Chapter 23, Problem 23.16EX

Determining missing items from computations

Data for the North, South, East, and West divisions of Free Bird Company are as follows:

1. A. Determine the missing items, identifying each by the letters (A) through (L). (Round per­centages and investment turnover to one decimal place.)
2. B. Determine the residual income for each division, assuming that the minimum acceptable return on investment established by management is 12%.
3. C. Which division is the most profitable in terms of (1) return on investment and (2) residual income?

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:

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

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)

To compute: The missing items

Explanation of Solution

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.

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

To determine

Residual income of for each division

Explanation of Solution

1)

Determine 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)

Determine 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)

Determine 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)

Determine 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.

To determine

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%.