Suppose a borrower knows at time t = 0 that it will have available at time t = 1 an opportunity to invest $300 in a risky project that will pay off at time t = 2. The borrower knows that it will be able to invest in one of two mutually exclusive projects, S or R, each requiring a $300 investment. If the borrower invests in S at time t = 1, the project will yield a gross payoff of $590 with a probability of 0.8 and $200 with a probability of 0.2 at time t = 2. If the borrower invests in R at time t = 1, the project will yield a gross payoff of $670 with a probability of 0.6 and $50 with a probability of 0.4 at time t = 2. The borrowers project choice is not observable to the bank.

The riskless, single-period interest rate at time t = 0 is 3%. It is not known at time t = 0 what the riskless, single period interest rate at time t = 1 will be, but it is common knowledge that this rate will be 5% (with probability 0.60) or 9% (with probability 0.40). Assume universal risk neutrality and that the borrower has no assets than the project on which you (as the lender) can have a claim.

Suppose you are this borrowers bank and both you and the borrower recognize that this borrower has two choices: (1) it can do nothing at time t = 0 and simply borrow at the spot market at interest rate prevailing for it at time t = 1, or (2) it can negotiate at time t = 0 with you (or some other bank) for a loan commitment that will permit it to borrow at predetermined terms at time t = 1.

What advice should you give this borrower? Assume a competitive loan market in which each bank is constrained to earn zero expected profit. Determine the NPV of the alternative(s) that you recommend.