Question

Assume that you have been hired as a consultant by CGT, a major producer of chemicals and plastics, including plastic grocery bags, styrofoam cups, and fertilizers, to estimate the firm's weighted average cost of capital. The balance sheet and some other information are provided below.
  Assets

Current assets	$38,000,000
Net plant, property, and equipment	$101,000,000
Total assets	$139,000,000

Liabilities and Equity

Accounts payable	$10,000,000
Accruals	$9,000,000
Current liabilities	$19,000,000
Long-term debt (40,000 bonds, $1,000 par value)	$40,000,000
Total liabilities	$59,000,000
Common stock (10,000,000 shares)	$30,000,000
Retained earnings	$50,000,000
Total shareholders' equity	$80,000,000
Total liabilities and shareholders' equity	$139,000,000

The stock is currently selling for $17.75 per share, and its noncallable $3,319.97 par value, 20-year, 1.70% bonds with semiannual payments are selling for $881.00. The beta is 1.29, the yield on a 6-month Treasury bill is 3.50%, and the yield on a 20-year Treasury bond is 5.50%. The required return on the stock market is 11.50%, but the market has had an average annual return of 14.50% during the past 5 years. The firm's tax rate is 40%.

What is the best estimate of the after-tax cost of debt?

Answer 1

1]	Before tax cost of debt = YTM.
	YTM, by approximate formula = ((17+(1000-881)/20)/((1000+881)/2) =	2.44%
	YTM is that discount rate at which the cash flows
	from the bond will equal the current price.
	Such a rate has to be found out by trial and error.
	Discounting with 3%/2 = 1.5%:
	PV = 1000/1.015^40+8.5*(1.015^40-1)/(0.015*1.015^40) =	$     805.55
	Discounting with 2%/2 = 1%:
	PV = 1000/1.01^40+8.5*(1.01^40-1)/(0.01*1.01^40) =	$     950.75
	The YTM lies between 1% and 1.5%.
	By simple interpolation, YTM = 1%+0.5%*(950.75-881)/(950.75-805.55) =	1.24%
	Annualized YTM = 1.24%*2 =	2.48%
2]	After tax cost of debt = Before tax cost of debt*(1-t) = 2.48%*(1-40%) =	1.49%
	NOTE:
	YTM using a financial calculator = 2.46%. The after tax cost of debt would then be, 2.46%*(1-40%) =	1.48%