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19.1 Calculate a Break-Even Point in Units and Dollars

Understanding Cost Behavior​

Before calculating break-even points, we must understand how costs behave.

Variable Costs​

Variable costs are costs that change in total in direct proportion to changes in activity level (volume).

Characteristics:

  • Total variable costs increase as volume increases
  • Total variable costs decrease as volume decreases
  • Variable cost per unit remains constant
  • Examples: Direct materials, direct labor (if paid per unit), sales commissions

Example: Marie's restaurant uses €5 of ingredients per meal served.

  • 100 meals: €5 × 100 = €500 total variable cost
  • 200 meals: €5 × 200 = €1,000 total variable cost
  • Variable cost per meal: €5 (constant)

Formula: Total Variable Costs = Variable Cost per Unit × Number of Units

Fixed Costs​

Fixed costs are costs that remain constant in total regardless of changes in activity level (volume).

Characteristics:

  • Total fixed costs remain constant as volume changes
  • Fixed cost per unit decreases as volume increases
  • Fixed cost per unit increases as volume decreases
  • Examples: Rent, salaries (fixed), insurance, depreciation

Example: Marie's restaurant pays €3,000 per month in rent.

  • 100 meals: €3,000 total fixed cost (€30 per meal)
  • 200 meals: €3,000 total fixed cost (€15 per meal)
  • 500 meals: €3,000 total fixed cost (€6 per meal)
  • Total fixed cost: €3,000 (constant)

Formula: Total Fixed Costs = Constant Amount (regardless of volume)

Mixed Costs​

Mixed costs (also called semi-variable costs) have both fixed and variable components.

Characteristics:

  • Part fixed, part variable
  • Total cost changes with volume, but not proportionally
  • Examples: Utilities (base charge + usage), phone (monthly fee + per-minute charges)

Example: Marie's restaurant has electricity costs: €200 base charge + €0.50 per meal.

  • 100 meals: €200 + (€0.50 × 100) = €250
  • 200 meals: €200 + (€0.50 × 200) = €300
  • 500 meals: €200 + (€0.50 × 500) = €450

Formula: Total Mixed Costs = Fixed Component + (Variable Rate × Volume)

Contribution Margin​

Contribution margin is the amount remaining from sales revenue after variable expenses have been deducted. It represents the amount available to cover fixed costs and provide profit.

Contribution Margin per Unit: Contribution Margin per Unit = Selling Price per Unit - Variable Cost per Unit

Total Contribution Margin: Total Contribution Margin = Total Sales Revenue - Total Variable Costs

Contribution Margin Ratio: Contribution Margin Ratio = Contribution Margin per Unit ÷ Selling Price per Unit or Contribution Margin Ratio = Total Contribution Margin ÷ Total Sales Revenue

Example: Marie's restaurant sells meals for €20 each. Variable cost per meal is €8.

  • Selling price per unit: €20
  • Variable cost per unit: €8
  • Contribution margin per unit: €20 - €8 = €12
  • Contribution margin ratio: €12 ÷ €20 = 0.60 or 60%

This means for every €1 of sales, €0.60 is available to cover fixed costs and profit.

Break-Even Point​

The break-even point is the level of sales at which total revenue equals total costs, resulting in zero profit (or zero loss).

At Break-Even:

  • Total Revenue = Total Costs
  • Profit = €0
  • Contribution Margin = Fixed Costs

Calculating Break-Even Point in Units​

Formula: Break-Even Point (Units) = Total Fixed Costs ÷ Contribution Margin per Unit

Example: Marie's restaurant has:

  • Fixed costs: €6,000 per month
  • Selling price per meal: €20
  • Variable cost per meal: €8
  • Contribution margin per meal: €20 - €8 = €12

Break-Even Point (Units) = €6,000 ÷ €12 = 500 meals per month

Marie must sell 500 meals per month to break even.

Verification:

  • Revenue: 500 meals × €20 = €10,000
  • Variable costs: 500 meals × €8 = €4,000
  • Contribution margin: €10,000 - €4,000 = €6,000
  • Fixed costs: €6,000
  • Profit: €6,000 - €6,000 = €0 ✓

Calculating Break-Even Point in Dollars​

Formula: Break-Even Point (Dollars) = Total Fixed Costs ÷ Contribution Margin Ratio

or

Break-Even Point (Dollars) = Break-Even Point (Units) × Selling Price per Unit

Example: Using the same data:

  • Fixed costs: €6,000 per month
  • Contribution margin ratio: 60% (0.60)

Break-Even Point (Dollars) = €6,000 ÷ 0.60 = €10,000 per month

or

Break-Even Point (Dollars) = 500 meals × €20 = €10,000 per month

Marie must generate €10,000 in revenue per month to break even.

Break-Even Analysis Graph​

A break-even graph visually shows the relationship between costs, revenue, and volume:

Graph Components:

  • X-axis: Volume (units sold)
  • Y-axis: Costs and Revenue (euros)
  • Fixed Cost Line: Horizontal line at fixed cost level
  • Total Cost Line: Starts at fixed costs, slopes upward (fixed + variable)
  • Revenue Line: Starts at origin, slopes upward (price × volume)
  • Break-Even Point: Intersection of revenue and total cost lines

Graph Interpretation:

  • Area below break-even: Loss zone
  • Area above break-even: Profit zone
  • Distance to break-even: Safety margin

Target Profit Analysis​

Target profit is the desired level of profit. We can calculate the sales volume needed to achieve a target profit.

Formula: Sales Volume (Units) = (Fixed Costs + Target Profit) ÷ Contribution Margin per Unit

Example: Marie wants to earn €3,000 profit per month.

  • Fixed costs: €6,000
  • Target profit: €3,000
  • Contribution margin per unit: €12

Sales Volume (Units) = (€6,000 + €3,000) ÷ €12 = 750 meals per month

Marie must sell 750 meals per month to earn €3,000 profit.

Verification:

  • Revenue: 750 meals × €20 = €15,000
  • Variable costs: 750 meals × €8 = €6,000
  • Contribution margin: €15,000 - €6,000 = €9,000
  • Fixed costs: €6,000
  • Profit: €9,000 - €6,000 = €3,000 ✓

Margin of Safety​

Margin of safety is the amount by which actual or expected sales exceed break-even sales. It indicates how much sales can drop before the business incurs a loss.

Formula: Margin of Safety (Units) = Actual Sales (Units) - Break-Even Sales (Units)

Margin of Safety (Dollars) = Actual Sales (Dollars) - Break-Even Sales (Dollars)

Margin of Safety Ratio = Margin of Safety ÷ Actual Sales

Example: Marie's restaurant sells 800 meals per month. Break-even is 500 meals.

  • Actual sales: 800 meals
  • Break-even sales: 500 meals
  • Margin of safety: 800 - 500 = 300 meals
  • Margin of safety (dollars): (800 × €20) - (500 × €20) = €6,000
  • Margin of safety ratio: 300 ÷ 800 = 37.5%

Marie can sell 300 fewer meals (or €6,000 less revenue) before incurring a loss.

Luxembourg Compliance Note​

When calculating break-even in Luxembourg:

  • Consider VAT in pricing (selling price may include or exclude VAT)
  • Fixed costs may include VAT (if not recoverable)
  • Variable costs should exclude recoverable VAT
  • Break-even analysis helps with VAT planning
  • Consider Luxembourg-specific costs (social charges, etc.)

Think It Through​

Why is it important to understand the break-even point? How can this information help a business owner make decisions about pricing, costs, or sales volume?