Break-even charts

The break-even point can also be found by plotting total costs and total revenues on a break-even chart.

The first step is to calculate total costs and total revenues for a number of different levels of output. (As an absolute minimum, two levels of output should be chosen – zero and one other.) In a break-even chart, output or sales are measured on the horizontal (x) axis, while costs and revenues are measured on the vertical (y) axis. Break-even output is found at the point at which the total revenue line crosses the total cost line. The area between the two lines represents a loss when TC is greater than TR, and a profit when TC is less than TR.

‘What if’ analysis

Break-even chart is a useful business-planning tool because it allows managers to project what might happen to the break-even output and profits if costs alter, or if the price of the product is changed. For example, if prices are cut, the break-even level of output will rise, since more units will need to be sold to cover production costs.

The margin of safety

Once a business has forecast the level of sales it must achieve at a given price in order to break even, it must then attempt to exceed this level in order to make a profit. In the example above, Geoff's Knitwear might plan to sell 10,000 jumpers next year – 2,000 more than required to breakeven.

The firm would then be operating above break-even output and will therefore be in the area of profit. This difference between forecast sales and break-even output is known as the margin of safety. In other words, Geoff's Knitwear has incorporated a margin of safely of 2,000 units into its sales forecast. Sales of jumpers can therefore fall short of the forecast by up to 2,000 (or 20%) before the firm will start to make losses.

Cost-based pricing methods

If a firm is to survive in the long run, it must be able to cover its costs of production. If revenues do not exceed costs, it will make a loss. It may be able to sustain a loss for a while, but in order to continue operating, it must generate enough revenue to cover wage bills and pay for materials and power, rent and rates, and other overheads.

Cost-plus pricing. This involves calculating the cost of producing each unit of output, and then adding a mark-up for profit. For example, if a firm produced 10,000 units of a product costing £20,000, the average cost would be £2. A 10% profit mark-up would mean that units would be priced for sale at £2.20 each.

Contribution pricing. It is relatively easy to calculate the variable costs of producing each unit of output. However, it is often difficult to calculate what proportion of fixed costs such as rent and rates, heating, night-time security, etc., to apportion to each product. Contribution pricing, therefore, involves setting a price for each unit that covers its variable cost and makes a contribution towards total fixed costs, as well as a mark-up for profit. The contribution per unit of output can be calculated as follows:

Contribution per Unit = Selling Price – Variable Cost

The selling price of each unit of output will be chosen so that the total contribution covers fixed costs and yields an acceptable profit, where:

Profit = Total Contribution – Total Fixed Costs

Contribution pricing can also be used to find the level of output at which a firm will break even. For example, returning to the case of Geoffs Knitwear Ltd, we can calculate the contribution each jumper makes towards fixed costs as follows:

Contribution per Jumper Sold = 30 – 5 = 25

At the break-even output of 8,000 jumpers, the total contribution will be £200,000 (i.e. £8,000 * 25) – exactly equal to total fixed costs. Profit is zero. However, the 8,001^st jumper sold will yield a profit of £25 and so on.

The break-even level of output can therefore be calculated using the following formula: