Perform break-even analysis to determine the sales volume or revenue needed to cover all costs. Use this skill when the user needs to calculate break-even point, assess margin of safety, evaluate operating leverage, or decide pricing and volume trade-offs — even if they say 'how many units do we need to sell', 'when will we be profitable', or 'what happens if we lower the price'.
Break-even analysis finds the point where total revenue equals total costs — zero profit, zero loss. It separates costs into fixed and variable, then calculates the volume (units or revenue) needed to cover fixed costs through contribution margin.
IRON LAW: Fixed vs Variable Classification Must Be Rigorous
Fixed costs do NOT change with volume (rent, salaries, insurance).
Variable costs change PROPORTIONALLY with volume (materials, shipping per unit, commissions).
"Salaries" is NOT always fixed — a sales commission is variable.
"Rent" is NOT always fixed — a percentage-rent lease is variable.
Misclassification directly corrupts the break-even calculation.
Contribution Margin per Unit = Selling Price - Variable Cost per Unit
Break-Even Units = Fixed Costs / Contribution Margin per Unit
Break-Even Revenue = Fixed Costs / Contribution Margin Ratio
Contribution Margin Ratio = Contribution Margin per Unit / Selling Price
Margin of Safety = (Actual Sales - Break-Even Sales) / Actual Sales
Degree of Operating Leverage (DOL) = Contribution Margin / Net Income
Separate every cost line into fixed or variable. For semi-variable costs (e.g., electricity with a base charge + usage), split into fixed and variable portions.
How far above break-even are current sales? Higher margin of safety = more resilience to downturns.
Test: What happens if price drops 10%? If volume drops 20%? If fixed costs increase? Build a scenario table.
# Break-Even Analysis: {Product/Business}
## Cost Structure
| Category | Amount | Fixed/Variable |
|----------|--------|---------------|
| {item} | ${X} | F/V |
## Break-Even Calculation
- Fixed Costs: ${X}/period
- Variable Cost per Unit: ${X}
- Selling Price per Unit: ${X}
- Contribution Margin: ${X} ({X%})
- **Break-Even: {N} units / ${X} revenue**
- Margin of Safety: {X%}
## Scenario Analysis
| Scenario | BEP Units | Margin of Safety |
|----------|-----------|-----------------|
| Base case | {N} | {X%} |
| Price -10% | {N} | {X%} |
| Volume -20% | N/A | {X%} |
| Fixed costs +15% | {N} | {X%} |
Scenario: Break-even for a Taiwanese bubble tea shop
| Script | Description | Usage |
|---|---|---|
scripts/breakeven.py | Compute break-even quantity, revenue, and contribution margin | python scripts/breakeven.py --help |
Run python scripts/breakeven.py --verify to execute built-in sanity tests.
references/multi-product-bep.md