Question

Pearce’s Cricket Farm issued a 15-year, 8% semiannual bond 3 years ago. The bond currently sells for 96% of its face value. The company’s tax rate is 35%.

Suppose the book value of the debt issue is $60 million. In addition, the company has a second debt issue on the market, a zero coupon bond with 10 years left to maturity; the book value of this issue is $35 million and the bonds sell for 51% of par. Assume the par value of the bond is $1,000.

What is the company’s total book value of debt? (Enter the answer in dollars. Omit $ sign in your response.)

Total book value           $ _____

What is the company’s total market value of debt? (Enter the answer in dollars. Omit $ sign in your response.)

Total market value           $ _____

What is your best estimate of the after-tax cost of debt? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places.)

Cost of debt _____%

Answer 1

a). Book value of debt = 60+35 = 95 million or 95,000,000

b). Market value of debt = (96%*60) + (51%*25) = 75.45 million or 75,450,000

c). Cost of debt for semi-annual bond: FV = 1,000; PV = 96%*1,000 = 960; PMT (semi-annual coupon) = 8%*1,000/2 = 40; N = 15*2 = 30, solve for RATE.

Semi-annual rate = 4.24% so annual YTM = 2*4.24% = 8.48%

After-tax cost of debt = 8.48%*(1-35%) = 5.51%

Cost of zero-coupon bond: FV = 1,000; PV = 51%*1,000 = 510; N = 10, solve for RATE. YTM = 6.97%

After-tax cost of debt = 6.97%*(1-35%) = 4.53%

Weight of semi-annual bond = market value of bond/total market value of bond = (96%*60)/75.45 = 76.34%

Weight of zero-coupon bond = 1-76.34% = 23.66%

After-tax cost of debt = sum of weighted costs of debt = (76.34%*5.51%) + (23.66%*4.53%) = 5.28%