CHAPTER 13
RISK, COST OF CAPITAL, AND CAPITAL
BUDGETING
Answers to Concepts Review and Critical Thinking Questions
2. Interest expense is tax-deductible. There is no difference between pretax and aftertax equity costs.
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
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
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.
7. RSup = .12 + .75(.08) = .1800, or 18.00%
Both should proceed. The appropriate discount rate does not depend on which company is investing;
8. 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
9. The discount rate for the projects should be lower than the rate implied by the security market line.
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
(3) Financial leverage. Financial leverage arises from the use of debt in the firm’s capital structure. A
levered firm must make fixed interest payments regardless of its revenues. The effect of financial
leverage on beta is analogous to the effect of operating leverage on beta. Fixed interest payments cause
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.
Basic
1. With the information given, we can find the cost of equity using the CAPM. The cost of equity is:
2. The pretax cost of debt is the YTM of the company’s bonds, so:
P0 = $950 = $30(PVIFAR%,34) + $1,000(PVIFR%,34)
RB = 6.49%
3. a. The pretax cost of debt is the YTM of the company’s bonds, so:
P0 = $1,060 = $29.50(PVIFAR%,54) + $1,000(PVIFR%,54)
b. The aftertax cost of debt is:
4. The book value of debt is the total par value of all outstanding debt, so:
BVB = $25,000,000 + 60,000,000
BVB = $85,000,000
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:
The YTM of the zero coupon bonds is:
So, the aftertax cost of the zero coupon bonds is:
Aftertax cost of debt = .0433(1 – .22)
5. Using the equation to calculate the WACC, we find:
6. Here we need to use the debt-equity ratio to calculate the WACC. Doing so, we find:
7. Here we have the WACC and need to find the debt-equity ratio of the company. Setting up the WACC
equation, we find:
RWACC = .0910 = .11(S/V) + .064(B/V)(1 – .21)
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 = 7,600,000($4) = $30,400,000
Debt = $80,000,000 + 65,000,000 = $145,000,000
b. The market value of equity is the share price times the number of shares, so:
S = 7,600,000($67) = $509,200,000
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:
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:
Next, we need to find the YTM on both bond issues. Doing so, we find:
To find the weighted average aftertax cost of debt, we need the weight of each bond as a percentage
of the total debt. We find:
XB1 = 1.095($80,000,000)/$160,660,000 = .545
10. a. Using the equation to calculate WACC, we find:
RWACC = .101 = (1/1.38)(.12) + (.38/1.38)(1 – .25)RB
11. We will begin by finding the market value of each type of financing. We find:
B = 17,000($2,000)(1.05) = $35,700,000
S = 425,000($67) = $28,475,000
Now, we can find the cost of equity using the CAPM. The cost of equity is:
And the aftertax cost of debt is:
RB = (1 – .21)(.0452)
12. a. We will begin by finding the market value of each type of financing. We find:
B = 175,000($1,000)(1.06) = $185,500,000
S = 6,400,000($53) = $339,200,000
And the total market value of the firm is:
b. For projects equally as risky as the firm itself, the WACC should be used as the discount rate.
First we can find the cost of equity using the CAPM. The cost of equity is:
And the aftertax cost of debt is:
RB = (1 – .22)(.0574)
13. a. Projects Y and Z.
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
14. a. He should look at the weighted average flotation cost, not just the debt cost. If the company uses
only debt to fund this project, it will have to issue equity later to maintain its capital structure.
b. The weighted average flotation cost is the weighted average of the flotation costs for debt and
equity, so:
15. We first need to find the weighted average flotation cost. Doing so, we find:
fA = .70(.07) + .05(.04) + .25(.03)
16. Using the debt-equity ratio to calculate the WACC, we find:
RWACC = (.65/1.65)(.043) + (1/1.65)(.11)
RWACC = .0836, or 8.36%
Since the project is riskier than the company, we need to adjust the project discount rate for the
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. The market value of the firm’s financing is:
BB1 = 40,000($1,000)(1.065) = $42,600,000
BB2 = 40,000($10,000)(.218) = $87,200,000
R = 2.154%
YTM = 2.154% × 2 = 4.31%
And the aftertax cost of debt is:
Even though the zero coupon bonds make no payments, the calculation for the YTM (or price) still
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:
18. The total cost of the equipment including flotation costs was:
Total costs = $30,000,000 + 1,900,000
Total costs = $31,900,000
Using the equation to calculate the total cost including flotation costs, we get:
19. a. Using the dividend discount model, the cost of equity is:
RS = [(.75)(1.045)/$84] + .045
RS = .0543, or 5.43%
20. We are given the total cash flow for the current year. To value the company, we need to calculate the
cash flows until the growth rate levels off at a constant perpetual rate. So, the cash flows each year
will be:
Year 1: $7,100,000(1 + .10) = $7,810,000
Year 2: $7,810,000(1 + .10) = $8,591,000
We can calculate the terminal value in Year 5 since the cash flows begin a perpetual growth rate. Since
we are valuing Arras, we need to use the cost of capital for that company since this rate is based on
the risk of Arras. The cost of capital for Schultz is irrelevant in this case. So, the terminal value is:
Now we can discount the cash flows for the first 5 years as well as the terminal value back to today.
Again, using the cost of capital for Arras, we find the value of the company today is:
V0 = $7,810,000/1.09 + $8,591,000/1.092 + $9,450,100/1.093 + $10,395,110/1.094
+ ($11,434,621 + 237,840,117)/1.095
V0 = $191,068,855
The market value of the equity is the market value of the company minus the market value of the debt,
or:
21. a. To begin the valuation of Joe’s, we will begin by calculating the RWACC for Happy Times. Since
both companies are in the same industry, it is likely that the RWACC for both companies will be
the same. The weights of debt and equity are:
XB = $115,000,000/($115,000,000 + 360,000,000) = .2421, or 24.21%
XS = $360,000,000/($115,000,000 + 360,000,000) = .7579, or 75.79%
Next, we need to calculate the cash flows for each year. The EBIT will grow at 10 percent per
year for 5 years. Net working capital, capital spending, and depreciation are 9 percent, 15 percent,
and 8 percent of EBIT, respectively. So, the cash flows for each year over the next 5 years will
be:
Year 1
Year 2
Year 4
Year 5
EBIT
$17,300,000
$19,030,000
$23,026,300
$25,328,930
Taxes*
3,633,000
3,996,300
4,835,523
5,319,075
OCF
$15,051,000
$16,556,100
$20,032,881
$22,036,169
– Capital spending
2,595,000
2,854,500
3,453,945
3,799,340
– Change in NWC
1,557,000
1,712,700
2,072,367
2,279,604
CFA*
$10,899,000
$11,988,900
$14,506,569
$15,957,226
After Year 5 the cash flows will grow at 3 percent in perpetuity. We can find the terminal value
of the company in Year 5, using the cash flow in Year 6, as:
Now we can discount the cash flows and terminal value to today. Doing so, we find:
V0 = $10,899,000/1.0948 + $11,988,900/1.09482 + $13,187,790/1.09483
The market value of the equity is the market value of the company minus the market value of the
debt, or:
To find the maximum offer price, we divide the market value of equity by the shares outstanding,
or:
b. To calculate the terminal value using the EV/EBITDA multiple we need to calculate the Year 5
EBITDA, which is EBIT plus depreciation, or:
Net income
Depreciation
1,384,000
1,522,400
1,674,640
1,842,104
2,026,314
We can now calculate the terminal value of the company using the Year 5 EBITDA, which will
be:
Note, this is the terminal value in Year 5 since we used the Year 5 EBITDA. We need to calculate
the present value of the cash flows for the first 4 years, plus the present value of the Year 5
terminal value. We do not need to include the Year 5 cash flow since it is included in the Year 5
terminal value. So, the value of the company today is:
V0 = $10,899,000/1.0948 + $11,988,900/1.09482 + $13,187,790/1.09483
+ $14,506,569/1.09484 + ($15,957,226 + 246,197,200)/1.09485
V0 = $196,604,093
22. We can use the debt-equity ratio to calculate the weights of equity and debt. For the debt of the
company, there is a weight for long-term debt and a weight for accounts payable. We can use the target
ratio given for accounts payable to calculate the weight of accounts payable and the weight of long–
term debt. The weight of each will be:
Accounts payable weight = .20/1.20 = .17
We will use the same equation to calculate the weighted average flotation cost, except we will use the
flotation cost for each form of financing. Doing so, we get:
Flotation costs = (1/1.40)(.07) + (.40/1.40)[(.20/1.2)(0) + (1/1.2)(.02)] = .0548, or 5.48%
The total amount we need to raise to fund the new equipment will be:
23. We can use the debt-equity ratio to calculate the weights of equity and debt. The weight of debt in the
capital structure is:
XB = .65/1.65 = .3939, or 39.39%
And the weight of equity is:
Now we can calculate the weighted average flotation costs for the various percentages of internally
raised equity. To find the portion of equity flotation costs, we can multiply the equity costs by the
percentage of equity raised externally, which is one minus the percentage raised internally. So, if the
company raises all equity externally, the flotation costs are:
If the company uses 60 percent internally generated equity, the flotation cost is:
fA = (.6061)(.08)(1 – .60) + (.3939)(.035)
fA = .0332, or 3.32%
And the initial cash flow will be:
24. The $7.3 million cost of the land 3 years ago is a sunk cost and irrelevant; the $7.5 million appraised
value of the land is an opportunity cost and is relevant. The $7.9 million land value in 5 years is a
relevant cash flow as well. The fact that the company is keeping the land rather than selling it is
unimportant. The land is an opportunity cost in 5 years and is a relevant cash flow for this project. The
market value capitalization weights are:
B = 130,000($2,000)(1.04) = $270,400,000
The total market value of the company is:
The weight of each form of financing in the company’s capital structure is:
XB = $270,400,000/$978,400,000 = .2764
Next we need to find the cost of funds. We have the information available to calculate the cost of
equity using the CAPM, so:
RS = .031 + 1.20(.07)
RS = .1150, or 11.50%
The cost of debt is the YTM of the company’s outstanding bonds, so:
The cost of preferred stock is:
a. The weighted average flotation cost is the sum of the weight of each source of funds in the capital
structure of the company times the flotation costs, so:
The initial cash outflow for the project needs to be adjusted for the flotation costs. To account for
the flotation costs:
Amount raised(1 – .0546) = $55,000,000
So the cash flow at time zero will be:
CF0 = –$7,500,000 – 58,177,399 – 2,500,000
CF0 = –$68,177,399
There is an important caveat to this solution. This solution assumes that the increase in net
working capital does not require the company to raise outside funds; therefore the flotation costs
are not included. However, this is an assumption and the company could need to raise outside
funds for the NWC. If this is true, the initial cash outlay includes these flotation costs, so:
Total cost of NWC including flotation costs:
b. To find the required return on this project, we first need to calculate the WACC for the company.
The company’s WACC is:
The company wants to use the subjective approach to this project because it is located overseas.
The adjustment factor is 2 percent, so the required return on this project is:
Project required return = 9.29% + 2%
c. The annual depreciation for the equipment will be:
$55,000,000/8 = $6,875,000
So, the book value of the equipment at the end of five years will be:
d. Using the tax shield approach, the OCF for this project is:
OCF = [(P – v)Q – FC](1 – TC) + TCD
e. The accounting break-even sales figure for this project is:
QA = (FC + D)/(P – v)
f. We have calculated all cash flows of the project. We need to make sure that in Year 5 we add
back the aftertax salvage value and the recovery of the initial NWC. The cash flows for the project
are:
Year Flow Cash
0 –$68,177,399
1 21,312,500
Using the required return of 11.29 percent, the NPV of the project is:
NPV = –$68,177,399 + $21,312,500(PVIFA11.29%,4) + $43,543,750/1.11295
NPV = $23,053,458
And the IRR is:
If the initial NWC is assumed to be financed from outside sources, the cash flows are:
Year Flow Cash
0 –$68,321,827
1 21,312,500
2 21,312,500
With this assumption, and the required return of 11.29 percent, the NPV of the project is:
NPV = –$68,321,827 + $21,312,500(PVIFA11.29%,4) + $43,543,750/1.11295
NPV = $22,909,030.76
And the IRR is: