Mudvayne, Inc., is trying to determine its cost of debt. The firm has a debt iss

Question

Mudvayne, Inc., is trying to determine its cost of debt. The firm has a debt issue outstanding with 11 years to maturity that is quoted at 104 percent of face value. The issue makes semiannual payments and has an embedded cost of 4 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))

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

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))

Explanation / Answer

1.

Stated interest rate = 4%

Semi-annual interest payment = $1,000 * 4% * ½ = $20

Market value = $1000 *104% = $1040

Years to maturity = 11 years

Number of Interest payments to maturity = 11 years * 2 = 22

Market value of debt is the sum of present value of interest payments to be paid over the life of debt and the face value to be redeemed on maturity. The present value shall be determined by using the cost of debt as the discount rate. Let the cost of debt be r.

Present value of annuity = Annuity * {1 – (1+r)-n}/r

Present value of annuity of 22 interest payments = $20 * {1 – (1+r)-22}/r

Present value of face value to be received after 22 half years = $1,000/(1+r)22

Hence,

$1,040 = $20 * {1 – (1+r)-22}/r + $1,000/(1+r)22

Solving above equation for r, we get r = 0.0178 = 1.78%

This is semi-annual rate.

Pretax cost of debt = 1.78% *2 = 3.56%

2.

After tax cost of debt = pretax cost of debt * (1 – tax rate) = 3.56% * (1-0.35) = 2.31%

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