A project costs $100 to finance and yields success with probability .7 (and failure with complementary probability). In the success state, it gives a profit of $180 and in the failure state it gives a profit of $0. Assume the time-premium is 10%, capital markets are perfect, and investors are risk-neutral. Assume that an entrepreneur (i.e. the manager of the project) can choose how much debt he(she) uses to fund the project. That is, he(she) can choose to self-finance 0 ≤ y ≤ 100 and finance the left-over 100 − y with a bond.
i. What is the promised repayment on a bond that costs 100 − y today?
ii. Find an expression for the expected value of the “levered equity” financing scheme, where the entrepreneur self-finances y/100 of the costs him(her)- self and the left-over with a bond.
iii. What is the optimal (i.e. profit-maximizing) choice of y?