A and F-using Accounting Info Tcm4-117030 (2)

NATIONAL QUALIFICATIONS CURRICULUM SUPPORT

INTRODUCTION

NATIONAL QUALIFICATIONS CURRICULUM SUPPORTAccounting and Finance

Using Accounting Information

Break-even Analysis

Profit Maximisation

Financial Analysis

[INTERMEDIATE 2]

Dorothy Brown

First published 1998

Electronic version 2002

Scottish Consultative Council on the Curriculum 1998

This publication may be reproduced in whole or in part for educational purposes by educational establishments in Scotland provided that no profit accrues at any stage.

Acknowledgement

Learning and Teaching Scotland gratefully acknowledge this contribution to the National Qualifications support programme for Accounting and Finance.

ISBN 1 85955 653 1

Learning and Teaching Scotland

Gardyne Road

Dundee

DD5 1NY

www.LTScotland.com

contents

Section One

Break-even Analysis

1-53

Section Two

Profit Maximisation

57-94

Section Three

Financial Analysis

97-144

introductionThis publication contains both summary notes and a range of computational exercises covering break-even analysis, profit maximisation and financial analysis. It also includes questions covering the underpinning knowledge and understanding of the unit and suggested solutions to all questions and exercises. At the end of each section, there are extension exercises which are designed to stretch more able students and take them in the direction of Higher level. The exercises are not intended to be used for assessment purposes.

The publication is targeted at students who are undertaking the Higher Still Using Accounting Information Unit at Intermediate 2 level. It covers the basic knowledge required in dealing with break-even analysis, limiting factors for profit maximisation and ratio calculation for financial analysis. Teachers and lecturers are expected to augment these as, where and when they deem it appropriate.

For simplicity of use the publication has been divided into three sections:

Section One - Break-even Analysis

Section Two - Profit Maximisation

Section Three - Financial Analysis

Section OneBreak-even AnalysisContentsBreak-even analysis - summary notes, example, tasks and

suggested solutions1-6

Break-even charts - summary notes, example, tasks and suggested

solutions7-9

Exercises 1-6 with suggested solutions10-18

Contribution and profit in break-even analysis - summary notes,

examples, tasks with suggested solutions19-27

Break-even analysis - theory questions with suggested solutions28-30


Extension exercises 1-3 with suggested solutions48-53

Section oneBreak-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.

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 unit3

Selling price per unit

8

We can draw up a table to show the information.

Units ofFixedVariableTotalSalesProfit

outputcostscostscostsrevenue(loss)

01,0001,000(1,000)

1001,0003001,300800(500)

2001,0006001,6001,600

3001,0009001,9002,400500

4001,0001,2002,2003,2001,000

5001,0001,5002,5004,0001,500

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.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 ofBEPMargin of safetySelling priceMargin of safety

output(units)(units)per unit(sales revenue)

3002001008800

40020020081,600

50020030082,400The 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.

SalesBEPMargin of safety

revenue(sales revenue)

2,4001,600800

3,2001,6001,600

4,0001,6002,400Formulae:

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

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:

materials7

wages512


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?

(c)How much is the profit when 3,000 units are produced?

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?

(c)How much is the profit at an output of 2,500 units?

Suggested solution to Task 1



012,00012,000(12,000)

50012,0006,00018,00010,000(8,000)

1,00012,00012,00024,00020,000(4,000)

1,50012,00018,00030,00030,000

2,00012,00024,00036,00040,0004,000

2,50012,00030,00042,00050,0008,000

3,00012,00036,00048,00060,00012,000(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=12,000Suggested solution to Task 2



012,00012,000(12,000)

50012,0006,00018,0009,000(9,000)

1,00012,00012,00024,00018,000(6,000)

1,50012,00018,00030,00027,000(3,000)

2,00012,00024,00036,00036,000

2,50012,00030,00042,00045,0003,000

3,00012,00036,00048,00054,0006,000(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

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

the area of loss is to the left of break-even point.

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 shownsales 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 titlethe 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.

Suggested solution to Task 3(a)

Suggested solution to Task 3(b)

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


25

Projected output levels

100700 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


24


1,0007,000 units


(i)units of output

(ii)sales value

(c)Find the profit at outputs of 5,000 and 7,000 units.

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: materials10

labour

15


40

Total fixed costs

60,000


1,0008,000 units


(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

(f)Find the new profit expected at outputs of 4,000 and 6,000 units.

Exercise 4

(a)Using the following information prepare a break-even chart, labelling break-even point.

Data


1,0007,000 units

Total fixed costs

40,000


materials12

wages

10


30


(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

(f)Find the new profit expected at outputs 5,000 and 7,000 units.

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.

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.

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=3,000Exercise 2(a)

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

(c)Profit at 5,000 units=12,000

Profit at 7,000 units=36,000

Exercise 3

(a)




(d)

(e)Break-even point=3,000 units; 120,000

(f)Profit at 4,000 units=20,000


Exercise 4

(a)




(d)

(e)New break-even point=4,000 units; 120,000

(f)Profit at 5,000 units=10,000


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=2,000

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.

ExampleLightwell makes lamps and is investigating the profitability of producing a new design. The following figures are available.

Estimated variable cost per lamp40

Selling price per lamp60

Total fixed costs4,000

(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)=

fixed costs

unit contribution

=

4,000

20

=200 lamps

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

BEP in sales revenue=selling price number of lamps

=60 200 lamps

=12,000

Check:

Sales revenue of 200 units=60 200=12,000

Less variable cost of 200 units=40 200=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

Task 4

Complete the figures in the following table.

FirmSelling priceVariable costContributionFixedBEPBEP

per unitper unitper unitcosts(units)(revenue)

a3015

15,000

b53

5,000

c87

4,000

d14090

50,000

e380260

240,000


FirmSelling priceVariable costContributionFixed BEPBEP

per unitper unitper unitcosts(units)(revenue)

a30151515,0001,00030,000

b5325,0002,50012,500

c8714,0004,00032,000

d140905050,0001,000140,000

e38026080240,0003,0001,140,000

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 550 units.

OutputBEPMarginContributionProfit

level(units)of safetyper unit

(units)

(units)

25020050201,000

320200120202,400

400200200204,000

480200280205,600

550200350207,000Check:

OutputUnitTotalFixedProfit

levelcontributioncontributioncosts

(units)

250205,0004,0001,000

320206,4004,0002,400

400208,0004,0004,000

480209,6004,0005,600

5502011,0004,0007,000Contribution 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:


30


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=3,000

10

=300 units

Check:

Break-even point

=2,000

10

=200 units

Profit required

=1,000

Unit contribution

=10

Number of profitable units=1,000

10

=100 units

Total output required

=break-even point + profitable units

=200 + 100 units

=300 units

Task 5

Complete the figures in the following table using the information in the example on p. 24.

ProfitFixedTotalUnitRequired

requiredcostscontributioncontributionoutput

(units)

1,0002,0003,00010300

1,8002,000

10

2,300

10

3,000

3,500

Check:

RequiredUnitProfitableBreak-evenRequired

profitcontributionoutputpointoutput

(units)(units)(units)

1,00010100200300

1,80010180200

2,30010

200

3,000

3,500


ProfitFixedTotalUnitRequired

requiredcostscontributioncontributionoutput

(units)

1,0002,0003,00010300

1,8002,0003,80010380

2,3002,0004,30010430

3,0002,0005,00010500

3,5002,0005,50010550

Check:

RequiredUnitProfitableBreak-evenRequired

profitcontributionoutputpointoutput

(units)(units)(units)

1,00010100200300

1,80010180200380

2,30010230200430

3,00010300200500

3,50010350200550

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.

Break-even analysis: suggested solutions to theory questions

Question 1

Three uses of break-even analysis are:

1to calculate the break-even point in units of output and in sales revenue for a product

2to estimate the profit/loss that will result from any given level of output

3to find the level of output needed for a given profit figure.

Question 2

Four assumptions made in the use of break-even analysis are:

1all costs are either fixed or variable

2the selling price remains unchanged for the entire range of output regardless of different markets and conditions

3costs remain unchanged because there are no changes in materials, wages or methods

4there 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-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.

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.

Contribution in break-even analysis: exercises

Exercise 1

Three firms have supplied the following information:

A AndersonB BensonC Cameron

Variable costs per unit3.004.506.80

Selling price per unit6.008.5011.80

Fixed costs4,5006,40017,500

(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 unit40



(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

(ii)sales revenue ()?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:





(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:


21.00


materials

6.50

wages

4.50

Total fixed costs

33,000

(a)Calculate the contribution per shirt.


(c)What is the sales revenue of these units?

(d)What is the new contribution per shirt if they could be sold at 22 each?

(e)Calculate the new break-even point in units at the increased selling price.

(f)What is the sales revenue of these units?

Exercise 5

Novelties plc assembles novel clocks and has estimated the following figures for a new style:


34


component parts

12

wages

6

Total fixed costs

8,960

(a)Calculate the contribution per clock.


(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:




(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 revenue?

Exercise 7

J Jones has supplied the following figures:


materials36

wages15

expenses3



(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:





(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.Exercise 9

Deeside Woodworkers produces clocks and the following figures are available:




(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:



materials30

fastenings and locks12

wages25


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

(d)the output level required to give a profit of 7,920.

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 tree36

Variable costs per tree20

(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:


materials80

component parts120

wages100


(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?

(d)How much is the profit at output of 5,000 units?

Contribution in break-even analysis: suggested solutions to exercises

Exercise 1

A AndersonB BensonC Cameron

(a)Selling price per unit6.008.5011.80

Variable costs per unit3.004.506.80

Contribution per unit3.004.005.00

(b)BEP =

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

units

units

units

(c)Sales revenue1,500 61,600 8.503,500 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 3,500 units

=140,000(d)Margin of safety(i)=sales break-even point

=8,000 3,500 units

=4,500 units

(ii)=40 4,500 units

=180,000Exercise 3


=850 480


=

=

=220 units(c)Sales revenue

=850 220 units

=187,000(d)Margin of safety(i)=sales break-even point

=400 220 units

=180 units

(ii)=850 180 units

=153,000

Exercise 4

(a)Contribution per shirt=selling price variable costs

=21 11

=10

(b)Break-even point

=

=

=3,300 units

(c)Sales revenue

=21 3,300 units

=69,300

(d)Contribution per shirt=22 11

=11

(e)Break-even point

=

=3,000 units(f)Sales revenue

=22 3,000 units

=66,000Exercise 5


=34 18


=

=

=560 units(c)Sales revenue

=34 560 units

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

=14(e)New break-even point=

=640 units

Sales revenue

=34 640

=21,760 Exercise 6

(a)Contribution per quilt

=selling price variable costs

=85 54

=31(b)Break-even point(i)=

=

=6,400 units

(ii)=85 6,400 quilts

=544,000(c)Margin of safety(i)=20,000 6,400 units

=13,600 units

(ii)=85 13,600 units

=1,156,000(d)New break-even point(i)=

=5,800 units

(ii)=85 5,800

=493,000Exercise 7


=78 54

=24(b)Break-even point=

=

=2,500 units(c)Sales revenue=78 2,500 units

=195,000(d)OutputBEPMargin ofProfit

level(units)safety

(units)

(units)

3,0002,500500500 24 = 12,000

4,0002,5001,5001,500 24 = 36,000

Exercise 8

(a)Contribution per unit

=selling price variable costs

=52 28

=24(b)Break-even point(i)=

=

=580 units

(ii)=52 580 units

=30,160(c)OutputBEPMargin ofProfit

level(units)safety

(units)

(units)

6405806024 60 = 1,440

72058014024 140 = 3,360

Exercise 9

(a)Contribution per clock=80 55


=

=480 clocks

Sales revenue=80 480

=38,400

(c)OutputBEPMargin ofProfit

level(units)safety

(units)

(units)

5004802020 25 =500

600480120120 25 =3,000

(d)New contribution=85 55

=30

(e)New break-even point=

=400 units

Sales revenue=85 400

=34,000

Exercise 10


=139 67


=

=275 units

Sales revenue=139 275 units

=38,225(c)OutputBEPMargin ofProfit

level(units)safety

(units)

(units)

3002752572 25 = 1,800

40027512572 125 = 9,000

(d)Total contribution required=fixed costs + profit

=19,800 + 7,920

=27,720


Output required=

=

=385 units

Exercise 11


=36 20


=

=405 units

Sales revenue=36 405 units

=14,580

(c)FixedProfitTotalUnitOutput

costsrequiredcontributioncontributionrequired

required

6,4801,3607,84016

= 490 units

6,4805,04011,52016

= 720 units

(d)OutputBEPMargin ofProfit

level(units)safety

(units)

(units)

4504054516 45 = 720

58040517516 175 = 2,800

Exercise 12


=580 300


=

=2,450 units

Sales revenue=580 2,450 units

=1,421,000

(c)FixedProfitTotalUnitOutput

costsrequiredcontributioncontributionrequired

required

686,00016,800702,800280

= 2,510 units

686,00064,400750,400280

= 2,680 units

(d)OutputBEPMargin ofProfit

level(units)safety

(units)

(units)

5,0002,450550280 550 = 154,000

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 costs157,500

Variable costs:

materials80

component parts350

wages140

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:materials80

labour40


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.

Exercise E3

Stonehaven Clocks makes alarm clocks and has supplied the following figures.

Output6,000 clocks


Selling price per clock37

Variable costs per clock:

materials6

component parts4

labour12

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.

Contribution in break-even analysis: suggested solutions to extension exercises

Exercise E1


=1,200 570


=

=

=250 units

Sales value=1,200 250 units

=300,000

(c)OutputBEPMargin ofProfit

level(units)safety

(units)

(units)

32025070630 70 =44,100

425250175630 175= 110,250

(d)Total contribution required=fixed costs + required profit

=157,500 + 75,600

=233,100


Output required=

=

=370 units(e)New contribution=1,095 570

=525(f)New break-even point=

=300 units(g)Total contribution required=233,100


Output required=

=444 units

Exercise E2

(a)Unit contribution=200 120

=80

Break-even point = =

=1,200 units

Sales revenue=1,200 200

=240,000(b)Profit = (output BEP) x unit contribution

Output1,400 units2,000 units

1,400 1,2002,000 1,200

200 80800 80

16,00064,000

(c)New selling price=220

New contribution=220 120

=100

New break-even point=

=960 units

New sales revenue=960 220

=211,200

(d)New profit

Output1,400 units2,000 units

1,400 9602,000 960

440 1001,040 100

44,000104,000

Exercise E3

(a)Unit contribution=37 22

=15

Break-even point=

=

=4,000 units


=148,000(b)Profit =(6,000 BEP) 15

=(6,000 4,000) 15

=2,000 15

=30,000(c)New variable costs=21

New contribution=37 21

=16

New break-even point=

=3,750 units


=138,750

(d)New profit=(8,000 BEP) 16

=(8,000 3,750) 16

=4,250 16

=68,000Section TwoProfit MaximisationContentsProfit maximisation limiting factor, summary note, tasks, suggested solutions57-64



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.ExampleTwo products, A and B, are being produced and details are as follows:

AB

Contribution per unit1212

Number of labour hours per unit42

Number of units demanded10,00012,000

Total labour hours available60,000 hoursTotal fixed costs160,000

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

Product AProduct B

10,000 4+12,000 2

40,000+24,000

=

64,000 hoursThe 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.

AB

Contribution per unit1212

Number of labour hours42

Contribution per labour hour36

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:

1Product B24,000 hours/2

= 12,000 units

2Product A60,000 24,000 hours = 36,000 hours/4= 9,000 unitsHow much profit will be made?

ABTotal

Number of labour hours36,00024,00060,000

Contribution per labour hour36Total contribution3 36,000 6 24,000

108,000144,000252,000

Less fixed costs

160,000

Profit (maximised)92,000Task 6

Skye Weavers plc produces 2 items, rugs and scarves. Figures available are as follows:

Total labour hours available20,000


ProductRugsScarves

Selling price per unit8020Variable costs per unit408

Labour hours per unit21

Number of units demanded5,00012,000

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)?

Task 6: worksheet

RugsScarvesTotal

(a)Units demanded5,00012,000

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) ........ ........

Total contribution ........ ........ ........

(g)Total fixed costs

........

Profit

........

(h)Scarves and rugs made....................

Suggested solution to task 6

RugsScarvesTotal

(a)Units demanded5,00012,000


Total labour hours required10,00012,00022,000

Labour hours available

20,000

Shortage of labour hours

2,000(b)The limiting factor is labour hours(c)Contribution per unit4012


Contribution per labour hour2012

(d)Order of priority:first:

rugs

second:scarves

ReasonRugs 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 production10,00010,00020,000

(f)Contribution per labour hour

(from (c) above)2012

Total contribution200,000120,000320,000

(g)Total fixed costs

200,000

Profit

120,000(h)Scarves and rugs made5,00010,000Task 7

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

Total machine hours available22,000


ProductXYZ


Variable cost per unit163240

Number of machine hours per unit121.5

Number of units demanded4,0006,0005,000

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.

(h)How many of each product would be made in the hours in (e)?

Task 7: worksheet

XYZTotal

(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..............................

Suggested solution to task 7

XYZTotal

(a)Units demanded4,0006,0005,000

Machine hours per unit121.5

Total machine hours required4,00012,0007,50023,500

Machine hours available

22,000

Shortage of machine hours

1,500

(b)The limiting factor is machine hours(c)Contribution per unit101618

Machine hours per unit121.5

Contribution per machine hour10812

(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

production4,00010,5007,50022,000

(f)Contribution per machine hour10812

Total contribution40,00084,00090,000214,000

(g)Less total fixed costs

140,000

Profit

74,000(h)Number of units made4,0005,2505,000Limiting 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:

XY

(Per unit)

Contribution46

Labour hours 22

Units demanded5,0007,000


(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

(e)the number of units of each product that can be made.

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:

GeorgianVictorian

(Per unit)

Selling price150200

Variable costs60100

Labour hours 1.52




(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

(f)the number of units of each product that can be made.

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:

ClassicCityCasual

(Per unit)Selling price283022

Variable cost131610

Machine hours0.50.50.5

Units demanded10,00012,00016,000


(a)the machine hours required to meet current demand


(c)the contribution per machine hour for each product


(e)the machine hours available for each style

(f)the number of units of each style that can be made.

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:

KelsoSelkirkMelrose

(Per unit)

Selling price360280250

Variable cost180140100

Machine hours53.53

Units demanded200300180







(f)the number of units of each style that can be made.

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:

DunkeldAberfeldy

(Per unit)

Selling price1,200800

Variable costs600360

Labour hours 54







(e)the labour hours available for each style

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

(g)the total contribution

(h)the profit after deduction of fixed costs.

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:

RelaxRelax-plus

(Per unit)

Selling price130150

Variable costs7090

Machine hours1.52











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

Dornoch1,600 units

Beauly1,000 units.

The following figures are also available:

MorayDornochBeauly

(Per unit)


Variable costs6011080

Labour hours 21.52










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 1Class 2Class 3

(Per unit)


Variable cost 300240200

Labour hours 201815











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:

ABC

(Per unit)

Selling price123024

Variable cost81512

Machine hours0.250.50.5

Units demanded 6,0008,0004,000










Exercise 10

The expected demand for the toys made by Terry & Son is as follows:

Model 100:2,000 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 100Model 200Model 300

(Per unit)

Selling price252042

Variable cost151226

Machine hours0.50.251










Exercise 11

The following information has been supplied by Davidson & Williams:

total fixed costs: 40,000

labour hours available: 6,500

ProductABCD

(Per unit)


Variable cost206123

Labour hours20.510.25

Units demanded1,0003,0002,2004,800










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:

Single2-candle3-candle5-candle

(Per unit)

Machine hours0.250.250.50.5

Variable cost8131518












Limiting factor: suggested solutions to exercises

Exercise 1

XYTotal

(a)Labour hours required2 hours 5,0002 hours 7,000

10,000 hours14,000 hours24,000 hours

(b)Contribution per unit46

Labour hours per unit 22

Contribution per labour

hour

23

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

Second:X

(d)Labour hours 6,000 hours14,000 hours20,000 hours

available(20,000 14,000)

(e)Units produced

3,000 units7,000 units

Exercise 2

GeorgianVictorianTotal

(a)Labour hours required1.5 hours 2,0002 hours 1,500

3,000 hours3,000 hours6,000 hours

(b)Contribution per unit150 60200 100

(selling price variable

costs)90

100

(c)Contribution per 90

100

labour hour1.5 hours

2 hours

60

50

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

Second:Victorian

(e)Labour hours3,0002,5005,500

available

(5,500 3,000)

(f)Units produced3,000 hours2,500 hours

1.5 hours 2 hours

2,000 units1,250 units

Exercise 3

ClassicCityCasualTotal

(a)Machine hours 0.5 10,0000.5 12,0000.5 16,000

required5,000 hours6,000 hours8,000 hours19,000 hours

(b)Contribution28 1330 1622 10

per unit151412

(c)Contribution 151412

per machine hour0.50.50.5

302824

(d)First:Classic

Second:City

Third:Casual

(e)Machine hours5,000 hours6,000 hours7,000 hours18,000 hours

available

(18,000 11,000)

(f)Units produced5,0006,0007,000

0.5 0.5 0.5

10,000 units12,000 units14,000 units

Exercise 4

KelsoSelkirkMelroseTotal

(a)Machine hours5 hours 2003.5 hours 3003 hours 180

required1,000 hours1,050 hours540 hours2,590 hours

(b)Contribution 360 180280 140250 100

per unit180140150


per machine 5 3.5 3

hour

364050

(d)First: Melrose

Second:Selkirk

Third: Kelso(e)Machine hours 610 hours1,050 hours540 hours2,200 hours

available(2,200 1,590)

(f)Units produced6101,050540

5 3.5 3

122 units300 units180 units

Exercise 5

DunkeldAberfeldyTotal

(a)Labour hours 5 hours 4004 hours 800

required2,000 hours3,200 hours5,200 hours

(b)Contribution 1,200 600800 360

per unit600440


per labour hour 5 4

120110

(d)First:Dunkeld

Second:Aberfeldy

(e)Labour hours2,0003,0005,000

available

(5,000 2,000)

(f)Units produced2,0003,000

5 4

400 units750 units(g)Contribution per labour hour120110

Labour hours2,0003,000

Total contribution120 2,000110 3,000

240,000330,000570,000(h)Fixed costs

400,000

Profit

170,000

Exercise 6

RelaxRelax-plusTotal

(a)Machine hours required1.5 hours x 800 2 hours x 400

1,200 hours800 hours2,000 hours(b)Contribution130 70150 90

per unit6060


per machine hour1.5 2

4030(d)First: Relax

Second:Relax-plus

(e)Machine hours 1,2006001,800

available

(1,800 1,200)

(f)Units produced1,200600

1.5 2

800 units300 units

(g)Contribution per

machine hour4030

Machine hours1,200600

Total contribution48,00018,00064,000

(h)Fixed costs

30,000

Profit

34,000

Exercise 7

MorayDornochBeaulyTotal

(a)Labour hours 2 hours 2,0001.5 hours 1,600 2 hours 1,000


(b)Contribution120 60200 110150 80

per unit609070

(c)Contribution per609070

labour hour 21.5 2

306035

(d)First:Dornoch

Second:Beauly

Third:Moray

(e)Labour hours3,600 hours2,400 hours2,000 hours8,000 hours



2 1.5 2


(g)Total contribution30 x 3,60060 x 2,40035 x 2,000

108,000144,00070,000322,000(h)Fixed costs

180,000

Profit

142,000

Exercise 8

Class 1Class 2Class 3Total

(a)Labour hours20 hours 2018 hours 4015 hours 80

required400 hours720 hours1,200 hours2,320 hours(b)Contribution480 300420 240320 200

per unit180180120(c)Contribution180180120

per labour hour 20 18 15

9108(d)First:Class 2

SecondClass 1

Third:Class 3(e)Labour hours400 hours720 hours900 hours2,020 hours

available

(2,020 1,120)

(f)Units produced400720900

20 18 15

20 units40 units60 units(g)Total contribution9 40010 7208 900

3,6007,2007,20018,000(h)Fixed costs

8,000

Profit

10,000

Exercise 9

ABCTotal

(a)Machine hours0.25 hours 6,0000.5 hours 8,0000.5 hours 4,000


(b)Contribution12 830 1524 12

per unit41512(c)Contribution 41512

per machine hour0.250.50.5

163024(d)First:B

Second:C

Third:A(e)Machine hours1,000 hours4,000 hours2,000 hours7,000 hours



0.25 0.5 0.5


(g)Total contribution16 1,00030 4,00024 2,000

16,000120,00048,000184,000(h)Fixed costs

90,000

Profit

94,000

Exercise 10

Model 100Model 200Model 300Total

(a)Machine hours0.5 2,0000.25 5,0001 4,000


(b)Contribution 25 1520 1242 26

per unit10816(c)Contribution10 816

per machine hour0.50.25 1

203216(d)First:Model 200

Second:Model 100

Third:Model 300(e)Machine hours1,000 hours1,250 hours3,750 hours6,000 hours

available

(6,000 2,250)


0.5 0.25 1

2,000 units5,000 units3,750 units(g)Total contribution20 1,00032 1,25016 3,750

20,00040,00060,000120,000(h)Fixed costs

70,000

Profit

50,000

Exercise 11

ABCDTotal

(a)Labour hours2 1,0000.5 3,0001 2,2000.25 4,800

required2,000 hours1,500 hours2,200 hours1,200 hours6,900 hours(b)Contribution40 2010 618 128 3

per unit20465(c)Contribution20 46 5

per labour hour 20.5 10.25

108620(d)First:D

Second:A

Third:B

Fourth:C(e)Labour hours2,000 hours1,500 hours1,800 hours1,200 hours6,500 hours

available

(6,500 4,700)

(f)Units produced 2,000 1,500 1,800 1,200

2 hours0.5 hours1 hour0.25 hours

1,000 units3,000 units1,800 units4,800 units(g)Total contribution10 2,0008 1,5006 1,80020 1,200

20,00012,00010,80024,00066,800(h)Fixed costs

40,000

Profit

26,800

Exercise 12

Single2-candle3-candle5-candleTotal

(a)Machine hours0.25 1,6000.25 6000.5 1,4000.5 500

required400 hours150 hours700 hours250 hours1,500 hours(b)Contribution15 818 1326 1530 18

per unit751112(c)Contribution 7 51112

per machine hour0.250.250.50.5

28202224(d)First:Single

Second:5-candle

Third: 3-candle

Fourth:2-candle(e)Machine hours400 hours50 hours700 hours250 hours1,400 hours

available

(1,400 1,350)

(f)Units produced400 50700250

0.250.250.50.5

1,600 units200 units1,400 units500 units

(g)Total contribution28 40020 5022 70024 250

11,2001,00015,4006,00033,600(h)Fixed costs

14,000

Profit

19,600

Limiting factor: extension exercises

Exercise E1

Forth Valley Products uses machines that are equally suitable for making any of its products. There is a total machining capacity of 22,000 hours and total fixed costs are 360,000.

Sales demand for its 4 products is expected to be as follows:

J:18,000 units

K:16,000 units

L:20,000 units

M:10,000 units.

The following additional data is also given:

ProductSellingVariableMachine

pricecostshours

(per unit)(per unit)(per unit)

J24180.25

K18100.25

L25130.5

M20120.5

Using the above information, you are required to carry out the following tasks.

(a)Calculate the contribution per unit of the limiting factor.

(b)Decide which product(s), if any, should be cut back. Give a reason for your choice.

(c)Calculate how many machine hours are necessary to satisfy current demand.

(d)Calculate how many machine hours will be used for making each of the 4 products in order to maximise profit.

(e)Calculate the total contribution and the final profit from this output.

(f)How many units of each product will be made?

(g)Find the sales revenue of these units.

Exercise E2

Main & Morrison plc have a limited labour force that provides 4,200 labour hours per year. Four products are made in the factory, which has fixed costs of 70,000. Maximum demand for the 4 products is expected to be as follows:

A:200 units

B:150 units

C:400 units

D:320 units.

Budgeted figures for the 4 products have been supplied.

ProductVariableSellingLabour

costspricehours

(per unit)(per unit)(per unit)

A1603004

B1102303

C2253505

D1752954

Answer each of the following questions.

(a)How many labour hours are necessary to meet current demand? Why is it essential to calculate this figure?

(b)Can current demand be met with existing resources?

(c)If current demand cannot be met, state which product(s) should be cut back, showing calculations to support your answer.

(d)Calculate the number of labour hours available for each product.

(e)Calculate the number of units that will be produced.

(f)Calculate the maximum contribution and profit obtainable from this level of output.

(g)What is the sales revenue of the units produced?

Exercise E3

Crieff Wood Products plc produces 4 styles of garden seat de Luxe Double, Standard Double, de Luxe Single and Standard Single for which demand is expected to be 200, 500, 100 and 150 units, respectively. The number of labour hours available is 3,300 and fixed costs total 50,000.

The following figures are available.

ProductSellingMaterialsWagesLabour

pricecostcosthours

(per unit)(per unit)(per unit)(per unit)

de Luxe Double25040705

Standard Double18230484

de Luxe Single18028564

Standard Single13025363

Answer each of the following questions.

(a)The limiting factor is labour. Explain what is meant by the limiting factor.

(b)Calculate the labour hours needed to satisfy current demand. Compare your answer with the number of hours available and calculate the shortage of hours.

(c)Find the contribution per unit and the contribution per labour hour for each style.

(d)Calculate the labour hours to be spent on each style in order to maximise profit.

(e)Calculate the total contribution and maximum profit from your suggested output.

(f)Calculate the total sales revenue of the output.

Suggested solutions to extension exercises

Exercise E1

JKLMTotal

(a)Contribution24 1818 1025 1320 12

per unit68128

Contribution 6 8128

per machine hour0.250.250.50.5

24322416(b)Product M should be cut back because it has the lowest contribution per labour hour. Machine hours are scarce (only 22,000 are available) therefore the products given priority are those with the highest contribution per unit of the limiting factor.

(c)Machine hours0.25 18,0000.25 16,0000.5 20,0000.5 10,000

required4,500 hours4,000 hours10,000 hours5,000 hours23,500 hours

(d)Machine hours4,500 hours4,000 hours10,000 hours3,500 hours22,000 hours

available

(22,000 18,500)

(e)Total24 4,50032 4,00024 10,00016 3,500

contribution108,000128,000240,00056,000532,000

Less fixed costs

360,000

Profit

172,000(f)Units produced4,5004,00010,0003,500

0.25 0.25 0.5 0.5

18,000 units16,000 units20,000 units7,000 units(g)Sales revenue24 18,00018 16,00025 20,00020 7,000

432,000288,000500,000140,0001,360,000Exercise E2

ABCDTotal

(a)Labour hours4 hours 2003 hours 1505 hours 4004 hours 320

required800 hours450 hours2,000 hours1,280 hours4,530 hours

This figure must be calculated when labour is in scarce supply. It will tell the firm whether or not there are enough labour hours to fully meet current demand. If not, a level of output will have to be fixed to maximise profit within the limitations.

(b)No. Only 4,200 hours are available but 4,530 are required to meet current demand.

(c)Contribution300 160230 110350 225295 175

per unit140120125120

Contribution140120125120

per labour hour 4 3 5 4

35402530

Product C should be cut back because it has the lowest contribution per labour hour.

(d)Labour hours800 hours450 hours1,670 hours1,280 hours4,200 hours

available

(4,300 2,530)

(e)Units produced8004501,6701,280

4 3 5 4

200 units150 units334 units320 units(f)Total 35 80040 45025 1,67030 1,280

contribution28,00018,00041,75038,400126,150

Less fixed costs

70,000

Profit

56,150(g)Sales revenue300 200230 150350 334295 320

60,00034,500116,90094,400305,800Exercise E3

(a)The limiting factor is a resource that is in short supply, e.g. labour. This means that production has to be planned so that the highest possible profit will be made from the existing labour supply. Output levels will be such that those products which give the highest contribution per labour hour will be given priority.

(b)

de Luxe DoubleStandard Doublede Luxe SingleStandard SingleTotal

Labour hours5 hours 2004 hours 5004 hours 1003 hours 150

required1,000 hours2,000 hours400 hours450 hours3, 850 hours

Labour hours

available

3,300 hours

Shortage

550 hours

(c)Contribution250 110182 78180 84130 61

per unit1401049669

Contribution 1401049669

per labour hour5443

28262423(d)Labour hours1,000 hours2,000 hours300 hours3,300 hours

available

(3,300 3,000)

(e)Total 28 1,00026 2,00024 300

contribution28,00052,0007,20087,200

Less fixed costs

50,000

Profit

37,200

(f)Units produced200 units500 units75 units

Sales revenue250 200182 500180 75

50,00091,00013,500

154,500

Section ThreeFinancial AnalysisContentsSummary note and example97-103



Section Three

Ratios and percentages

At the end of each financial year Final Accounts are prepared that show the firms profitability and its financial position at that date. These accounts are a record of the firms performance and, by themselves, have limited use since they give no indication of whether the results are favourable or unfavourable. For example, they show the profit/loss figure but there is nothing to indicate whether that figure is satisfactory for the firm concerned. The assets are listed in the Balance Sheet but, again, there is nothing to show that they are being used effectively for example, is a bank balance of 10,000 a healthy sign and is an overdraft of 5,000 unhealthy?

Management needs to know whether or not:

(i)performance is satisfactory

(ii)performance is showing improvement on previous years

(iii)there are problem areas that should be investigated.

It may also be desirable to compare figures with those of competitors or with the average for the industry.

A straightforward comparison of figures is usually unhelpful. A profit of 20,000 may be acceptable for one firm but entirely unacceptable for another: if it is related to the capital employed it becomes more meaningful. A return of 20,000 on capital of 100,000 (20%) is obviously better than a return of 20,000 on capital of 200,000 (10%). Ratios and percentages are therefore normally used for the purpose of comparison.

Parties who would be interested in the firms ratios are:

owners/shareholders who want to see how profitable their investment is

potential creditors such as suppliers and banks who would be interested to know if the firm is credit worthy

staff who are interested in wage rates, bonuses and profit-sharing, which must be considered in the light of profitability

companies interested in take-over bids who want to see profitability and efficient use of assets.

The main types of ratio are those relating to profitability and liquidity.

Profitability

Profitability ratios show how successful a firm is in relation to capital and sales revenue.Example 1

Year 1Year 2

Capital at start20,00022,000

Add net profit4,0005,500

24,00027,500

Less drawings2,0003,000

Capital at end22,00024,500

Return on capital employed =net profit100

opening capital

1

Return on capital employedYear 1Year 2

4,0001005,500100

20,000

122,000

1

= 20%

= 25%This ratio shows there has been adequate return on investment. In the second year profit has increased and the improved ratio indicates that assets have been more effectively employed. This may be due to factors such as economic purchasing procedures, increased advertising and reduced expenses.

Example 2

Year 1Year 2

Sales60,00080,000

Less cost of goods sold40,00050,000

Gross profit20,00030,000

Less expenses8,00012,000

Net profit12,00018,000

Gross profit % =gross profit100

sales1

Gross profit %Year 1Year 2

20,00010030,000100

60,000

180,000

1

= 33.3%

= 37.5%Gross profit arises from buying and selling stock and the gross profit % shows how much of every 100 of sales is profitable. It is possible for sales volume to increase without a corresponding increase in profitability.

In Year 2 there has been an increase in profitability. This may have arisen from buying stock at a lower price because of influences such as a change of buying policy or a change in market prices. On the other hand, it may be the result of selling at an increased price without any increase in costs.

Net profit % ==net profit100

Sales1

Net profit %Year 1Year 2

12,00010018,000100

60,000

180,000

1

= 20%

= 22.5%

Expenses % ==total expenses100

sales1

Expenses %Year 1Year 2

8,00010012,000100

60,000

180,000

1

= 13.3%

= 15%

The net profit % and the expenses % are linked because net profit is the result of deducting expenses from gross profit. The improvement in gross profit ratio is reflected to some extent in the net profit % but there has been an increase in expenses. There may have been an increase in advertising costs, wages or other running costs and these would be examined to see if they can be reduced.Liquidity

Liquidity ratios show whether the firm can meet its liabilities when they are due. Generally, current assets should cover current liabilities. Potential creditors and lenders will not support a firm whose current liabilities are greater than its current assets and the firm may be forced to close because it is bankrupt. Working capital finances the day-to-day trading and if a firm tries to boost sales to a level beyond its capacity, working capital is reduced. This is called overtrading and is a common reason for insolvency.Example 3

Year 1Year 2

Current assets:stock2,0005,000

debtors2,5005,000

bank 1,500

6,00010,000

Current liabilities:creditors3,0008,000

bank

3,000

3,00011,000

Current ratio

= current assets

current liabilitiesCurrent ratioYear 1Year 2

6,00010,000

3,00011,000

= 2:1= 0.9:1The current ratio has fallen in Year 2 and the firm is now unable to meet the debts that are due within the next few months. This may be because the increased stock level has been financed by borrowing from the bank or because increased credit sales mean a higher debtors figure.

Example 4

Year 1Year 2

Total credit sales60,00075,000

Average debtors 2,0004,000

Debtors collection period =debtors

sales

Debtors collection periodYear 1Year 2

2,000

4,000

60,000

75,000

= 12 days= 19 daysThe debtors collection period is how long on average it has taken debtors to pay for their goods. In Year 2 they have been allowed 7 days longer than in Year 1 therefore credit control policy may need to be investigated. It may be that sales were only increased by allowing longer credit to customers.

Example 5

Year 1Year 2

Total credit purchases50,00060,000

Average creditors3,0002,500

Creditors payment period

= creditors

purchases

Creditors payment periodYear 1Year 2

3,000

2,500

50,000

60,000

= 21 days= 15 days

This ratio shows how long the firm is taking on average to pay for its credit purchases. In Year 2 the time has been shortened by 6 days which means that creditors have tightened their credit terms. It is also possible that the firm is not making full use of the credit facilities available to it and is paying too quickly.Example 6

Year 1Year 2

Stock at start14,00012,000

Add purchases40,00049,000

Goods available54,00061,000

Less stock at end12,00010,000

Cost of goods sold42,00051,000

Rate of stock turnover =cost of goods sold

average stock

Rate of stock turnoverYear 1Year 2

42,00051,000

13,00011,000

= 3.2 times= 4.6 timesThe rate of stock turnover gives the number of times stock has been changed during the year. The stock figure used is the average of the stock figures available the opening and closing stocks divided by 2.

A firm with a fast-moving stock (for example a bakery) will have a very high rate of stock turnover while one with a slow-moving stock (for example a furniture supplier) will have a low figure.

In Year 2 the rate of stock turnover has increased because a lower amount of stock is being held while output has risen. Further investigation would show if this trend was favourable and has led to higher profits.

Financial analysis: exercises

Exercise 1

From the following information calculate the return on capital employed for each year.

Year 1Year 2Year 3

Capital at start50,00054,00060,000

Add profit5,0008,10015,000

55,00062,10075,000

Less drawings1,0002,1001,500

Capital at end54,00060,00073,500

Exercise 2

Copy and complete the following table. Calculate the return on capital employed for each year.

Year 1Year 2Year 3

Capital at start100,000

Add profit25,00024,00021,000

125,000

Less drawings5,0004,000

Capital at end

155,000

Exercise 3

Use the information below to calculate the following for each year:

(a)gross profit %

(b)net profit %

(c)expenses %.

Year 1Year 2Year 3

Sales60,00072,00096,000

Less cost of goods sold40,00054,00067,200

Gross profit20,00018,00028,800

Less expenses8,0007,2009,600

Net profit12,00010,80019,200

Exercise 4

Copy and complete the following table then calculate gross profit %, net profit %, expenses % and rate of stock turnover.

Year 1Year 2Year 3

Sales120,000160,000220,000

Less cost of goods sold90,000

132,000

Gross profit32,000

Less expenses18,0008,000

Net profit

66,000

Exercise 5

Trading and Profit and Loss Accounts for year ended 31 March

Year 1Year 2

Sales

80,000

94,000

Less cost of sales

Stock at start6,000

8,000

Add purchases50,000

69,800

56,000

77,800

Less stock at end8,00048,00012,00065,800

Gross profit

32,000

28,200Less expenses

16,000

11,280

Net profit

16,000

16,920

Calculate the following ratios for each year:

(a)gross profit %

(b)net profit %

(c)expenses %

(d)rate of stock turnover.Exercise 6

Trading and Profit and Loss Accounts for year ended 31 July

Year 1Year 2

000s000s000s000sSales

120

140

Less cost of sales

Stock at start8

6

Add purchases70

74

78

80

Less stock at end6721070

Gross profit

48

70Less expenses

18

28

Net profit

30

42

Calculate the following ratios for each year and give one possible reason for any increase/decrease in Year 2:

(a)gross profit %

(b)net profit %

(c)expenses %

(d)rate of stock turnoverExercise 7

Using the following information, calculate the debtors collection period and the creditors payment period for each of the 3 firms.

BlackWhiteGray

Credit purchases100,00048,000235,000

Credit sales150,00075,000342,500

Average creditors10,0002,40014,500

Average debtors12,0003,50013,200

Exercise 8

Use the following figures to calculate the debtors collection period and the creditors payment period for each year and comment on any increase/decrease in the ratios in Year 2.

Year 1Year 2

Credit sales88,50096,800

Credit purchases54,20068,800

Average debtors4,6007,200

Average creditors2,6002,500

Exercise 9

From the following Balance Sheet extracts calculate the current ratio for each year and suggest a reason for any differences that have arisen.

Balance Sheet as at 28 February

Year 1Year 2Year 3

Current assetsStock4,0003,0004,000

Debtors2,5001,6001,400

Bank4,0001,400

10,5006,0005,400

Current liabilitiesCreditors3,5003,0003,200

Bank

4,000

3,5003,0007,200

Exercise 10

Study the ratios given for Years 1 and 2 then give one possible reason for each of the differences that have arisen.

Year 1Year 2

(a)Return on capital employed18%18.5%(b)Gross profit %30%40%

(c)Net profit %20%22%

(d)Current ratio2:12.5:1

(e)Debtors collection period25 days32 days

Exercise 11

Study the following set of final accounts provided by D Matthews and calculate the ratios listed below.

(a)Gross profit %

(b)Net profit %

(c)Expenses %

(d)Return on capital employed

(e)Rate of stock turnover

(f)Current ratio

(g)Debtors collection period

(h)Creditors payment period

Trading and Profit and Loss Accounts for year ended 31 December

Sales

48,000

Less cost of goods sold

Stock at start2,000

Add purchases36,800

Goods available38,800


Gross profit

12,000

Less expenses

4,800

Net profit

7,200

Exercise 11 (contd)

Balance Sheet as at 31 December

FIXED ASSETS

Machinery

12,200

Delivery van

3,80016,000

CURRENT ASSETS

Stock2,800

Debtors2,000

Bank1,000

Cash2006,000

LESS CURRENT LIABILITIES

Creditors

2,800

NET CURRENT ASSETS

3,200

TOTAL ASSETS

19,200

FINANCED BY

Capital at start

12,000

Add net profit

7,200

19,200

Exercise 12

You have been given the final accounts of A S Wilson and the following figures and for the average firm in this type of business:

(a)gross profit %27%

(b)net profit %9.5%

(c)return on capital employed16%

(d)rate of stock turnover8 times

(e)current ratio2:1

From the final accounts prepare ratios similar to those above and in each case give one possible reason for the difference (if any) between A S Wilsons figures and those of the average firm.

Trading and Profit and Loss Accounts for year ended 30 June

Sales

40,000


Stock at start4,000

Add purchases32,000

Goods available36,000


Gross profit

10,000

Less expenses

6,000

Net profit

4,000

Exercise 12 (contd)

Balance Sheet as at 30 June

FIXED ASSETS

Machinery

20,000

Delivery van

12,00032,000

CURRENT ASSETS

Stock6,000

Debtors8,00014,000


Creditors10,000

Bank2,00012,000

NET CURRENT ASSETS

2,000

TOTAL ASSETS

34,000

FINANCED BY

Capital at start

30,000

Add net profit

4,000

34,000

Exercise 13

(a)From the information below calculate the following figures:

(i)gross profit %

(ii)net profit %

(iii)current ratio

(iv)debtors collection period

(v)creditors payment period

(vi)rate of stock turnover

Trading and Profit and Loss Accounts for year ended 30 September

000s000sSales

60


Stock at start4

Add purchases40

Goods available44

Less stock at end836

Gross profit

24

Less expenses

12

Net profit

12

Exercise 13 (contd)

Balance Sheet as at 30 September

000s000s000sFIXED ASSETS

Motor lorry

36

Machinery

1046

CURRENT ASSETS

Stock8

Debtors614


Creditors8

Bank210

TOTAL ASSETS

4

50

FINANCED BY

Capital at start

40

Add net profit

12

52Less drawings

2

50

(b)Compare your answers with the figures given below for the average business in this line and give one possible reason for each difference shown.

(i)Gross profit %

40%

(ii)Net profit %

25%

(iii)Current ratio

1.5:1

(iv)Debtors collection period

30 days

(v)Creditors payment period

90 days

(vi)Rate of stock turnover

7 times

Exercise 14

The following final accounts have been supplied by Western Builders plc.

You are requir

Documents

A and F-using Accounting Info Tcm4-117030 (2)