Corporate Finance & Decision Making

Corporate finance Theory and practice

In memory of Glynne Jones

For Vanessa and her friend Tommy

Steve Lumby and Chris Jones

Corporate finance Theory & practice seventh edition

Australia • Canada • Mexico • Singapore • Spain • United Kingdom • United States

Corporate Finance:Theory and Practice Copyright © 1981, 1984, 1991, 1994, 1999, 2003 The Lumby Family Partnership The Thomson logo is a registered trademark used herein under licence All rights reserved. No part of this work which is copyright may be reproduced or used in any form or by any means – graphic, electronic, or mechanical, including photocopying, recording, taping or information storage and retrieval systems – without the written permission of the Publisher, except in accordance with the provisions of the Copyright Designs and Patents Act 1988. Whilst the Publisher has taken all reasonable care in the preparation of this book the Publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions from the book or the consequences thereof. Products and services that are referred to in this book may be either trademarks and/or registered trademarks of their respective owners. The Publisher/s and Author/s make no claim to these trademarks. British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library First edition published by Chapman & Hall 1981 Sixth edition published by International Thomson Business Press 1999 Reprinted 2000 and 2001 by Thomson Learning Seventh edition published as Corporate Finance: Theory and Practice 2003 Typeset by Saxon Graphics Ltd, Derby Printed in Croatia by ZRINSKI d.d. ISBN 1–86152–926–0 Thomson High Holborn House 50/51 Bedford Row London WC1R 4LR http://www.thomsonlearning.co.uk

Brief contents Preface Book plan

PART 1

PART 2

PART 3

PART 4

xvii xx

INTRODUCTION

1

1

Financial decision making

3

2

Decision objectives

14

INVESTMENT DECISIONS

31

3

Traditional methods of investment appraisal

33

4

Investment–consumption decision model

50

5

The discounted cash flow approach

67

6

Net present value and internal rate of return

94

7

Project cash flows

125

8

Capital rationing

148

RISK ANALYSIS

177

9

179

Simple risk techniques

10 Risk and return

204

11 Portfolio theory

226

12 The capital asset pricing model

255

13 Option valuation

291

14 Interest rate risk

325

FINANCING DECISIONS

353

15 Financial markets

355

16 The cost of capital

379

17 Weighted average cost of capital

420

18 Capital structure in a simple world

442

vi

PART 5

PART 6

BRIEF CONTENTS

19 Capital structure in a complex world

462

20 Capital structure in practice

488

21 Investment and financing interactions

506

22 The dividend decision

534

MERGERS AND ACQUISITIONS

551

23 Acquisition decisions

553

24 Company valuation

577

INTERNATIONAL ISSUES

593

25 Foreign exchange

595

26 Foreign exchange hedging

615

27 Foreign direct investment

642

Tables

667

Answers to quickie questions

673

Answers to problems

699

Index

783

Detailed contents xvii

Preface

xx

Book plan PART 1

PART 2

INTRODUCTION

1

Chapter 1

3

Financial decision making

The nature of financial decisions The decision process Financial decision making Technology and financial decision making Summary Notes Quickie questions

3 4 6 11 12 12 13

Chapter 2

14

Decision objectives

Wealth maximization and the company Ownership and control Regulation of the relationship between directors and shareholders Incentive scheme criteria When incentive schemes and regulation are ineffective Conclusion Summary Notes Further reading Quickie questions Problems

14 15 16 23 26 27 28 29 29 30 30

INVESTMENT DECISIONS

31

Chapter 3

33

Traditional methods of investment appraisal

Introduction The payback method Return on capital employed Conclusions Summary Notes Further reading Quickie questions Problems

33 34 41 44 44 45 47 47 48

viii

DETAILED CONTENTS

Chapter 4

Investment–consumption decision model

50

Introduction to the model The time value of money The basic graphical analysis Introduction of capital markets The separation theorem The conclusions of the basic model Payback and ROCE Summary Notes Further reading Quickie questions Problem

50 51 53 55 57 61 62 62 63 65 65 66

Chapter 5

67

The discounted cash flow approach

Net present value Alternative interpretations of NPV Internal rate of return Discounted payback Truncated NPV Summary Appendix: compounding and discounting Notes Further reading Quickie questions Problems

67 73 78 83 84 85 85 89 90 90 91

Chapter 6

94

Net present value and internal rate of return

NPV and project interdependence IRR rule and interdependent projects Extending the time horizon Multiple IRRs Other problems with the IRR rule The modified IRR NPV versus IRR: Conclusion The replacement cycle problem Summary Notes Further reading Quickie questions Problems

94 99 108 109 113 114 115 116 119 120 121 121 122

Chapter 7

125

Project cash flows

Investment appraisal and inflation Inflation and the IRR rule Investment appraisal and taxation

125 130 131

ix

DETAILED CONTENTS

PART 3

Financing cash flows Investment appraisal and the relevant cash flow Summary Appendix: the UK corporate tax system Notes Further reading Quickie questions Problems

132 136 141 141 142 143 143 144

Chapter 8

148

Capital rationing

Introduction Hard and soft capital rationing Single-period capital rationing Multi-period capital rationing Summary Appendix: linear programming Notes Further reading Quickie questions Problems

148 150 152 158 168 169 171 171 172 173

RISK ANALYSIS

177

Chapter 9

179

Simple risk techniques

Risk and return Expected net present value The abandonment decision Sensitivity analysis The risk-adjusted discount rate Summary Notes Further reading Quickie questions Problems

179 180 186 191 194 196 197 197 198 199

Chapter 10 Risk and return

204

Introduction to uncertainty The expected utility model Risk, return and the investment decision Summary Notes Further reading Quickie questions Problem

204 206 213 222 223 223 224 224

x

DETAILED CONTENTS

Chapter 11 Portfolio theory

226

Two-asset portfolios Multi-asset portfolios Introduction of a risk-free investment The capital market line Diversification within companies Summary Notes Further reading Quickie questions Problems

226 234 237 243 248 249 251 251 252 252

Chapter 12 The capital asset pricing model

255

The security market line The CAPM expression The beta value The validity of the CAPM Arbitrage pricing theory Betas and project investment appraisal Summary Appendix: The security market line Notes Further reading Quickie questions Problems

255 259 262 271 276 278 281 282 285 285 286 287

Chapter 13 Option valuation

291

Introduction The basic characteristics of options Option terminology The valuation of options The Black and Scholes model The building blocks of investment Put–call parity theorem Using share options The option ‘Greeks’ The binomial model Summary Appendix: the area under the normal curve Notes Further reading Quickie questions Problems

291 291 293 293 298 302 307 310 314 318 320 321 323 323 323 323

DETAILED CONTENTS

PART 4

xi

Chapter 14 Interest rate risk

325

Introduction The money markets Forward forward loans Forward rate agreements Interest rate guarantees Option contract markets Interest rate futures Caps, collars and floors Interest rate swaps Summary Notes Further reading Quickie questions Problems

325 325 327 328 331 333 334 343 344 348 348 349 349 350

FINANCING DECISIONS

353

Chapter 15 Financial markets

355

Introduction Market efficiency Market efficiency and share dealing The empirical evidence of EMH The term structure of interest rates Pure expectations hypothesis Summary Notes Further reading Quickie questions Problems

355 355 358 360 365 369 375 376 377 378 378

Chapter 16 The cost of capital

379

The financing decision The cost of equity capital Expected return, dividends and market price Applying the dividend valuation model CAPM and the cost of equity capital CAPM versus the DVM The cost of debt capital Cost of preference shares Convertible debt Summary Notes Further reading Quickie questions Problems

379 380 383 385 393 395 397 409 410 414 414 416 416 417

xii

DETAILED CONTENTS

Chapter 17 Weighted average cost of capital

420

The project discount rate The calculation of K0 The WACC and project risk Summary Appendix: Differing corporate and private costs of debt Notes Further reading Quickie questions Problems

420 423 427 430 431 437 437 438 438

Chapter 18

442

Capital structure in a simple world

Introduction An optimal capital structure Business and financial risk The arbitrage proof Summary Notes Further reading Quickie questions Problems

442 442 446 450 457 458 458 459 459

Chapter 19 Capital structure in a complex world

462

Taxation and capital structure Using the M and M equations M and M in the real world Further views on capital structure Conclusion Summary Notes Further reading Quickie questions Problems

462 467 472 477 482 482 483 484 484 485

Chapter 20 Capital structure in practice

488

The pecking order theory Real-world considerations Earnings per share and gearing Degree of operating gearing Summary Notes Further reading Quickie questions Problems

488 491 493 496 500 501 501 501 502

DETAILED CONTENTS

PART 5

xiii

Chapter 21 Investment and financing interactions

506

Company valuation and investment appraisal The dividend and interest valuation model Adjusted present value model The M and M valuation model The traditional valuation model Approaches to investment appraisal Asset betas and gearing Risk-adjusted WACC Lease or purchase decision Summary Notes Further reading Quickie questions Problems

506 507 507 508 508 509 514 521 524 529 529 529 530 531

Chapter 22 The dividend decision

534

Dividend policy in perfect capital markets Traditional view of the dividend decision Dividend policy in an imperfect market The empirical evidence Conclusion Summary Notes Further reading Quickie questions Problems

534 538 542 544 545 546 547 547 548 548

MERGERS AND ACQUISITIONS

551

Chapter 23 Acquisition decisions

553

Introduction Synergy Valuing synergy Acquisition premiums Organic growth versus growth via acquisition The coinsurance effect Bootstrapping EPS Diversification Takeover defence Financing acquisitions Summary Notes Further reading Quickie questions Problems

553 554 557 558 560 562 564 567 568 571 572 574 574 574 575

xiv

PART 6

DETAILED CONTENTS

Chapter 24 Company valuation

577

Introduction Asset basis Earnings basis Dividend basis Free cash flow basis Intellectual capital Summary Further reading Quickie questions Problems

577 577 579 582 582 584 586 587 587 588

INTERNATIONAL ISSUES

593

Chapter 25 Foreign exchange

595

Introduction Exchange rates Foreign exchange markets Exchange rate systems Determinants of FX rates Summary Notes Further reading Quickie questions Problems

595 595 600 605 608 612 613 613 613 614

Chapter 26 Foreign exchange hedging

615

Definitions Transaction risk hedging FX futures contracts Forward versus futures FX options contracts Setting up an option hedge Early exercise Contingent exposure to FX risk Traded options versus OTC options Summary Notes Further reading Quickie questions Problems

615 616 621 626 627 629 634 635 635 636 637 637 637 639

Chapter 27 Foreign direct investment

642

Introduction Project cash flows Project discount rate

642 644 648

DETAILED CONTENTS

xv

Translation risk Economic risk Country/political risk Management charges and transfer pricing Summary Notes Further reading Quickie questions Problems

653 656 659 660 661 662 662 663 663

Tables

667

Answers to quickie questions

673

Answers to problems

699

Index

783

xvii

Preface

There is a popular feeling that ‘theory’ is opposed to ‘practice’ and the merits lie with ‘practice’. This is a false conclusion, based on a false supposition. If practice has long been successful and does not conform to theory, the theory is bad and in need of revision... The distinction should not be between theory and practice; it should be between good theory and bad theory, between good practice and bad practice... Practice is brick; theory is mortar. Both are essential and both must be good if we are to erect a worthy structure. d. paarlberg, great myths of economics

The description in plain language will be a criterion of the degree of understanding that has been reached. w. heisenberg, physics and philosophy

This book takes these two quotations as its starting point. Its subject matter covers some of the major financial decisions that face companies: investment, financing, the dividend decision, acquisitions and the management of risk. These are areas of vital importance to companies because they represent the main ways by which firms can enhance the worth of the owners. This importance is reflected in the fact that corporate finance is a standard element of most degree courses that are concerned with industrial or commercial decision-making, as well as being a prominent element in professional accountancy examinations. It is with all these groups of people in mind that this book has been written. However, we hope that practising financial decision-makers will also find its contents of interest, in that it may help to provoke thoughtful reflection on how financial decisions are actually made. The book’s origins lie in the courses we have taught at various universities at both undergraduate and postgraduate level and in the courses taught to students studying for professional accountancy qualifications. In reality, this is the seventh edition of Investment Appraisal and Financial Decisions, but we have taken the opportunity of a new edition to change the title to Corporate Finance, in order to reflect better its scope and contents. In many ways this is not our book, but our students’ book. Their searching questions have often prompted us to think through the subject matter in greater

xviii

PREFACE

depth and to seek out alternative ways of providing clear and full explanations of the subject matter. In this new edition we have made a number of substantial additions, as well as several more minor amendments, revisions and rearrangements. The main extension has been to include the area of mergers and acquisitions, with a new chapter on the valuation of companies for purposes of acquisition and a chapter that covers a number of aspects of acquisition activity. Mergers and acquisitions are amongst the most important events that occur in the life of a company and this is an area that takes a central role in the preoccupations of corporate treasurers and other finance professionals. In addition to these new chapters, the chapter on option valuation theory has been rewritten to improve the clarity with which this complex subject matter is developed. We have also extended the chapter on the capital structure decision in the real world to include a discussion of the so-called ‘pecking order’ theory and have revised and updated several other areas within the book, including the ever-developing issue of corporate governance and the potential conflicts of interest between shareholders and managers. Finally, the layout of the book has been entirely redesigned to help enhance its ease of use. It is all too easy for authors to lose sight of just how difficult some topics can be to the new reader. Familiarity, if not exactly breeding contempt, can sometimes lead to an over-concise exposition of the subject being discussed. Hopefully we have managed to avoid this pitfall, and we are confident that the book’s new design further enhances the clarity of presentation of the subject matter. What has been retained from previous editions are the end-of-chapter summaries, together with suggestions on selected further reading, sets of ‘Quickie questions’ (and answers) and full-length ‘exam-style’ questions. The summaries are designed to give a general overview of the topics covered in each chapter and to give just a quick snapshot picture of the main points. The suggested further reading has been compiled with particular emphasis on providing articles that are, in the main, accessible to those readers who do not posses a higher degree in mathematics! The Quickie questions are designed to test both recall and understanding and to give the reader essential feedback – the Quickie answers are tucked away at the back of the book, in order to reduce the temptation to cheat! Finally, the exam-style questions - all 60 of them have been selected to try and cover the major elements of each chapter’s subject matter. These questions are either of our own design, or have been culled from the examination papers of various professional accountancy bodies. Collectively these examiners have set some splendid questions in the past, and we are grateful to the accountancy bodies concerned for their kind permission to use them. One other change to this new edition - and this is in response to reader demands - is that many of the answers to these questions are now included at the end of the book! The book’s website: www.thomsonlearning.co.uk/accountingandfinance/ lumbyandjones/, contains an extensive multiple-choice question bank to provide further opportunities for testing and feedback. Although solutions to most of the exam-style questions are given at the end of the book, the solutions to certain questions have been placed in a ‘lecturers only’ area of the website.

PREFACE

xix As before, we should make it clear that this is not a ‘how-to-do-it’ book of corporate financial management. Such a book is not really a possibility in the complex, practical and ever-changing area of corporate finance. Instead, it is an attempt at a fairly detailed, reasoned discussion of the normative theory of corporate finance. Examples that have used real-world data are there for the purposes of exposition, rather than to encourage unthinking application of the theory to practical decision-making. It is not our aim to put forward theoretical solutions to practical problems, but to promote thought and reflection on how decisions are actually made and, perhaps, how they can be improved. As far as possible, the presentation has been argued in descriptive and graphical terms rather than using a strict mathematical analysis. The reasons for this are two-fold. First, a mathematical treatment often excludes a great many potential enquirers and reduces the subject matter to a degree of terseness that makes unrealistic demands upon the concentration of the reader. Second, a mathematical treatment, although often rather elegant, can sometimes fail to make clear the full significance of important conclusions. However, it has been impossible to exclude mathematics completely - indeed it would have been counterproductive to do so in some areas - but its complexity has been kept to an absolute minimum. We have resisted the temptation to derive formulas and relationships just for the sake of it and have only done so where the mathematical derivation leads to a greater understanding for the reader. All that remains is to thank the people at Thomson Learning, in particular Pat Bond as editor, Fiona Freel as production manager and Katie Thorn, who is concerned with the marketing, for all their help, understanding and general prodding to get the book written and onto the bookshelves. Most of all our thanks go to our students who make writing and teaching so enjoyable!

Book plan Part 1 1 Financial decision making

Part 2 3 Traditional methods of investment appraisal

Part 3 9 Simple risk technique

Part 4 15 Financial markets

Part 5 23 Acquisition decisions

Part 6 25 Foreign exchange

Introduction 2 Decision objectives

Investment decisions 4 Investment– consumption decision model

5 The discounted cash flow approach

6 Net present value and internal rate of return

7 Project cash flows

8 Capital rationing

12 The capital asset pricing model

13 Option valuation

14 Interest rate risk

18 Capital structure in a simple world

19 Capital stucture in a complex world

20 Capital structure in practice

Risk analysis 10 Risk and return

11 Portfolio theory

Financing decisions 16 The cost of capital

17 Weighted average cost of capital

Mergers and acquisitions 24 Company valuation

International issues 26 Foreign exchange hedging

27 Foreign direct investment

21 Investment and financing interactions

22 The dividend decision

Part 1 Introduction

3

1

Financial decision making

The nature of financial decisions An overview This book covers a particular area of managerial economics: the theory of financial decision making by business corporations. It is concerned with how management within companies1 should make2 financial decisions,3 and so it can be said to adopt a normative approach because it sets out to establish a standard, or norm. But such a theory cannot hope to succeed in its task if it is developed in isolation from what actually does happen in practice, and so we shall also examine how financial decisions are made in order to guide and enrich the development of our normative approach.

The value base Financial decisions are no different in their fundamental aspects from other decisions of a non-financial nature, be they in industry or commerce (such as marketing decisions) or elsewhere (such as decisions to transfer footballers, or even international diplomacy decisions). In essence, all decisions are based on the concept of the comparison of alternatives, and it is in this sense that the theory of financial decisions really has its roots in valuation theory, because all the alternatives in any decision-making situation have to be valued in order to be compared. Therefore, although we can say that all types of decisions involve the same fundamental process, each is given its own unique characteristics by the valuation base that it employs. The financial decision theory developed in this book is founded on the valuation bases that come from capitalism4 and the idea of the free market economy. It is important that this is specified from the outset, because a different valuation base would be likely to produce a different overall theory of financial decisions. However, many parts of our financial theory will be applicable to other types of economic organization, and you may wish to consider and reflect upon the implications of our theory for more social value bases, such as those that might be appropriate to the public sector and, in particular, state-owned public enterprises. This is especially interesting because the past 20 years have seen an

4

FINANCIAL DECISION MAKING

apparent change in value bases in those particular areas and a transfer of many public sector enterprises into the private sector.

The ‘model’ approach and the structure of the text We have structured this text in six parts: 1. 2. 3. 4. 5.

Introduction to the context of financial decisions – Chapters 1 and 2. The capital investment decision – Chapters 3 to 8. The impact of uncertainty on financial decisions – Chapters 9 to 14. Financing decisions – Chapters 15 to 22. Decisions by one company to purchase another company – Chapters 23 and 24. 6. Financial decisions in an international context – Chapters 25 to 27. In the course of our development of a normative approach to financial decisions, a considerable number of abstractions from and simplifications of the ‘real world’ will be made, in order to distil the difficulties and focus attention on areas of major importance. Adopting this type of ‘modelling’ approach is normal in the study of economics and related areas. However it brings with it a danger that it is seen as fully describing a ‘real’ world and providing simple solutions to real-world problems. It is important to remember that we are developing a normative theory and are therefore attempting to give advice on how financial decisions should be taken. In general we will work with simplified models and if the theory were to be followed in practice, without recognizing the full range of possible complicating factors, the quality of financial decisions made in business might deteriorate rather than improve. The difficulties caused by taxation, inflation and capital scarcity will all be taken into account, as will the concept of risk and the fact that the future is uncertain.5 All these real-world complexities will be added layer by layer to the simplified model with which we start. Even though that model might be a poor reflection of the real world, it provides a logically sound framework upon which to build.

A warning As a final point, the reader should be constantly aware that the theory of financial decisions presented here is neither in a state of general detailed agreement, nor does it yet provide complete solutions to many of the important problems of financial decision making. In order to reflect this state of affairs, we shall examine the causes and evidence of these controversies and point out the irrationalities, ambiguities and inconsistencies that necessarily accompany the development of any theory that aspires to real-world application.

The decision process In order to examine the decision process and to answer the question, ‘How do we make a decision?’, we have first to discuss the circumstances in which a

THE DECISION PROCESS

5

decision needs to be made. We can specify two necessary conditions for a decision situation: the existence of alternatives and the existence of an objective or goal.

The first necessary condition The existence of alternatives is necessary because, if there are no alternatives from which to choose, then there is no need for a decision. This condition can be specified further in that not only must alternatives exist, but they must be seen to exist by the potential decision maker. There are two points of interest here. First, notice that we talk of a decision situation and of a potential decision maker. This is because the mere existence of perceived alternatives does not necessarily mean that a decision will be made. For instance, the potential decision maker may well procrastinate, and therefore the passage of time takes him (or her) out of a decision situation and into a situation where there is only one possible course of action and no alternatives are available. (Death is the ultimate example of the passage of time removing a decision situation from an individual.) The second point of interest is that we are not specifying that all possible alternatives are perceived; if they were, we could call this an optimal decision situation. We are, rather, examining how decisions are made, given that a particular decision situation exists. Whether the decision is truly optimal or non-optimal is of no concern at present.

The second necessary condition The second necessary condition for a decision situation arises from the fact that the actual process of ‘making a decision’ is liable to cause the decision maker to expend both time and effort. Rationally decision makers will be unwilling to do so unless they expect that some of the perceived alternatives will be preferred to others in relation to attaining the desired objective. Thus the existence of an objective is the second necessary condition: without it, there will be no purpose in making a decision.6

Valuation of alternatives Together, these two necessary conditions provide the rationale for making decisions: if the decision maker does not perceive alternatives, or sees no reason to choose between the alternatives if they are perceived, then no decision will be made (except one of a totally arbitrary kind, as in note six). But once these conditions do exist, a decision cannot actually be made until values are placed upon the alternatives. In fact, we can assert that the only reason why any alternative course of action is ever evaluated is in order to make a decision about it; therefore, the valuation method used must be related to the objective involved in making the decision and the way in which that objective is expressed. For example, if our objective were to drive from A to B in the shortest possible time, then we should value the alternative routes from A to B by a

6

FINANCIAL DECISION MAKING

common value criterion that was related to our objective of time, and choose whichever route took the shortest time. Suppose there were three alternative routes and one we valued by time, one by distance and one by scenic beauty. We obviously could not make a decision because the alternatives have different measures or yardsticks of value and so cannot be compared. Alternatively, if all three routes were measured in terms of scenic beauty, we should again be unable to make a decision, even though we could compare the routes, because the basis of the comparison is not the one that gives the rationale for the deci7 sion: the value base of the objective, which in this example is ‘time’. Therefore, any decision-making process consists of these three components: a series of perceived alternatives, an expectation that these alternatives are not all equally desirable in terms of attaining an objective held by the decision maker, and a common value base related to the decision objective. So it is with all financial decisions made in business.

Financial decision making This book focuses attention on only two of the three components that we have identified in the decision process and examines how they relate to the making of financial decisions: the expectation that the perceived alternatives are not all equally desirable in terms of attaining a specific objective, and the common value base that is related to this objective and is used to compare the alternatives. The remaining component of the decision process is the series of perceived alternatives. We shall not be examining it in the main body of the text as it is primarily a condition for the decision situation, and we are concentrating on the actual decision making, assuming that the decision situation already exists. However, this omission does not mean that the ‘search process’ (as it is called) for alternatives is unimportant. It is in fact extremely important. If this search process is not efficient in seeking out alternatives, then there is a grave danger that the decision itself will not be optimal because the ‘most preferred’ alternative may go unperceived.

The decision objective Turning to the two decision process components that we shall examine in detail, we immediately become involved in value judgements, because the objective we use for financial decision making, and the consequent value base, will determine the decision reached as to which alternative is selected. Therefore, what objective are we going to use and what valuation base are we going to set up for our theory of financial decisions? We stated earlier that the fundamental value judgement upon which our approach is based is capitalism. The approach is thus most appropriate in largely unregulated, competitive economies. In such economies, it is reasonable to assume that companies exist for one overriding purpose: in order to benefit their owners.8 While companies provide income for their employees and the wider local community, supply the needs of a particular market, and

FINANCIAL DECISION MAKING

7

provide other benefits such as technological advance, the fact remains that the fundamental rationale for their existence must be to bring benefit to their owners. This rationale for existence undoubtedly holds true for the great majority of privately owned9 companies (and also, to some extent, for state-owned indus10 tries although their rationale for existence can be more complex ). Therefore, management’s objective in making financial decisions should be to further the very reason for the company’s existence, of benefiting the owners, i.e. the shareholders. We shall see that there might be other managerial objectives but, in essence, we will treat those as deviating from what they should be (this is consistent with the idea of adopting a normative approach). So if the decision objective is to benefit the owners, what is the value base to be used for the comparison of alternatives? To answer this question, we have to examine the decision objective more closely. It is obvious from what we have already said that not only should company managements make financial decisions so as to benefit the shareholders but they should also strive to maximize that benefit, otherwise shareholders will be interested in replacing them with a set of decision makers who will do this. Therefore, what is meant by the term ‘maximizing owners’ or shareholders’ benefit’?

Maximizing shareholder wealth We are going to assume that maximizing benefit means maximizing wealth. Although there is nothing surprising about this, we have to be careful here because we are going to assume that maximizing the increase in the owners’ wealth is the only way in which management decisions can benefit owners. This is a slight simplification of the real world, because it is quite possible for shareholders to gain benefit from a company other than by increases in wealth. For example, shareholders of a company such as Body Shop may gain benefit from ownership in terms of pride in the fact that the company has a proactive stance towards protecting the environment, and this is also reflected in various investment vehicles such as ethical unit trusts. However, this is a comparatively minor point and we shall proceed on the relatively sound assumption that increase in wealth is the main, if not the sole source of benefit from company ownership. What about firms selling military arms to countries that have repugnant policies, or firms causing pollution to land, air or water resources? Do these types of activity enter into consideration of our decision objective? On the basis of our underlying assumption about the nature of the economy, our answer must be that they should not, because if these activities were thought to be truly undesirable, governments would legislate to constrain companies’ decision-choice alternatives so as to exclude them (as in many cases they do). Company decision makers should only need to perceive and analyse the decision alternatives in terms of maximizing the owners’ wealth. From this viewpoint we can treat financial decisions as not being anything to do with morality. Morality, the law and other things might act as constraints on what a company does but they are entirely different issues and are generally assessed using different criteria.

8

FINANCIAL DECISION MAKING

In market economies, we can develop a theory of financial decisions for privately owned firms in this way because of the workings of the market system for company capital. Ordinary share capital, the substance of ownership, is normally provided through supply and demand markets (e.g. stock exchanges), which means that potential shareholders can buy shares in companies that they expect will provide them with the greatest possible increase in wealth (i.e. shareholders have to make financial decisions in much the same way as management, choosing between alternative ownership opportunities), and existing shareholders can sell their shares if they see other companies providing greater increases to their owners’ wealth than they are receiving. (An important concept here, and one we have yet to deal with, is that the future is uncertain and so any decision amongst alternatives usually has a risk attached to it: the risk that the alternative chosen may not turn out as expected. Some alternatives are riskier than others and so shareholders will really want to own companies that they expect will give them the greatest possible increase in wealth, for a given level of risk. This concept will be considered much more fully later.) Therefore, if a company were to make its decisions on bases other than that of maximizing shareholder wealth, the whole rationale for the company’s existence – so far as shareholders are concerned – would be in doubt and they would be likely to take their investment funds elsewhere. In the extreme case, company law provides the opportunity for shareholders to replace a company’s decision makers if enough of them believe that decisions are not being taken in their best interests.

Defining wealth However, we still cannot determine the value base for financial decision making until we have defined ‘wealth’, because the purpose of the value base is to act as a common denominator with which to make the alternative courses of action directly comparable and to see which one leads furthest towards the decision objective. As the objective of financial decisions is assumed to be to ‘maximize the increase in owners’ wealth’, let us define ‘wealth’ and so determine the value base. Wealth can be defined as the capacity to consume, or, to put it in more straightforward terms, money or cash.11 Thus the objective of management becomes the maximization of shareholders’ purchasing power, which can be achieved by maximizing the amount of cash paid out to shareholders in the form of dividends. But which dividends should a company’s management try to maximize: this year’s, next year’s or what? The point here is that it would be a relatively easy task for a company to maximize a single year’s dividend, simply by selling up all the assets and paying a final liquidation dividend! (We are ignoring the niceties of company law here, but the point still remains.) Obviously this is not what is meant by our decision objective of maximizing dividends, and the trouble arises through the omission of the time dimension. When fully defined, including the time dimension, the objective of a company’s financial decision makers becomes the maximizing of the flow of dividends to shareholders over or through time.

FINANCIAL DECISION MAKING

9

The role of accounting profit There are two points of fundamental importance that arise from the development of this decision objective. First, the word ‘profit’ has not been mentioned and the emphasis has been laid on wealth defined as cash. Secondly, the introduction of time means that decisions must be analysed not only in terms of immediate cash gains and losses, but also in terms of future gains and losses. These two points are interlinked. Profit, when used in a business sense, is a concept developed by financial accountants in order to assist them with their auditing and reporting functions, performed on behalf of shareholders. Accounting has developed over hundreds of years from a base called ‘stewardship’. It was really designed to provide evidence that people holding responsibility for other people’s assets could account for them (i.e. demonstrate where the resources went). In many ways this still lies at the heart of financial accounting. Although financial reports are produced each year and contain the figure ‘profit’ it should not be interpreted as being the same thing as the increase in the value of the company during the year. Annual reports are produced using a number of conventions and rules, the most important of which is that the figures are expressed in terms of historic cost (with one or two possible exceptions). There is also a certain amount of judgement exercised in the production of the statement and it has been said that profit is the invention rather than the discovery of the accountant. The Accounting Standards Board (the UK body that defines many of the rules used by accountants) has expressed the view that accounting should not be seen as being concerned with value or worth. As we will see, wealth, worth and value are all concepts related to the future (and cash flows in the future) but profit is related to the past. Financial decisions are basically economic or resource allocation decisions. Management have to decide whether they should allocate the firm’s scarce resources (land, labour, machinery, etc.) to a particular project. The economic ‘unit of account’ is cash, not accounting profit, because it is cash which gives power to command resources (i.e. resources are purchased with cash, not profit). Thus to use the accounting profit concept in financial decision making would be to use an entirely inappropriate concept – a concept specially developed for reporting the outcome of decisions and not developed for helping to take the actual decision itself. However, we cannot discard the accounting profit concept completely. To do so would be rather like a sports team whose policy is that they do not mind whether they win or lose, so long as in playing they give maximum entertainment to their supporters. This is fine, and it is probably the correct attitude; but often it is on the winning or losing that the success of the team is ultimately judged and therefore that part of the game cannot be ignored. So it is with accounting profit. The company’s financial decision makers should have as their major concern the maximization of the flow of cash through time to the shareholders, but they should always do so with an eye to reported profit. Profitability, as expressed in annual published accounts, forms a major criterion by which shareholders and prospective shareholders judge a company’s success and, as we shall see later, it is important that people do form correct judgements about a company’s performance.

10

FINANCIAL DECISION MAKING

A further reason why the effects of financial decisions on reported profits cannot be completely ignored is provided by the fact that the level of retained profit, in company law, can form a very substantial maximum barrier to an annual dividend payment. Thus a company that wishes to maximize its dividend flow must ensure that its dividend payout intentions are legally within the confines of company law. Therefore, with the exception of these two provisos, we can say that the financial decision theory developed here is built on an analytical framework that is largely devoid of the accounting profit concept, although it would be correct to assume that, in the longer run, good company cash flows will result in good reported profits.

The time dimension Turning to the second point of importance in our decision objective, the introduction of the time dimension, we have already noted that the arbitrary time segmentation of a continuous flow process has been the cause of major problems for the accounting profit concept, but to see the true significance of the introduction of this factor we have to return to our discussion on value. An asset (such as a machine or a share in a company) is valued on the basis of the gains, or losses, that the owner receives. Furthermore, these gains and losses do not refer to just a single time period, but to the whole period of future time for which the asset will exist. (This concept is sometimes referred to as the asset’s earning power.) Let us consider an asset of company ownership: an ordinary share. Ordinary shares are traded (i.e. bought and sold) in supply and demand markets and so a share’s market valuation represents an equilibrium value, a value at which demand for the share by people who wish to buy it equates with the supply of the share by people who wish to sell it. But what process actually gives a share its equilibrium price, what makes prospective purchasers wish to buy it at that price and what makes prospective sellers willing to sell it at that price? Let us examine the prospective purchaser’s reasons. Suppose an ordinary share of XYZ plc has a stock market price of 150p.12 Prospective owners of that share would only be willing to buy it if they thought it was worth 150p. In other words, they would expect that the gains to be received from ownership would have a value of at least 150p. These gains of ownership consist of two elements: the stream of dividends received for as long as the share is owned, and the selling price received when the share is sold (and so ownership relinquished) at some future point in time. However, it is important to note that this future selling price of the XYZ share is itself based on the value the succeeding owner in turn puts on the benefits expected to be received from ownership – the dividend flow received and the selling price that will be received upon selling the share at some future point in time. So the process goes on ad infinitum. Therefore, although there are two benefits of ownership, the dividends received and the future selling price, this latter benefit is itself determined by the flow of dividends expected to be generated by the share subsequent to its sale. (We can treat the cash flow received if the company were to be wound up or liquidated as a final dividend.)

TECHNOLOGY AND FINANCIAL DECISION MAKING

11

Given this argument, our theory will assume that shares derive their (equilibrium) stock market price on the basis of the sum of the dividend flow that they will produce through time. (As the future is uncertain, it is more correct to talk of valuation based on the expected dividend flow, but we shall return to this later.) Thus the greater the future dividend flow, the more highly are the shares valued. Therefore if our financial decision makers are taking decisions so as to maximize dividend flow through time, then via the direct link between dividend flow and a share’s market price, this action will result in the maximization of the market value of the company’s shares. It is this that we shall take as being the operational objective of financial management decision making.13

The objective hierarchy So let us summarize our assumed hierarchy of decision objectives: 1. Decisions are taken by companies so as to maximize owners’ wealth. 2. Owners’ wealth can be maximized through maximizing owners’ purchasing power. 3. Purchasing power can be maximized through maximizing the amount of cash the company pays out to shareholders in the form of dividends. 4. With the introduction of the time dimension the objective becomes the maximizing of the value of the dividend flow through time to the shareholders. 5. The maximization of the value of the dividend flow through time maximizes the stock market’s valuation of the company’s ordinary share capital. However, it is important to realize that although it is this ‘fifth level’ of objective we shall use in developing the theory of financial decision making, it is really only a surrogate objective for the fundamental, underlying objective of maximizing shareholders’ wealth.

A fundamental assumption As a final point, let us state the assumptions about the shareholder that have been implied in the analysis. It was earlier argued that the maximization of shareholders’ wealth had to be the fundamental decision objective, because of the nature of the capital markets. However, the validity of this assertion depends entirely upon the assumption that shareholders perceive wealth in the way we have postulated and that in this perception they are rational. In essence this means that we have assumed that shareholders see wealth as the receipt of cash flows through time and that they will always prefer a greater to a lesser cash flow. These appear reasonably safe assumptions, but we shall consider situations where they may not hold when we look later at dividend policies.

Technology and financial decision making The past 20 years have seen what amounts to a technological revolution. This has been described as an information revolution on a par with the industrial

12

FINANCIAL DECISION MAKING

revolution of the 18th and 19th centuries. It is now most unlikely that decision makers will not have access to computer facilities and the power of the typical desktop machine is now such that sophisticated software can be used to aid their decisions. In most cases the type of software used will be based on spreadsheets such as Microsoft Excel and you are encouraged to use the software available to you when answering the problems set throughout the text. However, it is important that you understand the underlying principles so it is not advisable to rely solely on the financial functions embedded in the software. It is also worth mentioning that some of the functions can be somewhat problematical as we will see.

Summary

Notes

• The decision process consists of three elements: 1. a series of perceived alternatives; 2. an expectation that these alternatives are not all equally desirable in terms of attaining an objective held by the decision maker; 3. a common value base, related to the objective, by which the alternatives may be compared. • As far as financial management is concerned, it is assumed that the objective of financial management decision making is the maximization of shareholder wealth. This is normally translated to mean maximizing the current worth of the company’s shares. • Given that shareholder wealth is seen in terms of an ability to consume goods and services and that it is cash that provides consumption power, so share value can be maximized by maximizing the sum of the expected stream of dividends through time generated by the share. • Accounting profit is essentially an inappropriate concept within the context of financial management decision making because it is a reporting device, not a decision-making device. Finance decisions are economic or resource allocation decisions and the economic unit of account is cash; hence decisions are evaluated in terms of their cash flow impact. However, the reported profit impact of financial decisions remains an important consideration in terms of the correct communication of management’s actions to shareholders and others.

1. Be these large stock exchange quoted companies such as BP or Unilever, or small unquoted companies such as a local printing company or car rental company. 2. The terms decision ‘making’ and decision ‘taking’ can be used synonymously. However, the term decision ‘making’ will be used in this book because of its more positive emphasis on deliberate creative action. 3. We will carefully define just what financial decisions are, but for now this covers such things as a decision to invest in a new machine, to borrow money from the bank or a decision to ‘pass’ (i.e. not pay) an annual dividend that shareholders may have been expecting. 4. There are many variants of capitalism (which in itself is just one type of economic system; for example, alternatives could include socialist, feudal and primitive communal economies) but its two general features are the private ownership of property and the

QUICKIE QUESTIONS

13

allocation of the economy’s resources (land, labour and machinery) through a supply and demand price mechanism. 5. Indeed, we shall also occasionally allude to the psychological processes behind firms’ financial decisions where conflicts of interest arise. 6. In a way, in specifying this second necessary condition, we are ignoring the situation where a decision has to be made, even though this second condition does not exist. For instance, if you are out for a walk with no particular destination in mind and you come to a crossroads, a decision has to be taken on which direction to take, even though the second necessary condition is really unfulfilled. Such situations are of little interest as far as the decision process is concerned; we could call them indifference decisions. 7. For the present, we shall ignore the possibility of multiple objectives, although we shall touch upon it later. However we may observe that where multiple objectives exist in real life, one objective is often regarded (either implicitly or explicitly) as being of overriding importance, with the other objectives acting as constraining factors or considerations. 8. In abstract terms we can define a company as a collection of assets. The owners of the company have therefore pooled their funds to assemble such a collection and are logically only likely to do so in order to bring benefit (either directly or indirectly) to themselves. 9. The term ‘privately owned companies’ can be a source of confusion. It refers to all companies that are owned by individuals, either singly or collectively, whether or not they are ‘publicly quoted’ (plc) on a stock exchange or otherwise. Thus both public and private companies (in financial nomenclature) are privately owned companies. 10. See, for instance, Ivy Papps, Government and Enterprise, Hobart Paper No. 61, Institute of Economic Affairs, 1975. 11. We shall be ignoring the effects of inflation until later. 12. This is obviously a simplification, as in practice each share has two equilibrium prices, a buying price and a selling price. The former will be the higher of the two, and the difference constitutes the market-maker’s ‘turn’. However, for simplicity, we will ignore this complication and use a ‘middle’ value. 13. Of course, if the company’s shares are not quoted on a stock exchange, then the objective simply reduces to the maximization of the value of the company’s shares. This, however, still leaves the problem of how the shares are to be valued. In fact they should be valued on exactly the same basis as quoted shares: the future expected dividend flow. It is one of the great advantages of a stock market quotation that this value is ‘automatically’ and continuously provided for use both by management and by investors.

Quickie questions

1. 2. 3. 4. 5.

What are the three major areas of financial decisions? What is the search process? What is the fundamental objective of financial management decision making? Why is accounting profit an inappropriate criterion for financial decision making? How are shares valued?

(See the ‘Answers to quickie questions’ section at the back of the book.)

667

Tables

Compounding and discounting tables TABLE A Compound interest factor (1 + i)N

TABLE B Present value factor (1 + i)–N

i N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

i N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

1.0400 1.0816 1.1249 1.1699 1.2167 1.2653 1.3159 1.3686 1.4233 1.4802 1.5395 1.6010 1.6651 1.7317 1.8009

1.0600 1.1236 1.1910 1.2625 1.3382 1.4185 1.5036 1.5939 1.6895 1.7909 1.8983 2.0122 2.1329 2.2609 2.3966

1.0800 1.1664 1.2597 1.3605 1.4693 1.5869 1.7138 1.8509 1.9990 2.1589 2.3316 2.5182 2.7196 2.9372 3.1722

1.1000 1.2100 1.3310 1.4641 1.6105 1.7716 1.9487 2.1436 2.3580 2.5937 2.8531 3.1384 3.4523 3.7975 4.1773

1.1200 1.2544 1.4049 1.5735 1.7623 1.9738 2.2107 2.4760 2.7731 3.1058 3.4785 3.8960 4.3635 4.8871 5.4736

1.1400 1.2996 1.4815 1.6890 1.9254 2.1950 2.5023 2.8526 3.2519 3.7072 4.2262 4.8179 5.4924 6.2613 7.1379

1.1600 1.1800 1.2000 1.3456 1.3924 1.4400 1.5609 1.6430 1.7280 1.8106 1.9338 2.0736 2.1003 2.2878 2.4883 2.4364 2.6996 2.9860 2.8262 3.1855 3.5832 3.2784 3.7589 4.2998 3.8030 4.4335 5.1598 4.4114 5.2338 6.1917 5.1173 6.1759 7.4301 5.9360 7.2876 8.9161 6.8858 8.5994 10.6993 7.9875 10.1472 12.8392 9.2655 11.9737 15.4070

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.9615 0.9246 0.8890 0.8548 0.8219 0.7903 0.7599 0.7307 0.7026 0.6756 0.6496 0.6246 0.6006 0.5775 0.5553

0.9434 0.8900 0.8396 0.7921 0.7473 0.7050 0.6651 0.6274 0.5919 0.5584 0.5268 0.4970 0.4686 0.4423 0.4173

0.9259 0.8573 0.7938 0.7350 0.6806 0.6302 0.5835 0.5403 0.5002 0.4632 0.4289 0.3971 0.3677 0.3405 0.3152

0.9091 0.8264 0.7513 0.6830 0.6209 0.5645 0.5132 0.4665 0.4241 0.3855 0.3505 0.3186 0.2897 0.2633 0.2394

0.8929 0.7972 0.7118 0.6355 0.5674 0.5066 0.4532 0.4039 0.3606 0.3220 0.2875 0.2567 0.2292 0.2046 0.1827

0.8772 0.7695 0.6750 0.5921 0.5194 0.4556 0.3996 0.3506 0.3075 0.2697 0.2366 0.2076 0.1821 0.1597 0.1401

0.8621 0.7432 0.6407 0.5523 0.4761 0.4014 0.3538 0.3050 0.2630 0.2267 0.1954 0.1685 0.1452 0.1252 0.1079

0.8475 0.7182 0.6086 0.5158 0.4371 0.3704 0.3139 0.2660 0.2255 0.1911 0.1619 0.1372 0.1163 0.0985 0.0835

0.8333 0.6944 0.5787 0.4823 0.4019 0.3349 0.2791 0.2326 0.1938 0.1615 0.1346 0.1122 0.0935 0.0779 0.0649

668 TABLE C Present value of an annuity AN¬ i

TABLES

i N

TABLE D Terminal value of an annuity SN¬ i

0.04 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

i N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.9434 1.8334 2.6730 3.,4651 4.2124 4.9173 5.5824 6.2098 6.8017 7.3601 7.8869 8.3838 8.8527 9.2950 9.7122

0.9259 1.7833 2.5771 3.3121 3.9927 4.6229 5.2064 5.7466 6.2469 6.7101 7.1390 7.5361 7.9038 8.2442 8.5595

0.9091 1.7355 2.4869 3.1699 3.7908 4.3553 4.8684 5.3349 5.7590 6.1446 6.4951 6.8137 7.1034 7.3667 7.6061

0.8929 1.6901 2.4018 3.0373 3.6048 4.1114 4.5638 4.9676 5.3282 5.6502 5.9377 6.1944 6.4235 6.6282 6.8109

0.8772 1.6467 2.3216 2.9137 3.4331 3.8887 4.2883 4.6389 4.9464 5.2161 5.4527 5.6603 5.8424 6.0021 6.1422

0.8621 1.6052 2.2459 2.7982 3.2743 3.6847 4.0386 4.3436 4.6065 4.8332 5.0286 5.1971 5.3423 5.4675 5.5755

0.8475 1.5656 2.1743 2.6901 3.1272 3.4976 3.8115 4.0776 4.3030 4.4941 4.6560 4.7932 4.9095 5.0081 5.0916

0.8333 1.5278 2.1065 2.5887 2.9906 3.3255 3.6046 3.8372 4.0310 4.1925 4.3271 4.4392 4.5327 4.6106 4.6755

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

1.0000 2.0400 3.1216 4.2465 5.4163 6.6330 7.8983 9.2142 10.5828 12.0061 13.4864 15.0258 16.6268 18.2919 20.0236

1.0000 2.0600 3.1836 4.3746 5.6371 6.9753 8.3938 9.8975 11.4913 13.1808 14.9716 16.8699 18.8821 21.0151 23.2760

1.0000 2.0800 3.2464 4.5061 5.8666 7.3359 8.9228 10.6366 12.4876 14.4866 16.6455 18.9771 21.4953 24.2149 27.1521

1.0000 2.1000 3.3100 4.6410 6.1051 7.7156 9.4872 11.4359 13.5795 15.9374 18.5312 21.3843 24.5227 27.9750 31.7725

1.0000 2.1200 3.3744 4.7793 6.3528 8.1152 10.0890 12.2997 14.7757 17.5487 20.6546 24.1331 28.0291 32.3926 37.2797

1.0000 2.1400 3.4396 4.9211 6.6101 8.5355 10.7305 13.2328 16.0853 19.3373 23.0445 27.2707 32.0887 37.5811 43.8424

1.0000 2.1600 3.5056 5.0665 6.8771 8.9775 11.4139 14.2401 17.5185 21.3215 25.7329 30.8502 36.7862 43.6720 51.6595

1.0000 2.1800 3.5724 5.2154 7.1542 9.4420 12.1415 15.3270 19.0859 23.5213 28.7551 34.9311 42.2187 50.8180 60.9653

1.0000 2.2000 3.6400 5.3680 7.4416 9.9299 12.9159 16.4991 20.7989 25.9587 32.1504 39.5805 48.4966 59.1959 72.0351

0.9615 1.8861 2.7751 3.6299 4.4518 5.2421 6.0021 6.7327 7.4353 8.1109 8.7605 9.3851 9.9856 10.5631 11.1184

669

COMPOUNDING AND DISCOUNTING TABLES

TABLE E Annual equivalent –1 factor A N¬ i

i N

TABLE F Sinking fund factor –1 S N¬ i

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

i N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

1.0400 0.5302 0.3603 0.2755 0.2446 0.1908 0.1666 0.1485 0.1345 0.1233 0.1141 0.1066 0.1001 0.0947 0.0899

1.0600 0.5454 0.3741 0.2886 0.2374 0.2034 0.1791 0.1610 0.1470 0.1359 0.1268 0.1193 0.1130 0.1076 0.1030

1.0800 0.5608 0.3880 0.3019 0.2505 0.2163 0.1921 0.1740 0.1601 0.1490 0.1401 0.1327 0.1265 0.1213 0.1168

1.1000 0.5762 0.4021 0.3155 0.2638 0.2296 0.2054 0.1874 0.1736 0.1627 0.1540 0.1468 0.1408 0.1357 0.1315

1.1200 0.5917 0.4163 0.3292 0.2774 0.2432 0.2191 0.2013 0.1877 0.1770 0.1684 0.1614 0.1557 0.1509 0.1468

1.1400 0.6073 0.4307 0.3432 0.2913 0.2572 0.2332 0.2156 0.2022 0.1917 0.1834 0.1767 0.1712 0.1666 0.1628

1.1600 0.6230 0.4453 0.3574 0.3054 0.2714 0.2476 0.2302 0.2171 0.2069 0.1989 0.1924 0.1872 0.1829 0.1794

1.1800 0.6387 0.4599 0.3717 0.3198 0.2859 0.2624 0.2452 0.2324 0.2225 0.2148 0.2086 0.2037 0.1997 0.1964

1.2000 0.6545 0.4747 0.3863 0.3344 0.3007 0.2774 0.2606 0.2481 0.2385 0.2311 0.2253 0.2206 0.2169 0.2139

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

1.0000 0.4902 0.3203 0.2355 0.1846 0.1508 0.1266 0.1085 0.0945 0.0833 0.0741 0.0666 0.0601 0.0547 0.0499

1.0000 0.4854 0.3141 0.2286 0.1774 0.1343 0.1191 0.1010 0.0870 0.0759 0.0668 0.0593 0.0530 0.0476 0.0430

1.0000 0.4808 0.3080 0.2219 0.1705 0.1363 0.1121 0.0940 0.0801 0.0690 0.0601 0.0527 0.0465 0.0413 0.0368

1.0000 0.4762 0.3021 0.2155 0.1638 0.1296 0.1054 0.0874 0.0736 0.0627 0.0540 0.0468 0.0408 0.0357 0.0315

1.0000 0.4717 0.2963 0.2092 0.1574 0.1232 0.0991 0.0813 0.0677 0.0570 0.0484 0.0414 0.0357 0.0309 0.0268

1.0000 0.4673 0.2907 0.2032 0.1513 0.1172 0.0932 0.0756 0.0622 0.0517 0.0434 0.0367 0.0312 0.0266 0.0228

1.0000 0.4630 0.2853 0.1974 0.1454 0.1114 0.0876 0.0702 0.0571 0.0469 0.0389 0.0324 0.0272 0.0229 0.0194

1.0000 0.4587 0.2799 0.1917 0.1398 0.1059 0.0824 0.0652 0.0524 0.0425 0.0348 0.0286 0.0237 0.0197 0.0164

1.0000 0.4545 0.2747 0.1863 0.1344 0.1007 0.0774 0.0606 0.0481 0.0385 0.0311 0.0253 0.0206 0.0169 0.0139

670 TABLE G Compound interest N–0.5 factor (1 + i) Present value of £1 received evenly through year

TABLES

i N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.9806 0.9429 0.9066 0.8717 0.8382 0.8060 0.7750 0.7452 0.7165 0.6889 0.6624 0.6370 0.6125 0.5889 0.5663

0.9713 0.9163 0.8644 0.8155 0.7693 0.7258 0.6847 0.6460 0.6094 0.5749 0.5424 0.5117 0.4827 0.4554 0.4296

0.9623 0.8910 0.8250 0.7639 0.7073 0.6549 0.6064 0.5615 0.5199 0.4814 0.4457 0.4127 0.3821 0.3538 0.3276

0.9535 0.8668 0.7880 0.7164 0.6512 0.5920 0.5382 0.4893 0.4448 0.4044 0.3676 0.3342 0.3038 0.2762 0.2511

0.9449 0.8437 0.7533 0.6726 0.6005 0.5362 0.4787 0.4274 0.3816 0.3407 0.3042 0.2716 0.2425 0.2165 0.1933

0.9366 0.8216 0.7207 0.6322 0.5545 0.4864 0.4267 0.3743 0.3283 0.2880 0.2526 0.2216 0.1944 0.1705 0.1496

0.9285 0.8004 0.6900 0.5948 0.5128 0.4421 0.3811 0.3285 0.2832 0.2441 0.2105 0.1814 0.1564 0.1348 0.1162

0.9206 0.7801 0.6611 0.5603 0.4748 0.4024 0.3410 0.2890 0.2449 0.2075 0.1759 0.1491 0.1263 0.1071 0.0907

0.9129 0.7607 0.6339 0.5283 0.4402 0.3669 0.3057 0.2548 0.2123 0.1769 0.1474 0.1229 0.1024 0.0853 0.0711

Using this discount factor actually assumes that the cash flows take place in the middle of the year. However this is a very good approximation for cash flows that are spread evenly during the year. TABLE H Present value of an annuity AN–·05¬i Present value of £1 received each year evenly throughout the year

i N

2% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0.9901 1.9609 2.9126 3.8456 4.7604 5.6572 6.5364 7.3984 8.2435 9.0720 9.8842 10.6806 11.4613 12.2267 12.9771

4% 0.9806 1.9234 2.8300 3.7018 4.5400 5.3460 6.1209 6.8661 7.5826 8.2715 8.9340 9.5709 10.1834 10.7723 11.3386

6%

8%

10%

12%

14%

16%

18%

20%

0.9713 1.8876 2.7520 3.5675 4.3369 5.0627 5.7474 6.3934 7.0028 7.5777 8.1200 8.6317 9.1144 9.5698 9.9994

0.9623 1.8532 2.6782 3.4421 4.1493 4.8042 5.4106 5.9721 6.4920 6.9733 7.4190 7.8317 8.2138 8.5677 8.8953

0.9535 1.8202 2.6082 3.3246 3.9758 4.5678 5.1060 5.5953 6.0401 6.4445 6.8121 7.1463 7.4501 7.7262 7.9773

0.9449 1.7886 2.5419 3.2144 3.8149 4.3511 4.8298 5.2573 5.6389 5.9796 6.2839 6.5555 6.7980 7.0146 7.2079

0.9366 1.7582 2.4788 3.1110 3.6655 4.1520 4.5787 4.9530 5.2813 5.5693 5.8219 6.0435 6.2379 6.4085 6.5580

0.9285 1.7289 2.4189 3.0137 3.5265 3.9686 4.3497 4.6782 4.9614 5.2055 5.4160 5.5975 5.7539 5.8887 6.0050

0.9206 1.7007 2.3619 2.9222 3.3970 3.7994 4.1404 4.4294 4.6743 4.8818 5.0577 5.2068 5.3331 5.4401 5.5309

0.9129 1.6736 2.3075 2.8358 3.2761 3.6429 3.9486 4.2034 4.4157 4.5926 4.7401 4.8629 4.9653 5.0506 5.1217

Using this discount factor actually assumes that the cash flows take place in the middle of each year. However this is a very good approximation for cash flows that are spread evenly during each year. It will be noticed that at 10% over 10 years, the annuity factor is 6.4445 whilst using the year-end cash flow assumption (Table C) produces a factor of 6.1446. It is a matter of judgement as to whether or not this difference (of 5%) is seen as being significant.

671

AREA UNDER THE NORMAL CURVE

Area under the normal curve

TABLE I Areas under the normal distribution

z

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0

.0000 .0398 .0793 .1179 .1554 .1915 .2257 .2580 .2881 .3159 .3413 .3643 .3849 .4032 .4192 .4332 .4452 .4554 .4641 .4713 .4773 .4821 .4861 .4893 .4918 .4938 .4953 .4965 .4974 .4981 .4987

.0040 .0438 .0832 .1217 .1591 .1950 .2291 .2611 .2910 .3186 .3438 .3665 .3869 .4049 .4207 .4345 .4463 .4564 .4649 .4719 .4778 .4826 .4864 .4896 .4920 .4940 .4955 .4966 .4975 .4982 .4987

.0080 .0478 .0871 .1255 .1628 .1985 .2324 .2642 .2939 .3212 .3461 .3686 .3888 .4066 .4222 .4357 .4474 .4573 .4656 .4726 .4783 .4830 .4868 .4898 .4922 .4941 .4956 .4967 .4976 .4982 .4987

.0120 .0517 .0910 .1293 .1664 .2019 .2357 .2673 .2967 .3238 .3485 .3708 .3907 .4082 .4236 .4370 .4484 .4582 .4664 .4732 .4788 .4834 .4871 .4901 .4925 .4943 .4957 .4968 .4977 .4982 .4988

.0160 .0557 .0948 .1331 .1700 .2054 .2389 .2704 .2995 .3264 .3508 .3729 .3925 .4099 .4251 .4382 .4495 .4591 .4671 .4738 .4793 .4838 .4875 .4904 .4927 .4945 .4959 .4969 .4977 .4984 .4988

.0199 .0596 .0987 .1368 .1736 .2088 .2422 .2734 .3023 .3289 .3531 .3749 .3944 .4115 .4265 .4394 .4505 .4599 .4678 .4744 .4798 .4842 .4878 .4906 .4929 .4946 .4960 .4970 .4978 .4984 .4989

.0239 .0636 .1026 .1406 .1772 .2123 .2454 .2764 .3051 .3315 .3554 .3770 .3962 .4131 .4279 .4406 .4515 .4608 .4686 .4750 .4803 .4846 .4881 .4909 .4931 .4948 .4961 .4971 .4979 .4985 .4989

.0279 .0675 .1064 .1443 .1808 .2157 .2486 .2794 .3078 .3340 .3577 .3790 .3980 .4147 .4292 .4418 .4525 .4616 .4693 .4756 .4808 .4850 .4884 .4911 .4932 .4949 .4962 .4972 .4979 .4985 .4989

.0319 .0714 .1103 .1480 .1844 .2190 .2517 .2823 .3106 .3365 .3599 .3810 .3997 .4162 .4306 .4429 .4535 .4625 .4699 .4761 .4812 .4854 .4887 .4913 .4934 .4951 .4963 .4973 .4980 .4986 .4990

.0359 .0753 .1141 .1517 .1879 .2224 .2549 .2852 .3133 .3389 .3621 .3830 .4015 .4177 .4319 .4441 .4545 .4633 .4706 .4767 .4817 .4857 .4890 .4916 .4936 .4952 .4964 .4974 .4981 .4986 .4990

672

Natural logarithms TABLE J N

0

1.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 2.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 3.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 4.0 .1 .2 .3 .4 .5 .6 .7 .8 .9

0.0000 .0953 .1823 .2623 .3364 .4054 .4700 .5306 .5877 .6418 0.6931 .7419 .7884 .8329 .8754 .9162 .9555 .9932 1.0296 .0647 1.0986 .1314 .1631 .1939 .2237 .2527 .2809 .3083 .3350 .3609 1.3862 .4109 .4350 .4586 .4816 .5040 .5260 .5475 .5686 .5892

1

2

3

4

5

6

7

8

9

.0099 .1043 .1906 .2700 .3435 .4121 .4762 .5364 .5933 .6471 .6981 .7466 .7929 .8372 .8796 .9202 .9593 .9969 a .0331 .0681 .1019 .1346 .1662 .1969 .2267 .2556 .2837 .3110 .3376 .3635 .3887 .4134 .4374 .4609 .4838 .5063 .5282 .5496 .5707 .5912

.0198 .1133 .1988 .2776 .3506 .4187 .4824 .5423 .5988 .6523 .7031 .7514 .7975 .8415 .8837 .9242 .9631 a .0006 .0367 .0715 .1052 .1378 .1693 .1999 .2296 .2584 .2864 .3137 .3402 .3660 .3912 .4158 .4398 .4632 .4861 .5085 .5303 .5518 .5727 .5933

.0295 .1222 .2070 .2851 .3576 .4252 .4885 .5481 .6043 .6575 .7080 .7561 .8020 .8458 .8878 .9282 .9669 a .0043 .0402 .0750 .1085 .1410 .1724 .2029 .2325 .2613 .2892 .3164 .3428 .3686 .3937 .4182 .4422 .4655 .4884 .5107 .5325 .5539 .5748 .5953

.0392 .1310 .2151 .2926 .3646 .4317 .4947 .5538 .6097 .6626 .7129 .7608 .8064 .8501 .8920 .9321 .9707 a .0079 .0438 .0784 .1118 .1442 .1755 .2059 .2354 .2641 .2919 .3190 .3454 .3711 .3962 .4207 .4445 .4678 .4906 .5129 .5347 .5560 .5769 .5973

.0487 .1397 .2231 .3001 .3715 .4382 .5007 .5596 .6151 .6678 .7178 .7654 .8109 .8542 .8960 .9360 .9745 a .0116 .0473 .0818 .1151 .1474 .1786 .2089 .2383 .2669 .2947 .3217 .3480 .3737 .3987 .4231 .4469 .4701 .4929 .5151 .5368 .5581 .5789 .5993

.0582 .1484 .2311 .3074 .3784 .4446 .5068 .5653 .6205 .6729 .7227 .7701 .8153 .8586 .9001 .9400 .9783 a .0152 .0508 .0851 .1184 .1505 .1817 .2119 .2412 .2697 .2974 .3244 .3506 .3762 .4011 .4255 .4492 .4724 .4951 .5173 .5390 .5602 .5810 .6014

.0676 .1570 .2390 .3148 .3852 .4510 .5128 .5709 .6259 .6780 .7275 .7747 .8197 .8628 .9042 .0439 .9820 a .0188 .0543 .0885 .1216 .1537 .1847 .2149 .2441 .2725 .3001 .3270 .3532 .3787 .4036 .4279 .4516 .4747 .4973 .5195 .5411 .5623 .5830 .6034

.0769 .1655 .2468 .3220 .3920 .4574 .5187 .5766 .6312 .6831 .7323 .7793 .8241 .8671 .9082 .9477 .9858 a .0224 .0577 .0919 .1249 .1568 .1878 .2178 .2470 .2753 .3029 .3297 .3558 .3812 .4061 .4303 .4539 .4770 .4996 .5217 .5433 .5644 .5851 .6054

.0861 .1739 .2546 .3293 .3987 .4637 .5247 .5822 .6365 .6881 .7371 .7839 .8285 .8712 .9122 .9516 .9895 a .0260 .0612 .0952 .1281 .1600 .1908 .2208 .2499 .2781 .3056 .3323 .3584 .3837 .4085 .4327 .4562 .4793 .5018 .5238 .5454 .5665 .5871 .6074

a. Add 1.0 to indicated figure.

673

Answers to quickie questions Chapter 1

1. (a) The capital investment decision.

2. 3.

4.

5.

(b) The financing and capital structure decision. (c) The dividend decision. The process by which the company seeks out alternative courses of action, alternative projects, etc. The assumed objective of financial decision making is maximization of shareholder wealth. While recognizing that this is a simplification of the real world, it is reasonable to accept that this should be the main objective, other things being equal. It is a reporting concept, not a decision-making concept. Its purpose is to report on the success or failure of decisions taken. It has only a secondary role in the decision-making process itself. Accounting profit is also based on historic cost whereas financial management is concerned with value. The two things are very different. Finally, profit as reported is subject to the judgement of the accountant and cannot be regarded as entirely reliable. On the basis of the expected flow of dividends they will generate in the future.

Chapter 2

1. The problem is one of control. How does the principal control the agent to ensure that the agent acts in the principal’s best interests? 2. Fiduciary responsibilities; independent external audit; London Stock Exchange Yellow Book listing rules and ‘Model Code’ for directors’ share dealings; Companies Act regulations on directors’ transactions; and the Combined Code best corporate governance practice. 3. Reward managerial ability, not luck; rewards should have a significant impact on managerial remuneration; reward system should work two ways; concept of risk should be taken into account; the shareholders’ time horizon should be taken into account; scheme should be simple, inexpensive and difficult to manipulate.

Chapter 3

1. Stage one: The best of the alternative projects has the shortest payback. Stage two: Accept the best project as long as its payback period satisfies the decision criterion. 2. Working capital is excluded from the analysis. Net cash flow: 0 1 2 3 4 5

–11 000 + 4 000 + 4 000 + 4 000 + 3 000 + 3 000

Payback = 2.75 years

3. (a) Quick and simple to calculate. (b) Thought to automatically select less risky projects in mutually exclusive decision situations.

674

ANSWERS TO QUICKIE QUESTIONS

4. 5.

6. 7.

8.

9.

(c) Saves management the trouble of having to estimate project cash flows beyond the maximum payback time period. (d) Convenient method to use in capital rationing. The payback criterion is reduced until total capital expenditure equates with the amount of finance available. (a) Management’s experience of successful projects within the firm. (b) Industry practice. (c) Reflects the limit of management’s forecasting skills. However, none of these can be seen as being really objective. The payback decision rule, adjusted to take account of the time value of money. Ignores cash flows outside the payback time period. (The fact that ‘normal’ payback ignores the time value of money is equally important but this criticism can, of course, be easily overcome through the use of discounted payback.) Money has a time value because it can earn a rate of interest/a rate of return. This has nothing to do with inflation although that might have an effect on the levels of return expected. The question does not specify which ARR/ROCE to calculate, so both are given: Annual depreciation: (£11 000 – £1 000) ÷ 5 = £2 000. Profit:

£4 000 4 000 4 000 3 000 2 000 Total profit

– – – – –

£2 000 2 000 2 000 2 000 2 000

= = = = = = =

£2 000 Yr 1 2 000 Yr 2 2 000 Yr 3 1 000 Yr 4 0 Yr 5 £7 000 ÷ 5 = £1 400 Av. ann. profit

Average capital employed: £11 000 – £1 000 + £1 000 + £4 000 = £10 000 2 Return on initial capital employed = £1 400 ÷ £15 000 = 9 13% Return on average capital employed = £1 400 ÷ £10 000 = 14% 10. (a) Evaluates via a percentage rate of return. (b) Evaluates on the basis of profitability. (c) Appears logical to evaluate projects on the same basis as management have their own performance evaluated by shareholders. 11. (a) Ignores the time value of money. (b) Evaluates on the basis of profit, not cash flow.

Chapter 4

1. This is an example of the economic concept of diminishing marginal utility. Each additional £1 of t0 consumption forgone, through investment, is likely to be of increasing value in terms of consumption benefits forgone. Each additional £1 of future consumption gained is likely to be of decreasing value. Hence, the time value of money rises. 2. The complete range of maximum consumption combinations that the firm owner can obtain at t0 and t1. 3. The marginal return on the investment opportunity at any particular point. 4. A curve of constant utility. All combinations of consumption at t0 and t1 that lie along a single indifference curve would provide the same level of utility or satisfaction.

675

CHAPTER 5

5. It invests until the return on the marginal investment equates with the owner’s marginal time value of money. 6. Lending at t0 would reduce the amount of money available for consumption at t0 and increase the amount available at t1, hence the move would be up the financial investment line. 7. The firm should continue to invest in projects as long as the marginal rate of return is not less than the market rate of interest. This rule is, of course, obvious. There would be little point in investing money in a project that gave a lower return than could be obtained by lending the money on the capital market. The cash (dividend) distribution to shareholders in t0 and t1 that arises out of the firm’s investment decision can then be redistributed by shareholders, using the capital markets, to suit their own set of indifference curves. 8. A risky investment is one where the outcome is uncertain. 9. Ensure that any project earns at least the capital market rate of return that is available for investments of equivalent risk to the project. 10. (a) single time horizon; (b) infinitely divisible projects; (c) all independent projects; (d) rational investors. 11. Investors dislike risk: they are said to be risk-averse. Hence they require a reward for taking on a risk, which is the expectation (but, of course, not the certainty) of a higher return. 12. In these circumstances, the market rate of return offers you greater compensation than you require to forgo current consumption. Therefore you would want to lend money.

Chapter 5

1. 0

–1 000



1

=

1 2 3

+ 500 + 600 + 400

  

0.8772= 0.7695= 0.6750=

–1 000 + + + +

438.60 461.70 270 170.30 NPV

2. There are several interpretations: (a) It produces a return > 10%. (b) It produces £120 more (in t0 terms) than a £1000 capital market investment of similar risk. (c) The project would produce a sufficient cash flow to repay its outlay, pay its financing charges and provide an additional £120 in t0 terms. (d) If accepted, shareholder wealth would increase by £120. 3. At 4% discount rate: NPV = +147.48 At 20% discount rate: NPV = –9.28 147.48   Therefore IRR = 4% +   (20% – 4%) = 19.05% approx. 147.48 – (–9.28)  With any problem like this it is a good idea to use a computer to arrive at an answer. In this case the solution, using the IRR function of a spreadsheet, is 18.825%. 4. Year Cash flow. Discount factor 0 –500  1 = –500 1 +200  0.9091 = +181.82 2 +300  0.8264 = +247.92 3 +200  0.7513 = +150.26

676

ANSWERS TO QUICKIE QUESTIONS

500 – 181.82 – 247.92 = 70.26 ÷ 150.26 = 0.47. Therefore payback is 2.47 years approx. 5. The return available elsewhere on the capital market on a similar risk investment. 6. For the same project they should be identical. In both cases they are the opportunity cost return referred to in the answer to question five. 7. +350 A4¬0.10 = 350  3.1699 = +1109.47. 8. (a) annuity due; (b) immediate annuity; (c) deferred annuity. 9. Given that the PV of a perpetuity is: Annual amount , then: Discount rate IRR =

£100 = 0.10 or 10% £1 000

because: –£1 000 + 10.

Chapter 6

£100 = 0 NPV 0.10

–1 000 + 200 A2¬0.16 + 500 A3¬0.16 (1 + 0.16)–2 = NPV –1 000 + (200  1.6052) + (500  2.2459  0.7432) = +£155.62

1. The NPV rule is to accept whichever project has the largest positive NPV. Differences in magnitude, duration and risk can be ignored. Hence Project A should be accepted. 2. The assumptions made are: (a) There is a perfect capital market so that the firm can finance the large project just as easily as it can finance the small project. (b) The projects represent independent decisions in that they are not part of a continuous replacement chain. (c) The discount rates used do correctly reflect the risk of each project. 3. NPV and IRR both make assumptions about the rate of return at which project-generated cash flows are reinvested. NPV assumes that the rate is the market discount rate, while IRR assumes that it is equal to the IRR of the project generating those cash flows. Given a perfect capital market, the NPV method is making the correct assumption. 4. Non-conventional cash flows, where there is more than one change in sign. The problem can be avoided by using the ‘extended yield technique’ or the ‘modified IRR’. 5. Using the extended yield technique: Year 3: –20 (1 + 0.10)–3 = –15.02 at Year 0 Therefore the revised cash flow is: 0 –115.02 1 + 60 2 + 80 At a 4% discount rate: +16.64 NPV At a 20% discount rate: –9.46 NPV 16.64   ∴ IRR = 4%  (20% – 4%) = 14.2% 16.64 – (–9.46)  

677

CHAPTER 7

+ NPV

NPV: B NPV: B IRR: A 0 NPV

Discount rate Discount rate

IRR: B IRR of differential cash flow

NPV profile A NPV profile B

– NPV

7. If IRR diff. c/f > hurdle rate: accept project smallest IRR. If IRR diff. c/f < hurdle rate: accept project largest IRR. 8. 1 +40 (1.10)2 = 2 +80 (1.10)1 = 3 –3 0 = Year 3 Terminal value

(£) +60.5 +88 –30 +118.50

Modified cash flow of the project:

Year 0 3

(£) – 80 +118.50

Estimating the IRR using linear interpolation: NPV at 5% = +22.36 NPV at 20% = –11.42 22.36   IRR = 5% +   (20% – 5%) = 14.9%. 22.36 – (–11.42) 

Chapter 7

1.

(1.13) – 1 = 0.086 or 8.6% (1.04)

2. Either: (a) Project money cash flows discounted at the market discount rate to NPV; or (b) project money cash flows discounted at the general rate of inflation and then at the real discount rate to NPV. 3. The money cash flow, deflated (discounted) by the general rate of inflation. 1.155 4. – 1 = 0.10 = real discount rate 1.05 (a) £10 000 (1.05)2 = £11 025 (b) £10 000 (a) £11 025 (1.155)–2 = £11 025 (1.10)–2 (1.05)–2 = £8263.73 (b) £10 000 (1.155)–2 = £10 000 (1.10)–2 (1.05)–2 = £7495.45

678

ANSWERS TO QUICKIE QUESTIONS

5. 500 125 375 93.75 281.25



0.25

=

WDA +125

 0.35

=

Tax relief +43.75

Timing Year 2



0.25

=

+ 93.75  0.35

=

+32.81

Year 3

–

0

=

+281.25  0.35

=

+98.44

Year 4

6. Historic cost: £60 000, irrelevant, sunk cost. Written-down book value: £10 000, irrelevant non-economic figure. Scrap now: £3000. Rent and then scrap: £2500 + £800 = £3300. Therefore, if the machine is used to undertake the project, the best opportunity forgone is the ‘rent and then scrap’ alternative. So this is the opportunity cost of using the machine on the project: –£3300. 7. Discount the after-tax cash flows by the after-tax discount rate. 8. They are non-incremental. 9. Market price of factory space: £2 per m2 (external opportunity cost). Contribution £15 per m2 (internal opportunity cost). Cost to project: 150  (£15 + £2) = £2550.

Chapter 8

1. Hard and soft capital rationing. 2. The firm cannot necessarily accept a project just because it has a positive NPV, nor can it necessarily reject a project just because it has a negative NPV. Hence the standard NPV decision rule breaks down. In theory capital rationing should not exist because we assume that cash will be available for investments at an appropriate rate of return. In another sense it causes no problem for NPV because we could assume that the appropriate discount rate is the return on the alternative investments (i.e. opportunity cost of capital). 3. The benefit–cost ratios are: A: B: C: D: 200 –100 100 – 40 60 – 60 —

+60 +90 +20 –10

÷ ÷ ÷ ÷

100 200 40 100

= = = =

+0.60 +0.45 +0.50 –0.10

(1) (3) (2) (–)

available invest in A, producing

:

+ 60 NPV

invest in C, producing

:

+ 20 NPV

invest in 30% B, producing

:

+ 27 NPV +107 Total NPV

4. The benefit–cost ratios are: A: B: C: D: 240 –50 190 –190 0

+60 +90 +20 –10

÷ ÷ ÷ ÷

50 200 150 —

= = = =

+1.200 +0.450 +0.133 —

available invest in A, producing

(1) (2) (3)

:

invest in 95% of B, producing :

+ 60 NPV + 85.5 NPV +145.5 Total NPV

679

CHAPTER 8

As D has a cost–benefit ratio of: –10 ÷ 20 = –0.50 and B, the marginal project, has a benefit–cost ratio of 0.45, further investment is not worthwhile. 5. Benefit–cost ratios: A: *B: *C: D: E:

÷ ÷ ÷ ÷ ÷

40 30 50 10 4

300 –100 200 –100 100 –100 0

100 100 200 100 50

= = = = =

0.40 0.30 0.25 0.10 0.08

(1) (2) (3) (4) (5)

available invest in A, producing

:

+40 NPV

invest in B, producing

:

+30 NPV

invest in D, producing

:

+10 NPV +80 Total NPV

available invest in A, producing

:

+40 NPV

invest in C, producing

:

+50 NPV +90 Total NPV

alternatively: 300 –100 200 –200 0

Therefore, the best alternative is to undertake projects A and C. 6.

40a 100a 200a 30c

– 20b + 150b + 120c

+ 50c + 200c

a, b, c a, b, c 7.

Dual values 1.86 0.73 0.64 1.21

+ + + + +

⭐ ⭐ ⭐ ⭐ ⭓

10% discount factor 1.0000 0.9091 0.8264 0.7513

Max. 190 110 + 70b 50a + 70b 1 0 = = = = =

Total opportunity cost of cash 2.8600 t0 1.6391 t1 1.4664 t2 1.9613 t3

Gain from an extra £1 at t1: £1  1.6391 = £1.6391 Loss from repayment of £1, plus interest (i) at t2 £(1 + i)  1.4664 = £1.4664 + 1.4664i The maximum interest rate would occur at the point where the gain equals the loss: 1.6391 = 1.4664 + 1.4664i 1.6391 –1.4664 = 1.4664i 1.6391 –1.4664 = i = 0.118 or 11.8% max. 1.4664

680

ANSWERS TO QUICKIE QUESTIONS

8. NPV: –100  + 40  + 90 

1 0.9091 0.8264

= = =

–100.00 + 36.36 + 74.38 + 10.74 NPV

Internal opportunity cost: –100  1.86 = + 40  0.73 = + 90  0.64 =

–186.00 + 29.20 + 57.60 – 99.20

Total opportunity cost: +10.74 NPV –99.20 Internal opportunity cost –88.46 Net total opportunity cost As this net figure is negative, the additional project will not be a worthwhile investment, so reject.

Chapter 9

– 1 000 + 500 A3¬0.10 = + 243 NPV – 1 000 + 350 A3¬0.10 = –130 NPV

1. Success: Failure: State I II

Prob. 0.45 0.55

2. Survey indicates State I State II

 

NPV +243 –130

Action Accept Reject

Prob. 0.45 0.55

ENPV with survey ENPV without survey Max. worth of survey 3. Survey indicates State I correctly State I incorrectly State II correctly State II incorrectly State A B C D

Action Accept Accept Reject Reject

: : :

Probability 0.45  0.75 0.45  0.25 0.55  0.75 0.55  0.25 Prob. 0.3375 0.1125 0.4125 0.1375

ENPV with survey ENPV without survey Max. worth of survey

= =

Outcome +243 NPV = 0 NPV =

  +109 + 37 + 72 = = = =

: : :

+41 +37 + 4

State A B C D

0.3375 0.1125 0.4125 0.1375

Outcome +243 NPV – 72 NPV 0 NPV –243 NPV ENPV

   

+109 – 72 + 37 ENPV

= = = =

+82 – 8 0 –33 +41

+109 0 +109 ENPV

681

CHAPTER 9

4.

State I II III

Prob. 0.3 0.5 0.2

NPV +100 + 50 –300 ENPV

  

= = =

+30 +25 –60 – 5

Therefore, without the survey we would not accept the project and so incur a zero NPV. Survey indicates State I State II State III

Action Accept Accept Reject

Prob. 0.3 0.5 0.2

ENPV with survey ENPV without survey Max. worth of survey

   : : :

Outcome +100 + 50 + 0 ENPV

= = =

+30 +25 0 +55

+55 0 +55

5. If the machine is bought and, at the end of Yr 1, the decision is taken not to abandon the project, then the outcome will be: State I II III

Yr 1 –60 –60 –60

Yr 2 +100 + 60 + 40

NPV +23.43 – 6.81 –21.93

Decision Don’t abandon Abandon Abandon

The investment decision is therefore: State I II

Yr 0 –140 –140

III

–140

Yr 1 +100 + 60 + 60 + 40 + 60

Yr 2 +100      

NPV +22.57 –35.65

 

Prob. 0.70 = +15.80 0.10 = – 3.56

–53.04



0.20 = –10.61

ENPV

+ 1.63

The complete decision is that the company should purchase the machine but, if either states II or III occur, then the machine should be sold off at the end of the first year. 6. –1 000 + 280 A5¬0.10 = +61.42 NPV Life = x

At 5 year life: +61.42 NPV At 4 year life: –1000 + 280 A4¬0.10 = –112.40 NPV

Using linear interpolation:  112.40  x = 4+  (5 – 4 ) = 4.65 yrs. 61.42+112.40  Thus the life of the project can be reduced by up to 0.35 of a year (approx 4¼ months) before the original decision advice is incorrect. This represents a maximum change of 0.35 ÷ 5 = 7%. Net cash flow = x –1000 + x A5¬0.10 = 0 NPV x = 1000 ÷ A5¬0.10 = 264

682

ANSWERS TO QUICKIE QUESTIONS

Thus the annual net cash flow can fall by up to 16 per year, or 16 ÷ 280 = 5.7% before the original decision advice is incorrect.

Chapter 10

1. (a) How to measure the project’s risk. (b) How to find the return available on the capital market for that level of risk. 2. Transitivity means that choice between alternatives is consistent: if X is preferred to Y and Y is preferred to Z then X must be preferred to Z if the choice is to exhibit transitivity. 3. It is the guaranteed outcome that is regarded as being of equal value to the expected value of an uncertain investment. The guaranteed outcome will be smaller in cash terms than the equivalent uncertain outcome with the same perceived value so long as the investor is risk-averse. 4. U (+10 000) = 1 U (–5 000) = 0 U (C – E) = pU (+10 000) + (1 – p) U (–5 000) U (3 500) = (0.60  1) + (0.40  0) = 0.60 5. Risk aversion. 6. Linear. However, it is likely that any individual will be risk-averse. 7. Certainty-equivalent < expected outcome. 8. 9.

(Selling price – Purchase price) + Dividends received = Return Purchase price State of world I II III (Return)2 (40%)2 (15%)2 (–10%)2 2

Prob. 0.20 0.60 0.20

  

Return +40% +15% –10%

  

Prob. 0.20 0.60 0.20

= = =

2

2

= = =

+ 8% + 9% – 2% +15% = E(r)

320 135 20 475 = E(r2) 2

σ = E(r ) – E(r) = 475 – (15%) = 475 – 225 = 250 2

σ = √σ = √250 = 15.81% Solution: Expected return: 15% Risk (std. dev.): 15.81% 10. Downside risk is concerned with the possibility that an investment might do worse than expected. 11. In this situation the variance or standard deviation of the returns are not adequate descriptors of risk. An investment with a lower variance might also be the investment that bears the greater chance of a loss.

Chapter 11

1. 2.

The correlation coefficient. The further away it is from +1, the greater the degree of risk-reduction effect. σp = √[x2σ2A + (1 – x)2 σ2B + 2x(1 – x)Cov(rA, rB)], or σp = √[x2σ2A + (1 – x)2 σ2B + 2x(1 – x)σA σB ρA, B].

683

CHAPTER 11

3.

A: 0.3 0.4 0.3

  

= = = =

28% 18% 6% E(rA)

  

(28% – 17.4%) (18% – 17.4%) (6% – 17.4%) A: 0.3 0.4 0.3

(28%)2 (18%)2 (6%)2 E(r2A)

= = = =

B:

0.3 0.4 0.3

(35% – 22.5%) (15% – 22.5%) (20% – 22.5%) 235.2 129.6 10.8 375.6

B:

0.3 0.4 0.3

  

35% 15% 20% E(rB)

  

0.3 = 0.4 = 0.3 = Cov(rA, rB)

 (35%)2  (15%)2  (20%)2 E(r2B)

σ A = [ E ( rA2 ) −E ( rA )2 ]

σ B = [ E ( rB2 ) −E ( rB )2 ]

σ A = ( 375.6 –17.4 2 ) = 8.5%

σ B = (577.5 – 22.5 2 ) = 8.4%

ρ A, B = 4.

  

8.4% 7.2% 1.8% 17.4%

= = = =

= = = =

10.5% 6% 6% 22.5% +39.75 – 1.80 + 8.55 +46.50 367.5 90.0 120.0 577.5

Cov.( rA , rB ) 46.50 = = 0.65 σA  σB 8.5  8.4

E(rp) = xE(rA) + (1 – x) E(rB) 20% = x  17.4% + (1 – x) 22.5% 20 = 17.4x + 22.5 – 22.5x 20 – 22.5 = 17.4x – 22.5x –2.5 = –5.1x –2.5 = x = 0.49. –5.1 Therefore invest 49% of the funds in investment A, and the remaining 51% in B. 20% = (0.49  17.4%) + (0.51  22.5%).

5. N

E ( ri ) = ∑ x iρ i . i=1

N

σp = 6.

N

∑∑x x i=1 j=1

i

j

σ i σ jρ ij

A portfolio which lies along the capital market line (CML). It provides either (a) the maximum level of expected return for a given level of risk; or (b) the minimum level of risk for a given level of return.

7. E ( r j ) = rF + λσ j or E ( r j ) = rF + 8.

E ( rM ) – rF σ j. σM

An efficient portfolio consists of investing in the market portfolio and government stock (or borrowing at the risk-free interest rate). Thus, using: E(rp) = xE(rM) + (1 – x)rF 15% = x  16% + (1 – x) 10% 15 = 16x + 10 – 10x 15 – 10 = 16x – 10x 5 = x 6

684

ANSWERS TO QUICKIE QUESTIONS

Therefore 83
 % of the funds should be placed in the market portfolio and the balance, 16 %, should be invested in government stock. The resulting portfolio’s risk can be calculated from: E ( rp ) = rF +

E ( rM ) – rF σp σM

15% = 10% =

16% – 10% σp 3%

15% – 10% = σ p = 2.5%. 2% 9.

20% 20 20 – 10 10 10 6

= = = = =

x  16% + (1 – x) 10% 16x + 10 – 10x 16x – 10x 6x x = 1.66.

Therefore borrow 66 % of own personal funds at the risk-free interest rate of 10%: Borrow £1000  0.66 = £666.67. Invest your own funds (£1000) plus the borrowed funds (£666.67) in the market portfolio. Risk of the portfolio would be: 20% = 10% +

16% – 10% σp 3%

20% – 10% = σ p = 5% 2% 10. The market portfolio is the ultimate diversified portfolio and so contains only non-diversifiable risk. It consists of shares in all companies quoted on the stock exchange, held in proportion to the companies’ total market values.

Chapter 12

1. rA = rF + [E(rM) – rF] βA.

2. 3.

4.

5.

The market portfolio has a beta of 1 so a portfolio with a beta of 0.5 would only be half as risky as the market portfolio. The systematic risk of an investment, relative to the risk of the market portfolio. Unsystematic risk is that part of an investment’s total risk that can be diversified away. Its sources are those factors that are specific to the investment, such as its management’s ability and the quality of its research and development activities. There are three principal factors: (a) the sensitivity of the firm’s revenues to the level of economic activity in the economy; (b) the proportion of fixed to variable costs; (c) the amount of debt finance (gearing). 20%  0.6 = 12% = systematic risk 8% = unsystematic risk 20% = total risk βB =

20%  0.6 12% = = 1.20. 10% 10%

685

CHAPTER 14

6. βC = Cov (rC, rM) ÷ σ2M = 73.5 ÷ [7%  7%] = 73.5 ÷ 49 = 1.5. 7. βcompany + project = (1.20  0.90) + (1.70  0.10) = 1.25. 8. If a share is overvalued, it is giving an expected return of less than it should. Hence, it would lie below the CAPM. 9. The CAPM is a single-factor model: expected return is determined by a single factor – systematic risk or beta. The arbitrage pricing model is a multi-factor model: expected return is determined by more than a single factor. 10. E(rproject) = 8% + (12% – 8%)  1.75 = 15% –100 (1.15)0 + 60(1.15)–1 + 50(1.15)–2

= = =

–100.00 + 52.18 + 37.80 – 10.02 NPV

The project has a negative NPV when discounted at 15%. Thus it produces a return of less than 15%. As the CAPM indicates that the minimum return from an investment with this level of systematic risk (estimated by the beta value of the industry group into which the project can be classified) is 15%, the project should be rejected.

Chapter 13

1. An option to sell shares that can only be exercised on the expiry date. 2. An option to buy shares that can be exercised at any time up to the expiry date. 3. At expiry. 4. Use a straddle. Simultaneously buy both call options and put options at the same exercise price and expiry date. 5. The effect is the same as if the underlying shares had been bought: if the share price goes up, you gain; if the share price falls you make a loss. However, buying a call and selling a put is significantly cheaper than buying the underlying shares instead. 6. The intrinsic value of the option and the time value of the option. 7. The Black and Scholes model is a function of: (a) the current share price; (b) the future exercise price; (c) the risk-free rate of interest; (d) the time to expiry; (e) the volatility of the market price of the underlying shares. 8. Shares, risk-free bonds, call options on the shares and put options on the shares. The fundamental equality relationship is: S + P = B + C. –T

9. S – X (1 + rF) = C – P or S – Xe –rF. T = C – P. 10. Delta risk is the hedge ratio of the option. It measures the sensitivity in the value of the option to changes in the value of the shares. It is given by N(d1). The greater the delta risk, the greater the sensitivity of the option’s value to changes in the underlying share price, and vice versa.

Chapter 14

1. 8% ÷ 4 = 2% per three months. £1 million  0.02 = £20 000. 2. Borrow £5 million now for five months and place the money on deposit for the next two months until it is required. 3. You would receive compensation equal to: £10mn  6/12  (0.07 – 0.065) = £25 000.

686

ANSWERS TO QUICKIE QUESTIONS

4. FRAs provide a hedge against adverse and favourable interest rate movements. IRGs provide a hedge against adverse movements, but allow advantage to be taken of a favourable movement in interest rates. 5. You require a short hedge: you would sell futures. 6. Futures are priced on an indexed basis and so this implies: 100 – 92.75 = 7.25%. 7. $1 million  3/12  0.0001 = $25. 8. It is the risk that the futures price will not move precisely in line with interest rate movements. 9. Because of basis risk and because only whole contracts can be traded. 10. No. For there to be an advantage to an interest rate swap there must be a quality spread differential. Here, the QSD is zero. Fixed interest: 12.75% – 11% = 1.75%; LIBOR: 2.75% – 1% = 1.75%; QSD = 1.75% – 1.75% = 0.

Chapter 15

1. (a) Weak efficiency.

2.

3.

4.

5.

6. 7. 8.

9.

10.

(b) Semi-strong efficiency. (c) Strong efficiency. (a) Share prices will reflect management decisions as long as they are communicated to the stock market. (b) Shares are never overvalued or undervalued from the point of view of the timing of capital raising. (c) A takeover of a quoted company is unlikely to represent a positive NPV investment. With weak efficiency, technical analysis is worthless; with semi-strong efficiency, so too is fundamental analysis; and with strong efficiency investors cannot even expect to gain from inside information. Share prices react to the disclosure of new, relevant information. New information arises at random intervals of time and can be randomly either good or bad. Hence share price movements themselves occur at random. A technical analyst tries to identify patterns that recur in past share price movements. Then if one of those patterns is observed starting to develop, the technical analyst hopes that this will provide an ability to predict the future share price movement as the pattern develops more fully. Upward sloping. See Fig. 15.4 in the text. This states that the shape of the yield curve is determined by expected future interest rates. This states that the normal yield curve is upward sloping because investors prefer short-term bonds – they have a preference for liquidity. Thus they are willing to accept a low interest rate on short-term bonds, but have to be offered a higher interest rate to attract them to the less-preferred long-term bonds. According to the Fisher Effect, market interest rates are determined by inflation rates. Thus if the market expects future interest rates to be lower – based on the pure expectations hypothesis and a falling yield curve – this implies that inflation rates are also expected to fall in future. Suppose you invest £100 in a two-year bond. At the end of two years you will have: £100 (1.07)2 = £114.49. If you invest £100 in a one-year bond, at the end of one year you will have: £100(1.06)1 = £106. This implies that the market expects the yield on one-year bonds next year to be: (£114.49 ÷ £106) – 1 = 0.08 or 8%, so that £106(1.08)1 = £114.49 (approx.).

687

CHAPTER 16

Chapter 16

1. PE = 147 – 13 = 134p ex div 11¼(1 + g)3 = 13 1

g = (13÷11 41 ) 3 – 1 = 0.049 KE =

13(1 + 0.049) + 0.049 = 0.154 or 15.4%. 130

2. (a) Both r and b remain constant values. (b) All-equity financed company. (c) All projects financed out of retained earnings. 3. PB = £128 – £15 = £113 ex int. –4

+ 113 – 15(1 – 0.35) A4¬K DAT + 110 (1 + K DAT ) = 0 NPV At 5%, NPV = –12.07 At 15%, NPV = +22.28 12.07   KD = 5% +   (15% – 5%) = 8.5% 22.28 +12.07  VB = £12m  1.13 = £13.56mn. 4. 12(1 – 0.35) A3¬0.085 + 100(1.085)–3   = £92.08 = PB (7.8  2.5540) + (100  0.7216)  £10mn  0.9208 = £9.208mn = VB. 5. Given note 19 and the fact that: PB = £118 – £18 = £100 ex int. and the debt is redeemable at par then the coupon rate equals KD and so K DAT = 18% (1 – 0.35) = 11.7%. 6. 87 = 100 (1 + KD)–3 87 = (1 + KD)–3 = 0.87 100 1 =1.149 (1 + KD)3 = 0.87 KD = 1.149
 – 1 = 0.0475 or 4.75%. 7. (a) The bonds are issued at par and are redeemable at par and carry a coupon rate reflecting the market interest rate at the time of issue. (b) The bonds are issued at a substantial discount on par but are redeemed at par value. They pay zero interest. Thus the investor receives a return purely in the form of a capital gain. (c) The conversion ratio is the number of shares into which each unit of convertible debt can be converted. (d) The conversion price is effectively the exercise price of the call options on the company’s shares which is contained in an issue of convertible debt. (e) The conversion premium is the percentage by which the conversion price exceeds the current share price (normally, at the time of issue). 8. Convertibles have advantages from both the investor’s and the company’s viewpoint. From the investor’s viewpoint they offer the security of a fixed rate of interest, plus the possibility of making a significant capital gain on conversion, together with the security of being able to have the debt redeemed if they so wish. From the company’s viewpoint convertibles have the twin advantages of paying a

688

ANSWERS TO QUICKIE QUESTIONS

lower coupon than straight debt and, with luck, never having to repay the loan (as investors will convert). 9. In four years’ time, the share price is likely to be: 165p (1.08)4 = 224.5p. Thus 50 shares will be worth: 50  224.5p = £112.25. Therefore we would expect investors to convert. The coupon rate is 5% and so the after-tax interest payments payable by the company are: £5  (1 – 0.33) = £3.35. The after-tax cost of the convertible debt is given by the internal rate of return on the following cash flow: Year:

0 88

1

→ (3.35)

4

4 (112.25)

NPV at 4% = –20.11 NPV at 12% = +6.49.  –20.11  K D AT = 4%  (12% – 4%) = 10%.  –20.11 – 6.49  10. The minimum value of a convertible is the greater of its value as straight debt and its conversion value.

Chapter 17

1. KE = K DQ =

5(1.07) + 0.07 = 13.4% 83 15(1 – 0.35) = 8.9% 110

VE = 24 mn  83p = £19.92mn V B Q = £25 mn  1.10 = £27.5mn

K D UQ = K DQ = 8.9% (assuming similar risk). PBUQ

12(1 – 0.35) = = £87.64 ∴ VB UQ = £10 mn  0.8764 = £8.76 0.089 KL = 14%(1–0.35) = 9.1% VL = £3mn V0 = £19.92mn + £27.5mn + £3mn = £59.18mn 19.92   27.5   8.75   +  8.9%   +  8.9%   K 0 = 13.4%   59.18   59.18   59.18  3   = 10.4%. +  9.1%   59.18 

2. In the medium to long term the company will maintain a fixed capital structure and it is the overall return on this mix of capital that projects must be able to generate to allow the company to continue in existence. 3. (a) Project is small relative to the size of the company. (b) Project will be financed in such a way as not to change the capital structure. (c) Project has the same degree of systematic risk as that of the company’s existing cash flows. (d) All level-perpetuity cash flows. 4. Its WACC will reflect its average level of systematic risk, and not the particular level of systematic risk of any one of its individual business activities. Thus the WACC is an unsuitable NPVdiscount rate with which to evaluate projects in any one of the company’s areas of activity. 5. The CAPM produces an NPVdiscount rate which is tailor-made to the level of systematic risk of the individual project. The WACC only reflects the company’s existing, average systematic risk level. 6. Because companies, but not individual investors, can get tax relief on debt interest.

689

CHAPTER 18

7. Companies should finance themselves almost entirely with debt capital. 8. The gearing or leverage ratio is usually measured as VB  VE, although it is sometimes measured, as a percentage, as: VB ÷ V0.

Chapter 18

1. Given K E g = K E ug + ( K E ug – KD )

VB then VE

20% = K E ug = ( K E ug – 10%)

1 4

20% = K E ug + 0.25 K E ug – 2.5% 20% + 2.5% = 1.25 K E ug 22.5% = K E ug = 18%. 1.25 2. Again using the M and M equation: K E g = 18% + (18% – 10%)

3 = 22.8%. 5

In a no-tax world, the gearing ratio does not affect the WACC. So the change in capital structure will leave K0 unchanged: K 0 = 20% 

4 1 + 10%  = 18%. 5 5

K 0 = 22.8% 

5 3 + 10%  = 18%. 8 8

3. Sell your shares in company A for £100 cash and buy £25 of debt in company B and £75 of company B’s equity. 4. In arbitrage it is necessary to show the pure gain that can be made with no change in either business or financial risk. Business risk does not cause problems as the two companies involved in the arbitrage would be in the same business risk class (same asset betas). However, if a shareholder in a geared company wished to arbitrage into another company, care must be taken in order to preserve the existing degree of financial risk held. This is maintained by substituting home-made for corporate gearing. 5. Financial risk is borne by the shareholders in a geared company. It arises out of the fact that, because debt interest has to be paid in full before equity dividends can be paid, then shareholders are at risk that the company may have insufficient cash flow to pay dividends because it has all gone out in interest payments. This is financial risk. 6. As KD = rF = 10%, then we can assume βdebt = 0 Using CAPM, 20% = 10% + (15% – 10%) βequity therefore

20% – 10% = β equity = 2.0 (15% – 10%)

β assets = 2.0  7.

β assets = β assets 

2 1 + 0  = 1.33 3 3

7 V0 = 1.33  = 1.87. 5 VE

690

ANSWERS TO QUICKIE QUESTIONS

8. For two companies to be in the same business risk class, they should have the same asset betas and – in a no-tax world – the same WACC. As the WACCs of the two companies are not the same, we can conclude that they are not in the same business risk class: K 0 = 20% 

2 1 + 10%  = 16.67%. 3 3

K 0 = 20% 

5 2 + 10%  = 17.14%. 7 7

Alternatively, the asset beta of the question 6 company is 1.33. The asset beta of the question 8 company is:  2.0  5  +  0  2  = β assets = 1.43.  7 7 

Chapter 19

1. Using: K E g = K E ug + ( K E ug + K D )

VB (1 – TC ) VE

then: 1(1 – 0.35) 3 – 2.17%

25% = K E ug + ( K E ug – 10%) 25% = K E ug + 0.217 K E ug 25% = 2.17 = 1.217 K E ug

27.17% ÷ 1.217 = K E ug = 22.32%. 2.  VT  K 0 g = K E ug 1 – B C  , therefore: V0   1  0.35  K 0 g = 22.32%1 –   1+ 2  K 0 = 22.32%  0.8833 = 19.7%. 3. V0 g = VE ug + VBTC, therefore V0 g = £40mn + (£10  0.35) = £43.5mn. Shareholder wealth would have increased by the value of the tax shield: VBTC = £10mn  0.35 = £3.5mn. 4.  VT  K 0 g = K 0 ug 1 – B C  .  V0  5. The tax shield represents the present value of the tax relief on debt interest. It is the source of the increase in shareholders’ wealth that arises from increasing the level of gearing. 6. Debt capacity describes an asset’s ability to act as security for a loan. Specifically, an asset’s percentage debt capacity indicates the size of loan it would act as security for, expressed as a percentage of the asset’s worth. 7. Using: V0 g = VE ug + VBTC – E(b/c) then: £40mn = VE ug + (£10mn  0.35) – (0.05  £1mn) £40mn – £3.5mn + £0.05mn = VE ug = £36.55mn.

691

CHAPTER 21

8.  (1 – TC )(1 – TE )  V0 g = V0 ug + VB 1 – . 1 – TD  

Chapter 20

1.

Long-term debt and short-term debt – Cash balances. Shareholders’ funds However, the definitions of debt, etc. are not entirely unproblematical and thought needs to be given to items such as the capitalized value of leases.

2.

Earnings available for shareholders (after tax and interest). Number of shares in issue

3. Gearing ratios cannot be viewed as being high or low in absolute terms (within reason), but only in relative terms. Thus whether, at 50%, a company could be considered to have a high or low level of gearing would depend on the gearing ratio of other companies in its industry group. This is likely to be related to the business risk of the particular industry, cost structures, etc. 4. Financial risk is all systematic. It is not unsystematic. 5. There are two main factors: (a) the revenue sensitivity of the company; (b) the proportion of fixed to variable operating costs. 6.

Revenues – Variable operating costs. Earnings before interest and tax

7. DOG gives the percentage change in EBIT for every 1% change in revenues. 8. The greater the DOG value, the greater the systematic business risk of a company in comparison with similar companies. Thus the company with a DOG of 2.50 has a greater degree of systematic business risk than a similar company whose DOG value is only 1.50.

Chapter 21

1. Because the project’s NPV will add to the market value of the equity. 2. The return required from the project which purely reflects its systematic business risk (i.e. it assumes the project is all-equity financed). 3. What the NPV of the project would be, if it was all-equity financed. 4. An operating lease is essentially a marketing device to encourage sales and can be viewed as an operating cash flow. A financial lease is a particular method of project financing. 5. 5 2(1 – 0.35) β assets 1.45  + 0.25  = 1.20. 5 + 2(1 – 0.35) 5 + 2(1 – 0.35) 6. The equity beta reflects both the business and financial systematic risk. The asset beta purely reflects the business systematic risk. Therefore the financial systematic risk is reflected in a beta value of: 1.45 – 1.20 = 0.25. 7. Debt capacity concerns an asset’s ability to act as security for a loan. 8. The PV of the tax shield is based on debt capacity. Therefore the PV of the tax shield can be calculated as: £2500  0.10 = £250  0.35 = £87.50 = Annual tax relief PV of tax relief: £87.50 A5¬0.10 (1.10)–1 = £301.54.

692

ANSWERS TO QUICKIE QUESTIONS

Chapter 22

1. The dividend decision could be said to be irrelevant because it does not affect the overall return on the shares, but simply determines how that return is split up between dividend and capital gain. 2. Given the irrelevancy argument of the dividend decision, a company should invest as much of its retained earnings as possible in positive NPV projects. If all earnings cannot be utilized in this way, then the residual should be paid out as a dividend. In this way, shareholder wealth will be maximized. 3. If dividends are to be truly irrelevant, then companies must be indifferent between financing projects with retained earnings and financing via cash raised externally. For this to be the case, the company’s capital structure must also be an irrelevant consideration. 4. The bird-in-the-hand argument is that dividends, because they represent a certain current cash flow, are worth more than retained earnings which represent an uncertain future cash flow. Hence dividends are preferred to capital gains. 5. Investors with high marginal rates of personal tax are likely to prefer capital gains to dividends. There are two reasons. The first is that the marginal rate of capital gains tax is likely to be less than the marginal rate of tax on dividends. Secondly, the investor can control the time at which he takes his capital gains to give the greatest degree of tax efficiency. In contrast dividends must be taken when the company decides to pay them. 6. The clientele effect implies that companies should follow a consistent dividend policy to attract a specific clientele of investors. 7. There are two main classes of evidence. One is that companies seem reluctant to face a situation where they have to reduce dividends from one year to the next. Thus dividend growth lags behind earnings growth. The other evidence suggests that share prices react significantly to unexpected changes in dividends. 8. Given the evidence on signalling, to retain an expected dividend for capital investment purposes might be thought of as unwise. The market might interpret the decision as a signal about an unfavourable financial position. There is, however, evidence that so long as shareholders are properly prepared by the company, the withholding of a dividend for investment purposes can be seen as a good thing.

Chapter 23

1. Increased revenues, reduced operating costs, tax savings and financing savings. 2. By generating economies of scale and so lowering unit costs of production, increased efficiency through coordination of activities, use of complementary resources and the elimination of weak management teams. 3. No, unless it helps to reduce the volatility of the company’s cash flow and so lower its risk of debt default, resulting in increased debt capacity and a lower cost of debt capital. 4. Offer: One A share for four B shares. One A share is worth 480p ÷ 4 B shares = 120p bid value. Acquisition premium 120p – 100p = 20p per share or 20p/110p = 20%. 5. Post-acquisition A’s share price is likely to fall as a result of payment of the acquisition premium. However, synergy benefits might offset this effect. 6. The key advantages of an acquisition-led growth strategy are: speed, achievement of critical mass, use of company’s own shares to finance the strategy; allows the acquisition of the intellectual assets as well as the tangible assets of the business. 7. Because of the coinsurance effect. 8. It will harm the position of shareholders as it will result in a transfer of wealth from shareholders to debt holders.

693

CHAPTER 25

9. Two factors. One is the variability of the company’s cash flows – the greater the variability, the greater the potential for a reduction in variability, and so the greater the potential gain to shareholders. The other factor is the correlation coefficient of the two companies cash flows. The further away it is from +1, the greater will be the coinsurance effect and the greater the consequent gain to debt holders. 10. When A bids for B through a share-for-share exchange and B is valued on a lower PER than A. 11. The post-acquisition PER of the predator company will be an average of the pre-acquisition PERs of the two companies, weighted by their earnings. 12. They will try to: (a) argue that the value of the bid undervalues the company and (b) question the desirability of the terms of the offer. 13. If the post-acquisition market share is in excess of 25% and there are significant barriers to new entrants to the industry. 14. The value of the cash alternative will typically be around 10% below the value of the share-for-share exchange. The main reason for this is to account for the fact that the value of the cash offer is certain, whilst the value of the share-for-share exchange varies as the predator’s share price changes.

Chapter 24

1. The technique ignores the company’s intellectual capital. 2. The replacement cost of the assets of £9 million would be the most appropriate valuation on a ‘going concern’ basis. 3. You would look to adjust it for differences in gearing, earnings growth and company size. 4. As the company being valued is much smaller, it would be perceived as being more risky and so a lower PER should be used. 5. Its weighted average cost of capital: Ko. 6. Data identification: actually identifying the free cash flow. 7. Human capital, relationship capital and organizational capital. 8. It is trying to predict which companies are most likely to want to invest for future growth.

Chapter 25

1. Spot:

2.

3. 4. 5.

6. 7.

187.50 – 192.40

less premium: 1.20 – 1.10 Forward: 186.30 – 191.30 As the forward rate is at a premium, the first currency (¥) is appreciating against the second currency (£). Therefore, it follows that the £ must be depreciating against the ¥. £350 000  187.50 = ¥65.625mn cost. ¥3.5mn ÷ 191.30 = £18 296 receipt. $/£: 1.5280 E/£: 1.6240 1.6240 E/$: 1.5280 E/$ 1.0628 ¥187.50 × [1 – 0.03]4 × [1 + 0.10]2 = 200.85: Year 6 forward. Using the IRPT: 1.5815  US bills yield = 1.05   – 19.18%.  1.5210 

8. Using the PPPT:

694

ANSWERS TO QUICKIE QUESTIONS

Future $/£ spot: 9.

0.05 – 0.06 = –0.0094 1.06 1.5835(1 – 0.0094) = 1.5686 0.07 – 0.07 =0 1.07 1.5686(1 + 0) = 1.5686 0.09 – 0.05 = +0.038 1.05 1.5686(1 + 0.038) = 1.6282 Current $/£ spot Year 1 forecast Year 2 forecast Year 3 forecast

Chapter 26

1.

1.05  1.4550 = 1.4832. 1.03

Year 1

Year 2

Year 3 : : : :

1.5835 1.5686 1.5686 1.6282

Spot:

1.1020 – 1.1050

less Premium: Forward

180 165 1.0840 – 1.0885

$150 000 × 1.0885 = E163 275 payable in one month’s time. 2. (a) Forces of supply and demand for currencies from (i) ‘hot money’; (ii) international trade and investment. (b) Differences in interest rates between countries (IRPT). Movements in FXrates will take up differences in interest rates.Thus the currency of the country with high interest rates can be expected to depreciate. (c) Differences in inflation rates between countries (PPPT). Movements in FX rates will take up differences in inflation rates. Thus the currency of the country with higher inflation can be expected to depreciate. 3. (a) Sell E100 000, one month forward: E100 000 ÷ 1.0885 = $91 869 received in one month’s time.  0.10  (b) Borrow Ex. 1 + = E100 000 12   Ex = 99 173 Sell E99 173 at spot to give: E99 173 ÷ 1.1050 = $89 750 received now.  0.11  = 90 573 (c) $89 750. 1 + 12   As the forward market hedge produces $91 869 in one month’s time, the forward market hedge is best. 4. $ /£ =

9.8040 = 1.9216. 5.1020

5. Exercise of put option will generate $100 000 ÷ 1.80 = £55 555.56. (a) (i) A spot sale of $100 000 at 1.95 will produce only £51 282.05. Therefore, exercise option.

695

CHAPTER 26

(ii) A spot sale of $100 000 at 1.70 will yield: £58 823.53 therefore allow option to lapse and sell currency in spot market. (b) (i) A spot purchase of $100 000 at 1.95 will only cost £51 282.05. Therefore spot purchase $100 000 and then sell them through exercising the option to yield a profit of: £55 555.56 – £51 282.05 = £4273.51. (ii) A spot purchase of $100 000 at 1.70 would cost £58 823.53, therefore it is not worth exercising the option – allow it to lapse. 6. The deal will be done at the worst rate to forward sell the dollar: 1.7650. 7. (a) OTC options available in large numbers of currencies, traded currency options available only in major currencies. (b) OTC options available in cross currencies, traded currency options are only available against dollars. (c) OTC options are available for any reasonable exercise date; traded currency options only 3/6/9 months forward. (d) OTC option prices determined by bank. Thus a big company can use its financial strength to strike a better deal. (e) A very large transaction may be difficult to arrange on a traded currency option exchange (LIFFE). (f) OTC currency options are not dependent on the option exchange being open to deal or exercise. (g) OTC currency options are available for any amount of currency; traded currency options come in standardized amounts (i.e. £25 000 is the unit in sterling options). 8. (a) Target receipt: $526 000 ÷ 1.1050 = E476 081 Number of contracts: $526 000 ÷ 1.1060 =

E 475 587 = 9.51 → 10 contracts. E50 000

Buy or sell? • contract size currency: E (E50 000 per contract); • cash market: sell 526 000 and buy E; • therefore: buy futures. Hedge: buy 10 $/E futures for September at $1.1060. (b) In August, the company receives $526 000 which it sells at spot: $526 000 ÷ 1.0580 = Target receipt: Profit on target:

E497 164 E476 018 E 21 146

Close out the futures position: sell 10 $/E September futures at $1.0595. Loss on futures: Bought: 10 × E50 000 × 1.1060 = Sold: 10 × E50 000 × 1.0550 = Loss:

$553 000 cost. $529 750 receipt $ 23 250

Buying these $ at spot (to pay off the loss) costs: $23 250 ÷ 1.0550 = E22 038. Hedge efficiency:

E21146 = 95.9%. E22 038

9. (a) Buy $297 500 forward to October at a rate of $1.7000. Cost: $297 500 ÷ 1.7000 = £175 000.

696

ANSWERS TO QUICKIE QUESTIONS

(b) Number of futures:

£175 000 = 14 contracts. £12 500

Hedge position: sell 14 sterling December futures at $1.70 each. In October, close out the futures position by buying 14 December sterling futures contracts at the going price. At same time buy $297 500 on spot market to pay supplier. (c) Cost of paying invoice: $297 500 ÷ 1.7800 = £167 135. Outcome of futures market deals: Bought 14  £12 500  1.78 Sold 14  £12 500  1.70

= =

$311 500 Cost $297 500 Received $ 14 000 Loss

These dollars would then have to be bought at spot to pay off the loss: $14 000 ÷ 1.3800 = £7865 cost. Therefore the net cost of invoice: £167 135 + £7865 = £175 000, which is the same as the outcome of the forward market hedge.

Chapter 27

1. 2. 3. 4.

5.

6. 7. 8.

9. 10.

1 + inflation $ Forward rate $ inflation – £ inflation = or 1+ inflation $ Spot rate 1+ £ inflation 1.8420  1.25 –1 = 0.209 or 20.9% approx. 1.9050 1.9280(1 – 0.07)3 = 1.5508. $1.7940 less 150 $1.7790 = two-month forward rate (a) Project’s dollar cash flows are discounted by dollar discount rate to give a dollar NPV which is then converted at spot to a sterling NPV; or (b) project’s dollar cash flows are converted into sterling cash flows and then discounted at the sterling discount rate to give a sterling NPV. Because they may well affect the cash flow available to be remitted back to the parent. Property fixed assets and working capital finance in the overseas currency. Non-property fixed assets finance via the export of sterling. (a) Dividends; (b) interest; (c) management charges; (d) royalty payments; (e) transfer prices. The risk that the host government might adversely change the ‘rules of the game’ after the company have undertaken the investment. Economic risk describes the risk that a company is exposed to from unexpected FX rate movements and their resulting impact on the sterling worth of a foreign project’s cash flows.

697

Answers to Problems Chapter 2

Decision objectives problem 1

If shareholders want to ensure that their managers act in the best interests of shareholders, then it is vital that an attempt is made to bring managers’ own personal objectives into line with their shareholders’ objectives. This can be done through a variety of schemes designed to give the management an incentive to be wealth maximizers rather than just satisficers. One obvious approach would be to link management pay to profitability. This could be done either in absolute terms or in relative terms via earnings per share. However, this raises two problems. The first concerns the undoubted conflict that can occur between short-term and long-term profitability. It is difficult to devise an incentive scheme based on long-term profitability – managers are often in their positions for a relatively short time and want to be rewarded via an incentive scheme on a yearly basis – and therefore there is always the temptation to sacrifice long-term profitability for short-term profitability. (An example would be where the use of lower quality raw materials increases product contribution, but damages the longer-term reputation of the product.) The second difficulty with incentive schemes based on profit is that the level of profitability is not solely a function of managerial ability and effort. A large number of external macroeconomic factors that are outside the control of management – such as the rate of national economic growth – affect the profitability of the firm. A fundamental principle of any incentive scheme is that it should be related directly to effort and should not be affected by other factors. Thus, to reward management for a rise in profitability that is unconnected with their efforts – or to penalize them for a fall in profitability that has been caused by external economic influences outside their control – would mean that the incentive scheme was not performing its intended task. To avoid both these problems, it would be better to link the incentive scheme to the share price of the company (or, in the case of a company not quoted on a stock market, link the incentive scheme to a periodic private valuation of the shares). In so doing, this gets over the problem of a possible conflict between the long and short term (to some extent) as the share price should reflect all the implications of management’s actions. In addition, if the incentive scheme was linked to relative share price performance, this would then ensure that only the superior or inferior actions of the management’s performance would be rewarded or penalized. What is meant by linking the incentive scheme to relative share price performance is that the link should be between the performance (i.e. increase or decrease) in the company’s share price relative to the share price of its competitors. In this way macroeconomic influences on the company’s share price (which are largely beyond the control of the management) can be ‘screened out’ of the incentive reward system. In essence, a perfect incentive scheme would be almost impossible to devise in that it should try to take the following factors into account.

1. It should reward ability, not luck. 2. It should potentially form a significant part of the manager’s overall renumeration if it is to modify behaviour.

698

ANSWERS TO PROBLEMS

3. It should work both ways: rewarding good performance and penalizing poor. 4. It should take into account the maximum level of risk to which shareholders are willing to expose themselves. This is to avoid a potential problem (particularly with a ‘one-way’ scheme) where managers take very high risks in the hope that they will pay off and so they generate a large bonus, with the knowledge that if a risky venture fails, managers can always leave and find a job elsewhere (leaving the mess for the shareholders to clean up). 5. The incentive scheme should operate over the same time horizon as that used by shareholders for decision making, so as to avoid the problem (referred to above) of short term versus long term. 6. The scheme should be simple in structure and easy to understand by all parties and it should be cheap to monitor. 7. Management should not be able to artificially manipulate the scheme’s criteria.

problem 2

Strictly speaking, risk means measurable uncertainty. In other words, we cannot be sure what the outcome of a decision will be, but we have some estimate of likely outcomes derived from past experience. More generally, risk means that a decision – in this context, an investment decision – can result in a range of outcomes. We tend to concentrate on the risk of loss (downside risk) because it is this that hurts. Some investments are more risky than others because of the nature of the business involved. For example, an investment in a supermarket chain such as Sainsbury’s is less risky than an investment in a heavy engineering company such as Sheffield Forgemasters because the demand for the goods sold by the supermarket is less volatile. We will see later in the text that there are other things that determine total risk.

problem 3

We have seen that the assumed objective for commercial companies is the maximization of shareholder wealth. This, in turn, can be translated into meaning the maximization of the value of the company’s shares. When we turn to the situation of a state-owned company we could argue that this objective remains unchanged, but now we need to consider the ‘shareholders’ as meaning society at large. In such circumstances, the financial manager may be faced with the complication that financial decision making is not something that can be seen simply in terms of cash flow (or profits), but that the wider impacts of a decision have to be taken into account. An example might help to clarify this point. A commercial company would evaluate a decision to relocate its factory from a rural area to an urban area on the basis of the decision’s cash flow impact on the company. It may be that the urban location would be nearer to the raw material source and so produce a significant transportation cost saving. However from the viewpoint of a state-owned company, such a decision would be much more complex in that many more factors would have to be taken into consideration. These might include such things as the impact of the loss of jobs on the rural community and the increased congestion and pollution that might result from locating in the urban area. In conclusion therefore, although we might be able to say that financial managers in a state-owned company can be seen to have the same objective as their counterparts in a commercial organization, the efficient achievement of that objective is likely to require a much more complex and wide-ranging analysis.

Chapter 3

Traditional methods of investment appraisal problem 1

Given that the total outlay for the electronics project is £2 million, the project pays back a total of £1.6 million at Year 3 and £2.4 million at Year 4. Therefore, breakeven is achieved at approximately Year 3.5. The decision advice here is ambiguous.

CHAPTER 3

TRADITIONAL METHODS OF INVESTMENT APPRAISAL

699

On the one hand the project does not pay back within three years of the project’s starting date, while on the other hand it does pay back within three years (actually 2.5 years) of the completion of the capital expenditure. Property project The property project has a straight three-year payback and so just meets the decision criterion. Mining project Again, the decision advice is ambiguous. The project pays back its outlay in two years and so, on that criterion, is acceptable. However, a further outlay is required at Year 4. (b) The best choice here is not clear. One interpretation would be to accept the Electronics project as it pays back in 2.5 years as opposed to three years for the Property project. An alternative interpretation would be that the Property project pays back by Year 3 while the Electronics project pays back by Year 3.5. Therefore, the former should be accepted. A further factor to consider is the post-payback cash flows. Post-payback, the Electronics project generates a further £1.2 million. The Property project only generates a further £400 000 post-payback. Quite simply, there is no clearly correct decision using payback. (c) The Mining project, on one basis, has a payback of two years against a payback of three years for the Property project. However, the Mining project requires an extra £0.75 million outlay and only generates a net £0.05 million post-payback. In contrast, the Property project does not require any further capital expenditure and generates £0.4 million post-payback. Again the correct decision advice is unclear. (d) The payback decision criterion should really take the project risk into account. The more risky the project (that is, the more uncertain its expected future cash flows) the shorter should be the maximum permitted payback. Almost certainly, these three projects are of unequal risk. Clearly the property project, with its rent-paying tenant already installed, has much less uncertain cash flows than the other two projects. Thus the company’s use of the same decision criterion for all three divisions does not appear sensible.

problem 2 (a) Payback calculation (excluding working capital) Year 0 1 2 3 4

Net cash flow (200 000) 50 000 60 000 110 000 20 000   80 000 

Scrap value

Therefore the project has less than a three-year payback and is acceptable. However, it is debatable whether, in this example, working capital should be excluded from the analysis as it is not fully recovered. If it were to be included, then the analysis would be:

700

ANSWERS TO PROBLEMS

Year 0

Net cash flow  (200 000)   (50 000) 50 000 60 000 110 000 20 000 80 000   40 000 

1 2 3 4

Scrap value Working capital recovery

The project now takes longer than three years to pay back and should not be accepted. ROCE calculation Annual depreciation: (200 000 – 80 000) ÷ 4 = 30 000 Year 1 2 3 4

Net cash flow 50 000 60 000 110 000 20 000

– – – – –

Depreciation 30 000 30 000 30 000 30 000

= = = = =

‘Profit’ 20 000 30 000 80 000 (10 000)

Total profit

=

120 000

Average annual profit = 120 000 ÷ 4 = 30 000 Return on initial capital employed:

30000 = 0.12 250000

As the project only has a ROCE of 12%, against a decision criterion of 13%, it is unacceptable. Advice The project does not meet the firm’s ROCE criterion and, on one interpretation, nor does it satisfy the payback criterion. Therefore, on balance, the advice would be to reject. (b) Normally, working capital (WC) is excluded from the payback analysis on the basis that it is automatically paid back whenever the project is terminated: the stocks are eliminated and the debtors pay up. However, in the project currently under consideration, working capital is not fully recovered. In such circumstances there is a strong argument for including working capital expenditure (i.e. expenditure on current assets) along with expenditure on fixed assets (capital expenditure) in the payback calculation. (c) In many ways, the return on average capital employed is a more sensible measure of profitability than the return on initial capital employed. Average annual profits are compared to the average capital employed in generating those profits. The average annual profit is £30 000. The average capital employed is given by Capital expenditure   Scrap value      + +  +   WC expenditure  WC recovered  = 2 (200 000 + 50 000 ) + (80 000 + 40 000 ) = £185000 2

CHAPTER 4

701

INVESTMENT–CONSUMPTION DECISION MODEL

Therefore the return on average capital employed is £30 000 = 0.162 or 16.2% £185 000 On this basis, given the firm’s decision criterion, the project should be accepted. I hope that I get that promotion! (d) There are two major drawbacks with the ROCE/ARR as an investment appraisal decision rule. One is that it ignores the time value of money. The other is that it tries to use a reporting concept – accounting profit – in a decision-making context. In contrast, the payback technique does use a cash flow analysis of the decision, which is correct. A capital investment decision is an economic, resource allocation decision and the economic unit of account in such circumstances is cash or cash flow. Thus, between the two appraisal techniques, payback is to be preferred, even though it too ignores the concept of the time value of money. However, this criticism can easily be overcome by using a variation on payback: discounted payback – see Chapter 5.

Chapter 4

Investment–consumption decision model problem 1 (a) Fig. P4.1 shows the physical investment line facing the firm. (b) From the graph in (a) it can be seen that the point of tangency between the physical investment line (PIL) and the financial investment line (FIL) indicates the firm’s investment decision. At t0, the firm will undertake project I and II only, and reject project III. This will result in a cash flow of £200 at t0 and a cash flow of £420 at t1. (c) The graphical decision in (b) is such because projects I and II both give a return in excess of the market return of 8%, while project III gives a return that is less than the market return:

FIG. P4.1

£ t1

630

III 420 I 300

FIL II PIL 200

300

(1.08) 500

£ t0

702

ANSWERS TO PROBLEMS

Market return = 0.08 Project I: (120/100) – 1 = 0.20 Project II: (300/200) – 1 = 0.50 Project III: (210/200) – 1 = 0.05 (i)

If the market interest rate moved to 4%, then all three projects would be accepted. (ii) If the market interest rate moved to 25% then only Project II would be accepted. (iii) If the market interest rate moved to 20% then Project II would be accepted and Project III would be rejected. However, the firm would be indifferent between accepting or rejecting Project I as it gives the same return as the market. (d) The new project produces a return of 32% (330/250) – 1 = 0.32. Thus the firm would now undertake Projects I, II and IV. However this would require a total investment of £550 at t0. As the firm only has £500 available at t0, it should borrow the additional £50 required at the market interest rate of 8%. If the firm cannot borrow additional resources, or does not wish to do so, then the optimal investment decision is to accept Projects II and IV and 50% of Project I, as Fig. P4.2 shows. FIG. P4.2

£ t1

960

III 750 I 660

IV

300

II

–250

–50

0

50

300

500

£ t0

CHAPTER 5

Chapter 5

703

THE DISCOUNTED CASH FLOW APPROACH

The discounted cash flow approach problem 1 (a) NPV calculation (£mn) Capital expenditure – 1.8

Year 0 1 . . . . 6 7 . . . 10

Net revenue + 0.5 . . . . . + 0.5 + 0.3 . . . + 0.3

+ 0.5 –6

–10

–1.8 + 0.5A ¬6 0 .18 + 0.3A ¬4 0 .18 (1.18) + 0.5 (1.18)

–1.8 + (0.5 × 3.4976) + (0.3 × 2.6901 × 0.3704) + (0.5 × 0.1911) –1.8 + 1.7488 + 0.2989 + 0.0955= + £343 200 NPV. (b) ROCE calculation (£mn) Depreciation: Annual profit:

(1.8 – 0.5) ÷ 10 = £0.13mn/year 0.5 – 0.13 = £0.37 mn/year, Years 1 to 6 0.3 – 0.13 = £0.17mn/year, Years 7 to 10 Average annual profit: [(0.37 × 6) + (0.17 × 4)] ÷ 10 = £0.29 million 1.8 + 0.5 = £1.15 million 2 0.29 = 0.252 or 25.2 % Return on average capital employed = 1.15 0.29 Return on initial capital employed = = 0.161 or 16.1% 1.8 Average capital employed:

(c) The project pays back its outlay on capital expenditure after 3.6 years. (d) Report to the chairman Trionym PLC Subject: Chocolate-coating machine decision It is advised that the capital expenditure proposal should be evaluated on the basis of the net present value (NPV) decision rule. This decision rule, given certain assumptions outlined below, will ensure that projects are selected only if they lead to an increase in the market value of the company’s shares. On this basis, the chocolate-coating machine currently under consideration should be undertaken as it has a positive NPV of £343 200. This indicates that, as a result of acceptance, the total market value of Trionym’s equity should rise by this amount (and so increase shareholders’ wealth). The NPV investment appraisal decision rule can be justified on the basis of a number of interconnected reasons. First, it evaluates investment proposals on the basis of cash

704

ANSWERS TO PROBLEMS

flow, rather than profitability. This is important because a capital investment decision is an economic (or resource allocation) decision and the economic unit of account is cash, not accounting profit. This is because it is cash, not profit, which gives power to command resources. Accounting profit is not, in fact, a decision-making concept at all. It is a reporting concept, used to report on the outcome of investment (and other) decisions. The second reason to justify the use of NPV is that it takes account of the ‘time value’ or ‘opportunity cost’ of cash through the discounting process. Money has a time value in the sense that a rate of interest or rate of return can be earned by investing money (the return expected from such an investment being determined by the risk involved). Therefore, when money is invested in a particular project, the opportunity cost or the rate of return available elsewhere from a similar risk investment that is forgone must be taken into account. This is achieved through the discounting process used by the NPV technique. As a result, the magnitude of the NPV indicates how much extra return that particular project produces (in current terms) over and above the return available elsewhere from a similar risk investment. Therefore, by having a £343 200 positive NPV, when discounted at 18%, the chocolate-coating machine can be said to produce an extra return of that amount, over and above the 18% return available elsewhere. This leads directly on to the third justification for the use of the NPV decision rule. The magnitude of the NPV indicates the increase in the company’s total equity market value – or the increase in shareholder wealth – that will arise from the project. Thus the decision rule can be seen to link in directly with the company’s overall objective. However, there are two important reservations that should be mentioned about the advice given above. The first is that it is assumed that the company is not facing any form of effective capital expenditure constraint (either internally or externally imposed). The second is that an 18% discount rate does correctly reflect the project’s risk and so represents the return available elsewhere on the capital market from an investment with a similar degree of risk. (e) Discounted payback (£mn)

Year 0 1 2 3 4 5 6 7 . .

Capital Net expenditure cash flow – 1.8 + 0.5 + 0.5 + 0.5 + 0.5 + 0.5 + 0.5 + 0.3 . .

× × × × × × × ×

18% Present value discount cash flow 1.0 = 0.8475 = 0.7182 = 0.6086 = 0.5158 = 0.4371 = 0.3704 = 0.3139 =

– 1.8 + 0.4237 + 0.3591 + 0.3043 + 0.2579 + 0.2185 + 0.1852 + 0.0942. . .

Discounted payback: 6.5 years (approx.) Memo to the chairman: Discounted payback (i) Discounted payback is a ‘truncated’ version of NPV. In other words, instead of calculating a project’s NPV over the whole of its expected life, an artificial time horizon (or cut-off point) is applied: the maximum acceptable payback time period. Under these circumstances, the project is undertaken only if it manages to produce at least a zero NPV by the cut-off point.

CHAPTER 5

705

THE DISCOUNTED CASH FLOW APPROACH

(ii) In the case of the chocolate-coating machine, given a five-year payback criterion, the project will not produce a positive NPV at the end of five years: only after 6.5 years will it reach the zero NPV breakeven point. (iii) Discounted payback has all the advantages of the normal NPV technique, but with one important addition. Many companies feel that they only have a limited ability to forecast accurately future project cash flows and so are uncomfortable at making a decision on a project based on forecasted cash flows over the whole of its life, when some of the estimated cash flows in later years may be more like guesses rather than estimates. Discounted payback can be used to acknowledge this reality by placing on the project’s evaluation an artificial time horizon, which may be used to indicate the perceived limits of the management’s forecasting ability. (iv) However, this additional advantage of discounted payback is also a disadvantage. The technique does not take into account project cash flows that arise outside the maximum acceptable payback criterion. Thus the decision-making process may be seriously biased towards shorter-term rather than longer-term projects. (f) Decision criteria The main problem with the current investment appraisal procedures of Trionym plc is that the decision rules can give conflicting advice. Under these circumstances, it is not at all clear how the company would resolve such conflicts nor is it clear whether such a resolution would necessarily lead to optimal decisions being taken.

problem 2 (a) Calculations Project 1 £000

Project 2 £000

(a) (i) Accounting rate of return Cash flow – Depreciation (see below)

200 100

500 263

= Average accounting profit

100

237

Initial investment – Scrap value

556 56

1 616 301

Total depreciation

500

1 315

÷5 = Annual depreciation

100

263

Average book value of investment 556 + 56 2

306

1616 + 301 2 (ii)

Accounting rate of return Net present value Year Initial outlay 1–5 200 × 3.4331 500 × 3.4331 5 Residual value 56 × 0.5194 301 × 0.5194

958.5 32.7% (556) 687

24.7% (1 616) 1 717

29 156

706

ANSWERS TO PROBLEMS

Net present value

+ 160

+ 257

(iii) Internal rate of return Project 1 At 14% NPV = + 160 At 20% NPV = + 64 IRR = Project 2 At 14% At 20% IRR =

 160  14% +  × (20% –14%) = 24% 160 – 64  NPV = + 257 NPV = + 0 20%

(iv) Payback period Annual cash flows Initial investment Payback period in years Project (i) Accounting rate of return (ii) Net present value (£000s) (iii) Internal rate of return (iv) Payback period (years) Rankings (i) (ii) (iii) (iv)

Accounting rate of return Net present value Internal rate of return Payback period

200 556 2.8 Project 1 32.7% + 160 24% 2.8

500 1 616 3.2 Project 2 24.7% + 257 20% 3.2

Best project 1 2 1 1

(b) On the basis of the calculations made in answer to part (a), Congo Ltd should undertake Project 2. In doing so they would be following the advice given by the NPV decision rule and would be rejecting the advice given by the other three decision criteria. The NPV decision advice should be accepted because it provides the correct decision advice, given a perfect capital market. Project 2 will lead to the greatest increase in shareholder wealth as it has the largest positive NPV. All three of the other investment appraisal techniques can be faulted and so give unreliable decision advice. (i) The ARR evaluates the projects in percentage terms and so ignores differences in outlay. It does not use any discounting process and so ignores the time value of money. It evaluates the projects on the basis of their profitability, which is incorrect. Accounting profit is a reporting concept, not a decision-making concept. (ii) The IRR method cannot be relied upon to give the correct decision advice in a situation such as this which involves mutually exclusive projects. This is for two reasons. One is because, like the ARR, it evaluates on the basis of a percentage and so ignores differences in project outlay. The other is that it employs an incorrect assumption about the rate at which project-generated cash flows are reinvested. (iii) The payback method can be criticized on two grounds. First, as discounted payback has not been used, the time value of money has been ignored. Secondly, the approach does not evaluate project cash flows that lie beyond the project payback time period.

CHAPTER 6

NET PRESENT VALUE AND INTERNAL RATE OF RETURN

707

Chapter Chapter66 Net Netpresent presentvalue valueand andinternal internalrate rateofofreturn return problem problem11 (a)

Type A At 4% NPV = +558 (approx.) At 20% NPV = + 47 (approx.)  558  IRR = 4% +   (20% – 4%)= 21.5% 558 – 47 

Type B At 4% NPV = +849 (approx.) At 20% NPV = –86 (approx.)  849  IRR = 4% +   (20% – 4%)= 18.5% 849 – 86  Differential cash flow (A – B) +1 000 –290 A¬ 5 i = O NPV At 4% NPV = –291 At 20% NPV = +133  −291  IRR = 4% +   (20% – 4%)= 15.0%  −291 + 133  The decision rule is that: If the IRR of the differential cash flow is less than the ‘hurdle rate’, accept the project with the greatest IRR; and if the IRR of the differential cash flow is greater than the hurdle rate, accept the project with the smallest IRR. In this case, Saucy Steamboats’ hurdle rate is 10%. As the IRR of the differential cash flow is 15.0% then the project with the smallest IRR – the Type B boat – should be accepted. (b) There are a number of problems concerning the use of the internal rate of return decision rule for investment appraisal purposes. A problem that is common to both decisions involving single independent projects and decisions involving mutually exclusive projects is that of multiple internal rates of return. Any investment project’s cash flow is likely to have multiple internal rates of return if the cash flow is of a non-standard form, i.e. where the cash flow contains more than one change of sign. As a rule of thumb, a cash flow will have as many IRRs as it has changes in sign. One particular non-standard cash flow is extremely common because of the fact that tax is chargeable 12 months in arrears; after-tax project cash flows will then typically exhibit the signs: – + + + + … + + – – + + + + … + + –

In this cash flow there are two changes in sign and so two IRRs can be expected. The problem is that in such circumstances, the IRR decisions rules break down absolutely and cannot be operated reliably. Another serious problem with the IRR is confined to decisions concerning mutually exclusive projects. Under these circumstances the ‘normal’ IRR decision rule – i.e. accept whichever alternative project produces the largest IRR (given that it exceeds the cut-off rate) – cannot be relied upon to give the correct investment decision advice. The problem is caused by the fact that the IRR calculation for a project implicitly assumes that the project cash flows possess an opportunity cost equal to the IRR of the generating project.

708

ANSWERS TO PROBLEMS

Thus, when comparing mutually exclusive projects with different IRRs, the implicit assumption becomes inconsistent and, as a result, the decision rule fails. A modified decision rule can be used (as in (a) above) but the rule is really no more than a rule of thumb with very little underlying logic to sustain it. In contrast, given the circumstances surrounding Saucy Steamboats Ltd, the net present value decision rule evades these difficulties and can be relied upon to produce correct investment decision advice, given the assumption that the discount rate used reflects the project’s risk level correctly.

problem problem22 (a) £000s Project A Discount rate 4% 8% 12% 18%

NPV +21 +14 + 7 – 2

Project B Discount rate 4% 8% 12% 18%

NPV +26 +14 + 3 –10

(b) From the graph shown in Fig. P6.1, the internal rate of return of Project A is approximately 17% and the internal rate of return of Project B is approximately 13%. (c) Based on the information given and the graph, the following advice should be given to Mr Cowdrey: (i) if his discount rate is 6%, Project B should be undertaken, because at a 6% discount rate the NPV of Project B is higher than for Project A; (ii) if his discount rate is 12%, Project A should be chosen, because the NPV of Project A is higher than the NPV for Project B. (d) The following additional information would be useful to Mr Cowdrey in making the decision: (i) The degree of accuracy of the cash flow estimates. (ii) Tax implications and how these might affect the project’s cash flows. (iii) Riskness of each project. (iv) Effects, if any, of each project’s acceptance on the overall business risk. (v) Existence of other projects not included in the current appraisal. (vi) More general social effects that acceptance of the project would impose on the firm, its employees and its surrounding environment. (vii) Cut-off rate required by Mr Cowdrey. (e) The decision rule under the NPV method is to accept all projects that yield positive NPVs when discounted at the specified discount rate. Under the IRR method, all projects with IRRs that exceed the required rate should be accepted. Both methods give the same decision advice in simple accept/reject situations. However, we have argued that, theoretically, the NPV method should be preferred. The NPV approach is more consistent with the assumed objective of maximization of shareholders’ wealth than the IRR method. In a simple accept/reject situation, knowledge of the project’s NPV is sufficient to ensure that the shareholders’ wealth will be maximized when the present value of the future stream of cash flows received by the shareholders is maximized. However, knowledge of a project’s IRR is not in itself sufficient for optimal investment decisions, nor is it necessary; the IRR method makes economic sense only because in simple accept/reject situations it gives the same decision as the NPV method.

CHAPTER 6

NET PRESENT VALUE AND INTERNAL RATE OF RETURN

FIG. P6.1

709

+NPV (£000) 28 26 24 22 20 18 16 14 12 10 8 6 13%

4

17%

2 0 –2 –4

4

8

12

18

Discount rate % Project A

–6 –10 –14

Project B

–NPV (£000)

The two methods may give different decision advice when choosing between two mutually exclusive investments. This difference stems from the different assumptions made regarding the reinvestment rates of intermediate cash flows. The NPV approach assumes that intermediate cash flows can be reinvested at a rate of interest equivalent to that used as the discount rate. The IRR method assumes that these can be reinvested and earn a return equal to the project’s IRR. Of the two, it appears that the NPV assumption is more realistic, given a perfect capital market. When viewed in a ranking situation, the NPV approach assumes that the discount rate reflects the opportunity cost of capital. The opportunity cost concept under the IRR method is less valid because of the IRR reinvestment assumption. In fact, the actual opportunity cost of funds does not even enter into the IRR method when the method is used for ranking. The NPV method gives an absolute measure that may be more meaningful than the average concept used in the IRR method. Also, the NPV method is generally more flexible. It can be easily adjusted to include multiple discount rates over time. Multiple rates of return are possible under the IRR method. The presence of multiple rates of return makes interpretation difficult, and, for some patterns of cash flows, under the IRR method it may not be possible to derive a meaningful IRR at all. All that said, however, it is often argued that the theoretical difficulties of the IRR method are outweighed by its practical advantages. For instance, being based on a rate of return concept, the method is more easily understood and accepted by managers. It is also argued that the method obviates the decision maker from having to work out the firm’s

710

ANSWERS TO PROBLEMS

discount rate, which in itself poses a number of problems. The NPV method, on the other hand, requires the decision maker to determine the discount rate to be used from the start.

problem 3 (a) As funds are readily available at the market interest rate of 10%, you should accept all projects having a positive net present value (NPV) when discounted at 10%. Justification for the NPV rule is based on two main assumptions: (i) that the company’s objective is to maximize the wealth of its shareholders, as measured by the current market value of its ordinary shares; (ii) that the discount rate used (the company’s cost of capital) reflects the return available elsewhere on similar-risk investments. If these assumptions hold, the net present value of a project measures the amount by which the wealth of a company’s shareholders will change if the project is accepted (an increase if the NPV is positive and vice versa). The NPVs of the four projects under consideration are NPV Project 1 Project 2 Project 3 Project 4

–2 500 + 1 000 A¬3 0 .10 –2 500 + (1 000 × 2.4869) –1 –1 000 + 100 (1 + 0.1) –1 000 + (100 × 0.9091) –1 –1 000 + 800 (1 + 0.1) –1 000 + (800 × 0.9091) –3 –4 000 + 5 000 (1 + 0.1) –4 000 + (5 000 × 0.7513)

= – 13 –2 + 1 400 (1 + 0.1) + (1 400 × 0.8264) = + 248 –2 + 600 (1 + 0.1) + (600 × 0.8264) = + 223 = – 243

(Reject) (Accept) (Accept) (Reject)

(b) The decision rule would then be: accept whichever project has the largest positive NPV. This is Project 2. The decision rule does not have to take account of (i) differing project lives or (ii) differing capital outlays because it is assumed that (i) all considerations of risk are allowed for in the discount rate and (ii) there is a perfect capital market. (c) Project 2 10% discount rate NPV +248 20% discount rate NPV + 55  248  IRR = 10% +   (20% – 10%)=23% 248 – 55  Project 3 10% discount rate NPV +223 20% discount rate NPV + 83  223  IRR = 10% +   (20% – 10%)=26% 223 – 83  It would not be valid to use the normal IRR decision rule for mutually exclusive projects: accept whichever project has the largest IRR, given that it is greater than the cut-off rate. This is because the IRR decision rule makes an incorrect assumption concerning the opportunity cost of project-generated cash flows which makes its decision advice unreliable when faced with mutually exclusive projects. The alternative decision rule, making use of the IRR of the differential cash flow is: (i) If IRR (differential cash flow) > cut-off rate, accept the project with the smallest IRR.

CHAPTER 6

711

NET PRESENT VALUE AND INTERNAL RATE OF RETURN

(ii)

If IRR (differential cash flow) < cut-off rate, accept the project with the largest IRR. Therefore: Project 2 – 1 000 + 100 +1 400 + 500 23 % + 248

Net undiscounted cash flow IRR NPV10%

Project 3 – 1 000 + 800 + 600 + 400 26% + 223

2 minus 3 0 – 700 + 800 14 1% 3

(The IRR of the incremental cash flow is found by solving: −700 800 + = 0 NPV 1 + i (1 + i )2 Multiplying each side by (1 +i): 800 =0 1+ i 800 = 700 (1 + i) 800 – 700 = 700i

−700 +

100 = i = 0143 . , or14 13 %) 700 As the IRR (2 minus 3) > 10%, accept the project with the smallest IRR (Project 2) which is, of course, the project with the largest positive NPV. The result is shown graphically in Fig. P6.2. (d) The principal reasons for the managerial preference for IRR over NPV are as follows. (i) Management are familiar with a decision rule that uses a percentage rate of return. FIG. P6.2 +NPV +500

+400 +248 +223

0

10 141/3

23

26

–NPV

Discount rate % 3

2

712

ANSWERS TO PROBLEMS

(ii)

With IRR, the discount/cut-off rate does not have to be specified in the calculations, but only at the time of the final decision. Even then, an exact cut-off rate does not need to be specified. The decision can be made in reply to the question: Is this project’s IRR sufficiently high to make it acceptable? (iii) Many managements (incorrectly) see a link between a project’s IRR, current market interest rates and accounting rates of return. (iv) Many managements believe (incorrectly) that the capital rationing problem can more easily be overcome by using IRR instead of NPV (see Chapter 8). Using IRR instead of NPV may well lead to the wrong project being selected when a mutually exclusive choice has to be made among alternatives, but it should not lead to a project being accepted that has a negative NPV (i.e. the IRR decision rule will help select investments that will increase shareholder wealth, but not necessarily maximize it). Of course, this ignores the problem of multiple IRRs where such a choice is possible, but probably unlikely. Furthermore, both DCF methods only evaluate a project in terms of their quantifiable financial effects. Most managements have a high level of qualitative factor inputs into a decision, such as strategic reasons or competitiveness.

Chapter 7

Project cash flows problem 1

In assembling the project’s cash flows the following should be ignored.

(i) (ii)

depreciation – this is a non-cash cost and so is irrelevant to the analysis; allocated fixed overheads – on the assumption that these represent non-incremental cash flows; (iii) interest payments (plus their associated tax relief) – financing charges are never included in project cash flows, but instead they are implicitly reflected in the required after-tax rate of return/discount rate, which in this example is 10%; (iv) dividend payments – these too are part of the financing charges and are never explicitly included as part of a project’s cash flows. Writing-down allowances

£1 200 000 300 000 900 000 225 000 675 000 168 750 506 250 126 562 379 688 94 922 284 766 200 000 84 766

×

0.25 =

£300 000

×

0.4

=

Tax credit Year £120 000 1

×

0.25 =

£225 000

×

0.4

=

£90 000

2

×

0.25 =

£168 750

×

0.4

=

£67 500

3

×

0.25 =

£126 562

×

0.4

=

£50 625

4

×

0.25 =

£94 922

×

0.4

=

£37 969

5

= =

Sale proceeds Balancing allowance × 0.4 = £33 906

Tax on trading profits/year Sales £1 400 000 Materials (300 000) Labour (500 000) Taxed profit 600 000 Tax at 40% 240 000

Net trading cash flow

CHAPTER 7

713

PROJECT CASH FLOWS

Project cash flow (£000s) Year Machine Machine Trading Tax on Working cost tax c/f trading capital relief 0 (1200) (150) 1 120 600 2 90 600 (240) 3 67.5 600 (240) 4 50.625 600 (240) 5 200 37.969 600 (240) 150 6 33.906 (240) NPV calculation Year Net cash flow × 10% Discount factor = 0 (1 350 000) × 1 = 1 720 000 × 0.9091 = 2 450 000 × 0.8264 = 3 427 500 × 0.7513 = 4 410 625 × 0.6830 = 5 747 969 × 0.6209 = 6 (206 094) × 0.5645 =

Net project cash flow = = = = = = =

Net present value +

(1 350) 720 450 427.5 410.625 747.969 (206.094)

PV cash flow (1 350 000) 654 552 371 880 321 181 280 457 464 414 (116 340) £ 626 144

problem 2 Contract 1: PV costs (£000s) Special materials Other materials Skilled labour Unskilled labour

0 30

Total direct costs Variable overheads (6% direct costs) Total net cash flows Discount factors

30 1

1

2

100 42 58.8

110 46.2 64.7

200.8

220.9

12.05

13.25

212.85

234.15

0.9091

0.9091 × 0.8621

30

193.50

183.51

0

1 120 42 66.15

2 132 46.2 72.75

Direct costs Variable overheads (6% direct costs)

228.15 13.7

250.95 15.05

Total net cash flows Discount factors

241.85 0.9091

266.0 0.9091 × 0.8621

PV cash flows

219.87

208.47

PV: £407.01 Contract 2: PV costs (£000s) Other materials Skilled labour Unskilled labour

PV: £428.34

714

ANSWERS TO PROBLEMS

NPV of Contract 1 produced in-house +700 000 – 407 010 = +£292 990 NPV NPV of Contract 2 produced in-house +680 000 – 428 340 = +£251 660 NPV NPV of Contract 1 when subcontracted –1 PV cost: 245 000 + 245 000(1.10) Revenue

= =

–467 730 +700 000 +£232 270 NPV

NPV of Contract 2 when subcontracted –1 PV cost: 265 000 + 265 000(1.10) Revenue

= =

–505 911 +680 000 +£174 089 NPV

The possible combinations open to Sparrow Ltd are: Produce Contract 1 + 292 990 NPV Subcontract Contract 2 + 174 089 NPV +£467 079 Total NPV Produce Contract 2 Subcontract Contract 1

+ 251 660 NPV + 232 270 NPV +£483 930 Total NPV

Therefore the best option, given the constraints, is to produce Contract 2 in-house and subcontract Contract 1. This results in the greatest amount of aggregate NPV.

Chapter 8

Capital rationing problem 1 (a) The conflict arises from the differing assumptions that the NPV and IRR methods make about the opportunity cost (or reinvestment rate) of generated cash flows. Given a perfect capital market, the NPV’s assumption that their opportunity cost is equal to the market interest rate (for that level of risk) is correct. The IRR’s assumption that their opportunity cost is equal to the IRR of the project which generates the cash flows is incorrect. Therefore the company should accept the alternative with the largest positive NPV: the electrically powered vans. This selection will provide the greatest increase to shareholder wealth. (b) Given that the situation is one of single-period capital rationing, the capital allocation problem can be solved using benefit–cost ratios: Project A B C D Petrol fleet (P-F) Electrical fleet (E-F)

Benefit–cost ratio 60/50 = 1.2 40/80 = 0.5 84/140 = 0.6 32/80 = 0.4 80/100 = 0.8 110.5/170 = 0.65

Ranking 1 5 4 6 2 3

CHAPTER 8

715

CAPITAL RATIONING

As projects P-F and E-F are mutually exclusive (the two van fleets) two alternative combinations of projects have to be evaluated, each containing one of the mutually exclusive alternatives: Project A P-F C

Outlay at t0 50 100 140 290

Project A E-F 0.5C

Outlay at t0 50 170 70 290

NPV: 60 + 80 + 84 = +£224 000

NPV: 60 + 110.5 + 42 = £212 500

Therefore, projects A, C and the petrol-powered van fleet should be accepted as this will provide the largest total of positive NPV, given the capital constraint. (c) If the delivery fleet project were delayed by one year, their NPVs become: P-F E-F

£80/1.15 £110.5/1.15

= =

£69 565 £96 087

Clearly, the electrically powered van fleet is the best alternative. Therefore, excluding the above from the capital rationing problem: Project A C B 1D 4

Outlay at t0 50 140 80 20 290

NPV: 60 + 84 + 40 + 8 = £192 000

Hence, the total NPV would be: £192 000 + £96 087 = +£288 087, which represents a gain of £64 087 over the original solution. This is the additional gain in shareholder wealth.

problem 2 (a) Accept all projects with NPV ≥ 0. Project A B C D E

NPV (£000s) +58.5 +39.3 –20.7 +109.1 +38.8

(b) Using benefit–cost ratios:

   Therefore, accept A, B, D and E.   NPV Rationed investment

716

ANSWERS TO PROBLEMS

£000s A + 58.5/100 = 0.585 3 B + 39.3/50 = 0.786 2 C – 20.7/100 = –0.207 5 D + 109.1/100 = 1.091 1 E + 38.8/200 = 0.194 4 £225 000 available, therefore accept D, B, 75% of A.

   Ranking  

(c) The two alternative project combinations are: D, B, 37 12% of E

£000s 109.1 + 39.3 + 14.55

D, A, 12 12% of E

109.1 + 58.5 + 4.85

=

£000s 162.95 NPV

=

172.45 NPV

1 2

Therefore the best combination is D, A and 12 % of E. (d) Examining all the different ‘whole project’ combinations shows that A and D produce the maximum amount of total NPV. (e) Recalculating the benefit–cost ratios, now using t1 outlays: A B C D E

+58.5/100 +39.3/100 –20.7/— +109.1/50 +38.8/50

= = = = =

0.585 0.393 — 2.182 0.776

3 4 — 1 2

   Ranking  

If project C is accepted, this makes an extra £100 000 of investment finance available at t1; however, in doing so, a negative NPV (–£20 700) is incurred. Thus we will have to examine whether the extra +NPV generated by the additional investment finance outweighs this cost. £150 000 of capital: accept D, E and 50% of A. Total NPV = £177 150. £150 000 + £100 000 of capital: accept D, E, A, 50% of B and C. Total NPV = £205 350. This is the optimal combination. (f) Let a equal the proportion of Project A undertaken, b be the proportion of Project B undertaken, c be the proportion of Project C undertaken, d be the proportion of Project D undertaken, and e be the proportion of Project E undertaken. Objective function 58.5a + 39.3b – 20.7c + 109.1d + 38.8e Max Constraints 100a + 50b + 200c + 100d + 200e 100a + 100b + 50d + 50e a, b, c, d, e

ⱕ 225 ⱕ 150 + 100c ⱕ1

Non-negativity conditions a, b, c, d, e ≥ 0

ⱕ 1a, b, c, d, e

CHAPTER 9

717

SIMPLE RISK TECHNIQUES

(g) Year 0 Year 1 Year 2

DV of cash

+

10% Discount factor

=

Total opportunity cost

0.92 0.84 0

+ + +

1.0 0.9091 0.8264

= = =

1.9200 1.7491 0.8264

The circumstances when a deposit account facility would be worthwhile would be when £1 × 1.9200 < £(1 + i) × 1.7491. (h) £1 × 1.7491 = £1(1 + i) × 0.8264 1.7491 = 0.8264 + 0.8264i 1.7491 – 0.8264 = 0.8264i 1 ⋅ 7491 – 0.8264 0.8264

= i = 1.17 or 117% approximately.

Therefore, the company would have to be offered a minimum rate of interest of 117% before they would be willing to transfer money from t1 to t2.

Chapter 9

Simple risk techniques problem 1 (a) The first task with this type of complex ENPV question is to identify the different ‘states of the world’ and their associated probabilities. Once this is done, the project’s NPV in each state of the world can be calculated. These state of the world NPVs are then each multiplied by their associated probabilities and added together to give the overall expected NPV or ENPV of the project. The states of the world There are three stages involved with this project. Stage 1

Stage 2

Stage 3

The seismic survey. There is a 50% chance that this will reveal that the geology indicates the possibility of oil. If it does, we proceed to the next stage. But there is also a 50% chance (i.e. 1.0 – 0.50 = 0.50) that the geology indicates that there will be no oil. Under these circumstances, the company goes no further and abandons the project. The exploration wells. If the seismic survey indicates the possibility of oil then the company will proceed to drill exploration wells to see if oil does actually occur. There is a 30% chance that the exploration well will discover oil, in which case we proceed to stage 3. However, there is a 70% chance (i.e. 1.0 – 0.30 = 0.70) that the exploration well will indicate no oil is present. Under the circumstances, the company will go no further and abandon the project. The appraisal wells. If the exploration wells indicate oil then we will proceed to drill appraisal wells to identify just what quantity of oil is there. There is a 60% chance that the oil will be in negligible quantities (what the question refers to as type I). In those circumstances, the project is then obviously abandoned. However, there is a 32% chance that the appraisal wells will indicate the presence of 42 million barrels of oil (type II) and an 8% chance that 2250 million barrels of oil will be indicated (type III). Under each of these last two circumstances the company will then proceed to extract the oil.

As a result, there are five possible outcome combinations, or states of the world. State A

Seismic survey indicates no oil and the project is abandoned.

718

ANSWERS TO PROBLEMS

State B State C

State D State E

Seismic survey indicates that there may be oil, an exploration well is drilled and finds no oil. The project is then abandoned. Seismic survey indicates that there may be oil, an exploration well is drilled and also indicates oil. Therefore an appraisal well is drilled, but a negligible amount of oil is found. The project is abandoned. This is the same as for State C, except the appraisal well discovers 42 million barrels of oil which the company then extracts. Again, the same as for State C, except the appraisal well discovers 2250 million barrels of oil which the company then extracts.

The probability of occurence of each of these five states can be found from the product of the probability of each event in each state. State A

0.50 or 50%

State B

0.50 × 0.70 = 0.35 or 35%

State C

0.50 × 0.30 × 0.60 = 0.09 or 9%

State D

0.50 × 0.30 × 0.32 = 0.048 or 4.8%

State E

0.50 × 0.30 × 0.08 = 0.012 or 1.2%.

The required information Having identified the separate states of the world and their associated probabilities, the next stage is to work out the project’s NPV under each state. However, before doing that, we need to assemble the required information. (i) The first item of information is to identify the annual oil production pattern in the two states (D and E) where oil is actually produced. From the information in the question, the following can be derived. State D

State E

14 million barrels per year output for the first two years of the oilfield’s life and 7 million barrels per year for the second two years: 14 million + 14 million + 7 million + 7 million = 42 million 300 million barrels per year output for the first five years of the oilfield’s life and then 150 million barrels per year for each of the remaining five years: (5 × 300 million) + (5 × 150 million) = 2250 million.

(ii) As all the other financial figures are provided in £ terms, we need to express the oil revenues similarly. At $26.40 a barrel and an exchange rate of $1.20 = £1, the £ revenue from a barrel is $26.40 ÷ 1.20 = £22. (iii) The operating net cash flow (pre-tax) per barrel is: £22 × 0.45 = £9.90. (iv) The annual revenues (pre-tax) will be: 7 million barrels = £69.3 million 14 million barrels = £138.6 million 140 million barrels = £1 485 million 300 million barrels = £2 970 million (v) The annual tax cash flow on these net revenues are as follows: £69.3 million × 0.77 = £53.361 million £138.6 million × 0.77 = £106.722 million £1 485.0 million × 0.77 = £1 143.45 million £2 970.0 million × 0.77 = £2 286.9 million (vi) Finally, there is the timing of cash flows and the discount rate. The licence fee of £20 million and the seismic survey cost of £2 million both occur at Year 0. The appraisal wells cost of £100 million and the exploration well cost of £10 million both occur at Year

CHAPTER 9

719

SIMPLE RISK TECHNIQUES

1. All exploration costs receive tax relief at 50%. The first oil production revenues occur at Year 2 and the first tax charge occurs at Year 3. The discount rate is 16%. The NPV calculations (£ millions) In these calculations (which really test your discounting ability), use can be made of the fact that a lot of the cash flows are annuities. State A Year 0 Year 1

–20

–2 +10

=–22 –1 =+11(1.16)

+1

=–22.00 =+ 9.48 NPV

State B Year 0 Year 1 Year 2

–20

–2 +10

+1

–10 +5

=–22 –1 =+(1.16) –2 =+5(1.16)

=–22.00 =+ 0.86 =+ 3.72 NPV

State C Year 0 Year 1 Year 2 Year 0 Year 1 Year 2

–20

–2 +10

+1

–10 +5

–100 +50

–22 = –22.00 –1 –99(1.16) = –85.35 –2 +55(1.16) =+40.88 NPV = –66.47

State D –1 –2 –1 –22 –99(1.16) +55(1.16) +138.6A¬ 2 0 .16 (1.16) –2 –3 –106.722 A¬ + 69.3 A¬ 2 0 .16 (1.16) 2 0 .16 (1.16) –4 –53.361 A¬ 2 0 .16 (1.16) –22 – 85.35 + 40.88 + 191.80 –137.32 + 71.27 –47.31 = +11.97 NPV State E –1 –2 –1 –22 –99(1.16) + 55(1.16) + 2 970 A¬ 5 0 .16 (1.16) –2 –6 –2 286.9 A¬ + 1 485 A¬ 5 0 .16 (1.16) 5 0 .16 (1.16) –7 –1 143 A¬ 5 0 .16 (1.16) –22 – 85.35 + 40.88 + 8 383.64 –5 565.08 + 1 964.37 –1 324.10 = +3 892.86 NPV Expected NPV £mn NPV –12.52 –17.42 –66.47 +11.97 +3 892.86

× Probability × 0.50 = × 0.35 = × 0.09 = × 0.048 = × 0.012 =

– 6.26 – 6.10 – 5.98 + 0.57 + 46.71 +£28.94mn ENPV

=–12.52

=–17.42 =–22 =–99 =+55

720

ANSWERS TO PROBLEMS

FIG.P 9.1

Probability 0.6

C

9%

0.32

D

4.8%

0.08

E

1.2%

B

15%

A

70%

I II

: oil lore Exp 0.50 Exp lore : no oil 0.50

il y: o rve u S 0 0.3 Su rve y: n 0.7 o oil 0

III

(b) Revised probability tree The revised probability tree is shown in Fig. P9.1. The survey only changes the probabilities of States A and B. Therefore its worth should be determined by the difference the change in probabilities makes to the ENPV of these two outcomes, plus the cost of the existing survey: State A B

NPV × £mn –12.52 × –17.42 ×

Existing probability 0.50 0.35

State =–6.26 =–6.10

ENPV

–12.36

A B

NPV × £mn –12.52 × –17.42 ×

Revised probability 0.70 =–8.76 0.15 =–2.61 ENPV –11.37

The difference between is: £mn 12.36 11.37 0.99 2.00 (0.86) =

Plus cost of existing survey: Less PV of tax relief:

£2.13mn =

–1

£2.0mn × 0.50 × (1.16)

Max after-tax value of new survey

Let χ = gross cost of the new survey, then: –1

χ – χ × 0.50 × (1.16) = 0.569χ = χ =

2.13 2.13 2.13/0.569 = £3.74mn (approx.)

problem 2 (a) The market research cost has already been incurred and so can be ignored for decision purposes. NPV analysis Outlay: £200 000 Revenue: £250 000 per year Variable costs: £150 000 per year Fixed costs: £25 000 per year Scrap value: £2 000 Life: 4 years Discount rate: 10%

CHAPTER 9

721

SIMPLE RISK TECHNIQUES

–200 + (250 – 150 – 25 ) A ¬4 0 .10 + 2(110 . )−4  + £39 108 NPV  = ∴ accept –200 + (75  31699 . ) + (2  0.6830 )  Sensitivity analysis Let outlay = χ –4

–χ +75 A¬ = 0 NPV 4 0 .10 + 2(1.10) –4

–χ = –75 A¬ = –£239 108 4 0 .10 – 2(1.10) % change:

239 108 – 200 000 = 0.196 200 000

Let revenue = χ –4

–200 + χ A¬ =0 4 0 .10 – 175 A¬ 4 0 .10 + 2(1.10) χ=

200 + 175 A ¬ 2(110 . )−4 4 0 .10 − A¬ 4 0 .10

% change:

= £237662

250000 – 237662 = 0.049 250 000

Let variable costs = χ –4

=0 –200 + 250 A¬ 4 0 .10 – χ A¬ 4 0 .10 – 25 A¬ 4 0 .10 + 2(1.10) –χ =

200 – 250 A ¬ . )−4 4 0 .10 + 25 A ¬ 4 0 .10 – 2(110 = –£162 337 4 0 .10 A¬ % change:

162 337 – 150 000 = 0.082 150 000

Let fixed costs = χ –4

–200 + 250 A¬ =0 4 0 .10 – 150 A¬ 4 0 .10 – χ A¬ 4 0 .10 + 2(1.10) –χ =

. )−4 200 – 250 A ¬ 4 0 .10 + 150 A ¬ 4 0 .10 – 2(110 = –£37 337 A¬ 4 0 .10 % change:

37 337 – 25000 = 0.494 25000

Let life = χ years –χ

–200 + 75 A¬ =0 X 0 .10 + 2(1.10) When χ = 4 NPV = +£39 108 When χ = 2 NPV = –200 + (75 × 1.7355) + (2 × 0.8264) = –£68 185 –68 185   χ = 2+   ( 4 – 2) = 3.27 years  –68 185 – 39 108  % change:

4 – 327 . = 0.182 4

Let sales price = χ –4

–200 + 50χ A¬ =0 4 0 .10 – 175 A¬ 4 0 .10 + 2(1.10) χ=

200 + 175 A ¬

4 0 .10

50A ¬

– 2(1.10 )–4

4 0 .10

= £4.75

722

ANSWERS TO PROBLEMS

£5 – £4.75 = 0.05 £5

% change: Let sales volume = χ

–4

=0 –200 + (5 –3)χ A¬ 4 0 .10 – 25 A¬ 4 0 .10 + 2(1.10) χ=

. ) 200 + 25 A ¬ 4 0 .10 – 2(110 (5 – 3) A ¬ 4 0 .10 % change:

–4

= 43 831 bottles

50 000 – 43 831 = 0.123 43 831

Let variable cost/bottle = χ –4

=0 –200 + 250 A¬ 4 0 .10 – 50χ A¬ 4 0 .10 – 25 A¬ 4 0 .10 + 2(1.10) χ=

−4 200 – 250 A ¬ 4 0 .10 + 25 A ¬ 4 0 .10 + 2(1.10 ) = £3.25 50 A ¬ 4 0 .10

% change:

£3.25 – £3 = 0.083 £3

(b) Sensitivity table Forecast Outlay Revenue Variable cost Fixed cost Life Sales price Sales volume Variable cost/unit

Max. % change 19.6% rise 4.9% fall 8.2% rise 49.4% rise 18.2% fall 5.0% fall 12.3% fall 8.3% rise

The sensitivity table indicates that the ‘accept’ advice given by the NPV analysis is most sensitive to changes in the estimates of the annual revenue and the sales price. Management should go back and ensure that they cannot significantly improve their confidence in the reliability of both estimates. (c) Expected Year 6 sales: Successful: 28 000 × 0.5 = 9 000 × 0.5 =

14 000 4 500 18 500

Unsuccessful:

12 000 × 0.5 = 5 000 × 0.5 =

6 000 2 500 8 500

Contribution/sale: £5 – £3 = £2 ENPV of contribution (£000s): 5 6 –5 –6 +70(1.10) +37(1.10) –5 –6 +14(1.10) +17(1.10)

= =

PV 64 350 18 289

× ×

Probability 0.6 = 38 610 0.4 = 7 316 +45 926

PV of fixed costs (£000s): –5

–6

–25(1.10) –25(1.10) = –29 635

CHAPTER 9

723

SIMPLE RISK TECHNIQUES

Therefore the PV of the life extension would be: £45 926 – £29 635 = +16 291 PV cost of trade advertising (£000s): –5

–6

–10(1.10) –10(1.10) = –11 854 PV cost of price reduction (£000s): –5

–6

–35 × 0.40(1.10) – 18.5 × 0.40(1.10) = –12 870 × 0.6 = –7 722 –5 –6 – 7 × 0.40(1.10) – 8.5 × 0.40(1.10) = – 3 658 × 0.4 = –1 463 –9 185 NPV of life extension with trade advertising: £16 291 – £11 854 = +£4 437 NPV of life extension with price reduction: £16 291 – £9 185 = +£7 106 Therefore, although either alternative would be worthwhile, the ‘price reduction’ alternative leads to the largest additional amount of positive NPV.

problem 3 (a) Report Assuming that the investment in Goer is undertaken, is it better to continue with the project at the end of the first year, or to abandon it? If it is decided not to abandon the project at Year 1, there is an opportunity cost of £141 000 – the payment from Goer that is forgone. In Year 2, there are four possible outcomes: a cash flow of £80 000, £90 000, £100 000 or £110 000, plus £81 000 ‘final’ payment. The NPV of deciding not to abandon at Year 1 is as follows: Year 1 cash flow: £80 000 Year 1 (141 000)

Year 2 80 000   81 000 

NPV at 18% (3 867)

×

Prob. 0.6

=

(2 320)

(141 000)

90 000   81 000 

3 314

×

0.4

=

1 326

ENPV

(994)

Year 1 cash flow: £100 000 Year 1

Year 2

(141 000) 100 000   81 000  (141 000) 110 000   81 000 

NPV at 18%

Prob.

10 497

×

0.6

=

6 298

17 679

×

0.4

=

7 072

ENPV

13 370

Therefore if, at the end of Year 1, the company receives a cash flow of £80 000, the best course of action is then to abandon the project (for to continue incurs a negative ENPV of £994). However, if at the end of Year 1, the company receives a cash flow of £100 000, the best course of action is to continue the project (for continuing generates a positive ENPV of £13 370).

724

ANSWERS TO PROBLEMS

Now that the optimal action at Year 1 is known, the overall investment decision can be evaluated. There are three possible ‘states of the world’. State 1 is where the company receives an £80 000 cash inflow at Year 1 and so abandons the project. The probability of this state is 0.60. State II is where the company receives a £100 000 cash inflow at Year 1, continues with the project and receives another £100 000 cash inflow at Year 2. The probability of this state is: 0.40 × 0.60 = 0.24. State III is where the company receives a £100 000 cash inflow at Year 1, continues with the project and receives a £110 000 cash inflow at Year 2. The probability of this state is: 0.40 × 0.40 = 0.16. NPV analysis State

Year 0

Year 1

I

(201 000)

80 000   141 000 

II

(201 000)

100 000

III (201 000)

100 000

Year 2

NPV at 18% (13 702)

Probability ×

0.6

=

(8 221)

100 000  13 744  81 000 

×

0 .24

=

3 299

110 000  20 926  81 000 

×

0.16

=

3 348

ENPV £(1 574) Therefore, despite the abandonment option at Year 1, the overall project is not worthwhile. The company would do better to invest its £20 000 in the money market, which represents a zero NPV investment. (b) The practical problems of abandonment analysis relate primarily to the estimation of the relevant cash flows. It is difficult, if not impossible, to accurately estimate: (i) annual net cash flows – cash flows are usually estimated to be single figures, e.g. £80 000 or £100 000, whereas in reality they might take various alternative values; (ii) the conditional probabilities associated with the cash flows; (iii) the actual abandonment value – unless contractual agreements exist, the abandonment value estimated may be subject to substantial error. Estimates of NPV are likely to be less accurate as the number of years that an abandonment opportunity exists increases. Abandonment is normally advocated in the first year that the present value of abandonment exceeds the present value of expected cash flows from continued operation. However, abandonment at a later date might produce an even greater expected present value. The normal abandonment rule might lead, therefore, to a sub-optimal decision. Abandonment part-way through the expected economic life might occur for many reasons, which results in the present value of abandonment exceeding the expected present value of continuing. Important factors might include unexpected unfavourable changes in inflation, exchange rates, taxation, labour, material and other costs, the development of new technology, labour disputes and increased competition.

CHAPTER 10

Chapter 10

725

RISK AND RETURN

Risk and return problem 1 (a) The utility function can be derived by arbitrarily defining the utility of two levels of income and then using the relationships the investor has provided to calculate the utilities of the remaining levels of income. Define U(500) = 0 and U(4500) = 1. Then using the expected utility hypothesis it is possible to calculate the utility of £2500 which must equal the expected utility of £500 with probability 0.4 and £4500 with probability 0.6. Thus: (i)

U(2 500) = 0.4 U(500) + 0.6 U(4 500) U(2 500) = 0.4 × 0 + 0.6 × 1 = 0.6

Similarly: (ii)

U(2 500) = 0.75 U(1 600) + 0.25 U(4 500) 0.6 = 0.75 U(1 600) + 0.25 × 1 U(1 600) = 0.35/0.75 = 0.467

(iii) U(2 500) = 0.55 U(1 600) + 0.45 U(3 500) 0.6 = 0.55 × 0.467 + 0.45 U(3 500) U(3 500) = (0.6 – 0.55 × 0.467)/0.45 = 0.763 (iv) U(2 500) = 0.75 U(2 000) + 0.25 U(3 500) 0.6 = 0.75 U(2 000) + 0.25 × 0.763 U(2 000) = (0.6 – 0.25 × 0.763)/0.75 = 0.546 (v)

U(2 500) = 0.5 U(2 000) + 0.5 U(3 000) 0.6 = 0.5 × 0.546 + 0.5 U(3 000) U(3 000) = (0.6 – 0.5 × 0.546)/0.5 = 0.654

(vi) U(2 500) = 0.85 U(2 000) + 0.15 U(4 000) 0.6 = 0.85 × 0.546 + 0.15 U(4 000) U(4 000) = (0.6 – 0.85 × 0.546)/0.15 = 0.906 FIG. P10.1 Ut

1.0

0.8

0.6

0.4

0.2

0

0

1 000

2 000

3 000

4 000

Total income

£

726

ANSWERS TO PROBLEMS

Therefore we have the following data: U(500) = 0 U(1 600) = 0.467 U(2 000) = 0.546 U(2 500) = 0.6 U(3 000) = 0.654 U(3 500) = 0.763 U(4 000) = 0.906 U(4 500) = 1.0 Figure P10.1 illustrates this utility function. As can be seen from the graph, for a total income level of between (approximately) £0 and £2500 the utility function is concave to the origin, indicating risk-aversion. However, for income levels of between £2500 and £4000 the utility function is convex to the origin, suggesting that the investor becomes a risk-seeker/risk-lover. (b) Note that the alternative activities are additional. As the utility function was drawn up using total income it can be used to compare the total incomes given by different alternatives. Thus with (i) the total incomes will be £2500 (1500 + 1000 already received), probability of 0.5, and £3000 (2000 + 1000), probability of 0.5. The expected utility of (i) is thus: 0.5 U(2 500) + 0.5 U(3 000) = 0.5 (0.6 + 0.654) = 0.627 Similarly the total incomes from (ii) are £2000 and £3500 each with a probability of 0.5. The expected utility of (ii) is thus: 0.5 U(2 000) + 0.5 U(3 500) = 0.5 (0.546 + 0.763) = 0.655 Thus (ii) is preferred by the investor as it has a higher utility. (c) Expected values (i) 2 500 × 0.5 = 3 000 × 0.5 = Expected value

(ii) 2 000 × 0.5 = 3 500 × 0.5 =

1 250 1 500 2 750

1 000 1 750 2 750

Variances (i) 2 (2 500 – 2 750) × 0.50 2 (3 000 – 2 750) × 0.50

= 31 250 = 31 250

(ii) 2 (2 000 – 2 750) × 0.5 2 (3 500 – 2 750) × 0.5

= 281 250 = 281 250

Variance

= 62 500

Variance

= 562 500

(d) (ii) is preferred by the investor even though it has a greater variance than (i) and the same expected value. Variance is a successful measure of risk where individuals are risk-averse. The investor is not risk-averse over the range of utilities of (i) and (ii).

CHAPTER 11

Chapter 11

727

PORTFOLIO THEORY

Portfolio theory problem 1 (a) In Fig. P11.1 AB, BC and AC are joined by straight lines since they are perfectly positively correlated. The shaded area represents possible risky portfolios. CML represents the capital market line. The market portfolio is risky Security B. (b) The market price of risk is represented by the slope of CML: 015 . – 0.08 0.07 = = 175 . 0.04 0.04 Therefore, investors will receive an expected return of 1.75% (in addition to the risk-free return) for every 1% increase in risk (standard deviation of return) that they accept, if they hold an efficient portfolio. (c) Investors would only be willing to hold risky Security B in possible combination with the risk-free security, assuming that all investors were risk-averse. This is because Security B gives the best ‘price for risk’, i.e. the maximum slope for the capital market line. Since A and C do not give as good a price for risk there must be a temporary disequilibrium; they are both giving a return that is too low for the risk involved. (d)

E(rp) E(rM) rF E(rp) 0.10 0.10 0.02 0.02

= = = = = = =

x ⋅ E(rM) + (1 – x)rF 0.15 0.08 0.10 0.15x + (1 – x) 0.08 0.15x + 0.08 – 0.08x 0.07x

0.07 = x = 0.286 Thus the investor would place 28.6% of his investment capital in Security B and the remainder (71.4%) in the risk-free security. The risk of the resulting portfolio can either be calculated via the market price of risk: 0.10 – 0.08 = 0.011 1.75 or via: 2

2

σ p = √x 2 ⋅ σ 2Μ = √(0.286 × 0.04 ) = 0.011 (e) As the market portfolio yields an expected return of only 15% per period, to gain a 20% return, the investor will have to borrow additional funds at an interest cost of 8% per period: E(rp) = x ⋅ E(rM) + (1 – x)rF E(rp) = 0.20 E(rM) = 0.15 rF = 0.08 (borrowing cash) 0.20 = 0.15x + (1 – x) 0.08 0.20 = 0.15x + 0.08 – 0.08x 0.12 = 0.07x 0.12 0.07

=

x = 1.714

728

ANSWERS TO PROBLEMS

FIG. P11.1

E(rp ) %

CML

20

C

B

15

10 8

A

0

2

4

σp

7

Therefore an investor will borrow an amount equivalent to 71.4% of his own funds. These borrowings, together with his own investment funds, will be placed in Security B. The risk attached to this portfolio yielding a 20% expected period return is as follows: via the market price of risk σp =

0.20 – 0.08 = 0.0686 1.75

or: 2

σp = √x ⋅ σ

2

2

M

2

= √(1.714 × 0.04 ) = 0.0686

The main assumptions are: (f) (i) The investor’s objective is to maximize the utility of wealth. (ii) Investors make choices on the basis of risk and return. Return is measured by the arithmetic mean return from a portfolio of assets, and risk is measured by the standard deviation or variance of those returns. (iii) All investors can lend and borrow unlimited amounts of cash at the risk-free interest rate. (iv) No taxation, transaction costs or other market imperfections. (v) All investors have the same knowledge and expectations about the future and have access to the complete range of investment opportunities. Investors are all price-takers and have free access to all relevant information. (vi) All investors have the same decision-making time horizon, i.e. the expected return on investments arises from expectations over the same time period. Portfolio theory is important to companies as far as investment decision making is concerned because it illuminates the risk reduction effect of diversification and, more importantly, it indicates that the reward for risk-taking is only linked to systematic risk, rather than total risk.

problem 3 (a)

E[rp] = x ⋅ E[rA] + (1 – x) ⋅ E[rB] E[rp] = (0.8 × 12) + (0.2 × 20) = 13.6%

CHAPTER 12

THE CAPITAL ASSET PRICING MODEL 2 2

(b) σp = √x σ

2 2

A 2

+ (1 – x) σ 2

B

729

+ 2x(1 – x)σAσBρAB

2

2

σp = √(0.8 × 3 ) + (0.2 × 7 ) + (2 × 0.8 × 0.2 × 3 × 7 × 0.1) σp = 2.9% (c) The weighted average risk of the portfolio is: (0.8 × 3%) + (0.2 × 7%) = 3.8% The actual risk of the portfolio, as calculated in part (b) above, is 2.9%. Thus a significant amount of risk reduction has been achieved through portfolio diversification. The reason for such a significant degree of risk reduction (0.9% as a percentage of 3.8% represents 23.7% risk reduction) is that the correlation coefficient, at a value of +0.1, is well away from +1. (d) It is possible to construct a zero-risk two-asset portfolio, if the correlation coefficient is perfectly negative: –1. In such circumstances, the equation for portfolio risk reduces to: σp = xσA – (1 – x)σB Therefore, solving for x: 0 0 7% 7%

= = =

x ⋅ 3% – (1 – x) 7% 3%x – 7% + 7%x 10%x

10% = x = 0.70 Therefore 70% of the funds should be placed in Project A and the other 30% in Project B.

Chapter 12

The capital asset pricing model problem 1 (a) Given: β SHARES =

Systematic risk of shares Risk of market portfolio

then: Systematic risk of shares = βSHARES × Risk of market portfolio Also given: βx + y = βx ⋅

x y +βy ⋅ x+ y x+ y

Therefore: 62   4  β V + A = 0.67   + 0.67   = 0.67 66   66   62   4  β V + B = 0.67   + 1.14   = 0.698 66 66     62   4  β V + C = 0.67   + 0.88   = 0.683 66   66  

730

ANSWERS TO PROBLEMS

And so: Systematic β × σM risk V+A = 0.67 × 16% V+B = 0.698 × 16% V+C = 0.683 × 16% In all three cases, the new market value of the £62 million + £4 million = £66 million.

= 10.72% = 11.17% = 10.93% company would be expected to be:

(b) Portfolio theory shows that when assets are combined, the total risk of the combination (measured as standard deviation of returns) is less than a weighted average of the risks of the individual assets, as long as the assets are less than perfectly positively correlated with each other. The further away the correlation coefficient is from being perfectly positive (i.e. +1), the greater will be the amount of risk reduction. The simplest type of portfolio is a two-asset portfolio. Vanhal, plus an acquired company, could be viewed as such a portfolio. For example, if Vanhal were to acquire company A, then the total risk of the enlarged company would be given by: 2 2

σV+A = √x σ

V

+ 2x(1 – x)σVσAρV,A

where x and (1 – x) represent the proportions of Vanhal and A represented in the enlarged company. As long as the correlation coefficient (ρV,A) is less than + 1, then σV+A will be less than (σV ⋅ x) + σA ⋅ (1 – x). In other words, Vanhal will have been able to reduce its total risk (in the sense that the resulting total risk will be less than a weighted average of the total risk of the components) through the diversification process. (c) There could be a large number of possible reasons why the directors of Vanhal might wish to diversify, but the question indicates that the primary reason is to broaden the company’s activities. In this respect, the desire of the directors to diversify arises from their wish to reduce the total risk of the company. How this may be done – in relation to the company’s stock exchange return – has been shown in the answer to part (b). However, from the directors’ viewpoint, risk reduction through diversification would manifest itself in a reduction in the variability of the company’s operating cash flow and therefore resulting (in stock market parlance) in an increase in the perceived ‘quality’ of the company’s earnings. The directors would be interested in trying to bring about such an effect for two reasons. One would be to hope for an enhancement of the stock market price of the company’s shares through the increased earnings quality leading to a higher price–earnings ratio multiple being applied to the company’s earnings per share. However, such an effect would only come about if the market valued total risk, rather than just systematic risk. The second reason for the directors’ interest in such a policy would be the benefits that a more stable corporate cash flow would bring to the job of management. For example, there would be a reduced probability of insolvency (and the consequential costs for directors); there may be opportunities for increasing the company’s gearing; a stable dividend policy might be able to be maintained with greater ease; and generally the task of managing the overall company would become less demanding. To suggest which of the three companies under consideration best meets the directors’ requirements is difficult, given the information available. As all three are in the same area of industry, any one of the three would presumably provide the required broadening of the company’s activities. However, assuming that the directors are interested in such a move in order to reduce total corporate risk, then they may not be indifferent between the three companies. Given that all three companies have the same value,

CHAPTER 12

THE CAPITAL ASSET PRICING MODEL

731

and assuming that they all have the same correlation coefficient with Vanhal (which is not unrealistic, given the circumstances), then company A is likely to be preferable as it has the smallest amount of total risk and specific risk. (Non-specific or systematic risk cannot be diversified away.) If the assumption about the correlation coefficient is unsafe, then the company best suiting the directors’ requirements would be that whose combination of total risk and correlation coefficient – used in the expression given in answer to part (b) above – would result in the lowest level of total risk for the enlarged company. (d) Portfolio theory and the capital asset pricing model suggest that investors should only be interested in systematic risk. As systematic risk cannot be diversified away, there would be no risk reduction benefits accruing to shareholders as a result of the merger, assuming that they already hold well diversified investment portfolios. In fact such a move as that contemplated by Vanhal may be unwelcome to shareholders if it were to significantly change the total market value and beta of the company. In such circumstances, a shareholder holding a diversified portfolio with a desired beta value would have to adjust his/her portfolio (and so incur transaction costs) in the light of the change to Vanhal. Despite the foregoing, shareholders might still welcome the takeover, even given the assumption in part (a) of the question that there are no synergy benefits. For example, shareholders holding non-fully diversified portfolios would gain some risk reduction effect. Alternatively, if the company taken over was worth more than the £4 million purchase price, then Vanhal’s shareholders’ wealth would increase. Again if, as a result of the takeover, Vanhal were able to increase their debt capacity, then the tax shield benefits (if they exist) would also accrue to the shareholders (see Chapter 19). However, given a reasonably efficient capital market with shareholders holding well diversified investment portfolios, the value to shareholders of such a takeover as that proposed is likely to be minimal. In fact, the costs (both internally and externally to Vanhal) associated with the takeover may result in shareholders suffering an actual reduction in their wealth.

problem 2 (a) Given that Mr Swift has a well diversified portfolio, it will be safe to assume that most of the unsystematic risk that is attached to the individual securities in the portfolio will have been diversified away. Thus his portfolio risk will largely consist of systematic risk and so the variance of returns on his portfolio will essentially measure systematic risk. If he wishes to include shares that will reduce his portfolio variance, then he will be concerned with the covariance of returns between any new share and his existing portfolio. In other words, he is interested in selecting the shares of that company which would help to bring the greatest reduction in portfolio risk. This would be indicated by looking at the product of the standard deviation of returns and the correlation with Mr Swift’s existing portfolio: Dove: Jay:

σD × ρD,S = 35% × 0.16 = 5.6% σJ × ρJ,S = 30% × 0.21 = 6.3%

Under these circumstances, the optimal course of action for Mr Swift – given his objective – would be to invest in the shares of Dove plc. (b) The CAPM shows that there is a positive relationship between the expected return on a security and its degree of systematic risk – which is normally measured by its beta value. Thus, the greater the amount of systematic risk the greater will be the expected return demanded by investors in an equilibrium stock market. The systematic risk of

732

ANSWERS TO PROBLEMS

individual securities can be measured as the product of their standard deviation of return and their correlation coefficient with the market portfolio. In the case of Dove and Jay, this gives values for systematic risk of: Dove: Jay:

σD × ρD,M = 35% × 0.3 = 10.5% σJ × ρJ,M = 30% × 0.25 = 7.5%

As Dove plc has the higher level of systematic risk, it would follow that Dove should have the higher expected return, as indeed it does: 9% as against only 7% for Jay plc. (c) If Mr Swift’s portfolio contained shares in a few companies only, then he would be holding a largely undiversified portfolio. Hence, the variance of returns of the portfolio would reflect both the systematic and unsystematic risk components as there would be insufficient diversification to wash out the unsystematic risk. Without passing comment on whether such a portfolio is wise (although it would appear sensible for Mr Swift to diversify further), in order to meet his objective on portfolio variance Mr Swift would be most interested in selecting that company which would help to bring the greatest reduction to the total risk of his existing portfolio. However, in these particular circumstances a problem arises from the fact that with small portfolios a security’s contribution to portfolio risk can arise out of its own variance, as well as from its covariance with the existing portfolio. Thus, although Dove plc, as was seen in the answer to (a), has the smaller covariance with the existing portfolio, it has a higher variance (or standard deviation) than Jay: σ

2 D

= 0.1225

2

σ J = 0.09

Therefore the final choice between the two companies will depend upon the existing components of Mr Swift’s portfolio and their weights and the resulting changes brought about through the introduction of the new security. (d) Shareholders, assuming that they hold well diversified efficient portfolios, will be interested in the effect on the risk of their portfolio of the addition to it of any particular security. However, because the portfolio is fully diversified, when a new share is added (again, assuming that only a marginal investment is made), then that new share’s unsystematic risk is eliminated, or is washed out, and it is only the systematic risk that is added to the portfolio. It is therefore for this reason that the relevant measure of risk for a company’s shareholders is the amount of systematic risk. This is most conveniently measured in relative terms via the beta value. Debt holders are also interested in the systematic risk of their investment which, again, could be measured by beta. However, as most debt is unquoted, beta does not provide a convenient measure of risk. Hence debt holders attempt to measure the risk of a company’s debt through a series of alternative measures including the degree of capital gearing, the interest cover ratio, the amount of tangible assets held by the company and the stability, or otherwise, of the company’s annual net cash flow. Just which of these factors contribute to systematic risk and which to unsystematic risk is somewhat unclear. What evidence there is available suggests that all four factors – with the possible exception of the amount of tangible assets held – are likely to contribute to systematic risk. Finally, managers, as far as their labour is concerned, hold undiversified portfolios. Therefore, unlike outside investors, they are interested in the total risk of a company and – in particular – the likelihood that it will fall. Thus, managers are likely to measure risk by the variability of net annual cash flows (i.e. by the variance of corporate net cash flows), the skew of those cash flows and by the degree of capital gearing. All three factors will have a bearing on the riskiness of the company as seen from management’s viewpoint.

CHAPTER 13

733

OPTION VALUATION

problem 3 (a) (i) Expected return on Cemenco equity Average % annual capital gain: 1

[16.42 ÷ 9.50] – 1= 20% 3

Average % dividend yield: [10% + 12% + 8% + 10%] ÷ 4 = 10% Therefore, expected return on Cemenco shares = 20% + 10% = 30% (ii) Expected return on TSE Index Average % annual capital gain: 1

[1983 ÷ 1490] – 1 = 0% 3

Average % dividend yield: [16% + 15% + 10% + 18%] ÷ 4 = 15% Therefore, expected return on the TSE Index = 10% + 15% = 25% (iii) Return on government stocks 15% + 16% + 14% + 15% ÷ 4 = 15% Therefore, risk-free return = rf = 15% (iv) Beta value of Cemenco equity E[rc] = rf + (E[rm] – rf) . βc Therefore: E [ rc ] – rf E [ rm ] – rf

= βc

30% – 15% 15 = – 1.50 25% – 15% 10

(b) It is difficult to predict with any accuracy whether the government’s action will make Cemenco Ltd more or less systematically risky. Although in total risk terms the risk of the company will be reduced, it is difficult to be certain what will be the effect on systematic risk. The company’s revenues will, as always, be fairly sensitive to the level of Trinka’s economic activity and this is unlikely to change by being given a monopoly. However, there will be price control and this may therefore result in increasing the company’s systematic risk exposure.

Chapter 13

Option valuation problem 1 (i) In order to answer this question, we need to use the Black and Scholes model to value the Pear call options, where: S = 415p X = 400p; T = 0.25 years Rf = 0.05 ␴ = 0.22.

734

ANSWERS TO PROBLEMS

and the Black and Scholes model is: –Rf × T

C = S × N (d1) – [X × e

] × N (d2)

where:

( d1 ) =

S log e   + ( Rf  T )  X σ T

+ (0.5  σ  T

)

and (d2) = (d1) – ␴ × √T We will do the calculations, item by item: log e S/X = log e 415/400 = log e 1.0375 = 0.0368 Rf × T = 0.05 × 0.25 = 0.0125 ␴ × √T = 0.22 × √0.25 = 0.22 × 0.50 = 0.11 0.5 × ␴ × √T = 0.5 × 0.11 = 0.055 0.0368 + 0.0125 (d1) = + 0.055 = 0.5032 0.11 (d2) = 0.5032 – 0.11 = 0.3932 Using the area under the normal curve tables: N (d1) = N (0.50) = 0.5 + 0.1915 = 0.6915 N (d2) = N (0.39) = 0.5 + 0.1517 = 0.6517 and so finally: –0.25× 0.05

C = 415p × 0.6915 – (400p × e ) × 0.6517 C = 286.97p – (400p × 0.9876) × 0.6517 C = 286.97p – (395.03p × 0.6517) C = 286.97p – 257.44p = 29.5p The Black and Scholes model suggests that the Pear calls should have a value of 29.5p. (ii) We can use the put–call parity equation to value the pear put options: P = C + [X × e

–Rf × T

]–S

where: C = 29.5p X = 400p S = 415p e

–Rf × T

–0.05 × 0.25

=e

= 0.9876

Therefore: P = 29.5p + [400p × 0.9876] – 415p = 9.5p (iii) The delta or hedge ratio for the Pear calls is given by the value of N (d1) = 0.6915. Therefore, in order to construct a delta neutral hedge on the holding of 50 000 Pear shares, the investor would need to sell/write: 50 000 shares ÷ 0.6915 = 72 307 call options. As a result, any gains or losses on the shareholding should be exactly matched by offsetting losses or gains on the written call options.

CHAPTER 14

735

INTEREST RATE RISK

problem 2 e √T. ␴ Rf.T In S/X

One plc 0.988 0.15 0.0125 0.0513

Two plc 0.951 0.177 0.05 0

Three plc 0.963 0.173 0.0375 –0.0954

d1 d2

0.5003 0.3503

0.3710 0.1940

–0.2482 –0.4212

N(d1) N(d2)

0.6915 0.6368

0.6443 0.5753

0.4013 0.3372

C P

9.4p 3.3p

9.7p 4.8p

–Rf.T

Chapter 14

4.4p 10.3p

Interest rate risk problem 1 (a) Manling loan interest rate: 12% Swap: Manling pays: LIBOR + 11 2% Manling receives: 115 8% Net interest rate paid by Manling after the swap: LIBOR + 1 12% + 12% – 115 8% = LIBOR + 17 8% (i) LIBOR remains at 10% Without swap: interest rate paid = 12% With swap: interest rate paid = 10% + 17 8% = 117 8% Interest saving from swap: 1

8% on £14mn loan Less Bank fee

= £ 17 500 = £(20 000)

Net cost

= £( 2 500)

Net cost of swap after tax relief: £(2 500) × (1 – 0.35) = £(1 625) Therefore in this LIBOR scenario, the swap would not be worthwhile. (ii) LIBOR falls to 9% after six months Without swap: interest rate paid = 12% With swap: interest rate paid = 10% + 1 7 8 %  0.5   = 11 3 8 % 9% + 1 7 8 %  0.5  Interest saving from swap: 5 8% on £14mn loan Less Bank fee

Net saving

= £87 500 = £(20 000) = £ 67 500

Net saving from swap after tax relief: £67 500 × (1 – 0.35) = £43 875

736

ANSWERS TO PROBLEMS

Therefore, in this LIBOR scenario, the swap is worthwhile. (b) Manling Swap partner

Fixed interest loan 12% 11 3 4 % 1

Interest differentials

4

Floating rate loan LIBOR + 2% LIBOR + 11 8% ⫽

%

7

%

8

As the interest differentials between the two types of loan are not the same, there is a benefit to be gained from a swap agreement equal, in total, to the difference between the two interest differentials: 7

%–

8

1

4

% = 5 8% interest saving

Given that this benefit is to be equally shared, each company will gain an interest saving of 5 8% ÷ 2 = 5 16 %. The swap arrangement is put together as follows: 1. Greatest interest differential: floating rate loan. 2. The ‘swap partner’ can raise this type of loan most cheaply: LIBOR + 11 8%. 3. Therefore the swap partner borrows £14mn at LIBOR + 11 8% and Manling keeps its existing loan at a fixed interest rate of 12%. 4. Manling wants a floating rate loan and we know that through a swap, such a loan can be arranged at a 5 16 % interest saving on the normal interest rate that Manling would pay for that type of loan: LIBOR + 2% – 5 16 % = LIBOR + 111 16 %. 5. Manling therefore pays LIBOR + 111 16 % interest to the swap partner and, in exchange, receives a fixed 12% interest rate from the swap partner (which can then be used to pay the interest on their fixed rate loan). 6. The swap partner therefore: (i) Pays interest on its own loan : LIBOR + 11 8% (ii) Receives from Manling : LIBOR + 111 16 % Gain from swap (iii) Pays Manling Net interest cost

9

16 % 12% 117 16 %

: : :

Therefore, like Manling, the swap partner ends up with a loan at a on the normal interest rate paid: Swap partner: Normal fixed interest loan rate Effective swap interest rate Interest saving

: : :

5

16

% interest saving

11 3 4 % 117 16 % 5 16 %

Now, if LIBOR remains at 10%: Manling With swap: £14mn × (10% = 111 16 %) Without swap: £14mn × 12% Interest saving Less bank fee Net interest saving Net interest saving after tax: £23 750 × 0.65 = £15 438

= =

Interest £1 636 250 £1 680 000 £ 43 750 £ (20 000) £23 750

CHAPTER 14

737

INTEREST RATE RISK

Swap partner With swap: Without swap:

£14mn × 117 16 % £14mn × (10% = 11 8%)

= =

Interest £1 601 250 £1 557 500

Interest cost Plus bank fee

£ (43 750) £ (20 000)

Total cost

£ (63 750)

Net interest cost after tax relief: £(63 750) × 0.65 = £(41 438) Therefore, with the benefit of hindsight, although the swap deal results in a gain for Manling, it results in a loss for the swap partner.

problem 2 (a) Omniown faces interest rate risk: the risk of an adverse movement in interest rates over the next three months. All three techniques will help hedge their exposure, but in different ways. A forward rate agreement can be used to lock the company into a specific rate of interest, say 14%, so that whatever happens to interest rates over the next three months, Omniown will not be affected. An FRA agreement works on the basis that the company pays the market rate of interest on its loan but, if that rate is above the agreed 14%, then they receive ‘compensation’ to bring their net effective interest rate down to the agreed 14%. Conversely, if market interest rates fall then they will have to pay compensation to bring their interest costs up to an effective 14%. Interest rate futures have the same hedging effect as an FRA in that they hedge the company against both a rise and a fall in interest rates. However, unlike an FRA, futures are not tailor-made to the company’s precise requirements but are standardized contracts and so may not provide a perfect hedge effect. A futures hedge works by ensuring that whatever happens to interest rates, there will be an offsetting effect from the futures contracts. Thus, for example, if interest rates rise over the next three months, Omniown will make an offsetting profit on their futures market contracts and vice versa. In contrast to the first two hedging techniques, interest rate guarantees only hedge the company against a rise in interest rates, but allow the company to take advantage of a fall in rates. In other words, interest rate guarantees work as an option which the company exercises if rates rise, to enable the company to borrow at 14%. On the other hand, if rates fall, the company allows its option to lapse as it can borrow more cheaply at the open market rate. The only problem with interest rate guarantees is that this advantage that they have over forward rate agreements and futures means that they are a significantly more expensive hedging device. (b) Value of a tick: £500 000 × 3 12× 0.0001 = £12.50 Target interest charge: £5mn × 6 12× 0.14 = £350 000 Hedge: As the company wishes to hedge against the risk of a rise in interest rates, it needs to sell futures and then, in March, to ‘close out’ its futures position it will reverse the effects of this initial deal by buying futures. Number of contracts involved:

£5mn = 10 contracts £500 000

738

ANSWERS TO PROBLEMS

But to allow for the ‘maturity mismatch’ – three month futures used to hedge a six-month loan – the number of contracts involved will have to be doubled: 10 × 2 = 20 contracts. Therefore Omniown will sell 20 futures contracts at 86.25. (i) Interest rates rise to 16% and, it is assumed, the futures price falls by 2% to 84.25 Interest on loan: £5mn × 6 12× 0.16

= £400 000

Target interest

= £350 000

Loss on target

= £ 50 000

Profit on futures: Bought at Sold at

84.25 86.25

Profit

2.00 = 200 ticks/contract

Total profit: 20 × 200 × £12.50 = £50 000 Interest on loan Less profit on futures

= =

£400 000 £(50 000)

Net interest cost

=

£350 000

Hedge efficiency:

Profit £50 000 = = 100% Loss £50 000

(ii) Interest rates rise to 16% and, it is assumed, the futures price falls by 1.5% to 84.75 Interest on loan: £5mn × 6 12× 0.16 = £400 000 Target interest = £350 000 Loss on target

= £ 50 000

Profit on futures: Bought at Sold at

84.75 86.25

Profit 1.50 = 150 ticks/contract Total profit: 20 × 150 × £12.50 = £37 500 Interest on loan Less profit on futures

= £400 000 = £(37 500)

Net interest cost

= £362 500 Hedge efficiency:

Profit £37 500 = = 75% Loss £50 000

(iii) Interest rates fall to 13% and futures price rises by 0.75% to 87.00. Interest on loan: £5mn × 6 12× 0.13 Target interest

= £325 000 = £350 000

Profit on target

= £ 25 000

CHAPTER 15

739

FINANCIAL MARKETS

Loss on futures: Bought at Sold at

87.00 86.25

Loss

0.75 = 75 ticks/contracts

Total loss: 20 × 75 × £12.50 = £18 750 Interest on loan Plus loss on futures

= £325 000 = £ 18 750

Total interest costs

= £343 750 Hedge efficiency:

Profit £25 000 = = 133.3% Loss £18 750

(c) Cost of the guarantee: £5mn × 0.002 = £10 000 (i)

Interest rate: Guarantee rate: Exercise the guarantee:

16% 14%

Interest cost: £5mn × 6 12× 0.14 Plus guarantee cost

= £350 000 = £ 10 000

Total interest cost

= £360 000

Interest cost with futures (ii)

(iii)

Interest rate: Guarantee rate: Exercise the guarantee:

= £350 000 16% 14%

Interest cost: £5mn × 6 12× 0.14 Plus guarantee cost

= £350 000 = £ 10 000

Total interest cost

= £360 000

Interest cost with futures

= £362 500

Interest rate: Guarantee rate: Allow the guarantee to lapse:

13% 14%

Interest cost: £5mn × 6 12× 0.13 Plus guarantee cost

= £325 000 = £ 10 000

Total interest cost

= £335 000

Interest cost with futures

= £343 750

The outcome of this analysis shows that, with the benefit of hindsight, the interest rate guarantee would provide the best outcome in scenarios (ii) and (iii), but in scenario (i) futures provide the best outcome.

Chapter 15

Financial markets problem 1

The statement can be divided into five separate sentences. However, before we discuss these we need to consider the meaning of the word ‘correct’. All it means is that, given all the available information, the price set for shares is the best estimate available. It does not mean that the price will turn out to have been correct with the benefit of hindsight.

740

ANSWERS TO PROBLEMS

1. The efficient market hypothesis demonstrates how different levels of information efficiency have different implications. In the strong form, it would not be possible to identify a mispriced investment even if one had access to information about the company that was not publicly available. If this were true then prices of shares would be correct (given our definition of the word). However, it is difficult to imagine a situation where privileged information would consistently have no value. 2. The second sentence is also not true. Share prices should respond to new information in an appropriate manner. In other words, the market should adjust the share prices in a way that values the new information appropriately. It is the information that arises in a random manner and not the valuation of the information. 3. The third sentence is also incorrect. In an efficient market, share prices should move in response to the disclosure of all relevant information, and not just accounting information. 4. Whilst there is no evidence that technical analysts contribute to market efficiency, there is every reason to suppose that fundamental analysts do. They invest a great deal of time, effort and resources in acquiring an information network and the ability to interpret that information. They cannot predict share prices but they do help to ensure that new information is correctly interpreted. 5. If we return to point one, corporate managers will often be aware of information that has not yet been made public and they will thus be in a position to predict share price movements.

problem 2 (a) The spot interest rates can be estimated on the basis that the return on a two-year bond should be the same as the yield on two consecutive one-year bonds. Therefore: Year 2 spot rate estimate: 2

£100 (1 + 0.0575) = £111.83 1 £100 (1 + 0.06) (1 + S2) = £111.83 1 S2 = [£111.83/£100 (1 + 0.06) ] – 1 = 5.5% Year 3 spot rate estimate: 3

£100 (1 + 0.055) = £117.42 £100(1.06)(1.055)(1 + S3) = £117.42 S3=[£117.42/£100(1.06)(1.055)] – 1 = 5% Year 4 spot rate estimate: 4

£100(1 + 0.05) = £121.55 £100(1.06)(1.055)(1.05)(1 + S4) = £121.55 S4=[£121.55/£100(1.06)(1.055)(1.05)] – 1 = 3.5% Year 5 spot rate estimate: 5

£100(1 + 0.045) = 124.62 £100(1.06)(1.055)(1.05)(1.035)(1 + S5) = £124.62 S5=[£124.62/£100(1.06)(1.055)(1.05)(1.035)] – 1 = 2.5% Estimated spot rates: Year 1 2 3 4

Rate 6% 5.5% 5% 3.5%

CHAPTER 15

741

FINANCIAL MARKET

FIG. P15.1 Yield Falling yield curve

6%

5%

4% 1

2

3

5

4

5

2.5%

(b) The yield curve is plotted in Fig. P15.1. (c) Given the relationship: (1 + Real).(1 + Inflation) = (1 + Market) 1+ Market  then: Inflation =   –1  1+ Real 

Therefore:

Year 1:

106 . –1 102 .

=

3.92%

Year 2:

1055 . –1 102 .

=

3.43%

Year 3:

105 . –1 102 .

=

2.94%

Year 4:

1035 . –1 102 .

=

1.47%

Year 5:

1025 . –1 102 .

=

0.49%

Year 1 2 3 4 5

Inflation forecast 3.92% 3.43% 2.94% 1.47% 0.49%

(d) Return from a £100 two-year bond:

Years to redemption

742

ANSWERS TO PROBLEMS 2

£100(1 + 0.0575) = £111.83 Return from two consecutive one-year bonds as specified: £100(1 + 0.06)(1 + 0.07) = £113.42. This is equivalent to a compound annual rate of return of:  £113.42   £100 

1

2

= 6.5%

whereas the compound annual rate of return on a two-year bond is only 5.75%.

Chapter 16

The cost of capital problem 1 (a) (i)

Price/share = 35.8p × 28 = 1 002.4p 1

Dividend growth rate = (11 ÷ 4.86) Cost of equity capital = (ii)

4

– 1 = 22.7%

11(1 + 0.227 ) + 0.227 = 24% 1002.4

Proportion of retained earnings: Return on capital employed:

35.8 – 11 = 0.693 35.8

35.8 = 0.188 190

∴ Dividend growth rate = 0.693 × 0.188 = 13% Cost of equity capital =

11(1 + 0.13) + 0.13 = 14.2% 1 002.4

(iii) Cost of equity capital = 10% + [9% × 0.80] = 17.2% (b) The dividend growth model used contains three principal assumptions: (i) shares are valued on the basis of the present value sum of future expected dividends; (ii) the share price used is in equilibrium; (iii) the estimated dividend growth rate will continue indefinitely. The first of these assumptions could be assumed to be reasonably realistic. The second assumption is, however, open to some doubt, as the company’s P/E multiple is substantially different from the average of what is a reasonably homogeneous industry group. Nevertheless, the most serious doubts concern the third assumption. Forecasting the future on the basis of what has occurred in the past is never satisfactory unless there are positive reasons to believe that the past will replicate itself in the future. In this case this may be particularly unrealistic, given that the company has achieved a very high rate of dividend growth in the recent past. It is doubtful whether such a trend would be maintained indefinitely. The ‘Gordon’ model also makes three specific assumptions: (i)

the proportion of retained earnings and the company’s ROCE remain constant in the future; (ii) the company is all-equity financed; (iii) projects are only financed out of retained earnings. In the example in question, although the retention rate has remained reasonably constant over the recent past, the firm’s ROCE has changed significantly, growing steadily from 15.6% to 18.8%. Thus doubt must be cast on the realism of the assumption that this will remain constant in the future.

CHAPTER 16

THE COST OF CAPITAL

743

As far as the second assumption is concerned, Thamos is indeed all-equity financed at present – but it may not necessarily remain so in the future. The third assumption also holds at present, but again it may be unrealistic to assume that the firm will not wish to raise additional equity finance at some future point in time. It is because of the questionable nature of some of the assumptions that lie behind these models that it is not surprising that the two estimates of future dividend growth, approximately 23% and 13%, are so different. This, in turn, then feeds through into the estimate of the cost of equity capital. Finally, the CAPM-based estimate of the company’s cost of equity capital is also founded on a number of assumptions, the realism of which might be open to question. Principal amongst these would be: (i) beta is the sole determinant of return; (ii) tax has been correctly taken into account; (iii) the risk-free return and the market risk premium have been correctly identified; (iv) investors have homogeneous expectations and a one-period time horizon; (v) betas are stable over time. These, and many other assumptions behind the CAPM, are of questionable real-world validity. However, the real question concerning the applicability of CAPM to generate a firm’s cost of equity capital is: is it empirically valid and does it work in practice? Although this evidence has come in for recent criticism, the best-known study of this question is by Black, Jensen and Scholes (1972) which does tend to suggest that the CAPM is, at least approximately, correct in relation to reality – although it may be that the model is just too simplistic and a model using multi-factor determinants of return may be more applicable to the real world. In many ways the three models used are not competitors, but just take different views of the same problem. However, given the data input difficulties that are associated with all the models, it is not surprising that the diversity of results obtained in part (a) has actually occurred. (c) In pure finance theory, it is highly debatable whether managers do need to know their firm’s cost of equity capital and, in practice, many managers may well believe that cost of capital numbers produced as in part (a) owe more to fiction than reality. It is conceivable that a company operating in a single area of business and wishing to evaluate an investment project that is in the same area may require knowledge of the cost of equity capital as an input into the weighted average cost of capital (WACC) computation, in order to obtain a discount rate. Additionally, a manager might also want to identify the company’s cost of equity capital as an input into a WACC calculation in an attempt to observe the effect on the WACC (and on the cost of equity) of a change in the company’s capital structure (see Chapter 17). However, perhaps the most useful information imparted to managers by a company’s cost of equity capital is its opportunity cost implications. The cost of equity capital represents the return available to shareholders, elsewhere on the capital markets, from an investment of a similar level of risk to that of investing in the company’s shares. Thus it could be interpreted as being the minimum return that management should earn on investing shareholders’ funds. As an investment criterion, this has only a restricted validity because the risk level has to be held constant. However, it does have the advantage of clearly bringing home to management the fact that retained earnings – forming as they do part of shareholders’ funds – cannot be considered ‘costless’ or ‘free’ capital, but have a very significant opportunity cost.

744

ANSWERS TO PROBLEMS

problem 2 (a) (i)

The dividend valuation model is: KE =

d 0 (1 + g ) +g PE

The total dividend payout is given as £2.14mn and the number of shares in issue is 10mn. Thus the dividend per share, d0, is: £2.14mn ÷ 10mn = 21.4p. The market price per share, PE, is given as 321p (assumed to be ex div) and the dividend growth rate, g, is given as 11%. Therefore: KE =

21.4 (1 + 0.11) + 0.11 = 0.184 or 18.4% 321

The company’s cost of equity capital is 18.4%. (ii) The CAPM is: Rcompany = Rf + (Rm – Rf) βcompany The company’s beta for its equity is not given and so has to be calculated from first principles using the beta equation: β company = σ company  ρ company, market σ market The question gives:

σcompany σmarket portfolio ρcompany, market

Therefore βcompany =

= = =

20% 10% +0.7

20%  0.7 14% = = 1.40 10% 10%

Also, given that the risk-free return (Rf) is 12% and the return on the market portfolio (Rm) is 16%, then the CAPM can be used to find the company’s cost of equity capital (Rcompany): Rcompany = 12% + (16% – 12%) × 1.40 = 17.6% Assumptions made: 1. The quoted share price is ex div. 2. The share price represents an equilibrium value in an efficient market. 3. The dividend growth rate is expected to remain constant in perpetuity. (b) Under normal circumstances, we would not expect the dividend valuation model (DVM) and the CAPM to give the same estimates for the KE of a company. The reasons for this are as follows: 1. CAPM is a normative model. It indicates what should be the company’s cost of equity capital, given the systematic risk involved. In contrast, the DVM is a positive model. It indicates what is the company’s cost of equity capital. 2. CAPM is a single time period model. It looks at the return on equity over a single time period. In contrast, the DVM is a multitime period model as it involves a discounting process and looks at the expected dividend flow over each future time period. 3. The CAPM, being a normative or predictive model, may be incomplete. That is to say, the model is a single-factor model in that it assumes that there is only one factor which determines the return on equity: beta or systematic risk. It may well be that other factors, such as company size and dividend policy, also determine the

CHAPTER 17

745

WEIGHTED AVERAGE COST OF CAPITAL

return. If this is so, then the estimate of KE given by CAPM would not be correct. (Notice that this problem of possibly being an incomplete model does not apply to the DVM as it is a positive or deterministic model. Only predictive models run the risk of being incomplete.) 4. Finally, both models require data which has to be estimated. Obviously if any of these estimates are incorrect, the values produced for the cost of equity capital would not be correct. Thus despite points 1 to 3, only if all the estimated variables were correct: (g, Rf, Rm and β) would the two models produce the same value for the cost of equity capital.

Chapter 17

Weighted average cost of capital problem 1 (a) Cost of equity capital KE

d 0 (1 + g ) +g PE

where PE = 135 p 1

g = (13.6 / 10 ) 4 – 1 = 0.08 d 0 = 13.6 p ∴ KE =

13.6(1 + 0.08) + 0.08 = 0.189 135

Cost of debentures VB = £800 000 × 0.825 = £660 000 KD is found by solving: + £82.50 – £8 ⋅ [ A¬4 K D

–£100(1 + K D )

=0

–4

Using linear interpolation: At 10%: + 82.50 – 8 ⋅A¬4 0 .10−100(1 + 010 . )−4 = –11.16 At 16%: + 82.50 – 8 ⋅A¬4 0 .16 −100(1 + 016 . )−4 = + 4.88   –11.16 ∴ K D앓10% +   6% = 0.142   –11.16 – 4.88 Cost of bank loan As the interest rate is variable with market rate movements: VL = £900 000 KL = 0.165 Weighted average cost of capital (K0) K0 =

VE ⋅ K E + VB ⋅ K D + VL K L VE + VB + VL

where: VE = £1.35 × 3mn = £4.05mn VD = £0.66mn VL = £0.9mn ∴ K0 =

KE =18.9% KD =14.2% KL =16.5%

(4.05  18.9%) + (0.66 + 14.2%) + (0.9 + 16.5%) = 18% 4.05 + 0.66 + 0.9

(b) Apart from the obvious assumptions that the market values and the costs of capital used in the calculation of the WACC are correct, there are three major assumptions that

746

ANSWERS TO PROBLEMS

have to be made if the WACC is to be a reliable discount rate for project appraisal. They are: (i) the project is marginal; (ii) the company will maintain its existing gearing ratio; (iii) the project has the same degree of (systematic) risk as the company’s existing cash flows. The project should be marginal (i.e. small relative to the size of the firm) because the WACC is a marginal cost of capital figure. It is so because each of the individual costs of capital that go up to make the WACC are themselves marginal costs of capital. For example, the cost of equity capital of (approximately) 19% represents the return that the market would require from a marginal (i.e. relatively small) investment in the company’s equity. Thus the WACC is an appropriate discount rate or minimum required rate of return for a relatively small capital investment project. As can be seen in the calculation of the WACC in part (a) above, it is based on the company’s existing capital structure (gearing ratio). If the company were to change its gearing, then the WACC could be expected to change also, for two reasons. First, changing the gearing would change the weights applied to the individual costs of capital, and second, changing the gearing would also change the degree of financial risk held by ordinary shareholders and would thus, in turn, change the cost of equity capital. [Only in a Modigliani and Miller world of no taxes and perfect markets would this assumption prove unnecessary (see next chapter)]. Finally, the company’s WACC relates to the degree of risk surrounding the company’s existing cash flows. Therefore it would be appropriate to use this as an investment appraisal discount rate only if the investment project has a similar level of risk. (c) A number of practical problems are likely to be encountered in the calculation of real world WACCs. However, there are three principal problems. The first is that capital structures are often far more complex in practice than in textbook examples/calculations, with some securities causing really difficult valuation problems. Examples would include convertible debentures, loan stocks in foreign currencies (Eurobonds, etc.) and unquoted, fixed interest capital. The second problem specifically concerns the calculation of the cost of equity capital. To obtain this number, estimates are normally required of the market value of the equity and of the future dividend growth rate. With the market value of the equity there is a problem in deciding what value to take if the share price is relatively volatile, but the real problem concerns the dividend growth rate estimate. The past dividend growth rate may be highly erratic, or it might have been depressed because of legal restraints on dividends, or it may be non-existent in the sense that no dividends have been paid in recent years. In all cases, estimating the future dividend growth rate becomes highly problematical. The Gordon approach (where the growth rate g = b × r) may be of some help in such circumstances, but again it is hedged around by a number of assumptions such as constant earnings retention percentages and constant rates of return on reinvested earnings which severely limit its usefulness. One other approach to calculating the cost of equity capital would be to use the capital asset pricing model rather than the dividend valuation model, but that too has its operational difficulties, in particular the specification of the risk-free interest rate and the rate of return on the overall market. The final major problem with the real-world calculation of WACC is caused by taxation. In a taxed world what is required is an after-tax WACC, but the corporate tax regime is now so complex and specific in terms of how it affects individual companies that major problems are posed in trying to arrive at a reliable after-tax WACC estimate.

CHAPTER 17

747

WEIGHTED AVERAGE COST OF CAPITAL

problem 2 (a) (i)

Equity capital KE = 18% (given) VE = 8mn × £1.10 = £8.8mn

(ii)

Irredeemable debentures KIRR =

Annual Int. (1 – Tc ) £3(1 – 0.35) 1.95 = = 0.068 = Mkt. value, ex. int. £31.60 – £3 28.6 VIRR = £1.4mn × 0.286 = £0.4004mn

(iii) Redeemable debentures KRED is found by solving the internal rate of return of the following cash flow: −10 =0 (£10326 . – £9 ) – 9(1 – 0.35 )A¬ 10K RED−£100(1 + K RED )

At 10% discount rate: NPV = +19.76 At 4% discount rate: NPV = – 20.75 Interpolating: −20.75   KRED 앓 4% +   (10% – 4%) = 7.07%   −20.75 – 19.76 VRED = £1.5mn × 0.9426 = £1.4139mn (iv) Loan stock Current value of each £100 unit of loan stock: £6 A¬ . )−10 = £75.42 10 0 .10 + £100(1 + 010 VL = £2mn × 0.7542 = £1.5084mn KL is found by solving the IRR of the following cash flow: –10

+£75.42 – £6(1 – 0.35)A¬10 KL – £100(1 + KL)

=0

At 4% discount rate: NPV = –23.77 At 10% discount rate: NPV = +13.74 Interpolating: −2377 .   K L앓 4% +   (10% – 4%) = 7.8% . – 1374 .   −2377 (v) Bank loans KB = 13%(1 – 0.35) = 8.45% VB = £1.54mn (vi) Weighted average cost of capital (WACC) K0 =

{(18% × 8.8) + (6.8% × 0.4004) + (7.07% × 1.4139) + (7.8% × 1.5084) + (8.45% × 1.54)}/ {(8.8+ 0.4004 + 1.4139 + 1.5084 + 1.54)} K0 =

195.9 = 14.3% 1366 .

(b) In order to estimate a company’s weighted average cost of capital it is necessary to estimate the after-tax market return and market capitalization (or equivalent) of each type of long-term capital. Thus in judging the difficulty encountered with any one particular type of capital, both aspects should be taken into account.

748

ANSWERS TO PROBLEMS

The presence of bank overdrafts in the capital structure do not cause much difficulty as long as the amount of the overdraft remains reasonably stable. The interest rate charged on the overdraft can be expected to vary with changes in market interest rates and so the current ‘market value’ of the overdraft will remain equal to its nominal amount. Furthermore, given that the overdraft is repaid at par, the after-tax market return will simply be the current actual overdraft interest rate, adjusted for the tax relief on the interest payments. Convertible loan stock causes greater difficulties. Such stock may well have a market quotation, and in such circumstances finding its capitalized market value causes no problems. However, if it is unquoted an equivalent valuation must be estimated. The valuation of this type of security can be approached by splitting it into two elements, the loan stock itself and the convertible option, which is a call option on the company’s equity. Thus its market value can be estimated as whichever is the greater between its value as a simple loan stock and its value if converted immediately, plus the value of the call option. Apart from these difficulties, whether or not a market value exists, there is still the problem of estimating the market return on the security, which requires the determination of the point in time at which conversion is expected to take place, and the expected gain that the stockholders can be expected to make upon conversion. (c) There are four fundamental assumptions that are made when a company’s weighted average cost of capital (WACC) is used as an NPV discount rate. These are: (i) the project under evaluation is marginal; (ii) the project, if accepted, is financed in such a way as not to change the company’s existing capital structure; (iii) level-perpetuity cash flows; (iv) the project has the same degree of systematic risk as the company’s existing projects. The assumption that the project should be marginal, i.e. that it is small relative to the size of the company is necessary because the WACC itself is a marginal rate of return. The WACC is made up of the ‘cost’ of each individual source of the company’s capital, and each of these costs represents the required return on a marginal investment in that security. For example, the company’s cost of equity capital represents the required market return from a marginal investment in the company’s equity. Hence the WACC should only be applied to evaluating relatively small capital investment projects. The second assumption is required (except in a Modigliani and Miller world with no taxation) because a change in the company’s capital structure can be expected to change its WACC. There are two reasons for this. First, changing the gearing ratio will change the amount of financial risk borne by ordinary shareholders and hence will change the ‘cost of equity capital’ value in the WACC calculation, and secondly, changing the gearing will in turn change the weights (assuming market value weights) used in the WACC calculation. The third fundamental assumption arises from the fact that, strictly speaking, the WACC calculation is a level-perpetuity model. Hence the different types of company capital should involve only level-perpetuity cash flows, as so too should the cash flows of the project being evaluated. Finally, and perhaps most important, is the assumption about a constant level of systematic risk. A company’s WACC represents the overall return that the company earns, given the systematic risk of the existing collection of assets. It therefore follows that its WACC is applicable only to the evaluation of new investment opportunities that have a similar level of systematic risk. It is this last requirement in particular that makes the WACC of Redskins especially unsuitable for investment appraisal purposes, as it is a holding company consisting of a number of different subsidiaries in (presumably) different industries, and with the

CHAPTER 18

749

CAPITAL STRUCTURE IN A SIMPLE WORLD

likelihood of different levels of systematic risk. Thus the WACC represents the required return on the average of these risks, but it cannot be thought to reflect the systematic risk of any one particular subsidiary.

Chapter 18

Capital structure in a simple world problem 1 (a) Earnings Interest

Alpha £ 5.0mn £ 0.72mn

Beta £ 5.0mn ––

Dividends PE PB VE VB KE KD K0

£ 4.28mn 100p £ 50 £ 17.2mn £ 4mn 0.249 0.18 0.236

£

5.0mn 50p –– £ 23.2mn –– 0.216 –– 0.216

Beta shareholding: 464 000 shares = 1% ∴ Annual divs. = £50 000 Arbitrage to Alpha: Sell Beta for £232 000, and either: Alpha geared 4:17.2 ∴ Buy £ 43 774 debt × 0.18 and £188 226 equity × 0.249

= =

£ 7 879 interest £46 838 dividends £54 717 income

∴£4 717/year better off Buy 1% Alpha debt, plus the balance in equity: £ 40 000 debt × 0.18 = £ 7 200 interest £192 000 equity × 0.249 = £47 808 dividends £55 008 income ∴ £5 008/year better off As a shareholder in Beta, Ms Gamma holds no financial risk as Beta is an all-equity company. In order to be able to compare like with like it is necessary for her to maintain this zero exposure to financial risk when she moves into Alpha. Thus she wishes to buy into the earnings probability distribution of Alpha (which, by definition, has the same degree of business risk as Beta’s dividend distribution). The simplest way would be to buy debt and equity in Alpha in proportion to the company’s existing gearing ratio. However, this is not a perfect answer as Alpha’s equity – and hence the gearing ratio – is in disequilibrium. Therefore the alternative arbitraging mechanism that is shown above may be preferred, as it effectively has Ms Gamma buying into Alpha in proportion to the equilibrium gearing ratio. (b) In equilibrium, given that the earnings of the two companies have the same magnitude: V0α = V0β = VEβ

=

£23.2mn

750

ANSWERS TO PROBLEMS

VBα

=

£ 4.0mn

∴ VEα

=

£19.2mn

PEα = £19.2mn/17.2mn

=

£1.12/share

problem 2 (a) If two companies are in the same business risk class then their asset betas will be the same. Given that these two companies are in the same business risk class, this condition should hold. Furthermore, as Chardonnay is all-equity, its equity beta will equal its asset beta. Hence its equity beta can be estimated as Cabernet’s asset beta: β Cabernet assets = 1.6 ×

3

4

= 1.2 = β Chardonnay equity

(b) Cabernet: KE = 10% + (6% × 1.6) = 19.6% KD = 10% K0 = (19.6% × 0.75) + (10% × 0.25) = 17.2% Chardonnay: KE = 10% + (6% × 1.2) = 17.2% = K0 This is just the result that the Modigliani and Miller no-tax capital structure hypothesis would expect: companies in the same business risk class have the same weighted average costs of capital. (c) Given the information in (b) above, a regular £150 per year dividend should have a value of £150/0.172 = £872.09. Thus the shareholder is, in effect, being offered a disequilibrium price for his shares. This price implies a WACC of: £150/£1 000 = 15%. Hence there would be a gain to be made by arbitraging into Cabernet. This can be achieved as follows. (i) Sell shares in Chardonnay for £1 000 cash. (ii) Use the money to buy both the debt and equity of Cabernet in the same proportion as Cabernet’s own debt: equity ratio (1:3). Thus the investor should purchase £250 of Cabernet debt and £750 of Cabernet equity. This would have the effect of maintaining a zero financial risk level (as at present) and would produce an annual income of: £250 × 0.10 £750 × 0.196

= =

£ 25 £147 £172/year

Thus the investor is £172 – £150 = £22/year better off, with no change in risk. (d) In these circumstances, Cabernet’s WACC value of 17.2% is an equilibrium value. Hence Chardonnay’s WACC (and hence KE also, as it is an all-equity company) should equal 17.2%. Thus the equilibrium value of the investor’s shareholding in Chardonnay is £150/0.172 = £872.09.

Chapter 19

Capital structure in a complex world problem 1 (a) Mandina plc Using the asset beta, the CAPM can be used to calculate what would be the company’s cost of capital, if it were all-equity financed:

CHAPTER 19

CAPITAL STRUCTURE IN A COMPLEX WORLD

751

7% + (15% – 7%) × 0.50 = 11% Hence Mandina, if it were all-equity financed, would have a value of: £500 000(1 – 0.35) = £2.954mn 0.11 Using the Modigiani and Miller (M and M) expression for the total market value of a geared company in a taxed world, the actual total market value of Mandina can be estimated: Total market value: £2.954mn + (£1mn × 0.35) = £3.304mn As Mandina’s debt is worth £1mn, its equity will be worth: £3.304mn – £1mn = £2.304mn. As there is an 8% chance of bankruptcy and a cost of bankruptcy of £0.5mn, the expected cost of bankruptcy will be: £0.5mn × 0.08 = £40 000, and so the total market value of the equity will be reduced to £2.264mn. Therefore: Total market value of equity

= £2.364mn

Total market value of debt

= £1mn

Total market value of company

= £3.264mn

Debt:equity ratio = 1:2.264 Clarice plc Company’s cost of capital, assuming all-equity financing: 7% + (15% – 7%) × 1.50 = 19% Value of company if all-equity financed: £1.2mn(1 – 0.35) = £4.105mn 0.19 Total market value of company: £4.105mn + £1mn × 0.35 = £4.455mn Total market value of company: Less: total market value debt:

£4.455mn £1.000mn

Total market value equity:

£3.455mn

Less expected cost of bankruptcy: 10% × £0.5mn = £50 000 Total market value of equity:

£3.405mn

Total market value of debt:

£1mn

Total market value of company:

£4.405mn

Debt:equity ratio

= 1:3.405

(b) There are, perhaps, four principal determinants behind the capital structure decision in practice: (i) bankruptcy costs; (ii) agency costs; (iii) debt capacity; (iv) tax exhaustion. Each of these will be discussed in turn to examine how they affect the capital structure decision. Debt finance involves firms in a contractual agreement to pay interest and repay the capital sum. If the firm defaults on the agreement, debt holders can appoint receivers and effectively bankrupt the firm. Except in the case of fraud, firms are only going to

752

ANSWERS TO PROBLEMS

default on loan agreements when there is insufficient cash flow. Thus, the more highly geared the company, the greater the chance of a shortfall in cash flow and hence the greater the chance of bankruptcy. Although shareholders (and others, such as employees) no doubt bear a cost in such circumstances – as the question illustrates – the actual cost of bankruptcy is likely to represent only a very small loss in the wealth of a shareholder who has a well-diversified portfolio. However, in contrast, a very substantial loss would be suffered by the company directors in such circumstances – loss of office and loss of confidence in their professional abilities – and this would particularly be the case for the finance director whose responsibility it is for the company’s gearing level. Thus directors are going to be cautious about the level of corporate gearing so as to keep the probability of bankruptcy and the associated costs that they would bear at an acceptably low level. Whether this results in low gearing or higher gearing depends not only upon the risk attitudes of the directors concerned, but also on the volatility of the company’s pre-interest cash flow. Thus the directors of a property company, with its very stable (rental income) cash flow, may well be willing to gear the company up to high levels because even then the probability of loan default and consequent bankruptcy is relatively low. On the other hand, an engineering company’s directors may only indulge in a low level of gearing because of that type of company’s much more volatile cash flow. The second factor is agency costs. When a company raises debt capital, the loan is made under a trust deed which has attached to it a series of restrictive conditions. These conditions represent part of the lender’s efforts to control the actions of the management to ensure that they act responsibly with the money lent. In essence, these conditions represent ‘agency costs’. Generally speaking, the more highly geared the company, the more restrictive become these conditions. (Restrictions may be placed on such things as dividend growth, asset sales, diversification and further increases in gearing.) Thus once again management may wish to restrict the level of gearing simply to avoid the more onerous of these agency costs being imposed. The third factor is concerned with the fact that most corporate lending is secured against the assets of the firm. However, different assets have different levels of ability to act as security for a loan. This is referred to as an asset’s debt capacity. The main determinants of debt capacity are, first, the efficiency/quality of the second-hand market and, secondly, the rate of depreciation. The greater the former and the slower the latter, the better will be an asset’s ability to act as security. Thus, property assets will have a high debt capacity and industrial machinery will have a low debt capacity. Therefore the directors’ choice as to the company’s gearing level may well be dictated by the debt capacity of the firm’s assets and hence the capital market’s willingness to supply debt capital. Returning to the example used earlier, even if an engineering company’s directors were willing to ignore bankruptcy costs, it is likely that they would be prevented from gearing the firm up to high levels by the low debt capacity. However, the capital markets would be willing to gear up the property company’s capital structure more highly because of its high debt capacity. The final determinant of the gearing ratio arises from the fact that the main attraction of debt capital is the tax-deductibility of the interest payments. Tax exhaustion refers to the situation where the firm has insufficient tax liability to take the tax relief available. In such circumstances, much of the attractiveness of debt, relative to equity, disappears. Thus companies may well restrict their level of gearing to avoid the possibility of moving into a situation of tax exhaustion. Finally, no mention has been made in this discussion of the weighted average cost of capital (WACC). The reason for this is that first most companies are unable to measure their WACC with any confidence (principally because of valuation difficulties), and even

CHAPTER 19

CAPITAL STRUCTURE IN A COMPLEX WORLD

753

when they do, the WACC is such a volatile figure that company directors cannot realistically indulge in the static analysis of the ‘traditional view’ of capital structure, seeking to identify the minimum point on the WACC function. Certainly companies might try to identify some ‘optimal’ capital structure, but its optimality is more likely to be based on managerial judgement arising out of the four factors discussed earlier, rather than on an estimate of the WACC function. Also, mention should also be made of the M and M analysis. M and M suggested that, in a taxed world, companies should gear up as high as possible in order to take advantage of debt interest tax relief. Implicit in the foregoing discussion is the assumption that this is the policy that directors would wish to pursue, but they are prevented from always following this advice because of the factors discussed. In addition, the later Miller analysis (1977) throws all this analysis into some confusion. Miller argued that in a world of corporate and personal taxes and a perfect market for corporate debt capital, the capital structure decision (from an M and M viewpoint) is irrelevant. However, such circumstances – if they hold good in the real world – still do not negate the impact of the four factors discussed on the capital structure decision.

problem 3

Modigliani and Miller show that companies that have the same earnings stream and the same level of business risk will have the same total market values (V0) in the absence of taxation, whatever their individual capital structures. Dora and Bella are two such companies and so it is not surprising that in t–3, when there was no taxation in Despina, their total market values were identical: Dora: VE = V0 = $1mn Bella: VE + VB = V0 = $0.8m + $0.2mn = $1mn In the following year taxation was introduced on company profits and therefore company market values could be expected to fall. However, under the t–2 regime there was no difference between the tax treatment of equity dividends and debt interest. Therefore the tax charge was unaffected by a company’s capital structure. Consequently, the total market values of the two companies should remain the same, despite their different gearing ratios. This was the case: Dora: VE = V0 = $0.51mn Bella: VE + VB = V0 = $0.51mn In t–1 the tax regime was changed so that debt interest was treated differently from equity dividends. Specifically, debt interest was now allowable against taxation. Thus a geared company would have a lower tax charge than a similar ungeared company and, as a result, the geared company would have a higher total market value. Again Modigliani and Miller showed that under such a tax regime with two identical companies, except that one was geared while the other was ungeared, then the total market value of the geared company would be: V0 (geared) = V0 (ungeared) + VB ⋅ Tc where Tc is the rate of corporation tax. Therefore it would be expected that Bella (the geared company) would have a greater market value than Dora: Dora: VE = V0 = $0.52mn Bella: VE + VB = V0 + $0.60mn and this value for Bella can be shown to fit in with the M and M expression: V0 (Bella) = V0 (Dora) + (VB (Bella) × Tc) $0.6mn = $0.52mn + ($0.16mn × 0.50)

754

ANSWERS TO PROBLEMS

Finally, in t0, although the tax regime remained unchanged from t–1, there is effectively no corporation tax as tax allowances shield operating earnings fully. Therefore, once again, the total market values of the two companies would be expected to equate, as they do: Dora: VE = V0 = $0.98mn Bella: VE + VB = V0 = $0.98mn

Chapter 20 Capital structure in practice problem 1 Calculations Current EPS: £5.778mn = 57.78p 10mn Current gearing (debt:equity using book values): £12m+ £6mn = 817 . % £22.02mn Impact on EPS and gearing of the three different sources of finance This question gives no indication as to the impact on earnings of the extra £10 million of investment. Thus it will be assumed that it will generate the same return on investment as at present. Operating profit: Capital employed:

£11.17mn = £32.8% £34.02mn

Thus the extra £10 million of capital will generate extra operating profits of: £10mn × 0.328 = £3.28mn (i) Ordinary share financing It is assumed that the new shares will be issued at a 10% discount on the current share price of 350p: 315p. Thus, the number of new shares issued will be: £10mn/315p = 3 175 00 approx. Also, it is assumed that the company will maintain its current dividend per share payout of: £3.467mn = 34.67p / share 10mn Operating profit Interest

11.17 + 3.28 =

Pre-tax profit Tax at 35% Earnings Dividends Retained earnings

£mn 14.45 (2.28) 12.17 (4.26)

(10mn + 3.175mn) ×34.67p =

7.91 (4.57) 3.34

CHAPTER 20

755

CAPITAL STRUCTURE IN PRACTICE

£7.91mn = 60 p 13175 . mn

Revised EPS: Revised gearing:

£12mn + £6mn = 50.9% £22.02mn + £10mn + £3.34mn

(ii) Preference share financing Operating profit Interest

£mn 14.45 (2.28)

Pre-tax profit Tax at 35%

12.17 (4.26)

Earnings Preference dividends

7.91 (1.40)

Earnings available for shareholders Dividends

6.51 (3.467)

Retained earnings

3.043 £6.51mn = 65.1p 10mn

Revised EPS:

£12mn + £6mn + £10mn = 1117 . % £22.02mn + £3.043mn

Revised gearing: (iii) Loan stock financing Operating profit Interest

£mn 14.45 2.28 + 1.2 = (3.48)

Pre-tax profit Tax at 35%

10.97 (3.84)

Earnings Dividend

7.13 (3.467)

Retained earnings

3.663 £7.13mn = 71.3p 10mn

Revised EPS: Revised gearing:

£12mn + £6mn + £10mn = 109% £22.02mn + £3.663mn

Report to the Directors of Latost plc Dear Sirs We have analysed the probable impact of the three proposed financing packages of the company’s EPS and gearing levels. The results are shown below: Current situation Equity financing Preference financing Loan stock financing

EPS 57.78p 60p 65.1p 71.3p

Gearing 81.7% 50.9% 111.7% 109%

All three financing packages will result in an increase in EPS. Financing via preference shares or loan stock will increase the level of gearing, while financing with equity will reduce the gearing.

756

ANSWERS TO PROBLEMS

The decision as to which financing package should be chosen is not clear-cut. However, the analysis would appear to suggest that loan stock financing is a better alternative to preference share financing as the loan stock alternative provides a significantly higher EPS and a marginally lower level of gearing. This then narrows the choice between equity financing and loan stock financing. It is here that the directors must judge the trade-off that their shareholders will find acceptable between risk and return. Equity financing results in a small increase in EPS from 57.78p to 60p, but does provide a substantial reduction in gearing (and hence, a reduction in the riskiness of ordinary shares) from 81.7% to 50.9%. In contrast, loan stock financing results in a substantial increase in EPS from 57.78p to 71.3p, but it also increases the level of gearing from an already high 81.7% up to 109%. We would suggest that the final choice be made after investigating the gearing levels of Latost’s competitors. If the competitors have gearing levels of around 100%, then it would be reasonable to assume that such a high level of gearing is acceptable and, on balance, the loan stock option should be selected. However, if Latost’s competitors generally have a much lower level of gearing, then the equity financing alternative may represent the more acceptable course of action. Yours faithfully B.E.R. Tie Accountants

problem 2 (a) ‘Business risk’ arises out of the risky nature of the company’s business, which manifests itself in the variability of the company’s earnings stream (before interest and tax). Quite simply, some companies have very stable earnings streams because of the steady, low-risk nature of their businesses. A supermarket company might be one such example. In contrast, some other companies have highly volatile earnings, again because of the very variable high-risk nature of their businesses. A small oil-exploration company might serve as a suitable example of a company with a high degree of business risk. Portfolio theory shows that risks can be divided up into systematic risk and unsystematic risk. Systematic risk is that part of total risk that cannot be diversified away, while unsystematic risk is the risk that can be diversified away. Therefore business risk is partially systematic and partially unsystematic. The systematic element of business risk is largely (but not completely) out of the control of the individual company management. The unsystematic element of business risk arises out of factors which are specific to the individual company and are directly under the control of management. The two main determinants of a company’s exposure to systematic business risk would be the sensitivity of the company’s revenues to the level of economic activity in the economy (and its sensitivity to macroeconomic events in general), and its proportion of fixed-to-variable ‘operating’ costs, i.e. the costs incurred in generating those revenues – principally material, labour and energy costs. The greater its revenue sensitivity and the greater its proportion of fixed costs, the greater its exposure to systematic business risk. Such factors as revenue sensitivity and fixed-to-variable operating costs are largely out of management’s control, and arise out of the nature of the market and the production technology. Thus a carpet manufacturing business can do very little about the highly revenue-sensitive nature of the business (people buy new carpets when the

CHAPTER 20

CAPITAL STRUCTURE IN PRACTICE

757

economy booms and not otherwise). Nor can the manufacturer do much about the high proportion of fixed costs involved in carpet production technology. However, it should be noted that these factors are not entirely out of management’s control. For example, the carpet manufacturer may try to lock his customers into long-term deals to bring greater stability to the revenues. Similarly they may try to subcontract out as much of the manufacturing process as they can, on short-term contracts, to keep as many of their costs variable as possible. The unsystematic aspects of business risk arise from such factors as the skill of the top management team, the training of the workforce, the state of labour relations and the ability of the marketing department. Obviously, such factors are largely under the direct control of the management. (b) An investor with a well diversified share portfolio will have eliminated all unsystematic risk. Therefore such an investor is only going to be interested in the systematic element of business risk which, together with financial risk, goes to make up the beta value of the shares. (c) (1) Degree of operating gearing (DOG) DOG at a given level of turnover is: Turnover – Variables costs Profit before interest and tax At the start of the current financial year: DOG =

3381 – 2193 = 2.57 462

Assume that variable costs comprise wages and salaries, raw materials and direct selling expenses. (In reality these are not all likely to vary directly with turnover.) One interpretation of a 2.57 DOG may be that a 1% change in sales will lead to a 2.57% change in profit before interest and tax (in the same direction). At the end of the financial year, the expected profit and loss account, assuming no price changes except those stated, is: (£000s) (£000s) Turnover (15% increase) 3 888 Operating expenses: Wages and salaries (1 220 × 0.80 × 1.15) 1 122 Raw materials (15% increase) 1 004 Direct selling prices (15% increase) 115 General administration (no increase) 346 Other fixed costs (£85 000 increase) 465 3 052 Profit before interest and tax

836

Therefore expected DOG at the end of the year is: 3888 – 2241 = 1.97 836 The degree of operating gearing is expected to fall. If a high percentage of a company’s total costs are fixed, that company will have a high degree of operating gearing. If other factors are held constant the higher the operating gearing the higher will be the business risk of a company. In this case other factors have not been held constant; the unit variable cost of wages and salaries and also the level of fixed costs are expected to change. The overall result is a lower DOG at the sales level of £3 888 000.

758

ANSWERS TO PROBLEMS

Financial gearing As an accounting-based analysis of the company is being undertaken, an accounting-based measure of financial gearing will be used: Balance sheet value of debt Shareholders' funds At the start of the year financial gearing is

570 = 37.7% 1510

At the end of the year profit before interest and tax has been estimated to be £836 000. (£000s) Profit before interest and tax 836 Interest (207) Profit before tax Tax

629 (252)

Profit available to ordinary shareholders Estimated dividend

377 (189)

Retained earnings

188 Estimated financial gearing

570 + 820 = 81.8%. 1510 + 188

The expected financial gearing more than doubles by the end of the year. The higher the level of financial gearing, the higher the financial risk placed on the ordinary shareholders. (c) (2) (i) If turnover increases by 15%, the expected profit available to ordinary shareholders is £377 000. There are 3 200 000 issued ordinary shares resulting in an expected earnings per share of 11.78 pence. The earnings per share at the start of the year is £227 000 = 7.09 pence per share. 3 200 000 Because of the financial and operating gearing effects, earnings per share are expected to increase by 66%. (c) (2) (ii) If turnover falls by 10% (£000s) (£000s) Turnover 3 043 Operating expenses: Wages and salaries (1 220 × 0.90 × 0.80) 878 Raw materials (10% fall) 786 Direct selling expenses (10% fall) 90 General administration (no change) 346 Other fixed costs (£85 000 increase) 465 2 565 Profit before interest and tax Interest

478 (207)

Profit before tax Tax

271 (108)

Profit available to ordinary shareholders

163

CHAPTER 21

759

INVESTMENT AND FINANCING INTERACTIONS

The estimated earnings per share is

£163 000 = 5.09 pence. 3 200 000

This is 28% lower than the current earnings per share. The changes in the operating and financial gearing have increased the risks for the shareholders.

Chapter 21 Investment and financing interactions problem 1 (a) Base-case discount rate 1(1 – 0.35)  3    + 0.10  = 1.26   – 3 + 1(1 – 0.35 )  3 + 1(1 0.35)    β Asset = 1 ⋅ 036 + 0.018 = 1.054

β Asset

project

project

E[rProject] = 7% + [15.5% – 7%] × 1.054 = 16% approx. Base-case present value –10 000 + 6 700 (1 – 0.35) A¬

3 0 .16

= 219 PV

Financing side-effects PV tax shield 3 000 × 0.14 × 0.35 + A¬

3 0 .14

= 341 PV

Issue costs 3 000 × 0.01 × (1 – 0.35) =

–19.5

4 000 × 0.02 × (1 – 0.35) =

–52 –71.5PV

Note that the project gains the tax shield and incurs the issue costs based on how the project would be financed as a free-standing entity. Hence, assuming that £3000 of retained earnings would be used and its 30% debt capacity would allow £3000 of debt financing, this means that, under normal circumstances, £4000 of equity finance (via a rights issue) would be raised. Adjusted present value: –219 + 341 – 71.5 = +50.5 APV Accept (b) Effect of cheap loan Interest saved: 10 000 × 0.14 × A¬3 0 .14

=

Less lost tax shield: 10 000 × 0.14 × 0.35A¬3 0 .14

=

Net saving

+3 250 –1 138 +2 112

Revised APV: –219 + 2 112 – 71.5 = +1 821.5 APV. Note, as the cheap loan is specifically attached to this project, all of its net benefits are taken into account.

760

ANSWERS TO PROBLEMS

problem 2 (a) Calculation of an asset beta for project VE VB(1 – TC ) + β Debt  VE + VB(1 – TC ) VE + VB(1 – TC ) 3 2(1 – 0.35 ) = 2.29  + 0.15  3 + 2(1 – 0.35 ) 3 + 2(1 – 0.35 )

β Asset = β Equity  β Asset

. + 0.04 = 164 . β Asset = 160 Calculation of base-case discount rate for project Base-case discount rate = rF + [E(rM) – rF] × βAsset 8.5% + [15.5% – 8.5%] × 1.64 = 20% approx. Calculation of base-case present value for project Data Capital expenditure: £1mn Scrap value: £0.6mn Working capital requirement: £0.3mn Revenues: £1.1mn/year for 5 years Operating expenses: Materials: £0.25mn/year Labour: £0.165mn/year Supervisory labour: £0.056mn/year Training: £0.270mn at Year 1 Variable overheads: £0.076mn/year Rent: £0.012mn/year Var. selling expenses: £0.095mn/year (Note: Labour has been costed on an incremental basis. Depreciation has been excluded as it is a non-cash item. Financing cash flows – interest – have been excluded. All other non-incremental/allocated expenses have been excluded.) Total operating expenses £0.654mn/year Net revenues £1.1mn – £0.654mn = £0.446mn/year pre-tax Capital allowance tax relief Capital allowances £1mn

Tax relief

Year

× 0.25

=

£0.25mn

× 0.40

=

£0.1mn

1

× 0.25

=

£0.1875mn

× 0.40

=

£0.075mn

2

× 0.25

=

£0.1406mn

× 0.35

=

£0.0492mn

3

× 0.25

=

£0.1055mn

× 0.35

=

£0.0369mn

4

× 0.25

=

£0.0791mn

× 0.35

=

£0.0277mn

5

(£0.3627mn)

× 0.35

=

(£0.1269mn)

6

0.25mn £0.75mn 0.1875mn £0.5625mn 0.1406mn £0.4219mn 0.1055mn £0.3164mn 0.0791mn £0.2373

–£0.6m =

CHAPTER 21

761

INVESTMENT AND FINANCING INTERACTIONS

Cash flow analysis (£mn) Machinery Scrap CA tax relief WC Training Tax relief Net revenues Tax

0 (1)

1

2

3

4

5

0.1

0.075

0.0492

0.0369

0.6 0.0277 0.3

(0.3)

6

(0.1269)

(0.270) 0.108 0.446 0.446 0.446 0.446 (0.1784) (0.1561) (0.1561) (0.1561) (0.1561)

0.446

Net cash flow 20% discount rate

(1.3)

0.276

0.4506

0.3391

0.3268

1.2176

(0.283)

0.8333

0.6944

0.5787

0.4823

0.4019

0.3349

PV cash flow

(1.3)

0.23

0.3129

0.1962

0.1576

0.4893

(0.1061)

Base-case present value: (£20 100) Calculation of present value of financing side-effects The debt capacity of the project is: Capital expenditure: WC expenditure:

£1mn × 0.50 = £0.3mn × 0.10 =

£0.5mn £0.03mn

Total

£0.53mn

Therefore the tax shield will only be calculated as a total of £530 000 of debt financing at 10% interest. PV tax shield £530 000 × 0.10 = £53 000/year interest for 5 years. £ 53 000 × 0.40 = £21 200 tax relief in Year 1. £ 53 000 × 0.35 = £18 550 tax relief/year thereafter PV: £21 200 (1 + 0.10) £18 550 A ¬

4 0.10

–2

(1+ 0.10)–2

= £17 520 = £48 594 £66 114

Adjusted present value Base-case present value PV of tax shield

£ (20 100) £ 66 114 APV + £ 46 014

As the APV is positive, the project should be accepted. (b) The evaluation carried out in part (a) differs in two fundamental ways from the analysis carried out by the production director. First, the project was evaluated on the basis of incremental cash flows. Therefore, a number of irrelevant items were excluded from the analysis. Secondly, the project was evaluated on the basis of APV and not NPV, to capture better the impact of the finance package proposed for the project. (c) Net present value is a capital expenditure evaluation technique. In contrast, adjusted present value is able to evaluate not only the capital expenditure decisions, but also the financing package with which it is proposed to undertake the project. In this way, therefore, APV is a more powerful form of analysis than the rather limited NPV analysis.

762

ANSWERS TO PROBLEMS

Chapter 22 The dividend decision problem 1 (a) (i) Cum dividend price after declaration of £150 000 dividend = 140p. The total value of Pulini plc will be £1.4 million. (ii) The current price reflects the expected dividend of £150 000. The share price should increase by the NPV of the contract. Dividend 15 = = 12% Ex div value 125 £80 000 £22400 – = +560 000 NPV = £80 000 + 0.12 012 . KE =

Share price should increase by £560 000 ÷ 1mn = 56p; Revised cum dividend price = 196p; Revised total value = £1.96mn. (iii) By using the £80 000 revenue from the project Pulini can increase its current dividend from 15p to 23p per share. The way in which the market responds to this will depend upon whether it is efficient in the semi-strong or strong form. (1) Semi-strong. The revised price will depend upon whether the market supposes that the increased dividend is a one-off payment for this year only, or, based on Pulini’s past record of constant dividends, anticipates the increased dividend to continue indefinitely: One-off:

Cum-div price = 140p + 8p = 148p Total value £1.48mn.

Continuing:

23p +

23p = 215 p 0.12

Total value £2.15mn. (2) Strong form. If the market is efficient in the strong form it will learn of the project and the share price will adjust to 196p as calculated in part (ii) above. (b) In theory, dividends are a passive residual in the context of financial decision making. As the positive net present value of investment projects accrues to shareholders it must necessarily be the company’s aim to undertake all projects giving a positive net present value even if this entails reductions in dividends below previously existing levels. Funds not required for investment will be paid out as dividends. For these ideas to be valid there must be perfect information about company activities available to shareholders, who must understand and believe the information. They will then accept any reduction in dividend as being in their own interest and the share price will in fact rise to reflect this improvement in the value of the company. In the short term at least, the reduction of dividends to finance beneficial investment would in theory substitute a capital gain for dividends. Shareholders must be prepared to accept this distribution. They will do so only if they can borrow at the same rate as the company (and repay later out of a future enhanced dividend) or if they can realize the capital gain to obtain cash in substitution for the dividend. These will only be adequate substitutes if there are no transaction costs or distorting taxes. If the conditions necessary to uphold the ‘dividend irrelevancy theory’ were met in practice then dividends would truly be a residual and not a determining factor in the

CHAPTER 22

THE DIVIDEND DECISION

763

valuation of a company. However, in reality, they do not hold well and it is necessary to examine those aspects of dividend policy which may in practice affect a company’s market value. It is information which determines share price and one of the principal pieces of objective information available to investors to assist them in pricing shares is the level of dividend. Whilst published accounts and reported earnings are extremely useful, they are both historical, indicating what the company has done rather than what it is doing or will do. Dividends are, by contrast, an indicator of the current state of the company and its future prospects. The amount of, and trends in, dividends are thus strongly reacted to by the market. This is strikingly illustrated by the different reactions to reduced dividends in theory and practice. In theory this could well herald further beneficial investment and increased company value whereas in practice it is likely to be seen as evidence of severe difficulties and the share price is likely to drop. Even if the management set out clearly their intentions for the use of funds, it is possible that the message will not be fully understood, or may be treated with scepticism. In view of these practical realities, company management are likely to pursue a policy of dividend stability and, where possible, steady growth at a prudent rate. Above all shareholders require a consistent policy. Where this is possible, uncertainty, and hence risk, is reduced. The rate of return required by investors may therefore be adjusted downwards leading to higher market capitalization. In summary, investors are not indifferent between current dividends and the retention of earnings with the prospect of future dividends, capital gains, or both. They prefer the resolution of uncertainty and are willing to pay a higher price or a share that pays a greater current dividend, all other things being equal. (c) The factors that will influence company management’s dividend policy relate essentially to prudence, company funding requirements and regard for individual shareholders’ requirements. With regard to prudence, it might well be that whilst a company makes good profits, a significant proportion of these may not be realized in cash terms and it is therefore not possible to pay substantial dividends without placing strains on the company’s liquidity. Dividends must be budgeted for as an integral part of the cash flow forecast and where necessary further funds obtained for the purpose of dividend payments. The alternative to this is a more restrained payout policy. Company management will also have regard to future funding requirements. Use of retained earnings is one of the simplest and cheapest ways of obtaining finance for expansion, and it is therefore quite attractive to management to pursue a relatively low payout policy in order to retain funds for expansion. The company’s access to capital markets will also play a large part in the decision on retention policy. A company with ready access to capital markets may in practice prefer a higher payout policy coupled with regular rights issues rather than keep dividends deliberately low to provide a large pool of retained earnings. Smaller companies cannot count on this advantage and therefore in practice will seek funding largely from retained earnings. In financial management it is generally assumed that the objective of company management is to follow a policy of maximizing the wealth of shareholders. To this end dividend policy is of vital importance. Clearly a high retentions policy is commensurate with high capital growth in share value whilst high payouts will benefit shareholders who require high income. Whilst in a perfect capital market with no taxes this differentiation of policy would be irrelevant, in actuality the tax position of shareholders will significantly influence their accumulation of wealth through shareholdings. Whilst in large companies researching shareholders’ preferences and setting policy accordingly might be impracticable, this will not necessarily be so in small companies where tax considerations may well play an extremely important part in setting dividend policy.

764

ANSWERS TO PROBLEMS

It should not be forgotten that dividends can only be paid regularly where the company is inherently profitable and hence management must examine profitability in setting dividend policy, and in particular the stability of earnings. Where earnings are very stable the company will be less at risk in following a high percentage payout policy than if earnings are extremely volatile. Dividend cuts are usually anathema to company management as the market is likely to consider that this presages bad news, with consequent disastrous effects on share price. Hence companies with volatile earnings are unlikely to risk dividend cuts by pursuing a high payout policy. Indeed good dividend policy is to pursue the ideals of stability and consistency. Variable dividends are uncertain dividends, giving rise to an increased risk perception in shareholders. This feeds through into a higher required return and hence lower market capitalization, defeating the company aim of shareholder wealth maximization. While the conventional models assume the objective of maximization of shareholder wealth this may not be the objective being pursued by particular companies. It may be that corporate managers are pursuing alternative objectives such as sales maximization, market share maximization or the maximization of managerial discretion subject to the constraint of providing an acceptable return to investors. Alternatively managers may not be maximizing at all but may be ‘satisficing’, i.e. pursuing a battery of parallel objectives. In such circumstances they will need to modify their dividend policies to suit the objectives they are pursuing. In any event they will need to know what constitutes an acceptable return to their investors and this in turn requires a knowledge of what can be earned on similar risk investments elsewhere, i.e. the opportunity cost of capital. Finally it cannot be forgotten that there are legal requirements governing dividend payments and company management must have regard to the legal definitions of distributable profits.

problem 3 (a) Net present value to Charles Pooter (Contractors) Ltd: –2

–3

NPV = –3 000 + 800(1.04) + 1 000(1.04) + 1 700(1.04) NPV = –3 000 + 769 + 925 + 1 511 = +£205

(b) (i) Lupin is satisfied (as stated in the question). Charles can borrow one half of the present value of the cash inflows from the project (i.e. he can borrow the present value of the dividends he expects to receive): Charles can borrow ( 12 × £3 205) £1 602 at 4% (and go on the cruise) Interest Year 1 at 4%

64

Repay end Year 1 ( 12 × £800)

1 666 400

Interest Year 2 at 4%

1 266 51

Repay end Year 2 ( 12 × £1 000)

1 317 500

Interest Year 3 at 4%

817 33

Repay end Year 3 ( 12 × £1 700)

850 850

By borrowing, and using his dividends to repay the loan, Charles is £102 better off if the project is accepted than if it is rejected. So the company is acting in the best interests of both shareholders by accepting the project.

CHAPTER 23

765

ACQUISITION DECISIONS

(ii) Lupin is still satisfied (as stated in the question). The present value of Charles’s dividends at a 10% discount rate is: –1

–2

–3

400(1.10) + 500(1.10) + 850(1.10) = 400(0.9091) + 500(0.8264) + 850(0.7513) = £1 415 which is the maximum amount he could borrow and repay out of his share of the project dividends. He would be better off with an immediate dividend of £1500. So the company is not acting in the best interests of both shareholders. (c) The above analysis suggests that the net present value rule results in correct investment decisions provided that all shareholders have the same ‘cost of capital’ as the company, even if their consumption preferences vary. Any shareholder can adjust his dividend receipts to fit his desired consumption pattern by lending or borrowing. (b)(ii) suggests that the net present value rule needs to be applied cautiously where shareholders’ costs of capital differ from the company’s (e.g. where capital markets are imperfect). In this case it may not be possible for shareholders to adjust their consumption patterns by lending or borrowing without incurring an interest cost different from the company’s.

Chapter 23 Acquisition decisions problem 1 After a merger of Peden and Tulen

Value of debt (45 + 10) Value of equity (bal fig) Total value

Recession (p = 0.15) (£mn) 55 50 105

Slow growth (p = 0.65) (£mn) 55 80 135

Rapid growth ( p = 0.2) (£mn) 55 140 195

Expected value (£mn) 55 87.5 142.5

42 — 42

45 10 55

45 30 75

44.55 12.5 57.05

10 53 63

10 70 80

10 110 120

10 75.45 85.45

Without a merger of the two companies: Peden Value of debt Value of equity Total value Tulen Value of debt Value of equity Total value

Since no operational synergy has occurred on the merger, the total value of the merged company is equal to the sum of the values of the individual companies: £57.05mn + £85.45mn = £142.5mn However, there has been a transfer in total value from the shareholders to the debt holders. The total of the individual companies’ debt is 44.55 + 10 = £54.55 million, while the value of the merged company’s debt is £55 million. Conversely, the total of the individual companies’ equity is 12.5 + 75.45 = £87.95 million, while the value of the merged company’s equity is £87.5 million. This transfer arises from the position of Peden’s debt in a time of recession. Peden would have total net assets to be financed of £42 million, but £45 million of debt. In such

766

ANSWERS TO PROBLEMS

a situation the equity is worthless and £3 million of debt is unable to be repaid. There is a 0.15 probability that debt holders will lose £3 million, i.e. an expected loss of £450 000. In the merged company there is no longer any risk that the debt will be unable to be repaid in full. Therefore the debt holders can expect to be £450 000 better off, as the above calculations show. In practice the merged company is likely to have cash flows that are less risky than each of the individual companies, so both the cost of equity and cost of debt may reduce after the merger. This would offer a gain to both the equity holders and the debt holders, even in the absence of any operational synergy.

problem 2

The bid will be viewed favourably by the shareholders of Savealot if it offers a premium above the current share price. It will be viewed favourably by the shareholders of Minprice if it will increase the value of their shares. Consider the shareholders of Savealot first. The current share price of Savealot is 4 295p. At its current share price Minprice is offering shares worth 3 × 232p = 309p. This is only 14p or 4.7% above the current share price of Savealot, which is probably not enough to entice a majority of the Savealot shareholders to accept the offer. Factors likely to influence the decision include: (i) Recent annual growth trends. Savealot is currently growing faster than Minprice in both dividends and EPS, indicating that Savealot has good prospects. This is confirmed by the companies’ PE ratios:

PE ratio

Minprice £2.32 = 13.9 £50mn / 300mn

Savealot £2.95 = 14.75. £8mn / 40mn

The shareholders of Savealot will be unwilling to swap into the shares of a company with worse prospects, unless they are given a proper incentive. (ii) The intrinsic value of Savealot’s shares. Using the dividend valuation model, the shares of Savealot have an intrinsic value of: P=

D1 12.5p  1.08 = 270p. = ke – g 13% – 8%

This suggests that Savealot’s shares are currently overvalued at their current price of 295p, and would be a reason encouraging the Savealot shareholders to get out for this value while they can. (iii) The different financial profiles of the two companies. Minprice has much higher gearing than Savealot, e.g. at book values: Minprice 314 = 141% 222

Loans Gearing = Shareholders' funds

Savealot 17.5 = 32%. 54.7

Minprice has a higher dividend cover than Savealot (2.1 times rather than 1.6 times), and a lower dividend yield (3.4% rather than 4.2%). If a shareholder was worried about financial gearing, he would be happier owning Savealot than Minprice. If a shareholder was most interested in the dividend stream from his investment he would take account of the dividend statistics calculated above. Consider now the shareholders of Minprice. Using PE ratios we can estimate the share price of the combined company. If we first ignore the effects of the rationalization: Combined earnings Combined number of shares ∴ Expected combined EPS

= = =

50 + 8 = £58mn 300mn + (4 3 × £40mn) = 353.3mn 16.4p

CHAPTER 24

767

COMPANY VALUATION

Expected combined PE ratio

=

Current market value of Minprice Current market value of Savealot

= =

∴ Combined PE ratio

=

∴ Combined share price

=

Weighted average of the PERs of the two companies 300mn × £2.32 = £696mn 40mn × £2.95 = £118mn 696 118 × 13.9 + × 14.75 = 14.0 814 814 14.0 × 16.4p = 230p

This is marginally below the current share price of 232p, so would not be attractive. However, the effects on the value of the combined company would be: Sale of warehouse Redundancy Wage savings 2.7 × Annuity (12%, 5 years) = 2.7 × 3.605

The effect on the combined share price will be

£mn 6.8 (9.0) 9.7 7.5

£7.5mn = 2.1p 353.3mn

This takes the expected share price after the combination to 232p, i.e. the same as before the combination. There is no financial reason for the shareholders of Minprice to want the scheme to go ahead. However, if the wage savings could last longer than the five years used in the calculation, or if there are other possible synergies from the combination, then Minprice’s shareholders would look favourably at the scheme.

Chapter 24 Company valuation problem 1 Bid 7 September by BZO: 2 for 3 share exchange The value of this bid equates to £5.20 per Demast share (Working 6). The true value per Demast share is likely to be in the region of £4.43 (Working 5). Thus it appears that BZO are paying approximately £5.20 – £4.43 = 77p too much. This is largely borne out by the reaction of BZO’s shareholders to the bid as its share price falls 70p from £7.80 to £7.10 once the bid is announced. It appears that BZO’s shareholders value Demast at around the £4.50 mark so the bid is not financially prudent from their perspective. BZO is a conglomerate so no great synergies would be expected as a result of the acquisition and a purchase price of £5.20 per share would not appear an undervaluation. Bid 2 October by Nadion: 170p plus £100 convertible per £6.25 nominal value of shares The value of the bid equates to £5.70 per share ignoring the value of the option (Working 6). The true value of the share is likely to be around £4.43. It appears that Nadion is offering a premium of approximately £5.70 – £4.43 = £1.27 per share. Upon announcement the Nadion share price increases 15p from £3.20 to £3.35. It is surprising that the Nadion share price did not go higher because a combination of two companies in the same industry often results in considerable synergies. Bid 19 October by BZO: 600p per share The value of the bid is £6 per share. The value of the share is approximately £4.43. After announcement of the bid the BZO share price falls by 100p from its original value of £7.80 to £6.80. This is a substantial fall. It appears that BZO’s shareholders

768

ANSWERS TO PROBLEMS

think the bid is considerably higher than the true value of the shares. The bid is not therefore prudent from the point of view of the company’s shareholders. This is probably exacerbated by two further problems. • BZO’s gearing will increase substantially as a result of taking a loan to finance the cash purchase. • Directorships will be given to Demast’s current directors. As BZO is a conglomerate they may not have the relevant experience to run other subsidiaries effectively. Working 1: Book value of net assets acquired From the balance sheet this is £6 500 000. Reservations are as follows: • The predators are likely to run Demast as a going concern so are more likely to be concerned with its income than with its assets. • A historical cost balance sheet is not a valuation device. Working 2: Net realisable value of net assets acquired Book value of net assets Less stock devaluation (5 500 000 × 10%) Net realizable value

£ 6 500 000 (550 000) 5 950 000

Working 3: Valuation by price–earnings multiple This is a practical and common method of valuing a target in a takeover situation. Companies in the same industry tend to have similar PERs because a PER partly reflects growth prospects and the perceived risk of the company. In the absence of Demast’s own PER (it is not a listed company), Nadion’s will be used instead as it is also a games manufacturer. PER ratio of Nadion = Value of Demast shares = Total value of equity acquired =

320 ÷ 58 = 5.5 80.5p × 5.5 = 442.75p 442.75 ÷ 100 × 1 000 000 × 4 (25p nominal) = £17.71mn

Comments and reservations include: • An income-based valuation is presumably more consistent with the purchaser’s intentions (i.e. to run Demast as a going concern). • Nadion’s PER may not be representative of the industry. Further information on similar companies is required. • The calculation assumes that Demast’s current earnings would be unchanged after a change of ownership. The true value to the predator is the value of the earnings under their control. The following specific comments can be made: – The directors own 25% of Demast. Thus they may be paying themselves inflated management salaries which would not continue after a change of ownership. – The earnings may change after a change of ownership because of synergistic benefits. These are unlikely to be major in the case of BZO as its operations are dissimilar to those of Demast. However Demast and Nadion are in the same industry so considerable synergies could result from cost savings, sharing of know-how and reduced competition. Working 4: Dividend valuation approach The intrinsic value of a share is thought to be the present value of the future dividend stream. Therefore by estimating a value of the future dividends of Demast and discounting at an appropriate discount rate a share price can be obtained.

CHAPTER 24

769

COMPANY VALUATION

PV of dividends do/Ke – g do G Ke

= = = = =

Value of shares Value of shares £1 500 000 9% per annum 16% per annum

Value of shares =

£1 500 000  [1+ 0.09] = £23.3mn 0.16 – 0.09

Comments and reservations include: • An income-based method is more consistent with the predator’s intentions. • The dividend valuation approach is theoretical and subject to a number of criticisms. Working 5: Summary of valuations In total Book value of net assets (Working 1) NRV of net assets (Working 2) PER basis (Working 3) Discounted dividend approach (Working 4)

£6.5mn £5.95mn £17.71mn £23.3mn

Per share £1.63 £1.49 £4.43 £5.83

In practice the PER multiple is probably the most common valuation method so the main body of this answer assumes this to be the most accurate valuation. This gives a price for one Demast share (£17.7mn ÷ 4mn) = £4.43. Reservations include: • As stated above the predators are more likely to value Demast on an earnings basis. • Insufficient information is available to value Demast properly. The current market value, for example, of land and buildings is required. Working 6: Value of bids Bid 7 September by BZO Value of bid per share = 2 × £7.80 ÷ 3 = £5.20. Bid 2 October by Nadion Value of bid per share = £1.70 +

£100 = £5.70. 6.25  4

The value of the option cannot be quantified. Bid 19 October by BZO Value of bid per share = £6.00.

problem 2

The current market price of 410 pence per share, or a total market value of £123 million, is likely to be the lowest that shareholders of Omnigen would accept, and a premium over the current market price will normally be payable. If industry PERs are used to value Omnigen, the range of values would be £182 million to £210 million. (Omnigen’s total earnings after tax of £14 million, multiplied by the PERs of 13:1 and 15:1.) The realizable value of assets, £82 million, is substantially below the estimates based upon PERs. This shortfall in value is likely to be caused by the fact that the value of Omnigen’s intellectual capital is being ignored. A better method of estimating the value of Omnigen is to use the cash flow projections to find the present value of Omnigen to Laceto. This will be based upon the free

770

ANSWERS TO PROBLEMS

cash flow after replacement expenditure and expenditure required to achieve the forecast growth levels. Financial year Net sales Cost of goods sold (50%) Selling and administrative expenses Capital allowances Taxable Taxation (30%)

Year 1

(£mn) Year 2 Year 3

Year 4

230 115

261 131

281 141

298 149

32 40 187 43 12.9 30.1 40

34 42 207 54 16.2 37.8 42

36 42 219 62 18.6 43.4 42

38 42 229 69 20.7 48.3 42

Year 5 onwards

Add back capital allowances Less cash flow needed for asset Replacement and forecast growth (50) (52) (55) (58) Net cash flow 20.1 27.8 30.4 32.3 1 Discount factors (14%) 0.877 0.769 0.675 0.592 Present values 17.6 21.4 20.5 19.1

19.1(1.03) = 178.8 .14–.03 Total present value is £257.4 million (the sum of the present values for each year). This value is the value of the entire entity, i.e. equity plus debt. The value of debt will depend upon the final gearing, and will vary between approximately £45 million and £58 million (18%–23% gearing), giving a value of equity between £19.4 million and £212.4 million. If growth is 5% the present value of the entity would be £297.2 million, and the value of equity between £228.8 million and £243.7 million. Assuming these cash flow projections are reasonably accurate (which itself must be subject to serious doubt – e.g. can the imbalance after Year 5 between capital allowances and replacement capital expenditure continue indefinitely), it is clearly worth Laceto offering a premium over the current market price for the shares of Omnigen. In theory, using present values to infinity, it could afford to offer a premium of more than 50% above the current market price, but in order to increase its own value it would offer the lowest price that would attract more than 50% of the shareholders of Omnigen. It is not possible to know what this price would be. An initial bid might offer a 25–30% premium above the current price, or between £154 million and £160 million. If that bid was refused then there is scope for increasing it up to a maximum of the estimated equity present values discussed above. It must be stressed that all of the above estimates are subject to significant margins of error, and that valuation for takeover is not a precise science. 1

Discount rate: Using the capital asset pricing model Ke = 6% + (14% – 6%) 1.3 = 16.4% Omnigen’s cost of equity after the acquisition is used as this is likely to reflect the systematic risk of the activities of Omnigen within Laceto. As the range of expected gearing levels is quite small (18–23%), and gearing is relatively low, it is assumed that the cost of equity will not significantly change over this range of gearing, other than the change already reflected in the increase in the equity beta by 0.1. The cost of debt is not given but may be estimated from the data regarding Laceto’s debenture. As Omnigen currently has a lower gearing than Laceto, it is assumed

CHAPTER 25

771

FOREIGN EXCHANGE

increasing Omnigen’s gearing should not have a significant effect on Laceto’s cost of debt, even if the overall gearing increases to 23%. The cost of debt, using linear interpolation is: At 6% interest 12(1 – 0.3) × 2.673 100 × 0.840

= =

22.45 84.00 106.45

At 5% interest 12(1 – 0.3) × 2.723 100 × 0.864

= =

22.87 86.40 109.27

By interpolation: 5% +

0.47 × 1% = 5.17%. 0.47 + 2.35

The weighted average cost of capital may be estimated for the full range of expected gearing: At 18% gearing: The weighted average cost of capital is 16.4 × 0.82 + 5.17% × 0.18 = 14.38% At 23% gearing: The weighted average cost of capital is 16.4 × 0.77 + 5.17% × 0.23 = 13.82% The estimated WACC does not change dramatically over the possible range in gearing. 14% will be used as the discount rate.

Chapter 25 Foreign exchange problem 1

There are three basic causes of movements in FX rates:

1. forces of supply and demand; 2. interest rate differentials; 3. inflation rate differentials. Exchange rates represent the price of one currency in terms of another currency, and the price of currencies responds to the forces of supply and demand in exactly the same way as the price of anything else. Thus if lots of people want to buy the Japanese yen, the yen FX rate appreciates relative to other currencies. If people are selling the US$, then the $ FX rate depreciates. These supply and demand market forces arise out of the needs of international trade (a UK importer receives an invoice in US$ and therefore has to buy $ in order to pay the invoice) and investment (a US company wants to build a factory in Germany and therefore has to buy euros in order to pay for the investment). However, it is thought that the most important source of supply and demand market forces arises out of speculation. The second cause of FX movements is interest rate differentials between different countries. This idea is represented by the interest rate parity theorem which states that exchange rates should move to effectively bring about interest rate parity. Thus if the loan interest rate in US$ is 6% and in £ is 10% then IRPT states that the US$ should appreciate against £ by approximately the interest differential of 4%. The reasoning that lies behind IRPT is that international financial markets are efficient and, in such markets, there is no such thing as cheap finance. Thus a UK company

772

ANSWERS TO PROBLEMS

wishing to borrow money might be tempted to borrow $ rather than £. But IRPT holds that what they gain from a more favourable rate of interest they are likely to lose in an adverse movement in exchange rates: over time it would cost more and more in £ terms to pay the 6% $ interest and repay the $ loan. The third cause of FX movements is inflation rate differentials between countries. This is the purchasing power parity theorem which states that the currency of the country with the lower rate of inflation will appreciate against the currency of the country with the higher rate of inflation by an amount approximately equal to the difference between the two inflation rates. What lies behind the PPPT is the law of one price which states that the price of a good in one particular currency, times the exchange rate, should equal the price of that same good in another currency. If not, there is an opportunity for arbitrage gain. Therefore as inflation affects the price of the good in each country, the differences in inflation rates cause the exchange rate to move in compensation so as to maintain the law of one price.

problem 2

The two extreme types of exchange rate system are a system of fixed exchange rates and a system of freely floating exchange rates. Between these two extremes are a whole series of semi-fixed/semi-floating type systems. In a fixed rate system, exchange rates between different currencies are fixed by agreement between the countries concerned. Such a system makes importing and exporting much more straightforward as there is no foreign exchange risk. An importer invoiced in the overseas currency knows exactly how much that import deal will cost in his own currency because the exchange rate between the two currencies is fixed and unchanging. Exporters invoicing in the foreign currency would be equally certain about the outcome of that export deal in their own currency. The problem with fixed exchange rate systems is that they try to deny the forces of supply and demand by attempting to have a fixed price for one currency in terms of another. Such a system, almost by definition, is going to be unstable unless the economic conditions are such – equality of interest and inflation rates and a balance between imports and exports – to enable currency price stability to be maintained. A freely floating exchange rate system does not try to deny these supply and demand market forces as the exchange rate is allowed to float to wherever these forces push it. Therefore the system is stable in as much as it is a sustainable system, but it has two main problems. The first is that, in such a system, international trade is not encouraged because importers and exporters are exposed to the risk of adverse movements in exchange rates: foreign exchange risk. The second problem is that the exchange rate plays an important role in the macroeconomic affairs of an economy. As a result, most governments are not willing to allow their currency’s exchange rate to be determined solely by supply and demand market forces (as in a freely floating or ‘clean’ floating system). Because all of these extremes have both advantages and disadvantages, there are many examples, throughout the world, of semi-fixed exchange rate systems that try to capture the advantages of each extreme whilst avoiding their disadvantages. One such system was the Exchange Rate Mechanism (ERM) of the European Union which was set up in 1979. In such a system the exchange rates between the member country currencies are fixed, but those rates then are allowed to appreciate or depreciate, in response to supply and demand market forces, to a very limited (and specified) extent. Such a system is designed to encourage international trade between member countries by having (approximately) fixed exchange rates. The problem is that market forces in foreign exchange markets can be enormous. With such potentially large market forces it is very difficult to maintain only a limited movement in exchange rates unless economic

CHAPTER 26

FOREIGN EXCHANGE HEDGING

773

conditions (convergence of interest and inflation rates between member countries) can control them.

Chapter 26 Foreign exchange hedging problem 1 (a) As the question gives only the S$/US$ and US$/£FX rates, we first have to calculate the S$/£ cross rate: Two months forward: S$/US$ US$/£

= 2.0964 = 1.5047

∴ £/US$

= 1/1.5047 = 0.6646 20964 . = 3.1544 = 0.6646

∴ S$/£

Three months forward: S$/US$ US$/£

= 2.0915 = 1.5105

∴ £/US$

= 1/1.5105 = 0.6620 20915 . = = 3.1592 0.6620

∴ S$/£

There are basically two ways an exporter can hedge against FX risk if they have to invoice customers in the overseas currency. One is to use the forward market and the other is to use the money market. Singapore sale With Oxlake, as far as the Singapore sale is concerned, they could investigate either approach. However, due to the uncertainty as to when the customer will pay and the fact that the company wishes to hedge ‘without taking any risks’, this means that only the forward market approach is possible. The reason for this is that, with a money market hedge, the company would be open to risk in that it doesn’t know whether to take out a two- or three-month loan. If they just take out a two-month loan, there is the risk that the customer will not pay until three months have elapsed. Thus the loan would have to be extended for a month (subjecting the company to interest rate risk) and the increased level of interest payable (three months rather than two) would also expose the firm to a small FX risk on the difference. In order for Oxlake to hedge the Singapore contract without any risk they will need to take out an option forward contract as the timing of the S$ receipts is uncertain and could arise at any time between two and three months. Option forward contract rates are always set at the least favourable rate to the company. A two-month forward contract has an exchange rate of 3.1544, whilst the three-month contract is at a rate of 3.1592. As it is the latter which is the least favourable to Oxlake, this will be the rate they are charged on their option forward contract. Hence the company will take out an option forward contract to sell S$715 500 at some time between two and three months in the future, at an exchange rate of 3.1592. Thus the expected £ cash flow will be: S$715 500 ÷ 3.1592 = £226 481

774

ANSWERS TO PROBLEMS

Indonesian sale As there is no forward market in Indonesian rupiahs against £, and no rupiah loans are available, Oxlake must accept their customer’s offer of US$125 000 in three months if they wish to be able to hedge the FX risk. The US$ could be sold three months forward as a FX hedge to yield: US$125 000 ÷ 1.5105 = £82 754 received in three months. The alternative is to use the money market to hedge by taking out a three-month US$ loan for US$x: such that: US$x (1 + 0.03) = US$125 000. Therefore they should take out a loan for: US$x = 125 000 ÷ 1.03 = US$121 359. This loan will be repaid (capital, plus interest, will amount to US$125 000) with the money received from the customer in three months’ time. The US$ loan can be converted into £ at spot: US$121 359 ÷ 1.4875 = £81 586 available now. In order to compare this alternative with the forward market deal, we need to be able to compare like with like (i.e. £82 754 in three months’ time as against £81 586 now). Therefore, assuming that the £81 586 is placed on three-month £ deposit then this will yield in three months’ time: £81 586 (1 + 0.01625) = £82 912. As this amounts to marginally more than Oxlake could obtain from the forward market transaction, the company should hedge the Indonesian sale through the use of the money market. Summary Singapore sale: Expected £ revenues in three months’ time = £226 481. Indonesian sale: £ revenues immediately = £81 586 (or £82 912 in three months’ time) The Singapore hedge is achieved through a two-to-three month option forward sale contract. The Indonesian hedge is achieved through a three-month US$ loan (a so-called currency overdraft). (b) Standard sale price: 100 000 × 2 246 = 224.6mn rupiahs. Discount price: 224.6mn × 0.95 = 213.37mn rupiahs. The R/US$ spot rate is the cross rate of the R/£ and the US$/£ spot rates: 2481 = 1 668 = R / US$ spot rate. 1.4875 Therefore the Indonesian customer will pay immediately: US$ = 213.37mn ÷ 1 668 = 127 920 which Oxlake can sell at spot for: US$127 920 ÷ 1.4875 = £85 996.

CHAPTER 26

FOREIGN EXCHANGE HEDGING

775

As this is more than the £81 586 available immediately from use of the money market, the offer made by the Indonesian importer is likely to be accepted by Oxlake. (c) There are three main reasons why it may be advantageous for a company to invoice an export sale in a foreign currency. First, the foreign currency might be expected to appreciate (i.e. the forward rates would be at a premium) and therefore the company could expect a favourable FX movement. The second reason is that the exporter may have an existing liability in that overseas currency. Therefore, by invoicing the customer in that currency, some hedging of the FX risk can be gained through the matching principle. Finally, it may be advantageous to agree to invoice in the foreign currency in order to gain a competitive advantage over your rival suppliers. Export markets are often very competitive and offering to invoice in the customer’s currency may be an effective marketing device. The main disadvantage of invoicing in a foreign currency is the exposure it creates to foreign exchange risk. This exposure may be difficult to hedge (because no forward market exists and there is no convenient ‘proxy’ currency to invoice in instead) or, if hedging is possible, then the company has to incur the transaction costs involved, which can be significant.

problem 2 (a) Four FX hedging techniques are: 1. 2. 3. 4.

forward market hedge; money market or financial hedge; futures market hedge; options market hedge.

With a forward market hedge an exporter who is due to receive payment in a foreign currency arranges with a bank to sell that currency at a specific rate of exchange for delivery on a specific future date (or, sometimes, between two specific future dates) which coincides with the expected payment of the invoice. With a money market hedge the exporter would borrow an amount of money in the foreign currency for the period of the credit granted to the customer, such that the principal sum plus the accumulated interest at the end of the loan’s term would exactly equal the amount of foreign currency due from the customer on payment of the invoiced amount. The amount borrowed is sold at spot for £ and represents the outcome of the export deal. The principal plus interest is then repaid using the money received from the customer at the end of the credit period. If the company were to use a futures market hedge, the exporter would open up a position on the futures market such that any profit or loss made on the futures when the position is subsequently closed out approximately offsets the loss or gain made on the invoiced amount arising out of a movement on exchange rates over the credit period. Finally an options market hedge guarantees the company a minimum rate of exchange for its future foreign currency receipt, known as the option ‘exercise’ or ‘strike’ price. Thus, when the foreign currency is received from the export customer, if a better rate of exchange is available on the spot market, then the option is allowed to lapse and the currency is sold spot. On the other hand, if the spot market provides a less favourable rate of exchange, then the option is exercised to take advantage of its guaranteed minimum rate of exchange. Each of the first three of these hedging techniques hedges the company against both an adverse and a favourable movement in exchange rates over the credit period granted to the customer. In contrast, the FX options hedge the exporter against an adverse

776

ANSWERS TO PROBLEMS

movement in exchange rates, but allows him to take advantage of any favourable movement. (b) The $/£ rates are: Spot: 3 months forward: 6 months forward:

1.7106 – 1.7140 1.7024 – 1.7063 1.6967 – 1.7006

(i) Fidden has the following transactions due: Due to pay Due to receive Due to pay Due to receive Net payment due

: : : : :

£116 000 $197 000 $447 000 $154 000 $293 000

– – –   –

No FX risk Requires hedge Net out for a ‘natural’ hedge, leaving the balance Requires hedge

[a]

[b]

(1) Forward market hedge [a] Sell $197 000 at 1.7063 = £115 454 receivable in 3 months. [b] Buy $293 000 at 1.6967 = £172 688 payable in 6 months. (2) Money market hedge [a] Borrow $x for 3 months at 9% ÷ 4 = 2[1/4]% so that: $x(1 + 0.0225) = $197 000 $x = $197 000 ÷ 1.0225 = $192 665 Sell the $192 665 spot, at 1.7140, to give £112 407 received immediately. Use the $197 000 received in three months time to repay loan, plus accumulated interest. [b] Deposit

$x for 6 months at 6% ÷ 2 = 3% so that: $x(1 + 0.03) = $293 000 $x = $293 000 ÷ 1.03 = $284 466

Purchase the $284 466 spot, at 1.7106, to give £166 296 payable now. The net payment of $293 000 due in six months time can be made with the contents (capital plus interest) of the $ deposit account. Therefore the net £ position from the forward markets will be: (i) Three months’ time: Pay: Receive:

£116 000 £115 454

Net pay:

£

546

(ii) Six months’ time: Pay:

£172 688

The net £ position for the money markets will be: (i) Immediately: Receive: Pay:

£112 407 £166 296

Net pay:

£ 53 889

(ii) Three months’ time: Pay:

£116 000

CHAPTER 26

777

FOREIGN EXCHANGE HEDGING

(ii) As the question only gives details of the spot rate in six months’ time, it is assumed that the question only refers to the net payment of $293 000, payable in six months’ time. To hedge this FX risk in the option market we will need to buy £ June put options. June options are involved because the payment is due in June (although September options could possibly be used). Put options are involved because in the ‘cash’ market we will need to buy $293 000 to pay the invoice by selling £. Therefore we need to buy options to sell £: £ puts. With £ June puts, there is a choice of two exercise prices. (Notice that the more favourable the exercise price is to the company – $1.80 – the more expensive will be the option cost.) However, we can see that in this case we would not select the $1.70 exercise price, the reason being that the cost of paying the invoice at this exercise price would be: $293 000 ÷ $1.70 = £172 353. This is only marginally cheaper than the cost of paying the invoice through a forward market hedge: £172 688. The cost of the £ July options will certainly be in excess of this saving of £335, therefore we can ignore the $1.70 exercise price in this case. Therefore, we would hedge with £ June puts at an exercise price of $1.80. Paying the invoice at this rate of exchange would have a £ cost of: $293 000 ÷ $1.80 = £162 778. Given the size of £ option contracts, to hedge the FX risk we would need: £ 162 778 ÷ £12 500 = 13.02 contracts. We are now faced with a choice of two alternatives: 1. hedge with just 13 option contracts and leave a very small amount unhedged; 2. over-hedge by using 14 option contracts. Assuming that the company wants no FX risk, it will go for the over-hedge. Therefore we will hedge by buying 14 £ June puts at an exercise price of $1.80 and a cost of: 14 × £12 500 × 9.32¢ = $16 310 In June, we also have a choice. We either allow the option to lapse and buy $293 000 on the spot market in order to pay the amount due or, alternatively, buy $ through the exercise of the option contracts. As the June $/£ spot rate is 1.6967–1.7006, it is obviously better to buy $ by exercising the option as they can be bought at a more favourable rate of exchange – $1.80 – than the 1.6967 rate on the spot market. Exercising the option contracts: Buy: 14 ×

£ 12 500 × $1.80 = $315 000 at a £ cost of: $315 000 ÷ $1.80 = £175 000.

The invoice of $293 000 can then be paid out of these purchased $, leaving a surplus of: $315 000 – $293 000 = $22 000. The surplus can then be used to pay the option cost of $16 310. This leaves a residual of: $22 000 – $16 310 = $5690 which can be sold spot at 1.7006 to yield: $5690 ÷ 1.7006 = £3346. Therefore, overall: £ cost of exercising option contracts Less the proceeds from sale of surplus $

: :

£175 000 £ 3 346

Net cost

:

+£171 654

778

ANSWERS TO PROBLEMS

As this net cost, payable in six months’ time, is less than the forward market hedge cost of £172 688, the option hedge is preferred. (However, note you can only tell with the benefit of hindsight whether the option hedge is more or less favourable than the forward market hedge. In this question the option turns out to be the better alternative, but this will not always be the case.) (iii) A forward market hedge locks the company into a specific future exchange rate (as does a futures hedge). Therefore the company is hedged against a favourable move in FX rates, as well as hedged against an adverse movement. With options, the company has additional flexibility. The option allows the company to hedge against an adverse move in FX rates (by exercising the option), but at the same time the company can take advantage of a favourable movement in FX rates (by allowing the option to lapse). This extra flexibility means that options are more expensive than forward contracts, but they are particularly useful where a company has a contingent exposure to FX risk.

Chapter 27 Foreign direct investment problem 1 (a) Discount rate Given: βA =

σ A ⋅ ρ A, M σM

then: β Subsidiary

σ Subsidiary ⋅ ρ Subsidiary, Market σ Market

β Subsidiary

0.65  0.885 = 1.198 0.48

Using CAPM: E [ rSubsidiary ] = rf + ( E [ rMarket ] – rf )β Subsidiary E [ rSubsidiary ] = 8% + [13% – 8%]  1.198 = 14% Writing-down allowances Assuming that the capital expenditure is incurred on the first day of the company’s accounting year: £mn 15 3.75 11.25 2.81 8.44 2.11 6.33 1.58 4.75

£mn

WDA ×

0.25

=

3.75

×

0.35

=

1.312

Year 2

×

0.25

=

2.81

×

0.35

=

0.984

Year 3

×

0.25

=

2.11

×

0.35

=

0.739

Year 4

×

0.25

=

1.58

×

0.35

=

0.553

Year 5

–

10

=

(5.25)

×

0.35

=

(1.837)

Year 6

        

Writing-down allowance tax relief

Balancing charge

CHAPTER 27

779

FOREIGN DIRECT INVESTMENT

Contribution/gallon £300 – £140 £160(1.04) £166.4(1.03) £171.39(1.03) £176.53(1.04)

= £160/gal. = £166.4/gal. = £171.39/gal. = £176.53/gal. = £183.59/gal.

Annual contribution Year Contrib/gal. 1 £160 2 166.4 3 171.39 4 176.53 5 183.59 Annual fixed costs Year 1 2 3 4 5

× × × × × ×

2 2(1.04) 2.08(1.03) 2.142(1.03) 2.206(1.04)

Sales 20 000 50 000 50 000 50 000 50 000

1.4725 (1 – 0.05) 1.3989 (1 – 0.05) 1.3289 (1 – 0.05) 1.2625 (1 – 0.05)

Royalty payments Year Sales 1 20 000 × $50 = 2 50 000 × $50 = 3 50 000 × $50 = 4 50 000 × $50 = 5 50 000 × $50 =

$mn ÷ 1.0 ÷ 2.5 ÷ 2.5 ÷ 2.5 ÷ 2.5 ÷

Tax charges (£mn) Year Contrib. – Fixed costs 1 3.2 – 2 2 8.32 – 2.08 3 8.57 – 2.142 4 8.827 – 2.206 5 9.18 – 2.294

=

– – – – –

= = = = =

£m 3.2 8.32 8.57 8.827 9.18

£mn 2 2.08 2.142 2.206 2.294 = = = = = =

Exchange rate 1.4725 1.3989 1.3289 1.2625 1.1994

– Royalties 0.679 1.787 1.881 1.980 2.084

= = = = = =

= = = = =

Exchange rates forecast Spot Year 1 Year 2: Year 3: Year 4: Year 5:

Year 1 Year 2 Year 3 Year 4 Year 5

Taxable c/f 0.521 4.453 4.547 4.641 4.802

1.5500 1.4725 1.3989 1.3289 1.2625 1.1994 £mn 0.679 1.787 1.881 1.980 2.084

= = = = = × × × × × ×

Tax rate 0.35 0.35 0.35 0.35 0.35

= Tax Tax charge timing = 0.182 2 = 1.558 3 = 1.591 4 = 1.624 5 = 1.681 6

780

ANSWERS TO PROBLEMS

Project cash flows (£ mn) 0 1 Outlay –15 Grant +3 Scrap WDA T/R Contribution +3.2 Fixed costs –2 Tax charge

2

+1.312 +8.32 –2.08 –0.182

3

+0.984 +8.57 –2.142 –1.558

4

+0.739 +8.827 –2.206 –1.591

5

+10 +0.553 +9.18 –2.294 –1.624

6

–1.837

–1.681

Net cash flow Discount factor

–12 1

+1.2 +7.37 0.8772 0.7695

+5.854 +5.769 +15.815 –3.518 0.6750 0.5921 0.5194 0.4556

PV c/f

–12

+1.053

+3.951

+5.671

+3.416

+8.214

–1.603

NPV of proposed UK subsidiary: +£8.702 million. The royalty cash flow has been excluded from this calculation (but not the impact of the royalty payments on the corporate tax charge) because it is a cash flow which is internal to the company. In US dollar terms, the project could be expected to have a positive NPV of: £8.702 million × 1.55 = $13.488 million. In addition, there is a further opportunity benefit arising out of the project. At present the UK market is supplied from the US where there is no spare production capacity. The UK project will make some spare production capacity become available in the US, which will allow the company to exploit the Scandinavian market and so generate an after-tax net cash flow of £1.5mn. On the assumption that the Scandinavian market ‘project’ has the same risk as the UK project, then the interest rate parity theorem could be used to estimate a suitable discount rate to apply to these incremental after-tax US$ cash flows: 1+ $ discount rate 12 month forward $ / £ = 1+ £ discount rate Spot $ / £ 1+ $ discount rate 1.4725 = 1+ 0.14 1.5500 1.14  1.4725 $ discount rate = – 1 = 0.083 or 8.3%. 1.5500 Thus the present value of the Scandinavian market could be estimated as: $15 . mn = $18.07 mn PV. 0.083 Note: As an alternative, the present value of this opportunity benefit could be calculated over just five years, the project’s planning horizon, giving $5.94million. (b) Investment in any overseas project is likely to expose the parent company to FX translation risk. In this particular case Blue Grass Distillery Inc would have sterling assets and, if it finances the project by exporting dollars, dollar liabilities. The easiest way to avoid this risk is to match the overseas currency assets with a liability in that same currency. However, such a perfect hedge may not be legally possible (the project’s host country might insist that at least some of the finance should be exported by the parent) or may not be seen to be advisable from a public relations viewpoint. In such circumstances, the standard advice is that a project’s non-property fixed assets should be financed with sterling, while the property fixed assets, together with the working capital, should be financed in the currency of the host country. The reasoning

CHAPTER 27

781

FOREIGN DIRECT INVESTMENT

behind this advice is that the company can hedge part of its foreign exchange risk through matching assets and liabilities in the same currency, while at the same time it gets some protection from foreign exchange risk on its unmatched assets through the workings of the law of one price. The reason why the non-property fixed assets are left unmatched is that they are the most likely assets to react to the law of one price. Therefore if sterling depreciates against the US dollar (as it is expected to do) it might be reasonable to assume that the sterling worth of the non-property fixed assets may rise in order to counteract the reduced worth of sterling, assuming that those assets are capable of being traded internationally.

problem 2 (a) Base-case present value Base-case discount rate (£ terms) β assets = 1.40 

4 = 1.20 4 + 1(1 – 0.35 )

Base-case discount rate = 7.1% + (17.85% – 7.1%) × 1.20 = 20% A$ project tax charge (A$mn) Years Revenue Operation costs – Depreciation =

1–4 18 (5) (3.75)

Taxable profit Tax charge

9.25 4.625

A$ project cash flows (A$mn) Year 0 Capital equipment (15) Working capital (5) Revenues Costs Taxation Net cash flow

1

(20)

(20) 8.375 8.375 8.375 13.375

÷ ÷ ÷ ÷ ÷

2 1 2(1.10) 2 2(1.10) 3 2(1.10) 4 2(1.10)

3

4

18 (5) (4.625)

18 (5) (4.625)

18 (5) (4.625)

5 18 (5) (4.625)

8.375

8.375

8.375

13.375

£m base-case present value calculation Year A$mn ÷ Exchange = n rate 0 1 2 3 4

2

= = = = =

£mn

×

(10) 3.807 3.461 3.146 4.568

× × × × ×

20% disount rate 1 0.833 0.694 0.579 0.482

Base case PV

=

= = = = =

£m PV cash flows (10) 3.171 2.402 1.821 2.202

=

(£0.404mn)

PV of financing side-effects PV of tax shield £5mn × 0.10 £500 000 × 0.35

= =

PV of tax relief: £175 000 A ¬

4 0 .10

£500 000 £175 000 =

£554 750

= =

Annual interest Annual tax relief

782

ANSWERS TO PROBLEMS

PV of issue costs £5mn × 0.025 × (1 – 0.35) = (£81 250) Adjusted present value Base-case PV PV tax shield PV issue costs

£mn (0.404) 0.555 (0.081)

Adjusted present value

£0.07mn or + £70 000 approx.

Therefore, the project should be accepted. (b) The company’s proposed financing plans for the Australian project can be criticized on the basis that they have not taken the opportunity to arrange them so as to help limit exposure to foreign exchange risk. By having a long-lived Australian dollar (A$) asset the company is exposing itself to both foreign exchange translation and transaction risk. This risk can be reduced by matching the A$ assets as closely as possible to an A$ liability. The standard advice – given on the assumption that the company will have to finance some part of its overseas project by exporting sterling – is that the project’s non-property fixed assets should be financed with sterling, while the property fixed assets, together with the working capital, should be financed in the currency of the host country. The reasoning behind this advice is that the company can hedge part of its foreign exchange risk through matching assets and liabilities in the same currency, while at the same time it gets some protection from foreign exchange risk on its unmatched assets through the workings of the law of one price. The reason why the non-property fixed assets are left unmatched is that they are the most likely assets to react to the law of one price. Therefore if the A$ depreciates against sterling (as it is expected to do) it might be reasonable to assume that the A$ worth of the non-property fixed assets may rise in order to counteract the reduced worth of the A$, assuming that those assets are capable of being traded internationally.

783

Index abandonment decision, ENPV 186–91 accounting role, profit 9–10 acquisition decisions 553–76 acquisition premiums 558–60 all-equity situation 562–3 ‘anti-competitive’ defence 570–1 bootstrapping EPS 564–7 ‘City Code’ 19 coinsurance effect 562–4 cost synergy 555–6 defence document 569–70 diversification 567–8 EPS 564–7 financial synergy 557 financing acquisitions 571–2 geared situation 563–4 organic growth vs. acquisition growth 560–2 revenue synergy 554–5 synergy 554–8 takeover defence 568–71 tax synergy 556–7 valuing synergy 557–8 ‘White Knight’ defence 571 adjusted present value (APV) applying 516–21 company valuation 507–8 investment and financing interactions 507–8, 513 maintaining gearing ratio 510–11 agency costs bankruptcy costs 473–5 debt capital 472–3 all-equity financed companies, WACC 420–1 all-equity situation, acquisition decisions 562–3 alpha coefficient, beta value 267–8 alternatives valuation, decision making 5–6 ‘American’ options, option valuation 293, 296–7 annual equivalent factors compounding and discounting 88 table 669

annual reports, decision objectives 17 annuities compounding and discounting 87–8 defined 87 present value 87–8 tables 668 terminal value 88 answers, problems 699–786 answers, quickie questions 673–98 ‘anti-competitive’ defence, acquisition decisions 570–1 appraisal, investment see investment appraisal appreciation, foreign exchange 602–3 APT see arbitrage pricing theory APV see adjusted present value arbitrage capital structure 450–4, 471–2 criticism 539–40 reverse arbitrage 453–4 taxation 471–2 arbitrage pricing theory (APT), CAPM 276–7 area under the normal curve option valuation 321–2 tables 671 Arthur Andersen 26–7 asset basis, company valuation 577–9 asset betas capital structure 447–8 gearing 447–8, 514–21 investment and financing interactions 514–21 taxation 515–16 assumptions, decision making, financial 11 at-the-money (ATM), option valuation 296 audits, decision objectives 17 bankruptcy costs, capital structure 473–5 base-case discount rate, investment and financing interactions 513–14 benefit-cost ratios, capital rationing 152–7

784

INDEX

beta value adjusting beta 279–80 alpha coefficient 267–8 beta stability 269–70 CAPM 262–71 information sources 276 interpreting 262–4 investment appraisal 278–81 measuring 265–6 portfolio betas 264–5 project beta 278–9 project discount rate 278–81 bid prices, cost of capital 386 binomial model, option valuation 318–20 Black and Scholes model assumptions 301 dividends 302 option valuation 298–302, 321–2 bonds discount 403–4 low coupon 404–5 ‘plain vanilla’ bonds 398–9 pricing 399 zero coupon 403–4 bootstrapping EPS, acquisition decisions 564–7 borrowing possibility, portfolio theory 240–2 business risk, capital structure 446–50, 496–9 buying rates, exchange rates 595–8 Cadbury Code 19–21 calculated intangible value (CIV), intellectual capital 585 call options Black and Scholes model 298–302 combining puts 312–13 foreign exchange hedging 629 gamma 316 option valuation 293, 294, 304 speculating with calls 310 vega 317 capital asset pricing model (CAPM) 255–90 APT 276–7 assumptions 271–3 beta value 262–71 CAPM expression 259–71 DVM 393–7 empirical evidence 273–5 investment appraisal 278–81

KE 393–7 M and M 497–8 NPV 278 PER 275 Roll’s critique 273–4 SML 255–9 systematic risk 259–62 unsystematic risk 259–62 validity 271–6 capital, cost of see cost of capital capital market borrowing, capital rationing 148–50 capital market line (CML) portfolio theory 243–8 SML 255–9 capital markets, investment-consumption decision model 55–6 capital rationing 148–75 benefit-cost ratios 152–7 capital market borrowing 148–50 divisibility assumption 157 hard 150–1 LP 160–8 multi-period 158–68 mutually exclusive investments 157 opportunity costs 159–60 single-period 152–8 soft 150–1, 158–9 capital structure arbitrage 471–2 arbitrage proof 450–4 asset betas 447–8 assumptions 455–6 bankruptcy costs 473–5 business risk 446–50 complex world 462–87 corporate taxes 479–82 debt capacity 475–6 debt, consideration 490 DOG 496–500 EPS 493–6 financial risk 446–50 financing dilemma 490 gearing 444–5 interest cover ratio 496 judgement 495–6 M and M 443, 455–7, 477–82 market signals 489–90 optimal 442–6 pecking order theory 488–91 in practice 488–505 principal-agent problem 472–3

785

INDEX

real-world considerations 491–3 rising cost of debt 456–7 risk 446–50 risk and return 493–5 simple world 442–61 tax exhaustion 476 taxation 462–7 timing 489 total market value model 443–6 traditional view 477–9 views, further 477–82 CAPM see capital asset pricing model caps, interest rate risk 343–4 cash alternative, acquisition decisions 572 cash flows FCF basis 582–4 incremental 99–103 timing 71–2 see also discounted cash flow; project cash flows cash offers, acquisition decisions 571, 572 CGPP see current general purchasing power ‘City Code’ acquisition decisions 19 takeover defence 569 CIV see calculated intangible value clean floats, foreign exchange 606 ‘clientele’ effect, dividend decision 542–3 CML see capital market line coinsurance effect, acquisition decisions 562–4 collars, interest rate risk 343–4 combined borrowing and lending, portfolio theory 242 Combined Code 21–3 combining calls/puts 312–13 combining risk-free and risky investment, portfolio theory 239–40 Company Securities (Insider Dealing) Act 1985; 18 company valuation 506–8, 577–91 APV 507–8 asset basis 577–9 current EAIT 580–2 dividend basis 582 DVM 507 earnings basis 579–82 FCF basis 582–4 intellectual capital 584–6 M and M see Modigliani and Miller capital structure hypothesis

owner-managers 580 PER 580–1 suitable multiple 580–1 traditional valuation model 508 see also investment and financing interactions; investment appraisal compound interest factors compounding and discounting 85–6 table 667, 670 compounding and discounting annual equivalent factors 88 annuities 87–8 compound interest factors 85–6 perpetuities 86–7 present value factors 86 sinking fund factors 89 tables 667–70 constant capital structure, WACC 422–3 contingent exposure, foreign exchange hedging 635 control and ownership, decision objectives 15–16 convertible debt advantages 411 cost of capital 410–13 corporate debt costs 431–7 corporate taxes, capital structure 479–82 corporation tax see taxation cost of capital 379–419 convertible debt 410–13 cum dividend 386–7 dividend growth model 388–9 dividend growth rate 389–92 dividend valuation model 385–93 dividends 383–5 ex dividend 386–7 expected return 383–5 financing decision 379–80 graphical relationship 466–7 interest valuation model 398 M and M 466–76 market price 383–5 ‘plain vanilla’ bonds 398–9 preference shares 409–10 retained earnings 392–3 share price-return relationship 384–5 see also weighted average cost of capital cost of debt capital 397–409 vs. equity capital 397–8 cost of equity capital (KE) 380–2 CAPM 393–7 gearing 449, 466

786

INDEX

cost synergy, acquisition decisions 555–6 country/political risk, foreign direct investment 642, 659–60 covariance, portfolio theory 227–9 cross rates, exchange rates 598–600 cum dividend, shares 386–7 currency finance, overseas, foreign direct investment 646–7 current EAIT, company valuation 580–2 current general purchasing power (CGPP) 127–30 DCF see discounted cash flow debt capacity, capital structure 475–6 debt capital agency costs 472–3 explicit costs 409 extreme use 435–6 financing via 431 imperfect markets 433–5 implicit costs 409 irredeemable 401 opportunity costs 399–400 perfect markets 432–3 taxation 431–2 debt costs corporate 431–7 private 431–7 decision making, financial 3–13 accounting profit 9–10 alternatives valuation 5–6 assumptions 11 maximizing shareholder wealth 7–8 process 4–6 technology 11–12 time dimension 10–11 value base 3–4 wealth 7–8 decision objectives 6–7, 11, 14–30 annual reports 17 audits 17 directors’ transactions 18 fiduciary responsibilities 16–17 incentive scheme criteria 23–6 ownership and control 15–16 relationship, directors/shareholders 14–15, 16–23 stock exchange rules 17–23 wealth maximization 14–15 decision pivot point, sensitivity analysis 191–3

defence document, acquisition decisions 569–70 degree of operating gearing (DOG) capital structure 496–500 defined 498 meaning 499–500 delta, option valuation 314 depreciation foreign exchange 602–3 non-cash flow 137 directors good governance 22 shareholder relationship 14–15, 16–23 see also management directors’ transactions, decision objectives 18 dirty floats, foreign exchange 606 discount bonds 403–4 discount rate base-case 513–14 beta value 278–81 foreign direct investment 648–53 risk-adjusted 194–6 WACC 420–3 discounted cash flow (DCF) 67–124 assumptions 95–6 compounding and discounting 85–90 IRR 78–85, 94–124 NPV 67–77, 94–124 discounted payback, IRR 83–4 discounting and compounding see compounding and discounting discounts, foreign exchange 601–2 diversification, acquisition decisions 567–8 diversification within companies, portfolio theory 248–9 dividend basis, company valuation 582 dividend decision 534–50 ‘clientele’ effect 542–3 dividend patterns 537–8 empirical evidence 544–5 external finance 540–1 policy, imperfect markets 542–4 policy, perfect capital markets 534–8 taxation 544 traditional view 538–41 valuation model 537–8 dividend flow approach, maintaining gearing ratio 510 dividend growth model, cost of capital 388–9

787

INDEX

dividend growth rate changing 391–2 cost of capital 389–92 ‘dividend irrelevancy hypothesis’ 536 dividend valuation model (DVM) CAPM 393–7 company valuation 507 cost of capital 385–93 dividends Black and Scholes model 302 cost of capital 383–93 probability distribution 446–7 as a residual 535–7 signalling effect 543 DOG see degree of operating gearing domestic vs. foreign projects, foreign direct investment 642 dominance, portfolio theory 233 downside risk option valuation 310–11 risk and return 218–19 dual values, LP 162–8 DVM see dividend valuation model EAIT, company valuation 580–2 early exercise, foreign exchange hedging 634–5 earnings basis, company valuation 579–82 earnings per share (EPS) acquisition decisions 564–7 capital structure 493–6 gearing 493–6 economic risk foreign direct investment 656–9 foreign exchange hedging 615, 616 efficient markets hypothesis (EMH) 355–65 see also market efficiency EMU see European Monetary Union ENPV see expected net present value Enron 26–7 EPS see earnings per share equity capital cost 380–2, 393–7, 464–6 vs. cost of debt capital 397–8 ERM see Exchange Rate Mechanism European Monetary Union (EMU) 606–7 ‘European’ options, option valuation 293, 296–7 ex dividend, shares 386–7 exchange/delivery of currencies, foreign exchange 603–5

Exchange Rate Mechanism (ERM) 606–7 exchange rate systems, foreign exchange 605–7 exchange rates buying rates 595–8 cross rates 598–600 forecasting 612 inverting 598 selling rates 595–8 see also foreign exchange exchange-traded options, option valuation 293 exercise price, foreign exchange hedging 629 expected net present value (ENPV) abandonment decision 186–91 additional information 184–6 limitations 183–4 risk techniques 180–91 see also net present value expected returns cost of capital 383–5 risk and return 214–16 expected utility model, risk and return 206–12, 219–20 explicit costs, debt capital 409 ‘extended yield’, IRR 112 external finance, dividend decision 540–1 FCF basis see free cash flow basis fiduciary responsibilities, decision objectives 16–17 finance, external, dividend decision 540–1 financial investments, cf. physical investments 380 financial leases 524–9 financial market line, investment-consumption decision model 56 financial markets 355–78 market efficiency 355–65 pure expectations hypothesis 369–75 term structure, interest rates 365–9 yield to maturity 366 financial risk, capital structure 446–50, 496–9 financial synergy, acquisition decisions 557 financing acquisitions 571–2 financing and investment interactions see investment and financing interactions financing decision, cost of capital 379–80

788

INDEX

financing via debt capital 431 Fisher Effect 126–30 interest rates 371–2 fixed forward contracts, foreign exchange 603–5 floating rate debt 407–9 floors, interest rate risk 343–4 forecasting exchange rates 612 foreign direct investment 642–66 basic approach 643–4 country/political risk 642, 659–60 domestic vs. foreign projects 642 economic risk 656–9 management charges 660–1 overseas currency finance 646–7 project cash flows 644–7 project discount rate 648–53 taxation 649–53 transfer pricing 660–1 translation risk 653–6 foreign exchange 595–614 appreciation 602–3 clean floats 606 depreciation 602–3 determinants, FX rates 608–12 dirty floats 606 discounts 601–2 EMU 606–7 ERM 606–7 exchange/delivery of currencies 603–5 exchange rate systems 605–7 exchange rates 595–614 fixed forward contracts 603–5 forward contracts 603–5 inflation 610–12 interest rates 609–10 markets 600–5 option forward contracts 603–5 premiums 601–2 time option forward contracts 603–5 see also exchange rates foreign exchange hedging 615–41 comparing hedges 619–20 contingent exposure 635 definitions 615–16 early exercise 634–5 economic risk 615, 616 exercise price 629 forward market hedging 618 forward vs. futures 626–7 futures contracts 621–6 importer case 631–2

leading hedge 620–1 LIFFE 626 margin 626 money market hedging 618–19, 621 netting 617 option hedging, setting up 629–34 options contracts 627–9 OTC options 628, 635–6 risk, contingent exposure 635 risk types 615 swaps 617–18 techniques 616–21 traded currency options 628–9, 635–6 transaction risk hedging 615, 616–21 translation risk 615–16 variation 633–4 forward contracts, foreign exchange 603–5 forward forward loans, interest rate risk 327–8 forward interest rates 370–1 forward market hedging, foreign exchange hedging 618 forward rate agreements (FRAs) interest rate risk 328–31 vs. IRGs 333 market in 331 forward vs. futures, foreign exchange hedging 626–7 FRAs see forward rate agreements free cash flow (FCF) basis, company valuation 582–4 futures contracts foreign exchange hedging 621–7 vs. forward market hedging 626–7 ‘ticks’ 335–6 FX see foreign exchange gamma, option valuation 316 geared situation, acquisition decisions 563–4 gearing asset betas 447–8, 514–21 assumptions 445 capital structure 443–5 defined 443 DOG 496–500 EPS 493–6 KE 449, 464–6 maintaining gearing ratio 509–11 no-tax world 444–5 see also capital structure

789

INDEX

Gordon’s approach, dividend growth rate 389–91 governance, corporate 15–27 graphical analysis, investment-consumption decision model 53–5 graphical derivation, decision rule, investment-consumption decision model 57–9 graphical interpretation, NPV 75–7 ‘Greeks’, option 314 Greenbury Code 21 growth, organic vs. acquisition 560–2 Hampel Report 21 hard capital rationing 150–1 hedge efficiency, interest rate risk 338–40 hedge ratio, option valuation 314–16 Hirshliefer single-period investment-consumption model see investment-consumption decision model imperfect markets debt capital 433–5 dividend decision 542–4 implicit costs, debt capital 409 importer case, foreign exchange hedging 631–2 in-the-money (ITM), option valuation 296 incentive schemes criteria 23–6 decision objectives 23–7 ineffective 26–7 types 25–6 incremental cash flows, IRR 99–103 indifference curves, investment-consumption decision model 54–5 individual choice, risk and return 211–12 inflation foreign exchange 610–12 investment appraisal 125–30 IRR 130–1 project cash flows 125–31 insider dealing, Company Securities (Insider Dealing) Act 1985; 18 intellectual capital CIV 585 company valuation 584–6 defined 584

market to book 585 Tobin’s ‘q’ quotient 585 value 584–5 interdependent projects IRR 99–108 NPV 94–9 interest cover ratio, capital structure 496 interest rate futures, interest rate risk 334–43 interest rate guarantees (IRGs) vs. FRAs 333 interest rate risk 331–3 interest rate options (IROs) see interest rate guarantees interest rate risk 325–51 caps 343–4 collars 343–4 defined 325 floors 343–4 forward forward loans 327–8 FRAs 328–31 hedge efficiency 338–40 interest rate futures 334–43 interest rate swaps 344–7 IRGs 331–3 margin 342–3 maturity mis-match 340–1 money markets 325–7 option contract markets 333–4 strip hedge 342 interest rates Fisher Effect 371–2 foreign exchange 609–10 forward 370–1 liquidity preference 373–4 ‘market’ 126–30 ‘real’ 126–30 segmented markets 374–5 spot rates 367–9 taxation 372–3 term structure 365–9 transaction costs 372–3 yield curve 366–7 yield to maturity 366 interest valuation model cost of capital 398 investment and financing interactions 507 internal rate of return (IRR) 78–85 decision rule 82 discounted payback 83–4 estimating 79–82

790

INDEX

‘extended yield’ 112 incremental cash flows 99–103 inflation 130–1 interdependent projects 99–108 investment-consumption decision model 82–3 linear interpolation 79–82 model 78–9 modified 114–15 multiple 109–12 mutually exclusive projects 94–124 and NPV 94–124 vs. NPV 115–16 ‘opportunity cost of cash’ assumption 105–8 problems 113–14 rates of return, average/marginal 109 single-period capital rationing 157–8 time horizon extension 108–9 truncated NPV 84–5 use of 101 intrinsic value, option valuation 295, 297 inverting, exchange rates 598 investing in call options in the shares 304 put options in the shares 305 risk-free bonds 303–4 shares 303 investment and financing interactions 506–33 adjusted present value model 507–8 asset betas 514–21 base-case discount rate 513–14 capital structure, changing 511–13 company valuation 506–7 DVM 507 investment appraisal approaches 509–14 lease or purchase decision 524–9 risk-adjusted WACC 521–4 traditional valuation model 508 investment appraisal approaches 509–14 beta value 278–81 CAPM 278–81 company valuation 506–8 inflation 125–30 investment-consumption decision model 50–66 IRR 78–90 NPV 67–77 payback method 34–41

project cash flows 125–47 relevant cash flow 136–41 ROCE 41–4 taxation 131–2 traditional methods 33–49 investment building blocks, option valuation 302–7 investment-consumption decision model 50–66 assumptions 50–1 capital markets 55–6 financial market line 56 graphical analysis 53–5 graphical derivation, decision rule 57–9 indifference curves 54–5 IRR 82–3 multi-owner firms 59–61 NPV 74–5 separation theorem 57–61 single-owner firms 53–4 TVM 51–5 uncertainty 61–2 investment decision, risk and return 212–22 investors’ behaviour axioms, risk and return 206–7 IRGs see interest rate guarantees IROs see interest rate guarantees IRR see internal rate of return irredeemable debt capital, cost 401 ITM see in-the-money judgement, capital structure 495–6 K0 calculation, WACC 423–6 KE see cost of equity capital leading hedge, foreign exchange hedging 620 lease or purchase decision, investment and financing interactions 524–9 leases financial 524–9 operating 524–5 legal issues Company Securities (Insider Dealing) Act 1985; 18 governance, corporate 15–27 lending and borrowing combined, portfolio theory 242 leverage see gearing LIFFE, foreign exchange hedging 626

791

INDEX

linear programming (LP) 169–70 assumptions 162 capital rationing 160–8 dual values 162–8 liquidity preference, interest rates 373–4 logarithms, natural, tables 672 London Stock Exchange ‘Model Code’ 17–23 rules 17–23 long-term finance types 380 see also cost of capital low coupon bonds 404–5 LP see linear programming M and M see Modigliani and Miller capital structure hypothesis M and M valuation model, investment and financing interactions 508 management incentive schemes 23–7 shareholder relationship 14–15, 16–23 see also directors management charges, foreign direct investment 660–1 margin foreign exchange hedging 626 interest rate risk 342–3 market efficiency defined 355–6 empirical evidence 360–5 financial markets 355–65 importance 356–7 levels 357–8 semi-strong efficiency 361–3 share dealing 358–60 strong efficiency 364 weak efficiency 360–1 ‘market’ interest rates 126–30 market portfolio, portfolio theory 244–6 market portfolio risk, portfolio theory 248 market price, cost of capital 383–5 market price of risk, portfolio theory 247–8 market to book, intellectual capital 585 market value, option valuation 296–7, 298 markets financial see financial markets foreign exchange 600–5 maturity mis-match, interest rate risk 340–1

maximizing shareholder wealth 7–8, 14–15 mergers see acquisition decisions mixed capital structure companies, WACC 421–2 ‘Model Code’, London Stock Exchange 17–23 Modigliani and Miller (M and M) capital structure hypothesis 443, 455–7, 477–82 CAPM 497–8 company valuation 508 cost of capital 466–76 ‘dividend irrelevancy hypothesis’ 536 M and M valuation model 508 real world 472–6 money market hedging, foreign exchange hedging 618–19, 621 money markets, interest rate risk 325–7 multi-asset portfolios, portfolio theory 234–7 multi-period capital rationing 158–68 mutually exclusive investments, capital rationing 157 mutually exclusive projects, IRR 94–124 natural logarithms, tables 672 net present value (NPV) 67–77 alternative interpretations 73–7 CAPM 278 decision rule 72–3 discounting example 69–70 discounting process 68–9 graphical interpretation 75–7 investment-consumption decision model 74–5 and IRR 94–124 vs. IRR 115–16 maintaining gearing ratio 511 mutually exclusive projects 94–124 present values, calculating 71 project interdependence 94–9 rates of return, average/marginal 109 repair vs. replace 118 replacement cycle problem 116–19 time horizon extension 108–9 timing, cash flows 71–2 truncated 84–5 see also expected net present value netting, foreign exchange hedging 617 NPV see net present value

792

INDEX

objectives, decision making 6–7, 11, 14–30 offer prices, cost of capital 386 Office of Fair Trading (OFT), acquisition decisions 570 operating leases 524–5 ‘opportunity cost of cash’ assumption, internal rate of return (IRR) 105–8 opportunity costs capital rationing 159–60 debt capital 399–400 optimal capital structure 442–6 option contract markets interest rate risk 333–4 OTC options 333–4 option forward contracts, foreign exchange 603–5 option ‘Greeks’, option valuation 314 option hedging, setting up, foreign exchange hedging 629–34 option valuation 291–324 ‘American’ options 293, 296–7 area under the normal curve 321–2 ATM 296 binomial model 318–20 Black and Scholes model 298–302, 321–2 building blocks, investment 302–7 call options 293, 294 characteristics, options 291–2 delta 314 downside risk 310–11 ‘European’ options 293, 296–7 exchange-traded options 293 fundamental relationship 305–6 gamma 316 hedge ratio 314–16 intrinsic value 295, 297 ITM 296 market value 296–7, 298 option ‘Greeks’ 314 OTC options 293 put-call parity theorem 307–10 put options 293, 294–5, 302 rho (phi) 317 risk-free investment portfolio 306–7 share options 310–14 speculating with calls 310 speculating with puts 311–12 terminology 293 theta 316–17 time value 296, 297–8

types, options 292 vega 317 writing (selling) options 313–14 options contracts, foreign exchange hedging 627–9 organic growth vs. acquisition growth 560–2 over-the-counter (OTC) options foreign exchange hedging 628, 635–6 option contract markets 333–4 option valuation 293 overseas currency finance, foreign direct investment 646–7 owner-managers, company valuation 580 ownership and control, decision objectives 15–16 payback method, investment appraisal 34–41 advantages 36–7 decision criterion 38 disadvantages 38–9 ROCE 62 TVM 39–40 pecking order theory, capital structure 488–91 PER see price-earnings ratio perfect markets debt capital 432–3 dividend decision 534–8 perpetuities, compounding and discounting 86–7 personal taxation 479–82 phi (rho), option valuation 317 physical investment line (PIL), investment-consumption decision model 53–5 physical investments, cost of capital 380 PIL see physical investment line ‘plain vanilla’ bonds, cost of capital 398–9 political/country risk, foreign direct investment 642, 659–60 ‘pool of funds’, WACC 423 portfolio betas, beta value 264–5 portfolio, risk-free investment 306–7 portfolio theory 226–54 assumptions 246–7 borrowing possibility 240–2 CML 243–8 combined borrowing and lending 242 combining risk-free and risky investment 239–40

793

INDEX

covariance 227–9 diversification within companies 248–9 dominance 233 graphical representation 235–6 market portfolio 244–6 market portfolio risk 248 market price of risk 247–8 multi-asset portfolios 234–7 practicality considerations 236–7 risk and return 227 risk-free investment 237–42 risk-reduction effect 229–32 riskless asset plus risky portfolio 239–40 risky-riskless boundary 237–9 separation theorem 243–4 three-asset portfolios 234–5 two-asset portfolios 226, 237 PPPT see purchasing power parity theorem preference shares, cost of capital 409–10 premiums, foreign exchange 601–2 present value factors compounding and discounting 86 tables 667–8, 670 price-earnings ratio (PER) CAPM 275 company valuation 580–1 principal-agent problem, capital structure 472–3 private debt costs 431–7 problems, answers to 699–786 profit, accounting role 9–10 project cash flows 125–47 financing cash flows 132–6 foreign direct investment 644–7 inflation 125–31 investment appraisal 125–47 ‘profit’ tax charge 134–6 relevant cash flow 136–41 taxation 131–2 WDAs 133–4 project discount rate beta value 278–81 foreign direct investment 648–53 WACC 420–3 project interdependence IRR 99–108 NPV 94–9 project investment appraisal, CAPM 278–81 project risk, WACC 427–9

purchase or lease decision, investment and financing interactions 524–9 purchasing power parity theorem (PPPT) 610–11 pure expectations hypothesis, financial markets 369–75 put-call parity theorem option valuation 307–10 put-call parity equation 309–10 put options combining calls 312–13 foreign exchange hedging 629 option valuation 293, 294–5, 302, 305 speculating with puts 311–12 quickie questions, answers to 673–98 rates of return, average/marginal, IRR/NPV 109 ‘real’ interest rates 126–30 real-world considerations, capital structure 472–6, 491–3 redeemable debt, cost 402 regulation 15–27 ineffective 26–7 repair vs. replace 118 replacement cycle problem, NPV 116–19 required return on equity capital 380–2, 383–4 retained earnings, cost of capital 392–3 return on capital employed (ROCE) advantages 41–3 disadvantages 43–4 investment appraisal 41–4 payback method, investment appraisal 62 return on equity capital 380–2 return on investment, risk and return 212–16 revenue synergy, acquisition decisions 554–5 reverse arbitrage 453–4 see also arbitrage rho (phi), option valuation 317 risk business 446–50, 496–9 capital structure 446–50 country/political risk 642, 659–60 financial 446–50, 496–9 interest rate see interest rate risk systematic/unsystematic 259–62 see also uncertainty

794

INDEX

risk-adjusted discount rate 194–6 risk-adjusted WACC, investment and financing interactions 521–4 risk and return 204–25 assumptions 220–1 capital structure 493–5 downside risk 218–19 expected returns 214–16 expected utility model 206–12, 219–20 individual choice 211–12 investment decision 212–22 investors’ behaviour axioms 206–7 limitations 221–2 portfolio theory 227 return on investment 212–16 risk techniques 179–80, 194–5 uncertainty 204–5 upside potential 218–19 utility function 207–10 risk-free investment portfolio 306–7 portfolio theory 237–42 risk-free bonds 303–4 risk, interest rate see interest rate risk risk, project, WACC 427–9 risk-reduction effect, portfolio theory 229–32 risk techniques 179–203 certainty-equivalents 195–6 ENPV 180–91 risk-adjusted discount rate 194–6 risk and return 179–80, 194–5 sensitivity analysis 191–4 risk types, foreign exchange hedging 615 riskless asset plus risky portfolio, portfolio theory 239–40 risky-riskless boundary, portfolio theory 237–9 ROCE see return on capital employed Roll’s critique, CAPM 273–4 satisficing shareholder wealth 14–15 security market line (SML) 282–5 CAPM 255–9 CML 255–9 derivation 256–7 segmented markets, interest rates 374–5 selling rates, exchange rates 595–8 selling (writing) options, option valuation 313–14 semi-annual interest payments 403 sensitivity analysis

decision pivot point 191–3 limitations 193–4 risk techniques 191–4 separation theorem investment-consumption decision model 57–61 portfolio theory 243–4 share dealing, market efficiency 358–60 share-for-share exchange, acquisition decisions 571–2 share options, option valuation 310–14 shareholders management relationship 14–15, 16–23 markets 385 maximizing shareholder wealth 7–8, 14–15 shares cum dividend 386–7 ex dividend 386–7 single-owner firms, investment-consumption decision model 53–4 single-period capital rationing 152–8 IRR 157–8 sinking fund factors compounding and discounting 89 table 669 SML see security market line soft capital rationing 150–1, 158–9 speculating with calls, option valuation 310 speculating with puts, option valuation 311–12 spot rates, interest rates 367–9 Stiglitz, J 26–7 stock exchange rules, decision objectives 17–23 stock market, workings 383 strip hedge, interest rate risk 342 structure, this book’s 4 suitable multiple, company valuation 580–1 swaps, interest rate 344–7 advantages/disadvantages 347 quality spread 345–7 ‘swaptions’ 345 synergy, acquisition decisions 554–8 systematic risk, CAPM 259–62 tables 667–72 area under the normal curve 671 compounding and discounting 667–70

795

INDEX

natural logarithms 672 takeover defence acquisition decisions 568–71 ‘City Code’ 569 early warning system 568–9 three-stage strategy 569–71 takeovers see acquisition decisions tax exhaustion, capital structure 476 tax synergy, acquisition decisions 556–7 taxation arbitrage 471–2 asset betas 515–16 capital structure 462–7 corporate taxes 479–82 corporation tax 131–2, 141–2, 405–7 debt capital 431–2 dividend decision 544 foreign projects 649–53 gearing 444–5 interest rates 372–3 investment appraisal 131–2 personal 479–82 project cash flows 131–2, 134–6 pure expectations hypothesis 372–3 V0 464–7 WACC 429, 464–7 technology, decision making, financial 11–12 term structure, interest rates 365–9 terminal value, annuities 88 table 668 theta, option valuation 316–17 three-asset portfolios, portfolio theory 234–5 ‘ticks’, futures contracts 335–6 time dimension, decision making, financial 10–11 time horizon extension, IRR/NPV 108–9 time option forward contracts, foreign exchange 603–5 time value of money (TVM) investment-consumption decision model 51–5 payback method, investment appraisal 39–40 time value, option valuation 296, 297–8 timing capital structure 489 cash flows 71–2 Tobin’s ‘q’ quotient, intellectual capital 585 total market value model (V0)

assumptions 445 capital structure 443–6 no-tax world 444–5 traded currency options, foreign exchange hedging 628–9, 635–6 traditional valuation model, investment and financing interactions 508 transaction costs interest rates 372–3 pure expectations hypothesis 372–3 transaction risk hedging defined 615 foreign exchange hedging 616–21 transfer pricing, foreign direct investment 660–1 translation risk foreign direct investment 653–6 foreign exchange hedging 615–16 ‘transmission vehicle’, company as 14–15 TVM see time value of money two-asset portfolios, portfolio theory 226, 237 uncertainty investment-consumption decision model 61–2 risk and return 204–5 see also risk unquoted debt 407–8 unsystematic risk, CAPM 259–62 upside potential, risk and return 218–19 utility function construction 207–8 risk and return 207–10 shape 209–11 utility model, expected, risk and return 206–12 V0 see total market value model valuation, company see company valuation valuing synergy, acquisition decisions 557–8 vega, option valuation 317 WACC see weighted average cost of capital WDAs (writing-down allowances) 133–4 wealth defining 8 maximization, decision objectives 14–15 maximizing shareholder 7–8

796

INDEX

weighted average cost of capital (WACC) 420–41 all-equity financed companies 420–1 assumptions 421, 425–6 constant capital structure 422–3 formal derivation 424 investment and financing interactions 521–4 K0 calculation 423–6 mixed capital structure companies 421–2 ‘pool of funds’ 423 project discount rate 420–3 project risk 427–9 risk-adjusted 521–4 role 436–7

taxation 429, 464–7 see also cost of capital ‘White Knight’ defence, acquisition decisions 571 working capital, payback method, investment appraisal 35–6 WorldCom 26–7 writing-down allowances (WDAs) 133–4 writing (selling) options, option valuation 313–14 Yellow Book 18–19 yield curve, interest rates 366–7 yield to maturity, interest rates 366 zero coupon bonds 403–4