Question

Fanny’s Farm issued a 25-year, 6 percent semiannual bond four years ago. The bond currently sells for 102 percent of its face value. The company’s tax rate is 21 percent.

a.         What is the pretax cost of debt?

b.         What is the after-tax cost of debt?

c.         Which is more relevant, the pretax or the after-tax cost of debt? Why?

Answer 1

a.

We will use the 'yield' function in Excel to calculate the Yield to Maturity (YTM) of the bond. Since YTM represents the intereste rate at which Fanny's Farm's bond security is trading in the market, it is the firm's pretax cost of debt.

Please find attached below the snapshot from Excel to calculate bond's YTM.

mat Painter Merge & Center Conditional Format as Cel S% 00 .0 Formatting Table Style Font Alignment Number Styles fr X =+YIELD(E3,E4,E5,E6,E7,E8,E9) B C E F G H J K Settlement date 11/2/2019 Maturity date 11/2/2040 Coupon rate 6.000% Price 102 Redemption price 100 Coupon Frequency 2 Day-count basis 0 5.834% Yield

Settlement date is today's date. Since the bond was issued 4 years ago, Maturity date will be 21 years from today's date. Coupon rate is given as 6%. Current price is given as 102% of face value. Redemption price is the price at which bond will be redeemed which the bond's face value. Day-count basis is used to calculate the number of days between the settlement date and maturity date. We have used '0' which represents the standard convention for US bonds and assumes that a month has 30 days and a year has 360 days.

As can be seen from the snapshot, YTM = 5.834%.

Hence, pretax cost of debt = 5.834%

b.

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

Tax rate = 21%

Hence, after-tax cost of debt = 5.834% * (1-21%) = 4.609%

c.

Since interest on debt is tax-deductible, the after-tax cost of debt is the effective rate that a company pays on its debt after taking into account the tax savings. Thus, after-tax cost of debt is a more relevant measure. While calculating a firm's weighted average cost of capital, after-tax cost of debt is used.