Ponderosa's bonds sell for $846.04. The coupon rate is 8%, the bonds mature in 25 years, and interest is paid semi-annually. The tax rate is 34%. What is Ponderosa's after-tax cost of debt?

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 can be calculated using the following formula:YTM = (C + (FV - PV) / N) / ((FV + PV) / 2)where:C = coupon paymentFV = face value of the bondPV = present value of the bondN = number of periods to maturityIn this case, the coupon payment is $40 (8% of $500), the face value is $500, the present value is $846.04, and the number of periods to maturity is 50 (25 years * 2 semi-annual payments per year).Plugging these values into the formula, we get:YTM = (40 + (500 - 846.04) / 50) / ((500 + 846.04) / 2)YTM = 0.0499 = 4.99%Therefore, the after-tax cost of debt is 4.99% * (1 - 0.34) = 3.18%.

Ponderosa's Bonds Sell for $846