Definition
The breakeven point is the sales level at which total revenue equals total costs. At that point a business (or a specific product line) has zero profit and zero loss. It is a threshold used to judge minimum sales needed to avoid an operating loss.
Key formulas (assumptions: one product or product mix with constant unit price and constant variable cost per unit)
– Break-even units = Fixed costs ÷ (Price per unit − Variable cost per unit)
– “Fixed costs” are expenses that do not change with output (rent, salaried payroll, insurance).
– “Variable cost per unit” changes with output (materials, direct labor per unit).
– The denominator is the unit contribution margin (what each unit contributes to covering fixed costs).
– Break-even sales dollars = Fixed costs ÷ Contribution margin ratio
– Contribution margin ratio = (Price − Variable cost) ÷ Price
– Or multiply break-even units × Price to get break-even sales dollars.
Why it matters (applications)
– Business planning: sets a minimum sales target for viability and helps with pricing and cost-control decisions.
– Budgeting and forecasting: shows sensitivity to price, cost, or volume changes.
– Investment/trading contexts: an analogous breakeven concept exists for securities and options (e.g., for a long call, breakeven = strike price + premium paid).
– Decision making: used to evaluate whether a new product, project, or promotional discount can reach a viable sales level.
Step-by-step checklist for a basic breakeven calculation
1. Identify fixed costs for the period (month, quarter, year).
2. Determine selling price per unit.
3. Calculate variable cost per unit.
4. Compute unit contribution margin = Price − Variable cost.
5. Apply break-even units formula: Fixed ÷ Contribution margin.
6. Optionally compute break-even sales dollars = Break-even units × Price, or Fixed ÷ Contribution margin ratio.
7. Review assumptions: linear costs, constant price, no inventory buildup, single product or constant product mix.
Worked numeric example — bakery
Given:
– Fixed costs = $50,000 per month
– Variable cost per cake = $10
– Selling price per cake = $50
Steps:
1. Unit contribution margin = 50 − 10 = $40 per cake.
2. Break-even units = 50,000 ÷ 40 = 1,250 cakes.
3. Break-even sales dollars = 1,250 × 50 = $62,500.
Interpretation: the bakery must sell 1,250 cakes each month (or generate $62,500 in cake sales) to cover all fixed and variable costs. Sales above that level produce operating profit; sales below produce operating loss.
Small example from trading — long call option
– Strike price = $300
– Premium paid = $50
Breakeven stock price at expiration = Strike + Premium = $350.
If the stock is above $350 at expiration, the option holder begins to profit (ignoring commissions and slippage).
Benefits of breakeven analysis
– Simple and quick way to see minimum performance needed to avoid losses.
– Helps compare scenarios: price changes, cost reductions, or promotions.
– Useful for planning financing needs until breakeven is reached.
Limitations and common pitfalls
– Assumes costs are strictly fixed or strictly variable and that they behave linearly; many costs are only partly fixed or change stepwise with volume.
– Ass
sumes a linear relationship between cost and output; many costs change in steps (e.g., hiring, renting additional space) or behave partly fixed/partly variable. Other limitations include:
– Ignores time and cash-flow timing. Breakeven counts unit sales or revenue but does not discount future cash flows; funding needs before breakeven can differ from the simple breakeven estimate.
– Assumes selling price and variable cost per unit are constant; in reality price discounts, economies of scale, or volume-based supplier pricing change these.
– Assumes a single product or a fixed sales mix; multiple products require a weighted approach and that mix must remain stable.
– Omits capacity limits and operational constraints that can prevent reaching the mathematically computed breakeven point.
– Does not account for taxes, financing costs, or non-cash charges (depreciation) unless these are explicitly included in fixed costs.
Practical formulas (definitions first)
– Fixed costs: costs that do not change with output in the relevant range (e.g., rent, salaried wages).
– Variable cost per unit: cost that rises with each unit produced (e.g., materials).
– Contribution margin per unit: Price − Variable cost per unit. This is the amount each unit contributes toward covering fixed costs and then profit.
– Contribution margin ratio (CM ratio): Contribution margin per unit / Price. This is contribution expressed as a share of sales.
Core formulas
– Break-even units = Fixed costs / Contribution margin per unit.
– Break-even sales ($) = Fixed costs / CM ratio.
– Required units for target profit = (Fixed costs + Target profit) / Contribution margin per unit.
– For multiple products: use Weighted Average Contribution Margin (WACM) per “sales mix unit.”
Worked numeric examples
1) Simple product example (units)
Assume fixed costs = $50,000; price = $20; variable cost = $12.
– Contribution margin = 20 − 12 = $8 per unit.
– Break-even units = 50,000 / 8 = 6,250 units.
2) Break-even in dollars (same numbers)
– CM ratio = 8 / 20 = 0.40 (40%).
– Break-even sales = 50,000 / 0.40 = $125,000 (which equals 6,250 units × $20).
3) Target profit example
Target profit = $10,000.
– Required units = (50,000 + 10,000) / 8 =
7,500 units.
– In dollars: 7,500 units × $20 = $150,000 in sales required to earn the $10,000 target profit.
Multiple-products (weighted average contribution margin) — worked example
– Setup: two products sold in a constant sales mix.
– Product A: price = $50; variable cost = $30 → contribution margin (CM)A = $20.
– Product B: price = $80; variable cost = $60 → CM B = $20.
– Sales mix: 3 units of A for every 2 units of B (i.e., 3:2).
– Fixed costs = $100,000.
– Step 1 — compute WACM (weighted average contribution margin) per “sales-mix unit”:
– Total CM per mix = (3 × 20) + (2 × 20) = 60 + 40 = 100.
– Units in one mix = 3 + 2 = 5.
– WACM per mix unit = 100 / 5 = $20.
– Step 2 — break-even in mix units:
– Break-even mix units = Fixed costs / WACM = 100,000 / 20 = 5,000 mixes.
– Step 3 — convert to product units:
– Product A required = 3 × 5,000 = 15,000 units.
– Product B required = 2 × 5,000 = 10,000 units.
– In dollars (optional): total break-even sales = (15,000 × $50) + (10,000 × $80) = $750,000 + $800,000 = $1,550,000.
Margin of safety (MOS) — quick definition and example
– Definition: MOS = Actual (or budgeted) sales − Break-even sales. It measures how far sales can fall before the firm incurs a loss.
– Example (using the earlier single-product break-even of $125,000):
– If actual sales = $200,000, MOS = $200,000 − $125,000 = $75,000.
– MOS percentage = MOS / Actual sales = $75,000 / $200,000 = 37.5%.
How to draw a simple break-even chart (step-by-step)
1. X-axis: units sold (or sales dollars). Y-axis: dollars (costs and revenue).
2. Plot fixed cost as a horizontal line.
3. Plot total cost line starting at the fixed-cost intercept with slope = variable cost per unit.
4. Plot total revenue line from the origin with slope = price per unit.
5. Intersection of total revenue and total cost = break-even point.
6. Optional: mark MOS and target-profit revenue (fixed cost + target profit) / CM ratio.
Common assumptions and limitations (checklist)
– Prices and variable cost per unit are constant over the relevant range.
– Fixed costs remain fixed over the relevant range (no step-fixed costs).
– All units produced are sold (no inventory carrying or spoilage effects).
– Sales mix is constant (for multi-product WACM calculations).
– Short-term, linear approximation — real businesses may have non-linear behavior, volume discounts, or capacity constraints.
– Checklist: validate each assumption for your case; if an assumption fails, consider sensitivity analysis or a more detailed model.
Excel/Google Sheets formulas (cell examples)
– Let Fixed = cell B1, Price = B2, VarCost = B3.
– CM per unit = =B2 – B3
– Break-even units = =B1 / (B2 – B3)
– Break-even dollars = =B1 / ((B2 – B3) / B2)
– Required units for target profit (Target in B4) = =(B1 + B4) / (B2 – B3)
– For WACM with two products (mix counts in C2 and C3):
– WACM = =((C2*(B2-B3)) + (C3*(D2-D3))) / (C2 + C3)
Summary of key formulas
– Contribution margin per unit = Price − Variable cost per unit.
– Contribution margin ratio = (Price − Variable cost) / Price.
– Break-even units = Fixed costs / Contribution margin per unit.
– Break-even sales (dollars) = Fixed costs / Contribution margin ratio.
– Required units for target profit = (Fixed costs + Target profit) / Contribution margin per unit.
– WACM per mix unit = (Sum of (CM_i × mix_i)) / (Sum of mix_i).
– Margin of safety = Actual sales − Break-even sales.
Practical tips
– Use scenario testing: change price, variable cost, or fixed cost to see effects on break-even.
– Monitor CM ratio closely; small changes materially affect break-even.
– For multi-product firms,
For multi-product firms, allocate fixed costs and compute a weighted-average contribution measure using your expected sales mix. Work in “mix bundles” (one bundle = the set of products in the sales mix) to keep units and revenue consistent.
Step-by-step example (two products)
– Assumptions:
– Fixed costs = $120,000 per period.
– Product A: price = $50, variable cost = $30 → contribution per unit = $20.
– Product B: price = $80, variable cost = $50 → contribution per unit = $30.
– Expected sales mix = 3 units A : 2 units B (bundle size = 5 units).
– Calculate bundle totals:
– Contribution per bundle
– Contribution per bundle = (3 × $20) + (2 × $30) = $60 + $60 = $120.
– Price (revenue) per bundle = (3 × $50) + (2 × $80) = $150 + $160 = $310.
– Variable cost per bundle = (3 × $30) + (2 × $50) = $90 + $100 = $190.
– Contribution margin ratio for the bundle = contribution per bundle / revenue per bundle = $120 / $310 ≈ 0.3871 (38.71%).
Step 4 — Compute break-even in bundles and convert to units
– Break-even bundles = Fixed costs / Contribution per bundle = $120,000 / $120 = 1,000 bundles.
– Break-even units of Product A = 3 × 1,000 = 3,000 units.
– Break-even units of Product B = 2 × 1,000 = 2,000 units.
– Break-even revenue = Revenue per bundle × 1,000 = $310 × 1,000 = $310,000.
(Alternate revenue check: Fixed costs / bundle CM ratio = $120,000 / 0.3871 ≈ $310,000 — same result.)
Interpretation
– You must sell the bundle mix (3 A : 2 B) 1,000 times — equivalently 3,000 of A and 2,000 of B — to cover $120,000 of fixed costs.
– If actual sales deviate from the planned mix, the weighted-average contribution will change and the break-even point will shift.
Quick checklist for multi-product break-even analysis
1. Confirm period and that fixed costs are relevant to that period.
2. Choose the expected sales mix (express as units per bundle or percentage of total units).
3. Compute contribution per unit for each product (price − variable cost).
4. Sum contributions and revenues across the bundle to get contribution per bundle and revenue per bundle.
5. Break-even bundles = fixed costs / contribution per bundle. Convert bundles to units and revenue as needed.
6. Test sensitivity: re-run with alternate mixes, prices, or costs.
Worked sensitivity example (small change)
– If Product B’s variable cost rises from $50 to $55, B contribution falls to $25.
– New contribution per bundle = (3 × $20) + (2 × $25) = $60 + $50 = $110.
– New break-even bundles = $120,000 / $110 ≈ 1,090.9 → 1,091 bundles (round up for whole bundles).
– New break-even revenue ≈ 1,091 × $310 = $338,210.
This shows small cost changes can materially increase required sales.
Key assumptions and limitations
– Prices, variable costs, and sales mix are constant over the period.
– Fixed costs are truly fixed for the analysis period.
– Contribution per unit is constant (no quantity discounts, step-fixed costs, or capacity constraints).
– This is an accounting break-even (covering costs), not a profitability target (no required profit margin included). For target profit, add desired profit to fixed costs before division.
Further reading (introductory and reference)
– Investopedia — Break-Even Point: https://www.investopedia.com/terms/b/breakevenpoint.asp
– Corporate Finance Institute (CFI) — Break-Even Analysis: https://corporatefinanceinstitute.com/resources/knowledge/finance/break-even-analysis/
– AccountingCoach — Contribution Margin and Break-Even Analysis: https://www.accountingcoach.com/blog/contribution-margin
Educational disclaimer
This is educational information, not individualized investment or business advice. Use your own data and, when appropriate, consult an accountant or financial professional before making decisions.