Question

Jiminy's Cricket Farm issued a 20-year, 7 percent, semiannual bond four years ago. The bond

currently sells for 108 percent of its face value. What is the company’s pretax cost of debt? What

is the company’s aftertax cost of debt if the tax rate is 23 percent?

Answer 1

1)	Pretax cost of debt is the bonds YTM.
	YTM is that discount rate which equates the cash flows from the
	bond with the price of $1080 if it is held for 16 years, its maturity.
	The cash flows are the maturity value of $1000 at EOY 16 and
	the semi-annual interest of $35.00 for 32 half years.
	The relevant discount rate (half year) has to be found by trial and error, so that the PV of the expected cash flows equals the price of the bond.
	Discounting with 4.0%, PV of the cash flows =
	= 1000/1.04^32+35.00*(1.04^32-1)/(0.04*1.04^32) =	$      910.63
	Discounting with 3%, the PV will be:
	= 1000/1.03^32+35.00*(1.03^32-1)/(0.03*1.03^32) =	$   1,101.94
	The value of r lies between 4% and 3%.
	The exact value can be ascertained by simple interpolation as below:
	r = 3+(1101.94-1080.00)/(1101.94-910.63) =	3.11
	YTM = 3.11*2 =	6.22
	Using an online calculator, the YTM = 6.20%
	Pre-tax cost = 6.22% (more accurately 6.20%)
2)	After tax cost = 6.22%*(1-23%) =	4.79%
	[or 6.20%*(1-23%) = 4.77%]