Break-even calculator

How do you calculate the break-even point?

The break-even point is the volume of sales at which total revenue equals total cost, so profit is exactly zero. Every unit sold earns its selling price minus its variable cost, an amount called the contribution per unit, and the business breaks even once those contributions add up to its fixed costs:

Break-even units = fixed costs / (selling price per unit - variable cost per unit)

With the calculator's opening figures, a price of $25 and a variable cost of $15 leave a contribution of $10 a unit. Fixed costs of $40,000 divided by $10 give a break-even point of 4,000 units. Sell one unit fewer and the business makes a $10 loss; sell one more and it makes $10 of profit.

Worked example: break-even set out as an exam answer

A written answer usually proves the break-even point with a marginal costing statement, which lists contribution before fixed costs. Here is the default product at break-even and at its budget of 6,000 units:

The first column proves the answer: contribution exactly covers fixed costs. The second shows the point of the layout, since every unit beyond break-even adds its whole $10 contribution to profit. The calculator builds the same statement for your inputs, with a third column for the target profit.

Break-even in units or in sales revenue: what is the C/S ratio?

To find break-even as an amount of revenue rather than a count of units, divide fixed costs by the contribution to sales (C/S) ratio, also called the contribution margin ratio. It is contribution as a share of the selling price: $10 / $25 = 40% for the default product, so break-even revenue is $40,000 / 0.40 = $100,000. That is the same as 4,000 units x $25.

The revenue form is the one to use when a business sells many items at different prices but its mix stays steady, because the C/S ratio can be read from the accounts. An example in pounds: a product sells at £40, costs £22 a unit to make and carries £54,000 of fixed costs. Contribution is £18, the C/S ratio is 45%, and break-even is £54,000 / £18 = 3,000 units, or £54,000 / 0.45 = £120,000 of sales.

How do you calculate the margin of safety?

The margin of safety measures how far sales can fall before the business starts to lose money: margin of safety = budgeted sales - break-even sales. It is usually given three ways. For the default product, budgeted at 6,000 units:

• In units: 6,000 - 4,000 = 2,000 units.
• In revenue: 2,000 x $25 = $50,000.
• As a percentage: 2,000 / 6,000 = 33.33% of budgeted sales.

The pound example above, budgeted at 3,600 units, has a margin of safety of only 600 units, or £24,000 of sales and 16.67% of the budget, and budgets a profit of £10,800. The percentage is the figure to compare across products of different sizes. If budgeted sales are below break-even the margin is negative, and the calculator says how big the loss on the budget would be.

How many units do you need to sell for a target profit?

Add the profit you want to the fixed costs, because contribution now has to cover both: units for target profit = (fixed costs + target profit) / contribution per unit. For the default product, a $20,000 profit needs ($40,000 + $20,000) / $10 = 6,000 units, or $150,000 of sales, which is exactly its budget.

A dirham example: a product sells for AED 120 with a variable cost of AED 75, so contribution is AED 45 and the C/S ratio is 37.5%. With AED 270,000 of fixed costs it breaks even at 6,000 units, or AED 720,000 of sales. A target profit of AED 90,000 needs (AED 270,000 + AED 90,000) / AED 45 = 8,000 units, which is AED 960,000 of revenue.

How do you draw a break-even chart?

Put units sold on the horizontal axis and money on the vertical axis. Draw fixed costs as a flat line, total cost as a line that starts at the fixed-cost level and rises by the variable cost per unit, and sales revenue as a line from zero that rises by the selling price per unit. Break-even is where the revenue and total cost lines cross; the gap between them to the right is profit and to the left is loss. The chart beside the result is drawn this way and marks the break-even point and your budget.

The profit-volume chart further down condenses the same picture into a single line. It begins at a loss equal to the fixed costs when nothing is sold and climbs by the contribution per unit, so its slope is the contribution and it crosses zero at the break-even volume.

How do you calculate break-even in Excel?

Put the price in B1, the variable cost in B2 and fixed costs in B3. Then:

• Break-even units: =B3/(B1-B2), which returns 4,000 for the default figures.
• Break-even units rounded up to whole units: =ROUNDUP(B3/(B1-B2),0).
• Break-even revenue: =B3/((B1-B2)/B1), which returns 100,000.
• Units for a target profit in B4: =(B3+B4)/(B1-B2).

To work backward, for instance to find the price that breaks even at a set volume, put a profit formula such as =B5*(B1-B2)-B3 in a cell, with units in B5. Then use Goal Seek, under Data, What-If Analysis: set the profit cell to 0 by changing the price cell. Google Sheets accepts the same formulas.

How do price, variable cost and fixed costs move the break-even point?

A 10% change does not move break-even by 10%. Price and variable cost work through the contribution, and because contribution is the smaller number, a change in either one swings the result harder than the same percentage change in fixed costs. When the answer is not a whole number the calculator rounds up, since 4,705 units would still leave a small loss.

Does sales tax or VAT go into break-even?

No. Use the selling price before sales tax or VAT, because the tax is collected for the government and is not revenue to the business. If your price list includes tax, divide by one plus the rate first. In the UK the standard VAT rate is 20%, so a £48 shelf price is £48 / 1.20 = £40 of revenue. In the UAE the rate is 5%, so a shelf price of AED 126 is AED 120 to the business. In the US, general sales tax is a state and local tax on retail sales; where a price includes it, divide by one plus the rate charged where the sale takes place.

Treat cost-side tax the same way. VAT a registered business can reclaim on its purchases is not a cost, so variable costs should exclude it too.

Common mistakes, what the calculator leaves out, and a glossary

• Putting fixed costs into the variable cost per unit, for example by dividing rent over last year's output. That counts them twice.
• Using gross profit per unit instead of contribution. Gross profit often has fixed production overhead inside it.
• Rounding break-even down. Round up to the next whole unit.
• Mixing periods, such as monthly fixed costs against annual sales.

The calculator assumes one product, a price and a variable cost that hold at every volume, and fixed costs that do not step up as output grows. Several products need a weighted average C/S ratio for a fixed sales mix, and a capacity limit or a price discount for volume changes the lines into curves or steps. Read the answer as a guide to the volume needed, not as a forecast of what will sell.

Contribution: selling price minus variable cost. C/S ratio: contribution / sales. Fixed costs: costs that do not change with volume in the period. Margin of safety: budgeted sales above break-even. Marginal costing: a costing method that charges only variable costs to units and treats fixed costs as a cost of the period.

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