Question

Debt:

Number of bonds outstanding = 24,000
Face Value = \$1,000
Current Price = 107% * \$1,000 = \$1,070

Value of Debt = 24,000 * \$1,070
Value of Debt = \$25,680,000

Annual Coupon Rate = 7.30%
Semiannual Coupon Rate = 3.65%
Semiannual Coupon = 3.65% * \$1,000 = \$36.50

Time to Maturity = 18 years
Semiannual Period to Maturity = 36

Let semiannual YTM be i%

\$1,070 = \$36.50 * PVIFA(i%, 36) + \$1,000 * PVIF(i%, 36)

Using financial calculator:
N = 36
PV = -1070
PMT = 36.50
FV = 1000

I = 3.31%

Semiannual YTM = 3.31%
Annual YTM = 2 * 3.31%
Annual YTM = 6.62%

Before-tax Cost of Debt = 6.62%
After-tax Cost of Debt = 6.62% * (1 - 0.24)
After-tax Cost of Debt = 5.03%

Common Stock:

Number of shares outstanding = 570,000
Current Price = \$75

Value of Common Stock = 570,000 * \$75
Value of Common Stock = \$42,750,000

Cost of Common Equity = Risk-free Rate + Beta * Market Risk Premium
Cost of Common Equity = 4.9% + 1.19 * 6.0%
Cost of Common Equity = 12.04%

Preferred Stock:

Number of shares outstanding = 25,500
Current Price = \$96
Annual Dividend = 5.10% * \$100 = \$5.10

Value of Preferred Stock = 25,500 * \$96
Value of Preferred Stock = \$2,448,000

Cost of Preferred Stock = Annual Dividend / Current Price * 100
Cost of Preferred Stock = \$5.10 / \$96 * 100
Cost of Preferred Stock = 5.31%

Value of Firm = Value of Debt + Value of Common Stock + Value of Preferred Stock
Value of Firm = \$25,680,000 + \$42,750,000 + \$2,448,000
Value of Firm = \$70,878,000

Weight of Debt = \$25,680,000 / \$70,878,000
Weight of Debt = 0.3623

Weight of Common Stock = \$42,750,000 / \$70,878,000
Weight of Common Stock = 0.6031

Weight of Preferred Stock = \$2,448,000 / \$70,878,000
Weight of Preferred Stock = 0.0345

WACC = Weight of Debt*After-tax Cost of Debt + Weight of Common Stock*Cost of Common Stock + Weight of Preferred Stock*Cost of Preferred Stock
WACC = (0.3623 * 5.03%) + (0.6031 * 12.04%) + (0.0345 * 5.31%)
WACC = 9.27%

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