Question

A customer has apprached a bank for $20,000 one-year loan at a 18% interest rate. If the bank does not approve this loan application the $20,000 will be invested in bonds that earn a 5% annual return. The bank will charge the customer an up-front $200 legal fee if the loan is granted. The bank believes that there a p% chance that this customer will default on the loan, assuming that the loan is approved. If the customer defaults on the loan tha banl will lose $10,000. Should the bank make the loan?..

If the objective is to maximize the bank's profit, whar is the smallest value of p for the which the bank should not grant the loan? (Obviously as p decreases, the profitability of the loan increases.)

Explain please

Answer 1

Considering the fact that the payable upfront fee is payable by the customer and taking the analysis format.

The analysis is based on equating the min earning profit (i.e by investing in bonds ) to the interest earned by giving to the customer at a defaulting rate.

The net profit one can earn in one next by investing in bonds is 5%, i.e 1000. Therefore the probability of max defaulting is such that it should give a profit of 1000.

Please go through the analysis.

The P- the probability of defaulting is 0.191 i.e 19.1% is the max probability or the smallest p that bank should not grant the loan. Up of 19.1% can lead to unpredictive losses.