Question 2 (25 marks). This question is about debt, equity, and the irrelevance of capital structure

(a) [3 marks] Consider a firm that operates for one period only and pays cash flow X next period. The firm has face value of debt BL. Explain, why the final payoffs of debt and equity can be expressed as min(BL,X) and max(X- BL,0), respectively.

(b) [7 marks] The current value of the ABC corporations assets is 100 million. The value of assets either goes up by 15% or down by 10% each period. The riskless interest rate per period is 2%. Calculate the risk-neutral probabilities of the up and down moves. The corporation has debt with face value K=102 million that matures at date T=1 (next period). Calculate the time-0 value of the companys debt and equity. Verify that the combined value of debt and equity is the same as the value of the firms assets. Explain your result.

(c) [7 marks] Assume that the CAPM and the Modigliani and Miller propositions hold. Assume also that firm debt is riskless and its rate of return is 10%. Consider a firm that has a debt-to- equity ratio of 0.8 and return on equity of 15%. Equity beta is 1.3. What is the return on assets for this firm? What is the beta of the assets?

(d) [8 marks] Suppose, a firm has cash flow X at the final date T. The firm issues equity and debt with face value B. However, default is costly. In particular, if the firm defaults on its debt, its cash flow after default goes down by a% due to various bankruptcy costs. Show that the Modigliani- Miller Proposition 1 does not hold in this case.