Difficulty: Intermediate | Prerequisites: Basic cost classification (fixed vs. variable costs), contribution margin concept
Break-even analysis sits at the intersection of cost accounting and managerial decision-making. It answers a deceptively simple question: how much must a firm sell before it stops losing money? This is one of the first tools managers reach for when planning production volumes, setting prices, or evaluating whether a new product line is viable. You should already be comfortable classifying costs as fixed or variable, and understand what a contribution margin is, before working through this material.
Break-even analysis tells you the minimum sales revenue (or quantity) a firm needs to cover all its costs, earning zero profit and zero loss. You calculate it by dividing total fixed costs by the contribution margin ratio (for revenue) or by the per-unit contribution margin (for quantity). A firm's cost structure, whether it leans towards fixed or variable costs, shapes where the break-even point falls and what pricing strategy makes sense.
Break-even point (BEP)
The level of sales at which total revenue exactly equals total costs, producing neither profit nor loss. Think of it as the line where the business goes from bleeding money to starting to earn.
Fixed costs
Costs that remain constant regardless of production volume: rent, salaried staff, insurance, depreciation. In simple terms, these are the bills you pay even if you sell nothing.
Variable costs
Costs that rise or fall in direct proportion to the number of units produced or sold: raw materials, per-unit labour, sales commissions. The more you make, the more you spend.
Contribution margin (contribution profit)
Sales revenue minus total variable costs. This is the portion of each sale that goes towards covering fixed costs and, once those are covered, becomes profit. In simple terms, it is what each unit "contributes" to paying the overhead.
Contribution margin ratio (CM ratio)
Contribution margin expressed as a percentage of sales revenue. If the CM ratio is 75%, then 75 pence of every pound of revenue goes towards fixed costs and profit.
Variable cost ratio
Total variable costs divided by total sales revenue. The complement of the CM ratio (Variable cost ratio + CM ratio = 100%).
Net profit
Contribution margin minus total fixed costs. What remains after every cost, fixed and variable, has been paid.
Cost structure
The relative proportion of fixed costs to variable costs in a business. A "high fixed cost" structure (hotels, cinemas) behaves very differently from a "high variable cost" structure (retail, raw material trading) at the break-even point.
The contribution margin income statement
Before computing break-even, you need a contribution margin income statement. This rearranges costs by behaviour (variable vs. fixed) rather than by function. Using the PT Eliona example:
Sales revenue: IDR 172,000,000 (1,000 kg at IDR 172,000 per kg)
Total variable costs: IDR 43,000,000 (25% of revenue)
Variable manufacturing: IDR 25,000,000
Variable marketing: IDR 8,000,000
Variable admin and general: IDR 10,000,000
Contribution margin: IDR 129,000,000 (75% of revenue)
Total fixed costs: IDR 77,400,000
Fixed factory overhead: IDR 37,400,000
Fixed marketing: IDR 15,000,000
Fixed admin and general: IDR 25,000,000
Net profit: IDR 51,600,000
Computing break-even revenue
The formula divides total fixed costs by the contribution margin ratio:
BEP (revenue) = Fixed Costs / (1 - Variable Cost Ratio)
Or equivalently: BEP (revenue) = Fixed Costs / CM Ratio
For PT Eliona:
Variable cost ratio = IDR 43,000,000 / IDR 172,000,000 = 0.25 (25%)
CM ratio = 1 - 0.25 = 0.75 (75%)
BEP = IDR 77,400,000 / 0.75 = IDR 103,200,000
This means PT Eliona must generate at least IDR 103,200,000 in sales before it stops making a loss.
When you need units, not revenue
Management often wants to know the minimum number of units to sell, not just the revenue target. The formula swaps the CM ratio for the per-unit contribution margin:
BEP (units) = Fixed Costs / (Selling Price per Unit - Variable Cost per Unit)
For PT Eliona:
Selling price per kg: IDR 172,000
Variable cost per kg: IDR 43,000,000 / 1,000 kg = IDR 43,000
Contribution margin per kg: IDR 172,000 - IDR 43,000 = IDR 129,000
BEP = IDR 77,400,000 / IDR 129,000 = 600 kg
What happens after break-even
Once PT Eliona sells 600 kg, every additional kilogram sold earns a profit of IDR 129,000 (the full contribution margin per unit). All fixed costs have already been absorbed by the first 600 kg. This is why the profit line on a break-even chart rises steeply once you pass the BEP.
Reading a break-even chart
A break-even chart plots total revenue and total costs against sales volume. The point where the two lines cross is the BEP. Below that point the firm is in a loss zone; above it, in a profit zone.
The total cost line starts at the level of fixed costs (its y-intercept) and rises with a slope equal to the variable cost per unit.
The total revenue line starts at zero and rises with a slope equal to the selling price per unit.
The vertical distance between the two lines at any volume equals the profit (or loss) at that volume.
How cost structure shifts the break-even point
High fixed costs, low variable costs (hotels, cinemas, telecoms): The break-even point occurs at a high sales volume. The total cost line is steep at the start (high y-intercept) but climbs slowly. Once past break-even, profits accumulate quickly because each additional sale has a large contribution margin.
High variable costs, low fixed costs (retailers, commodity traders): The break-even point occurs at a lower sales volume. The cost line starts low but climbs steeply. Profits grow more slowly beyond break-even because each unit carries a smaller contribution margin.
Pricing strategy for high-fixed-cost businesses
Businesses with heavy fixed costs focus on maximising revenue. Hotels, for example, offer discounted rates during off-peak periods. Even a reduced rate is profitable as long as it exceeds the variable cost per room night, because it generates positive contribution margin that chips away at the fixed cost base.
\text{BEP (revenue)} = \frac{\text{Total Fixed Costs}}{1 - \frac{\text{Total Variable Costs}}{\text{Total Sales Revenue}}}\text{BEP (units)} = \frac{\text{Total Fixed Costs}}{\text{Selling Price per Unit} - \text{Variable Cost per Unit}}\text{CM Ratio} = \frac{\text{Sales Revenue} - \text{Total Variable Costs}}{\text{Sales Revenue}} = 1 - \text{Variable Cost Ratio}\text{Net Profit} = \text{Contribution Margin} - \text{Total Fixed Costs}Note: the revenue BEP formula and the unit BEP formula are algebraically equivalent. If you multiply the unit BEP by the selling price per unit, you get the revenue BEP.
Hotels and cinemas are textbook high-fixed-cost businesses. Their buildings, staff, and equipment cost the same whether occupancy is 10% or 90%. This is why hotels slash room rates during quiet periods and cinemas run cheap Tuesday screenings: any revenue above the tiny variable cost per guest (cleaning, utilities) generates contribution margin that offsets the enormous fixed base.
Manufacturing firms use break-even analysis when deciding whether to accept a special order at a lower-than-usual price. If the price exceeds variable cost per unit and the firm has spare capacity, the order contributes to fixed costs even at a discount.
Students often think break-even means the company is doing well. It does not. Break-even is the bare minimum: zero profit, zero loss. It is a floor, not a target.
Students sometimes confuse the contribution margin with net profit. Contribution margin is revenue minus variable costs only. Net profit subtracts fixed costs as well. The contribution margin is always larger than net profit (unless fixed costs are zero, which is unrealistic).
A common error is dividing fixed costs by the selling price to get the break-even quantity. You must divide by the contribution margin per unit (selling price minus variable cost per unit), not by the selling price alone.
Students occasionally assume that once a company passes break-even, every pound of additional revenue is pure profit. It is not. Each additional unit still carries its variable cost. The profit per additional unit equals the contribution margin per unit, not the selling price.
⚠️ You will almost certainly be asked to compute BEP in both revenue and units from a contribution margin income statement. Practise both formulas until they are automatic.
⚠️ Expect a question on how cost structure (high fixed vs. high variable) affects the break-even point and the firm's risk profile.
⚠️ Be prepared to explain why a high-fixed-cost firm might rationally discount its prices during slow periods, and connect this to the contribution margin concept.
⚠️ Know how to read a break-even chart: identify the loss zone, profit zone, BEP, fixed cost intercept, and the slopes of the revenue and cost lines.
True or false: A firm at its break-even point is making a small profit.
False. Break-even means exactly zero profit, zero loss.
Fill in the blank: BEP in revenue = Total Fixed Costs / ______.
Contribution Margin Ratio (or equivalently, 1 minus the variable cost ratio).
True or false: If a hotel's variable cost per room night is IDR 20,000 and it offers a rate of IDR 50,000 during off-peak, that discounted rate is unprofitable.
False. The rate exceeds the variable cost, so it generates IDR 30,000 of contribution margin per room night.
Fill in the blank: Once a firm passes break-even, the profit on each additional unit equals the ______ per unit.
Contribution margin.
True or false: A firm with very high fixed costs will break even at a lower sales volume than a firm with low fixed costs, all else equal.
False. Higher fixed costs push the break-even point to a higher sales volume, not a lower one.
Q: A company has fixed costs of IDR 50,000,000, a selling price of IDR 100,000 per unit, and variable costs of IDR 40,000 per unit. What is its break-even point in units?
A: BEP = IDR 50,000,000 / (IDR 100,000 - IDR 40,000) = IDR 50,000,000 / IDR 60,000 = 833.33 units. The firm must sell at least 834 units to avoid a loss (you round up because you cannot sell a fraction of a unit).
Q: Using the same company, what is the break-even revenue?
A: CM ratio = IDR 60,000 / IDR 100,000 = 0.60 (60%). BEP revenue = IDR 50,000,000 / 0.60 = IDR 83,333,333. Alternatively, 833.33 units x IDR 100,000 = IDR 83,333,333.
Q: PT Eliona's break-even quantity is 600 kg. If PT Eliona sells 800 kg in fiscal year 20X1, what is its net profit?
A: The first 600 kg cover all fixed costs. The remaining 200 kg each contribute IDR 129,000 (the CM per kg). Net profit = 200 x IDR 129,000 = IDR 25,800,000.
Q: Why would a hotel offer rooms at a steep discount during off-peak season rather than keeping them empty?
A: The hotel's costs are overwhelmingly fixed (building, staff, maintenance). The variable cost per occupied room is minimal. Any rate above that variable cost generates a positive contribution margin, which reduces the net loss from the fixed cost base. An empty room earns nothing and still costs the same in fixed overheads.
Q: Company A has a cost structure of 80% fixed / 20% variable. Company B has 20% fixed / 80% variable. Both have the same total costs and revenue. Which breaks even at a higher volume, and which earns profit faster after break-even?
A: Company A breaks even at a higher volume because its large fixed costs require more sales to cover. However, once past break-even, Company A's profits grow faster because its high CM ratio (80%) means most of each additional sale is profit. Company B breaks even sooner but accumulates profit more slowly.
Break-even analysis connects directly to cost-volume-profit (CVP) analysis, which extends the same framework to answer "what-if" questions: what profit results from a given volume, or what volume is needed for a target profit. If your course covers CVP later, this material is its foundation.
The contribution margin concept reappears in relevant costing and special order decisions. When a firm decides whether to accept a one-off order at a reduced price, or whether to make or buy a component, the contribution margin per unit is the key figure.
Cost structure links to operating leverage, a topic in both managerial accounting and corporate finance. A firm with high fixed costs has high operating leverage: small changes in revenue produce large swings in profit. This is the same dynamic that makes the break-even chart steeper for high-fixed-cost firms.
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