Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
CHAPTER 12
RISK, COST OF CAPITAL, AND
VALUATION
Answers to Concepts Review and Critical Thinking Questions
1. No. The cost of capital depends on the risk of the project, not the source of the money.
2. Interest expense is tax-deductible. There is no difference between pretax and aftertax equity costs.
3. You are assuming that the new project’s risk is the same as the risk of the firm as a whole, and that the
firm is financed entirely with equity.
4. 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 DCF model, since the SML
doesn’t make any assumptions about the firm’s dividends. The primary disadvantages of the SML
by analysts and investment firms.
5. The appropriate aftertax cost of debt to the company is the interest rate it would have to pay if it were
to issue new debt today. Hence, if the YTM on outstanding bonds of the company is observed, the
company has an accurate estimate of its cost of debt. If the debt is privately-placed, the firm could still
6. 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.
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
7. RSup = .12 + .75(.08) = .1800, or 18.00%
Both should proceed. The appropriate discount rate does not depend on which company is investing;
$1 million regardless of who takes it.
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
9. The discount rate for the projects should be lower than the rate implied by the security market line.
The security market line is used to calculate the cost of equity. The appropriate discount rate for
projects is the firm’s weighted average cost of capital. Since the firm’s cost of debt is generally less
that the firm’s cost of equity, the rate implied by the security market line will be too high.
10. Beta measures the responsiveness of a security's returns to movements in the market. Beta is
determined by the cyclicality of a firm's revenues. This cyclicality is magnified by the firm's operating
and financial leverage. The following three factors will impact the firm’s beta. (1) Revenues. The
cyclicality of a firm's sales is an important factor in determining beta. In general, stock prices will rise
when the economy expands and will fall when the economy contracts. As we said above, beta measures
the responsiveness of a security's returns to movements in the market. Therefore, firms whose revenues
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.
Basic
1. With the information given, we can find the cost of equity using the CAPM. The cost of equity is:
RS = .041 + 1.13(.11 – .041)
RS = .1190, or 11.90%
P0 = $950 = $32(PVIFAR%,28) + $1,000(PVIFR%,28)
R = 3.482%
RB = 2 × 3.482% = 6.96%
P0 = $1,040 = $29(PVIFAR%,46) + $1,000(PVIFR%,46)
R = 2.746%
RB = 2 × 2.746% = 5.49%
Aftertax cost of debt = 5.49%(1 – .35)
Aftertax cost of debt = 3.57%
4. The book value of debt is the total par value of all outstanding debt, so:
BVB = $55,000,000 + 75,000,000
BVB = $130,000,000
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:
B = 1.04($55,000,000) + .63($75,000,000)
B = $104,450,000
RWACC = .75(.121) + .25(.063)(1 – .35)
RWACC = .1010, or 10.10%
RWACC = .13(1/1.45) + .07(.45/1.45)(1 – .35)
RWACC = .1038, or 10.38%
equation, we find:
RWACC = .0860 = .112(S/V) + .064(B/V)(1 – .35)
Rearranging the equation, we find:
.0860(V/S) = .112 + .064(.65)(B/S)
Now we must realize that the V/S is just the equity multiplier, which is equal to:
8. 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:
Equity = 6,400,000($4)
Equity = $25,600,000
Debt = $60,000,000 + 50,000,000
Debt = $110,000,000
Equity/Value = $25,600,000/$135,600,000
Equity/Value = .1888
S = 6,400,000($59)
S = $377,600,000
Using the relationship that the total market value of debt is the price quote times the par value of
the bond, we find the market value of debt is:
B = 1.083($60,000,000) + 1.089($50,000,000)
B = $119,430,000
c. The market value weights are more relevant.
9. First, we will find the cost of equity for the company. The information provided allows us to solve for
the cost of equity using the CAPM, so:
RS = .031 + 1.2(.07)
RS = .1150, or 11.50%
XB1 = .544
Now we can multiply the weighted average cost of debt times one minus the tax rate to find the
weighted average aftertax cost of debt. This gives us:
RB = (1 – .35)[(.544)(.0522) + (.456)(.0612)]
RB = .0366, or 3.66%
Using these costs and the weight of debt we calculated earlier, the WACC is:
RWACC = .7597(.1150) + .2403(.0366)
RWACC = .0962, or 9.62%
10. a. Using the equation to calculate WACC, we find:
RWACC = .096 = (1/1.45)(.124) + (.45/1.45)(1 – .35)RB
RWACC = .096 = (1/1.45)RS + (.45/1.45)(.064)
11. We will begin by finding the market value of each type of financing. We find:
B = 7,000($1,000)(1.05)
B = $7,350,000
S = 180,000($58)
S = $10,440,000
And the total market value of the firm is:
V = $7,350,000 + 10,440,000
V = $17,790,000
RB = (1 – .35)(.0558)
RB = .0363, or 3.63%
Now we have all of the components to calculate the WACC. The WACC is:
B = 230,000($1,000)(1.04)
B = $239,200,000
S = 9,100,000($41)
S = $373,100,000
And the total market value of the firm is:
V = $239,200,000 + 373,100,000
V = $612,300,000
First we can find the cost of equity using the CAPM. The cost of equity is:
RS = .031 + 1.20(.07)
RS = .1150, or 11.50%
RB = (1 – .35)(.0586)
RB = .0381, or 3.81%
b. Using the CAPM to consider the projects, we need to calculate the expected return of each project
given its level of risk. This expected return should then be compared to the expected return of the
project. If the return calculated using the CAPM is lower than the project expected return, we
should accept the project; if not, we reject the project. After considering risk via the CAPM:
E[W] = .035 + .75(.11 – .035) = .0913 < .094, so accept W
E[X] = .035 + .90(.11 – .035) = .1025 > .101, so reject X
E[Y] = .035 + 1.15(.11 – .035) = .1213 > .119, so reject Y
14. a. He should look at the weighted average flotation cost, not just the debt cost.
b. The weighted average flotation cost is the weighted average of the flotation costs for debt and
equity, so:
fT = .03(.65/1.65) + .07(1/1.65)
fT = .0542, or 5.42%
Amount raised(1 – .0542) = $25,000,000
Amount raised = $25,000,000/(1 – .0542)
Amount raised = $26,433,835
fT = .65(.07) + .05(.04) + .30(.03)
fT = .0565, or 5.65%
And the total cost of the equipment including flotation costs is:
Amount raised(1 – .0565) = $55,000,000
Amount raised = $55,000,000/(1 – .0565)
16. Using the debt-equity ratio to calculate the WACC, we find:
RWACC = (.55/1.55)(.049) + (1/1.55)(.124)
RWACC = .0974, or 9.74%
Since the project is riskier than the company, we need to adjust the project discount rate for the
additional risk. Using the subjective risk factor given, we find:
Project discount rate = 9.74% + 2%
Project discount rate = 11.74%
17. We will begin by finding the market value of each type of financing. We will use B1 to represent the
coupon bond, and B2 to represent the zero coupon bond. So, the market value of the firm’s financing
is:
BB1 = 90,000($1,000)(1.064)
BB1 = $95,760,000
BB2 = 280,000($1,000)(.158)
BB2 = $44,240,000
P = 150,000($84)
S = $176,800,000
And the total market value of the firm is:
V = $95,760,000 + 44,240,000 + 12,600,000 + 176,800,000
V = $329,400,000
YTM = 2.735% × 2 = 5.47%
RB1 = (1 – .40)(.0547)
RB1 = .0328, or 3.28%
P0 = $158 = $1,000(PVIFR%,60)
R = 3.123%
YTM = 3.123% × 2 = 6.25%
assumes semiannual compounding, consistent with a coupon bond. Also remember that, even though
the company does not make interest payments, the accrued interest is still tax deductible for the
company.
To find the required return on preferred stock, we can use the preferred stock pricing equation, which
is the level perpetuity equation, so the required return on the company’s preferred stock is:
RP = D1/P0
RP = $4/$84
