Four years ago, the Moore Co. issued 15-year, 7.5 percent semiannual coupon bonds at par. Today, the bonds are quoted at 101.6. What is this firm's pre-tax cost of debt?

Question

Quizplus · Accepted Answer

When the bonds were issued, they were sold at par, which means the coupon rate of 7.5% matched the yield to maturity (YTM) of the bonds. Since the bonds are now trading at 101.6, which is a premium to par, we can assume that the current YTM is lower than 7.5%. We can use the bond pricing formula to calculate the current YTM:

PV = (C / r) x [1 - 1 / (1 + r)^n] + F / (1 + r)^n

Where:
PV = present value of the bond = 1016
C = semiannual coupon payment = 0.075 x 1000 / 2 = 37.5
r = YTM (in decimal)
n = number of semiannual periods = 15 x 2 = 30
F = face value of the bond = 1000

Rearranging the equation and solving for r gives:

r = 7.29%

This is the pre-tax cost of debt for Moore Co.

Four Years Ago, the Moore Co