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Solutions Manual - Chapter 19: Cost-Volume-Profit Analysis

Multiple Choice Questions - Solutions​

  1. Variable costs are costs that:

    • Answer: b) Variable costs change in total in direct proportion to volume.

  2. Contribution margin is:

    • Answer: b) Contribution margin = Sales - Variable costs.

  3. Break-even point occurs when:

    • Answer: c) Break-even occurs when revenue equals total costs.

  4. If selling price is €20, variable cost is €8, and fixed costs are €6,000, break-even in units is:

    • Answer: b) Break-even = €6,000 ÷ (€20 - €8) = 500 units.

  5. Margin of safety is:

    • Answer: b) Margin of safety = Actual sales - Break-even sales.

  6. High operating leverage means:

    • Answer: c) High operating leverage = High fixed costs relative to variable costs.

  7. Sales mix is:

    • Answer: b) Sales mix is the relative proportion of different products sold.

  8. Variable costing includes in product costs:

    • Answer: b) Variable costing includes only variable manufacturing costs.

  9. Absorption costing is required for:

    • Answer: b) Absorption costing is required for external financial reporting.

  10. In Luxembourg, break-even analysis should:

  • Answer: b) VAT should be handled consistently in break-even analysis.

Questions - Solutions​

  1. CVP purpose: CVP analysis evaluates how changes in volume, costs, and price affect profit so managers can plan sales targets, set prices, and evaluate new initiatives.
  2. Cost behavior categories: Variable costs change in total with activity, fixed costs stay constant within the relevant range, and mixed costs contain both components (often split using high-low or regression methods).
  3. Break-even formulas: Units = Fixed Costs ÷ Contribution Margin per Unit; Sales € = Fixed Costs ÷ Contribution Margin Ratio.
  4. Margin of safety: Actual sales − Break-even sales (in units or €). Dividing by actual sales yields the margin of safety ratio, indicating how much sales can drop before incurring losses.
  5. Operating leverage: Measures sensitivity of profit to volume changes (CM ÷ Net Income). High leverage (high fixed costs) magnifies profit and loss swings.
  6. Sales mix effects: For multi-product firms, break-even depends on the weighted average contribution margin; shifts toward higher-margin products lower the break-even point.
  7. Variable vs. absorption costing: Variable costing assigns only variable manufacturing costs to products; absorption costing assigns both variable and fixed manufacturing costs (required for external reporting).
  8. Income differences: When production ≠ sales, absorption costing defers or releases fixed overhead in inventory, causing income to differ from variable costing. When production = sales, incomes match.
  9. Luxembourg considerations: Include social charges, RCS/compliance fees, and high rents in fixed costs; treat VAT consistently (usually exclude it for internal analysis); consider multilingual markets and high labor costs.
  10. Using CVP for pricing: Managers can test price scenarios by recalculating contribution margins and break-even points, evaluating whether expected volume changes maintain or improve profit.

Problems Set A - Solutions​

Problem A-1: Break-Even Calculation​

  • Contribution margin per unit = €30 − €12 = €18
  • Contribution margin ratio = 18 ÷ 30 = 60%
  • Break-even units = 18,000 ÷ 18 = 1,000 units
  • Break-even revenue = 18,000 ÷ 0.60 = €30,000

Problem A-2: Target Profit​

  • Units for €6,000 profit = (18,000 + 6,000) ÷ 18 = 1,334 units (round up)
  • Revenue for €6,000 profit = (18,000 + 6,000) ÷ 0.60 = €40,000
  • Profit at 1,500 units: CM = 1,500 × 18 = 27,000 → Profit = 27,000 − 18,000 = €9,000

Problem A-3: What-If Analysis​

Base CM = €25 − €10 = €15; fixed costs €15,000; profit at 1,200 units = 18,000 − 15,000 = €3,000.

  • a) Price €28: CM = 28 − 10 = 18; break-even = 15,000 ÷ 18 = 834 units; profit at 1,200 units = 21,600 − 15,000 = €6,600
  • b) Variable cost €8: CM = 25 − 8 = 17; break-even = 15,000 ÷ 17 = 882 units; profit at 1,200 units = 20,400 − 15,000 = €5,400
  • c) Fixed costs €18,000: Break-even = 18,000 ÷ 15 = 1,200 units; profit at 1,200 units = 18,000 − 18,000 = €0 (no cushion)

Problem A-4: Margin of Safety​

  • Margin of safety (units) = 2,000 − 1,500 = 500 units
  • Margin of safety (€) = 500 × €20 = €10,000
  • Margin of safety ratio = 500 ÷ 2,000 = 25%

Problem A-5: Operating Leverage​

  • Degree of operating leverage = Contribution margin ÷ Net income = 12,000 ÷ 4,000 = 3
  • Profit increase for 20% sales growth = DOL × % change = 3 × 20% = 60% (new profit ≈ €6,400)

Problems Set B - Solutions​

Problem B-1: Multiple Products​

  • CM per unit: A = €20; B = €15
  • Weighted CM = 0.60(20) + 0.40(15) = €18
  • Weighted price = 0.60(40) + 0.40(30) = €36
  • CM ratio = 18 ÷ 36 = 50%
  • Break-even composite units = 24,000 ÷ 18 = 1,334 units
  • Break-even revenue = 24,000 ÷ 0.50 = €48,000
  • Units by product (approx.): Product A = 1,334 × 60% ≈ 800 units; Product B = 1,334 × 40% ≈ 534 units (round upward to maintain coverage)

Problem B-2: Variable vs. Absorption Costing​

  • Sales revenue = 1,800 × €50 = €90,000
  • Variable COGS = 1,800 × €20 = €36,000
  • Variable selling = 1,800 × €5 = €9,000
  • CM = €45,000
  • Fixed costs (mfg + selling) = 30,000 + 10,000 = €40,000
  • Variable-costing income = €5,000

Absorption COGS includes fixed OH: rate = 30,000 ÷ 2,000 = €15/unit. COGS = 1,800 × (€20 + €15) = €63,000.

  • Gross margin = 90,000 − 63,000 = €27,000
  • Selling costs = 9,000 + 10,000 = €19,000
  • Absorption income = €8,000

Difference €3,000 equals fixed OH deferred in inventory (200 units × €15).

Problem B-3: Complete CVP Analysis​

  • CM per meal = 25 − 9 = €16
  • Break-even meals = 12,000 ÷ 16 = 750 meals
  • Break-even revenue (ex VAT) = 750 × 25 = €18,750
  • Meals for €8,000 profit = (12,000 + 8,000) ÷ 16 = 1,250 meals
  • At 1,000 meals: profit = (1,000 × 16) − 12,000 = €4,000
    • Margin of safety units = 1,000 − 750 = 250
    • Margin of safety € = 250 × 25 = €6,250
    • MOS ratio = 250 ÷ 1,000 = 25%

Problem B-4: Cost Structure Analysis​

Model A: CM = 15 − 5 = €10

  • Break-even = 20,000 ÷ 10 = 2,000 units
  • Profit at 3,000 units = (3,000 × 10) − 20,000 = €10,000
  • DOL = 30,000 ÷ 10,000 = 3

Model B: CM = 15 − 10 = €5

  • Break-even = 10,000 ÷ 5 = 2,000 units
  • Profit at 3,000 units = (3,000 × 5) − 10,000 = €5,000
  • DOL = 15,000 ÷ 5,000 = 3

Model A carries more risk (higher fixed costs) but delivers double the profit at the same volume; Model B is safer but offers lower upside.

Comprehensive Problem 19 - Solutions​

1. Cost Behavior & Averages​

  • Fixed costs = €9,500 (rent, salaries + social charges, insurance, fiduciaire, utilities, other)
  • Weighted average selling price = 0.40(25) + 0.35(15) + 0.25(12) = €18.25
  • Weighted average variable cost = 0.40(10) + 0.35(6) + 0.25(5) = €7.35
  • Weighted average contribution margin = €10.90 (CM ratio ≈ 59.7%)

2. Break-Even​

  • Break-even meals = 9,500 ÷ 10.90 ≈ 872 meals
  • Break-even revenue (ex VAT) = 872 × 18.25 ≈ €15,914
  • Meals by product: Signature 349, Lunch 305, Light 218 (rounded)
  • Break-even graph: intercept at 9,500 (fixed costs); total cost line slope = 7.35; sales line slope = 18.25; intersection near 872 meals

3. Current Performance (900 meals)​

  • CM = 900 × 10.90 = €9,810
  • Profit = 9,810 − 9,500 = €310
  • Margin of safety = 900 − 872 = 28 meals (≈ €511, ratio 3.1%)
  • Degree of operating leverage = 9,810 ÷ 310 ≈ 31.6 (profits highly sensitive to volume)

4. Target Profit (€6,000)​

  • Required CM = 9,500 + 6,000 = 15,500
  • Required meals = 15,500 ÷ 10.90 ≈ 1,422 meals
  • Required revenue = 1,422 × 18.25 ≈ €25,973
  • Feasibility: requires ~58% volume growth over current 900 meals; significant marketing/operational improvements needed.

5. What-If Scenarios​

Scenario 1 – Signature price €28, mix 50/30/20:

  • Weighted price = €20.90; weighted VC = €7.80; CM = €13.10
  • Break-even meals = 9,500 ÷ 13.10 ≈ 725 meals (improves break-even)

Scenario 2 – Variable costs ↓10%:

  • New weighted VC = 0.40(9) + 0.35(5.4) + 0.25(4.5) = €6.615
  • CM = 18.25 − 6.615 = €11.64
  • Break-even = 9,500 ÷ 11.64 ≈ 817 meals

Scenario 3 – Fixed costs +€2,000 (new cook):

  • Fixed costs = 11,500; CM unchanged = 10.90
  • Break-even meals = 11,500 ÷ 10.90 ≈ 1,055 meals
  • Requires ~183 extra meals just to break even; ensure expected volume gain exceeds this.

6. Sales Mix Shift (50/30/20)​

  • Weighted CM = 0.50(15) + 0.30(9) + 0.20(7) = €11.60
  • Break-even = 9,500 ÷ 11.60 ≈ 819 meals
  • Beneficial because higher-margin signature dishes dominate.

7. 10% Price Increase (all items)​

  • New prices: Signature €27.50, Lunch €16.50, Light €13.20
  • New CMs: 17.5, 10.5, 8.2 → Weighted CM = €12.73
  • Break-even = 9,500 ÷ 12.73 ≈ 747 meals
  • Benefits break-even, but must assess demand elasticity and potential VAT-inclusive price impact.

8. Luxembourg Considerations​

  • VAT is excluded from internal CVP but affects cash flows; ensure consistent treatment.
  • Fixed costs include Luxembourg-specific items (fiduciaire, RCS fees, high rents).
  • Social charges increase both variable (hourly staff) and fixed (salaried staff) labor costs.
  • Compliance (eCDF, inspections) adds fixed overhead; budgeting should include these items.

9. Recommendations​

  • Emphasize high-margin signature dishes (menu engineering, promotions).
  • Explore moderate price increases paired with enhanced value messaging; monitor customer response.
  • Pursue cost controls (supplier negotiations, waste reduction) to improve CM.
  • Build marketing/operational plans to reach at least 1,100–1,200 meals before taking on new fixed costs.
  • Track CVP metrics monthly and update assumptions as VAT rules or social charges change.

Case Solutions​

Case 19-1: Pricing Decision​

  • Current CM = €20 − €8 = €12
  • Proposed price (−15%) = €20 × 0.85 = €17 → CM = 17 − 8 = €9
  • Break-even after price cut = 9,500 ÷ 9 ≈ 1,056 meals (up from 792)
  • Profit at 1,170 meals = (1,170 × 9) − 9,500 = €1,030 (below current profit ≈ €2,200)
  • Recommendation: Do not reduce price unless volume gains exceed 30% or other strategic reasons exist.
  • Considerations: brand positioning, capacity, service quality, competitive response, VAT-inclusive pricing, marketing effectiveness.
  • Alternatives: targeted promotions, upselling, menu mix optimization, loyalty programs.

Case 19-2: Expansion Decision​

  • Current break-even = 9,500 ÷ 12 = 792 meals
  • Post-expansion fixed costs = 9,500 + 4,000 = 13,500 → break-even = 13,500 ÷ 12 = 1,125 meals
  • Additional meals required to cover new fixed costs = 4,000 ÷ 12 ≈ 334 meals
  • If only 400 extra meals achievable, incremental profit = (400 × 12) − 4,000 = €800 (positive but modest).
  • Minimum extra volume to justify expansion ≈ 334 meals per month; higher buffer recommended.
  • Risks: demand uncertainty, staffing challenges, higher VAT remittances, capital needs, potential quality issues. Perform sensitivity analysis before committing.

End of Chapter 19 Solutions