Question

15-10 A firm has 60,000 shares whose current price is $45.90. Those stockholders expect a return of 14%. The firm has a 3-year loan of $1,900,000 at 7.3%. It has issued 22,000 bonds with a face value of 1000, 20 years left to maturity, semiannual compounding, a coupon interest rate of 7%, and a current price of $925. Using market values for debt and equity, what is the firm’s cost of capital: A) Before taxes? B) After taxes with a tax rate of 21%?

Answer 1

Answer:

before taxes:

WACC 8.74959%

after a 21% tax-rate:

WACC 7.23587%

Explanation:

Equity:       60,000 x $45.90 = 2,754,000

Liabilities:   1,900,000 + 22,000 x 925 = 22,250,000

Value:      25,004,000

We solve for weights:

Ew =    2,754,000 / 25,004,000 =  0,1101423772196449

Lw = 22,250,000 / 25,004,000 =   0,8898576227803551

Cost of debt will be the market value rate of the bond That is the rate at which the future coupon payment and maturity matches the market price of the bond

we solve this using excel goal seek:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 35.00

time 20

rate 0.040545327

$35 \times \frac{1-(1+0.0405453269606019)^{-20} }{0.0405453269606019} = PV$

PV $473.3728

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity  $1,000.00

time  20.00

rate  0.04055

$\frac{1000}{(1 + 0.0405453269606019)^{20} } = PV$  

PV   451.6270

PV c $473.3728

PV m  $451.6270

Total $924.9998

a semiannual rate of 0.04055 is the market rate thus, cost of debt is

0.04055 x 2 = 0.081

Now we can solve for the WACC without taxes:

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

Ke 0.14000

Equity weight 0.1101

Kd 0.081

Debt Weight 0.8899

t 0

$WACC = 0.14(0.1101) + 0.081(1-0)(0.8899)$

WACC 8.74959%

wiht taxes of 21%

t 0.21

$WACC = 0.14(0.1101) + 0.081(1-0.21)(0.8899)$

WACC 7.23587%