Answer:
1. See the calculations under part 1 below.
2. We have:
Division A's Residual Income (loss) = $395,200
Division B's Residual Income (loss) = (105,600)
Division C's Residual Income (loss) = $0
3.a. Only Division B will accept the investment opportunity.
3.b. Divisions A and B will accept the investment opportunity.
Explanation:
Given:
Division A Division B Division C
Sales $15,200,000 $35,200,000 $25,200,000
Average operating assets $3,040,000 $7,040,000 $5,040,000
Net operating income $668,800 $563,200 $655,200
Min. req'd rate of return 9.00% 9.50% 13.00%
Therefore, we have:
1. Compute the margin, turnover, and return on investment (ROI) for each division.
The formulae for calculating these are:
Margin = Net Operating Income / Sales
Turnover = Sales / Average Operating Assets
Return on Investment = Margin * Turnover
Therefore, we have:
Division A:
Margin = $668,800 / $15,200,000 = 0.0440, or 4.40%
Turnover = $15,200,000 / $3,040,000 = 5 times
Return on Investment = 4.40% * 5 = 22%
Division B:
Margin = $563,200 / $35,200,000 = 0.0160, or 1.60%
Turnover = $35,200,000 / $7,040,000 = 5 times
Return on Investment = 1.60% * 5 = 8%
Division C:
Margin = $655,200 / $25,200,000 = 0.0260, or 2.60%
Turnover = $25,200,000 / $5,040,000 = 5 times
Return on Investment = 2.60% * 5 = 13%
2. Compute the residual income (loss) for each division.
The formula for calculating this is:
Residual Income (loss) = Net Operating Income - Minimum Required Return * Average Operating Assets
Therefore, we have:
Division A's Residual Income (loss) = $668,800 - (9.00% * $3,040,000) = $395,200
Division B's Residual Income (loss) = $563,200 - (9.50% * $7,040,000) = (105,600.00)
Division C's Residual Income (loss) = $655,200 - (13.00% * $5,040,000) = $0
3-a. If performance is being measured by ROI, which division or divisions will probably accept the opportunity?
The decision criterion is for a division to accept the investment opportunity if its Return on Investment (ROI) is lower than 10%. Otherwise, reject.
Based on the Return on Investment results in part 1 above, only Division B will accept the investment opportunity.
3-b. 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 10%. Otherwise, reject.
Based on the information on minimum required rate of returns given in the question, Divisions A and B will accept the investment opportunity.
