Key Takeaways
- Contribution margin (CM) = Sales - Variable Costs; represents amount available to cover fixed costs and profit.
- Break-even point occurs where total revenue equals total costs (CM covers all fixed costs).
- Margin of safety measures how far sales can drop before reaching break-even.
- Operating leverage indicates how sensitive operating income is to sales changes.
- Multi-product CVP requires weighted-average contribution margin based on sales mix.
Cost-Volume-Profit Analysis
Quick Answer: CVP analysis studies the relationship between costs, volume, and profit. Key formulas: Break-even units = Fixed Costs ÷ CM per unit; Break-even sales = Fixed Costs ÷ CM ratio. Target profit units = (Fixed Costs + Target Profit) ÷ CM. Margin of safety = Actual Sales - Break-even Sales.
Cost-volume-profit (CVP) analysis is a powerful tool for planning, pricing, and decision-making. It shows how changes in costs, sales volume, and prices affect operating income.
CVP Assumptions
CVP analysis relies on several simplifying assumptions:
| Assumption | Explanation |
|---|---|
| Linear costs | Total variable costs and revenues are linear |
| Fixed classification | Costs are clearly fixed or variable |
| Constant selling price | Price doesn't change with volume |
| Constant sales mix | Product mix remains stable |
| Inventory unchanged | Production equals sales |
Contribution Margin
The contribution margin is the amount remaining after variable costs to cover fixed costs and generate profit.
Contribution Margin Formulas
Total Contribution Margin:
CM = Sales Revenue - Total Variable Costs
Contribution Margin Per Unit:
CM per unit = Selling Price per Unit - Variable Cost per Unit
Contribution Margin Ratio:
CM Ratio = CM per Unit ÷ Selling Price per Unit
= Total CM ÷ Total Sales
Contribution Margin Income Statement
| Item | Amount |
|---|---|
| Sales Revenue | $500,000 |
| Less: Variable Costs | ($300,000) |
| Contribution Margin | $200,000 |
| Less: Fixed Costs | ($150,000) |
| Operating Income | $50,000 |
Analysis:
- CM Ratio = $200,000 ÷ $500,000 = 40%
- Every $1 of sales contributes $0.40 to fixed costs and profit
Break-Even Analysis
The break-even point is where total revenue equals total costs—no profit or loss.
Break-Even Formulas
Break-Even in Units:
Break-Even Units = Fixed Costs ÷ CM per Unit
Break-Even in Sales Dollars:
Break-Even Sales = Fixed Costs ÷ CM Ratio
Break-Even Example
| Data | Amount |
|---|---|
| Selling Price | $50 per unit |
| Variable Cost | $30 per unit |
| Fixed Costs | $100,000 |
Calculations:
CM per Unit = \$50 - \$30 = \$20
CM Ratio = \$20 ÷ \$50 = 40%
Break-Even Units = \$100,000 ÷ \$20 = 5,000 units
Break-Even Sales = \$100,000 ÷ 0.40 = \$250,000
Verification:
| Item | Amount |
|---|---|
| Sales (5,000 × $50) | $250,000 |
| Variable Costs (5,000 × $30) | ($150,000) |
| Contribution Margin | $100,000 |
| Fixed Costs | ($100,000) |
| Operating Income | $0 |
Target Profit Analysis
To find the volume needed to achieve a target profit:
Target Profit in Units:
Required Units = (Fixed Costs + Target Profit) ÷ CM per Unit
Target Profit in Sales Dollars:
Required Sales = (Fixed Costs + Target Profit) ÷ CM Ratio
Target Profit Example
Using the previous data, find units needed for $60,000 profit:
Required Units = (\$100,000 + \$60,000) ÷ \$20 = 8,000 units
Required Sales = 8,000 × \$50 = \$400,000
Target Profit After Tax
If target profit is after-tax, convert to pre-tax:
Pre-Tax Profit = After-Tax Profit ÷ (1 - Tax Rate)
Example: Target $45,000 after-tax profit, 25% tax rate:
Pre-Tax Profit = \$45,000 ÷ (1 - 0.25) = \$45,000 ÷ 0.75 = \$60,000
Margin of Safety
The margin of safety measures how far sales can decline before reaching break-even.
Formulas:
Margin of Safety (units) = Actual Units - Break-Even Units
Margin of Safety (dollars) = Actual Sales - Break-Even Sales
Margin of Safety (%) = Margin of Safety ÷ Actual Sales
Margin of Safety Example
| Data | Amount |
|---|---|
| Actual Sales | $400,000 |
| Break-Even Sales | $250,000 |
Margin of Safety = \$400,000 - \$250,000 = \$150,000
Margin of Safety % = \$150,000 ÷ \$400,000 = 37.5%
Interpretation: Sales can decline by 37.5% before the company incurs a loss.
Operating Leverage
Operating leverage measures how sensitive operating income is to changes in sales.
Degree of Operating Leverage (DOL)
DOL = Contribution Margin ÷ Operating Income
Operating Leverage Example
| Item | Amount |
|---|---|
| Contribution Margin | $200,000 |
| Operating Income | $50,000 |
DOL = \$200,000 ÷ \$50,000 = 4.0
Interpretation: A 10% increase in sales will result in a 40% increase in operating income (10% × 4.0 = 40%).
Operating Leverage and Risk
| Leverage Level | Characteristics |
|---|---|
| High DOL | High fixed costs, volatile profits |
| Low DOL | High variable costs, stable profits |
Risk Insight: Companies with high operating leverage experience larger profit swings from sales changes. They benefit more from sales increases but suffer more from sales decreases.
Multi-Product CVP Analysis
When a company sells multiple products, CVP analysis requires a weighted-average contribution margin.
Weighted-Average CM Calculation
Weighted-Average CM = Σ (CM per Unit × Sales Mix %)
Multi-Product Example
| Product | Price | VC | CM | Sales Mix |
|---|---|---|---|---|
| A | $40 | $24 | $16 | 60% |
| B | $80 | $40 | $40 | 40% |
Weighted-Average CM:
WACM = (\$16 × 0.60) + (\$40 × 0.40) = \$9.60 + \$16.00 = \$25.60
Break-Even ($128,000 fixed costs):
Break-Even Units = \$128,000 ÷ \$25.60 = 5,000 total units
Product A: 5,000 × 60% = 3,000 units
Product B: 5,000 × 40% = 2,000 units
CVP Graphical Analysis
The CVP graph (profit-volume chart) shows the relationship visually:
| Point/Line | Meaning |
|---|---|
| Total Revenue Line | Starts at origin, slope = selling price |
| Total Cost Line | Starts at fixed costs, slope = variable cost |
| Break-Even Point | Where lines intersect |
| Loss Area | Below break-even |
| Profit Area | Above break-even |
Sensitivity Analysis
CVP analysis helps evaluate "what-if" scenarios:
| Change | Impact on Break-Even |
|---|---|
| ↑ Selling Price | ↓ Break-even (if VC constant) |
| ↑ Variable Costs | ↑ Break-even |
| ↑ Fixed Costs | ↑ Break-even |
| ↑ Sales Mix (high CM products) | ↓ Break-even |
A company sells a product for $80 per unit with variable costs of $48 per unit and fixed costs of $160,000. How many units must be sold to break even?
A company has a contribution margin ratio of 35% and fixed costs of $175,000. What sales revenue is needed to earn a target profit of $70,000?
If a company has a contribution margin of $300,000 and operating income of $75,000, what is the degree of operating leverage?
A company has actual sales of $600,000 and break-even sales of $450,000. What is the margin of safety percentage?