A firm\'s current balance sheet is as follows: Assets $100 Debt $10 Equity $90 A

Question

A firm's current balance sheet is as follows:

Assets              $100                               Debt                           $10

                                                                Equity                         $90

A.) What is the firm's weighted-average cost of capital at various combinations of debt and equity, given the following information?

Debt/Assets      After-Tax Cost of Debt   Cost of Equity     Cost of Capital

0%                         8%                                          12%                                ?

10%                          8%                                          12%                                ?

20%                          8%                                          12%                                ?

30%                           8%                                          13%                                ?

40%                           9%                                          14%                                ?

50%                           10%                                        15%                                ?

60%                           12%                                        16%                                ?

B.) Construct a pro forma balance sheet that indicates the firm's optimal capital structure. Compare this balance sheet with the firm's current balance sheet. What course of action should the firm take?

Assets                               $100                  Debt                 $?

                                                                    Equity              $?

C.) As a firm initially substitutes debt for equity financing, what happens tot he cost of capital, and why?

D.) If a firm uses too much debt financing, why does the cost of capital rise?

Please be detailed in explaing the answer and show all the work please. Thank you for your help:-)

Explanation / Answer

The cost of capital (k) is a weighted average:

       k = (weight)(cost of debt) + weight(cost of equity)

      Debt/      Weight x +   Weight x    =   Cost of

      Assets      Cost           Cost          Capital

                 of Debt       of Equity     

       0%       (.0)(.08) + (1.0)(.12)   =   .120   

      10        (.1)(.08) + (.9)(.12)    =   .116

      20        (.2)(.08) + (.8)(.12)    =   .112

      30        (.3)(.08) + (.7)(.13)    =   .115

      40        (.4)(.09) + (.6)(.14)    =   .120

      50        (.5)(.10) + (.5)(.15)    =   .125

      60        (.6)(.12) + (.4)(.16)    =   .136

    b. The optimal capital structure is that combination, which minimizes the firm's cost of capital. In this case that occurs where debt is 20% of capital and the cost of capital is 11.2%. The balance sheet is

         Assets      $100    Liabilities   $20

                             Equity         80

Since the firm is currently using only 10% debt financing, it is not at its optimal capital structure and should substitute some debt for equity.

    c. The cost of capital initially declines because the effective cost of debt is less than the cost of equity.

    d. As the firm continues to substitute debt for equity, the firm becomes more financially leveraged and riskier. This causes the interest rate to rise and the cost of equity to increase. These increases in the cost of debt and equity cause the cost of capital (i.e., the weighted average) to increase.

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