Key Idea: At HL, Topic 5.5 is about using break-even analysis accurately and then interpreting what the result means for risk, pricing and planning. Strong HL answers show disciplined method, clear chart technique and balanced evaluation of the limitations.
🔢 Key formulas: **Break-even output —** fixed costs ÷ contribution per unit. **Margin of safety —** actual sales minus break-even output. **Profit —** total contribution minus fixed costs. **Target output —** (fixed costs + target profit) ÷ contribution per unit.
📊 Key chart rules: **TR line —** starts at the origin. **TC line —** starts at the fixed cost level. **BEP —** where TR and TC cross. **Profit zone —** where TR is above TC.
[Diagram: break-even-chart]
✅ Strengths: **Useful because —** simple, visual, helps planning, shows effect of price or cost changes. **Good for start-ups and short-term planning**.
⚠️ Limits: **Limitations —** assumes all output is sold. **Limitations —** assumes prices and costs stay constant. **Limitations —** often assumes one product only. **Limitations —** ignores wider strategic and market factors.
HL exam tip: Always show every step of your working. Markschemes repeatedly reward correct method even when the final answer is wrong.
Chart tip: A fully labelled break-even chart must show the axes, the total revenue line, the total cost line and the break-even point clearly. If the question says to draw to scale, that matters.
Past-paper tip: Examiners often reward comments like fixed costs remain constant, margin of safety is forecast sales minus break-even output, and break-even quantity falls when selling price rises because contribution per unit increases.
Example: A strong answer: If variable costs rise, contribution per unit falls, so the business must sell more units to break even. This increases risk because the margin of safety is likely to shrink unless sales also increase.
Important: Common triggers: calculate break-even output, margin of safety, profit, target output or target price, draw or interpret a break-even chart, explain the effect of cost or price changes, or evaluate the usefulness of break-even analysis.
- Identify whether it is a formula, chart or interpretation question
- Write the correct formula first
- Substitute numbers carefully
- Show full working
- Explain what the result means for the business
- For HL, add one limitation or judgement if the question is analytical or evaluative