John is the owner and CEO of a company. He has two options for a project but can choose only one due to staff limitations. Both projects cost $1mill. But the risk and payoffs are different. Project a is risky, and the payoff in a year is either $2mill (probability 35%) or $800k (probability 65%). Project b on the other hand has a payoff of either $1.5mill (prob. 50%) or $1.9mill (prob. 50%). Everyone is risk neutral, the market doesn't know John's decision until a year later, and the interest rate is 9% a. If John is providing the $1mill equity money for the project, based on NPV, what will he choose?

b. If John borrows the money from the bank (interest rate 9%) and promises to take the less risky project (and keeps his promise), what is the NPV of the bank?

c. If John borrows the money from the bank, but might break his promise- based of calculations of his expected gains in a year, which project will he choose if there is limited liability and John only cares about himself. What is the NPV for the bank?

d. What is the maximum amount the bank should lend to John to make sure he chooses the project it prefers?