Viserion, Inc., is trying to determine its cost of debt. The firm has a debt issue outstanding with 24 years to maturity that is quoted at 92 percent of face value. The issue makes semiannual payments and has an embedded cost of 4 percent annually.

a. What is the company's pretax cost of debt? b. If the tax rate is 23 percent, what is the aftertax cost of debt?

A) 4.51%

B) 3.47%

Explanation:

The pretax cost of debt will be the yield to maturity of the bonds.

YTM = {C + [ (F - P) / n]} / [ (F + P) / 2]

C = 4%/2 = 2% ⇒ 20 F = 1,000 P = 920 n = 24 years x 2 = 48

YTM = {20 + [ (1000 - 920) / 48]} / [ (1000 + 920) / 2]

YTM = 21.67 / 960 = 2.257% x 2 = 4.51% annual

pretax cost of debt = 4.51%

after tax cost of debt = pretax cost x (1 - tax rate) = 4.51% x (1 - 23%) = 3.47%