SUGGESTED SOLUTIONS TO CHAPTER 14 PROBLEMS
1. A firm with a corporate-wide debt/equity ratio of 1:2, an after-tax cost of debt of 7 percent, and a cost of equity
capital of 15 percent is interested in pursuing a foreign project. The debt capacity of the project is the same as for the
company as a whole, but its systematic risk is such that the required return on equity is estimated to be about 12
percent. The after-tax cost of debt is expected to remain at 7 percent.
a.
What is the project's weighted average cost of capital? How does it compare with the parent's WACC?
ANSWER. The weighted average cost of capital for the project is
kI = (1 - w) x ke' + w x id(1 - t)
where w is the ratio of debt to total assets, ke' is the required risk-adjusted return on project equity, and id(1 - t) is the
after-tax cost of debt for the project. Substituting in the numbers provided yields
kI = 2/3 x 12% + 1/3 x 7% = 10.33%
b.
If the project's equity beta is 1.21, what is its unlevered beta?
ANSWER. The following approximation is usually used to unlever beta:
Unlevered beta = levered beta/[1 + (1 - t)D/E]
where t is the firm's marginal tax rate and D/E is its debt/equity ratio. Without knowing the firm's marginal tax rate,
we cannot unlever beta. Assuming that the marginal tax rate is about 40%, the unlevered beta is
Unlevered beta = 1.21/[1 + (1 - .4)½] = .93
2. Suppose that a foreign project has a beta of 0.85, the risk-free return is 12 percent, and the required return on the
market is estimated at 19 percent. What is the cost of capital for the project?
ANSWER. The cost of capital for the project is
k* = Rf + β*[E(Rm) - Rf]
where Rf is the risk-free required return, β* is the project beta, and E(Rm) is the expected return on the market.
Substituting in the numbers provided in the problem yields
k* = .12 + .85(.19 - .12) = 17.95%
3. IBM is considering having its German affiliate issue a 10-year, $100 million bond denominated in euros and
priced to yield 7.5 percent. Alternatively, IBM’s German unit can issue a dollar-denominated bond of the same size
and maturity and carrying an interest rate of 6.7 percent..
a. If the euro is forecast to depreciate by 1.7 percent annually, what is the expected dollar cost of the eurodenominated bond? How does this compare to the cost of the dollar bond?
ANSWER. According to Chapter 14, the pre-tax dollar cost of borrowing in a foreign currency at an interest rate of
rL, where the currency is expected to appreciate (depreciate) against the dollar at an annual rate of c, is rL(1 + c) + c.
Substituting the numbers in the problem to this formula yields an expected dollar cost of borrowing euros of 5.67%
[7.5% x (1 - 0.017) - 1.7%). This figure is substantially below the 6.7% cost of borrowing dollars.
b. At what rate of euro depreciation will the dollar cost of the euro-denominated bond equal the dollar cost of the
dollar-denominated bond?
ANSWER. The answer to this question is the solution to 7.5% x (1 + c) + c = 6.7%, or c = (6.7% - 7.5%)/1.075 = 0.74%.
c. Suppose IBM’s German unit faces a 35 percent corporate tax rate. What is the expected after-tax dollar cost of
the euro-denominated bond?
ANSWER. According to Chapter 14, the effective after-tax dollar cost of borrowing a local currency at an interest
rate of rL, annual currency appreciation (depreciation) of c, and a corporate tax rate of ta, is r = rL(1 + c)(1 - ta) + c.
Substituting in the numbers from the question yields a solution of r = 7.5% x (1 - 0.017)(1 - 0.35) - 0.017 = 4.78%.
4. Suppose that the cost of borrowing restricted euros is 7 percent annually, whereas the market rate for these
funds is 12 percent. If a firm can borrow €10 million of restricted funds, how much will it save annually in beforetax franc interest expense?
ANSWER. The annual interest savings on €10 million of restricted funds at 7% when the market rate is 12% equals
€10,000,000(0.12 - 0.07) or €500,000.
5. Suppose that one of the inducements provided by Taiwan to woo Xidex into setting up a local production
facility is a ten-year, $12.5 million loan at 8 percent interest. The principal is to be repaid at the end of the tenth
year. The market interest rate on such a loan is about 15 percent. With a marginal tax rate of 40 percent, how
much is this loan worth to Xidex?
ANSWER. By borrowing at 8% when the market rate is 15%, Xebec saves 8% annually. This translates into annual
before-tax savings of $12,500,000(.15 - .08) = $875,000. With a marginal tax rate of 40%, this yields annual
after-tax savings of $525,000. The value of this ten-year annuity, discounted at Xebec's after-tax debt cost of 9%
(15% x .6), is $525,000 x 6.4177 = $3,369,293.