Corporate Finance, Module 18: Weighted Average Cost of Capital

Homework Assignment

(The attached PDF file has better formatting.)


A firm has debt of $25 million paying 9.5% interest. The firm has 2 million shares outstanding, selling at $40 per share. The company expects to earn $18 million before interest and taxes each year in perpetuity. The marginal tax rate is 35%.

A.    What is the after-tax cost of debt capital? (The pre-tax cost times the complement of the corporate tax rate.)
B.    What is the earnings of the firm after interest payments but before tax payments? (Subtract the par value of the debt times the coupon rate from the earnings before interest and taxes.)
C.    What is the after-tax earnings of the firm available to shareholders? (Earnings after interest payments times the complement of the corporate tax rate.)
D.    What is the market value of the equity? (Number of share times market price per share.)
E.    What is the return on (market value) equity (re)? (After-tax earnings to shareholders divided by market value of equity.)
F.    What is the return on assets? Use the weighted average cost of capital method. (Weight the after-tax cost of debt capital with the cost of equity capital, where the market value of debt and equity are the weights.)

What do you think about this?

A. After-tax cost of debt capital = (Pre-tax cost)(1 - Corporate tax rate) = (25 million x 9.5%)(1-35%) = $1,543,750

B. Earnings after interest pmts, before tax pmts = Earnings before intetrest - (Par value of debt)(Coupon rate) = 18 million - (25 million)(9.5%) = $15,625,000

C. After-tax earnings avail. to shareholders = Earnings after interest x (1 - tax rate) = 15,625,000 - (1-35%) = $10,156,250

D. Market value of equity = # shares x Market price per share = 2 million x $40 = $80 million

E. Return on market value equity (re) = After-tax earnings to shareholders / Market value of equity = 10,156,250 / 80,000,000 = 12.6953%

F. Return on assets using WACC method = [(After-tax cost of debt) x (MV debt) + (Cost of equity) x (MV equity)] / [MV debt + MV equity] = [(1,543,750/25,000,000) x 25,000,000 + 12.6953% x 80,000,000] / [25,000,000 + 80,000,000] = 11.1429%

I agree with the answers for homework parts B through F as posted above by al1835 on 12/30/06. I have a different answer for homework part A, however. In other postings in this Module, NEAS expresses the after-tax cost of debt capital as a percentage (interest rate), not as a dollar amount. See the Practice Problems, Solution 18.1, Part A, for example.

So, I think the solution to homework part A should be 9.5% x (1 - 35%) = 6.175%.

It may be worth noting that, as in Practice Problem 18.1, you can check your answer to F. by calculating the pretax cost of capital $18 million/$105 million, and then multiply that by the complement of the tax rate to get the after tax cost of capital. The answer should match that of part F.

I agree with the above answers B-F and with Rick Sutherland that part A = 6.175%

You will notice that WACC stands for "weighted average cost of capital" and is a percentage, so based on this logic and all of the past assignments (look at Module 17 homework for an example), it is fair to assume the "cost of (debt) capital" is also a percentage.