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Transcript of 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.