Question

Galvatron Metals has a bond outstanding with a coupon rate of 6.7 percent and semiannual payments. The bond currently sells for $1,863 and matures in 21 years. The par value is $2,000 and the company's tax rate is 40 percent. What is the company's aftertax cost of debt?

A. 7.22%

B. 4.33%

C. 4.00%

D. 6.74%

E. 4.59%

Answer 1

Answer is 4.33%

Face Value = $2,000
Current Price = $1,863

Annual Coupon Rate = 6.7%
Semiannual Coupon Rate = 3.35%
Semiannual Coupon = 3.35%*$2,000
Semiannual Coupon = $67

Time to Maturity = 21 years
Semainnual Period to Maturity = 42

Let semiannual YTM be i%

$1,863 = $67 * PVIFA(i%, 42) + $2,000 * PVIF(i%, 42)

Using financial calculator:
N = 42
PV = -1863
PMT = 67
FV = 2000

I = 3.673%

Semiannual YTM = 3.673%
Annual YTM = 2 * 3.673%
Annual YTM = 7.346%

Before-tax Cost of Debt = 7.346%
After-tax Cost of Debt = 7.346%*(1 - 0.40)
After-tax Cost of Debt = 4.40%

So, after-tax cost of debt is closet to 4.33%