Question

You are given the following information concerning Parrothead Enterprises: Debt: 9,100 6.3 percent coupon bonds outstanding, with 24 years to maturity and a quoted price of 104.25. These bonds pay interest semiannually. Common stock: 230,000 shares of common stock selling for $64.60 per share. The stock has a beta of .86 and will pay a dividend of $2.80 next year. The dividend is expected to grow by 5.1 percent per year indefinitely. Preferred stock: 8,100 shares of 4.55 percent preferred stock selling at $94.10 per share. Market: An expected return of 11.9 percent, a risk-free rate of 5.05 percent, and a 34 percent tax rate. Calculate the WACC for Parrothead Enterprises. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) WACC

Answer 1

Debt:

Number of bonds outstanding = 9,100
Face Value = $1,000
Current Price = 104.25%*$1,000 = $1,042.50

Value of Debt = 9,100 * $1,042.50
Value of Debt = $9,486,750

Annual Coupon Rate = 6.30%
Semiannual Coupon Rate = 3.15%
Semiannual Coupon = 3.15%*$1,000 = $31.50

Time to Maturity = 24 years
Semiannual Period to Maturity = 48

Let semiannual YTM be i%

$1,042.50 = $31.50 * PVIFA(i%, 48) + $1,000 * PVIF(i%, 48)

Using financial calculator:
N = 48
PV = -1042.50
PMT = 31.50
FV = 1000

I = 2.98%

Semiannual YTM = 2.98%
Annual YTM = 2 * 2.98%
Annual YTM = 5.96%

Before-tax Cost of Debt = 5.96%
After-tax Cost of Debt = 5.96% * (1 - 0.34)
After-tax Cost of Debt = 3.934%

Preferred Stock:

Number of shares outstanding = 8,100
Current Price = $94.10
Annual Dividend = 4.55%*$100 = $4.55

Value of Preferred Stock = 8,100 * $94.10
Value of Preferred Stock = $762,210

Cost of Preferred Stock = Annual Dividend / Current Price
Cost of Preferred Stock = $4.55 / $94.10
Cost of Preferred Stock = 4.835%

Equity:

Number of shares outstanding = 230,000
Current Price = $64.60

Value of Equity = 230,000 * $64.60
Value of Equity = $14,858,000

Using DDM:

Cost of Equity = Expected Dividend / Current Price + Growth Rate
Cost of Equity = $2.80 / $64.60 + 0.051
Cost of Equity = 0.09434 or 9.434%

Using CAPM:

Cost of Equity = Risk-free Rate + Beta * (Market Return - Risk-free Rate)
Cost of Equity = 5.05% + 0.86 * (11.90% - 5.05%)
Cost of Equity = 10.941%

Expected Cost of Equity = (9.434% + 10.941%) / 2
Expected Cost of Equity = 10.1875%

Value of Firm = Value of Debt + Value of Preferred Stock + Value of Equity
Value of Firm = $9,486,750 + $762,210 + $14,858,000
Value of Firm = $25,106,960

Weight of Debt = $9,486,750 / $25,106,960
Weight of Debt = 0.3779

Weight of Preferred Stock = $762,210 / $25,106,960
Weight of Preferred Stock = 0.0304

Weight of Equity = $14,858,000 / $25,106,960
Weight of Equity = 0.5917

WACC = Weight of Debt * After-tax Cost of Debt + Weight of Preferred Stock * Cost of Preferred Stock + Weight of Equity * Cost of Equity
WACC = 0.3779 * 3.934% + 0.0304 * 4.835% + 0.5917 * 10.1875%
WACC = 7.66%