Question

Assuming the tax rate is 40%, estimate Lightyear’s Weighted Average Cost of Capital.  Do not implement the bond?yield?plus?risk?premium approach in the process. The following information regarding Lightyear Corp.’s outstanding securities is available.

1.) 8 5 /8 % bonds: 10,000 bonds outstanding with 5 years to maturity, currently selling at $970.00 (coupons are paid semiannually)  

2.) common stock: 1,000,000 shares outstanding; currently priced at $20/share; ?=1.20; next (annual) dividend expected to be $1.00/share; dividends expected to grow at 9.5% per year indefinitely.

Answer 1

Debt:

Number of Bonds = 10,000

Face Value = $1,000
Current Price = $970

Value of Debt = 10,000 * $970
Value of Debt = $9,700,000

Annual Coupon Rate = 8.625%
Semiannual Coupon Rate = 8.625%/2
Semiannual Coupon Rate = 4.3125%
Semiannual Coupon = 4.3125%*$1,000 = $43.125

Time to Maturity = 5 years
Semiannual Period to Maturity = 10

Let semiannual YTM be i%

$970 = $43.125 * PVIFA(i%, 10) + $1,000 * PVIF(i%, 10)

Using financial calculator:
N = 10
PV = -970
PMT = 43.125
FV = 1000

I = 4.70%

Semiannual YTM = 4.70%
Annual YTM = 2 * 4.70%
Annual YTM = 9.40%

Before-tax Cost of Debt = 9.40%
After-tax Cost of Debt = 9.40%*(1-0.40)
After-tax Cost of Debt = 5.64%

Equity:

Number of shares = 1,000,000
Current Price = $20
Expected Dividend = $1.00
Growth Rate = 9.50%

Value of Equity = 1,000,000 * $20
Value of Equity = $20,000,000

Cost of Equity = Expected Dividend / Current Price + Growth Rate
Cost of Equity = $1.0 / $20 + 0.095
Cost of Equity = 14.50%

Total Value of Firm = Value of Debt + Value of Equity
Total Value of Firm = $9,700,000 + $20,000,000
Total Value of Firm = $29,700,000

Weight of Debt = $9,700,000 / $29,700,000
Weight of Debt = 0.3266

Weight of Equity = $20,000,000 / $29,700,000
Weight of Equity = 0.6734

WACC = Weight of Debt * After-tax Cost of Debt + Weight of Equity * Cost of Equity
WACC = 0.3266 * 5.64% + 0.6734 * 14.50%
WACC = 11.61%