Question

The current stock price for a company is $39 per share, and there are 7 million shares outstanding. The beta for this firms stock is 0.9, the risk-free rate is 4.3, and the expected market risk premium is 5.7%. This firm also has 100,000 bonds outstanding, which pay interest semiannually. These bonds have a coupon interest rate of 5%, 15 years to maturity, a face value of $1,000, and a current price of 1,010.44. If the corporate tax rate is 38%, 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.

The formula is given below:

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

Where:

Rf=risk-free rate of return which is the yield on default free debt like treasury notes

Rm=expected rate of return on the market.

Rm-Rf= Market risk premium

b= Stock’s beta

Ke= 4.3% + 0.9*5.7%

     = 4.3% + 5.13%

     = 9.43%.

The cost of debt is calculated by computing the yield to maturity

Face value= $1,000

Coupon arte= 5%/2= 2.5%

Coupon payment= 0.0250*1,000= $25

Time= 15 years*2= 30 semi-annual periods

Current price= present value= $1,010.44

The below has to be entered in a financial calculator to compute the yield to maturity:

FV= 1,000

PV= -1,010.44

PMT= 25

N= 30

Press the CPT key and I/Y to compute the yield to maturity.

The value obtained is 2.4504.

Therefore, the yield to maturity is 2.4504%*2= 4.90%

Market value of equity= $39*7,000,000= $273,000,000

Market value of debt=$1,010.44*100,000= $101,044,000.

Total firm capital= $273,000,000 + $101,044,000

                                 = $374,044,000.

Weight of equity= $273,000,000/ $374,044,000

                                = 0.7299*100

                                = 72.99%

Weight of debt= $101,044,000/ $374,044,000

                            = 0.2701*100

                            = 27.01%

WACC is calculated by using the formula below:

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= 0.2701*4.90*(1- 0.38) + 0.7299*9.43%

            = 0.8206 + 6.8830

            = 7.7036%   7.70%

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