Chapter 19, Problem 23E

To determine

Calculate return on sales (ROS), asset turnover (AT), and return on investment (ROI) for each division and also for the business as a whole for each of the three years 2016, 2017 and 2018.

Explanation of Solution

Return on Investment (ROI) is a calculation of income split in the business unit by some amount of investment.

Return on sales (ROS), or profit per dollar, indicators the capacity of the manager

Controlling expenses and raising revenue to increase profits.

Asset turnover (AT), the sales dollars generated per dollar investment, assesses the ability of managers to raise revenue from a specified investment level.

	2016		2017	2018
Revenue
Southwest	$  14,900		$   22,000	$   26,000
Midwest	6,700		7,000	7,200
Southeast	12,400		13,000	13,300
Total	$  34,000		$  42,000	$   46,500
Net Operating Income
Southwest	$    1,100	$    1,200				$     1,350
Midwest	1,250	1,600				1,550
Southeast	1,000	1,200				1,600
Total	$    3,350	$    4,000				$     4,500
Average Total Assets
Southwest	$   14,000	$  14,200			$    16,800
Midwest	4,700	4,200			4,200
Southeast	5,300	5,600			5,600
Total	$24,000	$24,000			$26,600

The formula to calculate return on sales is:

$\text{ROS}=\frac{\text{Net operating income}}{\text{Sales}}$

The formula to calculate asset turnover (AT) is:

$\text{AT}=\frac{\text{Sales}}{\text{Average total assets}}$

The formula to calculate return on investment (ROI) is:

$\text{ROI}=\text{ROS}\times \text{AT}$

OR

$\text{ROI}=\text{Net operating income}÷\text{Average total assets}$

The following table shows the ROI; AT and ROI:

2016		2017	2018
Return on Sales (ROS)
Southwest	7.4%	5.5%	5.2%
Midwest	18.7%	22.9%	22.5%
Southeast	8.1%	9.2%	12.0%
Firm	9.9%	9.5%	9.7%
Asset Turnover (AT)
Southwest	1.064	1.549	1.548
Midwest	1.426	1.667	1.714
Southeast	2.340	2.321	2.375
Firm	1.417	1.750	1.748
Return on Investment (ROI)
Southwest	7.9%	8.5%	8.0%
Midwest	26.6%	38.1%	36.9%
Southeast	18.9%	21.4%	28.6%
Firm-wide	14.0%	16.7%	16.9%

Working Notes:

Calculate ROS:

For 2016, Southwest

$\begin{array}{c}\text{ROS}=\frac{\text{1,100}}{\text{14,900}}\\ =7.4\%\end{array}$

For 2016, Midwest

$\begin{array}{c}\text{ROS}=\frac{\text{1,250}}{\text{6,700}}\\ =18.7\%\end{array}$

For 2016, Southeast

$\begin{array}{c}\text{ROS}=\frac{\text{1,000}}{\text{12,400}}\\ =8.1\%\end{array}$

For 2016, Firm

$\begin{array}{c}\text{ROS}=\frac{\text{3,350}}{\text{34,000}}\\ =9.9\%\end{array}$

For 2017, Southwest

$\begin{array}{c}\text{ROS}=\frac{\text{1,200}}{\text{22,000}}\\ =5.5\%\end{array}$

For 2017, Midwest

$\begin{array}{c}\text{ROS}=\frac{\text{1,600}}{\text{7,000}}\\ =22.9\%\end{array}$

For 2017, Southeast

$\begin{array}{c}\text{ROS}=\frac{\text{1,200}}{\text{13,000}}\\ =9.2\%\end{array}$

For 2017, Firm

$\begin{array}{c}\text{ROS}=\frac{\text{4,000}}{\text{42,000}}\\ =9.5\%\end{array}$

For 2018, Southwest

$\begin{array}{c}\text{ROS}=\frac{\text{1,350}}{\text{26,000}}\\ =5.2\%\end{array}$

For 2018, Midwest

$\begin{array}{c}\text{ROS}=\frac{\text{1,550}}{\text{7,200}}\\ =21.5\%\end{array}$

For 2018, Southeast

$\begin{array}{c}\text{ROS}=\frac{\text{1,600}}{\text{13,300}}\\ =12.0\%\end{array}$

For 2018, Firm

$\begin{array}{c}\text{ROS}=\frac{\text{4,500}}{\text{46,500}}\\ =9.7\%\end{array}$

Calculate AT:

For 2016, Southwest

$\begin{array}{c}\text{AT}=\frac{\text{14,900}}{\text{14,000}}\\ =1.064\end{array}$

For 2016, Midwest

$\begin{array}{c}\text{AT}=\frac{\text{6,700}}{\text{4,700}}\\ =1.426\end{array}$

For 2016, Southeast

$\begin{array}{c}\text{AT}=\frac{\text{12,400}}{\text{5,300}}\\ =2.340\end{array}$

For 2016, Firm

$\begin{array}{c}\text{AT}=\frac{\text{34,000}}{\text{24,000}}\\ =1.417\end{array}$

For 2017, Southwest

$\begin{array}{c}\text{AT}=\frac{\text{22,000}}{\text{14,200}}\\ =1.549\end{array}$

For 2017, Midwest

$\begin{array}{c}\text{AT}=\frac{\text{7,000}}{\text{4,200}}\\ =1.667\end{array}$

For 2017, Southeast

$\begin{array}{c}\text{AT}=\frac{\text{13,000}}{\text{5,600}}\\ =2.321\end{array}$

For 2017, Firm

$\begin{array}{c}\text{AT}=\frac{\text{42,000}}{\text{24,000}}\\ =1.750\end{array}$

For 2018, Southwest

$\begin{array}{c}\text{AT}=\frac{\text{26,000}}{\text{16,800}}\\ =1.548\end{array}$

For 2018, Midwest

$\begin{array}{c}\text{AT}=\frac{\text{7,200}}{\text{4,200}}\\ =1.714\end{array}$

For 2018, Southeast

$\begin{array}{c}\text{AT}=\frac{\text{13,300}}{\text{5,600}}\\ =2.375\end{array}$

For 2018, Firm

$\begin{array}{c}\text{AT}=\frac{\text{46,500}}{\text{26,600}}\\ =1.748\end{array}$

Calculate ROI:

For 2016, Southwest

$\begin{array}{l}\text{ROI}=\text{1,100}÷\text{14,000}\\ \text{ROI}=7.9\%\end{array}$

For 2016, Midwest

$\begin{array}{l}\text{ROI}=\text{1,250}÷\text{4,700}\\ \text{ROI}=26.6\%\end{array}$

For 2016, Southeast

$\begin{array}{l}\text{ROI}=\text{1,000}÷\text{5,300}\\ \text{ROI}=18.9\%\end{array}$

For 2016, Firm

$\begin{array}{l}\text{ROI}=\text{3,350}÷\text{24,000}\\ \text{ROI}=14.0\%\end{array}$

For 2017, Southwest

$\begin{array}{l}\text{ROI}=\text{1,200}÷\text{14,200}\\ \text{ROI}=8.5\%\end{array}$

For 2017, Midwest

$\begin{array}{l}\text{ROI}=\text{1,600}÷\text{4,200}\\ \text{ROI}=38.1\%\end{array}$

For 2017, Southeast

$\begin{array}{l}\text{ROI}=\text{1,200}÷\text{5,600}\\ \text{ROI}=21.4\%\end{array}$

For 2017, Firm

$\begin{array}{l}\text{ROI}=\text{4,000}÷\text{24,000}\\ \text{ROI}=16.7\%\end{array}$

For 2018, Southwest

$\begin{array}{l}\text{ROI}=\text{1,350}÷\text{16,800}\\ \text{ROI}=8.0\%\end{array}$

For 2018, Midwest

$\begin{array}{l}\text{ROI}=\text{1,550}÷\text{4,200}\\ \text{ROI}=36.9\%\end{array}$

For 2018, Southeast

$\begin{array}{l}\text{ROI}=\text{1,600}÷\text{5,600}\\ \text{ROI}=28.6\%\end{array}$

For 2018, Firm

$\begin{array}{l}\text{ROI}=\text{4,500}÷\text{26,600}\\ \text{ROI}=16.9\%\end{array}$