A firm has an income of $20. A firm with 30% debt and 70% equity is valued at $240 whereas an all equity firm is valued at $200. Show that in a M-M world without frictions this will lead to an arbitrage opportunity. The risk free rate is 0.05. Assume that the correct value of the firm is $220. A corporate tax of 30% is imposed. If the firm takes on $100 of debt, what should its value be? What is the value of equity? How much tax is the firm paying? Assume that now that in addition to corporate taxes, equity income is taxed at 20% and there is no tax on debt income. Please explain what should the optimal captial structure of the firm be (you can either prove verbally or show with a calculation).