Brealey−Meyers: Principles of Corporate Finance, 7th Edition - Chapter 9 pot

Weshall see that it is the right hurdle rate for those projects that have the same risk as the firm’s exist-ing business; however, if a project is more risky than the firm as a whole, th

C A P I T A L

B U D G E T I N G

A N D R I S K

LONG BEFORE THE development of modern theories linking risk and expected return, smart financialmanagers adjusted for risk in capital budgeting They realized intuitively that, other things beingequal, risky projects are less desirable than safe ones Therefore, financial managers demanded ahigher rate of return from risky projects, or they based their decisions on conservative estimates ofthe cash flows.

Various rules of thumb are often used to make these risk adjustments For example, many panies estimate the rate of return required by investors in their securities and then use this companycost of capital to discount the cash flows on new projects Our first task in this chapter is to explainwhen the company cost of capital can, and cannot, be used to discount a project’s cash flows Weshall see that it is the right hurdle rate for those projects that have the same risk as the firm’s exist-ing business; however, if a project is more risky than the firm as a whole, the cost of capital needs to

com-be adjusted upward and the project’s cash flows discounted at this higher rate Conversely, a lowerdiscount rate is needed for projects that are safer than the firm as a whole

The capital asset pricing model is widely used to estimate the return that investors require.1Itstates

We used this formula in the last chapter to figure out the return that investors expected from a ple of common stocks but we did not explain how to estimate beta It turns out that we can gain someinsight into beta by looking at how the stock price has responded in the past to market fluctuations.Beta is difficult to measure accurately for an individual firm: Greater accuracy can be achieved bylooking at an average of similar companies We will also look at what features make some investments

sam-riskier than others If you know why Exxon Mobil has less risk than, say, Dell Computer, you will be in

a better position to judge the relative risks of different capital investment opportunities

Some companies are financed entirely by common stock In these cases the company cost of ital and the expected return on the stock are the same thing However, most firms finance themselvespartly by debt and the return that they earn on their investments must be sufficient to satisfy boththe stockholders and the debtholders We will show you how to calculate the company cost of capi-tal when the firm has more than one type of security outstanding

cap-There is still another complication: Project betas can shift over time Some projects are safer inyouth than in old age; others are riskier In this case, what do we mean by the project beta? Theremay be a separate beta for each year of the project’s life To put it another way, can we jump fromthe capital asset pricing model, which looks one period into the future, to the discounted-cash-flowformula for valuing long-lived assets? Most of the time it is safe to do so, but you should be able torecognize and deal with the exceptions

We will use the capital asset pricing model, or CAPM, throughout this chapter But don’t infer that

it is therefore the last word on risk and return The principles and procedures covered in this chapterwork just as well with other models such as arbitrage pricing theory (APT)

Expected return⫽ r ⫽ r f ⫹ 1beta2 1rm⫺ r f2

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 projectsthat have similar risk to that of the firm as a whole For example, in Table 8.2 weestimated that investors require a return of 9.2 percent from Pfizer common stock

If Pfizer is contemplating an expansion of the firm’s existing business, it wouldmake sense to discount the forecasted cash flows at 9.2 percent.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 Each project should in

prin-ciple be evaluated at its own opportunity cost of capital This is a clear implication

of the value-additivity principle introduced in Chapter 7 For a firm composed ofassets A and B, the firm value is

Here PV(A) and PV(B) are valued just as if they were mini-firms in which holders could invest directly Investors would value A by discounting its fore-casted cash flows at a rate reflecting the risk of A They would value B by dis-counting at a rate reflecting the risk of B The two discount rates will, in general, bedifferent If the present value of an asset depended on the identity of the company

stock-that bought it, present values would not add up Remember, a good project is a

good project is a good project

If the firm considers investing in a third project C, it should also value C as if Cwere a mini-firm That is, the firm should discount the cash flows of C at the ex-pected rate of return that investors would demand to make a separate investment

in C The true cost of capital depends on the use to which that capital is put.

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 9.1 If the projecthas a high risk, Pfizer needs a higher prospective return than if the project has alow risk Now contrast this with the company cost of capital rule, which is to ac-

cept any project regardless of its risk as long as it offers a higher return than the pany’s cost of capital In terms of Figure 9.1, the rule tells Pfizer to accept any proj-

com-ect above the horizontal cost of capital line, that is, any projcom-ect offering a return ofmore than 9.2 percent

It is clearly silly to suggest that Pfizer should demand the same rate of returnfrom 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 poorhigh-risk projects It is also silly to suggest that just because another company has

a low company cost of capital, it is justified in accepting projects that Pfizerwould reject

The notion that each company has some individual discount rate or cost of ital is widespread, but far from universal Many firms require different returns

cap-⫽ sum of separate asset values Firm value⫽ PV1AB2 ⫽ PV1A2 ⫹ PV1B29.1 COMPANY AND PROJECT COSTS OF CAPITAL

2 Debt accounted for only about 0.3 percent of the total market value of Pfizer’s securities Thus, its cost

of capital is effectively identical to the rate of return investors expect on its common stock The cations caused by debt are discussed later in this chapter.

compli-from different categories of investment For example, discount rates might be set

as follows:

Project beta

Company cost of capital

Security market line showing required return on project

Average beta of the firm's assets = 71

to beta.

Category Discount Rate Speculative ventures 30%

Expansion of existing business 15 (company cost of capital)

Cost improvement, known technology 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?

There are two reasons First, many (maybe, most) projects can be treated as

av-erage risk, that is, no more or less risky than the avav-erage of the company’s other

as-sets For these projects the company cost of capital is the right discount rate

Sec-ond, 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

com-pany cost of capital than to estimate each project’s cost of capital from scratch

There is a good musical analogy here.3Most of us, lacking perfect pitch, need a

well-defined reference point, like middle C, before we can sing on key But anyone

who can carry a tune gets relative pitches right Businesspeople have good intuition

about relative risks, at least in industries they 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

3 The analogy is borrowed from S C Myers and L S Borucki, “Discounted Cash Flow Estimates of

the Cost of Equity Capital—A Case Study,” Financial Markets, Institutions, and Investments 3 (August

1994), p 18.

Suppose that you are considering an across-the-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 fromthe company’s common stock In Chapter 8 we used the capital asset pricing model

to do this This states

An obvious way to measure the beta (␤) of a stock is to look at how its price has sponded in the past to market movements For example, look at the three left-handscatter diagrams in Figure 9.2 In the top-left diagram we have calculated monthly re-turns from Dell Computer stock in the period after it went public in 1988, and we haveplotted these returns against the market returns for the same month The second dia-gram on the left shows a similar plot for the returns on General Motors stock, and thethird shows a plot for Exxon Mobil In each case we have fitted a line through thepoints The slope of this line is an estimate of beta.4It tells us how much on averagethe stock price changed for each additional 1 percent change in the market index.The right-hand diagrams show similar plots for the same three stocks during thesubsequent period, February 1995 to July 2001 Although the slopes varied from thefirst period to the second, there is little doubt that Exxon Mobil’s beta is much lessthan Dell’s or that GM’s beta falls somewhere between the two If you had used thepast beta of each stock to predict its future beta, you wouldn’t have been too far off.Only a small portion of each stock’s total risk comes from movements in the mar-ket The rest is unique risk, which shows up in the scatter of points around the fitted

re-lines in Figure 9.2 R-squared (R2) measures the proportion of the total variance in thestock’s returns that can be explained by market movements For example, from 1995

to 2001, the R2for GM was 25 In other words, a quarter of GM’s risk was market riskand three-quarters was unique risk The variance of the returns on GM stock was 964.5

So we could say that the variance in stock returns that was due to the market was

and the variance of unique returns was The estimates of beta shown in Figure 9.2 are just that They are based on thestocks’ returns in 78 particular months The noise in the returns can obscure the true

beta Therefore, statisticians calculate the standard error of the estimated beta to show the extent of possible mismeasurement Then they set up a confidence interval of the

estimated value plus or minus two standard errors For example, the standard error

of GM’s estimated beta in the most recent period is 20 Thus the confidence intervalfor GM’s beta is 1.00 plus or minus 2 ⫻ 20 If you state that the true beta for GM is

between 60 and 1.40, you have a 95 percent chance of being right Notice that we can

be more confident of our estimate of Exxon Mobil’s beta and less confident of Dell’s.Usually you will have more information (and thus more confidence) than thissimple calculation suggests For example, you know that Exxon Mobil’s estimated

sim-tain nonsense results.

5

This is an annual figure; we annualized the monthly variance by multiplying by 12 (see footnote 17 in Chapter 7) The standard deviation was 2964 ⫽ 31.0 percent.

-10 -20

-30 -40

-20 -10 0 10 20 30 40 50

-40 -30 -20 -10 0 10 20 30 40 50

-30 -20 -10 0 10 20 30

-30 -20 -10 0 10 20 30

-10 0 10 20

-10 0 10 20

R 2 = 11

Dell Computer return %

February 1995–

July 2001

β = 2.02 (.38)

R 2 = 13

February 1995–

July 2001

General Motors return %

β = 1.00 (.20)

R 2 = 28

Exxon Mobil return %

β = 42 (.11)

beta was well below 1 in the previous period, while Dell’s estimated beta was wellabove 1 Nevertheless, there is always a large margin for error when estimating thebeta for individual stocks.

Fortunately, the estimation errors tend to cancel out when you estimate betas of

portfolios.6That is why financial managers often turn to industry betas For example,

Table 9.1 shows estimates of beta and the standard errors of these estimates for thecommon stocks of four large railroad companies Most of the standard errors areabove 2, large enough to preclude a precise estimate of any particular utility’s beta.However, the table also shows the estimated beta for a portfolio of all four railroadstocks Notice that the estimated industry beta is more reliable This shows up inthe lower standard error

The Expected Return on Union Pacific Corporation’s Common Stock

Suppose that in mid-2001 you had been asked to estimate the company cost of ital of Union Pacific Corporation Table 9.1 provides two clues about the true beta

cap-of Union Pacific’s stock: the direct estimate cap-of 40 and the average estimate for theindustry of 50 We will use the industry average of 50.7

In mid-2001 the risk-free rate of interest r fwas about 3.5 percent Therefore, ifyou had used 8 percent for the risk premium on the market, you would have con-cluded that the expected return on Union Pacific’s stock was about 7.5 percent:8

Standard

Burlington Northern & Santa Fe 64 20 CSX Transportation 46 24 Norfolk Southern 52 26 Union Pacific Corp .40 21 Industry portfolio 50 17

T A B L E 9 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.

8

This is really a discount rate for near-term cash flows, since it rests on a risk-free rate measured by the yield on Treasury bills with maturities less than one year Is this, you may ask, the right discount rate for cash flows from an asset with, say, a 10- or 20-year expected life?

Well, now that you mention it, possibly not In 2001 longer-term Treasury bonds yielded about 5.8 percent, that is, about 2.3 percent above the Treasury bill rate.

The risk-free rate could be defined as a long-term Treasury bond yield If you do this, however, you should subtract the risk premium of Treasury bonds over bills, which we gave as 1.8 percent in Table 7.1 This gives a rough-and-ready estimate of the expected yield on short-term Treasury bills over the life of the bond:

The expected average future Treasury bill rate should be used in the CAPM if a discount rate is

needed for an extended stream of cash flows In 2001 this “long-term r f” was a bit higher than the Treasury bill rate.

⫽ 058 ⫺ 019 ⫽ 039, or 3.9%

Expected average T-bill rate ⫽ T-bond yield ⫺ premium of bonds over bills

We have focused on using the capital asset pricing model to estimate the

ex-pected returns on Union Pacific’s common stock But it would be useful to get a

check on this figure For example, in Chapter 4 we used the constant-growth

DCF formula to estimate the expected rate of return for a sample of utility

stocks.9You could also use DCF models with varying future growth rates, or

perhaps arbitrage pricing theory (APT) We showed in Section 8.4 how APT can

be used to estimate expected returns

⫽ 3.5 ⫹ 518.02 ⫽ 7.5%

Expected stock return⫽ r f ⫹ ␤1r m ⫺ r f2

9 The United States Surface Transportation Board uses the constant-growth model to estimate the cost

of equity capital for railroad companies We will review its findings in Chapter 19.

9.3 CAPITAL STRUCTURE AND THE COMPANY COST

OF CAPITAL

In the last section, we used the capital asset pricing model to estimate the return

that investors require from Union Pacific’s common stock Is this figure Union

Pa-cific’s company cost of capital? Not if Union Pacific has other securities

outstand-ing The company cost of capital also needs to reflect the returns demanded by the

owners of these securities

We will return shortly to the problem of Union Pacific’s cost of capital, but first

we need to look at the relationship between the cost of capital and the mix of debt

and equity used to finance the company Think again of what the company cost of

capital is and what it is used for We define it as the opportunity cost of capital for

the firm’s existing assets; we use it to value new assets that have the same risk as

the old ones

If you owned a portfolio of all the firm’s securities—100 percent of the debt

and 100 percent of the equity—you would own the firm’s assets lock, stock, and

barrel You wouldn’t share the cash flows with anyone; every dollar of cash the

firm paid out would be paid to you You can think of the company cost of

capi-tal as the expected return on this hypothetical portfolio To calculate it, you just

take a weighted average of the expected returns on the debt and the equity:

For example, suppose that the firm’s market-value balance sheet is as follows:

Equity value (E) 70

Note that the values of debt and equity add up to the firm value (D ⫹ E ⫽ V) and

that the firm value equals the asset value (These figures are market values, not book

values: The market value of the firm’s equity is often substantially different from

its book value.)

debt⫹ equity rdebt⫹ equity

debt⫹ equity requity Company cost of capital⫽ rassets⫽ rportfolio

If investors expect a return of 7.5 percent on the debt and 15 percent on the uity, then the expected return on the assets is

eq-If the firm is contemplating investment in a project that has the same risk as thefirm’s existing business, the opportunity cost of capital for this project is the same

as the firm’s cost of capital; in other words, it is 12.75 percent

What would happen if the firm issued an additional 10 of debt and used the cash

to repurchase 10 of its equity? The revised market-value balance sheet is

Equity value (E) 60

The change in financial structure does not affect the amount or risk of the cashflows on the total package of debt and equity Therefore, if investors required a re-turn of 12.75 percent on the total package before the refinancing, they must require

a 12.75 percent return on the firm’s assets afterward

Although the required return on the package of debt and equity is unaffected, the

change in financial structure does affect the required return on the individual curities Since the company has more debt than before, the debtholders are likely

se-to demand a higher interest rate We will suppose that the expected return on thedebt rises to 7.875 percent Now you can write down the basic equation for the re-turn on assets

and solve for the return on equity

Increasing the amount of debt increased debtholder risk and led to a rise in the

return that debtholders required (rdebtrose from 7.5 to 7.875 percent) The higherleverage also made the equity riskier and increased the return that shareholders re-

quired (requityrose from 15 to 16 percent) The weighted average return on debt andequity remained at 12.75 percent:

Suppose that the company decided instead to repay all its debt and to replace itwith equity In that case all the cash flows would go to the equity holders The com-

pany cost of capital, rassets, would stay at 12.75 percent, and requitywould also be12.75 percent

How Changing Capital Structure Affects Beta

We have looked at how changes in financial structure affect expected return Let us

now look at the effect on beta

The stockholders and debtholders both receive a share of the firm’s cash flows,

and both bear part of the risk For example, if the firm’s assets turn out to be

worth-less, there will be no cash to pay stockholders or debtholders But debtholders

usu-ally bear much less risk than stockholders Debt betas of large blue-chip firms are

typically in the range of 1 to 3.10

If you owned a portfolio of all the firm’s securities, you wouldn’t share the cash

flows with anyone You wouldn’t share the risks with anyone either; you would

bear them all Thus the firm’s asset beta is equal to the beta of a portfolio of all the

firm’s debt and its equity

The beta of this hypothetical portfolio is just a weighted average of the debt and

equity betas:

Think back to our example If the debt before the refinancing has a beta of 1 and

the equity has a beta of 1.1, then

What happens after the refinancing? The risk of the total package is unaffected, but

both the debt and the equity are now more risky Suppose that the debt beta

in-creases to 2 We can work out the new equity beta:

You can see why borrowing is said to create financial leverage or gearing Financial

leverage does not affect the risk or the expected return on the firm’s assets, but it

does push up the risk of the common stock Shareholders demand a

correspond-ingly higher return because of this financial risk.

Figure 9.3 shows the expected return and beta of the firm’s assets It also shows

how expected return and risk are shared between the debtholders and equity

hold-ers before the refinancing Figure 9.4 shows what happens after the refinancing

Both debt and equity are now more risky, and therefore investors demand a higher

return But equity accounts for a smaller proportion of firm value than before As

a result, the weighted average of both the expected return and beta on the two

components is unchanged

Now you can see how to unlever betas, that is, how to go from an observed

␤equityto ␤assets.You have the equity beta, say, 1.2 You also need the debt beta, say,

.2, and the relative market values of debt (D/V) and equity (E/V) If debt accounts

for 40 percent of overall value V,

␤assets⫽ 1.4 ⫻ 22 ⫹ 1.6 ⫻ 1.22 ⫽ 8

␤equity⫽ 1.2 8⫽ 1.4 ⫻ 22 ⫹ 1.6 ⫻ ␤equity2

10 For example, in Table 7.1 we reported average returns on a portfolio of high-grade corporate bonds.

In the 10 years ending December 2000 the estimated beta of this bond portfolio was 17.

This runs the previous example in reverse Just remember the basic relationship:

Capital Structure and Discount Rates

The company cost of capital is the opportunity cost of capital for the firm’s

as-sets That’s why we write it as rassets.If a firm encounters a project that has the

␤assets⫽ ␤portfolio⫽ D V␤debt⫹ V E␤equity

Beta

0 b debt = 1 b assets = 8 b equity = 1.1

Expected return, percent

rdebt = 7.5

rassets = 12.75

requity = 15

F I G U R E 9 3

Expected returns and betas

before refinancing The

expected return and beta

of the firm’s assets are

weighted averages of the

expected return and betas

of the debt and equity.

Beta

Expected return, percent

same beta as the firm’s overall assets, then rassetsis the right discount rate for the

project cash flows

When the firm uses debt financing, the company cost of capital is not the same

as requity, the expected rate of return on the firm’s stock; requityis higher because of

financial risk However, the company cost of capital can be calculated as a

weighted average of the returns expected by investors on the various debt and

eq-uity securities issued by the firm You can also calculate the firm’s asset beta as a

weighted average of the betas of these securities

When the firm changes its mix of debt and equity securities, the risk and

ex-pected returns of these securities change; however, the asset beta and the company

cost of capital do not change

Now, if you think all this is too neat and simple, you’re right The

complica-tions are spelled out in great detail in Chapters 17 through 19 But we must note

one complication here: Interest paid on a firm’s borrowing can be deducted from

taxable income Thus the after-tax cost of debt is rdebt(l ⫺ T c ), where T cis the

marginal corporate tax rate When companies discount an average-risk project,

they do not use the company cost of capital as we have computed it They use

the after-tax cost of debt to compute the after-tax weighted-average cost of

cap-ital or WACC:

More—lots more—on this in Chapter 19

Back to Union Pacific’s Cost of Capital

In the last section we estimated the return that investors required on Union

Pa-cific’s common stock If Union Pacific were wholly equity-financed, the company

cost of capital would be the same as the expected return on its stock But in

mid-2001 common stock accounted for only 60 percent of the market value of the

com-pany’s securities Debt accounted for the remaining 40 percent.11Union Pacific’s

company cost of capital is a weighted average of the expected returns on the

dif-ferent securities

We estimated the expected return from Union Pacific’s common stock at 7.5

per-cent The yield on the company’s debt in 2001 was about 5.5 perper-cent.12Thus

Union Pacific’s WACC is calculated in the same fashion, but using the after-tax cost

11

Union Pacific had also issued preferred stock Preferred stock is discussed in Chapter 14 To keep

mat-ters simple here, we have lumped the preferred stock in with Union Pacific’s debt.

12

This is a promised yield; that is, it is the yield if Union Pacific makes all the promised payments Since

there is some risk of default, the expected return is always less than the promised yield Union Pacific

debt has an investment-grade rating and the difference is small But for a company that is hovering on

the brink of bankruptcy, it can be important.

We have shown how the CAPM can help to estimate the cost of capital for tic investments by U.S companies But can we extend the procedure to allow forinvestments in different countries? The answer is yes in principle, but naturallythere are complications.

domes-Foreign Investments Are Not Always Riskier

Pop quiz: Which is riskier for an investor in the United States—the Standard andPoor’s Composite Index or the stock market in Egypt? If you answer Egypt, you’re

right, but only if risk is defined as total volatility or variance But does investment

in Egypt have a high beta? How much does it add to the risk of a diversified

port-folio held in the United States?

Table 9.2 shows estimated betas for the Egyptian market and for markets inPoland, Thailand, and Venezuela The standard deviations of returns in these mar-kets were two or three times more than the U.S market, but only Thailand had abeta greater than 1 The reason is low correlation For example, the standard devi-ation of the Egyptian market was 3.1 times that of the Standard and Poor’s index,but the correlation coefficient was only 18 The beta was 3.1 ⫻ 18 ⫽ 55

Table 9.2 does not prove that investment abroad is always safer than at home.But it should remind you always to distinguish between diversifiable and marketrisk The opportunity cost of capital should depend on market risk

Foreign Investment in the United States

Now let’s turn the problem around Suppose that the Swiss pharmaceutical pany, Roche, is considering an investment in a new plant near Basel in Switzerland.The financial manager forecasts the Swiss franc cash flows from the project and dis-counts these cash flows at a discount rate measured in francs Since the project isrisky, the company requires a higher return than the Swiss franc interest rate How-ever, the project is average-risk compared to Roche’s other Swiss assets To esti-mate the cost of capital, the Swiss manager proceeds in the same way as her coun-terpart in a U.S pharmaceutical company In other words, she first measures therisk of the investment by estimating Roche’s beta and the beta of other Swiss phar-

com-maceutical companies However, she calculates these betas relative to the Swiss ket index Suppose that both measures point to a beta of 1.1 and that the expected

mar-9.4 DISCOUNT RATES FOR INTERNATIONAL

PROJECTS

Ratio of Standard Correlation Deviations* Coefficient Beta †

Egypt 3.11 18 56 Poland 1.93 42 81 Thailand 2.91 48 1.40 Venezuela 2.58 30 77

T A B L E 9 2

Betas of four country indexes versus the U.S market,

calculated from monthly returns, August 1996–July 2001.

Despite high volatility, three of the four betas are less

than 1 The reason is the relatively low correlation with

the U.S market.

*Ratio of standard deviations of country index to Standard

& Poor’s Composite Index.

† Beta is the ratio of covariance to variance Covariance can be

written as ␴ IM ⫽ ␳ IM ␴ I ␴ M ; ␤ ⫽ ␳ IM ␴ I ␴ M /␴ M2⫽ ␳ (␴ I /␴ M ), where

I indicates the country index and M indicates the U.S market.

risk premium on the Swiss market index is 6 percent.13Then Roche needs to

dis-count the Swiss franc cash flows from its project at 1.1 ⫻ 6 ⫽ 6.6 percent above the

Swiss franc interest rate

That’s straightforward But now suppose that Roche considers construction of a

plant in the United States Once again the financial manager measures the risk of

this investment by its beta relative to the Swiss market index But notice that the

value of Roche’s business in the United States is likely to be much less closely tied

to fluctuations in the Swiss market So the beta of the U.S project relative to the

Swiss market is likely to be less than 1.1 How much less? One useful guide is the

U.S pharmaceutical industry beta calculated relative to the Swiss market index It

turns out that this beta has been 36.14If the expected risk premium on the Swiss

market index is 6 percent, Roche should be discounting the Swiss franc cash flows

from its U.S project at 36 ⫻ 6 ⫽ 2.2 percent above the Swiss franc interest rate

Why does Roche’s manager measure the beta of its investments relative to the

Swiss index, whereas her U.S counterpart measures the beta relative to the U.S

index? The answer lies in Section 7.4, where we explained that risk cannot be

con-sidered in isolation; it depends on the other securities in the investor’s portfolio

Beta measures risk relative to the investor’s portfolio If U.S investors already hold

the U.S market, an additional dollar invested at home is just more of the same

But, if Swiss investors hold the Swiss market, an investment in the United States

can reduce their risk That explains why an investment in the United States is

likely to have lower risk for Roche’s shareholders than it has for shareholders in

Merck or Pfizer It also explains why Roche’s shareholders are willing to accept

a lower return from such an investment than would the shareholders in the U.S

companies.15

When Merck measures risk relative to the U.S market and Roche measures risk

relative to the Swiss market, their managers are implicitly assuming that the

share-holders simply hold domestic stocks That’s not a bad approximation, particularly

in the case of the United States.16Although investors in the United States can

re-duce their risk by holding an internationally diversified portfolio of shares, they

generally invest only a small proportion of their money overseas Why they are so

shy is a puzzle.17It looks as if they are worried about the costs of investing

over-seas, but we don’t understand what those costs include Maybe it is more difficult

to figure out which foreign shares to buy Or perhaps investors are worried that a

13 Figure 7.3 showed that this is the historical risk premium on the Swiss market The fact that the

real-ized premium has been lower in Switzerland than the United States may be just a coincidence and may

not mean that Swiss investors expected the lower premium On the other hand, if Swiss firms are

gen-erally less risky, then investors may have been content with a lower premium.

14 This is the beta of the Standard and Poor’s pharmaceutical index calculated relative to the Swiss

mar-ket for the period August 1996 to July 2001.

15 When investors hold efficient portfolios, the expected reward for risk on each stock in the portfolio is

proportional to its beta relative to the portfolio So, if the Swiss market index is an efficient portfolio for

Swiss investors, then Swiss investors will want Roche to invest in a new plant if the expected reward

for risk is proportional to its beta relative to the Swiss market index.

16 But it can be a bad assumption elsewhere For small countries with open financial borders—

Luxembourg, for example—a beta calculated relative to the local market has little value Few

in-vestors in Luxembourg hold only local stocks.

17 For an explanation of the cost of capital for international investments when there are costs to

interna-tional diversification, see I A Cooper and E Kaplanis, “Home Bias in Equity Portfolios and the Cost of

Capital for Multinational Firms,” Journal of Applied Corporate Finance 8 (Fall 1995), pp 95–102.

foreign government will expropriate their shares, restrict dividend payments, orcatch them by a change in the tax law.

However, the world is getting smaller, and investors everywhere are increasingtheir holdings of foreign securities Large American financial institutions have sub-stantially increased their overseas investments, and literally dozens of funds havebeen set up for individuals who want to invest abroad For example, you can nowbuy funds that specialize in investment in emerging capital markets such as Viet-nam, Peru, or Hungary As investors increase their holdings of overseas stocks, itbecomes less appropriate to measure risk relative to the domestic market and moreimportant to measure the risk of any investment relative to the portfolios that theyactually hold

Who knows? Perhaps in a few years investors will hold internationally versified portfolios, and in later editions of this book we will recommend thatfirms calculate betas relative to the world market If investors throughout theworld held the world portfolio, then Roche and Merck would both demand thesame return from an investment in the United States, in Switzerland, or inEgypt

di-Do Some Countries Have a Lower Cost of Capital?

Some countries enjoy much lower rates of interest than others For example, as wewrite this the interest rate in Japan is effectively zero; in the United States it is above

3 percent People often conclude from this that Japanese companies enjoy a lowercost of capital

This view is one part confusion and one part probable truth The confusionarises because the interest rate in Japan is measured in yen and the rate in theUnited States is measured in dollars You wouldn’t say that a 10-inch-high rabbitwas taller than a 9-foot elephant You would be comparing their height in differentunits In the same way it makes no sense to compare an interest rate in yen with arate in dollars The units are different

But suppose that in each case you measure the interest rate in real terms Then

you are comparing like with like, and it does make sense to ask whether the costs

of overseas investment can cause the real cost of capital to be lower in Japan

Japan-ese citizens have for a long time been big savers, but as they moved into a new tury they were very worried about the future and were saving more than ever Thatmoney could not be absorbed by Japanese industry and therefore had to be in-

cen-vested overseas Japanese investors were not compelled to invest overseas: They

needed to be enticed to do so So the expected real returns on Japanese investmentsfell to the point that Japanese investors were willing to incur the costs of buyingforeign securities, and when a Japanese company wanted to finance a new project,

it could tap into a pool of relatively low-cost funds

9.5 SETTING DISCOUNT RATES WHEN YOU

CAN’T CALCULATE BETAStock or industry betas provide a rough guide to the risk encountered in variouslines of business But an asset beta for, say, the steel industry can take us only sofar Not all investments made in the steel industry are typical What other kinds ofevidence about business risk might a financial manager examine?

In some cases the asset is publicly traded If so, we can simply estimate its beta

from past price data For example, suppose a firm wants to analyze the risks of

holding a large inventory of copper Because copper is a standardized, widely

traded commodity, it is possible to calculate rates of return from holding copper

and to calculate a beta for copper

What should a manager do if the asset has no such convenient price record?

What if the proposed investment is not close enough to business as usual to justify

using a company cost of capital?

These cases clearly call for judgment For managers making that kind of

judg-ment, we offer two pieces of advice

1 Avoid fudge factors Don’t give in to the temptation to add fudge factors to

the discount rate to offset things that could go wrong with the proposed

investment Adjust cash-flow forecasts first

2 Think about the determinants of asset betas Often the characteristics of

high-and low-beta assets can be observed when the beta itself cannot be

Let us expand on these two points

Avoid Fudge Factors in Discount Rates

We have defined risk, from the investor’s viewpoint, as the standard deviation of

portfolio return or the beta of a common stock or other security But in everyday

usage risk simply equals “bad outcome.” People think of the risks of a project as a

list of things that can go wrong For example,

• A geologist looking for oil worries about the risk of a dry hole

• A pharmaceutical manufacturer worries about the risk that a new drug which

cures baldness may not be approved by the Food and Drug Administration

• The owner of a hotel in a politically unstable part of the world worries about

the political risk of expropriation

Managers often add fudge factors to discount rates to offset worries such as these

This sort of adjustment makes us nervous First, the bad outcomes we cited

ap-pear to reflect unique (i.e., diversifiable) risks that would not affect the expected

rate of return demanded by investors Second, the need for a discount rate

adjust-ment usually arises because managers fail to give bad outcomes their due weight

in cash-flow forecasts The managers then try to offset that mistake by adding a

fudge factor to the discount rate

Example Project Z will produce just one cash flow, forecasted at $1 million at

year 1 It is regarded as average risk, suitable for discounting at a 10 percent

com-pany cost of capital:

But now you discover that the company’s engineers are behind schedule in

devel-oping the technology required for the project They’re confident it will work, but

they admit to a small chance that it won’t You still see the most likely outcome as

$1 million, but you also see some chance that project Z will generate zero cash flow

next year

PV⫽ C1

1⫹ r⫽

1,000,0001.1 ⫽ $909,100