Question

The approximate after-tax cost of debt for a 20-year, 7 percent, $1,000 par value bond selling at $960 (assume a marginal tax rate of 40 percent) is

Select one:

a. 4.41 percent.

b. 5.15 percent.

c. 7 percent.

d. 7.35 percent.

Answer 1

Solution :

The formula for calculating the cost of debt of a bond is

= [ C + ( ( F – P ) / N ) ] / [ ( F + P ) / 2 ]

Where C = Annual coupon

F = Face value of the bond    ;   P = Market price of the bond     ;   N = No. of years to maturity

As per the information given in the question

C =$ 1000 * 7 % = $ 70 ;   F = $ 1,000   ; P = $ 960 ; N = 20

Applying the above values in the formula we have

= [ 70 + ( ( 1000 – 960 ) / 20 ) ] / [ ( 1000 + 960 ) / 2 ]

= [ 70 + ( 40 / 20 ) ] / [ 1960 / 2 ]

= ( 70 + 2 ) / 980

= 72 / 980

= 0.0735

= 7.35 %

Thus the pre tax cost of debt of the bond is 7.35 %

The formula for calculation of post tax cost of debt of the bond is

= Pre tax cost of debt * ( 1 – Tax rate )

As per the information available we have

Pre tax cost of debt = 7.35 %   ;   Tax rate = 40 %

Applying the above values in the formula we have

= 7.35 % * ( 1 – 40 % )

= 7.35 % * 60 %

= 4.41 %

Thus the after tax cost of debt of the bond = 4.41 %

The solution is Option A. 4.41 percent