A total of $50,000 was allocated to a project to detect and reduce insider theft in the ZipCar auto parts store. Two alternatives identified as Y and Z are under consideration. The overall ROR on the

(a) The first step is to calculate the amount allocated to alternative Z. Since it is stated that Z is the higher first-cost alternative, we can assume that its cost is $30,000 ($50,000 - $20,000). We know that the incremental difference between Y and Z is $20,000 and the rate of return on this increment is 15%, therefore the investment required in Y can be calculated as follows: Investment in Y = $30,000 - ($20,000 / 1.15) Investment in Y = $30,000 - $17,391.30 Investment in Y = $12,608.70 Therefore, the size of the investment required in Y is $12,608.70. (b) The overall ROR on the $50,000 is expected to be 40%, which means that the total return on investment is $20,000 ($50,000 x 40%). We know that the cost of alternative Y is $12,608.70, therefore the remaining amount of return to be earned on Y is $7,391.30 ($20,000 - $12,608.70). The rate of return on Y can be calculated using the following formula: Rate of return on Y = (Return on investment / Investment) x 100% Rate of return on Y = ($7,391.30 / $12,608.70) x 100% Rate of return on Y = 58.56% Therefore, the rate of return on Y is 58.56%.