Question

Suppose your firm just issued a 20-year $1000 par value bond with semiannual coupons. The coupon interest rate is 6%. The bonds sold for par valuebut costs amounted to 5% of the priceYou have a 21% corporate tax rate. What is your firm’s cost of debt?

Answer 1

Face Value = $1,000
Current Price = $1,000-5%*$1000 = $950

Annual Coupon Rate = 6%
Semiannual Coupon Rate = 3%
Semiannual Coupon = 3%*$1,000 = $30

Time to Maturity = 20 years
Semiannual Period to Maturity = 40

Let semiannual YTM be i%

$950 = $30 * PVIFA(i%, 40) + $1,000 * PVIF(i%, 40)

Using financial calculator:
N = 40
PV = -950
PMT = 30
FV = 1000

I = 3.22%

Semiannual YTM = 3.22%
Annual YTM = 2 * 3.22%
Annual YTM = 6.44%

Before-tax Cost of Debt = 6.44%
After-tax Cost of Debt = 6.44% * (1 - 0.21)
After-tax Cost of Debt = 5.09%