edition
2
FOUNDATIONS OF
CORPORATE FINANCE
Kent A. Hickman
Gonzaga University
Hugh O. Hunter
San Diego State University
John W. Byrd
Fort Lewis College
chapter
8
Cost of Capital
“You tell the governor that if he doesn’t come up with some subsidized financing,
258
free land, a tax deferment, a new highway and airport, it’s no deal!”
Chapter 8 • Cost of Capital
259
CHAPTER 8 IN FOCUS
THE FINANCIAL BALANCE SHEET
Investments
made by
the firm
Capital supplied
for
corporate
investments
Bonds
Preferred stock
Common stock
Cash returned to capital supplied
Capital suppliers are exposed to risk and their returns must reflect that risk. The corporation’s cost of capital
is the weighted average of the returns required by suppliers of capital. This weighted average cost of capital is
the discount rate for corporate investments.
C
hapter 7 described the various capital budgeting techniques employed by
corporate managers. Among the techniques, net present value (NPV)
emerges as the best measure of a project’s contribution to shareholder
wealth. In NPV analysis, the present value of a project’s expected future cash
flows is compared to the initial investment, and the project is accepted if the present value exceeds the initial investment. Calculation of NPV requires the analyst
to estimate cash flows and an appropriate discount rate. Techniques for estimating cash flows were covered in Chapter 7. In this chapter you will learn how to
estimate the discount rate. The same estimates of cash flows and discount rate
are also used in internal rate of return (IRR) analysis. Used in IRR, the discount
rate becomes a hurdle rate against which to compare the project’s IRR.
Estimating the Discount Rate
To illustrate the calculation and use of the discount rate, we continue with the
Chapter 7 example of Pacific Offshore Ltd. (POL). The NPV of POL’s harness
project is $9,110, which was found by discounting the project’s net cash flows
by 12.5%. The project’s internal rate of return of 17.2% is greater than the
12.5% required rate of return on the harness project. Therefore, whether we use
NPV or IRR, the harness project appears to be acceptable because it meets the
respective decision criteria. Had the required return been 20%, for example, the
project would have been rejected using either criterion.
We have referred to the 12.5% as the harness project’s required rate of return. To be more specific, 12.5% is the weighted average return demanded by
the company’s investors. The weightings reflect the proportional values of their
investments. From Chapter 7, the cost of the harness project is $64,384, meaning that Paula Bauer must raise that amount from her investors to fund tools,
equipment, and working capital and to pay the cost of reconfiguring the plant.
Paula has decided to fund future projects using the firm’s current proportional
mix of debt and preferred and common stock. POL’s current capital mix is 28%
debt, 7.8% preferred stock, and 64.2% common stock. POL, therefore, will
raise about $18,000 in debt and about $5,000 in preferred stock. The balance
of the funding will come from residual cash flows that belong to the firm’s
The required return on an investment
is the weighted average of the returns
demanded by the company’s investors.
260
Chapter 8 • Cost of Capital
FIGURE 8.1
FINANCING MIX
AND
CASH FLOWS
FOR THE
POGO HARNESS PROJECT
$64,384
$18,028
Pogo Harness Project
tools, equipment, working
capital, plant
$5,022
Preferred
stockholders
$41,334
Common
stockholders
Harnesses
Consumers
Bondholders
Cash Flows
Visit Ibbotson Associates at
http://www.ibbotson.com
to see how they estimate the cost of
capital. To learn more about how to select the appropriate discount rate, click
on Managing Your Business Finances,
Major Purchases and Projects, and Discount Rate.
The basic discount rate for capital
investments is the company’s cost
of capital.
shareholders.1 Cash from the harness project will flow to these investors in order
of the priority of their claims: first to bondholders, then to preferred stockholders,
and finally to common stockholders. Figure 8.1 illustrates the flow of capital and
cash flows, assuming that the harness project produces its expected cash flows.
POL raises capital by selling these securities to investors, who expect to receive a return on their investment. Any investor purchasing POL’s securities must
expect that the returns will be at least equal to, and preferably greater than, the required return on an investment having the same risk as the harness project. If expected returns were lower than required, investors would look elsewhere, or they
may be persuaded to buy POL’s securities at a discount, which would increase their
expected returns. Thus, Paula must be confident that the discount rate she uses to
value the project will provide the required return to each class of POL’s investors.
This discount rate is known as the cost of capital for the project because the returns investors require are the cost, like rent, that is paid for the use of the capital.
The Weighted Average
Cost of Capital
Calculating the Weighted Average Cost of Capital
The weighted average cost of capital
(WACC) is the weighted average of the
required returns for each capital
source. Weightings are the proportional
contributions from each capital source.
The cost of capital is a weighted average of the required returns for each capital
source. For the harness project, the weighted average cost of capital (WACC) is
the after-tax2 required returns on POL’s bonds, preferred stock, and common eq1Accountants refer to these as retained earnings, but we prefer cash flows, since earnings, as far as we know, are
not legal tender.
2Interest on bonds or any other debt is tax deductible, thus lowering the cost of debt to the firm.
Chapter 8 • Cost of Capital
uity, weighted by their proportional contribution to the project. As you can see
in Exhibit 8.1, of the $64,384 being raised, the bondholders contribute $18,028
(28%), the preferred stockholders contribute $5,022 (7.8%), and the common
stockholders contribute the remaining $41,334 (64.2%) in residual cash flows.
Later we will explain how Paula estimated the costs of debt preferred stock
and common equity. First, though, we present her worksheet for computing
POL’s cost of capital. Exhibit 8.1 shows that she multiplied the proportion of
each capital source by its after-tax required return. She then summed these results to arrive at the 12.5% cost of capital.
Paula’s worksheet may be summarized by a formula for the weighted average cost of capital.
WACC 5 (Wd)(after-tax cost of debt)
(8.1)
1 (Wpfd)(cost of preferred stock)
1 (We)(cost of common equity)
where
Wd 5 the desired proportion of financing provided by debt
Wpfd 5 the desired proportion of financing provided by preferred stock
We 5 the desired proportion of financing provided by common equity
This formula is adaptable to any combination of financing sources. For example, if preferred stock were not used, then Wpfd 5 0 and preferred stock would
drop out of the formula. Some companies borrow from many sources. They may
have several bond issues and perhaps long-term loans from banks or insurance
companies. The only source of capital that is common to all companies is common equity. The WACC formula for a company with no preferred stock, but
with two types of debt, would be
WACC 5 (WB)(after-tax cost of bonds)
(8.2)
1 (WL)(after-tax cost of loan)
1 (We)(cost of equity)
No matter how many sources of capital there are, the weights always sum to 1
(WB 1 WL 1 We 5 1). This ensures that all capital sources have been included in
the calculation of WACC.
Discounting expected cash flows by the weighted average cost of capital
gives Paula the information she needs to make her investment decision on the
harness project. If the NPV 5 0, then the project should provide all investors
EXHIBIT 8.1
WORKSHEET FOR COMPUTING POL’S COST
CAPITAL
COMPONENT
Debt (bonds)
Preferred stock
Common equity
(A)
TARGETED
PROPORTION
OR WEIGHT
28.0%
7.8%
64.2%
100.0%
(B)
PROJECT
COST
$64,384
64,384
64,384
OF
CAPITAL
(A) 3 (B)
DOLLARS
RAISED
$18,028
5,022
41,334
$64,384
(D)
AFTER TAX
REQUIRED
RETURNS
6.93%
11.96%
15.00%
(A) 3 (D)
WEIGHTED
AVERAGE
1.94%
0.93%
9.63%
12.50%
261
262
Chapter 8 • Cost of Capital
Discounting project cash flows by the
WACC means that projects will be accepted only if they are expected to provide at least the required returns to all
investors.
with their required returns but with nothing more. This is the minimally acceptable outcome. The harness project is expected to do better than that, meaning
that it should add value because its NPV is $9,110.
To summarize, discounting project cash flows at the WACC ensures that the
minimal needs of each class of investor are met. We may rewrite the NPV and
IRR equations from Chapter 7 to include WACC.
n
OCFt
TCFn
NPV 5 2II 1 a
t 1
s1 1 Rsrd d n
t51 s1 1 Rsrd d
(7.1)
where
II 5 initial investment
OCFt 5 operating cash flows in year t
TCF 5 terminal cash flows
t 5 year
n 5 life span (in years) of the project
r 5 project required rate of return
Equation (7.1) may be simplified to
n
CFt
NPV 5 a
t 2 II
t51 s1 1 rd
(8.3)
By substituting WACC for r, the equation becomes
n
CFt
NPV 5 a
t 2 II
t51 s1 1 WACCd
(8.4)
where CFt 5 total net cash flow for period t. The company should accept projects with NPV > 0.
The equation for IRR is
n
CFt
a s1 1 IRRd t 2 II 5 0
(8.5)
t51
The company should accept projects with IRR > WACC.
In the following section, we explain how Paula estimated the cost of each
capital component.
The Cost of Debt
The cost of debt is the yield-tomaturity (YTM) on the company’s
bonds or other long-term debt
securities.
The cost of debt is the current yield-to-maturity (YTM) on the company’s bonds
or other long-term debt securities. YTM reflects current credit market conditions
and investors’ expectation, and therefore it is the best indicator of returns investors require on the sale of new bonds. Recall from Chapter 5 that YTM is the
discount rate applied to the expected cash flows from a bond. This discount rate
is the cost of debt for the project.
Kd 5 YTM
The current market price of POL’s bonds is $1,003. The bonds mature in 6 years,
bear a 9.5% coupon rate, and make coupon payments semiannually. Their par
value is $1,000.
Kd is found by solving for YTM in the following equation, which sets the
price of the bonds equal to the present value of future cash flows. We may think
of the YTM as the internal rate of return (IRR) of a bond.
Chapter 8 • Cost of Capital
$1,003 5
263
$47.50
$47.50
$47.50
1
1...1
1
2
s1 1 YTMd
s1 1 YTMd
s1 1 YTMd 12
$1,000
1
s1 1 YTMd 12
Note that each coupon payment, $47.50, equals one-half of the coupon rate
(9.5%) times par value ($1,000) because the bond pays coupons semiannually
[(0.095)($1,000)/2 5 $47.50]. There are 12 payments because the bonds mature
in 6 years and pay interest twice per year. The yield to maturity on these bonds
equals 4.72% semiannually, or 9.44% on an annual basis.3
Because interest on debt is tax deductible, the YTM must be adjusted for the
tax effect. The tax deduction lowers the effective cost of debt to the company.
We adjust YTM for taxes by multiplying YTM by (1 2 t), where t is the firm’s
marginal tax rate. Substituting Kd for YTM gives us
after-tax cost of debt 5 Kd (1 2 t)
(8.6)
POL’s marginal tax rate is 30%. Therefore
Kd (1 2 t) 5 9.44% (1 2 0.30) 5 9.44% (0.7) 5 6.61%
The Cost of Preferred Stock
Preferred stock combines features of debt and equity. Preferred dividends are fixed,
like bond interest, but also have an infinite life like common stock dividends. From
Chapter 4, we recognize this as a perpetuity—a perpetual annuity—which greatly
simplifies the calculation. The cost of preferred stock equals its required rate of return, which is its annual dividend divided by its current market price.
The dividend on POL’s preferred stock is $2.50 and its current market price
is $21.50 per share. Therefore, the required return on the stock is 11.63%.
Kpfd 5
dividend
$2.50
5
5 0.1163 5 11.63%
share price
$21.50
The cost of preferred stock is its
annual dividend divided by its current
market price.
(8.7)
No tax adjustment is necessary for preferred stock.
The Cost of Common Equity
The cost of common equity is the most difficult of the component costs to estimate. Chapter 6 presented the capital asset pricing model (CAPM) as one means
of estimating investors’ required return for risky assets. Although this risk-return
model is the most frequently used method for estimating returns to common
stock, other models may also be used, most notably the discounted cash flow
model introduced in Chapter 5. As a general rule, the analyst should approach
the problem of estimating common stock returns from several directions and
hope to generate a consensus estimate from these varying approaches. In this section, we cover three approaches: CAPM, the discounted cash flow model, and
the equity-debt risk premium.
The CAPM Approach to Ke
Ke is the cost of common equity. Chapter 6 built on portfolio theory to show the relationship between required returns
3YTM,
like IRR, must be solved with the aid of a financial calculator or computer.
The cost of common equity may be estimated using the CAPM, a discounted
cash flow (dividend growth) model, or
an equity-debt risk premium.
264
Chapter 8 • Cost of Capital
on investments and their market risk. The CAPM states that the required return
on a risky investment equals the risk-free rate plus the product of the asset’s beta
and the market risk premium. The CAPM is
R(r)i 5 rf 1 bi(market risk premium)
or
R(r)i 5 ri 1 bi[E(rm) 2 rf]
(8.8)
where
R(r)i 5 the required return for asset i
rf 5 the risk-free rate of return
bi 5 asset i’s beta
market risk premium 5 market’s expected return minus the risk-free return
Value Line can be accessed at
http://www.valueline.com.
Let’s look at the information needed to solve the CAPM. First is the risk-free
return. Although no asset is totally free of risk, U.S. government t-bills are considered nearly riskless. Thus, t-bills are a widely used proxy for the true risk-free rate.4
T-bill returns are widely available in print and on the Web. Next, we need an estimate of the equity beta. Brokerage and other investment service firms estimate betas for many publicly traded stocks. Betas may be obtained on the Web and in print
from Value Line, Standard & Poor’s, and Bloomberg.5 As we saw in Chapter 6, we
may also estimate beta ourselves using data on past returns.
The expected market return is difficult to forecast directly. Therefore, we
must rely on historical market returns and the historical market risk premium as
our best guide to the future. Stock market indexes, especially the S&P 500, are
generally used as market proxies. Since 1926, the average annual return on the
S&P 500 is about 13%. This number, or one close to it, is often used in the
CAPM as the market’s expected return. The current t-bill rate is subtracted from
the market return to derive the market risk premium.
Other practitioners prefer to avoid estimating the market return and choose,
instead, to use the historical equity market risk premium. The historical market
risk premium is found by calculating the average amount by which the market
return has exceeded t-bill returns. For example, the difference between the S&P
500 return and the t-bill return for each of the last 70 years could be averaged
and used as the historical market risk premium. From the Ibbotson data in Chapter 6, we see that over the past 70 years the market risk premium has averaged
about 9.4% per year.
For POL, Paula gathered the following estimates for the risk-free return,
POL’s beta, the market return, and the market risk premium. Notice that she
used two different forms for the CAPM, one using the historical S&P return and
one using the historical market risk premium. The result is two estimates of
POL’s cost of equity, both using the CAPM.
POL’S COST
OF
EQUITY ESTIMATES USING THE CAPM
Risk free return: T-bills (from the Wall Street Journal)
BetaPOL (from POL’s investment banker)
Market return: historical S&P 500 return (from Ibbotson)
Market risk premium: historical equity market risk premium
(from Ibbotson)
4For
a discussion of the appropriate proxy for the risk-free rate, see the chapter appendix.
such site is Yahoo Finance, http://quote.yahoo.com.
5One
rf 5 4%
bPOL 5 1.2
E(rm) 5 13%
9.4%
Chapter 8 • Cost of Capital
Paula’s first CAPM estimate was:
R(r)POL 5 rf 1 bPOL 1 [E(rm) 2 rf]
5 4% 1 1.2(13% 2 4%)
5 14.8%
Her second CAPM estimate was:
R(r)POL 5 rf 1 bPOL(market risk premium)
5 4% 1 1.2(9.4%)
5 15.28%
These two estimates are similar because the same model was used for both. In
fact, the difference in the estimates boils down to the risk-free rate. In the second
estimate the market risk premium is based on a historical rf and the first estimate
uses a current rf . We now turn to a second model for estimating the cost of equity.
The Discounted Cash Flow Approach to Ke In Chapter 5 the
constant dividend growth model for valuing common stock was introduced.
P0 5
D1
Ke 2 gn
(8.9)
The current price equals next year’s dividend divided by the difference between
equity’s required return and the long-run dividend growth rate. This equation
may also be solved for Ke the cost of equity.
Ke 5
D1
1 gn
P0
(8.10)
The dividend growth model for estimating the required return on common stock
reflects the discounted cash flow approach to valuation, as do the YTM for debt
and the preferred stock perpetuity model.
This approach requires a current market price, an estimate of next year’s
dividend per share, and an estimate of the long-run dividend growth rate. Prices
for traded firms’ stock are easily obtained. Value Line and many brokerage firms
forecast dividends and dividend growth rates for large and actively traded companies. For smaller companies, such as POL, published forecasts are generally
not available, so we must rely on our own resources. Forecasts should begin by
looking at a company’s dividend history. If we have enough data, we can calculate historical growth rates. The historical growth rate is the compound rate that
equates a dividend paid several years ago with a recent dividend payment. This
process is nothing more than an application of the future value of a single cash
flow formula, given in Chapter 4.
FVn 5 PV0 (1 1 r)n
The difference is that rather than looking forward, we are looking back. To use
the model, we must change the definition of its components. FVn is the most recent dividend, D0. PV0 is the beginning historical dividend, D2n. The rate of return, r, is the compound growth rate, gn.
D0 5 D2n (1 1 gn)n
(8.11)
265
266
Chapter 8 • Cost of Capital
Fortunately, POL has paid a dividend for 5 years, so we are able to calculate a
growth rate. The dividend 5 years ago (D25,) was $0.60 and the most recent dividend (D0) was $0.84.
D0 5 D25(1 1 gn)5
0.84 5 0.60(1 1 gn)5
(1.4)1/5 5 1 1 gn
1.07 5 1 1 gn
0.07 5 gn ,
gn 5 7%
The current market price of POL’s common stock is about $11.25.6 Next year’s
dividend, D1, should equal D0 (1 1 gn). D1 5 $0.84(1.07) 5 $0.90. Now, we
may solve for Ke.
P0 5 $11.25
gn 5 7% 5 0.07
D1 5 $0.90
Ke 5
$0.90
1 0.07 5 0.15 5 15%
11.25
Having estimated Ke using the constant growth formula, we must remember
that this formula assumes a constant growth rate into perpetuity. Therefore, this
method may not be appropriate for firms whose growth is unstable or unsustainable. Cyclical firms, such as lumber companies, often have earnings that fluctuate dramatically with the business cycle. Exceptionally high initial growth rates
of startup companies will eventually fall to more sustainable levels as the industry matures. For these types of firms the constant growth assumption is quite difficult to apply. In practice, companies appear to favor the CAPM approach to the
discounted cash flow approach for determining their cost of equity.7
The Equity-Debt Risk Premium Approach to Ke
The difference between returns to
equity and returns to debt is the
equity-debt-risk premium.
The final
method for estimating the cost of equity is to add a risk premium to the cost of
debt. Because equity is a residual claim with a lower priority than debt, equity is
riskier than debt; therefore investors require that Ke exceed Kd. The difference
between Ke and Kd is the equity-debt-risk premium.
Ke 5 Kd 1 RP
The risk premium, RP, is generally in the range of 3% to 6%. The method is ad hoc
but works fairly well as a benchmark because the needed data are easily obtained.
Estimates of Ke, using CAPM and discounted cash flow models, that fall outside
the range [Kd 1 (3% to 6%)] should prompt the analyst to revisit her estimates.
For POL, the equity-debt-risk premium approach yields the following range for Ke.
(Kd 1 3%) < Ke < (Kd 1 6%)
(9.4% 1 3%) < Ke < (9.4% 1 6%)
12.4% < Ke < 15.4%
6We used the word about on purpose because POL is a small company whose stock is infrequently traded in the
over-the-counter market.
7See Robert Bruner, Kenneth Eades, Robert Harris, and Robert Higgins, “Best Practices in Estimating the Cost of
Capital: Survey and Synthesis,” Financial Practice and Education, Spring/Summer 1998.
Chapter 8 • Cost of Capital
267
Paula’s estimates of Ke using the CAPM were 14.8% and 15.28%. Her discounted cash flow method produced a 15% cost of equity. All three of these estimates are within the range prescribed by the equity-debt premium, which more
or less confirms Paula’s estimates. All three estimates of Ke clustered about 15%,
so Paula elected 15% as POL’s cost of equity. As with preferred stock, no tax adjustment is necessary.
The Cost of Selling Securities
Each component cost reflects returns required by investors who are supplying
capital to the firm. These returns reflect the amount the investors paid for their
respective securities. However, when a company raises funds by selling securities,
it usually employs a company to assist it in marketing its securities. Companies
that specialize in selling new securities issues, called investment banks, take a cut
for marketing and underwriting the issue. A securities issue is underwritten when
the investment bank buys securities from the company and resells them to investors for a higher price. The difference between the price paid to the company
and the sale price is called the underwriting spread. Of course, the sale price must
approximate the security’s market value. For example, POL is selling bonds to
pay for the harness project. Investors will buy the bonds for approximately
$1,003, their current market price. However, the underwriting spread reduces
POL’s proceeds from the bond sale and raises POL’s effective cost of debt above
the 9.44% YTM.
Costs associated with selling securities are called flotation costs. In the lingo
of Wall Street, firms are said to be floating an issue. Aside from the underwriting
spread, flotation costs include fees paid to the investment banker for consultation, document preparation, and so on. They also include costs of filing with regulators such as the Securities and Exchange Commission, legal fees, and accounting fees. Flotation costs as a percentage of the value of the securities issue are
greater for equity than for debt, reflecting the increased risk of underwriting
stocks. Flotation costs are also proportionally greater for issues of small dollar
value. There are significant scale economies to securities issues. Some fees and
other costs are relatively fixed.
With the high cost of issuing securities for smaller companies, it would seem
that small firms might have a tough time raising outside capital. Historically, this
has been the case with small firms having to rely largely on private sources of
capital. However, the rapid development and dissemination of technology, and
the deregulation of financial services, transportation, and telecommunications
have spurred a virtual renaissance in entrepreneurial activity in the United States,
creating new investment opportunities. Venture capital firms have sprung up by
the hundreds to supply early financing to promising companies. Not wishing to
miss out on these opportunities, large investment banks and other companies,
such as General Electric, have gotten into the venture capital business. This capital market specializes in high-risk investments, but the returns can be astonishing. Venture capitalists generally expect rates of return of 40% to 50%! Through
the 1990s, we were entertained by stories of billions of dollars of instant wealth
created in initial public offerings (IPOs) of heretofore unknown companies. Venture capitalists and other early investors who take a share of the company’s equity are beneficiaries of successful IPOs. Venture capital firms generally take a
25% or larger stake in a company.
Flotation costs siphon money from the securities issue, raising the effective
cost of capital. Therefore, the cost to the company is greater than the return to
Investment banks assist companies in
marketing new securities offerings.
When an investment bank buys securities from the issuing company and
resells them to investors, it is underwriting the securities offering. The difference between the price paid to the
company and sale price to investors is
the underwriting spread.
Flotation costs are the costs associated with selling securities.
Venture capital firms supply high-risk
capital to small firms prior to an initial public offering of stock.
268
Chapter 8 • Cost of Capital
the investor. This means that the cost of each component must be adjusted to reflect flotation costs. Net proceeds to the company equal the sale price to the investors minus flotation costs.
Pnet 5 P 2 (flotation costs)
(8.12)
Virtually all financing with bonds and preferred stock represents new issues
and therefore includes flotation costs. Common equity financing may be done
through stock sales, but more often it comes from retained earnings, which carry
no flotation costs. POL is selling bonds and preferred stock to finance the harness project. Common equity financing comes from retained earnings. POL’s investment banker estimates that flotation costs will be $20 for every bond sold
and $0.60 for each share of preferred stock. Paula adjusts the cost of debt and
preferred stock to reflect these flotation costs.
For bonds:
Kdnew 5 YTM
(YTM was calculated using Pnet for bonds) (8.13)
Pnet for bonds 5 $1,003 2 $20 5 $983
Based on the Pnet of $983, we recalculate YTM:
YTM* 5 4.94% semiannually
Kdnew 5 9.9% annually
Kdnew (1 2 t) 5 (9.9%)(0.7) 5 6.93%
We now have calculated four numbers masquerading as the cost of debt. We have
costs before and after the tax adjustment, and with and without flotation costs.
Without flotation costs
Including flotation costs
BEFORE TAX
AFTER TAX
9.44%
9.88%
6.61%
6.93%
The actual YTM of the bonds is 9.44%, but after adjusting for taxes and flotation, the cost of debt to POL is 6.93%. The tax savings reduces the cost of debt,
but flotation costs take back some of that savings.
For preferred stock:
Pnet 5 $21.50 2 $0.60 5 $20.90
new
5
Kpdf
D
$2.50
5
5 11.96%
Pnet
$20.90
Because there are no flotation costs associated with retained earnings, POL’s cost
of common equity remains at 15%.
Kret earn 5 15%
For the record, the following equation shows how flotation costs would affect
the cost of a new stock issue. The effect of flotation cost is most easily illustrated
with the constant dividend growth model. As with the preferred stock adjustment, we reduce the stock price by the amount of the flotation costs, which raises
the cost of equity to the company.
Chapter 8 • Cost of Capital
Knew stock 5
D1
1 gn
Pnet
269
(8.14)
where
Pnet 5 P 2 (flotation costs)
Note that POL’s after-tax cost of debt (6.93%), the cost of preferred 11.96%),
and the cost of equity (15%) are the component costs that Paula used in her
WACC worksheet, Exhibit 8.1. Using Equation (8.1), she multiplied these component costs by their desired proportions to derive the WACC. We have not
described in detail how Paula decided on the mix of common equity, preferred
stock, and bonds to finance the harness project. In the next section, we show how
she determined her financing mix. The financing mix is called capital structure.
Capital refers to long-term financing, such as that used to fund the harness project. Determining the best capital structure for a company raises some rather complicated issues, which we leave for Chapter 10.
Capital structure is the mix of debt,
preferred equity, and common equity.
Short-term financing is excluded.
The Financing Mix and Weights in the WACC
The weights in the WACC formula could reflect any target or desired financing
mix. Paula has chosen to finance the harness project using POL’s current mix of
capital. Generally, firms that are satisfied with their current capital mix will attempt to maintain those proportions.
The existing mix of capital can be determined by examining the right-hand side
(RHS) of the financial balance sheet. Recall that the financial balance sheet reflects
market values, unlike the accounting balance sheet’s book values. Current market
values are certainly closer to actual values than are historical accounting values. A
company’s common stock with a book value of $5 may have a current market value
of $100. If it decides to sell stock to finance an investment, it will surely not sell new
shares for $5. Public companies tend to use market rather than book values.8
Paula determined the current financing mix by estimating the market values
for each of POL’s capital sources. She first obtained the current prices for the
company’s bonds, preferred stock, and common stock. Next, she multiplied these
prices by the number of bonds or shares of stock outstanding to compute the
market value of each component. Summing these market values gave her the total market value of POL’s capital. The calculations are shown in Exhibit 8.2.
When possible, the proportions of each
component in the capital structure
should be calculated using market
rather than book weights.
Finance in the Firm
EXPLAINING A CHANGING COST OF CAPITAL
As mentioned in Chapter 7, project analysis involves virtually every unit within a company and
cuts across many disciplines. By necessity, cost of
capital calculations are performed centrally, often
in the office of the corporate treasurer, and are
provided to the various company units. Managers and analysts in these units may protest that
8Bruner,
et al., p. 17.
changing discount rates make planning nearly
impossible. They are especially upset when the
discount rate increases, placing some of their
planned investments in jeopardy. It is therefore
important that cost of capital calculations be
fully explained and changes justified by changing
capital market rates of return.
270
Chapter 8 • Cost of Capital
EXHIBIT 8.2
CALCULATING THE MARKET WEIGHTINGS
OF
EACH CAPITAL SOURCE
CAPITAL
COMPONENT
PRICE PER
NUMBER
TOTAL MARKET
BOND OR SHARE OUTSTANDING VALUE OF COMPONENT
Debt (bonds)
Preferred stock
Equity (retained cash)
$1,003.00
$21.50
$11.25
1,537
20,068
313,867
$1,541,611
$ 431,462
$3,531,004
$5,504,077
PROPORTION
28.0%
7.8%
64.2%
100.0%
Paula calculated the proportion for each component by dividing its market value
by the total market value of capital, $5,504,077.
proportion of common equity financing 5
3,531,004
5 64.2%
5,504,077
proportion of preferred stock financing 5
431,462
5 7.8%
5,504,077
proportion of debt financing 5
1,541,611
5 28.0%
5,504,077
Paula intends to finance the harness project using capital from these three
sources in these proportions. As we saw in Exhibit 8.1, the WACC for the harness project is 12.5%. We may confirm this with the WACC formula.
WACC 5 (Wd)(Kdnew)(1 2 t) 1 (Wpfd)(Kpfdnew) 1 (Wret earn)(Kret earn)
(8.15)
5 (0.28)(9.9)(1 2 0.30) 1 (0.078)(11.96) 1 (0.642)(.15)
5 1.94% 1 0.93% 1 9.63%
5 12.5%
Glancing at Equation 8.15, you may wonder why Paula doesn’t finance the entire project with debt and discount it at the after tax cost of debt. The after-tax
cost of debt is only (9.9%) (1 2 0.30) 5 6.93%. Discounting at 6.93% rather
than 12.5% would certainly raise the harness project’s NPV. The problem with
Finance in the Firm
ACCOUNTING VS. FINANCE
The widespread use of market rather than book
weights is a rather recent phenomenon. Book
weights have the advantages of being relatively
stable over time and being observable by anyone
with access to company financial statements.
Market weights change continually, and, for
many not schooled in finance, the calculations
are opaque because they require monitoring of
capital markets. This provides ample opportunity for mistrustful accountants and others to
believe that the calculation is performed more
with smoke and mirrors than with solid numbers. Of course, their suspicions are confirmed if
they discover that, in a year when no new capital was raised, their debt weighting fell from
30% to 20% of capital.
Chapter 8 • Cost of Capital
this scheme is that POL must maintain some balance between debt and equity.9
If debt were used this year, equity may have to be used next year to achieve the
desired balance. If POL financed next year’s project with equity, then to be consistent, it would discount that project at the 15% cost of equity. Consider two
projects, perhaps quite similar in most respects, one accepted and the other rejected just because POL is seeking some balance to its capital structure and not
because one project is better or worse than the other. This illustrates why it is important to discount all projects at the cost of capital and not at the cost of debt
one time and the cost of equity the next time, regardless of how a particular
project is financed.
WACC reflects the firm’s long-term capital mix. A firm that finances a project with either debt or equity will temporarily unbalance its capital structure and,
we can assume, will attempt to rebalance it the next time around. Firms often unbalance their capital structure temporarily to take advantage of scale economies
of large securities issues. In reality, POL would never fund such a small project by
selling both preferred stock and bonds, because flotation costs would be prohibitive. This project would probably be funded entirely from retained earnings,
meaning that POL would temporarily unbalance its capital structure.
271
A project should be discounted at the
WACC, rather than at the costs of individual capital components, regardless of how the project is financed.
Estimating the Discount Rate
for Individual Projects
For many, perhaps most, projects, the appropriate discount rate to use in the
NPV calculation is the firm’s weighted average cost of capital (WACC), as outlined in the previous section. However, there are circumstances in which WACC
is not the appropriate discount rate. Every company, of course, is risky, and this
risk is reflected in its WACC. Investors in a particularly risky company demand
higher returns on their securities, which increases the company’s WACC. In project analysis, we are actually interested in the risk of the particular project rather
than the company as a whole, and we would like the discount rate to reflect the
risk of the project. When we discount a project by the company’s WACC, we implicitly assume that project risk and company risk are identical. If they are not,
then we should adjust the project discount rate up or down accordingly. For example, if a company increases its risk by investing in high-risk projects, investors
expect a higher return; therefore these risky projects should carry a higher discount rate.
Paula believes that the harness project has the same risk as POL’s existing
business. Paula reasons that the harness is simply another product to add to
POL’s existing line of hardware and sailing gear. Therefore, the business risk of
the harness project is essentially identical to that of the company’s existing products. She understands that there are uncertainties, to be sure, in producing a new
product, but no more than in the normal course of extending and upgrading an
existing line of products. Paula also realizes that the relevant risk for estimating
required returns are the marketwide or nondiversifiable risks of the business.
(She apparently read Chapter 6.) The new harness is probably about as sensitive
to marketwide forces as are POL’s current products. All are sensitive to economic
recession (in which case sales of discretionary products will decline), changing
tastes, changes in tax codes, and so on.
9If
you don’t believe that the company must maintain some balance in its capital structure, read Chapter 10.
WACC is the appropriate discount rate
for projects whose risk is about equal
to the risk of the company as a whole.
272
Chapter 8 • Cost of Capital
Why a Project’s Risk May Differ
from the Company’s Overall Risk
While the harness fits neatly into POL’s existing product line, there are many occasions when this is not the case. In such instances we must estimate a discount
rate that reflects the project’s risk. This section describes why differences in risk
might arise and how discount rates for individual projects might be estimated.
Consider Campbell Soup. The company has a dominant position in its industry
and produces a product for which there is fairly constant demand. Thus we
would expect that Campbell Soup has average or slightly below-average risk.
Now suppose that Campbell’s managers propose two projects. The first is a
tomato soup with a spicy Mexican taste. This soup follows the successful introduction of a spicy Italian tomato soup in 1992. The second proposal is to start a
chain of small soup cafes—tentatively called “17 Flavors Soup Cafes.” The cafes
would feature 17 flavors (hence the name) of Campbell’s soups ready for immediate serving.
Do these two proposals have the same risk? Probably they do not. The spicy
Mexican soup is a standard Campbell’s product. Campbell Soup has enormous
experience evaluating, producing, marketing, and distributing such products. It
also has recent experience with a similar soup—the spicy Italian tomato soup. By
contrast, a chain of fast-food restaurants differs markedly from any of Campbell’s other businesses. The fast-food industry is very competitive, with several
dominant chains vying for market share. Campbell’s managers have little experience in this industry. Also, the two projects will probably respond differently to
economywide risk factors. For example, in a recession individuals tend to eat out
less but may consume more canned soup at home.
Campbell’s managers may reasonably conclude that the new soup flavor
project should be discounted at the company’s WACC. The new soup is analogous to POL’s harness project. Campbell’s managers would judge that the soup
cafes add risk to company, and therefore should take a higher discount rate.
Estimating a Risk-Adjusted
Discount Rate for NPV Analysis
Chapter 6 introduced the capital asset pricing model (CAPM) and the idea that
the capital markets price only market risk. This follows from the notion that
unique risk is generally absent from well-diversified portfolios. Projects also contain mostly market risk; therefore, we may use the CAPM to determine a project’s discount rate.
required return on a project 5 risk-free rate
(8.16)
1 (project beta) (market return 2 risk-free rate)
An asset beta is a measure of market
risk for a project.
The project beta, commonly called an asset beta, is not the same as the common
stock beta from Chapter 6; it is actually a measure of a project’s market risk. In
the next section we discuss how to estimate a project’s beta.
Estimating a Project’s Beta
Recall from Chapter 6 that beta is a measure of the extent to which the returns
on a stock move with changes in the returns of a market portfolio, such as the
S&P 500. Of course, there is no convenient market index for soup cafes, so we
Chapter 8 • Cost of Capital
273
Finance in the Firm
USE AND MISUSE OF RISK-ADJUSTED DISCOUNT RATES
The risk-adjusted discount rate (RADR) calculation depends on identifying pure-play companies.
Because such companies are illusory, the calculation is subject to second-guessing and criticism,
especially by those units in the company that are
assigned a high RADR. Unit managers may cry
foul and claim that the calculation is unreliable
and discriminatory. The only defense against such
charges is to make explicit the assumptions and
calculations that generated the RADR. Although
the process is inevitably flawed, it must be shown
to be as free of bias as possible. Top managers
may also use arbitrary RADRs as a pretext for altering the allocation of resources within the company. In this case, the distrust of the technique by
unit managers is fully justified.
cannot directly calculate the beta for Campbell’s project. Therefore, the analyst
must look for clues regarding the project’s risk. One widely used technique for
estimating a project’s cost of capital is the pure-play method. A pure-play is a
publicly traded firm that engages primarily in the same line of business as the
project being considered. The beta of this pure-play’s equity may then be found
and used as a proxy for the project’s beta.10 The pure-play’s beta may be fed
into the CAPM to estimate the appropriate risk-adjusted discount rate (RADR)
for the project.
Identifying a publicly traded pure-play firm is seldom easy. For the soup
cafes, Campbell’s managers may begin with small chains of specialized fast-food
restaurants. Another chain of soup cafes would be ideal, but none probably exists. Wendy’s would likely be a better proxy than McDonald’s because of size.
Perhaps Baskin-Robbins would be better yet: Baskin-Robbins is not too large,
and has a specialized menu, and ice cream is somewhat seasonal, as is soup. Ideally, several publicly traded pure-play firms would be identified.
Aside from identifying appropriate business lines for the pure-play firms,
Campbell’s managers must also consider their capital mix. The best choice is an
all equity-financed firm. If a pure-play can be found with no debt, the project’s
required return may be estimated directly using the CAPM. The project’s required return could then be used as the discount rate for NPV or as the hurdle
rate for IRR. Suppose, for example, there exists a chain of soup cafes that is all
equity financed. The beta for this company is 1.3. This beta may then be transferred to Campbell’s cafe project and a RADR could then be estimated.
We will assume rf 5 4% and E(Rm) 5 13%.
A pure-play is a publicly traded firm
that engages primarily in the same
line of business as the project being
considered.
The risk-adjusted discount rate
(RADR) applies to projects whose risk
is substantially different from company risk.
RADR 5 required Returnsoup cafes 5 rf 1 basset[E(Rm) 2 rf)]
5 4% 1 1.3(13% 2 4%) 5 15.7%
If the capital structure of the pure-play firm includes debt, we may estimate the
asset beta using the Hamada equation.11
basset 5
10Here
bequity
1 1 sD>Ed s1 2 td
(8.17)
we are assuming that the pure-play engages in the same business and uses the same mix of debt and equity
in its financing.
Robert Hamada, “The Effect of the Firm’s Capital Structure on the Systematic Risk of Common Stock,”
Journal of Finance, May 1972, 435–452.
11See
The Hamada equation may be used to
convert the equity beta of a pure-play
firm into an asset beta.
274
Chapter 8 • Cost of Capital
Here bequity is the beta of the pure-play’s common stock. The pure-play’s tax
rate is t and D/E is the ratio of the firm’s debt to equity, both at market value.
If we find a pure-play with debt of $1 million and equity worth $2 million, a tax
rate of 30%, and bequity equal to 1.5, we can estimate its asset beta as follows.
bassets 5
1.5
5 1.11
1 1 s1 2 0.3d 12
This beta could then be used to estimate the project’s appropriate discount rate.
RADR 5 4% 1 1.11(13% 2 4%) 5 13.99, or 14%
Of course, for many projects a pure-play cannot be found. The methods for estimating the RADR under such circumstances range from ad hoc techniques (like adding
or subtracting a few percentage points to the firm’s existing WACC) to developing
betas based on accounting information. Ad hoc estimates require careful judgment
on the part of the analyst. Should Campbell Soup, for example, add 2% to its current WACC to reflect the added risk of the cafes, or should it add 5%? Other new
projects may be perceived as being less risky than existing lines of business, so a few
percentage points would be subtracted from the current WACC. The difficulties encountered using this method are obvious, but at times there is no choice. Accounting betas are found by measuring the comovement of an accounting-based standard
of performance for a pure-play firm with a benchmark performance standard from
a broad sample of other firms. This technique is beyond the scope of this text but is
useful when a pure-play firm does not have publicly traded stock.
Ideally, each project will have its own discount rate reflecting its risk. In practice, large companies use divisional hurdle rates, so that, for example, projects in a
home appliances division carry a different RADR than do projects in broadcasting
division.
Summary
Choosing the correct rate at which to discount project cash flows is crucial to
valuing a capital project. The discount rate is the weighted average of the required return for each class of investor. The principal investor classes are the
bondholders, preferred stockholders, and common stockholders. Each of these
investor classes contributes capital to the firm as a whole, rather than to individual projects, and each is compensated for the risk that it incurs by investing in
the firm. The discount rate that provides each investor class with its required rate
of return is the weighted average cost of capital (WACC).
The WACC is the appropriate discount rate for a project whose risk is equal
to that of the firm as a whole. However, the cash flows of projects that increase
firm risk—and, therefore, the risk of its investors—should be discounted at a rate
greater than the WACC. In the same way, cash flows of projects that reduce firm
risk should be discounted at a rate less than the WACC. The rate that reflects
project specific risk is the risk adjusted discount rate (RADR).
Key Terms
cost of capital
weighted average cost of capital
(WACC)
cost of debt
cost of preferred stock
cost of common equity
Chapter 8 • Cost of Capital
equity-debt-risk premium
investment banks
underwriting
underwriting spread
flotation costs
venture capital firms
capital structure
asset beta
pure-play method
risk-adjusted discount rate (RADR)
Key Formulas
Cost of Debt
Kd 5 Yield to Maturity
the after-tax cost of debt 5 Kd (1 2 t)
Kd new 5 YTM
YTM calculated using Pnet for Bonds
Cost of Preferred Stock
Kpfd 5
dividend
share price
PNet 5 P 2 (flotation costs)
Cost of Common Equity
CAPM
Ke 5 rf 1 bi[E(rm) 2 rf ]
Dividend Growth
Ke 5
D1
1 gn
P0
Equity-Debt Risk Premium
Ke 5 Kd 1 RP
Knew stock 5
D1
1 gn
Pnet
Weighted Average Cost of Capital
WACC 5 (Wd) (Kdnew) (1 2 t) 1 (Wpfd) (Kpfdnew) 1 (Wret earn) (Kret earn)
Calculating the Asset Beta
bassets 5
bequity
1 1 sD>Ed s1 2 td
Questions
1. A fellow student comments that if a project has an NPV equal to zero, then
the project will generate no cash flows for the common stockholders. You argue that it will produce such cash flows. What is your argument? (By the
way, you are correct. It will produce cash for the common stockholders.)
275
276
Chapter 8 • Cost of Capital
2. Accounting balance sheets reflect the book values of claims, based on the
historical contributions of capital suppliers. Suppose a firm raised its initial
capital 10 years ago, and its accounting statements currently reflect a capital
mix of half debt and half equity. No more debt has been issued since the
original bonds were sold. Interest rates have not changed, but the firm has
been exceptionally successful.
a. Do you think common stockholders would be willing to sell their stock
today for its book value?
b. Interest rates have not changed, but the firm’s bonds are selling at a premium, above their book values. Why?
c. If the firm has been wildly successful, and given your answers to parts (a)
and (b), what do you think has happened to the total market value of the
firm? Is it above or below its total book value?
d. How do you think the firm’s capital mix, based on market values, compares to the 50–50 mix reflected on the accounting balance sheet?
3. Explain why (1 2 t) does not appear in the cost of preferred and the cost of
common equity formulas.
4. Suppose a firm uses all equity financing, but half that financing is internal equity and half is external equity.
a. Name the capital components for the firm.
b. What will be the weights for each component?
c. Write the firm’s WACC formula.
5. Which of the following hypothetical projects would appropriately use the
firm’s current WACC as the discount rate in capital budgeting, and which do
you feel require some risk adjustment?
a. Boeing is considering producing a new version of the 777 aircraft, altered
for use as a cargo plane. It will be called the 777C.
b. Pogo Offshore Ltd., discussed in this chapter, is analyzing the market for
producing windsurfing equipment.
c. AT&T is considering the production of fax machines.
d. McDonald’s is analyzing the addition of a new menu item, onion rings.
6. A project with an NPV 5 0 provides all corporate investors with their required return; therefore all investors are satisfied. Do you agree or disagree
with this statement?
7. Consider a project for which NPV 5 $18,000. Which investors have a claim
on this net present value amount?
8. There are three methods of estimating the cost of corporate equity. Name or
briefly describe two of these methods.
9. Flotation costs __________ (raise/lower) the corporate cost of capital.
10. (True/False.) A project beta provides a way to estimate the required return to
reflect project risk.
11. The corporate weighted average cost of capital is the appropriate required
rate of return for which of the following?
a. All corporate projects
b. Projects whose risk is about equal to overall corporate risk
c. Projects whose risk is generally less than overall corporate risk
d. Projects whose risk is generally greater than overall corporate risk
e. None of the above
Chapter 8 • Cost of Capital
Demonstration Problem
Stan & Ollie’s WACC
Stan and Ollie’s Popcorn is considering a new, fat-free product for distribution in
movie theaters. The firm’s management believes that the new product has about
the same risk as the firm’s current product line. Management therefore believes
the firm’s current WACC is the appropriate discount rate for finding the project’s
NPV. The RHS of the firm’s financial balance sheet, shown here, reflects the market value of each capital component.
CAPITAL SOURCE
MARKET VALUE
Bonds, 100,000 outstanding; 8% annual coupon rate;
payable semiannually; mature in 15 years
Preferred stock, $5 annual dividend, 2,000,000 shares outstanding
Common stock, 13,000,000 shares outstanding
Total
$ 64,636,183
$ 71,420,000
$312,000,000
$448,056,183
The common stock just paid a dividend of $2.25 per share. Dividends are expected to grow at 6% annually. Find Stan and Ollie’s WACC if the tax rate is
34%.
solution
WACC 5 Wd Kd (1 2 t) 1 WpfdKpfd 1 WeKe
step 1
Find the weights of each capital source.
Wd 5
5
value debt
total value
$64,636,183
$448,056,183
5 0.1443
Wpfd 5
5
We 5
5
value preferred
total value
$71,420,000
5 0.1594
$448,056,183
value equity
total value
$312,000,000
5 0.6963
$448,056,183
Check:
Wd 1 Wpfd 1 We 5 1.0000
0.1443 1 0.1594 1 0.6963 5 1.0000
1.0000 5 1.0000
277
278
Chapter 8 • Cost of Capital
Now, we know:
WACC 5 (0.1443) Kd (1 2 t) 1 (0.1594) Kpfd 1 (0.6963) Ke
step 2
Find the costs.
a. Kd 5 YTM on bonds. The price of each bond is $64,636,183 divided by the
total number of bonds outstanding, 100,000: $64,636,1834100,000 5
$646.
$646 5
$40
$40
$40
1
1...1
s1 1 YTMd 1
s1 1 YTMd 2
s1 1 YTMd 30
$1,000
1
s1 1 YTMd 30
Because the annual coupon rate is 8%, the annual coupon payment is $80, but
payments are made semiannually and therefore equal $40 each. Because there are
15 years to maturity, there will be 30 semiannual periods until the bond matures.
In absence of a stated maturity or par value, $1,000 is assumed. Solving for
YTM results in a solution of
YTM 5 6.79% semiannually or
YTM 5 13.58% per year
Kd 5 13.58%
b. The price per share of the preferred can be found by dividing the total market value by the number of preferred shares outstanding,
price per share 5
Kpfd 5
$71,420,000
5 $35.71
2,000,000
$5
5 14%
$35.71
c.
Ke 5
D1
1 gn
P0
gn 5 6% 5 0.06
D1 5 D0(1 1 gn) 5 $2.25(1.06) 5 $2.385
P0 5
$312,000,000
5 $24
13,000,000
Ke 5
$2.385
1 0.06 5 0.1594 5 15.94%
$24
step 3
Insert the costs and tax rate, and solve.
WACC 5 (0.1443)(0.1358)(1 2 0.34) 1 (0.1594)(0.14) 1 (0.6963)(0.1594)
5 0.01293 1 0.02232 1 0.11099
5 0.14624
5 14.624%
279
Chapter 8 • Cost of Capital
Problems
1. Cost of Debt
Three years ago, Ron’s Rubbish Service issued 30-year bonds at par with a
coupon rate of 8%, payable semiannually. Today, these bonds are selling for
$875 each. What is Ron’s after-tax cost of debt if the company is in the 28%
tax bracket?
2. Cost of Equity
Dr. Watson’s Frosty Mornin’ Spring Water, Inc., has an equity beta of 1.5. Assuming t-bills are yielding 7% annually and the market risk premium is 5%,
what is Watson’s cost of equity?
3. Cost of Equity
Telebrations is a rapidly growing business. Its niche is allowing virtual parties by providing a closed-circuit video linkup for people all across the country. Thus, grandparents in New Jersey can attend Tommy’s first birthday in
Arizona. Telebrations’ dividends have been growing at an 8% rate annually.
The last dividend paid was $1.15 and the stock is selling for $9.50 per share.
a. What is Telebrations’ cost of retained earnings?
b. If flotation costs are 30¢ per share, what is Telebrations’ cost of new
stock?
4. Cost of Equity
If Telebrations’ (see Problem 3) bonds yield 13%, what would be a reasonable range, in your estimation, for the firm’s cost of equity?
5. Cost of Preferred Stock
What is a firm’s cost of preferred stock if it pays an annual dividend of $3 a
share and is selling for $18 per share?
6. Calculating Weights
A corporation’s capital structure consists of bonds and common stock. There
are $8 million in corporate bonds outstanding, selling at par value. Book
value of the common equity is $6 million. There are 1 million shares of common stock outstanding. Currently, the market price per share is $18.
a. What are the proportions of debt and equity using book values?
b. What are the proportions of debt and equity using market values?
c. Which is preferred for calculating WACC, book or market values?
7. Calculating Weights
A company has a capital structure as reflected on the following balance sheet.
Bonds ($1000 par)
500 outstanding
Preferred stock ($3 coupon)
100,000 shares outstanding
Common stock
100,000 shares outstanding
$ 500,000
$ 300,000
$1,000,000
a. What are the firm’s capital structure proportions based on book values?
b. The bonds pay interest semiannually, have an 8% annual coupon rate,
and mature in 10 years. Currently, investors require a 6% annual return
from these bonds. What is the current price of each bond? What is the total current value of these bonds?
c. The required return for the preferred stock is 8%. What is the current
price per share of the preferred and what is the preferred stock total value?
excel
280
Chapter 8 • Cost of Capital
d. Common stock is expected to pay a $1.10 dividend next year. Dividends are
expected to grow at an 8% rate for the foreseeable future. Investors require
a 10% return from their investment in securities that have the same risk as
this stock. What is the stock’s current price and total value?
e. Construct the RHS of this corporation’s financial balance sheet. Then
find the weights, based on market values that would be used in finding
this firm’s WACC.
8. Calculating WACC
Mainsail Corporation is financed by the following proportions of capital:
Long-term debt
Preferred stock
Common equity (retained cash)
Mainsail’s corporate tax rate is
excel
30%
5%
65%
30%
a. The yield to maturity on long-term debt is 9%. What is the after-tax cost
of this debt to Mainsail?
b. The preferred stock dividend is $6.50 per share. The price of the preferred stock is $50. What is the cost of preferred stock to Mainsail?
c. The risk-free interest rate is 8%. The market risk premium is 5%. The
company’s beta is 1.3. What is the cost of common equity to Mainsail?
d. Calculate the weighted average cost of capital for Mainsail.
e. If the project is financed solely by debt, what is the required rate of return
for the project, assuming its risk is the same as that of the overall company and the firm will maintain its current capital structure as its longterm target?
9. Comprehensive WACC
Santa Fe Industries manufactures frozen tamales, which are distributed throughout the Southwest. The corporation is considering a geographic expansion
into New England. The project requires additional processing capacity in the
Santa Fe factory. Total initial investment will be $2,000,000. You have been
hired by Santa Fe to estimate the cost of capital for the project. The firm
wishes to maintain its current capital mix and considers the project to have
risk equal to its existing business. Santa Fe’s management has provided the following details of its existing capital from its accounting balance sheet.
Long-term debt
Bank loan*
Bonds (originally sold at par)†
Equity
Common stock, $1 per share par
Additional paid in capital
Retained earnings
*The
$ 1,500,000
$ 6,000,000
$ 1,000,000
$ 9,000,000
$13,000,000
bank loan floats at the prime rate.
are $1,000 par value, mature 12 years from today, and pay coupons annually at a 9% rate.
†Bonds
You have done some research on your own. The following notes reflect the
pertinent information.
281
Chapter 8 • Cost of Capital
Bonds: Santa Fe’s bonds are selling for $920. Investment bankers charge $50
per bond to sell a new issue.
Bank loan: The bank is willing to extend a long-term loan to Santa Fe at 9%
current APR, with interest paid monthly. The bank will waive any loan origination fees.
Equity: Santa Fe has no internal cash flow available for investment in the
project. Common stock is selling for $24 per share. Dividends were $1.20
last year and were $0.50 per share 10 years ago. Investment bankers will
charge $3 per share to market a new issue of stock.
a. What are the components of capital for Santa Fe?
b. What are the weights of each component?
c. Of the $2,000,000, how many dollars must be raised from each capital
source?
d. For the new bonds to be sold at par value ($1,000 each), what annual
coupon rate should they carry?
e. How many bonds must Santa Fe sell? (Round up to the next bond if your
answer is not a whole number.)
f. How many shares of stock must be sold to raise the needed capital?
(Round up if you have a fractional answer.)
g. What is the cost of bond debt? What is the after tax cost of bond debt if
Santa Fe is in the 34% marginal tax bracket?
h. What is the cost of bank debt? What is the after tax cost of bank debt?
i. What is the cost of equity?
j. Does the cost of equity you calculated in part (i) fall within the range
found using the equity-debt risk premium?
k. What is the WACC?
10. RADR
Santa Fe (Problem 9) is also considering starting a new chain of fast-food
restaurants, to be called the Santa Fe Cafe. These will be funded using 100%
equity, all of it internally generated cash. To calculate the risk-adjusted discount
cost of capital for this project, you have found the betas of two pure-plays:
Tijuana Tacos
The Big Burrito
beta 5 1.6
beta 5 1.4
You note that Tijuana Tacos’ capital mix is 20% debt and 80% equity, while The
Big Burrito uses no debt in its capital structure. Tijuana Taco’s tax rate is 33%.
a. Estimate Santa Fe Cafe’s beta.
b. The market risk premium has historically been close to 6%, and t-bills are
yielding 5.7%. What is the cost of equity for the cafe project?
c. Will the WACC for the project differ from the cost of equity in this case?
11. Calculating NPV and IRR
If the Santa Fe Cafe project (Problem 10) requires an initial investment of
$1,500,000 and is expected to generate cash flows of $180,000 in year 1,
$250,000 in year 2, and $300,000 in each of the next 8 years, what is the
project’s NPV? What is its IRR? Would you recommend that the project be
pursued? Why or why not?
12. RADR
Suppose that Campbell Soup finds a comparable firm with which it can estimate the beta of the 17 Flavors Soup Cafes project (see text for a complete
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Chapter 8 • Cost of Capital
excel
description). The pure-play firm is called Chicago Soup Kitchens. Chicago’s
equity beta is 1.30, its tax rate is 35%, and its debt-equity ratio based on
market values is 13. What is your estimate of the 17 Flavors’ asset beta?
13. Calculating WACC
Barnstorm Aircraft, Inc. has a target capital structure of 45% debt and 55%
equity. Its cost of equity is 19%, its tax rate is 34%, and its cost of debt is
13%. What is Barnstorm’s WACC?
14. Calculating Weights
The management of Blue Thumb Tools believes the firm’s current capital
structure is optimal and intends to maintain it in the future. Blue Thumb’s
bonds are selling for $950 each. Its common stock is selling for $37 a share
and its preferred stock is selling for $88 per share. There are 50,000 bonds
outstanding, 10,000,000 shares of stock, and 3,000,000 shares of preferred
stock outstanding, respectively. What are the current weights of Blue
Thumb’s capital sources?
15. Calculating WACC
Blue Thumb’s (see Problem 14) stock has a beta of 1.2. The current t-bill
yield is 5.5% and the expected return on the market portfolio is 11.5%. The
company’s preferred stock pays a $8.50-per-share dividend each year. The
yield to maturity of Blue Thumb’s bonds is currently 9.7%. If Blue Thumb is
in the 29% tax bracket, what is the company’s WACC?
16. NPV
Suppose Blue Thumb Tools (Problem 15) is considering the introduction of a
new, heavier hammer to be used for driving spikes. The new hammer is called
the Black Thumb. Use the WACC you found in Problem 15 to find the NPV
of the Black Thumb project. The project’s projected cost and cash flows are
given here.
cost 5 $459,000
YEAR
CASH FLOW
1
2
3
4
$178,000
$239,000
$225,000
$180,000
Internet Exercise
Cost of Capital Data
Ibbotson Associates provides financial data for commercial and academic use.
Log on to the Ibbotson Web site, http://www.ibbotson.com. View the Cost of
Capital Center and Cost of Capital Yearbook pages.
a. Summarize the cost of capital information provided by Ibbotson.
b. Why do you think that clients would be willing to pay such high prices for
this information? What might they use if for?
c. From the Cost of Capital Center, click on Research Papers and read the abstracts of the papers. Looking at the data provided by Ibbotson and the topics of the research papers, is there more focus on cost of debt or cost of equity? Why do you think this is true?
appendix
8
The Best Proxy for
the Risk-Free Rate
T
raditionally, returns on the 3-month treasury bill have been used as the
risk-free rate in calculating a company’s cost of equity. The bill is not only
free of default risk, it is also virtually free of interest-rate risk because of
its short life span. Today practitioners favor use of a long-term treasury bond,
primarily because it more closely matches the long-term character of common
stocks. In a widely used practitioner’s guide to valuation, Tom Copeland et al.
suggest using the 10-year treasury bond rate.12 In an article summarizing practices in estimating a firm’s cost of capital, Bruner et al. report that only 4% of
responding companies used the 3-month treasury bill rate, while 70% used rates
on treasury bonds of 10 or more years’ maturity.13
The choice of a risk-free rate can significantly alter the calculated cost of equity. Returns on 10-year treasury bonds have averaged about 1.5% higher than
those on treasury bills.14 Reworking the cost of equity calculation, with a beta of
1.2, the cost of equity for Pacific Offshore Ltd., we get the following.
Risk-free rate
Market return
Market risk premium
USING THE T-BILL RATE
USING THE T-BOND RATE
4%
13%
9%
5.5%
13%
7.5%
Using the two estimates of the risk-free rate to calculate POL’s cost of equity
gives us
R(r)POL 5 rf 1 bPOL 1 [E(rm) 2 rf]
R(r)POL 5 4% 1 1.2(9%) 5 14.8% (t-bill rate)
R(r)POL 5 5.5% 1 1.2(7.5%) 5 14.5% (t-bond rate)
The magnitude of the differences in these estimates is dependent on beta. With a
beta of 1, it does not matter which risk-free rate is used. In either case, the cost
of equity is 13%. For betas below or above 1, the cost of equity estimates will
differ, depending on which risk-free rate is used; the greater the distance from 1,
the greater the difference. In the POL example, if beta 5 1.8, the cost of equity
would be 20.2% using t-bills and 19% using t-bonds.
12Tom Copeland, Tim Koller, and Jack Murrin, Valuation: Measuring and Managing the Value of Companies
(New York: John Wiley & Sons, 1996), Chapter 8.
13Bruner, et al., 13–28.
14Bruner, et al., 19.
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