The firm is considering alternative capital structures. The unlevered firm beta

Question

The firm is considering alternative capital structures. The unlevered firm beta is 0.85 and the firm’s tax rate is 40%. The expected return on the market is 11.5% and the risk-free rate is 4%. Each level of debt has a corresponding cost of debt, as indicated below. Select the best capital structure for the firm and state why.

                  Debt    Kd                    Equity

            a.         $ 0       na                    $100

      b.         $40      5%                   $60

      c.         $50      7%                   $50

      d.         $60      8%                   $40

e.         $70      9%                   $30

Explanation / Answer

a. 100% equity

Cots of capital =Re = 4 + 0.85*(11.5-4) = 10.375%

b. 40% debt and 60% equity

Levered Beta = BU*(1+(1-t)*D/E) = 0.85(1+0.6*40/60) = 1.19

Cost of equity = 4 + 1.19*(11.5-4) = 12.925%

Cost of debt = 5%(1-0.4) = 3%

Cost of capital = 0.4* 3 + 0.6*12.925 = 8.955%

c. 50% debt and 50% equity

Levered Beta = BU*(1+(1-t)*D/E) = 0.85(1+0.6*50/50) = 1.36

Cost of equity = 4 + 1.36*(11.5-4) = 14.2%

Cost of debt = 7%(1-0.4) = 4.2%

Cost of capital = 0.5* 4.2 + 0.5*14.2 = 9.2%

d. 60% debt and 40% equity

Levered Beta = BU*(1+(1-t)*D/E) = 0.85(1+0.6*60/40) = 1.615

Cost of equity = 4 + 1.615*(11.5-4) = 16.1125%

Cost of debt = 8%*(1-0.4) = 4.8%

Cost of capital = 0.6* 4.8 + 0.4*16.1125 = 9.325%

e. 70% debt and 30% equity

Levered Beta = BU*(1+(1-t)*D/E) = 0.85(1+0.6*70/30) = 2.04

Cost of equity = 4 + 2.04*(11.5-4) = 19.3%

Cost of debt = 9%*(1-0.4) = 5.4%

Cost of capital = 0.7* 5.4 + 0.3*19.3 = 9.57%

Hence bes capital structure : is "b" ($40 debt and $60 equity) with a cost of 8.955%

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