Chappelle Systems has 8 percent semiannual coupon bonds outstanding with a $1,000 face value that sell for $1,072.66. The bonds have 15 years to maturity, but can be called in 5 years at a call price of $1,030. Chappelle's tax rate is 40 percent. What is Chappelle's after-tax cost of debt if interest rates are assumed to remain at their current level?

Question

Quizplus · Accepted Answer

The after-tax cost of debt is the yield to maturity (YTM) of the bond multiplied by (1 - tax rate). The YTM of the bond is the annual coupon payment divided by the bond price plus the present value of the principal payment divided by the bond price. The annual coupon payment is $80 ($1,000 face value x 8% coupon rate x 1/2 year). The present value of the principal payment is $1,000 divided by (1 + YTM)^30 (15 years to maturity x 2 semiannual periods per year). The bond price is $1,072.66. Therefore, the YTM is:YTM = ($80 + $1,000 / (1 + YTM)^30) / $1,072.66YTM = 0.0756 or 7.56%The after-tax cost of debt is:After-tax cost of debt = YTM x (1 - tax rate)After-tax cost of debt = 0.0756 x (1 - 0.40)After-tax cost of debt = 0.0454 or 4.54%

Chappelle Systems Has 8 Percent Semiannual Coupon Bonds Outstanding with a $1,000