Question

The current stock price for a company is $38 per share, and there are 8 million shares outstanding. The beta for this firms stock is 0.8, the risk-free rate is 4.3, and the expected market risk premium is 6.2%. This firm also has 230,000 bonds outstanding, which pay interest semiannually. These bonds have a coupon interest rate of 7%, 28 years to maturity, a face value of $1,000, and an annual yield to maturity of 8%. If the corporate tax rate is 35%, what is the Weighted Average Cost of Capital (WACC) for this firm? (Answer to the nearest hundredth of a percent, but do not use a percent sign).

Answer 1

The cost of equity is calculated using the Capital Asset Pricing Model (CAPM) which is calculated using the formula below:

Ke=Rf+b[E(Rm)-Rf]

Where:

Rf=risk-free rate of return

Rm=expected rate of return on the market.

Rm- Rf= Market risk premium

b= stock’s beta

Ke= 4.3% + 0.8*6.2%

     = 4.3% + 4.96%

     = 9.26%

The bond price is calculated by computing the present value.

Face value= future value= $1,000

Coupon rate= 7%/2= 3.5%

Coupon payment= 0.035*1,000= $35

Time= 28 years*2= 56 semi-annual periods

Yield to maturity= 8%/2= 4%

The yield to maturity is calculated by entering the below in a financial calculator:

FV= 1,000

PMT= 35

N= 56

I/Y= 4

Press the CPT key and PV to compute the price of the bond.

The value obtained is 888.90.

Therefore, the price of the bond is $888.90.

Market value of debt= $888.90*230,000= $204,447,000.

Market value of equity= $38*8,000,000= $304,000,000.

Total firm value= $204,447,000 + $304,000,000= $508,447,000.

Weight of debt in the capital structure= $204,447,000/ $508,447,000

                                                                          = 0.4021*100

                                                                          = 40.21%

Weight of equity in the capital structure= $304,000,000/ $508,447,000

                                                                             = 0.5979*100

                                                                             = 59.79%.

WACC= wd*kd(1-t)+we*ke

Where:

Wd=percentage of debt in the capital structure

We=percentage of equity in the capital structure

Kd=cost of debt

Ke=cost of equity

t= tax rate

WACC= 0.4021*8%*(1 – 0.35) + 0.5979*9.26%

            = 2.0909 + 5.5366

           = 7.6275%   7.63%

In case of any query, kindly comment on the solution.