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Margin of Safety - Cost Accounting

  1. A company has a margin of safety of ($120,000). The company's contribution margin ratio is 25%. What is the company's current operating income?
    Answer: ($30,000) Operating income is the profit generated on sales above the break-even point. The margin of safety in dollars represents exactly this volume of sales. Therefore, operating income can be calculated directly by multiplying the margin of safety in dollars by the contribution margin ratio. Operating Income = $120,000∗0.25=$30,000\$120,000 * 0.25 = \$30,000.
  2. Sales $600,000, VC $360,000, FC $120,000. Margin of safety in dollars?
    Answer: $300,000 Contribution margin is 600,000 - 360,000 = 240,000, so the CM ratio is 240,000 / 600,000 = 0.4. Break-even sales are 120,000 / 0.4 = 300,000. Margin of safety is actual sales minus break-even sales: 600,000 - 300,000 = 300,000. The tempting 240,000 is just the contribution margin, not the margin of safety.
  3. Price $50, VC $30, FC $60,000, budgeted sales 4,000 units. Margin of safety in dollars?
    Answer: $50,000 Each unit contributes 50 - 30 = 20 toward fixed costs, so breakeven is 60,000 / 20 = 3,000 units. Budgeted sales are 4,000 units, giving a 1,000-unit margin of safety. At $50 per unit, that is 1,000 x 50 = $50,000. A tempting wrong answer is $150,000, but that is breakeven sales dollars, not the margin of safety.
  4. Breakeven sales $240,000, MOS 25%, CM ratio 35%. Net operating income?
    Answer: $28,000 A 25% margin of safety means breakeven sales are 75% of actual sales, so actual sales are 240,000 / 0.75 = 320,000. Contribution margin is 320,000 × 35% = 112,000. Fixed costs equal breakeven sales × CM ratio = 240,000 × 35% = 84,000, so net operating income is 112,000 - 84,000 = 28,000. The tempting $84,000 is just fixed costs, not net income.
  5. Zenith Innovations has a margin of safety of ($200,000). The company's contribution margin ratio is 40%, and its current sales are ($800,000). What are Zenith's total fixed costs?
    Answer: ($240,000) The margin of safety in dollars is the difference between total sales and break-even sales. We can find the break-even sales: Break-Even Sales = Total Sales - Margin of Safety = $800,000−$200,000=$600,000\$800,000 - \$200,000 = \$600,000. The formula for break-even sales is Fixed Costs / Contribution Margin Ratio. We can rearrange this to solve for fixed costs: Fixed Costs = Break-Even Sales * Contribution Margin Ratio = $600,000∗0.40=$240,000\$600,000 * 0.40 = \$240,000.
  6. DOL is 4 and current sales are 10,000 units. Margin of safety in units?
    Answer: 2,500 units DOL equals current sales units divided by margin of safety in units. So with DOL of 4 and 10,000 units, margin of safety = 10,000 / 4 = 2,500 units. The tempting 7,500 is the breakeven point, not the margin of safety.
  7. At a sales level of 5,000 units, Sterling Corp. incurred total costs of ($190,000). At a sales level of 8,000 units, total costs were ($280,000). The company sells its product for ($50) per unit. If the company is currently operating at a sales level of 9,000 units, what is its margin of safety in units?
    Answer: 7,000 units First, use the high-low method to find variable and fixed costs. Variable cost per unit = ($280,000−$190,000\$280,000 - \$190,000) / (8,000−5,0008,000 - 5,000) = $90,000/3,000\$90,000 / 3,000 units = ($30) per unit. Fixed costs = Total Costs - (Variable Cost per unit * Units) = $280,000−($30∗8,000)\$280,000 - (\$30 * 8,000) = ($40,000). The contribution margin per unit is $50−$30=$20\$50 - \$30 = \$20. The break-even point is $40,000/$20=2,000\$40,000 / \$20 = 2,000 units. The margin of safety at 9,000 units is 9,000−2,000=7,0009,000 - 2,000 = 7,000 units.
  8. Price $50, variable cost $30, fixed costs $240,000, sales 15,000 units. Fixed costs rise 20%. Margin of safety in units?
    Answer: 600 units Contribution per unit is 50 - 30 = 20. Fixed costs rise 20%, so they become 240,000 x 1.2 = 288,000. Break-even is 288,000 / 20 = 14,400 units. Margin of safety is sales minus break-even: 15,000 - 14,400 = 600 units. The 3,000-unit trap comes from using the old fixed costs of 240,000 and forgetting the 20% increase.
  9. Pavo Enterprises has fixed costs of ($100,000) for production up to 20,000 units. If production exceeds 20,000 units, fixed costs increase by ($30,000). The product sells for ($25), with variable costs of ($15) per unit. If the company plans to sell 24,000 units, what is its margin of safety in units?
    Answer: 11,000 units Since planned sales are 24,000 units, which is above the 20,000-unit threshold, the relevant total fixed costs are $100,000+$30,000=$130,000\$100,000 + \$30,000 = \$130,000. The contribution margin per unit is $25−$15=$10\$25 - \$15 = \$10. The break-even point is calculated using the relevant fixed costs: $130,000/$10=13,000\$130,000 / \$10 = 13,000 units. The margin of safety is the difference between planned sales and the break-even point: 24,000−13,000=11,00024,000 - 13,000 = 11,000 units.
  10. Sales $500,000, VC $300,000, FC $150,000. Margin of safety percentage?
    Answer: 25% Contribution margin is 500,000 - 300,000 = 200,000, so the CM ratio is 40%. Break-even sales revenue is fixed costs / CM ratio = 150,000 / 0.40 = 375,000. Margin of safety is 500,000 - 375,000 = 125,000, and as a percentage of actual sales that is 125,000 / 500,000 = 25%. The tempting 40% is the contribution margin ratio, not the margin of safety.
  11. Nova Corporation has been operating with a margin of safety ratio of 20%. The company sells a single product for $50 per unit with a contribution margin ratio of 60%. If the company wants to maintain the same margin of safety ratio but plans to increase its fixed costs by $36,000 to improve product quality, by what percentage must sales volume increase?
    Answer: 15.0% Let current sales = S. Current breakeven = 0.80S (since margin of safety ratio = 20%, breakeven ratio = 80%). Current fixed costs = 0.80S × 0.60 = 0.48S. New fixed costs = 0.48S + $36,000. To maintain 20% margin of safety ratio, new breakeven must be 80% of new sales. Let new sales = 1.15S (assuming 15% increase). New breakeven = 0.80 × 1.15S = 0.92S. For this to work: 0.92S × 0.60 = 0.48S + $36,000. Solving: 0.552S = 0.48S + $36,000. Therefore: 0.072S = $36,000, so S = $500,000. Verification: If sales increase by 15%, new sales = $575,000. New breakeven = $460,000. New fixed costs = $460,000 × 0.60 = $276,000. Original fixed costs = $240,000. Increase = $36,000 ✓. Choice A is correct.
  12. Margin of safety is 25% of sales; fixed costs are $135,000; CM ratio is 45%. What is the margin of safety in dollars?
    Answer: $100,000 Break-even sales equals fixed costs divided by CM ratio: 135,000 / 0.45 = 300,000. If margin of safety is 25% of sales, break-even sales must be 75% of sales, so total sales are 300,000 / 0.75 = 400,000. Margin of safety is 25% of that, or 100,000. The trap is multiplying 135,000 by 45% to get 60,750, which misuses fixed costs.
  13. Sales are $800,000; CM ratio is 40%; fixed costs are $250,000. If CM ratio drops to 30%, margin of safety percentage?
    Answer: -4.17% With the new CM ratio of 30%, breakeven sales are 250,000 / 0.30 = 833,333. Margin of safety is (800,000 - 833,333) / 800,000 = -33,333 / 800,000 = -4.17%. The tempting mistake is to keep the old 40% ratio, which gives 21.88%, but the CM ratio has dropped to 30%.
  14. Sales are $500,000; variable costs 60% of sales; fixed costs $150,000. Sales fall 20%. Margin of safety in dollars?
    Answer: $25,000 After a 20% fall, sales are 400,000. Variable costs are 60% of sales, so the contribution margin ratio is 40%; fixed costs of 150,000 divided by 0.40 gives breakeven sales of 375,000. Margin of safety is 400,000 minus 375,000 = 25,000. The tempting 125,000 is the margin before the sales decline, so recalculate with the new sales level.
  15. Using the information from the Keystone Co. passage, if total sales are projected to be 10,000 units, what is the margin of safety in dollars?
    Answer: ($360,000) First, determine the weighted-average contribution margin (CM) per 'bundle' of 3 Alphas and 2 Betas. Alpha's CM is ($40) and Beta's is ($60). The bundle CM is (3∗$40)+(2∗$60)=$120+$120=$240(3 * \$40) + (2 * \$60) = \$120 + \$120 = \$240. The break-even point in bundles is $336,000/$240=1,400\$336,000 / \$240 = 1,400 bundles. This equals 4,200 units of Alpha (1,400*3) and 2,800 units of Beta (1,400*2). Projected sales are 6,000 Alphas (10,000*3/5) and 4,000 Betas (10,000*2/5). The margin of safety in units is 1,800 Alphas (6,000-4,200) and 1,200 Betas (4,000-2,800). In dollars, this is (1,800∗$100)+(1,200∗$150)=$180,000+$180,000=$360,000(1,800 * \$100) + (1,200 * \$150) = \$180,000 + \$180,000 = \$360,000.
  16. Nova Manufacturing plans to sell 15,000 units of its product at ($50) per unit. Current variable costs are ($30) per unit, and total fixed costs are ($180,000). Management believes that a new production process can decrease variable costs by 10%. If this change is implemented, what will be the new margin of safety in units?
    Answer: 7,174 units First, calculate the new variable cost: $30∗(1−0.10)=$27\$30 * (1 - 0.10) = \$27 per unit. The new contribution margin is $50−$27=$23\$50 - \$27 = \$23 per unit. Next, calculate the new break-even point in units: $180,000/$23≈7,826\$180,000 / \$23 ≈ 7,826 units. The new margin of safety in units is the difference between planned sales and the new break-even point: 15,000−7,826=7,17415,000 - 7,826 = 7,174 units.
  17. Breakeven sales are $600,000; margin of safety is 20% of actual sales. What is the margin of safety in dollars?
    Answer: $150,000 Margin of safety equals actual sales minus breakeven sales and is 20% of actual sales. Let actual sales be S: S - 600,000 = 0.20S, so 0.80S = 600,000 and S = 750,000. Then margin of safety = 0.20 x 750,000 = 150,000. The tempting wrong $120,000 is 20% of breakeven, but the percent applies to actual sales.
  18. Price $20, VC $12, FC $80,000. Planned 12,000 units; fixed costs rise 20%. MOS units?
    Answer: Zero units Contribution margin per unit is 20 - 12 = 8. Fixed costs rise 20%, from 80,000 to 96,000, so break-even is 96,000 / 8 = 12,000 units. Planned volume is also 12,000 units, so margin of safety is 12,000 - 12,000 = 0 units. The tempting 2,000 units comes from using old fixed costs of 80,000, but the increase must be included.
  19. For the upcoming year, Hydrus Inc. projects sales of ($1,200,000), a contribution margin ratio of 40%, and fixed costs of ($360,000). If actual sales are 15% lower than projected, what will be the actual margin of safety in dollars?
    Answer: ($120,000) First, calculate the break-even point in dollars: BEP = Fixed Costs / CM Ratio = $360,000/0.40=$900,000\$360,000 / 0.40 = \$900,000. Next, calculate the actual sales revenue: Actual Sales = $1,200,000×(1−0.15)=$1,020,000\$1,200,000 × (1 - 0.15) = \$1,020,000. The actual margin of safety is the difference between actual sales and break-even sales: MOS = $1,020,000−$900,000=$120,000\$1,020,000 - \$900,000 = \$120,000. Note that distractor A (($300,000)) represents the original projected margin of safety, and distractor D (($180,000)) represents the sales decrease amount.
  20. Orbital Corp manufactures two products using the same facilities. Product Alpha has a margin of safety of 800 units and represents 40% of total company sales in units. Product Beta has a margin of safety of 1,200 units and represents 60% of total company sales in units. If the company's overall margin of safety percentage is 25%, what is the total number of units sold by the company?
    Answer: 8,000 units Let total units sold = T. Product Alpha sales = 0.40T, Product Beta sales = 0.60T. Alpha's margin of safety = 800 units, so Alpha's breakeven = 0.40T - 800. Beta's margin of safety = 1,200 units, so Beta's breakeven = 0.60T - 1,200. Total breakeven = (0.40T - 800) + (0.60T - 1,200) = T - 2,000. Overall margin of safety = T - (T - 2,000) = 2,000 units. Overall margin of safety percentage = 2,000 ÷ T = 25% = 0.25. Solving: 2,000 = 0.25T, therefore T = 8,000 units. Verification: Alpha sales = 3,200 units, breakeven = 2,400 units, margin of safety = 800 ✓. Beta sales = 4,800 units, breakeven = 3,600 units, margin of safety = 1,200 ✓. Total margin of safety = 2,000 ÷ 8,000 = 25% ✓.

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