Chapter 9, Problem 20PSB

a.

To determine

Calculate the profit margin of Corporation S.

Explanation of Solution

Operating profit margin: This ratio gauges the operating profitability by quantifying the amount of income earned from business operations from the sales generated.

Formula of operating profit margin:

$\text{Operating profit margin}=\frac{\text{Operating income}}{\text{Sales}}$

Calculate the profit margin of Corporation S, if operating income is $16,000 and sales is $320,000.

$\begin{array}{c}\text{Operating profit margin =}\frac{\text{Operating income}}{\text{Sales}}\\ \text{= }\frac{\text{\$16,000}}{\text{\$320,000}}\\ \text{= 0}\text{.05 or 5\%}\end{array}$

Conclusion

Thus, the profit margin of Corporation S is 5%.

b.

To determine

Calculate the turnover of Corporation S.

Explanation of Solution

Investment turnover: This ratio gauges the operating efficiency by quantifying the amount of sales generated from the assets invested.

Formula of investment turnover:

$\text{Investment turnover}=\frac{\text{Sales}}{\text{Operating assets}}$

Calculate the turnover of Corporation S, if operating assets is $200,000 and sales is $320,000.

$\begin{array}{c}\text{Turnover =}\frac{\text{Sales}}{\text{Operating assets}}\\ \text{= }\frac{\text{\$320,000}}{\text{\$200,000}}\\ \text{= 1}\text{.6 times}\end{array}$

Conclusion

Thus, the turnover of Corporation S is 1.6 times.

c.

To determine

Calculate the return on investment (ROI) of Corporation S.

Explanation of Solution

Calculate the ROI of Corporation S, if operating income is $16,000, and operating assets are $200,000.

$\begin{array}{c}\text{Return on investment = }\frac{\text{Operating income}}{\text{Operating assets}}\\ \text{=}\frac{\text{\$16,000}}{\text{\$200,000}}\\ \text{= 0}\text{.08 or 8\%}\end{array}$

Conclusion

Thus, the ROI of Corporation S is 8%.

d-1.

To determine

Calculate the ROI of Corporation S, if operating income increases to $18,000, and sales increases to $360,000.

Explanation of Solution

Formula of ROI according to DuPont formula:

$\begin{array}{c}\text{Return on investment = Profit margin × Investment turnover}\\ \text{=}\frac{\text{Operating income}}{\text{Sales}}\times \frac{\text{Sales}}{\text{Operating assets}}\\ \text{=}\frac{\text{Operating income}}{\text{Operating assets}}\end{array}$

Calculate the ROI of Corporation S, if operating income increases to $18,000, sales increases to $360,000, and operating assets remain at $200,000.

$\begin{array}{c}\text{Return on investment =Profit margin × Investment turnover}\\ \text{=}\frac{\text{Operating income}}{\text{Sales}}\times \frac{\text{Sales}}{\text{Operating assets}}\\ =\frac{\$18,000}{\$360,000}\times \frac{\$360,000}{\$200,000}\\ \text{= }5\%\times 1.8\\ \text{= 0}\text{.09 or 9\%}\end{array}$

Conclusion

Thus, ROI of Corporation S is 9%.

2.

To determine

Calculate the ROI of Corporation S, if operating income increases to $16,800.

Explanation of Solution

Calculate the ROI of Corporation S, if operating income increases to $16,800, sales remain at $320,000, and operating assets remain at $200,000.

$\begin{array}{c}\text{Return on investment =Profit margin × Investment turnover}\\ \text{=}\frac{\text{Operating income}}{\text{Sales}}\times \frac{\text{Sales}}{\text{Operating assets}}\\ =\frac{\$16,800}{\$320,000}\times \frac{\$320,000}{\$200,000}\\ \text{= }5.25\%\times 1.6\\ \text{= 0}\text{.084 or 8}\text{.4\%}\end{array}$

Conclusion

Thus, ROI of Corporation S is 8.4%.

3.

To determine

Calculate the ROI of Corporation S, if operating assets decreases to $160,000.

Explanation of Solution

Calculate the ROI of Corporation S, if operating assets decreases to $160,000, sales remain at $320,000, and operating income remains at $16,000.

$\begin{array}{c}\text{Return on investment =Profit margin × Investment turnover}\\ \text{=}\frac{\text{Operating income}}{\text{Sales}}\times \frac{\text{Sales}}{\text{Operating assets}}\\ =\frac{\$16,000}{\$320,000}\times \frac{\$320,000}{\$160,000}\\ \text{= }5\%\times 2\\ \text{= 0}\text{.01 or 10\%}\end{array}$

Conclusion

Thus, ROI of Corporation S is 10%.