Question

ZipCar auto parts store has $92,000 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 $34,000 and will exhibit a rate of return of 20% per year. Z requires an investment of $92,000. They expect a rate of return on the S92000 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?
The size of the investment required in Y is________.
The rate of return on Y is__________.

Answer 1

a). The investment size -- Y

As we know, Z has higher a first cost alternative and also the incremental difference is 34,000. Therefore, the investment of Y is lower than that of Z by 34,000. Thus, the investment of Y = $ 92,000 - $ 34,000

= $ 58,000

b). Rate of return for Y

The question also mentions that the incremental 34,000 returned only 20 % while Z cumulatively generated 34%

Therefore, 34,000 at the rate of 20% return =
`$34000 * (120)/(100) = 40,800$`

92,000 at the rate of 34% return =
`$92000 * (134)/(100) = 123,280$`

The difference between the 92,000 and 32,000 is the investment of Y i.e. 58,000. Thus we check the difference between the 40800 and 123280 to find out how much 58000 (Y's investment ) would have generated.

123480 - 40800 = 82,480

`$(82480)/(58000)-1 = 0.420269$`

Therefore, the return of Y is 42.03%