The default rate of Don's new customers has been running at 20%. The average sale for each new customer amounts to $500, generating a profit of $200 and a 30% chance of a repeat order next year. The default rate on repeat orders is only 5%. If the interest rate is 6%, what is the expected profit from each new customer?

Question

Quizplus · Accepted Answer

To calculate the expected profit from each new customer, we need to consider the three possible outcomes: no default or repeat purchase, default only, and default with no repeat purchase.

The probability of no default or repeat purchase is 0.7 (1-0.2-0.1) and the profit from each customer in this case is $200+($500*0.3*0.95) = $347.50.

The probability of default only is 0.2, and the profit from each customer in this case is -$500.

The probability of default with no repeat purchase is 0.1*0.2, and the profit from each customer in this case is -$500.

Therefore, the expected profit from each new customer is (0.7*$347.50) + (0.2*(-$500)) + (0.1*0.2*(-$500)) = $149.53.

Thus, the best choice is B.

The Default Rate of Don's New Customers Has Been Running