Question

ZipCar auto parts store has $84,000 to invest in a project to detect and reduce insier theft in their stores. They have considering investing in one of two alternatives, identified as Y and Z. Z is the higher first-cost alternative, and the incremental initial investment between the two is $26,000 and will exhibit a rate of return of 8% per year. Z requires an investment of $84,000. They expect a rate of return on the $84,000 investment of 34 percent. Answer the following questions; (a) what is the size of the investment required in Y?, and, (b) what is the rate of return on Y?

What is the size of the investment required in Y ?

What is the rate of return on Y?

Answer 1

Solution:-

A) Investment size of Y: We know that, Z is higher first cost alternative and the incremental difference is 26,000. Hence Y's investment is lower than Z by 26,000. Hence Y's investment is 84000-26000= 58000

B) Rate of return for Y: The question also mentions that incremental 26,000 returned 8% only while Z cumulatively generated 34% return.

26000 @ 8% return would be 26000*108/100 = 28080

84000 @ 34% return would be 84000*134/100 = 112560

Difference between 84000 and 26000 is Y's investment 58000. We need to check the difference between 28080 and 112560 to figure out how much 58000 (Y's investment) would have generated.

112560 - 28080= 84480

(84480/58000) - 1= 0.456552, that is 45.66% is Y's returns