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19.2 Apply Cost-Volume-Profit Analysis for Single-Product Companies

CVP Analysis Assumptions​

CVP analysis is based on several assumptions:

  1. Cost Behavior: Costs can be accurately classified as fixed or variable
  2. Linear Relationships: Costs and revenues are linear within the relevant range
  3. Constant Selling Price: Selling price per unit remains constant
  4. Constant Variable Cost: Variable cost per unit remains constant
  5. Constant Sales Mix: For multi-product companies, sales mix remains constant
  6. Inventory Levels: Inventory levels don't change significantly (production = sales)

CVP Income Statement​

A CVP income statement (contribution format income statement) organizes costs by behavior (variable vs. fixed) rather than by function.

Format:

Sales Revenue                    €XX,XXX
Less: Variable Costs             (XX,XXX)
────────────────────────────────────────
Contribution Margin               XX,XXX
Less: Fixed Costs                (XX,XXX)
────────────────────────────────────────
Net Income                       €XX,XXX

Example: Marie's restaurant CVP income statement for 600 meals:

Sales Revenue (600 × €20)        €12,000
Less: Variable Costs (600 × €8)   (4,800)
────────────────────────────────────────
Contribution Margin                7,200
Less: Fixed Costs                 (6,000)
────────────────────────────────────────
Net Income                       € 1,200

Using CVP for Decision-Making​

Scenario 1: What-If Analysis - Change in Selling Price​

Question: What if Marie increases price from €20 to €22?

Analysis:

  • New selling price: €22
  • Variable cost per unit: €8 (unchanged)
  • New contribution margin: €22 - €8 = €14
  • Fixed costs: €6,000 (unchanged)
  • New break-even: €6,000 ÷ €14 = 429 meals (down from 500)

Impact:

  • Break-even decreases (good)
  • But sales volume may decrease due to higher price
  • Need to consider price elasticity

Scenario 2: What-If Analysis - Change in Variable Costs​

Question: What if variable costs increase from €8 to €9 per meal?

Analysis:

  • Selling price: €20 (unchanged)
  • New variable cost: €9
  • New contribution margin: €20 - €9 = €11
  • Fixed costs: €6,000 (unchanged)
  • New break-even: €6,000 ÷ €11 = 545 meals (up from 500)

Impact:

  • Break-even increases (bad)
  • Profit decreases for any given sales volume
  • Need to find ways to reduce variable costs or increase price

Scenario 3: What-If Analysis - Change in Fixed Costs​

Question: What if fixed costs increase from €6,000 to €7,500 (e.g., higher rent)?

Analysis:

  • Selling price: €20 (unchanged)
  • Variable cost: €8 (unchanged)
  • Contribution margin: €12 (unchanged)
  • New fixed costs: €7,500
  • New break-even: €7,500 ÷ €12 = 625 meals (up from 500)

Impact:

  • Break-even increases significantly
  • Need to sell 125 more meals to break even
  • May need to increase prices or reduce other costs

Scenario 4: What-If Analysis - Change in Sales Volume​

Question: What if sales increase from 600 to 750 meals per month?

Analysis:

  • Selling price: €20
  • Variable cost: €8
  • Contribution margin: €12
  • Fixed costs: €6,000

At 600 meals:

  • Contribution margin: 600 × €12 = €7,200
  • Fixed costs: €6,000
  • Profit: €1,200

At 750 meals:

  • Contribution margin: 750 × €12 = €9,000
  • Fixed costs: €6,000
  • Profit: €3,000

Impact:

  • Profit increases by €1,800 (150 meals × €12 contribution margin)
  • Each additional meal contributes €12 to profit (after covering variable costs)

Operating Leverage​

Operating leverage measures how sensitive net income is to changes in sales volume. Companies with high fixed costs relative to variable costs have high operating leverage.

Degree of Operating Leverage: Degree of Operating Leverage = Contribution Margin ÷ Net Income

Example: At 600 meals:

  • Contribution margin: €7,200
  • Net income: €1,200
  • Degree of operating leverage: €7,200 ÷ €1,200 = 6.0

This means a 10% increase in sales will result in a 60% increase in profit (10% × 6.0).

High Operating Leverage:

  • High fixed costs, low variable costs
  • Large profit increases when sales increase
  • Large profit decreases when sales decrease
  • Higher risk, higher potential reward

Low Operating Leverage:

  • Low fixed costs, high variable costs
  • Smaller profit changes when sales change
  • Lower risk, lower potential reward

CVP Analysis with Taxes​

When considering taxes, we need to adjust our target profit calculations.

After-Tax Profit: After-Tax Profit = Before-Tax Profit × (1 - Tax Rate)

Before-Tax Profit: Before-Tax Profit = After-Tax Profit ÷ (1 - Tax Rate)

Sales Volume for After-Tax Target: Sales Volume = (Fixed Costs + [After-Tax Target ÷ (1 - Tax Rate)]) ÷ Contribution Margin per Unit

Example: Marie wants €2,400 after-tax profit. Tax rate is 20%.

  • After-tax target: €2,400
  • Tax rate: 20%
  • Before-tax target: €2,400 ÷ (1 - 0.20) = €3,000
  • Fixed costs: €6,000
  • Contribution margin: €12
  • Sales volume: (€6,000 + €3,000) ÷ €12 = 750 meals

Luxembourg Compliance Note​

For Luxembourg SMEs:

  • Consider corporate income tax (impôt sur le revenu des collectivités)
  • Consider municipal business tax (impôt commercial communal)
  • Effective tax rates vary by entity type and location
  • VAT is not an income tax (it's a consumption tax)
  • Social charges affect total costs but are not income taxes

Think It Through​

How does operating leverage affect a business's risk and potential reward? Would a restaurant typically have high or low operating leverage? Why?