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Contribution Margin - Managerial Accounting

  1. What would be the projected impact on operating income if the campaign is implemented?
    Answer: An increase of $10,000 The correct answer is an increase of $10,000. The incremental contribution margin from the increased sales must be compared to the incremental fixed costs. The contribution margin per unit is $50−$30=$20\$50 - \$30 = \$20. The expected increase in sales volume is 10,000 units×20%=2,00010,000 \text{ units} \times 20\% = 2,000 units. The incremental total contribution margin is 2,000 units×$20/unit=$40,0002,000 \text{ units} \times \$20/\text{unit} = \$40,000. The incremental fixed cost is $30,000. The net impact on operating income is the incremental contribution margin minus the incremental fixed cost: $40,000−$30,000=$10,000\$40,000 - \$30,000 = \$10,000.
  2. How much can the company's actual sales revenue fall short of the projection before the company incurs an operating loss?
    Answer: $100,000 The correct answer is $100,000. This question is asking for the margin of safety in dollars. First, calculate the break-even point in sales dollars: Break-Even Sales = Fixed Costs / Contribution Margin Ratio = $120,000 / 0.40 = $300,000. The margin of safety is the difference between projected sales and break-even sales: $400,000 - $300,000 = $100,000. This is the amount by which sales can fall before a loss occurs. Distractor A is the break-even point itself. Distractor D is the projected operating income ($400,000 * 0.40 - $120,000 = $40,000).
  3. Due to supply chain constraints, TechAssembly must reduce total monthly production by 3,000 units. From a contribution margin perspective, how should the company allocate this production reduction between the two lines to minimize the impact on total contribution margin?
    Answer: Reduce Line B by 3,000 units and maintain Line A at current levels, as Line B has higher variable costs per unit Line A CM per unit: $45 - $25 = $20. Line B CM per unit: $45 - $30 = $15. To minimize impact on total contribution margin, reduce production of the line with lower contribution margin per unit first. Line B has lower CM per unit ($15 vs $20), so reduce Line B production first. Reducing Line B by 3,000 units (from 8,000 to 5,000) is feasible and would reduce total CM by $45,000. Reducing Line A by 3,000 units would reduce total CM by $60,000. Choice B correctly identifies reducing Line B production. Choices A and C would result in larger CM reductions. Choice D partially correct but doesn't optimize the reduction.
  4. The company is currently producing and selling 7,500 units per month. A new client offers to buy 1,500 units per month on a long-term basis. What is the minimum number of units from this new order that the company must sell to cover the incremental fixed cost of the additional facility?
    Answer: 600 units The correct answer is 600 units. The new order for 1,500 units would bring total production to 9,000 units (7,500 + 1,500), which exceeds the current capacity of 8,000 units. Therefore, the company must incur the incremental fixed cost of $9,000 for the additional facility. The number of units required to cover this cost is calculated by dividing the incremental fixed cost by the contribution margin per unit: $9,000 / $15 per unit = 600 units. Distractor C incorrectly uses the current production level (7,500) to find the units over capacity (9,000 - 7,500 = 1,500; 8,000 - 7,500 = 500). Distractor D incorrectly uses the total fixed costs ($20,000 + $9,000) instead of the incremental cost.
  5. Assuming sales revenue for both companies increases by 15% in the coming year and their cost structures remain unchanged, which of the following statements is most accurate?
    Answer: Innovate Corp.'s operating income will increase by a greater dollar amount than Praxis Inc.'s. The correct answer is that Innovate Corp.'s operating income will increase by a greater dollar amount. Since fixed costs are constant, the increase in operating income is equal to the increase in total contribution margin. The increase in contribution margin is calculated by multiplying the increase in sales revenue by the contribution margin ratio. Because Innovate Corp. has a higher contribution margin ratio (70% vs. 40%), it will generate more contribution margin (and thus more operating income) from the same dollar increase in sales.
  6. What would be the impact on Delta Corp.'s monthly operating income if the special order is accepted?
    Answer: A decrease of $1,400 The correct answer is a decrease of $1,400. To analyze a special order, we compare incremental revenues to incremental costs. The allocated fixed overhead of $10 is not relevant. The relevant variable cost per unit is the sum of direct materials, direct labor, and variable overhead: $40+$25+$15=$80\$40 + \$25 + \$15 = \$80. The contribution margin per unit on the special order is $82−$80=$2\$82 - \$80 = \$2. The total incremental contribution margin is 800 units×$2/unit=$1,600800 \text{ units} \times \$2/\text{unit} = \$1,600. However, the order requires an additional fixed cost of $3,000 for the special tool. The net impact is $1,600−$3,000=−$1,400\$1,600 - \$3,000 = -\$1,400, a decrease in operating income. Distractor A ignores the cost of the tool. Distractor C incorrectly includes the allocated fixed cost in the analysis ($82−$90)∗800=−$6,400\$82 - \$90) * 800 = -\$6,400. Distractor D incorrectly includes the allocated fixed cost AND the tool cost (−$6,400−$3,000=−$9,400-\$6,400 - \$3,000 = -\$9,400).
  7. Management wants to incentivize customers to upgrade to higher tiers by offering a 20% discount on Premium plans and a 15% discount on Enterprise plans, while keeping Basic pricing unchanged. They estimate this will shift the customer mix to 40% Basic, 35% Premium, and 25% Enterprise, with total customers increasing to 5,500. What is the percentage change in total contribution margin from this strategy?
    Answer: Total contribution margin increases by approximately 19.2% due to the favorable shift toward higher-value customer tiers despite the pricing discounts Current CM: Basic (3,000 × $7) + Premium (1,500 × $17) + Enterprise (500 × $35) = $21,000 + $25,500 + $17,500 = $64,000. New pricing: Premium = $20 (CM = $12), Enterprise = $42.50 (CM = $27.50). New CM: Basic (2,200 × $7) + Premium (1,925 × $12) + Enterprise (1,375 × $27.50) = $15,400 + $23,100 + $37,813 = $76,313. Percentage change = ($76,313 - $64,000)/$64,000 = 19.2%.
  8. A company is analyzing a product line that has a positive contribution margin of $100,000 but a reported segment loss of $20,000 after allocation of common corporate fixed costs. If the product line is eliminated, the traceable fixed costs of $40,000 associated with the line can be avoided. What would be the impact on the company's overall operating income if this product line is dropped?
    Answer: A decrease of $60,000 The correct answer is a decrease of $60,000. When considering dropping a product line, the key is to analyze its segment margin, which is its contribution margin less its traceable fixed costs. Common allocated costs are irrelevant as they will persist even if the line is dropped. The segment margin for this product line is $100,000 (Contribution Margin) - $40,000 (Traceable Fixed Costs) = $60,000. Since the segment margin is positive, the product line contributes $60,000 towards covering common corporate costs. Eliminating the line would result in losing this $60,000 contribution, thus decreasing overall company operating income by that amount.
  9. A company anticipates that its selling price per unit will increase by 5% and its variable cost per unit will increase by 8% in the next year. This year, the selling price is $40 and the variable cost is $25. If sales volume in units remains constant, what will be the percentage change in the contribution margin per unit?
    Answer: A decrease of 6.7% The correct answer is a decrease of 6.7%. This requires calculating the contribution margin per unit for both years and then finding the percentage change. Current CM per unit = $40 - $25 = $15. Next year's selling price = $40 \times 1.05 = $42. Next year's variable cost = $25 \times 1.08 = $27. Next year's CM per unit = $42 - $27 = $14. The change in CM per unit is $14 - $15 = -$1. The percentage change is (Change / Original Amount) = (-$1 / $15) = -0.0667, or a decrease of 6.7%. A common mistake is to simply net the percentages (5% - 8% = -3%), which leads to distractor A.
  10. A company is currently operating at a profit. If its sales volume increases and the per-unit selling price, per-unit variable costs, and total fixed costs all remain constant, which of the following will occur?
    Answer: The total contribution margin will increase, and the operating income will increase. The correct answer is that the total contribution margin will increase, and the operating income will increase. If sales volume (number of units) increases while per-unit amounts are constant, the total contribution margin (Unit CM x Quantity) will increase. Since total fixed costs remain constant, the increase in total contribution margin will flow directly to operating income (OI = Total CM - Fixed Costs), causing it to increase as well. The contribution margin ratio and per unit CM will remain constant, not increase. The margin of safety will increase, not decrease. Total fixed costs are stated to be constant.
  11. A company's operating income decreased by $15,000 in a period where its sales revenue increased by $75,000. During this period, the company's variable cost per unit and selling price per unit remained constant, but total fixed costs increased by $45,000. What is the company's contribution margin ratio?
    Answer: 40% The correct answer is 40%. The formula relating the changes is: Change in Operating Income = Change in Contribution Margin - Change in Fixed Costs. We can solve for the change in contribution margin: −$15,000=Change in CM−$45,000-\$15,000 = \text{Change in CM} - \$45,000, so Change in CM = $30,000. The contribution margin ratio is the change in contribution margin divided by the change in sales revenue: $30,000 / $75,000 = 0.40, or 40%. Distractor A (20%) results from dividing the change in operating income by the change in sales, ignoring the fixed cost increase. Distractor C (60%) incorrectly uses the fixed cost increase as the numerator. Distractor D (80%) results from incorrectly adding the income decrease to the fixed cost increase ($45,000 + $15,000) and dividing by the sales increase.
  12. If a company's total contribution margin is exactly equal to its total fixed expenses, which of the following must be true?
    Answer: The company's operating income is zero. The correct answer is that the company's operating income is zero. The fundamental profit equation is: Operating Income = Total Contribution Margin - Total Fixed Expenses. If Total Contribution Margin = Total Fixed Expenses, then Operating Income = 0. This situation describes the break-even point. Distractor B is incorrect; the contribution margin per unit must be positive to generate any total contribution margin. Distractor C is a restatement of the premise, but A is the more precise conclusion in accounting terminology. Distractor D is not necessarily true; the contribution margin ratio (CM/Sales) being equal to the fixed cost ratio (FC/Sales) is a consequence of breaking even, not a separate truth.
  13. How will this change most likely affect the company's unit contribution margin and its gross margin per unit, as calculated under absorption costing?
    Answer: Unit contribution margin will increase; the effect on gross margin per unit is indeterminate. The correct answer is that the unit contribution margin will increase, while the effect on gross margin per unit is indeterminate. Unit contribution margin (Sales Price - All Variable Costs) will increase because a variable cost (hourly labor) is being replaced by a fixed cost, thus reducing the total variable cost per unit. Gross margin per unit (Sales Price - COGS per unit) is more complex. Under absorption costing, COGS per unit includes both variable and allocated fixed manufacturing costs. The change decreases the variable manufacturing cost but increases the total fixed manufacturing cost, which is then allocated over the units produced. The net effect on the total COGS per unit, and thus the gross margin per unit, depends on the production volume used for allocation and the relative magnitudes of the cost changes.
  14. Which of the following statements best interprets the meaning of a positive contribution margin?
    Answer: It measures the amount of revenue remaining to cover fixed costs and generate profit. The correct answer is that it measures the amount of revenue remaining to cover fixed costs and then contribute to profit. This is the definition of contribution margin. A positive contribution margin does not guarantee overall profitability (Distractor A), as total fixed costs could still exceed the total contribution margin. It is not related to equity (Distractor B) and does not involve full absorption cost (Distractor D), which includes an allocation of fixed costs.
  15. If the company's variable costs per unit decrease by 10%, but the selling price and fixed costs remain unchanged, what will be the new total contribution margin?
    Answer: $368,000 The correct answer is $368,000. First, calculate the original total contribution margin: $800,000 (Sales) - $480,000 (Variable Costs) = $320,000. Next, calculate the new total variable costs. The variable costs decrease by 10%: $480,000 \times 10\% = $48,000. The new variable costs will be $480,000 - $48,000 = $432,000. The new total contribution margin is calculated as Sales - New Variable Costs: $800,000 - $432,000 = $368,000. Distractor A is the original contribution margin. Distractor B results from increasing the original CM by 10% ($320,000 1.1), which is incorrect. Distractor D incorrectly decreases the original CM by 10% ($320,000 0.9).
  16. What is the company's margin of safety in units?
    Answer: 1,000 units The correct answer is 1,000 units. The margin of safety is the difference between current sales and break-even sales. First, calculate the break-even point in units: Break-Even Units = Fixed Expenses / Contribution Margin per Unit = $84,000 / $12 per unit = 7,000 units. The margin of safety in units is then Current Sales Units - Break-Even Sales Units = 8,000 units - 7,000 units = 1,000 units. Distractor A is the break-even point in units. Distractor C is the current sales level. Distractor D represents the current total contribution margin in dollars ($12*8000 = $96,000) minus fixed costs ($12,000 profit), not units.
  17. The company wants to achieve a target operating income of $100,000. Management believes that increasing the advertising budget by $50,000 will allow them to reach this target. How many units must the company sell to achieve the target operating income under these new conditions?
    Answer: 14,500 units The correct answer is 14,500 units. The formula for target sales in units is (Fixed Costs + Target Operating Income) / Contribution Margin per Unit. First, calculate the contribution margin per unit: $150 - $90 = $60. Next, determine the new total fixed costs, which includes the additional advertising: $720,000 + $50,000 = $770,000. Now apply the formula: ($770,000 + $100,000) / $60 = $870,000 / $60 = 14,500 units. Distractor A (12,000) represents the original break-even point ($720,000 / $60). Distractor B (14,000) represents the units needed for the target income before the advertising increase.
  18. Phoenix Manufacturing's monthly income statement shows sales of $500,000, variable costs of $320,000, and fixed costs of $150,000. The company is considering outsourcing its delivery function, which would eliminate $25,000 of fixed costs but add $0.08 per unit in variable costs. If Phoenix currently sells 10,000 units per month, what is the net effect on monthly contribution margin from this outsourcing decision?
    Answer: Contribution margin decreases by $800, calculated as the additional variable cost per unit multiplied by monthly unit sales Contribution margin is sales minus variable costs. The outsourcing decision adds $0.08 × 10,000 = $800 in variable costs per month. Fixed costs don't affect contribution margin calculation - they affect operating income. So contribution margin decreases by $800. Choice B incorrectly includes fixed cost impact in contribution margin. Choice C adds amounts incorrectly. Choice D incorrectly suggests no change.
  19. A firm has an opportunity to sell 1,000 units of a product at a special price of $25 per unit. The product normally sells for $40. The firm has sufficient idle capacity to produce the units. The product's costs per unit are $18 variable and $10 fixed (based on normal volume). If the firm accepts the order, how will its operating income be affected?
    Answer: It will increase by $7,000. The correct answer is an increase of $7,000. For a special order with idle capacity, fixed costs are irrelevant. The decision should be based on the incremental contribution margin. The incremental revenue is $25 per unit. The incremental cost is the variable cost of $18 per unit. The contribution margin per unit for this order is $25−$18=$7\$25 - \$18 = \$7. The total increase in operating income is 1,000 units×$7/unit=$7,0001,000 \text{ units} \times \$7/\text{unit} = \$7,000. Distractor B results from incorrectly including the fixed cost in the analysis ($25 price - $28 total cost = -$3 per unit). Distractor C incorrectly compares the special price to the normal price ($25 - $40 = -$15 per unit).
  20. To maximize profitability, which product should the company prioritize, and what is the contribution margin per hour of machine time for that product?
    Answer: Prioritize Alpha, with a contribution margin of $40 per machine hour. The correct answer is to prioritize Alpha. When a resource is constrained, profitability is maximized by prioritizing the product with the highest contribution margin per unit of the constrained resource. For Alpha: Unit CM = $100−$60=$40\$100 - \$60 = \$40. CM per machine hour = $40 / 1 hour = $40/hour. For Beta: Unit CM = $200−$155=$45\$200 - \$155 = \$45. CM per machine hour = $45 / 3 hours = $15/hour. Since Alpha generates a higher contribution margin per machine hour, it should be prioritized. Distractor B is incorrect because it focuses on the higher unit contribution margin of Beta, ignoring the constrained resource. Distractor C correctly calculates Beta's CM per hour but makes the wrong prioritization decision.

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