Question

Exhibit 10.1

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%.

Refer to Exhibit 10.1. What is the best estimate of the after-tax cost of debt?

	a.	5.62%
	b.	7.11%
	c.	6.77%
	d.	6.39%
	e.	6.07%

Answer 1

Before tax cost of debt is the bond’s yield to maturity; we have following formula for calculation of bond’s yield to maturity

Bond price P0 = C* [1- 1/ (1+i) ^n] /i + M / (1+i) ^n

Where,

M = value at maturity, or Face value = $3,319.97

Current market price of the bond, P0 = $881.00

C = coupon payment = 1.70%/2 * $3,319.97 = $28.22 semiannual coupon

n = number of payments = 20 years *2 = 40

i = interest rate, or yield to maturity =?

Putting all the values into formula, we get

$881.00 = $28.22 * [1 – 1 / (1+i) ^40] /i + $3,319.97 / (1+i) ^40

By trial and error method we got the value of i = 5.32%

[Or you can use excel function for YTM calculation in following manner

“= Rate(N,PMT,PV,FV)”

“Rate(40,-28.22,881,-3319.97)” = 5.32%]

And annual rate I = 5.32% *2 = 10.64%

The company's pretax cost of debt is 10.64% per annum

If the tax rate is 40 percent, then the best estimate of the after-tax cost of debt

After tax cost of debt = pretax cost of debt * (1- Tax Rate)

= 10.64% * (1- 40%)

= 10.64% * 0.60

= 6.39%

After-tax cost of debt is 6.39%

Therefore correct answer is option d. 6.39%