What is Cost‑Volume‑Profit (CVP) analysis — short definition
– CVP analysis (also called breakeven analysis) is a simple model that links a product’s selling price, sales volume, fixed costs, and variable costs to operating profit. It answers questions like “How many units must we sell to cover costs?” and “What sales level gives a target profit?”
Key terms (defined)
– Fixed costs: expenses that don’t change with production volume within a relevant range (e.g., rent, salaried staff).
– Variable costs: costs that vary directly with output (e.g., materials per unit).
– Contribution margin (per unit): selling price per unit minus variable cost per unit. It is the amount each unit contributes to covering fixed costs and then to profit.
– Contribution margin ratio: contribution margin per unit divided by selling price per unit (or total contribution divided by total sales). Expressed as a percentage.
– Breakeven point: the sales level (units or revenue) where total revenue equals total costs (zero operating profit).
Basic formulas (accurate and practical)
– Contribution margin per unit = Price per unit − Variable cost per unit
– Contribution margin ratio = Contribution margin per unit ÷ Price per unit
– Breakeven (units) = Fixed costs ÷ Contribution margin per unit
– Breakeven (sales dollars) = Fixed costs ÷ Contribution margin ratio
– Target sales to achieve a desired operating profit = (Fixed costs + Target profit) ÷ Contribution margin ratio
How to run a CVP analysis — step‑by‑step checklist
1. Identify the relevant period and scope (product line, plant, or company).
2. List fixed costs for that period.
3. Calculate variable cost per unit and selling price per unit.
4. Compute contribution margin per unit and the contribution margin ratio.
5. Calculate breakeven units and breakeven sales revenue.
6. If you have a target profit, add it to fixed costs and recompute required sales (using the formula above).
7. Test sensitivity: change price, volume, or costs to see how breakeven and profit targets shift.
8. Review assumptions (see limitations below) and, if needed, split mixed costs using a method such as high‑low, scatter plot, or regression.
Worked numeric examples (two quick cases)
Example A — revenue breakeven using a CM ratio
– Given: Fixed costs = $100,000; Contribution margin ratio = 40% (0.40).
– Breakeven sales dollars = Fixed costs ÷ CM ratio = $100,000 ÷ 0.40 = $250,000.
– Interpretation: the business must generate $250,000 of sales to cover all fixed and variable costs.
If the company wants $50,000 of operating profit:
– Required sales = (Fixed costs + Target profit) ÷ CM ratio = ($100,000 + $50,000) ÷ 0.40 = $375,000.
Example B — breakeven in units using per‑unit numbers
– Assume: Price = $20 per unit; Variable cost = $12 per unit → Contribution margin per unit = $8.
– Fixed costs = $100,000.
– Breakeven units = Fixed costs ÷ CM per unit = $100,000 ÷ $8 = 12,500 units.
– Interpretation: sell 12,500 units to break even; any additional units contribute $8 each toward profit.
What CVP analysis is used for (practical applications)
– Setting minimum sales targets and revenue budgets.
– Testing pricing changes and their profit impact.
– Evaluating whether a new product is economically feasible.
– Supporting “make or buy” and discontinuation decisions.
– Short‑term capacity and staffing decisions where cost behavior can be approximated as linear.
Key assumptions and common limitations (check before relying on results)
– Selling price per unit is constant over the relevant range.
– Unit variable costs are constant and linear with volume.
– Total fixed costs remain unchanged within the analyzed range.
– All units produced are assumed to be sold (no inventory effects).
– Relationships are linear; therefore CVP is mainly a short‑term tool.
– Mixed (semi‑variable) costs must be separated into fixed and variable portions — common methods: high‑low method, scatter plot analysis, or statistical regression.
– Because of these assumptions, CVP provides a useful approximation but can mislead if costs or prices vary significantly with scale.
Quick sanity checks to run after computing CVP results
– Does the required sales volume seem achievable given market size and production capacity?
– Would a small change in price or variable cost drastically change the breakeven result? If yes,
If yes, run a sensitivity (what‑if) analysis before acting. Small changes in price, variable cost, sales mix, or volume can move breakeven a lot. Recompute breakeven and profit under plausible alternative scenarios (±5–20%) and note how quickly margin of safety disappears.
Quick practical checklist for CVP follow‑up
– Define the analysis period and the relevant range for costs.
– Separate fixed and variable costs (use high‑low or regression if needed).
– Compute contribution margin (CM) per unit = Price − Variable cost per unit.
– Compute CM ratio = CM per unit ÷ Price (useful for sales‑dollar formulas).
– Find breakeven: units = Fixed costs ÷ CM per unit; sales dollars = Fixed costs ÷ CM ratio.
– Compute target‑profit sales: required sales dollars = (Fixed costs + Target profit) ÷ CM ratio.
– Compute margin of safety = Actual (or budgeted) sales − Breakeven sales; express as percent of actual sales.
– Perform sensitivity tests for changes in price, variable cost, fixed cost, and mix.
– For multi‑product firms, use weighted‑average CM or CM ratio based on expected sales mix.
Worked numeric example (single product)
Assumptions:
– Price = $20 per unit
– Variable cost = $12 per unit
– Fixed costs = $50,000
– Expected sales = 10,000 units
Step calculations:
1. CM per unit = 20 − 12 = $8.
2. CM ratio = 8 ÷ 20 = 0.40 (40%).
3. Breakeven units = 50,000 ÷ 8 = 6,250 units.
4. Breakeven sales dollars = 6,250 × 20 = $125,000 (or 50,000 ÷ 0.40).
5. Expected profit = CM per unit × Expected units − Fixed = 8×10,000 − 50,000 = $30,000.
6. Margin of safety (units) = 10,000 − 6,250 = 3,750 units; margin of safety % = 3,750 ÷ 10,000 = 37.5%.
Sensitivity example (price falls 5% to $19):
– New CM = 19 − 12 = $7.
– New breakeven units = 50,000 ÷ 7 ≈ 7,143 units.
– Profit at 10,000 units = 7×10,000 − 50,000 = $20,000.
Interpretation: a 5% price cut increases breakeven by ≈14.3% (from 6,250 to ~7,143), and cuts profit by $10,000.
Multi‑product note
– Calculate a weighted‑average CM per unit or CM ratio using expected sales mix.
– Use that weighted CM in the usual breakeven and target‑profit formulas.
Useful formulas (summary)
– CM per unit = Price − Variable cost per unit
– CM ratio = CM per unit ÷ Price (also called contribution margin percentage)
– Breakeven (units) = Total fixed costs ÷ CM per unit
– Breakeven (sales dollars) = Total fixed costs ÷ CM ratio
– Target‑profit (units) = (Total fixed costs + Target profit) ÷ CM per unit
– Target‑profit (sales dollars) = (Total fixed costs + Target profit) ÷ CM ratio
– Margin of safety (units) = Actual (or budgeted) sales units − Breakeven units
– Margin of safety (%) = (Actual sales − Breakeven sales) ÷ Actual sales
– Degree of operating leverage (DOL) = Contribution margin ÷ Operating income
– Using totals: DOL = (Sales − Variable costs) ÷ (Sales − Variable costs − Fixed costs)
– Approximate use: % change in operating income ≈ DOL × % change in sales
– Weighted‑average CM per unit (multi‑product) = Σ(CM_i × mix share_i)
– Weighted‑average CM ratio (multi‑product) = Σ(CM ratio_i × mix share_i)
– Breakeven (multi‑product sales dollars) = Total fixed costs ÷ Weighted‑average CM ratio
Worked numeric examples
1) Target profit (units) — single product
– Price = $25; Variable cost = $15; CM per unit = $10.
– Fixed costs = $80,000; Target profit = $40,000.
– Units = (80,000 + 40,000) ÷ 10 = 12,000 units.
2) Weighted average CM and breakeven — two products
– Product A: Price $30, Var cost $18 → CM_A = $12; expected mix 60% of units.
– Product B: Price $20, Var cost $12 → CM_B = $8; expected mix 40% of units.
– Weighted CM per unit = 12×0.6 + 8×0.4 = 7.2 + 3.2 = $10.4.
– If fixed costs = $52,000, breakeven units (total) = 52,000 ÷ 10.4 ≈ 5,000 total units.
– Allocate by mix: A = 5,000×0.6 = 3,000 units; B = 2,000 units.
3) Degree of operating leverage example
– Sales = $200,000; Variable costs = $120,000; Fixed costs = $50,000.
– Contribution margin = 200,000 − 120,000 = $80,000.
– Operating income = 80,000 − 50,000 = $30,000.
– DOL = 80,000 ÷ 30,000 ≈ 2.67.
– If sales rise 10%, estimated operating income change ≈ 2.67 × 10% = 26.7%.
Step‑by‑step CVP checklist (practical)
1. Classify costs — separate fixed vs. variable; verify cost drivers.
2. Choose relevant range — ensure assumptions about linearity hold at planned volumes.
3. Calculate unit CM and/or CM ratio.
4. Compute breakeven and/or target‑profit levels (units and dollars).
5. For multi‑product, compute weighted CM using expected sales mix.
6. Compute margin of safety and DOL to gauge risk and sensitivity.
7. Run sensitivity scenarios (price, volume, variable cost, fixed cost changes).
8. Document assumptions and update periodically as business conditions change.
Key assumptions and limitations (be explicit)
– Linearity: Prices and variable costs are assumed constant per unit within the relevant range.
– Fixed costs are assumed constant over the relevant range.
– Sales mix is assumed constant for multi‑product analysis.
– Uses contribution approach (variable costing logic) — inventory accounting method can change reported profit under absorption costing.
– CVP ignores timing, cash flows, taxes, and financing effects; treat it as short‑term decision support, not full valuation.
Quick practical tips
– Use CM ratio for decisions expressed in dollars (e.g., pricing changes, sales-dollar breakeven).
– Use unit CM for operations planning (production schedules, unit targets).
– Recompute CVP when major changes occur: new products, step fixed costs, bulk discounts.
– When uncertainty is high, present ranges (best/worst case) rather than single-point results.
Reputable references for further reading
– Investopedia — Cost‑Volume‑Profit (CVP) Analysis: https://www.investopedia.com/terms/c/cost-volume-profit-analysis.asp
– Corporate Finance Institute — Cost‑Volume‑Profit (CVP) Analysis: https://corporatefinanceinstitute.com/resources/knowledge/finance/cost-volume-profit-analysis/
– OpenStax — Principles of Managerial Accounting (Chapter on cost behavior and CVP): https://openstax.org/books/principles-managerial-accounting/pages/5-introduction
– AccountingCoach — Contribution Margin: https://www.accountingcoach.com/blog/contribution-margin
Educational disclaimer
This explanation is educational and not individualized investment or accounting advice. Check your own numbers, consult professional accountants or financial advisors for business decisions, and adapt formulas to your context.