1. Break-even Analysis Learning Aim E
Mr. Barry
A-level Accounting Year 13

2. A-level Accounting Year 13
Important
Contribution = is of fundamental importance in marginal costing, and the term contribution is really short for contribution towards covering fixed overheads and making a profit.
Sales – Variable costs = Contribution
Mr. Barry
A-level Accounting Year 13

3. A-level Accounting Year 13
CONTRIBUTION – is the difference between selling price and variable costs
Contribution should more properly be termed contribution
towards fixed costs and profit, are once fixed costs are all
covered contribution becomes profit.
WORKED EXAMPLE 1
The selling price of a unit of BMX
Variable costs per unit - direct materials
Direct labour
Royalties
Fixed Costs
REQUIRED: Calculate the contribution made by the sale
of one unit of BMX
Mr. Barry
A-level Accounting Year 13

4. A-level Accounting Year 13
ANSWER
Contribution per unit =
Selling price per unit - Variable cost per
unit
£ £67 (£27 + £32 + £8)
Contribution per unit = £33
Mr. Barry
A-level Accounting Year 13

5. A-level Accounting Year 13
WORKED EXAMPLE 2
Elia produces a single product. The information below
relates to the production and sales of the product in
October:
Costs and Revenues per unit £
Sales revenue
Costs - direct materials
Direct labour 12
Royalties
Fixed Costs 20
Production and sales 1,000 units
REQUIRED Prepare an income statement for October,
showing the total contribution and profit.
Mr. Barry
A-level Accounting Year 13

6. A-level Accounting Year 13
ANSWER Income Statement
£ £
Sales ,000
LESS
Direct materials 15,000
Direct labour 12,000
Royalties 5, ,000
CONTRIBUTION ,000
LESS FIXED costs ,000
Profit ,000
Mr. Barry
A-level Accounting Year 13

7. Fixed and Variable Costs A-level Accounting Year 13
Fixed Costs
Variable Costs
Fixed costs remain fixed over a range of output levels in the short-term
Variable costs vary directly with changes in output levels
For example: materials and labour
For example: factory rent
There are also ‘semi-variable costs’ which combine both a fixed and variable element eg a telephone bill which has fixed rental and variable call charges.
Mr. Barry
A-level Accounting Year 13

8. A-level Accounting Year 13
The Break-Even Point
The break-even point is the output level (in units) at which the income from sales is just enough to cover all the costs, and the profit (or loss) is therefore zero.
The formula for break-even in units of output is:
fixed costs (£) contribution per unit (£)
contribution per unit (£) =
selling price per unit – variable costs per unit
Mr. Barry
A-level Accounting Year 13

9. A-level Accounting Year 13
Break-even point by calculation
Jason Sports Limited manufactures golf clubs and is able to sell all that is produced.
Fixed costs of running the business = £10,000 per month
Selling price of each golf club = £30 each
Variable costs (materials and direct labour) = £10 per unit
What is the break-even point?
Using the formula, the break-even point in units of output is:
Fixed costs 4
£10,000 =
500 units
Selling price per unit less 4 variable costs per unit
£30 - £10
Break-even point in units per month
Mr. Barry
A-level Accounting Year 13

10. A-level Accounting Year 13
Break-even point by the graph method
JASON SPORTS LIMITED: BREAK-EVEN GRAPH
break-even point (500 units) where the total costs line crosses the sales revenue line.
sales revenue
£20,000
area of profit
total costs
£15,000
variable costs
costs and revenues
area of loss
£10,000
fixed costs
£5,000
100
200
300
400
500
600
700
units of output (per month)
Mr. Barry
A-level Accounting Year 13

11. A-level Accounting Year 13
Interpretation of break-even
The break-even graph can show not only the break-even point but also the profit or loss at any level of output/sales contained within the graph.
To calculate profit or loss from the graph simply measure the gap between sales revenue and total costs at a chosen number of units, and read the money amounts off the vertical axis.
Another way to calculate the profit or loss at any level of output/sales is the use the following formula:
(the level of output or activity)
Profit/(loss) =
(selling price – variable costs) per unit x volume – fixed costs
For example, for Jason Sports Ltd, the profit at 600 units =
(£30 - £10) x £10,000
= £12,000 - £10,000
= £2,000
Mr. Barry
A-level Accounting Year 13

12. A-level Accounting Year 13
Limitations of break-even analysis
The main limitations are:
The relationship between sales revenue, variable costs and fixed costs may not always remain constant because:
- sales prices may differ at different quantities sold (for example because of discounts).
- variable costs may alter at different levels of output (for example due to bulk buying of materials).
- fixed costs do not remain fixed at all levels of output (for example if extra premises are needed).
The assumption that all output is sold may not be true.
The presumption that there is only one product may not be correct.
External factors (such as rate of inflation) are not considered.
Mr. Barry
A-level Accounting Year 13

13. A-level Accounting Year 13
Margin of safety
The margin of safety is the amount by which sales exceed the break-even point.
The margin of safety is important to management as it shows the ‘cushion’ which current production/sales gives beyond the break-even point.
The margin of safety may be expressed:
In units
sales volume (units) – break-even point (units)
eg Jason Sports Ltd at output of 700 units: 700 – 500 = 200 units
In £
margin of safety in units x selling price (£)
eg Jason Sports Ltd at output of 700 units: 200 x £30 = £6,000
margin of safety in units x sales volume (units)
As a %
Mr. Barry
A-level Accounting Year 13

14. A-level Accounting Year 13
Target profit
It is also possible to calculate the output that needs to be sold in order to give a certain amount of profit (called the target profit).
The formula for this is:
fixed costs (£) + target profit (£) contribution per unit (£)
Number of units output =
eg If Jason Sports Ltd requires a profit of £4,000 per month, the calculation is:
£10,000 + £ cont£20
700 units with a sales value of £21,000 =
700 units at £30 each
Mr. Barry
A-level Accounting Year 13

15. A-level Accounting Year 13
Target profit (continued)
The target profit of £4,000 can also be shown by means of a profit statement:
Jason Sports Limited £
sales revenue (700 units at £30 each) ,000
less variable costs (700 units at £10 each) ,000
equals contribution (to fixed costs and profit) 14,000
less monthly fixed costs ,000
equals target profit for month ,000
Note that target profit can also be calculated by making use of the contribution sales ratio (see next two slides).
Mr. Barry
A-level Accounting Year 13

16. A-level Accounting Year 13
Contribution Sales Ratio
The contribution sales (CS) ratio - also known as the profit volume (PV) ratio - expresses the amount of contribution in relation to the amount of the selling price.
The formula for contribution sales ratio is:
contribution (£)
selling price (£)
Referring to Jason Sports Ltd the CS ratio (per unit) is:
£20£30 =
or 66.66%
In break-even analysis, if fixed costs are known, then the CS ratio can be used to find the sales value at which the business breaks even, or the sales value to give a target amount of profit (see next slide).
Mr. Barry
A-level Accounting Year 13

17. A-level Accounting Year 13
Contribution Sales Ratio (continued)
To find the sales value at which Jason Sports Ltd will break-even using the CS ratio:
Fixed costs (£) CS ratio
£10,000 = =
£15,000
0.6666
To find the sales value at which Jason Sports Ltd will achieve a target amount of profit (say £2,000) using the CS ratio:
fixed costs (£) + target profit c CS ratio
£10,000 + £2000 =
0.6666 =
£18,000
As the selling price is £30 the units of output to achieve the £2,000 profit above is £18,000 / £30 = 600 units.
Mr. Barry
A-level Accounting Year 13

18. A-level Accounting Year 13
When to use break-even analysis
Before starting a new business:
In order to see the level of sales needed to cover costs or to make a particular level of profit.
When making changes within the business:
Break-even analysis will be used as part of the planning process to ensure the business remains profitable.
To answer ‘what if?’ questions:
Questions such as ‘what if sales fall by 15%?’ and ‘what if fixed costs increase by £1,000?’ can be answered.
To evaluate alternative management viewpoints:
For example assessing how automation may affect profit.
Mr. Barry
A-level Accounting Year 13

19. Contribution per unit benefits and limitations
Straightforward to calculate
Does not take into account fixed costs
Allows for the calculation of break-even
level of output
Assumes that prices remain constant
Can be used to inform decisions, e.g. what price to charge
Does not take into account any unexpected
changes to variables, e.g. selling price and
variable costs can fluctuate
Can be used to carry out what-if analysis
Mr. Barry
A-level Accounting Year 13

20. Advantages and disadvantages of break-even
Mr. Barry
A-level Accounting Year 13