10 the cost of capital

If Allied raises new capital to finance asset expansion, and if it is to keep its capital structure inbalance that is, if it is to keep the same percentage of debt, pre-ferred stock, and

SOURCE: IPIX™ Used with permission from Interactive Pictures Corporation www.ipix.com.

General Electric has long been recognized as one of the world’s best-managed companies, and it has rewarded its shareholders with outstanding returns.

Given its performance, it is not surprising that GE is always at or near the top of the list of companies in generating EVA Thus, GE has been able to consistently find projects that earn more than their costs of capital.

Estimating the cost of capital for a company like GE

is a fairly straightforward exercise, but it does require judgment Since GE’s capital comes largely from equity, its cost of capital depends to a large extent on the cost

of its equity, which is in essence its shareholders’

required return One must recognize that when investors purchase GE stock, they are investing in a company that operates many different divisions throughout the world.

Each division has a different level of risk, hence a different cost of capital GE’s appliance division’s cost of capital is likely to be different than that of its NBC subsidiary, or than that of its aircraft engine division.

Likewise, an overseas project may have different risks and thus a different cost of capital than an otherwise similar domestic project.

As we will see in this chapter, estimating a project’s cost of capital is an important process, and one that requires judgment Companies that manage this process well will probably produce positive economic value for

n Chapter 2 we discussed the concept of EVA —

Economic Value Added — which is used by an

increasing number of companies to measure

corporate performance Developed by the consulting firm

Stern Stewart & Company, EVA is designed to measure a

corporation’s true profitability, and it is calculated as

after-tax operating profits less the annual after-tax cost

of all the capital a firm uses.

The idea behind EVA is simple — firms are truly

profitable and create value if and only if their income

exceeds the cost of all the capital they use to finance

operations The conventional measure of performance,

net income, takes into account the cost of debt, which

shows up on financial statements as interest expense,

but it does not reflect the cost of equity Therefore, a

firm can report positive net income yet still be

unprofitable in an economic sense if its net income is

less than its cost of equity EVA corrects this flaw by

recognizing that to properly measure performance, it is

necessary to account for the cost of equity capital.

A variety of factors influence a firm’s cost of capital.

Some, such as the level of interest rates, state and

federal tax policies, and the regulatory environment, are

outside of the firm’s control However, the firm’s

financing and investment policies, especially the types

of capital it uses and the types of investment projects it

undertakes, have a profound effect on its cost of capital.

C R E AT I N G VA L U E

AT G E

GENERAL ELECTRIC

$ I

461

In the last two chapters, we discussed the values of and required rates of return

on stocks and bonds When companies issue stocks or bonds, they are raising

capital for investment in various projects Capital is a necessary factor of

pro-duction, and like any other factor, it has a cost This cost is equal to the

mar-ginal investor’s required return on the security in question With this in mind,

we now consider the process of estimating the cost of capital

The firm’s primary objective is to maximize shareholder value, and companies

can increase shareholder value by investing in projects that earn more than the

cost of capital For this reason, the cost of capital is sometimes referred to as

a hurdle rate: For a project to be accepted, it must earn more than its hurdle

rate

Although its most important use is in capital budgeting, the cost of capital is

also used for at least three other purposes: (1) It is a key input used to calculate

a firm’s or division’s economic value added (EVA) (2) Managers estimate and use

the cost of capital when deciding if they should lease or purchase assets And (3),

the cost of capital is important in the regulation of monopoly services provided by

electric, gas, and telephone companies These firms are natural monopolies in the

sense that one firm can supply service at a lower cost than could two or more

firms Since it has a monopoly, your electric or telephone company could, if it

were unregulated, exploit you Therefore, regulators (1) determine the cost of the

capital investors have provided to the utility and (2) then set rates designed to

permit the company to earn its cost of capital, no more and no less

It should be noted that the cost of capital models and formulas used in this

chapter are the same ones we developed in Chapters 8 and 9, where we were

con-cerned with the rates of return investors require on different securities The same

factors that affect investors’ required rates of return also determine the cost of

capital to a firm, so investors and corporate treasurers often use exactly the same

models ■

Assume that Allied Food Products has a 10 percent cost of debt and a 13.4percent cost of equity Further, assume that Allied has made the decision to fi-nance next year’s projects with debt The argument is sometimes made that thecost of capital for these projects is 10 percent because only debt will be used tofinance them However, this position is incorrect If Allied finances a particularset of projects with debt, the firm will be using up some of its capacity for bor-rowing in the future As expansion occurs in subsequent years, Allied will atsome point find it necessary to raise additional equity to prevent the debt ratiofrom becoming too large.

To illustrate, suppose Allied borrows heavily at 10 percent during 2002,using up its debt capacity in the process, to finance projects yielding 11.5 per-cent In 2003, it has new projects available that yield 13 percent, well abovethe return on 2002 projects, but it cannot accept them because they would

have to be financed with 13.4 percent equity money To avoid this problem,

Al-lied should be viewed as an ongoing concern, and the cost of capital used in capital budgeting should be calculated as a weighted average, or composite, of the various types of funds it generally uses, regardless of the specific financing used to fund a par- ticular project.

B A S I C D E F I N I T I O N S

Ohio State University has

a web site with video clips

of business professionals

discussing various topics

of interest in finance The site can be

found at

http://fisher.osu.edu/fin/clips.htm.

The two video clips relevant to capital

budgeting come from Steve Walsh,

assistant treasurer of JCPenney: “How

We Do Capital Budgeting” and “On the

Cost of Capital and Debt.” Be

forewarned that these files are quite

large and are best downloaded using a

rapid Internet link.

S E L F - T E S T Q U E S T I O N

Why should the cost of capital used in capital budgeting be calculated as aweighted average of the various types of funds the firm generally uses, notthe cost of the specific financing used to fund a particular project?

B A S I C D E F I N I T I O N S

The items on the right side of a firm’s balance sheet — various types of debt,

preferred stock, and common equity — are called capital components Any

in-crease in total assets must be financed by an inin-crease in one or more of thesecapital components

The cost of each component is called the component cost of that particular

type of capital; for example, if Allied can borrow money at 10 percent, its

Capital Component

One of the types of capital used by

firms to raise money.

component cost of debt is 10 percent Throughout this chapter, we trate on these three major capital components: debt, preferred stock, and com-mon equity The following symbols identify the cost of each:

concen-kd
interest rate on the firm’s new debt
before-tax component cost

of debt For Allied, kd
10%

kd(1  T)
after-tax component cost of debt, where T is the firm’s marginal

tax rate kd(1  T) is the debt cost used to calculate the weightedaverage cost of capital For Allied, T
40%, so kd(1  T)
10%(1  0.4)
10%(0.6)
6.0%

kp
component cost of preferred stock For Allied, kp
10.3%

ks
component cost of common equity It is identical to the ksoped in Chapters 6 and 9 and defined there as the rate of returninvestors require on a firm’s common stock Equity capital israised in two ways: (1) by retaining earnings (internal equity) or(2) by issuing new common stock (external equity) It is generallydifficult to estimate ks, but, as we shall see shortly, a reasonablygood estimate for Allied is ks
13.4%

devel-WACC
the weighted average cost of capital If Allied raises new capital to

finance asset expansion, and if it is to keep its capital structure inbalance (that is, if it is to keep the same percentage of debt, pre-ferred stock, and common equity funds), then it must raise part ofits new funds as debt, part as preferred stock, and part as commonequity (with equity coming either from retained earnings or by is-suing new common stock).2 We will calculate WACC for AlliedFood Products shortly

These definitions and concepts are explained in detail in the remainder of thechapter Later, in Chapter 13, we extend the analysis to determine the mix of se-curities that will minimize the firm’s cost of capital and thereby maximize its value

The after-tax cost of debt, k d (1 ⴚ T), is used to calculate the weighted

aver-age cost of capital, and it is the interest rate on debt, kd, less the tax savings that

After-tax Cost of Debt,

k d (1 ⴚ T)

The relevant cost of new debt,

taking into account the tax

deductibility of interest; used to

calculate the WACC.

want to maximize, depends on after-tax cash flows Because interest is a

de-ductible expense, it produces tax savings that reduce the net cost of debt, ing the after-tax cost of debt less than the before-tax cost We are concernedwith after-tax cash flows, and since cash flows and rates of return should beplaced on a comparable basis, we adjust the interest rate downward to take ac-count of the preferential tax treatment of debt.4

mak-Note that the cost of debt is the interest rate on new debt, not that on ready outstanding debt; in other words, we are interested in the marginal cost

al-of debt Our primary concern with the cost al-of capital is to use it for capitalbudgeting decisions — for example, would a new machine earn a returngreater than the cost of the capital needed to acquire the machine? The rate

at which the firm has borrowed in the past is irrelevant — we need the cost of

4

The tax rate is zero for a firm with losses Therefore, for a company that does not pay taxes, the

cost of debt is not reduced; that is, in Equation 10-1, the tax rate equals zero, so the after-tax cost

of debt is equal to the interest rate.

Strictly speaking, the after-tax cost of debt should reflect the expected cost of debt While Allied’s

bonds have a promised return of 10 percent, there is some chance of default, so its bondholders’ expected return (and consequently Allied’s cost) is a bit less than 10 percent For a relatively strong company such as Allied, this difference is quite small As we discuss later in the chapter, Allied must also incur flotation costs when it issues debt, but like the difference between the promised and the expected rate of return, flotation costs are generally small Finally, note that these two factors tend

to offset one another — not including the possibility of default leads to an overstatement of the cost

of debt, but not including flotation costs leads to an understatement For all these reasons, k d is generally a good approximation of the before-tax cost of debt capital.

C O S T O F P R E F E R R E D S T O C K , kp

The component cost of preferred stock used to calculate the weighted age cost of capital, k p, is the preferred dividend, Dp, divided by the currentprice of the preferred stock, Pp:5

aver-(10-2)

For example, Allied has preferred stock that pays a $10 dividend per share andsells for $97.50 per share in the open market Therefore, Allied’s cost of pre-ferred stock is 10.3 percent:

kp
$10/$97.50
10.3%

As we can see from Equation 10–2, calculating the cost of preferred stock isgenerally quite simple This is particularly true when we consider the tradi-tional, “plain vanilla” form of preferred stock that pays a fixed dividend in per-petuity We mentioned, however, in Chapter 9 that some preferred stock has afixed maturity date, and we described how to calculate the expected return onthese issues These expected returns would also represent the cost of preferredstock for these fixed-maturity issues In some other instances, preferred stockmay include an option to convert to common stock In these cases, calculatingthe cost of preferred stock becomes considerably more complicated We willleave these more complicated cases for advanced classes and restrict ourselves

to “plain vanilla” preferred issues, such as the ones issued by Allied

No tax adjustments are made when calculating kp because preferred

divi-dends, unlike interest on debt, are not deductible Therefore, there are no tax

savings associated with the use of preferred stock However, as we discuss in theaccompanying box entitled “Funny-Named Preferred-Like Securities,” somecompanies have tried to come up with ways to issue securities that are similar

to preferred stock but that are structured in ways that enable them to deductthe payments made on these securities

Component cost of preferred stock
kp
Dp

Pp

Cost of Preferred Stock, k p

The rate of return investors

require on the firm’s preferred

stock k p is calculated as the

the current price, P p

S E L F - T E S T Q U E S T I O N

Is a tax adjustment made to the cost of preferred stock? Why or why not?

C O S T O F R E T A I N E D E A R N I N G S , ks

The costs of debt and preferred stock are based on the returns investors require

on these securities Similarly, the cost of common equity is based on the rate ofreturn investors require on a company’s common stock Note, though, that newcommon equity is raised in two ways: (1) by retaining some of the current year’searnings and (2) by issuing new common stock As we shall see, equity raised byissuing stock has a somewhat higher cost than equity raised as retained earnings

due to the flotation costs involved with new stock issues We use the symbol k s

to designate the cost of retained earnings and k eto designate the cost of mon equity raised by issuing new stock, or external equity.6

com-C O S T O F R E T A I N E D E A R N I N G S , k

Cost of Retained Earnings, k s

The rate of return required by

stockholders on a firm’s common

stock.

6The term retained earnings can be interpreted to mean either the balance sheet item “retained

earnings,” consisting of all the earnings retained in the business throughout its history, or the come statement item “addition to retained earnings.” The income statement item is used in this

in-chapter; for our purpose, retained earnings refers to that part of the current year’s earnings not paid

out in dividends, hence available for reinvestment in the business this year.

F U N N Y- N A M E D P R E F E R R E D - L I K E S E C U R I T I E S

Wall Street’s “financial engineers” are constantly trying to

develop new securities with appeal to issuers and

in-vestors One such new security is a special type of preferred

stock created by Goldman Sachs in the mid-1990s These

secu-rities trade under a variety of colorful names, including MIPS

(modified income preferred securities), QUIPS (quarterly income

preferred securities), and QUIDS (quarterly income debt

securi-ties) The corporation that wants to raise capital (the “parent”)

establishes a trust, which issues fixed-dividend preferred stock.

The parent then issues bonds (or debt of some type) to the

trust, and the trust pays for the bonds with the cash raised

from the sale of preferred At that point, the parent has the

cash it needs, the trust holds debt issued by the parent, and

the investing public holds preferred stock issued by the trust.

The parent then makes interest payments to the trust, and the

trust uses that income to make the preferred dividend

pay-ments Because the parent company has issued debt, its

inter-est payments are tax deductible.

If the dividends could be excluded from taxable income by

corporate investors, this preferred would really be a great deal

— the issuer could deduct the interest, corporate investors

could exclude most of the dividends, and the IRS would be the

loser The corporate parent does get to deduct the interest paid

to the trust, but IRS regulations do not allow the dividends on

these securities to be excluded.

Because there is only one deduction, why are these new

se-curities attractive? The answer is as follows: (1) Since the

par-ent company gets to take the deduction, its cost of funds from the preferred is k p (1  T), just as it would be if it used debt (2) The parent generates a tax savings, and it can thus afford

to pay a relatively high rate on trust-related preferred; that is,

it can pass on some of its tax savings to investors to induce them to buy the new securities (3) The primary purchasers of the preferred are low-tax-bracket individuals and tax-exempt in- stitutions such as pension funds For such purchasers, not being able to exclude the dividend from taxable income is not impor- tant (4) Due to the differential tax rates, the arrangement re- sults in a net tax savings Competition in capital markets re- sults in a sharing of the savings between investors and corporations.

A recent SmartMoney Online article argued that these hybrid

securities are a good deal for individual investors for the reason set forth above and also because they are sold in small incre- ments — often as small as $25 However, these securities are relatively complex, which increases their risk and makes them hard to value There is also risk to the issuing corporations The IRS has expressed concerns about these securities, and if at some point the IRS decides to disallow interest paid to the trusts, that will have a profound negative effect on the corpo- rations that have issued them.

SOURCES: Kerry Capell, “High Yields, Low Cost, Funny Names,” Business Week,

Sep-tember 9, 1996, 122; and Leslie Haggin, “SmartMoney Online: MIPS, QUIDS, and

QUIPS,” SmartMoney Interactive, April 6, 1999.

k e

The designation for the cost of

common equity raised by issuing

new stock, or external equity.

A corporation’s management might misguidedly thinkthat retained ings are “free” because they represent money that is “left over” after payingdividends While it is true that no direct costs are associated with capitalraised as retained earnings, this capital still has a cost The reason we must as-

earn-sign a cost of capital to retained earnings involves the opportunity cost principle.

The firm’s after-tax earnings belong to its stockholders Bondholders are pensated by interest payments, and preferred stockholders by preferred divi-dends All earnings remaining after interest and preferred dividends belong tothe common stockholders, and these earnings serve to compensate stockhold-ers for the use of their capital Management may either pay out earnings inthe form of dividends or else retain earnings and reinvest them in the busi-

com-ness If management decides to retain earnings, there is an opportunity cost

volved — stockholders could have received the earnings as dividends and vested this money in other stocks, in bonds, in real estate, or in anything else

in-Thus, the firm should earn on its retained earnings at least as much as the holders themselves could earn on alternative investments of comparable risk.

stock-What rate of return can stockholders expect to earn on equivalent-risk ments? First, recall from Chapter 9 that stocks are normally in equilibrium, withexpected and required rates of return being equal: ˆks
ks Thus, we can assumethat Allied’s stockholders expect to earn a return of kson their money Therefore,

invest-if the firm cannot invest retained earnings and earn at least k s , it should pay these funds

to its stockholders and let them invest directly in other assets that do provide this return.7

Whereas debt and preferred stocks are contractual obligations that have ily determined costs, it is difficult to measure ks However, we can employ theprinciples developed in Chapters 6 and 9 to produce reasonably good cost ofequity estimates Recall that if a stock is in equilibrium, then its required rate

eas-of return, ks, must be equal to its expected rate of return, ˆks Further, its required

return is equal to a risk-free rate, kRF, plus a risk premium, RP, whereas the

ex-pected return on a constant growth stock is the stock’s dividend yield, D1/P0,plus its expected growth rate, g:

Required rate of return
Expected rate of return

Step 1.Estimate the risk-free rate, kRF, generally taken to be either the U.S

Treasury bond rate or the short-term (30-day) Treasury bill rate

Step 2.Estimate the stock’s beta coefficient, bi, and use it as an index of the

stock’s risk The i signifies the ith company’s beta.

7 Dividends and capital gains are taxed differently, with long-term capital gains being taxed at a lower rate than dividends for most stockholders That makes it beneficial for companies to retain earnings rather than pay them out as dividends, and that, in turn, tends to lower the cost of capital for retained earnings This point is discussed in detail in Chapter 14.

Step 3.Estimate the expected rate of return on the market, or on an

“aver-age” stock, kM

Step 4.Substitute the preceding values into the CAPM equation to estimate

the required rate of return on the stock in question:

Equation 10-4 shows that the CAPM estimate of ksbegins with the risk-freerate, kRF, to which is added a risk premium set equal to the risk premium on anaverage stock, kM kRF, scaled up or down to reflect the particular stock’s risk

as measured by its beta coefficient

To illustrate the CAPM approach, assume that kRF
8%, kM
13%, and

bi
0.7 for a given stock This stock’s ksis calculated as follows:

ac-as we saw in Chapter 6, if a firm’s stockholders are not well diversified, they

may be concerned with stand-alone risk rather than just market risk In that case,

the firm’s true investment risk would not be measured by its beta, and theCAPM procedure would understate the correct value of ks Further, even if theCAPM method is valid, it is hard to obtain correct estimates of the inputs re-quired to make it operational because (1) there is controversy about whether touse long-term or short-term Treasury yields for kRF, (2) it is hard to estimatethe beta that investors expect the company to have in the future, and (3) it isdifficult to estimate the market risk premium

BO N D- YI E L D-P L U S- RI S K- PR E M I U M AP P R O A C H

Analysts who do not have confidence in the CAPM often use a subjective, adhoc procedure to estimate a firm’s cost of common equity: they simply add ajudgmental risk premium of 3 to 5 percentage points to the interest rate on thefirm’s own long-term debt It is logical to think that firms with risky, low-rated,and consequently high-interest-rate debt will also have risky, high-cost equity,

C O S T O F R E T A I N E D E A R N I N G S , k

and the procedure of basing the cost of equity on a readily observable debtcost utilizes this logic For example, if an extremely strong firm such asBellSouth had bonds that yielded 8 percent, its cost of equity might be esti-mated as follows:

ks
Bond yield  Risk premium
8%  4%
12%

The bonds of a riskier company such as Continental Airlines might carry ayield of 12 percent, making its estimated cost of equity 16 percent:

ks
12%  4%
16%

Because the 4 percent risk premium is a judgmental estimate, the estimatedvalue of ksis also judgmental Empirical work in recent years suggests that therisk premium over a firm’s own bond yield has generally ranged from 3 to 5percentage points, so while this method does not produce a precise cost of eq-uity, it will “get us into the right ballpark.”

DI V I D E N D- YI E L D-P L U S- GR O W T H- RAT E, O R

DI S C O U N T E D CA S H FL O W ( D C F ) , AP P R O A C H

In Chapter 9, we saw that both the price and the expected rate of return on a share

of common stockdepend, ultimately, on the dividends expected on the stock:

(10-5)

Here P0is the current price of the stock; Dtis the dividend expected to be paid

at the end of Year t; and ks is the required rate of return If dividends are pected to grow at a constant rate, then, as we saw in Chapter 9, Equation 10-5reduces to this important formula:

ex-(10-6)

We can solve for ks to obtain the required rate of return on common equity,which, for the marginal investor, is also equal to the expected rate of return:

(10-7)

Thus, investors expect to receive a dividend yield, D1/P0, plus a capital gain,

g, for a total expected return of ˆks, and in equilibrium this expected return

is also equal to the required return, ks This method of estimating the cost

of equity is called the discounted cash flow, or DCF, method Henceforth, we

will assume that equilibrium exists, and we will use the terms ks and ˆks terchangeably

in-It is easy to determine the dividend yield, but it is difficult to establish theproper growth rate If past growth rates in earnings and dividends have beenrelatively stable, and if investors appear to be projecting a continuation of past

trends, then g may be based on the firm’s historic growth rate However, if the

company’s past growth has been abnormally high or low, either because of its own

P0
D1(1 ks)1  D2

(1 ks)2  # # #

unique situation or because of general economic fluctuations, then investors will not project the past growth rate into the future In this case, g must be estimated in

some other manner

Security analysts regularly make earnings and dividend growth forecasts,looking at such factors as projected sales, profit margins, and competitive factors

For example, Value Line, which is available in most libraries, provides growth

rate forecasts for 1,700 companies, and Merrill Lynch, Salomon Smith Barney,and other organizations make similar forecasts Therefore, someone making acost of equity estimate can obtain several analysts’ forecasts, average them, usethe average as a proxy for the growth expectations of investors in general, andthen combine this g with the current dividend yield to estimate ˆksas follows:

Again, note that this estimate of ˆksis based on the assumption that g is expected

to remain constant in the future.8

Another method for estimating g involves first forecasting the firm’s average

future dividend payout ratio and its complement, the retention rate, and then

multiplying the retention rate by the company’s expected future rate of return

on equity (ROE):

g
(Retention rate)(ROE)
(1.0  Payout rate)(ROE) (10-8)

Intuitively, firms that are more profitable and retain a larger portion of theirearnings for reinvestment in the firm will tend to have higher growth rates thanfirms that are less profitable and pay out a higher percentage of their earnings

as dividends Security analysts often use Equation 10-8 when they estimategrowth rates For example, suppose a company is expected to have a constantROE of 13.4 percent, and it is expected to pay out 40 percent of its earningsand to retain 60 percent In this case, its forecasted growth rate would be g
(0.60)(13.4%)
8.0%

To illustrate the DCF approach, suppose Allied’s stock sells for $23; its nextexpected dividend is $1.24; and its expected growth rate is 8 percent Allied’sexpected and required rate of return, hence its cost of retained earnings, wouldthen be 13.4 percent:

5.4%  8.0%

13.4%

This 13.4 percent is the minimum rate of return that management must expect

to justify retaining earnings and plowing them back in the business rather thanpaying them out to stockholders as dividends Put another way, since investors

Return,” Financial Management, Spring 1986.

Note also that two organizations — IBES and Zacks — collect the forecasts of leading analysts for most larger companies, average these forecasts, and then publish the averages The IBES and Zacks data are available over the Internet through on-line computer data services.

C O S T O F N E W C O M M O N S T O C K , ke

Companies generally hire an investment banker to assist them when they issuecommon stock, preferred stock, or bonds In return for a fee, the investmentbanker helps the company structure the terms and set a price for the issue, and

then sells the issue to investors The banker’s fees are often referred to as

flota-tion costs, and the total cost of capital should reflect both the required return

paid to investors and the flotation fees paid to the investment banker

As you can see in the accompanying box, “How Much Does It Cost to RaiseExternal Capital?,” flotation costs are often substantial, and they vary depending

on the size and riskof the issuing firm and on the type of capital raised So far, wehave ignored flotation costs when estimating the component costs of capital, butsome would argue that these costs should be included in a complete analysis ofthe cost of capital [The counter-argument is that flotation costs are not highenough to worry about because (1) most equity comes from retained earnings, (2)most debt is raised in private placements and hence involves no flotation costs,and (3) preferred stockis rarely used.] A more complete discussion of flotation

cost adjustments can be found in Eugene F Brigham and Phillip R Daves,

Inter-mediate Financial Management, 7th ed., and other advanced texts, but we describe

below two alternative approaches that can be used to account for flotation costs.The first approach simply adds the estimated dollar amount of flotation costsfor each project to the project’s up-front cost The estimated flotation costs arefound as the sum of the flotation costs for the debt, preferred, and common stockused to finance the project Because of the now-higher investment cost, the proj-ect’s expected rate of return and NPV are decreased For example, consider aone-year project that has an up-front cost (not including flotation costs) of $100million After one year, the project is expected to produce an inflow of $115 mil-lion Therefore, its expected return is $115/$100 1
0.15
15% However,

S E L F - T E S T Q U E S T I O N S

Why must a cost be assigned to retained earnings?

What three approaches are used to estimate the cost of common equity?Identify some problems with the CAPM approach

What is the reasoning behind the bond-yield-plus-risk-premium approach?Which of the two components of the constant growth DCF formula, the div-idend yield or the growth rate, is more difficult to estimate? Why?

have an opportunity to earn 13.4 percent if earnings are paid to them as dends, then the company’s opportunity cost of equity from retained earnings is

divi-13.4 percent

People experienced in estimating equity capital costs recognize that bothcareful analysis and sound judgment are required It would be nice to pretendthat judgment is unnecessary and to specify an easy, precise way of determiningthe exact cost of equity capital Unfortunately, this is not possible — finance is

in large part a matter of judgment, and we simply must face that fact

if the project requires the company to issue new capital with an estimated $2 lion of flotation costs, the total up-front cost is $102 million, and the expectedrate of return is only $115/$102 1
0.1275
12.75%

mil-The second approach involves adjusting the cost of capital rather than creasing the project’s cost If the firm plans to continue to use the capital in thefuture, as is generally true for equity, then this second approach is better Theadjustment process is based on the following logic If there are flotation costs,the issuing company receives only a portion of the total capital raised from in-vestors, with the remainder going to the underwriter When calculating thecost of common equity, the DCF approach can be adapted to account for flota-

in-tion costs For a constant growth stock, the cost of new common stock, k e ,

can be expressed as:9

(10-9)

Cost of equity from new stock issues
ke
D1

P0(1 F) g.

C O S T O F N E W C O M M O N S T O C K , k

Cost of New Common Stock, k e

The cost of external equity; based

on the cost of retained earnings,

but increased for flotation costs.

T R E N D S I N T E C H N O L O G Y: E S T I M AT I N G T H E C O S T O F C A P I TA L F O R I N T E R N E T C O M PA N I E S

hard to find reliable estimates of key inputs, such as the

firm’s expected growth rate and beta Internet companies face

an especially difficult challenge Volatile Internet stock prices

cause the parameters needed to calculate the cost of capital

to change quickly and dramatically, producing wide swings in

the estimated cost of capital When the estimated hurdle rate

is constantly fluctuating, firms have difficulty evaluating

pro-posed projects.

At the same time, however, the high market valuations of Internet companies seem to have reduced their costs of capital High demand for these stocks has made it easy for them to raise large amounts of low-cost capital to finance internal growth and acquire other companies Indeed, even analysts who believe that Internet companies are wildly overvalued still note that they can use their overvalued stock to acquire reasonably priced companies, and that this very action tends to make them less overvalued.

9 Equation 10-9 is derived as follows:

Step 1.The old stockholders expect the firm to pay a stream of dividends, Dt, that will be derived from existing assets with a per-share value of P0 New investors will likewise expect to receive the same stream of dividends, but the funds available to invest in assets will be less than P0

because of flotation costs For new investors to receive their expected dividend stream out impairing the D t stream of the old investors, the new funds obtained from the sale of stock

with-must be invested at a return high enough to provide a dividend stream whose present value

is equal to the net price the firm will receive:

Here F is the percentage flotation cost required to sell the new stock, so

P0(1  F) is the net price per share received by the company

Assuming that Allied has a flotation cost of 10 percent, its cost of newcommon equity, ke, is computed as follows:

6.0%  8.0%
14.0%

Investors require a return of ks
13.4% on the stock However, because of

flotation costs the company must earn more than 13.4 percent on the net funds

obtained by selling stockin order to give investors a 13.4 percent return on themoney they put up Specifically, if the firm earns 14 percent on funds obtained

by issuing new stock, then earnings per share will remain at the previously pected level, the firm’s expected dividend can be maintained, and, as a result, theprice per share will not decline If the firm earns less than 14 percent, then earn-ings, dividends, and growth will fall below expectations, causing the stockprice

ex-to decline If the firm earns more than 14 percent, the sex-tockprice will rise

$20.70$1.24  8.0%

ke
$23(1$1.24

 0.10) 8.0%

H OW M U C H D O E S I T C O S T TO R A I S E E X T E R N A L C A P I TA L ?

how much it costs U.S corporations to raise external

capi-tal Using information from the Securities Data Company, they

found the average flotation cost for debt and equity issued in

the 1990s as presented below.

The common stock flotation costs are for non-IPOs Costs

as-sociated with IPOs are even higher — flotation costs are about

17 percent of gross proceeds for common equity if the amount

raised in the IPO is less than $10 million and about 6 percent

if more than $500 million is raised The data shown below clude both utility and nonutility companies If utilities were ex- cluded, flotation costs would be somewhat higher.

in-SOURCE: Inmoo Lee, Scott Lochhead, Jay Ritter, and Quanshui Zhao, “The Costs of

Raising Capital,” The Journal of Financial Research, Vol XIX, No 1, Spring 1996,

59–74 Reprinted with permission.

AVERAGE FLOTATION COST AVERAGE FLOTATION COST

(MILLIONS OF DOLLARS) (% OF TOTAL CAPITAL RAISED) (% OF TOTAL CAPITAL RAISED)

The percentage cost of issuing

new common stock.

Because of flotation costs, dollars raised by selling new stock must “workharder” than dollars raised by retaining earnings Moreover, since no flotationcosts are involved, retained earnings have a lower cost than new stock There-fore, firms should utilize retained earnings to the extent possible to avoid thecosts of issuing new common stock However, if a firm has more good invest-ment opportunities than can be financed with retained earnings and debt sup-ported by retained earnings, it may find it necessary to issue new common

stock The retained earnings breakpoint represents the total amount of

fi-nancing that can be raised before the firm is forced to sell new common stock.This breakpoint can be calculated as follows:

(10-11)

Allied’s addition to retained earnings in 2002 is expected to be $68 million(see Table 4-3 in Chapter 4), and its capital structure consists of 45 percentdebt, 2 percent preferred, and 53 percent equity Therefore, its retained earn-ings breakpoint is $68/0.53
$128 million If Allied’s capital budget called forspending exactly $128 million, then 0.45($128)
$57.6 million would be fi-nanced with debt, 0.02($128)
$2.6 million with preferred stock, and0.53($128)
$67.8 million with equity raised from retained earnings If Allied’scapital budget exceeded the $128 million “breakpoint,” the amount of equityrequired would exceed the amount of available retained earnings, so the com-pany would have to obtain equity by issuing new, high-cost common stock

It is important to recognize that this breakpoint is only suggestive — it is notwritten in stone For example, rather than issuing new common stock, the com-pany could use more debt (hence, less equity), or it could increase its additionalretained earnings by reducing its dividend payout ratio Both actions would in-crease the retained earnings breakpoint In any event, firms that have a largenumber of good investment opportunities generally maximize their retainedearnings by paying out a smaller percentage of income as dividends than firmswith fewer good investment opportunities We will discuss dividend policy inmore detail in Chapter 14

Flotation cost adjustments can also be made for preferred stock and debt.For preferred stock, the flotation-adjusted cost is the preferred dividend, Dp,divided by the net issuing price, Pn, the price the firm receives on preferredafter deducting flotation costs Similarly, if debt is issued to the public andflotation costs are incurred, the after-tax cost is found by calculating the after-tax yield to maturity, where the issue price is the bond’s par value less the flota-tion expense.10

Retained earningsbreakpoint
Addition to retained earningsEquity fraction

C O S T O F N E W C O M M O N S T O C K , k

Retained Earnings Breakpoint

The amount of capital raised

beyond which new common stock

must be issued.

10 More specifically, the solution value of k d in this formula is used as the after-tax cost of debt:

Here F is the percentage amount of the bond flotation cost, N is the number of periods to rity, INT is the dollars of interest per period, T is the corporate tax rate, M is the maturity value

matu-of the bond, and k d is the after-tax cost of debt adjusted to reflect flotation costs If we assume that the bond in the example calls for annual payments, that it has a 20-year maturity, and that F
2%, then the flotation-adjusted, after-tax cost of debt is 6.18 percent versus 6 percent before the flota-

tion adjustment Also see Eugene F Brigham and Phillip R Daves, Intermediate Financial ment, 7th ed (Fort Worth, TX: Harcourt College Publishers, 2002), Chapter 9.

Manage-M(1  F)
aN

t
1

INT(1  T) (1  k d ) t  M

(1  k d ) N

C O M P O S I T E , O R W E I G H T E D AV E R A G E ,

C O S T O F C A P I T A L , WA C C

As we shall see in Chapter 13, each firm has an optimal capital structure, fined as that mix of debt, preferred, and common equity that causes its stockprice to be maximized Therefore, a value-maximizing firm will determine its

de-optimal capital structure, use it as a target, and then raise new capital in a

manner designed to keep the actual capital structure on target over time In thischapter, we assume that the firm has identified its optimal capital structure, that

it uses this optimum as the target, and that it finances so as to remain on get How the target is established will be examined in Chapter 13

tar-The target proportions of debt, preferred stock, and common equity, along

with the costs of those components, are used to calculate the firm’s weighted

average cost of capital, WACC To illustrate, suppose Allied Food has a

tar-get capital structure calling for 45 percent debt, 2 percent preferred stock, and

53 percent common equity (retained earnings plus common stock) Its tax cost of debt, kd, is 10 percent; its after-tax cost of debt
kd(1  T)
10%(0.6)
6.0%; its cost of preferred stock, kp, is 10.3 percent; its cost ofcommon equity, ks, is 13.4 percent; its marginal tax rate is 40 percent; and all

before-of its new equity will come from retained earnings We calculate Allied’sweighted average cost of capital, WACC, as follows:

A weighted average of the

component costs of debt,

preferred stock, and common

equity.

Target (Optimal) Capital

Structure

The percentages of debt,

preferred stock, and common

equity that will maximize the

While flotation costs may seem high, their per-project cost is usually tively small For example, if a company issues common stock only once every

rela-10 years, the flotation costs should be spread over all the projects funded ing the 10-year period If flotation costs are charged only during the years inwhich external capital is raised, a project evaluated during those years wouldappear worse than the same project analyzed in a year when no external capital

dur-is radur-ised Since flotation costs are not normally very important, unless statedotherwise, we will leave a detailed discussion of flotation costs to advanced fi-nance courses

Note that when calculating the firm’s target capital structure, total debtincludes both long-term debt and bank debt (notes payable) Recall fromChapter 2, that investor-supplied capital does not include other current liabili-ties such as accounts payable and accruals Therefore, these other items are notincluded as part of Allied’s capital structure.

a Long-term debt only.

Stewart & Company regularly estimates EVAs and MVAs for

large U.S corporations To obtain these estimates, Stern

Stew-art must calculate a WACC for each company The table below

presents some recent WACC estimates as calculated by Stern

Stewart for a sample of corporations, along with their long-term

debt-to-total-capital ratios.

These estimates suggest that a typical company has a WACC

somewhere in the 7.5 percent to 12.5 percent range and that

the WACC varies considerably depending on (1) the company’s

risk and (2) the amount of debt it uses Companies in riskier

businesses, such as Intel, presumably have higher costs of

com-mon equity Moreover, they tend not to use as much debt These

two factors, in combination, result in higher WACCs than those

of companies that operate in more stable businesses, such as BellSouth We will discuss the effects of capital structure on WACC in more detail in Chapter 13.

Note that riskier companies may also have the potential for producing higher returns, and what really matters to sharehold- ers is whether a company is able to generate returns in excess

of its cost of capital, resulting in a positive EVA Therefore, a high cost of capital is not necessarily bad if it is accompanied

by projects with high rates of return.

SOURCE: “The 2000 Stern Stewart Performance 1000,” http://www.sternstewart.com/

performance/rankings.shtml; and Value Line Investment Survey, February 23, 2001.

As long as Allied keeps its capital structure on target, and as long as its debthas an after-tax cost of 6 percent, its preferred stock costs 10.3 percent, and itscommon equity costs 13.4 percent, then its weighted average cost of capital will

be WACC
10%.11Each dollar the firm raises will consist of some long-termdebt, some preferred stock, and some common equity, and the cost of the

whole dollar will be 10 percent Therefore, the WACC represents the

mar-ginal cost of capital (MCC), because it indicates the cost of raising an

addi-tional dollar.12

S E L F - T E S T Q U E S T I O N S

Write out the equation for the weighted average cost of capital, WACC

Is short-term debt included in the capital structure used to calculate WACC?Why or why not?

Why does the WACC at every amount of capital raised represent the marginalcost of that capital?

11 The 10 percent WACC assumed that Allied’s equity capital came exclusively from retained ings and had a cost of 13.4 percent If Allied expanded so rapidly and required so much new capi- tal that it had to issue new common stock at a cost of ke
14%, then its WACC would rise to 10.3 percent:

so the breakpoint itself is flexible, not set in stone.

12 As noted in Footnote 11, at times the marginal cost of capital will not remain constant but will instead increase as the firm raises more and more capital This situation exists for large, estab- lished firms if they require so much capital that they are required to issue new common stockto the public Note, though, that large firms rarely issue common stock— they typically obtain all

the equity they need by retaining earnings See Brigham and Daves, Intermediate Financial agement, 7th ed., Chapter 9.

Man-Marginal Cost of Capital (MCC)

The cost of obtaining another

dollar of new capital; the weighted

average cost of the last dollar of

new capital raised.

F A C T O R S T H A T A F F E C T

T H E C O M P O S I T E C O S T O F C A P I T A L

The cost of capital is affected by a number of factors Some are beyond afirm’s control, but others are influenced by its financing and investmentdecisions

T a x R a t e s

Tax rates, which are largely beyond the control of an individual firm (althoughfirms can and do lobby for more favorable tax treatment), have an important ef-fect on the cost of capital Tax rates are used in the calculation of the compo-nent cost of debt In addition, there are other less apparent ways in which taxpolicy affects the cost of capital For example, lowering the capital gains tax raterelative to the rate on ordinary income makes stocks more attractive, and thatreduces the cost of equity That would lower the WACC, and, as we will see inChapter 13, it would also lead to a change in a firm’s optimal capital structure(toward less debt and more equity)

in the WACC equation will tend to lower the WACC However, an increase inthe use of debt will increase the riskiness of both the debt and the equity, and theseincreases in component costs will tend to offset the effects of the change in theweights In Chapter 13, we will discuss this concept in more depth, and we willdemonstrate that a firm’s optimal capital structure minimizes its cost of capital

D i v i d e n d P o l i c y

As we indicated earlier, firms can obtain new equity either through retainedearnings or by issuing new common stock, but because of flotation costs, new

F A C T O R S T H A T A F F E C T T H E C O M P O S I T E C O S T O F C A P I T A L

common stock is more expensive than retained earnings For this reason, firmsissue new common stockonly after they have invested all of their retainedearnings Since retained earnings is income that has not been paid out as divi-dends, it follows that dividend policy can affect the cost of capital because it af-fects the level of retained earnings As we will see in Chapter 14, firms take cost

of capital effects into account when they establish their dividend policies

I n v e s t m e n t P o l i c y

When we estimate the cost of capital, we use as the starting point the requiredrates of return on the firm’s outstanding stock and bonds Those cost rates re-flect the riskiness of the firm’s existing assets Therefore, we have implicitlybeen assuming that new capital will be invested in assets of the same type andwith the same degree of risk as is embedded in the existing assets This as-sumption is generally correct, as most firms do invest in assets similar to thosethey currently operate However, it would be incorrect if the firm dramaticallychanged its investment policy For example, if a firm invests in an entirely newline of business, its marginal cost of capital should reflect the riskiness of thatnew business To illustrate, ITT Corporation recently sold off its finance com-pany and purchased Caesar’s World, a casino gambling firm This dramaticshift in corporate focus almost certainly affected ITT’s cost of capital Likewise,Disney’s purchase of the ABC television network changed the nature and risk

of the company in a way that might also influence its cost of capital The effect

of investment decisions on capital costs is discussed in detail in the next section

must have a cost of capital similar to that faced by their

in-ternational competitors In the past, many experts argued that

U.S firms were at a disadvantage In particular, Japanese firms

enjoyed a lower cost of capital, which lowered their total costs

and thus made it harder for U.S firms to compete Recent

events, however, have considerably narrowed cost of capital

dif-ferences between U.S and Japanese firms In particular, the

U.S stock market has outperformed the Japanese market in

re-cent years, which has made it easier and cheaper for U.S firms

to raise equity capital.

As capital markets become increasingly integrated, country differences in the cost of capital are disappearing Today, most large corporations raise capital throughout the world, hence we are moving toward one global capital market rather than distinct capital markets in each country Although government policies and market conditions can affect the cost

cross-of capital within a given country, this primarily affects smaller firms that do not have access to global capital markets, and even these differences are becoming less important as time goes by What matters most is the risk of the individual firm, not the market in which it raises capital.

As we saw in Chapter 6, investors require higher returns for riskier ments Consequently, a company that is raising capital to take on risky projectswill have a higher cost of capital than a company that is investing in safer proj-ects Figure 10-1 illustrates the trade-off between risk and the cost of capital.Firm L is a low-risk business and has a WACC of 8 percent, whereas Firm H

invest-is exposed to high rinvest-isks and has a WACC of 12 percent Thus, Firm H will cept a typical project only if its expected return is above 12 percent The cor-responding hurdle rate for Firm L’s typical project is only 8 percent

ac-It is important to remember that the cost of capital values at points L and H

in Figure 10-1 represent the overall, or composite, WACCs for the two firms,and, thus, only represent the hurdle rate of a “typical” project for each firm.Different projects generally have different risks Indeed, the hurdle rate foreach project should reflect the risk of the project itself, not the risks associated

A D J U S T I N G T H E C O S T O F C A P I T A L F O R R I S K

F I G U R E 1 0 - 1 Risk and the Cost of Capital

RiskL RiskAverage RiskH Risk

WACC Acceptance Region

Rejection Region

0

Rate of Return

(%)