Question

Merrill Lee Limited has the following information and a tax rate of 30 percent.

Debt	3,000, 6 percent coupon bonds outstanding, $1000 par value, 12 years to maturity, selling for 80 percent of par, the bonds make semiannual payments
Common stock	100,000 shares outstanding, selling for $55 per share; the beta is 1.20
Preferred stock	19,000 shares of 6 percent preferred stock outstanding, currently selling for $110 per share
Market	6 percent market risk premium and 4 percent risk-free rate

Determine the following for the company:

1. Total market value
2. After-tax cost of debt
3. Cost of common stock
4. Cost of preferred stock
5. WACC= 8.77%

PLEASE EXPLAIN THE CALCULATIONS

Answer 1

Debt:

Number of bonds outstanding = 3,000
Face Value = $1,000
Current Price = 80%*$1,000 = $800

Value of Debt = 3,000 * $800
Value of Debt = $2,400,000

Annual Coupon Rate = 6%
Semiannual Coupon Rate = 3%
Semiannual Coupon = 3%*$1,000 = $30

Time to Maturity = 12 years
Semiannual Period to Maturity = 24

Let semiannual YTM be i%

$800 = $30 * PVIFA(i%, 24) + $1,000 * PVIF(i%, 24)

Using financial calculator:
N = 24
PV = -800
PMT = 30
FV = 1000

I = 4.361%

Semiannual YTM = 4.361%
Annual YTM = 2 * 4.361%
Annual YTM = 8.722%

Before-tax Cost of Debt = 8.722%
After-tax Cost of Debt = 8.722% * (1 - 0.30)
After-tax Cost of Debt = 6.105%

Preferred Stock:

Number of shares outstanding = 19,000
Current Price = $110
Annual Dividend = 6%*$100 = $6

Value of Preferred Stock = 19,000 * $110
Value of Preferred Stock = $2,090,000

Cost of Preferred Stock = Annual Dividend / Current Price
Cost of Preferred Stock = $6 / $110
Cost of Preferred Stock = 5.455%

Equity:

Number of shares outstanding = 100,000
Current Price = $55

Value of Common Stock = 100,000 * $55
Value of Common Stock = $5,500,000

Cost of Common Equity = Risk-free Rate + Beta * Market Risk Premium
Cost of Common Equity = 4% + 1.20 * 6%
Cost of Common Equity = 11.200%

Value of Firm = Value of Debt + Value of Preferred Stock + Value of Common Stock
Value of Firm = $2,400,000 + $2,090,000 + $5,500,000
Value of Firm = $9,990,000

Weight of Debt = $2,400,000 / $9,990,000
Weight of Debt = 0.2402

Weight of Preferred Stock = $2,090,000 / $9,990,000
Weight of Preferred Stock = 0.2092

Weight of Common Stock = $5,500,000 / $9,990,000
Weight of Common Stock = 0.5506

WACC = Weight of Debt * After-tax Cost of Debt + Weight of Preferred Stock * Cost of Preferred Stock + Weight of Common Stock * Cost of Common Stock
WACC = 0.2402 * 6.105% + 0.2092 * 5.455% + 0.5506 * 11.200%
WACC = 8.77%