Chapter 19 – Exercises & Cases
Multiple Choice Questions
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Variable costs are costs that:
a) Remain constant in total
b) Change in total in direct proportion to volume
c) Change per unit as volume changes
d) Are always fixed
Answer: b) Variable costs change in total in direct proportion to volume. -
Contribution margin is:
a) Sales minus fixed costs
b) Sales minus variable costs
c) Sales minus total costs
d) Fixed costs minus variable costs
Answer: b) Contribution margin = Sales - Variable costs. -
Break-even point occurs when:
a) Revenue equals variable costs
b) Revenue equals fixed costs
c) Revenue equals total costs
d) Contribution margin equals zero
Answer: c) Break-even occurs when revenue equals total costs. -
If selling price is €20, variable cost is €8, and fixed costs are €6,000, break-even in units is:
a) 300 units
b) 500 units
c) 750 units
d) 1,000 units
Answer: b) Break-even = €6,000 ÷ (€20 - €8) = 500 units. -
Margin of safety is:
a) Break-even sales minus actual sales
b) Actual sales minus break-even sales
c) Contribution margin minus fixed costs
d) Selling price minus variable cost
Answer: b) Margin of safety = Actual sales - Break-even sales. -
High operating leverage means:
a) Low fixed costs
b) High variable costs
c) High fixed costs relative to variable costs
d) Low contribution margin
Answer: c) High operating leverage = High fixed costs relative to variable costs. -
Sales mix is:
a) Total sales volume
b) Proportion of different products sold
c) Average selling price
d) Total contribution margin
Answer: b) Sales mix is the relative proportion of different products sold. -
Variable costing includes in product costs:
a) All manufacturing costs
b) Only variable manufacturing costs
c) Only fixed manufacturing costs
d) No manufacturing costs
Answer: b) Variable costing includes only variable manufacturing costs. -
Absorption costing is required for:
a) Internal decision-making
b) External financial reporting
c) CVP analysis
d) Break-even analysis
Answer: b) Absorption costing is required for external financial reporting. -
In Luxembourg, break-even analysis should:
a) Ignore VAT
b) Handle VAT consistently
c) Only consider fixed costs
d) Exclude social charges
Answer: b) VAT should be handled consistently in break-even analysis.
Questions
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Explain the difference between variable costs and fixed costs. Give examples of each.
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What is contribution margin? How is it calculated and why is it important?
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How do you calculate the break-even point in units? In dollars?
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What is margin of safety? How is it calculated and what does it tell you?
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Explain operating leverage. What does high operating leverage mean for a business?
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How does sales mix affect break-even analysis for a multi-product company?
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What is the difference between variable costing and absorption costing?
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When will net income differ between variable costing and absorption costing?
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What are the key considerations for break-even analysis in Luxembourg SMEs?
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How can a business use CVP analysis to make pricing decisions?
Problems Set A
Problem A-1: Break-Even Calculation
A business has:
- Selling price: €30 per unit
- Variable cost: €12 per unit
- Fixed costs: €18,000 per month
Calculate:
a) Contribution margin per unit
b) Contribution margin ratio
c) Break-even point in units
d) Break-even point in dollars
Problem A-2: Target Profit
Using the data from Problem A-1, calculate:
a) Units needed to earn €6,000 profit
b) Revenue needed to earn €6,000 profit
c) If 1,500 units are sold, what is the profit?
Problem A-3: What-If Analysis
A business has:
- Selling price: €25
- Variable cost: €10
- Fixed costs: €15,000
- Current sales: 1,200 units
Calculate the impact of:
a) Increasing price to €28
b) Reducing variable cost to €8
c) Increasing fixed costs to €18,000
Problem A-4: Margin of Safety
A business has:
- Actual sales: 2,000 units
- Break-even sales: 1,500 units
- Selling price: €20 per unit
Calculate:
a) Margin of safety in units
b) Margin of safety in dollars
c) Margin of safety ratio
Problem A-5: Operating Leverage
At 1,000 units:
- Contribution margin: €12,000
- Net income: €4,000
Calculate:
a) Degree of operating leverage
b) If sales increase 20%, what is the percentage increase in profit?
Problems Set B
Problem B-1: Multiple Products
A business sells two products:
- Product A: Price €40, Variable cost €20, 60% of sales
- Product B: Price €30, Variable cost €15, 40% of sales
- Fixed costs: €24,000
Calculate:
a) Weighted average contribution margin
b) Weighted average selling price
c) Weighted average contribution margin ratio
d) Break-even point in total units
e) Break-even point in dollars
f) Break-even units for each product
Problem B-2: Variable vs. Absorption Costing
A company:
- Produced: 2,000 units
- Sold: 1,800 units
- Selling price: €50
- Variable manufacturing cost: €20
- Fixed manufacturing overhead: €30,000
- Variable selling: €5 per unit
- Fixed selling: €10,000
Calculate net income under:
a) Variable costing
b) Absorption costing
c) Explain the difference
Problem B-3: Complete CVP Analysis
A Luxembourg restaurant:
- Fixed costs: €12,000 per month
- Variable cost per meal: €9
- Selling price per meal: €25 (excluding VAT)
- VAT rate: 17%
Calculate:
a) Break-even in meals (excluding VAT consideration for internal analysis)
b) Break-even in revenue (excluding VAT)
c) Meals needed for €8,000 profit
d) If 1,000 meals are sold, calculate profit and margin of safety
Problem B-4: Cost Structure Analysis
Compare two business models:
- Model A: Fixed costs €20,000, Variable cost €5 per unit, Price €15
- Model B: Fixed costs €10,000, Variable cost €10 per unit, Price €15
Calculate for each:
a) Break-even point
b) Profit at 3,000 units
c) Degree of operating leverage at 3,000 units
d) Which model has higher risk? Higher potential reward?
Comprehensive Problem
Comprehensive Problem 19: Complete CVP Analysis for Le Petit Bistro
Marie wants to perform a complete CVP analysis for her restaurant to make better decisions.
Current Situation:
- Fixed costs per month: €9,500
- Rent: €3,500
- Salaries (fixed): €4,000
- Social charges (24%): €960
- Insurance: €200
- Fiduciaire: €300
- Utilities (base): €150
- Other: €390
Menu Items:
- Signature Dish: Price €25 (excl. VAT), Variable cost €10, 40% of sales
- Lunch Special: Price €15 (excl. VAT), Variable cost €6, 35% of sales
- Light Meal: Price €12 (excl. VAT), Variable cost €5, 25% of sales
- VAT rate: 17% (all meals)
Current Performance:
- Average 900 meals per month
- Current sales mix as stated above
Required:
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Cost Behavior Analysis:
a) Classify all costs as fixed or variable
b) Calculate total variable cost per meal (weighted average)
c) Calculate weighted average selling price
d) Calculate weighted average contribution margin -
Break-Even Analysis:
a) Calculate break-even point in total meals
b) Calculate break-even point in revenue (excluding VAT)
c) Calculate break-even for each menu item
d) Create a break-even graph (describe key points) -
Current Performance Analysis:
a) Calculate current profit at 900 meals
b) Calculate margin of safety
c) Calculate degree of operating leverage
d) Analyze current performance -
Target Profit Analysis:
Marie wants €6,000 profit per month: a) Calculate required meals
b) Calculate required revenue
c) Analyze feasibility -
What-If Scenarios:
a) Scenario 1: Increase Signature Dish price to €28- Calculate new break-even
- Assume sales mix changes to 50% Signature, 30% Lunch, 20% Light b) Scenario 2: Reduce variable costs by 10%
- Calculate new break-even
- Analyze impact c) Scenario 3: Increase fixed costs by €2,000 (hire another cook)
- Calculate new break-even
- Determine if additional volume justifies cost
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Sales Mix Analysis:
a) Current weighted average contribution margin
b) If sales mix shifts to 50% Signature, 30% Lunch, 20% Light- Calculate new weighted average contribution margin
- Calculate new break-even
- Analyze impact
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Pricing Strategy:
Marie is considering a 10% price increase across all items: a) Calculate new prices
b) Calculate new contribution margins
c) Calculate new break-even
d) Analyze impact (consider potential volume decrease) -
Luxembourg Considerations:
a) How does VAT affect the analysis?
b) What Luxembourg-specific costs are included?
c) How do social charges affect the cost structure?
d) What compliance considerations are there? -
Recommendations:
Based on the analysis, provide recommendations for: a) Pricing strategy
b) Cost management
c) Sales mix optimization
d) Profit improvement
Cases
Case 19-1: Pricing Decision
Marie is considering whether to lower prices to attract more customers. Currently:
- Average price: €20 (weighted average)
- Variable cost: €8
- Fixed costs: €9,500
- Current sales: 900 meals/month
- Profit: €2,200/month
She's considering a 15% price reduction, which she believes will increase volume by 30%.
Questions for Analysis:
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Calculate the impact of the price reduction on contribution margin per meal.
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Calculate the new break-even point.
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Calculate profit at the new volume (900 × 1.30 = 1,170 meals).
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Should Marie reduce prices? Why or why not?
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What other factors should she consider?
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What alternative strategies might be better?
Case 19-2: Expansion Decision
Marie is considering expanding her restaurant to increase capacity. The expansion would:
- Increase fixed costs by €4,000/month (additional rent, utilities)
- Allow her to serve 500 more meals per month
- Require hiring additional staff (variable cost)
Questions for Analysis:
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What is the current break-even point?
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What would be the new break-even point after expansion?
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How many additional meals must she sell to cover the additional fixed costs?
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If she can sell 400 additional meals, should she expand?
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What is the minimum additional volume needed to justify expansion?
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What risks should she consider?
Solutions are published in supplementary/instructor/solutions/chapter_19_solutions.md.