Risk, Cost of Capital, and Capital Budgeting

CHAPTER 12

RISK, COST OF CAPITAL, AND CAPITAL BUDGETING

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:

RE = .045 + 1.30 (.12 – .045) = .1425 or 14.25%

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

BVD = $20M + 80M = $100M

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:

MVD = 1.08($20M) + .58($80M) = $68M

The YTM of the zero coupon bonds is:

PZ = $580 = $1,000(PVIFR%,7)

R = 8.09%

So, the aftertax cost of the zero coupon bonds is:

RZ = .0809(1 – .35) = .0526 or 5.26%

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 = .0595($21.6/$68) + .0526($46.4/$68) = .0548 or 5.48%

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

WACC = .55(.16) + .45(.09)(1 – .35) = .1143 or 11.43%

6.Here we need to use the debt-equity ratio to calculate the WACC. Doing so, we find:

WACC = .18(1/1.60) + .10(.60/1.60)(1 – .35) = .1369 or 13.69%

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

MVD = 4,000($1,000)(1.03) = $4,120,000

MVE = 90,000($57) = $5,130,000

And the total market value of the firm is:

V = $4,120,000 + 5,130,000 = $9,250,000

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

RE = .06 + 1.10(.08) = .1480 or 14.80%

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

P0 = $1,030 = $35(PVIFAR%,40) + $1,000(PVIFR%,40)

R = 3.36%

YTM = 3.36% × 2 = 6.72%

And the aftertax cost of debt is:

RD = (1 – .35)(.0672) = .0437 or 4.37%

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

WACC = .0437(4.12/9.25) + .1480(5.13/9.25) = .1015 or 10.15%

Notice that we didn’t include the (1 – tC) term in the WACC equation. We simply used the aftertax cost of debt in the equation, so the term is not needed here.