Assume that you have two investment alternatives: the first project produces $125 for sure, and the second project produces $150 with probability 2/5. You can borrow $110 from your financial institution for one project (investment) if you show an asset as a collateral. Suppose that you maximize your expected profit, what would be the minimum level of collateral that make you select the safe project?
Expected profit is the profit expected
by the investor on the investment made. This expected profit is computed based on past trends ans various variables and probabilities.
Collateral is a security which is submitted by the debtor to the creditor as a security against loan. In case the debtor fails pay the loan the collateral acts as a compensation for the unpaid loan.
It is given that first project's return is 100% sure. Therefore
Expected profit out of first project is
It is given that second project produces a return of . Therefore,
Expected profit out of second project is
It is evidently seen that the first projects yields 100% profit and the expected profit $125 of the first project is more than the second project's expected return of $60.
Therefore the first project is chose to loaned against a loan amount of $110.
It is seen that since the expected probability of the return produced is 100%, the minimum collateral to be presented against should not be more than the 50% of the expected profit of the project.
The minimum collateral to be placed is
It can also be seen that collateral to be placed is well within the loan borrowing limits.