Study Guide 2018 Principles of Corporate Finance

Principles of corporate finance
H. Zhong, P. Frantz, R. Payne, J. Favilukis
FN2191
2018
Undergraduate study in
Economics, Management,
Finance and the Social Sciences
This subject guide is for a 200 course offered as part of the University of London
undergraduate study in Economics, Management, Finance and the Social
Sciences. This is equivalent to Level 5 within the Framework for Higher Education
Qualifications in England, Wales and Northern Ireland (FHEQ). For more information,
see: www.london.ac.uk
This guide was prepared for the University of London by:
Dr Hongda Zhong, Assistant Professor of Finance, The London of Economics and Political
Science and Dr. J. Favilukis, Lecturer, The London School of Economics and Political Science
This is one of a series of subject guides published by the University. We regret that due
to pressure of work the authors are unable to enter into any correspondence relating to,
or arising from, the guide. If you have any comments on this subject guide, favourable or
unfavourable, please use the form at the back of this guide.
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Contents
Contents
Introduction to the subject guide........................................................................... 1
Aims of the course.......................................................................................................... 1
Learning outcomes......................................................................................................... 1
Syllabus.......................................................................................................................... 2
Essential reading............................................................................................................ 2
Further reading............................................................................................................... 2
Online study resources.................................................................................................... 4
Subject guide structure and use...................................................................................... 5
Examination advice........................................................................................................ 6
Glossary of abbreviations used in this subject guide........................................................ 7
Chapter 1: Present value calculations and the valuation of physical investment
projects.................................................................................................................... 9
Aim of this chapter ........................................................................................................ 9
Learning objectives......................................................................................................... 9
Essential reading............................................................................................................ 9
Further reading............................................................................................................... 9
Overview........................................................................................................................ 9
Introduction................................................................................................................. 10
Fisher separation and optimal decision-making............................................................. 10
Fisher separation and project evaluation....................................................................... 13
The time value of money............................................................................................... 14
The net present value rule............................................................................................. 15
Other project appraisal techniques................................................................................ 17
Using present value techniques to value stocks and bonds............................................ 21
A reminder of your learning outcomes........................................................................... 23
Key terms..................................................................................................................... 23
Sample examination questions...................................................................................... 23
Chapter 2: Real options......................................................................................... 25
Aim of the chapter........................................................................................................ 25
Learning objectives....................................................................................................... 25
Essential reading.......................................................................................................... 25
Further reading............................................................................................................. 25
Introduction................................................................................................................. 25
Decision tree, source of option value and early exercise................................................. 26
Three types of real options............................................................................................ 30
A reminder of your learning outcomes........................................................................... 36
Key terms..................................................................................................................... 36
Sample examination questions...................................................................................... 37
Chapter 3: The choice of corporate capital structure............................................ 39
Aim of the chapter........................................................................................................ 39
Learning objectives....................................................................................................... 39
Essential reading.......................................................................................................... 39
Further reading............................................................................................................. 39
Overview...................................................................................................................... 39
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FN2191 Principles of corporate finance
Basic features of debt and equity.................................................................................. 40
The Modigliani–Miller theorem..................................................................................... 41
Modigliani–Miller and corporate taxation...................................................................... 43
Modigliani–Miller with corporate and personal taxation................................................ 46
Summary...................................................................................................................... 48
A reminder of your learning outcomes........................................................................... 48
Key terms..................................................................................................................... 48
Sample examination questions...................................................................................... 49
Chapter 4: Leverage, WACC and the Modigliani-Miller 2nd proposition.............. 51
Aim of the chapter........................................................................................................ 51
Learning objectives....................................................................................................... 51
Essential reading.......................................................................................................... 51
Further reading............................................................................................................. 51
Overview...................................................................................................................... 51
Weighted average cost of capital.................................................................................. 52
Modigliani and Miller’s 2nd proposition........................................................................ 54
A CAPM perspective (optional)..................................................................................... 58
Summary...................................................................................................................... 59
Key terms..................................................................................................................... 60
A reminder of your learning outcomes........................................................................... 60
Sample examination questions...................................................................................... 61
Chapter 5: Asymmetric information, agency costs and capital structure............. 63
Aim of the chapter........................................................................................................ 63
Learning objectives....................................................................................................... 63
Essential reading.......................................................................................................... 63
Further reading............................................................................................................. 63
Overview...................................................................................................................... 64
Capital structure, governance problems and agency costs.............................................. 64
Agency costs of outside equity and debt....................................................................... 64
Agency costs of free cash flows..................................................................................... 70
Firm value and asymmetric information......................................................................... 71
Summary...................................................................................................................... 75
Key terms..................................................................................................................... 76
A reminder of your learning outcomes........................................................................... 76
Sample examination questions...................................................................................... 76
Chapter 6: Equity financing................................................................................... 79
Aim of the chapter........................................................................................................ 79
Learning objectives....................................................................................................... 79
Essential reading.......................................................................................................... 79
Further reading............................................................................................................. 79
Introduction................................................................................................................. 79
Private equity financing................................................................................................ 80
Initial public offerings and seasoned equity offerings..................................................... 85
IPO underpricing and winner’s curse............................................................................. 89
A reminder of your learning outcomes........................................................................... 92
Key terms..................................................................................................................... 92
Sample examination questions...................................................................................... 93
ii
Contents
Chapter 7: Dividend policy.................................................................................... 95
Aim of the chapter........................................................................................................ 95
Learning objectives....................................................................................................... 95
Essential reading.......................................................................................................... 95
Further reading............................................................................................................. 95
Overview...................................................................................................................... 96
How to return capital to equity holders?....................................................................... 96
Modigliani–Miller meets dividends................................................................................ 97
Prices, dividends and share repurchases........................................................................ 98
Dividend policy: stylised facts........................................................................................ 99
Taxation and clientele theory...................................................................................... 100
Asymmetric information and dividends........................................................................ 102
Agency costs and dividends........................................................................................ 103
Summary.................................................................................................................... 103
A reminder of your learning outcomes......................................................................... 104
Key terms................................................................................................................... 104
Sample examination questions.................................................................................... 104
Chapter 8: Mergers and takeovers...................................................................... 105
Aim of the chapter...................................................................................................... 105
Learning objectives..................................................................................................... 105
Essential reading........................................................................................................ 105
Further reading........................................................................................................... 105
Overview.................................................................................................................... 106
Merger motivations.................................................................................................... 106
Payment method in takeover....................................................................................... 107
The market for corporate control................................................................................. 110
The impossibility of efficient takeovers........................................................................ 110
Two ways to get efficient takeovers............................................................................. 112
Empirical evidence...................................................................................................... 113
Summary.................................................................................................................... 114
A reminder of your learning outcomes......................................................................... 115
Key terms................................................................................................................... 115
Sample examination questions.................................................................................... 116
Chapter 9: Risk management and hedging......................................................... 117
Aim of the chapter...................................................................................................... 117
Learning objectives..................................................................................................... 117
Essential reading........................................................................................................ 117
Further reading........................................................................................................... 117
Introduction............................................................................................................... 117
Why do firms hedge? ................................................................................................. 118
Typical financial instruments for hedging..................................................................... 123
Cost of risk management............................................................................................ 126
Interest rate parity and carry trade.............................................................................. 127
A reminder of your learning outcomes......................................................................... 129
Key terms................................................................................................................... 129
Sample examination questions.................................................................................... 130
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FN2191 Principles of corporate finance
Notes
iv
Introduction to the subject guide
Introduction to the subject guide
This subject guide provides you with an introduction to the modern theory
of corporate finance. As such, it covers a broad range of topics and aims
to give a general background to any student who wishes to do further
academic or practical work in finance or accounting after graduation.
We begin with project valuation methods and then examine issues that
come under the broad heading of corporate finance. We will study how
key decisions made by firms affect firm value and empirical evidence on
these issues. The areas involved include:
•
the capital structure decision
•
dividend policy
•
mergers and acquisitions
•
raising equity
•
risk management.
By studying these areas, you should gain an appreciation of:
•
optimal financial policy on a firm level
•
conditions under which an optimal policy actually exists
•
how the actual financial decisions of firms may be explained in
theoretical terms.
Aims of the course
This course provides a theoretical framework used to address issues
in project appraisal and financing, payout policy, capital structure,
mergers and acquisitions, equity offerings and risk management. It
provides students with the tools required for further studies in financial
intermediation and investments.
Learning outcomes
At the end of this course, and having completed the Essential reading and
activities, you should be able to:
•
explain how to value projects, and use key capital budgeting
techniques (for example: NPV and IRR)
•
understand and apply real option theory as an advanced technique of
capital budgeting
•
understand and explain the relevance, facts and role of the payout
policy, and calculate how payouts affect the valuation of securities
•
understand the trade-off firms face between tax advantages of debt
and various costs of debt
•
calculate and apply different costs of capital in valuation
•
understand and explain different capital structure theories, including
information asymmetry and agency conflict
•
understand how companies issue new shares, and calculate related
price impact in security offerings
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FN2191 Principles of corporate finance
•
discuss why merger and acquisition activities exist, and calculate the
related gains and losses
•
understand risk, hedging, and numerous financial securities as tools to
manage risk.
Syllabus
Students may bring into the examination hall their own hand-held
electronic calculator. If calculators are used they must satisfy the
requirements listed in the General Regulations.
The up-to-date course syllabus for can be found in the course information
sheet, which is available on the course virtual learning environment (VLE)
page or on the LSE website: www.lse.ac.uk/study-at-lse/uolip/courseinformation-sheets
Essential reading
There are a number of excellent textbooks that cover this area. However,
the following text has been chosen as the core text for this course due
to its extensive treatment of many of the issues covered and up-to-date
discussions:
Brealey, R., S. Myers and F. Allen Principles of Corporate Finance. (Boston, MA,
London: McGraw-Hill, 2016) 12th edition [ISBN 9781259253331].
At the start of each chapter of this guide, we will indicate the reading that
you need to do from Brealey, Myers and Allen (2016).
Detailed reading references in this subject guide refer to the editions of the
set textbooks listed above. New editions of one or more of these textbooks
may have been published by the time you study this course. You can use
a more recent edition of any of the books; use the detailed chapter and
section headings and the index to identify relevant readings. Also check the
VLE regularly for updated guidance on readings.
Further reading
Please note that as long as you read the Essential reading you are then free
to read around the subject area in any text, paper or online resource. You
will need to support your learning by reading as widely as possible and by
thinking about how these principles apply in the real world. To help you
read extensively, you have free access to the VLE and University of London
Online Library (see below).
As further material, we will also direct you to the relevant chapters in
two other texts. You may wish to look at the following two texts that are
standard for many undergraduate finance courses:
Grinblatt, M. and S. Titman Financial Markets and Corporate Strategy. (Boston,
MA: McGraw Hill, 2011) 2nd edition [ISBN 9780077129422].
Copeland, T., J. Weston and K. Shastri Financial Theory and Corporate
Policy. (Reading, MA; Wokingham: Addison-Wesley, 2005) 4th edition
[ISBN 9780321223531].
A full list of all Further reading referred to in the subject guide is presented
here for ease of reference.
2
Introduction to the subject guide
Journal articles
Allen, F. and R. Michaely ‘Dividend policy’ in Jarrow R.A., V. Maksimovic and
W.T. Ziemba (eds) Handbooks in Operational Research and Management
Science Volume 9 1995, pp.793–837.
Asquith, P. and D. Mullins ‘The impact of initiating dividend payments on
shareholders’ wealth’, Journal of Business 56(1) 1983, pp.77–96.
Ball, R. and P. Brown ‘An empirical evaluation of accounting income numbers’,
Journal of Accounting Research 6(2) 1968, pp.159–78.
Bhattacharya, S. ‘Imperfect information, dividend policy, and “the bird in the
hand” fallacy’, Bell Journal of Economics 10(1) 1979, pp.259–70.
Blume, M., J. Crockett and I. Friend ‘Stock ownership in the United States:
characteristics and trends’, Survey of Current Business 54(11) 1974,
pp.16–40.
Bradley, M., A. Desai and E. Kim ‘Synergistic gains from corporate acquisitions
and their division between the stockholders of target and acquiring firms’,
Journal of Financial Economics 21(1) 1988, pp.3–40.
Grossman, S. and O. Hart ‘Takeover bids, the free-rider problem and the theory
of the corporation’, Bell Journal of Economics 11(1) 1980, pp.42–64.
Healy, P. and K. Palepu ‘Earnings information conveyed by dividend initiations
and omissions’, Journal of Financial Economics 21(2) 1988, pp.149–76.
Healy, P., K. Palepu and R. Ruback ‘Does corporate performance improve after
mergers?’, Journal of Financial Economics 31(2) 1992, pp.135–76.
Jarrell, G. and A. Poulsen ‘Returns to acquiring firms in tender offers: evidence
from three decades’, Financial Management 18(3) 1989, pp.12–19.
Jarrell, G., J. Brickley and J. Netter ‘The market for corporate control: the
empirical evidence since 1980’, Journal of Economic Perspectives 2(1) 1988,
pp.49–68.
Jensen, M. ‘Agency costs of free cash flow, corporate finance, and takeovers’,
American Economic Review 76(2) 1986, pp.323–29.
Jensen, M. and W. Meckling ‘Theory of the firm: managerial behaviour, agency
costs and capital structure’, Journal of Financial Economics 3(4) 1976,
pp.305–60.
Jensen, M. and R. Ruback ‘The market for corporate control: the scientific
evidence’, Journal of Financial Economics 11(1–4) 1983, pp.5–50.
Lintner, J. ‘Distribution of incomes of corporations among dividends, retained
earnings and taxes’ American Economic Review 46(2) 1956, pp.97–113.
Masulis, R. ‘The impact of capital structure change on firm value: some
estimates’, Journal of Finance 38(1) 1983, pp.107–26.
Miles, J. and J. Ezzell ‘The weighed average cost of capital, perfect capital
markets and project life: a clarification’, Journal of Financial and
Quantitative Analysis (15) 1980, pp.719–30.
Miller, M. ‘Debt and taxes’, Journal of Finance 32 1977, pp.261–75.
Modigliani, F. and M. Miller ‘The cost of capital, corporation finance and the
theory of investment’, American Economic Review (48)3 1958, pp. 261–97.
Modigliani, F. and M. Miller ‘Corporate income taxes and the cost of capital: a
correction’, American Economic Review (5)3 1963, pp. 433–43.
Myers, S. ‘Determinants of corporate borrowing’, Journal of Financial Economics
5(2) 1977, pp.147–75.
Myers, S. and N. Majluf ‘Corporate financing and investment decisions when
firms have information that investors do not have’, Journal of Financial
Economics 13(2) 1984, pp.187–221.
Poterba, J. and L. Summers ‘Mean reversion in stock prices: evidence and
implications’, Journal of Financial Economics 22(1) 1988, pp.27–59.
Ross, S. ‘The determination of financial structure: the incentive signalling
approach’, Bell Journal of Economics 8(1) 1977, pp.23–40.
Shleifer, A. and R. Vishny ‘Large shareholders and corporate control,’ Journal of
Political Economy 94(3) 1986, pp.461–88.
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FN2191 Principles of corporate finance
Shleifer, A. and R. Vishny ‘Managerial entrenchment: the case of managementspecific investment,’ Journal of Financial Economics 25 1989, pp.123–39.
Travlos, N. ‘Corporate takeover bids, methods of payment, and bidding firms’
stock returns’, Journal of Finance 42(4) 1990, pp.943–63.
Warner, J. ‘Bankruptcy costs: some evidence’, Journal of Finance 32(2) 1977,
pp.337–47.
Books
Ravenscraft, D. and F. Scherer Mergers, selloffs, and economic efficiency.
(Washington D.C.: Brookings Institution, 1987) [ISBN 9780815773481].
Online study resources
In addition to the subject guide and the Essential reading, it is crucial that
you take advantage of the study resources that are available online for this
course, including the VLE and the Online Library.
You can access the VLE, the Online Library and your University of London
email account via the Student Portal at:
https://my.london.ac.uk
You should have received your login details for the Student Portal with
your official offer, which was emailed to the address that you gave
on your application form. You have probably already logged in to the
Student Portal in order to register! As soon as you registered, you will
automatically have been granted access to the VLE, Online Library and
your fully functional University of London email account.
If you have forgotten these login details, please click on the ‘Forgotten
your password’ link on the login page.
The VLE
The VLE, which complements this subject guide, has been designed to
enhance your learning experience, providing additional support and a
sense of community. It forms an important part of your study experience
with the University of London and you should access it regularly.
The VLE provides a range of resources for EMFSS courses:
4
•
Course materials: Subject guides and other course materials
available for download. In some courses, the content of the subject
guide is transferred into the VLE and additional resources and
activities are integrated with the text.
•
Readings: Direct links, wherever possible, to essential readings in the
Online Library, including journal articles and ebooks.
•
Video content: Including introductions to courses and topics within
courses, interviews, lessons and debates.
•
Screencasts: Videos of PowerPoint presentations, animated podcasts
and on-screen worked examples.
•
External material: Links out to carefully selected third-party
resources
•
Self-test activities: Multiple-choice, numerical and algebraic
quizzes to check your understanding.
•
Collaborative activities: Work with fellow students to build a body
of knowledge.
•
Discussion forums: A space where you can share your thoughts
and questions with fellow students. Many forums will be supported by
Introduction to the subject guide
a ‘course moderator’, a subject expert employed by LSE to facilitate the
discussion and clarify difficult topics.
•
Past examination papers: We provide up to three years’ of
past examinations alongside Examiners’ commentaries that provide
guidance on how to approach the questions.
•
Study skills: Expert advice on getting started with your studies,
preparing for examinations and developing your digital literacy skills.
Note: Students registered for Laws courses also receive access to the
dedicated Laws VLE.
Some of these resources are available for certain courses only, but we
are expanding our provision all the time and you should check the VLE
regularly for updates.
Making use of the Online Library
The Online Library (http://onlinelibrary.london.ac.uk) contains a huge
array of journal articles and other resources to help you read widely and
extensively.
To access the majority of resources via the Online Library you will either
need to use your University of London Student Portal login details, or you
will be required to register and use an Athens login.
The easiest way to locate relevant content and journal articles in the
Online Library is to use the Summon search engine.
If you are having trouble finding an article listed in a reading list, try
removing any punctuation from the title, such as single quotation marks,
question marks and colons.
For further advice, please use the online help pages (http://onlinelibrary.
london.ac.uk/resources/summon) or contact the Online Library team:
onlinelibrary@shl.london.ac.uk
Subject guide structure and use
You should note that, as indicated above, the study of the relevant chapter
should be complemented by at least the Essential reading given at the
chapter head.
The content of the subject guide is as follows.
•
Chapter 1: here we focus on the evaluation of real investment
projects using the net present value technique and provide a
comparison of NPV with alternative forms of project evaluation.
•
Chapter 2: here we focus on what real options are and why they are
important in project valuation. We discuss the source of option value
and detail three types of real options: options to abandon, to expand
and to wait.
•
Chapter 3: here we study a corporation’s capital structure. The
essential issue is what levels of debt and equity finance should be
chosen in order to maximise firm value.
•
Chapter 4: this chapter is complementary to Chapter 3, however
rather than looking at values, as in Chapter 3, this chapter analyses
discount rates. We learn that if there are no taxes, while the return on
equity gets riskier as the level of debt increases, the average rate the
firm pays to raise money is unchanged. In the presence of taxes, as
debt increases, the average rate the firm pays to raise money decreases
due to tax shields.
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FN2191 Principles of corporate finance
•
Chapter 5: we look at more advanced issues in capital structure theory
and focus on the use of capital structure to mitigate governance problems
known as agency costs and how capital structure and financial decisions
are affected by asymmetric information.
•
Chapter 6: here we analyse several different ways to issue new equity,
some prominent features in equity offerings, and well-known frictions
associated with equity issuance. The topics include staged financing in the
private equity market, initial public offerings, seasoned equity offerings,
rights offerings and the winner’s curse problem.
•
Chapter 7: here we examine dividend policy. What is the empirical
evidence on the dividend pay-out behaviour of firms, and theoretically,
how can we understand the empirical facts?
•
Chapter 8: we look at mergers and acquisitions, and ask what motivates
firms to merge or acquire, what are the potential gains from this activity,
and how can this be theoretically treated? We also explore how hostile
acquisitions may serve as a discipline device to mitigate governance
problems.
•
Chapter 9: this chapter answers why and how companies manage risks
in their course of operation. We will discuss the reasons, typical financial
instrument, and the associated costs of risk management.
There is no specific chapter about corporate governance, but the agency
related topics of Chapters 5 and 8 are inherently motivated by the
existence of such problems. See also Grinblatt and Titman (2002) Chapter
18 for a broad overview on governance-related issues.
Examination advice
Important: the information and advice given here are based on the
examination structure used at the time this guide was written. Please
note that subject guides may be used for several years. Because of this we
strongly advise you to always check both the current Regulations for relevant
information about the examination, and the VLE where you should be advised
of any forthcoming changes. You should also carefully check the rubric/
instructions on the paper you actually sit and follow those instructions.
This course will be evaluated solely on the basis of a three-hour examination.
Although the examiners will attempt to provide a fairly balanced coverage of
the course, there is no guarantee that all of the topics covered in this guide
will appear in the examination. Examination questions may contain both
numerical and discursive elements. Finally, each question will carry equal
weight in marking and, in allocating your examination time, you should pay
attention to the breakdown of marks associated with the different parts of
each question.
Remember, it is important to check the VLE for:
6
•
up-to-date information on examination and assessment arrangements for
this course
•
where available, past examination papers and Examiners’ commentaries
for the course which give advice on how each question might best be
answered.
Introduction to the subject guide
Glossary of abbreviations used in this subject guide
ARR
accounting rate of return
CAPM
capital asset pricing model
IRR
internal rate of return
MM
Modigliani–Miller
NPV
net present value
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FN2191 Principles of corporate finance
Notes
8
Chapter 1: Present value calculations and the valuation of physical investment projects
Chapter 1: Present value calculations
and the valuation of physical investment
projects
Aim of this chapter
The aim of this chapter is to introduce the Fisher separation theorem, which
is the basis for using the net present value (NPV) for project evaluation
purposes. With this aim in mind, we discuss the optimality of the NPV
criterion and compare this criterion with alternative project evaluation
criteria.
Learning objectives
At the end of this chapter, and having completed the Essential reading and
activities, you should be able to:
•
analyse optimal physical and financial investment in perfect capital
markets and derive the Fisher separation result
•
justify the use of the NPV rules via Fisher separation
•
compute present and future values of cash-flow streams and appraise
projects using the NPV rule
•
evaluate the NPV rule in relation to other commonly used evaluation
criteria
•
value stocks and bonds via NPV.
Essential reading
Brealey, R., S. Myers and F. Allen Principles of Corporate Finance. (Boston,
MA; London: McGraw-Hill, 2016) Chapters 2 (Present Values), 3 (How to
Calculate Present Values), 5 (The Value of Common Stocks), 6 (Why NPV
Leads to Better Investment Decisions) and 7 (Making Investment Decisions
with the NPV Rule).
Further reading
Copeland, T. and J. Weston Financial Theory and Corporate Policy. (Reading, MA;
Wokingham: Addison-Wesley, 2005) Chapters 1 and 2.
Grinblatt, M. and S. Titman Financial Markets and Corporate Strategy. (Boston,
MA: McGraw-Hill, 2011) Chapters 9 (Discounting and Valuation), 10
(Investing in Risk-Free Projects), 11 (Investing in Risky Projects).
Roll, R. ‘A critique of the asset pricing theory’s texts. Part 1: on past and
potential testability of the theory’, Journal of Financial Economics 4(2) 1977,
pp.129–76.
Overview
In this chapter we present the basics of the present value methodology
for the valuation of investment projects. The chapter develops the NPV
technique before presenting a comparison with the other project evaluation
criteria that are common in practice. We will also discuss the optimality of
NPV and give a number of extensive examples.
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FN2191 Principles of corporate finance
Introduction
What do firms do? They use resources to produce outputs. Often there are
many different projects available, for example:
•
an engine manufacturer can choose to supply engines to Airbus or to
Boeing
•
a school can offer different courses to students
•
and, similar to a firm, an individual can choose to supply labour to
different companies.
How do companies select projects? In this chapter, we answer this
fundamental question.
For the purposes of this chapter, we will consider a firm to be a package
of investment projects. The key question, therefore, is how do the
firm’s shareholders or managers decide on which investment projects to
undertake and which to discard? Developing the tools that should be used
for project evaluation is the emphasis of this chapter.
It may seem, at this point, that our definition of the firm is rather limited.
It is clear that, in only examining the investment operations of the firm,
we are ignoring a number of potentially important firm characteristics.
In particular, we have made no reference to the financial structure or
decisions of the firm (i.e. its capital structure, borrowing or lending
activities, or dividend policy). The first part of this chapter presents what
is known as the Fisher separation theorem. What follows is a statement
of the theorem. This theorem allows us to say the following: under
certain conditions (which will be presented in the following section), the
shareholders can delegate to the management the task of choosing which
projects to undertake (i.e. determining the optimal package of investment
projects), whereas they themselves determine the optimal financial
decisions. Hence, the theory implies that the investment and financing
choices can be completely disconnected from each other and justifies our
limited definition of the firm for the time being.
Fisher separation and optimal decision-making
Consider the following scenario. A firm exists for two periods
(imaginatively named period 0 and period 1). The firm has current funds
of m and, without any investment, will receive no money in period 1.
Investments can be of two forms. The firm can invest in a number of
physical investment projects, each of which costs a certain amount of cash
in period 0 and delivers a known return in period 1. The second type of
investment is financial in nature and permits the firm to borrow or lend
unlimited amounts at rate of interest r. Finally the firm is assumed to have
a standard utility function in its period 0 and period 1 consumption. (By
consumption we mean the use of any funds available to the firm net of any
costs of investment.)
Let us first examine the set of physical investments available. The firm
will logically rank these investments in terms of their return, and this will
yield a production opportunity frontier (POF) that looks as given in Figure
1.1. This curve represents one manner in which the firm can transform
its current funds into future income, where c0 is period 0 consumption,
and c1 is period 1 consumption. Using the assumed utility function for the
firm, we can also plot an indifference map on the same diagram to find the
optimal physical investment plan of a given firm. The optimal investment
policies of two different firms are shown in Figure 1.1.
10
Chapter 1: Present value calculations and the valuation of physical investment projects
It is clear from Figure 1.1 that the specifics of the utility function of
the firm will impact upon the firm’s physical investment policy. The
implication of this is that the shareholders of a firm (i.e. those whose
utility function matters in forming optimal investment policy) must dictate
to the managers of the firm the point to which it invests. However, until
now we have ignored the fact that the firm has an alternative method for
investment (i.e. using the capital market).
Figure 1.1
The financial investment allows firms to borrow or lend unlimited
amounts at rate r. Assuming that the firm undertakes no physical
investment, we can define the firm’s consumption opportunities quite
easily. Assume the firm neither borrows nor lends. This implies that
current consumption (c0) must be identically m, whereas period 1
consumption (c1) is zero. Alternatively, the firm could lend all of its funds.
This leads to c0 being zero and c1 = (1 + r) m. The relationship between
period 0 and period 1 consumption is therefore:
c1 = (1 + r)(m – c0).
(1.1)
This implies that the curve which represents capital market investments
is a straight line with slope –(1 + r). This curve is labeled CML on
Figure 1.2. Again, we have on Figure 1.2 plotted the optimal financial
investments for two different sets of preferences (assuming that no
physical investment is undertaken).
Figure 1.2
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FN2191 Principles of corporate finance
Now we can proceed to analyse optimal decision-making when firms
invest in both financial and physical assets. Assume that the firm is at the
beginning of period 0 and trying to decide on its investment plan. It is
clear that, to maximise firm value, the projects undertaken should be those
with the greatest return. Knowing that the return on financial investment
is always (1+r), the firm will first invest in all physical investment projects
with returns greater than (1+r ). These are those projects on the
production possibility frontier (PPF) between points m and I on Figure
1.3.1 Projects above I on the PPF have returns that are dominated by the
return from financial investment.
Hence, the firm physically invests up to point I. Note that, at this point,
we have not mentioned the firm’s preferences over period 0 and period
1 consumption. Hence, the decision to physically invest to I will be taken
by all firms regardless of the preferences of their owners. Preferences
come into play when we consider what financial investments should be
undertaken.
The firm’s physical investment policy takes it to point I, from where it can
borrow or lend on the capital market. Borrowing will move the firm to the
south-east along a line starting at I and with slope –(1+r); lending will
take the firm north-west along a similarly sloped line. Two possible optima
are shown on Figure 1.3. The optimum at point X is that for a firm whose
owners prefer period 1 consumption relative to period 0 consumption (and
have hence lent on the capital market), whereas a firm locating at Y has
borrowed, as its owners prefer date 0 to date 1 consumption.
Figure 1.3 demonstrates the key insight of Fisher separation. All firms,
regardless of preferences, will have the same optimal physical investment
policy, investing to the point where the PPF and capital market line are
tangent. Preferences then dictate the firm’s borrowing or lending policy
and shift the optimum along the capital market line. The implication of
this is that, as it is physical investment that alters firm value, all agents
(i.e. regardless of preferences) agree on the physical investment policy that
will maximise firm value. More specifically, the shareholders of the firm
can delegate choice of investment policy to a manager whose preferences
may differ from their own, while controlling financial investment policy in
order to suit their preferences.
Figure 1.3
12
1
The absolute value of
the slope of the PPF
can be equated with
the return on physical
investment. For all points
below I on the PPF, this
slope exceeds that of
the capital market line
and hence defines the
set of desirable physical
investment projects.
Chapter 1: Present value calculations and the valuation of physical investment projects
Fisher separation and project evaluation
Fisher separation can also be used to justify a certain method of project
appraisal. Figure 1.3 shows a suboptimal physical investment decision (I’)
and the capital market line that borrowing and lending from point I’ would
trace out. Clearly this capital market line always lies below that achieved
through the optimal physical investment policy. Hence, one could say that
optimal physical investment should maximise the horizontal intercept of
the capital market line on which the firm ends up. Let us, then, assume a
firm that decides to invest a dollar amount of I0. Given that the firm has
date 0 income of m and no date 1 income, aside from that accruing from
physical investment, the horizontal intercept of the capital market line
upon which the firm has located is:
where Π(I0) is the date 1 income from the firm’s physical investment.
Maximising this is equivalent to the following maximisation problem:
.
The prior objective is the NPV rule for project appraisal. It says that an
optimal physical investment policy maximises the difference between
investment proceeds divided by one plus the interest rate and the
investment cost. Here, the term ‘optimal’ is being defined as that which
leads to maximisation of shareholder utility. We will discuss the NPV rule
more fully (and for cases involving more than one time period) later in
this chapter.
The assumption of perfect capital markets is vital for our Fisher separation
results to hold. We have assumed that borrowing and lending occur at the
same rate and are unrestricted in amount and that there are no transaction
costs associated with the use of the capital market. However, in practical
situations, these conditions are unlikely to be met. A particular example
is given in Figure 1.4. Here we have assumed that the rate at which
borrowing occurs is greater than the rate of interest paid on lending (as
the real world would dictate). Figure 1.3 shows that there are now two
points at which the capital market lines and the production opportunities
frontier are tangential. This then implies that agents with different
preferences will choose differing physical investment decisions and,
therefore, Fisher separation breaks down.
Figure 1.4
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FN2191 Principles of corporate finance
Agents with strong preferences for future consumption will physically
invest to point X and then financially invest to an optimum on the capital
market lending line (CML). Those with strong preferences for current
consumption physically invest to point Y and borrow (along CML’). Finally,
a set of agents may exist who value current and future consumption
similarly, and these will optimise by locating directly on the PPF and not
using the capital market at all. An example of an optimum of this type is
point Z on Figure 1.4.
The time value of money
In the preceding section we demonstrated the Fisher separation theorem
and the manner in which physical and financial investment decisions can
be disconnected. The major implication of this theorem is that the set of
desirable physical investment projects does not depend on the preferences
of individuals. In the following sections we shall focus on the way in
which individual physical investment projects should be evaluated. Our
key methodology for this will be the NPV rule, mentioned in the preceding
section. In the following sections we will show you how to apply the rule
to situations involving more than one period and with time-varying cash
flows.
To begin, let us consider a straightforward question. Is $1 received today
worth the same as $1 received in one year’s time? A naïve response to
this question would assert that $1 is $1 regardless of when it is received,
and hence the answer to the question would be yes. A more careful
consideration of the question brings the opposite response however. Let’s
assume I receive $1 now. If I also assume that there is a risk-free asset in
which I can invest my dollar (e.g. a bank account), then in one year’s time
I will receive $(1+r), assuming I invest. Here, r is the rate of return on the
safe investment. Hence $1 received today is worth $(1+r) in one year. The
answer to the question is therefore no. A dollar received today is worth
more than a dollar received in one year or at any time in the future.
The above argument characterises the time value of money. Funds are
more valuable the earlier they are received. In the previous paragraph we
illustrated this by calculating the future value of $1. We can similarly
illustrate the time value of money by using present values. Assume I
am to receive $1 in one year’s time and further assume that the borrowing
and lending rate is r. How much is this dollar worth in today’s terms?
To answer this second question, put yourself in the position of a bank.
Knowing that someone is certain to receive $1 in one year, what is the
maximum amount you would lend him or her now? If I, as a bank, were to
lend someone money for one year, at the end of the year I would require
repayment of the loan plus interest (at rate r). Hence if I loaned the
individual $x, I would require a repayment of $x(1+r). This implies that
the maximum amount I should be willing to lend is implicitly defined by
the following equation:
$x(1+r) = $1
(1.2)
such that:
(1.3)
The value for x defined in equation 1.3 is the present value of $1
received in one year’s time. This quantity is also termed the discounted
value of the $1.
14
Chapter 1: Present value calculations and the valuation of physical investment projects
You can see the present and future value concepts pictured in Figure 1.2.
If you recall, Figure 1.2 just plots the CML for a given level of initial funds
(m) assuming no funds are to be received in the future. The future value
of this amount of money is simply the vertical intercept of the CML (i.e.
m(1+r)), and obviously the present value of m(1+r) is just m.
The present and future value concepts are straightforwardly extended
to cover more than one period. Assume an annual compound interest rate
of r. The present value of $100 to be received in k year’s time is:
(1.4)
whereas the future value of $100 received today and evaluated k years
hence is:
FVK (100) = 100(1 + r)K
(1.5)
Activity
Below, there are a few applications of the present and future value concepts. You should
attempt to verify that you can replicate the calculations.
Assume a compound borrowing and lending rate of 10 per cent annually.
a. The present value of $2,000 to be received in three years’ time is $1,502.63.
b. The present value of $500 to be received in five years’ time is $310.46.
c. The future value of $6,000 evaluated four years hence is $8,784.60.
d. The future value of $250 evaluated 10 years hence is $648.44.
The net present value rule
In the previous section we demonstrated that the value of funds depends
critically on the time those funds are received. If received immediately,
cash is more valuable than if it is to be received in the future.
The NPV rule was introduced in simple form in the section on Fisher
separation. In its more general form, it uses the discounting techniques
provided in the previous section in order to generate a method of evaluating
investment projects. Consider a hypothetical physical investment project,
which has an immediate cost of I. The project generates cash flows to the
firm in each of the next k years, equal to Ck. In words, all that the NPV rule
does is to compute the present value of all receipts or payments. This allows
direct comparisons of monetary values, as all are evaluated at the same
point in time. The NPV of the project is then just the sum of the present
values of receipts, less the sum of the present values of the payments.
Using the notation given above and again assuming a rate of return of r,
the NPV can be written as:
(1.6)
Note that the cash flows to the project can be positive and negative,
implying that the notation employed is flexible enough to embody both
cash inflows and outflows after initiation.
Once we have calculated the NPV, what should we do? Clearly, if the NPV
is positive, it implies that the present value of receipts exceeds the present
value of payments. Hence, the project generates revenues that outweigh its
costs and should therefore be accepted. If the NPV is negative the project
should be rejected, and if it is zero the firm will be indifferent between
accepting and rejecting the project.
15
FN2191 Principles of corporate finance
This gives a very straightforward method for project evaluation. Compute
the NPV of the project (which is a simple calculation), and if it is greater
than zero, the project is acceptable.
Example
Consider a manufacturing firm, which is contemplating the purchase of a new piece of
plant. The rate of interest relevant to the firm is 10 per cent. The purchase price is £1,000.
If purchased, the machine will last for three years and in each year generate extra revenue
equivalent to £750. The resale value of the machine at the end of its lifetime is zero. The
NPV of this project is:
NPV = 750 + 750 + 750 – 1000 = 865.14.
(1.1)3 (1.1)2 (1.1)1
As the NPV of the project exceeds zero, it should be accepted.
In order to familiarise yourself with NPV calculations, attempt the following
activities by calculating the NPV of each project and assessing its desirability.
Activity
Assume an interest rate of 5 per cent. Compute the NPV of each of the following projects,
and state whether each project should be accepted or not.
•• Project A has an immediate cost of $5,000, generates $1,000 for each of the next six
years and zero thereafter.
•• Project B costs £1,000 immediately, generates cash flows of £600 in year 1,
£300 in year 2 and £300 in year 3.
•• Project C costs ¥10,000 and generates ¥6,000 in year 1. Over the following years, the
cash flows decline by ¥2,000 each year, until the cash flow reaches zero.
•• Project D costs £1,500 immediately. In year 1 it generates £1,000. In year 2 there is a
further cost of £2,000. In years 3, 4 and 5 the project generates revenues of £1,500
per annum.
Up to this point we have just considered single projects in isolation,
assuming that our funds were enough to cover the costs involved. What
happens, first of all, if the members of a set of projects are mutually
exclusive?2 The answer is simple. Pick the project that has the greatest
NPV. Second, what should we do if we have limited funds? It may be the
case that we are faced with a pool of projects, all of which have positive
NPVs, but we only have access to an amount of money that is less than the
total investment cost of the entire project pool. Here we can rely on
another nice feature of the NPV technique. NPVs are additive across
projects (i.e. the NPV of taking on projects A and B is identical to the NPV
of A plus the NPV of B). The reason for this should be obvious from the
manner in which NPVs are calculated. Hence, in this scenario, we should
calculate all project combinations that are feasible (i.e. the total investment
in these projects can be financed with our current funds). Then calculate
the NPV of each combination by summing the NPVs of its constituents, and
finally choose the combination that yields the greatest total NPV.
Finally, we should devote some time to discussion of the ‘interest rate’
we have used to discount future cash flows. Until now we have just
referred to r as the rate at which one can borrow or lend funds. A more
precise definition of r is that r is the opportunity cost of capital. If we are
considering the use of the NPV rule within the context of a firm, we have to
recognise that the firm has several sources of capital, and the cost of each
of these should be taken into account when evaluating the firm’s overall
16
By this we mean that
taking on any one of the
set of projects precludes
us from accepting any of
the others.
2
Chapter 1: Present value calculations and the valuation of physical investment projects
cost of capital. The firm can raise funds via equity issues and debt issues,
and it is likely that the costs of these two types of funds will differ. Later
on in this chapter and in those that follow, we will present techniques by
which the firm can compute the overall cost of capital for its enterprise.
Other project appraisal techniques
The NPV methodology for project appraisal is by no means the only
technique used by firms to decide on their physical investment policy. It is,
however, the optimal technique for corporate management to use if they
wish to maximise expected shareholder wealth. This result is obvious from
our Fisher separation analysis. In this section we talk about three of NPV’s
competitors, the payback rule, the internal rate of return (IRR) rule,
and the multiples method, which are sometimes used in practice.
The payback rule
Payback is a particularly simple criterion for deciding on the desirability of
an investment project. The firm chooses a fixed payback period, for example,
three years. If a project generates enough cash in the first three years of its
existence to repay the initial investment outlay, then it is desirable, and if it
doesn’t generate enough cash to cover the outlay, it should be rejected. Take
the cash-flow stream given in the following table as an example.
Year
Cash flow
0
1
2
3
4
–1,000
250
250
250
500
Table 1.1
A firm that has chosen a payback period of three years and is faced with
the project shown in Table 1.1 will reject it as the cash flow in years 1 to
3 (750) doesn’t cover the initial outlay of 1,000. Note, however, that if the
firm used a payback period of four years, the project would be acceptable,
as the total cash flow to the project would be 1,250, which exceeds the
outlay. Hence, it’s clear that the crucial choice by management is of the
payback period.
We can also use the preceding example to illustrate the weaknesses of
payback. First, assume that the firm has a payback period of three years.
Then, as previously mentioned, the project in Table 1.1 will not be accepted.
However, assume also that, instead of being 500, the project cash flow in
year 4 is 500,000. Clearly, one would want to revise one’s opinion on the
desirability of the project, but the payback rule still says you should reject it.
Payback is flawed, as a portion of the cash-flow stream (that realised after
the payback period is up) is always ignored in project evaluation.
The second weakness of payback should be obvious, given our earlier
discussion of NPV. Payback ignores the time value of money. Sticking
with the example in Table 1.1, assume a firm has a payback period of
four years. Then the project as given should be accepted (as total cash
flow of 1,250 exceeds investment outlay of 1,000). But what’s the NPV
of this project? If we assume, for example, a required rate of return of 10
per cent, then the NPV can be shown to be negative. (In fact the NPV is
–36.78. As a self-assessment activity, show that this is the case.) Hence
application of the payback rule tells us to accept a project that would
decrease expected shareholder wealth (as shown by application of the
NPV rule). This flaw could be eliminated by discounting project cash flows
that accrue within the payback period, giving a discounted payback
rule, but such a modification still wouldn’t solve the first problem we
highlighted.
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FN2191 Principles of corporate finance
The internal rate of return criterion
The IRR rule can be viewed as a variant on the apparatus we used in the
NPV formulation. The IRR of a project is the rate of return that solves the
following equation:
(1.7)
where Ci is the project cash flow in year i, and I is the initial (i.e. year 0)
investment outlay. Comparison of equation 1.7 with 1.6 shows that the
project IRR is the discount rate that would set the project NPV to zero.
Once the IRR has been calculated, the project is evaluated by comparing
the IRR to a predetermined required rate of return known as a hurdle
rate. If the IRR exceeds the hurdle rate, then the project is acceptable,
and if the IRR is less than the hurdle rate it should be rejected. A graphical
analysis of this is presented in Figure 1.5, which plots project NPV against
the rate of return used in NPV calculation. If r* is the hurdle rate used
in project evaluation, then the project represented by the curve on the
figure is acceptable as the IRR exceeds r*. Clearly, if r* is also the correct
required rate of return, which would be used in NPV calculations, then
application of the IRR and NPV rules to assessment of the project in Figure
1.5 gives identical results (as at rate r* the NPV exceeds zero).
Figure 1.5
Calculation of the IRR need not be straightforward. Rearranging equation
1.7 shows us that the IRR is a solution to a kth order polynomial in r.
In general, the solution must be found by some iterative process, for
example, a (progressively finer) grid search method. This also points to
a first weakness of the IRR approach; as the solution to a polynomial,
the IRR may not be unique. Several different rates of return might satisfy
equation 1.7; in this case, which one should be used as the IRR? Figure 1.6
gives a graphical example of this case.
18
Chapter 1: Present value calculations and the valuation of physical investment projects
Figure 1.6
The graphical approach can also be used to illustrate another weakness
of the IRR rule. Consider a firm that is faced with a choice between two
mutually exclusive investment projects (A and B). The locus of NPV-rate of
return pairings for each of these projects is given on Figure 1.7.
The first thing to note from the figure is that the IRR of project A exceeds
that of B. Also, both IRRs exceed the hurdle rate, r*. Hence, both projects
are acceptable but, using the IRR rule, one would choose project A as
its IRR is greatest. However, if we assume that the hurdle rate is the
true opportunity cost of capital (which should be employed in an NPV
calculation), then Figure 1.7 indicates that the NPV of project B exceeds
that of project A. Hence, in the evaluation of mutually exclusive projects,
use of the IRR rule may lead to choices that do not maximise expected
shareholder wealth.
Figure 1.7
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FN2191 Principles of corporate finance
The multiples method
An alternative to using forecasts of a firm’s or project’s cash flows to
calculate value, it is possible to use market information to estimate the
value. The multiples method assesses the firm’s value based on the value
of a comparable publically traded firm. For example, consider the firm’s
market value to earnings ratio, this ratio tells us how much a dollar
of earnings contributes to the present value according to the market’s
consensus view. For publically traded firms, this ratio is available. The
firm we wish to value may not have a publically available market value,
however we are likely to know its earnings. If we assume that these two
firms should have similar market value to earnings ratios, then we can
value the firm by taking the publically available ratio and multiplying it by
the firm’s earnings.
Common multiples to use are market value to earnings, market value to
EBITDA, market value to cash flow, and market value to book value. Some
firms, especially younger firms, have no earnings or even negative
earnings. In this case it may be better to value the firm as of some future
date in which the firm’s cash flows have stabilised, and then to discount to
today’s value. An alternative is to use more creative multiples, for example
price to patent ratio, price to subscribers ratio, or price to Ph.D.’s ratio. It is
often better to take an average over several comparable firms to calculate
the multiple. If you believe the firm being valued is better or worse than
the comparable firms, you can shade the multiple down or up, as in the
example below. The multiples method is not an exact science but rather a
convenient way to incorporate market beliefs. It should always be used in
conjunction with another method, such as NPV.
Example
Below are the equity values, debt values, and earnings (in billions) for several large US
retailers. Additionally provided is earnings growth for the past 10 years.
Equity
Debt
E
∆E (10 yr) %
JCP
17.48
3.81
1.10
7.8
COST
24.08
2.22
1.10
15.5
HD
82.08
12.39
6.01
21.2
WMT
?
47.44
11.88
15.7
TGT
50.14
14.14
2.58
19.2
Walmart’s (WMT’s) equity value is excluded as this is the quantity we wish to estimate.
We can first calculate the market value of equity to earnings ratio for the average firm
in the industry (excluding Walmart), this is: [(17.48/1.1) + (24.08/1.1) + (82.08/6.01) +
(50.14/2.58)]/4 = 17.72
We now multiply this number by Walmart’s earnings to get Walmart’s equity value
estimate: 17.72*11.88=210.49. Walmart’s actual equity value was $192.48 billion.
In the example above we used multiples to value equity, we sometimes
wish to the value of the full business (sometimes called enterprise value),
in this case we would need to use the full business value (for example,
debt plus equity) in the numerator instead of just equity value.
Notice that the debt to equity ratio of Costco (COST) was 9.2 per cent
while that of Target (TGT) was 28.2 per cent. In this example, we have
ignored the effects of leverage (debt in the capital structure), however
as we will see in a later chapter, leverage affects both firm value and the
expected return on equity. Therefore, firms with different leverage ratios
20
Chapter 1: Present value calculations and the valuation of physical investment projects
that look otherwise similar may have very different value to earnings
ratios. We will learn how to adjust the multiples method for the effects of
leverage later.
The multiples method allows us to check whether the value of a
conglomerate is equal to the sum of its parts. To estimate the value of
each business division of a conglomerate we can calculate each division’s
earnings and multiply it by the average value to earnings multiple of stand
alone firms in the same sector. Adding up the value of all divisions gives
us an estimated value for the conglomerate, this estimate is on average
12 per cent greater than the traded value of the conglomerate. This is
called the conglomerate discount. The reasons for the conglomerate
discount are not fully understood. It is possible that conglomerates are
a less efficient form of organisation due to inefficient capital markets. It
is also possible that the multiples method is inappropriate here because
single segment firms are too different from divisions of a conglomerate
operating in the same industry.
The strength of the multiples approach is that it incorporates a lot of
information in a simple way. It does not require assumptions on the
discount rate and growth rate (as is necessary with the NPV approach)
but just uses the consensus estimates from the market. A weakness is
the assumption that the comparable companies are truly similar to the
company one is trying to value; there is no simple way of incorporating
company specific information. However, its strength is also its biggest
weakness. By using market information, we are assuming that the market
is always correct. This approach would lead to the biggest mistakes
in times of biggest money making opportunities: when the market is
overvalued or undervalued.
The lesson of this section is therefore as follows. The most commonly
used alternative project evaluation criteria to the NPV rule can lead to
poor decisions being made under some circumstances. By contrast, NPV
performs well under all circumstances and thus should be employed.
Using present value techniques to value stocks and
bonds
To end this chapter, we will discuss very briefly how to value common
stocks and bonds through the application of present value techniques.
Stocks
Consider holding a common equity share from a given corporation. To
what does this equity share entitle the holder? Aside from issues such as
voting rights, the share simply delivers a stream of future dividends to
the holder. Assume that we are currently at time t, that the corporation is
infinitely long-lived (such that the stream of dividends goes on forever)
and that we denote the dividend to be paid at time t+i by Dt+i. Also
assume that dividends are paid annually. Denoting the required annual
rate of return on this equity share to be re, then a present value argument
would dictate that the share price (P) should be defined by the following
formula:
.
(1.8)
Note that in the above representation we have assumed that there is no
dividend paid at the current time (i.e. the summation does not start at
zero). In plain terms, what equation 1.8 says is that an equity share is
worth only the discounted stream of annual dividends that it delivers.
21
FN2191 Principles of corporate finance
A simplification of the preceding formula is available when we assume
that the dividend paid grows at constant percentage rate g per annum.
Then, assuming that a dividend of D0 has just been paid, the future stream
of dividends will be D0(1+g), D0(1+g)2, D0(1+g)3 and so on. This type
of cash-flow stream is known as a perpetuity with growth, and its
present value can be calculated very simply.3 In this setting the price of the
equity share is:
0
3
See Appendix 1.
(1.9)
.
This is the Gordon growth model of equity valuation. As is obvious
from the preceding discussion, it is only valid if you can assert that
dividends grow at a constant rate.
Note also that if you have the share price, dividend just paid and an
estimate of dividend growth, you can rearrange equation 1.9 to give the
required rate of return on the stock – that is:
.
(1.10)
The first term in 1.10 is the expected dividend yield on the stock, and the
second is expected dividend growth. Hence, with empirical estimates of
the previous two quantities, we can easily calculate the required rate of
return on any equity share.
Activity
Attempt the following questions:
1. An investor is considering buying a certain equity share. The stock has just paid a
dividend of £0.50, and both the investor and the market expect the future dividend to
be precisely at this level forever. The required rate of return on similar equities is 8 per
cent. What price should the investor be prepared to pay for a single equity share?
2. A stock has just paid a dividend of $0.25. Dividends are expected to grow at
a constant annual rate of 5 per cent. The required rate of return on the share
is 10 per cent. Calculate the price of the stock.
3. A single share of XYZ Corporation is priced at $25. Dividends are expected
to grow at a rate of 8 per cent, and the dividend just paid was $0.50. What is
the required rate of return on the stock?
Bonds
In principle, bonds are just as easy to value.
•
A discount or zero coupon bond is an instrument that promises
to pay the bearer a given sum (known as the principal) at the end
of the instrument’s lifetime. For example, a simple five-year discount
bond might pay the bearer $1,000 after five years have elapsed.
•
Slightly more complex instruments are coupon bonds. These not
only repay the principal at the end of the term but in the interim
entitle the bearer to coupon payments that are a specified percentage
of the principal. Assuming annual coupon payments, a three-year bond
with principal of £100 and coupon rate of 8 per cent will give annual
payments of £8, £8 and £108 in years 1, 2 and 3.
In more general terms, assuming the coupon rate is c, the principal is P
and the required annual rate of return on this type of bond is rb, the price
of the bond can be written as:4
22
4
In our notation a coupon
rate of 12 per cent, for
example, implies that
c = 0.12; the discount
rate used here, rb , is
called the yield to maturity
of the bond.
Chapter 1: Present value calculations and the valuation of physical investment projects
.
(1.11)
Note that it is straightforward to value discount bonds in this framework
by setting c to zero.
Activity
Using the previous formula, value a seven-year bond with principal $1,000, annual
coupon rate of 5 per cent and required annual rate of return of 12 per cent.
(Hint: the use of a set of annuity tables might help.)
A reminder of your learning outcomes
Having completed this chapter, and the Essential reading and activities,
you should be able to:
•
analyse optimal physical and financial investment in perfect capital
markets and derive the Fisher separation result
•
justify the use of the NPV rules via Fisher separation
•
compute present and future values of cash-flow streams and appraise
projects using the NPV rule
•
evaluate the NPV rule in relation to other commonly used evaluation
criteria
•
value stocks and bonds via NPV.
Key terms
capital market line (CML)
consumption
Fisher separation theorem
Gordon growth model
indifference curve
internal rate of return (IRR) criterion
investment policy
net present value (NPV) rule
payback rule
production opportunity frontier (POF)
production possibility frontier (PPF)
time value of money
utility function
Sample examination questions
1. The Toyundai Motor Company has the opportunity to invest in new
production line equipment, which would have a working lifetime of 10
years. The new equipment would generate the following increases in
Toyundai’s net cash flows.
In the first year of usage the new plant would decrease costs by
$200,000. For the following six years the cost saving would fall
at a rate of 5 per cent per annum. In the remaining years of the
equipment’s lifetime, the annual cost saving would be $140,000.
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FN2191 Principles of corporate finance
Assuming that the cost of the equipment is $1,000,000 and that
Toyundai’s cost of capital is 10 per cent, calculate the NPV of the
project. Should Toyundai take on the investment?
2. Describe two methods of project evaluation other than NPV. Discuss
the weaknesses of these methods when compared to NPV.
3. The CEO and other top executives of a firm with no nearby commercial
airports make approximately 300 flights per year with an average
cost per flight of $5,000. The firm is considering buying a Gulfstream
jet for $15 million. The jet will reduce the cost of travel to $300,000
(including fuel, maintenance, and other jet-related expenses).
The firm expects to be able to resell the jet in five years for $12.5
million. The firm pays a 25 per cent corporate tax on its profits and
can offset its corporate liabilities by using straight line depreciation on
its fixed assets. The opportunity cost of capital is 4 per cent.
a. Should the firm buy this jet if it has sufficient taxable profits in
order to take advantage of all tax shields?
b. Should the firm buy this jet if it does not have sufficient taxable
profits in order to take advantage of new tax shields?
c. Suppose the firm could lease an airplane for the first year, with
an option to extend the lease. Within that year they would find
out whether the local government has decided to build an airport
nearby which would reduce travel costs. How would this change
your calculations?
4. Suppose that you have a £10,000 student loan with a 5 per cent
interest rate. You also have £1,000 in your zero interest checking
account which you do not plan to use in the foreseeable future. You
are considering three strategies: (i) pay off as much of the loan as
possible, (ii) invest the money in a local bank at 3.5 per cent interest,
(iii) invest in the stock market. The expected return on the stock
market is 6 per cent for the foreseeable future. Your personal discount
rate is 4 per cent for risk-free investments. For simplicity assume all
investments are perpetuities.
a. What is the NPV of strategy (i)?
b. What is the NPV of strategy (ii)?
c. What is the NPV of strategy (iii) if you are risk neutral?
24
Chapter 2: Real options
Chapter 2: Real options
Aim of the chapter
The aim of this chapter is to understand what real options are and how to
quantify the option value. With this aim in mind, we study three types of
real options (options to abandon, to expand and to wait) through several
representative examples.
Learning objectives
At the end of this chapter, and having completed the Essential reading and
activities, you should be able to:
•
explain what real options are
•
explain why real options are important in project valuation
•
explain and calculate the source of option value
•
explain three types of real options: options to abandon, to expand, and
to wait.
Essential reading
Brealey, R., S. Myers and F. Allen Principles of Corporate Finance. (Boston, MA;
London: McGraw-Hill, 2016) Chapters 10.4 (Real Options and Decision
Trees) and 22 (Real Options).
Further reading
Brealey, R., S. Myers and F. Allen Principles of Corporate Finance. (Boston, MA;
London: McGraw-Hill, 2016) Chapters 20 (Understanding Options) and 21
(Valuing Options).
Introduction
In Chapter 1 we examined the use of present-value techniques in the
evaluation of investment projects. A key assumption is that if managers
decide to carry out a project, they never revise it subsequently. Clearly,
this is not realistic. Managers may terminate the project early if things
go wrong or may follow up with a new investment, if a trial is successful.
Analogously, movie directors may decide to film a sequel of a movie if the
original one performs well, but may decide not to if the first part performs
poorly.
In finance, we define real option as the right but not the obligation to
modify the project in the future. Real options are valuable if the future
is random, since they give us the flexibility to undertake projects only
when it is beneficial to do so. This flexibility can be in the form of an
opportunity to make more money or an opportunity to avoid losses. This
‘cherry-picking’ feature of real options is the main source of their value.
Note that in case of deterministic future, the flexibility provided by real
options, is meaningless. When there is no randomness, one can optimise
all future actions (what, when or how much to invest) upfront and simply
not deviate from this plan. Hence, there is no need for real options. In real
life, however, the future is non-deterministic in most cases and real options
are valuable.
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FN2191 Principles of corporate finance
In this chapter, we will consider decision trees – the key element to assess
real options. We will explore the source of real option value and analyse
whether it is optimal to exercise the option early.
Then we will go over the three main types of real options: option to
abandon, option to expand and option to wait.
Decision tree, source of option value and early exercise
Decision trees are simply a diagram of sequential decisions and possible
outcomes. They are a key element to value real options and they illustrate
the answers to three main questions:
•
What are the available actions?
•
When do you have them?
•
What is the payoff if an action is taken?
Figure 2.1 shows a typical decision tree. The manager has the option to
not test the project at the beginning or to stop the project in case of a
failure. In both cases, the manager avoids a loss and the decision has 0
NPV instead of a negative one.
Success
Test
Pursue project
Invest $200,000
NPV=$2million
Failure
Manager
has a
choice
Don’t test
Stop project
NPV=0
NPV=0
Figure 2.1: A typical decision tree.
In the remainder of this section, we conduct a case study on a coffee shop
project. Through this case, we will see a full-blown example of real options,
the source of option value and when early exercise of the option is optimal.
Example: Coffee shop case
We consider building a coffee shop in London. The initial investment costs
are £50,000 (in 2019). Cash flows will last for 10 years. Assume a risk-free
rate of 2.1 per cent and a discount rate for the project of 10.5 per cent
(timeline illustrated in Figure 2.2):
Year 1 CF Year 2 CF ...
Year 9 CF
Year 10 CF
Year 0 Investment –50k
Figure 2.2: Coffee shop benchmark timeline.
The cash flows in years 1–10 are uncertain and there are two main sources
of risk: market type risks and cash flow risks. The coffee market in London
may be similar to either the one in Berkeley, CA, where the demand is
generally stronger, or the one in Cleveland, OH, featuring weaker demand.
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Chapter 2: Real options
In addition to this market risk, the cash flow in each year can be high,
medium or low in each market type. Table 2.1 summarises the probabilities
of each market type and the cash flow outcomes.
Type of market
Probability of
market type
(Idiosyncratic)
Demand
Probability of
demand type
(Systematic)
Annual cash
flow (£ ‘000)
Berkeley, CA
0.8
High
0.25
16
0.8
Med
0.50
11
0.8
Low
0.25
6
0.2
High
0.25
11
0.2
Med
0.50
6
0.2
Low
0.25
1
Cleveland, OH
Table 2.1: Coffee-shop case risk analysis.
Note that unlike the projections we had in Chapter 1, now the cash flow is
random. This introduces uncertainty in the future and hence creates value for
real options. But for the beginning, let us ignore the optionality and calculate
the NPV for the benchmark case with no real options.
First, let us find the NPV of the coffee shop project given each market type.
Using the probabilities of each demand type from column 4, we can calculate
the expected cash flows for years 1–10:
E[Cash flow | Berkeley-type market ] = 0.25*6 + 0.50*11 + 0.25*16 = £11,000
E[ Cash flow | Cleveland-type market ] = 0.25*1 + 0.50*6 + 0.25*11 = £6,000
Then, the NPV of the project given each type is:
10
NPV
Berkeley
= − 50 +
∑
t=1
10
NPV
= − 50 +
Cleveland
∑
t=1
11
(1 + 0.105) t
6
(1 + 0.105) t
= 16.2
= −13.9
Hence, the unconditional NPV at year 0 is:
0.8*NPVB + 0.2*NPVC = 0.8*16.2 + 0.2*(–13.9) = 10.1
The NPV is positive, so we should build the coffee shop. But can we do
better? Yes, if we could hire a marketing research firm to learn the market
type before investing, in Year –1. The new timeline is shown in Figure 2.3:
Old Timeline
Year 1 CF Year 2 CF ...
Year 9 CF
Year 10 CF
Year 0 Investment –50k
Timeline with Market Research:
Year -1
Market Research
Year 1 CF
Year 2 CF ...
Year 9 CF
Year 10 CF
Year 0 Investment –50k
Figure 2.3: Coffee shop: time line with the market research.
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FN2191 Principles of corporate finance
If the research says that the market is Berkeley-type, we build the coffee
shop as the NPV is positive. On the other hand, if the market is Cleveland,
we withdraw as the NPV is negative. Thus, the new information creates
real option – we have the right but not the obligation to build the coffee
shop. The market research allows us to avoid losses in case of a Clevelandtype market. Figure 2.4 depicts the decision tree.
Build
Berkeley
~Build
0.8
0.2
Build
Cleveland
~Build
Figure 2.4: Coffee shop: decision tree with the market research.
Let us now find out the value of the project with the market research. The
NPV at year –1 is:
NPV =
0.8 ∗ 16.2 + 0.2 ∗ 0
= 12.7
1 + 0.021
Now, instead of –13.9 (NPVC), we simply do not build the coffee shop and
have a cash flow of 0 in the case of a Cleveland-type market. We discount
at the risk-free rate, because from year –1 to year 0, we just hold cash (no
risk). The project becomes more valuable with the real option: the NPV
without research at year –1 is 10.1/1.021 = 9.9 < 12.7.
How much are we ready to pay for the market research? We would be
willing to pay up to the additional benefit that we obtain due to the
research: 12.7 – 9.9 = £2.8,000. This is the first view of the source of option
value: the difference between the NPV with and without the real option.
An alternative view of the option value is to think of it as the marginal
effect of change in action. How does the research change our investment
decision? Without the option value, we cannot avoid losses in case of
Cleveland-type market. However, with the option to withdraw from the
project, we can avoid the negative NPV of building the shop. The NPV
of savings evaluated at year –1 is 0.2*(0 – 13.9)/1.021 = £2.8,000. This is
exactly the same as the previous figure!
Until now, we have assumed that we can only start the project at year 0,
even without research. In reality, however, market research takes time
(say one year, in this example) and without research, the project starts
immediately. The question is therefore, should we wait (start at year 0) or
should we start immediately (at year –1) without research? Recall option
theory:
28
•
early exercise is never optimal for a US call option on a non-dividend
paying stock
•
but early exercise may be optimal for a dividend paying stock.
Chapter 2: Real options
Let us see whether it is optimal to exercise our real option early. To
emphasise the cost of waiting, suppose we only have the lease for the
coffee shop for 10 years (year 0–9). If we do market research, we would
lose one year’s cash flow (Figure 2.5).
Year -1
Market Research
Year 1 CF
Year 2 CF
...
Year 9 CF
Year 2 CF
...
Year 9 CF
Year 0 Investment
-50K
Year 1 CF
Year 0 CF
Year -1 Investment
-50K
Figure 2.5: Coffee shop: timeline with the market research and waiting.
As our lease runs for 10 years, we give up one year of cash flow by
waiting. Let us re-calculate the NPV with market research:
9
PV
Berkeley
PV =
= − 50 +
∑
t=1
11
(1 + 0.105)t
0.8 * 12.1 + 0.2 * 0
1 + 0.021
= 12.1
= 9.48 < 10.1
The £4.1,000 = (16.2 – 12.1) drop in value is analogous to a dividend
payment for a stock. It is the cost of sacrificing one year of cash flows. We
miss out on the dividend by not exercising early. Analogously to a US option
on a dividend-paying stock, in this case it is optimal to exercise before
maturity. In other words, the foregone benefit (one-year cash flow) is greater
than the loss we avoid (taking a negative NPV project if a Cleveland-type
market) and it is optimal to build the shop immediately (exercise early)
rather than to wait for the outcome of the market research (delay exercise).
To sum up, real options are valuable because they give us the flexibility to
avoid bad projects. However, waiting can be costly if valuable production
opportunities are sacrificed. This is similar to losing dividend when
delaying the exercise of a stock option.
Activities
1. Which of the following examples are applications of real options:
I) An investment in the IT business
II) The valuation of an option to purchase additional handset units for resale
III) The option to develop a new drug
IV) The decision to abandon a test facility
Select one:
a. I, II, III and IV
b. I, II, and III only
c. I only
d. I and II only
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FN2191 Principles of corporate finance
2. You are thinking about an investment opportunity. To implement the opportunity,
you need to invest $5 million (C0). The investment will produce Q = 30,000 units of
products every year. The price of the product P is $40 per unit and the unit cost is $25.
Your discount rate is 6 per cent per year. Calculate the NPV if you invest today.
Select one:
a. +7.5 million
b. + 4 million
c. None of the above
d. +2.5 million
3. Following the same setup as in Question 2 but the only difference is that the price of
the product is random. Suppose the unit price P is either $60 or $30 next year with
equal probability, then expected NPV of the project if postponed by one year is:
Select one:
a. +5 million
b. +5.9 million
c. None of the above
d. –2.5 million
Three types of real options
In this section, we study three types of real options commonly observed in
practice – option to abandon, option to expand, and option to wait.
The option to abandon gives us the flexibility to withdraw from the project
in case it is no longer profitable. This option is used to disengage from
failing deals. The option to expand gives us the right to expand an existing
project. This option is beneficial if, for example, investment turns out to
be more profitable than expected. In that case, it is valuable to be able to
put more money on it. The option to wait is beneficial if we have a positive
NPV project, which, if implemented in the future, may have an even
higher NPV. It is valuable if we have the option to delay investment. Let us
consider each of these three options in more detail.
Option to abandon
There are two main subcategories of this option: temporary abandonment
and permanent abandonment. To understand the temporary abandonment
option, consider the following example.
Example: Gold mine
We have the rights to operate a gold mine for three years, starting now.
The mine produces 50,000 ounces of gold per year. The costs of extraction
are $230/ounce and the current price of gold is $220/ounce. The discount
rate is 5 per cent. The price of gold in each period has two equally likely
outcomes: it either rises by 20 per cent, or falls by 10 per cent (shown in
Figure 2.6).
30
Chapter 2: Real options
317
264
220
0.5
0.5
0.5
238
0.5
238
198
0.5
0.5
178
Figure 2.6: Gold mine – gold price dynamics.
Let us first calculate the plain NPV without any real options. First, let us
find the expected price of gold in the first and the second period:
E0 [P1Gold] = 0.5*264 + 0.5*198 = 231
E0 [P2Gold] = 0.25*317 + 0.5 * 238 + 0.25*178 = 242.75
Then, the NPV is:
NVGold mine = 50(220 − 230) +
50 (231−230)
1.05
+
50 ( 242.75 − 230)
1 .05
2
= 126
The cash flows are calculated as the price of gold less the cost multiplied
with the amount produced.
4350
1700
−500
0.5
= (317 − 230)(50)
0.5
0.5
400
= (238 − 230)(50)
0.5
400
= (238 − 230)(50)
−2600
= (178 − 230)(50)
−1600
0.5
0.5
Figure 2.7: Gold mine cash flows.
As we see, we make a loss from the mine if the gold price drops in the first
period and also if it drops in the second period. Can we avoid these losses?
Yes, if we have the option to temporarily stop extraction. Suppose we can
temporarily abandon production (close down the mine) if the gold price is
too low. Let us recalculate the cash flows by inserting zeros at nodes where
the profit is negative, and recalculate the NPV.
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FN2191 Principles of corporate finance
4350
1700
0
= (317 − 230)(50)
0.5
0.5
0.5
400
= (238 − 230)(50)
0.5
400
= (238 − 230)(50)
0.5
0.5
0
0
Figure 2.8: Gold mine cash flows with abandonment option.
With 0.5*0.5 = 0.25 probability, the price continues to rise and the cash
flow is 1,700 in the first period, 4,350 in the second period. Analogously,
with 0.25 probability, the price goes ‘up and down’ and the cash flow is
1,700 in the first period, 400 in the second period. Using the same logic
for ‘down and up’ and ‘down and down’, the final NPV is:
+ 0.25 0 +
4350
(1 + 0.05)2
[
1 + 0.05
+
400
(1 + 0.05)2
[
1700
400
+ 0.25 1 + 0.05 +
(1 + 0.05)2
[
[
[
1700
= 1978 > 126
With the abandonment option, the project is much more valuable because
we can avoid the losses in case the price of gold is low. What is the source
of the option value? Just like in the coffee shop example, there are two
ways to calculate it. We can get it either as the difference between the two
NPVs (1978 – 126 = 1852), or, alternatively, as the NPV of the negative cash
flows that is saved by the abandonment option, which also gives 1,852.
Now let us consider permanent abandonment. Consider the following
example. Suppose we have set up our own company. Now we receive a
nonretractable offer from an outside investor, to buy our company for
$150 million at or before year 1. The company’s cash flow projection is
illustrated in Figure 2.9. The discount rate is 10 per cent. The questions we
need to answer are:
1. what is the value of the offer?
2. when should we abandon the company for good?
Year 0
Year 1
Year 2
120(.6)
100 (.6)
90(.4)
0
70(.6)
50 (.4)
40(.4)
Figure 2.9: Projected cash flow (year 1 and 2) of the company.
32
[
NVGold mine = 0 + 0.25
+
Chapter 2: Real options
To answer these questions, let us calculate the NPV at all nodes.
At node 100, the NPV is:
100 + [120(0.6) + 90(0.4)] / 1.1 = 198 > 150.
The NPV is greater than the value of the offer, so we do not sell.
At node 50, the NPV is:
50 + [70(0.6) + 40(0.4)] / 1.1 = 102.72 < 150.
The NPV is less than the value of the offer, so we sell.
At year 0, the NPV is:
[198(0.6)+102.72(0.4)] / 1.1 = 145.4 < 150.
Do you want to sell? No! Why? Let us think carefully.
Note that unlike the temporary abandonment, the key in permanent
abandonment is to decide when the project should be abandoned. We use
backward induction: given the optimal abandonment decision at day 1,
what’s the day 0 NPV? Drawing a new decision tree illustrates the situation.
Year 0
Year 1
Year 2
120(.6)
100 (.6)
90(.4)
0
150 (.4)
Figure 2.10: Permanent abandonment – backward induction.
The new NPV is:
NPV0 = [198(0.6) + 150(0.4)]/1.1 = 162.
We do not want to sell at year 0 since 162>150.
The option value can be calculated again either as the difference between
the two NPVs (162 – 145 = 17) or as the present value of the marginal
changes: we can dump the firm at 150 million when the continuation cash
flows are worth only 102.72 million. The latter occurs with 0.4 probability
and the PV of the gain is (150 – 102.72)*0.4/1.1 = 17. This again gives the
same option value.
Option to expand
As outlined at the beginning of this section, this option gives us the right
to expand an existing project if it turns out to be profitable. In that case,
we would be willing to invest more money in it.
Example: Executive flying business
You are thinking about starting an executive flying business. The first-year
demand will be high with probability 60 per cent and low with probability
40 per cent. If the first-year demand was high, subsequent-year demand
will be also high with probability 80 per cent and low with probability 20
per cent. On the other hand, if the first-year demand was low, subsequentyear demand will be high with probability 40 per cent and low with
probability of 60 per cent. The risk-free rate is 10 per cent. One option is
33
FN2191 Principles of corporate finance
to purchase a Turboprop plane for $550,000 that will generate the following
cash flows (see Figure 2.11).
960 (.8)
+150(.6)
220(.2)
-550
930(.4)
+30(.4)
140(.6)
Figure 2.11: Executive flying business – Turboprop plane.
Let us find the NPV of the Turboprop plane:
NPV = − 550 +
.6(150) + .4 (30)
1.10
+
.6[.8(960) + .2(220)] + .4[.4(930) + .6(140)]
1.102
= 96.12
The project is positive NPV. But can we do better? Suppose we have another
option: purchase a Piston-engine (smaller) plane for $250,000 today and
another for $150,000 if demand is high. The latter has an implicit option to
expand if demand is high. The cash flows are depicted in Figure 2.12.
800(.8)
+100(.6)
{
-150
or
100(.2)
410(.8)
0
-250
180(.2)
220(.4)
+50(.4)
100(.6)
Figure 2.12: Executive flying business – Piston engine.
First, let us find out whether we should buy a second plane when demand is
high. The upper node on Figure 2.12 shows the cash flows if we purchase the
second plane:
.8 * 800 + .2 * 100
1.1
− 150 = 450.
This is greater than the cash flow without buying it: 450 >
.8 * 410 + .2 * 180
1.1
so we decide to expand by purchasing a second Piston-engine plane. Then
the NPV of the resulting Piston-engine strategy is:
NPV = − 250 +
.6(−50) + .4(50)
1.10
+
.6[.8(800) + .2(100) + .4[.4(220) + .6(100)]
1.102
As we see from this example, staged implementation is usually better:
NPVPISTON = $117,000,
NPVTURBO = $96,000. What is the source of option value? Suppose we ignore
the option to expand, then
NPVPISTON/NE = $52,000.
Hence, we can calculate the value of the option to expand as the difference
between the two NPVs, analogously to before: 117,000 – 52,000 = $65,000.
Alternatively, we can calculate it again as the present value of the marginal
changes. The option value comes from the ability to invest $150,000 for a
34
= 117.11
Chapter 2: Real options
second Piston plane and get incremental cash flow of 800 – 410 = 390 with
probability 0.8, and of 100 –180= –80 with probability 0.2. This opportunity
exists with probability 0.6. Hence, the present value of this investment is
[(390*0.8 – 80*0.2)/1.1 – 150]*0.6/1.1 = $65,000. This is again the same as
the previous option value.
Option to wait
As outlined at the beginning, this option gives us the flexibility to delay
investment. Even when the project currently has a positive NPV, it may be
more valuable if we wait for a better timing. Recall the stock option: you
can exercise now and pocket profits (if any) or you have the option to
exercise later, hoping for even larger profit. We can decompose the option
value into intrinsic value and time premium: option value = intrinsic
value + time premium. The intrinsic value is the profit if you exercise now.
For example, for a call option, it is max(Stock Price – Strike Price,0). The
time premium is the value of being able to wait (shown in Figure 2.13).
The black curve is the intrinsic value, and the gap between the dotted
and black curves is the value of the option to wait (the time premium).
Essentially, the time premium is the additional benefit of the stock option
that gives us the flexibility to exercise with larger profits in the future.
Option
Price
Intrinsic
Value
Option value
Time Premium
Stock Price
Figure 2.13: Intrinsic value and time premium of an option.
An important idea in the option to wait is the optimal timing of exercising
the option. For example, it might be optimal to exercise a US option on
a dividend-paying stock before maturity, if the additional benefit from
the dividend exceeds the benefit from being able to wait. The same logic
applies to real options. Even projects with positive NPV may be more
valuable if deferred. The actual NPV is then the current value of some
future value of the deferred project:
Net future value as of date t
Current NPV =
(1 + r)t
Consider the following example.
Example: Tree harvest
Suppose we may harvest a set of trees at any time over the next five years.
The net future values are shown in the table below. Assume a 10 per
cent discount rate. Given the future values of delaying the harvest, which
harvest date maximises the current NPV?
Harvest year
0
1
2
3
4
5
Net FV ($1000s)
50
64.4
77.5
89.4
100
109.4
28.8
20.3
15.4
11.9
9.4
% change in value
Table 2.2: Tree harvest: future values.
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FN2191 Principles of corporate finance
Let us calculate the current NPVs for years 0–5:
64.4
NPV if harvested in year 1=
= 58.5
1.10
Analogously, we get the NPVs if harvested in years 0–5 (shown in Table
2.3):
Harvest year
0
1
2
3
4
5
NPV ($1000s)
50
58.5
64.0
67.2
68.3
67.9
Table 2.3: Tree harvest: NPVs.
Hence, it is optimal to harvest in year 4 (highest NPV).
Activities
4. Are the following statements true or false?
a. The option to expand increases NPV
b. High abandonment value decreases NPV
c. If a project has positive NPV, the firm should always invest immediately
5. An abandonment option, in effect (select one):
a. Limits the flexibility of management’s decision-making.
b. Applies only to new projects.
c. Limits the profit potential of a proposed project.
d. Limits the downside risk of an investment project.
A reminder of your learning outcomes
At the end of this chapter, and having completed the Essential reading and
activities, you should be able to:
•
explain what real options are
•
explain why real options are important in project valuation
•
explain and calculate the source of option value
•
explain three types of real options: options to abandon, to expand, and
to wait.
Key terms
Decision tree
Early exercise
Option to abandon
Option to expand
Option to wait
Option value
36
Chapter 2: Real options
Sample examination questions
1. You are deciding between two technologies for production of a Marley
Richards’ motorcycle: Technology A uses state-of-the-art customdesigned techniques to produce the complex shapes required for the
motorcycles in high volumes and at low cost. But if the motorcycle
does not sell, the equipment will be worthless. Technology B uses
standard machine tools. Labour costs are much higher, but the
machinery can be sold for $100 million if the motorcycle does not sell.
Payoffs from Producing Outboard ($ millions)
Technology A
Technology B
Buoyant demand
185
180
Sluggish demand
85
80
Assume that the present value of the project is $115 million at year 0 if
Technology A is used. What is the present value in year 0 if Technology
B is used, ignoring the abandonment value? The risk free rate is 7 per
cent.
2. The R&D division at your company has just synthesised new lowtemperature resistant material. You decide to go ahead and produce
this material commercially as there is high demand for such materials
in the space industry. It will take five years to find out whether the
material is commercially viable, and you estimate that the risk neutral
probability of success is 25 per cent. Development will cost $100
million per year, paid at the beginning of each year. If development
is successful and you decide to produce the material, the factory will
be built immediately. It will cost $10 billion to put in place, and will
generate risk-free profits of $1 billion at the end of every year in
perpetuity.
The five-year risk-free interest rate today is 10 per cent per year, and
the yield on a perpetual risk-free bond will be 5 per cent, 8 per cent,
10 per cent or 12 per cent in five years. The risk-neutral probability of
each rate is 25 per cent. What is the value today of this project?
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FN2191 Principles of corporate finance
Notes
38
Chapter 3: The choice of corporate capital structure
Chapter 3: The choice of corporate
capital structure
Aim of the chapter
The aim of this chapter is to analyse and explain the choices of corporate
capital structures made by firms’ managers. With this aim in mind, we
first introduce a stylised model in which capital structure is irrelevant
(Modigliani–Miller). We then relax some of the assumptions made in this
stylised model in order to explain empirical evidence on firms’ capital
structures.
Learning objectives
By the end of this chapter, and having completed the Essential reading and
activities, you should be able to:
•
outline the main features of risky debt and equity
•
derive and discuss the Modigliani–Miller theorem
•
analyse the impact of taxes on the Modigliani–Miller propositions.
Essential reading
Brealey, R., S. Myers and F. Allen Principles of Corporate Finance. (Boston,
MA; London: McGraw-Hill, 2016) Chapter 19 (How Much Should a Firm
Borrow?).
Further reading
Copeland, T. and J. Weston Financial Theory and Corporate Policy. (Reading,
MA; Wokingham: Addison-Wesley, 2005) Chapter 15.
Grinblatt, M. and S. Titman Financial Markets and Corporate Strategy. (Boston,
MA: McGraw-Hill, 2011) Chapters 14 (How Taxes Affect Financing Choices)
and 16 (Bankruptcy Costs and Debt Holder-Equity Holder Conflicts).
Modigliani, F. and M. Miller ‘The cost of capital, corporation finance and the
theory of investment’, American Economic Review (48)3 1958, pp.261–97.
Modigliani, F. and M. Miller ‘Corporate income taxes and the cost of capital: a
correction’, American Economic Review (5)3 1963, pp.433–43.
Warner, J. ‘Bankruptcy costs: some evidence’, Journal of Finance 32(2) 1977,
pp.337–47.
Overview
In the preceding chapters of this guide we studied capital budget – the
choice of investment projects assuming the firm has required capital
to implement these projects. In particular, we have considered how a
manager should evaluate projects given projected future cash flows and
possible future actions that the manager may take.
Thus far, however, we have said nothing about how the firm can raise the
required investment capital, typically the mix of securities actually issued
by corporations. Should firms aim to use a large proportion of debt in
their financing or, conversely, should they employ equity financing in the
main? In this chapter and the next we examine the firm’s decision over
which types of claim to issue. The most important result we will find is
that, under a certain set of assumptions, the firm is indifferent about the
39
FN2191 Principles of corporate finance
mix of debt and equity that it uses in its financing. This result is the first
Modigliani–Miller theorem (MM1). We go on to explore deviations
from the MM1 assumptions and how this affects the debt–equity choice
through the introduction of taxation effects, costly bankruptcy and
information asymmetries.
Basic features of debt and equity
Before moving into our analysis it is useful to introduce the most basic
securities actually issued by corporations: risky debt and equity.
Corporations hold debt in many forms. They borrow money from banks
through straightforward loan and overdraft facilities, they issue corporate
debt, and they have trade credit with their trading partners. The bonds
issued by firms can have complicated features, such as convertibility,
the ability to be called and differences in seniority. To simplify matters,
however, we will think of corporate debt as being composed of a number
of bonds. Each bond entitles the holder to claim a fixed amount of cash
from the firm at a given maturity date. The amount reclaimed is termed
the face value of the debt.
Two important features of corporate debt are as follows.
1. In times of corporate bankruptcy (the cash flow to the firm being
less than the claims upon it), bond-holders have priority over equityholders (i.e. they get their share of the cash first).
2. Interest paid to debt claims is deductible from a corporation’s
corporate tax bill.
The latter point will not be used at present but will come in later. The
first of the preceding pair of points implies that corporate debt has the
following payoff function.
Payoff
[Xt , B] –
B
0
B
Xt
Figure 3.1: Debt holders payoff.
The horizontal axis of the graph above represents the cash flow to the firm
(X), and the vertical axis shows the payoff to debt assuming the amount
promised to the group of all debt-holders (the face value) is denoted B.
When the cash flow to the firm is less than the face value, the debt-holders
gain the entire amount. For values of the cash flow at and above the face
value, the payoff to debt-holders is constant at B.
40
Chapter 3: The choice of corporate capital structure
The holders of corporate equity receive the residual cash flow accruing to
the firm after payments to debt-holders. However, despite having a claim
that is junior to that of debt-holders, equity-holders elect the board of a
firm and have voting rights over corporate activities and are hence the true
owners of the corporation. Equity also comes in many forms, but we will
focus on the characteristics of common stock.1
Stock-holders receive cash income in the form of dividend payments.
These payments, unlike payments to service debt, are not deductible from
corporation tax obligations. Given the residual nature of the equity claim,
the payoff to equity is as given in Figure 3.2.
1
Other types of equity
include preferred stock
and warrants.
Payoff
[Xt – B, 0]+
0
B
Xt
Figure 3.2: Equity holders payoff.
When the firm’s cash flow (X) is at or less than the face value of debt (B),
equity-holders receive nothing. However, they receive every dollar of cash
flow greater than B. This gives the kinked payoff function shown in Figure
6.2, which (anticipating future developments) is of precisely the same
form as that of a European call option.
The Modigliani–Miller theorem
We now know what corporate debt and equity claims look like. One
unanswered question, however, is what mix of debt versus equity should
firms issue? In finance parlance, the ratio of the market value of debt
to that of equity is known as the leverage or gearing ratio. Hence,
the preceding question can be rephrased as follows. What is the optimal
leverage ratio that a firm should aim for? This question was addressed in
the 1950s by Franco Modigliani and Merton Miller. They showed the result
that is the focus of the current section: under given assumptions, firms are
indifferent about their leverage. This is because firms with differing debtto-equity ratios but the same investment policies have identical values, and
hence there is no value to leverage.
The assumptions underlying MM1 are as follows:
•
capital markets have no frictions (including no taxes or transactions
costs)
•
investors have perfect information and homogeneous expectations
•
investors care only about their wealth
•
financing decisions do not affect investment outcomes.
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FN2191 Principles of corporate finance
To prove their indifference proposition, Modigliani and Miller used the
notion of absence of arbitrage, meaning that the two different assets that
generate the exact same payoffs in the future must share the same price
today.
Consider two firms. The first is entirely equity-financed, and we call it firm
U. A second firm has an identical set of investment projects but has issued
both debt and equity. We shall refer to the second firm as firm L and
assume it has issued B units of debt that earn interest at rate rd. Finally,
assume for simplicity’s sake that everything in our world lasts for one
period only.
Consider an investor who holds a proportion α of firm U’s equity. As this
firm is solely equity-financed, our individual always earns a proportion α
of firm U’s cash flow (X). Assume that the same agent also buys α of firm
L’s equity and α of firm L’s debt. When the cash flow to firm L is less than
the face value of its debt (B) obligations, our investor earns α of the cash
flows through his share of total debt. When cash flow exceeds the face
value of debt, he also gets a payoff on his equity claim.
In Table 3.1 we show the payoff to our investors’ positions in both firms
under two scenarios. The first represents the case where the cash flows to
the two firms are smaller than the face value of firm L’s debt. The second
case is when firm U’s cash flows exceed firm L’s debt obligations. Note
that, in both cases, the investor earns an identical amount from their two
positions, regardless of the actual cash-flow outcome. Hence, in line with
the absence of arbitrage argument, the two positions must be identically
priced.
Type of claim
Debt
Payoff from position in U
X < B(1 + rd) X > B(1 + rd)
0
0
Payoff from position in L
X < B(1 + rd) X > B(1 + rd)
αX
αB(1 + rd)
Equity
αX
αX
0
α(X–B(1 + rd))
Total
αX
αX
αX
αX
Table 3.1
The price of the position in the unlevered firm is just αVU where the
value of the unlevered firm is denoted VU. The value of the position in
the levered firm is αE + αD = α(E+D), where E is the market value of the
levered firm’s equity, and D is the market value of the levered firm’s debt.
Of course, the total value of the levered firm (VL) must be the sum of E and
D. Hence, the price of the levered position is αVL. Equating the price of
levered and unlevered position yields the result that VU = VL, which is the
MM capital structure irrelevance proposition.
The key to the above result is that financing decisions do not affect
investment outcomes. Hence, two firms with identical investment policies
will derive identical returns regardless of their financing. As their
investment proceeds are the same, they should have the same value.2
Another key point is that none of their cash flow goes to anyone outside
those who own debt and equity.
An alternative way to show the MM capital structure irrelevance
proposition is to show that stakeholders in the firm are indifferent to
changes in the firm’s capital structure. The reason for this is that stakeholders can, without cost, undo any changes the firm makes through their
own trading in the firm’s securities.
Consider once more an investor who owns a proportion α of firm L’s
equity. The payoff associated with this position is α(X – B(1+rd)). Firm
42
2
You can think of this
result in the following
way: when you slice a
cake, you do not reduce
the size of the cake you
sliced. Debt and equity
are just different slices
of firm cash flow and,
based on the preceding
logic, the value of the
firm (size of the cake)
is independent of the
leverage ratio (way in
which you slice the cake).
Chapter 3: The choice of corporate capital structure
L now chooses to repurchase half of its equity (costing E/2) and funds
the repurchase with the issue of new debt. Hence, the face value of debt
outstanding becomes B1 = B + E/2. Assuming that none of our investor’s
equity was repurchased, their payoff would be 2α(X – B1(1 + rd)) after the
repurchase. This is obviously different to that prior to the capital structure
change.
However, our investor can restore their original payoff profile using the
following strategy. Sell one-half of their equity stake and use the proceeds to
buy debt. The payoff from the new position is α(X – B1(1 + rd)) + α(1 + rd)E/2
= α(X – B(1 + rd)). Hence our investor can, without cost, undo any change
the firm makes in its capital structure. This implies that investors will be
indifferent to such changes, and hence the valuation of a firm will not
depend on the specific debt–equity ratio it chooses (i.e. the MM irrelevance
proposition is valid).
Example
Consider an entrepreneur with a project which requires an initial investment of $100m
and which will have perpetual cash flows of $20m forever or $5m forever with equal
probability. Assume that all investors are risk neutral and require a 10 per cent expected
rate of return. We can show that the entrepreneur is indifferent between raising $100m
with debt, equity, or a mix of debt and equity.
•• Debt: the entrepreneur must promise investors a coupon such that in expectations
they receive interest of 100*.1 = $10m every year. Since in the bad state of the
world investors will receive no more than $5m, it must be the case that .5*c + .5*5
= 10 and c = 15. The entrepreneur will receive the remainder: 0 in the bad state of
the world and 20 – 15 = 5 in the good state of the world. In expectation, the present
value of this is .5*5/.1 = $25m.
•• Equity: the entrepreneur must promise investors a fraction α of future equity
payouts. In expectation, outside equity investors will receive α*(.5*5 + .5*20) =
12.5α each year. The present value of this is 12.5α/.1 = 125α. This must equal to the
amount they put in: 100 = 125α and α = 80 per cent. The entrepreneur receives the
remainder of the equity, (1 – α)*12.5 = $2.5m every year. The present value of this
is $25m.
•• Mix: the entrepreneur raises $50m through debt. They must promise investors a
coupon such that in expectations they receive interest of 50*.1 = $5m every year.
Since even in the bad state of the world the firm can pay $5m, they promise them a
coupon of $5m. The total equity payout is the remainder: 0 in the bad state of the
world and 20 – 5 = $15m in the good state of the world; this is equal to .5*15 =
$7.5m in expectation. The entrepreneur promises equity investors a fraction α of
future equity payouts. In expectation outside equity investors will receive 7.5α, per
year, or 7.5α/.1 = 75α in present value. This must equal to the $50m they have
contributed, resulting in α = 66.7 per cent. The entrepreneur is left with (1 – α)*75
= $25m.
The entrepreneur is indifferent to the choice of capital structure because capital structure
does not affect total cash flows produced by the firm.
Modigliani–Miller and corporate taxation
One of the assumptions underlying MM’s irrelevance proposition is that
there are no frictions in capital markets. One very pertinent and realistic
friction is taxation, however. Firms are taxed on their profits and investors
on their income from dividends, capital gains and interest income.
Incorporating taxation into our analysis will result in the irrelevance of
capital structure breaking down. The reason underlying this problem is
that dividend and interest payments are not treated symmetrically in the
43
FN2191 Principles of corporate finance
calculation of a firm’s corporation tax bill, and similarly investors are taxed
differentially on their income from interest and from capital gains. Hence,
the choice of firm capital structure will affect the after-tax stream of
payments to all stakeholders and hence change the value of the firm.
To start, consider a world in which investors are not taxed at all on their
personal incomes. However, firm profits are taxed. Interest payments to
debt, however, are made prior to the calculation of the corporation tax
bill, whereas dividend payments must be paid out of after-tax income.
As suggested above, the fact that debt service payments are made out of
pre-tax cash flow and payments to equity out of post-tax cash flow will
cause the breakdown of the irrelevance proposition. Debt is now a more
favourable security to issue than equity.
To illustrate, consider an infinitely lived, levered firm. Assume that the
firm earns net cash flow Xt in period t, and that interest of rdB must be paid
every period. Finally, assume that the probability of defaulting on the debt
is always zero.3 In period t, the following funds are paid to investors in the
firm:
Ct = rd B + (1 – τc )(Xt – rdB) = (1 – τc) Xt + τcrd B,
(3.1)
where τc is the corporation tax rate. The first term on the right-hand side
of equation 3.1 is precisely the payment made by an unlevered firm with
cash flow Xt in period t. The second term is the gain made by the levered
firm in saving on its corporation tax bill through using debt in the capital
structure. This is known as the tax shield advantage of debt finance.
As our firm is infinitely lived, its market value is calculated as the present
value of the perpetual stream of payments to investors. Discounting and
adding up the stream of payments represented by the first term on the
right-hand side of equation 3.1 gives us the value of an unlevered firm
(VU), with identical cash flows to our levered firm. Discounting the stream
of payments represented by the second term on the right-hand side of
equation 3.1 gives τcD, where D is the market value of debt. Hence the
value of the levered firm can be written as:
VU = VL + τcD.
(3.2)
The value of a firm increases linearly with the market value of its debt
and, as such, firms should aim to have as high a leverage as possible.
Note that, when the corporation tax rate is zero, the MM proposition is
satisfied once more. In the following section, we show how firm valuation
is affected by the introduction of personal taxes on investor income as well
as taxes on corporate profits.
Example
Consider the same entrepreneur as in the previous example but now living in a world
where corporate taxes are 15 per cent. We can show that the entrepreneur wishes to
raise as much money as possible through debt.
•• Debt: the coupon payment offered to creditors is c = $15m, exactly as before. The
entrepreneur will receive the remainder, but must pay taxes on it. This is 0 in the bad
state of the world and (20 – 15)*(1 – .15) = 4.25 in the good state of the world. In
expectation the present value of this is .5*4.25/.1 = $21.25m.
44
•• Equity: the entrepreneur must promise investors a fraction α of future equity
payouts. In expectation, outside equity investors will receive α*(.5*5 + .5*20)
(1 – .85) = 10.625α each year. The present value of this is 10.625α/.1=106.25α.
This must equal to the amount they put in: 100 = 106.25α and α = 94.12%. The
entrepreneur receives the remainder of the equity, (1 – α)*10.625 = $.625m every
year. The present value of this is $6.25m.
3
For this to hold we
must have Xt > rd B in
every period t.
Chapter 3: The choice of corporate capital structure
•• Mix: the coupon payment offered to creditors is $5m, exactly as above. The total
equity payout is the remainder: 0 in the bad state of the world and (20 – 5)*
(1 – .15) = $12.75m in the good state of the world; this is equal to .5*12.75 =
$6.375m in expectation. The entrepreneur promises equity investors a fraction α of
future equity payouts. In expectation outside equity investors will receive 6.375 α, per
year, or 6.375α/.1 = 63.75α in present value. This must equal to the $50m they have
contributed, resulting in α = 78.43%. The entrepreneur is left with (1 – α)*63.75 =
$13.75m.
The entrepreneur is best off raising money with 100 per cent debt, next best off with a
50/50 mix, and worst off raising money with 100 per cent equity.
As noted above, the addition of corporation tax to the MM analysis implies
that firms should choose leverage ratios as large as possible. However, this
is a clearly counterfactual implication. It has been suggested that relaxing
another of MM’s assumptions can reconcile the facts with our analysis. The
assumption that we relax is that bankruptcy is a cost-less process for firms
to undergo.4 MM assume that, if a firm’s cash flow is insufficient to cover
debt service (bankruptcy), then all funds are transferred immediately and
without cost to bond-holders. However, in reality bankruptcy involves
direct costs, such as lawyers’ fees, and indirect costs, such as debt-holder–
equity-holder conflicts in financially distressed firms.
For empirical
evidence on the costs
of bankruptcy in US
railroad firms, see
Warner (1977).
4
Figure 3.3: Optimal leverage under trade-off theory.
As a result, we once more modify our analysis to allow for the effects of
bankruptcy costs. We assume that firms with higher levels of debt in their
capital structure incur greater costs of financial distress and that, at very
high debt levels, the effect of such costs may outweigh tax shield effects.5
You will find a diagrammatic analysis of this situation in Figure 3.3, which
plots firm value against leverage under three different scenarios. The first
is when corporation tax and bankruptcy costs are both zero. Scenario 2
introduces non-zero corporation tax, and the third scenario allows for
non-zero costs of bankruptcy.
High debt levels imply
large fixed nominal
payments every period
and hence expose
the firm to financial
distress if cash flows are
unexpectedly low.
5
Figure 3.3 makes the point quite well. When debt levels become too large,
the costs of financial distress outweigh tax shield gains and imply a finite
optimal leverage ratio. This is in contrast to the case when bankruptcy is
costless as firm value then increases without bound as leverage rises.
Example
Consider the same entrepreneur as in the previous example who still faces a 15 per
cent corporate tax, but now also a drop of 40 per cent in all future income in case of
bankruptcy. We can show that the entrepreneur wishes to raise money through a mix of
45
FN2191 Principles of corporate finance
debt and equity because using all equity results in losses of tax shields while too much
debt results in paying bankruptcy costs.
•• Debt: the entrepreneur must promise investors a coupon such that in expectations
they receive interest of 100*.1 = $10m every year. In the bad state of the world
the firm is unable to fully pay its creditors and the firm will default. At this point, the
creditors will take over the firm, but 20 per cent is lost to bankruptcy costs so their
annual payout is 5*(1 – .4) = 3. It must be the case that .5*c + .5*3 = 10 and c
= 17. The entrepreneur will receive the remainder, after taxes. This is 0 in the bad
state of the world and (20 – 17)*(1 – .15) = 2.55 in the good state of the world. In
expectation the present value of this is .5*2.55/.1 = $12.75m.
•• Equity: the firm cannot be bankrupt since it carries no debt, therefore the solution is
identical to the previous example. The entrepreneur receives $6.25m.
•• Mix: note that in the previous example the coupon payment was just low enough
for the firm to not default (in the bad state of the world equity is left with zero but
creditors are fully paid, this is not default). Since no bankruptcy costs are paid, the
solution is identical to the previous example. The entrepreneur receives $13.75m
The entrepreneur is best off raising money by a mix of debt and equity so that they can
take advantage of the tax benefits of debt without having leverage so high as to suffer
bankruptcy costs.
The idea that firm value is maximised by some intermediate leverage which
balances out the tax benefit of debt and the costs of financial distress is
called trade-off theory. However trade-off theory is out of favour because
empirically the costs of bankruptcy appear to be too low to observe the low
amounts of debt firms typically have in their capital structure. The average
leverage ratio for large US firms is 1/3. Estimates of direct costs have been
estimated as 7.5 per cent of market value for small firms by Ang (1982)
but only 2.9 per cent for firms listed on AMEX and NYSE by Weiss (1990).
Indirect costs are likely to be somewhat larger, but are harder to estimate.
Modigliani–Miller with corporate and personal taxation
Before closing this chapter, we briefly examine how personal taxation
affects the Modigliani–Miller analysis when introduced in conjunction
with corporate taxation. For the analysis in this section, we revert to the
assumption that bankruptcy costs are zero.
Consider a world with the following tax structure. Corporate profits are
taxed at τc. Personal income, including that obtained from corporate
interest payments, is taxed at rate τd. Finally, personal income from
holdings of equity is taxed at rate τe. Assume that firms are infinitely
lived, and consider a firm that pays rD B of its gross income at any point as
interest. As interest payments are tax-deductible, the amount of interest
that reaches the firm’s bond-holders’ bank accounts is:
rDB(1 – τd).
(3.3)
In period t, the firm pays out an amount Xt – rD B to equity-holders. This
amount is taxed twice: first at the corporate level and second at the personal
level. Hence, the net amount that reaches equity-holders’ pockets is:
(Xt – rD B)(1 – τc)(1 – τe).
(3.4)
Hence, in total, in period t, the firm pays out the following amount:
Ct = (Xt – rD B) (1 – τc)(1 – τe) + rDB(1 – τd).
46
(3.5)
Chapter 3: The choice of corporate capital structure
This expression can be rearranged to yield the following:
Ct = Xt (1 –τc)(1 – τe) + rD B[(1 – τd) – (1 – τe)(1 – τc)].
(3.6)
Note that the first term in equation 3.6 is precisely the cash-flow stream
accruing to equity-holders in an unlevered firm (with identical cash flows to
the levered firm). Hence, discounting this stream of funds at the appropriate
rate yields a present value of VU. The second term is the extra money paid
out, as the firm has debt in its capital structure. This should be discounted
at the after-tax rate of return on debt (i.e. (1 – τd)rD). The sum of the present
values of these two terms is clearly the value of the levered firm. Hence we
can write:
(3.7)
This generalises equation 3.2 to the personal (as well as corporate) taxation
case. Note that equation 3.2 can be retrieved as a special case of equation
3.7, when both personal tax rates are set to zero. The second term on the
right-hand side of 3.7 is the taxation gain of debt. It is increasing in the
corporate tax rate and the tax rate on equity income and decreasing in the
tax rate on debt income. Note that, if (1 – τc)(1 – τe) > (1 – τd), then the tax
advantage is negative, such that the optimal capital structure choice is to be
all equity. If the preceding inequality is reversed, though, the tax advantage
is clearly positive and, as such, optimal capital structure involves a firm
issuing as much debt as possible.
The Miller equilibrium
Let us consider again the Modigliani–Miller setting with corporate
and personal taxes. The Miller equilibrium is derived in such a setting
when investors differ in their tax rates on personal income. The Miller
equilibrium is obtained by stating that demand for debt must be equal to
supply for debt in equilibrium.
Let us denote respectively the (expected) rates of return offered by debt
and equity, gross of personal taxes, but after adjusting for risk premiums,
by rD and rE. In this new setting, firms are willing to issue debt exclusively
as long as, after adjusting for risk premiums, the cost of debt after
corporate taxes is strictly lower than the cost of equity, that is, as long as:
rD (1 – τc) < rE.
(3.8)
Investors are willing to hold debt as long as, after adjusting for risk
premiums, the return after personal income taxes offered by debt is weakly
higher than the return after personal taxes on equity income offered by
equity, that is, as long as:
rD (1 – τd) ≥ rE (1 – τe).
(3.9)
In order to understand the Miller equilibrium, let us first assume that
the pre-tax return on debt, rD, offered by firms is equal to the pre-tax
return on equity, rE. In this case, firms are willing to issue debt which
tax-exempt investors are willing to buy as both inequalities (equations 3.8
and 3.9) are satisfied. Firms have an incentive to increase leverage and
will continue to replace equity with debt, moving up the demand curve by
increasing the return rD they offer to attract investors with higher personal
income tax rates, until:
rD = [rE(1 –τe)]/(1 – τd) = rE /(1 – τc).
(3.10)
If the rate of return offered on debt is lower than rE /(1 – τc), firms have still
incentives to issue more debt as, at this point, it is still profitable to issue
47
FN2191 Principles of corporate finance
debt to investors with marginally higher personal income tax rates. In
contrast, if the rate of return offered on debt is higher than rE/(1 – τc), firms
would be better off issuing equity than debt as it is cheaper.
In equilibrium, there is thus no advantage for firms to issue debt as the
equilibrium rate of return offered to debt-holders is such that firms are
indifferent between issuing debt and equity. In equation 3.7, the value of
the levered firm, VL, is equal to the value of the unlevered firm, VU, as:
(1 – τc) (1 – τe) = 1 – τd.
(3.11)
The after-tax Miller’s theory hence implies that there is an equilibrium
aggregate amount of debt outstanding in the economy which is
determined by relative corporate and personal tax rates. The amount of
debt issued by any particular firm is, however, a matter of indifference.
Summary
In this chapter we have presented a fundamental analysis of the capital
structure of a firm. Initially we show that, under the MM assumptions,
capital structure does not affect firm value. We then present relaxations of
the MM assumptions and demonstrate how the MM result is altered. With
the introduction of corporate taxation it becomes clear that firm value is
increasing with the level of debt in the capital structure. Also allowing for
costly bankruptcy, we find that an optimal, finite capital structure may result.
When personal taxes and corporate taxes are included, then the prescriptions
for optimal capital structure are unclear. The optimum depends on the
particular constellation of corporate and personal taxation rates.
In the next chapter we will explore the same relationships but from the
perspective of returns rather than values. In the following chapter we will
examine how conflicts between debt and equity-holder interests will also
imply that the MM result is violated. The analysis presented focuses on
simple cases in which the choices of equity-holders (those who dictate the
firm’s investment policy) are not aligned with the interests of debt-holders.
A reminder of your learning outcomes
Having completed this chapter, and the Essential reading and activities,
you should be able to:
•
outline the main features of risky debt and equity
•
derive and discuss the Modigliani–Miller theorem
•
analyse the impact of taxes on the Modigliani–Miller propositions.
Key terms
bankruptcy costs
capital structure
corporate taxes
leverage
Miller equilibrium
Modigliani–Miller irrelevance theorem
personal taxes
tax shield of debt
48
Chapter 3: The choice of corporate capital structure
Sample examination questions
1. What assumptions underlie Modigliani and Miller’s proposition that
firm value should be independent of capital structure?
2. Using a simple two-period model of an unlevered firm and a levered
firm with B units of riskless debt outstanding, demonstrate the
Modigliani–Miller proposition. In the same framework, show that an
investor is indifferent to the firm altering its capital structure.
3. Demonstrate the impact of corporate and personal taxation on the
relationship between firm value and capital structure using a simple
infinite horizon framework. What would be the optimal capital
structure for firms if the only form of taxation was corporate?
4. A start-up firm needs $100 million to launch its product. It has already
signed a contract to provide its services to one major customer, this
will result in $5 million in profits annually in perpetuity, starting this
year. There is a 50 per cent chance the firm will sign a contract with a
second customer with expected profits of $15 million in annual profits.
If this deal is not signed, the firm only has $5 million in profits.
The corporate tax is 15 per cent. In case of bankruptcy, 40 per cent of
firm value is lost. Everyone is risk neutral with a 10 per cent discount
rate.
a. Suppose the start-up funds the $100 million through equity. What
share of equity must be offered to outside investors? What is the
present value of the initial investors’ stake.
b. Suppose the start-up funds the $100 million through debt
(perpetuity). What coupon payment must be offered to creditors?
What is the present value of the initial investors’ stake.
c. Suppose the start-up funds half of the $100 million through
debt and the rest through equity. What coupon payment must
be offered to creditors? What share of equity must be offered to
outside investors? What is the present value of the initial investors’
stake. What is the best way to finance this project? Comment on
trade-off theory.
d. Suppose there were no bankruptcy costs. What would be the
optimal choice of financing?
5. Firm A pays ¥15 million in the good state and ¥10 million in the bad
state. It is an all equity firm and you own 10 per cent of the equity.
Assume there are no taxes. The price per share is ¥10 with one million
shares outstanding.
a. What is your payout in the good state and in the bad state?
b. The other owners have decided to recapitalise the firm. They raise
¥6 million by selling riskless bonds with a face value ¥7 million.
They use this money to repurchase equity at the market price.
You did not sell any of your shares. How much equity did they
repurchase? What share of equity do you now on? What is your
payout in the good state and in the bad state?
c. Compare the expected return on your investment before and after
the transaction. Why did the expected return change?
d. You are risk averse and do not like the change to your return
profile. Describe what you can do to get your payoff to be just the
same as before the transaction. Comment on what the Modigliani–
Miller 1st proposition in relation to this question.
49
FN2191 Principles of corporate finance
Notes
50
Chapter 4: Leverage, WACC and the Modigliani-Miller 2nd proposition
Chapter 4: Leverage, WACC and the
Modigliani-Miller 2nd proposition
Aim of the chapter
The aim of this chapter is to derive relationships between the rate of
return on a firm’s equity, the rate of return on a firm’s debt, and the rate
of return on the firm’s total assets (WACC). We will derive the Modigliani
and Miller 2nd proposition to analyse these relationships in the presence
of corporate taxes.
Learning objectives
By the end of this chapter, and having completed the Essential reading and
activities, you should be able to:
•
write down the relationship between debt, equity, the unlevered return
on the firm, and the levered return on the firm
•
understand what happens to equity returns, and the weighted average
cost of capital as leverage increases with and without taxes
•
draw a link between Modigliani–Miller’s 1st and 2nd propositions
•
find the equity beta of a firm by unlevering and relevering the equity
beta of a comparable firm with different capital structure.
Essential reading
Brealey, R., S. Myers and F. Allen Principles of Corporate Finance. (Boston, MA;
London: McGraw-Hill, 2016) Chapters 18 (Does Debt Policy Matter?) and
20 (Financing and Valuation).
Further reading
Grinblatt, M. and S. Titman Financial Markets and Corporate Strategy. (Boston,
MA: McGraw-Hill, 2011) Chapters 13 (Corporate Taxes and the Impact
of Financing on Real Asset Valuation), 14 (How Taxes Affect Financing
Choices) and 15 (How Taxes Affect Dividends and Share Repurchases).
Miles, J. and J. Ezzell ‘The weighed average cost of capital, perfect capital
markets and project life: a clarification’, Journal of Financial and
Quantitative Analysis (15) 1980, pp.719–30.
Modigliani, F. and M. Miller ‘The cost of capital, corporation finance and the
theory of investment’, American Economic Review (48)3 1958, pp.261–97.
Modigliani, F. and M. Miller ‘Corporate income taxes and the cost of capital: a
correction’, American Economic Review (5)3 1963, pp.433–43.
Overview
In Chapter 1 we learned how to calculate the value of a project by
computing the present value of the project’s future cash flows. This was
done by discounting the cash flows by the appropriate discount rate. In
this chapter we will see how this discount rate changes as the capital
structure of the firm changes.
We will see that as the firm increases its leverage, its equity becomes more
risky. The required rate of return on equity therefore increases. However
the overall return on the firm’s assets (WACC) does not change if there are
51
FN2191 Principles of corporate finance
no corporate taxes. This is analogous to results from the previous chapter:
Modigliani–Miller’s 1st proposition stated that the firm’s value did not
change with leverage when there were no corporate taxes. We will see that
because taxes result in a safe cash flow returned to the firm in the form
of a reduced tax liability, in the presence of corporate taxes the expected
return on the firm’s assets decreases with leverage as the assets become
safer due to increased tax shields. This is also analogous to results from
the previous chapter: as the firm increases leverage, its value increases in
the presence of corporate taxes.
Weighted average cost of capital
In this section, we first derive the weighted average cost of capital in a
world without corporate tax. Then we introduce tax and study how it
affects the cost of capital.
Let’s first consider a world without corporate tax. A firm with total asset V
is financed by both equity E and debt (or bond) B, and hence:
V = E + B.
(4.1)
The equity and debt holders require returns of re and rd respectively. When
the capital market is competitive, these returns are also the expected
returns to the respective security holders. From the firm’s perspective,
resources that must be paid to the equity and debt investors in order
to generate these returns are the cost of financing the productive asset.
Therefore, the expected returns to equity and debt are also known as the
cost of equity and cost of debt. Our firm is currently financed by
a mixture of debt and equity, so we naturally want to know its average
financing cost, which is also the discount rate we shall use to calculate the
present value of all future cash flows generated by the productive assets.
The total resource that must be paid to equity and debt investors is:
reE + rdB.
(4.2)
which must be generated from operating the asset. Therefore, to make the
production worthwhile, the asset must deliver a minimum return of:
( B +E E r + ( B +E E r
=
(
V
e
(
(reE + rdB)
d
(4.3)
This is the rate of return which should discount the total cash flow coming
from the firm (that is, the cash flows to debt and equity) in order to
calculate the total value of the firm (that is, the value of debt plus equity).
Expression (4.3) is known as the weighted average cost of capital
(WACC). From the expression, it is clear that WACC is the average cost of
equity and cost of debt weighed by their respective composition in the
total asset value.
Now we introduce corporate income tax. If interest payment to the debt
holders is tax deductible, then the cost of borrowing through debt becomes
cheaper, as it lowers the tax bill of the company. Hence, the average cost of
capital should therefore lower.
Consider a firm with pre-tax annual cash flows Xt. Its value today is V0
and its value next year, after X1 has been paid out, is V1. If this firm has
outstanding debt with market value B0, then its equity is valued E0=V0–
B0. Suppose that the appropriate returns on debt and equity are rd and re
respectively.
Recall from the previous chapter that if this firm has perpetual outstanding
debt with face value B then rdB will be distributed to the creditors in the
52
Chapter 4: Leverage, WACC and the Modigliani-Miller 2nd proposition
form of a dividend, and the rest (Xt – rdB)(1 – τC) will be distributed to
equity holders after corporate taxes. Define the free cash flow (FCF) as the
after-tax cash flow available to be distributed by a similar but all equity
firm. In this case, the firm’s FCF each year is Xt(1 – τC). Let us calculate the
discount rate r, which would make the discounted present value of the FCF
equal to V0, the combined value of the debt and equity.
By definition of a return:
V0 = [Xt(1 – τc) + V1]/(1 + r).
(4.4)
which can be rewritten as:
r = (Xt(1 – τc) + V1 – V0)/V0.
(4.5)
We wish to solve for the r in equation 4.5 as a function of the return on
debt, return on equity, and the tax rate.
Note that the expected increase in value between years 0 and 1 is:
(Xt – rdB0) (1 – τc) + rdB0+ V1 – V0 = [X1(1 – τc) + V1 – V0] + τcrdB0 (4.6)
where the first term is the payment to equity holders, the second term is the
payment to creditors, and the third term is the value of all assets remaining
in the firm. The formulation on the right of 4.6 merely rearranges terms on
the left hand side. Note that this increase in expected value must be split
between the return to equity holders and the return to debt holders:
[X1(1 – τc) + V1 – V0]+ τcrdB0 = E0 rd + B0re.
(4.7)
[X1(1 – τc) + V1 – V0]/V0 = (E0 rd + (1 – τc)B0re)/V0.
Finally, substitute equation 4.5 for the left hand side, and note that
V0 = E0 + B0 to find the WACC:
0
0
0
(
( E E+ B
re + (1 – τC)
( E B+ B
0
0
0
(
WACC = r =
rd
(4.8)
Thus, the WACC is the discount rate at which the FCF needs to be
discounted in order to calculate the firm’s value. The FCF is the cash flow
to a hypothetical all equity firm, while the WACC accounts for the firm’s
leverage.
When corporate taxes are zero, equation 4.8 collapses to 4.3, however in
the presence of taxes, WACC decreases as leverage increases. The intuition
is similar to the Modigliani–Miller 1st proposition. For every extra dollar of
debt in its capital structure, the firm receives τcrd back as a tax refund. This
tax refund is a riskless payment, therefore the firm appears less risky and
the average rate of return it pays to raise money decreases. Because of the
refund, effectively, the firm is paying (1 – τc)rd instead of rd to raise money
through debt.
Example
Walmart has an expected equity return of re = 8.5%. Walmart has AA debt
which matures in 2023 and has a yield of 5.9%. Walmart’s tax rate is 35%
so Walmart is paying (1 – τc )rd =(1 – 0.35) * 5.9 = 3.835% to raise money
through debt.
Walmart’s outstanding debt has a value of $22.7 billion. Walmart has 4,269
million shares outstanding with a price of $55.69 per share, implying an
equity market capitalization of 4.269 * 55.69 = $237.7 billion. Walmart’s
weight of debt in the capital structure is 22.7/(237.7 + 22.7) = 8.7% and
its weight of equity is 237.7/(237.7 + 22.7) = 91.3%. Walmart’s WACC is
0.087 * 3.835 + .913 * 8.5 = 8.09%.
53
FN2191 Principles of corporate finance
Modigliani and Miller’s 2nd proposition
In the previous section we derived the relationship between the return
on the firm’s debt, the return on its equity, and the average cost of capital
for that firm. In this section we will make a distinction between the firm’s
unlevered (or asset return), which is the return this firm would pay to raise
capital if it was an all equity firm, and the firm’s actual cost of capital, once
we account for leverage, this is the WACC from the previous section. We will
also find a relationship between the firm’s equity return and its unlevered
return.
In the absence of taxes, the MM 2nd proposition states that:
re = ru + (B/E)(ru – rd ),
(4.9)
where B/E is the debt to equity ratio in the firm’s capital structure, re is
the return on the firm’s equity, rd is the return on the firm’s debt, and ru is
the unlevered return, or the return on a hypothetical firm that is financed
by all equity (or unlevered) but otherwise similar to the firm we are
considering.
As leverage increases, the expected return on equity grows because equity
becomes riskier. Equity is riskier because it is a residual payment, it is paid
last after all other claims (such as debt) have been settled. When leverage
is high, equity is only a small portion of the firm, but must take the brunt
of most of the firm’s losses. This makes the equity of a highly levered firm
very risky.
Let us illustrate this fact by a simple example which shows how higher
leverage can boost earnings per share, increase volatility and expected
return to equity.
Example. Miller’s Firm
Professor Miller has an unlevered firm (no debt). The firm information is
summarised in Table 4.1:
Number of shares
1,000
Price per share ($)
10
Market value of shares ($)
10,000
Outcomes
A
B
C
D
Operating income ($)
500
1,000
1,500
2,000
Earnings per share
0.5
1.0
1.5
2.0
Return on shares (%)
5
10
15
20
Table 4.1: Professor Miller’s firm without leverage.
Column C is the average outcome, i.e. average earnings per share (EPS)
are 1.5 and average return on shares is 15 per cent. Now, assume Professor
Miller raises the leverage to 50 per cent debt at 10 per cent interest:
Data
54
Number of shares
500
Price per share ($)
10
Market value of shares ($)
5,000
Chapter 4: Leverage, WACC and the Modigliani-Miller 2nd proposition
Outcomes
A
B
C
D
Operating income ($)
500
1,000
1,500
2,000
Interest ($)
500
500
500
500
Equity earnings ($)
0
500
1,000
1,500
Earnings per share ($)
0
1
2
3
Return on shares (%)
0
10
20
30
Table 4.2: Professor Miller’s firm with leverage.
Looking at column C of Table 4.2, which is the expected outcome, we
can see that higher leverage increases average EPS and return on shares:
the average EPS are 2, and the average return on shares is 20 per cent.
However, it also increases the variance of returns, thus making returns
also more risky. Figure 4.1 illustrates the result from Tables 4.1 and 4.2
graphically. The dashed line shows the EPS as a function of operating
income for Table 4.1 and the black line for Table 4.1. For the same range
on the x-axis (say, 500 to 1,500), the black graph gives a wider set of
values on the y-axis (0 to 2.5) compared to the dotted one (0.5 to 1.5).
This is evidence of higher variance (risk):
Earnings per share
(EPS), dollars
3.00
2.50
2.00
Equal proportions
debt and equity
Expected EPS with
debt and equity
Expected EPS
with all equity
1.50
All equity
1.00
Expected
operating
income
0.50
0.00
500
1000
1500
2000
Operating
income, dollars
Figure 4.1: Effect of leverage on EPS.
Changing leverage does change the return, but not the firm value. It also
does not change the WACC
Notice that equation 4.9 is identical to equation 4.3 if we substitute WACC
for ru and rearrange terms. When there are no taxes (or other frictions), as
leverage increases, the equity return becomes riskier and its expectation
grows to compensate investors for that risk. However, the average return that
the firm pays to borrow does not change. This is because although equity
returns grow, equity is a smaller part of the firm and carries less weight. Thus
the firm is borrowing more through debt, which has a lower rate of return.
The weighted average does not change. In the absence of corporate taxes,
55
FN2191 Principles of corporate finance
the average rate at which the firm raises money, the WACC, is equal to the
rate at which an all equity (or unlevered) firm raises money, ru. The WACC is
independent of capital structure, analogous to the MM 1st proposition in the
absence of taxes. The relationship between equity, debt, WACC and leverage
in the absence of taxes is illustrated graphically in Figure 4.1.
r
rE
rA = WACC
rD
D
E
Figure 4.2: Weighted average cost of capital without tax.
We will now derive a more general version of the MM 2nd proposition, in
the presence of taxes. Consider a firm that lives for one period. It has both
debt and equity in its capital structure and its value is V0 = E0 + B0 today
and V1 = E1 + B1 next period. Also note that from the definition of return,
E1 = (1 + re)E0 and B1 = (1 + rd)B0 as there are no intermediate payments.
This firm will have a cash flow X1 which it will distribute to its debt and
equity holders in period 1. Also consider a similar firm that is all equity
owned. This unlevered firm has value V0U today; for this firm B = 0.
Since next period the cash flows will be distributed first to creditors, and
then to equity-holders (after taxes), we can write the value of the firm as
the value of the total distributions:
V1 = (X1 – B1)(1 – τC) + B1 = X1 (1 – τC) + τCB1 = V1U + τC B1,
(4.10)
where the first term is the payout to equity-holders and the second term is
the payout to creditors. The last equality uses the fact that the value of the
unlevered firm next period is just equal to its after-tax cash flows.
From the definitions of debt and equity we know that:
V1 = E1 + B1 = (1 + re)E0 + (1 + rd)B0.
(4.11)
Setting equations 7.10 and 7.11 equal to each other and substituting
V1U = (1 + ru)V0U and B1 = (1 + rd)B0 we get the following equation:
(1 + ru)V0U + τC (1 + rd)B0 = (1 + re)E0 + (1 + rd)B0.
(4.12)
Now, we can rearrange the terms of this to solve for the return on equity:
1 + re = (1 + ru)(V0U/E0) – (1 – τC)(1 + rd)(B0 /E0).
(4.13)
Finally, we can use the fact that V0U = V0 – τCB0 = E0 + B0 – τC B0 (this is just
the present value of equation 4.10) to rewrite this as:
re = ru + (1 – τC)(B0 / E0)(ru – rd).
(4.14)
Equation 4.14 is the MM 2nd proposition in the presence of corporate
taxes. When τC = 0 this equation becomes identical to equation 4.9.
However when τC > 0, the expected return on equity rises by less in
comparison to equation 4.9 as leverage (B/E) increases. This is because
56
Chapter 4: Leverage, WACC and the Modigliani-Miller 2nd proposition
even though extra leverage makes equity more risky for the same
arguments as before, tax shield reduce some of this risk. This can also be
seen by comparing the equity return in Figure 4.2 to that of Figure 4.3
which has the same returns in the presence of taxes.
r
rE
After-tax WACC
(1 – Tc) rD
D
E
Figure 4.3: Weighted average cost of capital with tax.
The MM 2nd proposition gives us a relationship between the unlevered
return on a firm, and the return on the debt and equity of a similar but
levered firm. The WACC is the average rate of return the firm pays to raise
money, it is defined as a function of the returns on debt and equity. We
can combine the MM 2nd proposition (equation 4.14) with the definition
of WACC (equation 4.8) to find the WACC as a function of the unlevered
return on the firm:
WACC = ru(1 – τC (B0 / V0)).
(4.15)
Activity
Combine equations 4.14 and 4.8 to derive equation 4.15.
We can split up the risk investors of a firm face into two types of risk. The
first is business risk, this depends on the risk of the firm’s underlying assets
and activities. All similar firms should have similar business risk regardless
of capital structure. The second is financial risk, this is additional risk that
the firm faces due to its choice of capital structure. The return on an
unlevered firm ru is based on the firm’s business risk, since this firm has no
leverage. WACC is the return on the levered firm, this combines business
and financial risk. From equation 4.15, it is evident that without taxes
financial risk is irrelevant. The WACC of any firm is equal to the return on
an unlevered firm, regardless of the amount of leverage. This is analogous
to the 1st proposition of MM: the value of any firm is equal to the value of
an unlevered firm, regardless of the amount of leverage. In the presence of
taxes, the WACC decreases as we add leverage because of additional tax
shields. With more leverage, the firm becomes safer, its borrowing rate
decreases (equation 4.15), and its value increases. The MM 1st and 2nd
propositions are flip sides of the same coin.
Example
Consider two firms with the same unlevered return on asset ru = 4.5 per cent. The
corporate tax rate is 35 per cent.
Firm A has no debt. Current pre-tax earnings are $23 million with no growth prospects.
57
FN2191 Principles of corporate finance
Firm B has AAA-rated long-term debt with 4 per cent yield to maturity and market value
$50 million. Current pre-tax earnings are $8.75 million with no growth prospects.
What are the WACC, equity return, total firm value, and equity value for each firm?
The FCF of firm A is 23*(1 – .35) = $23.98 million. We use ru = 4.5% as the discount
rate and find an unlevered firm value of VU = 23.98/.045 = $332.2 million.
Since this firm is debt free, its equity value and its total value are the same as the
unlevered value. Again, because this firm is unlevered, its WACC and its equity return are
both equal to ru.
The FCF of firm B is 8.75*(1 – 0.35) = $5.69 million. We use ru = 4.5% as the discount
rate and find an unlevered firm value of VU = 5.69/ 0.045 = $126.4 million.
Using the MM 1st proposition, we can calculate the levered value as the unlevered value
plus the present value of tax shields where the present value of tax shields is given by τcB:
V = 126.4 + 0.35*50 = $143.9 million. The equity value is the total firm value minus
the value of the debt: 143.9 – 50 = $93.9 million.
We can use the MM 2nd proposition (4.14) to calculate the return on equity:
re = ru + (1 – τC)(B0 / E0)(ru – rd) = 4.5 + (1 – 0.35)*(50/93.9)*(4.5 – 4) = 4.67%.
We can now calculate the WACC either through equation 4.8 or 4.15. Both give the same
answer. First using equation 4.8:
WACC = (E/(E + B))re + (1 – τC)(B/ (E + B))rd
WACC = (50/143.9)*(1 – 0.35)*4 + (93.9/143.9)*4.67 = 3.95%
Alternately using 4.15:
WACC = ru(1 – τC(B/V)) = 4.5*(1 – 0.35*(50/143.9)) = 3.95%.
A CAPM perspective (optional)
So far we have looked at the relationships between returns implied by the
Modigliani–Miller 2nd proposition. According to the Capital Asset Pricing
Model (CAPM), the expected return of a security is linearly related to its
correlation with the return on the market portfolio, one that comprises
all assets in the market. This correlation is denoted by the betas of the
securities, which reflect the correlation of the returns and the market risk
premium, i.e. the expected return over and above the risk-free rate. The
higher the beta of a security, the more correlated is the security with the
market portfolio, and hence the higher the risk. To compensate investors
for the higher risk, the security is expected to deliver a higher return. As a
result, the relationship among the expected returns can be translated into
the relationships between betas.
A full understanding of CAPM is beyond this course (it is introduced in
a typical asset pricing course). All we need to know is that the expected
returns of the unlevered asset, equity, and risk-free bond returns vary
linearly with the market risk premium and the coefficient is beta:
ru = rf + βu (rm – rf)
re = rf + βe (rm – rf)
rd = rf + βd (rm – rf)
(4.16)
(4.17)
(4.18)
By plugging equation 4.16 into equation 4.14 (MM 2nd proposition) and
then rearranging terms, we can rewrite the return on equity as:
re = rf + [βu+ (1 – τC )(B/E)(βu – βd )](rm – rf)
58
(4.19)
Chapter 4: Leverage, WACC and the Modigliani-Miller 2nd proposition
This itself is a CAPM equation, by comparing equation 4.19 to 4.17 we can
see that βe must equal to the term in brackets from equation 4.19:
βe = βu + (1 – τC )(B/E)(βu – βd).
(4.20)
In the special case when the firm’s debt is riskless and therefore βd = 0, this
equation simplifies to:
βe = βu (1 + (1 – τC)(B/E)).
(4.21)
With equation 4.21 we can compare the β of an unlevered firm to the
β of a levered firm. We can also use the equation backwards to find the
unlevered β for a levered firm. Suppose you wish to find the expected
equity return for a firm with no past financial data. It is possible to
find a comparable publically trading firm with the same business risk
(for example a firm in the same industry), however this firm may have
different financial risk (different leverage).
Using historical market information we can find the β of the comparable
firm by running a regression of its excess return on the excess market
return. (The regression is similar to equation 4.17.) The slope from
this regression is the equity β of the comparable firm. However, due to
different leverage, the β we are looking for may be different from this β.
Using equation 4.21 with the capital structure of the publically traded
firm, we can unlever this β and find the unlevered (asset) β, which is the
same for both firms. We can then again use equation 4.21, this time with
the leverage ratio of the firm whose β we wish to know, to get the desired
equity β.
Example
Firm A is looking to do an IPO with a debt to value ratio of 0.7. The average equity beta of
similar, publically traded firms is 0.85 and the average debt to value ratio is 0.22. The tax
rate is 35 per cent. What rate of return should we use to discount Firm A’s expected equity
cash flows?
Using equation 4.21 backwards with the capital structure of the comparables, we find
that the unlevered (asset) β of this industry is:
βu = βe/(1 + (1 – τC)(B/E)) = 0.85/(1 + (1 – 0.35)*.22/(1 – 0.22)) = 0.718
Now we can use equation 4.21 forwards, with the target leverage of firm A:
βe = βu(1 + (1 – τC)(B/E)) = 0.718*(1 + (1 – 0.35)* 0.7/(1 – 0.7)) = 1.81
With a 4 per cent historical risk-free rate and a 6 per cent historical market premium, the
required equity return is: 4 + 1.81*6 = 14.86%.
Summary
In this chapter we derived relationships between the return on a firm’s
equity, a firm’s debt and a firm’s total assets. We saw that if there are no
taxes, increasing leverage makes equity riskier and increases expected
returns. However, the return on the firm’s total assets does not change
because more weight is given to the safe debt return. However, in the
presence of taxes, the increase of expected equity returns with leverage
was smaller, due to a tax refund. The return on the firm’s total asset
actually declined with leverage in the presence of taxes, because tax
refunds make the firm safer. This is analogous to firm value rising with
leverage in the presence of taxes, as we saw in the previous chapter.
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FN2191 Principles of corporate finance
Key terms
business risk
financial risk
leverage
tax shields
weighted average cost of capital (WACC)
unlevered (asset) return
unlevered β
A reminder of your learning outcomes
Having completed this chapter, and the Essential reading and activities,
you should be able to:
60
•
write down the relationship between debt, equity, the unlevered return
on the firm, and the levered return on the firm
•
understand what happens to equity returns, and the weighted average
cost of capital as leverage increases with and without taxes
•
draw a link between Modigliani and Miller’s 1st and 2nd propositions
•
find the equity beta of a firm by unlevering and relevering the equity
beta of a comparable firm with different capital structure.
Chapter 4: Leverage, WACC and the Modigliani-Miller 2nd proposition
Sample examination questions
1. Consider an all equity firm with an equity β of 0.7. The risk-free rate
is 3 per cent and the market risk premium is 6 per cent. The company
is considering a recapitalisation to a debt-to-value ratio of 0.25; at this
ratio the before-tax cost of debt will be 5 per cent. For a tax rate of 35
per cent, what is the WACC at this new level of leverage?
2. Stagnant Inc. is a swimming pool supply company that is currently
unlevered with a P/E ratio of 12. The company has no growth
prospects. The tax rate is 35 per cent.
a. What is Stangant’s cost of capital?
b. Stagnant is considering adopting a new capital structure with 50
per cent debt. It has consulted with a bank which is willing to lend
at a 5 per cent rate. What will be the new return on equity, WACC
and P/E ratio?
3. The earnings for firm A and firm B are given below (year –5 indicates
5 years ago, year 0 indicates this year’s dividend, which has not been
paid out yet but is already known, year +1 indicates the forecast of
next year’s dividend). All numbers are in millions of dollars.
Year
–5
–4
–3
–2
–1
0
+1
+2
A
–11
0
1
2
21
22
23
23
B
5
13
7
4
15
13
3
10
4. Both firms pay out nearly 100 per cent of their after-tax cash flows
to the owner. A has no debt. B has AAA-rated long-term debt with 4
per cent yield to maturity and market value of 50 million. The asset
(unlevered) β for firms in the same industry as A and B is 0.5. The
corporate tax rate is 35 per cent, assume no personal taxes. The
historical risk-free rate is 3 per cent and the historical return on the
stock market is 6 per cent.
a. For each firm calculate the WACC, the firm (enterprise) value, and
the equity value. Give justification for your calculation.
b. What changes to capital structure would you make for firm A?
Firm B?
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Notes
62
Chapter 5: Asymmetric information, agency costs and capital structure
Chapter 5: Asymmetric information,
agency costs and capital structure
Aim of the chapter
The aim of this chapter is to analyse and explain the choices of corporate
capital structures made by firms’ managers through theories involving
agency costs or asymmetries of information.
Learning objectives
By the end of this chapter, and having completed the Essential reading and
activities, you should be able to:
•
understand the concept of agency costs and governance problems in
general
•
discuss the intuition behind the agency costs of debt, equity and free
cash-flows
•
calculate the agency cost of debt in stylised settings
•
discuss the effects of asymmetric information on capital structure
•
explain the intuition behind the pecking order theory of finance.
Essential reading
Brealey, R., S. Myers and F. Allen Principles of Corporate Finance. (Boston, MA;
London: McGraw-Hill, 2016) Chapters 13 (Agency Problems, Management
Compensation, and the Measurement of Performance) and 19 (How Much
Should a Firm Borrow?).
Further reading
Copeland, T. and J. Weston Financial Theory and Corporate Policy. (Reading,
MA; Wokingham: Addison-Wesley, 2005) Chapter 15.
Grinblatt, M. and S. Titman Financial Markets and Corporate Strategy. (Boston,
MA; London: McGraw-Hill, 2011) Chapters 16 (Bankruptcy Costs and Debt
Holder – Equity Holder Conflicts), 17 (Capital Structure and Corporate
Strategy), 18 (How Managerial Incentives Affect Financial Decisions) and
19 (The Information Conveyed by Financial Decisions).
Jensen, M. ‘Agency costs of free cash flow, corporate finance, and takeovers’,
American Economic Review 76(2) 1986, pp.323–29.
Jensen, M. and W. Meckling ‘Theory of the firm: managerial behaviour, agency
costs and capital structure’, Journal of Financial Economics 3(4) 1976,
pp.305–60.
Masulis, R. ‘The impact of capital structure change on firm value: some
estimates’, Journal of Finance 38(1) 1983, pp.107–26.
Miller, M. ‘Debt and taxes’, Journal of Finance 32, 1977, pp.261–75.
Modigliani, F. and M. Miller ‘The cost of capital, corporate finance and the
theory of investment’, American Economic Review 48(3) 1958, pp.261–97.
Myers, S. ‘Determinants of corporate borrowing’, Journal of Financial Economics
5(2) 1977, pp.147–75.
Myers, S. and N. Majluf ‘Corporate financing and investment decisions when
firms have information that investors do not have’, Journal of Financial
Economics 13(2) 1984, pp.187–221.
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FN2191 Principles of corporate finance
Ross, S. ‘The determination of financial structure: the incentive signalling
approach’, Bell Journal of Economics 8(1) 1977, pp.23–40.
Overview
In Chapter 3 we introduced the capital irrelevance proposition first put
forward by Miller and Modigliani (1958). We also explored cases in which
the capital structure of a firm did matter in its valuation due to relaxations
of the MM assumptions (e.g. the introduction of corporation tax and
bankruptcy costs). In this chapter we will focus on two classes of problem in
which MM1 does not hold. In the first, firms are subject to agency problems
between outside stakeholders and insiders (managers). The second class of
problem allows the possibility that insiders to the firm are better informed
about its quality than the market or potential external investors.
Capital structure, governance problems and agency
costs
In most Western corporations, ownership and control are separate, in that
the owners of a firm (the firm’s security-holders) entrust the day-to-day
running of the firm to managers. In general, although owners may have an
idea of what the optimal strategy for the firm is, it is impossible to force
managers to follow this plan. Managers may then behave opportunistically,
taking inflated salaries, investing in pet projects and enjoying other
perquisites (perks). Hence, in such scenarios, managers can corporate
policy to maximise their own utility rather than setting the policy which
would maximise shareholder wealth. This is the agency problem that
arises in modern corporations and was first talked about in relation to
capital structure by Jensen and Meckling (1976).
Agency costs of outside equity and debt
Jensen and Meckling (1976) argue that understanding of two types of
agency cost is important in understanding why firm value is not invariant
to capital structure. The first of these is an agency cost associated with
outside equity.
Assume a firm that is financed solely by equity. A proportion of the
equity is held by the management of the firm, whereas the rest is held
by outsiders to the firm. Jensen and Meckling argue that such a situation
leads to firm values which are lower than that which would obtain if
the manager was the sole owner of the firm. To see why this is the case,
consider the rewards and costs facing the manager/equity-holder.
The manager is the agent who undertakes activities that add value to
the firm. Let’s call these activities ‘effort’. Increased effort supply leads
to greater firm value and vice versa. However, supplying effort is also
costly to the manager (it takes up their time and tires them mentally and
physically, for example). In situations where a proportion α of the firm’s
equity is held by outsiders, the manager bears the entire cost of effort
supply but reaps only a portion (1 – α) of the benefit. Hence, the outside
equity-holders gain from the manager increasing effort but don’t bear any
costs. This induces the manager to supply lower levels of effort for higher
values of α (i.e. when the proportion of profits the manager appropriates is
low, their incentive is to supply little amounts of effort). Hence, firm value
is decreased when the proportion of equity held by outsiders is increased,
and MM1 does not hold. This is the agency cost of outside equity.
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Chapter 5: Asymmetric information, agency costs and capital structure
Jensen and Meckling argue that the agency cost of outside equity is
decreasing in the leverage ratio of the firm (where leverage is the ratio of
debt to equity values). The argument runs as follows: assume that the firm
repurchases some of the equity held by outsiders, funding this with a debt
issue – hence, leverage is increased. Also, the proportion of outstanding
equity held by the manager is now increased. Thus, as his share of the
residual value of the firm is increased, the manager chooses to supply
more effort, leading to increased firm value. Then, as leverage rises,
agency costs of outside equity fall.
Example
In this example we will see that when issuing outside equity, a project’s owner is worse
off because she uses too little effort. On the other hand, when using debt, she uses
optimal effort.
Consider an entrepreneur with a project that next year pays $20 million with probability
p and $10 million with probability 1 – p. This project requires an initial investment of
$11 million.
The entrepreneur can pick the probability of success p to be any number they want
between 0.25 and 0.75. However, choosing a higher p requires effort e, which the
entrepreneur dislikes; e = k*p. In this case k = 4 is the disutility of raising probability of
success by 1 expressed in millions of dollars. In particular, if X is the monetary the utility
function is:
U = E[X] – k*e
The required discount rate is zero and everyone is risk neutral.
Suppose the entrepreneur finances the project with equity by promising a share α of
equity to outside investors in return for them paying the $11 million necessary for the
initial investment. Then their expected payoff is:
E[X] = (1 – α)(20p + 10(1 – p)) = (1 – α)(10p + 10),
and the utility is:
U = E[X] – e = (1 – α)(10p + 10) – k*p = 10*(1 – α) + [10*(1 – α) – k]*p.
Therefore, the entrepreneur will choose p to be as small as possible if 10*(1 – α ) – k
< 0. Suppose outside investors believe that the entrepreneur will choose p = 0.75, then
their expected payout is: α(0.75*20 + 0.25*10) = 17.5α.
This must equal to their initial investment of 11, implying α = 62.9%. However, that
implies that 10*(1 – α) – k = 3.71 – k < 0 and the entrepreneur would choose
p = 0.25, therefore this cannot be an equilibrium.
Suppose outside investors believe our investor will choose p = 0.25, then their expected
payout is: α(0.25*20 + 0.75*10) = 12.5α.
This must equal their initial investment of 11, implying α = 88%. Indeed 10*(1 – α) – k
= 1.2 – k < 0, thus the entrepreneur will choose p = 0.25, consistent with the beliefs of
outside equity-holders.
The entrepreneur’s utility is:
U = 10*(1 – α) + [10*(1 – α) – k]*p = 1.5 – k*p = 0.5.
Suppose instead the entrepreneur financed this investment with debt by promising a face
value F to creditors in return for $11 million to cover the initial investment. In this case
the entrepreneur’s equity will always be bankrupt in the bad state of the world and they
will receive zero; in this case creditors receive the full $10 million. In the good state of the
world, the entrepreneur will receive 20 – F. Their utility is:
U = E[X] – e = p(20 – F) – k*p = (20 – F – k)*p.
They will choose p to be as large as possible as long as 20 – F – k > 0.
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FN2191 Principles of corporate finance
Suppose creditors believe that p = 0.25. Then their expected payout is:
p*F + (1 – p)*10 = 0.25F + 7.5
This must equal their initial investment of 11, implying F = 14. However, this implies that
20 – F – k > 0 and the entrepreneur would choose p = 0.75, therefore this cannot be
an equilibrium.
Suppose creditors believe that p = 0.75. Then their expected payout is:
p*F + (1 – p)*10 = 0.75F + 2.5.
This must equal to their initial investment of 11, implying F = 11.33. Indeed, 20 – F – k
> 0 and the entrepreneur chooses p = 0.75, consistent with the beliefs of outside equityholders.
The entrepreneur’s utility is:
U = (20 – F – k)*p = 6.50 – k*p = 3.5.
Note that this is much higher than when the entrepreneur uses equity. In this example
the MM proposition did not hold because one type of security was better than another.
As we increased the proportion of debt used to finance the firm, the entrepreneur chose
to exert more effort and increased value. Increasing leverage reduced the agency cost of
outside equity because it aligned the payoff to the entrepreneur with their cost of effort.
With a fraction α of outside equity, for every dollar of value they took out of the firm due
to decreased effort, the entrepreneur lost only (1 – α) of wealth.
Activity
First, show that in the above example, if the entrepreneur could commit to using the
optimal amount of effort, then they could get maximum utility even when using equity.
Next, show that in the above example if the entrepreneur is less averse to effort, for
example k = 3, then two possible equilibria can arise in the equity financing case. Thus
market beliefs may play an important role.
The second agency cost highlighted by Jensen and Meckling is that
associated with debt finance. It is also known as the asset substitution or
risk-shifting problem associated with debt finance. To illustrate the
problem, consider the following example.
Example
Assume that a firm that is financed by both debt and equity. A manager runs the firm in
the interest of current equity-holders (i.e. the manager sets investment policy in order
to maximise the expected shareholder payoff). The manager is faced with the choice
between two investment projects, A and B. These projects are assumed to have zero cost
and are mutually exclusive. The cash flows to projects A and B are given in Table 5.1.
State 1
State 2
State 3
Probabilities
0.25
0.5
0.25
Cash flow A
40
50
60
Cash flow B
20
40
80
Table 5.1
Clearly, both projects have positive expected NPV. Project A has the lowest risk and the
higher expected NPV (50), whereas project B is the riskier and its expected NPV is 45.1
We assume that debt-holders have a claim of 50 that must be repaid out of
the cash flow to the chosen project. Given this debt claim, which project
will the manager choose?
66
1
When we say that
project B is riskier, we
mean that it has higher
cash-flow variance than
project A.
Chapter 5: Asymmetric information, agency costs and capital structure
Let us start our analysis with Project A. From the cash flows of the project,
we see that, with a debt obligation of 50, only in state 3 will equityholders get any pay-off, this pay-off being 60 – 50=10. This implies that
the expected pay-off from Project A to shareholders is 10*0.25 = 2.5. The
expected pay-off to debt-holders from A is equal to (0.25*40) + (0.5*50)
+ (0.25*50) = 47.5.
Moving on to the analysis of Project B, again equity-holders only get
some cash in state 3 and their expected pay-off is 0.25*(80 – 50) = 7.5.
The pay-off to debt-holders from Project B is (0.25*20) + (0.5*40) +
(0.25*50) = 37.5. Hence, from the equity-holders point of view, Project
B maximises expected pay-off as 7.5>2.5 and, as a result, this will be the
project chosen by the manager. Note that the choice of this project implies
that debt-holders are worse off and firm value lower than in the case
where Project A is chosen.
When the face value of debt is 50, the firm invests in the project with
the lower expected NPV and higher risk, as this project maximises the
expected return to equity. What would happen if the debt repayment
outstanding were 30 instead of 50? In this case the expected payoffs to
equity-holders are 20 from project A and 17.5 from project B. Therefore,
the manager will choose project A. This choice also implies that debtholders are happy as project A maximises their expected payoff (they get
30 rather than the 27.5 that they would expect to receive if project B were
chosen). Note that, when the face value of debt is lower, the manager
switches and chooses the low-risk, high-expected-return project. This, in
turn, implies that, when face value of debt is lower, firm value is higher.
Example
In this example we will see that when issuing debt, a project’s owner is worse off because
they choose to take on too much risk. On the other hand, when using outside equity, they
choose the optimal amount of risk.
Consider an entrepreneur with a choice of one of two projects. Project A pays $5
million or $15 million with equal probability. Project B pays 0 or $18 million with equal
probability.
Each project requires an initial investment of $3 million. The entrepreneur will have the
freedom to choose the project after they raise financing.
The required discount rate is zero and everyone is risk neutral. There are no taxes or
bankruptcy costs.
Note that the expected value of project A is 0.5*5 + 0.5*15 = 10 while the expected
value of project B is 0.5*0 + 0.5*18 = 9 so project A is better. Project A is also less
volatile; in this example investors are risk neutral but typically they would prefer less
volatile projects.
Consider debt financing. For any face value of debt F shareholders receive the residual
after creditors have been paid. From project A their expected payout is:
0.5*(5 – F) + 0.5*(15 – F) = 10 – F if F < 5
0.5*0 + 0.5*(15 – F) = 7.5 – 0.5F if 5 < F < 15.
From project B their expected payout is:
0.5*(18 – F) = 9 – 0.5F if F < 18.
Comparing these two equations we can see that project B is preferred by equity-holders
for any F > 2, this can also be seen graphically in Figure 8.1. Project B is preferred
because equity-holders have a limited downside but care very much about the upside.
On the other hand, creditors expected payout from project A is:
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FN2191 Principles of corporate finance
F if F < 5
0.5*5 + 0.5*F = 2.5 + 0.5F if 5 < F < 15.
From project B their expected payout is:
0.5*F if F < 18.
Comparing these two equations we can see that project A is preferred by creditors for any
F, this can also be seen graphically in Figure 8.1. Project A is preferred because creditors
have no upside, and care only about limiting losses in the downside.
Since the necessary initial investment is 3, the face value of debt will have to be at least
3. This leads equity-holders to choose project B. Knowing this, creditors will ask for a face
value of debt such that they receive their initial investment back in expectation:
3 = 0.5*F and F = 6.
With this F, the initial entrepreneur’s payout is:
0.5*(18 – 6) = $6 million
Suppose the entrepreneur could credibly commit to choose project A. In that case
creditors would ask for a smaller face value of debt, F = 3, because even in the bad
scenario, project A will be more than enough to repay the initial investment. The payout
to equity-holders would be:
10 – F = $7 million.
The shareholders would be better off if they could ex-ante commit to invest in A because
A has higher NPV. However, as we saw earlier, with F = 3 they are ex-post better off
choosing B. Since the creditors have no reason to trust them, creditors will assume B will
be chosen and ask for F = 6.
Now consider using outside equity to finance this project. Outside equity-holders
are promised a fraction α of the project and the entrepreneur receives the rest. The
entrepreneur’s payoff from choosing A is:
(1 – α)[0.5*5 + 0.5*15] = (1 – α)*10,
and from choosing B it is:
(1 – α)[0.5*0 + 0.5*18] = (1 – α)*9.
Clearly the entrepreneur always chooses A. Knowing this, outside equity-holder will ask
for α such that their expected payoff 10α is equal to their initial investment of 3. This
implies that α = 30% and the entrepreneur’s share is worth (1 – 0.3)*10 = 7. This is just
as good as the commitment case and better than the debt financing case.
In this example the MM proposition did not hold because one type of security was better
than another. Debt financing caused the entrepreneur to choose a very risky project (risk
shift) because their downside was limited. As a result, creditors asked for a very high
interest rate to protect their investment and the entrepreneur was worse off for this.
Equity financing did not face this problem because the entrepreneur was just receiving
a fixed share of total profits, therefore it was in their interest to maximise total profits
both ex-ante and ex-post. Commitment was a possible substitute to equity, but it may be
difficult to implement in a real world situation.
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Chapter 5: Asymmetric information, agency costs and capital structure
Shareholder value
10
Project A
Project B
5
Creditor value
0
0
5
10
F
15
20
10
8
6
4
25
Project A
Project B
2
0
0
5
10
F
15
20
25
Figure 5.1: Payoff to the shareholder and to the creditor.
Jensen and Meckling argue that the agency costs of debt are increasing in
the level of debt outstanding and hence in corporate leverage. Combining
the two agency costs then allows us to argue that an optimal (in the sense
of maximising firm value) capital structure might exist. We contended
that the agency cost of outside equity was decreasing in leverage, whereas
the agency cost of debt increased with leverage. Firm value would be
maximised where total agency costs are minimised, and this leads to the
optimal leverage ratio shown on Figure 5.2.
Cost
Total
cost
Cmin
Agency cost
of debt
0
Agency cost
of equity
D/E*
D/E
Figure 5.2: Optimal leverage under agency costs.
The Myers (1977) debt overhang problem
Another agency cost of debt was pointed out by Myers (1977). Rather than
arguing that debt obligations induce managers to invest in excessively
risky projects, Myers argues that the management of firms with large
levels of debt outstanding will choose to reject some positive NPV projects.
As a result, heavily indebted firms will see reductions in corporate value,
and MM1 is violated. This is known as the debt overhang problem.
To illustrate the previous argument consider the situation depicted in Table
5.2. A given firm is presented with the opportunity to invest in a certain
project at the current time. The payoff of this investment is $20,000 at time
t + 1 regardless of the state of nature, and the cost at time t is $10,000. We
assume, for simplicity, that interest rates are zero such that the investment
has a positive NPV. Further, the firm receives cash flow at time t, which
reflects its past investments. This cash flow is uncertain. As depicted in
Table 5.2, with probability 0.25 it will be $50,000; it will be $80,000 with
probability 0.5 and, finally, with probability 0.25 it will be $120,000.
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FN2191 Principles of corporate finance
The firm is run by a manager who acts in the interest of current
shareholders. In the past, the firm issued debt with a face value of
$100,000. This debt must be repaid out of the cash flow to the firm, after
the investment decision has been made and any payoffs realised. Note
that, if the project is accepted by the manager, its cost must be met out of
the pockets of equity-holders.
State 1
State 2
State 3
0.25
0.5
0.25
Cash flow existing assets
50
80
120
Cost new project
10
10
10
Return new project
20
20
20
Probabilities
Table 5.2
When the face value of debt is $100,000, the manager will reject the new
project. Why is this? Note that, in states 1 and 2, the new project pays
$20,000, but this simply goes straight into the pockets of debt-holders
through the required payment of $100,000. It is only in state 3 that the
$20,000 payoff of the new project accrues to equity-holders. Hence, in this
case the expected net payoff to equity-holders is:
(0.25 * 20) – 10 = –5.
As this is negative, the manager rejects the new project. The implication
of this is that, when debt levels are high, a firm may reject a project with
positive NPV, as little of that project’s payoff accrues to equity-holders.
To confirm this, consider the case in which the required debt payment is
$80,000 rather than $100,000. In this case, the payoff from existing assets
is sufficient to service the debt in both states 2 and 3. Hence, in both these
states the equity-holders reap all of the rewards from the new project,
whereas the new project payoff goes to debt-holders in state 1. Hence, the
expected net return to equity-holders from the new project is:
(0.5*20) + (0.25*20) – 10 = 5.
As this is positive, the manager will accept the project as it increases
expected shareholder wealth.
Activity
Compute the expected payoff to equity-holders if the required debt repayment is 90. Will
the manager accept or reject the project?
The preceding example illustrates the debt overhang argument. Managers
that run heavily indebted corporations in the interest of equity-holders
may reject positive NPV projects as the cash flows from such projects
accrue mostly to debt-holders, whereas equity-holders bear the costs. The
rejection of such projects implies that firm values are suboptimal.
Agency costs of free cash flows
Although debt may generate agency costs, as discussed in the previous
section, Jensen (1986) argues that debt may also alleviate agency costs
of free cash flows. In this framework, debt is valuable as it motivates
managers to disgorge cash (in the form of interest and principal payments)
rather than investing it at below the cost of capital or wasting it on
organisation inefficiencies.
Jensen argues that growth is associated with increases in managers’
compensation and power. Managers have thus incentives to grow their
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Chapter 5: Asymmetric information, agency costs and capital structure
firms beyond their optimal size; that is, to engage in ‘empire-building’.
Managers of firms with substantial free cash flow, that is, cash flows
in excess of that required to fund all projects with non-negative NPVs,
are thus tempted to invest it at below the cost of capital or waste it on
organisation inefficiencies rather than return the cash to shareholders
through the payment of dividends or repurchase of shares. The agency cost
of free cash flows is the negative NPV of the investments made at below
the cost of capital. In this context, debt creation, without the retention
of the proceeds of the issue, enables managers to bond their promise to
pay out future cash flows in the form of interest and principal payments.
Although increases in dividends can be reversed, an issue of debt used to
repurchase equity is a credible bond as debt-holders are given the right
to take the firm into bankruptcy court if managers do not respect their
promise to make interest and principal payments. Debt thus reduces the
agency costs of free cash flow by decreasing the cash flow available for
spending at the discretion of managers.
Firm value and asymmetric information
The preceding sections emphasised the point that agency problems may
lead to departures from MM1. An alternative reason for such departures is
the presence of information asymmetries between corporate insiders and
outsiders. The role played by asymmetric information is emphasised by
Ross (1977) and Myers and Majluf (1984).
Ross (1977) signalling argument for debt
The crux of Ross’ argument is as follows. Assume firms differ according
to their future cash-flow prospects. High-quality firms expect large future
cash flows, whereas low-quality firms expect cash flows to be small. Firm
quality is not observable to outsiders to the firm. The managers of highquality firms have an incentive to attempt to signal their quality to the
market, as in the absence of signals the market can’t distinguish high- and
low-quality firms and will value them identically.
One way the management can signal is through debt policy. High-quality
firms choose large leverage ratios and lower quality firms choose low
leverage ratios. The market can observe leverage and hence values firms
accordingly (assigning firm values increasing in leverage.) Leverage is a
credible signal, as it is assumed that firm managers are averse (in terms
of their own utility) to bankruptcy. High levels of debt imply a higher
probability of bankruptcy, and only managers in charge of high-quality
firms are willing to expose themselves to this probability.
The preceding intuition can be formalised with the following model, which
is a simplified version of that contained in Ross (1977). Assume a
population of firms, each of which has future cash flow that is uniformly
distributed.2 Firm quality varies, as the upper bound of the cash flow
distribution (call this parameter t) varies across firms (i.e. a high-quality
firm may have cash flow distributed on [0, t1] and a low-quality firm might
have cash flow distributed on [0, t2] where t1 exceeds t2). Managers of firms
know the value of t for their own firms, but the market as a whole does not.
Managerial utility is increasing in date 0 firm value and date 1 firm value,
but is decreasing in the expected cost of bankruptcy. In line with the prior
argument, managers will try to use debt to signal their quality. However,
non-zero debt levels imply that bankruptcy is possible. Hence, we can
write the managerial optimisation problem as follows:
2
If cash flow is
uniformly distributed
on [a, b] it means that
the probability density
of cash flow is constant
from a to b and zero
elsewhere. This implies
that the probability
distribution function of
cash flow is F(x)=(x–a)/
(b–a) for x between a
and b.
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FN2191 Principles of corporate finance
(5.1)
where we have assumed firm quality of t, V0(B) is date 0 firm value, L is a
parameter reflecting the cost (in managerial utility terms) of bankruptcy
and γ is a weight parameter. Given that the manager knows the true
t
distribution of firm cash flow, his assessment of date 1 firm value is 2 .
Similarly, if a debt level of B is chosen, the manager knows the firm will be
B
bankrupt with probability t and the expected utility cost of bankruptcy is
hence
.
Assume that the market assigns a firm with debt level B a date 0 value of
f(B). Substituting this into equation 5.1 gives:
(5.2)
To compute the optimal level of debt, we compute the first order condition
of 5.2 with respect to B. After rearrangement this yields:
.
(5.3)
Finally, we assume that in equilibrium, the market’s beliefs about firm
quality (based on a firm’s debt level) are correct. Hence, we have the
condition f (B(t)) = 2t where we have also acknowledged the dependence
of the debt level, B, on firm quality through managerial actions.
Differentiating this condition yields:
f’(B)B’(t) = ½.
(5.4)
Substituting f’(B) from 5.4 into 5.3 yields the following differential
equation:
.
(5.5)
This differential equation has the following general solution:
(5.6)
where c is a constant term. The constant c can be assigned a value through
noting that the lowest quality firm in the population has no incentive
to signal and will hence elect not to have any debt. Denoting the lowest
quality by tc, use of this intuition in 5.6 gives:
(5.7)
.
Substitution of 5.7 in 5.6 gives the final debt rule:
.
(5.8)
Equation 5.8 gives us the key results from the Ross (1977) model. Debt level
(B) is increasing in firm quality (t). Clearly then, firms with higher debt levels
will have greater date 0 market values and MM1 is violated once more.
In more loose terms, the arguments in Ross (1977) are that debt is a
costly signal (due to the possibility of bankruptcy it entails), and hence its
use implies higher-quality firms. From an empirical standpoint, evidence
that supports this notion can be found in Masulis (1983). This paper
demonstrates that firms which swap debt for equity (hence increasing
leverage) experience positive stock price returns whereas firms swapping
equity for debt experience negative stock returns. The stock price reactions
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Chapter 5: Asymmetric information, agency costs and capital structure
are interpreted as implying that leverage-increasing transactions are good
news whereas leverage-decreasing transactions are bad news, consistent
with the asymmetric information story.
The Myers–Majluf (1984) pecking order theory of finance
Another study that generates departures from MM1 through information
asymmetries is Myers and Majluf (1984). Although Ross focuses on the
level of the debt–equity ratio as a signal of firm quality, Myers–Majluf
concentrate on the information revealed by security issues. The intuition
behind their arguments is as follows.
We start by assuming a population of firms differing in both the quality
(value) of their assets in place and the quality (NPV) of their investment
projects. Any investment project has to be financed through an issue of
equity. Assume also that the managers of any firm are better informed
about both the quality of their firm’s assets in place and the quality of their
firm’s investment project than are outsiders. Furthermore, assume that
managers act in the interests of their firm’s existing equity-holders.
Only managers know whether the equity of their firm is over- or underpriced though, and this creates an opportunity for them to exploit the market
in order for existing shareholders to profit. The existence of information
asymmetries thus implies that the market can misprice corporate equity:
some firms’ equity may be over priced and others will be under priced.
In this setting, managers may raise equity for two reasons.
•
They may wish to invest in a positive NPV investment, which would
result in an increase in the value of the firm’s equity.
•
Alternatively, they may wish to issue overpriced equity, which would
result in a transfer of wealth from the new to the old equity-holders.
Given rational expectations, the financial market correctly recognises
both incentives to raise equity. In equilibrium, managers of low-quality
firms (i.e. managers of firms with assets in place whose true worth is low
enough – and are hence overvalued), raise equity in order to take projects
with a small but negative NPV. The benefit to the existing equity-holders
that results from issuing overvalued equity exceeds the cost resulting
from taking the negative NPV project. Similarly, managers of high-quality
firms (i.e. managers of firms with assets in place whose true worth is high
enough – and are hence undervalued), abstain from raising equity and
hence from taking projects with a small but positive NPV. The dilution to
the existing equity-holders that results from issuing undervalued equity
exceeds the benefit resulting from the positive NPV generated by taking
the project. The presence of information asymmetries between managers
and equity-holders hence leads to distortions in investments.
Issue decisions affect prices as they reveal information on firm quality.
Managers are more likely to issue equity when their firm’s assets in place
are overvalued, as opposed to undervalued. On average, equity issues thus
lead to stock price drops. Furthermore, the highest quality firms avoid
issues at all costs.
Generalising the above somewhat, we can fit riskless debt, risky debt and
other securities into our pecking order. Obviously, issuing riskless debt to
finance investments conveys no information to the market, as there is no
possibility of exploitation (as there is no risk). Thus, stock prices should
not react to riskless debt issues and the highest quality firms will issue riskless debt in order to finance any investments. Low-quality firms don’t issue
riskless debt, as they cannot exploit new investors through its issue. Risky
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FN2191 Principles of corporate finance
debt comes with a possibility of default and hence could be overpriced if
the market underestimates the probability of default. Issues of risky debt,
therefore, convey some information, but clearly less than issues of equity.
Putting this all together leads to a model in which equity issues cause
stock prices to drop a lot (as the market infers that firms that issue are
very poor quality), risky debt issues cause small price decreases (as fairly
low-quality firms issue risky debt) and riskless debt issues cause no price
impact (as only high-quality firms issue riskless debt). Hence, in a dynamic
sense, Myers–Majluf implies that capital structure decisions do affect firm
values. This is the pecking order theory of finance.
There is a fair amount of empirical evidence that supports the pecking
order theory. First, the event study results on exchange offers detailed
above are consistent with the pecking order theory. Second, event study
evidence on new security issues confirms the theory too. Common stock
issues lead to price impacts of around –3 per cent, for example, whereas
risky debt issues cause small price drops, which are not statistically
different from zero. Hence, the intuition that underlies the model is
regarded by many as very plausible.
Example
Project Universe Industries (PUI), an all equity firm, currently has 20 million shares
outstanding. The value of the company is the sum of the value of the assets in place and the
NPV of the project. As shown in the following table, both the value of the assets in place
and the NPV from the project crucially depend on the price of oil:
Valuation
Assets
State A (cheap oil) State B (expensive oil)
Assets in place
£130m
£220m
NPV of the project’s cash flows
£10m
£40m
The positive NPV project requires an initial investment of K = £600m irrespective of the
state of nature. In order to fund its project, PUI must raise £600m in equity. Assume that
managers maximise the wealth of the existing shareholders and that the states are equally
likely.
a. If managers must issue equity prior to knowing the price of oil, how many shares should
the firm issue and at which price will they sell for?
In each state, the post-issue firm value will be equal to the sum of the value of the
assets in place, the NPV of the project, and the capital (K = $600m) contributed by
the new equity-holders. In state A, the post-issue firm value is thus £740m. In state B,
the post-issue firm value is thus £860m. As both states are equally likely, the expected
post-issue firm value is thus £800m (derived as 50%*£740m + 50%*£860m). The
fraction of the value of the firm that the new shareholder should be getting is hence
£600m/£800m = 75%. The value of the firm’s equity prior to the share issue is thus
£600m, and the share price is thus £200m/20m = £10. As ex-post, all the shares have
an equal claim, the firm must thus issue 60 million new shares (derived as £600m/£10).
b. If the manager knew the state of the world before investing, in which state (A or B)
would the manager raise equity and invest in the project? In order to answer this
question, let us assume that the capital can be raised under the terms found in part a)
of this example and that the market does not know the state of the world.
Let us derive the ex-post payoffs to the existing shareholders in each state of nature
when the manager raises equity and invests in the project and when the manager
abstains from raising any equity and does not invest in the project. These payoffs can be
found in the following table:
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Chapter 5: Asymmetric information, agency costs and capital structure
Payoff to existing shareholders
Do nothing
Issue equity invested in
the project
State A (cheap oil)
State B (expensive oil)
£130m
£220m
(1 – 75%) * £740m
(1 – 75%) * £860m
Table 5.3
The manager, when informed about the realisation of the state of nature, will issue
equity and invest in the positive NPV project in state A as (1 − 75%)*£740m =
£185m is strictly higher than £130m and refrain from issuing equity and forego the
positive NPV project in state B as (1 − 75%)*£860m = £215m is strictly lower than
£220m.
The manager of the firm hence abstains from issuing any equity and does not invest
in the strictly positive NPV project in the favourable state of nature. The intuition
behind this result is as follows. Although taking this project would increase the value
of the firm overall as it has a strictly positive NPV, it also leads to a reduction in the
wealth of the existing shareholders. The reason for this is that, in the favourable
state of nature, the financial market undervalues both the NPV of the project and the
intrinsic value of the firm’s existing assets. The effect of the dilution of the existing
shareholders, resulting from issuing undervalued shares, turns out to be so high that
the existing shareholders are better off without the project whenever the project has
to be financed through outside equity.
c. Now let us assume that the market knows that managers will make a decision after
observing the state of the world. When managers announce that they will not issue
equity to fund the project, the stock price of the firm may change. How would you
expect it to change? In order to answer this question, let us assume that the firm
does not have any other source of capital to take the project and that the market
does not know the state of the world.
Upon the announcement that equity will not be issued and the investment project will
not be taken, the market updates its estimate of the value of the firm, infers that state
B is obtaining, and hence prices the firm’s stock at £11 per share (£220m/20m),
hence rises by 10 per cent.
Summary
In this chapter we have examined theoretical models (and examples),
which imply that firm value does depend on the financing choices it
makes and on capital structure choices in particular. First, we examined
arguments based on agency costs and then looked at a model of
asymmetric information. The empirical evidence for these models is
mixed. Evidence for agency problems can be found in the specification
of corporate debt contracts, which contain clauses aimed specifically at
preventing debt overhang and asset substitution problems. The previously
discussed evidence on exchange offers is supportive of asymmetric
information models (although it would contradict the implications of a
debt overhang model). Research in these areas still proceeds. The most
recent strand of literature on capital structure builds on the agency cost
approach and examines incomplete contracts as the source of violations of
MM1.
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FN2191 Principles of corporate finance
Key terms
agency costs of debt
agency costs of free cash flows
agency costs of outside equity
asset substitution problem
asymmetric information
capital structure
debt-overhang problem
event study
governance problems
overinvestment
pecking order theory
risk-shifting problem
separation of ownership and control
signalling
underinvestment
A reminder of your learning outcomes
Having completed this chapter, and the Essential reading and activities,
you should be able to:
•
understand the concept of agency costs and governance problems in
general
•
discuss the intuition behind the agency costs of debt, equity and free
cash-flows
•
calculate the agency cost of debt in stylised settings
•
discuss the effects of asymmetric information on capital structure
•
explain the intuition behind the pecking order theory of finance.
Sample examination questions
1. Explain the debt-overhang problem.
2. What are the agency costs of equity? Explain.
3. A firm has £100m in cash on hand and a debt obligation of £100m
due next period. With this cash, it can take one of two projects (A
and B) which cost £100m each. Assume that the firm cannot raise
any additional funds. If the economy is favourable, project A will pay
£120m and project B will pay £101m. If the economy is unfavourable,
project A will pay £60m and project B will pay £101m. Assume
that investors are risk-neutral, there are no taxes or direct costs of
bankruptcy, the risk-free rate of interest is nil, and the probability of
each state of nature obtaining is equal.
a. What is the NPV of each project?
b. Which project will equity-holders want the firm’s manager to take?
c. Show that debt-holders would find it incentive-compatible to cut
the face value of their claim to £82m.
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Chapter 5: Asymmetric information, agency costs and capital structure
4. What are the consequences of asymmetries of information between
managers and investors, as in Myers and Majluf, for investments and
the funding of investments?
5. Consider an entrepreneur who has a project that will cost $20 million
to implement and will produce cash flows of either $3 million or $5
million per year in perpetuity with equal probability. The entrepreneur
does not have the $20 million and must raise it externally. Assume risk
neutrality and a 10 per cent opportunity cost of capital.
a. Calculate the annual cash flow to the entrepreneur and its present
value if they raise the $20 million through perpetual debt.
b. Calculate the annual cash flow to the entrepreneur and its present
value if they raise the initial investment with equity.
c. As CEO of the firm the entrepreneur is able to spend $200,000
per year on a marketing relationship with their favourite celebrity.
This advertising relationship is worth only $150,000 annually
for a net loss of $50,000. However, the CEO receives utility from
the relationship, in particular, they would be willing to spend up
to $30,000 of their own money purely to spend time with this
celebrity. Show that if the entrepreneur uses equity to raise money,
they will engage in the wasteful advertising relationship but if they
use debt, they will not.
d. Suppose the outside investors are aware of the CEO’s penchant for
spending time with celebrities. What share of equity would they
demand? What would be the present value of the entrepreneur’s
total payoff?
5. A firm’s productive assets will be worth either $100 million in a good
state or $10 million in a bad state with equal probability. Additionally,
the firm has $15 million in cash, which it could pay out as a dividend,
and outstanding debt with a face value of $35 million due next year.
The firm also has a project which would require an investment of $15
million this year and produce $22 million with certainty regardless
of the state of the world. Assume risk neutrality and a 10% cost of
capital.
a. Do stockholders choose to take this positive NPV project? What is
the present value of the creditors payoff?
b. Suppose creditors suggest to financially restructure by reducing
the face value of debt to 24 if the shareholders promise to use
the $15 million to invest. Will the shareholders agree? Will the
creditors prefer to do this?
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FN2191 Principles of corporate finance
Notes
78
Chapter 6: Equity financing
Chapter 6: Equity financing
Aim of the chapter
The aim of this chapter is to understand and analyse several different ways
to issue new equity, some prominent features in equity offerings, and wellknown frictions associated with equity issuance. With this aim in mind, we
study staged financing in the private equity market, initial public offerings,
seasoned equity offerings, rights offerings, and the winner’s curse problem.
Learning objectives
At the end of this chapter, and having completed the essential reading and
activities, you should be able to:
•
explain venture capital and equity issuance in the public market
•
perform valuation with multiple financing rounds
•
explain the calculate ownership structure in initial public offerings and
seasoned equity offerings
•
explain and evaluate the winners’ curse problem.
Essential reading
Brealey, R., S. Myers and F. Allen Principles of Corporate Finance. (Boston,
MA; London: McGraw-Hill, 2016) Chapters 15 (How Corporations Issue
Securities).
Further reading
Grinblatt, M. and S. Titman Financial Markets and Corporate Strategy. (Boston,
MA; London: McGraw-Hill, 2011) Chapters 3 (Equity Financing)
Rock, K. ‘Why new issues are underpriced’, Journal of Financial Economics 15
(1–2) 1986, pp.187–212.
Introduction
Corporate finance is mostly about how firms raise money to conduct
their activities. Broadly speaking, there are two categories of financing
securities: debt and equity. Financing a project through debt results in a
liability to creditors that can take the form of a bank loan, notes payable
or bonds issued to the public. This is an obligation that must be serviced,
independent of the project’s success as debt holders are senior to equity
holders. Debt comes with benefits for the firm (tax shield, less information
sensitive claim), but it might also cause conflicts of interest (recall the
debt overhang problem in Chapter 5), and as a result, some positive NPV
projects might not get financed.
Equity financing is usually in the form of selling company shares to
investors. It is less risky than debt with respect to cash flow commitments,
but causes a dilution of share ownership and control. Moreover, equity
holders are junior claimholders compared to debt holders. In Chapters
3–5, we focused on debt financing. Now we will turn to equity financing.
In this chapter, we will consider three main topics. First, we will see how
start-up companies finance themselves. We will talk about the main stages
of equity financing and their characteristics. Then, we will analyse how
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FN2191 Principles of corporate finance
firms issue new shares. Our main focus will be IPO (initial public offering)
and SEO (seasoned equity offerings). Finally, we will consider one of the
most prominent features in IPO market – underpricing – and one of its
explanations.
Private equity financing
In this section, we will consider the main features of private equity.
We will focus on venture capitalists. First, we will talk about the main
characteristics of these funds. Then, we will see how they provide
financing to firms, and why they have the incentives to monitor the firms.
Last, we will talk about the typical VC structure and the compensation
scheme.
Consider a small start-up company. Suppose you have a brilliant idea in
mind. How do you finance your endeavor? Young small firms often begin
with self-financing: equity and ‘informal finance’, debt from family, friends.
As the firm grows, the ability/willingness of informal finance fails to meet
the needs of the business and firms look for other sources of financing.
There are three main ways companies finance their future operations:
•
retained earnings
•
bank debt
•
private equity.
We say that firms use retained earnings for financing if they reinvest their
profits. This might appear to be the easiest and most natural source of
funds for the firm, but clearly the amount of money may not be enough,
especially, for fast-growing companies. The next source of financing
is banks. This is the predominate source of small-business finance but
there are limits here as well. Banks usually require tangible assets and/
or performance records. However, typically young firms often do not meet
the eligibility criteria and fail to obtain bank financing. The alternative is
private equity – equity financing that is not publicly traded. This type of
financing usually comes from venture capitalists (VCs).
Venture capital is one increasingly important alternative institution
specialising in financing risky and opaque firms. Let us consider the
key features. First, it is an equity investor, and hence inherits all the
characteristics of equity holders. This is in contrast to bank investors,
who are debt holders. Second, as outlined above, VCs invest in risky
firms. Hence, they have a low success probability but much higher than
usual returns (recall the usual risk-return trade-off: higher risk should be
compensated by higher returns). Third, venture capital comes in the form
of staged financing – funds are usually dispersed in stages, after a certain
level of success is achieved. Finally, VCs are active investors. They usually
hold a large stake in the firm and have incentive to monitor/ advise the
start-up company. Let us now elaborate on the last two features — staged
financing and active investors.
Why do VCs use staged financing? Why don’t they just finance the projects
by giving entrepreneurs a lump sum? Let us think about it. If the VC
gives a lot of money to young small firms at once, that creates several
problems. For example, the entrepreneur might have no incentive to
develop their idea, and can simply abandon the project. Alternatively,
they can take riskier decisions. In other words, providing all the funds at
once creates higher risks for the VC. Using staged financing allows the VC
to minimise the risk. If the small firm fails to meet the eligibility criteria
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Chapter 6: Equity financing
for the next financing stage, the VC can cut financing or even withdraw
from the project. This creates strong incentives for entrepreneurs to be
more efficient in order to get to the next financing stage. Essentially,
staged financing creates real options for the VC by providing them with
the flexibility to adjust funding decisions in the future. If the new firms
are unsuccessful, the VC has the option to abandon the project. If the
firms turn out to be successful, the VC has the option to expand profitable
projects by injecting more money.
How does one calculate the ownership structure with multiple rounds of
equity finance? Let us take a simple example. You have just started your
own company (say, a website or a social network) by investing $K. For
simplicity, there were no sunk costs related to setting up the company,
so the company is also worth $K. After some time, you realise you need
new funding to expand the operations, for example to buy new servers
or hardware. You present your business plan to a couple of potential
investors, and one of them, impressed by your presentation, decides to
contribute $L to the company. Now, the firm is worth $K+$L, and your
K
fraction of the firm is s =
. After some more time, your website
K+ L
gets even more popular and attracts the attention of a VC. The VC decides
to contribute $X to your startup. After contribution, the startup is worth
$V=$K+$L+$X.
As an original investor (OI), you hold 0 < s < 1 fraction of the precontribution firm. What fraction of the post-contribution company do you
(OI) and the VC own? The VC simply owns $X in something worth $V, so
x
his fraction is VCfrac = . The OI owns a fraction s of whatever is left
v
x
in the company, excluding the VC’s share: OIfrac= s *[1 –
. As the OI
v ]
attracts more and more funds from outside investors, the value of the firm
keeps growing, but your fraction decreases, everything else equal. Let us
illustrate the staged financing with an example where we will see how to
calculate the fraction of the company that belongs to different investors in
each stage.–
(
(
Example. Staged finance
We decide to start our own company by investing $2K of our own money
at the beginning. The firm is all-equity financed, with a value of $2K. After
a year, a VC contributes another $2K, and our company is worth $4K.
However, our own share drops from 100 per cent originally, to 50 per cent
(see Table 6.1).
Assets
Liabilities
Cash from new equity
2.0
New equity from venture capital
2.0
Other assets
2.0
Your original equity
2.0
Value
4.0
Value
4.0
Table 6.1: First stage market value balance sheet ($K).
Your fraction:
2
4 = 50%
2
(Recall that if the VC contributes X to a start-up
4 = 50%
worth V, his fractions is simply X/V. Here X=2 and V=4)
VC1 fraction:
Suppose we expand the business and in one year the market value
increases to $20K. A new VC2 contributes $8K.
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FN2191 Principles of corporate finance
Assets
Liabilities
Cash from new equity
8.0
New equity from 2nd stage
8.0
Fixed assets
2.0
Equity from 1st stage
??
Other assets
18.0
Your original equity
??
Value
28.0
Value
28.0
Table 6.2: Second stage market value balance sheet ($K).
8
28 = 29%
VC1 fraction: half the old firm = ½ (1 − 29%) = 35% of the new firm
VC2 fraction:
To calculate your fraction, we use s=1/2 as you had 1/2 of the company
at the first stage, and X/V = 29% – the share of the new VC:
X
s ∗ [1− ( )] = ½ (1 − 29%) = 35% ($10K)
V
VCs often specialise in certain industries or in a certain stage of firms.
In practice, many VCs focus on high-tech high growth industries such as
information technology, biotechnology, etc. These industries are opaque
and very risky, since it is not so straightforward to calculate the value of
new products and ideas in these areas. Many of these firms have very low
success probability – usually only two out of 10 turn out to be profitable
investments. As discussed before, VCs have low success probability but
larger than usual return on the firms that turn out to be profitable. A
typical stage list is:
•
Angel investor:
Usually the firm has only raw ideas at this stage and there is no
product yet.
•
Seed capital:
There is a prototype of the product and a business plan to illustrate
the main ideas.
•
Early stage venture capital:
At this stage, the firm starts to generate revenue but is still perhaps
not profitable.
•
Late stage venture capital:
The company is profitable but needs additional cash to invest.
•
Mezzanine stage:
This is the last stage before IPO (VC exit). Often, there are multiple
securities used for financing: debt, convertibles and so on.
Now, let us move on to the last feature of VCs – active investors. Recall
that private equity is equity financing that is not publicly traded.
Compared to public equity, there are two main differences. First, private
equity is not as easily tradable as public equity. Private equity projects
are often illiquid as VCs usually know much better about the quality of
the project compared to outside investors. Hence, it might be hard for
VCs to sell their stake to the general public. Public equity in this sense is
more liquid. Second, private equity is characterised by concentrated large
investors, compared to the dispersed and small owners of large public
companies. This creates some problems. Usually, the many small owners of
public equity have no skill or incentive to monitor the company. They have
to exert the full cost of monitoring, but enjoy only a very small fraction
of the benefits. This is called externality: one does not fully bear the
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Chapter 6: Equity financing
consequences of one’s action. Hence, it is rational for them to not monitor
(as the costs exceed the benefits). This is the famous free-riders problem.
VCs can solve this problem. They are big shareholders of a company, so
they enjoy a big part of the benefits from monitoring. Hence, for them,
it is rational to monitor the entrepreneur (benefits exceed the costs). Let
us illustrate this intuition in a simple case where we will see why small
investors have no incentive to monitor, whereas large investors have.
Example. VC monitoring
Suppose there is a firm that next period generates a cash flow of 10 if
an equity holder monitors or 0 otherwise. The cost of monitoring is 4. If
you are a small investor with 20 per cent stake, then you do not monitor
because:
•
The payoff from monitoring is 20%*10 – 4 = –2 (if you monitor,
then the firm value is 10, and you get 20 per cent of the total firm
value. On the other hand, you exert monitoring effort of 4 – the full
cost of monitoring. Hence, the net payoff to you as the monitoring
shareholder is: 20%*10 – 4 = –2).
•
On the other hand, your payoff from not monitoring is simply 0 as
the firm value without monitoring is 0. Since your payoff from not
monitoring exceeds the one from monitoring (0>–2), you do not
monitor.
If every investor holds less than 20 per cent, then no one monitors. In
public companies, this is almost always true, so we have the free-riders
problem.
On the other hand, if you are a large investor with a 70 per cent stake,
then you will monitor because:
•
you anticipate that no one else monitors
•
your payoff from monitoring is: 70%*10 – 4 = 3
•
payoff from not monitoring is 0<3. Thus, you are better off monitoring.
VCs are usually large investors with a big stake in the company; hence,
they have the incentives to monitor.
Now, let us talk about how VC funds raise money for their investments.
VCs belong to the private equity industry and are usually organised in
limited partnership structure. There are two types of partners: general
partners (GPs) and limited partners (LPs). GPs are responsible for choosing
and monitoring the portfolio of firms. They contribute mainly skill and
around 2 per cent of the total capital of the VC. LPs provide capital for
the partnership. They do not directly make investment decisions but
contribute the majority of capital: around 98 per cent. To understand the
fund structure, let us consider the following example. Suppose you have
brilliant skills in choosing successful start-ups, but do not have enough
money to invest in all of them. However, some outside investors (for
example your friends) have large amounts of money and are looking
for high return projects. One possibility is to set up a VC, where you are
the GP and your wealthy investors are the LPs. A typical fund structure
is depicted in Figure 6.1. The institutional investors are the LPs – they
contribute funds to the VC and expect larger than usual returns. The VCs
are the GPs – they buy the equity of a portfolio of start-ups.
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FN2191 Principles of corporate finance
Institutional Investors
Returns
Funds
VCs
Cash
Equity
Portfolio Firms
Figure 6.1: Typical VC structure.
Now let us talk about the benefits of the VC structure. Private equity
funds are limited-duration funds – they normally last for 10–12 years.
The limited duration provides a strong incentive for the GP to perform
well because it would be much harder to raise money for the next fund
without a good track record. For example, new LPs would be reluctant to
contribute funds to GPs that performed poorly in previous venture capital
situations. Private equity funds are a closed-end type of funds. This means
that no shares can be redeemed or created after the fund is structured. If,
for example, the fund performs well, the fund cannot create new shares.
If, on the other hand, the fund performs poorly, LPs cannot usually redeem
their money back or sell their stakes. This feature of PE funds makes
them illiquid, but also creates the benefit of more stable fund structure
compared to public equity.
VC compensation usually has two parts: fixed fees and incentive fees.
Fixed fees, as the name suggests, are pre-specified and do not depend
on performance. They are akin to a management fee and are quoted as a
fraction (usually 2 per cent) of the committed capital annually. Incentive
fees are similar to carry and are specified as a fraction (typically 20 per
cent) of any profit made above some promised return (hurdle rate).
Compared to GP’s contribution, these are big numbers. Let us illustrate the
compensation to LPs and GPs with a simple example.
Example. VC compensation
Suppose you are the GP of a VC. You open a fund with 1 per cent
contribution of $1M (as GP). LPs contribute $99M. Ten years later, you
manage to increase the fund value by $100M. Assume 2 per cent annual
fixed fees and 20 per cent carry. What are the payoffs to GP and LP?
The payoff to you as a GP consists of three components. First, since you
hold 1 per cent of the fund (as you contributed $1M out of the original
$100M), now you get 1 per cent of the new value of the fund: $200M.
Second, you get the fixed fees of 2 per cent for each of the 10 years. Third,
you are entitled to the carry which is 20 per cent of the fund profits. All in
all, you get:
1%*(200M) (stake in the fund) + 2%*100M*10 (fixed fees) + 20%*(200M –
99M – 2M – 20M) (carry) = 37.8M
The payoff to LPs is their original stake plus the rest of the profits:
99M + 80% * (200M – 99M – 2M – 20M) = 162.2M
Note the huge return to the GP: $37.8M on $1M investment. This is due to
the effective leverage taken on by the LP fund structure.
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Chapter 6: Equity financing
Finally, let us consider how VCs exit the portfolio of firms. There are
two ways: M&A and IPO. In M&A, the company is acquired by another
(potentially bigger) company. For example, recall the 2014 acquisition of
WhatsApp by Facebook. In an IPO, a company’s equity becomes available
to the general public for the first time. We will discuss this in detail in the
next section.
Activities
You founded your own IT firm five years ago. Initially you invested $2 million of your own
money and in return you received 20 million shares in the company. Last year you sold
10 million shares of stock to angel investors. Now you decide to obtain funding from a
VC which would invest $50 million and would receive 20 million newly issued shares in
return. What is the post-money valuation of your IT firm?
Select one:
a. $52 million
b. $125 million
c. $50 million
d. $100 million
Initial public offerings and seasoned equity offerings
In this section, we study IPOs and SEOs. An IPO (initial public offering) is
a first sale of a company’s equity to the general public, i.e. the company
goes from being private to public. A SEO (seasoned equity offerings) is a
sale of securities by a firm that is already publicly traded. Both of these
operations take place at the primary market (firms sell to investors). This
is different to the secondary market offerings, unrelated to the company
(investors sell to investors). Why would a company go public? There
are certain benefits of doing so. First, the company attracts funds for
investment. By selling shares to new investors, the firm can raise money
for new projects. Second, IPO helps to diversify the initial set of investors.
Founders can cash out by selling their shares and use the money for other
ventures. However, current equity holders usually sell a fraction of their
shares, but not a large fraction. Why don’t they sell everything? Let us
think about it. If the original owner sells all his shares in an IPO, this is
usually a bad sign about the quality of the firm. Moreover, if the owner
dumps all their shares, they would have fewer incentives to work hard
for the company as they would no longer be compensated by an increase
in the share price. The third reason why firms go public is because IPOs
provide an exit strategy for VCs and other investors. Founders of the
company would rather have dispersed shareholders and want VCs and
banks out (recall the free rider problem: with many small shareholders,
nobody has the incentive to monitor the entrepreneur). VCs and other
early investors might also want to cash out. Typically, as we mentioned
before, they have a five-to-10-year timeframe so might want to realise
returns and move on. An IPO gives them the possibility to cash-in profits
and go to the next start-up.
There are also certain costs of going public. First, there are monetary costs.
Among these, administrative costs account for two to10 per cent. Usually,
the bigger the IPO, the lower the fraction of administrative costs – there
are big economies of scale in IPOs. Furthermore, following the IPO, it is
expensive for the firm to comply with regulatory filing requirements after
becoming a publicly traded company. The firm has to hire new employees
to prepare and to handle these reports, which costs money. Underwriting
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FN2191 Principles of corporate finance
costs are usually in the range of seven to 11 per cent. This is the fee that
investment bankers (usually big reputable banks) charge for their services.
They agree to buy the shares from the company and to place them to
the general public. However, the most dramatic monetary cost is the IPO
underpricing. A prominent feature of almost all IPOs is that the IPO price
is typically lower than the day one closing price. This is a cost to existing
shareholders as they could have sold the shares at a higher price than the
IPO price.
Second, there are disclosure requirements. Public companies are legally
obliged to file honest reports. This information is publicly available, and
can be used by the company’s competitors. Thus, disclosure requirements
may make public firms more vulnerable to competitors. Lastly, companies
that go public lose freedom as there is now oversight by the regulator.
A prominent feature of most US IPOs is the seven per cent underwriting
fee puzzle (see Figure 6.2). As we see, after 1988, 7 per cent is the
predominant underwriting fee for most IPOs in the USA.
100.0%
90.0%
80.0%
Percentage of IPOs
70.0%
60.0%
Below 7%
7%
50.0%
Above 7%
40.0%
30.0%
20.0%
10.0%
0.0%
85 86 87 88 89 90 91 92 93 94 95 96 97 98
Year
Figure 6.2: The seven per cent underwriting fee puzzle.
Let us next perform a case study on flows of cash during an IPO. Through
this case, we will see a full-blown example of direct and indirect IPO costs.
We will analyse who gets what and who wins and who loses (bears the
costs) of a potential underpricing.
Example. IPO: flow of cash
Suppose you have a company and are planning to go public. Before the IPO,
there are 34M shares outstanding and the firm is valued at $1.9805B. The
value per share before the IPO is thus $1.9805B/34M shares = $58.25/
share. Suppose you want to raise $130.2M net equity for investment. The
direct issuance cost is approximately $9.8M or 7% of gross proceeds.
a. What is the post-issue stock price (Pnew) and how many shares should
be issued? How much equity did the original stockholders give up?
What is the value of the founders’ shares after the IPO? What is the
value of (new) investors’ shares after the IPO?
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Chapter 6: Equity financing
b. Suppose the issue is underpriced at $28/share. How much equity was
sold? How much did existing shareholders give away?
c. The total amount of cash we need to raise is the sum of the new net
equity and the issuance costs. Since the net equity is $130.2M and the
direct costs are $9.8M, we get:
Pnew * [N shares] = $130.2M + $9.8M = $140M
The market value of the company after the IPO will be the product of a
new number of shares and the new share price. As we had 34M shares
before the IPO, and we issue N new shares, the total number of shares
after the IPO will be $34M + N:
[(34,000,000 + N)shares]* Pnew = $1.9805B + $130.2M
Solving this, we get Pnew = $57.96/share and N = 2,415,385 shares. Hence,
the firm has to issue 2,415,385 new shares, and the price will drop
from $58.25 to $57.96.
Original stockholders gave up 2,415,385 /(2,415,385 + 34,000,000) =
6.63% of the value of the firm (before they had 100 per cent of all the
stocks: 34M out of 34M, now they hold a lower fraction: 34M out of
34M+2.415385M).
The value of founders’ shares after the IPO is the product of the
number of shares they have and the new share price: This is exactly
the same as their original wealth less the direct financing costs: .
The value of (new) investors’ shares after the IPO is the product of
the number of shares they acquired and the new share price $57.96 *
2,415,385 shares = $140M
Bottom line: As long as the issue is fairly priced, existing shareholders
only lose issuing costs ($9.8M in this case).
d. As the share price is $28 and we still have to attract the same amount
of money, we issue shares. Since there were 34M shares originally, the
total number of new shares will be 5M+34M=39M. Hence, we issue
5/(5+34) = 12.82% of the new company. The amount of money that
existing shareholders give away is the product of the number of newly
issued shares and the loss on each share (since they sold the shares at
a much lower price than the fair value):
Shares issued* (True stock value preIPO – IPO price) = 5,000,000*(58.25–
28) = $151.25M
Thus, the underpricing costs of $151.25M are much higher than the
direct costs of $9.8M. This example illustrates that the underpricing
costs can be a very substantial part of the total IPO costs faced by
existing shareholders. We will elaborate more on this in the next
section when we consider IPO underpricing and winner’s curse.
Next, we turn to a SEO. Remember, a SEO is when an already public
company decides to issue additional shares. In contrast with IPOs,
SEOs are used by already public companies. Compared to secondary
market offerings, SEOs take place on the primary market as it is the
firm who sells to investors.
There are three main ways to issue seasoned equity:
general cash offer
private placement
rights issue.
General cash offer is a sale of securities open to all investors. In
contrast, private placement, as the name suggests, is a sale of
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FN2191 Principles of corporate finance
securities to a limited number of investors without a public offering.
Lastly, rights issue is an issue of securities offered only to current
stockholders. It is usually quoted in terms of ‘X for Y shares’. This type
of rights offer means that for every Y shares you own, you have the
option to buy X more shares from the company. For example, 4 for 17
rights issue means that for every 17 shares that you own, you have
the right (but not the obligation) to buy 4 in addition. Since rights
issues effectively create new shares, they increase the total number
of shares and thus may entail dilution effect to existing shareholders.
Hence, one should consider the dilution effect when evaluating the
value of rights. Let us elaborate with an example that illustrates how
to calculate the value of a rights issue and the potential effects for the
share price.
Example. Rights issue
Suppose we need to raise €1.28billion of new equity. The market price is
€60 per share. We decide to raise the additional funds via a 4 for 17 rights
offer at €41 per share. If we assume 100 per cent subscription, what is the
value of each right?
To answer this question, first we have to calculate the value of the right. It
is easy to think of the rights issue as an option that gives you the right to
buy shares of the company at a discounted price. We would exercise this
option only when the issue price is below the market price. The value of
this option is then the true value of the stock less the strike price (akin to a
payoff of in-the-money call option).
Value of right = true value of stock – strike price
Let us calculate the value of the stock after the rights issue. We can obtain
it by dividing the market value of the company by the new number of
shares after the issue. The current market value of the firm (suppose only
17 shares outstanding for simplicity) is 17 × €60 = €1,020. The total
number of shares will increase to 17 + 4 = 21 if everyone subscribes for
the rights issue (recall that for every 17 shares existing, there are four
newly created). The amount of funds after the issue is the market value
plus funds attracted from investors of the rights issue. Since we sell 4
shares at the price of 41, this is 1,020 + (4 × 41) = €1,184. Finally, the
new share price is 1,184/21 = €56.38 and the value of a right, calculated
using the above formula is: 56.38 – 41 = €15.38.
In general, the formula for the value of right is:
N ,
Value of right = (Current Price – Issue price) ∗
N +1
where N is the number of shares per right.
The equation takes into account both the price discount and the dilution.
Let us check for the example above:
€15.38 = (60 − 41) ∗
88
, where N=17/4
+1
Chapter 6: Equity financing
Activities
Big Burger Corporation has 1 million shares outstanding. It wishes to issue 500,000 new
shares using rights issue. The current stock price is $500 and the subscription price is
$470/share. What is the value of a right?.
Select one:
a. $25/right
b. $20/right
c. $4/right
d. $50/right
IPO underpricing and winner’s curse
Recall the IPO: flow of cash example from the previous section. As we saw
there, underpricing can be a substantial part of the IPO costs. This section
will elaborate more on this.
(P − P )
In practice, IPO underpricing is the day 1 return of the stock: 1 0
P0
Why? Because it measures the costs to existing shareholders from dilution
and from selling shares too cheaply. If the day 1 return is positive, existing
shareholders lost money from selling their shares to the new investors
at a lower price. Empirically, the day 1 return of an IPO is 16 per cent
on average. This is underpricing: firms could have sold the shares for 16
per cent more. These returns are risky though – they vary widely by year
(1960–1987). The worst year was 1973 when IPOs returned –18% (105
issues). The best year was 1968 when the return was +56% (368 issues).
You might think 16 per cent is a small number, but once we convert it into
actual money left on the table by firms going public, the figures become
gigantic. VISA is the company with the largest IPO underpricing costs so
far. Shareholders of VISA have left $5.075B on the table on the first day of
trading! With $406M shares offered at an IPO price of $44, the closing day
1 price was $56.50.
Underpricing varies also with uncertainty about the stock’s value. Larger
firms are usually underpriced less. Based on data from Ritter’s website
(https://site.warrington.ufl.edu/ritter/ipo-data/) and Loughran, Ritter
and Rydqvist (1994)1, firms with sales less than $1M had initial excess
returns of 31 per cent on an IPO. Firms with sales exceeding $25M had
initial excess returns of only 5 per cent. Underpricing is smaller for older
firms as they have longer track record.
Moreover, IPO underpricing is an international phenomenon. Underpricing
occurs in almost every country with IPOs and, again, smaller issues are
underpriced more than bigger issues. (see Figure 6.3). One interesting
observation is that the maturity of countries’ equity market does not
explain the magnitude of the initial underpricing. For example, developed
countries such as Canada, USA, the UK and Japan have well-established
equity markets, but these markets feature dramatically different sizes of
IPO underpricing. On the other hand, less developed equity markets, such
as the ones in Russia, Iran and China, exhibit underpricing with similar
magnitude and dispersion.
1
Loughran, T.,
J.R. Ritter, and K.
Rydqvist ‘Initial
public offerings:
international
insights’, Pacific Basin
Finance Journal 3
1994, pp.139–40.
Long-run returns of IPO firms go in the opposite direction: shares of firm
that went public perform poorly in the long run after three years. From a
sample of 1,500 IPO’s the three-year returns were 34 per cent, compared
with a 62 per cent return on a portfolio of small stocks in similar
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FN2191 Principles of corporate finance
industries. Thus, holding shares of firms that recently went public, for a
long period after the IPO, proofs to be a bad investing strategy.
Russia
Argentina
Austria
Canada
Denmark
Chile
Norway
Netherlands
France
Turkey
Spain
Portugal
Nigeria
Belgium
Israel
Hong Kong
Mexico
UK
Italy
USA
Finland
S. Africa
New Zealand
Philippines
Iran
Australia
Poland
Cyprus
Ireland
Germany
Indonesia
Sweden
Singapore
Switzerland
Sri Lanka
Brazil
Bulgaria
Thailand
Taiwan
Japan
Greece
Korea
Malaysia
India
China
Small underpricing
Medium underpricing
High
underpricing
0
20
40
60
80
100
Figure 6.3: IPO underpricing – international evidence.
Why are IPOs underpriced? Why do private firms leave money on the table
when they go public? There are several potential explanations:
•
Underwriter price supports. Underwriters can support the price
of an IPO by buying shares at the IPO price or lower. This can lead
to underpricing because, to minimise the costs and to decrease the
probability of potential price support transactions, underwriters might
prefer lower IPO price.
•
Benefit the underwriter. Lower IPO price favors the clients of the
underwriters – they can buy at the offer price and realise gains on the
first day of trading. This might be beneficial for the reputation of the
underwriter and clients might be more willing to subscribe to further
IPOs of the same underwriter.
•
Risk averse owners. The original owners might perceive the IPO as
a once-in-a-lifetime very positive NPV project where they can become
rich immediately. Owners may be afraid that too high a price could
cause the IPO to fail or to attract fewer investors; hence the offered
price is set lower.
•
Information asymmetry (winner’s curse). There are two types
of investors: informed (they know for sure whether the firm is bad or
good) and uninformed (they have no idea whether the firm is good
or bad). Informed investors stay away from bad deals. Uninformed
investors get 100 per cent of bad IPOs but only a fraction in good IPOs.
To break even, uninformed investors need a discount on the fair price.
The winner’s curse problem is one of the most prevalent explanations for
the IPO underpricing. Let us elaborate more on this story. The winner’s
curse problem is typical in auctions: when bidders have different private
90
120
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Chapter 6: Equity financing
information, the winner of the auction tends to overpay for the item.
How does this relate to an IPO? Analogously, in an IPO, uninformed
investors tend to overpay for bad firms. To the contrary, informed investors
participate in an IPO only if the firm is good. Now, assume you are
uninformed investor and your average evaluations are correct. If you bid
the average estimates in an IPO, and the IPO is a good deal, you get small
(or no) allocation in the issue because informed investors also participate.
However, when the IPO is bad, informed investors withdraw and you are
the only buyer. You end up with a big allocation in a bad firm, for which
you paid a higher price than the fair one (since the average between a
good and a bad deal is larger than a bad deal). Thus, on average, when
you win a lot of allocation, it means it is a bad IPO – winner’s curse
problem. Moreover, your expected return is negative. Hence, in order
to break even, you bid at a discount which means that the day 1 closing
price should be higher than the IPO price. This leads to IPO underpricing.
In some sense, the IPO underpricing is a form of a ‘bribe’ to attract the
uninformed investors to the offering. Let us consider an example which
shows us why uninformed investors need a lower-than fair price at the IPO
to break even.
Example. IPO underpricing
Suppose you want to participate in an IPO but you don’t know whether
it is a good or a bad deal – you are uninformed. You think that the shares
are equally likely to go to $0 (bad deal) or to $2 (bad deal) after the IPO.
There is also an informed trader who knows the outcome. There are two
shares available to subscribe. Both you and the informed can choose to
buy the new shares. If both of you choose to buy, each gets one share. If
only you choose to buy, you get two shares. Are you willing to buy at the
average price of $1? No! Why? Let us think.
Consider the strategy of the informed investor and the allocation outcome.
If the IPO is bad, the informed investor withdraws and we ‘win’ all of the
shares. The ultimate payoff will be $0 and our total payoff is $–2 (since we
paid $1 for 2 shares worth nothing). If the IPO is good, both you and the
informed investor get 1 share worth $2. Thus, the payoff to you is:
0.5*(–1 + 2) + 0.5*(–2 + 0) = $–0.5 <$0 (you get $0 if you do not
participate in the IPO).
This is the winner’s curse issue: you cannot break even if you bid for
the shares. Hence, the IPO price should be lower than $1 to attract you
which explains the IPO underpricing. Consider yet another example which
shows that the expected day 1 return on an IPO has to be positive in an
environment with both bad and good IPO deals.
Example. Winner’s curse
MM Enterprises is going public with an offer of 1,000 shares at $1/
share. With 40 per cent chance, MM Enterprises will turn out to be a bad
company which we will refer to as a ‘Dog’ and with 60 per cent chance
it will be good, which we will call a ‘Jewel’. Assume ‘Dogs’ have an initial
return of –20%. There is no discounting and everyone is risk neutral.
There exist both informed (very small group for any given issue) and
uninformed investors. Informed investors know whether or not MM is
a dog or a jewel, and subscribe only to jewels. Informed investors have
capacity to buy 500 shares. Uninformed investors subscribe to all issues. In
the event of oversubscription, shares are rationed (Table 6.3).
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FN2191 Principles of corporate finance
Dog
(40% Probability)
Jewel
(60% Probability)
Informed
0
500
Uninformed
1,000
500
Table 6.3 Shares rationing.
We need participation by uniformed investors; otherwise the IPO will not
go through. They must earn an average 1–day return of 0 per cent. What is
the required return from a ‘Jewel’ for uniformed investors to participate in
the IPO?
Assume is the day 1 return from ‘Jewel’. Then the expected day 1 return
for an uninformed investor is:
.4($1000)(1 – .20) + .6(500)(1 + Rj) + .6(500)(1 + 0) = 1000 (1 + 0)
The first term on the left-hand side of the equation above is the return on
allocated shares in a bad IPO, the second the return on allocated shares in
a good IPO, and the last the return on unused cash. The right-hand side is
the return from not participating in the IPO. Solving yields . What is the
expected return on the IPO then?
E(RIPO) = .4*(–20%) + .6*(26.67%) = 8%
This is the average day 1 return (underpricing)!
A reminder of your learning outcomes
At the end of this chapter, and having completed the Essential reading and
activities, you should be able to:
•
explain venture capital and equity issuance in the public market
•
perform valuation with multiple financing rounds
•
explain the calculate ownership structure in initial public offerings and
seasoned equity offerings
•
explain and evaluate the winners’ curse problem.
Key terms
Initial public offerings
IPO underpricing
Private equity
Rights offerings
Seasoned equity offerings
Staged financing
Venture capital
Winner’s curse problem
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Chapter 6: Equity financing
Sample examination questions
1. Swipechat recently completed its IPO. The stock was offered at a price
of $1.40 per share. On the first day of trading, the stock closed at
$1.90 per share.
a. What was the initial return on Swipechat?
b. Who benefited from this underpricing?
c. Who lost, and why?
2. In 2017 the Duckdonalds Corporation made a rights issue at $50 a
share of one new share for every four shares held. There were 10
million shares outstanding before this issue and the share price was
$60. For Parts (a) - (c) assume that all rights were exercised.
a. What was the total amount of new money raised?
b. What was the prospective stock price after the issue?
c. What was the value of the right to buy one new share?
d. How far could the stock price decrease after the issue before
shareholders would be unwilling to take up their rights?
e. Assume that the rights issue is at $40 rather than $50 per share.
How many new shares would it have needed to sell to raise the
same amount of money? How do your answers to (c) and (d)
change? Are the shareholders any better or worse off with the $40
exercise price?
3. Two years ago, you founded Pineapple Computers, Inc., a retailer
specialising in the sale of IT equipment. So far your company has gone
through three funding rounds:
Round
Date
Investor
Shares Issued
Share Price ($)
Series A
Feb 2011
You
50,000
10
Series B
Aug 2012
Angels
100,000
20
Series C
Sept 2013
Venture Capital
200,000
35
It is 2015 and you need to raise additional funding to expand your
business. You have decided to take your firm public through an IPO.
You would like to issue an additional 650,000 shares at this IPO. If
your firm successfully completes its IPO, the 2015 net income will be
$750,000.
a. Your investment banker advises you that the prices of other
recent IPOs have been set such that the P/E ratios based on 2015
forecasted earnings average 20.0. Assuming that your IPO is set at
a price that implies a similar multiple, what will your IPO price per
share be?
b. What percentage of the firm will you own after the IPO?
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FN2191 Principles of corporate finance
Notes
94
Chapter 7: Dividend policy
Chapter 7: Dividend policy
Aim of the chapter
The aim of this chapter is to analyse and explain the choices of dividend
policies made by firms’ managers. With this aim in mind, we first introduce
a stylised model in which dividend policy is irrelevant (Modigliani–Miller).
We then relax some of the assumptions made in this stylised model in
order to explain empirical evidence on firms’ dividend policies.
Learning objectives
By the end of this chapter, and having completed the Essential reading and
activities, you should be able to:
•
show that dividend policy (and share repurchases) are irrelevant to
firm valuation under the Modigliani–Miller assumptions
•
discuss the stylised facts of dividend policy provided by Lintner
•
present the clientele model of dividends
•
discuss the effects of asymmetric information and agency costs on
dividend behaviour.
Essential reading
Brealey, R., S. Myers and F. Allen Principles of Corporate Finance. (Boston, MA;
London: McGraw-Hill, 2016) Chapter 17 (Payout Policy).
Further reading
Allen, F. and R. Michaely ‘Dividend Policy’ in Jarrow, R.A., V. Maksimovic and
W.T. Ziemba (eds) Handbooks in Operational Research and Management
Science: Volume 9: Finance. (Amsterdam: North Holland, 1995).
Bhattacharya, S. ‘Imperfect information, dividend policy, and “the bird in the
hand” fallacy’, Bell Journal of Economics 10(1) 1979, pp.259–70.
Blume, M., J. Crockett and I. Friend ‘Stock ownership in the United States:
characteristics and trends’, Survey of Current Business 54(11) 1974,
pp.16–40.
Copeland, T. and J. Weston Financial Theory and Corporate Policy. (Reading,
MA; Wokingham: Addison-Wesley, 2005) Chapter 16.
Grinblatt, M. and S. Titman Financial Markets and Corporate Strategy. (Boston,
MA; London: McGraw-Hill, 2011) Chapters 15 (How Taxes Affect Dividends
and Share Repurchases) and 19 (The Information Conveyed by Financial
Decisions).
Healy, P. and K. Palepu ‘Earnings information conveyed by dividend initiations
and omissions’, Journal of Financial Economics 21(2) 1988, pp.149–76.
Jensen, M. and W. Meckling ‘Theory of the firm: managerial behaviour, agency
costs and capital structure’, Journal of Financial Economics 3(4) 1976,
pp.305–60.
Lintner, J. ‘Distribution of incomes of corporations among dividends, retained
earnings and taxes’, American Economic Review 46(2) 1956, pp.97–113.
Myers, S. ‘Determinants of corporate borrowing’, Journal of Financial Economics
5(2) 1977, pp.147–75.
Ross, S. ‘The determination of financial structure: the incentive signalling
approach’, Bell Journal of Economics 8(1) 1977, pp.23–40.
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Overview
The dividend is a cash payment (usually made on an annual or semiannual basis) to the owners of corporate equity and is the basic financial
inducement for individuals to hold shares. In Chapter 1, when analysing
discounted cash-flow techniques, we demonstrated how to price an
equity share, given knowledge of the future dividend stream that would
accrue to the share. Such an analysis might be undertaken by an investor
in order to assess the ‘value’ of an equity share. The current chapter
analyses dividends from the opposite perspective, that of the manager
of a corporation who must decide on the level of dividends to pay out.
In a similar vein to the analysis of capital structure in Chapters 5 and 6,
the fundamental question we wish to answer is: what dividend policy is
optimal for management in that its adoption results in maximum firm
value?
How to return capital to equity holders?
There are two main ways in which companies return money to equity
holders: dividends and share repurchases. Let us focus first on dividends.
There are two types of dividends: cash dividends and stock dividends.
In the first type, a firm pays cash to shareholders: for example, for every
share they have, shareholders receive $1 of cash paid from the company’s
account. If the stock price is $100 in that case, the dividend yield is 1 per
cent. Cash dividends are paid either regularly (quarterly, (semi-)annually),
or as a one-time payout – special cash dividends. Stock dividends, on the
other hand, do not involve any actual cash flows from the company to
the investors. In a stock dividend, the firm just creates new shares and
distributes them among existing shareholders.
For example, for every 100 shares an investor has, she receives one new
share. Stock dividends are hardly a ‘payout’, as the company does not pay
actual money from its account to equity holders. This type of dividend
is similar to a stock split, but with a smaller order of magnitude. In the
previous example, every 100 shares receive one new share, whereas in a
typical stock split, much more shares are created. For example, in a twofor-one split every 100 shares receive 100 new shares. Typically, when
firms announce a stock dividend, the share price drops.
Think about the following analogy of a one per cent stock dividend:
suppose you have your money split into 100 wallets. Now you decide to
split the same amount of money in 101 wallets. The total sum of money
in all wallets is the same but the amount of money in each of the 101
wallets is lower than the amount of money in each of the 100 wallets
before. Analogously, the share price after the stock dividend (101 shares
outstanding) is lower than the price before the dividend (100 shares
outstanding).
Now let us talk about the timing of dividend payments. There are several
important dates in a typical dividend payment. First, the announcement
date is the date when the firm states the dividend amount. In the
announcement, usually, firms also specify the payment date and the record
date. The payment date is the day on which dividends are actually paid. The
record date is the date on which the firm takes a snapshot of all investors
who own shares of the company: it is only these investors who will receive
the dividend. For example, suppose at t=0 the firm announces a dividend
payment taking place at t=7 with a record date at t=5. Suppose that it
takes two days to settle a buy-sell transaction of a firm’s shares. If you
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Chapter 7: Dividend policy
buy a share of the company any time before t=3, you will be eligible for a
dividend as at t=5 the transaction will be settled and you will be holding
shares in the company. However, if you buy the share at, say, t=4, you will
not receive the dividend as you will only become an official shareholder at
t=4+2=6, which is after the record date. In relation to this, the first day
the stock trades without the dividend, is called the ex-dividend date (t=4
in our example). The day before the ex-dividend day, is called the cumdividend date (t=3 in our example). Figure 7.1 illustrates the timeline of a
typical dividend payment. If you buy the share on or after the ex-dividend
date, you will not receive the declared dividend. If you buy the share on or
before the cum-dividend date, you will receive the dividend.
Figure 7.1: Timeline of a dividend.
Now let us talk about the second way firms distribute capital to equity
holders: share repurchases. In a share repurchase, firms use cash to buy
back stocks. The most popular way is via open market repurchases: firms
buy shares on the public market anonymously and then cancel these shares.
In a share repurchase, firms may sometimes treat different shareholders
heterogeneously: for example, they can buy most of the shares from one
or a small group of investors, and not buy any shares from other investors.
Open market repurchases provide some tax flexibility: investors can delay
the tax by not selling the shares, for example. In contrast, with a dividend
payment, shareholders cannot avoid the tax because, as soon as the
dividend is paid, they are obliged to pay the tax. Lastly, these repurchases
are usually spread over time: they can last up to three years.
The next way to do a share repurchase is a tender offer. In this operation,
the firm offers to buy a certain number of shares at a specified price.
For example, it offers to buy 1 million shares at the price of $1. Then,
shareholders can choose whether to participate by subscribing for the offer
or not. If there are enough subscriptions, the offer goes through. If there
are more shares in the subscription, say, 2 million, the company can either
randomly pick 1 million from these, or ration the shares on a pro-rata
basis: each investor sells 50 per cent of the shares they initially intended to
sell as part of the tender offer.
Modigliani–Miller meets dividends
In Chapter 5 we argued that, under a given set of assumptions, firm value
is independent of capital structure (i.e. the MM theorem was valid). These
assumptions include the following:
•
frictionless markets (no taxes or transaction costs)
•
symmetric information
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FN2191 Principles of corporate finance
•
no agency costs
•
investment outcomes independent of financing decisions.
The assumptions that give us MM1 actually yield a far more powerful
result than just the irrelevancy of debt policy. They imply that the entire
financial policy followed by a firm is irrelevant for its valuation; all that
matters is the firm’s portfolio of investment projects. Hence, capital
structure, dividend policy and risk management activities (among other
things) are all ineffectual in altering firm value. We have restated the
theorem and application of its logic to dividend policy, below.
Consider a firm that has fixed its investment policy. In each period, it is left
with a net cash flow, which is simply the difference between operating
income and investment costs. A straightforward corporate dividend
policy would just be to pay out this net cash flow to the holders of equity.
However, consider a firm that desires to pay a dividend in excess of its
net cash flow. In order to do this, the firm can raise funds by issuing
new equity. Alternatively, the firm could borrow money which, assuming
perfect capital markets, is a transaction with NPV of zero. Conversely, a
firm wishing to pay a smaller dividend might spend the balance of its net
cash flow on repurchasing equity. The key idea here is that a firm can
choose whatever payout policy it desires, funding the policy through share
issues/repurchases; hence, dividend policy is irrelevant.
From the individual investor’s point of view we can show that dividend
policy is irrelevant too. To do this we can use a similar argument to that
employed in our argument that shareholders are indifferent to capital
structure changes; shareholders are indifferent to dividend policy as,
through appropriate purchases or sales of shares, they can replicate any
dividend policy they wish. Hence, investors will not value a firm paying a
particular dividend policy different to any other firm such that firm
value does not depend on dividends. We will pick up this theme in the
following section.
Prices, dividends and share repurchases
It is straightforward to show that investors are indifferent to cash received
through dividends or share repurchases. To see this, consider an all-equity
firm, which has a current market value of $100,000. There are 2,000
shares outstanding, such that the current share price is $50. The firm is
due to pay a $10 per share dividend tomorrow. In this scenario (i.e. just
before the payment of a dividend) the current share price of $50 is called
the cum-dividend share price.
First, let’s analyse what would happen to the share price after dividend
payment. The total dividend payment is $10*2,000 = $20,000. Hence, after
a dividend payment, the total firm value will be $100,000 – $20,000 =
$80,000. As there are still 2,000 shares outstanding, the share price after
dividend payment is $80,000/2,000 = $40. This is called the ex-dividend
share price. Note the obvious result that the sum of dividend paid and exdividend share price is equal to the cum-dividend share price ($80,000 +
$20,000 = $100,000).
Activity
A firm has current share price of £2.50 and will pay a £0.15 per share dividend
tomorrow. What is the share price immediately after dividend payment?
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Chapter 7: Dividend policy
Consider the cash position of an individual who originally held five shares
in our firm. The value of their shareholding was originally $250. After
the dividend payment, they have cash of $50, and the value of their
shareholding is $200. Hence, the dividend has just altered the composition
of their wealth rather than changing its dollar amount.
What happens if, instead, the firm decides to use the cash it had originally
earmarked for dividend payment for a share repurchase instead? As
mentioned above, the total dividend amount was $20,000. As the
original share price was $50, this implies that the firm can repurchase
$20,000/$50 = 400 shares. As a result, after the share repurchase, there
are 1,600 shares outstanding, and the firm is again worth $80,000 in total.
Therefore, the post-share repurchase share price must be $80,000/1,600
= $50. Note that a share repurchase (at a fair price) does not alter share
prices.
Again, consider the position of our individual who originally owned
five shares. The firm repurchases 400 shares, which is one-fifth of all
equity. Now, assume that one share of this individual’s holding of five
is repurchased. The repurchase thus gives them $50 and, after the
repurchase, their four remaining shares are worth $200 in all. As a result,
in this case also, their $250 invested in equity has been changed into
$50 of cash and $200 still in equity. This is identical to the case where
dividends were paid.
Thus, the individual is indifferent between dividends and share
repurchases. The manner in which the firm chooses to distribute cash does
not matter to them and, as a result, they will not discriminate (in value
terms) between stocks that do and do not pay dividends.
Dividend policy: stylised facts
Our prior discussion led to the conclusion that dividend policy is irrelevant
(i.e. the choice of policy doesn’t affect firm value). However, certain formal
and casual empirical observations point in the opposite direction. In this
section we will provide a brief and selective review of such empirical
research on dividend policy.
Perhaps the most famous set of results on actual dividend policy was
compiled and presented by John Lintner (1958). Lintner interviewed the
management of a sample of US corporations in order to determine what
lay behind their dividend-setting decisions. His research led to the four
following stylised facts.
1. Managers seem to have a target dividend payout level.
2. This payout level is determined as a proportion of long-run
(i.e. sustainable) earnings of the firm.
3. Managers are more concerned with changes in dividends rather than
the actual level of dividends.
4. Managers prefer not to make dividend changes that might need to
be reversed (e.g. cutting dividends after having raised them in the
previous period).
As the second fact implies, it is not current but long-run earnings
that matter in setting dividends such that dividends can be seen to be
smoothed relative to earnings. These observations led Lintner to develop
the characterisation of dividend behaviour that is given in equation 7.1. It
is a simple partial adjustment model:
ΔDt = λ(αEPSt – Dt–1), 0 < α < 1, 0 < λ < 1
(7.1)
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FN2191 Principles of corporate finance
where Dt is the time t dividend per share, EPSt is earnings per share at t, α
is the target payout ratio, and λ is the parameter governing the degree of
dividend smoothing. In line with facts 1 and 2, equation 7.1 embodies a
target payout, which is a simple proportion of earnings. Also, the change
in dividends appears on the left-hand side of 7.1 in line with fact 3.
Note that, if λ was equal to one, then the dividend change at time t would
always ensure that dividends were at precisely their target level (i.e. we
would have Dt = α EPSt). However, for values of λ less than one, dividends
change towards their target level gradually. This reflects the smoothing of
dividends that Lintner’s stylised facts indicate.
The other major source of empirical observations on the effects of dividend
policy has been the event study literature, which has also emphasised the
vast importance of changes in dividends. A wide range of studies for equity
from many different countries has demonstrated that dividend cuts lead to
drops in stock price on average, whereas dividend increases on average
lead to stock price rises.1 The interested reader can consult Healy and
Palepu (1988), among other writers.
Clearly then, putting together the empirical evidence from interviews and
event studies yields an impressive case for the relevance of dividend policy.
The results of Lintner (1956) indicate that corporate managers do not
perceive dividend policy as irrelevant. Rather, they seem to follow similar
plans in their payout policy. Further, the event study evidence tells us that
the market interprets unexpected dividend increases as good news for a
stock, whereas unexpected dividend cuts are regarded as bad news.
1
No change in dividends
is (as one might expect)
associated with little or
no effect on stock prices
on average.
Hence, we have a case for arguing that the dividend version of the MM
theorem is invalid. However, we have not yet come up with reasons for
why it is invalid. In the following two sections we will explore three sets
of reasons (similar to those put forward to explain the relevancy of capital
structure): namely, the existence of taxation, asymmetric information and
agency costs.
Taxation and clientele theory
An obvious omission from our story of dividend policy irrelevancy is
taxation. Previously we argued that, with no taxes, share-holders should
be indifferent between income in the form of dividends or income from
capital gains. This would still be true if dividends and capital gains were
taxed symmetrically, that is both the tax rate and the timing of taxes
are the same. However, it is generally true that the dividend payments
accruing to individuals are taxed more heavily than capital gains. We
would therefore expect individuals to prefer income in the form of capital
gains. Corporations, on the other hand, are taxed very favourably on
dividend income on the shares of other firms that they hold. Corporations,
therefore, should prefer dividend income to capital gains income. Finally,
some institutions pay no taxes whatsoever. These institutions will not care
whether income is earned as either dividends or capital gains.
The preceding observations on taxes lay the foundations for the clientele
theory of dividends. The notion behind this theory is straightforward.
Given the three groups above, we might expect some stocks to pay high
dividends (with these stocks held by corporations), some stocks to pay
medium dividend levels (and these are held by tax-exempt institutions)
and finally certain firms to pay low dividends (and their shares are held by
individuals). Each type of stock (classified according to dividend levels)
caters to its own ‘clientele’ of investor. A numerical example will yield
further insights.2
100
This example is based
on that given in Allen
and Michaely (1995).
2
Chapter 7: Dividend policy
Assume an economy populated by risk-neutral agents. Individuals pay
a tax rate of 50 per cent on dividend income and 20 per cent on capital
gains. Corporations pay tax at rate 10 per cent on dividend income and 35
per cent on capital gains. Three types of stock exist in the economy: high,
medium and low payout stocks. Each stock has earnings per share of 100.
Payout policies, stock prices and after-tax payoffs are given in Table 7.1.
Payout policy
High
Medium
Low
100
50
0
0
50
100
Individuals
50
65
80
Corporations
90
77.5
65
Institutions
100
100
100
1,000
1,000
1,000
Dividend
Capital gain
After tax payoffs
Equilibrium price
Table 7.1
Clearly, given the after-tax payoffs to each group, individuals will hold low
payout stocks, corporations will hold high payout stocks, and institutions
are indifferent. Assume that in equilibrium the total holdings of each
group are as given in Table 7.2.
Payout policy
High
Medium
Low
0
0
320m
Corporations
110m
0
0
Institutions
500m
730m
220m
Total
610m
730m
540m
Individuals
Table 7.2
Note that in Table 7.1 we displayed the equilibrium price of each equity
share as 1,000. Why is this the case? To see this, assume that the price of
low payout stock is 1,050, whereas the price of all other stock is 1,000.
This would imply that high and medium dividend level firms have an
incentive to switch to low dividend policies (to take advantage of the high
share prices). Such actions would increase the supply of low dividend
stocks and hence depress their price.
A reinforcing effect comes from the demand side. The return that
individuals get from holding low payout stock is 80/1,050 = 7.62%.
This exceeds the returns they would gain from holding medium and high
payout stocks (which are 6.5 per cent and 5 per cent respectively), and
hence individuals continue to demand low dividend stocks. Institutions, on
the other hand, only get a return of 9.52 per cent from holding low payout
stock (100/1,050 = 9.52 per cent), whereas they get a return of 10 per
cent on other types of equity. Thus, institutions rationally sell their low
dividend equity. This further depresses the price. It is only when the price
of low dividend stock is 1,000 that equilibrium is reached.
The clientele model leads to the same main result as MM. Firm values (or
stock prices) are unaffected by dividend policy. There are obviously
underlying differences to these theories though. For example, the clientele
theory implies that investors in high tax brackets should hold portfolios
with low dividend yields and vice versa.3
3
The dividend yield on
a stock is the ratio of
dividend payment to
stock price. Evidence for
this prediction is given
in Blume, Crockett and
Friend (1974).
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FN2191 Principles of corporate finance
Let us elaborate more on the timing of dividend and the tax deferral of
capital gain. Suppose a company has a current share price of 100 and has
an additional income at 5 per cent every year. The company can choose
between two dividend policies: in policy A, it pays 5 per cent dividend
every year so that the share price stays constant at 100. In policy B, it does
not pay any dividend, but reinvests the additional income in the firm so
that the share price grows by 5 per cent per year. Suppose both dividend
and capital gain tax rates are 40 per cent. As a shareholder of the company
with an investment horizon of 10 years, are we indifferent between the
two payout methods? No, because we can defer capital gain tax under
policy B. How? Recall dividends are immediately taxable upon payment,
and investors can only use after-tax dividend to reinvest. Then, the
dividend on the reinvestment is again taxed in the next round of payout
after it generates some new profits. However, if the capital is returned
in the form of repurchase, such a repeated taxation problem would not
appear. Investors are only taxed once upon the liquidation of their shares.
This is the crucial difference between the two payout methods. Thus,
even if the tax rates are the same, paying dividends still incurs higher tax
liability. Let us see why this is the case by calculating the gain under the
two different policies. If the company chooses policy A, we as shareholders
receive after tax dividend of 3 = 5 * (1 – 40%) in year 1. Then, we
reinvest the dividend and get 3 per cent after tax return every year. After
10 years, our proceeds are 100 * 1.0310 = 134.4. If the firm chooses policy
B, we do not pay any taxes over the next 10 years as we receive zero
dividends. After 10 years, we sell the stock at a price of 100 * 1.0510 =
162.9. After paying tax of 40% on the capital gain (162.9 – 100), our final
proceeds are 162.9 – (162.9 – 100) * 40% = 137.7 which is higher than
the gain under policy A.
Asymmetric information and dividends
A popular version of the asymmetric information story for the relevance
of dividends is very similar to the reasoning underlying the relevance
of capital structure in Ross (1977). This model argued that debt policy
was relevant as, in a world where firm quality was not observable to the
market, the level of debt chosen by a firm’s management signalled the
quality of the firm. High-quality firms would choose high debt levels (as
they could afford the interest payments without running into cash-flow
problems), whereas poor firms would choose low levels of debt. Hence,
debt acted as an observable signal of firm quality upon which the market
would base its valuation of a firm.
Exactly the same type of logic can be applied to dividend policy. If we
again assume that corporate managers’ objective function is increasing in
expected firm value but decreasing in expected bankruptcy costs then, in
a world where firm quality is not observable to outsiders, dividend policy
can be used as a signal. High-quality firms (i.e. firms with large average
cash flows) can afford to pay large dividends, as they worry less about
bankruptcy than low-quality firms. The latter pay low dividends to avoid
bankruptcy. Interpretation of such signals by investors means that firms
paying high dividends are valued more highly in the market than those
paying low amounts.
In empirical terms, the prior argument would then imply a positive
relationship between dividend levels and firm value. Further, we might
also expect that cuts in dividends would result in share price reductions,
as this might be interpreted as a signal of reductions in a firm’s quality.
Conversely, dividend increases should correlate with share price rises. Such
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Chapter 7: Dividend policy
empirical predictions fit quite nicely with those empirical results discussed
earlier in the chapter.
Agency costs and dividends
Consider a situation where the ownership and control of corporations
are separated. Organisations are assumed to be controlled by managers,
who can only be imperfectly monitored by owners/shareholders and, as
a result, there is scope for managers to behave opportunistically. In such
situations, our analysis of the results of Jensen and Meckling (1976)
and Myers (1977) indicated that capital structure changes may alter
firm value, such that MM1 was violated. The same situation may imply
that dividend policy affects firm value. Here, we give only the briefest
treatment of this possibility.
Both of the agency cost models of capital structure referenced above
include situations where managers, acting in the interest of equity-holders,
transfer value away from debt-holders towards those who own shares.4
Similar activities may be undertaken with dividend policy. Managers may
pay out large levels of dividends (benefiting equity-holders), financing
these payments by rejecting positive NPV projects or by increasing debt
levels. If debt-holders do not anticipate this behaviour, the value of debt
will be reduced while the value of equity increases. Note that, in both
cases, ‘excessive’ dividend payments will lead to lower firm values.
4
Asset substitution
and debt overhang
are examples of such
behaviour.
An interesting feature of this argument is that it predicts that dividend
increases should be reflected in higher market values for equity but
lower market values for debt. This contrasts with the implications of the
asymmetric information-based theories, which, as dividend increases are
good news in general, predict that they should lead to increases in the
values of both debt and equity.
From the preceding section we know that dividend increases result
in higher equity values empirically, consistent with both agency- and
information-based theories. However, recent empirical evidence suggests
that, at least for US firms, corporate bond prices drop when dividends are
cut and don’t change significantly when dividend increases are announced.
Such results would seem to indicate that theories of dividend policy based
on asymmetric information are more realistic than those based on agency
costs.
Summary
We started this chapter by arguing that, like capital structure, dividend
policy should not affect firm value. Subsequent to this, however, we
pointed out several sources of real world imperfection that might lead to
optimal dividend policies (in the sense of firm value maximisation). Such
imperfections included taxation, information asymmetries and agency
costs.
We also explored some of the empirical results on dividend policy.
Empirical evidence shows that equity prices tend to rise after unexpected
dividend increases and fall after unexpected dividend cuts (with bond
prices following a similar pattern). This, we argued, seemed most
supportive of dividend models based on asymmetric information.
The dividend puzzle is far from resolved, however. Much research
work remains to be done in the area to clarify our understanding of the
fundamental determinants of corporate dividend policy. Lintner’s stylised
facts and results from event studies have given us a good empirical basis
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FN2191 Principles of corporate finance
upon which to construct realistic theories of dividend behaviour, and it is
precisely this task that currently confronts finance theorists.
A reminder of your learning outcomes
Having completed this chapter, and the Essential reading and activities,
you should be able to:
•
show that dividend policy (and share repurchases) are irrelevant to
firm valuation under the Modigliani–Miller assumptions
•
discuss the stylised facts of dividend policy as provided by Lintner
•
present the clientele model of dividends
•
discuss the effects of asymmetric information and agency costs on
dividend behaviour.
Key terms
agency costs
asymmetric information
capital structure
clientele model
dividend policy
frictionless markets
Lintner’s stylised facts
Modigliani–Miller irrelevance theorem
personal taxes
share repurchases
target dividend payout level
taxes on capital gains
taxes on dividends
Sample examination questions
1. Describe the model of dividend policy formulated by Lintner (1956)
and detail the stylised facts upon which this model is based.
2. ‘The Modigliani–Miller theorems imply that firms’ dividend policy does
not affect their value in the slightest.’ What assumptions underlie this
statement? Give two scenarios in which the statement is invalid.
3. For tax reasons it is cheaper to pay equity-holders through share
repurchases than with dividends. Nevertheless, many firms use
dividends to pay their investors. What is the signaling explanation for
this?
104
Chapter 8: Mergers and takeovers
Chapter 8: Mergers and takeovers
Aim of the chapter
The aim of this chapter is to explain why managers of firms are engaging
in mergers and acquisitions. With this aim in mind, we first introduce
a stylised model in which efficient takeovers cannot possibly obtain
(Grossman–Hart). We then introduce institutional mechanisms which
enable takeovers to occur. Finally, we investigate whether or not mergers
and acquisitions create value and provide empirical evidence on returns to
shareholders of bidding and target firms.
Learning objectives
By the end of this chapter, and having completed the Essential reading,
you should be able to:
•
discuss motivations for merger activity
•
analyse simple numerical examples of efficient takeover activity
•
detail the argument of Grossman­–Hart (1980) regarding the
impossibility of efficient takeovers
•
present ways in which this analysis can be modified to permit
takeovers to occur.
Essential reading
Brealey, R., S. Myers and F. Allen Principles of Corporate Finance. (Boston, MA;
London: McGraw-Hill, 2016) Chapter 32 (Mergers).
Further reading
Bradley, M., A. Desai and E. Kim ‘Synergistic gains from corporate acquisitions
and their division between the stockholders of target and acquiring firms’,
Journal of Financial Economics 21(1) 1988, pp.3–40.
Copeland, T. and J. Weston Financial Theory and Corporate Policy. (Reading,
MA; Wokingham: Addison-Wesley, 2004) Chapter 18.
Grinblatt, M. and S. Titman Financial Markets and Corporate Strategy. (Boston,
MA; London: McGraw-Hill, 2011) Chapter 20 (Mergers and Acquisitions).
Grossman, S. and O. Hart ‘Takeover bids, the free-rider problem and the theory
of the corporation’, Bell Journal of Economics 11(1) 1980, pp.42–64.
Healy, P., K. Palepu and R. Ruback ‘Does corporate performance improve after
mergers?’, Journal of Financial Economics 31(2) 1992, pp.135–76.
Jarrell, G., J. Brickley and J. Netter ‘The market for corporate control: the
empirical evidence since 1980’, Journal of Economic Perspectives 2(1) 1988,
pp.49–68.
Jarrell, G. and A. Poulsen ‘Returns to acquiring firms in tender offers: evidence
from three decades’, Financial Management 18(3) 1989, pp.12–19.
Jensen, M. ‘Agency costs of free cash flow, corporate finance, and takeovers’,
American Economic Review 76(2) 1986, pp.323–29.
Jensen, M. and W. Meckling ‘Theory of the firm: managerial behaviour, agency
costs and capital structure’, Journal of Financial Economics 3(4) 1976,
pp.305–60.
Jensen, M. and R. Ruback ‘The market for corporate control: the scientific
evidence’, Journal of Financial Economics 11(1–4) 1983, pp.5–50.
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Myers, S. and N. Majluf ‘Corporate financing and investment decisions when
firms have information that investors do not have’, Journal of Financial
Economics 13(2) 1984, pp.187–221.
Ravenscraft, D. and F. Scherer Mergers, selloffs, and economic efficiency.
(Washington D.C.: Brookings Institution, 1987).
Shleifer, A. and R. Vishny ‘Large shareholders and corporate control’, Journal of
Political Economy 94(3) 1986, pp.461–88.
Shleifer, A. and R. Vishny ‘Managerial entrenchment: The case of managementspecific investment’, Journal of Financial Economics 25 1989, pp.123–39.
Travlos, N. ‘Corporate takeover bids, methods of payment, and bidding firms’
stock returns’, Journal of Finance 42(4) 1987, pp.943–63.
Overview
The post-Second World War period has seen an unprecedented amount
of corporate activity resulting in the combination of two or more firms
under a single corporate banner and legal status. Such activity comes in
many forms and is initiated for varying reasons. This chapter gives an
introduction to the concepts underlying merger/takeover/acquisition
activity and provides a basic review of the theory of takeover activity, and
supplies empirical evidence on returns to takeovers.
In line with the arguments presented throughout this guide, we argue
that merger activity should be judged in terms of the value it delivers.
Mergers should be undertaken if they are positive NPV transactions. A
mathematical way of stating this is that:
VXY > VX + VY,
(8.1)
that is, the value of the merged firm created from firms X and Y (VXY)
exceeds the sum of pre-merger values of X and Y (i.e. VX + VY). Such value
may come about through the exploitation of scale economies or elimination
of inefficiencies. We will give a classification of merger and acquisition
behaviour based on the source of value in the following section.
Merger motivations
Following Grinblatt and Titman (2002), we will split merger and takeover
activity into three distinct sub-groups:
•
financial activity
•
strategic activity
•
conglomerate activity.
1. Financial mergers: these are takeovers or acquisitions that are
initiated to take advantage of corporate inefficiencies that lead to the
under-valuation of firms. This allows an acquiring firm to buy assets
cheaply, implement strategies that increase the value of the acquired
firm and then sell on the acquired assets at a profit (if so desired).
Such activity yields a positive net present value. Opportunities
for financial mergers are likely to come about due to managers of
acquired firms following their own, rather than shareholders’, goals
and hence not maximising firm value. In this way, the market for
corporate control is said to exert discipline on a firm’s management.1
The merger wave of the 1980s may be thought of as largely comprised
of such activity. An active market for corporate control (in the form
of hostile takeovers) is therefore an important force that mitigates
the problems arising from the separation of ownership and control in
modern corporations.
106
This is because, if
a takeover occurs,
incumbent management
are likely to lose their
jobs. Hence, assuming
management would prefer
to retain their jobs, the
possibility of takeover
limits managerial scope for
inefficiency.
1
Chapter 8: Mergers and takeovers
2. Strategic mergers: financial mergers generate value through
eliminating corporate inefficiency induced by bad management.
Strategic mergers yield value through the taking advantage of
economies of scale and scope in production, purchasing and
marketing. Hence, horizontal integration activity undertaken to
increase and exploit market power and to take advantage of scale
economies fall into this category. Also, acquisitions that are vertically
integrating may be thought of as strategic activity due to their yielding
lower production costs or marketing expenses. A recent example of
such activity might be the announced link-ups within the French
banking sector in February 1999.2
3. Conglomerate mergers: certain mergers are clearly not motivated
by scale economies and are not attempts to take advantage of
corporate mismanagement. The most obvious examples of such
activity are between firms in very different industries and these
link-ups are known as conglomerate mergers. This type of activity was
very popular in the 1960s and 1970s (although much of the
conglomeration that occurred in these decades was reversed in the
1980s). Motivations for conglomerate merger are unclear. Some have
stated that the element of diversification that conglomeration yields
adds to value. However, given that investors can diversify their own
portfolios in order to reduce risk (i.e. they don’t need firms to diversify
for them), the idea that value is added for this reason is flawed. Along
similar lines, some have argued that a gain from conglomeration is
derived due to lower interest rates that conglomerates are charged.3
Again, however, this argument doesn’t stand up to close scrutiny. One
reason why conglomeration may occur is that it allows firms with large
amounts of cash (who do not want to increase dividends or repurchase
equity) to profitably employ this cash in positive NPV projects.
In early February
1999, BNP and Société
Générale announced
plans to merge. Later,
Paribas entered the
fray, announcing that
it would take over the
other two banks.
2
3
Conglomerates may be
charged lower interest rates
as cash-flow risk is reduced
through precisely the
diversification argument
already mentioned.
Payment method in takeover
Just like we need to pay for our everyday purchases, acquiring companies
need to pay owners (shareholders) of target firms in takeover and merger
deals. Quite often, acquiring companies pay even more than the current
market price of the target firm. This premium is the cost of takeover for
the acquirer.
The payment method in our daily purchases is straightforward: we pay
cash to the seller in exchange for goods. The acquiring company can do
the same. It can simply pay cash to the target’s shareholders who sell the
company. This type of takeover is known as a cash deal. It is important
to note that in such a deal the purchase price is paid out from the firm’s
assets. Hence, the total firm value after the takeover should exclude the
purchase price.
Alternatively, instead of using cash, the acquiring company can offer new
shares to compensate the target shareholders. This type of takeover is
known as a stock deal. Such a deal is often structured as an exchange
offer: for example, every 10 shares of the target company can be
exchanged for three shares of the acquiring company. Once the exchange
is complete, the target company’s shares no longer exist and the acquiring
company’s shares become the only equity claim on the entire post-takeover
company. It is crucial to recognise that the shares offered to target
shareholders do not usually come from the current shareholders of the
acquiring company. Instead, these shares are newly created claims on the
post-takeover company. As we shall see in the following examples, the fair
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share price is the total firm value post-takeover divided by the new total
number of shares outstanding. The new number of shares is calculated
as a pre-takeover number of shares plus new shares offered to the target
shareholders. Note that, unlike in cash deals, stock deals typically do not
involve the transfer of resource from the firm to the target shareholders.
The owners of the target company merely join those of the acquiring
company and also become shareholders of the post-takeover firm.
Example 1:
Consider two firms, X and Y, that compete in the same product market.
Corporation X currently has one million shares outstanding, each with
value $2. Firm Y has 500,000 shares on offer and share price $10. Firm Y
is contemplating a takeover of corporation X, as it knows that corporation
X is being run inefficiently. Firm Y estimates that, if it takes corporation X
over, it could increase firm X’s net cash flow by $300,000 per year. Assume
that these firms are infinitely lived. The relevant cost of capital for firm X
is 10 per cent.
Given the prior information, it is clear that, if firm Y does take over
corporation X, the increase in X’s value would be the present value of a
perpetuity paying $300,000 each year. This present value is $3m, which
represents the gain from the merger.4 It is clear that, given that the merger
creates value, it is socially desirable. However, the terms by which the
merger actually occurs will dictate the net payoffs to the shareholders of X
and Y. For the merger to occur, both net payoffs must be positive.
4
Make sure you can
derive this PV for
yourself.
Assume, for example, that the merger is to occur by firm Y agreeing to
purchase every share in firm X at a price of $3 per share. This implies that
(as there are one million shares in firm X in issue) X’s shareholders get a
total payout of $3m, which exceeds the value of their initial shareholding
(i.e. $2m). Hence firm X’s shareholders are happy to participate in the
merger, as their payoff is $1m. Firm Y’s shareholders are paying $3m for a
firm which, under their management, will be worth $2m + $3m = $5m.
Hence their gain is also positive at $2m, and they are happy to participate.
Note that, quite obviously, the sum of the gains to X and Y shareholders is
the total value creation of $3m.
Another way in which this merger could have been financed is if firm Y
offered to issue a certain amount of new shares and gave these to the
shareholders of firm X instead of cash. Consider the following offer as an
example. One new share in firm Y is exchanged for every four existing firm
X shares. Note that this freshly issued equity will be a claim on the value of
the merged enterprise and hence priced as such.
The value of the merged firm will be the sum of the pre-merger values of X
and Y plus the value created of $3m. The pre-merger value of X is $2m
and that of Y is $5m. Hence the total value of the firm after the merger is
$10m. After the merger there are 0.75m shares in issue. This comprises
the original 0.5m shares in firm Y plus the 250,000 new shares issued.5
Hence the share price of the merged enterprise is:
$
(8.2)
The original shareholders of Y hold two-thirds of the equity of the merged
enterprise, which has a value $6.67m. The value of their original position
is $5m and hence they gain to the tune of $1.67m. The old X shareholders
own one-third of the equity of the merged enterprise, which is worth
$3.33m. Their gain is hence $1.33m, as the value of firm X pre-merger
was $2m. Both sets of shareholders are winners therefore, and hence the
108
5
One new share was
offered for every four old
X shares. As there were
originally one million X
shares outstanding, this
implies 250,000 new Y
shares must be issued.
Chapter 8: Mergers and takeovers
merger goes ahead. Again, note that the sum of the gains is $3m, the total
value created.
Example 2:
Suppose you are the treasurer of Company A and you are investigating the
possible acquisition of Company B. You have the following basic data:
Company
A
B
Next year’s expected earnings per share
£5.00
£1.50
Next year’s expected dividends per share
£3.00
£0.80
1,000,000
600,000
£90
£20
Number of shares
Stock price
You estimate that investors currently expect a steady growth of about 6 per
cent in B’s earnings and dividends. Under new management this growth
rate would be increased to 8 per cent per year, without any additional
capital investment required.
Let us first calculate the gain from the acquisition. To find the appropriate
discount rate (r) for the common stock of Company B, we use the
perpetual growth model of stock valuation:
0.80 = 20 ⇒ r = 0.10
r – 0.06
Under the new management, the value of the merged firm (call it AB)
would be the value of Company A before the merger plus the value of B
after the merger, or:
( 0.10$0.80
– 0.08
(
PVAB = (1,000,000 * $90) + 600,000 *
= $114,000,000.
The gain from the acquisition is then:
Gain = PVAB – (PVA + PVB) = $114,000,000 – ($90,000,000 + $12,000,000) = $12,000,000.
It is clear that, given that the merger creates value, it is again socially
desirable. However, the costs of the merger for A will be typically different
in a cash deal and in a stock deal. Let us calculate these costs under the
two different payment methods.
Let us start with the cost of acquisition in case of a cash deal. Suppose A
pays $25 in cash for each share of B. Then:
Cost = Cash Paid – PVB = ($25 * 600,000) – $12,000,000 = $3,000,000.
Since the acquisition gain is larger than this cost, shareholders of both
companies would be happy to make such a deal. Shareholders of B
are paid $25 for their stock worth $20, and get in total the cost of the
acquisition: ($25 – $20) * 600,000 = $3,000,000. The owners of A get the
rest of the gain $12,000,000 – $3,000,000 = $9,000,000.
Now let us see what happens in a stock deal. Suppose A offers one share
of A for every three shares of B. Because this acquisition is financed
with stock, we have to take into consideration the effect of the merger
on the stock price of A. After the merger, there will be 1,200,000 shares
outstanding (1,000,000 old shares plus 600,000/3 new shares given to the
owners of B). Hence, the share price will be the value of AB after merger
divided by the new total number of shares: $114,000,000/1,200,000 =
$95.00. Therefore, the cost will be the number of shares sold to owners
of B times the new price, minus PVB: Cost = ($95 * 200,000) – ($20
*600,000) = $7,000,000. This cost is more than twice the cost of the
previous cash deal. However, the gain from the acquisition is still larger
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FN2191 Principles of corporate finance
and shareholders of both firms would be happy to perform it. Shareholders
of B exchange three shares worth 3 * $20 = $60 for one share worth
$95 and thus receive again the cost of the acquisition of $7,000,000.
Shareholders of A get ($95 – $90) * 1,000,000 = $5,000,000 which is
exactly the gain minus the cost of the stock deal.
Finally, let us see how the costs of the cash offer and the share offer alter if
expected growth rate of B is not changed by the merger. If the acquisition
is for cash, the cost would not be changed since we still pay $25 per each
share of B: Cost = $3,000,000. If the acquisition is for stock, the cost is
different from the one calculated before. This is because the new growth
rate affects the value of the merged company. This, in turn, affects the
stock price of the merged company and, hence, the cost of the merger.
It follows that the new value of the merged company is: PVAB = ($90 *
1,000,000) + ($20 * 600,000) = $102,000,000. The new share price
will be: $102,000,000/1,200,000 = $85.00. Therefore: Cost = ($85 *
200,000) – ($20 * 600,000) = $5,000,000. Note that this is lower than
the cost of $7,000,000 calculated before. The lower growth rate changes
the post-valuation of the merged company and lowers the price of AB.
Hence, the cost of a share deal goes down.
The market for corporate control
As a result of the separation of ownership and control, managers may not
act in the firm owners’ best interest. Managers may:
•
exercise insufficient effort
•
make extravagant investments (Jensen (1986))
•
use entrenchment strategies; that is, take actions that hurt shareholders
in order to secure their position (Shleifer and Vishny (1989))
•
increase their private benefits from running the firm by engaging in a
variety of self-dealing behaviour (Jensen and Meckling (1976)).
This moral hazard between firms’ managers and owners may be mitigated
through corporate governance. A firm’s board of directors in principle
monitors managers on behalf of owners. It is furthermore in charge of
managers’ compensation, audits and oversight of risk management.
Moral hazard between firms’ managers and owners may be mitigated
through the market for corporate control. In the market for control,
disciplinary takeovers, which are usually hostile, create value by
substituting efficient teams for entrenched money-wasting managers.
These disciplinary takeovers may be needed to keep managers on their
toes if the board of directors is an ineffective monitor and, more generally,
if corporate governance is failing. This is particularly important for firms
with a disperse mass of small shareholders. However, as we will see in the
following section, free-rider problems make hostile takeovers particularly
difficult when ownership is disperse.
The impossibility of efficient takeovers
In the previous sections, we examined the types of merger activity
commonly seen in reality and the motives for such activity generally given
by managers. In this section, we will introduce you to a simple theoretical
model of merger activity, which yields the result that any efficient takeover
bid will fail.6 This extreme outcome comes from rational shareholders
free-riding on the (effort and) firm value improvement delivered by a
takeover raider.
110
The model developed
in this section is based
on Grossman and
Hart (1980). Efficient
takeover activity is
defined as activity for
which the increase in
the market value of the
acquired firm exceeds
any associated costs.
6
Chapter 8: Mergers and takeovers
Assumptions
Our assumptions here are as follows:
•
the firm is subject to a takeover bid from an external takeover raider
•
firm value will improve, if the bid succeeds: the value increase is
common knowledge
•
the equity of the target firm is held by many, small shareholders
•
the raider incurs administrative takeover costs of c.
Assume that the current firm value is y, and let the firm value if the
takeover were to succeed be y + z. The takeover is efficient as the
following condition holds:
z > c.
(8.3)
The raider must gain at least 50 per cent of the shares to implement the
takeover. Note, however, that as shareholders are assumed to be identical,
if any one shareholder finds it profitable to tender their shares to the
raider then all will. The raider offers a premium p over the current firm
value to equity-holders for their shares. Hence, for the bid to be profitable
for the raider we must have:
z > p + c,
(8.4)
that is, the improvement in firm value must exceed the cost of takeover
and the premium paid to original equity-holders.
Consider the position of a single, small shareholder. As their shareholding
is minor relative to the sum of all equity, they do not consider their
decision to be pivotal. Assume that they believe that the bid will be
successful. Then they will only sell their shares to the raider if:
p > z,
(8.5)
that is, it is only in the shareholder’s interest to tender if the premium they
get outweighs the money they would make by hanging on to their equity
and profiting from the value improvement associated with the takeover.
If the shareholder believes that the takeover bid will fail, then they will
be indifferent between offering their shares to the raider and not offering
them.
Our key result can be derived from a comparison of equations 8.4 and
8.5. They are clearly contradictory, implying that the raider cannot
simultaneously succeed with the bid and make a profit. Hence, profitable
takeover activity cannot occur.
A crucial assumption here is that all shareholders are small in size.
This then implies that none of them perceive themselves to be pivotal
to the success of the takeover bid. This results in all small shareholders
attempting to free-ride on the value improvement offered by the raider
and, ultimately, the bid then fails.
Another way to see the result is as follows. A premium that allows the
raider to make a profit must satisfy the following condition:
p ∈ (0, z – c).
(8.6)
However, a premium in this region implies that shareholders are better off
not selling to the raider and hanging on to their equity as:
y + p < y + z – c < y + z.
(8.7)
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The first term in equation 8.7 is the money they get for selling to the
raider, and the final term is the value of their shareholding if they do not
sell (conditional on the bid being successful).
Two ways to get efficient takeovers
In light of casual and formal empirical evidence, the result of the previous
section seems untenable. Most would argue that at least some of the
takeovers that occur in reality lead to both the raider and the target
shareholders making some money. This section provides two ways in
which we can overturn the results from the previous section.
Dilution
Grossman and Hart (1980) first pointed out the free-riding problem we
discussed in the preceding section. In the same paper they also indicated a
solution to the free-riding problem. This solution was dilution.
Dilution is the ability of a raider to extract value from the target, if they
successfully complete the takeover. This might be done by placing themself
in charge and paying themself an astronomical salary, selling the firm’s
output to another corporation they own at a very low price, and other
diverse means. Hence, if the takeover is successful and the raider dilutes
the firm, the firm’s market value ends up being less than y + z (to use the
notation of the previous section).
To make the prior argument concrete, assume the raider can appropriate
an amount φ of firm value if the takeover is successful. Hence, if
shareholders believe the bid will be successful, they will be willing to
tender their shares if offered a premium (over current value) that satisfies
the following condition:
p > z – φ.
(8.8)
The raider makes money if equation 8.4 holds, and this leads to the
following condition for profitable takeover activity to occur:
z – c > p > z – φ | φ > c.
(8.9)
The interpretation of equation 8.9 is simple – takeovers can be
profitable if the amount the raider can grab through dilution exceeds the
administrative cost of takeover. Note also that, once they gain control,
the raider need not actually dilute the firm. Merely the threat of dilution
allows the takeover to proceed.
A final issue about dilution that should be addressed is the source of the
raider’s ability to dilute. Grossman and Hart assume that the target firm is
originally a private enterprise. The original owners of the firm then decide
to take the firm public and write provisions that allow dilution into the
corporate charter. These individuals do this in order to ensure that the firm
is efficiently run in future years (i.e. they write in dilution provisions to
allow efficient future takeover activity).
Large shareholders (toehold)
Another scenario in which efficient takeover activity might occur is when
a single shareholder owns a large block of equity. In such a situation we
can think of the large shareholder and the raider synonymously (i.e. it is
the large shareholder who can possibly implement an efficient takeover).
Sticking with the notation used in the Grossman and Hart (1980) analysis,
assume that the large shareholder originally owns a proportion α of firm
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Chapter 8: Mergers and takeovers
equity (toehold). Assuming no dilution, the condition for shareholders to
tender if they believe the bid will succeed is again:
p > z.
(8.10)
Hence, shareholders require a premium that exceeds the size of the value
improvement. The condition that must hold for the large shareholder to
profit is:
z > (1 – α)p + c,
(8.11)
that is, the value improvement must exceed the cost of takeover, plus the
premium the large shareholder must pay to buy the remaining (1 – α) of
firm equity. Both equations 8.10 and 8.11 are satisfied when the following
condition holds:
αz > c.
(8.12)
Hence, large shareholders can implement efficient takeovers, when the
proportion of the value improvement that accrues to their original holding
exceeds the takeover cost.
Thus our analysis tells us that large shareholders are important in that
their existence allows the free-rider problem to be circumvented. This is
exploited in Shleifer and Vishny (1986) who also relax the assumption
of perfect information. In their analysis, the value improvement is only
known by the large shareholder, and this provides another reason for
the existence of takeover activity in the model. The role of the large
shareholder is emphasised in some of the empirical predictions from their
model. They show, for example, that firm values increase with the size of
the large shareholding. The intuition for this is that a larger shareholding
means more efficient takeover decisions and hence a firm with larger
future values and hence greater current market value.
Empirical evidence
Are mergers and acquisitions value-enhancing? This section reviews
empirical evidence from two types of studies: accounting and event studies.
The first type, accounting studies, examine financial results
(accounting data) to draw inferences about the underlying economic
impact of mergers and acquisitions. These studies tend to investigate
whether acquirers outperform their non-acquirer peers. Alternatively, these
studies compare the performance of the combined firm following a merger
or an acquisition with the performance obtaining prior to the transaction.
Performance tends to be measured by net income, operating margin, or
return on equity or assets.
The second type, event studies, do not directly measure performance.
Instead, these studies attempt to measure the value created by the merger
or acquisition through abnormal stock returns around the announcement
date of a tender offer. Hence, event studies rely on financial markets being
efficient.
Accounting studies
The empirical evidence from accounting studies is mixed. Ravenscraft and
Scherer (1987) investigate more than 5,000 mergers occurring between
1950 and 1975, calculate and compare the post-merger performance of
acquiring firms with that of non-acquiring firms in the same industries,
with performance being measured as return on assets, and report that
performance is 1 to 2 per cent less for acquiring firms.
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FN2191 Principles of corporate finance
In contrast, Healy, Palepu and Ruback (1992) examine 50 large mergers
between 1979 and 1983 and report improvement in performance of the
combined firms following the mergers, where performance is measured
by sales and profits. Asset productivity is furthermore shown to improve
significantly following acquisitions.
The difference in findings between both accounting studies may be due to
differences in the motivation for mergers and acquisitions. The motivation
for many of the mergers in the 1960s and 1970s (and much fewer in the
1980s) was diversification and there can be efficiency losses associated
with diversification. Accounting studies are, however, vulnerable to
discrepancies introduced by accounting for mergers and acquisitions.
Event studies
Empirical evidence from event studies suggests that shareholders from
target firms gain from takeovers. This should not come as a surprise as
target shareholders require a premium in order to induce them to sell their
shares to the acquiring firm. Jensen and Ruback (1983) report that target
share prices increase, on average, by about 16 to 30 per cent around the
date of the announcement of a tender offer. Empirical evidence reported
by Jarrell, Brickley and Netter (1988) suggests that these returns increased
substantially during the 1980s to an average of about 53 per cent.
Jensen and Ruback (1983) furthermore report that the average return to
shareholders from target firms in negotiated mergers is, however, only
about 10 per cent.
The empirical evidence from event studies on returns to shareholders of
bidding firms tends to be quite mixed: returns to bidders are, on average,
small, time-varying, but may be positive or negative. For instance, Jarrell
and Poulsen (1989) show that the announcement return to bidder in
tender offers dropped from a statistically significant 5 per cent gain in
the 1960s to an insignificant 1 per cent loss in the 1980s. The means of
payment used for the transaction is furthermore shown to have a major
effect on returns to bidders. For instance, Travlos (1987) finds that the
average return on the two days around the announcement of a cash offer
is only marginally different from zero (+0.24 per cent). In contrast, in
acquisitions financed by an exchange of equity, stock prices of bidding
firms fall, on average, by about 1.5 per cent. The means of payment may
hence act as a signal for the quality of the bidder. Consistent with the
pecking order theory reviewed in Chapter 6 (Myers and Majluf (1984)),
bidders offer stock when they believe that their stock is overvalued. A
stock offer may furthermore indicate that the bidder was unable to get any
financial backing from a bank or another financial institution.
Adding the bidder and target returns generates positive returns, implying
that, on average, there is a net gain to shareholders around the time of the
merger or acquisition. For instance, Bradley, Desai and Kim (1988) provide
evidence suggesting that successful tender offers increase the combined
value of the merging firms by an average of 7.4 per cent or $117m (stated
in 1984 dollars). The empirical evidence from event studies hence suggests
that mergers and acquisitions are, on average, value enhancing.
Summary
In this chapter we have given you an overview of the facts involved in,
and theory surrounding, mergers and takeovers. The main lesson of
this chapter is that mergers that should go ahead (i.e. efficient merger
activity) are those that are positive NPV transactions. See equation 8.1.
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Chapter 8: Mergers and takeovers
Such positive NPV can come from exploitation of economies of scale in
production or sales (strategic mergers), removal of bad management and
elimination of inefficiencies (financial mergers) or possibly through the
purchase of firms in an unrelated industry but with a strong portfolio of
possible investment projects (conglomerate mergers).
We discussed theoretical models indicating that such efficient merger
activity may be blocked in economies without frictions or information
asymmetries. The source of problems here is shareholder free riding.
The prevention of profitable takeovers by free riding is shown to
disappear when allowances are made for dilution, large shareholders and
asymmetric information.
Towards the end of the chapter, we investigate whether mergers and
acquisitions are value-enhancing. Empirical evidence from event studies
suggests that mergers and acquisitions create, on average, joint value.
Most of the value created is, however, appropriated by the shareholders of
target firms.
A reminder of your learning outcomes
Having completed this chapter, and the Essential reading, you should be
able to:
•
discuss motivations for merger activity
•
analyse simple numerical examples of efficient takeover activity
•
detail the argument of Grossman­–Hart (1980) regarding the
impossibility of efficient takeovers
•
present ways in which this analysis can be modefied to permit
takeovers to occur.
Key terms
asymmetric information
bidders
capital structure
clientele model
conglomerate mergers
corporate governance
dilution
disciplinary takeover
efficient takeovers
event studies
financial mergers
free-riding
frictionless markets
Grossman–Hart model
large shareholders
mergers and acquisitions
strategic mergers
targets
takeover premium
toehold
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Sample examination questions
1. Present the assumptions behind, and give a derivation of, the
Grossman–Hart analysis, which implies that efficient takeover activity
is impossible.
2. Describe the dilution solution to the preceding solution as suggested
by Grossman and Hart.
3. How does the existence of a large shareholder affect the Grossman–
Hart result?
4. Exporting firm Euro Importing has a market value of €100 million.
There are one million shares outstanding, 20 per cent of them are
controlled by the CEO who is the original founder. The present value
of the firm’s profits is €130 million, however the CEO uses up €30
million of firm value for pet projects that do not add value to the firm.
All other shares are controlled by dispersed shareholders.
An asset management firm worth €500 million, and which has five
million shares outstanding, is considering acquiring Euro Importing.
a. What is the current price per share of Euro Importing?
b. If the acquirer buys 51 per cent of the shares, it would control the
firm and cancel wasteful perk spending. What is the maximum
the acquirer would be willing to pay for 51 per cent? What if
purchasing 51 per cent also involved €1 million in additional fees?
c. The acquirer announces that it will attempt a takeover of Euro
Importing by purchasing shares at the price in (b). Assume €1
million fees as in (b). What happens to the price per share if (i)
the market believes the raid will succeed; (ii) the market believes
the raid will fail. What does a rational investor do if the rest of the
market believes (i)? If the rest of the market believes (ii)? Is there
an inconsistency? What happens to the price per share of the asset
management firm if (i)? If (ii)?
d. Suppose half of the dispersed shareholders believe the acquirer
succeeds and half believe that he will fail. Does the raid succeed?
e. How many shareholders are willing to sell if the offer price is
€130? How many are willing to sell if the offer price is €100?
Assume you can linearly interpolate the probability that a
shareholder succeeds between these two extreme values. What
price must be paid for the raid to succeed? Is it worth it to the
acquirer? What if the fees were €6 million?
f.
Suppose that after buying the firm, the acquirer can also use
up €30 million on private benefits. At what price would the
shareholders now be willing to sell? Relate this to Grossman and
Hart’s solution to the free rider problem.
g. Explain why current ownership would be willing to outbid the
acquirer.
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Chapter 9: Risk management and hedging
Chapter 9: Risk management and
hedging
Aim of the chapter
The aim of this chapter is to understand why and how companies manage
risks in their course of operation. With this aim in mind, we will discuss
the reasons, typical financial instruments and the associated costs of risk
management.
Learning objectives
At the end of this chapter, and having completed the Essential reading and
activities, you should be able to:
•
explain why and how companies manage risk
•
explain and evaluate the cost of hedging
•
explain covered and uncovered interest rate parity, and analyse the
associated arbitrage possibilities.
Essential reading
Brealey, R., S. Myers and F. Allen Principles of Corporate Finance. (Boston, MA;
London: McGraw-Hill, 2016) Chapters 26 (Managing Risk).
Further reading
Grinblatt, M. and S. Titman Financial Markets and Corporate Strategy. (Boston,
MA; London: McGraw-Hill, 2011) Chapters 21 (Risk Management and
Corporate Strategy), 22 (The Practice of Hedging), and 23 (Interest Rate
Risk Management)
Introduction
In the previous chapters, we have analysed:
•
valuation and investment decisions
•
dividend decisions
•
financing decisions.
One of the most important roles of a CFO in running a business is to
manage the potential risks associated with the operations. In this chapter,
we study risk management and hedging. In particular, we would like to
understand which risks should be hedged, and how to find the appropriate
instruments to hedge these risks. We are going to talk about why and how
firms manage risks. We will consider three main reasons why firms hedge
their risks:
•
bankruptcy costs
•
cost of financial distress
•
risk averse managers.
Then we will analyse several possible instruments to reduce risks:
•
insurance
•
future contracts
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•
forward contracts
•
swaps.
We will elaborate on each of those and see how they can be beneficial to
reduce future uncertainty. However, managing risks via hedging is typically
not for free. We will talk about the two main costs of hedging:
•
transaction costs
•
risk premium.
Finally, we will briefly talk about one application of futures for hedging in
the foreign exchange market – the carry trade, and the resulting covered
and uncovered interest rate parity.
Why do firms hedge?
Let us first understand the definition of hedging: hedging is a set of
financial transactions which offset the risk of a real asset. When the real
asset rises in value, the hedge loses money. On the other hand, when the
real asset falls in value, the hedge makes money. For example, suppose
you have one share of Facebook, but are afraid that the share price might
drop. You can hedge this risk by buying a put option on the stock: when
the stock price rises, the put option loses money (all else equal); however,
when the price drops, the put is increasing in value, thereby offsetting
part of the losses on the stock. Essentially, the hedge should be negatively
correlated to the real asset as we will see later on. If the hedge is perfect,
the gains from the hedge and the losses from the real asset are perfectly
correlated. This means that the total return of the portfolio consisting of
the real asset and the hedge should be a constant. Imperfect hedge is when
the portfolio return still fluctuates so there are still some residual risks.
An example of a simple perfect hedge in the previous situation would be a
short sell of one Facebook share – the total return of the portfolio will then
be 0 (assuming no transaction costs).
What are the consequences of hedging? The most important one is that
risks are transferred, not eliminated. For example, suppose you are
worried about getting laid off from your job and want to hedge this risk by
buying unemployment insurance. The risk of getting laid off is still present
though: the fact that you own insurance does not eliminate the possibility
of getting unemployed. What changes is that now someone else is bearing
the risk – the government in this case. Another consequence of hedging
is that if the insurer cannot diversify the risk (the risk is systematic), then
the hedger has to compensate by paying a premium. Thus, even a perfect
hedge of a systematic risk loses money on average.
Unemployment insurance is one of the many hedging activities we are
involved in our everyday life (although we might not use the word
hedging to describe them). Individuals hedge personal risks all the time:
they buy health, home owner or auto insurance to reduce the risks of
losses. How does insurance work in practice? Quite simple: the individual
pays a fixed amount called the insurance premium, to the insurance
company. In exchange, the insurance company pays the variable cash
flow (the loss) in case of hazards: sickness, the home burns down or there
is a car accident. If there is no insurance event during the contract, the
individual just pays the insurance premium but gets nothing in return.
However, if there is an accident during the insurance contract, the
insurance company steps in and covers part or all of the losses. Hence,
by buying insurance, we perform a financial transaction that offsets the
risk of a real asset – we hedge. Insurance, as well as hedging in general,
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is not a zero-NPV transaction. As we briefly mentioned earlier, the hedger
pays a premium to the insurer. On top of that, insurance companies
have advantages and disadvantages in bearing risk. Let us talk about
advantages first.
One of the key advantages is that insurers have better skills in estimating
probabilities – they have more data and can evaluate more precisely the
likelihood of an insurance event. For example, they can estimate the
probability of your house burning down based on the location of the
house, the number of rooms, the number of houses burned down in the
area for the past years, etc. Insurance companies have also more skills in
identifying risk-reduction techniques. For example, in the USA, insurance
companies use software to evaluate the driving skills of the individuals
they insure; based on the evaluations, the insurance premium can be
higher or lower. In response, individuals driving the cars might reduce
their driving risk in order to get higher scores. Another key advantage of
insurance companies is that, by pooling many individual risks, they can
diversify the risks (recall the benefits of diversification and the law of large
numbers).
However, there are some disadvantages in bearing risk. First, just like
usual companies, insurers have to pay wages to their employees, and bear
other administrative costs. Second, and more important, insurance creates
a bulk of potential adverse selection and moral hazard problems. Let
us take house insurance as an example. Suppose there is a home owner
(Home Owner A) who knows better than the insurance company about
potential issues with their house that can cause an insurance event. For
example, they know that there are some electricity issues that can cause a
fire in the house but the insurance company is unaware of those. If there
are many home owners like Home Owner A in the market, the insurance
company will be unable to distinguish between them and honest owners.
As a result, it will be charging too high insurance premium assuming every
customer is like Home Owner A. This could lead to the entire insurance
market breaking down as nobody would find it optimal to buy insurance at
the high premium. This is the adverse selection problem.
To illustrate the moral hazard problem, let us take car insurance as an
example. Suppose there is a risky driver with a luxurious car who would
like to insure against a car crash. However, once fully insured, they
no longer find it rational to drive responsibly. Even if they crash their
expensive car, the insurance company will compensate them with money
to buy a new one, so why should they care about the damages? This is the
moral hazard problem – one does not fully bear the consequences of one’s
own actions.
The last disadvantage of bearing risk by insurance companies is that the
risk pool may have correlated risks. Remember, the crucial assumption of
the law of large numbers is that the random draws are uncorrelated. Once
this assumption is violated, we cannot use the law to estimate probabilities
correctly. Assuming no correlation was one of the most serious mistakes
in finance. In the financial crisis of 2008, one of the largest insurance
companies, AIG offered credit risk insurance to a pool of mortgages, which
was assumed to have uncorrelated defaults. However, many of these
mortgages were correlated which caused huge losses to AIG. For example,
the mortgage payers could default simultaneously if they lost their job at
the same time, or if the economy-wide house price went down. Some of
these mortgage payers worked for the same factory so when the factory
was closed down and workers laid off, their defaults suddenly became
highly correlated.
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Up to now, we looked at insurance from the insurance companies’
perspective. Let us now turn to the insuring side. Since hedging
transactions are not free (not zero-NPV transactions), do firms need to
hedge? In a Modigliani–Miller world, the answer is no. Why? First, there
should be no consequence of firm failure as all the failure risks should be
fairly priced. Thus, there should be no room for lowering bankruptcy costs
by hedging. Second, under the MM assumptions, investors can undertake
the same transactions as firms and hence, can hedge on their own.
Therefore, there should be no scope for separate insurance companies that
perform the hedging on behalf of investors. In practice, however, hedging
is an important aspect of firms’ operations. So why do firms hedge? Some
of the MM assumptions must be violated. In the remainder of this section,
we provide three reasons for that:
•
bankruptcy costs
•
cost of financial distress
•
risk averse manager.
Let us elaborate on each.
Bankruptcy costs
How do we reduce bankruptcy costs? One way to achieve this target is
by reducing the probability of default. Sometimes, however, the financial
market for the risk may not exist. For example, suppose you are a UK
company, and you want to hedge against unfavourable outcomes for
your activities in case London becomes a less important financial centre.
However, a contract that pays off in this case might simply not exist. A
possible way to hedge is then for the company to establish a subsidiary
outside the UK, thereby diversifying its activities.
Another obvious non-hedging approach to reduce the default probability
is to avoid any kind of leverage altogether. In the extreme case, when the
firm has no debt, there is zero probability of default. Would this be optimal
for the company? Not necessarily. Recall companies can increase their
value by taking debt because of the interest tax shield. Hence, they can
find it optimal to take on leverage to improve valuation indicators even
though this increases default risk. There are two main types of leverage
debts
that companies manage: financial leverage assets
, and operating
fixed costs
leverage total costs .
(
(
(
(
Alternatively, firms use financial contracts to lower the default probability
and thus, bankruptcy costs. By using financial arrangements with
other entities, a company can shift resources from good outcomes
to bad outcomes, thereby reducing the cash flow risk. The firm’s
aggregate performance (including the payment associated with the
financial arrangements) in the good state would be lower, but the firm’s
performance in the bad state would be less devastating. Hence, these
financial arrangements reduce the probability of bankruptcy in the bad
state. Let us illustrate the last point with a simple example which shows
how hedging activities can decrease the default probability.
Example. Hedging with financial contracts
Suppose two firms: A and B, have the following cash flows shown in Table
9.1. Both states are equally likely. Whenever the cash flow is less than 60,
the firm fails. Bankruptcy costs are 20 per cent of firm value, so if the cash
flow is 50, the firm fails and its value will be 40 due to bankruptcy.
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State 1
State 2
Firm A
50
100
Firm B
100
50
Table 9.1: Cash flows in the different states.
The firm value (for both A and B) without hedging (since the probability
of each state is 50 per cent) is 0.5*100 + 0.5*50*(1 – 20%) = 70
But can the firms do better than that? Can they write a contract that
allows them both to avoid bankruptcy and the loss of 20 per cent in the
bad state? Yes. Suppose the two firms can sign the following contract: in
state 1, firm B gives firm A 25; in state 2, firm A gives firm B 25. The new
cash flows are shown in Table 9.2.
State 1
State 2
Firm A
75
75
Firm B
75
75
Table 9.2: New cash flows in the different states.
In this case, there is no bankruptcy. The firm value is 0.5*75+0.5*75=75.
This is larger than the firm value without hedging (70). The value of
hedging is 75 – 70 = 5 for each firm, which are exactly the savings from
avoiding the bankruptcy loss of 20%*50 = 10 in the bad state. Since the
probability of each state is 50%, the expected savings are 50%*10 = 5.
Cost of financial distress
This type of cost arises if the company has investment opportunities at
a time when the company’s cash flow is low. The firm can have many
positive NPV projects but if there is not enough money to invest in them,
the company might be forced to sell securities at lower prices in order to
attract funding for the projects. This is costly and can also lead to higher
perceived risk. In some cases, firms might be even forced to forego the
positive NPV projects because of a lack of capital to invest. Firms would
like to hedge against such unfavourable outcomes. A crucial point to
consider is the correlation between investment opportunities and cash
flows.
If investment opportunities and cash flows are not constant then hedging
can be value enhancing or value destroying. Let us elaborate on this. In
case cash flows and positive NPV opportunities are positively correlated,
hedging is not beneficial. If there are no positive NPV projects when a
firm’s cash flow is low, and, to the contrary, if there are many positive NPV
projects when a firm’s cash flow is high, the firm does not need to hedge.
It has enough money to invest in the good state but does not need money
in the bad state as there are no projects then either. Hence, in this case,
hedging does not create value.
On the other hand, if cash flows and positive NPV opportunities are
negatively correlated, hedging is beneficial. If the firm has many positive
NPV projects at a time when cash flows are low, and, to the contrary, has
few positive NPV projects at a time when cash flows are high, hedging
can be profitable because it pays off exactly when the firm needs cash the
most. Let us illustrate these crucial points with two simple examples which
show the importance of correlation for hedging activities. In the first one,
hedging creates no value, whereas in the second, it creates benefits for the
company.
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Example. Positive correlation and hedging
Suppose cash flows and investment opportunities are positively correlated.
The cash flow is either 60 or 100 with equal probability. A firm has an
investment project that costs 75 and returns NPV of 20 in the good state
(when cash flow is 100) only. If the firm hedges, it has cash flow of 0.5*60
+ 0.5*100 = 80 in both states. In the good state, it has also the positive NPV
project that gives additional 20 (see Table 9.3).
State 1
State 2
Unhedged Asset Cash flow
60
100 + 20
Hedged Asset Cash flow
80
80 + 20
Table 9.3: Cash flows with positive correlation.
If the firm hedges it has an expected cash flow of 0.5*80 + 0.5*(80 + 20) =
90. If it does not hedge, the expected cash flow is still 90: 0.5*60 + 0.5*120
= 90. Hence, there are no gains from hedging as the expected cash flow
from hedging equals that from not hedging. Let us now consider the
opposite case when hedging does create benefits.
Example. Negative correlation and hedging
Suppose now that cash flows and investment opportunities are negatively
correlated. The cash flow is again either 60 or 100 with equal probability.
However, the firm has an investment project that costs 75 and returns NPV
of 20 in the bad state (when cash flow is 60) only. If the firm hedges, it has
again a cash flow of 80 in both states. However, now in the bad state, it
also has the positive NPV project that gives additional 20 (see Table 9.4).
State 1
State 2
Unhedged Asset Cash flow
60
100
Hedged Asset Cash flow
80+20
80
Table 9.4: Cash flows with negative correlation.
Thus, if the firm hedges, it has an expected cash flow of 0.5*(80 + 20) +
0.5*80 = 90. If it does not hedge, the expected cash flow is only 80: 0.5*60
+ 0.5*100 = 80. Hence, there are gains from hedging as the expected cash
flow from hedging is larger than that from not hedging. Where does the
benefit come from? It is due to the fact that with hedging, the company
does not forego the positive NPV project and gets the full NPV of 20 with a
probability of 50%: 0.5*20 = 10 = 90 – 80.
Risk averse manager
Another reason for hedging is that firms’ managers are risk averse. As
such, they would be willing to diversify the risk of being dependent on
the success of their own company. However, it is not easy for them to
do so. Compared to outside investors who can easily buy a share of a
similar company, or buy downside protection with options, managers
cannot undertake such transactions. Why? Let us think. Suppose you are
an outside investor who holds shares in Google. You are worried that the
share price might drop so you decide to hedge your position by buying
put options (remember, these appreciate in value if the price drops).
This is a reasonable hedge that minimises the risk of Google doing badly.
Now suppose that you are one of Google’s managers and you decide to
perform the same transaction. Should the company allow you to do so?
If they do, then you might be incentivised to bring down the company
and profit on your put position. This simple example illustrates that it is
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optimal to expose managers to risks in order to maintain their incentives.
If managers’ compensation is tied to the firm’s success, this creates no
conflict of interest and forces managers to work hard to increase the firm’s
value. Hedging via bearish positions such as the put described above,
might create conflicts of interests and destroy managers’ incentives.
At the end of this section, let us discuss the potential danger of ‘overhedging’, that is speculation. Speculation is one of the bad reasons for
hedging. However, in practice, it is difficult to differentiate hedging
from speculation. Hedging risk requires sophistication but the treasury
departments of many firms do not have the knowledge and/or guidance
on how to reduce risk, especially at the highest level. In fact, firms may be
tempted to gamble as in many cases those hedging get more credit if they
make money rather than avoid losing money. This can be dangerous and, as
we are going to see in the example below, even detrimental in some cases.
Example. China Eastern Airlines
The largest costs for a typical airline company are fuel costs, which directly
depend on the oil price. Higher oil prices mean higher costs and lower
profits. To hedge the risk of high oil prices, airline companies bet on the
increase of oil prices. If the price increases, they make money on the bet
but lose money from their main business. To the contrary, if the oil price
tanks, they lose money on the hedge but get more profits from their airline
business. China Eastern Airlines decided to perform the hedge outlined
above. Prior to 2008, the oil price was rising and this hedge delivered
money to the company at the time when it was losing profits from the
airline business. Based on the good results, the company’s management
turned the usual hedge into speculation on oil prices. They over-hedged
in 2008, betting on oil price increase much more than what was necessary
for their normal demand of aviation oil. The oil price dropped and in usual
circumstances this would have been good news for the company as it
had to pay lower fuel costs. However, due to its speculation activities, the
company accumulated staggering loss of approximately 6 billion RMB on
top of an operating loss of 14 billion. This drove the firm’s leverage ratio
to 115 per cent. Ultimately, the firm went bankrupt. The example of China
Eastern Airlines illustrates the potential disastrous consequence of turning
hedging into speculation.
Activity
Which of the following firms may be more likely to hedge risks? Give a brief explanation:
a. Private firms where investors are not diversified.
b. Opaque firms with significant asymmetric information problems.
c. Intangible firms that are more exposed to costs of financial distress.
d. All of the above described firms.
Typical financial instruments for hedging
After we established several reasons for firms to manage risks via hedging,
the next question is: how to perform the hedge? In this section, we will
introduce four types of financial contracts that are commonly used for
hedging purposes:
•
insurance
•
future contracts (aka futures)
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•
forward contracts
•
swaps.
Futures, forward contracts and swaps belong to the asset class of
derivatives. Derivatives are financial agreements/instruments/contracts
whose returns are linked to, or derived from, the performance of
underlying assets such as equity, bonds, currencies or commodities. We
are already familiar with some basic derivatives: call and put options.
Remember, the call option gives you the right, but not the obligation to
buy the underlying asset in the future for a price fixed today; the put
option gives you a similar right but to sell the asset. The value of both
these simple derivatives is derived from the price of the underlying asset.
For the remainder of this section we are going to discuss each type of
financial contract used for hedging in more detail.
Let us start with insurance. We already briefly talked about the main
features of this type of hedging, so let us summarise the key points.
In an insurance contract, the firm pays a fixed amount (the insurance
premium) in exchange for the insurance company paying the variable
cash flow (the loss) instead of the firm. This exchanges a variable cash
flow for a fixed one. Insurance is against (mostly idiosyncratic) risk. By
selling many policies, the insurance company diversifies much of the risk
internally as it pools many idiosyncratic risks that cancel each other out.
Moreover, because of the law of large numbers, the insurance company is
able to predict the fraction of insurance events for the pool. Essentially, the
probability is no longer uncertain but deterministic. The only risk which
is left in the insurance company is the systematic risk, which is passed to
shareholders through the securities market, where the security holders
diversify the risk.
Forwards and futures are another way of hedging the future uncertainty.
They are agreements to sell an asset at a future date at a fixed price set
today. The transaction price set today is called the forward/future price.
For example, an airline company might be worried that in a year’s time the
price of oil might be too high, hence increasing costs. To hedge this risk,
the firm can buy a one-year futures contract, fixing the oil price today. This
allows the company to get rid of the uncertainty related to future prices.
Many assets have future markets including agricultural commodities (e.g.
corn and soybeans), non-agricultural commodities (e.g. gold or fuel oil)
and financial assets (e.g. 30-year government bonds or Swiss Francs).
In practice, most contracts are not physically settled, i.e. the actual
commodity is not usually delivered (sometimes delivery is not allowed for
commodities like wind, for example). Traders usually reverse their position
before the contract expires to have a net exposure of 0. For example, if
you enter in a long oil futures contract maturing in one year, you can enter
into a short futures contract with the same notional any time before the
maturity, which would cancel your long position.
Although quite similar, futures and forward contracts have some
differences. Most importantly, futures contracts are standardised and are
traded on exchanges. This means that the counterparty of your futures
contract is the exchange. This decreases the counterparty risk. To the
contrary, forward contracts are not standardised and are traded overthe-counter. This means that there is no intermediary between the long
and the short side of the contract and that the risk of the counterparty
defaulting is much higher.
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Futures prices are closely related to spot prices observed in the future. In
particular, future prices are one possible predictor of expected spot prices
in the future. Is this predictor good enough? Not always. Why? Because of
the risk premium. We will elaborate more on this in the next section.
Lastly, let us discuss swaps as a way to hedge risks. A swap is an exchange
of one set of cash flows (e.g. cash flows on a floating rate loan) for
another of equivalent market value (e.g. cash flows on a fixed rate loan).
Essentially, they are a sequence of futures contracts. Let us illustrate the
mechanics of swaps with a simple example that shows how swaps can be
beneficial in hedging mismatch between assets and liabilities.
Example. Swap
There are two firms: CRST and Hanson. CRST receives LIBOR (London
Interbank Offered Rate), which is floating, but CRST a fixed liability. Thus,
it is exposed to the risk that the floating rate might decrease and hence
the company will have insufficient assets to cover its fixed-rate liability.
Hanson, on the other hand, receives fixed rate but is liable for LIBOR.
Thus, it is exposed to the risk that the floating rate might increase and
hence Hansen will have insufficient assets to cover its floating-rate liability.
Can the two firms sign a contract that allows both of them to hedge the
floating versus fixed risk mismatch?
Yes! CRST and Hanson can enter into an interest rate swap: CRST agrees
to pay a floating rate to Hanson and Hanson agrees to pay a fixed interest
rate (called the swap rate) to CRST. This way, both of them get rid of the
uncertainty associated with the future LIBOR. The swap rate is always set
such that the transaction has zero NPV. Suppose, in our example, the swap
rate is 8 per cent. Figure 9.1 illustrates the mechanics of the contract.
CRST receives LIBOR and pays it immediately to Hansen as a part of the
swap contract. In return, CRST gets the fixed 8 per cent swap rate which
allows CRST to pay the fixed 8 per cent liability to the lender. Analogously,
Hansen receives the fixed rate of 8 per cent and pays it as a part of the
swap contract. In return, it receives LIBOR from CRST which allows
Hansen to cover the LIBOR liability:
LIBOR
Hanson PLC
CRST
Swap rate = 8%
8%
Lender
LIBOR
Lender
Figure 9.1: The swap contract between CRST and Hansen.
A final remark on swap contracts is that there is a significant counterparty
risk – that is, the risk that the hedge evaporates. In the example above,
either CRST or Hansen might run away from the swap contract.
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Cost of risk management
As mentioned earlier, risk management is not free. Usually, we have to pay
some costs to transfer our risks to someone else. In this section, we will
talk about two main costs of hedging: transaction costs and risk premium.
Let us start with transaction costs.
Typically, to complete a hedge, the firm will have to pay transaction
costs: e.g. brokerage commissions and losses to more informed traders.
Consider a simple example: you decide to buy an asset as a hedge, but
a second later want to reverse the hedge by selling the same asset. Even
assuming the price did not move in that one second, you will not be able
to sell the asset for the price you bought it. Why? Because of the bid–ask
spread. You buy at the ask price, but you sell at the bid price. Typically,
the ask is larger than the bid so you lose money if you reverse the trade
immediately. This loss is the profit of the market maker. In the early 1980s,
the bid–ask spread for swaps exceeded 100 basis points at times, which is
a significant number for firms that hedge frequently. A one per cent bid–
ask spread means that they would lose the entire capital in 100 roundtrip
transactions. By 1995, the bid–ask spread was significantly lower at 2 basis
points.
Now, let us talk about the risk premium. Let us take futures as an example.
The future price is set today but will be paid next year. The spot price is
the price at which you can buy the commodity today. Is the future price an
unbiased estimate of the future spot price? No. If there is a positive risk
premium, then the two will differ. Let us think why. Intuitively, when you
buy a futures contract, you eliminate the uncertainty about future spot
prices. No matter what the spot price is at the maturity of the contract,
you can buy at the futures price. However, your counterparty does have
to worry about the uncertainty. She has promised to sell the asset at the
futures price, but, assuming she does not have the asset, she has to buy
it at the spot price observed in the future. Hence, she bears the risk that
the spot price will increase a lot, thereby causing her to suffer losses. To
compensate her for this risk, we usually have to pay a premium, i.e. to
agree on a futures price that is different than the expected spot price. Now,
let us see the source of the premium (or the bias) mathematically.
A futures contract is a zero-sum game: the losses of the one party are
equal to the gains of the other party. In other words, the NPV of a futures
contract is always 0. Hence,
E (spot price)
Future price
0
=0
−
NPV(Future contract for seller) =
1+ r
1 + r commodity value
future
Assume no default, so rfuture = rrisk-free
Rearranging, we get: Future price = E0 (Spot price) * (1 + rF) / (1 + rC),
where rF is the risk free rate, rC is the commodity return.
According to the CAPM, rC = rF + β * Market Risk Premium.
β = 0 implies rC = rF and hence, Future price = E0 (spot price)
β > 0 implies rC> rF and hence, Future price < E0 (spot price)
β < 0 implies rC< rF and hence, Future price > E0 (spot price)
The intuition is that the seller contracts away a systematic risk, so he
offers a discount in future price as a compensation for risk to the buyer.
The discount may be positive (Future price < E0 (spot price)) or negative
(Future price > E0 (spot price)). The sign depends on whether the asset is a
pro-cyclical (tanks in bad times, positive) or counter-cyclical (increases in
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Chapter 9: Risk management and hedging
value in bad times, negative b). Consider, for example, an owner selling
gold through a futures contract. Gold is a good hedge against bad times, so
has a negative b. Hence, rC< rF and (1 + rF) / (1 + rC) > 1 which means (Future
price > E0 (spot price). The seller of a gold futures contract loses the benefit
of gold to appreciate in value in bad times by fixing the futures price today.
He requires compensation for this; hence, the future price is above the
expected spot price.
To conclude, the risk premium is an important cost of hedging. Depending
on the b of the asset, this premium may be positive or negative, causing
the future price to be different than the expected spot price.
Interest rate parity and carry trade
Finally, after talking about derivatives as a way of hedging, let us briefly
discuss some basics of the financial derivatives pricing. In this section,
we will focus on the foreign exchange market. The foreign exchange
market is the market where one currency is traded against another one.
It is, arguably, the biggest market on the planet and is populated by very
large institutional investors. There are also future contracts in this market
– investors can take long or short positions on the future exchange rate
between two currencies. What is the fair future price in the exchange
market? Let us think. Suppose you are a US investor who wants to borrow
for one year. You can directly borrow at the US interest rate. Alternatively,
you can borrow in any other country, say, the UK, for the same period
of time: you convert the pounds to dollars today, simultaneously fix the
future exchange rate by entering into a futures contract, and then convert
dollars to pounds in one year, to repay the UK loan. If there is no arbitrage,
these two ways of borrowing should cost you the same. Hence, the future
price should depend on the interest rates observed in the USA and UK. Let
us illustrate this arbitrage pricing argument with an explicit example.
Example. Interest rate parity
Company ABC has decided to borrow $10M for one year. It is currently
all equity financed, so we treat the debt as having zero default risk. If
it borrows in the US market, it will have to pay 6 per cent interest. If it
borrows in the UK market, however, it will have to pay only 2 per cent.
The current exchange rate is £1=$1.25. Should the company borrow at the
lower UK interest rate instead of at the higher US rate?
Let us first calculate ABC’s obligation if it borrows in pounds. It needs to
borrow $10M, which is equivalent to
10M
1 .25
= £8M. The principal and
interest payments due next year will be the amount borrowed times the
rate: 8*(1 + 0.02) = £8.16M.
What is ABC’s obligation if it borrows in US dollars? It is simply the
principal and interest payments in dollars: 10M*1.06 = $10.6M. It appears
that borrowing pounds is much cheaper, 2 per cent interest versus 6 per
cent interest. But is it? Not necessarily. It depends on the exchange rate
tomorrow. If the pound appreciates against the dollar and ABC borrows
pounds, then ABC may end up paying back a lot more in terms of dollars.
For example, suppose a year later, 1£ = $2. Then the total liability in
pounds is £8.16M * 2 = $16.32M. This is much higher than if borrowed in
dollars ($10.6M). By borrowing in another currency, ABC is exposed to the
exchange rate risk which might be substantial.
Suppose now that ABC wants to borrow in pounds (for example because
of better tax deals). Is it possible to hedge the exchange rate risk? Yes!
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The company can use a currency forward contract to lock down the FX
tomorrow. Suppose ABC can sign a currency forward contract on the £/$
exchange rate. How many contracts (face value) does the company need?
What is the forward price?
If ABC borrows in pounds, it needs to buy back £8.16M. The forward price
must make sure that the company is indifferent between borrowing in
pounds and in dollars, i.e. that £8.16M = $10.6M in a year’s time. Namely,
the forward price must be £1=$1.3. As today £1=$1.25<$1.3, the forward
price implies the pound will appreciate, making borrowing in pounds less
attractive.
What if the forward price is larger than $1.3, say, £1=$1.4? That is an
arbitrage. Take the following strategy: today, borrow $1.25, convert into
£1 and invest at the UK risk-free rate of 2%. Simultaneously, sign a forward
contract for £1.02 at the observed forward price of £1=$1.4. In a year’s
time, the investment returns £1.02, we use the forward contract to convert
it into dollars: 1.02*1.4 = $1.428. We use part of this money to repay the
dollar debt with 6 per cent interest: $1.25*1.06 = $1.325. The rest is the
arbitrage profit: $1.428-$1.325 = 0.103.
This example shows that the forward price should be uniquely linked
to the spot exchange rate and to the interest rates in the two countries.
Whenever this relationship is violated, we can construct an arbitrage.
Let us generalise this relationship, based on the logic in the ABC example.
Consider two ways to borrow $1 today:
1. Directly borrow $1 today and repay $(1+r$) in a year.
2. Borrow £fx£/$ today which is equivalent to $1 at today’s FX (foreign
exchange) rate. Need to repay £fx£/$ * (1+r£) in a year.
You can lock down the liability in dollars by entering a one-year forward
contract today. The dollar liability in a year will be £
By the no-arbitrage argument we saw before, it must be that the two ways
of borrowing are equivalent, i.e. (1+r$)=£fx£/$ * (1+r£)/F£/$. This is the
‘covered interest rate parity’.
In the ABC example, 1.06 = 1.25
−1
1.02
1.3
.
If covered interest rate parity
fails, then there is an arbitrage opportunity. In reality it holds very well.
Finally, what if we do not lock down the exchange rates in the future
through future contracts? If we believe the forward rate F should equal the
expected FX rate in a year, then the formula is called ‘uncovered interest
rate parity’: (1 + r$) = fx£/$ * (1 + r£) / E[fx£/$]. Note the use of the uncertain
instead of the deterministic E[fx£/$] in the formula F£/$.
If we hold the positions in foreign currency and close them using random
future spot exchange rate, then typically there is a non-zero return. In
other words, the uncovered interest rate parity fails in reality: currency
with higher interest rate tends to appreciate. Based on this, traders have
developed a strategy called the carry trade: borrow low interest currency,
buy government bond in high interest rate currency; then exchange
it back to low interest currency and pay back the debt. There are two
sources of profit in the strategy: from the interest rate spread and from
the currency appreciation. For instance, in 2016–2017, the exchange
rate increased, i.e. the pound depreciated against the dollar, although the
pound interest rate was lower than the dollars. Hence, if you borrowed
in pounds and invested in dollars over that period, you would not only
gain because of the interest rate difference, but also because the dollar
would be worth more in terms of pounds It is important to note, however,
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Chapter 9: Risk management and hedging
that the non-zero return is stochastic, hence the carry trade is not an
arbitrage opportunity – there is some risk. Historically, the carry trade has
experienced occasional very large losses when the exchange rates moved
dramatically over short periods of time.
Activities
1. Which of the following statements about futures contracts is false?
Select only one:
a. Futures contracts are generally more illiquid than forward contracts and are
traded anonymously on an exchange at a publicly observed market price.
b. Traders are required to post collateral, called margin, when selling or buying
commodities through futures contracts.
c. Both the seller and the buyer can get out of the contract at any time by selling it
to a third party at the current market price.
d. Futures prices are not prices that are paid today. They are prices agreed today, but
to be paid in the future.
2. In September 2004, the spot exchange rate for the Euro against the US Dollar was
$1.7188/€. At the same time the one-year interest rate in the USA was 4.85 per cent
and the one-year interest rate in Europe was 3.15 per cent. Based on these rates,
what is the one-year forward exchange rate that is consistent with no arbitrage?
Choose the closest answer.
Select one:
a. $1.6/€.
b. $1.9/€.
c. $1.7/€.
d. $1.5/€.
A reminder of your learning outcomes
At the end of this chapter, and having completed the Essential reading and
activities, you should be able to:
•
explain why and how companies manage risk
•
explain and evaluate the cost of hedging
•
explain covered and uncovered interest rate parity, and analyse the
associated arbitrage possibilities.
Key terms
Carry trade
Covered interest rate parity
Forward contracts
Future contracts
Hedging
Insurance
Swaps
Uncovered interest rate parity
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Sample examination questions
1. Large businesses spend significant amounts of money annually on
insurance. Why? Should they insure against all risks? Does insurance
make more sense for some risks than others?
2. A silver-mining firm is concerned about volatility in its revenues.
The price of silver is currently $65/ounce, but it is extremely volatile
and could fall as low as $63 or rise as high as high as $68 in the next
month. The company will bring 100 ounces to the market next month.
The one-month interest rate is 0.
a. What will be the total revenue if the firm remains unhedged for
silver prices of $60, $63, and $68 per ounce?
b. The future price of silver for delivery one month ahead is $66.
What will be the firm’s total revenues for each silver price if the
firm enters into a one-month futures contract to deliver 100
ounces of silver?
c. What will total revenues be if the firm buys a one-month put
option to sell silver for $65 an ounce? The put option costs $4.5.
3. A catering firm faces a 9 per cent chance of a potential loss of $1
million next year. If the firm purchases new equipment, it can reduce
the chance of this loss to 4 per cent, but this new equipment has an
upfront cost of $10,000. The beta of the loss is 0, and the risk-free
interest rate is 5 per cent.
a. If the firm decides to be uninsured, what is the NPV of purchasing
the new equipment?
b. If the firm decides to insure fully, what is the NPV of purchasing
the new equipment?
c. Given your answer to part (b), what is the actuarially fair cost of
full insurance?
d. What is the minimum-size deductible that would leave your firm
with an incentive to purchase the new equipment?
e. What is the actuarially fair price of insurance with the deductible
in part (d)?
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