Question

Collins Group The Collins Group, a leading producer of custom automobile accessories, has hired you to estimate the firm's weighted average cost of capital. The balance sheet and some other information are provided below. Assets Current assets $ 38,000,000 Net plant, property, and equipment 101,000,000 Total assets $139,000,000 Liabilities and Equity Accounts payable $ 10,000,000 Accruals 9,000,000 Current liabilities $ 19,000,000 Long-term debt (40,000 bonds, $1,000 par value) 40,000,000 Total liabilities $ 59,000,000 Common stock (10,000,000 shares) 30,000,000 Retained earnings 50,000,000 Total shareholders' equity 80,000,000 Total liabilities and shareholders' equity $139,000,000 The stock is currently selling for $15.25 per share, and its noncallable $1,000 par value, 20-year, 7.25% bonds with semiannual payments are selling for $875.00. The beta is 1.25, the yield on a 6-month Treasury bill is 3.50%, and the yield on a 20-year Treasury bond is 5.50%. The required return on the stock market is 11.50%, but the market has had an average annual return of 14.50% during the past 5 years. The firm's tax rate is 40%. Refer to the data for the Collins Group. What is the best estimate of the after-tax cost of debt? a. 5.14% b. 5.67% c. 5.40% d. 4.88% e. 4.64%

Answer 1

Bond:

Par Value = $ 1000, Tenure = 20 years or 40 half-years, Coupon Rate = 7.25 % or 3.625 %per half-year, Market Price = $ 875

Semi-Annual Coupon = 0.03625 x 1000 = $ 36.25

Let the yield to maturity be 2R %

Therefore, 875 = 36.25 x (1/R) x [1-{1/(1+R)^(40)}] + 1000 / (1+R)^(40)

Using EXCEL's Goal Seek Function/ Hit and Trial Method to solve the aboe equation, we get:

R = 0.04283 or 4.283 %

Therefore, Yield to Maturity = Before Tax Cost of Debt = 4.283 x 2 = 8.566 % per annum

Tax Rate = 40 %

After-Tax Cost of Debt = (1-0.4) x 8.556 = 5.14 %

Hence, the correct option is (a).