Answer:
Check the following calculations
Explanation:
Debt:
Number of bonds outstanding = 140,000
Face Value = $1,000
Current Price = 107%*$1,000 = $1,070
Value of Debt = 140,000 * $1,070
Value of Debt = $149,800,000
Annual Coupon Rate = 5.10%
Semiannual Coupon Rate = 2.55%
Semiannual Coupon = 2.55%*$1,000 = $25.50
Time to Maturity = 15 years
Semiannual Period to Maturity = 30
Let semiannual YTM be i%
$1,070 = $25.50 * PVIFA(i%, 30) + $1,000 * PVIF(i%, 30)
Using financial calculator:
N = 30
PV = -1070
PMT = 25.5
FV = 1000
I = 2.228%
Semiannual YTM = 2.228%
Annual YTM = 2 * 2.228%
Annual YTM = 4.456%
Before-tax Cost of Debt = 4.456%
After-tax Cost of Debt = 4.456% * (1 - 0.22)
After-tax Cost of Debt = 3.476%
Preferred Stock:
Number of shares outstanding = 250,000
Current Price = $103
Annual Dividend = 4.20%*$100 = $4.20
Value of Preferred Stock = 250,000 * $103
Value of Preferred Stock = $25,750,000
Cost of Preferred Stock = Annual Dividend / Current Price
Cost of Preferred Stock = $4.20 / $103
Cost of Preferred Stock = 4.078%
Equity:
Number of shares outstanding = 7,500,000
Current Price = $51
Value of Common Stock = 7,500,000 * $51
Value of Common Stock = $382,500,000
Cost of Equity = Risk-free Rate + Beta * Market Risk Premium
Cost of Equity = 2.40% + 1.15 * 7.50%
Cost of Equity = 11.025%
Answer a.
Value of Firm = Value of Debt + Value of Preferred Stock + Value of Common Stock
Value of Firm = $149,800,000 + $25,750,000 + $382,500,000
Value of Firm = $558,050,000
Answer b.
Weight of Debt = $149,800,000/$558,050,000
Weight of Debt = 0.2684
Weight of Preferred Stock = $25,750,000/$558,050,000
Weight of Preferred Stock = 0.0462
Weight of Equity = $382,500,000/$558,050,000
Weight of Equity = 0.6854
WACC = Weight of Debt*After-tax Cost of Debt + Weight of Preferred Stock*Cost of Preferred Stock + Weight of Equity*Cost of Equity
WACC = 0.2684 * 3.476% + 0.0462 * 4.078% + 0.6854 * 11.025%
WACC = 8.68%
