Blitz industries has a debt-equity ratio of .6. its wacc is 9.1 percent, and its cost of debt is 6.4 percent. the corporate tax rate is 22 percent.
a. what is the company's cost of equity capital?
b. what is the company's unlevered cost of equity capital?
c-1. what would the cost of equity be if the debt-equity ratio were 2?
c-2. what would the cost of equity be if the debt-equity ratio were 1.0?
c-3. what would the cost of equity be if the debt-equity ratio were zero?

a. WACC = Ke(E/V} + kd(D/V)(1-T)

                            9.1 = ke(100/160) + 6.4(60/160)(1-0.22)

                            9.1 = ke(0.625) + 2.4(0.78)

                            9.1 = 0.625ke + 1.872

                  9.1-1.872 = 0.625ke

                        7.228 = 0.625ke

                              ke = 7.228/0.625

                               ke = 11.56%

                b. WACC = Ke(E/V)

                          9.1   = ke(100/160)    

                          9.1   = 0.625ke

                           ke = 9.1/0.625

                           ke = 14.56%

                 c-1.    WACC = Ke(E/V} + kd(D/V)(1-T)

                                 9.1  = ke(1/3) + 6.4(2/3)(1-0.22)

                                 9.1  = 0.3333ke + 3.328

                     9.1 - 3.328 = 0.3333ke

                            5.772   = 0.3333ke

                                 ke = 5.772/0.3333

                                 ke = 17.32%

                    c-2.     9.1 = ke(1/2) + 6.4(1/2)(1-0.22)  

                                9.1 = 0.5ke   + 2.496

                   9.1 - 2.496 = 0.5ke

                           6.604 = 0.5ke

                                ke = 6.604/0.5

                                ke = 13.21%

                   c-3.  9.1 = ke (0/0) + kd (0/)

                            ke = 0%

Explanation:

a. in the a part of the question, the debt-equity ratio was 0.6 ie 60/100. Thus, the value of the firm equals 160. The figures given in the question were substituted in the formula. Cost of equity was not provided, therefore, it becomes the subject of the formula. The variables are defined as follows:

ke = Cost of equity = ?

kd = Cost of debt  = 6.4%

 E = Value of equity = 100

 D = Value of debt = 60

 V = Value of the firm ie E + D = 100 + 60 = 160

 T = Tax rate = 22% = 0.22

b. In this part of the question, only equity would be considered since we are calculating unlevered cost of equity. The part of the formula that deals with debt will be ignored.

c-1.  In this case, the debt-equity ratio is 2. Therefore, debt equals 2 while equity is 1. The value of the firm becomes 3. There is need to substitute these values in the original formula while other variables remain constant.

c-2. In this scenario, the debt-equity ratio is 1. Thus, equity is 1 and debt is also 1. The value of the company changes to 2. These new values would be substituted in the formula in order to obtain the new cost of equity.

c-3. since the debt-equity ratio is 0, therefore, the cost of equity equals 0.

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