Question

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.

A. Calculate total Expected return on each project for the entrepreneur

B. What is his net return (i.e. his profit = Expected return minus his investment) if he had his own money to invest in a project? Which project will he choose?

C. What is his net return if he borrows from a bank with limited liability at 10% interest rate? (in this example in the low payoff state he will pay $50 to the bank as his liability is limited to what he has in his business)? Which project will he choose?

D. What is Bank’s expected return in each case (assume 10% interest rate)? Which project will bank prefer?

E. What is social net return on each project (i.e. entrepreneur’s return and bank return)? Which project is optimal from societal point of view?

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

G. 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

Let safe project be S and risky project be R

Part A :

Expected return from safe project = $140 as there is 100% guarantee that the project will give return

Expected return from risky project = probability of success × return on success + probability of failure × returl on failure = .5 × 200 + .5 × 50 = $125

Part B :

Net return from safe project = return - investment = 140-100 = $40

Net return from risky project = return - investment= 125- 100= $25

If he had invested his own money, then he would chose safe prinecp as it gives a higher net return with the same amount of investment.

Part C:

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.