Question

J&R Renovation, Inc., is trying to determine its cost of debt. The firm has a debt issue outstanding with 20 years to maturity that is quoted at 109 percent of face value. The issue makes semiannual payments and has a coupon rate of 6 percent annually.

What is the company's pretax cost of debt? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Pretax cost of debt ?%

If the tax rate is 35 percent, what is the aftertax cost of debt? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Aftertax cost of debt ?%

Answer 1

What is the company's pretax cost of debt?

Let’s assume that face value of bond is $100, then the current market price of the bond is 109% of $100 = $109

Pretax cost of debt is the bond’s yield to maturity; we have following formula for calculation of bond’s yield to maturity

Bond price P0 = C* [1- 1/ (1+i) ^n] /i + M / (1+i) ^n

Where,

M = value at maturity, or Face value = $ 100

Current market price of the bond, P0 = $109

C = coupon payment = 6%/2 of $100 = $3 semiannual coupon

n = number of payments = 20 years *2 = 40

i = interest rate, or yield to maturity =?

Putting all the values into formula, we get

$109 = $3 * [1 – 1 / (1+i) ^40] /i + $100 / (1+i) ^40

By trial and error method we got the value of i = 2.63%

[Or you can use excel function for YTM calculation in following manner

“= Rate(N,PMT,PV,FV)”

“Rate(40,-3,109,-100)” = 2.63%]

And annual rate I = 2.63% *2 = 5.27%

The company's pretax cost of debt is 5.27% per annum

If the tax rate is 35 percent, what is the after-tax cost of debt?

Tax rate of J&R Renovation, Inc. is 35%

After tax cost of debt = pretax cost of debt * (1- Tax Rate)

= 5.27% * (1- 35%)

= 5.27% * 0.65

= 3.42%

After-tax cost of debt is 3.42%