Herb has an idea for a project. The great thing about the project is that it requires no work on Herb's part. But Herb does need $200,000 to pursue it. In one year, the project will either work out as hoped or not. If it works out, the project pays $240,000 (a $40,000 gain). If it doesn't work out, the project pays $140,000 (a $60,000 loss). There is a 70% probability the project will work out and a 30% probability it will not.

Herb and all others are risk neutral. The interest rate on 1-year U.S. discount bonds is 6%.

Start by assuming Herb has no assets to pledge as collateral, no net worth, and no reputational capital to lose. This means Herb will not be able to pay in full if the project doesn't work out as hoped and has nothing else to lose if he defaults.

 

a. If Herb can borrow $200,000 at 6%, would it make sense for him to pursue the project? Briefly explain.

 

b. What is the expected return on a 6% loan to Herb from the perspective of the lender?

 

c. Would a (risk-neutral) lender make the loan at 6% if she knew the project payouts and their probabilities? Briefly explain.

 

d. Is there an interest rate at which an informed lender would be willing to lend and at which Herb would be willing to borrow? Briefly explain.