Last Study Topics
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Qualification of Statements.
Examples.
CAPM
APT
Three Factors Model
Today’s Study Topics
• Company and Project Costs of Capital
• Measuring the Cost of Equity
Principles of
Corporate
Finance
Sixth Edition
Richard A. Brealey
Stewart C. Myers
McGraw Hill/Irwin
Chapter 9
Capital Budgeting and Risk
Introduction
• LONG BEFORE THE development of modern
theories linking risk and expected return,
smart financial managers adjusted for risk in
capital budgeting.
• How they should treat the element of risk
with respect to each and every projects of
different class?
Continue
• Various rules of thumb are often used to make
these risk adjustments.
– For example, many companies estimate the rate
of return required by investors in their securities
and then use this company cost of capital to
discount the cash flows on new projects.
COMPANY AND PROJECT COSTS OF
CAPITAL
• The company cost of capital is defined as the
expected return on a portfolio of all the
company’s existing securities.
• It is used to discount the cash flows on
projects that have similar risk to that of the
firm as a whole.
Continue
• We estimated that investors require a return
of 9.2% from Pfizer common stock.
• If Pfizer is contemplating an expansion of the
firm’s existing business, it would make sense
to discount the forecasted cash flows at 9.2 %.
• The company cost of capital is not the correct
discount rate if the new projects are more or
less risky than the firm’s existing business..
Company Cost of Capital
• A firm’s value can be stated as the sum of the
value of its various assets.
• Each project should in principle be evaluated
at its own opportunity cost of capital.
• For a firm composed of assets A and B, the
firm value is;
Firm value  PV(AB)  PV(A)  PV(B)
Continue
• Here PV(A) and PV(B) are valued just as if they
were mini-firms in which stockholders could
invest directly.
• Investors would value A by discounting its
forecasted cash flows at a rate reflecting the
risk of A.
• They would value B by discounting at a rate
reflecting the risk of B.
– The two discount rates will, in general, be
different.
Continue
• This means that Pfizer should accept any
project that more than compensates for the
project’s beta.
• In other words, Pfizer should accept any
project lying above the upward-sloping line
that links expected return to risk in Figure 1.
– If the project has a high risk, Pfizer needs a higher
prospective return than if the project has a low
risk.
Company Cost of Capital
• A company’s cost of capital can be compared
to the CAPM required return
SML
Required
return
13
Company Cost
of Capital
5.5
0
1.26
Project Beta
Understanding
• In terms of Figure1, the rule tells Pfizer to
accept any project above the horizontal cost
of capital line, that is, any project offering a
return of more than 9.2%.
– The company cost of capital rule, which is to
accept any project regardless of its risk as long as
it offers a higher return than the company’s cost
of capital.
Understanding
– It is clearly silly to suggest that Pfizer should
demand the same rate of return from a very safe
project as from a very risky one.
– If Pfizer used the company cost of capital rule, it
would reject many good low-risk projects and
accept many poor high-risk projects.
• Many firms require different returns from different
categories of investment.
Understanding
For example, discount rates might be set as
follows:
Category
Speculativ e ventures
New products
Expansion of existing business
Cost improvemen t, known tech nology
Discount Rate
30%
20%
15% (Company COC)
10%
Perfect Pitch and the Cost of Capital
• The true cost of capital depends on project
risk, not on the company undertaking the
project.
– So why is so much time spent estimating the
company cost of capital?
• First, many (maybe, most) projects can be
treated as average risk, that is, no more or less
risky than the average of the company’s other
assets.
– For these projects the company cost of capital is
the right discount rate.
Continue
• Second, the company cost of capital is a useful
starting point for setting discount rates for
unusually risky or safe projects.
– It is easier to add to, or subtract from, the
company cost of capital than to estimate each
project’s cost of capital from scratch.
• Anyone who can carry a tune gets relative pitches right.
Business People
• are used to, but not about absolute risk or
required rates of return.
• Therefore, they set a companywide cost of
capital as a benchmark.
• This is not the right hurdle rate for everything
the company does.
– But adjustments can be made for more or less
risky ventures.
MEASURING THE COST OF EQUITY
• Suppose that you are considering an acrossthe-board expansion by your firm.
• Such an investment would have about the
same degree of risk as the existing business.
• Therefore you should discount the projected
flows at the company cost of capital.
• Companies generally start by estimating the
return that investors require from the
company’s common stock.
Continue
• Used the capital asset pricing model to do the
working. This states;
– Expected stock return =rf + Beta(rm – rf)
• An obvious way to measure the beta (B) of a
stock is to look at how its price has responded
in the past to market movements.
Measuring Betas
• The SML shows the relationship between
return and risk.
• CAPM uses Beta as a proxy for risk.
• Other methods can be employed to determine
the slope of the SML and thus Beta.
• Regression analysis can be used to find Beta.
Dell Computer Stock
• Calculated monthly returns from Dell
Computer stock in the period, after it went
public in 1988, is given on the next slide.
• Also plotted returns against the market
returns for the same month, is given too.
• We have fitted a line through the points.
– The slope of this line is an estimate of beta.
Measuring Betas
Dell Computer
Dell return (%)
Price data – Aug 88- Jan 95
R2 = .11
B = 1.62
Slope determined from plotting the
line of best fit.
Market return (%)
Measuring Betas
Dell Computer
Dell return (%)
Price data – Feb 95 – Jul 01
R2 = .27
B = 2.02
Slope determined from plotting the
line of best fit.
Market return (%)
Other Stocks
• The next diagram shows a similar plot for the
returns on General Motors stock, and the
• Third shows a plot for Exxon Mobil.
• In each case we have fitted a line through the
points.
• The slope of this line is an estimate of beta.
– It tells us how much on average the stock price
changed for each additional 1% change in the
market index.
Measuring Betas
General Motors
GM return (%)
Price data – Aug 88- Jan 95
R2 = .13
B = 0.80
Market return (%)
Slope determined from plotting the
line of best fit.
Measuring Betas
General Motors
GM return (%)
Price data – Feb 95 – Jul 01
R2 = .25
B = 1.00
Slope determined from plotting the
line of best fit.
Market return (%)
Measuring Betas
Exxon Mobil
Exxon Mobil return (%)
Price data – Aug 88- Jan 95
R2 = .28
B = 0.52
Slope determined from plotting the
line of best fit.
Market return (%)
Measuring Betas
Exxon Mobil
Exxon Mobil return (%)
Price data – Feb 95 – Jul 01
R2 = .16
B = 0.42
Slope determined from plotting the
line of best fit.
Market return (%)
Understanding
• Diagrams show plots for the three stocks
during the subsequent period, February 1995
to July 2001.
• Although the slopes varied from the first
period to the second, there is little doubt that
Exxon Mobil’s beta is much less than Dell’s or
that GM’s beta falls somewhere between the
two.
– If you had used the past beta of each stock to
predict its future beta, you wouldn’t have been
too far off.
Understanding
• Only a small portion of each stock’s total risk
comes from movements in the market.
• The rest is unique risk, which shows up in the
scatter of points around the fitted
• lines in Diagrams.
– R-squared (R2) measures the proportion of the
total variance in the stock’s returns that can be
explained by market movements.
Table 1
• Estimated betas and costs of (equity) capital for a sample
of large railroad companies and for a portfolio of these
companies.
• The precision of the portfolio beta is much better than
that of the betas of the individual companies—note the
lower standard error for the portfolio.
Beta
Standard. Error
Burlington Northern
.64
.20
CSX Transporta tion
.46
.24
Norfolk Southern
.52
.26
Union Pacific
.40
.21
Industry Portfolio
.50
.17
Summary
• Company and Project Costs of Capital
• Beta As a Proxy