A break-even chart plots revenue and costs against output. The point where the revenue line meets the total cost line is the break-even point, where the firm makes neither profit nor loss. You may be asked to read values from a chart, to identify the lines, or to explain what the gaps mean.
This lesson builds on calculating contribution in costs, revenue and break-even. A chart is the same calculation drawn as lines.
What does each line on the chart mean?
Output (units) goes on the horizontal axis. Ringgit of cost and revenue go on the vertical axis. There are normally three or four lines:
- Fixed costs: a horizontal line, because the amount does not change with output.
- Variable costs: a line from the origin that rises steadily, because each unit adds the same cost.
- Total costs: starts at the fixed cost level on the vertical axis and rises in parallel with the variable cost line.
- Revenue: a line from the origin that rises more steeply than variable costs, because the price is higher than the variable cost per unit.
At any output, the vertical gap between revenue and total cost is the profit if revenue is higher, or the loss if total cost is higher. The horizontal distance between planned output and break-even output is the margin of safety, which the next lesson explains.
Worked example
Kedai Kopi Aman in Taiping sells coffee at RM10 a cup. Variable cost is RM4 a cup and fixed costs are RM6,000 a month. Rebuild the lines from this table.
| Cups sold | Revenue (RM) | Fixed cost (RM) | Variable cost (RM) | Total cost (RM) | Profit or loss (RM) |
|---|---|---|---|---|---|
| 0 | 0 | 6,000 | 0 | 6,000 | −6,000 |
| 500 | 5,000 | 6,000 | 2,000 | 8,000 | −3,000 |
| 1,000 | 10,000 | 6,000 | 4,000 | 10,000 | 0 |
| 1,500 | 15,000 | 6,000 | 6,000 | 12,000 | 3,000 |
| 2,000 | 20,000 | 6,000 | 8,000 | 14,000 | 6,000 |
Step 1, find the crossing. Revenue equals total cost at 1,000 cups, so the break-even output is 1,000 cups. The formula agrees: contribution is 10 − 4 = RM6, and 6,000 ÷ 6 = 1,000.
Step 2, read break-even revenue. On the vertical axis the crossing is at RM10,000.
Step 3, read a profit. At 1,800 cups, revenue is 18,000 and total cost is 6,000 + 7,200 = 13,200, so profit is RM4,800. Check: 1,800 × 6 = 10,800, and 10,800 − 6,000 = 4,800.
Step 4, read a loss. At 800 cups, total contribution is 800 × 6 = 4,800, so the loss is 6,000 − 4,800 = RM1,200.
Step 5, describe the zones. Output below 1,000 cups falls in the loss area, where total cost is above revenue. Output above 1,000 cups falls in the profit area.
The mistake to watch for
A common slip is to draw or read the total cost line as if it starts at the origin.
Mistaken reading: The total cost line starts at zero, so the firm has no costs when it makes nothing.
This would put the break-even point at output 0 and make every sale profitable.
A firm with no output still pays rent and salaries. The total cost line must start at the fixed cost level, RM6,000 here.
The related slip is reading RM10,000 as a number of cups, when it is a ringgit value read from the vertical axis. Always check which axis your reading comes from, and write the unit with the answer.
Check yourself
Use the Kedai Kopi Aman figures above.
1. Calculate the profit if 1,800 cups are sold, and read it as a gap on the chart.
Show answer
Revenue = 1,800 × 10 = RM18,000. Total cost = 6,000 + 1,800 × 4 = RM13,200. Profit = RM4,800. On the chart this is the vertical gap between the revenue line and the total cost line at 1,800 cups.
2. A student draws the total cost line starting at the origin. Explain what is wrong with that.
Show answer
The line should start at the fixed cost level, RM6,000, because fixed costs are paid even at zero output. Starting at the origin would suggest there are no fixed costs, which is not the case for this café, and the break-even point would be wrong.
3. At 800 cups, is the firm in profit or loss, and by how much?
Show answer
800 cups is below the break-even output of 1,000, so there is a loss. Loss = 6,000 − 800 × 6 = 6,000 − 4,800 = RM1,200.
Where this leads next
Once you can read a chart, you can ask how far sales could fall before the firm loses money. The next lesson shows how to explain a margin of safety. To see lines like these move when you change the inputs, try the break-even and contribution explorer, and compare the shape of profit with the timing of cash in the cash versus profit bridge.
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