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?

Question

Quizplus · Accepted Answer

To break even, Al needs to have a return rate of 100% since he invests in low-risk projects that hit 50% of the time. This means that he will earn $100,000 for every successful project. 
Bea's break-even point is trickier to calculate. Since she invests in high-risk projects that hit only 20% of the time, she will need a higher return rate to break even. Let x be the rate of return that a successful project for Bea needs to pay. She loses $100,000 on projects that fail, and earns $100,000(1+x) on projects that succeed. Therefore, to break even, we solve the equation: 
0 = (-$100,000)(0.8) + ($100,000)(1+x)(0.2)
Simplifying: 
80,000 = 20,000(1+x)
4 = 1+x 
x = 3
So, Bea needs a return rate of 300% to break even. Therefore, the answer is choice B, Al's rate is 100% and Bea's rate is 400%.

Investors Al and Bea Lend $100,000 to Each New Idea