WACC and Optimal Capital Structure (Challenging Problem)

F. Pierce Products Inc. is considering changing its capital structure. F. Pierce currently has no debt and no preferred stock, but it would like to add some debt to take advantage of low interest rates and the tax shield. its investment banker has indicated that the pre-tax cost of debt under various possible capital structuress would be as follows:

Market Debt to                     Market Equity to               Market Debt to                  Before Tax Cost

Value Ratio (Wd)                 Value Ratio (Ws)             Equity Ratio (D/S)              of Debt (rd)

0.0                                        1.0                                       0.00                                 6.0%

0.2                                         0.8                                       0.25                                 7.0

0.4                                         0.6                                        0.67                                8.0

0.6                                         0.4                                       1.50                                 9.0

0.8                                          0.2                                       4.00                                 10.0

F. Pierce uses CAPM to estimate its cost of common equity, r, and at the time of the analysis the risk free rate is 5%, the market risk premium is 6%, and the company's tax rate is 40%. F. Pierce estimates that its beta now (which is "unlevered" because it currently has no debt) is 0.8. Based on this information what is the firm's optimal capital structure, and what would be the weighted average cost of capital at the optimal capital structure? show all work and formulas to support answer.