Question

ou are given the following information on Parrothead Enterprises: Debt: 9,200 7.3 percent coupon bonds outstanding, with 22 years to maturity and a quoted price of 108.5. These bonds pay interest semiannually and have a par value of $2,000. Common stock: 315,000 shares of common stock selling for $66.30 per share. The stock has a beta of 1.08 and will pay a dividend of $4.50 next year. The dividend is expected to grow by 5.3 percent per year indefinitely. Preferred stock: 9,800 shares of 4.65 percent preferred stock selling at $95.80 per share. The par value is $100 per share. Market: 10.2 percent expected return, risk-free rate of 4.5 percent, and a 23 percent tax rate. Calculate the company's WACC.

Answer 1

Answer:

Debt:

Number of bonds outstanding = 9,200
Face Value = $2,000
Current Price = 108.5% * $2,000 = $2,170    

Value of Debt = 9,200 * $2,170
Value of Debt = $19,964,000

Annual Coupon Rate = 7.30%
Semiannual Coupon Rate = 3.65%
Semiannual Coupon = 3.65% * $2,000 = $73

Time to Maturity = 22 years
Semiannual Period to Maturity = 44

Let semiannual YTM be i%

$2,170 = $73 * PVIFA(i%, 44) + $2,000 * PVIF(i%, 44)

Using financial calculator:
N = 44
PV = -2170
PMT = 73
FV = 2000

I = 3.28%

Semiannual YTM = 3.28%
Annual YTM = 2 * 3.28%
Annual YTM = 6.56%

Before-tax Cost of Debt = 6.56%
After-tax Cost of Debt = 6.56% * (1 - 0.23)
After-tax Cost of Debt = 5.0512%

Preferred Stock:

Number of shares outstanding = 9,800
Current Price = $95.80
Annual Dividend = 4.65% * $100 = $4.65

Value of Preferred Stock = 9,800 * $95.80
Value of Preferred Stock = $938,840

Cost of Preferred Stock = Annual Dividend / Current Price
Cost of Preferred Stock = $4.65 / $95.80
Cost of Preferred Stock = 4.8539%

Equity:

Number of shares outstanding = 315,000
Current Price = $66.30

Value of Common Stock = 315,000 * $66.30
Value of Common Stock = $20,884,500

Using CAPM Model,
Cost of Common Equity = Risk-free Rate + Beta * Market Risk Premium
Cost of Common Equity = 4.5% + (1.08 * 10.2%)
Cost of Common Equity = 15.516%

Using Growth Model,
Cost of Equity = D1 / P0 + g
Cost of Equity = $4.50 / $66.30 + 0.053
Cost of Equity = 12.0873%

Average Cost of Equity = (15.516% + 12.0873%)/2
Average Cost of Equity = 13.8017%

Value of Firm = Value of Debt + Value of Preferred Stock + Value of Common Stock
Value of Firm = $19,964,000 + $938,840 + $20,884,500
Value of Firm = $41,787,340

Weight of Debt = $19,964,000 / $41,787,340
Weight of Debt = 0.4777

Weight of Preferred Stock = $938,840 / $41,787,340
Weight of Preferred Stock = 0.0225

Weight of Common Stock = $20,884,500 / $41,787,340
Weight of Common Stock = 0.4998

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 = (0.4777 * 5.0512%) + (0.0225 * 4.8539%) + (0.4998 * 13.8017%)
WACC = 9.42%