You are evaluating a loan request of $3.5 million from Precise Corp and the bank will require an expected return of 4.0 percent per annum. The firm has an existing debt repayment obligation of $4.5 million. It has $2.0 million in equity. The firm has two projects, A and B. An investment in A will yield a payoff of $5.5 million with a probability of 0.8 and $3.0 million with a probability of 0.2. An investment in B will yield a payoff of $8.0 million with a probability of 0.4 and $0.5 million with a probability of 0.6. The firm has assets-in-place that generates $5.0 million with a probability of 0.75 and $1.0 million with a probability of 0.25. Assume that the distributions of payoffs for A and B are common knowledge, and the payoff from A is statistically independent of the payoff for B. However, as a bank officer, you cannot observe the firm's project choice.

What rate should the bank charge in order to breakeven? Given this rate will a Nash equilibrium result?