Finance
Break-even Analysis
Finds the sales volume at which contribution covers fixed costs and a venture stops losing money, then reads the gap between expected sales and that point, the margin of safety, as a measure of how much room the plan has to be wrong.
Also known as Cost-volume-profit analysis, CVP analysis, Break-even point analysis. First set out by Walter Rautenstrauch (populariser), with earlier roots in Henry Hess and Charles E. Knoeppel in 1930; the primary source is cited in full below.
Where this is contested
Attribution is diffuse. Henry Hess published a graphical cost-volume analysis in 1903, Charles E. Knoeppel developed profit-graph methods from the 1910s, and Walter Rautenstrauch at Columbia coined 'break-even point' around 1930; the technique grew out of engineering economics rather than a single author's work.
- Format
- Scoring model
- Level
- Business unit · Product
- Best for
- Evaluate options · Plan execution · Assess risk
- Decision stage
- Explore options · Decide · Plan
- Difficulty
- Introductory
- Time to apply
- An hour with reliable cost data; longer if costs must first be separated into fixed and variable.
Plate · The model
The components
Fixed costs
Costs that do not move with volume across the relevant range: rent, salaries, insurance, equipment, licences. These are the hurdle the venture must clear, and they are what make the decision risky, because they are incurred whether or not customers turn up.
Signals of strength
Costs that would still be paid in a zero-sales month · Step changes lurking at higher volumes, such as a second member of staff · Allocated overheads masquerading as incremental costs
Contribution per unit
Selling price per unit minus variable cost per unit: the amount each sale contributes towards fixed costs and, past break-even, towards profit. It is the engine of the whole analysis, and small changes to it move the break-even point sharply.
Signals of strength
Discounting or wastage quietly eroding the net price · Variable costs such as card fees and delivery left out of the unit cost · A contribution margin ratio well below sector norms
Break-even point
The volume, in units or revenue, at which total contribution exactly covers fixed costs. Below it the venture loses money on the period; above it, each additional unit's contribution falls through to profit. It is a floor to clear, never a target to aim at.
Signals of strength
Break-even volume close to realistic capacity · Break-even revenue above credible demand for the site or channel · The point moving sharply under small price changes, a sign of high operating leverage
Margin of safety
The gap between expected sales and break-even sales, usually expressed as a percentage of expected sales. It converts the arithmetic into a risk statement: how wrong can the forecast be before the venture loses money?
Signals of strength
Expected sales only just above break-even · Forecasts built on best-case footfall or launch enthusiasm · High fixed costs magnifying losses below the break-even point
When it earns its keep
- You are weighing a discrete commitment with identifiable fixed costs, a new site, machine, product line or hire, and need to know the volume it must sustain before it pays.
- You are setting or changing prices and want to see how the required volume moves as price and contribution move.
- You need a fast viability screen before building a full financial model; break-even is the cheapest honest test a plan can fail.
- You want to compare cost structures, for instance renting versus buying, or fixed salaries versus commission, where the choice shifts costs between fixed and variable.
And when it doesn't
- Costs cannot be sensibly split into fixed and variable, for example project businesses where almost every cost is negotiated per job.
- The decision spans many products with shared costs and shifting mix; a single break-even point hides the mix problem that actually decides profitability.
- Volumes under consideration sit far outside the current relevant range, where the linear cost and price assumptions behind the arithmetic stop holding.
- The real question is cash survival rather than accounting profit. Break-even ignores timing; a business can trade above break-even and still run out of cash.
How to run it
Before starting, gather the inputs the analysis depends on:
- A reliable split of costs into fixed and variable for the decision at hand, including an honest treatment of semi-variable items such as utilities and casual labour.
- The expected selling price per unit, net of discounts, wastage and transaction fees, and the variable cost per unit.
- A credible sales forecast or capacity estimate against which to judge the break-even point.
- Clarity on which costs are genuinely incremental to the decision, rather than allocations of costs the business pays anyway.
- 1
Separate fixed from variable costs
List every cost the decision creates and classify it. Fixed costs stay constant across the relevant range of volumes (rent, salaries, insurance, licence fees); variable costs move with each unit sold (ingredients, packaging, card fees, piece-rate labour). Split semi-variable costs into their fixed and variable elements rather than dumping them in either pile.
- 2
Establish contribution per unit
Contribution per unit = selling price per unit minus variable cost per unit. Use the realistic net price, after discounts and wastage, that units actually achieve. Contribution is what each sale throws towards fixed costs; if it is negative, stop here, because volume only makes a negative contribution worse.
- 3
Calculate the break-even point
Break-even units = fixed costs divided by contribution per unit. A venture with fixed costs of 3,420 pounds and contribution of 5.70 pounds per unit breaks even at 600 units. Express it in whatever unit the business thinks in: covers, orders, billable days, seats filled.
- 4
Run the contribution-margin-ratio variant
Where units are awkward or the mix varies, work in revenue instead. Contribution margin ratio = contribution per unit divided by price. Break-even revenue = fixed costs divided by the contribution margin ratio. At a 60 per cent ratio, 3,420 pounds of fixed costs needs 5,700 pounds of revenue to break even.
- 5
Calculate the margin of safety
Margin of safety = (expected sales minus break-even sales) divided by expected sales. It states how far sales can fall short of forecast before the venture makes a loss. A thin margin of safety on a confident forecast is a warning, since forecasts are the least reliable number in the whole calculation.
- 6
Stress-test and decide
Recompute the break-even point under pessimistic assumptions: price down 10 per cent, variable costs up, fixed costs higher than quoted. If the decision only works in the base case, the analysis has told you something. The output is a judgement about viability and risk, and it should change what you commit to.
Reading the result
A break-even point in units and in revenue, a margin of safety against the expected sales forecast, and a sensitivity view showing how the point moves as price, variable cost and fixed cost assumptions flex.
- Compare the break-even point with capacity and credible demand, never with the forecast alone. A point the site physically cannot serve is a decision already made.
- Read the margin of safety as the plan's tolerance for error. Under about 20 per cent, the venture depends on the forecast being right, and forecasts rarely are.
- Watch operating leverage. High fixed costs mean profits grow fast above break-even and losses grow fast below it; the same arithmetic that makes the upside attractive makes the downside dangerous.
A worked example
A street-food trader weighs a second pitch
A Leeds street-food trader runs a profitable weekend stall selling bao and rice boxes at an outdoor market. A city-centre food hall has offered a midweek pitch on a twelve-month licence. The trader runs a break-even analysis on the second pitch as an incremental decision: only the costs and sales the new pitch creates.
- Fixed costs
- Incremental fixed costs of the new pitch: food-hall licence fee 1,200 pounds a month, a part-time server 1,850 pounds, extra insurance and prep-kitchen hire 370 pounds. Total 3,420 pounds a month, payable whether anyone buys a bao or not. The trader's own time is excluded but noted as a real opportunity cost.
- Contribution per unit
- Average spend per customer is 9.50 pounds. Variable costs per cover: ingredients 2.90 pounds, packaging 0.40, card fees and food-hall commission 0.50, making 3.80 pounds. Contribution is 5.70 pounds per cover, a 60 per cent contribution margin ratio, healthy for street food.
- Break-even point
- 3,420 divided by 5.70 = 600 covers a month. Trading 20 days a month, that is 30 covers a day. In revenue terms, 3,420 divided by 0.60 = 5,700 pounds a month. The food hall's footfall data suggests comparable vendors serve 40 to 50 covers a day midweek.
- Margin of safety
- Taking 45 covers a day, 900 a month, as the expected case: margin of safety = (900 minus 600) / 900 = 33 per cent. Sales can come in a third below the comparable-vendor benchmark before the pitch loses money. At the cautious case of 35 covers a day the margin of safety falls to 14 per cent, which is thin for a twelve-month commitment.
The read. The pitch clears break-even comfortably on the food hall's own benchmark, but the benchmark is the seller's number, and the licence binds for a year. The analysis says negotiate before committing: a three-month break clause or a stepped licence fee would matter more than any plausible saving on ingredients, because the risk sits in the fixed costs, and only January footfall will show whether 45 covers a day is real.
Pitfalls
- Treating semi-variable costs as wholly fixed or wholly variable. Casual labour, utilities and maintenance usually have both elements, and misclassifying them biases the break-even point in whichever direction flatters the plan.
- Using list price instead of achieved price. Discounts, wastage, refunds and platform commissions all reduce contribution, and leaving them out understates the break-even point.
- Applying a single-product calculation to a multi-product business without fixing the sales mix. The break-even point of a mix is only valid while the mix holds.
- Treating break-even as a target. Break-even is the floor at which the venture merely stops losing money; a plan whose ambition is the floor is not a plan.
- Extrapolating outside the relevant range. Linear costs and constant prices hold over a limited band of volumes; beyond it come step costs, overtime and price pressure the model does not see.
What the critics say
The classical model is deterministic, yet every input is uncertain. Jaedicke and Robichek showed that ignoring the probability distributions of price, cost and volume can make a higher-break-even alternative wrongly look safer, and argued CVP analysis should be done explicitly under uncertainty.
Jaedicke, R. K. and Robichek, A. A. (1964) 'Cost-Volume-Profit Analysis Under Conditions of Uncertainty', The Accounting Review, 39(4), pp. 917-926.
The fixed-versus-variable dichotomy misdescribes modern cost structures. Cooper and Kaplan argued that many so-called fixed costs vary with the range and complexity of activity rather than with volume, so simple volume-based break-even analysis can misprice products and decisions.
Cooper, R. and Kaplan, R. S. (1988) 'Measure Costs Right: Make the Right Decisions', Harvard Business Review, 66(5), September-October 1988.
The accountant's linear model conflicts with the economist's cost and revenue curves, which bend with scale and price elasticity. The linear version is defensible only within a narrow relevant range, a caveat that practice routinely forgets.
Work it through
Enter the fixed costs the decision creates, the realistic net price and variable cost per unit, and your expected sales. The break-even point and margin of safety compute below. Read the break-even point against capacity and credible demand, and the margin of safety as the plan's tolerance for a wrong forecast.
Inputs
Result
- Contribution per unit
- £5.7
- Contribution margin ratio
- 60%
- Break-even point
- 600 units
- Break-even revenue
- £5,700
- Margin of safety
- 33.3%
Break-even chart
Sources and further reading
- Rautenstrauch, W. (1930) The Successful Control of Profits. New York: B. C. Forbes.
- Hess, H. (1903) 'Manufacturing: Capital, Costs, Profits and Dividends', The Engineering Magazine, December 1903, an early graphical treatment of cost-volume relationships and a recognised precursor of the break-even chart.
- Drury, C. (2018) Management and Cost Accounting. 10th edn. Andover: Cengage Learning, chapter on cost-volume-profit analysis.
- Wikipedia: Walter Rautenstrauch (provenance of the break-even chart and the term 'break-even point'). ↗