Question

Drogo, 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 104 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 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?

Answer 1

(Assuming Excel and Financial Calculator are not allowed)

a) pretax cost of debt is the YTM of the bond issuance. We would use the approximate YTM formula, in order to calculate the YTM.

Now, for our question with semi-annual payments

Assume face value, F =100; Hence Price, P = 104

C = 8/2 (semi-annual) = 4

n = 14 * 2 (semi-annual periods) = 28

Approx YTM = 3.8571/102

Approx YTM = 3.78% (semi-annual)

Hence, Annual YTM = 3.78% * 2 = 7.56% (Annual)

(Using Excel, the YTM is calculated as 7.53%, which is closer to our approximate measure)

Hence, pretax cost of debt = 7.56%

b) After tax cost of debt = pretax cost of debt * (1 - tax rate)

After tax cost of debt = 7.56% * (1 - 35%) = 4.92%