Williamson, Inc., has a debt–equity ratio of 2.54. The firm’s weighted average c

Question

Williamson, Inc., has a debt–equity ratio of 2.54. The firm’s weighted average cost of capital is 9 percent, and its pretax cost of debt is 7 percent. Williamson is subject to a corporate tax rate of 40 percent.

What is Williamson’s unlevered cost of equity capital? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

What would Williamson’s weighted average cost of capital be if the firm’s debt–equity ratio were .80 and 1.70? (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))

Explanation / Answer

a)WACC =( cost of equity **Weight of equity ) +(After tax cost of debt *Wd)

   9 = (X *.2825 )+( 4.20*.7175)

   9 = .2825X = 3.0135

.2825X = 9 - 3.0135

   X= 5.9865 / .2825

     = 21.19%

**after tax cost of debt = 7 (1-.40) =4.2%

**Weight of debt= 2.54 /(1+2.54) = 2.54 /3.54 = .7175

weight of equity = 1- .7175 = .2825

2)unlevered cost of equity = WACC /(1 - debt ratio* tax rate)

                                     = 9 / (1- .7175 *.30)

                                   = 9 /(1- .2153)

                                  =9 / .7848

                                = 11.47%

3) WACC= (21.19 *.5556) +(4.20*.4444)

              = 11.77 + 1.87

             = 13.64%

**weight of debt = .8/(1+.8) = .8/1.8

                      =.4444

equity = 1-.4444 = .5556

3b)WACC= (21.19*.3704 )+(4.2*.6296)

              = 7.85+ 2.64

              = 10.49%

**weight of debt = 1.7 /(1+1.7) = 1.7 /2.7

                         = .6296

weight of equity = 1-.6296 = .3704

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