Chapter 9, Problem 16E

(a)

To determine

Compute the missing terms.

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:

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

Residual income: The remaining income from operations after deducting the desired acceptable income is referred to as residual income.

Formula of residual income:

Income from operations	XXX
Less minimum acceptable income from operations as a percent of invested assets	XXX
Residual income	XXX

Table (1)

1)

Compute income from operations.

  $\begin{array}{c}\text{Profit margin}=\frac{\text{Income from operations}}{\text{Sales}}\\ 7\%=\frac{\text{Income from operations}}{\$860,000}\\ \text{Income from operations}=\$860,000\times 7\%\\ =\$60,200\end{array}$

2)

Compute invested assets.

  $\begin{array}{c}\text{Return on investment = }\frac{\text{Income from operations}}{\text{Invested assets}}\\ 17.5\%=\frac{\$60,200}{\text{Invested assets}}\\ \text{Invested assets}=\frac{\$60,200}{17.5\%}\\ =\$344,000\end{array}$

Note: Refer to missing amount (a) for value of income from operations.

3)

Compute investment turnover.

  $\begin{array}{c}\text{Investment turnover}=\frac{\text{Sales}}{\text{Invested assets}}\\ =\frac{\$860,000}{\$344,000}\\ =2.5\end{array}$

4)

Compute sales value.

  $\begin{array}{c}\text{Profit margin}=\frac{\text{Income from operations}}{\text{Sales}}\\ 4.5\%=\frac{\text{\$51,300}}{\text{Sales}}\\ \text{Sales}=\frac{\text{\$51,300}}{4.5\%}\\ =\$1,140,000\end{array}$

5)

Compute sales value.

  $\begin{array}{c}\text{Investment turnover}=\frac{\text{Sales}}{\text{Invested assets}}\\ 3.8=\frac{\$1,140,000}{\text{Invested assets}}\\ \text{Invested assets}=\frac{\$1,140,000}{3.8}\\ =\$300,000\end{array}$

Note: Refer to missing amount (d) for value of sales.

6)

Compute ROI.

  $\begin{array}{c}\text{Return on investment = }\frac{\text{Income from operations}}{\text{Invested assets}}\\ \text{= }\frac{\text{\$51,300}}{\text{\$300,000}}\\ \text{= 0}\text{.171 or 17}\text{.1\%}\end{array}$

Note: Refer to missing amount (e) for value of invested assets.

7)

Compute income from operations.

  $\begin{array}{c}\text{Return on investment = }\frac{\text{Income from operations}}{\text{Invested assets}}\\ \text{15\% = }\frac{\text{Income from operations}}{\text{\$680,000}}\\ \text{Income from operations}\text{= \$680,000}\times \text{15\%}\\ \text{=\$102,000}\end{array}$

8)

Compute profit margin.

  $\begin{array}{c}\text{Profit margin}=\frac{\text{Income from operations}}{\text{Sales}}\\ \text{= }\frac{\text{\$102,000}}{\text{\$1,020,000}}\\ \text{= \$1,140,000}\\ \text{= 0}\text{.1 or 10\%}\end{array}$

Note: Refer to missing amount (g) for value of income from operations.

9)

Compute investment turnover.

  $\begin{array}{c}\text{Investment turnover}=\frac{\text{Sales}}{\text{Invested assets}}\\ =\frac{\$1,020,000}{\text{\$680,000}}\\ =1.5\end{array}$

10)

Compute ROI.

  $\begin{array}{c}\text{Return on investment = }\frac{\text{Income from operations}}{\text{Invested assets}}\\ \text{= }\frac{\text{\$89,600}}{\text{\$560,000}}\\ \text{= 0}\text{.16 or 16\%}\end{array}$

11)

Compute profit margin.

  $\begin{array}{c}\text{Profit margin}=\frac{\text{Income from operations}}{\text{Sales}}\\ \text{= }\frac{\text{\$89,600}}{\text{\$1,120,000}}\\ \text{= \$1,140,000}\\ \text{= 0}\text{.08 or 8\%}\end{array}$

12)

Compute investment turnover.

  $\begin{array}{c}\text{Investment turnover}=\frac{\text{Sales}}{\text{Invested assets}}\\ =\frac{\$1,120,000}{\text{\$560,000}}\\ =2.0\end{array}$

(b)

To determine

Ascertain the residual income of for each division

Explanation of Solution

1)

Ascertain the residual income of N Division.

Step 1: Compute minimum acceptable income from operations as a percent of invested assets for N Division.

  $\begin{array}{c}\begin{array}{l}\text{Minimum acceptable income }\\ \text{from operations as a percent }\\ \text{of invested assets}\end{array}\}\text{ = }\left\{\begin{array}{l}\text{Invested assets }\times \\ \text{Minimum acceptable return on assets}\end{array}\right\}\\ \text{= \$344,000 × 12\%}\\ \text{= \$41,280}\end{array}$

Note: Refer to missing amount (b) of part (a) for value of invested assets.

Step 2: Determine residual income of N Division.

Particulars	Amount ($)
Income from operations	$60,200
Less minimum acceptable income from operations as a percent of invested assets	41,280
Residual income	$18,920

Table (2)

Note: Refer to missing amount (a) of part (a) for value of income from operations, and Step 1 for value and computation of minimum acceptable income.

2)

Ascertain the residual income of S Division.

Step 1: Compute minimum acceptable income from operations as a percent of invested assets for S Division.

  $\begin{array}{c}\begin{array}{l}\text{Minimum acceptable income }\\ \text{from operations as a percent }\\ \text{of invested assets}\end{array}\}\text{ = }\left\{\begin{array}{l}\text{Invested assets }\times \\ \text{Minimum acceptable return on assets}\end{array}\right\}\\ \text{= \$300,000 × 12\%}\\ \text{= \$36,000}\end{array}$

Note: Refer to missing amount (e) of part (a) for value of invested assets.

Step 2: Determine residual income of S Division.

Particulars	Amount ($)
Income from operations	$51,300
Less minimum acceptable income from operations as a percent of invested assets	36,000
Residual income	$15,300

Table (3)

Note: Refer to Step 1 for value and computation of minimum acceptable income.

3)

Ascertain the residual income of E Division.

Step 1: Compute minimum acceptable income from operations as a percent of invested assets for E Division.

  $\begin{array}{c}\begin{array}{l}\text{Minimum acceptable income }\\ \text{from operations as a percent }\\ \text{of invested assets}\end{array}\}\text{ = }\left\{\begin{array}{l}\text{Invested assets }\times \\ \text{Minimum acceptable return on assets}\end{array}\right\}\\ \text{= \$680,000 × 12\%}\\ \text{= \$81,600}\end{array}$

Step 2: Determine residual income of E Division.

Particulars	Amount ($)
Income from operations	$102,000
Less minimum acceptable income from operations as a percent of invested assets	81,600
Residual income	$20,400

Table (4)

Note: Refer to missing amount (g) of part (a) for value of income from operations, and Step 1 for value and computation of minimum acceptable income.

4)

Ascertain the residual income of W Division.

Step 1: Compute minimum acceptable income from operations as a percent of invested assets for W Division.

  $\begin{array}{c}\begin{array}{l}\text{Minimum acceptable income }\\ \text{from operations as a percent }\\ \text{of invested assets}\end{array}\}\text{ = }\left\{\begin{array}{l}\text{Invested assets }\times \\ \text{Minimum acceptable return on assets}\end{array}\right\}\\ \text{= \$560,000 × 12\%}\\ \text{= \$67,200}\end{array}$

Step 2: Determine residual income of W Division.

Particulars	Amount ($)
Income from operations	$89,600
Less minimum acceptable income from operations as a percent of invested assets	67,200
Residual income	$22,400

Table (5)

Note: Refer to missing amount (g) of part (a) for value of income from operations, and Step 1 for value and computation of minimum acceptable income.

(c) 1

To determine

Ascertain the profitable division in terms of ROI.

Explanation of Solution

The division with highest return on investment is considered as the most profitable division. Hence, N Division is the most profitable division with highest ROI of 17.5%.

(c) 2

To determine

Ascertain the division with highest residual income

Explanation of Solution

The division with highest residual income is considered as the most profitable division. Hence, W Division is the most profitable division with the highest residual income of $22,400.