Consider a self-made entrepreneur in IT industry, Mr. Dragon, who has two possible investment projects that offer the following payoffs:

Project 1: Investment of $12m is required now, and the payoff one year from now is going to be $15m with probability of 1.

Project 2: Investment of $12m is required now, and the payoff one year from now is either $24m with probability 0.4 or $0 with probability 0.6.

a. Calculate the expected payoffs to the bank and Mr. Dragon in each project if the bank lends the present value of $10. Which project would Mr. Dragon undertake?

b. What is the maximum amount the bank could lend that would induce Mr. Dragon to take a project that benefits the bank?