Question

Suspect Corp. issued a bond with a maturity of 10 years and a semiannual coupon rate of 8 percent 3 years ago. The bond currently sells for 96 percent of its face value. The book value of the debt issue is $50 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 $30 million and the bonds sell for 55 percent of par. The company’s tax rate is 35 percent.

(a) What is the company’s total book value of debt? (Do not round intermediate calculations. Enter your answer in dollars, not millions of dollars, e.g., 1,234,567.)

(b) What is the company’s total market value of debt? (Do not round intermediate calculations. Enter your answer in dollars, not millions of dollars, e.g., 1,234,567.)

(c) What is your best estimate of the aftertax cost of debt? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

1^st Issue of Bonds:

Face Value = $50,000,000

Market Value = 96% * $50,000,000
Market Value = $48,000,000

Semiannual Coupon Rate = 8%
Semiannual Coupon = 8% * $50,000,000
Semiannual Coupon = $4,000,000

Time to Maturity = 7 years
Semiannual Period to Maturity = 14

Let semiannual YTM be i%

$48,000,000 = $4,000,000 * PVIFA(i%, 14) + $50,000,000 * PVIF(i%, 14)

Using financial calculator:
N = 14
PV = -48000000
PMT = 4000000
FV = 50000000

I = 8.50%

Semiannual YTM = 8.50%
Annual YTM = 2 * 8.50%
Annual YTM = 17.00%

Before-tax Cost of Debt = 17.00%
After-tax Cost of Debt = 17.00% * (1 - 0.35)
After-tax Cost of Debt = 11.05%

2^nd Issue of Bonds:

Face Value = $30,000,000

Market Value = 55% * $30,000,000
Market Value = $16,500,000

Time to Maturity = 10 years
Semiannual Period to Maturity = 20

Let semiannual YTM be i%

$16,500,000 = $30,000,000 * PVIF(i%, 20)

Using financial calculator:
N = 20
PV = -16500000
PMT = 0
FV = 30000000

I = 3.034%

Semiannual YTM = 3.034%
Annual YTM = 2 * 3.034%
Annual YTM = 6.068%

Before-tax Cost of Debt = 6.068%
After-tax Cost of Debt = 6.068% * (1 - 0.35)
After-tax Cost of Debt = 3.94%

Answer a.

Total Book Value of Debt = $50,000,000 + $30,000,000
Total Book Value of Debt = $80,000,000

Answer b.

Total Market Value of Debt = $48,000,000 + $16,500,000
Total Market Value of Debt = $64,500,000

Answer c.

Weight of 1^st Issue of Debt = $48,000,000 / $64,500,000
Weight of 1^st Issue of Debt = 0.7442

Weight of 2^nd Issue of Debt = $16,500,000 / $64,500,000
Weight of 2^nd Issue of Debt = 0.2558

Estimated After-tax Cost of Debt = 0.7442 * 11.05% + 0.2558 * 3.94%
Estimated After-tax Cost of Debt = 9.23%