2 R.A. Hill

Strategic Financial Management

Exercises

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3 Strategic Financial Management Exercises

1st edition© 2009 R.A. Hill &

bookboon.com

ISBN 978-87-7061-426-9Download free eBooks at bookboon.com

4 Contents

Contents

About the Author

7 Part One: An Introduction

81 Finance Œ An Overview

9 Introduction

9 Exercise 1.1: Modern Finance ˜eory

9 Exercise 1.2: ˜e Nature and Scope of Financial Strategy

14 Summary and Conclusions

16 Part Two: ˜e Investment Decision

172

Capital Budgeting Under Conditions of Certainty

18 Introduction

18 Exercise 2.1: Liquidity, Pro˚tability and Project PV

19 Exercise 2.2: IRR Inadequacies and the Case for NPV

22 Summary and Conclusions

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5 Contents

3

Capital Budgeting and the Case for NPV

26 Introduction

26 Exercise 3.1: IRR and NPV Maximisation

26 Exercise 3.2: Relevant Cash Flows, Taxation and Purchasing Power Risk

31 Summary and Conclusions

374 ˜e Treatment of Uncertainty

38 Introduction

38 Exercise 4.2: Decision Trees and Risk Analyses

46 Summary and Conclusions

51 Part ˜ree: ˜e Finance Decision

525

Equity Valuation the Cost of Capital

53 Introduction

53 Exercise 5.1: Dividend Valuation and Capital Cost

53 Exercise 5.2: Dividend Irrelevancy and Capital Cost

61 Summary and Conclusions

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6 Contents

6

Debt Valuation and the Cost of Capital

69 Introduction

69 Exercise 6.1: Tax-Deductibility of Debt and Issue Costs

70 Exercise 6.2: Overall Cost (WACC) as a Cut-o˛ Rate

73 Summary and Conclusions

777

Debt Valuation and the Cost of Capital

78 Introduction

78 Exercise 7.1: Capital Structure, Shareholder Return and Leverage

79 Exercise 7.2: Capital Structure and the Law of One Price

83 Summary and Conclusions

96 Part Four: ˜e Wealth Decision

988

Shareholder Wealth and Value Added

99 Introduction

99 Exercise 8.1: Shareholder Wealth, NPV Maximisation and Value Added

100 Exercise 8.2: Current Issues and Future Developments

105 Summary and Conclusions

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7 About the Author

About the Author

With an eclectic record of University teaching, research, publication, consultancy and curricula

development, underpinned by running a successful business, Alan has been a member of national

academic validation bodies and held senior external examinerships and lectureships at both undergraduate

and postgraduate level in the UK and abroad.

With increasing demand for global e-learning, his attention is now focussed on the free provision of a

˚nancial textbook series, underpinned by a critique of contemporary capital market theory in volatile

markets, published by bookboon.com.

To contact Alan, please visit Robert Alan Hill at

www.linkedin.com

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8 Part One

An Introduction

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9 Finance Œ An Overview

1 Finance Œ An Overview

Introduction

It is a basic assumption of ˚nance theory, taught as fact in Business Schools and advocated at the highest

level by vested interests, world-wide (governments, ˚nancial institutions, corporate spin doctors, the

press, media and ˚nancial web-sites) that stock markets represent a pro˚table long-term investment.

˜roughout the twentieth century, historical evidence also reveals that over any ˚ve to seven year period

security prices invariably rose.

˜is happy state of a˛airs was due in no small part (or so the argument goes) to the

e˜cient

allocation

of resources based on an

e˜cient

interpretation of a

free ˚ow

of information. But nearly a decade into

the new millennium, investors in global markets are adapting to a new world order, characterised by

economic recession, political and ˚nancial instability, based on a

communication breakdown

for which

strategic ˚nancial managers are held largely responsible.

˜e root cause has been a breakdown of

agency theory

and the role of

corporate governance

across global

capital markets. Executive managers motivated by their own greed (short-term bonus, pension and share

options linked to short-term, high-risk pro˚tability) have abused the complexities of the ˚nancial system

to drive up value. To make matters worse, too many companies have also ˝attered their reported pro˚ts

by adopting

creative accounting

techniques to cover their losses and discourage predators, only to be

found out.

We live in strange times

. So let us begin our series of Exercises with a critical review of the traditional

market

assumptions that underpin the Strategic Financial Management function and also validate its

decision models. A fundamental re-examination is paramount, if companies are to regain the trust of

the investment community which they serve.

Exercise 1.1: Modern Finance Theory

We began our companion text:

Strategic Financial Management

(SFM

henceforth) with an idealised picture

of shareholders as wealth maximising individuals, to whom management are ultimately responsible. We

also noted the theoretical assumption that shareholders

should

be rational, risk-averse individuals who

demand higher returns to compensate for the higher risk strategies of management.

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10 Finance Œ An Overview

What

should be

(rather than

what is

) is termed

normative theory

. It represents the bedrock of modern

˚nance. ˜us, in a sophisticated mixed market economy where the ownership of a company™s investment

portfolio is divorced from its control, it follows that:

The over-arching, normative objective of strategic ˜nancial management should be an optimum

combination of investment and ˜nancing policies which maximise shareholders™ wealth as

measured by the overall return on ordinary shares (dividends plus capital gains).

But what about the ﬁreal worldﬂ of

what is

rather than

what should be

?A fundamental managerial problem is how to retain funds for reinvestment without compromising the

various income requirements of innumerable shareholders at particular points in time.

As a benchmark

, you recall from

SFM

how Fisher (1930) neatly resolved this dilemma. In

perfect markets

, where all participants can borrow or lend at the same market rate of interest, management can maximise

shareholders™ wealth irrespective of their consumption preferences, providing that:

The return on new corporate investment at least equals the shareholders™ cost of borrowing,

or their desired return earned elsewhere on comparable investments of equivalent risk.

Yet, eight decades on, we all know that markets are

imperfect

, characterised by

barriers to trade

and

populated by

irrational

investors, each of which may invalidate Fisher™s

Separation ˛eorem

.As a consequence, the questions we need to ask are whether an

imperfect

capital market is still

e˜cient

and whether its constituents exhibit

rational

behaviour?

-If so,

shares will be correctly priced according to a ˚rm™s investment and ˚nancial decisions.

-If not

, the global capital market may be a ﬁcastle built on sandﬂ.

So, before we review the role of Strategic Financial Management, outlined in Chapter One of our

companion text, let us evaluate the case

for and against

stock market

e˜ciency

, investor

rationality

and

summarise its future implications for the investment community, including management.

As a springboard, I suggest reference to Fisher™s Separation ˜eorem (

SFM

: Chapter One). Next, you

should key in the following terms on the internet and itemise a

brief

de˚nition of each that you feel

comfortable with.

Perfect Market; Agency ˛eory; Corporate Governance; Normative ˛eory; Pragmatism; Empiricism;

Rational Investors; E˜cient Markets; Random Walk; Normal Distribution; EMH; Weak, Semi-Strong,

Strong; Technical, Fundamental (Chartist) and Speculative Analyses.

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11 Finance Œ An Overview

Armed with this information, answer the questions below. But keep them brief by using the previous

terms at appropriate points

without

their de˚nitions. Assume the reader is familiar with the subject.

Finally, compare your answers with those provided and if there are points that you do not understand,

refer back to your internet research and if necessary, download other material.

The Concept of Market E˚ciency as ﬁBad Scienceﬂ

1. How does Fisher™s Separation Theorem underpin modern ˜nance?

2. If capital markets are imperfect does this invalidate Fisher™s Theorem?

3. E˚cient markets are a necessary but not su˚cient condition to ensure

that NPV maximisation elicits shareholder wealth maximisation. Thus,

modern capital market theory is not premised on e˚ciency alone. It is

based on three pragmatic concepts.

De˜ne these concepts and critique their purpose.

4. Fama (1965) developed the concept of e˚cient markets in three forms

that comprise the E˚cient Market Hypothesis (EMH) to justify the use

of linear models by corporate management, ˜nancial analysts and stock

market participants in their pursuit of wealth.

Explain the characteristics of each form and their implications for technical,

fundamental and speculative investors.

5. Whilst governments, markets and companies still pursue policies

designed to promote stock market e˚ciency, since the 1987 crash

there has been increasing unease within the academic and investment

community that the EMH is ﬁbad scienceﬂ.

Why is this?

6. What are your conclusions concerning the E˚cient Market Hypothesis?

An Indicative Outline Solution (Based on Key Term Research)

1. Fisher™s Separation ˜eorem

In corporate economies where ownership is divorced from control, ˚rms that satisfy consumer

demand should generate money pro˚ts that create value, increase equity prices and hence

shareholder wealth.

To achieve this position, corporate management must optimise their internal investment

function and their external

˚nance function. ˜ese are interrelated by the ˚rm™s cost of capital

compared to the return that investors can earn elsewhere.

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12 Finance Œ An Overview

To resolve the dilemma, Fisher (1930) states that in

perfect

markets

a company™s investment

decisions can be made independently of its shareholders™ ˚nancial decisions without

compromising their wealth, providing that returns on investment at least equal the shareholders™

opportunity cost of capital.

But how perfect is the capital market?

2. Imperfect Markets and E˚ciency

We know that capital markets are not perfect but are they reasonably e˙cient? If so, pro˚table

investment undertaken by management on behalf of their shareholders (the

agency principle

supported by

corporate governance

) will be communicated to market participants and the

current price of shares in issue should rise. So, conventional theory states that ˚rms should

maximise the cash returns from all their projects to maximise the market value of ordinary

shares

3. Capital Market ˜eory

Modern capital market theory is based on three

normative

concepts that are also

pragmatic

because they were accepted without any

empirical

foundation.

-Rational investors

-E˜cient markets

-Random walks

To prove the point, we can question the ˚rst two:

investors are ﬁirrationalﬂ (think Dot.Com)

and markets are ﬁine˙cientﬂ (insider dealing, ˚nancial meltdown and governmental panic)).

So, where does the concept of ﬁrandom walkﬂ ˚t in?

If investors react rationally to new information within e˙cient markets it should be impossible

to ﬁbeat the marketﬂ except by luck, rather than judgement. ˜e ˚rst two concepts therefore

justify the third, because if ﬁmarkets

have no

memoryﬂ the past and future are ﬁindependentﬂ

and security prices and returns exhibit a random

normal distribution

.So, why do we have a multi-trillion dollar ˚nancial services industry that reads the news of

every strategic corporate ˚nancial decision throughout the world?

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13 Finance Œ An Overview

4. ˜e E˚cient Market Hypothesis (EMH)

Anticipating the need for this development, Eugene Fama (1965

˝.) developed the E˙cient

Market Hypothesis (

EMH) over forty years ago in three forms (

weak, semi-strong and strong

). Irrespective of the form of market e˙ciency, he explained how:

-Current share prices re˝ect all the information used by the market.

-Share prices only change when new information becomes available.

As markets strengthen, or so his argument goes, any investment strategies designed to ﬁbeat

the marketﬂ weaken, whether they are

technical (i.e. chartist),

fundamental

or a combination

of the two. Like

speculation

, without insider information (illegal) investment is a ﬁfair game

for allﬂ unless you can a˛ord access to market information before the competition (i.e. semi-

strong e˙ciency).

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14 Finance Œ An Overview

5. ˜e EMH as ﬁBad Scienceﬂ

Today, despite global recession, governments, markets and companies continue to promote

policies premised on semi-strong e˙ciency. But since the 1987 crash there has been an

increasing awareness within the academic community that the EMH in any form is ﬁbad scienceﬂ.

It placed the ﬁcart before the horseﬂ by relying on three simplifying assumptions, without any

empirical evidence that they are true. Financial models premised on rationality, e˙ciency and

random walks, which are the bedrock of modern ˚nance, therefore attract legitimate criticism

concerning their real world applicability.

6. Conclusion

Post-modern behavioural theorists believe that markets have a memory, take a

ﬁnon-linearﬂ

view of society and dispense with the assumption that we can maximise anything with their

talk of speculative bubbles, catastrophe theory and market incoherence. Unfortunately, they

too, have not yet developed alternative ˚nancial models to guide corporate management in

their quest for shareholder wealth

via

equity prices.

So, who knows where the ﬁnewﬂ ˚nance will take us?

Exercise 1.2: The Nature and Scope of Financial Strategy

Although the capital market assumptions that underpin modern ˚nance theory are highly suspect,

it is still widely accepted that the normative objective of ˚nancial management is the maximisation

of shareholder wealth. We observed in Chapter One of our companion text (

SFM

) that to satisfy this

objective a company requires a ﬁlong-term course of actionﬂ. And this is where

strategy

˚ts in.

Financial Strategy and Corporate Objectives

Using

SFM

supplemented by any other reading:

1. De˜ne Corporate Strategy

2. Explain the meaning of Financial Strategy?

3. Summarise the functions of Strategic Financial Management.

An Indicative Outline Solution

1. Corporate Strategy

Strategy

is a course of action that speci˚es the monetary and physical resources required to

achieve a predetermined objective, or series of objectives.

Corporate Strategy

is an overall, long-term plan of action that comprises a portfolio of functional

business strategies (˚nance, marketing etc.) designed to meet the speci˚ed objective(s).

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15 Finance Œ An Overview

2. Financial Strategy

Financial Strategy

is the portfolio constituent of the corporate strategic plan that embraces the

optimum investment and ˚nancing decisions required to attain an overall speci˚ed objective(s).

It is also useful to distinguish between strategic, tactical and operational planning.

-Strategy is a long-run course of action.

-Tactics are an intermediate plan designed to satisfy the objectives of the agreed strategy.

-Operational activities are short-term (even daily) functions (such as inventory

control) required to satisfy the speci˚ed corporate objective(s) in accordance with

tactical and strategic plans.

Needless to say, senior management decide strategy, middle management decide tactics and

line management exercise operational control.

3. ˜e Functions of Strategic Financial Management

We have observed ˚nancial strategy as the area of managerial policy that determines the

investment and ˚nancial decisions, which are preconditions for shareholder wealth maximisation.

Each type of decision can also be subdivided into two broad categories; longer term (strategic or

tactical) and short-term (operational). ˜e former may be unique, typically involving signi˚cant

˚xed asset expenditure but uncertain future gains. Without sophisticated periodic forecasts of

required outlays and associated returns that model the

time value of money

and an allowance

for risk, the subsequent penalty for error can be severe, resulting in corporate liquidation.

Conversely, operational decisions (the domain of working capital management) tend to be

repetitious, or in˚nitely divisible, so much so that funds may be acquired piecemeal. Costs

and returns are usually quanti˚able from existing data with any weakness in forecasting easily

remedied. ˜e decision itself may not be irreversible.

However, irrespective of the time horizon, the investment and ˚nancial decision functions of

˚nancial management should always involve:

-˜e continual search for investment opportunities.

-˜e selection of the most pro˚table opportunities, in absolute terms.

-˜e determination of the optimal mix of internal and external funds required to ˚nance

those opportunities.

-˜e establishment of a system of ˚nancial controls governing the acquisition and

disposition of funds.

-˜e analysis of ˚nancial results as a guide to future decision-making.

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16 Finance Œ An Overview

None of these functions are independent of the other. All occupy a pivotal position in the decision

making process and naturally require co-ordination at the highest level.

Summary and Conclusions

˜e implosion of the global free-market banking system (and the domino e˛ect throughout world-wide

corporate sectors starved of ˚nance) required consideration of the assumptions that underscore modern

˚nancial theory. Only then, can we place the following Exercises that accompany the companion

SFM

text within a topical framework.

However, we shall still adhere to the traditional objective of shareholder wealth maximisation, based on

agency theory

and

corporate governance

, whereby the owners of a company entrust management with

their money, who then act on their behalf in their best long-term interests.

But remember, too many ˚nancial managers have long abused this trust for personal gain.

So, whilst what follows is a

normative

series of Exercises based on ﬁwhat shouldﬂ be rather than ﬁwhat

isﬂ, it could be some time before Strategic Financial Management and the models presented in this text

receive a good press.

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17 Part Two

The Investment Decision

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18 Capital Budgeting Under Conditions of Certainty

2

Capital Budgeting Under

Conditions of Certainty

Introduction

If we assume that the strategic objective of corporate ˚nancial management is the maximisation of

shareholders™ wealth, the ˚rm requires a consistent model for analysing the pro˚tability of proposed

investments, which should incorporate an appropriate criterion for their acceptance or rejection. In

Chapter Two of

SFM

(our companion text) we examined

four common techniques

for selecting capital

projects where a choice is made between alternatives.

-Payback

(PB) is useful for calculating how quickly a project™s cash ˝ows recoups its capital

cost but says nothing about its overall pro˚tability or how it compares with other projects.

-Accounting Rate of Return

(ARR) focuses on project pro˚tability but contains serious

computational defects, which relate to accounting conventions, ignores the

true

net cash

in˝ow and also the time value of money.

When the time value of money is incorporated into investment decisions using

discounted cash ˚ow

(DCF) techniques based on

Present Value

(PV), the real

economic

return di˛ers from the accounting

return (ARR). So, the remainder of our companion chapter explained how DCF is built into investment

appraisal using one of two PV models:

-Internal Rate of Return

(IRR) -Net Present Value

(NPV).

In practice, which of these models management choose to maximise project pro˚tability (and hopefully

wealth) oˆen depends on how they de˚ne ﬁpro˚tabilityﬂ. If management™s objective is to maximise

the

rate of return in percentage terms

they will use IRR. On the other hand, if management wish to maximise

pro˙t in absolute cash terms

they will use NPV.

But as we shall discover in this chapter and the next, if management™s over-arching objective is wealth

maximisation then the IRR may be

sub-optimal

relative to NPV. ˜e problem occurs when ranking

projects in the presence of

capital rationing

, if projects are

mutually exclusive

and a choice must be made

between alternatives.

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19 Capital Budgeting Under Conditions of Certainty

Exercise 2.1: Liquidity, Pro˜tability and Project PV

Let us begin our analysis of pro˚table, wealth maximising strategies by comparing the four methods of

investment appraisal outlined above (PB, ARR, IRR and NPV) applied to the same projects.

˜e Bryan Ferry Company operates regular services to the Isle of Avalon. To satisfy demand, the Executive

Board are considering the purchase of an idle ship (the ﬁRoxyﬂ) as a temporary strategy before their new

super-ferry (the ﬁMusicﬂ) is delivered in four years time.

Currently, laid up, the Roxy is available for sale at a cost of $2 million. It can be used on one of two

routes: either an existing route (Route One) subject to increasing competition, or a new route (Two)

which will initially require discounted fares to attract custom.

Based on anticipated demand and pricing structures, Ferry has prepared the following pro˚t forecast

($000) net of straight-line depreciation with residual values and capital costs.

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20 Capital Budgeting Under Conditions of Certainty

Route

One Two

Pre-Tax Pro˜ts

Year:

One

800 300 Two

800 500 Three

400 900 Four

400 1,200 Residual Value 400 400

Cost of Capital 16% 16%

Required:

Using this data, information from Chapter Two of the

SFM

text, and any other assumptions:

1. Summarise the results of your calculations for each route using the following criteria.

Payback (PB); Accounting Rate of Return (ARR);

Internal Rate of Return (IRR); Net Present Value (NPV)

2. Summarise your acceptance decisions using each model™s maximisation criteria.

To answer this question and others throughout the text you need to

access Present Value (PV) tables from your recommended readings, or the

internet. Compound interest and zstatistic tables should also be accessed

for future reference. To get you started, however, here is a highlight from

the appropriate PV table for part of your answer (in $).

Present Value Interest Factor ($1 at

r % for

n years) = 1/ (1+r)

nFactor

16% Year One

1.000 Year Two

0.862 Year Three

0.743 Year Four

0.552 Year Five

0.476An Indicative Outline Solution

Your analyses can be based on either four or ˚ve years, depending on when the Roxy is sold (realised).

Is it at the end of Year 4 or Year 5? ˜ese assumptions a˛ect IRR and NPV investment decision criteria

but not PB. Even though all three are

cash-based

, remember that

PB only relates to

liquidity

and

not

pro˙tability

. ˜e ARR will also di˛er, according to your accounting formula. For consistency, I have used

a simple

four-year

formula ($m) throughout. For example, with Route One:

Average Lifetime Pro˚t / Original Cost less Residual Value = 0.6 / 2.0 = 30%

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21 Capital Budgeting Under Conditions of Certainty

˜e following results are therefore illustrative but not exhaustive. Your answers may di˛er in places but

this serves to highlight the importance of stating the assumptions that underpin any ˚nancial analyses.

1: Results

Let us assume the Roxy is sold in

Year

Five

(with ARR as a cost-based four-year average).

Criteria

PB(Yrs)

ARR(%) IRR(%)

NPV($000)Route 1

1.67

30.00

42.52

1,101.55Route 2

2.31

36.25

38.70

1,209.73Now assume the Roxy is realised in Year

Four

(where PB and ARR obviously stay the same).

Criteria

PB(Yrs)

ARR(%) IRR(%)

NPV ($000)

Route 1

1.67

30.00

41.49

1,071.08Route 2

2.31

36.25

37.88

1,179.262: Project Acceptance

According to our four investment models (irrespective of when the Roxy is sold) project selection based

upon their respective criteria can be summarised as follows:

Criteria

PB(Yrs)

ARR(%) IRR(%)

NPV($000)Objective

(Max. Liq.)

(Max. %)

(Max. %)

(Max. $)

Route

1

2

1

2Unfortunately, if Bryan Ferry™s objective is wealth maximisation, we have a dilemma. Which route do

we go for?

We can dispense with PB that maximises liquidity but reveals nothing concerning pro˚tability and wealth.

˜e ARR is also dysfunctional because it is an average percentage rate based on accrual accounting that

also ignores project size and the time value of money. Unfortunately, this leaves us with the IRR, which

favours Route One and the NPV that selects Route 2.

So, give some thought to which route should be accepted before we move on to the next exercise and a

formal explanation of our ambiguous conclusion in Chapter ˜ree.

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22 Capital Budgeting Under Conditions of Certainty

Exercise 2.2: IRR Inadequacies and the Case for NPV

Pro˚table investments opportunities are best measured by DCF techniques that incorporate the time

value of money. Unfortunately, with more than one DCF model at their disposal, which may also give

con˝icting results when ranking alternative investments, management need to de˚ne their objectives

carefully before choosing a model.

You will recall from the

SFM

text that in a free market economy, ˚rms raise funds from various providers

of capital who expect an appropriate return from e˙cient asset investment. Under the assumptions of

a perfect capital market, explained in Part One, the ˚rm™s investment decision can be separated from

the owner™s personal preferences without compromising wealth maximisation, providing projects are

valued on the basis of their opportunity cost of capital. If the cut-o˛ rate for investment corresponds to

the market rate of interest, which shareholders can earn elsewhere on similar investments:

Projects that produce an IRR greater than their opportunity cost of capital (i.e. positive NPV)

should be accepted. Those with an inferior return (negative NPV) should be rejected.

Even in a world of zero in˝ation, the DCF concept also con˚rms that in today™s terms the PV of future

sums of money is worth progressively less, as its receipt becomes more remote and interest rates rise.

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23 Capital Budgeting Under Conditions of Certainty

˜is phenomenon is supremely important to management in a situation of

capital rationing

, or if

investments are

mutually exclusive

where projects must be ranked in terms of the timing and size of

prospective pro˚ts which they promise. ˜eir respective PB and ARR computations may be uniform.

˜eir initial investment cost and total net cash in˝ows over their entire lives may be identical. But if one

delivers the bulk of its return earlier than any other, it may exhibit the highest present value (PV). And

providing this project™s return covers the cost and associated interest payments of the initial investment

it should therefore be selected. Unfortunately, this is where modelling optimum strategic investment

decisions using the IRR and NPV con˝ict.

Required:

Refer back to Chapter Two of the companion text (and even Chapter ˜ree) and without using any

mathematics summarise in your own words:

1. ˜e IRR concept.

2. ˜e IRR accept-reject decision criteria.

3. ˜e computational and conceptual defects of IRR.

An Indicative Outline Solution

1. ˜e IRR Concept

˜e IRR methodology

solves

for an

average

discount rate, which equates future net cash in˝ows

to the present value (PV) of an investment™s cost. In other words, the IRR equals the

hypothetica

l rate at which an investment™s NPV would equal zero.

2. IRR Accept-Reject Decision Criteria.

˜e solution for IRR can be interpreted in one of two ways.

-˜e time-adjusted rate of return on the funds committed to project investment.

-˜e maximum rate of interest required to ˚nance a project if it is not to make a loss.

˜e IRR for a given project can be viewed, therefore, as a

˙nancial break-even point

in relation

to a cut-o˛ rate for investment predetermined by management. To summarise:

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24 Capital Budgeting Under Conditions of Certainty

Individual

projects are acceptable if:

IRR

a target rate of return

IRR > the cost of capital, or a rate of interest.

Collective

projects can be ranked according to the size of their IRR. So, under conditions

of capital rationing

, or where projects are

mutually exclusive

and management™s

objective is IRR

maximisation, it follows that if:

IRRA > IRRB >–IRRNProject A would be selected, subject to the proviso that it at least matched the ˜rm™s

cut-o˛ rate criterion for investment.

3. ˜e Computational and Conceptual Defects of IRR.

Research the empirical evidence and you will ˚nd that the IRR (relative to PB, ARR and NPV)

oˆen represents the preferred method of strategic investment appraisal throughout the global

business community. Arguments in favour of IRR are that

-Pro˚table investments are assessed using

percentages

which are

universally

understood.

-If the annual net cash in˝ows from an investment are equal in amount, the IRR can

be determined by a simple formula using factors from PV annuity tables.

-Even if annual cash ˝ows are complex and a choice must be made between

alternatives, commercial soˆware programs are readily available (oˆen as freeware)

that perform the chain calculations to derive each project™s IRR

Unfortunately, these practical selling points overstate the case for IRR as a pro˚t maximisation criterion.

You will recall from our discussion of ARR that percentage results fail to discriminate between projects

of di˛erent

timing and size

and may actually con˝ict with wealth maximisation. Firms can maximise

their rate of return by accepting a ﬁquickﬂ pro˚t on the smallest ﬁrichestﬂ project. However, as we shall

discover in Chapter ˜ree, high returns on low investments (albeit liquid) do not necessarily maximise

absolute

pro˚ts.

When net cash in˝ows are equal in amount, a factor computation may not correspond exactly to an

appropriate ˚gure in a PV annuity table, therefore requiring some method of interpolation. Even with

access to computer soˆware, it soon emerges that where cash ˝ows are variable a project™s IRR may be

indeterminate

, not a

real number

or with

imaginary roots

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25 Capital Budgeting Under Conditions of Certainty

Computational di˙culties apart, conceptually the IRR also assumes that even under conditions of

certainty when capital costs, future cash ˝ows and life are known and correctly de˚ned:

-All ˚nancing will be undertaken at a cost equal to the project™s IRR.

-Intermediate net cash in˝ows will be reinvested at a rate of return equal to the IRR.

˜e implication is that inward cash ˝ows can be reinvested at the

hypothetical

interest rate used to ˚nance

the project and in the calculation of a zero NPV. Moreover, this borrowing-reinvestment rate is assumed

to be constant over a project™s life. Unfortunately, relax either assumption and the IRR will change.

Summary and Conclusions

Because the precise derivation of a project™s IRR present a number of computational and conceptual

problems, you may have concluded (quite correctly) that a

real

rather than

assumed

cut-o˛ rate for

investment should be incorporated directly into present value calculations. Presumably, if a project™s

NPV based on a real rate is positive, we should accept it. Negativity would signal rejection, unless other

considerations (perhaps non-˚nancial) outweigh the emergence of a residual cash de˚cit.

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26 Capital Budgeting and the Case for NPV

3

Capital Budgeting and the Case

for NPV

Introduction

If management invest resources e˙ciently, their

strategic shareholder wealth maximising objectives

should be satis˚ed. Chapter Two of both the

SFM

and

Example

texts explain the superiority of the NPV

decision model over PB, ARR and IRR as a strategic guide to action. Neither PB, nor ARR, maximise

wealth. IRR too, may be

sub-optimal

unless we are confronted by a single project with a ﬁnormalﬂ

series of cash in˝ows. We concluded, therefore, that under conditions of certainty with known price

level movements:

Managerial criteria for wealth maximisation should conform to an NPV maximisation model

that discounts

incremental

money cash ˝ows at their

money (market) rate of interest.

Chapter ˜ree of

SFM

compares NPV and IRR project decision rules. We observed that di˛erences arise

because the NPV is a measure of

absolute

money wealth,

whereas

IRR is a

relative

percentage measure

. NPV is also free from the computational di˙culties frequently associated with IRR. ˜e validity of the

two models also hinges upon their respective assumptions concerning borrowing and reinvestment rates

associated with individual projects.

Unlike NPV, IRR assumes that re-investment and capital cost rates equal a project™s IRR without any

economic foundation whatsoever and important consequences for project rankings. We shall consider

this in our ˚rst Exercise.

Of course, NPV is still a ˚nancial

model

, which is an

abstraction

of the real world. Select simple data from

complex situations and even NPV loses detail. But as we shall observe in our second Exercise, incorporate

real-world considerations into NPV analyses (relevant cash ˝ows, taxation, price level changes) and we

can prove its strategic wealth maximising utility.

Exercise 3.1: IRR and NPV Maximisation

˜e Jovi Group is deciding whether to proceed with one of two projects that have a three-year life. ˜eir

respective IRR (highlighted) assuming relevant cash ˝ows are as follows (£000s):

Cost

Annual

NetIn˝ows

IRRYear

0123Project 1

1,00050070090043 %Project 2

1,0001,00050050054 %Download free eBooks at bookboon.com

27 Capital Budgeting and the Case for NPV

Required:

Given that Jovi™s cost of capital is a uniform 10 percent throughout each project:

1. Calculate the appropriate PV discount factors.

2. Derive each project™s NPV compared to IRR and highlight which (if any) maximises

corporate wealth according to both investment criteria.

3. Use the NTV concept to prove that NPV maximises wealth in

absolute money terms

.4. Explain why IRR and NPV rank projects di˛erently using a graphical analysis.

An Indicative Outline Solution

Your answer should con˚rm that individually each project will

increase

wealth because both IRRs

exceed the cost of capital (i.e. the discount rate) and both NPVs are positive. But if a choice must be

made between the alternatives, only one project

maximises

wealth. And to complicate matters further,

NPV maximisation and IRR maximisation criteria rank the projects di˛erently. So, which model should

management use?

1: PV Factor Calculations for 1/ (1+r)

t (£1 at 10% for t years where t = 0 to 3)

1/(1.1)0 = 1.000 1 1/(1.1)1 = 0.909 1/(1.1)2 = 0.826 1/(1.1)3 = 0.7512: NPV (£ 000s ) and IRR (%) Highlighted Comparisons

NPV IRRProject 1(10%): (1,000) + 500 × 0.909 + 700 × 0.826 + 900 × 0.751

= 709 43%Project 2(10%): (1,000) + 1,000 × 0.909 + 500 × 0.826 + 500 × 0.751

= 698 54%NPV maximisation selects one project but IRR maximisation selects the other; but why?

3: NTV (£ 000s)

Assume that Jovi borrows £1 million at an interest rate of 10 per cent to invest in either project but not

both. ˜ey are

mutually exclusive

. ˜ereaˆer, reinvestment opportunities also yield 10 per cent. ˜e

bank

overdraˆ

formulation below reveals that if project funds are reinvested at the market rate of interest,

NPV not only favours Project 1 but also

maximises wealth

because it produces a higher

cash surplus

(NTV) at the end of three years.

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28 Capital Budgeting and the Case for NPV

Project ( £000s )

1 2Cost

-1,000-1,000Interest year 1

-- 100 1,100-

- 1001,100Receipt year 1

+- 500

600+-1,000 100Interest year 2

-- 60 660-- 10 110Receipt year 2

++ 700 40++ 500

390Interest year 3

+

+ 4 44+

+ 39 429Receipt year 3

+ 900+ 500Summary (£ 000s)

Net Terminal Value (NTV)

1 944 2 929NTV = NPV (1+r)

3NPV = NTV/(1+r)

3 709 698Of course, the above data set could be formulated using each project™s IRR as their respective borrowing

and reinvestment rates (43 per cent for Project 1 and 54 per cent for Project 2). In both cases the bank

surplus (NTV) and its discounted equivalent (NPV) would equal zero. And as we know from the original

question, IRR maximisation would select Project 2. Perhaps you can con˚rm this?

But what is the point, if the company actually borrows at a

real world

(rather than

hypothetical break-

even

) rate of 10 per cent for each project? It also seems unreasonable to assume that there are any real

world reinvestment opportunities yielding 54 per cent, let alone 43 per cent!

4: A Graphical Analysis

Both NPV and IRR models employ common simplifying assumptions that you should be familiar with,

one of which is that borrowing and lending rates are equal. But note that

-NPV assumes that projects are ˚nanced and intermediate net cash in˝ows are reinvested at

the discount rate.

-IRR assumes that ˚nance and reinvestment occur at that rate where the project breaks even

and the NPV equals zero (i.e. the project™s IRR).

Given the di˛erence between actual discount rates (r) applied to projects and their IRR, you should also

appreciate their impact on the timing and size (pattern) of project cash ˝ows.

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29 Capital Budgeting and the Case for NPV

To visualise why a particular discount rate applied to di˛erent cash patterns determine their PV and hence NPV

and IRR, you could refer to a DCF table for 1/ (1+r)

t. This reveals the e˛ect of discounting £1.00, $1.00, or whatever

currency, at increasing interest rates over longer time periods. Now draw a diagonal line from the top left-hand

corner to the bottom right-hand corner of the table (where the ˜gures disappear altogether)? Finally, graph the line.

Without being too mathematical, can you summarise its characteristics?

Note that your graph is not only

non-linear

but also

increasingly

curvi-linear

. If you are in di˙culty, think

compound

interest (not

simple

interest) and reverse its logic. DCF is its

mirror image

, which reveals that

for a given discount rate, the longer the discount period, the lower the PV. And for a given discount

period, the higher the discount rate, the lower the PV. So, increase the discount rate and extend the

discount period and the PV of £1.00 (say) evaporates at an increasing rate.

Applied to our Exercise, a graph should be sketched that compares the two projects, with NPV on the

vertical

axis and discount rates on the

horizonta

l axis, to reveal these characteristics

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30 Capital Budgeting and the Case for NPV

Figure 3.1:

IRR and NPV Comparisons

Figure 3:1 illustrates that at one extreme (the vertical axis) each project™s NPV is maximised when

r equals zero, since cash ˝ows are not discounted. At the other (the horizontal axis) IRR is maximised

because

r solves for a break-even point (zero NPV) beyond which, both projects under-recover because

their NPV is negative.

Using NPV and IRR criteria, the graph also con˚rms that in

isolation

both projects are acceptable

However, if a

choice

must be made between the two, Project 1 maximises NPV, whereas Project 2

maximises IRR. So, why do their NPV curves intersect?

˜e intersection (crossover point) between the two projects represents an

indi˝erence

point between the

two if that was their common discount rate. ˜e NPVs of Project 1 and 2 are the same (any idea of the

discount rate and the project NPVs)?. To the leˆ, lower discount rates favour Project 1, whilst to the

right; higher rates favour Project 2 leading to its signi˚cantly higher IRR.

Refer back to your analysis of PV tables and you should also be able to con˚rm that:

-NPV (a low discount rate) selects Project 1 because it delivers more money, but later.

-IRR (a high discount rate) selects Project 2 because it delivers less money, but earlier.

-Wealth maximisation equals NPV maximisation (in

absolute

in cash terms) but not

necessarily IRR maximisation (a

relative

overall percentage). So, Project 1 is accepted.

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31 Capital Budgeting and the Case for NPV

Finally, irrespective of the time value of money, if you are still confused about the di˛erence between

maximising wealth in

absolute money

terms

or maximising a

percentage

rate of return

, ask yourself the

following simple question:

Is a 20 percent return on £1 million preferable to a 10 percent return on £20 million?

Exercise 3.2: Relevant Cash Flows, Taxation and Purchasing Power Risk

To supply a university consortium with e-learning material on DVD over the next three years, the South

American Clever Publishing Company (CPC) needs to calculate a contract price.

Management believe that the contract™s acceptance will enable CPC to access a new area of pro˚table

investment characterised by future growth. ˜is would also reduce the company™s reliance on hard copy

texts for its traditional clientele. For these reasons management are willing to divert resources from

existing projects to meet production. ˜e company will also relax its normal strict terms of sale. ˜e

consortium would pay the contract price in two equal instalments; the ˚rst up front but the second only

when the CPC contract has run its course.

˜e following information has been prepared relating to the project:

1. Inventory

At today™s prices, component costs are expected to be $150,000 per annum. ˜e contract™s

importance dictates that the requisite stocks will be acquired prior to each year of production.

However, su˙cient items are currently held in inventory to cover the ˚rst year from an aborted

project. ˜ey originally cost $100,000 but due to their specialised nature, neither the supplier

nor competitors will repurchase them. ˜e only alternative is hazardous waste disposal at a

cost of $5,000.

2. Employee Costs

Each year the contract will require 3,000 hours of highly skilled technicians. Current wage

rates are $8.00 per hour. Because these skills are in short supply, the company would also lose a

pro˚t contribution of $2.00 per hour in Year 1 by diverting personnel from an existing project

if the contract is accepted.

3. Overheads

Fixed overheads (excluding depreciation) are estimated to be $50,000 at current prices. Variable

overheads are currently allocated to projects at a rate of $60.00 per hour of skilled labour.

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32 Capital Budgeting and the Case for NPV

4. Capital Investment

Fixed assets and working capital (net of inventory) for the project will cost $2 million

immediately. ˜e realisable value of the former will be negligible. Company policy is to

depreciate assets on a reducing balance basis. When the contract is ful˚lled $50,000 of working

capital will be recouped.

5. Taxation

Because the contract is marginal in size and the contract deadline is imminent, a decision has

been taken to ignore the net tax e˛ect upon the company™s revised portfolio of investments if

the contract is accepted. However, it is envisaged that the contract itself will attract a $255,000

government grant at the time of initial capital expenditure.

6. Anticipated Price Level Changes

˜e rate of in˝ation is expected to increase at an annual compound rate of 15 per cent. Employee

costs and overheads will track this ˚gure but component costs will increase at an annual

compound rateof 20 per cent.

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33 Capital Budgeting and the Case for NPV

Required:

Assuming that CPC employ a discount rate for new projects based upon an annual cost of capital of 4.5

per cent in

real

terms:

1. Calculate the Clever Company™s minimum contract price.

2. Explain your ˚gures.

3. Comment on other factors not re˝ected in your calculations which might a˛ect the price.

An Indicative Outline Solution

1: ˜e Calculations

˜e minimum price at which the Clever Company should implement the project is that which produces

a zero NPV. But because our analysis involves price level changes, we must initially ascertain the

Fisher

e˝ect

upon the real discount rate explained in Chapter ˜ree (page 46) of the

SFM

text. To the nearest

percentage point, this

money

rate (m) is given by:

(5) m = (1 + r) (1 + i) Œ 1= (1.045)(1.15) Œ 1 = 20%Next, the contract™s

real

current cash ˝ows must be in˝ated to

money

cash ˝ows, prior to discounting

at the 20 per cent

money

rate.

Using the opportunity cost concept, let us tabulate the contract™s

relevant

current cash ˝ows ($000s)

attached to their appropriate price level adjustments (in brackets):

Year

0123Cash˜ows

Capital Investment

-2,000+50Capital Allowance

+255Materials

+5-150(1.2)-150 (1.2)2Labour-24 (1.15)-24 (1.15)2-24 (1.15)3Contribution Foregone

-6 (1.15)Variable Overheads

-180 (1.15)-180 (1.15)2-180 (1.15)3Relevant Real Cash Flows and Price Level Adjustments

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34 Capital Budgeting and the Case for NPV

Leaving you to determine the contract™s relevant money cash ˝ows, you should now be able to con˚rm

that the application of the money discount rate to the company™s net money cash out˝ows produces the

following PV calculations. Using soˆware, a calculator, or DCF tables:

Year

0123PVNet Out˝ows

1,740.00421.50485.79260.20DCF (20%)1,740.00351.25337.35150.582,579.18PV Calculations ($000s)

˜us, the minimum contract PV under the conditions stated is $2,579,180. However, remember that the

university consortium will only pay this price in two

equal

instalments (Year 0 and Year 3). If the CPC

is to break even, we must divide the total payment as follows;

Let C represent the amount of each instalment and the money cost of capital equal 20 percent.

Algebraically, the two amounts are represented by the following PV equation ($000s):

$2,579.18 = C + C (1.2)3Rearranging terms and simplifying, we ˚nd that:

$2,579.18 = C = $1,634.46 1.578And because there is only

one unknown

in the equation, solving for C we can con˚rm that the minimum

contract price of $2,579,180 can be paid in two equal instalments of $1,634,460 now and $1,634,460 in

three years time without compromising the integrity of CPC™s investment strategy.

2: An Explanation

Our contract price calculation is based on the following

relevant

money cash ˝ows discounted at the

appropriate

money

cost of capital.

(i) Inventory

˜ere is su˙cient stock to maintain ˚rst year production. However, its original purchase price

is

irrelevant

to our appraisal. It is a

sunk

cost because the only alternative is disposal for $5,000

only avoidable if the contract were accepted. We therefore record this ˚gure as an

opportunity

bene˙t

. At the beginning of Year 2 and Year 3 components have to be purchased at their prevailing

prices of $180,000 and $216,000 respectively.

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35 Capital Budgeting and the Case for NPV

(ii) Employee Costs

3,000 hours of skilled labour will be required each year. If we assume that the company™s annual

pay award based upon the forecast rate of in˝ation is impending, the hourly wage rates over

three years would be $9.20, $10.58 and $12.17 respectively.

(iii) Contribution Foregone

Because of a skilled labour shortage, the contract™s acceptance would lose CPC a contribution

of $2 per skilled labour hour from another project in the ˚rst year. We must therefore include

$2 × 3,000 adjusted for in˝ation as an implicit contract cost.

(iv)

Overheads

If ˚xed overheads are incurred irrespective of contract acceptance they are irrelevant to the

decision. Conversely, variable overheads are an incremental cost. ˜ey enter into our analysis

based on a cost of $60.00 per hour of skilled labour at $180,000 adjusted for in˝ation over each

of the three years in accordance with the company™s pay policy.

(v) Capital Investment

Depreciation is a

non-cash

expense. Except to the extent that it may act as a tax shield it is

therefore irrelevant to our decision. You will recall that since PV analyses are designed to recoup

the cost of an investment, depreciation is already incorporated into discounting $2 million at

Year 0 with a zero value for ˚xed assets at Year 3.

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36 Capital Budgeting and the Case for NPV

In contrast, that proportion of the $2 million investment represented by working capital is a cash

out˝ow, which will be released for use elsewhere in the company once the contract has run its

course. Assuming that $50,000 is the actual amount still tied up at the end of Year 3, we must

show this amount as a cash in˝ow in our calculations.

(vi)

Taxation

Because the project is marginal CPC ignored the net tax e˛ect on the overall revision to its

investment portfolio. However, we can incorporate the government grant of $255,000 as a cost

saving, providing the company proceeds with the project.

3: Other Factors

Diversi˚cation based on a core technology that uses existing resource elements is a sound business

strategy. In this case it should provide new experience in a new sector ripe for exploitation at little risk

(the project is marginal).

However, the contract costs (and price) bene˚t from a project that the company has already aborted. ˜is

may indicate a strategic forecasting weakness on the part of management. ˜e lost contribution from

diverting resources from any existing project may also entail future loss of goodwill from the company™s

existing clientele upon which it still depends.

Although the project is marginal, we must also consider whether the company will miss out on more

traditional pro˚table opportunities over the next three years. However, we could argue that if further

e-learning contracts follow, their returns will eventually outweigh the risk.

4: A Conceptual Review

Our contract appraisal assumes that the data is correct and that net money cash ˝ows can be discounted

at a 20 percent money cost of capital. It is based on the following

certainty

assumptions that underpin

all our previous PV analyses.

-˜e costs of investments are known.

-An investment™s life is known and will not change.

-Relevant future cash ˝ows are known.

-Price level changes are pre-determined.

-Discount rates based on money (market) rates of interest can be de˚ned and will not change.

-Borrowing and reinvestment rates equal the discount rates.

-˜e ˚rm can access the capital market at the market rate of interest if internal funds are

insu˙cient to ˚nance the project, or interim net cash ˝ows are available for reinvestment.

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37 Capital Budgeting and the Case for NPV

Uncertainty about any one of these assumptions is likely to invalidate our investment decision and

compromise shareholders™ wealth.

In the contract calculations, it may increase the minimum contract price far beyond $2,579,180.

Summary and Conclusions

A project™s NPV is equivalent to the PV of the net cash surplus at the end of its life (NTV). We observed

that this should equal the project™s

relevant

cash ˝ows

discounted at appropriate

price-adjusted

opportunity

cost of capital rates, using prevailing rates of interest or the company™s desired rate of return. To maximise

wealth, management should then select projects with the highest NPV to produce the highest lifetime

cash surplus (NTV).

It is also worth repeating from Exercise 3.1 that the NPV approach to investment appraisal based on

actual

DCF cost or return cut-o˛ rates should be more realistic than an IRR.

˜e IRR model is an

arithmetic

computation with little economic foundation. It is a

percentage averaging

technique

that merely establishes a project™s

overall break-even

discount rate where the NPV and NTV (the

cash surplus) equal zero. Moreover, IRR may rank projects in a di˛erent order to NPV. ˜is arises because

of di˛erent cash ˝ow patterns and the disparity between a project™s IRR and a company™s opportunity

capital cost (or return) each of which determines the borrowing and reinvestment assumptions of the

respective models.

Of course, the assumptions of NPV analyses presented so far ignore the uncertain world inhabited by

management, each of which may invalidate the model™s conclusions.

So, as a companion to the

SFM

text, let us develop the NPV capital budgeting model in Chapter 4 by

illustrating a number of formal techniques that can reduce, if not eliminate, the risk associated with

strategic investment appraisal.

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38 The Treatment of Uncertainty

4 The Treatment of Uncertainty

Introduction

For simplicity, our previous analyses of investment decisions assumed the future to be certain. But what

about the real world of uncertainty, where cash ˝ows cannot be speci˚ed in advance? How do management

maximise their strategic NPV wealth objectives?

In Chapter Four of your companion text (

SFM

) we evaluated risky projects where more than one set of

cash ˝ows are possible, based on two statistical parameters, namely the

mean

and

standard deviation

of

their distribution. But do you understand them?

One lesson from the recent ˚nancial meltdown is that irrespective of whether you are sitting an

examination, or dealing with multi-national sub-prime mortgages on Wall Street, a good memory for

formulae, access to a simple scienti˚c calculator, or the most sophisticated soˆware, is no substitute for

understanding what you are doing and its consequences.

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39 The Treatment of Uncertainty

Using mean-variance analysis as a springboard, the following exercises therefore emphasise: why you

should always be able to explain what you are calculating, know what the results mean, are critically

aware of their limitations and how the analysis may be improved. Real ˚nancial decisions should always

consider ﬁwhat isﬂ and ﬁwhat should beﬂ.

Exercise 4.1: Mean-Variance Analyses

Project

Mean NPV

Standard Deviation of NPV

• (000s)• (000s)A39 27B2727C 3933D4536˜e above table summarises statistical data for a series of

mutually exclusive

projects under review by

the Euro Song Company (ESCo).

Required:

1. Prior to analysing the data set, summarise in

your own words

: -˜e formal statistical assumptions that underpin mean-variance analysis.

-˜e de˚nition of a project™s mean, the variance and purpose of the standard deviation.

2. Reformulate the data set to select and critically evaluate the most e˙cient project based on

the various mean-variance criteria explained in Chapter Four of the

SFM

companion text.

3. Explain the limitations of your ˚ndings with reference to the

risk-return paradox

.An Indicative Outline Solution

1: Summary

- ˜e Formal Assumptions

For the purpose of risk analysis, most ˚nancial theorists and analysts accept the statistical assumptions

of

classical

probability theory, whereby:

-Cash ˝ows are

random

variables that are

normally

distributed around their

mean

value.

-Normal

variables display a

symmetrical

frequency distribution, which conforms to a bell

shaped curve (see below) based on the

Law of Large Numbers

. -˜e Law™s

Central Limit ˛eorem

states that as a sample of independent, identically

distributed (

IID) random numbers (i.e. cash ˝ow variables) approaches in˚nity, its

probability density function will conform to the normal distribution. If variables are

normally distributed, a ˚nite, statistical measure of their dispersion can be measured by

their

variance

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40 The Treatment of Uncertainty

Figure 4.1:

A Normal Distribution (£Cash Flows)

- De˛nitions

˜e

mean

(average) return from a project is a measure of

location

given by the weighted addition of

each return. Each weight represents the probability of occurrence, subject to the proviso that project™s

returns are random variables and the sum of probabilities equals one.

˜e

variance

of a project™s returns (risk) is a measure of

dispersion

equal to the weighted addition of

the squared deviations of each return from the mean return. Again, each weight is represented by the

probability of occurrence.

˜e

standard deviation

of a project is simply the

square root

of the variance.

So, what does the standard deviation contribute to our analysis of risk?

Because the distribution of normal returns is

symmetrical

, having calculated the deviation of each return

from the project mean, we cannot simply weight the deviations by their probabilities to arrive at a mean

deviation as a measure of dispersion. Unless the investment is

riskless

, some deviations will be positive,

others negative, but

collectively

the mean deviation would still equal zero. We also know that the sum of

all probabilities always equals one, so the mean deviation remains zero.

So, if we ˚rst square the deviations, we eliminate the minus signs and derive the

variance

. But in relation

to the original mean of the distribution, we now have a

scale

problem.

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41 The Treatment of Uncertainty

˜e increased scale, through squaring, is remedied by calculating the

square root of the variance

. ˜is

equals the

standard deviation

, which is a measure of dispersion expressed in the

same units

as the mean

of the distribution.

˜us, management have an NPV risk-return model where both parameters are in the same monetary

denomination (• in our current example). ˜us, if a choice must be made between alternatives, the ˚rm™s

wealth maximisation objective can be summarised as follows:

Maximise project returns at minimum risk by comparing their expected

net present value (ENPV) with their standard deviation (

NPV).

2: E˚cient Project Selection

As a summary measure of project risk based on the dispersion of cash ˝ows around their mean, the

interpretation of the standard deviation seems obvious: the higher its value, the greater the risk and

vice versa

.However, projects that produce

either

the highest mean return (ENPV)

or the lowest dispersion of returns

(NPV) are not necessarily the least risky. ˜e

total

risk of a project must be assessed by reference to

both

parameters and compared with alternative investments.

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42 The Treatment of Uncertainty

To evaluate projects that are either

mutually exclusive

or subject to

capital rationing

, the depth of variability

around the mean must be incorporated into our analysis. We can either maximise the expected return

for a given level of risk, or minimise risk for a given expected return

MAX: ENPV, given ˇNPV or MIN: ˇNPV, given ENPV

Ideally, we should also maximise ENPV and minimise ˇ NPV using a

risk-free

discount rate to avoid

double counting. So, let us refer to the data set and analyse its risk- return pro˚le.

Project A has a higher expected rate of return than project B but the standard deviation is the same, so

project A is preferable. Project C has the same mean as project A but has a larger standard deviation, so

it is inferior. ˜e most e˙cient choice between A, B and C is therefore project A.

However, we encounter a problem when comparing projects A and D, since D has a higher mean

and

a higher standard deviation. So, which one of these projects should ESCo accept?

- ˜e z statistic

You will recall from the

SFM

text that if cash ˝ows (C

i) are normally distributed, we can use the statistical

table for the

area under the standard normal curve

to establish the probability that any value will lie within

a given number of standard deviations away from their mean (EMV) by calculating the

z statistic. ˜e

mechanistic procedure is as follows:

Calculate how many standard deviations away from the mean is the requisite value. ˜is is given by the

z statistic,

which measures the actual deviation from the mean divided by the standard deviation. So,

using Equation (5) from the

SFM

text:

(5) z = Ci Œ EMV / (Ci)Next, consult the table to establish the area under the normal curve between the right

or leˆ of

z (plus

or minus) by ˚nding the absolute value of

z to two decimal places.

For example, the area one standard deviation above the mean is found by cross-referencing the ˚rst two

signi˚cant ˚gures in the leˆ hand column (1.0) with the third ˚gure across the top (0).˜erefore, the

probability of a value lying between the mean and one standard deviation above the mean is 0.3413,

which equals 34.13 per cent.

Since a normal distribution is symmetrical, 2

z represents the probability of a variable deviating above

or below the mean. ˜erefore, the probability of a value +ˇ, or -ˇ, away from the mean corresponds to

68.26 percent of the total area under the normal curve, i.e. twice 34.13 percent.

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43 The Treatment of Uncertainty

As a measure of risk, the standard deviation has a further convenient property in relation to the normal

curve. Assuming normality, we have estimated the percentage probability that any variable will lie within

a given number of standard deviations from the mean of its distribution by calculating the

z statistic.

Reversing this logic, from a table of

z statistics we can observe that any normal distribution of random

variables about their mean measured by the standard deviation will conform to prescribed

con˙dence

limits

, which we can express as a percentage probability.

For example, the percentage probability of any cash ˝ow (C

i) lying one, two or three standard deviations

above or below the EMV of its distribution is given by:

EMV n (where n equals the number of standard deviations)

2 x 0.3413 for -

to +

= 68.26% 2 x 0.4772 for -2

to +2

= 95.44% 2 x 0.4987 for -3

to +3

= 99.74%(Perhaps you can con˜rm these ˜gures by reference to a

z table?)Returning to our data set, let us assume that the management of ESCo wish to choose between projects

A and D using an approximate con˚dence limit of 68 percent. ˜e basis for their accept reject decisions

can be summarised as follows: (•000s)

Probability

ENPV ± nˇ (where n equals one)

2 × 0.3413 = 68.26% for

-ˇ to

+ˇProject A: ENPV

39-27 =12 39+27 = 66Project D: ENPV

45-36 = 9 45+36 = 81Unfortunately, the company still cannot conclude which project is less risky. Explained simply, should

it opt for project A with the likelihood of •12,000 (compared to only •9,000 from project D) or project

D with an equal likelihood of •81,000 (compared to •66,000 from project A)?

- ˜e Coe˚cient of Variation

To resolve the problem, one solution (or so it is argued) is to measure the

depth

of variability from the

mean using a

relative

measure of risk (rather than the standard deviation alone, which is an

absolute

measure). Using Equation (6) from the

SFM

text, we could therefore apply the

coe˜cient of variation

to

our project data set (•000s) as follows:

(6) Coe˛.Var. = (

NPV) / (ENPV)

Project: A 27/39 = 0.69; B 27/27 = 1.00; C 33/39 = 0.85; D 36/45 = 0.80.

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44 The Treatment of Uncertainty

˜ese ˚gures now con˚rm that projects B and C are more risky than A and D. Moreover, D is apparently

more risky than A because it involves •0.80 of risk (standard deviation of NPV) for every •1.00 of ENPV,

whereas project A only involves •0.69 for every •1.00 of ENPV. So, should the management of ESCo

now select project A?

- ˜e Pro˛tability Index

Unfortunately, we still don™t know. ˜e coe˙cient of variation (like the IRR under certainty) ignores the

size

of projects, thereby assuming that risk attitudes are

constant

. Add zeros to the previous project data

and note that the coe˙cients would still remain the same. Yet, intuitively, we all know that investors

(including management) become increasingly risk averse as the stakes rise. Explained simply, is a low

coe˙cient on a high capital investment better than a high coe˙cient on a low capital investment or

vice versa

?To overcome the problem, an alternative solution is for management to predetermine a desired

minimum

ENPV for investment (I

o) expressed as a

pro˙tability index

with which they feel comfortable. ˜is

benchmark

can then be compared to

expected

indices for proposed investments, which also incorporate

con˙dence limits

(as de˚ned earlier) to re˝ect

subjective

managerial risk attitudes. So, the company™s

objective function for project selection using Equation (7) from the

SFM

text becomes:

(7) MAX: (ENPV Œ nˇNPV) / I

0 MIN: NPV / I0Download free eBooks at bookboon.com

45 The Treatment of Uncertainty

Assume that ESCo apply a benchmark [MIN:NPV / I

0] = •0.12 to satisfy stakeholders. Use

the initial data to derive the left-hand side of Equation (7) one standard deviation from the

mean for projects A and D, assuming that they cost •100k and •75k, respectively. Now use

the whole equation to compare their acceptability to management.

Recall that mean-variance analysis alone (or the

z statistic and con˚dence limits) could not discriminate

between project A or D. Using the coe˙cient of variation, Project A seemed preferable to D. Note now,

however, using the expected pro˚tability index with the same con˚dence interval (68.26% probability)

that both projects are equally acceptable (• 000s).

Project

(ENPV Œ ˇNPV) / I

0 ˘ MIN: £NPV / I0 Decision

A

39 Œ 27 /100 = 0.12 =

0.12

Accept

D

45 Œ 36 / 75 = 0.12 =

0.12

Accept

But is this true?

- ˜e Risk-Return Paradox

From your reading you should be aware that modern ˚nancial theory de˚nes investors (including

management) as rational, risk-averse investors who seek maximum returns at minimum risk. But

throughout our example, we have a statistical-behavioural

paradox

based on the

symmetric normality

of returns and their

depth

of variability around the mean, however we de˚ne it.

ESCo still cannot conclude which project is less risky. Explained simply, one standard deviation from the

mean, should it opt for project A with the likelihood of •12,000 (compared to only •9,000 from project

D) or project D with an equal likelihood of •81,000 (compared to •66,000 from project A)?

Whilst project A maximises

downside

returns there is also an equal probability that project D maximises

upside

returns. So, is project A less risky than project D?

Below the mean, risk aversion would select the former, (why?). Above the mean, project D is clearly

more attractive, (to whom?). Presumably, rational, risk-averse investors would say ﬁyesﬂ to project A.

But those prepared to gamble would opt for project D?

˜e

risk-return paradox

cannot be resolved by formal, statistical analyses of the mean, variance or

standard deviation, con˚dence limits,

z statistics, and coe˙cients of variation, or pro˚tability indices.

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46 The Treatment of Uncertainty

We also need to know the

behavioural

attitudes of decision-makers (in our example, the corporate

management of ESCo) towards risk (aversion, indi˛erence, or preference). And for this you must refer

back to Chapter Four of the

SFM

text for the concept of

investor utility

and the application of

certainty

equivalent

analysis within the context of investment appraisal.

Exercise 4.2: Decision Trees and Risk Analyses

Our previous exercise considered statistical techniques for selecting investments based on their

predetermined

pattern of probabilistic cash ˝ows However, companies are sometimes faced with more

complex

sequential

decisions where:

Management need to make a strategic choice between alternative courses of action

with the possibility of future alternative courses of action occurring dependant upon

their previous choices.

In Chapter Four of the

SFM

text, we therefore mentioned a diagrammatic technique termed ﬁdecision

treeﬂ analysis to clarify this problem. ˜e diagram begins with the investment decision (trunk) which is

then channelled through alternative strategies (branches) arising from subsequent managerial decisions

(control

factors) or pure chance. As each branch divides, (

nodal

points) monetary values and

conditional

probabilities are attached until all possible outcomes are exhausted. Each

node

represents a

decision point

that departs from previous decisions, stretching back to the initial investment. Moving up the tree, the

branch structure therefore reveals eventual possible pro˚ts (or losses) in terms of EMV. NPV techniques

using mean-variance analyses can then be applied to assess an optimum investment decision.

So, let us illustrate the technique using the following information.

˜e Chilli Pepper Group (CPG) needs a new productive process, the cost of which is either £2 million

or £3 million depending on future demand. ˜e following forecast data is available.

£2m Project

£3m Project

Probability

Years

Annual cash ˜ow (£m)

Probability

Years

Annual cash ˜ow (£m)

0.4 1Œ4 0.60 0.3 1Œ4 1.00 5Œ10 0.50 5Œ10 0.70 0.4 1Œ4 0.60 0.5 1Œ4 0.80 5Œ10 0.20 5Œ10 0.40 0.2 1Œ10 0.20 0.2 1Œ10 0.10˙Pi =1.0˙Pi =1.0 Cost of Capital 10%

Cost of Capital 10%

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47 The Treatment of Uncertainty

Required:

1. Prior to analysing the data set, refer to appropriate DCF tables and summarise the factors

necessary for your analysis.

2. Use the data set and your DCF factors to determine the probabilistic cash ˝ows for both

investment opportunities (£2m and £3m).

3. Analyse all the above information in the form of decision trees.

4. Comment on the statistical validity of your ˚ndings.

An Indicative Outline Solution

1. ˜e Present Value of £1.00 received annually for the requisite number of years.

Years

10% DCF Factor

1Œ43.175Œ102.981Œ106.15Download free eBooks at bookboon.com

48 The Treatment of Uncertainty

2. ˜e Present Value of Probabilistic Cash Flows Discounted at 10 per cent (£m)

£2mProject

£3mProject

Years

PV Factor

Cash Flows

PVCash Flows

PV 1Œ4 3.17 0.60 1.90 1.00 3.17 5Œ10 2.98 0.50 1.50 0.702.09 1Œ4 3.17 0.60 1.90 0.802.54 5Œ10 2.98 0.20 0.60 0.401.191Œ106.15 0.201.230.100.623. ˜e Decision Trees (£m)

All the previous information for either project can be graphically reformulated as a decision tree

summarised below. Each diagram (£m) begins with the initial decision (£2m or £3m), moving

through the branches associated with their alternative strategic pay-o˛s. For convenience, their

respective ENPV at 10 per cent is also shown.

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49 The Treatment of Uncertainty

˜e two decision trees reveal that the ENPV of the £2 million investment is marginally

superior to that for £3 million. So, presumably, the incremental investment of £1 million is

not worthwhile? However, look closely at the data and you will see a larger range of possible

outcomes for the larger investment (i.e. a greater chance of lower cash ˝ows

but also

a greater

chance of higher cash ˝ows). So, is the smaller investment really preferable?

4. Statistical Commentary

˜e ˚rst point to note is that if the worst and best

states of the world

materialise, the £2 million

investment

minimises

losses whilst £3 million

maximises

pro˚ts.

Worst Case Scenario

£2 million Project

£3 million Project

Cash ˝ow

1.230.62Investment

(2.00)(3.00)NPV(0.77)(2.38)Best Case Scenario

£2 million Project

£3 million Project

Cash ˝ow

3.405.26Investment

(2.00)(3.00)NPV1.402.36˜us, we might conclude that if CPC wish to take a chance it could opt for the larger investment.

However, any risk assessment should be guided by the investment™s size relative to the scale of

the company™s other operations. If £3 million represents a

marginal

investment in a diverse,

multi-project ˚rm, then management need not worry unduly. But if CPC is small with a narrow

investment portfolio, the failure of this one project could be catastrophic.

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50 The Treatment of Uncertainty

So, let us focus on the

downside

risk for each project using mean-variance analysis, given:

EMV = ENPV (@ £2m) = 0.61 > ENPV (@ £3m) = 0.57Each project™s standard deviation is calculated using the PV of cash ˝ows for their branches For example,

the C

i of 3.4 in the ˚rst cell below equals 1.9 plus 1.5 (£ million) used earlier.

C i Pi C i Pi (C

i Œ EMV)

2 Pi(C

i Œ EMV)

2 Pi 3.40 0.4 1.36 0.62 0.4 0.248 2.50 0.4 1.00 0.012 0.4 0.005 1.23 0.2 0.25 1.90 0.2 0.380 S Pi 1.0 1.0Expected Monetary Value (EPV) 2.61

Variance (VAR =

2 ) = 0.633ENPV = EPV Œ I0 = 2.61 Œ 2.00 = 0.61 S.D. (ˆVAR =

) = 0.796Mean-Variance Analysis at £2 Million

C i Pi C i Pi (C

i Œ EMV)

2 Pi(C

i Œ EMV)

2 Pi 5.26 0.3 1.58 2.86 0.3 0.858 3.73 0.5 1.87 0.03 0.5 0.015 0.62 0.2 0.12 8.70 0.2 1.740 S Pi 1.0 1.0Expected Monetary Value (EPV) 3.57

Variance (VAR =

2 ) = 2.613ENPV = EPV Œ I0 = 3.57 Œ 3.00 = 0.57 S.D. (ˆVAR =

) = 1.615Mean-Variance Analysis at £3 Million

You might care to con˚rm that the £2 million investment minimises downside returns at all

con˚dence levels.

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51 The Treatment of Uncertainty

Summary and Conclusions

Our ˚rst Exercise dealt with risky projects where more than one set of cash ˝ows are possible, based

on two classical statistical parameters, namely the

mean

and

standard deviation

of their distribution.

However, despite the increasing sophistication of our analyses, none of the models speci˚ed investors risk

attitudes (for example managerial reaction to con˚dence intervals).We therefore suggested reference to an

even more sophisticated approach to investment appraisal, covered in Chapter Four of your companion

text (

SFM

) namely:

˜e PV maximisation of the expected utility of cash equivalents

However, this model too, is problematical. Its validity still depends upon how basic ˚nancial data feeds

into complex ENPV calculations. And this is where our second Exercise ˚ts in.

Decision trees (like sensitivity analysis and computer simulation also covered in the

SFM

text) are not

selection criteria, but an aid to judgement. ˜ey do not provide

new

information. However, they do

clarify

crucial

information using sequential decision points and their probabilistic outcomes in

simple

˚nancial terms. Perhaps strategic management ought to return to this technique and adopt a more

ﬁhands onﬂ approach to investment appraisal, rather than rely on ﬁhands o˛ﬂ computer programs, which

use incomprehensible models that precipitated the ongoing 2008 global and ˚nancial and economic

meltdown, so oˆen referred to throughout our study.

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52 Part Three

The Finance Decision

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53 Equity Valuation the Cost of Capital

5

Equity Valuation the Cost of

Capital

Introduction

Having explained how ENPV investment models can maximise shareholder wealth, we need to consider

how management actually ˚nance investments, since their cost of capital determines project discount

rates and hence corporate value. Part ˜ree of the

SFM

text reveals how funds can be raised from a

variety of sources at di˛erent costs with important implications for a company™s

overall

discount rate

and shareholder wealth. However, even the derivation of a

single

discount rate in

all-equity

˚rms poses

problems. To maximise wealth, management need to know their shareholders™ desired rate of return and

then only accept projects with a positive ENPV discounted at this rate. But this not only presupposes a

share valuation model that determines the current return on equity but also the nature of the return. Is

it a dividend or earnings stream?

Chapter Five of our companion text touched on this problem in the Review Activity. ˜e following

exercises examine its complexity in more detail. Each question begins with an exposition of the theories

required for its solution. And because of their complexity, we shall develop the data throughout both

exercises in a ﬁcase studyﬂ format (so you can retrace your steps back from the second exercise to the

˚rst if necessary). To tackle the sequence of questions throughout this chapter you also need to refer to

the

SFM

text, other readings you are familiar with, plus your knowledge of share price listings in the

˚nancial press.

Exercise 5.1: Dividend Valuation and Capital Cost

You will recall that Chapter Five of

SFM

de˚nes a company™s current

ex div

share price (P

o) in a variety

of ways using the present value model. Each price corresponds to a dividend or earnings stream (D

t or E

t) under growth (g) or non-growth conditions, discounted at an appropriate cost of equity (K

e) i.e.

shareholder return within a speci˚ed time continuum.

For example, if shares are held in

perpetuity

and the latest reported dividend per share remains

constant

inde˚nitely (i.e. g = zero) the current

ex div

price can be expressed using K

e as the shareholders™

capitalisation rate for a

perpetual annuity

.P0 = D1 / KeLikewise, a corresponding earnings valuation based on earnings per share (EPS) is given by:

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54 Equity Valuation the Cost of Capital

However, rearrange either equation to de˚ne the shareholders™ return (K

e) as a managerial cut-o˛ for

investment (project discount rate) and we encounter a fundamental problem.

Assume funds are retained for reinvestment, i.e. dividends are lower than earnings (which characterises

the ˚nancial policy of most real world companies). Because the

same

share cannot trade at

di˝erent

prices at the

same

time, the equity capitalisation rate (discount rate) must

di˝er

in the two equations.

Summarised mathematically, if:

Dt < Et but P

0 = Dt / Ke = P0 = Et / Ke then

Ke = Dt / P0 < Ke = Et / P0Moreover, if P

0 is common to both value equations, then not only must the equity yield for dividends

and earnings (K

e) di˛er, but a

unique

relationship must also exist between the two.

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55 Equity Valuation the Cost of Capital

˜e ˜eoretical Background

˜roughout the 1950s and 1960s, Myron J. Gordon (referenced in

SFM

) formalised the relationship

between dividend-reinvestment policies, their associated returns and current share prices under

conditions of

certainty

and

uncertainty

. Using a

constant growth

formula:

The Gordon dividend growth valuation model determines the current ex-div price of a share

by capitalising next year™s dividend at the amount by which the shareholders™ desired rate of

return exceeds the constant annual growth rate of dividends.

Using Gordon™s notation, where K

e is the equity capitalisation rate; E

1 equals next year™s post-tax earnings;

b is the proportion retained; [E

1 (1-b)] is next year™s dividend; r is the return on reinvestment and rb

equals the constant annual growth in dividends, we can de˚ne:

P 0 = [E1(1-b)] / Ke Œ rbIn most Finance texts the equation™s notation is simpli˚ed as follows, with D

1 and g representing Gordon™s

dividend term and growth rate respectively:

P 0 = D1 / Ke Œ gSubject to the non-negativity constraint that K

e > rb = g (for share price to be

˙nite

) we can also rearrange

the terms of the Gordon

valuation

model and solve for Ke to produce an

investment

model.

Ke = [{E1(1-b)} / P0] + rb = (D1 / P0) + gAccording to Gordon, the managerial cut-o˛ (project discount) rate for new investment is

de˜ned by the shareholders™ total return, which equals a dividend expectation divided by

current share price, plus a premium for growth (capital gain).

Gordon then analysed the behaviour of his models, assuming a perfect world of

certainty

and came

to the same conclusions as Irving Fisher thirty years earlier (see Chapter One of

SFM

). According to

Fisher™s

Separation ˛eorem

, price movements and returns relate to pro˚table investment policy and not

dividend policy. Speci˚cally:

(i) Shareholder wealth (price and return) will stay the same if r equals K

e(ii) Shareholder wealth (price and return) will increase if r is greater than K

e(iii) Shareholder wealth (price and return) will decrease if r is lower than K

e˜us, dividend policy is a

residual

managerial decision only made once a company™s pro˚table reinvestment

opportunities are exhausted.

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56 Equity Valuation the Cost of Capital

A Practical Illustration Œ Certainty

To gauge the impact of corporate reinvestment policy on share price and returns using the Gordon

growth model under conditions of

certainty

consider the following data.

Because of recession, the share price of Jovi plc tumbled from £2.00 to 75 pence throughout 2009 and

market capitalisation fell from £20 million to £7.5 million. EPS and dividend cover also halved, falling

from 10 pence to 5 pence and from two to one, respectively. With economic revival, however, Jovi intends

to declare a 10 pence dividend per share (covered once) equivalent to a dividend yield of 2.5 per cent.

Required:

1. Calculate the new equilibrium price for Jovi™s shares based on its dividend intentions.

2. Calculate the new

equilibrium

price if Jovi retained 50 per cent of its annual earnings

3. Comment on your results with regard to shareholder returns and the managerial cut-o˛ rate.

An Indicative Outline Solution

1. ˜e Equilibrium Price (zero growth)

Without further injections of capital, a 10 pence dividend covered once not only implies an

EPS of 10 pence but an intention to pursue a policy of

full distribution

with

zero

growth. If

shareholders are satis˚ed with a 2.5 per cent yield on this investment, we can de˚ne their

current share price by using the capitalisation of a

perpetual annuity

.P0 = E1 / Ke = D1 / Ke = 10 pence / 0.025 = £4.00

2. ˜e Equilibrium Price (growth)

With the same EPS forecast of 10 pence but 50 percent reinvested in perpetuity, new project

returns should

at least equal

the original equity capitalisation rate of 2.5 per cent (Fisher™s

˜eorem). So, using this ˚gure for the annual reinvestment rate we can determine an annual

growth rate to incorporate into the Gordon valuation model as follows:

P 0 = [E1(1-b)] / Ke Œ rb = P0 = D1 / Ke Œ g = 5 pence / 0.025 Œ 0.0125 = £4.00

3. Commentary

Despite changing mathematical formulae from the capitalisation of a perpetual annuity to

a model that accommodates retentions and reinvestment (growth) share price remains the

same. Moreover, reformulate the growth equation solving for K

e and it is still equivalent to the

original dividend yield; but why?

Ke = (D1 / P0) + g = (5 pence / £4.00) + 0.0125 = 2.5%

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57 Equity Valuation the Cost of Capital

According to Gordon, movements in share price relate to the pro˚tability of corporate

investment opportunities and not alterations in dividend policy. So, if the company™s rate of

return on reinvestment (r) equals the shareholders™ original capitalisation rate, share price and

Ke remain the same (in Jovi™s case, 2.5 per cent). ˜us, it also follows logically that:

(i) Shareholder wealth (price and return) will

increase

if r is greater than the original K

e(ii) Shareholder wealth (price and return) will

decrease

if r is lower than the original K

eGiven P

0 = £4.00, Ke = 2.5 per cent and b = 0.5, perhaps you can con˜rm that if Jovi™s reinvestment

rate (r) moves from 2.5 per cent

up to 4.0 per cent or

down

to 1.0 per cent:

P0 moves to £10.00 or £2.50 with corresponding revisions to the cut-o˛ rate (K

e) of 3.25 per cent

and 1.75 per cent, respectively.

A Practical Illustration Œ Uncertainty

Gordon™s initial value-investment model depends on

certainty

assumptions in perfect markets. He begins

with a

constant

equity capitalisation rate (K

e) equivalent

to a managerial assessment of a

constant

return

(r) on new projects ˚nanced by a

constant

retention rate (b).When he changes the variables, they too,

remain the same in perpetuity. However, these simplifying assumptions do not invalidate his analysis.

Like most ˚nancial models they are a

means to an end

. With simple policy prescriptions as

benchmarks

, Gordon moves into the real world by asking ﬁwhat if the future is

uncertain

ﬂ?Download free eBooks at bookboon.com

58 Equity Valuation the Cost of Capital

According to Gordon, most real-world market participants are still

rational

-risk averse

investors who

subscribe to a ﬁbird in the handﬂ philosophy. ˜ey prefer

more

dividends

now

rather than later, even

if future retentions are more pro˚table than their current capitalisation rate (r > K

e). Consequently,

near dividends are valued more highly. Investors discount

current

dividends at a lower rate than

future

dividends (K

e1<Ke2<Ke3–.) because they expect a higher overall return on equity (K

e0) from ˚rms that

retain a greater proportion of their earnings. ˜e inevitable implication of this

risk- return trade-o˝

is

that share price will fall because equity values are:

-Positively

related to the dividend payout ratio

-Inversely

related to dividend cover

-Inversely related to the retention rate

-Inversely

related to the dividend growth rate.

In a world of

uncertainty

Gordon therefore reverses the logic of his

certainty

argument. He

hypothesises

that

dividend policy, rather than investment policy, should motivate management to maximise shareholder

wealth. ˜e overall equity capitalisation rate is no longer a

constant

but a function of the

timing and size

of the dividend payout ratio.

Increased

retention rates (delayed dividend payments) result in the most

signi˚cant

rise

in periodic dividend capitalisation rates and corresponding

fall

in current shares values

(or

vice versa

).To summarise Gordon™s uncertainty hypothesis

, current shareholder returns and managerial cut-o˛ rates

are functionally related to the dividend payout ratio, or equivalent retention rate, as follows:

Ke0 = f (Ke1 < Ke2 < – Ken)Because the greatest periodic inequalities relate to the non-payment of dividends, an

all-equity

˚rm

should

maximise

its dividend payout to

minimise

the equity capitalisation (cut-o˛) rate and

maximise

share price and corporate wealth.

So, let us focus on the

uncertain

relationships between dividend-investment policies, share price behaviour

and managerial discount rates in the presence of retention ˚nanced growth.

Consider the following data set for Jovi plc in a world of

uncertainty

. ˜e ˚rst line (1) represents a full

distribution policy (like our previous example). ˜e second (2) re˝ects a rational managerial decision to

withhold half the dividend (like before). And note, that the company™s revised return on reinvestment not

only exceeds the company™s original capitalisation rate (2.5 per cent) but also the shareholders™ upward

risk-return revision.

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59 Equity Valuation the Cost of Capital

Forecast EPS

Retention Rate

Dividend Payout

Return on

Investment

Growth Rate

Shareholder

Return

E1(b)

(1-b)

(r)rb = g

Ke1: £0.1001.0--0.0252: £0.100.50.50.0750.03750.050Required:

1. Explain why the basic requirements of the Gordon growth model under conditions of

uncertainty are satis˚ed by the data set.

2. Con˚rm whether share prices derived from the data set support Gordon™s hypothesis.

3. Summarise the conceptual and statistical weakness of on your ˚ndings.

An Indicative Outline Solution

In Gordon™s world of

uncertainty

, share price, equity capitalisation and managerial cut-o˛ rates are a

function of dividends-retention policies that are

imperfect

economic substitutes.

1: ˜e Gordon Model

Moving from full to partial distribution, our data set

satis˙es all the requirements

of the Gordon

model. Withholding dividends [E

1(1Œb)=D1], to ˚nance new investment not only accords with

Fisher™s wealth maximisation criterion (r>K

e) but also satis˚es the mathematical constraint that

Ke > rb = g. ˜e equity capitalisation rate (K

e) also rises with the increased rate of return (r)

on retentions (b) i.e. the growth rate (g).

But has share price (P

0) fallen, given the reduction in the dividend payout, the increase in

growth and K

e and as Gordon predicts?

2: Gordon™s Predictions

Rational, risk-averse investors may prefer dividends now, rather than later (a ﬁbird in the handﬂ

philosophy that values current consumption more highly than future investment). But using

our data set, which

satis˙es all the requirements

of the Gordon dividend growth model under

conditions of uncertainty, you should have discovered that:

Despite a change in dividend policy, share price remains the same

P 0 = [E1(1-b)] / Ke Œ rb = P0 = D1 / Ke Œ g = £4.00Download free eBooks at bookboon.com

60 Equity Valuation the Cost of Capital

Of course, the series of variables in the data set were deliberately chosen to ensure that share

price remained unchanged. But the important point is that they all satisfy the requirements

of the Gordon model, yet contradict his prediction that share price should fall. Moreover, it

would be just as easy to produce other data sets, which satisfy his requirement that share price

should apparently rise but actually stay the same, (or even fall).

3: ˜e Gordon Weakness

˜e dividend growth model confuses ˚nancial policy (

˙nancial risk

) with investment policy

(business risk

). An increase in the dividend payout ratio, without any additional ˚nance, reduces

a ˚rm™s investment capability and

vice versa

. Consider the basic equation:

P0 = D1 / Ke Œ gChange D

1, then you change K

e and g.. So, how do you unscramble the di˛erential e˛ects on

price (P

0) when all the variables on the

right hand side

of the equation are now a˛ected?

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61 Equity Valuation the Cost of Capital

Gordon encountered this problem when empirically testing his model, being unable to conclude

that dividends determine share price and return. Yet, statisticians among you will recognise the

phenomena, termed

multicolinearity

. Change one variable and you change them all because

they are all interrelated. No wonder subsequent research, even using sensitivity analysis cannot

prove conclusively that dividend policy determines share price.

Exercise 5.2: Dividend Irrelevancy and Capital Cost

˜e purpose of this Exercise is to evaluate Gordon™s case for dividend policy as a determinant of corporate

value and capital cost in a wider context by introducing the comprehensive critique of Franco Modigliani

and Merton H. Miller (MM henceforth) to the debate. Since 1958, their views on the

irrelevance of ˙nancial

policy

(which includes dividend policy) based on their Nobel Prize winning economic ﬁlaw of one priceﬂ

and a wealth of empiricism has proved to be a watershed for the development of modern ˚nance.

˜e ˜eoretical Background

According to MM, dividend policy is not a determinant of share price in reasonably e˙cient markets

because dividends and retentions are

perfect economic substitutes

. -If shareholders forego a dividend to bene˜t from a retention-˜nanced capital gain, they

can still create their own home made dividends to match their consumption preferences

by the sale of shares and be no worse o˛.

- If companies choose to distribute a dividend they can still ful˜l their investment

requirements by a new issue of equity, rather than use retained earnings, so that the

e˛ect on shareholders™ wealth is also neutral.

˜eoretically and mathematically, MM have no problem with Gordon™s model under conditions of

certainty

. ˜ey too, support Fisher™s Separation ˜eorem that share price is a function of pro˚table

corporate investment (business risk) and not dividend policy (˚nancial risk).But where MM depart

company from Gordon is under conditions of

uncertainty

.MM maintain that Gordon™s model fails to discriminate between ˚nancial policy (˚nancial risk) and

investment policy (business risk). For example, an increase in the dividend payout ratio, without any

additional ˚nance, reduces a ˚rm™s reinvestment capability and

vice versa

.Using the earlier notation for the dividend growth model:

P0 = D1 / Ke Œ gDownload free eBooks at bookboon.com

62 Equity Valuation the Cost of Capital

Change D

1, you change b and as a consequence g = br also changes. And if K

e also changes as Gordon

hypothesises, MM legitimately ask our earlier question:

How are the di˛erential e˛ects of dividend policy and investment policy on price (P

0) measured when all the right hand variables of the Gordon equation are a˛ected?

Perhaps you recall from our previous exercise that this represented a real problem for Gordon and others,

who empirically encountered what statisticians formally term

multicolinearity

.MM also assert (quite correctly) that because uncertainty is

non-quanti˙able

, it is logically impossible

for Gordon to capitalise a

multi-period

future stream of dividends, where K

e1 < Ke2 < Ke3 etc., according

to the investors™ ˚nancial perception of the unknown. A

one-period

model, where K

e re˝ects the ˚rm™s

current

investment opportunities (business risk) is obviously more appropriate.

Finally, according to MM, if shareholders do not like the ˚nancial risk of their dividend stream they can

always sell their holdings. So, why revise K

e?˜e MM Model

Unlike Gordon, MM de˚ne an

ex-div

share price using a

one period model

. Moreover, their shareholder

return (K

e) equals the company™s cut-o˛ (discount) rate applicable to the business risk of its current

investment policy.

P0 = D1 + P1 / 1 + KeFor a given investment policy, a change in dividend policy cannot alter current share

price. According to MM, the future

ex div price increases by the reduction in the

dividend and vice versa.

To see why, let us return to the data set for Jovi plc in the previous exercise where the company ˚rst

pursues a dividend policy of

maximum distribution

with:

E1 = D1 = 10 pence in perpetuity and K

e = 2.5%MM would de˚ne an equivalent price to Gordon:

P0 = D1 + P1 / 1 + ke = £0.10 + £4.00 / 1.025 = £4.00But now, let us assume that the company pursues a policy of

maximum retention

to ˚nance future

investment of equivalent risk and see where this takes us.

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63 Equity Valuation the Cost of Capital

According to MM, if the cut-o˛ rate for investment still equals K

e then the

ex div

price rises by the

corresponding fall in the dividend, leaving P

0 unchanged.

P0 = D1 + P1 / 1 + ke = £0 + £4.10 / 1.025 = £4.00˜e Shareholders™ Reaction

You will recall that Gordon argues if dividends

fall

, the capitalisation rate should

rise

, causing share price

to fall

. However, MM maintain that both return and price should remain the same.

If shareholders

do not like the heat, they can get out of the kitchen

by creating

home-made

dividends through the sale of either part, or all of their holdings.

To prove the point, assume you own a number of Jovi™s shares (let us say, n = 10,000) with the company™s

initial policy of full distribution. From the previous section, it follows that:

nP0 = nD1 + nP1 / 1 + Ke = £1,000 + £40,000 / 1.025 = £40,000Now assume the ˚rm withholds all dividends for reinvestment. What do you do if your income

requirements (consumption preferences) equal the non-payment of your dividend (£1,000)?

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64 Equity Valuation the Cost of Capital

According to MM, there is no problem. ˜e

ex div

share price increases by the reduction in dividends,

so, your holding is now valued as follows, with no overall change:

nP0 = nD1 + nP1 / 1 + Ke = £0 + £41,000 / 1.025 = £40,000However, you still need to satisfy your income preference for £1,000 at time period one.

So, MM would suggest that you sell 250 shares for £41,000 / 10,000 at £4.10 apiece.

You now have £1,025, which means that you can take the income of £1,000 and reinvest the balance of

£25 on the market at your desired rate of return (K

e=2.5%). And remember you still have 9,750 shares

valued at £4.10. To summarise your new equilibrium position:

Shareholding 9,750: Market value £39,975: Homemade Dividends £1,000: Cash £25

So, have you lost out? According to MM,

of course not

, because future income and value are unchanged:

£nP1 = 9,750 x £4.1039,975Cash reinvested at 2.5%

25Total Investment

40,000Total annual return at 2.5%

1,000˜e Corporate Perspective

Let us now turn or attention to what is now regarded as the

proof

of the MM dividend

irrelevancy

hypothesis. ˜is is

usually liˆed

verbatim

from the mathematics of their original article and relegated to

an Appendix in the appropriate chapter of most ˚nancial texts, with little if any numerical explanation.

So, where do we start?

˜e MM case for

dividend neutrality

suggests that shareholders can create their own

home-made

dividends, if needs be, by selling part or all of their holdings at an enhanced e

x-div

price. For its part

too, the ˚rm can resort to new issues of equity in order to ˚nance any shortfall in its investment plans.

To illustrate the dynamics, consider Jovi plc that now has a policy of maximum retention (nil distribution)

and a dedicated investment policy, whose shares are currently valued at £4.00 with an

ex-div

price of

£4.10 at time period one:

P0 = D1 + P1 / 1 + Ke = £0 + £4.10 / 1.025 = £4.00Download free eBooks at bookboon.com

65 Equity Valuation the Cost of Capital

Assuming Jovi has one million shares in issue (n) we can then derive its market capitalisation of equity:

nP0 = nD1 + nP1 / 1 + Ke = £0 + £4.1m / 1.025 = £4m˜e ˚rm now decides

to distribute all earnings as dividends

(10 pence per share on one million issued).

If investment projects are still to be implemented, the company must therefore raise new equity capital

equal to the proportion of investment that is no longer funded by retained earnings. From the MM proof:

mP1 = nD1 = £100,000Based on all the shares outstanding at time period one, (n + m) P

1, we can rewrite the equation for the

total market value of the original shares in issue as follows:

nP0 = [nD1 + (n + m)P1 Œ mP1] / 1 + KeAnd because mP

1 = nD1, this simpli˚es to the

fundamental

equation of their proof containing

no dividend term

.nP0 = (n + m) P1 / 1 + Ke = (nP1 + £100,000) / 1.025 = £4mSince there is also only one unknown in the equation (i.e. P

1) then dividing throughout by the number

of shares originally issued (n = one million).

P0 = (P1 + £0.10) / 1.025 = £4.00And rearranging terms and solving for P

1:P1 = £4.00˜us, as MM hypothesise:

-˜e

ex-div

share price at the end of the period (P

1) falls

from its initial value of £4.10 to £4.00,

which is exactly the same as the 10 pence

rise

in dividend per share (D

1) leaving P

0 unchanged.

-Because the dividend term has completely disappeared from their value equation, it is

impossible to conclude that share price is a function of dividend policy.

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66 Equity Valuation the Cost of Capital

˜e MM Dividend Hypothesis: A Practical Illustration

To con˚rm the logic of the MM hypothesis yourself, let us modify Jovi™s previous

nil

distribution policy

to assess shareholder and corporate implications if management now adopt a policy of

partial

dividend

distribution, say 50 per cent? So we begin with:

P0 = (0 + £4.10) / 1.025 = £4.00And from our data set, we know the company now intends to pay a dividend of 5 pence per share next

year on one million currently issue. Without compromising its investment policy,

P0 = (0.10 + £4.00) / 1.025 = £4.00Required:

Explain why the ˚rm™s equity value is independent of its dividend payout ratio.

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67 Equity Valuation the Cost of Capital

An Indicative Outline Solution

Our second exercise provides an opportunity to evaluate the role of investment and ˚nancial criteria

that underpin the normative objective of shareholder wealth maximisation under conditions of certainty

and uncertainty. Our reference point is the Gordon-MM controversy concerning the determinants of

share price and capital cost in an all-equity ˚rm. Are dividends and retentions

perfect substitutes,

leaving

shareholder wealth and the corporate cut-o˛ rate for investment una˛ected by changes in dividend

distribution policy?

Points to Cover

1. ˜e Shareholders™ Reaction

˜e MM case for

dividend neutrality

suggests that if a ˚rm

reduces

its dividend payout, then

shareholders can create their own

home-made

dividends by selling part or all of their holdings

at an enhanced

ex-div

price. But in our question, the company has

increases

its dividend payout

ratio. So, do the shareholders have a problem?

2. Dividend Irrelevancy

For a given investment policy, a change in dividend policy (either way) does not alter current

share price. ˜e future

ex div

price falls by the rise in the dividend for a given investment

policy of equivalent business risk and

vice versa

, leaving the current

ex div

price unchanged.

Using our data set, where Jovi pursues an initial policy of

nil distribution

and K

e = 2.5%.P0 = D1 + P1 / 1 + Ke = £0 + £4.10 / 1.025 = £4.00But now assume that the ˚rm pursues a policy of 50 per cent retention to reinvest in projects

of equivalent business risk (i.e. K

e = 2.5 per cent). MM would de˚ne:

P0 = D1 + P1 / 1 + Ke = £0.05 + £4.05 / 1.025 = £4.003. ˜e Corporate Perspective

For its part too, Jovi can resort to new issues of equity in order to ˚nance any shortfall in

investment plans. To illustrate, consider the company™s original policy of

nil

distribution but

a dedicated investment policy, with shares currently valued at £4.00 but at £4.10 next year

P0 = D1 + P1 / 1 + Ke = £0 + £4.10 / 1.025 = £4.00Download free eBooks at bookboon.com

68 Equity Valuation the Cost of Capital

Management now decide to distribute 50 per cent of corporate earnings as dividends (5

pence per share on one million shares currently in issue). If investment projects are still to

be implemented, the company must therefore raise new equity equal to the proportion of

investment that is no longer funded by retained earnings. From our MM proof:

mP1 = nD1 = £50,000˜e substitution of this ˚gure into the MM equation for the total market value of the original

shares, based on all shares outstanding at time period one, equals:

nP0 = [nD1 + (n + m)P1 Œ mP1] / 1 + KeAnd because mP

1 = nD1, the MM proof simpli˚es to an equation with

no dividend term

.nP0 = (n + m) P1 / 1 + Ke = (nP1 + £50,000) / 1.025 = £4mSince there is only one unknown in this equation (P

1) then dividing through by the number

of shares originally in issue (n = one million) and solving for P

1:P0 = (P1 + £0.05) / 1.025 = £4.00P1 = £4.05So, as MM hypothesise; the

ex-div

share price at the end of the period has fallen from its initial

value of £4.10 to £4.05, which is exactly the same as the 5 pence rise in dividend per share,

leaving P

0 unchanged.

Summary and Conclusions

MM criticise the Gordon growth model under conditions of uncertainty from both a

proprietary

and

entity

perspective by focussing on home-made dividends and corporate investment policy, respectively.

According to MM, the current value of a ˚rm™s equity is independent of its dividend distribution policy,

or alternatively its retention policy, because they are

perfect economic substitutes:

˜e quality of earnings (business risk), rather than how they are packaged for distribution (˚nancial

risk), determines the shareholders™ desired rate of return and management™s cut-o˛ rate for investment

(project discount rate) in an all-equity ˚rm and hence its share price.

Consequently, dividend policy is a

passive residual

, whereby unused funds are returned to shareholders

because management has failed in their search for new investment opportunities, which at least elicit

project ENPVs that maintain shareholder wealth intact.

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69 Debt Valuation and the Cost of Capital

6

Debt Valuation and the Cost of

Capital

Introduction

Chapter Six of our

SFM

text explains why corporate borrowing is attractive to management. Interest

rates on debt are typically lower than equity yields. Debt (bond) holders accept lower returns than

shareholders because their investment is less risky. Unlike dividends, interest is a

guaranteed

prior claim

on pro˚ts. In the event of liquidation, bond holders like other

creditors

are also paid from the sale of

any assets before shareholders. Finally, in many countries, interest payments on debt (unlike dividends)

also qualify for corporate

tax relief

, reducing their

real

cost to the ˚rm and widening the yield gap with

equity still further.

The introduction of borrowing into the corporate ˜nancial structure, termed capital

gearing or leverage

, can therefore lower the overall return (cut-o˛ rate) that management need to earn on

new investments. Consequently, the ENPV of geared projects should be greater than their all

equity counterparts, producing a corresponding increase corporate wealth.

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70 Debt Valuation and the Cost of Capital

Our ˚rst exercise therefore reviews the ˚scal bene˚ts conferred on companies that issue corporate bonds

(debentures) whilst the second deals with the derivation of an overall cost of capital from a combination

of debt and equity as a managerial discount rate for project appraisal.

Because the development of the real world equations required to answer the ˚rst question are quite

complex, you might need to refer back to their origins in Chapter Six of the

SFM

text. To aid cross-

referencing, I have applied the original number to the equations where appropriate.

Exercise 6.1: Tax-Deductibility of Debt and Issue Costs

If management can generate su˙cient taxable pro˚ts to claim the tax relief on debt interest, the higher

the rate of corporation tax, the greater the ˚scal bene˚t conferred on the company through issuing

debt, rather than equity, to ˚nance investment. To prove the point, in the

SFM

text we de˚ned the

price of

irredeemable

debt incorporating the tax e˛ect by using the PV model for the capitalisation of a

perpetual annuity.

(6) P0 = I(1Œt) / KdtRearranging terms, the ﬁrealﬂ cost of debt for the company aˆer tax:

(7) Kdt

= I(1Œt) / P0And because the investors™

gross

return (K

d) equals the company™s cost of debt before tax, it follows that

with a tax rate (t) we can also rewrite Equation (7) as follows;

(8) Kdt = Kd (1Œt)In a world of corporate taxation, the capital budgeting implications for management are clear.

(9) Kdt < KdTo maximise corporate wealth, the post-tax cost of debt should be incorporated into any overall discount

rate as a cut-o˛ rate for investment.

Turning to

redeemable

debt, the company still receives tax relief on interest but oˆen the redemption

payment is not allowable for tax. To calculate the post-tax cost of capital it is necessary to determine an

IRR that incorporates tax relief on interest alone. ˜us, we derive K

dt in the following

˙nite

equation:

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71 Debt Valuation and the Cost of Capital

Irrespective of whether debt is irredeemable or redeemable, its tax adjusted cost of (K

dt) is the IRR that represents the true corporate cost of new debt issues. If the ENPV of a

prospective debt-˜nanced project discounted at this IRR is positive, then its return will

exceed the cost of servicing that debt and management should accept it.

Taxation Lags and Issue Costs

˜e introduction of tax

bias

into our analysis of debt costs is only one real world adjustment. ˜ere are

others, namely the

timing

of the tax bene˚t, set against the actual cost of

issuing

debt.

As we explained in

SFM

, corporate taxation might not be payable until well aˆer pro˚ts are earned. We

can therefore introduce greater realism into our calculations by incorporating a

time lag

associated with

the interest set-o˛ against corporate tax liability. Although this delay reduces the present value of the

tax deduction to the company, the

net cost of corporate debt will still be lower than the

gross

return to

the investor.

Let us assume a

one-year

time lag between the payment of annual interest and the receipt of the tax

bene˚t. ˜e post-tax cost of redeemable debt, K

dt can be found by solving for the IRR in the following

value equation:

˜us, the value of debt is equal to the discounted

pre-tax

cash ˝ows on the right-hand side of Equation (10),

less

the discounted sum of tax bene˚ts from the

second

year of issue to the year

aˆer

redemption (the

˚nal term on the right hand side of the above equation).

Of course, in the real world, the ﬁrealﬂ price of loan stock and marginal cost of debt to the company is

o˛set by issue costs, which can represent between three and six per cent of the capital raised.

˜is is best understood if we ˚rst substitute issue costs (C) into the cost of

irredeemable

debt in a

taxless

world (Equation 5 in

SFM

). ˜e denominator of the equation is reduced by the issue costs, so the

corporate cost or debt rises.

(13) Kd = I / P0 (1ŒC

)If we now assume that interest is tax deductible (with no time lag) the post-tax cost of debt originally

given by Equation (7) also rises.

(14) Kdt = I (1-t) / P0(1ŒC)Download free eBooks at bookboon.com

72 Debt Valuation and the Cost of Capital

But what if issue costs, as well as interest payments, are also tax deductible?

Using redeemable debentures, let us assume a one-year time lag for tax-deductibility associated with:

initial

issue costs and

annual

interest. Substituting this ˚scal policy into the previous

time lag

equation

should produce a lower corporate tax bill.

Indeed this debt valuation equation reveals how the tax deductibility associated with issue costs (the

discounted leˆ-hand term in brackets) works in the company™s favour, just like tax relief on interest (the

˚nal right-hand term of the equation).

To comprehend the complexities of the previous post-tax, issue cost equation and con˚rm the di˛erence

between an investor™s gross return and the company™s aˆer-tax cost of debt capital, consider the following

information.

˜e Sambora Company intends to issue a new ˚ˆeen year corporate bond in £100 blocks at a coupon rate

of 10 per cent with a redemption premium of 20 per cent. Issue costs are £3.00 per cent. ˜e corporate

tax rate is 50 per cent. Fiscal relief is staggered by one year.

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73 Debt Valuation and the Cost of Capital

Required:

1. Calculate the investors

yield to redemption

.2. Calculate the company™s

post-tax

cost of debt.

An Indicative Outline Solution

1. ˜e Redemption Yield

˜e investor yield to maturity solves for K

d using Equation (5) from the

SFM

text. Annual

interest payments and the redemption price are discounted back to a present value as follows:

P0 = 100 = 12 / (1+r) + 12 / (1+r)2 – + – 12 / (1+r)15 + 120 / (1+r)15˜e IRR of the equation (yield to redemption) is approximately 12.5 per cent per annum.

2. ˜e Corporate Cost of Issue

With regard to the company, the cost of debt is lower than the cost to its clientele because issue

costs and interest payments are tax deductible.

˜e value of any £100 bond allowing for

net

transaction costs (the di˛erence between £3.00

and the discounted 50 per cent tax relief on £3.00) is equal to the discounted interest payments

from year one to ˚ˆeen less the tax deductible interest bene˚t of £6 per annum, discounted

from year two through sixteen. ˜us, using the time-lag equation that incorporates issue costs:

And solving for the IRR, we ˚nd that the corporate post-tax cost of debentures (K

dt) is

approximately 7.4 percent per annum (compared with 12.5 per cent for investors).

Exercise 6.2: Overall Cost (WACC) as a Cut-o˛ Rate

With your knowledge of equity and debt valuation and their component costs we are now in a position

to combine them to derive a company™s weighted average cost of capital (WACC) as an overall cut-o˛

(discount rate) for investment. Consider the following information:

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74 Debt Valuation and the Cost of Capital

˜e summarised Balance Sheet of Winehouse plc is as follows ($m).

Ordinary Share Capital

1,600Fixed Assets

2,800Reserves

800Net Current Assets

200Debentures

600Totals

3,0003,000Two proposals have been placed before the Board by the new Finance Director, each requiring an initial

investment of $600,000 and the one piece of vacant land that the company has available, so that only

one investment can be chosen.

Project I will generate net cash ˝ows of $240,000 per annum for the ˚rst three years of its life and $100,000

per annum for the remaining two. Project II will generate net cash ˝ows of $200,000 per annum during

its life, which is also ˚ve years. Neither project has any residual value but the ˚rst project is regarded

as the less risky of the two. ˜ere is £$80,000 of internally generated funds available and the remainder

will have to be raised through the issue of ordinary shares and loan stock. However, Winehouse wishes

to maintain its original capital structure. ˜e current equity yield is 15% but a new issue of ordinary

shares at $5 per share will result in net proceeds per share of $4.75. It is also envisaged that 8% bonds

can be sold at par. ˜e company has a marginal corporate tax rate of 25%.

Required:

1. Derive the marginal WACC applicable to each investment.

2. Determine the NPV of each project with an explanation of which (if either) maximises wealth.

3. Summarise the conditions that must be satis˚ed to validate WACC as a cut-o˛ rate for

investment.

An Indicative Outline Solution

˜e calculation of both projects™ NPV requires the derivation of a discount rate, based upon the

mathematical concept of a

weighted average

applied to the formulation of a company™s

WACC

as an

appropriate cut-o˛ rate for investment. For example, with only two sources of capital (equity and debt

say) and using standard notation, a general formula for WACC is given by:

K = Ke(VE/V) + K

d(VD/V)

Computationally, the component costs of capital are weighted as a proportion of the company™s total

market value and the results summated (i.e. added together).

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75 Debt Valuation and the Cost of Capital

1. ˜e WACC Computation

Incremental ˚nance and capital costs using the desired capital structure.

Finance

($000)Weight

Cost

Component

Derivation

Equity: Internal

800.1315.0%1.95%given

External

4000.6715.8%10.59%less issue costs

Debt

1200.206.0%1.20%post taxTotals

6001.00WACC

13.74%2. NPV Analysis

Rounding up the WACC to a 14 per cent discount rate, you should be able to derive the

following NPVs for the two projects using the now familiar present value of the summation

of discounted cash ˝ows minus the cost of the investment.

[(PV@ 14%) Œ I0] = NPV = $70,200 for Project 1 < $88,000 for Project 2

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76 Debt Valuation and the Cost of Capital

Assuming that the normative objective of Winehouse is shareholder wealth maximisation, then

a NPV maximisation approach to project appraisal means that Project 2 should be accepted

if the investments are mutually exclusive and capital is rationed. Note, however, that the ˚rst

project is less risky. But is this important, given the small scale of the projects relative to the

company™s overall size? ˜e

marginal

nature of the projects also leads one to ask why the ˚rm

wishes to retain its existing capital structure when debt is the cheapest source of ˚nance, only

costing the company 6 per cent aˆer tax?

3. ˜e WACC Assumptions

To maximise NPV, it is a function of management to establish a discount rate, having acquired

capital in the most e˙cient (least costly) manner. If funds are acquired from a miscellany of

e˙cient sources to ˚nance projects, it also seems reasonable to assume that the derivation of

a marginal WACC should represent the optimum discount rate.

In an e˚cient capital market, optimum projects should produce returns in excess

of their minimum WACC at a maximum NPV that not only exceeds shareholders™

expectations of a dividend and capital gain but also the returns required by all

other providers of capital (Fisher™s Theorem again).

However, the use of WACC as an appropriate discount rate in project appraisal must satisfy the

following conditions:

-˜e selected investment is

homogenous

with respect to the overall business risk that

already confronts the ˚rm; otherwise the returns required by investors will change.

-˜e capital structure is reasonably

stable

; otherwise the weightings applied to the

component costs of the WACC calculation will be invalid.

-As a consequence, the investment should be

marginal

to the ˚rm™s existing operations.

With regard to the calculation itself, the overall cost of capital is found

via

the identi˚cation

of all types of capital used (including opportunity costs) which are weighted according to the

existing capital structure) and then summated to produce the WACC.

-˜e weights are based on the market value of securities, rather than their book values, so

as to re˝ect current rather than historical costs.

-˜e costs of equity are the returns expected by the shareholders on their funds invested

in the business (reserves and new issues) adjusted for issue costs.

-˜e cost of debt is the current market rate of interest net of tax relief, which can be

derived from existing borrowing.

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77 Debt Valuation and the Cost of Capital

Summary and Conclusions

In Chapter One our study of strategic ˚nancial management began with a hypothetical explanation of

a company™s overall cost of capital as an investment criterion designed to maximise shareholder wealth.

By Chapter Five we demonstrated that an

all equity

company should accept capital projects using the

marginal cost of equity as a discount rate, because the market value of ordinary shares will increase by

the project™s NPV.

In this chapter we considered the implications for a project discount rate if funds are obtained from a

variety of sources other than the equity market, each of which requires a rate of return that may be unique.

For the purpose of exposition, we analysed the most signi˚cant alternative to ordinary shares as an

external source of funding, namely redeemable and irredeemable loan stock. We observed that corporate

borrowing is attractive to management because interest rates on debt are typically lower than equity

yields. ˜e impact of corporate tax relief on debenture interest widens the gap further, although the

tax-deductibility of debt is partially o˛set by the costs of issuing new capital, which are common to all

˚nancial securities.

In this newly

leveraged

situation, the company™s overall cost of capital (rather than its cost of equity)

measured by a

weighted average cost

of capital

(WACC) seems a more appropriate investment criterion.

However, we observed that a number of conditions must be satis˚ed to legitimise its use as a project

discount rate. In the next chapter we shall examine these further.

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78 Debt Valuation and the Cost of Capital

7

Debt Valuation and the Cost of

Capital

Introduction

For the purpose of exposition, the derivation of a company™s weighted average cost of capital (WACC)

in Chapter Six was kept simple. Given ˚nancial management™s strategic objective is to maximise the

market value of ordinary shares, our analysis assumed that:

-˜e value attributed by the market to any class of ˚nancial security (debt or equity) is the

PV of its cash returns, discounted at an opportunity rate that re˝ects the ˚nancial risk

associated with those returns.

-˜e NPV of a project, discounted at a company™s WACC (based on debt plus equity) is the

amount by which the market value of the company will increase if the project is accepted;

subject to the constraint that acceptance does not change WACC.

We speci˚ed

three

necessary conditions that underpin this constraint and justify the use of WACC as a

cut-o˛ rate for investment.

-˜e project has the same business risk as the company™s existing investment portfolio.

-˜e company intends to retain its existing capital structure (i.e. ˚nancial risk is constant).

-˜e project is small, relative to the scale of its existing operations.

Yet, we know that even if business risk is

homogenous

and projects are

marginal

, the ˚nancial risk of future

investments is rarely

stable

. As the global meltdown of 2007 through to 2009 con˚rms, the availability of

funds (debt and equity) is

the

limiting factor

. ˜e component costs of project ˚nance (and hence WACC)

are also susceptible to change as

external

forces unfold.

So, let us develop a

dynamic critique of the overall cost of capital (WACC) and ask ourselves

whether management can increase the value of the ˜rm, not simply by selecting an optimal

investment

, but also by manipulating its

˜nance

. If so, there may be an optimal capital

structure arising from a debt-equity

trade-o˚

, which elicits a least-cost combination of

˜nancial resources that minimises the ˜rm™s WACC and maximises its total value.

In the summary to Chapter Seven of the

SFM

text we touched on the case for and against an optimal

capital structure and WACC based on ﬁtraditionalﬂ theory and the MM economic ﬁlaw of one priceﬂ

respectively. ˜e second exercise will pick up on these con˝icting analyses in detail. Speci˚cally, we

shall examine the MM

arbitrage

proof, whereby investors can pro˚tably trade securities with di˛erent

prices between companies with di˛erent leverage until their WACC and overall value are in

equilibrium

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79 Debt Valuation and the Cost of Capital

Unlike the traditionalists, MM maintain that the equilibrium value of any company is

independent

of its

capital structure and derived by capitalising expected project returns at a

constant

WACC appropriate

to their class of business risk. Yet both theories begin with a common assumption. Because of higher

˚nancial risk the cost of equity is higher than the cost of debt and rises with increased leverage (gearing).

So, before we analyse why the two theories part company, our ˚rst exercise will explain how increased

gearing a˛ects shareholder returns by graphing the relationship between earnings yields and EBIT (net

operating income) when ˚rms incorporate cheaper debt into their capital structure.

Like our approach to the questions in Chapter Five, we shall accompany each of the current exercises

with an exposition of the theories required for their solution, where appropriate. And because of their

complexity, we shall (again) develop a data set throughout Exercise Two using a ﬁcase studyﬂ format.

To tackle its sequential exposition (just like Chapter Five) you may need to refer back and forth,

supplementing your readings with any other texts, purchased or downloaded from the internet.

Exercise 7.1: Capital Structure, Shareholder Return and Leverage

To assess the impact of a changing capital structure on capital costs and corporate values, let us begin

with a fundamental assumption of capital market theory, which you ˚rst encountered in Chapter One,

namely that investors are

rational

and

risk averse

. Companies must o˛er them a return, which is inversely

related to the probability of its occurrence. ˜us, the crucial question for ˚nancial management is whether

a combination of stakeholder funds, related to the earnings capability of the ˚rm, can minimise the risk

which confronts each class of investor. If so, a ˚rm should be able to minimise its own discount rate

(WACC) and hence, maximise total corporate value for the mutual bene˚t of all.

We know from previous Chapters that

total

risk

comprises two inter-related components with which

you are familiar,

business risk

and

˙nancial risk

. So, even when a ˚rm is ˚nanced by equity alone, the

pattern of shareholder returns not only depends upon periodic post-tax pro˚ts (business risk) but also

managerial decisions to withhold dividends and retain earnings for reinvestment (˚nancial risk). As we

explained in Chapter Five, if rational (risk averse) investors prefer dividends now, rather than later, the

question arises as to whether their equity capitalisation rate is a positive function of a ˚rm™s retention

ratio. In otherwords, despite the prospect of a capital gain, does a ﬁbird in the handﬂ philosophy elicit

a premium for the ˚nancial risk associated with any diminution in the dividend stream? If so, despite

investment

policy, corporate

˙nancial

policy must a˛ect the overall discount rate which management

applies to NPV project analyses and therefore the market value of ordinary shares.

When a ˚rm introduces debt into its capital structure we can apply the same logic to arrive at similar

conclusions. Financial policies

matter

because the degree of leverage (like the dividend payout ratio)

determines the level of ˚nancial risk that confronts the investor.

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80 Debt Valuation and the Cost of Capital

˜e ˜eoretical Background

Initially, when a ˚rm borrows, shareholder wealth (dividend plus capital gain) can be increased if

the e˛ective cost of debt is lower than the original earnings yield. In e˙cient capital markets such an

assumption is not unrealistic:

-Debt holders receive a guaranteed return and in the unlikely event of liquidation are usually

given security in the form of a prior charge over the assets.

-From an entity viewpoint, debt interest quali˚es for tax relief.

You should note that the productivity of the ˚rm™s resources is unchanged. Irrespective of the ˚nancing

source, the same overall income is characterised by the same degree of business risk. What has changed is

the mode of ˚nancing which increases the investors™ return in the form of EPS at minimum ˚nancial risk.

So, if this creates demand for equity and its market price rises proportionately, the equity capitalisation

rate should remain

constant

. For the company, the bene˚cial e˛ects of cheaper ˚nancing therefore

outweigh the costs and as a consequence, its overall cost of capital (WACC) falls and total market

value rises.

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81 Debt Valuation and the Cost of Capital

Of course, the net bene˚ts of gearing cannot be maintained inde˚nitely. As a ˚rm introduces more

debt into its capital structure, shareholders soon become exposed to greater ˚nancial risk (irrespective

of dividend policy and EPS), even if there is no realistic chance of liquidation. So much so, that the

demand for equity

tails o˛ and its price begins to fall, taking total corporate value with it. At this point,

WACC begins to rise.

˜e increased ˚nancial risk of higher gearing arises because the returns to debt and equity holders

are interdependent stemming from the same investment. Because of the contractual obligation to pay

interest, any variability in operating income (EBIT) caused by business risk is therefore transferred to the

shareholders who must bear the inconsistency of returns. ˜is is ampli˚ed as the gearing ratio rises. To

compensate for a higher level of ˚nancial risk, shareholders require a higher yield on their investment,

thereby producing a lower capitalised value of earnings available for distribution (i.e. lower share price).

At extremely high levels of gearing the situation may be further aggravated by debt holders. ˜ey too,

may require ever-higher rates of interest per cent as their investment takes on the characteristics of equity

and no longer represents a prior claim on either the ˚rm™s income or assets.

Even without increasing the interest rate on debt, the impact of leverage on shareholder yields can be

illustrated quite simply. Consider the following data:

Company

Ulrich (£ million)Hammett (£ million)MARKET VALUES

Equity

10060Debt

Œ40Total

100100NET OPERATING INCOME

EBIT8.010.012.08.010.012.0Interest (10%)

ŒŒŒ4.04.04.0EBT

8.010.012.04.06.08.0Corporation Tax (25%)

2.02.53.01.01.52.0EAT

6.07.59.03.04.56.0Earnings Yield (%)

6%7.5%9%5%7,5%10%˜e two companies (Ulrich and Hammett) are identical in every respect except for their methods of

˚nancing. Ulrich is an all-equity ˚rm. Hammett has £40 million of 10 per cent debt in its capital structure.

A comparison of net operating income (EBIT) and shareholder return (earnings yield) is also shown if

business conditions deviate 20 per cent either side of the norm.

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82 Debt Valuation and the Cost of Capital

What the table reveals is that the returns to ordinary shareholders in the all-equity company only ˝uctuate

between 6 per cent and 9 per cent as EBIT (business risk) ˝uctuates between £8 million and £12 million.

However, for the geared company the existence of a ˚xed interest component ampli˚es business risk in

terms of the total risk borne by the ordinary shareholder. Despite the bene˚ts conferred on Hammett

and its shareholders by the tax deductibility of debt, the greater range of equity returns (5Œ10 per cent)

implies greater ˚nancial risk.

˜us, if shareholders act rationally and business prospects are poor, they may well sell their holdings

in the geared company, thereby depressing its share price and buy into the all-equity ˚rm causing its

price to rise.

Our preceding discussion suggests that for a given level of earnings a company might be able to trade

the costs and bene˚ts of debt by a combination of fund sources that achieve a lower WACC and hence a

higher value for equity. To implement this strategy, however, management obviously need to be aware of

shareholder attitudes to its existing ˚nancial policy and

those of competitors under prevailing economic

conditions. Even ﬁblue chip ﬁcompanies with little chance of liquidation are not immune to ˚nancial risk,

Required:

Use the previous data for Ulrich and Hammett to:

1. Graph the relationship between the respective earnings yield (vertical axis) and EBIT

(horizontal axis) and establish the

indi˝erence point

between their shareholder clienteles.

2. Summarise what your graph illustrates concerning shareholder preferences.

An Indicative Outline Solution

From the raw data you should have observed that if shareholders require a 7.5 per cent return and

the EBIT (NOI) of both companies equals 10 million, they would be indi˛erent to investing in either,

irrespective of current ˚nancial policies. By plotting a graph, however, you can also see that the relationship

between earnings yield and EBIT is positive and linear for both companies but

di˝erent

. For the all-

equity ˚rm it is less severe, with a shareholder™s return of zero corresponding to an EBIT ˚gure of zero

that passes through the origin in Figure 9.1. For the geared company, the EBIT ˚gure which equates to

a zero earnings yield intersects the horizontal axis at the value of 10 percent debenture interest payable

(£4 million) and rises more steeply.

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83 Debt Valuation and the Cost of Capital

Figure 7.1:

Capital Gearing and the Relationship between EBIT and Earnings Yield

˜e intersection of the two straight lines represents the point of indi˛erence between the two companies.

To the leˆ of this point, shareholders would prefer to invest in Ulrich (ungeared) since they receive a

better return for a lower level of EBIT. To the right, they would prefer Hammett (geared) for the same

reasons. What we are observing is that leverage, which here means the incorporation of 10 per cent loan

stock into a ˚rm™s capital structure, increases shareholders™ sensitivity to changes in EBIT (business risk)

and therefore the ˚nancial risk associated with equity; hence the steepness of the line.

Exercise 7.2: Capital Structure and the Law of One Price

˜e previous exercise illustrates why rational risk averse investors prefer the ordinary shares of higher

geared companies when economic conditions are good or improving but switch to lower geared ˚rms

when recession looms. Both strategies represent a rational risk-return trade o˛ because:

-Ordinary shares represent a more speculative investment when there is a contractual

obligation on the part of the company to pay periodic interest on debt

-As a general rule, the higher the gearing and more uncertain a ˚rm™s overall pro˚tability

(EBIT) the greater the ˝uctuation in dividends plus reserves.

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84 Debt Valuation and the Cost of Capital

As we mentioned earlier, the returns to debt and equity holders are interdependent, stemming from the

same resources. So, what we are observing is the transfer of business risk to shareholders who must bear

the inconsistency of returns as the ˚rm gears up. ˜us, it would seem that management should ˚nance

its investments so that the shareholders, to whom they are ultimately responsible, receive the highest

return for a given level of earnings and risk. And this is where MM disagree with traditional theorists.

˜e Traditional ˜eory of Capital Gearing and WACC

Traditionalists believe that if a ˚rm substitute™s lower-cost debt for equity into its capital structure WACC

will fall and value rise to a point of indebtedness where both classes of investor will require higher

returns to compensate for increasing ˚nancial risk. ˜ereaˆer, WACC rises and value falls, suggesting

an optimum level of gearing that minimises WACC and maximises value.

Figure 7.2 sketches these phenomena using the notation from our

SFM

text. ˜e debt-equity ratio (V

D/VE) is plotted along the horizontal axes of both diagrams. ˜e costs of both types of capital (setting K

d < Ke) are given on the vertical axis of the upper graph. ˜e vertical axis on the lower graph plots total

market value (V=V

E+VD).To keep the analysis simple K

d is held constant and its tax deductibility is

ignored. Our aim is not to develop a real world model (more of which later) but to illustrate the basic

relationships between capital costs, corporate value and leverage.

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85 Debt Valuation and the Cost of Capital

Figure 9.2:

Traditional Theory with a Constant Cost of Debt in a Taxless World

Figure 9.2 con˚rms the traditional view that WACC is characterised by a U-shaped average cost curve

K (familiar to economists).˜is is because the bene˚ts of cheaper debt ˚nance (K

d<Ke) are eventually

o˛set by an increasing cost of equity as the ˚rm gears up.

Turning to total market value V, (equity plus debt) if we de˚ne the relationship:

(1) V = NOI / K

where:

V = VE + VD = total market value

VE = market value of equity

VD = market value of debt

NOI = net operating income (earnings before interest)

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86 Debt Valuation and the Cost of Capital

K = WACC,

= Ke (VE / VE + VD) + Kd (VD / VE + VD)= Ke (VE / V) + K

d (VD / V)Ke = cost of equity

Kd = cost of debt

We now observe an

inverse

relationship exists between V and K, given NOI. As one rises, the other falls

and

vice versa.

˜us, the lower graph of Figure 9.2 illustrates that relative to the degree of leverage, the

total market value of the ˚rm has an

inverted

U-shaped function. As K (WACC) responds to changes

in the gearing ratio and the rising cost of equity, V presents us with a mirror image. So, according

to traditional theory, if companies borrow at an interest rate lower than their returns to equity, the

implications for ˚nancial management are clear.

For a given investment policy, there exists an optimal ˜nancial policy (debt-equity ratio) which

de˜nes a least-cost combination of ˜nancial resources.

At the point where overall cost of capital is minimised, total corporate value is maximised and

so is the market value of ordinary shares.

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87 Debt Valuation and the Cost of Capital

˜e MM Cost of Capital Hypothesis

Like much else in ˚nance, the traditional case for an optimal capital structure did not arise from hard

empirical evidence, or mathematical precision, but merely plausible assumptions concerning the cost

of equity at di˛erent levels of gearing. But what if the overall relationship between the two is mistaken?

Would an optimal WACC and corporate value still emerge?

To answer both these questions MM developed an alternative hypothesis, which produced two startling

conclusions that confounded both traditional theorists and ˚nancial analysts.

The total value of a ˜rm represented by the NPV of an income stream discounted at a rate

appropriate to its business risk, should be una˛ected by shifts in ˜nancial structure.

Any rational debt-equity ratio should also produce the same cut-o˛ rate for investment (WACC).

Unlike many of their contemporaries, MM based their conclusions not on anecdote but

partial equilibrium

analysis, preceded by a number of rigorous assumptions, which they then substantiated by empirical

research. ˜e assumptions should be familiar, since they are based on

perfect markets

˚rst outlined in

Chapter One of the

SFM

text.

-Investors are rational.

-Information is freely available.

-Transaction costs are zero.

-Debt is risk-free.

-Investors are indi˛erent between corporate and personal borrowing.

MM also based their analysis on the traditional equation for total market value:

(1) V = NOI / K

However, where they disagree with traditional theory relates to their de˚nition of WACC, which hinges

on the behaviour of the equity capitalisation rate

MM reason that WACC (K) re˝ects the business risk associated with total earnings (NOI) rather than

their ˚nancial risk, i.e. how they are packaged for distribution in the form of dividends, retentions or

interest. Assuming that NOI is constant, they maintain that irrespective of the debt-equity ratio (V

D / VE) the company™s WACC (K) and hence overall value (V) must be constant.

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88 Debt Valuation and the Cost of Capital

Based on their ﬁeconomic law of one priceﬂ MM further reasoned that irrespective of leverage, because

shares in similar companies cannot sell at di˛erent prices, two companies with the same total income

and business risk will have the same total market value and WACC, even if their gearing ratios di˛er.

Expressed algebraically, if:

V1 = V2 = the value for two companies.

I1 = I2 = their common NOI.

˜e WACC for any company in the same risk class:

(2) K = I1/V1 = I2/V2And because K = K

e in the unlevered ˚rm, the WACC for the geared company must also equal the cost

of equity capital K

e of the all equity ˚rm.

˜us, if the cost of debt K

d is constant (an assumption that MM later relax) all that needs to be resolved

is the precise relationship between the rising cost of equity K

e and the debt-equity ratio V

D/VE when a

˚rm gears up. Is it

exponentia

l, as the traditionalists suggest (Figure 9.2) or not.

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89 Debt Valuation and the Cost of Capital

Figure 9.3:

The MM Theory with a Constant Cost of Debt in a Taxless World

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90 Debt Valuation and the Cost of Capital

According to MM, if we ignore corporate tax and tax relief on interest, the equity capitalisation rate K

e will still increase but not exponentially as the traditionalists believe. ˜e rise

exactly o˝sets

the bene˚ts

of increasing the proportion of cheaper loan stock in a ˚rm™s capital structure leaving WACC unchanged.

˜is

linear

relationship is sketched in the upper graph of Figure 9.3, which translates into the following

equation.

(2) Keg = Keu + [(VD / VE ) ( Keu Œ Kd )]where:

Keg = the cost of equity in a geared company

Keu = the cost of equity in an ungeared company

Kd = the cost of debt capital

VD = the market value of debt in the geared company

VE = the market value of equity in the geared company

Keg (leveraged) is equivalent to K

eu, the capitalisation rate for an all-equity stream of the same class of

business risk, plus a premium related to ˚nancial risk. ˜is is measured by the debt-equity ratio (V

D/VE) multiplied by the spread between K

eu and K

d.˜e ˚nancial risk premium (the second term on the right of our preceding equation) causes equity yields

to rise at a

constant

rate as compensation for ˚nancial risk when the ˚rm gears up.

Since the WACC in companies of equivalent business risk is the same, irrespective of leverage, their

total market value (V) will also be the same if the companies are identical in every respect except their

gearing ratio. ˜us:

(3) VU = VG = VE +VDwhere:

VU = the market value of an ungeared all equity company

VG = market value of an identical geared company (equity plus debt)

˜e lower graph of Figure 9.3 plots constant value (V) against an increasing debt-equity ratio (V

D/VE).If WACC and overall corporate value are una˛ected by leverage as MM hypothesise, the implication

for strategic ˚nancial management are profound. As we mentioned in Chapter One of the

SFM

text,

˚nancial decisions (which include the dividend policy of Chapter Five, as well as gearing) are irrelevant

to investment decisions (project valuation and selection).

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91 Debt Valuation and the Cost of Capital

Reading and Review

In a subject still dominated by the work of Modigliani and Miller it is important that you refer to their original articles

if only to con˜rm what you read elsewhere.

MM™s 1958 paper ﬁThe Cost of Capital, Corporation Finance and the Theory of Investmentﬂ sets out their original case

for the irrelevance of ˜nancial structure to corporate valuation and capital cost (WACC) in a perfect capital market.

Find it and skim through to get the broad thrust of their arguments (even if you ˜nd the mathematics complex). Then

produce brief answers to the following questions before we move on to our second exercise.

a) There are three

propositions

advanced by MM. What are they and how are they proved?

b) How do MM™s conclusions di˛er from a traditional view of capital structure in a taxless world where the cost

of debt is constant?

c) Within the context of investment appraisal, what are the implications of MM™s hypothesis for ˜nancial

management?

MM: A Review

a) ˜e Propositions

Using our own notation, the three propositions advanced by MM are:

Proposition I:

Overall market value (V) is

independent

of the debt-equity ratio (V

D/VE)Proposition II:

To o˛set ˚nancial risk, the equity capitalisation rate (K

eg) increases at

a constant

rate as V

D/VE rises, with the corollaries:

-K is una˛ected by V

D/VE -K = Keu for an unlevered ˚rm.

Proposition III:

Shareholder wealth is maximised by

substituting

an equity capitalisation

rate (K

eu) of an unlevered ˚rm for the cut-o˛ rate (K) of a levered ˚rm.

MM then explain how:

(i) Proposition I can be proved by

arbitrage

(more of which later).

(ii)

Proposition I can be used to prove Proposition II which states that K is una˛ected by

VD/VE.(iii)

Proposition III follows logically from Positions II and III, since market value equals

equity value (V = V

E) and therefore K = K

e in an unlevered ˚rm.

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92 Debt Valuation and the Cost of Capital

b) ˜e Conclusions

Even in a world of zero taxation with a constant cost of debt, a comparison of Figure 9.2 with

Figure 9.3 reveals that MM™s conclusions contrast sharply to a traditional view. WACC does

not vary with gearing. ˜ere is no optimal debt-equity ratio and the market value of the ˚rm

remains constant. According to MM, the cost of equity capital is no longer an exponential

function of increasing leverage. Given MM™s contention that K is constant, K

e rises

linearly

as

VD/VE increases.

c) ˜e Investment Implications

If MM™s hypothesis is correct, the ﬁtraditionalﬂ ˜nancial decisions that confront management

when investment decisions include debt are eliminated. The net result is that WACC (the cut-o˛

rate for investment) and total corporate value remain the same. Gearing is therefore irrelevant

to project evaluation and shareholder wealth maximisation.

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93 Debt Valuation and the Cost of Capital

Proposition I and the Arbitrage Process

Your reading should con˚rm that that the logic of MM™s cost of capital hypothesis stems from their ˚rst

proposition that corporate value is independent of capital structure because of

arbitrage

.Arbitrage occurs when investors sell ˜nancial securities to buy cheaper perfect

substitutes, thereby depressing the price of the former and increasing the price of

the latter, until their market prices are in equilibrium.

MM maintain that if a traditional view of capital structure were to exist it should only be a short-run

dis-equilibrium

phenomenon in perfect markets. Rational (risk-averse)

arbitrageurs

will respond quickly

to prevent the existence of the two ˚rms with identical risk and the same NOI from selling at di˛erent

prices.

Shareholders in an over-valued company (what the traditionalists would call highly geared) will change

its total value by selling shares in that company and buying shares in an under-valued (i.e. ungeared)

company. In the process shareholders will even undertake personal borrowing to maximise their stake

in the ungeared company at a level where their personal investment portfolios have the same degree of

leverage as the overvalued ˚rm.

As a result of what MM term

home-made

leverage

(personal borrowing), investor income is increased

at no greater ˚nancial risk. Eventually, through supply and demand forces, the price of shares in the

overvalued company will fall, while that of the undervalued company will rise until no further ˚nancial

advantage is gained. At this

equilibrium

overall market value, the overall cost of capital (WACC) for the

two companies will also be the same.

For the mathematically minded, we could illustrate the whole arbitrage process by reference to formidable

algebraic

relationships that compare MM to a traditional view, in a tax-free world where the cost of debt

is constant. For ease of exposition, however, we shall restrict our second exercise to a

numerical

example

with a modest series of equations.

Let us begin with a series of

traditional

˚nancial relationships between two ˚rms (Elbow and Dimebag)

that are identical in every respect, except for their capital structure (•000s).

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94 Debt Valuation and the Cost of Capital

Elbow (ungeared)

Dimebag (geared)

Distributable Earnings (No Tax)

NOI100=100Debt Interest (Kd = 5%)

-10Shareholder Income

100>90Market Values

Equity (VE)

1000>900Debt (VD)

-200Total Value (V)

1000<1,100Capital Costs

Equity Yield (Ke)

10%=10%Cost of Debt (Kd)

-5%WACC (K = NOI / V)

10%>9.09%Required:

1. Use the previous data to illustrate the bene˚ts of arbitrage for an investor who currently

owns 10 per cent of Dimebag™s shares.

2. Summarise the e˛ects of arbitrage as more investors enter the process.

An Indicative Outline Solution

From the data you should have observed what MM term

disequilibrium

. ˜e total market value and

WACC of equivalent companies di˛er. So, arbitrage is a pro˚table strategy for all investors in the

geared ˚rm.

1. ˜e Arbitrage Process

Now let us consider a series of arbitrage transactions for a single investor who holds 10 per cent

of the equity in Dimebag (the higher valued geared ˚rm) whose annual income is therefore

•9,000 (•90,000 x 0.10).1. She sells her total shareholding for •90,000 (10 per cent of •900,000) which reduces the

˚nancial risk of investing in the geared company to zero.

2. She now buys shares in Elbow (the ungeared, all-equity ˚rm) but how much should she

spend?

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95 Debt Valuation and the Cost of Capital

3. In order to compare like with like, it is important to hold the investor™s exposure to ˚nancial

risk at the same level as her original investment in Dimebag. With a •90,000 equity stake

in that company, management presumably used this as collateral to borrow •20,000 of

corporate debt on her behalf (i.e.10 per cent of •200,000). So, in a perfect capital market

where private investors can borrow on the same terms as the company, she can substitute

homemade

leverage for

corporate

leverage to ˚nance her new investment in the all-equity

˚rm.

4. She borrows •20,000 at 5 per cent per annum, an amount equal to 10 per cent of the ˚rm™s

debt.

5. As a result, the investor now has a total of •110,000 (•90,000 cash, plus •20,000 of personal

borrowing) with which to purchase the ungeared shares in Elbow.

6. Because Elbow™s yield is 10 per cent, the investor will receive an annual return of •11,000

(•110,000 × 0.10). However, she must pay annual interest on her personal loan (•20,000 ×

0.05 = •1000).˜erefore, her annual net income will be •10,000 (•11,000 Œ •1,000).

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96 Debt Valuation and the Cost of Capital

So, to conclude, is our investor better o˛? We can measure her change in income as follows:

•Shareholder income in Elbow (ungeared)

11,000Shareholder income in Dimebag (geared)

9,000Change in income

2,000Interest on borrowing (5%)

1,000Net Gain from

Arbitrage

1,000The Arbitrage Process

˜us, shareholder income has increased with no change in ˚nancial risk. ˜e reason the investor

has bene˚ted is because the leveraged shares of Dimebag are overvalued relative to those of

Elbow. If proof be needed, you should be able to con˚rm that the equity capitalisation rates for

both ˚rms originally equalled 10 per cent, despite di˛erences in their total shareholder income.

2. Summary

As more investors enter the arbitrage process (trading shares to pro˚t from disequilibrium) the

equity value of geared ˚rms will fall, whilst those of their ungeared counterparts will rise. To

similar but opposite e˛ect, their equity capitalisation rates will rise and fall respectively, until

their overall cost of capital (WACC) is equal. ˜us, MM™s message to ﬁtraditionalistsﬂ is clear.

Inequilibrium, shareholders will be indi˛erent to the degree of leverage

and the arbitrage process becomes irrelevant to management™s strategic

evaluation of project investment and its wealth maximisation implications.

Summary and Conclusions

We have considered whether a company can implement ˚nancial policies concerning capital structures

that minimise weighted average cost of capital (WACC) and maximise total corporate value. Given

your knowledge of equity valuation (Chapter Five) and the derivation of debt cost (Chapter Six) we

focussed upon the controversial question of whether optimal ˚nancial decisions contribute to optimum

investment decisions.

˜e traditional view states that if a ˚rm trades lower-cost debt for equity, WACC will fall and value rise

to a point of indebtedness where both classes of investor will require higher returns to compensate for

increasing ˚nancial risk. ˜ereaˆer, WACC rises and value falls, suggesting an optimum capital structure.

In 1958, Modigliani and Miller (MM) discredited this view under the assumptions of perfect markets

with no barriers to trade, by proving that WACC and total value are independent of ˚nancial policy.

Based on the economic

law of one price

, they used

arbitrage

to demonstrate that close ˚nancial substitutes,

such as two ˚rms in the same class of business risk with identical net operating income (NOI), cannot

sell at di˛erent prices; thereby negating ˚nancial risk.

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97 Debt Valuation and the Cost of Capital

˜e MM proof confounded the traditional investment community who argued that their assumption

of perfect markets, particularly a neutral tax system without tax relief on debenture interest invalidated

their conclusions. However, MM were the ˚rst to concede that an allowance for tax relief will reduce

the cost of loan stock, lower WACC and increase total value as a ˚rm gears up. ˜e whole point of their

hypothesis was to provide a

benchmark

to assess the impact of incorporating more realistic assumptions

as a basis for more complex analyses. For example:

-Do personal as well as corporate ˚scal policies a˛ect capital structure?

-Are corporate borrowing and investment rates equal?

-How do investor returns behave with extreme leverage?

-Are management better informed than stock market participants?

-Do managerial objectives con˝ict those of investors

-And if so, do management prefer di˛erent sources of ˚nance (think share options).

Unfortunately, we still have few de˚nitive answers. ˜e capital structure debate has ebbed and ˝owed since

MM published their original hypothesis in 1958 with a surprising lack of consensus among academics,

researchers and practitioners. To complicate matters further, historical research has obviously focussed

on observable, modest (rational) debt equity ratios, rather than the extreme (irrational) leverage that

has created global ˚nancial distress and bankruptcy since 2007.

To learn the lessons of the recent past, perhaps the debate will take a new turn. If so, real world management

could learn from their mistakes by returning to ˚rst principles and revive MM™s basic propositions on

the irrelevance of ˚nancial policy. ˜ey provide a sturdy framework for rational investment. Moreover,

their cost of capital hypothesis is entirely consistent with their 1961 dividend irrelevancy hypothesis

covered in Chapter Five (for which there is considerable empirical support).

˜us, it seems reasonable to conclude that if we are to emerge from the current global, economic crisis

ﬁall singing from the same old song sheetﬂ.

-Corporate value should depend on the agency principle (Chapter One) characterised by an

investor-managerial consensus on the level of earnings and their degree of risk, rather than the

proportion distributed.

-Dividend and retention decisions should be irrelevant to the marketprice of a share (Chapter Five).

-The division of returns between debt and equity asa determinant of WACC and total corporate

value should also be perfect substitutes.

Reference

1. Modigliani, F. and Miller, M.H., ﬁ˜e Cost of Capital, Corporation Finance and the ˜eory

of Investmentﬂ,

American Economic Review,

Vol. XLVIII, No. 3, June, 1958.

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98 Part Four

The Wealth Decision

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99 Shareholder Wealth and Value Added

8

Shareholder Wealth and Value

Added

Introduction

Our study of Strategic Financial Management has revealed a series of controversial, theoretical

relationships between shareholder wealth, dividend policy and the derivation of WACC as a cut-o˛ rate

for investment. Unfortunately, even if the di˛erences between competing theories were resolved, there

might still be no guarantee that real-world managerial self-interest would coincide with shareholder

wealth maximisation. Time and again throughout the

SFM

text, when projects are being evaluated and

modelled, we have used recent ˚nancial crises to prove the point.

In Chapter Eight we therefore explained how two American consultants, Joel Stern and Bennett Stewart

have long sought to minimise any

principle-agency

problems for their corporate clients through the

application of value added techniques.

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100 Shareholder Wealth and Value Added

According to Stern-Stewart, what companies require is an

internal

, incentive-based earnings driver, which

shareholders can con˚rm from periodic

external

˚nancial data to vet managerial performance.

Economic

value added

(EVA) provides the internal metric. Moreover, they maintain that it is highly correlated to

increases in shareholder wealth measured by the company™s

market value added

(MVA).

So, how do they work?

Exercise 8.1: Shareholder Wealth, NPV Maximisation and Value Added

Consider the Grohl Company that is currently committed to NPV maximisation in order to satisfy its

overall shareholder wealth maximisation objective. ˜e new Finance Director proposes that the company

should appraise all future investment projects using the dual Stern-Stewart concepts of EVA and MVA.

You are not convinced that substituting value added analyses for the company™s existing investment

model will contribute anything to its wealth maximisation objective.

Required:

Based on your reading of the

SFM

text

1. Outline how a company maximises the NPV of all its projects as a basis for shareholder

wealth maximisation.

2. Present the

three

Stern-Stewart equations required to prove the inter-relationship between

value added and NPV.

3. Manipulate these equations to illustrate whether the Stern-Stewart model is ˚nancially

equivalent to NPV maximisation.

4. Summarise your thoughts on the case for value added.

An Indicative Outline Solution

˜roughout most of our text and exercises we have assumed that companies

should

maximise wealth

using the NPV investment model and optimum ˚nancing, a combination of which maximises cash

in˝ows at minimum cost. We can summarise the approach as follows.

1. NPV Maximisation and Shareholder Wealth

A NPV project calculation requires the derivation of a discount rate, based upon the

mathematical concept of a

weighted average

to formulate a company™s

WACC

as an appropriate

cut-o˛ rate for investment. For example, with only two sources of capital (equity and debt say)

and using our standard notation, a general formula for WACC is given by:

K = Ke (VE / V) + K

d (VD / V)

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101 Shareholder Wealth and Value Added

Computationally, the component costs of capital are weighted as a proportion of the company™s

total market value and the results summated (i.e. added together).

We can then derive any project™s NPV by discounting its cash ˝ow series at the company™s

WACC (i.e. K) and subtracting the cost of the investment.

[(PV@WACC Œ I

0 ] = NPVNow assume that the normative objective of our company (Grohl) is to maximise shareholder

wealth. ˜e NPV maximisation approach to investment appraisal means that if a choice must

be made between alternatives (because projects are mutually exclusive, or capital is rationed)

the highest NPV should be selected, subject to a comparison of their risk-return pro˚les using

mean variance analysis.

To maximise NPV, it is also the company™s responsibility to acquire capital from various sources

in the most e˙cient (least-costly) manner to establish an overall discount rate. ˜e derivation

of this marginal WACC (whether it be traditional or MM based) should represent the optimum

discount rate. ˜e project which then produces the highest return in excess of this WACC

should therefore maximise NPV and not only exceed shareholders™ expectations of a dividend

or capital gain but also the returns required by all other providers of capital.

2. ˜e Value Added Equations

Optimum investment and ˚nancial decision models employed by ˚nancial managers under

risk and non-risk conditions should maximise corporate wealth through the in˝ow of cash at

minimum cost. It is a basic tenet of ˚nancial theory that the NPV maximisation of all a ˚rm™s

projects satis˚es this objective. So, what does the Stern-Stewart model o˛er the Grohl company,

over and above the universally accepted NPV decision rule?

According to Stern-Stewart, economic value added (EVA) is a periodic, incentive-based

earnings performance driver that is correlated to increased shareholder value measured by

market value added (MVA). Whilst Stern-Stewart™s precise derivation of value added has

remained highly

secretive

since they adopted it as their own in 1982

(perhaps explaining, why it

has captured the corporate imagination and attracted media comment world-wide) the concept

has a long academic and empirical pedigree. Like much else in ˚nance, it can be traced back

to the ﬁgolden ageﬂ of the 1960s.

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102 Shareholder Wealth and Value Added

˜e economic rationale for the Stern-Stewart model is best explained to the Grohl Company

by reference to Chapter Eight of the

SFM

text, which de˚nes all the constituent components,

notation and purpose of the following three equations:

EVA = NOPAT (free cash ˝ow) less the

money

cost of total capital investment =

NOPAT Œ C.K

MVA = Market value less total capital = V Œ C

V = Market value = Capital plus the present value of all future EVA = C + PV(EVA)

3. ˜e Financial Equivalence between Value Added and NPV Maximisation

˜e inter-relationship between the Stern-Stewart model, NPV maximisation and shareholder

wealth can now be explained by manipulating the relationships between the previous three

equations asfollows. Given:

1. EVA

= NOPAT Œ C.K

2. MVA

= V Œ C3. V

= C + PV(EVA)

First take the di˛erence between Equations (2) and (3) to rede˚ne MVA.

4. MVA

= PV (EVA)

Next, because the EVA equation represents a current cash surplus aˆer subtracting the money

cost of capital investment from NOPAT (what Stern-Stewart term

free cash ˚ow

) it must equal

the NPV of all a ˚rm™s projects if they are discounted using K as a common WACC.

According to Stern-Stewart the MVA of Equation (4) may be rede˚ned as follows

5. MVA

= PV of all future EVA = S NPV

4. Summary

Your initial dispute with the Finance Director of the Grohl Company who recommends the

substitution of value added concepts for NPV to pursue shareholder maximisation appears

justi˚able. ˜eoretically, the two models should be

˙nancially equivalent

, so why change over?

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103 Shareholder Wealth and Value Added

Presumably, the Finance Director™s preference for value added re˝ects the views of Stern-

Stewart. Because management do not provide project NPVs based on

internal

cash ˝ow data

for

external

users of published accounts, what markets require is an

equivalent

model, which

they can derive from the data actually contained in those accounts. Only then can investors

assess corporate performance on the same terms that management initially justi˚ed project

decisions on their behalf. According to Stern-Stewart, value added provides such a measure

and as a consequence, it also acts as a

control

on dysfunctional management behaviour (the

agency principle).

Figure 8.1:

Strategic Financial Management and the Stern-Stewart Model

Figure 8.1 (reproduced from the

SFM

text) illustrates how the Stern-Stewart model should ˚t seamlessly

into a managerial framework of

internal

NPV analyses and

external

shareholder wealth maximisation.

However, there are still nagging doubts concerning its practical application.

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104 Shareholder Wealth and Value Added

A long-standing criticism is that because the Stern-Stewart consultancy is secretive (for sound commercial

reasons) it does make it di˙cult to verify their claims. For example, the EVA formula

de-leverages

published post-tax accounting pro˚ts to derive NOPAT based on numerous cash ˝ow adjustments that

are not in the public domain. And even where the value added computation of public companies is

transparent, it is rarely measured in the same way (see Weaver 2001).

Prior to the current wave of ˚nancial crises and market volatility, which now makes

trend

research

di˙cult, Gri˙th (2004) also sampled the EVA ˚gures of 63 corporate consultancy clients available on

the Stern-Stewart web page at

www.sternstewart.com.

He con˚rmed too, that neither EVA, nor MVA,

were good indicators of performance.

Even if the pro˚tability side of the EVA equation corresponds to the periodic cash ˝ow of NPV

calculations, (

free cash ˚ow

explained in Chapter Eight of

SFM

) a fundamental problem remains. How

do Stern-Stewart measure the WACC (i.e. K) in the third term of their formula?

EVA = NOPAT Œ C.K

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105 Shareholder Wealth and Value Added

EVA calculations, like NPV, are based on the common assumption that an optimum WACC (central to

the ˚nance function outlined in Figure 8.1) can be satisfactorily de˚ned, either as a money cost of capital

in the previous equation, or the NPV discount rate (r =K) in the following equation.

However, as we observed in Chapter Seven there are two schools of thought. ˜e

traditional

approach

to investment ˚nance subscribes to a ﬁpecking orderﬂ framework.

WACC falls with leverage because ˜rms prefer cheaper internal to external ˜nancing and then

cheaper debt to equity, if they need to issue ˜nancial securities to support their investment.

Alternatively, we have the MM hypothesis.

WACC is constant, irrespective of leverage, because any change in the gearing ratio produces a

compensatory change in the cost of equity to counter the change in the level of ˜nancial risk.

Exercise 8.2: Current Issues and Future Developments

Whilst the value added debate continues, it is worth noting that the Stern-Stewart model does provide

support for the MM capital structure hypothesis. Both of their WACC derivations are driven by earnings

(business risk). By implication, Stern-Stewart must also support the MM dividend hypothesis that

˚nancial risk is irrelevant.

Perhaps you recall from previous chapters that the MM capital structure and dividend irrelevancy

theories are entirely consistent with one another. Based on their economic ﬁlaw of one priceﬂ and ﬁperfect

substitutionﬂ:

-Personal (home made) leverage is equivalent to corporate leverage.

-Capital gains (home made dividends) are equivalent to corporate dividends.

It therefore seems reasonable to assume that if Stern-Stewart accept the MM dividend

irrelevancy hypothesis:

Value added is dependent upon investor agreement on the level of de-leveraged post-tax

earnings (NOPAT. or what MM term NOI) and their degree of business risk, rather than the

˜nancial risk associated with proportion distributed.

If the dividend-retention decision is irrelevant to the marketpricing of shares, then so too, is the

division of returns between debt and equity, which determines WACC (K) in the EVA equation.

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106 Shareholder Wealth and Value Added

So, let us conclude our analysis of the value added concept by illustrating the relationship between the

capital structure and dividend irrelevancy hypotheses of MM. Both underpin the Stern-Stewart model

and remain at the heart of modern ˚nancial management (summarised in Figure 8.1).

For the purposes of uniformity, we shall ignore the tax deductibility of debt. ˜is follows logically from

our analysis of MM™s basic propositions in Chapter Seven. Besides, if their theory fails the test at a

rudimentary level of logic, why bother with greater realism?

Consider the Edge Company, an all-equity ˚rm ˚nanced by 100,000 £1 shares (nominal). Total earnings

are £100,000 and the market price per share is £10.00.

Using familiar notation from previous chapters:

£Earnings

E1= 100,000Equity:

Market value

VE1=1,000,000Capitalisation rate

K e1 = E1 / V

E1=10%Total value

VU = VE1=1,000,000Now consider the Bono Company, an identical ˚rm in terms of business risk with the same level of

earnings. It di˛ers only in the manner by which it ˚nances its operations. 50 per cent of the market

value of capital is represented by bonds that yield 5 per cent. According to MM, because identical assets

cannot sell at di˛erent prices in the same market (i.e. total corporate value and the price per share are

the same) it follows that:

Earnings

E2=100,000Debt :

Market value

VD=500,000Interest (£)

I =Kd VD=25,000Interest (%)

Kd = I / V

D= 5%Equity:

Market value

VE2=500,000Capitalisation rate

Ke2 = (E2 Œ Kd VD) / V

E2=75,000 / 500,000=15%Total value

VG = V

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107 Shareholder Wealth and Value Added

Required:

Based on your reading of the

SFM

text and previous exercises:

1. Derive the WACC for Edge and Bono respectively.

2. Explain the implications of your ˚ndings.

An Indicative Outline Solution

In previous exercises we observed that if management maximise shareholder wealth, using either EVA or

NPV decision models, their optimal ˚nancial policy should represent a uniform, least-cost combination

of debt and equity that maximises cash in˝ows at minimum cost.

1. ˜e Derivation of a Uniform WACC

We can derive the WACC for both ˚rms using either of the following general formulations.

K = Ke (VE / V) + K

d (VD / V)

K = Ke (WE) + Kd (WD)(where W

E and W

D represent the weightings applied to equity and debt respectively).

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108 Shareholder Wealth and Value Added

Now, let us apply the data to the previous equations, where K

u and K

g represent the WACC for

the ungeared and geared ˚rm respectively.

Edge K

u = (10% × 1.0) = 10%Bono K

g = (15% × 0.5) + (5% × 0.5) = 10%˜us, irrespective of gearing, the WACC for both companies is identical.

2. ˜e Implications

˜e previous analysis follow logically from the MM

arbitrage

proof in our last chapter. ˜e

equity capitalisation rate has risen with gearing to o˛set

exactly

the lower cost of debt, which

also explains MM™s proposition that two identical assets (shares and corporate value in our

example) cannot exhibit di˛erent prices. Consequently, the WACC or cut-o˛ rate for investment

for any ˚rm in a particular class of business risk equals the equity capitalisation rate for an

all-equity ˚rm in that class. In general terms if:

VEU = VU = VGIt follows that:

Keu = Ku = KgSo, given the MM hypotheses that the market value of investment is independent of a

company™s ˜nancial policy (because dividend-retention and debt-equity ratios are

perfect

economic substitutes

) the Stern-Stewart model should con˜rm that a company™s overall cost of

capital subtracted from its income and hence market value is divorced from its gearing.

Summary and Conclusions

Our study of ˚nance began with an

idealised

picture of rational, risk-averse investors. ˜ey should

formally analyse the pro˚tability of one course of action in relation to another in pursuit of their wealth

maximisation objectives. In a sophisticated mixed economy outlined in Figure 8.2 where the ownership

of companies is divorced from control (the

agency

principle), we then de˚ned the strategic,

normative

goal of ˚nancial management as follows.

The implementation of investment and ˜nancing decisions using risk-adjusted wealth

maximising techniques, such as expected net present value (ENPV) and certainty equivalents,

which generate money pro˜ts in the form of retentions and distributions that satisfy the ˜rm™s

owners

(a multiplicity of ordinary shareholders) thereby maximising share price.

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109 Shareholder Wealth and Value Added

Figure 8:2:

The Mixed Market Economy

You will recall that if ˚rms make money pro˚ts that

exceed

their overall cost of funds (a positive NPV)

they create what is termed

economic value added

(EVA), which provides a ﬁrealﬂ surplus at no expense to

their stakeholders. In a

perfect capital market with no barriers to trade

, demand for a company™s shares,

driven by its EVA, should then exceed supply. Share price will rise, thereby creating

market value added

(MVA) for the mutual bene˚t of the ˚rm, its owners and prospective investors.

Of course, the price of shares can fall, as well as rise, depending on economic circumstances. Companies

engaged in ine˙cient or irrelevant activities, which produce losses (negative NPV and EVA) are

gradually starved of ˚nance because of reduced dividends, inadequate retentions and the capital market™s

unwillingness to replenish their asset base at current market prices (negative MVA).

Figure 8.3 distinguishes the ﬁwinnersﬂ from the ﬁlosersﬂ in their drive to add value by summarising why

some companies fail. ˜ese may then fall prey to take-over as share values plummet (or they may even

go into liquidation).

Figure 8.3:

Corporate Economic Performance: Winners and Losers

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110 Shareholder Wealth and Value Added

˜roughout the remainder of the text, we de˚ned successful management policies of wealth maximisation,

which increase share price, in terms of two distinct but nevertheless

inter-related

functions

-˜e

investment function

, which identi˚es and selects a portfolio of investment opportunities

that

maximise

anticipated net cash in˝ows commensurate with risk.

-˜e ˙nance function

, which identi˚es potential fund sources (internal and external, debt

or equity, long or short) required to sustain investments, evaluates the risk-adjusted return

expected by each, then selects the optimum mix that will

minimise

their overall weighted

average cost of capital (WACC).

˜e managerial investment function and ˚nance function are linked by the company™s WACC. You will

recall that from a ˚nancial perspective, it represents the overall cost incurred in the acquisition of funds.

A complex concept, it not only concerns explicit interest on borrowings or dividends paid to shareholders.

Companies also ˚nance their operations by utilising funds from a variety of sources, both long and short

term, at an implicit or opportunity cost, notably retained earnings, without which companies would

presumably have to raise funds elsewhere. In addition, there are implicit costs associated with depreciation

and other non-cash expenses. ˜ese too, represent retentions that are available for reinvestment.

Finally, in terms of the corporate investment decision, we reconciled the NPV maximisation of all a ˚rm™s

projects with EVA and MVA maximisation using WACC as an appropriate cut-o˛ rate for investment.

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111 Shareholder Wealth and Value Added

In our

ideal world

characterised by rational investors and perfect markets, the strategic objectives of

˚nancial management relative to the investment and ˚nance decisions that enhance shareholder wealth

can be characterised as follows:

Funds from any source should only be invested in capital projects if their marginal yield at least equals the

rate of return that the ˚nance provider can earn elsewhere on comparable investments of equivalent risk.

Cash pro˚ts should then exceed the overall cost of investment (WACC) producing either a positive NPV

or EVA which can either be distributed as a dividend or retained to ˚nance future investments.

If management wish to increase shareholder wealth, (MVA) using share price as a

vehicle

, then earnings

(measured by NPV or EVA) rather than dividends should be the

driver

.So, there you have it. An introduction to strategic ˚nancial management based on established theories.

But as we observed in Chapter One of this and the

SFM

companion text, such theories attract legitimate

criticism in a world that is

far from ideal

characterised by geo-political and economic instability, ˚nancial

meltdown and recession.

So, whilst the exercises presented in this text support a sturdy framework for the analysis of investment

and ˚nance decisions, it remains to be seen whether it is a ﬁcastle built on sandﬂ.

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