Break-Even Analysis
Finding the point where revenue equals costs.
Why This Matters
Before you commit to a business, a product, a price point, or an expansion, one question must be answered first: how much do you need to sell just to survive?
The break-even point is the exact volume at which total revenue equals total costs โ zero profit, zero loss. Every unit sold above break-even generates profit. Every unit below break-even contributes to a loss.
Break-even analysis is the most immediately actionable CVP tool. It converts abstract financial projections into a concrete, operational target: you need to sell X cups per day to keep the lights on. That number tells a manager whether a business is viable, whether a new location makes sense, whether a price change is worth making, and how close to the edge the business operates on a bad week.
Break-even is the financial equivalent of asking "can I survive?" before you ask "can I thrive?" It's the minimum viable economics of any business decision.
The Break-Even Formulas
BREAK-EVEN IN UNITS
Break-Even Units = Fixed Costs รท Contribution Margin per Unit
= FC รท (SP โ VC)
BREAK-EVEN IN SALES DOLLARS
Break-Even Revenue = Fixed Costs รท Contribution Margin Ratio
= FC รท CM%
Where CM% = CM per unit รท Selling Price per unit
These are equivalent: Break-Even Revenue = Break-Even Units ร Selling Price
Full Calculation: ABC Coffee Shop
INPUTS
Selling Price (SP): $2.00/cup
Variable Cost (VC): $1.20/cup
Contribution Margin: $0.80/cup
CM Ratio: 40% ($0.80 รท $2.00)
Fixed Costs (annual): $33,500
BREAK-EVEN IN UNITS
= $33,500 รท $0.80 = 41,875 cups/year
BREAK-EVEN IN REVENUE
= $33,500 รท 0.40 = $83,750/year
Operational Translation
Per Month
3,490
cups/month
Per Week
805
cups/week
Per Day
140
cups/day (300 open days)
"ABC needs to sell at least 140 cups per day just to cover all costs." โ the number the owner posts in the back office.
Verification: Does It Check Out?
Always verify break-even by plugging back into the profit equation:
VERIFICATION
Revenue: 41,875 ร $2.00 = $83,750
Variable costs: 41,875 ร $1.20 = ($50,250)
Contribution margin: $33,500
Fixed costs: ($33,500)
Profit: $0 โ
The Break-Even Graph
The graph makes break-even intuitive โ two lines converging at a single point.
Break-Even Graph โ Profit and Loss Zones
- โ Revenue starts at $0; total cost starts at $33,500 (fixed)
- โ Lines intersect at break-even (41,875 units, $83,750)
- โ Gap above intersection = profit; gap below = loss
How Break-Even Changes with Key Variables
Understanding how break-even responds to input changes is the most powerful application of break-even analysis.
Effect of Price Changes
| Scenario | Price | VC | CM | Fixed | BE Units |
|---|---|---|---|---|---|
| Base | $2.00 | $1.20 | $0.80 | $33,500 | 41,875 |
| Price up 12.5% ($2.25) | $2.25 | $1.20 | $1.05 | $33,500 | 31,905 โ (โ9,970) |
| Price down 10% ($1.80) | $1.80 | $1.20 | $0.60 | $33,500 | 55,833 โ (+13,958) |
Insight
A 12.5% price increase reduces break-even by 23.8%. A 10% price decrease increases break-even by 33.3%. Price is the most leveraged break-even driver โ a small increase dramatically lowers the hurdle, but a small decrease dramatically raises it.
Effect of Variable Cost Changes
| Scenario | Price | VC | CM | Fixed | BE Units |
|---|---|---|---|---|---|
| Base | $2.00 | $1.20 | $0.80 | $33,500 | 41,875 |
| VC up 12.5% ($1.35) | $2.00 | $1.35 | $0.65 | $33,500 | 51,538 โ (+9,663) |
| VC down 10% ($1.08) | $2.00 | $1.08 | $0.92 | $33,500 | 36,413 โ (โ5,462) |
If coffee bean costs rise 12.5%: break-even jumps to 51,538 cups. ABC currently sells 85,000 โ still profitable, but the buffer shrinks.
Effect of Fixed Cost Changes
| Scenario | Price | VC | CM | Fixed | BE Units |
|---|---|---|---|---|---|
| Base | $2.00 | $1.20 | $0.80 | $33,500 | 41,875 |
| Fixed up $6K (new location) | $2.00 | $1.20 | $0.80 | $39,500 | 49,375 โ (+7,500) |
| Fixed down $5K (manager cuts) | $2.00 | $1.20 | $0.80 | $28,500 | 35,625 โ (โ6,250) |
Important
Fixed cost changes shift break-even proportionately. Every $1 of additional fixed cost requires $1 รท CM = $1.25 of additional revenue to break even ($1 รท $0.80 = 1.25 additional cups).
Interactive Tool
Model your own break-even and see sensitivity to price, variable cost, and fixed cost changes in real time.
Break-Even Calculator with Sensitivity
Pre-filled with ABC Coffee Shop. Adjust base inputs, then model how break-even shifts when price, variable cost, or fixed costs change.
Sensitivity adjustments
Base BE Units
41,875
Base BE Revenue
$83,750
CM per Unit
$0.80
CM Ratio
40.0%
| Scenario | Price | VC | CM | Fixed | BE Units | ฮ vs Base |
|---|---|---|---|---|---|---|
| Base case | $2.00 | $1.20 | $0.80 | $33,500 | 41,875 | โ |
FORMULA
Break-Even Units = FC รท (SP โ VC)
Every $1 of additional fixed cost requires $1 รท CM additional units to break even. At $0.80 CM: $1 รท 0.80 = 1.25 extra units per $1 FC.
Break-Even for New Investment Decisions
Break-even analysis is critical for evaluating capital investments.
Scenario
ABC Coffee Shop โ Second Location Expansion
ABC is considering opening a second location. Additional fixed costs: $28,000/year (new rent + additional staff). Variable costs and price remain the same.
Additional fixed costs: $28,000
CM per cup: $0.80
Break-even: $28,000 รท $0.80 = 35,000 cups/year
= 2,917 cups/month = 97 cups/day (300 open days)
"The second location must sell at least 97 cups/day to be worthwhile โ otherwise it loses money and drags down overall business profit."
If location averages 120 cups/day
(120 โ 97) ร 300 ร $0.80 = $5,520/year profit
Positive but thin margin โ high risk if volume expectations are optimistic.
Compare to first location
First location sells 85,000 cups with 50.7% margin of safety. Second location needs only 35,000 but has much less buffer at 120 cups/day.
After-Tax Break-Even
When target profit must be earned after taxes, the formula adjusts:
AFTER-TAX BREAK-EVEN
Target Pre-Tax Income = Target After-Tax Income รท (1 โ Tax Rate)
Then: Units = (FC + Target Pre-Tax Income) รท CM
ABC: Owner wants $15,000 after-tax income. Tax rate: 25%
Required pre-tax = $15,000 รท 0.75 = $20,000
Units = ($33,500 + $20,000) รท $0.80 = 66,875 cups/year
Verification: Pre-tax $20,000 โ Tax 25% ($5,000) = After-tax $15,000 โ
Break-Even in Service Businesses
Break-even applies beyond product businesses โ any business with fixed and variable costs can use it.
Freelance Graphic Designer โ Monthly
- Software subscriptions$150
- Home office allocation$200
- Health insurance$400
- Total Fixed$750/month
Variable rate: $15/hour ยท Billing rate: $85/hour
CM per hour: $85 โ $15 = $70/hour
Monthly break-even: $750 รท $70 = 10.7 hours/month
Powerful insight: With low fixed costs, break-even is reached quickly โ the rest is pure profit upside at $70/hour. This is the appeal of low-overhead service businesses.
Interpreting Break-Even Results
What break-even tells you
- โ The minimum sales volume to avoid losses
- โ Whether a new investment is economically viable
- โ How price or cost changes shift the survival threshold
- โ A daily/weekly operational target for managers
What it does NOT tell you
- โ Expected profit at planned volume (use CVP for that)
- โ Cash flow timing (profitability โ liquidity)
- โ Competitive dynamics or demand elasticity
- โ Optimal price โ only the survival floor
Common Mistakes
Mistake 1: Forgetting Mixed Costs
โ Wrong
Using total cost รท units as "variable cost per unit" and treating all remaining cost as fixed. Electricity: $150 base + $0.003/cup treated as entirely fixed โ VC understated, FC overstated โ wrong break-even.
โ Right
Use high-low method (or regression) to separate mixed costs into fixed and variable components before running CVP.
Mistake 2: Using Break-Even for Unequal Periods
โ Wrong
"Annual break-even is 41,875 cups โ if we sell 4,000 cups every month, we're fine." Ignores cash flow timing when costs and revenue don't align month-to-month.
โ Right
Break-even = profitability analysis, not cash flow analysis. A business can be above break-even on paper but cash-flow-negative due to timing.
Mistake 3: Ignoring Sales Mix in Multi-Product Break-Even
โ Wrong
Using espresso CM ($0.80) when 29% of sales are pastries (CM $0.69). Single-product BE: 41,875. Actual multi-product BE: 43,620 โ underestimates by 1,745 units.
โ Right
Calculate weighted average CM using actual sales mix before computing multi-product break-even.
Key Takeaway
Break-even analysis finds the exact sales volume where total revenue equals total costs โ the boundary between profit and loss. The formula is simple: Fixed Costs รท Contribution Margin per Unit. What makes it powerful is its applications: sizing new investments, testing price changes, modeling cost increases, and translating abstract annual targets into daily operational numbers. Break-even doesn't tell you how much profit to expect โ it tells you the minimum viable performance level, which is the first question any decision-maker must answer.
Test Your Understanding
Break-even formulas, fixed cost changes, and after-tax targets โ check your answers below.
Question 1: Fixed costs = $50,000. Selling price = $25. Variable cost = $15. What is break-even in units?
Question 2: Fixed costs increase from $50,000 to $60,000. CM stays at $10. How does break-even change?
Question 3: A business wants $18,000 after-tax profit. Tax rate = 40%. Fixed costs = $42,000. CM per unit = $6. How many units must be sold?
Ready to Practice?
Calculate break-even, test price and cost sensitivity, and evaluate investment decisions in the Practice Lab.
Try the Practice LabWhat's Next?
Contribution Margin โ The full deep-dive into the metric at the heart of CVP: how it's calculated, reported, and used to analyze product profitability.
Contribution Margin
The metric at the heart of break-even
CVP Analysis
Costs, volume, and profit together