If Wild Widgets, Inc., were an all-equity company, it would have a beta of 1.05. The company has a target debt-equity ratio of .55. The expected return on the market portfolio is 10 percent and Treasury bills currently yield 3.2 percent. The company has one bond issue outstanding that matures in 30 years, a par value of $1,000, and a coupon rate of 6.1 percent. The bond currently sells for $1,055. The corporate tax rate is 24 percent.

What is the company’s weighted average cost of capital? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e. g., 32.16.)

WACC is 10.18%

Explanation:

In order to compute the WACC for Wild Widgets,Inc,we need first of all ascertain the cost of debt kd and the cost of equity ke.

The cost of debt is the same the yield to maturity where yield to maturity can be computed using rate formula in excel:

=rate(nper,pmt,-pv,fv)

nper is  the number of years before maturity which is 30

pmt is the coupon payable on the bond,6.1%*$1000=$61

pv is the current price of the bond at $1,055

fv is the face value of the bond at $1,000

=rate(30,61,-1055,1000)

rate=5.71%

pretax cost of debt is 5.71%

In order to calculate levered cost of equity,we need to re-lever the beta value of 1.05 using the below formula:

Levered β=Unlevered β×(1 + [(D/E) × (1−t) )

Unlevered β=1.05

D/E=0.55

tax=tax =24%=0.24

Levered β=1.05*(1+(0.55)*(1-0.24)

                =1.05*(1+(0.55)*(0.76)

                =1.49

Levered cost of equity is then computed using the levered beta of 1.49

      Ke=risk free rate+Levered beta*(market return-risk-free rate)

risk free rate is 3.2%          

market return is 10%

ke=3.2%+1.49(10%-3.2%)

ke=13.33%

WACC=Ke*(E/V)+Kd*(D/V)*(1-t)

Ke is 13.33%

kd is 5.71%

D/E=0.55=0.55/1 which means that debt has 0.55 equity has 1

D/V=D/E+V=0.55/1+0.55=0.35

E/V=E/E+V=1/(1+0.55)=0.65

WACC=13.33%*0.65+5.71%*(0.35)*(1-0.24)

           =13.33%*0.65+5.71%*(0.35)*(0.76)

           =0.086645 +0.0151886

           =10.18%

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