Chapter 9, Problem 20PSB

a.

To determine

Calculate the profit margin of Corporation B.

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 B, if operating income is $24,000 and sales is $480,000.

$\begin{array}{c}\text{Operating profit margin =}\frac{\text{Operating income}}{\text{Sales}}\\ \text{= }\frac{\text{\$24,000}}{\text{\$480,000}}\\ \text{= 0}\text{.05 or 5\%}\end{array}$

Conclusion

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

b.

To determine

Calculate the turnover of Corporation B.

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 B, if operating assets is $320,000 and sales is $480,000.

$\begin{array}{c}\text{Turnover =}\frac{\text{Sales}}{\text{Operating assets}}\\ \text{= }\frac{\text{\$480,000}}{\text{\$320,000}}\\ \text{= 1}\text{.5 times}\end{array}$

Conclusion

Thus, the turnover of Corporation B is 1.5 times.

c.

To determine

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

Explanation of Solution

Calculate the ROI of Corporation B, if operating income is $24,000, and operating assets are $320,000.

$\begin{array}{c}\text{Return on investment = }\frac{\text{Operating income}}{\text{Operating assets}}\\ \text{=}\frac{\text{\$24,000}}{\text{\$320,000}}\\ \text{= 0}\text{.075 or 7}\text{.5\%}\end{array}$

Conclusion

Thus, the ROI of Corporation B is 7.5%.

d-1.

To determine

Calculate the ROI of Corporation B, if operating income increases to $28,000, and sales increases to $560,000.

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 B, if operating income increases to $28,000, sales increases to $560,000, and operating assets remain at $320,000.

$\begin{array}{c}\text{Return on investment =Profit margin × Investment turnover}\\ \text{=}\frac{\text{Operating income}}{\text{Sales}}\times \frac{\text{Sales}}{\text{Operating assets}}\\ =\frac{\$28,000}{\$560,000}\times \frac{\$560,000}{\$320,000}\\ \text{= }5\%\times 1.75\\ \text{= 0}\text{.875 or 8}\text{.75\%}\end{array}$

Conclusion

Thus, ROI of Corporation B is 8.75%.

2.

To determine

Calculate the ROI of Corporation B, if operating income increases to $25,920.

Explanation of Solution

Calculate the ROI of Corporation B, if operating income increases to $25,920, sales remain at $560,000, and operating assets remain at $320,000.

$\begin{array}{c}\text{Return on investment =Profit margin × Investment turnover}\\ \text{=}\frac{\text{Operating income}}{\text{Sales}}\times \frac{\text{Sales}}{\text{Operating assets}}\\ =\frac{\$25,920}{\$480,000}\times \frac{\$480,000}{\$320,000}\\ \text{= }5.4\%\times 1.5\\ \text{= 0}\text{.081 or 8}\text{.1\%}\end{array}$

Conclusion

Thus, ROI of Corporation B is 8.1%.

3.

To determine

Calculate the ROI of Corporation B, if operating assets decreases to $300,000.

Explanation of Solution

Calculate the ROI of Corporation B, if operating assets decreases to $300,000, sales remain at $480,000, and operating income remains at $24,000.

$\begin{array}{c}\text{Return on investment =Profit margin × Investment turnover}\\ \text{=}\frac{\text{Operating income}}{\text{Sales}}\times \frac{\text{Sales}}{\text{Operating assets}}\\ =\frac{\$24,000}{\$480,000}\times \frac{\$480,000}{\$300,000}\\ \text{= }5\%\times 1.6\\ \text{= 0}\text{.08 or 8\%}\end{array}$

Conclusion

Thus, ROI of Corporation B is 8%.