Question

You are given the following information concerning a firm:

• Debt:7,500, 6.8 coupon bonds outstanding, with 11 years to maturity and a quoted price of 927.9. These bonds pay interest semiannually

• Common stock: 284,000 shares of common stock selling for $68 per share. The stock has a beta of 1.04 and will pay a dividend of $2.62 next year. The dividend is expected to grow by 2.5% per year indefinitely.

• Preferred stock: 9,000 shares of $8 preferred stock selling at $88 per share

• Market: 14.6% expected return, 4.1% risk-free rate

• Company: 34% tax rate

Calculate the WACC for this firm.

Answer 1

Debt:

Number of bonds outstanding = 7,500
Face Value = $1,000
Current Price = $927.90

Value of Debt = 7,500 * $927.90
Value of Debt = $6,959,250

Annual Coupon Rate = 6.80%
Semiannual Coupon Rate = 3.40%
Semiannual Coupon = 3.40%*$1,000 = $34

Time to Maturity = 11 years
Semiannual Period to Maturity = 22

Let semiannual YTM be i%

$927.90 = $34 * PVIFA(i%, 22) + $1,000 * PVIF(i%, 22)

Using financial calculator:
N = 22
PV = -927.90
PMT = 34
FV = 1000

I = 3.894%

Semiannual YTM = 3.894%
Annual YTM = 2 * 3.894%
Annual YTM = 7.788%

Before-tax Cost of Debt = 7.788%
After-tax Cost of Debt = 7.788% * (1 - 0.34)
After-tax Cost of Debt = 5.14%

Preferred Stock:

Number of shares outstanding = 9,000
Current Price = $88
Annual Dividend = $8

Value of Preferred Stock = 9,000 * $88
Value of Preferred Stock = $792,000

Cost of Preferred Stock = Annual Dividend / Current Price
Cost of Preferred Stock = $8 / $88
Cost of Preferred Stock = 9.091%

Equity:

Number of shares outstanding = 284,000
Current Price = $68

Value of Equity = 284,000 * $68
Value of Equity = $19,312,000

Using CAPM:

Cost of Equity = Risk-free Rate + Beta * (Market Return - Risk-free Rate)
Cost of Equity = 4.10% + 1.04 * (14.60% - 4.10%)
Cost of Equity = 15.02%

Using DDM:

Cost of Equity = Expected Dividend / Current Price + Growth Rate
Cost of Equity = $2.62 / $68 + 0.025
Cost of Equity = 0.06353 or 6.353%

Expected Cost of Equity = (15.02% + 6.353%) / 2
Expected Cost of Equity = 10.6865%

Value of Firm = Value of Debt + Value of Preferred Stock + Value of Equity
Value of Firm = $6,959,250 + $792,000 + $19,312,000
Value of Firm = $27,063,250

Weight of Debt = $6,959,250 /$27,063,250
Weight of Debt = 0.2571

Weight of Preferred Stock = $792,000/$27,063,250
Weight of Preferred Stock = 0.0293

Weight of Equity = $19,312,000/$27,063,250
Weight of Equity = 0.7136

WACC = Weight of Debt*After-tax Cost of Debt + Weight of Preferred Stock*Cost of Preferred Stock + Weight of Equity*Cost of Equity
WACC = 0.2571*5.14% + 0.0293*9.091% + 0.7136*10.6865%
WACC = 9.21%