Answer: 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.
