Howard RH (ed) Risk and regulated firms. Mich. State Univ. Div. Res. Grad. Sch. Bus, East Lansing, MI, USA, pp 32–46 Myers SC (1974) Interactions of corporate financing and investment decisions: implications for capital budgeting. J Financ 29:1–25 Myers SC (1984a) Finance theory and financial strategy. Interfaces 14:126–137 Myers SC (1984b) The capital structure puzzle. J Financ 39:575–592 Myers SC (1988) Fuzzy efficiency. Inst Investig:8–9 Myers SC (1989) Still searching for optimal capital structure. In: Kopke RW, Rosengren ES (eds) Are the distinctions between debt and equity disappearing? Fed. Reserve Bank, Boston, MA, USA, pp 80–95 Myers SC (1999) Financial architecture. Eur Financ Manag 5:133–141 Myers SC (2000) Outside equity. J Financ 55:1005–1037 Myers SC (2001) Capital structure. J Econ Perspect 15:81–102 Myers SC (2015) Finance, theoretical and applied. Annu Rev Financ Econ 7:1–34 Myers SC, Cohn R (1987) A discounted cash flow approach to property-liability insurance rate regulation. In: Cummings JD, Harrington S (eds) Fair rate of return in property liability insurance. Kluwer-Nijhoff, Dordrecht, The Netherlands, pp 55–78 Myers SC, Howe C (1997) A life cycle model of pharmaceutical R&D. Cambridge, MA, USA, Work. Pap.; Progr. Pharm. Ind.; Massachusetts Institute of Technology Myers SC, Majd S (1990) Abandonment value and project life. In: Fabozzi F (ed) Advances in futures and options research, vol 4. JAI, Greenwich, CT, USA, pp 1–21

50

2

Capital Structure Theory: Past, Present, Future

Myers SC, Majluf NS (1984) Corporate financing and investment decisions when firms have information that investors do not have. J Financ Econ 13:187–221 Myers SC, Pogue GA (1974) A programming approach to corporate financial management. J Financ 29:579–599 Myers SC, Rajan R (1998) The paradox of liquidity. Q J Econ 113:733–771 Myers SC, Read JA Jr (2001) Capital allocation for insurance companies. J Risk Insur 68:545–580 Myers SC, Read JA Jr (2014) Real options, taxes and leverage. Work. Pap.; Massachusetts Institute of Technology, Cambridge, MA, USA Myers SC, Shyam-Sunder L (1996) Measuring pharmaceutical industry risk and the cost of capital. In: Helms RB (ed) Competitive strategies in the pharmaceutical industry. Am. Enterp. Inst, Washington, DC, USA, pp 208–237 Myers SC, Turnbull SM (1977) Capital budgeting and the capital asset pricing model: good news and bad news. J Financ 32:321–333 Myers SC, Dill DA, Bautista AJ (1976) Valuation of financial lease contracts. J Financ 31:799–819 Myers SC, Kolbe AL, Tye WB (1984) Regulation and capital formation in the oil pipeline industry. Transp J 23:25–49 Myers SC, Kolbe AL, Tye WB (1985) Inflation and rate of return regulation. Res Transp Econ 2: 83–119 Robichek AA, Myers SC (1965) Optimal financing decisions. Prentice-Hall, Upper Saddle River, NJ, USA Robichek AA, Myers SC (1966a) Conceptual problems in the use of risk-adjusted discount rates. J Financ 21:727–730 Robichek AA, Myers SC (1966b) Problems in the theory of optimal capital structure. J Financ Quant Anal 1:1–35 Robichek AA, Myers SC (1966c) Valuation of the firm: effects of uncertainty in a market context. J Financ 21:215–227 Rosenbaum J, Pearl J (2013) Investment banking, 2nd edn. Wiley, New York, NY, USA Rubinstein M (1973) A mean–variance synthesis of corporate financial theory. J Financ 28:167– 181 Schwartz E (1959) The theory of the capital structure of the firm. J Financ 14:18–39 Sethi S, Derzko N, Lehoczky J (1991) A stochastic extension of the Miller-Modigliani framework. Math Financ 1:57–76. https://ssrn.com/abstract=1082940 Sharpe WF (1965) Capital asset prices: a theory of market equilibrium under conditions of risk. J Financ 19:425–442 Shleifer A, Summers LH (1988) Breach of trust in hostile takeovers. In: Auerbach AJ (ed) Corporate takeovers: causes and consequences. Univ. Chic. Press, Chicago, IL, USA, pp 33–56 Shyam-Sunder L, Myers SC (1999) Testing static tradeoff against pecking order models of capital structure. J Financ Econ 51:219–244 Skinner DJ (2008) The evolving relation between earnings, dividends and stock repurchases. J Financ Econ 87:582–609 Solomon E, Laya J (1967) Measurement of company profitability: some systematic errors in the accounting rate of return. In: Robichek AA (ed) Financial research and management decisions. Wiley, New York, NY, USA, pp 152–183 Stiglitz J (1969) A re–examination of the Modigliani–Miller theorem. Am Econ Rev 59(5):784–793 Van Horne J (1966) Capital budgeting decisions involving combinations of risky assets. Manag Sci 19:B84–B92 Williams JB (1938) The theory of investment value. Harvard. Univ. Press, Cambridge, MA, USA

Chapter 3

Main Theories of Capital Structure

Keywords Main theories of capital structure · Brusov–Filatova–Orekhova (BFO) theory · The Modigliani–Miller theory and its modifications · The traditional approach Under the capital structure, one understands the relationship between equity and debt capital of the company. Does capital structure affect the company’s main settings, such as the cost of capital, profit, value of the company and the other, and, if affected, how? Choice of an optimal capital structure, i.e., a capital structure, which minimizes the weighted average cost of capital and maximizes the value of the company, is one of the most important tasks solving by financial manager and the management of a company. The first serious study (and first qualitative study) of capital structure of the company influence on its indicators of activities was the work by Modigliani–Miller (Мodigliani and Мiller 1958). Until this study, the approach existed (let us call it traditional), which was based on empirical data analysis. The Modigliani–Miller theory and its numerous modifications are discussed.

3.1

The Traditional Approach

The traditional (empirical) approach told to businessmen, that weighted average cost of capital, WACC, and the associated company capitalization, V = CF/WACC depend on the capital structure, the level of leverage. Debt cost always turns out to be lower, than equity cost, because first one has lower risk, because in the event of bankruptcy creditor claims are met prior to shareholders’ claims. As a result an increase in the proportion of lower-cost debt capital in the overall capital structure up to the limit which does not cause violation of financial sustainability and growth in risk of bankruptcy, leads to lower weighted average cost of capital, WACC. The profitability required by investors (the equity cost) is growing; however, its growth has not led to compensation benefits from the use of more low-cost debt capital. Therefore, the traditional approach welcomes the increased leverage L = D/ © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_3

51

52

3

Main Theories of Capital Structure

S, and the associated increase in company capitalization. The traditional (empirical) approach has existed up to the appearance of the first quantitative theory by Modigliani and Miller in 1958 (Мodigliani and Мiller 1958).

3.2 3.2.1

Modigliani–Miller Theory Modigliani–Miller Theory Without Taxes

Modigliani and Miller (ММ) in their first paper (Мodigliani and Мiller 1958) come to conclusions which are fundamentally different from the conclusions of traditional approach. Under assumptions (see Sect. 3.2.3 for details), that there is no taxes, no transaction costs, no bankruptcy costs, perfect market exists with symmetry information, equivalence in borrowing costs for both companies and investors etc. they showed that choosing of the ratio between the debt and equity capital does not affect company value as well as capital costs (Fig. 3.1). Under the above assumptions Modigliani and Miller have analyzed the impact of financial leverage, supposing the absence of any taxes (on corporate profit as well as individual one). They have formulated and proven two following statements.

Fig. 3.1 Dependence of company capitalization, UL, equity cost, ke, debt cost, kd, weighted average cost of capital, WACC, in traditional (empirical) approach

3.2

Modigliani–Miller Theory

53

Without taxes the total cost of any company is determined by the value of its EBIT—Earnings Before Interest and Taxes, discounted with fix rate k0, corresponding to group of business–risk of this company: VL = VU =

EBIT : k0

ð3:1Þ

Index L means financially dependent company (using debt financing), while index U means a financially independent company. Authors suppose that both companies belong to the same group of business–risk and k0 corresponds to required profitability of financially independent company, having the same business risk. Because, as it follows from the formula (Eq. 3.1), value of the company does not depend on the value of debt, then according to Modigliani–Miller theorem (Мodigliani and Мiller 1958), in the absence of taxes value of the company is independent of the method of its funding. This means as well that weighted average cost of capital WАСС of this company does not depend on its capital structure and equal to the capital cost, which this company will have under the founding by equity capital only. V0 = VL; CF/k0 = CF/WACC, and thus WACC = k0. Note, that first Modigliani–Miller theorem is based on suggestion about independence of weighted average cost of capital and debt cost on leverage level. From the first Modigliani–Miller theorem (Мodigliani and Мiller 1958) it is easy to derive an expression for the equity cost WACC = k0 = ke we þ kd wd :

ð3:2Þ

Finding from here ke, one gets ke =

k ðS þ DÞ k0 D w D - kd d = 0 - kd = k 0 þ ðk0- kd Þ = k0 þ ðk 0- k d ÞL ð3:3Þ S S we we S

Here D—value of debt capital of the company S—value of equity capital of the company kd , wd = DDþS—cost and fraction of debt capital of the company S ke , we = Dþ S—cost and fraction of equity capital of the company L = D/S—financial leverage Thus, we come to second statement (theorem) of Modigliani–Miller theory about the equity cost of financially dependent (leverage) company (Мodigliani and Мiller 1958). Equity cost of leverage company ke could be found as equity cost of financially independent company k0 of the same group of risk, plus premium for risk, which value is equal to production of difference (k0 - kd) on leverage level L:

54

3

Main Theories of Capital Structure

ke = k 0 þ ðk0- kd ÞL:

ð3:4Þ

Fig. 3.2 Dependence of equity cost ke and WACC on leverage level L within Modigliani–Miller theory without taxes

Formula (Eq. 3.4) shows that equity cost of the company increases linearly with leverage level (Fig. 3.2). The combination of these two Modigliani–Miller statements implies that the increasing level of debt in the capital structure of the company does not lead to an increased value of firms, because the benefits gained from the use of more low-cost debt capital markets will be exactly offset by an increase in risk (we are speaking about the financial risk, the risk of bankruptcy), and, therefore, by an increase in cost of equity capital firms: investors will increase the required level of profitability under increase the risk, by which a higher level of debt in the capital structure is accompanied. In this way, the Modigliani–Miller theorem argues that, in the absence of taxes the capital structure of the company does not affect the value of the company and on its weighted average cost of capital, WACC, and equity cost increasing linearly with the increasing financial leverage. Explanations, given by Modigliani–Miller under receiving of their conclusions, are the following (Мodigliani and Мiller 1958). Value of the company depends on profitability and risk only and does not depend on the capital structure. Based on the principle of preservation of the value, they postulate that the value of the company, which is equal to the sum of its own and borrowed funds, is not changed when the ratio between its parts is changed. An important role in justification of Modigliani– Miller statements plays an existence of an arbitral awards opportunities for the committed markets. Two identical companies, differing only by the leverage level, must have the same value. If this is not the case, the arbitration aligns business cost: investors of less cost company can invest capital in a company of more value. Selling

3.2

Modigliani–Miller Theory

55

of shares of the first company and buying of stock of the second company will continue until the value of both companies is not equalized. Most of Modigliani and Miller’s assumptions (Мodigliani and Мiller 1958), of course, are unrealistic. Some assumptions can be removed without changing the conclusions of the model. However, assuming no costs of bankruptcy and the absence of taxes (or the presence of only corporate taxes) are crucial–the change of these assumptions alters conclusions. The last two assumptions rule out the possibility of signaling and agency costs and, thus, also constitute a critical prerequisite.

3.2.2

Modigliani–Miller Theory with Taxes

In the real situation taxes on profit of companies always exist. Since the interest paid on debt, are excluded from the tax base—it leads to the so-called effect of “tax shield”: value of the company, used the borrowed capital (leverage company), is higher than the value of the company, financed entirely by the equity (non-leverage company). The value of the “tax shield” for 1 year is equal to kdDt, where D is the value of debt, t—the income tax rate, kd—the interest on the debt (or debt capital cost) (Мodigliani and Мiller 1963). The value of the “tax shield” for perpetuity company for all time of its existence is equal to (we used the formula for the sum of terms of an infinitely decreasing geometric progression), ðPVÞTS = kd Dt

1 X

ð1 þ kd Þ - t = Dt

ð3:5Þ

t=1

and the cost of leverage company is equal to V = V 0 þ Dt,

ð3:6Þ

where V0 is the value of financially independent company. Thus, we obtain the following result obtained by Modigliani and Miller in 1963 (Мodigliani and Мiller 1963). The value of financially dependent company is equal to the value of the company of the same risk group used no leverage, increased by the value of tax shield arising from financial leverage and equal to the product of rate of corporate income tax T and the value of debt D. Let us get now the expression for the equity capital cost of the company under the existing corporate taxes. Accounting, that V0 = CF/k0, and that the ratio of debt capital wd = D/V, one gets

56

3

Main Theories of Capital Structure

V = CF=k0 þ wd VT:

ð3:7Þ

Because the value of leverage company V = CF/WACC, for weighted average cost of capital, WACC, we get WACC = k 0 ð1- wd T Þ:

ð3:8Þ

From here the dependence of WACC on leverage L = D/S becomes the following WACC = k 0 ð1- LT=ð1 þ LÞÞ

ð3:9Þ

On the other hand, on definition of the weighted average cost of capital with “tax shield” accounting we have WACC = k 0 we þ kd wd ð1- T Þ:

ð3:10Þ

Equating Eqs. (3.9) and (3.11), one gets k0 ð1- wd T Þ = k 0 we þ kd wd ð1- T Þ,

ð3:11Þ

and from here for equity cost, we get the following expression ð 1 - wd T Þ w 1 w D - kd d ð1 - T Þ = k 0 - k 0 d T - kd ð1 - T Þ = we we we we S DþS D D = k0 - k 0 T - kd ð1 - T Þ = k 0 þ Lð1 - T Þðk0 - kd Þ: S S S

ke = k0

ð3:12Þ

So, we get the following statement, obtained by Modigliani and Miller (Мodigliani and Мiller 1963). Equity cost of leverage company ke paying tax on profit could be found as equity cost of financially independent company k0 of the same group of risk, plus premium for risk, which value is equal to production of difference (k0 - kd) on leverage level L and on tax shield (1-T). It should be noted that the formula (Eq. 3.12) is different from the formula (Eq. 3.4) without tax only by the multiplier (1-T ) in term, indicating premium for risk. As the multiplier is less than unit, the corporate tax on profits leads to the fact that capital is growing with the increasing of financial leverage slower than it would have been without them. Analysis of formulas (Eqs. 3.4, 3.9, and 3.12) leads to following conclusions. With leverage grows: 1. Value of company increases 2. Weighted average cost of capital WACC decreases from k0 (at L = 0) up to k0(1 - T )(at L = 1) (when the company is funded solely by borrowed funds). 3. Equity cost Increasing linearly from k0 (at L = 0) up to 1 (at L = 1).

3.2

Modigliani–Miller Theory

57

Fig. 3.3 Dependence of equity capital cost, debt cost, and WACC on leverage in Modigliani– Miller theory without taxes (t = 0) and with taxes (t ≠ 0)

Within their theory, Modigliani and Miller (Мodigliani and Мiller 1963) had come to the following conclusions. With the growth of financial leverage (Fig. 3.3): 1. The company value increases. 2. The weighted average cost of capital decreases from k0 (for L = 0) up to k0(1 - T ) (for L = 1, when the company is financed entirely with borrowed funds). 3. The cost of equity capital increases linearly from k0 (for L = 0) up to 1 (for L = 1).

3.2.3

Main Assumptions of Modigliani–Miller Theory

The most important assumptions of the Modigliani–Miller theory are as follows: 1. Investors are behaving rationally and instantaneously see profit opportunity, inadequate investment risk. Therefore, the possibility of a stable situation of the

58

2.

3.

4.

5. 6.

7.

8. 9. 10. 11.

3

Main Theories of Capital Structure

arbitration, i.e., obtain the risk–free profit on the difference in prices for the same asset can not be kept any length of time—a reasonable investors quickly take advantage of it for their own purposes and equalize conditions in the market. This means that in a developed financial market, capital with the same risk should be rewarded by the same rate of return. Investment and financial market opportunities should be equally accessible to all categories of investors—whether institutional or individual investors, large or small, rapidly growing or stable, experienced or relatively inexperienced. Transaction costs associated with funding, are very small. In practice, the magnitude of transaction costs is inversely proportional to the amount of finance involved, so this assumption is more consistent with reality than the large sums involved: i.e., in attracting small amounts the transaction costs can be high, while, as in attracting large loans, as well as during placement of shares at a significant amount the transaction costs can be ignored. Investors get money and provide funds to borrowers at risk-free rate. In all probability, this assumption is due to the fact that the lender seeks to protect himself by using one or other guarantees, pledge of assets, the right to pay claims on third parties, the treaty provisions restricting the freedom of the borrower to act to the detriment of the creditor. Lender’s risk is really small, but its position can be considered risk-free with respect to the position of the borrower and, accordingly, should be rewarded by a risk-free rate of return. Companies have only two types of assets: risk–free lending and risk their own. There is no possibility of bankruptcy, i.e., irrespective of what level to bring its financial leverage of the company–borrowers, bankruptcy is threatening them. Thus, bankruptcy costs are absent. There are no corporate taxes and taxes on personal income of investors. If the personal income tax can indeed be neglected, because the assets of the company separated from the assets of shareholders, the corporate income taxes should be considered in the development of more realistic theories (which was done by Modigliani and Miller in the second paper devoted to the capital structure. Companies are in the same class of risky companies. All financial flows are perpetuity. Companies have the same information. Management of the company maximizes the equity of the company.

3.2.4

Modifications of Modigliani–Miller Theory

Taking into Account Market Risk: Hamada Model Robert Hаmаdа (1969) unites Capital Asset Pricing Model (CAPM) with Modigliani–Miller model taxation. As a result, he derived the following formula for calculating the equity cost of financially dependent company, including both financial and business risk of company:

3.2

Modigliani–Miller Theory

59

k e = kF þ ðkM- kF ÞbU þ ðkM- kF ÞbU

D ð1- T Þ, S

ð3:13Þ

where bU—β- coefficient of the company of the same group of business risk, that the company under consideration, but with zero financial leverage. The formula (Eq. 3.13) represents the desired profitability of equity capital ke as a sum of three components: risk-free profitability kF, compensating to shareholders a temporary value of their money, premium for business risk (kM - kF)bU and premium for financial risk ðk M- kF ÞbU DS ð1- T Þ. If the company does not have borrowing (D = 0), the financial risk factor will be equal to zero (the third term is drawn to zero), and its owners will only receive the premium for business risk. To apply the Hamada equation, specialists in practice in most cases use book value of equity capital as its approach of market value. Nevertheless, the Hamada formula implies the use of market value of the assets. It should be noted also that the formula (Eq. 3.13) can be used to derive of other equations, using which you can analyze the impact of financial leverage on β-factor of company shares. Equating CAPM formula to equity cost we get: k F þ ðk M- k F ÞbU = kF þ ðkM- kF ÞbU þ ðkM- kF ÞbU

D ð1- T Þ S

ð3:14Þ

or   D b = bU 1 þ ð1- T Þ : S

ð3:15Þ

In this way, at the assumptions on which Modigliani–Miller theory and CAPM are based, β-factor of equity capital of financially dependent company is equal to βfactor of financially independent company, corrected on tax on profit rate and applied leverage level. Consequently, market risk of the company, measured by a factor b, depends on both the business risk of the company, a measure of which is bU, and on the financial risk, which is calculated by the formula (Eq. 3.15). In conclusion, here are the formulas for calculating the capital costs within the CAPM model (in parenthesis there are formulas within the Modigliani–Miller theory (Мodigliani and Мiller 1958, 1963, 1966)). The equity cost for company without debt capital:   k e = k F þ k M - k F βU , The equity cost for company with debt capital:

ðke= k0 Þ:

ð3:16Þ

60

3

  ke = k F þ kM - kF βe ,

Main Theories of Capital Structure

ðk e= k0 þ ð1- T Þðk0- kd ÞLÞ:

ð3:17Þ

The debt cost:   kd = k F þ kM - kF βd ,

ðkd= k F ; βd = 0Þ:

ð3:18Þ

The weighted average cost of capital WACC WACC = k e we þ k d wd ð1- T Þ,

ðWACC= k0 ð1- Twd ÞÞ

ð3:19Þ

The Cost of Capital Under Risky Debt Another hypothesis of Modigliani and Miller was the suggestion about free-of-risk debt (in their theory, there are two types of assets: risky equity and free-of-risk debt. However, if we assume the risk of bankruptcy of company (and, accordingly, the ability to non-payment of loans), the situation may change. Stiglitz (1969) and Rubinstein (1973) have shown that the conclusions concerning the total value of company do not change as compared to the findings derived by Modigliani and Miller under assumptions about free-of-risk debt (Мodigliani and Мiller 1958, 1963, 1966). However, the debt cost is changed. If previously under assumption about the free-of-risk debt it (debt cost) was regarded as a constant kd = kF, now it is not a constant. This claim is based on the work by Hsia (1981), where based on the models of pricing options, Modigliani–Miller and CAPM it was shown, that, if one uses the formula for the net discount income, a term, reflecting tax protection on debt, should be discounted at the rate 1 , wd

ð3:20Þ

- ln wd þ kF t 1 pffi pffi kF þ σ t, 2 σ t

ð3:21Þ

k0d = kF þ ðk0- k F ÞN ð- d1 Þ where d1 =

here t—a moment of payment a credit, N(-d1)- cumulative normal distribution of probability of random value d1. The Account of Corporate and Individual Taxes (Miller Model) In the second article, Modigliani and Miller (1958) considered taxation of corporate profits but did not take into account the presence in the economy of individual taxes of investors. Merton Miller in 1997 introduced the model, demonstrating the impact of leverage on the company value with account of the corporate and individual taxes (Miller 1976). To describe his model we will enter the following legend: TC—tax on corporate profits rate, TS—the tax rate on income of an individual investor from his ownership by stock of corporation, TD—tax rate on interest income from the provision of investor—individuals of credits to other investors and companies. Income from

3.2

Modigliani–Miller Theory

61

shares partly comes in the form of a dividend, and in part as capital profits, so that TS is a weighted average value of effective rates of tax on dividends and capital profits on shares, while the income from the provision of loans usually comes in the form of the interests. The last are usually taxed at a higher rate. In the light of the individual taxes, and with the same assumptions that have been made for Modigliani–Miller models previously, the financially independent company value can be determined as follows: VU =

EBITð1 - T C Þð1 - T S Þ : k0

ð3:22Þ

A term (1 - TS) allows to take into account the individual taxes in the formula. In this way, numerator indicates which part of the operating company’s profit remains in possession of the investors, after the company will pay taxes on their profits, and its shareholders then will pay individual taxes on income from stock ownership. Since individual taxes reduce profits, remaining in the disposal of investors, the last, at other things being equal circumstances, also reduce and an overall assessment of the financially independent company value. We will assess the financially dependent company under condition of a double taxation of income investors. To start let us divide the annual cash flows of financially dependent company CFL into flows sent to its shareholders CFe, and the flows, belonging to debt owners CFd, with account of both corporation tax on profits, and on the income of individuals: CFL = CFe þ CFd = ðEBIT- I Þð1- T C Þð1- T S Þ þ I ð1- T D Þ,

ð3:23Þ

where I is the annual interest payments on debt. The formula (Eq. 3.23) can also be rewritten as follows: CFL = CFe þ CFd = EBITð1- T C Þð1- T S Þ - I ð1- T C Þð1- T S Þ þ I ð1- T D Þ:

ð3:24Þ

The first term of the equation (Eq. 3.24) corresponds to cash flow after taxes for financially independent company, shown in equation (Eq. 3.22), which shows its present value. The second and the third terms of the equation, reflecting the financial dependence, corresponds to cash flows related to the debt financing, which, as previously, is considered as free of risk. Their present values are obtained by discounting by risk-free nominal rate on debt kd. By combining the present values of all three terms, we get the company value under using debt financing and in the presence of all types of taxation:

62

3

VU =

Main Theories of Capital Structure

EBITð1 - T C Þð1 - T S Þ I ð1 - T C Þð1 - T S Þ I ð1 - T d Þ þ : k0 kd kd

ð3:25Þ

First term in (Eq. 3.25) is identical to VU in formula (Eq. 3.22). Accounting this and combining two last terms, we get the following formula: VL = VU þ

  ð1 - T C Þð1 - T S Þ I ð1 - T d Þ 1: kd ð1 - T d Þ

ð3:26Þ

The amount of paid interests with taking into account the taxation, divided by the desired profitability of debt capital, I ð1 - T d Þ kd

ð3:27Þ

is equal to market value of the debt D. Substituting D in the previous formula, we get the final expression, which is known as a formula of a Miller model: 

 ð1 - T C Þð1 - T S Þ D: V L = V U þ 1ð1 - T d Þ

ð3:28Þ

The Miller model allows you to obtain an estimate of the value of financially dependent company, taking into account the corporate tax, as well as tax on individuals. The Miller formula (3.28) has several important consequences: 1. Second term of sum, 

 ð1 - T C Þð1 - T S Þ 1D, ð1 - T d Þ

ð3:29Þ

represents the gains from use of debt capital. This term replaces the tax on the profit of corporation rate in the Modigliani–Miller model with corporate taxes: V L = V U þ TD:

ð3:30Þ

2. If we ignore taxes, a term (Eq. 3.29) will be equal to zero. Thus, in this case, the formula (Eq. 3.28) is transformed into the original version of the Modigliani– Miller model without taxes. 3. If we neglect taxes on individuals, the considering term becomes 1 - (1 TC) = TC, so, in this case (Eq. 3.28) is becoming a Modigliani–Miller model with corporate taxes (Eq. 3.30).

3.2

Modigliani–Miller Theory

63

4. If the shareholder receives profit only in the form of dividend, and if effective tax rates on income from shares and bonds are equal (TS = TD), the terms 1 - TS and 1 - TD are shrinking, and the factor for D in (Eq. 3.29) again is equal to TC. 5. If the shareholder receives dividends, and income from capital, the situation is changed. In this case, effective tax rates on income from shares and bonds are not equal. Let us take a look at common case, when individual taxes on income for the company shares are less than individual taxes of creditors. This encourages investors to purchase the shares of the company compared to purchasing the bonds of the company. In this case TS < TD. Then factor in D in (Eq. 3.28) β has a look ð1 - T C Þð1 - T S Þ = 1 - ð1 - T C Þα = 1 - ð1 - T C Þð1 þ γ Þ = ð1 - T d Þ = T C þ γ ð T C - 1Þ < T C :

β=1-

ð3:31Þ

It is less than TC, because γ > 0, TC < 1; therefore, in this case, the effect of using of debt financing, although there is, but it is less, than in the absence individual taxes. In other words, the effect of tax shields for the company in this case decreases, and it becomes the less than above individual taxes of creditors (individual taxes for the obligations of the company) in comparison with the individual income tax on shares. 6. Let us take a look at case TS > TD, when individual income taxes on shares are bigger than individual taxes creditors. The factor β takes view ð1 - T C Þð1 - T S Þ = 1 - ð1 - T C Þα = 1 - ð1 - T C Þð1 - γ Þ = ð1 - T d Þ = T C þ γ ð1 - T C Þ > T C :

β=1-

ð3:32Þ

It is bigger than TC, because γ > 0, TC < 1; therefore, in this case, the effect of use of debt financing is increased compared with the case of the absence of individual taxes. 7. If (1 - TC)(1 - TS) = 1 - TD, then this term is zero, and the effect of using of debt financing will also be zero. This means, that the benefits of the use of tax shields as a result of the application of debt financing will be fully offset by additional losses of investors, associated with a higher tax rate on interest on income of individuals. In this case, the capital structure will not affect the company value and its capital cost,—in other words, you can apply Modigliani– Miller theory without tax (Мodigliani and Мiller 1958). In his report, Miller (1976) claimed that companies on average will use issuance of shares and debt securities in such a way as to result in taxation of investors income to be optimal. In such an equilibrium state will occur equality

64

3

Main Theories of Capital Structure

ð1- T C Þð1- T S Þ = 1 - T D ,

ð3:33Þ

and thus, as we have pointed out above, capital structure will not affect the market company value and its capital cost. Thus, by Miller, the conclusions on the irrelevance of the capital structure, made on the base of the original Modigliani–Miller model with zero taxes remain in force. Subsequently, researchers adapted and checked the Miller results. Their works, as a rule, have been devoted to Miller’s conclusion concerning the absence of the gains from the use of the debt capital by the company. In the United States an effective tax rate on the income of shareholders is lower than the income of creditors, but, nevertheless, the product (1 - TC)(1 - TS) is less than 1 - TD. Consequently, the companies may receive the benefit from the use of debt financing. However, in Miller work in fact has been shown that the distinction of rates of individual taxes on income of shareholders and creditors to some extent compensates of the advantages of use of debt financing, and, in this way, the tax benefits of debt are less than anticipated at a more earlier Modigliani–Miller model where only corporate taxes have been taken into account. In conclusion, we present in Table 3.1 a classification and summary of the main theories of capital structures of company. Table 3.1 The main theories of the company’s capital structure: classification and summary Theory Traditional theory

Modigliani–Miller theory (ММ)

Without taxes

With taxes

Main thesis Before appearance of the first quantitative theory of capital structures (Modigliani– Miller theory) in 1958 (Modigliani and Miller 1958, 1963, 1966) empirical theory existed. Weighted average cost of capital, WACC, and company value, V, depends on capital structures of company. Within the based on existing practical experience traditional approach the competition between the advantages of debt financing at a low leverage level and its disadvantages at a high leverage level forms the optimal capital structure, defined as the leverage level, at which WACC is minimal and company value, V, is maximum. Under many constraints, Modigliani and Miller concluded that the cost of raising capital and capitalization of a company do not depend on the company’s capital structure at all. Under corporate taxation, the weighted average cost of capital WACC decreases with the level of leverage, the cost of equity ke increases linearly with the level of (continued)

3.2

Modigliani–Miller Theory

65

Table 3.1 (continued) Theory

Brusov–Filatova– Orekhova theory (BFO–1)

Main thesis

For arbitrary age Without inflation

For arbitrary age With inflation

For arbitrary age With increased financial distress costs and risk of bankruptcy For arbitrary lifetime

leverage, and the value of company V increases continuously with the level of leverage. In 2008, BFO theory (Brusov and Filatova 2011; Brusov et al. 2011a–c, 2012a, b, 2013, 2014a, b; Filatova et al. 2008; Brusova 2011) has replaced the famous Modigliani and Miller theory (1958, 1963, 1966). The authors have moved from the assumption of Modigliani–Miller concerning the perpetuity (infinite time of life) of companies and elaborated the quantitative theory of valuation of main indicators of financial activities of arbitrary age companies. Results of modern BFO theory turn out to be quite different from that of Modigliani– Miller theory. It shows that later, via its perpetuity, underestimates the valuation of cost of raising capital for the company and substantially overestimates the valuation of the company value. Such an incorrect valuation of main financial parameters of companies has led to an underestimation of risks involved, and impossibility, or serious difficulties in adequate managerial decision-making, which was one of the implicit reasons of the 2008 global financial crisis. In the BFO theory, in investments at certain values of return-on-investment, there is an optimum investment structure. As well a new mechanism of formation of the company optimal capital structure, different from suggested by trade-off theory has been developed. Inflation has a twofold effect on the costs of raising capital: (1) increases the equity cost and the weighted average cost of capital, (2) changes their dependence on leverage, increasing, in particular, the rate of growth of the cost of equity with leverage. The company value decreases under accounting of inflation. In BFO theory, with increased financial costs and bankruptcy risk, there is no optimal capital structure, which means that the trade-off theory does NOT work. In the Modigliani–Miller theory (in the limit of eternity), the lifetime of a company and (continued)

66

3

Main Theories of Capital Structure

Table 3.1 (continued) Theory Brusov–Filatova– Orekhova theory (BFO–2)

Brusov–Filatova– Orekhova theory (BFO–3)

Main thesis

For rating needs

the age of a company mean the same thing: they are both infinite. When moving to a company with a finite age, the terms “company lifetime” and “company age” become different, and they should be distinguished when generalizing the Modigliani–Miller theory to a finite n. Thus Brusov et al. have developed two kinds of finite n—theories: BFO–1 and BFO–2. BFO–1 theory is related to companies with arbitrary age and BFO–2 theory is related to companies with arbitrary lifetime companies. In other words, BFO–1 is applicable to most interesting case of companies that reached the age of n–years and continue to exist on the market and allows to analyze the financial condition of the operating companies. BFO–2 theory allows examine the financial status of the companies which ceased to exist, i.e., of those for which n means not age, but a lifetime, i.e., the time of existence. In real economy, there are a lot of schemes for the termination of activities of the company: bankruptcy, merger, acquisition, etc. One of those schemes, when the value of the debt capital D becomes zero at the time of termination of activity of company n, is considered in Brusov et al. (2015), where as well where the results of BFO-1 and BFO-2 are also compared. A new approach to rating methodology (for non-financial issuers and for long-term project rating), within both BFO and MM theories has been developed be Brusov et al. The key factors of a new approach are: (1) the adequate use of discounting of financial flows virtually not used in existing rating methodologies, (2) the incorporation of rating parameters (financial “ratios”) into these theories. This, on the one hand, allows the use of the powerful tools of these theories in the rating, and on the other hand, it ensures the correct discount rates when discounting of financial flows. The interplay between rating ratios and leverage level which is quite important in rating. This creates a new base for rating methodologies, which allows to issue more correct ratings of issuers, makes the rating (continued)

3.2

Modigliani–Miller Theory

67

Table 3.1 (continued) Theory

Trade-off theory

Main thesis

Static

Dynamic

methodologies more understandable and transparent. During decades one of the main theory of capital structure was the trade-off theory. There are two modifications of trade-off theory: static and dynamic. Static The static trade-off theory accounts the income tax and cost of bankruptcy. Within this theory, the optimal capital structure is formed by the balancing act between the benefits of debt financing at low leverage level (from the tax shield from interest deduction) and the disadvantage of debt financing at high leverage level (from the increased financial distress and expected bankruptcy costs). The tax shield benefit is equal to the product of the corporate income tax rate and the market value of debt and the expected bankruptcy costs are equal to the product of probability of bankruptcy and the estimated bankruptcy costs. The static version of the trade-off theory does not take into account the costs of adapting the capital structure to the optimal one, economic behavior of managers, owners, and other participants of economical process, as well as a number of other factors. As it has been shown in BFO theory, the optimal capital structure is absent in tradeoff theory The dynamic version of trade-off theory suggests that the costs of adjusting the capital structure are high, and therefore companies will only change their capital structure if the benefits outweigh the costs. Therefore, there is an optimal range that varies on the outside of each lever but remains the same on the inside. Companies try to adjust their leverage when it reaches the edge of the optimal range. Depending on the type of adaptation costs, companies reach the target ratio faster or slower. Proportional changes involve a small adjustment, while fixed changes imply significant costs. In the dynamic version of the trade-off theory, company capital structure decision in (continued)

68

3

Main Theories of Capital Structure

Table 3.1 (continued) Theory

Accounting of transaction cost

Accounting of asymmetry of information

Signaling theory

Pecking order theory

Main thesis current period depends on the waiting company income in the next period. As it has been shown within BFO theory Brusov et al. (2013), under increased financial distress costs and bankruptcy risk, the optimal capital structure is absent. This means that the trade-off theory does NOT work in either the static or dynamic version. In BFO theory, with increased financial distress costs and risk of bankruptcy, the optimal capital structure is absent, which means that trade-off theory does NOT work: in static version as well as in dynamic one If the cost of changing the capital structure to its optimal value is high, the company may decide not to change the capital structure and maintain the current capital structure. The company may decide that it is more cost-effective not to change the capital structure, even if it is not optimal, for a certain period of time. Because of this, the actual and target capital structure may differ. In real financial markets, information is asymmetric (company managers have more reliable information than investors and creditors), and the rationality of economic entities is limited. Information asymmetry can be reduced based on certain signals for lenders and investors related to the behavior of managers in the capital market. It should take into account the previous company development and the current and projected profitability of the activity. The pecking order theory describes a preferred sequence of funding types for raising capital. That is, companies first use financing from retained earnings (internal equity), the second source is debt, and the last source is the issuance of new shares of common stock (external equity). Empirical data on the leverage level of non-financial companies, combined with the decisionmaking process of top management and the board of directors, indicate a greater commitment to pecking order theory. Note that (continued)

3.2

Modigliani–Miller Theory

69

Table 3.1 (continued) Theory

Theories of conflict of interests

Main thesis

Theory of agency costs

Theory of corporate control and costs monitoring

Theory of stakeholders

Behavioral theories

Manager investment autonomy

this theory contradicts both MM and BFO theory, which underline the quite importance of debt financing. The company management may make decisions that are contrary to the interests of shareholders or creditors, respectively; expenses are necessary to control its actions. For solving the agency problem the correct choice of compensation package (the agent’s share in the property, bonus, stock options) is needed, which allows you to link the manager’s profit with the dynamics of equity capital and ensure the motivation of managers for preservation and growth of equity capital. In the presence of information asymmetry, creditors providing capital are interested in the possibility of self-control of the effectiveness of its use and return. Monitoring costs are usually passed on to company owners by being included in the loan rate. The level of monitoring costs depends on the scale of the business; therefore, with the increase in the scale of the business, the company weighted average capital cost increases, and the company market value decreases. Stakeholder theory is a theory that defines and models the groups that are the stakeholders of a company. The diversity and intersection of interests of stakeholders, their different assessments of acceptable risk give rise to conditions for a conflict of their interests, that is, they make adjustments to the process of capital structure optimizing. Company managers implement those decisions that, from their point of view, will be positively perceived by investors and, accordingly, will positively affect the market value of companies: when the market value of the company’s shares and the degree of consensus between the expectations of managers and investors is high, the company conducts an additional share issue, and in the opposite situation uses debt instruments. Thus, the company capital structure is more influenced by investors, (continued)

70

3

Main Theories of Capital Structure

Table 3.1 (continued) Theory

Main thesis

The equity market timing theory

Information cascades

whose expectations are taken into account by company managers. The level of leverage is determined by market dynamics. Equity market timing theory means that a company should issue shares at a high price and repurchase them at a low price. The idea is to take advantage of the temporary fluctuations in the value of equity relative to the value of other forms of capital. To save costs and avoid mistakes, the company’s capital structure can be formed not on the basis of calculations of the optimal capital structure (this is a non-trivial task and its correct solution could be found within the framework of the BFO theory) or depending on the available sources of financing of the company, but borrowed from other companies, having successful, proven managers (heads of companies), as well as using (following the majority) the most popular methods of managing the capital structure, or even simply by copying of the capital structure of successful companies in a similar industry.

References Brusov PN, Filatova ТV (2011) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Financ Credit 435:2–8 Brusov P, Filatova T, Orehova N, Brusova A (2011a) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Appl Financ Econ 21(11): 815–824 Brusov P, Filatova T, Orehova N et al (2011b) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Bus ICT 2:16–21 Brusov P, Filatova T, Orehova N et al (2011c) Influence of debt financing on the effectiveness of the investment project within the Modigliani–Miller theory. Res J Econ Bus ICT (UK) 2:11–15 Brusov P, Filatova T, Eskindarov M, Orehova N (2012a) Influence of debt financing on the effectiveness of the finite duration investment project. Appl Financ Econ 22(13):1043–1052 Brusov P, Filatova T, Eskindarov M, Orehova N (2012b) Hidden global causes of the global financial crisis. J Rev Glob Econ 1:106–111 Brusov P, Filatova P, Orekhova N (2013) Absence of an optimal capital structure in the famous tradeoff theory! J Rev Glob Econ 2:94–116 Brusov P, Filatova P, Orekhova N (2014a) Mechanism of formation of the company optimal capital structure, different from suggested by trade off theory. Cogent Econ Financ 2:1–13. https://doi. org/10.1080/23322039.2014.946150

References

71

Brusov P, Filatova T, Orehova N (2014b) Inflation in Brusov–Filatova–Orekhova theory and in its perpetuity limit – Modigliani – Miller theory. J Rev Glob Econ 3:175–185 Brusov PN, Filatova TV, Orekhova NP, Eskindarov MA, Kulik VL (2015) Modern theory of capital cost and capital structure by Brusov–Filatova–Orekhova (BFO Theory) for companies, which ceased to exist at the time moment n. J Rev Glob Econ 4:87–95 Brusova A (2011) А comparison of the three methods of estimation of weighted average cost of capital and equity cost of company. Financ Anal Probl Sol 34(76):36–42 Filatova Т, Orehova N, Brusova А (2008) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Bull FU 48:68–77 Hamada R (1969) Portfolio analysis, market equilibrium, and corporate finance. J Financ 24(1): 13–31 Hsia С (1981) Coherence of the modern theories of finance. Financ Rev 16(1):27–42 Miller M (1976) Debt and taxes. J Financ 32(2):261–275 Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Modigliani F, Miller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391 Rubinstein M (1973) A mean–variance synthesis of corporate financial theory. J Financ 28:167– 181 Stiglitz J (1969) A re–examination of the Modigliani–Miller theorem. Am Econ Rev 59(5):784–793

Chapter 4

Modern Theory of Capital Cost and Capital Structure: Brusov–Filatova–Orekhova Theory (BFO Theory)

Keywords Brusov–Filatova–Orekhova (BFO) theory · The Modigliani–Miller theory · The weighted average cost of capital · Company capitalization · A qualitatively new anomalous effect One of the serious limitations of the Modigliani–Miller theory is the suggestion about perpetuity of the companies. In 2008, Brusov–Filatova–Orekhova (Filatova et al. 2008) have lifted up this limitation and shown, that the accounting of the finite lifetime (finite age) of the company leads to significant changes in all Modigliani– Miller results (Мodigliani and Мiller 1958, 1963, 1966): capitalization of the company is changed, as well as the equity cost, ke, and the weighted average cost of capital, WACC, in the presence of corporative taxes. Besides a number of qualitatively new effects in corporate finance, obtained in Brusov–Filatova– Orekhova theory (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011), is absent in Modigliani–Miller theory. Only in the absence of corporative taxes we give a rigorous proof of the Brusov– Filatova–Orekhova theorem, that cost of company equity, ke, as well as its weighted average cost, WACC, does not depend on the lifetime or age of the company, so the Modigliani–Miller theory could be generalized for arbitrary lifetime companies. Until recently (before 2008, when the first paper by Brusov–Filatova–Orekhova (Filatova et al. 2008) has appeared) the basic theory (and the first quantitative one) of the cost of capital and capital structure of companies was the theory of Nobel Prize winners Modigliani and Miller (Мodigliani and Мiller 1958, 1963, 1966). One of the serious limitations of the Modigliani–Miller theory is the suggestion about perpetuity of the companies. We lift up this limitation and show, that the accounting of the finite lifetime of the company leads to change of the equity cost, ke, as well as of the weighted average cost of capital WACC in the presence of corporative taxes. The effect of leverage on the cost of equity capital of the company, ke, with an arbitrary lifetime, and its weighted average cost of WACC is investigated. We give a rigorous proof of the Brusov–Filatova–Orekhova theorem, that in the absence of corporative taxes cost of company equity, ke, as well as its weighted average cost, WACC, does not depend on the lifetime of the company.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_4

73

74

4.1

4

Modern Theory of Capital Cost and Capital Structure:. . .

Companies with Arbitrary Lifetime. Brusov–Filatova– Orekhova Equation

Let us consider the situation with finite lifetime companies. First of all, we will find the value of tax shields, TS, of the company for n years TS = k d DT

n X

ð1 þ k d Þ - t = DT½1- ð1 þ kd Þ - n :

ð4:1Þ

t=1

(We used the formula for the sum of n terms of a geometric progression).Here, D is the value of debt capital; kd—the cost of debt capital, T—income tax rate. Next, we use the Modigliani–Miller theorem (Мodigliani and Мiller 1958, 1963, 1966): The value of financially dependent company is equal to the value of the company of the same risk group used no leverage, increased by the value of tax shield arising from financial leverage and equal to the product of rate of corporate income tax T and the value of debt D. V = V 0 þ DT

ð4:2Þ

This theorem was formulated by Modigliani and Miller for perpetuity companies, but we modify it for a company with a finite lifetime. V = V 0 þ TS = V 0 þ kd DT

1 X

ð1 þ k d Þ - t =

t=1

= V 0 þ wd VT ½1- ð1 þ kd Þ - n  V ð1- wd VT ½1- ð1 þ k d Þ

-n

Þ = V 0 :

ð4:3Þ ð4:4Þ

There is a common use of the following two formulas for the cost of the financially independent and financially dependent companies (Мodigliani and Мiller 1958, 1963, 1966): V 0 = CF=k 0

and V = CF=WACC:

ð4:5Þ

However, these almost always used formulas were derived for perpetuity company and in case of a company with a finite lifetime they must be modified in the same manner as the value of tax shields (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011; Filatova et al. 2008) V 0 = CF½1- ð1 þ k0 Þ - n =k0 ; V = CF½1- ð1 þ WACCÞ - n =WACC

ð4:6Þ

4.1

Companies with Arbitrary Lifetime. Brusov–Filatova–Orekhova Equation

75

From formula (Eq. 4.4), we get Brusov–Filatova–Orekhova equation for WACC (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011; Filatova et al. 2008) 1 - ð1 þ k 0 Þ - n 1 - ð1 þ WACCÞ - n : = WACC k 0 ½1 - ωd T ð1 - ð1 þ kd Þ - n Þ

ð4:7Þ

D —the share Here, S—the value of own (equity) capital of the company, wd = DþS S of debt capital; ke , we = DþS—the cost and the share of the equity of the company, L = D/S—financial leverage. At n = 1 we get Myers (2001) formula for 1-year company

WACC = k0 -

ð1 þ k0 Þk d wd T 1 þ kd

ð4:8Þ

For n = 2 one has 1 - ð1 þ k 0 Þ - 2 1 - ð1 þ WACCÞ - 2  i : = h WACC k 0 1 - ω d T 1 - ð1 þ k d Þ - 2

ð4:9Þ

This equation can be solved for WACC analytically: pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 - 2α ± 4α þ 1 , WACC = 2α

ð4:10Þ

where α=

2 þ k0 h i: 2k d þk 2d ð1 þ k0 Þ 1 - ωd T ð1þk 2 Þ 2

ð4:11Þ

d

For n = 3 and n = 4 equation for the WACC becomes more complicate, but it still can be solved analytically, while for n > 4 it can be solved only numerically. We would like to make an important methodological notice: taking into account the finite lifetime of the company, all formulas, without exception, should be received with use formulas (Eq. 4.6) instead of their perpetuity limits (Eq. 4.5). Below, we will describe the algorithm for the numerical solution of the equation (Eq. 4.7). Algorithm for Finding of WACC in Case of Arbitrary Lifetime of the Project Let us return back to n-year project (n-year company). We have the following equation for WACC in n-year case

76

4

Modern Theory of Capital Cost and Capital Structure:. . .

1 - ð1 þ WACCÞ - n - AðnÞ = 0, WACC

ð4:12Þ

where AðnÞ =

1 - ð1 þ k 0 Þ - n : k 0 ½1 - ωd T ð1 - ð1 þ kd Þ - n Þ

ð4:13Þ

The algorithm of the solving of the Eq. (4.12) should be as follows: 1. Putting the values of parameters k0, ωd, T and given n, we calculate A(n) 2. We determine two WACC values, for which the left part of the Eq. (4.12) has opposite signs. It is obviously that as these two values we can use WACC1 and WACC1, because WACC1 > WACCn > WACC1 for finite n ≥ 2 3. Using, for example, the bisection method, we can solve the Eq. (4.12) numerically

4.2

Comparison of Modigliani–Miller Results (Perpetuity Company) with Myers Results (1-Year Company) and Brusov–Filatova–Orekhova Ones (Company with Arbitrary Lifetime)

Myers (1974) has compared his result for 1-year project (Eq. 4.8) with Modigliani and Miller’s result for perpetuity limits (Eq. 3.8). He has used the following values of parameters: k0 = 8% ÷ 24%; kd = 7%; T = 50%; wd = 0% ÷ 60% and estimated the difference in the WACC values following from the formulas (Eq. 4.8) and (Eq. 3.8). We did make similar calculations for 3-, 3-, 5-, and 10-year project for the same set of parameters and we have gotten the following results, shown in Tables (Table 4.1 (second line (bulk)), Table 4.2 (second line (bulk)), and Table 4.3) and corresponding Figures (Figs. 4.1, 4.2, and 4.3). Note, that data for equity cost k0 = 8% turn out to be a little bit uncertain: this could be related to the fact that this value of equity cost is quite close to the value of interest rate of the debt kd = 7%. For all other values of equity cost the results are reproducible and very informative and are discussed below. For a graphic illustration of the results, we use data for n = 1, 2, 1, that adequately reflect the results we obtained. Discussion of Results 1. From Table 4.1 and Fig. 4.2, it is obviously that WACC has a maximum for 1-year project and decreases with the lifetime of the project, reaching the

4.2

Comparison of Modigliani–Miller Results (Perpetuity Company) with. . .

77

Table 4.1 WACC dependence on debt share wd for different values of equity cost k0 for companies with different lifetime n k0 k0 = 8% k0 = 10% k0 = 12%

k0 = 16%

k0 = 20%

k0 = 24%

n n=1 n=2 n=1 n=1 n=2 n=1 n=1 n=2 n=3 n=5 n = 10 n=1 n=1 n=2 n=3 n=5 n = 10 n=1 n=1 n=2 n=3 n=5 n = 10 n=1 n=1 n=2 n=3 n=5 n = 10 n=1

wd = 10% 7.6% 7.52 7.6 9.7 9.51 9.5 11.6 11.51 11.46 11.42 11.396 11.4 15.62 15.52 15.44 15.38 15.34 15.2 19.6 19.45 19.41 19.35 19.27 19.0 23.6 23.46 23.39 23.31 23.21 22.8

20% 7.3 7.08 7.2 9.3 9.05 9.0 11.3 11.02 10.93 10.83 10.786 10.8 15.2 14.99 14.88 14.76 14.67 14.4 19.2 18.97 18.82 18.69 18.54 18.0 23.2 22.94 22.77 22.61 22.40 21.6

30% 6.9 6.6 6.8 8.9 8.59 8.5 10.9 10.54 10.39 10.25 10.1695 10.2 14.9 14.5 14.31 14.14 13.99 13.6 18.8 18.45 18.23 18.03 17.80 17.0 22.8 22.37 22.15 21.91 21.60 20.4

40% 6.6 6.17 6.4 8.6 8.13 8.0 10.5 10.07 9.85 9.66 9.5455 9.6 14.5 13.98 13.75 13.51 13.31 12.8 18.4 17.93 17.64 17.36 17.05 16.0 22.4 21.80 21.54 21.21 20.78 19.2

50% 6.2 5.67 6.0 8.2 7.64 7.5 10.2 9.6 9.31 9.06 8.914 9.0 14.1 13.47 13.18 12.88 12.62 12.0 18.1 17.37 17.05 16.70 16.30 15.0 22.0 21.30 20.91 20.51 19.96 18.0

60% 5.9 5.21 5.6 7.8 7.16 7.0 9.8 9.09 8.77 8.46 8.2745 8.4 13.7 12.96 12.61 12.24 11.92 11.2 17.7 16.86 16.45 16.03 15.54 14.0 21.6 20.75 20.29 19.80 19.13 16.8

minimum in the Modigliani–Miller perpetuity case. Dependence of all WACC values on debt share wd turns out to be linear at any equity cost k0 for all considered durations of the project (lifetime values of the companies). It is natural for 1-year project, because it is described by Myers linear formula (4.8) as well as in the Modigliani–Miller perpetuity case, describing by the formula (3.8), which is linear too, but it is surprised for 2-year project, where formula for WACC (4.7) is obviously nonlinear. The negative slope in WACC increases with the equity cost k0. 2. As it follows from the Table 4.2 and Fig. 4.3, the dependence of the average ratios r = < Δ1 =Δ2 > on debt share wd is quite weak and can be considered as almost constant. The value of this constant increases practically linear with the equity cost k0 from 1.22 at k0 = 10% up to 5.69 at k0 = 24% (see Fig. 4.4).

78

4

Table 4.2 Dependence of the differences Δ1 = WACC1 WACC1 (first line), Δ2 = WACC1 - WACC2 (second line (bulk)) and their ratio r = Δ1/Δ2 (third line) on debt share wd for different values of equity cost k0

Modern Theory of Capital Cost and Capital Structure:. . .

k0 = 10% k0 = 12% k0 = 16% k0 = 20% k0 = 24%

wd = 10% 0.20 0.19 1.05 0.2 0.09 2.22 0.4 0.08 5.0 0.6 0.15 4.0 0.8 0.14 5.7

20% 0.30 0.25 1.2 0.5 0.28 1.76 0.8 0.21 3.81 1.2 0.23 5.22 1.6 0.26 6.15

30% 0.4 0.31 1.29 0.7 0.36 1.94 1.3 0.4 3.25 1.8 0.35 5.14 2.4 0.43 5.58

40% 0.60 0.47 1.28 0.9 0.43 2.09 1.7 0.52 3.27 2.4 0.47 5.11 3.2 0.6 5.33

50% 0.7 0.56 1.25 1.2 0.6 2 2.1 0.63 3.33 3.1 0.73 4.25 4.0 0.7 5.71

60% 0.8 0.64 1.25 1.4 0.71 1.97 2.5 0.74 3.38 3.7 0.84 4.4 4.8 0.85 5.65

Table 4.3 Average (by debt share wd) values of ratios r = < Δ1 =Δ2 > for k0 = 10 % ; 12 % ; 16 % ; 20% and 24% k0 r = < Δ1 =Δ2 >

10% 1.22

12% 2.00

16% 3.67

20% 4.69

24% 5.69

3. The relative difference between 1-year and 2-year projects increases when the equity cost k0 decreases. This means that the error in 1-year project WACC for 2-year project increases when the equity cost k0 decreases as well. At the same time the relative difference between 2-year project and perpetuity MM project increases with the equity cost k0.

4.3

Brusov–Filatova–Orekhova Theorem

Case of Absence of Corporate Taxes Modigliani–Miller theory in case of absence of corporate taxes gives the following results for dependence of WACC and equity cost ke on leverage 1. V0 = VL; CF/k0 = CF/WACC, and thus WACC = k0 :

ð4:14Þ

W A CC

4.3

Brusov–Filatova–Orekhova Theorem

79

25,00 24,00 23,00 22,00 21,00 20,00 19,00 18,00 17,00 16,00 15,00 14,00 13,00 12,00 11,00 10,00 9,00 8,00 7,00 6,00 5,00 0

10

20

30

40

50

60 Wd

Fig. 4.1 The dependence of the WACC on debt share wd for companies with different lifetimes for different cost of equity, k0 (from Table 4.1)

Fig. 4.2 Dependence of the ratio r = Δ1/Δ2 of differences Δ1 = WACC1 - WACC1, Δ2 = WACC1 - WACC2 on debt share wd for different values of equity cost k0 (from Table 4.2)

80

4

r

Modern Theory of Capital Cost and Capital Structure:. . .

7,00 6,00 5,00 4,00 3,00 2,00 1,00 0,00

10,00

12,00

16,00

20,00

24,00

Ko

Fig. 4.3 Dependence of the average values of ratio r = < Δ1 =Δ2 > on the equity cost, k0

Fig. 4.4 The dependence of the WACC on leverage in the absence of corporate taxes (the horizontal line (t = 0)), as well as in the presence of corporate taxes (for 1-year (n = 1) and perpetuity companies (n = 1)). Curves for the WACC of companies with an intermediate lifetime (1 < n < 1) lie within the shaded region

4.3

Brusov–Filatova–Orekhova Theorem

81

2. WACC = we  ke + wd  kd; and thus L k k0 WACC - wd  k d 1 þ L d =: ke = = 1 we 1þL = k0 þ Lðk0 - kd Þ

ð4:15Þ

For the finite lifetime companies Modigliani–Miller theorem about equality of value of financially independent and financially dependent companies (V0 = VL) has the following view (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011) V 0 = V L; CF 

½ 1 - ð1 þ k 0 Þ - n  ½1 - ð1 þ WACCÞ - n  : = CF  k0 WACC

ð4:16Þ

Using this relation, we prove an important Brusov–Filatova–Orekhova theorem: Under absence of corporate taxes the equity cost of the company, ke, as well as its weighted average cost of capital, WACC, does not depend on the lifetime of the company and is equal, respectively, to ke = k0 þ Lðk0- kd Þ; WACC = k0

ð4:17Þ

Let us consider first the 1- and 2-year companies (a) for 1-year company one has from (4.16) 1 - ð1 þ k 0 Þ - 1 1 - ð1 þ WACCÞ - 1 = , k0 WACC

ð4:18Þ

1 1 = : 1 þ k0 1 þ WACC

ð4:19Þ

WACC = k0 :

ð4:20Þ

and thus

Hence

Formula for equity cost ke = k0 + L(k0 - kd) now obtained by substituting WACC = k0 into (4.15)

82

Modern Theory of Capital Cost and Capital Structure:. . .

4

(b) for 2-years company one has from (4.16) h

1 - ð1 þ k 0 Þ - 2 k0

i

h =

1 - ð1 þ WACCÞ - 2

i

WACC

,

and thus 2 þ k0 2 þ WACC = : ð1 þ k 0 Þ2 ð1 þ WACCÞ2 Denoting α =

2þk0 , ð1þk 0 Þ2

ð4:21Þ

we get the following quadratic equation for WACC:

α  WACC2 þ ð2α - 1Þ  WACC þ ðα - 2Þ = 0:

ð4:22Þ

It has two solutions pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 - 2α ± 4α þ 1 : WACC1,2 = 2α Substituting α =

2þk 0 , ð1þk0 Þ2

ð4:23Þ

we get 

 k20 - 3 ± ðk0 þ 3Þð1 þ k 0 Þ WACC1,2 = : 2ð 2 þ k 0 Þ

ð4:24Þ

2k0 þ 3 < 0: k0 þ 2

ð4:25Þ

WACC1 = k 0 ; WACC2 = -

The second root is negative, but the weighted average cost of capital can only be positive, so only one value remains WACC1 = k 0 : (c) For company with arbitrary lifetime n Brusov–Filatova–Orekhova–Orekhova formula (4.16) gives 1 - ð1 þ k 0 Þ - n 1 - ð1 þ WACCÞ - n = : k0 WACC

ð4:26Þ

For a fixed k0 (4.26) is an equation of n-degree relative to WACC. It has n roots (in general complex). One of the roots, as shown by direct substitution, is always WACC = k0. Investigation of the remaining roots is difficult and not part of our problem.

4.4

From Modigliani–Miller to General Theory of Capital Cost and. . .

83

Formula for equity cost ke = k0 + L(k0 - kd) now obtained by substituting WACC = k0 into (4.15) Thus, we have proved the Brusov–Filatova–Orekhova theorem. Case of the Presence of Corporate Taxes Modigliani–Miller theory in case of presence of corporate taxes gives the following results for dependence of WACC and equity cost ke on leverage 1. WACC V L = V 0 þ Dt; D = wd V L

ð4:27Þ

CF=WACC = CF=k0 þ Dt = CF=k 0 þ wd tCF=WACC;

ð4:28Þ

1 1 - wd t = ; WACC k 0  WACC = k 0 ð1- wd t Þ = k0 1-

ð4:29Þ  L t : 1þL

ð4:30Þ

Thus, WACC decreases with leverage from k0 (in the absence of debt financing (L = 0)) up to k0(1 - t) (at L = 1). 2. The equity cost ke WACC = k 0 ð1- wd t Þ = we  ke þ wd  kd ð1- t Þ; and thus WACC - wd  k d  ð1 - t Þ = we L k0 ð1 - wd t Þ k ð1 - t Þ 1þL d = k 0 þ Lðk0 - kd Þð1 - t Þ: 1 1þL ke =

4.4

ð4:31Þ

From Modigliani–Miller to General Theory of Capital Cost and Capital Structure

Let us consider how the weighted average cost of capital, WACC, and the cost of equity capital, ke, will be changed under taking into account the finite lifetime of the company.

84

4

Modern Theory of Capital Cost and Capital Structure:. . .

(a) 1-year company From (4.20) one has 1 - ð1 þ k 0 Þ - n 1 - ð1 þ WACCÞ - n : = WACC k 0 ½ 1 - w d t ð1 - ð1 þ k d Þ - n Þ

ð4:32Þ

For 1-year company we get 1 - ð1 þ k 0 Þ - 1 1 - ð1 þ WACCÞ - 1  i = h WACC k 0 1 - wd t 1 - ð1 þ k d Þ - 1

ð4:33Þ

From (Eq. 4.33), we obtain the well-known Myers formula (Eq. 4.8), which is the particular case of Brusov–Filatova–Orekhova formula (Eq. 4.7). WACC = k0 -

1 þ k0 k w t: 1 þ kd d d

Thus   ð1 þ k 0 Þ  k d L  WACC = k0 1t : ð1 þ k d Þ  k 0 1 þ L

ð4:34Þ

Thus, WACC decreases with  leverage from k0 (in the absence of debt financing ð1þk 0 Þkd (L = 0)) up to k 0 1- ð1þkd Þk0 t (at L = 1). Equating the right part to general expression for WACC WACC = we  ke þ wd  kd ð1- t Þ,

ð4:35Þ

1 þ k0 k w t = we  ke þ wd  kd ð1- t Þ: 1 þ kd d d

ð4:36Þ

one gets k0 Thus

1 1 þ k0 kk w t - kd wd ð1- t Þ = ke = we 0 1 þ k d d d

4.4

From Modigliani–Miller to General Theory of Capital Cost and. . .

85

Fig. 4.5 Dependence of the equity cost, ke, on leverage in the absence of corporate taxes (the upper line (t = 0)), as well as in the presence of corporate taxes (for 1–year (n = 1) and perpetuity companies (n = 1)). Dependences of the cost of equity capital of companies, ke, with an intermediate lifetime (1 < n < 1) lie within the shaded region

kd ½ð1 þ k 0 Þt þ ð1 þ kd Þð1 - t Þ = 1 þ kd   kd t : = k 0 þ Lðk0 - kd Þ 1 1 þ kd   kd t : k e = k0 þ Lðk 0- k d Þ 11 þ kd

= ð1 þ LÞk 0 - L

ð4:37Þ

So, we see, that in case of 1-year company the perpetuity limit ke = k0 + L(k0 - kd)(1 - t) is replaced by (Eq. 4.37). Difference is due to different values of the tax shield for a 1-year company and perpetuity one (Fig. 4.5). Let us investigate the question of the tax shields value for companies with different lifetime in more detail. Tax Shield General expression for the tax shield has the form (Brusov–Filatova–Orekhova) TS =

n X i=1

k d Dt ½1 - ð1 þ kd Þ - n  k d Dt   = Dt ½1- ð1 þ k d Þ - n : ð4:38Þ = ð1 þ kd Þi ð1 þ kd Þ 1 - ð1 þ kd Þ - 1

1. In perpetuity limit (n → 1) tax shield is equal to TS1 = Dt, which leads to the so-called effect of the tax shield associated with the appearance of a factor (1 - t) in the equity cost ke = k0 + L(k0 - kd)(1 - t). 2. For the 1-year company tax shield value is equal to

86

4

Modern Theory of Capital Cost and Capital Structure:. . .

  TS1 = Dt 1- ð1 þ k d Þ - 1 = Dtk d =ð1 þ k d Þ:  This leads to appearance of a factor 1  kd ke = k 0 þ Lðk0- kd Þ 1- 1þk t : d

kd 1þk d

ð4:39Þ

 t

in the equity cost (Eq. 4.37)

3. Tax shield for a 2-year company is equal to   TS2 = Dt 1- ð1 þ kd Þ - 2 = Dtkd ð2 þ kd Þ=ð1 þ kd Þ2

ð4:40Þ

and if the analogy with the 1-year company will keep, then factor (1 - t) in the Modigliani–Miller theory would be replaced by the factor ! k d ð2 þ k d Þ 1t : ð1 þ k d Þ2

ð4:41Þ

However, due to a nonlinear relation between WACC and k0 and kd in Brusov– Filatova–Orekhova formula (Eqs. 4.9–4.11) fora 2-year company (and companies with longer lifetime), such a simple analogy is no longer observed, and the calculations become more complex.

4.5

Conclusions

In this chapter, an important step toward a general theory of capital cost and capital structure of the company has been done. For this perpetuity theory of Nobel Prize winners Modigliani and Miller, which was until recently the basic theory of capital cost and capital structure of companies, extended to the case of companies with an arbitrary lifetime, as well as for projects of arbitrary duration. We show that taking into account the finite lifetime of the company in the presence of corporate taxes leads to a change in the equity cost of the company, ke, as well as in its weighted average cost, WACC. Thus, we have removed one of the most serious limitations of the theory of Modigliani–Miller connected with the assumption of perpetuity of the companies. The effect of leverage on the cost of equity capital of the company with an arbitrary lifetime, ke, and its weighted average cost, WACC, is investigated. We give a rigorous proof of an important Brusov–Filatova–Orekhova theorem, that in the absence of corporate tax equity cost of companies, ke, as well as its weighted average cost, WACC, does not depend on the lifetime of the company. We summarize the difference in results obtained within modern Brusov– Filatova–Orekhova theory and within classical Modigliani–Miller one in Table 4.4.

References

87

Table 4.4 Comparison of results, obtained within Modigliani–Miller theory and general Brusov– Filatova–Orekhova theory Financial parameter Capitalization of financially independent company Capitalization of leverage (financially dependent) company Tax shield Modigliani–Miller theorem with taxes Weighted average cost of capital, WACC

Equity cost, ke

Modigliani–Miller (MM) results V0 = CF/k0

Brusov–Filatova–Orekhova (BFO) results

V = CF/WACC

V=

(TS)1 = DT V = V0 + DT

(TS)n = DT[1 - (1 + kd)-n] V = V0 + DT[1 - (1 + kd)-n]

WACC = = k 0 ð1 - wd t Þ

1 - ð1 þ WACCÞ - n = WACC 1 - ð1 þ k 0 Þ - n = k 0 ½1 - ωd T ð1 - ð1 þ k d Þ - n Þ k e = ð1 þ LÞ  WACC - k d Lð1 - T Þ

ke = k0 þ þLðk0 - kd Þð1 - t Þ

V0 =

CF k 0 ½1- ð1

þ k0 Þ - n 

CF WACC ½1- ð1

þ WACCÞ - n 

The first four formulas from the right-hand column are sometimes used in practice, but there are several significant nuances. The first—these formulas do not take account of the residual value of the company and only take into account the operating flows and this must be borne in mind. The second—these formulas contain the weighted average cost of capital of the company, WACC. If it is estimated within the traditional approach or the theory of Modigliani–Miller, it gives a lower WACC value, than the real, and, therefore, overestimates the capitalization of both financially dependent and financially independent companies. Therefore, in order to assess the company capitalization by the first two formulas one needs to use Brusov–Filatova–Orekhova formulas for weighted average cost of capital, WACC, and equity cost, ke. To calculate the equity cost in BFO approximation (last line in Table) one needs to first use Brusov–Filatova–Orekhova formula for weighted average cost of capital, WACC (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011; Filatova et al. 2008).

References Brusov PN, Filatova ТV (2011) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Financ Credit 435:2–8 Brusov P, Filatova T, Orehova N, Brusova A (2011a) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Appl Financ Econ 21(11): 815–824 Brusov P, Filatova T, Orehova N et al (2011b) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Bus ICT 2:16–21 Brusov P, Filatova T, Orehova N et al (2011c) Influence of debt financing on the effectiveness of the investment project within the Modigliani–Miller theory. Res J Econ Bus ICT (UK) 2:11–15

88

4

Modern Theory of Capital Cost and Capital Structure:. . .

Brusov P, Filatova T, Orehova N, Brusov PP, Brusova N (2011d) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Bus ICT 2:16–21 Brusov P, Filatova T, Eskindarov M, Orehova N (2012a) Influence of debt financing on the effectiveness of the finite duration investment project. Appl Financ Econ 22(13):1043–1052 Brusov P, Filatova T, Eskindarov M, Orehova N (2012b) Hidden global causes of the global financial crisis. J Rev Glob Econ 1:106–111 Brusov P, Filatova P, Orekhova N (2013a) Absence of an optimal capital structure in the famous tradeoff theory! J Rev Glob Econ 2:94–116 Brusov P, Filatova T, Orehova N (2013b) A qualitatively new effect in corporative finance: abnormal dependence of cost of equity of company on leverage. J Rev Glob Econ 2:183–193 Brusov P, Filatova P, Orekhova N (2014a) Mechanism of formation of the company optimal capital structure, different from suggested by trade off theory. Cogent Econ Financ 2:1–13. https://doi. org/10.1080/23322039.2014.946150 Brusov P, Filatova T, Orehova N (2014b) Inflation in Brusov–Filatova–Orekhova theory and in its perpetuity limit – Modigliani – Miller theory. J Rev Glob Econ 3:175–185 Filatova Т, Orehova N, Brusova А (2008) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Bull FU 48:68–77 Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Modigliani F, Miller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391 Myers S (2001) Capital structure. J Econ Perspect 15(2):81–102

Chapter 5

Bankruptcy of the Famous Trade-Off Theory

Keywords Brusov–Filatova–Orekhova (BFO) theory · Trade-off theory · The weighted average cost of capital · Equity cost · Company capitalization · A qualitatively new anomalous effect Within modern theory of capital structure and capital cost by Brusov–Filatova– Orekhova (Brusova 2011; Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011; Filatova et al. 2008) the analyses of wide known trade-off theory have been made. It is shown that suggestion of risky debt financing (and growing credit rate near the bankruptcy) in opposite to waiting result does not lead to growing of weighted average cost of capital, WACC, which still decreases with leverage. This means the absence of minimum in the dependence of WACC on leverage as well as the absence of maximum in the dependence of company capitalization on leverage. Thus, it means that the optimal capital structure is absent in famous trade-off theory. The explanation to this fact has been done. Under condition of proved by us insolvency of well–known classical trade-off theory question of finding of new mechanisms of formation of the company optimal capital structure, different from one, suggested by trade-off theory, becomes very important. One of the real such mechanisms has been developed by us in next Chapter.

5.1

Optimal Capital Structure of the Company

Choosing of optimal capital structure of the company, i.e., proportion of debt and equity, which minimizes weighted average cost of capital and maximizes the company capitalization, is one of the most important tasks of financial manager and the management of a company. The search for an optimal capital structure, like the search for a “golden fleece,” attracts attention of economists and financiers during many tens of years. And it is clear why: one can, nothing making, but only by changing the proportion between the values of equity capital and debt one of the company, significantly enhance the company capitalization, by other words to fulfill © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_5

89

90

5 Bankruptcy of the Famous Trade-Off Theory

the primary task, to reach critical goal of the business management. Spend a little less of your own, loan slightly more (or vice versa), and company capitalization reaches a maximum. Note, that the problem of capital structure is studied very intensively. There are theories, which consider the perfect market (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011; Filatova et al. 2008; Мodigliani and Мiller 1958, 1963, 1966) and other ones, considering the imperfect market (Brennan and Schwartz 1978, 1984; Leland 1994; Kane et al. 1984; Dittmar and Thakor 2007; Bikhchandani et al. 1998; Post et al. 2002; Filbeck et al. 1996; Jenter 2005; Baker and Wurgler 2002; Graham and Harvey 2001; Hovakimian et al. 2001; Myers and Majluf 1984; Myers 1984; Fama and French 2004; Jensen and Meckling 1976). Among former ones agent cost theory (Jensen and Meckling 1976), stakeholders theory (Post et al. 2002), manager investment autonomy (Dittmar and Thakor 2007), information cascades (Bikhchandani et al. 1998), behavioral theories (Filbeck et al. 1996; Jenter 2005; Baker and Wurgler 2002; Graham and Harvey 2001), signaling theory (Myers and Majluf 1984), and pecking order theory (Myers 1984; Hovakimian et al. 2001; Fama and French 2004). Historically the conceptions of the influence of capital structure on the well-being of shareholders have developed not monotonically. We consider the traditional (empirical) approach (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011; Filatova et al. 2008), the Modigliani and Miller theory (Мodigliani and Мiller 1958, 1963, 1966), trade-off theory (Brennan and Schwartz 1978, 1984; Leland 1994; Kane et al. 1984), and modern Brusov–Filatova–Orekhova theory of capital cost and capital structure (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011; Filatova et al. 2008). The Traditional Approach The traditional (empirical) approach told to businessmen, that weighted average cost of capital, WACC, and the associated company capitalization, V = CF/WACC depend on the capital structure, the level of leverage. Debt cost always turns out to be lower, than equity cost, because first one has lower risk, because in the event of bankruptcy creditor claims are met prior to shareholders claims. As a result an increase in the proportion of lower-cost debt capital in the overall capital structure up to the limit which does not cause violation of financial sustainability and growth in risk of bankruptcy, leads to lower weighted average cost of capital, WACC. The required by investors profitability (the equity cost) is growing, however, its growth has not led to compensation benefits from use of more low-cost debt capital. Therefore, the traditional approach welcomes the increased leverage L = D/S, and the associated increase of company capitalization. The traditional (empirical) approach has existed up to the appearance of the first quantitative theory by Modigliani and Miller in 1958 (Мodigliani and Мiller 1958). Modigliani–Miller Theory Modigliani and Miller (ММ) in their first paper (without taxes) (Мodigliani and Мiller 1958) come to conclusion, that under assumptions, that there are no taxes, no transaction costs, no bankruptcy costs, perfect market

5.1

Optimal Capital Structure of the Company

91

exists with symmetry information, equivalence in borrowing costs for both companies and investors, etc., the choosing of proportion of debt and equity does not affect WACC and company value as well. Most of Modigliani and Miller assumptions (Мodigliani and Мiller 1958), of course, are unrealistic. Some assumptions can be removed without changing the conclusions of the model. However, assuming no costs of bankruptcy and the absence of taxes (or the presence of only corporate taxes) are crucial—the change of these assumptions alters conclusions. The last two assumptions rule out the possibility of signaling and agency costs and, thus, also constitute a critical prerequisite. Modigliani–Miller theory with taxes (see Chap. 3) leads to conclusion, that in accordance to obtained by them formula WACC = k 0 ð1- wd T Þ

ð5:1Þ

weighted average cost of capital WАСС decreases continuously (Fig. 3.3) (WACC decreases from k0 (for L = 0) up to k0(1 - T ) (for L = 1, when the company is financed entirely with borrowed funds). So, there is no optimal capital structure within this theory. Below we modify Modigliani–Miller theory with taxes by taken off the suggestion about riskless of debt capital, modeling the growth in risk of bankruptcy by increase of a credit rate, and show that optimal capital structure of the company is still absent. Trade-Off Theory Reduction in financial sustainability of companies and increase of bankruptcy risk, which relate to the use of different forms of borrowing in the formation of financial capital structure of the company, is increased with the increasing of debt. Modigliani–Miller theory did not take into account the bankruptcy risk and related costs. From its version with the tax on profit it follows that, debt financing brings only some benefits associated with tax benefits (tax shield). Because company capitalization grows with leverage and there is no compensating increase in the debt cost, increasing the capitalization requires use of debt financing only. This obvious contradiction with the real economy has created many theories, which had tried to find a balance between the advantages and disadvantages of using by the companies of debt financing. The advantage is a reduction of weighted average cost of capital, WACC, and the corresponding increase of capitalization of the companies, V, and the drawback—reduce with the increase of debt financing of financial sustainability of the companies and increased financial distress costs and risk of bankruptcy. One of this theory is trade-off theory (Brennan and Schwartz 1978; Leland 1994). There are two versions of this theory: static and dynamic. Former one is based on the fact that at the low leverage level the benefits of debt financing are manifested: WACC drops with leverage, a company capitalization is growing. Starting with a certain leverage level financial distress costs and risk of bankruptcy are growing, the WACC begins to grow and the value of the company begins

92

5 Bankruptcy of the Famous Trade-Off Theory

to fall. The leverage level, at which the value of tax benefits is approximately equal to the cost of bankruptcy, determines the optimal (objective) capital structure. While the static trade-off theory is single-period model (Brennan and Schwartz 1978; Leland 1994), in the dynamic trade-off theory (Brennan and Schwartz 1984) the financing decision depends on what the company anticipates in the next periods, which will be a capital structure.

5.2

Absence of the Optimal Capital Structure in Modified Modigliani–Miller Theory (MMM Theory)

Let us show first that in Modigliani–Miller theory (Мodigliani and Мiller 1958, 1963) modified by us by taken off the suggestion about riskless of debt capital, the optimal capital structure is still absent. Consider the case of arbitrary dependence of debt cost on leverage f(L) . Suppose that debt cost kd is described by the following function:
kd =

kd0 = const; at L ≤ L0 kd0 þ f ðLÞ; at L > L0

 ð5:2Þ

Here f(L ) is an arbitrary (growing or decreasing) function of leverage level L. We are interested in leverage levels L > L0, because at L < L0 the standard Modigliani– Miller theory works and weighted average cost of capital, WACC, is decreased with leverage WACC = k0 ð1- wd t Þ

ð5:3Þ

while an equity cost grows linearly with leverage k e = k0 þ Lðk 0- k d Þð1- t Þ:

ð5:4Þ

Here ke is an equity cost; k0 is an equity cost of financially independent company; kd is debt cost; t is tax on profit rate; WACC is a weighted average cost of capital. In this case for WACC one has WACC = ke we þ kd wd ð1 - t Þ = ke =

1 ½k þ kd Lð1 - t Þ 1þL e

1 L þ kd ð1 - t Þ = 1þL 1þL

ð5:5Þ

Substituting Eqs. (5.2) and (5.4) into Eq. (5.5), one has finally for weighted average cost of capital, WACC,

5.3

Analysis of the Trade-Off Theory Within the Brusov–Filatova–Orekhova Theory

WACC

=

1 ½k þ Lðk0 - kd Þð1 - t Þþ 1þL 0

þ Lk d ð1 - t Þ = =

93

1 ½k þ k0 Lð1 - t Þ = 1þL 0

k 0 ½1 þ Lð1 - t Þ = k0 ½we þ wd ð1 - t Þ = k0 ð1 - wd t Þ 1þL

ð5:6Þ

One can see, that weighted average cost of capital, WACC, does not depend on f(L). Moreover, it is described by the same expression (Eq. 5.3), as in case of riskless debt capital. Note that obtained result consistent with conclusions of Rubinstein (1973) and Stiglitz (1969), that cost of company within Modigliani–Miller theory is not changed upon introduction of debt riskiness. In our approximation, as well as at Hsia (1981) debt cost is not already constant. For derivative from weighted average cost of capital, WACC, on leverage level one has ðWACCÞ0L = k0

½ð1 - t Þð1 þ LÞ - 1 - Lð1 - t Þ t = - k0 < 0: 2 ð1 þ LÞ2 ð1 þ LÞ

ð5:7Þ

We have proved the following theorem: In modified Modigliani–Miller theory (allowing riskiness debt capital) under arbitrary change of debt cost with leverage (growing, as well as decrease) weighted average cost of capital, WACC always falls down with leverage. This means the absence of the company optimal capital structure and proves insolvency well–known classical trade-off in its original formulation.

5.3

Analysis of the Trade-Off Theory Within the Brusov– Filatova–Orekhova Theory

Modigliani and Miller (1958, 1963, 1966) assumed that all financial flows are perpetuity. Because, in reality the lifetime of the companies are always, of course, finite, this condition is one of the weaknesses of the Modigliani and Miller theory. Account of the finite lifetime of the companies changes all the formulas of Modigliani and Miller drastically. The solution of the problem of weighted average cost of capital, WACC, for the companies with arbitrary lifetime has been done for the first time by Brusov–Filatova–Orekhova with coauthors (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011; Filatova et al. 2008). Their theory allows to find hidden global causes of the global financial crisis (Brusov et al. 2012b). The main formula, received by them, is an algebraic equation of n + 1 power (n— a term of life of company) to calculate weighted average cost of capital, WACC, taking the form

94

5

Bankruptcy of the Famous Trade-Off Theory

1 - ð1 þ k 0 Þ - n 1 - ð1 þ WACCÞ - n : = WACC k 0 ½1 - ωd T ð1 - ð1 þ kd Þ - n Þ

ð5:8Þ

For n > 3 this equation can be solved numerically only. It is easy to use for this a function “matching parameters” in the Excel. Using equation (Eq. 5.8), let us investigate the optimal capital structure in the trade-off theory. We are modeling the emergence of a financial volatility and of bankruptcy risk by the growth of the cost of debt capital kd, indicating that kd becomes risky and its growth represents a fee for the state of financial volatility and bankruptcy risk. It is impossible to study such effects, as the growth of credit rate with leverage in the theory of Modigliani and Miller, because: – MM theory considers two types of assets: risky equity capital and free of risk debt capital – weighted average cost of capital, WACC, in the theory of Modigliani and Miller is determined by the following expression (Eq. 5.3), which depends on k0, wd, T and does NOT depend on kd. This is due to the fact that discounted value of tax shields for an infinite period of time

ðPVÞTS = kd DT

1 X

ð1 þ kd Þ - t = DT

ð5:9Þ

t=1

with the use of kd as discount rate does NOT depend on kd. In contrast to the theory of the Modigliani and Miller, in a modern theory of capital cost and capital structure of the company by Brusov–Filatova–Orekhova (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011; Filatova et al. 2008) discounted value of tax shields is valuated for finite period of time n (lifetime of company or the time from the establishment of companies up to the present moment (n)) and depends on kd ðPVÞTS = kd DT

n X

ð1 þ kd Þ - t = DT½1- ð1 þ k d Þ - n ,

ð5:10Þ

t=1

as well as capitalization of financially independent company V 0 = CF½1- ð1 þ k0 Þ - n =k0

ð5:11Þ

and capitalization of financially dependent company V = CF½1- ð1 þ WACCÞ - n =WACC:

ð5:12Þ

5.3

Analysis of the Trade-Off Theory Within the Brusov–Filatova–Orekhova Theory

95

Table 5.1 Dependence of WACC on L n

L

0

1

2

3

4

5

6

7

8

9

3

kd

0.07

0.07

0.07

0.08

0.11

0.16

0.23

0.32

0.43

0.56

10 0.71

k0

A

1.9813

2.0184

2.0311

2.0445

2.0703

2.1075

2.1520

2.1988

2.2438

2.2842

2.3186

0.24

WACC

0.2401

0.2279

0.2238

0.2195

0.2111

0.1997

0.1864

0.1730

0.1605

0.1496

0.1406

WACC(L) 0.3000 0.2500 0.2000 0.1500 0.1000 0.0500 0.0000

0

1

2

3

4

5

6

7

8

9

10

11

Fig. 5.1 Dependence of WACC on L

As a result, for weighted average cost of capital WACC the formula BFO is derived 1 - ð1 þ k 0 Þ - n 1 - ð1 þ WACCÞ - n = WACC k0 ½1 - ωd T ð1 - ð1 þ k d Þ - n Þ

ð5:13Þ

and WACC now depends on kd. We consider linear and quadratic growth of debt cost kd with leverage, starting from some value (with different coefficients), different values of k0 and different terms of life of the companies. Let us find WACC values. 1. n = 3; t = 20 % ; L = 0, 1, 2, . . .10
k0 = 24%; kd =

0:07; at L ≤ 2 0:07 þ 0:01ðL - 2Þ2 ; at L > 2

 ð5:14Þ

Dependence of WACC on L for case (1) is shown in Table 5.1 and Fig. 5.1.

96

5

Bankruptcy of the Famous Trade-Off Theory

Table 5.2 Dependence of WACC on L n

L

0

1

2

3

4

5

6

7

8

9

5

kd

0.07

0.07

0.07

0.08

0.11

0.16

0.23

0.32

0.43

0.56

10 0.71

k0

A

2.7454

2.8265

2.8546

2.8835

2.9364

3.0080

3.0866

3.1605

3.2225

3.2703

3.3052

0.24

WACC

0.2400

0.2261

0.2215

0.2168

0.2083

0.1973

0.1858

0.1753

0.1669

0.1605

0.1560

WACC(L) 0.3000 0.2500 0.2000 0.1500 0.1000 0.0500 0.0000

0

1

2

3

4

5

6

7

8

9

10

11

Fig. 5.2 Dependence of WACC on L

2. n = 5; t = 20 % ; L = 0, 1, 2, . . .10
k0 = 24%; kd =



0:07; at L ≤ 2 0:07 þ 0:01ðL - 2Þ2 ; at L > 2

ð5:15Þ

Dependence of WACC on L for case (2) is shown in Table 5.2 and Fig. 5.2. 3. n = 3; t = 20 % ; L = 0, 1, 2, . . .10
k0 = 24%; kd =

0:07; at L ≤ 2 0:07 þ 0:1ðL - 2Þ2 ; at L > 2

 ð5:16Þ

Dependence of WACC on L for case (3) is shown in Table 5.3 and Fig. 5.3. 4. n = 5; t = 20 % ; L = 0, 1, 2, . . .10
k0 = 24%; kd =

0:07; at L ≤ 2 0:07 þ 0:1ðL - 2Þ2 ; at L > 2

 ð5:17Þ

Dependence of WACC on L for case (4) is shown in Table 5.4 and Fig. 5.4.

5.3

Analysis of the Trade-Off Theory Within the Brusov–Filatova–Orekhova Theory

97

Table 5.3 Dependence of WACC on L n

L

0

1

2

3

4

5

6

7

8

9

3

kd

0.07

0.07

0.07

0.17

0.47

0.97

1.67

2.57

3.67

4.97

10 6.47

k0

A

1.9813

2.0184

2.0311

2.0996

2.2253

2.3170

2.3655

2.3904

2.4046

2.4137

2.4203

0.24

WACC

0.2401

0.2279

0.2238

0.2021

0.1656

0.1410

0.1289

0.1228

0.1193

0.1171

0.1156

WACC(L) 0.3000 0.2500 0.2000 0.1500 0.1000 0.0500 0.0000

0

1

2

3

4

5

6

7

8

9

10

11

Fig. 5.3 Dependence of WACC on L

Table 5.4 Dependence of WACC on L n

L

0

1

2

3

4

5

6

7

8

9

5

kd

0.07

0.07

0.07

0.17

0.47

0.97

1.67

2.57

3.67

4.97

10 6.47

k0

A

2.7454

2.8265

2.8546

2.9893

3.1801

3.2724

3.3084

3.3265

3.3387

3.3479

3.3554

0.24

WACC

0.2400

0.2261

0.2215

0.2001

0.1726

0.1603

0.1556

0.1533

0.1517

0.1506

0.1496

WACC(L) 0.3000 0.2500 0.2000 0.1500 0.1000 0.0500 0.0000

0

1

2

3

Fig. 5.4 Dependence of WACC on L

4

5

6

7

8

9

10

11

98

5

Bankruptcy of the Famous Trade-Off Theory

Table 5.5 Dependence of WACC on L n

L

0

1

2

3

4

5

6

7

8

9

3

kd

0.07

0.07

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0.14

10 0.15

k0

A

1.9813

2.0184

2.0311

2.0445

2.0563

2.0670

2.0770

2.0865

2.0957

2.1044

2.1129

0.24

WACC

0.2401

0.2279

0.2238

0.2195

0.2159

0.2122

0.2090

0.2061

0.2033

0.2006

0.1981

WACC(L) 0.3000 0.2500 0.2000 0.1500 0.1000 0.0500 0.0000 0

1

2

3

4

5

6

7

8

9

10

11

Fig. 5.5 Dependence of WACC on L

5. n = 3; t = 20 % ; L = 0, 1, 2, . . .10
k0 = 24%; kd =



0:07; at L ≤ 2

ð5:18Þ

0:07 þ 0:01ðL - 2Þ; at L > 2

Dependence of WACC on L for case (5) is shown in Table 5.5 and Fig. 5.5. 6. n = 5; t = 20 % ; L = 0, 1, 2, . . .10
k0 = 24%; kd =



0:07; at L ≤ 2 0:07 þ 0:01ðL - 2Þ; at L > 2

ð5:19Þ

Dependence of WACC on L for case (6) is shown in Table 5.6 and Fig. 5.6. 7. n = 3; t = 20 % ; L = 0, 1, 2, . . .10
k0 = 24%; kd =

0:07; at L ≤ 2 0:07 þ 0:1ðL - 2Þ; at L > 2

 ð5:20Þ

Dependence of WACC on L for case (7) is shown in Table 5.7 and Fig. 5.7.

5.3

Analysis of the Trade-Off Theory Within the Brusov–Filatova–Orekhova Theory

99

Table 5.6 Dependence of WACC on L n

L

0

1

2

3

4

5

6

7

8

9

5

kd

0.07

0.07

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0.14

10 0.15

k0

A

2.7454

2.8265

2.8546

2.8835

2.9083

2.9305

2.9511

2.9702

2.9883

3.0054

3.0216

0.24

WACC

0.2400

0.2261

0.2215

0.2168

0.2128

0.2093

0.2060

0.2031

0.2003

0.1977

0.1952

WACC(L) 0.3000 0.2500 0.2000 0.1500 0.1000 0.0500 0.0000

0

1

2

3

4

5

6

7

8

9

10

11

Fig. 5.6 Dependence of WACC on L

Table 5.7 Dependence of WACC on L n

L

0

1

2

3

4

5

6

7

8

9

3

kd

0.07

0.07

0.07

0.17

0.27

0.37

0.47

0.57

0.67

0.77

10 0.87

k0

A

1.9813

2.0184

2.0311

2.0996

2.1580

2.2060

2.2450

2.2768

2.3028

2.3242

2.3420

0.24

WACC

0.2401

0.2279

0.2238

0.2021

0.1847

0.1710

0.1602

0.1516

0.1447

0.1391

0.1346

WACC(L) 0.3000 0.2500 0.2000 0.1500 0.1000 0.0500 0.0000

0

1

2

3

Fig. 5.7 Dependence of WACC on L

4

5

6

7

8

9

10

11

100

5

Bankruptcy of the Famous Trade-Off Theory

Table 5.8 Dependence of WACC on L n

L

0

1

2

3

4

5

6

7

8

9

5

kd

0.07

0.07

0.07

0.17

0.27

0.37

0.47

0.57

0.67

0.77

10 0.87

k0

A

2.7454

2.8265

2.8546

2.9893

3.0902

3.1634

3.2164

3.2553

3.2843

3.3063

3.3232

0.24

WACC

0.2400

0.2261

0.2215

0.2001

0.1853

0.1749

0.1677

0.1625

0.1587

0.1559

0.1537

WACC(L) 0.3000 0.2500 0.2000 0.1500 0.1000 0.0500 0.0000

0

1

2

3

4

5

6

7

8

9

10

11

Fig. 5.8 Dependence of WACC on L

8. n = 5; t = 20 % ; L = 0, 1, 2, . . .10
k0 = 24%; kd =

0:07; at L ≤ 2

 ð5:21Þ

0:07 þ 0:1ðL - 2Þ; at L > 2

Dependence of WACC on L for case (8) is shown in Table 5.8 and Fig. 5.8. 9. n = 3; t = 20 % ; L = 0, 1, 2, . . .10
k0 = 12%; kd =

0:07; at L ≤ 2 0:07 þ 0:01ðL - 2Þ2 ; at L > 2

 ð5:22Þ

Dependence of WACC on L for case (9) is shown in Table 5.9 and Fig. 5.9.

5.3

Analysis of the Trade-Off Theory Within the Brusov–Filatova–Orekhova Theory

101

Table 5.9 Dependence of WACC on L n

L

0

1

2

3

4

5

6

7

8

9

3

kd

0.07

0.07

0.07

0.08

0.11

0.16

0.23

0.32

0.43

0.56

10 0.71

k0

A

2.4018

2.4468

2.4621

2.4785

2.5098

2.5548

2.6087

2.6655

2.7200

2.7690

2.8107

0.12

WACC

0.1200

0.1093

0.1057

0.1019

0.0948

0.0849

0.0734

0.0615

0.0506

0.0412

0.0333

WACC(L) 0.1400 0.1200 0.1000 0.0800 0.0600 0.0400 0.0200 0.0000 0

1

2

3

4

5

6

7

8

9

10

11

Fig. 5.9 Dependence of WACC on L

10. n = 5; t = 20 % ; L = 0, 1, 2, . . .10
k 0 = 12%; kd =



0:07; at L ≤ 2 0:07 þ 0:01ðL - 2Þ2 ; at L > 2

ð5:23Þ

Dependence of WACC on L for case (10) is shown in Table 5.10 and Fig. 5.10. 11. n = 3; t = 20 % ; L = 0, 1, 2, . . .10
k0 = 12%; kd =

0:07; at L ≤ 2 0:07 þ 0:1ðL - 2Þ2 ; at L > 2

 ð5:24Þ

Dependence of WACC on L for case (11) is shown in Table 5.11 and Fig. 5.11. 12. n = 5; t = 20 % ; L = 0, 1, 2, . . .10
k0 = 12%; kd =

0:07; at L ≤ 2 0:07 þ 0:1ðL - 2Þ2 ; at L > 2

 ð5:25Þ

Dependence of WACC on L for case (12) is shown in Table 5.12 and Fig. 5.12.

102

5

Bankruptcy of the Famous Trade-Off Theory

Table 5.10 Dependence of WACC on L n

L

0

1

2

3

4

5

6

7

8

9

5

kd

0.07

0.07

0.07

0.08

0.11

0.16

0.23

0.32

0.43

0.56

10 0.71

k0

A

3.6048

3.7113

3.7482

3.7862

3.8556

3.9496

4.0528

4.1498

4.2312

4.2940

4.3399

0.12

WACC

0.1200

0.1084

0.1045

0.1005

0.0934

0.0841

0.0744

0.0655

0.0584

0.0530

0.0492

WACC(L) 0.1400 0.1200 0.1000 0.0800 0.0600 0.0400 0.0200 0.0000

0

1

2

3

4

5

6

7

8

9

10

11

Fig. 5.10 Dependence of WACC on L

Table 5.11 Dependence of WACC on L n

L

0

1

2

3

4

5

6

7

8

9

3

kd

0.07

0.07

0.07

0.17

0.47

0.97

1.67

2.57

3.67

4.97

10 6.47

k0

A

2.4018

2.4468

2.4621

2.5452

2.6976

2.8087

2.8676

2.8978

2.9150

2.9260

2.9340

0.12

WACC

0.1200

0.1093

0.1057

0.0870

0.0551

0.0337

0.0230

0.0176

0.0146

0.0127

0.0113

WACC(L) 0.1400 0.1200 0.1000 0.0800 0.0600 0.0400 0.0200 0.0000 0

1

2

3

Fig. 5.11 Dependence of WACC on L

4

5

6

7

8

9

10

11

5.3

Analysis of the Trade-Off Theory Within the Brusov–Filatova–Orekhova Theory

103

Table 5.12 Dependence of WACC on L n

L

0

1

2

3

4

5

6

7

8

9

5

kd

0.07

0.07

0.07

0.17

0.47

0.97

1.67

2.57

3.67

4.97

10 6.47

k0

A

3.6048

3.7113

3.7482

3.9250

4.1755

4.2968

4.3440

4.3678

4.3838

4.3959

4.4058

0.12

WACC

0.1200

0.1084

0.1045

0.0866

0.0633

0.0528

0.0489

0.0468

0.0455

0.0445

0.0437

WACC(L) 0.1400 0.1200 0.1000 0.0800 0.0600 0.0400 0.0200 0.0000 0

1

2

3

4

5

6

7

8

9

10

11

Fig. 5.12 Dependence of WACC on L

One can see (Figs. 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9, 5.10, 5.11 and 5.12) that WACC(L) is a monotonically diminishing function. In spite of the fact that the rise in the cost of debt financing was assumed, and fairly significant, WACC is not growing with leverage. In dependence of WACC(L ) a cupped zone (in the mathematical sense, WACC00L2 < 0) appears only, which more or less corresponds to the leverage level, at which the increase in the cost of debt capital begins (in our case, L = 2). Note that distortion of the WACC(L ) dependence is mostly determined by the function kd(L ) (linear or quadratic) and by the factors at (L - 2) or (L - 2)2. Linear dependence of kd(L) distorts the WACC(L ) dependence less than square one, as well as the smaller factor (0.01). The change of the company lifetime (from 3 to 5 years) has a smaller effect, although a bigger lifetimes may lead to more substantial changes in WACC(L ) dependence. The reduction of a difference k0 - kd between k0 and kd leads to an increase of effect. The main conclusion that can be drawn from the obtained results is the following: the optimal capital structure in well-known “trade off” theory is missing, contrary to hopes and expectations of its creators and supporters. The question immediately appears: why this turned out to be possible, and how this can be? How can the weighted average cost of capital not grow

104

5

Bankruptcy of the Famous Trade-Off Theory

WACC = we k e þ wd kd ð1- T Þ,

ð5:26Þ

if both kd and ke are growing ke is growing with leverage in accordance with (Eq. 5.4) and kd is growing in accordance with our assumption? The answer will be received in the next paragraph, where we are investigating the dependence of equity cost ke on leverage L with the same assumptions about the risky of debt capital and growth as a consequence of its cost with the leverage.

5.4

The Causes of Absence of the Optimum Capital Structure in Trade-Off Theory

So, we will investigate the dependence of the equity cost ke on leverage L at the same assumptions about the risky of the debt and growth of its cost with leverage. In the Modigliani–Miller theory equity cost ke always grows with leverage, as well as in Brusov–Filatova–Orekhova theory. In the former one, however, an abnormal effect, discovered by us, exists (Brusov et al. 2013a, b): decreasing of equity cost ke with leverage L. This effect, which is absent in perpetuity Modigliani– Miller limit, takes place under account of finite lifetime of the company at tax on profits rate, which exceeds some value T*. At some ratios between debt cost and equity capital cost the discovered effect takes place at tax on profits rate, existing in western countries and Russia. But this effect has been obtained under condition of a constant debt cost kd. Let us see, how the growth of debt cost kd with leverage affects the equity cost ke dependence on leverage. We will consider the same cases as above for the calculations of dependences WACC(L). 1. n = 3; t = 20 % ; L = 0, 1, 2, . . .10
k0 = 24%; kd =

0:07; at L ≤ 2

 ð5:27Þ

0:07 þ 0:01ðL - 2Þ2 ; at L > 2

Dependence of equity cost ke on L for case (1) is shown in Table 5.13 and Fig. 5.13. 2. n = 5; t = 20 % ; L = 0, 1, 2, . . .10
k0 = 24%; kd =

0:07; at L ≤ 2 0:07 þ 0:01ðL - 2Þ2 ; at L > 2

 ð5:28Þ

Dependence of equity cost ke on L for case (2) is shown in Table 5.14 and Fig. 5.14.

5.4

The Causes of Absence of the Optimum Capital Structure in Trade-Off Theory

105

Table 5.13 Dependence of equity cost ke on L n

L

0

1

2

3

4

5

6

3

kd

0.07

0.07

0.07

0.08

0.11

0.16

0.23

7 0.32

8 0.43

9 0.56

10

k0

A

1.9813

2.0184

2.0311

2.0445

2.0703

2.1075

2.1520

2.1988

2.2438

2.2842

0.24

ke

0.2401

0.3997

0.5594

0.6861

0.7036

0.5581

0.2011

-0.4081

-1.3075

-2.5356

0.71 2.3186 -4.133

Ke(L) 0.8000 0.7000 0.6000 0.5000 0.4000 0.3000 0.2000 0.1000 0.0000

0

1

2

3

4

5

6

7

Fig. 5.13 Dependence of equity cost ke on L

Table 5.14 Dependence of equity cost ke on L n

L

0

1

2

3

4

5

6

5

kd

0.07

0.07

0.07

0.08

0.11

0.16

0.23

7 0.32

8 0.43

9 0.56

10

k0

A

2.7454

2.8265

2.8546

2.8835

2.9364

3.0080

3.0866

3.1605

3.2225

3.2703

0.24

ke

0.2400

0.3962

0.5524

0.6750

0.6897

0.5438

0.1966

-0.3892

-1.2501

-2.4267

0.71 3.3052 -3.964

Ke(L) 0.8000 0.7000 0.6000 0.5000 0.4000 0.3000 0.2000 0.1000 0.0000 0

1

2

Fig. 5.14 Dependence of equity cost ke on L

3

4

5

6

7

106

5

Bankruptcy of the Famous Trade-Off Theory

3. n = 3; t = 20 % ; L = 0, 1, 2, . . .10
k0 = 24%; kd =



0:07; at L ≤ 2

ð5:29Þ

0:07 þ 0:1ðL - 2Þ2 ; at L > 2

Dependence of equity cost ke on L for case (3) is shown in Table 5.15 and Fig. 5.15. 4. n = 5; t = 20 % ; L = 0, 1, 2, . . .10
k0 = 24%; kd =

0:07; at L ≤ 2 0:07 þ 0:1ðL - 2Þ2 ; at L > 2

 ð5:30Þ

Dependence of equity cost ke on L for case (4) is shown in Table 5.16 and Fig. 5.16. 5. n = 3; t = 20 % ; L = 0, 1, 2, . . .10
k0 = 24%; kd =

0:07; at L ≤ 2 0:07 þ 0:01ðL - 2Þ; at L > 2

 ð5:31Þ

Dependence of equity cost ke on L for case (5) is shown in Table 5.17 and Fig. 5.17. 6. n = 5; t = 20 % ; L = 0, 1, 2, . . .10
k0 = 24%; kd =



0:07; at L ≤ 2 0:07 þ 0:01ðL - 2Þ; at L > 2

ð5:32Þ

Dependence of equity cost ke on L for case (6) is shown in Table 5.18 and Fig. 5.18. 7. n = 3; t = 20 % ; L = 0, 1, 2, . . .10
k0 = 24%; kd =

0:07; at L ≤ 2 0:07 þ 0:1ðL - 2Þ; at L > 2

 ð5:33Þ

Dependence of equity cost ke on L for case (7) is shown in Table 5.19 and Fig. 5.19.

n 3 k0 0.24

L kd A ke

0 0.07 1.9813 0.2401

1 0.07 2.0184 0.3997

2 0.07 2.0311 0.5594

Table 5.15 Dependence of equity cost ke on L 3 0.17 2.0996 0.4003

5 0.97 2.3170 -3.0339

4 0.47 2.2253 -0.6760

1.67 2.3655 -7.1136

6 2.57 2.3904 -13.4098

7

3.67 2.4046 -22.4140

8

4.97 2.4137 -34.6126

9

6.47 2.4203 -50.489

10

5.4 The Causes of Absence of the Optimum Capital Structure in Trade-Off Theory 107

108

5

Bankruptcy of the Famous Trade-Off Theory

Ke(L) 0.8000 0.6000 0.4000 0.2000 0.0000 -0.2000

0

1

2

3

5

4

-0.4000 -0.6000 -0.8000

Fig. 5.15 Dependence of equity cost ke on L

8. n = 5; t = 20 % ; L = 0, 1, 2, . . .10
k0 = 24%; kd =

0:07; at L ≤ 2

 ð5:34Þ

0:07 þ 0:1ðL - 2Þ; at L > 2

Dependence of equity cost ke on L for case (8) is shown in Table 5.20 and Fig. 5.20. 9. n = 3; t = 20 % ; L = 0, 1, 2, . . .10
k0 = 12%; kd =

0:07; at L ≤ 2 0:07 þ 0:01ðL - 2Þ2 ; at L > 2

 ð5:35Þ

Dependence of equity cost ke on L for case (9) is shown in Table 5.21 and Fig. 5.21. 10. n = 5; t = 20 % ; L = 0, 1, 2, . . .10
k0 = 12%; kd =

0:07; at L ≤ 2 0:07 þ 0:01ðL - 2Þ2 ; at L > 2

 ð5:36Þ

Dependence of equity cost ke on L for case (10) is shown in Table 5.22 and Fig. 5.22.

n 5 k0 0.24

L kd A ke

0 0.07 2.7454 0.2400

1 0.07 2.8265 0.3962

2 0.07 2.8546 0.5524

Table 5.16 Dependence of equity cost ke on L 3 0.17 2.9893 0.3926

5 0.97 3.2724 -2.9184

4 0.47 3.1801 -0.6408

1.67 3.3084 -6.9268

6 2.57 3.3265 -13.1658

7

3.67 3.3387 -22.1224

8

4.97 3.3479 -34.2784

9

6.47 3.3554 -50.114

10

5.4 The Causes of Absence of the Optimum Capital Structure in Trade-Off Theory 109

110

5

Bankruptcy of the Famous Trade-Off Theory

Ke(L) 0.8000 0.6000 0.4000 0.2000 0.0000

0

-0.2000

1

2

3

4

5

-0.4000 -0.6000 -0.8000

Fig. 5.16 Dependence of equity cost ke on L

Table 5.17 Dependence of equity cost ke on L n

L

0

1

2

3

4

5

6

7

8

9

10

3

kd

0.07

0.07

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0.14

0.15

k0

A

1.9813

2.0184

2.0311

2.0445

2.0563

2.0670

2.0770

2.0865

2.0957

2.1044

2.1129

0.24

ke

0.2401

0.3997

0.5594

0.6861

0.7913

0.8730

0.9353

0.9767

0.9976

0.9982

0.9787

Ke(L) 0.8000 0.7000 0.6000 0.5000 0.4000 0.3000 0.2000 0.1000 0.0000 0

1

2

3

4

5

6

7

Fig. 5.17 Dependence of equity cost ke on L Table 5.18 Dependence of equity cost ke on L n

L

0

1

2

3

4

5

6

7

8

9

10

5

kd

0.07

0.07

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0.14

0.15

k0

A

2.7454

2.8265

2.8546

2.8835

2.9083

2.9305

2.9511

2.9702

2.9883

3.0054

3.0216

0.24

ke

0.2400

0.3962

0.5524

0.6750

0.7759

0.8555

0.9143

0.9525

0.9706

0.9689

0.9477

5.4 The Causes of Absence of the Optimum Capital Structure in Trade-Off Theory

111

Ke(L) 1.2000 1.0000 0.8000 0.6000 0.4000 0.2000 0.0000 0

1

2

3

4

5

6

7

8

9

10

11

Fig. 5.18 Dependence of equity cost ke on L

Table 5.19 Dependence of equity cost ke on L n

L

0

1

2

3

4

5

6

7

8

9

3

kd

0.07

0.07

0.07

0.17

0.27

0.37

0.47

0.57

0.67

0.77

10 0.87

k0

A

1.9813

2.0184

2.0311

2.0996

2.1580

2.2060

2.2450

2.2768

2.3028

2.3242

2.3420

0.24

ke

0.2401

0.3997

0.5594

0.4003

0.0594

-0.4542

-1.1348

-1.9792

-2.9855

-4.1526

-5.48

Ke(L) 0.6000 0.5000 0.4000 0.3000 0.2000 0.1000 0.0000

0

1

2

Fig. 5.19 Dependence of equity cost ke on L

3

4

5

112

5

Bankruptcy of the Famous Trade-Off Theory

Table 5.20 Dependence of equity cost ke on L n

L

0

1

2

3

4

5

6

7

8

9

10

5

kd

0.07

0.07

0.07

0.17

0.27

0.37

0.47

0.57

0.67

0.77

0.87

k0

A

2.7454

2.8265

2.8546

2.9893

3.0902

3.1634

3.2164

3.2553

3.2843

3.3063

3.3232

0.24

ke

0.2400

0.3962

0.5524

0.3926

0.0624

-0.4304

-1.0822

-1.8920

-2.8596

-3.9853

-5.269

Ke(L) 0.6000 0.5000 0.4000 0.3000 0.2000 0.1000 0.0000

0

1

2

3

4

5

Fig. 5.20 Dependence of equity cost ke on L

11. n = 3; t = 20 % ; L = 0, 1, 2, . . .10
k 0 = 12%; kd =

0:07; at L ≤ 2 0:07 þ 0:1ðL - 2Þ2 ; at L > 2

 ð5:37Þ

Dependence of equity cost ke on L for case (11) is shown in Table 5.23 and Fig. 5.23. 12. n = 5; t = 20 % ; L = 0, 1, 2, . . .10
k 0 = 12%; kd =

0:07; at L ≤ 2 0:07 þ 0:1ðL - 2Þ2 ; at L > 2

 ð5:38Þ

Dependence of equity cost ke on L for case (12) is shown in Table 5.24 and Fig. 5.24. An analysis of the obtained results (Figs. 5.13, 5.14, 5.15, 5.16, 5.17, 5.18, 5.19, 5.20, 5.21, 5.22, 5.23 and 5.24) leads to the following conclusions. Under the turning on the growth of debt cost kd with leverage, the dependence of equity cost ke on leverage is undergoing significant changes. The linear growth of equity cost ke at low leverage level is changed by its fall, starting with some value L0.

5.4

The Causes of Absence of the Optimum Capital Structure in Trade-Off Theory

113

Table 5.21 Dependence of equity cost ke on L n

L

0

1

2

3

4

5

6

7

8

9

10

3

kd

0.07

0.07

0.07

0.08

0.11

0.16

0.23

0.32

0.43

0.56

0.71

k0

A

2.4018

2.4468

2.4621

2.4785

2.5098

2.5548

2.6087

2.6655

2.7200

2.7690

2.8107

0.12

ke

0.1200

0.1626

0.2051

0.2157

0.1222

-0.1307

-0.5904

-1.2998

-2.2963

-3.6202

-5.313

Ke(L) 0.8000 0.7000 0.6000 0.5000 0.4000 0.3000 0.2000 0.1000 0.0000 0

1

2

3

4

5

6

7

Fig. 5.21 Dependence of equity cost ke on L Table 5.22 Dependence of equity cost ke on L n

L

0

1

2

3

4

5

6

7

8

9

10

5

kd

0.07

0.07

0.07

0.08

0.11

0.16

0.23

0.32

0.43

0.56

0.71

k0

A

3.6048

3.7113

3.7482

3.7862

3.8556

3.9496

4.0528

4.1498

4.2312

4.2940

4.3399

0.12

ke

0.1200

0.1607

0.2014

0.2100

0.1152

-0.1352

-0.5829

-1.2677

-2.2267

-3.5020

-5.139

Ke(L) 0.2500 0.2000 0.1500 0.1000 0.0500 0.0000

0

1

2

Fig. 5.22 Dependence of equity cost ke on L

3

4

5

114

5 Bankruptcy of the Famous Trade-Off Theory

Table 5.23 Dependence of equity cost ke on L n

L

0

1

2

3

4

5

6

7

8

9

3

kd

0.07

0.07

0.07

0.17

0.47

0.97

1.67

2.57

3.67

4.97

10 6.47

k0

A

2.4018

2.4468

2.4621

2.5452

2.6976

2.8087

2.8676

2.8978

2.9150

2.9260

2.9340

0.12

ke

0.1200

0.1626

0.2051

-0.0601

-1.2286

-3.6778

-7.8553

-14.2512

-23.3566

-35.6572

-51.636

Ke(L) 0.4000 0.2000 0.0000 0

-0.2000

1

2

3

5

4

-0.4000 -0.6000 -0.8000 -1.0000 -1.2000 -1.4000 Fig. 5.23 Dependence of equity cost ke on L Table 5.24 Dependence of equity cost ke on L n

L

0

1

2

3

4

5

6

7

8

9

10

5

kd

0.07

0.07

0.07

0.17

0.47

0.97

1.67

2.57

3.67

4.97

6.47

k0

A

3.6048

3.7113

3.7482

3.9250

4.1755

4.2968

4.3440

4.3678

4.3838

4.3959

4.4058

0.12

ke

0.1200

0.1607

0.2014

-0.0615

-1.1876

-3.5634

-7.6740

-14.0175

-23.0784

-35.3389

-51.279

The L0 value sometimes exactly correlates with the starting point of kd growth with leverage (L0= 2), but sometimes takes values which are significantly higher (up to L0 = 8.5). The speed of decreasing of equity cost ke with leverage increases with increasing growth factor of debt cost kd as well as under the transition to quadratic growth. This is especially noticeable in the case 6, where there is a ke growing, up to the leverage level L = 8.5. So, we come to the conclusion that the increase in the cost of debt capital kd with leverage leads to the decrease of equity cost ke with leverage, starting with some value L0. This is the cause of the absence of weighted average capital cost growth with leverage at all its values.

5.5

Conclusion

115

Ke(L) 0.4000 0.2000 0.0000

-0.2000 0

1

2

3

4

5

-0.4000 -0.6000 -0.8000 -1.0000 -1.2000 -1.4000

Fig. 5.24 Dependence of equity cost ke on L

Note that the results remain qualitatively the same if we use different dependence of kd on leverage. For example, for the case of exponential growing of kd with leverage n = 5; t = 20%; L = 0, 1, 2, . . . 6, 
0:12; at L ≤ 1 k 0 = 22%; k d = 0:12 þ 0:01  3L - 1 ; at L > 1

ð5:39Þ

one gets the following dependence of kd, kd and WACC on leverage level (Fig. 5.25). So, the conclusions made are independent of rate of growing of kd with leverage.

5.5

Conclusion

The analysis of well-known trade-off theory, conducting with the help of modern theory of capital structure and capital cost by Brusov–Filatova–Orekhova, has shown that suggestion of risky debt financing (and growing credit rate near the bankruptcy) in opposite to waiting result does not lead to growing of WACC, which still decreases with leverage. This means the absence of minimum in the dependence of WACC on leverage as well as the absence of maximum in the dependence of capitalization V on leverage. Thus, it seems that the optimal capital structure is absent in famous trade-off theory. The explanation to this fact has been done within the same Brusov–Filatova–Orekhova theory by study of the dependence of the equity cost ke with leverage. It turned out that the growth of debt cost kd with leverage leads to decrease of equity cost ke with leverage, starting from some leverage level, which is higher than starting point of debt cost growth. This paradox conclusion gives the explanation of the absence of the optimal capital structure in the

116

5

Bankruptcy of the Famous Trade-Off Theory

n=5 0.5 0.4 0.3 0.2 0.1 0

Kd Kd

Wacc

Ke 0

2

4

6

Wacc 8

Ke

L Fig. 5.25 Dependence of equity cost ke, debt cost kd and WACC on leverage L

famous trade-off theory. This means that competition of benefits from using of debt financing and of financial distress cost (or a bankruptcy cost) is NOT balanced and hopes that trade-off theory gives us the optimal capital structure, unfortunately, do not realized. The absence of the optimal capital structure in the trade-off theory questioned the existence of an optimal capital structure of the company (but as authors have shown, the optimal capital structure for the investment still exists (Brusov et al. 2011b, c)). In the search for the “golden fleece” one needs to switch to study of other mechanisms for formation of the capital structure of the company, different from ones considering in trade-off theory.

References Baker M, Wurgler J (2002) Market timing and capital structure. J Financ 57(1):1–32 Bikhchandani S, Hirshleifer D, Welch I (1998) Learning from the behavior of others: conformity, fads, and informational cascades. J Econ Perspect 12(3):151–170 Brennan M, Schwartz E (1978) Corporate income taxes, valuation, and the problem of optimal capital structure. J Bus 51:103–114 Brennan M, Schwartz E (1984) Optimal financial policy and firm valuation. J Financ 39:593–607 Brusov PN, Filatova ТV (2011) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Financ Credit 435:2–8 Brusov P, Filatova T, Orehova N, Brusova A (2011a) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Appl Financ Econ 21(11): 815–824 Brusov P, Filatova T, Orehova N et al (2011b) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Bus ICT 2:16–21 Brusov P, Filatova T, Orehova N et al (2011c) Influence of debt financing on the effectiveness of the investment project within the Modigliani–Miller theory. Res J Econ Bus ICT (UK) 2:11–15 Brusov P, Filatova T, Orehova N, Brusov PP, Brusova N (2011d) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Bus ICT 2:16–21 Brusov P, Filatova T, Eskindarov M, Orehova N (2012a) Influence of debt financing on the effectiveness of the finite duration investment project. Appl Financ Econ 22(13):1043–1052 Brusov P, Filatova T, Eskindarov M, Orehova N (2012b) Hidden global causes of the global financial crisis. J Rev Glob Econ 1:106–111

References

117

Brusov P, Filatova P, Orekhova N (2013a) Absence of an optimal capital structure in the famous tradeoff theory! J Rev Glob Econ 2:94–116 Brusov P, Filatova T, Orehova N (2013b) A qualitatively new effect in corporative finance: abnormal dependence of cost of equity of company on leverage. J Rev Glob Econ 2:183–193 Brusov P, Filatova P, Orekhova N (2014a) Mechanism of formation of the company optimal capital structure, different from suggested by trade off theory. Cogent Econ Financ 2:1–13. https://doi. org/10.1080/23322039.2014.946150 Brusov P, Filatova T, Orehova N (2014b) Inflation in Brusov–Filatova–Orekhova theory and in its perpetuity limit – Modigliani–Miller theory. J Rev Glob Econ 3:175–185 Brusova A (2011) А comparison of the three methods of estimation of weighted average cost of capital and equity cost of company. Financ Anal Probl Sol 34(76):36–42 Dittmar A, Thakor A (2007) Why do firms issue equity? J Financ 62(1):1–54 Fama E, French K (2004) Financing decisions: who issues stock? Working paper Filatova Т, Orekhova N, Brusova А (2008) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life-time company. Bull FU 48:68–77 Filbeck G, Raymond F, Preece D (1996) Behavioral aspects of the intra-industry capital structure decision. J Financ Strateg Decis 9(2):55–66 Graham J, Harvey C (2001) The theory and practice of corporate finance: evidence from the field. J Financ Econ 60:187–243 Hovakimian A, Opler T, Titman S (2001) The debt-equity choice. J Financ Quant Anal 36(1):1–24 Hsia С (1981) Coherence of the modern theories of finance. Financ Rev 16(1):27–42 Jensen M, Meckling W (1976) Theory of the firm: managerial behavior, agency costs, and ownership structure. J Financ Econ 3(4):305–360 Jenter D (2005) Market timing and managerial portfolio decisions. J Financ 60(4):1903–1949 Kane A, Marcus A, McDonald R (1984) How big is the tax advantage to debt? J Financ 39:841–853 Leland H (1994) Corporate debt value, bond covenants, and optimal capital structure. J Financ 49(4):1213–1252 Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Modigliani F, Miller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391 Myers S (1984) The capital structure puzzle. J Financ 9(3):574–592 Myers S, Majluf N (1984) Corporate financing and investment decisions when firms have information that investors do not have. J Financ Econ 13:187–221 Post J, Preston L, Sachs S (2002) Redefining the corporation: stakeholder management and organizational wealth. Stanford University Press, Stanford Rubinstein M (1973) A mean–variance synthesis of corporate financial theory. J Financ 28:167– 181 Stiglitz J (1969) A re–examination of the Modigliani–Miller theorem. Am Econ Rev 59(5):784–793

Chapter 6

New Mechanism of Formation of the Company Optimal Capital Structure, Different from Suggested by Trade-off Theory

Keywords Brusov–Filatova–Orekhova (BFO) theory · Trade-off theory · The weighted average cost of capital · Equity cost · Company capitalization · A new mechanism · Optimal capital structure Under condition of proved by us insolvency of well-known classical trade-off theory question of finding of new mechanisms of formation of the company optimal capital structure, different from one, suggested by trade-off theory, becomes very important. One of the real such mechanisms has been developed by us in this Chapter. It is based on the decrease of debt cost with leverage, which is determined by growth of debt volume. This mechanism is absent in perpetuity Modigliani–Miller theory, even in modified version, developed by us, and exists within more general modern theory of capital cost and capital structure by Brusov–Filatova–Orekhova (BFO theory).

6.1

Absence of Suggested Mechanism of Formation of the Company Optimal Capital Structure Within Modified Modigliani–Miller Theory (MMM Theory)

Analyzing the validity of well-known trade-off theory (Brennan and Schwartz 1978, 1984; Leland 1994), we have investigated the problem of existing of company optimal capital structure within Modigliani–Miller theory (Мodigliani and Мiller 1958, 1963, 1966), modified by us by taken off the suggestion about riskless of debt capital (MMM theory), as well as within modern theory of capital cost and capital structure by Brusov–Filatova–Orekhova (BFO theory) applicable to companies with arbitrary lifetime and investment projects of arbitrary duration (Brusov et al. 2011a– d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011; Filatova et al. 2008). Within both theories (МММ and BFO) the absence of the optimal capital structure has been proved under the modelling of financial distressed and danger of bankruptcy by increase in debt cost. This proves the insolvency of the classical trade-off theory (Brusov et al. 2013a), which is based on the following suggestions (Brennan and Schwartz 1978, 1984; Leland 1994): © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_6

119

120

6

New Mechanism of Formation of the Company Optimal Capital Structure,. . .

At low leverage levels the advantages of using of debt financing (which is cheaper than equity one) is connected to the fact that the weighted average cost of capital, WACC, decreases with leverage and consequently the company capitalization is growing. Starting from some leverage level financial distressed appears and grows, bankruptcy risk grows as well. The increase of WACC and consequently decrease of the company capitalization starts. The leverage level, at which profits of debt capital using are approximately equal to the bankruptcy cost, determines the company optimal capital structure. As our investigations show (Brusov et al. 2013a), within both theories (MMM and BFO), grows of WACC and consequently decrease of the company capitalization are absent. We have given the explanation of a such phenomenon: for leverage levels above some value L
the equity cost decreases with leverage, providing continuously (at all leverage levels) fall down of WACC. The conclusion, made by us, is as follows: the mechanism of formation of the company optimal capital structure, suggested in the trade-off theory about 40 years ago turns out to be insolvent (Brusov et al. 2013a). From other side continuously and unlimited fall down of weighted average cost of capital, WACC, and consequently unlimited growing of the company capitalization with leverage seems contradict to the existing experience. Willing to study the problem of the existing of the company optimal capital structure, we investigate the influence of debt cost on equity cost and on weighted average cost of capital, WACC. We have discovered the presence of correlations between debt cost and equity cost, which could give another mechanism of formation of the company optimal capital structure (different from the trade-off one) at leverage levels which are far enough from the “critical” levels, at which financial distressed appears and the bankruptcy risk increases. The detailed description of such a mechanism is the main purpose of this Chapter. Suggested mechanism of formation of the company optimal capital structure is based on the decrease of debt cost, which (in some range of leverage levels) is determined by growing of the debt volume. As it has been shown in previous Chapter, in modified Modigliani–Miller theory (MMM theory) (allowing riskiness debt capital) under arbitrary change of debt cost with leverage (growing, as well as decrease) weighted average cost of capital, WACC, always falls down with leverage. If one considers the growing of debt cost with leverage, this means the absence of the company optimal capital structure and proves insolvency of well-known classical trade-off in its original formulation. If one considers the decrease of debt cost with leverage, this means the absence of suggested mechanism of formation of the company optimal capital structure within modified (by us) Modigliani–Miller theory. But, as it will be seen below, situation turns out to be another in modern theory of capital cost and capital structure by Brusov–Filatova–Orekhova (BFO theory).

Formation of the Company Optimal Capital Structure. . .

6.2

6.2

121

Formation of the Company Optimal Capital Structure Within Brusov–Filatova–Orekhova (BFO Theory)

The situation is different in modern theory of capital cost and capital structure by Brusov–Filatova–Orekhova (BFO theory) (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011; Filatova et al. 2008). As it will be shown below, decrease of debt cost with leverage leads to formation of minimum in dependence of WACC on leverage at moderate leverage levels far from the “critical” levels, at which financial distressed appears and the bankruptcy risk increases. Existence of such minimum leads to appearance of maximum in capitalization of the company. So, we suggest a new mechanism of formation of the company optimal capital structure, different from one, suggested by (already insolvent) trade-off theory. Before studying the problem within BFO theory (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011; Filatova et al. 2008) let us consider 1-year companies, which have been studied by Myers (2001). This case is the particular case of more general BFO theory. For weighted average cost of capital, WACC of 1-year company one has WACC = k0 -

1 þ k0 k w t: 1 þ kd d d

ð6:1Þ

Here wd is the debt fraction. The debt cost kd still has the following form  kd =

 kd0 = const; atL ≤ L0 , k d0 þ f ðLÞ; atL > L0

ð6:2Þ

Thus, weighted average cost of capital, WACC, at leverage levels L > L0 is equal to WACC = k0 -

1 þ k0 L ðkd0 þ f ðLÞÞ t 1 þ L 1 þ kd0 þ f ðLÞ

ð6:3Þ

and, obviously, depends on the form of f(L). Thus, the difference of the simplest case of 1-year companies from perpetuity ones, which, as we have shown above in previous Chapter, is independent of form of f(L ), becomes obvious. We will not analyze here 1-year companies in details, but instead we will go now to analysis of companies with arbitrary lifetime, described by BFO theory (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011; Filatova et al. 2008). Let us consider a few types of dependences of debt cost on leverage f(L ).

122

6.2.1

6

New Mechanism of Formation of the Company Optimal Capital Structure,. . .

Decrease of Debt Cost at Exponential Rate

We have the following parameters: L0 = 1; k 0 = 0, 22; kd = 0, 12; t = 0, 2, and the debt cost has the form  kd =

kd0 = const; atL ≤ L0 = 1 kd0 þ α - α  3L - L0 ; atL > L0 = 1

 ð6:4Þ

Calculation of the weighted average cost of capital, WACC, will be done, using the BFO formula 1 - ð1 þ k 0 Þ - n 1 - ð1 þ WACCÞ - n    =  -n WACC L k0 1 - t ð1þL ð ð Þ Þ 1 1 þ k d Þ

ð6:5Þ

By the function “Matching parameter” in Excel we will find the weighted average cost of capital, WACC values. Then, using obtained values of WACC, we will find the cost of equity values ke by the formula: WACC = KeWe þ KdWd ð1- t Þ Ke = WACCð1 þ LÞ - KdLð1- t Þ

ð6:6Þ

Formula (Eq. 6.6) is the definition of the weighted average cost of capital, WACC, for the case of existing of taxing. The application of BFO formula (Eq. 6.5) is very wide: authors have applied it in corporate finance, in investments, in taxing, in business valuation, in banking, and some other areas (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011; Filatova et al. 2008). Using this formula (Eq. 6.5), one can study the dependence of the weighted average cost of capital, WACC, as well as the equity cost ke on leverage level L, on tax on profit rate t, on lifetime of the company n. The case α = 0, 01. Let us consider first the case α = 0, 01. We will study below the dependence of debt cost kd, equity cost ke and weighted average cost of capital, WACC, on leverage level L in case of kd exponential decrease (Table 6.1, Figs. 6.1, 6.2, 6.3, 6.4, 6.5, 6.6 and 6.7). The case α = 0.1. Let us consider now the caseα = 0.1 (Table 6.2, Figs. 6.8, 6.9, 6.10, 6.11, 6.12, and 6.13). Let us valuate the optimum position L* and its depth ΔWACC, using obtained results (see Table 6.3).

6.2

Formation of the Company Optimal Capital Structure. . .

123

Table 6.1 kd, ke and weighted average cost of capital, WACC, for companies of age n = 1; 3;5;10 L kd WACC (n = 1) ke (n = 1) WACC (n = 3) ke (n = 3) WACC (n = 5) ke (n = 5) WACC (n = 10) ke (n = 10)

0 0.12 0.220 0.220 0.219 0.219 0.220 0.220 0.220

0.5 0.12 0.211 0.257 0.208 0.252 0.206 0.250 0.206

1 0.12 0.207 0.294 0.201 0.281 0.200 0.279 0.199

1.1 0.1188 0.206 0.302 0.201 0.291 0.199 0.287 0.198

1.3 0.1161 0.205 0.320 0.199 0.307 0.197 0.303 0.196

1.6 0.1107 0.206 0.358 0.199 0.340 0.197 0.335 0.196

2 0.1 0.206 0.417 0.198 0.395 0.196 0.388 0.194

3 0.04 0.214 0.736 0.209 0.716 0.207 0.710 0.205

4 -0.14 0.252 1.819 0.279 1.955 0.301 2.067 0.383

0.220

0.249

0.277

0.285

0.301

0.332

0.383

0.699

2.474

Fig. 6.1 Dependence of debt cost kd on leverage level L in case of its exponential decrease at α = 0.01

Kd(L) 1 0,8 0,6 0,4 0,2 0 -0,2 0 -0,4 -0,6 -0,8

1

3

2

4

5

L Fig. 6.2 Dependence of weighted average cost of capital, WACC, on leverage level L in case of exponential decrease of debt cost at α = 0.01

The Quadratic Decrease of Debt Cost kd with Leverage Level Let us consider the quadratic decrease of debt cost kd with leverage. We will study below the dependence of debt cost kd, equity cost ke and weighted average cost of capital, WACC, on leverage level L in case of kd quadratic decrease. We use the same parameters, as above

124

6

New Mechanism of Formation of the Company Optimal Capital Structure,. . .

Fig. 6.3 Dependence of equity cost ke on leverage level L in case of its exponential decrease at α = 0.01

Fig. 6.4 Dependence of debt cost kd, equity cost ke and weighted average cost of capital, WACC, on leverage level L in case of exponential decrease of debt cost kd, at α = 0.01 for 1-year company

Fig. 6.5 Dependence of debt cost kd, equity cost ke and weighted average cost of capital, WACC, on leverage level L in case of exponential decrease of debt cost kd, at α = 0.01 for 3-year company

Fig. 6.6 Dependence of debt cost kd, equity cost ke and weighted average cost of capital, WACC, on leverage level L in case of exponential decrease of debt cost kd, at α = 0.01 for 5-year company

n=5 0.4 Ke

0.3 Wacc

0.2 0.1 0

Kd 0

0.5

1

1.5

L

2

2.5

3

3.5

6.2

Formation of the Company Optimal Capital Structure. . .

125

Fig. 6.7 Dependence of debt cost kd, equity cost ke and weighted average cost of capital, WACC, on leverage level L in case of exponential decrease of debt cost kd, at α = 0.01 for 10-year company

Table 6.2 Debt cost kd and weighted average cost of capital, WACC, for companies of age n = 1; 3;5;10 L kd WACC (n = 1) ke (n = 1) WACC (n = 3) ke (n = 3) WACC (n = 5) ke (n = 5) WACC (n = 10) ke (n = 10)

0 0.12 0.220 0.220 0.219 0.219 0.220 0.220 0.220 0.220

0.5 0.12 0.211 0.257 0.207 0.251 0.207 0.250 0.206 0.249

0.7 0.12 0.209 0.272 0.204 0.264 0.204 0.262 0.203 0.261

1 0.12 0.207 0.294 0.201 0.281 0.200 0.279 0.199 0.277

1.1 0.108 0.207 0.316 0.202 0.304 0.200 0.301 0.199 0.299

1.3 0.081 0.210 0.377 0.205 0.365 0.203 0.362 0.201 0.357

1.5 0.047 0.213 0.463 0.210 0.455 0.208 0.451 0.206 0.446

2 -0.08 0.233 0.860 0.244 0.892 0.252 0.916 0.272 0.976

4 -2.48 -0.107 9.384 0.079 10.314 0.132 10.578 0.170 10.768

Fig. 6.8 Dependence of weighted average cost of capital, WACC, on leverage level L in case of exponential decrease of debt cost kd, at α = 0.1

L0 = 1; k 0 = 0:22; kd = 0:12; t = 0:2 with the following dependence of debt cost kd on leverage  kd =

kd0 = const; atL ≤ L0 = 1 k d0 - α  ðL - L0 Þ2 ; atL > L0 = 1

 ð6:7Þ

126

6

New Mechanism of Formation of the Company Optimal Capital Structure,. . .

Fig. 6.9 Dependence of equity cost ke on leverage level L in case of exponential decrease of debt cost kd, at α = 0.1

Fig. 6.10 Dependence of debt cost kd, equity cost ke and weighted average cost of capital, WACC, on leverage level L in case of exponential decrease of debt cost kd, at α = 0.1 for 1-year company

Fig. 6.11 Dependence of debt cost kd, equity cost ke and weighted average cost of capital, WACC, on leverage level L in case of exponential decrease of debt cost kd, at α = 0.1 for 3-year company

Fig. 6.12 Dependence of debt cost kd, equity cost ke and weighted average cost of capital, WACC, on leverage level L in case of exponential decrease of debt cost kd, at α = 0.1 for 5-year company

6.2

Formation of the Company Optimal Capital Structure. . .

127

Fig. 6.13 Dependence of debt cost kd, equity cost ke and weighted average cost of capital, WACC, on leverage level L in case of exponential decrease of debt cost kd, at α = 0.1 for 10-year company

Table 6.3 Optimum position L* and its depth ΔWACC for lifetimes n = 1;3;5;10 n α = 0.01 α = 0.1

Optimum position L* 1 3 5 1.3 2 2 1–1.1 1 1–1.1

10 2 1–1.1

Optimum depth ΔWACC 1 3 5 1.7% 2.2% 2.4% 1.5% 2.1% 2.2%

10 2.6% 2.3%

Table 6.4 kd and WACC for 1-year companies α

0.01 0.1 0.01 0.1 0.01 0.1

L wd we kd kd WACC WACC ke ke

0 0.000 1.000 0.12 0.12 0.220 0.220 0.22 0.22

0.2 0.167 0.833 0.12 0.12 0.213 0.213 0.24 0.24

0.4 0.286 0.714 0.12 0.12 0.208 0.208 0.25 0.25

0.6 0.375 0.625 0.12 0.12 0.204 0.204 0.27 0.27

0.8 0.444 0.556 0.12 0.12 0.201 0.201 0.29 0.29

1 0.500 0.500 0.12 0.12 0.199 0.199 0.3 0.3

2 0.667 0.333 0.11 0.02 0.193 0.213 0.4 0.61

3 0.750 0.250 0.08

4 0.800 0.200 0.03

0.195

0.207

0.59

0.94

1-year companies. Let us start from 1-year companies. For them we get the following results (Table 6.4, Figs. 6.14 and 6.15). 3-year companies. For 3-year companies we get the following results (Table 6.5, Figs. 6.16 and 6.17). 5-year companies. For 5–year companies we get the following results (Table 6.6, Figs. 6.18 and 6.19). 10-year companies. For 10-year companies we get the following results (Table 6.7, Figs. 6.20 and 6.21). Let us valuate the optimum position L* and its depth ΔWACC, using obtained results (Table 6.8). Discussion of Results Thus, we have considered the impact of reducing of the cost of debt kd with increases of debt volume. The article deals with two cases: quadratic and an exponential dependence of cost of debt kd on leverage. We have considered as well other dependences, giving similar results. It is shown that in considered cases, the equity capital cost of firm correlates with the debt cost, that leads to the emergence of an optimal capital structure of

128

6

New Mechanism of Formation of the Company Optimal Capital Structure,. . .

WACC(L), Ke(L), Kd(L) at α =0.01 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%

0

1

2

L

3

4

5

Fig. 6.14 Dependence of debt cost kd, equity cost ke and weighted average cost of capital, WACC, on leverage level L in case of quadratic decrease of debt cost kd, at α = 0.01 for 1-year company

companies. Cause of the emergence of an optimal structure is that the speed of increase of equity cost ke of the firm begins to grow, starting from some leverage level L
, that not only compensates of the fall in cost of debt kd with leverage, but it has also led to an increase in weighted average cost of capital WACC with leverage, starting from some leverage level. This leverage level determines the optimal capital structure of company. Found that, in all examined cases (quadratic as well as exponential one fall of debt cost) in case of weak drops in debt cost with leverage (α = 0.01) the optimal capital structure of the company is formed at bigger leverage values, than the beginning of the fall (in our case L
/ 2L0), and in the case of a stronger fall of kd (α = 0.1) the optimal capital structure of the company is formed directly near the start point of the fall of kd (L
≈ L0). It turns out that the depth of optimum (and, accordingly, the achieved in optimum company capitalization) is bigger at weak drops of debt cost with leverage (α = 0, 01), that is due to the more long-term fall in this case of the weighted average cost of capital WACC with leverage L.

6.3

Simple Model of Proposed Mechanism

129

WACC(L), Ke(L), Kd(L) at α =0.1 70% 60% 50% 40% 30% 20% 10% 0%

0

1

2

L

3

4

5

Fig. 6.15 Dependence of debt cost kd, equity cost ke and weighted average cost of capital, WACC, on leverage level L in case of quadratic decrease of debt cost kd, at α = 0.1 for 1-year company Table 6.5 kd and WACC for 3-year companies α

0.01 0.1 0.01 0.1 0.01 0.1

6.3

L wd we kd kd WACC WACC ke ke

0 0.000 1.000 0.12 0.12 0.220 0.220 0.22 0.22

0.2 0.167 0.833 0.12 0.12 0.214 0.214 0.24 0.24

0.4 0.286 0.714 0.12 0.12 0.210 0.210 0.26 0.26

0.6 0.375 0.625 0.12 0.12 0.207 0.207 0.27 0.27

0.8 0.444 0.556 0.12 0.12 0.205 0.205 0.29 0.29

1 0.500 0.500 0.12 0.12 0.203 0.203 0.31 0.31

2 0.667 0.333 0.11 0.02 0.199 0.215 0.42 0.61

3 0.750 0.250 0.08

4 0.800 0.200 0.03

0.202

0.212

0.62

0.97

Simple Model of Proposed Mechanism

The features of the proposed mechanism can be demonstrated at its simplest example of step-like dependence of debt cost on leverage in the BFO model. Let us suppose

130

6

New Mechanism of Formation of the Company Optimal Capital Structure,. . .

WACC(L), Ke(L), Kd(L) at α =0.01 120% 100% 80% 60% 40% 20% 0%

0

1

2

L

3

4

5

Fig. 6.16 Dependence of debt cost kd, equity cost ke and weighted average cost of capital, WACC, on leverage level L in case of quadratic decrease of debt cost kd, at α = 0.01 for 3-year company

 kd =

k d1 = 0:12 = const; atL ≤ L0 k d2 = 0:06 = const; atL > L0

 ; k0 = 0:18; L0 = 5

ð6:8Þ

We will find the dependence WACC(L ) for 2-year and 4-year companies at T = 0.2. The calculations will be done in MS Excel using BFO formula 1 - ð1 þ K 0 Þ - n 1 - ð1 þ WACCÞ - n , = WACC K 0 × ð1 - W d × T × ð1 - ð1 þ K d Þ - n ÞÞ where wd =

ð6:9Þ

L : 1þL

For 2-year company one gets the following results (Table 6.9). These results are shown on Fig. 6.22. Similar calculations for 4-year company is given at Fig. 6.23. Let us compose the mutual figure for 2-year company and for 4-year company (see Fig. 6.24). It can be easily seen that weighted average cost of capital WACC, decreasing with leverage, in descending point of cost of credit has a gap (jump up), and then continues to decrease, however, at a slower speed, corresponding to the higher leverage levels. This means that there is an optimum (minimum) in the dependence

6.3

Simple Model of Proposed Mechanism

131

WACC(L), Ke(L), Kd(L) at α =0.1 70% 60% 50% 40% 30% 20% 10% 0%

0

2

1

L

3

4

5

Fig. 6.17 Dependence of debt cost kd, equity cost ke and weighted average cost of capital, WACC, on leverage level L in case of quadratic decrease of debt cost kd, at α = 0.1 for 3-year company Table 6.6 kd and WACC for 5-year companies α

0.01 0.1 0.01 0.1 0.01 0.1

L wd we kd kd WACC WACC ke ke

0 0.000 1.000 0.12 0.12 0.220 0.220 0.22 0.22

0.2 0.167 0.833 0.12 0.12 0.213 0.213 0.24 0.24

0.4 0.286 0.714 0.12 0.12 0.208 0.208 0.25 0.25

0.6 0.375 0.625 0.12 0.12 0.205 0.205 0.27 0.27

0.8 0.444 0.556 0.12 0.12 0.202 0.202 0.29 0.29

1 0.500 0.500 0.12 0.12 0.200 0.200 0.3 0.3

2 0.667 0.333 0.11 0.02 0.194 0.214 0.41 0.61

3 0.750 0.250 0.08

4 0.800 0.200 0.03

0.197

0.210

0.6

0.95

of weighted average cost of capital WACC on leverage. The optimum depth in this model is equal to the gap value in point of descending of cost of credit. With increase of the lifetime of companies the total lower of graph takes place: weighted average cost of capital WACC decreases. The optimum depth does not change: for biennial and quadrennial companies it remains equal 1.32% (for this values set of k0, kd, Δkd, L0).

132

6

New Mechanism of Formation of the Company Optimal Capital Structure,. . .

WACC(L), Ke(L), Kd(L) at α =0.01 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%

0

1

2

L

3

4

5

Fig. 6.18 Dependence of debt cost kd, equity cost ke and weighted average cost of capital, WACC, on leverage level L in case of quadratic decrease of debt cost kd, at α = 0.01 for 5-year company

It should be noted that, this model with step-like decrease of debt cost in spite of its simplicity turns out to be a realistic: many credit organizations use this scheme. For continuous descending of credit cost weighted average cost of capital WACC is also continuous, and minimum is described by a more familiar bowl, as it was shown above for exponential and quadratic decrease of credit cost.

6.4

Conclusion

1. The Modigliani–Miller theory in its classical version in principle does not consider risky debt funds, therefore, within this theory it is not possible to investigate the current problem. 2. In the modified (by us) theory of Modigliani–Miller with the modelling of riskiness of debt funds by dependence of their cost of leverage level, as shown in this article, at arbitrary change of debt cost with leverage (the growing as well as the fall) the weighted average cost of capital WACC always decreases with leverage, that demonstrates the absence of the optimal capital structure and proves insolvency of well-known classical trade-off theory in its original formulation as well as the inability to implement the proposed in this article mechanism of formation of an optimal capital structure.

6.4

Conclusion

133

WACC(L), Ke(L), Kd(L) at α =0.1 70% 60% 50% 40% 30% 20% 10% 0%

0

1

2

L

3

4

5

Fig. 6.19 Dependence of debt cost kd, equity cost ke and weighted average cost of capital, WACC, on leverage level L in case of quadratic decrease of debt cost kd, at α = 0.1 for 5-year company Table 6.7 kd and WACC for 10-year companies α

0.01 0.1 0.01 0.1 0.01 0.1

L wd we kd kd WACC WACC ke ke

0 0.000 1.000 0.12 0.12 0.220 0.220 0.22 0.22

0.2 0.167 0.833 0.12 0.12 0.213 0.213 0.24 0.24

0.4 0.286 0.714 0.12 0.12 0.208 0.208 0.25 0.25

0.6 0.375 0.625 0.12 0.12 0.205 0.205 0.27 0.27

0.8 0.444 0.556 0.12 0.12 0.202 0.202 0.29 0.29

1 0.500 0.500 0.12 0.12 0.200 0.200 0.3 0.3

2 0.667 0.333 0.11 0.02 0.194 0.214 0.41 0.61

3 0.750 0.250 0.08

4 0.800 0.200 0.03

0.197

0.210

0.6

0.95

3. Within modern theory of capital cost and capital structure by Brusov–Filatova– Orekhova (BFO theory) it is shown, that decrease of debt cost with leverage leads to formation of minimum in dependence of the weighted average cost of capital WACC on leverage at moderate leverage levels far from critical ones, at which financial distressed appears and the bankruptcy risk increases. Existence of minimum in dependence of the weighted average cost of capital WACC on leverage leads to maximum in company capitalization.

134

6

New Mechanism of Formation of the Company Optimal Capital Structure,. . .

WACC(L), Ke(L), Kd(L) at α =0.01 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%

0

1

2

L

3

4

5

Fig. 6.20 Dependence of debt cost kd, equity cost ke and weighted average cost of capital, WACC, on leverage level L in case of quadratic decrease of debt cost kd, at α = 0.01 for 10-year company

Thus, a new mechanism of formation of the company optimal capital structure, different from one, suggested by trade-off theory (now insolvent) and which is based on the decrease of debt cost with leverage, has developed by us in this Chapter. The cause of optimum formation is as follows: decrease of debt cost with leverage leads to more significant grows of equity cost, which is not compensated by the fall of the debt cost and WACC starts to increase with leverage at some (moderate) leverage level. From other side the increase of debt cost with leverage at higher leverage level leads, as we have shown before (Brusov et al. 2013a), to the fall of WACC with leverage. Thus, within BFO theory under suggestion of decrease of debt cost at moderate leverage levels and of its increase at high leverage levels WACC first decreases with leverage, then, going through minimum, starts to grow and finally fall again already continuously (under growing or constant debt cost) (see Fig. 6.25). Note that continuously fall of WACC with leverage at high leverage levels has been proved by us in our previous paper (Brusov et al. 2013a), where the insolvency of well-known classical trade-off theory has been demonstrated. Obtained conclusions do not depend qualitatively on velocity of debt cost fall. Only optimum depth and its position (but not its existence) depend on the particular form of dependence of debt cost on leverage (mainly on velocity of debt cost fall and significantly less on the particular form of function f(L )).

6.4

Conclusion

135

WACC(L), Ke(L), Kd(L) at α =0.1 70%

60%

50%

40%

30%

20%

10%

0%

0

2

1

L

3

4

5

Fig. 6.21 Dependence of debt cost kd, equity cost ke and weighted average cost of capital, WACC, on leverage level L in case of quadratic decrease of debt cost kd, at α = 0.1 for 10-year company Table 6.8 Optimum position L* and its depth ΔWACC for lifetimes n = 1;3;5;10 Optimum position L* 1 3 5 2 2 2 1–1.1 1 1–1.1

n α = 0.01 α = 0.1

10 2 1–1.1

Optimum depth ΔWACC 1 3 5 2.7% 2.1% 2.6% 2.1% 1.7% 2.2%

10 2.6% 2.2%

Table 6.9 Dependence WACC(L ) for company with lifetime n = 2 L WACC, %

0 18

1 16.33

2 15.8

3 15.52

4 15.35

5 15.23

6 16.45

7 16.42

8 16.39

9 16.37

10 16.35

136

6

New Mechanism of Formation of the Company Optimal Capital Structure,. . .

WACC(L); n=2 18.50% 18.00%

WACC

17.50% 17.00% 16.50% 16.00% 15.50% 15.00%

0

2

4

6

8

10

L Fig. 6.22 Dependence of weighted average cost of capital, WACC, on leverage level L in case of step-like decrease of debt cost for 2-year company

WACC(L); n=4 18.50%

WACC

17.50% 16.50% 15.50% 14.50% 13.50%

0

2

4

6

8

10

L Fig. 6.23 Dependence of weighted average cost of capital, WACC, on leverage level L in case of step-like decrease of debt cost for 4-year company

6.4

Conclusion

137

WACC(L); n=2 & n=4 18.50%

WACC

17.50% 16.50% 15.50% 14.50% 13.50%

0

2

4

6

8

10

L Fig. 6.24 Dependence of weighted average cost of capital, WACC, on leverage level L in case of step-like decrease of debt cost for 2-year and 4-year companies

Fig. 6.25 Mechanism of formation of the company optimal capital structure, different from one, suggested by trade-off theory. Decrease of debt cost with increase credit volume in leverage range from L0 up to L1 leads to formation of optimum in dependence WACC(L) at L = Lopt

138

6

New Mechanism of Formation of the Company Optimal Capital Structure,. . .

References Brennan M, Schwartz E (1978) Corporate income taxes, valuation, and the problem of optimal capital structure. J Bus 51:103–114 Brennan M, Schwartz E (1984) Optimal financial policy and firm valuation. J Financ 39:593–607 Brusov PN, Filatova ТV (2011) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Financ Credit 435:2–8 Brusov P, Filatova T, Orehova N, Brusova A (2011a) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Appl Financ Econ 21(11): 815–824 Brusov P, Filatova T, Orehova N et al (2011b) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Bus ICT 2:16–21 Brusov P, Filatova T, Orehova N et al (2011c) Influence of debt financing on the effectiveness of the investment project within the Modigliani–Miller theory. Res J Econ Bus ICT (UK) 2:11–15 Brusov P, Filatova T, Orehova N, Brusov PP, Brusova N (2011d) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Bus ICT 2:16–21 Brusov P, Filatova T, Eskindarov M, Orehova N (2012a) Influence of debt financing on the effectiveness of the finite duration investment project. Appl Financ Econ 22(13):1043–1052 Brusov P, Filatova T, Eskindarov M, Orehova N (2012b) Hidden global causes of the global financial crisis. J Rev Glob Econ 1:106–111 Brusov P, Filatova P, Orekhova N (2013a) Absence of an optimal capital structure in the famous tradeoff theory! J Rev Glob Econ 2:94–116 Brusov P, Filatova T, Orehova N (2013b) A qualitatively new effect in corporative finance: abnormal dependence of cost of equity of company on leverage. J Rev Glob Econ 2:183–193 Brusov P, Filatova P, Orekhova N (2014a) Mechanism of formation of the company optimal capital structure, different from suggested by trade off theory. Cogent Econ Financ 2:1–13. https://doi. org/10.1080/23322039.2014.946150 Brusov P, Filatova T, Orehova N (2014b) Inflation in Brusov–Filatova–Orekhova theory and in its perpetuity limit – Modigliani–Miller theory. J Rev Glob Econ 3:175–185 Filatova Т, Orehova N, Brusova А (2008) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Bull FU 48:68–77 Leland H (1994) Corporate debt value, bond covenants, and optimal capital structure. J Financ 49(4):1213–1252 Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Modigliani F, Miller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391 Myers (2001) Capital structure. J Econ Perspect 15:81–102

Chapter 7

The Global Causes of the Global Financial Crisis

Keywords The global financial crisis · Brusov–Filatova–Orekhova (BFO) theory · Trade-off theory · The weighted average cost of capital · Equity cost · Company capitalization Hopes of ending the financial crisis did not materialize. Recent events (the problems of the euro zone, the threat of default in the USA, the collapse of the financial market after a reduction of the credit rating of the USA, debt problems in the world (Europe, USA), etc.) show that the crisis deepened, affecting new areas and taking on a systemic character. It becomes clear that we need in-depth analysis of its general, systemic causes. In this Chapter, we describe recent results in this field, obtained by the authors. Analysts have called a lot of particular specific reasons that have led in 2008 to the financial crisis: the crisis in mortgage lending in the USA, unscrupulous financial statements of a number of leading investment funds, problems in the booming derivatives market in recent years, and others. But, as recent researches by us show, that there are also global, fundamental causes of the current and future financial crises. And one important cause of this is the wrong long-term systematic assessment of key financial parameters of companies: their capitalization, the value of attracting funds, including the cost of equity and weighted average cost of capital. To illustrate the importance of a correct evaluation of financial parameters we give only one example, associated with a reduction of the credit rating of the USA. When the agency Standard & Poor’s said to the Obama administration about the decision to lower credit ratings, the White House has pointed out to representatives of S & P an errors in its calculations in the trillions of dollars. After the official downgrade of the U.S. credit rating government has publicly stated about these errors. The representative of the U.S. Treasury Department stated: «Built on an error in the $2 trillion in the analysis of S & P, which led to a decrease in the rating speaks for itself». Last month, S & P warned that only spending budget cuts by $4 trillion

Whether it is possible to manage the finance, being unable to properly assess them © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_7

139

140

7 The Global Causes of the Global Financial Crisis

will be able to prevent a fall. However, Congress approved the plan, which included a reduction by only $2.4 trillion over 10 years. According to the estimates S & P, this means that U.S. foreign debt could reach 74% of GDP by the end of 2011, 79% by 2015, and 85% by 2021. Moody’s and Fitch Ratings, in turn, affirmed the top rating U.S. after Barack Obama signed the bill, prevented default on August 2. Thus, we have, on the one hand, the White House, President Obama (stated that America always will be the country with the AAA rating), agency Moody’s and Fitch, and, on the other hand, agency Standard & Poor’s, whose decision brought down the markets on August 8, 2011 and the difference in the assessment of about $2 trillion. Leaving aside the question of a possible trade insider information, we note that this is a striking example which demonstrates the great importance of quantitative assessments in the finance areas and the utmost responsibility in financial calculations. Let us pose the rhetorical question: whether it is possible to manage by the finance, being unable to properly consider them. The current system of assessment of key financial parameters of the companies goes back to Nobel Prize winners Modigliani and Miller (1958, 1963, 1966), who a half a century ago, replaced existed at that time empirical intuitive approach (let us call it by traditional). The theory of Modigliani–Miller has been established under a number of limitations, which obviously had a rough model character and had a very weak relationship to the real economy. Among the limitations it is sufficient to mention the lack of corporate and individual income taxes, perpetuity (infinite lifetime) of the companies, the existence of perfect markets, etc. Some restrictions (such as a lack of corporate and individual income taxes, etc.) were removed later by the authors themselves and their followers, while others (such as perpetuity of companies) remained in the approach of Modigliani–Miller, until recently. However, since the theory of Modigliani–Miller (Мodigliani and Мiller 1958, 1963, 1966) was the first quantitative theory, and since finance are essentially a quantitative science, the theory has become widely used in practice, since it gave even inaccurate, even rude, but at least some quantitative estimates of key financial parameters of companies, thus it was necessary as an air for forecasting activities of the companies and to make informed management decisions. Widely spread of the Modigliani–Miller theory, as usual, led to the neglect of the restrictions which it is based on, and the absolutization of the theory. As it has been shown by Brusov–Filatova–Orekhova (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011; Filatova et al. 2008), the theory of Modigliani–Miller (Мodigliani and Мiller 1958, 1963, 1966), to put it mildly, does not adequately evaluate the most important financial indicators of the company. It yields significantly lower estimates of weighted average cost of capital and of the value of its equity, compared with the actual estimates. This underestimation leads to the overestimate values of capitalization of the company. More theory by Brusov–Filatova–Orekhova can be seen, for example, in the following articles (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011; Filatova et al. 2008).

7

The Global Causes of the Global Financial Crisis

141

Fig. 7.1 Dependence of the equity cost, ke, on leverage L in the absence of corporate taxes (the upper line (t = 0)), as well as in the presence of corporate taxes (for 1-year (n = 1) and perpetuity companies (n = 1)). Dependences of the cost of equity capital of companies, ke, with an intermediate lifetime (1 < n < 1) lie within the shaded region

The first researcher, who drew attention to the fact that the calculation of weighted average cost of capital in the theory of Modigliani–Miller is inaccurate, was Myers (2001), who derived a formula for the average cost of capital for 1-year project. He suggested that the estimate given by the theory of Modigliani–Miller, is a lowest bound estimate of average cost of capital. The general solution of the problem of weighted average cost of capital for companies with an arbitrary finite lifetime was first obtained by Brusov–Filatova– Orekhova (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011; Filatova et al. 2008). Note that the results of their theory is applicable not only to companies with a finite lifetime, which had completed its work, but also to existing companies, giving the opportunity to assess the real value of equity cost and its weighted average capital cost, supposing that the company existed to date n years. Let us give a couple graphic illustrations of their results, for equity cost and for weighted average capital cost (Figs. 7.1 and 7.2). Obtained by Brusov–Filatova–Orekhova results (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011; Filatova et al. 2008) show that the theory of Modigliani–Miller (Мodigliani and Мiller 1958, 1963, 1966), due to its perpetuity underestimates (and often significantly) an assessment of average cost of capital, cost of equity of the company and inflating (also often significant) estimate of the capitalization of leverage as well financially independent companies.

W ACC

142

7

The Global Causes of the Global Financial Crisis

25,00 24,00 23,00 22,00 21,00 20,00 19,00 18,00 17,00 16,00 15,00 14,00 13,00 12,00 11,00 10,00 9,00 8,00 7,00 6,00 5,00 0

10

20

30

40

50

60 Wd

Fig. 7.2 The dependence of the WACC on debt share wd for companies with different lifetimes for different cost of equity, k0 (in each triplet upper curve corresponds to n = 1, middle one—to n = 2, and bottom one—to n = 1)

Such incorrect estimations of the basic financial parameters of companies lead to an underestimation of the financial risks, the impossibility, or severe difficulties in making appropriate management decisions, which is one of the implicit reasons for the financial crisis. Brusova Nastya (Brusova 2011) has made a comparative analysis of the calculation of the cost of equity and weighted average cost of capital of one of the leading telecom companies in Russia by three methods: traditional, Modigliani–Miller method, and Brusov–Filatova–Orekhova one. She has shown that the least accurate is the traditional approach. Better results are obtained by the method of Modigliani– Miller (and this determined his half-century of use in the world). And the most relevant results and provides by the Brusov–Filatova–Orekhova method (Fig. 7.3). See Chap. 18 for more details. Note that the present methods of estimating of the main financial parameters of companies are a blend of the traditional approach and the method of Modigliani– Miller. If we will continue use the existing system of evaluation of financial

7

The Global Causes of the Global Financial Crisis

143

k,%

60

ke ke

50 4

40

5 6 30

ke WACC

1 2 3

20

WACC WACC

10 L

0 0

0,5

1

1,5

2

2,5

3

Fig. 7.3 Dependence of the weighted average cost of capital of the company, WACC, equity cost, ke, on leverage by traditional method (lines 3, 6), by Modigliani–Miller method (lines 2, 5), and by Brusov–Filatova–Orekhova method (lines 1, 4)

indicators, it will inevitably be the hidden global cause of new financial crises because it does not allow make informed management decisions. The danger of the situation is that the found by us causes for the crisis do not lie on the surface, they are implicit, hidden, though no less important and significant. Therefore, the problem of their identification, disclosure is extremely important and relevant. Informed—so protected. Authors are working now on development of methodology for assessing the key financial parameters of the companies on the basis of the Brusov–Filatova– Orekhova theory. The conclusion is that we must globally transform the system of assessment of key financial parameters of companies: their capitalization, the cost of equity, and weighted average cost of capital, in order to lower the financial risks. This will lower the dangerous of global financial crisis. The authors are aware of the complexity of the task—to transform the world system of evaluation of the basic financial parameters of the companies to a new, more realistic basis, it will take years and years, but there is no other way for the world economic community.

144

7

The Global Causes of the Global Financial Crisis

References Brusov PN, Filatova ТV (2011) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Financ Credit 435:2–8 Brusov P, Filatova T, Orehova N, Brusova A (2011a) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Appl Financ Econ 21(11): 815–824 Brusov P, Filatova T, Orehova N et al (2011b) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Bus ICT 2:16–21 Brusov P, Filatova T, Orehova N et al (2011c) Influence of debt financing on the effectiveness of the investment project within the Modigliani–Miller theory. Res J Econ Bus ICT (UK) 2:11–15 Brusov P, Filatova T, Orehova N, Brusov PP, Brusova N (2011d) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Bus ICT 2:16–21 Brusov P, Filatova T, Eskindarov M, Orehova N (2012a) Influence of debt financing on the effectiveness of the finite duration investment project. Appl Financ Econ 22(13):1043–1052 Brusov P, Filatova T, Eskindarov M, Orehova N (2012b) Hidden global causes of the global financial crisis. J Rev Glob Econ 1:106–111 Brusov P, Filatova P, Orekhova N (2013a) Absence of an optimal capital structure in the famous tradeoff theory! J Rev Glob Econ 2:94–116 Brusov P, Filatova T, Orehova N (2013b) A qualitatively new effect in corporative finance: abnormal dependence of cost of equity of company on leverage. J Rev Glob Econ 2:183–193 Brusov P, Filatova P, Orekhova N (2014a) Mechanism of formation of the company optimal capital structure, different from suggested by trade off theory. Cogent Econ Financ 2:1–13. https://doi. org/10.1080/23322039.2014.946150 Brusov P, Filatova T, Orehova N (2014b) Inflation in Brusov–Filatova–Orekhova theory and in its perpetuity limit – Modigliani–Miller theory. J Rev Glob Econ 3:175–185 Brusova A (2011) А comparison of the three methods of estimation of weighted average cost of capital and equity cost of company. Financ Anal Prob Sol 34:36–42 Filatova Т, Orehova N, Brusova А (2008) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Bull FU 48:68–77 Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Modigliani F, Miller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391 Myers S (2001) Capital structure. J Econ Perspect 15(2):81–102

Chapter 8

The Role of Taxing and Leverage in Evaluation of Capital Cost and Capitalization of the Company

Keywords Brusov–Filatova–Orekhova (BFO) theory · Taxing · Leverage level · Debt financing · The weighted average cost of capital · Equity cost · Company capitalization In this Chapter, the role of tax shield, taxes, and leverage in the modern theory of the corporative finance is investigated. Modigliani–Miller theory, as well as modern theory of capital cost and capital structure by Brusov–Filatova–Orekhova is considered. It is shown that the equity cost as well as the weighted average cost of capital decreases with the tax rate, while the capitalization increases. The detailed investigation of the dependence of the weighted average cost of capital WACC and the equity cost ke on the tax rate at fix leverage (debt capital fraction wd) and on the leverage level at fix tax rate, as well as the dependence of WACCand ke on company lifetime is made. We have introduced the concept of tax operation leverage. For companies with finite lifetime a number of important qualitative effects, which have no analogies at perpetuity companies are found. In Chap. 3 it has been noted that Modigliani and Miller in their paper in 1958 (Мodigliani and Мiller 1958) have come to the conclusions, which are fundamentally different from the conclusions of traditional approach. They have shown that, in the framework of assumptions made by them the ratio between equity and debt capital in the company does not affect neither the cost of capital, nor company value. In the context of the studies of the impact tax on the cost of capital and the company’s capitalization, we raised among the numerous assumptions Modigliani and Miller two of the most important: 1. Corporate taxes and taxes on personal income of investors are absent 2. All financial flows are perpetuity ones From the first of these assumptions Modigliani and Miller subsequently refused themselves and have modified their theory to the case of presence of corporate taxes and taxes on personal income of investors that have significantly altered the conclusions of their theory (Мodigliani and Мiller 1963, 1966). The failure of the second assumption has led to the creation of modern theory of capital cost and capital structure by Brusov–Filatova–Orekhova (Brusov et al. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_8

145

146

8

The Role of Taxing and Leverage in Evaluation of Capital Cost. . .

2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011; Filatova et al. 2008).

8.1

The Role of Taxes in Modigliani–Miller Theory

We analyze now the role of taxes in the Modigliani–Miller theory, studying the dependence of weighted average cost of capital WACC and the equity cost ke of tax on profit rate T. With this purpose we analyze the following formulas: 1. For weighted average cost of capital WACC one has WACC = k0 ð1- wd T Þ,

ð8:1Þ

WACC = k0 ð1- LT=ð1 þ LÞÞ; 2. For the equity cost ke one has ke = k 0 þ Lð1- T Þðk0- kd Þ:

ð8:2Þ

Both dependences are linear: both costs of capital decrease linearly with the increase of tax on profit rate T. For dependence of weighted average cost of capital WACC on tax on profit rate T negative tangent of tilt angle in tgβ = - k0L/(1 + L) is growing in the module with the increase of the leverage level L, achieving maximum, equal k0 at an infinite leverage level L = 1 (share of equity capital is insignificantly small compared with the fraction of debt funds) (Fig. 8.1).

Fig. 8.1 The dependence of weighted average cost of capital WACC on tax on profit rate T at different fixed leverage level L

8.1

The Role of Taxes in Modigliani–Miller Theory

147

Let us give a few examples: 1. In accordance with expression tgβ = - k0L/(1 + L ) one gets, that at k0 = 10% and L = 1, i.e. D = S increase of tax on profit rate T on 10% leads to decrease of weighted average cost of capital WACC on 0.5%. 2. This dependence of weighted average cost of capital WACC on tax on profit rate T will be even more significant at a higher leverage level L and higher value k0. For example, at k0 = 20% and L = 2, the increase in T on 10% leads to a decrease in WACC on 1.33%. For dependence of the equity cost ke on tax on profit rate T from the analysis of formula ke = k0 + L(1 - T)(k0 - kd) it is seen that negative tangent of tilt angle tgγ = - L(k0 - kd) is also increase in the module with the increase of the leverage level, in which connection all dependences at the different leverage levels Li, based on the different points ke = k0 + Li(k0 - kd) when T = 0, at T = 1 converge at the point. k0; 3. In accordance with the formula tgγ = - L(k0 - kd) we get that, when k0 kd = 6% and L = 1, i.е. D = S, the increase of tax on profit rate T on 10% leads to a reduction in the equity capital cost ke on 0.6%. 4. This dependence of the equity cost ke on tax on profit rate T will be even more significant at a higher leverage level L and higher value k0 - kd. For example, at k0 - kd = 10% and L = 2, the increase in T on 10% leads to a decrease in ke on 2%. It should be noted that with the rising of tax on profit rate T the difference in the equity cost ke at various levels leverage decreases, disappearing at T = 1. This procedure recalls operational analysis, which examined dependence of financial results of the activities of the company on the costs and volumes of production and the implementation of the products, goods, and services. The key elements of operational analysis of any enterprise are: operating lever; the threshold of cost-effectiveness; stock financial strength of enterprise. The operational arm is reflected in the fact that any change proceeds from the disposal always gives rise to a more severe change in earnings. In the present case, as the effects of tax operational lever can be taken the ratio of change of weighted average cost of capital WACC to the change of tax on profit rate T, and the ratio of change of equity capital cost ke to the change of tax on profit rate T, i.е. we can introduce for the first time two tax operating levers: – For weighted average cost of capital WACC: LWACC = ΔWACC=ΔT; – For equity capital cost ke:

148

8

The Role of Taxing and Leverage in Evaluation of Capital Cost. . .

Fig. 8.2 Dependence of equity capital cost ke on tax on profit rate T at different leverage level L

Lke = Δk e =ΔT: For the earlier examples, the power of the lever is: 1. 2. 3. 4.

LWACC = 0.05; LWACC = 0.133; Lke = 0:06; Lke = 0:2.

The higher value of the tax operational lever causes the greater change in capital cost of the company at fixed change of tax on profit rate T (Fig. 8.2).

8.2

The Role of Taxes in Brusov–Filatova–Orekhova Theory

The solution of the problem of evaluation of the weighted average cost of capital WACC for companies with arbitrary lifetime, as it was noted in Chap. 4, has been done for the first time by Brusov, Filatova, and Orekhova (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011; Filatova et al. 2008). Following them, consider the situation for the finite lifetime of the company. In this case the Modigliani–Miller theorem V L = V 0 þ DT is changed by

8.2

The Role of Taxes in Brusov–Filatova–Orekhova Theory

V = V 0 þ ðPV ÞTS = V 0 þ DT ½1- ð1 þ kd Þ - n ,

149

ð8:3Þ

where ðPV ÞTS = kd DT

n X

ð1 þ k d Þ - t = DT ½1- ð1 þ kd Þ - n 

ð8:4Þ

t=1

represents a tax shield for n-years. It is seen that the capitalization of financially dependent (leverage)company linearly increasing with the growth of the tax on profit rate (as well as in the limited case of Modigliani–Miller), however, the tilt angle of the linear function VL(T ) is less than in the perpetuity case: tgδ = T ½1- ð1 þ k d Þ - n  ≤ T:

ð8:5Þ

We will carry out the study of the dependence of weighted average cost of capital of the company WACC and its equity cost ke on tax on profit rate in two ways: 1. We will study the dependence of weighted average cost of capital of the company WACC and its equity cost ke on tax on profit rate at fixed leverage level and at different lifetime of the company 2. We will study the dependence of weighted average cost of capital of the company WACC and its equity cost ke on leverage level at fixed tax on profit rate and at different lifetime of the company In both cases, we will use Brusov–Filatova–Orekhova formula for weighted average cost of capital of the company WACC (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011; Filatova et al. 2008): 1 - ð1 þ k 0 Þ - n 1 - ð1 þ WACCÞ - n : = WACC k 0 ½1 - ωd T ð1 - ð1 þ kd Þ - n Þ

8.2.1

ð8:6Þ

Weighted Average Cost of Capital of the Company WACC

Dependence of Weighted Average Cost of Capital of the Company WACC on Tax on Profit Rate Т at Fixed Leverage Level L For n = 2, k0 = 18 % , kd = 10% the dependences of weighted average cost of capital of the company WACC on tax on profit rate Т at fixed leverage level L (fraction of debt capital wd) are shown at Fig. 8.3. It is quite obvious that dependences are very similar to that in Fig. 8.1, differing by the tilt angle α and the distance between curves (in fact, the dependences are very

150

8

The Role of Taxing and Leverage in Evaluation of Capital Cost. . .

WACC

0.2000

1 0.1500

2

0.1000

3 4

0.0500

5 0.0000

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1 6 1.1

-0.0500

T Fig. 8.3 Dependence of weighted average cost of capital of the company WACC on tax on profit rate Т at fixed leverage level L (fraction of debt capital wd): 1—wd = 0; 2—wd = 0.2; 3—wd = 0.4; 4—wd = 0.6; 5—wd = 0.8; 6—wd = 1

close to the linear ones). With the increase of debt capital fraction wd the curves become more steep, the relevant tax operating lever decreases, which means the raise of the impact of the change of the tax on profit rate on the weighted average cost of capital. Dependence of Weighted Average Cost of Capital of the Company WACC on Debt Capital Fraction wd at Fixed Tax on Profit Rate Т Dependences of weighted average cost of capital of the company WACC on debt capital fraction wd at fixed tax on profit rate Т turn out to be linear ones as well. For example, for n = 3, k0 = 24 % , kd = 20% we got the dependences, represented in Fig. 8.4. The dependences, shown in Fig. 8.4 are not surprising, because the fraction of debt capital and tax on profit rate are included in the Brusov–Filatova–Orekhova formula (Eq. 8.5) in a symmetrical manner. With the increase of the tax on profit rate Т the curves become more steep, which means the raise of the impact of the change of the debt capital fraction wd on the weighted average cost of capital WACC. Dependence of Weighted Average Cost of Capital of the Company WACC on Leverage Level L at Fixed Tax on Profit Rate Т Dependence of weighted average cost of capital of the company WACC on leverage level L at fixed tax on profit rate Т becomes an essentially nonlinear. For example, for n = 3; k0 = 18 % , kd = 12% we got the dependences, represented in Fig. 8.5. With the increase of the tax on profit rate Т the curve of the dependence of weighted average cost of capital of the company WACC on leverage level

8.2

The Role of Taxes in Brusov–Filatova–Orekhova Theory

151

WACC

0.3000 0.2500

1

0.2000

2

0.1500 3

0.1000

4

0.0500 0.0000 -0.0500

5 0

0.2

0.4

0.6

0.8

1

1.2 6

-0.1000

Wd Fig. 8.4 Dependence of weighted average cost of capital of the company WACC on debt capital fraction wd at different tax on profit rates Т: 1—Т = 0; 2—Т = 0.2; 3—Т = 0.4; 4—Т = 0.6; 5—Т = 0.8; 6—Т = 1

WACC

0.2000 0.1800

1

0.1600 2

0.1400 0.1200

3

0.1000 0.0800

4

0.0600 0.0400

5

0.0200 6

0.0000 0

1

2

3

4

5

6

7

8

9

10

L Fig. 8.5 Dependence of weighted average cost of capital of the company WACC on leverage level L at different fixed tax on profit rates Т: 1—Т = 0; 2—Т = 0.2; 3—Т = 0.4; 4—Т = 0.6; 5—Т = 0.8; 6—Т = 1

L becomes more steep, i.e. at the same leverage level L its change leads to bigger change of WACC at higher tax on profit rate Т. At tax on profit rate T ≤ 40% weighted average cost of capital of the company WACC locates within kd ≤ WACC ≤ k0.

152

The Role of Taxing and Leverage in Evaluation of Capital Cost. . .

8

At tax on profit rate T ≥ 40% weighted average cost of capital of the company WACC falls below kd at certain leverage level L, which decreases with increase of T.

8.2.2

Equity Cost ke of the Company

Dependence of Equity Cost ke of the Company on Tax on Profit Rate Т at Fixed Leverage Level L Here are three figures, showing the dependence of equity cost ke on tax on profit rate at different (fixed) leverage level (debt capital fraction wd) for different parameter sets n, k0, kd (Figs. 8.6, 8.7, and 8.8). It should be noted that: 1. All dependencies are linear and ke decreases with increasing tax on profit rate Т. 2. With the increase of the debt capital fraction wd initial values ke significantly grow and exceed k0. 3. Lines, corresponding to the different values of the debt capital fraction wd intersect at the same point (at a certain value of tax on profit rate T), dependent on parameters n, k0, kd (Figs. 8.6 and 8.7).

Ke 0.2700 0.2500 0.2300 0.2100 0.1900 0.1700 5

0.1500

4

0.1300

3 2

0.1100 0.0900 0.0700

1 0

0.2

0.4

0.6

0.8

1

T

1.2

Fig. 8.6 Dependence of equity cost ke of the company on tax on profit rate Т at fixed debt capital fraction wd (n = 5, k0 = 10 % , kd = 6%): 1—wd = 0; 2—wd = 0.2; 3—wd = 0.4; 4—wd = 0.6; 5— wd = 0.8

8.2

The Role of Taxes in Brusov–Filatova–Orekhova Theory

153

Ke

0.2000 0.1500 1 2 3

0.1000 0.0500 0.0000

4

0

0.2

0.4

0.6

0.8

1

1.2

-0.0500 5 -0.1000

T

Fig. 8.7 Dependence of equity cost ke of the company on tax on profit rate Т at fixed debt capital fraction wd (n = 10, k0 = 10 % , kd = 8%): 1—wd = 0; 2—wd = 0.2; 3—wd = 0.4; 4—wd = 0.6; 5—wd = 0.8

Ke

0.6500 0.6000 0.5500 0.5000 0.4500 0.4000 0.3500

5

0.3000 0.2500

4 3 2 1

0.2000 0.1500

0

0.2

0.4

0.6

0.8

1

T

1.2

Fig. 8.8 Dependence of equity cost ke of the company on tax on profit rate Т at fixed debt capital fraction wd (n = 3, k0 = 20 % , kd = 10%): 1—wd = 0; 2—wd = 0.2; 3—wd = 0.4; 4—wd = 0.6; 5—wd = 0.8

154

8

The Role of Taxing and Leverage in Evaluation of Capital Cost. . .

4. At some values of parameters n, k0, kd the crossing of all lines at a single point cannot take a place at any tax on profit rate 0 < T ≤ 100%. With a large gap between k0 and kd a point of crossing of all the lines lies in the non-existent (the “non-financial”) region T > 100% (Fig. 8.8). For data of Fig. 8.8 T ≈ 162%. Dependence of Equity Cost ke of the Company on Leverage Level L on Fixed Tax on Profit Rate Т The results of the calculations of dependence of equity cost ke of the company on the leverage level L in Excel for the case: n = 7, k0 = 20 % , kd = 10% (at a fixed tax on profit rate Т) are presented in the Table 8.1 and in Fig. 8.9. Dependence of equity cost ke of the company on leverage level L on fixed tax on profit rate Т with a good accuracy is linear. When the tilt angle decreases with increasing tax on profit rate Т, as in the perpetuity case (Fig. 8.9). However, for companies with finite lifetime, along with the behavior ke(L ), similar to behavior in case of Modigliani–Miller perpetuity companies (Fig. 8.9), for some sets of parameters n, k0, kd there is a different dependence ke(L). For example, starting with some of the values of tax on profit rate T (in this case  T = 40%, although for the other parameter sets n, k0, kd a critical tax rate Tcould be even less) one has not the growth of the equity capital cost of the company but its descending (Fig. 8.10). Let us repeat once more that existence or absence of this effect depends on a set of parameters k0, kd, n. Note that this is a principally new effect, which may take place only for the company with the finite lifetime and which is not observed in perpetuity limit. For example, from the formula k e = k 0 þ Lð1- T Þðk0- kd Þ

ð8:7Þ

it follows, that at T = 1(100%) equity cost ke does not change with leverage: ke = k0, i.e. descending of equity cost ke with leverage does not occur at any tax on profit rate T. Thus, discovered effect does NOT take place in perpetuity Modigliani–Miller limit.

8.2.3

Dependence of WACC and ke on Lifetime of Company

The issue of dependency of WACC and keon the length of life of the company within the theory of Modigliani–Miller even though it is not possible to place: in their theory the parameter “time” is absent, since all the companies are perpetuity ones. Within the modern Brusov–Filatova–Orekhova theory, it become possible to study the dependence of WACC and ke on the company lifetime. Below we will undertake a detailed study of this problem: the dependences WACC(n) and ke(n) will be examined at different tax on profit rate T and leverage level L for different sets of parameters k0, kd, T, wd.

T 0.0 0.2 0.4 0.6 0.8 1.0

L 0.0 0.2000 0.2000 0.2000 0.2000 0.2000 0.2000

1.0 0.3000 0.2842 0.2677 0.2504 0.2323 0.2132

2.0 0.4000 0.3682 0.3344 0.2984 0.2601 0.2185

3.0 0.5000 0.4522 0.4008 0.3457 0.2861 0.2210

4.0 0.6000 0.5362 0.4672 0.3928 0.3117 0.2223

5.0 0.7000 0.6202 0.5335 0.4397 0.3369 0.2229

6.0 0.8000 0.7042 0.5998 0.4865 0.3619 0.2231

7.0 0.9000 0.7874 0.6661 0.5334 0.3867 0.2233

8.0 1.0000 0.8713 0.7323 0.5802 0.4116 0.2231

9.0 1.1000 0.9551 0.7986 0.6265 0.4364 0.2228

Table 8.1 Dependence of equity cost ke of the company on leverage level L on fixed tax on profit rate Т for the case n = 7, k0 = 20 % , kd = 10% 10 1.2000 1.0389 0.8649 0.6731 0.4612 0.2224

8.2 The Role of Taxes in Brusov–Filatova–Orekhova Theory 155

156

8

The Role of Taxing and Leverage in Evaluation of Capital Cost. . .

Ke 1.4000 1.2000

1

1.0000

2 3

0.8000

4

0.6000 0.4000

5

0.2000

6

0.0000

0

1

2

3

4

5

6

7

8

9

10

11

L Fig. 8.9 Dependence of equity cost ke of the company on leverage level L on fixed tax on profit rate Т for the case n = 7, k0 = 20 % , kd = 10%: 1—T = 0; 2—T = 0.2; 3—T = 0.4; 4—T = 0.6; 5— T = 0.8; 6—T = 1

Dependence of Weighted Average Cost of Capital of the Company WACC on Lifetime of Company at Different Fixed Tax on Profit Rate T Considering dependence is shown in Fig. 8.11. Weighted average cost of capital of the company WACC decreases with increasing of company lifetime n, in an effort to its perpetuity limit. The initial values WACC (at n = 1) will decrease with increasing of tax on profit rate T (in accordance with the received previously dependencies WACC(T )), and a range of WACC changes is growing with increasing T. Dependence of Weighted Average Cost of Capital of the Company WACC on Lifetime of Company at Different Fixed Fraction of Debt Cpital wd Considering dependence is shown in Fig. 8.12. The weighted average cost of capital of the company WACC decreases with the lifetime of company n, tending to its perpetuity limit. The initial values WACC (at n = 1) decrease with the increase of fraction of debt capital (in accordance with the previously received dependencies WACC(wd)), and a range of WACC changes is growing with increasing of wd. Dependence of Equity Cost of the Company ke on Lifetime of Company n at Different Fixed Fraction of Debt Capital wd Considering dependence is represented in Fig. 8.13. The equity cost of the company ke decreases with the lifetime of company n, tending to its perpetuity limit. The initial values ke (at n = 1) decrease significantly

8.2

The Role of Taxes in Brusov–Filatova–Orekhova Theory

157

Ke

0.4000 0.3000

1

0.2000

2

0.1000

3

0.0000

4 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 1010.5

-0.1000 5 -0.2000 6 -0.3000

L

Fig. 8.10 Dependence of equity cost ke of the company on leverage level L on fixed tax on profit rate Т for the case: n = 5, k0 = 10 % , kd = 8%: 1—T = 0; 2—T = 0.2; 3—T = 0.4; 4—T = 0.6; 5— T = 0.8; 6—T = 1

WACC

0.1200 0.1000

1 2

0.0800

3

0.0600

4

0.0400

5

0.0200 0.0000

6 0

5

10

15

20

25

30

n Fig. 8.11 Dependence of weighted average cost of capital of the company WACC on lifetime of company at different fixed tax on profit rate T (wd = 0, 7, k0 = 10 % , kd = 8%): 1—T = 0; 2— T = 0.2; 3—T = 0.4; 4—T = 0.6; 5—T = 0.8; 6—T = 1

158

The Role of Taxing and Leverage in Evaluation of Capital Cost. . .

8

WACC

0.1200 0.1000

1 2 3 4 5 6

0.0800 0.0600 0.0400 0.0200 0.0000 0

5

10

15

20

n

25

30

Fig. 8.12 Dependence of weighted average cost of capital of the company WACC on lifetime of company at different fixed fraction of debt capital wd (T = 40 % , k0 = 10 % , kd = 8%): 1—wd = 0; 2—wd = 0.2; 3—wd = 0.4; 4—wd = 0.6; 5—wd = 0.8

Ke 0.2000 0.1800 0.1600

5

0.1400

4 3 2 1

0.1200 0.1000 0.0800 0.0600 0.0400 0.0200 0.0000

0

5

10

15

20

25

30

n Fig. 8.13 Dependence of equity cost of the company ke on lifetime of company n at different fixed fraction of debt capital wd (T = 20 % , k0 = 10 % , kd = 8%): 1—wd = 0; 2—wd = 0.2; 3—wd = 0.4; 4—wd = 0.6; 5—wd = 0.8

with the increase of fraction of debt capital wd. A range of ke changes is growing with increasing of wd. It should be noted that the differences in equity cost of the company at a fixed n, starting from wd = 0, 5, become and remain significant (and constant for a fixed change in the fraction of debt capital Δwd and at n ≥ 6).

8.3

Conclusions

159

Ke 0.1900 0.1700 0.1500 0.1300

5 4 3 2 1

0.1100 0.0900

0

5

10

15

20

25

30

n Fig. 8.14 Dependence of equity cost of the company ke on lifetime of company n at different fixed fraction of debt capital wd (T = 40 % , k0 = 10 % , kd = 8%):1—wd = 0; 2—wd = 0.2; 3—wd = 0.4; 4—wd = 0.6; 5—wd = 0.8

The situation will change with increase of tax on profits rate T. To demonstrate this fact we show the similar data, increasing tax on profit rate T twice (from 20 up to 40%) (Fig. 8.14). It can be observed that with increase in tax on profits rates in two times, the region, where the differences in equity cost of capital ke of the company are feeling at various fractions of debt capital wd have narrowed down to 6 years, while at n ≥ 6 equity cost of capital ke remains virtually equal k0, only slightly fluctuates around this value. Dependence of Equity Cost of the Company ke on Lifetime of Company n at Different Fixed Tax on Profit Rate T Considering dependence is represented in Fig. 8.15. The equity cost of the company ke decreases with the lifetime of company n, tending to its perpetuity limit. Under growing of tax on profit rates T the equity cost of the company ke decreases (at fixed fraction of debt capital wd, while range of ke changes increases.

8.3

Conclusions

In this chapter, the role of tax shields, taxes, and leverage is investigated within the theory of Modigliani–Miller as well as within the modern theory of corporate finance by Brusov–Filatova–Orekhova (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011; Filatova et al. 2008). It is shown that equity cost of the

160

8

The Role of Taxing and Leverage in Evaluation of Capital Cost. . .

Ke 0.3000

1 2 3

0.2500 0.2000

4 0.1500

5

0.1000

6

0.0500 0.0000

0

5

10

15

20

25

30

n Fig. 8.15 Dependence of equity cost of the company ke on lifetime of company n at different fixed tax on profit rates T (wd = 0, 7, k0 = 16 % , kd = 12%): 1—T = 0; 2—T = 0.2; 3—T = 0.4; 4— T = 0.6; 5—T = 0.8; 6—T = 1

company as well as weighted average cost of capital decreases with the growth of tax on profits rates. A detailed study of the dependence of weighted average cost of capital WACC and equity cost of the company keon tax on profits rates at fixed leverage level (fixed debt capital fraction wd) as well as on leverage level (debt capital fraction wd) at fixed tax on profits rate has been done. The dependences of weighted average cost of capital WACC and equity cost of the company keon company lifetime have been investigated as well. The concept “tax operating lever” has been introduced. For companies with finite lifetime a number of important qualitative effects that do not have analogs for perpetuity companies have been detected. One such effect—decreasing of equity cost with leverage level at values of tax on profits rate T, which exceeds some critical value T*—is described in detail in Chap. 11 (at certain ratios between the debt cost and equity capital discovered effect takes place at tax on profits rate, existing in the western countries and in Russia, that provides practical value effect). Its accounting is important in improving tax legislation and may change dividend policy of the company.

References

161

References Brusov PN, Filatova ТV (2011) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Financ Credit 435:2–8 Brusov P, Filatova T, Orehova N, Brusova A (2011a) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Appl Financ Econ 21(11): 815–824 Brusov P, Filatova T, Orehova N et al (2011b) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Bus ICT 2:16–21 Brusov P, Filatova T, Orehova N et al (2011c) Influence of debt financing on the effectiveness of the investment project within the Modigliani–Miller theory. Res J Econ Bus ICT (UK) 2:11–15 Brusov P, Filatova T, Orehova N, Brusov PP, Brusova N (2011d) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Bus ICT 2:16–21 Brusov P, Filatova T, Eskindarov M, Orehova N (2012a) Influence of debt financing on the effectiveness of the finite duration investment project. Appl Financ Econ 22(13):1043–1052 Brusov P, Filatova T, Eskindarov M, Orehova N (2012b) Hidden global causes of the global financial crisis. J Rev Glob Econ 1:106–111 Brusov P, Filatova P, Orekhova N (2013a) Absence of an optimal capital structure in the famous tradeoff theory! J Rev Glob Econ 2:94–116 Brusov P, Filatova T, Orehova N (2013b) A qualitatively new effect in corporative finance: abnormal dependence of cost of equity of company on leverage. J Rev Glob Econ 2:183–193 Brusov P, Filatova P, Orekhova N (2014a) Mechanism of formation of the company optimal capital structure, different from suggested by trade off theory. Cogent Econ Financ 2:1–13. https://doi. org/10.1080/23322039.2014.946150 Brusov P, Filatova T, Orehova N (2014b) Inflation in Brusov–Filatova–Orekhova theory and in its perpetuity limit – Modigliani–Miller theory. J Rev Glob Econ 3:175–185 Filatova Т, Orehova N, Brusova А (2008) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Bull FU 48:68–77 Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Modigliani F, Miller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391

Chapter 9

A Qualitatively New Effect in Corporate Finance: Abnormal Dependence of Equity Cost of Company on Leverage

Keywords Brusov–Filatova–Orekhova (BFO) theory · Debt financing · The weighted average cost of capital · Equity cost · Debt cost · Company capitalization · A qualitatively new effect in corporate finance Qualitatively new effect in corporative finance is discovered: decreasing of cost of equity ke with leverage L. This effect, which is absent in perpetuity Modigliani– Miller limit, takes place under account of finite lifetime of the company at tax on profit rate, which exceeds some value T*. At some ratios between cost of debt and cost of equity the discovered effect takes place at tax on profit rate, existing in western countries and Russia. This provides the practical meaning of discussed effect. Its accounting is important at modification of tax low and can change the dividend policy of the company. In this Chapter, the complete and detailed investigation of discussed effect, discovered within Brusov–Filatova–Orekhova theory, has been done. It has been shown that the absence of the effect at some particular set of parameters is connected to the fact, that in these cases T* exceeds 100% (tax on profit rate is situated in “non– financial” region).

9.1

Introduction

The structure of this Chapter is as follows: first, we consider the value of the cost of equity ke in the theory of Modigliani and Miller, its dependence on leverage L and tax on profit rate T to show that, in this perpetuity limit the cost of equity ke is always growing with leverage (for any tax on profit rate T). Then we consider the cost of equity ke within the modern Brusоv–Filаtоvа– Orekhоvа theory and show that for companies with finite lifetime a qualitatively new effect takes place: decreasing of the cost of equity with the leverage. The effect takes place at tax on profit rate T, exceeding a value T*.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_9

163

164

9

A Qualitatively New Effect in Corporate Finance: Abnormal Dependence. . .

Next, we make a complete study of the discovered effect: we investigate the dependence of T* on company lifetime n, on cost of equity of financially independent company k0 and on debt rate kd as well as on ratio of these parameters. We separately consider a 1-year company and analyze their special feature in connection with the discussed effect. An explanation of the absence of this effect for such companies will be given. In the conclusion the importance of the discovered effect in various areas, including improving of tax legislation and dividend policies of companies, as well as the practical value of the effect is discussed.

9.2

Equity Cost in the Modigliani–Miller Theory

For weighted average cost of capital WACC in the Modigliani–Miller theory the following expression has been obtained (Мodigliani and Мiller 1958, 1963, 1966) WACC = k 0 ð1- wd T Þ:

ð9:1Þ

Dependence of WACC on financial leverage L = D/S is described by the formula WACC = k0 ð1- LT=ð1 þ LÞÞ

ð9:2Þ

In accordance with the definition of the weighted average cost of capital accounting the tax shield one has WACC = k 0 we þ kd wd ð1- T Þ:

ð9:3Þ

Equating (Eqs. 9.1) to (9.3), we get k0 ð1- wd T Þ = k 0 we þ kd wd ð1- T Þ,

ð9:4Þ

From where for cost of equity one has ke = k 0 þ Lð1- T Þðk0- kd Þ:

ð9:5Þ

Note that the formula (Eq. 9.5) is different from the corresponding formula without tax only by multiplier (1–T ) in the term, indicating premium for risk. As the multiplier is less than unit, the appearance of corporate tax on profits leads to the fact that cost of equity increases with leverage slowly comparing to the case of taxes absence. Analysis of formulas (Eqs. 9.1) and (9.5) leads to the following conclusions:

9.2

Equity Cost in the Modigliani–Miller Theory

165

Fig. 9.1 Dependence of cost of equity, cost of debt, and WACC on leverage without taxes (t = 0) and with taxes (t ≠ 0)

With the Increasing of Financial Leverage 1. Value of the company increases 2. Weighted average cost of capital decreases from k0 (at L = 0) up to k0(1 - T ) (at L = 1, when the company is funded solely by borrowing, or its own capital is negligible) 3. Cost of equity increases linearly from k0 (at L = 0) up to 1 (at L = 1) Let us analyze now the influence of taxes on cost of equity in Modigliani–Miller theory by study of the dependence of cost of equity on tax on profit rate. For this we will analyze the formula ke = k 0 þ Lð1- T Þðk0- kd Þ:

ð9:6Þ

It is seen from Fig. 9.1, that dependence is linear: cost of equity decreases linearly with tax on profit rate. The module of negative tilt angle tangent tgγ = - L(k0 - kd) increases with leverage, and besides all dependences at different leverage level Li,

166

9

A Qualitatively New Effect in Corporate Finance: Abnormal Dependence. . .

Fig. 9.2 Dependence of cost of equity on tax on profit rate T at different leverage level Li

Fig. 9.3 Dependence of cost of equity on tax on profit rate T at different leverage level Li for the case k0 = 10 % ; kd = 8%. (1— L = 0; 2—L = 2; 3—L = 4; 4—L = 6; 5—L = 8)

Ke (T), at fix L

Ke 0.3000

5

0.2500

4

0.2000

3

0.1500

2

0.1000

1

0.0500

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

1.1

0.0000

T

coming from different points ke = k0 + Li(k0 - kd) at T = 0, at T = 1 converge at the point k0 (Fig. 9.2). This means that the difference in cost of equity at different leverage level Li decreases with tax on profit rate T, disappearing at T = 1. Let us illustrate these general considerations by the example k0 = 10 % ; kd = 8% (Figs. 9.3, 9.4 and 9.5). From Fig. 9.2 it is seen that dependence is linear: cost of equity decreases linearly with tax on profit rate. The module of negative tilt angle tangent tgγ = - L(k0 - kd) increases with leverage, and besides all dependences at different leverage level Li, coming from different points ke = k0 + Li(k0 - kd) at T = 0, at T = 1 converge at the point k0 (Fig. 9.2).

9.2

Equity Cost in the Modigliani–Miller Theory

Fig. 9.4 Dependence of cost of equity on leverage L at different tax on profit rates T for the case k0 = 10 % ; kd = 8% (1— T = 0; 2—T = 0.1; 3— T = 0.2; 4—T = 0.3; 5— T = 0.4; 6—T = 0.5; 7— T = 0.6; 8—T = 0.7; 9— T = 0.8; 10—T = 0.9; 11— T = 1)

167

Ke (L), at fix T

Ke 0.3000

1 2 3 4 5 6 7 8 9 10 11

0.2500 0.2000 0.1500 0.1000 0.0500 0.0000

Ke

0.0

1.0

2.0

3.0

4.0 L

5.0

6.0

7.0

8.0

9.0

Ke (L,T)

0.3000 0.2500 0.2000 0.1500 0.1000 0.0500 0.0000 0 0.1 0.2 0.3 8,0 0.4 0.5 6,0 0.6 0.7 4,0 0.8 0.9 2,0 T 1 0,0 L Fig. 9.5 Dependence of cost of equity on leverage L and on tax on profit rate T for the case k0 = 10 % ; kd = 8%

From Fig. 9.4, it is seen that cost of equity increases linearly from k0 (at L = 0) up to 1 (at L = 1), and besides tilt angle tangent decreases with tax on profit rate T, becoming zero at T = 100%. By other words, with increase of tax on profit rate T, dependence of cost of equity on leverage L becomes smaller, disappearing at T = 100%, i.e. within perpetuity Modigliani–Miller theory there is not any anomaly—effect, announced in the title of paper is absent.

168

9

A Qualitatively New Effect in Corporate Finance: Abnormal Dependence. . .

In conclusion, here is a three-dimensional graph of dependence of cost of equity on leverage L and on tax on profit rate T for the case k0 = 10 % ; kd = 8%.

9.3

Cost of Equity Capital Within Brusov–Filatova– Orekhova Theory (BFO Theory)

The general solution of the problem of weighted average cost of capital and the cost of equity for the company with finite lifetime has been received for the first time by Brusov–Filatova–Orekhova with coauthors (Brusov et al. 2011–d, 2012a, b, 2013, b, 2014, b; Brusov and Filatova 2011; Filatova et al. 2008). They have gotten (now already famous) formula for WACC 1 - ð1 þ WACCÞ - n 1 - ð1 þ k 0 Þ - n : = WACC k 0 ½1 - ωd T ð1 - ð1 þ kd Þ - n Þ

ð9:7Þ

At n = 1 one gets Myers formula (Myers 2001) for 1-year company which is a particular case of Brusov–Filatova–Orekhova formula (Eq. 9.6) WACC = k 0 -

1 þ k0 k w T: 1 þ kd d d

ð9:8Þ

We will study the dependence of cost of equity ke on tax on profit rate T and leverage level L by three methods: 1. We will study the dependence of cost of equity ke on tax on profit rate T at fix leverage level L for different lifetime n of the company. 2. We will study the dependence of cost of equity ke on leverage level L at fix tax on profit rate T for different lifetime n of the company. 3. We will explore the influence of simultaneous change of leverage level L and tax on profit rate T on cost of equity ke for different lifetime n of the company. In this case, the results will be presented as 3D graphs. In these studies, a qualitatively new effect has been discovered, and it is visible in each of the applicable types of studies (1–3).

9.3.1

Dependence of Cost of Equity ke on Tax on Profit Rate T at Different Fix Leverage Level L

Dependence of cost of equity ke on tax on profit rate T at fix leverage level L Below we show three figures (Figs. 9.6, 9.7, and 9.8) of the dependence of cost of equity ke

9.3 Cost of Equity Capital Within Brusov–Filatova–Orekhova Theory (BFO Theory)

169

Ke(T), at fix Wd

Ke 0.2700 0.2500 0.2300 0.2100 0.1900 0.1700 0.1500 0.1300 0.1100

1 2 3 4 5

0.0900 0.0700

0

0.2

0.4

0.6

T

0.8

1

1.2

Fig. 9.6 Dependence of cost of equity ke on tax on profit rate T at different fix leverage level L (n = 5, k0 = 10 % , kd = 6%) (1—wd = 0; 2—wd = 0.2; 3—wd = 0.4; 4—wd = 0.6; 5—wd = 0.8)

on tax on profit rate T at different fix leverage L for different sets of parameters n, k0, kd. On the basis of the analysis of the three figures (Figs. 9.6, 9.7, and 9.8), and other data we come to the following conclusions: 1. All dependences are linear: cost of equity decreases linearly with tax on profit rate. 2. The initial values of ke grow significantly with the level of leverage (the share of debt capital wd) and exceed k0. 3. Lines, corresponding to the different values of leverage level (the share of debt capital wd) intersect at one point (at some value of tax on profit rate T), depending on parameters n, k0, kd (Figs. 9.7 and 9.8). At fix tax on profit rate T > T increasing of leverage level corresponds to moving from line 1 to 2, 3, 4, 5, i.е. decreasing ke, this means the discovery of qualitatively new effect in corporative finance: decreasing of equity cost ke with leverage. In a more obvious form, it will manifest itself in studies depending on cost of equity of the company on the leverage level, carried out by us below. At some values of parameters n, k0, kd the intersection of all lines at one point could not happened at any tax on profit rate 0 < T ≤ 100%. From the Fig. 9.9 it is seen that with a large gap between k0 and kd the intersection of the lines lies in the non-existent (“non-financial”) region T > 100% (for data of Fig. 9.9 T ≈ 162%).

170

9

A Qualitatively New Effect in Corporate Finance: Abnormal Dependence. . .

Ke(T), at fix Wd

Ke 0.2000 0.1500 0.1000

1 2 3

0.0500

4

0.0000

0

0.2

0.4

0.6

-0.0500 -0.1000

0.8

1

1.2 5

T

Fig. 9.7 Dependence of cost of equity ke on tax on profit rate T at different fix leverage level L (n = 10, k0 = 10 % , kd = 8%) (1—wd = 0; 2—wd = 0.2; 3—wd = 0.4; 4—wd = 0.6; 5— wd = 0.8)

9.3.2

Dependence of Cost of Equity ke on Leverage Level L (the Share of Debt Capital wd) at Different Fix Tax on Profit Rate T

Below we show the results on calculation of dependence of cost of equity ke on leverage level L (the share of debt capital wd) in Excel at different fix tax on profit rate T in the form of a table, and in the form of a graph for the case n = 7, k0 = 20 % , kd = 10%, as well as in the form of a graph for the case n = 5, k0 = 10 % , kd = 8% (Table 9.1). From Fig. 9.9 it is seen that dependence of cost of equity ke on leverage level L with a good accuracy is linear. The tilt angle decreases with tax on profit rate like the perpetuity case. However, for the finite lifetime of companies along with the behavior ke(L ), similar to the perpetuity behavior of the Modigliani–Miller case (Fig. 9.9), for some sets of parameters n, k0, kd there is an otherwise behavior ke(L ). From the Fig. 9.10, it is seen that starting from some values of tax on profit rate T (in this case from T = 40%, although at other sets of parameters n, k0, kd critical values of tax on profit rate T could be lower) there is not the rise in the cost of equity of the company with leverage, but descending. Once again, the presence or the absence of such an effect depends on a set of parameters k0, kd, n.

9.3

Cost of Equity Capital Within Brusov–Filatova–Orekhova Theory (BFO Theory)

171

Ke(T), at fix Wd

Ke 0.6500 0.6000 0.5500 0.5000 0.4500 0.4000 0.3500

5

0.3000 0.2500

4 3 2 1

0.2000 0.1500

0

0.2

0.4

0.6

T

0.8

1

1.2

Fig. 9.8 Dependence of cost of equity ke on tax on profit rate T at different fix leverage level L (n = 3, k0 = 20 % , kd = 10%) (1—wd = 0; 2—wd = 0.2; 3—wd = 0.4; 4—wd = 0.6; 5— wd = 0.8)

Ke(L), at fix T

Ke

1.4000 1.2000

1

1.0000

2

0.8000

3

0.6000

4

0.4000

5

0.2000

6

0.0000

0

1

2

3

4

5

L

6

7

8

9

10

11

Fig. 9.9 Dependence of cost of equity ke on leverage level L at different tax on profit rate T (n = 7, k0 = 20 % , kd = 10%) (1—T = 0; 2—T = 0.2; 3—T = 0.4; 4—T = 0.6; 5—T = 0.8; 6—T = 1)

TL 0 0.2 0.4 0.6 0.8 1

0.0 0.2000 0.2000 0.2000 0.2000 0.2000 0.2000

1.0 0.3000 0.2842 0.2677 0.2504 0.2323 0.2132

2.0 0.4000 0.3682 0.3344 0.2984 0.2601 0.2185

3.0 0.5000 0.4522 0.4008 0.3457 0.2861 0.2210

4.0 0.6000 0.5362 0.4672 0.3928 0.3117 0.2223

5.0 0.7000 0.6202 0.5335 0.4397 0.3369 0.2229

6.0 0.8000 0.7042 0.5998 0.4865 0.3619 0.2231

7.0 0.9000 0.7874 0.6661 0.5334 0.3867 0.2233

8.0 1.0000 0.8713 0.7323 0.5802 0.4116 0.2231

9.0 1.1000 0.9551 0.7986 0.6265 0.4364 0.2228

10 1.2000 1.0389 0.8649 0.6731 0.4612 0.2224

9

Table 9.1 Dependence of cost of equity ke on leverage level L at different fix tax on profit rates T for the case n = 7, k0 = 20 % , kd = 10%

172 A Qualitatively New Effect in Corporate Finance: Abnormal Dependence. . .

9.4

Dependence of the Critical Value of Tax on Profit Rate T. . .

Ke

173

Ke(L), at fix T

0.4000 0.3000

1

0.2000

2

0.1000

3

0.0000

4 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 1010.5

-0.1000

5

-0.2000 6 -0.3000

L

Fig. 9.10 Dependence of cost of equity ke on leverage level L at different tax on profit rate T (n = 5, k0 = 10 % , kd = 8%) (1—T = 0; 2—T = 0.2; 3—T = 0.4; 4—T = 0.6; 5—T = 0.8; 6—T = 1)

This effect has been observed above in the dependence of cost of equity ke on tax on profit rate T at fix leverage level, but it is more clearly visible, depending on value of cost of equity of the company on the leverage for various values of tax on profit rate T. Note that this is a new effect, which may take place only for the finite lifetime company and which is not observed in perpetuity Modigliani–Miller limit. It is easy to see from the Modigliani–Miller formula (9.5) k e = k0 þ Lð1- T Þðk0- kd Þ, that at T = 1(100%) cost of equity ke does not change with leverage: ke = k0, i.е. there is no decreasing of ke with leverage at any tax on profit rate T.

9.4

Dependence of the Critical Value of Tax on Profit Rate T on Parameters n, k0, kd of the Company

In this section, we study the dependence of the critical value of tax on profit rate T on parameters n, k0, kd of the company. First we study the dependence of the critical value of tax on profit rate T on the lifetime of the company under variation of the difference between k0and kd.

174

9

A Qualitatively New Effect in Corporate Finance: Abnormal Dependence. . .

Table 9.2 The dependence of the critical value of tax on profit rate T on the lifetime of the company under variation of the difference between k0 and kd ke(t)\n kd = 6%. k0 = 8% kd = 6%. k0 = 10% kd = 6%. k0 = 12% kd = 6%. k0 = 14% kd = 6%. k0 = 16% kd = 6%. k0 = 20% kd = 6%. k0 = 24%

T*

2 0.9575

3 0.6600

5 0.5200 0.9110

7 0.4800 0.8225

10 0.4640 0.7650 0.9800

15 0.4710 0.7332 0.9040

20 0.4903 0.7249 0.8693 0.9671

25 0.5121 0.7260 0.8504 0.9324

T*(n)

1.0 0.9 0.8 0.7

4 3 2

0.6 0.5

1

0.4 0.3 0.2 0.1 0.0

n 0 1 2 3 4 5 6 7 8 9 10111213141516171819202122232425

Fig. 9.11 The dependence of the critical value of tax on profit rate T on the lifetime of the company under variation of the difference between k0 and kd (Δk = k0 - kd = 2 % ; 4 % ; 6 % ; 8%) (1—kd = 6%, k0 = 8%;2—kd = 6%, k0 = 10%; 3—kd = 6%, k0 = 12%; 4—kd = 6%, k0 = 14%)

The results of calculations are shown in Table 9.2, empty cells means, that the critical value of tax on profit rate T > 100%, i.е. we are in “non–financial” region. The conclusions from Fig. 9.11 are as follows: 1. It is seen that the critical value of tax on profit rate T increases with the difference Δk = k0 - kd, therefore a small difference between the value of cost of equity

9.4

Dependence of the Critical Value of Tax on Profit Rate T. . .

175

Table 9.3 The dependence of the critical value of tax on profit rate T on the lifetime of the company under different values of k0 and kd at constant difference between them Δk = k0 kd = 2% ke(t)\n kd = 6%. k0 = 8% kd = 8%. k0 = 10% kd = 10%. k0 = 12% kd = 12%. k0 = 14% kd = 14%. k0 = 16% kd = 18%. k0 = 20% kd = 22%. k0 = 24%

2 0.9575 0.7313 0.6000

3 0.6600 0.5125 0.4280

5 0.5200 0.4140 0.3510

7 0.4800 0.3905 0.3392

10 0.4640 0.3892 0.3467

15 0.4710 0.4138 0.3840

20 0.4903 0.4453 0.4285

25 0.5121 0.4803 0.4733

0.5125

0.3687

0.3110

0.3043

0.3218

0.3697

0.4239

0.4788

0.4437

0.3266

0.2810

0.2821

0.3043

0.3636

0.4277

0.4904

0.3625

0.2710

0.2435

0.2549

0.2895

0.3677

0.4468

0.5221

0.3100

0.2370

0.2220

0.2400

0.2875

0.3818

0.4759

0.5588

(at L = 0) k0 of the company and the credit rate kd favors to existence of a new effect. 2. The critical value of tax on profit rate T decreases monotonically with the lifetime of the company (only for 10 years in case of Δk = k0 - kd = 2% it has a minimum). Therefore, the probability of the anomaly effect is higher for “adult” companies. 3. Recapitulating 1 and 2, one can note, that a small difference between the value of cost of equity (at L = 0) k0 of the company and the credit rate kd as well as old enough age of the company favors to existence of a new effect. We calculated as well T at different values of k0 and kd at constant difference between them Δk = k0 - kd = 2%. The data are shown in Table 9.3. The conclusions in current case are as follows (Fig. 9.12): All curves are convex and the critical value of tax on profit rate T* reaches minimum, which value decreases with k0. Min T* = 22.2% at k0 = 24%, min T* = 24.35% at k0 = 20%, min T* = 28.1% at k0 = 16%, min T* = 30.43% at k0 = 14%, min T* = 33.92% at k0 = 12%, min T* = 38.92% at k0 = 10%, min T* = 46.4% at k0 = 8%. Therefore, the higher value of k0 and the higher value of kd at constant difference between them Δk = k0 kd = const favor for existence of a new effect. 1. The critical value of tax on profit rate T reaches minimum at company lifetime, decreasing with k0: n = 4, 5 years at k0 = 24%, n = 5, 5 years at k0 = 16%, n = 6, 5 years at k0 = 12% and n = 10, 5 years at k0 = 8%. 2. Thus, a parallel shift up of rates k0 and kd favor a for new effect, while company age, favorable a new effect, decreases with k0. III. Now let us investigate the dependence of critical value of tax on profit rate T on k0 for the second considerable case (at constant difference between k0 and kd Δk = k0 - kd = 2%).

176

9

A Qualitatively New Effect in Corporate Finance: Abnormal Dependence. . .

T*(n)

T*

1.0

1 0.9 0.8 0.7 0.6 0.5

2

3 7 6 1 4 5 2 3

4 5

0.4 0.3 0.2

6 7

0 1 2 3 4 5 6 7 8 9 10 11 12 1314 15 16 17 18 19 2021 22 23 24 25

n

Fig. 9.12 The dependence of the critical value of tax on profit rate T on the lifetime of the company under different values of k0 and kd at constant difference between them Δk = k0 kd = 2% (1—k0 = 8%; 2—k0 = 10%; 3—k0 = 12%; 4—k0 = 14%; 5—k0 = 16%; 6—k0 = 20%; 7—k0 = 24%)

For this we consider Fig. 9.13. For companies with lifetime up to 10–15 years, the decreasing of critical value of tax on profit rate T with k0 is observed. At further increase of company lifetime one observes in dependence of T on k0 a smooth transition to a low growing function T on k0. So, for companies with lifetime up to 10–15 years monotonic growing of k0 favors to new effect, while for companies with longer lifetime rates of order k0 ≈ 12 % - 15% favors to new effect.

9.5

Practical Value of Effect

80

177

T*(k0)

T*

70 60

8

50

7

40

6 1 5 2 4 3

30 20 10 0

k0 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Fig. 9.13 The dependence of the critical value of tax on profit rate T on k0 at constant difference between them Δk = k0 - kd = 2% (1—n = 2; 2—n = 3; 3—n = 5; 4—n = 7; 5—n = 10; 6— n = 15; 7—n = 20; 8—n = 25)

9.5

Practical Value of Effect

What is the practical value of effect? Does it exist in real life or its discovery has a purely theoretical interest? Because a new effect takes place at tax on profit rate, which is bigger some value T*, it is necessary to compare this value with real tax on profit rates established in the different countries. The biggest tax on profits of corporation rate is in the USA—39.2%. In Japan, it exceeds a little bit 38%. In France, tax on profits of corporation rate varies from 33.3% for small- and medium-sized companies, up to 36% for the major. In England, tax on profits of corporation rate is in the range of 21–28%. In the Russian Federation, tax on profits of corporation rate is installed in the amount of 20%. In considered by us examples the value T* strongly depends on the ratio between k0, kd, n and reaches a minimal value of 22.2%, and it is quite likely even lower values of T* with other ratios between k0, kd, n. In this way, we come to the conclusion, that at some ratios between equity cost, debt cost, and company lifetime k0, kd, n discovered by us effect takes place at tax on profits of corporation rate established in most developed countries, that provides the practical value of effect.

178

9

A Qualitatively New Effect in Corporate Finance: Abnormal Dependence. . .

Its account is important in improving tax legislation and may change dividend policies of the company. Opening the effect expands our view of the rules of the game in the economy. If prior to that it was widely known that, with the rising of leverage the cost of equity is always growing, that is associated with the decrease in financial sustainability of the companies, with an increase in the share of borrowing, when the shareholders require higher rate of return on the share. But now it becomes clear that this is not always the case, and the dependence of cost of equity on leverage depends on the ratio between the parameters k0, kd, n, and, ultimately, on the tax on profit rate. This effect has never been known, therefore, it was not taken into account by controls tax legislation, but possibilities here are opening tremendous. The effect is also important for the development of the dividend policy of the company. It turns out that the rule taken by the shareholders since immemorial time to require higher rate of return on the share with an increase in the share of debt capital now does not always work. This will allow company management to hold a more realistic dividend policy, limiting appetites of shareholders by economically founded value of dividends.

9.6

Equity Cost of 1-Year Company

The dependence of the cost of equity on tax on profit rate T for 1-year company has some features considered below. Interest in the 1-year companies is associated also with the fact that a great number of companies, both in developed countries and in developing ones go bankrupt or no longer exist in the first year or two after the creation. For 1-year company the Brusov–Filatova–Orekhova (BFO) equation for weighted average cost of capital is simplified and can be expressed in apparent form (Brusov et al. 2011–d, 2012a, b, 2013, b, 2014, b; Brusov and Filatova 2011; Filatova et al. 2008) (Eq. 9.8) WACC = k0 -

1 þ k0 k w T: 1 þ kd d d

This formula has been obtained for the first time by Meyers (Myers 2001) and is the particular case of the Brusov–Filatova–Orekhova (BFO) equation at n = 1. By definition for weighted average cost of capital with accounting “the tax shield” one has WACC = k e we þ kd wd ð1- T Þ:

ð9:9Þ

9.6

Equity Cost of 1-Year Company

179

Ke (T)

Fig. 9.14 Dependence of cost of equity ke of the company on tax on profit rate T at fix leverage level for 1-year company (n = 1, k0 = 10 % , kd = 8%)

Ke 0.3000

5 4

0.2500 0.2000

3 2 1

0.1500 0.1000 0.0500

0

0.2

0.4

0.6

0.8

1

1.2

0.0000

T

Substituting here the expression for WACC of 1-year company, let us find the expression for cost of equity ke of the company ke =

  WACC - wd k d ð1 - T Þ kd : = k0 þ Lðk0- kd Þ 1- T we 1 þ kd

ð9:10Þ

It is seen that cost of equity ke decreases linearly with tax on profit rate. The module of negative tilt angle tangent is equal to tgα = Lðk 0- kd Þ

kd 1 þ kd

ð9:11Þ

However, the calculation for the case k0 = 10 % , kd = 8% gives practically independence of cost of equity ke of the company tax on profit rate T at fix leverage level (Fig. 9.14). kd , which in our case is equal This is due to the low value of coefficient ðk0- kd Þ 1þk d to 0.00148.. Therefore, descending becomes visible only at significant higher leverage (Fig. 9.14). Note that such a weak dependence (virtually independence) of cost of equity ke of the company on tax on profit rate T at fix leverage level takes place for 1-year company only. Already for 2-year company with the same parameters dependence of cost of equity ke of the company on tax on profit rate T at fix leverage level becomes significant. Below we give an example for 2-year company with other parameters n = 2, k0 = 24 % , kd = 22% (Fig. 9.15). Finding a Formula for T* In case of 1-year company it is easy to find a formula for T*. Putting in (Eq. 9.10) ke = k0, one gets

180

9

A Qualitatively New Effect in Corporate Finance: Abnormal Dependence. . .

Ke (t), n = 2, Kd = 22%, K0 = 24%

Ke

0.4000

0.3000

0.2000

0.1000

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

0.0000

-0.1000

-0.2000

T

Fig. 9.15 Dependence of cost of equity ke of the company on tax on profit rate T at fix leverage level for 2-year company (n = 2, k0 = 24 % , kd = 22%)

 k0 = k0 þ Lðk 0- kd Þ 1- T

kd 1 þ kd

 ð9:12Þ

From where T =

1 þ kd kd

ð9:13Þ

It is seen, that T does not depend on L, i.е. all the direct lines, corresponding to different L, intersect at a single point. From the data for the older companies (n > 1 year) it follows that similar situation takes place for them as well, however, to prove this fact becomes more difficult and in case n > 3practically impossible. Note, that equation (Eq. 9.13) allows to evaluate the value T, which depends now on credit rate only and is equal to: for kd = 8% T = 13.5 for kd = 10% T = 11 for kd = 15% T = 7.7 for kd = 25% T = 5 for kd = 100% T = 2

9.6

Equity Cost of 1-Year Company

181

Ke(t,L) for n = 1

Ke 0.3000

0.2500

0.2500-0.3000

0.2000

0.2000-0.2500 0.1500-0.2000

0.1500

0.1000-0.1500 0.0500-0.1000

0.1000

0.0000-0.0500

0.0500

0.0000

0

0.2

0.4

T

0.6

0.8

01

4

2

6

8

L

Fig. 9.16 Dependence of cost of equity ke of the company on tax on profit rate T and leverage level L (n = 1, k0 = 10 % , kd = 8%)

It is clear that for all (reasonable and unreasonable) credit rate values tax on profit rate T* is situated in “nonfinancial” region (exceeds 1 (100%)), that is the cause of the absence of effect. Analysis of the formula (Eq. 9.13) shows that at very large credit rate values T, T* tends to 1(100%), always remaining greater than 1. This means, that found by us effect is absent for 1-year company. Let us show the 3D picture for dependence of cost of equity ke of the company on tax on profit rate T and leverage level L for 1-year company (Fig. 9.16). It is seen that all dependences of cost of equity ke of the company on tax on profit rate T and leverage level L are linear, and abnormal effect for 1-year company (as well as for perpetuity one) is absent.

182

9.7

9

A Qualitatively New Effect in Corporate Finance: Abnormal Dependence. . .

Conclusions

Qualitatively new effect in corporative finance is discovered: decreasing of cost of equity ke with leverage L. This effect, which is absent in perpetuity Modigliani– Miller limit, takes place under account of finite lifetime of the company at tax on profit rate, which exceeds some value T* (Brusov et al. 2011–d, 2012a, b, 2013, b, 2014, b; Brusov and Filatova 2011; Filatova et al. 2008). At some ratios between debt cost and equity cost the discovered effect takes place at tax on profit rate, existing in western countries and Russia. This provides the practical meaning of discussed effect. Its accounting is important at modification of tax low and can change the dividend policy of the company. In this Chapter, the complete and detailed investigation of discussed effect, discovered within Brusov–Filatova–Orekhova (BFO) theory, has been done (Brusov et al. 2011–d, 2012a, b, 2013, b, 2014, b; Brusov and Filatova 2011; Filatova et al. 2008). It has been shown that the absence of the effect at some particular set of parameters is connected to the fact, that in these cases T* exceeds 100% (tax on profit rate is situated in a “non–financial” region). In future, the papers and monographs will be devoted to discussion of discovered abnormal effect, but it is already now clear, that we will have to abandon of some established views in corporative finance.

References Brusov PN, Filatova ТV (2011) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Financ Credit 435:2–8 Brusov P, Filatova T, Eskindarov M, Orehova N (2012a) Influence of debt financing on the effectiveness of the finite duration investment project. Appl Financ Econ 22(13):1043–1052 Brusov P, Filatova T, Eskindarov M, Orehova N (2012b) Hidden global causes of the global financial crisis. J Rev Glob Econ 1:106–111 Brusov P, Filatova T, Orehova N (2013) A qualitatively new effect in corporative finance: abnormal dependence of cost of equity of company on leverage. J Rev Glob Econ 2:183–193 Brusov P, Filatova T, Orehova N (2014) Inflation in Brusov–Filatova–Orekhova theory and in its perpetuity limit – Modigliani – Miller theory. J Rev Glob Econ 3:175–185 Brusov P, Filatova T, Orehova N, Brusov PP, Brusova N (2011) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Bus ICT 2:16–21 Brusov P, Filatova T, Orehova N, Brusova A (2011) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Appl Financ Econ 21(11): 815–824 Brusov P, Filatova T, Orehova N et al (2011b) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Bus ICT 2:16–21 Brusov P, Filatova T, Orehova N et al (2011c) Influence of debt financing on the effectiveness of the investment project within the Modigliani–Miller theory. Res J Econ Bus ICT (UK) 2:11–15 Brusov P, Filatova P, Orekhova N (2013) Absence of an optimal capital structure in the famous tradeoff theory! J Rev Glob Econ 2:94–116

References

183

Brusov P, Filatova P, Orekhova N (2014) Mechanism of formation of the company optimal capital structure, different from suggested by trade off theory. Cogent Econ Financ 2:1–13. https://doi. org/10.1080/23322039.2014.946150 Filatova Т, Orehova N, Brusova А (2008) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Bull FU 48:68–77 Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Modigliani F, Miller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391 Myers S (2001) Capital structure. J Econ Perspect 15(2):81–102

Chapter 10

Inflation in Brusov–Filatova–Orekhova Theory and in Its Perpetuity Limit: Modigliani–Miller Theory

Keywords Brusov–Filatova–Orekhova (BFO) theory · Modigliani–Miller theory · Inflation · Debt financing · The weighted average cost of capital · Equity cost · Debt cost · Company capitalization In this Chapter, the influence of inflation on capital cost and capitalization of the company within modern theory of capital cost and capital structure—Brusov– Filatova–Orekhova theory (BFO theory) (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011; Filatova et al. 2008) and within its perpetuity limit—Modigliani–Miller theory (Мodigliani and Мiller 1958, 1963, 1966) is investigated. By direct incorporation of inflation into both theories, it is shown for the first time, that inflation not only increases the equity cost and the weighted average cost of capital, but as well it changes their dependence on leverage. In particular, it increases growing rate of equity cost with leverage. Capitalization of the company is decreased under accounting of inflation.

10.1

Introduction

Created more than half a century ago by Nobel Prize winners Modigliani and Miller theory of capital cost and capital structure (Мodigliani and Мiller 1958, 1963, 1966) did not account a lot of factors of a real economy, such as taxing, bankruptcy, unperfected capital markets, inflation, and many others. But while taxing has been included into consideration by authors themselves and some other limitations have been taken off by their followers, direct incorporation of inflation to Modigliani– Miller theory is absent still now. The influence of inflation on valuation of capital cost of company and its capitalization is investigated within Modigliani–Miller theory (ММ) (Мodigliani and Мiller 1958, 1963, 1966), which is now outdate, but still widely used at the West, as well as within modern theory of capital cost and capital structure—Brusov– Filatova–Orekhova theory (BFO theory) (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011; Filatova et al. 2008), which should replace © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_10

185

186

10

Inflation in Brusov–Filatova–Orekhova Theory and in Its Perpetuity Limit:. . .

Modigliani–Miller theory (Мodigliani and Мiller 1958, 1963, 1966). It is shown that inflation not only increases the equity cost and the weighted average cost of capital, but as well it changes their dependence on leverage. In particular, it increases growing rate of equity cost with leverage. Capitalization of the company is decreased under accounting of inflation. We start from the study of inflation within Modigliani–Miller theory without taxing (Мodigliani and Мiller 1958), than with taxing (Мodigliani and Мiller 1963) and finally within modern theory of capital cost and capital structure—Brusov– Filatova–Orekhova theory (BFO theory) (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011; Filatova et al. 2008).

10.2

Accounting of Inflation in Modigliani–Miller Theory Without Taxes

Note that any modification of Modigliani–Miller theory, as well as of any other one, requires going behind the frame of modified theory. Thus, in current case we should go behind the frame of perpetuity of the company (remind to reader, that Modigliani–Miller theory describes only perpetuity companies—companies with infinite lifetime), come to the companies with finite lifetime, make necessary calculations and then use the perpetuity limit. As known, in profit approach capitalization of the company is equal to discounted sum of profits of the company. Suppose that profit is constant for all periods and equal to CF, one gets for capitalization of the financially independent company V0, existing n years at market V0 =

CF CF CF þ þ⋯þ : 1 þ k 0 ð1 þ k 0 Þ2 ð1 þ k 0 Þn

ð10:1Þ

Here k0 capital cost of the financially independent company. Under inflation with rate α the capitalization of the financially independent company V 0 becomes equal to V 0 =

CF CF CF þ⋯þ : þ ð1 þ k 0 Þð1 þ αÞ ½ð1 þ k0 Þð1 þ αÞ2 ½ð1 þ k0 Þð1 þ αÞn

ð10:2Þ

Using the formula for sum of the terms of indefinitely diminishing geometrical progression with the first term a1 = and denominator

CF ð1 þ k 0 Þð1 þ α Þ

ð10:3Þ

10.2

Accounting of Inflation in Modigliani–Miller Theory Without Taxes

q=

1 ð1 þ k0 Þð1 þ αÞ

187

ð10:4Þ

one gets for capitalization of the financially independent company V 0 the following expression: V 0 = =

CF a1 h i= = 1 - q ð1 þ k Þð1 þ αÞ 1 - ðð1 þ k Þð1 þ αÞÞ - 1 0 0

CF CF = : ð1 þ k0 Þð1 þ αÞ - 1 k 0 ð1 þ αÞ þ α V 0 =

CF : k 0 ð1 þ αÞ þ α

ð10:5Þ

It is seen, that under accounting of inflation the capitalization of the company decreases. At discount rate k0 = 10% and inflation rate α = 3% the decrease is equal to 5.7%, and at discount rate k0 = 15% and inflation rate α = 7% the decrease is equal to 35%. One can see that influence of inflation on the company capitalization could be significant enough and negative. For leverage company, using debt capital one has without inflation

VL =

CF CF CF þ þ⋯þ , 1 þ WACC ð1 þ WACCÞ2 ð1 þ WACCÞn

ð10:6Þ

and in perpetuity limit VL =

CF WACC

ð10:7Þ

Under accounting of inflation the capitalization of the company is equal to V L = þ

CF CF þ þ⋯ ð1 þ WACCÞð1 þ αÞ ½ð1 þ WACCÞð1 þ αÞ2

CF : ½ð1 þ WACCÞð1 þ αÞn

ð10:8Þ

Summing the infinite set, we get for leverage company capitalization under accounting of inflation in Modigliani–Miller limit

188

10

V L = =

Inflation in Brusov–Filatova–Orekhova Theory and in Its Perpetuity Limit:. . .

CF a1 h i= = 1 - q ð1 þ WACCÞð1 þ αÞ 1 - ðð1 þ WACCÞð1 þ αÞÞ - 1

CF CF = ð1 þ WACCÞð1 þ αÞ - 1 WACCð1 þ αÞ þ α V L =

CF : WACCð1 þ αÞ þ α

ð10:9Þ

It is seen, that similar to the case of the financially independent company inflation decreases the company capitalization and the decrease could be significant. From the formulas (Eqs. 10.7) and (10.9), it follows that effective values of capital costs (equity and WACC) are equal to k0 = k0 ð1 þ αÞ þ α

ð10:10Þ

WACC = WACC  ð1 þ αÞ þ α

ð10:11Þ

Note that both capital costs increase under inflation. We can compare obtained results with Fisher formula for inflation. i =

i-α : 1þα

ð10:12Þ

Solving this equation with respect to nominal rate i, one gets equation, similar to (Eqs. 10.10) and (10.11) i = i  ð1 þ αÞ þ α:

ð10:13Þ

Thus, effective capital costs in our case have meaning of nominal ones, accounting inflation. From the Modigliani–Miller theorem, that the weighted average cost of capital WACC does not depend on leverage level (without taxing), formulating under accounting of inflation, it is easy to get expression for the equity cost: WACC = k0 = ke we þ kd wd :

ð10:14Þ

Finding from here ke , one gets:  D k0 k ðS þ DÞ w D - kd d = 0 = k0 - kd = k 0 þ k 0 - kd we we S S S   þ k 0 - k d L

ke =

Putting instead of k0 , k d their expressions, one gets finally

ð10:15Þ

10.2

Accounting of Inflation in Modigliani–Miller Theory Without Taxes

189

Fig. 10.1 Dependence of the equity cost and the weighted average cost of capital on leverage in the Modigliani–Miller theory without taxing under accounting of inflation. It is seen, that growing rate of equity cost increases with leverage. Axis y means capital costs–C.C

  ke = k0 þ k 0 - kd L = k 0 ð1 þ αÞ þ αþ þLðk0 - kd Þð1 þ αÞ = ð1 þ αÞ½k 0 þ α þ Lðk0 - kd Þ ke = k0 ð1 þ αÞ þ α þ Lðk 0- k d Þð1 þ αÞ:

ð10:16Þ

It is seen that inflation not only increases the equity cost, but as well it changes its dependence on leverage. In particular, it increases growing rate of equity cost with leverage by multiplier (1 + α). The growing rate of equity cost with leverage, which is equal to (k0 - kd) without inflation becomes equal to (k0 - kd)(1 + α) under accounting of inflation (Fig. 10.1). Thus, we come to conclusion, that it is necessary to modify the second statement of the Modigliani–Miller theory (Мodigliani and Мiller 1958) concerning the equity cost of leverage company. 2-nd Original MM Statement Equity cost of leverage company ke could be found as equity cost of financially independent company k0 of the same group of risk, plus premium for risk, which value is equal to production of difference (k0 - kd)on leverage level L.

190

10

Inflation in Brusov–Filatova–Orekhova Theory and in Its Perpetuity Limit:. . .

2-nd Modified MM-BFO Statement Under existing of inflation with rate α equity cost of leverage company ke could be found as equity cost of financially independent company k0 of the same group of risk, multiplied by (1 + α), plus inflation rate α and plus premium for risk, which value is equal to production of difference (k0 - kd) on leverage level L and on multiplier (1 + α).

10.3

Accounting of Inflation in Modigliani–Miller Theory with Corporate Taxes

Let us calculate first the tax shield for perpetuity company under accounting of inflation ðPVÞTS = kd DT

1  X t=1

1 þ kd

-t

= DT

ð10:17Þ

It is interesting to note that inspite of dependence of each term of set on effective credit rate kd tax shield turns out to be independent of it and equal to “inflationless” value DТ and Modigliani–Miller theorem under accounting of inflation takes the form (Мodigliani and Мiller 1963) V L = V 0 þ DT:

ð10:18Þ

V L = CF=k0 þ wd V L T

ð10:19Þ

V L ð1- wd T Þ = CF=k 0 :

ð10:20Þ

Substituting D = wd V L , one gets

or

Because leverage company capitalization is equal to V L = CF=WACC for the weighted average cost of capital one has WACC = k0 ð1- wd T Þ:

ð10:21Þ

From (Eq. 10.21), we get the dependence of WACC on leverage level L = D/S: WACC = k0 ð1=LT ð1 þ LÞÞ:

10.3

Accounting of Inflation in Modigliani–Miller Theory with Corporate Taxes

WACC = ½k0 ð1 þ αÞ þ α  ð1- wd T Þ

191

ð10:22Þ

On definition of the weighted average cost of capital with accounting of the tax shield one has WACC = k0 we þ k d wd ð1- T Þ:

ð10:23Þ

Equating right hand parts of expressions (Eqs. 10.21) and (10.23), we get k0 ð1- wd T Þ = k 0 we þ kd wd ð1- T Þ,

ð10:24Þ

from where one obtains the following expression for equity cost: ð1 - w d T Þ w 1 w D - kd d ð1 - T Þ = k e - k0 d T - kd ð1 - T Þ = we S we we we ke   D þ S D D = k 0 - k 0 T - kd ð1 - T Þ = k0 þ Lð1 - T Þ k0 - kd : S S S      = k 0 þ Lð1- T Þ k0 - kd = ½k 0 ð1 þ αÞ þ α þ Lð1- T Þðk 0- k d Þ  ð1 þ α Þ

ke = k0

ð10:25Þ It is seen, that similar to the case without taxes inflation not only increases the equity cost, but as well it changes its dependence on leverage (Fig. 10.2). In particular, it increases growing rate of equity cost with leverage by multiplier (1 + α). The growing rate of equity cost with leverage, which is equal to (k0 - kd) (1 - T ) without inflation becomes equal to (k0 - kd)(1 + α)(1 - T) under accounting of inflation. We can now reformulate the fourth statement of the Modigliani–Miller theory (Мodigliani and Мiller 1963) concerning the equity cost of leverage company for case of accounting of inflation. 4-th Original MM Statement Equity cost of leverage company ke paying tax on profit could be found as equity cost of financially independent company k0 of the same group of risk, plus premium for risk, which value is equal to production of difference (k0 - kd)on leverage level L and on tax shield (1-T) and on multiplier (1 + α). 4-th Modified MM-BFO Statement Equity cost of leverage company ke paying tax on profit under existing of inflation with rate α could be found as equity cost of financially independent company k0 of the same group of risk, multiplied by (1 + α), plus inflation rate α and plus premium for risk, which value is equal to production of difference (k0 - kd) on leverage level L, on tax shield (1-T) and on multiplier (1 + α).

192

10

Inflation in Brusov–Filatova–Orekhova Theory and in Its Perpetuity Limit:. . .

Fig. 10.2 Dependence of the equity cost and the weighted average cost of capital on leverage in the Modigliani–Miller theory with taxing under accounting of inflation. It is seen, that growing rate of equity cost increases with leverage. Axis y means capital costs–C.C

10.4 Accounting of Inflation in Brusov–Filatova–Orekhova Theory with Corporate Taxes 10.4.1 Generalized Brusov–Filatova–Orekhova Theorem Brusov–Filatova–Orekhova, generalized the Modigliani–Miller theory for the case of the companies with arbitrary lifetime (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011; Filatova et al. 2008), have proved the following important theorem in case of absence of corporate taxing: Without corporate taxing the equity cost k0, as well as the weighted average cost of capital WACC does not depend on company lifetime and is equal to

10.4

Accounting of Inflation in Brusov–Filatova–Orekhova Theory. . .

ke = k0 þ Lðk0- kd Þ

and WACC = k0 :

193

ð10:26Þ

consequently. Thus, the theorem has been proved, that without corporate taxes (say, in offshore zones) the Modigliani–Miller results for capital costs, in spite of the fact, that they have been obtained in perpetuity limit, remain in force for companies with arbitrary lifetime, describing by Brusov–Filatova–Orekhova theory (BFO theory). To prove this theorem Brusov, Filatova, and Orekhova, of course, had to go behind Modigliani–Miller approximation. Under accounting of inflation we can generalize this theorem (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011; Filatova et al. 2008): Generalized Brusov–Filatova–Orekhova Theorem Under accounting of inflation without corporate taxing the equity cost k 0, as well as the weighted average cost of capital WACC does not depend on company lifetime and is equal to   ke = k0 þ L k 0 - k d = k 0 ð1 þ αÞ þ α þ Lðk0- kd Þð1 þ αÞ and WACC = k 0 = k 0 ð1 þ αÞ þ α:

ð10:27Þ

consequently. Following to Brusov–Filatova–Orekhova (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011; Filatova et al. 2008), let us consider the situation for arbitrary lifetime companies with account of corporate taxing. They have derived the famous formula for weighted average cost of capital of companies with arbitrary lifetime 1 - ð1 þ k 0 Þ - n 1 - ð1 þ WACCÞ - n = WACC k0 ½1 - ωd T ð1 - ð1 þ kd Þ - n Þ

ð10:28Þ

The application of BFO formula (10.28) is very wide: authors have applied it in corporate finance, in investments, in taxing, in business valuation, in banking, and some other areas (Brusov et al. 2011a, b, 2013a). Using this formula (10.28), one can study the dependence of the weighted average cost of capital, WACC, as well as the equity cost ke on leverage level L, on tax on profit rate t, on lifetime of the company n, and on relation between equity and debt cost. The qualitatively new effect in corporate finance has been discovered: decrease of the equity cost ke on leverage level L, which is quite important for corporate finance in general and, in particular, for creating the adequate dividend policy. Below we generalize formula (10.28) under existing of inflation.

194

10

10.5

Inflation in Brusov–Filatova–Orekhova Theory and in Its Perpetuity Limit:. . .

Generalized Brusov–Filatova–Orekhova Formula Under Existing of Inflation

Under existing of inflation it is necessary to replace all capital costs: the equity, the debt, and the weighted average cost of capital k0, kd, WACC by effective ones k 0 , k d , WACC , where k0 = k0 ð1 þ αÞ þ α k d = kd ð1 þ αÞ þ α WACC = WACC  ð1 þ αÞ þ α Rewriting the equations for tax shield (TS)n, capitalization of financially independent company V 0 as well as for financially dependent company V L for the case of existing of inflation, one gets ðPVÞTS = ðTSÞn = kd DT V 0 = CF V L = CF

n X

n  X t=1

n  X t=1

1 þ k d

1 þ k 0

-t

-t

   - n = DT 1- 1 þ k d

   - n  =k0 = CF 1- 1 þ k 0

ð1 þ WACC Þ - t = CF½1- ð1 þ WACC Þ - n =WACC

ð10:29Þ ð10:30Þ ð10:31Þ

t=1

V L = V 0 þ ðTSÞn ,

ð10:32Þ

After substitution D = wd V L we have V L = CF=k0 þ wd V L T

ð10:33Þ

From here after some transformations we get generalized Brusov–Filatova– Orekhova formula under existing of inflation  -n 1 - 1 þ k 0 1 - ð1 þ WACC Þ - n     - n  , =  WACC k0 1 - ωd T 1 - 1 þ kd or after substitutions k0 = k0 ð1 þ αÞ þ α; one gets finally

kd = k d ð1 þ αÞ þ α

ð10:34Þ

10.5

Generalized Brusov–Filatova–Orekhova Formula Under Existing of Inflation

195

WACC(wd), k0=20%, kd=12%, T=20%

WACC 0.35 0.30 0.25

4 3 2 1

0.20 0.15 0.10 0.05 0.00

0

0.1

0.2

0.3

0.4

0.5 0.6 Wd

0.7

0.8

0.9

1

1.1

Fig. 10.3 Dependence of the weighted average cost of capital WACC on debt ratio wd at different inflation rate α (1—α = 3%; 2—α = 5%; 3—α = 7%; 4—α = 9%) for 5-year company

1 - ð1 þ WACC Þ - n WACC 1 - ½ð1 þ k 0 Þð1 þ αÞ - n = ðk0 ð1 þ αÞ þ αÞ  ½1 - ωd T ð1 - ðð1 þ k d Þð1 þ αÞÞ - n Þ

ð10:35Þ

Formula (10.35) is the generalized Brusov–Filatova–Orekhova formula under existing of inflation. Let us show some figures, illustrating obtained results. At Figs. 10.3 and 10.4, the dependence of the weighted average cost of capital WACC on debt ratiowdat different inflation rate α (1—α = 3%; 2—α = 5%; 3—α = 7%; 4—α = 9%) for 5-year company as well as for 2-year company. It is seen that with increase of inflation rate lines, showing the dependence of WACC (wd) shifts practically homogeneously to higher values. It is seen that difference in results for 2-year company and 5-year company is very small. More obviously it could be observed from below tables (Tables 10.1 and 10.2).

196

10

Inflation in Brusov–Filatova–Orekhova Theory and in Its Perpetuity Limit:. . .

WACC(wd), k0=20%, kd=12%, T=20%

WACC

0.35 0.30 0.25

4 3 2 1

0.20 0.15 0.10 0.05 0.00

Wd 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Fig. 10.4 Dependence of the weighted average cost of capital WACC on debt ratio wd at different inflation rate α (1—α = 3%; 2—α = 5%; 3—α = 7%; 4—α = 9%) for 2-year company

Below we show the dependences of the weighted average cost of capital WACC on debt ratio wd at different tax on profit rate from T = 10% up to T = 100% at different inflation rate α = 3, 5, 7, 9% for 5-year company (Figs. 10.5, 10.6, 10.7, and 10.8) as well as for 2-year company (Figs. 10.9, 10.10, 10.11, and 10.12). Tax on profit rate increases from T = 0.1 (upper line) up to T = 1 (lowest line) with the step 0.1. The analysis of Figs. 10.5, 10.6, 10.7, 10.8, 10.9, 10.10, 10.11, and 10.12 shows that the weighted average cost of capital WACC decreases with debt ratio wd faster with increase of tax on profit rate. The space between lines, corresponding to different tax on profit rates, increases with inflation rate. The variation range of WACC increases with inflation rate as well as with lifetime of the company.

10.6

Irregular Inflation

Above we considered inflation rate as constant. Really, as a rule, the inflation rate is a variable. It is possible to generalize all above consideration for the case of non-homogeneous inflation, introducing effective inflation for a few periods. The effective inflation rate for a few periods t = t1 + t2 + ⋯ + tn is equal to

0.1 0.2318 0.2557 0.2786 0.3020

0.2 0.2276 0.2503 0.2733 0.2960

0.3 0.2233 0.2455 0.2679 0.2900

0.4 0.2191 0.2406 0.2626 0.2839

0.5 0.2149 0.2358 0.2573 0.2779

0.6 0.2106 0.2309 0.2514 0.2720

0.7 0.2064 0.2261 0.2459 0.2661

0.8 0.2021 0.2212 0.2404 0.2602

0.9 0.1979 0.2164 0.2350 0.2537

1 0.1937 0.2115 0.2295 0.2476

α\wd 0.03 0.05 0.07 0.09

0.1 0.2311 0.2546 0.2781 0.3015

0.2 0.2262 0.2491 0.2718 0.2947

0.3 0.2213 0.2434 0.2657 0.2879

0.4 0.2163 0.2379 0.2595 0.2812

0.5 0.2113 0.2323 0.2534 0.2744

0.6 0.2064 0.2267 0.2472 0.2676

0.7 0.2013 0.2210 0.2408 0.2608

0.8 0.1963 0.2154 0.2346 0.2539

0.9 0.1912 0.2097 0.2283 0.2471

1 0.1863 0.2040 0.2219 0.2400

Table 10.2 Dependence of the weighted average cost of capital WACC on debt ratio wd at different inflation rate α = 3; 5; 7; 9% for 5-year company

α\wd 0.03 0.05 0.07 0.09

Table 10.1 Dependence of the weighted average cost of capital WACC on debt ratio wd at different inflation rate α = 3; 5; 7; 9% for 2-year company

10.6 Irregular Inflation 197

198

10

Inflation in Brusov–Filatova–Orekhova Theory and in Its Perpetuity Limit:. . .

WACC(wd), k0=20%, kd=12%, a=3%

WACC 0.35

0.25

0.15

0.05

-0.05

0

0.1

0.2

-0.15

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Wd

Fig. 10.5 Dependence of the weighted average cost of capital WACC on debt ratio wd at different tax on profit rate at inflation rate α = 3% for 5-year company. Tax on profit rate increases from T = 0.1 (upper line) up to T = 1 (lowest line) with step 0.1

α = ð1 þ α1 Þð1 þ α2 Þ⋯ð1 þ αn Þ - 1,

ð10:36Þ

where α1, α2, . . ., αn are inflation rates for periods t1, t2, . . ., tn. The proof of the formula (10.36) will be done below in 10.6. In the case of non-homogeneous inflation it could be accounted in both theories: Modigliani–Miller and Brusov–Filatova–Orekhova theory (BFO theory) either through effective inflation rate or directly upon discounting of financial flow.

10.7

Conclusions

In this Chapter, the influence of inflation on capital cost and capitalization of the company within modern theory of capital cost and capital structure—Brusov– Filatova–Orekhova theory (BFO theory) (Brusov et al. 2011a–d, 2012a, b, 2013a, b, 2014a, b; Brusov and Filatova 2011; Filatova et al. 2008) and in its perpetuity limit—Modigliani–Miller theory (Мodigliani and Мiller 1958, 1963, 1966), which is now outdate, but still widely used at the West, is investigated. All basic results of Modigliani–Miller theory were modified. It is shown that inflation not only increases the equity cost and the weighted average cost of capital, but as

10.7

Conclusions

199

WACC(wd), k0=20%, kd=12%, a=5%

WACC 0.35

0.25

0.15

0.05

-0.05

0

0.1

0.2

0.3

0.4

-0.15

0.5

0.6

0.7

0.8

0.9

1

1.1

Wd

Fig. 10.6 Dependence of the weighted average cost of capital WACC on debt ratio wd at different tax on profit rate at inflation rate α = 5% for 5-year company. Tax on profit rate increases from T = 0.1 (upper line) up to T = 1 (lowest line) with step 0.1

WACC(wd), k0=20%, kd=12%, a=7%

WACC 0.35 0.25 0.15

Wd

0.05 -0.05 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

-0.15 Fig. 10.7 Dependence of the weighted average cost of capital WACC on debt ratio wd at different tax on profit rate at inflation rate α = 7% for 5-year company. Tax on profit rate increases from T = 0.1 (upper line) up to T = 1 (lowest line) with step 0.1

well it changes their dependence on leverage. In particular, it increases growing rate of equity cost with leverage. Capitalization of the company is decreased under accounting of inflation.

200

10

Inflation in Brusov–Filatova–Orekhova Theory and in Its Perpetuity Limit:. . .

WACC(wd), k0=20%, kd=12%, a=9%

WACC 0.35 0.30 0.25 0.20 0.15 0.10 0.05

Wd

0.00

0

-0.05

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

-0.10 -0.15 Fig. 10.8 Dependence of the weighted average cost of capital WACC on debt ratio wd at different tax on profit rate at inflation rate α = 9% for 5-year company. Tax on profit rate increases from T = 0.1 (upper line) up to T = 1 (lowest line) with step 0.1

WACC(wd), k0=20%, kd=12%, a=3%

WACC 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00

Wd 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

-0.05 Fig. 10.9 Dependence of the weighted average cost of capital WACC on debt ratio wd at different tax on profit rate at inflation rate α = 3% for 2-year company. Tax on profit rate increases from T = 0.1 (upper line) up to T = 1 (lowest line) with step 0.1

10.7

Conclusions

201

WACC(wd), k0=20%, kd=12%, a=5%

WACC 0.35 0.25 0.15 0.05

Wd

-0.05 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Fig. 10.10 Dependence of the weighted average cost of capital WACC on debt ratio wd at different tax on profit rate at inflation rate α = 5% for 2-year company. Tax on profit rate increases from T = 0.1 (upper line) up to T = 1 (lowest line) with step 0.1

WACC(wd), k0=20%, kd=12%, a=7%

WACC 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 -0.05

Wd 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Fig. 10.11 Dependence of the weighted average cost of capital WACC on debt ratio wd at different tax on profit rate at inflation rate α = 7% for 2-year company. Tax on profit rate increases from T = 0.1 (upper line) up to T = 1 (lowest line) with step 0.1

Within modern theory of capital cost and capital structure—Brusov–Filatova– Orekhova theory (BFO theory) the modified equation for the weighted average cost of capital, WACC, applicable to companies with arbitrary lifetime under accounting of inflation has been derived. Modified BFO equation allows to investigate the dependence of the weighted average cost of capital, WACC, and equity cost, ke, on leverage level L, on tax on profit rate t, on lifetime of the company n, on equity

202

10

Inflation in Brusov–Filatova–Orekhova Theory and in Its Perpetuity Limit:. . .

WACC(wd), k0=20%, kd=12%, a=9%

WACC 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 -0.05

Wd 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Fig. 10.12 Dependence of the weighted average cost of capital WACC on debt ratio wd at different tax on profit rate at inflation rate α = 9% for 2-year company. Tax on profit rate increases from T = 0.1 (upper line) up to T = 1 (lowest line) with step 0.1

cost of financially independent company, k0, and debt cost, kd, as well as on inflation rate α . Using modified BFO equation the analysis of the dependence of the weighted average cost of capital, WACC, on debt ratio, wd, at different tax on profit rate t, as well as inflation rate α has been done. It has been shown that WACC decreases with debt ratio, wd, faster at bigger tax on profit rate t. The space between lines, corresponding to different values of tax on profit rate at the same step (10%), increases with inflation rate α. The variation region (with change of tax on profit rate t) of the weighted average cost of capital, WACC, increases with inflation rate α, as well as with lifetime of the company n.

10.8

Inflation Rate for a Few Periods

Suppose that the inflation rate for the consistent time periods t1, t2, . . ., tn is equal to α1, α2, . . ., αn consequently. Let us find the inflation rate α for total time period t = t1 + t2 + ⋯ + tn. Common sense dictates that inflation rate is an additive value, so that α, at least approximately, is equal to the sum of the inflation rates α1, α2, . . ., αn

References

203

α ≈ α1 þ α2 þ ⋯ þ αn :

ð10:37Þ

Below we will get an exact expression for inflation rate for the total period of time t, and will see how it is different from an intuitive result (10.37). At the end of the first commitment period the gained sum will be equal to the amount S1 = S0(1 + i), and with the account of inflation S1α = S0 ð1 þ iÞt1 =ð1 þ α1 Þ. At the end of the second commitment period the gained sum will be equal to the and with the account of inflation amount S2 = S0 ð1 þ iÞt1 þt2 , S2α = S0 ð1 þ iÞt1 þt2 =ð1 þ α1 Þð1 þ α2 Þ. At the end of the n-th commitment period the gained sum will be equal to the amount Sn = S0 ð1 þ iÞt1 þt2 þ⋯þtn , and with the account of inflation Snα = S0 ð1 þ iÞt1 þt2 þ⋯þtn =ð1 þ α1 Þð1 þ α2 Þ⋯ð1 þ αn Þ:

ð10:38Þ

On the other hand, at inflation rate α for the total period at t = t1 + t2 + ⋯ + tn at the end of this period t gained sum will be equal to Snα = S0 ð1 þ iÞt =ð1 þ αÞ:

ð10:39Þ

Equating the right-hand part of (10.38) and (10.39), we get ð1 þ α1 Þð1 þ α2 Þ⋯ð1 þ αn Þ = 1 þ α:

ð10:40Þ

α = ð1 þ α1 Þð1 þ α2 Þ⋯ð1 þ αn Þ - 1:

ð10:41Þ

From where

It is easy to get a strict proof of this formula by the method of mathematical induction. Note that inflation rate for the n–periods does not depend on both of the length of constituting periods and on the period t. For equal inflation rates α1 = α2 = ⋯ = αn (it is interesting to note, that herewith the time intervals t1, t2, . . ., tn can be arbitrary and do not equal each other) one has α = ð1 þ α1 Þn - 1:

ð10:42Þ

References Brusov PN, Filatova ТV (2011) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Financ Credit 435:2–8 Brusov P, Filatova T, Orehova N, Brusova A (2011a) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Appl Financ Econ 21(11): 815–824

204

10

Inflation in Brusov–Filatova–Orekhova Theory and in Its Perpetuity Limit:. . .

Brusov P, Filatova T, Orehova N et al (2011b) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Bus ICT 2:16–21 Brusov P, Filatova T, Orehova N et al (2011c) Influence of debt financing on the effectiveness of the investment project within the Modigliani–Miller theory. Res J Econ Bus ICT (UK) 2:11–15 Brusov P, Filatova T, Orehova N, Brusov PP, Brusova N (2011d) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Bus ICT 2:16–21 Brusov P, Filatova T, Eskindarov M, Orehova N (2012a) Influence of debt financing on the effectiveness of the finite duration investment project. Appl Financ Econ 22(13):1043–1052 Brusov P, Filatova T, Eskindarov M, Orehova N (2012b) Hidden global causes of the global financial crisis. J Rev Glob Econ 1:106–111 Brusov P, Filatova P, Orekhova N (2013a) Absence of an optimal capital structure in the famous tradeoff theory! J Rev Glob Econ 2:94–116 Brusov P, Filatova T, Orehova N (2013b) A qualitatively new effect in corporative finance: abnormal dependence of cost of equity of company on leverage. J Rev Glob Econ 2:183–193 Brusov P, Filatova P, Orekhova N (2014a) Mechanism of formation of the company optimal capital structure, different from suggested by trade off theory. Cogent Econ Financ 2:1–13. https://doi. org/10.1080/23322039.2014.946150 Brusov P, Filatova T, Orehova N (2014b) Inflation in Brusov–Filatova–Orekhova theory and in its perpetuity limit – Modigliani–Miller theory. J Rev Glob Econ 3:175–185 Filatova Т, Orehova N, Brusova А (2008) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Bull FU 48:68–77 Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Modigliani F, Miller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391

Chapter 11

Benefits of Advance Payments of Tax on Profit: Consideration Within Brusov– Filatova–Orekhova (BFO) Theory

Keywords Generalized Brusov–Filatova–Orekhova (BFO) theory · The Modigliani–Miller theory · Advance payments of income tax · Equity cost · The weighted average cost of capital · Company capitalization · A qualitatively new anomalous effect

11.1

Introduction

The importance of accounting for upfront payments rests on two points: (1) companies can pay tax payments upfront with subsequent adjustments if they earn a stable and predictable income; (2) the development of a methodology for advance payments allows the regulator to expand this practice, which ensures an increase in the stability of budget revenues. As results of this chapter show, the advance payments of tax on income are quite important for both parties: for companies and for regulator. We give below a short review of evolution of the theory of capital cost and capital structure. 1. The Modigliani-Miller (MM) theory, created by Nobel Prize winners in 1958 (Мodigliani and Мiller 1958), was the first quantitative theory of capital structure. It was based on many restrictions, the main of which were the absence of taxes and the perpetual nature of all financial flows and companies. The first limitation was removed by the MMs themselves (Мodigliani and Мiller 1963, 1966) and the following formulas were obtained: For tax shield, TS : TS = DT;

ð11:1Þ

For company value, V (financially independent company V0, leverage company, V:

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_11

205

206

11

Benefits of Advance Payments of Tax on Profit: Consideration. . .

V 0 = CF=k 0 and

V = CF=WACC:

ð11:2Þ

For weighted average cost of capital, WACC: WACC = k 0  ð1- wd t Þ;

ð11:3Þ

k e = k0 þ Lðk e- kd Þ  ð1- t Þ:

ð11:4Þ

For equity cost, ke:

2. Hаmаdа (1969) has derived the following formula for the leveraged company equity cost, accounting both financial and business risk of company, united the Modigliani–Miller theory with capital asset pricing model (CAPM): k e = kF þ ðkM- kF ÞbU þ ðkM- kF ÞbU

D ð1- T Þ, S

ð11:5Þ

where bU is the β-coefficient of the company of the same group of business risk, that the considering company, but with L = 0. 3. Merton Miller (1977) took into account the corporate and individual taxes. He got for the capitalization of the financially independent company the following formula:
 ð1 - T C Þð1 - T S Þ D V = V 0 þ 1ð1 - T D Þ

ð11:6Þ

Here, TC—the tax on corporate income rate, TS—the tax rate on income of an individual investor from his ownership by corporation stock, TD—tax rate on interest income from the provision of investor–individuals of credits to other investors and companies. 4. In 2008, Brusov–Filatova–Orekhova (Brusov et al. 2018, 2022) have lifted up the limitation concerning the perpetuity of flows and companies and created the modern theory of capital cost and capital structure—BFO theory—which describes the companies of arbitrary age (and arbitrary lifetime). The generalization of MM theory for the companies of arbitrary age (and arbitrary lifetime) required the modification of the valuation of the tax shield TS, as well as of the valuation of the company capitalization: financially independent, V0 as well as financially dependent, V. The following formulas were obtained: for the tax shield, TS, company value, V, and for the weighted average cost of capital WACC:

11.1

Introduction

207

TS = k d DT

n X

ð1 þ k d Þ - t = DT½1- ð1 þ kd Þ - n :

ð11:7Þ

t=1

V = CF½1- ð1 þ WACCÞ - n =WACC:

V 0 = CF½1- ð1 þ k0 Þ - n =k0 ; 1 - ð1 þ WACCÞ WACC

-n

=

-n

1 - ð1 þ k 0 Þ : k 0 ½1 - ωd T ð1 - ð1 þ kd Þ - n Þ

ð11:8Þ ð11:9Þ

D —the share of debt Here, S—the value of equity capital of the company, wd = DþS S capital, ke , we = DþS —the cost and the share of the equity capital of the company, and L = D/S—financial leverage, D—the value of debt capital. At n = 1, from BFO formula for WACC we get Myers (2001) formula for 1-year company.

WACC = k0 -

ð1 þ k0 Þkd wd T; 1 þ kd

ð11:10Þ

and at n = 1 we get Modigliani–Miller formula for WACC (Мodigliani and Мiller 1963): WACC = k0  ð1- wd t Þ

ð11:11Þ

Note that before BFO discovery (in 2008) there were two results only: Modigliani–Miller for perpetuity companies (Мodigliani and Мiller 1958, 1963, 1966) and Myers one for a year companies (Myers 2001). The accounting of the company’s finite age, as it was shown by BFO authors, leads to significant changes of all Modigliani–Miller results (Мodigliani and Мiller 1958, 1963, 1966). Besides, a number of qualitatively new effects in corporate finance, obtained in Brusov– Filatova–Orekhova theory (Brusov et al. 2018, 2022) are absent in Modigliani– Miller theory. 5. Recently, we have modified the Modigliani–Miller theory for the case of advanced payments of income tax (Brusov et al. 2020, 2022) and have shown that obtained results are quite different from the ones in “classical” Modigliani– Miller theory.

208

11

11.2

Benefits of Advance Payments of Tax on Profit: Consideration. . .

Modification of the Brusov–Filatova–Orekhova (BFO) Theory for Companies with Frequent Payments of Tax on Income

11.2.1

Calculation of the Tax Shield

Let us calculate the tax shield within Brusov–Filatova–Orekhova theory for the case of advance payments of tax on profit. The tax shield, TS, for period of n-years is equal to sum of the discounted values of benefits from the use of tax incentives ðTSÞn = k d Dt þ

k d Dt k d Dt kd Dt þ⋯þ þ ð 1 þ k d Þ ð1 þ k d Þ2 ð1 þ k d Þn - 1

ð11:12Þ

This expression represents a geometric progression with denominator q=

1 ð1 þ k d Þ

ð11:13Þ

After summing the progression, one obtains: ðTSÞn =

kd Dt ð1 - ð1 þ kd Þ - n Þ   = Dt ð1- ð1 þ k d Þ - n Þð1 þ kd Þ 1 - ð1 þ k d Þ - 1

ð11:14Þ

In classical Brusov–Filatova–Orekhova theory under payments at the end of periods one has ðTSÞn = Dt ð1- ð1 þ kd Þ - n Þ

11.2.2

ð11:15Þ

Company Value

For the financially dependent company value V we have V = V 0 þ ðTSÞn

ð11:16Þ

V = V 0 þ Dt ð1- ð1 þ kd Þ - n Þ  ð1 þ kd Þ:

ð11:17Þ

This formula differs from the equation for company value V in case of payments of income tax at the end of the year

11.2

Modification of the Brusov–Filatova–Orekhova (BFO) Theory for. . .

V = V 0 þ Dt ð1- ð1 þ kd Þ - n Þ:

11.2.3

209

ð11:18Þ

The Weighted Average Cost of Capital, WACC

Substituting D = wd V

ð11:19Þ

  V 1- wd t ð1- ð1 þ kd Þ - n Þ  ð1 þ kd Þ = V 0

ð11:20Þ

into (11.17), we get

Using the values of financially dependent company, V, and financially independent company, V0, V=

CFð1 - ð1 þ WACCÞ - n Þ CF ; V0 =  ð1- ð1 þ k 0 Þ - n Þ, WACC k0

ð11:21Þ

we come to the following intermediate equation  CFð1 - ð1 þ WACCÞ - n Þ   1- wd t  ð1- ð1 þ k d Þ - n Þ  ð1 þ k d Þ WACC CF =  ð1- ð1 þ k0 Þ - n Þ ð11:22Þ k0 and then to the final Brusov–Filatova–Orekhova equation for WACC for the case of advanced payments of income tax ð1 - ð1 þ WACCÞ - n Þ ð1 - ð1 þ k 0 Þ - n Þ  : =  WACC k 0 1 - wd t  ð 1 - ð 1 þ k d Þ - n Þ  ð 1 þ k d Þ

ð11:23Þ

This formula differs from the classical Brusov–Filatova–Orekhova equation by the factor (1 + kd) in the left denominator ð1 - ð1 þ WACCÞ - n Þ ð1 - ð1 þ k 0 Þ - n Þ  =  WACC k 0 1 - wd t  ð1 - ð1 þ k d Þ - n Þ

11.2.3.1

ð11:24Þ

Calculation of the Equity Cost

To calculate the equity cost ke one should use the equation of WACC definition

210

11

Benefits of Advance Payments of Tax on Profit: Consideration. . .

WACC = k e we þ k d wd ð1- t Þ

ð11:25Þ

from where one gets the expression for ke ke =

WACC kd ð1 - t Þwd = WACCð1 þ LÞ - Lkd ð1- t Þ: we we

ð11:26Þ

One should substitute WACC from the formula (11.12), calculating the equity cost ke for the case of advanced payments of income tax and from the formula (11.13), calculating the equity cost ke for the case of payments of income tax at the end of the year.

11.3

Results

Here, the dependence of the weighted average cost of capital, WACC, capital value, V, equity cost, ke, on leverage level L for 3-year and 6-year companies, using Microsoft Excel is being studied. We consider two types of payments of income tax: (1) at the end of the year and (2) in advance. As we mentioned above, for WACC we use formulas (11.12) and (11.13), for capital value, V, we use formulas (11.6) and (11.7), and for equity cost, ke, we use formula (11.15). We use the following parameters: k0 = 0.2; kd = 0.18; t = 0.2; n = 3; 6; CF = 100.

11.3.1

Dependence of the Weighted Average Cost of Capital, WACC, Capital Value, V, Equity Cost, ke, on Leverage Level L for 3-Year Company

Table 11.1 Dependence of the weighted average cost of capital, WACC, equity cost, ke, and company value, V, on leverage level L in the cases of payments of tax on profit at the end of the year (1) and in the beginning of the year (2) for 3-year company n=3 L 1 2 3 4 5 6 7 8 9 10

WACC 1 0.1749 0.1664 0.1622 0.1596 0.1579 0.1567 0.1558 0.1551 0.1545 0.1541

2 0.1703 0.1603 0.1553 0.1523 0.1503 0.1489 0.1478 0.1469 0.1463 0.1457

ke 1 0.2057 0.2113 0.2168 0.2222 0.2277 0.2331 0.2386 0.2440 0.2495 0.2549

2 0.1966 0.1930 0.1892 0.1855 0.1817 0.1780 0.1742 0.1704 0.1666 0.1628

V 1 219.2281 222.2455 223.7856 224.7199 225.3471 225.7973 226.1361 226.4003 226.6122 226.7858

2 220.8472 224.4700 226.3263 227.4549 228.2136 228.7586 229.1691 229.4893 229.7462 229.9568

11.3

Results

211

WACC (L) (1;2) n=3

WACC (L)

0.18 0.17 n=3 (1)

0.16

n=3 (2)

0.15 0.14 1

2

3

4

5

6

7

8

9

10

Fig. 11.1 Dependence of the weighted average cost of capital, WACC, on leverage level L in the cases of payments of tax on profit at the end of the year (1) and in the beginning of the year (2) for 3-year company

V (L) (1;2) n=3 229

V (L)

227 225

n=3 (1)

223

n=3 (2)

221 219 1

2

3

4

5

6

7

8

9

10

Fig. 11.2 Dependence of the company value, V, on leverage level L in the cases of payments of tax on profit at the end of the year (1) and in the beginning of the year (2) for 3-year company

Ke (L) (1;2) n=3 0.26

Ke (L)

0.24 0.22

n=3 (1)

0.2

n=3 (2)

0.18 0.16

1

2

3

4

5

6

7

8

9

10

Fig. 11.3 Dependence of the equity cost, ke on leverage level L in the cases of payments of tax on profit at the end of the year (1) and in the beginning of the year (2) for 3-year company

212

11

11.3.2

Benefits of Advance Payments of Tax on Profit: Consideration. . .

Dependence of the Weighted Average Cost of Capital, WACC, Capital Value, V, Equity Cost, ke, on Leverage Level L for 6-Year Company

Table 11.2 Dependence of the weighted average cost of capital, WACC, equity cost, ke and company value, V, on leverage level L in the cases of payments of tax on profit at the end of the year (1) and in the beginning of the year (2) for 6-year company n=6 L 1 2 3 4 5 6 7 8 9 10

WACC 1 0.1743 0.1657 0.1613 0.1586 0.1569 0.1556 0.1547 0.1539 0.1534 0.1529

ke 1 0.2047 0.2090 0.2131 0.2172 0.2213 0.2254 0.2294 0.2335 0.2376 0.2416

2 0.1697 0.1593 0.1542 0.1510 0.1489 0.1474 0.1463 0.1454 0.1447 0.1442

V 1 354.8940 363.0242 367.2305 369.8015 371.5355 372.7841 373.7261 374.4620 375.0529 375.5377

2 0.1953 0.1900 0.1846 0.1791 0.1736 0.1680 0.1624 0.1569 0.1513 0.1457

2 359.2385 369.1124 374.2557 377.4110 379.5443 381.0830 382.2451 383.1540 383.8841 384.4836

WACC (L) (1;2) n=6 0.18

WACC (L)

0.17 n=6 (1)

0.16

n=6 (2)

0.15 0.14

1

2

3

4

5

6

7

8

9

10

Fig. 11.4 Dependence of the weighted average cost of capital, WACC, on leverage level L in the cases of payments of tax on profit at the end of the year (1) and in the beginning of the year (2) for 6-year company

11.3

Results

213

V (L) (1;2) n=6 383

V (L)

378 373

n=6 (1)

368

n=6 (2)

363 358 353

1

2

3

4

5

6

7

8

9

10

Fig. 11.5 Dependence of the company value, V, on leverage level L in the cases of payments of tax on profit at the end of the year (1) and in the beginning of the year (2) for 6-year company

Ke (L) (1;2) n=6 0.26 0.24 Ke (L)

0.22 0.2

n=6 (1)

0.18

n=6 (2)

0.16 0.14 1

2

3

4

5

6

7

8

9

10

Fig. 11.6 Dependence of the equity cost, ke on leverage level L in the cases of payments of tax on profit at the end of the year (1) and in the beginning of the year (2) for 3-year company

214

11

11.4

Benefits of Advance Payments of Tax on Profit: Consideration. . .

Comparison of Results for 3-Year and 6-Year Companies WACC (L) (1;2) n=3 , n=6 0.174

WACC (L)

0.169 0.164

n=6 (1)

0.159

n=6 (2)

0.154

n=3 (1)

0.149

n=3 (2)

0.144 1

2

3

4

5

6

7

8

9

10

Fig. 11.7 Dependence of the weighted average cost of capital, WACC, on leverage level L in the cases of payments of tax on profit at the end of the year (1) and in the beginning of the year (2) for 3-year and 6-year companies

V (L)

V (L) (1;2) n=3 , n=6 378 368 358 348 338 328 318 308 298 288 278 268 258 248 238 228 218

n=3 (1) n=3 (2) n=6 (1) n=6 (2)

1

2

3

4

5

6

7

8

9

10

Fig. 11.8 Dependence of the company value, V, on leverage level L in the cases of payments of tax on profit at the end of the year (1) and in the beginning of the year (2) for 3-year and 6-year companies

11.5

Discussion

215

Ke (L) (1;2) n=3 , n=6 0.26

Ke (L)

0.24 0.22

n=3 (1)

0.2

n=3 (2)

0.18

n=6 (1) n=6 (2)

0.16 0.14

1

2

3

4

5

6

7

8

9

10

Fig. 11.9 Dependence of the equity cost, ke, on leverage level L in the cases of payments of tax on profit at the end of the year (1) and in the beginning of the year (2) for 3-year and 6-year companies

11.5

Discussion

We derive BFO formulas for WACC, V, ke for the case of advanced payments of income tax. Making the calculations using these formulas within Microsoft Excel, we get the following results (see Tables 11.1 and 11.2 and Figs. 11.1, 11.2, 11.3, 11.4, 11.5, 11.6, 11.7, 11.8, and 11.9). 1. WACC(L ) decreases with L in both cases: advanced payments of income tax and payments at the end of years. This means that debt financing is important and should be used by company—it leads to decrease of attracting capital cost with L. 2. WACC turns out to be lower in the case of advanced payments of income tax, this tells about the importance of the use of advanced payments of income tax for companies. 3. WACC decreases with company age: this is one of the important results of classical BFO theory. 4. Company value, V, increases with L in both cases, this follows from the decrease of attracting capital cost with L. 5. Company value, V, turns out to be bigger in the case of advanced payments of income tax: this tells about the importance of the use of advanced payments of income tax for companies. 6. Company value, V, increases with company age. 7. Equity cost ke decreases with company age in both cases: this is one of the important results of classical BFO theory. 8. Equity cost ke increases with leverage level L in the case of payments of income tax at the end of the year. 9. Equity cost ke decreases with leverage level L in the case of advanced payments of income tax. This means the appearance of a qualitatively new effect can greatly change the company’s dividend policy, because the economically justified amount of dividends is equal to the equity cost.

216

11.6

11

Benefits of Advance Payments of Tax on Profit: Consideration. . .

Summary and Conclusions

Advance income tax payments are beneficial to both parties: to companies, because they lead to decrease of cost of attracting capital and increase of company values; to regulator, because earlier replenishment of the budget ensures an increase in the stability of budget revenues. Thus, the regulator should extend the practice of tax payments in advance by the companies. An important conclusion drawn in this chapter is that the tax shield is very important and the way it is formed (payments at the end of the year or in advance) leads to very important consequences, changing all the financial indicators of the company, such as the cost of raising capital and company value and radically changing the company’s dividend policy. If with payments at the end of the year, the amount of dividends should increase with the increase in the use of debt financing, with advance payments of income tax the amount of dividends should decrease with the increase in the use of debt financing: this is a pioneering result that radically changes the company’s dividend policy.

References Brusov P, Filatova T, Orehova N, Eskindarov M (2018) Modern corporate finance, investments, taxation and ratings, 2nd edn. Springer, Cham, Switzerland, pp 1–571 Brusov PN, Filatova TV, Orekhova NP, Kulik VL, Chang S-I, Lin YCG (2020) Modification of the Modigliani– Miller theory for the case of advance payments of tax on profit. J Rev Glob Econ 2020(9):257–267 Brusov P, Filatova T, Orehova N (2022) Generalized Modigliani–Miller theory. Applications in corporate finance, investments, taxation and ratings. Springer, Cham, Switzerland, pp 1–362. https://rd.springer.com/book/10.1007/978-3-030-93893-2 Hamada R (1969) Portfolio analysis, market equilibrium, and corporate finance. J Financ:13–31 Miller M (1977) Debt and taxes. J Financ 32(2):261–275. https://doi.org/10.1111/j.1540-6261. 1977.tb03267.x Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Modigliani F, Miller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391 Myers S (2001) Capital structure. J Econ Perspect 15(2):81–102

Chapter 12

The Generalization of the Brusov–Filatova– Orekhova Theory for the Case of Payments of Tax on Profit with Arbitrary Frequency

Keywords Generalized Brusov–Filatova–Orekhova (BFO) theory · The Modigliani–Miller theory · Frequency of payment of income tax · Equity cost · The weighted average cost of capital · Company capitalization · A qualitatively new anomalous effect

12.1

Introduction

The chapter has the following structure: In the Introduction, we describe some approaches to the capital structure theory: traditional approach, Modigliani–Miller theory and some of its modifications. We generalize the Brusov–Filatova–Orekhova (BFO) theory for the case of arbitrary frequency of payments of income tax and get generalized Brusov–Filatova– Orekhova (BFO) formulas for the weighted average cost of capital, WACC, for the equity cost, ke, and for the capitalization of the company, V. Within the generalized Brusov–Filatova–Orekhova (BFO) theory the dependence of the main financial parameters of the company (the weighted average cost of capital, WACC, equity cost, ke, company capitalization, V ) on leverage level L at different frequencies of payments of income tax p is studied. Obtained results allow come to some very important conclusions and give recommendations on how frequently company should pay income tax in order to decrease the cost of attracting capital and to increase its capitalization.

12.1.1

Capital Structure of the Company

This chapter is devoted to one of the most important problem of financial management—problem of capital cost and capital structure of the company. The management by capital structure of the company (the relationship between equity and debt capital of the company) allows to company’s management to solve the main task—increase the company value. This relates as well with the problem of the optimal capital structure, i.e., with the capital structure, which minimizes the © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_12

217

218

12 The Generalization of the Brusov–Filatova–Orekhova Theory for the. . .

Fig. 12.1 Historical aspects of capital cost and capital structure theory: here empirical traditional approach—TA, Modigliani–Miller theory—MM, Brusov–Filatova–Orekhova theory—BFO

weighted average cost of capital, WACC, and maximizes the value of the company, V, which is one of the most important problem in financial management. The first quantitative study of influence of capital structure of the company on its (company) financial indicators was the work by Nobel Prize winners Modigliani and Miller (1958). Before their work, the traditional approach existed, based on empirical data analysis. In 2008 the modern capital cost and capital structure theory—Brusov– Filatova–Orekhova (BFO) theory has been developed (Filatova et al. 2008), which made Modigliani–Miller theory its particular case. Within BFO theory many qualitatively new effects have been discovered, which are absent within Modigliani– Miller theory. Some main existing principles of financial management have been destroyed by BFO theory, among them the world-famous trade-off theory (Brennan and Schwartz 1978, 1984; Leland 1994), which was considered as keystone of the formation of optimal capital structure of the company during many decades. Brusov–Filatova–Orekhova have proven the bankruptcy of trade-off theory and have found the cause of this (Chap. 4 in monograph (Brusov et al. 2018)). Below we briefly describe the historical development of the theory of capital cost and capital structure. Figure 12.1 shows the historical development of capital cost and capital structure theory (from the empirical traditional approach, through perpetuity Modigliani– Miller theory to general capital cost and capital structure theory—Brusov–Filatova– Orekhova (BFO) theory (Brusov et al. 2018). Myers (Myers 2001) in 2001 has considered the one-year company case and show that the weighted average cost of capital, WACC, in this case is higher than in Modigliani–Miller case, and the capitalization of the company, V, is less than in Modigliani–Miller case. So, before 2008 only two results for capital structure of the company were available: Modigliani–Miller for perpetuity company (Мodigliani and Мiller 1958, 1963, 1966) and Myers (2001) for one-year company (see Fig. 12.2). Wherein Brusov–Filatova–Orekhova theory has filled out whole interval between t = 1 and t=1. Brusov–Filatova–Orekhova theory allows to calculate the company value, V, the weighted average cost of capital, WACC, the equity cost ke and other financial parameters for arbitrary age companies and for arbitrary lifetime companies. BFO theory has led to a lot of new meaningful effects in modern capital structure theory, absent in Modigliani–Miller theory (Brusov et al. 2018). The main purpose of this chapter is to generalize and further develop the Brusov– Filatova–Orekhova (BFO) theory, taking into account the case of paying income tax

12.1

Introduction

219

Fig. 12.2 Myers result describes one-year company, Modigliani–Miller theory (MM) corresponds to perpetuity limit, while Brusov–Filatova–Orekhova (BFO) theory fills the whole numeric axis (from n = 1 up to perpetuity limit n = 1)

with an arbitrary frequency (monthly, quarterly, semi-annual, or annual payments), which takes place in real economic practice. Note that both major theories on the cost of capital and capital structure of the Brusov–Filatova–Orekhova (BFO) theory and its perpetuity limit, the Modigliani–Miller theory, take into account annual income tax payments. The latter was recently generalized by us to the case of an arbitrary periodicity in the payment of income tax (Tatiana et al. 2022), which showed a significant change in the results of the classical Modigliani–Miller theory. Here we make this generalization for the Brusov–Filatova–Orekhova (BFO) theory. Below we discuss the traditional approach, the Modigliani–Miller theory and its different modifications, and the Brusov–Filatova–Orekhova (BFO) theory.

12.1.2

The Modigliani–Miller Theory

Before the Modigliani–Miller work, the traditional approach existed, based on empirical data analysis. In the traditional approach weighted average cost of capital, WACC, and the company value, V, depend on the capital structure, on the leverage level, L. The cost of debt is lower than cost of equity via the fact that first one has lower risk, because creditor claims are met prior to shareholders’ claims in the event of bankruptcy. Thus the increase of the share of lower-cost debt capital up to the values which does not cause violation of financial sustainability and growth of risk of bankruptcy leads to lower weighted average cost of capital, WACC. The required by investors profitability, which is equal to the equity cost, is growing; but its growth does not compensate for the benefits from the use of lower-cost debt capital. Therefore, in the traditional approach the increase of leverage level (at low leverage level) leads to decrease in WACC and to the associated increase of the value of company V. At a high leverage level, financial difficulties and the risk of bankruptcy appear. The debt capital cost increases as well as the equity cost (which always increases with leverage level) and these lead to an increase of WACC and decrease of company value V. Thus, competition between the advantages of debt financing at a low level of leverage and its disadvantages at a high level of leverage forms the optimal capital structure, when WACC reaches minimum and capital value V reaches maximum. This is the main point of the traditional approach as well as trade-off theory. This empirical approach has existed up to the creation of the first quantitative theory by Nobel Prize Winners Modigliani and Miller (1958).

12 The Generalization of the Brusov–Filatova–Orekhova Theory for the. . .

220

Modigliani and Miller (ММ) in their first chapter (Мodigliani and Мiller 1958) have come to conclusions which were fundamentally different from the conclusions of traditional approach. Under assumptions that there are no taxes, no transaction costs, no bankruptcy costs, perfect financial markets exist with symmetry information, equivalence in borrowing costs for both companies and investors, etc., they have showed that choosing of the ratio between the debt and equity capital does not affect company value V, as well as weighted average cost of capital, WACC. Modigliani and Miller analyzing the influence of financial leverage on V and V0, weighted average cost of capital, WACC and ke, get the following results: (here, EBIT–earnings before interest and taxes, k0 is discount rate, V and V0 are the values of levered and unlevered companies, ke is the equity cost) V = V0 =

EBIT k0

ð12:1Þ

This leads to the following expressions for weighted average cost of capital, WACC: WACC = k0 :

ð12:2Þ

Note that k0 here and below is the equity cost for financially independent company. For financially dependent company k0 is the equity cost at zero leverage level (L = 0). From (12.1), and formula for WACC definition WACC = k 0 = k e we þ k d wd

ð12:3Þ

it is easy to derive an expression for the equity capital cost. Finding ke, one gets ke =

k ðS þ DÞ w D k0 D - kd = k0 þ ðk 0- k d Þ = k 0 - kd d = 0 S we we S S

þ ðk0- kd ÞL

ð12:4Þ

Here, D S k d , wd = k e , we = L = D/S WACC

D DþS S DþS

Value of debt capital of the company Value of equity capital of the company Cost and fraction of debt capital of the company Cost and fraction of equity capital of the company Financial leverage Weighted average cost of capital.

Thus, we have the following formula for equity cost

12.1

Introduction

221

ke = k0 þ Lðk0- kd Þ

ð12:5Þ

Formula (12.5) shows that equity cost of the company increases linearly with leverage level. In 1963, Мodigliani and Мiller (1963) accounted for the tax on profit and get the following formula for the cost of financially dependent company, V, V = V 0 þ DT,

ð12:6Þ

where V0 is the value of financially independent company, D is debt value and T is the tax on profit. Below we get the expression for WACC and the equity capital cost ke of the company under the existence of corporate taxes. Weighted Average Cost of Capital, WACC Substituting into (12.6) D = wdV, one gets V ð1- wd T Þ = V 0 : Putting V =

CF WACC ;

V0 =

CF k0

ð12:7Þ

into formula (12.7), we get

CF CF ð1- wd T Þ = : k0 WACC

ð12:8Þ

Here CF is the income of the company for one period. And from (12.8) we arrive to the expression for weighted average cost of capital, WACC WACC = k0  ð1- wd t Þ

ð12:9Þ

This formula for WACC is one of the main result of Modigliani–Miller theory with taxes. The Equity Cost Let us derive formula for equity cost. On definition of the weighted average cost of capital WACC in the presence of corporate taxes, we have WACC = k 0 we þ kd wd ð1- T Þ:

ð12:10Þ

Equating Eqs. (12.9) and (12.10), one gets k0 ð1- wd T Þ = k0 we þ kd wd ð1- T Þ

ð12:11Þ

12 The Generalization of the Brusov–Filatova–Orekhova Theory for the. . .

222

Fig. 12.3 Impact of leverage level on equity capital cost ke, and WACC within the Modigliani– Miller theory without taxes (t = 0) and with taxes (t ≠ 0)

and from here, for equity cost, ke we get the following expression (Мodigliani and Мiller 1963): ð 1 - wd T Þ w 1 w D - k d d ð1 - T Þ = k 0 - k 0 d T - k d ð1 - T Þ we we we we S DþS D D = k0 - k0 T - kd ð1 - T Þ = k 0 þ Lð1 - T Þðk0 - kd Þ: S S S

ke = k0

ð12:12Þ

The formula (12.12) is different from the formula (12.5) without tax only by the multiplier (1 – T ) in term, indicating a premium for risk. As the multiplier is less than unit, the corporate income tax leads to decrease in the slope of the curve ke(L ) with respect to L–axis. From formulas (12.5), (12.9), and (12.12) we get the following conclusions (see Fig. 12.3). When leverage level grows:

12.2

Some Modifications of Modigliani–Miller Theory

223

1. Value of company, V, increases. 2. Weighted average cost of capital, WACC decreases from k0 up to k0(1 - T ) (at L = 1). 3. Equity cost increases linearly from k0 up to infinity.

12.2 12.2.1

Some Modifications of Modigliani–Miller Theory Hamada Model: Accounting Market Risk

The Modigliani–Miller theory was united with Capital Asset Pricing Model (CAPM) in 1969 (Hamada 1969) by R. Hаmаdа, who has derived the following formula for the leveraged company equity cost, accounting both financial and business risk of company: k e = kF þ ðkM- kF ÞbU þ ðkM- kF ÞbU

D ð1- T Þ, S

ð12:13Þ

where bU is the β–coefficient of the same group of business risk company, that the considering company, but with L = 0. The formula (12.13) represents the desired equity capital ke profitability as a sum of three components: risk–free profitability kF, compensating to shareholders a temporary value of their money, premium for business risk (kM - kF)bU, and premium for financial risk ðk M- kF ÞbU DS ð1- T Þ. If the company does not have debt financing, the financial risk factor will be equal to zero (the third term is drawn to zero), and only the premium for business risk will be received by shareholders.

12.2.2

The Account of Corporate and Individual Taxes (Miller Model)

In 1963 Modigliani and Miller (1963) have accounted the taxation of corporate income, but the individual taxes of investors were not taken into account. The account of the corporate and individual taxes has been done by Merton Miller in 1977 (Miller 1977), who study the influence of debt financing on company capitalization. In Miller model, the following definitions have been used: TC–the tax on corporate income rate, TS–the tax rate on income of an individual investor from his ownership by corporation stock, TD–tax rate on interest income from the provision of investor–individuals of credits to other investors and companies. Because the income from shares partly comes in the form of a dividend and, in part, as capital profits, so TS is a weighted average value of the rates of tax on capital profits on shares and on dividends, while the profit from the provision of loans

224

12 The Generalization of the Brusov–Filatova–Orekhova Theory for the. . .

usually comes in the form of the interests. The former are usually taxed at a higher rate. For the capitalization of the financially independent company one has: VU =

EBITð1 - T C Þð1 - T S Þ : k0

ð12:14Þ

A term (1 - TS) allows to take into account the individual taxes in the formula. In this way, numerator indicates which part of the operating company’s profit remains in the possession of the investors, after the company will pay taxes on their profits, and its shareholders then will pay individual taxes on income from stock ownership. Since individual taxes reduce profits, remaining in the disposal of investors, the last, at other things being equal circumstances, also reduce and an overall assessment of the financially independent company value.

12.2.3

More General Case for WACC Formula

In (Farber et al. 2006; Fernandez 2006; Berk and DeMarzo 2007; Harris and Pringle 1985) more general than Modigliani–Miller (MM) formula for the WACC has been derived: it is described by the following formula (Farber et al. 2006) WACC = k0 ð1- wd T Þ - kd twd þ k TS twd :

ð12:15Þ

Here k0, kd, and kTS are the expected returns, respectively, on the financially independent company, the debt and the tax shield, V is the capitalization of the financially dependent company, VTS is the tax shield value, D is the debt value and TC is the rate of corporate tax. Formula (12.15) is derived from the WACC definition and the balance identity (see as well Berk and DeMarzo 2007). Although Eq. (12.15) is general enough, some additional conditions are required its practical applicability. If the WACC is constant over time, as it stated in (Farber et al. 2006) the levered company value can be found by discounting with the WACC for the unlevered free cash flows. The resulting formulas, which describe the special cases, where the WACC is constant, can be found in textbooks (Berk and DeMarzo 2007; Harris and Pringle 1985). First, Modigliani and Miller in 1963 (Мodigliani and Мiller 1963) assume that the level of debt D is constant. Then, as the expected after-tax cash flow of the unlevered firm is fixed, V0 is also constant. By assumption, kTS = kD and the value of the tax shield is TS = tD. Therefore, the company value V is a constant and the general WACC formula (12.15) simplifies to a constant WACC: WACC = k 0 ð1- wd T Þ We think that the “classical” Modigliani–Miller (MM) theory, which suggests that the expected returns on the debt kd and the tax shield kTS are equals (because

12.2

Some Modifications of Modigliani–Miller Theory

225

both of them have debt nature), is much more reasonable and namely the “classical” Modigliani–Miller (MM) theory, which is still widely used in practice, has been modified by us in Tatiana et al. (2022).

12.2.4

Fiscal Pressure, Financial Liquidity, Financial Solvency, and Financial Leverage

The problem of fiscal pressure is more current than ever in most countries. The article by Batrancea (Batrancea 2021a) was the first empirical study of the impact of fiscal pressure on the financial equilibrium of energy companies listed on the New York Stock Exchange. Empirical results obtained by econometric models showed that fiscal pressure had a stronger impact on the short-term and long-term equilibrium of electricity and oil companies than on the equilibrium of gas companies. The research could be useful for the managers of energy companies interested in estimating the evolution of company equilibrium state when considering different possible financial crises. How financial liquidity and financial solvency influenced the performance of healthcare companies that are publicly traded on the New York Stock Exchange has been studied by Batrancea (Batrancea 2021b), who used econometric models with two-stage least squares (2SLS) panel and panel generalized method of moments (GMM). Empirical evidence showed that the financial indicators’ current liquidity ratio, quick liquidity ratio, and financial leverage significantly influenced company performance measured by return on assets, gross margin ratio, operating margin ratio, earnings before interest, tax, depreciation, and amortization. Strategies intended to improve business performance based on liquidity and solvency insights were also addressed.

12.2.5

Brusov–Filatova–Orekhova (BFO) Theory

The suggestion about perpetuity of the companies and of all financial flows is the most serious limitations of the Modigliani–Miller theory. This limitation have been lifted up in 2008 by Brusov, Filatova, and Orekhova (Brennan and Schwartz 1984), who have created the modern theory of capital cost and capital structure, generalizing the Modigliani–Miller theory for the companies of arbitrary age (arbitrary lifetime). They have shown that in this case all Modigliani–Miller results (Мodigliani and Мiller 1958; Filatova et al. 2008; Brennan and Schwartz 1978) significant changes: in the presence of corporative taxes capitalization of the company V is changed, as well as the equity cost, ke, and the weighted average cost of capital, WACC. A number of qualitatively new effects in corporate finance, obtained in

226

12 The Generalization of the Brusov–Filatova–Orekhova Theory for the. . .

Brusov–Filatova–Orekhova theory (Brennan and Schwartz 1984), are absent in Modigliani–Miller theory (Мodigliani and Мiller 1958, 1963, 1966). The Brusov–Filatova–Orekhova formula for weighted average cost of capital, WACC for the company of arbitrary age n, takes the following form (Brennan and Schwartz 1984) 1 - ð1 þ k 0 Þ - n 1 - ð1 þ WACCÞ - n : = WACC k 0 ½1 - wd T ð1 - ð1 þ k d Þ - n Þ

ð12:16Þ

D —the share of debt Here, S—the equity capital of the company value, wd = DþS S capital; k e , we = DþS —the cost and the share of the equity capital of the company, L = D/S—leverage level. Substituting in (12.14) n → 1, we easily arrive to the perpetuity (Modigliani– Miller) limit formula for weighted average cost of capital, WACC.

WACC = k 0 ð1- wd T Þ:

ð12:17Þ

Results of BFO theory are well known in the world literature (for example, see references (Dimitropoulos 2014; Luiz et al. 2015; Massimiliano 2011; Pavel 2018; Justyna et al. 2021; Angotti et al. 2018; Cristian et al. 2018)). Some chapters (Cristian et al. 2018) use the BFO theory in practical calculations. The similarities and differences between BFO and MM results are shown in Table 12.1.

12.2.6

Trade-off Theory

As we mentioned above, the main theory of optimal capital structure of the company during many decades was the world-famous trade-off theory (Brennan and Schwartz 1978, 1984; Leland 1994), which is still used now for decision on capital structure making. But, in 2013 Brusov et al. (2018) have proven the trade-off theory’s bankruptcy. In opposite to waiting result, it was shown that suggestion of risky debt financing which causes the growing of the credit rate near bankruptcy, does not lead to the growing of weighted average cost of capital, WACC, which still decreases with leverage level. Thus, the minimum in the dependence of WACC on leverage level is absent as well. This means, that the world-famous trade-off theory lacks an optimal capital structure. Brusov et al. in 2013 (Brusov et al. 2018) have given the explanation of this fact by analyzing the equity capital cost dependence on the leverage level on the risky debt capital assumption.

12.3

Modification of the Brusov–Filatova–Orekhova (BFO) Theory for. . .

227

Table 12.1 The similarities and differences between BFO and MM results Time parameter, n

Company age and lifetime Dependence of all main financial indicators: WACC, V, ke on time parameter, n All main financial indicators: WACC, V, ke depend on debt cost kd WACC

V

Equity cost ke Equity cost ke: The slope of the curve ke(L ) ke: the slope of the curve ke (L )

Golden and silver age effects (Brusov et al. 2018)

12.3

BFO Arbitrary age of companies, Arbitrary lifetime of companies Are different

MM Perpetuity companies, perpetuity financial flows; n=1

Allow to study these dependences

Are the same and equal infinity Time parameter, n is absent

Yes

None

Correct estimation; Decreases with leverage level L Correct estimation; Increases with leverage level L Increases linearly with leverage level L Less than in MM theory

Underestimation; Decreases with leverage level L Overestimation; Increases with leverage level L Increases linearly with leverage level L Bigger than in BFO theory

Could be negative at T > T* (qualitatively new effect) Exist

Always is positive New effect is absent Absent

Modification of the Brusov–Filatova–Orekhova (BFO) Theory for Companies with Frequent Payments of Tax on Income

Below we use the following definitions: D S k d , wd = k e , we = L = D/S WACC

D DþS S DþS

Value of debt capital of the company Value of equity capital of the company Cost and fraction of debt capital of the company Cost and fraction of equity capital of the company Financial leverage Weighted average cost of capital

k0 is the equity cost for financially independent company; p is the number of payments of tax on profit per year; T is tax on profit.

12 The Generalization of the Brusov–Filatova–Orekhova Theory for the. . .

228

12.3.1 Calculation of the Tax Shield We start from the calculation of the tax shield within Brusov–Filatova–Orekhova theory for the case of p payments of tax on profit per year (payments are made at the end of periods). The tax shield, TS, for period of n-years is equal to the sum of discounted values of benefits from the use of tax incentives ðTSÞn =

k d Dt pð 1 þ k d Þ

1= p

þ

kd Dt pð 1 þ k d Þ

2= p

þ :... þ

kd Dt np= p

pð 1 þ k d Þ

We have a geometric progression with denominator q =

ð12:18Þ

1 1= . ð1þkd Þ p

After summing the progression, one obtains: ðTSÞn = =

k d Dt ð1 - ð1 þ k d Þ - n Þ
pð 1 þ k d Þ

1= p

1 - ð1 þ k d Þ -

1= p



kd Dt ð1 - ð1 þ kd Þ - n Þ
 1= p ð1 þ k d Þ p - 1

ð12:19Þ

In classical Brusov–Filatova–Orekhova theory (at p = 1): ðTSÞn = Dt ð1- ð1 þ kd Þ - n Þ

ð12:20Þ

It is easy to obtain this result from (12.19), putting the frequency of payments of tax on profit p = 1.

12.3.2

Derivation of the Modified BFO Formula for Weighted Average Cost of Capital (WACC)

We derive now the modified formula BFO for weighted average cost of capital (WACC) for the case of p payments of tax on profit per year (payments at the end of periods). One has for the financially dependent company value V: V = V 0 þ ðTSÞn

ð12:21Þ

Here V0 is the value of a financially independent company. Putting expression (12.19) for TS, one has:

12.3

Modification of the Brusov–Filatova–Orekhova (BFO) Theory for. . .

V = V0 þ

kd Dt ð1 - ð1 þ kd Þ - n Þ
 1= p ð1 þ k d Þ p - 1

229

ð12:22Þ

After substituting D = wdV, we get: 0 V@

1 - kd wd tð1 - ð1 þ kd Þ
 1= p ð1 þ k d Þ p - 1

-n

1 ÞA

= V0

ð12:23Þ

Accounting, that the values of financially dependent company, V, and financially independent company, V0, are respectively equal to V=

CFð1 - ð1 þ k0 Þ - n Þ CFð1 - ð1 þ WACCÞ - n Þ ; V0 = WACC k0

ð12:24Þ

one gets: 0 1 CFð1 - ð1 þ WACCÞ - n Þ @1 - k d wd tð1 - ð1 þ k d Þ - n ÞA
  1= WACC p ð1 þ k d Þ p - 1 =

CF  ð1 - ð1 þ k 0 Þ - n Þ k0

ð12:25Þ

From here we derive now the modified formula BFO for weighted average cost of capital (WACC) for company of age n years for the case of p payments of tax on profit per year (payments at the end of periods) 1 - ð1 þ WACCÞ - n = WACC

CFð1 - ð1 þ k0 Þ - n Þ   1 - k d wd tð1 - ð1þkd Þ - n Þ   k0 1= p ð1þk d Þ

p

ð12:26Þ

-1

At p = 1 we get classical BFO formula 1 - ð1 þ k 0 Þ - n 1 - ð1 þ WACCÞ - n = WACC k 0  ð1 - wd t ½1 - ð1 þ k d Þ - n Þ

12.3.3

ð12:27Þ

Formulas for Capital Value, V, and Equity Cost, ke

Below in Sect. 12.3 we will investigate the dependence of the weighted average cost of capital, WACC, capital value, V, equity cost, ke, on leverage level L at different frequencies of payment of tax on profit p for 3-year and 6-year companies, using

12 The Generalization of the Brusov–Filatova–Orekhova Theory for the. . .

230

Microsoft Excel. For WACC we will use formula (12.10) and for capital value, V, and equity cost, ke, we will use formulas (12.28) and (12.29), respectively, (see below). Company of age n capitalization could be calculated by the following formula V=

CF  ð1 - ð1 þ WACCÞ - n Þ : WACC

ð12:28Þ

ke should be found from the equation WACC = k e we þ k d wd ð1- t Þ

ke =

WACC kd ð1 - t Þwd = WACCð1 þ LÞ - Lkd ð1- t Þ we we

ð12:29Þ

where one should substitute WACC from the formula (12.26).

12.4

Results

In this section, we study the dependence of the weighted average cost of capital, WACC, capital value, V, equity cost, ke, on leverage level L at different frequencies of payment of tax on profit p for 3-year and 6-year companies, using Microsoft Excel. As we mentioned above, for WACC we use formula (12.10) and for capital value, V, and equity cost, ke, we use formulas (12.11) and (12.13), respectively. We use the following parameters: k0 = 0.2; kd = 0.18; t = 0.2; n = 3; 6; CF = 100.

12.4.1

Dependence of the Weighted Average Cost of Capital, WACC, Capital Value, V, Equity Cost, ke, on Leverage Level L at Different Frequency of Payment of Tax on Profit p for 3-year Company

12.4.1.1

Dependence of The Weighted Average Cost of Capital, WACC, on Leverage Level L at Different Frequency of Payment of Tax on Profit p for 3-year Company

Dependence of the weighted average cost of capital, WACC, on leverage level L at different frequencies of payments of tax on profit p for 3-year company is shown in Table 12.2 and Fig. 12.4. The weighted average cost of capital, WACC, decreases with leverage level L at any frequency of payments of tax on profit p. The difference between the WACC(L)

12.4

Results

231

Table 12.2 Dependence of the weighted average cost of capital, WACC, on leverage level L at different frequencies of payments of tax on profit p for 3-year company L 1 2 3 4 5 6 7 8 9 10

WACC p=1 0.1749 0.1664 0.1622 0.1596 0.1579 0.1567 0.1558 0.1551 0.1545 0.1541

Wd 0.5 0.666667 0.75 0.8 0.833333 0.857143 0.875 0.888889 0.9 0.909091

p=2 0.1738 0.1650 0.1605 0.1579 0.1561 0.1548 0.1539 0.1532 0.1526 0.1521

p=4 0.1732 0.1642 0.1597 0.1570 0.1552 0.1539 0.1529 0.1522 0.1515 0.1511

p=6 0.1730 0.1640 0.1594 0.1567 0.1549 0.1536 0.1526 0.1518 0.1512 0.1507

p = 12 0.1728 0.1637 0.1591 0.1564 0.1545 0.1532 0.1522 0.1515 0.1509 0.1504

WACC(L) at different p at n=3 0.1750

WACC (L)

0.1700 p=1

0.1650

p=2 p=4

0.1600

p=6 p=12

0.1550 0.1500

1

2

3

4

5

6

7

8

9

10

Fig. 12.4 Dependence of the weighted average cost of capital, WACC, on leverage level L at different frequencies of payments of tax on profit p for 3-year company

curves is maximum when moving from annual ( p = 1) to semi-annual ( p = 2) income tax payments and decreases when moving from semi-annual ( p = 2) to quarterly ( p = 4) payments and from quarterly ( p = 4) to monthly ( p = 12) payments.

12.4.1.2

Dependence of the Company Value, on Leverage Level L at Different Frequencies of Payment of Tax on Profit p for 3-year Company

Dependence of the company value, V, on leverage level L at different frequencies of payments of tax on profit p for 3-year company is shown in Table 12.3 and Fig. 12.5. The value of company V increases with the frequency p. The largest increase occurs when moving from annual ( p = 1) to semi-annual ( p = 2) income tax

12 The Generalization of the Brusov–Filatova–Orekhova Theory for the. . .

232

Table 12.3 Dependence of the company value, V, on leverage level L at different frequencies of payments of tax on profit p for 3-year company L 1 2 3 4 5 6 7 8 9 10

wd 0.5 0.666667 0.75 0.8 0.833333 0.857143 0.875 0.888889 0.9 0.909091

V p=1 219.2281 222.2455 223.7856 224.7199 225.3471 225.7973 226.1361 226.4003 226.6122 226.7858

p=2 219.6139 222.7746 224.3893 225.3694 226.0275 226.5000 226.8557 227.1331 227.3555 227.5378

p=4 219.8116 223.0459 224.6989 225.7025 226.3766 226.8606 227.2250 227.5091 227.7370 227.9238

p=6 219.8781 223.1373 224.8033 225.8149 226.4944 226.9822 227.3495 227.6360 227.8657 228.0540

p = 12 219.9451 223.2292 224.9082 225.9278 226.6127 227.1045 227.4747 227.7635 227.9951 228.1849

V(L) at different p at n=3

V (L)

230.0000 228.0000

p=1

226.0000

p=2

224.0000

p=4

222.0000

p=6

220.0000

p=12

218.0000

1

2

3

4

5

6

7

8

9

10

Fig. 12.5 Dependence of the company value, V, on leverage level L at different frequencies of payments of tax on profit p for 3-year company

payments and decreases when moving from semi-annual ( p = 2) to quarterly ( p = 4) payments and from quarterly ( p = 4) to monthly ( p = 12) payments.

12.4.1.3

Dependence of the Equity Cost, ke, on Leverage Level L at Different Frequency of Payment of Tax on Profit p for 3-year Company

Dependence of the equity cost, ke, on leverage level L at different frequencies of payments of tax on profit p for 3-year company is shown in Table 12.4 and Fig. 12.6. The cost of equity ke increases linearly with the level of leverage L. The slope of the curve ke(L ) depends on the frequency of paying income tax: it decreases with increasing p, most rapidly when moving from annual ( p = 1) to semi-annual ( p = 2) payments of income tax and slower in the transition from semi-annual ( p = 2) to quarterly ( p = 4) payments and from quarterly ( p = 4) to monthly ( p = 12) payments.

12.4

Results

233

Table 12.4 Dependence of the equity cost, ke, on leverage level L at different frequencies of payments of tax on profit p for 3-year company L 1 2 3 4 5 6 7 8 9 10

Ke p=1 0.2057 0.2113 0.2168 0.2222 0.2277 0.2331 0.2386 0.2440 0.2495 0.2549

wd 0.5 0.666667 0.75 0.8 0.833333 0.857143 0.875 0.888889 0.9 0.909091

p=2 0.2036 0.2069 0.2102 0.2134 0.2167 0.2199 0.2232 0.2264 0.2296 0.2329

p=4 0.2024 0.2046 0.2068 0.2089 0.2111 0.2132 0.2153 0.2174 0.2195 0.2216

p=6 0.2021 0.2039 0.2057 0.2074 0.2092 0.2109 0.2126 0.2144 0.2161 0.2178

p = 12 0.2017 0.2031 0.2045 0.2059 0.2073 0.2086 0.2100 0.2113 0.2127 0.2140

ke(L) at different p at n=3

ke (L)

0.2600 0.2500

p=1

0.2400

p=2

0.2300

p=4 p=6

0.2200

p=12

0.2100 0.2000

1

2

3

4

5

6

7

8

9

10

Fig. 12.6 Dependence of the equity cost, ke, on leverage level L at different frequencies of payments of tax on profit p for 3-year company

12.4.2

Dependence of the Weighted Average Cost of Capital, WACC, Capital Value, V, Equity Cost, ke, on Leverage Level L at Different Frequency of Payment of Tax on Profit p for 6-year Company

12.4.2.1

Dependence of The Weighted Average Cost of Capital, WACC, on Leverage Level L at Different Frequency of Payment of Tax on Profit p for 6-year Company

Dependence of the weighted average cost of capital, WACC, on leverage level L at different frequencies of payments of tax on profit p for 6-year company is shown in Table 12.5 and Fig. 12.7. We use the following parameters: k0 = 0.2; kd = 0.18; t = 0.2; n = 6;

12 The Generalization of the Brusov–Filatova–Orekhova Theory for the. . .

234

Table 12.5 Dependence of the weighted average cost of capital, WACC, on leverage level L at different frequencies of payments of tax on profit p for 6-year company L 1 2 3 4 5 6 7 8 9 10

WACC p=1 0.1743 0.1657 0.1613 0.1586 0.1569 0.1556 0.1547 0.1539 0.1534 0.1529

wd 0.5 0.666667 0.75 0.8 0.833333 0.857143 0.875 0.888889 0.9 0.909091

p=2 0.1732 0.1641 0.1596 0.1568 0.1550 0.1537 0.1527 0.1519 0.1513 0.1508

p=4 0.1726 0.1634 0.1587 0.1559 0.1540 0.1527 0.1517 0.1509 0.1502 0.1497

p=6 0.1725 0.1631 0.1584 0.1556 0.1537 0.1523 0.1513 0.1505 0.1499 0.1494

p = 12 0.1723 0.1629 0.1581 0.1553 0.1534 0.1520 0.1510 0.1502 0.1495 0.1490

WACC(L) at different p at n=6 0.1730

WACC (L)

0.1680 p=1

0.1630

p=2 p=4

0.1580

p=6

0.1530 0.1480

p=12 1

2

3

4

5

6

7

8

9

10

Fig. 12.7 Dependence of the weighted average cost of capital, WACC, on leverage level L at different frequencies of payments of tax on profit p for 6-year company

The weighted average cost of capital, WACC, decreases with leverage level L at any frequency of payments of tax on profit p. The difference between the WACC(L) curves is maximum when moving from annual ( p = 1) to semi-annual ( p = 2) income tax payments and decreases when moving from semi-annual ( p = 2) to quarterly ( p = 4) payments and from quarterly ( p = 4) to monthly ( p = 12) payments.

12.4.2.2

Dependence of the Company Value, V, on Leverage Level L at Different Frequency of Payment of Tax on Profit p for 6-year Company

Dependence of the company value, V, on leverage level L at different frequencies of payments of tax on profit p for 6-year company is shown in Table 12.6 and in Fig. 12.8.

12.4

Results

235

Table 12.6 Dependence of the company value, V, on leverage level L at different frequencies of payments of tax on profit p for 6-year company L 1 2 3 4 5 6 7 8 9 10

wd 0.5 0.666667 0.75 0.8 0.833333 0.857143 0.875 0.888889 0.9 0.909091

V p=1 354.8940 363.0242 367.2305 369.8015 371.5355 372.7841 373.7261 374.4620 375.0529 375.5377

p=2 355.9256 364.4649 368.8900 371.5971 373.4240 374.7399 375.7330 376.5090 377.1322 377.6435

p=4 356.4549 365.2052 369.7435 372.5210 374.3960 375.7468 376.7664 377.5632 378.2031 378.7283

p=6 356.6333 365.4550 370.0315 372.8329 374.7242 376.0869 377.1154 377.9193 378.5648 379.0947

p = 12 356.8127 365.7063 370.3214 373.1468 375.0545 376.4291 377.4667 378.2776 378.9289 379.4635

V(L) at different p at n=6

V (L)

383.0000 378.0000

p=1

373.0000

p=2

368.0000

p=4 p=6

363.0000

p=12

358.0000 353.0000

1

2

3

4

5

6

7

8

9

10

Fig. 12.8 Dependence of the company value, V, on leverage level L at different frequencies of payments of tax on profit p for 6-year company

The value of company V increases with the frequency p. The largest increase occurs when moving from annual ( p = 1) to semi-annual ( p = 2) income tax payments and decreases when moving from semi-annual ( p = 2) to quarterly ( p = 4) payments and from quarterly ( p = 4) to monthly ( p = 12) payments.

12.4.2.3

Dependence of the Equity Cost, ke, on Leverage Level L at Different Frequencies of Payment of Tax on Profit p for 6-year Company

Dependence of the equity cost, ke, on leverage level L at different frequencies of payments of tax on profit p for 6-year company is shown in Table 12.7 and Fig. 12.9. The cost of equity ke increases linearly with the level of leverage L. The slope of the curve ke(L ) depends on the frequency of paying income tax: it decreases with increasing p, most rapidly when moving from annual ( p = 1) to semi-annual ( p = 2)

12 The Generalization of the Brusov–Filatova–Orekhova Theory for the. . .

236

Table 12.7 Dependence of the equity cost, ke, on leverage level L at different frequencies of payments of tax on profit p for 6-year company L 1 2 3 4 5 6 7 8 9 10

ke p=1 0.2047 0.2090 0.2131 0.2172 0.2213 0.2254 0.2294 0.2335 0.2376 0.2416

wd 0.5 0.666667 0.75 0.8 0.833333 0.857143 0.875 0.888889 0.9 0.909091

p=2 0.2024 0.2044 0.2063 0.2081 0.2099 0.2117 0.2134 0.2152 0.2169 0.2187

p=4 0.2013 0.2021 0.2028 0.2035 0.2041 0.2047 0.2052 0.2058 0.2064 0.2070

p=6 0.2009 0.2013 0.2016 0.2019 0.2021 0.2023 0.2025 0.2027 0.2029 0.2030

p = 12 0.2005 0.2006 0.2005 0.2003 0.2001 0.1999 0.1997 0.1995 0.1993 0.1991

ke(L) at different p at n=6 0.2450 p=1

Ke (L)

0.2350

p=2

0.2250

p=4

0.2150

p=6

0.2050

p=12

0.1950

1

2

3

4

5

6

7

8

9

10

Fig. 12.9 Dependence of the equity cost, ke, on leverage level L at different frequencies of payments of tax on profit p for 6-year company

payments of income tax and slower in the transition from semi-annual ( p = 2) to quarterly ( p = 4) payments and from quarterly ( p = 4) to monthly ( p = 12) payments. One can see, that for a 6-year-old company with monthly income tax payments a qualitatively new anomalous effect takes place: ke(L) decreases with an increase in the level of leverage L. This radically changes the company’s dividend policy, since the economically justified amount of the dividends is equal to the cost of equity.

12.5

The Discussion and Conclusions

The main purpose of the chapter is to bring the Brusov–Filatova–Orekhova (BFO) theory closer to economic practice, taking into account one of the features of the real functioning of companies—the frequent payments of tax on profit. We generalize for

12.5

The Discussion and Conclusions

237

the first time the Brusov–Filatova–Orekhova (BFO) theory for the case of tax on profit payments with an arbitrary frequency. We derive modified BFO formulas and show that: (1) all BFO formulas change; (2) all main financial parameters of the company, such as company value, V, the weighted average cost of capital, WACC, and equity cost, ke, depend on the frequency of tax on profit payments. It turns out that the increase in the number of payments of tax of profit per year leads to decrease in the cost of attracting capital and increase in the company value. More frequent payments of income tax are beneficial for both parties—for the company and for the tax regulator: for the company, this leads to an increase in the value of the company, and for the tax regulator, earlier payments are beneficial due to the time value of money. We numerically studied the dependence of the weighted average cost of capital WACC, value of company, V, cost of equity ke on the level of leverage L at different frequencies of income tax payments p for 3- and 6-year companies and obtained the following results. The calculation of financial indicators is made for some typical parameters of enterprises (equity and debt costs, etc.). The weighted average cost of capital, WACC, decreases with leverage level L at any frequency of payments of tax on profit p. The difference between the WACC(L ) curves is maximum when moving from annual ( p = 1) to semi-annual ( p = 2) income tax payments and decreases when moving from semi-annual ( p = 2) to quarterly ( p = 4) payments and from quarterly ( p = 4) to monthly ( p = 12) payments. The value of company V increases with the frequency p. The largest increase occurs when moving from annual ( p = 1) to semi-annual ( p = 2) income tax payments and decreases when moving from semi-annual ( p = 2) to quarterly ( p = 4) payments and from quarterly ( p = 4) to monthly ( p = 12) payments. The cost of equity ke increases linearly with the level of leverage L. The slope of the curve ke(L ) depends on the frequency of paying income tax: it decreases with increasing p, most rapidly when moving from annual ( p = 1) to semi-annual ( p = 2) payments of income tax and slower in the transition from semi-annual ( p = 2) to quarterly ( p = 4) payments and from quarterly ( p = 4) to monthly ( p = 12) payments. At a certain age of the company, a qualitatively new anomalous effect takes place: ke(L) decreases with an increase in the level of leverage L. We obtain this result for a 6-year-old company with monthly income tax payments, but it is clear that this effect should take place for the companies of different ages and at different frequencies of income tax payment. This radically changes the company’s dividend policy, since the economically justified amount of the dividends is equal to the cost of equity. Note that this result reminds discovery, made by us earlier (Chap. 8 in monograph (Brusov et al. 2018)): the abnormal dependence of equity cost, ke, on leverage level L: above some value of tax on income, T*, equity cost ke decreases with the leverage level L. Thus, it is interesting to note, that increase in frequency of income tax payments p and increase in tax on profit T lead to a similar abnormal effect: decrease in equity cost ke with leverage level L. If in the first case there are threshold values for the

238

12 The Generalization of the Brusov–Filatova–Orekhova Theory for the. . .

Table 12.8 Comparison of the impact of the frequency of income tax payments in BFO theory and in MM theory Theorems, statements, and formulas All main financial indicators: WACC, V, ke All main financial indicators: WACC, V, ke All main financial indicators: WACC, V, ke depend on debt cost kd WACC V ke: the slope of the curve ke(L ) ke: The slope of the curve ke(L )

BFO Change

MM Change

Depend on the frequency of tax on profit payments p Value of the effect of p on all indicators is higher, than in MM At all p

Depend on the frequency of tax on profit payments p Value of the effect of p on all indicators is smaller, than in BFO At p ≠ 1 only

Decreases with p Increases with p Decreases with increasing p Could be negative (qualitatively new effect)

Decreases with p Increases with p Decreases with increasing p Always is positive

frequency of paying income tax, p*, and the age of the company, n*, then in the second case there is a threshold value for income tax T*. In Table 12.8 we compare the impact of the frequency of income tax payments in BFO theory and in MM theory. Recommendations From the analysis of the results of the current chapter the following recommendations could be done: For company: company should pay tax on profit as frequently as it is possible, because in this case company value increases. For regulator: should encourage more frequent payments of tax on profit, because earlier payments are beneficial for budget due to the time value of money.

References Angotti M, de Lacerda R, Moreira JH, do Nascimento B, de Almeida Bispo ON (2018) Analysis of an equity investment strategy based on accounting and financial reports in Latin American markets. Reficont 5(2) Batrancea L (2021a) An econometric approach regarding the impact of fiscal pressure on equilibrium: evidence from electricity, gas and oil companies listed on the New York Stock Exchange. Mathematics 9(6):630. https://doi.org/10.3390/math906063 Batrancea L (2021b) The influence of liquidity and solvency on performance within the healthcare industry: evidence from publicly listed companies. Mathematics 9:2231. https://doi.org/10. 3390/math9182231 Berk J, DeMarzo P (2007) Corporate finance. Pearson–Addison Wesley, Boston

References

239

Brennan M, Schwartz E (1978) Corporate income taxes, valuation, and the problem of optimal capital structure. J Bus 51:103–114 Brennan M, Schwartz E (1984) Optimal financial policy and firm valuation. J Financ 39:593–607 Brusov P, Filatova T, Orehova N, Eskindarov M (2018) Modern corporate finance, investments, taxation and ratings. Springer Nature Publishing, Cham Cristian V-N, Juan PS-R, Alfaro Miguel D, Nicolás R (2018) Cost of capital estimation for highway concessionaires in Chile. J Adv Transp 2018:9. https://doi.org/10.1155/2018/2153536 Dimitropoulos P (2014) Capital structure and corporate governance of soccer clubs: European evidence. Manag Res Rev 37(7):658–678. https://doi.org/10.1108/MRR-09-2012-0207 Farber A, Gillet R, Szafarz A (2006) A general formula for the WACC. Int J Bus 11(2):211–218 Fernandez P (2006) A general formula for the WACC: a comment. Int J Bus 11/2:219 Filatova Т, Orehova N, Brusova А (2008) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Bull FU 48:68–77 Hamada R (1969) Portfolio analysis, market equilibrium, and corporate finance. J Financ 24(1): 13–31 Harris R, Pringle J (1985) Risk–adjusted discount rates – extension form the average–risk case. J Financ Res 8(3):237–244 Justyna F-D et al (2021) Energy sector risk and cost of capital assessment—companies and investors perspective. Energies 14(6):1613. https://doi.org/10.3390/en14061613 Leland H (1994) Corporate debt value, bond covenants, and optimal capital structure. J Financ 49(4):1213–1252 Luiz K, Cruz M et al (2015) The relevance of capital structure on firm performance: a multivariate analysis of publicly traded Brazilian companies. REPeC Brasília 9(4):384–401. https://doi.org/ 10.17524/repec.v9i4.1313 Massimiliano B (2011) On the risk-neutral value of debt tax shields. Appl Financ Econ 22(3): 251–258. https://doi.org/10.1080/09603107.2011.613754 Miller M (1977) Debt and taxes. J Financ 32(2):261–275. https://doi.org/10.1111/j.1540-6261. 1977.tb03267.x Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Modigliani F, Miller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391 Myers S (2001) Capital structure. J Econ Perspect 15(2):81–102 Pavel Z (2018) The impact of cash flows and weighted average cost of capital to enterprise value in the oil and gas sector. J Rev Glob Econ 7:138–145 Tatiana F, Brusov P, Orekhova N (2022) Impact of advance payments of tax on profit on effectiveness of investments. Mathematics 10(4):666. https://doi.org/10.3390/math10040666

Chapter 13

Influence of Method and Frequency of Profit Tax Payments on Company Financial Indicators

Keywords Generalized Brusov–Filatova–Orekhova (BFO) theory · Frequent advance profit tax payments · Abnormal dependence effects of equity costs on leverage level · New approach to company dividend policies

13.1

Introduction

In practice, profit tax payments are (1) made more frequently than annually and (2) can be made in advance. Recently, the Brusov–Filatova–Orekhova (BFO) theory (Brusov et al. 2022) was generalized for the case of profit tax payments with an arbitrary frequency. Using modified BFO formulae, it was shown that all financial indicators of a company depend on the frequency of profit tax payments. The weighted average cost of capital (WACC) decreases with the payments and the company value increases with the payments. A new effect was thus discovered: the decrease in equity cost with an increase in the level of leverage (L ). Due to the fact that the economically justified amount of dividends is equal to the equity cost, this can significantly change the dividend policy of a company. More frequent profit tax payments are beneficial for both parties: the company and the tax regulator. For the company, this practice increases the company value and it helps the tax regulator due to the time value of money. In the current chapter, for the first time, the Brusov–Filatova–Orekhova (BFO) theory was generalized for the case of advance profit tax payments with an arbitrary frequency. We compared the obtained results to those that we described recently for profit tax payments at the end of the financial period (Brusov et al. 2022) and found them to be totally different. We showed that in spite of the fact that the WACC decreases with the payments and the company value increases with the payments in this case (Brusov et al. 2022), the WACC values turned out to be bigger and the company value turned out to be smaller than in case of advance profit tax payments of any frequency. This underlined the importance of advance profit tax payments. The novelty and originality of this study lie in the fact that the simultaneous influence of two effects was investigated for the first time: (1) advance profit tax payments and (2) frequent profit tax payments. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_13

241

242

13

Influence of Method and Frequency of Profit Tax Payments on. . .

Before this study, we generalized the Brusov–Filatova–Orekhova (BFO) theory to (1) the case of frequent profit tax payments at the end of the financial period and (2) the case of advance annual profit tax payments. In this article, we also compared the obtained results to the results of consideration (1) and found a large difference between the results. Thus, in this chapter, an in-depth study of frequent profit tax payments was carried out for both possible cases of payments: advance and at the end of the financial period. The robustness of the outcomes was provided by the use of the modern Brusov– Filatova–Orekhova (BFO) theory of capital cost and capital structure, which has been tested in real economic practice and its correct generalization for the case of frequent advance profit tax payments has been proven. The structure of the chapter is as follows. In the introduction, we present a literature review of the development of the capital structure and capital cost theory (Sect. 13.1.1). The Brusov–Filatova– Orekhova (BFO) theory is generalized for frequent advance profit tax payments for the first time in Sect. 13.2. The modified formulae are derived for the tax shield in Sect. 13.2.1, company value in Sect. 13.2.2, and the equity cost and WACC in Sect. 13.2.3. In Sect. 13.3, using the generalized BFO formulae that were obtained in Sect. 13.2 and Microsoft Excel, we numerically calculate the dependence of a company’s financial parameters, such as WACC, company value, and equity cost, on the level of leverage for an arbitrary frequency of profit tax payment for three- and six-year-old companies (Sects. 13.3.1 and 13.3.2, respectively). We considered frequent advance profit tax payments. In Sect. 13.3, we also compare the obtained results to those that were found previously for frequent profit tax payments tax at the end of the financial period (Brusov et al. 2022). This section also compares the results for companies of different ages (three- and six-year-old companies). In Sect. 13.4, the discussion and conclusions are presented.

13.1.1

A Literature Review on the Development of the Capital Cost and Capital Structure Theory

In this section, we present an overview of the development of the capital cost and capital structure theory. Following the traditional empirical approaches, the first quantitative theory of capital cost and capital structure was proposed by the Nobel Prize winners Modigliani and Miller (the MM theory) in 1958 (Мodigliani and Мiller 1958). Among the many limitations of this theory, two main shortcomings can be distinguished: the non-accounting of taxes and the infinite lifetime of companies. The first constraint was removed by Modigliani and Miller themselves (Мodigliani and Мiller 1963, 1966), who obtained the following formulae. The tax shield (TS) had the following form:

13.1

Introduction

243

TS = DT

ð13:1Þ

Company value (V ) and financially independent companies (V0) were expressed as: V 0 = CF=k 0 and

V = CF=WACC:

ð13:2Þ

For WACC, Modigliani and Miller obtained the following formula: WACC = k0  ð1- wd t Þ

ð13:3Þ

For equity cost (ke), they had: k e = k0 þ Lðke- kd Þ  ð1- t Þ

ð13:4Þ

In 1969, the capital asset pricing model (CAPM) was combined with the Modigliani–Miller theory by Hamada (Hamada 1969), which accounted for both the business and financial risk of companies and used the below formula for the equity cost (ke) of financially dependent companies: ke = k F þ ðkM- kF ÞbU þ ðkM- k F ÞbU

D ð1- T Þ, S

ð13:5Þ

where bU is the β-coefficient of a company with L = 0. Corporate and individual taxes were then taken into account by Miller in 1977 (Miller 1977). The following formula was obtained for unleveraged company value:


 ð1 - T C Þð1 - T S Þ D V = V 0 þ 1ð1 - T D Þ

ð13:6Þ

where TS is the profit tax rate for an individual investor for their ownership of corporation stock, TC is the tax rate for corporate profit, and TD is the profit tax interest rate for the provision of credit to other investors or companies. In Farber et al. (2006); Fernandez (2006); Berk and De Marzo (2007); Harris and Pringle (1985), a more general expression for WACC than the Modigliani–Miller (MM) version was obtained (Farber et al. 2006): WACC = k0 ð1- wd t Þ - kd wd t þ k TS twd

ð13:7Þ

where k0 is the equity cost of the unleveraged company, kd is the debt cost, kTS is the expected return on the tax shield, V is the leveraged company value, VTS is the value of the tax shield, and D is the debt value. Derived in Berk and De Marzo (2007), Formula (13.7) is more general than the Modigliani–Miller (MM) expression, so some additional conditions are necessary for its use in practice. When the WACC value is constant over time, the leveraged

244

13

Influence of Method and Frequency of Profit Tax Payments on. . .

company value can be found by discounting the WACC from the unleveraged company cash flows. For this specific case, the formulae can be found in textbooks (Berk and De Marzo 2007; Harris and Pringle 1985). In 1963, Modigliani and Miller (1963) supposed that the level of debt was constant. The expected after-tax cash flow of a financially independent company was also fixed, thus V0 was constant. By that assumption, kTS = kd and the tax shield value was TS = tD. Thus, for the financially dependent company value, we used the ordinary Modigliani–Miller (MM) formula for WACC instead of Formula (13.7): WACC = k0 ð1- wd t Þ

ð13:8Þ

From our point of view, the “classical” Modigliani–Miller (MM) theory supposed that the debt cost and expected return on the tax shield were equal (due to the fact that both of them are debt-like in nature), which is much more reasonable and so we modified the “classical” Modigliani–Miller (MM) in Brusov et al. (2020). A study on the influence of tax pressure on the financial balance of energy companies was carried out in Batrancea (2021a). The results showed that tax pressure has a stronger influence on the financial equilibrium (both in the short term and long term) of oil and electricity companies than gas companies. These results are useful for the managers of energy companies who underestimate the evolution of the financial equilibrium of the company because they take into account various possible financial crises. A study on the influence of financial liquidity and financial solvency on the performance of healthcare companies was conducted in Batrancea (2021b) using econometric models. From the empirical evidence, it follows that certain financial parameters such as current liquidity ratio, quick liquidity ratio, and financial leverage significantly influence company performance, as measured by the return on assets, gross margin ratio, operating margin ratio, taxes, earnings before interest, amortization, and depreciation. The limitation that was related to the infinite lifetime of companies was removed in 2008 by Brusov, Filatova, and Orekhova (Brusov et al. 2018), who developed the modern theory of capital cost and capital structure (the BFO theory), which is applicable to companies of all ages. Modifications to the calculations for the tax shield and company value (unleveraged, V0; leveraged, V ) were required for the generalization of the MM theory (see the formulae below): TS = kd DT

n X

ð1 þ k d Þ - t = DT½1- ð1 þ kd Þ - n :

ð13:9Þ

t=1

V 0 = CF½1- ð1 þ k0 Þ - n =k0 ;

V = CF½1- ð1 þ WACCÞ - n =WACC:

ð13:10Þ

13.1

Introduction

245

1 - ð1 þ k 0 Þ - n 1 - ð1 þ WACCÞ - n : = WACC k 0 ½1 - ωd T ð1 - ð1 þ k d Þ - n Þ

ð13:11Þ

D S is the debt capital, ke , we = DþS is the where S is the equity capital value, wd = DþS equity capital, L = D/S is the value of financial leverage, and D is the debt value. The Myers formula for a one-year company (Myers 2001) can be easily obtained from Formula (13.11) by substituting n = 1:

WACC = k 0 -

ð1 þ k 0 Þk d wd T 1 þ kd

ð13:12Þ

Then, by substituting n = 1, we arrive at the Modigliani–Miller formula for WACC (Мodigliani and Мiller 1958): WACC = k0  ð1- wd t Þ

ð13:13Þ

Until 2008, when the BFO theory was created, there were only two options: the Modigliani–Miller theory for perpetual companies (Мodigliani and Мiller 1958, 1963, 1966) and the Myers theory for one-year companies (Myers 2001). As the authors of the BFO showed, taking the finite age of a company into account leads to significant changes in all Modigliani–Miller results (Мodigliani and Мiller 1958, 1963, 1966). In addition, a number of the new effects that are observed within corporate finance using the Brusov–Filatova–Orekhova theory (Brusov et al. 2018) are absent in the Modigliani–Miller theory. In Brusov et al. (2020), the Modigliani-Miller theory was modified for the case of advance profit tax payments and significant differences were found between the modified theory and the “classical” Modigliani-Miller theory. In the literature, the methodology and results of the Brusov–Filatova–Orekhova (BFO) theory are well known (for example, see references Dimitropoulos (2014); Luiz and Cruz (2015); Barbi (2011); Zhukov (2018); Franc-Dąbrowska et al. (2021); Angotti et al. (2018); Vergara-Novoa et al. (2018); Mundi et al. (2022); Sadiq et al. (2022); Becker (2022); El-Chaarani et al. (2022); Huang et al. (2020)). A number of chapters (see, for example, Vergara-Novoa et al. (2018); Mundi et al. (2022); Sadiq et al. (2022)) have used the BFO theory in practical calculations. The authors Franc-Dąbrowska et al. (2021) valuated the capital costs of energy companies by including an investor and market risk approach. The study also concerned a WACC intra-industry analysis of the companies, which was related to the sector characteristics of revenue, total assets, company age, and market capitalization. In Mundi et al. (2022), the influence of the overconfidence of finance managers on the capital structure decisions of family-run businesses in India was studied. It was shown that the capital structure decisions of managers could be explained by measurable managerial characteristics. In Sadiq et al. (2022), the correlation between company risk and capital structure was explored using datasets from sugar and

246

13

Influence of Method and Frequency of Profit Tax Payments on. . .

cement companies in Pakistan. It was shown that the role of risk assessment and capital structure is vital for the sustainable growth of companies and the increase in the wealth of shareholders. The author Becker (2022) considered the adjusted present value method, the free cash flow (FCF) method, the flow-to-equity method, and the relationships between these methods. The authors departed from Modigliani and Miller method and used a stationary FCF method and the Miles and Ezzell method to consider FCF as a firstorder autoregressive possession. The authors derived DCF valuation formulae for annuities. The authors found (1) the correct discount rate for the tax shield when the free cash flow is a first-order autoregressive annuity and (2) the tax shield valuation of a first-order autoregressive free cash flow annuity. The author El-Chaarani et al. (2022) studied the impacts of internal and external corporate governance mechanisms on the financial performance of banks in the MENA region during the COVID-19 pandemic. The results showed that the corporate governance measures of the presence of independent members on the board of directors, strong legal protection, a high concentration of ownership, and the lack of political pressure on board members had positive effects on the financial indicators of banks. In Huang et al. (2020), the influence of leverage level on the expected equity returns of listed companies was studied. The existence of an optimal capital structure to maximize the expected equity returns was discussed. The authors thought that this problem should be discussed from the perspective of maximizing shareholder wealth and not from the perspective of maximizing company value due to the existence of financial distress costs and agency costs. Using Gebhardt–Lee–Swaminathan (GLS) model to measure the implied capital costs and to measure the expected equity returns, the authors empirically found that the leverage level had a positive correlation with the equity returns of a listed company. The relationship between the leverage level and the expected equity returns appeared to an inverse “U”: • When the leverage level fell below the optimal level, increasing the leverage could increase the expected equity returns; • When the leverage level was higher than the optimal level, deleveraging was beneficial to increase the expected equity returns. Within a standard capital structure model, the authors Islam and Khandaker (2015) investigated the leverage decisions of over 1500 companies that were listed in the ASX for 2000–2012 and divided the sample into mining and non-mining industries. Applying a dummy variable approach, the authors showed that there were fundamental differences between these two types of companies when making leverage decisions. It turned out that mining companies were more sensitive to profitability and asset tangibility, whereas neither profitability nor asset tangibility was significant for non-mining companies. The obtained results suggested that industry type matters for companies when making leverage decisions. In Barbi (2011), the author discussed the disagreement in the financial literature about the meaning of the “value of tax shields.” Although it is accepted that the tax deductibility of interest increases the value of a firm, the correct valuation of this

The Modified Brusov–Filatova–Orekhova (BFO) Theory for the Case. . .

13.2

247

added value is controversial. Using a risk-neutral approach, the authors derived a general formula for the valuation of tax shields, which shows that this value equals the summation of the discounted future tax savings. As soon as the authors specified a leverage level policy and cash flow dynamics, they obtained some well-known formulae for the calculation of tax shields.

13.2

The Modified Brusov–Filatova–Orekhova (BFO) Theory for the Case of Frequent Advance Profit Tax Payments

In this section, we generalize the Brusov–Filatova–Orekhova (BFO) theory for the case of frequent advance profit tax payments. The expressions for the tax shield, company value, WACC, and equity cost are presented in Sects. 13.2.1, 13.2.2, and 13.2.3, respectively. In this section, we use the following definitions. D S k d , wd = k e , we =

Debt Capital Value Equity Capital Value Debt Capital Cost and Share

D DþS S DþS

Equity Capital Cost and Share

L = D/S WACC

Leverage Level Weighted Average Cost of Capital

k0, the equity cost for a financially independent company; p, the number of payments per year; T, profit tax

13.2.1

The Tax Shield Calculation

We started with the calculation of the tax shield for the case of frequent advance profit tax payments using the Brusov–Filatova–Orekhova theory (where p is the number of payments per year when payments are made at the beginning of the financial period). For a period of n years, the tax shield (TS) was equal to the sum of the discounted values of benefits from the use of tax incentives: ðTSÞn =

k d Dt kd Dt kd Dt kd Dt þ þ :... þ þ 1= 2= np= p p p pð 1 þ k d Þ pð 1 þ k d Þ pð 1 þ k d Þ p

We used a geometric progression with the denominator q = After summation, we obtained:

1 1. ð1þkd Þ =p

ð13:14Þ

248

13

Influence of Method and Frequency of Profit Tax Payments on. . .

k d Dt ð1 - ð1 þ k d Þ - n Þ kd Dt ð1 - ð1 þ kd Þ - n Þ  ð1 þ kd Þ    = ðTSÞn =  1= 1= p ð1 þ k d Þ p - 1 p 1 - ð1 þ k d Þ - p

1= p

ð13:15Þ

Using the classical Brusov–Filatova–Orekhova theory at p = 1, we obtained: ðTSÞn = Dt ð1- ð1 þ kd Þ - n Þ  ð1 þ kd Þ

ð13:16Þ

It was easy to obtain this result from Formula (13.15) by inputting the value of p = 1 for the number of profit tax payments.

13.2.2

Derivation of the Modified BFO Formula for the Weighted Average Cost of Capital (WACC)

We now present the modified BFO formula for the weighted average cost of capital (WACC) for the case of frequent advance profit tax payments (where p is the number of payments per year when the payments are made at the beginning of the financial period). For the value of a leveraged company (V ), we obtained: V = V 0 þ ðTSÞn

ð13:17Þ

where V0 is the value of an unleveraged company. By substituting Formula (13.19) for TS, we obtained: V = V0 þ

k d Dt ð1 - ð1 þ k d Þ - n Þ  ð1 þ k d Þ   1= p ð1 þ k d Þ p - 1

1= p

ð13:18Þ

After substituting D = wdV, we obtained: 0

1 1= -n p w t ð 1 ð 1 þ k Þ Þ  ð 1 þ k Þ k 1 d d d d A = V0   V@ 1= p ð1 þ k d Þ p - 1

ð13:19Þ

Assuming that the values of a leveraged company (V ) and an unleveraged company (V0) were equal to: V=

CFð1 - ð1 þ k0 Þ - n Þ CFð1 - ð1 þ WACCÞ - n Þ ; V0 = WACC k0

respectively, we obtained:

ð13:20Þ

13.2

The Modified Brusov–Filatova–Orekhova (BFO) Theory for the Case. . .

249

0 1 1= CFð1 - ð1 þ WACCÞ - n Þ @1 - k d wd tð1 - ð1 þ k d Þ - n Þ  ð1 þ k d Þ p A    1= WACC p ð1 þ k d Þ p - 1 =

CF  ð1 - ð1 þ k 0 Þ - n Þ k0

ð13:21Þ

From there, we could derive the modified BFO formula for the WACC of a company of age n years for the case of p profit tax payments per year (payments at the beginning of the financial period): 1 - ð1 þ WACCÞ - n = WACC

 k0

CFð1 - ð1 þ k0 Þ - n Þ 1=p

1 - k d wd tð1 - ð1þk d Þ - n Þð1þkd Þ



1=p

p ð1þkd Þ

-1





ð13:22Þ

For p = 1, we obtained the modified BFO formula for advance annual profit tax payments: 1 - ð1 þ k 0 Þ - n 1 - ð1 þ WACCÞ - n = WACC k 0  ð1 - wd t ½1 - ð1 þ k d Þ - n   ð1 þ k d ÞÞ

13.2.3

ð13:23Þ

Formulae for the Capital Value and Equity Cost

In Sect. 13.3, we present our investigation into the impact of the frequency of profit tax payments on the dependence of the WACC, capital value, and equity cost on the leverage level of companies of different ages (3 or 6 years) using Microsoft Excel. For the WACC, we used Formula (13.10) and for capital value and equity cost, we used Formulae (13.24) and (13.25), respectively (see below). The value of a company of age n could be calculated using the following formula: V=

CF  ð1 - ð1 þ WACCÞ - n Þ WACC

ð13:24Þ

Then, the equity cost could be found using the following equation: WACC = k e we þ k d wd ð1- t Þ ke =

WACC kd ð1 - t Þwd = WACCð1 þ LÞ - Lkd ð1- t Þ we we

where the WACC value is found using Formula (13.22).

ð13:25Þ

250

13.3

13

Influence of Method and Frequency of Profit Tax Payments on. . .

Results and Discussions

We studied the impact of the frequency of advance profit tax payments on the dependence of the WACC, capital value, and equity cost on the leverage level of companies of different ages (3 or 6 years) using Microsoft Excel. We considered the advance profit tax payments using the formulae that were obtained above: Formula (13.22) was used for WACC, Formula (13.24) was used for capital value, and Formula (13.25) was used for equity cost. By using the BFO theory, we could study companies of any age. Three- and six-year-old companies were considered as examples to estimate the impact of age on the financial parameters of a company. We used a large database, which can be made available to interested readers upon request. We used data that showed the influence of advance profit tax payments with an arbitrary frequency on the financial parameters of the selected companies. Then, we compared the results of the calculations of two types of profit tax payments: (1) payments at the end of the financial period (Brusov et al. 2022) and (2) at the beginning of the financial period (i.e., in advance). The following parameters were used: k0 = 0.2; kd = 0.18; t = 0.2; n = 3 or 6; CF = 100. The chosen parameters were typical for companies and the results that were obtained using other parameters were similar and did not show any qualitative differences.

13.3.1

The Impact of the Frequency of Profit Tax Payments on the Dependence of the Weighted Average Cost of Capital, Capital Value, and Equity Cost on the Leverage Level of a Three-Year-Old Company

In Tables 13.1, 13.2, and 13.3, we present the results of our study on the impact of the frequency of profit tax payments on the dependence of the WACC, capital value, and equity cost on the leverage level of a three-year-old company with payment frequencies of p = 1, 2, 4, 6, and 12. As can be seen from Fig. 13.1, the WACC decreased with L for all frequencies (annual, semi-annual, quarterly, monthly, etc.) of advance profit tax payments. So, the debt financing led to a decrease in the corresponding capital cost with L and thus, its use by the company was important. The WACC values increased with the frequency of payments, which meant that more infrequent payments were beneficial for the company. The influence of the payment frequency was stronger for annual, semi-annual, and quarterly payments and decreased for monthly payments. As can be seen from Fig. 13.2, the company value (V ) increased with L for all frequencies (annual, semi-annual, quarterly, monthly, etc.) of advance profit tax payments. So, the debt financing led to an increase in the company value with L and thus, its use by the company was important. This was consistent with the decrease in WACC with the leverage level, as shown in the previous section. The company

13.3

Results and Discussions

251

Table 13.1 The dependence of the WACC on the leverage level (L ) of a three-year-old company for advance profit tax payments with frequencies of p = 1, 2, 4, 6, and 12 L 1 2 3 4 5 6 7 8 9 10

Wd 0.5 0.666667 0.75 0.8 0.833333 0.857143 0.875 0.888889 0.9 0.909091

WACC, n = 3 (2) p=1 p=2 0.1703 0.1715 0.1603 0.1619 0.1553 0.1571 0.1523 0.1542 0.1503 0.1523 0.1489 0.1509 0.1478 0.1499 0.1469 0.1491 0.1463 0.1484 0.1457 0.1479

p=4 0.1721 0.1627 0.1580 0.1552 0.1533 0.1519 0.1509 0.1501 0.1495 0.1490

p=6 0.1723 0.1629 0.1583 0.1555 0.1536 0.1522 0.1512 0.1505 0.1498 0.1493

p = 12 0.1725 0.1632 0.1586 0.1558 0.1539 0.1526 0.1516 0.1508 0.1502 0.1497

Table 13.2 The dependence of the company value (V ) on the leverage level (L ) of a three-year-old company for advance profit tax payments with frequencies of p = 1, 2, 4, 6, and 12 L 1 2 3 4 5 6 7 8 9 10

Wd 0.5 0.666667 0.75 0.8 0.833333 0.857143 0.875 0.888889 0.9 0.909091

V p=1 220.8472 224.4700 226.3263 227.4549 228.2136 228.7586 229.1691 229.4893 229.7462 229.9568

p=2 220.4234 223.8866 225.6593 226.7365 227.4603 227.9802 228.3717 228.6771 228.9220 229.1228

p=4 220.2163 223.6018 225.3339 226.3861 227.0930 227.6007 227.9829 228.2811 228.5202 228.7162

p=6 220.1479 223.5079 225.2266 226.2705 226.9719 227.4756 227.8548 228.1506 228.3878 228.5823

p = 12 220.0800 223.4144 225.1199 226.1557 226.8515 227.3512 227.7274 228.0208 228.2561 228.4490

Table 13.3 The dependence of the equity cost (ke) on the leverage level (L ) of a three-year-old company for advance profit tax payments with frequencies of p = 1, 2, 4, 6, and 12 L 1 2 3 4 5 6 7 8 9 10

Wd 0.5 0.666667 0.75 0.8 0.833333 0.857143 0.875 0.888889 0.9 0.909091

ke p=1 0.1966 0.1930 0.1892 0.1855 0.1817 0.1780 0.1742 0.1704 0.1666 0.1628

p=2 0.1990 0.1977 0.1964 0.1951 0.1937 0.1923 0.1910 0.1896 0.1882 0.1868

p=4 0.2002 0.2001 0.1999 0.1998 0.1996 0.1994 0.1992 0.1990 0.1988 0.1986

p=6 0.2005 0.2008 0.2011 0.2013 0.2015 0.2017 0.2019 0.2021 0.2023 0.2025

p = 12 0.2009 0.2016 0.2022 0.2028 0.2034 0.2040 0.2046 0.2052 0.2058 0.2063

252

Influence of Method and Frequency of Profit Tax Payments on. . .

13

WACC(L) at different p (n=3)

WACC (L)

0.1700 0.1650

p=1 p=2 p=4 p=6 p=12

0.1600 0.1550 0.1500 0.1450

1

2

3

4

5

6

7

8

9

10

Fig. 13.1 The dependence of the WACC on the leverage level (L ) of a three-year-old company for advance profit tax payments with frequencies of p = 1, 2, 4, 6, and 12

V(L) at different p (n=3) 232.0000 230.0000 V (L)

228.0000

p=1 p=2 p=4 p=6 p=12

226.0000 224.0000 222.0000 220.0000

1

2

3

4

5

6

7

8

9

10

Fig. 13.2 The dependence of the company value (V ) on the leverage level (L ) of a three-year-old company for advance profit tax payments with frequencies of p = 1, 2, 4, 6, and 12

value decreased with the frequency of payments, which meant that more infrequent payments were beneficial for the company. The influence of the payment frequency was stronger for annual, semi-annual, and quarterly payments and decreased for monthly payments. This was consistent with the WACC behavior that was shown in the previous section. As can be seen from Fig. 13.3, the equity cost (ke) depended on the leverage level in a linear manner. It was not expected for ke(L ) to be linear because the BFO equation for the WACC was an n + 1 power equation. However, as can be seen from the figures and tables for the equity cost results, this occurred with a high accuracy. We called the relationship quasi-linear (or practically linear). Our entire extensive database showed that this was the case. The equity cost decreased for annual ( p = 1), semi-annual ( p = 2), and quarterly ( p = 4) payments and increased for monthly ( p = 12) and bi-monthly payments ( p = 6). The tilt angle of ke(L ) increased with p and the transition from ke increasing with L to ke decreasing with L occurred at p = 4.

13.3

Results and Discussions

253

ke(L) at different p (n=3) 0.2100 0.2000 Ke (L)

0.1900

p=1 p=2 p=4 p=6 p=12

0.1800 0.1700 0.1600 0.1500

1

2

3

4

5

6

7

8

9

10

Fig. 13.3 The dependence of the equity cost (ke) on the leverage level (L ) of a three-year-old company for advance profit tax payments with frequencies of p = 1, 2, 4, 6, and 12

WACC(L): Comparison of (1) and (2) at p=2,4,6,12 0.1750

WACC (L)

0.1700

(1) p=2 (1) p=4 (1) p=6 (2) p=2 (2) p=4 (2) p=6 (1) p=12 (2) p=12

0.1650 0.1600 0.1550 0.1500 0.1450

1

2

3

4

5

6

7

8

9

10

Fig. 13.4 The comparison of the dependence of the WACC on the leverage level (L ) of a threeyear-old company for profit tax payments that were (1) made at the end of the financial period and (2) made at the beginning of the financial period (i.e., advance payments) with frequencies of p = 2, 4, 6, and 12

The economically justified amount of dividends was equal to the equity cost; therefore, the decrease in the equity cost with the leverage level signaled the discovery of a new effect that could significantly change the company’s dividend policy. Below, we compare the dependence of the WACC, company value, and equity cost on the leverage level of a three-year-old company for profit tax payments that were (1) made at the end of the financial period (data from Ref. (Brusov et al. 2022)) and (2) made at the beginning of the financial period (i.e., advance payments) with frequencies of p = 2, 4, 6, and 12. The comparison of the dependence of the WACC on the leverage level (L ) of a three-year-old company for profit tax payments that were (1) made at the end of the financial period and (2) made at the beginning of the financial period (i.e., advance payments) with frequencies of p = 2, 4, 6, and 12 is shown in Fig. 13.4.

254

Influence of Method and Frequency of Profit Tax Payments on. . .

13

V(L): Comparison of (1) and (2) at p=2,4,6,12 231.0000 229.0000

(1) p=2 (1) p=4 (1) p=6 (2) p=2 (2) p=4 (2) p=6 (1) p=12 (2) p=12

V (L)

227.0000 225.0000 223.0000 221.0000 219.0000

1

2

3

4

5

6

7

8

9

10

Fig. 13.5 The comparison of the dependence of the company value (V ) on the leverage level (L ) of a three-year-old company for profit tax payments that were (1) made at the end of the financial period and (2) made at the beginning of the financial period (i.e., advance payments) with frequencies of p = 2, 4, 6, and 12 is shown in Fig. 13.4

The WACC(L ) decreased with L in both cases: advance profit tax payments and payments at the end of the financial year. This meant that debt financing was important and should be used by the company as it led to a decrease in the corresponding capital cost with L. In the case of profit tax payments that were made at the end of the financial year, the WACC(L ) decreased with p, while in the case of advance profit tax payments, the WACC(L ) increased with p. However, in spite of this, the WACC(L ) always turned out to be lower in the case of advance profit tax payments. From Fig. 13.4, it can be seen, for example, that WACC(L = 10) = 0.1504 at p = 12 for profit tax payments that were made at the end of the financial year while WACC (L = 10) = 0.1497 at p = 12 for advance profit tax payments. The WACC(L ) curves for these two cases never crossed, i.e., the WACC values for advance profit tax payments always turned out to be lower than in the case of profit tax payments that were made at the end of the financial year. This demonstrated the importance of the use of advance profit tax payments for companies because the lower values of WACC corresponded to higher company values. The comparison of the dependence of the company value (V ) on the leverage level (L ) of a three-year-old company for profit tax payments that were (1) made at the end of the financial period and (2) made at the beginning of the financial period (i.e., advance payments) with frequencies of p = 2, 4, 6, and 12 is shown in Fig. 13.5. Figure 13.5 shows that the company value increased with L for all payment frequencies (annual, semi-annual, quarterly, monthly, etc.) in both cases: advance profit tax payments and payments at the end of the financial period. So, the debt financing led to an increase in the company value with L and thus, it was important and should be used by the company. This was consistent with the decrease in the WACC with L, as shown in the previous section. The company value decreased with

13.3

Results and Discussions

255

ke (L)

ke(L): Comparison (1) and (2) at p=2,4,6,12 0.2350 0.2300 0.2250 0.2200 0.2150 0.2100 0.2050 0.2000 0.1950 0.1900 0.1850

(1) p=2 (1) p=4 (1) p=6 (2) p=2 (2) p=4 (2) p=6 (1) p=12 (2) p=12 1

2

3

4

5

6

7

8

9

10

Fig. 13.6 The comparison of the dependence of the equity cost (ke) on the leverage level (L ) of a three-year-old company for profit tax payments that were (1) made at the end of the financial period and (2) made at the beginning of the financial period (i.e., advance payments) with frequencies of p = 2, 4, 6, and 12

the frequency of payments in the case of profit tax payments being made at the beginning of the financial period (i.e., advance payments), which meant that more infrequent payments were beneficial for the company. The company value increased with the frequency of payments in the case of profit tax payments being made at the end of the financial period. However, in spite of this, V(L ) always turned out to be bigger in the case of advance profit tax payments. From Fig. 13.5, it can be seen, for example, that V(L = 10) = 228.1849 at p = 12 for profit tax payments that were made at the end of the financial year, while V(L = 10) = 228.4490 at p = 12 for advance profit tax payments. Note that the V(L ) curves that corresponded to these two cases never crossed. The influence of the payment frequency was stronger for annual, semi-annual, and quarterly payments and decreased for monthly payments. This was consistent with the WACC behavior that was shown in the previous section. The comparison of the dependence of the equity cost (ke) on the leverage level (L ) of a three-year-old company for profit tax payments that were (1) made at the end of the financial period and (2) made at the beginning of the financial period (i.e., advance payments) with frequencies of p = 2, 4, 6, and 12 is shown in Fig. 13.6. From Fig. 13.6, it can be seen that the equity cost (ke) depended on the leverage level (L ) in a linear manner in both cases ((1) and (2)) for all values of p. In the case of profit tax payments being made at the end of the financial period, the tilt angle of ke(L) decreased with p but ke(L) continued to increase with L for all values of p. In the case of advance profit tax payments, the tilt angle of ke(L) increased with p and the transition from ke increasing with L to ke decreasing with L occurred at p = 4. Additionally, ke(L ) decreased with L for annual ( p = 1), semi-annual ( p = 2), and quarterly ( p = 4) payments and increased for monthly ( p = 12) and bi-monthly payments ( p = 6). The economically justified amount of dividends was equal to the equity cost; therefore, the decrease in the equity cost with the leverage level signaled the discovery of a new effect that could significantly change the dividend policy of a

256

13

Influence of Method and Frequency of Profit Tax Payments on. . .

company. This effect only occurred in the case of advance profit tax payments. Note that with the increase in p, the ke(L ) curves for the two cases ((1) and (2)) approached each other but never crossed.

13.3.2

The Impact of the Frequency of Profit Tax Payments on the Dependence of the Weighted Average Cost of Capital, Capital Value, and Equity Cost on the Leverage Level of a Six-Year-Old Company

In Tables 13.4, 13.5, and 13.6, we present the results of our study on the impact of the frequency of profit tax payments on the dependence of the WACC, capital value,

Table 13.4 The dependence of the WACC on the leverage level (L ) of a six-year-old company for advance profit tax payments with frequencies of p = 1, 2, 4, 6, and 12 L 1 2 3 4 5 6 7 8 9 10

Wd 0.5 0.666667 0.75 0.8 0.833333 0.857143 0.875 0.888889 0.9 0.909091

WACC, n = 6 (2) p=1 p=2 0.1697 0.1709 0.1593 0.1610 0.1542 0.1560 0.1510 0.1530 0.1489 0.1510 0.1474 0.1496 0.1463 0.1485 0.1454 0.1477 0.1447 0.1470 0.1442 0.1464

p=4 0.1715 0.1618 0.1569 0.1540 0.1520 0.1506 0.1496 0.1487 0.1481 0.1475

p=6 0.1717 0.1621 0.1572 0.1543 0.1524 0.1510 0.1499 0.1491 0.1484 0.1479

p = 12 0.1719 0.1623 0.1575 0.1546 0.1527 0.1513 0.1503 0.1495 0.1488 0.1483

Table 13.5 The dependence of the company value (V ) on the leverage level (L ) of a six-year-old company for advance profit tax payments with frequencies of p = 1, 2, 4, 6, and 12 L 1 2 3 4 5 6 7 8 9 10

Wd 0.5 0.666667 0.75 0.8 0.833333 0.857143 0.875 0.888889 0.9 0.909091

V p=1 359.2385 369.1124 374.2557 377.4110 379.5443 381.0830 382.2451 383.1540 383.8841 384.4836

p=2 358.0973 367.5078 372.4010 375.4000 377.4263 378.8871 379.9901 380.8525 381.5452 382.1139

p=4 357.5406 366.7265 371.4988 374.4222 376.3969 377.8201 378.8947 379.7347 380.4093 380.9631

p=6 357.3571 366.4692 371.2017 374.1003 376.0581 377.4690 378.5342 379.3669 380.0356 380.5845

p = 12 357.1746 366.2133 370.9064 373.7805 375.7214 377.1201 378.1761 379.0014 379.6643 380.2084

13.3

Results and Discussions

257

Table 13.6 The dependence of the equity cost (ke) on the leverage level (L ) of a six-year-old company for advance profit tax payments with frequencies of p = 1, 2, 4, 6, and 12 L 1 2 3 4 5 6 7 8 9 10

ke p=1 0.1953 0.1900 0.1846 0.1791 0.1736 0.1680 0.1624 0.1569 0.1513 0.1457

Wd 0.5 0.666667 0.75 0.8 0.833333 0.857143 0.875 0.888889 0.9 0.909091

p=2 0.1978 0.1950 0.1920 0.1891 0.1860 0.1830 0.1799 0.1769 0.1738 0.1707

p=4 0.1990 0.1974 0.1957 0.1939 0.1921 0.1903 0.1885 0.1867 0.1848 0.1830

p=6 0.1994 0.1982 0.1969 0.1955 0.1941 0.1927 0.1913 0.1899 0.1885 0.1870

p = 12 0.1997 0.1990 0.1981 0.1971 0.1961 0.1951 0.1941 0.1931 0.1921 0.1911

WACC(L) at different p (n=6) 0.1750 0.1700 WACC (L)

0.1650

p=1

0.1600

p=2

0.1550

p=4

0.1500

p=6

0.1450 0.1400

p=12 1

2

3

4

5

6

7

8

9

10

Fig. 13.7 The dependence of the WACC on the leverage level (L ) of a six-year-old company for advance profit tax payments with frequencies of p = 1, 2, 4, 6, and 12

and equity cost on the leverage level of a six-year-old company with payment frequencies of p = 1, 2, 4, 6, and 12. As can be seen from Fig. 13.7, the WACC decreased with L in the case of advance profit tax payments for all payment frequencies (annual, semi-annual, quarterly, monthly, etc.). So, debt financing led to a decrease in the corresponding capital cost with L and thus, should be used by the company. The WACC values increased with the frequency of payments, which meant that more infrequent payments were beneficial for the company. The influence of the payment frequency was stronger for annual, semi-annual, and quarterly payments and decreased for monthly payments. As can be seen from Fig. 13.8, the company value (V ) increased with L in the case of advance profit tax payments for all payment frequencies (annual, semi-annual, quarterly, monthly, etc.). This was consistent with the decrease in the WACC with

258

Influence of Method and Frequency of Profit Tax Payments on. . .

13

V(L) at different p (n=6) 390.0000 385.0000

V (L)

380.0000

p=1 p=2 p=4 p=6 p=12

375.0000 370.0000 365.0000 360.0000 355.0000

1

2

3

4

5

6

7

8

9

10

Fig. 13.8 The dependence of the company value (V ) on the leverage level (L ) of a six-year-old company for advance profit tax payments with frequencies of p = 1, 2, 4, 6, and 12

ke(L) at different p (n=6) 0.2000

Ke (L)

0.1900 0.1800

p=1 p=2 p=4 p=6 p=12

0.1700 0.1600 0.1500 0.1400

1

2

3

4

5

6

7

8

9

10

Fig. 13.9 The dependence of the equity cost (ke) on the leverage level (L ) of a six-year-old company for advance profit tax payments with frequencies of p = 1, 2, 4, 6, and 12

the leverage level, as shown in the previous section. The company value decreased with the frequency of payments, which meant that more infrequent payments were beneficial for the company. The influence of the payment frequency was stronger for annual, semi-annual, and quarterly payments and decreased for monthly payments. This was consistent with the WACC behavior that was shown in the previous section. As can be seen from Fig. 13.9, the equity cost (ke) depended on the leverage level (L ) in a linear manner. It decreased for annual ( p = 1), semi-annual ( p = 2), and quarterly ( p = 4) payments and increased for monthly ( p = 12) and bi-monthly payments ( p = 6). The economically justified amount of dividends was equal to the equity cost; therefore, the decrease in the equity cost with the leverage level signaled the discovery of a new effect that could significantly change the dividend policy of the company. Note that for the three-year-old company, ke increased with L for

13.3

Results and Discussions

259

WACC(L): Comparison of (1) and (2) at p=2,4,6,12 0.1750

(1) p=2

WACC (L)

0.1700

(1) p=4

0.1650

(1) p=6

0.1600

(2) p=2

0.1550

(2) p=4 (2) p=6

0.1500 0.1450

(1) p=12 1

2

3

4

5

6

7

8

9

10

(2) p=12

Fig. 13.10 The comparison of the dependence of the WACC on the leverage level (L ) of a sixyear-old company for profit tax payments that were (1) made at the end of the financial period and (2) made at the beginning of the financial period (i.e., advance payments) with frequencies of p = 2, 4, 6, and 12

monthly ( p = 12) and bi-monthly payments ( p = 6) and the transition from decreasing to increasing behavior occurred at p = 4. The comparison of the dependence of the WACC on the leverage level (L ) of a six-year-old company for profit tax payments that were (1) made at the end of the financial period and (2) made at the beginning of the financial period (i.e., advance payments) with frequencies of p = 2, 4, 6, and 12 is shown in Fig. 13.10. The WACC(L ) decreased with L in both cases: profit tax payments that were made at the beginning of the financial period and payments that were made at the end of the financial period. This meant that the debt financing led to a decrease in the corresponding capital cost with L and should be used by the company. The WACC(L ) decreased with p in the case of profit tax payments being made at the end of the financial period, while in the case of profit tax payments being made at the beginning of the financial period (i.e., advance payments), the WACC(L ) increased with p. However, in spite of this, the WACC(L ) always turned out to be lower in the latter case. From Fig. 13.10, it can be seen, for example, that WACC (L = 10) = 0.1490 at p = 12 for profit tax payments that were made at the end of the financial year while WACC(L = 10) = 0.1483 at p = 12 for advance profit tax payments. The WACC(L ) curves for these two cases never crossed, i.e., the WACC values for advance profit tax payments always turned out to be lower than in the case of profit tax payments that were made at the end of the financial year. Thus, the use of advance profit tax payments was quite important for the company because lower values of WACC corresponded to higher company values. This conclusion is valid for companies of any age. The comparison of the dependence of the company cost (V ) on the leverage level (L ) of a six-year-old company for profit tax payments that were (1) made at the end of the financial period and (2) made at the beginning of the financial period (i.e., advance payments) with frequencies of p = 2, 4, 6, and 12 is shown in Fig. 13.11.

260

Influence of Method and Frequency of Profit Tax Payments on. . .

13

V(L): Comparison of (1) and (2) at p=2,4,6,12 385.0000 (1) p=2 (1) p=4 (1) p=6 (2) p=2 (2) p=4 (2) p=6 (1) p=12 (2) p=12

380.0000 V (L)

375.0000 370.0000 365.0000 360.0000 355.0000

1

2

3

4

5

6

7

8

9

10

Fig. 13.11 The comparison of the dependence of the company value (V ) on the leverage level (L ) of a six-year-old company for profit tax payments that were (1) made at the end of the financial period and (2) made at the beginning of the financial period (i.e., advance payments) with frequencies of p = 2, 4, 6, and 12

As can be seen from Fig. 13.11, the company value (V ) increased with L for all payment frequencies (annual, semi-annual, quarterly, monthly, etc.) in both cases: profit tax payments that were made at the beginning of the financial period (i.e., advance payments) and profit tax payments that were made at the end of the financial period. So, the debt financing led to an increase in the company value with the leverage level and thus should be used by the company. This was consistent with the decrease in the WACC with the leverage level, as shown in the previous section. The company value decreased with the frequency of payments in the case of advance profit tax payments, which meant that more infrequent payments were beneficial for the company and increased with the frequency of payments in the case of profit tax payments that were made at the end of the financial period. However, in spite of this, the V(L ) always turned out to be bigger in the case of advance profit tax payments. From Fig. 13.11, it can be seen, for example, that V(L = 10) = 379.4635 at p = 12 for profit tax payments that were made at the end of the financial year while V(L = 10) = 380.2084 at p = 12 for advance profit tax payments. Note that the V(L) curves that corresponded to these two cases never crossed. The influence of the payment frequency was stronger for annual, semiannual, and quarterly payments and decreased for monthly payments. This was consistent with the WACC behavior that was shown in the previous section. The comparison of the dependence of the equity cost (ke) on the leverage level (L ) of a six-year-old company for profit tax payments that were (1) made at the end of the financial period and (2) made at the beginning of the financial period (i.e., advance payments) with frequencies of p = 2, 4, 6, and 12 is shown in Fig. 13.12. From Fig. 13.12, it can be seen that the equity cost (ke) depended on the leverage level (L ) in a linear manner in both cases ((1) and (2)) for all values of p (similar to the case of the three-year-old company). In the case of profit tax payments that were made at the end of the financial period, the tilt angle of ke(L ) decreased with p, but

13.4

Conclusions

261

ke (L)

ke(L): Comparison of (1) and (2) at p=2,4,6,12 0.2200 0.2150 0.2100 0.2050 0.2000 0.1950 0.1900 0.1850 0.1800 0.1750 0.1700

(1) p=2 (1) p=4 (1) p=6 (2) p=2 (2) p=4 (2) p=6 (1) p=12

1

2

3

4

5

6

7

8

9

10

(2) p=12

Fig. 13.12 The comparison of the dependence of the equity cost (ke) on the leverage level (L ) of a six-year-old company for profit tax payments that were (1) made at the end of the financial period and (2) made at the beginning of the financial period (i.e., advance payments) with frequencies of p = 2, 4, 6, and 12

ke(L) continued to increase with L at p = 2, 4, and 6 and we only observed the transition to a slight decrease with leverage level at p = 12. Note that for the threeyear-old company, this transition was absent and ke(L) increased with L for all values of p. In the case of profit tax payments that were made at the beginning of the financial period (i.e., advance payments), the tilt angle of ke(L ) increased with p, but ke(L ) decreased with L for all payment frequencies. The economically justified amount of dividends was equal to the equity cost; thus, the discovery of the decrease in equity cost with the leverage level represented a new effect that could greatly change the company’s dividend policy. This effect only occurred in the case of advance profit tax payments. Note that with the increase in p, the ke(L ) curves for the two cases ((1) and (2)) approached each other but never crossed.

13.4

Conclusions

In this chapter, we studied the influence of frequent advance profit tax payments on the main financial indicators of a company. For this, we generalized the Brusov– Filatova–Orekhova (BFO) theory for the case of advance profit tax payments with an arbitrary frequency for the first time. We derived modified BFO formulae and showed that (1) all BFO formulae could change and (2) all of the financial parameters of a company, such as WACC, company value, and equity cost, depended on the frequency of profit tax payments. The weighted average cost of capital (WACC) increased with the payments and the company value decreased with the payments. This meant that more infrequent payments were beneficial for the companies. The tilt angle of the equity cost (ke(L )) also increased with the payments. Depending on the company age, ke(L ) either decreased with L for all payment frequencies or a

262

13

Influence of Method and Frequency of Profit Tax Payments on. . .

transition from the decrease to an increase in ke with L occurred for some frequencies. We compared the obtained results to those that we recently obtained for frequent profit tax payments that were made at the end of the financial period (Brusov et al. 2022) and found them to be totally different. We showed that in spite of the fact that the WACC decreased with the payments and the company value increased with the payments in this case (Brusov et al. 2022), the WACC values turned out to be bigger and the company values turned out to be smaller than in the case of frequent advance profit tax payments for all payment frequencies. This underlined the importance of advance profit tax payments. Regulators should extend the practice of advance income tax payments to profit tax payments. The economically justified amount of dividends was equal to the equity cost; thus, the discovered decrease in the equity cost with the leverage level represented a new effect that could greatly change a company’s dividend policy. In the case of profit tax payments that were made at the end of the financial period, the tilt angle of ke(L) decreased with the payments, but ke(L ) continued to increase with L at p = 2, 4, and 6 and we only observed the transition to a slight decrease with leverage level at p = 12. Note that for the three-year-old company, this transition was absent and ke(L) increased with L for all values of p. In the case of advance profit tax payments, the tilt angle of ke(L ) increased with the payments, but ke(L ) decreased with L for all payment frequencies for the sixyear-old company. For the three-year-old company, ke(L ) decreased at p = 1, 2, and 4 and increased at p = 6 and 12. Thus, for the three-year-old company, the transition from the decreasing ke(L ) behavior to the ke(L ) increasing behavior occurred at p = 6, while for the six-year-old company, this transition was absent. The novelty of the chapter is as follows: 1. We generalized the BFO theory for the case of advance profit tax payments with an arbitrary frequency for the first time; 2. By comparing the obtained results to those for frequent profit tax payments at the end of the financial period, we showed that in spite of the fact that the WACC decreased with the payments and the company value increased with the payments, the WACC value in this case turned out to be bigger and the company value turned out to be smaller than in case of frequent advance profit tax payments for all payment frequencies, which underlined the importance of advance profit tax payments; 3. A new effect of the dependence of equity cost on leverage level was discovered and this pioneering result could radically change the company dividend policies. In the case of advance profit tax payments, the tilt angle of ke(L ) increased with the payments, but ke(L) decreased with L for all payment frequencies for the sixyear-old company and at p = 1, 2, and 4 for the three-year-old company, although it increased at p = 6 and 12. Thus, for the three-year-old company, the transition from the decreasing ke(L ) behavior to the increasing ke(L) behavior occurred at p = 6, while this transition was absent for the six-year-old company;

References

263

4. Regulator recommendations were developed to expand the practice of advance profit tax payments, which would be beneficial to both parties, the companies and the state, (1) this practice would lead to a decrease in the cost of raising capital and an increase in the company value for companies and (2) ensure an increase in the stability of budget revenues for the regulators. There was one limitation of the current consideration: the BFO theory was used with the assumption of a constant income. We will generalize the BFO theory for the case of variable incomes in the next chapter.

References Angotti M, de Lacerda Moreira R, Hipólito Bernardes do Nascimento J, Neto de Almeida Bispo O (2018) Analysis of an equity investment strategy based on accounting and financial reports in Latin American markets. Reficont 5:22–40 Barbi M (2011) On the risk-neutral value of debt tax shields. Appl Financ Econ 22:251–258 Batrancea L (2021a) An econometric approach regarding the impact of fiscal pressure on equilibrium: evidence from electricity, gas and oil companies listed on the New York stock exchange. Mathematics 9:630 Batrancea L (2021b) The influence of liquidity and solvency on performance within the healthcare industry: evidence from publicly listed companies. Mathematics 9:2231 Becker DM (2022) Getting the valuation formulas right when it comes to annuities. Manag Financ 48:470 Berk J, De Marzo P (2007) Corporate finance. Pearson–Addison Wesley, Boston, MA Brusov P, Filatova T, Orehova N, Eskindarov M (2018) Modern corporate finance, investments, taxation and ratings, 2nd edn. Springer Nature Publishing, Cham, pp 1–571 Brusov PN, Filatova TV, Orekhova NP, Kulik VL, Chang SI, Lin YCG (2020) Modification of the Modigliani–Miller theory for the case of advance payments of tax on profit. J Rev Glob Econ 9: 257–267 Brusov PN, Filatova TV, Orekhova NP, Kulik VL, Chang SI, Lin YCG (2022) The generalization of the Brusov–Filatova–Orekhova theory for the case of payments of tax on profit with arbitrary frequency. Mathematics 10:1343. https://doi.org/10.3390/math10081343 Dimitropoulos P (2014) Capital structure and corporate governance of soccer clubs: European evidence. Manag Res Rev 37:658–678 El-Chaarani H, Abraham R, Skaf Y (2022) The impact of corporate governance on the financial performance of the banking sector in the MENA (middle eastern and north African) region: an immunity test of banks for COVID-19. J Risk Financ Manag 15:82 Farber A, Gillet R, Szafarz AA (2006) General formula for the WACC. Int J Bus 11:211–218 Fernandez PA (2006) General formula for the WACC: a comment. Int J Bus 11:219 Franc-Dąbrowska J, Mądra-Sawicka M, Milewska A (2021) Energy sector risk and cost of capital assessment—companies and investors perspective. Energies 14:1613 Hamada R (1969) Portfolio analysis, market equilibrium, and corporate finance. J Financ 24:13–31 Harris R, Pringle J (1985) Risk-adjusted discount rates–extension from the average-risk case. J Financ Res 8:237–244 Huang S, Sun H, Zhao H, Zhang Y (2020) Influence of leverage on the return on equity. Syst Eng Theory Pract 40:355 Islam SZ, Khandaker S (2015) Firm leverage decisions: does industry matter? N Am J Econ Financ 31:94

264

13

Influence of Method and Frequency of Profit Tax Payments on. . .

Luiz K, Cruz M (2015) The relevance of capital structure on firm performance: a multivariate analysis of publicly traded Brazilian companies. REPeC Brasília 9:384–401 Miller M (1977) Debt and taxes. J Financ 32:261–275. https://doi.org/10.1111/j.1540-6261.1977. tb03267.x Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Modigliani F, Miller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391 Mundi HS, Kaur P, Murty RLN (2022) A qualitative inquiry into the capital structure decisions of overconfident finance managers of family-owned businesses in India. Qual Res Financ Mark 14: 357–379 Myers S (2001) Capital structure. J Econ Perspect 15:81–102 Sadiq M, Alajlani S, Hussain MS, Bashir F, Chupradit S (2022) Impact of credit, liquidity, and systematic risk on financial structure: comparative investigation from sustainable production. Environ Sci Pollut Res Int 29:20963–20975 Vergara-Novoa C, Sepúlveda-Rojas JP, Miguel DA, Nicolás R (2018) Cost of capital estimation for highway concessionaires in Chile. J Adv Transp 2018:2153536 Zhukov P (2018) The impact of cash flows and weighted average cost of capital to enterprise value in the oil and gas sector. J Rev Glob Econ 7:138–145

Chapter 14

Generalization of the Brusov–Filatova– Orekhova Theory for the Case of Variable Income

Keywords Generalized Brusov–Filatova–Orekhova theory · Growth rate · Variable income · Company’s capitalization · The weighted average cost of capital · WACC · Equity cost

14.1

Introduction

Among the theories of capital structure, the two main ones are the Brusov–Filatova– Orekhova (BFO) theory and the Modigliani–Miller (MM) theory, which is the eternal limit of the BFO theory. Both of them consider the case of constant income, although in practice, a company’s income is, of course, variable. The generalization of these two theories of capital structure for the case of variable income is very important, since it allows them to expand their applicability in practice. Recently, we have generalized the case of variable income the Modigliani–Miller theory (Brusov et al. 2021a), and here we have generalized for the first time the case of variable income of the Brusov–Filatova–Orekhova theory. This generalization significantly expands the applicability of the modern capital structure theory, which is valid for companies of any age and, in practice, for investments, corporate finance, business valuation, banking, ratings, etc.

14.1.1

Literature Review

The Brusov–Filatova–Orekhova (BFO) theory and its perpetual limit—the theory of Nobel laureates Modigliani and Miller—study capital structure problems. Capital structure is the ratio between the company’s own and borrowed capital and asks whether capital structure affects key company metrics, such as weighted average cost of capital, WACC, cost of equity, ke, earnings, company value, and others, and if so, how? The determination of the optimal capital structure, that is, the determination of capital structure in which WACC is minimal and the company value is maximized, is one of the main problems, solved by the company’s management. The Modigliani and Miller chapter (Мodigliani and Мiller 1958) was the first © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_14

265

266

14

Generalization of the Brusov–Filatova–Orekhova Theory for the Case. . .

quantitative study of the influence of capital structure on a company’s financial parameters. Prior to this, there was a traditional approach based on empirical data analysis.

14.1.2

Before the Modigliani and Miller Work

In the traditional approach, the WACC and the value of the company, V, depend on the level of leverage, L (and, therefore, on the capital structure). Debt is always cheaper than equity, since the former has less risk, and because in the event of bankruptcy, the claims of creditors are satisfied earlier than the claims of shareholders. Thus, an increase in the share of cheaper borrowed capital of the total capital structure to the limit that does not violate financial stability and does not increase the risk of bankruptcy leads to a decrease in the WACC and an increase in the value of the company, V. Further increase of debt financing could lead to financial stability violation and an increase in the bankruptcy risk. WACC increases and the company value, V, decreases. The competition of advantages of debt financing and its shortcomings at low and at high leverage levels forms the optimal capital structure where WACC is minimal and the company value, V, is maximum. These traditional approach results have been used in the trade-off theory.

14.1.3

Modigliani–Miller Theory

14.1.3.1

Modigliani–Miller Theory Without Taxes

Modigliani and Miller (MM) (Мodigliani and Мiller 1958), under a lot of assumptions, including the absence of corporate and individual taxes, the perpetuity of all companies and all cash flows, etc., obtained results that are completely different from the results of the traditional approach: capital structure does not affect capital cost and company value. Under the above restrictions, Modigliani and Miller have shown that without taxes, the company value, V, is equal V = V0 =

EBIT k0

ð14:1Þ

Here, EBIT is Earnings Before Interest and Taxes, k0 is the discount rate, and V0 stands for the unlevered company value. From (14.1) it is easy to obtain WACC:

14.1

Introduction

267

WACC = k0

ð14:2Þ

k0 is the cost of equity for a company without borrowed funds, and for a company with borrowed capital, k0 is the cost of equity with a zero level of borrowed funds (L = 0). From (14.1) and the expression for WACC WACC = k 0 = k e we þ k d wd :

ð14:3Þ

One can obtain the cost of equity, ke ke =

k ðS þ DÞ w D k0 D - kd = k0 þ ðk 0- k d Þ = k 0 - kd d = 0 S we we S S

þ ðk0- kd ÞL

ð14:4Þ

Here, WACC is weighted average cost of capital; L is the leverage level; D is the debt capital value; S is the equity capital value; kd and wd are the cost and share of the company’s debt capital; and ke and we are the equity capital cost and share. From (14.4), it follows that the equity cost increases linearly with the leverage level.

14.1.3.2

Modigliani–Miller Theory with Taxes

Taking into account income tax, in 1963, Modigliani and Miller (1963, 1966) obtained the following result for the value of the levered company, V, V = V0 þ D  t

ð14:5Þ

Here, V0 stands for the unlevered company value, t is the tax on income, and D is the debt value. From (14.5), it is easy to derive the expression for the WACC WACC = k0  ð1- wd t Þ

ð14:6Þ

From (14.6), one can obtain the formula for equity cost, ke, within the Modigliani–Miller theory with taxes k e = k0 þ L  ðk0- k d Þð1- t Þ

ð14:7Þ

Formula (14.7) differs from formula (14.4) (MM without taxes) by the factor (1 - t), which is called the tax corrector. This is less than one, so the tilt of the ke(L ) curve decreases with taxes.

268

14.1.4

14

Generalization of the Brusov–Filatova–Orekhova Theory for the Case. . .

Unification of Capital Asset Pricing Model (CAPM) with Modigliani–Miller Model

Unification of capital asset pricing model (CAPM) with the Modigliani–Miller model was done in 1969 (Hamada 1969). Hamada derived the below formula for the cost of equity of a levered company, which included the financial and business risks of a company: k e = k F þ ðkM- kF ÞbU þ ðkM- k F ÞbU

D ð1- T Þ, S

ð14:8Þ

where bU is the β-coefficient of the company of the same group of business risk, that the company under consideration, but with L = 0. The formula (14.8) consists of three terms: risk-free income ability kF, compensating shareholders time value of their money, business risk premium (kM - kF)bU, and financial risk premium ðk M- k F ÞbU DS ð1- T Þ. For a financially independent company, the financial risk is equal to zero (the third term disappears), and its owners will only receive the business risk premium.

14.1.4.1

Miller Model

In Miller (1977), he has accounted for corporate and individual taxes to obtain the following formula for unlevered company value, VU, VU =

EBITð1 - T C Þð1 - T S Þ : k0

ð14:9Þ

Here, TC—tax rate on corporate income, TS—the tax rate on incomes of an individual investor from his ownership through corporation stocks.

14.1.5

Brusov–Filatova–Orekhova (BFO) Theory

The perpetuity of all company cash flow and of a company’s lifetime was one of the main restrictions of the Modigliani–Miller (MM) theory, which has been lifted up in 2008 by Brusov–Filatova–Orekhova (Brusov et al. 2018, 2021b). They generalized the MM theory for the case of the company of any age, n, and derived the following Brusov–Filatova–Orekhova formula for the WACC

14.1

Introduction

269

1 - ð1 þ k 0 Þ - n 1 - ð1 þ WACCÞ - n = WACC k0 ½1 - wd T ð1 - ð1 þ kd Þ - n Þ

ð14:10Þ

To obtain the Modigliani–Miller formula for the WACC from (14.10), one should substitute n → 1. It was shown (Brusov et al. 2018, 2021b) that a number of innovative effects, discovered in the BFO theory, are absent in the MM theory (Мodigliani and Мiller 1958, 1963, 1966). Some main existing principles of financial management spanning many decades have been destroyed by the BFO theory; among them is the keystone of optimal capital structure formation—trade-off theory, and the bankruptcy of this theory has been proven within the BFO theory (Brusov et al. 2018, 2021b).

14.1.6

Alternate WACC Formula

An alternate formula for the WACC has been suggested (Farber et al. 2006; Fernandez 2006; Berk and DeMarzo 2007; Harris and Pringle 1985). It has the form below (Eq. (14.18) in Farber et al. (2006)) WACC = k 0 ð1- wd t Þ - k d twd þ kTS twd

ð14:11Þ

Here, k0, kd, and kTS are the returns on the financially independent company, the debt, and the tax shield, respectively, t is the corporate tax rate, and wd is the debt share. Although Eq. (14.11) is quite general, additional conditions are needed for practical applicability. When the WACC remains constant over time, the value of a leveraged company can be found by discounting the unleveraged free cash flows using the WACC. In this case, specific formulas can be found in textbook (Berk and DeMarzo 2007). In the Modigliani–Miller theory (Мodigliani and Мiller 1963), the debt value D is constant. V0 is also constant, as the expected after-tax cash flow of the financially independent company is fixed. By assumption, kTS = kd and the tax shield value is TS = tD. Therefore, the company value V is a constant and the alternate WACC formula (14.11) simplifies the MM formula: WACC = k0 ð1- wd t Þ The “classical” MM theory, suggesting that the returns on the debt kd and the tax shield kTS are equal (both these values have debt nature), is much more reasonable, so this is why in Brusov et al. (2021a), we modify the “classical” MM theory, namely.

270

14.1.7

14

Generalization of the Brusov–Filatova–Orekhova Theory for the Case. . .

Trade-off Theory

In the study of the problem of optimal capital structure of the company during many decades, the cornerstone was the world famous trade-off theory. It is still widely used now for decisions on capital structure. In Frank and Goyal (2009), the relative importance of different factors in capital structure decisions of publicly traded American companies has been studied. The most important factors to explain leverage level are: median industry leverage (+ effect on leverage), log of assets (+), market-to-book assets ratio (-), inflation (+), tangibility (+), and incomes (-). It was noted that companies that pay dividends tend to have lower leverage levels. The related effects have been found under considering book leverage. The authors found empirical data consistent with some trade-off theory versions. In Sheridan and Wessels (1988), the authors compare the applicability of the trade-off theory and pecking order theory for small and medium-sized companies’ decisions about capital structure. It was found that the most lucrative and oldest companies have smaller leverage levels, which confirms the forecasts of the pecking order theory. Larger companies have a higher level of leverage, which is consistent with the predictions of the trade-off theory and pecking order theory. It is concluded that the trade-off theory and pecking order theory for small and medium-sized companies are not mutually exclusive when explaining capital structure decisions. However, in 2013, Brusov et al. (2018, 2021b) proved the inconsistency of the trade-off theory in the framework of the BFO theory they created. It is shown that the assumption of risky debt financing does not lead to an increase in the WACC, which still decreases with increasing leverage. Thus, there is no minimum depending on the level of WACC leverage and no maximum depending on the value of the company from the level of leverage. Therefore, in the world famous theory of trade-offs, there is no optimal capital structure. Brusov et al., in 2013 (Brusov et al. 2018, 2021b), having analyzed the equity cost dependence on the level of leverage under the assumption that debt capital is risky, gave an explanation for this fact. The Modigliani–Miller theory proved that tax shields provided substantial gains to the company. In Harry and Masulis (1980), the theoretical study of tax shields was continued. It was noted that companies may have tax deductibles other than debt. Such non-debt tax shields are investment tax credits, depreciation, and net-loss carry forward. In Bradley et al. (1984), the tax effects suggested in Harry and Masulis (1980) have been tested. In contrast to the prediction in Harry and Masulis (1980), it was shown that debt is positively related to non-debt tax shields, as measured by investment tax credits and depreciation. The results of Sheridan and Wessels (1988) do not provide support for an effect on debt ratios arising from non-debt tax shields. In Graham (2003), it was pointed out that a positive relationship between such proxies for non-debt tax shield and debt may result if a company invests heavily and borrows to invest. Any substitution effects between debt and non-debt tax shields could be suppressed by a mechanical positive relation of this type. The Brusov–Filatova–Orekhova (BFO) theory methodology and results are well known in the literature (for example, see references Dimitropoulos (2014); Luiz and

14.1

Introduction

271

Cruz (2015); Barbi (2011); Franc-Dąbrowska et al. (2021); Angotti et al. (2018); Vergara-Novoa et al. (2018); Mundi et al. (2022); Becker (2022); El-Chaarani et al. (2022); Sadiq et al. (2022); Singhal et al. (2022)). Chapters (Angotti et al. 2018; Vergara-Novoa et al. 2018; Mundi et al. 2022; Singhal et al. 2022) use the BFO theory in practice. The impact on capital structure decisions of the overconfidence of finance managers of family-run businesses in India has been studied in VergaraNovoa et al. (2018). The study concludes that manager decisions about capital structure could be explained by measurable managerial characteristics. In Mundi et al. (2022), the correlation between capital structure and company risk was studied using datasets from Pakistani companies. It was shown that the role of capital structure and risk valuation is vital for the increase in the wealth of shareholders and the sustainable growth of companies. In Becker (2022), the adjusted present value method, the free cash flow (FCF) method, the flow-to-equity method, and the relationships between these methods have been considered. The authors used a stationary FCF method and the Miles and Ezzell method instead of the Modigliani– Miller method to derive DCF valuation formulas for annuities. In El-Chaarani et al. (2022), the influence of internal and external corporate governance mechanisms on the financial performance of banks in the MENA region is studied. It was shown that the corporate governance had positive effects on the financial indicators of banks. The energy companies capital costs by including an investor and market risk approach have been evaluated in Sadiq et al. (2022). The WACC intra-industry analysis of the companies has been done. The connection of capitalization and income ability in the BRICS banking sector has been examined in Singhal et al. (2022) under the signaling theory, the bankruptcy cost theory, the agency theory, the pecking order theory, the Modigliani and Miller theory, and the general theory of the cost of capital and capital structure—the Brusov–Filatova–Orekhova (BFO) theory. Over the past two years, the theory of capital structure has received a new impetus. A large-scale modification of both main theories of the capital structure, BFO and MM, has been carried out and continues in order to better take into account the conditions for the real functioning of companies, such as variable income, advance income tax payments, frequent income tax payments, their combinations, etc. (Brusov et al. 2021a; Brusov and Filatova 2022, 2013). A study of different aspects of emerging markets was carried out in Durana et al. (2022, 2021); Virglerova et al. (2021); Xu and Liu (2020); Valaskova et al. (2020, 2021a, b); Białek-Jaworska and Klapkiv (2021). In Xu and Liu (2020), the impact of intellectual capital on firm performance within a modified and extended VAIC model has been studied. In the near future, the authors plan to publish a large review, which will examine in detail the problems of capital structure.

272

14.1.8

14

Generalization of the Brusov–Filatova–Orekhova Theory for the Case. . .

Materials and Methods

We combine analytical and numerical methods. First, we derive formulas for the company’s leveraged value, V; the leverage less value of the company, V0; the tax shield TS; and finally the WACC in the case of variable income. Then, using Microsoft Excel, we study the dependences of the following values: weighted average cost of capital, WACC, discount rate, WACC-g, company value, V, and the cost of equity, ke, on the level of leverage, L, at different values of the growth rate, g. We have created a large database for sets of cost of equity k0 and cost of debt kd, which is available upon request.

14.2 14.2.1

Modification of the BFO Theory for the Case of Companies with Variable Incomes The Levered Company Value, V

Below, for the first time, we generalize the modern theory of the capital cost and capital structure—the Brusov–Filatova–Orekhova theory—to the case of variable income. We start by deriving the capitalization formula for a financially dependent company, assuming that income for the period grows with the growth rate g. When accounting for the cost of any asset being equal to the sum of discounted values of incomes generated by this asset, one could write the capitalization for a financially dependent company’s V of age, n, as the following expression V= þ

CFð1 þ gÞ CFð1 þ gÞ2 CF þ þ ... þ 2 1 þ WACC ð1 þ WACCÞ ð1 þ WACCÞ3 CFð1 þ gÞn - 1 ð1 þ WACCÞn

ð14:12Þ

Here, WACC is the weighted average cost of capital, CF is an annual income of company, and (14.12) is the geometric progression with denominator g=

ð1 þ gÞ ð1 þ WACCÞ

ð14:13Þ

Summarizing (14.12), we get the expression for the capitalization, V, of the levered company of age n

14.2

Modification of the BFO Theory for the Case of Companies with Variable Incomes

V=

CF  1 þ WACC

1-



273

n

1þg 1þWACC 1þg 1 - 1þWACC

  n  CF 1þg =  1WACC - g 1 þ WACC

ð14:14Þ

In the perpetuity limit (n → 1), we get the following formula for the levered company value, V, V=

CF WACC - g

ð14:15Þ

This formula shows that the discount rate is WACC-g, and not WACC.

14.2.2

The Unlevered Company Value, V0

Let us now derive the capitalization formula for a financially independent company, assuming that income for the period grows with the growth rate g. 2

V0 =

n-1

CFð1 þ gÞ CFð1 þ gÞ CFð1 þ gÞ CF þ þ þ ... þ 3 1 þ k 0 ð1 þ k 0 Þ 2 ð1 þ k 0 Þn ð1 þ k 0 Þ

ð14:16Þ

(14.16) is the geometric progression with denominator g=

ð 1 þ gÞ ð1 þ k 0 Þ

ð14:17Þ

Summarizing (14.16), we get the expression for the value V0 of unlevered company of age n CF  V0 = 1 þ k0

1-



n

1þg 1þk 0 1þg 1 - 1þk 0

  n  1þg CF =  11 þ k0 k0 - g

ð14:18Þ

In the perpetuity limit (n → 1), we get the following formula for the unlevered company value, V0, V0 =

CF k0 - g

This formula shows that the discount rate is k0 - g, and not k0.

ð14:19Þ

274

14.2.3

14

Generalization of the Brusov–Filatova–Orekhova Theory for the Case. . .

The Tax Shield Value

The tax shield for n-years is equal to ðTSÞn =

tk d D tk d D tk d D þ þ ... þ 1 þ k d ð1 þ k d Þ2 ð1 þ kd Þn

ð14:20Þ

(14.20) is the geometric progression with denominator g=

1 ð1 þ k d Þ

ð14:21Þ

Summarizing (14.20), for the tax shield, we have ðTSÞn =

tk d D 1 - ð1 þ kd Þ  1 1 þ kd 1 - 1þk

-n

= Dt ð1- ð1 þ kd Þ - n Þ

ð14:22Þ

d

ðTSÞn = Dt ð1- ð1 þ kd Þ - n Þ

ð14:23Þ

Using an analog of the first theorem by Modigliani–Miller for finite time, one gets V = V 0 þ ðTSÞn

ð14:24Þ

D = wd V

ð14:25Þ

Substituting

we arrive to the following expression V ð1- wd t ð1- ð1 þ kd Þ - n ÞÞ = V 0

ð14:26Þ

Substituting into this equation the values of an unlevered company, V0 (14.18) and of levered company, V, (14.14) one gets the following expression   n  1þg CF  1 - 1þWACC  ð1 - wd t ½1 - ð1 þ k d Þ - n Þ 

=

CF  1 -



WACC - g n 

1þg 1þk 0

ð k 0 - gÞ

ð14:27Þ

Dividing both parts by (1 - wdt(1 - (1 + kd)-n)), we get the BFO equation for the WACC of the company with variable income

14.3

Results and Discussions

1-



1þg 1þWACC

275

n

WACC - g

=

1-



1þg 1þk 0

n

ðk 0 - gÞ  ð1 - wd t ½1 - ð1 þ k d Þ - n Þ

ð14:28Þ

This is the main theoretical result of the current chapter. In the perpetuity limit (n → 1), we get the following equation for WACC in the case of variable income (Brusov et al. 2021a)

14.3

WACC - g = ðk0- gÞ  ð1- wd t Þ

ð14:29Þ

WACC = ðk0- gÞ  ð1- wd t Þ þ g

ð14:30Þ

Results and Discussions

In order to understand the impact of a variable growth rate g on the main financial indicators of a company within the framework of the generalized theory of Brusov– Filatova–Orekhova (GBFO), we study the dependences of the following values: weighted average cost of capital, WACC, discount rate, WACC-g, company value, V, and the cost of equity, ke, on the level of leverage L at different values of the growth rate, g. We have created a large database for sets of cost of equity k0 and cost of debt kd, which is available upon request. To illustrate the results obtained and the conclusions drawn below, we present below the results for the following financial parameters of the company: k 0 = 0:18; k d = 0:16; t = 0:2; CF = 100; n = 2 and n = 4; g = 0:2; 0:1; 0:0; - 0:1; - 0:2 Here, k0 is the equity cost at zero leverage level; kd is the debt cost; t is the tax on income; CF is the income per period; n is the company age; L is the leverage level; and g is the growth rate. Note that if the results for different parameters could be and are numerically different, then the qualitative effect of the variable growth rate g on the main financial indicators is similar.

14.3.1

Calculations for Two-Year Company

14.3.1.1

Calculations of Weighted Average Cost of Capital, WACC

As can be seen from Table 14.1 and Fig. 14.1, for different values of g all curves WACC(L ) start from one point (0; k0 = 0.18). These curves WACC(L) demonstrate

276

Generalization of the Brusov–Filatova–Orekhova Theory for the Case. . .

14

Table 14.1 The WACC depending on the level of leverage L at different growth rates g in Generalized Brusov–Filatova–Orekhova theory (GBFO theory) WACC, n = 2 g = 0.2 0.1799864 0.1583502 0.15084 0.1472744 0.1451307 0.1436999 0.142677 0.1419093 0.141312 0.140834 0.1404427

L 0 1 2 3 4 5 6 7 8 9 10

g = -0.1 0.1799858 0.1583545 0.1513935 0.1478992 0.1457982 0.1443958 0.1433932 0.1426408 0.1420553 0.1415867 0.1412033

g=0 0.179995 0.1591545 0.1521805 0.148688 0.1465907 0.1451917 0.1441921 0.1434421 0.1428587 0.1423919 0.1420099

g = 0.1 0.1799849 0.1594954 0.1523026 0.1489255 0.1468947 0.1455391 0.1445699 0.1438425 0.1432764 0.1428234 0.1424527

g = 0.2 0.1799844 0.1597882 0.1526805 0.1493521 0.1473505 0.1460143 0.145059 0.144342 0.1437841 0.1433376 0.1429721

WACC (L), n=2 0.18 0.175

WACC

0.17 0.165 0.16 0.155 0.15 0.145 0.14

0

WACC, g=-0.2

1

2

3

WACC, g=-0.1

4

5 L

WACC, g=0

6

7

8

WACC, g=0.1

9

10

WACC, g=0.2

Fig. 14.1 The WACC depending on the level of leverage L at different growth rates g in Generalized Brusov–Filatova–Orekhova theory (GBFO theory)

the decrease of WACC with leverage level L at all g values. The curves WACC(L ) increase with growth rate, g. The results for a two-year company differ from the results for a perpetual limit— the theory of Modigliani and Miller (Brusov et al. 2021a). In the latter case, the WACC(L ) curves decrease with the level of leverage L at g < k0 and increase at g > k0. k0 is the threshold value g separating the increasing WACC(L ) curves from

14.3

Results and Discussions

277

the decreasing ones, and for g = k0 WACC = const = k0. In the first case (BFO theory), the WACC(L ) curves decrease with increasing leverage L for all values of the growth rate g. The WACC(L ) curves increase with the rate g both in the Brusov– Filatova–Orekhova theory and in the Modigliani and Miller theory. This is the first indication that WACC is no longer a discount rate, since it is intuitive that the discount rate must decrease in order to increase the value of company V. As we will see below, WACC-g and WACC-k0 play the role of the discount rate. The discount rate moves for a financially dependent company from the weighted average cost of capital, WACC, to WACC-g (where g is the growth rate), for a financially independent company from k0 to k0–g. As we intuitively understood above, this means that WACC and k0 are no longer discount rates, as is the case for the classical Brusov–Filatova–Orekhova constant income theory. Below, we study the dependence of the discount rate WACC-g on the level of leverage L in the Generalized theory of Brusov–Filatova–Orekhova (the GBFO theory) at k0 = 0.18 and different values of g (-0.2; -0.1; 0.0; 0.1; 0.2) for a two- and four-year company.

14.3.1.2

Calculations of the Discount Rate, WACC-g

As can be seen from Table 14.2 and Fig. 14.2, the curves (WACC-g)(L ) demonstrate the decrease of WACC-g with leverage level L at all g values. The curves (WACC-g) (L ) decrease with growth rate, g. This behavior of the (WACC-g)(L ) curves can be explained as follows: all WACC(L ) curves originate from the same point (L = 0; WACC = 0.18). The (WACC-g)(L ) curves will be ordered as follows for L = 0: the larger g, the lower the starting point and hence the entire graph lies, since the curves do not intersect. As

Table 14.2 The discount rate WACC-g depending on the level of leverage L at different growth rates g in Generalized Brusov–Filatova–Orekhova theory (GBFO theory) L 0 1 2 3 4 5 6 7 8 9 10

(WACC-g), n = 2 g = -0.2 g = -0.1 0.3799864 0.2799858 0.3583502 0.2583545 0.35084 0.2513935 0.3472744 0.2478992 0.3451307 0.2457982 0.3436999 0.2443958 0.342677 0.2433932 0.3419093 0.2426408 0.341312 0.2420553 0.340834 0.2415867 0.3404427 0.2412033

g=0 0.179995 0.1591545 0.1521805 0.148688 0.1465907 0.1451917 0.1441921 0.1434421 0.1428587 0.1423919 0.1420099

g = 0.1 0.0799849 0.0594954 0.0523026 0.0489255 0.0468947 0.0455391 0.0445699 0.0438425 0.0432764 0.0428234 0.0424527

g = 0.2 -0.020016 -0.040212 -0.047319 -0.050648 -0.052649 -0.053986 -0.054941 -0.055658 -0.056216 -0.056662 -0.057028

278

14

Generalization of the Brusov–Filatova–Orekhova Theory for the Case. . .

(WACC-g) (L), n=2 0.4 0.35 0.3

WACC-g

0.25 0.2 0.15 0.1 0.05 0 -0.05

0

1

2

3

-0.1

4

5

6

7

8

9

10

L WACC-g, g=-0.2 WACC-g, g=0.1

WACC-g, g=-0.1 WACC-g, g=0.2

WACC-g, g=0

Fig. 14.2 The discount rate WACC-g depending on the level of leverage L at different growth rates g in Generalized Brusov–Filatova–Orekhova theory (GBFO theory

we will see below, the decrease of (WACC-g)(L) with growth rate, g, will lead to an increase of the company value, V, with g.

14.3.1.3

Calculations of the Company Value, V

It is seen from Table 14.3 and Fig. 14.3 that the company value V at fixed growth rate g increases with leverage level L in the Generalized Brusov–Filatova–Orekhova theory (GBFO theory). The company value V as well increases with growth rate g. This is a consequence of a decrease in the discount rate (WACC-g)(L) with an increase in the growth rate g. Below, we have studied the dependence of cost of equity, ke, on leverage level L and on growth rate, g, in the Generalized Brusov–Filatova–Orekhova theory (GBFO theory) at k0 = 0.18; kd = 0.16; and g = 0; ±0.1;±0.2.

14.3.1.4

Calculations of the Equity Cost, ke

As is seen from Table 14.4 and Fig. 14.4, the equity cost, ke, practically linearly grows with leverage level L at all growth rate g values. The tilt angle ke(L) grows with g.

14.3

Results and Discussions

279

Table 14.3 The company value, V, depending on the level of leverage L at different growth rates g in Generalized Brusov–Filatova–Orekhova theory (GBFO theory) V, n = 2 g = -0.2 142.20282 145.95218 147.29627 147.94237 148.3333 148.5953 148.78312 148.92435 149.03442 149.12261 149.19486

L 0 1 2 3 4 5 6 7 8 9 10

g = -0.1 149.38493 153.40417 154.73958 155.41792 155.82837 156.10344 156.30063 156.44891 156.56448 156.65707 156.73293

g=0 156.56518 160.69451 162.12039 162.84303 163.27978 163.57228 163.78186 163.93941 164.06217 164.16051 164.24106

g = 0.1 163.74916 168.06349 169.62647 170.36931 170.81878 171.12001 171.33596 171.49835 171.6249 171.7263 171.80938

g = 0.2 170.93128 175.43476 177.07002 177.84511 178.31411 178.62842 178.85374 179.02318 179.15523 179.26104 179.34772

V(L), n=2 185 180 175 170 V

165 160 155 150 145 140

0

1

V, g=-0.2

2

3

V, g=-0.1

4

5 L V, g=0

6

7 V, g=0.1

8

9

10

V, g=0.2

Fig. 14.3 The company value, V, depending on the level of leverage L at different growth rates g in Generalized Brusov–Filatova–Orekhova theory (GBFO theory)

14.3.2

Calculations for Four-Year Company

Below, we study the dependence of WACC, WACC-g, V, and ke on leverage level L in the Generalized Brusov–Filatova–Orekhova theory (GBFO theory) at k0 = 0.18; kd = 0.16; t = 0.2; g = 0.2; 0.1; 0.0; -0.1; -0.2 for a four-year company and compare obtained results with ones for a two-year company (see above).

280

14

Generalization of the Brusov–Filatova–Orekhova Theory for the Case. . .

Table 14.4 The equity cost, ke, depending on the level of leverage L at different growth rates g in Generalized Brusov–Filatova–Orekhova theory (GBFO theory) ke, n = 2 g = -0.2 0.1799864 0.1887005 0.19652 0.2050974 0.2136535 0.2221991 0.2307387 0.2392746 0.247808 0.2563397 0.2648701

L 0 1 2 3 4 5 6 7 8 9 10

g = -0.1 0.1799858 0.1887091 0.1981805 0.2075966 0.2169911 0.2263748 0.2357525 0.2451264 0.2544978 0.2638674 0.2732358

g=0 0.179995 0.1903091 0.2005415 0.2107521 0.2209535 0.2311504 0.2413446 0.2515371 0.2617285 0.271919 0.282109

g = 0.1 0.1799849 0.1909909 0.2009079 0.2117018 0.2224736 0.2332344 0.243989 0.2547397 0.2654878 0.2762342 0.2869792

g = 0.2 0.1799844 0.1915764 0.2020416 0.2134083 0.2247527 0.236086 0.2474131 0.2587362 0.2700568 0.2813755 0.292693

ke (L), n=2 0.31 0.29 0.27

ke

0.25 0.23 0.21 0.19 0.17 0.15

0

1

ke, g=-0.2

2

3

ke, g=-0.1

4

5 L ke, g=0

6

7 ke, g=0.1

8

9

10

ke, g=0.2

Fig. 14.4 The equity cost, ke, depending on the level of leverage L at different growth rates g in Generalized Brusov–Filatova–Orekhova theory (GBFO theory)

14.3.2.1

Calculations of Weighted Average Cost of Capital, WACC

From Table 14.5 and Fig. 14.5, it follows that different values of g all curves WACC (L ) start from one point (0; k0 = 0.18). These curves WACC(L ) demonstrate the decrease of WACC with leverage level L at all g values. The curves WACC(L ) increase with growth rate, g. In this part, the results for a four-year company are similar to ones for a two-year company. There is quantitative difference between them; the splitting of the curves WACC(L ) Δ for g = 0.2 and g = -0.2 increases

14.3

Results and Discussions

281

Table 14.5 The WACC depending on the level of leverage L at different growth rates g in Generalized Brusov–Filatova–Orekhova theory (GBFO theory) WACC g = -0.2 0.1799864 0.1538597 0.1450677 0.1406528 0.1379983 0.1362263 0.1349595 0.1340088 0.1332689 0.1326768 0.1321922

L 0 1 2 3 4 5 6 7 8 9 10

g = -0.1 0.1799858 0.1554667 0.1472039 0.1430555 0.1405609 0.1388955 0.1377048 0.1368112 0.1361157 0.1355592 0.1351036

g=0 0.179995 0.1567983 0.1489781 0.1450509 0.1426891 0.1411122 0.1399846 0.1391383 0.1384797 0.1379526 0.1375212

g = 0.1 0.1799849 0.1579005 0.1504635 0.1467206 0.1444691 0.1429656 0.1418905 0.1410836 0.1404555 0.1399529 0.1395414

g = 0.2 0.1799844 0.1588493 0.1517081 0.1481196 0.145877 0.1445542 0.1434877 0.1427137 0.1421113 0.1416291 0.1412344

WACC (L), n=4 0.18 0.17

WACC

0.16 0.15 0.14 0.13 0.12

0

1

2

3

4

5

6

7

8

9

10

L WACC, g=-0.2 WACC, g=0.1

WACC, g=-0.1 WACC, g=0.2

WACC, g=0

Fig. 14.5 The WACC depending on the level of leverage L at different growth rates g in Generalized Brusov–Filatova–Orekhova theory (GBFO theory

with g (at L = 10 Δ = 0.0018 for n = 2, while for n = 4 Δ = 0.009). In the perpetual case, (n = 1) Δ = 0.073) (Brusov et al. 2021a). The results for a four-year company, as it was seen for a two-year company, differ from the results for the perpetual limit—the theory of Modigliani and Miller (Brusov et al. 2021a); the WACC(L ) curves decrease with increasing leverage L for all values

282

14

Generalization of the Brusov–Filatova–Orekhova Theory for the Case. . .

of the growth rate g. As is known from Brusov et al. (2021a), in the case of Modigliani and Miller, the WACC(L ) curves decrease with the level of leverage L for g < k0 and increase for g > k0. Therefore, k0 is the threshold value g separating the increasing WACC(L ) curves from the decreasing ones, and for g = k0 WACC = const = k0. As we mentioned above, the increase in WACC(L ) with the growth rate of g is the first indication that WACC is no longer a discount rate, since it is intuitive that the discount rate must decrease with growth rate g in order to increase the value of company V. As we will see below, WACC-g and WACC-k0 play the role of the discount rates and satisfy the above condition.

14.3.2.2

Calculations of the Discount Rate, WACC-g

Table 14.6 and Fig. 14.6 show all the curves (WACC-g)(L ) with leverage level L at all g values. The (WACC-g) values at fixed leverage level L decrease with growth rate g. This means that WACC-g is a suitable candidate for the discount rate. As in the case of the two-year company, the behavior of (WACC-g)(L ) with g growth can be explained as follows: all WACC(L ) curves originate from the same point (L = 0; WACC = 0.18). The (WACC-g)(L) curves will be ordered as follows for L = 0: the larger g, the lower the starting point and hence the entire graph lies, since the curves do not intersect. As we will see below, the decrease of (WACC-g) (L ) with growth rate, g, will lead to an increase of the company value, V, with g.

14.3.2.3

Calculations of the Company Value, V

As can be seen from Table 14.7 and Fig. 14.7, the company value V at fixed growth rate g increases with leverage level L in Generalized Brusov–Filatova–Orekhova Table 14.6 The discount rate, WACC-g, depending on the level of leverage L at different growth rates g in Generalized Brusov–Filatova–Orekhova theory (GBFO theory) L 0 1 2 3 4 5 6 7 8 9 10

(WACC-g), n = 4 g = -0.2 g = -0.1 0.3799864 0.2799858 0.3538597 0.2554667 0.3450677 0.2472039 0.3406528 0.2430555 0.3379983 0.2405609 0.3362263 0.2388955 0.3349595 0.2377048 0.3340088 0.2368112 0.3332689 0.2361157 0.3326768 0.2355592 0.3321922 0.2351036

g=0 0.179995 0.1567983 0.1489781 0.1450509 0.1426891 0.1411122 0.1399846 0.1391383 0.1384797 0.1379526 0.1375212

g = 0.1 0.0799849 0.0579005 0.0504635 0.0467206 0.0444691 0.0429656 0.0418905 0.0410836 0.0404555 0.0399529 0.0395414

g = 0.2 -0.020016 -0.041151 -0.048292 -0.05188 -0.054123 -0.055446 -0.056512 -0.057286 -0.057889 -0.058371 -0.058766

14.3

Results and Discussions

283

(WACC-g) (L), n=4 0.4 0.35 0.3

WACC-g

0.25 0.2 0.15 0.1 0.05 0 -0.05

0

1

2

3

-0.1

4

5

6

7

8

9

10

L WACC-g, g=-0.2 WACC-g, g=0.1

WACC-g, g=-0.1 WACC-g, g=0.2

WACC-g, g=0

Fig. 14.6 The discount rate, WACC-g, depending on the level of leverage L at different growth rates g in Generalized Brusov–Filatova–Orekhova theory (GBFO theory) Table 14.7 The company value, V, depending on the level of leverage L at different growth rates g in Generalized Brusov–Filatova–Orekhova theory (GBFO theory) L 0 1 2 3 4 5 6 7 8 9 10

V, n = 4 g = -0.2 207.56615 217.29735 220.75339 222.5253 223.60263 224.32687 224.84716 225.23902 225.54478 225.79 225.99105

g = -0.1 236.28862 247.3597 251.2914 253.30558 254.53001 255.35305 255.94428 256.38954 256.73695 257.01557 257.244

g=0 269.00881 281.61599 286.08901 288.37987 289.7723 290.70818 291.38042 291.88667 292.28165 292.59842 292.85811

g = 0.1 306.05136 320.39442 325.47139 328.07604 329.65911 330.72309 331.48732 332.06283 332.51185 332.87195 333.16716

g = 0.2 347.71061 363.9946 369.77167 372.72979 374.59742 375.70606 376.60369 377.25722 377.7671 378.176 378.51122

theory (GBFO theory). The company value V increases at fixed leverage level L with growth rate g at fixed as well. This is the consequence of a decrease in the discount rate (WACC-g)(L ) with an increase in the growth rate g. Comparing with the results for the two-year-old company, we see that the value of the company V increases with the age of the company: we have a range from 149 to 157 with L = 1 for g from -0.2

284

14

Generalization of the Brusov–Filatova–Orekhova Theory for the Case. . .

V(L), n=4 440 390

V

340 290 240 190 140

0 V, g=-0.2

1

2

3

V, g=-0.1

4

5 L V, g=0

6

7 V, g=0.1

8

9

10

V, g=0.2

Fig. 14.7 The company value, V, depending on the level of leverage L at different growth rates g in Generalized Brusov–Filatova–Orekhova theory (GBFO theory)

to 0.2 for the two-year-old company and a range from 217 to 364 with L = 1 for g from -0.2 to 0.2 for a four-year-old company. This is the obvious conclusion, because it is well known that the value of any asset (company, stock, bond, etc.) is equal to the sum of the discounted returns generated by this asset. Since this value is proportional to the lifetime of this asset, the capitalization of the company will grow with its age. The dependence of the cost of equity ke on the level of leverage L in the Generalized theory of Brusov–Filatova–Orekhova (GBFO theory) was studied below for a four-year company with growth rates g = 0; ±0.1; and ± 0.2.

14.3.2.4

Calculations of the Cost of Equity ke

From Table 14.8 and Fig. 14.8, it can be seen that the cost of equity ke increases practically linearly with leverage level L at all growth rates g (except for g = -0.2 where we see a decrease in ke with leverage level L ). The slope angle ke(L ) increases with g. This should change the dividend policy of an enterprise with variable income since, economically, the reasonable amount of dividends is equal to the cost of equity. However, the biggest change in the company’s dividend policy is related to the discovery of a qualitatively new effect in corporate finance: at a rate g < g*, the slope of the ke(L ) curve turns out to be negative (one can observe this effect here for g = 0.2 where a decrease in ke with leverage level L takes place). This effect, which is

14.3

Results and Discussions

285

Table 14.8 The equity cost, ke, depending on the level of leverage L at different growth rates g in Generalized Brusov–Filatova–Orekhova theory (GBFO theory) ke , n = 4 g = -0.2 0.1799864 0.1797193 0.1792032 0.1786111 0.1779915 0.1773581 0.1767166 0.1760702 0.1754204 0.1747682 0.1741143

L 0 1 2 3 4 5 6 7 8 9 10

g = -0.1 0.1799858 0.1829333 0.1856116 0.1882219 0.1908046 0.1933733 0.1959339 0.1984895 0.2010417 0.2035915 0.2061396

g=0 0.179995 0.1855967 0.1909343 0.1962038 0.2014454 0.2066729 0.2118923 0.2171066 0.2223176 0.2275261 0.2327328

g = 0.1 0.1799849 0.187801 0.1953906 0.2028824 0.2103453 0.2177938 0.2252338 0.2326686 0.2400999 0.2475287 0.2549558

g = 0.2 0.1799844 0.1896985 0.1991244 0.2084783 0.2173852 0.2273252 0.2364136 0.2457093 0.2550015 0.2642911 0.2735789

ke (L), n=4 0.29 0.27 0.25

ke

0.23 0.21 0.19 0.17 0.15

0 ke, g=-0.2

1

2

3

ke, g=-0.1

4

5 L ke, g=0

6

7 ke, g=0.1

8

9

10

ke, g=0.2

Fig. 14.8 The equity cost, ke, depending on the level of leverage L at different growth rates g in Generalized Brusov–Filatova–Orekhova theory (GBFO theory)

absent in the classical Modigliani–Miller theory and the classical Brusov–Filatova– Orekhova theory with constant income, exists in the Modigliani–Miller theory with variable income and in the Brusov–Filatova–Orekhova theory with variable income at a certain age of the company, n, which exceeds some cutoff age value, n*. The latter effect is similar to a qualitatively new effect in corporate finance, discovered by Brusov–Filatova–Orekhova within the framework of the BFO theory (Brusov et al. 2018, 2021b): anomalous dependences of the cost of equity ke on the

286

14

Generalization of the Brusov–Filatova–Orekhova Theory for the Case. . .

leverage level L when income tax T exceeds a certain value T*. This discovery also significantly changes the principles of the company’s dividend policy.

14.3.3

Comparison with the Theory of Modigliani and Miller with Variable Income

The main difference between the Modigliani–Miller (MM) theory and the Brusov– Filatova–Orekhova (BFO) theory is that the latter describes companies of an arbitrary age, whereas the former represents the eternal limit of the BFO theory and is valid only for perpetual companies (with an infinite lifetime). If there is no time factor in the MM theory, then within the framework of the modern BFO theory, it is possible to analyze the financial condition of a company of any age; in this chapter, this is done for two company ages—two and four years. Since the MM theory is the eternal BFO limit, it is important to note that some of the results, such as the change in the discount rate from WACC to WACC-g, etc., are general, and this emphasizes the correctness of both theories and the connection between them as a connection between a general theory and its limiting case. Along with the fundamental differences between the results of the two theories indicated above, there are also qualitative and quantitative differences. One of them is the next. The BFO results for a four-year company, as it was seen for a two-year company as well, differ from the results for the perpetual limit—the theory of Modigliani and Miller (Brusov et al. 2021a), where the WACC(L) curves decrease with increasing leverage L for all values of the growth rate g. As is known from Brusov et al. (2021a), in the case of Modigliani and Miller, the WACC(L ) curves decrease with the level of leverage L for g < k0 and increase for g > k0. Therefore, k0 is the threshold value g separating the increasing WACC(L ) curves from the decreasing ones, and for g = k0 WACC = const = k0 (see Fig. 14.9 below). We would like to emphasize an important observation. If in the classical versions of the Brusov–Filatova–Orekhova (BFO) theory and its perpetual limit, the theory of Nobel laureates Modigliani and Miller, where the case of constant income was considered, and where the gap between these two theories is huge (many qualitative effects that take place in the first theory, missing in the second), when taking into account the variable income, some effects of the BFO theory also take place in the Modigliani–Miller theory. This means that taking into account some effects that are present in economic practice (for example, variable income) brings both theories closer, and even the Modigliani–Miller theory, with all its many limitations, becomes more applicable in economic practice. However, it should be remembered that the Modigliani–Miller theory is only true for perpetual companies, whereas the BFO theory is valid for companies of any age, and from this point of view, they never coincide.

14.4

Conclusions

287

WACC(L), ko=0.3 0.33 0.31 0.29 g=0.4

0.27

g=0.3

WACC

0.25

g=0.2 g=0

0.23 0.21

g=-0.2 g=-0.3

0.19

g=-0.4

0.17 0.15

0

1

2

3

4

5 L

6

7

8

9

10

Fig. 14.9 WACC depending on leverage level L in Generalized Modigliani–Miller theory (GMM theory) at k0 = 0.3 and g = 0; ± 0.2; ± 0.3; ± 0.4 (from Brusov et al. (2021a))

14.4

Conclusions

The Brusov–Filatova–Orekhova (BFO) theory of capital cost and capital structure as well as the theory by Nobel Prize winners Modigliani and Miller (perpetuity limit of BFO theory) considers the case of constant income, whereas in practice, the income of a company is, of course, variable. Recently, we have generalized the latter for the case of variable income, and here we have generalized for the first time the Brusov– Filatova–Orekhova theory for the case of variable income. This generalization significantly expands the applicability of this modern capital structure theory, which is valid for companies of any age, and in practice for corporate finance, business valuation, investments, banking, ratings, etc. We have derived the generalized BFO formula for WACC and this consists of a main theoretical result of the current chapter. From this formula d as well as from using this formula in MS Excel, we show that the role of the discount rate shifts from WACC to WACC-g (where g is the growth rate) for financially dependent companies and from k0 to k0–g (for financially independent companies). Whereas the WACC increases with g, the actual discount rates WACC-g and k0-g decrease with g and, accordingly, the company value, V, increases with g. For the cost of equity ke, the slope of the curve ke(L ) increases with g. Since the cost of equity determines the economically justified amount of dividends, this should change the company’s dividend policy. It turns out that at the rate g < g*, the slope of the curve ke(L ) becomes negative, which can significantly change the company’s dividend policy principles. This means a qualitatively new effect on discoveries in corporate finance.

288

14

Generalization of the Brusov–Filatova–Orekhova Theory for the Case. . .

The novelty of the work is the generalization of the theory of Brusov–Filatova– Orekhova to the case of variable income, the derivation of generalized BFO formulas for the weighted average cost of capital, WACC, cost of equity, ke, company value, V, and the use of these formulas to study the influence of the growth rate g on the dependence of the main financial performance of the company on debt financing. The importance of the current consideration is due to a couple of points: • gives an idea of the behavior of the main financial indicators of the company with a change in the growth rate g for both cases—an increase in g and a decrease in g; • creates a developed methodology that allows the researcher to analyze the main financial indicators of the company (capital costs, company value, etc.) for the actual conditions of the company’s functioning. Limitations of the study: a generalization of the BFO theory was carried out for the case of paying income tax at the end of reporting periods. However, in practice, these payments may also be made in advance. This determines the further direction of the study: consideration of the case of variable income when income tax is paid in advance.

References Angotti M, de Lacerda Moreira R, Hipólito Bernardes do Nascimento J, Neto de Almeida Bispo O (2018) Analysis of an equity investment strategy based on accounting and financial reports in Latin American markets. Reficont 5:22–40 Barbi M (2011) On the risk–neutral value of debt tax shields. Appl Financ Econ 22:251–258 Becker DM (2022) Getting the valuation formulas right when it comes to annuities. Manag Financ 48:470 Berk J, DeMarzo P (2007) Corporate finance. Pearson–Addison Wesley, Boston, MA Białek-Jaworska A, Klapkiv L (2021) Does withholding tax on interest limit international profit– shifting by FDI? Equilib Q J Econ Econ Policy 16:11–44. https://doi.org/10.24136/eq.2021.001 Bradley M, Jarrell GA, Kim EH (1984) On the existence of an optimal capital structure: theory and evidence. J Financ 39:857–878 Brusov P, Filatova T (2013) Veniamin Kulik benefits of advance payments of tax on profit: consideration within the Brusov–Filatova–Orekhova (BFO) theory. Mathematics 2022:10. https://doi.org/10.3390/math10122013 Brusov P, Filatova T (2022) Influence of Method and Frequency of Profit Tax Payments on Company Financial Indicators. Mathematics 10:2479. https://doi.org/10.3390/math10142479 Brusov P, Filatova T, Orehova N, Eskindarov M (2018) Modern corporate finance, investments, taxation and ratings, 2nd edn. Springer Nature Publishing, Cham, pp 1–571 Brusov PN, Filatova TV, Orekhova NP, Kulik VL, Chang SI, Lin YCG (2021a) Generalization of the Modigliani–Miller theory for the case of variable income. Mathematics 9:1286. https://doi. org/10.3390/math9111286 Brusov P, Filatova T, Orehova N (2021b) Ratings: critical analysis and new approaches of quantitative and qualitative methodology. Springer Nature Publishing, Cham, pp 1–369. Available online: https://www.springer.com/de/book/9783030562427 Dimitropoulos P (2014) Capital structure and corporate governance of soccer clubs: European evidence. Manag Res Rev 37:658–678

References

289

Durana P, Ginevicius R, Urbanski M, Podhorska I, Tumpach M (2021) Parallels and differences in earnings management of the Visegrad four and the Baltics. J Compet 13:39–55. https://doi.org/ 10.7441/joc.2021.03.03 Durana P, Valaskova K, Blazek R, Palo J (2022) Metamorphoses of earnings in the transport sector of the V4 region. Mathematics 10:1204. https://doi.org/10.3390/math10081204 El-Chaarani H, Abraham R, Skaf Y (2022) The impact of corporate governance on the financial performance of the banking sector in the MENA (middle eastern and north African) region: an immunity test of banks for COVID–19. J Risk Financ Manag 15:82 Farber A, Gillet R, Szafarz A (2006) A general formula for the WACC. Int J Bus 11:211–218 Fernandez P (2006) A general formula for the WACC: a comment. Int J Bus 11:219 Franc-Dąbrowska J, Mądra-Sawicka M, Milewska A (2021) Energy sector risk and cost of capital assessment—companies and investors perspective. Energies 14:1613 Frank M, Goyal V (2009) Capital structure decisions: which factors are reliably important? Financ Manag 38:1–37. https://doi.org/10.1111/j.1755-053X.2009.01026.x Graham JR (2003) Taxes and corporate finance: a review. Rev Financ Stud 16:1075–1129 Hamada R (1969) Portfolio analysis, market equilibrium, and corporate finance. J Financ 24:13–31 Harris R, Pringle J (1985) Risk–adjusted discount rates—extension form the average–risk case. J Financ Res 8:237–244 Harry DA, Masulis RW (1980) Optimal capital structure under corporate and personal taxation. J Financ Econ 8:3–29 Luiz K, Cruz M (2015) The relevance of capital structure on firm performance: a multivariate analysis of publicly traded Brazilian companies. REPeC Brasília 9:384–401 Miller M (1977) Debt and taxes. J Financ 32:261–275. https://doi.org/10.1111/j.1540-6261.1977. tb03267.x Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Modigliani F, Miller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391 Mundi HS, Kaur P, Murty RLN (2022) A qualitative inquiry into the capital structure decisions of overconfident finance managers of family–owned businesses in India. Qual Res Financ Mark 14:357–379 Sadiq M, Alajlani S, Hussain MS, Bashir F, Chupradit S (2022) Impact of credit, liquidity, and systematic risk on financial structure: Comparative investigation from sustainable production. Environ Sci Pollut Res Int 29:20963–20975 Sheridan T, Wessels R (1988) The determinants of capital structure choice. J Financ 43:1–19 Singhal N, Goyal S, Sharma D, Kumari S, Nagar S (2022) Capitalization and profit ability: applicability of capital theories in BRICS banking sector. Future Bus J 8:30. https://doi.org/ 10.1186/s43093-022-00140-w Valaskova K, Gavurova B, Durana P, Kovacova M (2020) Alter ego only four times? The case study of business profits in the Visegrad Group. EM Econ Manag 23:101–119. https://doi.org/ 10.15240/tul/001/2020-3-007 Valaskova K, Androniceanu A-M, Zvarikova K, Olah J (2021a) Bonds between earnings management and corporate financial stability in the context of the competitive ability of enterprises. J Compet 13:167–184. https://doi.org/10.7441/joc.2021.04.10

290

14

Generalization of the Brusov–Filatova–Orekhova Theory for the Case. . .

Valaskova K, Kliestik T, Gajdosikova D (2021b) Distinctive determinants of financial indebtedness: evidence from Slovak and Czech enterprises. Equilib Q J Econ Econ Policy 16:639–659. https://doi.org/10.24136/eq.2021.023 Vergara-Novoa C, Sepúlveda-Rojas JP, Miguel DA, Nicolás R (2018) Cost of capital estimation for highway concessionaires in Chile. J Adv Transp 2018:2153536 Virglerova Z, Ivanova E, Dvorsky J, Belas J, Krulický T (2021) Selected factors of internationalisation and their impact on the SME perception of the market risk. Oeconomia Copernic 12:1011–1032. https://doi.org/10.24136/oc.2021.033 Xu J, Liu F (2020) The impact of intellectual capital on firm performance: a modified and extended VAIC model. J Compet 12:161–176. https://doi.org/10.7441/joc.2010.01.10

Chapter 15

BFO Theory with Variable Profit in Case of Advance Payments of Tax on Profit

Keywords Generalized BFO theory · Variable income · Advance tax on income payments · Company value · WACC · Cost of equity

15.1

Introduction

Two main capital structure theories—Brusov–Filatova–Orekhova (BFO) and its perpetuity limit—theory by Nobel Prize winners Modigliani and Miller—consider the companies with constant profit, while in practice profit of the company is, of cause, variable. Recently the Modigliani–Miller (MM) theory has been generalized for the case of variable profit (Brusov et al. 2021), and in current chapter we have generalized for the first time BFO theory for the companies with variable profit and advance tax on profit payments. After such a generalization, the applicability of the BFO theory, which is valid for companies of any age, significantly expands in practice, in particular, in corporate finance, in investments, in business valuation, in banking, in ratings, etc.

15.1.1

Review of Literature

The capital structure is the ratio between the equity and debt value. Whether the capital structure affects main financial parameters and if so, how? The main task solved by the company’s management is to determine the optimal capital structure, in which the cost of raising capital is minimal, and the value of the company V is maximum. The first quantitative work on this topic was that of Modigliani and Miller (1958) (Мodigliani and Мiller 1958). Before this, there was the so-called traditional (empirical) approach.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_15

291

292

15

BFO Theory with Variable Profit in Case of Advance Payments of Tax on Profit

15.1.2

The Basis of the Traditional Approach (TA)

In TA, WACC and company value V depend on the level of leverage L (capital structure). Debt is cheaper than equity, because the former has less risk, since in the event of bankruptcy, the claims of creditors are satisfied before the shareholders’ ones. Thus, increasing the share of cheaper debt capital in the total capital structure to a limit that does not violate financial stability and does not increase the risk of bankruptcy reduces WACC and increases the value of the company, V. A further increase in debt financing leads to a violation of financial stability and to the risk of bankruptcy increase. WACC goes up, while company capitalization, V, goes down. The optimal capital structure is formed as a result of competition between the advantages of debt financing with a low level of leverage and its disadvantages with a high level of leverage. The trade-off theory has come to similar conclusions.

15.1.3

Modigliani–Miller Theory

15.1.3.1

Modigliani–Miller Theory Without Taxes

Modigliani and Miller (1958), under numerous restrictions, came to the conclusion that, without taxes, the value of a company is constant and equal to V = V0 =

EBIT , k0

ð15:1Þ

where EBIT is earnings before interest and taxes, k0 is the discount rate. This contradicts the findings of TA. From (15.1) one obtains for WACC: WACC = k0 :

ð15:2Þ

WACC = k 0 = k e we þ k d wd :

ð15:3Þ

k0 is the equity cost at L = 0. Using

and (15.1) we get for equity cost, ke

15.1

Introduction

ke =

293

k ðS þ D Þ w D k0 D - kd = k 0 þ ðk0- kd Þ = k0 - kd d = 0 S we we S S

þ ðk0- kd ÞL,

ð15:4Þ

where L stands for leverage level; D is debt capital value of the company; WACC stands for weighted average cost of capital; S stands for equity value; kd and wd stand for the debt cost and share; ke and we stand for the equity capital cost and share. From (15.4), it follows that the equity cost increases linearly with the level of leverage.

15.1.3.2

Modigliani–Miller Theory with Taxes

Taking into account the income tax. In 1963 Modigliani and Miller (Мodigliani and Мiller 1963, 1966), accounting the tax on profit, have obtained for the levered company value, V, V = V0 þ D  t

ð15:5Þ

where D stands for the debt value, V0 stands for the unlevered company value, and T stands for the tax on income rate. From (15.5) one gets WACC = k0  ð1- wd t Þ

ð15:6Þ

One gets from (15.6) for equity cost ke k e = k0 þ L  ðk0- k d Þð1- t Þ

ð15:7Þ

Formula (15.7) (MM with taxes) differs from formula (15.4) (MM without taxes) by the factor (1 – t) (tax corrector). It is less than unity, so the ke(L ) curve slope decreases when taxes are included.

15.1.4

Unification of Capital Asset Pricing Model (CAPM) with Modigliani–Miller Model

The Modigliani–Miller theory with accounting taxes has been united with CAPM (Capital Asset Pricing Model) in 1961 by Hamada (1969). For the cost of equity of leveraged company, the below formula has been derived

294

15

BFO Theory with Variable Profit in Case of Advance Payments of Tax on Profit

ke = k F þ ðkM- kF ÞbU þ ðkM- k F ÞbU

D ð1- T Þ, S

ð15:8Þ

Here, bU is the β-coefficient of the unlevered company. First term represents riskfree profitability kF, second term—business risk premium, (kM - kF)bU, and third term—financial risk premium ðkM- kF ÞbU DS ð1- T Þ. In the case of a unlevered company (D = 0), the financial risk (the third term) is zero, and its shareholders receive only a business risk premium.

15.1.5

Miller Model

Corporate and individual taxes were taken into account by Miller (1977), and the following formula was obtained for the value of a company without borrowed funds, VU, VU =

EBITð1 - T C Þð1 - T S Þ : k0

ð15:9Þ

Here, TC stands for the corporate tax on income rate, TS stands for the tax rate on profits of an individual investor from his ownership by stock of corporation, TD-tax rate on interest profits from the provision of investor–individuals of credits to other investors and companies. A factor (1 - TS) accounts the individual taxes.

15.1.6

Brusov–Filatova–Orekhova (BFO) Theory

One of the most important limitations of the Modigliani–Miller theory, removed in 2008 by Brusov–Filatova–Orekhova (Brusov et al. 2018, 2020), is the perpetual nature of the company. The authors generalized the Modigliani–Miller theory for companies of arbitrary age and obtained the famous BFO formula for WACC. 1 - ð1 þ k 0 Þ - n 1 - ð1 þ WACCÞ - n = WACC k0 ½1 - wd T ð1 - ð1 þ kd Þ - n Þ

ð15:10Þ

To get Modigliani–Miller limit one should substitute n → 1. A number of new effects, obtained in Brusov–Filatova–Orekhova theory (Brusov et al. 2018, 2020), are absent in Modigliani–Miller theory (Brusov et al. 2021; Мodigliani and Мiller 1958, 1963). The BFO theory destroyed some of the main principles of financial management that have existed for many decades: among them, one of the cornerstones of the formation of an optimal capital structure—trade-off theory—the failure of which was proved by Brusov–Filatova–Orekhova (Brusov et al. 2018, 2020).

15.1

Introduction

15.1.7

295

Alternative Expression for WACC

Alternative formula for the WACC, different from Modigliani–Miller one, has been derived in Farber et al. (2006); Fernandez (2006); Berk and De Marzo (2007); Harris and Pringle (1985) from the WACC definition and the balance identity (see Farber et al. 2006): WACC = k0 ð1- wd T Þ - kd twd þ kTS twd ,

ð15:11Þ

where k0, kd, and kTS are the expected returns, respectively, on the unlevered company, the debt, and the tax shield. Some additional conditions are required for practical applicability of Eq. (15.11) practical applicability. If the WACC is constant over time, as it stated in Farber et al. (2006) the levered company capitalization is found by discounting with the WACC of the unlevered company. In textbooks (Berk and De Marzo 2007; Harris and Pringle 1985) formulas for the special cases, where the WACC is constant, could be found. In 1963 Modigliani and Miller assume that the debt value D is constant. Then, as the expected after-tax cash-flow of the unlevered firm is fixed, V0 is constant as well. By assumption, kTS = kD and the value of the tax shield is TS = tD. Thus, the capitalization of the company V is a constant and the alternative formula (15.11) becomes a formula for a constant WACC: WACC = k 0 ð1- wd T Þ Because the debt kd and the tax shield kTS have debt nature it seems reasonable that the expected returns on them are equal as suggested by “classical” Modigliani– Miller (MM) theory, which has been modified by Brusov et al. (2021) for cases of practical meanings.

15.1.8

Trade-off Theory

The world famous trade-off theory was the cornerstone for many decades and is popular now (see, for example, Frank and Goyal (2009; Sheridan and Wessels (1988)). However, in 2013 the trade-off theory bankruptcy has been proved by Brusov et al. (2018, 2020). The risky debt financing does not lead to the WACC growth, and WACC still decreases with leverage. Thus, the minimum in the WACC(L) curve and of maximum in the V(L ) are absent. This means that within the world famous tradeoff theory the optimal capital structure is absent. Brusov et al. (2018, 2020) gave an explanation for this fact. Modigliani–Miller stressed the importance of the tax shield. In Sheridan and Wessels (1988); Harry and Masulis (1980); Bradley et al. (1984); Graham (2003),

296

15

BFO Theory with Variable Profit in Case of Advance Payments of Tax on Profit

the study of the tax shield was continued, including non-debt tax shield (Graham 2003). It was shown that the effects of substitution between debt and non-debt tax shields are suppressed by a positive relation of this type. The Brusov–Filatova–Orekhova (BFO) theory, its methodology, and results are widely known (see, for example, Dimitropoulos (2014); Luiz and Cruz (2015); Barbi (2011); Franc-Dąbrowska et al. (2021); Angotti et al. (2018); Vergara-Novoa et al. (2018); Mundi et al. (2022); Sadiq et al. (2022); Becker (2022); El-Chaarani et al. (2022)). A lot of authors of (Angotti et al. 2018; Vergara-Novoa et al. 2018; Mundi et al. 2022) use the BFO theory in practice.

15.2

15.2.1

Modification of the Brusov–Filatova–Orekhova (BFO) Theory to the Case of Companies with Variable Incomes and Advance Payments of Tax on Profit The Financially Dependent Company Value, V

Below, for the first time, we generalize the BFO theory for the case of variable profit. Assuming that income for the period grows with rate g, we derive the formula for a financially dependent company value. V= þ

CFð1 þ gÞ CFð1 þ gÞ2 CF þ þ ... þ 2 1 þ WACC ð1 þ WACCÞ ð1 þ WACCÞ3 CFð1 þ gÞn - 1 ð1 þ WACCÞn

ð15:12Þ

where CF is an annual profit of company. (15.12) is the geometric progression with denominator g=

ð 1 þ gÞ ð1 þ WACCÞ

ð15:13Þ

Summing (15.12), one gets for V 1-



CF  1 þ WACC   n  1þg  11 þ WACC

V=

n

1þg 1þWACC 1þg 1 - 1þWACC

=

In perpetuity (MM) limit (n → 1) one gets for V,

CF WACC - g ð15:14Þ

15.2

Modification of the Brusov–Filatova–Orekhova (BFO) Theory to the Case. . .

V=

CF WACC - g

297

ð15:15Þ

This means that WACC-g plays the role of the discount rate, not WACC.

15.2.2

The Value of a Financially Independent Company, V0

Let us, assuming that profit for the period grows with the rate g, derive formula for a financially independent company value V0, 2

V0 =

n-1

CFð1 þ gÞ CFð1 þ gÞ CFð1 þ gÞ CF þ þ þ ... þ 3 1 þ k 0 ð1 þ k 0 Þ 2 ð1 þ k 0 Þn ð1 þ k 0 Þ

ð15:16Þ

(15.16) is the geometric progression with denominator g=

ð 1 þ gÞ ð1 þ k 0 Þ

ð15:17Þ

Summing (15.16), one gets for a financially independent company value, V

V0 =

CF  1 þ k0

1-



n

1þg 1þk0 1þg 1 - 1þk 0

=

  n  CF 1þg :  1k0 - g 1 þ k0

ð15:18Þ

In perpetuity (MM) limit (n → 1) one gets for a financially independent company value, V0, V0 =

CF : k0 - g

ð15:19Þ

This formula shows that discount rate is k0-g, and not k0.

15.2.3

The Tax Shield Value

The tax shield for n-year company for advance payments of tax on income is equal ðTSÞn = tk d D þ

tk d D tk d D þ ... þ 1 þ kd ð1 þ k d Þn - 1

(15.20) is the geometric progression with denominator

ð15:20Þ

298

15

BFO Theory with Variable Profit in Case of Advance Payments of Tax on Profit

g=

1 ð1 þ k d Þ

ð15:21Þ

Summing (15.20), one gets for tax shield 1 - ð1 þ k d Þ - n = Dt ð1- ð1 þ k d Þ - n Þ  ð1 þ k d Þ 1 1 - 1þk d

ðTSÞn = tk d D 

ð15:22Þ

ðTSÞn = Dt ð1- ð1 þ kd Þ - n Þ  ð1 þ kd Þ

ð15:23Þ

Generalizing the first Modigliani–Miller theorem for finite company age, we get V = V 0 þ ðTSÞn

ð15:24Þ

D = wd V,

ð15:25Þ

Substituting

we arrive to the following expression: V ð1- wd t ð1- ð1 þ kd Þ - n Þ  ð1 þ kd ÞÞ = V 0

ð15:26Þ

Substituting here the values of a financially independent company, V0 (15.18) and of a financially dependent company, V, (15.14) one gets   n  1þg CF  1 - 1þWACC  ð1 - wd t ½1 - ð1 þ k d Þ - n   ð1 þ k d ÞÞ 

=

CF  1 -



1þg 1þk 0

n 

WACC - g ð15:27Þ

ðk 0 - gÞ

From (15.27) we arrive to the BFO equation for the case of the company variable profit 1-



1þg 1þWACC

n

WACC - g

=

1-



1þg 1þk0

n

ðk0 - gÞ  ð1 - wd t ½1 - ð1 þ kd Þ - n   ð1 þ kd ÞÞ

:

ð15:28Þ

This formula is the main theoretical result of the article. For the Modigliani–Miller theory with the variable profit (Brusov et al. 2021), one gets

15.3

Results and Discussions

15.3

299

WACC - g = ðk0- gÞ  ð1- wd t  ð1 þ kd ÞÞ

ð15:29Þ

WACC = ðk0- gÞ  ð1- wd t  ð1 þ kd ÞÞ þ g

ð15:30Þ

Results and Discussions

Below we study within Microsoft Excel the impact of a growth rate g on the company financial parameters (WACC; WACC-g; V; ke) using the formula (15.28), under investigating their dependences on the level of leverage L. We present the results for the following financial parameters of the company: k0 = 0:26; kd = 0:22; t = 0:2; CF = 100; n = 5 Here, k0 stands for the equity cost at zero leverage level; kd stands for the debt cost; t stands for the tax on profit; CF stands for the profit per period; n stands for the company age; L stands for the leverage level. Note that the qualitative effect of the growth rate g on the main financial parameters is similar, while the results for different parameters are different numerically.

15.3.1

Five-year Company

15.3.1.1

Weighted Average Cost of Capital, WACC

As it could be seen from Fig. 15.1, all curves WACC(L) for different values of g start from one point (0; k0 = 0.26). All curves WACC(L) decrease with leverage level L at all g values. The curves WACC(L) increase with g. The five-year company results differ from the results for a perpetual limit—the theory of Modigliani and Miller (Brusov et al. 2021). In the latter case, the WACC (L ) curves decrease with the level of leverage L at g < k0 and increase at g > k0. k0 is the threshold value g separating the increasing WACC(L ) curves from the decreasing ones, and for g = k0 WACC = const = k0. In the first case (BFO theory), the WACC(L ) curves decrease with increasing leverage L for all values of the growth rate g. The WACC(L ) curves increase with the rate g both in the Brusov–Filatova– Orekhova theory and in the Modigliani and Miller theory. This means that WACC is no longer a discount rate. As it will be seen below, the role of the discount rate play WACC-g and WACC–k0. Below we study the dependence of WACC-g on L in the generalized theory of Brusov–Filatova–Orekhova (the GBFO theory) at k0 = 0.18 and different values of g (-0.2; -0.1; 0.0; 0.1; 0.2) for two- and four-year company.

300

15

BFO Theory with Variable Profit in Case of Advance Payments of Tax on Profit

WACC(L), ko=0.26; kd = 0.22; n=5 0.265 0.255 0.245 0.235 0.225 0.215 0.205 0.195 0.185 0.175

0

1 g=0 g=0,15

2

3 g=0,05 g=-0,15

4

5

6

g=-0,05 g=0,2

7 g=0,1 g=-0,2

8

9

10 g=-0,1

Fig. 15.1 The dependence of WACC on leverage level L in Generalized Brusov–Filatova– Orekhova theory (GBFO theory) with advance payments of tax on profit at k0 = 0.26; kd = 0.22; t = 0.2; g = 0.2; 0.15; 0.1; 0.05; 0.0; -0.05;–0.1; -0.15; -0.2 for five-year company

15.3.1.2

Calculations of the Discount Rate, WACC-g

As it is seen from Fig. 15.2. the curves (WACC-g)(L ) decrease with leverage level L at all g values. The curves (WACC-g)(L) decrease with growth rate, g. The explanation of the behavior of the (WACC-g)(L ) curves is as follows: all WACC(L ) curves originate from the same point (L = 0; WACC = 0.26). The (WACC-g)(L ) curves will be ordered as follows for L = 0: the larger g, the lower the starting point and hence the entire graph lies, since the curves do not intersect. As we’ll see below the decrease of (WACC-g)(L ) with growth rate, g, will lead to increase of the company value, V, with g.

15.3.1.3

Calculations of the Company Value, V

It is seen from Fig. 15.3 that the company value V at fixed growth rate g increases with leverage level L. The company value V increases with growth rate g as well.

15.3

Results and Discussions

301

WACC-g(L), k0=0.26; kd = 0.22; n=5 0.44 0.39 0.34 0.29 0.24 0.19 0.14 0.09 0.04 -0.01

0

1

2

3

4

5

6

7

8

g=0

g=0,05

g=-0,05

g=0,1

g=-0,1

g=0,15

g=-0,15

g=0,2

g=-0,2

9

10

Fig. 15.2 The dependence of discount rate, WACC-g, on leverage level L in Generalized Brusov– Filatova–Orekhova theory (GBFO theory) with advance payments of tax on profit at k0 = 0.26; kd = 0.22; t = 0.2; g = 0.2; 0.15; 0.1; 0.05; 0.0; -0.05;–0.1; -0.15; -0.2 for five-year company

Below we study the equity cost, ke, dependence on leverage level L and on growth rate, g, at k0 = 0.18; kd = 0.16 and g = 0; ± 0.1;±0.2.

15.3.1.4

Calculations of the Equity Cost, ke

As it is seen from Fig. 15.4 the equity cost, ke, practically linearly grows with leverage level L at all growth rate g values. The tilt angle ke(L ) increases with g.

302

15

BFO Theory with Variable Profit in Case of Advance Payments of Tax on Profit

V(L), k0=0.26; kd=0.22; n=5

390 g=0 g=0,05 g=-0,05 g=0,1

340

g=-0,1 g=0,15 g=-0,15 g=0,2

290

g=-0,2

240

190

0

1

2

3

4

5

6

7

8

9

10

Fig. 15.3 The dependence of discount rate, WACC-g, on leverage level L in Generalized Brusov– Filatova–Orekhova theory (GBFO theory) with advance payments of tax on profit at k0 = 0.26; kd = 0.22; t = 0.2; g = 0.2; 0.15; 0.1; 0.05; 0.0; -0.05;–0.1; -0.15; -0.2 for five-year company

15.3.2

Study the Dependence of Financial Indicators on kd

15.3.2.1

The Weighted Average Cost of Capital, WACC

It is seen from Fig. 15.5 that all curves WACC(L) at all values of kd start from one point (0; 0.26). WACC(L) decreases with leverage level L at all values of kd. WACC (L ) decreases with the increase of debt cost kd. This means that tax shield advantages the decrease of the cost of raising capital.

15.3.2.2

The Discount Rate, WACC-g

It is seen from Fig. 15.6 that all curves of discount rate (WACC-g) (L) at all values of kd start from one point (0; 0.21). (WACC-g) (L ) decreases with leverage level L at all values of kd. (WACC-g)(L ) decreases with the increase of debt cost kd. This means that the tax shield tends to lower the value of the discount rate (WACC-g) and hence (as we will see below in Sect. 15.3.2.3) increase the value of the company, V.

15.3

Results and Discussions

303

ke(L), k0=0.26; kd = 0.22; n=5 0.43

0.38 g=0 g=0,05 g=-0,05

0.33

g=0,1 g=-0,1 g=0,15 g=-0,15

0.28

g=0,2 g=-0,2 0.23

0.18

0

1

2

3

4

5

6

7

8

9

10

Fig. 15.4 The dependence of equity cost, ke, on leverage level L in Generalized Brusov–Filatova– Orekhova theory (GBFO theory) with advance payments of tax on profit at k0 = 0.26; kd = 0.22; t = 0.2; g = 0.2; 0.15; 0.1; 0.05; 0.0; -0.05;–0.1; -0.15; -0.2 for five-year company

15.3.2.3

The Company Value, V

From Fig. 15.7 it follows that all curves of company value V (L) at all values of kd start from one point (0; 285). V (L ) increases with leverage level L at all values of kd. V(L ) increases with the increase of debt cost kd. This means that tax shield advantages the increase of the company value, V. It follows from Fig. 15.8 that all curves of equity cost, ke(L), at all values of kd start from one point (0; 0.26) and ke increases with leverage level L at all values of kd. The slope of the straight line ke(L ) decreases with the cost of debt kd. This means that debt cost kd impacts the dividend policy of the company, because the equity cost ke determines the economically justified amount of dividends.

304

15

BFO Theory with Variable Profit in Case of Advance Payments of Tax on Profit

WACC(L), k0=0.26; g=0.05; n=5 0.27 0.26 0.25 0.24 0.23 0.22 0.21 0.2 0.19

0

1

2

3 kd=0,22

4

5 kd=0,2

6

7

8

9

10

kd=0,18

Fig. 15.5 The dependence of WACC on leverage level L in Generalized Brusov–Filatova– Orekhova theory (GBFO theory) with advance payments of tax on profit at k0 = 0.26; kd = 0.22; 0.2; 0.18; t = 0.2; g = 0.05 for five-year company

15.3.3

Impact of Company Age, n, on Main Financial Indicators of the Company

Below we study the impact of company age, n, on main financial indicators of the company: WACC; WACC-g; V; ke. We investigate the dependence of WACC; WACC-g; company value, V, and equity cost, ke on leverage level L in Generalized Brusov–Filatova–Orekhova theory (GBFO theory) with advance payments of tax on profit at k0 = 0.26; kd = 0.22; t = 0.2; g = 0.2 and g = -0.2 for five-year and ten-year companies. We found a huge difference between the behavior of the main financial indicators of the company with a positive and negative growth rate g. This allows you to explore companies with growing profits and companies with decreasing profits. Also it allows to study the companies whose profits rise and fall in different periods.

15.3

Results and Discussions

305

WACC-g(L), k0=0.26; g=0.05; n=5 0.21

0.2

0.19

0.18

0.17

0.16

0.15

0.14

0

1

2

3

kd=0,22

4

6 kd=0,2

7

8

9

10

kd=0,18

Fig. 15.6 The dependence of discount rate, WACC-g, on leverage level L in Generalized Brusov– Filatova–Orekhova theory (GBFO theory) with advance payments of tax on profit at k0 = 0.26; kd = 0.22; 0.2; 0.18; t = 0.2; g = 0.05 for five-year company

15.3.3.1

WACC(L)

We investigate the dependence of WACC on L for companies of two ages: five and ten years old at two values of growth rates (g = 0.2 and g = -0.2) (see Figs. 15.9 and 15.10). In both cases, the two WACC(L ) curves start from the point (0; 0.26) and decrease with L. For positive growth rate (g = 0.2) WACC is lower for five-year company, while for negative growth rate (g = -0.2) WACC is lower for ten-year company. We are seeing this effect for the first time.

15.3.3.2

Discount Rate WACC-g

We investigate the dependence of discount rate WACC-g on L for companies of two ages: five and ten years old at two values of growth rates (g = 0.2 and g = -0.2)

306

15

BFO Theory with Variable Profit in Case of Advance Payments of Tax on Profit

V(L), k0=0.26; g=0.05; n=5 335 330 325 320 315 310 305 300 295 290 285

0

1

2

3 kd=0,22

4

5 kd=0,2

6

7

8

9

10

kd=0,18

Fig. 15.7 The dependence of company value, V, on leverage level L in Generalized Brusov– Filatova–Orekhova theory (GBFO theory) with advance payments of tax on profit at k0 = 0.26; kd = 0.22; 0.2; 0.18; t = 0.2; g = 0.05 for five-year company

(see Figs. 15.11 and 15.12). In both cases, the two WACC(L ) curves start from one point: (0; 0.06) for g = 0.2 and (0; 0.46) for g = -0.2 and decrease with L. For positive growth rate (g = 0.2) discount rate WACC-g is lower for five-year company, while for negative growth rate (g = -0.2) discount rate WACC-g is lower for ten-year company. We are seeing this effect for the first time.

15.3.3.3

Company Value, V

Let us study the dependence of the value of a company V on L for companies of two ages: five and ten years old at two values of growth rates (g = 0.2 and g = -0.2). In both cases, the value of the company V increases with the growth of L, and the greater the age of the company corresponds to the greater value of the company V. But if, with a positive growth rate (g = 0.2), the difference in the value of V for a five-year company and a ten-year company is about 400, with negative growth rate (g = -0.2), this difference is 45 (ten times less) (see Figs. 15.13 and 15.14). So, in the competition between the age of the company and the size of the growth rate, the growth rate wins.

15.3

Results and Discussions

307

ke(L), k0=0.26; g=0.05; n=5 0.8

0.7

0.6

0.5

0.4

0.3

0.2

0

1

2

3 kd=0,22

4

5 kd=0,2

6

7

8

9

10

kd=0,18

Fig. 15.8 The dependence of equity cost, ke, on leverage level L in Generalized Brusov–Filatova– Orekhova theory (GBFO theory) with advance payments of tax on profit at k0 = 0.26; kd = 0.22; 0.2; 0.18; t = 0.2; g = 0.05 for five-year company

15.3.3.4

Equity Cost, ke

Let us study the dependence of the equity cost, ke, on L for companies of two ages: five and ten years old at two values of growth rates (g = 0.2 and g = -0.2). In the case of a positive growth rate (g = 0.2), the cost of equity ke increases linearly with L, and the slope ke(L ) for a ten-year company is greater than for a five-year one. With a negative growth rate (g = -0.2), the cost of equity ke decreases linearly with increasing L, and the negative slope for a ten-year company is greater than for a fiveyear one. Since the cost of equity determines the economically justified amount of dividends, this means that the dividend policy of the company when increasing profits and when decreasing profits should be completely different. This is a qualitatively new effect, discovered by us for the first time (Figs. 15.15 and 15.16).

308

15

BFO Theory with Variable Profit in Case of Advance Payments of Tax on Profit

WACC(L), kd = 0.22, g = 0.2

0.255

0.245

0.235

0.225

0.215

0.205

0.195 0

1

2

3

4 n=5

5

6

7

8

9

10

n=10

Fig. 15.9 The dependence of WACC on leverage level L in Generalized Brusov–Filatova– Orekhova theory (GBFO theory) with advance payments of tax on profit at k0 = 0.26; kd = 0.22; t = 0.2; g = 0.2 for five-year and ten-year companies

15.3.3.5

Results Summary

The curves (WACC-g)(L ) decrease with leverage level L at all g values. The curves (WACC-g)(L ) decrease with growth rate, g. The company value V increases with leverage level L at fixed growth rate g. The company value V increases with growth rate g as well. This is a consequence of a decrease of the discount rate (WACC-g)(L ) with an increase of g. The equity cost, ke, practically linearly increases with leverage level L at all g values. The tilt angle ke(L ) increases with g. Studying the impact of the debt cost kd on the main financial indicators, we found the following:

15.3

Results and Discussions

309

WACC(L), kd = 0.22, g = -0.2 0.265 0.255 0.245 0.235 0.225 0.215 0.205 0.195 0.185 0.175 0.165 0

0.5

1

1.5

2

2.5 n=10

3

4

5

6

7

8

9

10

n=5

Fig. 15.10 The dependence of WACC on leverage level L in Generalized Brusov–Filatova– Orekhova theory (GBFO theory) with advance payments of tax on profit at k0 = 0.26; kd = 0.22; t = 0.2; g = -0.2 for five-year and ten-year companies

• all curves WACC(L ) at all values of kd start from one point (0; 0.26). WACC(L ) decreases with leverage level L at all values of kd. WACC(L ) decreases with the increase of debt cost kd. This means that tax shield advantages the decrease of the cost of raising capital. • All curves of discount rate (WACC-g) (L ) at all values of kd start from one point (0; 0.21). (WACC-g) (L ) decreases with leverage level L at all values of kd. (WACC-g)(L ) decreases with the increase of debt cost kd. This means that the tax shield tends to lower the value of the discount rate (WACC-g) and hence increase the value of the company, V. • All curves of company value V (L ) at all values of kd start from one point (0; 285). V (L ) increases with leverage level L at all values of kd. V(L ) increases with the increase of debt cost kd. This means that tax shield advantages the increase of the company value, V.

310

15

BFO Theory with Variable Profit in Case of Advance Payments of Tax on Profit

WACC-g(L), kd = 0.22, g = -0,2 0.465 0.455 0.445 0.435 0.425 0.415 0.405 0.395 0.385 0.375 0.365 0

1

2

3

4 n=10

5

6

7

8

9

10

n=5

Fig. 15.11 The dependence of discount rate, WACC-g, on leverage level L in Generalized Brusov– Filatova–Orekhova theory (GBFO theory) with advance payments of tax on profit at k0 = 0.26; kd = 0.22; t = 0.2; g = -0.2 for five-year and ten-year companies

• All curves of equity cost, ke(L ), at all values of kd start from one point (0; 0.26) and ke increases with leverage level L at all values of kd. The slope of the straight line ke(L ) decreases with the cost of debt kd. This means that debt cost kd impacts the dividend policy of the company, because the equity cost ke determines the economically justified amount of dividends. Studying the impact of company age, n, on main financial indicators of the company: WACC; WACC-g; V; ke, we found a huge difference between the behavior of the main financial indicators of the company with a positive and negative growth rate g. This allows you to explore companies with growing profits and companies with decreasing profits. Also it allows to study the companies whose profits rise and fall in different periods. Particular results here are as follows: We investigate the dependence of WACC on L for companies of two ages: five and ten years old at two values of growth rates (g = 0.2 and g = -0.2). In both cases, the two WACC(L) curves start from the point (0; 0.26) and decrease with L. For positive growth rate (g = 0.2) WACC is lower for five-year company, while for negative growth rate (g = -0.2) WACC is lower for ten-year company. We are seeing this effect for the first time. We investigate the dependence of discount rate WACC-g on L for companies of two ages: five and ten years old at two values of growth rates (g = 0.2 and g = -0.2).

15.3

Results and Discussions

311

WACC-g(L), kd = 0.22, g = 0.2 0.06 0.05 0.04 0.03 0.02 0.01 0 0

1

2

3

4

5

6

7

8

9

10

-0.01 n=10

n=5

Fig. 15.12 The dependence of discount rate, WACC-g, on leverage level L in Generalized Brusov– Filatova–Orekhova theory (GBFO theory) with advance payments of tax on profit at k0 = 0.26; kd = 0.22; t = 0.2; g = 0.2 for five-year and ten-year companies

In both cases, the two WACC(L) curves start from one point: (0; 0.06) for g = 0.2 and (0; 0.46) for g = -0.2 and decrease with L. For positive growth rate (g = 0.2) discount rate WACC-g is lower for five-year company, while for negative growth rate (g = -0.2) discount rate WACC-g is lower for ten-year company. We are seeing this effect for the first time. Let us analyze the dependence of the value of a company V on L for companies of two ages: five and ten years old at two values of growth rates (g = 0.2 and g = -0.2). In both cases, the value of the company V increases with the growth of L, and the greater the age of the company corresponds to the greater value of the company V. But if, with a positive growth rate (g = 0.2), the difference in the value of V for a five-year company and a ten-year company is about 400, with negative growth rate (g = -0.2), this difference is 45 (ten times less). So, in the competition between the age of the company and the size of the growth rate, the growth rate wins. We study the dependence of the equity cost, ke, on L for companies of two ages: five and ten years old at two values of growth rates (g = 0.2 and g = -0.2). In the case of a positive growth rate (g = 0.2), the cost of equity ke increases linearly with

312

15

BFO Theory with Variable Profit in Case of Advance Payments of Tax on Profit

V(L), kd = 0.22, g = -0.2 270 260 250 240 230 220 210 200 190 0

1

2

3

4 n=10

5

6

7

8

9

10

n=5

Fig. 15.13 The dependence of company value, V, on leverage level L in Generalized Brusov– Filatova–Orekhova theory (GBFO theory) with advance payments of tax on profit at k0 = 0.26; kd = 0.22; t = 0.2; g = -0.2 for five-year and ten-year companies

L, and the slope ke(L ) for a ten-year company is greater than for a five-year one. With a negative growth rate (g = -0.2), the cost of equity ke decreases linearly with increasing L, and the negative slope for a ten-year company is greater than for a fiveyear one. Since the cost of equity determines the economically justified amount of dividends, this means that the dividend policy of the company when increasing profits and when decreasing profits should be completely different. This is a qualitatively new effect, discovered by us for the first time.

15.4

Conclusions

The Brusov–Filatova–Orekhova (BFO) theory has been generalized for the case of variable income and advance payments of tax on profit. The generalized Brusov– Filatova–Orekhova formula for WACC has been derived. Using this formula the

15.4

Conclusions

313

V(L), kd = 0.22, g = 0.2 800 750 700 650 600 550 500 450 400 350 300 0

1

2

3

4 n=5

5

6

7

8

9

10

n=10

Fig. 15.14 The dependence of company value, V, on leverage level L in Generalized Brusov– Filatova–Orekhova theory (GBFO theory) with advance payments of tax on profit at k0 = 0.26; kd = 0.22; t = 0.2; g = 0.2 for five-year and ten-year companies

dependence of WACC, discount rate, WACC-g, company capitalization, V, the equity cost, ke, on leverage level L at different values of the growth rate, g, on cost of debt capital, kd, and on company age, n has been studied. It turns out that the WACC is no longer a discount rate. The role of the discount rate is played by WACC-g, which decreases with g, while the company’s value increases with g. The slope of the curve ke(L ) increases with g. It turns out that at the growth rate g < g* the slope of the curve ke(L ) becomes negative, which can significantly change the principles of the company’s dividend policy, since the economically justified amount of dividends is equal to the cost of equity. WACC(L) as well as the discount rate, WACC-g, decreases with the increase of debt cost kd. V (L ) increases with leverage level L at all values of kd. And V(L ) increases with the increase of debt cost kd. This means that tax shield advantages the decrease of the cost of raising capital. Examining the behavior of the main financial parameters of the company with positive (g = 0.2) and negative (g = -0.2) growth rates, we found a huge difference in their behavior. This allows you to explore companies with growing profits and companies with decreasing profits. It also allows you to study companies whose profits rise and fall in different periods.

314

15

BFO Theory with Variable Profit in Case of Advance Payments of Tax on Profit

ke(L), kd = 0.22, g = -0.2 0.3

0.25

0.2

0.15

0.1

0.05

0

1

2

3

4 n=10

5

6

7

8

9

10

n=5

Fig. 15.15 The dependence of equity cost, ke, on leverage level L in Generalized Brusov–Filatova– Orekhova theory (GBFO theory) with advance payments of tax on profit at k0 = 0.26; kd = 0.22; t = 0.2; g = -0.2 for five-year and ten-year companies

References

315

ke(L), kd = 0.22, g = 0.2 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0

1

2

3

4 n=10

5

6

7

8

9

10

n=5

Fig. 15.16 The dependence of equity cost, ke, on leverage level L in Generalized Brusov–Filatova– Orekhova theory (GBFO theory) with advance payments of tax on profit at k0 = 0.26; kd = 0.22; t = 0.2; g = 0.2 for five-year and ten-year companies

References Angotti M, de Lacerda Moreira R, Hipólito Bernardes do Nascimento J, Neto de Almeida Bispo O (2018) Analysis of an equity investment strategy based on accounting and financial reports in Latin American markets. Reficont 5:22–40 Barbi M (2011) On the risk–neutral value of debt tax shields. Appl Financ Econ 22:251–258 Becker DM (2022) Getting the valuation formulas right when it comes to annuities. Manag Financ 48:470 Berk J, De Marzo P (2007) Corporate finance. Pearson-Addison Wesley, Boston Bradley M, Jarrell GA, Kim EH (1984) On the existence of an optimal capital structure: theory and evidence. J Financ 39:857–878 Brusov P, Filatova T, Orehova N, Eskindarov M (2018) Modern corporate finance, investments, taxation and ratings, 2nd edn. Springer Nature Publishing, Cham, pp 1–571 Brusov P, Filatova T, Orehova N (2020) Ratings: critical analysis and new approaches of quantitative and qualitative methodology. Springer Nature Publishing, pp 1–369. https://www. springer.com/de/book/9783030562427 Brusov PN, Filatova TV, Orekhova NP, Kulik VL, Chang SI, Lin YCG (2021) Generalization of the Modigliani–Miller theory for the case of variable profit. Mathematics 9(11):1286. https:// doi.org/10.3390/math9111286 Dimitropoulos P (2014) Capital structure and corporate governance of soccer clubs: European evidence. Manag Res Rev 37:658–678

316

15

BFO Theory with Variable Profit in Case of Advance Payments of Tax on Profit

El-Chaarani H, Abraham R, Skaf Y (2022) The impact of corporate governance on the financial performance of the banking sector in the MENA (middle eastern and north African) region: an immunity test of banks for COVID-19. J Risk Financ Manag 15:82 Farber A, Gillet R, Szafarz A (2006) A general formula for the WACC. Int J Bus 11(2):211–218 Fernandez P (2006) A general formula for the WACC: a comment. Int J Bus 11(2):219 Franc-Dąbrowska J, Mądra-Sawicka M, Milewska A (2021) Energy sector risk and cost of capital assessment—companies and investors perspective. Energies 14:1613 Frank M, Goyal V (2009) Capital structure decisions: which factors are reliably important? Financ Manag 38(1):1–37. https://doi.org/10.1111/j.1755-053X.2009.01026.x Graham JR (2003) Taxes and corporate finance: a review. Rev Financ Stud 16:1075–1129 Hamada R (1969) Portfolio analysis, market equilibrium, and corporate finance. J Financ 24(1): 13–31 Harris R, Pringle J (1985) Risk–adjusted discount rates – extension form the average–risk case. J Financ Res 8/3:237–244 Harry DA, Masulis RW (1980) Optimal capital structure under corporate and personal taxation. J Financ Econ 8:3–29 Luiz K, Cruz M (2015) The relevance of capital structure on firm performance: a multivariate analysis of publicly traded Brazilian companies. REPeC Brasília 9:384–401 Miller M (1977) Debt and taxes. J Financ 32(2):261–275. https://doi.org/10.1111/j.1540-6261. 1977.tb03267.x Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Modigliani F, Miller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391 Mundi HS, Kaur P, Murty RLN (2022) A qualitative inquiry into the capital structure decisions of overconfident finance managers of family–owned businesses in India. Qual Res Financ Mark 14:357–379 Sadiq M, Alajlani S, Hussain MS, Bashir F, Chupradit S (2022) Impact of credit, liquidity, and systematic risk on financial structure: comparative investigation from sustainable production. Environ Sci Pollut Res Int 29:20963–20975 Sheridan T, Wessels R (1988) The determinants of capital structure choice. J Financ 43:1–19 Vergara-Novoa C, Sepúlveda-Rojas JP, Miguel DA, Nicolás R (2018) Cost of capital estimation for highway concessionaires in Chile. J Adv Transp 2018:2153536

Chapter 16

BFO Theory with Variable Profit: Two Types of Payments of Tax on Profit: Advanced Payments and at the Ends of Periods

Keywords Generalized Brusov–Filatova–Orekhova theory · Advance payments of tax on profit · Variable profit · Company value · Equity cost · The weighted average cost of capital · WACC

16.1

Introduction

The classical versions of the two main capital structure theories—Brusov–Filatova– Orekhova (BFO), which is valid for companies of arbitrary age, and the Modigliani– Miller theory, a perpetual version of the BFO theory, are limited to the case of constant profit. But in practice, the profit of the company, of course, is variable. Recently, both theories have been generalized to the case of variable income (Brusov et al. 2021; Brusov and Filatova 2022), which expands significantly the applicability of both theories of capital structure in practice. In the Brusov–Filatova–Orekhova (BFO) theory, generalized to the case of variable income (Brusov and Filatova 2022), income tax payments are made at the end of periods, while in practice these payments can be made as well in advance. Here we consider two modifications of the Brusov–Filatova–Orekhova (BFO) theory with variable income: (1) with the payment of income tax at the end of periods and (2) with advance payments of income tax (this case is considered here for the first time). For these two cases, BFO formulas were derived for the weighted average cost of capital, WACC, for the value of the company, V, and within these formulas, a comprehensive analysis of the dependence of WACC, of the discount rate, WACC–g (here g is the growth rate), company capitalization, V, cost of equity, ke, on debt financing at different values of the growth rate, g, at different values of the cost of debt capital, kd, and at different values of the age of the company, n. The results for cases (1) and (2) are compared, which allows us to conclude that case (2) is always preferable for both the company and the regulator. This makes it possible to develop recommendations for both parties to expand the practice of advance income tax payments in the framework of real economic practice. The structure of the chapter is as following. In 16.1 (Introduction) the formulation of the problem is discussed as well as the novelty of the study. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_16

317

318

16 BFO Theory with Variable Profit: Two Types of Payments of Tax on Profit:. . .

In 16.1.1 A review of the literature on capital structure is given. In 16.2 we consider the modification of the Brusov–Filatova–Orekhova (BFO) theory to the case of companies with variable incomes and advance payments of tax on profit. We derive here formulas for the value of a financially dependent company, V, for the value of a financially independent company, V0, for the tax shield value, TS, for the weighted average cost of capital, WACC. The formulas are derived simultaneously for two cases: for income tax payments at the end of the periods and in advance in order to compare them. The latter are obtained here for the first time. In 16.3 we describe the results of the study the dependences of the following values: weighted average cost of capital, WACC, discount rate, WACC–g, company value, V, and the equity cost, ke, on the debt financing L at different values of the growth rate, g, at different values of the debt cost, kd and at different ages of the companies.

16.1.1

A Literature Review

From a historical point of view, five stages in the development of the capital structure theory can be distinguished: First (before 1958)—the traditional approach that existed before the appearance of the first quantitative theory by Modigliani and Miller (the second stage) (1958–1963)(Мodigliani and Мiller 1958, 1963, 1966). The third stage (1964–2008) is the numerous attempts of scientists to modify the Modigliani–Miller theory. The fourth stage (2008–2019) is the appearance of the Brusov–Filatova–Orekhova (BFO) theory, which removed the main restriction of the Modigliani–Miller (MM) theory associated with the infinite lifetime of the company (Brusov et al. 2018). And, finally, the fifth stage (2019 up to now), which began a couple of years ago and is associated with the adaptation of the two main theories of the capital structure (Brusov–Filatova–Orekhova and Modigliani– Miller) to the established financial practice of the company’s functioning by taking into account the real conditions of their work (Brusov et al. 2021; Brusov and Filatova 2022). The traditional approach is based on existing practical experience. From a theoretical point of view, the advantages of debt financing at a low level of leverage and its disadvantages at a high level of leverage are taken into account, the competition between which forms the optimal capital structure. The optimal capital structure is defined as the level of leverage at which WACC is lowest and company value, V, is highest. There are two versions of the Modigliani–Miller theory: without taxes and with taxes. Without taxes the following expressions for V, WACC and ke V = V0 =

EBIT , k0

ð16:1Þ

where V0 stands for the unlevered company value, EBIT stands for earnings before interest and taxes, and k0 stands for the equity cost at zero leverage level L.

16.1

Introduction

319

From (16.1) one gets for the weighted average cost of capital WACC: WACC = k0 :

ð16:2Þ

From the expression for WACC WACC = k 0 = k e we þ k d wd :

ð16:3Þ

and accounting (16.1), one gets for the equity cost, ke ke =

k ðS þ DÞ w D k0 D - kd d = 0 - kd = k0 þ ðk 0- k d Þ = k 0 S we we S S

þ ðk0- kd ÞL

ð16:4Þ

Here, D stands for debt capital value; S stands for equity capital value; kd and wd stand for the cost and share of the company’s debt capital; ke and we stand for the equity capital cost and share. It is seen from (4), that the equity increases linearly with the leverage level. Within the framework of the Modigliani–Miller theory with taxes (Мodigliani and Мiller 1963), the following expression was postulated for the value of a company using borrowed funds, V, V = V 0 þ D  t:

ð16:5Þ

The expression for WACC immediately follows from (16.5) WACC = k0  ð1- wd t Þ

ð16:6Þ

The following formula for the cost of equity ke can be obtained from (16.6) within the framework of the Modigliani–Miller theory with taxes k e = k0 þ L  ðk0- k d Þð1- t Þ

ð16:7Þ

Two formulas (16.7) (MM with taxes) and (16.4) (MM without taxes) differ by the multiplier (1–t), called the tax corrector. It is less than unit, thus the ke(L ) curve slope decreases with accounting the taxes. In Hamada (1969), the Modigliani–Miller theory was combined with the CAPM (Capital Asset Pricing Model). This took into account both the financial and business risk of the company and was described by the formula below for the company’s leveraged cost of equity, ke

320

16 BFO Theory with Variable Profit: Two Types of Payments of Tax on Profit:. . .

ke = k F þ ðkM- kF ÞbU þ ðkM- k F ÞbU

D ð1- T Þ, S

ð16:8Þ

where bU is the β–coefficient of the unlevered company. In Miller (1977), both corporate and individual taxes were taken into account. The following formula for the leveraged value of a company, V, was derived in 1977 by Miller (Miller 1977):


 ð1 - T C Þð1 - T S Þ D V = V 0 þ 1ð1 - T D Þ

ð16:9Þ

where TS stands for the tax on income of an individual investor from his ownership by corporation stock rate, TC stands for the tax rate on corporate income, TD stands for the tax rate on interest income from the provision of investor–individuals of credits to other investors and companies. Authors of (Farber et al. 2006; Fernandez 2006; Berk and De Marzo 2007; Harris and Pringle 1985) have supposed more general expression for WACC than the Modigliani–Miller (MM) one: WACC = k0 ð1- wd t Þ - kd wd t þ k TS twd

ð16:10Þ

where D stands for the debt value, k0 stands for the equity cost at zero leverage level, kd stands for the debt cost and kTS stands for the tax shield returns, V stands for the levered company value, and VTS stands for the tax shield value. While formula (16.10) derived in (Berk and De Marzo 2007) is more general than the Modigliani–Miller (MM) one, for its use in practice additional conditions are necessary. The levered company value can be found by discounting with the WACC for the unlevered company cash flows, in case when the WACC value is constant over time. For this special case, the formulas could be found in textbooks (Berk and De Marzo 2007; Harris and Pringle 1985). Because, as it has been supposed by Modigliani and Miller in 1963 (Мodigliani and Мiller 1963), the debt value, D, is constant, the unlevered company expected after-tax cash flow is fixed, thus V0 is also constant. By assumption, kTS = kd and the tax shield value is TS = tD. Thus, for the levered company value, V, one gets the ordinary Modigliani–Miller (MM) formula for WACC instead of formula (16.10): WACC = k0 ð1- wd t Þ We believe that the cost of debt kd and the expected return of the tax shield kTS are equal, since both of them are debt-based and thus the “classical” Modigliani–Miller (MM) theory is much more reasonable. The influence of tax pressure on the financial balance of energy companies was studied in Batrancea (2021a). As it was shown tax pressure has a stronger effect on the equilibrium of oil and electricity companies than of gas companies. In Batrancea

16.1

Introduction

321

(2021b), by studying the impact of financial liquidity and solvency on the performance of healthcare companies within the framework of econometric models, it was shown that such financial indicators as the current liquidity ratio, quick ratio and leverage level significantly affect the performance of the company. The restriction associated with the infinite life of companies and the eternity of cash flows within the framework of the MM theory was removed in 2008 by Brusov, Filatova, and Orekhova (Brusov et al. 2018), who created the modern theory of the cost of capital and capital structure—the BFO theory, which is valid both for companies of arbitrary age, as well as for companies with an arbitrary lifetime. A generalization of the assessment of the tax shield TS and the value of the company: without leverage V0 and with leverage V was required to modify the theory of MM (see the formulas below): TS = k d DT

n X

ð1 þ kd Þ - t = DT½1 - ð1 þ kd Þ - n :

t=1

V 0 = CF½1 - ð1 þ k0 Þ - n =k0 ; V = CF½1 - ð1 þ WACCÞ - n =WACC: ð16:11Þ 1 - ð1 þ k 0 Þ - n 1 - ð1 þ WACCÞ - n : = WACC k0 ½1 - ωd T ð1 - ð1 þ kd Þ - n Þ D Here, S stands for the equity capital value, wd = DþS stands for the debt capital S share, k e , we = DþS stands for the equity cost and the equity capital share, and L = D/S stands for the value of financial leverage, D stands for the debt capital value. For a 1-year company Steve Myers (Myers 2001) has derived formula, which could be obtained easily from formula (16.11) by substituting n = 1

WACC = k 0 -

ð1 þ k 0 Þk d wd T 1 þ kd

and by substituting n = 1 we arrive to the Modigliani–Miller formula for WACC (Мodigliani and Мiller 1963): WACC = k0  ð1- wd t Þ The methods and the conclusions of the Brusov–Filatova–Orekhova (BFO) theory are well known in the scientific literature (for example, see references (Dimitropoulos 2014; Luiz and Cruz 2015; Barbi 2011; Zhukov 2018; FrancDąbrowska et al. 2021; Angotti et al. 2018; Vergara-Novoa et al. 2018; Mundi et al. 2022; Sadiq et al. 2022; Becker 2022; El-Chaarani et al. 2022; Huang et al. 2020; Islam and Khandaker 2015; Singhal et al. 2022)). In a number of works (see, for example, (Vergara-Novoa et al. 2018; Mundi et al. 2022; Sadiq et al. 2022; Singhal et al. 2022)), the BFO theory is used in practical calculations.

322

16.1.1.1

16 BFO Theory with Variable Profit: Two Types of Payments of Tax on Profit:. . .

Methods and Materials

We use both analytical and numerical methods. We derive analytically (from first principles) all the formulas for the main financial indicators of the company, and then using them in Microsoft Excel calculate the dependence of these indicators on debt financing, L, growth rate, g, cost of debt, kd, age of the company, n, etc.

16.2

16.2.1

The Brusov–Filatova–Orekhova (BFO) Theory Modification to the Case of Companies with Variable Incomes and Advance Payments of Tax on Profit The Value of a Financially Dependent Company, V

Below, for the first time, we generalize the modern theory of capital cost and capital structure—the Brusov–Filatova–Orekhova theory—for the case of variable profit upon advance payments of tax on income. We simultaneously consider two modifications of the Brusov–Filatova–Orekhova (BFO) theory with variable income: (1) with the payment of income tax at the end of periods (formulas with ‘) and (2) with advance payments of income tax (this case is considered here) to see the difference in their derivation and in the resulting formulas. Let us start by deriving the capitalization formula for a financially dependent company, assuming that income for the period grows with the growth rate g. Note, that below (up to formula (16.20)) all derivations for the two cases (1) and (2) are similar, starting from formula (16.20) there will be big differences. Accounting, that the cost of any asset is equal to the sum of discounted values of incomes, generated by this asset, one could write for the capitalization for a financially dependent company V of age n the following expression V= þ

CFð1 þ gÞ2 CFð1 þ gÞ CF þ þ ... þ 2 1 þ WACC ð1 þ WACCÞ ð1 þ WACCÞ3 CFð1 þ gÞn - 1 ð1 þ WACCÞn

ð16:12Þ

Here WACC is the weighted average cost of capital, CF is an annual profit of company, (16.12) is geometric progression with denominator. g=

ð1 þ gÞ : ð1 þ WACCÞ

ð16:13Þ

Summing (16.12), we get the expression for the capitalization for a financially dependent company V of age n

16.2

The Brusov–Filatova–Orekhova (BFO) Theory Modification to the Case. . .

V=

1-



n

1þg 1þWACC 1þg 1 - 1þWACC

CF  1 þ WACC   1-

323

1þg 1 þ WACC

=

n 

CF  WACC - g ð16:14Þ

In perpetuity limit (n → 1) we get the following formula for a financially dependent company value, V, V=

CF WACC - g

ð16:15Þ

This formula shows, that discount rate is WACC–g, and not WACC.

16.2.2

The Value of a Financially Independent Company, V0

Let us now derive the capitalization formula for a financially independent company, assuming that income for the period grows with the growth rate g. 2

V0 =

n-1

CFð1 þ gÞ CFð1 þ gÞ CFð1 þ gÞ CF þ þ þ ... þ 3 1 þ k 0 ð1 þ k 0 Þ 2 ð1 þ k 0 Þn ð1 þ k 0 Þ

ð16:16Þ

(16.16) is geometric progression with denominator g=

ð 1 þ gÞ ð1 þ k 0 Þ

ð16:17Þ

Summing (16.16), we get the expression for the capitalization for a financially independent company V of age n

V0 =

CF  1 þ k0

1-



n

1þg 1þk0 1þg 1 - 1þk 0

=

  n  1þg CF :  11 þ k0 k0 - g

ð16:18Þ

In perpetuity limit (n → 1) we get the following formula for a financially independent company value, V0, V0 =

CF : k0 - g

This formula shows, that discount rate is k0–g, and not k0.

ð16:19Þ

16 BFO Theory with Variable Profit: Two Types of Payments of Tax on Profit:. . .

324

16.2.3

The Tax Shield Value, TS

Starting from this place formulas for two cases (1) and (2) become different (formulas for the payments of income tax at the end of periods are marked with ‘). The tax shield for n years in case of advance payments of tax on profit is equal ðTSÞn = tk d D þ

tk d D tk d D þ ... þ 1 þ kd ð1 þ k d Þn - 1

ð16:20Þ

The tax shield for n years in case of payments of tax on profit at the ends of periods is equal ðTSÞn =

tk d D tk d D tk d D þ þ ... þ 1 þ k d ð1 þ k d Þ2 ð1 þ kd Þn

ð16:20’Þ

(16.20) is geometric progression with denominator g=

1 ð1 þ k d Þ

ð16:21Þ

Summing (16.20), one gets for tax shield ðTSÞn = tk d D  ðTSÞn =

1 - ð1 þ k d Þ - n = Dt ð1- ð1 þ k d Þ - n Þ  ð1 þ k d Þ 1 1 - 1þk d

tk d D 1 - ð1 þ k d Þ  1 1 þ kd 1 - 1þk

-n

= Dt ð1- ð1 þ k d Þ - n Þ

ð16:22Þ ð16:22’Þ

d

ðTSÞn = Dt ð1- ð1 þ kd Þ - n Þ  ð1 þ kd Þ

ð16:23’Þ

Using an analog of the first theorem by Modigliani–Miller for finite time, one gets V = V 0 þ ðTSÞn

ð16:24Þ

D = wd V,

ð16:25Þ

Substituting

we arrive to the following expression V ð1- wd t ð1- ð1 þ kd Þ - n Þ  ð1 þ kd ÞÞ = V 0 V ð1- wd t ð1- ð1 þ kd Þ

-n

ÞÞ = V 0

ð16:26Þ ð16:26’Þ

16.2

The Brusov–Filatova–Orekhova (BFO) Theory Modification to the Case. . .

325

Substituting into this equation the values of a financially independent company, V0 (16.18) and of a financially dependent company, V, (16.14) one gets the following expression   n  1þg CF  1 - 1þWACC  ð1 - wd t ½1 - ð1 þ k d Þ - n   ð1 þ k d ÞÞ 

=

CF  1 -



1þg 1þk 0

n 

WACC - g

ðk 0 - gÞ   n  1þg CF  1 - 1þWACC  ð1 - wd t ½1 - ð1 þ kd Þ - n Þ

=

WACC - g   n  1þg CF  1 - 1þk0

ð16:27Þ

ð16:27’Þ

ð k 0 - gÞ

Dividing both parts by (1 - wdt(1 - (1 + kd)-n)  (1 + kd)), (1 - wdt(1 - (1 + kd)-n)), we get the BFO equation for the case of variable profit of the company 1-



1þg 1þWACC

n

1-



1þg 1þk0

n

: = WACC - g ðk0 - gÞ  ð1 - wd t ½1 - ð1 þ kd Þ - n   ð1 þ kd ÞÞ  n  n 1þg 1þg 1 - 1þWACC 1 - 1þk 0 : = WACC - g ðk 0 - gÞ  ð1 - wd t ½1 - ð1 þ kd Þ - n Þ

ð16:28Þ

ð16:28’Þ

These two formulas differ in the factor (1 + kd) in the denominator of the right side. This is the main theoretical result of the current Chapter. In perpetuity limit (n → 1) we get the following equation for WACC in the Modigliani–Miller theory in the case of variable profit (Brusov et al. 2021) WACC - g = ðk0- gÞ  ð1- wd t  ð1 þ kd ÞÞ

ð16:29Þ

WACC - g = ðk0- gÞ  ð1- wd t Þ

ð16:29’Þ

WACC = ðk0- gÞ  ð1- wd t  ð1 þ kd ÞÞ þ g

ð16:30Þ

WACC = ðk0- gÞ  ð1- wd t Þ þ g

ð16:30’Þ

k e = WACCð1 þ LÞ - Lk d ð1- t Þ

ð16:31Þ

16 BFO Theory with Variable Profit: Two Types of Payments of Tax on Profit:. . .

326

16.3

Results and Discussions

Below we describe the results of the study of the dependences of the following values: weighted average cost of capital, WACC, discount rate, WACC–g, company value, V, and the equity cost, ke, on the debt financing L at different values of the growth rate, g, at different values of the debt cost, kd and at different ages of the companies. A large database of results for different pairs (k0, kd) (k0 is the equity cost and kd is the debt cost) has been created and is available upon request. To illustrate the obtained results and the conclusions, the results for the following typical financial indicators of the 5- and 10-year companies are presented: k0 = 0.26; kd = 0.22; t = 0.2; g = 0.1; 0.05; 0.0; -0.05; CF = 100, where k0 stands for the equity cost at zero leverage level; kd stands for the debt cost; t stands for the tax on income; CF stands for income per period; n stands for the company age; L stands for the leverage level; g stands for the growth rate. Although the results for different values of the indicators may be numerically different, the detected qualitative effects are similar. For both types of payments of tax on profit (at the ends of periods (1) and advance payments (2)), as it could be seen from Fig. 16.1. for different values of g all curves WACC(L ) start from one point (L = 0; k0 = 0.26). These curves WACC(L ) demonstrate the decrease of WACC with leverage level L at all g values. The curves WACC(L ) increase with growth rate, g. This is the first manifestation of the fact that under variable income, the weighted average cost of capital, WACC, is no longer a discount rate. As we will see below, the role of the discount rate has been taken over by WACC–g (here g is the growth rate). The results for a 5-year company differ from the results for a perpetual limit—the theory of Modigliani and Miller with variable income (Brusov et al. 2021). In the

WACC(L), k0=0.26; Kd=0.22; n=5

0.255 0.245

g1=0 g1=0,05 g1=-0,05 g1=0,1 g2=0 g2=0,05 g2=-0,05 g2=0,1

0.235 0.225 0.215 0.205 0.195 0.185

0

1

2

3

4

5

6

7

8

9

10

Fig. 16.1 The dependence of WACC on leverage level L in Generalized Brusov–Filatova– Orekhova theory (GBFO theory) with payments of tax on profit at the ends of periods (1) and advance payments (2) at k0 = 0.26; kd = 0.22; t = 0.2; g = 0.1; 0.05; 0.0; -0.05 for 5-year company

16.3

Results and Discussions

327

WACC-g (L), k0 = 0.26; kd=0.22; n =5 0.29 g1=0 g1=0,05 g1=-0,05 g1=0,1 g2=0 g2=0,05 g2=-0,05 g2=0,1

0.24 0.19 0.14 0.09

0

1

2

3

4

5

6

7

8

9

10

Fig. 16.2 The dependence of discount rate, WACC–g, on leverage level L in Generalized Brusov– Filatova–Orekhova theory (GBFO theory) with payments of tax on profit at the ends of periods (1) and advance payments (2) at k0 = 0.26; kd = 0.22; t = 0.2; g = 0.1; 0.05; 0.0; -0.05 for 5-year company

latter case, the WACC(L) curves decrease with the level of leverage L at g < k0 and increase at g > k0. k0 is the threshold value g separating the increasing WACC(L ) curves from the decreasing ones, and for g = k0 WACC = const = k0. In the first case (BFO theory), the WACC(L) curves decrease with increasing leverage L for all values of the growth rate g. Note that the WACC(L ) curves increase with the rate g both in the Brusov–Filatova–Orekhova theory and in the Modigliani–Miller theory. As it could be seen from Fig. 16.2. the curves (WACC–g)(L ) demonstrate the decrease of the discount rate, WACC–g, with leverage level L at all g values. The curves (WACC–g)(L ) decrease with growth rate, g. Thus, as it will be seen below, the company value, V, will increase with g. This behavior of the (WACC–g)(L ) curves can be explained as follows: all WACC(L ) curves originate from the same point (L = 0; WACC = 0.26). The (WACC–g)(L ) curves will be ordered as follows for L = 0: the larger g, the lower the starting point and hence the entire graph lies, since the curves do not intersect. As we’ll see below the decrease of (WACC–g)(L) with growth rate, g, will lead to increase in the company value, V, with g. Now, for each value of g, the two curves (WACC–g)(L ) corresponding to two different types of income tax payments ((1) and (2)), start from the same point (k0– g), and they are then split into two curves, and the income tax advances correspond to the lower curve. This means that advance income tax payments result in lower WACC–g values for any growth rate g. It could be seen from Fig. 16.3, that the company value V at fixed growth rate g increases with leverage level L in Generalized Brusov–Filatova–Orekhova theory (GBFO theory) for both types of payments of tax on profit: at the ends of periods

16 BFO Theory with Variable Profit: Two Types of Payments of Tax on Profit:. . .

328

V(L), k0=0.26; Kd=0.22; n=5 370 350 330

g1=0 g1=0,05 g1=-0,05 g1=0,1 g2=0 g2=0,05 g2=-0,05 g2=0,1

310 290 270 250 230

0

1

2

3

4

5

6

7

8

9

10

Fig. 16.3 The dependence of discount rate, WACC–g, on leverage level L in Generalized Brusov– Filatova–Orekhova theory (GBFO theory) with payments of tax on profit at the ends of periods (1) and advance payments (2) at k0 = 0.26; kd = 0.22; t = 0.2; g = 0.1; 0.05; 0.0; -0.05 for 5-year company

(1) and advance payments (2). The company value V as well increases with growth rate g. This is a consequence of a decrease in the discount rate (WACC–g)(L ) with an increase in the growth rate g. Note that for each value of g, two V(L ) curves corresponding to two different types of income tax payments ((1) and (2)) start from the same point CF/(k0–g), they are then split into two curves, and the income tax advances correspond to the upper curve. This means that advance payments of income tax result in a higher value for company V at any growth rate g. Below we have studied the dependence of cost of equity, ke, on leverage level L and on growth rate, g, in Generalized Brusov–Filatova–Orekhova theory (GBFO theory) at k0 = 0.26; kd = 0.22 and g = 0.1; 0.05; 0.0; -0.05 for 5-year company for two types of payments of tax on profit: at the ends of periods (1) and advance payments (2).

16.3.1

Calculations of the Equity Cost, ke

As it is seen from Fig. 16.4 the equity cost, ke, practically linearly grows with leverage level L at all growth rate g values. All curves ke(L ) start from one point (L = 0; ke = k0 = 0.26). The tilt angle ke(L ) grows with g. The slope of all curves ke(L) corresponding to the payment of income tax at the end of periods (1) is greater than that of the curves with advance payments of income tax.

16.3

Results and Discussions

329

ke(L), k0=0.26; Kd=0.22; n=5 0.5 0.45 g1=0 g1=0,05 g1=-0,05 g1=0,1 g2=0 g2=0,05 g2=-0,05 g2=0,1

0.4 0.35 0.3 0.25

0

1

2

3

4

5

6

7

8

9

10

Fig. 16.4 The dependence of equity cost, ke, on leverage level L in Generalized Brusov–Filatova– Orekhova theory (GBFO theory) with payments of tax on profit at the ends of periods (1) and advance payments (2) at k0 = 0.26; kd = 0.22; t = 0.2; g = 0.1; 0.05; 0.0; -0.05 for 5-year company

Given that the cost of equity capital determines the economically justified amount of dividends, we can draw the following conclusions regarding the dividend policy of the company: 1. Higher growth rate g justifies higher dividends. 2. If a company pays income tax at the end of periods, it must pay large dividends. 3. If the company pays income tax in advance, dividends should be less. One important remark can be made: when income tax is paid in advance, the dividends paid by the company should be less. In addition, as we saw above, the value of the company in this case is higher. So, advance payments on income tax are beneficial to the enterprise.

16.3.2

Study the Dependence of Financial Indicators on kd

16.3.2.1

The Weighted Average Cost of Capital, WACC

It is seen from Fig. 16.5 that all curves WACC(L) at all values of kd start from one point (0; 0.26). WACC(L) decreases with leverage level L at all values of kd. WACC (L ) decreases with the increase of debt cost kd. This means that tax shield advantages the decrease in the cost of raising capital. All curves WACC(L) in the case of advance income tax payments lie below the curves in the case of income tax payments at the end of periods.

16 BFO Theory with Variable Profit: Two Types of Payments of Tax on Profit:. . .

330

WACC(L), k0=0.26; g=0.05; n=5 0.22 0.21 0.2 0.19

kd1=0,22 kd1=0,2 kd1=0,18 kd2=0,22 kd2=0,2 kd2=0,18

0.18 0.17 0.16 0.15 0.14 0.13

0

1

2

3

4

5

6

7

8

9

10

Fig. 16.5 The dependence of WACC on leverage level L in Generalized Brusov–Filatova– Orekhova theory (GBFO theory) with payments of tax on profit at the ends of periods (1) and advance payments (2) at k0 = 0.26; kd = 0.22; 0.2; 0.18 t = 0.2; g = 0.05 for 5-year company

WACC-g (L), k0=0.26; g=0.05; n=5 0.22 0.21 0.2 0.19

kd1=0,22 kd1=0,2 kd1=0,18 kd2=0,22 kd2=0,2 kd2=0,18

0.18 0.17 0.16 0.15 0.14

0

1

2

3

4

5

6

7

8

9

10

Fig. 16.6 The dependence of discount rate, WACC–g, on leverage level L in Generalized Brusov– Filatova–Orekhova theory (GBFO theory) with payments of tax on profit at the ends of periods (1) and advance payments (2) at k0 = 0.26; kd = 0.22; 0.2; 0.18; t = 0.2; g = 0.05 for 5-year company

16.3.2.2

The Discount Rate, WACC–g

It is seen from Fig. 16.6 that all curves of discount rate (WACC–g) (L ) at all values of kd start from one point (L = 0; ke = 0.21). (WACC–g) (L ) decrease with leverage

16.3

Results and Discussions

331

level L at all values of kd. (WACC–g)(L ) decrease with the increase of debt cost kd. This means that the tax shield tends to lower the value of the discount rate (WACC– g) and hence (as we will see below in 16.3.2.3) increase the value of the company, V. All curves (WACC–g) (L ) in the case of advance income tax payments lie below the curves in the case of income tax payments at the end of periods.

16.3.2.3

The Company Value, V

From Fig. 16.7 it follows that all curves of company value V (L) at all values of kd for 5-year company start from one point (0; 285). V (L ) increases with leverage level L at all values of kd. V(L ) increases with the increase of debt cost kd. This means that tax shield advantages the increase of the company value, V. All curves V(L) in the case of advance payments of income tax lie above the curves in the case of payment of income tax at the end of periods. This means that advance income tax payments are beneficial for the company, increasing its capitalization. It follows from Fig. 16.8 that all curves of equity cost, ke(L), at all values of kd start from one point (L = 0; ke = k0 = 0.26) and ke increases with leverage level L at all values of kd. The slope of the straight line ke(L) decreases with the cost of debt kd. This means that debt cost kd impacts the dividend policy of the company, because the equity cost ke determines the economically justified amount of dividends. At a fixed cost of debt kd, the slope of the straight line ke(L ) in the case of paying income tax at the end of the periods is higher than in the case of advance payments.

V(L), k0 = 0.26; g=0.05; n =5 335 330 325 320 kd1=0,22 kd1=0,2 kd1=0,18 kd2=0,22 kd2=0,2 kd2=0,18

315 310 305 300 295 290 285

0

1

2

3

4

5

6

7

8

9

10

Fig. 16.7 The dependence of company value, V, on leverage level L in Generalized Brusov– Filatova–Orekhova theory (GBFO theory) with payments of tax on profit at the ends of periods (1) and advance payments (2) at k0 = 0.26; kd = 0.22; 0.2; 0.18; t = 0.2; g = 0.05 for 5-year company

16 BFO Theory with Variable Profit: Two Types of Payments of Tax on Profit:. . .

332

ke (L), k0 = 0.26; g=0.05; n=5 1 0.9 0.8 0.7

kd1=0,22 kd1=0,2 kd1=0,18 kd2=0,22 kd2=0,2 kd2=0,18

0.6 0.5 0.4 0.3 0.2

0

1

2

3

4

5

6

7

8

9

10

Fig. 16.8 The dependence of equity cost, ke, on leverage level L in Generalized Brusov–Filatova– Orekhova theory (GBFO theory) with payments of tax on profit at the ends of periods (1) and advance payments (2) at k0 = 0.26; kd = 0.22; 0.2; 0.18 t = 0.2; g = 0.05 for 5-year company

16.3.3

Impact of Company Age, n, on Main Financial Indicators of the Company

Below we study the impact of company age, n, on main financial indicators of the company. We investigate the dependence of WACC; WACC–g; company value, V, and equity cost, ke on leverage level L in Generalized Brusov–Filatova–Orekhova theory (GBFO theory) with advance payments of tax on profit at k0 = 0.26; kd = 0.22; t = 0.2; g = 0.2 and g = -0.2 for 5-year and 10-year companies. We found a huge difference between the behavior of the main financial indicators of the company with a positive and negative growth rate g. This allows you to explore companies with growing profits and companies with decreasing profits. And also it allows to study the companies whose profits rise and fall in different periods.

16.3.3.1

WACC(L)

We investigate the dependence of WACC on L for companies of two ages: 5- and 10-year old at two values of growth rates (g = 0.2 and g = -0.2) (see Figs. 16.9 and 16.10). In both cases, the two WACC(L ) curves start from the point (0; 0.26) and decrease with L. For positive growth rate (g = 0.2) WACC is lower for 5-year company, while for negative growth rate (g = -0.2) WACC is lower for 10-year company. We are seeing this effect for the first time.

16.3

Results and Discussions

333

WACC(L), k0=0.26; kd=0.22; g=0.2 0.26 0.25 0.24 0.23 n1=5 n1=10 n2=5 n2=10

0.22 0.21 0.2 0.19

0

1

2

3

4

5

6

7

8

9

10

Fig. 16.9 The dependence of WACC on leverage level L in Generalized Brusov–Filatova– Orekhova theory (GBFO theory) with payments of tax on profit at the ends of periods (1) and advance payments (2) at k0 = 0.26; kd = 0.22; t = 0.2; g = 0.2 for 5-year and 10-year companies

WACC(L), k0=0.26; kd=0.22; g=-0,2 0.26 0.25 0.24 0.23 0.22 0.21

n1=5 n1=10 n2=5 n2=10

0.2 0.19 0.18 0.17 0.16

0

1

2

3

4

5

6

7

8

9

10

Fig. 16.10 The dependence of WACC on leverage level L in Generalized Brusov–Filatova– Orekhova theory (GBFO theory) with payments of tax on profit at the ends of periods (1) and advance payments (2) at k0 = 0.26; kd = 0.22; t = 0.2; g = -0.2 for 5-year and 10-year companies

16 BFO Theory with Variable Profit: Two Types of Payments of Tax on Profit:. . .

334

Discount Rate WACC–g

16.3.3.2

We investigate the dependence of discount rate WACC–g on L for companies of two ages: 5- and 10-year old at two values of growth rates (g = 0.2 and g = -0.2) (see Figs. 16.11 and 16.12). In both cases, the two WACC(L ) curves start from one

WACC-g(L), k0=0.26; kd=0.22; g=-0,2 0.46 0.45 0.44 0.43 0.42 0.41

n1=5 n1=10 n2=5 n2=10

0.4 0.39 0.38 0.37 0.36

0

1

2

3

4

5

6

7

8

9

10

Fig. 16.11 The dependence of discount rate, WACC–g, on leverage level L in Generalized Brusov–Filatova–Orekhova theory (GBFO theory) with payments of tax on profit at the ends of periods (1) and advance payments (2) at k0 = 0.26; kd = 0.22; t = 0.2; g = -0.2 for 5-year and 10-year companies

WACC-g(L), k0=0.26; kd=0.22; g=0,2 0.06 0.05 0.04 0.03 n1=5 n1=10 n2=5 n2=10

0.02 0.01 0

0

1

2

3

4

5

6

7

8

9

10

-0.01

Fig. 16.12 The dependence of discount rate, WACC–g, on leverage level L in Generalized Brusov–Filatova–Orekhova theory (GBFO theory) with payments of tax on profit at the ends of periods (1) and advance payments (2) at k0 = 0.26; kd = 0.22; t = 0.2; g = 0.2 for 5-year and 10-year companies

16.3

Results and Discussions

335

point: (0; 0.06) for g = 0.2 and (0; 0.46) for g = -0.2 and decrease with L. For positive growth rate (g = 0.2) discount rate WACC–g is lower for 5-year company, while for negative growth rate (g = -0.2) discount rate WACC–g is lower for 10-year company. This effect has been observed here for the first time.

16.3.3.3

Company Value, V

Let us study the dependence of the value of a company V on L for companies of two ages: 5- and 10-year old at two values of growth rates (g = 0.2 and g = -0.2). In both cases, the value of company V increases with the growth of L, and the greater the age of the company corresponds to the greater value of company V. But if, with a positive growth rate (g = 0.2), the difference in the value of V for a 5-year company and a 10-year company is about 400, with negative growth rate (g = -0.2), this difference is 45 (ten times less) (see Figs. 16.13 and 16.14). So, in the competition between the age of the company and the size of the growth rate, the growth rate wins.

16.3.3.4

Equity Cost, ke

Let us study the dependence of the equity cost, ke, on L for companies of two ages: 5and 10-year old at two values of growth rates (g = 0.2 and g = -0.2) (see Figs. 16.15 and 16.16). In the case of a positive growth rate (g = 0.2), the cost of equity ke increases linearly with L, and the slope ke(L ) for a 10-year company is

V(L), k0=0.26; kd=0.22; g=-0,2 270 260 250 240 230

n1=5 n1=10 n2=5 n2=10

220 210 200 190

0

1

2

3

4

5

6

7

8

9

10

Fig. 16.13 The dependence of company value, V, on leverage level L in Generalized Brusov– Filatova–Orekhova theory (GBFO theory) with payments of tax on profit at the ends of periods (1) and advance payments (2) at k0 = 0.26; kd = 0.22; t = 0.2; g = -0.2 for 5-year and 10-year companies

16 BFO Theory with Variable Profit: Two Types of Payments of Tax on Profit:. . .

336

V(L), k0=0.26; kd=0.22; g=0,2 800 750 700 650 600 n1=5 n1=10 n2=5 n2=10

550 500 450 400 350

0

1

2

3

4

5

6

7

8

9

10

Fig. 16.14 The dependence of company value, V, on leverage level L in Generalized Brusov– Filatova–Orekhova theory (GBFO theory) with payments of tax on profit at the ends of periods (1) and advance payments (2) at k0 = 0.26; kd = 0.22; t = 0.2; g = 0.2 for 5-year and 10-year companies

ke, k0=0.26; kd=0.22; g=-0,2 0.4 0.35 0.3 0.25 n1=5

0.2

n1=10

0.15

n2=5 n2=10

0.1 0.05

0

1

2

3

4

5

6

7

8

9

10

Fig. 16.15 The dependence of equity cost, ke, on leverage level L in Generalized Brusov–Filatova– Orekhova theory (GBFO theory) with payments of tax on profit at the ends of periods (1) and advance payments (2) at k0 = 0.26; kd = 0.22; t = 0.2; g = -0.2 for 5-year and 10-year companies

greater than for a 5-year one. With a negative growth rate (g = -0.2), the cost of equity ke decreases linearly with increasing L, and the negative slope for a 10-year company is greater than for a 5-year one.

16.3

Results and Discussions

337

ke, k0=0.26; kd=0.22; g=0,2 0.65 0.6 0.55 0.5 0.45

n1=5

0.4

n1=10 n2=5

0.35

n2=10

0.3 0.25

0

1

2

3

4

5

6

7

8

9

10

Fig. 16.16 The dependence of equity cost, ke, on leverage level L in Generalized Brusov–Filatova– Orekhova theory (GBFO theory) with payments of tax on profit at the ends of periods (1) and advance payments (2) at k0 = 0.26; kd = 0.22; t = 0.2; g = 0.2 for 5-year and 10-year companies

Since the cost of equity determines the economically justified amount of dividends, this means that the dividend policy of the company when increasing profits and when decreasing profits should be completely different. This is a qualitatively new effect, discovered by us for the first time.

16.3.3.5

Results Summary

The curves (WACC–g)(L ) demonstrate the decrease of WACC–g with leverage level L at all g values. The curves (WACC–g)(L ) decrease with growth rate, g. The company value V at fixed growth rate g increases with leverage level L in Generalized Brusov–Filatova–Orekhova theory (GBFO theory). The company value V as well increases with growth rate g. This is a consequence of a decrease in the discount rate (WACC–g)(L ) with an increase in the growth rate g. The equity cost, ke, practically linearly grows with leverage level L at all growth rate g values. The tilt angle ke(L ) grows with g. Studying the impact of the debt cost kd on the main financial indicators, we found the following: • All curves WACC(L ) at all values of kd start from one point (0; 0.26). WACC(L ) decreases with leverage level L at all values of kd. WACC(L ) decreases with the increase of debt cost kd. This means that tax shield advantages the decrease in the cost of raising capital. • All curves of discount rate (WACC–g) (L) at all values of kd start from one point (0; 0.21). (WACC–g) (L ) decrease with leverage level L at all values of kd.

338

16 BFO Theory with Variable Profit: Two Types of Payments of Tax on Profit:. . .

(WACC–g)(L ) decrease with the increase of debt cost kd. This means that the tax shield tends to lower the value of the discount rate (WACC–g) and hence increase the value of the company, V. • All curves of company value V (L ) at all values of kd start from one point (0; 285). V (L ) increases with leverage level L at all values of kd. V(L ) increases with the increase of debt cost kd. This means that tax shield advantages the increase of the company value, V. • All curves of equity cost, ke(L ), at all values of kd start from one point (0; 0.26) and ke increases with leverage level L at all values of kd. The slope of the straight line ke(L ) decreases with the cost of debt kd. This means that debt cost kd impacts the dividend policy of the company, because the equity cost ke determines the economically justified amount of dividends. Studying the impact of company age, n, on main financial indicators of the company: WACC; WACC–g; V; ke, we found a huge difference between the behavior of the main financial indicators of the company with a positive and negative growth rate g. This allows you to explore companies with growing profits and companies with decreasing profits. And also it allows to study the companies whose profits rise and fall in different periods. Particular Results Here Are as Following We investigate the dependence of WACC on L for companies of two ages: 5- and 10-year old at two values of growth rates (g = 0.2 and g = -0.2). In both cases, the two WACC(L ) curves start from the point (0; 0.26) and decrease with L. For positive growth rate (g = 0.2) WACC is lower for 5-year company, while for negative growth rate (g = -0.2) WACC is lower for 10-year company. We are seeing this effect for the first time. We investigate the dependence of discount rate WACC–g on L for companies of two ages: 5- and 10-year old at two values of growth rates (g = 0.2 and g = -0.2). In both cases, the two WACC(L ) curves start from one point: (0; 0.06) for g = 0.2 and (0; 0.46) for g = -0.2 and decrease with L. For positive growth rate (g = 0.2) discount rate WACC–g is lower for 5-year company, while for negative growth rate (g = -0.2) discount rate WACC–g is lower for 10-year company. We are seeing this effect for the first time. We study the dependence of the value of a company V on L for companies of two ages: 5- and 10-year old at two values of growth rates (g = 0.2 and g = -0.2). In both cases, the value of the company V increases with the growth of L, and the greater the age of the company corresponds to the greater value of the company V. But if, with a positive growth rate (g = 0.2), the difference in the value of V for a 5-year company and a 10-year company is about 400, with negative growth rate (g = -0.2), this difference is 45 (ten times less). So, in the competition between the age of the company and the size of the growth rate, the growth rate wins. The dependence of the equity cost, ke, on L is studied for companies of two ages: 5- and 10-year old at two values of growth rates (g = 0.2 and g = -0.2). In the case of a positive growth rate (g = 0.2), the cost of equity ke increases linearly with L, and the slope ke(L ) for a 10-year company is greater than for a 5-year one. With a

16.4

Conclusions

339

negative growth rate (g = -0.2), the cost of equity ke decreases linearly with increasing L, and the negative slope for a 10-year company is greater than for a 5-year one. Since the cost of equity determines the economically justified amount of dividends, this means that the dividend policy of the company when increasing profits and when decreasing profits should be completely different. This is a qualitatively new effect, discovered by us for the first time. As it is seen from Table 16.1 the most significant qualitative differences between cases (1) and (2) occur for the dependence of financial indicators on the age of the company. For the cases of influence g and kd, despite the fact that the financial parameters for cases (1) and (2) move in the same direction, there are significant differences between cases (1) and (2) from the quantitative point of view as well as with respect to interposition of the financial parameters.

16.4

Conclusions

Two modifications of the Brusov–Filatova–Orekhova (BFO) theory with variable income have been considered: (1) with the payment of income tax at the end of periods and (2) with advance payments of income tax (for the first time). BFO formulas for the weighted average cost of capital, WACC, for company value, V, were derived for these two cases and within these formulas a comprehensive analysis of the dependence of WACC, of discount rate, WACC–g, company value, V, the equity cost, ke, on the debt financing at different values of the growth rate, g, at different values of the cost of debt capital, kd, and at different values of company age, n was carried out. The results for cases (1) and (2) are compared, which allows us to conclude that case (2) is always preferable for both the company and the regulator. This allows developing recommendations for both parties to expand the practice of advance payments of income tax. Chapter novelties are as follows: 1. Generalization of the Brusov–Filatova–Orekhova theory to the case of variable income with advance payments of income tax. 2. Derivation of generalized BFO formulas for weighted average cost of capital, WACC, cost of equity, ke, company value, V. 3. Using the obtained formulas, investigate the influence of the growth rate g, the cost of debt, kd, the company’s age, n, on the dependence of the company’s financial performance on debt financing. 4. Comparison of the obtained results with those for the case of paying income tax at the end of the periods. 5. Developing the recommendations for both companies and regulators on how to pay income tax.

#

"

"

#

"

"

WACC– g

V

ke

WACC

Advance payments (2) "

g Growth rate Payments at the ends of periods (1) "

#

"

#

kd Debt cost Payments at the ends of periods (1) #

#

"

#

Advance payments (2) #

n Company age Payments at the ends of periods (1) g≥0 " g≤0 # g≥0 " g≤0 # g≥0 " g≤0 " g≥0 " g≤0 #

Advance payments (2) " # " # " " " #

1≤2

1≤2

1≥2

1≥2

Comparison of (1) and (2)

Table 16.1 Comparison of the results in Generalized Brusov–Filatova–Orekhova theory (GBFO theory) with payments of tax on profit at the ends of periods (1) and advance payments (2) for parameters g (growth rate), kd (debt cost) and n (company age (for 5-year and 10-year companies)) (" means an increase in the indicator with the current parameter; # means a decrease in the indicator with the current parameter)

340 16 BFO Theory with Variable Profit: Two Types of Payments of Tax on Profit:. . .

References

341

6. The developed methodology makes it possible to study companies with growing profits and companies with decreasing profits, which is quite important for practice. And also it allows to study the companies whose profits rise and fall in different periods. Regarding the direction of future research: The proposed theory will be used in the future for a more detailed study of companies with both rising and falling profits.

References Angotti M, de Lacerda Moreira R, Hipólito Bernardes do Nascimento J, Neto de Almeida Bispo O (2018) Analysis of an equity investment strategy based on accounting and financial reports in Latin American markets. Reficont 5:22–40 Barbi M (2011) On the risk–neutral value of debt tax shields. Appl Financ Econ 22:251–258 Batrancea L (2021a) An econometric approach regarding the impact of fiscal pressure on equilibrium: evidence from electricity, gas and oil companies listed on the New York Stock Exchange. Mathematics 9:630 Batrancea L (2021b) The influence of liquidity and solvency on performance within the healthcare industry: evidence from publicly listed companies. Mathematics 9:2231 Becker DM (2022) Getting the valuation formulas right when it comes to annuities. Manag Financ 48:470 Berk J, De Marzo P (2007) Corporate finance. Pearson–Addison Wesley, Boston, MA Brusov P, Filatova T (2022) Generalization of the Brusov–Filatova–Orekhova theory for the case of variable income. Mathematics 10(19):3661. https://doi.org/10.3390/math10193661 Brusov P, Filatova T, Orehova N, Eskindarov M (2018) Modern corporate finance, investments, taxation and ratings, 2nd edn. Springer Nature, Cham, pp 1–571 Brusov P, Filatova T, Orekhova N, Kulik V, Chang S-I, Lin G (2021) Generalization of the Modigliani–Miller theory for the case of variable profit. Mathematics 9:1286. https://doi.org/ 10.3390/math9111286 Dimitropoulos P (2014) Capital structure and corporate governance of soccer clubs: European evidence. Manag Res Rev 37:658–678 El-Chaarani H, Abraham R, Skaf Y (2022) The impact of corporate governance on the financial performance of the banking sector in the MENA (middle eastern and north African) region: an immunity test of banks for COVID–19. J Risk Financ Manag 15:82 Farber A, Gillet R, Szafarz AA (2006) General formula for the WACC. Int J Bus 11:211–218 Fernandez PA (2006) General formula for the WACC: a comment. Int J Bus 11:219 Franc-Dąbrowska J, Mądra-Sawicka M, Milewska A (2021) Energy sector risk and cost of capital assessment—companies and investors perspective. Energies 14:1613 Hamada R (1969) Portfolio analysis, market equilibrium, and corporate finance. J Financ 24:13–31 Harris R, Pringle J (1985) Risk-adjusted discount rates-extension from the average–risk case. J Financ Res 8:237–244 Huang S, Sun H, Zhao H, Zhang Y (2020) Influence of leverage on the return on equity. Syst Eng Theory Pract 40:355 Islam SZ, Khandaker S (2015) Firm leverage decisions: does industry matter? N Am J Econ Financ 31:94 Luiz K, Cruz M (2015) The relevance of capital structure on firm performance: a multivariate analysis of publicly traded Brazilian companies. REPeC Brasília 9:384–401 Miller M (1977) Debt and taxes. J Financ 32:261–275 Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297

342

16 BFO Theory with Variable Profit: Two Types of Payments of Tax on Profit:. . .

Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Modigliani F, Miller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391 Mundi HS, Kaur P, Murty RLN (2022) A qualitative inquiry into the capital structure decisions of overconfident finance managers of family–owned businesses in India. Qual Res Financ Mark 14:357–379 Myers S (2001) Capital structure. J Econ Perspect 15:81–102 Sadiq M, Alajlani S, Hussain MS, Bashir F, Chupradit S (2022) Impact of credit, liquidity, and systematic risk on financial structure: comparative investigation from sustainable production. Environ Sci Pollut Res Int 29:20963–20975 Singhal N, Goyal S, Sharma D, Kumari S, Nagar S (2022) Capitalization and profitability: applicability of capital theories in BRICS banking sector. Future Bus J 8:1. https://doi.org/10. 1186/s43093-022-00140-w Vergara-Novoa C, Sepúlveda-Rojas JP, Miguel DA, Nicolás R (2018) Cost of capital estimation for highway concessionaires in Chile. J Adv Transp 2018:2153536 Zhukov P (2018) The impact of cash flows and weighted average cost of capital to Enterprise value in the oil and gas sector. J Rev Glob Econ 7:138–145

Part II

Investments

Chapter 17

Investment Models with Debt Repayment at the End of the Project and their Application

Keywords Investment models · Debt repayment at the end of the project · Efficiency of investments · Brusov–Filatova–Orekhova (BFO) theory · Modigliani · Miller theory · Debt financing In this chapter, the modern investment models, which will be used in following chapters for investigation of different problems of investments, such as the influence of debt financing, leverage level, taxing, project duration, method of financing, and some other parameters on the efficiency of investments and other problems, are built.

17.1

Investment Models

The effectiveness of the investment project is considered from two perspectives: the owners of equity and debt as well as the equity holders only. For each of these cases, NPV is calculated in two ways: with the division of credit and investment flows (and thus discounting the payments at two different rates) and without such a division (in this case, both flows are discounted at the same rate as which, obviously, can be chosen WACC). For each of the four situations, two cases are considered: 1) a constant value of equity S; 2) a constant value of the total invested capital I = S + D (D is value of debt funds). As it was stated above, the effectiveness of the investment project is considered from two perspectives: the owners of equity and debt as well as equity holders only. In the first case, the interest and duty paid by owners of equity (negative flows), returned to the project because they are exactly equal to the flow (positive), obtained by owners of debt capital. The only effect of leverage in this case—the effect of the tax shield generated from the tax relief: interest on the loan is entirely included in the cost and, thus, reduce the tax base. After tax flow of capital for each period in this case is

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_17

345

346

17 Investment Models with Debt Repayment at the End of the Project and. . .

NOIð1- t Þ þ kd Dt,

ð17:1Þ

and value of investments at the initial time moment T = 0 are equal to –I = –S–D. Here NOI–Net Operating Income (before taxes). In the second case, investments at the initial time moment T = 0, are equal to –S, and the flow of capital for the period (in addition to the tax shields kdDt it includes a payment of interest on a loan -kdD) ðNOI- k d DÞð1- t Þ:

ð17:2Þ

Here, for simplicity, we suppose that interest on the loan will be paid in equal shares kdD during all periods. Note, that principal repayment is made at the end of last period. Some variety of repayment of long-term loans will be considered below. We will consider two different ways of discounting: 1. Operating and financial flows are not separated and both are discounted at the general rate (as which, obviously, can be selected the weighted average cost of capital, WACC). The Modigliani–Miller formula (Мodigliani and Мiller 1958, 1963, 1966) for WACC for perpetuity projects will be used and for projects of finite (arbitrary) duration Brusov–Filatova–Orekhova formula will be used (Brusov and Filatova 2011; Brusov et al. 2011a, b, c; 2012a, b; 2013a, b; 2014a, b; Filatova et al. 2008). 2. Operating and financial flows are separated and are discounted at different rates: the operating flow at the rate equal to the equity cost ke, depending on leverage, and credit flow –at the rate equal to the debt cost kd, which until fairly large values of leverage remains constant and starts to grow only at high values of leverage L, when there is a danger of bankruptcy. Note that, loan capital is the least risky, because interest on credit is paid after tax in the first place. Therefore, the cost of credit will always be less than the equity cost, whether of ordinary or of preference shares ke > kd; kp > kd. Here ke; kp—equity cost of ordinary or of preference shares consequently.

17.2 17.2.1

The Effectiveness of the Investment Project from the Perspective of the Equity Holders Only With the Division of Credit and Investment Flows

Projects of finite (arbitrary) duration In this case, the expression for NPV has a view

17.2

The Effectiveness of the Investment Project from the Perspective of. . .

347

n n X NOIð1 - t Þ X - kd Dð1 - t Þ D þ = -S i i 1 þ k d Þn ð ð1 þ k d Þ i = 1 ð1 þ k e Þ i=1     NOIð1 - t Þ 1 D 1 - Dð1- t Þ 1þ 1ð17:3Þ ke ð1 þ k e Þn ð1 þ k d Þ n ð1 þ k d Þn

NPV = - S þ

The last term in the first line—discounted (present) value of credit, extinguished a one-off payment at the end of the last period n. Below we will look at two cases: 1. A constant value of invested capital I = S + D (D—debt value) 2. A constant value of equity capital S We will start with the first case. At a constant value of invested capital (I = const) In case of a constant value of invested capital (I = const), taking into account D = IL/(1 + L ), S = I/(1 + L), one gets      1 I 1 1 þ L ð1 - t Þ 1 þ þ 1þL ð1 þ k d Þn ð1 þ k d Þn   NOIð1 - t Þ 1 : 1þ ke ð1 þ k e Þn NPV = -

ð17:4Þ

For one-year project Putting at the equation (Eq. 17.4) n = 1, one gets for NPV NPV = -

   1 þ k d ð1 - t Þ NOIð1 - t Þ I þ : 1þL 1 þ ke 1þL ð1 þ k d Þ

ð17:5Þ

At a constant value of equity capital (S = const) Accounting, that in case S = const NOI is proportional to invested capital, NOI = βI = βS(1 + L ), we get      1 1 þ þ NPV = - S 1 þ L ð1 - t Þ 1 ð1 þ kd Þn ð1 þ k d Þn   βSð1 þ LÞð1 - t Þ 1 þ : 1ke ð1 þ k e Þ n For one-year project Putting at the equation (Eq. 17.6) n = 1, one gets for NPV

ð17:6Þ

348

17 Investment Models with Debt Repayment at the End of the Project and. . .

   βSð1 þ LÞð1 - t Þ 1 þ k d ð1 - t Þ þ NPV = - S 1 þ L : 1 þ kd 1 þ ke

17.3

ð17:7Þ

Without Flows Separation

In this case, operating and financial flows are not separated and are discounted at the general rate (as which, obviously, can be selected the weighted average cost of capital, WACC). The credit reimbursable at the end of the project (at the end of the period (n)) can be discounted either at the same rate WACC, or that is more logical,—at the debt cost rate kd. Now we choose a uniform rate and the first option. n X NOIð1 - t Þ - kd Dð1 - t Þ D = -S i ð 1 þ WACC Þn ð 1 þ WACC Þ i=1   NOIð1 - t Þ - kd Dð1 - t Þ 1 D 1: þ WACC ð1 þ WACCÞn ð1 þ WACCÞn

NPV = - S þ

ð17:8Þ

At a constant value of invested capital (I = const) In case of a constant value of invested capital (I = const), taking into account D = IL/(1 + L ), S = I/(1 + L), one gets     k d ð1 - t Þ 1 L I þ þ 11þL NPV = WACC 1þL ð1 þ WACCÞn ð1 þ WACCÞn   NOIð1 - t Þ 1 : þ 1WACC ð1 þ WACCÞn ð17:9Þ For one-year project Putting into the equation (Eq. 17.9) n = 1, one gets for NPV   NOIð1 - t Þ 1 þ k d ð1 - t Þ I þ : 1þL NPV = 1 þ WACC 1 þ WACC 1þL

ð17:10Þ

At a constant value of equity capital (S = const) Accounting, that in case S = const NOI is proportional to invested capital, I, NOI = βI = βS(1 + L ), and substitute D = LS, we get

17.4

Modigliani–Miller Limit (Perpetuity Projects)

349

  NOIð1 - t Þ - kd Dð1 - t Þ 1 1NPV = - S þ WACC ð1 þ WACCÞn D ð17:11Þ ð1 þ WACCÞn     Lk d ð1 - t Þ 1 L 1þ þ NPV = - S 1 þ WACC ð1 þ WACCÞn ð1 þ WACCÞn   ð17:12Þ βSð1 þ LÞð1 - t Þ 1 þ 1: WACC ð1 þ WACCÞn -

For one-year project Putting into the equation (Eq. 17.12) n = 1, one gets for NPV     Lk d ð1 - t Þ 1 L 1þ þ NPV = - S 1 þ WACC ð1 þ WACCÞn ð1 þ WACCÞn   βSð1 þ LÞð1 - t Þ 1 ð17:13Þ þ : 1WACC ð1 þ WACCÞn NOIð1 - t Þ - kd Dð1 - t Þ - D : NPV = - S þ 1 þ WACC Substituting D = LS, NOI = βI = βS(1 + L), we get   Lðk d ð1 - t Þ - 1Þ βSð1 þ LÞð1 - t Þ þ NPV = - S 1 þ : 1 þ WACC 1 þ WACC

17.4 17.4.1

ð17:14Þ

Modigliani–Miller Limit (Perpetuity Projects) With Flows Separation

In perpetuity limit (Modigliani–Miller limit) (turning to the limit n → 1 in the relevant equations) we have NPV = - S þ

NOIð1 - t Þ - Dð1- t Þ: ke

ð17:15Þ

At a constant value of invested capital (I = const) At a constant value of invested capital (I = const), accounting D = IL/(1 + L ), S = I/(1 + L ), we get

17 Investment Models with Debt Repayment at the End of the Project and. . .

350

NPV = NPV = -

NOIð1 - t Þ I : ð1 þ Lð1- t ÞÞ þ ke 1þL

NOIð1 - t Þ I ð1 þ Lð1- t ÞÞ þ : 1þL k0 þ ðk 0 - k d ÞLð1 - t Þ

ð17:16Þ ð17:17Þ

In order to obtain equation (Eq. 17.17) from (Eq. 17.16) we used the Modigliani– Miller formula (Мodigliani and Мiller (1963)) for equity cost ke for perpetuity projects: k e = k0 þ ðk0- k d ÞLð1- t Þ:

ð17:18Þ

At a constant value of equity capital (S = const) Accounting D = LS, we get in perpetuity limit (n → 1) (Modigliani–Miller limit) NPV = - Sð1 þ Lð1- t ÞÞ þ

17.4.2

βSð1 þ LÞð1 - t Þ : k 0 þ ðk 0 - k d ÞLt

ð17:19Þ

Without Flows Separation

In perpetuity limit (n → 1) (Modigliani–Miller limit) (turning to the limit n → 1 in the relevant equations) we have NPV = - S þ

NOIð1 - t Þ - k d Dð1 - t Þ : WACC

ð17:20Þ

At a constant value of invested capital (I = const) At a constant value of invested capital (I = const), accounting D = IL/(1 + L ), S = I/(1 + L ), we get L NOIð1 - t Þ - I 1þL k d ð1 - t Þ 1 1 þ = -I  NPV = - I  1þL WACC 1þL   Lkd ð1 - t Þ NOIð1 - t Þ þ  1þ : k0 ð1 - Lt=ð1 þ LÞÞ k0 ð1 - Lt=ð1 þ LÞÞ

ð17:21Þ

At a constant value of equity capital (S = const) NPV = - S þ Substituting D = LS, we get

NOIð1 - t Þ - kd Dð1 - t Þ : WACC

ð17:22Þ

The Effectiveness of the Investment Project from the perspective of. . .

17.5

 NOIð1 - t Þ Lk d ð1 - t Þ þ = NPV = - S 1 þ WACC WACC   βSð1 þ LÞð1 - t Þ Lkd ð1 - t Þ -S 1 þ þ : k 0 ð1 - Lt=ð1 þ LÞÞ k 0 ð1 - Lt=ð1 þ LÞÞ

351



17.5

ð17:23Þ

The Effectiveness of the Investment Project from the perspective of the Owners of Equity and Debt

17.5.1

With Flows Separation

Projects of arbitrary (finite) duration In this case, operating and financial flows are separated and are discounted at different rates: the operating flow at the rate equal to the equity cost ke, depending on leverage, and credit flow –at the rate equal to the debt cost kd, which until fairly large values of leverage remains constant and starts to grow only at high values of leverage L, when there is a danger of bankruptcy. n n X NOIð1 - t Þ X kd Dt NOIð1 - t Þ þ i i = -I þ ke 1 þ k ð Þ ð Þ 1 þ k e d i=1 i=1     1 1 þ Dt 1:  1ð1 þ k e Þn ð1 þ k d Þn

NPV = - I þ

ð17:24Þ

Below we will consider two cases: 1. At a constant value of invested capital (I = S + D (D is the debt value) 2. At a constant value of equity capital S We will start with the first case. At a constant value of invested capital (I = const) At a constant value of invested capital (I = const), accounting D = IL/(1 + L ), S = I/(1 + L ), we get     NOIð1 - t Þ ILt 1 1 þ 11NPV = - I þ ke 1þL ð1 þ k e Þn ð1 þ k d Þn      NOIð1 - t Þ Lt 1 1 þ : = - I 111ke 1þL ð1 þ k d Þn ð 1 þ k e Þn At a constant value of equity capital (S = const) Accounting D = LS, I = S(1 + L ), we get

ð17:25Þ

17 Investment Models with Debt Repayment at the End of the Project and. . .

352

    NOIð1 - t Þ 1 1 þ Dt 1: ð17:26Þ NPV = - S - LS þ 1ke ð 1 þ k e Þn ð1 þ k d Þn Accounting, that in case S = const NOI is not a constant, but is proportional to invested capital, NOI = βI = βS(1 + L ), we get   NPV = - S 1 þ L - tL 1  1-

 1 : ð1 þ k e Þn

1 ð1 þ k d Þn

 þ

βSð1 þ LÞð1 - t Þ ke ð17:27Þ

For one-year project 

 βSð1 þ LÞð1 - t Þ kd þ : NPV = - S 1 þ L - tL 1 þ ke 1 þ kd

17.5.2

ð17:28Þ

Without Flows Separation

In this case, operating and financial flows are not separated and both are discounted at the general rate (as which, obviously, can be selected the weighted average cost of capital, WACC). n X NOIð1 - t Þ þ kd Dt NOIð1 - t Þ þ kd Dt = -I þ i WACC ð1 þ WACCÞ i=1   1  1: ð1 þ WACCÞn

NPV = - I þ

At a constant value of invested capital (I = const) At a constant value of invested capital (I = const) we have   NOIð1 - t Þ þ kd Dt 1 : 1NPV = - I þ WACC ð1 þ WACCÞn Accounting D = IL/(1 + L ), S = I/(1 + L ), we get

ð17:29Þ

17.6

Modigliani–Miller Limit

353

2

0 13 L 1 6 7 1 þ L  B1 -   n C NPV = - I 41 -  @ A5 þ L L 1 þ k0 1 - γ 1þL t k0 1 - γ t 1þL 0 1 ð17:30Þ kd t

þ

NOIð1 - t Þ B 1  n C   @1 -  A: L L 1 þ k0 1 - γ 1þL t k0 1 - γ t 1þL

For one-year project Putting at the equation (Eq. 17.30) n = 1, one gets for NPV 

 L kd t 1þL NOIð1 - t Þ þ NPV = - I 1: 1 þ WACC 1 þ WACC

ð17:31Þ

At a constant value of equity capital (S = const) NPV

= =

  NOIð1 - t Þ þ kd Dt 1 1-I þ WACC ð1 þ WACCÞn    k Lt 1 -S 1 þ L- d 1WACC ð1 þ WACCÞn   βSð1 þ LÞð1 - t Þ 1 : þþ 1WACC ð1 þ WACCÞn

ð17:32Þ

For one-year project   NOIð1 - t Þ þ kd Dt kd Lt = -S 1 þLNPV = - I þ 1 þ WACC 1 þ WACC þ

17.6 17.6.1

NOIð1 - t Þ : 1 þ WACC

ð17:33Þ

Modigliani–Miller Limit With Flows Separation

In perpetuity limit (n → 1) (Modigliani–Miller limit) we have NPV = - I þ

NOIð1 - t Þ þ Dt: ke

ð17:34Þ

354

17 Investment Models with Debt Repayment at the End of the Project and. . .

At a constant value of invested capital (I = const) accounting D = IL/(1 + L ), we have  NPV = - I 1- t

 NOIð1 - t Þ L : þ ke 1þL

ð17:35Þ

For equity cost ke and the weighted average cost of capital, WACC in Modigliani–Miller theory we have consequently ke = k0 þ ðk 0- k d ÞLð1- t Þ,

ð17:36Þ

WACC = k0 ð1- wd t Þ = k 0 ð1- Lt=ð1 þ LÞÞ:

ð17:37Þ

Putting (Eq. 17.36) into (Eq. 17.37), we get  NPV = - I 1- t

 NOIð1 - t Þ L : þ 1þL k0 þ ðk0 - kd ÞLð1 - t Þ

ð17:38Þ

At a constant value of equity capital (S = const) Accounting D = LS, I = S(1 + L ), in perpetuity limit (n → 1) (Modigliani–Miller limit) we have: NPV = - Sð1 þ Lð1- t ÞÞ þ

NOIð1 - t Þ : k0 þ ðk 0 - k d ÞLt

ð17:39Þ

Note, that in case S = const NOI is not a constant, but is proportional to invested capital, NOI = βI = βS(1 + L ).. In this case, the equation (Eq. 17.38) is replaced by NPV = - Sð1 þ Lð1- t ÞÞ þ

17.6.2

βSð1 þ LÞð1 - t Þ , k0 þ ðk 0 - k d ÞLt

ð17:40Þ

Without Flows Separation

In perpetuity limit (n → 1) (Modigliani–Miller limit) we have NPV = - I þ

NOIð1 - t Þ þ kd Dt : WACC

At a constant value of invested capital (I = const), we have

ð17:41Þ

References

355

0 NPV = - I þ þ

1 L kd t 1þL

NOIð1 - t Þ þ k d Dt = - I @1-  WACC k0 1 -

L 1þL t

A

NOIð1 - t Þ  : L k0 1 - 1þL t

ð17:42Þ

At a constant value of equity capital (S = const) In perpetuity limit (n → 1) (Modigliani–Miller limit) we have   NOIð1 - t Þ k Lt þ NPV = - S 1 þ L - d : WACC WACC 2 3 βSð1 þ LÞð1 - t Þ Lt k 5 þ   : NPV = - S41 þ L -  d L L k0 1 - 1þL t k 0 1 - 1þL t

ð17:43Þ ð17:44Þ

References Brusov PN, Filatova ТV (2011) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Finance and Credit 435:2–8 Brusov P, Filatova T, Orehova N, Brusova A (2011a) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Appl Financ Econ 21(11): 815–824 Brusov P, Filatova T, Orehova N et al (2011b) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Bus ICT 2:16–21 Brusov P, Filatova T, Orehova N et al (2011c) Influence of debt financing on the effectiveness of the investment project within the Modigliani–Miller theory. Res J Econ Bus ICT 2:11–15 Brusov P, Filatova T, Eskindarov M, Orehova N (2012a) Influence of debt financing on the effectiveness of the finite duration investment project. Appl Financ Econ 22(13):1043–1052 Brusov P, Filatova T, Eskindarov M, Orehova N (2012b) Hidden global causes of the global financial crisis. J Rev Glob Econ 1:106–111 Brusov P, Filatova P, Orekhova N (2013a) Absence of an optimal capital structure in the famous Tradeoff theory! J Rev Glob Econ 2:94–116 Brusov P, Filatova T, Orehova N (2013b) A qualitatively new effect in corporative finance: abnormal dependence of cost of equity of company on leverage. J Rev Glob Econ 2:183–193 Brusov P, Filatova P, Orekhova N (2014a) Mechanism of formation of the company optimal capital structure, different from suggested by trade off theory. Cogent Econ Finance 2:1–13. https://doi. org/10.1080/23322039.2014.946150 Brusov P, Filatova T, Orehova N (2014b) Inflation in Brusov–Filatova–Orekhova theory and in its perpetuity limit – Modigliani – Miller theory. J Rev Glob Econ 3:175–185

356

17 Investment Models with Debt Repayment at the End of the Project and. . .

Filatova Т, Orehova N, Brusova А (2008) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Bullet FU 48:68–77 Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Modigliani F, Miller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391

Chapter 18

Investment Models with Uniform Debt Repayment and their Application

Keywords Investment models · Uniform debt repayment · Efficiency of investments · Brusov–Filatova–Orekhova (BFO) theory · Debt financing In previous chapters, we have established investment models with debt repayment at the end of the project, well proven in the analysis of real investment projects. In practice, however, a scheme of uniform debt repayment during the duration of the project is more extended. In this chapter, we describe new investment models with uniform debt repayment during the duration of the investment project, quite adequately describing real investment projects. Within these models it is possible, in particular, to analyze the dependence of the effectiveness of investment projects on debt financing and taxation. We will work on the modern theory of capital cost and capital structure developed by Brusov–Filatova–Orekhova (Brusov 2018a, b; Brusov et al. 2015a, b; Brusov et al. 2018a, b, c, d, e, f, g; Brusov et al. 2019; Brusov et al. 2020; Filatova et al. 2018a, b; Brusov et al. 2014a, b; Filatova et al. 2008; Brusova 2011) as well as on perpetuity limit (Мodigliani and Мiller 1958, 1963, 1966). In Chap. 30, we consider the application of the investment models with uniform debt repayment to rating methodology.

18.1

Investment Models with Uniform Debt Repayment

As in the case of debt repayment at the end of the project, the effectiveness of the investment project is considered from two perspectives: the owners of equity and debt and the equity holders only. In the first case, the interest and duty paid by owners of equity (negative flows) returned to the project because they are exactly equal to the flow (positive), obtained by owners of debt capital. The only effect of leverage in this case is the effect of tax shield, generated from the tax relief: interest on the loan is entirely included into the net cost and, thus, reduces the tax base. For each of these cases, NPV is calculated in two ways: with the division of credit and investment flows (and thus discounting the payments, using two different rates) and © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_18

357

358

18

Investment Models with Uniform Debt Repayment and their Application

Table 18.1 The sequence of debt and interest values and credit values

Period number Debt

1 D

Interest

kdD

2

3

D  n -n 1 k d D  n -n 1

D  n -n 2 k d D  n -n 2

... ...

D  1n

...

k d D  1n

n

without such a division (in this case, both flows are discounted at the same rate as which, obviously, WACC can be chosen). For each of the four situations, two cases are considered: (1) a constant value of equity S and (2) a constant value of the total invested capital I = S + D (D is value of debt funds). The main debt repayment occurs evenly (by equal parts) at the end of each period, and the remaining debt at the end of each period is an arithmetic progression with the difference -D/n n D, D-

o o n     2D D n-1 n-2 D D , ..., = D, D ,D , ..., ,Dn n n n n n

ð18:1Þ

Interest constitutes a sequence: n kd D, k d D

o     D n-1 n-2 : , kd D , . . . , kd n n n

ð18:2Þ

In the case of consideration from the point of view of equity owners and debt owners, the after-tax flow of capital for each period is equal to NOIð1- t Þ þ kd Di t,

ð18:3Þ

n - ð i - 1Þ , n

ð18:4Þ

where Di = D

and investments at time moment T = 0 are equal to -I = -S - D. Here NOI stands for net operating income (before tax). In the second case (from the point of view of equity owners only), investments at the initial moment T = 0 are equal to -S, and the flow of capital for the ith period (apart from tax shields kdDt it includes payment of interest on the loan -kdDi) is equal to ðNOI- k d Di Þð1- t Þ -

Di : n

ð18:5Þ

We suppose that the interest on the loan and the loans itself are paid in tranches i kdDi and D  n n consequently during the all ith periods. We cite in Table 18.1 the sequence of debt and interest values and credit values. As in the case of debt repayment at the end of the project, we will consider two different ways of discounting:

18.2

The Effectiveness of the Investment Project from the Perspective of. . .

359

1. Operating and financial flows are not separated and both are discounted, using the general rate (as which, obviously, the weighted average cost of capital (WACC) can be selected). For perpetuity projects, the Modigliani–Miller formula (Мodigliani and Мiller 1963) for WACC will be used and for projects of finite duration Brusov–Filatova–Orekhova formula for WACC (Brusov et al. 2014a, b; Filatova et al. 2008). 2. Operating and financial flows are separated and are discounted at different rates: the operating flow at the rate equal to the equity cost ke, depending on leverage, and credit flow–at the rate equal to the debt cost kd, which until fairly large values of leverage remain constant and start to grow only at high values of leverage L, when there is a danger of bankruptcy. Note once again that loan capital is the least risky, because interest on credit is paid after tax in the first place. Therefore, the cost of credit will always be less than the equity cost, whether of ordinary or of preference shares ke > kd; kp > kd. Here ke; kp is equity cost of ordinary or of preference shares consequently. One can show that the present value of interest can be calculated by using the following formula, which we have been able to derive: að 1 - a - n Þ 3 n n 1 2 : þ 2þ 3þ⋯þ n = 2 a a a ð a 1Þan a ð a - 1Þ

ð18:6Þ

Here a = 1 + i. We will use this formula in further calculations.

18.2 18.2.1

The Effectiveness of the Investment Project from the Perspective of the Equity Holders Only With the Division of Credit and Investment Flows

To obtain an expression for NPV, the discounted flow values for one period, given by formulas (Eq. 18.3) and (Eq. 18.5), must be summed, using our obtained formula (Eq. 18.6), in which a = 1 + i, where i is the discount rate. Its accurate assessment is one of the most important advantages of BFO theory (Brusov–Filatova–Orekhova) (Brusov et al. 2014a, b; Filatova et al. 2008) over its perpetuity limit–Modigliani– Miller theory (Мodigliani and Мiller 1958, 1963, 1966). In this case, the expression for NPV has a view

360

18

NPV = - S þ

Investment Models with Uniform Debt Repayment and their Application

n X NOIð1 - t Þ i=1

ð1 þ k e Þi

þ

n - kd D X i=1

n þ 1-i D ð1 - t Þ n n ð1 þ k d Þi

NOIð1 - t Þð1 - ð1 þ k e Þ - n Þ = -S þ ke   1 - ð1 þ k Þ - n D nþ1 d þ kd D ð1 - t Þ kd n n   ð1 þ kd Þ½1 - ð1 þ k d Þ - n  n D þk d ð1 - t Þ n k d ð1 þ k d Þn k 2d

ð18:7Þ

In perpetuity limit (let us call it Modigliani–Miller limit), one has NPV = - S þ

18.2.2

NOIð1 - t Þ - Dð1- t Þ: ke

ð18:8Þ

Without Flows Separation

In this case, operating and financial flows are not separated and are discounted, using the general rate (as which, obviously, WACC can be selected). The main debt repayment, which occurs evenly (by equal parts) at the end of each period, can be discounted either at the same rate WACC or at the debt cost rate kd. Now we choose a uniform rate and the first option. We still consider the effectiveness of the investment project from the perspective of the equity holders only.

NPV

=

=

n þ 1-i D ð1 - t Þ n n -S þ i ð 1 þ WACC Þ i=1 nþ1 D  NOIð1 - t Þ - - kd D ð1 - t Þ  1 n n -S þ   1WACC ð1 þ WACCÞn  -n ð1 þ WACCÞ½1 - ð1 þ WACCÞ  k D þ þ d ð1 - t Þ n WACC2 n g WACCð1 þ WACCÞn ð18:9Þ n NOIð1 - t Þ - k d D X

18.3

The Effectiveness of the Investment Project from the Perspective of. . .

361

In perpetuity limit (Modigliani–Miller limit) (turning to the limit n → 1 in the relevant equations), we have NPV = - S þ

NOIð1 - t Þ - k d Dð1 - t Þ : WACC

ð18:10Þ

Note, that formula (18.10) as well as other formulas for perpetuity limit (18.12) and (18.14) could be applied to analyze the effectiveness of long-term investment projects.

18.3

The Effectiveness of the Investment Project from the Perspective of the Owners of Equity and Debt

18.3.1

With Flows Separation

18.3.1.1

Projects of Arbitrary (Finite) Duration

In the case of consideration from the perspective of the owners of equity and debt

NPV = - I þ

n X NOIð1 - t Þ i=1

ð1 þ k e Þi

þ

n þ 1-i t n i ð1 þ k d Þ

n kd D X i=1

NOIð1 - t Þð1 - ð1 þ ke Þ - n Þ = -I þ ke nþ1 þD t  ½1 - ð1 þ k d Þ - n  n  -n D ð1 þ kd Þ½1 - ð1 þ k d Þ  n - kd t n k d ð1 þ k d Þn k 2d

ð18:11Þ

In perpetuity limit (Modigliani–Miller limit) (turning to the limit n → 1 in the relevant equations), we have NOI = - I þ

18.3.2

NOIð1 - t Þ þ Dt: ke

ð18:12Þ

Without Flows Separation

We still consider the effectiveness of the investment project from the perspective of the owners of equity and debt.

362

18

Investment Models with Uniform Debt Repayment and their Application

n þ 1-i t n NPV = - I þ ð1 þ WACCÞi i=1 nþ1   t NOIð1 - t Þ þ k d D 1 n 1= -I þ WACC ð1 þ WACCÞn  -n k D ð1 þ WACCÞ½1 - ð1 þ WACCÞ  - d t n WACC2  n WACCð1 þ WACCÞn n NOIð1 - t Þ þ k d D X

ð18:13Þ

In perpetuity limit (Modigliani–Miller limit) (turning to the limit n → 1 in the relevant equations), we have NPV = - I þ

18.4

NOIð1 - t Þ þ kd Dt : WACC

ð18:14Þ

Example of the Application of the Derived Formulas

As an example of the application of the obtained formulas, let us take a look at the dependence of the NPV of project on the leverage level at three values of the tax on profit rates in the case of consideration from the perspective of the equity holders only without flows separation on operating and finance ones. We use formula (Eq. 18.10) and the next parameters values NOI = 800; S = 500; k 0 = 22 %; k d = 19 %; T = 15 %; 20%; 25 %: Making the calculations in Excel, we get the data, which are shown in Fig. 18.1. From the calculations and Fig. 18.1, one can make the following conclusions: 1. With growth of the tax on profit rate, the NPV of the project decreases and our model makes it possible to assess, for how many percent, with growth of tax on profit rate, for example, by 1%. It should be noted that the possibility of such evaluations is unique. 2. The effect of taxation on the NPV significantly depends on the leverage level: With its increase, the impact of changing of tax on profit rate is greatly reduced. This is valid for increasing of the tax on profit rate and for its reduction. 3. At tax on profit rates 20% (as in Russia) and 25%, there is an optimum in NPV dependence on leverage. Investors should take into account the invested capital structure: in this case, they may, without special effort (only changing this structure), obtain (sometimes very substantial) gains in NPV. Note that at tax

18.5

Conclusions

363

Fig. 18.1 Dependence of NPV of the project on the leverage level at three values of the tax on profit rates NOI = 800; S = 500; k0 = 22 % ; kd = 19 % ; T = 15 % ; 20 % ; 25 %

on profit rate 15%, there is no optimum in NPV dependence on leverage: NPV descends monotonically with leverage.

18.5

Conclusions

New investment models with uniform debt repayment during the duration of the project, quite adequately describing real investment projects, are described. Within these models, it is possible, in particular, to analyze the dependence of the effectiveness of investment projects on debt financing and taxation. We work on the modern theory of capital cost and capital structure developed by Brusov–Filatova– Orekhova as well as on perpetuity limit–MM theory. As in the case of debt repayment at the end of the project, the effectiveness of the investment project is considered from two perspectives: the owners of equity and debt and the equity holders only. For each of these cases, NPV is calculated in two ways: with the division of credit and investment flows (and thus discounting the payments, using two different rates) and without such a division (in this case, both flows are discounted at the same rate as which, obviously, WACC can be chosen). For each of the four situations, two cases are considered: (1) a constant value of equity S and (2) a constant value of the total invested capital I = S + D (D is value of debt funds). As an example of the application of the obtained formulas, the dependence of the NPV of project on the leverage level at three values of the tax on profit rate has been investigated in the case of consideration from the perspective of the equity holders only and without flows separation on operating and financial ones. It has been shown that effect of taxation on the NPV significantly depends on the leverage level: with its increase, the impact of changing of tax on profit rates is greatly reduced. This is valid for increasing of the tax on profit rate and for its reduction. The model allows investigating the dependence of effectiveness of the investment project on leverage level, on the tax on profit rate, on credit rate, on equity cost, etc.

364

18

Investment Models with Uniform Debt Repayment and their Application

References Brusov P (2018a) Editorial: introduction on special issue on the banking system and financial markets of Russia and other countries: problems and prospects. J Rev Glob Econ 7:i–vi Brusov P (2018b) Editorial. J Rev Glob Econ 7:i–v Brusov P, Filatova P, Orekhova N (2014a) Mechanism of formation of the company optimal capital structure, different from suggested by trade off theory. Cogent Econ Financ 2:1–13 Brusov P, Filatova T, Orehova N (2014b) Inflation in Brusov–Filatova–Orekhova theory and in its perpetuity limit–Modigliani–Miller theory. J Rev Glob Econ 3:175–118 Brusov P, Filatova T, Orehova N, Eskindarov M (2015a) Modern corporate finance, investments and taxation. Springer International Publishing. 373 p. monograph, https://www.springer.com/ gp/book/9783319147314 Brusov P, Filatova T, Orehova N, Eskindarov M (2015b) Modern corporate finance, investment and taxation, 1st edn. Springer, pp 1–368 Brusov P, Filatova T, Orehova N, Eskindarov M (2018a) Modern corporate finance, investments, taxation and ratings. Springer Nature Publishing. 571 p. monograph Brusov PN, Filatova TV, Orekhova NP (2018b) Modern corporate finance and investments, monograph. Knorus Publishing House, Moscow, p 517 Brusov PN, Filatova TV, Orekhova NP, Kulik VL (2018c) Rating: new approach. J Rev Glob Econ 7:37–62 Brusov PN, Filatova TV, Orekhova NP, Kulik VL (2018d) A “golden age” of the companies: conditions of its existence. J Rev Glob Econ 7:88–103 Brusov PN, Filatova TV, Orekhova NP, Kulik VL (2018e) Rating methodology: new look and new horizons. J Rev Glob Econ 7:63–87 Brusov PN, Filatova TV, Orekhova NP, Kulik VL, Weil I (2018f) New meaningful effects in modern capital structure theory. J Rev Glob Econ 7:104–122 Brusov P, Filatova T, Orekhova N, Kulik V, Weil I, Brailov A (2018g) The impact of the central bank key rate and commercial banks credit rates on creating and maintaining of a favorable investment climate in the country. J Rev Glob Econ 7:360–376 Brusov PN, Filatova TV, Orekhova NP, Kulik VL, Weil I (2019) Ratings of the investment projects of arbitrary durations: new methodology. J Rev Glob Econ 8:437–448 Brusov PN, Filatova TV, Orekhova NP, Kulik VL, Chang S-I, Lin YCG (2020) Modification of the Modigliani–Miller theory for the case of advance payments of tax on profit. J Rev Glob Econ 9: 257–268 Brusova A (2011) А comparison of the three methods of estimation of weighted average cost of capital and equity cost of company. Financ Anal Prob Solut 34(76):36–42 Filatova Т, Orehova N, Brusova А (2008) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Bull FU 48:68–77 Filatova TV, Brusov PN, Orekhova NP, Kulik VL (2018a) Ratings of the long–term projects: new approach. J Rev Glob Econ 7:645–661 Filatova TV, Brusov PN, Orekhova NP, Kulik VL (2018b) Ratings of the long–term projects: new approach. J Rev Glob Econ 7:645–666 Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Modigliani F, Miller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391

Chapter 19

The Analysis of the Exploration of Efficiency of Investment Projects of Arbitrary Duration (within Brusov– Filatova–Orekhova Theory)

Keywords Efficiency of arbitrary duration investment projects · Brusov · Filatova · Orekhova (BFO) theory Earlier (see in Brusov et al. 2022) we have conducted the analysis of the effectiveness of investment projects within the perpetuity (Modigliani–Miller) approximation (Modigliani et al. 1958, 1963, 1966). In this chapter the analysis of the obtained results on the exploration of efficiency of investment projects of arbitrary duration (within Brusov–Filatova–Orekhova theory (Brusov et al. 2011a, b, c; 2012a, b; 2013a, b; 2014a, b; Filatova et al. 2008)) is conducted.

19.1 19.1.1

The Effectiveness of the Investment Project from the Perspective of the Equity Holders Only With the Division of Credit and Investment Flows

At a constant investment value(I = const) For NPV in this case the following expression has been obtained (Brusov et al. 2011a, b, c; 2012a, b; 2013a, b; 2014a, b) 

  I 1 1 þ þ NPV = 1 þ L ð1 - t Þ 1 1þL ð1 þ k d Þn ð1 þ k d Þn
 NOIð1 - t Þ 1 þ : 1ke ð1 þ k e Þn

ð19:1Þ

Dependence of NPV on leverage level at fixed values of k0 and kd at a constant investment value (I = const) is shown in Table 19.1 and Figs. 19.1 and 19.2. 1. At the constant values of Δk = k0 - kd NPV decreases with leverage at low values of k0 (up to 20%) and grows at higher values of k0 (from 25%–30%). All curves

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_19

365

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

k0 0.08 0.10 0.14 0.18 0.24 0.30 0.36 0.40 0.44 0.10 0.12 0.16 0.20 0.24 0.30 0.36 0.40 0.44

kd\L 0.06 0.08 0.12 0.16 0.22 0.28 0.34 0.38 0.42 0.06 0.08 0.12 0.16 0.20 0.26 0.32 0.36 0.40

0.0 711.9 666.6 580.9 503.0 398.5 306.5 225.0 175.6 129.7 666.6 622.6 541.1 466.2 398.5 306.5 225.0 175.6 129.7

0.5 700.7 660.2 581.9 510.6 414.0 328.6 251.3 206.1 163.0 635.3 596.5 524.3 456.8 396.6 318.4 237.9 193.9 151.7

1.0 686.2 649.4 576.5 509.8 418.6 337.3 264.7 221.0 179.5 602.0 567.1 501.8 441.5 385.1 308.1 238.8 197.2 157.5

Table 19.1 n = 2, t = 0.2, NOI = 1200; I = 1000, k0-kd = const 1.5 670.6 637.0 568.5 505.7 418.9 340.6 272.0 229.6 189.5 568.7 537.1 477.7 422.5 370.2 298.0 234.1 194.7 157.1

2.0 654.6 623.9 559.4 499.9 417.1 344.0 276.4 235.1 196.1 536.1 507.3 453.2 402.5 353.8 285.9 226.8 189.3 153.7

2.5 638.5 610.5 549.6 493.4 414.0 344.2 279.0 236.2 200.7 504.4 478.2 428.8 382.2 336.9 275.8 218.2 179.9 148.5

3.0 622.4 597.0 539.5 486.3 410.2 343.5 280.5 238.8 204.3 473.6 449.9 404.8 362.1 319.7 263.0 208.7 172.2 142.4

3.5 606.5 583.6 529.3 478.9 406.0 342.3 281.3 240.6 207.0 443.9 422.4 381.4 342.1 302.6 249.9 198.8 164.0 135.6

4.0 590.8 570.2 519.0 471.3 401.4 340.6 281.6 242.0 209.1 415.2 395.7 358.4 322.5 285.6 236.7 188.6 155.5 128.5

4.5 575.3 556.9 508.7 463.7 396.6 338.6 283.5 242.9 210.9 387.5 369.9 336.1 303.2 268.9 223.6 178.3 146.7 121.1

366 19 The Analysis of the Exploration of Efficiency of Investment Projects. . .

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

k0 0.08 0.10 0.14 0.18 0.24 0.30 0.36 0.40 0.44 0.10 0.12 0.16 0.20 0.24 0.30 0.36 0.40 0.44

kd\L 0.06 0.08 0.12 0.16 0.22 0.28 0.34 0.38 0.42 0.06 0.08 0.12 0.16 0.20 0.26 0.32 0.36 0.40

5.0 560.0 543.7 498.4 455.9 391.7 336.3 284.4 243.5 212.4 360.7 344.9 314.4 284.4 252.4 210.6 168.0 137.9 118.6

5.5 544.9 525.7 488.2 448.2 386.6 334.0 280.7 244.0 218.6 334.8 320.6 293.2 266.0 236.2 197.7 155.9 129.0 106.0

6.0 530.1 512.5 478.0 440.4 381.5 331.5 280.0 244.2 214.6 309.8 297.2 272.7 248.1 220.4 185.0 145.7 120.2 98.3

6.5 515.5 499.5 468.0 432.6 376.3 328.9 279.1 244.3 215.5 285.6 274.5 252.7 230.6 204.9 172.5 140.4 111.3 90.7

7.0 501.1 486.6 458.0 424.9 371.1 326.2 278.2 244.3 216.3 262.2 252.5 233.3 218.5 189.7 160.1 127.2 102.6 83.0

7.5 487.0 474.0 448.1 417.2 365.9 323.4 277.2 244.2 217.0 239.6 231.1 214.4 196.8 174.9 148.0 117.2 93.9 75.4

8.0 473.1 461.5 438.3 409.6 360.7 320.7 276.1 244.0 217.6 217.7 210.5 196.0 180.5 160.3 136.1 107.4 85.2 67.9

8.5 459.4 449.2 428.6 402.0 355.4 317.8 274.9 243.7 218.2 196.5 190.4 178.1 164.6 146.1 124.4 97.7 76.7 60.4

9.0 445.9 437.1 419.0 394.4 350.2 315.0 273.7 243.4 218.6 176.0 171.0 160.8 149.1 132.2 112.9 88.1 68.3 53.0

9.5 432.7 425.1 409.5 386.9 345.0 312.1 272.5 243.1 219.1 156.1 152.2 143.9 134.0 118.6 101.6 78.7 59.9 45.6

10.0 419.7 418.4 400.1 379.5 339.8 309.2 271.2 242.7 219.4 136.9 133.9 127.4 119.3 105.3 90.5 69.4 51.7 38.3

19.1 The Effectiveness of the Investment Project from the Perspective of. . . 367

368

19

The Analysis of the Exploration of Efficiency of Investment Projects. . .

NPV(L), t = 20%

NPV 800

1 2

700 600

3 4

500

5

400

6

300

7 8 9

200 100

0

1

2

3

4

5

6

7

8

9

10

11

0

L Fig. 19.1 Dependence of NPV on leverage level at fixed values of k0 and kd

NPV(L ) are shifted down with the growth of k0. At small leverage levels L there is an optimum in the dependence of NPV(L ). 2. At the constant values of k0 NPV practically always decreases with leverage. Higher values of kd (at the same value of k0) correspond to higher lying curves NPV(L ). At small leverage levels L at high value of k0 (36%–40%) there is an optimum in the dependence of NPV(L ). 3. At the constant values of kd NPV practically always decreases with leverage. Higher values of k0 (at the same value of kd) correspond to lower lying curves NPV(L ). At small leverage levels L for some pairs of values k0 and kd (for example, k0 (18%) and kd (16%)) there is an optimum in the dependence of NPV(L ). At the constant equity value (S = const) For NPV in this case the following expression has been obtained (Brusov et al. 2011a, b, c; 2012a, b; 2013a, b; 2014a, b)

19.1

The Effectiveness of the Investment Project from the Perspective of. . .

NPV(L), t = 20%

369

NPV

700

10 11

600

12 500

13 14

400

15

300

16

200

17 18

100

0

1

2

3

4

5

6

7

8

9

10

11

0

L Fig. 19.2 Dependence of NPV on leverage level at fixed values of k0 and kd



  1 1 þ þ NPV = - S 1 þ L ð1 - t Þ 1 ð1 þ kd Þn ð1 þ k d Þn
 βSð1 þ LÞð1 - t Þ 1 : 1þ ke ð1 þ k e Þ n

ð19:2Þ

Dependence of NPV on leverage level at fixed values of k0 and kd at a constant equity value (S = const) is shown in Table 19.2 and Figs. 19.3 and 19.4. 1. At the constant values of Δk = k0 - kd NPV, as a rule, decreases with leverage. All curves NPV(L) are shifted down with the growth of k0 sometimes at small leverage level L values there is an optimum in the dependence of NPV(L ). As it will be shown in Chap. 18 at the example with “Nastcom Plus” company, the dependence of NPV(L ) strongly depends on the β parameter value and can have a marked optimum. 2. At the constant values of k0 NPV practically always decreases with leverage. Higher values of kd (lower values of Δk = k0 - kd) at the same value of k0 correspond to higher lying curves NPV(L ). Like the previous paragraph, the dependence of NPV(L) strongly depends on the β parameter value and can have a marked optimum.

k0 0.08 0.10 0.14 0.18 0.24 0.30 0.36 0.40 0.44 0.10 0.12 0.16 0.20 0.24 0.30 0.36 0.40 0.44 k0 0.08 0.10 0.14 0.18 0.24 0.30

kd\L 0.06 0.08 0.12 0.16 0.22 0.28 0.34 0.38 0.42 0.06 0.08 0.12 0.16 0.20 0.26 0.32 0.36 0.40 kd\L 0.06 0.08 0.12 0.16 0.22 0.28

0.0 0.5 1.0 -1.4 -7.3 -23.6 -27.8 -41.4 -63.8 -77.8 -107.4 -143.9 -123.2 -167.5 -217.2 -184.2 -249.1 -317.6 -237.9 -321.3 -407.4 -285.4 -386.7 -487.6 -314.2 -424.8 -535.9 -341.0 -461.4 -581.9 -27.8 -64.5 -121.8 -53.5 -97.1 -159.8 -101.1 -157.8 -231.0 -144.7 -214.6 -296.8 -184.2 -265.3 -358.6 -237.9 -335.4 -443.1 -285.4 -399.1 -519.3 -314.2 -436.2 -565.0 -341.0 -471.9 -608.7 5.0 5.5 6.0 -494.2 -591.7 -697.1 -537.5 -649.7 -752.6 -671.0 -764.3 -863.3 -797.3 -891.4 -990.0 -992.4 -1092.0 -1194.8 -1160.4 -1263.4 -1368.4 6.5 -810.2 -862.5 -967.9 -1093.1 -1300.8 -1475.2

1.5 -50.0 -94.9 -187.3 -272.2 -389.7 -496.3 -589.6 -647.5 -702.4 -198.6 -240.6 -319.7 -393.4 -463.6 -560.7 -647.0 -700.4 -751.3

2.0 2.5 3.0 3.5 -86.1 -131.8 -186.8 -250.8 -134.4 -182.1 -237.9 -301.5 -237.3 -294.0 -357.0 -426.4 -332.3 -397.5 -467.8 -542.9 -465.4 -544.7 -627.4 -718.6 -583.0 -674.4 -767.7 -862.9 -692.5 -796.5 -901.4 -1007.3 -759.5 -877.3 -990.8 -1104.8 -822.9 -943.5 -1064.0 -1184.7 -293.5 -405.7 -534.0 -677.6 -338.4 -452.2 -581.2 -724.6 -423.1 -540.6 -671.4 -814.8 -502.8 -624.4 -757.7 -902.1 -579.9 -706.9 -844.3 -991.6 -688.0 -818.1 -960.5 -1111.1 -782.0 -924.2 -1073.2 -1229.0 -842.1 -995.4 -1150.0 -1310.5 -899.4 -1053.0 -1212.0 -1376.1 7.0 7.5 8.0 8.5 9.0 -930.6 -1058.3 -1193.0 -1334.6 -1482.9 -979.1 -1102.3 -1232.0 -1367.9 -1510.0 -1077.9 -1193.3 -1314.0 -1439.8 -1570.7 -1200.7 -1312.5 -1428.6 -1548.9 -1673.4 -1410.0 -1522.3 -1637.8 -1756.3 -1877.8 -1583.8 -1694.4 -1806.8 -1921.0 -2037.0

4.0 -323.5 -372.8 -501.9 -623.0 -803.2 -960.2 -1114.3 -1219.3 -1305.3 -835.6 -881.6 -970.3 -1057.2 -1148.5 -1269.5 -1391.2 -1476.8 -1545.3 9.5 -1637.7 -1658.0 -1706.5 -1801.8 -2002.3 -2154.9

4.5 -404.7 -451.5 -583.5 -707.8 -896.1 -1059.3 -1216.1 -1334.3 -1426.0 -1007.3 -1051.5 -1137.3 -1222.4 -1314.5 -1435.4 -1559.8 -1648.7 -1719.4 10.0 -1798.8 -1811.9 -1847.2 -1934.3 -2129.7 -2274.5

19

1 2 3 4 5 6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Table 19.2 n = 2, t = 0.2, S = 1000; β = 0.7, k0-kd = const

370 The Analysis of the Exploration of Efficiency of Investment Projects. . .

7 8 9 10 11 12 13 14 15 16 17 18

0.36 0.40 0.44 0.10 0.12 0.16 0.20 0.24 0.30 0.36 0.40 0.44

0.34 0.38 0.42 0.06 0.08 0.12 0.16 0.20 0.26 0.32 0.36 0.40

-1320.0 -1449.8 -1546.7 -1191.8 -1233.5 -1315.2 -1397.5 -1489.3 -1608.7 -1734.5 -1826.0 -1898.3

-1441.0 -1565.7 -1667.4 -1388.5 -1427.2 -1503.5 -1581.9 -1672.5 -1789.0 -1922.0 -2008.5 -2082.0

-1551.9 -1682.1 -1788.2 -1596.8 -1631.8 -1701.8 -1775.2 -1863.9 -1976.2 -2108.6 -2196.3 -2270.2

-1663.7 -1799.0 -1909.0 -1816.0 -1846.9 -1909.6 -1977.2 -2063.1 -2169.9 -2279.8 -2389.1 -2463.0

-1776.6 -1916.3 -2029.8 -2045.5 -2071.9 -2126.4 -2187.4 -2269.8 -2370.1 -2491.2 -2586.7 -2660.1

-1890.4 -2034.1 -2150.6 -2284.9 -2306.4 -2352.0 -2405.4 -2483.7 -2576.4 -2694.0 -2789.2 -2861.5

-2005.2 -2152.4 -2271.5 -2533.7 -2549.9 -2585.8 -2631.1 -2704.6 -2788.8 -2902.0 -2996.3 -3067.1

-2120.9 -2271.2 -2392.4 -2791.3 -2801.9 -2827.5 -2864.1 -2932.2 -3006.9 -3115.0 -3207.9 -3276.7

-2237.6 -2390.5 -2518.3 -3057.4 -3062.1 -3076.8 -3104.0 -3166.3 -3230.7 -3332.9 -3424.0 -3490.4

-2355.3 -2510.2 -2634.2 -3331.6 -3330.1 -3333.3 -3350.7 -3406.6 -3459.9 -3555.6 -3644.3 -3708.0

-2473.9 -2630.3 -2755.2 -3618.4 -3605.5 -3596.8 -3603.9 -3653.0 -3694.4 -3782.8 -3868.9 -3929.4

19.1 The Effectiveness of the Investment Project from the Perspective of. . . 371

372

19

The Analysis of the Exploration of Efficiency of Investment Projects. . .

NPV(L), t = 20% 0

1

2

3

4

5

6

7

8

9

10

11

NPV 0

-500

-1000

-1500 1 2 3 4 5 6 7 8 9

-2000

-2500

-3000

L Fig. 19.3 Dependence of NPV on leverage level at fixed values of k0 and kd

3. At the constant values of kd NPV practically always decreases with leverage. Higher values of k0 (higher values of Δk = k0 - kd) at the same value of kd correspond to lower lying curves NPV(L ). At small leverage levels L for projects with durations above 2 years for some pairs of values k0 and kd (for example, for 5-year and 7-year projects with k0 (8%) and kd (6%); k0 (10%) and kd (6%)) there is an optimum in the dependence of NPV(L ). This optimum could be a marked one at other values of parameter β.

19.1.2

Without Flows Separation

At a constant investment value(I = const) For NPV in this case the following expression has been obtained (Brusov et al. 2011a, b, c; 2012a, b; 2013a, b; 2014a, b)

19.1

The Effectiveness of the Investment Project from the Perspective of. . .

373

NPV(L), t = 20% 0

1

2

3

4

5

6

7

8

9

11

10

NPV 0 -500 -1000 -1500 -2000 -2500 -3000

10 11 12 13 14 15 16 17 18

-3500 -4000 -4500

L Fig. 19.4 Dependence of NPV on leverage level at fixed values of k0 and kd

 
 k d ð1 - t Þ 1 L I 1þ þ NPV = 1þL WACC 1þL ð1 þ WACCÞn ð1 þ WACCÞn
 NOIð1 - t Þ 1 þ : 1WACC ð1 þ WACCÞn ð19:3Þ Dependence of NPV on leverage level at fixed values of k0 and kd at a constant investment value (I = const) is shown in Table 19.3 and Figs. 19.5 and 19.6. 1. At the constant values of Δk = k0 - kd NPV demonstrates a limited growth with leverage with output into saturation regime. The main increase in NPV occurs at small values of leverage levels L ≤ 3. With growth of k0 (and kd) the сurves NPV (L ) are lowered. Optimum in the dependence of NPV(L) is absent. 2. At the constant values of k0 NPV demonstrates a limited growth with leverage with output into saturation regime. All curves NPV(L ) at the constant values of k0 and different values of kd are started (at L = 0) from one point, the higher values of kd (and, respectively, the lower values of Δk = k0 - kd) correspond to lower

k0 0.08 0.10 0.14 0.18 0.24 0.30 0.36 0.40 0.44 0.10 0.12 0.16 0.20 0.24 0.30 0.36 0.40 0.44 k0 0.08 0.10 0.14 0.18 0.24 0.30

kd\L 0.06 0.08 0.12 0.16 0.22 0.28 0.34 0.38 0.42 0.06 0.08 0.12 0.16 0.20 0.26 0.32 0.36 0.40 kd\L 0.06 0.08 0.12 0.16 0.22 0.28

0.0 711.9 666.6 580.9 503.0 398.5 306.5 225.0 175.6 129.7 666.6 622.6 541.1 466.2 398.5 306.5 225.0 175.6 129.7 5.0 772.1 734.1 661.3 593.7 500.9 417.6

5.5 772.7 734.4 661.9 594.4 501.6 418.3

0.5 740.5 699.5 621.2 549.5 452.1 365.7 287.8 241.2 197.2 706.0 666.0 591.1 521.6 458.5 371.9 293.7 247.1 202.9 6.0 773.2 734.9 662.5 595.0 502.2 418.9

1.0 752.6 718.0 637.3 567.7 472.8 387.9 311.9 265.5 222.0 723.5 684.8 612.2 545.1 482.8 397.7 321.3 274.7 231.0 6.5 773.7 735.4 663.0 595.5 502.7 419.4

1.5 759.1 720.2 645.7 577.0 483.1 398.9 323.5 277.3 233.9 733.3 695.2 623.6 557.3 495.6 411.0 335.1 288.6 244.9 7.0 774.1 735.8 663.4 596.0 503.2 419.8

2.0 763.1 724.6 650.7 582.5 489.1 405.6 330.0 283.8 240.4 739.5 701.8 630.6 564.7 503.3 418.9 343.2 296.7 253.0 7.5 774.4 736.1 663.8 596.3 503.5 420.1

2.5 765.8 727.5 654.0 586.1 492.9 409.6 334.1 287.6 244.5 743.8 706.2 635.4 569.7 508.4 424.4 348.5 301.5 258.1 8.0 774.7 736.5 664.1 596.7 503.8 420.4

3.0 767.8 729.6 656.3 588.6 495.6 412.3 336.8 290.3 247.1 746.9 709.5 638.8 573.2 512.0 428.1 352.1 305.1 261.6 8.5 775.0 736.7 664.4 597.0 504.1 420.7

3.5 769.2 731.1 658.1 590.4 497.5 414.2 338.8 292.3 248.9 749.3 712.0 641.4 575.9 514.6 430.7 354.7 307.7 264.1 9.0 775.2 737.0 664.7 597.2 504.4 420.9

4.0 770.4 732.3 659.4 591.8 498.9 415.6 340.2 293.7 250.3 751.2 718.9 643.4 577.9 516.7 432.8 356.7 309.7 265.9 9.5 775.4 737.2 664.9 597.4 504.6 421.1

4.5 771.3 733.3 660.4 592.9 500.0 416.7 341.3 294.7 251.3 752.7 715.5 645.0 579.5 518.3 434.4 358.2 311.2 267.4 10.0 775.6 737.4 665.1 597.6 504.8 421.3

19

1 2 3 4 5 6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Table 19.3 n = 2, t = 0.2, NOI = 1200; I = 1000, k0-kd = const

374 The Analysis of the Exploration of Efficiency of Investment Projects. . .

7 8 9 10 11 12 13 14 15 16 17 18

0.36 0.40 0.44 0.10 0.12 0.16 0.20 0.24 0.30 0.36 0.40 0.44

0.34 0.38 0.42 0.06 0.08 0.12 0.16 0.20 0.26 0.32 0.36 0.40

342.2 295.5 252.0 754.0 716.8 646.3 580.9 519.6 435.6 359.4 312.4 268.5

342.7 296.2 252.6 755.1 717.8 647.4 582.0 520.7 436.7 360.3 318.4 269.4

343.3 296.7 253.1 755.9 718.7 648.4 582.9 521.6 437.6 361.2 314.2 270.2

343.7 297.1 253.5 756.7 719.5 649.2 583.7 522.4 438.3 362.1 314.9 270.8

344.1 297.5 253.8 757.4 720.2 649.8 584.3 523.1 438.9 362.6 315.4 271.3

344.4 297.8 254.1 758.0 720.8 650.4 584.9 523.6 439.5 363.1 315.9 271.8

344.7 298.0 254.3 758.5 721.3 651.0 585.5 524.1 440.0 363.5 316.4 272.2

344.9 298.2 254.5 759.0 721.8 651.4 585.9 524.6 440.4 363.9 316.7 272.5

345.1 298.4 254.7 759.4 722.2 651.8 586.3 525.0 440.8 364.2 317.1 272.8

345.3 298.6 254.8 759.7 722.6 652.2 586.7 525.4 441.1 364.5 317.3 273.1

345.4 298.7 254.9 760.1 722.9 652.6 587.0 525.7 441.4 364.8 317.6 273.3

19.1 The Effectiveness of the Investment Project from the Perspective of. . . 375

376

19

The Analysis of the Exploration of Efficiency of Investment Projects. . .

NPV(L), t = 20%

NPV 900 800

1 2

700

3 4

600

5

500

6

400

7 8 9

300 200 100

0

1

2

3

4

5

6

7

8

9

10

11

0

L Fig. 19.5 Dependence of NPV on leverage level at fixed values of k0 and kd

lying curves NPV(L ). Optimum in the dependence of NPV(L ) is absent. With growth of NOI all curves NPV(L) are shifted practically parallel upwards. Is of interest the crossing of individual curves NPV(L ) at certain leverage levels. This means the equivalence of projects with different pairs of k0 and kd at this leverage level (see, for example, n = 7; L = 2.5; (k0 and kd) = (18;14) and (24;10). 3. At the constant values of kd NPV shows a limited growth with leverage with output into saturation regime. All curves NPV(L) at the constant values of k0 and different values of kd are started (at L = 0) from one point, the higher values of k0 (and, respectively, the higher values of Δk = k0 - kd) correspond to lower lying curves NPV(L ). Optimum in the dependence of NPV(L ) is absent. The crossing of individual curves NPV(L ) at certain leverage levels (like point 2)) was not observed up to 10-year projects. At a constant equity value (S = const) For NPV in this case the following expression has been obtained (Brusov et al. 2011a, b, c; 2012a, b; 2013a, b; 2014a, b)

19.1

The Effectiveness of the Investment Project from the Perspective of. . .

377

NPV(L), t = 20%

NPV 800 10 11

700

12 600

13 14

500

15

400

16 17 18

300 200 100

0

1

2

3

4

5

6

7

8

9

10

11

0

L Fig. 19.6 Dependence of NPV on leverage level at fixed values of k0 and kd


  Lk ð1 - t Þ 1 L þ þ NPV = - S 1 þ d 1WACC ð1 þ WACCÞn ð1 þ WACCÞn
 ð19:4Þ βSð1 þ LÞð1 - t Þ 1 : þ 1WACC ð1 þ WACCÞn Dependence of NPV on leverage level at fixed values of k0 and kd at a constant equity value (S = const) is shown in Table 19.4 and Figs. 19.7 and 19.8. 1. At the constant values of Δk = k0 - kd NPV shows as an unlimited growth with leverage and unlimited descending with leverage. It is interesting to note, that the credit rate value kd ≈ 12% turns out to be a boundary at all surveyed values of Δk = k0 - kd, equal to 2%, 4%, 6%, and 10% (it separates the growth of NPV with leverage from descending of NPV with leverage) for 2-year projects. In other words, with growth of kd the transition from the growth of NPV with leverage to its descending with leverage takes place, and at the credit rate kd ≈ 12% NPV does not depend on the leverage level at all surveyed values of k0. For 5-year projects, this boundary credit rate is equal to 16–18%, for 7-year and 10-year projects it is equal to 12–15%.

k0 0.08 0.10 0.14 0.18 0.24 0.30 0.36 0.40 0.44 0.10 0.12 0.16 0.20 0.24 0.30 0.36 0.40 0.44 k0 0.08 0.10 0.14 0.18 0.24 0.30

kd\L 0.0 0.06 -1.4 0.08 -27.8 0.12 -77.8 0.16 -123.2 0.22 -184.2 0.28 -237.9 0.34 -285.4 0.38 -314.2 0.42 -341.0 -27.8 0.06 0.08 -53.5 0.12 -101.1 0.16 -144.7 0.20 -184.2 0.26 -237.9 0.32 -285.4 0.36 -314.2 0.40 -341.0 kd\L 5.0 0.06 272.6 0.08 135.3 0.12 -123.4 0.16 -363.4 0.22 -691.5 0.28 -987.4

298.1 149.4 -131.6 -391.9 -748.0 -1069.1

5.5

32.9 -2.5 -69.8 -131.6 -215.3 -289.8 -356.7 -396.9 -434.8 9.6 -25.0 -89.8 -149.8 -204.4 -279.4 -346.8 -387.3 -425.5

0.5

1.5 2.0 2.5 3.0 3.5 62.7 90.6 117.5 143.9 170.0 195.9 16.9 33.8 49.6 64.6 79.2 93.5 -70.1 -73.7 -79.1 -85.4 -92.4 -99.8 -150.2 -173.0 -198.0 -224.2 -251.2 -278.8 -259.2 -308.4 -360.4 -418.9 -468.4 -523.6 -356.6 -429.7 -505.9 -584.2 -663.6 -743.8 -444.0 -538.7 -637.0 -737.6 -839.5 -942.3 -497.4 -605.4 -717.3 -831.3 -946.9 -1063.6 -547.3 -667.9 -792.6 -919.7 -1048.4 -1178.1 42.6 73.7 103.9 133.7 163.0 192.2 -2.2 18.2 37.4 56.0 74.1 92.0 -86.4 -86.4 -88.0 -90.6 -93.8 -97.3 -164.2 -183.1 -204.2 -226.5 -249.5 -273.1 -236.3 -273.0 -312.2 -352.8 -394.3 -436.4 -334.8 -396.0 -460.2 -526.1 -593.2 -661.0 -423.3 -506.6 -593.5 -682.4 -772.6 -863.6 -477.3 -574.4 -675.2 -778.0 -882.2 -987.5 -527.9 -637.9 -751.8 -868.1 -985.8 -1104.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 323.4 348.8 374.1 399.3 424.6 449.8 475.0 163.1 176.8 190.4 204.1 217.6 231.2 244.7 -139.8 -148.2 -156.6 -165.1 -173.6 -182.2 -190.8 -420.6 -449.4 -478.3 -507.2 -536.2 -565.3 -594.4 -804.6 -861.4 -918.2 -975.2 -1032.2 -1089.2 -1146.3 -1151.1 -1233.2 -1315.5 -1397.8 -1480.2 -1562.7 -1645.3

1.0 221.6 107.6 -107.4 -306.7 -579.3 -824.6 -1045.8 -1180.9 -1308.6 221.2 109.6 -101.2 -297.0 -478.9 -729.3 -955.2 -1093.4 -1223.9 9.5 500.2 258.2 -199.4 -623.5 -1203.5 -1727.9

4.0

247.1 121.5 -115.3 -335.0 -635.3 -905.8 -1150.1 -1298.7 -1439.6 250.1 127.1 -105.3 -321.2 -521.8 -798.1 -1047.3 -1199.7 -1343.8 10.0 525.4 271.7 -208.0 -652.7 -1260.7 -1810.6

4.5

19

1 2 3 4 5 6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Table 19.4 n = 2, t = 0.2, S = 1000; β = 0.7, k0-kd = const

378 The Analysis of the Exploration of Efficiency of Investment Projects. . .

7 8 9 10 11 12 13 14 15 16 17 18

0.36 0.40 0.44 0.10 0.12 0.16 0.20 0.24 0.30 0.36 0.40 0.44

0.34 0.38 0.42 0.06 0.08 0.12 0.16 0.20 0.26 0.32 0.36 0.40

-1254.7 -1417.0 -1571.0 278.9 144.5 -109.5 -345.6 -564.9 -867.1 -1139.8 -1306.5 -1464.2

-1358.6 -1535.5 -1702.7 307.6 161.8 -118.9 -370.1 -608.1 -936.3 -1232.0 -1418.5 -1584.8

-1463.4 -1654.3 -1834.7 336.3 179.1 -118.3 -394.7 -651.5 -1005.7 -1324.9 -1520.8 -1705.6

-1568.4 -1773.3 -1966.9 365.0 196.3 -122.9 -419.5 -695.1 -1075.3 -1419.3 -1628.3 -1826.7

-1673.5 -1892.5 -2099.3 393.6 218.4 -127.5 -444.3 -738.7 -1145.0 -1511.6 -1735.9 -1947.9

-1778.7 -2011.7 -2231.8 422.1 230.5 -132.1 -469.2 -782.4 -1214.7 -1604.9 -1843.6 -2069.2

-1884.1 -2131.1 -2364.4 450.7 247.6 -136.8 -494.2 -826.1 -1284.6 -1698.3 -1951.4 -2190.7

-1989.5 -2250.6 -2497.1 479.2 264.6 -141.5 -519.2 -869.9 -1354.5 -1791.8 -2059.3 -2312.2

-2094.9 -2370.1 -2629.8 507.8 281.7 -146.2 -544.2 -918.8 -1424.5 -1885.3 -2167.3 -2433.8

-2200.5 -2489.7 -2762.7 536.3 298.7 -151.0 -569.3 -957.7 -1494.5 -1978.9 -2275.3 -2555.5

-2306.1 -2609.4 -2895.6 564.8 315.7 -155.8 -594.4 -1001.6 -1564.6 -2072.5 -2383.4 -2677.2

19.1 The Effectiveness of the Investment Project from the Perspective of. . . 379

380

19

The Analysis of the Exploration of Efficiency of Investment Projects. . .

NPV(L), t = 20%

NPV 1000 1

500

2 0

1

2

3

4

5

6

7

8

9

10 3 11 4

0 -500 -1000

5 -1500 6 7 8 9

L

-2000 -2500 -3000 -3500

Fig. 19.7 Dependence of NPV on leverage level at fixed values of k0 and kd

Thus, we come to conclusion, that for arbitrary duration projects NPV grows with leverage at a credit rate kd < 12 % - 18% and NPV decreases with leverage at a credit rate kd > 12 % - 18% (project remains effective up to leverage levels L = L0, NPV(L0) = 0). Optimum in the dependence of NPV(L ) is absent. 2. At the constant values of kd NPV shows two types of behavior: a) an unlimited growth with leverage, b) NPV reaches maximum at relatively low leverage level (L < 1), then it unlimited descends with leverage. NPV grows with leverage at a credit rate kd < 8 % - 10% and NPV decreases with leverage at a credit rate kd < 8 % - 10% (project remains effective up to leverage levels L = L0, NPV(L0) = 0). All curves NPV(L ) at the constant values of k0 and different values of kd are started (at L = 0) from one point, the higher values of k0 (and higher values of Δk = k0 - kd) correspond to more low-lying curves NPV(L ). Optimum in dependence of NPV(L ) is absent. This is observed for projects of all analyzed duration frames. The first type of dependence of NPV (L ) has a place mainly for pairs of values k0 and kd up to 16%–18%, while the second type—for higher pairs of values k0 and kd and irrespective of the duration of the project.

19.1

The Effectiveness of the Investment Project from the Perspective of. . .

NPV(L), t = 20%

381

NPV 1000 10

500

11 0

1

2

3

4

5

6

7

8

9

10 12 11 13

0 -500

14

-1000

15

-1500

16 17 18

L

-2000 -2500 -3000

Fig. 19.8 Dependence of NPV on leverage level at fixed values of k0 and kd

Thus, for the projects of all analyzed durations the second type of dependence of NPV(L ) has a place for kd = 16 % ; k0 = 18 % ÷ 24 % ; kd = 20 % ; k0 = 24 % ÷ 44 % ; kd = 24 % ; k0 = 30 % ÷ 44 % ; in the case 2-year project another pair (kd = 12 % ; k0 = 14%) is added yet. 3. At the constant values of k0 NPV as well as in case of constant values of Δk = k0 kd shows as an unlimited growth with leverage and unlimited descending with leverage. An analysis of the data leads to the same conclusion, that and, in paragraph 1): at arbitrary duration of project NPV is growing with leverage at the credit rate kd < 18% and NPV decreases with leverage at a credit rate kd < 18% (project remains effective up to leverage levels L = L0, NPV(L0) = 0). It should be noted that this pattern should be taken into account by the Regulator which should regulate normative base in such a way that credit rates, that are associated with central bank basic rate, not exceed, say, 18%. All curves NPV(L) at the constant values of k0 and different values of kd are started (at L = 0) from one point, the higher values of kd (and lower values of Δk = k0 - kd) correspond to more low-lying curves NPV(L ). Optimum in dependence of NPV(L) is absent.

382

19.2 19.2.1

19

The Analysis of the Exploration of Efficiency of Investment Projects. . .

The Effectiveness of the Investment Project from the Perspective of the Owners of Equity and Debt With the Division of Credit and Investment Flows

At a constant investment value (I = const) For NPV in this case the following expression has been obtained (Brusov et al. 2011a, b, c; 2012a, b; 2013a, b; 2014a, b)  NPV = - I 1-



 NOIð1 - t Þ 1 Lt 1 þ ð19:5Þ 11ke 1þL ð1 þ kd Þn ð 1 þ k e Þn

Dependence of NPV on leverage level at fixed values of k0 and kd at a constant investment value (I = const) is shown in Table 19.5 and Figs. 19.9 and 19.10. 1. At the constant values of Δk = k0 - kd NPV, as a rule, reaches an optimum at relatively low leverage level (L < 1), then decreases with leverage. All curves NPV(L ) for the same values of k0 are started at the same point, but with growth of Δk = k0 - kd (respectively, decreasing of kd) they are shifted into region of lower values of NPV, and descending speed decreases with leverage and for not too high values of k0 and kd curves NPV(L) practically output into saturation regime. For higher values of k0 and kd saturation regime does not occur and after optimum (sometimes, but more seldom, without optimum) falling trend is still present. 2. At the constant values of k0 NPV practically always decreases with leverage, very rarely only (for individual values of k0 and kd) demonstrating the presence of optimum at low leverage levels (L < 1) (it should be noted that, with the increase of the duration of the project the number of curves NPV(L ) having optimum is growing, while remaining to be not very large). All curves NPV(L ) at the constant values of k0 and different values of kd are started (at L = 0) from one point, the higher values of kd (and lower values of Δk = k0 - kd) correspond to higher lying curves NPV(L ). Descending speed decreases with leverage. 3. At the constant values of kd NPV practically always decreases with leverage, and the existence of optimum at low levels leverage (L < 1) is a rare exception. All curves NPV(L ) at the constant values of k0 and different values of kd are started (at L = 0) from one point, the higher values of k0 (and higher values of Δk = k0 kd) correspond to lower lying curves NPV(L ). Descending speed increases with leverage. At a constant equity value (S = const) For NPV in this case the following expression has been obtained (Brusov et al. 2011a, b, c; 2012a, b; 2013a, b; 2014a, b)

1 2 3 4 5 6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

k0 0.08 0.10 0.14 0.18 0.24 0.30 0.36 0.40 0.44 0.10 0.12 0.16 0.20 0.24 0.30 0.36 0.40 0.44 k0 0.08 0.10 0.14 0.18 0.24 0.30

kd\L 0.06 0.08 0.12 0.16 0.22 0.28 0.34 0.38 0.42 0.06 0.08 0.12 0.16 0.20 0.26 0.32 0.36 0.40 kd\L 0.06 0.08 0.12 0.16 0.22 0.28

0.0 711.9 666.6 580.9 503.0 398.5 306.5 225.0 175.6 129.7 666.6 622.6 541.1 466.2 398.5 306.5 225.0 175.6 129.7 5.0 560.0 543.7 498.4 455.9 391.7 336.3

5.5 544.9 525.7 488.2 448.2 386.6 334.0

0.5 700.7 660.2 581.9 510.6 414.0 328.6 251.3 206.1 163.0 635.3 596.5 524.3 456.8 396.6 318.4 237.9 193.9 151.7 6.0 530.1 512.5 478.0 440.4 381.5 331.5

1.0 686.2 649.4 576.5 509.8 418.6 337.3 264.7 221.0 179.5 602.0 567.1 501.8 441.5 385.1 308.1 238.8 197.2 157.5 6.5 515.5 499.5 468.0 432.6 376.3 328.9

Table 19.5 n = 2, t = 0.2, NOI = 1200; I = 1000, k0-kd = const 1.5 670.6 637.0 568.5 505.7 418.9 340.6 272.0 229.6 189.5 568.7 537.1 477.7 422.5 370.2 298.0 234.1 194.7 157.1 7.0 501.1 486.6 458.0 424.9 371.1 326.2

2.0 654.6 623.9 559.4 499.9 417.1 344.0 276.4 235.1 196.1 536.1 507.3 453.2 402.5 353.8 285.9 226.8 189.3 153.7 7.5 487.0 474.0 448.1 417.2 365.9 323.4

2.5 638.5 610.5 549.6 493.4 414.0 344.2 279.0 236.2 200.7 504.4 478.2 428.8 382.2 336.9 275.8 218.2 179.9 148.5 8.0 473.1 461.5 438.3 409.6 360.7 320.7

3.0 622.4 597.0 539.5 486.3 410.2 343.5 280.5 238.8 204.3 473.6 449.9 404.8 362.1 319.7 263.0 208.7 172.2 142.4 8.5 459.4 449.2 428.6 402.0 355.4 317.8

3.5 606.5 583.6 529.3 478.9 406.0 342.3 281.3 240.6 207.0 443.9 422.4 381.4 342.1 302.6 249.9 198.8 164.0 135.6 9.0 445.9 437.1 419.0 394.4 350.2 315.0

4.0 590.8 570.2 519.0 471.3 401.4 340.6 281.6 242.0 209.1 415.2 395.7 358.4 322.5 285.6 236.7 188.6 155.5 128.5 9.5 432.7 425.1 409.5 386.9 345.0 312.1

The Effectiveness of the Investment Project from the Perspective of. . . (continued)

4.5 575.3 556.9 508.7 463.7 396.6 338.6 283.5 242.9 210.9 387.5 369.9 336.1 303.2 268.9 223.6 178.3 146.7 121.1 10.0 419.7 418.4 400.1 379.5 339.8 309.2

19.2 383

7 8 9 10 11 12 13 14 15 16 17 18

k0 0.36 0.40 0.44 0.10 0.12 0.16 0.20 0.24 0.30 0.36 0.40 0.44

kd\L 0.34 0.38 0.42 0.06 0.08 0.12 0.16 0.20 0.26 0.32 0.36 0.40

Table 19.5 (continued)

5.0 284.4 243.5 212.4 360.7 344.9 314.4 284.4 252.4 210.6 168.0 137.9 118.6

5.5 280.7 244.0 218.6 334.8 320.6 293.2 266.0 236.2 197.7 155.9 129.0 106.0

6.0 280.0 244.2 214.6 309.8 297.2 272.7 248.1 220.4 185.0 145.7 120.2 98.3

6.5 279.1 244.3 215.5 285.6 274.5 252.7 230.6 204.9 172.5 140.4 111.3 90.7

7.0 278.2 244.3 216.3 262.2 252.5 233.3 218.5 189.7 160.1 127.2 102.6 83.0

7.5 277.2 244.2 217.0 239.6 231.1 214.4 196.8 174.9 148.0 117.2 93.9 75.4

8.0 276.1 244.0 217.6 217.7 210.5 196.0 180.5 160.3 136.1 107.4 85.2 67.9

8.5 274.9 243.7 218.2 196.5 190.4 178.1 164.6 146.1 124.4 97.7 76.7 60.4

9.0 273.7 243.4 218.6 176.0 171.0 160.8 149.1 132.2 112.9 88.1 68.3 53.0

9.5 272.5 243.1 219.1 156.1 152.2 143.9 134.0 118.6 101.6 78.7 59.9 45.6

10.0 271.2 242.7 219.4 136.9 133.9 127.4 119.3 105.3 90.5 69.4 51.7 38.3

384 19 The Analysis of the Exploration of Efficiency of Investment Projects. . .

19.2

The Effectiveness of the Investment Project from the Perspective of. . .

385

NPV(L), t = 20%

NPV 800

1 2

700 600

3 4

500

5

400

6

300

7

200

8 9

100

0

1

2

3

4

5

6

7

8

9

10

11

0

L Fig. 19.9 Dependence of NPV on leverage level at fixed values of k0 and kd




NPV = - S 1 þ L - tL 1
 1-

1 ð1 þ k e Þn



1 ð1 þ k d Þn

 þ

βSð1 þ LÞð1 - t Þ ke ð19:6Þ

Dependence of NPV on leverage level at fixed values of k0 and kd at a constant equity value (S = const) is shown in Table 19.6 and Figs. 19.11 and 19.12. 1. At the constant values of Δk = k0 - kd NPV always decreases with leverage (existence of an optimum (at relatively low leverage level (L < 1)), practically has not been observed. All curves NPV(L) for the same values of k0 are started at the same point, but with growth of k0 (and, respectively, growth of kd) they are shifted into region of lower values of NPV, and descending speed increases with leverage. The values of Δk = k0 - kd, equal to 2%; 4%; 6%; and 10% have been used. With growth of Δk = k0 - kd a narrowing of NPV(L ) curve cluster takes place (the width of cluster is decreased), the difference between curvers becomes less and less, and at Δk = 10% curve cluster is practically transformed into one wide

386

The Analysis of the Exploration of Efficiency of Investment Projects. . .

19

NPV(L), t = 20%

NPV 700

10 11

600

12 500

13 14

400

15

300

16

200

17 18

100

0

1

2

3

4

5

6

7

8

9

10

11

0

L Fig. 19.10 Dependence of NPV on leverage level at fixed values of k0 and kd

line. The marked pattern has a place for projects of all examined duration projects (2, 5, 7, and 10 years). 2. At the constant values of k0 NPV always decreases with leverage. All curves NPV (L ) for the same values of k0 are started at the same point, but with growth of kd (and, respectively, decrease of Δk = k0 - kd) they are shifted into region of higher values of NPV, and descending speed decreases with leverage. The width of the NPV(L ) curves cluster is decreased with increase of the duration of the project. 3. At the constant values of k0 NPV always decreases with leverage. All curves NPV (L ) for the same values of k0 are started at the same point, but with growth of k0 (and, respectively, increase of Δk = k0 - kd) they are shifted into region of lower values of NPV, and descending speed increases with leverage. The width of the NPV(L ) curves cluster is decreased with increase of the duration of the project.

1 2 3 4 5 6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

k0 0.08 0.10 0.14 0.18 0.24 0.30 0.36 0.40 0.44 0.10 0.12 0.16 0.20 0.24 0.30 0.36 0.40 0.44 k0 0.08 0.10 0.14 0.18 0.24 0.30

kd\L 0.0 0.06 -1.4 0.08 -27.8 0.12 -77.8 0.16 -123.2 0.22 -184.2 0.28 -237.9 0.34 -285.4 0.38 -314.2 0.42 -341.0 -27.8 0.06 0.08 -53.5 0.12 -101.1 0.16 -144.7 0.20 -184.2 0.26 -237.9 0.32 -285.4 0.36 -314.2 0.40 -341.0 kd\L 5.0 0.06 -494.2 0.08 -537.5 0.12 -671.0 0.16 -797.3 0.22 -992.4 0.28 -1160.4

5.5 -591.7 -649.7 -764.3 -891.4 -1092.0 -1263.4

0.5 -7.3 -41.4 -107.4 -167.5 -249.1 -321.3 -386.7 -424.8 -461.4 -64.5 -97.1 -157.8 -214.6 -265.3 -335.4 -399.1 -436.2 -471.9 6.0 -697.1 -752.6 -863.3 -990.0 -1194.8 -1368.4

1.0 -23.6 -63.8 -143.9 -217.2 -317.6 -407.4 -487.6 -535.9 -581.9 -121.8 -159.8 -231.0 -296.8 -358.6 -443.1 -519.3 -565.0 -608.7

1.5 2.0 2.5 3.0 3.5 -50.0 -86.1 -131.8 -186.8 -250.8 -94.9 -134.4 -182.1 -237.9 -301.5 -187.3 -237.3 -294.0 -357.0 -426.4 -272.2 -332.3 -397.5 -467.8 -542.9 -389.7 -465.4 -544.7 -627.4 -718.6 -496.3 -583.0 -674.4 -767.7 -862.9 -589.6 -692.5 -796.5 -901.4 -1007.3 -647.5 -759.5 -877.3 -990.8 -1104.8 -702.4 -822.9 -943.5 -1064.0 -1184.7 -198.6 -293.5 -405.7 -534.0 -677.6 -240.6 -338.4 -452.2 -581.2 -724.6 -319.7 -423.1 -540.6 -671.4 -814.8 -393.4 -502.8 -624.4 -757.7 -902.1 -463.6 -579.9 -706.9 -844.3 -991.6 -560.7 -688.0 -818.1 -960.5 -1111.1 -647.0 -782.0 -924.2 -1073.2 -1229.0 -700.4 -842.1 -995.4 -1150.0 -1310.5 -751.3 -899.4 -1053.0 -1212.0 -1376.1 6.5 7.0 7.5 8.0 8.5 9.0 -810.2 -930.6 -1058.3 -1193.0 -1334.6 -1482.9 -862.5 -979.1 -1102.3 -1232.0 -1367.9 -1510.0 -967.9 -1077.9 -1193.3 -1314.0 -1439.8 -1570.7 -1093.1 -1200.7 -1312.5 -1428.6 -1548.9 -1673.4 -1300.8 -1410.0 -1522.3 -1637.8 -1756.3 -1877.8 -1475.2 -1583.8 -1694.4 -1806.8 -1921.0 -2037.0

Table 19.6 n = 2, t = 0.2, S = 1000; β = 0.7, k0-kd = const 4.0 -323.5 -372.8 -501.9 -623.0 -803.2 -960.2 -1114.3 -1219.3 -1305.3 -835.6 -881.6 -970.3 -1057.2 -1148.5 -1269.5 -1391.2 -1476.8 -1545.3 9.5 -1637.7 -1658.0 -1706.5 -1801.8 -2002.3 -2154.9

The Effectiveness of the Investment Project from the Perspective of. . . (continued)

4.5 -404.7 -451.5 -583.5 -707.8 -896.1 -1059.3 -1216.1 -1334.3 -1426.0 -1007.3 -1051.5 -1137.3 -1222.4 -1314.5 -1435.4 -1559.8 -1648.7 -1719.4 10.0 -1798.8 -1811.9 -1847.2 -1934.3 -2129.7 -2274.5

19.2 387

7 8 9 10 11 12 13 14 15 16 17 18

k0 0.36 0.40 0.44 0.10 0.12 0.16 0.20 0.24 0.30 0.36 0.40 0.44

kd\L 0.34 0.38 0.42 0.06 0.08 0.12 0.16 0.20 0.26 0.32 0.36 0.40

5.0 -1320.0 -1449.8 -1546.7 -1191.8 -1233.5 -1315.2 -1397.5 -1489.3 -1608.7 -1734.5 -1826.0 -1898.3

Table 19.6 (continued)

5.5 -1441.0 -1565.7 -1667.4 -1388.5 -1427.2 -1503.5 -1581.9 -1672.5 -1789.0 -1922.0 -2008.5 -2082.0

6.0 -1551.9 -1682.1 -1788.2 -1596.8 -1631.8 -1701.8 -1775.2 -1863.9 -1976.2 -2108.6 -2196.3 -2270.2

6.5 -1663.7 -1799.0 -1909.0 -1816.0 -1846.9 -1909.6 -1977.2 -2063.1 -2169.9 -2279.8 -2389.1 -2463.0

7.0 -1776.6 -1916.3 -2029.8 -2045.5 -2071.9 -2126.4 -2187.4 -2269.8 -2370.1 -2491.2 -2586.7 -2660.1

7.5 -1890.4 -2034.1 -2150.6 -2284.9 -2306.4 -2352.0 -2405.4 -2483.7 -2576.4 -2694.0 -2789.2 -2861.5

8.0 -2005.2 -2152.4 -2271.5 -2533.7 -2549.9 -2585.8 -2631.1 -2704.6 -2788.8 -2902.0 -2996.3 -3067.1

8.5 -2120.9 -2271.2 -2392.4 -2791.3 -2801.9 -2827.5 -2864.1 -2932.2 -3006.9 -3115.0 -3207.9 -3276.7

9.0 -2237.6 -2390.5 -2518.3 -3057.4 -3062.1 -3076.8 -3104.0 -3166.3 -3230.7 -3332.9 -3424.0 -3490.4

9.5 -2355.3 -2510.2 -2634.2 -3331.6 -3330.1 -3333.3 -3350.7 -3406.6 -3459.9 -3555.6 -3644.3 -3708.0

10.0 -2473.9 -2630.3 -2755.2 -3618.4 -3605.5 -3596.8 -3603.9 -3653.0 -3694.4 -3782.8 -3868.9 -3929.4

388 19 The Analysis of the Exploration of Efficiency of Investment Projects. . .

19.2

The Effectiveness of the Investment Project from the Perspective of. . .

389

NPV(L), t = 20% 0

1

2

3

4

5

6

7

8

9

11

10

NPV 0

-500

-1000

-1500 1 2 3 4 5 6 7 8 9

-2000

-2500

-3000

L Fig. 19.11 Dependence of NPV on leverage level at fixed values of k0 and kd

19.2.2

Without Flows Separation

At a constant investment value (I = const) For NPV in this case the following expressions have been obtained (Brusov et al. 2011a, b, c; 2012a, b; 2013a, b; 2014a, b)

390

19

The Analysis of the Exploration of Efficiency of Investment Projects. . .

NPV(L), t = 20% 0

1

2

3

4

5

6

7

8

9

11

10

NPV 0 -500 -1000 -1500 -2000 -2500 -3000

10 11 12 13 14 15 16 17 18

-3500 -4000 -4500

L Fig. 19.12 Dependence of NPV on leverage level at fixed values of k0 and kd

NPV = - I þ


 NOIð1 - t Þ þ kd Dt 1 1WACC ð1 þ WACCÞn 0

1

NOIð1 - t Þ þ kd Dt B 1  n C   @1 -  A L L 1 þ k0 1 - γ 1þL k0 1 - γ 1þL 2 13 0 L kd t 1 7 6 1 þ L  B1 -   n C NPV = - I 41 -  A5 þ @ L L 1 þ k0 1 - γ 1þL t t k0 1 - γ 1þL 1 0 NPV = - I þ

þ

ð19:7Þ

NOIð1 - t Þ B 1  n C   @1 -  A: L L 1 þ k0 1 - γ 1þL t k0 1 - γ t 1þL

Dependence of NPV on leverage level at fixed values of k0 and kd at a constant investment value (I = const) is shown in Table 19.7 and Figs. 19.13 and 19.14.

1 2 3 4 5 6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

k0 0.08 0.10 0.14 0.18 0.24 0.30 0.36 0.40 0.44 0.10 0.12 0.16 0.20 0.24 0.30 0.36 0.40 0.44 k0 0.08 0.10 0.14 0.18 0.24 0.30

kd\L 0.06 0.08 0.12 0.16 0.22 0.28 0.34 0.38 0.42 0.06 0.08 0.12 0.16 0.20 0.26 0.32 0.36 0.40 kd\L 0.06 0.08 0.12 0.16 0.22 0.28

0.0 711.9 666.6 580.9 503.0 398.5 306.5 225.0 175.6 129.7 666.6 622.6 541.1 466.2 398.5 306.5 225.0 175.6 129.7 5.0 762.0 731.4 670.5 618.9 535.3 465.1

5.5 762.8 731.4 671.9 615.7 537.5 467.7

0.5 731.8 692.1 615.9 546.2 451.5 367.3 291.2 246.0 203.1 686.0 647.4 575.2 507.9 447.3 363.6 287.9 243.0 200.3 6.0 763.5 732.3 673.1 617.2 539.4 470.0

1.0 741.8 705.0 633.9 568.4 478.8 398.7 326.7 283.0 241.7 695.8 660.0 592.7 530.4 472.4 393.1 321.6 278.3 237.4 6.5 764.1 733.0 674.2 618.6 541.1 471.9

Table 19.7 n = 2, t = 0.2, NOI = 1200; I = 1000, k0-kd = const 1.5 747.8 712.9 644.7 581.9 495.5 417.7 348.5 305.8 265.6 701.8 667.6 603.2 543.6 487.7 411.0 342.3 300.1 260.2 7.0 764.6 733.7 675.1 619.7 542.5 473.6

2.0 751.9 718.1 652.0 590.9 506.8 431.7 363.2 321.2 281.7 705.7 672.7 610.3 552.4 498.0 423.0 356.3 314.8 275.8 7.5 765.1 734.3 675.9 620.7 543.8 475.1

2.5 754.8 721.9 657.3 597.5 514.9 441.1 373.8 331.5 293.4 708.6 676.3 615.4 558.8 505.5 432.8 366.3 324.5 287.0 8.0 765.5 734.8 676.7 621.7 544.9 476.5

3.0 757.0 724.7 661.2 602.4 521.0 448.3 381.8 340.0 302.3 710.7 679.1 619.3 563.6 511.1 439.5 373.9 332.7 295.5 8.5 765.8 735.3 677.3 622.5 546.0 477.7

3.5 758.6 726.9 664.3 606.2 525.7 453.9 388.1 346.7 309.2 712.4 681.2 622.3 567.3 515.4 444.7 379.9 339.1 302.1 9.0 766.1 735.7 677.9 623.2 546.9 478.7

4.0 760.0 728.7 666.7 609.3 529.5 458.4 393.1 352.1 314.8 718.7 682.9 624.7 570.3 518.9 448.9 384.6 344.2 307.4 9.5 766.4 736.0 678.4 623.9 547.7 479.7

The Effectiveness of the Investment Project from the Perspective of. . . (continued)

4.5 761.1 730.2 668.8 611.8 532.7 462.0 397.6 356.6 319.4 714.8 684.3 626.6 572.8 521.8 452.3 388.5 348.4 311.8 10.0 766.7 736.4 678.9 624.5 548.5 480.6

19.2 391

7 8 9 10 11 12 13 14 15 16 17 18

k0 0.36 0.40 0.44 0.10 0.12 0.16 0.20 0.24 0.30 0.36 0.40 0.44

kd\L 0.34 0.38 0.42 0.06 0.08 0.12 0.16 0.20 0.26 0.32 0.36 0.40

Table 19.7 (continued)

5.0 401.3 360.2 323.2 715.7 685.5 628.3 574.8 524.2 455.2 391.8 351.9 315.5

5.5 403.6 363.4 326.4 716.5 686.5 629.7 576.6 526.2 457.6 394.1 354.9 318.6

6.0 406.1 366.1 329.2 717.2 687.3 630.9 578.1 528.0 459.7 396.6 357.5 321.3

6.5 408.3 368.4 331.7 717.7 688.1 631.9 579.4 529.5 461.6 399.7 359.7 323.6

7.0 410.2 370.5 333.8 718.2 688.7 632.8 580.5 530.8 463.2 400.8 361.7 325.7

7.5 411.8 372.3 335.7 718.7 689.3 633.6 581.5 532.0 464.6 402.4 363.4 327.5

8.0 418.3 373.9 337.4 719.1 689.8 634.3 582.4 533.0 465.8 403.8 364.9 329.1

8.5 414.7 375.3 338.9 719.4 690.2 634.9 583.2 533.9 466.9 405.1 366.3 330.5

9.0 415.9 376.6 340.2 719.8 690.7 635.5 583.9 534.8 467.9 406.3 367.5 331.8

9.5 417.0 377.8 341.4 720.0 691.0 636.0 584.6 535.5 468.9 407.3 368.7 333.0

10.0 418.0 378.9 342.6 720.3 691.4 636.5 585.2 536.2 469.7 408.2 369.7 334.0

392 19 The Analysis of the Exploration of Efficiency of Investment Projects. . .

19.2

The Effectiveness of the Investment Project from the Perspective of. . .

393

NPV(L), t = 20%

NPV 900

800

1 2

700

3 4

600

5 500

6 7 8 9

400 300 200 100

0

1

2

3

4

5

6

7

8

9

10

11

0

L Fig. 19.13 Dependence of NPV on leverage level at fixed values of k0 and kd

1. At the constant values of Δk = k0 - kd NPV demonstrates a limited growth with leverage with output into saturation regime. The main increase in NPV occurs at small values of leverage levels L ≤ 3 ÷ 4. With growth of k0 (and kd) the сurves NPV(L ) are lowered. Optimum in the dependence of NPV(L ) is absent. 2. At the constant values of k0 NPV demonstrates a limited growth with leverage with output into saturation regime. The main increase in NPV occurs at low values of leverage levels L ≤ 4 ÷ 5. All curves NPV(L ) at the constant values of k0 and different values of kd are started (at L = 0) from one point, the higher values of kd (and, respectively, the lower values of Δk = k0 - kd correspond to higher lying curves NPV(L ). This distinguishes this case from consideration from the point of view of equity capital owners, where ordering of curves NPV(L ) with growth of kd is an opposite. Optimum in the dependence of NPV(L ) is absent. With growth of project duration the distance between curves NPV(L ), corresponding to different pairs of values k0 and kd, increases. 3. At the constant values of kd NPV growth with leverage with output into saturation regime. All curves NPV(L) at the constant values of k0 and different values of kd are started (at L = 0) from one point, the higher values of k0 (and, respectively, the higher values of Δk = k0 - kd correspond to lower lying curves NPV(L ). With the

394

19

The Analysis of the Exploration of Efficiency of Investment Projects. . .

NPV(L), t = 20%

NPV 800 10 11

700

12

600

13 14

500

15 16 17 18

400 300 200 100 0

0

1

2

3

4

5

6

7

8

9

10

11

L Fig. 19.14 Dependence of NPV on leverage level at fixed values of k0 and kd

growth of Δk = k0 - kd the distance between curves NPV(L ), corresponding to different pairs of values k0 and kd, decreases. Optimum in the dependence of NPV(L ) is absent. At a constant equity value (S = const) For NPV in this case the following expression has been obtained (Brusov et al. 2011a, b, c; 2012a, b; 2013a, b, 2014a, b) 
 1 k Lt þ 1NPV = - S 1 þ L - d WACC ð1 þ WACCÞn
 βSð1 þ LÞð1 - t Þ 1 : 1þ WACC ð1 þ WACCÞn

ð19:8Þ

Dependence of NPV on leverage level at fixed values of k0 and kd at a constant equity value (S = const) is shown in Table 19.8 and Figs. 19.15 and 19.16. 1. At the constant values of Δk = k0 - kd NPV shows as an unlimited growth with leverage and unlimited descending with leverage. There is a boundary credit rate value, which separates the growth of NPV with leverage from descending of NPV

1 2 3 4 5 6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

k0 0.08 0.10 0.14 0.18 0.24 0.30 0.36 0.40 0.44 0.10 0.12 0.16 0.20 0.24 0.30 0.36 0.40 0.44 k0 0.08 0.10 0.14 0.18 0.24 0.30

kd\L 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.06 -1.4 19.8 41.1 62.5 83.9 105.3 126.8 0.08 -27.8 -18.6 1.0 15.6 30.3 45.1 59.9 0.12 -77.8 -77.7 -77.0 -76.1 -75.1 -74.0 -72.9 0.16 -123.2 -136.4 -148.8 -160.8 -172.6 -184.3 -196.0 0.22 -184.2 -216.3 -247.1 -277.3 -307.3 -337.1 -366.8 0.28 -237.9 -287.3 -335.2 -382.5 -427.6 -473.6 -519.5 0.34 -285.4 -351.6 -414.4 -476.2 -537.6 -598.7 -659.6 0.38 -314.2 -389.7 -462.5 -534.1 -605.1 -677.6 -748.0 0.42 -341.0 -426.0 -508.0 -588.6 -668.7 -748.3 -827.7 -27.8 -20.4 -12.7 -5.1 2.7 10.4 18.2 0.06 0.08 -53.5 -52.8 -51.9 -50.9 -49.9 -48.8 -47.6 0.12 -101.1 -118.6 -125.5 -137.3 -148.9 -160.5 -172.0 0.16 -144.7 -170.2 -193.6 -217.4 -241.0 -264.6 -288.1 0.20 -184.2 -221.2 -257.1 -292.6 -327.8 -362.9 -397.9 0.26 -237.9 -291.7 -344.2 -396.1 -447.8 -496.9 -547.6 0.32 -285.4 -355.6 -422.6 -488.7 -554.4 -619.8 -685.1 0.36 -314.2 -393.4 -470.1 -545.7 -620.8 -697.6 -772.2 0.40 -341.0 -429.5 -515.1 -599.6 -683.5 -767.0 -850.3 kd\L 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 0.06 212.6 234.0 255.5 277.0 298.5 319.9 341.4 362.9 0.08 119.1 130.1 144.6 159.1 173.6 188.1 202.6 217.1 0.12 -68.2 -67.0 -65.8 -64.6 -63.3 -62.1 -60.9 -59.6 0.16 -242.3 -253.8 -265.3 -276.8 -288.3 -299.8 -311.3 -322.8 0.22 -485.2 -514.8 -544.3 -573.8 -603.3 -632.8 -662.3 -691.8 0.28 -702.3 -747.9 -793.5 -839.0 -884.6 -930.1 -975.6 -1021.1

Table 19.8 n = 2, t = 0.2, S = 1000; β = 0.7, k0-kd = const 3.5 4.0 148.2 169.7 74.7 89.5 -71.8 -70.6 -207.6 -219.2 -396.5 -426.1 -565.3 -611.0 -720.4 -781.2 -818.3 -888.5 -906.9 -986.0 26.0 33.7 -46.5 -45.4 -183.5 -195.0 -311.5 -334.9 -432.9 -467.8 -598.2 -648.7 -750.3 -815.5 -846.6 -920.9 -933.4 -1016.4 9.0 9.5 384.3 405.8 231.6 246.1 -58.4 -57.2 -334.2 -345.7 -721.3 -750.7 -1066.6 -1112.1

The Effectiveness of the Investment Project from the Perspective of. . . (continued)

191.1 104.3 -69.4 -230.7 -455.7 -656.7 -840.5 -958.6 -1065.1 41.5 -44.2 -206.5 -358.3 -502.7 -699.2 -880.5 -995.2 -1099.3 10.0 427.3 260.6 -55.9 -357.2 -780.2 -1157.6

4.5

19.2 395

7 8 9 10 11 12 13 14 15 16 17 18

k0 0.36 0.40 0.44 0.10 0.12 0.16 0.20 0.24 0.30 0.36 0.40 0.44

kd\L 0.34 0.38 0.42 0.06 0.08 0.12 0.16 0.20 0.26 0.32 0.36 0.40

Table 19.8 (continued)

5.0 -900.1 -1028.7 -1144.0 49.3 -43.1 -218.0 -381.6 -537.5 -749.6 -945.6 -1069.4 -1182.2

5.5 -963.2 -1098.7 -1222.9 57.1 -41.9 -229.4 -405.0 -572.4 -800.1 -1012.2 -1143.6 -1265.0

6.0 -1023.8 -1168.7 -1301.8 64.9 -40.7 -240.9 -428.3 -607.2 -850.5 -1077.2 -1217.8 -1347.8

6.5 -1084.3 -1238.6 -1380.6 72.7 -39.6 -252.3 -451.7 -642.0 -900.9 -1137.5 -1291.9 -1430.6

7.0 -1144.9 -1308.6 -1459.4 80.5 -38.4 -263.8 -475.0 -676.8 -951.3 -1205.5 -1366.0 -1518.3

7.5 -1205.5 -1378.5 -1538.2 88.2 -37.2 -275.2 -498.3 -711.6 -1001.6 -1270.4 -1440.1 -1596.0

8.0 -1266.0 -1448.4 -1617.0 96.0 -36.1 -286.6 -521.6 -746.5 -1052.0 -1335.4 -1514.2 -1678.7

8.5 -1326.5 -1518.3 -1695.7 103.8 -34.9 -298.1 -544.9 -781.2 -1102.3 -1400.3 -1588.3 -1761.4

9.0 -1387.0 -1588.2 -1774.4 111.6 -33.7 -309.5 -568.3 -816.0 -1152.7 -1465.2 -1662.4 -1844.1

9.5 -1447.5 -1658.1 -1853.2 119.4 -32.6 -320.9 -591.6 -850.8 -1203.0 -1530.1 -1736.4 -1926.7

10.0 -1508.1 -1727.9 -1931.9 127.2 -31.4 -332.4 -614.9 -885.6 -1253.4 -1595.0 -1810.5 -2009.4

396 19 The Analysis of the Exploration of Efficiency of Investment Projects. . .

19.2

The Effectiveness of the Investment Project from the Perspective of. . .

397

NPV(L), t = 20%

NPV 1000 500

1 2 0

1

2

3

4

5

6

7

8

9

10

3 4

11

0 -500

5 6 7

-1000 -1500

8 9

-2000 -2500

L Fig. 19.15 Dependence of NPV on leverage level at fixed values of k0 and kd

with leverage. This rate depends on the values Δk = k0 - kd, equal to 2%, 4%, 6%, and 10%, weakly depends on project duration and are within region 8–20%. Thus, we come to conclusion, that for arbitrary duration projects NPV grows with leverage at a credit rate kd < 8 % - 20% and NPV decreases with leverage at a credit rate kd > 8 % - 20% (project remains effective up to leverage levels L = L0, NPV(L0) = 0). Optimum in the dependence of NPV(L ) is absent. 2. At the constant values of k0 (similar to the case of Δk = k0 - kd) NPV shows as an unlimited growth with leverage and unlimited descending with leverage. 3. All curves NPV(L ) at the constant values of k0 and different values of kd are started (at L = 0) from one point, the higher values of kd (and lower values of Δk = k0 - kd) correspond to higher lying curves NPV(L ). Optimum in dependence of NPV(L ) is absent. 4. At the constant values of kd NPV as well as in case of constant values of Δk = k0 kd shows as an unlimited growth with leverage and unlimited descending with leverage. There is a boundary credit rate value, which separates the growth of NPV with leverage from descending of NPV with leverage. This rate depends on the values Δk = k0 - kd, equal to 2%, 4%, 6%, and 10%, weakly depends on project duration and is within region 8%–20%. Thus, we come to conclusion, that for arbitrary duration projects NPV grows with leverage at a credit rate kd < 8 % -

398

19

The Analysis of the Exploration of Efficiency of Investment Projects. . .

NPV(L), t = 20%

0

1

2

3

4

5

6

NPV 500

7

8

9

10

10 11

11

0

12 13 14

-500

-1000

15 16

-1500

17 18

-2000

-2500

L Fig. 19.16 Dependence of NPV on leverage level at fixed values of k0 and kd

20% and NPV decreases with leverage at a credit rate kd > 8 % - 20% (project remains effective up to leverage levels L = L0, NPV(L0) = 0). Optimum in the dependence of NPV(L) is absent.

19.3

19.3.1

The Elaboration of Recommendations on the Capital Structure of Investment of Enterprises, Companies, Taking into Account all the Key Financial Parameters of Investment Project General Conclusions and Recommendations on the Definition of Capital Structure of Investment of Enterprises

As indicates the dependence NPV(L ) at different I, NOI, S, β, the changing of first two parameters, as a rule, leads to the shift of curves NPV(L ) in the vertical direction

19.3

The Elaboration of Recommendations on the Capital Structure of. . .

399

only (parallel offset), without changing of characteristic points of these curves, of type L* (value of L, where NPV(L) reaches optimum (if available). Only the maximum permissible leverage level L0 is changed (in case of descending of NPV with leverage). This opens the way for tabulation of the results obtained in the case of constant value of investment. In other words, this fact is the basis for the use of our tables and graphs to estimate the optimal debt level for the investor. Thus, obtained by us tables and graphs allows to determine the value of L*, knowing only k0 and kd for investment project. kd- is the credit rate, which is determined by creditor, but determination of parameter k0 is always a complicate problem. This has been noted by several researchers, and we can also add that the parameter k0 is one of the most important parameter in both used theories Modigliani–Miller (Modigliani and Miller 1958, 1963, 1966) and Brusov–Filatova–Orekhova (Brusov et al. 2011a, b, c; 2012a, b; 2013a, b; 2014a, b; Filatova et al. 2008). In contrast to the parameters I, NOI a change of parameters S, β, both individually and simultaneously, can significantly change the nature of the curves NPV(L ), i.e., the dependence of NPV on the leverage level. Thus, with change of β NPV(L ) can be changed from decreasing functions to function, having an optimum. Such studies have been conducted on the example of “Nastcom Plus” company. This means the inability of tabulation of the results obtained in the case of constant value of equity capital S: in this case, one will need to use the formulas we have received to determine the NPV at the existing level leverage, as well as to optimizing the existing investment structure. In the case of a constant invested capital I with the division of flows (with using of two discount rates) in the case of finite duration projects the descending of NPV with leverage is possible, as well as the existence of optimum. Without flows separation a moderate growth of NPV(L )—output to saturation has been observed. This indicates the limitations of the approach associated with the use of a single discount rate, which veils different variants of the NPV(L ) dependence at different cost of equity and borrowed capital. At constant equity value S with using of one discount rate (WACC approximation) one has either growth or decrease of NPV depending on credit rate kd. We have found the boundary rates kd, determining transition from growth to decrease of NPV. Because application of two discount rates (at flow separation) demonstrates the existence of optimum in this case, WACC approximation changes the type of dependence of NPV(L ). Thus, one can make the following general recommendations: 1. It is necessary to use an assessment of the efficiency of investment projects with flows separation. 2. In the case of a constant value of investment I a tabulation of the obtained results is possible, i.e., one can use obtained by us tables and graphs to estimate the optimal for investor level of borrowing. Thus, obtained by us tables and graphs allows to determine value of L*, knowing only k0 and kd for investment project.

400

19

The Analysis of the Exploration of Efficiency of Investment Projects. . .

3. At a constant equity value S as well as to determine the NPV at the existing level leverage, and to estimate the optimal for investor level of borrowing received by us analytical expressions (formulas) should be used because the behavior of NPV (L ) in this case depends strongly on S and β.

References Brusov P, Filatova T, Orehova N, Brusova A (2011a) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Appl Financ Econ 21(11): 815–824 Brusov P, Filatova T, Orehova N et al (2011b) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Business ICT 2:16–21 Brusov P, Filatova T, Orehova N et al (2011c) Influence of debt financing on the effectiveness of the investment project within the Modigliani–Miller theory. Res J Econ Business and ICT 2:11–15 Brusov P, Filatova T, Eskindarov M, Orehova N (2012a) Influence of debt financing on the effectiveness of the finite duration investment project. Appl Financ Econ 22(13):1043–1052 Brusov P, Filatova T, Eskindarov M, Orehova N (2012b) Hidden global causes of the global financial crisis. J Rev Glob Econ 1:106–111 Brusov P, Filatova P, Orekhova N (2013a) Absence of an optimal capital structure in the famous tradeoff theory! J Rev Glob Econ 2:94–116 Brusov P, Filatova T, Orehova N (2013b) A qualitatively new effect in corporative finance: abnormal dependence of cost of equity of company on leverage. J Rev Glob Econ 2:183–193 Brusov P, Filatova P, Orekhova N (2014a) Mechanism of formation of the company optimal capital structure, different from suggested by trade off theory. Cogent Econ Finance 2:1–13. https://doi. org/10.1080/23322039.2014.946150 Brusov P, Filatova T, Orehova N (2014b) Inflation in Brusov–Filatova–Orekhova theory and in its perpetuity limit – Modigliani – Miller theory. J Rev Glob Econ 3:175–185 Brusov P, Filatova T, Orekhova N (2022) Generalized Modigliani–Miller theory: applications in corporate finance, investments, taxation and ratings. Springer Nature, Cham, p 362 Filatova Т, Orehova N, Brusova А (2008) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Bulletin of the FU 48:68–77 Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Modigliani F, Miller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391

Chapter 20

Whether it Is Possible to Increase Taxing and Conserve a Good Investment Climate in the Country?

Keywords Investment climate · Taxing · Efficiency of investments · Brusov– Filatova–Orekhova (BFO) theory · Modigliani–Miller theory · Debt financing Within investment models, developed by Brusov, Filatova, Orekhova earlier (Brusov et al. 2011a, b, c; 2012a, b; 2013a, b; 2014a, b; Brusov and Filatova 2011; Brusova 2011; Filatova et al. 2008) the influence of tax on profit rate on the effectiveness of long-term investment projects at different debt levels is investigated. It is shown, that increase of tax on profit rate from one side leads to decrease in project NPV, but from other side it leads to decrease in sensitivity of NPV with respect to leverage level. At high leverage level L the influence of tax on profit rate increase on the effectiveness of investment projects becomes significantly less. We come to conclusion, that taxing could be differentiated depending on debt level of investment projects of the company: for projects with high debt level L it is possible to apply a higher tax on profit rate.

20.1

Influence of Tax on Profit Rates on the Efficiency of the Investment Projects

Basis of the modern tax systems are the following taxes: tax on profit of organizations, income tax (tax on the income of individuals), social tax (contributions into state extra-budgetary funds), the sales tax (the value-added tax), tax on property of the organization. In this chapter we investigate the influence of tax on profit rates on the efficiency of investment projects. The problems that we are currently investigating now, those questions which we can analyze now in all of their complexity and diversity and to which we give answers, not be tractable by analysis and assessment previously, for them one was not able to give an answer, they even not been raised in such a setting. What should be the taxes scale: flat, progressive or otherwise, differentiated, as well as tax rate has an impact on the cost of attract of company capital, its capitalization. What is cumulative effect of increase in taxes: whether the system “state–employer” will © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_20

401

402

20 Whether it Is Possible to Increase Taxing and Conserve a Good. . .

win, or will lose as a whole from the tax growth, and if it will lose, then how much. Whether the redistribution of income in favor of the state does not destroy the spirit of enterprise, its driving force. If tax on profit rate will increase by 1%, for how much does the cost of attractive capital of company will increase, for how much its capitalization will decrease. If by 3–6%, it should be serious reasons for such increase, but if by 0.5–1.5%, it is possible to discuss such increase. How taxation affects the efficiency of investment? How much does the NPV of investment project will decrease, if tax on profit rate will increase by 1%? If on 5–10%, it has a strong negative impact on investment, if on the 1%, or 0.5%, or 0.25%, Regulator can accept this: this will help to the state and do not exert much to investment programs of companies. One of the main reasons for which it has become possible to carry out such studies, has been a progress in corporate finance, has been made in recent years. It relates primarily to the establishment of a modern theory of capital cost and capital structure by Brusov, Filatova, and Orekhova (BFO theory) (Brusov et al. 2011a, b, c; 2012a, b; 2013a, b; 2014a, b; Filatova et al. 2008) and to the creation by them in the framework of this theory of modern investment models. The BFO theory allows making correct assessment of the financial performance of companies with arbitrary lifetime and of efficiency of investment projects of arbitrary duration. This distinguishes BFO theory from Мodigliani–Мiller theory (Modigliani and Miller 1958, 1963, 1966), which is a perpetuity limit of BFO theory. Archived after the appearance of BFO theory the Мodigliani -Miller theory, still heavily used in the West, despite of its obvious limitations, may, mutatis mutandis, be applied to long living stable companies and long-term investment projects. In its framework in this chapter effects of taxation on the effectiveness of long-term investment will be investigated. So, at present, there are two main theories, that allow exploring the effects of taxation on the efficiency of investments: perpetuity Modigliani–Miller theory (Modigliani and Miller 1958, 1963, 1966) and the modern theory of capital cost and capital structure developed by Brusov, Filatova, Orekhova (Brusov et al. 2011a, b, c; 2012a, b; 2013a, b; 2014a, b; Filatova et al. 2008). In this chapter, we describe the first real results obtained by us within created by us investment projects in perpetuity limit, which can be applied to long-term projects. The effectiveness of the investment project is considered from the perspectives of the equity holders. For this case, NPV is calculated in two ways: with the division of credit and investment flows (and thus discounting the payments at two different rates) and without such a division (in this case, both flows are discounted at the same rate as which, obviously, can be chosen WACC). For each of the four situations two cases are considered: 1) a constant value of equity S; 2) a constant value of the total invested capital I = S + D (D is the value of debt funds). We start first from the case with the division of credit and investment flows and then consider the case without the division of flows.

20.2

20.2

Investment Models

403

Investment Models

Let us remind shortly the main points of the investment models with debt repayment at the end of the project, well-proven in the analysis of real investment projects. Investments at the initial time moment T = 0, are equal to –S, and the flow of capital for the period (in addition to the tax shields kdDt it includes a payment of interest on a loan -kdD) ðNOI- k d DÞð1- t Þ:

ð20:1Þ

Here, for simplicity, we suppose that interest on the loan will be paid in equal shares kdD during all periods. Note, that principal repayment is made at the end of last period. Here NOI—Net Operating Income (before taxes), kd– debt cost, t– tax on profit rate. Let us first consider the case with the division of credit and investment flows. In this case in perpetuity limit (Modigliani–Miller approximation) expression for NPV takes a following form (Brusov et al. 2011a, b, c; 2012a, b; 2013a, b; 2014a, b; Filatova et al. 2008) NPV = - S þ

NOIð1 - t Þ - Dð1- t Þ: ke

ð20:2Þ

We will consider two cases: 1) a constant value of the total invested capital I = S + D (D is the value of debt funds); 2) a constant value of equity S. At a constant value of the total invested capital (I = const), accounting D = IL/ (1 + L ), S = I/(1 + L ), one gets NOIð1 - t Þ I : ð1 þ Lð1- t ÞÞ þ ke 1þL

ð20:3Þ

NOIð1 - t Þ I ð1 þ Lð1- t ÞÞ þ , 1þL k0 þ ðk 0 - k d ÞLð1 - t Þ

ð20:4Þ

NPV = NPV = -

where L = D/S—leverage level; ke—equity cost of leverage company (which uses the debt financing); k0—equity cost of non-leverage company (which does not use the debt financing). Under the transition from the equation (Eq. 20.3) to (Eq. 20.4) we have used the dependence of equity capital on leverage, received by Modigliani and Miller (Modigliani and Miller 1958, 1963, 1966): k e = k0 þ ðk0- k d ÞLð1- t Þ:

ð20:5Þ

20 Whether it Is Possible to Increase Taxing and Conserve a Good. . .

404

NPV(L) 3000.00

1 2 3

2500.00 NPV

2000.00 1500.00 1000.00 500.00 0.00 0

2

4

6

8

10

12

L Fig. 20.1 Dependence of NPV on leverage level L at three values of tax on profit rate (1—t = 0.15; 2—t = 0.20; 3—t = 0.25), NOI = 800

∆NPV(L) 0.00 -100.00

0

2

4

6

8

10

∆NPV

-200.00 -300.00 -400.00 -500.00 -600.00

1 2 3 L

Fig. 20.2 Dependence of ΔNPV on leverage level L at three values of tax on profit rate (1— t = 0.25; 2—t = 0.20; 3—t = 0.15). NOI = 800, I = 1000

So, we explore the equation (Eq. 20.4). A number of conclusions can be drawn from the study of dependence of NPV of the project on leverage level at different values of tax on profit rates t (Fig. 20.1). It is clear that the increase of tax on profit rates leads not only to reduce of NPV of the project, but as well to decrease of the sensitivity of effectiveness of investment projects NPV to the leverage level L. At high leverage levels the influence of the growth of tax on profit rates on the effectiveness of investment projects is significantly reduced. Hence, in particular, it should be noted that taxation can be differentiated depending on the debt financing level in the company investment projects: for projects with a high leverage level L the higher tax on profit rates t can be used. The foregoing is illustrated also in Fig. 20.2, where it is clear that the change of NPV

20.3

Borrowings Abroad

405

NPV

NPV(L) 5000.00 4500.00 4000.00 3500.00 3000.00 2500.00 2000.00 1500.00 1000.00 500.00 0.00

1 2 3

0

1

2

3

4

5

L Fig. 20.3 Dependence of NPV on leverage level L at three values of tax on profit rate (1—t = 0.15; 2—t = 0.20; 3—t = 0.25), NOI = 1200, I = 1000

(ΔNPV) with leverage level decreases when the tax on profit rate t grows, and as well when leverage level increases. Let us increase our return on investment in 1.5 times (NOI = 1200 instead of 800) (Fig. 20.3). Still, the impact of the tax on profit rate on the NPV value significantly depends on the level of debt financing. So the increase in tax on profit rate by 1% from the existing (in Russia) (20%) leads to a reduction in the NPV by 44.5 units at L = 0, by 27.7 units at L = 1, by 12.2 units at L = 3, by 5 units at L = 5. I.e. for companies with a high level of debt financing (for example, companies in the telecommunication sector and other) an increase in tax on profit rate will have less impact on the effectiveness of their investment projects and will be less painful, than for companies with low leverage level in investment. It should be noted that the increase of NOI in 1.5 times increases NPV in 1.7 times (from 2555 up to 4333), and increases ΔNPV(L ) in 1.62 at L = 0, and in 1.5 times when L = 9 (Fig. 20.4). It is clear also that, with the increase of the leverage level L curves, describing the dependence ΔNPV(L ), virtually converge, which demonstrates once again the reduction of impact of the change of the tax on profit rate t on the efficiency of investment projects with the increase of the leverage level L.

20.3

Borrowings Abroad

Until recently, Russian companies have preferred to borrow abroad, because overseas credits are much cheaper than domestic ones. Although relevance of studies using such loans now is not so high in connection with the West sanctions, all same, realizing that, in the not-too-distant future, all will return to its circles, here is a

20 Whether it Is Possible to Increase Taxing and Conserve a Good. . .

406

Δ NPV(L) 0.00 -100.00 0

2

4

6

8

10

-200.00 ∆NPV

-300.00 -400.00 -500.00

1

-600.00 -700.00

2

-800.00 -900.00

3 L

Fig. 20.4 Dependence of ΔNPV on leverage level L at three values of tax on profit rate (1— t = 0.25; 2—t = 0.20; 3—t = 0.15), NOI = 1200, I = 1000

NPV(L) 8000.00

1

NPV

6000.00 4000.00 2000.00

2

0.00 0

2

4

6

8

10

12

L Fig. 20.5 Comparison of dependences of NPV on leverage level L at typical values of credit rates with borrowings abroad (1—k0 =0.1; kd = 0.07) and with borrowings at domestic (Russian) credit market (2—k0 = 0.18; kd = 0.14), NOI = 800, I = 1000, t = 15%

comparison of NPV dependencies on leverage at typical values of rates on credit, with borrowings abroad (k0 =0.1; kd =0.07) and with borrowings at domestic (Russian) credit market (k0 =0.18; kd =0.14). (Here k0—equity cost of financially independent company (Fig. 20.5). The growing of effectiveness of investment when using cheaper foreign credit is obvious. The stabilization of the situation on the external credit market a detailed analysis of this case, as well as of the case of the use of domestic and overseas credits can be done. We analyze now the impact of the tax on profit rates on dependence of NPV on leverage level at typical values of credit rates with borrowings abroad and with borrowings at domestic (Russian) credit market (Fig. 20.6).

20.3

Borrowings Abroad

407

NPV(L) 7000.00 6000.00

1 2 3

NPV

5000.00 4000.00

4 5 6

3000.00 2000.00 1000.00 0.00 0

2

4

6

8

10

12

L Fig. 20.6 Influence of tax on profit rates on dependence of NPV on leverage level at typical values of credit rates with borrowings abroad (lines 1–2–3) and with borrowings at domestic (Russian) credit market (lines 4–5–6)

1. 2. 3. 4. 5. 6.

k0 = 0.1; kd = 0.07; T = 0.15 k0 = 0.1; kd = 0.07; T = 0.2 k0 = 0.1; kd = 0.07; T = 0.25 k0 = 0.18; kd = 0.14; T = 0.15 k0 = 0.18; kd = 0.14; T = 0.2 k0 = 0.18; kd = 0.14; T = 0.25

It is clear that at low leverage levels influence of tax on profit rates is very significant: at zero leverage the NPV drops by 80 units at increase of tax on profit rates on 1% when one borrows abroad and on 44 units when one borrows at domestic (Russian) credit market. It would seem that this could be one of the signals for borrowing within the country, however, taking into account the different values of NPV at two considering cases (ratio is 2.1), we come to the conclusion that the impact of tax on profit rates is in close proportions (ratio is 80/44 = 1.8). So it seems that after the West sanctions will be over, to borrow at the West will be more advantageous for a long time.

20 Whether it Is Possible to Increase Taxing and Conserve a Good. . .

408

20.4

Dependence of NPV on Tax on Profit Rates at Different Leverage Levels

From Fig. 20.7 it is seen that dependence of NPV on tax on profit rates significantly depends on the leverage level L. When there is no borrowing NPV linearly decreases with t with a factor— 43.44 units at 1%. When L = 1 this factor (at t = 20%) is equal to—27.7 units at 1%, when L = 3 this factor (when t = 20%) is equal to—12.3 units at 1%, and when L = 5 this factor (at t = 20%) is equal to—5.8 units. at 1%. It can be seen that the influence of tax on profit rate on efficiency of investment projects drops significantly with increase of the leverage level L used in investments. This is particularly seen in Fig. 20.8 in the dependence of ΔNPV on tax on profit rate at different leverage levels L (here ΔNPV—increment of NPV under change of t for 10%). When there is no borrowing ΔNPV = –450 and does not depend on tax on profit rate. At t = 20%: at L = 1 ΔNPV = -276.6; at L = 3 ΔNPV = -122.6; at L = 5 ΔNPV = –49. It is clear that the change of tax on profit rate affect mostly the effectiveness of the projects, funded by equity capital only, and if you use debt financing to finance the projects impact of the change of tax on profit rate drops very substantially (up to ten times).

NPV(t) 4000.00

1

3000.00

2 3

NPV

2000.00 1000.00 0.00 -1000.00 -2000.00

4 0

0.2

0.4

0.6

0.8

1

1.2

t

Fig. 20.7 Dependence of NPV on tax on profit rate at different leverage levels L (1—L = 0; 2— L = 1; 3—L = 3; 4—L = 5), NOI = 800, I = 1000

20.5

At a Constant Value of Equity Capital (S = Const)

∆NPV (t)

1

0.00

∆NPV

-100.002

409

0

0.2

0.4

0.6

0.8

1

1.2

-200.00

3

-300.00 -400.00

-500.004

t

Fig. 20.8 Dependence of ΔNPV on tax on profit rate at different leverage levels L (1—L = 5; 2— L = 3; 3—L = 1; 4—L = 0), NOI = 800, I = 1000

20.5

At a Constant Value of Equity Capital (S = Const)

At a constant value of equity capital (S = const), when investment growth is associated with the increased borrowing only, the dependence of NPV on leverage level is qualitatively different in nature, rather than in the case of a constant value of invested capital. Now, depending on the values of the coefficient β = NOI/I NPV can grow with leverage level. It should be noted that, in this case (at large values of the coefficient β) the optimal structure of invested capital, in which NPV is maximized could take place. NPV in this case is described by the following expression NPV = - Sð1 þ Lð1- t ÞÞ þ

βSð1 þ LÞð1 - t Þ : k 0 þ ðk 0 - k d ÞLðt - 1Þ

ð20:6Þ

It is seen from Fig. 20.9 that with the increase of the coefficients β value NPV and its optimal (maximum) values grow. It follows from Fig. 20.10, that with the increase of the leverage level ΔNPV drops and either goes to the saturation (ΔNPV = 0), or becomes negative (ΔNPV0 at small leverage level L). In Figs. 20.11 and 20.12 the dependencies of ΔNPV and NPV on tax on profit rate at different leverage levels and at S = 500, β = 0,8 are shown. From Fig. 20.11 as well as from Fig. 20.9, it is seen that at fixed tax on profit rate NPV grows with leverage level. With the increasing of tax on profit rate NPV drops, and curves, corresponding to the different leverage level converge in one point at t = 100% and NPV = -S in accordance to equation (Eq. 20.6). Change of ΔNPV with increasing of t also depends on the leverage level: with the growth of the leverage level it changes from constant (at L = 0) up to the increasingly growing at t > 30%–40% at L = 1;3;5.

20 Whether it Is Possible to Increase Taxing and Conserve a Good. . .

410

NPV

NPV(L) 10000.00 9000.00 8000.00 7000.00 6000.00 5000.00 4000.00 3000.00 2000.00 1000.00 0.00

1

2

0

2

4

6

8

10

12

L Fig. 20.9 Dependence of NPV on leverage level L at three values of β-coefficient (1—β = 1.5; 2—β = 1.2; 3—β = 0.8), S = 500

∆NPV(L) 2500.00 2000.00

1

∆NPV

1500.00 1000.00

2

500.00 0.00 -500.00

0

2

4

6

8

10

12

L

Fig. 20.10 Dependence of ΔNPV on leverage level L at three values of β- coefficient (1—β = 1.5; 2—β = 1.2; 3—β = 0.8), S = 500

20.6

Without Flows Separation

Let us consider the case without the division of credit and investment flows. In this case, both flows are discounted at the same rate as which, obviously, can be chosen WACC). In perpetuity limit. (n → 1) one has

20.6

Without Flows Separation

411

NPV(t) 4000.00 3500.00

1

3000.00 2500.00

2

NPV

2000.00 1500.00

3

1000.00 500.00

4

0.00

-500.00 0

0.2

0.4

-1000.00

0.6

0.8

1

1.2

t

Fig. 20.11 Dependence of NPV on tax on profit rate at different leverage levels L (1—L = 5; 2— L = 3; 3—L = 1; 4—L = 0), S = 500, β = 0.8

∆NPV(t) 0.00

0

0.2

0.4

0.6

0.8

∆NPV

-200.00

1

1.2

1

-400.00

2

-600.00

3

-800.00 -1000.00

t

Fig. 20.12 Dependence of ΔNPV on tax on profit rate at different leverage levels L (1—L = 0; 2— L = 1; 3—L = 3; 4—L = 5), S = 500, β = 0.8

NPV = - S þ

NOIð1 - t Þ - kd Dð1 - t Þ : WACC

ð20:7Þ

20 Whether it Is Possible to Increase Taxing and Conserve a Good. . .

412

20.6.1

At a Constant Value of the Total Invested Capital (I = Const) (Fig. 20.13)

In case of a constant value of the total invested capital (I = const), accounting D = IL/(1 + L ), S = I/(1 + L), we get NPV = - I 

  Lkd ð1 - t Þ NOIð1 - t Þ 1 þ : 1þ 1þL k 0 ð1 - Lt=ð1 þ LÞÞ k0 ð1 - Lt=ð1 þ LÞÞ

ð20:8Þ

It should be noted that, in contrast to the case with the division of flows, described above, in a situation without the division of flows NPV is growing with leverage level. It is seen, that, while NOI increases in 1.5 times NPV increases in 1.68 times (Fig. 20.14). NPV rather quickly goes to the saturation, at L > 4 it varies weakly, and the leverage level, at which the saturation of NPV(L ) takes place, practically does not depend on NOI (Fig. 20.15). NPV falls down with the growth of tax on profits rate at different leverage levels: At L = 0 at change of tax on profits rate on 1%, NPV falls down on 1.74%. At L = 1 at change of tax on profits rate on 1%, NPV falls down on 0.85%. At L = 3 at change of tax on profits rate on 1%, NPV falls down on 0.43%. At L = 5 at change of tax on profits rate on 1%, NPV falls down on 0.29%. It is seen that, with the rising of the tax on profit rate by 1%, NPV drops less at the higher leverage level. This confirms the conclusion, made in the previous section, that with the increase of the leverage level a negative impact of the growth of the tax

NPV(L) 7000.00

1

6000.00 NPV

5000.00 4000.00 3000.00 2000.00 1000.00 0.00

0

2

4

6

8

10

12

L Fig. 20.13 Dependence of NPV on leverage level L at two values of NOI (1—NOI = 1200; 2— NOI = 800), I = 1000

20.6

Without Flows Separation

413

∆NPV

∆NPV(L) 700.00 600.00 500.00 400.00 300.00 200.00 100.00 0.00

1

2 0

2

4

6

8

10

12

L Fig. 20.14 Dependence of ΔNPV on leverage level L at two values of NOI (1—NOI = 1200; 2— NOI = 800), I = 1000

NPV(t)

NPV

4000.00 3000.00

1

2000.00

2

1000.00 0.00 -1000.00 -2000.00

3 0

0.2

0.4

0.6

4

0.8

1

1.2

t

Fig. 20.15 Dependence of ΔNPV on tax on profit rate at different leverage levels L (1—L = 5; 2— L = 3; 3—L = 1; 4—L = 0), NOI = 800, I = 1000

on profit rate declines in a few times, allowing to the Regulator to establish the differentiated tax on profit rates (as can be seen from Fig. 20.16, the founded conclusions are true up to tax on profit rate values of 70–80%).

20 Whether it Is Possible to Increase Taxing and Conserve a Good. . .

414

∆NPV (t) 0.00

-200.00 0

0.2

0.4

0.6

0.8

∆NPV

-400.00

1

4 3

-600.00 -800.00 -1000.00 -1200.00

2

-1400.00 -1600.00 t

1

Fig. 20.16 Dependence of ΔNPV on tax on profit rate at different leverage levels L (1—L = 5; 2— L = 3; 3—L = 1; 4—L = 0), NOI = 800, I = 1000

20.6.2

At a Constant Value of Equity Capital (S = Const)

NPV = - S þ

NOIð1 - t Þ - kd Dð1 - t Þ : WACC

ð20:9Þ

Substituting D = LS, one gets  NPV = - S 1 þ

 βSð1 þ LÞð1 - t Þ Lkd ð1 - t Þ þ : k 0 ð1 - Lt=ð1 þ LÞÞ k0 ð1 - Lt=ð1 þ LÞÞ

ð20:10Þ

From Fig. 20.17 it follows that NPV grows linearly with leverage level and speed of its growth increases with grows of coefficient β. From Fig. 20.18 it follows, that ΔNPV practically does not depend on leverage level L and at decrease of β—coefficient in 1.25 times (the transition from line 1 to line 2) ΔNPV is decreased in 1.28 times (practically so), and at decrease of β— coefficient in 1.5 times (the transition from line 2 to line 3) ΔNPV is decreased in 1.59 times (practically so). As in case of constant value of investments (I = const), at constant equity capital value (S = const) NPV falls down with the growth of tax on profit rate t at different leverage levels L. Let us take a look at the region of changes of tax on profits rates from 0% up to 60%. In this region: At L = 0 at change of tax on profits rate on 1%, NPV falls down on 3.6%. At L = 1 at change of tax on profits rate on 1%, NPV falls down on 1.23%. At L = 3 at change of tax on profits rate on 1%, NPV falls down on 0.46%. At L = 5 at change of tax on profits rate on 1%, NPV falls down on 0.22%.

20.6

Without Flows Separation

415

NPV(L) 50000.00

1

NPV

40000.00 30000.00

2

20000.00 10000.00 0.00

0

2

4

6

8

10

12

L Fig. 20.17 Dependence of NPV on leverage level L at three values of β—coefficient (1—β = 1.5; 2—β = 1.2; 3—β = 0.8), S = 500

∆NPV

∆NPV(L) 4000.00 3500.00 3000.00 2500.00 2000.00 1500.00 1000.00 500.00 0.00

1 2 3

0

2

4

6

8

10

12

L Fig. 20.18 Dependence of ΔNPV on leverage level L at three values of β—coefficient (1—β = 1.5; 2—β = 1.2; 3—β = 0.8), S = 500

And so, with the increasing of the tax on profits rates at 1%, NPV drops less for the higher leverage level. This correlates with the conclusion made above and in the previous section, that with the increase of the leverage level a negative impact of the growth of the tax on profit rates declines in a few times, allowing the regulator to introduce differentiated tax on profits rate (as it can be seen from Figs. 20.19 and 20.20, the findings are true up to values of tax on profits rates 60%). At higher rates (that, however, is a purely theoretical interest) the situation will be different.

20 Whether it Is Possible to Increase Taxing and Conserve a Good. . .

416

NPV(t) 12000.00

1

10000.00

NPV

8000.00

2

6000.00 4000.00

3

2000.00 0.00 -2000.00

4 0

0.2

0.4

0.6

0.8

1

1.2

t

Fig. 20.19 Dependence of NPV on tax on profit rate t at different leverage levels L (1—L = 5; 2— L = 3; 3—L = 1; 4—L = 0), S = 500

∆NPV(t) 0.00

∆NPV

-1000.00

0

0.2

0.4

0.6

0.8

1

1

1.2

2

-2000.00

3

-3000.00 -4000.00 -5000.00

t

Fig. 20.20 Dependence of NPV on tax on profit rate t at different leverage levels L (1—L = 0; 2— L = 1; 3—L = 3; 4—L = 5), S = 500

20.7

Conclusions

Within investment models, developed by Brusov, Filatova, Orekhova earlier (Brusov et al. 2011a, b, c; 2012a, b; 2013a, b; 2014a, b; Filatova et al. 2008) the influence of tax on profit rate on effectiveness of long-term investment projects at different debt levels is investigated. The ability to obtain quantitative estimates of such impact on the projects with various costs of equity and debt capital, at an arbitrary structure of invested capital has been demonstrated. It is shown, that increase of tax on profit rate from one side leads to decrease of project NPV, but from other side it leads to decrease in sensitivity of NPV with respect to leverage

References

417

level. At high leverage level L the influence of tax on profit rate increase on effectiveness of investment projects becomes significantly less. We come to conclusion, that taxing could be differentiated depending on debt level of investment projects of the company: for projects with high debt level L it is possible to apply a higher tax on profit rate. These recommendations, in particular, may be addressed to the Regulator. Effects of taxation on the effectiveness of investment projects depend on the level of leverage, of the project duration, of the equity cost, as well as of the level of returns on investment (NOI) and of methods of forming of invested capital. Study of all these problems, as the results of this chapter show, may be successfully carried out within developed by Brusov, Filatova, Orekhova investment models, using discount rates, derived from the Brusov–Filatova–Orekhova (BFO) theory.

References Brusov PN, Filatova ТV (2011) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Finance Credit 435:2–8 Brusov P, Filatova T, Orehova N, Brusova A (2011a) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Appl Financ Econ 21(11): 815–824 Brusov P, Filatova T, Orehova N et al (2011b) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Bus ICT 2:16–21 Brusov P, Filatova T, Orehova N et al (2011c) Influence of debt financing on the effectiveness of the investment project within the Modigliani–Miller theory. Res J Econ Bus ICT 2:11–15 Brusov P, Filatova T, Eskindarov M, Orehova N (2012a) Influence of debt financing on the effectiveness of the finite duration investment project. Appl Financ Econ 22(13):1043–1052 Brusov P, Filatova T, Eskindarov M, Orehova N (2012b) Hidden global causes of the global financial crisis. J Rev Glob Econ 1:106–111 Brusov P, Filatova P, Orekhova N (2013a) Absence of an optimal capital structure in the famous Tradeoff theory! J Rev Glob Econ 2:94–116 Brusov P, Filatova T, Orehova N (2013b) A qualitatively new effect in corporative finance: abnormal dependence of cost of equity of company on leverage. J Rev Glob Econ 2:183–193 Brusov P, Filatova P, Orekhova N (2014a) Mechanism of formation of the company optimal capital structure, different from suggested by trade off theory. Cogent Econ Finance 2:1–13. https://doi. org/10.1080/23322039.2014.946150 Brusov P, Filatova T, Orehova N (2014b) Inflation in Brusov–Filatova–Orekhova theory and in its perpetuity limit – Modigliani – Miller theory. J Rev Glob Econ 3:175–185 Brusova A (2011) А comparison of the three methods of estimation of weighted average cost of capital and equity cost of company. Financ Anal Prob Solut 34(76):36–42 Filatova Т, Orehova N, Brusova А (2008) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Bullet FU 48:68–77 Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Modigliani F, Miller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391

Chapter 21

Whether It Is Possible to Increase the Investment Efficiency, Increasing Tax on Profit Rate? An Abnormal Influence of Growth of Tax on Profit Rate on the Efficiency of the Investment Keywords Investment projects · Taxing · Efficiency of investments · Brusov– Filatova–Orekhova (BFO) theory · Modigliani–Miller theory · Debt financing

Dependence of NPV on Leverage Level L at Fixed Levels of Tax on Profit Rates t

21.1 21.1.1

The Effectiveness of the Investment Project from the Perspective of the Equity Holders Only

Investigations will be done with the division of credit and investment flows: operating and finance flows are divided and discounted using different rates: operating flows—by the rate equal to equity cost ke, depending on leverage, and credit ones— by the rate equal to debt cost kd, which, until sufficiently large values of leverage levels, remains constant and starts to grow only at sufficiently high leverage values L, when a risk of bankruptcy will appear. The consideration has been done upon constant value of investment capital I. In this case, NPV is described by the following formula (Brusov et al. 2011a, b, c, d, 2012a, b, 2013a, b, 2014a, b; Brusova 2011; Filatova et al. 2008) NPV = -

     1 I 1 þ 1 þ L ð1 - t Þ 1 1þL ð1 þ k d Þn ð1 þ k d Þn   NOIð1 - t Þ 1 1þ : ke ð1 þ k e Þn

ð21:1Þ

Using it we calculate NPV and ΔNPV at fixed levels of tax on profit rates t. 5-Year Project For 5-year projects we get the following results (Tables 21.1, 21.2, 21.3, 21.4, 21.5, 21.6, 21.7, Figs. 21.1 and 21.2).

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_21

419

420

21

Whether It Is Possible to Increase the Investment Efficiency, Increasing. . .

Table 21.1 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 5-year project at t = 0.3 L 0 1 2 3 4 5 6 7 8 9 10

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3

n 5 5 5 5 5 5 5 5 5 5 5

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.197488 0.214367 0.231082 0.24773 0.264343 0.280937 0.297518 0.314091 0.330658 0.34722

NPV 751.22 756.14 719.28 674.51 628.39 582.93 538.90 496.60 456.10 417.41 380.49

ΔNPV 4.922709 -36.8599 -44.7663 -46.126 -45.4549 -44.027 -42.3084 -40.4978 -38.6879 -36.9239

Table 21.2 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 5-year project at t = 0.4 L 0 1 2 3 4 5 6 7 8 9 10

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4

n 5 5 5 5 5 5 5 5 5 5 5

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.189578 0.19803 0.206172 0.214184 0.22213 0.230037 0.23792 0.245786 0.253642 0.261488

NPV 501.04 565.18 569.91 560.40 545.62 528.52 510.35 491.73 472.98 454.30 435.81

ΔNPV 64.13345 4.73089 -9.5017 -14.7815 -17.1025 -18.1709 -18.6246 -18.7461 -18.6762 -18.4911

One can see from Fig. 21.1 that the nature of the NPV dependence on leverage at t* = 0.5: there is a transition from diminishing function NPV(L) when t < t* to growing function NPV(L) at t > t*. 10-Year Project For 10-year projects, we get the following results (Tables 21.8, 21.9, 21.10, 21.11, 21.12, 21.13, 21.14, Figs. 21.3 and 21.4). Perpetuity Limit In perpetuity limit n → 1 (Мodigliani and Мiller limit (Modigliani et al. 1958, 1963, 1966)) formula for NPV is as following (Brusov et al. 2011a, b, c, d, 2012a, b, 2013a, b, 2014a, b; Filatova et al. 2008)

21.1

Dependence of NPV on Leverage Level L at Fixed Levels of Tax on Profit Rates t

421

Table 21.3 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 5-year project at t = 0.5 L 0 1 2 3 4 5 6 7 8 9 10

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

n 5 5 5 5 5 5 5 5 5 5 5

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.181448 0.181065 0.180162 0.179041 0.177806 0.176505 0.175162 0.173792 0.172401 0.170996

NPV 250.87 366.94 408.07 430.65 445.84 457.37 466.82 474.98 482.28 488.99 495.28

ΔNPV 120.0669 41.1323 22.57738 15.19888 11.52994 9.446706 8.154973 7.302458 6.713275 6.291579

Table 21.4 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 5-year project at t = 0.6 L 0 1 2 3 4 5 6 7 8 9 10

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6

NPV = - S þ

n 5 5 5 5 5 5 5 5 5 5 5

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.173086 0.163424 0.15296 0.142153 0.131168 0.120078 0.108922 0.097721 0.086488 0.075231

NPV 0.69 160.76 231.71 281.50 323.63 362.63 400.49 438.23 476.49 515.66 556.05

NOIð1 - t Þ - Dð1- t Þ: ke

ΔNPV 160.0655 70.95083 49.78654 42.12961 39.00243 37.85743 37.74625 38.25211 39.17065 40.39427

ð21:2Þ

At constant value of investment capital (I = const), accounting D = IL/(1 + L ), S = I/(1 + L ), one gets NOIð1 - t Þ I : ð1 þ Lð1- t ÞÞ þ 1þL ke

ð21:3Þ

NOIð1 - t Þ I , ð1 þ Lð1- t ÞÞ þ 1þL k0 þ ðk 0 - k d ÞLð1 - t Þ

ð21:4Þ

NPV = NPV = -

here L = D/S—leverage level; ke—equity cost of leverage company (use the debt capital); k0—equity cost of financially independent company.

422

21

Whether It Is Possible to Increase the Investment Efficiency, Increasing. . .

Table 21.5 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 5-year project at t = 0.7 L 0 1 2 3 4 5 6 7 8 9 10

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7

n 5 5 5 5 5 5 5 5 5 5 5

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.16448 0.145057 0.124461 0.103355 0.081982 0.060453 0.038822 0.017124 -0.00462 -0.0264

NPV -249.48 -54.09 38.32 108.00 171.20 233.63 298.10 366.37 439.79 519.62 607.09

ΔNPV 195.3877 92.40829 69.68464 63.19622 62.43475 64.46977 68.26526 73.42597 79.82524 87.47314

Table 21.6 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 5-year project at t = 0.8 L 0 1 2 3 4 5 6 7 8 9 10

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8

n 5 5 5 5 5 5 5 5 5 5 5

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.155616 0.125907 0.094544 0.062454 0.029979 -0.00272 -0.03557 -0.06852 -0.10154 -0.13462

NPV -499.65 -278.46 -175.24 -96.55 -22.89 53.22 136.16 229.45 336.64 461.80 609.93

ΔNPV 221.1945 103.2179 78.69376 73.65304 76.11182 82.93806 93.28915 107.1925 125.1636 148.1245

In the transition from the equation (Eq. 21.3) to (Eq. 21.4) we have used the formula for equity capital cost, received by Мodigliani and Мiller (1958, 1963, 1966) k e = k0 þ ðk0- k d ÞLð1- t Þ:

ð21:5Þ

For perpetuity projects we get the following results (Tables 21.15, 21.16, 21.17, 21.18, 21.19, 21.20, 21.21, Figs. 21.5 and 21.6).

21.1

Dependence of NPV on Leverage Level L at Fixed Levels of Tax on Profit Rates t

423

Table 21.7 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 5-year project at t = 0.9 L 0 1 2 3 4 5 6 7 8 9 10

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9

n 5 5 5 5 5 5 5 5 5 5 5

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.14648 0.105908 0.063074 0.019228 -0.02516 -0.06987 -0.11479 -0.15985 -0.20501 -0.25024

NPV -749.83 -513.29 -412.88 -341.38 -276.02 -207.47 -129.54 -36.24 79.64 227.94 422.90

ΔNPV 236.5329 100.4127 71.49601 65.36206 68.55205 77.93497 93.29474 115.8841 148.3017 194.9563

Fig. 21.1 Dependence of NPV on leverage level L at fixed levels of tax on profit rates t for 5-year project

21.1.2

The Effectiveness of the Investment Project from the Perspective of the Equity and Debt Holders

In this case, we use the following expression for NPV (Brusov et al. 2011a, b, c, d, 2012a, b, 2013a, b, 2014a, b; Filatova et al. 2008)  NPV = - I 1-

    NOIð1 - t Þ Lt 1 1 þ ð21:6Þ 111þL ke ð1 þ kd Þn ð 1 þ k e Þn

Using it we calculate the dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t.

424

21

Whether It Is Possible to Increase the Investment Efficiency, Increasing. . .

Fig. 21.2 Dependence of ΔNPV on leverage level L at fixed levels of tax on profit rates t for 5-year project Table 21.8 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 10-year project at t = 0.3 L 0 1 2 3 4 5 6 7 8 9 10

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3

n 10 10 10 10 10 10 10 10 10 10 10

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.19907 0.217182 0.235022 0.252747 0.270413 0.288045 0.305654 0.323249 0.340834 0.358411

NPV 1520.69 1464.75 1363.28 1258.44 1158.18 1064.36 977.25 896.57 821.89 752.72 688.58

ΔNPV -51.935 -101.47 -104.843 -100.263 -93.8156 -87.1129 -80.6768 -74.6812 -69.1705 -64.1369

5-Year Project For 5-year projects we get the following results (Tables 21.22, 21.23, 21.24, 21.25, 21.26, 21.27, 21.28, Figs. 21.7 and 21.8). 10-Year Project For 10-year projects we get the following results (Tables 21.29, 21.30, 21.31, 21.32, 21.33, 21.34, 21.35, Figs. 21.9 and 21.10).

21.1

Dependence of NPV on Leverage Level L at Fixed Levels of Tax on Profit Rates t

425

Table 21.9 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 10-year project at t = 0.4 L 0 1 2 3 4 5 6 7 8 9 10

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4

n 10 10 10 10 10 10 10 10 10 10 10

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.191455 0.201083 0.210169 0.21902 0.22775 0.236408 0.24502 0.253602 0.262161 0.270705

NPV 1157.16 1218.26 1199.74 1163.95 1122.81 1080.17 1037.56 995.70 954.91 915.37 877.15

ΔNPV 61.10029 -18.517 -35.7995 -41.1321 -42.6427 -42.6081 -41.8669 -40.7844 -39.5386 -38.2228

Table 21.10 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 10-year project at t = 0.5 L 0 1 2 3 4 5 6 7 8 9 10

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

n 10 10 10 10 10 10 10 10 10 10 10

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.219687 0.255351 0.290005 0.32421 0.358168 0.391982 0.425702 0.459362 0.492979 0.526564

NPV 797.63 753.43 648.73 545.06 451.45 368.78 296.06 232.03 175.46 125.26 80.52

ΔNPV -44.2013 -104.707 -103.671 -93.6005 -82.6797 -72.7174 -64.0269 -56.5734 -50.1953 -44.7383

Table 21.11 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 10-year project at t = 0.6 L 0 1 2 3 4 5 6 7 8 9 10

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6

n 10 10 10 10 10 10 10 10 10 10 10

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.175084 0.165407 0.154162 0.142206 0.129869 0.117304 0.10459 0.091775 0.078888 0.065947

NPV 438.11 682.67 808.10 909.47 1005.41 1102.43 1203.76 1311.47 1427.17 1552.38 1688.58

ΔNPV 244.5668 125.4304 101.3662 95.93652 97.02629 101.3309 107.7015 115.7055 125.2046 136.2059

426

21

Whether It Is Possible to Increase the Investment Efficiency, Increasing. . .

Table 21.12 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 10-year project at t = 0.7 L 0 1 2 3 4 5 6 7 8 9 10

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7

n 10 10 10 10 10 10 10 10 10 10 10

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.166255 0.145497 0.122295 0.097953 0.072986 0.04764 0.022047 -0.00372 -0.0296 -0.05558

NPV 78.58 389.06 566.25 726.79 896.70 1088.62 1312.79 1580.19 1904.18 2301.94 2796.25

ΔNPV 310.4744 177.1979 160.5402 169.9063 191.9196 224.1724 267.4019 323.9861 397.7601 494.3094

Table 21.13 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 10-year project at t = 0.8 L 0 1 2 3 4 5 6 7 8 9 10

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8

n 10 10 10 10 10 10 10 10 10 10 10

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.156938 0.123925 0.087223 0.048741 0.009262 -0.03083 -0.07133 -0.11211 -0.1531 -0.19424

NPV -280.95 74.32 279.16 477.65 710.43 1008.26 1409.19 1969.56 2779.06 3986.48 5847.59

ΔNPV 355.2633 204.8466 198.4863 232.7806 297.8303 400.9259 560.3743 809.4944 1207.425 1861.112

Table 21.14 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 10-year project at t = 0.9 L 0 1 2 3 4 5 6 7 8 9 10

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9

n 10 10 10 10 10 10 10 10 10 10 10

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.147081 0.100417 0.048303 -0.00655 -0.06297 -0.12039 -0.17847 -0.23701 -0.2959 -0.35504

NPV -640.47 -265.38 -71.16 115.79 355.37 711.85 1295.45 2327.83 4295.04 8349.38 17464.72

ΔNPV 375.0978 194.2145 186.9461 239.586 356.4744 583.6021 1032.383 1967.211 4054.338 9115.336

21.2

Dependence of NPV on Tax on Profit Rates at Fixed Leverage Levels L

427

Fig. 21.3 Dependence of NPV on leverage level L at fixed levels of tax on profit rates t for 10-year project

Fig. 21.4 Dependence of NPV on leverage level L at fixed levels of tax on profit rates t for 10-year project

21.2

Dependence of NPV on Tax on Profit Rates at Fixed Leverage Levels L

Below we study the dependence of NPV on tax on profit rates at fixed leverage levels L.

428

21

Whether It Is Possible to Increase the Investment Efficiency, Increasing. . .

Table 21.15 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for perpetuity project at t = 0.3 L 0 1 2 3 4 5 6 7 8 9 10

t 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

NOI 800 800 800 800 800 800 800 800 800 800 800

NPV 2111.111 1842.308 1572.881 1346.212 1157.808 1000 866.3383 751.8617 652.8053 566.2963 490.1186

ΔNPV -268.803 -269.426 -226.669 -188.404 -157.808 -133.662 -114.477 -99.0564 -86.509 -76.1777

Table 21.16 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for perpetuity project at t = 0.4 L 0 1 2 3 4 5 6 7 8 9 10

t 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

NOI 800 800 800 800 800 800 800 800 800 800 800

NPV 1666.667 1552.941 1371.93 1204.762 1059.13 933.3333 824.3386 729.3103 645.8781 572.1212 506.4935

ΔNPV -113.725 -181.011 -167.168 -145.631 -125.797 -108.995 -95.0283 -83.4322 -73.7569 -65.6277

Table 21.17 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for perpetuity project at t = 0.5 L 0 1 2 3 4 5 6 7 8 9 10

t 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

NOI 800 800 800 800 800 800 800 800 800 800 800

NPV 1222.222 1250 1151.515 1041.667 938.4615 845.2381 761.9048 687.5 620.915 561.1111 507.177

ΔNPV 27.77778 -98.4848 -109.848 -103.205 -93.2234 -83.3333 -74.4048 -66.585 -59.8039 -53.9341

21.2

Dependence of NPV on Tax on Profit Rates at Fixed Leverage Levels L

429

Table 21.18 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for perpetuity project at t = 0.6 L 0 1 2 3 4 5 6 7 8 9 10

t 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

NOI 800 800 800 800 800 800 800 800 800 800 800

NPV 777.7778 932.6531 909.434 853.5088 791.4754 730.7692 673.706 620.8904 572.2944 527.6543 486.631

ΔNPV 154.8753 -23.2191 -55.9252 -62.0334 -60.7062 -57.0632 -52.8156 -48.596 -44.6401 -41.0233

Table 21.19 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for perpetuity project at t = 0.7 L 0 1 2 3 4 5 6 7 8 9 10

t 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

NOI 800 800 800 800 800 800 800 800 800 800 800

NPV 333.3333 600 643.1373 636.1111 612.6316 583.3333 552.381 521.5909 491.7874 463.3333 436.3636

ΔNPV 266.6667 43.13725 -7.02614 -23.4795 -29.2982 -30.9524 -30.79 -29.8035 -28.4541 -26.9697

Table 21.20 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for perpetuity project at t = 0.8 L 0 1 2 3 4 5 6 7 8 9 10

t 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

NOI 800 800 800 800 800 800 800 800 800 800 800

NPV -111.111 251.0638 349.6599 384.3137 394.717 393.9394 387.4687 377.9661 366.8488 354.9206 342.6573

ΔNPV 362.1749 98.59603 34.65386 10.40326 -0.77759 -6.47072 -9.50257 -11.1173 -11.9282 -12.2633

430

21

Whether It Is Possible to Increase the Investment Efficiency, Increasing. . .

Table 21.21 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for perpetuity project at t = 0.9 L 0 1 2 3 4 5 6 7 8 9 10

t 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

NOI 800 800 800 800 800 800 800 800 800 800 800

NPV -555.556 -115.217 25.53191 91.66667 128.1633 150 163.5854 172.1154 177.3585 180.3704 181.8182

ΔNPV 440.3382 140.7493 66.13475 36.4966 21.83673 13.58543 8.52995 5.243106 3.01188 1.447811

Fig. 21.5 Dependence of NPV on leverage level L at fixed levels of tax on profit rates t for perpetuity project

21.2.1

The Effectiveness of the Investment Project from the Perspective of the Equity Holders Only

5-Year Project For 5-year projects we get the following results (Tables 21.36, 21.37, 21.38, 21.39, 21.40, 21.41, Figs. 21.11 and 21.12). 10-Year Project For 10-year projects we get the following results (Tables 21.42, 21.43, 21.44, 21.45, 21.46, 21.47, Figs. 21.13 and 21.14).

21.2

Dependence of NPV on Tax on Profit Rates at Fixed Leverage Levels L

431

Fig. 21.6 Dependence of ΔNPV on leverage level L at fixed levels of tax on profit rates t for perpetuity project

Perpetuity Limit For perpetuity projects we get the following results (Tables 21.48, 21.49, Fig. 21.15).

21.2.2

The Effectiveness of the Investment Project from the Perspective of the Equity and Debt Holders

5-Year Project For 5-year projects we get the following results (Tables 21.50, 21.51, 21.52, 21.53, 21.54, 21.55, Figs. 21.16 and 21.17). 10-Year Projects For 10-year projects we get the following results (Tables 21.56, 21.57, 21.58, 21.59, 21.60, 21.61, Figs. 21.18, 21.19, 21.20, 21.21). Or more detailed It is seen from Fig. 21.19, that falling trend at L = 0, 2, and 4 alternates by growing trend at higher leverage levels L = 6, 8, and 10. The observed at high leverage levels (starting from L = 6) increase of NPV with growth of the tax on profit rate t takes place at all values of t, that means that this is an entirely new effect in investments which can be applied in a real economic practice for optimizing of the management of investments. Or more detailed Conclusions Within modern theory of capital cost and capital structure by Brusov– Filatova–Orekhova (BFO theory) and created within this theory modern investment

L 0 1 2 3 4 5 6 7 8 9 10

WACC 0.18 0.14774 0.13679 0.13127 0.12795 0.12572 0.12413 0.12294 0.12201 0.12127 0.12066

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3

n 5 5 5 5 5 5 5 5 5 5 5

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.197488 0.214367 0.231082 0.24773 0.264343 0.280937 0.297518 0.314091 0.330658 0.34722

NPV 751.2158 756.1385 719.2786 674.5122 628.3863 582.9313 538.9044 496.596 456.0982 417.4103 380.4865

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 0 1 2 3 4 5 6 7 8 9 10

WACC 0.18 0.13679 0.12201 0.11454 0.11004 0.10702 0.10486 0.10324 0.10198 0.10096 0.10014

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4

n 5 5 5 5 5 5 5 5 5 5 5

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.189578 0.19803 0.206172 0.214184 0.22213 0.230037 0.23792 0.245786 0.253642 0.261488

NPV 501.0421 565.1755 569.9064 560.4047 545.6233 528.5208 510.3499 491.7254 472.9793 454.3031 435.812

ΔNPV 64.13345 4.73089 -9.5017 -14.7815 -17.1025 -18.1709 -18.6246 -18.7461 -18.6762 -18.4911

ΔNPV 4.922709 -36.8599 -44.7663 -46.126 -45.4549 -44.027 -42.3084 -40.4978 -38.6879 -36.9239

21

Table 21.23 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 5-year project at t = 0.4

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

Table 21.22 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 5-year project at t = 0.3

432 Whether It Is Possible to Increase the Investment Efficiency, Increasing. . .

L 0 1 2 3 4 5 6 7 8 9 10

WACC 0.18 0.12572 0.10702 0.09754 0.09181 0.08797 0.08522 0.08315 0.08153 0.08024 0.07918

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

n 5 5 5 5 5 5 5 5 5 5 5

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.181448 0.181065 0.180162 0.179041 0.177806 0.176505 0.175162 0.173792 0.172401 0.170996

NPV 250.8684 366.9353 408.0676 430.645 445.8439 457.3738 466.8205 474.9755 482.278 488.9912 495.2828

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 0 1 2 3 4 5 6 7 8 9 10

WACC 0.18 0.11454 0.09181 0.08024 0.07323 0.06853 0.06515 0.06262 0.06064 0.05905 0.05775

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6

n 5 5 5 5 5 5 5 5 5 5 5

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.173086 0.163424 0.15296 0.142153 0.131168 0.120078 0.108922 0.097721 0.086488 0.075231

NPV 0.694727 160.7602 231.711 281.4976 323.6272 362.6296 400.487 438.2333 476.4854 515.656 556.0503

Table 21.25 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 5-year project at t = 0.6

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

Table 21.24 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 5-year project at t = 0.5

ΔNPV 160.0655 70.95083 49.78654 42.12961 39.00243 37.85743 37.74625 38.25211 39.17065 40.39427

ΔNPV 120.0669 41.1323 22.57738 15.19888 11.52994 9.446706 8.154973 7.302458 6.713275 6.291579

21.2 Dependence of NPV on Tax on Profit Rates at Fixed Leverage Levels L 433

L 0 1 2 3 4 5 6 7 8 9 10

WACC 0.18 0.10324 0.07635 0.06262 0.05427 0.04866 0.04464 0.0416 0.03924 0.03734 0.03578

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7

n 5 5 5 5 5 5 5 5 5 5 5

NOI 800 800 800 800 800 800 800 800 800 800 800 0.18 0.16448 0.145057 0.124461 0.103355 0.081982 0.060453 0.038822 0.017124 -0.00462 -0.0264

ke

NPV -249.479 -54.0913 38.31702 108.0017 171.1979 233.6326 298.1024 366.3677 439.7936 519.6189 607.092

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 0 1 2 3 4 5 6 7 8 9 10

WACC 0.18 0.09181 0.06064 0.04464 0.03489 0.02833 0.02361 0.02005 0.01728 0.01505 0.01322

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8

n 5 5 5 5 5 5 5 5 5 5 5

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.155616 0.125907 0.094544 0.062454 0.029979 -0.00272 -0.03557 -0.06852 -0.10154 -0.13462

NPV -499.653 -278.458 -175.24 -96.5465 -22.8934 53.21839 136.1565 229.4456 336.6381 461.8017 609.9262

ΔNPV 221.1945 103.2179 78.69376 73.65304 76.11182 82.93806 93.28915 107.1925 125.1636 148.1245

ΔNPV 195.3877 92.40829 69.68464 63.19622 62.43475 64.46977 68.26526 73.42597 79.82524 87.47314

21

Table 21.27 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 5-year project at t = 0.8

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

Table 21.26 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 5-year project at t = 0.7

434 Whether It Is Possible to Increase the Investment Efficiency, Increasing. . .

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 0 1 2 3 4 5 6 7 8 9 10

WACC 0.18 0.08024 0.04464 0.02627 0.01505 0.00747 0.00202 -0.0021 -0.0053 -0.0079 -0.01

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9

n 5 5 5 5 5 5 5 5 5 5 5

NOI 800 800 800 800 800 800 800 800 800 800 800 0.18 0.14648 0.105908 0.063074 0.019228 -0.02516 -0.06987 -0.11479 -0.15985 -0.20501 -0.25024

ke

NPV -749.826 -513.293 -412.881 -341.385 -276.023 -207.471 -129.536 -36.2409 79.64322 227.945 422.9012

Table 21.28 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 5-year project at t = 0.9 ΔNPV 236.5329 100.4127 71.49601 65.36206 68.55205 77.93497 93.29474 115.8841 148.3017 194.9563

21.2 Dependence of NPV on Tax on Profit Rates at Fixed Leverage Levels L 435

436

21

Whether It Is Possible to Increase the Investment Efficiency, Increasing. . .

Fig. 21.7 Dependence of NPV on leverage level L at fixed levels of tax on profit rates t for 5-year project

Fig. 21.8 Dependence of ΔNPV on leverage level L at fixed levels of tax on profit rates t for 5-year project

models influence of growth of tax on profit rate on the efficiency of the investment is investigated. It has been shown that for arbitrary duration projects as well as for perpetuity projects the growth of tax on profit rate change the nature of the NPV dependence on leverage at some value t*: there is a transition from diminishing function NPV(L) when t < t* to growing function NPV(L). The t* value depends on the duration of the project, cost of capital (equity and debt) values and other parameters of the project. At high leverage levels, this leads to qualitatively new effect in investments: growth of the efficiency of the investments with growth of tax on profit rate.

L 0 1 2 3 4 5 6 7 8 9 10

WACC 0.18 0.14854 0.13773 0.13226 0.12895 0.12674 0.12515 0.12396 0.12303 0.12228 0.12167

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3

n 10 10 10 10 10 10 10 10 10 10 10

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.19907 0.217182 0.235022 0.252747 0.270413 0.288045 0.305654 0.323249 0.340834 0.358411

NPV 1520.688 1464.753 1363.283 1258.441 1158.178 1064.362 977.2493 896.5725 821.8913 752.7207 688.5839

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 0 1 2 3 4 5 6 7 8 9 10

WACC 0.18 0.13773 0.12303 0.11554 0.111 0.10796 0.10577 0.10413 0.10284 0.10182 0.10097

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4

n 10 10 10 10 10 10 10 10 10 10 10

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.191455 0.201083 0.210169 0.21902 0.22775 0.236408 0.24502 0.253602 0.262161 0.270705

NPV 1157.161 1218.262 1199.745 1163.945 1122.813 1080.17 1037.562 995.6955 954.9111 915.3725 877.1497

Table 21.30 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 10-year project at t = 0.4

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

Table 21.29 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 10-year project at t = 0.3

ΔNPV 61.10029 -18.517 -35.7995 -41.1321 -42.6427 -42.6081 -41.8669 -40.7844 -39.5386 -38.2228

ΔNPV -51.935 -101.47 -104.843 -100.263 -93.8156 -87.1129 -80.6768 -74.6812 -69.1705 -64.1369

21.2 Dependence of NPV on Tax on Profit Rates at Fixed Leverage Levels L 437

L 0 1 2 3 4 5 6 7 8 9 10

WACC 0.18 0.14484 0.13178 0.125 0.12084 0.11803 0.116 0.11446 0.11326 0.1123 0.11151

k0 0.18 0.20056 0.20836 0.21253 0.21513 0.2169 0.21819 0.21917 0.21994 0.22055 0.22106

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

n 10 10 10 10 10 10 10 10 10 10 10

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.219687 0.255351 0.290005 0.32421 0.358168 0.391982 0.425702 0.459362 0.492979 0.526564

NPV 797.6345 753.4333 648.7259 545.0552 451.4547 368.775 296.0576 232.0307 175.4573 125.262 80.52365

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 0 1 2 3 4 5 6 7 8 9 10

WACC 0.18 0.11554 0.09247 0.08054 0.07324 0.06831 0.06476 0.06207 0.05998 0.05829 0.0569

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6

n 10 10 10 10 10 10 10 10 10 10 10

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.175084 0.165407 0.154162 0.142206 0.129869 0.117304 0.10459 0.091775 0.078888 0.065947

NPV 438.1076 682.6744 808.1048 909.471 1005.408 1102.434 1203.765 1311.466 1427.172 1552.376 1688.582

ΔNPV 244.5668 125.4304 101.3662 95.93652 97.02629 101.3309 107.7015 115.7055 125.2046 136.2059

ΔNPV -44.2013 -104.707 -103.671 -93.6005 -82.6797 -72.7174 -64.0269 -56.5734 -50.1953 -44.7383

21

Table 21.32 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 10-year project at t = 0.6

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

Table 21.31 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 10-year project at t = 0.5

438 Whether It Is Possible to Increase the Investment Efficiency, Increasing. . .

L 0 1 2 3 4 5 6 7 8 9 10

WACC 0.18 0.10413 0.0765 0.06207 0.05319 0.04716 0.04281 0.03951 0.03692 0.03484 0.03313

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7

n 10 10 10 10 10 10 10 10 10 10 10

NOI 800 800 800 800 800 800 800 800 800 800 800 0.18 0.166255 0.145497 0.122295 0.097953 0.072986 0.04764 0.022047 -0.00372 -0.0296 -0.05558

ke

NPV 78.58071 389.0551 566.253 726.7932 896.6995 1088.619 1312.791 1580.193 1904.18 2301.94 2796.249

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 0 1 2 3 4 5 6 7 8 9 10

WACC 0.18 0.09247 0.05998 0.04281 0.03215 0.02488 0.0196 0.01558 0.01243 0.00989 0.0078

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8

n 10 10 10 10 10 10 10 10 10 10 10

NOI 800 800 800 800 800 800 800 800 800 800 800

0.18 0.156938 0.123925 0.087223 0.048741 0.009262 -0.03083 -0.07133 -0.11211 -0.1531 -0.19424

ke

NPV -280.946 74.31716 279.1638 477.6501 710.4306 1008.261 1409.187 1969.561 2779.056 3986.481 5847.593

Table 21.34 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 10-year project at t = 0.8

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

Table 21.33 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 10-year project at t = 0.7

ΔNPV 355.2633 204.8466 198.4863 232.7806 297.8303 400.9259 560.3743 809.4944 1207.425 1861.112

ΔNPV 310.4744 177.1979 160.5402 169.9063 191.9196 224.1724 267.4019 323.9861 397.7601 494.3094

21.2 Dependence of NPV on Tax on Profit Rates at Fixed Leverage Levels L 439

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 0 1 2 3 4 5 6 7 8 9 10

WACC 0.18 0.08054 0.04281 0.02258 0.00989 0.00117 -0.0052 -0.0101 -0.0139 -0.017 -0.0195

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9

n 10 10 10 10 10 10 10 10 10 10 10

NOI 800 800 800 800 800 800 800 800 800 800 800 0.18 0.147081 0.100417 0.048303 -0.00655 -0.06297 -0.12039 -0.17847 -0.23701 -0.2959 -0.35504

ke

NPV -640.473 -265.375 -71.1609 115.7852 355.3712 711.8456 1295.448 2327.831 4295.041 8349.379 17464.72

ΔNPV 375.0978 194.2145 186.9461 239.586 356.4744 583.6021 1032.383 1967.211 4054.338 9115.336

21

Table 21.35 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 10-year project at t = 0.9

440 Whether It Is Possible to Increase the Investment Efficiency, Increasing. . .

21.2

Dependence of NPV on Tax on Profit Rates at Fixed Leverage Levels L

441

Fig. 21.9 Dependence of NPV on leverage level L at fixed levels of tax on profit rates t for 5-year project

Fig. 21.10 Dependence of ΔNPV on leverage level L at fixed levels of tax on profit rates t for 5-year project

Discovered effects take place under consideration from the point of view of owners of equity capital as well as from the point of view of owners of equity and debt capital. The observed at high leverage levels (starting from L = 6) increase of NPV with growth of the tax on profit rate t takes place at all values of t, that means that this is an entirely new effect in investments which can be applied in a real economic practice for optimizing of the management of investments. So, two very important qualitatively new effects in investments has been discovered:

442

21

Whether It Is Possible to Increase the Investment Efficiency, Increasing. . .

Table 21.36 Dependence of NPV and ΔNPV on tax on profit rate t at fixed leverage level L for 5-year project at L = 0 I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 0 0 0 0 0 0 0 0 0 0 0

WACC 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0 0 0 0 0 0 0 0 0 0

t 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

n 5 5 5 5 5 5 5 5 5 5 5

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

NPV 1501.74 1251.56 1001.39 751.22 501.04 250.87 0.69 -249.48 -499.65 -749.83 -1000.00

ΔNPV -250.174 -250.174 -250.174 -250.174 -250.174 -250.174 -250.174 -250.174 -250.174 -250.174

1. Change the character of NPV dependence on leverage 2. Growth of the efficiency of the investments with growth of tax on profit rate. Both effects could be used in practice to optimize investments.

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 2 2 2 2 2 2 2 2 2 2 2

WACC 0.18 0.16577 0.15137 0.13679 0.12201 0.10702 0.09181 0.07635 0.06064 0.04464 0.02833

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667

t 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

n 5 5 5 5 5 5 5 5 5 5 5

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.26 0.245315 0.230116 0.214367 0.19803 0.181065 0.163424 0.145057 0.125907 0.105908 0.084989

Table 21.37 Dependence of NPV and ΔNPV on tax on profit rate t at fixed leverage level L for 5-year project at L = 2 NPV 1108.06 987.07 857.87 719.28 569.91 408.07 231.71 38.32 -175.24 -412.88 -679.58

ΔNPV -120.983 -129.204 -138.59 -149.372 -161.839 -176.357 -193.394 -213.557 -237.64 -266.698

21.2 Dependence of NPV on Tax on Profit Rates at Fixed Leverage Levels L 443

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 4 4 4 4 4 4 4 4 4 4 4

WACC 0.18 0.16291 0.14556 0.12795 0.11004 0.09181 0.07323 0.05427 0.03489 0.01505 -0.0053

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8

t 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

n 5 5 5 5 5 5 5 5 5 5 5

NOI 800 800 800 800 800 800 800 800 800 800 800 0.34 0.31053 0.279807 0.24773 0.214184 0.179041 0.142153 0.103355 0.062454 0.019228 -0.02658

ke

NPV 808.33 757.29 698.00 628.39 545.62 445.84 323.63 171.20 -22.89 -276.02 -615.49

ΔNPV -51.044 -59.2842 -69.6148 -82.763 -99.7794 -122.217 -152.429 -194.091 -253.129 -339.472

21

Table 21.38 Dependence of NPV and ΔNPV on tax on profit rate t at fixed leverage level L for 5-year project at L = 4

444 Whether It Is Possible to Increase the Investment Efficiency, Increasing. . .

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 6 6 6 6 6 6 6 6 6 6 6

WACC 0.18 0.16168 0.14306 0.12413 0.10486 0.08522 0.06515 0.04464 0.02361 0.00202 -0.0202

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0.85714 0.85714 0.85714 0.85714 0.85714 0.85714 0.85714 0.85714 0.85714 0.85714 0.85714

t 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

n 5 5 5 5 5 5 5 5 5 5 5

NOI 800 800 800 800 800 800 800 800 800 800 800 0.42 0.375729 0.329434 0.280937 0.230037 0.176505 0.120078 0.060453 -0.00272 -0.06987 -0.14147

ke

Table 21.39 Dependence of NPV and ΔNPV on tax on profit rate t at fixed leverage level L for 5-year project at L = 6 NPV 574.85 568.61 557.30 538.90 510.35 466.82 400.49 298.10 136.16 -129.54 -588.03

ΔNPV -6.23744 -11.31 -18.3975 -28.5544 -43.5294 -66.3335 -102.385 -161.946 -265.692 -458.495

21.2 Dependence of NPV on Tax on Profit Rates at Fixed Leverage Levels L 445

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 8 8 8 8 8 8 8 8 8 8 8

WACC 0.18 0.16099 0.14167 0.12201 0.10198 0.08153 0.06064 0.03924 0.01728 -0.0053 -0.0286

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0.88889 0.88889 0.88889 0.88889 0.88889 0.88889 0.88889 0.88889 0.88889 0.88889 0.88889

t 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

n 5 5 5 5 5 5 5 5 5 5 5

NOI 800 800 800 800 800 800 800 800 800 800 800 0.5 0.440923 0.379039 0.314091 0.245786 0.173792 0.097721 0.017124 -0.06852 -0.15985 -0.25759

ke

NPV 389.30 412.78 435.38 456.10 472.98 482.28 476.49 439.79 336.64 79.64 -572.77

ΔNPV 23.47489 22.6083 20.71462 20.88106 9.298693 -5.79258 -36.6918 -103.156 -256.995 -652.415

21

Table 21.40 Dependence of NPV and ΔNPV on tax on profit rate t at fixed leverage level L for 5-year project at L = 8

446 Whether It Is Possible to Increase the Investment Efficiency, Increasing. . .

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 10 10 10 10 10 10 10 10 10 10 10

WACC 0.18 0.16056 0.14078 0.12066 0.10014 0.07918 0.05775 0.03578 0.01322 -0.01 -0.034

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0.90909 0.90909 0.90909 0.90909 0.90909 0.90909 0.90909 0.90909 0.90909 0.90909 0.90909

t 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

n 5 5 5 5 5 5 5 5 5 5 5

NOI 800 800 800 800 800 800 800 800 800 800 800 0.58 0.506115 0.428635 0.34722 0.261488 0.170996 0.075231 -0.0264 -0.13462 -0.25024 -0.37429

ke

Table 21.41 Dependence of NPV and ΔNPV on tax on profit rate t at fixed leverage level L for 5-year project at L = 10 NPV 239.23 282.73 329.61 380.49 435.81 495.28 556.05 607.09 609.93 422.90 -563.06

ΔNPV 43.49836 46.87962 50.87829 55.32552 59.47085 60.76747 51.04171 2.834166 -187.024 -985.964

21.2 Dependence of NPV on Tax on Profit Rates at Fixed Leverage Levels L 447

448

21

Whether It Is Possible to Increase the Investment Efficiency, Increasing. . .

Fig. 21.11 Dependence of NPV on tax on profit rate t at fixed leverage level L for 5-year project

Fig. 21.12 Dependence of ΔNPV on tax on profit rate t at fixed leverage level L for 5-year project

21.2

Dependence of NPV on Tax on Profit Rates at Fixed Leverage Levels L

449

Table 21.42 Dependence of NPV and ΔNPV on tax on profit rate t at fixed leverage level L for 10-year project at L = 0 I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 0 0 0 0 0 0 0 0 0 0 0

WACC 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0 0 0 0 0 0 0 0 0 0

t 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

n 10 10 10 10 10 10 10 10 10 10 10

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

NPV 2595.27 2235.74 1876.22 1520.69 1157.16 797.63 438.11 78.58 -280.95 -640.47 -1000.00

ΔNPV -359.527 -359.527 -359.527 -359.527 -359.527 -359.527 -359.527 -359.527 -359.527 -359.527

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 2 2 2 2 2 2 2 2 2 2 2

WACC 0.18 0.16618 0.1521 0.13773 0.12303 0.10796 0.09247 0.0765 0.05998 0.04281 0.02488

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667

t 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

n 10 10 10 10 10 10 10 10 10 10 10

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.26 0.24654 0.232299 0.217182 0.201083 0.183875 0.165407 0.145497 0.123925 0.100417 0.074631

NPV 1771.84 1646.71 1511.27 1363.28 1199.74 1020.58 808.10 566.25 279.16 -71.16 -513.16

ΔNPV -125.137 -135.437 -147.987 -163.538 -183.17 -208.47 -241.852 -287.089 -350.325 -442.002

21

Table 21.43 Dependence of NPV and ΔNPV on tax on profit rate t at fixed leverage level L for 10-year project at L = 2

450 Whether It Is Possible to Increase the Investment Efficiency, Increasing. . .

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 4 4 4 4 4 4 4 4 4 4 4

WACC 0.18 0.18316 0.17256 0.15772 0.14072 0.12227 0.10261 0.08181 0.0598 0.0364 0.01135

k0 0.18 0.20056 0.20836 0.21253 0.21513 0.2169 0.21819 0.21917 0.21994 0.22055 0.22106

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8

t 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

n 10 10 10 10 10 10 10 10 10 10 10

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.34 0.411801 0.414791 0.396579 0.367589 0.331331 0.289071 0.241069 0.186991 0.126013 0.056769

Table 21.44 Dependence of NPV and ΔNPV on tax on profit rate t at fixed leverage level L for 10-year project at L = 4 NPV 1226.89 751.26 611.77 537.31 482.43 430.34 370.14 289.66 168.91 -33.11 -415.80

ΔNPV -475.625 -139.495 -74.4553 -54.8815 -52.0879 -60.1971 -80.4792 -120.753 -202.021 -382.685

21.2 Dependence of NPV on Tax on Profit Rates at Fixed Leverage Levels L 451

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 6 6 6 6 6 6 6 6 6 6 6

WACC 0.18 0.16218 0.14392 0.12515 0.10577 0.08569 0.06476 0.04281 0.0196 -0.0052 -0.032

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0.85714 0.85714 0.85714 0.85714 0.85714 0.85714 0.85714 0.85714 0.85714 0.85714 0.85714

t 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

n 10 10 10 10 10 10 10 10 10 10 10

NOI 800 800 800 800 800 800 800 800 800 800 800 0.42 0.379295 0.335473 0.288045 0.236408 0.179813 0.117304 0.04764 -0.03083 -0.12039 -0.22431

ke

NPV 847.62 884.68 927.22 977.25 1037.56 1111.80 1203.76 1312.79 1409.19 1295.45 -374.07

ΔNPV 37.06285 42.53552 50.03126 60.31305 74.23617 91.96624 109.0267 96.39537 -113.739 -1669.51

21

Table 21.45 Dependence of NPV and ΔNPV on tax on profit rate t at fixed leverage level L for 10-year project at L = 6

452 Whether It Is Possible to Increase the Investment Efficiency, Increasing. . .

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 8 8 8 8 8 8 8 8 8 8 8

WACC 0.18 0.16152 0.14255 0.12303 0.10284 0.08188 0.05998 0.03692 0.01243 -0.0139 -0.0426

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0.88889 0.88889 0.88889 0.88889 0.88889 0.88889 0.88889 0.88889 0.88889 0.88889 0.88889

t 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

n 10 10 10 10 10 10 10 10 10 10 10

NOI 800 800 800 800 800 800 800 800 800 800 800 0.5 0.445653 0.386973 0.323249 0.253602 0.17692 0.091775 -0.00372 -0.11211 -0.23701 -0.38375

ke

Table 21.46 Dependence of NPV and ΔNPV on tax on profit rate t at fixed leverage level L for 10-year project at L = 8 NPV 572.25 640.00 720.91 821.89 954.91 1142.05 1427.17 1904.18 2779.06 4295.04 -350.88

ΔNPV 67.74227 80.91054 100.9849 133.0198 187.1372 285.1235 477.0078 874.876 1515.986 -4645.92

21.2 Dependence of NPV on Tax on Profit Rates at Fixed Leverage Levels L 453

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 10 10 10 10 10 10 10 10 10 10 10

WACC 0.18 0.16109 0.14168 0.12167 0.10097 0.07944 0.0569 0.03313 0.0078 -0.0195 -0.0496

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0.90909 0.90909 0.90909 0.90909 0.90909 0.90909 0.90909 0.90909 0.90909 0.90909 0.90909

t 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

n 10 10 10 10 10 10 10 10 10 10 10

NOI 800 800 800 800 800 800 800 800 800 800 800 0.58 0.512008 0.438456 0.358411 0.270705 0.173857 0.065947 -0.05558 -0.19424 -0.35504 -0.54557

ke

NPV 365.08 450.10 553.96 688.58 877.15 1169.53 1688.58 2796.25 5847.59 17464.71 -336.13

ΔNPV 85.01433 103.8568 134.6286 188.5659 292.3814 519.0512 1107.667 3051.344 11617.12 -17800.8

21

Table 21.47 Dependence of NPV and ΔNPV on tax on profit rate t at fixed leverage level L for 10-year project at L = 10

454 Whether It Is Possible to Increase the Investment Efficiency, Increasing. . .

21.2

Dependence of NPV on Tax on Profit Rates at Fixed Leverage Levels L

455

Fig. 21.13 Dependence of NPV on tax on profit rate t at fixed leverage level L for 10-year project

Fig. 21.14 Dependence of ΔNPV on tax on profit rate t at fixed leverage level L for 10-year project

456

21

Whether It Is Possible to Increase the Investment Efficiency, Increasing. . .

Table 21.48 Dependence of NPV and ΔNPV on tax on profit rate t at fixed leverage level L for perpetuity project at L = 8 t 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

L 8 8 8 8 8 8 8 8 8 8 8

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

NOI 800 800 800 800 800 800 800 800 800 800 800

NPV -32111.1 -37114.8 -44,828 -57487.2 -81067.2 -138,333 -464,667 352294.1 129828.3 80567.25 59,000

ΔNPV -5003.72 -7713.12 -12659.2 -23,580 -57266.1 -326,333 816960.8 -222,466 -49,261 -21567.3

Table 21.49 Dependence of NPV and ΔNPV on tax on profit rate t at fixed leverage level L for perpetuity project at L = 10 t 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

L 10 10 10 10 10 10 10 10 10 10 10

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

NOI 800 800 800 800 800 800 800 800 800 800 800

NPV -41,000 -50090.9 -66,000 -98692.3 -198,143 -8.6E+19 202,750 103117.6 70111.11 53736.84 44,000

ΔNPV -9090.91 -15909.1 -32692.3 -99450.5 -8.6E+19 8.65E+19 -99632.4 -33006.5 -16374.3 -9736.84

21.2

Dependence of NPV on Tax on Profit Rates at Fixed Leverage Levels L

457

Fig. 21.15 Dependence of ΔNPV on tax on profit rate t at fixed leverage level L for perpetuity project Table 21.50 Dependence of NPV and ΔNPV on tax on profit rate t at fixed leverage level L for 5-year project at L = 0 I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 0 0 0 0 0 0 0 0 0 0 0

WACC 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0 0 0 0 0 0 0 0 0 0

t 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

n 5 5 5 5 5 5 5 5 5 5 5

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

NPV 1501.737 1251.563 1001.389 751.2158 501.0421 250.8684 0.694727 -249.479 -499.653 -749.826 -1000

ΔNPV -250.174 -250.174 -250.174 -250.174 -250.174 -250.174 -250.174 -250.174 -250.174 -250.174

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 2 2 2 2 2 2 2 2 2 2 2

WACC 0.18 0.16577 0.15137 0.13679 0.12201 0.10702 0.09181 0.07635 0.06064 0.04464 0.02833

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667

t 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

n 5 5 5 5 5 5 5 5 5 5 5

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.26 0.245315 0.230116 0.214367 0.19803 0.181065 0.163424 0.145057 0.125907 0.105908 0.084989

NPV 1108.057 987.0733 857.869 719.2786 569.9064 408.0676 231.711 38.31702 -175.24 -412.881 -679.579

ΔNPV -120.983 -129.204 -138.59 -149.372 -161.839 -176.357 -193.394 -213.557 -237.64 -266.698

21

Table 21.51 Dependence of NPV and ΔNPV on tax on profit rate t at fixed leverage level L for 5-year project at L = 2

458 Whether It Is Possible to Increase the Investment Efficiency, Increasing. . .

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 4 4 4 4 4 4 4 4 4 4 4

WACC 0.18 0.16291 0.14556 0.12795 0.11004 0.09181 0.07323 0.05427 0.03489 0.01505 -0.0053

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8

t 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

n 5 5 5 5 5 5 5 5 5 5 5

NOI 800 800 800 800 800 800 800 800 800 800 800 0.34 0.31053 0.279807 0.24773 0.214184 0.179041 0.142153 0.103355 0.062454 0.019228 -0.02658

ke

Table 21.52 Dependence of NPV and ΔNPV on tax on profit rate t at fixed leverage level L for 5-year project at L = 4 NPV 808.3293 757.2853 698.0011 628.3863 545.6233 445.8439 323.6272 171.1979 -22.8934 -276.023 -615.495

ΔNPV -51.044 -59.2842 -69.6148 -82.763 -99.7794 -122.217 -152.429 -194.091 -253.129 -339.472

21.2 Dependence of NPV on Tax on Profit Rates at Fixed Leverage Levels L 459

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 6 6 6 6 6 6 6 6 6 6 6

WACC 0.18 0.16168 0.14306 0.12413 0.10486 0.08522 0.06515 0.04464 0.02361 0.00202 -0.0202

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0.85714 0.85714 0.85714 0.85714 0.85714 0.85714 0.85714 0.85714 0.85714 0.85714 0.85714

t 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

n 5 5 5 5 5 5 5 5 5 5 5

NOI 800 800 800 800 800 800 800 800 800 800 800 0.42 0.375729 0.329434 0.280937 0.230037 0.176505 0.120078 0.060453 -0.00272 -0.06987 -0.14147

ke

NPV 574.8492 568.6118 557.3019 538.9044 510.3499 466.8205 400.487 298.1024 136.1565 -129.536 -588.03

ΔNPV -6.23744 -11.31 -18.3975 -28.5544 -43.5294 -66.3335 -102.385 -161.946 -265.692 -458.495

21

Table 21.53 Dependence of NPV and ΔNPV on tax on profit rate t at fixed leverage level L for 5-year project at L = 6

460 Whether It Is Possible to Increase the Investment Efficiency, Increasing. . .

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 8 8 8 8 8 8 8 8 8 8 8

WACC 0.18 0.16099 0.14167 0.12201 0.10198 0.08153 0.06064 0.03924 0.01728 -0.0053 -0.0286

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0.88889 0.88889 0.88889 0.88889 0.88889 0.88889 0.88889 0.88889 0.88889 0.88889 0.88889

t 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

n 5 5 5 5 5 5 5 5 5 5 5

NOI 800 800 800 800 800 800 800 800 800 800 800 0.5 0.440923 0.379039 0.314091 0.245786 0.173792 0.097721 0.017124 -0.06852 -0.15985 -0.25759

ke

Table 21.54 Dependence of NPV and ΔNPV on tax on profit rate t at fixed leverage level L for 5-year project at L = 8 NPV 389.3004 412.7753 435.3836 456.0982 472.9793 482.278 476.4854 439.7936 336.6381 79.64322 -572.772

ΔNPV 23.47489 22.6083 20.71462 20.88106 9.298693 -5.79258 -36.6918 -103.156 -256.995 -652.415

21.2 Dependence of NPV on Tax on Profit Rates at Fixed Leverage Levels L 461

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 10 10 10 10 10 10 10 10 10 10 10

WACC 0.18 0.16056 0.14078 0.12066 0.10014 0.07918 0.05775 0.03578 0.01322 -0.01 -0.034

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0.90909 0.90909 0.90909 0.90909 0.90909 0.90909 0.90909 0.90909 0.90909 0.90909 0.90909

t 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

n 5 5 5 5 5 5 5 5 5 5 5

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.58 0.506115 0.428635 0.34722 0.261488 0.170996 0.075231 -0.0264 -0.13462 -0.25024 -0.37429

NPV 239.2302 282.7286 329.6082 380.4865 435.812 495.2828 556.0503 607.092 609.9262 422.9017 -563.062

ΔNPV 43.49836 46.87962 50.87829 55.32552 59.47085 60.76747 51.04171 2.834166 -187.024 -985.964

21

Table 21.55 Dependence of NPV and ΔNPV on tax on profit rate t at fixed leverage level L for 5-year project at L = 10

462 Whether It Is Possible to Increase the Investment Efficiency, Increasing. . .

21.2

Dependence of NPV on Tax on Profit Rates at Fixed Leverage Levels L

463

Fig. 21.16 Dependence of NPV on tax on profit rate t at fixed leverage level L for 5-year project

Fig. 21.17 Dependence of ΔNPV on tax on profit rate t at fixed leverage level L for 5-year project

464

21

Whether It Is Possible to Increase the Investment Efficiency, Increasing. . .

Table 21.56 Dependence of NPV and ΔNPV on tax on profit rate t at fixed leverage level L for 10-year project at L = 0 I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 0 0 0 0 0 0 0 0 0 0 0

WACC 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0 0 0 0 0 0 0 0 0 0

t 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

n 10 10 10 10 10 10 10 10 10 10 10

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

NPV 2595.269 2235.742 1876.215 1520.688 1157.161 797.6345 438.1076 78.58071 -280.946 -640.473 -1000

ΔNPV -359.527 -359.527 -359.527 -359.527 -359.527 -359.527 -359.527 -359.527 -359.527 -359.527

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 2 2 2 2 2 2 2 2 2 2 2

WACC 0.18 0.16618 0.1521 0.13773 0.12303 0.10796 0.09247 0.0765 0.05998 0.04281 0.02488

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667

t 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

n 10 10 10 10 10 10 10 10 10 10 10

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.26 0.24654 0.232299 0.217182 0.201083 0.183875 0.165407 0.145497 0.123925 0.100417 0.074631

Table 21.57 Dependence of NPV and ΔNPV on tax on profit rate t at fixed leverage level L for 10-year project at L = 2 NPV 1771.845 1646.708 1511.27 1363.283 1199.745 1020.575 808.1048 566.253 279.1638 -71.1609 -513.163

ΔNPV -125.137 -135.437 -147.987 -163.538 -183.17 -208.47 -241.852 -287.089 -350.325 -442.002

21.2 Dependence of NPV on Tax on Profit Rates at Fixed Leverage Levels L 465

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 4 4 4 4 4 4 4 4 4 4 4

WACC 0.18 0.18316 0.17256 0.15772 0.14072 0.12227 0.10261 0.08181 0.0598 0.0364 0.01135

k0 0.18 0.20056 0.20836 0.21253 0.21513 0.2169 0.21819 0.21917 0.21994 0.22055 0.22106

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8

t 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

n 10 10 10 10 10 10 10 10 10 10 10

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.34 0.411801 0.414791 0.396579 0.367589 0.331331 0.289071 0.241069 0.186991 0.126013 0.056769

NPV 1226.885 751.2601 611.7654 537.3101 482.4286 430.3407 370.1436 289.6644 168.9112 -33.1095 -415.795

ΔNPV -475.625 -139.495 -74.4553 -54.8815 -52.0879 -60.1971 -80.4792 -120.753 -202.021 -382.685

21

Table 21.58 Dependence of NPV and ΔNPV on tax on profit rate t at fixed leverage level L for 10-year project at L = 4

466 Whether It Is Possible to Increase the Investment Efficiency, Increasing. . .

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 6 6 6 6 6 6 6 6 6 6 6

WACC 0.18 0.16218 0.14392 0.12515 0.10577 0.08569 0.06476 0.04281 0.0196 -0.0052 -0.032

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0.85714 0.85714 0.85714 0.85714 0.85714 0.85714 0.85714 0.85714 0.85714 0.85714 0.85714

t 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

n 10 10 10 10 10 10 10 10 10 10 10

NOI 800 800 800 800 800 800 800 800 800 800 800 0.42 0.379295 0.335473 0.288045 0.236408 0.179813 0.117304 0.04764 -0.03083 -0.12039 -0.22431

ke

Table 21.59 Dependence of NPV and ΔNPV on tax on profit rate t at fixed leverage level L for 10-year project at L = 6 NPV 847.6197 884.6825 927.218 977.2493 1037.562 1111.799 1203.765 1312.791 1409.187 1295.448 -374.066

ΔNPV 37.06285 42.53552 50.03126 60.31305 74.23617 91.96624 109.0267 96.39537 -113.739 -1669.51

21.2 Dependence of NPV on Tax on Profit Rates at Fixed Leverage Levels L 467

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 8 8 8 8 8 8 8 8 8 8 8

WACC 0.18 0.16152 0.14255 0.12303 0.10284 0.08188 0.05998 0.03692 0.01243 -0.0139 -0.0426

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0.88889 0.88889 0.88889 0.88889 0.88889 0.88889 0.88889 0.88889 0.88889 0.88889 0.88889

t 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

n 10 10 10 10 10 10 10 10 10 10 10

NOI 800 800 800 800 800 800 800 800 800 800 800 0.5 0.445653 0.386973 0.323249 0.253602 0.17692 0.091775 -0.00372 -0.11211 -0.23701 -0.38375

ke

NPV 572.2536 639.9958 720.9064 821.8913 954.9111 1142.048 1427.172 1904.18 2779.056 4295.041 -350.883

ΔNPV 67.74227 80.91054 100.9849 133.0198 187.1372 285.1235 477.0078 874.876 1515.986 -4645.92

21

Table 21.60 Dependence of NPV and ΔNPV on tax on profit rate t at fixed leverage level L for 10-year project at L = 8

468 Whether It Is Possible to Increase the Investment Efficiency, Increasing. . .

I 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

L 10 10 10 10 10 10 10 10 10 10 10

WACC 0.18 0.16109 0.14168 0.12167 0.10097 0.07944 0.0569 0.03313 0.0078 -0.0195 -0.0496

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0.90909 0.90909 0.90909 0.90909 0.90909 0.90909 0.90909 0.90909 0.90909 0.90909 0.90909

t 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

n 10 10 10 10 10 10 10 10 10 10 10

NOI 800 800 800 800 800 800 800 800 800 800 800 0.58 0.512008 0.438456 0.358411 0.270705 0.173857 0.065947 -0.05558 -0.19424 -0.35504 -0.54557

ke

NPV 365.0841 450.0984 553.9552 688.5839 877.1497 1169.531 1688.582 2796.249 5847.593 17464.71 -336.131

Table 21.61 Dependence of NPV and ΔNPV on tax on profit rate t at fixed leverage level L for 10-year project at L = 10 ΔNPV 85.01433 103.8568 134.6286 188.5659 292.3814 519.0512 1107.667 3051.344 11617.12 -17800.8

21.2 Dependence of NPV on Tax on Profit Rates at Fixed Leverage Levels L 469

470

21

Whether It Is Possible to Increase the Investment Efficiency, Increasing. . .

Fig. 21.18 Dependence of NPV on tax on profit rate t at fixed leverage level L for 10-year project

Fig. 21.19 Dependence of NPV on tax on profit rate t at fixed leverage level L for 10-year project (more detailed)

References

471

Fig. 21.20 Dependence of ΔNPV on tax on profit rate t at fixed leverage level L for 10-year project

Fig. 21.21 Dependence of ΔNPV on tax on profit rate t at fixed leverage level L for 10-year project (more detailed)

References Brusov P, Filatova T, Orehova N, Brusova A (2011a) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life-time company. Appl Financ Econ 21(11): 815–824 Brusov P, Filatova T, Orehova N et al (2011b) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Bus ICT 2:16–21 Brusov P, Filatova T, Orehova N et al (2011c) Influence of debt financing on the effectiveness of the investment project within the Modigliani–Miller theory. Res J Econ Bus ICT (UK) 2:11–15

472

21

Whether It Is Possible to Increase the Investment Efficiency, Increasing. . .

Brusov PN, Filatova ТV et al (2011d) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Finance Credit 435:2–8 Brusov P, Filatova T, Eskindarov M, Orehova N (2012a) Influence of debt financing on the effectiveness of the finite duration investment project. Appl Financ Econ 22(13):1043–1052 Brusov P, Filatova T, Eskindarov M, Orehova N (2012b) Hidden global causes of the global financial crisis. J Rev Glob Econ 1:106–111 Brusov P, Filatova P, Orekhova N (2013a) Absence of an optimal capital structure in the famous tradeoff theory! J Rev Glob Econ 2:94–116 Brusov P, Filatova T, Orehova N (2013b) A qualitatively new effect in corporative finance: abnormal dependence of cost of equity of company on leverage. J Rev Glob Econ 2:183–193 Brusov P, Filatova P, Orekhova N (2014a) Mechanism of formation of the company optimal capital structure, different from suggested by trade off theory. Cogent Econ Finance 2:1–13. https://doi. org/10.1080/23322039.2014.946150 Brusov P, Filatova T, Orehova N (2014b) Inflation in Brusov–Filatova–Orekhova theory and in its perpetuity limit – Modigliani–Miller theory. J Rev Glob Econ 3:175–185 Brusova A (2011) А comparison of the three methods of estimation of weighted average cost of capital and equity cost of company. Financ Anal Prob Solutions 34(76):36–42 Filatova Т, Orehova N, Brusova А (2008) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life-time company. Bull FU 48:68–77 Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Modigliani F, Miller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391

Chapter 22

Optimizing the Investment Structure of the Telecommunication Sector Company

Keywords Investment projects · Efficiency of investments · Optimal investment structure · Telecommunication sector · Brusov–Filatova–Orekhova (BFO) theory · Modigliani–Miller theory · Debt financing In this chapter developed by the authors models on the evaluation of the dependence of the effectiveness of investments on debt financing are applied for the analysis of investments of one of the telecommunication company for 2010–2012 from the point of view of optimal structure of investment. The analysis revealed that only in 2011, the company’s investment structure was close to the optimal.

22.1

Introduction

Investments in tangible and intangible assets play an important role in the activities of any company. They are a necessary condition for structural adjustment and economic growth and provide the creation of new and enhancement of existing basic funds and industries. The role of investment, which is always one of the most important, is increased many times at the current stage. For example, in Russia, a priority of budget will be reduced dependence of the price of oil and gas. The main issue that helps at least to start the movement on this way is, of course, investments. In this way, the role of investment at the present stage is indeed increasing dramatically. In this regard, the role of the evaluation of the efficiency of investment projects, which in the context of scarcity and limited investment resources allows the realization of the most effective projects, increases. Since virtually all investment projects use debt financing, the purpose of the study of the impact of debt financing and capital structure on the efficiency of investment projects, determining the optimal level leverage, is especially actual at the present time. The hope to determine the optimal capital structure, in which one or more parameters of the efficiency of the project (NPV, IRR, etc.) are maximum, more than half a century has encouraged researchers to deal with the issue. Some of the © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_22

473

474

22

Optimizing the Investment Structure of the Telecommunication Sector Company

major problems in the assessment of the effectiveness of the projects are the following: – What are financial flows and why are they necessary to take into account when calculating parameters of efficiency of the project (NPV, IRR, etc.)? – How many discount rates should be used for financial flows associated with investments? – How can these discount rates be accurately determined? Discussion concerning the first two problems is ongoing. On the third issue, one needs to note that, in recent years, there has been a significant progress in the accurate determination of the cost of the equity capital of the company and its weighted average cost, which as time and are the discount rate when evaluating the NPV of the project. The progress is associated with work performed by Brusov, Filatova, and Orekhova (Brusov et al. 2015; Brusov et al. 2018a, b, c, d; Brusov and Filatova 2011; Brusov et al. 2011a, b, c, 2012a, b, 2013a, b, 2014a, b; Filatova et al. 2008; Brusova 2011), in which the general theory of capital cost of the company (equity cost as well as weighted average cost) was established and its dependence on leverage and on lifetime (age) of company was found for the companies with arbitrary lifetime (age). The main difference between their theory and theory by Modigliani and Miller is that the former one waives from the perpetuity of the companies, which leads to significant differences of a new theory from theory of Nobel laureates Modigliani and Miller (1958, 1963, 1966). The lack of modern methods of evaluation of effectiveness of investment projects with account of the debt financing, with the correct assessment of discount rate, used in investment models, has identified the need for research. The establishment of such modern models, considering problem from the point of view of equity capital owners as well as from the point of view of equity and debt capital owners, with the use of modern theory by Brusov, Filatova, and Orekhova that assesses the equity capital cost and weighted average cost of capital of the company (Мodigliani and Мiller 1958, 1963, 1966), which play the role of discount rate in the investment models, can significantly contribute to the problem of the assessment of investment projects’ effectiveness.

22.2

Investment Analysis and Recommendations for Telecommunication Company “Nastcom Plus”

Based on the method, developed by the authors (Brusov and Filatova 2011; Brusov et al. 2011a, b, c, 2012a, b, 2013a, b, 2014a, b; Filatova et al. 2008), let us analyze the efficiency of investments of one of the leading companies in the telecommunication sector “Nastcom Plus” for 2010–2012 from the point of view of optimal structure of investment. The source data for the analysis are presented in Table 22.1.

Investment Analysis and Recommendations for Telecommunication. . .

22.2

475

Table 22.1 Data of “Nastcom Plus” for 2010–2012 Indicator Investment I, million dollars Revenue, million dollars Net operating income for the year before taxing, NOI, million dollars Equity cost at zero leverage, k0, % Debt cost k d , % Return on investment for 1 year, β = I/NOI Amount of debt financing, % Amount of equity, % Leverage level, L Amount of equity capital S, million dollars

60

2010 1.124 7204.335 2161.3

2011 2.05 8232.172 2469.174

2012 2.763 9418.773 2826

23.67 8.26

23.67 7.4

23.67 6.69

1.92 35 65 0.54 730.6

1.204 50 50 1 1025

1.02 50 50 1 1381.5

K ke

50

ke

40

4 5 6

30

ke WACC WACC

1 2 3

20

WACC

10

L 0

0.5

1

1.5

2

2.5

3

Fig. 22.1 Dependence of weighted average cost of capital WACC and the equity cost ke on leverage: 1, 4 within Brusov–Filatova–Orekhova theory; 2, 5 within Modigliani–Miller theory; 3, 6 within traditional approach

Quantity k0 is the equity cost of financially independent company (or equity cost at zero leverage) and for “Nastcom Plus” is equal to 23.67% (Brusova 2011). Here are also calculated dependence of weighted average cost of capital WACC and the equity cost ke on leverage (Fig. 22.1).

476

22

Optimizing the Investment Structure of the Telecommunication Sector Company

22.2.1

The Dependence of NPV on Investment Capital Structure

Analysis of investment will be continued with use of the formula provided in the works (Brusov and Filatova 2011; Brusov et al. 2011a, b, c, 2012a, b, 2013a, b, 2014a, b; Filatova et al. 2008):      1 1 þ NPV = - S 1 þ L ð1 - t Þ 1 ð1 þ k d Þn ð1 þ k d Þn   βSð1 þ LÞð1 - t Þ 1 , 1þ ke ð1 þ k e Þn

ð22:1Þ

where NPV—net present value S—equity capital amount L—leverage level t—tax on profit rate kd—debt cost n—project duration β—return on investment for 1 year ke—equity cost Analysis of Investments in 2010 Using company’s data (Table 22.1), we compute the WACC, ke, and NPV (Tables 22.2, 22.3, 22.4, Figs. 22.1 and 22.2). In the company’s investment in 2010, equity capital accounted for 65%, and debt 35%, i.e., the leverage level was equal to L = 0.54. The term for hardware depreciation, into establishment of which investment was done, was 5 years. Curve 2 (Fig. 22.2) corresponds to the dependence of NPV on leverage level for the 5-year project. Optimum NPV is achieved when L = 2. At this leverage level, NPV = 3624.5 million dollars. The level leverage with which “Nastcom Plus” has carried out its investment projects (L = 0.54) was lying far from optimum and provided NPV = 2979.2 million dollars, which is approximately 645 million dollars less than the optimal value of NPV. Since the equipment can be operated, after depreciation, one can estimate the NPV for a more long-term perspective. For example, for the 7-year project, the optimal leverage value is L = 2.0, when the NPV = 4157.6 million dollars, which is 562.8 million dollars more than non-optimal values of NPV = 3594.8 million dollars, obtained by the company. For the 10-year project, the optimal leverage level is L = 1.5, with NPV = 4509.1 million dollars, which is 422.9 million dollars more than non-optimal values of NPV = 4086.2 million dollars, obtained by the company (Fig. 22.2, Tables 22.2, 22.3, and 22.4).

Leverage level L 0 0.5 0.2367 0.2284 0.2367 0.2262 0.2367 0.2256 0.2366 0.2250

Leverage level L 0 0.5 0.2367 0.3096 0.2367 0.3063 0.2367 0.3053 0.2366 0.3044 1 0.3824 0.3758 0.3738 0.3720

1 0.2242 0.2209 0.2199 0.2190

Project duration n 2 5 7 10

Leverage level L 0 0.5 910.5 1181.8 2371.6 2979.2 2939.0 3594.8 3444.5 4086.2 1 1358.3 3347.7 3955.1 4396.9

Table 22.4 Net present value, NPV, in 2010, million dollars

Project duration n 2 5 7 10

Table 22.3 Equity cost, ke, in 2010

Project duration n 2 5 7 10

1.5 1458.5 3547.1 4121.6 4509.1

1.5 0.4552 0.4452 0.4423 0.4396

1.5 0.2217 0.2177 0.2166 0.2155

Table 22.2 Weighted average cost of capital, WACC, in 2010

2 1496.3 3624.5 4157.6 4497.4

2 0.5280 0.5147 0.5107 0.5071

2 0.2201 0.2156 0.2143 0.2131

2.5 1482.8 3612.4 4103.6 4405.3

2.5 0.6008 0.5841 0.5791 0.5746

2.5 0.2189 0.2141 0.2127 0.2114

3 1426.6 3533.6 3981.6 4258.9

3 0.6736 0.6536 0.6480 0.6422

3 0.2180 0.2130 0.2116 0.2101

3.5 1334.6 3404.2 3821.6 4074.9

3.5 0.7464 0.7230 0.7165 0.7097

3.5 0.2173 0.2121 0.2106 0.2091

4 1212.4 3236.1 3619.9 3863.8

4 0.8192 0.7925 0.7850 0.7772

4 0.2167 0.2114 0.2099 0.2083

4.5 1064.5 3038.0 3397.1 3632.7

4.5 0.8920 0.8619 0.8535 0.8447

4.5 0.2163 0.2108 0.2093 0.2076

Investment Analysis and Recommendations for Telecommunication. . . 894.5 2816.2 3155.1 3386.5

5

5 0.9649 0.9314 0.9220 0.9122

5 0.2159 0.2103 0.2087 0.2071

22.2 477

478

22

5 000

Optimizing the Investment Structure of the Telecommunication Sector Company

NPV

4 000

4 3 2

3 000 2 000 1 000

1

L

0 0

1

2

3

4

5

6

Fig. 22.2 Dependence of NPV on leverage L at t = 20% in 2010: 1 for 2-year income from investments; 2 for 5-year income from investments (the term for hardware depreciation); 3 for 7 years of investment income; 4 for 10 years of investment income

Analysis of Investments in 2011 Using company’s data, we compute the WACC, ke, and NPV (Tables 22.5, 22.6, 22.7, and Fig. 22.3). In the company’s investment in 2011, equity capital accounted for 50%, and debt capital for 50% as well, i.e., the leverage level was equal to L = 1. The term for hardware depreciation, into establishment of which investment was done, was 5 years. Curve 2 (Fig. 22.3) corresponds to dependence of NPV on leverage level for the 5-year project. Optimum NPV is achieved approximately at L = 1. More accurate calculations show that the optimal value of NPV = 2133.7 million dollars is achieved when L = 1.1. The level leverage with which “Nastcom Plus” has carried out its investment projects (L = 0.1) was lying in the vicinity of optimum and provided NPV = 2131.8 million dollars, which is just 2 million dollars less than the optimal value of NPV. You can take it that, in 2011, investment in “Nastcom Plus” company has been carried out with almost optimal structure. Analysis of Investments in 2012 Using company’s data, we compute the WACC, ke, and NPV (Tables 22.8, 22.9, and 22.10, Fig. 22.4). The company’s investment structure in 2012 was the same as in 2011: equity capital accounted for 50%, and debt capital for 50%, i.e., the leverage level was equal to L = 1. The term hardware for depreciation, into the establishment of which investment was done, was 5 years. Curve 2 (Fig. 22.4) corresponds to dependence of NPV on leverage level for the 5-year project. Optimum NPV is achieved when L = 0.5. More accurate calculations show that the optimal value of NPV = 1987.7 million dollars is achieved when L = 0.7 (Table 22.11, Fig. 22.5). The level leverage, with which “Nastcom Plus” has carried out its investment projects (L = 0.1), did not correspond to optimum value (L = 0.7) and provided NPV = 1954.6 million dollars, which is 31.7 million dollars less than the optimal value of NPV (Figs. 22.4 and 22.5; Tables 22.10 and 22.11).

Project duration n 2 5 7 10

Leverage level L 0 0.5 0.2367 0.3096 0.2367 0.3063 0.2367 0.3053 0.2366 0.3044 1 0.3824 0.3758 0.3738 0.3720

1.5 0.4552 0.4452 0.4423 0.4396

Table 22.5 Weighted average cost of capital, WACC, in 2011 2 0.5280 0.5147 0.5107 0.5071

2.5 0.6008 0.5841 0.5791 0.5746

3 0.6736 0.6536 0.6480 0.6422

3.5 0.7464 0.7230 0.7165 0.7097

4 0.8192 0.7925 0.7850 0.7772

4.5 0.8920 0.8619 0.8535 0.8447

5 0.9649 0.9314 0.9220 0.9122

22.2 Investment Analysis and Recommendations for Telecommunication. . . 479

Project duration n 2 5 7 10

Leverage level L 0 0.5 0.2367 0.3142 0.2367 0.3110 0.2367 0.3100 0.2366 0.3091 1 0.3916 0.3853 0.3833 0.3813

1.5 0.4690 0.4595 0.4565 0.4536

2 0.5464 0.5338 0.5297 0.5258

2.5 0.6239 0.6080 0.6029 0.5980

3 0.7013 0.6822 0.6761 0.6702

3.5 0.7787 0.7565 0.7493 0.7424

4 0.8561 0.8307 0.8230 0.8146

4.5 0.9335 0.9049 0.8963 0.8868

5 1.0110 0.9791 0.9695 0.9589

22

Table 22.6 Equity cost, ke, in 2011

480 Optimizing the Investment Structure of the Telecommunication Sector Company

Project duration n 2 5 7 10

Leverage level L 0 0.5 418.8 460.5 1704.2 2025.4 2203.4 2558.0 2648.2 2982.3 415.8 2131.8 2650.5 3028.1

1

1.5 302.3 2089.9 2576.1 2907.1

2 133.3 1943.2 2392.2 2685.2

Table 22.7 Net present value, NPV, of the company in 2011, million dollars 2.5 -80.9 1721.0 2134.4 2399.5

3 -332.5 1443.5 1825.6 2071.6

3.5 -615.0 1124.7 1480.7 1715.0

4 -923.5 774.8 1105.7 1338.0

4.5 -1254.0 400.9 715.0 946.0

5 -1603.1 8.5 309.8 542.9

22.2 Investment Analysis and Recommendations for Telecommunication. . . 481

482

22

Optimizing the Investment Structure of the Telecommunication Sector Company

NPV

4 000 3 000 2 000 1 000

4 3 2

0

L

-1 000 1

-2 000 0

1

2

3

4

5

6

Fig. 22.3 Dependence of NPV on leverage L at t = 20% in 2011: 1 for 2-year income from investments; 2 for 5-year income from investments (the term for hardware depreciation); 3 for 7 years of investment income; 4 for 10 years of investment income

Since the equipment can be operated after depreciation, one can estimate the NPV for a more long-term perspective. For example, for the 7-year project, the optimal leverage value is L = 0.65, when the NPV = 2580.6 million dollars, which is 51.7 million dollars more than non-optimal values of NPV = 2528.9 million dollars, obtained by the company. For the 10-year project, the optimal leverage level L = 0.55, with NPV = 3043.5 million dollars, which is 98 million dollars more than non-optimal values of NPV = 2945.5 million dollars, obtained by the company.

22.2.2

The Dependence of NPV on the Equity Capital Value and Coefficient β

Let us investigate the dependence of NPV on the equity capital value and coefficient β (Tables 22.12, 22.13, 22.14, and 22.15; Figs. 22.6, 22.7, 22.8, and 22.9). With increase of the equity value, optimum is observed for all of the values S when leverage level is approximately equal to L = 0.7, and the optimum value as well as the NPV value is growing with increasing S, as long as the project remains effective (up to the leverage level approximately L = 3.7). With the decrease of the return on investment (β = 0.5), the dependence of the NPV on leverage changes significantly: now NPV monotonically decreases with the leverage at all values of equity capital S (Fig. 22.7). With the increase of the return on investment (β = 1.5), the NPV of the project has an optimum at all values of equity capital S at leverage level L = 1.5, and NPV (L ) curve is going up with the increase in S until the project remains effective (up to the leverage level approximately L = 7). The optimum position (value L0) almost does not depend on the equity value S (L0 = 1.5). This means the possibility of a

Project duration n 2 5 7 10

Leverage level L 0 0.5 0.2367 0.2298 0.2367 0.2278 0.2367 0.2272 0.2366 0.2265 1 0.2264 0.2234 0.2224 0.2213

1.5 0.2243 0.2207 0.2195 0.2183

Table 22.8 Weighted average cost of capital, WACC, in 2012 2 0.2229 0.2189 0.2176 0.2162

2.5 0.2219 0.2176 0.2162 0.2147

3 0.2212 0.2167 0.2152 0.2136

3.5 0.2206 0.2159 0.2143 0.2127

4 0.2202 0.2153 0.2137 0.2120

4.5 0.2198 0.2148 0.2132 0.2115

5 0.2195 0.2144 0.2127 0.2110

22.2 Investment Analysis and Recommendations for Telecommunication. . . 483

Project duration n 2 5 7 10

Leverage level L 0 0.5 0.2367 0.3180 0.2367 0.3150 0.2367 0.3140 0.2366 0.3130 1 0.3992 0.3933 0.3913 0.3892

1.5 0.4805 0.4715 0.4685 0.4653

2 0.5617 0.5497 0.5457 0.5415

2.5 0.6430 0.6279 0.6229 0.6177

3 0.7242 0.7062 0.7001 0.6938

3.5 0.8055 0.7844 0.7772 0.7699

4 0.8867 0.8626 0.8544 0.8461

4.5 0.9680 0.9408 0.9316 0.9222

5 1.0492 1.0190 1.0088 0.9983

22

Table 22.9 Equity cost, ke, in 2012

484 Optimizing the Investment Structure of the Telecommunication Sector Company

Project duration n 2 5 7 10

Leverage level L 0 0.5 267.0 200.9 1734.8 1968.9 2304.7 2566.9 2812.6 3041.6 33.4 1954.6 2528.9 2945.5

1

1.5 -214.0 1771.8 2304.4 2667.4

Table 22.10 Net present value, NPV, in 2012, million dollars 2 -525.3 1472.1 1960.4 2281.9

2.5 -888.3 1089.6 1537.2 1829.9

3 -1293.4 647.1 1060.3 1335.0

3.5 -1733.4 160.6 545.9 811.1

4 -2202.4 -358.9 4.7 266.8

4.5 -2695.8 -903.4 -556.0 -292.2

5 -3209.9 -1467.2 -1131.2 -862.1

22.2 Investment Analysis and Recommendations for Telecommunication. . . 485

486

22

Optimizing the Investment Structure of the Telecommunication Sector Company

NPV

5 000 3 000 1 000 0 -1 000

L

4 3 2

-3 000

1

-5 000 0

1

2

3

4

5

6

Fig. 22.4 Dependence of NPV on leverage L at t = 20% in 2012: 1 for 2-year income from investments; 2 for 5-year income from investments (the term for hardware depreciation); 3 for 7 years of investment income; 4 for 10 years of investment income

tabulation of obtained results by the known values k0 and kd for large values β ≥ 1, when in dependence of NPV(L) there is an optimum. With the further increase of the return on investment (β = 2), NPV of the project has an optimum for all values S at leverage level which is already approximately equal to L = 1.8, and the value of optimum as well as of NPV in general is growing with increasing S, until the project remains effective (up to leverage level of order L = 8.5, see Fig. 22.9). In this way, the analysis of the dependence of NPV on the equity value S and on the return on investment β allows us to conclude that in contrast to the parameters I and NOI, the change of parameters S and β, both individually and simultaneously, can significantly change the nature of the dependence of NPV on leverage level. With the increase of return on investment (with the increased β), there is a transition from the monotonic decrease of NPV of the project with leverage (Fig. 22.7) to the existing optimum at all values of S (see Figs. 22.6 and 22.8). The growth of β leads to the growth of NPV as well as to the growth of the limit leverage value, up to which the project remains effective. This means the inability of tabulation of the results, obtained in the general case of a constant value of equity capital; in this case, it is necessary to use the formulas obtained by authors in their works (Brusov and Filatova 2011; Brusov et al. 2011a, b, c, 2012a, b, 2013a, b, 2014a, b; Filatova et al. 2008) to determine the NPV at the existing leverage level as well as for optimization of existing investment structure. Tabulation is possible only in the case of large β values (β ≥ 1), when there is an optimum in the dependence of NPV on the leverage level.

Project duration n 2 5 7 10

Leverage level L 0.5 0.55 200.9 188.3 1968.9 1977.0 2566.9 2574.2 3041.6 3043.5 0.6 174.8 1982.8 2578.8 3042.4

0.65 160.2 1986.3 2580.6 3038.5

0.7 144.8 1987.7 2580.0 3032.0

0.75 128.4 1987.0 2576.9 3023.1

0.8 111.1 1984.2 2571.5 3011.7

Table 22.11 Net present value, NPV, at leverage level from 0.5 up to 1.05 in 2012, million dollars 0.85 92.9 1979.5 2563.9 2998.2

0.9 73.9 1973.0 2554.2 2982.6

0.95 54.1 1964.6 2542.5 2965.0

33.4 1954.6 2528.9 2945.5

1

1.05 12.0 1942.8 2513.5 2924.3

22.2 Investment Analysis and Recommendations for Telecommunication. . . 487

488

22

Optimizing the Investment Structure of the Telecommunication Sector Company

NPV 4 000 4

3 000

3 2

2 000 1 000

1

L

0 0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

Fig. 22.5 Dependence of NPV on leverage L at t = 20% in 2012 in the vicinity of optimum: 1 for 2-year income from investments; 2 for 5-year income from investments (the term for hardware depreciation); 3 for 7 years of investment income; 4 for 10 years of investment income

22.3

Effects of Taxation on the Optimal Capital Structure of Companies in the Telecommunication Sector

We continue the analysis of activity of “Nastcom Plus.” In this paragraph, we examine the effect of change of tax on profit rate, both in the case of its increase and decrease, on the optimal structure of investments at different project durations. It is shown that the increase of tax on profit rate leads to the degradation (decreasing) of NPV, and the degradation is reduced with an increase in project duration. In particular, for the 5-year project (amortization period), when the tax on profit rate decreases by 1%, NPV decreases by 1.5–2.34% in different years. The impact of change of tax on the profit rate on the optimum position while it exists (change optimum position) is changed for 2-year and 10-year projects in 2010 and for the 5-year project in 2012[for 0.5–1 (in L units)]; nevertheless, the optimum position turns out to be sufficiently stable (Figs. 22.10, 22.11, 22.12, 22.13, 22.14, 22.15, 22.16, 22.17, 22.18, 22.19, 22.20, and 22.21; Tables 22.16, 22.17, 22.18, 22.19, 22.20, and 22.21). It is shown that the increase of tax on profit rate leads to the degradation (decreasing) of NPV, and the degradation is reduced with an increase in project duration. Note that for the 5–year project (amortization period), when the tax on profit rate decreases by 1 %, NPV decreases by 2.34 % in 2012, by 2.04 % in 2011, and by 1.49 % in 2010.

Leverage level L 0 0.5 1734.8 1968.9 1255.7 1425.2 1506.8 1710.2 2009.1 2280.3 2260.3 2565.3

1 1954.6 1414.8 1697.8 2263.7 2546.7

1.5 1771.8 1282.5 1539.0 2052.0 2308.5

Equity S 1382 1000 1200 1600 1800

Leverage level L 0 0.5 146.1 -71.8 105.7 -52.0 126.9 -62.4 169.2 -83.2 190.3 -93.6

1 -411.5 -297.9 -357.4 -476.6 -536.2

1.5 -833.8 -603.5 -724.2 -965.6 -1086.3

2 1472.1 1065.6 1278.7 1705.0 1918.1

2 -1313.3 -950.7 -1140.8 -1521.0 -1711.2

Table 22.13 Net present value, NPV, at β = 0.5, million dollars

Equity S 1382 1000 1200 1600 1800

Table 22.12 Net present value, NPV, at β = 1.02, million dollars

2.5 -1833.5 -1327.2 -1592.6 -2123.5 -2388.9

2.5 1089.6 788.7 946.4 1261.9 1419.7

3 -2383.1 -1725.0 -2070.0 -2760.0 -3105.0

3 647.1 468.4 562.1 749.5 843.2

3.5 -2954.2 -2138.4 -2566.1 -3421.5 -3849.2

3.5 160.6 116.2 139.5 186.0 209.2

4 -3541.6 -2563.6 -3076.3 -4101.7 -4614.4

4 -358.9 -259.8 -311.8 -415.7 -467.6

4.5 -4141.1 -2997.6 -3597.1 -4796.1 -5395.6

4.5 -903.4 -653.9 -784.7 -1046.3 -1177.1

5 -4750.2 -3438.4 -4126.1 -5501.4 -6189.1

5 -1467.2 -1062.0 -1274.4 -1699.2 -1911.6

22.3 Effects of Taxation on the Optimal Capital Structure of Companies in. . . 489

1 4138.6 2995.8 3594.9 4793.2 5392.4

1.5 4176.9 3023.5 3628.2 4837.6 5442.3

Equity S 1382 1000 1200 1600 1800

Leverage level L 0 0.5 4728.8 5814.9 3423.0 4209.1 4107.5 5050.9 5476.7 6734.5 6161.3 7576.4

1 6413.7 4642.6 5571.1 7428.1 8356.6

1.5 6682.3 4837.0 5804.4 7739.2 8706.6

Table 22.15 Net present value, NPV, at β = 2.0, million dollars

Leverage level L 0 0.5 3201.2 3852.6 2321.2 2788.7 2780.7 3346.5 3707.5 4462.0 4171.0 5019.7

2 6721.7 4865.5 5838.6 7784.8 8757.9

2 4043.3 2926.8 3512.1 4682.8 5268.2

2.5 6598.5 4776.3 5731.6 7642.1 8597.4

2.5 3787.8 2741.8 3290.2 4386.9 4935.3

3 6357.9 4602.2 5522.6 7363.4 8283.9

3 3444.2 2493.1 2991.7 3989.0 4487.6

3.5 6030.8 4365.4 5238.5 6984.7 7857.8

3.5 3035.8 2197.5 2637.0 3515.9 3955.4

4 5639.2 4081.9 4898.3 6531.1 7347.4

4 2578.9 1866.7 2240.1 2986.8 3360.1

4.5 5198.5 3762.9 4515.5 6020.6 6773.2

4.5 2085.3 1509.4 1811.3 2415.1 2716.9

5 4720.0 3416.6 4099.9 5466.6 6149.9

5 1563.3 1131.6 1357.9 1810.6 2036.9

22

Equity S 1382 1000 1200 1600 1800

Table 22.14 Net present value, NPV, at β = 1.5, million dollars

490 Optimizing the Investment Structure of the Telecommunication Sector Company

22.4

Conclusions

491

NPV

4 000 2 000 1 000

5

4

1

2

3

0 -1 000 -2 000 1

2

3

4

5

6

L

Fig. 22.6 Dependence of NPV on leverage at different values of equity cost S at β = 1.02, million dollars: 1 S = 1382.2 million dollars; 2 S = 1000 million dollars; 3 S = 1200 million dollars; 4 S = 1600 million dollars; 5 S = 1800 million dollars

1 000

NPV

0 -1 000 -2 000 -3 000

2 3 1 4 5

-4 000 -5 000 -6 000 -7 000 1

2

3

4

5

6

L

Fig. 22.7 Dependence of NPV on leverage at different values of equity cost S at β = 0.5, million dollars: 1 S = 1382.2 million dollars; 2 S = 1000 million dollars; 3 S = 1200 million dollars; 4 S = 1600 million dollars; 5 S = 1800 million dollars

22.4

Conclusions

In 2010, the company “Nastcom Plus” worked at leverage level L = 0.54 instead of optimal value L = 2.0. The NPV loss amounted to 645 million dollars. In 2012, the company worked at leverage level L = 1.0 instead of optimal value L = 0.7. The NPV loss amounted to 32–98 million dollars, depending on the term of operation of equipment. The authors have evaluated the effectiveness of investment at existing level of debt financing and have developed recommendations on the optimum level of leverage for the Russian company “Nastcom Plus” in 2010–2012. The results indicate that if in 2011 the financial structure of the investment of “Nastcom Plus” was close to the optimal and NPV was only 2 million dollars less than the optimal value, in 2010, when the leverage level was L = 0.54, NPV was

492

22

6 000

Optimizing the Investment Structure of the Telecommunication Sector Company

NPV

5 000 4 000 3 000 5 4 1 3 2

2 000 1 000 0

1

2

3

4

5

6

L

Fig. 22.8 Dependence of NPV on leverage at different values of equity cost S at β = 1.5, million dollars: 1 S = 1382.2 million dollars; 2 S = 1000 million dollars; 3 S = 1200 million dollars; 4 S = 1600 million dollars; 5 S = 1800 million dollars

NPV

10 000 9 000 8 000 7 000 6 000 5 000 4 000 3 000 2 000 1 000 0

1

2

3

4

5

6

L

Fig. 22.9 Dependence of NPV on leverage at different values of equity cost S at β = 2, million dollars: 1 S = 1382.2 million dollars; 2 S = 1000 million dollars; 3 S = 1200 million dollars; 4 S = 1600 million dollars; 5 S = 1800 million dollars

645 million dollars less than optimal value (the optimal leverage level should be equal to L = 2). In 2012 the leverage level, with which “Nastcom Plus” has carried out its investment projects (L = 0.1), did not correspond to optimum value (L = 0.7) and provided NPV = 1954.6 million dollars, which is 31.7 million dollars less than the optimal value of NPV (Tables 22.10 and 22.11; Figs. 22.4 and 22.5). Since the equipment can be operated after depreciation, one can estimate the NPV for a more long-term perspective. For example, for the 7–year project, the optimal leverage value is L = 0.65, when the NPV = 2580.6 million dollars, which is 51.7 million dollars more than non-optimal values of NPV = 2528.9 million dollars, obtained by the company. For the 10-year project, the optimal leverage level L = 0.55, with NPV = 3043.5 million dollars, which is 98 million dollars more than non-optimal values of NPV = 2945.5 million dollars, obtained by the company.

22.4

Conclusions

493

Fig. 22.10 Dependence of NPV on leverage level L for three values of tax on profit rate: T = 15%, 20%, 25% for the 2-year project in 2010

Fig. 22.11 Dependence of NPV on leverage level L for three values of tax on profit rate: T = 15%, 20%, 25% for the 5-year project in 2010

494

22

Optimizing the Investment Structure of the Telecommunication Sector Company

Fig. 22.12 Dependence of NPV on leverage level L for three values of tax on profit rate: T = 15%, 20%, 25% for the 7-year project in 2010

Fig. 22.13 Dependence of NPV on leverage level L for three values of tax on profit rate: T = 15%, 20%, 25% for the 10-year project in 2010

22.4

Conclusions

495

Fig. 22.14 Dependence of NPV on leverage level L for three values of tax on profit rate: T = 15%, 20%, 25% for the 2-year project in 2011

Fig. 22.15 Dependence of NPV on leverage level L for three values of tax on profit rate: T = 15%, 20%, 25% for the 5-year project in 2011

496

22

Optimizing the Investment Structure of the Telecommunication Sector Company

Fig. 22.16 Dependence of NPV on leverage level L for three values of tax on profit rate: T = 15%, 20%, 25% for the 7-year project in 2011

Fig. 22.17 Dependence of NPV on leverage level L for three values of tax on profit rate: T = 15%, 20%, 25% for the 10-year project in 2011

22.4

Conclusions

497

Fig. 22.18 Dependence of NPV on leverage level L for three values of tax on profit rate: T = 15%, 20%, 25% for the 2-year project in 2012

Fig. 22.19 Dependence of NPV on leverage level L for three values of tax on profit rate: T = 15%, 20%, 25% for the 5-year project in 2012

498

22

Optimizing the Investment Structure of the Telecommunication Sector Company

Fig. 22.20 Dependence of NPV on leverage level L for three values of tax on profit rate: T = 15%, 20%, 25% for the 7-year project in 2012

Fig. 22.21 Dependence of NPV on leverage level L for three values of tax on profit rate: T = 15%, 20%, 25% for the 10-year project in 2012 Table 22.16 Dependence of optimum position L0 of investment structure in 2010 on tax on profit rate and project duration

2010, t 15% 20% 25%

n 2 3 2 2

5 2 2 2

7 2 2 2

10 2 1.5 2

References Table 22.17 Absolute and relative change of NPV with increase/decrease of tax on profit rate on 5% (1%) in 2010

Table 22.18 Dependence of optimum position L0 of investment structure in 2011 on tax on profit rate and project duration

Table 22.19 Absolute and relative change of NPV with increase/decrease of tax on profit rate on 5% (1%) in 2011

Table 22.20 Dependence of optimum position L0 of investment structure in 2010 on tax on profit rate and project duration

Table 22.21 Absolute and relative change of NPV with increase/decrease of tax on profit rate on 5% (1%) in 2012

499 2010 n=2 5 7 10

2011, t 15% 20% 25%

2011 n=2 5 7 10

2012, t 15% 20% 25%

2012 n=2 5 7 10

t = 20–15% 418/487 266 263 245

t = 25–20% 204 273 271 256

n 2 0.5 0.5 0.5 t = 20–15% 119 222 236 238

n 2 0 0 0 t = 20–15% 104 229 253 269

5 1 1 1

On 5% 34% 7.45% 6.88% 5.56%

7 1 1 1

t = 25–20% 118 223 239 242

On 5% 25.8% 10.2% 8.75% 7.7%

5 1 0.5 0.5

7 0.5 0.5 0.5

t = 25–20% 103 229 256 271

On 5% 39% 11.7% 9.9% 8.9%

On 1% 6.8% 1.49% 1.37% 1.11%

10 1 1 1

On 1% 5.16% 2.04% 1.75% 1.54%

10 0.5 0.5 0.5

On 1% 7.8% 2.34% 1.98% 1.74%

References Brusov PN, Filatova ТV (2011) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Finance Credit 435:2–8 Brusov P, Filatova T, Orehova N, Brusova A (2011a) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Appl Financ Econ 21(11): 815–824 Brusov P, Filatova T, Orehova N et al (2011b) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Bus ICT 2:16–21 Brusov P, Filatova T, Orehova N et al (2011c) Influence of debt financing on the effectiveness of the investment project within the Modigliani–Miller theory. Res J Econ Bus ICT (UK) 2:11–15 Brusov P, Filatova T, Eskindarov M, Orehova N (2012a) Influence of debt financing on the effectiveness of the finite duration investment project. Appl Financ Econ 22(13):1043–1052

500

22

Optimizing the Investment Structure of the Telecommunication Sector Company

Brusov P, Filatova T, Eskindarov M, Orehova N (2012b) Hidden global causes of the global financial crisis. J Rev Global Econ 1:106–111 Brusov P, Filatova P, Orekhova N (2013a) Absence of an optimal capital structure in the famous tradeoff theory! J Rev Global Econ 2:94–116 Brusov P, Filatova T, Orehova N (2013b) A qualitatively new effect in corporative finance: abnormal dependence of cost of equity of company on leverage. J Rev Global Econ 2:183–193 Brusov P, Filatova P, Orekhova N (2014a) Mechanism of formation of the company optimal capital structure, different from suggested by trade off theory. Cogent Econ Finance 2:1–13. https://doi. org/10.1080/23322039.2014.946150 Brusov P, Filatova T, Orehova N (2014b) Inflation in Brusov–Filatova–Orekhova theory and in its perpetuity limit – Modigliani–Miller theory. J Rev Global Econ 3:175–185 Brusov P, Filatova T, Orehova N, Eskindarov M (2015) Modern corporate finance, investment and taxation, 1st edn. Springer, New York, pp 1–368 Brusov P, Filatova T, Orehova N, Kulk WI (2018a) New meaningful effects in modern capital structure theory. J Rev Global Econ 7:104–122 Brusov P, Filatova T, Orehova N, Kulk V (2018b) A “golden age” of the companies: conditions of its existence. J Rev Global Econ 7:88–103 Brusov P, Filatova T, Orehova N, Kulk V (2018c) Rating methodology: new look and new horizons. J Rev Global Econ 7:63–87 Brusov P, Filatova T, Orehova N, Kulk V (2018d) Rating: new approach. J Rev Global Econ 7:37– 62 Brusova A (2011) А comparison of the three methods of estimation of weighted average cost of capital and equity cost of company. Financ Anal Prob Sol 34(76):36–42 Filatova Т, Orehova N, Brusova А (2008) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Bull FU 48:68–77 Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Мodigliani F, Мiller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391

Chapter 23

Innovative Investment Models with Frequent Payments of Tax on Income and of Interest on Debt

Keywords Innovative investment models · Effectiveness of the investment project · Frequent payments of interest on debt and of tax on income · The Modigliani–Miller theory · The Brusov–Filatova–Orekhova theory

23.1

Introduction

Investments play a crucial role in economy and finance. Investments in tangible and intangible assets are a necessary condition for structural adjustment and economic growth. They provide the enhancement of existing basic funds and industries and the creation of new ones. The role of investment is increased many times at the current stage. In this respect, the role of the evaluation of the efficiency of investment projects, which allows for the realization of the most effective projects in the context of scarcity and limited investment resources, increases. Since virtually most investment projects use debt financing, the study of the influence of capital structure and debt financing on the efficiency of investment projects and determining the optimal capital structure is especially important at the present time. This is why in spite of the fact that a lot of different types of investment models have been developed— stochastic, dynamics (Bond and Meghir 1994), investment banking valuation models (Rosenbaum and Pearl 2013), etc.—the main problem, which has been discussed during the last few decades, is the impact of debt financing on the efficiency of investment projects and on the investment decisions of companies. Below we review some approaches to these problems.

23.1.1

The Literature Review

Lang et al. (1996) used the so-called “Tobin’s q ratio” and considered companies with low Tobin’s q ratios as well as high ones. Note that the q ratio, or Tobin’s q ratio, equals the market value of a company divided by its assets’ replacement cost. The equilibrium takes place when market value equals replacement cost. The q ratio expresses the relationship between market valuation and intrinsic value. It is a means © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_23

501

502

23 Innovative Investment Models with Frequent Payments of Tax on Income. . .

of estimating the fact of whether a given business or market is undervalued or overvalued. The authors have shown that there is a negative correlation between future growth and leverage level at the company level and, for diversified companies, at the level of business segments. This negative correlation between growth and leverage level holds for companies with low Tobin’s q ratio, but not for high-q companies or companies in high-q industries. Therefore, for companies known to have good investment opportunities, leverage does not reduce growth, but it is negatively correlated to growth for companies whose growth opportunities are either not recognized by the capital markets or are not valuable enough to overcome the effects of their debt load. Whited (1992) studied the influence of debt financing on companies’ investment decisions with pharmaceutical firms in India for 11 years, from 1998 to 2009. To study the impact of debt financing on the firms’ investment decisions, Whited used pooling regression as well as random and fixed effect models. Leverage level, retained earnings, Tobin’s q, sales, Return on Asset, cash flow, and liquidity were considered as independent variables and investment as the dependent one. Whited considered three types of companies, depending on their size: small companies, medium companies, and large companies. He showed that there is a significant positive correlation between leverage level and investment for large companies, while for medium companies a negative correlation between leverage level and investment took place. Kang (1995) studied the connection between leverage level and investment decisions. “Interdependent tax models” were used to try to explain the specifics of company leverage levels by analyzing the interdependency between financing decisions and investment. These models account for the so-called “investment effect”: the influence of investment on debt tax benefit and financial risk. One of the questions is how the “investment effect” influences bond financing decisions and hence the leverage level. Different “Interdependent tax models” lead to different connections between investments and leverage levels. Some authors mentioned a positive connection via the fact that the financial risk and hence the cost of bond financing decrease with an increase in investment at a given leverage level. A negative connection has been mentioned by DeAngelo and Masulis (1980) and Dotan and Ravid (1985). The first authors concluded this since the tax benefits of debt compete with those of capital investment. The second authors refer to the fact that financial risk and thus the cost of bond financing will increase with investment increase. The impact of investment increase on financial risk may depend on companyspecific factors, like company-specific technology Dammon and Senbet 1988). An analysis of the impact of corporate and personal taxes on a firm’s optimal investment and financing decisions under uncertainty is provided in this paper. By endogenizing firms’ investment decisions, it extends the DeAngelo and Masulis capital structure model. The authors’ results indicate that the existing predictions about the relationship between investment-related and debt-related tax shields must be modified in cases where investment is allowed to adjust optimally. The authors show that

23.1

Introduction

503

increases in investment-related tax shields due to changes in the corporate tax code are not necessarily associated with reductions in leverage level at the individual company level. Companies with higher investment-related tax shields (as crosssectional analysis shows) need not have lower debt-related tax shields (normalized by expected earnings) unless all companies utilize the same production technology. Differences in production technologies across companies may thus explain why the empirical results of recent cross-sectional studies have not conformed to the predictions of DeAngelo and Masulis (1980). A model of company leverage level choice is formulated in this paper, in which corporate and differential personal taxes exist and supply-side adjustments by companies enter into the determination of equilibrium prices of debt and equity. The presence of corporate tax shield substitutes for debt such as depletion allowances, accounting depreciation, and investment tax credits are shown to imply a market equilibrium in which each company has a unique interior optimum leverage level decision. The optimal leverage level model yields a number of interesting predictions regarding crosssectional and time-series properties of firms’ capital structures. Below we discuss some portfolio investment models as well as behavioral aspects of investors, which play an important role in investments. Among those portfolio investment models is the well-known Black–Litterman model, which was created by Fischer Black and Robert Litterman (1992). They developed the model to address the problems that institutional investors have encountered the during application of modern portfolio theory in practice. Starting with an asset allocation based on the equilibrium assumption, the model then modifies that allocation by accounting the investors’ opinions with respect to future asset performance. Anthony Loviscek (2021) has applied the Black–Litterman model of modern portfolio theory to well-known index mutual funds—one guided by the classic 60%/ 40% stock/bond allocation and one based on an all-equity allocation. The period under their study is from 2000 to 2020. Although statistical evidence supports that the efficacy of a precious metal allocation is elusive, the results suggest an average allocation of about 2% for “buy-and-hold” investors who seek one. He has shown that, from 2003 to 2010 and from 2016 to 3Q2020, the allocations were in the range of 5–10%. Other periods, however, register only a little more than 0%. Nusret Cakici and Adam Zaremba (2021), using data on 65,000 stocks from 23 countries, reconsidered the performance of the Fama–French factors in global markets. As their results showed, the value, profitability and investment factors are far less reliable than what is commonly thought. Their performance depends strongly on the geographical regions and periods examined. Moreover, most factor returns are driven by the smallest companies. Virtually no value or investment effects are present among the big companies representing most of the total market capitalization worldwide. These results cast doubt on the five-factor model’s applicability in international markets, citing that the smallest companies are typically not invested in by major financial institutions. A growing number of investors want to use firm sustainability information in their investment decision processes to avoid risk, satisfy their own asset preference,

504

23 Innovative Investment Models with Frequent Payments of Tax on Income. . .

or find a new alpha-generating factor. Not too many users of environment, social, and governance (ESG) data understand how ESG ratings change over time. Bahar Gidwani (2020) used the CSRHub data set to show that ESG ratings regress strongly toward the mean. These ratings include both data from 640 sources and from most commercial ESG ratings firms. The observed regression persists during 9 years within the ratings data, for a sample set of more than 8000 firms. Newly rated firms show even more reversion than “seasoned” firms. Firms can only rarely maintain an especially high or low ESG rating. Investors and firm managers should understand that ESG ratings are likely to change toward the mean. This however does not mean that a good firm is getting worse or a bad one is getting better. Brown et al. (2021) have developed statistics (holdings-based) to estimate the volatility with time of investment style characteristics of funds. They found that funds with lower levels of style volatility significantly outperform funds with higher levels of style volatility on a risk-adjusted basis. The authors have shown that style volatility has a distinct impact on fund performance in the future compared to expenses of funds or past risk-adjusted returns, with the level of indirect style volatility being the primary determinant of the overall effect. It was concluded that deciding to maintain a less volatile investment style is an important aspect of the portfolio management process. Some behavioral aspects of investors have been considered by Marcos EscobarAnel et al. (2020), who introduced a strategy generalizing the CPPI (Constant Proportion Portfolio Insurance) approach. The target of this strategy is to guarantee the investment goal or floor during participation in the performance of the assets and limiting the downside risk of the portfolio at the same time. The authors show that the strategy accounts for the following behavioral aspects of investors: a risk-averse behavior for gains, distorted probabilities recognition and a risk-seeking behavior for losses. The developed strategy turns out to be optimal within the Cumulative Prospect Theory framework by Kahneman and Tversky (1996).

23.1.2

Some Problems Under the Evaluation of the Effectiveness of the Investment Projects

Some of the major problems under the evaluation of the effectiveness of investment projects are suggested as follows: 1. Which financial flows should be taken into account when calculating the parameters of efficiency of a project (NPV, IRR, etc.)? 2. How many discount rates should be used for discounting various cashflows? 3. How can these discount rates be accurately evaluated? The first two problems are still under intensive discussion. Concerning the third issue, we need to note that, in the last decade, significant progress in the accurate determination of the cost of the equity and company weighted average cost, which

23.1

Introduction

505

just are the discount rates when evaluating the effectiveness of the project, has been achieved. The progress is mainly associated with the studies by Brusov, Filatova, and Orekhova (BFO theory) (Brusov et al. 2015, 2018b; Filatova et al. 2008), in which a general theory of capital cost of the company and its capital structure was established, and the dependence of capital cost on leverage level and on the age of a company was found for the companies of arbitrary age. The main difference between their theory and Modigliani–Miller theory is that the former one removes the assumption of perpetuity for the companies under discussion, which leads to a significantly different new theory from the theory established by the Nobel laureates Modigliani and Miller (1958, 1963, 1966). In modern conditions, the requirements for improving the quality of assessing the effectiveness of investments have increased. The modern investment models, which have been well-tested in real economic situations, have been developed by Brusov et al. (2015; Filatova et al. 2008). They have created long-term as well as arbitrary duration models and have considered the effectiveness of the investment project from two points of view: from the equity holders and from the owners of equity and debt. NPV in each of these cases could be calculated by two different methods: with the division of credit and investment flows and using two different discounting rates, and without such a division and using a general discounting rate (for which WACC can, obviously, be chosen). Applying their modern investment models on the evaluation of the dependence of the effectiveness of investments on debt financing of one telecommunication company in 2010–2012 from the point of view of optimal structure of investment, the authors showed that in 2012, the company lost 675 million USD on average, because the investment structure had been far from the optimal one. The ability to calculate the correct optimal capital structure is one important feature implied by the Brusov, Filatova, and Orekhova modern investment models (Brusov et al. 2015; Filatova et al. 2008).

23.1.3

The Discount Rates

As we mentioned above, one of the most important elements of calculating the effectiveness of investment projects is the assessment of the discount rate. In the case of long-term investment models without the division of credit and investment flows, the discount rate WACC has been calculated using the Modigliani–Miller formula (Мodigliani and Мiller 1958, 1963, 1966) WACC = k 0
ð1- wd t Þ

ð23:1Þ

while in the case of arbitrary duration models, the Brusov–Filatova–Orekhova formula for WACC (Black and Litterman 1992; Loviscek 2021; Cakici and Zaremba 2021).

506

23 Innovative Investment Models with Frequent Payments of Tax on Income. . .

1 - ð1 þ k 0 Þ - n 1 - ð1 þ WACCÞ - n = WACC k0
ð1 - wd t ½1 - ð1 þ kd Þ - n Þ

ð23:2Þ

has been used. Here and below, WACC is the weighted average cost of capital; k0 is the equity cost at zero leverage (L = 0); kd is the debt cost; wd is the debt share; t is the tax on profit; n is the project duration; ke is the equity cost; and L is the leverage level. In the case of long-term investment models with the division of credit and investment flows, the discount rate for discounting the investment flows (equity cost ke) has been calculated using the Modigliani–Miller formula (Мodigliani and Мiller 1958, 1963, 1966). k e = k0 þ L
ðk0- k d Þð1- t Þ

ð23:3Þ

while in the case of arbitrary duration models, equity cost ke has been calculated from the formula WACC = k e we þ k d wd ð1- t Þ

ð23:4Þ

using the Brusov–Filatova–Orekhova value for WACC (Brusov et al. 2015, 2018b; Filatova et al. 2008). The calculation methods of the discount rates (WACC, equity cost ke) have been generalized in Brusov and Filatova (2021) for the real conditions of the implementation of investment projects: for arbitrary frequency of payment of tax on profit. In this paper, new modern investment models, both long-term and arbitrary duration, will be created, as close as possible to real investment conditions. They will account for the payments of interest on debt and of tax on income a few times per year (semi-annually, quarterly, monthly), which are applied in real economic practice. Their verification will lead to the creation of a comprehensive system of adequate and correct assessment of the effectiveness of the company’s investment program and its investment strategy.

23.1.4

The Structure of the Paper

The structure of the paper is as follows: 1. In Sect. 23.1 above, we presented: 1.1 The literature review 1.2 Some problems under the evaluation of the effectiveness of the investment projects 1.3 Discount rates

23.2

The Effectiveness of the Investment Project from the Perspective of. . .

507

2. In Sect. 23.1.1, we consider the effectiveness of the investment project from the perspective of the equity holders only. In Sect. 23.1.2, we consider a case with flow separation. In Sect. 23.1.3, we consider a case without flow separation. 3. In Sect. 23.2, we consider the effectiveness of the investment project from the perspective of the owners of equity and debt. In Sect. 23.2.1, we consider a case with flow separation. In Sect. 23.2.2, we consider a case without flow separation. 4. In Sect. 23.3, the problem of calculation of discount rates is discussed and expressions for their modified values are obtained. 5. In Sect. 23.4, we study numerically with the use of Microsoft Excel the effectiveness of the four models, created by us in this paper. We consider long-term projects as well as projects of arbitrary duration from two perspectives: the owners of equity and debt and the equity holders only without the division of credit and investment flows. 6. In Conclusions, we discuss obtained results and their impact on the correctness of the valuation of efficiency of investment projects.

23.2

The Effectiveness of the Investment Project from the Perspective of the Equity Holders Only

We will consider the effectiveness of the investment project from two points of view: from the equity holders and from the owners of equity and debt. NPV in each of these cases could be calculated by two different methods: with the division of credit and investment flows and using two different discounting rates, and without such a division and using a general discounting rate (for which WACC can, obviously, be chosen). The following designations are used below: The equity value S, the investment value I, the net operating income NOI, the leverage level L, the profitability of investments β, the tax on profit t, the project duration n, the equity cost k0, the debt cost kd and the number of payments of interest on debt p1 and of tax on income p2; D is the debt value. In the first case (from the perspective of the equity holders), at the initial moment in time, T = 0 investments are equal to –S and the flow of capital, CF, for the period is equal to: CF = ðNOI- kd DÞð1- t Þ:

ð23:5Þ

In addition to the tax shields, kdDt includes a payment of interest on a loan, -kdD.

508

23 Innovative Investment Models with Frequent Payments of Tax on Income. . .

We suppose below that interests on the loan are paid in equal shares of kdD during all periods and principal repayment is made at the end of the project. In the second case (from the perspective of the equity holders), the negative flows (the interest and duty paid by owners of equity) are returned to the project and they are exactly equal to the positive flows obtained by owners of debt capital. Thus, in this case, the only effect of debt financing is the effect of the tax shield, generated from the tax relief: interest on the loan is entirely included in the cost and thus reduces the tax base. After-tax flow of capital, CF, for each period is equal to CF = NOIð1- t Þ þ kd Dt

ð23:6Þ

and the value of investments at the initial moment in time T = 0 is equal to -I = S - D. Below are two different ways of discounting will be considered: 1. If operating and financial flows are not separated, both flows are discounted by the general rate. In this case, the weighted average cost of capital (WACC) can be selected as a discounting rate. For long-term projects, we will use the Modigliani– Miller formula for WACC (Мodigliani and Мiller 1958, 1963, 1966), modified by us for the case of payments of interest on debt and of tax on income a few times per year (semi-annually, quarterly, monthly) and for projects of finite (arbitrary) duration we will use the Brusov–Filatova–Orekhova formula for WACC (Brusov et al. 2018b; Filatova et al. 2008), modified by us for the case of payments of interest on debt and of tax on income a few times per year (semi-annually, quarterly, monthly). 2. Operating and financial flows are separated and are discounted at different rates: the operating flow at the rate which is equal to the equity cost ke, depending on leverage and on the number of payments of interest on debt and of tax on income, and credit flow at the rate which is equal to the debt cost kd. Note that loan capital is the least risky because the credit (including the interest on credit) is paid after taxes in the first place. Therefore, the cost of credit will always be less than the equity cost, whether for ordinary or for preference shares ke > kd; kp > kd. Here ke; kp is the equity cost of ordinary or of preference shares consequently.

23.2.1

With Flow Separation

In this case, the expression for NPV (net present value) per period has a view NPV = NOIð1- t Þ - kd Dð1- t Þ = NOIð1- t Þ þ k d Dt - kd D:

ð23:7Þ

23.2

The Effectiveness of the Investment Project from the Perspective of. . .

509

Here, the first term is the value of operating income from the investment project after tax deduction, the second term is the value of the tax shield, the third term is the value of interest on debt for one period. We will need the following auxiliary formulas for summing the reduced values of financial flows (23.7) when calculating NPV: For annual payments of interest on debt and of tax on income: n X i=1

1 - ð1 þ k d Þ 1 1 i = 1þk
1 1 - 1þk d ð1 þ k d Þ d

-n

=

1
ð1- ð1 þ kd Þ - n Þ kd

ð23:8Þ

For more frequent payments ( p times per period) of interest on debt and of tax on income (semi-annually, quarterly, monthly): np X

R

i=1

pð 1 þ k d Þ = p i

=

=

R pð 1 þ k d Þ

R ð1 - ð1 þ k d Þ
1= p ð1 þ k d Þ p

-n

Þ

1= p




1 - ð1 þ k d Þ - n 1 - 1 1=p ð1þk d Þ

- 1:

ð23:9Þ

Similar formulas are obtained using the cost of equity ke and WACC as the discount rates. Summing up the given values of financial flows for each period (23.7), we obtain for NPV of n-years project in the case of separated flows: NPV = - S þ -

n n n X X NOIð1 - t Þ X kd Dt kd D i þ i 1 þ k ð Þ ð Þ ð 1 þ k 1 þ k d Þi e d i=1 i=1 i=1

D ð1 þ k d Þn

ð23:10Þ

Here, the second term is the reduced value of operating income from the investment project, the second term is the reduced value of the tax shield, the third term is the reduced value of interest paid annually (at the end of the year), and the fourth term is the reduced value of the debt paid at the end of the project. After summing, we have the following expression for NPV: NPV = - S þ

  n  NOIð1 - t Þ 1 þ Dt ð1- ð1 þ kd Þ - n Þ
1ke 1 þ ke

- Dð1- ð1 þ kd Þ - n Þ -

D ð1 þ k d Þn

ð23:11Þ

In the case of more frequent ( p-times per year) payment of income taxes ( p1) and frequent payments of interest on debt ( p2) we have:

23 Innovative Investment Models with Frequent Payments of Tax on Income. . .

510

NPV = - S þ 

np np n X X NOIð1 - t Þ X kd Dt þ i i=p i = 1 p1 ð 1 þ k d Þ 1 i=1 i = 1 ð1 þ k e Þ

kd D p2 ð 1 þ k d Þ

i=p

2

D ; ð1 þ k d Þn

ð23:12Þ

After summing, we have the following expression for NPV:   n  k d Dt ð1 - ð1 þ k d Þ - n Þ 1 NOIð1 - t Þ  þ 
1NPV = - S þ 1= 1 þ ke ke p ð 1 þ k d Þ p1 - 1 1

D k d Dð1 - ð1 þ kd Þ - n Þ  -  1= ð1 þ k d Þn p2 ð 1 þ k d Þ p2 - 1

ð23:13Þ

Long-term investment projects To obtain the expression for NPV of long-term investment projects, one should find the limit of (23.13) n → 1. NPV = - S þ -

23.2.2

NOIð1 - t Þ kd Dt  þ  1= ke p1 ð 1 þ k d Þ p1 - 1

kd D   1= p 2 ð 1 þ k d Þ p2 - 1

ð23:14Þ

Without Flow Separation

In the case of no separation between operating and financial flows, both flows are discounted by the general rate WACC. The credit reimbursable at the end of the project can be discounted either at the same rate WACC or at the debt cost rate kd. Below, a uniform rate for WACC has been used. Summing up the given values of financial flows for each period (23.3), we obtain for NPV of n-years project in the case without separated flows: NPV = - S þ 

n n n X X X NOIð1 - t Þ k d Dt iþ i i = 1 ð1 þ WACCÞ i = 1 ð1 þ WACCÞ i=1

kd D D n ð1 þ WACCÞi ð1 þ WACCÞ

After summing, we have the following expression for NPV:

ð23:15Þ

23.2

The Effectiveness of the Investment Project from the Perspective of. . .

511

  n  k Dt ð1 - ð1 þ WACCÞ - n Þ NOIð1 - t Þ 1 þ d NPV = - S þ
1WACC WACC 1 þ WACC -

k d Dð1 - ð1 þ WACCÞ - n Þ D WACC ð1 þ WACCÞn ð23:16Þ

In the case of more frequent ( p-times per year) payment of income taxes and frequent payments of interest on the debt we have: np n X X NOIð1 - t Þ k d Dt þ i i ð 1 þ WACC Þ ð 1 þ WACCÞ=p1 p i=1 1 i=1 np X kd D D i=p - ð1 þ WACCÞn 2 ð 1 þ WACC Þ p i=1

NPV = - S þ

ð23:17Þ

2

After summing, we have the following expression for NPV: NPV = - S þ

 n   NOIð1 - t Þ 1 kd Dt ð1 - ð1 þ WACCÞ - n Þ 
1þ  1= WACC 1 þ WACC p ð1 þ WACCÞ p1 - 1 -

-n

1

D kd Dð1 - ð1 þ WACCÞ Þ   1= p2 ð 1 þ WACC Þn p2 ð1 þ WACCÞ - 1 ð23:18Þ

Long-term investment projects To obtain the expression for NPV of long-term investment projects, one should find the limit of (23.18) n → 1. NPV = - S þ -

kd Dt NOIð1 - t Þ  þ  1= WACC p1 ð1 þ WACCÞ p1 - 1

kd D   1= p2 ð1 þ WACCÞ p2 - 1

ð23:19Þ

23 Innovative Investment Models with Frequent Payments of Tax on Income. . .

512

23.3

The Effectiveness of the Investment Project from the Perspective of the Owners of Equity and Debt

23.3.1

With Flow Separation

In this case, operating and financial flows are separated and are discounted using different rates: the operating flow at the rate equal to the equity cost ke, depending on leverage, and credit flow at the rate equal to the debt cost kd, which remain constant until fairly large values of leverage and start to grow only at high values of leverage L, when there is a danger of bankruptcy. After-tax flow of capital for each period in this case is equal to (23.6): ð23:20Þ

CF = NOIð1- t Þ þ kd Dt

After summing over n-periods, one gets the following expression for NPV: NPV = - I þ

n n X NOIð1 - t Þ X kd Dt NOIð1 - t Þ i þ i = -I þ ke ð Þ ð Þ 1 þ k 1 þ k e d i=1 i=1

 ð1- ð1 þ k e Þ - n Þ þ Dt ð1- ð1 þ kd Þ - n Þ

ð23:21Þ

In the case of a few ( p) payments of tax on profit per period, the expression for NPV will be modified: NPV = - I þ

np n X NOIð1 - t Þ X kd Dt þ i i=p 1 þ k ð Þ e i = 1 pð 1 þ k d Þ i=1

ð23:22Þ

After summing over n-periods, one gets the following modified expression for NPV: NPV = - I þ

NOIð1 - t Þ½1 - ð1 þ k e Þ - n  kd Dt ½1 - ð1 þ kd Þ - n  h þ 1 ke p ð1 þ k Þ =p - 1 

ð23:23Þ

d

To obtain the expression for NPV of long-term investment projects, one should find the limit of (23.23) n → 1. NPV = - I þ

NOIð1 - t Þ kd Dt þ h 1 ke p ð1 þ k Þ =p - 1  d

ð23:24Þ

23.4

Discount Rates

23.3.2

513

Without Flow Separation

In the case of no separation between operating and financial flows, both flows are discounted by the general rate WACC. After summing the expression (23.6) over n-periods, one gets the following expression for NPV: NPV = - I þ

n n X X NOIð1 - t Þ k d Dt þ i i i = 1 ð1 þ WACCÞ i = 1 ð1 þ WACCÞ

NOIð1 - t Þ k Dt ð1- ð1 þ WACCÞ - n Þ þ d WACC WACC  ð1- ð1 þ WACCÞ - n Þ

ð23:25Þ

NPV = - I þ

ð23:26Þ

In the case of a few ( p) payments of tax on profit per period, the expression for NPV will be modified: NPV = - I þ

np n X X NOIð1 - t Þ k d Dt þ i i=p i = 1 pð1 þ WACCÞ i = 1 ð1 þ WACCÞ

ð23:27Þ

After summing over n-periods, one gets the following modified expression for NPV:   n  NOIð1 - t Þ 1
1NPV = - I þ WACC 1 þ WACC þ

k d Dt ð1 - ð1 þ WACCÞ - n Þ  1 p ð1 þ WACCÞ =p - 1 Þ

ð23:28Þ

To obtain the expression for NPV of long-term investment projects, one should find the limit of (23.28) n → 1. NPV = - I þ

23.4

NOIð1 - t Þ kd Dt
þ  1 WACC p ð1 þ WACCÞ =p - 1 Þ

ð23:29Þ

Discount Rates

In the case without the division of credit and investment flows (both flows are discounted using the same rate, for which WACC can obviously be chosen), WACC is calculated by the following formulas:

514

23 Innovative Investment Models with Frequent Payments of Tax on Income. . .

For arbitrary project duration (Kahneman and Tversky 1996): 1 - ð1 þ WACCÞ - n = WACC

1 - ð1 þ k 0 Þ - n  -n k0
1 - kd pwd t ½1 - ð1þk1=pd -Þ 1 Þ

ð23:30Þ

ð1þk d Þ

For long-term projects (Kahneman and Tversky 1996): WACC = k 0


1-

k d wd t 1 Þ p ð1 þ k d Þ1=p - 1

ð23:31Þ

In the case of the division of credit and investment flows (and thus discounting of the payments using two different rates, equity cost ke and debt cost kd), ke should be found from the equation WACC = k e we þ k d wd ð1- t Þ

ð23:32Þ

where we substitute WACC from the formula (23.30) for a project with arbitrary duration and from the formula (23.31) for a long-term project. Note that formulas (23.30) and (23.31) are quite different from the original formulas by Brusov–Filatova–Orekhova (Brusov et al. 2018b; Filatova et al. 2008) and Modigliani–Miller (Мodigliani and Мiller 1958, 1963, 1966), where payments of interest on debt and of tax on income are made once per year and are turned into them if we put p = 1: 1 - ð1 þ k 0 Þ - n 1 - ð1 þ WACCÞ - n = WACC k 0
ð1 - wd t ½1 - ð1 þ k d Þ - n Þ WACC = k0
ð1- wd t Þ

23.5

ð23:33Þ ð23:34Þ

Results and Discussions

In this section, we study numerically with the use of Microsoft Excel the effectiveness of the four models created above by us. We consider long-term projects as well as projects of arbitrary duration from two perspectives: the owners of equity and debt and the equity holders only. We will study the case without flow separation. In this case, operating and financial flows are not separated and both are discounted, using the general rate, for which we select the weighted average cost of capital, WACC. Let us start from the study numerically on the dependence of the discount rates (weighted average cost of capital, WACC) on leverage level L at different frequencies of payment of tax on profit p.

23.5

Results and Discussions

515

23.5.1

Numerical Calculation of the Discount Rates

23.5.1.1

The Long-Term Investment Projects

For long-term investment projects (the Modigliani–Miller limit), the discount rate (WACC) in the case of arbitrary frequency of payment of tax on profit p is described by formula (23.31) (Brusov and Filatova 2021): WACC = k 0


k d wd t 1 1-1 p ð1 þ kd Þ1=p

!

For WACC calculation, we will use the following parameters: k0 = 0.22; kd = 0.14; t = 20%; L = 0; 1; 2...; 10. Dependence of WACC on leverage level L at k0 = 0.22, kd = 0.14 and different p = 1, 6, 12 is shown in Table 23.1 and Fig. 23.1.

23.5.1.2

The Arbitrary Duration Investment Projects

For arbitrary duration investment projects, the discount rate (WACC) in the case of arbitrary frequency of payment of tax on profit p is described by formula (23.30) (modified BFO formula (Brusov and Filatova 2021)). For WACC calculation, we will use the following parameters: k0 = 0.22; kd = 0.14; t = 20%; L = 0; 1; 2...; 10; p = 1; 6; 12; n = 3

Table 23.1 Dependence of WACC on leverage level L at k0 = 0.22, kd = 0.14 and different p = 1, 6, 12

L 0 1 2 3 4 5 6 7 8 9 10

WACC p=1 0.2200 0.1980 0.1907 0.1870 0.1848 0.1833 0.1823 0.1815 0.1809 0.1804 0.1800

p=6 0.2200 0.1967 0.1890 0.1851 0.1828 0.1812 0.1801 0.1793 0.1787 0.1781 0.1777

p = 12 0.2200 0.1966 0.1888 0.1849 0.1826 0.1810 0.1799 0.1791 0.1784 0.1779 0.1775

516

23 Innovative Investment Models with Frequent Payments of Tax on Income. . .

Fig. 23.1 Dependence of the weighted average cost of capital, WACC, on leverage level L at different frequencies of payments of tax on profit, p = 1; 6; 12 Table 23.2 Dependence of WACC on leverage level L at k0 = 0.22, kd = 0.14 and different p = 1, 6, 12 for a threeyear company

L 0 1 2 3 4 5 6 7 8 9 10

1 - ð1 þ WACCÞ - n = WACC

WACC p=1 0.2200 0.1987 0.1915 0.1879 0.1858 0.1843 0.1833 0.1825 0.1819 0.1815 0.1811



p=6 0.2200 0.1974 0.1899 0.1861 0.1838 0.1823 0.1812 0.1804 0.1798 0.1793 0.1788

1 - ð1 þ k 0 Þ - n

k0
1 -

-n k d wd t ½1 - ð1þkd Þ  1=p p ð1þk d Þ

p = 12 0.2200 0.1973 0.1897 0.1859 0.1836 0.1821 0.1810 0.1802 0.1795 0.1790 0.1786

 -1

Dependence of WACC on leverage level L at k0 = 0.22, kd = 0.14 and different p = 1, 6, 12 for a three-year company is shown in Table 23.2 and Figs. 23.2 and 23.3. Note that the dependences of WACC on leverage level L obtained above will be used below under a study of the effectiveness of long-term as well arbitrary duration

23.5

Results and Discussions

517

Fig. 23.2 Dependence of WACC on leverage level L at k0 = 0.22, kd = 0.14 and different p = 1, 6, 12 for a three-year project

Fig. 23.3 Dependence of WACC on leverage level L at k0 = 0.22, kd = 0.14 and different p = 1, 6, 12 for a three-year project (larger scale)

518

23 Innovative Investment Models with Frequent Payments of Tax on Income. . .

investment projects, from the perspective of the owners of equity capital and of the owners of equity and debt.

23.5.2

The Effectiveness of the Long-Term Investment Project from the Perspective of the Owners of Equity Capital

For long-term investment projects, the discount rate (WACC) in the case of arbitrary frequency of payment of tax on profit p is described by formula (23.19) and for NPV one has: NPV = - S þ -

kd Dt NOIð1 - t Þ  þ  1= WACC p1 ð1 þ WACCÞ p1 - 1

kd D   1= p2 ð1 þ WACCÞ p2 - 1

For NPV calculation, we will use the following parameters: k0 = 0.22; kd = 0.14; t = 20%; L = 0; 1; 2...; 10; p1 = p2 = p = 1; 6; 12; S = 1000; D = LS; NOI = 800. It is seen from Figs. 23.4 and 23.5 that in the case of considering the effectiveness of long-term investment projects for owners of equity capital, NPV will vary with the change of p, but with not much variation (it is seen from Table 23.3 and from Fig. 23.5, but not from Fig. 23.4).

23.5.3

The Effectiveness of the Long-Term Investment Project from the Perspective of the Owners of Equity and Debt

For long-term investment projects, NPV in the case of arbitrary frequency of payment of tax on profit p is described by formula (23.29): NPV = - I þ

NOIð1 - t Þ kd Dt  þ  1= WACC p ð1 þ WACCÞ p - 1

For NPV calculation, we will use the following parameters: k0 = 0.22; kd = 0.14; t = 20%; L = 0; 1; 2...; 10; p1 = p2 = p = 1; 6; 12; S = 1000; D = LS; NOI = 800. Dependence of NPV on leverage level L at k0 = 0.22, kd = 0.14 and different p = 1, 6, 12 for a long-term project is shown in Table 23.4 and Figs. 23.6 and 23.7.

23.5

Results and Discussions

519

NPV(L) at different p 35000 30000 25000

NPV

20000 NPV (p=1) 15000

NPV (p=6) NPV (p=12)

10000 5000 0

1

2

3

4

5

6

7

8

9

10

L Fig. 23.4 Dependence of NPV on leverage level L at k0 = 0.22, kd = 0.14 and different p = 1, 6, 12 for a long-term project

NPV(L) at different p 29000 28500 28000

NPV

27500 NPV (p=1) 27000

NPV (p=6)

NPV (p=12)

26500 26000 25500 10

9

L Fig. 23.5 Dependence of NPV on leverage level L at k0 = 0.22, kd = 0.14 and different p = 1, 6, 12 for a long-term project (larger scale)

520

23 Innovative Investment Models with Frequent Payments of Tax on Income. . .

Table 23.3 Dependence of WACC and NPV on leverage level L at k0 = 0.22, kd = 0.14 and different p = 1, 6, 12

Table 23.4 Dependence of NPV on leverage level L at k0 = 0.22, kd = 0.14 and different p = 1, 6, 12

23.5.4

L 0 1 2 3 4 5 6 7 8 9 10

NPV p=1 1909 4899 7895 10,893 13,892 16,891 19,890 22,890 25,889 28,889 31,889

p=6 1909 4891 7883 10,878 13,874 16,871 19,868 22,865 25,863 28,860 31,858

p = 12 1909 4891 7882 10,877 13,873 16,869 19,866 22,863 25,860 28,858 31,855

L 0 1 2 3 4 5 6 7 8 9 10

NPV p=1 1909 4606 7364 10,139 12,922 15,709 18,498 21,289 24,081 26,874 29,667

p=6 1909 4659 7478 10,316 13,163 16,015 18,870 21,726 24,583 27,441 30,300

p = 12 1909 4665 7489 10,334 13,188 16,047 18,908 21,771 24,635 27,500 30,365

The Effectiveness of the Arbitrary Duration Investment Projects from the Perspective of the Owners of Equity Capital

For the arbitrary duration investment projects, NPV in the case of arbitrary frequency of payment of tax on profit p is described by formula (23.18):   n  kd Dt ð1 - ð1 þ WACCÞ - n Þ 1 NOIð1 - t Þ  þ 
1NPV = - S þ 1= WACC 1 þ WACC p ð1 þ WACCÞ p1 - 1 1

D kd Dð1 - ð1 þ WACCÞ - n Þ  -  1= ð1 þ WACCÞn p2 ð1 þ WACCÞ p2 - 1

23.5

Results and Discussions

521

NPV(L) at different p 30000 25000

NPV

20000 NPV (p=1)

15000

NPV (p=6) NPV (p=12)

10000 5000 0

1

2

3

4

5

6

7

8

9

10

L Fig. 23.6 Dependence of NPV on leverage level L at k0 = 0.22, kd = 0.14 and different p = 1, 6, 12 for a long-term project

NPV(L) (I = const) at different p 28000 27000

NPV

26000 25000 NPV (p=1) 24000

NPV (p=6)

NPV (p=12)

23000 22000 21000 8

9

10

L Fig. 23.7 Dependence of NPV on leverage level L at k0 = 0.22, kd = 0.14 and different p = 1, 6, 12 for a long-term project (larger scale)

23 Innovative Investment Models with Frequent Payments of Tax on Income. . .

522

Table 23.5 Dependence of NPV on leverage level L at k0 = 0.22, kd = 0.14 and different p = 1, 6, 12 for a threeyear project

NPV p=1 307 885 1438 1985 2530 3072 3615 4156 4698 5239 5780

L 0 1 2 3 4 5 6 7 8 9 10

p=6 307 869 1406 1937 2464 2991 3516 4042 4566 5091 5615

p = 12 307 867 1403 1932 2458 2983 3506 4030 4553 5076 5599

NPV(L) (S = const) at different p 6000 5000

NPV

4000 3000

NPV (p=1) NPV (p=6)

2000

NPV (p=12)

1000 0

1

2

3

4

5

6

7

8

9

10

L Fig. 23.8 Dependence of NPV on leverage level L at k0 = 0.22, kd = 0.14 and different p = 1, 6, 12 for a three-year project

For NPV calculation, we will use the following parameters: k0 = 0.22; kd = 0.14; t = 20%; L = 0; 1; 2...; 10; p1 = p2 = p = 1; 6; 12; S = 1000; D = LS; NOI = 800; n = 3. Dependence of NPV on leverage level L at k0 = 0.22, kd = 0.14 and different p = 1, 6, 12 for a 3-year project is shown in Table 23.5 and Figs. 23.8 and 23.9.

23.5

Results and Discussions

523

NPV(L) at different p 5200 5000

NPV

4800 NPV (p=1)

4600

NPV (p=6) NPV (p=12)

4400 4200 4000

8

9

10

L Fig. 23.9 Dependence of NPV on leverage level L at k0 = 0.22, kd = 0.14 and different p = 1, 6, 12 for a three-year project (larger scale)

23.5.5

The Effectiveness of the Arbitrary Duration Investment Project from the Perspective of the Owners of Equity and Debt

For the arbitrary duration investment projects, NPV in the case of arbitrary frequency of payment of tax on profit p is described by formula (23.28): NPV = - I þ

  n  k Dt ð1 - ð1 þ WACCÞ - n Þ NOIð1 - t Þ 1
1þ d  1 WACC 1 þ WACC p ð1 þ WACCÞ =p - 1 Þ

For NPV calculation, we will use the following parameters: k0 = 0.22; kd = 0.14; t = 20%; L = 0; 1; 2...; 10; p1 = p2 = p = 1; 6; 12; S = 1000; D = LS; NOI = 800; n = 3. Dependence of NPV on leverage level L at k0 = 0.22, kd = 0.14 and different p = 1, 6, 12 for a three-year project is shown in Table 23.6 and Figs. 23.10 and 23.11.

23 Innovative Investment Models with Frequent Payments of Tax on Income. . .

524

Table 23.6 Dependence of NPV on leverage level L at k0 = 0.22, kd = 0.14 and different p = 1, 6, 12 for a threeyear project

NPV p=1 307 761 1218 1676 2135 2594 3053 3511 3970 4429 4888

L 0 1 2 3 4 5 6 7 8 9 10

p=6 307 771 1238 1707 2175 2644 3113 3582 4051 4520 4989

p = 12 307 772 1240 1710 2179 2649 3119 3589 4059 4529 4999

NPV(L) (I = const) at different p 5000 4500 4000 3500

NPV

3000 2500

NPV (p=1)

2000

NPV (p=6) NPV (p=12)

1500 1000 500 0 1

2

3

4

5

6

7

8

9

10

L Fig. 23.10 Dependence of NPV on leverage level L at k0 = 0.22, kd = 0.14 and different p = 1, 6, 12 for a three-year project

23.5.6

Discussions

The analysis of results from Tables 23.1–23.6 and Figs. 23.1–23.11 shows that: 1. The weighted average cost of capital, WACC, decreases with leverage level L at all values of frequency of payments of tax on profit p (see Tables 23.1 and 23.2 and Figs. 23.1–23.3);

23.5

Results and Discussions

525

NPV(L) (I = const) at different p 4600

4400

NPV

4200

4000

NPV (p=1) NPV (p=6)

3800

NPV (p=12)

3600

3400 8

9

10

L Fig. 23.11 Dependence of NPV on leverage level L at k0 = 0.22, kd = 0.14 and different p = 1, 6, 12 for a three-year project (larger scale)

2. With an increase in p, WACC decreases: WACC(L) curves lie lower with increase of p; 3. The difference between curves corresponding to p = 1 and p = 6 is much more than the difference between the curves corresponding to p = 6 and p = 12. This difference decreases with p. It turns out that an increase in the number of payments of tax on profit per year p leads to a decrease in the cost of attracting capital (WACC). Will this decrease in the discount rate increase the effectiveness of investment projects? As we see from Tables 23.3–23.6 and Figs. 23.4– 23.11, the situation is different for owners of equity capital and for owners of equity and debt capital. 4. NPV practically linearly increases with leverage level at all values of frequency of payments of tax on profit p and all frequency of payments of interest on debt. 5. In the case of considering the effectiveness of long-term investment projects for owners of equity capital, NPV is changed with a change of p (both p1 and p2 are equal everywhere below) but by a very small value (it is seen in the Tables, but not in the Figures). 6. In the case of considering the effectiveness of long-term investment projects for owners of equity and debt, NPV is changed with a change of p more significantly (it is seen in the Tables and in the Figures).

526

23 Innovative Investment Models with Frequent Payments of Tax on Income. . .

7. For arbitrary duration projects, this difference in NPV with a change of p is more significant and should be accounted under valuation of the effectiveness of an investment project. 8. In the case of considering the effectiveness of an investment project for owners of equity capital, we need to note that an increase in p leads to a decrease in NPV: this means that the effectiveness of an investment project decreases with p. 9. In the case of considering the effectiveness of an investment project for owners of equity and debt capital, we need to note that the situation is opposite and an increase in p leads to increase in NPV: this means that the effectiveness of an investment project increases with p. 10. The above results show that in the former case, companies should pay tax on profit and interest on debt once per year, while in the latter case, more frequent payments are profitable for the effectiveness of an investment. 11. Thus, while for long-term projects’ NPV, the impact of more frequent payments of both values p1 and p2 is insignificant, for arbitrary duration projects the account of the frequency of both types of payments could be important and could lead to more significant influence on the effectiveness of an investment project, decreasing it (in the former case), or increasing it (in the latter case). Note that the specific value of the effect depends on the values of the parameters in the project (k0, kd, n, t, S, etc.).

23.6

Conclusions

There are too few investment models which can numerically valuate the effectiveness of investment projects, among them the investment models developed by the authors of this paper. Moreover, investment models are practically absent which account for the conditions of the real functioning of investment projects. This paper covers this gap in the literature and science in the field of investments and develops innovative investment models which are much closer to economic practice. We developed here for the first time eight innovative investment models: longterm (described by Eqs. (23.14), (23.19), (23.24), and (23.29)) as well as arbitrary duration (described by Eqs. (23.13), (23.18), (23.23) and (23.28)), which account payments of interest on debt and of tax on income a few times per year (semiannually, quarterly, monthly) as it happened in practice. Note that no one before had investigated the impact of the frequency of payments of taxes and of debt interest on the effectiveness of investment projects. These investment models allow for investigation of the impact of all main parameters of investment projects (equity value S, investment value I, net operating income NOI, leverage level L, profitability of investments β, tax on profit t, project duration n, equity cost k0, debt cost kd and number of payments of interest on debt p1 and of tax on income p2) on the main indicator of effectiveness of investment projects NPV (net present value). They could be used for investigation of different problems of investments, such as the

Conclusions

527

influence of debt financing, leverage level, taxing, project duration, method of financing, number of payments of interest on debt and of tax on income and some other parameters on efficiency of investments and other problems. In particular, they will improve the issue of project ratings (Brusov et al. 2018a). These new models allow for making more correct evaluations of effectiveness of investment projects long-term as well as of arbitrary duration. Numerical calculations, conducted for four investment models (without flow separation) show that: • In the case of considering the effectiveness of an investment project for owners of equity capital, the increase in the number of payments of tax on income and of interest on debt p leads to an decrease in NPV: this means that the effectiveness of an investment project decreases with p. • In the case of considering the effectiveness of an investment project for owners of equity and debt capital, the increase in the number of payments of tax on income and of interest on debt p leads to an increase in NPV: this means that the effectiveness of an investment project increases with p. In the former case, companies should pay tax on profit and interest on debt once per year, while in the latter case, more frequent payments are profitable for the effectiveness of an investment. Thus, while for long-term projects’ NPV, the impact of more frequent payments of both values p1 and p2 is insignificant, for arbitrary duration projects the account of the frequency of both types of payments could be important and could lead to more significant influence on the effectiveness of an investment project, decreasing it (in the former case), or increasing it (in the latter case). Note that the specific value of the effect depends on the values of the parameters in the project (k0, kd, n, t, S, etc.). There are some limitations of the applicability of the proposed models: 1. For long-term projects, they are connected with the limitations of the Modigliani– Miller theory. 2. For consideration of without flow separation, they are connected with the wellknown limitations of the WACC approach. 3. For arbitrary duration projects (using BFO theory), they are connected with the fact that not all the conditions of real investments are accounted yet. The contribution of this study to finance and economics is mainly related to the goal that new modern investment models have been created to be as close as possible to real investment conditions. Our models, namely, models with payments of interest on debt and of tax on income which occur a few times per year (semi-annually, quarterly or monthly), could be more successfully applied in real economic practice.

528

23 Innovative Investment Models with Frequent Payments of Tax on Income. . .

References Black F, Litterman R (1992) Global Portfolio Optimization. Financ Anal J 48:28–43 Bond S, Meghir C (1994) Dynamic investment models and the firm’s financial policy. Rev Econ Study 67:197–222 Brown K, Harlow W, Zhang H (2021) Investment style volatility and mutual fund performance. J Invest Manag 19:78 Brusov P, Filatova T (2021) The Modigliani-Miller theory with arbitrary frequency of payment of tax on profit. Mathematics 9:1198. https://doi.org/10.3390/math9111198 Brusov P, Filatova T, Orehova N, Eskindarov M (2015) Modern corporate finance, investments and taxation. Springer, Cham, Switzerland, pp 1–373. https://www.springer.com/gp/book/978331 9147314. Accessed on 29 April 2021 Brusov P, Filatova T, Orehova N (2018a) Ratings: critical analysis and new approaches of quantitative and qualitative methodology. Springer, Cham, Switzerland, pp 1–379. https:// www.springer.com/de/book/9783030562427. Accessed 29 April 2021 Brusov P, Filatova T, Orehova N, Eskindarov M (2018b) Modern corporate finance, investments, taxation and ratings, 2nd edn. Springer, Cham, Switzerland, pp 1–571 Cakici N, Zaremba A (2021) Size, value, profitability, and investment effects in international stock returns: are they really there? J Invest 30:65–86. https://doi.org/10.3905/joi.2021.1.176 Dammon R, Senbet L (1988) The effect of taxes and depreciation on corporate investment and financial leverage. J Financ 43:357–373. https://doi.org/10.1111/j.1540-6261.1988.tb03944.x DeAngelo H, Masulis R (1980) Optimal capital structure under corporate and personal taxation. J Financ Econ 8:3–29 Dotan A, Ravid S (1985) On the interaction of real and financial decisions of the firm under uncertainty. J Financ 40:501–517 Escobar-Anel M, Lichtenstern A, Zagst R (2020) Behavioral portfolio insurance strategies. Financ Mark Portf Manag 34:353–399 Filatova TV, Orekhova NP, Brusova АP (2008) Weighted average cost of capital in the theory of Modigliani-Miller, modified for a finite life–time company. Bull FU 48:68–77 Gidwani B (2020) Some issues with using ESG ratings in an investment process. J Invest 29:76–84. https://doi.org/10.3905/joi.2020.1.147 Kahneman D, Tversky A (1996) On the reality of cognitive illusions. Psychol Rev 103:582–591. https://doi.org/10.1037/0033-295X.103.3.582 Kang J (1995) The conditional relationship between financial leverage and corporate investment: further clarification. J Bus Financ Account 22:1211–1219. https://doi.org/10.1111/j.1468-5957. 1995.tb00902.x Lang LE, Ofek E, Stulz R (1996) Leverage, investment, and firm growth. J Financ Econ 40:3–29 Loviscek A (2021) How much to invest, if any, in precious metals? A 21st-century perspective. J Invest 30:95–111. https://doi.org/10.3905/joi.2021.1.179 Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Modigliani F, Miller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391 Rosenbaum J, Pearl J (2013) Investment banking valuation models. Wiley, New York, NY, pp 1–342 Whited T (1992) Debt, liquidity constraints and corporate investment: evidence from panel data. J Financ 47:1425–1461

Chapter 24

The Role of the Central Bank and Commercial Banks in Creating and Maintaining a Favorable Investment Climate in the Country

Keywords The Central Bank · Commercial banks · Innovative investment models · Effectiveness of the investment project · The Brusov–Filatova–Orekhova theory · Favorable investment climate In this chapter, we study the role of the Central Bank and commercial banks in creating and maintaining a favorable investment climate in the country. Within the framework of modern investment models created by the authors, the dependence of the efficiency of investments on the level of debt financing within a wide range of values of equity costs and debt capital costs under different project terms (long-term projects as well as projects of arbitrary duration) and different investment profitability coefficients β is investigated. The effectiveness of investments is determined by Net Present Value, NPV. The study is conducted within the framework of investment models with debt repayment at the end of the project term. It is found that NPV depends practically linearly on leverage level L, increasing or decreasing depending on profitability coefficient β and credit rate values kd. The cutoff credit rate values kd*, separating the range of increasing NPV(L) from range of decreasing NPV(L), are determined. The Central Bank should keep its key rate at the level which allows commercial banks to keep their credit rates below the cutoff credit rate kd* values in order to create and maintain a favorable investment climate in the country.

24.1

Introduction

The investments play a very important role in an economy of each country. As a rule the debt financing is always used in the investments. In the current paper, we determine the role of the Central Bank and commercial banks in creating and maintaining a favorable investment climate in the country. Within the framework of modern investment models created by the authors, the dependence of the efficiency of investments on the level of debt financing within a wide range of values of equity capital costs and debt capital costs under different project terms (long-term © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_24

529

530

24

The Role of the Central Bank and Commercial Banks in Creating. . .

projects as well as projects of arbitrary duration) and different investment profitability coefficients β is investigated. The effectiveness of investments is determined by Net Present Value, NPV. The study is conducted within the framework of investment models with debt repayment at the end of the project term. It is found that NPV depends practically linearly on leverage level L, increasing or decreasing depending on profitability coefficient β and credit rate values kd. The cutoff credit rate values kd*, separating the range of increasing NPV(L) from range of decreasing NPV(L), are determined. The Central Bank should keep its key rate at the level which allows commercial banks to keep their credit rates below the cutoff credit rate values kd* in order to create and maintain a favorable investment climate in the country.

24.2

Investment Models with Debt Repayment at the End of the Project

The effectiveness of the investment project could be considered from two perspectives: the owners of equity and debt and the equity holders only. For each of these cases, NPV could be calculated in two ways: with the division of credit and investment flows (and thus discounting of the payments using two different rates) and without such a division (in this case, both flows are discounted using the same rate, as which can be, obviously, chosen WACC). For each of the four situations, two cases could be considered: (1) a constant value of equity S and (2) a constant value of the total invested capital I = S + D (D is the value of debt funds). As it was stated above, the effectiveness of the investment project is considered from two perspectives: the owners of equity and debt and the equity holders only. In the first case, the interest and duty paid by owners of equity (negative flows) returned to the project because they are exactly equal to the flow (positive), obtained by owners of debt capital. The only effect of leverage in this case is the effect of the tax shield, generated from the tax relief: interest on the loan is entirely included into the cost and thus reduces the tax base. After-tax flow of capital for each period in this case is equal to NOIð1- t Þ þ k d Dt

ð24:1Þ

and the value of investments at the initial time moment T = 0 is equal to -I = -S D. Here, NOI stands for net operating income (before taxes). In the second case, investments at the initial time moment T = 0 are equal to -S and the flow of capital for the period (in addition to the tax shields kd Dt it includes a payment of interest on a loan -kdD):

24.2

Investment Models with Debt Repayment at the End of the Project

ðNOI- k d DÞð1- t Þ:

531

ð24:2Þ

Here, for simplicity, we suppose that interest on the loan will be paid in equal shares kd D during all periods. Note that principal repayment is made at the end of the last period. We will consider the case of discounting, when operating and financial flows are not separated and both are discounted, using the general rate (as which, obviously, the weighted average cost of capital (WACC) can be selected). In this case for longterm (perpetuity) projects, the Modigliani–Miller formula (Мodigliani and Мiller 1958, 1963, 1966) for WACC will be used and for projects of finite (arbitrary) duration Brusov–Filatova–Orekhova formula will be used (Brusov et al. 2015; Brusov et al. 2018a, b, c, d; Brusov and Filatova 2011; Brusov et al. 2011a, b, c, 2012a, b, 2013a, b, 2014a, b; Filatova et al. 2008; Brusova 2011). Note that debt capital is the least risky, because interest on credit is paid after taxes in the first place. Therefore, the cost of credit will always be less than the equity cost, whether of ordinary or of preference shares ke > kd; kp > kd. Here, ke; kp is the equity cost of ordinary or of preference shares consequently.

24.2.1

The Effectiveness of the Investment Project from the Perspective of the Equity Holders Only (Without Flows Separation)

In this case operating and financial flows are not separated and are discounted, using the general rate (as which, obviously, WACC can be selected). The credit reimbursable at the end of the project (at the end of the period (n)) can be discounted either at the same rate WACC or at the debt cost rate kd. Now we choose a uniform rate and the first option. n X NOIð1 - t Þ - kd Dð1 - t Þ

D ð 1 þ WACC Þn ð1 þ WACCÞ i=1   NOIð1 - t Þ - k d Dð1 - t Þ 1 D 1= -S þ : WACC ð1 þ WACCÞn ð1 þ WACCÞn

NPV = - S þ

i

-

ð24:3Þ At a Constant Value of Equity Capital (S = const) Accounting that in the case S = const NOI is proportional to the invested capital, I, NOI = βI = βS(1 + L ), and substituting D = LS, we get

532

24

The Role of the Central Bank and Commercial Banks in Creating. . .

  NOIð1 - t Þ - kd Dð1 - t Þ 1 1NPV = - S þ WACC ð1 þ WACCÞn D , ð1 þ WACCÞn     Lk d ð1 - t Þ 1 L 1þ NPV = - S 1 þ WACC ð1 þ WACCÞn ð1 þ WACCÞn   βSð1 þ LÞð1 - t Þ 1 þ 1: WACC ð1 þ WACCÞn -

24.2.1.1

ð24:4Þ

ð24:5Þ

Modigliani–Miller Limit (Long-Term (Perpetuity) Projects

In perpetuity limit (n → 1) (Modigliani–Miller limit) (turning to the limit n → 1 in the relevant equations), we have NPV = - S þ

NOIð1 - t Þ - kd Dð1 - t Þ : WACC

ð24:6Þ

At a Constant Value of Equity Capital (S = const) NPV = - S þ

NOIð1 - t Þ - k d Dð1 - t Þ WACC

ð24:7Þ

Substituting D = LS, we get 

 NOIð1 - t Þ Lkd ð1 - t Þ þ NPV = - S 1 þ WACC WACC   Lk d ð1 - t Þ βSð1 þ LÞð1 - t Þ = -S 1 þ þ : k0 ð1 - Lt=ð1 þ LÞÞ k 0 ð1 - Lt=ð1 þ LÞÞ

ð24:8Þ

In the last equation we substituted the perpetuity (Modigliani–Miller) formula for WACC  WACC = k 0 1-

 Lt : 1þL

ð24:9Þ

Below we will investigate the dependence of the efficiency of investments on the level of debt financing within a wide range of values of equity costs k0 and debt capital costs kd under different project terms (long-term projects as well as projects of arbitrary duration) and different investment profitability coefficients β.

24.3

Modigliani–Miller Limit (Long-Term (Perpetuity) Projects)

533

For long-term project calculations we use formulas (24.8) and (24.9), while for arbitrary duration project calculations we use formula (24.5) for NPV and BFO formula for WACC 1 - ð1 þ k 0 Þ - n 1 - ð1 þ WACCÞ - n : = WACC k 0 ½ 1 - ω d T ð 1 - ð 1 þ k d Þ - n Þ

ð24:10Þ

D —the share of Here, S is the value of equity capital of the company, wd = DþS S debt capital, ke , we = DþS —the cost and the share of the equity capital of the company, and L = D/S—financial leverage.

24.3

Modigliani–Miller Limit (Long-Term (Perpetuity) Projects)

Let us start with the long-term projects. We will study the dependence of the efficiency of investments on the level of debt financing L for the values of equity costs k0 from 6% up to 32% and for different debt capital costs and different investment profitability coefficient β values.

24.3.1

The Dependence of the Efficiency of Investments NPV on the Level of Debt Financing L for the Values of Equity Costs k0 = 0.2

Below we represent the results of calculations for equity costs k0 = 0.2; debt capital costs kd = 0.18; 0.16; 0.14; 0.12; 0.10; 0.08; 0.06; S = 250; tax on profit rate t = 0.2. Results are shown in Tables 24.1, 24.2, and 24.3 and Figs. 24.1, 24.2, and 24.3. 1. β = 0.1 From Table 24.1 and Fig. 24.1, it is seen that NPV depends practically linearly on leverage level L, increasing or decreasing depending on credit rate value kd. NPV (L) increases at credit rate kd = 0.06 and kd = 0.08. The cutoff credit rate kd* value, separating the range of increasing NPV(L) from range of decreasing NPV(L) for investment profitability coefficient β = 0.1, is equal to 0.1. At higher credit rate kd values NPV(L) represents decreasing function. 2. β = 0.12 From Table 24.2 and Fig. 24.2 it is seen that NPV depends practically linearly on leverage level L, increasing or decreasing depending on credit rate value kd. NPV (L) increases at credit rate kd = 0.06; kd = 0.08 and kd = 0.1. The cutoff credit rate value kd*, separating the range of increasing NPV(L) from range of decreasing NPV

NPV (kd = 0.18) -150.00 -227.78 -319.23 -414.71 -511.90 -610.00 -708.62 -807.58 -906.76 -1006.10 -1105.56

NPV (kd = 0.16) -150.00 -205.56 -273.08 -344.12 -416.67 -490.00 -563.79 -637.88 -712.16 -786.59 -861.11

NPV (kd = 0.14) -150.00 -183.33 -226.92 -273.53 -321.43 -370.00 -418.97 -468.18 -517.57 -567.07 -616.67

NPV (kd = 0.12) -150.00 -161.11 -180.77 -202.94 -226.19 -250.00 -274.14 -298.48 -322.97 -347.56 -372.22

NPV (kd = 0.1) -150.00 -138.89 -134.62 -132.35 -130.95 -130.00 -129.31 -128.79 -128.38 -128.05 -127.78

NPV (kd = 0.08) -150.00 -116.67 -88.46 -61.76 -35.71 -10.00 15.52 40.91 66.22 91.46 116.67

NPV (kd = 0.06) -150.00 -94.44 -42.31 8.82 59.52 110.00 160.34 210.61 260.81 310.98 361.11

24

L 0 1 2 3 4 5 6 7 8 9 10

Table 24.1 The dependence of NPV on the level of debt financing L for the values of equity costs k0 = 0.2 and for different debt capital costs kd = 0.18; 0.16; 0.14; 0.12; 0.10; 0.08; 0.06; S = 250; tax on profit rate t = 0.2 and investment profitability coefficient β = 0.1

534 The Role of the Central Bank and Commercial Banks in Creating. . .

L 0 1 2 3 4 5 6 7 8 9 10

NPV (kd = 0.18) -130.00 -183.33 -250.00 -323.59 -392.86 -466.00 -539.66 -613.64 -687.84 -762.20 -836.67

NPV (kd = 0.16) -130.00 -161.11 -203.85 -250.00 -297.62 -346.00 -394.83 -443.94 -493.24 -542.68 -592.22

NPV (kd = 0.14) -130.00 -138.89 -157.69 -179.41 -202.38 -226.00 -250.00 -274.24 -298.65 -323.17 -347.78

NPV (kd = 0.12) -130.00 -116.67 -111.54 -108.82 -107.14 -106.00 -105.17 -104.55 -104.05 -103.66 -103.33

NPV (kd = 0.1) -130.00 -94.44 -65.38 -38.24 -11.90 14.00 39.66 65.15 90.54 115.85 141.11

NPV (kd = 0.08) -130.00 -72.22 -19.23 32.35 83.33 134.00 184.48 234.85 285.14 335.37 385.56

NPV (kd = 0.06) -130.00 -50.00 26.92 102.94 178.57 254.00 329.31 404.55 479.73 554.88 630.00

Table 24.2 The dependence of NPV on the level of debt financing L for the values of equity costs k0 = 0.2 and for different debt capital costs kd = 0.18; 0.16; 0.14; 0.12; 0.10; 0.08; 0.06; S = 250; tax on profit rate t = 0.2 and investment profitability coefficient β = 0.12

24.3 Modigliani–Miller Limit (Long-Term (Perpetuity) Projects) 535

NPV (kd = 0.18) -110.00 -138.89 -180.77 -226.47 -273.81 -322.00 -370.69 -419.70 -468.92 -518.29 -567.78

NPV (kd = 0.16) -110.00 -116.67 -134.62 -155.88 -178.57 -202.00 -225.86 -250.00 -274.32 -298.78 -323.33

NPV (kd = 0.14) -110.00 -94.44 -88.46 -85.29 -83.33 -82.00 -81.03 -80.30 -79.73 -79.27 -78.89

NPV (kd = 0.12) -110.00 -72.22 -42.31 -14.71 11.90 38.00 63.79 89.39 114.86 140.24 165.56

NPV (kd = 0.1) -110.00 -50.00 3.85 55.88 107.14 158.00 208.62 259.09 309.46 359.76 410.00

NPV (kd = 0.08) -110.00 -27.78 50.00 126.47 202.38 278.00 353.45 428.79 504.05 579.27 654.44

NPV (kd = 0.06) -110.00 -5.56 96.15 197.06 297.62 398.00 498.28 598.48 698.65 798.78 898.89

24

L 0 1 2 3 4 5 6 7 8 9 10

Table 24.3 The dependence of NPV on the level of debt financing L for the values of equity costs k0 = 0.2 and for different debt capital costs kd = 0.18; 0.16; 0.14; 0.12; 0.10; 0.08; 0.06; S = 250; tax on profit rate t = 0.2 and investment profitability coefficient β = 0.14

536 The Role of the Central Bank and Commercial Banks in Creating. . .

24.3

Modigliani–Miller Limit (Long-Term (Perpetuity) Projects)

537

Fig. 24.1 The dependence of the Net Present Value, NPV on the leverage level L for the equity value k0 = 20% and for different debt capital costs kd = 0.18; 0.16; 0.14; 0.12; 0.10; 0.08; 0.06; S = 250; tax on profit rate t = 0.2 and investment profitability coefficient β = 0.1

Fig. 24.2 The dependence of the Net Present Value, NPV, on the leverage level L for the equity value k0 = 20% and for different debt capital costs kd = 0.18; 0.16; 0.14; 0.12; 0.10; 0.08; 0.06; S = 250; tax on profit rate t = 0.2 and investment profitability coefficient β = 0.12

(L) for investment profitability coefficient β = 0.12, is equal to 0.12. At higher credit rate kd values NPV(L) represents decreasing function.

538

24

The Role of the Central Bank and Commercial Banks in Creating. . .

Fig. 24.3 The dependence of the Net Present Value, NPV, on the leverage level L for the equity value k0 = 20% and for different debt capital costs kd = 0.18; 0.16; 0.14; 0.12; 0.10; 0.08; 0.06; S = 250; tax on profit rate t = 0.2 and investment profitability coefficient β = 0.14

3. β = 0.14 From Table 24.3 and Fig. 24.3 it is seen that NPV depends practically linearly on leverage level L, increasing or decreasing depending on credit rate value kd. NPV (L) increases at credit rate kd = 0.06; kd = 0.08; kd = 0.1; and kd = 0.12. The cutoff credit rate kd* value separating the range of increasing NPV(L) from range of decreasing NPV(L) for investment profitability coefficient β = 0.14 is equal to 0.14. At higher credit rate kd values NPV(L) represents decreasing function. One can see that the cutoff credit rate kd* values separating the range of increasing NPV(L) from range of decreasing NPV(L) strongly correlate with investment profitability coefficient β and practically linearly depend on it. For long-term projects (Modigliani–Miller limit) it was found that the cutoff credit rate values kd* are proportional to investment profitability coefficient β: it turns out that for equity capital cost k0 = 0.2 the cutoff credit rate values kd* separating the range of increasing NPV(L) from range of decreasing NPV(L) are approximately equal to investment profitability coefficient β: for investment profitability coefficient β = 0.1 kd* is equal to 0.1; for β = 0.12 kd* is equal to 0.12; and for investment profitability coefficient β = 0.14 kd* is equal to 0.14. The slope of the curve NPV(L) increases with investment profitability coefficient β for the same value of credit rate kd.

24.3

Modigliani–Miller Limit (Long-Term (Perpetuity) Projects)

24.3.2

539

The Dependence of the Efficiency of Investments NPV on the Level of Debt Financing L for the Value of Equity Costs k0 = 0.28

Let us consider also the case of equity capital cost k0 = 0.28 and debt capital cost kd = 6%;8%;10%;12%;14%;16%;18%;20%;22%;24%. It is seen from Fig. 24.4 that the cutoff credit rate kd* value separating the range of increasing NPV(L) from range of decreasing NPV(L) is equal to 10%. It is seen from Fig. 24.5 that the cutoff credit rate value kd*, separating the range of increasing NPV(L) from range of decreasing NPV(L), is equal to 20%. From Figs. 24.4 and 24.5 it follows that for β = 0.1 kd* is equal to 0.1; and for investment profitability coefficient β = 0.2 kd* is equal to 0.2. We could come to the conclusion that in perpetuity limit for both cases for the equity values k0 = 20% and k0 = 28% it turns out that the cutoff credit rate kd* values are equal to investment profitability coefficient β (and do not depend on the equity values k0). As we will see below this statement is not valid for the projects of arbitrary durations.

Fig. 24.4 The dependence of the Net Present Value, NPV on the leverage level L for the equity value k0 = 28% and for different debt capital costs kd = 6%;8%;10%;12%;14%;16%;18%;20%;22%;24%; S = 250; tax on profit rate t = 0.2 and investment profitability coefficient β = 0.1

540

24

The Role of the Central Bank and Commercial Banks in Creating. . .

Fig. 24.5 The dependence of the Net Present Value, NPV on the leverage level L for the equity value k0 = 28% and for different debt capital costs kd = 6%; 8%; 10%; 12%; 14%; 16%; 18%; 20%; 22%; 24%; S = 250; tax on profit rate t = 0.2 and investment profitability coefficient β = 0.2

24.4

Projects of Finite (Arbitrary) Duration

Let us consider now the projects of arbitrary durations. We will study the dependence of the efficiency of investments on the level of debt financing L for the same values of equity costs k0 from 6% up to 32%; for different debt capital costs kd and different investment profitability coefficient β values as well as for different project durations. For arbitrary duration project calculations, we use formula (24.5) for NPV     Lkd ð1 - t Þ 1 L 1þ NPV = - S 1 þ WACC ð1 þ WACCÞn ð1 þ WACCÞn   βSð1 þ LÞð1 - t Þ 1 : þ 1WACC ð1 þ WACCÞn and BFO formula (24.10) for WACC 1 - ð1 þ WACCÞ - n 1 - ð1 þ k 0 Þ - n : = WACC k 0 ½1 - ωd T ð1 - ð1 þ kd Þ - n Þ

24.4

Projects of Finite (Arbitrary) Duration

24.4.1

541

The Dependence of the Efficiency of Investments NPV on the Level of Debt Financing L for the Values of Equity Costs k0 = 0.2

Below we represent the results of calculations for equity costs k0 = 0.2; debt capital costs kd = 0.18; 0.16; 0.14; 0.12; 0.10; 0.08; 0.06; S = 250; tax on profit rate t = 0.2 and project duration n = 5. In the next part, we will compare the results for project durations n = 5 and n = 3. For arbitrary duration project calculations, we use formula (24.5) for NPV and BFO formula for WACC (24.10). Results are shown in Tables 24.4, 24.5, and 24.6 and Figs. 24.4, 24.5, and 24.6. 1. β = 0.325 From Table 24.4 and Fig. 24.6 it is seen that NPV depends practically linearly on leverage level L, increasing or decreasing depending on credit rate value kd. NPV (L) increases at credit rate kd = 0.06; kd = 0.08; kd = 0.1; and kd = 0.12. The cutoff credit rate value kd*, separating the range of increasing NPV(L) from range of decreasing NPV(L) for investment profitability coefficient β = 0.325, is equal to 0.14. At higher credit rates kd values NPV(L) represents decreasing function. 2. β = 0.345 From Table 24.5 and Fig. 24.7 it is seen that NPV depends practically linearly on leverage level L, increasing or decreasing depending on credit rate value kd. NPV (L) increases at credit rates kd = 0.06; kd = 0.08; kd = 0.1; kd = 0.12; and kd = 0.14. The cutoff credit rate value kd*, separating the range of increasing NPV(L) from range of decreasing NPV(L) for investment profitability coefficient β = 0.345 is equal to 0.16. At higher credit rates kd values NPV(L) represents decreasing function. 3. β = 0.365 From Table 24.6 and Fig. 24.8 it is seen that NPV depends practically linearly on leverage level L, increasing or decreasing depending on credit rate value kd. NPV (L) increases at credit rate kd = 0.06; kd = 0.08; kd = 0.1; kd = 0.12; kd = 0.14; and kd = 0.16. The cutoff credit rate value kd*, separating the range of increasing NPV (L) from the range of decreasing NPV(L) for investment profitability coefficient β = 0.365, is equal to 0.18. At higher credit rates kd values NPV(L) represents decreasing function. One can see that the cutoff credit rate values kd*, separating the range of increasing NPV(L) from the range of decreasing NPV(L), strongly correlate with investment profitability coefficient β and practically linearly depend on it: kd* linearly increases with profitability coefficient β. For arbitrary duration projects results are as follows. The efficiency of investments strongly depends on project duration and increases with duration. One can see that the slope of the curve NPV(L) at project duration n = 5 is always higher than for

NPV (kd = 0.18) -55.62 -64.27 -84.87 -109.00 -134.55 -160.82 -187.68 -214.48 -241.83 -269.07 -296.16

NPV (kd = 0.16) -55.62 -51.88 -58.97 -69.04 -80.39 -92.33 -104.63 -117.19 -129.90 -142.72 -155.62

NPV (kd = 0.14) -55.62 -39.78 -33.37 -29.55 -26.81 -24.61 -22.73 -21.05 -19.51 -18.06 -16.68

NPV (kd = 0.12) -55.62 -27.84 -8.12 9.40 26.01 42.16 58.04 73.87 89.50 105.05 123.54

NPV (kd = 0.1) -55.62 -16.10 16.70 47.74 78.04 107.96 137.67 167.24 196.72 226.13 255.50

NPV (kd = 0.08) -55.62 -4.63 41.06 85.35 129.06 172.47 215.71 258.85 301.91 344.92 387.89

NPV (kd = 0.06) -55.62 6.60 64.88 122.14 178.95 235.56 292.05 348.47 404.83 461.15 517.45

24

L 0 1 2 3 4 5 6 7 8 9 10

Table 24.4 The dependence of NPV on the level of debt financing L for the values of equity costs k0 = 0.2 and for different debt capital costs kd = 0.18; 0.16; 0.14; 0.12; 0.10; 0.08; 0.06; S = 250; tax on profit rate t = 0.2; β = 0.325 and project duration n = 5

542 The Role of the Central Bank and Commercial Banks in Creating. . .

L 0 1 2 3 4 5 6 7 8 9 10

NPV (kd = 0.18) -43.66 -38.96 -46.07 -56.74 -68.82 -81.62 -94.98 -108.32 -122.17 -135.93 -149.58

NPV (kd = 0.16) -43.66 -26.63 -23.39 -17.11 -15.10 -13.68 -12.63 -11.83 -11.18 -10.64 -10.18

NPV (kd = 0.14) -43.66 -14.64 4.97 22.02 37.99 53.42 68.53 83.45 98.22 112.91 127.53

NPV (kd = 0.12) -43.66 -2.83 29.97 60.58 90.29 119.54 148.51 177.41 206.13 234.77 263.36

NPV (kd = 0.1) -43.66 8.77 54.50 98.47 141.71 184.58 227.22 269.74 312.16 354.52 396.83

NPV (kd = 0.08) -43.66 23.08 78.55 135.61 192.09 248.28 304.31 360.22 416.07 471.86 527.61

NPV (kd = 0.06) -43.66 31.15 102.02 171.89 241.28 310.49 379.58 448.59 517.55 586.48 655.38

Table 24.5 The dependence of NPV on the level of debt financing L for the values of equity costs k0 = 0.2 and for different debt capital costs kd = 0.18; 0.16; 0.14; 0.12; 0.10; 0.08; 0.06; S = 250; tax on profit rate t = 0.2; β = 0.345 and project duration n = 5

24.4 Projects of Finite (Arbitrary) Duration 543

NPV (kd = 0.18) -31.70 -13.65 -7.27 -4.48 -3.08 -2.41 -2.27 -2.17 -2.50 -2.79 -3.01

NPV (kd = 0.16) -31.70 -1.39 18.20 34.82 50.20 64.96 79.37 93.53 107.54 121.44 135.26

NPV (kd = 0.14) -31.70 10.49 43.32 73.59 102.79 131.45 159.80 187.94 215.96 243.87 271.73

NPV (kd = 0.12) -31.70 22.18 68.06 111.76 154.56 196.91 238.99 280.94 322.76 364.50 406.18

NPV (kd = 0.1) -31.70 33.65 92.30 149.21 205.39 261.19 316.78 372.24 427.60 482.91 538.16

NPV (kd = 0.08) -31.70 44.80 116.03 185.87 255.13 324.10 392.90 461.60 530.22 598.80 667.33

NPV (kd = 0.06) -31.70 55.69 139.16 221.64 303.62 385.43 467.11 548.72 630.28 711.81 793.30

24

L 0 1 2 3 4 5 6 7 8 9 10

Table 24.6 The dependence of NPV on the level of debt financing L for the values of equity costs k0 = 0.2 and for different debt capital costs kd = 0.18; 0.16; 0.14; 0.12; 0.10; 0.08; 0.06; S = 250; tax on profit rate t = 0.2; β = 0.365 and project duration n = 5

544 The Role of the Central Bank and Commercial Banks in Creating. . .

24.4

Projects of Finite (Arbitrary) Duration

545

Fig. 24.6 The dependence of the Net Present Value, NPV, on the leverage level L for the equity value k0 = 20% and for different debt capital costs kd = 0.18; 0.16; 0.14; 0.12; 0.10; 0.08; 0.06; S = 250; tax on profit rate t = 0.2; investment profitability coefficient β = 0.325 and project duration n = 5

Fig. 24.7 The dependence of the Net Present Value, NPV, on the leverage level L for the equity value k0 = 20% and for different debt capital costs kd = 0.18; 0.16; 0.14; 0.12; 0.10; 0.08; 0.06; S = 250; tax on profit rate t = 0.2; investment profitability coefficient β = 0.345 and project duration n = 5

project duration n = 3. The efficiency of investments increases with project duration and is less than for long-term (perpetuity) projects. Transition to increasing NPV (L) behavior for finite duration projects requires much higher values of investment profitability coefficient β than in case of long-term (perpetuity) projects, where kd* is

546

24

The Role of the Central Bank and Commercial Banks in Creating. . .

Fig. 24.8 The dependence of the Net Present Value, NPV, on the leverage level L for the equity value k0 = 20% and for different debt capital costs kd = 0.18; 0.16; 0.14; 0.12; 0.10; 0.08; 0.06; S = 250; tax on profit rate t = 0.2; investment profitability coefficient β = 0.365 and project duration n = 5

approximately equal to β: for five-year projects the cutoff credit rate value kd* for investment profitability coefficient β = 0.325 is equal to 0.14; for investment profitability coefficient β = 0.345 is equal to 0.16; for investment profitability coefficient β = 0.365 is equal to 0.18. Thus, for finite duration projects as well as for the long-term projects cutoff credit rate values kd* turn out to be proportional to investment profitability coefficient β, but investment profitability coefficient β is approximately twice higher than kd*.

24.4.2

The Dependence of the Efficiency of Investments NPV on the Level of Debt Financing L for the Values of Equity Costs k0 = 0.28

Below in Figs. 24.9, 24.10, 24.11, and 24.12 we present the results of calculations of the dependence of the Net Present Value, NPV, on the leverage level L for the equity value k0 = 28% and for different debt capital costs kd = 0.24; 0.22; 0.20; 0.18; 0.16; 0.14; 0.12; 0.10; 0.08; 0.06; S = 250; tax on profit rate t = 0.2; investment profitability coefficient β = 0.1 and project durations n = 3 and n = 5. From Figs. 24.9, 24.10, 24.11, and 24.12 one can make the following conclusions: 1. NPV decreases with debt capital cost kd. 2. NPV increases with investment profitability coefficient β as well as with project duration.

24.4

Projects of Finite (Arbitrary) Duration

547

n=3, E=0,1 0,00 1

2

3

4

5

6

7

8

9

10

NPV

-500,00

NPV (kd=0,24) NPV (kd=0,22) NPV (kd=0,20) NPV (kd=0,18) NPV (kd=0,16) NPV (kd=0,14) NPV (kd=0,12) NPV (kd=0,10) NPV (kd=0,08) NPV (kd=0,06)

-1000,00 -1500,00 -2000,00 -2500,00

L Fig. 24.9 The dependence of the Net Present Value, NPV on the leverage level L for the equity value k0 = 28% and for different debt capital costs kd = 0.24; 0.22; 0.20; 0.18; 0.16; 0.14; 0.12; 0.10; 0.08; 0.06; S = 250; tax on profit rate t = 0.2; investment profitability coefficient β = 0.1 and project duration n = 3

n=3, E=0,2 0,00 -200,00

1

2

3

4

5

6

8

9

10 NPV (kd=0,24)

-400,00

NPV (kd=0,22)

-600,00

NPV (kd=0,20)

-800,00

NPV

7

NPV (kd=0,18)

-1000,00

NPV (kd=0,16)

-1200,00

NPV (kd=0,14)

-1400,00

NPV (kd=0,12)

-1600,00

NPV (kd=0,10)

-1800,00

NPV (kd=0,08)

-2000,00

NPV (kd=0,06)

L

Fig. 24.10 The dependence of the Net Present Value, NPV on the leverage level L for the equity value k0 = 28% and for different debt capital costs kd = 0.24; 0.22; 0.20; 0.18; 0.16; 0.14; 0.12; 0.10; 0.08; 0.06; S = 250; tax on profit rate t = 0.2; investment profitability coefficient β = 0.2; and project duration n = 3

3. The cutoff value kd* has been reached in Figs. 24.9, 24.10, 24.11, and 24.12 only at profitability coefficient β = 0.2 for 5-year project and is equal to 6%; it will increase with investment profitability coefficient β. Bigger values of β, and/or longer durations n, and/or bigger values of equity capital S are required in order to demonstrate the presence of a cutoff value kd* for particular project.

548

24

The Role of the Central Bank and Commercial Banks in Creating. . .

n=5, E=0,1 0,00

1

2

3

4

5

6

7

8

9

10 NPV (kd=0,24) NPV (kd=0,22) NPV (kd=0,20) NPV (kd=0,18) NPV (kd=0,16) NPV (kd=0,14) NPV (kd=0,12) NPV (kd=0,10) NPV (kd=0,08) NPV (kd=0,06)

-500,00

NPV

-1000,00 -1500,00 -2000,00 -2500,00

L

Fig. 24.11 The dependence of the Net Present Value, NPV on the leverage level L for the equity value k0 = 28% and for different debt capital costs kd = 0.24;0.22;0.20;0.18; 0.16; 0.14; 0.12; 0.10; 0.08; 0.06; S = 250; tax on profit rate t = 0.2; investment profitability coefficient β = 0.1; and project duration n = 5

n=5, E=0,2 0,00

1

2

3

4

5

6

7

8

9

10

-200,00 NPV (kd=0,24) NPV (kd=0,22) NPV (kd=0,20) NPV (kd=0,18) NPV (kd=0,16) NPV (kd=0,14) NPV (kd=0,12) NPV (kd=0,10) NPV (kd=0,08) NPV (kd=0,06)

-400,00

NPV

-600,00 -800,00

-1000,00 -1200,00 -1400,00 -1600,00

L

Fig. 24.12 The dependence of the Net Present Value, NPV, on the leverage level L for the equity value k0 = 28% and for different debt capital costs kd = 0.24; 0.22; 0.20; 0.18; 0.16; 0.14; 0.12; 0.10; 0.08; 0.06; S = 250; tax on profit rate t = 0.2; investment profitability coefficient β = 0.2; and project duration n = 5

24.5

24.5

The Dependence of the Net Present Value, NPV, on the Leverage Level l. . .

549

The Dependence of the Net Present Value, NPV, on the Leverage Level l for Projects of Different Durations

We consider the case of equity cost (at L = 0) k0 = 14% and fixed value of debt cost kd = 0.04; 0.06; 0.08; 0.1; 0.12 and compare the results for projects of different duration: n = 3 years and n = 5 years (Tables 24.7, 24.8, 24.9, 24.10, 24.11, 24.12, 24.13, 24.14, Figs. 24.13, 24.14, 24.15, 24.16). kd = 0.1 One can see that at fixed credit rates k0 NPV increases with project duration. The (negative) slope of NPV(L) curves decreases with project duration.

Table 24.7 The dependence of the Net Present Value, NPV, on the leverage level L for the equity cost value k0 = 14% and for debt capital costs kd = 0.04; S = 250; tax on profit rate t = 0.2; investment profitability coefficient β = 0.1 and for project durations n = 3 S 250 250 250 250 250 250 250 250 250 250 250

L 0 1 2 3 4 5 6 7 8 9 10

WACC 14.00% 13.34% 13.11% 13.00% 12.94% 12.89% 12.86% 12.84% 12.82% 12.80% 12.79%

k0 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

kd 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04

wd 0.00 0.50 0.67 0.75 0.80 0.83 0.86 0.88 0.89 0.90 0.91

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 3 3 3 3 3 3 3 3 3 3 3

β 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

ke 0.14 0.23 0.33 0.42 0.52 0.61 0.71 0.80 0.90 0.99 1.09

NPV -203.57 -346.60 -491.78 -637.53 -783.49 -929.57 -1075.71 -1221.89 -1368.10 -1514.33 -1660.57

Table 24.8 The dependence of the Net Present Value, NPV, on the leverage level L for the equity cost value k0 = 14% and for debt capital costs kd = 0.04; S = 250; tax on profit rate t = 0.2; investment profitability coefficient β = 0.1 and for project durations n = 5 S 250 250 250 250 250 250 250 250 250 250 250

L 0 1 2 3 4 5 6 7 8 9 10

WACC 14.00% 13.26% 13.01% 12.88% 12.80% 12.75% 12.72% 12.69% 12.67% 12.65% 12.64%

k0 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

kd 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04

wd 0.00 0.50 0.67 0.75 0.80 0.83 0.86 0.88 0.89 0.90 0.91

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 5 5 5 5 5 5 5 5 5 5 5

β 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

ke 0.14 0.23 0.33 0.42 0.51 0.61 0.70 0.79 0.88 0.98 1.07

NPV -181.34 -272.31 -366.58 -461.70 -557.17 -652.81 -748.55 -844.36 -940.21 -1036.09 -1131.99

550

24

The Role of the Central Bank and Commercial Banks in Creating. . .

Table 24.9 The dependence of the Net Present Value, NPV, on the leverage level L for the equity cost value k0 = 14% and for debt capital costs kd = 0.04; S = 250; tax on profit rate t = 0.2; investment profitability coefficient β = 0.2; and for project durations n = 3 S 250 250 250 250 250 250 250 250 250 250 250

L 0 1 2 3 4 5 6 7 8 9 10

WACC 14.00% 13.34% 13.11% 13.00% 12.94% 12.89% 12.86% 12.84% 12.82% 12.80% 12.79%

k0 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

kd 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04

wd 0.00 0.50 0.67 0.75 0.80 0.83 0.86 0.88 0.89 0.90 0.91

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 3 3 3 3 3 3 3 3 3 3 3

β 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

ke 0.14 0.23 0.33 0.42 0.52 0.61 0.71 0.80 0.90 0.99 1.09

NPV -157.14 -252.69 -350.39 -448.64 -547.12 -645.71 -744.36 -843.05 -941.77 -1040.51 -1139.26

Table 24.10 The dependence of the Net Present Value, NPV, on the leverage level L for the equity cost value k0 = 14% and for debt capital costs kd = 0.04; S = 250; tax on profit rate t = 0.2; investment profitability coefficient β = 0.2; and for project durations n = 5 S 250 250 250 250 250 250 250 250 250 250 250

24.6

L 0 1 2 3 4 5 6 7 8 9 10

WACC 14.00% 13.26% 13.01% 12.88% 12.80% 12.75% 12.72% 12.69% 12.67% 12.65% 12.64%

k0 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

kd 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04

wd 0.00 0.50 0.67 0.75 0.80 0.83 0.86 0.88 0.89 0.90 0.91

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 5 5 5 5 5 5 5 5 5 5 5

β 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

ke 0.14 0.23 0.33 0.42 0.51 0.61 0.70 0.79 0.88 0.98 1.07

NPV -112.68 -132.50 -155.57 -179.49 -203.76 -228.20 -252.73 -277.33 -301.97 -326.65 -351.34

Conclusions

We study the role of the Central Bank and commercial banks in creating and maintaining a favorable investment climate in the country. Within the framework of modern investment models created by the authors, the dependence of the efficiency of investments on the level of debt financing within a wide range of values of equity capital costs and debt capital costs under different project terms (long-term projects as well as projects of arbitrary duration) and different investment profitability coefficients β is investigated. The effectiveness of investments is determined by net present value (NPV). The study is conducted within the framework of investment models with debt repayment at the end of the project term.

24.6

Conclusions

551

Table 24.11 The dependence of the Net Present Value, NPV, on the leverage level L for the equity cost value k0 = 14% and for debt capital costs kd = 0.1; S = 250; tax on profit rate t = 0.2; investment profitability coefficient β = 0.2; and for project durations n = 3 S 250 250 250 250 250 250 250 250 250 250 250

L 0 1 2 3 4 5 6 7 8 9 10

WACC 14.00% 12.51% 12.01% 11.76% 11.61% 11.51% 11.44% 11.39% 11.35% 11.31% 11.28%

k0 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

kd 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10

wd 0.00 0.50 0.67 0.75 0.80 0.83 0.86 0.88 0.89 0.90 0.91

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 3 3 3 3 3 3 3 3 3 3 3

β 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

ke 0.14 0.17 0.20 0.23 0.26 0.29 0.32 0.35 0.38 0.41 0.44

NPV -203.57 -377.91 -557.74 -739.00 -923.85 -1103.00 -1285.31 -1467.73 -1650.23 -1832.77 -2015.35

Table 24.12 The dependence of the Net Present Value, NPV, on the leverage level L for the equity cost value k0 = 14% and for debt capital costs kd = 0.1; S = 250; tax on profit rate t = 0.2; investment profitability coefficient β = 0.1; and for project durations n = 5 S 250 250 250 250 250 250 250 250 250 250 250

L 0 1 2 3 4 5 6 7 8 9 10

WACC 14.00% 12.41% 11.88% 11.61% 11.45% 11.34% 11.26% 11.20% 11.16% 11.12% 11.09%

k0 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

kd 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10

wd 0.00 0.50 0.67 0.75 0.80 0.83 0.86 0.88 0.89 0.90 0.91

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 5 5 5 5 5 5 5 5 5 5 5

β 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

ke 0.14 0.17 0.20 0.22 0.25 0.28 0.31 0.34 0.36 0.39 0.42

NPV -181.34 -317.91 -462.97 -610.30 -758.57 -907.31 -1056.33 -1205.52 -1354.83 -1504.22 -1653.67

It is found that NPV depends practically linearly on leverage level L, increasing or decreasing depending on profitability coefficient β and credit rate value kd. The cutoff credit rate values kd* separating the range of increasing NPV(L) from range of decreasing NPV(L) are determined. For long-term projects (Modigliani–Miller limit) it was found that the cutoff credit rate values kd* are proportional to investment profitability coefficient β: it turns out that for equity capital cost k0 = 0.2 the cutoff credit rate value kd* separating the range of increasing NPV(L) from range of decreasing NPV(L) is approximately equal to investment profitability coefficient β: for investment profitability coefficient β = 0.1 kd* is equal to 0.1; for β = 0.12 kd* is equal to 0.12; and for investment profitability coefficient β = 0.14 kd* is equal to 0.14. The slope of the

552

24

The Role of the Central Bank and Commercial Banks in Creating. . .

Table 24.13 The dependence of the Net Present Value, NPV, on the leverage level L for the equity cost value k0 = 14% and for debt capital costs kd = 0.1; S = 250; tax on profit rate t = 0.2; investment profitability coefficient β = 0.2; and for project durations n = 3 S 250 250 250 250 250 250 250 250 250 250 250

L 0 1 2 3 4 5 6 7 8 9 10

WACC 14.00% 12.51% 12.01% 11.76% 11.61% 11.51% 11.44% 11.39% 11.35% 11.31% 11.28%

k0 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

kd 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10

wd 0.00 0.50 0.67 0.75 0.80 0.83 0.86 0.88 0.89 0.90 0.91

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 3 3 3 3 3 3 3 3 3 3 3

β 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

ke 0.14 0.17 0.20 0.23 0.26 0.29 0.32 0.35 0.38 0.41 0.44

NPV -157.14 -282.68 -413.66 -546.07 -679.06 -812.35 -945.80 -1079.36 -1212.99 -1346.67 -1480.38

Table 24.14 The dependence of the Net Present Value, NPV, on the leverage level L for the equity cost value k0 = 14% and for debt capital costs kd = 0.1; S = 250; tax on profit rate t = 0.2; investment profitability coefficient β = 0.2; and for project durations n = 5 S 250 250 250 250 250 250 250 250 250 250 250

L 0 1 2 3 4 5 6 7 8 9 10

WACC 14.00% 12.41% 11.88% 11.61% 11.45% 11.34% 11.26% 11.20% 11.16% 11.12% 11.09%

k0 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

kd 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10

wd 0.00 0.50 0.67 0.75 0.80 0.83 0.86 0.88 0.89 0.90 0.91

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 5 5 5 5 5 5 5 5 5 5 5

β 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

ke 0.14 0.17 0.20 0.22 0.25 0.28 0.31 0.34 0.36 0.39 0.42

NPV -112.68 -175.18 -246.02 -319.09 -393.09 -467.55 -542.29 -617.20 -692.22 -767.32 -842.47

curve NPV(L) increases with investment profitability coefficient β for the same value of credit rate kd. We come to the conclusion that for long-term projects (in perpetuity limit) for both cases for the equity values k0 = 20% and k0 = 28% it turns out that the cutoff credit rate values kd* are equal to investment profitability coefficient β (and do not depend on the equity values k0). This statement is not valid for the projects of arbitrary (finite) durations. For arbitrary duration projects results are as follows. The efficiency of investments strongly depends on project duration and increases with duration. One can see that the slope of the curve NPV(L) at project duration n = 5 is always higher than for project duration n = 3. The efficiency of investments increases with project duration and is less than for long-term (perpetuity) projects. Transition to increasing NPV

24.6

Conclusions

553

NPV(L), kd=0,04, E=0,1 0,00 -200,00

0

1

2

3

4

5

6

7

8

9

10

-400,00

NPV

-600,00 -800,00 -1000,00 -1200,00 -1400,00 -1600,00 -1800,00

L NPV (n=3)

NPV (n=5)

Fig. 24.13 The dependence of the Net Present Value, NPV, on the leverage level L for the equity cost value k0 = 14% and for debt capital costs kd = 0.04; S = 250; tax on profit rate t = 0.2; investment profitability coefficient β = 0.1; and for two project durations n = 3 and n = 5

NPV(L), kd=0,04, E=0,2 0,00 0

1

2

3

4

5

6

7

8

9

10

-200,00

NPV

-400,00 -600,00 -800,00 -1000,00 -1200,00

L NPV (n=3)

NPV (n=5)

Fig. 24.14 The dependence of the Net Present Value, NPV, on the leverage level L for the equity cost value k0 = 14% and for debt capital costs kd = 0.04; S = 250; tax on profit rate t = 0.2; investment profitability coefficient β = 0.2; and for two project durations n = 3 and n = 5

(L) behavior for finite duration projects requires much higher values of investment profitability coefficient β than in case of long-term (perpetuity) projects, where kd* is approximately equal to β: for example, for equity cost k0 = 0.20 and five-year projects the cutoff credit rate value kd* for investment profitability coefficient

554

24

The Role of the Central Bank and Commercial Banks in Creating. . .

NPV(L), kd=0,1, E=0,1 0,00 0

1

2

3

4

5

6

7

8

9

10

NPV

-500,00 -1000,00 -1500,00 -2000,00 -2500,00

L NPV (n=3)

NPV (n=5)

Fig. 24.15 The dependence of the Net Present Value, NPV, on the leverage level L for the equity cost value k0 = 14% and for debt capital costs kd = 0.1; S = 250; tax on profit rate t = 0.2; investment profitability coefficient β = 0.1; and for two project durations n = 3 and n = 5

NPV(L), kd=0,1, E=0,2 0,00 -200,00

0

1

2

3

4

5

6

7

8

9

10

-400,00

NPV

-600,00 -800,00 -1000,00 -1200,00 -1400,00 -1600,00

L NPV (n=3)

NPV (n=5)

Fig. 24.16 The dependence of the Net Present Value, NPV, on the leverage level L for the equity cost value k0 = 14% and for debt capital costs kd = 0.1; S = 250; tax on profit rate t = 0.2; investment profitability coefficient β = 0.2; and for two project durations n = 3 and n = 5

β = 0.325 is equal to 0.14; for investment profitability coefficient β = 0.345 is equal to 0.16; for investment profitability coefficient β = 0.365 is equal to 0.18. Thus, for finite duration projects as well as for the long-term projects cutoff credit rate values

References

555

kd* turn out to be proportional to investment profitability coefficient β, but investment profitability coefficient β is approximately twice higher than kd*. We develop a method of determination of the cutoff credit rate values kd*, separating the range of increasing NPV(L) from range of decreasing NPV(L). We have found the cutoff credit rate kd* values within a wide range of values of equity costs k0 and debt capital costs kd under different project terms (long-term projects as well as projects of arbitrary duration) and different investment profitability coefficients β. Obtained results will help the Central Bank to keep its key rate at the level, which allows commercial banks to keep their credit rates below the cutoff credit rate values kd* in order to create and maintain a favorable investment climate in the country.

References Brusov PN, Filatova ТV (2011) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Finance Credit 435:2–8 Brusov P, Filatova T, Orehova N, Brusova A (2011a) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Appl Financ Econ 21(11): 815–824 Brusov P, Filatova T, Orehova N et al (2011b) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Bus ICT 2:16–21 Brusov P, Filatova T, Orehova N et al (2011c) Influence of debt financing on the effectiveness of the investment project within the Modigliani–Miller theory. Res J Econ Bus ICT (UK) 2:11–15 Brusov P, Filatova T, Eskindarov M, Orehova N (2012a) Influence of debt financing on the effectiveness of the finite duration investment project. Appl Financ Econ 22(13):1043–1052 Brusov P, Filatova T, Eskindarov M, Orehova N (2012b) Hidden global causes of the global financial crisis. J Rev Global Econ 1:106–111 Brusov P, Filatova P, Orekhova N (2013a) Absence of an optimal capital structure in the famous tradeoff theory! J Rev Global Econ 2:94–116 Brusov P, Filatova T, Orehova N (2013b) A qualitatively new effect in corporative finance: abnormal dependence of cost of equity of company on leverage. J Rev Global Econ 2:183–193 Brusov P, Filatova P, Orekhova N (2014a) Mechanism of formation of the company optimal capital structure, different from suggested by trade off theory. Cogent Econ Finance 2:1–13. https://doi. org/10.1080/23322039.20946150 Brusov P, Filatova T, Orehova N (2014b) Inflation in Brusov–Filatova–Orekhova theory and in its perpetuity limit – Modigliani–Miller theory. J Rev Global Econ 3:175–185 Brusov P, Filatova T, Orehova N, Eskindarov M (2015) Modern corporate finance, investments and taxation, monograph, 1st edn. Springer, New York, p 368 Brusov P, Filatova T, Orehova N, Kulk WI (2018a) New meaningful effects in modern capital structure theory. J Rev Global Econ 7:104–122 Brusov P, Filatova T, Orehova N, Kulk V (2018b) A “golden age” of the companies: conditions of its existence. J Rev Global Econ 7:88–103 Brusov P, Filatova T, Orehova N, Kulk V (2018c) Rating methodology: new look and new horizons. J Rev Global Econ 7:63–87 Brusov P, Filatova T, Orehova N, Kulk V (2018d) Rating: new approach. J Rev Global Econ 7:37– 62 Brusova A (2011) А comparison of the three methods of estimation of weighted average cost of capital and equity cost of company. Financ Anal Prob Sol 34(76):36–42

556

24

The Role of the Central Bank and Commercial Banks in Creating. . .

Filatova Т, Orehova N, Brusova А (2008) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Bull FU 48:68–77 Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Мodigliani F, Мiller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391

Chapter 25

The Golden Age of the Company (Three Colors of Company’s Time)

Keywords The golden age of the company · The Brusov–Filatova–Orekhova theory · The weighted average cost of capital, WACC In this Chapter we return back to corporate finance in order to describe a very important discovery, made by us recently (Brusov et al. 2015a, b). We investigate the dependence of attracting capital cost on the age of company n at various leverage levels, at various values of capital costs with the aim of defining minimum cost of attracting capital. All calculations have been done within modern theory of capital cost and capital structure by Brusov–Filatova–Orekhova (Brusov and Filatova 2011; Brusov et al. 2011a, b, c, 2012a, b, 2013a, b, 2014a, b; Filatova et al. 2008; Brusova 2011). It is shown for the first time that the valuation of weighted average cost of capital (WACC) in the Modigliani–Miller theory (Мodigliani and Мiller 1958, 1963, 1966) is not minimal and valuation of the company capitalization is not maximal, as all financiers supposed up to now: at some age of the company, its WACC value turns out to be lower than in Modigliani–Miller theory and company capitalization V turns out to be greater than V in Modigliani–Miller theory. It is shown that, from the point of view of cost of attracting capital, there are two types of dependences of WACC on the age of company n: monotonic descending of WACC with n and descending of WACC with passage through minimum, followed by a limited growth (Brusov et al. 2015a, b). The companies with the latter type of dependence of WACC on the age of company n can take advantage of the benefits given at a certain stage of development by discovered effect. Moreover, since the “golden age” of company depends on the company’s capital costs, ke and kd, by controlling them (e.g., by modifying the value of dividend payments that reflect the equity cost, etc.), the company may extend its “golden age” when the cost to attract capital becomes minimal (less than perpetuity limit) and the capitalization of companies becomes maximal (above than perpetuity assessment) up to a specified time interval. It has been concluded that existing presentations concerning the results of the theory of Modigliani–Miller (Мodigliani and Мiller 1958, 1963, 1966) in these aspects are incorrect. We discuss the use of opened effects in economics. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_25

557

558

25

The Golden Age of the Company (Three Colors of Company’s Time)

WACC WACC1

M

BFO

MM

WACC∞

0

1

∞

n

Fig. 25.1 Monotonic dependence of WACC on the lifetime (age) of the company n

Introduction It is well known that the company goes through several stages in its development process: adolescence, maturity, and old age. Within the modern theory of capital cost and capital structure by Brusоv–Filаtоvа–Orekhоvа (BFO theory) (Brusov et al. 2018a, b, c, d; Brusov and Filatova 2011; Brusov et al. 2011a, b, c, 2012a, b, 2013a, b, 2014a, b; Filatova et al. 2008; Brusova 2011), it is shown that the problem of the company development has an interpretation, which is absolutely different from the generally accepted one. One of the most important problems in corporate finance is the problem of capital cost and capital structure. Before 2008 there were just two kinds of valuations of cost of capital: the first one was the first quantitative theory by Nobel Prize winners Modigliani and Miller (1958, 1963, 1966), applicable to perpetuity (with infinite lifetime) companies, and the second one was the valuation applicable to 1-year companies by Steve Myers (1984). So, before 2008, when the modern theory of capital cost and capital structure by Brusоv–Filаtоvа–Orekhоvа (BFO theory) has been created (Brusov and Filatova 2011; Brusov et al. 2011a, b, c, 2012a, b, 2013a, b, 2014a, b; Filatova et al. 2008; Brusova 2011), only two points in time interval have been known: 1 year and infinity. At that time Steve Myers (1984) has supposed that the Modigliani–Miller (MM) theory (Мodigliani and Мiller 1958, 1963, 1966) gave the lowest assessment for WACC and consequently, the highest assessment for company capitalization. This means that the WACC monotonically descends with the time of life of company, n, approaching its perpetuity limit (Fig. 25.1), and, consequently, company capitalization monotonically increases, approaching its perpetuity limit (Fig. 25.3).

25

The Golden Age of the Company (Three Colors of Company’s Time)

559

Created in 2008 the modern theory of capital cost and capital structure by Brusоv–Filаtоvа–Orekhоvа (BFO theory) (Brusov and Filatova 2011; Brusov et al. 2011a, b, c, 2012a, b, 2013a, b, 2014a, b; Filatova et al. 2008; Brusova 2011) turned out to be able to make valuation of capital cost and company capitalization for companies with arbitrary lifetime (of arbitrary age): this completes the whole time interval from n = 1 up to n = 1. A lot of qualitative effects in corporate finance, investments, taxations, etc. has been made within BFO theory. In this chapter with BFO theory it is shown that Steve Myers’ suggestion (Myers 1984) turns out to be wrong. Choosing of optimal capital structure of the company, i.e., proportion of debt and equity, which minimizes the weighted average cost of capital and maximizes the company capitalization, is one of the most important tasks of financial manager and the management of a company. The search for an optimal capital structure attracts the attention of economists and financiers during many tens of years. And it is clear why: one can, nothing making but only by changing the proportion between the values of equity capital and debt of the company, significantly enhance the company capitalization, in other words, fulfill the primary task, to reach the critical goal of business management. Spend a little less of your own, loan slightly more (or vice versa), and company capitalization reaches a maximum. Before, the search for an optimal capital structure was made by studying the dependence of WACC on leverage level in order to determine the optimal leverage level L0, at which the WACC is minimal and capitalization V is maximal. Here we apply an absolutely different method, studying the dependence of WACC on the time of life (age) of company n. Note that before the appearance of BFO theory, study of such kind of dependences was impossible due to the absence of “time” parameter in perpetuity Modigliani–Miller theory (Мodigliani and Мiller 1958, 1963, 1966). As it is shown in this chapter, from the point of view of cost of capital, there are two types of dependences of WACC on the time of life (age) of company n: monotonic descending of WACC with n and descending of WACC with passage through minimum, followed by a limited growth (Figs. 25.1 and 25.2) (Brusov et al. 2015a, b). The first type of behavior is linked with the comment by Myers (1984) that the Modigliani–Miller (MM) theory (Мodigliani and Мiller 1958, 1963, 1966) gives the lowest assessment for WACC that, as shown by us within the BFO theory, is, generally speaking, incorrect. The second type of behavior of dependence of WACC on the time of life (age) of company n is descending of WACC with passage through minimum, followed by a limited growth. Thus, in the general case, the comment by Myers (1984) turns out to be wrong, and in the life of company there is a “golden age” or “the golden century” when the cost of attracting capital becomes minimal and company capitalization becomes maximal (Figs. 25.2 and 25.3) (Brusov et al. 2015a, b). In the life of company, the same number of stages as usual can be allocated: youth, maturity, and old age. In youth, the WACC decreases with n; in maturity, the value of attracting capital cost becomes minimal; and in old age, this cost grows, approaching its perpetuity limit.

560

25

The Golden Age of the Company (Three Colors of Company’s Time)

WACC WACC1

M

BFO

MM

WACC∞ WACC0

0

1

n0

∞

n

Fig. 25.2 Dependence of WACC on the lifetime (age) of the company n, showing descending of WACC with passage through minimum and then showing a limited growth to perpetuity (MM) limit

So, figuratively speaking, a current investigation transforms “black and white business world” (with monotonic descending of WACC with the time of life of company n) into “color business world” (with descending of WACC with n with passage through minimum, followed by a limited growth): really there are three colors of company’s time. The conclusion made in this chapter for the first time that the assessment of the WACC in the theory of Modigliani and Miller (MM) (Мodigliani and Мiller 1958, 1963, 1966) is not the minimal and capitalization is not maximal seems to be very significant and important.

25.1

Dependence of WACC on the Age of the Company n at Different Leverage Levels

In this section we study the dependence of WACC on the age of the company n at different leverage levels (L = 1;2;3;5;7). The analysis in Tables 25.1, 25.2, 25.3, 25.4, and 25.5 and Fig. 25.4 allows us to make the following conclusions: 1. In all examined cases (at all leverage levels), at current values of capital costs (equity, k0, and debt, kd, ones), the second type of behavior of dependence of

25.2

Dependence of WACC on the Age of the Company n at Different. . .

561

CC,V 2'

V∞ V

WACC k0 (1-wdt)

1'

1 2

0

1

n0

n

Fig. 25.3 Two kinds of dependences of WACC and company capitalization, V, on the lifetime (age) of the company n: 1–1′—monotonic descending of WACC and monotonic increase of company capitalization, V, with the lifetime of the company n; 2–2′—descending of WACC with passage through minimum and then showing a limited growth, and increase of V with passage through maximum (at n0) and then a limited descending to perpetuity (MM) limit

WACC on the lifetime (age) of the company, n, takes place, namely, descending of WACC with n with passage through minimum with subsequent limited growth. 2. The minimum cost of attracting capital (WACC) is achieved at all leverage levels at the same company’s age at n = 6 (only when L = 1, minimum is spread for 2 years (n = 5 and n = 6)). 3. The value of minimum WACC, at a fixed n, significantly depends on the level of leverage, L, and, of course, decreases with increasing L.

25.2

Dependence of WACC on the Age of the Company n at Different Values of Capital Costs (Equity, k0, and Debt, kd) and Fixed Leverage Levels

The analysis in Tables 25.6, 25.7, 25.8, and 25.9 and Figs. 25.5 and 25.6 allows us to make the following conclusions: 1. The type of behavior of dependence of WACC on the age of the company, n, at fixed leverage level significantly depends on values of capital costs (equity, k0,

562

25

The Golden Age of the Company (Three Colors of Company’s Time)

Table 25.1 Dependence of WACC on the age of the company n at L = 1

L 1 1 1 1 1 1 1 1 1 1

WACC 0.1843 0.1798 0.1780 0.1772 0.1769 0.1769 0.1770 0.1771 0.1773 0.1775

Table 25.2 Dependence of WACC on the age of the company n at L = 2

L 2 2 2 2 2 2 2 2 2 2

WACC 0.1791 0.1731 0.1706 0.1696 0.1692 0.1691 0.1692 0.1694 0.1696 0.1699

Table 25.3 Dependence of WACC on the age of the company n at L = 3

L 3 3 3 3 3 3 3 3 3 3

WACC 0.1765 0.1697 0.1669 0.1657 0.1653 0.1651 0.1653 0.1655 0.1658 0.1661

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

kd 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

kd 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

wd 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

wd 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667

wd 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 1 2 3 4 5 6 7 8 9 10

ke 0.2487 0.2397 0.2360 0.2345 0.2339 0.2338 0.2340 0.2343 0.2346 0.2351

n 1 2 3 4 5 6 7 8 9 10

ke 0.2974 0.2793 0.2719 0.2687 0.2675 0.2672 0.2675 0.2681 0.2689 0.2697

n 1 2 3 4 5 6 7 8 9 10

ke 0.3461 0.3189 0.3078 0.3029 0.3010 0.3006 0.3010 0.3019 0.3030 0.3042

and debt, kd). At the values of capital costs that are specific to developing countries (including Russia) (k0 = 20 %, kd = 15 %), there is a second type of dependence of WACC on the age of the company, n, namely, descending of WACC with n with passage through minimum with subsequent limited growth. And at the capital cost values, characteristic to the West (k0 = 8 %, kd = 4 %), there is a first type of dependence of WACC on the age of company n, namely, the monotonic descending of WACC with n.

25.2

Dependence of WACC on the Age of the Company n at Different. . .

Table 25.4 Dependence of WACC on the age of the company n at L = 5

L 5 5 5 5 5 5 5 5 5 5

WACC 0.1739 0.1663 0.1632 0.1619 0.1613 0.1612 0.1613 0.1615 0.1619 0.1622

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Table 25.5 Dependence of WACC on the age of the company n at L = 7

L 7 7 7 7 7 7 7 7 7 7

WACC 0.1726 0.1646 0.1614 0.1599 0.1594 0.1592 0.1593 0.1596 0.1599 0.1603

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

kd 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

563

wd 0.83333 0.83333 0.83333 0.83333 0.83333 0.83333 0.83333 0.83333 0.83333 0.83333

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 1 2 3 4 5 6 7 8 9 10

ke 0.4435 0.3980 0.3795 0.3713 0.3680 0.3672 0.3679 0.3693 0.3711 0.3732

wd 0.875 0.875 0.875 0.875 0.875 0.875 0.875 0.875 0.875 0.875

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 1 2 3 4 5 6 7 8 9 10

ke 0.5409 0.4771 0.4511 0.4396 0.4349 0.4338 0.4347 0.4366 0.4392 0.4421

WACC(n) 0.1900 0.1850

WACC

0.1800

L=1

0.1750

L=2

0.1700

L=3

0.1650

L=5

0.1600

L=7

0.1550

0

2

4

6

n

8

10

12

Fig. 25.4 Dependence of WACC on the age of the company n at different leverage levels

Current suggestion has been made before the detailed investigation of condition of existing of gold age effect has been done. As we will see in the next Chapter, the existence of the “golden age” of company does not depend on

564

25

The Golden Age of the Company (Three Colors of Company’s Time)

Table 25.6 Dependence of WACC on the age of the company n at L = 1, k0 = 8%, kd = 4%

L 1 1 1 1 1 1 1 1 1 1

WACC 0.0758 0.0745 0.0738 0.0735 0.0732 0.0731 0.0729 0.0729 0.0728 0.0728

k0 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08

kd 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04

wd 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 1 2 3 4 5 6 7 8 9 10

ke 0.1197 0.1170 0.1157 0.1149 0.1144 0.1141 0.1139 0.1137 0.1136 0.1135

Table 25.7 Dependence of WACC on the age of the company n at L = 1, k0 = 20%, kd = 15%

L 1 1 1 1 1 1 1 1 1 1

WACC 0.1843 0.1798 0.1780 0.1772 0.1769 0.1769 0.1770 0.1771 0.1773 0.1775

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

wd 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 1 2 3 4 5 6 7 8 9 10

ke 0.2487 0.2397 0.2360 0.2345 0.2339 0.2338 0.2340 0.2343 0.2346 0.2351

Table 25.8 Dependence of WACC on the age of the company n at L = 3, k0 = 20%, kd = 15%

L 3 3 3 3 3 3 3 3 3 3

WACC 0.1765 0.1697 0.1669 0.1657 0.1653 0.1651 0.1653 0.1655 0.1658 0.1661

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

wd 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 1 2 3 4 5 6 7 8 9 10

ke 0.3461 0.3189 0.3078 0.3029 0.3010 0.3006 0.3010 0.3019 0.3030 0.3042

the value of capital costs of the company, but depends on the difference value between equity, k0, and debt, kd, costs. 2. The same features are observed in both considering cases: at the leverage values L = 1 and L = 3.

25.2

Dependence of WACC on the Age of the Company n at Different. . .

Table 25.9 Dependence of WACC on the age of the company n at L = 3, k0 = 8%, kd = 4%

L 3 3 3 3 3 3 3 3 3 3

WACC 0.0738 0.0717 0.0707 0.0702 0.0698 0.0696 0.0694 0.0693 0.0692 0.0691

k0 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08

kd 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04

wd 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75

565 t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 1 2 3 4 5 6 7 8 9 10

ke 0.1991 0.1909 0.1870 0.1847 0.1832 0.1822 0.1815 0.1810 0.1806 0.1803

WACC

WACC(n) 0.2000 0.1800 0.1600 0.1400 0.1200 0.1000 0.0800 0.0600 0.0400 0.0200 0.0000

k0=0.2; kd=0.15 k0=0.08, kd=0.04

0

2

4

6

n

8

10

12

Fig. 25.5 Dependence of WACC on the age of the company n at different values of capital costs (equity, k0, and debt, kd, ones) and fixed leverage level L = 1

WACC(n) 0.2000

WACC

0.1500 0.1000

k0=0.2; kd=0.15 k0=0.08, kd=0.04

0.0500 0.0000

0

2

4

6

8

10

12

n Fig. 25.6 Dependence of WACC on the age of the company n at different values of capital costs (equity, k0, and debt, kd) and fixed leverage level L = 3

566

25.3

25

The Golden Age of the Company (Three Colors of Company’s Time)

Dependence of WACC on the Age of the Company n at Different Values of Debt Capital Cost, kd, and Fixed Equity Cost, k0, and Fixed Leverage Levels

In this section we study the dependence of WACC on the age of the company n at different values of debt capital cost, kd, and fixed equity cost, k0, and fixed leverage levels. Put first L = 1. Put then L = 3. The analysis in Tables 25.10, 25.11, 25.12, 25.13, 25.14, 25.15, 25.16, and 25.17 and Figs. 25.7 and 25.8 allows us to make the following conclusions: 1. At fixed equity cost, k0, and at fixed leverage level, the type of behavior of dependence of WACC on the age of the company, n, significantly depends on value of debt capital cost, kd: with growth of kd it is changing from monotonic descending of WACC with n to descending of WACC with n with passage through minimum with subsequent limited growth. 2. At kd = 10% and kd = 12% (k0 = 20%), the monotonic descending of WACC with n is observed, while at higher debt costs, kd = 15% and kd = 17% Table 25.10 Dependence of WACC on the age of the company n at L = 1, k0 = 20%, kd = 15%

L 1 1 1 1 1 1 1 1 1 1

WACC 0.1843 0.1798 0.1780 0.1772 0.1769 0.1769 0.1770 0.1771 0.1773 0.1775

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

wd 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 1 2 3 4 5 6 7 8 9 10

ke 0.2487 0.2397 0.2360 0.2345 0.2339 0.2338 0.2340 0.2343 0.2346 0.2351

Table 25.11 Dependence of WACC on the age of the company n at L = 1, k0 = 20%, kd = 12%

L 1 1 1 1 1 1 1 1 1 1

WACC 0.1871 0.1832 0.1815 0.1807 0.1802 0.1799 0.1798 0.1798 0.1798 0.1798

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12

wd 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 1 2 3 4 5 6 7 8 9 10

ke 0.2783 0.2705 0.2670 0.2653 0.2644 0.2639 0.2636 0.2636 0.2635 0.2636

25.3

Dependence of WACC on the Age of the Company n at Different. . .

567

Table 25.12 Dependence of WACC on the age of the company n at L = 1, k0 = 20%, kd = 17%

L 1 1 1 1 1 1 1 1 1 1

WACC 0.1826 0.1777 0.1759 0.1752 0.1750 0.1751 0.1754 0.1757 0.1760 0.1763

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.17 0.17 0.17 0.17 0.17 0.17 0.17 0.17 0.17 0.17

wd 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 1 2 3 4 5 6 7 8 9 10

ke 0.2291 0.2194 0.2158 0.2144 0.2141 0.2143 0.2148 0.2154 0.2160 0.2167

Table 25.13 Dependence of WACC on the age of the company n at L = 1, k0 = 20%, kd = 10%

L 1 1 1 1 1 1 1 1 1 1

WACC 0.1891 0.1857 0.1841 0.1832 0.1827 0.1823 0.1821 0.1819 0.1818 0.1817

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

wd 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 1 2 3 4 5 6 7 8 9 10

ke 0.2982 0.2913 0.2881 0.2864 0.2853 0.2846 0.2842 0.2838 0.2836 0.2834

Table 25.14 Dependence of WACC on the age of the company n at L = 3, k0 = 20%, kd = 15%

L 3 3 3 3 3 3 3 3 3 3

WACC 0.1765 0.1697 0.1669 0.1657 0.1653 0.1651 0.1653 0.1655 0.1658 0.1661

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

wd 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 1 2 3 4 5 6 7 8 9 10

ke 0.3461 0.3189 0.3078 0.3029 0.3010 0.3006 0.3010 0.3019 0.3030 0.3042

(k0 = 20%), descending of WACC with n with passage through minimum with subsequent limited growth takes place. The optimum age of the company is growing with kd decreasing: it is equal to 5 years at kd = 17% and 6 years at kd = 15%. 3. The conclusions are saved at both considered values of leverage level: L = 1 and L = 3.

568

25

The Golden Age of the Company (Three Colors of Company’s Time)

Table 25.15 Dependence of WACC on the age of the company n at L = 3, k0 = 20%, kd = 12%

L 3 3 3 3 3 3 3 3 3 3

WACC 0.1807 0.1748 0.1722 0.1709 0.1702 0.1698 0.1696 0.1695 0.1695 0.1695

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12

wd 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 1 2 3 4 5 6 7 8 9 10

ke 0.4349 0.4113 0.4009 0.3955 0.3927 0.3911 0.3903 0.3900 0.3899 0.3900

Table 25.16 Dependence of WACC on the age of the company n at L = 3, k0 = 20%, kd = 17%

L 3 3 3 3 3 3 3 3 3 3

WACC 0.1738 0.1665 0.1637 0.1626 0.1624 0.1625 0.1628 0.1633 0.1638 0.1643

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.17 0.17 0.17 0.17 0.17 0.17 0.17 0.17 0.17 0.17

wd 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 1 2 3 4 5 6 7 8 9 10

ke 0.2874 0.2581 0.2469 0.2426 0.2415 0.2420 0.2433 0.2451 0.2470 0.2490

Table 25.17 Dependence of WACC on the age of the company n at L = 3, k0 = 20%, kd = 10%

L 3 3 3 3 3 3 3 3 3 3

WACC 0.1836 0.1785 0.1761 0.1747 0.1739 0.1734 0.1730 0.1727 0.1726 0.1724

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

wd 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 1 2 3 4 5 6 7 8 9 10

ke 0.4945 0.4739 0.4642 0.4588 0.4556 0.4535 0.4520 0.4510 0.4502 0.4496

25.4

Dependence of WACC on the Age of the Company n at Different. . .

569

WACC(n) 0.1900 0.1880

WACC

0.1860 0.1840

kd=0.15

0.1820 0.1800

kd=0.12

0.1780

kd=0.17

0.1760

kd=0.1

0.1740

0

2

4

6

n

8

10

12

Fig. 25.7 Dependence of WACC on the age of the company n at different values of debt capital cost, kd, and fixed equity cost, k0, and fixed leverage level L = 1

WACC(n) 0.1850

WACC

0.1800 0.1750

kd=0.15 kd=0.12

0.1700

kd=0.17 0.1650 0.1600

kd=0.1 0

2

4

6

n

8

10

12

Fig. 25.8 Dependence of WACC on the age of the company n at different values of debt capital cost, kd, and fixed equity cost, k0, and fixed leverage level L = 3

25.4

Dependence of WACC on the Age of the Company n at Different Values of Equity Cost, k0, and Fixed Debt Capital Cost, kd, and Fixed Leverage Levels

In this section we study the dependence of WACC on the age of the company n at different values of equity cost, k0, and fixed debt capital cost, kd, and fixed leverage levels. Put L = 1. Put L = 3. The analysis in Tables 25.18, 25.19, 25.20, 25.21, 25.22, and 25.23 and Figs. 25.9 and 25.10 allows us to make the following conclusions:

570

25

The Golden Age of the Company (Three Colors of Company’s Time)

Table 25.18 Dependence of WACC on the age of the company n at L = 1, k0 = 18%, kd = 15%

L 1 1 1 1 1 1 1 1 1 1

WACC 0.1646 0.1602 0.1585 0.1578 0.1576 0.1576 0.1578 0.1580 0.1583 0.1585

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

wd 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 1 2 3 4 5 6 7 8 9 10

ke 0.2092 0.2005 0.1970 0.1956 0.1952 0.1952 0.1955 0.1960 0.1965 0.1970

Table 25.19 Dependence of WACC on the age of the company n at L = 1, k0 = 20%, kd = 15%

L 1 1 1 1 1 1 1 1 1 1

WACC 0.1843 0.1798 0.1780 0.1772 0.1769 0.1769 0.1770 0.1771 0.1773 0.1775

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

wd 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 1 2 3 4 5 6 7 8 9 10

ke 0.2487 0.2397 0.2360 0.2345 0.2339 0.2338 0.2340 0.2343 0.2346 0.2351

Table 25.20 Dependence of WACC on the age of the company n at L = 1, k0 = 22%, kd = 15%

L 1 1 1 1 1 1 1 1 1 1

WACC 0.2041 0.1994 0.1975 0.1967 0.1963 0.1962 0.1962 0.1962 0.1964 0.1965

k0 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22

kd 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

wd 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 1 2 3 4 5 6 7 8 9 10

ke 0.2882 0.2789 0.2751 0.2733 0.2726 0.2723 0.2723 0.2725 0.2727 0.2730

1. At fixed debt capital cost, kd, and at fixed leverage level in all considered cases (at all equity costs k0 and all leverage levels L ), the second type of dependence of WACC on the age of the company, n, namely, descending of WACC with n with passage through minimum with subsequent limited growth, takes place. 2. The “golden age” of the company slightly fluctuates under change of the equity value k0; these fluctuations are described in Table 25.24 (age is in years).

25.4

Dependence of WACC on the Age of the Company n at Different. . .

571

Table 25.21 Dependence of WACC on the age of the company n at L = 3, k0 = 18%, kd = 15%

L 3 3 3 3 3 3 3 3 3 3

WACC 0.1569 0.1503 0.1477 0.1466 0.1462 0.1462 0.1464 0.1468 0.1471 0.1475

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

wd 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 1 2 3 4 5 6 7 8 9 10

ke 0.2677 0.2412 0.2307 0.2264 0.2249 0.2250 0.2258 0.2271 0.2286 0.2302

Table 25.22 Dependence of WACC on the age of the company n at L = 3, k0 = 20%, kd = 15%

L 3 3 3 3 3 3 3 3 3 3

WACC 0.1765 0.1697 0.1669 0.1657 0.1653 0.1651 0.1653 0.1655 0.1658 0.1661

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

wd 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 1 2 3 4 5 6 7 8 9 10

ke 0.3461 0.3189 0.3078 0.3029 0.3010 0.3006 0.3010 0.3019 0.3030 0.3042

Table 25.23 Dependence of WACC on the age of the company n at L = 3, k0 = 22%, kd = 15%

L 3 3 3 3 3 3 3 3 3 3

WACC 0.1961 0.1891 0.1862 0.1849 0.1843 0.1840 0.1840 0.1841 0.1843 0.1845

k0 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22

kd 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

wd 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 1 2 3 4 5 6 7 8 9 10

ke 0.4245 0.3965 0.3848 0.3795 0.3770 0.3762 0.3761 0.3766 0.3773 0.3781

572

25

The Golden Age of the Company (Three Colors of Company’s Time)

WACC(n) 0.2500

WACC

0.2000 0.1500 k0=0.2 k0=0.18 k0=0.22

0.1000 0.0500 0.0000 0

2

4

6

8

10

12

n Fig. 25.9 Dependence of WACC on the age of the company n at different values of equity cost, k0, and fixed debt capital cost, kd, and fixed leverage level L = 1

WACC(n) 0.2500

WACC

0.2000 0.1500 k0=0.2 k0=0.18

0.1000

k0=0.22 0.0500 0.0000 0

2

4

6

8

10

12

n Fig. 25.10 Dependence of WACC on the age of the company n at different values of equity cost, k0, and fixed debt capital cost, kd, and fixed leverage level L = 3 Table 25.24 Dependence of “golden age” of the company n on L and k0

L 1 3

k0 18% 5–6 5–6

20% 5–6 6

22% 6–8 6–7

25.5

Dependence of WACC on the Age of the Company n at High Values of. . .

573

WACC(n) 0.3700

WACC

0.3600 0.3500

L=1

0.3400

L=2 L=3

0.3300

L=5

0.3200 0.3100

L=7 0

10

20

30

40

50

n Fig. 25.11 Dependence of WACC on the age of the company n at high values of capital cost (equity, k0 = 40%, and debt, kd = 35%) at different leverage levels L (up to high values of lifetime of the company) Table 25.25 The difference between the optimal (minimal) value of WACC and its perpetuity limit L ΔWACC, %

25.5

1 -0.72

2 -0.99

3 -1.12

5 -1.25

7 -1.33

Dependence of WACC on the Age of the Company n at High Values of Capital Cost (Equity, k0, and Debt, kd) and High Lifetime of the Company

Let us study the dependence of WACC on the age of the company n at high values of capital cost (equity, k0, and debt, kd) and big age of the company. 1. At Fixed Leverage Level From Fig. 25.11 it follows that: 1. In all considered cases (at all leverage levels L) at high values of capital cost (equity, k0 = 40%, and debt, kd = 35%), the second type of dependence of WACC on the age of the company, n, namely, descending of WACC with n with passage through minimum with subsequent limited growth up to perpetuity limit, takes place. 2. A minimum value of attracting capital cost (WACC) is achieved at all leverage levels in the same age, when n = 4. This means that, at high value of capital costs, the company age, at which minimal value of attracting capital cost is achieved, is shifted forward lower (younger) values. We just remind that at k0 = 20% and kd = 15% (see above), the “golden age” was 6 years.

574

25

The Golden Age of the Company (Three Colors of Company’s Time)

WACC

WACC(n) 0.3700 0.3680 0.3660 0.3640 0.3620 0.3600 0.3580 0.3560 0.3540 0.3520 0.3500

kd=0.35 kd=0.3

0

10

20

30

40

50

n Fig. 25.12 Dependence of WACC on the age of the company n at fixed high value of equity cost, k0 = 40%, and two values of debt cost, kd = 30% and 35%, at leverage level L = 1

3. The shift of curves to lower values of WACC with increase of leverage level L is associated with decrease of WACC with leverage. 4. An interesting thing is the analysis of the value of detected effect, i.e., how much is the difference between the minimum of the attracting capital, found in the BFO theory, and its perpetuity limit value, which has been considered as minimal value up to now. In Table 25.25 the dependence of the difference between the minimum of the attracting capital and its perpetuity limit value on leverage level L is shown. Perpetuity limit value of WACC is calculated by using Modigliani–Miller formula (Мodigliani and Мiller 1958, 1963, 1966) with accounting of corporate taxes: WACC = k 0 ð1- wd  t Þ:

ð25:1Þ

From Fig. 25.11, it is seen that at high values of age of company (n ≥ 30), the WACC practically does not differ from its perpetuity limit. From Table 25.25 it is seen that the gain value is from 0.7% up to 1.5% and grows with the increase of the leverage level of company, L. 2. Under Change of the Debt Capital Cost, kd Under change of the debt capital cost, kd, a depth of pit in dependence of WACC on the age of the company, n, is changed as well: from Fig. 25.12 it is seen that pit (accounted from perpetuity value) is changed from 0.49% (at kd = 0.3) up to 0.72% (at kd = 0.35). Note that as it is seen from Fig. 25.12, a perpetuity limit of WACC does not depend on debt cost, kd, which is in accordance with the Modigliani–Miller formula (25.1) for WACC, which does not contain a debt capital cost, kd, that means independence of perpetuity limit of WACC values from kd, while the intermediate WACC values (for finite lifetime (age) of company, n) depend on the debt capital

25.5

Dependence of WACC on the Age of the Company n at High Values of. . .

575

WACC

WACC(n), k0=0.2 19.2000% 19.0000% 18.8000% 18.6000% 18.4000% 18.2000% 18.0000% 17.8000% 17.6000% 17.4000% 17.2000%

kd=0.18 kd=0.15 kd=0.10 kd=0.08 0

10

20

30

40

50

n Fig. 25.13 Dependence of WACC on the age of the company n at fixed value of equity cost, k0 = 20%, and at four values of debt cost, kd = 8%, 10%, 15%, and 18%, at leverage level L = 1 Table 25.26 Dependence of WACC on the age of the company n at L = 1, k0 = 20%, kd = 18%

a 24.2889% 17.4859% 17.4155% 17.4654% 17.5833% 17.8641% 17.9629% 17.9909%

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

L 1 1 1 1 1 1 1 1

n 1 3 5 7 10 20 30 40

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Table 25.27 Dependence of WACC on the age of the company n at L = 1, k0 = 20%, kd = 15%

WACC 24.4736% 17.8200% 17.6936% 17.6967% 17.7528% 17.9192% 17.9797% 17.9957%

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

L 1 1 1 1 1 1 1 1

n 1 3 5 7 10 20 30 40

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

cost, kd [see BFO theory (Brusov and Filatova 2011; Brusov et al. 2011a, b, c, 2012a, b, 2013a, b, 2014a, b; Filatova et al. 2008)]. From Fig. 25.13 it is seen, that with the increase of debt cost, kd, the character of dependence of WACC on the age of the company n is changed from monotonic descending of WACC with n to descending of WACC with n with passage through minimum, followed by a limited growth (Tables 25.26, 25.27, 25.28, 25.29, and 25.30).

576

25

The Golden Age of the Company (Three Colors of Company’s Time)

Table 25.28 Dependence of WACC on the age of the company n at L = 1, k0 = 20%, kd = 12%

WACC 24.6583% 24.1511% 24.0181% 17.9817% 17.9789% 24.0145% 24.0175% 24.0099%

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12

L 1 1 1 1 1 1 1 1

n 1 3 5 7 10 20 30 40

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Table 25.29 Dependence of WACC on the age of the company n at L = 1, k0 = 20%, kd = 10%

a 24.9082% 24.4030% 24.2615% 24.2045% 24.1678% 24.1146% 24.0669% 24.0330%

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

L 1 1 1 1 1 1 1 1

n 1 3 5 7 10 20 30 40

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Table 25.30 Dependence of WACC on the age of the company n at L = 1, k0 = 20%, kd = 8%

WACC 19.1087% 24.6716% 24.5297% 24.4692% 24.4040% 24.2594% 24.1532% 24.0813%

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08

L 1 1 1 1 1 1 1 1

n 1 3 5 7 10 20 30 40

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Table 25.31 Dependence of WACC on the age of the company n at L = 1, k0 = 25%, kd = 15%

WACC 24.2477% 22.6690% 22.5117% 22.4913% 22.4933% 22.5219% 22.5136% 22.5045%

k0 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

L 1 1 1 1 1 1 1 1

n 1 3 5 7 10 20 30 40

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

25.5

Dependence of WACC on the Age of the Company n at High Values of. . .

Table 25.32 Dependence of WACC on the age of the company n at L = 1, k0 = 22%, kd = 15%

WACC 20.3006% 19.7431% 19.6171% 19.6163% 19.6514% 19.7639% 19.7960% 19.8007%

k0 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22

Table 25.33 Dependence of WACC on the age of the company n at L = 1, k0 = 20%, kd = 15%

WACC 24.4717% 17.8015% 17.6938% 17.6972% 17.7592% 17.9192% 17.9797% 17.9957%

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Table 25.34 Dependence of WACC on the age of the company n at L = 1, k0 = 18%, kd = 15%

WACC 16.4350% 15.8519% 15.7610% 15.7793% 15.8561% 16.0683% 16.1586% 16.1884%

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

Table 25.35 Dependence of WACC on the age of the company n at L = 1, k0 = 16%, kd = 15%

WACC 14.4304% 13.9019% 13.8278% 13.8610% 13.9481% 14.2119% 14.3324% 14.3781%

k0 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16

kd 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

577

L 1 1 1 1 1 1 1 1

n 1 3 5 7 10 20 30 40

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

L 1 1 1 1 1 1 1 1

n 1 3 5 7 10 20 30 40

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

L 1 1 1 1 1 1 1 1

n 1 3 5 7 10 20 30 40

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

L 1 1 1 1 1 1 1 1

n 1 3 5 7 10 20 30 40

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

578

25

The Golden Age of the Company (Three Colors of Company’s Time)

Table 25.36 Dependence of depth of gap ΔWACC on k0 value k0 ΔWACC, %

0.16 0.55

0.18 0.43

0.20 0.30

0.22 0.18

0.25 0.03

WACC(n) 23.0000% 21.0000%

WACC

Ko=0.25

19.0000%

Ko=0.22 Ko=0.2

17.0000%

Ko=0.18 15.0000% 13.0000%

Ko=0.16

0

10

20

n

30

40

50

Fig. 25.14 Dependence of WACC on the age of the company n at fixed value of debt cost, kd = 15%, and five values of equity cost, k0 = 16%, 18%, 20%, 22%, and 25%, at leverage level L=1 Table 25.37 Dependence of WACC on the age of the company n at L = 2, k0 = 20%, kd = 15%, t = 20%

L 2 2 2 2 2 2 2 2

WACC 17.84% 17.07% 16.92% 16.92% 16.99% 17.12% 17.30% 17.33%

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 1 3 5 7 10 15 30 45

Table 25.38 Dependence of WACC on the age of the company n at L = 2, k0 = 20%, kd = 15%, t = 40%

L 2 2 2 2 2 2 2 2

WACC 15.72% 14.09% 13.76% 13.73% 13.86% 14.13% 14.56% 14.65%

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

t 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4

n 1 3 5 7 10 15 30 45

25.5

Dependence of WACC on the Age of the Company n at High Values of. . .

579

WACC(n) 18.00%

WACC

17.00% 16.00% t=0.2

15.00%

t=0.4

14.00% 13.00%

0

10

20

n

30

40

50

Fig. 25.15 Dependence of WACC on the age of the company n at fixed capital costs, k0 = 20%, kd = 15%, and two values of tax on profit rate t = 0.2 and t = 0.4 and at leverage level L = 2

WACC(n) 30.00% 29.00%

WACC

28.00% 27.00%

t=0

26.00%

t=0.1

25.00%

t=0.2

24.00%

t=0.3

23.00%

t=0.4

22.00% 0

10

20

n

30

40

50

Fig. 25.16 Dependence of WACC on the age of the company n at fixed capital costs, k0 = 30%, kd = 15%, and different values of tax on profit rate t = 0, 0.1, 0.2, 0.3, and 0.4 and at leverage level L=2

3. Under Change of the Equity Capital Cost, k0 (Tables 25.31, 25.32, 25.33, 25.34, 25.35, and 25.36) Depth of gap, ΔWACC, is decreased with equity cost, k0 (Fig. 25.14). 4. Under Change of the Tax on Profit Rate, t (Tables 25.37 and 25.38) The depth of gap in dependence of WACC on n, which is equal to 0.41% at t = 0.2, is increased in 2.2 times and becomes equal to 0.92% at t = 0.4, i.e., it is increased in 2.2 times, when tax on profit rate is increased in two times (Fig. 25.15). We see from Fig. 25.16 that at fixed capital costs, k0 = 30%, kd = 15%, and at different values of tax on profit rate, t, there is no minimum in WACC at finite age of the company: minimal value of WACC is reached at n = 1. Note that this is a

580

25

The Golden Age of the Company (Three Colors of Company’s Time)

Table 25.39 Dependence of WACC on the age of the company n at L = 1, k0 = 25%, kd = 15%

L 1 1 1 1 1 1 1 1 1

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Table 25.40 Dependence of WACC on the age of the company n at L = 2, k0 = 25%, kd = 15%

L 2 2 2 2 2 2 2 2 2

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

k0 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

k0 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

kd 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

kd 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

n 1 3 5 7 10 20 30 40 1

n 1 3 5 7 10 20 30 40 1

wd 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

WACC 24.2270% 22.6725% 22.5184% 22.4914% 22.4934% 22.5220% 22.5137% 22.5045% 21.50%

wd 0.6667 0.6667 0.6667 0.6667 0.6667 0.6667 0.6667 0.6667 0.6667

WACC 22.8255% 21.8935% 21.6843% 21.6431% 21.6448% 21.6895% 21.6842% 21.6742% 21.6665%

WACC

WACC(n) 23.4000% 23.2000% 23.0000% 22.8000% 22.6000% 22.4000% 22.2000% 22.0000% 21.8000% 21.6000% 21.4000%

L=1 L=2

0

10

20

n

30

40

50

Fig. 25.17 Dependence of WACC on the age of the company n at fixed capital costs, k0 = 25%, kd = 15%, and different values of leverage level L = 1 and L = 2

feature of particular values of capital costs (probably, too big difference between k0 and kd).

25.6

Further Investigation of Effect

581

WACC

WACC(n) 22.6000% 22.5000% 22.4000% 22.3000% 22.2000% 22.1000% 22.0000% 21.9000% 21.8000% 21.7000% 21.6000%

L=1 L=2

0

10

20

30

40

50

n Fig. 25.18 Dependence of WACC on the age of the company n at fixed capital costs, k0 = 25%, kd = 15%, and different values of leverage level L = 1 and L = 2 (lager scale)

WACC(n)

WACC

22.5300% 22.5250% 22.5200% 22.5150% 22.5100% 22.5050%

L=1 L=2

22.5000% 22.4950% 22.4900% 0

10

20

n

30

40

50

Fig. 25.19 Dependence of WACC on the age of the company n at fixed capital costs, k0 = 25%, kd = 15%, and different values of leverage level L = 1 and L = 2 (the largest scale)

25.6

Further Investigation of Effect

During further investigation of effect, we have discovered one more interesting feature of dependence of WACC on n, WACC(n): we have called this effect “Kulik effect” (Kulik is a graduate student of the Management Department of Financial University in Moscow, who has discovered this effect) (Brusov et al. 2015a, b) (Tables 25.39 and 25.40). Note that perpetuity limits for WACC(n), calculated by the Modigliani–Miller formula (Мodigliani and Мiller 1958, 1963, 1966) (25.1), are equal to: For L = 1 WACC(1) = 22.5% For L = 2 WACC(1) = 21.6665% (Figs. 25.17, 25.18 and 25.19)

582

25

The Golden Age of the Company (Three Colors of Company’s Time)

CC,V V∞

2' 1' 3'

V

WACC 3 1 2

k0 (1-wdt)

0

1

n0

n1

n

Fig. 25.20 “Kulik” effect: behavior 3 for WACC(n) and 3′ for V(n)

It turns out that at particular values of capital costs, for example, at k0 = 25%, kd = 15%, a third modification of dependences of WACC on the age of company n takes place: descending of WACC with passage through minimum, followed by a growth with passage through maximum, and finally with trend to perpetuity limit from bigger values (remind that at the second type of WACC(n) behavior, the curve WACC(n) tends to perpetuity limit from lower values). We have called this effect the “Kulik effect.” It gives a third type of dependence of WACC on the age of company n, which is represented in Fig. 25.20.

25.7

Conclusions

In this Chapter it is shown for the first time (Brusov et al. 2015a, b) within BFO theory (Brusov and Filatova 2011; Brusov et al. 2011a, b, c, 2012a, b, 2013a, b, 2014a, b; Filatova et al. 2008) that valuation of WACC in the Modigliani–Miller theory (Мodigliani and Мiller 1958, 1963, 1966) is not minimal and valuation of the company capitalization is not maximal, as all financiers supposed up to now: at some age of the company its WACC value turns out to be lower than in Modigliani–Miller theory and company capitalization V turns out to be greater than V in Modigliani– Miller theory (Мodigliani and Мiller 1958, 1963, 1966). Thus, existing presentations concerning the results of the Modigliani–Miller theory in this aspect (Myers 1984) turn out to be incorrect (Brusov et al. 2015a, b).

References

583

It is shown that from the point of view of cost of attracting capital, there are two (really three) types of dependences of WACC on the time of life (age) of company n: monotonic descending of WACC with n and descending of WACC with passage through minimum, followed by a limited growth [there is a third modification of dependences WACC(n) (“Kulik” behavior), which leaves all conclusions valid (Brusov et al. 2015a, b)]. A hypothesis was put forward (Brusov et al. 2015a, b) that the character of the WACC(n) dependence is determined by the equity cost k0. The first type takes place for the companies with low-cost capital, characteristic of Western companies. The second type takes place for higher-cost capital of the company, characteristic of companies from developing countries (including Russia). This means that the latter companies, in contrast to the Western ones, can take advantage of the benefits given at a certain stage of development by discovered effect (Brusov et al. 2015a, b). Whether or not this hypothesis turned out to be right we will see in next Chap. 20, where we investigate the conditions of existing of “the golden age” of the company effect and discover a new important effect, which we called “the silver age” of the company. It is important to note, that since the “golden age” of company depends on the company’s capital costs, by controlling them (e.g., by modifying the value of dividend payments that reflects the equity cost), the company may extend the “golden age” of the company when the cost to attract capital becomes minimal (less than perpetuity limit) and the capitalization of companies becomes maximal (above than perpetuity assessment) up to a specified time interval.

References Brusov PN, Filatova ТV (2011) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Finance Credit 435:2–8 Brusov P, Filatova T, Orehova N, Brusova A (2011a) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Appl Financ Econ 21(11): 815–824 Brusov P, Filatova T, Orehova N et al (2011b) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Bus ICT 2:16–21 Brusov P, Filatova T, Orehova N et al (2011c) Influence of debt financing on the effectiveness of the investment project within the Modigliani–Miller theory. Res J Econ Bus ICT (UK) 2:11–15 Brusov P, Filatova T, Eskindarov M, Orehova N (2012a) Influence of debt financing on the effectiveness of the finite duration investment project. Appl Financ Econ 22(13):1043–1052 Brusov P, Filatova T, Eskindarov M, Orehova N (2012b) Hidden global causes of the global financial crisis. J Rev Global Econ 1:106–111 Brusov P, Filatova P, Orekhova N (2013a) Absence of an optimal capital structure in the famous tradeoff theory! J Rev Global Econ 2:94–116 Brusov P, Filatova T, Orehova N (2013b) A qualitatively new effect in corporative finance: abnormal dependence of cost of equity of company on leverage. J Rev Global Econ 2:183–193 Brusov P, Filatova P, Orekhova N (2014a) Mechanism of formation of the company optimal capital structure, different from suggested by trade off theory. Cogent Econ Finance 2:1–13. https://doi. org/10.1080/23322039.2014.946150

584

25

The Golden Age of the Company (Three Colors of Company’s Time)

Brusov P, Filatova T, Orehova N (2014b) Inflation in Brusov–Filatova–Orekhova theory and in its perpetuity limit – Modigliani–Miller theory. J Rev Global Econ 3:175–185 Brusov P, Filatova T, Orehova N, Eskindarov M (2015a) Modern corporate finance, investment and taxation, 1st edn. Springer, New York, pp 1–368 Brusov P, Filatova T, Orehova N, Kulik V (2015b) The golden age of the company. J Rev Global Econ 4:21–42 Brusov P, Filatova T, Orehova N, Kulk WI (2018a) New meaningful effects in modern capital structure theory. J Rev Global Econ 7:104–122 Brusov P, Filatova T, Orehova N, Kulk V (2018b) A “golden age” of the companies: conditions of its existence. J Rev Global Econ 7:88–103 Brusov P, Filatova T, Orehova N, Kulk V (2018c) Rating methodology: new look and new horizons. J Rev Global Econ 7:63–87 Brusov P, Filatova T, Orehova N, Kulk V (2018d) Rating: new approach. J Rev Global Econ 7:37– 62 Brusova A (2011) А comparison of the three methods of estimation of weighted average cost of capital and equity cost of company. Financ Anal Prob Sol 34(76):36–42 Filatova Т, Orehova N, Brusova А (2008) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Bull FU 48:68–77 Myers S (1984) The capital structure puzzle. J Finance 39(3):574–592 Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Мodigliani F, Мiller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391

Chapter 26

A “Golden Age” of the Companies: Conditions of Its Existence

Keywords The golden age of the company · The Brusov–Filatova–Orekhova theory · The weighted average cost of capital, WACC A few years ago we have discovered the effect of the “golden age” of company (Brusov et al. 2015a, b): it was shown for the first time that valuation of the weighted average cost of capital, WACC, in the Modigliani–Miller theory (Мodigliani and Мiller 1958, 1963, 1966) is not minimal and valuation of the company capitalization is not maximal, as all financiers supposed up to this discovery: at some age of the company its WACC value turns out to be lower, than in Modigliani–Miller theory and company capitalization V turns out to be greater, than V in Modigliani–Miller theory. It was shown that, from the point of view of cost of attracting capital there are two types of dependences of weighted average cost of capital, WACC, on the company age n: monotonic descending with n and descending with passage through minimum, followed by a limited growth. In practice, there are companies with both types of dependences of WACC on the company age n. In this Chapter we continue to study this problem and investigate which companies have the “golden age,” i.e., obey the latter type of dependence of WACC on n (Brusov et al. 2018b). With this aim, we study the dependence of WACC on the age of company n at various leverage levels within a wide spectrum of capital costs values as well as the dependence of WACC on leverage level L at fixed company age n. All calculations have been done within modern theory of capital cost and capital structure BFO by Brusov–Filatova–Orekhova (Brusov et al. 2018a, b, c, d; Brusova 2011; Brusov et al. 2011a, b, c, d, 2012a, b, 2013a, b, 2014a, b; Filatova et al. 2008). We have shown that existence of the “golden age” of company does not depend on the value of capital costs of the company, but depends on the difference between equity k0 and debt kd costs. The “golden age” of company exists at small enough difference between k0 and kd costs, while at high value of this difference, the “golden age” of company is absent: curve WACC(n) monotonic descends with n. For the companies with the “golden age” curve WACC(L) for perpetuity companies lies between curves WACC(L) for company ages n = 1 and n = 3, while for the companies without the “golden age” curve WACC(L) for perpetuity companies is the lowest one. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_26

585

586

26

A “Golden Age” of the Companies: Conditions of Its Existence

In our paper (Brusov et al. 2015a, b) we have found also a third type of WACC (n) dependence: descending with passage through minimum, which lies below the perpetuity limit value, then going through maximum followed by a limited descending. We called this effect “Kulik effect.” In this Chapter, we have found a variety of “Kulik effect”: descending with passage through minimum of WACC, which lies above the perpetuity limit value, then going through maximum followed by a limited descending. We call this company age, where WACC has a minimum, which lies above the perpetuity limit value, “a silver age” of the company. Because the cost of attracting capital is used in rating methodologies as discounting rate under discounting of cash flows, study of WACC behavior is very important for rating procedures. The account of effects of the “golden (silver) age” could change the valuation of creditworthiness of issuers. Remind that, since the “golden age” of company depends on the company’s capital costs, by controlling them (for example, by modifying the value of dividend payments, that reflect the equity cost), company may extend the “golden age” of the company, when the cost to attract capital becomes a minimal (less than perpetuity limit), and capitalization of companies becomes maximal (above than perpetuity assessment) up to a specified time interval. We discuss the use of opened effects in developing economics.

26.1

Introduction

In this Chapter we answer the following question: which companies have “a golden age,” i.e., obey the following type of dependence of WACC on n: WACC (n) descending with passage through minimum, followed by a limited growth. With this aim we study the dependence of WACC on the age of company n at various leverage levels within a wide spectrum of capital costs values as well as the dependence of WACC on leverage level L at fixed company age n. All calculations have been done within modern theory of capital cost and capital structure BFO by Brusov–Filatova–Orekhova (Brusov et al. 2011a, b, c, d, 2012a, b, 2013a, b, 2014a, b; Filatova et al. 2008). We make calculations for equity cost k0 (at L = 0) between 6% and 30% and debt cost kd between 4% and 28% for a lot of pairs (k0, kd), accounting that the inequality k0 ≥ kd is always valid via the fact that equity cost is more risky than debt one. We present in paper only some examples of our calculations (one-two in each group) and readers should understand that other results in each group give more or less qualitatively similar results. We have shown that existence of the “golden age” of company depends not on the value of capital costs of the company, but on the difference between equity k0 and debt kd costs. The “golden age” of company exists at small enough difference between k0 and kd costs, while at high value of this difference, the “golden age” of company is absent: curve WACC(n) monotonic descends with n. For the companies with the “golden age” curve WACC(L) for perpetuity limit (n = 1) lies between curves WACC(L) for one year (n = 1) and three years (n = 3) companies, while for

26.2

Companies Without the “Golden Age” (Large Difference Between k0. . .

587

Fig. 26.1 Two kind of dependences of weighted average cost of capital, WACC, and company capitalization, V, on life-time of the company n

the companies without the “golden age” curve WACC(L) for perpetuity limit is the lowest one. The problem of the existence of the “golden age” of company is very important in ratings because the discount rate (WACC value), used in discounting of cash flows in ratings, depends on the existence or the nonexistence of the “golden age” of company (Fig. 26.1). 1–1′—monotonic dependence of weighted average cost of capital, WACC, and company capitalization, V, on life-time of the company n; 2–2′—showing descending of WACC with n, and with the passage through a minimum and then a limited growth and increase of V with the passage through a maximum (at n0) and then a limited descending.

26.2

Companies Without the “Golden Age” (Large Difference Between k0 and kd Costs)

As an example of companies without the “golden age”(with large difference between k0 and kd costs) we present the calculations for equity cost k0 (at L = 0) equals to 20% and debt cost kd equals to 9%.

588

26

26.2.1

A “Golden Age” of the Companies: Conditions of Its Existence

Dependence of Weighted Average Cost of Capital, WACC, on the Company Age n at Different Leverage Levels

We study below the dependence of weighted average cost of capital, WACC, on the company age n at different leverage levels (L = 1,2, 3), using the BFO formula ½1 - ð1 þ WACCÞ - n  ½1 - ð1 þ k 0 Þ - n  = : WACC k 0 ½1 - ωd t ð1 - ð1 þ k d Þ - n Þ

ð26:1Þ

Leverage level L is presented in BFO formula through the share of debt capital wd = L/(1 + L). The results of our calculations are shown in tables and figures. For L = 1 one has For L = 2 we have For L = 3 one has It is seen from Tables 26.1, 26.2, 26.3, and Fig. 26.2 that 1–1′—behavior (from Fig. 26.1) takes place: monotonic dependence of weighted average cost of capital, WACC, and company capitalization, V, on the company age n for all considered leverage levels (L = 1, 2, 3); this means that the “golden age” of company is absent. The ordering of curves is the following: the lower curve corresponds to the greater leverage level. Table 26.1 Dependence of WACC on the age of the company n at L = 1, k0 = 20%, kd = 9% n 1 2 3 4 5 6 7 8 9 10 20 30 40

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

L 1 1 1 1 1 1 1 1 1 1 1 1 1

WACC (L = 1) 0.19001348 0.18679105 0.18521681 0.18453895 0.18398934 0.18361179 0.18333561 0.18312210 0.18294855 0.18280097 0.18181178 0.18103559 0.18052092

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09

wd 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50

A(n) 0.840271 1.552355 2.155589 2.666482 3.099102 3.465420 3.775614 4.038322 4.260871 4.449469 5.305460 5.486207 5.532205

БФО 0.000055264 0.000242408 0.000643588 0.000008562 0.000019534 0.000038686 0.000068644 0.000111902 0.000170582 0.000246231 0.000013165 0.000041589 0.000065502

26.2

Companies Without the “Golden Age” (Large Difference Between k0. . .

589

Table 26.2 Dependence of WACC on the age of the company n at L = 2, k0 = 20%, kd = 9% n 1 2 3 4 5 6 7 8 9 10 20 30 40

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

L 2 2 2 2 2 2 2 2 2 2 2 2 2

WACC (L = 2) 0.18670845 0.18242414 0.18033977 0.17935211 0.17860838 0.17809570 0.17771992 0.17742943 0.17719390 0.17699457 0.17567694 0.17467722 0.17401430

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09

wd 0.67 0.67 0.67 0.67 0.67 0.67 0.67 0.67 0.67 0.67 0.67 0.67 0.67

A(n) 0.8426098 1.5607236 2.1724715 2.6934467 3.1370358 3.5147106 3.8362859 4.1101468 4.3434469 4.5422818 5.4686271 5.6790746 5.7372042

БФО 0.000057189 0.000239282 0.000618675 0.000007915 0.000018207 0.000036130 0.000064261 0.000105021 0.000160484 0.000232186 0.000012229 0.000039727 0.000064124

Table 26.3 Dependence of WACC on the age of the company n at L = 3, k0 = 20%, kd = 9% n 1 2 3 4 5 6 7 8 9 10 20 30 40

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

L 3 3 3 3 3 3 3 3 3 3 3 3 3

WACC (L = 3) 0.18506498 0.18024369 0.17789664 0.17675215 0.17590910 0.17532683 0.17489950 0.17456914 0.17430145 0.17407533 0.17259416 0.17148952 0.17075742

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09

wd 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75

A(n) 0.8437839 1.5649420 2.1810121 2.7071344 3.1563532 3.5398852 3.8673589 4.1470258 4.3859468 4.5901557 5.5540330 5.7806846 5.8455083

БФО 0.000051714 0.000228517 0.000607678 0.000007660 0.000017650 0.000035095 0.000062558 0.000101532 0.000155351 0.000225050 0.000011720 0.000038586 0.000063263

From Tables 26.4, 26.5, 26.6 and Fig. 26.3 it is seen that the ordering of curves WACC(L) is the following: the lower curve corresponds to the greater company age n. We will see below that under existence the “golden age” of company this ordering will be a different one. We keep here the case of n = 45 as the case which is closed to perpetuity limit. An alternative method is the using of the Modigliani–Miller formula WACC = k0 ð1- ωd t Þ, which follows from BFO formula (26.1) for perpetuity limit.

ð26:2Þ

590

26

A “Golden Age” of the Companies: Conditions of Its Existence

WACC(n) 0.19500000 0.19000000

WACC

0.18500000 0.18000000 0.17500000 0.17000000 0.16500000 0

5

10

15

20

25

30

35

40

45

n L=1

L=2

L=3

Fig. 26.2 The dependence of weighted average cost of capital, WACC, on the company age n at different leverage levels (L = 1,2, 3) Table 26.4 Dependence of WACC on the leverage level at the company age n = 1, k0 = 20%, kd = 9% n 1 1 1 1 1 1 1 1 1 1 1

26.3

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

L 0 1 2 3 4 5 6 7 8 9 10

WACC (n = 1) 0.19990871 0.18989673 0.18675471 0.18504185 0.18395964 0.18323424 0.18270822 0.18230907 0.18203277 0.18178544 0.18158213

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09

wd 0.00 0.50 0.67 0.75 0.80 0.83 0.86 0.88 0.89 0.90 0.91

A(n) 0.833333 0.840271 0.842610 0.843784 0.844490 0.844961 0.845298 0.845551 0.845748 0.845906 0.846034

БФО 0.000063399 0.000137715 0.000024342 0.000068187 0.000133490 0.000179952 0.000218846 0.000251369 0.000252248 0.000271780 0.000288455

Companies with the “Golden Age” (Small Difference Between k0 and kd Costs)

As an example of companies with the “golden age”(with small difference between k0 and kd costs) we present the calculations for equity cost k0 (at L = 0) equals to 27% and debt cost kd equals to 25% (Fig. 26.4).

26.3

Companies with the “Golden Age” (Small Difference Between k0. . .

591

Table 26.5 Dependence of WACC on the leverage level at the company age n = 3, k0 = 20%, kd = 9% n 3 3 3 3 3 3 3 3 3 3 3

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

L 0 1 2 3 4 5 6 7 8 9 10

WACC (n = 3) 0.19978349 0.18521867 0.18034194 0.17789941 0.17643254 0.17545407 0.17475488 0.17423034 0.17382227 0.17349576 0.17322858

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09

wd 0.00 0.50 0.67 0.75 0.80 0.83 0.86 0.88 0.89 0.90 0.91

A(n) 2.106481 2.155589 2.172471 2.181012 2.186169 2.189620 2.192092 2.193950 2.195397 2.196556 2.197505

БФО 0.000714376 0.000637220 0.000611094 0.000597961 0.000590059 0.000584783 0.000581010 0.000578178 0.000575974 0.000574210 0.000572766

Table 26.6 Dependence of WACC on the leverage level at the company age n = 45, k0 = 20%, kd = 9% n 45 45 45 45 45 45 45 45 45 45 45

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

L 0 1 2 3 4 5 6 7 8 9 10

WACC (n = 45) 0.19999699 0.18035710 0.17380207 0.17052242 0.16855385 0.16724112 0.16630328 0.16559980 0.16505258 0.16461477 0.16425654

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09

wd 0.00 0.50 0.67 0.75 0.80 0.83 0.86 0.88 0.89 0.90 0.91

A(n) 4.998633 5.541296 5.749351 5.859349 5.927391 5.973638 6.007115 6.032471 6.052340 6.068330 6.081476

БФО 0.000075004 0.000073385 0.000072648 0.000072233 0.000071966 0.000071780 0.000071642 0.000071536 0.000071451 0.000071382 0.000071325

It is seen from Tables 26.7, 26.8, 26.9 and Fig. 26.5 that 2–2′—behavior (from Fig. 26.1) takes place: descending of WACC with n, and with the passage through a minimum and then a limited growth and increase of V with the passage through a maximum (at n0 ≈ 4) and then a limited descending. This means the presence of the “golden age” of company. The ordering of curves is the following: the lower curve corresponds to the greater leverage level. From Tables 26.10, 26.11, 26.12, and Fig. 26.6 the quite new effect follows: the ordering of curves WACC(L) is the following: the top curve corresponds to the company age n = 1, the middle one corresponds to perpetuity company n0 = 1(we use n = 49 to approximate perpetuity limit), and bottom one corresponds to the company age n = 3. Thus, the curve WACC(L) for perpetuity company lies between curves corresponding to the company age n = 1, and n - 3.

592

26

A “Golden Age” of the Companies: Conditions of Its Existence

WACC(L) 0.21000000 0.20000000

WACC

0.19000000 0.18000000 0.17000000 0.16000000 0.15000000 0.14000000

0

1

2

3

4

5

6

7

8

9

10

L WACC(n=1)

WACC (n=3)

WACC(n=45)

Fig. 26.3 The dependence of weighted average cost of capital, WACC, on the leverage level at different company age n (n = 1, 3, 45)

WACC (n) 0.2500 0.2450

WACC

0.2400 0.2350

L=1

0.2300

L=2 L=3

0.2250 0.2200 0.2150 0

10

20

30

40

50

n Fig. 26.4 The dependence of weighted average cost of capital, WACC, on the company age n at different leverage levels (L = 1,2, 3)

26.3

Companies with the “Golden Age” (Small Difference Between k0. . .

593

Table 26.7 Dependence of WACC on the age of the company n at L = 1, k0 = 27%, kd = 25% n 1 2 3 4 5 6 7 8 9 10 20 30 40

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

L 1 1 1 1 1 1 1 1 1 1 1 1 1

WACC 0.2441 0.2381 0.2360 0.2357 0.2359 0.2363 0.2371 0.2377 0.2383 0.2389 0.2422 0.2429 0.2430

k0 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27

kd 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

wd 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50

A(n) 0.8035 1.4600 1.9928 2.4231 2.7688 3.0457 3.2668 3.4430 3.5830 3.6941 4.0755 4.1115 4.1149

BFO 0.000292 0.000038 0.000286 0.000046 0.000319 0.000877 0.000033 0.000070 0.000127 0.000204 0.000005 0.000009 0.000010

Table 26.8 Dependence of WACC on the age of the company n at L = 2, k0 = 27%, kd = 25% n 1 2 3 4 5 6 7 8 9 10 20 30 40

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

L 2 2 2 2 2 2 2 2 2 2 2 2 2

WACC 0.2361 0.2274 0.2246 0.2239 0.2244 0.2251 0.2259 0.2267 0.2276 0.2284 0.2328 0.2338 0.2340

k0 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27

kd 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

wd 0.67 0.67 0.67 0.67 0.67 0.67 0.67 0.67 0.67 0.67 0.67 0.67 0.67

A(n) 0.8090 1.4784 2.0275 2.4748 2.8370 3.1288 3.3630 3.5504 3.6999 3.8189 4.2301 4.2694 4.2731

BFO 0.000024 0.000164 0.000411 0.000753 -0.000018 -0.000026 -0.000037 -0.000046 -0.000054 -0.000063 -0.000110 -0.000124 -0.000128

Note, that this ordering is quite different from the case when the “golden age” of company is absent: in that case the lower curve corresponds to the greater company age n: the top curve corresponds to the company age n = 1, the middle one corresponds to the company age n = 3 and bottom one corresponds to the perpetuity company.

594

26

A “Golden Age” of the Companies: Conditions of Its Existence

Table 26.9 Dependence of WACC on the age of the company n at L = 3, k0 = 27%, kd = 25% n 1 2 3 4 5 6 7 8 9 10 20 30 40

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

L 3 3 3 3 3 3 3 3 3 3 3 3 3

WACC 0.2318 0.2219 0.2190 0.2183 0.2186 0.2193 0.2203 0.2212 0.2222 0.2231 0.2281 0.2293 0.2295

k0 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27

kd 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

wd 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75

A(n) 0.8118 1.4877 2.0453 2.5015 2.8723 3.1721 3.4133 3.6067 3.7612 3.8845 4.3120 4.3530 4.3569

BFO 0.000064 0.000412 -0.000020 -0.000044 -0.000076 -0.000112 -0.000154 -0.000195 -0.000234 -0.000271 -0.000497 -0.000570 -0.000590

WACC (L) 0.2700 0.2600

WACC

0.2500 0.2400

n=1 n=3

0.2300

n=49

0.2200 0.2100 0.2000 0

2

4

6 L

8

10

12

Fig. 26.5 The dependence of weighted average cost of capital, WACC, on leverage level L at different the company age n (n = 1, 3, 49)

26.4

Companies with Abnormal “Golden Age” (Intermediate Difference Between k0 and kd Costs)

One example, which is different from two considered above cases will be studied below, where we present the calculations for equity cost k0 (at L = 0) equals to 27% and debt cost kd equals to 16%. While in this case the “golden age” of the company is present but it is less pronounced: the minimal WACC value (at some leverage value: in this case at

26.4

Companies with Abnormal “Golden Age” (Intermediate Difference. . .

595

Table 26.10 Dependence of WACC on the leverage level at the company age n = 1, k0 = 27%, kd = 25% n 1 1 1 1 1 1 1 1 1 1 1

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

L 0 1 2 3 4 5 6 7 8 9 10

WACC 0.2697 0.2441 0.2360 0.2317 0.2290 0.2273 0.2260 0.2251 0.2243 0.2237 0.2232

k0 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27

kd 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

wd 0.00 0.50 0.67 0.75 0.80 0.83 0.86 0.88 0.89 0.90 0.91

A(n) 0.7874 0.8035 0.8090 0.8118 0.8134 0.8146 0.8154 0.8160 0.8164 0.8168 0.8171

BFO 0.000188 0.000292 0.000064 0.000153 0.000216 0.000263 0.000298 0.000326 0.000349 0.000367 0.000382

Table 26.11 Dependence of WACC on the leverage level at the company age n = 3, k0 = 27%, kd = 25% n 3 3 3 3 3 3 3 3 3 3 3

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

L 0 1 2 3 4 5 6 7 8 9 10

WACC 0.2697 0.2361 0.2246 0.2188 0.2154 0.2131 0.2114 0.2102 0.2092 0.2084 0.2078

k0 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27

kd 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

wd 0.00 0.50 0.67 0.75 0.80 0.83 0.86 0.88 0.89 0.90 0.91

A(n) 1.8956 1.9928 2.0275 2.0453 2.0561 2.0634 2.0687 2.0726 2.0757 2.0781 2.0802

BFO 0.000832 0.000174 0.000411 0.000542 0.000631 0.000694 0.000741 0.000778 0.000807 0.000830 0.000850

L = 1) lies above the perpetuity WACC value. We call this situation the “silver age” of the company (Tables 26.13–26.15 and Fig. 26.6). To be sure that the minimal WACC value at leverage level L = 1 lies above the perpetuity WACC value we make more detailed calculations for this case (see Table 26.16). We see that the minimal WACC value at n = 8.2 is equal to 0.243095889, while perpetuity limit is equal to 0.243 and lies below. Let us study the dependence of weighted average cost of capital, WACC, on the leverage level at different company age n (n = 1, 3, 1) (Fig. 26.7). It is seen from Tables 26.14, 26.15 and Fig. 26.6 that the following behavior takes place for L = 2 and 3: a third modification of dependences of weighted average cost of capital, WACC, on the company age n takes place: descending of WACC with passage through minimum at n = 8, followed by a growth with passage through maximum at n = 20 and finally with trend to perpetuity limit from bigger values

596

26

A “Golden Age” of the Companies: Conditions of Its Existence

Table 26.12 Dependence of WACC on the leverage level at the company age n = 49, k0 = 27%, kd = 25% n 49 49 49 49 49 49 49 49 49 49 49

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

L 0 1 2 3 4 5 6 7 8 9 10

WACC 0.2700 0.2430 0.2340 0.2295 0.2268 0.2250 0.2237 0.2227 0.2220 0.2214 0.2209

k0 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27

kd 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

WACC (n)

wd 0.00 0.50 0.67 0.75 0.80 0.83 0.86 0.88 0.89 0.90 0.91

A(n) 3.7037 4.1152 4.2735 4.3572 4.4091 4.4444 4.4699 4.4893 4.5045 4.5167 4.5267

BFO -0.000037 0.000041 0.000159 0.000273 0.000368 0.000444 0.000505 0.000556 0.000598 0.000633 0.000664

L=1 L=2 L=3

0.248

WACC

0.243

0.238

0.233

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

0.228

n

Fig. 26.6 The dependence of weighted average cost of capital, WACC, on the company age n at different leverage levels (L = 1, 2, 3)

(remind, that at second type of WACC(n) behavior, the curve WACC(n) tends to perpetuity limit from lower values). We have called this effect “Kulik effect.” The ordering of curves is the following: the lower curve corresponds to the greater leverage level. From Tables 26.16, 26.17, 26.18, and 26.19 and Fig. 26.6 it is seen that for L = 1 the following behavior takes place: descending of WACC with passage through

26.4

Companies with Abnormal “Golden Age” (Intermediate Difference. . .

Table 26.13 Dependence of WACC on the age of the company n at L = 1, k0 = 27%, kd = 16%

n 1 2 3 4 5 6 7 8 9 10 20 30 40 1

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

L 1 1 1 1 1 1 1 1 1 1 1 1 1 1

k0 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27

kd 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16

597

wd 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

WACC 0.252483428 0.247301552 0.245105573 0.244045922 0.243511488 0.243250247 0.24313388 0.243097298 0.243103247 0.243130071 0.243291667 0.243146312 0.243048121 0.243

WACC от L 0.27

WACC

0.26 0.25 n=1 n=3

0.24

n=∞

0.23 0.22 0

1

2

3

4

5

6

7

8

9

10

L Fig. 26.7 The dependence of weighted average cost of capital, WACC, on the leverage level at different company age n (n = 1, 3, 1)

minimum at n = 8.2 (which is higher than perpetuity limit), followed by a growth with passage through maximum at n = 20 and finally with trend to perpetuity limit from bigger values. This means that the “golden age” in its purest form presents at leverage levels for L = 2 and 3, while at L = 1 one has different effect: we call it “silver age.”

598

26

A “Golden Age” of the Companies: Conditions of Its Existence

Table 26.14 Dependence of WACC on the age of the company n at L = 2, k0 = 27%, kd = 16%

n 1 2 3 4 5 6 7 8 9 10 20 30 40 1

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

L 2 2 2 2 2 2 2 2 2 2 2 2 2 2

Table 26.15 Dependence of WACC on the age of the company n at L = 3, k0 = 27%, kd = 16%

n 1 2 3 4 5 6 7 8 9 10 20 30 40 1

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

L 3 3 3 3 3 3 3 3 3 3 3 3 3 3

k0 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27

k0 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27

kd 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16

kd 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16

wd 0.6(6) 0.6(6) 0.6(6) 0.6(6) 0.6(6) 0.6(6) 0.6(6) 0.6(6) 0.6(6) 0.6(6) 0.6(6) 0.6(6) 0.6(6) 0.6(6)

WACC 0.246644883 0.239710388 0.236752006 0.235311829 0.234578628 0.23421254 0.234046353 0.233991091 0.233996344 0.234032536 0.234316362 0.234174539 0.234059889 0.234

wd 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75

WACC 0.243725045 0.235910011 0.232564477 0.230926014 0.230090888 0.229669501 0.229475982 0.229409857 0.229414009 0.229454135 0.229812629 0.229682914 0.229564113 0.2295

The ordering of curves is the following: the lower curve corresponds to the greater company age. It turns out that at particular values of capital costs, for example, at k0 = 27%; kd = 16%, a third modification of dependences of weighted average cost of capital, WACC, on the company age n takes place: descending of WACC with passage through minimum, followed by a growth with passage through maximum and finally with trend to perpetuity limit from bigger values (remind, that at second type of WACC(n) behavior, the curve WACC(n) tends to perpetuity limit from lower values). We have called this effect “Kulik effect.”

26.5

Comparing with Results from Previous Chapter

Table 26.16 Dependence of WACC (more detailed) on the age of the company n at L = 1, k0 = 27%, kd = 16%

L 1 1 1 1 1 1 1 1 1 1 1 1

k0 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27

Table 26.17 Dependence of WACC on the leverage level L at age of the company n = 1, k0 = 27%, kd = 16%

n 1 1 1 1 1 1 1 1 1 1 1

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

26.5 26.5.1

kd 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16

L 0 1 2 3 4 5 6 7 8 9 10

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

k0 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27

599 n 7 7.2 7.4 7.6 7.8 8 8.2 8.4 8.6 8.8 9 1

kd 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16

wd 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50

WACC 0.243133854 0.243121633 0.243112185 0.243105150 0.243100256 0.243097246 0.243095889 0.243095979 0.243097328 0.243099771 0.243103156 0.243

wd 0 0.5 0.6(6) 0.75 0.8 0.8(3) 0.857142857 0.875 0.8(8) 0.9 0.(90)

BFO 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

WACC 0.270000213 0.252483428 0.246644883 0.243725045 0.241973361 0.24080557 0.239971433 0.239345829 0.238859248 0.238469982 0.238151492

Comparing with Results from Previous Chapter Under Change of the Debt Capital Cost, kd

From Fig. 26.8 it is seen that with increase of debt cost, kd, the character of dependence of weighted average cost of capital, WACC, on the company age n is changed from monotonic descending of WACC with n to descending of WACC with n with passage through minimum, followed by a limited growth. It is seen from Table 26.20 that the gap depth ΔWACC(the difference between the optimal (minimal) value of weighted average cost of capital, WACC, and its perpetuity limit) decreases with Δk = k0 - kd from 3.38% at Δk = 0.02 up to 1.89% at Δk = 0.5. At Δk = 0.10 and Δk = 0.12 the minimum in dependence of WACC(n) is absent (too big value of Δk = k0 - kd). This coincides with our conclusions in this Chapter.

600

26

A “Golden Age” of the Companies: Conditions of Its Existence

Table 26.18 Dependence of WACC on the leverage level L at age of the company n = 3, k0 = 27%, kd = 16%

n 3 3 3 3 3 3 3 3 3 3 3

Table 26.19 Dependence of WACC on the leverage level L for the perpetuity company (n = 1) at k0 = 27%, kd = 16%

n 1 1 1 1 1 1 1 1 1 1 1

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

L 0 1 2 3 4 5 6 7 8 9 10

L 0 1 2 3 4 5 6 7 8 9 10

k0 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27

kd 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16

wd 0 0.5 0.6(6) 0.75 0.8 0.8(3) 0.857142857 0.875 0.(8) 0.9 0.(90)

WACC 0.270000842 0.245105573 0.236752006 0.232564477 0.230048473 0.228369673 0.22716981 0.226269517 0.225569054 0.225008535 0.224549831

k0 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27

kd 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16

wd 0 0.5 0.(6) 0.75 0.8 0.8(3) 0.857142857 0.875 0.(8) 0.9 0.(90)

WACC 0.27 0.243 0.234 0.2295 0.2268 0.225 0.223714286 0.22275 0.222 0.2214 0.220909091

The same conclusion could be made from Fig. 26.9 and Table 26.21 for higher values of capital costs: it is seen, that with increase of debt cost, kd at fixed k0, i.e., with decrease Δk = k0 - kd the gap depth ΔWACCis increased from 1.08% at Δk = 0.10up to 1.85% at Δk = 0.05. This as well coincides with our conclusions in this paper.

26.5.2

Under Change of the Equity Capital Cost, k0

From Fig. 26.10 and Table 26.22 it is seen, that the gap depth ΔWACC (the difference between the optimal (minimal) value of weighted average cost of capital, WACC, and its perpetuity limit) decreases with Δk = k0 - kd from 0.55% at Δk = 0.01 up to 0.03% at Δk = 0.10. This as well coincides with our conclusions in this paper.

26.5

Comparing with Results from Previous Chapter

601

WACC(n), k 0=0.2 19.2000% 19.0000% 18.8000%

WACC

18.6000% 18.4000% Kd=0,18

18.2000%

Kd=0,15

18.0000%

Kd=0,10

17.8000%

Kd=0,08

17.6000% 17.4000% 17.2000% 0

5

10

15

20

25

30

35

40

45

n Fig. 26.8 Dependence of weighted average cost of capital, WACC, on life-time of the company n at fixed value of equity cost,k0 = 20%, and at four values of debt cost, kd = 8%;10%;15% and 18% at leverage level L = 1 Table 26.20 The dependence of the gap depth ΔWACC on Δk = k0 - kd

kd Δk = k0 - kd ΔWACC, %

0.18 0.02 3.38

0.15 0.05 1.89

0.10 0.10 NA

0.08 0.12 NA

WACC

WACC(n) 0.3700 0.3680 0.3660 0.3640 0.3620 0.3600 0.3580 0.3560 0.3540 0.3520 0.3500

kd=0,35 kd=0,3

0

5

10

15

20

25

30

35

40

45

n Fig. 26.9 Dependence of weighted average cost of capital, WACC, on life-time of the company n at fixed high value of equity cost,k0 = 40%, and two values of debt cost, kd = 30% and 35% at leverage level L = 1

602

26

Table 26.21 The dependence of the gap depth ΔWACC on Δk = k0 - kd

A “Golden Age” of the Companies: Conditions of Its Existence k0 = 0, 4; kd Δk = k0 - kd ΔWACC, %

0.35 0.05 1.85

0.3 0.10 1.08

WACC(n) 23.0000%

WACC

21.0000% Ko=0,25

19.0000%

Ko=0,22 Ko=0,2

17.0000%

Ko=0,18 Ko=0,16

15.0000% 13.0000% 0

5

10

15

20

25

30

35

40

45

n Fig. 26.10 Dependence of weighted average cost of capital, WACC, on life-time of the company n at fixed value of debt cost, kd = 15%, and five values of equity cost, k0 = 16%;18%; 20%; 22% and 25% at leverage level L = 1 Table 26.22 The dependence of the gap depth ΔWACC on Δk = k0 - kd

k0 Δk = k0 - kd ΔWACC, %

0.16 0.01 0.55

0.18 0.03 0.43

0.20 0.05 0.30

0.22 0.07 0.18

0.25 0.10 0.03

In conclusion we present in Fig. 26.11 both cases of “Kulik” effect: “the golden age” of the company and the “silver age” of the company.

26.6

Conclusions

In our previous paper a few years ago (Brusov et al. 2015a, b) we have discovered the effect of the “golden age” of company: it was shown for the first time that valuation of the weighted average cost of capital, WACC, in the Modigliani–Miller theory (Мodigliani and Мiller 1958, 1963, 1966) is not minimal and valuation of the company capitalization is not maximal, as all financiers supposed up to this discovery: at some age of the company its WACC value turns out to be lower, than in Modigliani–Miller theory and company capitalization V turns out to be greater, than

26.6

Conclusions

603

Fig. 26.11 Dependence of weighted average cost of capital, WACC, on company age of the company n, which illustrate the presence of “the golden age” of the company (curve 1) and of “the silver age” of the company (curve 2) under existence of “Kulik” effect. Here n0 is “the golden (silver) age” of the company and n1 is the age of local maximum in dependence of WACC(n)

V in Modigliani–Miller theory (see previous Chapter). It was shown that, from the point of view of cost of attracting capital there are two types of dependences of weighted average cost of capital, WACC, on the company age n: monotonic descending with n and descending with passage through minimum, followed by a limited growth. In practice, there are companies with both types of dependences of WACC on the company age n. In this Chapter we have continued the study of the effect of the “golden age” of company and have investigated which companies have the “golden age,” i.e., obey the latter type of dependence of WACC on n. With this aim we study the dependence of WACC on the age of company n at various leverage levels within a wide spectrum of capital costs values as well as the dependence of WACC on leverage level L at fixed company age n. All calculations have been done within modern theory of capital cost and capital structure BFO by Brusov–Filatova–Orekhova (Brusov et al. 2011a, b, c, d, 2012a, b, 2013a, b, 2014a, b; Filatova et al. 2008). We have shown that existence of the “golden age” of company does not depend on the value of capital costs of the company (as it was supposed in previous Chapter), but depends on the difference value between equity, k0, and debt, kd, costs. The “golden age” of company exists at small enough difference between k0 and kd costs, while at high value of this difference the “golden age” of company is absent: curve WACC(n) monotonic descends with company age n. For the companies with the “golden age” curve WACC(L) for perpetuity limit lies between curves WACC(L) at n = 1 and n = 3, while for the companies without the “golden age” curve WACC(L) for perpetuity limit (n = 1) is the lowest one. In other words, the ordering of curves WACC(L) is different for the companies with the “golden age” and without it.

604

26

A “Golden Age” of the Companies: Conditions of Its Existence

In the previous Chapter we have found also a third type of WACC (n) dependence: descending with passage through minimum, which lies below the perpetuity limit value, then going through maximum followed by a limited descending. We called this effect “Kulik effect” (this is last name of student, who have discovered this effect). In this paper, we have found a variety of “Kulik effect”: descending with passage through minimum of WACC, which lies above the perpetuity limit value, then going through maximum followed by a limited descending. We call this company age n, at which WACC has a minimum, which lies above the perpetuity limit value, “the silver age” of the company. It takes place at intermediate difference value between equity k0 and debt kd costs. Because the cost of attracting capital is used in rating methodologies as discounting rate under discounting of cash flows, study of WACC behavior is very important for rating procedures. The account of effects of the “golden (silver) age” could change the valuation of creditworthiness of issuers. Remind that, since the “golden age” of company depends on the company’s capital costs, by controlling them (for example, by modifying the value of dividend payments, that reflect the equity cost), company may extend the “golden (silver) age” of the company, when the cost to attract capital becomes a minimal (less (above) than perpetuity limit), and capitalization of companies becomes maximal (above (below) than perpetuity assessment) up to a specified time interval.

References Brusov P, Filatova T, Orehova N, Brusova A (2011a) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Appl Financ Econ 21(11): 815–824 Brusov P, Filatova T, Orehova N et al (2011b) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Bus ICT 2:16–21 Brusov P, Filatova T, Orehova N et al (2011c) Influence of debt financing on the effectiveness of the investment project within the Modigliani–Miller theory. Res J Econ Bus ICT (UK) 2:11–15 Brusov P, Filatova Т, Orehova N, Brusova P, Brusova N (2011d) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Finance Credit 435:2–8 Brusov P, Filatova T, Eskindarov M, Orehova N (2012a) Influence of debt financing on the effectiveness of the finite duration investment project. Appl Financ Econ 22(13):1043–1052 Brusov P, Filatova T, Eskindarov M, Orehova N (2012b) Hidden global causes of the global financial crisis. J Rev Glob Econ 1:106–111 Brusov P, Filatova P, Orekhova N (2013a) Absence of an optimal capital structure in the famous tradeoff theory! J Rev Glob Econ 2:94–116 Brusov P, Filatova T, Orehova N (2013b) A qualitatively new effect in corporative finance: abnormal dependence of cost of equity of company on leverage. J Rev Glob Econ 2:183–193 Brusov P, Filatova P, Orekhova N (2014a) Mechanism of formation of the company optimal capital structure, different from suggested by trade off theory. Cogent Econ Finance 2:1–13. https://doi. org/10.1080/23322039.2014.946150 Brusov P, Filatova T, Orehova N (2014b) Inflation in Brusov–Filatova–Orekhova theory and in its perpetuity limit – Modigliani–Miller theory. J Rev Glob Econ 3:175–185 Brusov P, Filatova T, Orehova N, Eskindarov M (2015a) Modern corporate finance, investments and taxation, monograph, 1st edn. Springer, New York, p 368

References

605

Brusov P, Filatova T, Orehova N, Kulik V (2015b) The Golden age of the company: (three colors of company’s time). J Rev Glob Econ 4:21–42 Brusov P, Filatova T, Orehova N, Kulk WI (2018a) New meaningful effects in modern capital structure theory. J Rev Global Econ 7:104–122 Brusov P, Filatova T, Orehova N, Kulk V (2018b) A “Golden Age” of the companies: conditions of its existence. J Rev Global Econ 7:88–103 Brusov P, Filatova T, Orehova N, Kulk V (2018c) Rating methodology: new look and new horizons. J Rev Global Econ 7:63–87 Brusov P, Filatova T, Orehova N, Kulk V (2018d) Rating: new approach. J Rev Global Econ 7:37– 62 Brusova A (2011) А comparison of the three methods of estimation of weighted average cost of capital and equity cost of company. Financ Anal Prob Solutions 34(76):36–42 Filatova Т, Orehova N, Brusova А (2008) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Bull FU 48:68–77 Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Modigliani F, Miller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391

Chapter 27

New Meaningful Effects in Modern Capital Structure Theory

Keywords Brusov–Filatova–Orekhova theory · Modigliani–Miller theory · Tradeoff theory · Ratings · New effects in corporate finance

27.1

Introduction

One of the main and the most important problems in corporate finance is the problem of cost of capital, the impact of capital structure on its cost and capitalization of the companies and problem of an optimal capital structure of the companies (at which the company capitalization is maximal, and weighted average cost of capital WACC is minimal). The importance of these problems is connected to the fact that one can do nothing, just by changing the ratio between debt and equity (by changing the capital structure) to increase the capitalization of the company, i.e., solve the main task of any company. However, to date, even the question of the existence of an optimal capital structure of the companies still remains open. Numerous theories and models, including the first and the only one until recently quantitative theory by Nobel laureates Modigliani and Miller (MM), not only does not solve the problem, but also because of the large number of restrictions (for example, theory of MM) have a weak relationship to the real economy. Herewith the qualitative theories and models, based on the empirical approaches, do not allow to carry out the necessary assessment. This special issue is devoted to recent development of capital structure theory and its applications. Discussions will be made within both main theories: modern theory by Brusov, Filatova, and Orekhova (BFO theory) and its perpetuity limit—classical Modigliani–Miller (MM) theory, which will be compared in detail. From 2008 the BFO theory has replaced the famous theory of capital cost and capital structure by Nobel laureates Modigliani and Miller. The authors of BFO have moved from the assumption of Modigliani–Miller concerning the perpetuity (infinite time of life) of companies and further elaborated quantitative theory of valuation of core parameters of financial activities of companies of arbitrary age as well as of the arbitrary time of life.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_27

607

608

27

New Meaningful Effects in Modern Capital Structure Theory

Results of modern BFO theory turn out to be quite different from the ones of Modigliani–Miller theory. Brusov, Filatova, and Orekhova show that later, via its perpetuity, underestimates the assessment of weighted average cost of capital, the equity cost of the company and substantially overestimates the assessment of the capitalization of the company. Such an incorrect assessment of key performance indicators of financial activities of companies has led to an underestimation of risks involved, and impossibility, or serious difficulties in adequate managerial decision-making, which was one of the implicit reasons for the global financial crisis of 2008. Within modern theory of capital cost and capital structure (BFO theory) a lot of qualitatively new results, described in this paper, have been obtained, among them: – Bankruptcy of the famous trade-off theory has been proven. BFO theory has destroyed some main existing principles of financial management: among them trade-off theory, which was considered as keystone of formation of optimal capital structure of the company during many decades. It would be a great pity if the optimal capital structure of the company does not exist in general, thus BFO authors have suggested the Mechanism of formation of the company optimal capital structure, different from suggested by trade-off theory. – –The qualitatively new effect in corporate finance has been discovered by BFO authors: abnormal dependence of equity cost on leverage, which significantly alters the principles of the company’s dividend policy. – Existence of “A golden age” of the companies has been discovered. It was shown for the first time that the valuation of WACC in the Modigliani–Miller theory is not minimal and valuation of the company capitalization is not maximal, as all financiers supposed up to now: at some age of the company its WACC value turns out to be lower, than in Modigliani–Miller theory (in perpetuity limit) and company capitalization V at some company age turns out to be greater, than company capitalization V in Modigliani–Miller theory. – The inflation in both Modigliani–Miller as well as in Brusov–Filatova– Orekhova theories has been taken into account in explicit form, with the detected its non-trivial impact on the dependence of equity cost on leverage. – Study of the role of taxes and leverage has been done, and obtained results allow to the Regulator set the tax on profits rate, and to businesses choose the optimal level of debt financing. – Investigation of the influence of tax on profit rate on effectiveness of investment projects at different debt levels showed, that increase of tax on profit rate from one side leads to decrease of project NPV, but from other side it leads to decrease in sensitivity of NPV with respect to leverage level. At high leverage level L the influence of tax on profit rate on effectiveness of investment projects becomes significantly less. – The influence of growth of tax on profit rate on the efficiency of the investment as well has led to two qualitatively new effects in investments:

27.2

Comparision of Modigliani–Miller (MM) and Brusov–Filatova–Orekhova. . .

609

1. The growth of tax on profit rate changes the nature of the NPV dependence on leverage L at some value t*: there is a transition from diminishing function NPV(L) at t < t*, to growing function NPV(L) at t > t*. 2. At high leverage levels the growth of tax on profit rate leads to the growth of the efficiency of the investments. Discovered effects in investments can be applied in a real economic practice for optimizing of the management of investments. Established BFO theory allows to conduct a valid assessment of the core parameters of financial activities of companies, such as weighted average cost of capital and equity capital cost of the company, its capitalization. It allows to management of company to make adequate decisions, which improve the effectiveness of the company management. More generally, the introduction of the new system of evaluation of the parameters of financial activities of companies into the systems of financial reporting (IFRS, GAAP, etc.) would lead to lower risk of global financial crisis. Corporate management in the modern world is the management of financial flows. The proposed Brusov–Filatova–Orekhova theory allows correctly to identify discount rates—basic parameters for discounting of financial flows to arbitrary time moment, compare financial flows with a view to adoption of literate managerial decisions. The discount rate is a key link of the existing financial system, by pulling on which modern finance can be adequately built, and BFO theory can assist in this. In this paper, we discuss numerous new meaningful effects in modern capital structure theory.

27.2 27.2.1

Comparision of Modigliani–Miller (MM) and Brusov– Filatova–Orekhova (BFO) Results The Traditional Approach

The traditional (empirical) approach told to businessmen, that weighted average cost of capital, WACC, and the associated company capitalization, V = CF/WACC depend on the capital structure, the level of leverage. Debt cost always turns out to be lower than equity cost, because first one has lower risk, because in the event of bankruptcy creditor claims are met prior to shareholders claims. As a result an increase in the proportion of lower-cost debt capital in the overall capital structure up to the limit which does not cause a violation of financial sustainability and growth in risk of bankruptcy leads to lower weighted average cost of capital, WACC. The required by investors profitability (the equity cost) is growing; however, its growth has not led to compensation benefits from use of more low-cost debt capital.

610

27

New Meaningful Effects in Modern Capital Structure Theory

Fig. 27.1 Dependence of company capitalization, UL, equity cost, ke, debt cost, kd, weighted average cost of capital, WACC, in traditional (empirical) approach

Therefore, the traditional approach welcomes the increased leverage L = D/S, and the associated increase in company capitalization. The traditional (empirical) approach has existed up to the appearance of the first quantitative theory by Мodigliani and Мiller (1958) (Fig. 27.1).

27.2.2 Modigliani–Miller Theory Modigliani–Miller theory with taxes is based on the following three formulae for capitalization V, WACC and equity cost ke (Fig. 27.2). V = V 0 þ Dt, WACC = k0 ð1- wd T Þ, ke = k 0 þ Lð1- T Þðk0- kd Þ: One of the most important assumptions of the Modigliani–Miller theory is that all financial flows are perpetuity.

27.2

Comparision of Modigliani–Miller (MM) and Brusov–Filatova–Orekhova. . .

611

Fig. 27.2 Dependence of equity capital cost, debt cost, and WACC on leverage in Modigliani– Miller theory without taxes (t = 0) and with taxes (t ≠ 0)

Fig. 27.3 Historical development of capital structure theory (here TA—traditional (empirical) approach, MM—Modigliani–Miller approach, BFO—Brusov–Filatova–Orekhova theory)

This limitation was lifted out by Brusov–Filatova–Orekhova in 2008, who created the BFO theory—modern theory of capital cost and capital structure for companies of arbitrary age (BFO–I) and for companies of arbitrary lifetime (BFO– II) (Brusov et al. 2015) (Fig. 27.3). Note, that before 2008 only two results for capital structure of company were available: Modigliani–Miller for perpetuity company and Myers for one-year company (see Fig. 27.4).

612

27

New Meaningful Effects in Modern Capital Structure Theory

Fig. 27.4 MM theory describes perpetuity limit, Myers paper describes one-year company while BFO theory fills the whole numeric axis (from n = 1 up to perpetuity limit n = 1)

BFO theory has filled out whole interval between t = 1 and t = 1. One got the possibility to calculate capitalization V, WACC and equity cost ke for companies of arbitrary age and for companies of arbitrary lifetime. BFO theory has led to a lot of new meaningful effects in modern capital structure theory, discussed in this paper. BFO theory is based on famous formula 1 - ð1 þ k 0 Þ - n 1 - ð1 þ WACCÞ - n : = WACC k 0 ½1 - ωd T ð1 - ð1 þ kd Þ - n Þ

ð27:1Þ

D —the share Here, S—the value of own (equity) capital of the company, wd = DþS S of debt capital; k e , we = DþS—the cost and the share of the equity of the company, L = D/S—financial leverage.

27.3

Comparision of Modigliani–Miller Results (Perpetuity Company) with Myers Results (One Year Company) and Brusov–Filatova–Orekhova Ones (Company of Arbitrary Age)

We could compare the Modigliani–Miller results (perpetuity company) with Myers results (one year company) and Brusov–Filatova–Orekhova ones (company with arbitrary age) under valuation of WACC and equity cost. From Tables 27.1, 27.2 and Fig. 27.5 it is obvious that WACC has a maximum for one-year company and decreases with the age (lifetime) of the company, reaching the minimum in the Modigliani–Miller perpetuity case. (Note, however, that this not always be so via the effect of “golden age” of the company (see below)). Results of modern BFO theory turn out to be quite different from ones of Modigliani–Miller theory. They show, that later, via its perpetuity, underestimates the assessment of weighted average cost of capital, the equity cost of the company and substantially overestimates the assessment of the capitalization of the company. Such an incorrect assessment of key performance indicators of financial activities of companies has led to an underestimation of risks involved, and impossibility, or serious difficulties in adequate managerial decision-making, which was one of the implicit reasons for the global financial crisis of 2008.

27.3

Comparision of Modigliani–Miller Results (Perpetuity Company) with. . .

613

Table 27.1 Dependence of WACC and ke on leverage level for n = 1, and n = 1 L 0 1 2 3 4 5 6 7 8 9 10

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

N 1 1 1 1 1 1 1 1 1 1 1

wd 0.00 0.50 0.67 0.75 0.80 0.83 0.86 0.88 0.89 0.90 0.91

WACC 20.00% 18.91% 18.55% 18.36% 18.25% 18.18% 18.13% 18.09% 18.06% 18.04% 18.02%

BFO 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

ke 0.2000 0.2982 0.3964 0.4945 0.5927 0.6909 0.7891 0.8873 0.9855 1.0836 1.1818

WACC MM 20.00% 18.00% 17.33% 17.00% 16.80% 16.67% 16.57% 16.50% 16.44% 16.40% 16.36%

MM ke 0.2000 0.2800 0.3600 0.4400 0.5200 0.6000 0.6800 0.7600 0.8400 0.9200 1.0000

Table 27.2 Dependence of WACC and ke on leverage level for n = 3, and n = 1 L 0 1 2 3 4 5 6 7 8 9 10

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 3 3 3 3 3 3 3 3 3 3 3

wd 0.00 0.50 0.67 0.75 0.80 0.83 0.86 0.88 0.89 0.90 0.91

WACC 20.00% 18.41% 17.87% 17.61% 17.44% 17.34% 17.26% 17.20% 17.16% 17.12% 17.09%

BFO 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

ke 0.2000 0.2881 0.3762 0.4642 0.5522 0.6402 0.7283 0.8163 0.9043 0.9923 1.0803

WACC MM 20.00% 18.00% 17.33% 17.00% 16.80% 16.67% 16.57% 16.50% 16.44% 16.40% 16.36%

MM ke 0.2000 0.2800 0.3600 0.4400 0.5200 0.6000 0.6800 0.7600 0.8400 0.9200 1.0000

20.00% 19.50% 19.00%

WACC

18.50% 18.00%

n=1 ko=0,2 kd=0,1

17.50%

n=3 ko=0,2 kd=0,1

17.00%

MM ko=0,2 kd=0,1

16.50% 16.00% 15.50% 15.00%

0

1

2

3

4

5

6

7

8

9

10

Fig. 27.5 Dependence of WACC on leverage level for n = 1, n = 3 and n = 1

614

27

New Meaningful Effects in Modern Capital Structure Theory

BFO theory allows making a correct assessment of key parameters of financial activities of companies of arbitrary age (arbitrary lifetime) that leads accordingly to adequate managerial decision-making.

27.4

Bankruptcy of the Famous Trade-off Theory

Within modern theory of capital structure and capital cost by Brusov–Filatova– Orekhova (Brusov et al. 2011a, b, c, d, 2012a, b, 2013a, b, 2014a, b; Brusova 2011; Filatova et al. 2008) the analyses of widely known trade-off theory has been made. It is shown that the suggestion of risky debt financing (and growing credit rate near the bankruptcy) in opposite to waiting result does not lead to growing of weighted average cost of capital, WACC, which still decreases with leverage. This means the absence of minimum in the dependence of WACC on leverage as well as the absence of maximum in the dependence of company capitalization on leverage. Thus, it means that the optimal capital structure is absent in famous trade-off theory. An explanation to this fact has been done. In modified Modigliani–Miller theory we have proved the following theorem: In modified Modigliani–Miller theory (allowing riskiness debt capital) under arbitrary change of debt cost with leverage (growing, as well as decrease) weighted average cost of capital, WACC always fall down with leverage. This means the absence of the company optimal capital structure and proves insolvency well-known classical trade-off in its original formulation. We consider linear and quadratic growth of debt cost kd with leverage, starting from some value (with different coefficients), different values of k0 and different terms of life of the companies. Let us find WACC values (Table 27.3 and Fig. 27.6). 1. n = 3; t = 20 % ; L = 0, 1, 2, ...10  k0 = 24%; kd =

0:07; at L ≤ 2

 ð27:2Þ

0:07 þ 0:01ðL - 2Þ2 ; at L > 2

Let us see how the growth of debt cost kd with leverage affects the equity cost ke dependence on leverage. We will consider the same cases as above for the calculations of dependences WACC(L) (Table 27.4 and Fig. 27.7). 1. n = 3; t = 20 % ; L = 0, 1, 2, . . .10  k0 = 24%; kd =

0:07; at L ≤ 2 0:07 þ 0:01ðL - 2Þ2 ; at L > 2

 ð27:3Þ

The analysis of well-known trade-off theory, conducted with the help of modern theory of capital structure and capital cost by Brusov–Filatova–Orekhova, has

n 3 k0 0.24

L kd A WACC

0 0.07 1.9813 0.2401

1 0.07 2.0184 0.2279

Table 27.3 Dependence of WACC on L 2 0.07 2.0311 0.2238

3 0.08 2.0445 0.2195

4 0.11 2.0703 0.2111

5 0.16 2.1075 0.1997

6 0.23 2.1520 0.1864

7 0.32 2.1988 0.1730

8 0.43 2.2438 0.1605

9 0.56 2.2842 0.1496

10 0.71 2.3186 0.1406

27.4 Bankruptcy of the Famous Trade-off Theory 615

616

27

New Meaningful Effects in Modern Capital Structure Theory

WACC(L) 0.3000 0.2500 0.2000 0.1500 0.1000 0.0500 0.0000

0

1

2

3

4

5

6

7

8

9

10

11

Fig. 27.6 Dependence of WACC on L

shown that the suggestion of risky debt financing (and growing credit rate near bankruptcy) in opposite to waiting result does not lead to growing of WACC, which still decreases with leverage. This means the absence of minimum in the dependence of WACC on leverage as well as the absence of maximum in the dependence of capitalization V on leverage. Thus, it seems that the optimal capital structure is absent in famous trade-off theory. The explanation to this fact has been done within the same Brusov–Filatova–Orekhova theory by studying the dependence of the equity cost ke with leverage. It turned out that the growth of debt cost kd with leverage led to decrease in equity cost ke with leverage, starting from some leverage level, which is higher than starting point of debt cost growth. This paradoxical conclusion gives the explanation of the absence of the optimal capital structure in the famous trade-off theory. This means that competition of benefits from using debt financing and financial distress cost (or a bankruptcy cost) are NOT balanced and hopes that trade-off theory gives us the optimal capital structure, unfortunately, do not realize. The absence of the optimal capital structure in the trade-off theory questioned the existence of an optimal capital structure of the company (but as authors have shown, the optimal capital structure for the investment still exists (Brusov et al. 2011b, c)). In the search for the “golden fleece” one needs to switch to study of other mechanisms for the formation of the capital structure of the company, different from the ones considering in trade-off theory.

n 3 k0 0.24

L kd A ke

0 0.07 1.9813 0.2401

1 0.07 2.0184 0.3997

2 0.07 2.0311 0.5594

Table 27.4 Dependence of equity cost ke on L 3 0.08 2.0445 0.6861

4 0.11 2.0703 0.7036

5 0.16 2.1075 0.5581

6 0.23 2.1520 0.2011

8 0.43 2.2438 -1.3075

7 0.32 2.1988 -0.4081

0.56 2.2842 -2.5356

9

10 0.71 2.3186 -4.133

27.4 Bankruptcy of the Famous Trade-off Theory 617

618

27

New Meaningful Effects in Modern Capital Structure Theory

Ke(L) 0.8000 0.7000 0.6000 0.5000 0.4000 0.3000 0.2000 0.1000 0.0000

0

1

2

3

4

5

6

7

Fig. 27.7 Dependence of equity cost ke on L

27.5

The Qualitatively New Effect in Corporate Finance

Qualitatively new effect in corporative finance is discovered: decreasing of cost of equity ke with leverage L. This effect, which is absent in perpetuity Modigliani– Miller limit, takes place under the account of finite lifetime of the company at tax on profit rate, which exceeds some value T*. At some ratios between cost of debt and cost of equity the discovered effect takes place at tax on profit rate, existing in western countries and Russia. This provides the practical meaning of discussed effect. Its accounting is important at modification of tax low and can change the dividend policy of the company.

27.5.1

Perpetuity Modigliani–Miller Limit

One sees from Fig. 27.8 that position limit of dependence of cost of equity on leverage L is horizontal line 11 at T = 1. Below we will see that in BFO theory the abnormal effect takes place (see Fig. 27.10) and dependence of cost of equity on leverage L line could have a negative slope (Fig. 27.9).

27.5.2

BFO Theory

From Fig. 27.10 it is seen, that dependence of cost of equity ke on leverage level L with a good accuracy is linear. The tilt angle decreases with tax on profit rate like the perpetuity case.

27.5

The Qualitatively New Effect in Corporate Finance

Fig. 27.8 Dependence of cost of equity on leverage L at different tax on profit rates T for the case k0 = 10 % ; kd = 8% (1— T = 0; 2—T = 0.1; 3— T = 0.2; 4—T = 0.3; 5— T = 0.4; 6—T = 0.5; 7— T = 0.6; 8—T = 0.7; 9–10—T = 0.9; 11—T = 1)

619

Ke (L), at fix T

Ke 0.3000

1 2 3 4 5 6 7 8 9 10 11

0.2500 0.2000 0.1500 0.1000 0.0500 0.0000

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

L

Ke(T), at fix Wd

Ke 0.2000 0.1500 0.1000

1 2 3

0.0500 0.0000

4

0

0.2

0.4

0.6

0.8

1

1.2

-0.0500 5 -0.1000

T

Fig. 27.9 Dependence of cost of equity ke on tax on profit rate T at different fix leverage level L (n = 10, k0 = 10 % , kd = 8%)(1—wd = 0; 2—wd = 0.2; 3—wd = 0.4; 4—wd = 0.6; 5—wd = 0.8)

However for the finite lifetime of companies along with the behavior ke(L ), similar to the perpetuity behavior of the Modigliani–Miller case (Fig. 27.8), for some sets of parameters n, k0, kd there is an otherwise behavior ke(L ).

620

27

Ke 0.4000

New Meaningful Effects in Modern Capital Structure Theory

Ke(L), at fix T

0.3000

1

0.2000

2

0.1000

3

0.0000

4 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 1010.5

-0.1000

5

-0.2000 6 -0.3000

L

Fig. 27.10 Dependence of cost of equity ke on leverage level L at different tax on profit rate T (n = 5, k0 = 10 % , kd = 8%)(1—T = 0; 2—T = 0.2; 3—T = 0.4; 4—T = 0.6; 5—T = 0.8; 6— T = 1)

From the Fig. 27.10 it is seen that starting from some values of tax on profit rate T (in this case from T = 40%, although at other sets of parameters n, k0, kd critical values of tax on profit rate T could be lower) there is not rise in the cost of equity of the company with leverage, but descending. Once again, the presence or the absence of such an effect depends on a set of parameters k0, kd, n. This effect has been observed above in the dependence of cost of equity ke on tax on profit rate T at fix leverage level, but it is more clearly visible, depending on value of cost of equity of the company on the leverage for various values of tax on profit rate T. Note that this is a new effect, which may take place only for the finite lifetime company and which is not observed in perpetuity Modigliani–Miller limit. It is easy to receive from the Modigliani–Miller formula for WACC WACC = ke we þ kd wd ð1- T Þ formula for ke k e = k0 þ Lð1- T Þðk0- kd Þ, from which one can see that at T = 1(100%) cost of equity ke does not change with leverage: ke = k0, i.е there is no decreasing of ke with leverage at any tax on profit rate T.

27.6

Mechanism of Formation of the Company Optimal Capital Structure

621

Conclusions Qualitatively new effect in corporative finance is discovered: decreasing of cost of equity ke with leverage L. This effect, which is absent in perpetuity Modigliani–Miller limit, takes place under account of finite lifetime of the company at tax on profit rate, which exceeds some value T* (Brusov et al. 2011a, b, c, d, 2012a, b, 2013a, b, 2014a, b; Filatova et al. 2008). At some ratios between debt cost and equity cost the discovered effect takes place at tax on profit rate, existing in western countries and Russia. This provides the practical meaning of discussed effect. Its accounting is important at modification of tax low and can change the dividend policy of the company. A complete and detailed investigation of discussed effect, discovered within Brusov–Filatova–Orekhova (BFO) theory, has been done (Brusov et al. 2011a, b, c, d, 2012a, b, 2013a, b, 2014a, b; Filatova et al. 2008). It has been shown that the absence of the effect at some particular set of parameters is connected to the fact, that in these cases T* exceeds 100% (tax on profit rate is situated in a “non-financial” region). In future, the papers and monographs will be devoted to the discussion of discovered abnormal effect, but it is already now clear, that we will have to abandon of some established views in corporative finance.

27.6

Mechanism of Formation of the Company Optimal Capital Structure

Under the condition of proven by us insolvency of well-known classical trade-off theory question of finding of new mechanisms of formation of the company optimal capital structure, different from one, suggested by trade-off theory, becomes very important. One of the real such mechanisms has been developed by us in this Chapter. It is based on the decrease of debt cost with leverage, which is determined by the growth of debt volume. This mechanism is absent in perpetuity Modigliani– Miller theory, even in modified version, developed by us, and exists within more general modern theory of capital cost and capital structure by Brusov–Filatova– Orekhova (BFO theory). Suggested mechanism of formation of the company optimal capital structure is based on the decrease of debt cost, which (in some range of leverage levels) is determined by growing of the debt volume. We will study below the dependence of equity cost ke and weighted average cost of capital, WACC, on leverage level L in case of debt cost kd exponential decrease (Table 27.5, Figs. 27.11, 27.12, and 27.13). The case α = 0.01. Let us consider first the case α = 0.01. The case α = 0.01. Let us consider first the case α = 0.01. We will study below the dependence of debt cost kd, equity cost ke and weighted average cost of capital, WACC, on leverage level L in case of kd exponential decrease (Table 27.6, Figs. 27.14, 27.15, and 27.16).

622

27

New Meaningful Effects in Modern Capital Structure Theory

Table 27.5 kd, ke and weighted average cost of capital, WACC, for companies with lifetimes n = 1; 3; 5; 10 L kd WACC (n = 1) ke (n = 1) WACC (n = 3) ke (n = 3) WACC (n = 5) ke (n = 5) WACC (n = 10) ke (n = 10)

0 0.12 0.220 0.220 0.219 0.219 0.220 0.220 0.220

0.5 0.12 0.211 0.257 0.208 0.252 0.206 0.250 0.206

1 0.12 0.207 0.294 0.201 0.281 0.200 0.279 0.199

1.1 0.1188 0.206 0.302 0.201 0.291 0.199 0.287 0.198

1.3 0.1161 0.205 0.320 0.199 0.307 0.197 0.303 0.196

1.6 0.1107 0.206 0.358 0.199 0.340 0.197 0.335 0.196

2 0.1 0.206 0.417 0.198 0.395 0.196 0.388 0.194

3 0.04 0.214 0.736 0.209 0.716 0.207 0.710 0.205

4 -0.14 0.252 1.819 0.279 1.955 0.301 2.067 0.383

0.220

0.249

0.277

0.285

0.301

0.332

0.383

0.699

2.474

Fig. 27.11 Dependence of debt cost kd on leverage level L in case of its exponential decrease at α = 0.01

Fig. 27.12 Dependence of weighted average cost of capital, WACC on leverage level L in case of exponential decrease of debt cost at α = 0.01

27.7 “A Golden Age” of the Company Authors of BFO theory have investigated the dependence of attracting capital cost on the time of life of company n at various leverage levels, at various values of capital costs with the aim of define of minimum cost of attracting capital. All calculations have been done within modern theory of capital cost and capital structure by

27.7

“A Golden Age” of the Company

623

Fig. 27.13 Dependence of equity cost ke on leverage level L in case of its exponential decrease at α = 0.01

Table 27.6 kd, ke and weighted average cost of capital, WACC, for companies with lifetimes n = 1; 3; 5; 10 L kd WACC (n = 1) ke (n = 1) WACC (n = 3) ke (n = 3) WACC (n = 5) ke (n = 5) WACC (n = 10) ke (n = 10)

0 0.12 0.220 0.220 0.219 0.219 0.220 0.220 0.220

0.5 0.12 0.211 0.257 0.208 0.252 0.206 0.250 0.206

1 0.12 0.207 0.294 0.201 0.281 0.200 0.279 0.199

1.1 0.1188 0.206 0.302 0.201 0.291 0.199 0.287 0.198

1.3 0.1161 0.205 0.320 0.199 0.307 0.197 0.303 0.196

1.6 0.1107 0.206 0.358 0.199 0.340 0.197 0.335 0.196

2 0.1 0.206 0.417 0.198 0.395 0.196 0.388 0.194

3 0.04 0.214 0.736 0.209 0.716 0.207 0.710 0.205

4 -0.14 0.252 1.819 0.279 1.955 0.301 2.067 0.383

0.220

0.249

0.277

0.285

0.301

0.332

0.383

0.699

2.474

Fig. 27.14 Dependence of debt cost kd on leverage level L in case of its exponential decrease at α = 0.01

Brusov–Filatova–Orekhova (Brusov et al. 2011a, b, c, d, 2012a, b, 2013a, b, 2014a, b, 2015; Filatova et al. 2008). It was shown for the first time that the valuation of WACC in the Modigliani– Miller theory (Мodigliani and Мiller 1958, 1963, 1966) is not minimal and valuation of the company capitalization is not maximal, as all financiers supposed up to now: at some age of the company its WACC value turns out to be lower, than in Modigliani–Miller theory and company capitalization V turns out to be greater, than V in Modigliani–Miller theory.

624

27

New Meaningful Effects in Modern Capital Structure Theory

Fig. 27.15 Dependence of weighted average cost of capital, WACC on leverage level L in case of exponential decrease of debt cost at α = 0.01

Fig. 27.16 Dependence of equity cost ke on leverage level L in case of its exponential decrease at α = 0.01

It was shown that from the point of view of cost of attracting capital there are two types of dependences of weighted average cost of capital, WACC, on the time of life of company n: monotonic descending with n and descending with passage through minimum, followed by a limited growth. The first type takes place for the companies with low cost capital, characteristic for western companies. The second type takes place for higher costs capital costs of the company, characteristic for Russian companies as well as for companies from other developing countries. This means that latter companies, in contrast to the western ones, can take advantage of the benefits, given at a certain stage of development of company by discovered effect. Moreover, since the “golden age” of company depends on the company’s capital costs, by controlling them (for example, by modifying the value of dividend payments, that reflect the equity cost), company may extend the “golden age” of the company, when the cost to attract capital becomes a minimal (less than perpetuity limit), and capitalization of companies becomes maximal (above than perpetuity assessment) up to a specified time interval. Concluded that existed up to the present conclusions of the results of the theory of Modigliani–Miller (Мodigliani and Мiller 1958, 1963, 1966) in these aspects are incorrect. We discuss the use of opened effects in developing economics. The conclusion made in this Paper for the first time, that the assessment of weighted average cost of capital of the company, WACC, in the theory of Modigliani and Miller (MM) (Мodigliani and Мiller 1958, 1963, 1966) is not the

27.7

“A Golden Age” of the Company

625

Fig. 27.17 Monotonic dependence of weighted average cost of capital, WACC, on lifetime of the company n

Fig. 27.18 Dependence of weighted average cost of capital, WACC, on lifetime of the company n, showing descending with n, and with the passage through a minimum and then a limited growth

minimal, and capitalization is not maximal, seems to be very significant and important (Figs. 27.17, 27.18, and 27.19).

626

27

New Meaningful Effects in Modern Capital Structure Theory

Fig. 27.19 Two kinds of dependences of weighted average cost of capital, WACC, and company capitalization, V, on lifetime of the company n: 1–1′—monotonic dependence of weighted average cost of capital, WACC, and company capitalization, V, on lifetime of the company n; 2–2′— showing descending of WACC with n, and with the passage through a minimum and then a limited growth and increase of V with the passage through a maximum (at n0) and then a limited descending

Below we show the dependence of weighted average cost of capital, WACC, on lifetime of the company n at fixed value of equity cost, k0 = 20%, and at four values of debt cost. From Fig. 27.20 it is seen that with increase in debt cost, kd, the character of dependence of weighted average cost of capital, WACC, on lifetime of the company n is changed from monotonic descending of WACC with n to descending of WACC with n with passage through minimum, followed by a limited growth. Conclusions Above it is shown for the first time within BFO theory (Brusov et al. 2011a, b, c, d, 2012a, b, 2013a, b, 2014a, b; Filatova et al. 2008), that valuation of WACC in the Modigliani–Miller theory (Мodigliani and Мiller 1958, 1963, 1966) is not minimal and valuation of the company capitalization is not maximal, as all financiers supposed up to now: at some age of the company its WACC value turns out to be lower, than in Modigliani–Miller theory and company capitalization V turns out to be greater, than V in Modigliani–Miller theory (Мodigliani and Мiller 1958, 1963, 1966). Thus, existing up to the present presentations concerning the results of the Modigliani–Miller theory in this aspect (Myers 2001) turn out to be incorrect. It is shown that from the point of view of cost of attracting capital there are two types of dependences of weighted average cost of capital, WACC, on the time of life of company n: monotonic descending with n and descending with passage through minimum, followed by a limited growth (there is a third modification of dependences

27.7

“A Golden Age” of the Company

627

WACC(n), k0=0.2 19.2000% 19.0000% 18.8000%

WACC

18.6000% 18.4000%

Kd=0,18

18.2000%

Kd=0,15

18.0000%

Kd=0,10

17.8000%

Kd=0,08

17.6000% 17.4000% 17.2000%

0

5

10

15

20

n

25

30

35

40

45

Fig. 27.20 Dependence of weighted average cost of capital, WACC, on lifetime of the company n at fixed value of equity cost, k0 = 20%, and at four values of debt cost, kd = 8%; 10%; 15% and 18% at leverage level L = 1

WACC(n), which leaves all conclusions valid). The first type takes place for the companies with low-cost capital, characteristic of western companies. The second type takes place for higher costs capital costs of the company, characteristic for Russian companies as well as for companies from other developing countries. This means that latter companies, in contrast to the western ones, can take advantage of the benefits, given at a certain stage of development of company by discovered effect. (For example, the capitalization of Russian oil company “Rosneft,” which has been valued in 2014 by the Modigliani–Miller method, could be higher, accounting for the discovered effect and BFO theory). Moreover, since the “golden age” of company depends on the company’s capital costs, by controlling them (for example, by modifying the value of dividend payments, that reflect the equity cost), company may extend the “golden age” of the company, when the cost to attract capital becomes a minimal (less than perpetuity limit), and capitalization of companies becomes maximal (above than perpetuity assessment) up to a specified time interval. It is important to note that “golden age” of company effect changes the dependence of WACC on L: the curve WACC(L) for perpetuity company turns out to be not lowest for company with this effect—as it is seen from Tables 27.7, 27.8 and Fig. 27.21 below the curve WACC(L) for 3 years company lies below the perpetuity curve.

628

27

New Meaningful Effects in Modern Capital Structure Theory

Table 27.7 Dependence of WACC and ke on leverage level for n = 1, and n = 1 L 0 1 2 3 4 5 6 7 8 9 10

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 1 1 1 1 1 1 1 1 1 1 1

wd 0.00 0.50 0.67 0.75 0.80 0.83 0.86 0.88 0.89 0.90 0.91

WACC 20.00% 18.43% 17.91% 17.65% 17.50% 17.39% 17.32% 17.26% 17.22% 17.18% 17.15%

BFO 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

ke 0.2000 0.2487 0.2974 0.3461 0.3948 0.4435 0.4922 0.5409 0.5896 0.6383 0.6870

WACC MM 20.00% 18.00% 17.33% 17.00% 16.80% 16.67% 16.57% 16.50% 16.44% 16.40% 16.36%

MM ke 0.2000 0.2400 0.2800 0.3200 0.3600 0.4000 0.4400 0.4800 0.5200 0.5600 0.6000

Table 27.8 Dependence of WACC and ke on leverage level for n = 3, and n = 1 L 0 1 2 3 4 5 6 7 8 9 10

27.8

k0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0,2

kd 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0,15

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0,2

n 3 3 3 3 3 3 3 3 3 3 3

wd 0.00 0.50 0.67 0.75 0.80 0.83 0.86 0.88 0.89 0.90 0,91

WACC 20.00% 17.80% 17.06% 16.69% 16.47% 16.32% 16.22% 16.14% 16.08% 16.03% 15,99%

BFO 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0,000

ke 0.2000 0.2360 0.2719 0.3078 0.3436 0.3795 0.4153 0.4511 0.4869 0.5228 0,5586

WACC MM 20.00% 18.00% 17.33% 17.00% 16.80% 16.67% 16.57% 16.50% 16.44% 16.40% 16,36%

MM ke 0.2000 0.2400 0.2800 0.3200 0.3600 0.4000 0.4400 0.4800 0.5200 0.5600 0,6000

Inflation in MM and BFO Theories

Here we describe the influence of inflation on capital cost and capitalization of the company within modern theory of capital cost and capital structure—Brusov– Filatova–Orekhova theory (BFO theory) (Brusov et al. 2011a, b, c, d, 2012a, b, 2013a, b, 2014a, b; Filatova et al. 2008) and within its perpetuity limit—Modigliani– Miller theory (Мodigliani and Мiller 1958, 1963, 1966). By direct incorporation of inflation into both theories, Brusov–Filatova–Orekhova have shown for the first time, that inflation not only increases the equity cost and the weighted average cost of capital, but as well it changes their dependence on leverage. In particular, it increases the growing rate of equity cost with leverage. Capitalization of the company is decreased under accounting of inflation. Under accounting of inflation all original MM (Modigliani–Miller) statements have been modified as it is done below. 2nd original MM statement:

27.8

Inflation in MM and BFO Theories

629

21.00% 20.00% 19.00% WACC

n=1 ko=0,2 kd=0,15

18.00%

n=3 ko=0,2 kd=0,15 MM ko=0,2 kd=0,15

17.00% 16.00% 15.00%

0

1

2

3

4

5

6

7

8

9

10

Fig. 27.21 The curve WACC(L ) for perpetuity company turns out to be not lowest for company with the effect of “golden age”: the curve WACC(L) for 3 years company lies below the perpetuity curve

equity cost of leverage company ke could be found as equity cost of financially independent company k0 of the same group of risk, plus premium for risk, which value is equal to production of difference (k0 - kd) on leverage level L. 2nd modified MM–BFO statement: under existing of inflation with rate α equity cost of leverage company ke could be found as equity cost of financially independent company k0 of the same group of risk, multiplied by (1 + α), plus inflation rate α and plus premium for risk, which value is equal to production of difference (k0 - kd) on leverage level L and on multiplier (1 + α). 4th original MM statement: equity cost of leverage company ke paying tax on profit could be found as equity cost of financially independent company k0 of the same group of risk, plus premium for risk, which value is equal to production of difference (k0 - kd) on leverage level L and on tax shield (1 – T) and on multiplier (1 + α). 4th modified MM–BFO statement: equity cost of leverage company ke paying tax on profit under existing of inflation with rate α could be found as equity cost of financially independent company k0 of the same group of risk, multiplied by (1 + α), plus inflation rate α and plus premium for risk, which value is equal to production of difference (k0 - kd) on leverage level L, on tax shield (1 - T) and on multiplier (1 + α) (Fig. 27.22). We generalized a very important Brusov–Filatova–Orekhova theorem under accounting of inflation.

630

27

New Meaningful Effects in Modern Capital Structure Theory

Fig. 27.22 Dependence of the equity cost and the weighted average cost of capital on leverage in the Modigliani–Miller theory with taxing under accounting of inflation. It is seen that growing rate of equity cost increases with leverage. Axis y means capital costs –C.C

Generalized Brusov–Filatova–Orekhova Theorem Under accounting of inflation without corporate taxing the equity cost k 0 , as well as the weighted average cost of capital WACC do not depend on company lifetime and are equal to
k e = k0 þ L k 0 - k d = k0 ð1 þ αÞ þ α þ Lðk 0- kd Þð1 þ αÞ and WACC = k 0 = k 0 ð1 þ αÞ þ α:

ð27:3Þ

consequently. It is shown that inflation not only increases the equity cost and the weighted average cost of capital, but as well it changes their dependence on leverage. In particular, it increases growing rate of equity cost with leverage. Capitalization of the company is decreased under accounting of inflation. Within modern theory of capital cost and capital structure—Brusov–Filatova– Orekhova theory (BFO theory) the modified equation for the weighted average cost of capital, WACC, applicable to companies with arbitrary lifetime under accounting

27.9

Effects, Connected with Tax Shields, Taxes and Leverage

631

of inflation has been derived. Modified BFO equation allow to investigate the dependence of the weighted average cost of capital, WACC, and equity cost, ke, on leverage level L, on tax on profit rate t, on lifetime of the company n, on equity cost of financially independent company, k0, and debt cost, kd, as well as on inflation rate α. Using modified BFO equation the analysis of the dependence of the weighted average cost of capital, WACC, on debt ratio, wd, at different tax on profit rate t, as well as inflation rate α has been done. It has been shown that WACC decreases with debt ratio, wd, faster at bigger tax on profit rate t. The space between lines, corresponding to different values of tax on profit rate at the same step (10%), increases with inflation rate α. The variation region (with change of tax on profit rate t) of the weighted average cost of capital, WACC, increases with inflation rate α, as well as with lifetime of the company n.

27.9

Effects, Connected with Tax Shields, Taxes and Leverage

The role of tax shields, taxes and leverage is investigated within the theory of Modigliani–Miller as well as within the modern theory of corporate finance by Brusov–Filatova–Orekhova (Brusov et al. 2011a, b, c, d, 2012a, b, 2013a, b, 2014a, b, Filatova et al. 2008). It is shown that equity cost of the company as well as weighted average cost of capital decrease with the growth of tax on profits rates. A detailed study of the dependence of weighted average cost of capital WACC and equity cost of the company ke on tax on profits rates at fixed leverage level (fixed debt capital fraction wd) as well as on leverage level (debt capital fraction wd) at fixed tax on profits rate has been done. The dependences of weighted average cost of capital WACC and equity cost of the company ke on company lifetime have been investigated as well. The concept “tax operating lever” has been introduced. For companies with finite lifetime a number of important qualitative effects that do not have analogues for perpetuity companies has been detected. One such effect—decreasing of equity cost with leverage level at values of tax on profits rate T, which exceeds some critical value T*—is described in detail in Chap. 11 (at certain ratios between the debt cost and equity capital discovered effect takes place at tax on profits rate, existing in the western countries and in Russia, that provides practical value effect.) Its accounting is important in improving tax legislation and may change dividend policy of the company.

632

27.10

27

New Meaningful Effects in Modern Capital Structure Theory

Effects, Connected with the Influence of Tax on Profit Rate on Effectiveness of Investment Projects

BFO authors have conducted the analysis of effectiveness of investment projects within the perpetuity (Modigliani–Miller) approximation (Мodigliani and Мiller 1958, 1963, 1966) as well as within BFO theory. They analyzed the effectiveness of investment projects for three cases: 1. At a constant difference between equity cost (at L = 0) and debt cost Δk = k0 - kd 2. At a constant equity cost (at L = 0) and varying debt cost kd 3. At a constant debt cost kd and varying equity cost (at L = 0) k0. The dependence of NPV on investment value and/or equity value will be also analyzed. The results have been represented in the form of tables and graphs. It should be noted that the obtained tables have played an important practical role in determining of the optimal, or acceptable debt level, at which the project remains effective. The optimal debt level there is for the situation, when in the dependence of NPV on leverage level L there is an optimum (leverage level value, at which NPV reaches a maximum value). An acceptable debt level there is for the situation, when NPV decreases with leverage. And, finally, it is possible that NPV is growing with leverage. In this case, an increase in borrowing leads to increased effectiveness of investment projects, and their limit is determined by financial sustainability of investing company.

27.11

Influence of Growth of Tax on Profit Rate

Within modern theory of capital cost and capital structure by Brusov–Filatova– Orekhova (BFO theory) (Brusov et al. 2011a, b, c, d, 2012a, b, 2013a, b, 2014a, b; Filatova et al. 2008) and created within this theory modern investment models influence of growth of tax on profit rate on the efficiency of the investment is investigated. It has been shown that for long-term investment projects, as well as for arbitrary duration projects the growth of tax on profit rate change the nature of the NPV dependence on leverage at some value t*: there is a transition from diminishing function NPV(L) when t < t* to growing function NPV(L). The t* value depends on the duration of the project, cost of capital (equity and debt) values and other parameters of the project. At high leverage levels this leads to qualitatively new effect in investments: growth of the efficiency of the investments with growth of tax on profit rate. Discovered effects take place under consideration from the point of view of owners of equity capital as well as from the point of view of owners of equity and debt capital (Tables 27.9, 27.10, and 27.11).

27.11

Influence of Growth of Tax on Profit Rate

633

Table 27.9 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 5-year project at t = 0.3 L 0 1 2 3 4 5 6 7 8 9 10

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3

n 5 5 5 5 5 5 5 5 5 5 5

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.197488 0.214367 0.231082 0.24773 0.264343 0.280937 0.297518 0.314091 0.330658 0.34722

NPV 751.22 756.14 719.28 674.51 628.39 582.93 538.90 496.60 456.10 417.41 380.49

ΔNPV 4.922709 -36.8599 -44.7663 -46.126 -45.4549 -44.027 -42.3084 -40.4978 -38.6879 -36.9239

Table 27.10 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 5-year project at t = 0.4 L 0 1 2 3 4 5 6 7 8 9 10

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4

n 5 5 5 5 5 5 5 5 5 5 5

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.189578 0.19803 0.206172 0.214184 0.22213 0.230037 0.23792 0.245786 0.253642 0.261488

NPV 501.04 565.18 569.91 560.40 545.62 528.52 510.35 491.73 472.98 454.30 435.81

ΔNPV 64.13345 4.73089 -9.5017 -14.7815 -17.1025 -18.1709 -18.6246 -18.7461 -18.6762 -18.4911

Table 27.11 Dependence of NPV and ΔNPV on leverage level L at fixed levels of tax on profit rates t for 5-year project at t = 0.5 L 0 1 2 3 4 5 6 7 8 9 10

k0 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

wd 0 0.5 0.66667 0.75 0.8 0.83333 0.85714 0.875 0.88889 0.9 0.90909

t 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

n 5 5 5 5 5 5 5 5 5 5 5

NOI 800 800 800 800 800 800 800 800 800 800 800

ke 0.18 0.181448 0.181065 0.180162 0.179041 0.177806 0.176505 0.175162 0.173792 0.172401 0.170996

NPV 250.87 366.94 408.07 430.65 445.84 457.37 466.82 474.98 482.28 488.99 495.28

ΔNPV 116.0669 41.1323 22.57738 15.19888 11.52994 9.446706 8.154973 7.302458 6.713275 6.291579

634

27

New Meaningful Effects in Modern Capital Structure Theory

Fig. 27.23 Dependence of NPV on leverage level L at fixed levels of tax on profit rates t for 5-year project

Fig. 27.24 Dependence of NPV on tax on profit rate t at fixed leverage level L for 10-year project

One can see from Figs. 27.23 and 27.24 that the nature of the NPV dependence on leverage at t* = 0.5: there is a transition from diminishing function NPV(L) when t < t* to growing function NPV(L) at t > t*. Within modern theory of capital cost and capital structure by Brusov–Filatova– Orekhova (BFO theory) and created within this theory modern investment models influence of growth of tax on profit rate on the efficiency of the investment is investigated. It has been shown that for arbitrary duration projects as well as for perpetuity projects the growth of tax on profit rate change the nature of the NPV dependence on leverage at some value t*: there is a transition from diminishing function NPV(L) when t < t* to growing function NPV(L). The t* value depends on

27.12

New Approach to Ratings

635

the duration of the project, cost of capital (equity and debt) values and other parameters of the project. At high leverage levels, this leads to qualitatively new effect in investments: growth of the efficiency of the investments with growth of tax on profit rate. Discovered effects take place under consideration from the point of view of owners of equity capital as well as from the point of view of owners of equity and debt capital. The observed at high leverage levels (starting from L = 6) increase of NPV with growth of the tax on profit rate t (Fig. 27.24) takes place at all values of t, which means that this is an entirely new effect in investments which can be applied in a real economic practice for optimizing of the management of investments. So, two very important qualitatively new effects in investments has been discovered: 1. Change the character of NPV dependence on leverage 2. Growth of the efficiency of the investments with growth of tax on profit rate Both effects could be used in practice to optimize the investments.

27.12

New Approach to Ratings

The first paper of this Special issue is devoted to application of the perpetuity limit of BFO theory (MM theory) to rating methodology: for the first time we will incorporate the main parameters of ratings—rating “ratios”—directly into modern capital structure theory. This allows to use the powerful methods and “toolkit” of this theory in rating and creates practically the new basis of a rating methodology, that allows making more correct ratings. A new approach to rating methodology has been suggested, key factors of which are: (1) The adequate use of discounting of financial flows virtually not used in existing rating methodologies, (2) The incorporation of rating parameters (financial “ratios”) into the modern theory of capital structure (BFO theory) (Brusov et al. 2015) (for beginning into its perpetuity limit). This, on the one hand, allows the use of the powerful tools of this theory in the rating, and on the other hand, it ensures the correct discount rates when discounting of financial flows. We discuss also the interplay between rating ratios and leverage level which can be quite important in rating. All these create a new base for rating methodologies. In conclusion remind again that the introduction of the new system of evaluation of the parameters of financial activities of companies into the systems of financial reporting (IFRS, GAAP, etc.) would lead to lower risk of global financial crisis.

636

27

New Meaningful Effects in Modern Capital Structure Theory

References Brusov P, Filatova T, Orehova N, Brusova A (2011a) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Appl Financ Econ 21(11): 815–824 Brusov P, Filatova T, Orehova N, Brusov PP, Brusova N (2011b) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Bus ICT 2:16–21 Brusov P, Filatova T, Orehova N et al (2011c) Influence of debt financing on the effectiveness of the investment project within the Modigliani–Miller theory. Res J Econ Bus ICT (UK) 2:11–15 Brusov PN, Filatova ТV et al (2011d) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Finance Credit 435:2–8 Brusov P, Filatova T, Eskindarov M, Orehova N (2012a) Influence of debt financing on the effectiveness of the finite duration investment project. Appl Financ Econ 22(13):1043–1052 Brusov P, Filatova T, Eskindarov M, Orehova N (2012b) Hidden global causes of the global financial crisis. J Rev Glob Econ 1:106–111 Brusov P, Filatova P, Orekhova N (2013a) Absence of an optimal capital structure in the famous tradeoff theory! J Rev Glob Econ 2:94–116 Brusov P, Filatova T, Orehova N (2013b) A qualitatively new effect in corporative finance: abnormal dependence of cost of equity of company on leverage. J Rev Glob Econ 2:183–193 Brusov P, Filatova P, Orekhova N (2014a) Mechanism of formation of the company optimal capital structure, different from suggested by trade off theory. Cogent Econ Finance 2:1–13. https://doi. org/10.1080/23322039.2014.946150 Brusov P, Filatova T, Orehova N (2014b) Inflation in Brusov–Filatova–Orekhova theory and in its perpetuity limit – Modigliani–Miller theory. J Rev Glob Econ 3:175–185 Brusov P, Filatova T, Orehova N, Eskindarov M (2015) Modern corporate finance, investment and taxation. Springer, New York, p 368 Brusova A (2011) А comparison of the three methods of estimation of weighted average cost of capital and equity cost of company. Financ Anal Probl Solutions 34(76):36–42 Filatova Т, Orehova N, Brusova А (2008) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Bull FU 48:68–77 Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Мodigliani F, Miller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391 Myers S (2001) Capital structure. J Econ Perspect 15(2):81–102

Part III

Ratings and Rating Methodologies of Non-financial Issuers

Chapter 28

Rating: New Approach

Keywords Brusov–Filatova–Orekhova theory · Modigliani–Miller theory · Ratings · Discounting of financial flows · Financial “ratios”

28.1

Introduction

In this chapter, a new approach to rating methodology is suggested. Chapters 28–30 are devoted to rating of non-financial issuers, while Chaps. 31 and 32 are devoted to investment project rating (Brusov et al. 2021). The key factors of a new approach are: (1) The adequate use of discounting of financial flows virtually not used in existing rating methodologies, (2) The incorporation of rating parameters (financial “ratios”) into the modern theory of capital structure (Brusov–Filatova–Orekhova (BFO) theory) (Brusov et al. 2015) in Chap. 29 (in this Chapter and in Chap. 30 into its perpetuity limit). This, on the one hand, allows to use the powerful tools of this theory in the rating and, on the other hand, it ensures the correct discount rates when discounting of financial flows. We discuss also the interplay between rating ratios and leverage level which can be quite important in rating. All these create a new base for rating methodologies. New approach to ratings and rating methodologies allows to issue more correct ratings of issuers and makes the rating methodologies more understandable and transparent. Rating agencies play a very important role in economics. Their analysis of issuer’s state, generated credit ratings of issuers, helps investors to make reasonable investment decision, as well as helps issuers with good enough ratings to get credits on lower rates, etc. But from time to time we listen about scandals involved rating agencies and their credit ratings: let us just remind the situation with sovereign rating of the USA in 2011 and of the Russia in 2015. Were these ratings an objective? And how objective could be issued credit ratings in principal? To answer this question, we need to understand how rating agencies (RA) consider, evaluate, analyze. But this is the secret behind the seven seals: rating agencies stand to the death, but did not reveal their secrets, even under the threat of multibillion–dollar sanctions. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_28

639

640

28 Rating: New Approach

Thus, rating agencies represent some “black boxes,” about which information on the methods of work is almost completely absent.

28.2

The Closeness of the Rating Agencies

The closeness of the rating agencies is caused by multiple causes: 1. The desire to preserve their “know-how.” Rating agencies get big enough money for generated ratings (mostly from issuers) to replicate its methodology. 2. On the other hand, closeness of rating agencies is caused by the desire to avoid public discussion of the ratings with anyone, including the issuer. It is very convenient position—rating agency “a priori” removes himself from beneath any criticism of generated ratings. 3. The absence of any external control and external analysis of the methodologies is resulted in the fact that shortcomings of methodologies are not subjected to serious critical analysis and stored long enough. The illustration of the closeness of rating agencies is the behavior of the S&P (Standard & Poor’s) Director after declining of the sovereign rating of the USA, who left his position but has not opened the methodology used. But even in this situation, it is still possible some analysis of the activities and findings of the rating agencies, based on knowledge and understanding of the existing methods of evaluation. Rating agencies cannot use methods other than developed up to now by leading economists and financiers.

28.3

The Use of Discounting in the Rating

One of the major flaws of all existing rating methodologies is a failure or a very narrow use of discounting. But even in those rare cases where it is used, it is not quite correct, since the discount rate when discounting financial flows is chosen incorrectly. The need to take into account the time factor in terms of discounting is obvious, because it is associated with the time value of money. The financial part of the rating is based on a comparison of generated income with the value of the debt and the interest payable. Because income and disbursement of debt and interest are separated in time, the use of discounting when comparing revenues with the value of debt and interest is absolutely necessary for assigning credit ratings for issuers. This raises the question about the value of discount rate. This question has always been one of the major and extremely difficult in many areas of Finance: corporate finance, investment, it is particularly important in business valuation, where a slight change in the discount rate leads to a significant change in the assessment of company capitalization, that is used by unscrupulous appraisers for artificial bankruptcy of the company. And the value of discount rate is extremely essential as well in rating.

28.4

28.4

Incorporation of Parameters, Using in Ratings, into Perpetuity Limit. . .

641

Incorporation of Parameters, Using in Ratings, into Perpetuity Limit of Modern Theory of Capital Structure by Brusov–Filatova–Orekhova

In quantification of the creditworthiness of the issuers the crucial role belongs to the so-called financial “ratios,” which constitute a direct and inverse ratios of various generated cash flows to debt values and interest ones. We could mention such ratios as DCF/Debt, FFO/Debt, CFO/Debt, FOCF/Debt, FFO/cash interest, EBITDA/interest, Interests/EBITDA, Debt/EBITDA, and some others. We incorporate these rating parameters (financial “ratios”) into the modern theory of capital structure—BFO theory (Brusov & Filatova 2011, Brusov et al. 2011a, b, c, d, 2012, 2013a, b, 2014a, b, 2018a, b, c; Filatova et al. 2008) (for beginning into its perpetuity limit) (Brusov et al. 2018d). The importance of such incorporation, which has been done by us for the first time, is in using this theory as a powerful tool when discounting of financial flows using the correct discounting rate in rating. Only this theory allows to valuate adequately the weighted average cost of capital WACC and equity cost of capital ke used when discounting of financial flows. Use of the tools of well-developed theories in rating opens completely new horizons in the rating industry, which could go from the mainly use of qualitative methods of the evaluation of the creditworthiness of issuers to a predominantly quantitative evaluation methods that will certainly enhance the quality and correctness of the rating. Currently, rating agencies just directly use financial ratios, while the new methodology will allow (knowing the values of these “relations” (and parameter k0)) to determine the correct values of discount rates (WACC and ke) that should be used when discounting the various financial flows, both in terms of their timing and forecasting. This has required the modification of the BFO theory (and its perpetuity limit— Modigliani—Miller theory), as used in financial management the concept of “leverage” as the ratio of debt value to the equity value substantially differs from the concept of “leverage” in the rating, where it is understood as the direct and inverse ratio of the debt value to the generated cash flow values (income, profit, etc.). The authors introduced some additional ratios, allowing full characterization of the issuer’s ability to repay debts and to pay interest thereon. Thus, the bridge is building between the discount rates (WACC, ke) used when discounting of financial flows and the “ratios” in the rating methodology. The algorithm for finding the discount rates for given ratio values is developed.

642

28.5

28 Rating: New Approach

Models

Two kinds of models of the evaluation of the creditworthiness of issuers, accounting the discounting of financial flows could be used in rating: one-period model and multi-period model.

28.5.1

One-Period Model

One-period model is described by the following formula (see Fig. 28.1) CFð1 þ iÞt2 - t ≥ D þ k d Dð1 þ iÞt2 - t1
 CFð1 þ iÞt2 - t ≥ D 1 þ kd ð1 þ iÞt2 - t1

ð28:1Þ

Here, CF is the value of income for period, D is the debt value, t, t1, t2 the moments of income, payment of interest, and payment of debt consequently, i is the discount rate, kd is the credit rate, and kdD is the interest on credit.

28.5.2

Multi-Period Model

One-period model of the evaluation of the creditworthiness of issuers, accounting the discounting of financial flows could be generalized for more interesting multiperiod case. Multi-period model is described by the following formula: X  t - t X h  t - t i CFj 1 þ ij 2j j ≥ Dj 1 þ kdj 1 þ ij 2j 1j j

ð28:2Þ

j

Here, CFj is the income for j-st period, Dj is the debt value in j-st period, tj, t1j, t2j the moments of income, payment of interest, and payment of debt consequently in j-st period, ij is the discount rate in j-st period, kdj is the credit rate in j-st period. There are several options to work with these models: 1. One can check the creditworthiness of the issuer, knowing parameters CFj, Dj, tj, t1j, t2j, kdj and defining discount rate i by the method described below.

Fig. 28.1 One-period model

CF

t

kd D

t

1

D

t

2

28.6

Theory of Incorporation of Parameters, Using in Ratings, into. . .

643

2. When the preset Dj, tj, t1j, t2j, kdj, one can determine which income CFj the issuer would require to ensure its creditworthiness. 3. When the preset Dj, tj, t1j, t2j, kdj, one can define an acceptable level of debt financing (including the credit value Dj and credit rates kdj) when issuer retains its creditworthiness.

28.6

Theory of Incorporation of Parameters, Using in Ratings, into Perpetuity Limit of Modern Theory of Capital Structure by Brusov–Filatova–Orekhova

For the first time we incorporate the below parameters, using in ratings, into perpetuity limit of modern theory of capital structure by Brusov–Filatova–Orekhova (BFO) theory. We’ll consider two kinds of ratios: coverage ratios and leverage ratios. Let us start with the coverage ratios.

28.6.1

Coverage Ratios

We will consider three kinds of coverage ratios: coverage ratios of debt, coverage ratios of interest on the credit, and coverage ratios of debt and interest on the credit.

28.6.1.1

Coverage Ratios of Debt

Here

i1 = CF=D

ð28:3Þ

Modigliani–Miller theorem for case with corporate taxes (Мodigliani and Мiller 1958, 1963, 1966) tells us that capitalization of leveraged company, VL, is equal to the capitalization of unleveraged company, V0, plus tax shield for perpetuity time, Dt, V L = V 0 þ Dt: Substituting the expressions for both capitalizations, one has CF CF þ Dt = WACC k0 Dividing both parts by D one gets

ð28:4Þ

644

28 Rating: New Approach

i i1 = 1 þt WACC k0 i k WACC = 1 0 i1 þ tk 0

ð28:5Þ

This ratio (i1) can be used to assess of the following parameters used in rating, DCF/Debt, FFO/Debt, CFO/Debt, FOCF/Debt, and some others. We will use the last formula to build a curve of dependence WACC(i1).

28.6.1.2

Coverage Ratios of Interest on the Credit

Here

i2 = CF=kd D

ð28:6Þ

Using the Modigliani–Miller theorem for case with corporate taxes V L = V 0 þ Dt, we derive the expression for WACC(i2) CF CF þ Dt = WACC k0 i i2 i = 2þ 2 WACC k0 k d i k k WACC = 2 0 d i2 kd þ tk 0

ð28:7Þ

This ratio (i2) can be used to assess the following parameters, used in rating, FFO/cashinterest, EBITDA/interest, and some others. We will use the last formula to build a curve of dependence WACC(i2).

28.6.1.3

Coverage Ratios of Debt and Interest on the Credit (New Ratios)

Let us consider the coverage ratios of debt and interest on the credit simultaneously: this is new ratio, introduced by us for the first time here. Here i3 =

CF D ð1 þ k d Þ

ð28:8Þ

Using as above the Modigliani–Miller theorem for case with corporate taxes

28.6

Theory of Incorporation of Parameters, Using in Ratings, into. . .

645

V L = V 0 þ Dt one gets the expression for WACC(i3) CF CF þ Dt = WACC k0 i i3 t = 3þ WACC k0 1 þ k d i k ð1 þ k d Þ WACC = 3 0 i3 ð1 þ kd Þ þ tk 0

ð28:9Þ

This ratio (i3) can be used to assess the following parameters used in rating, FFO/Debt + interest, EBITDA/Debt + interest, and some others. We will use the last formula to build a curve of dependence WACC(i3). Let us analyze the dependence of company’s weighted average cost of capital (WACC) on the coverage ratios on debt i1, on interest on the credit i2, and on coverage ratios on debt and interest on the credit with the following data: k0 = 12%; kd = 6%; t = 20%; ij run from 0 up to 10. The dependence of company’s weighted average cost of capital (WACC) on the coverage ratio on interest on the credit i2 is presented in Fig. 28.3. The dependence of company’s weighted average cost of capital (WACC) on the coverage ratio on debt and interest on the credit i2 is presented in Fig. 28.4. The dependence of company’s weighted average cost of capital (WACC) on the coverage ratio on debt i1, on interest on the credit i2, and on debt and interest on the credit i3 is presented in Fig. 28.5. It is seen from Figs. 28.2, 28.3, 28.4, and 28.5 that WACC(ij) is increasing function on ij with saturation around ij value of order 1 for ratios i1 and i3 and of order 4 or 5 for ratio i2. At saturation WACC reaches the value k0 (equity value at

WACC

WACC(i1) 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0

2

4

6

8

10

12

i1 Fig. 28.2 The dependence of company’s weighted average cost of capital (WACC) on the coverage ratio on debt i1

646

28 Rating: New Approach

WACC

WACC(i2) 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0

2

4

6

8

10

12

i2

WACC

Fig. 28.3 The dependence of company’s weighted average cost of capital (WACC) on the coverage ratio on interest on the credit i2

WACC(i3)

0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0

2

4

6

8

10

12

i3 Fig. 28.4 The dependence of company’s weighted average cost of capital (WACC) on the coverage ratio on debt and interest on the credit i3

zero leverage level). This means that for high values of ij one can choose k0 as a discount rate with a good accuracy. Thus, the role of parameter k0 increases drastically. The method of determination of parameter k0 has been developed by Anastasiya Brusova (2011). So, parameter k0 is the discount rate for limit case of high values of ij (see, however, below for more detailed consideration). It is clear from Figs. 28.2, 28.3, 28.4, and 28.5 that case of low values of ij requires more detailed consideration. Let us consider the situation with low values of ij which seems to be the case of the most interest.

28.6

Theory of Incorporation of Parameters, Using in Ratings, into. . .

647

WACC(i) 0.14 0.12 0.1

WACC

0.08 0.06 0.04 0.02 0

0

2

4

6

8

10

12

I WACC 1

WACC 2

WACC 3

Fig. 28.5 The dependence of company’s weighted average cost of capital (WACC) on the coverage ratio on debt i1, on interest on the credit i2, and on debt and interest on the credit i3

28.6.2

More Detailed Consideration

Below we consider the case of low values of ij with more details. ij will vary from zero up to 1 with all other parameters to be the same (Figs. 28.6, 28.7, 28.8 and 28.9).

More detailed consideration leads us to the following conclusions: 1. In case of coverage ratio on debt and interest on the credit i3, WACC goes to saturation very fast: with accuracy of 20% at i3 = 0.15 and with accuracy of 5% at i3 = 0.5. 2. In case of coverage ratio on debt i1, WACC practically linearly increases with parameter i1 and goes to saturation at i1 = 0.1. 3. In case of coverage ratio on interest on the credit i2, WACC increases with parameter i2 much more slowly than in two previous cases and goes to saturation at high values of i2: with accuracy of 10% at i2 = 4.

648

28 Rating: New Approach

WACC(i1) 0.1400 0.1200 0.1000 0.0800 WACC(i1)

0.0600 0.0400 0.0200 0.0000 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

Fig. 28.6 The dependence of company’s weighted average cost of capital (WACC) on the coverage ratio on debt and interest on the credit i1

WACC(i2) 0.0900 0.0800 0.0700 0.0600 0.0500 WACC(i2)

0.0400 0.0300 0.0200 0.0100 0.0000 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

Fig. 28.7 The dependence of company’s weighted average cost of capital (WACC) on the coverage ratio on debt and interest on the credit i2

28.6

Theory of Incorporation of Parameters, Using in Ratings, into. . .

649

WACC(i3) 0.1400 0.1200 0.1000 0.0800 WACC(i3)

0.0600 0.0400 0.0200 0.0000 0

0.1 0.2 0.3 0.4

0.5

0.6 0.7 0.8 0.9

1

Fig. 28.8 The dependence of company’s weighted average cost of capital (WACC) on the coverage ratio on debt and interest on the credit i3

0.1400 0.1200 0.1000 0.0800

WACC(i1) WACC(i2)

0.0600

WACC(i3)

0.0400 0.0200 0.0000

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Fig. 28.9 The dependence of company’s weighted average cost of capital (WACC) on the coverage ratio on debt i1, on interest on the credit i2, and on debt and interest on the credit i3

650

28.6.3

28 Rating: New Approach

Leverage Ratios

Let us consider now the leverage ratios. We will consider three kinds of leverage ratios: leverage ratios of debt, leverage ratios of interest on the credit, and leverage ratios of debt and interest on the credit.

28.6.3.1

Leverage Ratios for Debt

Here,

l1 = D=CF

ð28:10Þ

As above for coverage ratios we use the Modigliani–Miller theorem for case with corporate taxes V L = V 0 þ Dt, we derive the expression for WACC(l1) CF CF þ Dt = WACC k0 1 1 = þ l1 t WACC k0 k0 WACC = 1 þ tl1 k0

ð28:11Þ

This ratio (l1) can be used to assess the following parameters used in rating, Debt/ EBITDA and some others. We will use the last formula to build a curve of dependence WACC(l1).

28.6.3.2

Leverage Ratios for Interest on Credit Here l2 = kd D=CF

ð28:12Þ

We use again the Modigliani–Miller theorem for case with corporate taxes V L = V 0 þ Dt, we derive the expression for WACC(l2)

28.6

Theory of Incorporation of Parameters, Using in Ratings, into. . .

CF CF þ Dt = WACC k0 1 1 l t = þ 2 WACC k0 kd k0 kd WACC = kd þ tl2 k0

651

ð28:13Þ

This ratio (l2) can be used to assess the following parameters used in rating, Interests/EBITDA and some others. We will use the last formula to build a curve of dependence WACC(l2).

28.6.3.3

Leverage Ratios for Debt and Interest on Credit

Here

l3 = Dð1 þ k d Þ=CF

ð28:14Þ

Using the Modigliani–Miller theorem for case with corporate taxes V L = V 0 þ Dt, we derive the expression for WACC(l3) CF CF þ Dt = WACC k0 l t 1 1 = þ 3 WACC k0 1 þ k d k 0 ð1 þ k d Þ WACC = 1 þ k d þ tl3 k0

ð28:15Þ

This ratio (l3) can be used to assess the following parameters used in rating, Debt + interest/FFO, Debt + interest/EBIT, Debt + interest/EBITDA(R), and some others. We will use the last formula to build a curve of dependence WACC(l3). Let us analyze the dependence of company’s weighted average cost of capital (WACC) on the leverage ratios with the following data: k0 = 12%; kd = 6%; t = 20%; li runs from 0 up to 10. The dependence of company’s weighted average cost of capital (WACC) on the leverage ratio on debt l1 is presented in Fig. 28.10. The dependence of company’s weighted average cost of capital (WACC) on the leverage ratio on interest on credit l2 is presented in Fig. 28.11. The dependence of company’s weighted average cost of capital (WACC) on the leverage ratio on debt and interest on credit l3 is presented in Fig. 28.12.

652

28 Rating: New Approach

WACC

WACC (l1) 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0

0

2

4

6

8

10

12

l1 Fig. 28.10 The dependence of company’s weighted average cost of capital (WACC) on the leverage ratio on debt l1

WACC

WACC (l2) 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0

2

4

6

8

10

12

l2 Fig. 28.11 The dependence of company’s weighted average cost of capital (WACC) on the leverage ratio on interest on credit l2

The dependence of company’s weighted average cost of capital (WACC) on the leverage ratio on debt, l1, on interest on credit, l2, and on debt and interest on credit, l3 simultaneously is presented in Fig. 28.13. Analysis of the dependences of company’s weighted average cost of capital (WACC) on the leverage ratio on debt, l1, on interest on credit, l2, and on debt and interest on credit, l3 shows the following: for all leverage ratios the weighted average cost of capital (WACC) decreases with leverage ratios. For leverage ratio on debt l1 and leverage ratio on debt and interest on credit l3 WACC decreases very similarly and practically linearly from k0 = 12% at l1,3 = 0 up to 9,7% at l1,3 = 10. For leverage ratio on interest on credit l2 WACC decreases nonlinearly and much faster from k0 = 12% at l2 = 0 up to 2,4% at l2 = 10.

28.7

Equity Cost

653

WACC(l3) 0.14 0.12

WACC

0.1 0.08 0.06 0.04 0.02 0

0

2

4

6

8

10

12

l3 Fig. 28.12 The dependence of company’s weighted average cost of capital (WACC) on the leverage ratio on debt and interest on credit l3

WACC (l) 0.14 0.12

WACC

0.1 0.08 0.06 0.04 0.02 0 0

2

4

6

8

10

12

l WACC1

WACC2

WACC3

Fig. 28.13 The dependence of company’s weighted average cost of capital (WACC) on the leverage ratio on debt, l1, on interest on credit, l2, and on debt and on interest on credit, l3 simultaneously

28.7

Equity Cost

Equity cost plays a very important role in economy and finance because it is the essence of the dividend policy of companies, which should be accounted in rating. A modern approach to the dividend policy of companies, based on the real value of their equity capital cost, compared to its efficiency of planned investment is suggested in the article (Brusov et al. 2012a, b). This allows return to the economic essence of dividends, as the payment to shareholders for the use of equity capital.

654

28 Rating: New Approach

Equity cost ke determines the economically reasonable dividend value. Rating agencies will be able to compare payable dividend value with economically reasonable dividend level and make conclusion about the adequacy of the dividend policy of companies and its influence on company’s credit rating. For finding of the dependence of equity cost ke on coverage ratios and leverage ratios we consider consistently the dependence of equity cost ke on ratios i1, i2, i3, l1, l2, l3, using the following formula, which couples weighted average cost of capital WACC (calculated by us above: see Tables 28.1, 28.2, 28.3, 28.4, 28.5, 28.6, 28.7, 28.8, and 28.9) and equity cost ke k e = WACCð1 þ LÞ - Lk d ð1- t Þ:

ð28:16Þ

The Dependence of Equity Cost ke on Coverage Ratios i1, i2, i3 Let us study the dependence of equity cost ke on coverage ratios i1, i2, i3 for the same set of parameters as used above and for leverage levels L = 1 and L = 2 (Tables 28.10, 28.11 and 28.12). Table 28.1 The dependence of company’s weighted average cost of capital (WACC) on the coverage ratio on debt i1

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

i1 0 1 2 3 4 5 6 7 8 9 10

k0 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12

Table 28.2 The dependence of company’s weighted average cost of capital (WACC) on the coverage ratio on debt i2

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

i2 0 1 2 3 4 5 6 7 8 9 10

k0 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12

kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

WACC 0 0.1171875 0.1185771 0.1190476 0.1192843 0.1194268 0.1195219 0.11959 0.1196411 0.1196809 0.1197127

WACC 0 0.085714 0.1 0.105882 0.109091 0.111111 0.1125 0.113514 0.114286 0.114894 0.115385

28.7

Equity Cost

655

Table 28.3 The dependence of company’s weighted average cost of capital (WACC) on the coverage ratio on debt i3

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

i3 0 1 2 3 4 5 6 7 8 9 10

Table 28.4 The dependence of company’s weighted average cost of capital (WACC) on the coverage ratio on debt i1

i1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

k0 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12

Table 28.5 The dependence of company’s weighted average cost of capital (WACC) on the coverage ratio on debt i1

i2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Ko 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12

k0 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12

kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

WACC 0 0.1173432 0.1186567 0.1191011 0.1193246 0.1194591 0.1195489 0.1196131 0.1196613 0.1196989 0.1197289

Kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

WACC(i1) 0.0000 0.0117 0.0234 0.0352 0.0469 0.0586 0.0703 0.0820 0.0938 0.1055 0.1172

Kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

WACC(i2) 0.0000 0.0240 0.0400 0.0514 0.0600 0.0667 0.0720 0.0764 0.0800 0.0831 0.0857

656

28 Rating: New Approach

Table 28.6 The dependence of company’s weighted average cost of capital (WACC) on the coverage ratio on debt i3

i3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Ko 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12

Table 28.7 The dependence of company’s weighted average cost of capital (WACC) on the coverage ratio on debt l1

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

l1 0 1 2 3 4 5 6 7 8 9 10

Table 28.8 The dependence of company’s weighted average cost of capital (WACC) on the coverage ratio on debt l2

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

l2 0 1 2 3 4 5 6 7 8 9 10

Kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

WACC(i3) 0.0000 0.0978 0.1078 0.1116 0.1136 0.1148 0.1156 0.1162 0.1167 0.1171 0.1173

k0 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12

kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

WACC 0.12 0.117188 0.114504 0.11194 0.109489 0.107143 0.104895 0.10274 0.100671 0.098684 0.096774

k0 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12

kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

WACC 0.12 0.085714 0.066667 0.054545 0.046154 0.04 0.035294 0.031579 0.028571 0.026087 0.024

28.7

Equity Cost

657

Table 28.9 The dependence of company’s weighted average cost of capital (WACC) on the coverage ratio on debt l3

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Table 28.10 The dependence of equity cost ke on coverage ratio i1 at leverage level L = 1

L 1 1 1 1 1 1 1 1 1 1 1

i1 0 1 2 3 4 5 6 7 8 9 10

WACC(i1) 0.00000 0.11719 0.11858 0.11905 0.11928 0.11943 0.11952 0.11959 0.11964 0.11968 0.11971

Kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Ke -0.0480 0.1864 0.1892 0.1901 0.1906 0.1909 0.1910 0.1912 0.1913 0.1914 0.1914

Table 28.11 The dependence of equity cost ke on coverage ratio i1 at leverage level L = 2

L 2 2 2 2 2 2 2 2 2 2 2

i1 0 1 2 3 4 5 6 7 8 9 10

WACC(i1) 0.00000 0.11719 0.11858 0.11905 0.11928 0.11943 0.11952 0.11959 0.11964 0.11968 0.11971

Kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Ke -0.0960 0.2556 0.2597 0.2611 0.2619 0.2623 0.2626 0.2628 0.2629 0.2630 0.2631

l3 0 1 2 3 4 5 6 7 8 9 10

k0 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12

kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

WACC 0.12 0.117353 0.114819 0.112393 0.110068 0.107836 0.105693 0.103634 0.101654 0.099747 0.097911

658 Table 28.12 The dependence of equity cost ke on coverage ratio i2 at leverage level L = 1

28 Rating: New Approach L 1 1 1 1 1 1 1 1 1 1 1

i2 0 1 2 3 4 5 6 7 8 9 10

WACC(i2) 0.00000 0.11734 0.11866 0.11910 0.11932 0.11946 0.11955 0.11961 0.11966 0.11970 0.11973

Kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Ke -0.0480 0.1867 0.1893 0.1902 0.1906 0.1909 0.1911 0.1912 0.1913 0.1914 0.1915

1. L = 1 2. L = 2 We could make some conclusions, based on Tables 28.13, 28.14, and 28.15 and Figs. 28.14, 28.15, and 28.16. In all three cases equity cost ke increases with coverage ratios and goes to saturation at high values of coverage ratios. Saturation values increase with leverage level from 19% at L = 1 up to value above 26% at L = 2. Note that for coverage ratios i1 and i2 the saturation takes place at values i1,2 of order unit, while for coverage ratio i3 the saturation takes place at much higher i3 values of order 6 or 7. Equity cost ke should be used as discount rate for unleveraged (financially independent) companies. For coverage ratios i1 and i2 saturation values of equity cost ke could be used as discount rate above unit, while for coverage ratio i3 saturation values of equity cost ke could be used as discount rate at i3 value above 6 or 7. Table 28.13 The dependence of equity cost ke on coverage ratio i2 at leverage level L = 2

L 2 2 2 2 2 2 2 2 2 2 2

i2 0 1 2 3 4 5 6 7 8 9 10

WACC(i2) 0.00000 0.11734 0.11866 0.11910 0.11932 0.11946 0.11955 0.11961 0.11966 0.11970 0.11973

Kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Ke -0.0960 0.2560 0.2600 0.2613 0.2620 0.2624 0.2626 0.2628 0.2630 0.2631 0.2632

28.7

Equity Cost

659

Table 28.14 The dependence of equity cost ke on coverage ratio i3 at leverage level L = 1

L 1 1 1 1 1 1 1 1 1 1 1

i3 0 1 2 3 4 5 6 7 8 9 10

WACC(i3) 0.00000 0.08571 0.10000 0.10588 0.10909 0.11111 0.11250 0.11351 0.11429 0.11489 0.11538

Kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Ke -0.0480 0.1234 0.1520 0.1638 0.1702 0.1742 0.1770 0.1790 0.1806 0.1818 0.1828

Table 28.15 The dependence of equity cost ke on coverage ratio i3 at leverage level L = 2

L 2 2 2 2 2 2 2 2 2 2 2

i3 0 1 2 3 4 5 6 7 8 9 10

WACC(i3) 0.00000 0.08571 0.10000 0.10588 0.10909 0.11111 0.11250 0.11351 0.11429 0.11489 0.11538

Kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Ke -0.0960 0.1611 0.2040 0.2216 0.2313 0.2373 0.2415 0.2445 0.2469 0.2487 0.2502

Ke(i1) 0.3000 0.2500 0.2000 0.1500 0.1000

L=1

0.0500

L=2

0.0000 -0.0500

0

1

2

3

4

5

6

7

8

9

10

-0.1000 -0.1500

Fig. 28.14 The dependence of equity cost ke on coverage ratio i1 at two leverage level values L = 1 and L = 2

660

28 Rating: New Approach

Ke(i2) 0.3000 0.2500 0.2000 0.1500 0.1000

L=1

0.0500

L=2

0.0000 -0.0500

0

1

2

3

4

5

6

7

8

9

10

-0.1000 -0.1500

Fig. 28.15 The dependence of equity cost ke on coverage ratio i2 at two leverage level values L = 1 and L = 2

Ke(i3) 0.3000 0.2500 0.2000 0.1500 0.1000

L=1

0.0500

L=2

0.0000 -0.0500

0

1

2

3

4

5

6

7

8

9

10

-0.1000 -0.1500

Fig. 28.16 The dependence of equity cost ke on coverage ratio i3 at two leverage level values L = 1 and L = 2

The Dependence of Equity Cost ke on Leverage Ratios l1, l2, l3 We study below the dependence of equity cost ke on leverage ratios l1, l2, l3 for the same set of parameters as used above and for leverage levels L = 1 and L = 2.

28.8

How to Evaluate the Discount Rate?

661

The Dependence of Equity Cost ke on Leverage Ratio l1 1. L = 1 (Table 28.16) 2. L = 2 (Table 28.17 and Fig. 28.17) The Dependence of Equity Cost ke on Leverage Ratios l2 1. L = 1 (Table 28.18) 2. L = 2 (Table 28.19 and Fig. 28.18) The Dependence of Equity Cost ke on Leverage Ratios l3 1. L = 1 (Table 28.20) 2. L = 2 (Table 28.21 and Fig. 28.19)

28.8

How to Evaluate the Discount Rate?

Let us discuss now the algorithm of valuation of the discount rate, if we know one or a few ratios (coverage or leverage ones). The above developed method allows to estimate discount rate with the best accuracy characteristic used for theory of capital structure (perpetuity limit).

28.8.1

Using One Ratio

If one knows one ratio (coverage or leverage one), the algorithm of valuation of the discount rate is as follows: Table 28.16 The dependence of equity cost ke on leverage ratio l1 at leverage level L = 1

L 1 1 1 1 1 1 1 1 1 1 1

l1 0 1 2 3 4 5 6 7 8 9 10

WACC(l1) 0.12000 0.11719 0.11450 0.11194 0.10949 0.10714 0.10490 0.10274 0.10067 0.09868 0.09677

Kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Ke 0.1920 0.1864 0.1810 0.1759 0.1710 0.1663 0.1618 0.1575 0.1533 0.1494 0.1455

662

28 Rating: New Approach

Table 28.17 The dependence of equity cost ke on leverage ratio l1 at leverage level L = 2

L 2 2 2 2 2 2 2 2 2 2 2

WACC(l1) 0.12000 0.11719 0.11450 0.11194 0.10949 0.10714 0.10490 0.10274 0.10067 0.09868 0.09677

l1 0 1 2 3 4 5 6 7 8 9 10

Kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Ke 0.2640 0.2556 0.2475 0.2398 0.2325 0.2254 0.2187 0.2122 0.2060 0.2001 0.1943

Ke(l1) 0.3000 0.2500 0.2000 L=1

0.1500

L=2

0.1000 0.0500 0.0000

0

1

2

3

4

5

6

7

8

9

10

Fig. 28.17 The dependence of equity cost ke on leverage ratio l1 at two leverage level values L = 1 and L = 2

– determination of the parameter k0; – knowing k0, kd, and t, one builds the curve of dependence WACC(i) or WACC(l); – then, using the known value of coverage ratio (i0) or leverage ratio (l0) one finds the value WACC(i0) or WACC(l0), which represents the discount rate.

28.8.2

Using a Few Ratios

If we know say m values of coverage ratios (ij) and n values of leverage ratios (lk)

28.8

How to Evaluate the Discount Rate?

Table 28.18 The dependence of equity cost ke on leverage ratio l2 at leverage level L = 1

L 1 1 1 1 1 1 1 1 1 1 1

l2 0 1 2 3 4 5 6 7 8 9 10

Table 28.19 The dependence of equity cost ke on leverage ratio l2 at leverage level L = 2

L 2 2 2 2 2 2 2 2 2 2 2

l2 0 1 2 3 4 5 6 7 8 9 10

663 WACC(l2) 0.12000 0.08571 0.06667 0.05455 0.04615 0.04000 0.03529 0.03158 0.02857 0.02609 0.02400

WACC(l2) 0.12000 0.08571 0.06667 0.05455 0.04615 0.04000 0.03529 0.03158 0.02857 0.02609 0.02400

Kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Ke 0.1920 0.1234 0.0853 0.0611 0.0443 0.0320 0.0226 0.0152 0.0091 0.0042 0.0000

Ke 0.2640 0.1611 0.1040 0.0676 0.0425 0.0240 0.0099 -0.0013 -0.0103 -0.0177 -0.0240

Ke(l2) 0.3000 0.2500 0.2000 0.1500

L=1

0.1000

L=2

0.0500 0.0000 -0.0500

0

1

2

3

4

5

6

7

8

9

10

Fig. 28.18 The dependence of equity cost ke on leverage ratio l2 at two leverage level values L = 1 and L = 2

664

28 Rating: New Approach

Table 28.20 The dependence of equity cost ke on leverage ratio l2 at leverage level L = 1

L 1 1 1 1 1 1 1 1 1 1 1

l3 0 1 2 3 4 5 6 7 8 9 10

WACC(l3) 0.12000 0.11735 0.11482 0.11239 0.11007 0.10784 0.10569 0.10363 0.10165 0.09975 0.09791

Kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Ke 0.1920 0.1867 0.1816 0.1768 0.1721 0.1677 0.1634 0.1593 0.1553 0.1515 0.1478

Table 28.21 The dependence of equity cost ke on leverage ratio l2 at leverage level L = 2

L 2 2 2 2 2 2 2 2 2 2 2

l3 0 1 2 3 4 5 6 7 8 9 10

WACC(l3) 0.12000 0.11735 0.11482 0.11239 0.11007 0.10784 0.10569 0.10363 0.10165 0.09975 0.09791

Kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Ke 0.2640 0.2561 0.2485 0.2412 0.2342 0.2275 0.2211 0.2149 0.2090 0.2032 0.1977

Ke(l3) 0.3000 0.2500 0.2000 L=1

0.1500

L=2

0.1000 0.0500 0.0000

0

1

2

3

4

5

6

7

8

9

10

Fig. 28.19 The dependence of equity cost ke on leverage ratio l3 at two leverage level values L = 1 and L = 2

28.9

Influence of Leverage Level

665

– we find by the above algorithm m values of WACC(ij) and n values of WACC(lk) first; – then we find the average value of WACC by the following formula: " # m n X   X 1 WACC ij þ WACCðlk Þ : WACCav = m þ n j=1 k=1 This found value WACCav should be used when discounting the financial flows in rating.

28.9

Influence of Leverage Level

We discuss also the interplay between rating ratios and leverage level which can be quite important in rating.

28.9.1

The Dependence of Equity Cost ke on Leverage Level at Two Coverage Ratio Values ij = 1 and ij = 2

1. i1 = 1 2. i1 = 2 1. i2 = 1, 2. i2 = 2 1. i3 = 1, 2. i3 = 2 It is seen from Tables 28.22, 28.23, 28.24, 28.25, 28.26, and 28.27 and Figs. 28.20, 28.21, and 28.22 that equity cost ke increases practically linearly with leverage level for all coverage ratios i1, i2, i3. For each of the two coverage ratios i1, i2, curves ke (L ) for two values of ij (1 and 2) practically coincide. For coverage ratio i3 curves ke (L ) for value of i3 = 2 lie above one for i3 = 1 and angle of inclination for value of i3 = 2 is bigger.

666

28 Rating: New Approach

Table 28.22 The dependence of equity cost ke on leverage level L at coverage ratio i1 = 1

L 0 1 2 3 4 5 6 7 8 9 10

WACC(i1 = 1) 0.11719 0.11719 0.11719 0.11719 0.11719 0.11719 0.11719 0.11719 0.11719 0.11719 0.11719

Kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Ke 0.1172 0.1864 0.2556 0.3248 0.3939 0.4631 0.5323 0.6015 0.6707 0.7399 0.8091

Table 28.23 The dependence of equity cost ke on leverage level L at coverage ratio i1 = 2

L 0 1 2 3 4 5 6 7 8 9 10

WACC(i1 = 2) 0.11858 0.11858 0.11858 0.11858 0.11858 0.11858 0.11858 0.11858 0.11858 0.11858 0.11858

Kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Ke 0.1186 0.1892 0.2597 0.3303 0.4009 0.4715 0.5420 0.6126 0.6832 0.7538 0.8243

Table 28.24 The dependence of equity cost ke on leverage level L at coverage ratio i2 = 1

L 0 1 2 3 4 5 6 7 8 9 10

WACC(i2 = 1) 0.11734 0.11734 0.11734 0.11734 0.11734 0.11734 0.11734 0.11734 0.11734 0.11734 0.11734

Kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Ke 0.1173 0.1867 0.2560 0.3254 0.3947 0.4641 0.5334 0.6027 0.6721 0.7414 0.8108

28.9

Influence of Leverage Level

667

Table 28.25 The dependence of equity cost ke on leverage level L at coverage ratio i2 = 2

L 0 1 2 3 4 5 6 7 8 9 10

WACC(i2 = 2) 0.11866 0.11866 0.11866 0.11866 0.11866 0.11866 0.11866 0.11866 0.11866 0.11866 0.11866

Kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Ke 0.1187 0.1893 0.2600 0.3306 0.4013 0.4719 0.5426 0.6133 0.6839 0.7546 0.8252

Table 28.26 The dependence of equity cost ke on leverage level L at coverage ratio i3 = 1

L 0 1 2 3 4 5 6 7 8 9 10

WACC(i3 = 1) 0.08571 0.08571 0.08571 0.08571 0.08571 0.08571 0.08571 0.08571 0.08571 0.08571 0.08571

Kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Ke 0.0857 0.1234 0.1611 0.1989 0.2366 0.2743 0.3120 0.3497 0.3874 0.4251 0.4629

Table 28.27 The dependence of equity cost ke on leverage level L at coverage ratio i3 = 2

L 0 1 2 3 4 5 6 7 8 9 10

WACC(i3 = 2) 0.10000 0.10000 0.10000 0.10000 0.10000 0.10000 0.10000 0.10000 0.10000 0.10000 0.10000

Kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Ke 0.1000 0.1520 0.2040 0.2560 0.3080 0.3600 0.4120 0.4640 0.5160 0.5680 0.6200

668

28 Rating: New Approach

Ke(L) 0.7800 0.6800 0.5800 0.4800

i1=1

0.3800

i1=2

0.2800 0.1800 0.0800

0

1

2

3

4

5

6

7

8

9

10

Fig. 28.20 The dependence of equity cost ke on leverage level at two coverage ratio values i1 = 1 and i1 = 2

Ke(L) 0.9000 0.8000 0.7000 0.6000 0.5000 0.4000

i2=1

0.3000

i2=2

0.2000 0.1000 0.0000

0

1

2

3

4

5

6

7

8

9

10

Fig. 28.21 The dependence of equity cost ke on leverage level at two coverage ratio values i2 = 1 and i2 = 2

28.10

The Dependence of Equity Cost ke on Leverage Level at Two Leverage Ratio Values lj = 1 and lj = 2

Let us now study the dependence of equity cost ke on leverage level at two leverage ratio values lj = 1 and lj = 2 for leverage ratios l1, l2, l3. 1. l1 = 1,

28.10

The Dependence of Equity Cost ke on Leverage Level at. . .

669

Ke(L) 0.7000 0.6000 0.5000 0.4000

i3=1

0.3000

i3=2

0.2000 0.1000 0.0000

0

1

2

3

4

5

6

7

8

9

10

Fig. 28.22 The dependence of equity cost ke on leverage level at two coverage ratio values i3 = 1 and i3 = 2

2. l1 = 2 1. l2 = 1, 2. l2 = 2 1. l3 = 1, 2. l3 = 2 It is seen from Tables 28.28, 28.29, 28.30, 28.31, 28.32, and 28.33 and Figs. 28.23, 28.24, and 28.25 that equity cost ke increases practically linearly with leverage level for all leverage ratios l1, l2, l3. For each of the two leverage ratios l1, l3, Table 28.28 The dependence of equity cost ke on leverage level L at leverage ratio l1 = 1

L 0 1 2 3 4 5 6 7 8 9 10

WACC(l1 = 1) 0.11719 0.11719 0.11719 0.11719 0.11719 0.11719 0.11719 0.11719 0.11719 0.11719 0.11719

Kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Ke 0.1172 0.1864 0.2556 0.3248 0.3939 0.4631 0.5323 0.6015 0.6707 0.7399 0.8091

670

28 Rating: New Approach

Table 28.29 The dependence of equity cost ke on leverage level L at leverage ratio l1 = 2

L 0 1 2 3 4 5 6 7 8 9 10

WACC(l1 = 2) 0.11450 0.11450 0.11450 0.11450 0.11450 0.11450 0.11450 0.11450 0.11450 0.11450 0.11450

Kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Ke 0.1145 0.1810 0.2475 0.3140 0.3805 0.4470 0.5135 0.5800 0.6465 0.7130 0.7795

Table 28.30 The dependence of equity cost ke on leverage level L at leverage ratio l2 = 1

L 0 1 2 3 4 5 6 7 8 9 10

WACC(l2 = 1) 0.08571 0.08571 0.08571 0.08571 0.08571 0.08571 0.08571 0.08571 0.08571 0.08571 0.08571

Kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Ke 0.0857 0.1234 0.1611 0.1989 0.2366 0.2743 0.3120 0.3497 0.3874 0.4251 0.4629

Table 28.31 The dependence of equity cost ke on leverage level L at leverage ratio l2 = 2

L 0 1 2 3 4 5 6 7 8 9 10

WACC(l2 = 2) 0.06667 0.06667 0.06667 0.06667 0.06667 0.06667 0.06667 0.06667 0.06667 0.06667 0.06667

Kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Ke 0.0667 0.0853 0.1040 0.1227 0.1413 0.1600 0.1787 0.1973 0.2160 0.2347 0.2533

28.10

The Dependence of Equity Cost ke on Leverage Level at. . .

671

Table 28.32 The dependence of equity cost ke on leverage level L at leverage ratio l3 = 1

L 0 1 2 3 4 5 6 7 8 9 10

WACC(l3 = 1) 0.11735 0.11735 0.11735 0.11735 0.11735 0.11735 0.11735 0.11735 0.11735 0.11735 0.11735

Kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Ke 0.1174 0.1867 0.2561 0.3254 0.3948 0.4641 0.5335 0.6028 0.6722 0.7415 0.8109

Table 28.33 The dependence of equity cost ke on leverage level L at leverage ratio l3 = 2

L 0 1 2 3 4 5 6 7 8 9 10

WACC(l3 = 2) 0.11482 0.11482 0.11482 0.11482 0.11482 0.11482 0.11482 0.11482 0.11482 0.11482 0.11482

Kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Ke 0.1148 0.1816 0.2485 0.3153 0.3821 0.4489 0.5157 0.5826 0.6494 0.7162 0.7830

Ke(L) 0.9000 0.8000 0.7000 0.6000 0.5000

L1=1

0.4000

L1=2

0.3000 0.2000 0.1000 0.0000 0

1

2

3

4

5

6

7

8

9

10

Fig. 28.23 The dependence of equity cost ke on leverage level at two leverage ratio values l1 = 1 and l1 = 2

672

28 Rating: New Approach

Ke(L) 0.5000 0.4500 0.4000 0.3500 0.3000 0.2500

L2=1

0.2000

L2=2

0.1500 0.1000 0.0500 0.0000 0

1

2

3

4

5

6

7

8

9

10

Fig. 28.24 The dependence of equity cost ke on leverage level at two leverage ratio values l2 = 1 and l2 = 2

Ke(L) 0.9000 0.8000 0.7000 0.6000 0.5000

L3=1

0.4000

L3=2

0.3000 0.2000 0.1000 0.0000 0

1

2

3

4

5

6

7

8

9

10

Fig. 28.25 The dependence of equity cost ke on leverage level at two leverage ratio values l3 = 1 and l3 = 2

curves ke (L ) for two values of lj (1 and 2) practically coincide. For leverage ratio l2 curves ke (L ) for value of l3 = 1 lie above one for l3 = 2 and angle of inclination for value of l3 = 1 is bigger.

References

28.11

673

Conclusion

In this chapter, a new approach to rating methodology is suggested. Chapters 28–30 are devoted to rating of non-financial issuers, while Chaps. 31 and 32 are devoted to investment project rating. The key factors of a new approach are: (1) The adequate use of discounting of financial flows virtually not used in existing rating methodologies, (2) The incorporation of rating parameters (financial “ratios”) into the modern theory of capital structure BFO (and its perpetuity limit). This, on the one hand, allows to use the powerful tool of this theory in the rating and, on the other hand, it ensures the correct discount rates when discounting of financial flows. Two models for accounting of discounting of financial flows—one-period and multi-period are discussed. An algorithm of valuation of correct discount rate, accounting rating ratios is suggested. We discuss also the interplay between rating ratios and leverage level which can be quite important in rating. All the above create a new base for rating methodologies.

References Brusov PN, Filatova ТV (2011) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Financ Credit 435:2–8 Brusov P, Filatova T, Orehova N, Brusova A (2011a) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Appl Financ Econ 21(11): 815–824 Brusov P, Filatova T, Orehova N et al (2011b) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Bus ICT 2:16–21 Brusov P, Filatova T, Orehova N et al (2011c) Influence of debt financing on the effectiveness of the investment project within the Modigliani–Miller theory. Res J Econ Bus ICT (UK) 2:11–15 Brusov P, Filatova T, Orehova N, Brusov PP, Brusova N (2011d) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Bus ICT 2:16–21 Brusov P, Filatova T, Orekhova N, Brusov P, Brusova A (2012) Modern approach to dividend policy of company. Financ Credit 18(37):2012 Brusov P, Filatova T, Eskindarov M, Orehova N (2012a) Influence of debt financing on the effectiveness of the finite duration investment project. Appl Financ Econ 22(13):1043–1052 Brusov P, Filatova T, Eskindarov M, Orehova N (2012b) Hidden global causes of the global financial crisis. J Rev Glob Econ 1:106–111 Brusov P, Filatova P, Orekhova N (2013a) Absence of an optimal capital structure in the famous tradeoff theory! J Rev Glob Econ 2:94–116 Brusov P, Filatova T, Orehova N (2013b) A qualitatively new effect in corporative finance: abnormal dependence of cost of equity of company on leverage. J Rev Glob Econ 2:183–193 Brusov P, Filatova P, Orekhova N (2014a) Mechanism of formation of the company optimal capital structure, different from suggested by trade off theory. Cogent Econ Financ 2:1–13. https://doi. org/10.1080/23322039.2014.946150 Brusov P, Filatova T, Orehova N (2014b) Inflation in Brusov–Filatova–Orekhova theory and in its perpetuity limit–Modigliani–Miller theory. J Rev Glob Econ 3:175–185 Brusov P, Filatova T, Orekhova N (2021) Ratings: critical analysis and new approaches of quantitative and qualitative methodology. Springer Nature Publishing

674

28 Rating: New Approach

Brusov P, Filatova T, Orehova N, Eskindarov M (2015) Modern corporate finance, investment and taxation, 1st edn. Springer, pp 1–368 Brusov P, Filatova T, Orehova N, Kulk WI (2018a) New meaningful effects in modern capital structure theory. J Rev Global Econ 7:104–122 Brusov P, Filatova T, Orehova N, Kulk V (2018b) A “golden age” of the companies: conditions of its existence. J Rev Global Econ 7:88–103 Brusov P, Filatova T, Orehova N, Kulk V (2018c) Rating methodology: new look and new horizons. J Rev Global Econ 7:63–87 Brusov P, Filatova T, Orehova N, Kulk V (2018d) Rating: new approach. J Rev Global Econ 7:37– 62 Brusova A (2011) А comparison of the three methods of estimation of weighted average cost of capital and equity cost of company. Financ Anal Prob Solut 34(76):36–42 Filatova Т, Orehova N, Brusova А (2008) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Bull FU 48:68–77 Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Modigliani F, Miller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391

Chapter 29

Rating Methodology: New Look and New Horizons

Keywords Rating · Rating methodology · Discounting of financial flows · Brusov– Filatova–Orekhova theory · Coverage ratios · Leverage ratios

29.1

Introduction

In the previous chapter, we have offered fundamentally new approach to rating methodology, which includes adequate application of discounting of financial flows virtually not used in existing rating methodologies. The incorporation of rating parameters (financial “ratios”) into the perpetuity limit of modern theory of capital structure by Brusov–Filatova–Orekhova (BFO) theory has been done: it required a modification of perpetuity limit of BFO theory for rating needs. Two models (one-period and multi-period) for accounting of discounting of financial flows were discussed. An algorithm of valuation of discount rate, accounting rating ratios has been suggested. We discussed also the interplay between rating ratios and leverage level which can be quite important in rating (Brusov et al. 2021). As we discussed in a number of works (Brusov et al. 2011a, b, c, d, 2012a, 2012b, c, 2013a, b, 2014a, b, 2015; Brusov & Filatova 2011; Filatova et al. 2008) perpetuity limit of BFO theory–Modigliani–Miller theory (Modigliani and Miller 1958, 1963, 1966) underestimated the assessment of the attracting capital cost and therefore overestimated the assessment of the capitalization of the company. Besides, the time factor, which is very important, does not exist in the perpetuity limit. And therefore in this limit there is no concept of the age of the company, and their lifetime is infinite (perpetuity). In this Chapter, we generalize our approach to the rating methodology to the case of the application of the modern theory of capital structure and cost—the Brusov–Filatova–Orekhova (BFO) theory for companies and corporations of arbitrary age. This has required the modification of the BFO theory for the rating needs (much more complicate than it was done in the case of perpetuity limit—Modigliani–Miller theory), as used in financial management the concept of “leverage” as the ratio of debt value to the equity value substantially differs from the concept of “leverage” in the rating, where it is understood as the direct and inverse ratio of the debt value to © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_29

675

676

29 Rating Methodology: New Look and New Horizons

the generated cash flow values (income, profit, etc.). We introduce here some additional ratios, allowing full characterization of the issuer’s ability to repay debts and to pay interest thereon. As we mentioned in the previous paper, the bridge is building between the discount rates (WACC, ke) used when discounting of financial flows and the “ratios” in the rating methodology. The algorithm for finding the discount rates for given ratio values is developed. Application of BFO theory modified for rating purposes allow adequately produce the discounting of financial flows using the correct discount rates with taken into account when discounting the magnitude of rating ratios, and take into account the time factor missing in perpetuity limit and being the vital, i.e. to take into account the company age (in BFO–I theory) or the company lifetime (in the BFO–II theory).

29.2

The Analysis of Methodological and Systemic Deficiencies in the Existing Credit Rating of Non-financial Issuers

The analysis of methodological and systemic deficiencies in the existing credit rating of non-financial issuers has been conducted by us. We have analyzed the methodology of the big three (Standard & Poor’s, Fitch and Moody’s) and Russian national rating agency.

29.2.1

The Closeness of the Rating Agencies

The closeness of the rating agencies has been discussed by us in a previous paper (Brusov et al. 2018) and is caused by multiple causes. 1. The desire to preserve their “know-how.” Rating agencies get big enough money for generated ratings (mostly from issuers) to replicate its methodology. 2. The desire to avoid public discussion of the ratings with anyone, including the issuer. It is very convenient position—rating agency “a priori” removes himself from beneath any criticism of generated ratings. 3. The absence of any external control and external analysis of the methodologies is resulted in the fact that shortcomings of methodologies are not subjected to serious critical analysis and stored long enough.

29.2

The Analysis of Methodological and Systemic Deficiencies in the. . .

29.2.2

677

Discounting

One of the major flaws of all existing rating methodologies is a failure or a very narrow use of discounting. But even in those rare cases where it is used, it is not quite correct, since the discount rate when discounting financial flows is chosen incorrectly. The need to take into account the time factor in terms of discounting is obvious, because it is associated with the time value of money. The financial part of the rating is based on a comparison of generated income with the value of the debt and the interest payable. Because income and disbursement of debt and interest are separated in time, the use of discounting when comparing revenues with the value of debt and interest is absolutely necessary for assigning credit ratings for issuers. 1. In the existing rating methodologies, despite their breadth and detail, there are a lot of shortcomings. One of the major flaws of all existing rating methodologies, as mentioned in our previous paper, is a failure or a very narrow use of discounting. But even in those rare cases where it is used, it is not quite correct, since the discount rate when discounting financial flows is chosen incorrectly. The need to take into account the time factor in terms of discounting is obvious, because it is associated with the time value of money. The financial part of the rating is based on a comparison of generated income with the value of the debt and the interest payable. Because income and disbursement of debt and interest are separated in time, the use of discounting when comparing revenues with the value of debt and interest is absolutely necessary for assigning credit ratings for issuers. This raises the question about the discount rate. This question has always been one of the major and extremely difficult in many areas of finance: corporate finance, investment, it is particularly important in business valuation, where a slight change in the discount rate leads to significant changes in estimates of capitalization of the company, that is used by unscrupulous appraisers for artificial bankruptcy of companies. As well it is essential in rating, and when assigning a rating to an issuer, and forecasting. Therefore, as soon as we are talking about financial flows, it is necessary to account discounting, otherwise the time value of money does not take into account, i.e., any analysis of financial flows should take into account of discounting. 2. When we talk about using the rating reports for the 3 or 5 (GAAP) years, assuming the behavior indicators beyond that period “a flat”, discounting must be taken into account.

29.2.3

Dividend Policy of the Company

1. Dividend policy of the company must be taken into account (and account) when rating, because the financial policy is taken into account in rating. However, the existing methodologies for ranking estimate only the stability of the dividend

678

29 Rating Methodology: New Look and New Horizons

policy and do not estimate its reasonableness, how reasonable is the value of dividend payouts, how do they relate to the economically reasonable dividend values. 2. The reasonableness of dividend policy, its score is determined by comparing the values of paid dividends with their economically reasonable value, which is the cost of equity capital ke of the company. The calculation of ke is a rather difficult task. BFO theory allows you to make the correct assessment of the value of the equity capital cost of the company and thus to compare values of the paid by the company dividend to their economically reasonable value, it allows you to assess the reasonableness of dividend policy, which is clearly linked to the creditworthiness of the issuer. 3. For example, one of the varieties “cash flow,” taking into account the amount of paid dividends (Discretionary cash flow (DCF) S & P), should be compared with the “economically reasonable dividend values,” and this will affect the rating.

29.2.4

Leverage Level

1. Currently the rating agencies take into account the leverage level only from the perspective of assessing the financial stability and risk of bankruptcy. In fact, the leverage level significantly affects the main financial indicators of the company’s activity: the cost of equity capital, WACC, in other words, the cost of attraction of capital, as well as the capitalization of the company. The failure of this effect in the analysis of financial reports leads to incorrect conclusions based on it. Evaluation (by the BFO method) of the influence of the debt financing level on the effectiveness of investment projects for different values of capital costs can be used in the rating of investment projects and investment programs of companies.

29.2.5

Taxation

1. Taxation affects the rating of the issuers. Evaluation (by the BFO method) of the influence of taxation (tax on profit organization rate) on the financial performance of the company, on the effectiveness of investment projects can be used when rating companies and their investment programs, investment projects, as well as in the context of change of tax on profits of the organization rate for forecast predictions and in analysis of country risk. 2. Evaluation (by BFO the method) of the influence of the Central Bank base rate, credit rates of commercial banks on the effectiveness of investment projects, creation of a favorable investment climate in the country can be used to forecast predictions, as well as in country risk analysis.

29.2

The Analysis of Methodological and Systemic Deficiencies in the. . .

29.2.6

679

Account of the Industrial Specifics of the Issuer

Industrial specifics of the issuer in the existing rating methodologies, especially in newly established and taking into account the experience of predecessors, ignored. So in “‘the methodology of ACRA for assigning of credit ratings for non-financial companies on a national scale for the Russian Federation,’ own creditworthiness is determined by taking into account the characteristics of the industry in which the company operates. To assess the factor of the industry risk profile ACRA subdivides the industry into five groups according to their cyclical, barriers to entry, industry risk statistics, as well as trends and prospects. The weight of the factor of industry risk profile is determined individually for each group and varies depending on the level of credit risk. This creates a certain rating threshold for companies from industries with high risk and slightly rewards low risk industry.” However, the existing accounting of industry specifics of issuer is clearly insufficient. Ranking methodologies should better integrate industry peculiarities in the organization of finance of issuers. In particular, it is very important to define business needs in working capital, from the size of which financial soundness indicators, solvency, and creditworthiness depend directly. The latter is the key indicator in rating.

29.2.7

Neglect of Taking into Account the Particularities of the Issuer

In the existing rating methodologies, taking into account the particularities of the issuer, features of financial reports, taxation, legal and financial system is neglected in favor of achieving full comparability of financial reports, they smooth the distinctions (see Moody’s rating methodologies).

29.2.8

Financial Ratios

1. A necessary and sufficient quantity and mix of financial ratios are not determined, it appears that such questions are even not raised though valuation of the financial risk, the financial condition of the issuer largely depend on the quantity and quality of financial ratios, their correlation, or independence. 2. Some financial ratios define ambiguously the state of the issuer. For example, the ratio of cash flow/leverage is high at high cash flow value as well as at low leverage value. The question is how these two different states of the issuer, which is attributed to one value of financial risk, is really equally relate to credit risk.

680

29 Rating Methodology: New Look and New Horizons

Table 29.1 (After ACRA) Assessment of funding

Liquidity assessment 1 2 3 1 2 2 1 1 2 3 2 2 2 3 3 3 3 3 4 3 3 4 5

4 3 3 4 4 5

5 4 4 5 5 5

3. As recognized in the ACRA methodology “in some cases it is possible a formal hit of individual characteristics of factor/subfactor simultaneously in several categories of evaluation, particularly for qualitative factors. In this case, the score is based on expert opinion, taking into account the most important parameters.” 4. In connection with paragraph 3 it should be noted that the formalization of expert opinions is one of the most important tasks in improving the rating methodology, in making a peer-review process more objective. There are a few ways to solve this problem: using results of modern theory of measurement, using the formalism of fuzzy sets, fuzzy logic, and others. 5. Tabulate the composition of various risks, for example, CICRA (in S&P methodology) gives 6 × 6 matrix, which has 36 elements, i.e. generally CICRA should have 36 different values, but their total number is equal to 6. The question is how this is justified. The fact that total number is equal exactly to 6 shows that not very justified, or there are other considerations, but they must be well grounded. Similar examples abound. So in “the ACRA methodology for assigning of credit ratings for microfinance organizations on a national scale for the Russian Federation” Table 29.1 “Score of funding and liquidity” provides 5 × 5 matrix that has 25 elements, i.e. generally should be 25 different states but their total number is equal to 5. The question is whether it is justified. The fact that total number is equal exactly to 5 shows that not very justified. 6. Tabulating of mixes of different ratios in determining the financial risk has not been done quite correctly:

Minimal

FFO/ debt (%) 60+

Modest Intermediate Significant Aggressive Highly leveraged

45–60 30–45 20–30 12–20 Less than 12

Debt/ EBITDA (x) Less than 1.5 1.5–2 2–3 3–4 4–5 Greater than 5

FFO/cash interest(x) More than 13 9–13 6–9 4–6 2–4 Less than 2

EBITDA/ interest(x) More than 15 10–15 6–10 3–6 2–3 Less than 2

CFO/ debt (%) More than 50 35–50 25–35 15–25 10–15 Less than 10

FOCF/ debt(%) 40+

DCF/ debt (%) 25+

25–40 15–25 10–15 5–10 Less than 5

15–25 10–15 5–10 2–5 Less than 2

29.3

Modification of the BFO Theory for Companies and Corporations of. . .

681

ratios at least not completely correlated but used as fully correlated. So, one can see that the two lines Minimal

60+

Modest

45–60

Less than 1.5 1.5–2

More than 13 9–13

More than 15 10–15

More than 50 35–50

40+

25+

25–40

15–25

do not allow mixing between parameters of lines, although such mixing can occur, for example, 60+

Less than 1.5

More than 13

More than 15

More than 50

40+

25+

All these points are limiting the applicability of rating agency methods. They were introduced by the rating agencies for the purpose of simplifying the procedure of ranking (with or without understanding), and with a view of unification of methods to different reporting systems, different countries, with the objective of comparability of results. Mentioned ambiguity of evaluations already occurred when S&P has assigned a rating to Gazprom.

29.3

Modification of the BFO Theory for Companies and Corporations of Arbitrary Age for Purposes of Ranking

We will conduct below the modification of the BFO theory for companies and corporations of arbitrary age for purposes of ranking, which proved much more difficult than modification of its (BFO theory) perpetuity limit. As it turned out, use of the famous formula BFO ½1 - ð1 þ WACCÞ - n  ½ 1 - ð1 þ k 0 Þ - n  = WACC k0 ½1 - ωd T ð1 - ð1 þ kd Þ - n Þ

ð29:1Þ

is not possible, since it no longer includes cash flows CF and debt value D, and the leverage level L = D/S (in the same sense as it is used in financial management) is included only through the share of leveraged wd = L/(L + 1). For the modification of the general theory of BFO for ranking purposes, one must return to the initial assumptions under the derivation of the BFO formula. Modigliani–Miller theorem in case of existing of corporate taxes, generalized by us for the case of finite company age, states that capitalization of leveraged company (using the debt financing), VL, is equal to the capitalization of non-leveraged company (which does not use the debt financing), V0, increased by the amount of the tax shield for the finite period of time, TSn,

682

29 Rating Methodology: New Look and New Horizons

V L = V 0 þ TSn :

ð29:2Þ

where the capitalization of leveraged company CF ð1- ð1 þ WACCÞ - n Þ; WACC

VL =

ð29:3Þ

the capitalization of non-leveraged company. V0 =

CF ð1- ð1 þ k 0 Þ - n Þ; k0

ð29:4Þ

and the tax shield for the period of n years TSn = tDð1- ð1 þ kd Þ - n Þ:

ð29:5Þ

Substituting Eqs. (29.3)–(29.5) into Eq. (29.2), we obtain Eq. (29.6), which will be used by us in the future to modify the BFO theory for the needs of the ranking. CF  ð1 - ð1 þ WACCÞ - n Þ CF =  ð1- ð1 þ k 0 Þ - n Þ þ t  D WACC K0  ð1- ð1 þ k d Þ - n Þ

ð29:6Þ

Below we fulfill the incorporation of rating parameters (financial “ratios”) into the modern theory of capital structure (Brusov–Filatova–Orekhova (BFO) theory). As we noted in the previous paper (Brusov et al. 2018), in quantification of the creditworthiness of the issuers the crucial role belongs to the so-called financial ratios, which constitute direct and inverse ratios of various generated cash flows to debt values and interest ones. We could mention such ratios as DCF/Debt, FFO/Debt, CFO/Debt, FOCF/Debt, FFO/cashinterest, EBITDA/interest, Interests/ EBITDA, Debt/EBITDA, and some others. Let us consider two kinds of rating ratios: coverage ratios and leverage ratios.

29.4

Coverage Ratios

We start with the coverage ratios and will consider three kinds of coverage ratios: coverage ratios of debt, coverage ratios of interest on the credit, and coverage ratios of debt and interest on the credit. Note that the last type of ratios has been introduced by us for the first time for a more complete valuation of the issuer’s ability to repay debts and to pay interest thereon.

29.4

Coverage Ratios

29.4.1

683

Coverage Ratios of Debt

Here i1 = CF/D Let us consider the coverage ratios of debt first. Dividing the both parts of the formula (29.6) by the value of the debt D, enter the debt coverage ratio into the general BFO theory i1 = CF=D i1  ð1 - ð1 þ WACCÞ WACC

-n

i1  ð1 - ð1 þ k0 Þ k0

=

ð29:7Þ -n

þ t  ð1- ð1 þ kd Þ - n Þ ð29:8Þ

i1  A = i1  B þ t  C A=

ð1 - ð1 þ WACCÞ WACC

ð29:9Þ

-n

ð29:10Þ

;

ð1 - ð1 þ k 0 Þ - n ; k0

ð29:11Þ

C = ð1- ð1 þ kd Þ - n Þ;

ð29:12Þ

B=

This ratio (i1) can be used to assess the following parameters used in rating, DCF/Debt, FFO/Debt, CFO/Debt, FOCF/Debt, and some others. We will use formula (29.8) to study the dependence WACC(i1) and to build a curve of this dependence. Let us analyze the dependence of the weighted average cost of capital (WACC) on debt coverage ratio i1. We consider the case k0 = 8%; kd = 4%; t = 20%; i1 is changed from 1 up to 10, for two company ages n = 3 (Tables 29.2 and 29.3) n = 5. The dependence of company’s weighted average cost of capital (WACC) on the coverage ratio on debt i1 is shown in Figs. 29.1 and 29.2. Table 29.2 The dependence of the weighted average cost of capital (WACC) on debt coverage ratio i1 at n = 3

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

ko 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08

kd 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04

i1 1 2 3 4 5 6 7 8 9 10

WACC 0.075356711 0.077705469 0.078412717 0.078808879 0.079046807 0.079205521 0.079318935 0.079404022 0.079470216 0.07952318

684

29 Rating Methodology: New Look and New Horizons

Table 29.3 The dependence of the weighted average cost of capital (WACC) on debt coverage ratio i1 at n = 5

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

ko 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08

Fig. 29.1 The dependence of company’s weighted average cost of capital (WACC) on the coverage ratio on debt i1 at n = 3

kd 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04

i1 1 2 3 4 5 6 7 8 9 10

WACC 0.07663868 0.0783126 0.0788732 0.079154 0.07932264 0.07943518 0.0795156 0.07957594 0.07962287 0.07966043

WACC(i1) at n=3 0.08 0.079 0.078 0.077 0.076 0.075 0

Fig. 29.2 The dependence of company’s weighted average cost of capital (WACC) on the coverage ratio on debt i1 at n = 5

10

15

WACC(i1) at n=5

0.08 0.0795 0.079 0.0785 0.078 0.0775 0.077 0.0765 0.076 0

29.4.2

5

5

10

15

The Coverage Ratio on Interest on the Credit

Let us analyze now the dependence of company’s weighted average cost of capital (WACC) on the coverage ratio on interest on the credit i2. Dividing the both parts of the formula (29.6) by the value of the interest on the credit kdD, enter the coverage ratio on interest on the credit i2 into the general BFO theory

29.4

Coverage Ratios

685

Table 29.4 The dependence of the weighted average cost of capital (WACC) on the coverage ratio on interest on the credit i2 at n = 3

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Table 29.5 The dependence of the weighted average cost of capital (WACC) on the coverage ratio on interest on the credit i2 at n = 5

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

ko 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08

ko 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08

kd 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04

kd 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04

i2 1 2 3 4 5 6 7 8 9 10

i2 1 2 3 4 5 6 7 8 9 10

WACC -0.021238089 0.02529016 0.042483465 0.051456351 0.056965593 0.060692181 0.063380861 0.065412245 0.067001115 0.068277865

WACC 0.00793717 0.04111354 0.0533843 0.05974575 0.06365738 0.06630611 0.06821315 0.06966377 0.07078076 0.07168658

i2  ð1 - ð1 þ WACCÞ - n i2  ð1 - ð1 þ k 0 Þ - n = WACC k0 þ

t  ð1 - ð1 þ k d Þ - n Þ kd

ð29:13Þ

Here CF = i2 D  kd

i2  A = i2  B þ

ð29:14Þ

tC kd

ð29:15Þ

The dependences of company’s weighted average cost of capital (WACC) on the coverage ratio on interest on the credit i2 for company ages n = 3 and n = 5 are presented in Tables 29.4 and 29.5. The dependences of company’s weighted average cost of capital (WACC) on the coverage ratio on interest on the credit i2 at company ages n = 3 and n = 5 are shown in Figs. 29.3 and 29.4.

686

29 Rating Methodology: New Look and New Horizons

Fig. 29.3 The dependence of company’s weighted average cost of capital (WACC) on the coverage ratio on interest on the credit i2 at company age n = 3

WACC(i2) at n=3 0.08 0.06 0.04 0.02 0 -0.02 0 -0.04

Fig. 29.4 The dependence of company’s weighted average cost of capital (WACC) on the coverage ratio on interest on the credit i2 at company age n = 5

5

10

15

WACC(i2) at n=5 0.08 0.06 0.04 0.02 0 0

5

10

15

This ratio (i2) can be used to assess the following parameters, used in rating, FFO/cash interest, EBITDA/interest, and some others. We will use the last formula to build a curve of dependence WACC(i2).

29.4.3

Coverage Ratios of Debt and Interest on the Credit (New Ratios)

Let us now study the dependence of the company’s weighted average cost of capital (WACC) on the coverage ratios of debt and interest on the credit simultaneously i3: this is new ratio, introduced by us for the first time here for a more complete description of the issuer’s ability to repay debts and to pay interest thereon. Dividing the both parts of the formula (29.6) by the value of the debt and interest on the credit (1 + kd)D, enter the coverage ratio on debt and interest on the credit i3 into the general BFO theory CF = i3 D  ð1 þ k d Þ

ð29:16Þ

29.4

Coverage Ratios

687

Table 29.6 The dependence of the weighted average cost of capital (WACC) on the coverage ratio on debt and interest on the credit i3 at n=3

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

ko 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08

kd 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04

Table 29.7 The dependence of the weighted average cost of capital (WACC) on the coverage ratio on debt and interest on the credit i3 at n=5

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

ko 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08

kd 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04

i3  A = i3  B þ

i3 1 2 3 4 5 6 7 8 9 10

i3 1 2 3 4 5 6 7 8 9 10

tC 1 þ kd

WACC 0.075536724 0.077796177 0.078473634 0.078854621 0.079083426 0.079236052 0.079345114 0.079426934 0.079490586 0.079541516

WACC 0.07676703 0.07837722 0.07891638 0.07918642 0.07934861 0.07945683 0.07953417 0.07959218 0.07963732 0.07967343

ð29:17Þ

i3  ð1 - ð1 þ WACCÞ - n i3  ð1 - ð1 þ k 0 Þ - n = WACC k0 þ

t  ð1 - ð1 þ k d Þ - n Þ 1 þ kd

ð29:18Þ

The dependences of company weighted average cost of capital (WACC) on the coverage ratio on debt and interest on the credit i3 at company age n = 3 and n = 5 are presented in Tables 29.6 and 29.7. The dependences of company weighted average cost of capital (WACC) on the coverage ratio on debt and interest on the credit i3 at company age n = 3 and n = 3 are shown in Figs. 29.5 and 29.6.

688

29 Rating Methodology: New Look and New Horizons

Fig. 29.5 The dependence of company’s weighted average cost of capital (WACC) on the coverage ratio on debt and interest on the credit i3 at company age n=3

WACC (i3) at n=3 0.08 0.079 0.078 0.077 0.076 0.075 0

Fig. 29.6 The dependence of company’s weighted average cost of capital (WACC) on the coverage ratio on debt and interest on the credit i2 at company age n=5

5

10

15

WACC(i3) at n=5 0.08 0.0795 0.079 0.0785 0.078 0.0775 0.077 0.0765 0

5

10

15

WACC(i1), WACC(i2), WACC(i3) 0.1 0.08 0.06 0.04 0.02 0 0

2

4 WACC1

6

8

WACC2

10

12

WACC3

Fig. 29.7 Consolidated data of dependence of WACC on i1, i2, i3, at company age n = 3

29.4.4

All Three Coverage Ratios Together

Consolidated data of dependence of WACC on i1, i2, i3, at company age n = 3 and n = 5 are shown in Figs. 29.7 and 29.8.

29.5

Coverage Ratios (Different Capital Cost Values)

689

WACC( i1),(i2),(i3) 0.1 0.08 0.06 0.04 0.02 0 -0.02

0

2

4

6

8

10

12

-0.04 WACC1

WACC2

WACC3

Fig. 29.8 Consolidated data of dependence of WACC on i1, i2, i3, at company age n = 3

The analysis of Tables 29.1, 29.2, 29.3, 29.4, 29.5, 29.6, and 29.7 and Figs. 29.1, 29.2, 29.3, 29.4, 29.5, 29.6, 29.7 and 29.8 as well as conclusions will be made at the end of next paragraph.

29.5

Coverage Ratios (Different Capital Cost Values)

Let us analyze the dependence of company weighted average cost of capital (WACC) of coverage ratios (i1, i2, i3), for different capital cost values k0 = 14%, kd = 8%. Here as before t = 20%, n = 3; 5, the value of coverage ratios i is in the range from 1 to 10.

29.5.1

Coverage Ratios of Debt

As we have derived above the dependence of the weighted average cost of capital (WACC) on debt coverage ratio (i1) in the BFO theory is described by the following formula: i1 

ð1 - ð1 þ WACCÞ - n Þ ð1 - ð1 þ K 0 Þ - n Þ -t - i1  WACC K0

 ½1- ð1 þ K d Þ - n  = 0: Here

ð29:19Þ

690

29 Rating Methodology: New Look and New Horizons

Table 29.8 The dependence of the weighted average cost of capital WACC on debt coverage ratio i1 at company age n = 3

i1 1 2 3 4 5 6 7 8 9 10

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

k0 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

kd 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08

WACC 0.1298 0.1347 0.1365 0.1374 0.1379 0.1382 0.1385 0.1387 0.1388 0.1389

n 3 3 3 3 3 3 3 3 3 3

BFO 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

WACC (i1)

WACC

0.1400 0.1350 0.1300 0.1250

1

2

3

4

5

6

7

8

9

10

i1 Fig. 29.9 The dependence of the weighted average cost of capital WACC on debt coverage ratio i1 at company age n = 3 Table 29.9 The dependence of the weighted average cost of capital WACC on debt coverage ratio i1 at company age n = 5

i1 1 2 3 4 5 6 7 8 9 10

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

i1 =

K0 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

CF : D

Kd 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08

WACC 0.1324 0.1362 0.1374 0.1381 0.1385 0.1387 0.1389 0.1390 0.1391 0.1392

n 5 5 5 5 5 5 5 5 5 5

BFO 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

ð29:20Þ

Using it we get the following results, representing in Table 29.8 and Fig. 29.9 for company age n = 3 and in Table 29.9 and Fig. 29.10 for company age n = 5.

29.5

Coverage Ratios (Different Capital Cost Values)

691

WACC (i1) 0.1400

WACC

0.1380 0.1360 0.1340 0.1320 0.1300 0.1280

1

2

3

4

5

6

7

8

9

10

i1 Fig. 29.10 The dependence of the weighted average cost of capital WACC on debt coverage ratio i1 at company age n = 5

The dependence of the weighted average cost of capital WACC on debt coverage ratio i1 at company age n = 5 is shown in Table 29.9 and Fig. 29.10.

29.5.2

The Coverage Ratio on Interest on the Credit

As we have derived above the dependence of the weighted average cost of capital (WACC) on interests on credit coverage ratio (i2) in the BFO theory is described by the following formula: i2 

ð1 - ð1 þ WACCÞ - n Þ ð1 - ð1 þ K 0 Þ - n Þ - i2  WACC K0

-

ðt  ½1 - ð1 þ K d Þ - n Þ =0 Kd

ð29:21Þ

Here i2 =

CF : Kd  D

ð29:22Þ

Using it, we get the following results, representing in Table 29.10 and Fig. 29.11 for company age n = 3 and in Table 29.11 and Fig. 29.12 for company age n = 5.

692

29 Rating Methodology: New Look and New Horizons

Table 29.10 The dependence of the weighted average cost of capital (WACC) on interests on credit leverage ratio (i2) at company age n = 3

i2 1 2 3 4 5 6 7 8 9 10

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

K0 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

Kd 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08

WACC 0.0285 0.0795 0.0985 0.1084 0.1145 0.1186 0.1216 0.1238 0.1256 0.1270

n 3 3 3 3 3 3 3 3 3 3

BFO 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

WACC

WACC(i2) at n=3 0.1400 0.1200 0.1000 0.0800 0.0600 0.0400 0.0200 0.0000

1

2

3

4

5

6

7

8

9

10

i2 Fig. 29.11 The dependence of the weighted average cost of capital (WACC) on interests on credit leverage ratio (i2) at company age n = 3 Table 29.11 The dependence of the weighted average cost of capital (WACC) on interests on credit leverage ratio (i2) at company age n = 5

i2 1 2 3 4 5 6 7 8 9 10

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

k0 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

kd 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08

WACC 0.0583 0.0957 0.1096 0.1169 0.1213 0.1244 0.1265 0.1282 0.1295 0.1305

n 5 5 5 5 5 5 5 5 5 5

BFO 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

29.5

Coverage Ratios (Different Capital Cost Values)

693

WACC(i2) at n=5

WACC

0.1500 0.1000 0.0500 0.0000

1

2

3

4

5

6

7

8

9

10

i2 Fig. 29.12 The dependence of the weighted average cost of capital (WACC) on interests on credit leverage ratio (i2) at company age n = 5

29.5.3

Coverage Ratios of Debt and Interest on the Credit (New Ratios)

As we have derived above the dependence of the weighted average cost of capital (WACC) on debt and interests on credit coverage ratio (i3) in the BFO theory is described by the following formula: i3 

ð1 - ð1 þ WACCÞ - n Þ ð1 - ð1 þ K 0 Þ - n Þ - i3  WACC K0

-

t  ½ 1 - ð1 þ K d Þ - n  = 0: ð K d þ 1Þ

ð29:23Þ

Here i3 =

CF : ð K d þ 1Þ  D

ð29:24Þ

Using it, we get the following results, representing in Table 29.12 and Fig. 29.13 for company age n = 3 and in Table 29.13 and Fig. 29.14 for company age n = 5. Consolidated data of dependence of WACC on i1, i2, i3, at company age n = 3 and n = 5 are shown in Figs. 29.15 and 29.16.

29.5.4

Analysis and Conclusions

It is seen from Tables 29.1, 29.2, 29.3, 29.4, 29.5, 29.6, 29.7, 29.8, 29.9, 29.10, 29.11, 29.12, and 29.13 and Figs. 29.1, 29.2, 29.3, 29.4, 29.5, 29.6, 29.7, 29.8, 29.9,

694

29 Rating Methodology: New Look and New Horizons

Table 29.12 The dependence of the weighted average cost of capital (WACC) on debt and interests on credit leverage ratio (i3) at company age n=3

i3 1 2 3 4 5 6 7 8 9 10

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

K0 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

Kd 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08

WACC 0.1303 0.1351 0.1367 0.1376 0.1380 0.1384 0.1386 0.1388 0.1389 0.1390

n 3 3 3 3 3 3 3 3 3 3

BFO 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

WACC

WACC(i3) at n=3 0.1400 0.1380 0.1360 0.1340 0.1320 0.1300 0.1280 0.1260 0.1240

1

2

3

4

5

6

7

8

9

10

i3 Fig. 29.13 The dependence of the weighted average cost of capital (WACC) on debt and interests on credit leverage ratio (i3) at company age n = 3 Table 29.13 The dependence of the weighted average cost of capital (WACC) on debt and interests on credit leverage ratio (i3) at company age n=5

i3 1 2 3 4 5 6 7 8 9 10

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

K0 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

Kd 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08

WACC 0.1329 0.1364 0.1376 0.1382 0.1386 0.1388 0.1390 0.1391 0.1392 0.1393

n 5 5 5 5 5 5 5 5 5 5

BFO 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

29.10, 29.11, 29.12, 29.13, 29.14, 29.15, and 29.16 that WACC(ij) is increasing function on ij with saturation WACC = k0 at high values of ij. Note that this saturation for companies of finite age is a little bit more gradual than in case of perpetuity companies: in latter case the saturation takes place around ij value of order 1 for ratios i1 and i3 and of order 4 or 5 for ratios i2. In perpetuity case as well as in

29.5

Coverage Ratios (Different Capital Cost Values)

695

WACC(i3) at n=5 0.1400

WACC

0.1380 0.1360 0.1340 0.1320 0.1300 0.1280

1

2

3

4

5

6

7

8

9

10

i3 Fig. 29.14 The dependence of the weighted average cost of capital (WACC) on debt and interests on credit leverage ratio (i3) at company age n = 5

WACC

WACC (i1), WACC (i2), WACC (i3) at n=3 0.1600 0.1400 0.1200 0.1000 0.0800 0.0600 0.0400 0.0200 0.0000

1

2

3

4

5

6

7

8

9

10

WACC (i1) 0.1298 0.1347 0.1365 0.1374 0.1379 0.1382 0.1385 0.1387 0.1388 0.1389 WACC (i2) 0.0285 0.0795 0.0985 0.1084 0.1145 0.1186 0.1216 0.1238 0.1256 0.1270 WACC (i3) 0.1303 0.1351 0.1367 0.1376 0.1380 0.1384 0.1386 0.1388 0.1389 0.1390 i

Fig. 29.15 Consolidated data of dependence of WACC on i1, i2, i3, at company age n = 3

WACC

WACC (i1), WACC (i2), WACC (i3) at n=5 0.1600 0.1400 0.1200 0.1000 0.0800 0.0600 0.0400 0.0200 0.0000

1

2

3

4

5

6

7

8

9

10

WACC (i1) 0.1324 0.1362 0.1374 0.1381 0.1385 0.1387 0.1389 0.1390 0.1391 0.1392 WACC (i2) 0.0583 0.0957 0.1096 0.1169 0.1213 0.1244 0.1265 0.1282 0.1295 0.1305 WACC (i3) 0.1329 0.1364 0.1376 0.1382 0.1386 0.1388 0.1390 0.1391 0.1392 0.1393 i

Fig. 29.16 Consolidated data of dependence of WACC on i1, i2, i3, at company age n = 5

696

29 Rating Methodology: New Look and New Horizons

case of companies of finite age at saturation WACC reaches the value k0 (equity value at zero leverage level). This means that for high values of ij one can choose k0 as a discount rate with a very good accuracy in perpetuity case and with a little bit less accuracy in general case (companies of arbitrary ages). Thus the role of parameter k0 increases drastically. The method of determination of parameter k0 has been developed by Anastasiya Brusova (2011). So, parameter k0 is the discount rate for case of high values of ij. In case of ratio i2 in general case as well as in perpetuity case the saturation of WACC (i2) takes place at higher values of i2. In opposite to perpetuity case within BFO theory one could make calculations for companies of arbitrary age because a factor of time presents in this theory. Our calculations show that curve WACC (ij) for company of higher age lies above this curve for younger company. And with increase of ij value the WACC values for different company ages n become closer each other. Note that curves WACC(i1) and WACC(i3) are very close each other at small enough credit rates, but difference between them will become bigger at higher values of credit rates. Curve WACC(i2) turns out to be enough different from WACC(i1) and curves WACC(i3).

29.6

Leverage Ratios

29.6.1

Leverage Ratios for Debt

We will analyze the dependence of company weighted average cost of capital (WACC) on leverage ratios (l1, l2, l3). We will make calculation for capital costs k0 = 10%, kd = 6%, t = 20%, n = 3; 5; l values range from 0 to 10. Dividing the both parts of the formula (29.6) by the income value for one-period CF, we enter the leverage ratios l1 for debt into the general BFO theory ð1 - ð1 þ WACCÞ - n Þ ð1 - ð1 þ K 0 Þ - n Þ - t  ½1- ð1 þ K d Þ - n  WACC K0  l1 = 0:

ð29:25Þ

Here l1 =

D : CF

ð29:26Þ

Remind that here WACC is the weighted average cost of capital of the company, l1—the leverage ratios l1 for debt, t is the tax on profit rate for organizations (t = 20%), k0—equity cost of financially-independent company, kd is the debt capital cost; n is the company age, CF—income value for one period; D—debt capital value.

29.6

Leverage Ratios

697

Table 29.14 The dependence of company weighted average cost of capital (WACC) on debt leverage ratio, l1, at n = 3

l1 0 1 2 3 4 5 6 7 8 9 10

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

k0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

WACC(l1) 0.1000 0.0928 0.0857 0.0787 0.0720 0.0654 0.0587 0.0523 0.0461 0.0399 0.0339

n 3 3 3 3 3 3 3 3 3 3 3

BFO 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

WACC(l 1 ) at n=3 0.1000

WACC

0.0800 0.0600 0.0400 0.0200 0.0000

1

2

3

4

5

l1

6

7

8

9

10

Fig. 29.17 The dependence of company weighted average cost of capital (WACC) on debt leverage ratio at n = 3

The ratio (l2) can be used to assess the following parameters used in rating, Interests/EBITDA and some others. Using the above equation, we get the following results, representing in Table 29.14 and Fig. 29.17 for company age n = 3 and in Table 29.15 and Fig. 29.18 for company age n = 5.

29.6.2

Leverage Ratios for Interest on Credit

The dependence of company weighted average cost of capital (WACC) on leverage ratios on interests on credit l2 is described within BFO theory by the following formula:

698

29 Rating Methodology: New Look and New Horizons

Table 29.15 The dependence of company weighted average cost of capital (WACC) on debt leverage ratio, l1, at n = 5

l1 0 1 2 3 4 5 6 7 8 9 10

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

k0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

WACC(l1) 0.1000 0.0948 0.0898 0.0848 0.0799 0.0752 0.0705 0.0660 0.0615 0.0571 0.0528

n 5 5 5 5 5 5 5 5 5 5 5

BFO 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

WACC(l 1 )at n=5 0.1000

WACC

0.0800 0.0600 0.0400 0.0200 0.0000

1

2

3

4

5

L1

6

7

8

9

10

Fig. 29.18 The dependence of company weighted average cost of capital WACC on debt leverage ratios at n = 5

ð1 - ð1 þ WACCÞ - n Þ ð1 - ð1 þ K 0 Þ - n Þ WACC K0 -

ðt  l 2  ½ 1 - ð 1 þ K d Þ - n  Þ = 0: Kd

ð29:27Þ

Here l2 =

Kd  D : CF

ð29:28Þ

Using it, we find the dependence WACC(l2) at company ages n = 3 and n = 5. This ratio l2 can be used to assess the following parameters used in rating, Interests/EBITDA and some others. Using the above equation, we get the following results, representing in Table 29.16 and Fig. 29.19 for company age n = 3 and in Table 29.17 and Fig. 29.20 for company age n = 5.

29.6

Leverage Ratios

699

Table 29.16 The dependence of company weighted average cost of capital (WACC) on leverage ratio of interests on credit, l2, at company age n=3

l2 0 1 2 3 4 5 6 7 8 9 10

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

k0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

WACC(l2) 0.0998 -0.0036 -0.0804 -0.1403 -0.1888 -0.2289 -0.2629 -0.2922 -0.3178 -0.3404 -0.3605

n 3 3 3 3 3 3 3 3 3 3 3

BFO 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

WACC(l 2 ) at n=3 1

2

3

4

5

6

7

8

10

9

WACC

0.0000 -0.0500 -0.1000 -0.1500 -0.2000 -0.2500 -0.3000 -0.3500 -0.4000

L2

Fig. 29.19 The dependence of company weighted average cost of capital (WACC) on leverage ratio of interests on credit at company age n = 3 Table 29.17 The dependence of company weighted average cost of capital (WACC) on leverage ratio of interests on credit, l2, at company age n=5

l2 0 1 2 3 4 5 6 7 8 9 10

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

k0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

WACC(l2) 0.1000 0.0259 -0.0296 -0.0732 -0.1089 -0.1388 -0.1643 -0.1865 -0.2061 -0.2235 -0.2391

n 5 5 5 5 5 5 5 5 5 5 5

BFO 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

The dependence of company weighted average cost of capital (WACC) on leverage ratios on debt and interests on credit l3 is described within BFO theory by the following formula:

700

29 Rating Methodology: New Look and New Horizons

WACC

WACC(l 2 ) 0.0500 0.0000 -0.0500 -0.1000 -0.1500 -0.2000 -0.2500 -0.3000

1

2

3

4

5

6

7

8

9

10

L2

Fig. 29.20 The dependence of company weighted average cost of capital (WACC) on leverage ratio of interests on credit at company age n = 3

ð1 - ð1 þ WACCÞ - n Þ ð1 - ð1 þ K 0 Þ - n Þ WACC K0 -

t  l 3  ½ 1 - ð1 þ K d Þ - n  = 0: ðK d þ 1Þ

ð29:29Þ

Here l3 =

ð K d þ 1Þ  D : CF

ð29:30Þ

The ratio l3 can be used to assess the following parameters used in rating, Debt + interest/FFO, Debt + interest/EBIT, Debt + interest/EBITDA(R), and some others. Using the above equation, we get the following results for the dependence WACC(l3), representing in Table 29.18 and Fig. 29.21 for company age n = 3 and in Table 29.19 and Fig. 29.22 for company age n = 5. Below we represent the consolidated data of dependence of WACC on l1, l2, l3, at company age n = 3 (Figs. 29.23 and 29.24) n = 5.

29.7 29.7.1

Leverage Ratios (Different Capital Costs) Leverage Ratios for Debt

Below we analyze the dependence of company weighted average cost of capital (WACC) on leverage ratios l1, l2, l3, at capital costs values k0 = 12%, kd = 6%. As before t = 20%, company age n = 3; 5, leverage ratios values range from 0 to 10.

29.7

Leverage Ratios (Different Capital Costs)

Table 29.18 The dependence of company weighted average cost of capital (WACC) on leverage ratio on debt and interests on credit, l3, at company age n = 3

l3 0 1 2 3 4 5 6 7 8 9 10

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

701 k0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

WACC(l3) 0.1000 0.0930 0.0864 0.0798 0.0734 0.0671 0.0608 0.0548 0.0489 0.0430 0.0371

n 3 3 3 3 3 3 3 3 3 3 3

BFO 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

WACC(l 3 ) at n=3 0.1000

WACC

0.0800 0.0600 0.0400 0.0200 0.0000

1

2

3

4

5

L3

6

7

8

9

10

Fig. 29.21 The dependence of company weighted average cost of capital (WACC) on leverage ratio on debt and interests on credit at company age n = 3 Table 29.19 The dependence of company weighted average cost of capital (WACC) on leverage ratio on debt and interests on credit, l3, at company age n = 5

l3 0 1 2 3 4 5 6 7 8 9 10

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

k0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

WACC(l3) 0.1000 0.0951 0.0903 0.0856 0.0810 0.0765 0.0721 0.0678 0.0635 0.0593 0.0552

n 5 5 5 5 5 5 5 5 5 5 5

BFO 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

The dependence of company weighted average cost of capital (WACC) on leverage ratios on debt l1 is described within BFO theory by the following formula:

702

29 Rating Methodology: New Look and New Horizons

WACC(l 3 ) 0.1000 WACC

0.0800 0.0600 0.0400 0.0200 0.0000

1

2

3

4

5

L3

6

7

8

9

10

Fig. 29.22 The dependence of company weighted average cost of capital (WACC) on leverage ratio of debt and interests on credit at company age n = 5

WACC(l 1 ), WACC(l 2 ), WACC(l 3 ) 0.2000

WACC(l1)

WACC(l2)

WACC(l3)

0.1000

WACC

0.0000

0

2

4

6

8

10

12

-0.1000

-0.2000

-0.3000

-0.4000

L

Fig. 29.23 Consolidated data of dependence of WACC on l1, l2, l3, at company age n = 3

ð1 - ð1 þ WACCÞ - n Þ ð1 - ð1 þ k0Þ - n Þ – –t  c  l1 = 0 WACC k0 Here

ð29:31Þ

29.7

Leverage Ratios (Different Capital Costs)

703

WACC(l 1 ), WACC(l 2 ), WACC(l 3 ) WACC(l1)

0.1500

WACC(l2)

WACC(l3)

0.1000 0.0500

WACC

0.0000

0

2

4

6

8

10

12

-0.0500 -0.1000 -0.1500 -0.2000 -0.2500 -0.3000

l

Fig. 29.24 Consolidated data of dependence of WACC on l1, l2, l3, at company age n = 5

l1 =

D : CF

ð29:32Þ

Using it, we find the dependence WACC(l1) at company ages n = 3 (Table 29.20 and Fig. 29.25) and n = 5 (Table 29.21 and Fig. 29.26).

29.7.2

Leverage Ratios for Interests on Credit

The dependence of company weighted average cost of capital (WACC) on leverage ratios on interests on credit l2 is described within BFO theory by the following formula: ð1 - ð1 þ WACCÞ - n Þ ð1 - ð1 þ K0Þ - n Þ t  l2  ð1 - ð1 þ kd Þ - n Þ – – WACC k0 kd =0 Here

ð29:33Þ

704

29 Rating Methodology: New Look and New Horizons

Table 29.20 The dependence of company weighted average cost of capital (WACC) on leverage ratio of debt, l1, at company age n = 3

l1 0 1 2 3 4 5 6 7 8 9 10

k0 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12

kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

n1 3 3 3 3 3 3 3 3 3 3 3

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

WACC 0.119997 0.112294 0.104774 0.097444 0.090128 0.083078 0.076332 0.06959 0.062962 0.056492 0.050163

БФО 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

WACC (l1) at n=3

WACC

0.15 0.1 0.05 0

WACC

0

1

2

3

4

5

6

7

8

9

10

L1 Fig. 29.25 The dependence of company weighted average cost of capital (WACC) on leverage ratio of debt at company age n = 3 Table 29.21 The dependence of company weighted average cost of capital (WACC) on leverage ratio of debt, l1, at company age n = 5

l1 0 1 2 3 4 5 6 7 8 9 10

k0 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12

kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

n1 5 5 5 5 5 5 5 5 5 5 5

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

WACC 0.119994 0.114311 0.108927 0.103556 0.098332 0.093123 0.088164 0.083265 0.078452 0.073744 0.069

БФО 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

29.7

Leverage Ratios (Different Capital Costs)

705

WACC (l1) at n=5

WACC

0.15 0.1 0.05 0

WACC 0

1

2

3

4

5

6

7

8

9

10

L1 Fig. 29.26 The dependence of company weighted average cost of capital (WACC) on leverage ratio of debt at company age n = 3 Table 29.22 The dependence of company weighted average cost of capital (WACC) on leverage ratio of interests on credit, l2, at company age n=3

l2 0 1 2 3 4 5 6 7 8 9 10

k0 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12

l2 =

kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

n1 3 3 3 3 3 3 3 3 3 3 3

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

WACC 0.119997 0.010838 -0.06941 -0.13171 -0.18169 -0.22298 -0.25785 -0.28784 -0.31392 -0.33692 -0.35745

D  kd : CF

БФО 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

ð29:34Þ

Using it, we find the dependence WACC(l2) at company ages n = 3 (Table 29.22 and Fig. 29.27) and n = 5 (Table 29.23 and Fig. 29.28).

29.7.3

Leverage Ratios for Debt and Interests on Credit

The dependence of company weighted average cost of capital (WACC) on leverage ratios on debt and interests on credit l3 is described within BFO theory by the following formula:

706

29 Rating Methodology: New Look and New Horizons

WACC (l2) at n=3 0.2

WACC

0.1 0

-0.1 0

1

2

3

4

5

6

7

8

9

10

-0.2

WACC

-0.3 -0.4

L2

Fig. 29.27 The dependence of company weighted average cost of capital (WACC) on leverage ratio of interests on credit at company age n = 3 Table 29.23 The dependence of company weighted average cost of capital (WACC) on leverage ratio of interests on credit, l2, at company age n=5

k0 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12

l2 0 1 2 3 4 5 6 7 8 9 10

kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

n1 5 5 5 5 5 5 5 5 5 5 5

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

WACC 0.119994 0.040367 -0.01846 -0.06439 -0.10159 -0.13262 -0.15899 -0.18185 -0.20194 -0.21978 -0.23578

БФО 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

WACC (l2) at n=5 0.2

WACC

0.1 0 -0.1

0

1

2

3

4

5

6

7

8

9

10

WACC

-0.2 -0.3

L2

Fig. 29.28 The dependence of company weighted average cost of capital (WACC) on leverage ratio of interests on credit at company age n = 5

29.7

Leverage Ratios (Different Capital Costs)

707

ð1 - ð1 þ WACCÞ - n Þ ð1 - ð1 þ K0Þ - n Þ t  l3  ð1 - ð1 þ kd Þ - n Þ – – WACC K0 1 þ Kd = 0:

ð29:35Þ

Here l3 =

Dð1 þ kd Þ : CF

ð29:36Þ

Using it, we find the dependence WACC(l3) at company ages n = 3 (Table 29.24 and Fig. 29.29) and n = 5 (Table 29.25 and Fig. 29.30). Consolidated data of dependence of WACC on l1, l2, l3, at company age n = 3. (Fig. 29.31) and for n = 5 (Fig. 29.32).

29.7.4

Analysis and Conclusions

It is seen from Tables 29.14, 29.15, 29.16, 29.17, 29.18, 29.19, 29.20, 29.21, 29.22, 29.23, and 29.24 and Figs. 29.17, 29.18, 29.19, 29.20, 29.21, 29.22, 29.23, 29.24, 29.25, 29.26, 29.27, 29.28, 29.29, 29.30, 29.31, and 29.32 that WACC(lj) is decreasing function on lj. WACC decreases from value of k0 (equity value at zero leverage level) practically linearly for WACC(l1) and WACC(l3) and with higher speed for WACC(l2). In opposite to perpetuity case within BFO theory one could make calculations for companies of arbitrary age because a factor of time presents in this theory. Our calculations show that curve WACC (li) for company of higher age lies above this curve for younger company. Note that curves WACC(l1) and WACC(l3) are very close to each other at small enough credit rates, but difference between them will become bigger at higher values of credit rates.

Table 29.24 The dependence of company weighted average cost of capital (WACC) on leverage ratio of debt and interests on credit, l3, at company age n = 3

l3 0 1 2 3 4 5 6 7 8 9 10

k0 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12

kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

n 3 3 3 3 3 3 3 3 3 3 3

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

WACC 0.119997 0.112716 0.105604 0.098686 0.091785 0.085114 0.078654 0.072249 0.065828 0.059771 0.053729

BFO 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

708

29 Rating Methodology: New Look and New Horizons

WACC (l3) at n=3

WACC

0.15 0.1 0.05 0

WACC

0

1

2

3

4

5

6

7

8

9

10

L3 Fig. 29.29 The dependence of company weighted average cost of capital (WACC) on leverage ratio of debt and interests on credit at company age n = 3 Table 29.25 The dependence of company weighted average cost of capital (WACC) on leverage ratio of debt and interests on credit, l3, at company age n = 5

l3 0 1 2 3 4 5 6 7 8 9 10

k0 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12

kd 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

n 5 5 5 5 5 5 5 5 5 5 5

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

WACC 0.119994 0.114614 0.10954 0.104444 0.099512 0.094598 0.08988 0.0852 0.080618 0.076129 0.071733

BFO 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

WACC (L3) at n=5

WACC

0.15 0.1 0.05 0

WACC

0

1

2

3

4

5

6

7

8

9

10

L3 Fig. 29.30 The dependence of company weighted average cost of capital (WACC) on leverage ratio of debt and interests on credit at company age n = 5

29.8

Conclusions

709

WACC(l1, l2, l3) at n=3 0.2 0.1

WACC

0 -0.1

0

1

2

3

4

5

6

7

8

9

10

WACC (L1) WACC (L2)

-0.2

WACC (L3)

-0.3 -0.4

L

Fig. 29.31 Consolidated data of dependence of WACC on l1, l2, l3, at company age n = 3

WACC

WACC (l1, l2, l3) at n=5 0.15 0.1 0.05 0 -0.05 0 -0.1 -0.15 -0.2 -0.25 -0.3

1

2

3

4

5

6

7

8

9

10

WACC (L1) WACC (L2) WACC (L3)

L

Fig. 29.32 Consolidated data of dependence of WACC on l1, l2, l3, at company age n = 5

Curve WACC(l2) turns out to be enough different from WACC(l1) and curves WACC(l3).

29.8

Conclusions

In the current chapter, further development of a new approach to rating methodology has been done. We have generalized it for the general case of modern theory of capital structure (Brusov–Filatova–Orekhova (BFO) theory): for companies of arbitrary age. A serious modification of BFO theory in order to use it in rating procedure has been required. It allows to apply obtained results for real economics, where all companies have finite lifetime, introduce a factor of time into theory, estimate the

710

29 Rating Methodology: New Look and New Horizons

creditworthiness of companies of arbitrary age (or arbitrary lifetime), introduce discounting of the financial flows, using the correct discount rate, etc. This allows to use the powerful tools of BFO theory in the rating. All these create a new base for rating methodologies.

References Brusov PN, Filatova ТV (2011) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Financ Credit 435:2–8 Brusov P, Filatova T, Orehova N, Brusova A (2011a) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Appl Financ Econ 21(11): 815–824 Brusov P, Filatova T, Orehova N et al (2011b) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Bus ICT 2:16–21 Brusov P, Filatova T, Orehova N et al (2011c) Influence of debt financing on the effectiveness of the investment project within the Modigliani–Miller theory. Res J Econ Bus ICT (UK) 2:11–15 Brusov P, Filatova T, Orehova N, Brusov PP, Brusova N (2011d) From Modigliani–Miller to general theory of capital cost and capital structure of the company. Res J Econ Bus ICT 2:16–21 Brusov P, Filatova T, Orekhova N, Brusov P, Brusova A (2012a) Modern approach to dividend policy of company. Financ Credit 18(37):2012 Brusov P, Filatova T, Eskindarov M, Orehova N (2012b) Influence of debt financing on the effectiveness of the finite duration investment project. Appl Financ Econ 22(13):1043–1052 Brusov P, Filatova T, Eskindarov M, Orehova N (2012c) Hidden global causes of the global financial crisis. J Rev Glob Econ 1:106–111 Brusov P, Filatova P, Orekhova N (2013a) Absence of an optimal capital structure in the famous tradeoff theory! J Rev Glob Econ 2:94–116 Brusov P, Filatova T, Orehova N (2013b) A qualitatively new effect in corporative finance: abnormal dependence of cost of equity of company on leverage. J Rev Glob Econ 2:183–193 Brusov P, Filatova P, Orekhova N (2014a) Mechanism of formation of the company optimal capital structure, different from suggested by trade off theory. Cogent Econ Financ 2:1–13. https://doi. org/10.1080/23322039.2014.946150 Brusov P, Filatova T, Orehova N (2014b) Inflation in Brusov–Filatova–Orekhova theory and in its perpetuity limit–Modigliani–Miller theory. J Rev Glob Econ 3:175–185 Brusov P, Filatova T, Orekhova N (2021) Ratings: critical analysis and new approaches of quantitative and qualitative methodology. Springer Nature Publishing Brusov P, Filatova T, Orehova N, Eskindarov M (2015) Modern corporate finance, investment and taxation. Springer, pp 1–368 Brusov P, Filatova T, Orehova N, Kulik V (2018) Rating: new approach. J Rev Glob Econ 7:37–62 Brusova A (2011) А comparison of the three methods of estimation of weighted average cost of capital and equity cost of company. Financ Anal Prob Sol 34(76):36–42 Filatova Т, Orehova N, Brusova А (2008) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Bull FU 48:68–77 Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Modigliani F, Miller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391

Chapter 30

Application of the Modigliani–Miller Theory, Modified for the Case of Advance Payments of Tax on Profit, in Rating Methodologies

Keywords The Modigliani–Miller theory · Advance payments of tax on profit · Rating methodologies Recently we have generalized the Modigliani and Miller theory for a more realistic method of payments of tax on profit payments: for the case of advance payments of tax on profit, which is widely used in practice (Brusov et al. 2020a, b). Modigliani– Miller theory accounts these tax payments as annuity–immediate, while in practice these payments are making in advance and thus should be accounting as annuity due. We have shown that this generalization leads to some important consequences, which change seriously all the main statements by Modigliani and Miller. In the current chapter, we use the modified Modigliani–Miller theory (MMM theory) and apply it for rating methodology needs. A serious modification of MMM theory in order to use it in rating procedure has been required. The financial “ratios” (main rating parameters) were introduced into MMM theory. The necessity of an appropriate use of financial flows discounting in rating methodologies is discussed. The dependence of the weighted average cost of capital (WACC), which plays the role of discount rate, on coverage and leverage ratios is analyzed. Obtained results make possible to use the power of this theory in the rating and create a new base for rating methodologies; in other words, this allows development of a new approach to methodology of rating, requiring a serious modification of the existing rating methodologies (Brusov et al. 2021).

30.1

Introduction

In our previous chapters (Brusov et al. 2018a–g, 2019, 2020b) we have applied the theory of Nobel Prize winners Modigliani and Miller, which is the perpetuity limit of the general theory of capital cost and capital structure—Brusov–Filatova–Orekhova (BFO) theory (Brusov 2018a, b; Filatova et al. 2008, 2018; Brusov et al. 2014a, b, 2015, 2018a–g) for rating needs. It has become a very important step in developing a qualitatively new rating methodology. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_30

711

712

30 Application of the Modigliani–Miller Theory, Modified for the Case. . .

Recently we have generalized the Modigliani and Miller theory (Мodigliani and Мiller 1958, 1963, 1966) for a more realistic method of tax on profit payments: for the case of advance payments of tax on profit, which is widely used in practice (Brusov et al. 2020a, b). Modigliani–Miller theory accounts these tax payments as annuity–immediate, while in practice these payments are making in advance and thus should be accounting as annuity due. We have shown that this generalization leads to some important consequences, which change seriously all the main statements by Modigliani and Miller (Мodigliani and Мiller 1958, 1963, 1966). These consequences are as follows: WACC starts depend on debt cost kd, WACC turns out to be lower than in case of classical Modigliani–Miller theory and thus company capitalization becomes higher than in ordinary Modigliani–Miller theory. We show that equity dependence on leverage level L is still linear, but the tilt angle with respect to L-axis turns out to be smaller: this could lead to modification of the dividend policy of the company. In the current chapter, we use modified Modigliani–Miller theory (MMM theory) and apply it for rating methodology needs. A serious modification of MMM theory in order to use it in rating procedure has been required. The financial “ratios” (main rating parameters) were introduced into MMM theory. The necessity of an appropriate use of financial flows discounting in rating methodologies is discussed. The dependence of the weighted average cost of capital (WACC), which plays the role of discount rate, on coverage, and leverage ratios is analyzed. Obtained results make possible to use the power of this theory in the rating and create a new base for rating methodologies; in other words, this allows development of a new approach to methodology of rating, requiring a serious modification of the existing rating methodologies.

30.2

Modified Modigliani–Miller Theory

Let us shortly discuss some main points of modified Modigliani–Miller (MMM) theory and its features, which are different from ones of “classical” Modigliani– Miller theory (Brusov et al. 2020a, b). Tax Shield To calculate tax shield TS in case of advance tax payments one should use annuity due TS = k d Dt þ

k d Dt k d Dt k d Dt  þ⋯=  þ ð 1 þ k d Þ ð1 þ k d Þ2 1 - ð1 þ k d Þ - 1

= Dt ð1 þ k d Þ

ð30:1Þ

This expression is different from the case of classical Modigliani–Miller theory (which used annuity–immediate).

30.2

Modified Modigliani–Miller Theory

TS =

k d Dt k Dt k d Dt  d  = Dt þ ⋯= þ ð 1 þ k d Þ ð1 þ k d Þ2 ð1 þ k d Þ 1 - ð 1 þ k d Þ - 1

713

ð30:2Þ

Thus, in the former case tax shield TS is bigger by multiplier (1 + kd). This is connected with the time value of money: money today is more expensive than money tomorrow due to the possibility of their alternative investment. Weighted Average Cost of Capital (WACC) For WACC in MMM theory we have the following formula: WACC = k0 ð1- wd t ð1 þ kd ÞÞ: At

L→1

WACC = k 0 ð1- t ð1 þ kd ÞÞ:

ð30:3Þ ð30:4Þ

This expression is different from the similar one in classical Modigliani–Miller theory WACC = k0 ð1- wd t Þ

ð30:5Þ

At L → 1 WACC = k0(1 - t). From these expressions it is seen that WACC decreases with L, achieving lower value WACC = k0(1 - t(1 + kd)) at L → 1 in considering case comparing with classical Modigliani–Miller theory WACC = k0(1 - t). This means also that company capitalization becomes higher than in ordinary Modigliani–Miller theory. Let us compare the dependence of the weighted average cost of capital, WACC, on leverage level in “classical” Modigliani–Miller theory (MM theory) and in modified Modigliani–Miller theory (MMM theory) (Fig. 30.1). Study of such dependence is very important, because the weighted average cost of capital, WACC, plays the role of discount rate in operating financial flows discounting as well as of financial flows in rating methodologies. WACC’s value determines as well the capitalization of the company V = CF/WACC. – in “classical” Modigliani–Miller theory (curve WACC(0)) and – in modified Modigliani–Miller theory (MMM theory) at different values of debt cost: kd = 0.18; kd = 0.14; kd = 0.1 (curves WACC(0′)). From Fig. 30.1 it is seen that WACC in MMM theory turns out to be lower than in case of classical Modigliani–Miller theory and thus company capitalization becomes higher than in ordinary Modigliani–Miller theory. It is seen that WACC decreases with debt cost kd. In paper (Brusov et al. 2020a, b) we study as well the equity cost dependence on leverage level L and show that it is still linear, but the tilt angle with respect to L-axis turns out to be smaller in MMM theory tgα = (k0 - kd)  (1 - t) - k0kdt than in classical Modigliani–Miller theory tgα = (k0 - kd)  (1 - t). This could lead to modification of the dividend policy of the company, because the equity cost

30 Application of the Modigliani–Miller Theory, Modified for the Case. . .

714

WACC(L) 0.2100 0.2000

WACC

0.1900 WACC (0) WACC (0') kd=0,18 WACC (0') kd=0,14 WACC (0') kd=0,1

0.1800 0.1700 0.1600 0.1500

0

1

2

3

4

5

6

7

8

9

10

Fig. 30.1 Dependence of WACC on leverage level L

represents itself economically sound value of dividends. Thus, company could decrease the value of dividends, which they should pay to shareholders. Correct account of a method of tax on profit payments demonstrates that shortcomings of Modigliani–Miller theory are dipper than everybody suggested: the underestimation of WACC really turns out to be bigger, as well as overestimation of the capitalization of the company. This means that systematic risks arising from the use of modified Modigliani–Miller theory (MMM theory) (which is more correct than “classical” one) in practice are higher than it was suggested by the “classical” version of this theory. Because the advance payments of tax on profit is widely used in practice, modified Modigliani–Miller theory (MMM theory) should be used instead of classical version of this theory (MM theory). And below we apply the modified Modigliani–Miller theory for rating needs.

30.3

Application of Modified Modigliani–Miller Theory for Rating Needs

The financial “ratios” constitute direct and inverse ratios of various generated cash flows to debt values and interest ones and play quite significant role in quantification of the creditworthiness of the issuers. The examples of such ratios are as follows:

30.3

Application of Modified Modigliani–Miller Theory for Rating Needs

715

DCF/Debt, FFO/Debt, CFO/Debt, FOCF/Debt, FFO/cashinterest, EBITDA/interest, Interests/EBITDA, Debt/EBITDA, and some others. We introduce these financial “ratios” into the modified perpetuity limit of modern theory of capital structure—BFO theory (MMM theory), which is valid for companies of arbitrary age. This is quite important because it allows to use this theory as a powerful tool when discounting of financial flows using the correct discounting rate in rating. This has required the modification of the perpetuity limit of the BFO theory— modified Modigliani–Miller theory (MMM theory). The needs of modification are connected to the fact that used in financial management the concept of “leverage” as the ratio of debt value to the equity value substantially differs from the concept of “leverage” in the rating, where it is understood as ratio of the debt value to the generated cash flow values (income, profit, etc.). Developed by us recently (Brusov et al. 2020a, b) modified Modigliani–Miller theory (MMM theory) with corporate taxes (Modigliani and Miller 1966) shows that capitalization of financially dependent (leveraged) company, VL, is equal to the capitalization of financially independent (unleveraged) company, V0, increased by the size of the tax shield for perpetuity time, Dt(1 + kd), V L = V 0 þ Dt ð1 þ kd Þ:

ð30:6Þ

Substituting the expressions for both capitalizations, one has CF CF þ Dt ð1 þ k d Þ = WACC k0

ð30:7Þ

Let us now introduce the parameters, using in ratings (ratios), into modified Modigliani–Miller theory (MMM theory), which represents a perpetuity limit of modern theory of capital structure by Brusov–Filatova–Orekhova theory (BFO theory) (Brusov et al. 2015, 2018a–g, 2019). Two kinds of financial ratios will be considered: coverage ratios and leverage ratios. We will start from the coverage ratios.

30.3.1

Coverage Ratios

We will consider three kinds of coverage ratios: coverage ratio of debt, coverage ratio of interest on the credit, and coverage ratio of debt and interest on the credit.

30.3.1.1

Coverage Ratios of Debt

Let us consider first the coverage ratios of debt i1 = CF/D .

716

30 Application of the Modigliani–Miller Theory, Modified for the Case. . .

Dividing both parts of Eq. (30.7) by D one gets i1 i = 1 þ t ð1 þ k d Þ WACC k0 i þ k 0 t ð1 þ k d Þ i1 = 1 k0 WACC i1 k 0 WACC = i1 þ tk 0 ð1 þ kd Þ

ð30:8Þ

The coverage ratio of debt i1 = CF/D could be used for assessment of the following rating ratios: DCF/Debt, FFO/Debt, CFO/Debt, FOCF/Debt, and some others. Formula (30.8) will be used to find a dependence WACC(i1).

30.3.1.2

Coverage Ratios of Interest on the Credit

Consider now coverage ratio of interest on the credit i2 = CF/kdD . Using the modified Modigliani—Miller theory (MMM theory) for case with corporate taxes V L = V 0 þ Dt ð1 þ kd Þ, and dividing the both parts by kdD, one could derive the expression for dependence WACC(i2) CF CF þ Dt ð1 þ k d Þ = WACC k0 t ð1 þ k d Þ i i2 = 2þ kd WACC k0 i2 k 0 k d WACC = i2 kd þ tk 0 ð1 þ kd Þ

ð30:9Þ

This ratio (i2) could be used for assessment of the following parameters, used in rating, FFO/cashinterest, EBITDA/interest, and some others. Formula (30.9) will be used to find a dependence WACC(i2).

30.3.1.3

Coverage Ratios of Debt and Interest on the Credit

Below we consider the coverage ratios of debt and interest on the credit simultaCF neously i3 = Dð1þk . This is a new value, introduced by us here for the first time. dÞ Using the modified Modigliani–Miller theory (MMM theory) for case with corporate taxes

30.3

Application of Modified Modigliani–Miller Theory for Rating Needs

717

V L = V 0 þ Dt ð1 þ kd Þ and dividing the both parts by (1 + kd)D we get the dependence WACC(i3) CF CF þ Dt ð1 þ k d Þ = WACC k0 i i3 t = 3þ WACC k0 k d i k k WACC = 3 0 d i3 kd þ tk 0

ð30:10Þ

This ratio (i3) could be used for assessment of the following rating ratios: FFO/Debt + interest, EBITDA/Debt + interest, and some others. Formula (30.10) will be used to find a dependence WACC(i3).

30.3.2

Dependence of WACC on Leverage Ratios of Debt in “Classical” Modigliani–Miller Theory (MM Theory) and Modified Modigliani–Miller Theory (MMM Theory)

Below we study the dependences of WACC on leverage ratios of debt in “classical” Modigliani–Miller theory (MM theory) and modified Modigliani–Miller theory (MMM theory). We use Microsoft Excel and the following parameters: equity cost at L = 0 k0 = 0.2; tax on profit rate t = 0.2; debt cost kd = 0.1;0.14;0.18; leverage ratios of debt l1 = 0;1;2;3;4;5;6;7;8;9;10. Dependence of WACC on coverage ratios of debt in “classical” Modigliani–Miller theory is shown in Table 30.1.

Table 30.1 Dependence of WACC on coverage ratios of debt in “classical” Modigliani–Miller theory

ko 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

i1 0 1 2 3 4 5 6 7 8 9 10

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

WACC 0.0000 0.1923 0.1961 0.1974 0.1980 0.1984 0.1987 0.1989 0.1990 0.1991 0.1992

718

30 Application of the Modigliani–Miller Theory, Modified for the Case. . .

Table 30.2 Dependence of WACC on coverage ratios of debt in modified Modigliani– Miller theory (MMM theory) at kd = 0.18

ko 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

i1 0 1 2 3 4 5 6 7 8 9 10

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

WACC 0.0000 0.1910 0.1954 0.1969 0.1977 0.1981 0.1984 0.1987 0.1988 0.1990 0.1991

Table 30.3 Dependence of WACC on coverage ratios of debt in modified Modigliani– Miller theory (MMM theory) at kd = 0.14

ko 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

i1 0 1 2 3 4 5 6 7 8 9 10

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

WACC 0.0000 0.1913 0.1955 0.1970 0.1977 0.1982 0.1985 0.1987 0.1989 0.1990 0.1991

Dependence of WACC on coverage ratios of debt in modified Modigliani–Miller theory (MMM theory) at kd = 0.18 is shown in Table 30.2. Dependence of WACC on coverage ratios of debt in modified Modigliani–Miller theory (MMM theory) at kd = 0.14 is shown in Table 30.3. Dependence of WACC on coverage ratios of debt in modified Modigliani–Miller theory (MMM theory) at kd = 0.1 is shown in Table 30.4. Dependence of WACC on coverage ratios of debt in “classical” Modigliani– Miller theory and in modified Modigliani–Miller theory (MMM theory) at kd = 0.1;0.14;0.18 is shown in Fig. 30.2. Let us analyze the dependence of company’s weighted average cost of capital (WACC) on the coverage ratios on debt i1 . It is seen from Fig. 30.2 that the weighted average cost of capital, WACC, increases with coverage ratio of debt for both versions of Modigliani–Miller theory: for “classical” Modigliani–Miller theory (MM theory) as well as for modified Modigliani–Miller theory (MMM theory). WACC increases very rapidly at L increases from L = 0 to L = 1 and then comes to saturation very fast (after L = 3 WACC changes very weak). At saturation WACC reaches the value k0 (equity cost at zero leverage level). This means that for high values of ij one can choose k0 as a discount rate with a good accuracy. Thus, the role

30.3

Application of Modified Modigliani–Miller Theory for Rating Needs

Table 30.4 Dependence of WACC on coverage ratios of debt in modified Modigliani– Miller theory (MMM theory) at kd = 0.1

ko 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

i1 0 1 2 3 4 5 6 7 8 9 10

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

719

kd 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

WACC 0.0000 0.1916 0.1957 0.1971 0.1978 0.1983 0.1985 0.1988 0.1989 0.1990 0.1991

WACC(i1) 0.2000 0.1800 0.1600 0.1400 0.1200

WACC

WACC (1) WACC (1') kd=0,18

0.1000

WACC (1') kd=0,14

0.0800

WACC (1') kd=0,1

0.0600 0.0400 0.0200 0.0000

0

1

2

3

4

5

6

7

8

9

10

Fig. 30.2 Dependence of WACC on coverage ratios of debt in “classical” Modigliani–Miller theory (curve WACC(1)) and in modified Modigliani–Miller theory (MMM theory) (curves WACC (1′)) at kd = 0.1;0.14;0.18

of parameter k0 increases drastically. The method of determination of parameter k0 has been developed by Anastasiya Brusova (2011). So, parameter k0 is the discount rate for limit case of high values of i1. We observe that results for both versions of Modigliani–Miller theory are very close: only from tables it is seen that curve of dependence of WACC on leverage ratios of debt in “classical” Modigliani–Miller theory (curve WACC(2)) lies a little bit above all dependences of WACC on coverage ratio of debt in modified Modigliani–Miller theory. The WACC values are practically independent on kd.

720

30 Application of the Modigliani–Miller Theory, Modified for the Case. . .

As we will see below, the situation is quite different in case of leverage ratios, where the influence of kd on dependences of WACC on leverage ratios is significant.

30.3.3

Leverage Ratios

We will consider now the leverage ratios. Three kinds of leverage ratios will be considered: leverage ratios of debt, leverage ratios of interest on the credit, and leverage ratios of debt and interest on the credit.

30.3.3.1

Leverage Ratios for Debt

Here l1 = D=CF

ð30:11Þ

As above for coverage ratios we use the modified Modigliani–Miller theorem for case with corporate taxes one has V L = V 0 þ Dt ð1 þ kd Þ, and dividing the both parts by CF, we derive the expression for WACC(l1) CF CF þ Dt ð1 þ k d Þ = WACC k0 1 1 = þ l1 t ð1 þ k d Þ WACC k0 k0 WACC = 1 þ tl1 k 0 ð1 þ kd Þ

ð30:12Þ

This ratio (l1) can be used to assess the following parameters used in rating, Debt/ EBITDA and some others. We will use the last formula to build a curve of dependence WACC(l1).

30.3.3.2

Leverage Ratios for Interest on Credit

Here l2 = k d D=CF

ð30:13Þ

30.3

Application of Modified Modigliani–Miller Theory for Rating Needs

721

We use again modified Modigliani–Miller theory (MMM theory) for case with corporate taxes V L = V 0 þ Dt ð1 þ kd Þ, and dividing the both parts by CF/kd, we derive the expression for WACC(l2) CF CF þ Dt ð1 þ k d Þ = WACC k0 1 1 l t ð1 þ k d Þ = þ 2 kd WACC k0 k0 kd WACC = kd þ tl2 k0 ð1 þ kd Þ

ð30:14Þ

This ratio (l2) can be used to assess the following parameters used in rating, Interests/EBITDA and some others. We will use the last formula to build a curve of dependence WACC(l2).

30.3.3.3

Leverage Ratios for Debt and Interest on Credit

Here l3 = Dð1 þ kd Þ=CF

ð30:15Þ

Using the modified Modigliani–Miller theory (MMM theory) for case with corporate taxes V L = V 0 þ Dt ð1 þ kd Þ, and dividing the both parts by CF/(1 + kd), we derive the expression for WACC(l3) CF CF þ Dt ð1 þ k d Þ = WACC k0 1 1 = þ l3 t WACC k0 k0 WACC = 1 þ tl3 k 0

ð30:16Þ

This ratio (l3) can be used to assess the following parameters used in rating, Debt + interest/FFO, Debt + interest/EBIT, Debt + interest/EBITDA(R), and some others. We will use the last formula to build a curve of dependence WACC(l3).

722

30.3.3.4

30 Application of the Modigliani–Miller Theory, Modified for the Case. . .

Dependence of WACC on Leverage Ratios of Debt in “Classical” Modigliani–Miller Theory (MM Theory) and Modified Modigliani–Miller Theory (MMM Theory)

Below we study the dependences of WACC on leverage ratios of debt in “classical” Modigliani–Miller theory (MM theory) and modified Modigliani–Miller theory (MMM theory). We use Microsoft Excel and the following parameters: equity cost at L = 0 k0 = 0.2; tax on profit rate t = 0.2; debt cost kd = 0.1;0.14;0.18; leverage ratios of debt l1 = 0;1;2;3;4;5;6;7;8;9;10. Dependence of WACC on leverage ratios of debt in “classical” Modigliani– Miller theory is shown in Table 30.5. Dependence of WACC on leverage ratios of debt in modified Modigliani–Miller theory (MMM theory) at kd = 0.18 is shown in Table 30.6. Dependence of WACC on leverage ratios of debt in modified Modigliani–Miller theory (MMM theory) at kd = 0.14 is shown in Table 30.7. Dependence of WACC on leverage ratios of debt in modified Modigliani–Miller theory (MMM theory) at kd = 0.1 is shown in Table 30.8. Table 30.5 Dependence of WACC on leverage ratios of debt in “classical” Modigliani–Miller theory

ko 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Table 30.6 Dependence of WACC on leverage ratios of debt in modified Modigliani– Miller theory (MMM theory) at kd = 0.18

ko 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

l1 0 1 2 3 4 5 6 7 8 9 10

l1 0 1 2 3 4 5 6 7 8 9 10

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

WACC 0.2000 0.1923 0.1852 0.1786 0.1724 0.1667 0.1613 0.1563 0.1515 0.1471 0.1429

kd 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

WACC 0.2000 0.1910 0.1827 0.1752 0.1682 0.1618 0.1559 0.1503 0.1452 0.1404 0.1359

30.3

Application of Modified Modigliani–Miller Theory for Rating Needs

723

Table 30.7 Dependence of WACC on leverage ratios of debt in modified Modigliani– Miller theory (MMM theory) at kd = 0.14

ko 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

l1 0 1 2 3 4 5 6 7 8 9 10

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

WACC 0.2000 0.1913 0.1833 0.1759 0.1691 0.1629 0.1570 0.1516 0.1465 0.1418 0.1374

Table 30.8 Dependence of WACC on leverage ratios of debt in modified Modigliani– Miller theory (MMM theory) at kd = 0.1

ko 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

l1 0 1 2 3 4 5 6 7 8 9 10

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

kd 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

WACC 0.2000 0.1916 0.1838 0.1767 0.1701 0.1639 0.1582 0.1529 0.1479 0.1433 0.1389

Dependence of WACC on leverage ratios of debt in “classical” Modigliani– Miller theory and in modified Modigliani–Miller theory (MMM theory) at kd = 0.1;0.14;0.18 is shown in Fig. 30.3. Analysis of the dependences of company’s weighted average cost of capital (WACC) on the leverage ratio on debt, l1 shows the following: (see Fig. 30.3) the weighted average cost of capital, WACC, decreases with leverage ratios for both versions of Modigliani–Miller theory: for “classical” Modigliani–Miller theory (MM theory) and for modified Modigliani–Miller theory (MMM theory). But we observe that curve of dependence of WACC on leverage ratios of debt in “classical” Modigliani–Miller theory (curve WACC(2)) lies above all dependences of WACC on leverage ratios of debt in modified Modigliani–Miller theory. The WACC values decrease with kd. So we are observing the influence of kd on dependences of WACC on leverage ratios. This effect is absent in “classical” Modigliani–Miller theory. Thus, using the modified Modigliani–Miller theory (MMM theory) leads to more correct valuation of the weighted average cost of capital (WACC), which plays the role of discount rate in financial flows discounting in rating methodologies. Obtained results will help to improve the existing rating methodologies.

30 Application of the Modigliani–Miller Theory, Modified for the Case. . .

724

WACC(l1) 0.2200 0.2000

WACC

0.1800

WACC (2) WACC (2') kd=0,18 WACC (2') kd=0,14 WACC (2') kd=0,1

0.1600 0.1400 0.1200 0.1000

0

1

2

3

4

5

6

7

8

9

10

Fig. 30.3 Dependence of WACC on leverage ratios of debt in “classical” Modigliani–Miller theory (curve WACC(2)) and in modified Modigliani–Miller theory (MMM theory) (curves WACC(2′)) at kd = 0.1;0.14;0.18

30.4

Discussions

In the current paper, we use the modified Modigliani–Miller theory (MMM theory) and apply it for rating methodology needs. The financial “ratios” (main rating parameters) were introduced into MMM theory. The dependence of the weighted average cost of capital (WACC), which plays the role of discount rate in financial flows discounting in rating methodologies, on coverage and leverage ratios is analyzed. Obtained results will help to improve the existing rating methodologies. The analysis of the dependence of company’s weighted average cost of capital (WACC) on the coverage ratios on debt i1 shows that WACC increases with coverage ratio of debt for both versions of Modigliani–Miller theory: for “classical” Modigliani–Miller theory (MM theory) and for modified Modigliani–Miller theory (MMM theory). WACC increases very rapidly at L increases from L = 0 to L = 1 and then comes to saturation very fast (after L = 3 WACC changes very weak). At saturation WACC reaches the value k0 (equity cost at zero leverage level). This means that for high values of ij one can choose k0 as a discount rate with a good accuracy. Thus, the role of parameter k0 increases drastically. The method of determination of parameter k0 has been developed by Anastasiya Brusova (2011). So, parameter k0 is the discount rate for limit case of high values of i1. We observe that results for both versions of Modigliani–Miller theory are very close: only from tables it is seen that curve of dependence of WACC on leverage ratios of debt in “classical” Modigliani–Miller theory lies a little bit above all dependences of WACC on coverage ratio of debt in modified Modigliani–Miller theory. The WACC values are practically independent on kd. The situation is quite

References

725

different in case of leverage ratios, where the influence of kd on dependences of WACC on leverage ratios is significant. Analysis of the dependences of company’s weighted average cost of capital (WACC) on the leverage ratio on debt, l1 shows that WACC decreases with leverage ratios for both versions of Modigliani–Miller theory: for “classical” Modigliani– Miller theory (MM theory) and for modified Modigliani–Miller theory (MMM theory). We observe that curve of dependence of WACC on leverage ratios of debt in “classical” Modigliani–Miller theory lies above all dependences of WACC on leverage ratios of debt in modified Modigliani–Miller theory. The WACC values decreases with kd. So we are observing the influence of kd on dependences of WACC on leverage ratios. This effect is absent in “classical” Modigliani–Miller theory. Thus, the using of the modified Modigliani–Miller theory (MMM theory) leads to more correct valuation of the weighted average cost of capital (WACC), which plays the role of discount rate in financial flows discounting in rating methodologies. Obtained results will help to improve the existing rating methodologies, which are used for valuation of the creditworthiness of companies. Correct account of a method of tax on profit payments demonstrates that shortcomings of Modigliani–Miller theory are dipper than everybody suggested: the underestimation of WACC really turns out to be bigger, as well as overestimation of the capitalization of the company. This means that systematic risks arising from the use of modified Modigliani–Miller theory (MMM theory) (which is more correct than “classical” one) in practice are higher than it was suggested by the “classical” version of this theory.

References Brusov P (2018a) Editorial: introduction on special issue on the banking system and financial markets of Russia and other countries: problems and prospects. J Rev Glob Econ 7:i–vi. SCOPUS Brusov P (2018b) Editorial. J Rev Glob Econ 7:i–v. SCOPUS Brusov P, Filatova P, Orekhova N (2014a) Mechanism of formation of the company optimal capital structure, different from suggested by trade off theory. Cogent Econ Financ 2:1–13 Brusov P, Filatova T, Orehova N (2014b) Inflation in Brusov–Filatova–Orekhova theory and in its perpetuity limit–Modigliani–Miller theory. J Rev Glob Econ 3:175–118 Brusov P, Filatova T, Orehova N, Eskindarov M (2015) Modern corporate finance, investment and taxation, 1st edn. Springer, pp 1–368 Brusov P, Filatova T, Orehova N, Eskindarov M (2018a) Modern corporate finance, investments, taxation and ratings. Springer, Switzerland. 571 p. monograph Brusov PN, Filatova TV, Orekhova NP, Kulik VL (2018b) Rating: new approach. J Rev Glob Econ 7:37–62. SCOPUS. https://doi.org/10.6000/1929-7092.2018.029.05 Brusov PN, Filatova TV, Orekhova NP, Kulik VL (2018c) A “golden age” of the companies: conditions of its existence. J Rev Glob Econ 7:88–103. SCOPUS. https://doi.org/10.6000/ 1929-7092.2018.029.07 Brusov PN, Filatova TV, Orekhova NP, Kulik VL (2018d) Rating methodology: new look and new horizons. J Rev Glob Econ 7:63–829. SCOPUS. https://doi.org/10.6000/1929-7092.2018. 029.06

726

30 Application of the Modigliani–Miller Theory, Modified for the Case. . .

Brusov PN, Filatova TV, Orekhova NP, Kulik VL, Weil I (2018e) New meaningful effects in modern capital structure theory. J Rev Glob Econ 7:104–122. SCOPUS. https://doi.org/10. 6000/1929-7092.2018.029.08 Brusov P, Filatova T, Orekhova N, Kulik V, Weil I, Brailov A (2018f) The impact of the central bank key rate and commercial banks credit rates on creating and maintaining of a favorable investment climate in the country. J Rev Glob Econ 7:360–376. SCOPUS. https://doi.org/10. 6000/1929-7092.2018.029.31 Brusov PN, Filatova TV, Orekhova NP (2018g) Modern corporate finance and investments, monograph. Knorus Publishing House, Moscow. 517 p Brusov PN, Filatova TV, Orekhova NP, Kulik VL, Weil I (2019) Ratings of the investment projects of arbitrary durations: new methodology. J Rev Glob Econ 8:437–448. SCOPUS. https://doi. org/10.6000/1929-7092.2019.08.37 Brusov P, Filatova T, Orehova N (2020a) Ratings: critical analysis and new approaches of quantitative and qualitative methodology. Springer, Switzerland. 369 p. monograph, SCOPUS Brusov PN, Filatova TV, Orekhova NP, Kulik VL, Chang SI, Lin YCG (2020b) Modification of the Modigliani–Miller theory for the case of advance payments of tax on profit. J Rev Glob Econ 9: 257–268 Brusov P, Filatova T, Orekhova N (2021) Ratings: critical analysis and new approaches of quantitative and qualitative methodology. Springer Nature Publishing Brusova A (2011) А comparison of the three methods of estimation of weighted average cost of capital and equity cost of company. Financ Anal Prob Solut 34(76):36–42 Filatova Т, Orehova N, Brusova А (2008) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Bull FU 48:68–77 Filatova TV, Brusov PN, Orekhova NP, Kulik VL (2018) Ratings of the long–term projects: new approach. J Rev Glob Econ 7:645–661., SCOPUS. https://doi.org/10.6000/1929-7092.2018. 029.59 Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Modigliani F, Miller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1952. Am Econ Rev 56:333–391

Part IV

Ratings and Rating Methodologies of the Investment Projects

Chapter 31

Ratings of the Investment Projects of Arbitrary Durations: New Methodology

Keywords Brusov–Filatova–Orekhova (BFO) theory · Investment projects of arbitrary durations · Rating methodologies · Financial “ratios” In this chapter, we develop for the first time a new approach to ratings of the investment projects of arbitrary durations, applicable in particular to energy projects. The ratings of such energy projects, as “Turkish stream,” “Nord stream-2,” energy projects relating to clean, renewable, and sustainable energy, as well as relating to pricing carbon emissions could be done using new rating methodologies developed here. In our previous chapters, the new approach to the ratings of the long-term investment projects has been developed (Filatova et al. 2018). The important features of that consideration are as follows: (1) The incorporation of rating parameters (financial “ratios”), used in project rating and playing a major role in it, into modern long-term investment models, (2) The adequate use of discounting of financial flows virtually not used in existing rating methodologies. Here, for the first time, we incorporate the rating parameters (financial “ratios”), used in project rating, into modern investment models, describing the investment projects of arbitrary durations (Brusov et al. 2021). This was much more difficult task than in case of the long-term investment projects, considered by us in previous chapters. We work within investment models, created by authors. One of them describes the effectiveness of investment project from the perspective of equity capital owners, while other model describes the effectiveness of investment project from the perspective of equity capital and debt capital owners. The new approach allows to use the powerful instruments of modern theory of capital cost and capital structure (BFO) theory (Brusov et al. 2015, 2018a, b, c, d, e, f, g) and modern investment models, created by the authors and well tested in the real economy to evaluate investment project performance, including energy projects. In our calculations we use Excel technique in two aspects: (1) we calculate WACC at different values of equity costs k0, different values of debt costs kd and different values of leverage level L = D/S, using the famous BFO formula; (2) we calculate the dependences of NPV on coverage ratios as well as leverage ratios at different values of equity costs k0, different values of debt costs kd, and different values of leverage level L.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_31

729

730

31.1

31

Ratings of the Investment Projects of Arbitrary Durations: New Methodology

Introduction

The investments play a very important role in economics and finance. Wherein the role of energy projects in general and in particular relating to clean, renewable, and sustainable energy, as well as relating to pricing carbon emissions is rapidly increasing. In the conditions of limited financial resources, the selection of the most efficient projects from the point of view of investors becomes a very important task. Rating agencies are called upon to solve it. Rating agencies play a very important role in economics. Their analysis of issuer’s state, generated credit ratings of issuers, of investment projects helps investors to make reasonable investment decision, as well as helps issuer with good enough ratings to get credits on lower rates, etc. But the methodologies of leading rating agencies such as “The Big Three credit rating agencies” (Standard & Poor’s (S&P), Moody’s, and Fitch Group) as well as Russian rating agency (ACRA) and all other ones have a lot of shortcomings. A number of works by authors are devoted to eliminating some of these shortcomings (Brusov et al. 2018a, b, c, d, e, f, g, 2019, 2020). Besides the fact that RA represent some “black boxes,” the information about the methods of work of which is almost completely absent, there are some serious methodological and systematic errors in their activity. These errors and ways to their overcome have been discussed in a number of authors papers, as well as in monograph (Brusov et al. 2018a, b, c, d, e, f, g). The use of discounting in the rating. One of the major flaws of all existing rating methodologies is a failure or a very narrow use of discounting. But even in those rare cases where it is used, it is not quite correct, since the discount rate when discounting financial flows is chosen incorrectly. As Brusov et al. (2018a, b, c, d, e, f, g) have mentioned, “the need to take into account the time factor in terms of discounting is obvious, because it is associated with the time value of money. The financial part of the rating is based on a comparison of generated income with the value of the debt and the interest payable. Because income and disbursement of debt and interest are separated in time, the use of discounting when comparing revenues with the value of debt and interest is absolutely necessary for assigning credit ratings for issuers.” This raises the question about the value of discount rate. This question has always been one of the major and extremely difficult in many areas of finance: corporate finance, investment, it is particularly important in business valuation, where a slight change in the discount rate leads to a significant change in the assessment of company capitalization, that is used by unscrupulous appraisers for artificial bankruptcy of the company. It is extremely essential as well as in rating. Incorporation of financial “ratios,” using in ratings, into modern investment models. In quantification of the creditworthiness of the issuers as well as in valuation of effectiveness of investment projects the crucial role belongs to the so-called

31.2

Investment Models

731

financial ratios, which constitute direct and inverse ratios of various generated cash flows to debt values and interest ones. We incorporate these financial “ratios” into the modern theory of capital structure—Brusov–Filatova–Orekhova (BFO) theory (Brusov et al. 2018a, b, c, d, e, f, g) and as well into modern investment models, created by the authors. Such incorporation, which has been done by us for the first time, is very important because one can use this theory as a powerful tool when discounting of financial flows using the correct discounting rate in rating. Only this theory allows to valuate adequately the weighted average cost of capital WACC and equity cost ke used when discounting of financial flows. As Brusov et al. (2018a, b, c, d, e, f, g) have mentioned “use of the tools of welldeveloped theories in rating opens completely new horizons in the rating industry, which could be connected with transition from the main use of qualitative methods of the evaluation of the creditworthiness of issuers to a predominantly quantitative evaluation methods that will certainly enhance the quality and correctness of the rating.” Currently, RA just directly use financial ratios, while the new methodology will allow (knowing the values of these “relations” (and parameter k0)) to determine the correct values of discount rates (WACC and ke) that should be used when discounting the various financial flows, both in terms of their timing and forecasting. In relation to the rating of investment projects new methodology allows to correctly determine the values of project NPV (both in units of D and in NOI), using modern investment models and correct discount rate. As Brusov et al. (2018a, b, c, d, e, f, g) mentioned, “incorporation of financial ‘ratios’ has required the modification of the BFO theory (and its perpetuity limit— the so-called Modigliani–Miller theory), as used in financial management the concept of ‘leverage’ as the ratio of debt value to the equity value substantially differs from the concept of ‘leverage’ in the rating, where it is understood as the direct and inverse ratio of the debt value to the generated cash flow values (income, revenue, etc.). The authors introduced some additional ratios, allowing full characterization of the issuer’s ability to repay debts and to pay interest thereon.” Thus, the bridge is building between the discount rates (WACC, ke) used when discounting of financial flows and “ratios” in the rating methodology. The important features of current consideration as well as in previous studies are: (1) The adequate use of discounting of financial flows virtually not used in existing rating methodologies, (2) The incorporation of rating parameters (financial “ratios”), used in project rating, into considered modern investment models.

31.2

Investment Models

We work within investment models, created by authors. One of them describes the effectiveness of investment project from the perspective of equity capital owners, while other model describes the effectiveness of investment project from the perspective of equity capital and debt capital owners.

732

31

Ratings of the Investment Projects of Arbitrary Durations: New Methodology

In the former case, investments at the initial time moment T = 0 are equal to –S and the flow of capital for the period (in addition to the tax shields kdDt it includes a payment of interest on a loan -kdD): CF = ðNOI- kd DÞð1- t Þ:

ð31:1Þ

Here, for simplicity, we suppose that interest on the loan will be paid in equal shares kdD during all periods. Note that the principal repayment is made at the end of the last period. We will consider the case of discounting, when operating and financial flows are not separated and both are discounted, using the general rate (as which, obviously, the weighted average cost of capital (WACC) can be selected). In case for long-term (perpetuity) projects, the Modigliani–Miller formula (Мodigliani and Мiller 1958, 1963, 1966) for WACC has been used (Brusov et al. 2018a, b, c, d, e, f, g) and for projects of finite (arbitrary) duration Brusov–Filatova–Orekhova formula will be used (Brusov et al. 2014a, b; Filatova et al. 2008; Brusova 2011). Note that debt capital is the least risky, because interest on credit is paid after taxes in the first place. Therefore, the cost of credit will always be less than the equity cost, whether of ordinary or of preference shares ke > kd; kp > kd. Here ke, kp is the equity cost of ordinary or of preference shares consequently.

31.2.1

The Effectiveness of the Investment Project from the Perspective of the Equity Holders Only (Without Flows Separation)

In this case operating and financial flows are not separated and are discounted, using the general rate (as which, obviously, WACC can be selected). The credit reimbursable at the end of the project (at the end of the period (n)) can be discounted either at the same rate WACC or at the debt cost rate kd. Now we choose a uniform rate and the first option. n X NOIð1 - t Þ - kd Dð1 - t Þ

D ð 1 þ WACC Þn i=1   NOIð1 - t Þ - k d Dð1 - t Þ D 1 1= -S þ : n WACC ð1 þ WACCÞn ð1 þ WACCÞ

NPV = - S þ

ð1 þ WACCÞi

-

ð31:2Þ At a Constant Value of Equity Capital (S = const) Accounting that in the case S = const NOI is proportional to the invested capital, I, NOI = βI = βS(1 + L ) and substituting D = LS, we get

31.3

Incorporation of Financial Coefficients, Using in Project Rating. . .

733

  NOIð1 - t Þ - kd Dð1 - t Þ 1 1NPV = - S þ WACC ð1 þ WACCÞn D , ð1 þ WACCÞn     Lk d ð1 - t Þ 1 L 1þ NPV = - S 1 þ WACC ð1 þ WACCÞn ð1 þ WACCÞn   βSð1 þ LÞð1 - t Þ 1 þ 1: WACC ð1 þ WACCÞn     k Lð1 - t Þ 1 L 1NPV = - S 1 þ d þ WACC ð1 þ WACCÞn ð1 þ WACCÞn   βSð1 þ LÞð1 - t Þ 1 : þ 1WACC ð1 þ WACCÞn -

31.3

ð31:3Þ

ð31:4Þ

ð31:5Þ

Incorporation of Financial Coefficients, Using in Project Rating into Modern Investment Models, Describing the Investment Projects of Arbitrary Duration

Below for the first time we incorporate the financial coefficients, used in project rating, into modern investment models, describing the investment projects of arbitrary duration, created by authors. We will consider two kinds of financial coefficients: coverage ratios as well as leverage coefficients. In each group of financial coefficients we incorporate three particular quantities. For coverage ratios we incorporate: (1) coverage ratios of debt, i1 = NPV D ; (2) covNPV erage ratios of interest on the credit i2 = kd D ; (3) coverage ratios of debt and interest on the credit i3 = ð1NPV þkd ÞD. D For leverage ratios we incorporate: (1) leverage ratios of debt, l1 = NPV ; (2) leverkd D age ratios of interest on the credit l2 = NPV; (3) leverage ratios of debt and interest on d ÞD the credit l3 = ð1þk NPV .

734

31

Ratings of the Investment Projects of Arbitrary Durations: New Methodology

31.3.1

Coverage Ratios

31.3.1.1

Coverage Ratios of Debt

Let us first incorporate the coverage ratios, using in project rating, into modern investment models, describing the investment projects of arbitrary duration, created by authors. Dividing both parts of Eq. (31.5) by D one gets   1 1 NPV 1 ði1 - kd Þð1 - t Þ 1=- þ WACC D L ð1 þ WACCÞn ð1 þ WACCÞn Here,

31.3.1.2

i1 =

NPV D

ð31:6Þ ð31:7Þ

Coverage Ratios of Interest on the Credit

Dividing both parts of Eq. (31.5) by kdD one gets   ði 2 - k d Þð1 - t Þ NPV 1 1 =þ 1kd D kd L WACC ð1 þ WACCÞn -

1 k d ð1 þ WACCÞn

ð31:8Þ Here,

31.3.1.3

i2 =

NPV kd D

ð31:9Þ

Coverage Ratios of Debt and Interest on the Credit

Dividing both parts of Eq. (31.5) by (1 + kd)D one gets 1 NPV = ð1 þ k d ÞD ð1 þ kd Þ     1 ðð1 þ k d Þi3 - kd Þð1 - t Þ 1 1  - þ 1WACC L ð1 þ WACCÞn ð1 þ WACCÞn ð31:10Þ Here

i3 =

NPV ð1 þ k d ÞD

ð31:11Þ

31.3

Incorporation of Financial Coefficients, Using in Project Rating. . .

31.3.2

Leverage Ratios

31.3.2.1

Leverage Ratios for Debt

735

Now let us incorporate the leverage ratios, using in project rating, into modern investment models, created by authors. Dividing both parts of Eq. (31.5) by NOI one gets   1 NPV l1 ð1 - kd l1 Þð1 - t Þ 1=- þ WACC L NOI ð1 þ WACCÞn -

l1 ð1 þ WACCÞn

ð31:12Þ Here

31.3.2.2

l1 =

D NPV

ð31:13Þ

Leverage Ratios for Interest on Credit   ð1 - l2 Þð1 - t Þ 1 NPV l2 1þ =WACC kd L NOI ð1 þ WACCÞn -

l2 kd ð1 þ WACCÞn

ð31:14Þ Here

31.3.2.3

l2 =

kd D NPV

ð31:15Þ

Leverage Ratios for Debt and Interest on Credit

NPV 1 = NOI 1 þ kd     ð1 þ k d - k d l 3 Þð1 - t Þ l3 1 l 1 - 3þ WACC L ð1 þ WACCÞn ð1 þ WACCÞn ð31:16Þ Here

l3 =

ð1 þ k d ÞD : NPV

ð31:17Þ

Let us investigate below the effectiveness of investment projects of arbitrary duration studying the dependence of NPV on coverage ratios and on leverage ratios.

736

31

Ratings of the Investment Projects of Arbitrary Durations: New Methodology

We make calculations for coefficients i1 and l1. Calculations for the rest of coefficients (i2, i3 and l2, l3) could be made in a similar way. We start from the calculations of the dependence of NPV on coverage ratios. We consider different values of equity costs k0, different values of debt costs kd, and different values of leverage level L = D/S. Here, t is tax on profit rate, which in our calculations is equal to 20%.

31.4

Results and Analysis

31.4.1

Dependence of NPV/D on Coverage Ratios

Below we calculate the dependence of NPV (in units of D)(NPV D ) on coverage ratio on debt i1 at different equity costs k0 (k0 is the equity cost at zero leverage level L = 0). We will make calculations for two leverage levels L (L = 1 and L = 3), for two project durations (n = 2 and n = 5), and for different credit rates kd. In our calculations we use Excel technique in two aspects: (1) we calculate WACC at different values of equity costs k0, different values of debt costs kd, and different values of leverage level L = D/S, using the famous BFO formula; (2) we calculate the dependences of NPV on coverage ratios as well as leverage ratios at different values of equity costs k0, different values of debt costs kd, and different values of leverage level L. We use typical values of equity costs k0, of debt costs kd, and of leverage level L. For calculation of the dependence of NPV/D on coverage ratio on debt i1 within BFO approximation (arbitrary we use the formula (31.6).  duration projects)  ði1 - kd Þð1 - t Þ NPV 1 1 1 = þ 1n D L WACC ð1þWACCÞ ð1þWACCÞn

31.4.1.1

The Dependence of NPV on Coverage Ratio on Debt i1

Below we investigate the dependence of NPV/D on coverage ratio on debt i1 at different values of equity costs k0, at different values of debt costs kd at fixed value of equity cost, as well as at different values of leverage levels L. Let us start our calculations with the case of equity cost k0 = 14%. 1. We calculate WACC, using the famous BFO formula (Brusov et al. 2015, 2018a, b, c, d, e, f, g) ½1 - ð1 þ WACCÞ - n  ½ 1 - ð1 þ k 0 Þ - n  = WACC k0  ½1 - Wd  t  ð1 - ð1 þ kd Þ–n Þ

ð31:18Þ

31.4

Results and Analysis

737

Table 31.1 The dependence of NPV/D on coverage ratio on debt i1 at L = 1, k0 = 14%; kd = 12%; t = 20%, n = 2 Wd 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

L 1 1 1 1 1 1 1 1 1 1 1

ko 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

kd 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

i1 0 1 2 3 4 5 6 7 8 9 10

n 2 2 2 2 2 2 2 2 2 2 2

NPV/D (L = 1) -1.86035 -0.61682 0.626711 1.870243 3.113776 4.357308 5.600841 6.844373 8.087906 9.331438 10.57497

WACC 0.185838 0.185838 0.185838 0.185838 0.185838 0.185838 0.185838 0.185838 0.185838 0.185838 0.185838

Table 31.2 The dependence of NPV/D on coverage ratio on debt i1 at L = 1, k0 = 14%; kd = 12%; t = 20%, n = 5 L 1 1 1 1 1 1 1 1 1 1 1

ko 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

kd 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

i1 0 1 2 3 4 5 6 7 8 9 10

n 5 5 5 5 5 5 5 5 5 5 5

NPV/D (L = 1) -2.0942 1.161083 4.41637 7.671658 10.92694 14.18223 17.43752 20.69281 23.94809 27.20338 30.45867

WACC 0.072849 0.072849 0.072849 0.072849 0.072849 0.072849 0.072849 0.072849 0.072849 0.072849 0.072849

Here, k0 is the equity costs, kd is the debt costs; L = D/S is the leverage level; t is tax on profit rate, wd is the debt ratio, WACC is the weighted average capital cost, n is the project duration. 2. We calculate dependence of NPV/D (NPV in units D) on coverage ratio on debt i1, using obtained value of WACC, which depends on k0, kd, t, n, L. 3. We calculate NPV/NOI (NPV in units NOI) on leverage ratio on debt l1, using obtained value of WACC, which depends on k0, kd, t, n, L. The results are shown in tables and figures. We see from Tables 31.1, 31.2, 31.3, and 31.4 and from Fig. 31.1 that NPV (in units of D) (NPV D ) increases with i1. The features of this increase are as follows:

738

31

Ratings of the Investment Projects of Arbitrary Durations: New Methodology

Table 31.3 The dependence of NPV/D on coverage ratio on debt i1 at L = 3, k0 = 14%; kd = 12%; t = 20%, n = 2 L 3 3 3 3 3 3 3 3 3 3 3

ko 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

kd 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

i1 0 1 2 3 4 5 6 7 8 9 10

NPV/D (L = 1) -1.19238 0.049707 1.291792 2.533877 3.775963 5.018048 6.260133 7.502218 8.744303 9.986389 11.22847

n 2 2 2 2 2 2 2 2 2 2 2

WACC 0.186786 0.186786 0.186786 0.186786 0.186786 0.186786 0.186786 0.186786 0.186786 0.186786 0.186786

Table 31.4 The dependence of NPV/D on coverage ratio on debt i1 at L = 3, k0 = 14%; kd = 12%; t = 20%, n = 5 Wd 0,25 0,25 0,25 0,25 0,25 0,25 0,25 0,25 0,25 0,25 0,25

L 3 3 3 3 3 3 3 3 3 3 3

ko 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

kd 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

i1 0 1 2 3 4 5 6 7 8 9 10

n 5 5 5 5 5 5 5 5 5 5 5

NPV/D (L = 1) -1.42302 1.823185 5.069387 8.315588 11.56179 14.80799 18.05419 21.30039 24.5466 27.7928 31.039

WACC 0.073898 0.073898 0.073898 0.073898 0.073898 0.073898 0.073898 0.073898 0.073898 0.073898 0.073898

1. the angle NPV(i1) is determined by the project duration n: it increases with n. 2. with increase of leverage level L the curve NPV(i1) shifts practically parallel up. Thus, NPV increases with debt financing. This means that influence of the project duration n on the dependence of NPV/D on coverage ratio on debt i1 is more significant than influence of leverage level L.

31.4.1.2

The Dependence of NPV on Leverage Ratio on Debt l1

We see from Tables 31.5, 31.6, 31.7, and 31.8 and from Fig. 31.2 that NPV (in units of NOI) (NPV NOI ) decreases with l1. The features of this decrease are as follows:

31.4

Results and Analysis

739

NPV/D (i1) at L=1; 3 and n=2; 5 35 30 25 L=1,t=0,2,n=2

20

L=3, t=0,2 ,n=2

15

t=0,2, L=3, n=5

10

n=5, L=1,t=0,2

5 0 -5

0

2

4

6

8

10

12

Fig. 31.1 The dependence of NPV/D on coverage ratio on debt i1 at L = 1;3, k0 = 14%; kd = 12%; t = 20%, n = 2;5 Table 31.5 The dependence of NPV/NOI on leverage ratio on debt l1 at L = 1, k0 = 14%; kd = 12%; t = 20%, n = 2 L 1 1 1 1 1 1 1 1 1 1 1

l1 0 1 2 3 4 5 6 7 8 9 10

kd 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12

k0 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 2 2 2 2 2 2 2 2 2 2 2

wd 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

WACC 0.1231 0.1231 0.1231 0.1231 0.1231 0.1231 0.1231 0.1231 0.1231 0.1231 0.1231

NPV/NOI (L = 1) 1.346553406 -0.6078321 -2.5622176 -4.5166031 -6.47098861 -8.42537411 -10.3797596 -30.3341451 -14.2885306 -16.2429161 -18.1973016

1. the angle NPV(l1) is determined by the leverage level L: it increases with L. Thus, NPV increases with debt financing. 2. with increase of project duration n the curve NPV(l1) shifts practically parallel up. This means that influence of leverage level L on the dependence of NPV/NOI on leverage ratio on debt l1 is more significant than the influence of the project duration n. One can see that the dependence of NPV/NOI on leverage ratio on debt l1 is opposite to the dependence of NPV/D on coverage ratio on debt i1:

740

31

Ratings of the Investment Projects of Arbitrary Durations: New Methodology

Table 31.6 The dependence of NPV/NOI on leverage ratio on debt l1 at L = 3, k0 = 14%; kd = 12%; t = 20%, n = 2 L 3 3 3 3 3 3 3 3 3 3 3

l1 0 1 2 3 4 5 6 7 8 9 10

kd 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12

k0 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 2 2 2 2 2 2 2 2 2 2 2

wd 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

WACC 0.13203 0.13203 0.13203 0.13203 0.13203 0.13203 0.13203 0.13203 0.13203 0.13203 0.13203

NPV/NOI (L = 1) 1.330967788 0.057577565 -1.21581266 -2.48920288 -3.7625931 -5.03598332 -6.30937355 -7.58276377 -8.85615399 -10.1295442 -11.4029344

Table 31.7 The dependence of NPV/NOI on leverage ratio on debt l1 at L = 1, k0 = 14%; kd = 12%; t = 20%, n = 5 L 1 1 1 1 1 1 1 1 1 1 1

l1 0 1 2 3 4 5 6 7 8 9 10

kd 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12

k0 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 5 5 5 5 5 5 5 5 5 5 5

wd 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

WACC 0.121819 0.121819 0.121819 0.121819 0.121819 0.121819 0.121819 0.121819 0.121819 0.121819 0.121819

NPV/NOI (L = 1) 2.870871 0.963526 -0.94382 -2.85116 -4.75851 -6.66585 -8.5732 -10.4805 -30.3879 -14.2952 -16.2026

Table 31.8 The dependence of NPV/NOI on leverage ratio on debt l1 at L = 3, k0 = 14%; kd = 12%; t = 20%, n = 5 L 3 3 3 3 3 3 3 3 3 3 3

l1 0 1 2 3 4 5 6 7 8 9 10

kd 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12

k0 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 5 5 5 5 5 5 5 5 5 5 5

wd 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

WACC 0.130962 0.130962 0.130962 0.130962 0.130962 0.130962 0.130962 0.130962 0.130962 0.130962 0.130962

NPV/NOI (L = 1) 2.807196 1.596542 0.385889 -0.82476 -2.03542 -3.24607 -4.45672 -5.66738 -6.87803 -8.08868 -9.29934

31.4

Results and Analysis

741

NPV/NOI (l1) at L=1;3 and n=2;5 5 0

0

-5 -10

2

4

6

8

10

12

NPV/NOI L=1, t=0,2; n=2 NPV/NOI L=3,t=0,2;n=2 NPV/NOI L=1,n=5,t=0,2 NPV/NOI L=3, t=0,2 , n=5

-15 -20

Fig. 31.2 The dependence of NPV/NOI on leverage ratio on debt l1 at L = 1;3, k0 = 14%; kd = 12%; t = 20%, n = 2;5

1. the angle NPV(l1) is determined by the leverage level L, while the angle NPV(i1) is determined by the project duration n. 2. with increase of project duration n the curve NPV(l1) shifts practically parallel up, while such kind of behavior is typical for influence of the leverage level L in case of the curve NPV(i1). The only one common thing for both curves NPV(l1) and NPV(i1) is that NPV increases with debt financing (or with the leverage level L).

31.4.1.3

The Dependence of NPV on Coverage Ratio on Debt i1 at Different Values of kd

Let us investigate the dependence of NPV/D on coverage ratio on debt i1 at L = 3, k0 = 20%; kd = 18%; t = 20%, n = 2 (Fig. 31.3 and Tables 31.9, 31.10, and 31.11). The straight lines for different kd turn out practically to merge, which means that the influence of the variation of kd on such a scale of changes i1 is insignificant. In order to evaluate the ordering of straight lines corresponding to different kd, we increase the scale in the following figures, considering the values of i1 not from 0 to 10, but from 0 to 1. In Fig. 31.4, we consider the case of different project duration n, while in Fig. 31.5 the case of different leverage level L. One can see from Fig. 31.5 that the ordering of the NPV/D straight lines for different credit rates kd and different leverage level L turns out to be as follows: two triplets, corresponding to different leverage level L are well distinguished and upper triplet (with bigger NPV value) corresponds to bigger leverage level L = 3. This means that NPV increases with debt financing. Within each triplet NPV decreases with credit rates kd: the biggest NPV corresponds to kd = 14% and the smallest one corresponds to kd = 18%.

742

31

Ratings of the Investment Projects of Arbitrary Durations: New Methodology

NPV/D(i1) at n=2 and kd=14%;16%;18% 10 8

kd=18 L=1 kd=16

6

kd=14 4

kd=18 L=3 kd=16

2

kd=14 0

0

1

2

3

4

5

6

7

8

9

10

-2

Fig. 31.3 The dependence of NPV/D on coverage ratio on debt i1 at L = 1;3, k0 = 20%; kd = 14%, 16%, 18%; t = 20%, n = 2 (i1 changes from 0 to 10) Table 31.9 The dependence of NPV/D on coverage ratio on debt i1 at L = 3, k0 = 20%; kd = 18%; t = 20%, n = 2

31.4.1.4

NPV/D -1.281958725 -0.024284066 1.233390593 2.491065253 3.748739912 5.006414571 6.264089231 7.52176389 8.779438549 10.03711321 11.29478787

L 3 3 3 3 3 3 3 3 3 3 3

i1 0 1 2 3 4 5 6 7 8 9 10

kd 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

WACC 0.176679108 0.176679108 0.176679108 0.176679108 0.176679108 0.176679108 0.176679108 0.176679108 0.176679108 0.176679108 0.176679108

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 2 2 2 2 2 2 2 2 2 2 2

The Dependence of NPV/NOI on Leverage Ratio on Debt l1 at Different Values of kd

Let us investigate the dependence of NPV/NOI on leverage ratio on debt l1 at L = 1, k0 = 20%; kd = 18%; t = 20%, n = 2. We show below the detailed dependence of NPV/NOI on leverage ratio on debt l1 at L = 1; k0 = 20%; kd = 14%,!6%, 18%; t = 20%, n = 2;5 (i1 changes from 0 to 3). One can see from Fig. 31.6 that under increase of project duration n the NPV/NOI (l1) straight lines shift practically parallel up. The ordering of the NPV/NOI(l1) straight lines for different credit rates kd and different project duration n turns out to be as follows: two triplets, corresponding to different project duration n are well

31.5

Conclusion

743

Table 31.10 The dependence of NPV/D on coverage ratio on debt i1 at L = 3, k0 = 20%; kd = 16%; t = 20%, n = 2

NPV -1.249017883 0.000427777 1.249873438 2.499319098 3.748764758 4.998210418 6.247656078 7.497101739 8.746547399 9.995993059 11.24543872

L 3 3 3 3 3 3 3 3 3 3 3

Table 31.11 The dependence of NPV/D on coverage ratio on debt i1 at L = 3, k0 = 20%; kd = 14%; t = 20%, n = 2

NPV -1.221437995 0.025207969 1.271853932 2.518499896 3.76514586 5.011791823 6.258437787 7.505083751 8.751729714 9.998375678 11.24502164

L 3 3 3 3 3 3 3 3 3 3 3

i1 0 1 2 3 4 5 6 7 8 9 10

i1 0 1 2 3 4 5 6 7 8 9 10

kd 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16

kd 0.14 0.14 0.14 0.14 0.14 0.14 0,14 0,14 0,14 0,14 0,14

WACC 0.18198583 0.18198583 0.18198583 0.18198583 0.18198583 0.18198583 0.18198583 0.18198583 0.18198583 0.18198583 0.18198583

t 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

n 2 2 2 2 2 2 2 2 2 2 2

WACC 0.183805688 0.183805688 0.183805688 0.183805688 0.183805688 0.183805688 0,183,805,688 0,183,805,688 0,183,805,688 0,183,805,688 0,183,805,688

t 0.2 0.2 0.2 0.2 0.2 0.2 0,2 0,2 0,2 0,2 0,2

n 2 2 2 2 2 2 2 2 2 2 2

distinguished and upper triplet (with bigger NPV value) corresponds to bigger project duration n = 5. Within each triplet NPV decreases with credit rates kd: the biggest NPV corresponds to kd = 14% and the smallest one corresponds to kd = 18%. It is seen that influence of the value of credit rates kd increases with n, while in case of NPV/D the shift of NPV turns out to be the same for different leverage level L.

31.5

Conclusion

In this chapter we develop for the first time a new approach to ratings of the investment projects of arbitrary duration, applicable to energy projects. The ratings of such energy projects, as “Turkish stream,” “Nord stream-2,” energy projects relating to clean, renewable, and sustainable energy, as well as relating to pricing carbon emissions could be done using new rating methodologies developed here. This chapter generalizes the new approach to the ratings of the long-term investment

744

31

Ratings of the Investment Projects of Arbitrary Durations: New Methodology

NPV/D(i1) at L=1 1 0.5 0

0

1

kd=18 n=2 kd=16 kd=14

-0.5

kd=18 n=5 kd=16

-1

kd=14

-1.5 -2 Fig. 31.4 The detailed dependence of NPV/D on coverage ratio on debt i1 at L = 1, k0 = 20%; kd = 14%;16%; 18%; t = 20%, n = 2;5

NPV/D(i1) at n=2 , L=1;3 and kd=14%;16%;18% 0

-0.5

0

1

kd=18 L=1 kd=16

-1

kd=14 kd=18 L=3 kd=16

-1.5

kd=14

-2

Fig. 31.5 The detailed dependence of NPV/D on coverage ratio on debt i1 at L = 1;3, k0 = 20%; kd = 14%,!6%, 18%; t = 20%, n = 2 (i1 changes from 0 to 1)

31.5

Conclusion

745

NPV/NOI(l1) at L=1, n=2;5, kd=14%;16%;18% 1 0 -1 -2

1

2

3

kd=18 n=2 kd=16 kd=14 kd=18 n=5 kd=16

-3

kd=14

-4 -5

Fig. 31.6 The detailed dependence of NPV/NOI on leverage ratio on debt l1 at L = 1; k0 = 20%; kd = 14%,!6%, 18%; t = 20%, n = 2;5 (i1 changes from 0 to 3)

projects, which has been developed in our previous chapter (Brusov et al. 2018a, b, c, d, e, f, g). The important features of current consideration as well as in previous studies are: (1) The adequate use of discounting of financial flows virtually not used in existing rating methodologies, (2) The incorporation of rating parameters (financial “ratios”), used in project rating, into considered modern investment models. We use the modern investment models, created by us, with incorporated financial “ratios” to study the dependence of NPV on rating parameters (financial “ratios”) at different values of equity cost k0, at different values of credit rates kd as well as at different values of on leverage level L and project duration n. We study the dependence of NPV on two types of financial “ratios”: on the coverage ratios ij as well as on the leverage ratios lj. In our calculations we use Excel technique in two aspects: (1) we calculate WACC at different values of equity costs k0, different values of debt costs kd, and different values of leverage level L = D/S, using the famous BFO formula; (2) we calculate the dependences of NPV on coverage ratios as well as leverage ratios at different values of equity costs k0, different values of debt costs kd, and different values of leverage level L. Analyzing obtained results we have found: 1. NPV (in units of D) (NPV D ) increases with i1 with the following features: (a) the angle NPV(i1) is determined by the project duration n: it increases with n. (b) with increase of leverage level L the curve NPV(i1) shifts practically parallel up. Thus, NPV increases with debt financing. This means that influence of the project duration n on the dependence of NPV/D on coverage ratio on debt i1 is more significant than the influence of leverage level L.

746

31

Ratings of the Investment Projects of Arbitrary Durations: New Methodology

2. NPV (in units of NOI) (NPV NOI ) decreases with l1 with the following features: (a) the angle NPV(l1) is determined by the leverage level L: it increases with L. Thus, NPV increases with debt financing. (b) with increase of project duration n the curve NPV(l1) shifts practically parallel up. This means that influence of leverage level L on the dependence of NPV/NOI on leverage ratio on debt l1 is more significant than influence of the project duration n. One can see that the dependence of NPV/NOI on leverage ratio on debt l1 is opposite to the dependence of NPV/D on coverage ratio on debt i1: 1. the angle NPV(l1) is determined by the leverage level L, while the angle NPV(i1) is determined by the project duration n. 2. with increase of project duration n the curve NPV(l1) shifts practically parallel up, while such kind of behavior is typical for influence of the leverage level L in case of the curve NPV(i1). The only one common thing for both curves NPV(l1) and NPV(i1) is that NPV increases with debt financing (or with the leverage level L ). This means that debt financing of the projects of arbitrary duration favors effectiveness of the investment project as well as its creditworthiness. The obtained by us results allow to make adequate estimation of the effectiveness of the investment projects, NPV, knowing rating parameters (financial “ratios”). For all calculations we use the correct values of discount rate, WACC, which is calculated by use of the modern theory of capital cost and capital structure (BFO theory) (Brusov et al. 2018a, b, c, d, e, f, g). Investigations, conducting in the current chapter, creates a new approach to rating methodology with respect to the ratings of the investment project of arbitrary duration. It allows to use the financial “ratios” for adequate estimation of the effectiveness of the investment projects of arbitrary duration, including energy projects, such as “Turkish stream,” “Nord stream-2,” etc., energy projects relating to clean, renewable, and sustainable energy.

References Brusov P, Filatova T, Orehova N, Eskindarov M (2015) Modern corporate finance, investments and taxation. Springer, Cham. 373 p monograph, SCOPUS, https://www.springer.com/gp/book/ 9783319147314 Brusov P, Filatova T, Orehova N, Eskindarov M (2018a), Modern corporate finance, investments, taxation and ratings, Springer, Cham, 571 p. monograph Brusov PN, Filatova TV, Orekhova NP, Kulik VL (2018b) Rating: new approach. J Rev Glob Econ 7:37–62. SCOPUS. https://doi.org/10.6000/1929-7092.2018.07.05 Brusov PN, Filatova TV, Orekhova NP, Kulik VL (2018c) A “golden age” of the companies: conditions of its existence. J Rev Glob Econ 7:88–103. SCOPUS. https://doi.org/10.6000/ 1929-7092.2018.07.07

References

747

Brusov PN, Filatova TV, Orekhova NP, Kulik VL (2018d) Rating methodology: new look and new horizons. J Rev Glob Econ 7:63–87. SCOPUS. https://doi.org/10.6000/1929-7092.2018.07.06 Brusov PN, Filatova TV, Orekhova NP, Kulik VL, Weil I (2018e) New meaningful effects in modern capital structure theory. J Rev Glob Econ 7:104–122. SCOPUS. https://doi.org/10. 6000/1929-7092.2018.07.08 Brusov P, Filatova T, Orekhova N, Kulik V, Weil I, Brailov A (2018f) The impact of the central bank key rate and commercial banks credit rates on creating and maintaining of a favorable investment climate in the country. J Rev Glob Econ 7:360–376., SCOPUS. https://doi.org/10. 6000/1929-7092.2018.07.31 Brusov P, Filatova P, Orekhova N (2014a) Mechanism of formation of the company optimal capital structure, different from suggested by trade off theory. Cogent Econ Financ 2:1–13 Brusov P, Filatova T, Orehova N (2014b) Inflation in Brusov–Filatova–Orekhova theory and in its perpetuity limit–Modigliani–Miller theory. J Rev Glob Econ 3:175–118 Brusov PN, Filatova TV, Orekhova NP (2018g) Modern corporate finance and investments., monograph. Knorus Publishing House, Moscow, p 517 Brusov PN, Filatova TV, Orekhova NP, Kulik VL, Weil I (2019) Ratings of the investment projects of arbitrary durations: new methodology. J Rev Glob Econ 8:437–448. SCOPUS. https://doi. org/10.6000/1929-7092.2019.08.37 Brusov PN, Filatova TV, Orekhova NP, Kulik VL, Chang SI, Lin YCG (2020) Modification of the Modigliani–Miller theory for the case of advance payments of tax on profit. J Rev Glob Econ 9: 257–268 Brusov P, Filatova T, Orekhova N (2021) Ratings: critical analysis and new approaches of quantitative and qualitative methodology. Springer Nature Publishing Brusova A (2011) А comparison of the three methods of estimation of weighted average cost of capital and equity cost of company. Financ Anal Prob Solut 34(76):36–42 Filatova Т, Orehova N, Brusova А (2008) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Bull FU 48:68–77 Filatova TV, Brusov PN, Orekhova NP, Kulik VL (2018) Ratings of the long–term projects: new approach. J Rev Glob Econ 7:645–661., SCOPUS. https://doi.org/10.6000/1929-7092.2018. 07.59 Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Modigliani F, Miller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391

Chapter 32

Ratings of Investment Projects of Arbitrary Duration with a Uniform Debt Repayment: A New Approach

Keywords Brusov–Filatova–Orekhova (BFO) theory · Investment projects of arbitrary durations · Rating methodologies · Financial “ratios” · Uniform debt repayment

32.1

Introduction

Along with the rating of non-financial issuers, considered in previous Chaps. (28, 29, and 30), the rating of investment projects plays an important role in the modern economy and finance. It allows ranking and selection of the most effective investment projects, which is especially important for attracting both foreign and domestic investments. This chapter discusses the rating of investment projects of arbitrary duration with a uniform repayment of debt, investment model for which is described in Chap. 18. The methodology for rating investment projects has been modified. A fundamentally new approach to the project rating methodology has been developed, the key factors of which are: (1) adequate application of discounting when discounting the financial flows, which is practically not used in the existing project rating methodologies; (2) incorporation of financial ratios into modern investment models created by the authors; (3) use of rating parameters upon discounting; (4) the determination of the correct discount rate, taking into account financial ratios. We use modern investment model created by the authors (see Chap. 18), the modern theory of capital cost and capital structure by Brusov–Filatova–Orekhova (BFO) theory (Brusov 2018a, b; Brusov et al. 2015, 2018a, b, c, d, e, f, g, 2019, 2020; Filatova et al. 2008, 2018), its modification for rating needs, and rating coefficients (Brusov et al. 2021). Various theories of capital cost and capital structure are described in Chaps. 2, 3, 4, 5, and 6. The developed approach should be applied by rating agencies, both international and national ones, when rating investment projects. The modification of the methodology of the existing project rating systems will improve the accuracy of ratings of investment projects and make them more objective. The use of powerful tools of well-developed theories opens up new

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_32

749

750

32 Ratings of Investment Projects of Arbitrary Duration with a Uniform. . .

opportunities for the rating industry, which gets the opportunity to switch from using primarily qualitative methods for assessing the effectiveness of investment projects to using mainly quantitative methods for evaluating them.

32.2

Incorporation of Financial Ratios Used in Project Rating into Modern Investment Models with Uniform Repayment of Debt

Below we incorporate the financial coefficients, used in project rating, into modern investment models with a uniform repayment of debt, created by authors. We will consider two kinds of financial coefficients: coverage ratios as well as leverage coefficients. In each group of financial coefficients we incorporate three particular quantities. For coverage ratios we incorporate: (1) coverage ratios of debt, i1 = NPV D ; (2) cov; (3) coverage ratios of debt and interest erage ratios of interest on the credit i2 = NPV kd D NPV . on the credit i3 = ð1þk d ÞD D For leverage ratios we incorporate: (1) leverage ratios of debt, l1 = NPV ; (2) leverkd D age ratios of interest on the credit l2 = NPV; (3) leverage ratios of debt and interest on d ÞD the credit l3 = ð1þk NPV Note that the last type of ratios (i3 and l3) was introduced by us for the first time to more fully characterize the ability to repay debts and pay interest on them at the expense of operating income when implementing an investment project.

32.2.1

Coverage Ratios

32.2.1.1

Coverage Ratios of Debt

Let us first incorporate the coverage ratios, using in project rating, into modern investment models, created by authors. Dividing both parts of Eq. (10.9) by D one gets for the net present value of the project, NPV (in units of D), the following expression

32.2

Incorporation of Financial Ratios Used in Project Rating into. . .

751

nþ1 1   1 NPV 1 i i ð1 - t Þ - n - k d n ð1 - t Þ þ =- þ 1D L WACC ð1 þ WACCÞn   ð1 þ WACCÞ½1 - ð1 þ WACCÞ - n  n kd ð1 - t Þ n WACCð1 þ WACCÞn WACC2 ð32:1Þ Here, i1 = NOI/D, L = D/S—leverage level.

32.2.1.2

Coverage Ratios of Interest on the Credit

Dividing both parts of Eq. (10.9) by kdD one gets for the net present value of the project, NPV (in units of kdD), the following expression nþ1 1  i 2 ð1 - t Þ ð1 - t Þ  1 1 NPV n kd n þ =þ 1kd L WACC kd D ð1 þ WACCÞn   ð1 þ WACCÞ½1 - ð1 þ WACCÞ - n  1 n ð1 - t Þ n WACCð1 þ WACCÞn WACC2 ð32:2Þ Here, i2 = NOI/kdD.

32.2.1.3

Coverage Ratios of Debt and Interest on the Credit (New Parameter)

Dividing both parts of Eq. (10.9) by (1 + kd)D one gets for the net present value of the project, NPV (in units of (1 + kd)D), the following expression NPV = D ð1 þ k d Þ kd n þ 1 1  i3 ð1-t Þð1-t Þ  nð1 þ k d Þ ð1 þ kd Þ n 1 1 þ 1WACC Lð 1 þ k d Þ ð1 þ WACCÞn  ð1 þ WACCÞ½1- ð1 þ WACCÞ - n  kd n g ð1-t Þ þ 2 ð1 þ k d Þ  n WACC ð 1 þ WACCÞn WACC ð32:3Þ Here, i3 =

NOI Dð1þk d Þ :

32 Ratings of Investment Projects of Arbitrary Duration with a Uniform. . .

752

Analyzing the formulas (32.1), (32.2), and (32.3) we come to very important conclusion that NPV (in units of D) (NPV D ) depends only on equity cost k0, on credit rates kd, on leverage level L as well as on one of the coverage ratios ij and does not depend on equity value S, debt value D and NOI. This means that results on the dependence of NPV (in units of D) (NPV D ) on coverage ratios ij at different equity costs k0, at different credit rates kd, at different leverage levels L carry the universal character: these dependencies remain valid for investment projects with any equity value S, debt value D and NOI.

32.2.2

Leverage Ratios

32.2.2.1

Leverage Ratios for Debt

Now let us incorporate the leverage ratios, using in project rating, into modern investment models, created by authors. Dividing both parts of Eq. (32.9) by NOI one gets for the net present value of the project, NPV (in units of NOI), the following expression l1 nþ1   l 1 ð1 - t Þ - n - k d l 1 n ð1 - t Þ NPV 1 þ =- þ 1NOI L WACC ð1 þ WACCÞn   ð1 þ WACCÞ½1 - ð1 þ WACCÞ - n  k d l1 n ð1 - t Þ n WACCð1 þ WACCÞn WACC2 ð32:4Þ Here, l1 =

32.2.2.2

D NOI

Leverage Ratios for Interest on Credit

Dividing both parts of Eq. (32.9) by NOI one gets for the net present value of the project, NPV (in units of NOI), the following expression nþ1 l  ð1 - t Þ - 2 - l 2 ð1 - t Þ  1 NPV l2 kd n n þ =þ 1NOI kd L WACC ð1 þ WACCÞn   ð1 þ WACCÞ½1 - ð1 þ WACCÞ - n  l2 n ð1 - t Þ n WACCð1 þ WACCÞn WACC2 ð32:5Þ kd D Here, l2 NOI

32.2

Incorporation of Financial Ratios Used in Project Rating into. . .

32.2.2.3

753

Leverage Ratios for Debt and Interest on Credit

Dividing both parts of Eq. (32.9) by NOI one gets for the net present value of the project, NPV (in units of NOI), the following expression NPV NOI 1 þ Lð1þkd Þ =

ð1-t Þ-

k l nþ1 l3  ð1-t Þ  - d3 ð1þkd Þn ð1þkd Þ n 1 1WACC ð1þWACCÞn

 ð1þWACCÞ½1- ð1þWACCÞ -n  k d l3 ð1-t Þ ð1þk d Þn WACC2 n g WACCð1þWACCÞn

þ

ð32:6Þ d ÞD Здесь l3 = ð1þk NOI Analyzing the formulas (32.4), (32.5), and
(32.6) we come to very important conclusion that NPV (in units of NOI) NPV NOI depends only on equity cost k0, on credit rates kd, on leverage level L as well as on one of the leverage ratios lj and does not depend on equity value S, debt value D
and NOI. This means that results on the dependence of NPV (in units of NOI) NPV NOI on leverage ratios lj at different equity costs k0, at different credit rates kd, at different leverage levels L carry the universal character: these dependencies remain valid for investment projects with any equity value S, debt value D and NOI. We investigate below the effectiveness of long-term investment projects studying the dependence of NPV on coverage ratios and on leverage ratios. We make calculations for coefficients i1 and l1. Calculations for the rest of coefficients (i2, i3 and l2, l3) could be made in a similar way. We start from the calculations of the dependence of NPV on coverage ratios. We consider different values of equity costs k0, of debt costs kd, and of leverage level L = D/S. Here t is the tax on profit rate, which in our calculations is equal to 20%.

32.2.3

Perpetuity Limit

In the perpetuity limit (T = 0) from Eq. (10.9), or as limit expressions (32.1)–(32.6), we can obtain the following expressions for NPV (in units of D) and NPV (in units of NOI).

754

32 Ratings of Investment Projects of Arbitrary Duration with a Uniform. . .

NPV 1 i ð1 - t Þ - k d ð1 - t Þ =- þ 1 WACC D L

ð32:7Þ

ð1 - t Þ - k d l 1 ð1 - t Þ NPV l =- 1þ WACC L NOI

ð32:8Þ

Substituting instead of WACC its value in the theory of MM  WACC = k0 1-

 Lt ,, 1þL

ð32:9Þ

one gets for NPV (in units D) NPV 1 ðkd - i1 Þð1 - t Þ   = D L Lt k 0 1 - 1þL

ð32:10Þ

and for NPV (in units NOI) NPV - l 1 ð 1 - k d l 1 Þð 1 - t Þ   : = þ NOI L k 1 - Lt 0

ð32:11Þ

1þL

Here k0 is the equity cost at zero leverage. In the following paragraphs, we will study the dependence of the net present value, NPV, on financial ratios for companies of a given age n and for particular values of investment project parameters, demonstrating the possibility of performing calculations for companies of arbitrary age n and for any values of investment project parameters.

32.2.4

The Study of the Dependence of the Net Present Value of the Project, NPV, on Rating Parameters

32.2.4.1

Investigation of the Dependence of the Net Present Value of the Project, NPV (in Units of Debt D) on Coverage Ratios

First, we analyze the dependence of the net present value of the NPV/D project on coverage coefficients ij for companies of arbitrary age n in the framework of the modern theory of value and capital structure by Brusov–Filatova–Orekhova using modern investment models created by the authors and described above. We restrict ourselves to considering the dependence of NPV on the debt coverage coefficients i1 described by Eq. (32.1). Calculations for other coverage coefficients described by Eqs. (32.2)–(32.3) are carried out similarly. The calculations are carried out in two stages.

32.2

Incorporation of Financial Ratios Used in Project Rating into. . .

755

1. First, for a given set of project parameters, according to the famous Brusov– Filatova–Orekhova formula 1 - ð1 þ k 0 Þ - n 1 - ð1 þ WACCÞ - n = WACC k0  ð1 - wd  t  ð1 - ð1 þ kd Þ - n ÞÞ

ð32:12Þ

weighted average cost of capital, WACC, is calculated by Microsoft Excel using the “matching parameter” function. 2. The found WACC value is used in Eq. (32.1) to study the dependence of NPV/D on debt coverage coefficient i1 Similar studies can be carried out for other coverage coefficients (i2 and i3). When analyzing this formula, we will use the following parameter values: L = 1, 3; t = 20%; n is 3; 5; k0 = 18%; kd = 12%, 14%, 16%; i1 = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. The following conclusions can be drawn from the data in Tables 32.1 and 32.2: 1. The net present value of the project NPV/D increases linearly with an increase of debt coverage ratio i1. 2. The dependence of NPV/D (i1) for various values of the cost of debt capital kd has interesting features: for values of the coverage ratio for debt i1 from 0 to 3, an increase in the cost of debt capital kd leads to a decrease in NPV/D, and for the values of the cost of borrowed capital kd more than 3 (and up to 10) large values of the cost of borrowed capital kd correspond to large values of NPV/D. From Tables 32.1 and 32.2 it is also seen that the net present value of the project, NPV/D, for various values of debt capital kd (12%, 14%, 16%) differs slightly from each other (by approximately 0.02), due to that the graphs of the dependence NPV/D (i1) practically coincide, as shown in Fig. 32.1. To demonstrate the differences in the dependence of the net present value of the project NPV (in units of debt D) on the debt coverage ratio i1 for various L and kd, we give Fig. 32.1 on an enlarged scale (Fig. 32.2). From Fig. 32.2 and from Tables 32.1 and 32.2 we can come to the following conclusions: 1. The slope of the straight line NPV/D (i1) is determined by the duration of the project n and increases with the duration of the project. So, the slope of the straight line NPV/D (i1) for a 5-year project is greater than for a 3-year project. 2. When the leverage level L changes, the line NPV/D (i1) shifts almost in parallel: with the growth of L, the line shifts higher (in Fig. 32.2 it can be seen that for projects of the same term, lines with L = 3 lie above lines with L = 1.

WACC 0.1574 0.1596 0.1619 0.1461 0.1493 0.1528

i =0 1

-1.954 -1.925 -1.897 -1.30 -1.274 -1.243

d

16% 14% 12% 16% 14% 12%

k

1 -0.1493 -0.1273 -0.1057 0.53 0.5548 0.5749

2 1.6549 1.6705 1.6854 2.37 2.3833 2.3929

3 3.4592 3.4684 3.4764 4.21 4.2119 4.2109

4 5.2634 5.2663 5.2675 6.05 6.0405 6.0289

5 7.0677 7.0641 7.0585 7.89 7.8690 7.8469

6 8.8719 8.8620 8.8495 9.73 9.6976 9.6649

7 10.6762 10.6598 10.6406 11.57 11.5261 11.4830

8 12.4804 12.4577 12.4316 13.40 13.3548 13.3010

L=3 n=5

NPV/D L=1 n=5

WACC 0.1566 0.1586 0.1608 0.1448 0.1477 0.1510

kd 16% 14% 12% 16% 14% 12%

i1 = 0 -1.938 -1.899 -1.861 -1.296 -1.255 -1.213

1 0.7022 0.7288 0.7543 1.4190 1.4416 1.4626

2 3.3423 3.3569 3.3692 4.1341 4.1378 4.1380

3 5.9823 5.9849 5.9840 6.8492 6.8339 6.8133

4 8.6224 8.6130 8.5989 9.5643 9.5300 9.4886

5 11.2624 11.2410 11.2137 12.2794 12.2261 12.1639

6 13.9025 13.8691 13.8286 14.9945 14.9222 14.8393

7 16.5425 16.4971 16.4434 17.7096 17.6183 17.5146

8 19.1825 19.1252 19.0583 20.4247 20.3144 20.1899

Table 32.2 The dependence of NPV/D on debt coverage ratio i1 at L = 1.3, t = 20%, n = 5, k0 = 18%, kd = kd = 12%, 14%, 16%

L=3 n=3

NPV/D L=1 n=3

Table 32.1 The dependence of NPV/D on debt coverage ratio i1 at L = 1.3, t = 20%, n = 3, k0 = 18%, kd = kd = 12%, 14%, 16%

9 21.8226 21.7532 21.6731 23.1398 23.0105 22.8653

9 14.2847 14.2555 14.2227 15.24 15.1833 15.1190

10 24.4626 24.3813 24.2880 25.8549 25.7067 25.5406

10 16.0890 16.0534 16.0137 17.08 17.0119 16.9370

756 32 Ratings of Investment Projects of Arbitrary Duration with a Uniform. . .

32.2

Incorporation of Financial Ratios Used in Project Rating into. . .

757

NPV/D (i1) at L=1, t=20%, n=3 18 16 14 12 10 8 6 4 2 0 -2 0 -4

kd=16% kd=14% kd=12%

5

10

15

Fig. 32.1 The dependence of the net present value of the project NPV (in units of debt D) on the debt coverage ratio i1

32.2.4.2

Study of the Dependence of the Net Present Value of the Project NPV (in Units of Net Operating Income NOI) on Leverage Ratios

Now we analyze the dependence of the net present value of the project NPV/D on leverage coefficients lj for companies of arbitrary age n in the framework of the modern theory of value and capital structure of Brusov–Filatova–Orekhova using modern investment models created by the authors and described above. We restrict ourselves to considering the dependence of NPV on the leverage coefficient for debt l1, described by Eq. (32.4). Calculations for other leverage coefficients (l2 and l3) described by Eqs. (32.5)–(32.6) are carried out similarly. The calculations, as in the case of coverage coefficients, are carried out in two stages. 1. First, for a given set of project parameters according to the famous Brusov– Filatova–Orekhova formula: 1 - ð1 þ k 0 Þ - n 1 - ð1 þ WACCÞ - n = WACC k0  ð1 - wd  t  ð1 - ð1 þ kd Þ - n ÞÞ

ð32:13Þ

weighted average cost of capital, WACC, is calculated by Microsoft Excel using the “matching parameter” function. 2. The found WACC value is used in Eq. (32.4) to study the dependence of NPV/ NOI on the debt leverage coefficient l1. Similar studies can be carried out for other leverage coefficients (l2 and l3).

32 Ratings of Investment Projects of Arbitrary Duration with a Uniform. . .

758

NPV/D (i1) 28

26

24

22

NPV/D

20

18

16

14

12

10 5

6

7

L=1, t=20%, n=3, kd=16 L=1, t=20%, n=3, kd=12 L=3, t=20%, n=3, kd=14 L=1, t=20%, n=5, kd=14 L=3, t=20%, n=5, kd=16 L=3, t=20%, n=5, kd=12

8 i

9

10

11

L=1, t=20%, n=3, kd=14 L=3, t=20%, n=3, kd=16 L=3, t=20%, n=3, kd=12 L=1, t=20%, n=5, kd=12 L=3, t=20%, n=5, kd=14

Fig. 32.2 Dependence of the net present value of the project NPV (in units of debt D) on the debt coverage ratio i1 (increased scale)

WACC 0.1574 0.1596 0.1619 0.1461 0.1493 0.1528

kd 16% 14% 12% 16% 14% 12%

l1 = 0 1.8043 1.7979 1.7910 1.84 1.83 1.82

1 -0.149 -0.127 -0.106 0.53 0.55 0.57

2 -2.103 -2.053 -2.002 -0.77 -0.72 -0.67

3 -4.057 -3.978 -3.899 -2.07 -1.99 -1.91

4 -6.010 -5.903 -5.796 -3.38 -3.27 -3.15

5 -7.964 -7.828 -7.692 -4.68 -4.54 -4.40

6 -9.917 -9.753 -9.589 -5.99 -5.81 -5.64

7 -11.871 -11.678 -11.486 -7.29 -7.09 -6.88

8 -13.824 -13.603 -13.383 -8.60 -8.36 -8.13

9 -15.778 -15.529 -15.279 -9.90 -9.64 -9.37

10 -17.732 -17.454 -17.176 -11.21 -10.91 -10.61

L=3 n=5

NPV/NOI L=1 n=5

WACC 0.1566 0.1586 0.1608 0.1448 0.1477 0.1510

kd 16% 14% 12% 16% 14% 12%

l1 = 0 2.64 2.63 2.61 2.72 2.70 2.68 1 0.70 0.73 0.75 1.42 1.44 1.46

2 -1.24 -1.17 -1.11 0.12 0.19 0.25

3 -3.17 -3.07 -2.97 -1.17 -1.07 -0.96

4 -5.11 -4.97 -4.83 -2.47 -2.32 -2.18

5 -7.05 -6.87 -6.69 -3.77 -3.58 -3.39

6 -8.99 -8.77 -8.55 -5.06 -4.83 -4.60

7 -10.92 -10.67 -10.41 -6.36 -6.09 -5.81

8 -12.86 -12.57 -12.27 -7.65 -7.34 -7.03

9 -14.80 -14.47 -14.13 -8.95 -8.59 -8.24

10 -16.74 -16.36 -15.99 -10.25 -9.85 -9.45

Table 32.4 The dependence of the net present value of the project NPV (in units of net operating income NOI) on the leverage coefficient on debt l1 at L = 1.3, t = 20%, n = 5, k0 = 18%, kd = kd = 12%, 14%, 16%

L=3 n=3

NPV/NOI L=1 n=3

Table 32.3 The dependence of the net present value of the project NPV (in units of net operating income NOI) on the leverage coefficient on debt l1 at L = 1,3, t = 20%, n = 3, k0 = 18%, kd = kd = 12%, 14%, 16%

32.2 Incorporation of Financial Ratios Used in Project Rating into. . . 759

32 Ratings of Investment Projects of Arbitrary Duration with a Uniform. . .

760

NPV/NOI (l1) 5 0 NPV/NOI

0

2

4

6

8

10

12

-5 -10 -15 -20

l1 L=1, t=20%, n=3, kd=16

L=1, t=20%, n=3, kd=14

L=1, t=20%, n=3, kd=12

L=3, t=20%, n=3, kd=16

L=3, t=20%, n=3, kd=14

L=3, t=20%, n=3, kd=12

L=1, t=20%, n=5, kd=16

L=1, t=20%, n=5, kd=14

L=1, t=20%, n=5, kd=12

L=3, t=20%, n=5, kd=16

L=3, t=20%, n=5, kd=14

L=3, t=20%, n=5, kd=12

Fig. 32.3 Summary dependence of NPV/NOI on leverage ratio on debt l1 at different leverage level L, project duration n, and debt cost kd

Let us analyze the dependence of the net present value of the project NPV (in units of net operating income NOI) on the leverage coefficient on debt l1 for companies of a given age n and for specific values of investment project parameters, demonstrating the possibility of performing calculations for companies of arbitrary age n and for any values of investment project parameters. When analyzing Eq. (32.4), we will use the following parameter values: L = 1, 3; t = 0,20; n = 3,5; k0 = 18; kd = 16, 14, 12; l = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. From the data of Tables 32.3 and 32.4 and Figs. 32.3 and 32.4, the following conclusions can be drawn: 1. The net present value of the project NPV/NOI decreases linearly with increasing leverage on debt ratio l1. 2. The slope of the straight line NPV/NOI (l1) is determined by the leverage level L, while the absolute value of the slope decreases with increasing L: thus, lines with L = 3 are closer to the axis l1 than lines with L = 1. 3. An increase in the project duration n shifts the line NPV/NOI (l1) almost parallel higher (Figs. 32.3 and 32.4 show that for projects with the same level of leverage L, lines with n = 5 lie above lines with n = 3).

32.2

Incorporation of Financial Ratios Used in Project Rating into. . .

761

NPV/NOI (l1) -5 5

6

7

8

9

10

11

-7

NPV/NOI

-9

-11

-13

-15

-17

-19

l L=1, t=20%, n=3, kd=16

L=1, t=20%, n=3, kd=14

L=1, t=20%, n=3, kd=12

L=3, t=20%, n=3, kd=16

L=3, t=20%, n=3, kd=14

L=3, t=20%, n=3, kd=12

L=1, t=20%, n=5, kd=16

L=1, t=20%, n=5, kd=14

L=1, t=20%, n=5, kd=12

L=3, t=20%, n=5, kd=16

L=3, t=20%, n=5, kd=14

L=3, t=20%, n=5, kd=12

Fig. 32.4 Summary dependence of NPV/NOI on leverage ratio on debt l1 at different leverage level L, project duration n, and debt cost kd (in increased scale)

4. For equal project duration n and equal leverage levels L, the line NPV/NOI (l1) shifts almost parallel downward with an increase in the debt cost kd (12%, 14%, 16%).

762

32.3

32 Ratings of Investment Projects of Arbitrary Duration with a Uniform. . .

Conclusions

The chapter discusses the rating of investment projects of arbitrary duration with a uniform repayment of debt and a modification of the methodology of rating systems for investment projects. The development of a fundamentally new approach to the project rating methodology has been carried out, the key factors of which are: (1) adequate use of discounts when discounting the financial flows, which is practically not used in existing project rating methodologies; (2) incorporation of financial ratios into modern investment models created by the authors; (3) use of rating parameters upon discounting; (4) the correct determination of the discount rate, taking into account financial ratios. The chapter used modern investment models created by the authors, the modern theory of capital cost and capital structure by Brusov–Filatova–Orekhova (BFO) theory, its modification for rating needs, and rating coefficients. For the first time, incorporation of coverage ratios and leverage coefficients used in the rating was carried out into modern investment models created by the authors and designed to study the effectiveness of investment projects of arbitrary duration with uniform repayment of debt. The dependence of the net present value of the project, NPV/NOI, on the coverage coefficients ij (leverage coefficients lj) for companies of arbitrary age n is analyzed. When studying the dependence of NPV/D on coverage ratios ij, it was shown that the net present value of the project, NPV/D increases linearly with increasing debt coverage ratio ij. At the same time, the dependence NPV/D (i1) for various values of the debt cost kd has interesting features: for values of the coverage ratio for debt i1 from 0 to 3, an increase in the cost of debt capital kd leads to a decrease in NPV/D, and for values of the cost of debt capital kd more than 3 (and up to 10) to bigger values of the cost of debt capital kd correspond to bigger values of NPV/D. At the same time, the values of the net present value of the project NPV/D at various values of the cost of debt capital kd (12%, 14%, 16%) differ slightly from each other (by about 0.02), and therefore the NPV/D graphs (i1) almost coincide. The slope of the straight line NPV/D (i1) is determined by the duration of the project n and increases with the duration of the project. So, the slope of the straight line NPV/D (i1) for a 5-year project is greater than for a 3-year project. When the leverage level L changes, the line NPV/D (i1) shifts almost parallel: with the growth of L, the line shifts higher (for projects of the same term, lines with L = 3 lie above lines with L = 1). When studying the dependence of NPV/NOI on leverage coefficients lj, it is shown that the net present value of the project NPV/NOI decreases linearly with an increase of the leverage coefficient for debt l1. In this case, the slope of the straight line NPV/NOI (l1) is determined by the leverage level L, and the absolute value of the slope decreases with increasing L: thus, lines with L = 3 lie closer to the axis l1 than lines with L = 1. An increase of the project duration n shifts the line NPV/NOI (l1) almost parallel higher (for projects with the same level of leverage L, lines with

References

763

n = 5 lie above lines with n = 3). With equal project times and equal leverage levels L, the direct NPV/D (i1) shifts almost parallel to down with the growth of the debt cost kd (12%, 14%, 16%). It can be seen that the behavior of the NPV/NOI (lj) dependence is qualitatively different from the behavior of the NPV/D (ij) dependence. These dependencies should be taken into account and used when rating investment projects. The modification of the methodology of the existing project rating systems will improve the accuracy of issued ratings of investment projects and make them more objective. The use of powerful tools of well-developed theories opens up new opportunities for the rating industry, which gets the opportunity to switch from using mainly qualitative methods for assessing the effectiveness of investment projects to using mainly quantitative methods for evaluating them.

References Brusov P (2018a) Editorial: introduction on special issue on the banking system and financial markets of Russia and other countries: problems and prospects. J Rev Glob Econ 7:i–vi. SCOPUS Brusov P (2018b) Editorial. J Rev Glob Econ 7:i–v. SCOPUS Brusov P, Filatova T, Orehova N, Eskindarov M (2015) Modern corporate finance, investments and taxation. Springer, Cham, p 373. monograph, https://www.springer.com/gp/book/978331914 7314 Brusov P, Filatova T, Orehova N, Eskindarov M (2018a) Modern corporate finance, investments, taxation and ratings. Springer, Cham, p 571. monograph Brusov PN, Filatova TV, Orekhova NP, Kulik VL (2018b) Rating: new approach. J. Rev. Glob. Econ 7:37–62. https://doi.org/10.6000/1929-7092.2018.07.05 Brusov PN, Filatova TV, Orekhova NP, Kulik VL (2018c) A “golden age” of the companies: conditions of its existence. J Rev Glob Econ 7:88–103. https://doi.org/10.6000/1929-7092. 2018.07.07 Brusov PN, Filatova TV, Orekhova NP, Kulik VL (2018d) Rating methodology: new look and new horizons. J Rev Glob Econ 7:63–87. https://doi.org/10.6000/1929-7092.2018.07.06 Brusov PN, Filatova TV, Orekhova NP, Kulik VL, Weil I (2018e) New meaningful effects in modern capital structure theory. J Rev Glob Econ 7:104–122. https://doi.org/10.6000/ 1929-7092.2018.07.08 Brusov P, Filatova T, Orekhova N, Kulik V, Weil I, Brailov A (2018f) The impact of the central bank key rate and commercial banks credit rates on creating and maintaining of a favorable investment climate in the country. J Rev Glob Econ 7:360–376. https://doi.org/10.6000/ 1929-7092.2018.07.31 Brusov PN, Filatova TV, Orekhova NP (2018g) Modern corporate finance and investments, monograph. Knorus publishing house, Moscow, p 517 Brusov PN, Filatova TV, Orekhova NP, Kulik VL, Weil I (2019) Ratings of the investment projects of arbitrary durations: new methodology. J Rev Glob Econ 8:437–448. https://doi.org/10.6000/ 1929-7092.2019.08.37

764

32 Ratings of Investment Projects of Arbitrary Duration with a Uniform. . .

Brusov PN, Filatova TV, Orekhova NP, Kulik VL, Chang SI, Lin YCG (2020) Modification of the Modigliani–Miller theory for the case of advance payments of tax on profit. J Rev Glob Econ 9: 257–268 Brusov P, Filatova T, Orekhova N (2021) Ratings: critical analysis and new approaches of quantitative and qualitative methodology. Springer Nature Publishing Filatova Т, Orehova N, Brusova А (2008) Weighted average cost of capital in the theory of Modigliani–Miller, modified for a finite life–time company. Bull FU 48:68–77 Filatova TV, Brusov PN, Orekhova NP, Kulik VL (2018) Ratings of the long–term projects: new approach. J Rev Glob Econ 7:645–661., SCOPUS. https://doi.org/10.6000/1929-7092.2018. 07.59

Chapter 33

Conclusions

Keywords Brusov–Filatova–Orekhova (BFO) theory · Rating agencies · Central Bank · Financial economic · Principles of financial management · Right managerial decisions This book changes our understanding of corporate finance, investments, taxation, and rating procedures. It shows that the most used principles of financial management should be changed in accordance with Brusov–Filatova–Orekhova (BFO) theory (Brusov & Filatova 2021, 2022a, b; Brusova 2011). Many of the discoveries made within this theory still require interpretations and understanding as well as incorporation into real finance and economy. But it is clear now that without very serious modification of the conceptions of financial management, it is impossible to adequately manage manufacture, investments, taxation, and rating procedures, as well as finance in general. The book has destroyed some main existing principles of financial management: among them is the trade-off theory, which was considered as a keystone of formation of optimal capital structure of the company during many decades. It was proved by the authors that the balance between advantages and shortcomings of debt financing could not provide the optimal capital structure for the company at all (and an explanation (nontrivial) to this fact has been done). A new mechanism of formation of the company’s optimal capital structure, different from the ones suggested by trade-off theory, has been suggested in monograph. Let us also mention the discovered qualitatively new effect in corporate finance: decreasing of cost of equity ke with leverage L. This changes the conceptions of dividend policy of company very significantly. A very important discovery has been done recently by the authors within Brusov– Filatova–Orekhova (BFO) theory. It is shown for the first time that valuation of weighted average cost of capital (WACC) in the Modigliani–Miller theory (perpetuity limit of BFO theory) (Modigliani and Miller 1958, 1963, 1966) is not minimal and valuation of the company capitalization is not maximal, as all financiers supposed up to now: at some age of the company (“golden age”), its WACC value turns out to be lower than in Modigliani–Miller theory and company capitalization V turns out to be greater than V in Modigliani–Miller theory (see Chaps. 24 and 25). © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Brusov et al., The Brusov–Filatova–Orekhova Theory of Capital Structure, https://doi.org/10.1007/978-3-031-27929-4_33

765

766

33

Conclusions

Over the past couple of years, the BFO authors have obtained very important results related to the generalization of the two main theories of the capital structure (Brusov–Filatova–Orekhova and Modigliani–Miller) to take into account the current financial practice of the company’s functioning and taking into account the real conditions of their work (2012, 2013a, b, 2014a, b, 2015, 2018a–e, 2020a–c, 2021a). The Brusov–Filatova–Orekhova (BFO) and MM theories have been generalized to the case of variable income, to arbitrary frequency of income tax payments, to advance payments of income tax, etc., as well as to their combinations (Brusov et al. 2021a, b, 2022a, b, 2023; Brusov and Filatova 2021, 2022a, b, 2023; Filatova et al. 2022). These generalizations significantly expand the applicability of both theories in practice, in particular, in corporate finance, business valuation, investments, ratings, etc. The results on the generalized Modigliani–Miller theory can be found in the monograph (Brusov et al. 2022c). The generalization of Modigliani–Miller theory for the cases of practical interest leads to a much more significant change in Modigliani–Miller theory than all previous modifications, studied over the previous decades. Obtained results showed that under such a generalization there is some convergence of Modigliani–Miller theory and BFO theory: the former theory begins to have some new properties similar to those of BFO theory, which was not there in the classical Modigliani–Miller theory, between the properties of which and of the BFO theory was a huge gap. Most of the innovative effects existing in the BFO theory are absent in the classical Modigliani–Miller theory. All of the above means that the considered effects, such as the variable income of the company, frequent paying income tax, advance payment of income tax, the combinations of this conditions and others, are more important than the effects studied earlier and having much less influence on the Modigliani–Miller theory. Taking into account these effects leads to some convergence between Modigliani– Miller theory and the BFO theory. At the same time, one must understand that Modigliani–Miller theory remains perpetual and will never describe a company of arbitrary age, which is extremely important for the practical application of the theory. We could mention the directions for further research: • Generalization of the Brusov–Filatova–Orekhova (BFO) theory and MM theory to the case of a company’s variable in time income. • Generalization of the Brusov–Filatova–Orekhova (BFO) theory to the stochastic case and to the case of a company’s variable in time income. • Further generalization of the Brusov–Filatova–Orekhova (BFO) theory and MM theory on the conditions for the practical functioning of the company. • Study the dependence of the effects of the “golden and silver age of the company” on the growth rate of income in the case of a company’s variable income, on the frequency of income tax payment, on the advance payment of income tax, and on a combination of these conditions. • Incorporating CAPM, Hamada and Fama–French Models into Capital Structure Theories (both Brusov-Filatova-Orekhova and Modigliani–Miller ).This will take into account the business risk accounted for in these models, along with the financial risk accounted for in the BFO and MM theories.

33

Conclusions

767

Existing rating methodologies have a lot of shortcomings (Brusov et al. 2021c). One of the major flaws of all of them is a failure or a very narrow use of discounting. But even in those rare cases where it is used, it is not quite correct, since the discount rate when discounting financial flows is chosen incorrectly. In this book, a new approach to rating methodology is suggested. Chapters 28–30 are devoted to rating of non-financial issuers, while Chaps. 31 and 32 are devoted to ratings of the investment projects of arbitrary durations. The key factors of a new approach are: (1) The adequate use of discounting of financial flows virtually not used in existing rating methodologies, (2) The incorporation of rating parameters (financial “ratios”) into the modern theory of capital structure (Brusov–Filatova–Orekhova (BFO) theory). This, on the one hand, allows to use the powerful tools of this theory in the rating and, on the other hand, it ensures the correct discount rates when discounting of financial flows. We discuss also the interplay between rating ratios and leverage level which can be quite important in rating. All these create a new base for rating methodologies. The new approach to ratings and rating methodologies allows to issue more correct ratings of issuers and makes the rating methodologies more understandable and transparent. A distinctive feature of the book is the extensive and adequate use of mathematics that allows the reader to count various financial and economic parameters, including investment and taxation ones, up to the quantitative result. Application of Brusov–Filatova–Orekhova (BFO) theory in corporate finance, investments, taxation, business valuation, and ratings as well as in other areas of economy and finance allows to make correct assessment of main financial parameters of the objects and make the right managerial decisions. This will help to avoid financial crises like global financial crisis of 2008 in the future. And we can see similar influence of the obtained results in many areas of finance and economy. Not all results, obtained by authors, found reflection in a book via its limited volume. Readers should look for recent and coming papers by authors in journals. In conclusion, we mention the applications of BFO theory in corporate finance, investments, business valuation, taxation and ratings: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Companies and corporations Rating agencies Investment companies Banks and credit organizations Central banks Ministry of finance Business valuation Insurance companies Financial reports (ISFR, GAAP, etc.) Fiscal organizations

768

33

Conclusions

References Brusov P, Filatova T (2021) The Modigliani–Miller theory with arbitrary frequency of payment of tax on profit. Mathematics 9(11):1198. https://doi.org/10.3390/math9111198 Brusov P, Filatova T (2022a) Influence of method and frequency of profit tax payments on company financial indicators. Mathematics 10(14):2479. https://doi.org/10.3390/math10142479 Brusov P, Filatova T (2022b) Generalization of the Brusov–Filatova–Orekhova theory for the case of variable income. Mathematics 10:3661. https://doi.org/10.3390/math10193661 Brusov P, Filatova T (2023) Capital structure theory: past, present, future. Mathematics 11(3):616. https://doi.org/10.3390/math11030616 Brusov P, Filatova T, Eskindarov M, Orehova N (2012) Hidden global causes of the global financial crisis. J Rev Global Econ 1:106–111 Brusov P, Filatova P, Orekhova N (2013a) Absence of an optimal capital structure in the famous tradeoff theory! J Rev Global Econ 2:94–116 Brusov P, Filatova T, Orehova N (2013b) A qualitatively new effect in corporative finance: abnormal dependence of cost of equity of company on leverage. J Rev Global Econ 2:183–193 Brusov P, Filatova P, Orekhova N (2014a) Mechanism of formation of the company optimal capital structure, different from suggested by trade off theory. Cogent Econ Finance 2:1–13. https://doi. org/10.1080/23322039.2014.946150 Brusov P, Filatova T, Orehova N (2014b) Inflation in Brusov–Filatova–Orekhova theory and in its perpetuity limit–Modigliani–Miller theory. J Rev Global Econ 3:175–185 Brusov P, Filatova T, Orehova N, Eskindarov M (2015) Modern corporate finance, investment and taxation, 1st edn. Springer, pp 1–368 Brusov P, Filatova T, Orehova N, Eskindarov M (2018a) Modern corporate finance, investments, taxation and ratings, 2nd edn. Springer, Cham, pp 1–571 Brusov P, Filatova T, Orehova N, Kulk WI (2018b) New meaningful effects in modern capital structure theory. J Rev Global Econ 7:104–122 Brusov P, Filatova T, Orehova N, Kulk V (2018c) A “golden age” of the companies: conditions of its existence. J Rev Global Econ 7:88–103 Brusov P, Filatova T, Orehova N, Kulk V (2018d) Rating methodology: new look and new horizons. J Rev Global Econ 7:63–87 Brusov P, Filatova T, Orehova N, Kulk V (2018e) Rating: new approach. J Rev Global Econ 7:37– 62 Brusov PN, Filatova TV, Orekhova NP, Kulik VL, Chang SI, Lin YCG (2020a) Modification of the Modigliani–Miller Theory for the case of advance payments of tax on profit. J Rev Glob Econ 9: 257–267 Brusov PN, Filatova TV, Orekhova NP, Kulik VL, Chang SI, Lin YCG (2020b) Application of the Modigliani–Miller theory, modified for the case of advance payments of tax on profit, in rating methodologies. J Rev Glob Econ 9:282–292 Brusov PN, Filatova TV, Orekhova NP, Kulik VL, Chang SI, Lin YCG (2020c) Modification of the Modigliani–Miller theory for the case of advance payments of tax on profit. J Rev Glob Econ 9: 257–267 Brusov P, Filatova T, Chang S-I, Lin G (2021a) Innovative investment models with frequent payments of tax on income and of interest on debt. Mathematics 9(13):1491. https://doi.org/ 10.3390/math9131491 Brusov P, Filatova T, Orekhova N, Kulik V, Chang S–I, Lin G (2021b) Generalization of the Modigliani–Miller theory for the case of variable profit. Mathematics 9:1286 Brusov P, Filatova T, Orekhova N (2021c) Ratings: critical analysis and new approaches of quantitative and qualitative methodology. Springer Nature Publishing Brusov P, Filatova T, Orekhova N, Kulik V, Chang S-I, Lin G (2022a) The generalization of the Brusov–Filatova–Orekhova theory for the case of payments of tax on profit with arbitrary frequency. Mathematics 10(8):1343. https://doi.org/10.3390/math10081343

References

769

Brusov P, Filatova T, Kulik V (2022b) Benefits of advance payments of tax on profit: consideration within the Brusov–Filatova–Orekhova (BFO) Theory. Mathematics 10(12):2013. https://doi. org/10.3390/math10122013 Brusov P, Filatova T, Orekhova N (2022c) Generalized Modigliani–Miller theory: applications in corporate finance, investments, taxation and ratings. Springer Brusov P, Filatova T, Kulik V (2023) Two types of payments of tax on profit: advanced payments and at the end of periods: consideration within BFO Theory with variable profit. J Risk Financ Manag 16(3):1–20 Brusova A (2011) А comparison of the three methods of estimation of weighted average cost of capital and equity cost of company. Financ Anal Prob Sol 34(76):36–42 Filatova T, Brusov P, Orekhova N (2022) Impact of advance payments of tax on profit on effectiveness of investments. Mathematics 10(4):666. https://doi.org/10.3390/math10040666 Мodigliani F, Мiller M (1958) The cost of capital, corporate finance, and the theory of investment. Am Econ Rev 48:261–297 Мodigliani F, Мiller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:147–175 Мodigliani F, Мiller M (1966) Some estimates of the cost of capital to the electric utility industry 1954–1957. Am Econ Rev 56:333–391