Cost-Volume-Profit Analysis (CVP): Definition and Formula Explained

By Markets & Investing DeskUpdated Nov 10, 2026

Definition

Cost-volume-profit analysis is a management accounting method showing how operating profit changes when selling price, sales volume, variable costs or fixed costs change.

Key takeaways

Breakeven in units equals fixed costs divided by contribution margin per unit.
An after-tax profit target is converted to pretax by dividing it by one minus the tax rate.
In the example, a 10% price cut raises breakeven volume by a third because it comes entirely out of margin.
The formulas assume constant prices, constant unit variable costs, fixed costs within a relevant range and no inventory change.

Cost-volume-profit (CVP) analysis is a management accounting method that shows how a company’s operating profit changes when its selling price, sales volume, variable costs or fixed costs change. CVP stands for cost, volume and profit, the three quantities the model ties together. Its best-known output is the breakeven point, the sales level at which total revenue equals total costs and operating profit is zero. The same model also gives the sales needed to hit a target profit and how far sales can fall before a loss.

How CVP analysis works

CVP starts by reorganizing the income statement into a contribution format: sales minus all variable costs equals contribution margin, and contribution margin minus fixed costs equals operating profit. Costs are grouped by how they behave as volume moves, not by function.

The core profit equation is:

Operating profit = (Price per unit − Variable cost per unit) × Units sold − Fixed costs

Written with symbols: Profit = (P − V) × Q − F. Every other CVP formula is a rearrangement of this line.

Contribution margin

Contribution margin is what each sale leaves over after its variable costs, money that first covers fixed costs and then becomes profit. It can be expressed three ways:

Total contribution margin = total sales − total variable costs
Contribution margin per unit = unit selling price − unit variable cost
Contribution margin ratio = contribution margin ÷ sales

The contribution margin ratio is also called the profit-volume (P/V) ratio or contribution-to-sales (C/S) ratio. Because the model treats fixed costs as constant, each extra dollar of sales raises profit by exactly this ratio.

The CVP formulas

Goal	Formula
Breakeven in units	Fixed costs ÷ Contribution margin per unit
Breakeven in sales dollars	Fixed costs ÷ Contribution margin ratio
Units for a target profit	(Fixed costs + Target profit) ÷ Contribution margin per unit
Sales dollars for a target profit	(Fixed costs + Target profit) ÷ Contribution margin ratio
Margin of safety	Expected (or actual) sales − Breakeven sales

The target profit is added to fixed costs in total, not per unit. Taxes are ignored unless the target is stated after tax, in which case the after-tax target is first converted to pretax: target ÷ (1 − tax rate).

Worked example

Hypothetical company, for illustration only. A firm sells one product at $50. Variable costs (materials, direct labor, sales commission) are $30 per unit. Fixed costs (rent, salaries, insurance) are $100,000 per year.

Contribution margin per unit: $50 − $30 = $20
Contribution margin ratio: $20 ÷ $50 = 40%
Breakeven units: $100,000 ÷ $20 = 5,000 units
Breakeven sales: $100,000 ÷ 0.40 = $250,000 (5,000 × $50 confirms it)

Target profit. To earn $50,000 of operating profit: ($100,000 + $50,000) ÷ $20 = 7,500 units, or $150,000 ÷ 0.40 = $375,000 of sales.

Margin of safety. If the firm forecasts 8,000 units ($400,000), the margin of safety is $400,000 − $250,000 = $150,000, or 37.5% of forecast sales. Sales could fall that much before the firm reaches breakeven.

Sensitivity. CVP is often used to test “what if” changes. Assume the same costs:

Cut price to $45: contribution margin drops to $15, and breakeven rises to $100,000 ÷ $15 ≈ 6,667 units (rounded up, since a partial unit cannot be sold).
Raise fixed costs to $120,000 at the original $50 price: breakeven rises to 6,000 units.
Lower variable cost to $25: contribution margin becomes $25, and breakeven falls to 4,000 units.

The 10% price cut raises breakeven volume by a third because the whole cut comes out of the $20 contribution margin, not the $50 price.

Reading the CVP graph

A standard cost-volume-profit graph plots units on the horizontal axis and dollars on the vertical axis. It has three lines:

Fixed cost line, flat at the fixed cost level.
Total cost line, starting at the fixed cost level and rising at the variable cost per unit.
Total revenue line, starting at zero and rising at the selling price.

The breakeven point is where the revenue and total cost lines cross. To the right, the gap between them is profit; to the left, a loss. The simpler profit-volume (P/V) graph plots profit against volume as one line that starts at a loss equal to fixed costs and crosses zero at breakeven.

How CVP analysis is used

CVP is mainly a short-term planning tool. Managers use it to:

Judge whether a product is worth making, by comparing projected sales with the volume needed to cover costs plus a target profit.
Set prices, by seeing how far volume must rise to offset a discount.
Choose a cost structure, such as automation (higher fixed, lower variable cost) versus outsourcing (lower fixed, higher variable cost). More fixed costs mean higher operating leverage: profit grows faster above breakeven and falls faster below it.
Set sales targets and budgets, and measure risk through the margin of safety.
Evaluate special orders: any price above variable cost adds contribution if fixed costs and capacity are unaffected.

For several products, analysts use a weighted average contribution margin based on the sales mix. The result holds only as long as that mix stays the same.

Assumptions and limitations

The formulas hold only under these assumptions:

Selling price per unit is constant at all volumes, with no volume discounts.
Variable cost per unit is constant, ignoring bulk purchasing savings or overtime premiums.
Fixed costs stay fixed within a relevant range of activity. A new factory or extra shift moves them to a new level.
All units produced are sold, so inventory levels do not change.
Volume is the only driver of cost changes.
In multi-product firms, the sales mix is constant.

Real costs are often semi-variable (mixed), such as a utility bill with a fixed monthly charge plus usage. They must be split into fixed and variable parts first, typically with the high-low method, a scatter plot or statistical regression, and errors in that split flow straight into the breakeven figure.

CVP also ignores the time value of money. For long-lived investments, methods such as net present value and internal rate of return are better suited.

CVP vs. breakeven analysis: The terms are often used interchangeably. Strictly, breakeven analysis is one application of CVP; CVP also covers target profit, margin of safety and sensitivity testing.
Contribution margin vs. gross margin: Gross margin subtracts cost of goods sold, which includes fixed manufacturing overhead and excludes variable selling costs. Contribution margin subtracts all variable costs and no fixed costs, so the two figures generally differ.
Operating profit vs. net income: CVP models profit before interest and taxes unless a tax adjustment is added explicitly.

The Bottom Line

CVP analysis suits managers making short-term decisions on pricing, product viability, cost structure, sales targets and special orders. The contribution format shows how much each sale covers fixed costs and how much risk sits in the margin of safety. Results depend on a careful split of mixed costs and a stable sales mix, and long-lived investments call for methods that account for the time value of money.