Question

A company's 7% coupon rate, semiannual payment, $1,000 par value bond that matures in 30 years sells at a price of $624.57. The company's federal-plus-state tax rate is 30%. What is the firm's after-tax component cost of debt for purposes of calculating the WACC?

Answer 1

We know that,

Price of the bond = Present value of all thesemi annual coupon and face value discounted at semi annual ytm.

FV = 1000

Price = 624.57

Number of payments = 30*2 = 60

Semi annual coupon amount = 0.07*1000/2 = 35

624.57 = 35/(1+semi annual ytm)^1 +35/(1+semi annual ytm)^2 +35/(1+semi annual ytm)^3 +35/(1+semi annual ytm)^4 +35/(1+semi annual ytm)^5 +35/(1+semi annual ytm)^6 +35/(1+semi annual ytm)^7 +35/(1+semi annual ytm)^8 + ............ 35/(1+semi annual ytm)^60 +1000/(1+semi annual ytm)^60

On Solving above equation,

Semi annual YTM = 5.73%

YTM = 11.46%

After tax cost = (11.46)*(1-0.3) = 8.02% Answer