A firm wants to undertake an investment project which costs $25,000, which it wants to finance through a bank loan. The project has a 60 percent probability of success. If the project succeeds the firm will make a cash flow of $75,000 after a year. If it fails the firm will get a cash flow of $10,000 and will be required to pay the whole amount to the bank. The bank has a required return of 25%.

(a) What will be the bank's loan rate at which it will be willing to lend? Explain. (4 marks)

(b) How much will be the bank's safe income? (1 mark)

(c) How is the bank's lending rate related to the probability of failure? Explain your answer. (2 marks)

(d) What will be the firm's expected profit at the rate in (a)? Will the firm be willing to participate at that rate? (4 marks)

(e) How much will be the bank's uncertain income? What will be the expected values of these incomes? (4 marks)