Question

Shanken Corp. issued a 30-year, 4.8 percent semiannual bond 3 years ago. The bond currently sells for 95 percent of its face value. The company's tax rate is 23 percent.

a.	What is the pretax cost of debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
b.	What is the aftertax cost of debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

a]	Before tax cost of debt = YTM
	YTM using the approximate formula = ((48+(1000-950)/27)/((1000+950)/2) =	5.11%
	YTM is that discount rate for which the
	PV of the expected cash flows from the
	bond will equal its price [here $950]
	The expected cash flows are:
	*maturity value of $1000 receivable at
	EOY 27
	*the semiannual interest of $24 [54 half years]
	which is an annuity.
	Such a discount rate [half yearly] is to be found
	out by trial and error.
	Discounting with 2.50%, the PV of the expected
	cash flows are:
	=1000/1.025^54+24*(1.025^54-1)/(0.025*1.025^54) =	$         970.54
	Discounting with 2.75%, the PV of the expected
	cash flows are:
	=1000/1.0275^54+24*(1.0275^54-1)/(0.0275*1.0275^54) =	$         902.14
	The half yearly discount rate lies between 2.5% and 2.75%.
	It is = 2.5%+0.25%*(970.54-950)/(970.54-902.14) =	2.5751%
	YTM = 2.5751%*2 =	5.15%
	YTM using a financial calculator =	5.14%
	Before tax cost of debt =	5.14%
b]	After tax cost of debt = Before tax cost*(1-tax rate) = 5.14%*(1-23%) =	3.96%