978-1259709685 Chapter 13 Solution Manual Part 1

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CHAPTER 13

RISK, COST OF CAPITAL, AND CAPITAL

BUDGETING

Answers to Concepts Review and Critical Thinking Questions

3. You are assuming that the new project’s risk is the same as the risk of the firm as a whole, and that

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

method are (1) three parameters (the risk-free rate, the expected return on the market, and beta) must

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 estimate its cost of debt by (1) looking at the cost of debt for similar firms in similar risk

b. This is the current yield only, not the promised yield to maturity. In addition, it is based on the

c. Equity is inherently riskier than debt (except, perhaps, in the unusual case where a firm’s assets

7. RSup = .12 + .75(.08) = .1800, or 18.00%

Both should proceed. The appropriate discount rate does not depend on which company is investing;

it depends on the risk of the project. Since Superior is in the business, it is closer to a pure play.

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

for investment projects, since their return would exceed the hurdle rate despite the fact that they may

9. The discount rate for the projects should be lower that 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 the

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.

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 = $35(PVIFAR%,26) + $1,000(PVIFR%,26)

R = 3.806%

3. a. The pretax cost of debt is the YTM of the company’s bonds, so:

P0 = $1,080 = $29.50(PVIFAR%,48) + $1,000(PVIFR%,48)

b. The aftertax cost of debt is:

c. The aftertax rate is more relevant because that is the actual cost to the company.

4. The book value of debt is the total par value of all outstanding debt, so:

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:

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:

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:

Now we must realize that the V/S is just the equity multiplier, which is equal to:

V/S = 1 + B/S

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 = 8,300,000($4) = $33,200,000

b. The market value of equity is the share price times the number of shares, so:

S = 8,300,000($53) = $439,900,000

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:

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:

Next, we need to find the YTM on both bond issues. Doing so, we find:

P2 = $1,089 = $37.50(PVIFAR%,54) + $1,000(PVIFR%,54)

R = 3.389%

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:

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:

Using these costs and the weight of debt we calculated earlier, the WACC is:

10. a. Using the equation to calculate WACC, we find:

b. Using the equation to calculate WACC, we find:

11. We will begin by finding the market value of each type of financing. We find:

And the total market value of the firm is:

Now, we can find the cost of equity using the CAPM. The cost of equity is:

The cost of debt is the YTM of the bonds, so:

And the aftertax cost of debt is:

Now we have all of the components to calculate the WACC. The WACC is:

Notice that we didn’t include the (1 – tC) term in the WACC equation. We used the aftertax cost of

12. a. We will begin by finding the market value of each type of financing. We find:

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:

The cost of debt is the YTM of the bonds, so:

And the aftertax cost of debt is:

RB = (1 – .35)(.0605)

RB = .0393, or 3.93%

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

c. Project X would be incorrectly rejected; Project Z would be incorrectly accepted.

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:

c. The total cost of the equipment including flotation costs is:

15. We first need to find the weighted average flotation cost. Doing so, we find:

And the total cost of the equipment including flotation costs is:

Amount raised(1 – .057) = $55,000,000

Intermediate

16. Using the debt–equity ratio to calculate the WACC, we find:

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:

We would accept the project if the NPV is positive. The NPV is the PV of the cash outflows plus the

PV of the cash inflows. Since we are seeking the breakeven initial cost, we just need to find the PV

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:

And the total market value of the firm is:

Now, we can find the cost of equity using the CAPM. The cost of equity is:

The cost of debt is the YTM of the bonds, so:

And the aftertax cost of debt is:

And the aftertax cost of the zero coupon bonds 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.

Notice that the required return on the preferred stock is lower than the required return on the bonds.

This result is not consistent with the risk levels of the two instruments, but is a common occurrence.

There is a practical reason for this: Assume Company A owns stock in Company B. The tax code

Now we have all of the components to calculate the WACC. The WACC is: