Question

R.S. Green has 250,000 shares of common stock outstanding at a market price of $28 a share. Next year’s annual dividend is expected to be $1.55 a share. The dividend growth rate is 2 percent. The firm also has 7,500 bonds outstanding with a face value of $1,000 per bond. The bonds carry a 7 percent coupon, pay interest semiannually, and mature in 7.5 years. The bonds are selling at 98 percent of face value. The company’s tax rate is 34 percent. What is the firm’s weighted average cost of capital?

Answer 1

Answer:

WACC 6.18%

Explanation:

to get the cost of capital we solve using the gordon model:

$\frac{divends}{return-growth} = Intrinsic \: Value$

$\frac{divends}{Price} = return-growth$

$\frac{divends}{Price} + growth = return$

$Cost of Equity =\frac{D_1}{P)} +g$

D1 1.55

P 28

f 0.00

g 0.02

$Cost of Equity =\frac{1.55}{28} +0.02$

Ke 0.075357143

Then for the cost of debt, we need to calculate the YTM of the bonds:

which is the rate at which the present value of the coupon payment and maturity equals the market price:

For the complexity this is done with excel or a financial calculator there is also an approximation formula

YTM with excel: 0.073516565

now that we good this we need to determinate the weigth of equity and debt:

250,00 shares x 28 dollars each = 7,000,000

1,500 bonds of $1,000 each at 98% = 7,350,000

value of the company: 7,000,000 + 7,350,000 = 14,350,000

Ew: 7,000,000 / 14,350,000 = 0.487804878

Dw: 7,350,000 / 14,350,000 =0.512195122

Now we got all values and we can determinate the WACC:

$WACC = K_e(\frac{E}{E+D}) + K_d(1-t)(\frac{D}{E+D})$

Ke 0.075357143

Equity weight 0.487804878

Kd 0.074

Debt Weight 0.512195122

t 0.34

$WACC = 0.075357143(0.48780487804878) + 0.074(1-0.34)(0.51219512195122)$

WACC 0.0617752 = 6.18%