Answer:
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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