The default rate of Demurrage Associates' new customers has been running at 10%. The average sale for each new customer amounts to $800, generating a profit of $100 and a 40% chance of a repeat order next year. The default rate on repeat orders is only 2%. If the interest rate is 9%, what is the expected profit from each new customer?

Question

Quizplus · Accepted Answer

To calculate the expected profit from a new customer, we need to take into account the different possible outcomes and their probabilities:

1. The customer pays on time and does not place a repeat order: Probability = 0.6 (100% - 40%), net profit = $100 - $72 (interest cost) = $28
2. The customer pays on time and places a repeat order: Probability = 0.4 * 0.98 (40% * 98% repeat order rate), net profit = $200 - $81 (interest cost) = $119
3. The customer defaults and does not place a repeat order: Probability = 0.1 * (100% - 40%), net loss = -$800
4. The customer defaults but places a repeat order: Probability = 0.1 * 40%, net loss = -$400

Expected profit = (0.6 * $28) + (0.4 * 0.98 * $119) + (0.1 * (100% - 40%) * -$800) + (0.1 * 40% * -$400) = $50.83

Therefore, the best choice is D ($50.83).

The Default Rate of Demurrage Associates' New Customers Has Been