Revision point: Fixed costs are those that do not change with changes in production levels, e.g. rent.

Transcription

1 SECTION ONE BREAK-EVEN ANALYSIS Break-even point What is meant by the term break even? A firm breaks even when income is sufficiently high to exactly cover total costs therefore neither a profit nor a loss is made. However, break-even analysis is not usually applied to the whole firm but rather to a single product, studying its profitability by comparing its estimated revenue and costs. Break-even analysis does more than just estimate the break-even point (BEP): it also shows how much profit or loss should be made at various levels of activity. It is therefore seen as a valuable tool for the management accountant. To use break-even analysis several assumptions must be made: there is only one product all costs can be classified as either fixed or variable costs remain constant over the whole range of output selling price remains constant for the whole range of output production is equal to sales so there is no adjustment for stock figures there are no changes in materials, labour, design or manufacturing methods. Revision point: Fixed costs are those that do not change with changes in production levels, e.g. rent. Variable costs vary in proportion to changes in production levels, e.g. raw materials. A simple table can be drawn up to show: increasing levels of activity estimated costs of production at these levels estimated revenue at these levels the resulting profit/loss for each level. ACCOUNTING AND FINANCE 1

2 BREAK-EVEN ANALYSIS Example 1 The following figures have been supplied by A Gardiner, who is considering making plant pots. He is particularly concerned to know how many he must make before the product becomes profitable. Total fixed costs 1,000 Variable costs per unit 3 Selling price per unit 8 We can draw up a table to show the information. Units of Fixed Variable Total Sales Profit output costs costs costs revenue (loss) 0 1,000 1,000 (1,000) 100 1, , (500) 200 1, ,600 1, , ,900 2, ,000 1,200 2,200 3,200 1, ,000 1,500 2,500 4,000 1,500 At an output of 200 units, where both sales revenue and total costs amount to 1,600, he is making neither a profit nor a loss on the plant pots. < Any output below 200 units will result in a loss. Any output above 200 units will result in a profit. Break-even point is therefore at a sales volume of 200 units and a sales revenue of 1, ACCOUNTING AND FINANCE

3 BREAK-EVEN ANALYSIS Profit/loss Profit/loss (the difference between sales revenue and total costs) at various output levels is shown in the final column of the table on p. 2. At 100 units of output the loss is ( 500) and at 400 units of output a profit of 1,000 is made. Break-even analysis is thus useful in forecasting profit/loss figures for different production levels. Margin of safety Output above BEP which gives a profit is the margin of safety. This margin can be measured by comparing the level of output with BEP and it can be expressed in units or in sales revenue. Units of BEP Margin of safety Selling price Margin of safety output (units) (units) per unit (sales revenue) , ,400 The margin of safety in sales revenue can also be calculated by comparing the sales revenue for the output level with the sales revenue at BEP. Sales BEP Margin of safety revenue (sales revenue) 2,400 1, Formulae: 3,200 1,600 1,600 4,000 1,600 2,400 Margin of safety (units) = actual units BEP units Margin of safety (revenue) = actual revenue BEP revenue or actual units BEP units x selling price per unit ACCOUNTING AND FINANCE 3

4 BREAK-EVEN ANALYSIS Task 1 Use the following information supplied by Julie Carter to complete the table and answer the questions that follow. Total fixed costs 12,000 Variable costs per unit: materials 7 wages 5 12 Selling price per unit 20 Units of Fixed Variable Total Sales Profit output costs costs costs revenue (loss) ,000 1,500 2,000 2,500 3,000 (a) (b) (c) What is the break-even point in units and sales revenue? What is the margin of safety (in units and sales revenue) at an output of 2,000 units? How much is the profit when 3,000 units are produced? 4 ACCOUNTING AND FINANCE

5 BREAK-EVEN ANALYSIS Task 2 Julie is considering reducing the selling price to 18 per unit although the costs would remain unchanged. Draw up another table to show the effect of this change on the figures then answer the following questions. (a) (b) (c) What is the break-even point in units and sales revenue? What is the margin of safety (in units and sales revenue) at an output of 2,500 units? How much is the profit at an output of 2,500 units? ACCOUNTING AND FINANCE 5

6 BREAK-EVEN ANALYSIS Suggested solution to Task 1 Units of Fixed Variable Total Sales Profit output costs costs costs revenue (loss) 0 12,000 12,000 (12,000) ,000 6,000 18,000 10,000 (8,000) 1,000 12,000 12,000 24,000 20,000 (4,000) 1,500 12,000 18,000 30,000 30,000 2,000 12,000 24,000 36,000 40,000 4,000 2,500 12,000 30,000 42,000 50,000 8,000 3,000 12,000 36,000 48,000 60,000 12,000 (a) Break-even point = 1,500 units or 30,000 sales revenue. (b) Margin of safety at 2,000 units = 2,000 1,500 = 500 units 500 units x 20 = 10,000 sales revenue (c) Profit at 3,000 units = 12,000 Suggested solution to Task 2 Units of Fixed Variable Total Sales Profit output costs costs costs revenue (loss) 0 12,000 12,000 (12,000) ,000 6,000 18,000 9,000 (9,000) 1,000 12,000 12,000 24,000 18,000 (6,000) 1,500 12,000 18,000 30,000 27,000 (3,000) 2,000 12,000 24,000 36,000 36,000 2,500 12,000 30,000 42,000 45,000 3,000 3,000 12,000 36,000 48,000 54,000 6,000 (a) Break-even point = 2,000 units or 36,000 sales revenue (b) Margin of safety = 2,500 2,000 units = 500 units 500 units x 20 = 10,000 sales revenue (c) Profit at 2,500 units = 3,000 6 ACCOUNTING AND FINANCE

7 BREAK-EVEN ANALYSIS Break-even charts A chart is a simple method of conveying information, particularly where there are many figures to be read. A line chart is considered the most suitable way of showing the data in the previous tables. A break-even chart displays the following details: fixed costs shown as a horizontal line total costs (fixed + variable costs) shown as a straight line sloping upwards from the start of the fixed costs line revenue (sales) an upward sloping line starting from the origin (indicated by 0) of the graph where no output results in no revenue. It has been constructed from the table on page 2, and shows fixed costs, total costs, revenue lines and the BEP. Break-even chart S a l e s 4,000 3,000 a n d c o s t s 2,000 1,000 BEP Output (units) Fixed costs Total costs Sales revenue Break-even point is where the sales revenue and total costs lines cross. The area of profit/loss at any level of output can be measured between the sales revenue and total costs lines: the area of profit, known as the margin of safety, is to the right of breakeven point the area of loss is to the left of break-even point. ACCOUNTING AND FINANCE 7

8 BREAK-EVEN ANALYSIS Constructing a break-even chart Before a break-even chart is produced, the following points should be considered: the level of activity is always shown on the horizontal axis and it must allow for all levels of production to be shown sales revenue and costs (in ) are shown on the vertical axis: the scale chosen should allow for the highest possible figure (usually the highest sales figure) the chart must have a title the axes (vertical and horizontal) must be clearly labelled a key must be shown to identify each line (or the lines can be labelled) the sales revenue line will always begin at the origin of the graph (no sales = no revenue) the fixed costs line is horizontal (fixed costs do not change with changes in production levels) the total costs line starts at the same point as the fixed costs line the break-even point must be clearly labelled. Task 3 (a) Using graph paper, draw a break-even chart to illustrate the figures in the table for Task 1 (p. 4). Label clearly the fixed costs, total costs and revenue lines and the break-even point. (b) On the same chart, add the new sales revenue line for the figures in Task 2 (p. 5), showing the new break-even point. 8 ACCOUNTING AND FINANCE

9 BREAK-EVEN ANALYSIS Suggested solution to Task 3(a) 60,000 Break-even chart S a l e s a n d c o s t s 50,000 40,000 30,000 20,000 10,000 BEP ,000 1,500 2,000 2,500 3,000 Output (units) Fixed costs Total costs Sales revenue Suggested solution to Task 3(b) 60,000 Break-even chart S a l e s a n d c o s t s 50,000 40,000 30,000 20,000 10,000 BEP 1 BEP ,000 1,500 2,000 2,500 Output (units) Fixed costs Total costs Sales revenue 3,000 Sales revenue (b) ACCOUNTING AND FINANCE 9

10 BREAK-EVEN ANALYSIS Break-even charts: exercises Exercise 1 (a) Using the data given below prepare a break-even chart to show fixed costs, total costs, sales and break-even point. Data Total fixed costs 4,000 Variable costs per unit 15 Selling price per unit 25 Projected output levels units (b) From your chart find the break-even point in (i) units of output (ii) sales value. (c) Find the profit at output levels of 500 and 700 units. Exercise 2 (a) Using the data given below prepare a break-even chart to show fixed costs, total costs, sales and break-even point. Data Total fixed costs 48,000 Variable costs per unit 12 Selling price per unit 24 Projected output levels 1,000 7,000 units (b) From your chart find the break-even point in (i) units of output (ii) sales value (c) Find the profit at outputs of 5,000 and 7,000 units. 10 ACCOUNTING AND FINANCE

11 BREAK-EVEN ANALYSIS Exercise 3 (a) Prepare a break-even chart to show fixed costs, total costs and sales revenue lines. Indicate the break-even point. Data Variable costs per unit: materials 10 labour 15 Selling price per unit 40 Total fixed costs 60,000 Projected output levels 1,000 8,000 units (b) From your chart find the break-even point in (i) units of output (ii) sales value (c) (d) (e) Find the profit expected at outputs of 6,000 and 8,000 units. Management are considering increasing the selling price to 45 per unit. Add this new sales line to your chart and show the new break-even point. State the new break-even point in (i) units of output (ii) sales value (f) Find the new profit expected at outputs of 4,000 and 6,000 units. ACCOUNTING AND FINANCE 11

12 BREAK-EVEN ANALYSIS Exercise 4 (a) Using the following information prepare a break-even chart, labelling break-even point. Data Projected output levels 1,000 7,000 units Total fixed costs 40,000 Variable costs per unit: materials 12 wages 10 Selling price per unit 30 (b) From your chart find the break-even point in (i) units of output (ii) sales value (c) (d) (e) Find the profit expected at outputs of 6,000 and 7,000 units. It may be possible to reduce the cost of materials to 10 per unit. Add the new total costs line to your chart and show the new break-even point. State the new break-even point in (i) units of output (ii) sales value (f) Find the new profit expected at outputs 5,000 and 7,000 units. 12 ACCOUNTING AND FINANCE

13 BREAK-EVEN ANALYSIS Exercise 5 Study the break-even chart below and answer the questions that follow. S a l e s a n d c o s t s 14,000 12,000 BEP 8,000 6,000 4,000 2, Output (units) Fixed costs Total costs Sales revenue 10,000 Break-even chart 700 (a) (b) How much are the fixed costs? What is the total variable cost of making 100 units? (c) What is the total cost of producing (i) 100 units (ii) 300 units? (d) What revenue is received from (i) 200 units (ii) 500 units? (e) Give the break-even point in units of output and in sales revenue. (f) Find the profit made at the following levels of output: 500 units, 600 units and 700 units. ACCOUNTING AND FINANCE 13

14 BREAK-EVEN ANALYSIS Exercise 6 Study the break-even chart below and answer the questions that follow. S a l e s a n d c o s t s 25,000 20,000 15,000 10,000 5,000 Break-even chart Output (units) Fixed costs Total costs BEP 600 Sales revenue (a) (b) How much are the fixed costs? What is the total variable cost of making 300 units? (c) What is the total cost of producing (i) 300 units (ii) 600 units? (d) What revenue is received from (i) 300 units (ii) 600 units? (e) Give the break-even point in units of output and in sales revenue. (f) Find the profit made at the following levels of output: 700 units and 800 units. 14 ACCOUNTING AND FINANCE

15 BREAK-EVEN ANALYSIS Break-even charts: suggested solutions to exercises Exercise 1 (a) S a l e s a n d c o s t s (b) Break-even point = 400 units; 10,000 (c) Profit at 500 units = 1,000 Profit at 700 units = 3,000 Exercise 2 (a) S a l e s a n d c o s t s 18,000 16,000 14,000 12,000 10,000 Fixed costs Total costs (b) Break-even point = 4,000 units; 96,000 (c) Profit at 5,000 units = 12,000 Profit at 7,000 units = 36,000 Break-even chart BEP 8,000 6,000 4,000 2, , , ,000 Fixed costs Output (units) Break-even chart 120,000 BEP 100,000 80,000 60,000 40,000 20, ,000 2,000 3,000 4,000 5,000 Sales revenue Sales revenue Output (units) Total costs 6,000 7,000 ACCOUNTING AND FINANCE 15

16 BREAK-EVEN ANALYSIS Exercise 3 (a) S a l e s a n d c o s t s (b) Break-even point = 4,000 units; 160,000 (c) Profit at 6,000 units = 30,000 Profit at 8,000 units = 60,000 (d) S a l e s a n d c o s t s 400, , , , , , , ,000 Fixed costs Total costs Fixed costs Total costs (e) Break-even point = 3,000 units; 120,000 (f) Profit at 4,000 units = 20,000 Profit at 6,000 units = 60,000 Break-even chart BEP 0 0 1,000 2,000 3,000 4,000 5,000 Output (units) Break-even chart Output (units) Sales BEP 0 0 1,000 2,000 3,000 4,000 5,000 Sales 6,000 6,000 7,000 7,000 Sales 2 8,000 8, ACCOUNTING AND FINANCE

17 BREAK-EVEN ANALYSIS Exercise 4 (a) S a l e s a n d c o s t s Fixed costs Total costs (b) Break-even point = 5,000 units; 150,000 (c) Profit at 6,000 units = 8,000 Profit at 7,000 units = 16,000 (d) S a l e s a n d c o s t s 250, , , ,000 50, , , , , ,000 2,000 3,000 4,000 5,000 50,000 Fixed costs (e) New break-even point = 4,000 units; 120,000 (f) Profit at 5,000 units = 10,000 Profit at 7,000 units = 30,000 Break-even chart BEP Output (units) Break-even chart 0 0 1,000 2,000 3,000 4,000 5,000 Sales 6,000 BEP Output (units) Total costs 6,000 Total costs 2 7,000 7,000 Sales ACCOUNTING AND FINANCE 17

18 BREAK-EVEN ANALYSIS Exercise 5 (a) Total fixed costs = 4,000 (b) Variable cost of 100 units = 1,000 (c) Total cost of 100 units = 5,000 Total cost of 300 units = 7,000 (d) Revenue from 200 units = 3,600 Revenue from 500 units = 9,000 (e) Break-even point = 500 units; 9,000 (f) Profit at 500 units = 0 Profit at 600 units = 800 Profit at 700 units = 1,600 Exercise 6 (a) Total fixed costs = 6,000 (b) Variable cost of 300 units = 6,000 (c) Total cost of 300 units = 12,000 Total cost of 600 units = 18,000 (d) Revenue from 300 units = 9,000 Revenue from 600 units = 18,000 (e) Break-even point = 600 units; 18,000 (f) Profit at 700 units = 1,000 Profit at 800 units = 2, ACCOUNTING AND FINANCE

19 BREAK-EVEN ANALYSIS Contribution in break-even analysis calculation of BEP Although break-even charts are easily produced and interpreted, it is not necessary to have a chart to find the profitability of a product at different output levels. This can be done by simple calculation. The word contribute is familiar in its usual meaning of give or donate. In break-even analysis the word contribution is used for the amount which the sale of each unit gives towards meeting the fixed costs. In other words, the amount left over after meeting the variable costs can be put towards the fixed costs. Once the fixed costs have been covered, that contribution becomes profit. Example Lightwell makes lamps and is investigating the profitability of producing a new design. The following figures are available. Estimated variable cost per lamp 40 Selling price per lamp 60 Total fixed costs 4,000 (a) How much is the contribution per lamp? Contribution per lamp = selling price variable costs = = 20 (b) If each lamp can contribute 20 towards meeting the fixed costs, how many lamps need to be sold in order to break even? Break-even point (BEP) = fixed costs unit contribution = 4, = 200 lamps (c) What is the sales revenue of these lamps? BEP in sales revenue = selling price x number of lamps = 60 x 200 lamps = 12,000 ACCOUNTING AND FINANCE 19

20 BREAK-EVEN ANALYSIS Check: Sales revenue of 200 units = 60 x 200 = 12,000 Less variable cost of 200 units = 40 x 200 = 8,000 Total contribution from 200 units = 12,000 8,000 = 4,000 Fixed costs = 4,000 At break-even point, total contribution equals total fixed costs. Formulae: BEP (units) = fixed costs/unit contribution BEP (revenue) = fixed costs/unit contribution x selling price per unit 20 ACCOUNTING AND FINANCE

21 BREAK-EVEN ANALYSIS Task 4 Complete the figures in the following table. Firm Selling price Variable cost Contribution Fixed BEP BEP per unit per unit per unit costs (units) (revenue) a ,000 b 5 3 5,000 c 8 7 4,000 d ,000 e ,000 ACCOUNTING AND FINANCE 21

22 BREAK-EVEN ANALYSIS Suggested solution to Task 4 Firm Selling price Variable cost Contribution Fixed BEP BEP per unit per unit per unit costs (units) (revenue) a ,000 1,000 30,000 b ,000 2,500 12,500 c ,000 4,000 32,000 d ,000 1, ,000 e ,000 3,000 1,140, ACCOUNTING AND FINANCE

23 BREAK-EVEN ANALYSIS Contribution in break-even analysis calculation of profit Break-even analysis can be used to estimate profit or loss at various levels of output. On a break-even chart, the margin of safety is the area to the right of break-even point where output is greater than break-even point and a profit is shown. The margin of safety is the excess of sales over break-even point and can be expressed in sales volume (units) and sales revenue ( ). At break-even point fixed costs have been covered therefore in the margin of safety contribution becomes profit. The calculation of profit is therefore very simple. In the Lightwell example on p. 19, break-even point is 200 units therefore all output above 200 units results in profit. The table below shows how much profit will be made at output levels of 250, 320, 400, 480 and 500 units. Output BEP Margin Contribution Profit level (units) of safety per unit (units) (units) , , , , ,000 Check: Output Unit Total Fixed Profit level contribution contribution costs (units) ,000 4,000 1, ,400 4,000 2, ,000 4,000 4, ,600 4,000 5, ,000 4,000 7,000 ACCOUNTING AND FINANCE 23

24 BREAK-EVEN ANALYSIS Contribution in break-even analysis calculation of required output As well as being used to forecast profit or loss at different levels of output, breakeven analysis is also useful in calculating the output required to give a certain amount of profit. After break-even point, contribution becomes profit therefore: total contribution required = fixed costs + desired profit. Example M Morrison has provided the following information: Selling price per unit 30 Variable costs per unit 20 Contribution per unit 10 Total fixed costs 2,000 (a) What is the total contribution required to give a profit of 1,000? (b) Total contribution required = fixed costs + profit = 2, ,000 = 3,000 How many units will give this total contribution? Total contribution required = 3,000 Unit contribution = 10 Output required = 3, = 300 units 24 ACCOUNTING AND FINANCE

25 BREAK-EVEN ANALYSIS Check: Break-even point = 2, = 200 units Profit required = 1,000 Unit contribution = 10 Number of profitable units = = 1, units Total output required = break-even point + profitable units = units = 300 units ACCOUNTING AND FINANCE 25

26 BREAK-EVEN ANALYSIS Task 5 Complete the figures in the following table using the information in the example on p. 24. Profit Fixed Total Unit Required required costs contribution contribution output (units) 1,000 2,000 3, ,800 2, , ,000 3,500 Check: Required Unit Profitable Break-even Required profit contribution output point output (units) (units) (units) 1, , , ,000 3, ACCOUNTING AND FINANCE

27 BREAK-EVEN ANALYSIS Suggested solution to Task 5 Profit Fixed Total Unit Required required costs contribution contribution output (units) 1,000 2,000 3, ,800 2,000 3, ,300 2,000 4, ,000 2,000 5, ,500 2,000 5, Check: Required Unit Profitable Break-even Required profit contribution output point output (units) (units) (units) 1, , , , , ACCOUNTING AND FINANCE 27

28 BREAK-EVEN ANALYSIS Break-even analysis: theory questions Question 1 Break-even analysis is seen as a valuable tool for the management accountant. List 3 of its uses. Question 2 List 4 assumptions made in the use of break-even analysis. Question 3 Explain what is meant by the following terms used in break-even analysis: (a) unit contribution (b) margin of safety (c) break-even point (d) fixed and variable costs. Question 4 Describe how each of the following lines can be shown on a break-even chart: (a) fixed costs (b) total costs (c) sales. Question 5 After break-even point, contribution becomes profit. Explain what is meant by this statement. 28 ACCOUNTING AND FINANCE

29 BREAK-EVEN ANALYSIS Break-even analysis: suggested solutions to theory questions Question 1 Three uses of break-even analysis are: 1 to calculate the break-even point in units of output and in sales revenue for a product 2 to estimate the profit/loss that will result from any given level of output 3 to find the level of output needed for a given profit figure. Question 2 Four assumptions made in the use of break-even analysis are: 1 all costs are either fixed or variable 2 the selling price remains unchanged for the entire range of output regardless of different markets and conditions 3 costs remain unchanged because there are no changes in materials, wages or methods 4 there is no adjustment for stock figures because production is equal to sales. Question 3 (a) (b) (c) (d) Unit contribution is the difference between the selling price and the variable costs of one unit. It is the amount the unit can give towards meeting the fixed costs and, after fixed costs are covered, towards profit. Margin of safety is the profitable output above break-even point and can be expressed in units or sales revenue. It is shown to the right of breakeven point on a break-even chart. Break-even point is the point at which fixed costs are covered and neither a profit nor a loss is made. Total contribution is equal to fixed costs and total revenue is equal to total costs. Fixed costs remain unchanged regardless of changes in the level of production. Variable costs vary in proportion to changes in production levels. ACCOUNTING AND FINANCE 29

30 BREAK-EVEN ANALYSIS Question 4 (a) (b) (c) The fixed costs line is horizontal because fixed costs remain constant at different output levels. The total costs line slopes upward to the right from the start of the fixed costs line. The sales line slopes upward to the right from the origin of the graph where no sales shows no revenue. Question 5 Contribution is the difference between selling price and variable costs and, in the first place, goes towards meeting fixed costs. Once fixed costs have been covered, i.e. at break-even point, any further contribution that arises from additional sales is profit as only the variable costs have to be met. 30 ACCOUNTING AND FINANCE

31 BREAK-EVEN ANALYSIS Contribution in break-even analysis: exercises Exercise 1 Three firms have supplied the following information: A Anderson B Benson C Cameron Variable costs per unit Selling price per unit Fixed costs 4,500 6,400 17,500 (a) (b) (c) Calculate the contribution per unit for each firm. For each firm find the break-even point in units of output. For each firm find the sales revenue at break-even point. Exercise 2 A manufacturing firm expects to sell 8,000 units in the next year and has provided the following figures: Selling price per unit 40 Variable costs per unit 22 Total fixed costs 63,000 (a) (b) (c) (d) Calculate the contribution per unit. Find the break-even point in units of output. What is the sales revenue of these units? What is the margin of safety in (i) units (ii) sales revenue ( )? ACCOUNTING AND FINANCE 31

32 BREAK-EVEN ANALYSIS Exercise 3 Alert plc installs burglar alarm systems and expects to install 400 units of System A in the next year. Costs are estimated as follows: Total fixed costs 81,400 Selling price per unit 850 Variable costs per unit 480 (a) (b) (c) (d) Calculate the contribution per unit. Find the break-even point in units. Find the sales revenue of these units. What is the margin of safety in (i) units (ii) sales revenue ( )? Exercise 4 The following data has been supplied by D Denver, who is considering manufacturing a new style of shirt: Selling price per unit Variable costs per unit: materials 6.50 wages 4.50 Total fixed costs 33,000 (a) (b) (c) (d) (e) (f) Calculate the contribution per shirt. Find the break-even point in units of output. What is the sales revenue of these units? What is the new contribution per shirt if they could be sold at 22 each? Calculate the new break-even point in units at the increased selling price. What is the sales revenue of these units? 32 ACCOUNTING AND FINANCE

33 BREAK-EVEN ANALYSIS Exercise 5 Novelties plc assembles novel clocks and and has estimated the following figures for a new style: Selling price per unit 34 Variable costs per unit: component parts 12 wages 6 Total fixed costs 8,960 (a) (b) (c) (d) (e) Calculate the contribution per clock. Find the break-even point in units of output. Find the sales revenue of these units. If the cost of the component parts is increased to 14, what is the new contribution per unit? Find the new break-even point in units and in sales revenue. Exercise 6 Downies plc makes quilts and has budgeted the following figures for an output of 20,000 units: Total fixed costs 198,400 Selling price per unit 85 Variable costs per unit 54 (a) (b) (c) (d) Calculate the contribution per quilt. Find the break-even point in (i) units and (ii) sales revenue. What is the margin of safety in (i) units and (ii) sales revenue? If fixed costs were decreased to 179,800 what would be the new breakeven point in (i) units and (ii) sales revenue? ACCOUNTING AND FINANCE 33

34 BREAK-EVEN ANALYSIS Exercise 7 J Jones has supplied the following figures: Variable costs per unit: materials 36 wages 15 expenses 3 Selling price per unit 78 Total fixed costs 60,000 (a) (b) (c) (d) How much is the contribution per unit? Find the break-even point in units. What would be the sales revenue of these units? Calculate the profit at output levels of 3,000 and 4,000 units. Exercise 8 Outdoor Relaxing plc produces loungers and hopes to sell 1,000 in the coming year. The following figures are forecast: Selling price per unit 52 Variable costs per unit 28 Total fixed costs 13,920 (a) (b) (c) Calculate the contribution per unit. Find the break-even point in (i) units and (ii) sales revenue. Calculate the profit at output levels of 640 and 720 units. 34 ACCOUNTING AND FINANCE

35 BREAK-EVEN ANALYSIS Exercise 9 Deeside Woodworkers produces clocks and the following figures are available: Selling price per unit 80 Variable costs per unit 55 Total fixed costs 12,000 (a) (b) Calculate the contribution per clock. Find the break-even point in units and in sales revenue. (c) Calculate the profit achieved at the following output levels: 500 and 600 units. (d) (e) If the selling price is increased to 85 while costs remain the same, what is the new contribution per clock? Find the new break-even point in units and in sales revenue. Exercise 10 A leather company produces briefcases and has provided the following data: Total fixed costs 19,800 Variable costs per unit: materials 30 fastenings and locks 12 wages 25 Selling price per unit 139 You are required to find the following: (a) (b) (c) contribution per unit break-even point in units and in sales revenue profit at output levels of 300 and 400 units (d) the output level required to give a profit of 7,920. ACCOUNTING AND FINANCE 35

36 BREAK-EVEN ANALYSIS Exercise 11 The following figures relate to ornamental trees supplied by nurserymen J & M Dawson, who have fixed costs of 6,480: Selling price per tree 36 Variable costs per tree 20 (a) (b) (c) (d) Find the contribution per unit. Find the break-even point in units and in sales revenue. How many trees would need to be sold in order to achieve the following profit levels: 1,360 and 5,040? How much is the profit at output levels of 450 and 580 units? Exercise 12 Soundsleep plc produces beds which sell at 580 each. The following details of costs have been supplied: Variable costs per unit: materials 80 component parts 120 wages 100 Total fixed costs 686,000 (a) (b) (c) (d) Find the contribution per unit. Find the break-even point in units and in sales revenue. How many beds would need to be sold in order to achieve the following profit levels: 16,800 and 64,400? How much is the profit at output of 5,000 units? 36 ACCOUNTING AND FINANCE

37 BREAK-EVEN ANALYSIS Contribution in break-even analysis: suggested solutions to exercises Exercise 1 A Anderson B Benson C Cameron (a) Selling price per unit Variable costs per unit Contribution per unit (b) BEP = fixed costs unit contribution 4, , ,500 5 = 1,500 = 1,600 = 3,500 units units units (c) Sales revenue 1,500 x 6 1,600 x ,500 x = 9,000 = 13,600 = 41,300 Exercise 2 (a) Contribution per unit = selling price variable costs = = 18 fixed costs (b) Break-even point = unit contribution = 63, = 3,500 units (c) Sales revenue = 40 x 3,500 units = 140,000 (d) Margin of safety (i) = sales break-even point = 8,000 3,500 units = 4,500 units (ii) = 40 x 4,500 units = 180,000 ACCOUNTING AND FINANCE 37

38 BREAK-EVEN ANALYSIS Exercise 3 (a) Contribution per unit = selling price variable costs = = 370 (b) Break-even point = = fixed costs unit contribution 81, = 220 units (c) Sales revenue = 850 x 220 units = 187,000 (d) Margin of safety (i) = sales break-even point = units = 180 units (ii) = 850 x 180 units = 153, ACCOUNTING AND FINANCE

39 BREAK-EVEN ANALYSIS Exercise 4 (a) Contribution per shirt = selling price variable costs = = 10 fixed costs (b) Break-even point = unit contribution 33,000 = 10 = 3,300 units (c) Sales revenue = 21 x 3,300 units = 69,300 (d) Contribution per shirt = = 11 (e) Break-even point 33,000 = 11 = 3,000 units (f) Sales revenue = 22 x 3,000 units = 66,000 ACCOUNTING AND FINANCE 39

40 BREAK-EVEN ANALYSIS Exercise 5 (a) Contribution per unit = selling price variable costs = = 16 (b) Break-even point = fixed costs unit contribution = 8, = 560 units (c) Sales revenue = 34 x 560 units = 19,040 (d) New contribution = = 14 (e) New break-even point = 8, = 640 units Sales revenue = 34 x 640 = 21, ACCOUNTING AND FINANCE

41 BREAK-EVEN ANALYSIS Exercise 6 (a) Contribution per quilt = selling price variable costs = = 31 (b) Break-even point (i) = = fixed costs unit contribution 198, = 6,400 units (ii) = 85 x 6,400 quilts = 544,000 (c) Margin of safety (i) = 20,000 6,400 units = 13,600 units (ii) = 85 x 13,600 units = 1,156,000 (d) New break-even point (i) 179,800 = 31 = 5,800 units (ii) = 85 x 5,800 = 493,000 ACCOUNTING AND FINANCE 41

42 BREAK-EVEN ANALYSIS Exercise 7 (a) Contribution per unit = selling price variable costs = = 24 (b) Break-even point fixed costs = unit contribution = 60, = 2,500 units (c) Sales revenue = 78 x 2,500 units = 195,000 (d) Output BEP Margin of Profit level (units) safety (units) (units) 3,000 2, x 24 = 12,000 4,000 2,500 1,500 1,500 x 24 = 36, ACCOUNTING AND FINANCE

43 BREAK-EVEN ANALYSIS Exercise 8 (a) Contribution per unit = selling price variable costs = = 24 (b) Break-even point (i) = fixed costs unit contribution = 13, = 580 units (ii) = 52 x 580 units = 30,160 (c) Output BEP Margin of Profit level (units) safety (units) (units) x 60 = 1, x 140 = 3,360 ACCOUNTING AND FINANCE 43

44 BREAK-EVEN ANALYSIS Exercise 9 (a) Contribution per clock = = 25 (b) Break-even point = = = 480 clocks Sales revenue = 80 x 480 = 38,400 (c) Output BEP Margin of Profit level (units) safety (units) (units) x 25 = x 25 = 3,000 (d) New contribution = = 30 (e) New break-even point = fixed costs unit contribution 12, , = 400 units Sales revenue = 85 x 400 = 34, ACCOUNTING AND FINANCE

45 BREAK-EVEN ANALYSIS Exercise 10 (a) Contribution per unit = selling price variable costs = = 72 fixed costs (b) Break-even point = unit contribution 19,800 = 72 = 275 units Sales revenue = 139 x 275 units = 38,225 (c) Output BEP Margin of Profit level (units) safety (units) (units) x 25 = 1, x 125 = 9,000 (d) Total contribution required = fixed costs + profit = 19, ,920 = 27,720 Unit contribution = 72 total contribution Output required = unit contribution = 27, = 385 units ACCOUNTING AND FINANCE 45

46 BREAK-EVEN ANALYSIS Exercise 11 (a) Contribution per unit = selling price variable costs = = 16 (b) Break-even point fixed costs = unit contribution 6,480 = 16 = 405 units Sales revenue = 36 x 405 units = 14,580 (c) Fixed Profit Total Unit Output costs required contribution contribution required required 6,480 1,360 7, , = 490 units 11,520 6,480 5,040 11, = 720 units (d) Output BEP Margin of Profit level (units) safety (units) (units) x 45 = x 175 = 2, ACCOUNTING AND FINANCE

47 BREAK-EVEN ANALYSIS Exercise 12 (a) Contribution per unit = selling price variable costs = = 280 fixed costs (b) Break-even point = unit contribution 686,000 = 280 = 2,450 units Sales revenue = 580 x 2,450 units = 1,421,000 (c) Fixed Profit Total Unit Output costs required contribution contribution required required 686,000 16, , ,800 = 2,510 units , ,000 64, , = 2,680 units 280 (d) Output BEP Margin of Profit level (units) safety (units) (units) 5,000 2, x 550 = 154,000 ACCOUNTING AND FINANCE 47

48 BREAK-EVEN ANALYSIS Contribution in break-even analysis: extension exercises Exercise E1 Wondersew produces sewing machines that are sold at 1,200 each. The following costs are incurred. Fixed costs 157,500 Variable costs: materials 80 component parts 350 wages 140 You are required to calculate the following: (a) the contribution per sewing machine (b) the break-even point in units and sales revenue (c) the profit at output levels of 320 and 425 units (d) the output level required to give a profit of 75,600 (e) the new contribution per unit if the selling price is reduced to 1,095 (f) the break-even point at the new selling price (g) the new output level required to give the same profit of 75,600. Exercise E2 Scotstoun Display Stands estimates that it can sell 2,000 display stands at 200 each. The costs of production are shown below. Variable costs per unit: materials 80 labour 40 Total fixed costs 96,000 You are required to find: (a) the break-even point in units and in sales revenue (b) the profit at the following levels of production: 1,400 units and 2,000 units (c) the new break-even point if the selling price is increased by 10% (d) the new profit at output levels of 1,400 and 2,000 units. 48 ACCOUNTING AND FINANCE

49 BREAK-EVEN ANALYSIS Exercise E3 Stonehaven Clocks makes alarm clocks and has supplied the following figures. Output 6,000 clocks Total fixed costs 60,000 Selling price per clock 37 Variable costs per clock: materials 6 component parts 4 labour 12 You are required to calculate the following: (a) the break-even point in units and sales revenue (b) the present profit figure. Stonehaven Clocks is considering increasing output to 8,000 clocks and estimates that the cost of materials per unit will be reduced to 5. Calculate: (c) the new break-even point in units and sales revenue (d) the new profit figure. ACCOUNTING AND FINANCE 49

50 BREAK-EVEN ANALYSIS Contribution in break-even analysis: suggested solutions to extension exercises Exercise E1 (a) Contribution per unit = selling price variable costs = 1, = 630 fixed costs (b) Break-even point = unit contribution 157,500 = 630 = 250 units Sales value = 1,200 x 250 units = 300,000 (c) Output BEP Margin of Profit level (units) safety (units) (units) x 70 = 44, x 175 = 110,250 (d) Total contribution required = fixed costs + required profit = 157, ,600 = 233,100 Unit contribution = 630 total contribution Output required = unit contribution 233,100 = 630 = 370 units (e) New contribution = 1, = 525 (f) New break-even point 157,500 = 525 = 300 units 50 ACCOUNTING AND FINANCE

51 BREAK-EVEN ANALYSIS (g) Total contribution required = 233,100 Unit contribution = 525 Output required 233,100 = 525 = 444 units ACCOUNTING AND FINANCE 51

52 BREAK-EVEN ANALYSIS Exercise E2 (a) Unit contribution = = 80 fixed costs Break-even point = = unit contribution 96, = 1,200 units Sales revenue = 1,200 x 200 = 240,000 (b) Profit = (output BEP) x unit contribution Output 1,400 units 2,000 units 1,400 1,200 2,000 1, x x 80 16,000 64,000 (c) New selling price = 220 New contribution = = 100 New break-even point = 96, = 960 units New sales revenue = 960 x 220 = 211,200 (d) New profit Output 1,400 units 2,000 units 1, , x 100 1,040 x , , ACCOUNTING AND FINANCE

53 BREAK-EVEN ANALYSIS Exercise E3 (a) Unit contribution = = 15 Break-even point = = fixed costs unit contribution 60, = 4,000 units Sales revenue = 4,000 x 37 = 148,000 (b) Profit = (6,000 BEP) x 15 = (6,000 4,000) x 15 = 2,000 x 15 = 30,000 (c) New variable costs = 21 New contribution = = 16 60,000 New break-even point = 16 = 3,750 units Sales revenue = 3,750 x 37 = 138,750 (d) New profit = (8,000 BEP) x 16 = (8,000 3,750) x 16 = 4,250 x 16 = 68,000 ACCOUNTING AND FINANCE 53

54 54 ACCOUNTING AND FINANCE

55 Section Two Profit Maximisation Contents Profit maximisation - limiting factor, summary note, tasks, suggested solutions Exercises 1-12 with suggested solutions Extension exercises 1-3 with suggested solutions ACCOUNTING AND FINANCE 55

56 56 ACCOUNTING AND FINANCE

57 SECTION TWO PROFIT MAXIMISATION Profit maximisation: limiting factor Most businesses are set up with a view to making a profit, preferably as high a profit as possible. Maximising profit simply means making as much profit as possible from the resources available. This is usually achieved by making as much as can be sold if demand for a product is limited there is no point in making more even though it may be possible to do so. Sometimes demand for a product may be high but production may be limited by factors such as: scarcity of materials scarcity of labour limited machine capacity limited number of machines limited space. These factors are called limiting factors (or key factors). If a limiting factor exists, management will have to decide which level of output will make most profit, taking into account the limiting factor. Instead of studying the contribution per unit, contribution must be considered in the light of the limiting factor. Example Two products, A and B, are being produced and details are as follows: A B Contribution per unit Number of labour hours per unit 4 2 Number of units demanded 10,000 12,000 Total labour hours available 60,000 hours Total fixed costs 160,000 ACCOUNTING AND FINANCE 57

58 PROFIT MAXIMISATION If demand is to be satisfied the total number of labour hours required would be: Product A Product B 10,000 x ,000 x 2 40, ,000 = 64,000 hours The number of labour hours required is 64,000 but only 60,000 labour hours are available. Since there is a shortage of 4,000 hours, labour is the limiting factor. How will this problem be solved? Should one or both products be cut back? B has a lower unit contribution than A so should only B be reduced? Before a decision is taken, the contribution per labour hour must be examined. A B Contribution per unit Number of labour hours 4 2 Contribution per labour hour 3 6 Only now can the order of priority be decided. Since the product giving the highest contribution per labour hour is B, the full demand for B will be met and the production of A will be cut by 4,000 hours. Production will be planned thus: 1 Product B 24,000 hours/2 = 12,000 units 2 Product A 60,000 24,000 hours = 36,000 hours/4 = 9,000 units How much profit will be made? A B Total Number of labour hours 36,000 24,000 60,000 Contribution per labour hour 3 6 Total contribution 3 x 36,000 6 x 24, , , ,000 Less fixed costs 160,000 Profit (maximised) 92, ACCOUNTING AND FINANCE

59 PROFIT MAXIMISATION Task 6 Skye Weavers plc produces 2 items, rugs and scarves. Figures available are as follows: Total labour hours available 20,000 Total fixed costs 200,000 Product Rugs Scarves Selling price per unit Variable costs per unit 40 8 Labour hours per unit 2 1 Number of units demanded 5,000 12,000 Use the accompanying worksheet to carry out the following tasks: (a) (b) (c) (d) (e) (f) (g) (h) Compare the hours available with the hours required to find the shortage of labour hours. What is the limiting factor for Skye Weavers plc? Calculate the contribution per labour hour for each product. Show the order of priority for production. Give a reason for your answer. Show how many labour hours would be used in the production of both rugs and scarves. Find the total contribution from rugs and scarves. Subtract the total fixed costs to find the profit from production. How many scarves and rugs would be made in the hours in (e)? ACCOUNTING AND FINANCE 59

60 PROFIT MAXIMISATION Task 6: worksheet Rugs Scarves Total (a) Units demanded 5,000 12,000 Labour hours per unit Total labour hours required Labour hours available... Shortage of labour hours... (b) The limiting factor is... (c) Contribution per unit Labour hours per unit Contribution per labour hour (d) Order of priority: first second Reason (e) Labour hours available for production ,000 (f) Contribution per labour hour (from (c) above) Total contribution (g) Total fixed costs... Profit... (h) Scarves and rugs made ACCOUNTING AND FINANCE

61 PROFIT MAXIMISATION Suggested solution to task 6 Rugs Scarves Total (a) Units demanded 5,000 12,000 Labour hours per unit 2 1 Total labour hours required 10,000 12,000 22,000 Labour hours available 20,000 Shortage of labour hours 2,000 (b) The limiting factor is labour hours (c) Contribution per unit Labour hours per unit 2 1 Contribution per labour hour (d) Order of priority: first: rugs second: scarves Reason Rugs have higher contribution per labour hour, which is the limiting factor. The demand for rugs must therefore be met if possible. (e) Labour hours available for production 10,000 10,000 20,000 (f) Contribution per labour hour (from (c) above) Total contribution 200, , ,000 (g) Total fixed costs 200,000 Profit 120,000 (h) Scarves and rugs made 5,000 10,000 ACCOUNTING AND FINANCE 61

62 PROFIT MAXIMISATION Task 7 Islay Woodcarvers plc makes 3 products, X, Y and Z, and has provided the following information: Total machine hours available 22,000 Total fixed costs 140,000 Product X Y Z Selling price per unit Variable cost per unit Number of machine hours per unit Number of units demanded 4,000 6,000 5,000 Use the accompanying worksheet to carry out the following tasks: (a) (b) (c) (d) (e) (f) (g) (h) Compare the hours available with the hours required to find the shortage of machine hours. What is the limiting factor for Islay Woodcarvers plc? Calculate the contribution per machine hour for each product. Show the order of priority for production. Give a reason for your answer. Show how many machine hours would be used in the production of each of the 3 products. Find the total contribution. Find the total profit. How many of each product would be made in the hours in (e)? 62 ACCOUNTING AND FINANCE

63 PROFIT MAXIMISATION Task 7: worksheet X Y Z Total (a) Units demanded Machine hours per unit Total machine hours required Machine hours available... Shortage of machine hours... (b) The limiting factor is... (c) Contribution per unit Machine hours per unit Contribution per machine hour (d) Order of priority: first: second: Reason (e) Machine hours available for production (f) Contribution per machine hour Total contribution (g) Less total fixed costs... Profit... (h) Number of units made ACCOUNTING AND FINANCE 63

64 PROFIT MAXIMISATION Suggested solution to task 7 X Y Z Total (a) Units demanded 4,000 6,000 5,000 Machine hours per unit Total machine hours required 4,000 12,000 7,500 23,500 Machine hours available 22,000 Shortage of machine hours 1,500 (b) The limiting factor is machine hours (c) Contribution per unit Machine hours per unit Contribution per machine hour (d) Order of priority: first: Z second: X third: Y Reason: Highest contribution per machine hour must take priority, followed by second highest if profit is to be maximised because machine hours are the limiting factor. (e) Machine hours available for production 4,000 10,500 7,500 22,000 (f) Contribution per machine hour Total contribution 40,000 84,000 90, ,000 (g) Less total fixed costs 140,000 Profit 74,000 (h) Number of units made 4,000 5,250 5, ACCOUNTING AND FINANCE

65 PROFIT MAXIMISATION Limiting factor: exercises Exercise 1 The total number of labour hours available in AB Components is 20,000. The firm has provided the following additional figures for products X and Y: X Y (Per unit) Contribution 4 6 Labour hours 2 2 Units demanded 5,000 7,000 You are required to find the following: (a) the labour hours required to meet current demand (b) (c) (d) (e) the contribution per labour hour for each product the order of priority for production the labour hours available for each product the number of units of each product that can be made. ACCOUNTING AND FINANCE 65

66 PROFIT MAXIMISATION Exercise 2 The total number of labour hours available in Quality Doors plc is 5,500. The firm has provided the following additional figures for 2 designs, Georgian and Victorian: Georgian Victorian (Per unit) Selling price Variable costs Labour hours Units demanded 2,000 1,500 You are required to find the following: (a) the labour hours required to meet current demand (b) (c) (d) (e) (f) the contribution per unit for each product the contribution per labour hour for each product the order of priority for production the labour hours available for each product the number of units of each product that can be made. 66 ACCOUNTING AND FINANCE

67 PROFIT MAXIMISATION Exercise 3 City Shirts plc produces 3 designs Classic, City and Casual for which 18,000 machine hours are available. The following figures have been provided: Classic City Casual (Per unit) Selling price Variable cost Machine hours Units demanded 10,000 12,000 16,000 You are required to find the following: (a) the machine hours required to meet current demand (b) (c) (d) (e) (f) the contribution per unit for each product the contribution per machine hour for each product the order of priority for production the machine hours available for each style the number of units of each style that can be made. ACCOUNTING AND FINANCE 67

68 PROFIT MAXIMISATION Exercise 4 County Suits plc produces 3 designs Kelso, Selkirk and Melrose for which 2,200 machine hours are available. The following figures have been provided: Kelso Selkirk Melrose (Per unit) Selling price Variable cost Machine hours Units demanded You are required to find the following: (a) the machine hours required to meet current demand (b) (c) (d) (e) (f) the contribution per unit for each product the contribution per machine hour for each product the order of priority for production the machine hours available for each style the number of units of each style that can be made. 68 ACCOUNTING AND FINANCE

69 PROFIT MAXIMISATION Exercise 5 Scottish Greenhouses plc makes 2 products Dunkeld and Aberfeldy. Total fixed costs are 400,000 and 5,000 labour hours are available. The following figures are available: Dunkeld Aberfeldy (Per unit) Selling price 1, Variable costs Labour hours 5 4 Units demanded You are required to find the following: (a) the labour hours required to meet current demand (b) (c) (d) (e) (f) (g) (h) the contribution per unit for each product the contribution per labour hour for each product the order of priority for production the labour hours available for each style the number of units of each style that can be made the total contribution the profit after deduction of fixed costs. ACCOUNTING AND FINANCE 69

70 PROFIT MAXIMISATION Exercise 6 Rockers Ltd makes 2 styles of chair Relax and Relax-plus for which 1,800 machine hours are available. Total fixed costs amount to 30,000. The following additional information has been provided: Relax Relax-plus (Per unit) Selling price Variable costs Machine hours Units demanded You are required to find the following: (a) the machine hours required to meet current demand (b) (c) (d) (e) (f) (g) (h) the contribution per unit for each product the contribution per machine hour for each product the order of priority for production the machine hours available for each style the number of units of each style that can be made the total contribution the profit after deduction of fixed costs. 70 ACCOUNTING AND FINANCE