Question

One Step, Inc., is trying to determine its cost of debt. The firm has a debt issue outstanding with 30 years to maturity that is quoted at 108 percent of face value. The issue makes semiannual payments and has a coupon rate of 7 percent.

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

If the tax rate is 21 percent, what is 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

Face Value = $1,000

Current Price = 108% * $1,000
Current Price = $1,080

Annual Coupon Rate = 7%
Semiannual Coupon Rate = 3.50%
Semiannual Coupon = 3.50% * $1,000
Semiannual Coupon = $35

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

Let semiannual YTM be i%

$1,080 = $35 * PVIFA(i%, 60) + $1,000 * PVIF(i%, 60)

Using financial calculator:
N = 60
PV = -1080
PMT = 35
FV = 1000

I = 3.20%

Semiannual YTM = 3.20%
Annual YTM = 2 * 3.20%
Annual YTM = 6.40%

Before-tax Cost of Debt = 6.40%

After-tax Cost of Debt = 6.40% * (1 - 0.21)
After-tax Cost of Debt = 5.06%