interpret a break-even chart

4.4.3 Break‑even analysis

What is a break‑even chart? 📈

A break‑even chart is a visual tool that shows the relationship between sales volume, revenue, costs and profit. Think of it as a map that tells you where your business stops losing money and starts making a profit. The chart usually has two lines: Revenue (upward slope) and Total Costs (starting high, then rising). The point where the two lines cross is the break‑even point.

Key components of the chart

  • Units sold (Q) – the horizontal axis.
  • Revenue (R) – calculated as $R = P \times Q$, where $P$ is the selling price.
  • Variable cost per unit (VC) – costs that change with each unit sold.
  • Fixed cost (FC) – costs that stay the same regardless of sales.
  • Total cost (TC) – $TC = FC + (VC \times Q)$.
  • Profit/Loss – the vertical difference between Revenue and Total Cost.

How to read the chart

  1. Locate the break‑even point (BE) where the Revenue line meets the Total Cost line.
  2. Read the units sold at that intersection – that’s the minimum sales needed to avoid loss.
  3. Anything to the right of BE means profit; to the left means loss.
  4. Check the slope of the Revenue line – it shows how much revenue increases per extra unit sold.
  5. Check the slope of the Total Cost line – it shows how much cost increases per extra unit sold.

Example: Toy Store 🧸

Suppose a toy store sells a toy for $25. The variable cost per toy is $10 and fixed costs (rent, salaries) are $5,000 per month. Let’s see how the break‑even chart looks.

Units Sold (Q) Revenue ($) Total Cost ($) Profit / Loss ($)
0 0 5,000 -5,000
100 2,500 6,000 -3,500
200 5,000 7,000 -2,000
300 7,500 8,000 -500
350 8,750 8,500 +250

The break‑even point is between 300 and 350 units. Using the formula: $$BE = \frac{FC}{P - VC} = \frac{5,000}{25 - 10} = \frac{5,000}{15} \approx 333 \text{ units}.$$ So the store needs to sell about 333 toys to break even. Selling more than that brings profit.

Exam Tips 💡

Remember:

  • Identify fixed costs and variable costs from the question.
  • Use the break‑even formula: $BE = \frac{FC}{P - VC}$.
  • Show the calculation step‑by‑step and state the final answer in units or money.
  • If a chart is given, read the intersection point directly and explain what it means.
  • Check for any rounding instructions – round to the nearest whole unit if required.

Revision

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