Question

Mudvayne, Inc., is trying to determine its cost of debt. The firm has a debt issue outstanding with 14 years to maturity that is quoted at 106 percent of face value. The issue makes semiannual payments and has an embedded cost of 8 percent annually. What is the company’s pretax cost of debt? (Do not round intermediate calculation and round your answer to 2 decimal places. (e.g., 32.16)) Cost of debt % If the tax rate is 35 percent, what is the aftertax cost of debt?

Answer 1

Answer:

Pre-tax   Cost of debt 7.35%

After-tax Cost of debt 4.78%

Explanation:

We will calculate the cost of debt which is the rate at which the present value of the coupon payment and maturirty matches with the market value.

$YTM = \frac{C + \frac{F-P}{n }}{\frac{F+P}{2}}$

Coupon payment =100 x 8% / 2 = 4

Face value= 100

market Value = P= 106

n= total payment = 14 years x 2 payment per year = 28

$YTM = \frac{4 + \frac{100-106}{28}}{\frac{100-106}{2}}$

YTM = 3.6754508%

As  this rate will be semiannually we multiply by 2

3.6754508 x 2 = 7.3509015 = 7.35%

Then we calcualte the cost of debt after tax:

pretax (1-t)

7.35 (1-.35) = 7.35(0.65) =4,7775‬ = 4.78%