Answer:
1. See part 1 below for the calculations.
2. We have:
Division A's Residual Income (loss) = $180,000
Division B's Residual Income (loss) = ($140,000)
Division C's Residual Income (loss) = $0
3.a. Only Division B will probably accept the investment opportunity.
3.b. Divisions A and B will probably accept the investment opportunity.
Explanation:
Note: This question is not complete as the part 3-b of the requirement is omitted. The question is therefore completed before answering the question by providing the part 3-b as follows:
b. If performance is being measured by residual income, which division or divisions will probably accept the opportunity?
The explanation of the answer is now provided as follows:
The following are given:
Division A Division B Division C
Sales $12,000,000 $14,000,000 $25,000,000
Average operating assets $3,000,000 $7,000,000 $5,000,000
Net operating income $600,000 $560,000 $800,000
Min. req'd rate of return 14% 10% 16%
1. Compute the return on investment (ROI) for each division using the formula stated in terms of margin and turnover.
The relevant formulae are as follows:
Margin = Net Operating Income / Sales
Turnover = Sales / Average Operating Assets
Return on Investment = Margin * Turnover
Therefore, we have:
Division A:
Margin = $600,000 / $12,000,000 = 0.05, or 5%
Turnover = $12,000,000 / $3,000,000 = 4 times
Return on Investment = 5% * 4 = 0.20, or 20%
Division B:
Margin = $560,000 / $14,000,000 = 0.04, or 4%
Turnover = $14,000,000 / $7,000,000 = 2 times
Return on Investment = 4% * 2 = 0.08, or 8%
Division C:
Margin = $800,000 / $25,000,000 = 0.032, or 3.20%
Turnover = $25,000,000 / $ 5,000,000 = 5 times
Return on Investment = 3.2% * 5 = 0.16, or 16%
2. Compute the residual income (loss) for each division.
The following is the formula to use:
Residual Income (loss) = Net Operating Income - (Minimum Required Return * Average Operating Assets)
Therefore, we have:
Division A's Residual Income (loss) = $600,000 - (14% * $3,000,000) = $180,000
Division B's Residual Income (loss) = $560,000 - (10% * $7,000,000) = ($140,000)
Division C's Residual Income (loss) = $800,000 - (16% * $5,000,000) = $0
3-a. Assume that each division is presented with an investment opportunity that would yield a 15% rate of return. If performance is being measured by ROI, which division or divisions will probably accept the opportunity?
If a division's Return on Investment (ROI) is less than 15%, the decision criterion is to accept the investment opportunity. Otherwise, it will be rejected. Therefore, only Division B is will probably accept the investment opportunity, based on the results of Part 1 above. Division A and C will reject it.
3-b. Assume that each division is presented with an investment opportunity that would yield a 15% rate of return. If performance is being measured by residual income, which division or divisions will probably accept the opportunity?
The decision criterion is for a division to accept the investment opportunity if its minimum required rate of return is lower than 15%. Otherwise, it will be rejected.
Based on the information in the question, Divisions A and B will probably accept the investment opportunity. Division C will reject it.
