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Weighted-Average Contribution Margin - Managerial Accounting

  1. Based on the sales mix from the most recent period, what is the company's weighted-average contribution margin per unit?
    Answer: $48.00 First, calculate the contribution margin (CM) per unit for each product. CM = Selling Price - Variable Costs. CM for Alpha = $100 - $60 = $40. CM for Beta = $150 - $90 = $60. Next, determine the sales mix based on units sold. Total units = 6,000 (Alpha) + 4,000 (Beta) = 10,000 units. The sales mix is 60% for Alpha (6,000 / 10,000) and 40% for Beta (4,000 / 10,000). The weighted-average contribution margin (WACM) is calculated as: WACM = (CM_Alpha × Mix_Alpha) + (CM_Beta × Mix_Beta) = ($40 × 0.60) + ($60 × 0.40) = $24 + $24 = $48.00. Distractor B ($50) represents a simple average of the two contribution margins (($40+$60)/2), which is also what one would get by incorrectly using the revenue mix (both products generated $600,000 in revenue, a 50/50 mix). Distractor C ($52) results from incorrectly swapping the sales mix percentages. Distractor D ($480,000) is the total contribution margin, not the per-unit average.
  2. Which of the following expressions correctly represents the company's weighted-average contribution margin per unit?
    Answer: 23CMA+13CMB \frac{2}{3}CM_A + \frac{1}{3}CM_B The sales mix is 2 units of Alpha for every 1 unit of Beta, meaning there are 3 total 'parts' in the sales mix. Therefore, Alpha constitutes 2/3 of the units sold, and Beta constitutes 1/3 of the units sold. The weighted-average contribution margin is the sum of each product's contribution margin multiplied by its sales mix percentage. This is correctly represented by (2/3)CM_A + (1/3)CM_B. Distractor B represents an unweighted, simple average based on a 1:1 mix. Distractor C represents the contribution margin of a composite unit or 'bundle' (2 Alphas and 1 Beta), not the per-unit average. Distractor D represents the formula for the break-even point in total units, not the weighted-average contribution margin itself.
  3. If Aurora expects the same sales mix percentages to continue next quarter but plans to increase total unit sales by 20%, what will be the weighted-average contribution margin per unit?
    Answer: $61.00 The weighted-average contribution margin per unit is independent of the total volume increase - it depends only on the sales mix ratios. Current mix is 300:200:100 or 3:2:1. Weighted-average CM = [(3 × $45) + (2 × $72) + (1 × $108)] ÷ (3 + 2 + 1) = [$135 + $144 + $108] ÷ 6 = $387 ÷ 6 = $61.00. Choice A incorrectly applies the 20% increase to the contribution margin. Choice C uses incorrect weights. Choice D appears to be a simple average of the three contribution margins.
  4. What is the projected weighted-average contribution margin per unit for this year?
    Answer: $84.00 The question asks for this year's projected WACM. The projected sales are 12,000 units of Alpha and 8,000 units of Beta, for a new total of 20,000 units. The new sales mix is 12,000/20,000 = 60% for Alpha and 8,000/20,000 = 40% for Beta. The projected WACM is calculated as: WACM = ($60 × 0.60) + ($120 × 0.40) = $36 + $48 = $84.00. Distractor B ($75.00) is the WACM from last year based on the old mix of 15,000:5,000 (a 75%/25% mix). Distractor C ($90.00) is the simple average of the two contribution margins. Distractor D ($81.00) is the result of averaging the old and new WACMs, which is not a meaningful metric.
  5. What is the company's weighted-average contribution margin per can sold?
    Answer: $0.42 The sales mix is 3 soda to 2 seltzer, for a total of 5 cans in the mix. The mix percentage for soda is 3/5 = 60%, and for seltzer is 2/5 = 40%. The weighted-average contribution margin (WACM) per can is calculated as: WACM = (CM_soda × Mix_soda) + (CM_seltzer × Mix_seltzer) = ($0.50 × 0.60) + ($0.30 × 0.40) = $0.30 + $0.12 = $0.42. Distractor B ($0.40) is the simple average of the two contribution margins. Distractor C ($2.10) is the total contribution margin for the entire variety pack (3 × $0.50 + 2 × $0.30 = $1.50 + $0.60), not the weighted average per can. Distractor D ($0.80) is the sum of the two per-unit contribution margins, ignoring weighting.
  6. What would be the weighted-average contribution margin per unit if the promotional effort is successful?
    Answer: $46.00 The question asks for the new WACM after the promotional effort. The new sales mix is 3 standard to 2 premium, for a total of 5 units in the mix. The new mix percentages are 3/5 (60%) for standard and 2/5 (40%) for premium. The new WACM is calculated as: New WACM = ($30 × 0.60) + ($70 × 0.40) = $18 + $28 = $46.00. Distractor A ($38.00) is the original WACM, calculated with the 4:1 mix. Distractor C ($50.00) is the simple average of the two contribution margins. Distractor D ($54.00) results from inverting the new mix percentages.
  7. What is the contribution margin per unit for Product A?
    Answer: $30 First, determine the known information. The sales mix is 3:2, meaning 3/5 (60%) of sales are Product A and 2/5 (40%) are Product B. The contribution margin for Product B is $150 - $60 = $90. Let CM_A be the unknown contribution margin for Product A. The WACM formula is: WACM = (CM_A × Mix_A) + (CM_B × Mix_B). Substitute the known values: $54 = (CM_A × 0.60) + ($90 × 0.40). This gives $54 = 0.60 × CM_A + $36. Solving for CM_A: $54 - $36 = $18 = 0.60 × CM_A. Therefore, CM_A = $18 / 0.60 = $30. Distractor B ($45) is what you get if you assume a simple 50/50 average. Distractor C ($90) is the contribution margin for Product B. Distractor D ($36) is the weighted contribution of Product B to the total WACM, not the CM of Product A.
  8. What was Fusion Electronics' weighted-average contribution margin per unit last year?
    Answer: $45.00 First, calculate the contribution margin (CM) for each product. CM_Spark = $800,000 - $500,000 = $300,000. CM_Bolt = $900,000 - $600,000 = $300,000. CM_Amp = $1,200,000 - $900,000 = $300,000. Total contribution margin = $300,000 + $300,000 + $300,000 = $900,000. Total units sold = 10,000 + 6,000 + 4,000 = 20,000 units. Weighted-average contribution margin per unit = $900,000 ÷ 20,000 = $45.00. Distractor B ($51.67) is the simple average of the individual per-unit CMs: ($30 + $50 + $75) ÷ 3. Distractor C ($50.00) represents an error in calculation. Distractor D ($42.50) results from excluding one product from the calculation.
  9. The company's weighted-average contribution margin per unit is closest to:
    Answer: $28.40 First, calculate the contribution margin (CM) per unit for each part. CM_101 = $80 × 25% = $20. CM_202 = $120 × 40% = $48. Next, determine the sales mix. Total units = 7,000 + 3,000 = 10,000. Mix_101 = 7,000 / 10,000 = 70%. Mix_202 = 3,000 / 10,000 = 30%. The WACM per unit is ($20 × 0.70) + ($48 × 0.30) = $14.00 + $14.40 = $28.40. Distractor B ($32.50) is the simple average of the two CMs. Distractor C (32.5%) is the simple average of the two CM ratios, which is conceptually different from the WACM per unit. Distractor D ($34.00) incorrectly inverts the sales mix weights, calculating ($20 × 0.30) + ($48 × 0.70).
  10. Nexus Industries is analyzing a potential change in product mix. Currently, they sell Product X (contribution margin ratio 35%, 70% of sales dollars) and Product Y (contribution margin ratio 28%, 30% of sales dollars). The proposed new mix would be Product X (60% of sales dollars) and Product Y (40% of sales dollars). If total sales dollars remain constant at $400,000, what is the change in total contribution margin under the new mix?
    Answer: $2,800 decrease Current weighted-average CM ratio = (0.70 × 35%) + (0.30 × 28%) = 24.5% + 8.4% = 32.9%. Current total CM = $400,000 × 32.9% = $131,600. New weighted-average CM ratio = (0.60 × 35%) + (0.40 × 28%) = 21% + 11.2% = 32.2%. New total CM = $400,000 × 32.2% = $128,800. Change = $128,800 - $131,600 = -$2,800 (decrease). Choice B and C incorrectly calculate the direction of change. Choice D has the wrong magnitude.
  11. What is the per-unit contribution margin of a Painted Frame?
    Answer: $20.00 First, find the known values. CM_Box = $90 - $50 = $40. The sales mix is 1:4, meaning 1/5 (20%) of units are Boxes and 4/5 (80%) are Frames. Let CM_Frame be the unknown. Using the WACM formula: $24 = (CM_Box × Mix_Box) + (CM_Frame × Mix_Frame). Substitute values: $24 = ($40 × 0.20) + (CM_Frame × 0.80). Simplify: $24 = $8 + 0.80 × CM_Frame. Solve: $16 = 0.80 × CM_Frame. Therefore, CM_Frame = $16 / 0.80 = $20.00. Distractor A ($22.50) represents a calculation error. Distractor B ($40.00) is the CM for Boxes. Distractor D ($16.00) results from forgetting to divide by the weight (0.8).
  12. What is the weighted-average contribution margin per unit for the company?
    Answer: $19.00 The sales mix of 5:3:2 means there is a total of 5 + 3 + 2 = 10 'parts' in the mix. The sales mix percentages are: X = 5/10 (50%), Y = 3/10 (30%), and Z = 2/10 (20%). The weighted-average contribution margin (WACM) is the sum of the weighted CMs: WACM = ($10 × 0.50) + ($20 × 0.30) + ($40 × 0.20) = $5.00 + $6.00 + $8.00 = $19.00. Distractor B ($23.33) is the simple average of the three CMs (($10+$20+$40)/3). Distractor C ($190.00) is the contribution margin of a composite unit or 'bundle' containing 5 units of X, 3 of Y, and 2 of Z. Distractor D ($21.00) is the result of swapping the weights of Y and Z in the calculation.
  13. What is the weighted-average contribution margin per bag for Garden Co.?
    Answer: $19.20 First, calculate the contribution margin (CM) per unit for each product. For Premium, CM = Selling Price × CM Ratio = $50 × 60% = $30. For Standard, CM = Selling Price - Variable Cost = $30 - $18 = $12. The sales mix is 2:3, meaning the mix percentages are 2/5 (40%) for Premium and 3/5 (60%) for Standard. The weighted-average contribution margin (WACM) is ($30 × 0.40) + ($12 × 0.60) = $12.00 + $7.20 = $19.20. Distractor B ($21) is the simple average of the two CMs (($30+$12)/2). Distractor C ($39) incorrectly calculates the Standard CM ratio as 40% and then applies a simple average. Distractor D ($42) is the sum of the two contribution margins ($30+$12), ignoring the weighting.
  14. What is the weighted-average contribution margin per unit sold?
    Answer: $100.00 The weighted-average contribution margin (WACM) per unit can be calculated by dividing the total contribution margin by the total number of units sold. The extraneous information includes total sales revenue, the tax rate, and fixed costs. Total units sold = 8,000 chairs + 2,000 desks = 10,000 units. Total contribution margin = $1,000,000. WACM per unit = $1,000,000 / 10,000 units = $100.00 per unit. Distractor B ($400) is the after-tax operating income ($1,000,000 - $600,000). Distractor C (40.0%) is the company's overall contribution margin ratio ($1,000,000 / $2,500,000). Distractor D ($75) is the after-tax contribution margin per unit (a meaningless concept), calculated as $100 * (1-0.25).
  15. Meridian Corp sells two products with the following data: Product X has a contribution margin ratio of 40% and accounts for 60% of total sales dollars. Product Y has a contribution margin ratio of 25% and accounts for 40% of total sales dollars. If total sales are expected to be $500,000, what is the weighted-average contribution margin ratio?
    Answer: 34.0% The weighted-average contribution margin ratio is calculated using sales dollar weights: (0.60 × 40%) + (0.40 × 25%) = 24% + 10% = 34%. Choice A (32.5%) incorrectly averages the ratios without weights. Choice C (30%) uses equal weights of 50% each. Choice D (35.5%) appears to reverse the product weights.
  16. Which of the following is the most likely cause of the increase in the weighted-average contribution margin per unit?
    Answer: The proportion of High-Margin products in the sales mix has increased. The weighted-average contribution margin (WACM) is an average of the individual product contribution margins, weighted by their respective proportions in the sales mix. If selling prices and variable costs per unit are constant, the individual contribution margins are also constant. Therefore, the only way for the WACM to change is for the weights (the sales mix) to change. An increase in the WACM indicates that a higher proportion of products with a higher contribution margin are being sold. Distractor B is incorrect because fixed costs do not affect the contribution margin. Distractor C would cause the WACM to decrease. Distractor D is incorrect because the problem states total units sold remained constant; furthermore, economies of scale typically affect fixed or variable costs, which were also stated to be constant.
  17. Given this information, what must be the contribution margin per unit for the Deluxe model?
    Answer: $40.00 The sales mix of 3 Standard to 2 Deluxe means there are 5 total 'parts' in the mix. The sales mix percentage for Standard is 3/5 = 60%, and for Deluxe is 2/5 = 40%. Let CM_Deluxe be the unknown contribution margin. The formula for the weighted-average contribution margin (WACM) is: $31 = (CM_Standard × Mix_Standard) + (CM_Deluxe × Mix_Deluxe). Plugging in the known values: $31 = ($25 × 0.60) + (CM_Deluxe × 0.40). This simplifies to $31 = $15 + 0.40 × CM_Deluxe. Solving for CM_Deluxe: $16 = 0.40 × CM_Deluxe, so CM_Deluxe = $16 / 0.40 = $40.00. Distractor B ($35) results from incorrectly inverting the sales mix weights (using 40% for Standard and 60% for Deluxe). Distractor C ($37) incorrectly assumes a simple unweighted average, where if one is $6 below the average ($31-$25), the other must be $6 above ($31+$6). Distractor D ($26.67) results from an algebraic error, dividing $16 by 0.60 instead of 0.40.
  18. What will be the new weighted-average contribution margin for the company after the Basic product line is discontinued?
    Answer: $31.25 First, calculate the original WACM for context (though not required for the answer). Total units = 8,000. Mix = 50% Basic, 37.5% Plus, 12.5% Pro. Original WACM = ($10×0.5) + ($25×0.375) + ($50×0.125) = $5 + $9.375 + $6.25 = $20.625. After discontinuing Basic, the new total units sold will be 3,000 (Plus) + 1,000 (Pro) = 4,000 units. The new sales mix is based on this new total: Mix_Plus = 3,000 / 4,000 = 75%. Mix_Pro = 1,000 / 4,000 = 25%. The new WACM is: New WACM = ($25 × 0.75) + ($50 × 0.25) = $18.75 + $12.50 = $31.25. Distractor A ($21.88) is an incorrect calculation. Distractor C ($37.50) is the simple average of the remaining products' CMs. Distractor D ($28.75) results from using the original total units (8,000) as the denominator for the new sales mix, an error in reasoning.
  19. What is the weighted-average contribution margin per unit if TechStart maintains this sales mix?
    Answer: $41.00 Calculate contribution margins: Basic = $50 - $30 = $20; Standard = $100 - $65 = $35; Premium = $180 - $126 = $54. With a 5:3:2 mix, weighted-average = [(5 × $20) + (3 × $35) + (2 × $54)] ÷ (5 + 3 + 2) = [$100 + $105 + $108] ÷ 10 = $313 ÷ 10 = $41.00. Choice A uses incorrect contribution margins. Choice C reverses some of the mix ratios. Choice D uses simple averaging instead of weighted averaging.
  20. What is the weighted-average contribution margin per unit for this company?
    Answer: $6.25 The sales mix is 3:1, so the mix percentages are 3/4 (75%) for Product A and 1/4 (25%) for Product B. The weighted-average contribution margin (WACM) is calculated by summing the weighted CMs, being careful with the negative sign for Product B. WACM = (CM_A × Mix_A) + (CM_B × Mix_B) = ($10 × 0.75) + (-$5 × 0.25) = $7.50 - $1.25 = $6.25. Distractor B ($2.50) is the simple average of the two CMs (($10 - $5)/2). Distractor C ($7.50) is the contribution from Product A alone, ignoring the negative impact of Product B. Distractor D ($5.00) results from incorrectly adding instead of subtracting the negative contribution of B ($7.50 + $1.25 = $8.75), or some other calculation error. For instance, ($10 - $5) / 1 = $5.

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