Problem
1. You are evaluating a loan request of $13.0 million from Precise Corp (The bank will generously only require an expected return of the principal). The firm has an existing debt repayment obligation of $5.0 million. It has $4.0 million in equity. The firm has two projects, A and B. An investment in A will yield a payoff of $11.5 million with a probability of 0.8 and $6.0 million with a probability of 0.2. An investment in B will yield a payoff of $14.0 million with a probability of 0.4 and 2.5 million with a probability of 0.6. The firm has assets-in-place that generates $10 million with a probability of 0.75 and $2.5 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?
2. Consider the case if an investment in B had a revised payoff of $18.0 million with a probability of 0.4 and 2.5 million with a probability of 0.6.