Question

You are given the following information on Parrothead Enterprises: Debt: 9,400 7.2 percent coupon bonds outstanding, with 24 years to maturity and a quoted price of 108.25. These bonds pay interest semiannually and have a par value of $2,000. Common stock: 325,000 shares of common stock selling for $66.50 per share. The stock has a beta of 1.10 and will pay a dividend of $4.70 next year. The dividend is expected to grow by 5.5 percent per year indefinitely. Preferred stock: 10,000 shares of 4.75 percent preferred stock selling at $96.00 per share. The par value is $100 per share. Market: 10.5 percent expected return, risk-free rate of 4.6 percent, and a 25 percent tax rate.

Answer 1

Debt: Number of Bonds = 9400, Coupon Rate = 7.2 %, Coupon Frequency: Semi-Annual, Tenure = 24 years or (24 x 2) = 48 semi-annual periods, Par Value = $ 2000, Bond Price = 108.25 % of Par Value = 1.0825 x 2000 = $ 2165

Semi-Annual Coupon = 0.072 x 0.5 x 2000 = $ 72

Let the yield to maturity be 2y%

Therefore, 2165 = 72 x (1/y) x [1-{1/(1+y)^(48)}] + 2000 / (1+y)^(48)

Using EXCEL's Goal Seek Function to solve the above equation, we get:

y = 0.03258 or 3.258 % ~ 3.26 %

Cost of Debt = Yield to Maturity = kd = 3.258 x 2 = 6.516 %

Market Value of Debt = 9400 x 2165 = $ 20351000

Common Stock: Number of Shares Outstanding = 325000 and Price per Share = $ 66.5

Market Value of Equity = 325000 x 66.5 = $ 21612500

Current Stock Price = P0 = $ 66.5, Expected Dividend = D1 = $ 4.7, Perpetual Dividend Growth Rate = g = 5.5 %

Therefore, Cost of Equity by Gordon Growth Model = ke1 = (D1/P0) + g = (4.7/66.5) + 0.055 = 0.12568 or 12.568%

Beta = B = 1.1, Market Return = Rm = 10.5 % and Risk-Free Rate = Rf = 4.6 %

Cost of Equity as per CAPM = ke2 = Rf + B x (Rm - Rf) = 4.6 + 1.1 x (10.5 - 4.6) = 11.09 %

Overall Cost of Equity = ke = Average (ke1,ke2) = 11.8288 %

Preferred Stock :

Number of Preferred Stock = 10000, Par Value = $ 100, Dividend = 4.75 % of Par Value = 0.0475 x 100 = $ 4.75 and Price = $ 96

Cost of Preferred Stock = kp = (4.75/96) = 0.049479 or 4.9479 %

Market Value of Preferred Stock = 96 x 10000 = $ 960000

Total Market Value of Firm = 20351000 + 21612500 + 960000 = $ 42923500

Debt Proportion = (20351000/42923500) = 0.4741 = D

Common Stock Proportion = E = (21612500/42923500) = 0.5035

Preferred Stock Proportion = P = (960000/42923500) = 0.0224

Tax Rate = t = 25 %

WACC = D x (1-t) x kd + E x ke + P x kp = 0.4741 x (1-0.25) x 6.516 + 0.5035 x 11.8288 + 0.0224 x 4.9479 = 8,3835 % ~ 8.38 %