ch13

Chapter 13

The Cost of Capital

Learning Objectives

1. Explain what the weighted average cost of capital for a firm is and why it is often

used as a discount rate to evaluate projects.

2. Calculate the cost of debt for a firm.

3. Calculate the cost of common stock and the cost of preferred stock for a firm.

4. Calculate the weighted average cost of capital for a firm, explain the limitations of

using a firm’s weighted average cost of capital as the discount rate when evaluating

a project, and discuss the alternatives that are available.

I. Chapter Outline

13.1 The Firm’s Overall Cost of Capital

Since unique risk can be eliminated by holding a diversified portfolio, systematic risk

is the only risk that investors require compensation for bearing.

We concluded in Chapter 7 that we could rely on the CAPM to arrive at the expected

rate of return for a particular investment.

In this chapter, we address the practical concerns that can make that concept

difficult to implement.

Firms do not issue publicly traded shares for individual projects.

As a result, firms have no way to directly estimate the discount rate that

reflects the risk of the incremental cash flows from a particular project.

Financial managers deal with this problem by estimating the cost of capital

for the firm as a whole and then requiring analysts within the firm to use

this cost of capital to discount the cash flows for all projects.

o A problem with this approach is that it ignores the fact that a

firm is really a collection of projects with varying levels of risk.

A. The Finance Balance Sheet

The finance balance sheet is based on market values rather than book values.

The total book value of the assets reported on an accounting balance sheet

does not necessarily reflect the total market value of those assets since the

book value is largely based on historical costs, while the total market

value of the assets equals the present value of the total cash flows that

those assets are expected to generate in the future.

The left-hand side of the accounting balance sheet reports the book values of a

firm’s assets, while the right-hand side reports how those assets were financed.

The value of the claims that investors hold must equal the value of the cash flows that

they have a right to receive.

This is because the total market value of the debt and the equity at a firm equals

the present value of the cash flows that the debt holders and the stockholders

have the right to receive.

o The people who have lent money to a firm and the people who have

purchased the firm’s stock have the right to receive all of the cash

flows that the firm is expected to generate in the future.

MV of assets = MV of liabilities + MV of equity

B. How Firms Estimate Their Cost of Capital

If analysts at a firm could estimate the betas for each of the firm’s

individual projects, they could estimate the beta for the entire firm as a

weighted average of the betas for the individual projects.

o Unfortunately, because analysts are not typically able to

estimate betas for individual projects, they generally cannot use

this approach.

o Instead, analysts must use their knowledge of the finance

balance sheet, along with the concept of market efficiency, to

estimate the cost of capital for the firm.

Rather than perform the calculations for the individual projects

represented on the left-hand side of the finance balance sheet, analysts

perform a similar set of calculations for the different types of financing

(debt and equity) on the right-hand side of the finance balance sheet.

o As long as they can estimate the cost of each type of financing

by observing that cost in the capital markets, they can compute

the cost of capital for the firm by using the following equation:

o If we divide the costs of capital into debt and equity portions of

the firm, then we can use the above to arrive at the weighted

average cost of capital (WACC) for the firm:

kFirm = xDebtkDebt + xEquitykEquity

13.2 The Cost of Debt

Analysts often cannot directly observe the rate of return that investors require for

a particular type of financing and instead must rely on the security prices they can

observe in the financial markets to estimate that required rate.

o It makes sense to rely on security prices only if you believe that the

financial markets are reasonably efficient at incorporating new

information into these prices.

o If the markets were not efficient, estimates of expected returns that were

based on market security prices would be unreliable.

A. Key Concepts for Estimating the Cost of Debt

With regard to the cost associated with each type of debt that a firm uses

when we estimate the cost of capital for a firm, we are particularly

interested in the cost of the firm’s long-term debt.

When we refer to debt we usually mean the debt that, when it was

borrowed, was set to mature in more than one year.

Debt with a maturity of more than one year can typically be viewed as

permanent debt because firms often borrow the money to pay off this debt

when it matures.

The cost of a firm’s long-term debt are estimated on the date on which the

analysis is done.

This is important because the interest rate (or historical interest rate

determined at the time of original debt issuance) that the firm is

paying on its outstanding debt does not necessarily reflect its

current cost of debt.

The current cost of long-term debt is the appropriate cost of debt for

WACC calculations.

This is the relevant cost because the WACC is the opportunity cost

of capital for the firm’s investors as of today.

B. Estimating the Current Cost of a Bond or an Outstanding Loan

The current cost of debt for a publicly traded bond is the yield-to-maturity

calculation.

o To estimate this cost, we first convert the bond data to reflect

semiannual compounding as well as account for the effective annual

interest rate (EAR) to account for the actual current annual cost of the

debt.

We must also account for the cost of issuing the bond—

issuance costs using the net proceeds that the company receives

for the bond rather than the price that is paid by the investor.

For the current cost of long-term bank or other private debt, the firm may

simply call its banker and ask what rate the bank would charge if it decided to

refinance the debt today.

C. Taxes and the Cost of Debt

Firms can deduct interest payments for tax purposes.

The after-tax cost of interest payments equals the pretax cost times 1 minus

the tax rate: kDebt after-tax = kDebt pretax (1 – t)

D. Estimating the Cost of Debt for a Firm

To estimate the firm’s overall cost of debt when it has several debt issues

outstanding, we must first estimate the costs of the individual debt issues and

then calculate a weighted average of these costs.

13.3 The Cost of Equity

The cost of equity for a firm is a weighted average of the costs of the different

types of stock that the firm has outstanding at a particular point in time.

A. Common Stock

o Just as information about market rates of return is used to estimate the cost of

debt, market information is also used to estimate the cost of equity.

There are several ways to do this, and the most appropriate approach will

depend on what information is available and how reliable the analyst

believes it is.

o The text discusses three alternative methods for estimating the cost of common

stock.

o Method 1: Using the Capital Asset Pricing Model (CAPM)

Using the CAPM equation, E(Ri) = Rrf + βi[E(Rm) – Rrf], we find that the

cost of common stock equals the risk-free rate of return plus compensation

for the systematic risk associated with the common stock.

Some practical considerations must be considered when choosing the

appropriate risk-free rate, beta, and market risk premium for the above

calculation.

The recommended risk-free rate to use is the risk-free rate on a

long-term Treasury security because the equity claim is a long-

term claim on the firm’s cash flows.

o A long-term risk-free rate better reflects long-term inflation

expectations and the cost of getting investors to part with

their money for a long period of time than a short-term rate.

You can estimate the beta for that stock using a regression

analysis.

o Identifying the appropriate beta is much more complicated

if the common stock is not publicly traded.

o This problem may be overcome by identifying a

“comparable” company with publicly traded stock that is in

the same business and that has a similar amount of debt.

o When a good comparable company cannot be identified, it

is sometimes possible to use an average of the betas for the

public firms in the same industry.

It is not possible to directly observe the market risk premium since

we don’t know what rate of return investors expect for the market

portfolio.

o For this reason, financial analysts generally use a measure

of the average risk premium investors have actually earned

in the past as an indication of the risk premium they might

require today.

o From 1926 through the end of 2006, actual returns on the

U.S. stock market exceeded actual returns on long-term

U.S. government bonds by an average of 6.51 percent per

year.

If a financial analyst believes that the market risk

premium in the past is a reasonable estimate of the

risk premium today, then he or she might use 6.51

percent (or a value close to it) as the market risk

premium for the future.

o Method 2: Using the Constant-Growth Dividend Model

Using Equation 9.5, , we can rearrange to solve for R—or kcs as

we now prefer to call it:

In order to solve for the cost of common stock, we must estimate the

dividend that stockholders will receive next period, D1, as well as the rate

at which the market expects dividends to grow over the long run, g.

This approach is useful for a firm that pays dividends that will grow at

a constant rate.

This approach might be consistent for an electric utility but not

for a fast growing high-tech firm.

o Method 3: Using a Multistage-Growth Dividend Model

The multistage-growth dividend model allows for faster dividend growth

rates in the near term, followed by a constant long-term growth rate.

The approach is based on the supernormal growth dividend model

discussed in Chapter 9.

o The complexity of this approach lies in choosing the

correct number of stages of forecasted growth as well as

how long each stage will last.

Because of the algebraic complexity in solving for the required rate

of return, the value is generally solved for using a trial-and-error

method, after forecasting the different stages of dividend growth.

o Which Method Should We Use?

In practice, most people use the CAPM (Method 1) to estimate the cost of

equity if the result is going to be used in the discount rate for evaluating a

project.

B. Preferred Stock

The characteristics of preferred stock allow us to use the perpetuity model,

Equation 6.3, to estimate the cost of preferred equity.

o Just as with common stock, we can find the cost of preferred equity by

rearranging the pricing equation for preferred shares:

o Note that the CAPM can be used to estimate the cost of preferred equity,

just as it can be used to estimate the cost of common equity.

12.4 Using the WACC in Practice

The after-tax version of the formula for the weighted-average cost of capital

is: .

The financial analyst should use market values rather than book values to

calculate WACC.

A. Limitations of WACC as a Discount Rate for Evaluating Projects

Financial theory tells us that the rate that should be used to discount these

incremental cash flows is the rate that reflects their systematic risk.

This means that the WACC is going to be the appropriate discount rate for

evaluating a project only when the project has cash flows with systematic risks

that are exactly the same as those for the firm as a whole.

o When a single rate, such as the WACC, is used to discount cash flows for

projects with varying levels of risk, the discount rate will be too low in

some cases and too high in others.

o When the discount rate is too low, the firm runs the risk of accepting a

negative-NPV project.

The estimated NPV will be positive even though the true NPV is

negative.

o When the discount rate is too high, the firm runs the risk of rejecting a

positive-NPV project.

The estimated NPV will be negative even though the true NPV

is positive.

The key point is that it is correct to use a firm’s WACC to discount the cash flows

for a project only if the following conditions hold.

o Condition 1: A firm’s WACC should be used to evaluate the cash flows

for a new project only if the level of systematic risk for that project is the

same as that for the portfolio of projects that currently comprise the firm.

o Condition 2: A firm’s WACC should be used to evaluate a project only if

that project uses the same financing mix—the same proportions of debt,

preferred shares, and common shares—used to finance the firm as a

whole.

B. Alternatives to Using WACC for Evaluating Projects

If the discount rate for a project cannot be estimated directly, a financial analyst

might try to find a public firm that is in a business that is similar to the project.

o This public company would be what financial analysts call a pure-play

comparable because it is exactly like the project.

o This approach is generally not feasible due to the difficulty of finding a

public firm that is only in the business represented by the project.

Financial managers sometimes classify projects into categories based on their

systematic risks.

o They then specify a discount rate that is to be used to discount the cash

flows for all projects within each category.

II. Suggested and Alternative Approaches to the Material

Chapter 13 concentrates on the tools needed to understand the firm’s cost of capital as well as the

complications and corresponding limitations associated with this value. On first glance, it

appears to be a relatively simple concept that is described by a static equation. Instead, the

chapter describes the weighted average cost of capital (WACC) as a snapshot that is based on the

firmwide systematic risk, which is affected by the current portfolio of projects as well as the

financial leverage that the firm is employing. After introducing the concept of WACC, the text

then provides an understanding of the subcomponents of WACC: the cost of debt, the cost of

common equity, and the cost of preferred equity for the firm. While the cost of debt and cost of

preferred equity for the firm are relatively easy calculations, the cost of common equity is

somewhat tricky due to the many assumptions required to estimate the future cash flows

associated with common shareholder ownership.

This material is required in order for the student to be able to proceed to the later capital

budgeting chapters in the text. The current chapter also includes material that is commonly

misunderstood by finance practitioners. As such, careful attention to the conditions required for

using WACC for a firm’s new projects should be discussed and understood.

III. Summary of Learning Objectives

1. Explain what the weighted average cost of capital for a firm is and why it is often used

as a discount rate to evaluate projects.

The weighted average cost of capital (WACC) for a firm is a weighted average of the current

costs of the different types of financing that a firm has used to finance the purchase of its

assets. When the WACC is calculated, the cost of each type of financing is weighted

according to the fraction of the total firm value represented by that type of financing. The

WACC is often used as a discount rate in evaluating projects because it is not possible to

directly estimate the appropriate discount rate for many projects. As we also discuss in

Section 13.4, having a single discount rate reduces inconsistencies that can arise when

different analysts in the firm use different methods to estimate the discount rate and can also

limit the ability of analysts to manipulate discount rates to favor pet projects.

2. Calculate the cost of debt for a firm.

The cost of debt can be calculated by solving for the yield to maturity of the debt using the

bond pricing model (Equation 8.1), computing the effective annual yield, and adjusting for

taxes using Equation 13.3.

3. Calculate the cost of common stock and the cost of preferred stock

for a firm.

The cost of common stock can be estimated using the CAPM, the constant-growth dividend

formula, and a multistage-growth dividend formula. The cost of preferred stock can be

calculated using the perpetuity model for the present value of cash flows.

4. Calculate the weighted average cost of capital for a firm, explain the limitations of

using a firm’s weighted average cost of capital as the discount rate when evaluating a

project, and discuss the alternatives that are available.

The weighted average cost of capital is estimated using either Equation 13.2 or Equation

13.7, with the cost of each individual type of financing estimated using the appropriate

method.

When a firm uses a single rate to discount the cash flows for all of its projects, some

project cash flows will be discounted using a rate that is too high and other project cash flows

will be discounted using a rate that is too low. This can result in the firm’s rejecting some

positive-NPV projects and accepting some negative-NPV projects. It will bias the firm

toward accepting more risky projects and can cause the firm to create less value for

stockholders than it would have if the appropriate discount rates had been used.

One approach to using the WACC is to identify a firm that engages in business activities

that are similar to those associated with the project under consideration and that has publicly

traded stock. The returns from this pure-play firm’s stock can then be used to estimate the

common stock’s beta for the project. In instances where pure-play firms are not available,

financial managers can classify projects according to their systematic risks and can use a

different discount rate for each classification. This is the type of classification scheme

illustrated in Exhibit 13.4.

IV. Summary of Key Equations

Equation Description Formula

13.1 Finance balance sheet identity

MV of assets = MV of liabilities + MV of equity

13.2

General formula for weighted average cost of capital (WACC) for a firm

13.3 After-tax cost of debt kDebt after-tax = kDebt pretax × (1 – t)

13.4 CAPM formula for the cost of common stock

kcs = Rrf + (βcs × Market risk premium)

13.5Constant-growth dividend formula for the cost of common stock

13.6Perpetuity formula for the cost of preferred stock

13.7 Traditional WACC formula

V. Before You Go On Questions and Answers

Section 13.1

1. Why does the market value of the claims on the assets of a firm equal the market value of

the assets?

The investors who own the debt and equity claims on the assets of a firm have the right to

receive all of the after-tax cash flows that the assets of the firm produce. Since the market

value of the assets equals the present value of the cash flows the assets produce, the market

value of the assets must equal the value of the claims on those assets.

2. How is the WACC for a firm calculated?

The WACC is calculated as the weighted average of the different types of claims on the

firm’s assets. The weights in this calculation are the fractions of the total value of the

financing that is represented by each individual type of financing. Equation 13.2 is the

general form of the WACC calculation.

3. What does the WACC for a firm tell us?

The WACC tells us the average cost of the money that has been used to finance the firm.

Section 13.2

1. Why do analysts care about the current cost of long-term debt when estimating a firm’s

cost of capital?

Managers care about the current cost of long-term debt because the opportunity cost of

capital that is relevant when discounting future cash flows is the opportunity cost of capital

as of today. Managers focus on long-term debt because firms generally use it to finance their

long-term assets, and it is the long-term assets that they are concerned about when they think

about the value of a firm’s assets.

2. How do you estimate the cost of debt for a firm with more than one type of debt?

When a firm has more than one type of debt, its overall cost of debt is estimated as a

weighted average of the costs of each type of debt. The weights in this calculation are the

fractions of the total value of the debt represented by each individual type of debt.

3. How do taxes affect the cost of debt?

In the United States, the ability of firms to deduct interest payments when they compute their

taxes actually reduces the cost of using debt. The after-tax cost of debt equals the pretax cost

of debt times one minus the firm’s marginal tax rate.

Section 13.3

1. What information do you need in order to use the CAPM to estimate kcs or kps?

In order to use the CAPM to estimate kcs or kps, you need to know the risk-free rate, the

market risk premium, and the beta for the stock.

2. Under what circumstances can you use the constant-growth dividend formula to estimate

kcs?

The constant-growth dividend formula can be used to estimate kcs if you can observe the

current market price of the common stock and you can estimate the dividend that

stockholders will receive next period, D1, and the rate at which the market expects dividends

to grow over the long run, g. Of course, it only makes sense to use this model if dividends

are expected to grow at a constant rate for the foreseeable future and this growth rate is not

greater than the long-term growth rate of the economy.

3. What is the advantage of using a multistage-growth dividend model, rather than the

constant-growth dividend model, to estimate kcs?

A multistage model allows dividends to grow at different rates over time, while the constant-

growth model allows for only a single growth rate in perpetuity.

Section 13.4

1. Do analysts use book values or market values to calculate the weights when they use

Equation 13.7? Why?

Analysts use market values because this is what the theory underlying the calculation says

they should use. Book values are relevant only if they just happen to equal the market values.

2. What kinds of errors can be made when the WACC for a firm is used as the discount rate

for evaluating all projects in the firm?

Using the WACC to discount cash flows for projects that are less risky than the firm can

result in managers rejecting positive-NPV projects. Using the WACC to discount cash flows

for projects that are more risky than the firm can result in managers accepting negative-NPV

projects.

3. Under what conditions is the WACC the appropriate discount rate for a project?

The WACC is the appropriate discount rate for a project when the project has the same level

of systematic risk as the firm and when the project will be financed with the same proportion

of debt, preferred shares, and common shares that have been used to finance the assets of the

firm.

VI. Self-Study Problems

13.1 The market value of a firm’s assets is $3 billion. If the market value of the firm’s liabilities

is $2 billion, what is the market value of the stockholders’ investment and why?

Solution:

Since the accounting identity that Assets = Liabilities + Equity holds for market values as

well as book values, then we know that the market value of the firm’s equity is $3 billion

—$2 billion, or $1 billion.

13.2 Berron Comics, Inc., has borrowed $100 million and is required to pay investors $8 million

in interest this year. If Berron is in the 35 percent marginal tax bracket, then what is the

after-tax cost of debt (in dollars as well as in annual interest) to Berron.

Solution:

Since Berron enjoys a tax deduction for its interest charges, the after-tax interest expense for

Berron is $8 million × (1 – 0.35) = $5.2 million, which translates into an annual interest

expense of $5.2/$100 = 0.052, or 5.2 percent.

13.3 Explain why the after-tax cost of equity (common or preferred) does not have to be

adjusted by the marginal income tax rate for the firm.

Solution:

The U.S. tax code allows a deduction for interest expense incurred on borrowing.

Preferred and common shares are not considered debt and, thus, do not benefit from an

interest deduction. As a result, there is no distinction between the before-tax and after-tax

cost of equity capital.

13.4 Mike’s T-Shirts, Inc., has debt claims of $400 (market value) and equity claims of $600

(market value). If the cost of debt financing (after tax) is 11 percent and the cost of equity

is 17 percent, then what is Mike’s weighted average cost of capital?

Solution:

Mike’s T-Shirts’ total firm value = $400 + $600 = $1,000. Therefore,

Debt = 40 percent of financing

Equity = 60 percent of financing

WACC = xDebtkDebt(1-t) + xpskps + xcskcs

WACC = (0.4 x 0.11) + (0.6 x 0.17) = 0.146, or 14.6%

13.5 You are analyzing a firm that is financed with 60 percent debt and 40 percent equity. The

current cost of debt financing is 10 percent, but due to a recent downgrade by the rating

agencies, the firm’s cost of debt is expected to increase to 12 percent immediately. How

will this change the firm’s weighted average cost of capital if you ignore taxes?

Solution:

The pretax debt contribution to the cost of capital is xDebt × kDebt, and since the firm’s pretax

cost of debt is expected to increase by 2 percent, we know that the effect on WACC

(pretax) will be 0.6 × 0.02 = 0.012, or 1.2 percent. Incidentally, if we assume that the firm

is subject to the 40 percent marginal tax rate, then the after-tax contribution to the cost of

capital for the firm would be 0.012 × (1 – 0.4) = 0.0072, or 0.72 percent.

VII.Critical Thinking Questions

13.1 Explain why the required rate of return on a firm’s assets must be equal to the weighted

average cost of capital associated with its liabilities and equity.

Solution:

In order to conceptualize the answer to this question, it helps to think of the case in which

the firm has raised all of its capital needs from a single source who owns all of the

liability and all of the equity claims on the firm. Assume that this source has no other

investments. If we were to measure the rate of return on the combined portfolio of

investments for this source, we would find that it is exactly equal to the return on the total

assets of the firm since that is the ultimate source of the returns. Therefore, the weighted

return of that portfolio, which is the weighted average cost of capital for the firm (if for

the time being we abstract away tax effects), is the return on the assets of the firm.

13.2 Which is easier to calculate directly, the expected rate of return on the assets of a firm or

the expected rate of return on the firm’s debt and equity? Assume that you are an outsider

to the firm.

Solution:

As an outsider to the firm, you will not be privy to the complete information about the

projected cash flows of each of the firm’s assets, and so that is a somewhat difficult

proposition. However, the collective market has made an inference concerning the

expected cash flows of each of the financing claims of the firm, and by pricing those cash

flows has given us an expected return for each of those claims. Therefore, finding the

expected return on the debt and equity claims of the firm is much easier than finding the

expected return on the assets of the firm, although that return can then be calculated from

the expected return on the financing claims of the firm.

13.3 With respect to the level of risk and the required return for a firm’s portfolio of projects,

discuss how the market and firm’s management can have inconsistent information and

expectations.

Solution:

Firm management will be fully informed concerning the firm’s project risks, but their

ability to accurately predict the required return for the firm’s projects depends on the

market’s assessment of those project risks. Alternatively, the collective market is not fully

informed (as outsiders) concerning the firm’s project risks and yet uses its incomplete

information set to dictate a required return for the firm’s projects. This suggests that if the

firm were able to better inform the market, and thereby reduce the market’s perceived risk

on the firm’s projects, then the firm might be able to reduce the required rate of return on

the firm’s projects.

13.4 Your friend has recently told you that the federal government effectively subsidizes the

cost of debt (compared to equity use) for corporations. Do you agree with that statement?

Explain.

Solution:

Your friend is correct. Because interest expense on debt is tax deductible, whereas

dividend payments on equity are not, the firm effectively gets a rebate on interest paid

through a lowered tax bill. Two firms with identical EBIT amounts with different interest

expenses will have different cash flow available to its collective set of investors. The firm

with greater interest expense (assuming it is less than the EBIT amount) will have greater

cash flow available to all of its investors.

13.5 Your firm will have a fixed interest expense for the next 10 years. You recently found out

that the marginal income tax rate for the firm will change from 30 percent to 40 percent

next year. Describe how the change will affect the cash flow available to investors.

Solution:

Let’s compare our firm to the firm with no interest expense. In order to make a concrete

example, assume that our firm has interest expense of $100 per year. Since the after-tax

cost of debt for the firm is equal to kdebt × (1 – t), then we can calculate the tax benefit to

using debt to be kdebt × t. In order to calculate that benefit in dollar terms, we would just

multiply (interest expense) × t. Therefore, the current dollar benefit to the interest expense

is $100 × 0.3 = $30. Next year, the dollar benefit is $100 × 0.4 = $40. The net benefit of

interest expense from the increased marginal corporate tax rate is $10, and that is a

positive benefit. Note that the analysis isolates the effect on debt and does not consider

the lower operating earnings figure caused by the increased tax rate. Overall, the increase

in tax rate will result in less cash flows available to investors, but for the leveraged (debt

holding) firm the reduction in cash flow is mitigated by the benefit from being able to

deduct interest expenses.

13.6 Describe why it is not usually appropriate to use the coupon rate on a firm’s bonds to

estimate the pretax cost of debt for the firm.

Solution:

The pretax cost of debt for the firm is the current annual economic cost of borrowing for

the firm (before any tax effects). That cost is better measured by the current yield to

maturity on the firm’s debt than by the coupon rate that is currently paid on that debt.

Since most firms try to issue new bonds very close to par, the coupon rate on a bond is an

indication of the yield to maturity on the bond issue at the time of issue. Unless the

market-determined borrowing rate for the firm is the same as when the bond was issued,

then the current yield to maturity of a bond will not be equal to the current coupon rate on

the bond.

13.7 Maltese Falcone, Inc., has not checked its weighted average cost of capital for four years.

Firm management claims that since Maltese has not had to raise capital for new projects

since that time, they should not have to worry about their current weighted average cost

of capital since they have essentially locked in their cost of capital. Critique that

statement.

Solution:

That is a false statement. Maltese is assuming that since it does not have to raise capital

for new projects, then it has essentially locked in its cost of capital. However, in a liquid

capital market every firm competes for capital everyday since the firm’s investors have

the opportunity to sell their investments to other investors. If a firm does not provide

investors with an ample return, then the investors will sell their investments in the firm,

which, in aggregate, will have the effect of actually raising the cost of capital for the firm

(since the current price of the securities will move down). Therefore, a firm that ignores

its current cost of capital by thinking that it has locked in a cost of capital might even be

raising its cost of capital by making that incorrect assumption.

13.8 Ten years ago, the Edson Water Company issued preferred stock with a price equal to the

par amount of $100. If the dividend yield on that issue was 12 percent, explain why the

firm’s current cost of preferred capital is likely not equal to 12 percent.

Solution:

Since the price of the preferred shares at issue was $100 and the dividend yield was 12

percent, then we know that the annual dividend on the shares is $12. We also then know

that the required rate of return at the time of issue was 12 percent. If during the last 10

years, the required rate of return on Edson preferred shares has changed at all, the current

required rate of return will not be 12 percent. This will, in turn, change the price of the

shares to some amount other than $100.

13.9 Discuss under what circumstances you might be able to use a model that assumes

constant growth in dividends to calculate the current cost of equity capital for a firm.

Solution:

In order to be completely correct, a firm must grow its dividends at a constant rate into

the indefinite future. If one expects the growth in dividends to change in the future, then

using a constant-growth dividend assumption is incorrect and only an estimation.

13.10 Your manager just completed the computation for your firm’s weighted average cost of

capital. He is relieved because he says that he can now use that cost of capital to evaluate

all projects that the firm is considering for the next four years. Evaluate that statement.

Solution:

Your manager is incorrect. A firm is always subject to revisions to its cost of capital due

to current market and firm conditions. In addition, the firm could also be making an error

by using the same cost of capital for all of its future projects. For that particular error to

not be made, two conditions must be met. That is, future projects must be financed with

the same mix of capital (debt, preferred shares, and common shares) with which the entire

firm is currently financed. In addition, the future projects must contain the same level of

systematic risk as that of the average project that the firm is currently operating.

VIII. Questions and Problems

BASIC

13.1 Finance balance sheet: KneeMan Markup Company has total debt obligations with a

book and market value equal to $30 million and $28 million, respectively. It also has total

equity with a book and market value equal to $20 million and $70 million, respectively. If

you were going to buy all of the assets of KneeMan Markup today, how much should you

be willing to pay?

Solution:

The price you should be willing to pay for all of the assets of the firm is the market value

of those assets. Using the market price version of the balance sheet identity, we can add

the market price of the debt obligations and the equity to find the market price of the

assets. That is, $28 million + $70 million = $98 million.

13.2 WACC: What is the weighted average cost of capital?

Solution:

The weighted average cost of capital (WACC) is the weighted average of the costs to the

different sources of capital used to fund a firm, The WACC is often used as an estimate

of the cost of financing a new project given the firm’s current mix of debt and equity.

13.3 Current cost of a bond: You are analyzing the cost of debt for a firm. You know that the

firm’s 14-year maturity, 8.5 percent coupon bonds are selling at a price of $823.48. The

bonds pay interest semiannually. If these bonds are the only debt outstanding for the firm,

what is the after-tax cost of debt for this firm if the firm is in the 30 percent marginal tax

rate?

Solution: The current YTM for the bonds can be calculated as follows.

$823.48 = $42.50 x PVIFA(28, YTM/2) + $1,000 x PVIF(28, YTM/2)

Solving, we find that YTM = 0.11, and therefore the after-tax cost of debt is equal to:

0.11 x (1 – 0.3) = 0.077, or 7.7%

13.4 Taxes and the cost of debt: How are taxes accounted for when we calculate the cost of

debt?

Solution:

When we calculate the cost of debt for a U.S. firm, we must take into account the tax

subsidy given in the United States for interest payments on debt. For every dollar the firm

pays in interest, the firm’s tax bill will decline by ($1 * t), where t is the firm’s marginal

tax rate. We adjust for this tax benefit by multiplying the pretax cost of debt by (1 - t).

This calculation gives us the after-tax cost of debt. We use the after-tax cost of debt for

cost of capital calculations such as when we calculate the WACC.

13.5 Taxes and the cost of debt: ProFarma, Inc., has earnings before interest and taxes equal

to $500. If the firm incurred interest expense of $200 and pays taxes at the 35 percent

marginal tax rate, what amount of cash is available for ProFarma’s investors?

Solution:

EBIT $500

Interest Exp 200

EBT $300

Taxes (35%) 105

Net income $195

Interest expense 200

Cash for investors $395

13.6 Cost of common equity: List and describe each of the three methods used to calculate

the cost of common equity.

Solution:

1) The Capital Asset Pricing Model (CAPM) formula for the cost of common stock,

given in Equation 13.4, can be used to calculate the return investors will demand on

investment in the company’s common stock. See Chapter 7 for further discussion of

the CAPM.

2) The constant-growth dividend model can be used to calculate the cost of equity

implied by the firm’s current stock price. In an efficient market, the current price of

the company’s stock should reflect the cash flows (dividends) that investors will

receive in the future from holding equity in the firm, discounted by an appropriate

rate (the cost of equity). By knowing the current dividend paid by the firm and the

expected growth rate of dividends, we can use Equation 13.5 to compute the cost of

capital that is implied in the firm’s current stock price. The constant-growth dividend

model is only appropriate when there is a reasonable expectation that the firm’s

dividend will continue growing at approximately the same rate forever. For example,

it might be used to calculate the cost of equity for a mature company whose growth

rate is similar to that of the economy.

3) The multistage-growth dividend model is very similar to the constant-growth

dividend model, but the multistage-growth dividend model can be applied in

situations when the growth rate is expected to change—for example, a small, fast

growing company whose growth will certainly slow as the company becomes larger.

See Section 13.3 for discussion of the calculation of cost of equity using the

multistage-growth dividend model.

13.7 Cost of common stock: Whitewall Tire Co. just paid a $1.60 dividend on its common

shares. If Whitewall is expected to increase its annual dividend by 2 percent per year into

the foreseeable future and the current price of Whitewall’s common shares is $11.66, then

what is the cost of common equity for Whitewall?

Solution:

The cost of common equity for Whitewall can be found using the constant-growth

assumption equation:

Solving for kcs, we find it is equal to 0.16 or 16 percent.

13.8 Cost of common stock: Seerex Wok Co. is expected to pay a dividend of $1.10 one year

from today on its common shares. That dividend is expected to increase by 5 percent

every year thereafter. If the price of Seerex is $13.75, then what is Seerex’s cost of

common equity?

Solution:

We can use the formula to find the cost of common equity assuming constant growth.

13.9 Cost of common stock: Two-Stage Rocket’s common stock is expected to pay an annual

dividend equal of $1.25, and it is commonly known that the firm expects dividends paid

to increase by 8 percent for the next two years and by 2 percent thereafter. If the current

price of Two-Stage’s common shares is $17.80, then what is the cost of common equity

capital for the firm?

Solution:

,

Using a spreadsheet to solve for the value of kcs, we find that the cost of common equity

capital is 10 percent.

13.10 Cost of preferred stock: Fjord Luxury Liners has preferred shares outstanding that pay an

annual dividend equal to $15 per year. If the current price of Fjord preferred shares is

$107.14, then what is the after-tax cost of preferred shares for Fjord?

Solution:

Using the equation for finding the cost of preferred equity, we have

13.11 Cost of preferred stock: Kresler Autos has preferred shares outstanding that pay annual

dividends of $12, and the current price of the shares is $80. What is the after-tax cost of

new preferred shares for Kresler if the flotation (issuance) costs for a new issue of

preferred are 5 percent?

Solution:

Kresler will only receive 95 percent of the proceeds, so we know that we can use the

equation to solve for the cost of preferred equity by adjusting the denominator for the

reduced proceeds from the sale of new equity. We then have:

13.12 WACC: Describe the alternatives to using a firm’s WACC as a discount rate when

evaluating a project.

Solution:

There are two major reasons why WACC may not be used to discount new projects:

1. It is not appropriate to use a firm’s WACC to discount a project’s free cash flows if the

systematic risk of the project is very different from the systematic risk of the firm. To

account for this potential problem, some firms estimate discount rates that directly reflect

the risk involved in the project’s cash flows. For example, a risky project might be

assigned a discount rate that is significantly higher then the firm’s WACC.

2). It is not appropriate to use a firm’s WACC when a project that has the same

systematic risk as the firm is not being financed using the same mix of debt and equity as

the firm—for example, if a project will be financed entirely with equity. The project’s

cash flows should be discounted using the cost of equity rather than the firm’s WACC.

These two rates will be the same only if the firm has no debt.

13.13 WACC for a firm: Capital Co. has a capital structure that is financed, based on current

market values, with 50 percent debt, 10 percent preferred shares, and 40 percent common

shares. If the return offered to the investors for each of those sources is 8 percent, 10

percent, and 15 percent for debt, preferred shares, and common shares, respectively, then

what is Capital’s after-tax WACC? Assume that the firm’s marginal tax rate is 40

percent.

Solution:

=

13.14 WACC: What are direct out-of-pocket costs?

Solution:

Direct out-of-pocket costs are the actual out-of-pocket costs that a firm incurs when it

raises capital. They include such things as fees paid to investment bankers and legal and

accounting expenses.

INTERMEDIATE

13.15 Finance balance sheet: Describe why the total value of all of the securities financing the

firm must be equal to the value of the firm.

Solution :

The value of the firm’s assets is equal to the present value of the future cash flows

expected to be generated by those assets. The cash flow claim on those assets is

prioritized by the financing of those assets. Therefore, the financing claims on the assets

of the firm fully account for the entire value of the assets, and the value of the financing

claims must equal the value of the assets that are carved up by those claims.

13.16 Finance balance sheet: Describe why the cost of capital for the firm is equal to the

expected rate of return to the investors of the firm.

Solution:

If we view the firm as a conduit for the cash flows provided by the assets of the firm, then

it is easy to see that the cash flows provided by the assets of the firm must equal the cash

flows provided to the aggregate investor group of the firm. We also know that the capital

invested in the firm must equal the capital invested by the firm. Therefore, we then know

that the rate of return for the investors of the firm must equal the cost of capital provided

to the firm. The expected return to investors will also equal the expected cost of capital

for the firm.

13.17 Current cost of a bond: You know that the after-tax cost of debt capital for Bubbles

Champagne is 7 percent. If the firm has only one issue of five-year maturity bonds

outstanding, what is the current price of the bonds if the coupon rate on those bonds is 10

percent? Assume the bonds make semiannual coupon payments and the marginal tax rate

is 30 percent.

Solution:

We know the after-tax cost of debt, and from that we can find the pretax cost of debt by

multiplying by 1 minus the tax rate. This becomes 0.07 / (1 – .3) = 0.10.

Since the YTM on the bonds is equal to the coupon rate, then we know the bonds are

priced at par, or $1,000.

13.18 Current cost of a bond: Perpetual Ltd. has issued bonds that never require the principal

amount to be repaid to investors. Correspondingly, Perpetual must make interest

payments into the infinite future. If the bondholders receive annual payments of $75 and

the current price of the bonds is $882.35, then what is the after-tax cost of this borrowing

for Perpetual if the firm is in the 40 percent marginal tax rate?

Solution:

Since the bonds represent a perpetuity, we know that the pretax cost of debt can be

solved using the following:

and the after-tax cost is 0.085 × (1 - .4) = 0.051, or 5.1%

13.19 Taxes and the cost of debt: Holding all other things constant but assuming that the

marginal tax rate for a firm decreases, does that provide incentive for the firm to increase

its use of debt or decrease that use?

Solution:

The after-tax cost of debt for the firm is equal kDebt x (1 – t). We can then calculate the tax

benefit to using debt to be kDebt x t. Therefore, the value of the tax benefit to debt increases

with the marginal tax rate. If the marginal tax rate decreases, then the tax benefit to debt

decreases as well. Therefore, the incentive to borrow actually decreases with a decrease in

the marginal tax rate.

13.20 Cost of debt for a firm: You are analyzing the after-tax cost of debt for a firm. You

know that the firm’s 12-year maturity, 9.5 percent coupon bonds are selling at a price of

$1,200. If these bonds are the only debt outstanding for the firm, what is the after-tax cost

of debt for this firm if the marginal tax rate for the firm is 34 percent? What if the bonds

are selling at par?

Solution:

The current YTM for the bonds can be calculated as follows.

$1,200 = $47.50 x PVIFA(24, YTM/2) + $1,000 x PVIF(24, YTM/2)

Solving, we find that YTM = 0.07008 and therefore the after-tax cost of debt is equal to

0.07008 x (1 – .34) = 0.046253, or 4.63%

If the bonds are priced at par, then the YTM on the bonds is 9.5 percent and then the

after-tax cost of debt would be 6.27%

13.21 Cost of common stock: Underestimated Inc.’s common shares currently sell for $36 per

share. The firm believes that its shares should really sell for $54 per share. If the firm just

paid an annual dividend of $2.00 per share and the firm expects those dividends to

increase by 8 percent per year forever (and this is common knowledge to the market),

then what is the current cost of common equity for the firm and what does the firm

believe is a more appropriate cost of common equity for the firm?

Solution:

The current cost of equity for the firm is

But the firm believes that its cost of capital is more appropriately

13.22 Cost of common stock: Write out the general equation for the price of a stock that will

grow dividends very rapidly for four years after our next predicted dividend and

thereafter at a constant, but lower, rate for the foreseeable future. Discuss the problems in

estimating the cost of equity capital for such a stock.

Solution:

It is easy to see that in order to solve for a cost of capital, kcs, you must have a good idea

of what g1 and g2 are. If those growth rates are poor estimates, then the calculation for kcs,

will also be a poor estimate.

13.23 Cost of common stock: You have calculated the cost of common equity using all three

methods described in the chapter. Unfortunately, all three methods have yielded different

answers. Describe which answer (if any) is most appropriate.

Solution:

Two of the methods involve an estimate of the growth rate in dividends for the firm. If

you are confident in your estimate of the growth rate, then those methods might be most

appropriate. Otherwise, utilizing the CAPM, which does not involve any dividend growth

rate estimates, would probably be the best. You may choose to average the results of all

three methods.

13.24 WACC for a firm: A firm financed totally with common equity is evaluating two

distinct projects. The first project has a large amount of nonsystematic risk and a small

amount of systematic risk. The second project has a small amount of nonsystematic risk

and a large amount of systematic risk. Which project, if taken, will have a tendency to

increase the firm’s cost of capital?

Solution:

Markets adjust the cost of capital according to the level of systematic risk in a project.

Therefore, the project with the greatest level of systematic risk will have the greatest

positive impact on the cost of capital for the firm, even if it has the lowest level of

nonsystematic risk.

13.25 WACC for a firm: The Imaginary Products Co. currently has $300 million of market

value debt outstanding. The 9 percent coupon bonds (semiannual pay) have a maturity of

15 years and are currently priced at $1,440.03 per bond. The firm also has an issue of 2

million preferred shares outstanding with a market price of $12.00. The preferred shares

offer an annual dividend of $1.20. Imaginary also has 14 million shares of common stock

outstanding with a price of $20.00 per share. The firm is expected to pay a $2.20 common

dividend one year from today, and that dividend is expected to increase by 5 percent per

year forever. If Imaginary is subject to a 40 percent marginal tax rate, then what is the

firm’s weighted average cost of capital?

Solution:

Step 1: Total amount of debt, common equity, and preferred equity:

Debt = $300,000,000 (given)

Preferred equity = $12 x 2,000,000 = $24,000,000

Common equity = $20 x 14,000,000 = $280,000,000

Total capital = $604,000,000

xDebt = 300/604 = 0.4967

xps = 24/604 = 0.0397

xcs = 280/604 = 0.4636

Step 2: Cost of capital components:

Cost of debt:

$1,440.03 = $45 x PVIFA(30, YTM/2) + $1,000 x PVIF(30, YTM/2)

Solving, we find that YTM = 0.0484 (this is a pretax number).

Cost of preferred equity:

Cost of common equity:

Step 3: Combine using the WACC formula.

=

13.26 Choosing a discount rate: For the Imaginary Products firm in Problem 13.25, calculate

the appropriate cost of capital for a new project that is financed with the same proportion

of debt, preferred shares, and common shares as the firm’s current capital structure. Also

assume that the project has the same degree of systematic risk as the average project that

the firm is currently undertaking (the project is also in the same general industry as the

firm’s current line of business).

Solution:

Since Imaginary will be financing the project with the same mix of capital that the firm is

currently utilizing for its projects, we will have met the first restriction concerning

financing mix. In addition, the new project will have the same degree of systematic risk

(in addition to being in the same general line of business). Therefore, Imaginary can use

the 9.26 percent cost of capital to evaluate its project.

13.27 Choosing a discount rate: If a firm anticipates financing a project with a capital mix

different than the firm’s current capital structure, describe in realistic terms how the firm

is subjecting itself to a calculation error if it chooses to use its historical WACC to

evaluate the project.

Solution:

Since the firm is financing the project with a different capital mix than it has historically

used, we know that the weights and rates for debt, preferred, and common shares in the

WACC formula will be different. We know that the cost of capital for each component is

a function of the individual weights and rates. Therefore, we know that the WACC will

be different for the overall firm versus that of the individual project. Therefore, using its

historical WACC can result in an error in the NPV estimate for the project.

ADVANCED

13.28 You are analyzing the cost of capital for MacroSwift Corporation, which develops

software operating systems for computers. The firm’s dividend growth rate has been a

very constant 3 percent per year for the past 15 years. Competition for the firm’s current

products is expected to develop in the next year, and MacroSwift is currently expanding

its revenue stream into the multimedia industry. Evaluate using a 3 percent growth rate in

dividends for MacroSwift in your cost of capital model.

Solution:

While the growth in dividends has been extremely constant for Macroswift over the last

15 years, it is appropriate to assume a constant-growth rate only if that same rate will

continue in the future. Two factors will act to alter that growth in the future. MacroSwift

will have competition for its current product list in the near future, and that could alter the

firm’s growth rate. In addition, the firm is expanding its product line into an area that will

probably not yield the same level of growth. It is therefore, unlikely that MacroSwift’s

dividend growth rate will continue at a 3 percent annual rate. This suggests that we

should consider something other than constant growth in our modeling.

13.29 You are an external financial analyst evaluating the merits of a stock. Since you are using

a dividend discount model approach to calculate a cost of equity capital, you need to

estimate the dividend growth rate for the firm in the future. Describe how you might go

about that process.

Solution:

One source for this data would be to measure the firm’s dividend growth rate in recent

history. If we could assume that such a growth in dividends will continue into the future,

then our measure would be reasonable. One additional source would be to read a financial

analyst’s report in which the author of the report may have a better estimate of the firm’s

future prospects.

13.30 You know that the return of Momentum Cyclicals’ common shares reacts to

macroeconomic information 1.6 more times than the return of the market. If the risk-free

rate of return is 4 percent and the market risk premium is 6 percent, then what is

Momentum Cyclicals’ cost of common equity capital?

Solution:

We know that the beta for Momentum Cyclicals is 1.6, and we can use the remaining

information in the CAPM as follows:

(AU: Italics ok for everything in above equation? See Summary of Key Equations, p. 455))

13.31 In your analysis of the cost of capital for a common stock, you calculate a cost of capital

using a dividend discount model that is much lower than the calculation for the cost of

capital using the CAPM model. Explain a possible source for the discrepancy.

Solution:

Comparing the two formulas for the two methods, we have:

and

Given these two sources of information, we see that the only variable that we are not able

to get directly from the market is the growth rate in dividends (note that future dividends

are also a function of this growth rate), which is an estimate. Since our dividend discount

method provided a lower cost of capital than the CAPM, it seems likely that we estimated

the growth rate lower than what the aggregate market has assumed. Of course, this

assumes that the market is efficiently pricing the stock. If the market price is incorrect,

then this might lead to a difference.

13.32 RetRyder Hand Trucks has a preferred share issue outstanding that pays an annual

dividend of $1.30 per year. The current cost of preferred equity for RetRyder is 9 percent.

If RetRyder issues additional preferred shares that pay exactly the same dividend and the

investment banker retains 8 percent of the sale price proceeds, what is the cost of new

preferred shares for RetRyder?

Solution:

The current cost of preferred shares for RetRyder is

and then RetRyder would receive 92 percent of the proceeds. We could then adapt the

cost of preferred equity to the following:

13.33 Enigma Corporation’s management believes that the firm’s cost of capital (WACC) is too

high because the firm has been too secretive with the market concerning its operations.

Evaluate that statement.

Solution:

The WACC is a function of the perceived risk involved in the cash flows of the projects

that the firm is currently operating. If the market perceives that risk to be higher than the

actual risk due to a lack of information concerning those projects, then the firm might be

able to lower that perceived risk by sharing more information with the market. That could

have the effect of lowering the firm’s WACC.

13.34 Discuss what valuable information would be lost if you decided to use book values in

order to calculate the cost of each capital component within a firm’s capital structure.

Solution:

Market returns are impounded in market prices. If those prices are ignored, then the

efficiency of the market’s information process is essentially thrown away. Since the

market adjusts securities prices according to the expected return for investing in a

security, then ignoring that information is the same as ignoring what the market deems to

be an appropriate cost of capital for the firm.

CFA Problems

13.35 The cost of equity is equal to the

a. expected market return.

b. rate of return required by stockholders.

c. cost of retained earnings plus dividends.

d. risk the company incurs when financing.

Solution:

B is correct. The cost of equity is defined as the rate of return required by stockholders.

13.36 Dot.Com has determined that it could issue $1,000 face value bonds with an 8 percent

coupon paid semiannually and a five-year maturity at $900 per bond. If Dot.Com’s

marginal tax rate is 38 percent, its after-tax cost of debt is closest to

a. 6.2 percent

b. 6.4 percent.

c. 6.6 percent.

d. 6.8 percent.

Solution:

C is correct.

FV = $1,000; PMT = $40; N = 10; PV = $900

Solve for i. The six-month yield, i, is 5.3149%

YTM = 5.3149% 2 = 10.6298%

rd(1 – t)= 10.6298%( 1 – 0.38) = 6.5905%

13.37 Morgan Insurance Ltd. issued a fixed-rate perpetual preferred stock three years ago and

placed it privately with institutional investors. The stock was issued at $25 per share with

a $1.75 dividend. If the company were to issue preferred stock today, the yield would be

6.5 percent. The stock’s current value is

a. $25.00

b. $26.92

c. $37.31

d. $40.18

Solution:

B is correct. The company can issue preferred stock at 6.5%.

Pp = $1.75/0.065 = $26.92

Note: Dividends are not tax deductible so there is no adjustment for taxes.

13.38 The Gearing Company has an after-tax cost of debt capital of 4 percent, a cost of

preferred stock of 8 percent, a cost of equity capital of 10 percent, and a weighted average

cost of capital of 7 percent. Gearing intends to maintain its current capital structure as it

raises additional capital. In making its capital-budgeting decisions for the average-risk

project, the relevant cost of capital is

a. 4 percent

b. 7 percent

c. 8 percent

d. 10 percent

Solution:

B is correct. The weighted average cost of capital, using weights derived from the current capital

structure, is the best estimate of the cost of capital for the average-risk project of a

company.

13.39 Suppose the cost of capital of the Gadget Company is 10 percent. If Gadget has a capital

structure that is 50 percent debt and 50 percent equity, its before-tax cost of debt is 5

percent, and its marginal tax rate is 20 percent, then its cost of equity capital is closest to

a. 10 percent

b. 12 percent

c. 14 percent

d. 16 percent

Solution:

C is correct.

re = ra + (ra – rd) (D/E)

Note:

If D/(D + E) = 0.50, then D/E = 1.0

re = 0.10 + (0.10 – 0.05)(1.0)(1 – 0.2)

re = 0.10 + [0.05(0.90)] = 0.10 + 0.04 = 0.14, or 14%

Sample Test Problems

13.1 The Balanced, Inc., has three different product lines of business. Its least risky product

line has a beta of 1.7, while its middle risk product line has a beta of 1.8, and its most

risky product line has a beta of 2.1. The market value of the assets invested in each

product line is $1 billion for the least risky line, $3 billion for the middle risk line, and $7

billion for the riskiest product line. What is the beta of The Balanced, Inc.?

Solution:

Using the formula for the beta of an n asset portfolio, we know

.

We have $1 billion + $3 billion + $7 billion = $11 billion, so

x1 = $1 billion / $11 billion = 0.09091

x2 = $3 billion / $11 billion = 0.27273

x1 = $7 billion / $11 billion = 0.63637

Then (0.09091 × 1.7) + (0.27273 × 1.8) + (0.63637 × 2.1) = 1.9818

13.2 Ellwood Corp. has a five-year bond issue outstanding with a coupon rate of 10 percent

and a price of $1,039.56. If the bonds pay coupons semiannually, what is the pretax cost

of the debt and what is the after-tax cost of the debt? Assume the marginal tax rate for the

firm is 40 percent.

Solution:

$1,039.56 = $50 PVIFA (i%/2, 10) + $1,000 PVIFA (i%/2, 10)

Using trial and error, we find that i%/2 = 4.5% ==> i% = 9% which is the pretax cost of

the debt. The after-tax cost of the debt is 9% × (1 - 0.4) = 5.4%.

13.3 Miron’s Copper Corp. expects its growth in common share dividends to be a very steady

1.5 percent per year for the indefinite future. The firm’s shares are currently selling for

$18.45, and the firm just paid a dividend of $3.00 yesterday. What is the cost of common

share equity for this firm?

Solution:

(

13.4 Micah’s Time Portals has a preferred stock issue outstanding that pays an annual

dividend of $2.50 per year and is currently selling for $27.78 a share. What is the cost of

preferred equity for this firm?

Solution:

13.5 The Old Time New Age Co. has a portfolio of projects that has a beta of 1.25. The firm is

currently evaluating a new project that involves a new product in a new competitive

market. Briefly discuss what adjustment Old Time New Age might make to its 1.25 beta

in order to evaluate this new project.

Solution:

As discussed in the chapter, the best method for evaluating the new project would be to

determine the level of systematic risk for the new project. If that is not ascertainable, the

firm might have a predetermined range of modifications for projects that do not have the

same level of systematic risk as the firm’s current portfolio of projects. That is, the firm

would adjust the beta downward, to the greatest extent, for an efficiency-type project,

with a lessened downward adjustment for product extension type project. The firm would

adjust its beta upward for a new market project and the greatest upward adjustment for

new products. The situation for Old Time New Age would dictate a large upward

adjustment. The exact amount of the adjustments would be determined by experienced

management of the firm.