Break-Even Chart and Limitations

(a) Fixed cost line — begins at the fixed cost level and runs horizontally. (b) Total cost line — begins at the same fixed cost level and slopes upward. (c) Sales revenue line — begins at the origin (zero) and slopes upward.

The break-even point is where the sales revenue line crosses the total cost line (revenue = total cost, profit = 0). Reading down to the x-axis gives the break-even output; reading across to the y-axis gives the break-even revenue.

To the left of the break-even point the total cost line is above the revenue line, so the business makes a loss. To the right, the revenue line is above the total cost line, so it makes a profit. The size of the profit (or loss) at a given output is the vertical gap between the two lines at that output.

The margin of safety is the amount by which actual (or budgeted) output exceeds the break-even output — it shows how far output can fall before the business makes a loss. On the chart it is the horizontal distance along the x-axis from the break-even output to the actual output.

A P/V chart plots profit or loss (vertical axis) against output or sales (horizontal axis). At zero output the line starts at minus the fixed costs (a loss equal to fixed costs). It slopes upward with a gradient equal to the contribution per unit, and it crosses the horizontal axis at the break-even point (profit = 0).

Break-even point = 6,000 units / $300,000. Margin of safety = 8,000 − 6,000 = 2,000 units. Budgeted profit = margin of safety × contribution = 2,000 × 20 = $40,000 (every unit beyond break-even adds $20 of profit).

1. Linearity. It assumes the selling price and variable cost per unit are constant, so the lines are straight. In reality bulk discounts, price cuts to sell more and overtime make these relationships curved, so break-even figures are only approximate. 2. Constant fixed costs. Fixed costs are assumed constant, but they step up beyond capacity (more machinery/supervisors), so the chart understates cost at high output. 3. All output sold. It assumes there is no change in inventory — everything produced is sold — which is often untrue. 4. Single product / constant mix. A simple chart assumes one product or an unchanging sales mix. Conclusion: these assumptions make break-even analysis a useful but approximate planning tool. It works best over a narrow output range and the short term; managers should treat its results with caution and consider non-financial factors too.

Break-even analysis assumes the selling price per unit is constant, giving a straight sales revenue line. Because this manufacturer gives quantity discounts, the average selling price falls as more is sold, so the real revenue line would bend/flatten — the chart would overstate revenue and understate the true break-even point at higher volumes.

It may also assume constant variable cost per unit (untrue if it pays overtime) and constant fixed costs (which step up beyond capacity).

Advice: the manufacturer can use break-even analysis as a quick guide and for what-if planning, but should not rely on it precisely for pricing, especially for large discounted orders. It should treat the figures as approximate, perhaps recalculating break-even at the specific discounted prices, and also weigh non-financial factors such as customer relationships.

1. Planning and target-setting — it shows the output needed to break even or to reach a target profit, so the business can set realistic sales targets.
2. 'What-if' and risk analysis — managers can quickly test the effect of changing price, costs or volume on profit, and the margin of safety shows how far sales can fall before a loss.

Advantage: a P/V chart shows the profit or loss at any output directly as a single line, making the net result easy to read (and easy to compare products). Limitation: it does not show the separate cost and revenue lines, so it does not reveal how fixed and variable costs build up.