Question

1. Assume an entrepreneur has two projects to choose. Both require $100 investment. Assume the entrepreneur is risk-neutral. Safe project: returns $140 for sure Risky project: Returns $ 200 with 50% chance and $50 with 50% chance.

If bank required collateral of $100, what would be entrepreneur’s return in each case? Which project will entrepreneur choose?

If 50% of all borrowers are safe and 50% are risky, what interest rate bank will need to charge to break even if no collateral is required?

Answer 1

If the investor borrows from the bank at limited liability then he would have to pay an interest of 10% on $100 i.e $10.

As his liability to return the money is limited he will go for the risky project as the net return he or she will get is higher than that of safe project if it's successful

Expected net return = .5(200-110)+ .5(50-50)= $45 which greater than the one with safe project i.e 140 - 110 = $30. As he has limited liability he does not have to worry about returning the money to the bank. Therefore, it is clear that the investor will chose the risky project.

Part D:

Bank's expected return on safe project = principal + interest = ?110

Bank's expected return on risky project= 1/2 ( principal + interest) + 1/2 ( liability amount) = .5(110) + .5 ( 50) = $80

Bank will prefer the safe project.