A vital part of any business plan is to see what output level or sales level is necessary before you are going to break-even. Break-even does not specify a time that it will take to reach this level. This will depend on how quickly sales are generated. In some cases it can be many years before a firm would reach its break-even sales level. A bank or other investor will almost certainly want to see break-even information. To work out break-even we need to know various bits of information:
- The price you are charging
- The variable costs (direct costs) of each unit - these are the costs of raw materials, labour and so on that can be directly attributed to each unit.
- The fixed costs (or indirect costs/overheads) - these are the costs that stay the same whatever the level of output and will be things like rent, marketing costs, admin costs and so on.
Once we have this information, we can work out the break-even level of output. Let's look at an example:
Price = £5
Variable costs = £3 per unit
Fixed costs = £1,000
From this information we can see that every time we sell one more unit we have an excess of income over variable costs of £2. We call this figure the contribution. However, this is NOT the same as profit, because we still have to pay the fixed costs of £1,000. We therefore need to work out how many we need to sell for the total contribution to be equal to the fixed costs. In this case, the contribution is £2 per unit and the fixed costs are £1,000, so if we can sell 500 units then we will have had enough contribution to pay the fixed costs. Any units we sell beyond that level will then make a profit of £2 each. So if we sell 501 units, our total profit will be £2. If we sell 502 units our total profit will be £4 and so on.
The break-even level of output can therefore be calculated from the following formula:
| Break-even output = | Fixed costs |
|
| Contribution (per unit) |
However, we can also work out the break-even level of information by plotting the figures on a graph. To do this, we need to go through the following steps:
Stage 1
Plot the total cost line - remember this will be the sum of the fixed costs and variable costs. This means that it will start from part way up the y-axis because of the fixed costs.
Stage 2
Add the total revenue curve. This can be plotted by working out the total revenue at the maximum capacity of the firm, e.g. if they can produce 50,000 units of a good and they sell them at £28 each, then the TR line will go from the origin to a point given by 50,000 units and £1.4m.
The diagram should now look like this:

Stage 3
The point where the TR and TC lines cross is the break-even level of output. At this point the firm will break-even. Any level of output above this point they will make a profit, but any level of output below this point they will make a loss. We can see this from the diagram below:

Stage 4
We can also identify from the diagram the margin of safety of the firm. The margin of safety shows how far from break-even output the firm is currently producing. It shows, in other words, how much output could fall before the firm started making a loss. We can see the margin of safety on the diagram below:

On the diagram below, estimate the company's position if it produced 10,000 and 20,000 units respectively.
| | £ ( 10,000 units) | £ (20,000 units) |
| Total Revenue | 0.2m | 0.4m |
| Total cost | 0.42m | 0.5m |
| Profit/ loss | 0.22m (loss) | 0.1m (loss) |
The total revenue from selling 10,000 units would be £0.2m. The total cost of producing 10,000 units would however be £0.42m. The company would therefore be making a loss of £0.22m if it continued producing at this level. However, if it increased output and sales to 20,000 units, then the revenue would rise to £0.4m and the costs of producing 20,000 units would have risen (because of the variable costs) to £0.5m. The fixed costs of producing 10,000 units and 20,000 units are however the same so the revenue is rising at a faster rate than the costs. The loss at this level of sales therefore would be £0.1m. This figure is lower than the loss made at 10,000 units. If you follow through the logic here you can identify the level of profit or loss at different levels of sales and output.

This is all based on an assumption about the structure of the total revenue curve. Total revenue is price times the quantity sold (TR = P x Q). If the business decided to charge a different price, the total revenue curve would be a different shape. If the company decided to charge a lower price, the total revenue curve would be flatter. This would mean that the company needs to sell a greater volume before they will break-even. It does not mean that they will never sell enough, it merely means they have to sell more.

On the other hand, if they decided on setting price at a higher level, the TR curve would now be steeper. This would imply that the number of sales needed to break-even would be less. The decision on the price level will depend on a host of factors - the level of competition, the type of product and what market it is aimed at (for example, is the product aimed at groups A and B in the 'social class groupings' or at a mass market?) and the results of market research conducted by the company that may inform their decisions. Using break-even analysis therefore allows a business to be able to plan and be informed of the impact of its decisions.

Break-even analysis is therefore an example of a quantitative decision making technique. The decision on the actual price to charge will largely be a qualitative one albeit based on other forms of information such as the results of market research.






