Answer:
1. See the calculations under part 1 below.
2. We have:
Division A's Residual Income (loss) = $88,450
Division B's Residual Income (loss) = $0
Division C's Residual Income (loss) = ($50,600
3.a. Only Division C will accept the investment opportunity.
3.b. Divisions A and C will accept the investment opportunity.
Explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question as follows:
Selected sales and operating data for three divisions of different structural engineering firms are given as follows:
Division A Division B Division C
Sales $ 6,100,000 $ 10,100,000 $ 9,200,000
Average operating assets $ 1,525,000 $ 5,050,000 $ 2,300,000
Net operating income $ 317,200 $ 929,200 $ 225,400
Min. req'd rate of return 15.00 % 18.40 % 12.00 %
Required:
1. Compute the return on investment (ROI) for each division using the formula stated in terms of margin and turnover.
2. Compute the residual income (loss) for each division.
3. Assume that each division is presented with an investment opportunity that would yield a 17% rate of return. a. If performance is being measured by ROI, which division or divisions will probably accept or reject the opportunity? b. If performance is being measured by residual income, which division or divisions will probably accept the opportunity?
The explanation of the answers is now provided as follows:
1. Compute the return on investment (ROI) for each division using the formula stated in terms of margin and turnover.
The relevant formulae to use are as follows:
Margin = Net Operating Income / Sales
Turnover = Sales / Average Operating Assets
Return on Investment = Margin * Turnover
Therefore, we have:
Division A:
Margin = $317,200 / $6,100,000 = 0.0520, or 5.20%
Turnover = $6,100,000 / $1,525,000 = 4 times
Return on Investment = 5.2% * 4 = 0.2080, or 20.80%
Division B:
Margin = $929,200 / $10,100,000 = 0.0920, or 9.20%
Turnover = $10,100,000 / $5,050,000 = 2 times
Return on Investment = 9.20% * 2 = 0.1840, or 18.40%
Division C:
Margin = $225,400 / $9,200,000 = 0.0245, or 2.45%
Turnover = $9,200,000 / $2,300,000 = 4 times
Return on Investment = Margin * Turnover = 2.45% * 4 = 0.0980, or 9.80%
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) = $317,200 - (15.00 % * $1,525,000) = $88,450
Division B's Residual Income (loss) = $929,200 - (18.40 % * $5,050,000) = $0
Division C's Residual Income (loss) = $225,400 - (12.00 % * $2,300,000) = ($50,600)
3. Assume that each division is presented with an investment opportunity that would yield a 17% rate of return.
3-a. If performance is being measured by ROI, which division or divisions will probably accept or reject the opportunity?
The decision criterion is for a division to accept the investment opportunity if its Return on Investment (ROI) is lower than 17%.
Based on the results in part 1 above, only Division C 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 17%.
Based on the information in the question, Divisions A and C will accept the investment opportunity.
