Break-even, margin of safety and operating leverage for one illustrative company, and the gross-margin shortcut that gets break-even wrong.
Break-even revenue is total fixed costs divided by the contribution margin ratio, the share of each sale left after variable costs. For an illustrative company with 15,000,000 of fixed costs and a 40.0 per cent contribution margin, break-even revenue is 37,500,000. On current revenue of 48,000,000 that leaves a margin of safety of 21.88 per cent, which is also the reciprocal of operating leverage: 4.57 times.
Worked in full in Financial Planning and Analysis by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A manufacturer reports 48,000,000 of revenue. Its cost of sales holds 28,800,000 of variable cost, materials and volume-paid labour, plus 2,400,000 of fixed production overhead. Operating expenses of 12,600,000 are fixed over the relevant range. All figures are illustrative.
| Line | Amount | % of revenue |
|---|---|---|
| Revenue | 48,000,000 | 100.0% |
| Variable cost of sales | -28,800,000 | 60% |
| Contribution | 19,200,000 | 40.0% |
| Fixed production overhead | -2,400,000 | |
| Fixed operating expenses | -12,600,000 | |
| EBIT | 4,200,000 | 8.75% |
The split by behaviour is the work. A statutory income statement groups costs by function, cost of sales and operating expenses, and both groups contain fixed and variable items. Break-even needs them regrouped by whether they move with volume.
Contribution margin ratio = (revenue − variable costs) / revenue = 19,200,000 / 48,000,000 = 40.0%
Semi-variable lines, such as energy, overtime or freight, have to be split before this step. The usual method is to regress twelve to twenty-four months of the cost against revenue or volume: the slope is the variable rate and the intercept the fixed part. A judgement call made line by line is acceptable if it is documented, because the break-even figure is only as good as the classification behind it, and reviewers will ask where each line went.
At break-even, contribution exactly covers fixed costs, so revenue times the ratio equals fixed costs:
Break-even revenue = fixed costs / contribution margin ratio
= (2,400,000 + 12,600,000) / 40.0% = 15,000,000 / 40.0% = 37,500,000
Excel: =Fixed/((Revenue-Variable)/Revenue)
For a single product the same formula in units divides fixed costs by contribution per unit. For a multi-product business, the ratio is a weighted average, and it holds only at the current sales mix: a shift towards lower-margin lines raises break-even even if every price is unchanged.
Margin of safety = (revenue − break-even) / revenue = 10,500,000 / 48,000,000 = 21.88%
Degree of operating leverage = contribution / EBIT = 19,200,000 / 4,200,000 = 4.57x = 1 / 21.88%
The two measures are the same fact seen from two sides. Revenue can fall 21.9 per cent before the company loses money, and each 1 per cent of revenue moves EBIT by 4.57 per cent. A 10 per cent fall to 43,200,000 takes EBIT from 4,200,000 to 2,280,000, a fall of 45.7 per cent. That is why a forecast miss of a few points of revenue can become a profit miss of tens of points, and why a variance commentary should state the operating leverage before explaining the profit line. The reverse calculation gives the revenue for a target profit: 6,000,000 of EBIT needs (15,000,000 + 6,000,000) / 40.0% = 52,500,000, growth of 9.38 per cent.
| Fixed costs | CM 38% | CM 40% | CM 42% |
|---|---|---|---|
| 14,000,000 | 36,842,105 (23.2%) | 35,000,000 (27.1%) | 33,333,333 (30.6%) |
| 15,000,000 | 39,473,684 (17.8%) | 37,500,000 (21.9%) | 35,714,286 (25.6%) |
| 16,000,000 | 42,105,263 (12.3%) | 40,000,000 (16.7%) | 38,095,238 (20.6%) |
Two points of contribution margin move break-even about three-quarters as far as 1,000,000 of fixed cost does. Price is the fastest way to lose them: a 2 per cent price cut with no change in volume takes revenue to 47,040,000, the ratio to 38.78 per cent, break-even up to 38,684,211, and EBIT down to 3,240,000. The volume needed to recover a price cut is worked through in how much volume a price increase can lose, which runs the same arithmetic in the other direction.
Break-even assumes costs behave linearly over the range considered. A step in fixed costs, a second shift or a new site, moves the answer discontinuously; state the range for which the fixed-cost figure holds.
The shortcut takes the reported gross margin, 16,800,000 or 35.0 per cent, and divides operating expenses by it: 12,600,000 / 35.0% = 36,000,000. It understates break-even by 1,500,000 and overstates the margin of safety at 25.0 per cent. The error is treating the 2,400,000 of fixed production overhead as if it varied with sales, because it sits above the gross profit line. The same confusion runs through budget variance analysis, where a flexible budget must flex only the costs that actually move; see how to calculate a flexible budget variance.
The free workbook for this case computes the book's own company's operating leverage and its three breakevens on live formulas, including the reforecast breakeven on the unrounded margin.
Contribution margin deducts only variable costs; gross margin also deducts fixed production overhead inside cost of sales. Break-even must use contribution margin and all fixed costs. Here the contribution margin ratio is 40.0 per cent against a 35.0 per cent gross margin, and the gross-margin shortcut gives 36,000,000 instead of the true 37,500,000.
They are reciprocals. The degree of operating leverage, contribution over EBIT, equals one divided by the margin of safety. A 21.88 per cent margin of safety means operating leverage of 4.57x, so a 10 per cent fall in revenue cuts EBIT by 45.7 per cent, from 4,200,000 to 2,280,000.
Add the target profit to fixed costs and divide by the contribution margin ratio. For 6,000,000 of EBIT: (15,000,000 + 6,000,000) / 40.0 per cent = 52,500,000, which is 9.38 per cent above current revenue. The same formula with a target of zero gives break-even.
This article is one calculation from Financial Planning and Analysis. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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