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CVP with Sales Mix - Cost Accounting

  1. Phoenix Enterprises produces three products with identical variable cost ratios of 60% of selling price. Product P sells for $40, Product Q for $25, and Product R for $35. Current sales mix is 1:2:2. Fixed costs are $180,000. If the company shifts to a sales mix that maximizes contribution margin per composite unit while maintaining at least 10% of sales volume for each product, what is the optimal sales mix ratio?
    Answer: 8:1:1 ratio optimizing total contribution margin potential With 60% variable cost ratio, contribution margins are: P = $40 × 0.40 = $16, Q = $25 × 0.40 = $10, R = $35 × 0.40 = $14. Product P has highest CM, so maximize P while maintaining 10% minimum for Q and R. If total is 10 parts, minimum constraint gives 1 part each for Q and R, leaving 8 parts for P. Optimal ratio = 8:1:1 (P:Q:R). This maximizes weighted CM = (8/10 × $16) + (1/10 × $10) + (1/10 × $14) = $12.80 + $1.00 + $1.40 = $15.20. Other choices either violate the 10% minimum constraint or fail to maximize the contribution margin.
  2. If the company's sales mix remains constant, what is the target operating income if total sales reach 9,000 units?
    Answer: $65,000 The correct answer is $65,000. This is a multi-step problem. First, find the unknown contribution margin for Product C (CMCCM_C). At breakeven, Total CM = Fixed Costs. So, (2,000 × $15) + (3,000 × $20) + (1,000 × CM_C) = $130,000. This gives $30,000 + $60,000 + 1,000 CM_C = $130,000. So, 1,000 CM_C = $40,000, and CM_C = $40. Second, determine the unit sales of each product at the 9,000 total unit level. The breakeven sales mix is 2:3:1 (totaling 6 parts). At 9,000 units: A = (2/6)×9,000 = 3,000 units; B = (3/6)×9,000 = 4,500 units; C = (1/6)×9,000 = 1,500 units. Third, calculate the total contribution margin at this new level: Total CM = (3,000×$15)+(4,500×$20)+(1,500×$40) = $45,000+$90,000+$60,000 = $195,000. Finally, calculate operating income: Operating Income = Total CM - Fixed Costs = $195,000 - $130,000 = $65,000.
  3. To achieve its target profit under the supply constraint for Product B, how many units of Product A must the company sell?
    Answer: 15,834 units The correct answer is 15,834 units. First, determine the total contribution margin required to meet the profit target: Required CM = Fixed Costs + Target Profit = $95,000 + $20,000 = $115,000. Second, calculate the contribution margin that will be generated by selling the maximum number of the constrained product, B: 2,000 units × $10/unit = $20,000. Third, determine the remaining contribution margin that must be generated by Product A: $115,000 (Total Required) - $20,000 (from B) = $95,000. Finally, calculate the number of units of A required to generate this amount: $95,000 / $6 per unit = 15,833.33 units, which rounds up to 15,834 units.
  4. Assuming the total sales revenue remains constant, which of the following events would cause the company's overall breakeven point in sales dollars to decrease?
    Answer: A shift in the sales mix, with the Premium product accounting for a larger percentage of total revenue. The correct answer is B. The breakeven point in sales dollars is calculated as Fixed Costs / Weighted-Average Contribution Margin Ratio (WACMR). To decrease the breakeven point, the WACMR must increase. Shifting the sales mix towards the product with the higher contribution margin ratio (the Premium product) will increase the overall WACMR. Shifting towards the Standard product (A) would decrease the WACMR and increase the breakeven point. Increasing variable costs (C) or decreasing selling prices (D) would lower the contribution margin ratios, thus decreasing the WACMR and increasing the breakeven point.
  5. At what level of total unit sales would the company's operating income be identical under both the current and proposed plans?
    Answer: 8,000 units The correct answer is 8,000 units. To find the indifference point, set the profit equations for both scenarios equal to each other. Let U be the total units sold. Scenario 1 (Current): Mix is 75% A, 25% B. WACM₁ = (0.75 × $5) + (0.25 × $15) = $3.75 + $3.75 = $7.50. Profit₁ = $7.50U - $100,000. Scenario 2 (Proposed): Mix is 50% A, 50% B. WACM₂ = (0.50 × $5) + (0.50 × $15) = $2.50 + $7.50 = $10.00. Profit₂ = $10.00U - $120,000. Set Profit₁ = Profit₂: $7.50U - $100,000 = $10.00U - $120,000. Solving for U: $20,000 = $2.50U, so U = 8,000 units.
  6. If Farmstead wishes to achieve a target operating income of $40,000, what is the total sales revenue required, given that the selling price is $10 for a box of Apples and $25 for a basket of Berries?
    Answer: $300,000 The correct answer is $300,000. This requires multiple steps. First, calculate the contribution margin of a 'package' (5 boxes of Apples, 2 baskets of Berries): CM_pkg = (5 × $4) + (2 × $10) = $20 + $20 = $40. Second, determine the number of packages needed for the target profit: Packages = (Fixed Costs + Target Profit) / CM_pkg = ($80,000 + $40,000) / $40 = $120,000 / $40 = 3,000 packages. Third, calculate the selling price of one package: SP_pkg = (5 × $10) + (2 × $25) = $50 + $50 = $100. Finally, calculate the total required sales revenue: Total Revenue = 3,000 packages × $100/package = $300,000. Alternatively, one could calculate WACMR. Total CM of package = $40, Total SP of package = $100, so WACMR = 40%. Required Sales = ($80k+$40k)/0.40 = $300,000.
  7. What is the total sales revenue Clean Corp must generate to achieve an after-tax net income of $75,000, assuming the sales mix remains constant?
    Answer: $1,000,000 The correct answer is $1,000,000. First, convert the after-tax profit target to a pre-tax profit target: Pre-tax Profit = After-tax Profit / (1 - Tax Rate) = $75,000 / (1 - 0.25) = $100,000. Second, calculate the weighted-average contribution margin ratio (WACMR). The sales mix based on revenue is 60% Commercial ($600k/$1M) and 40% Residential ($400k/$1M). WACMR = (60% × 40%) + (40% × 60%) = 0.24 + 0.24 = 0.48. Finally, use the target profit CVP formula for sales dollars: Required Sales = (Fixed Costs + Target Pre-tax Profit) / WACMR = ($380,000 + $100,000) / 0.48 = $480,000 / 0.48 = $1,000,000.
  8. Based on the information provided, how many units of Product Beta must the company sell to achieve its breakeven point?
    Answer: 20,000 units The correct answer is 20,000 units. First, calculate the weighted-average contribution margin (WACM) per unit for a 'package' of products. A package consists of 3 units of Alpha and 2 units of Beta. The contribution margin of a package is (3 units × $10/unit) + (2 units × $15/unit) = $30 + $30 = $60. The package contains 5 units in total, so the WACM per unit is $60 / 5 units = $12. Second, calculate the breakeven point in total packages: Total Fixed Costs / WACM per package = $120,000 / $60 = 2,000 packages. Alternatively, using WACM per unit: $120,000 / $12 = 10,000 total units. Finally, determine the number of Beta units at breakeven: 2,000 packages × 2 Beta units/package = 20,000 units. Or, 10,000 total units × (2/5) = 20,000 units.
  9. What is the contribution margin per unit for the Economy chair?
    Answer: $25.00 The correct answer is $25.00. At the breakeven point, the total contribution margin equals total fixed costs. The total fixed costs are given as $240,000. Let CM_E be the unknown contribution margin for the Economy chair. The total contribution margin is the sum of the CM from both products: Total CM = (8,000 units × CM_E) + (2,000 units × $40/unit). Set this equal to the fixed costs: $240,000 = (8,000 × CM_E) + $80,000. Now, solve for CM_E: $240,000 - $80,000 = 8,000 × CM_E. This simplifies to $160,000 = 8,000 × CM_E. Therefore, CM_E = $160,000 / 8,000 = $25.00 per unit.
  10. If a company's actual sales mix shifts towards the product with the lowest contribution margin per unit, but the total number of units sold remains the same as budgeted, what is the effect on the company's breakeven point and operating income?
    Answer: The breakeven point increases, and operating income decreases. The correct answer is A. A shift in sales mix towards the product with the lowest contribution margin per unit will decrease the company's overall weighted-average contribution margin (WACM) per unit. The breakeven point in units is calculated as Fixed Costs / WACM. A lower WACM in the denominator will result in a higher breakeven point. Furthermore, since the total number of units sold is constant, a lower WACM means the company generates less total contribution margin for the same sales volume. Since Operating Income = Total Contribution Margin - Fixed Costs, a lower total contribution margin will result in a lower operating income.
  11. Vortex Industries sells three products with the following monthly data: Product 1 sells 1,000 units at $50 each with $30 variable cost per unit; Product 2 sells 1,500 units at $40 each with $28 variable cost per unit; Product 3 sells 500 units at $60 each with $35 variable cost per unit. Monthly fixed costs are $48,000. If Vortex discontinues Product 2 and redistributes its sales proportionally between Products 1 and 3 based on their current relative volumes, what will be the new monthly operating income?
    Answer: $17,000 monthly operating income with restructured product line Current CMs: Product 1 = $20, Product 2 = $12, Product 3 = $25. After discontinuing Product 2, redistribute 1,500 units proportionally: Product 1 currently represents 1,000/(1,000+500) = 2/3 of remaining products, Product 3 represents 1/3. New volumes: Product 1 = 1,000 + (2/3 × 1,500) = 2,000 units; Product 3 = 500 + (1/3 × 1,500) = 1,000 units. New total CM = (2,000 × $20) + (1,000 × $25) = $65,000. New operating income = $65,000 - $48,000 = $17,000.

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