Question

Daniel's Sound Systems has 300,000 shares of common stock outstanding at a market price of $50 a share. Daniel will pay in one year an annual dividend in the amount of $2.567 per share. The dividend growth rate is 5%. Daniel's also has 10,000 bonds outstanding with a par value of $1,000 per bond. The bonds carry a 8% coupon, pay interest semiannually, and mature in 10 years. The bonds are selling at a quoted price of 99.

The company's tax rate is 34%. What is Daniel's weighted average cost of capital?

Answer 1

Debt:

Number of bonds outstanding = 10,000
Face Value = $1,000
Current Price = 99% * $1,000 = $990

Value of Debt = 10,000 * $990
Value of Debt = $9,900,000

Annual Coupon Rate = 8%
Semiannual Coupon Rate = 4%
Semiannual Coupon = 4%*$1,000 = $40

Time to Maturity = 10 years
Semiannual Period to Maturity = 20

Let semiannual YTM be i%

$990 = $40 * PVIFA(i%, 20) + $1,000 * PVIF(i%, 20)

Using financial calculator:
N = 20
PV = -990
PMT = 40
FV = 1000

I = 4.07%

Semiannual YTM = 4.07%
Annual YTM = 2 * 4.07%
Annual YTM = 8.14%

Before-tax Cost of Debt = 8.14%
After-tax Cost of Debt = 8.14% * (1 - 0.34)
After-tax Cost of Debt = 5.37%

Equity:

Number of shares outstanding = 300,000
Current Price = $50

Value of Common Stock = 300,000 * $50
Value of Common Stock = $15,000,000

Cost of Common Equity = D1/P0 + g
Cost of Common Equity = $2.567 / $50 + 0.05
Cost of Common Equity = 10.13%

Value of Firm = Value of Debt + Value of Common Stock
Value of Firm = $9,900,000 + $15,000,000
Value of Firm = $24,900,000

Weight of Debt = $9,900,000/$24,900,000
Weight of Debt = 0.3976

Weight of Common Stock = $15,000,000/$24,900,000
Weight of Common Stock = 0.6024

WACC = Weight of Debt*After-tax Cost of Debt + Weight of Common Stock*Cost of Common Stock
WACC = 0.3976*5.37% + 0.6024*10.13%
WACC = 8.24%