Management accounting / CVP

Break-even analysis

Find the unit volume and revenue that exactly cover fixed and variable costs, then see how much room there is between break-even and your plan. The margin of safety and operating leverage are derived from the same contribution margin.

At planProfitablePlanned profit$84,000Operating leverage3.86

Break-even volume

8889 units

Units needed to cover fixed costs

Break-even revenue

$400,000

Sales value at that volume

Contribution margin

$27.00 · 60.0%

Per unit and as a share of price

Margin of safety

25.9%

Planned 1.200e+4 units vs break-even

Cost-volume-profit ladder

Revenue, total cost and profit at output levels around the break-even point.

8889 unit break-even

Cost-volume-profit ladder
Volume	Revenue	Variable cost	Fixed cost	Profit
4444 units	$200,000	$80,000	$240,000	-$120,000
6667 units	$300,000	$120,000	$240,000	-$60,000
8889 units	$400,000	$160,000	$240,000	+$0.00
1.111e+4 units	$500,000	$200,000	$240,000	+$60,000
1.333e+4 units	$600,000	$240,000	$240,000	+$120,000

At break-even volume the profit row is exactly zero — revenue covers variable and fixed costs with nothing left over.

Revenue, cost and profit

The crossing point of revenue and total cost is the break-even volume.

Break-even volume vs price

How sensitive the break-even point is to a 20% price move.

Canonical equations

The exact relationships implemented by this engine.

CM = P − V · what each unit contributes to fixed costs

Q* = F / (P − V) · undefined when price is below variable cost

F / CM ratio · equivalent to Q* · P

(Q − Q*) / Q · how far sales can fall before a loss

Show model notation and computationOpen the symbolic form, the variable definitions, and the step-by-step derivation when you need the detail.

A clear path from inputs to results.

Break-even is the volume at which revenue exactly covers fixed and variable costs. Everything below it is a loss; everything above contributes to profit at the rate of the contribution margin. This engine reports the break-even point, the profit at your planned volume, and how far sales can fall before you are underwater.

Step-by-step methodWorked exampleAssumptions explained

How to use

Enter total fixed costs for the period — rent, salaries, insurance, anything that does not move with volume.

Enter the price per unit.

Enter the variable cost per unit: materials, packaging, payment fees, delivery.

Set your planned volume to see the profit and the margin of safety at that level.

Check the contribution margin ratio — it is the share of each sale available to cover fixed costs.

Use the price-sensitivity chart before cutting price to win volume.

The formula

\mathrm{CM} = P - V, \qquad Q^{*} = \frac{F}{P-V}, \qquad \text{MoS} = \frac{Q - Q^{*}}{Q}, \qquad \pi = Q(P-V) - F

Reference: Horngren, Datar & Rajan, "Cost Accounting", ch. 3 (cost-volume-profit analysis).

Worked example

$240,000 fixed cost, $45 price, $18 variable cost (default inputs)

Inputs

Fixed costs $240,000.
Price $45 per unit.
Variable cost $18 per unit.
Planned volume 12,000 units.

Calculation path

1
Contribution margin: 45 − 18 = $27 per unit, or 60% of price.
2
Break-even volume: 240,000 / 27 = 8,889 units.
3
Break-even revenue: 8,889 × 45 = $400,000.
4
Profit at plan: 12,000 × 27 − 240,000 = $84,000.
5
Margin of safety: (12,000 − 8,889) / 12,000 = 25.9%.

Result

Break-even 8,889 units or $400,000 of revenue · profit at plan $84,000 · margin of safety 25.9%.

Interpreting the result

A 60% contribution margin means every sale above break-even drops 60 cents of each dollar to the bottom line. The margin of safety says sales can fall 25.9% before the business makes a loss — that is the buffer, and it is usually more informative than the break-even number itself. If price falls 10%, the break-even volume jumps by roughly 20%, which is why discounting is so dangerous for high-fixed-cost businesses.

Assumptions & limitations

Fixed costs stay fixed within the relevant range. Beyond a capacity threshold they step up, which invalidates the linear model.

Variable cost per unit is constant. Volume discounts and overtime both break this.

Price is constant across all units — no tiered pricing or promotional mix.

The product mix is a single product, or a fixed mix with a blended contribution margin.

No inventory effects: units produced equal units sold.

Frequently asked questions

What is contribution margin?

Price minus variable cost per unit. It is what each sale contributes toward fixed costs and then profit. A 60% ratio means 60 cents of every revenue dollar is available after variable costs.

What happens if I cut price to gain volume?

The contribution margin falls and the break-even volume rises — often faster than volume can grow. A 10% price cut on a 60% margin reduces the contribution to 55.6% of the new price, raising break-even volume by about 20%.

How do I handle multiple products?

Use a weighted-average contribution margin based on the sales mix, or compute break-even per product line. The single-product model assumes a fixed mix.

Why is the margin of safety more useful than break-even?

Because it is expressed relative to your actual plan. Break-even tells you the floor; margin of safety tells you how far above the floor you are operating. A business 5% above break-even is fragile regardless of how large the absolute numbers are.

Does break-even include the owner’s salary?

It should, if the owner works in the business. Treat it as a fixed cost; otherwise break-even understates the true requirement.

What if variable cost exceeds price?

Then the contribution margin is negative and no volume can break even — every additional sale increases the loss. The engine reports this as unreachable rather than returning a negative unit count.