Break Even in Plain Terms

What break even measures

Break even is the point at which total cost and total revenue are equal, so there is no profit and no loss. The U.S. Small Business Administration and the OpenStax managerial accounting textbook define it the same way. It can be stated in units sold or in sales dollars, and both answers describe the same point. We think it is the most useful single number a founder can compute before spending money, and one of the easiest to compute badly.

The inputs and the formulas

The calculation needs three inputs. The first is fixed costs, which the SBA describes as costs that do not rise or fall with production or service levels. Its examples include rent, salaries, property taxes, insurance, interest and depreciation, and it advises working in monthly figures. The second is variable cost per unit. The third is price. The SBA also describes semi-variable costs, which are fixed up to a production level and variable beyond it, and recommends splitting them into their fixed and variable parts where possible.

The formulas, as set out by OpenStax, are:

• Contribution margin per unit = Price - Variable cost per unit
• Contribution margin ratio = Contribution margin / Sales
• Break-even units = Fixed costs / Contribution margin per unit
• Break-even dollars = Fixed costs / Contribution margin ratio
• Units for a target profit = (Fixed costs + Desired profit) / Contribution margin per unit
• Pre-tax profit needed = After-tax profit / (1 - Tax rate)

A worked example

The numbers in this section are illustrative, not real data. Suppose a small studio sells a product at 120 dollars, with variable costs of 45 dollars per unit and fixed costs of 15,000 dollars a month. The contribution margin is 75 dollars per unit, or 62.5 percent of price. Break even is 15,000 / 75 = 200 units, or 24,000 dollars in sales. Both routes agree, as OpenStax notes they should. For comparison, the textbook's own example divides 18,000 dollars of fixed costs by an 80 dollar margin and reaches 225 units.

Now stress the inputs. A price cut to 110 dollars lowers the margin to 65 dollars and raises break even to about 231 units. A rise in fixed costs to 18,000 dollars raises it to 240 units. A target profit of 6,000 dollars needs (15,000 + 6,000) / 75 = 280 units. A price cut of under 10 percent raises break even by about 15 percent, which is why we run the sensitivities before trusting the base case.

Margin of safety and operating leverage

OpenStax defines the margin of safety as the difference between current sales and break-even sales. In our illustration, 260 units is 31,200 dollars of sales, so the margin is 7,200 dollars, or 23.1 percent of sales. Sales can fall by about that share before the studio loses money.

OpenStax also defines the degree of operating leverage as contribution margin divided by net operating income. Here, total contribution is 19,500 dollars and operating income is 4,500, so the degree is about 4.3. A 10 percent rise in sales would lift operating income by roughly 43 percent, and a 10 percent fall would cut it by the same amount. OpenStax says leverage is higher where fixed costs make up more of the cost structure. It adds that higher fixed costs typically mean higher risk, while the payoff is typically greater as volume grows.

What the number assumes

OpenStax states its assumptions plainly. Costs are linear and can be designated as fixed or variable, the selling price stays constant whatever the volume, all units produced are sold, and the sales mix is constant. The SBA suggests adding about 10 percent for unpredictable expenses and says the exercise is not intended to determine accounting or financing with full accuracy.

The figure also says nothing about demand. Bureau of Labor Statistics data show that of private-sector establishments born in March 2013, 79.6 percent were still operating a year later and 50.6 percent after five years. We do not claim break-even analysis explains those figures, and we do not know the causes. We offer them as context for why the arithmetic is worth doing early.

Going deeper

Because the SBA lists depreciation and interest among fixed costs, an accounting break even includes charges that are not cash payments. Our own extension is a cash break even, which removes non-cash fixed costs. If 1,500 dollars of the studio's 15,000 is depreciation, cash fixed costs are 13,500 and cash break even is 13,500 / 75 = 180 units. It answers a different question: how many units keep the bank balance level, not the profit and loss statement.

That is where EBITDA enters. A proposed SEC rule release on non-GAAP measures describes it as net income before interest, taxes, depreciation and amortization. As a formula: EBITDA = Net income + Interest + Taxes + Depreciation + Amortization. On illustrative figures of 4,000, 500, 1,000 and 1,500 dollars, EBITDA is 7,000 dollars. SEC staff guidance says that a company presenting EBIT or EBITDA as a performance measure should reconcile it to net income, that these measures must not be shown per share, and that differently calculated versions should carry a distinct name such as Adjusted EBITDA. Those rules govern companies reporting to the SEC. We think the practical lesson applies to anyone: EBITDA leaves out interest and the cost of replacing equipment, so a business can show positive EBITDA and still sit below break even.

MaxxForge is designed to serve outside founders as well as our own portfolio, which we treat as a worked example, not the limit. General information, not financial advice. If you find an error in the arithmetic or the sources, tell us and we will correct it.