2. The top panel assumes all earnings are reinvested from 2005 to 2009. In 2010 and later years, two-thirds

of earnings are paid out as dividends and one-third reinvested.

3. The bottom panel assumes two-thirds of earnings are paid out as dividends in all years.

4. Columns may not add up because of rounding.

Mike Gordon™s Saloon, where Francine Firewater, the company™s

current book value per share, but Mr. Breezeway had inter-

CFO, was having her usual steak-and-beans breakfast. He asked

vened and convinced the would-be seller to wait.

Ms. Firewater to prepare a formal report to Prairie Home stock-

Prairie Home™s value did not just depend on its current book

holders, valuing the company on the assumption that its shares

value or earnings, but on its future prospects, which were good.

were publicly traded.

One financial projection (shown in the top panel of Table 3.8)

Ms. Firewater asked two questions immediately. First, what

called for growth in earnings of over 100 percent by 2011. Un-

should she assume about investment and growth? Mr. Breezeway

fortunately this plan would require reinvestment of all of Prairie

suggested two valuations, one assuming more rapid expansion (as

Home™s earnings from 2006 to 2010. After that the company

in the top panel of Table 3.8) and another just projecting past

could resume its normal dividend payout and growth rate. Mr.

growth (as in the bottom panel of Table 3.8).

Breezeway believed this plan was feasible.

Second, what rate of return should she use? Mr. Breezeway said

He was determined to step aside for the next generation of

that 15 percent, Prairie Home™s usual return on book equity,

top management. But before retiring he had to decide whether

sounded right to him, but he referred her to an article in the Jour-

to recommend that Prairie Home Stores “go public””and be-

nal of Finance indicating that investors in rural supermarket

fore that decision he had to know what the company was worth.

chains, with risks similar to Prairie Home Stores, expected to earn

The next morning he rode thoughtfully to work. He left his

about 11 percent on average.

horse at the south corral and ambled down the dusty street to

452 SECTION FOUR

relative risks, at least in industries they are used to, but not about absolute risk or re-

quired rates of return. Therefore, they set a company- or industrywide cost of capital as

a benchmark. This is not the right hurdle rate for everything the company does, but

judgmental adjustments can be made for more risky or less risky ventures.

SOME COMMON MISTAKES

One danger with the weighted-average formula is that it tempts people to make logical

errors. Think back to your estimate of the cost of capital for Big Oil:

[ ]( )

D E

— (1 “ Tc)rdebt + — requity

WACC =

V V

= [.243 — (1 “ .35) 9%] + (.757 — 13.5%) = 11.6%

Now you might be tempted to say to yourself, “Aha! Big Oil has a good credit rating. It

could easily push up its debt ratio to 50 percent. If the interest rate is 9 percent and the

required return on equity is 13.5 percent, the weighted-average cost of capital would be

WACC = [.50 — (1 “ .35) 9%] + (.50 — 13.5%) = 9.7%

At a discount rate of 9.7 percent, we can justify a lot more investment.”

That reasoning will get you into trouble. First, if Big Oil increased its borrowing, the

lenders would almost certainly demand a higher rate of interest on the debt. Second, as

the borrowing increased, the risk of the common stock would also increase and there-

fore the stockholders would demand a higher return.

There are actually two costs of debt finance. The explicit cost of debt is the

rate of interest that bondholders demand. But there is also an implicit cost,

because borrowing increases the required return to equity.

When you jumped to the conclusion that Big Oil could lower its weighted-average cost

of capital to 9.7 percent by borrowing more, you were recognizing only the explicit cost

of debt and not the implicit cost.

Jo Ann Cox™s boss has pointed out that Geothermal proposes to finance its expansion

Self-Test 7

entirely by borrowing at an interest rate of 8 percent. He argues that this is therefore the

appropriate discount rate for the project™s cash flows. Is he right?

HOW CHANGING CAPITAL STRUCTURE

AFFECTS EXPECTED RETURNS

We will illustrate how changes in capital structure affect expected returns by focusing

on the simplest possible case, where the corporate tax rate Tc is zero.

Think back to our earlier example of Geothermal. Geothermal, you may remember,

has the following market-value balance sheet:

Assets Liabilities and Shareholders™ Equity

Assets = value of Geothermal™s $647 Debt $194 (30%)

existing business

Equity $453 (70%)

Total value $647 Value $647 (100%)

The Cost of Capital 453

Geothermal™s debtholders require a return of 8 percent and the shareholders require a

return of 14 percent. Since we assume here that Geothermal pays no corporate tax, its

weighted-average cost of capital is simply the expected return on the firm™s assets:

WACC = rassets = (.3 — 8%) + (.7 — 14%) = 12.2%

This is the return you would expect if you held all Geothermal™s securities and therefore

owned all its assets.

Now think what will happen if Geothermal borrows an additional $97 million and

uses the cash to buy back and retire $97 million of its common stock. The revised mar-

ket-value balance sheet is

Assets Liabilities and Shareholders™ Equity

Assets = value of Geothermal™s $647 Debt $291 (45%)

existing business

Equity 356 (55%)

Total value $647 Value $647 (100%)

If there are no corporate taxes, the change in capital structure does not affect the total

cash that Geothermal pays out to its security holders and it does not affect the risk of

those cash flows. Therefore, if investors require a return of 12.2 percent on the total

package of debt and equity before the financing, they must require the same 12.2

percent return on the package afterward. The weighted-average cost of capital is there-

fore unaffected by the change in the capital structure.

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

change in capital structure does affect the required return on the individual securities.

Since the company has more debt than before, the debt is riskier and debtholders are

likely to demand a higher return. Increasing the amount of debt also makes the equity

riskier and increases the return that shareholders require.

WHAT HAPPENS WHEN THE CORPORATE

TAX RATE IS NOT ZERO

We have shown that when there are no corporate taxes the weighted-average cost of cap-

ital is unaffected by a change in capital structure. Unfortunately, taxes can complicate

the picture.7 For the moment, just remember

• The weighted-average cost of capital is the right discount rate for average-

risk capital investment projects.

• The weighted-average cost of capital is the return the company needs to

earn after tax in order to satisfy all its security holders.

• If the firm increases its debt ratio, both the debt and the equity will

become more risky. The debtholders and equity holders require a higher

return to compensate for the increased risk.

7 There™snothing wrong with our formulas and examples, provided that the tax deductibility of interest pay-

ments doesn™t change the aggregate risk of the debt and equity investors. However, if the tax savings from

deducting interest are treated as safe cash flows, the formulas get more complicated. If you really want to dive

into the tax-adjusted formulas showing how WACC changes with capital structure, we suggest later

in R. A. Brealey and S. C. Myers, Principles of Corporate Finance, 6th ed. (New York: Irwin/McGraw-Hill,

2000).

454 SECTION FOUR

Flotation Costs and the Cost of Capital

To raise the necessary cash for a new project, the firm may need to issue stocks, bonds,

or other securities. The costs of issuing these securities to the public can easily amount

to 5 percent of funds raised. For example, a firm issuing $100 million in new equity

may net only $95 million after incurring the costs of the issue.

Flotation costs involve real money. A new project is less attractive if the firm must

spend large sums on issuing new securities. To illustrate, consider a project that will

cost $900,000 to install and is expected to generate a level perpetual cash-flow stream

of $90,000 a year. At a required rate of return of 10 percent, the project is just barely

viable, with an NPV of zero: “$900,000 + $90,000/.10 = 0.

Now suppose that the firm needs to raise equity to pay for the project, and that

flotation costs are 10 percent of funds raised. To raise $900,000, the firm actually

must sell $1 million of equity. Since the installed project will be worth only $90,000/.10

= $900,000, NPV including flotation costs is actually “$1 million + $900,000 =

“$100,000.

In our example, we recognized flotation costs as one of the incremental costs of un-

dertaking the project. But instead of recognizing these costs explicitly, some companies

attempt to cope with flotation costs by increasing the cost of capital used to discount

project cash flows. By using a higher discount rate, project present value is reduced.

This procedure is flawed on practical as well as theoretical grounds. First, on a

purely practical level, it is far easier to account for flotation costs as a negative cash

flow than to search for an adjustment to the discount rate that will give the right NPV.

Finding the necessary adjustment is easy only when cash flows are level or will grow

indefinitely at a constant trend rate. This is almost never the case in practice, however.

Of course, there always exists some discount rate that will give the right measure of the

project™s NPV, but this rate could no longer be interpreted as the rate of return available

in the capital market for investments with the same risk as the project.

The cost of capital depends only on interest rates, taxes, and the risk of the

project. Flotation costs should be treated as incremental (negative) cash flows;

they do not increase the required rate of return.

Summary

Why do firms compute weighted-average costs of capital?

They need a standard discount rate for average-risk projects. An “average-risk” project is

one that has the same risk as the firm™s existing assets and operations.

What about projects that are not average?

The weighted-average cost of capital can still be used as a benchmark. The benchmark is

adjusted up for unusually risky projects and down for unusually safe ones.

How do firms compute weighted-average costs of capital?

Here™s the WACC formula one more time:

The Cost of Capital 455

WACC = rdebt — (1 “ Tc) — D/V + requity — E/V

The WACC is the expected rate of return on the portfolio of debt and equity securities

issued by the firm. The required rate of return on each security is weighted by its proportion

of the firm™s total market value (not book value). Since interest payments reduce the firm™s

income tax bill, the required rate of return on debt is measured after tax, as rdebt — (1 “ Tc).

This WACC formula is usually written assuming the firm™s capital structure includes just

two classes of securities, debt and equity. If there is another class, say preferred stock, the

formula expands to include it. In other words, we would estimate rpreferred, the rate of return

demanded by preferred stockholders, determine P/V the fraction of market value accounted

,

for by preferred, and add rpreferred — P/V to the equation. Of course the weights in the WACC

formula always add up to 1.0. In this case D/V + P/V + E/V = 1.0.

How are the costs of debt and equity calculated?

The cost of debt (rdebt) is the market interest rate demanded by bondholders. In other words,

it is the rate that the company would pay on new debt issued to finance its investment

projects. The cost of preferred (rpreferred) is just the preferred dividend divided by the market

price of a preferred share.

The tricky part is estimating the cost of equity (requity), the expected rate of return on the

firm™s shares. Financial managers use the capital asset pricing model to estimate expected

return. But for mature, steady-growth companies, it can also make sense to use the constant-

growth dividend discount model. Remember, estimates of expected return are less reliable

for a single firm™s stock than for a sample of comparable-risk firms. Therefore, some

managers also consider WACCs calculated for industries.

What happens when capital structure changes?

The rates of return on debt and equity will change. For example, increasing the debt ratio

will increase the risk borne by both debt and equity investors and cause them to demand

higher returns. However, this does not necessarily mean that the overall WACC will

increase, because more weight is put on the cost of debt, which is less than the cost of

equity. In fact, if we ignore taxes, the overall cost of capital will stay constant as the

fractions of debt and equity change.

Should WACC be adjusted for the costs of issuing securities to finance a project?

No. If acceptance of a project would require the firm to issue securities, the flotation costs

of the issue should be added to the investment required for the project. This reduces project

NPV dollar for dollar. There is no need to adjust WACC.

www.geocities.com/WallStreet/Market/1839/irates.html Incorporating risk premiums into the

Related Web cost of capital

Links www.financeadvisor.com/coc.htm Another approach to calculating cost of capital

capital structure weighted-average cost of capital (WACC)

Key Terms

1. Cost of Debt. Micro Spinoffs, Inc., issued 20-year debt a year ago at par value with a coupon

Quiz rate of 9 percent, paid annually. Today, the debt is selling at $1,050. If the firm™s tax bracket

is 35 percent, what is its after-tax cost of debt?

456 SECTION FOUR

2. Cost of Preferred Stock. Micro Spinoffs also has preferred stock outstanding. The stock

pays a dividend of $4 per share, and the stock sells for $40. What is the cost of preferred

stock?

3. Calculating WACC. Suppose Micro Spinoffs™s cost of equity is 12.5 percent. What is its

WACC if equity is 50 percent, preferred stock is 20 percent, and debt is 30 percent of total

capital?

4. Cost of Equity. Reliable Electric is a regulated public utility, and it is expected to provide

steady growth of dividends of 5 percent per year for the indefinite future. Its last dividend

was $5 per share; the stock sold for $60 per share just after the dividend was paid. What is

the company™s cost of equity?

5. Calculating WACC. Reactive Industries has the following capital structure. Its corporate tax

rate is 35 percent. What is its WACC?

Security Market Value Required Rate of Return

Debt $20 million 8%

Preferred stock $10 million 10%