Break-Even Point and Margin of Safety

Finds the sales figure at which profit is exactly zero, as fixed costs ÷ the contribution margin ratio, where that ratio is 1 − variable costs ÷ sales. The margin of safety, showing how far current sales sit above the break-even point, is shown as well.

Business costs split into two kinds: those you pay whether or not you sell anything, and those you only pay when you do. The first are fixed costs, such as rent and salaried staff. The second are variable costs, such as materials and stock.

As sales rise, variable costs rise with them, but fixed costs do not. So beyond a certain level of sales the fixed costs are covered and the business moves into profit. That threshold is the break-even point.

S_0 = \dfrac{F}{1 - \dfrac{V}{S}}

$S_0$ is break-even sales
$F$ is fixed costs
$V$ is variable costs
$S$ is sales

The denominator $1 - V \div S$ is the contribution margin ratio: of each extra unit of sales, the share that is left over to put towards fixed costs.

Example

Take fixed costs of 3000000, sales of 10000000 and variable costs of 6000000.

Variable costs are 60% of sales, so the contribution margin ratio is 40%. Every unit sold leaves 0.4 towards fixed costs. Covering 3000000 of fixed costs therefore needs $3000000 \div 0.4$ , or 7500000 in sales. That is the break-even point.

Check it. At sales of 7500000 the variable costs are 60% of that, or 4500000, leaving 3000000. Subtract the 3000000 of fixed costs and the profit is exactly zero.

Current sales of 10000000 sit 2500000 above break-even and produce a profit of 1000000. The margin of safety is $(10000000 - 7500000) \div 10000000$ , or 25%. Sales could fall by a quarter before the business turns a loss.

Where it helps

It informs pricing. Cutting the price lowers the contribution margin ratio and raises the break-even point, and this formula shows in advance how many extra units are needed to make up for it.

It also informs spending on fixed costs. Hiring one person raises fixed costs and pushes break-even up by a matching amount. Dividing the extra fixed cost by the contribution margin ratio gives the extra sales required. At the 40% ratio here, every 400000 of added fixed cost needs 1000000 more in sales.

Points to watch

If variable costs reach or exceed sales, there is no break-even point. Every additional sale deepens the loss, so no volume ever covers the fixed costs. The thing to revisit then is the cost or the price, not the sales target.

Splitting costs into fixed and variable is rarely clean in practice. An electricity bill has a fixed standing charge and a variable usage charge. Treat the result as a guide rather than an exact figure.