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Unformatted text preview: © Cora Reed (http://www.fotolia.com/p/3819) Capital
Budgeting and
Business Valuation Capital budgeting and business valuation concern two subjects near and dear to
financial peoples’ hearts: What should we do with the firm’s money and how much
is the company worth? The two subjects are closely related because the decision
about what to do with the firm’s money often affects the value of the firm. Chapter
9, “The Cost of Capital,” begins this section with a discussion of how to estimate
the minimum rate of return that the firm must seek when it makes investments.
Chapter 10, “Capital Budgeting Decision Methods,” explains how to decide if
an investment meets the firm’s requirements and how to rank order competing
investments. Chapter 11, “Estimating Incremental Cash Flows,” goes on to describe
how to estimate the cash inflows and outflows associated with investments. Finally,
Chapter 12, “Business Valuation,” explains how to use the techniques in Chapters
9 through 11 (and those in Chapter 8) to estimate the market value of the firm. 237 CHAPTERS
9 The Cost of Capital
10 Capital Budgeting Decision
Methods
11 Estimating Incremental
Cash Flows
12 Business Valuation The Cost
of Capital
“There’s no such thing as a free lunch.”
—Milton Friedman You Can Almost Always Get Capital If Your
Idea Is Good Enough
This chapter on the cost of capital and the ones that follow on capital
budgeting are all interconnected. What return do the suppliers of capital
to a firm expect? To answer this we must assess the risk these wouldbe
suppliers of capital are facing. What expected return would be sufficient to
compensate for this risk?
The suppliers of equity capital have a greater required rate of return on
their investment than do the suppliers of debt capital because the former are
taking a greater risk. Equity investors are paid after lenders.
If capital is invested in good valueadding projects the suppliers of that
capital can be paid the rate of return they required to part with that capital.
If funds are not already in hand they can be raised. Raising funds will not
be difficult if the wouldbe suppliers of those funds expect to get a return on
their investment that is sufficient to justify the risk of their investment.
If a company has a history of not delivering to its capital suppliers the
returns they needed, considering the risk taken by these investors, then
this company will probably have difficulty in the future raising funds at a
reasonable cost.
Companies with good projects waiting to be financed will find it easier
to raise the funds needed for those projects. The cost of this capital will be
reasonable since wouldbe investors will want to be part of this successful
venture. 238 © Dušan Zidar (www.fotolia.com, eur 1, #113304) Chapter Overview Learning Objectives In capital budgeting decisions, financial managers must analyze many factors
to determine whether a project will add value to a firm, including estimated
incremental cash flows, the timing of those cash flows, risk, and the project’s
required rate of return.
One of the key components of the capital budgeting decision is the cost of
capital. Capital is the term for funds that firms use. Businesses, such as Amcor
Ltd., raise capital from creditors and owners. All capital raised has a cost because
the suppliers of capital demand compensation for the funds provided.
In this chapter we examine the costs of different types of capital. We see how
to estimate the cost of capital from a particular source, as well as the overall cost
of capital for a firm. We also see how estimating a firm’s cost of capital affects a
firm’s financing and investment decisions. The Cost of Capital
To properly evaluate potential investments, firms must know how much their capital
costs. Without a measure of the cost of capital, for example, a firm might invest in a
new project with an expected return of 10 percent, even though the capital used for
the investment costs 15 percent. If a firm’s capital costs 15 percent, then the firm
must seek investments that return at least that much. It is vital, then, that managers
know how much their firm’s capital costs before committing to investments.
Suppliers and users of capital use cost estimates before making short or longterm financial decisions. Investors must determine their required rate of return,
239 After reading this chapter,
you should be able to:
1. Describe the sources of
capital and how firms raise
capital.
2. Estimate the cost of capital
for each financing source.
3. Estimate the weighted
average cost of capital.
4. Use the marginal cost of
capital (MCC) schedule to
make capital budgeting
decisions.
5. Explain the importance
of the marginal cost of
capital (MCC) schedule in
financial decision making. 240 Part III Capital Budgeting and Business Valuation k, to value either a bond or stock before they invest. That required rate of return, k,
for each type of security issued is the cost of capital for that source. Overall, the cost
of capital is the compensation investors demand of firms that use their funds, adjusted
for taxes and transaction costs in certain cases, as we will explain later in this chapter.
In Chapter 10, we will see that firms determine their required rate of return before
deciding whether to accept a capital budgeting project. The discount rate or hurdle rate,
k, is the firm’s cost of capital for that project. Investors supply capital, so they require a
return, and firms use capital, so they must pay suppliers of capital for the use of those funds. Sources of Capital
A firm’s capital is supplied by its creditors and owners. Firms raise capital by borrowing
it (issuing bonds to investors or promissory notes to banks), or by issuing preferred or
common stock. The overall cost of a firm’s capital depends on the return demanded by
each of these suppliers of capital.
To determine a firm’s overall cost of capital, the first step is to determine the cost of
capital from each category of supplier. The cost of capital from a particular source, such
as bondholders or common stockholders, is known as the component cost of capital.
In the following sections, we estimate the cost of debt capital, kd; the cost of capital
raised through a preferred stock issue, kp; and the cost of equity capital supplied by
common stockholders, ks for internal equity and kn for new external equity. The Cost of Debt
When a firm borrows money at a stated rate of interest, determining the cost of debt, kd,
is relatively straightforward. As shown in Figure 91, the lender’s cost of capital is the
required rate of return on either a company’s new bonds or a promissory note. The firm’s
cost of debt when it borrows money by issuing bonds is the interest rate demanded by
the bond investors. When borrowing money from an individual or financial institution,
the interest rate on the loan is the firm’s cost of debt.
When the Financial Crisis hit companies with all but the highest credit ratings
found that they had to pay much higher interest rates to borrow money. Their cost of
debt increased significantly.
The AfterTax Cost of Debt (AT kd) The aftertax cost of debt, AT kd, is the cost to
the company of obtaining debt funds. Because the interest paid on bonds or bank loans
is a taxdeductible expense for a business, a firm’s AT kd is less than the required rate of
return of the suppliers of debt capital. For example, suppose Ellis Industries borrowed
$100,000 for one year at 10 percent interest paid annually. The interest rate on the loan
is 10 percent, so Ellis must pay the lender $10,000 in interest each year the loan is
outstanding (10 percent of $100,000). However, look at what happens when Ellis takes
its taxes for the year into account:
Before Borrowing
Operating Income
Interest Expense $50,000
0 After Borrowing
$50,000
10,000 BeforeTax Income 50,000 40,000 Income Tax (40% rate) 20,000 16,000 Net AfterTax Income 30,000 24,000 Chapter 9 The Cost of Capital 241 Capital Bond
Purchases,
Loans Compensation Firms Interest Figure 91 shows how debt
investors supply capital to and
receive interest from the firm. Lenders The $10,000 interest charge caused a $6,000 decrease in Ellis’s net aftertax income
($30,000 – $24,000 = $6,000). Therefore, assuming a tax rate of 40 percent, the true
cost of the loan is only $6,000 (6 percent), not $10,000 (10 percent).
The following formula converts kd into AT kd, the true aftertax cost of borrowing:
Formula for the AfterTax Cost of Debt
AT kd = kd (1 – T) (91) where: kd = The beforetax cost of debt
T = The firm’s marginal tax rate1
To solve for AT kd in our Ellis Industries example, recall that Ellis’s beforetax cost
of debt is 10 percent and its marginal tax rate is 40 percent. The aftertax cost of debt,
according to Equation 91, follows:
AT kd = .10 (1 – .40)
= .10 × .60
= .06, or 6%
Our calculations show that for Ellis Industries the aftertax cost of debt on a $100,000
loan at a 10 percent rate of interest is 6 percent.
We have seen that the cost of using borrowed money is the interest rate charged by
the lender. In addition, we discussed how the tax deductibility of interest lowers the firm’s
true cost of debt. Next, we turn to the cost of preferred stock and common stock equity. The tax rate used here should reflect the firm’s total combined federal, state, and/or local income tax rate. 1 Figure 91 The Flow of
Debt Capital from Investors
to Firms 242 Part III Capital Budgeting and Business Valuation The Cost of Preferred and Common Stock Funds
When corporations raise capital by issuing preferred or common stock, these investors
expect a return on their investments. If that return is not realized, investors will sell
their stock, driving the stock price down. Although the claim of preferred and common
stockholders may not be contractual, as it is for bondholders, there is a cost nonetheless.
To calculate the cost of using preferred and common stockholders’ money, then, the
firm must estimate the rate of return that these investors demand. Figure 92 shows how
firms raise capital from, and compensate, equity investors.
The Cost of Preferred Stock (kp) The cost of preferred stock (kp) is the rate of return
investors require on a company’s new preferred stock, plus the cost of issuing the stock.
Therefore, to calculate kp, a firm’s managers must estimate the rate of return that preferred
stockholders would demand and add in the cost of the stock issue. Because preferred
stock investors normally buy preferred stock to obtain the stream of constant preferred
stock dividends associated with the preferred stock issue, their return on investment
can normally be measured by dividing the amount of the firm’s expected preferred
stock dividend by the price of the shares. The cost of issuing the new securities, known
as flotation cost, includes investment bankers’ fees and commissions, and attorneys’
fees. These costs must be deducted from the preferred stock price paid by investors to
obtain the net price received by the firm. Equation 92 shows how to estimate the cost
of preferred stock:
Formula for the Cost of Preferred Stock
kp = Dp
(Pp  F) (92) where: kp = The cost of the preferred stock issue; the expected return
Dp = The amount of the expected preferred stock dividend
Pp = The current price of the preferred stock
F = The flotation cost per share
The cost of using the company’s preferred stock is kp. The value of kp, the expected
return from the preferred stock issue, is the minimum return the firm’s managers must
earn when they use the money supplied by preferred stockholders. If they cannot earn
this return, the preferred stockholders will sell their shares, causing the preferred stock’s
price to fall. This means the firm must issue more shares of the stock than before the
stock price fell to raise the same amount of funds.
Suppose Ellis Industries has issued preferred stock that has been paying annual
dividends of $2.50 and is expected to continue to do so indefinitely. The current price
of Ellis’s preferred stock is $22 a share, and the flotation cost is $2 per share. According
to Equation 92, the cost of Ellis’s preferred stock is as follows:
kp = $2.50
($22 $2) = .125, or 12.5% Chapter 9 The Cost of Capital 243 Capital Stock
Purchases Compensation Firms Dividends
Equity Investors We see that Ellis Industries’ cost of new preferred stock, assuming that stock pays
dividends of $2.50 per year and has a market price of $22, is 12.5 percent.
The cost of preferred stock, kp, is higher than the beforetax cost of debt, kd,
because a company’s bondholders and bankers have a prior claim on the earnings of
the firm and on its assets in the event of a liquidation. Preferred stockholders, as a
result, take a greater risk than bondholders or bankers and demand a correspondingly
greater rate of return.
Preferred stock prices tumbled during the financial crisis. This led to an increase
in the cost of preferred stock capital when companies tried to issue such securities to
investors who were looking primarily at safer investments such as U.S. Treasury scurities.
The Cost of Internal Common Equity (ks) The cost of internal common equity
(ks) is the required rate of return on funds supplied by existing common stockholders.
The cost of equity depends on the rate of return the common stockholders demand for
holding the company’s common stock. Calculating ks is more difficult than calculating
kp because common stockholders do not receive a constant stream of dividends. Instead,
investors own the firm, including the corporate earnings left over after other claimants
on the firm have been paid. Neither creditors nor preferred stockholders have a claim on
these residual earnings. Corporations may either retain the residual earnings or return
them in the form of common stock dividends. Retained earnings have a cost, however.
The cost of retained earnings, another name for the cost of internal equity, is the rate
of return that the company must earn to justify retaining the earnings instead of paying
them as dividends. These are internally generated (within the firm) equity funds.
As noted, common stock dividend payments change from year to year or may
not be paid at all. Ultimately, however, dividends are the only payments a corporation
makes to its common stockholders. The corporation may pay regular dividends, or it
may pay a liquidation dividend some time in the future. For companies that pay regular
dividends that grow at a constant rate, the constant dividend growth model may be used Figure 92 The Flow
of Capital from Equity
Investors to Firms
Figure 92 shows how equity
investors supply capital to the
firm and receive dividends
from it. Take Note
There is no tax adjustment
in the cost of preferred
stock calculation. Unlike
interest payments on
debt, firms may not
deduct preferred stock
dividends on their tax
returns. The dividends
are paid out of aftertax
profits. 244 Part III Capital Budgeting and Business Valuation to estimate the cost of equity. For companies that do not pay regular dividends, or when
the market approach to risk is more appropriate, the CAPM may be used to estimate
the cost of equity.
Using the Dividend Growth Model to Estimate ks. The dividend growth model
(sometimes called the Gordon Model after its developer, financial economist Myron
Gordon) uses the time value of money concepts in Chapter 8 to calculate the present
value of a continuing stream of future dividends:
P0 = D1
ks  g where: P0 = The current price of the common stock
D1 = The dollar amount of the common stock dividend expected one period
from now
ks = Required rate of return per period on this common stock investment
g = Expected constant growth rate per period of the company’s common
stock dividends2
Rearranging the terms in the dividend growth model to solve for ks, we rewrite the
formula as follows:
Formula for the Cost of Common Stock Equity (ks)
(Dividend Growth Model Approach)
ks = D1
+g
P0 (93) By making use of Equation 93, we can solve for ks, assuming we know the values
of the terms P0, D1, and g. The term D1/P0 in Equation 93 represents the stock’s dividend
yield, and the g term represents dividend growth rate from year to year.
To apply Equation 93, suppose that Ellis Industries’ common stock is selling for $40
a share. Next year’s common stock dividend is expected to be $4.20, and the dividend
is expected to grow at a rate of 5 percent per year indefinitely. Given these conditions,
Equation 93 tells us that the expected rate of return on Ellis’s common stock is as follows:
ks = $4.20
+ .05
$40 = .105 + .05
= .155, or 15.5% At a stock share price of $40, a dividend of $4.20, and an expected dividend growth
rate of 5 percent, the expected return from Ellis’ common stock is 15.5 percent. The
expected return of 15.5 percent is the minimum return the firm’s managers must earn
This is the constant growth version of the dividend growth model. It assumes that the company’s dividends grow at the same
rate indefinitely. 2 Chapter 9 The Cost of Capital when they use money supplied by common stockholders. If they cannot achieve this
return, common stockholders will sell their shares, causing the stock’s price to fall. This
will make it necessary to sell more shares to raise the desired amount of funds. The
cost of using money supplied by the company’s common stockholders, then, is 15.5
percent. Because dividends paid are not tax deductible to the corporation, there is no
tax adjustment to the ks calculation.
When common stock prices plunged during the financial crisis it took more shares
than before the plunge to raise the same amount of equity capital. This increased the cost
of common stock equity capital. With the economy in a bad recession, few companies
were looking to expand their operations. The higher cost of common equity capital they
faced made them even less interested in raising such capital.
The CAPM Approach to Estimating ks. A firm may pay dividends that grow at a
changing rate; it may pay no dividends at all; or the managers of the firm may believe
that market risk is the relevant risk. In such cases, the firm may choose to use the capital
asset pricing model (CAPM) to calculate the rate of return that investors require for
holding common stock. The CAPM solves for the rate of return that investors demand
for holding a company’s common stock according to the degree of nondiversifiable risk3
present in the stock. The CAPM formula, Equation 94, follows:
CAPM Formula for the Cost of Common Stock Equity (ks)
ks = krf + (km – krf) × β (94) where: ks = The required rate of return from the company’s common stock equity
krf = The riskfree rate of return
km = The expected rate of return on the overall stock market
β = The beta of the company’s common stock, a measure of the amount
of nondiversifiable risk
Suppose Ellis Industries has a beta of 1.39, the riskfree rate as measured by the
rate on shortterm U.S. Treasury bills is 3 percent, and the expected rate of return on the
overall stock market is 12 percent. Given those market conditions, according to Equation
94, the required rate of return for Ellis’s common stock is as follows:
ks = .03 + (.12 – .03) × 1.39
= .03 + (.09 × 1.39)
= .03 + .1251
= .1551, or about 15.5%
According to the CAPM, we see that the cost of using money supplied by Ellis’s
common stockholders is about 15.5 percent, given a company beta of 1.39, a riskfree
rate of 3 percent, and an expected market rate of return of 12 percent. According to the CAPM, common stockholders hold welldiversified portfolios, so the only relevant risk measure is
nondiversifiable (market) risk. 3 245 246 Part III Capital Budgeting and Business Valuation Deciding How to Estimate ks. Should you use the dividend growth model, Equation
93, or the CAPM, Equation 94, to estimate a firm’s cost of common equity? The choice
depends on the firm’s dividend policy, available data, and management’s view of risk.
As a financial manager, if you were confident that your firm’s dividends would grow at a
fairly constant rate in the future, you could apply the dividend growth model to calculate
ks. If your firm’s growth rate were erratic or difficult to determine, you might use the
CAPM instead, assuming that you agreed with the CAPM’s underlying hypothesis that
common stockholders hold welldiversified portfolios and that nondiversifiable risk is
what is priced in the market. When possible, practitioners apply both models and use
their business judgment to reconcile differences between the two outcomes.
The Cost of Equity from New Common Stock (kn) The cost incurred by a company
when new common stock is sold is the cost of equity from new common stock (kn).
In the preceding section, we discussed the cost of using funds supplied by the firm’s
existing stockholders. Capital from existing stockholders is internal equity capital. That
is, the firm already has these funds. In contrast, capital from issuing new stock is external
equity capital. The firm is trying to raise new funds from outside sources.
New stock is sometimes issued to finance a capital budgeting project. The cost of
this capital includes not only stockholders’ expected returns on their investment but also
the flotation costs incurred to issue new securities. Flotation costs make the cost of
using funds supplied by new stockholders slightly higher than using retained earnings
supplied by the existing stockholders.
To estimate the cost of using funds supplied by new stockholders, we use a variation
of the dividend growth model that includes flotation costs:
Formula for the Cost of New Common Stock Equity (kn)
kn = D1
+g
P0  F (95) where: kn = The cost of new common stock equity
P0 = The price of one share of the common stock
D1 = The amount of the common stock dividend expected to be paid
in one year
F = The flotation cost per share
g = The expected constant growth rate of the company’s common stock
dividends
Equation 95 shows mathematically how the cost of new common stock, kn, is greater
than the cost of existing common stock equity, ks. By subtracting flotation costs, F, from
the common stock price in the denominator, the kn term becomes larger.
Let’s look at the cost of new common stock for Ellis Industries. Suppose again
that Ellis Industries’ anticipated dividend next year is $4.20 a share, its growth rate is
5 percent a year, and its existing common stock is selling for $40 a share. New shares
of stock can be sold to the public for the same price, but to do so Ellis must pay its
investment bankers 5 percent of the stock’s selling price, or $2 per share. Given these
conditions, we use Equation 95 to calculate the cost of Ellis Industries’ new common
equity as follows: Chapter 9 kn = The Cost of Capital $4.20
+ .05
$40  $2 = .1105 + .05
= .1605, or 16.05% Because of $2 flotation costs, Ellis Industries keeps only $38 of the $40 per share
paid by investors. As a result, the cost of new common stock is higher than the cost of
existing equity—16.05 percent compared to 15.5 percent.
If the cost of new common equity is higher than the cost of internal common equity,
the cost of preferred stock, and the cost of debt, why use it? Sometimes corporations
have no choice.
Also, if the amount of debt a firm has incurred continues to increase, and internal
equity funds have run out, it may be necessary to issue new common stock to bring the
weight of debt and equity on the balance sheet into line.4
We have examined the sources of capital and the cost of each capital source. Next,
we investigate how to measure the firm’s overall cost of capital. The Weighted Average Cost of Capital (WACC)
To estimate a firm’s overall cost of capital, the firm must first estimate the cost for each
component source of capital. The component sources include the aftertax cost of debt,
AT kd; the cost of preferred stock, kp; the cost of common stock equity, ks; and the cost
of new common stock equity, kn. In the following section, we first discuss all component
sources except kn, which we discuss separately.
To illustrate the first step in estimating a firm’s overall cost of capital, let’s review
Ellis Industries’ component costs of capital. From our previous calculations, we know
the following costs of capital:
AT kd = 6%
kp = 12.5%
ks = 15.5% The next step in finding a firm’s overall cost of capital is assessing the firm’s capital
structure. In practice, the assets of most firms are financed with a mixture of debt,
preferred stock, and common equity. The mixture of capital used to finance a firm’s
assets is called the capital structure of the firm. To analyze the capital structure of a
business, we must find the percentage of each type of capital source.
To illustrate how to assess a firm’s capital structure, assume that Ellis Industries
finances its assets through a mixture of capital sources, as shown on its balance sheet:5
Total Assets $1,000,000 Long and ShortTerm Debt $ 400,000 Preferred Stock
Common Equity
Total Liabilities and Equity 100,000
500,000
$1,000,000 This issue will be discussed in detail in Chapter 13. 4 Ideally, the percentage of each component in the capital structure would be measured on the basis of market values instead of
accounting values. For the sake of simplicity, we use accounting values here, as do many realworld companies. 5 247 248 Part III Capital Budgeting and Business Valuation In percentage terms, then, the mixture of capital used to finance Ellis’s $1 million
worth of assets is as follows:
Debt: 400,000/1,000,000 = .40, or 40%
Preferred Stock: 100,000/1,000,000 = .10, or 10%
Common Equity: 500,000/1,000,000 = .50, or 50% Our calculations show that Ellis Industries’ capital structure consists of 40 percent
debt, 10 percent preferred stock, and 50 percent common equity. If Ellis Industries thinks
that this mixture is optimal and wants to maintain it, then it will finance new capital
budgeting projects with a mixture of 40 percent debt, 10 percent preferred stock, and 50
percent common equity. This mixture might not be used for each and every project. But in
the long run, the firm is likely to seek this capital structure if it is believed to be optimal.
The final step in estimating a firm’s overall cost of capital is to find the weighted
average of the costs of each individual financing source. The weighted average cost of
capital (ka or WACC) is the mean of all component costs of capital, weighted according
to the percentage of each component in the firm’s optimal capital structure. We find the
WACC by multiplying the individual source’s cost of capital times its percentage of
the firm’s capital structure, then adding these results. For Ellis Industries, the weighted
average of the financing sources follows:
(.40 × AT kd) + (.10 × kp) + (.50 × ks) = (.40 × .06) + (.10 × .125) + (.50 × .155)
= .024 + .0125 + .0775
= .114, or 11.4%
Ellis Industries’ weighted average cost of capital is 11.4 percent. The general
formula for any firm’s WACC is shown in Equation 96:
Formula for the Weighted Average Cost of Capital (WACC)
ka = (WTd × AT kd) + (WTp × kp) + (WTs × ks) where: (96) ka = The weighted average cost of capital (WACC)
WTd = The weight, or proportion, of debt used to finance the firm’s assets
AT kd = The aftertax cost of debt
WTp = The weight, or proportion, of preferred stock being used to finance
the firm’s assets
kp = The cost of preferred stock
WTs = The weight, or proportion, of common equity being used to finance
the firm’s assets
ks = The cost of common equity A firm must earn a return equal to the WACC to pay suppliers of capital the return
they expect. In the case of Ellis Industries, for instance, its averagerisk capital budgeting
projects must earn a return of 11.4 percent to pay its capital suppliers the return they expect.
To illustrate how earning the WACC ensures that all capital suppliers will be paid
their required cost of capital, let’s return to our example. Suppose Ellis Industries
undertakes a plant expansion program that costs $1 million and earns an annual return
of 11.4 percent, equal to Ellis’s WACC. Capital for the project is supplied as follows: Chapter 9 The Cost of Capital 249 • 40 percent of the $1 million, or $400,000, is supplied by lenders expecting a return
equal to beforetax kd, 10 percent. • 10 percent of the $1 million, or $100,000, is supplied by preferred investors at a cost
equal to kp, 12.5 percent.6 • 50 percent of the $1 million, or $500,000, is supplied by common stockholders
expecting a return equal to ks, 15.5 percent. If the project does in fact produce the expected 11.4 percent return, will all these
suppliers of capital receive the return they expect? The computations that follow show
how Ellis will pay its capital suppliers:
Firstyear return from the project: $1,000,000 × .114 = $114,000
$400,000 × .10 = $ 40,000 Interest at 10 percent paid to the bondholders:
Less tax savings on interest expense: $40,000 × firm’s tax rate of 40% = $ 16,000 Net interest cost to the firm: $40,000 – $16,000 = $ 24,000 Amount remaining to repay other sources of capital: $114,000 – $24,000 = $ 90,000 Preferred dividend paid to preferred stockholders: 5,000 shares × $2.50 = $ 12,500 Amount remaining for common stockholders: $90,000 – $12,500 = $ 77,500 Summar y:
Return realized by lenders $40,000/$400,000 = .10 or 10% Return realized by preferred stock investors $12,500/$100,000 = .125 or 12.5%7 Return realized by common stockholders $77,500/$500,000 = .155 or 15.5% We see that Ellis was able to pay all its capital suppliers by earning an overall return
of 11.4 percent, its WACC.
In the long run, companies generally try to maintain an optimal mixture of capital
from different sources. In the short run, however, one project may be financed entirely
from one source. Even if a particular project is financed entirely from one source, the
WACC should still be used as the required rate of return for an averagerisk project.
Say, for instance, such a project is entirely financed with debt, a relatively cheap source
of capital. The cost of debt should not be used as that project’s cost of capital. Why?
Because the firm’s risk would increase with the increase in debt, and the costs of all
sources of capital would increase. The Marginal Cost of Capital (MCC)
A firm’s weighted average cost of capital will change if one component cost of capital
changes. Often, a change in WACC occurs when a firm raises a large amount of capital.
For example, lenders may increase the interest rate they charge, kd, if they think the
firm’s debt load will be too heavy after new funds are borrowed. Or a firm’s cost of
equity may increase when new stock is issued after new retained earnings run out. This
is because of the flotation costs incurred when new stock is issued.
In this example, the firm sold 5,000 shares of preferred stock at $22 a share for a total of $110,000; $2 a share, or $10,000,
went to the investment bankers and attorneys in the form of flotation costs, leaving $100,000 for the capital budget. 6 To be precise, 12.5 percent is the return to the preferred stockholders plus the investment bankers’ and attorneys’ fees for
issuing the stock ($2). The net return realized by the preferred stock investors is the preferred dividend they receive ($2.50)
divided by the price they paid for the stock ($22), which is 11.36 percent. 7 Interactive Module
Go to www.textbookmedia.
com and find the free
companion material for this
book. Follow the instructions
there. Note how the cost of
a particular source of capital
depends on the risk being
taken by the supplier of
that capital. 250 Part III Capital Budgeting and Business Valuation Firms, then, must consider how increasing component costs of capital affect the
WACC. The weighted average cost of the next dollar of capital to be raised is the
marginal cost of capital (MCC). To find the MCC, financial managers must (1) assess
at what point a firm’s cost of debt or equity will change the firm’s WACC, (2) estimate
how much the change will be, and (3) calculate the cost of capital up to and after the
points of change. The Firm’s MCC Schedule
The marginal cost of the first dollar of capital a firm raises is the same as the firm’s
basic WACC. However, as the firm raises more capital, a point is reached at which the
marginal cost of capital changes. Why? Because one of the component sources of capital
changes. This point is the break point in the firm’s MCC schedule. Capital above the
break point can only be raised at a higher cost.
Finding the Break Points in the MCC Schedule To find break points in the MCC
schedule, financial managers determine what limits, if any, there are on the firm’s ability
to raise funds from a given source at a given cost. Break points in the MCC Schedule
consist of one or more debt break points and an equity break point.
Debt Break Points Suppose that Ellis Industries’ financial managers, after consulting
with bankers, determined that the firm can borrow up to $300,000 at an interest rate of
10 percent, but any money borrowed above that amount will cost 12 percent. To calculate
Ellis Industries’ aftertax cost of debt, assume the firm’s tax rate is 40 percent. We apply
Equation 91 as follows:
AT kd = kd (1 – T)
= .10 × (1 – .40)
= .06, or 6% We see that at an interest rate of 10 percent and a tax rate of 40 percent, Ellis’s
aftertax cost of debt is 6 percent. However, if Ellis Industries borrows more than
$300,000, then its interest rate increases to 12 percent. At a tax rate of 40 percent
and an interest rate of 12 percent, the firm’s aftertax kd for amounts borrowed over
$300,000 is
AT kd (for over $300,000 borrowed) = .12 (1 – .40)
= .072, or 7.2%
Because Ellis’s AT kd increases when it borrows more than $300,000, its MCC will
also increase when it borrows more than $300,000. (We’ll see how much it increases
in the next section.) The financial managers at Ellis Industries want to know how much
total capital they can raise before the debt portion reaches $300,000, causing an increase
in the AT kd and the MCC. Chapter 9 The Cost of Capital 251 Ellis Industries
Capital Structure 50% of total capital
is common stock Total Capital Raised Up
to Debt Break Point =
$750,000 10% of total capital
is preferred stock 40% of total capital
is debt Debt = $300,000 Figure 93 Ellis
Industries Debt Break Point
Figure 93 shows how Ellis
Industries can raise up to
$750,000 of total capital
before the $300,000 of
lowercost debt is exhausted. Ellis Industries’ marginal cost of capital break point is not $300,000 because the
firm’s capital structure is 40 percent debt, 10 percent preferred stock, and 50 percent
common stock. At $300,000, then, only 40 percent of that capital is debt. Instead, the
financial managers of Ellis Industries must figure out at what point the firm will use
$300,000 of debt capital.
To find a firm’s marginal cost of capital break point, we use Equation 97:
Formula for the Marginal Cost of Capital (MCC) Break Point
BP = where: Limit
Proportion of Total (97) BP = The capital budget size at which the MCC changes
(break point)
Limit = The point at which the cost of the source of capital
changes Proportion of Total = The percentage of this source of capital in the firm’s
capital structure 252 Part III Capital Budgeting and Business Valuation In our Ellis Industries example, we know that the firm has a $300,000 debt limit
before its aftertax cost of debt will increase and that debt is 40 percent of the firm’s
capital structure. Applying Equation 97 to our Ellis example, we see that its debt break
point is the following:
BPd = $300, 000
.40 = $750, 000 We find that Ellis Industries’ break point is $750,000. By applying Equation 97,
Ellis’s financial managers know that they may raise up to $750,000 in capital before
their borrowing costs will rise from 6 percent to 7.2 percent. Any capital raised over
$750,000 will reflect the higher cost of borrowing, as shown in Figure 93.
Notice we used subscript d with BP in Equation 97. That was to identify the break
point as a debt break point. There could be other debt break points for Ellis Industries.
If, for instance, the company’s lenders set additional limits on the company’s borrowing,
the debt break points would be denoted as BPd1, BPd2, and so on. For our example,
let’s assume that Ellis’s bankers will lend the firm an unlimited amount of money over
$300,000 at 7.2 percent, so there are no further debt break points.
The Equity Break Point The equity break point is the point at which the MCC changes
because the cost of equity changes. Equity costs may change because firms exhaust the
supply of funds from the firm’s existing common stockholders—that is, they exhaust
additions to retained earnings. After firms exhaust their supply of internal equity, which
has a capital cost of ks, they will have to raise additional equity funds by issuing new
stock, which has a higher cost, kn. This additional equity is external equity capital. The
MCC increases accordingly.
Let’s illustrate how the MCC increases because of changes in the cost of equity.
We’ll assume that Ellis Industries expects to realize $600,000 in income this year after
it pays preferred stockholders their dividends. The $600,000 in earnings belong to the
common stockholders. The firm may either pay dividends or retain the earnings. Let’s
assume Ellis retains the $600,000. The finite supply of capital from the existing common
stockholders is the $600,000 addition to retained earnings. To find the equity break point,
then, Ellis’s managers must know at what point the firm will exhaust the common equity
capital of $600,000, assuming existing common stock equity is 50 percent of the firm’s
capital budget. Figure 94 graphically depicts the Ellis equity break point analysis.
To find the equity break point, we apply Equation 97, the MCC break point formula.
We know that the existing common stock capital limit is $600,000 and that common
equity finances 50 percent of the total capital budget. Using Equation 97, we solve for
the equity break point, BPe, as follows:
BPe = $600, 000
.50 = $1,200, 000 Our calculations show that the Ellis equity break point is $1,200,000. If the capital
budget exceeds $1,200,000, the portion financed with common equity will exceed
$600,000. At that point, Ellis will need to issue new common stock to raise the additional Chapter 9 253 The Cost of Capital Ellis Industries
Capital Structure 50% of total capital
is common stock Common Stock =
$6000,000 Total Capital Raised Up
to Equity Break Point =
$1,200,000
10% of total capital
is preferred stock Figure 94 40% of total capital
is debt Ellis Industries Equity
Break point
Figure 94 shows how Ellis
Industries can raise up to
$1,200,000 of total capital
before the $600,000 of lowercost internal equity is exhausted. capital. The new common stock’s cost, kn, will be greater than the cost of internal
common equity, ks, so the MCC will rise when the capital budget exceeds $1,200,000,
as shown in Figure 94.
Calculating the Amount the MCC Changes To calculate MCC changes, we must
first identify the break points. In our Ellis Industries example, we identified two break
points at which the firm’s MCC will change:
Debt Break Point, BPd = $750,000
Equity Break Point, BPe = $1,200,000
The next step in the MCC analysis is to estimate how much the change in the MCC
will be for varying amounts of funds raised.
The MCC Up to the First Break Point Because the MCC is simply the weighted
average cost of the next dollar of capital to be raised, we can use the WACC formula,
Equation 96, to calculate the MCC as well. 254 Part III Capital Budgeting and Business Valuation We assume that Ellis Industries wants to maintain its current capital structure of 40
percent debt, 10 percent preferred stock, and 50 percent common equity. We assume
further that its aftertax cost of debt, AT kd, is 6 percent; its cost of preferred stock, kp,
is 12.5 percent; and its cost of internal common equity, ks, is 15.5 percent. With these
values, we use Equation 96 to find the Ellis MCC for capital raised up to the first break
point, BPd, as follows:
MCC up to BPd ($750,000) = (.40 × AT kd) + (.10 × kp) + ( .50 × ks)
= (.40 × .06) + (.10 × .125) + ( .50 × .155)
= .024 + .0125 + .0775
= .114, or 11.4%
We see from our calculations that up to the first break point, the Ellis MCC is 11.4
percent—the WACC we calculated earlier. We know, however, that the Ellis lenders will
raise the interest rate to 12 percent if the firm raises more than $750,000, at which point
the AT kd increases from 6 percent to 7.2 percent. So between the first break point, BPd,
and the second break point, BPe, the MCC is
MCC between BPd ($750,000)
and BPe ($1,200,000) = (.40 × AT kd) + (.10 × kp) + ( .50 × ks)
= (.40 × .072) + (.10 × .125) + ( .50 × .155)
= .0288 + .0125 + .0775
= .1188, or 11.88%
Our calculations show that the MCC between the first and second break points, $750,000
and $1,200,000, is 11.88 percent.
At the second break point, BPe, we know from our earlier Ellis discussion that ks
of 15.5 percent changes to kn, which has a value of 16.05 percent. Applying Equation
96, the MCC for amounts raised over $1,200,000 follows:
MCC over BPe ($1,200,000) = (.40 × AT kd) + (.10 × kp) + ( .50 × ks)
= (.40 × .072) + (.10 × .125) + ( .50 × .1605)
= .0288 + .0125 + .08025
= .1216, or 12.16%
We find that the Ellis MCC with a capital budget exceeding $1,200,000 is 12.16
percent. A graph of Ellis Industries’ marginal cost of capital is shown in Figure 95.
Now that we have learned to estimate the MCC for a firm, we examine how MCC
estimates affect capital budgeting decisions. The MCC Schedule and Capital Budgeting Decisions
Firms use the MCC schedule to identify which new capital budgeting projects should be
selected for further consideration and which should be rejected. For example, assume
that Ellis Industries has identified the following projects for possible adoption: Chapter 9 The Cost of Capital 255 20%
19%
18%
17%
Cost of Capital 16%
15%
14%
13%
12% 11.4% 12.16% 11.88% 11% Figure 95 Ellis
Industries Marginal Cost
of Capital Schedule 10%
9%
8%
$0 $500,000 $1,000,000 $1,500,000 $2,000,000 Capital Budget Size Project Initial
Investment
Required Project’s
Expected
Rate of Return A $500,000 18.00% B $300,000 14.00% C $200,000 12.05% D $300,000 11.50% E $700,000 9.00% The projects are ranked from highest to lowest expected rate of return. The list
of proposed capital budgeting projects ranked by expected rate of return is the firm’s
investment opportunity schedule (IOS). To determine which proposed projects should
be accepted, the Ellis financial managers determine which projects have expected rates
of return that exceed their respective costs of capital. To compare the projects’ expected
rates of return to the firm’s cost of capital, the financial managers plot the IOS on the
same graph as the MCC. Figure 96 shows this technique.
The projects with the highest expected rates of return are plotted first. The Ellis
financial managers should start with Project A, which has an expected rate of return of
18 percent. That project requires a capital investment of $500,000. Next, they should add
Project B, a project with an expected rate of return of 14 percent and an investment of
$300,000. The total capital budget with Projects A and B is $800,000. Then Project C,
with an expected rate of return of 12.05 percent, should be added. Project C’s investment
requirement of $200,000 increases the capital budget to $1,000,000. Figure 95 shows the marginal
cost of capital (MCC) schedule
that reflects the cost of debt and
cost of equity break points. 256 Part III Capital Budgeting and Business Valuation 20%
IOS Schedule 19%
18% MCC Schedule Project A return = 18% 17%
Cost of Capital 16%
15%
Project B return = 14% 14%
13%
12% MCC = 11.4% 11% Figure 96 Ellis
Industries MCC and IOS
Schedules
Figure 96 shows the MCC and
IOS schedules. Those projects
on the IOS schedule above the
MCC schedule are accepted. Project C return
= 12.05% MCC Schedule 10% MCC = 11.88% 9% MCC = 12.16%
Project D return
= 11.5% Project E return = 9% 8%
$0 $500,000 $1,000,000 $1,500,000 $2,000,000 Capital Budget Size The addition of Project D, a project with an expected rate of return of 11.5 percent
and investment of $300,000, results in a capital budget of $1,300,000. Notice, however,
that Project D’s expected rate of return is less than the marginal cost of capital at the
point at which it is added. If Project D were adopted, Figure 96 shows that it would
have to be financed with capital that costs 11.88 percent, even though the project’s
expected rate of return is only 11.5 percent. The Ellis financial managers, then, should
reject Project D. Project E has a lower expected rate of return of 9 percent and requires a
capital investment of $700,000. Project E is also rejected. Combining the IOS and MCC
schedules is an effective tool to see whether a firm should accept or reject a project. The Optimal Capital Budget
When we integrate the IOS and the MCC schedules, as shown in Figure 96, we see that
Ellis Industries’ optimal capital budget is $1 million, consisting of Projects A, B, and C.
The optimal capital budget is the list of all accepted projects and the total amount of
initial cash outlays for these projects. All projects on the IOS schedule that are above
the MCC schedule are accepted; the rest are rejected.
Table 91 summarizes the seven steps to calculate the optimal capital budget.
The Importance of MCC to Capital Budgeting Decisions
Analyzing the combined IOS and MCC schedules allows financial managers to examine
many projects at once, rather than each project in isolation. This way they choose the
best projects.
To demonstrate how important the MCC schedule is to capital budgeting decisions, look
at Figure 96 again. Notice that Project D is rejected because it is below the MCC line. The Chapter 9 The Cost of Capital Table 91 Determining the Optimal Capital Budget
STEPS ACTIONS Step 1 Calculate the costs of the firm’s sources of capital, AT kd, kp, ks, and kn.
Record any borrowing limits and the resulting changes in AT kd with
those limits. Step 2 Calculate the break points in the capital budget size at which the MCC
will change. There will always be an equity break point, BPe, and there
may be one or more debt break points, BPd1, BPd2, and so on. Step 3 Calculate the MCC up to, between, and above all the break points. The
MCC increases at each break point. Record the MCC values before and
after each break point. Step 4 Plot the MCC values on a graph with the capital budget size on the X
axis and cost of capital/IRR on the Y axis. Step 5 Identify the firm’s potential investment projects. Record each investment
project’s initial investment requirement and expected rate of return. Make
an investment opportunity schedule (IOS) by lining up the projects from
highest return to lowest. Step 6 Plot the IOS on the same graph with the MCC. Step 7 Note the point where the IOS and MCC schedules cross. Projects on the
IOS line above the MCC line should be accepted, and those below the
MCC line rejected. graph shows us that if Project D is accepted, it will have to be financed in part with capital
costing 11.88 percent and in part with capital costing 12.16 percent. Because Project D’s
expected rate of return is only 11.5 percent, it’s a poor investment. However, this statement is
only true because Projects A, B, and C were already considered before Project D. Together,
Projects A, B, and C require $1 million of capital investment. Given that $1 million has
already been spent for Projects A, B, and C, the $300,000 required for Project D can only
be raised at costs of 11.88 percent (the first $200,000) and 12.16 percent (the last $100,000).
If Project D were considered by itself, as if it were Ellis Industries’ only capital
budgeting project, then the $300,000 investment the project requires could have been
raised at the company’s initial WACC of 11.4 percent. Because the project’s expected
rate of return of 11.5 percent exceeds that WACC rate by .1 percent, the project looks
like a good investment. But because its expected rate of return was lower than those of
Projects A, B, and C, Project D is not a good investment, given the changes in Ellis’s
cost of capital due to the MCC break points.
This example illustrates the importance of using a firm’s MCC, not the firm’s initial
WACC, to evaluate investments. If all investment projects are treated in isolation and
evaluated using the firm’s initial WACC, then some of them may be overvalued. The
discrepancy will become apparent when the firm tries to raise the entire amount of
capital to support the complete capital budget and finds that the cost of the last dollar
raised exceeds the expected rate of return of the last project adopted. 257 258 Part III Capital Budgeting and Business Valuation What’s Next
In this chapter we learned how to calculate a firm’s individual component costs of capital
and how to calculate its WACC and its MCC. In Chapter 10, we discuss the decision
techniques that firms use to select projects. Summary
1. Describe the sources of capital and how firms raise capital.
Firms raise debt capital from lenders or bondholders. They also raise funds from preferred
stockholders, from current stockholders, and from investors who buy newly issued shares
of common stock. All suppliers of capital expect a rate of return proportionate to the risk
they take. To ensure a supply of capital to meet their capital budgeting needs, firms must
pay that return to capital suppliers. To compensate creditors, firms must pay the interest
and principal on loans. For bondholders, firms must pay the market required interest rate.
For preferred stockholders, the dividend payments serve as compensation. To compensate
common stock investors, firms pay dividends or reinvest the stockholders’ earnings.
2. Estimate the cost of capital for each financing source.
To find a firm’s overall cost of capital, a firm must first estimate how much each source
of capital costs. The aftertax cost of debt, AT kd, is the market’s required rate of return
on the firm’s debt, adjusted for the tax savings realized when interest payments are
deducted from taxable income. The beforetax cost of debt, kd, is multiplied by one
minus the tax rate (1 – T) to arrive at the firm’s aftertax cost of debt.
The cost of preferred stock, kp, is the investor’s required rate of return on that security.
The cost of common stock equity, ks, is the opportunity cost of new retained earnings,
the required rate of return on the firm’s common stock. The cost of new common stock,
kn (external equity), is the required rate of return on the firm’s common stock, adjusted
for the flotation costs incurred when new common stock is sold in the market.
3. Estimate the weighted average cost of capital.
The weighted average cost of capital, ka or WACC, is the overall average cost of
funds considering each of the component capital costs and the weight of each of those
components in the firm’s capital structure. To estimate WACC, we multiply the individual
source’s cost of capital times its percentage of the firm’s capital structure and then add
the results.
4. Use the MCC schedule to make capital budgeting decisions.
A firm’s WACC changes as the cost of debt or equity increases as more capital is raised.
Financial managers calculate the break points in the capital budget size at which the
MCC will change. There will always be an equity break point, BPe, and there may be
one or more debt break points, BPd1, BPd2, and so on. Financial managers then calculate
the MCC up to, between, and above all the break points and plot the MCC values on a
graph showing how the cost of capital changes as capital budget size changes.
Financial managers create an IOS by ranking all potential capital budgeting projects
from the highest internal rate of return to the lowest and then plotting the IOS on the
same graph with the MCC. To increase the value of the firm, projects on the IOS line
above the MCC line should be accepted and those below the MCC line rejected. Chapter 9 The Cost of Capital 5. Explain the importance of the MCC schedule in financial decision making.
The MCC schedule forces financial managers to match a project’s rate of return with the
cost of funds for that specific project. This marginal analysis prevents financial managers
from estimating a project’s value incorrectly because of faulty cost of capital estimates
that fail to consider how a larger capital budget increases capital costs. Equations Introduced in This Chapter
Equation 91. Formula for the AfterTax Cost of Debt (AT kd):
AT kd = kd (1 – T) where: kd = The beforetax cost of debt
T = The firm’s marginal tax rate
Equation 92. Formula for the Cost of Preferred Stock (kp):
kp = Dp
(Pp  F) where: kp = The cost of the preferred stock issue; the expected return
Dp = The amount of the expected preferred stock dividend
Pp = The current price of the preferred stock
F = The flotation cost per share
Equation 93. Formula for the Cost of Common Stock Equity (ks)
(Dividend Growth Model Approach):
ks = D1
+g
P0 where: P0 = The current price of the common stock
D1 = The amount of the common stock dividend expected one period
from now
g = The expected constant growth rate of the company’s common stock
dividends
Equation 94. CAPM Formula for the Cost of Common Equity (ks):
ks = krf + (km – krf) × β where:ks = The required rate of return from the company’s common stock equity
krf = The riskfree rate of return
km = The expected rate of return on the overall stock market
β = The beta of the company’s common stock, a measure of the amount
of nondiversifiable risk 259 260 Part III Capital Budgeting and Business Valuation Equation 95. Formula for the Cost of New Common Equity (kn):
kn = D1
+g
P0 − F where: kn = The cost of new common stock equity
P0 = The price of one share of the common stock
D1 = The amount of the common stock dividend expected to be paid in
one year
F = The flotation cost per share
g = The expected constant growth rate of the company’s common stock
dividends
Equation 96. Formula for the Weighted Average Cost of Capital (WACC):
ka = (WTd × AT kd) + (WTp × kp) + (WTs × ks) where: ka = The weighted average cost of capital (WACC)
WTd = The weight, or proportion, of debt used to finance the firm’s assets
AT kd = The aftertax cost of debt
WTp = The weight, or proportion, of preferred stock being used to finance
the firm’s assets
kp = The cost of preferred stock
WTs = The weight, or proportion, of common equity being used to finance
the firm’s assets
ks = The cost of common equity
Equation 97. Formula for the Marginal Cost of Capital (MCC) Break Point:
BP = Limit
Proportion of Total where: BP = The capital budget size at which the MCC changes (break point)
Limit = The point at which the cost of the source of capital changes
Proportion
of Total = The percentage of this source of capital in the firm’s capital
structure Chapter 9 The Cost of Capital 261 SelfTest
ST1. Jules’ Security Company can issue new bonds
with a market interest rate of 14 percent. Jules’
marginal tax rate is 32 percent. Compute the
aftertax cost of debt, AT kd, for this company. ST2. Mr. White’s company, The Problem Solvers,
wants to issue new preferred stock. The
preferred dividend is $3.00 per share, the stock
can be sold for $30, and the flotation costs are
$1. What is the cost of preferred stock, kp? ST3. Vincent’s Dance Studio, Inc., has a beta of 1.9.
The riskfree rate of interest is 4 percent. The
market portfolio has an expected rate of return
of 10 percent. What is the cost of internal
equity, ks, for this company using the CAPM
approach? ST4. Marsalis’s Entertainment Corporation has an
aftertax cost of debt of 8 percent, a cost of
preferred stock of 12 percent, and a cost of
equity of 16 percent. What is the WACC, ka,
for this company? The capital structure of
Marsalis’s company contains 20 percent debt,
10 percent preferred stock, and 70 percent
equity. ST5. Quinten’s Movie Company has been told by
its investment banking firm that it could issue
up to $8 million in bonds at an aftertax cost
of debt of 10 percent. But after that, additional
bonds would have a 12 percent aftertax cost.
Quinten’s company uses 40 percent debt
and 60 percent equity for major projects.
How much money could this company raise,
maintaining its preferred capital structure,
before the aftertax cost of debt would jump to
12 percent? Review Questions
1. Which is lower for a given company: the cost of
debt or the cost of equity? Explain. Ignore taxes in
your answer. 5. If dividends paid to common stockholders are not
legal obligations of a corporation, is the cost of
equity zero? Explain your answer. 2. When a company issues new securities, how do
flotation costs affect the cost of raising that capital? 6. What is the investment opportunity schedule (IOS)?
How does it help financial managers make business
decisions? 3. What does the “weight” refer to in the weighted
average cost of capital?
4. How do tax considerations affect the cost of debt
and the cost of equity? 7. What is a marginal cost of capital (MCC) schedule?
Is the schedule always a horizontal line? Explain.
8. For a given IOS and MCC, how do financial
managers decide which proposed capital budgeting
projects to accept and which to reject? 262 Part III Capital Budgeting and Business Valuation Build Your Communication Skills
CS1. Prepare a brief paper in which you explain to
the CEO of a fictional company why the cost of
equity is greater than either the cost of debt or
the cost of preferred stock. Be sure to explain
why equity funds have a cost even though those
costs are not reflected on the income statement.
Finally, discuss why it is important for a firm to
know its cost of capital. CS2. Write a short report that analyzes the role of
the MCC schedule in making capital budgeting
decisions. In your report, explain how the IOS
affects this decisionmaking process. Be sure
to explain your rationale for choosing some
proposed projects while rejecting others. Problems
Cost of Debt 91. a. What would be the aftertax cost of debt for a company with the following
yields to maturity for its new bonds, if the applicable tax rate were
40 percent?
(i) YTM = 7%
(ii) YTM = 11%
(iii) YTM = 13%
b. How would the cost of debt change if the applicable tax rate were
34 percent? Cost of Debt 92. Calculate the aftertax cost of debt for loans with the following effective
annual interest rates and corporate tax rates.
a. Interest rate, 10%; tax rate, 0%.
b. Interest rate, 10%; tax rate, 22%.
c. Interest rate, 10%; tax rate, 34%. Cost of Debt 93. What would be the cost of debt for the following companies given their
yields to maturity (YTM) for new bonds and the applicable corporate tax
rates?
Company 8% 34% B 11% 40% C 94 . Tax Rate A Cost of Debt YTM 14% 30% Mary Lynn Eatenton is the chief financial officer of Magnolia Steel, Inc. She
has asked Trudy Jones, one of the financial analysts, to calculate the aftertax
cost of debt based on different bond yield to maturity rates. Magnolia Steel’s
current tax rate is 34 percent, but increasing sales and profits will put them
in the 40 percent tax bracket by the end of the year. Calculate the aftertax
costofdebt figures that will be shown in Ms. Jones’s report at each tax rate
for the following YTM rates.
a. Yield to maturity, 8%.
b. Yield to maturity, 14%.
c. Yield to maturity, 16%. Chapter 9 263 The Cost of Capital 95. A firm is issuing new bonds that pay 8 percent annual interest. The market
required annual rate of return on these bonds is 13 percent. The firm has a
tax rate of 40 percent.
a. What is the beforetax cost of debt?
b. What is the aftertax cost of debt? Cost of Debt 96. A company’s creditors charge 9.5 percent annual interest on loans to the
company. The company’s combined federal and state tax rate is 35 percent.
What is the company’s aftertax cost of debt? AfterTax Cost
of Debt 97. A company can sell preferred stock for $26 per share, and each share of
stock is expected to pay a dividend of $2. If the flotation cost per share of
stock is $0.75, what would be the estimate of the cost of capital from this
source? Cost of
Preferred Stock 98. Leo Bloom, the treasurer of a manufacturing company, thinks that debt
(YTM = 11%, tax rate = 40%) will be a cheaper option for acquiring funds
compared to issuing new preferred stock. The company can sell preferred
stock at $61 per share and pay a yearly preferred dividend of $8 per share.
The cost of issuing preferred stock is $1 per share. Is Leo correct? 99. OneEyed Jacks Corporation needs money to fund a new production line of
playing cards. Rio Longworth, manager of the finance department, suggests
they sell preferred stock for $50 per share. They expect to pay $6 per share
annual dividends. What is the estimate of the cost of preferred stock if the
flotation cost is $2.25 per share? Cost of
Preferred Stock 910. El Norte Industries will issue $100 par, 12 percent preferred stock. The
market price for the stock is expected to be $89 per share. El Norte must pay
flotation costs of 5 percent of the market price. What is El Norte’s cost of
preferred stock? Cost of
Preferred Stock 911. A company’s investment bankers say that a proposed new issue of 7.5
percent cumulative preferred stock with a par value of $10 a share can be
sold to the public for $27 a share. The transaction costs will be $1 a share.
What is the company’s cost of preferred stock financing? Cost of Preferred
Stock Financing 912. Twister Corporation is expected to pay a dividend of $7 per share one year
from now on its common stock, which has a current market price of $143.
Twister’s dividends are expected to grow at 13 percent.
a. Calculate the cost of the company’s retained earnings.
b. If the flotation cost per share of new common stock is $4, calculate the
cost of issuing new common stock. Cost of Equity 913. Amy Jolly is the treasurer of her company. She expects the company will
grow at 4 percent in the future, and debt securities (YTM = 14%, tax rate =
30%) will always be a cheaper option to finance the growth. The current
market price per share of its common stock is $39, and the expected dividend
in one year is $1.50 per share. Calculate the cost of the company’s retained
earnings and check if Amy’s assumption is correct. Cost of Retained
Earnings Cost of Debt and
Preferred Stock 264 Part III Capital Budgeting and Business Valuation Cost of Equity
CAPM Approach 914. Free Willy, Inc., (Nasdaq: FWIC) has a beta of 1.4. If the rate on U.S.
Treasury bills is 4.5 percent and the expected rate of return on the stock
market is 12 percent, what is Free Willy’s cost of common equity financing? Challenge Problem 915. Pedro Muzquiz and Tita de la Garza are the CEOs of a large bakery chain,
Chocolates, Inc. The common stock sells on the NASDAQ with a current
market price of $65 per share. A $7 dividend is planned for one year from
now. Business has been good and they expect the dividend growth rate of
10 percent to continue.
a. Calculate the cost of the corporation’s retained earnings.
b. At the beginning of the year, 1 million shares were authorized, with
500,000 issued and outstanding. They plan to issue another 200,000
shares. Calculate the cost of capital of the new common stock if the
flotation cost per share is $3. Do you expect the cost of new common
equity (external) to be higher than the cost of the internal equity? Why? Cost of Equity
CAPM Approach 916. Margo Channing, the financial analyst for Eve’s Broadway Production
Company, has been asked by management to estimate a cost of equity for use
in the analysis of a project under consideration. In the past, dividends declared
and paid have been very sporadic. Because of this, Ms. Channing elects to use
the CAPM approach to estimate the cost of equity. The rate on the shortterm
U.S. Treasury bills is 3 percent, and the expected rate of return on the overall
stock market is 11 percent. Eve’s Broadway Production Company has a beta of
1.6. What will Ms. Channing report as the cost of equity? Cost of Common
Equity Financing 917. African Queen River Tours, Inc. has capitalized on the renewed interest
in riverboat travel. Charlie Allnut, the lone financial analyst, estimates the
firm’s earnings, dividends, and stock price will continue to grow at the
historical 5 percent rate. AQRT’s common stock is currently selling for
$30 per share. The dividend just paid was $2. They pay dividends every year.
The rate of return expected on the overall stock market is 12 percent.
a. What is AQRT’s cost of equity?
b. If they issue new common stock today and pay flotation costs of $2 per
share, what is the cost of new common equity?
c. If AQRT has a riskfree rate of 3 percent and a beta of 1.4, what will be
AQRT’s cost of equity using the CAPM approach? Weighted
Average Cost
of Capital 918. Alvin C. York, the founder of York Corporation, thinks that the optimal
capital structure of his company is 30 percent debt, 15 percent preferred
stock, and the rest common equity. If the company is in the 40 percent tax
bracket, compute its weighted average cost of capital given that: Chapter 9 265 The Cost of Capital • YTM of its debt is 10 percent. N • ew preferred stock will have a market value of $31, a dividend of $2 per
share, and flotation costs of $1 per share. Weighted
Average Cost
of Capital P • rice of common stock is currently $100 per share, and new common stock can be issued at the same price with flotation costs of $4 per share.
The expected dividend in one year is $4 per share, and the growth rate is
6 percent. Assume the addition to retained earnings for the current period is zero.
919. Weighted
Average Cost
of Capital A company has an optimal capital structure as follows:
Total Assets $600,000 Debt $300,000 Preferred Stock $100,000 Common Equity $200,000 What would be the minimum expected return from a new capital investment
project to satisfy the suppliers of the capital? Assume the applicable tax rate is 40
percent, YTM of its debt is 11 percent, flotation cost per share of preferred stock
is $0.75, and flotation cost per share of common stock is $4. The preferred and
common stocks are selling in the market for $26 and $143 a share, respectively,
and they are expected to pay a dividend of $2 and $7, respectively, in one year.
The company’s dividends are expected to grow at 13 percent per year. The firm
would like to maintain the foregoing optimal capital structure to finance the
new project.
920. Great Expectations, a wedding and maternity clothing manufacturer, has a
cost of equity of 16 percent and a cost of preferred stock of 14 percent. Its
beforetax cost of debt is 12 percent, and its marginal tax rate is 40 percent.
Assume that the most recent balance sheet shown here reflects the optimal
capital structure. Calculate Great Expectations’ aftertax WACC.
Great Expectations Balance Sheet
Dec. 31, 2009
Assets
Cash
Accounts Receivable Liabilities and Equity
$ 50,000
90,000 LongTerm Debt Inventories 300,000 Preferred Stock 250,000 Plant and Equipment, net 810,000 Common Stock 400,000 Total Assets $1,250,000 $ 600,000 Total Liabilities and Equity $ 1,250,000 Weighted
Average Cost
of Capital 266 Part III
Weighted
Average Cost
of Capital 921. Capital Budgeting and Business Valuation Puppet Masters is considering a new capital investment project. The
company has an optimal capital structure and plans to maintain it. The
yield to maturity on Puppet Masters’ debt is 10 percent, and its tax rate is
35 percent. The market price of the new issue of preferred stock is $25 per
share, with an expected per share dividend of $2 at the end of this year.
Flotation costs are set at $1 per share. The new issue of common stock has
a current market price of $140 per share, with an expected dividend in one
year of $5. Flotation costs for issuing new common stock are $4 per share.
Puppet Masters’ dividends are growing at 10 percent per year, and this
growth is expected to continue for the foreseeable future. Selected figures
from last year’s balance sheet follow:
Total Assets $1,000,000 LongTerm Debt 300,000 Preferred Stock 100,000 Common Stock 600,000 Calculate the minimum expected return from the new capital investment project
needed to satisfy the suppliers of the capital.
Weighted
Average Cost
of Capital 922. Jay Lo Enterprises finances its assets with 60 percent debt, 10 percent
preferred stock, and 30 percent common stock. Jay Lo’s aftertax cost of
debt is 5 percent, its cost of preferred stock is 8 percent, and its cost of
common equity financing is 12 percent. Given these conditions, what is Jay
Lo’s WACC? Weighted
Average Cost
of Capital 923. The law firm of Dewey, Cheatem, and Howe (DCH) has the following
balance sheet:
Assets
Cash
Receivables
Office Equipment
Total Assets Liabilities and Equity
$ 110,000 Accounts Payable $ 70,000 240,000 LongTerm Debt 160,000 80,000 Preferred Stock 100,000 $ 430,000 Common Equity
Total Liabilities and Equity 100,000
$ 430,000 DCH’s creditors charge 9.5 percent annual interest on loans to the company. It
can sell preferred stock with a $10 per share dividend to the public for $50 a
share (net to the company after commissions). The company’s combined federal
and state tax rate is 35 percent, its beta is 1.1, the riskfree rate is 4 percent,
and the expected rate of return on the stock market is 12 percent. Given these
conditions, what is DCH’s WACC? Chapter 9 The Cost of Capital 267 924. Fans By Fay Company has a capital structure of 60 percent debt and 40
percent common equity. The company expects to realize $200,000 in net
income this year and will pay no dividends. The effective annual interest rate
on its new borrowings increases by 3 percent for amounts over $500,000.
a. At what capital budget size will Fans By Fay’s cost of equity increase? In
other words, what is its equity break point?
b. At what capital budget size will its cost of debt increase (debt break
point)? Marginal Cost of
Capital Schedule 925. Babe’s Dog Obedience School, Inc., wants to maintain its current capital
structure of 50 percent common equity, 10 percent preferred stock, and
40 percent debt. Its cost of common equity is 13 percent, and the cost of
preferred stock is 12 percent. The bank’s effective annual interest rate is 11
percent for amounts borrowed that are less than or equal to $1 million and
13 percent for amounts between $1 million and $2 million. If more than $2
million is borrowed, the effective annual interest rate charged is 15 percent.
Babe’s tax rate is 40 percent. The firm expects to realize $2,750,000 in net
income this year after preferred dividends have been paid.
a. Calculate the MCC if $900,000 is needed for an upcoming project.
b. Calculate the MCC if $3,000,000 is needed for the project instead.
c. If a different project is adopted and $5,005,000 is needed for it, what is
the MCC?
Stone Wood Products has a capital structure of 35 percent debt and
65 percent common equity. The managers consider this mix to be optimal
and want to maintain it in the future. Net income for the coming year is
expected to be $1.2 million dollars. Duke Mantee, the loan officer at the
local bank, has set up the following schedule for Stone Wood Products’
borrowings. There are 40,000 shares of common stock outstanding. The
firm’s tax rate is 40 percent. Marginal Cost of
Capital Schedule 926. Loan Amount
$0 to $750,000
> $750,000 Interest Rate
10%
12% The market price per share of Stone Wood Products’ common stock is $50 per
share. They have declared a $5 dividend to be paid in one year. The company’s
expected growth rate is 9 percent. The flotation costs for new common stock
issued are set at 8 percent of the market price.
The managers are considering several investment opportunities for the
upcoming year. They have asked the senior financial analyst, Gabrielle Maple,
to recommend which of the following projects the firm should undertake.
Because you are the newest member of her team and need the experience, she
has passed this management request on to you. Comprehensive
Problem 268 Part III Capital Budgeting and Business Valuation
Investment Opportunities
Project Initial Investment
(in millions) Rate of
Return A $0.5 16% B $1.6 12% C $0.6 15% D $1.5 18% a. Calculate all of Stone Wood Products’ component costs of capital (aftertax
cost of debt, cost of equity, and cost of new equity).
b. Calculate all of the MCC break points.
c. Calculate all of the MCC figures.
d. Make an IOS by listing the projects from the highest to the lowest internal
rates of return.
e. Plot the MCC values and the IOS values on the same graph.
f. Which projects will you recommend management adopt for the next year? Answers to SelfTest
ST1. .14 × (1 – .32) = .0952 = 9.52% AT kd ST2. Using Equation 97, kp = Dp /(Pp – F) =
$3/($30 – $1) = .1034, or 10.34% ST3. .04 + (.10 – .04) × 1.9 = .154 = 15.4% ks ST4. (.08 × .2) + (.12 × .10) + (.16 × .70) = .14 = 14% ka ST5. The break point in the MCC schedule caused by the increase in the cost
of debt, BPd, after $8,000,000 is borrowed, equals $8,000,000 ÷ .40 =
$20,000,000. ...
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This note was uploaded on 11/17/2011 for the course BUS 330 taught by Professor Nugent during the Fall '08 term at SUNY Stony Brook.
 Fall '08
 Nugent
 Valuation

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