Modern corporate finance, investments, taxation and ratings, 2 edition

Within theframework of modern investment models created by the authors, the dependence ofthe efficiency of investments, determined by net present value NPV, on the level ofdebtfinancing wi

Peter Brusov · Tatiana Filatova 

Natali Orekhova · Mukhadin Eskindarov

Modern Corporate

Finance, Investments, Taxation and Ratings

Second Edition

Modern Corporate Finance, Investments, Taxation and Ratings

Peter Brusov • Tatiana Filatova •

Modern Corporate Finance, Investments, Taxation and Ratings

Second Edition

Peter Brusov

Financial University under

the Government of Russian Federation

Moscow, Russia

Tatiana FilatovaFinancial University underthe Government of Russian FederationMoscow, Russia

Natali Orekhova

Center of Corporate Finance, Investment,

Taxation and Ratings

The Research Consortium of Universities

of the South of Russia

Rostov-on-Don, Russia

Mukhadin EskindarovFinancial University underthe Government of Russian FederationMoscow, Russia

ISBN 978-3-319-99685-1 ISBN 978-3-319-99686-8 (eBook)

https://doi.org/10.1007/978-3-319-99686-8

Library of Congress Control Number: 2018955714

© Springer Nature Switzerland AG 2015, 2018

This work is subject to copyright All rights are reserved by the Publisher, whether the whole or part of the material is concerned, speci fically 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 speci fic 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, express 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 af filiations.

This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

under the Government of Russia Federation

Dedicated to our dear granddaughter Anyuta, who likes very much to sing and dance, and to her little sister So fi

Preface to the Second Edition

In the 3 years since thefirst edition, new results have been obtained by authors incorporatefinance, investment, and taxation as well as in a new area—ratings andrating methodologies—within the framework of Brusov, Filatova, and Orekhova(BFO) theory Some of them (not all) have been included in the second edition(Chaps.19,20,21,22,23, and24have been added)

Among them is the chapter entitled“A golden age of the companies: conditions

of its existence” (Chap.19) Also, we have found a modification of “Kulik effect”:descending of WACC with passage through minimum, which lies above the perpe-tuity limit value, and then going through maximum followed by a limiteddescending We call this company age, where WACC has a minimum, which liesabove the perpetuity limit value,“by a silver age” of the company

In Chap 20, we study the role of the Central Bank and commercial banks increating and maintaining a favorable investment climate in the country Within theframework of modern investment models created by the authors, the dependence ofthe efficiency of investments, determined by net present value (NPV), on the level ofdebtfinancing within a wide range of values of equity costs and debt capital costsunder different project terms (long-term projects as well as projects of arbitraryduration) and different investment profitability coefficients β is investigated Thestudy 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 onleverage level L, increasing or decreasing depending on profitability coefficient βand credit rate values kd The cutoff credit rate values k∗

d, separating the range ofincreasing NPV(L ) from the range of decreasing NPV(L ), are determined TheCentral Bank should keep its key rate at the level which allows commercial banks

to keep their credit rates below the cutoff credit rate k∗

d values in order to create andmaintain a favorable investment climate in the country

The most significant addition to the second edition is Part IV, devoted to thediscussion of ratings and rating methodologies The shortcomings of existing ratingmethodologies are discussed and analyzed, and a new approach to rating methodol-ogy has been suggested in Chaps.21,22, and23: Chaps.21and22are devoted to

vii

rating of non-financial issuers, while Chap.23is devoted to long-term project rating.The key factors of the new approach are (1) the adequate use of discounting offinancial flows virtually not used in existing rating methodologies and (2) theincorporation of rating parameters (financial “ratios”) into the modern theory ofcapital structure [Brusov–Filatova–Orekhova (BFO) theory] (in Chap 21 into itsperpetuity limit) This, on the one hand, allows us to use the powerful tools of thistheory in the rating, and on the other hand, it ensures the correct discount rates whendiscounting offinancial flows We discuss also the interplay between rating ratiosand leverage level, which can be quite important in rating All these create a newbase for rating methodologies.1

The new approach to ratings and rating methodologies allows issue more correctratings of issuers, making the rating methodologies more understandable andtransparent

We call the modified form of BFO theory for rating needs BFO-3 theory Thus, inthe monograph we describe three modifications of BFO theory:

BFO-1, which is applicable to describe the companies of arbitrary age;

BFO-2, which is applicable to describe companies of arbitrary lifetime when pany ceased to exist at the arbitrary time moment n;

com-BFO-3, which is applicable for rating needs

This book is intended for both undergraduate and postgraduate students, students

of MBA program, teachers of economic andfinancial universities, scientists, cial analysts,financial directors of company, managers of insurance companies andrating agencies, officials of regional and federal ministries and departments, andministers responsible for economic andfinancial management

23 June 2018

1 The study in Chaps 21 , 22 , and 23 was funded by RFBR according to the research project 06-00251A.

This book describes in detail the modern theory of corporatefinance, investment,and taxation, created by Brusov, Filatova, and Orekhova (BFO theory), which hasreplaced the famous theory of capital cost and capital structure by Nobel laureatesModigliani and Miller The authors have moved from the assumption of Modigliani–Miller concerning the perpetuity (infinite time of life) of companies and furtherelaborated quantitative theory of valuation of key parameters offinancial activities ofcompanies with arbitrary time of life (of arbitrary age)

Results of modern BFO theory turn out to be quite different from those ofModigliani–Miller theory They show that the latter, via its perpetuity, underesti-mates the assessment of weighted average cost of capital, WACC, and the equitycost of the company and substantially overestimates the assessment of the capital-ization of the company

Such an incorrect assessment of key performance indicators offinancial activities

of companies has led to an underestimation of risks involved, and impossibility, orserious difficulties in adequate managerial decision-making, which was one of theimplicit reasons of globalfinancial crisis in 2008

Within new modern theory of capital cost and capital structure (BFO theory), a lot

of qualitatively new results have been obtained, among them:

1 The qualitatively new effect in corporatefinance, discovered by authors: mal dependence of equity cost on leverage, which alters the main principles of thecompany’s dividend policy significantly

abnor-2 Bankruptcy of the famous trade-off theory has been proven

3 A very important discovery has been done recently: the valuation of WACC inthe Modigliani–Miller theory (perpetuity limit) is not minimal and valuation ofthe company capitalization is not maximal, as allfinanciers supposed up to now:

at some age of the company (“golden age”) its WACC value turns out to be lowerthan in perpetuity limit and company capitalization V turns out to be greater thanperpetuity limit of V

ix

4 Mechanism of formation of the company optimal capital structure, different fromthe one suggested by trade-off theory, has been suggested.

5 The inflation in both Modigliani–Miller as well as in Brusov–Filatova–Orekhovatheories has been taken into account in explicit form, which has a nontrivialimpact on the dependence of equity cost on leverage

6 Study of the role of taxes and leverage has been done, which allows the Regulator

to set up the tax on profits rate and allows businessmen to choose the optimallevel of debtfinancing

7 Investigation of the influence of tax on profit rate on the effectiveness of ment projects at different debt levels has showed that increase of tax on profit ratefrom one side leads to decrease of project NPV, but from other side it leads todecrease of sensitivity of NPV with respect to leverage level At high leveragelevel L, the influence of tax on profit rate change on effectiveness of investmentprojects becomes significantly less

invest-8 Studying the influence of growth of tax on profit rate on the efficiency of theinvestment as well has led to two qualitatively new effects in investments:– the growth of tax on profit rate changes the nature of the NPV dependence onleverage L: at some value t*, there is a transition from diminishing functionNPV(L ) at t < t*, to growing function NPV(L) at t > t*

– at high leverage levels, the growth of tax on profit rate leads to the growth ofthe efficiency of the investments

Discovered effects in investments can be applied in a real economic practice foroptimizing of the management of investments

Established BFO theory allows us conduct a valid assessment of the core eters offinancial activities of companies, such as weighted average cost of capital,equity capital cost of the company, and company’s capitalization It allows themanagement of a company to make adequate decisions, which improves the effec-tiveness of the company management More generally, the introduction of the newsystem of evaluation of the core parameters offinancial activities of companies intothe systems offinancial reporting (IFRS, GAAP, etc.) would lead to a lower risk ofglobalfinancial crisis

param-The second part of this book is devoted to the assessment of effectiveness ofinvestment projects created by the authors within the modern investment models.The determination of the optimal leverage level for investments is studied in thisbook from two points of view: from the point of view of owners of equity capital, aswell as from the point of view of owners of both equity and debt capital

Corporate management in the modern world is the management of financialflows The proposed Brusov–Filatova–Orekhova theory allows to correctly identifydiscount rates—basic parameters for discounting of financial flows to arbitrary timemoment, comparefinancial flows with a view to adopt literate managerial decisions.The discount rate is a key link to the existingfinancial system, on which the modernfinance can be adequately built, and this proposed book can be of substantialassistance

This book is intended for students, postgraduate students, teachers of economicandfinancial institutions, students of MBA program, scientists, financial analysts,financial directors of company, managers of insurance companies and rating agen-cies, officials of regional and federal ministries and departments, and ministersresponsible for economic andfinancial management.

4 February 2014

Part I Corporate Finance

1 Introduction 3

References 6

2 Capital Structure: Modigliani–Miller Theory 9

2.1 Introduction 9

2.2 The Traditional Approach 10

2.3 Modigliani–Miller Theory 11

2.3.1 Modigliani–Miller Theory Without Taxes 11

2.3.2 Modigliani–Miller Theory with Taxes 13

2.3.3 Main Assumptions of Modigliani–Miller Theory 16

2.3.4 Modifications of Modigliani–Miller Theory 17

References 27

3 Modern Theory of Capital Cost and Capital Structure: Brusov–Filatova–Orekhova Theory (BFO Theory) 29

3.1 Companies of Arbitrary Age and Companies with Arbitrary Lifetime: Brusov–Filatova–Orekhova Equation 30

3.2 Comparison of Modigliani–Miller Results (Perpetuity Company) with Myers Results (1-Year Company) and Brusov–Filatova– Orekhova Ones (Company of Arbitrary Age) 32

3.3 Brusov–Filatova–Orekhova Theorem 36

3.4 From Modigliani–Miller to General Theory of Capital Cost and Capital Structure 40

3.5 BFO Theory in the Case, When the Company Ceased to Exist at the Time Moment n (BFO-2 Theory) 43

3.5.1 Application of Formula BFO-2 44

3.5.2 Comparison of Results Obtained from Formulas BFO and BFO-2 46

xiii

3.6 Conclusions 47

References 49

4 Bankruptcy of the Famous Trade-Off Theory 51

4.1 Optimal Capital Structure of the Company 51

4.2 Absence of the Optimal Capital Structure in Modified Modigliani–Miller Theory (MMM Theory) 54

4.3 Analysis of the Trade-Off Theory Within the Brusov–Filatova– Orekhova Theory 55

4.4 The Causes of Absence of the Optimum Capital Structure in the Trade-Off Theory 74

4.5 Conclusion 95

References 96

5 New Mechanism of Formation of the Company’s Optimal Capital Structure, Different from Suggested by Trade-Off Theory 99

5.1 Absence of Suggested Mechanism of Formation of the Company’s Optimal Capital Structure Within Modified Modigliani–Miller Theory (MMM Theory) 99

5.2 Formation of the Company’s Optimal Capital Structure Within Brusov–Filatova–Orekhova (BFO) Theory 100

5.3 Simple Model of Proposed Mechanism 113

5.4 Conclusion 115

References 116

6 The Global Causes of the Global Financial Crisis 119

References 124

7 The Role of Taxing and Leverage in Evaluation of Capital Cost and Capitalization of the Company 125

7.1 The Role of Taxes in Modigliani–Miller Theory 126

7.2 The Role of Taxes in Brusov–Filatova–Orekhova Theory 129

7.2.1 Weighted Average Cost of Capital (WACC) of the Company 130

7.2.2 Equity Cost keof the Company 132

7.2.3 Dependence of WACC and keon the Age of Company 135

7.3 Conclusions 138

References 139

8 A Qualitatively New Effect in Corporate Finance: Abnormal Dependence of Equity Cost of Company on Leverage 141

8.1 Introduction 141

8.2 Equity Cost in the Modigliani–Miller Theory 141

8.3 Equity Cost Capital Within Brusov–Filatova–Orekhova Theory 145

8.3.1 Dependence of Equity Cost keon Tax on Profit Rate T at Different Fixed Leverage Level L 146

8.3.2 Dependence of Equity Cost keon Leverage Level

L (the Share of Debt Capital wd) at Different Fixed Tax

on Profit Rate T 148

8.4 Dependence of the Critical Value of Tax on Profit Rate T * on Parameters n, k0, and kdof the Company 150

8.5 Practical Value of Effect 153

8.6 Equity Cost of a 1-Year Company 154

8.7 Conclusions 157

References 158

9 Inflation in Brusov–Filatova–Orekhova Theory and in Its Perpetuity Limit Modigliani–Miller Theory 161

9.1 Introduction 161

9.2 Accounting of Inflation in the Modigliani–Miller Theory Without Taxes 162

9.3 Accounting of Inflation in Modigliani–Miller Theory with Corporate Taxes 166

9.4 Accounting of Inflation in Brusov–Filatova–Orekhova Theory with Corporate Taxes 168

9.4.1 Generalized Brusov–Filatova–Orekhova Theorem 168

9.5 Generalized Brusov–Filatova–Orekhova Formula Under Existence of Inflation 169

9.6 Irregular Inflation 176

9.7 Inflation Rate for a Few Periods 177

9.8 Conclusions 178

References 179

Part II Investments 10 A Portfolio of Two Securities 183

10.1 A Portfolio of Two Securities 183

10.1.1 A Case of Complete Correlation 183

10.1.2 Case of Complete Anticorrelation 185

10.1.3 Independent Securities 186

10.1.4 Three Independent Securities 188

10.2 Risk-Free Security 191

10.3 Portfolio of a Given Yield (or Given Risk) 193

10.3.1 Case of Complete Correlation (ρ12¼ 1) and Complete Anticorrelation (ρ12¼ 1) 194

References 195

11 Investment Models with Debt Repayment at the End of the Project and Their Application 197

11.1 Investment Models 197

11.2 The Effectiveness of the Investment Project from the Perspective of the Equity Holders Only 198

11.2.1 With the Division of Credit and Investment Flows 198

11.3 Without Flows Separation 200

11.4 Modigliani–Miller Limit (Perpetuity Projects) 201

11.4.1 With Flows Separation 201

11.4.2 Without Flows Separation 202

11.5 The Effectiveness of the Investment Project from the Perspective of the Owners of Equity and Debt 203

11.5.1 With Flows Separation 203

11.5.2 Without Flows Separation 204

11.6 Modigliani–Miller Limit 205

11.6.1 With Flows Separation 205

11.6.2 Without Flows Separation 206

References 207

12 Influence of Debt Financing on the Efficiency of Investment Projects: The Analysis of Efficiency of Investment Projects Within the Perpetuity (Modigliani–Miller) Approximation 209

12.1 The Effectiveness of the Investment Project from the Perspective of the Equity Holders Only 209

12.1.1 With the Division of Credit and Investment Flows 209

12.1.2 Without Flows Separation 217

12.2 The Effectiveness of the Investment Project from the Perspective of the Equity and Debt Owners 225

12.2.1 With the Division of Credit and Investment Flows 225

12.2.2 Without Flows Separation 233

References 241

13 The Analysis of the Exploration of Efficiency of Investment Projects of Arbitrary Duration (Within Brusov–Filatova– Orekhova Theory) 243

13.1 The Effectiveness of the Investment Project from the Perspective of the Equity Holders Only 243

13.1.1 With the Division of Credit and Investment Flows 243

13.1.2 Without Flow Separation 250

13.2 The Effectiveness of the Investment Project from the Perspective of the Owners of Equity and Debt 258

13.2.1 With the Division of Credit and Investment Flows 258

13.2.2 Without Flow Separation 266

13.3 The Elaboration of Recommendations on the Capital Structure of Investment of Enterprises, Companies, Taking into Account All the Key Financial Parameters of Investment Project 273

13.3.1 General Conclusions and Recommendations on the Definition of Capital Structure of Investment of Enterprises 273

References 275

14 Investment Models with Uniform Debt Repayment and Their

Application 277

14.1 Investment Models with Uniform Debt Repayment 277

14.2 The Effectiveness of the Investment Project from the Perspective of the Equity Holders Only 279

14.2.1 With the Division of Credit and Investment Flows 279

14.2.2 Without Flows Separation 280

14.3 The Effectiveness of the Investment Project from the Perspective of the Owners of Equity and Debt 281

14.3.1 With Flows Separation 281

14.3.2 Without Flows Separation 281

14.4 Example of the Application of the Derived Formulas 282

14.5 Conclusions 283

References 284

Part III Taxation 15 Is It Possible to Increase Taxing and Conserve a Good Investment Climate in the Country? 287

15.1 Influence of Tax on Profit Rates on the Efficiency of the Investment Projects 287

15.2 Investment Models 289

15.3 Borrowings Abroad 292

15.4 Dependence of NPV on Tax on Profit Rate at Different Leverage Levels 293

15.5 At a Constant Value of Equity Capital (S¼ Const) 294

15.6 Without Flow Separation 296

15.6.1 At a Constant Value of the Total Invested Capital (I¼ Const) 296

15.6.2 At a Constant Value of Equity Capital (S¼ Const) 298

15.7 Conclusions 300

References 300

16 Is It Possible to Increase the Investment Efficiency by Increasing Tax on Profit Rate? An Abnormal Influence of the Growth of Tax on Profit Rate on the Efficiency of the Investment 303

16.1 Dependence of NPV on Leverage Level L at Fixed Levels of Tax on Profit Rate t 303

16.1.1 The Effectiveness of the Investment Project from the Perspective of the Equity Holders Only 303

16.1.2 The Effectiveness of the Investment Project from the Perspective of the Equity and Debt Holders 314

16.2 Dependence of NPV on Tax on Profit Rate at Fixed Leverage

Levels L 321

16.2.1 The Effectiveness of the Investment Project from the Perspective of the Equity Holders Only 321

16.2.2 The Effectiveness of the Investment Project from the Perspective of the Equity and Debt Holders 328

References 335

17 Optimizing the Investment Structure of the Telecommunication Sector Company 337

17.1 Introduction 337

17.2 Investment Analysis and Recommendations for Telecommunication Company“Nastcom Plus” 338

17.2.1 The Dependence of NPV on Investment Capital Structure 339

17.2.2 The Dependence of NPV on the Equity Capital Value and Coefficient β 348

17.3 Effects of Taxation on the Optimal Capital Structure of Companies in the Telecommunication Sector 354

17.4 Conclusions 365

References 366

18 The Golden Age of the Company (Three Colors of Company’s Time) 367

18.1 Introduction 368

18.2 Dependence of WACC on the Age of the Company n at Different Leverage Levels 371

18.3 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 373

18.4 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 375

18.5 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 379

18.6 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 380

18.7 Further Investigation of Effect 389

18.8 Conclusions 391

References 393

19 A“Golden Age” of the Companies: Conditions of Its Existence 395

19.1 Introduction 396

19.2 Companies Without the“Golden Age” (Large Difference Between k0and kdCosts) 397

19.2.1 Dependence of the Weighted Average Cost of Capital, WACC, on the Company Age n at Different Leverage Levels 397

19.3 Companies with the“Golden Age” (Small Difference Between k0and kdCosts) 399

19.4 Companies with Abnormal“Golden Age” (Intermediate Difference Between k0and kdCosts) 403

19.5 Comparing with Results from Previous Chapter 410

19.5.1 Under Change of the Debt Capital Cost, kd 410

19.5.2 Under Change of the Equity Capital Cost, k0 411

19.6 Conclusions 411

References 414

20 The Role of the Central Bank and Commercial Banks in Creating and Maintaining a Favorable Investment Climate in the Country 415

20.1 Introduction 415

20.2 Investment Models with Debt Repayment at the End of the Project 416

20.2.1 The Effectiveness of the Investment Project from the Perspective of the Equity Holders Only (Without Flow Separation) 417

20.3 Modigliani–Miller Limit (Long-Term (Perpetuity) Projects) 419

20.3.1 The Dependence of the Efficiency of Investments NPV on the Level of Debt Financing L for the Values of Equity Costs k0¼ 0.2 419

20.3.2 The Dependence of the Efficiency of Investments NPV on the Level of Debt Financing L for the Value of Equity Costs k0¼ 0.28 422

20.4 Projects of Finite (Arbitrary) Duration 424

20.4.1 The Dependence of the Efficiency of Investments NPV on the Level of Debt Financing L for the Values of Equity Costs k0¼ 0.2 424

20.4.2 The Dependence of the Efficiency of Investments NPV on the Level of Debt Financing L for the Values of Equity Costs k0¼ 0.28 428

20.5 The Dependence of the Net Present Value, NPV, on the Leverage Level l for Projects of Different Durations 430

20.6 Conclusions 435

References 437

Part IV Ratings and Rating Methodologies

21 Rating: New Approach 441

21.1 Introduction 441

21.2 The Closeness of the Rating Agencies 442

21.3 The Use of Discounting in the Rating 442

21.4 Incorporation of Parameters, Used in Ratings, into Perpetuity Limit of Modern Theory of Capital Structure by Brusov–Filatova–Orekhova 443

21.5 Models 443

21.5.1 One-Period Model 444

21.5.2 Multi-period Model 444

21.6 Theory of Incorporation of Parameters, Used in Ratings, into Perpetuity Limit of Modern Theory of Capital Structure by Brusov–Filatova–Orekhova 445

21.6.1 Coverage Ratios 445

21.6.2 More Detailed Consideration 448

21.6.3 Leverage Ratios 450

21.7 Equity Cost 453

21.8 How to Evaluate the Discount Rate? 464

21.8.1 Using One Ratio 465

21.8.2 Using a Few Ratios 465

21.9 Influence of Leverage Level 465

21.9.1 The Dependence of Equity Cost keon Leverage Level at Two Coverage Ratio Values ij¼ 1 and ij¼ 2 465

21.10 The Dependence of Equity Cost keon Leverage Level at Two Leverage Ratio Values lj¼ 1 and lj¼ 2 468

21.11 Conclusion 472

References 473

22 Rating Methodology: New Look and New Horizons 475

22.1 Introduction 475

22.2 The Analysis of Methodological and Systemic Deficiencies in the Existing Credit Rating of Nonfinancial Issuers 476

22.2.1 The Closeness of the Rating Agencies 476

22.2.2 Discounting 476

22.2.3 Dividend Policy of the Company 477

22.2.4 Leverage Level 478

22.2.5 Taxation 478

22.2.6 Account of the Industrial Specifics of the Issuer 479

22.2.7 Neglect of Taking into Account the Particularities of the Issuer 479

22.2.8 Financial Ratios 479

22.3 Modification of the BFO Theory for Companies

and Corporations of Arbitrary Age for Purposes of Ranking 481

22.4 Coverage Ratios 482

22.4.1 Coverage Ratios of Debt 483

22.4.2 The Coverage Ratio on Interest on the Credit 483

22.4.3 Coverage Ratios of Debt and Interest on the Credit (New Ratios) 485

22.4.4 All Three Coverage Ratios Together 487

22.5 Coverage Ratios (Different Capital Cost Values) 490

22.5.1 Coverage Ratios of Debt 490

22.5.2 The Coverage Ratio on Interest on the Credit 492

22.5.3 Coverage Ratios of Debt and Interest on the Credit (New Ratios) 493

22.5.4 Analysis and Conclusions 495

22.6 Leverage Ratios 496

22.6.1 Leverage Ratios for Debt 496

22.6.2 Leverage Ratios for Interest on Credit 498

22.7 Leverage Ratios (Different Capital Costs) 499

22.7.1 Leverage Ratios for Debt 499

22.7.2 Leverage Ratios for Interests on Credit 500

22.7.3 Leverage Ratios for Debt and Interests on Credit 500

22.7.4 Analysis and Conclusions 500

22.8 Conclusions 509

References 509

23 Ratings of Long-Term Projects: A New Approach 511

23.1 Investment Models 512

23.1.1 The Effectiveness of the Investment Project from the Perspective of the Equity Holders Only (Without Flows Separation) 512

23.1.2 Modigliani–Miller Limit [Long-Term (Perpetuity) Projects] 513

23.2 Incorporation of Financial Coefficients, Used in Project Rating, into Modern Investment Models 514

23.2.1 Coverage Ratios 514

23.2.2 Leverage Ratios 516

23.3 Dependence of NPV on Coverage Ratios 517

23.3.1 Coverage Ratio on Debt 517

23.4 Dependence of NPV on Leverage Ratios 522

23.4.1 Leverage Ratio of Debt 522

23.5 Conclusions 533

References 535

24 New Meaningful Effects in Modern Capital Structure Theory 537

24.1 Introduction 537

24.2 Comparison of Modigliani–Miller (MM) and Brusov–Filatova–Orekhova (BFO) Results 539

24.2.1 The Traditional Approach 539

24.2.2 Modigliani–Miller Theory 540

24.3 Comparison of Modigliani–Miller Results (Perpetuity Company) with Myers Results (1-Year Company) and Brusov–Filatova–Orekhova Ones (Company of Arbitrary Age) 542

24.4 Bankruptcy of the Famous Trade-Off Theory 544

24.5 The Qualitatively New Effect in Corporate Finance 546

24.5.1 Perpetuity Modigliani–Miller Limit 548

24.5.2 BFO Theory 549

24.6 Conclusions 550

24.7 Mechanism of Formation of the Company Optimal Capital Structure 551

24.8 “A Golden Age” of the Company 554

24.9 Inflation in Modigliani–Miller and BFO Theories 557

24.10 Effects, Connected with Tax Shields, Taxes, and Leverage 560

24.11 Effects, Connected with the Influence of Tax on Profit Rate on Effectiveness of Investment Projects 561

24.12 Influence of Growth of Tax on Profit Rate 561

24.13 New Approach to Ratings 564

24.13.1 New Approach to Ratings: The Creditworthiness of the Non-Finance Issuers 564

24.13.2 New Approach to Long-Term Project Ratings 566

References 567

25 Conclusion 569

References 570

Petr Nickitovich Brusov is professor at the cial University under the Government of the Rus-sian Federation (Moscow) Originally a physicist,

Finan-he was tFinan-he cofounder of (togetFinan-her with VictorPopov) the theory of collective properties of super-fluids and superconductors In the areas of financeand economy, Peter Brusov has created a moderntheory of capital cost and capital structure, theBrusov—Filatova—Orekhova theory, togetherwith Tatiana Filatova and Natali Orekhova PeterBrusov has been visiting Professor of NorthwesternUniversity (USA), Cornell University (USA), andOsaka City University (Japan), among other places

He is the author of over 500 research publications,including six monographs, numerous textbooks,and articles

Tatiana Filatova is professor at the Financial versity under the Government of the Russian Fed-eration (Moscow) In the last 20 years, she has been

Uni-a deUni-an of the fUni-aculties of financial management,management, and state and municipal government,among others, at the Financial University TatianaFilatova is the author of over 250 research publica-tions, including five monographs, numerous text-books, and articles

xxiii

Natali Orekhova is professor of the Center ofCorporate Finance, Investment, Taxation and Rat-ing at the Research Consortium of Universities ofthe South of Russia Natali Orekhova has beenleading scientist of the Financial University underthe Government of the Russian Federation She isthe author of over 100 research publications,including three monographs, numerous textbooks,and articles.

Mukhadin Abdurakhmanovich Eskindarov isprofessor, honored scholar of the Russian Federa-tion, member of the Russian Academy of Education,and rector of the Financial University under theGovernment of the Russian Federation (Moscow).Mukhadin A Eskindarov has played crucial admin-istrative, teaching, and researcher roles at the Finan-cial University He is the author of over 200 researchpublications, including monographs, manuals, andarticles on issues related to labor and production

efficiency, financial and industrial groups, economicdevelopment of the third-world countries, and mod-ernization of the educational system As a member ofvarious state and public administration bodies,Mukhadin A Eskindarov has been honored withhighly recognized state and public awards, includingthe IV Class Order for Merit to the Fatherland, Order

of Friendship, Petr Stolypin II Class Medal, badge ofthe Honored Worker of the Higher Education Sys-tem of the Russian Federation, and Patriot of RussiaMedal, among others

Part I Corporate Finance

Chapter 1

Introduction

One of the main problems in corporatefinance is the problem of cost of capital andthe impact of capital structure on its cost and capitalization of the companies Todate, even the question of the existence of an optimal capital structure of thecompanies (at which the company capitalization is maximal, and weighted averagecost of capital is minimal) is open Numerous theories and models, including thefirstand the only one until recently quantitative theory by Nobel Laureates Modiglianiand Miller (MM) (Modigliani and Miller1958,1963,1966), not only do not solvethe problem but also because of the large number of restrictions (such as, e.g., theory

of MM) have a weak relationship with the real economy Herewith the qualitativetheories and models, based on the empirical approach, do not allow to carry out thenecessary assessment

In the monograph, the foundation of modern corporate finance, investment,taxation, and ratings is laid It is based on the author’s work on modifying 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 and Filatova2011; Brusov et al.2011a,

b,c,2012a,b,2013a,b,2014a,b,2015,2018a,b,c,d; Filatova et al.2008, Brusova

2011) The authors have moved from the assumption of Modigliani–Millerconcerning the perpetuity of companies (infinite time of life of companies) andfurther elaborated quantitative theory of valuation of core parameters offinancialactivities of companies of arbitrary age or arbitrary time of life

Results of modern BFO theory (Brusov and Filatova2011; Brusov et al.2011a,b,c,

2012a,b,2013a,b,2014a,b,2015,2018a,b,c,d; Filatova et al.2008; Brusova

2011) turn out to be quite different from that of Modigliani–Miller theory gliani and Miller1958,1963,1966) They show that the latter, via its perpetuity,underestimates (often significantly) the assessment of weighted average cost ofcapital and the equity cost of the company and substantially overestimates (alsooften significantly) the assessment of the capitalization of both financially indepen-dent company and the company using the debtfinancing

(Modi-© Springer Nature Switzerland AG 2018

P Brusov et al., Modern Corporate Finance, Investments, Taxation and Ratings,

https://doi.org/10.1007/978-3-319-99686-8_1

3

Such an incorrect assessment of key performance indicators offinancial activities

of companies has led to an underestimation of risks involved, and impossibility, orserious difficulties in adequate managerial decision-making, which was one of theimplicit reasons of globalfinancial crisis of the year 2008

Within new theory of capital cost and capital structure (BFO theory), a study ofthe role of taxes and leverage has been done, which allows the regulator to set the tax

on profit rate and businesses to choose the optimal level of debt financing Thequalitatively new effect in corporatefinance, discovered by authors, is described:abnormal dependence of equity cost on leverage, which significantly alters theprinciples of development of the company’s dividend policy (modern principles ofwhich 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 which they detected its nontrivial impact on the dependence of equity cost onleverage

The established BFO theory (Brusov and Filatova2011; Brusov et al.2011a,b,c,

2012a, b, 2013a,b,2014a, b, 2015,2018a, b, c, d; Filatova et al 2008) allowsconduct a valid assessment of the core parameters offinancial activities of compa-nies, such as weighted average cost of capital and equity capital cost of the company,its capitalization It allows the management of a company make adequate decisions,which improves the effectiveness of the company management More generally, theintroduction of the new system of evaluation of the parameters offinancial activities

of companies into the systems offinancial reporting (IFRS, GAAP, etc.) would lead

to lower risk of globalfinancial crisis, since, as is shown in the monograph, a primarycause of the crisis of 2008 was a mortgage crisis in the USA, which is associatedwith overvalued capitalization of mortgage companies by rating agencies, usingincorrect MM theory This reason is now understood by the US Government, whichrequires $1 billion from rating agency S&P for overvalued capitalization of mort-gage companies

Within Brusov–Filatova–Orekhova theory, the analysis of wide-known trade-offtheory has been made (Brusov et al.2013a) It is shown that suggestion of risky debtfinancing (and growing credit rate near the bankruptcy) in opposite to waiting resultdoes not lead to growth of weighted average cost of capital, WACC, which stilldecreases with leverage This means the absence of minimum in the dependence ofWACC on leverage as well as the absence of maximum in the dependence ofcompany capitalization on leverage This means that the optimal capital structure

is absent in famous trade-off theory, and this fact proves the insolvency of famoustrade-off theory

Under condition, proved by authors, of insolvency of well-known classical off theory, the question of finding a new mechanism of the formation of thecompany’s optimal capital structure, different from one suggested by trade-offtheory, becomes very important A new such mechanism has been developed bythe authors in this monograph It is based on the decrease of debt cost with leverage,which is determined by growth of debt volume This mechanism is absent inperpetuity Modigliani–Miller theory (Modigliani and Miller 1958, 1963, 1966),even in modified version, developed by us, and exists within more general BFOtheory

trade-The second part of this monograph is devoted to assess effectiveness of theinvestment projects (IP) The authors created the modern investment models ofevaluation of the efficiency of IP index, using, as a 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 mostimportant problems is the determination of the optimal leverage level for invest-ments The monograph studies this problem from two points of view: from the point

of view of owners of equity capital and from the point of view of owners of bothequity capital and debt capital The study has being conducted without division ofcashflows as well as with division of cash flows on the financial and operating plusinvestmentflows (Brusov et al.2011c,2012a)

Within the framework of the established models, the evaluation of the ness of investment from the point of view of their optimal capital structure has beenmade on the example of one of the largest telecommunication companies in Russia

effective-It has been shown that there is an optimum structure of investment capital Butcompany has lost from $98 million up to $645 million because the company hasworked at leverage levels, which were far from optimal values The procedureproposed by authors for evaluation of the efficiency of investment projects willavoid such losses in the future

In this monograph, the significant attention has been given to the study of taxesand taxation in manufacture as well as in investments Some recommendations forregulator concerning taxation (value of tax on profit rates, etc.) have been done.Investigation of the influence of tax on profit rate on effectiveness of investmentprojects at different debt levels showed that increase of tax on profit rate from oneside leads to decrease of project NPV, but from other side, it leads to decrease ofsensitivity of NPV with respect to leverage level At high leverage level L, the

influence of changes of tax on profit rate on effectiveness of investment projectsbecomes significantly less

Studying the influence of growth of tax on profit rate on the efficiency of theinvestment 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 onleverage 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 foroptimizing the management of investments

A very important discovery has been done recently by the authors within BFOtheory It is shown for thefirst time that valuation of WACC in the Modigliani–Miller theory (perpetuity limit) (Modigliani and Miller 1958,1963, 1966) is notminimal, and valuation of the company capitalization is not maximal, as allfinanciers

supposed up to now: at some age of the company (“golden age”), its WACC valueturns 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 Chap.18)

A distinctive feature of the book is the extensive and adequate use of mathematicsthat allows the reader to count variousfinancial and economic parameters, includinginvestment and taxation ones, up to the quantitative result

Corporate management in the modern world is the management of financialflows The proposed Brusov–Filatova–Orekhova theory (Brusov and Filatova

2011; Brusov et al.2011a,b,c,2012a,b,2013a,b,2014a,b,2015,2018a,b,c,d;Filatova et al.2008) allows the reader to correctly identify discount rates—basicparameters for discountingfinancial flows to arbitrary time moment—and to com-parefinancial flows with a view to adopt literate managerial decisions The discountrate is a key link of the existing financial system, by pulling on which modernfinance can be adequately built, and the proposed monograph can be of substantialassistance in this

Existing rating methodologies have a lot of shortcomings One of the majorflaws

of all of them is a failure or a very narrow use of discounting But even in those rarecases where it is used, it is not quite correct, since the discount rate when discountingfinancial flows is chosen incorrectly In book a new approach to rating methodology

is suggested Chapters21and22are devoted to rating of nonfinancial issuers, whileChap.23is devoted to long-term project rating The key factors of a new approachare (1) the adequate use of discounting of financial flows virtually not used inexisting rating methodologies and (2) the incorporation of rating parameters (finan-cial“ratios”) into the modern theory of capital structure (Brusov–Filatova–Orekhova(BFO) theory) This on the one hand allows use of the powerful tools of this theory inthe rating, and on the other hand it ensures the correct discount rates whendiscounting offinancial flows We discuss also the interplay between rating ratiosand leverage level which can be quite important in rating All these create a new basefor rating methodologies New approach to ratings and rating methodologies(Brusov et al.2018c,d) allows issue more correct ratings of issuers and makes therating methodologies more understandable and transparent

This monograph is intended for students, postgraduate students, teachers ofeconomic andfinancial institutions, students of MBA program, scientists, financialanalysts, financial directors of company, managers of insurance companies andrating agencies, officials of regional and federal ministries and departments, andministers responsible for economic andfinancial management

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) In fluence 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) In fluence 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

Brusov P, Filatova T, Orehova N (2014b) In flation 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 International Publishing, Berlin, pp 1 –368

Brusov P, Filatova T, Orehova N, Kulik V, Weil I (2018a) New meaningful effects in modern capital structure theory J Rev Global Econ 7:104 –122

Brusov P, Filatova T, Orehova N, Kulik 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, Kulik V (2018c) Rating methodology: new look and new horizons J Rev Global Econ 7:63 –87

Brusov P, Filatova T, Orehova N, Kulik 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.

Capital Structure: Modigliani –Miller

Theory

2.1 Introduction

Under the capital structure, one understands the relationship between equity and debtcapital 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 others, and, ifaffects, how? Choice of an optimal capital structure, i.e., a capital structure, whichminimizes the weighted average cost of capital, WACC, and maximizes the value ofthe company, V, is one of the most important tasks solved byfinancial manager and

by the management of a company The first serious study (and first quantitativestudy) of influence of capital structure of the company on its indicators of activitieswas the work by Modigliani and Miller (1958) Until this study, the approach existed(let us call it traditional), which was based on empirical data analysis

One of the most important assumptions of the Modigliani–Miller theory is that allfinancial flows are perpetuity This limitation was lift out by Brusov–Filatova–Orekhova in 2008 (Filatova et al (2008), who have created BFO theory—moderntheory of capital cost and capital structure for companies of arbitrary age (BFO-1theory) and for companies of arbitrary lifetime (BFO-2 theory) (Brusov et al.2015).See recent development of BFO theory and its new applications in papers (Brusov

et al.2011a,b,c,2012a,b,2013a,b,2014a,b,2015,2018a,b,c,d) In Fig.2.1 thehistorical development of capital structure theory from the traditional (empirical)approach, through perpetuity Modigliani–Miller approach to general capital struc-ture theory—Brusov–Filatova–Orekhova (BFO) theory, is shown

In2001Steve Myers has considered the case of a 1-year company and shown that

in this case the weighted average cost of capital, WACC, is higher than inModigliani–Miller case and the capitalization of the company, V, is less than inModigliani–Miller case

So, before 2008 only two results for capital structure of the company wereavailable: Modigliani–Miller for perpetuity company and Myers for a 1-year com-pany (see Fig.2.2) BFO theory hasfilled out whole interval between t ¼ 1 and

© Springer Nature Switzerland AG 2018

P Brusov et al., Modern Corporate Finance, Investments, Taxation and Ratings,

https://doi.org/10.1007/978-3-319-99686-8_2

9

t¼ 1 It gives the possibility to calculate the capitalization V; the weighted averagecost of capital, WACC; equity cost ke; and otherfinancial parameters for companies

of arbitrary age and for companies of arbitrary lifetime BFO theory has led to a lot ofnew meaningful effects in modern capital structure theory, discussed in thismonograph

2.2 The Traditional Approach

The traditional (empirical) approach told that weighted average cost of capital,WACC, and the associated company capitalization, V¼ CF/WACC, depend onthe capital structure, the level of leverage, L Debt cost always turns out to be lowerthan equity cost becausefirst one has lower risk, via the fact, that in the event ofbankruptcy creditor claims are met prior to shareholders claims

As a result, an increase in the proportion of lower-cost debt capital in the overallcapital structure up to the limit which does not cause violation offinancial sustain-ability and growth of risk of bankruptcy leads to lower weighted average cost ofcapital, WACC

The profitability required by investors (the equity cost) is growing; however, itsgrowth has not led to compensation of benefits from use of lower-cost debt capital.Therefore, the traditional approach welcomes the increased leverage L¼ D/S and theassociated increase of company capitalization The traditional (empirical) approachhas existed up to appearance of the first quantitative theory by Modigliani andMiller (1958)

Fig 2.1 Historical development of capital structure theory [here TA traditional (empirical) approach, MM Modigliani –Miller approach, BFO Brusov–Filatova–Orekhova theory]

Fig 2.2 MM theory describes perpetuity limit; Myers paper describes a 1-year company, while BFO theory fills the whole numeric axis (from n ¼ 1 up to perpetuity limit n ¼ 1)

2.3 Modigliani –Miller Theory

2.3.1 Modigliani –Miller Theory Without Taxes

Modigliani and Miller (ММ) in their first paper (Мodigliani and Мiller1958) havecome to the conclusions which were fundamentally different from the conclusions oftraditional approach Under assumptions (see Sect.2.3for details) that there are notaxes, no transaction costs, no bankruptcy costs, perfectfinancial markets exist withsymmetry information, equivalence in borrowing costs for both companies andinvestors, etc., they have showed that choosing of the ratio between the debt andequity capital does not affect company value as well as capital costs (Fig.2.3).Under above assumptions, Modigliani and Miller have analyzed the impact offinancial leverage, supposing the absence of any taxes (on corporate profit as well asindividual one) They have formulated and proven two following statements:Without taxes, the total cost of any company is determined by the value of itsEBIT-Earnings Before Interest and Taxes, discounted with fixed rate k0,corresponding to group of business risk of this company:

equity cost, ke; debt cost, kd;

and weighted average cost

of capital, WACC, in

traditional (empirical)

approach

Index L means financially dependent company (using debt financing), whileindex U means afinancially independent company.

Authors supposed 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.2.1), value of the company does notdepend on the value of debt, and thus according to Modigliani–Miller theorem(Modigliani and Miller 1958), in the absence of taxes, value of the company isindependent of the method of its funding This means as well that weighted averagecost of capital, WАСС, of this company does not depend on its capital structure and

is equal to the capital cost, which this company will have under the funding by equitycapital only

V0¼ VL; CF=k0¼ CF=WACC, and thus WACC ¼ k0:

Note thatfirst Modigliani–Miller theorem is based on suggestion about dence of weighted average cost of capital and debt cost on leverage level

indepen-From thefirst Modigliani–Miller theorem (Мodigliani and Мiller1958), it is easy

to derive an expression for the equity capital cost

ke¼ k0þ kð 0 kdÞL: ð2:4ÞThe formula (Eq.2.4) shows that equity cost of the company increases linearlywith leverage level (Fig.2.3).

The combination of these two Modigliani–Miller statements implies that theincreasing of level of debt in the capital structure of the company does not lead toincreased value offirms, because the benefits gained from the use of more low-costdebt capital markets will be exactly offset by an increase in risk (we are speakingabout thefinancial risk, the risk of bankruptcy) and, therefore, by an increase in cost

of equity capital offirms: investors will increase the required level of profitabilityunder increased risk, by which a higher level of debt in the capital structure isaccompanied

In this way, the Modigliani–Miller theorem argues that in the absence of thetaxes, the capital structure of the company does not affect the value of the companyand its weighted average cost of capital, WACC, and equity cost increases linearlywith the increase offinancial leverage

Explanations, given by Modigliani and Miller under receiving of their sions, are the following (Мodigliani and Мiller 1958) Value of the companydepends on profitability and risk only and does not depend on the capital structure.Based on the principle of preservation of the value, they postulated that the value ofthe company, which is equal to the sum of the equity and debt funds, is not changedwhen the ratio between its parts is changed An important role in justification ofModigliani–Miller statements an existence of an arbitral awards opportunities for thecommitted markets plays Two identical companies, differing only by the leveragelevel, must have the same value If this is not the case, the arbitration aligns businesscost: investors of less cost company can invest capital in a company of more value.Selling of shares of thefirst company and buying of stock of the second companywill continue until the values of both companies are not equalized

conclu-Most of Modigliani and Miller assumptions (Мodigliani and Мiller 1958), ofcourse, are unrealistic Some assumptions can be removed without changing theconclusions of the model However, assuming no costs of bankruptcy and theabsence of taxes (or the presence of corporate taxes only) are crucial, the change

of these assumptions alters conclusions The last two assumptions rule out thepossibility of signaling theory and agency cost theory and, thus, also constitute acritical prerequisite (Fig.2.4)

2.3.2 Modigliani –Miller Theory with Taxes

In the real situation, taxes on profit of companies always exist Since the interestspaid on debt are excluded from the tax base, t leads to the so-called effect of“taxshield”: value of the company that used the borrowed capital (leverage company) ishigher than the value of the company that 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; and kd,the interest on the debt(or debt capital cost) (Мodigliani and Мiller1963) The value of the“tax shield” forperpetuity company for all time of its existence is equal to (we used the formula forthe sum of terms of an infinitely decreasing geometric progression)

where V0is the value offinancially independent company

Thus, we obtain the following result obtained byМodigliani and Мiller (1963):The value of financially dependent company is equal to the value of thecompany of the same risk group used no leverage, increased by the value of taxshield arising fromfinancial leverage, and equal to the product of rate of corpo-rate income tax T and the value of debt D

Let us now get the expression for the equity capital cost of the company under theexistence of corporate taxes

Accounting that V0¼ CF/k0and that the ratio of debt capital wd¼ D/V, one gets

WACC

CC

L DS

=

k0

ke = k0+L (k0-kd)

Fig 2.4 Dependence of

equity cost keand WACC on

leverage level L within

Modigliani –Miller theory

without taxes

V¼ CF=k0þ wdVT: ð2:7ÞBecause the value of leverage company is V¼ CF/WACC, for weighted averagecost of capital, WACC, we get

k0ð1 wdTÞ ¼ k0weþ kdwdð1 TÞ ð2:11Þand from here, for equity cost, we get the following expression:

It should be noted that the formula (Eq 2.12) is different from the formula(Eq.2.4) without tax only by the multiplier (1 T) in term, indicating a premiumfor risk As the multiplier is less than unit, the corporate tax on profits leads to thefact that capital is growing with the increasing offinancial leverage, slower than itwould have been without them

Analysis of formulas (Eqs 2.4, 2.9, and 2.12) leads to following conclusions.When leverage grows:

1 Value of company increases

2 Weighted average cost of capital (WACC) decreases from k0(at L¼ 0) up to

k0(1 T) (at L ¼ 1) (when the company is funded solely by borrowed funds)

3 Equity cost increases linearly from k (at L¼ 0) up to 1 (at L ¼ 1)

Within their theory,Мodigliani and Мiller (1963) had come to the followingconclusions With the growth offinancial leverage (Fig.2.5):

1 The company value increases

2 The weighted average cost of capital decreases from k0(for L¼ 0) up to k0(1 T)(for L¼ 1, when the company is financed entirely with borrowed funds)

3 The cost of equity capital increases linearly from k0(for L¼ 0) up to 1 (for

L¼ 1)

2.3.3 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 opportunitywhich is inadequate to investment risk Therefore, the possibility of a stablesituation of the arbitration, i.e of obtaining the risk-free profit on the difference

in prices for the same asset cannot be kept any long time-reasonable investorsquickly take advantage of it for their own purposes and equalize conditions inthe market This means that in a developed financial market capital, the samerisk should be rewarded by the same rate of return

2 Investment andfinancial market opportunities should be equally accessible to allcategories of investors—whether institutional or individual investors, large orsmall, rapidly growing or stable, or experienced or relatively inexperienced

3 Transaction costs associated with funding are very small In practice, themagnitude of transaction costs is inversely proportional to the amount offinanceinvolved, so this assumption is more consistent with reality than the large sumsinvolved: i.e., in attracting small amounts, the transaction costs can be high,

Kd

Kd(1-t)

Fig 2.5 Dependence of

equity capital cost, debt

cost, and WACC on

leverage in Modigliani –

Miller theory without taxes

(t ¼ 0) and with taxes (t 6¼ 0)

while, as in attracting large loans, as well as during placement of shares at asignificant amount, the transaction costs can be ignored.

4 Investors get money and provide funds to borrowers at risk-free rate In allprobability, this assumption is due to the fact that the lender seeks to protecthimself by using one or other guarantees, pledge of assets, the right to payclaims on third parties, and the treaty provisions restricting the freedom of theborrower to act to the detriment of the creditor Lender’s risk is really small, butits position can be considered risk-free with respect to the position of theborrower and, accordingly, should be rewarded by a risk-free rate of return

5 Companies have only two types of assets: risk-free debt capital and risky equitycapital

6 There is no possibility of bankruptcy, i.e., irrespective of what the level offinancial leverage of the company—borrowers are reached—bankruptcy is notthreatening them Thus, bankruptcy costs are absent

7 There are no corporate taxes and taxes on personal income of investors If thepersonal income tax can indeed be neglected, because the assets of the companyseparated from the assets of shareholders, the corporate income taxes should beconsidered in the development of more realistic theories (which was done byModigliani and Miller in their second paper devoted to the capital structure(Modigliani and Miller1963)

8 Companies are in the same class of risky companies

9 Allfinancial flows are perpetuity

10 Companies have the same information

11 Management of the company maximizes the capitalization of the company

2.3.4 Modi fications of Modigliani–Miller Theory

Taking into Account Market Risk: Hamada Model Robert Hаmаdа (1969)united Capital Asset Pricing Model (CAPM) with Modigliani–Miller model withtaxation As a result, he derived the following formula for calculation of the equitycost offinancially dependent company, including both financial and business risks ofcompany:

ke¼ kFþ kð M kFÞbUþ kð M kFÞbU

D

Sð1 TÞ, ð2:13Þwhere bUis theβ-coefficient of the company of the same group of business risk, thatthe company under consideration, but with zero financial leverage The formula(Eq.2.13) represents the desired profitability of equity capital keas a sum of threecomponents: risk-free profitability kF, compensating to shareholders a temporaryvalue of their money, premium for business risk (kM  kF)bU, and premium forfinancial risk kð M kFÞbUDð1 TÞ

If the company does not have borrowing (D¼ 0), the financial risk factor will beequal to zero (the third term is drawn to zero), and its owners will only receive thepremium for business risk.

To apply the Hamada equation, specialists in practice, in most cases, use bookvalue of equity capital as its approach of market value Nevertheless, the Hamadaformula implies the use of market value of the assets

It should be noted also that the formula (Eq.2.13) can be used to derive otherequation, using which you can analyze the impact offinancial leverage on β-factor ofcompany shares

Equating CAPM formula to equity cost, we get

kFþ kð M kFÞbU¼ kFþ kð M kFÞbUþ kð M kFÞbU

D

Sð1 TÞ ð2:14Þor

In conclusion, here are the formulas for calculating the capital costs within theCAPM model [in parenthesis, there are formulas within the Modigliani–Millertheory (Modigliani and Miller1958,1963,1966)]

The equity cost for company without debt capital

kd¼ kFþkM kF



βd, kð d¼ kF; βd¼ 0Þ: ð2:18ÞThe weighted average cost of capital (WACC)

WACC¼ keweþ kdwdð1 TÞ, ðWACC¼ k0ð1 TwdÞÞ: ð2:19Þ

The Cost of Capital Under Risky Debt Another hypothesis of Modigliani andMiller 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 ofbankruptcy of company (and, accordingly, the ability to nonpayment of loans), thesituation may change Stiglitz (1969) and Rubinstein (1973) have shown that theconclusions concerning the total value of company do not change as compared to thefindings derived by Modigliani and Miller under assumptions about free of risk debt(Modigliani and Miller1958,1963,1966) However, the debt cost is changed Ifpreviously, under assumption about the free of risk debt, it (debt cost) was regarded

as a constant kd¼ kF; now it is not a constant This claim is based on the work byHsia (1981), where based on the models of pricing options, Modigliani–Miller andCAPM, 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

here t is a moment of payment a credit and N(d1), cumulative normal distribution

of probability of random value d1

The Account of Corporate and Individual Taxes (Miller Model) In the secondarticle, Modigliani and Miller (1963) considered taxation of corporate profits, but didnot take into account the presence in the economy of individual taxes of investors.Merton Miller (1997) has introduced the model, demonstrating impact of lever-age on the company value with account of the corporate and individual taxes (Miller

at other things being equal circumstances, also reduce and an overall assessment ofthefinancially independent company value.

We will assess thefinancially dependent company under condition of a doubletaxation of income investors To start, let us divide the annual cash flows offinancially dependent company CFLintoflows sent to its shareholders CFeand theflows belonging to debt owners CFd, with account of both corporation tax on profitsand on the income of individuals:

CFL¼ CFeþ CFd¼ EBIT  Ið Þ 1  Tð CÞ 1  Tð SÞ þ I 1  Tð DÞ, ð2:23Þwhere I is the annual interest payments on debt

The formula (Eq.2.23) can also be rewritten as follows:

CFL¼ CFeþ CFd¼ EBIT 1  Tð CÞ 1  Tð SÞ  I 1  Tð CÞ 1  Tð SÞ

Thefirst term of the equation (Eq.2.24) corresponds to cashflow after taxes forfinancially independent company, shown in equation (Eq 2.22), which shows itspresent value The second and the third terms of the equation, reflecting the financialdependence, corresponds to cash flows related to the debt financing, which, aspreviously, is considered as free of risk Their present values are obtained bydiscounting by risk-free nominal rate on debt kd

By combining the present values of all three terms, we get the company valueunder using the debtfinancing and in the presence of all types of taxation: