Chapter 10, Problem 4PB

(1)

To determine

Ascertain the Profit margin, investment turnover, and return on investment of E Division

Explanation of Solution

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:

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

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.

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

Prepare the income statements for E Division of Company M for the year ended December 31, for each of the three proposals, and compute invested assets for each proposal and also compute the invested assets for each proposal

Explanation of Solution

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

Industries G
Divisional Income Statements
For the Year Ended December 31
	Proposal 1	Proposal 2	Proposal 3
Sales	$1,575,000	(2) $1,395,000	$1,575,000
Cost of goods sold	(1) 859,600	(3)  771,450	(5) 702,000
Gross profit	715,400	623,550	873,000
Operating expenses	558,000	(4) 498,000	558,000
Income from operations	$157,400	$125,550	$315,000

Table (1)

Working Notes:

(1) Compute cost of goods sold under proposal 1.

  $\begin{array}{c}\text{Revised cost of goods sold = Cost of goods sold – Depreciation}\\ \text{= \$891,000–\$31,400}\\ \text{= \$859,600}\end{array}$

(2) Compute sales under proposal 2.

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

(3) Compute cost of goods sold under proposal 2.

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

(4) Compute operating expenses under proposal 2.

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

(5) Compute cost of goods sold under proposal 3.

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

Compute invested assets for each proposal:

Compute invested assets for proposal 1.

  $\begin{array}{c}\text{Invested assets for proposal 1 = Invested assets – Transferred book value}\\ \text{= \$1,050,000–\$300,000}\\ \text{= \$750,000}\end{array}$

Compute invested assets for proposal 2.

  $\begin{array}{c}\text{Invested assets for proposal 2 = Invested assets – Increased book value}\\ \text{= \$1,050,000–\$112,500}\\ \text{= \$937,500}\end{array}$

Compute invested assets for proposal 3.

  $\begin{array}{c}\text{Invested assets for proposal 3 = Invested assets + Transferred book value}\\ \text{= \$1,050,000+\$918,750}\\ \text{= \$1,968,750}\end{array}$

(3)

To determine

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

Explanation of Solution

Ascertain the 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.

Ascertain the 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

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

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

Explanation of Solution

Ascertain the 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%.

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

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

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)).

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