Question

Debt: 30,000 bonds outstanding currently trading at $950 per bond. The bonds have a 5.65% coupon rate that pays semi-annually. The bond has 20 years remaining to maturity.

Preferred Stock: 100,000 shares of preferred stock that pays $6.60 per share dividend and is currently trading for $90 per share.

Common Stock: 1,400,000 shares with current market price of $76 per share. The firm is expected to pay $4.55 per share dividend next year, the growth rate is 5.80%. The market risk premium is 7.70% and the risk free rate is 2.40%. The firm beta is 1.20.

Assume a 30% tax rate.

Calculate WACC.

Answer 1

Debt:

Number of bonds outstanding = 30,000
Face Value = $1,000
Current Price = $950

Value of Debt = 30,000 * $950
Value of Debt = $28,500,000

Annual Coupon Rate = 5.65%
Semiannual Coupon Rate = 2.825%
Semiannual Coupon = 2.825%*$1,000 = $28.25

Time to Maturity = 20 years
Semiannual Period to Maturity = 40

Let semiannual YTM be i%

$950 = $28.25 * PVIFA(i%, 40) + $1,000 * PVIF(i%, 40)

Using financial calculator:
N = 40
PV = -950
PMT = 28.25
FV = 1000

I = 3.043%

Semiannual YTM = 3.043%
Annual YTM = 2 * 3.043%
Annual YTM = 6.086%

Before-tax Cost of Debt = 6.086%
After-tax Cost of Debt = 6.086% * (1 - 0.30)
After-tax Cost of Debt = 4.26%

Preferred Stock:

Number of shares outstanding = 100,000
Current Price = $90
Annual Dividend = $6.60

Value of Preferred Stock = 100,000 * $90
Value of Preferred Stock = $9,000,000

Cost of Preferred Stock = Annual Dividend / Current Price
Cost of Preferred Stock = $6.60 / $90
Cost of Preferred Stock = 7.33%

Equity:

Number of shares outstanding = 1,400,000
Current Price = $76

Value of Common Stock = 1,400,000 * $76
Value of Common Stock = $106,400,000

Using CAPM:

Cost of Common Equity = Risk-free Rate + Beta * Market Risk Premium
Cost of Common Equity = 2.40% + 1.20 * 7.70%
Cost of Common Equity = 11.64%

Using DDM:

Cost of Common Equity = Expected Dividend / Current Price + Growth Rate
Cost of Common Equity = $4.55 / $76 + 0.0580
Cost of Common Equity = 0.1179 or 11.79%

Estimated Cost of Common Equity = (11.64% + 11.79%) / 2
Estimated Cost of Common Equity = 11.715%

Value of Firm = Value of Debt + Value of Preferred Stock + Value of Common Stock
Value of Firm = $28,500,000 + $9,000,000 + $106,400,000
Value of Firm = $143,900,000

Weight of Debt = $28,500,000 / $143,900,000
Weight of Debt = 0.1981

Weight of Preferred Stock = $9,000,000 / $143,900,000
Weight of Preferred Stock = 0.0625

Weight of Common Stock = $106,400,000 / $143,900,000
Weight of Common Stock = 0.7394

WACC = Weight of Debt * After-tax Cost of Debt + Weight of Preferred Stock * Cost of Preferred Stock + Weight of Common Stock * Cost of Common Stock
WACC = 0.1981 * 4.26% + 0.0625 * 7.33% + 0.7394 * 11.715%
WACC = 9.96%