A firm has applied for a loan with the goal to fund a risky project. The bank is considering whether to grant a loan to the firm. The bank knows that the rm may choose between two projects: A or B. The return of these two projects is described below. A: Invest 40 and obtain 100 with probability 0.6 and 50 with probability 0.4. B: Invest 40 and obtain 110 with probability 0.5 and 0 with probability 0.5. The choice, made by the rm, of which project to invest in is not veriable by the bank. However, the outcome of the project (i.e., whether the firm obtains 100, 110, 50, or 0) is veriable. The bank is a mon0polist in the lending market (that is, there is no other bank that can grant a loan to the rm) and the bank can guarantee to obtain 45 for lending 40 of its funds elsewhere. The rm does not have funds of its own to carry out the project, so that the rm gets a value of 0 if not funded by the bank. The rm operates with limited liability. That is, a loan contract specifies that the firm will have to pay ER in case the project realized return is larger than R. a) If R=60, calculate the firm's profit for choosing project A and project B. Which project would the rm choose? [5 marks] b) If R=30, calculate the rm's prot for choosing project A and project B. Which project would the firm choose? [5 marks] c) What amount R should the bank charge in order for the rm to be indifferent between choosing project A or project B? [5 marks] d) Which is the prot-maximizing amount R that the bank should charge the rm? Which project will be implemented? What is the firm's expected prot under this contract? [10 marllc'l