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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__________.

Respuesta :

Solution :

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 = [tex]$34000 \times \frac{120}{100} = 40,800$[/tex]

                   92,000 at the rate of 34% return = [tex]$92000 \times \frac{134}{100} = 123,280$[/tex]

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

[tex]$\frac{82480}{58000}-1 = 0.420269$[/tex]

Therefore, the return of Y is 42.03%

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