Suppose we have a bond issue currently outstanding that has 25 years left to maturity. the coupon rate is 9% and coupons are paid semiannually. the bond is currently selling for $908.72 per $1000 bond. if the firm's marginal tax rate is 30%. what's the firm's after-tax cost of

a) 3.5%

b) 5.0%

c) 6.3%

d) 7.0%

The after tax cost of debt is

D) 7.0%

Explanation:

In order to find the firms after tax cost of debt we have to find it's pre tax cost of debt, which is also the yield to maturity or interest rate of the bond. In order to find it we need 4 other variables, the par value or future value of the bond, the present value of the bond, the coupon payments and the number of maturity periods.  

The present value is 908.72, the future value is 1,000, the coupon payment is (0.09*1000*0.5)= 45. We multiply the 9% coupon rate with the future value of the bond and divide it by 2 as 9 is the coupon rate and because there are semi annual payments we will divide it by 2. The number of periods are (25*2) as there are 25 years to maturity and 2 payment periods each year so number of periods are 50.

We need to put all these values in a financial calculator

Pv= 908.72

FV=-1000

PMT= -45

N= 50

Compute I=5.00

This is the semi annual interest rate so we will multiply it by 2 to find the yearly interest rate so 5*2= 10.

10% is the pre tax cost of debt and now we will multiply it by (1-tax rate) to find the after tax cost of debt

0.1*0.7= 0.07= 7%