Chapter 23, Problem 23.4BPR

(1)

To determine

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

Formula of profit margin:

$\text{Profit margin}=\frac{\text{Income from operations}}{\text{Sales}}$

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

Formula of investment turnover:

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

Return on investment (ROI): This financial ratio evaluates how efficiently the assets are used in earning income from operations. So, ROI is a tool used to measure and compare the performance of a units or divisions or a companies.

Formula of ROI according to Dupont formula:

$\begin{array}{c}\text{Return on investment = Profit margin × Investment turnover}\\ \text{=}\frac{\text{Income from operations}}{\text{Sales}}\times \frac{\text{Sales}}{\text{Invested assets}}\\ \text{=}\frac{\text{Income from operations}}{\text{Invested assets}}\end{array}$

To determine: Profit margin, investment turnover, and return on investment of E Division

Explanation of Solution

Determine ROI of E Division, if income from operations is $126,000, sales are $1,575,000, and assets invested are $1,050,000.

$\begin{array}{c}\text{Return on investment = Profit margin × Investment turnover}\\ \text{=}\frac{\text{Income from operations}}{\text{Sales}}\times \frac{\text{Sales}}{\text{Invested assets}}\\ =\frac{\$126,000}{\$1,575,000}\times \frac{\$1,575,000}{\$1,050,000}\\ \text{= }8.0\%\times 1.5\\ \text{= 12}\text{.0\%}\end{array}$

(2)

To determine

Income statement: The financial statement which reports revenues and expenses from business operations and the result of those operations as net income or net loss for a particular time period is referred to as income statement.

To prepare: The income statements for E Division of Industries G for the year ended December 31, 2016, for each of the three proposals, and compute invested assets for each proposal

Explanation of Solution

Prepare divisional income statements for E Division of Industries G for the year ended December 31, 2016, for the three proposals.

Industries G
Divisional Income Statements
For the Year Ended December 31, 2016
	Proposal 1	Proposal 2	Proposal 3
Sales	$1,575,000	$1,395,000	$1,575,000
Cost of goods sold	859,600	771,450	702,000
Gross profit	715,400	623,550	873,000
Operating expenses	558,000	498,000	558,000
Income from operations	$157,400	$125,550	$315,000

Table (1)

Working Notes:

Compute cost of goods sold under proposal 1.

$\begin{array}{c}\text{Revised cost of goods sold = Cost of goods sold – <x-custom-btb-me data-me-id="391" class="microExplainerHighlight">Depreciation</x-custom-btb-me>}\\ \text{= \$891,000–\$31,400}\\ \text{= \$859,600}\end{array}$

Compute sales under proposal 2.

$\begin{array}{c}\text{Revised sales = Sales – Reduction}\\ \text{= \$1,575,000–\$180,000}\\ \text{= \$1,395,000}\end{array}$

Compute cost of goods sold under proposal 2.

$\begin{array}{c}\text{Revised cost of goods sold = Cost of goods sold – Depreciation}\\ \text{= \$891,000–\$119,550}\\ \text{= \$771,450}\end{array}$

Compute operating expenses under proposal 2.

$\begin{array}{c}\text{Revised operating expenses = Operating expenses – Reduction}\\ \text{= \$558,000–\$60,000}\\ \text{= \$498,000}\end{array}$

Compute cost of goods sold under proposal 3.

$\begin{array}{c}\text{Revised cost of goods sold = Cost of goods sold – Depreciation}\\ \text{= \$891,000–\$189,000}\\ \text{= \$702,000}\end{array}$

(3)

To determine

Profit margin, investment turnover, and return on investment of E Division under the three proposals

Explanation of Solution

Determine ROI of E Division, under proposal 1, if income from operations is $157,400, sales are $1,575,000, and assets invested are $750,000.

$\begin{array}{c}\text{Return on investment = Profit margin × Investment turnover}\\ \text{=}\frac{\text{Income from operations}}{\text{Sales}}\times \frac{\text{Sales}}{\text{Invested assets}}\\ =\frac{\$157,400}{\$1,575,000}\times \frac{\$1,575,000}{\$750,000}\\ \text{= }10.0\%\times 2.1\\ \text{= 21}\text{.0\%}\end{array}$

Note: Refer to part (1) for the values of income from operations and invested assets.

Determine ROI of E Division, under proposal 2, if income from operations is $125,550, sales are $1,395,000, and assets invested are $937,500.

$\begin{array}{c}\text{Return on investment = Profit margin × Investment turnover}\\ \text{=}\frac{\text{Income from operations}}{\text{Sales}}\times \frac{\text{Sales}}{\text{Invested assets}}\\ =\frac{\$125,550}{\$1,395,000}\times \frac{\$1,395,000}{\$937,500}\\ \text{= }9.0\%\times 1.5\\ \text{= 13}\text{.5\%}\end{array}$

Note: Refer to part (1) for the values of income from operations, sales, and invested assets.

Determine ROI of E Division, under proposal 3, if income from operations is $315,000, sales are $1,575,000, and assets invested are $1,968,750.

$\begin{array}{c}\text{Return on investment = Profit margin × Investment turnover}\\ \text{=}\frac{\text{Income from operations}}{\text{Sales}}\times \frac{\text{Sales}}{\text{Invested assets}}\\ =\frac{\$315,000}{\$1,575,000}\times \frac{\$1,575,000}{\$1,968,750}\\ \text{= }20.0\%\times 0.8\\ \text{= 16}\text{.0\%}\end{array}$

Note: Refer to part (1) for the values of income from operations and invested assets.

(4)

To determine

To indicate: The proposal which meets the desired ROI of 20%

Explanation of Solution

Proposal 1 meets desired ROI of 20% because the proposal has 21.0% ROI.

(5)

To determine

The increase in investment turnover to meet the desired return of 20%.

Explanation of Solution

Determine increase in investment turnover of E Division, if income from operations is $126,000 and sales are $1,575,000.

Step 1: Find the required investment turnover to earn desired ROI of 20%.

$\begin{array}{c}\text{Return on investment = Profit margin × Investment turnover}\\ \text{=}\frac{\text{Income from operations}}{\text{Sales}}\times \text{Investment turnover}\\ 20\%=\frac{\$126,000}{\$1,575,000}\times \text{Investment turnover}\end{array}$

$\begin{array}{c}\text{20\%}\text{ = }8.0\%\times \text{Investment turnover}\\ \text{Investment turnover}\text{= }\frac{20\%}{8\%}\\ =2.5\end{array}$

Step 2: Find the increase in investment turnover, if required investment turnover is 2.5 (From Step 1), and current investment turnover is 1.50 (From Part (1)).

$\begin{array}{c}\text{Increase in turnover = Required turnover – Current turnover}\\ \text{= 2}\text{.5–1}\text{.50}\\ \text{= 1}\text{.0}\end{array}$