- A division has a profit margin of 10% and an asset turnover of 1.5. The division manager is considering purchasing a new piece of equipment for $100,000 cash. The equipment is expected to generate additional annual sales of $80,000 and have additional annual operating expenses of $68,000. What is the effect on the division's profit margin and asset turnover?
Answer: Profit margin will increase and asset turnover will decrease.
Compare the components of the new project to the division's existing components.
1. Project's additional operating income = $80,000 (sales) - $68,000 (expenses) = $12,000.
2. Project's profit margin = $12,000 / $80,000 = 15%. Since the project's margin (15%) is higher than the division's current margin (10%), it will increase the overall profit margin.
3. Project's asset turnover = $80,000 (sales) / $100,000 (assets) = 0.8. Since the project's turnover (0.8) is lower than the division's current turnover (1.5), it will decrease the overall asset turnover.
- Division A: margin 8%, turnover 2.0. Division B: margin 10%, turnover 1.6. Which has higher ROI?
Answer: Both have 16%
ROI equals margin times turnover. Division A: 8% times 2.0 = 16%. Division B: 10% times 1.6 = 16%. Both are the same, so neither is higher. The tempting error is choosing Division B only because its margin is larger, which ignores the lower turnover.
- A division's balance sheet shows the following assets: Cash $20,000, Accounts Receivable $150,000, Inventory $200,000, Prepaid Expenses $10,000, Land held for future sale $100,000, and Net Property, Plant & Equipment $520,000. The division's operating income for the period was $135,000. Assuming these are average balances for the period, what is the division's ROI?
Answer: 15.0%
ROI is calculated using operating assets. An asset held for investment, such as 'Land held for future sale,' is not an operating asset and should be excluded from the calculation.
1. Sum the operating assets: $20,000 + $150,000 + $200,000 + $10,000 + $520,000 = $900,000.
2. Calculate ROI: Operating Income / Average Operating Assets = $135,000 / $900,000 = 0.15 or 15.0%.
- The Services Division of Tech Inc. reported operating income of $750,000. The division's profit margin was 15% and its asset turnover was 1.2. What are the division's average operating assets?
Answer: $4,166,667
This problem requires working backwards from operating income to find sales, and then from sales to find assets.
1. Find Sales: Profit Margin = Operating Income / Sales => 15% = $750,000 / Sales => Sales = $750,000 / 0.15 = $5,000,000.
2. Find Assets: Asset Turnover = Sales / Average Operating Assets => 1.2 = $5,000,000 / Assets => Assets = $5,000,000 / 1.2 = $4,166,667.
- Sales $1,200,000; variable costs $720,000; fixed costs $300,000; average operating assets $500,000. ROI?
Answer: 36%
First find net operating income: sales 1,200,000 - variable costs 720,000 = 480,000 contribution margin; then subtract fixed costs 300,000 = 180,000. ROI = 180,000 / 500,000 = 36%. The tempting 96% comes from dividing contribution margin 480,000 by operating assets and forgetting fixed costs.
- Division Manager Sarah wants to improve her division's ROI from 16% to 20% by reducing operating assets while maintaining the same operating income of $320,000. If she achieves this goal, what will be the division's new asset turnover ratio, given that the current asset turnover is 0.8?
Answer: 1.0
Current Assets = Operating Income ÷ Current ROI = $320,000 ÷ 16% = $2,000,000. Current Sales = Asset Turnover × Assets = 0.8 × $2,000,000 = $1,600,000. New Assets = Operating Income ÷ New ROI = $320,000 ÷ 20% = $1,600,000. Since operating income stays the same and profit margin = operating income ÷ sales, sales must remain $1,600,000. New Asset Turnover = Sales ÷ New Assets = $1,600,000 ÷ $1,600,000 = 1.0. Choice B assumes proportional increase with ROI improvement. Choice C incorrectly doubles the current turnover. Choice D assumes assets are cut in half.
- Price rises 10%; volume, total costs, and average operating assets are unchanged. What happens to ROI components?
Answer: All three ratios rise
Price up with volume unchanged means sales rise while total costs stay fixed. So net operating income rises and margin (NOI / sales) rises. Average operating assets are unchanged, so turnover (sales / assets) also rises. ROI = margin x turnover, so it rises too. The tempting error is picking margin and ROI only: turnover rises as well, not stays flat.
- Based on the information provided, which of the following statements is a correct interpretation of their performance?
Answer: Both divisions are providing the same return on investment, reflecting different but equally successful strategies.
Calculate the ROI for each division using the DuPont formula: ROI = Profit Margin × Asset Turnover.
* Lux Goods ROI = 25% × 0.8 = 20%.
* Value Goods ROI = 5% × 4.0 = 20%.
Both divisions have the same ROI of 20%. They achieve this result through different business strategies: Lux Goods uses a high-margin, low-turnover strategy, while Value Goods uses a low-margin, high-turnover strategy. From an ROI perspective, their performance is identical.
- The manager of Division X is evaluated based on ROI. The division currently has an ROI of 20% on an asset base of $1,000,000. The company's cost of capital is 12%. The manager is presented with an investment opportunity that requires an investment of $200,000 and is expected to generate an operating income of $32,000 per year. From the perspectives of the company and the division manager, what actions will be taken?
Answer: The company desires acceptance; the manager is motivated to reject.
This problem illustrates potential goal incongruence.
1. Company's Perspective: The project's ROI is $32,000 / $200,000 = 16%. Since the project's ROI (16%) exceeds the company's cost of capital (12%), the project is financially desirable for the company.
2. Manager's Perspective: The division's current ROI is 20%. Since the project's ROI (16%) is lower than the division's current ROI, accepting it would lower the division's overall performance metric. Therefore, the manager, who is evaluated on ROI, is motivated to reject the project.
- Division A's return on investment (ROI) increased from 20% to 22% this year. The division's asset turnover decreased from 1.6 to 1.5. Which of the following statements is a valid conclusion?
Answer: The division's profit margin increased by enough to offset the decline in turnover.
The DuPont formula states ROI = Profit Margin × Asset Turnover. We can calculate the profit margin for both years.
Last Year: 20% = Margin × 1.6 => Margin = 12.5%.
This Year: 22% = Margin × 1.5 => Margin = 14.67%.
Since the profit margin increased from 12.5% to 14.67%, this improvement more than compensated for the decrease in asset turnover, resulting in a higher overall ROI.
- On January 1, Division Z had operating assets of $4.5 million. During the year, the division acquired new equipment for $1.0 million and sold old equipment with a net book value of $500,000. There were no other transactions involving operating assets. The division's operating income for the year was $950,000. What is Division Z's ROI for the year, using the average of beginning and ending operating assets?
Answer: 20.0%
First, calculate the beginning and ending balances of operating assets. Then, find the average and compute ROI.
1. Beginning Assets = $4,500,000.
2. Ending Assets = Beginning Assets + Purchases - NBV of Disposals = $4,500,000 + $1,000,000 - $500,000 = $5,000,000.
3. Average Operating Assets = (Beginning + Ending) / 2 = ($4,500,000 + $5,000,000) / 2 = $4,750,000.
4. ROI = Operating Income / Average Operating Assets = $950,000 / $4,750,000 = 0.20 or 20.0%.
- The European division of a multinational corporation had operating income of €400,000. Its average operating assets for the year consisted of: Cash €50,000; Accounts Receivable €300,000; Inventory €450,000; and Net Plant & Equipment €1,200,000. The division's operations are financed in part by accounts payable of €250,000. Company policy defines operating assets as total operating current and noncurrent assets. What is the division's ROI according to company policy?
Answer: 20.0%
The key is to use the company's specific definition for the asset base. Company policy defines operating assets as total operating assets, without deducting operating liabilities like accounts payable.
1. Calculate total average operating assets: €50,000 (Cash) + €300,000 (A/R) + €450,000 (Inventory) + €1,200,000 (Net P&E) = €2,000,000.
2. Calculate ROI: Operating Income / Average Operating Assets = €400,000 / €2,000,000 = 0.20 or 20.0%.
- The Alpha Division has an ROI of 25%. The division's average operating assets are $800,000, and its profit margin is 10%. What were the division's total sales for the period?
Answer: $2,000,000
This can be solved in two ways.
Method 1: Use ROI to find turnover, then find sales.
1. ROI = Margin × Turnover => 25% = 10% × Turnover => Turnover = 2.5.
2. Turnover = Sales / Assets => 2.5 = Sales / $800,000 => Sales = $2,000,000.
Method 2: Use ROI to find operating income, then find sales.
1. ROI = OI / Assets => 25% = OI / $800,000 => OI = $200,000.
2. Margin = OI / Sales => 10% = $200,000 / Sales => Sales = $2,000,000.
- Sales $800k; income $80k; avg assets $400k. Compute ROI.
Answer: 20%
ROI is income divided by average assets: 80,000 / 400,000 = 0.20, or 20%. The tempting wrong answer is 10%, which is income divided by sales - that is profit margin, not return on investment.
- A division reported sales of $5,000,000, cost of goods sold of $3,200,000, and selling and administrative expenses of $1,000,000. The division's operating assets were $2,200,000 at the beginning of the year and $2,800,000 at the end of the year. What is the division's return on investment (ROI)?
Answer: 32.0%
Return on Investment (ROI) is calculated as Operating Income / Average Operating Assets.
1. Calculate Operating Income: Sales - COGS - S&A Expenses = $5,000,000 - $3,200,000 - $1,000,000 = $800,000.
2. Calculate Average Operating Assets: (Beginning Assets + Ending Assets) / 2 = ($2,200,000 + $2,800,000) / 2 = $2,500,000.
3. Calculate ROI: $800,000 / $2,500,000 = 0.32 or 32.0%.
- Profit margin 8%, asset turnover 2.5, average operating assets $300,000. What is operating income?
Answer: $60,000
Asset turnover of 2.5 means every $1 of assets generates $2.50 in sales, so sales are 2.5 times $300,000 = $750,000. Operating income is 8% of sales: 0.08 times $750,000 = $60,000. The tempting $24,000 wrongly applies the 8% margin directly to assets instead of to sales.
- Sales $2,000,000; avg assets $1,000,000; target ROI 16%. Required margin?
Answer: 8.0%
Asset turnover is $2,000,000 / $1,000,000 = 2. To earn the 16% target ROI, your margin times turnover must equal 16%, so margin = 16% / 2 = 8%. The tempting 16% just repeats your target ROI and ignores that assets turn over twice.
- Margin rises 40%; turnover falls 20%. ROI change?
Answer: Up 12%
ROI = margin × turnover. A 40% rise makes margin 1.4 times; a 20% fall makes turnover 0.8 times. Multiply: 1.4 × 0.8 = 1.12, so ROI is 12% higher. The tempting Up 20% just subtracts the percentages, but changes compound multiplicatively.
- A division manager has successfully implemented a lean manufacturing program. The primary effects have been a reduction in work-in-process and finished goods inventory levels and a slight reduction in production costs. Sales volume and prices have remained stable. Which of the following is the most likely impact on the division's ROI components?
Answer: Increased profit margin, increased asset turnover.
Analyze the impact on each component of ROI.
1. Profit Margin (Operating Income / Sales): Production cost reductions, with stable sales revenue, lead to higher operating income. This increases the profit margin.
2. Asset Turnover (Sales / Average Assets): Reduced inventory levels decrease the amount of average operating assets. With stable sales revenue and a lower asset base, the asset turnover ratio increases.
Therefore, both components improve.
- Margin is 12%; ROI is 18%. What is asset turnover?
Answer: 1.50x
Margin times asset turnover equals ROI, so divide ROI by margin: 0.18 / 0.12 = 1.50x. Asset turnover is a ratio, not a difference; 0.06x is wrong because it subtracts the percentages instead of dividing them.
