1. The Bank of America faces a investor who would like to borrow $10,000 for a p

Question

1. The Bank of America faces a investor who would like to borrow $10,000 for a project. If this is a good project, it has 4/5 chance of being succeed which lead to a return of $20,000 and 1/5 chance of being failed which lead to a return of $5,000. On the other hand if this is a bad project, it has 1/5 chance of being succeed which lead to a return of $85,000 and 4/5 chance of being failed which lead to a return of $0.
(1) If the bank can distinguish the two kinds of project, what is the minimal required repayment for each of the project? Hint: a failure of the project may lead to a default.       
(2) Now that the bank can not distinguish the two kinds of project and only knows that they will appear with equal chance. If the bank can not apply the collateral strategy, can the market not fail? Hint: the market fails as long as good projects can not be funded.       
(3) What if the bank can collect collaterals? What is the minimal required collateral given the bank still can not distinguish projects?  

Explanation / Answer

1) If it is a good project then minimal repayment will be = 4/5*20000+ 1/5*5000= $17000

If it is a bad project then minimal repayment will be = 1/5*80000+4/5*0 = $16000

2) If the project appear with equal chances then 50% probability can be assigned to both the projects and a joint probability can be found to appear at the desired NPV of the project. The market will not fail, if the project is funded for the investment.

3) The minimal collateral of $16000 can be given to the bank if the bank can not distinguish the project.

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