Shanken Corp. issued a 30-year, 6 percent semiannual bond 3 years ago. The bond

Question

Shanken Corp. issued a 30-year, 6 percent semiannual bond 3 years ago. The bond currently sells for 92 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 12 years left to maturity; the book value of this issue is $50 million and the bonds sell for 54 percent of par. The company’s tax rate is 40 percent.

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.)

Explanation / Answer

Bond 1:

Face Value = $50,000,000
Market Value = 92% * $50,000,000
Market Value = $46,000,000

Annual Coupon Rate = 6%
Semiannual Coupon Rate = 3%
Semiannual Coupon = 3%*$50,000,000 = $1,500,000

Time to Maturity = 30 years
Semiannual Period to Maturity = 60

Let semiannual YTM be i%

$46,000,000 = $1,500,000 * PVIFA(i%, 60) + $50,000,000 * PVIF(i%, 60)

Using financial calculator:
N = 60
PV = -46000000
PMT = 1500000
FV = 50000000

I = 3.308%

Semiannual YTM = 3.308%
Annual YTM = 2 * 3.308%
Annual YTM = 6.616%

Bond 2:

Face Value = $50,000,000
Market Value = 54% * $50,000,000
Market Value = $27,000,000

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

Let semiannual YTM be i%

$27,000,000 = $50,000,000 * PVIF(i%, 24)

Using financial calculator:
N = 24
PV = -27000000
PMT = 0
FV = 50000000

I = 2.60%

Semiannual YTM = 2.60%
Annual YTM = 2 * 2.60%
Annual YTM = 5.20%

Total Market Value of Bonds = $46,000,000 + $27,000,000
Total Market Value of Bonds = $73,000,000

Weight of Bond 1 = $46,000,000 / $73,000,000
Weight of Bond 1 = 0.6301

Weight of Bond 2 = $27,000,000 / $73,000,000
Weight of Bond 2 = 0.3699

Before-tax Cost of Debt = 0.6301 * 6.616% + 0.3699 * 5.200%
Before-tax Cost of Debt = 6.092%

After-tax Cost of Debt = 6.092% * (1 - 0.40)
After-tax Cost of Debt = 3.66%

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