provided the following information for two of its divisions for last year

Forchen, Inc., provided the following information for two of its divisions for last year:  Small Appliances Division Cleaning Products Division Sales $34,670,000 $31,320,000 Operating income 2,773,600 1,252,800 Operating assets, January 1 6,394,000 5,600,000 Operating assets, December 31 7,474,000 6,000,000 Required: 1. For the Small Appliances Division, Calculate: A. Average operating assets
Forchen, Inc., provided the following information for two of its divisions for last year:

 Small Appliances
Division Cleaning Products
Division
Sales $34,670,000 $31,320,000
Operating income 2,773,600 1,252,800
Operating assets, January 1 6,394,000 5,600,000
Operating assets, December 31 7,474,000 6,000,000
Required:ÂÂ

1. For the Small Appliances Division, Calculate:ÂÂ

A. Average operating assets

B. Margin

C. Turnover

D. ROI

2. For the Cleaning Products Division, calculate:ÂÂ

A. Average operating assets

B. Margin

C. Turnover

D. ROI

3. What if operating income for the small appliances division was $2,000,000? How would that affect average operating assets? Margin? Turnover? ROI? Calculate any changed ratios (round to four significant digits).ÂÂ

The Correct Answer and Explanation is :

1. Small Appliances Division:

A. Average Operating Assets

The average operating assets are calculated by taking the average of the operating assets at the beginning and end of the year:

[
\text{Average Operating Assets} = \frac{\text{Operating Assets at January 1} + \text{Operating Assets at December 31}}{2}
]
[
\text{Average Operating Assets} = \frac{6,394,000 + 7,474,000}{2} = \frac{13,868,000}{2} = 6,934,000
]

B. Margin

Margin is calculated by dividing operating income by sales:

[
\text{Margin} = \frac{\text{Operating Income}}{\text{Sales}} = \frac{2,773,600}{34,670,000} = 0.08 \text{ or } 8\%
]

C. Turnover

Turnover is calculated by dividing sales by average operating assets:

[
\text{Turnover} = \frac{\text{Sales}}{\text{Average Operating Assets}} = \frac{34,670,000}{6,934,000} = 5.00
]

D. ROI (Return on Investment)

ROI is calculated by multiplying margin and turnover:

[
\text{ROI} = \text{Margin} \times \text{Turnover} = 0.08 \times 5.00 = 0.40 \text{ or } 40\%
]

---

2. Cleaning Products Division:

A. Average Operating Assets

[
\text{Average Operating Assets} = \frac{\text{Operating Assets at January 1} + \text{Operating Assets at December 31}}{2}
]
[
\text{Average Operating Assets} = \frac{5,600,000 + 6,000,000}{2} = \frac{11,600,000}{2} = 5,800,000
]

B. Margin

[
\text{Margin} = \frac{\text{Operating Income}}{\text{Sales}} = \frac{1,252,800}{31,320,000} = 0.04 \text{ or } 4\%
]

C. Turnover

[
\text{Turnover} = \frac{\text{Sales}}{\text{Average Operating Assets}} = \frac{31,320,000}{5,800,000} = 5.40
]

D. ROI (Return on Investment)

[
\text{ROI} = \text{Margin} \times \text{Turnover} = 0.04 \times 5.40 = 0.216 \text{ or } 21.6\%
]

---

3. If Operating Income for the Small Appliances Division was $2,000,000

A. Average Operating Assets

The average operating assets would remain the same because they are calculated based on the operating assets at the start and end of the year. Therefore, the average operating assets remain 6,934,000.

B. Margin

[
\text{Margin} = \frac{\text{New Operating Income}}{\text{Sales}} = \frac{2,000,000}{34,670,000} = 0.0577 \text{ or } 5.77\%
]

C. Turnover

The turnover will remain unchanged because it depends on sales and average operating assets, both of which remain constant. Therefore, turnover is still 5.00.

D. ROI (Return on Investment)

[
\text{ROI} = \text{Margin} \times \text{Turnover} = 0.0577 \times 5.00 = 0.2885 \text{ or } 28.85\%
]

Explanation:

• Average Operating Assets represent the average capital invested in the division over the year and are unaffected by changes in income.
• Margin indicates how efficiently a division turns sales into profits. If operating income decreases, margin also decreases.
• Turnover measures how efficiently a division uses its assets to generate sales. In this case, turnover remains unchanged because only the income, not the sales or assets, changed.
• ROI is a combination of margin and turnover, indicating how well the division is using its assets to generate profits. A decrease in operating income causes a decrease in ROI, as seen in the scenario where the operating income for the Small Appliances Division drops to $2,000,000.