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

(1)

SECTION ONE

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

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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 1,000 300 1,300 800 (500) 200 1,000 600 1,600 1,600 — 300 1,000 900 1,900 2,400 500 400 1,000 1,200 2,200 3,200 1,000 500 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 £1,600.

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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)

£ £

300 200 100 8 800

400 200 200 8 1,600

500 200 300 8 2,400

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 1,600 800

3,200 1,600 1,600

4,000 1,600 2,400

Formulae:

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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

£ £ £ £ £ 0 500 1,000 1,500 2,000 2,500 3,000

(a) What is the break-even point in units and sales revenue?

(b) What is the margin of safety (in units and sales revenue) at an output of 2,000 units?

(5)

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) What is the break-even point in units and sales revenue?

(b) What is the margin of safety (in units and sales revenue) at an output of 2,500 units?

(6)

Suggested solution to Task 1

£ £ £ £ £ 0 12,000 — 12,000 — (12,000) 500 12,000 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

£ £ £ £ £ 0 12,000 — 12,000 — (12,000) 500 12,000 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

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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 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 break-even point ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 4,000 3,000 2,000 1,000 0 0 100 200 300 400 500

•

S a l e s a n d c o s t s £ Output (units)

•

Fixed costs ○

•

○ ○ Total costs Sales revenue

•

Break-even chart

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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.

(9)

Suggested solution to Task 3(a)

Suggested solution to Task 3(b)

○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 40,000 30,000 20,000 10,000 0 0 500 1,000 1,500 2,000 2,500

•

S a l e s a n d c o s t s £ Output (units)

•

Fixed costs Sales revenue

•

Break-even chart 3,000 50,000 60,000

•

○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 40,000 30,000 20,000 10,000

•

S a l e s a n d c o s t s

•

Break-even chart 50,000 60,000

•

BEP BEP 2 BEP 1 Total costs ○

•

○ ○

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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

Projected output levels 100–700 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

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.

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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) Find the profit expected at outputs of 6,000 and 8,000 units.

(d) 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.

(e) State the new break-even point in (i) units of output (ii) sales value

(12)

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

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) Find the profit expected at outputs of 6,000 and 7,000 units.

(d) 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.

(e) State the new break-even point in (i) units of output (ii) sales value

(13)

Exercise 5

Study the break-even chart below and answer the questions that follow.

(a) How much are the fixed costs?

(b) 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.

•

8,000 6,000 4,000 2,000 0 0 100 200 300 400 500 S a l e s a n d c o s t s £ Output (units)

Fixed costs Sales revenue 600 10,000 12,000 700 14,000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○

•

○

•

Break-even chart BEP Total costs ○

•

○ ○

(14)

Exercise 6

Study the break-even chart below and answer the questions that follow.

(a) How much are the fixed costs?

(b) 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.

•

10,000 5,000 0 0 100 200 300 400 500 S a l e s a n d c o s t s £ Output (units)

Fixed costs Sales revenue 600 15,000 20,000 700 25,000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○

•

○

•

Break-even chart 800

•

BEP Total costs ○

•

○ ○

(15)

Break-even charts: suggested solutions to exercises

Exercise 1

(a)

(b) Break-even point = 400 units; £10,000 (c) Profit at 500 units = £1,000

Profit at 700 units = £3,000

Exercise 2

(a)

(b) Break-even point = 4,000 units; £96,000

•

0 0 100 200 300 400 500 S a l e s a n d c o s t s £ Output (units)

600 700 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○

•

8,000 6,000 4,000 2,000 10,000 12,000 14,000 16,000 18,000

•

0 0 1,000 2,000 3,000 4,000 5,000 S a l e s a n d c o s t s £ Output (units)

6,000 7,000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○

•

80,000 60,000 40,000 20,000 100,000 120,000 140,000 160,000 180,000

•

BEP

•

BEP Total costs ○

•

○ ○ Total costs ○

•

○ ○

(16)

Exercise 3

(a)

(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)

•

100,000 0 0 _1,000 _2,000 _3,000 _4,000 _5,000 S a l e s a n d c o s t s £ Output (units)

Fixed costs Sales

6,000 200,000 300,000 7,000 400,000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○

•

○

•

Break-even chart 8,000

•

100,000 0 0 _1,000 _2,000 _3,000 _4,000 _5,000 S a l e s a n d c o s t s £ 6,000 200,000 300,000 7,000 400,000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○

•

Break-even chart 8,000

•

BEP BEP Total costs ○

•

○ ○

(17)

Exercise 4

(a)

(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)

(e) New break-even point = 4,000 units; £120,000 (f) Profit at 5,000 units = £10,000

•

100,000 50,000 0 0 1,000 2,000 3,000 4,000 5,000 S a l e s a n d c o s t s £ Output (units)

Fixed costs Sales

6,000 150,000 200,000 7,000 250,000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○

•

100,000 50,000 0 0 1,000 2,000 3,000 4,000 5,000 S a l e s a n d c o s t s £ Output (units)

Fixed costs Sales

6,000 150,000 200,000 7,000 250,000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○

•

Total costs 2

•

BEP

•

BEP Total costs ○

•

○ ○ Total costs ○

•

○ ○

(18)

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

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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

= £60 – £40 = £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) =

=

= 200 lamps (c) What is the sales revenue of these lamps?

BEP in sales revenue = selling price x number of lamps

fixed costs unit contribution

£4,000 £20

(20)

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

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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 30 15 15,000 b 5 3 5,000 c 8 7 4,000 d 140 90 50,000 e 380 260 240,000

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Firm Selling price Variable cost Contribution Fixed BEP BEP

per unit per unit per unit costs (units) (revenue)

£ £ £ £ £ a 30 15 15 15,000 1,000 30,000 b 5 3 2 5,000 2,500 12,500 c 8 7 1 4,000 4,000 32,000 d 140 90 50 50,000 1,000 140,000 e 380 260 80 240,000 3,000 1,140,000

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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) £ £ 250 200 50 20 1,000 320 200 120 20 2,400 400 200 200 20 4,000 480 200 280 20 5,600 550 200 350 20 7,000 Check:

Output Unit Total Fixed Profit

level contribution contribution costs

(units) £ £ £ £

250 20 5,000 4,000 1,000

320 20 6,400 4,000 2,400

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Contribution in break-even analysis – calculation of required

output

As well as being used to forecast profit or loss at different levels of output, break-even 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? Total contribution required = fixed costs + profit

= £2,000 + £1,000 = £3,000

(b) How many units will give this total contribution? Total contribution required = £3,000

Unit contribution = £10 Output required =

= 300 units £3,000

(25)

Check:

Break-even point =

= 200 units

Profit required = £1,000

Unit contribution = £10 Number of profitable units =

= 100 units

Total output required = break-even point + profitable units = 200 + 100 units = 300 units £2,000 £10 £1,000 £10

(26)

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 3,000 10 300 1,800 2,000 10 2,300 10 3,000 3,500 Check:

Required Unit Profitable Break-even Required

profit contribution output point output

£ £ (units) (units) (units)

1,000 10 100 200 300

1,800 10 180 200

2,300 10 200

3,000 3,500

(27)

Profit Fixed Total Unit Required

required costs contribution contribution output

£ £ £ £ (units) 1,000 2,000 3,000 10 300 1,800 2,000 3,800 10 380 2,300 2,000 4,300 10 430 3,000 2,000 5,000 10 500 3,500 2,000 5,500 10 550 Check:

Required Unit Profitable Break-even Required

profit contribution output point output

£ £ (units) (units) (units)

1,000 10 100 200 300

1,800 10 180 200 380

2,300 10 230 200 430

3,000 10 300 200 500

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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.

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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) 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. (b) 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 break-even point on a break-break-even chart.

(c) 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.

(d) Fixed costs remain unchanged regardless of changes in the level of production. Variable costs vary in proportion to changes in production levels.

(30)

Question 4

(a) The fixed costs line is horizontal because fixed costs remain constant at different output levels.

(b) The total costs line slopes upward to the right from the start of the fixed costs line.

(c) 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.

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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 £3.00 £4.50 £6.80 Selling price per unit £6.00 £8.50 £11.80

Fixed costs £4,500 £6,400 £17,500

(a) Calculate the contribution per unit for each firm.

(b) For each firm find the break-even point in units of output. (c) 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) Calculate the contribution per unit.

(b) Find the break-even point in units of output. (c) What is the sales revenue of these units? (d) What is the margin of safety in

(i) units

(32)

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) Calculate the contribution per unit. (b) Find the break-even point in units. (c) Find the sales revenue of these units. (d) 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 £21.00 Variable costs per unit:

materials £6.50

wages £4.50

Total fixed costs £33,000 (a) Calculate the contribution per shirt.

(b) Find the break-even point in units of output. (c) What is the sales revenue of these units?

(33)

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) Calculate the contribution per clock.

(b) Find the break-even point in units of output. (c) Find the sales revenue of these units.

(d) If the cost of the component parts is increased to £14, what is the new contribution per unit?

(e) 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) Calculate the contribution per quilt.

(b) Find the break-even point in (i) units and (ii) sales revenue. (c) What is the margin of safety in (i) units and (ii) sales revenue?

(d) If fixed costs were decreased to £179,800 what would be the new break-even point in (i) units and (ii) sales rbreak-evenue?

(34)

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) How much is the contribution per unit? (b) Find the break-even point in units.

(c) What would be the sales revenue of these units?

(d) 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) Calculate the contribution per unit.

(b) Find the break-even point in (i) units and (ii) sales revenue. (c) Calculate the profit at output levels of 640 and 720 units.

(35)

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) Calculate the contribution per clock.

(b) 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) If the selling price is increased to £85 while costs remain the same, what is the new contribution per clock?

(e) 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) contribution per unit

(b) break-even point in units and in sales revenue (c) profit at output levels of 300 and 400 units

(36)

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) Find the contribution per unit.

(c) How many trees would need to be sold in order to achieve the following profit levels: £1,360 and £5,040?

(d) 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

wages £100

Total fixed costs £686,000 (a) Find the contribution per unit.

(c) How many beds would need to be sold in order to achieve the following profit levels: £16,800 and £64,400?

(37)

Contribution in break-even analysis: suggested solutions to exercises

Exercise 1

A Anderson B Benson C Cameron

(a) Selling price per unit £6.00 £8.50 £11.80 Variable costs per unit £3.00 £4.50 £6.80

Contribution per unit £3.00 £4.00 £5.00

(b) BEP =

= 1,500 = 1,600 = 3,500

units units units

(c) Sales revenue 1,500 x £6 1,600 x £8.50 3,500 x £11.80

= £9,000 = £13,600 = £41,300

Exercise 2

(a) Contribution per unit = selling price – variable costs = £40 – £22

= £18 (b) Break-even point =

=

= 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 fixed costs unit contribution £4,500£3 £6,400 £4 fixed costs unit contribution £63,000 £18 £17,500 £5

(38)

Exercise 3

=

= 220 units (c) Sales revenue = £850 x 220 units

= £187,000

(d) Margin of safety (i) = sales – break-even point = 400 – 220 units = 180 units (ii) = £850 x 180 units = £153,000 fixed costs unit contribution £81,400 £370

(39)

Exercise 4

(a) Contribution per shirt = selling price – variable costs = £21 – £11

=

= £69,300 (d) Contribution per shirt = £22 – £11

= £11 (e) Break-even point =

= 3,000 units (f) Sales revenue = £22 x 3,000 units

= £66,000 fixed costs unit contribution £33,000 £10 £33,000 £11

(40)

Exercise 5

=

= 560 units (c) Sales revenue = £34 x 560 units

= £19,040 (d) New contribution = £34 – £20

= £14 (e) New break-even point =

= 640 units Sales revenue = £34 x 640 = £21,760 fixed costs unit contribution £8,960 £16 £8,960 14

(41)

Exercise 6

(a) Contribution per quilt = selling price – variable costs = £85 – £54

= £31 (b) Break-even point (i) =

=

= 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) =

= 5,800 units (ii) = £85 x 5,800 = £493,000 fixed costs unit contribution £198,400 £31 £179,800 £31

(42)

Exercise 7

=

= £195,000

(d) Output BEP Margin of Profit

level (units) safety

(units) (units) 3,000 2,500 500 500 x £24 = £12,000 4,000 2,500 1,500 1,500 x £24 = £36,000 fixed costs unit contribution £60,000 £24

(43)

Exercise 8

= £24 (b) Break-even point (i) =

=

= 580 units (ii) = £52 x 580 units

= £30,160

(c) Output BEP Margin of Profit

(units) (units) 640 580 60 £24 x 60 = £1,440 720 580 140 £24 x 140 = £3,360 fixed costs unit contribution £13,920 £24

(44)

Exercise 9

(a) Contribution per clock = £80 – £55 = £25 (b) Break-even point = = = 480 clocks Sales revenue = £80 x 480 = £38,400

(units) (units)

500 480 20 20 x £25 = £500

600 480 120 120 x £25 = £3,000

(d) New contribution = £85 – £55 = £30 (e) New break-even point =

= 400 units Sales revenue = £85 x 400 = £34,000 fixed costs unit contribution £12,000 £25 £12,000 £30

(45)

Exercise 10

=

= 275 units Sales revenue = £139 x 275 units

= £38,225

300 275 25 £72 x 25 = £1,800

400 275 125 £72 x 125 = £9,000

(d) Total contribution required = fixed costs + profit = £19,800 + £7,920 = £27,720 Unit contribution = £72 Output required = = = 385 units fixed costs unit contribution £19,800 £72 total contribution unit contribution £27,720 £72

(46)

Exercise 11

=

= 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 £7,840 £16 = 490 units

£6,480 £5,040 £11,520 £16 = 720 units

(units) (units) 450 405 45 £16 x 45 = £720 580 405 175 £16 x 175 = £2,800 fixed costs unit contribution £6,480 £16 £7,840 £16 £11,520 £16

(47)

Exercise 12

=

= 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 £702,800 £280 = 2,510 units £686,000 £64,400 £750,400 £280 = 2,680 units

(units) (units) 5,000 2,450 550 £280 x 550 = £154,000 fixed costs unit contribution £686,000 £280 £702,800 £280 £750,400 £280

(48)

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

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

(49)

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

(50)

Contribution in break-even analysis: suggested solutions to

extension exercises

Exercise E1

(a) Contribution per unit = selling price – variable costs = £1,200 – £570

=

= 250 units

Sales value = £1,200 x 250 units = £300,000

320 250 70 £630 x 70 = £44,100

425 250 175 £630 x 175 = £110,250

(d) Total contribution required = fixed costs + required profit = £157,500 + £75,600 = £233,100 Unit contribution = £630 Output required = = = 370 units (e) New contribution = £1,095 – £570

fixed costs unit contribution £157,500 £630 total contribution unit contribution £233,100 £630

(51)

(g) Total contribution required = £233,100 Unit contribution = £525 Output required = = 444 units £233,100 £525

(52)

Exercise E2

(a) Unit contribution = £200 – £120 = £80

Break-even point = =

= 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 – 1,200 200 x £80 800 x £80

£16,000 £64,000

(c) New selling price = £220

New contribution = £220 – £120 = £100

New break-even point =

= 960 units New sales revenue = 960 x £220

= £211,200 (d) New profit

Output 1,400 units 2,000 units 1,400 – 960 2,000 – 960 440 x £100 1,040 x £100 £44,000 £104,000 fixed costs unit contribution £96,000£80 £96,000 £100

(53)

Exercise E3

(a) Unit contribution = £37 – £22 = £15 Break-even point = = = 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 = £37 – £21 = £16 New break-even point =

= 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 fixed costs unit contribution £60,000 £15 £60,000 £16

(54)

(55)

Section Two

Profit Maximisation

Contents

Profit maximisation - limiting factor, summary note, tasks,

SECTION TWO

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 £12 £12

Number of labour hours per unit 4 2

Number of units demanded 10,000 12,000

Total labour hours available 60,000 hours

(58)

If demand is to be satisfied the total number of labour hours required would be:

Product A Product B

10,000 x 4 + 12,000 x 2

40,000 + 24,000 = 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 £12 £12

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

(59)

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 £80 £20

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) Compare the hours available with the hours required to find the shortage of labour hours.

(b) What is the limiting factor for Skye Weavers plc?

(c) Calculate the contribution per labour hour for each product. (d) Show the order of priority for production. Give a reason for your

answer.

(e) Show how many labour hours would be used in the production of both rugs and scarves.

(f) Find the total contribution from rugs and scarves.

(g) Subtract the total fixed costs to find the profit from production. (h) How many scarves and rugs would be made in the hours in (e)?

(60)

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 ... ... 20,000 (f) Contribution per labour hour

(from (c) above) £ ... £ ...

(61)

Suggested solution to task 6

Rugs Scarves Total

(a) Units demanded 5,000 12,000

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 £40 £12

Contribution per labour hour £20 £12

(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) £20 £12

Total contribution £200,000 £120,000 £320,000

(g) Total fixed costs £200,000

Profit £120,000

(62)

Task 7

Islay Woodcarvers plc makes 3 products, X, Y and Z, and has provided the following information:

Total machine hours available 22,000

Product X Y Z

Selling price per unit £26 £48 £58

Variable cost per unit £16 £32 £40

Number of machine hours per unit 1 2 1.5

Number of units demanded 4,000 6,000 5,000

Use the accompanying worksheet to carry out the following tasks:

(a) Compare the hours available with the hours required to find the shortage of machine hours.

(b) What is the limiting factor for Islay Woodcarvers plc?

(c) Calculate the contribution per machine hour for each product. (d) Show the order of priority for production. Give a reason for your

answer.

(e) Show how many machine hours would be used in the production of each of the 3 products.

(f) Find the total contribution. (g) Find the total profit.

(63)

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 £ ...

(64)

Suggested solution to task 7

X Y Z Total

(a) Units demanded 4,000 6,000 5,000

Machine hours per unit 1 2 1.5

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 £10 £16 £18

Machine hours per unit 1 2 1.5

Contribution per machine hour £10 £8 £12

(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 £10 £8 £12

(65)

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) the contribution per labour hour for each product (c) the order of priority for production

(d) the labour hours available for each product

(66)

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 £150 £200 Variable costs £60 £100 Labour hours 1.5 2 Units demanded 2,000 1,500

(a) the labour hours required to meet current demand (b) the contribution per unit for each product

(c) the contribution per labour hour for each product (d) the order of priority for production

(e) the labour hours available for each product

(67)

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 £28 £30 £22

Variable cost £13 £16 £10

Machine hours 0.5 0.5 0.5

Units demanded 10,000 12,000 16,000

(a) the machine hours required to meet current demand (b) the contribution per unit for each product

(c) the contribution per machine hour for each product (d) the order of priority for production

(e) the machine hours available for each style

(68)

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)

Machine hours 5 3.5 3

Units demanded 200 300 180

(69)

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 £1,200 £800 Variable costs £600 £360 Labour hours 5 4 Units demanded 400 800

(e) the labour hours available for each style

(f) the number of units of each style that can be made (g) the total contribution

(70)

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 £130 £150 Variable costs £70 £90 Machine hours 1.5 2 Units demanded 800 400

(71)

Exercise 7

Caledonian Souvenirs produces 3 quality souvenirs, Moray, Dornoch and Beauly. They are all hand-made and a total of 8,000 labour hours is available. Total fixed costs amount to £180,000.

Sales demand for the products is expected to be: Moray 2,000 units

Dornoch 1,600 units Beauly 1,000 units.

The following figures are also available:

Moray Dornoch Beauly

(Per unit)

Variable costs £60 £110 £80

Labour hours 2 1.5 2

(72)

Exercise 8

West Coast Models plc has a labour supply with a limit of 2,020 hours

available. It produces 3 different model boats – Class 1, Class 2 and Class 3 – and its fixed costs amount to £8,000.

The following figures have also been supplied:

Class 1 Class 2 Class 3

(Per unit)

Labour hours 20 18 15

Units demanded 20 40 80

(73)

Exercise 9

Troon Models, which has a total of 7,000 machine hours available, produces 3 items, coded A, B and C. Total fixed costs are £90,000.

The following figures have been supplied:

A B C (Per unit) Selling price £12 £30 £24 Variable cost £8 £15 £12 Machine hours 0.25 0.5 0.5 Units demanded 6,000 8,000 4,000

(74)

Exercise 10

The expected demand for the toys made by Terry & Son is as follows: Model 100: 2,000 units

Model 200: 5,000 units Model 300: 4,000 units

Two machines are available, each with a capacity limited to 3,000 hours per year. Total fixed costs amount to £70,000.

The following figures have also been supplied:

Model 100 Model 200 Model 300

(Per unit)

Machine hours 0.5 0.25 1

(75)

Exercise 11

The following information has been supplied by Davidson & Williams: total fixed costs: £40,000

labour hours available: 6,500

Product A B C D (Per unit) Selling price £40 £10 £18 £8 Variable cost £20 £6 £12 £3 Labour hours 2 0.5 1 0.25 Units demanded 1,000 3,000 2,200 4,800

(76)

Exercise 12

Conservatory Decor makes 4 styles of candleholder – single, 2-candle, 3-candle and 5-candle – and it has a total of 1,400 machine hours available. Fixed costs amount to £14,000. The following additional figures have been supplied:

Single 2-candle 3-candle 5-candle

(Per unit)

Machine hours 0.25 0.25 0.5 0.5

Variable cost £8 £13 £15 £18

Selling price £15 £18 £26 £30

Units demanded 1,600 600 1,400 500

(77)

Limiting factor: suggested solutions to exercises

Exercise 1

X Y Total

(a) Labour hours required 2 hours x 5,000 2 hours x 7,000

10,000 hours 14,000 hours 24,000 hours

(b) Contribution per unit £4 £6 Labour hours per unit 2 2 Contribution per labour

hour

£2 £3

(c) First: Y (highest contribution per labour hour)

Second: X

(d) Labour hours 6,000 hours 14,000 hours 20,000 hours

available (20,000 – 14,000) (e) Units produced

3,000 units 7,000 units £4 2 £62 6,000 hours 2 hours 14,000 hours 2 hours

(78)

Exercise 2

Georgian Victorian Total

(a) Labour hours required 1.5 hours x 2,000 2 hours x 1,500

3,000 hours 3,000 hours 6,000 hours

(b) Contribution per unit £150 – £60 £200 – £100 (selling price – variable

costs) £90 £100

(c) Contribution per labour hour

£60 £50

(d) First: Georgian (highest contribution per labour hour)

Second: Victorian

(e) Labour hours 3,000 2,500 5,500

available (5,500 – 3,000) (f) Units produced 2,000 units 1,250 units £90 1.5 hours 2 hours£100 3,000 hours 1.5 hours 2,500 hours 2 hours

(79)

Exercise 3

Classic City Casual Total

(a) Machine hours 0.5 x 10,000 0.5 x 12,000 0.5 x 16,000

required 5,000 hours 6,000 hours 8,000 hours 19,000 hours

(b) Contribution £28 – £13 £30 – £16 £22 – £10

per unit £15 £14 £12

(c) Contribution per machine hour

£30 £28 £24

(d) First: Classic

Second: City Third: Casual

(e) Machine hours 5,000 hours 6,000 hours 7,000 hours 18,000 hours

available (18,000 – 11,000)

(f) Units produced

10,000 units 12,000 units 14,000 units

£15 0.5 5,000 0.5 £14 0.5 £120.5 6,000 0.5 7,000 0.5

(80)

Exercise 4

Kelso Selkirk Melrose Total

(a) Machine hours 5 hours x 200 3.5 hours x 300 3 hours x 180

required 1,000 hours 1,050 hours 540 hours 2,590 hours

(b) Contribution £360 – £180 £280 – £140 £250 – £100 per unit £180 £140 £150 (c) Contribution per machine hour £36 £40 £50 (d) First: Melrose Second: Selkirk Third: Kelso

(e) Machine hours 610 hours 1,050 hours 540 hours 2,200 hours

available (2,200 – 1,590) (f) Units produced

122 units 300 units 180 units

£180 5 610 5 £140 3.5 £150 3 1,050 3.5 5403