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

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

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 100 Variable costs per unit - direct materials 27 Direct labour 32 Royalties 8 Fixed Costs 17 REQUIRED: Calculate the contribution made by the sale of one unit of BMX Mr. Barry A-level Accounting Year 13

A-level Accounting Year 13 ANSWER Contribution per unit = Selling price per unit - Variable cost per unit £100 - £67 (£27 + £32 + £8) Contribution per unit = £33 Mr. Barry A-level Accounting Year 13

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 70 Costs - direct materials 15 Direct labour 12 Royalties 5 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

A-level Accounting Year 13 ANSWER Income Statement £ £ Sales 70,000 LESS Direct materials 15,000 Direct labour 12,000 Royalties 5,000 32,000 CONTRIBUTION 38,000 LESS FIXED costs 20,000 Profit 18,000 Mr. Barry A-level Accounting Year 13

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

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

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

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

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 600 - £10,000 = £12,000 - £10,000 = £2,000 Mr. Barry A-level Accounting Year 13

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

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 100 sales volume (units) As a % Mr. Barry A-level Accounting Year 13

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 + £4000 cont£20 700 units with a sales value of £21,000 = 700 units at £30 each Mr. Barry A-level Accounting Year 13

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) 21,000 less variable costs (700 units at £10 each) 7,000 equals contribution (to fixed costs and profit) 14,000 less monthly fixed costs 10,000 equals target profit for month 4,000 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

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 = 0.6666 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

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

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

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

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