Break-Even Analysis
A quantitative tool for determining the minimum output needed to cover costs — and for planning pricing, profit targets, and financial risk. Core to both Units 3 and 5.
- Calculate contribution per unit, total contribution, and break-even output
- Calculate margin of safety in units and as a percentage
- Calculate target profit output and explain the effect of changes in price or costs on break-even
- Evaluate the usefulness and limitations of break-even analysis as a decision-making tool
What is Break-Even Analysis?
Break-even analysis determines the level of output (or sales) at which total revenue equals total costs — where the business makes neither a profit nor a loss. It is a core tool for financial planning, pricing decisions, and assessing business viability.
Key Terms and Formulas
The Core Formulas
Contribution is the amount each unit contributes first to covering fixed costs, then once all fixed costs are covered, each additional unit's contribution becomes profit. Think of it as: the business must sell enough units that their total contribution pays off all the fixed costs — then everything after that is profit.
Worked Example — Water Bottle Company
A company produces reusable water bottles.
- Selling price: $25
- Variable cost per unit: $10
- Fixed costs: $6,000
Step 1 — Contribution per unit:
CPU = $25 − $10 = $15
Step 2 — Break-even output:
BEQ = $6,000 ÷ $15 = 400 units
Step 3 — Profit at 500 units:
Total Contribution = $15 × 500 = $7,500
Profit = $7,500 − $6,000 = $1,500 profit
Step 4 — Impact of $2 increase in variable cost:
New VC = $12 → New CPU = $25 − $12 = $13
New BEQ = $6,000 ÷ $13 = 461.5 → 462 units (always round up)
The higher variable cost increases the break-even point by 62 units — the business needs to sell more to cover its fixed costs.
Margin of Safety
The margin of safety shows how much actual sales exceed break-even. It measures risk — how far sales can fall before the business starts making a loss.
Worked Example — Clothing Company
- Fixed costs: $20,000 | VC per T-shirt: $8 | Price: $20 | Actual sales: 2,000 T-shirts
CPU = $20 − $8 = $12
BEQ = $20,000 ÷ $12 = 1,667 T-shirts (rounded up)
MoS = 2,000 − 1,667 = 333 T-shirts
MoS% = (333 ÷ 2,000) × 100 = 16.7%
Sales can fall by 333 units (16.7%) before the business hits break-even.
The margin of safety percentage can be expressed in two ways:
- As % of actual sales: (MoS ÷ Actual Sales) × 100 → how far sales can fall
- As % above BEQ: (MoS ÷ BEQ) × 100 → how much above the minimum you are
Both are valid — just be clear which you're using.
The Break-Even Chart
A break-even chart plots output on the x-axis and costs/revenue on the y-axis. Three lines are drawn:
- Fixed costs (FC): Horizontal line — same at every output level
- Total costs (TC): Starts at the FC line (y-intercept = FC), rises with output
- Total revenue (TR): Starts at the origin (zero revenue at zero output), rises with output
The break-even point (BEP) is where TR crosses TC. To the left = loss zone. To the right = profit zone. The vertical distance between TR and TC at any output shows the profit or loss.
The margin of safety is shown as the horizontal distance between actual/forecast output and the BEP on the x-axis.
When constructing a break-even chart:
- Label both axes with units (e.g. "Output (units)" and "Revenue/Cost ($)")
- Label all three lines: FC, TC, TR
- Mark and label the BEP clearly
- Mark the margin of safety if asked
- Use a ruler — messy charts lose marks
Impact of Changes in Price or Costs
Break-even is dynamic — changes to price or costs shift the chart and the BEP:
| Change | Effect on CPU | Effect on BEQ | Effect on Chart |
|---|---|---|---|
| Price increases | ↑ CPU | ↓ BEQ (easier to cover FC) | TR line steeper; BEP moves left |
| Price decreases | ↓ CPU | ↑ BEQ | TR line shallower; BEP moves right |
| VC per unit increases | ↓ CPU | ↑ BEQ | TC line steeper; BEP moves right |
| VC per unit decreases | ↑ CPU | ↓ BEQ | TC line shallower; BEP moves left |
| Fixed costs increase | No change to CPU | ↑ BEQ | FC and TC lines shift up; BEP moves right |
| Fixed costs decrease | No change to CPU | ↓ BEQ | FC and TC lines shift down; BEP moves left |
Limitations of Break-Even Analysis
| Limitation | Why it matters | How to address it |
|---|---|---|
| Assumes all output is sold | In reality, unsold stock is common — revenue may be lower than modelled | Use realistic sales forecasts; model different occupancy/sales scenarios |
| Assumes constant prices and costs | Variable costs and prices change — input costs fluctuate, discounts are offered | Perform sensitivity analysis — model high/low scenarios |
| Assumes a single product | Multi-product businesses have complex cost allocation | Use contribution analysis per product line |
| Static model | Fixed costs aren't truly fixed forever — they step up with capacity increases | Update the model as the business scales |
| Based on estimates | Forecasts may be inaccurate — especially for new businesses | Build in a safety margin; update forecasts regularly |
| Ignores qualitative factors | It doesn't capture brand, customer loyalty, or staff morale | Use alongside qualitative analysis |
Key Terms
- CPU = Price − Variable Cost per unit
- BEQ = Fixed Costs ÷ CPU
- Profit = Total Contribution − Fixed Costs
- Margin of Safety = Actual Sales − BEQ
- Target profit output = (FC + Target Profit) ÷ CPU
- A break-even chart plots FC, TC, TR — BEP is where TR = TC
- Increasing price or reducing VC lowers BEQ; increasing FC raises BEQ
- Limitations: static model, assumes all output sold, based on estimates
(a) Calculate the contribution per latte.
(b) Calculate the break-even number of lattes per month.
(c) If the shop sells 2,000 lattes, calculate the total profit or loss.
(d) Calculate the margin of safety in units and as a percentage.
(e) Analyse how a 10% increase in fixed costs would affect the break-even point. [10 marks]
Show answer
(a) CPU = $5 − $2 = $3
(b) BEQ = $4,500 ÷ $3 = 1,500 lattes
(c) Total Contribution = $3 × 2,000 = $6,000
Profit = $6,000 − $4,500 = $1,500 profit
(d) MoS = 2,000 − 1,500 = 500 lattes
MoS% = (500 ÷ 2,000) × 100 = 25%
(e) New FC = $4,500 × 1.10 = $4,950
New BEQ = $4,950 ÷ $3 = 1,650 lattes (up from 1,500 — 150 more lattes needed)
Common mistake: Using total revenue or total cost instead of contribution per unit in the BEQ formula. BEQ = Fixed Costs ÷ CPU. Students sometimes divide fixed costs by price alone (forgetting to subtract variable cost) or divide by total variable cost instead of the per-unit figure.
(a) Calculate BEQ, MoS (units), and MoS%.
(b) Calculate the monthly profit.
(c) How many memberships must the gym sell to achieve a target profit of $9,000? [8 marks]
Show answer
(a) CPU = $75 − $30 = $45
BEQ = $15,000 ÷ $45 = 333.3 → 334 memberships
MoS = 400 − 334 = 66 memberships
MoS% = (66 ÷ 400) × 100 = 16.5%
(b) Total Contribution = $45 × 400 = $18,000
Profit = $18,000 − $15,000 = $3,000
(c) Target output = ($15,000 + $9,000) ÷ $45 = $24,000 ÷ $45 = 533.3 → 534 memberships
Common mistake: Forgetting to add target profit to fixed costs in the target output formula. The formula is (FC + target profit) ÷ CPU — not FC ÷ CPU. Also: always round non-integer break-even figures up (you can't sell 0.3 of a membership), and use the rounded figure when calculating margin of safety.
Mia owns Energise Fitness Studio. She runs group fitness classes (yoga, pilates, HIIT) with 20 people per session. All classes are fully booked.
Current data: Rent: $2,000/month | Cleaning: $1,000/month | Wages per class: $70 | Maintenance per class: $10 | Price per person: $10 | Classes per month: 40
(a) Calculate the price per class, variable cost per class, and contribution per class.
(b) Calculate total fixed costs per month.
(c) Calculate the break-even number of classes.
(d) Calculate the margin of safety in classes and as a percentage.
(e) Calculate monthly profit at 40 fully booked classes.
Expansion: Mia expands, increasing rent by $3,000/month, cleaning by $500/month, and maintenance per class by $5.
(f) Calculate the new total fixed costs and the new break-even point.
(g) If Mia still runs 40 fully booked classes, does she still break even?
(h) She plans to increase to 60 classes. Calculate the new margin of safety (units and %).
(i) How many classes must she run and fill to achieve a target profit of $6,000/month? [16 marks]
Show answer
Current situation:
(a) Price per class = 20 × $10 = $200
VC per class = $70 + $10 = $80
CPU = $200 − $80 = $120
(b) FC = $2,000 + $1,000 = $3,000/month
(c) BEQ = $3,000 ÷ $120 = 25 classes
(d) MoS = 40 − 25 = 15 classes
MoS% = (15 ÷ 40) × 100 = 37.5%
(e) Total Contribution = $120 × 40 = $4,800
Profit = $4,800 − $3,000 = $1,800
After expansion:
(f) New FC = $3,000 + $3,000 + $500 = $6,500
New VC per class = $80 + $5 = $85 → New CPU = $200 − $85 = $115
New BEQ = $6,500 ÷ $115 = 56.5 → 57 classes
(g) At 40 classes: Total Contribution = $115 × 40 = $4,600. This is less than FC of $6,500 → loss of $1,900. She does NOT break even.
(h) At 60 classes: MoS = 60 − 57 = 3 classes
MoS% = (3 ÷ 60) × 100 = 5% — very thin margin.
(i) Target output = ($6,500 + $6,000) ÷ $115 = $12,500 ÷ $115 = 108.7 → 109 classes
Common mistake: Using the original (pre-expansion) CPU and FC after the scenario changes. When fixed costs or variable costs change, you must recalculate CPU and BEQ from scratch — don't carry over numbers from part (a)–(e) into the expansion scenario.
Show answer
For: Break-even analysis gives a new business a clear minimum sales target before any revenue is earned. It helps the owner assess whether the business idea is financially viable, set pricing, and plan how much finance is needed to cover losses until break-even is reached. Banks often require it as part of a business plan.
Against: For a new business, all the inputs (price, variable costs, fixed costs, demand) are estimates, not known quantities. The model assumes all output is sold at a constant price, which is unlikely. Demand may be far below or above forecast, making the analysis unreliable. It also ignores qualitative factors (brand, location, competition) that matter hugely for new businesses.
Conclusion: Break-even is a useful starting framework for a new business but should be treated as a rough guide, not a precise plan. Sensitivity analysis (running the model with optimistic and pessimistic assumptions) increases its value. Award marks for balanced evaluation with reference to the specific context of a new business.
Common mistake: Evaluating break-even analysis in general rather than specifically for a new business. The question asks about new businesses — so the answer must highlight that inputs (costs, price, demand) are all estimates with no historical data, making the model particularly unreliable in this specific context.