The Break-even point is the point at which a business is not making a profit or loss it is simply breaking even. The money being made from sales is the same as the money being spent on  all costs (variable and fixed). Break even analysis is a very useful financial tool for all businesses. The main variables we need to consider are Revenue, Variable costs and fixed costs these are explained with the relevant formula below. 

Costs to a business can be categorised as follows:

Variable costs- these vary with the level of output, for example raw materials. If we make and sell T-shirts for £30 the business would have a variable cost for each T Shirt made, this would be made up of Cotton, Printing, Labels and Packaging. If it costs £15 in varaible costs to make one T-Shirt. We can calculate the variable costs for 10 T-Shirts by multiplying £15 by 10.

Semi-variable- part of the cost stays the same and part varies in relation to  the degree of business activity, for example a worker may be paid a fixed rate of pay but at busy times earn additional payments for working overtime.

Fixed costs- these do not vary with output, for example rent and salaries. These have to be paid whether or not a business sells a single item or not.

Total costs- fixed costs + variable costs

Sales by a business generate revenue; this is cash coming in to the business.  If we sell T Shirts for £30 and we sell 1200 in December the revenue would be £30x1200= £36,000. This is not all profit as we have to first cover the costs of the materials to make the t-shirts and then other costs which the business has.

Important terms in this topic are listed below with their formula:

Total Revenue- the total amount of money coming in from sales, calculated as quantity sold multiplied by selling price.

Total Sales- the amount of sales made in a set time period, for example a year, this can be expressed as value or volume.

Selling Price per Unit- The amount a customer pays for each unit bought

Sales in value- Sales expressed in monetary value, for example £'s, calculated as quantity sold multiplied by selling price per unit.

Sales in volume- Sales expressed as a quantity, for example tons or units.

Break-even is the point where total revenue (TR)=total costs(TC). This can be calculated as follows.

Break-even point =   fixed costs/contribution per unit

Contribution per unit= selling price - variable costs per unit

Total Contribution= Sales revenue - total variable costs

Total variable cost= variable cost per unit x quantity 

or Total variable cost= contribution per unit x number of units sold

If we sell T Shirts for £30 and each T-shirt has £15 varaible costs then the contribution per unit is (£30-£15)=£15. 

Scenario A

If the business has £3000 in fixed costs the break even in units= 

=£3000/15.

=200 units 

We must sell 200 units to cover the fixed costs, at which point we break even. If we sell 201 we would make a £15 profit.

Scenario B

If we know the company breaks even at 4800 units, we can calculate the fixed costs by multiplying 4800 by £15.

Fixed costs = 4800 x 15

Fixed Costs=£72000

The Formula method for calculating break even is explained in the worked example below. It is also explained with a few examples in the "Break Even Technique Video" a little further down the page.

Margin of safety is the actual number of units sold over and above the break-even point. This is calculated as:

If we need to sell 4000 units to break even and we sell (or sometimes predict to sell) 5200 units our margin of safety is the difference. 

5200-4000

1200 units

It can also be expressed in terms of revenue. If we need £50000 in revenue to break even and we have a revenue of £80000 our margin of safety is the difference. 

80000-50000

£30000

Margin of safety=actual sales in units-break-even level of output

To work out the break-even level you need to calculate: 

break-even point=fixed costs/ contribution per unit

contribution per unit=selling price-variable costs 

then

margin of safety=actual sales-break-even level of output

Break-even can also be calculated on a break-even chart. This plots the costs and revenues at each unit of output. The break-even point is where the total cost line crosses the total revenue line. A break-even chart can also be used to calcualte margin of safety and profit or loss at different levels of output.

You are the finance assistant at Deluxe Car Washing Services. Produce a break even chart and check your workings against the break-even formula for the following:

Car wash price=£12.50 per car

Overhead costs=£175 per week per week 

Labour costs per wash=£4.50 per car 

Materials and water cost=£1 per car

1. Label your graph in full and include the break even formula to show you are right

2. The business averaged 30 cars per week during July- work out the margin for safety

3. How much profit would they make if they washed 20 cars suring one week, and what recommendations would you make to them about this?

Break-even level of output is the level of output where the business is making neither a profit nor a loss. If the business sells less than the break-even level of output, then it is making a loss. For every item sold above the break-even point it is making a profit.

This is the difference between selling price per unit and variable cost per unit, it shows how much each unit contributes towards paying off the fixed costs of the business, once fixed costs have been paid the contribution per unit becomes profit as we have covered the fixed costs.

Contribution per unit= selling price per unit- variable cost per unit

Total contribution=contribution per unit x number of units sold.

This is used by businesses to help inform decision making. There are benefits and limitations to it as a decision-making tool.

Benefits

• Straightforward to calculate

• Allows for the calculation of break-even level of output

• Can be used to inform decisions, e.g. what price to change

• Can be used to carry out what-if analysis

Limitations

• Does not take into account fixed costs

• Assumes that prices remain constant

• Does not take into account any unexpected changes to variables, e.g. selling price and variable costs can fluctuate.

Break-even can be used as a managment tool for planning, monitoring, control and target setting.

Planning

• Set budgets for the amount of sales necessary and costs

• Forms part of a business plan to show at what point the business will start to make a profit.

• Informs pricing decisions

Monitoring

• Monitor progress towards achieving break-even point

• Identify changes to selling price of costs

• Take corrective action if targets look ublikely to be met

Control

• Keep costs within budget

• Motivate employees

• Manage sales accounts

Target Setting

• Set sales targets for individual employees, teams or products

• Set expenditure budgets

• Set profit budgets based upon sales targets and cost targets

You should now be able to prepare a break-even chart, calculate the break-even level of output and analkyse the effect on break-even and margin of safety if any of the variables, i.e. costs or selling prices vary.

Advantages

• The business knows how many items it needs to sell to break even

• Informs decisions on what selling price to change to 

• Can set targets for sales

• Identifies fixed and variable costs

• Can identify if costs are too high allowing business to look for savings

• Can set targets to help motivate employees

• Easy way to calculate profit or loss at different levels of output

Disadvantages

• Does not take account of variations in costs or selling price

• Forecast sales may not be achieved and hence even though the break-even point is known it may not be achieved

• Targets set may be too high causing stress.