Question

Mojo Mining has a bond outstanding that sells for $1,061 and matures in 25 years. The bond pays semiannual coupons and has a coupon rate of 6.1 percent. The par value is $1,000. If the company's tax rate is 39 percent, what is the aftertax cost of debt?

Multiple Choice 5.73% 3.70% 3.23% 5.35% 3.44%

please show work

Answer 1

Answer:

Face Value = $1,000
Current Price = $1,061

Annual Coupon Rate = 6.1%
Semiannual Coupon Rate = 3.05%
Semiannual Coupon = 3.05% * $1,000 = $30.50

Time to Maturity = 25 years
Semiannual Period to Maturity = 50

Let semiannual YTM be i%

$1,061 = $30.50 * PVIFA(i%, 50) + $1,000 * PVIF(i%, 50)

Using financial calculator:
N = 50
PV = -1061
PMT = 30.50
FV = 1000

I = 2.82%

Semiannual YTM = 2.82%
Annual YTM = 2 * 2.82%
Annual YTM = 5.64%

Before-tax Cost of Debt = 5.64%
After-tax Cost of Debt = 5.64% * (1 - 0.39)
After-tax Cost of Debt = 3.44%