a and f-using accounting info tcm4-117030

7/29/2019 A and F-using Accounting Info Tcm4-117030

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NATIONAL QUALIFICATIONS CURRICULUM SUPPORT

Accounting andFinance

Using Accounting

Information

Break-even AnalysisProfit Maximisation

Financial Analysis

[INTERMEDIATE 2]

Dorothy Brown


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INTRODUCTION

HISTORY 3

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 theNational Qualif ications support programme for Accounting and Finance.

ISBN 1 85955 653 1

Learning and Teaching Scotland

Gardyne RoadDundee

DD5 1NY

www.LTScotland.com


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ACCOUNTING AND FINANCE iv

CONTENTS

Section One Break-even Analysis 1-53

Section Two Profit Maximisation 57-94

Section Three Financial Analysis 97-144


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vi ACCOUNTING AND FINANCE

INTRODUCTION

This publication contains both summary notes and a range of computational

exercises covering break-even analysis, profit maximisation and financialanalysis. It also includes questions covering the underpinning knowledge andunderstanding of the unit and suggested solutions to all questions andexercises. At the end of each section, there are extension exercises which aredesigned to stretch more able students and take them in the direction ofHigher level. The exercises are not intended to be used for assessmentpurposes.

The publication is targeted at students who are undertaking the Higher StillUsing Accounting Information Unit at Intermediate 2 level. It covers thebasic knowledge required in dealing with break -even analysi s, limit ingfactors for profit maximisation and ratio calculation for financial analysis.

Teachers and lecturers are expected to augment these as, where and whenthey deem it appropriate.

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

Section One - Break-even AnalysisSection Two - Profit Maximisation

Section Three - Financial Analysis


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Section One

Break-even Analysis

Contents

Break-even analysis - summary notes, example, tasks andsuggested solutions 1-6

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

solutions 7-9

Exercises 1-6 with suggested solutions 10-18

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

examples, tasks with suggested solutions 19-27

Break-even analysis - theory questions with suggested solutions 28-30


Extension exercises 1-3 with suggested solutions 48-53


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BREAK-EVEN ANALYSIS

ACCOUNTING AND FINANCE 1

SECTION ONE

Break-even point

What is meant by the term break even? A firm breaks even when income issufficiently high to exactly cover total costs therefore neither a profit nor aloss is made. However, break-even analysis is not usually applied to thewhole firm but rather to a single product, studying its profitability bycomparing 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 ofactivity. It is therefore seen as a valuable tool for the managementaccountant. 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. rawmaterials.

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.


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BREAK-EVEN ANALYSIS

2 ACCOUNTING AND FINANCE

Example 1

The following figures have been supplied by A Gardiner, who is consideringmaking plant pots. He is particularly concerned to know how many he mustmake 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 Profitoutput 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 salesrevenue of 1,600.


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BREAK-EVEN ANALYSIS


Profit/loss

Profit/loss (the difference between sales revenue and total costs) at variousoutput levels is shown in the final column of the table on p. 2. At 100 unitsof output the loss is (500) and at 400 units of output a profit of 1,000 ismade. Break-even analysis is thus useful in forecasting profit/loss figures fordifferent production levels.

Margin of safety

Output above BEP which gives a profit is the margin of safety. This margincan be measured by comparing the level of output with BEP and it can beexpressed 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 thesales 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:

Margin of safety (units) = actual units BEP units

Margin of safety (revenue) = actual revenueBEP revenueoractual units BEP units x selling price per unit


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BREAK-EVEN ANALYSIS


Task 1

Use the following information supplied by Julie Carter to complete the tableand answer the questions that follow.


Variable costs per unit:

materials 7wages 5 12


Units of Fixed Variable Total Sales Profit

output costs costs costs revenue (loss)

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 of2,000 units?

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


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BREAK-EVEN ANALYSIS


Task 2

Julie is considering reducing the selling price to 18 per unit although thecosts would remain unchanged. Draw up another table to show the effect ofthis 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 of2,500 units?

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


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BREAK-EVEN ANALYSIS


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 units500 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

(a) Break-even point = 2,000 units or 36,000 sales revenue

(b) Margin of safety = 2,500 2,000 units = 500 units500 units x 20 = 10,000 sales revenue



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BREAK-EVEN ANALYSIS


Break-even charts

A chart is a simple method of conveying information, particularly where thereare many figures to be read. A line chart is considered the most suitable wayof 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 slopingupwards 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, totalcosts, 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 thesales revenue and total costs lines:

thearea 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.


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BREAK-EVEN ANALYSIS


Constructing a break-even chart

Before a break-even chart is produced, the following points should beconsidered:

the level of activity is always shown on the horizontal axis and it mustallow for all levels of production to be shown

sales revenue and costs (in ) are shown on the vertical axis: the scalechosen 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 inthe table for Task 1 (p. 4). Label clearly the fixed costs, total costs andrevenue lines and the break-even point.

(b) On the same chart, add the new sales revenue line for the figures inTask 2 (p. 5), showing the new break-even point.


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BREAK-EVEN ANALYSIS


Suggested solution to Task 3(a)

Suggested solution to Task 3(b)


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BREAK-EVEN ANALYSIS


Break-even charts: exercises

Exercise 1

(a) Using the data given below prepare a break-even chart to show fixedcosts, total costs, sales and break-even point.

Data

Total fixed costs 4,000Variable costs per unit 15Selling price per unit 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 fixedcosts, total costs, sales and break-even point.

Data

Total fixed costs 48,000Variable costs per unit 12Selling price per unit 24Projected output levels 1,0007,000 units


(i) units of output (ii) sales value

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


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BREAK-EVEN ANALYSIS


Exercise 3

(a) Prepare a break-even chart to show fixed costs, total costs and salesrevenue lines. Indicate the break-even point.

Data

Variable costs per unit: materials 10

labour 15

Selling price per unit 40Total fixed costs 60,000Projected output levels 1,0008,000 units



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

(d) Management are considering increasing the selling price to 45 perunit. Add this new sales line to your chart and show the new break-even point.

(e) State the new break-even point in


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


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BREAK-EVEN ANALYSIS


Exercise 4

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

Data

Projected output levels 1,0007,000 units

Total fixed costs 40,000Variable costs per unit: materials 12

wages 10Selling price per unit 30



(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. Addthe new total costs line to your chart and show the new break-evenpoint.

(e) State the new break-even point in


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


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BREAK-EVEN ANALYSIS


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 and800 units.


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Break-even charts: suggested solutions to exercises

Exercise 1

(a)

(b) Break-even point = 400 units; 10,000

(c) Profit at 500 units = 1,000Profit at 700 units = 3,000

Exercise 2

(a)

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


Profit at 7,000 units = 36,000


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BREAK-EVEN ANALYSIS


Exercise 3

(a)


(c) Profit at 6,000 units = 30,000Profit at 8,000 units = 60,000

(d)

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

(f) Profit at 4,000 units = 20,000Profit at 6,000 units = 60,000


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BREAK-EVEN ANALYSIS


Exercise 4

(a)


(c) Profit at 6,000 units = 8,000Profit at 7,000 units = 16,000

(d)

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

(f) Profit at 5,000 units = 10,000Profit at 7,000 units = 30,000


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BREAK-EVEN ANALYSIS


Exercise 5

(a) Total fixed costs = 4,000

(b) Variable cost of 100 units = 1,000

(c) Total cost of 100 units = 5,000Total cost of 300 units = 7,000

(d) Revenue from 200 units = 3,600Revenue from 500 units = 9,000

(e) Break-even point = 500 units; 9,000

(f) Profit at 500 units = 0Profit at 600 units = 800Profit 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 = 9,000Revenue from 600 units = 18,000

(e) Break-even point = 600 units; 18,000

(f) Profit at 700 units = 1,000Profit at 800 units = 2,000


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BREAK-EVEN ANALYSIS


Contribution in break-even analysis calculation of

BEP

Although break-even charts are easily produced and interpreted, it is notnecessary to have a chart to find the profitability of a product at differentoutput 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 whichthe 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 thefixed costs. Once the fixed costs have been covered, that contributionbecomes profit .

Example

Lightwell makes lamps and is investigating the profitability of producing anew design. The following figures are available.

Estimated variable cost per lamp 40

Selling price per lamp 60Total 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, howmany lamps need to be sold in order to break even?

Break-even point(BEP) = fixed costs

unit contribution

= 4,00020

= 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


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BREAK-EVEN ANALYSIS


Check:

Sales revenue of 200 units = 60 200 = 12,000Less variable cos t 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


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BREAK-EVEN ANALYSIS


Task 4

Complete the figures in the following table.

Firm Selling price Variable cost Contribution Fixed BEP BEP

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

a 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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BREAK-EVEN ANALYSIS



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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BREAK-EVEN ANALYSIS



profit

Break-even analysis can be used to estimate profit or loss at various levels ofoutput. On a break-even chart, the margin of safety is the area to the right ofbreak-even point where output is greater than break-even point and a profit isshown. The margin of safety is the excess of sales over break-even pointand can be expressed in sales volume (units) and sales revenue ().

At break-even point fixed costs have been covered therefore in the margin ofsafety contribution becomes profit. The calculation of profit is thereforevery 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 muchprofit will be made at output levels of 250, 320, 400, 480 and 550 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 F ixed Profitlevel contribution contribution costs

(units)

250 20 5,000 4,000 1,000

320 20 6,400 4,000 2,400

400 20 8,000 4,000 4,000

480 20 9,600 4,000 5,600

550 20 11,000 4,000 7,000


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BREAK-EVEN ANALYSIS



required output

As well as being used to forecast profit or loss at different levels of output,break-even analysi s is also useful in calculating the output required to give acertain amount of profit. After break-even point, contribution becomes profittherefore:

total contribution required = fixed costs + desired profit.

Example

M Morrison has provided the following information:

Selling price per unit 30Variable costs per unit 20Contribution per unit 10


(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 = 3,000Unit contribution = 10

Output required = 3,00010

= 300 units


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BREAK-EVEN ANALYSIS


Check:

Break-even point = 2,00010

= 200 units

Profit required = 1,000Unit contribution = 10

Number of profitable units = 1,00010

= 100 units

Total output required = break-even point + profitable units= 200 + 100 units= 300 units


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BREAK-EVEN ANALYSIS


Task 5

Complete the figures in the following table using the information in theexample 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 Requiredprofit 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


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BREAK-EVEN ANALYSIS


Break-even analysis: theory questions

Question 1

Break-even analysis is seen as a valuable tool for the managementaccountant. 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 meantby 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 revenuefor 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 outputregardless 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 towardsmeeting 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 ofbreak-even point on a break-even chart.

(c) Break-even point is the point at which fixed costs are covered andneither a profit nor a loss is made. Total contribution is equa l to fixedcosts and total revenue is equal to total costs.

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


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BREAK-EVEN ANALYSIS


Question 4

(a) The fixed costs line is horizontal because fixed costs remain constant atdifferent 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 graphwhere 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 beencovered, i.e. at break-even point, any further contribution that arises fromadditional sales is profit as only the variable costs have to be met.


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BREAK-EVEN ANALYSIS


Contribution in break-even analysis: exercises

Exercise 1

Three firms have supplied the following information:

A Anderson B Benson C Cameron

Variable costs per unit 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 hasprovided the following figures:




(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 ()?


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BREAK-EVEN ANALYSIS


Exercise 3

Alert plc installs burglar alarm systems and expects to install 400 units ofSystem 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 consideringmanufacturing a new style of shirt:

Selling price per unit 21.00Variable costs per unit:

materials 6.50wages 4.50


(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?


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BREAK-EVEN ANALYSIS


Exercise 5

Novel ties plc assembles novel clocks and has estimated the fo llowing figuresfor a new style:


Variable costs per unit:component parts 12

wages 6


(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 newcontribution 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 anoutput of 20,000 units:


Selling price per unit 85Variable 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 revenue?


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BREAK-EVEN ANALYSIS


Exercise 7

J Jones has supplied the following figures:

Variable costs per unit:materials 36

wages 15expenses 3



(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 thecoming year. The following figures are forecast:

Selling price per unit 52Variable costs per unit 28



(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.


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BREAK-EVEN ANALYSIS


Exercise 9

Deeside Woodworkers produces clocks and the following figures areavailable:




(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 and600 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:


Variable costs per unit:materials 30

fastenings and locks 12wages 25


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.


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BREAK-EVEN ANALYSIS


Exercise 11

The following figures relate to ornamental trees supplied by nurserymen J &M Dawson, who have fixed costs of 6,480:

Selling price per tree 36

Variable costs per tree 20

(a) 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 detailsof costs have been supplied:

Variable costs per unit:materials 80component parts 120

wages 100


(a) Find the contribution per unit.


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

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


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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 11.80Variable costs per unit 3.00 4.50 6.80

Contribution per unit 3.00 4.00 5.00

(b) BEP =oncontributiunit

costsfixed

3

500,4

4

400,6

5

500,7

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

units units units

(c) Sales revenue 1,500 6 1,600 8.50 3,500 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 =oncontributiunit

costsfixed

=18

000,63

= 3,500 units

(c) Sales revenue = 40 3,500 units= 140,000

(d) Margin of safety (i) = salesbreak-even point= 8,000 3,500 units

= 4,500 units

(ii) = 40 4,500 units= 180,000


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BREAK-EVEN ANALYSIS


Exercise 4

(a) Contribution per shirt = sel ling price variable costs= 21 11= 10


costsfixed

=10

000,33

= 3,300 units


(d) Contribution per shirt = 22 11= 11

(e) Break-even point =11

33,000

= 3,000 units

(f) Sales revenue = 22 3,000 units= 66,000


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BREAK-EVEN ANALYSIS


Exercise 5

(a) Contribution per unit = selling price variable costs= 34 18= 16


costsfixed

=16

8,960

= 560 units

(c) Sales revenue = 34 560 units= 19,040

(d) New contribut ion = 34 20= 14

(e) New break-even point =14

8,960

= 640 units

Sales revenue = 34 640= 21,760


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BREAK-EVEN ANALYSIS


Exercise 6

(a) Contribution per quilt = selling price variable costs= 85 54= 31

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

costsfixed

=31

198,400

= 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) =31

179,800

= 5,800 units

(ii) = 85 5,800= 493,000


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BREAK-EVEN ANALYSIS


Exercise 7

(a) Contribution per unit = selling price variable costs= 78 54= 24


costsfixed

=24

60,000

= 2,500 units


(d) Output BEP Margin of Profit

level (units) safety

(units) (units)

3,000 2,500 500 500 24 = 12,000

4,000 2,500 1,500 1,500 24 = 36,000


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BREAK-EVEN ANALYSIS


Exercise 8

(a) Contribution per unit = selling pricevariable costs= 52 28= 24

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

costsfixed

=24

13,920

= 580 units

(ii) = 52 580 units

= 30,160

(c) Output BEP Margin of Profit


(units) (units)

640 580 60 24 60 = 1,440

720 580 140 24 140 = 3,360


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BREAK-EVEN ANALYSIS


Exercise 9

(a) Contribution per clock = 80 55= 25


costsfixed

=25

12,000

= 480 clocks

Sales revenue = 80 480

= 38,400



(units) (units)

500 480 20 20 25 = 500

600 480 120 120 25 = 3,000

(d) New contribution = 85 55= 30

(e) New break-even point =30

12,000

= 400 units

Sales revenue = 85 400= 34,000


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BREAK-EVEN ANALYSIS


Exercise 10



costsfixed

=72

19,800

= 275 units

Sales revenue = 139 275 units= 38,225



(units) (units)

300 275 25 72 25 = 1,800

400 275 125 72 125 = 9,000

(d) Total contribution required = fixed costs + profit= 19,800 + 7,920= 27,720

Unit contribution = 72

Output required =oncontributiunit

oncontributitotal

=72

27,720

= 385 units


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BREAK-EVEN ANALYSIS


Exercise 11



costsfixed

=16

6,480

= 405 units

Sales revenue = 36 405 units= 14,580

(c) Fixed Profit Total Unit Output

costs required contribution contribution required

required

6,480 1,360 7,840 1616

7,840= 490units

6,480 5,040 11,520 1616

11,520= 720 units



(units) (units)

450 405 45 16 45 = 720

580 405 175 16 175 = 2,800


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BREAK-EVEN ANALYSIS


Exercise 12



costsfixed

=280

686,000

= 2,450 units

Sales revenue = 580 2,450 units= 1,421,000

(c) Fixed Profit Total Unit Output

costs required contribution contribution required

required

686,000 16,800 702,800 280280

702,800= 2,510 units

686,000 64,400 750,400 280280

750,400= 2,680 units



(units) (units)

5,000 2,450 550 280 550 = 154,000


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BREAK-EVEN ANALYSIS


Contribution in break-even analysis: extension exercises

Exercise E1

Wondersew produces sewing machines that are sold at 1,200 each. Thefollowing costs are incurred.

Fixed costs 157,500

Variable costs:materials 80component parts 350

wages 140

You are required to calculate the following:

(a) the contribution per sewing machine(b) the break-even point in units and sales revenue(c) the profit at output levels of 320 and 425 units

(d) the output level required to give a profit of 75,600(e) the new contribution per unit if the selling price is reduced to 1,095

(f) the break-even point at the new selling price(g) the new output level required to give the same profit of 75 ,600.

Exercise E2

Scotstoun Display Stands estimates that it can sell 2,000 display stands at200 each. The costs of production are shown below.

Variable costs per unit: materials 80labour 40


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.


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BREAK-EVEN ANALYSIS


Exercise E3

Stonehaven Clocks makes alarm clocks and has supplied the followingfigures.

Output 6,000 clocks

Total fixed costs 60,000Selling price per clock 37

Variable costs per clock:materials 6component parts 4labour 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 andestimates 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.


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BREAK-EVEN ANALYSIS


Contribution in break-even analysis: suggested solutions

to extension exercises

Exercise E1

(a) Contribution per unit = selling pricevariable costs= 1,200 570= 630


costsfixed

=630

157,500

= 250 units

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



(units) (units)

320 250 70 630 70 =44,100

425 250 175 630 175= 110,250

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

= 157,500 + 75,600= 233,100


Output required =oncontributiunit

oncontributitotal

=630

233,100

= 370 units

(e) New contribution = 1,095 570= 525

(f) New break-even point =525

157,500

= 300 units


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BREAK-EVEN ANALYSIS


(g) Total contribution required = 233,100


Output required =525

233,100

= 444 units


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BREAK-EVEN ANALYSIS


Exercise E2

(a) Unit contribution = 200120= 80

Break-even point =oncontributiunit

costsfixed=

80

96,000

= 1,200 units

Sales revenue = 1,200 200= 240,000

(b) Profit = (outputBEP) x unit contribution

Output 1,400 units 2,000 units

1,4001,200 2,000 1,200200 80 800 80

16,000 64,000

(c) New selling price = 220New contribution = 220 120

= 100

New break-even point =100

96,000

= 960 units

New sales revenue = 960 220= 211,200

(d) New profit

Output 1,400 units 2,000 units

1,400960 2,000 960440 100 1,040 100

44,000 104,000


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BREAK-EVEN ANALYSIS


Exercise E3

(a) Unit contribution = 3722= 15

Break-even point =oncontributiunit

costsfixed

=15

60,000

= 4,000 units

Sales revenue = 4,000 37= 148,000

(b) Profit = (6,000 BEP) 15= (6,000 4,000) 15= 2,000 15= 30,000

(c) New variable costs = 21New contribution = 37 21

= 16

New break-even point =16

60,000

= 3,750 units

Sales revenue = 3,750 37= 138,750

(d) New profit = (8,000 BEP) 16= (8,000 3,750) 16

= 4,250 16= 68,000


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Section Two

Profit Maximisation

Contents

Profit maximisation limiting factor, summary note, tasks, suggestedsolutions 57-64




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PROFIT MAXIMISATION


SECTI ON TWO

Profit maximisation: limiting factor

Most businesses are set up with a view to making a profit, preferably as higha profit as possible. Maximising profit simply means making as much profit

as possible from the resources available. This is usually achieved by makingas much as can be sold if demand for a product is limited there is no pointin making more even though it may be possible to do so.

Sometimes demand for a product may be high but production may be limitedby 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 factorexists, management will have to decide which level of output will make mostprofit , taking into account the limit ing factor. Instead of studying thecontribution per unit, contribution must be considered in the light of thelimiting factor.

Example

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

A B

Contribution per unit 12 12Number of labour hours per unit 4 2

Number of units demanded 10,000 12,000

Total labour hours available 60,000 hoursTotal fixed costs 160,000


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PROFIT MAXIMISATION


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

be:

Product A Product B

10,000 4 + 12,000 2

40,000 + 24,000 = 64,000 hours

The number of labour hours required is 64,000 but only 60,000 labour hoursare available. Since there is a shortage of 4,000 hours, labour is the limitingfactor. How will this problem be solved? Should one or both products be cutback? B has a lower unit contribution than A so should only B be reduced?Before a decision is taken, the contribution per labourhour must be

examined.

A B

Contribution per unit 12 12Number of labour hours 4 2Contribution per labour hour 3 6

Only now can the order of priority be decided. Since the product giving thehighest contribution per labour hour is B, the full demand for B will be metand the production of A will be cut by 4,000 hours. Production will beplanned thus:

1 Product B 24,000 hours/2 = 12,000 units

2 Product A 60,00024,000 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 60,000Contribution per labour hour 3 6Total contribution 3 36,000 6 24,000

108,000 144,000 252,000

Less fixed costs 160,000

Profit (maximised) 92,000


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PROFIT MAXIMISATION


Task 6

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

Total labour hours available 20,000


Product Rugs Scarves

Selling price per unit 80 20

Variable costs per unit 40 8Labour 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 theshortage 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 youranswer.

(e) Show how many labour hours would be used in the production of bothrugs 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)?


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PROFIT MAXIMISATION


Task 6: worksheet

Rugs Scarves Total

(a) Units demanded 5,000 12,000

Labour hours per unit .......... ..........

Total labour hours required .......... .......... ..........

Labour hours available ..........

Shortage of labour hours ..........

(b) The limiting factor is .............. ............ ............ ............ ............ ............ .

(c) Contribution per unit ........ ........

Labour hours per unit .......... ..........

Contribution per labour hour ........ ........

(d) Order of priority: first

second

Reason .................................................................................................

.............................................................................................................

(e) Labour hours available for production .......... .......... 20,000

(f) Contribution per labour hour(from (c) above) ........ ........

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

(g) Total fixed costs ........

Profit ........

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


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PROFIT MAXIMISATION


Suggested solution to task 6

Rugs Scarves Total

(a) Units demanded 5,000 12,000

Labour hours per unit 2 1

Total labour hours required 10,000 12,000 22,000

Labour hours available 20,000

Shortage of labour hours 2,000

(b) The limiting factor is labour hours

(c) Contribution per unit 40 12

Labour hours per unit 2 1

Contribution per labour hour 20 12

(d) Order of priority: first: rugs

second: scarves

Reason Rugs have higher contribution per labour hour, which isthe 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

(h) Scarves and rugs made 5,000 10,000


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PROFIT MAXIMISATION


Task 7

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

Total machine hours available 22,000


Product X Y Z

Selling price per unit 26 48 58Variable cost per unit 16 32 40Number 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 theshortage 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 youranswer.

(e) Show how many machine hours would be used in the production of eachof 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)?


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PROFIT MAXIMISATION


Task 7: worksheet

X Y Z Total

(a) Units demanded .......... .......... ..........

Machine hours per unit .......... .......... ..........

Total machine hours required .......... .......... .......... ..........

Machine hours available ..........

Shortage of machine hours ..........

(b) The limiting factor is .............. ............ ............ ............ ............ ..

(c) Contribution per unit ........ ........ ........

Machine hours per unit .......... .......... ..........

Contribution per machine hour ........ ........ ........

(d) Order of priority: first:

second:

Reason .....................................................................................

.................................................................................................

(e) Machine hours available for

production .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..

(f) Contribution per machine hour ........ ........ ........

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

(g) Less total fixed costs ........

Profit ........

(h) Number of units made .......... .......... ..........


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PROFIT MAXIMISATION


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 forproduction 4,000 10,500 7,500 22,000

(f) Contribution per machine hour 10 8 12

Total contribution 40,000 84,000 90,000 214,000

(g) Less total fixed costs 140,000

Profit 74,000

(h) Number of units made 4,000 5,250 5,000


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PROFIT MAXIMISATION


Limiting factor: exercises

Exercise 1

The total number of labour hours available in AB Components is 20,000. Thefirm has provided the following additional figures for products X and Y:

X Y

(Per unit)

Contribution 4 6Labour hours 2 2

Units demanded 5,000 7,000


(a) the labour hours required to meet current demand

(b) the contribut ion 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.


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PROFIT MAXIMISATION


Exercise 2

The total number of labour hours available in Quality Doors plc is 5,500.The firm has provided the following additional figures for 2 designs,Georgian and Victorian:

Georgian Victorian

(Per unit)

Selling price 150 200Variable costs 60 100Labour hours 1.5 2

Units demanded 2,000 1,500



(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.


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PROFIT MAXIMISATION


Exercise 3

City Shirts plc produces 3 designs Classic, City and Casual for which18,000 machine hours are available. The following figures have beenprovided:

Classic City Casual

(Per unit)

Selling price 28 30 22Variable cost 13 16 10Machine 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 contribut ion per unit for each product

(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.


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PROFIT MAXIMISATION


Exercise 4

County Suits plc produces 3 designs Kelso, Selkirk and Melrose for which2,200 machine hours are available. The following figures have beenprovided:

Kelso Selkirk Melrose

(Per unit)

Selling price 360 280 250Variable cost 180 140 100Machine hours 5 3.5 3

Units demanded 200 300 180







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


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PROFIT MAXIMISATION


Exercise 5

Scottish Greenhouses plc makes 2 products Dunkeld and Aberfeldy. Totalfixed costs are 400,000 and 5,000 labour hours are available. The followingfigures are available:

Dunkeld Aberfeldy

(Per unit)

Selling price 1,200 800Variable costs 600 360Labour 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

(h) the profit after deduction of fixed costs.


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PROFIT MAXIMISATION


Exercise 6

Rockers Ltd makes 2 styles of chairRelax and Relax-plus for which 1,800machine hours are available. Total fixed costs amount to 30,000. Thefollowing additional information has been provided:

Relax Relax-plus

(Per unit)

Selling price 130 150Variable costs 70 90Machine hours 1.5 2

Units demanded 800 400











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PROFIT MAXIMISATION


Exercise 7

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

Sales demand for the products is expected to be:

Moray 2,000 unitsDornoch 1,600 unitsBeauly 1,000 units.

The following figures are also available:

Moray Dornoch Beauly(Per unit)Selling price 120 200 150Variable costs 60 110 80Labour hours 2 1.5 2











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PROFIT MAXIMISATION


Exercise 8

West Coast Models plc has a labour supply with a limit of 2,020 hoursavailable. It produces 3 different model boats Class 1, Class 2 and Class 3and its fixed costs amount to 8,000.

The following figures have also been supplied:

Class 1 Class 2 Class 3

(Per unit)Selling price 480 420 320Variable cost 300 240 200Labour hours 20 18 15

Units demanded 20 40 80











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PROFIT MAXIMISATION


Exercise 9

Troon Models, which has a total of 7,000 machine hours available, produces3 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 24Variable cost 8 15 12Machine hours 0.25 0.5 0.5

Units demanded 6,000 8,000 4,000




(c) the contribution per machine hour for each produc t







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PROFIT MAXIMISATION


Exercise 10

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

Model 100: 2,000 unitsModel 200: 5,000 units

Model 300: 4,000 units

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

The following figures have also been supplied:

Model 100 Model 200 Model 300

(Per unit)Selling price 25 20 42Variable cost 15 12 26Machine hours 0.5 0.25 1











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PROFIT MAXIMISATION


Exercise 11

The following information has been supplied by Davidson & Williams:

total fixed costs: 40,000labour hours available: 6,500

Product A B C D

(Per unit)Selling price 40 10 18 8Variable cost 20 6 12 3Labour hours 2 0.5 1 0.25

Units demanded 1,000 3,000 2,200 4,800




(c) the contribut ion per labour hour for each product







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PROFIT MAXIMISATION


Exercise 12

Conservatory Decor makes 4 styles of candleholdersingle, 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 beensupplied:

Single 2-candle 3-candle 5-candle

(Per unit)Machine hours 0.25 0.25 0.5 0.5Variable cost 8 13 15 18Selling price 15 18 26 30

Units demanded 1,600 600 1,400 500











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PROFIT MAXIMISATION


Limiting factor: suggested solutions to exercises

Exercise 1

X Y Total

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

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

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

Contribution per labour

2

4

2

6hour

2 3

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

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

(e) Units produced

hours2

hours000,6

hours2

hours000,14

3,000 units 7,000 units


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PROFIT MAXIMISATION


Exercise 2

Georgian Victorian Total

(a) Labour hours required 1.5 hours 2,000 2 hours 1,5003,000 hours 3,000 hours 6,000 hours

(b) Contribution per unit 15060 200 100

(selling price variablecosts) 90 100

(c) Contribution per 90 100labour hour 1.5 hours 2 hours

60 50

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

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

(f) Units produced 3,000 hours 2,500 hours1.5 hours 2 hours

2,000 units 1,250 units


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PROFIT MAXIMISATION


Exercise 3

Classic City Casual Total

(a) Machine hours 0.5 10,000 0.5 12,000 0.5 16,000required 5,000 hours 6,000 hours 8,000 hours 19,000 hours

(b) Contribution 2813 30 16 22 10

per unit 15 14 12

(c) Contribution 15 14 12per machine hour 0.5 0.5 0.5

30 28 24

(d) First: ClassicSecond: City

Third: Casual

(e) Machine hours 5,000 hours 6,000 hours 7,000 hours 18,000hoursavailable (18,000 11,000)

(f) Units produced 5,000 6,000 7,0000.5 0.5 0.5

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


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PROFIT MAXIMISATION


Exercise 4

Kelso Selkirk Melrose Total

(a) Machine hours 5 hours 200 3.5 hours 300 3 hours 180required 1,000 hours 1,050 hours 540 hours 2,590 hours

(b) Contribution 360180 280 140 250 100

per unit 180 140 150

(c) Contribution 180 140 150per machine 5 3.5 3hour

36 40 50

(d) First: Melrose

Second: Selkirk

Third: Kelso

(e) Machine hours 610 hours 1,050 hours 540 hours 2,200hoursavailable (2,200 1,590)

(f) Units produced 610 1,050 5405 3.5 3

122 units 300 units 180 units


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PROFIT MAXIMISATION


Exercise 5

Dunkeld Aberfeldy Total

(a) Labour hours 5 hours 400 4 hours 800required 2,000 hours 3,200 hours 5,200 hours

(b) Contribution 1,200600 800 360

per unit 600 440

(c) Contribution 600 440per labour hour 5 4

120 110

(d) First: DunkeldSecond: Aberfeldy

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

(f) Units produced 2,000 3,0005 4

400 units 750 units

(g) Contribution per labour hour 120 110

Labour hours 2,000 3,000Total contribution 120 2,000 110 3,000

240,000 330,000 570,000

(h) Fixed costs 400,000

Profit 170,000


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PROFIT MAXIMISATION


Exercise 6

Relax Relax-plus Total

(a) Machine hours required 1.5 hours x 800 2 hours x 4001,200 hours 800 hours 2,000 hours

(b) Contribution 13070 150 90

per unit 60 60

(c) Contribution 60 60per machine hour 1.5 2

40 30

(d) First: RelaxSecond: Relax-plus

(e) Machine hours 1,200 600 1,800

available (1,800 1,200)

(f) Units produced 1,200 6001.5 2

800 units 300 units

(g) Contribution permachine hour 40 30

Machine hours 1,200 600Total contribution 48,000 18,000 64,000

(h) Fixed costs 30,000Profit 34,000


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PROFIT MAXIMISATION


Exercise 7

Moray Dornoch Beauly Total

(a) Labour hours 2 hours 2,000 1.5 hours 1,600 2 hours 1,000required 4,000 hours 2,400 hours 2,000 hours 8,400 hours

(b) Contribution 12060 200 110 150 80

per unit 60 90 70

(c) Contribution per 60 90 70labour hour 2 1.5 2

30 60 35

(d) First: DornochSecond: Beauly

Third: Moray

(e) Labour hours 3,600 hours 2,400 hours 2,000 hours 8,000 hoursavailable (8,000 4,400)

(f) Units produced 3,600 2,400 2,0002 1.5 2


(g) Total contribution 30 x 3,600 60 x 2,400 35 x 2,000

108,000 144,000 70,000 322,000



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PROFIT MAXIMISATION


Exercise 8

Class 1 Class 2 Class 3 Total

(a) Labour hours 20 hours 20 18 hours 40 15 hours 80required 400 hours 720 hours 1,200 hours 2,320 hours

(b) Contribution 480300 420 240 320 200

per unit 180 180 120

(c) Contribution 180 180 120per labour hour 20 18 15

9 10 8

(d) First: Class 2Second Class 1

Third: Class 3

(e) Labour hours 400 hours 720 hours 900 hours 2,020hoursavailable (2,020 1,120)

(f) Units produced 400 720 90020 18 15

20 units 40 units 60 units

(g) Total contribution 9 400 10 720 8 900

3,600 7,200 7,200 18,000



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PROFIT MAXIMISATION


Exercise 9

A B C Total

(a) Machine hours 0.25 hours 6,000 0.5 hours 8,000 0.5 hours 4,000required 1,500 hours 4,000 hours 2,000 hours 7,500 hours

(b) Contribution 12 8 30 15 24 12

per unit 4 15 12

(c) Contribution 4 15 12per machine hour 0.25 0.5 0.5

16 30 24

(d) First: BSecond: C

Third: A

(e) Machine hours 1,000 hours 4,000 hours 2,000 hours 7,000 hours available (7,000 6,000)

(f) Units produced 1,000 4,000 2,0000.25 0.5 0.5

4,000 units 8,000 units 4,000units

(g) Total contribution 16 1,000 30 4,000 24 2,00016,000 120,000 48,000 184,000



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Exercise 10

Model 100 Model 200 Model 300 Total

(a) Machine hours 0.5 2,000 0.25 5,000 1 4,000required 1,000 hours 1,250 hours 4,000 hours 6,250 hours

(b) Contribution 2515 20 12 42 26

per unit 10 8 16

(c) Contribution 10 8 16per machine hour 0.5 0.25 1

20 32 16

(d) First: Model 200Second: Model 100

Third: Model 300

(e) Machine hours 1,000 hours 1,250 hours 3,750 hours 6,000hoursavailable (6,000 2,250)

(f) Units produced 1,000 1,250 3,7500.5 0.25 1


(g) Total contribution 20 1,000 32 1,250 16 3,75020,000 40,000 60,000 120,000



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Exercise 11

A B C D Total

(a) Labour hours 2 1,000 0.5 3,000 1 2,200 0.25 4,800required 2,000 hours 1,500 hours 2,200 hours 1,200 hours 6,900 hours

(b) Contribution 40 20 10 6 18 12 8 3

per unit 20 4 6 5

(c) Contribution 20 4 6 5per labour hour 2 0.5 1 0.25

10 8 6 20

(d) First: DSecond: A

Third: B

Fourth: C

(e) Labour hours 2,000 hours 1,500 hours 1,800 hours 1,200 hours 6,500hoursavailable (6,500 4,700)

(f) Units produced 2,000 1,500 1,800 1,2002 hours 0.5 hours 1 hour 0.25 hours

1,000 units 3,000 units 1,800 units 4,800 units

(g) Total contribution 10 2,000 8 1,500 6 1,800 20 1,200

20,000 12,000 10,800 24,000 66,800

(h) Fixed costs 40,000

Profit 26,800


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Exercise 12

Single 2-candle 3-candle 5-candle Total

(a) Machine hours 0.25 1,600 0.25 600 0.5 1,400 0.5 500required 400 hours 150 hours 700 hours 250 hours 1,500 hours

(b) Contribution 158 18 13 26 15 30 18

per unit 7 5 11 12

(c) Contribution 7 5 11 12per machine hour 0.25 0.25 0.5 0.5

28 20 22 24

(d) First: SingleSecond: 5-candle

Third: 3-candle

Fourth: 2-candle

(e) Machine hours 400 hours 50 hours 700 hours 250 hours 1,400hoursavailable (1,400 1,350)

(f) Units produced 400 50 700 2500.25 0.25 0.5 0.5

1,600 units 200 units 1,400 units 500 units

(g) Total contribution 28 400 20 50 22 700 24 250

11,200 1,000 15,400 6,000 33,600



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Limiting factor: extension exercises

Exercise E1

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

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

J: 18,000 unitsK: 16,000 units

L: 20,000 unitsM: 10,000 units.

The following additional data is also given:

Product Selling Variable Machine

price costs hours

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

J 24 18 0.25

K 18 10 0.25

L 25 13 0.5

M 20 12 0.5

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

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

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

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

(d) Calculate how many machine hours will be used for making each of the4 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.


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Exercise E2

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

A: 200 units

B: 150 unitsC: 400 unitsD: 320 units.

Budgeted figures for the 4 products have been supplied.

Product Variable Selling Labourcosts price hours

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

A 160 300 4

B 110 230 3

C 225 350 5

D 175 295 4

Answer each of the following questions.

(a) How many labour hours are necessary to meet current demand? Why isit 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 cutback, showing calculations to support your answer.

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

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

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

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


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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 isexpected to be 200, 500, 100 and 150 units, respectively. The number oflabour hours available is 3,300 and fixed costs total 50,000.

The following figures are available.

Product Selling Materials Wages Labour

price cost cost hours

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

de Luxe Double 250 40 70 5

Standard Double 182 30 48 4

de Luxe Single 180 28 56 4

Standard Single 130 25 36 3

Answer each of the following questions.

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

(b) Calculate the labour hours needed to satisfy current demand. Compareyour answer with the number of hours available and calculate theshortage 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 tomaximise profit.

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

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


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Suggested solutions to extension exercises

Exercise E1

J K L M Total

(a) Contribution 24 18 18 10 25 13 20 12

per uni t 6 8 12 8Contribution 6 8 12 8

per machin e hou r 0.2 5 0.25 0.5 0.524 32 24 16

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

(c) Machine hours 0.25 18,000 0.25 16,000 0.5 20,000 0.5 10,000

required 4,500 hours 4,000 hours 10,000 hours 5,000 hours 23,500 hours

(d) Machine hours 4,500 hours 4,000 hours 10,000 hours 3,500 hours 22,000hours available (22,000 18,500)

(e) Total 24 4,500 32 4,000 24 10,000 16 3,500contribution 108,000 128,000 240,000 56,000 532,000


Profit 172,000

(f) Units produced 4,500 4,000 10,000 3,500

0.25 0.25 0.5 0.5

18,000 units 16,000 units 20,000 units 7,000 units

(g) Sales revenue 24 18,000 18 16,000 25 20,000 20 7,000

432,000 288,000 500,000 140,000 1,360,000


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Exercise E2

A B C D Total

(a) Labour hours 4 hours 200 3 hours 150 5 hours 400 4 hours 320required 800 hours 450 hours 2,000 hours 1,280 hours 4,530 hours

This figure must be calculated when labour is in scarce supply. It will tell the firm wh ether 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) Contribution 300 160 230 110 350 225 295 175

per u ni t 140 120 125 120

Contribution 140 120 125 120

per l abour h our 4 3 5 4

35 40 25 30

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

(d) Labour hours 800 hours 450 hours 1,670 hours 1,280hours 4,200 hours

available (4,300 2,530)

(e) Units produced 800 450 1,670 1,280

4 3 5 4

200 units 150 units 334 units 320 units

(f) Total 35 800 40 450 25 1,670 30 1,280contribution 28,000 18,000 41,750 38,400 126,150


Profit 56,150

(g) Sales revenue 300 200 230 150 350 334 295 32060,000 34,500 116,900 94,400 305,800


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Exercise 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 giv en pr io rit y.

(b) de Luxe Double Standard Double de Luxe Single Standard Single Total

Labour hours 5 hours 200 4 hours 500 4 hours 100 3 hours 150

required 1,000 hours 2,000 hours 400 hours 450 hours 3, 850 hoursLabour hours

available 3,300 hours

Shortage 550 hours

(c) Contribution 250 110 182 78 180 84 130 61

per u ni t 140 104 96 69

Contribution 140 104 96 69

per l abour h our 5 4 4 3

28 26 24 23

(d) Labour hours 1,000 hours 2,000 hours 300 hours 3,300hours

available (3,300 3,000)

(e) Total 28 1,000 26 2,000 24 300 contribution 28,000 52,000 7,200 87,200


Profit 37,200

(f) Units produced 200 units 500 units 75 units

Sales revenue 250 200 182 500 180 7550,000 91,000 13,500 154,500


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Section Three

Financial Analysis

Contents

Summary note and example 97-103




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SECTION THREE

Ratios and percentages

At the end of each financial year Final Accounts are prepared that show thefirms profitability and its financial position at that date. These accounts area record of the firms performance and, by themselves, have limited use sincethey give no indication of whether the results are favourable or unfavourable.For example, they show the profit/loss figure but there is nothing to indicatewhether 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 arebeing used effectively for example, is a bank balance of 10,000 a healthysign 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 withthe 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 returnof 20,000 on capital of 100,000 (20%) is obviously better than a return of20,000 on capital of 200,000 (10%). Ratios and percentages are thereforenormally 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 toknow 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.


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Profit

a and f-using accounting info tcm4-117030

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