please show all work involved in deriving the answer

5. (15) Lippo In. reports the following capital structure on its balance sheet: Debt \$ 20m, Preferred stock \$ 10m, Common stock \$ 20m The debt has 10 years to maturity, carries a coupon rate of 6%, and sells at 86.58% of face value. The preferred shares have a face value of $100 each and pay an annual dividend of $11. They sell at $105 each. There are 1 million shares of common stock with a market price of $30 each. The stock has a beta of 1.2. The risk-free rate is 5%. Assume that the risk premium on the market portfolio is 6%. The tax rate is 40%. (Assume that flotation costs are negligible.) a. What is the after-tax cost of debt, preferred stock and common stock? (4.8%,10.48%, 12.2% b. What is the weighted average cost of capital for the firm, if the current capital structure based on market values is the optimal capital structure? (9.67%)