Question

Shanken Corp. issued a 25-year, 5.9 percent semiannual bond 2 years ago. The bond currently sells for 110 percent of its face value. The book value of the debt issue is $45 million. In addition, the company has a second debt issue on the market, a zero coupon bond with 12 years left to maturity; the book value of this issue is $45 million and the bonds sell for 54 percent of par. The company’s tax rate is 24 percent.

a. What is the company's total book value of debt? (Do not round intermediate calculations and 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 and 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 and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

1^st Issue of Bonds:

Face Value = $45,000,000

Market Value = 110% * $45,000,000
Market Value = $49,500,000

Annual Coupon Rate = 5.90%
Semiannual Coupon Rate = 2.95%
Semiannual Coupon = 2.95% * $45,000,000
Semiannual Coupon = $1,327,500

Time to Maturity = 23 years
Semiannual Period to Maturity = 46

Let semiannual YTM be i%

$49,500,000 = $1,327,500 * PVIFA(i%, 46) + $45,000,000 * PVIF(i%, 46)

Using financial calculator:
N = 46
PV = -49500000
PMT = 1327500
FV = 45000000

I = 2.576%

Semiannual YTM = 2.576%
Annual YTM = 2 * 2.576%
Annual YTM = 5.152%

Before-tax Cost of Debt = 5.152%
After-tax Cost of Debt = 5.152% * (1 - 0.24)
After-tax Cost of Debt = 3.916%

2^nd Issue of Bonds:

Face Value = $45,000,000

Market Value = 54% * $45,000,000
Market Value = $24,300,000

Time to Maturity = 12 years
Semiannual Period to Maturity = 24

Let semiannual YTM be i%

$24,300,000 = $45,000,000 * PVIF(i%, 24)

Using financial calculator:
N = 24
PV = -24300000
PMT = 0
FV = 45000000

I = 2.601%

Semiannual YTM = 2.601%
Annual YTM = 2 * 2.601%
Annual YTM = 5.202%

Before-tax Cost of Debt = 5.202%
After-tax Cost of Debt = 5.202% * (1 - 0.24)
After-tax Cost of Debt = 3.954%

Answer a.

Total Book Value of Debt = $45,000,000 + $45,000,000
Total Book Value of Debt = $90,000,000

Answer b.

Total Market Value of Debt = $49,500,000 + $24,300,000
Total Market Value of Debt = $73,800,000

Answer c.

Weight of 1^st Issue of Debt = $49,500,000 / $73,800,000
Weight of 1^st Issue of Debt = 0.6707

Weight of 2^nd Issue of Debt = $24,300,000 / $73,800,000
Weight of 2^nd Issue of Debt = 0.3293

Estimated After-tax Cost of Debt = 0.6707 * 3.916% + 0.3293 * 3.954%
Estimated After-tax Cost of Debt = 3.93%