Investors Al and Bea lend $100,000 to each new idea. Al's history is that he selects low-risk projects or ideas that hit 50% of the time. Bea's history is that she takes on high-risk projects that hit 20% of the time

What rate of return must each successful project pay Al and Bea for them to break even?
A) Al's rate is 200% and Bea's rate is 450%.
B) Al's rate is 100% and Bea's rate is 400%.
C) Al's rate is 200% and Bea's rate is 400%.
D) Al's rate is 450% and Bea's rate is 100%.

Answer: B
Explanation: B) With Al's rate of success, we know that five out of ten projects are successful and that he is repaid the loan five out of ten times. Therefore, we must get enough funding from the five successful projects to cover the cost of all ten projects. So if we make ten loans of $100,000 each, we need to recover $1,000,000 from the five successful projects. Thus each successful project must repay $1,000,000 / 5 = $200,000. Therefore, the loan "return" rate is on each successful project must be: ($200,000 - $100,000) / $100,000 = 100%. With Beatrice's rate of success of 20%, we have two successful projects out of every ten and so: $1,000,000 / 2 = $500,000 needs to be recovered, giving a loan return rate of ($500,000 - $100,000) / $100,000 = 400% from the two successful projects.