Consider a borrow a that can choose between two projects, S and R, each of which will pay off a random amount one period hence. Project S will yield $280 with probability all 0.8 and zero with probability 0.2 one period hence. Project R will yield $340 with probability 0.5 and $60 with probability 0.5 one period hence. As a banker you cannot control the borrowers project choice. Assume the bank's cost of funds is equal to zero and the bank officer assumes universal risk neutrality. Moreover, you can charge a borrower 400 basis points above your break-even interest rate before the borrower switches to another bank.

Compute the expected payoffs of the borrower and the bank under the following two scenarios:

1. the bank and the borrower can contract with each other however over only one period and the borrower will request a single line of $150.
2. the borrower will need a sequence of two $150 loans, with the ability to choose between S and R in each period.

3. What should be the choice of the contracting horizon? Will the bank obtain its return?

(this is the full question. nothing is missing)