Question

Calculate the after-tax cost of debt using following bond information. A four year bond has a 7 percent coupon rate and a $1000 face value. If the market value of the bond is $788, assuming that the bond makes annual coupon payments and the tax rate is 35%.

a. 7.16 %
b. 14.32 %
c. 12.12 %
d. 9.31 %
e. 5.01 %

Answer 1

d. 9.31 %

Step-by-step explanation:

in order to solve this question you cannot use the approximate yield to maturity since it will yield an approximation, but not an exact answer:

approximate YTM = {70 + [(1,000 - 788)/4]} / [(1,000 - 788)/2] = 13.76%

after tax cost of debt = 13.76% x 0.65 = 8.94%, but that is not an option

we must determine the exact yield to maturity which is determined by the following formula:

$788 = $70/(1 + i) + $70/(1 + i)² + $70/(1 + i)³ + $1,070/(1 + i)⁴

the simplest way to solve this is by using a financial calculator since the math is complicated. The exact yield to maturity = 14.324%

after tax cost of debt = 14.324% x (1 - tax rate) = 14.324% x 0.65 = 9.31%