This is a model with two dates: t = 0, 1. An entrepreneur has an investment opportunity: investing A > 0 at t = 0 which generates a risky cash ow C at t = 1. The risk of C is diversifiable. The risk-free interest rate is rf > 0. The realization of C may be CL or CH: CL < A < CH; C = CH for probability p (0, 1) and C = CL for probability 1 p; pCH + (1 p)CL > A(1 + rf ). Suppose the entrepreneur starts a firm to make the investment and is the firm's only equityholder. The firm borrows D in a loan from competitive lenders. If D < A, the entrepreneur provides the remaining A D investment. If D > A, the firm pays the entrepreneur D A in dividend at t = 0. The loan is issued at a par. The interest rate on the loan is r. In case of bankruptcy, there is a cost (D (1 + r) C), where [0, 1] is a parameter. Earnings are defined as: w = C A rD. Positive earnings are taxed at rate > 0 (there is no tax credit in the case of losses): T = max (0, w). Solve for the equilibrium interest rate r on the loan as a function of D. What is the maximum amount of debt the firm is able to borrow, Dmax? (Assume CH A rDmax > 0.) 2. Use the following parameter values to build a spreadsheet to get values for r (D). Plot the function r (D) and discuss its property. CH = 150, CL = 75, rf = 5%, p = 0.5, = 0.1, = 0.2. 3. Express the total value of the levered firm V^L as a function of the unlevered firm value V^U, D and r (D). 4- Use the above parameter values to build a spreadsheet to nd the optimal borrowing. For a risky loan, does V^L increase or decrease with loan level? How does the slope compare with a risk-free loan and why? 5. How does the optimal borrowing change if the tax rate is = 0.15? How does the optimal borrowing change if tax rate is kept at = 0.2 but = 0.15? Explain your findings. 6. Express the net payoff to the entrepreneur E as a function of the unlevered firm value V^U, D and r (D). What is the relation between E and V^L? What does this relation tell us about how the entrepreneur makes the optimal borrowing decision