Cost Accounting Quiz: Operating Leverage
20 questions · exam conditions
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Operating LeverageQuestion 1 of 20

Price increases; FC, VC/unit, volume unchanged. DOL:

Unchanged
Increases
Decreases
Cannot tell
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Cost Accounting Quiz

Cost Accounting Quiz: Operating Leverage

Practice Operating Leverage in Cost Accounting with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Operating Leverage, giving you a quick way to practice the rules, question types, and explanations that matter most for Cost Accounting.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Price increases; FC, VC/unit, volume unchanged. DOL:

  1. Unchanged
  2. Increases
  3. Decreases (correct answer)
  4. Cannot tell
Explanation: Contribution per unit rises with price, so total contribution and operating income rise while fixed costs and volume stay unchanged. DOL equals contribution divided by operating income, or 1 divided by (1 minus fixed costs divided by contribution). As contribution grows, that ratio falls. The tempting wrong answer is increases because a higher price raises profit, but DOL measures earnings sensitivity, not the profit level.

Question 2

High DOL is riskier than low DOL mainly when:

  1. FC are low
  2. Sales volatile (correct answer)
  3. VC are high
  4. Sales constant
Explanation: High DOL means a large portion of costs are fixed, so operating income moves more than proportionally with sales. That magnification is only risky when sales fluctuate; volatile sales create larger swings in income. The tempting wrong answer is Sales constant, because with steady sales the leverage has no variability to amplify, so it is not riskier then.

Question 3

Margin of safety ratio is 20%. DOL?

  1. 1.25
  2. 0.20
  3. 0.80
  4. 5.0 (correct answer)
Explanation: Margin of safety ratio equals operating income divided by contribution margin, and DOL is the reciprocal: contribution margin divided by operating income. So DOL = 1 / 0.20 = 5.0. A common mistake is computing 1 / (1 - 0.20) = 1.25, which wrongly treats the 20% margin of safety as a 20% reduction instead of the income-to-contribution ratio.

Question 4

Firm X: DOL 4, sales vary 2%. Firm Y: DOL 2, sales vary 5%. Riskier?

  1. Firm Y (correct answer)
  2. Firm X
  3. Cannot tell
  4. Both equal
Explanation: Using each firm's DOL times its sales fluctuation gives operating income volatility. Firm X varies 4 × 2 = 8%, while Firm Y varies 2 × 5 = 10%. Higher income volatility means higher risk, so Firm Y is riskier. The tempting mistake is choosing Firm X only because its DOL is higher, while ignoring the larger sales swings at Firm Y.

Question 5

At 10,000 units DOL=5. CM/unit and FC fixed. At 12,000 units DOL?

  1. 3.0 (correct answer)
  2. 4.0
  3. 5.0
  4. 6.0
Explanation: At 10,000 units, DOL = 10,000c divided by profit = 5, so fixed cost = 8,000c. At 12,000 units, profit = 12,000c - 8,000c = 4,000c, so DOL = 12,000c / 4,000c = 3.0. The tempting wrong answer is 4.0, which assumes DOL scales inversely with units, but fixed costs must be solved for first.

Question 6

A: FC $80k, VC $20/unit; B: FC $40k, VC $40/unit. Price $100, volume 2,000. Higher DOL?

  1. Unknown
  2. Firm B
  3. Equal
  4. Firm A (correct answer)
Explanation: With 2,000 units, Firm A's contribution margin is 160,000 (80 per unit) and operating income is 80,000, so DOL = 160,000 / 80,000 = 2. Firm B's contribution margin is 120,000 (60 per unit) and operating income is 80,000, so DOL = 120,000 / 80,000 = 1.5. Firm A has higher DOL. The tempting 'equal' answer fails because equal operating income at this volume does not mean equal sensitivity; DOL compares contribution margin to operating income.

Question 7

FC increases; price, VC, volume unchanged; still above breakeven. DOL:

  1. Unchanged
  2. Decreases
  3. Increases (correct answer)
  4. Cannot tell
Explanation: DOL equals contribution margin divided by operating income. Price, variable cost, and volume are unchanged, so contribution margin stays the same. Higher fixed cost lowers operating income, making the denominator smaller and DOL larger. The tempting wrong answer is unchanged, which ignores that fixed costs affect operating income.

Question 8

Sales +15%; operating income +45%. DOL?

  1. 3.0 (correct answer)
  2. 0.33
  3. 6.75
  4. 1.5
Explanation: DOL equals percentage change in operating income divided by percentage change in sales: 45% divided by 15% = 3.0. This means operating income moves 3 times as fast as sales. The tempting error is 0.33, which reverses the ratio; DOL is income change over sales change, not sales over income.

Question 9

DOL = 3; fixed costs = $100,000. CM?

  1. $150,000 (correct answer)
  2. $300,000
  3. $50,000
  4. $100,000
Explanation: DOL equals CM divided by operating income, and operating income is CM minus fixed costs. So 3 = CM / (CM - 100,000). Solve: 3(CM - 100,000) = CM, giving 3CM - 300,000 = CM, so 2CM = 300,000 and CM = 150,000. The tempting $300,000 mistake treats fixed costs as operating income, but operating income is CM minus fixed costs, not fixed costs alone.

Question 10

An analyst is comparing four companies in the cyclical consumer goods industry. The analyst has gathered the following data on their degrees of operating leverage (DOL):

  • Company W: 1.8
  • Company X: 4.5
  • Company Y: 6.2
  • Company Z: 2.1

Based on the provided data, if the economy enters a significant recession causing a 20% decline in industry-wide sales, which company is expected to experience the most severe percentage decline in operating income?

  1. Company W
  2. Company X
  3. Company Y (correct answer)
  4. Company Z
Explanation: The degree of operating leverage (DOL) is a multiplier that shows how a percentage change in sales affects operating income. A higher DOL signifies greater sensitivity of operating income to changes in sales. In an economic downturn (sales decline), the company with the highest DOL will experience the largest percentage decrease in its operating income. Company Y has the highest DOL of 6.2, making it the most vulnerable to a sales decline.

Question 11

As sales approach breakeven from above, DOL:

  1. Falls to zero
  2. Grows forever (correct answer)
  3. Falls to one
  4. Stays fixed
Explanation: DOL equals contribution margin divided by operating profit. As sales drop toward breakeven from above, contribution margin is still positive but operating profit approaches zero, so the ratio grows without bound. Breakeven is a vertical asymptote. The tempting mistake is "falls to one," but DOL falls toward one only at very high sales, not near breakeven.

Question 12

Price $20, unit VC $12, volume 10,000, fixed costs $50,000. If price rises 10% with volume unchanged, DOL becomes:

  1. 2.7
  2. 2.0 (correct answer)
  3. 3.3
  4. 1.6
Explanation: Price rises 10% to $22, so unit contribution becomes 22 - 12 = 10. Total contribution is 10 x 10,000 = 100,000. Operating income is 100,000 - 50,000 = 50,000. DOL is contribution divided by operating income: 100,000 / 50,000 = 2.0. A tempting error is using the old contribution and income, 80,000 / 30,000 = 2.7, without updating for the price rise.

Question 13

A: sales $300,000, CM ratio 40%, fixed $60,000. B: sales $300,000, CM ratio 30%, fixed $30,000. Which is riskier?

  1. Firm B; DOL 1.5
  2. Firm A; DOL 1.5
  3. Firm B; DOL 2.0
  4. Firm A; DOL 2.0 (correct answer)
Explanation: Firm A's contribution margin is 40% of 300,000 = 120,000. After fixed costs of 60,000, operating income is 60,000, so DOL = 120,000 / 60,000 = 2.0. Firm B has contribution margin 90,000 and operating income 60,000, so DOL = 1.5. Higher DOL means more risk, so Firm A is riskier. The tempting Firm B answer has the right DOL but lower DOL is safer, not riskier.

Question 14

At volume 10% above break-even, DOL is 11. If volume falls 10%, operating income will:

  1. fall 100% to break-even
  2. fall 11% from income
  3. fall 110% to a loss (correct answer)
  4. fall 10% from income
Explanation: DOL of 11 means each 1% change in volume moves operating income 11% in the same direction. A 10% volume fall therefore cuts operating income by 110%, pushing it below zero into a loss. The tempting mistake is thinking 10% above break-even minus 10% equals break-even, but 10% off 110% of break-even is 99% of break-even, not 100%.

Question 15

CM ratio 40%, fixed costs $80,000, sales $300,000. After a 10% sales increase, operating income is:

  1. $52,000 (correct answer)
  2. $40,000
  3. $44,000
  4. $120,000
Explanation: At 40% CM, current contribution margin is 120,000 (300,000 x 40%), minus 80,000 fixed costs gives 40,000 operating income. A 10% sales increase adds 30,000 sales, and 40% of that is 12,000 more contribution margin, so new income is 40,000 + 12,000 = 52,000. The 44,000 trap simply raises current income by 10%, ignoring that fixed costs don't change.

Question 16

At current sales, DOL is 4.0 and fixed costs are $60,000. Contribution margin is:

  1. $20,000
  2. $80,000 (correct answer)
  3. $240,000
  4. $60,000
Explanation: DOL is contribution margin divided by operating income, and operating income is contribution margin minus fixed costs. So set 4 = CM / (CM - 60,000). Solving gives 4CM - 240,000 = CM, so 3CM = 240,000 and CM = 80,000. The $240,000 trap comes from multiplying DOL by fixed costs, but DOL compares CM to operating income, not to fixed costs.

Question 17

An analyst states that a company's degree of operating leverage is 3.5. Which of the following is the most accurate interpretation of this figure?

  1. A 1% increase in sales will cause operating income to increase by 3.5%. (correct answer)
  2. A 10% increase in operating income will result from a 35% increase in sales.
  3. For every $1 increase in sales, operating income will increase by $3.50.
  4. The company's contribution margin is 3.5 times its sales revenue.
Explanation: The degree of operating leverage (DOL) acts as a multiplier on the percentage change in sales to determine the percentage change in operating income. A DOL of 3.5 means that for any given percentage change in sales (from the current level), operating income will change by 3.5 times that percentage. Therefore, a 1% increase in sales will cause a 3.5% increase in operating income.

Question 18

AeroCorp manufactures a single product. For the most recent year, the company reported sales revenue of $1,200,000, a contribution margin ratio of 40%, and fixed costs of $360,000. What is AeroCorp's degree of operating leverage (DOL) at this sales level?

  1. 1.25
  2. 2.50
  3. 3.33
  4. 4.00 (correct answer)
Explanation: The degree of operating leverage (DOL) is calculated as Contribution Margin / Operating Income. First, calculate the contribution margin: $1,200,000 (Sales) * 40% (CM Ratio) = $480,000. Next, calculate operating income: $480,000 (Contribution Margin) - $360,000 (Fixed Costs) = $120,000. Finally, calculate DOL: $480,000 / $120,000 = 4.00.

Question 19

Veloce Inc. has a degree of operating leverage of 5.0. Current operating income is $80,000 on sales of $1,000,000. Management forecasts a 15% increase in sales for the upcoming year, with no changes to its cost structure. What is the forecasted operating income for the upcoming year?

  1. $92,000
  2. $120,000
  3. $140,000 (correct answer)
  4. $480,000
Explanation: First, calculate the expected percentage change in operating income: Degree of Operating Leverage * Percentage Change in Sales = 5.0 * 15% = 75%. Next, apply this percentage change to the current operating income: $80,000 * (1 + 0.75) = $140,000. The new forecasted operating income is $140,000.

Question 20

Company A is a highly automated manufacturer with fixed costs of $800,000 and variable costs of $20 per unit. Company B produces a similar product using a more labor-intensive process, with fixed costs of $200,000 and variable costs of $60 per unit. Both companies sell their product for $100 per unit and currently sell 20,000 units per year.

Based on the information provided in the passage, which of the following statements is most accurate regarding the companies' risk profiles?

  1. Company B has a higher degree of operating leverage, making it more sensitive to changes in sales volume.
  2. Company A has a higher degree of operating leverage, making it more sensitive to changes in sales volume. (correct answer)
  3. Both companies have the same degree of operating leverage because their total costs at the current sales volume are identical.
  4. Company A has a lower break-even point in units, indicating it has a lower risk profile than Company B.
Explanation: Operating leverage measures the sensitivity of operating income to changes in sales. It is higher for companies with a higher proportion of fixed costs. Let's calculate the DOL for each company. Company A: CM per unit = $100 - $20 = $80. Total CM = $80 * 20,000 = $1,600,000. OI = $1,600,000 - $800,000 = $800,000. DOL = $1,600,000 / $800,000 = 2.0. Company B: CM per unit = $100 - $60 = $40. Total CM = $40 * 20,000 = $800,000. OI = $800,000 - $200,000 = $600,000. DOL = $800,000 / $600,000 = 1.33. Company A has a higher DOL (2.0 vs 1.33), meaning its operating income is more sensitive to sales changes, which represents higher risk and higher potential reward.