Shanken Corp. issued a bond with a maturity of 20 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 $40 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 $40 million and the bonds sell for 52 percent of par. The company’s tax rate is 35 percent.
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).)
1st Issue of Bonds:
Face Value = $40,000,000
Market Value = 96% * $40,000,000
Market Value = $38,400,000
Annual Coupon Rate = 8%
Semiannual Coupon Rate = 4%
Semiannual Coupon = 4% * $40,000,000
Semiannual Coupon = $1,600,000
Time to Maturity = 17 years
Semiannual Period to Maturity = 34
Let semiannual YTM be i%
$38,400,000 = $1,600,000 * PVIFA(i%, 34) + $40,000,000 * PVIF(i%, 34)
Using financial calculator:
N = 34
PV = -38400000
PMT = 1600000
FV = 40000000
I = 4.224%
Semiannual YTM = 4.224%
Annual YTM = 2 * 4.224%
Annual YTM = 8.448%
Before-tax Cost of Debt = 8.448%
After-tax Cost of Debt = 8.448% * (1 - 0.35)
After-tax Cost of Debt = 5.491%
2nd Issue of Bonds:
Face Value = $40,000,000
Market Value = 52% * $40,000,000
Market Value = $20,800,000
Time to Maturity = 10 years
Semiannual Period to Maturity = 20
Let semiannual YTM be i%
$20,800,000 = $40,000,000 * PVIF(i%, 20)
Using financial calculator:
N = 20
PV = -20800000
PMT = 0
FV = 40000000
I = 3.324%
Semiannual YTM = 3.324%
Annual YTM = 2 * 3.324%
Annual YTM = 6.648%
Before-tax Cost of Debt = 6.648%
After-tax Cost of Debt = 6.648% * (1 - 0.35)
After-tax Cost of Debt = 4.321%
Answer a.
Total Book Value of Debt = $40,000,000 + $40,000,000
Total Book Value of Debt = $80,000,000
Answer b.
Total Market Value of Debt = $38,400,000 + $20,800,000
Total Market Value of Debt = $59,200,000
Answer c.
Weight of 1st Issue of Debt = $38,400,000 /
$59,200,000
Weight of 1st Issue of Debt = 0.6486
Weight of 2nd Issue of Debt = $20,800,000 /
$59,200,000
Weight of 2nd Issue of Debt = 0.3514
Estimated After-tax Cost of Debt = 0.6486 * 5.491% + 0.3514 *
4.321%
Estimated After-tax Cost of Debt = 5.08%
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