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.

B.
MV of assets = MV of liabilities + MV of equity
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 righthand 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:
kFirm 
o
n
xk
i 1
i i
 x1k1  x2 k2  x3k3 
 xn k n
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
The appropriate discount rate to use when evaluating a capital budgeting project depends largely
on the risk of the project. The new project will have a positive NPV only if its return exceeds
what the financial markets offer on investments of similar risk. We called this minimum required
return the cost of capital associated with the project. The weighted average cost of capital
(WACC) is the cost of capital for the firm as a whole, and it can be interpreted as the required
return on the overall firm. In discussing the WACC, we will recognize the fact that a firm will
normally raise capital in a variety of forms and that these different forms of capital may have
different costs associated with them. Taxes are an important consideration in determining the
required return on an investment, because we are always interested in valuing the aftertax cash flows
from a project. We will therefore discuss how to incorporate taxes explicitly into our estimates of the
cost of capital.
An accurate estimate of the cost of capital is important for various reasons:
 good capital budgeting decisions – neither the NPV rule nor the IRR rule can be
implemented without knowledge of the appropriate discount rate.
 financing decisions – the optimal/target capital structure minimizes the cost of capital.
 operating decisions – cost of capital is used by regulatory agencies in order to determine
the “fair” return in some regulated industries (e.g. electric utilities).

Required Return versus Cost of Capital: Cost of capital, required return, and
appropriate discount rate are different phrases that all refer to the opportunity cost of
using capital in one way as opposed to alternative financial market investments of the
same systematic risk. Required return is from an investor’s point of view; cost of
capital is the same return from the firm’s point of view; appropriate discount rate
is the same return used in a PV calculation.
The cost of capital depends primarily on the use of the funds, not the source.
The investment decisions of the firm are separate from the financing decisions.

13.2
Financial Policy and Cost of Capital: The particular mixture of debt and equity a firm
chooses to employ is referred to as its capital structure; this is a managerial variable.
For now, we will take the firm's financial policy as given. In particular, we will
assume that the firm has a fixed debt-equity ratio that it maintains. This ratio reflects
the firm's target or optimal capital structure. Given that a firm uses both debt and
equity capital, this overall cost of capital will be a mixture of the returns needed to
compensate its creditors and its stockholders. In other words, a firm's cost of capital
will reflect both its cost of debt capital and its cost of equity capital.
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.
Unlike a firm's cost of equity, its cost of debt can normally be observed either directly or
indirectly, because the cost of debt is simply the interest rate the firm must pay on new
borrowing, and we can observe interest rates in the financial markets. For example, if the firm
already has bonds outstanding, then the yield to maturity on those bonds is the market-required
rate on the firm's debt.
Alternatively, if we knew that the firm's bonds were rated, say, AA, then we could simply find
out what the interest rate on newly issued AA-rated bonds was. Either way, there is no need to
actually estimate a beta for the debt since we can directly observe the rate we want to know.
The coupon rate on the firm's outstanding debt is irrelevant here. That just tells us roughly what
the firm's cost of debt was back when the bonds were issued, not what the cost of debt is today.
This is why we have to look at the yield on the debt in today's marketplace.
Example: 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?
N = 14 x 2 = 28
PV = -823.48
PMT = (.085 x $1,000) / 2 = 42.50
FV = 1000
I/YR = ___ x 2 =
kDebt after-tax = kDebt pretax x (1 – t) =
7.7%
(Par Value - Bond Price)

 Coupon 
Years to Maturity
Estimated YTM  
Par Value  2(Bond Price)


3
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 longterm 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.
Betas are widely available and T-bond or T-bill rates are often used for Rf. The expected market
risk premium, E(Rm) – Rf, is the more difficult number to come up with. One of the problems is
that we really do need an expectation, but we only have past information, and market risk
premiums do vary through time. Early in 2000, Federal Reserve Chairman, Alan Greenspan,
indicated that part of his concern with the current state of the U.S. stock markets is the reduction
in the market risk premium. He felt that investors were either becoming less risk averse, or they
did not truly understand the risk they were taking by investing in the stock. Nonetheless, the
historical average is often used as an estimate for the expected market risk premium.
- This approach explicitly adjusts for risk in a fashion that is consistent with capital market
history.
- It is applicable to virtually all publicly-traded stocks for which the value of β can be
determined.
- The main disadvantage is that the past is not a perfect predictor of the future, and both beta and
the market risk premium vary through time.
o Method 2: Using the Constant-Growth Dividend Model

Using Equation 9.5, P0 =
D1
, we can rearrange to solve for R—or kcs as we
R-g
now prefer to call it: kcs =

D1
+g
P0
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.
Of the required data, only g is not directly observable [Note: D1 = D0(1 + g)]. The
deficiencies of this approach are (1) it assumes that dividends grow at a constant rate; (2) the
value of g must be estimated and forecasting errors impact the value of kcs; and (3) risk is not
explicitly considered.
To use the dividend growth model, we must come up with an estimate for g, the growth rate.
There are essentially two ways of doing this: (1) use historical growth rates or (2) use analysts'
forecasts of future growth rates. Analysts' forecasts are available from a variety of sources.
(Example from Yahoo! Finance: IBM; from Zack’s: IBM).
Alternatively, we might observe dividends for the previous, say, five years, calculate the year-toyear growth rates, and average them. For example, suppose we observe the following for some
company:
Year
2005
2006
2007
2008
2009
Dividend
$4.00
$4.40
$4.75
$5.25
$5.65
$ Change
$.40
$.35
$.50
$.40
% Change
10.00%
7.95%
10.53%
7.62%
Arithmetic average growth rate = (10.00% + 7.95% + 10.53% + 7.62%) / 4 = 9.025%
Geometric average growth rate = ($5.65 / $4.00)(1/4) – 1 = 9.018%
Example: 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?
Pcs  $11.66 
D1
kcs  g
16%
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.
Example: 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?
E(Rcs )  Rrf  β[E(Rm )  Rrf ]
13.6%
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. The cost of preferred stock financing can
also be observed in the financial markets. A firm which expects to issue preferred
stock would compute the yield for either its own currently outstanding preferred stock
issue or for preferred stock issued by other firms with ratings similar to the proposed
offering.
o Just as with common stock, we can find the cost of preferred equity by
rearranging the pricing equation for preferred shares: kps =
D ps
Pps
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.
Sixth Fourth Bank has an issue of preferred stock with a $6 stated dividend that just sold for $94 per
share. What is the bank's cost of preferred stock?
kps =
6.38%
12.4
Using the WACC in Practice

The after-tax version of the formula for the weighted-average cost of capital is:
WACC  xDebt kDebt pretax (1  t )  xps kps  xcs kcs .

The financial analyst should use market values rather than book values to calculate
WACC.
Example - 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).
N = 15 x 2 = 30
PV = -1440.03
PMT = (.09 x $1,000) / 2 = 45
FV = 1000
I/YR = 2.42 x 2 = 4.84
Cost of preferred equity:
D
$1.20
k ps 

 0.10
Pps $12.00
Cost of common equity:
D
$2.20
k cs  1  g 
 0.05  0.16
Pcs
$20.00
Step 3: Combine using the WACC formula.
WACC  x debt k debt (1  t )  x ps k ps  xcs k cs =
WACC   0.4967  0.0484  (1  0.4)    0.0397  0.10    0.4636  0.16   0.0926, or 9.26%
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.
Chapter 13 - Sample Problems
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1.
How firms estimate their cost of capital: You are analyzing the cost of capital for a firm
that is financed with 65 percent equity and 35 percent debt. The cost of debt capital is 8
percent, while the cost of equity capital is 20 percent for the firm. What is the overall cost of
capital for the firm?
a. 12.2%
b. 14.0%
c. 15.8%
d. 20.0%
2.
The cost of debt: Beckham Corporation has bonds outstanding with 13 years to maturity and
are currently priced at $746.16. If the bonds have a coupon rate of 8.5 percent, then what is
the after-tax cost of debt for Beckham if its marginal tax rate is 35%? Assume that your
calculation is made as on Wall Street.
a. 6.250%
b. 8.125%
c. 12.500%
d. 12.890%
3.
The cost of equity: Jacque Ewing Drilling, Inc., has a beta of 1.3 and is trying to calculate its
cost of equity capital. If the risk-free rate of return is 8 percent and the expected return on the
market is 12 percent, then what is the firm's after-tax cost of equity capital if the firm's
marginal tax rate is 40 percent?
a. 7.92%
b. 13.20%
c. 15.57%
d. 23.60%
4.
The cost of equity: Gangland Water Guns, Inc., is expected to pay a dividend of $2.10 one
year from today. If the firm's growth in dividends is expected to remain at a flat 3 percent
forever, then what is the cost of equity capital for Gangland if the price of its common shares
is currently $17.50?
a. 12.00%
b. 14.65%
c. 15.00%
d. 15.36%
5.
The cost of preferred equity: Billy's Goat Coats has a preferred share issue outstanding with
a current price of $38.89. The firm last paid a dividend on the issue of $3.50 per share. What
is the firm's cost of preferred equity?
a. 7%
b. 8%
c. 9%
d. 10%
6.
Using the WACC in practice: Ronnie's Comics has found that its cost of common equity
capital is 15 percent and its cost of debt capital is 12 percent. If the firm is financed with
$250,000,000 of common shares (market value) and $750,000,000 of debt, then what is the
after-tax weighted average cost of capital for Ronnie's if it is subject to a 35 percent marginal
tax rate?
a. 6.05%
b. 9.60%
c. 8.75%
d. 13.65%
7.
Using the WACC in practice: Droz's Hiking Gear, Inc., has found that its common equity
capital shares have a beta equal to 1.5 while the risk-free return is 8 percent and the expected
return on the market is 14 percent. It has 7-year maturity bonds outstanding with a price of
$767.03 that have a coupon rate of 7 percent.. If the firm is financed with $120,000,000 of
common shares (market value) and $80,000,000 of debt, then what is the after-tax weighted
average cost of capital for Droz's if it is subject to a 35 percent marginal tax rate? Calculate
the cost of debt as it would be done on Wall Street.
a. 10.20%
b. 11.76%
c. 11.88%
d. 13.32%
Chapter 13 - Sample Problems
Answer Section
MULTIPLE CHOICE
1.
ANS:
C
Learning Objective: LO 4
Level of Difficulty: Hard
Feedback: kFirm = xDebt kDebt + xEquity kEquity = (0.35 x 0.08) + (0.65 x 0.2) = 0.158
2.
ANS:
B
Learning Objective: LO 2
Level of Difficulty: Medium
Feedback: Using the formula for pricing bonds, we have
3.
ANS:
B
Learning Objective: LO 3
Level of Difficulty: Hard
Feedback:
Prepared by Jim Keys
22
4.
ANS:
C
Learning Objective: LO 3
Level of Difficulty: Medium
Feedback:
5.
ANS:
C
Learning Objective: LO 3
Level of Difficulty: Hard
Feedback:
6.
ANS:
B
Learning Objective: LO 4
Level of Difficulty: Hard
Feedback:
Noting that the proportion of debt and equity is:
xDebt = $750,000/($750,000 + $250,000) = 0.75
xcs = $2,000,000/($750,000 + $250,000) = 0.25
The formula for the WACC is:
WACC = xDebt kDebt pretax (1-T) + xcs kcs = [0.75 x .12 x (1 - .35)] + [0.25 x 0.15] = .0585 + .0375 = .096 = 9.60%
Prepared by Jim Keys
23
7.
ANS:
D
Learning Objective: LO 4
Level of Difficulty: Hard
Feedback:
Prepared by Jim Keys
24