# Business Math: Knowing How to Calculate the Break-even Point of your Business

Knowing how much in the way of gross sales (revenue) or units sold to break even is an essential formula that all business owners should know and keep an eye on. In the early stages of a growing business it’s vital to know how much is needed for the business to reach that break-even point. Break-even point is where all costs and expenses are covered by the revenue/sales generated. When you know this figure you can keep a close eye on sales each week to know if you’re under or over the break-even point, and make important decisions from that. Break-even point (BEP) is a valuable key performance indicator (KPI) and should be monitored closely in the early stages of a growing business, and is also a good formula to use for “what if” scenarios… ie what if we moved into new premises, or what if we hired a new employee – what would the new break-even point be?

### Calculating Break-even

Don’t be put off by the following formulas. Once you know all your fixed costs (business costs unlikely to change in a month) and variable costs, which are linked to the cost of goods and will change with an  increase/decrease in sales, you can work out the below formulas with ease.

Firstly we’ll need to define some variables below:

p is the price per unit,
x is the number of units,
v is variable cost per unit and
FC is total fixed cost.

Now let’s use some real-world figures as an example. All figures exclude VAT.

• Selling price per Unit [p] – R200 – ie what you will sell to your end user for
• Variable Cost per Unit [v] – R120 – ie all the costs that make up the goods to get to the “ready to sell” point.
• Total Fixed Cost [FC] – R13,220 – ie all your overhead costs like rent/leases, fixed salaries, advertising, office supplies etc. Anything that typical doesn’t change based on sales volume.

### Break-even point in Sales Units

At break-even point the profit is zero therefore the formula is simplified to:

 px = vx + FC

Solving the above equation for x which equals break-even point in sales units, we get:

 Break-even Sales Units = x = FC p − v

Breakeven Point in Sales Units (x)

= R13,220 ÷ (R200 − R120)
= R13,220 ÷ R80 *also known as contribution margin
= 165.25 units

We need to sell a little over 165 units to break-even and cover all the business costs. As you can see this is for a single unit, use your on hand inventory figures to get an accurate picture for the BEP of inventory you are currently holding; or if you’re not holding stock create an average Contribution Margin figure from your average sale figures. This can be calculated by taking your last 6 months of sales minus variable costs divided by 6 (or the period used to calculate the average). The idea is you’re trying to get the average sale figures to work out the below.

### Break-even point in Sales Rands

The formula is then represented as:

Break-even Sales Dollars = Price per Unit × Break-even Sales Units

R200 x 165.25 = R33,050.00

This means you’ll need to generate R33,050.00 in sales (at R200 per unit/sale) to cover all your costs and make break-even. That would then mean R1,101.66 per day in sales or R8,262.50 per week.