Without using Excel

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 the tax shield. Its investment banker has indicated that the pre-tax cost of debt under various possible capital structures would be as follows: Market Debt- Market Equity- Market Debt- to-Value to-Value to-Equity Ratio Ratio Ratio (wa) (w) (D/S) Before-Tax Cost of Debt (ra) 0.0 1.0 0.00 6.0% 0.10 0.90 0.1111 6.4 0.20 0.80 0.2500 7.0 0.30 0.70 0.4286 8.2 0.40 0.60 0.6667 10.0 F. Pierce uses the 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 25%. 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