# Limited factor and break-even analysis

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1 Chapter 7 Limited factor and break-even analysis Syllabus Content D - Marginal costing and decision-making 15% Contribution concept. Limiting factor analysis. Break-even charts, profit/volume graphs, break-even point, profit target, margin of safety, contribution/sales ratio. Page 1

2 7.1 Limiting factors A limiting factor (or principle budget factor) is a scarce resource which is in short supply. Limiting factor analysis is a technique which will maximise contribution for an organisation, by allocating a scarce resource that exists to producing goods or services that earn the highest contribution per unit of scarce resource available. Examples of limiting factors Shortage of material Shortage of labour hours Shortage of machine hours Shortage of money Steps to maximise contribution given the existence of a limiting factor 1. Work out the contribution per unit for each product produced. Contribution per unit = Sales price less variable cost per unit. 2. Divide the contribution per unit for each product, by the quantity of scarce resource required to make it. Contribution earned per unit of scarce resource for each product = Contribution per unit for each product Quantity of scarce resource required to make it 3. Rank the different products in order of how much contribution they earn per unit of scarce resource. Produce first the products that earn the highest contribution per unit of scarce resource, subject to the constraint of maximum demand. Page 2

3 Example 7.1 Cosmetics R Us perform three types of cosmetic surgery, face jobs, gut tucks and lipo suction. FJ GT LS Estimated maximum demand for one year Average consultancy fee 3,000 1,500 2,000 Surgeon cost per hour (paid 500 per hour) 1, Variable cost per operation Fixed overhead is incurred at 750,000 a month. Unfortunately due to most surgeons working within the NHS, Cosmetics R Us can only currently employ 20 consultants working a 42 week year, performing operations up to a maximum of 40 hours a week. Calculate the number of operations that Cosmetics R Us must perform each year to maximise contribution? What would be the profit earned? Page 3

4 Example 7.2 Because of intense competition, there is huge pressure on waiting lists for FJs and therefore Cosmetics R Us must fulfil all of these operations first (before undertaking any GT or LS operations), otherwise the reputation of the business could suffer. Calculate the number of operations that Cosmetics R Us would perform if this were the case? Page 4

5 7.2 Break even analysis or cost volume profit (CVP) analysis Break even or CVP analysis calculates a physical quantity of units or sales value that would earn no profit and no loss for an organisation. This will help the organisation to understand how many units of a product or service they would need to sell before they can earn profit. There are a number of formulae within this chapter that you need to be able to learn and apply. To break even would mean an organisation would be earning no profit and no loss. Sales revenue = Variable + Fixed cost A variable cost is a cost that can be avoided if a unit is not produced or would be incurred if a unit was produced. A fixed cost remains constant whether a unit is or is not produced. Assumptions of break even analysis 1. Single product or single mix of products being sold 2. Fixed cost, variable cost per unit and selling price per unit are constant 3. Production equals sales or stock levels do not change significantly 4. The volume sold is the only factor effecting variable cost and sales 5. Linearity of sales and costs Page 5

6 Formulae to learn Contribution per unit = Sales price less variable cost per unit Break-even volume = Fixed overhead Contribution per unit The number of units you would need to sell in order to earn enough contribution to cover fixed overhead e.g. contribution equals fixed overhead. Contribution to sales ratio (C/S ratio) A contribution to sales ratio would calculate how much contribution a product would earn for every 1 of sales, expressed as a decimal e.g. a 0.4 C/S ratio would mean 40 pence of contribution is generated or earned for every 1 of sales. C/S ratio = Contribution per unit Sales price per unit C/S ratio = Total contribution Total sales revenue Break-even revenue The sales revenue earned that would give no profit and no loss. It can be calculated by multiplying the break-even volume by the product selling price, or using the following formulae; = Fixed overhead C/S ratio Margin of safety The sensitivity of the forecast or budgeted sales compared to the break-even point. Margin of safety (units) = Budgeted sales volume less Break-even sales volume Margin of safety (%) = Budgeted sales less Break-even sales volume x 100 Budgeted sales volume Number of units sold to achieve a target profit = Fixed cost + Target profit Contribution per unit Page 6

7 Break-even charts Cost and revenue Sales revenue Total costs Variable costs 0 Breakeven point Margin of safety Budgeted or actual sales Fixed costs Output (units) Profit volume charts Profit 0 Sales Loss Loss = fixed costs at zero sales activity Breakeven point Page 7

8 Example 7.3 Z-Boxes sell for 299 and the variable cost of production is 99 a unit. Fixed production overhead for the year is 1.2 million. a) Calculate the break-even level of sales for both volume and revenue? b) Calculate the break-even revenue using the C/S ratio? c) The budgeted sales revenue is 2.99 million; calculate the margin of safety in units and as a percentage? d) Produce a break-even chart and profit-volume chart using the information above? e) How many Z-Boxes must be sold in order to achieve 500,000 profit? Page 8

9 Solutions to lecture examples Page 9

10 Example 7.1 FJ GT LS Labour hours per operation* Contribution per operation ( ) 900 1, Contribution per hour ( ) 300 2, RANKING 3 rd 1 st 2 nd * Surgeon cost per hour for each operation 500 per hour To maximise contribution and therefore profit the quantities of each service performed would be as follow; 1 st GT 0.5 Hrs x 2000 max demand = 1000 Hrs 2 nd LS 1.5 Hrs x 3000 max demand = 4500 Hrs 3 rd (28100 Hrs remaining/3 Hrs an operation 9367 operation performed x 3 Hrs = Hrs Hrs Budgeted profit will be 4.58 million 000s FJ 9367 x ( 3,000-2,100) = 8,430.3 GT 2000 x ( 1, ) = 2,300.0 LS 3000 x ( 2,000-1,050) = 2,850.0 Contribution 13,580.3 Fixed cost ( 750,000 x 12 months) (9,000.0) Profit 4,580.3 Note: An alternative method could have been used above for the calculation of budgeted profit e.g. on the basis of total surgeon hours x contribution per hour for each service. Page 10

11 Example 7.2 FJ (NO CHOICE) x 3 Hrs = GT 2000 x 0.5 Hrs (most profitable next) 1000 LS 2600 Hrs (balance)/1.5 Hrs = 1733 operations x 1.5 Hrs Note: if you produced a budget now, the profit would be lower due to less profitable FJ being substituted for more profitable LS. Page 11

12 Example 7.3 a) 1.2 million/ ( ) = 6000 units break-even volume or for breakeven sales revenue 6000 units x 299 = 1,794,000 b) 1.2 million/ ( 200/ 299 = C/S ratio) = 1,793,990 c) 2.99 million/ 299 = budget volume units (10000 units units) = 4000 units margin of safety or as a percentage 4000/10000 = 40% margin of safety d) See charts below Area of contribution (sales less variable cost) Sales Total Cost Area of profit (sales less total cost) m 1.2 m Variable cost Fixed Cost 6000 Units sold + 0.8m PROFIT LOSS Output -1.2 m e) (1.2m + 0.5m)/ ( ) = 8500 units sold to make profit of 0.5m Page 12

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