# Break Even Point: A Numbers Example

This is an article from P1M3 How Profit is Created in the Pillar 1 Your Key Numbers.

## Break Even Analysis: Moving From The Graph To The Numbers

We started to look at business performance as a graph to show how sales and costs normally vary with volume.

Loss to the left, profit to the right

We then recognised the graph can be simplified by taking away sales and variable costs which both depend on volume and replace them with Contribution, the difference between sales value and total variable costs.

Break Even Point – where Contribution = Fixed Costs

If you want to manage for profit, you need to be comfortable with the numbers.

Lucky we’ve taken it down to the minimum.

Let’s work through an example together to prove the idea that a business will break even when contribution equals fixed costs.

I’ve kept the arithmetic simple and the numbers small so you can work through with me but you may want to use a calculator if you feel uncomfortable.

### The Cost Volume Profit Example Assumptions

In this example we will assume sales volume can be anything from zero to one hundred units per month.

We have a sales price per unit of £100…that means total sales can be as high as 10,000 per month – one hundred units at a price of 100.

Variable costs are £60 per unit making our contribution £40 per unit. That’s the selling price of £100 minus the £60 variable costs.

We will also assume fixed costs are £2,000 per month

We can now work out what the profits will be at different levels of sales volume.

## The Calculated Numbers

We know that if the business doesn’t sell anything, there are no sales, no variable costs and no contribution…just the fixed costs of £2,000 giving us a loss of £2,000.

I’ve selected four levels of sales volume – 30 units, 50, 70 and 100.

Profit across a range of volumes

We will work through this together.

Sales value equals sales volume multiplied by the price per unit which is £100.

So sales value at 30 units is £3,000, that’s 30 multiplied by 100.

Then at 50 units, sales value is £5,000 and so on.

Variable cost works the same as sales value and the variable cost is £60 per unit.
So at 30 units, the variable cost is £1,800 and at 50 units it is £3,000.

Contribution is sales value minus variable costs.

That’s £1,200 at 30 units and £2,000 at 50 units.

Fixed costs are the same at all levels of sales – always £2,000.

When sales are 30 units you can see profit – that’s contribution minus fixed costs is a loss of £800 but the business breaks even at 50 units.

Because we know the contribution is £40 per unit, we know if we sell just one more, a total of 51 units, the profit will be £40.

If we sell twenty more – and jump from 50 to 70 units we make £800 extra profit – that’s 20 extra units multiplied by the contribution per unit of £40.

If we double our sales from 50 to our maximum 100, contribution doubles from £2000 to £4000 and the business makes £2,000 of profit for the month.

If you are not clear on the numbers, go back and read through it again.

I want to use this example to make it clear just how sensitive your profit is to changes in volume, contribution and fixed costs.

At 51 units, the business made a profit of £40 which would double if one more unit was sold and triple if two more unit sales were made.

Because profit is the difference between two big numbers – either contribution and fixed costs or sales minus total costs, small changes in the numbers can make a huge change to your profits.

If you are trading around your break even point, the percentage changes are astonishing.