Question

You are analyzing the after-tax cost of debt for a firm. You know that the firm's 12-year maturity, 15.50 percent semiannual coupon bonds are selling at a price of $1,117.25. These bonds are the only debt outstanding for the firm. (a1) Your answer is correct. What is the current YTM of the bonds? (Round final answer to 2 decimal places, e.g. 15.25%.) YTM 13.50 % e Textbook and Media Attempts: 1 of 2 used (22) What is the after-tax cost of debt for this firm if it has a marginal tax rate of 34 percent? (Round intermediate calculations to 4 decimal places, e.g. 1.2514 and final answer to 2 decimal places, e.g. 15.25%.) After-tax cost of debt

Answer 1

Given,

CMP of the bond = $1117.25

Semi-annual interest on the bond = $ 0.155*1000/2 =  $77.50

(a1) The cash flow pattern for the bond will be as follows:

Period	Cash Flow
Year 0	$ -1,117.25
	$         77.50
Year 1	$         77.50
	$         77.50
Year 2	$         77.50
	$         77.50
Year 3	$         77.50
	$         77.50
Year 4	$         77.50
	$         77.50
Year 5	$         77.50
	$         77.50
Year 6	$         77.50
	$         77.50
Year 7	$         77.50
	$         77.50
Year 8	$         77.50
	$         77.50
Year 9	$         77.50
	$         77.50
Year 10	$         77.50
	$         77.50
Year 11	$         77.50
	$         77.50
Year 12	$   1,077.50

Using Excel's IRR function, we find that the IRR is 6.75% for this schedule, which is a semi-annual one.

Hence, YTM = 6.75*2 = 13.5%.

(a2) After-tax cost of debt = YTM * (1-tax rate) = 13.5*(1-0.34) = 13.5*0.66 = 8.91%.