Question

Q3. Suppose Westerfield Co. has the following financial information: Debt: 50,000 bonds outstanding with a face value of $1,000. The bonds currently trade at 106% of par and have 10 years to maturity. The coupon rate equals 5%, and the bonds make semi-annual interest payments. Preferred stock: 500,000 shares of preferred stock outstanding; currently trading for $108 per share and it pays a dividend of $7.25 per share every year. Common stock: 1,250,000 shares of common stock outstanding; currently trading for $65 per share. Beta equals 0.88. Market and firm information: The expected return on the market is 10%, the risk-free rate is 1.5%, the tax rate is 21% Calculate the before-tax cost of debt. (Enter percentages as decimals and round to 4 decimals) Calculate the cost of common stock.  (Enter percentages as decimals and round to 4 decimals) Calculate the weighted average cost of capital.(Enter percentages as decimals and round to 4 decimals)

Answer 1

Answer of Part 1:

Number of bonds outstanding = 50,000
Face Value = $1,000
Current Price = 106% * $1,000 = $1,060

Value of Debt = 50,000 * $1,060
Value of Debt = $53,000,000

Annual Coupon Rate = 5%
Semiannual Coupon Rate = 2.50%
Semiannual Coupon = 2.50% * $1,000 = $25

Time to Maturity = 10 years
Semiannual Period to Maturity = 20

Let semiannual YTM be i%

$1,060 = $25 * PVIFA(i%, 20) + $1,000 * PVIF(i%, 20)

Using financial calculator:
N = 20
PV = -1060
PMT = 25
FV = 1000

I = 2.1285%

Semiannual YTM = 2.1285%
Annual YTM = 2 * 2.1285%
Annual YTM = 4.2570%

Before-tax Cost of Debt = 4.2570%
After-tax Cost of Debt = 4.2570% * (1 - 0.21)
After-tax Cost of Debt = 3.3630%

Answer of Part 2:

Number of shares outstanding = 1,250,000
Current Price = $65

Value of Common Stock = 1,250,000 * $65
Value of Common Stock = $81,250,000

Cost of Common Equity = Risk-free Rate + Beta * (Market Rate of Return – Risk free rate)
Cost of Common Equity = 1.5% + 0.88 * (10% - 1.5%)
Cost of Common Equity = 1.5% + 7.48%
Cost of Common Equity = 8.9800%

Answer of Part 3:

Number of shares outstanding = 500,000
Current Price = $108
Annual Dividend = $7.25

Value of Preferred Stock = 500,000 * $108
Value of Preferred Stock = $54,000,000

Cost of Preferred Stock = Annual Dividend / Current Price
Cost of Preferred Stock = $7.25 / $108    
Cost of Preferred Stock = 6.7130%

Value of Firm = Value of Debt + Value of Preferred Stock + Value of Common Stock
Value of Firm = $53,000,000 + $54,000,000 + $81,250,000
Value of Firm = $188,250,000

Weight of Debt = $53,000,000/$188,250,000
Weight of Debt = 0.2815

Weight of Preferred Stock = $54,000,000/$188,250,000
Weight of Preferred Stock = 0.2869

Weight of Common Stock = $81,250,000/$188,250,000
Weight of Common Stock = 0.4316

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 = (0.2815*3.3630%) + (0.2869*6.7130%) + (0.4316*8.9800%)
WACC = 6.7484%