COST OF CAPITAL
LO1 How to determine a firm’s cost of equity capital.
LO2 How to determine a firm’s cost of debt.
LO3 How to determine a firm’s overall cost of capital.
LO4 How to correctly include flotation costs in capital budgeting projects.
LO5 Some of the pitfalls associated with a firm’s overall cost of capital and what to do about them.
Answers to Concepts Review and Critical Thinking Questions
2. (LO3) Book values for debt are likely to be much closer to market values than are equity book values.
4. (LO3) Interest expense is tax-deductible. There is no difference between pretax and aftertax equity costs.
6. (LO1) Two primary advantages of the SML approach are that the model explicitly incorporates the relevant
risk of the stock and the method is more widely applicable than is the dividend discount model model, since
the SML doesn’t make any assumptions about the firm’s dividends. The primary disadvantages of the SML
method are (1) three parameters (the risk-free rate, the expected return on the market, and beta) must be
estimated, and (2) the method essentially uses historical information to estimate these parameters. The risk-free
rate is usually estimated to be the yield on very short maturity T-bills and is, hence, observable; the market risk
premium is usually estimated from historical risk premiums and, hence, is not observable. The stock beta,
which is unobservable, is usually estimated either by determining some average historical beta from the firm
and the market’s return data, or by using beta estimates provided by analysts and investment firms.
a. This only considers the dividend yield component of the required return on equity.
b. This is the current yield only, not the promised yield to maturity. In addition, it is based on the book
value of the liability, and it ignores taxes.
c. Equity is inherently more risky than debt (except, perhaps, in the unusual case where a firm’s assets have
a negative beta). For this reason, the cost of equity exceeds the cost of debt. If taxes are considered in this
case, it can be seen that at reasonable tax rates, the cost of equity does exceed the cost of debt.
10. (LO5) If the different operating divisions were in much different risk classes, then separate cost of capital
figures should be used for the different divisions; the use of a single, overall cost of capital would be
inappropriate. If the single hurdle rate were used, riskier divisions would tend to receive more funds for
investment projects, since their return would exceed the hurdle rate despite the fact that they may actually plot
below the SML and, hence, be unprofitable projects on a risk-adjusted basis. The typical problem encountered
in estimating the cost of capital for a division is that it rarely has its own securities traded on the market, so it is
difficult to observe the market’s valuation of the risk of the division. Two typical ways around this are to use a
pure play proxy for the division, or to use subjective adjustments of the overall firm hurdle rate based on the
perceived risk of the division.
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to
space and readability constraints, when these intermediate steps are included in this solutions manual, rounding
may appear to have occurred. However, the final answer for each problem is found without rounding during any
step in the problem.
1. (LO1) With the information given, we can find the cost of equity using the dividend growth model. Using this
model, the cost of equity is:
R E [$2.40(1.055)/$52] + .055 = .1037 or 10.37%
2. (LO1) Here we have information to calculate the cost of equity using the CAPM. The cost of equity is:
R E .053 + 1.05(.12 – .053) = .1234 or 12.34%
4. (LO1) To use the dividend growth model, we first need to find the growth rate in dividends. So, the increase in
dividends each year was:
g1= ($1.12 – 1.05)/$1.05 = .0667 or 6.67%
g2= ($1.19 – 1.12)/$1.12 = .0625 or 6.25%
g3= ($1.30 – 1.19)/$1.19 = .0924 or 9.24%
g4= ($1.43 – 1.30)/$1.30 = .1000 or 10.00%
So, the average arithmetic growth rate in dividends was:
g = (.0667 + .0625 + .0924 + .1000)/4 = .0804 or 8.04%
Using this growth rate in the dividend growth model, we find the cost of equity is:
R = [$1.43(1.0804)/$45.00] + .0804 = .1147 or 11.47%
Calculating the geometric growth rate in dividends, we find:
$1.43 = $1.05(1 + g)
g = .0803 or 8.03%
The cost of equity using the geometric dividend growth rate is:
R E [$1.43(1.0803)/$45.00] + .0803 = .1146 or 11.46%
6. (LO2) The pretax cost of debt is the YTM of the company’s bonds, so:
P0= $1,070 = $35(PVIFA R%,30 + $1,000(PVIF R%,30
R = 3.137%
YTM = 2 × 3.137% = 6.27%
And the aftertax cost of debt is:
R D .0627(1 – .35) = .0408 or 4.08%
8. (LO2) The book value of debt is the total par value of all outstanding debt, so:
BV D $80,000,000 + 35,000,000 = $115,000,000
To find the market value of debt, we find the price of the bonds and multiply by the number of bonds.
Alternatively, we can multiply the price quote of the bond times the par value of the bonds. Doing so, we find:
MV =D.95($80,000,000) + .61($35,000,000)
MV =D$76,000,000 + 21,350,000
14-2 The YTM of the zero coupon bonds is:
PZ= $610 = $1,000(PVIF R%,14
R = 3.594%
YTM = 2 × 3.594% = 7.19%
So, the aftertax cost of the zero coupon bonds is:
RZ= .0719(1 – .35) = .0467 or 4.67%
The aftertax cost of debt for the company is the weighted average of the aftertax cost of debt for all
outstanding bond issues. We need to use the market value weights of the bonds. The total aftertax cost of debt
for the company is:
RD= .0552($76/$97.35) + .0467($21.35/$97.35) = .0534 or 5.34%
10. (LO3) Here we need to use the debt-equity ratio to calculate the WACC. Doing so, we find:
WACC = .15(1/1.65) + .09(.65/1.65)(1 – .35) = .1140 or 11.40%
a. The book value of equity is the book value per share times the number of shares, and the book value of
debt is the face value of the company’s debt, so:
BV =E11,000,000($6) = $66,000,000
BV =D$70,000,000 + 55,000,000 = $125,000,000
So, the total value of the company is:
V = $66,000,000 + 125,000,000 = $191,000,000
And the book value weights of equity and debt are:
E/V = $66,000,000/$191,000,000 = .3455
D/V = 1 – E/V = .6545
b. The market value of equity is the share price time