Selected sales and operating data for three divisions of different structural engineering firms are given 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	$	16,000,000		$	36,000,000		$	20,800,000
Average operating assets	$	3,200,000		$	7,200,000		$	5,200,000
Net operating income	$	752,000		$	576,000		$	540,800
Minimum required rate of return		9.00	%		9.50	%		10.40	%

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 10% 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 or reject the opportunity?

Solution

1.

ROI computations:

ROI =	Net operating income	×	Sales
	Sales		Average operating assets

Division A:

ROI =	$752,000	×	$16,000,000	= 4.70% × 5.00 = 23.50%
	$16,000,000		$3,200,000

Division B:

ROI =	$576,000	×	$36,000,000	= 1.60% × 5.00 = 8.00%
	$36,000,000		$7,200,000

Division C:

ROI =	$540,800	×	$20,800,000	= 2.60% × 4.00 = 10.40%
	$20,800,000		$5,200,000

2.

	Division A			Division B			Division C
Average operating assets	$	3,200,000		$	7,200,000		$	5,200,000
Required rate of return	×	9.00	%	×	9.50	%	×	10.40	%
Minimum required return	$	288,000		$	684,000		$	540,800
Actual operating income	$	752,000		$	576,000		$	540,800
Minimum required return (above)		288,000			684,000			540,800
Residual income	$	464,000		$	(108,000	)	$	0

3.

a. & b.

	Division A	Division B	Division C
Return on investment (ROI)	23.50%	8.00%	10.40%
Therefore, if the division is presented with an investment opportunity yielding 10%, it probably would	Reject	Accept	Reject
Minimum required return for computing residual income	9.00%	9.50%	10.40%
Therefore, if the division is presented with an investment opportunity yielding 10%, it probably would	Accept	Accept	Reject

If performance is being measured by ROI, both Division A and Division C probably would reject the 10% investment opportunity. These divisions’ ROIs currently exceed 10%; accepting a new investment with a 10% rate of return would reduce their overall ROIs. Division B probably would accept the 10% investment opportunity because accepting it would increase the division’s overall rate of return.

If performance is measured by residual income, both Division A and Division B probably would accept the 10% investment opportunity. The 10% rate of return promised by the new investment is greater than their required rates of return of 9% and 10%, respectively, and would therefore add to the total amount of their residual income. Division C would reject the opportunity because the 10% return on the new investment is less than its 10% required rate of return.
Thank you!