ManagerialAccountAH_tcm4-322498

7/30/2019 ManagerialAccountAH_tcm4-322498

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NATIONAL QUALIFICATIONS CURRICULUM SUPPORT

Accounting

Managerial Accounting

[ADVANCED HIGHER]

Lindsay Mitchell


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The Scottish Qualifications Authority regularly reviews

the arrangements for National Qualifications. Users of

all NQ support materials, whether published by LT

Scotland or others, are reminded that it is their

responsibility to check that the support materials

correspond to the requirements of the current

arrangements.

Acknowledgement

Learning and Teaching Scotland gratefully acknowledge this contribution to the National

Qualifications support programme for Accounting.

First published 2005

Learning and Teaching Scotland 2005

This resource may be reproduced in whole or in part for educational purposes by educational

establishments in Scotland provided that no profit accrues at any stage.

2 MANAGERIAL ACCOUNTING (AH)



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Contents

Introduction 4

Section 1: Activity-Based Costing (ABC) 5

Section 2: Multi-Product Break-Even Analysis 30

Section 3: Contract Costing Statements 46

MANAGERIAL ACCOUNTING (AH) 3



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INTRODUCTION

Introduction

This pack contains notes and exercises for three topics activity-based

costing, multi-product break-even analysis and contract costing.

Activity-based costing and multi-product break-even analysis are both new

topics for Advanced Higher and it is intended that the enclosed material will

provide guidance to tutors as to what students are expected to know whencovering the topics.

Contract costing appeared in the old Higher Accounting and Finance

arrangements but is now included in the Advanced Higher content. As no

previous material on this topic has been produced it is hoped that this

package will fill the gap.

Each topic contains notes, exercises and full solutions.




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ACTIVITY-BASED COSTING (ABC)

Section 1

Activity-Based Costing (ABC)

In your studies in Higher Accounting one of the major topics in the

Cost/Management Accounting part of the syllabus was the treatment of

overhead costs within a business.

This involved the allocation and apportionment of overheads among cost

centres and the subsequent absorption of these cost-centre overheads into the

cost units produced in the cost centres.

The whole process described above can best be illustrated by the following

diagram.

Overhead Costs

Allocation Apportionment using

selected basis

Single Cost Centre Multiple Cost Centres

Production Cost Centres Service Cost Centres

Re-apportionment

using selected basis

Cost Units using

appropriate absorption rate

The above approach is sometimes referred to as the traditional approach to

overhead absorption. Activity-based costing has been developed within the

last 2030 years in an effort to avoid defects in the traditional system.




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The main characteristics of the traditional system are as follows:

it was developed in manufacturing industry

there were typically a narrow range of products

production processes were much simpler than now

direct material and labour costs were the main production costs

overhead costs were relatively small

inaccuracies due to arbitrary nature of process were therefore relatively

unimportant.

Activity-Based Costing (ABC) has therefore emerged due to the following:

product ranges have increased

overhead costs have become more significant

manufacturing concerns no longer dominate

service organisations account for a much larger share of economic activity

production is more complex and capital intensive.

The main ideas behind ABC are:

costs are caused by activities for example ordering, material handling,

scheduling, machining, assembling, etc.

production of products or supply of services creates the demand for these

activities

costs are therefore assigned to products or services on the basis of

consumption of these activities.




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Therefore ABC involves a number of stages.

1. Identify the major activities of the organisation.

2. Identify the factors which affect the cost of an activity. These factors

are known as COST DRIVERS e.g. the number of purchase orders

might be considered as the cost driver for the costs of a purchasing

department.

3. Collect the associated costs of each activity. This is known as the

COST POOL.

4. Allocate costs to products/services based on the demand created for the

cost drivers.

As with the traditional approach, ABC can be illustrated by a diagram:

Identify major activities

Create cost pool for each activity

Identify cost driver for each activity

Produce absorption rate for each pool based on cost driver

Overhead cost per unit

Let us now look at an example which will show both the traditional approach

to the treatment of overheads and then how ABC would treat the same

situation.




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Example

Deeside plc manufactures three products, A, B and C in their factory and usesa factory-wide absorption rate for absorbing overheads based on direct labour

hours. The following information relates to Period 5 of Year 3.

Product A B C

Production (units) 12,000 8,000 4,000

Direct Material Cost p.u. 40 30 20

Direct Labour Hours p.u. 4 6 2

Direct labour is paid at 8 per hour.

The overhead costs for Period 5 are as follows:

Machining 312,000

Set-up 56,000

Assembling 80,000

Goods Receiving 128,000

Dispatch 100,000

676,000

(a) Calculate the factory-wide absorption rate for Period 5.

(b) Calculate the cost p.u. of each product under the traditional approach to

treatment of overheads.

The company is considering using ABC as a method of arriving at the cost

per unit of their products and the following information is available for this

purpose:

The overheads have been investigated and while machining costs will be

absorbed on the basis of machine hours, cost drivers have been identified for

the other overheads.

Overhead Cost Driver

Set-up No. of production runs

Assembling No. of production orders

Goods Receiving No. of receipts

Dispatch No. of production orders




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The following additional information is also available:

Product A B CMachine hours per unit 2 3 1

No. of Production runs 1 2 5

No. of Material receipts 3 5 24

No. of Production orders 3 2 5

(c) Calculate a cost driver absorption rate for each of the above overheads.

(d) Calculate the cost per unit for each product under the ABC system.

This question contains a lot of information and lots of figures and therefore it

is important to read it carefully with a view to deciding which information

relates to each part of the question.

The purpose of this question is to show how the traditional method of

overhead absorption works and then to demonstrate the Activity-Based

Costing approach.

At the end of the question we will compare the two methods and see if we can

explain the differing results they produce.




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Solution

(a) This opening part of the question asks us to calculate a factory-wideoverhead absorption rate (sometimes called a blanket rate), based on

labour hours.

You should recall that the calculation of an overhead absorption rate divides

the relevant overhead (which may be for a cost centre or, as in this case, for

the whole factory) by the relevant units of the base selected. (There were

actually six possibilities, i.e. per unit, % on material, % on wages, % on

prime cost, per labour hour or per machine hour).

In this question we are using labour hours and therefore the calculation is as

follows:

Overhead Absorption Rate =Factory Overheads

Labour Hours

Although we know the total factory overheads we need to calculate the total

labour hours, i.e.

A 12,000 4 = 48,000

B 8,000 6 = 48,000

C 4,000 2 = 8,000104,000

We can now calculate the factory-wide rate

676,000=

104,000

= 6.50 per labour hour




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(b) In this next part we are asked to calculate the total cost per unit for each

product using the tradit ional approach.

This total cost will be the sum of the two direct costs material and labour,

plus overheads.

The question gives us the material cost p.u. for each product, but we will

have to calculate the figures for labour and overheads. For labour this will be

the number of labour hours per unit multiplied by the labour rate per hour.

For overheads it will be the number of labour hours per unit multiplied by the

overhead absorption rate calculated in part (a), i.e.

Cost per unit A B C

Material 40 30 20

Labour 32 (4 8) 48 (6 x 8) 16 (2 8)

Overheads 26 (4 6.50) 39 (6 x 6.50) 13 (2 6.50)

98 117 49

The remaining parts of the question now introduce the Activity-Based

Costing technique.

(c) This part asks us to calculate cost driver absorption rates for the

separate overheads.

The total overhead of the factory has been broken down into five activities.

For the first of these, machining, a traditional-style absorption rate is to be

used, i.e. machine hour rate.

Machine Hour Rate =Machine Overhead

Machine Hours

Once again we know the overhead but need to calculate the machine hours,

i.e.

A 12,000 2 = 24,000

B 8,000 3 = 24,000

C 4,000 1 = 4,000

52,000

Therefore the calculation is

312,000Machine Hour Rate =

52,000

= 6 per m/c hour




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For the other activities, which comprise the factory overheads, appropriate

cost drivers have been identified and we can use these to calculate the

relevant absorption rate.

The cost drivers identified are the number of production runs, the number of

production orders and the number of receipts. Therefore before we go any

further we must calculate the relevant figure for each driver.

Production Runs A 1

B 2

C 5

8

Production Orders A 3

B 2

C 5

10

Receipts A 3

B 5

C 24

32

Now we can calculate the absorption rate for each activity , based on therelevant cost driver.

Set-up56,000

=8

= 7,000 per run

Assembling80,000

=10

= 8,000 per order

Goods Receiving128,000

=

32

= 4,000 per receipt

Dispatch100,000

=10

= 10,000 per order




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(d) The final part requires us to use these figures to produce a cost per unit

for each product. Therefore we need to calculate the overhead cost perunit to add to the material and labour costs which we calculated in part

(b).

Machinery overhead is the simplest, i.e. machine hours per unit multiplied by

machine hour rate.

A 2 6 = 12

B 3 6 = 18

C 1 6 = 6

For the other overhead activities we need to relate the cost driver absorption

rate to the units produced.

A B C

Set-up 7,000 14,000 (7,000 2) 35,000 (7,000 5)

12,000 8,000 4,000

= 0.58 = 1.75 = 8.75

Assembling 24,000 (8,000 3) 16,000 (8,000 2) 40,000 (8,000 5)

12,000 8,000 4,000

=2 = 2 =10

Goods 12,000 (4,000 3) 20,000 (4,000 5) 96,000 (4,000 24)

Receiving 12,000 8,000 4,000

=1 = 2.50 = 24

Dispatch 30,000 (10,000 3) 20,000 (10,000 2) 50,000 (10,000 5)

12,000 8,000 4,000

= 2.50 = 2.50 = 12.50

Therefore using ABC total cost per unit for the products would be as follows:

A B C

Direct Materials 40 30 20

Direct Labour 32 48 16

Machinery 12 18 6

Set-up 0.58 1.75 8.75

Assembling 2 2 10

Goods Receiving 1 2.50 24

Dispatch 2.50 2.50 12.50

90.08 104.75 97.25




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Contrast these figures with the ones produced in the answer to part (b) of the

question. The most striking change is in the increase in the cost per unit of

Product C, although there is also a less substantial decrease in the cost perunit of the other two products. The increase in the cost of C has arisen

because most of the charges relating to C were not identified under the

traditional absorption system. The cost drivers identified in the ABC system

are responsible for generating these charges and thus we can suggest that the

ABC system produces a more accurate cost for each product.

The following examples will provide practice in applying the ABC system.

Solutions are provided at the end of this section.




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Question 1

Your company currently produces and sells 4 products, Alpha, Beta, Gammaand Delta. The following information relates to Period 3.

Alpha Beta Gamma Delta

Production (units) 180 150 120 180

Costs per unit:

Direct material 46 58 35 70

Direct labour 21 14 7 14

Machine hours per unit 4 3 2 3

Number of production runs 6 5 4 6

Number of requisit ions raised 30 30 30 30

Number of orders completed 18 15 12 18

Currently the production overhead is absorbed by the machine-hour rate

method and the following are the total production overhead costs for Period

3.

Machine Department 24,540

Set-up costs 6,300

Receiving costs 7,200

Inspection costs 3,150Despatch costs 7,560

48,750

Cost drivers have been identified as follows:

Set-up costs Number of production runs

Stores receiving Number of requisitions raised

Inspection Number of production runs

Despatch Number of orders completed

You are required to calculate:

(a) ( i) The machine-hour rate currently used to absorb the production

overhead.

(ii) The total cost per unit for each product if overheads are absorbed

by the method in (a)(i) .

(b) The cost per unit for each product using an ABC approach.




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Question 2

Jomit plc has budgeted for the following overhead costs for Period 6.

Material receipt costs 31,200

Power costs 39,000

Material handling costs 27,300

The company produces 3 products, P, Q and R for which the following

budgeted information is available for Period 6.

Product P Q R

Output (units) 4,000 3,000 1,600

Material batches 20 10 32

Per Unit

Direct material (kg) 4 6 3

Direct material () 6 5 9

Direct labour (hours) 0.2 0.5 1.0

Number of power operations 6 3 2

Direct labour rate per hour 8 8 8

Currently the overhead costs are each absorbed using a rate per direct labourhour.

However, the company is considering applying overheads using an ABC

approach and has identified drivers for the activities as follows:

Material receipt costs number of batches of material

Power costs number of power operations

Material handling costs kg of material handled

You are required to calculate:

(a) The total cost per unit for each product using the current overhead

absorption method.

(b) The total cost per unit for each product using the ABC method.




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Question 3

Your company currently produces a range of three products, D, E and F towhich the following details relate for Period 2.

D E F


Material cost per unit 18 10 20

Labour hours per unit 1 3 2

Machine hours per unit 3 2 6

Labour costs are 8 per hour and production overheads are currently absorbed

in the conventional system by reference to machine hours. Total production

overheads for Period 2 have been analysed as follows:

Set-up costs 327,250

Handling costs 187,000

Machining costs 140,250

Inspection costs 280,500

935,000

(a) Calculate the cost per unit for each product using conventional methods.

The introduction of an ABC is being considered and to that end the following

volume of activities have been identified with the current output levels.

D E F

Number of set-ups 90 138 576

Number of material issues 16 28 116

Number of inspections 180 216 804

(b) Calculate the cost per unit for each product using the ABC approach.




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Question 4

The following table summarises the details of the production levels, costs andcost drivers for Abtronics Ltd who have traditionally absorbed overheads into

production on the basis of a labour hour absorption rate. They wish to move

to an ABC system.

Product P Q R

Material cost per unit 20 15 10

Labour hours per unit 4 6 3

Machine hours per unit 4 3 6

Number of production runs 6 14 40

Number of production orders 45 30 75

Number of orders delivered 30 20 50

Number of receipts 12 28 80


Labour hours are paid for at 10 per hour.

Overheads Cost Driver

Machining 684,000 machine hours

Set-up costs 60,000 production runs

Receiving costs 240,000 number of receipts

Packing costs 300,000 number of orders deliveredEngineering costs 450,000 number of production orders

1,834,000

(a) Calculate the cost per unit for each product using the traditional

overhead absorption approach.

(b) Calculate the cost per unit using the ABC approach.




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Question 5

Param plc has incurred the following overheads in its factory during Period 6.

Quality control 90,000

Process set-ups 135,000

Purchasing 105,000

Order processing 120,000

Occupancy costs 150,000

Param plc produces a range of products, two of which are Product X and

Product Y. The following information relate to these two products.

X Y

Material costs per unit 5 8

Labour cost per unit 8 12

Number of process set-ups 150 210

Number of purchase orders issued 500 300

Number of customer orders 1,000 800

Machine hours per unit 3 2

Production (units) 10,000 6,000

Inspection takes place after each process set-up.

The cost drivers which have been identified for the factory are:

Quality control 450 inspections

Process set-ups 450 set-ups

Purchasing 1,000 purchase orders

Order processing 2,000 customer orders

Occupancy costs 75,000 machine hours

Calculate the cost per unit for Products X and Y using:

( i) exist ing overhead absorption rate per machine hour

( ii ) an act ivity-based costing approach.




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Solutions

Question 1

(a) (i) Total machine hours: Alpha 4 180 = 720

Beta 3 150 = 450

Gamma 2 120 = 240

Delta 3 180 = 540

= 1950

Total overheads = 48,750

48,750Machine hour absorption rate = 1,950

= 25

(ii) Cost per unit Alpha Beta Gamma Delta

Direct material 46 58 35 70

Direct labour 21 14 7 14

Production overhead 100 75 50 75

167 147 92 159

(b) Cost Driver Driver Cost per

transactions driver

Machine Dept 24,540 m/c hours 1950 12.58

Set-up 6,300 Runs 21 300

Receiving 7,200 Requisitions 120 60

Inspection 3,150 Runs 21 150

Despatch 7,560 Orders 63 120




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Overheads cost per unit

Alpha Beta Gamma Delta

Set-up1800

= 10180

1500= 10

150

1200= 10

120

1800= 10

180

Receiving1800

= 10180

1800= 12

150

1800= 15

120

1800= 10

180

Inspection900

= 5180

750= 5

150

600= 5

120

900= 5

180

Despatch2160

= 12180

1800= 12

150

1440= 12

120

2160= 12

180

Machine 4 12.58 3 12.58 2 12.58 3 12.58

Dept = 50.32 = 37.74 = 25.16 = 37.74

Total cost per unit Alpha Beta Gamma Delta

Materials 46.00 58.00 35.00 70.00

Labour 21.00 14.00 7.00 14.00

Set-up 10.00 10.00 10.00 10.00

Receiving 10.00 12.00 15.00 10.00

Inspection 5.00 5.00 5.00 5.00

Despatch 12.00 12.00 12.00 12.00Machine Dept 50.32 37.74 25.16 37.74

154.32 148.74 109.16 158.74




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Question 2

(a) Direct labour hours: P 4,000 0.2 = 800Q 3,000 0.5 = 1,500

R 1,600 1.0 = 1,600

3,900

Overhead absorption rates :

Material receipt31,200

= 8 per labour hour3,900

Power 39,000 = 10 per labour hour3,900

Material handling27,300

= 7 per labour hour3,900

Overhead cost per unit P Q R

Material receipt 8 0.2 8 0.5 8 1

= 1.60 = 4 = 8

Power 10 0.2 10 0.5 10 1

= 2 = 5 = 10

Material handling 7 0.2 7 0.5 7 1

= 1.40 = 3.50 = 7

Total cost per unit P Q R

Direct material 6.00 5.00 9.00

Direct labour 1.60 4.00 8.00Material receipt costs 1.60 4.00 8.00

Power costs 2.00 5.00 10.00

Material handling 1.40 3.50 7.00

12.60 21.50 42.00




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(b) ABC absorpt ion ra tes

Material receipt31,200

= 503.23 per batch62

Power39,000

= 1.08 per operation(W1)36,200

Material handling27,300

= 0.70 per kg(W2)38,800

W1 (4,000 6) + (3,000 3) + (1,600 2) = 36,200

W2 (4,000 4) + (3,000 6) + (1,600 3) = 38,800

Overhead costs

per unit P Q R

Material receipts503.23 20

4,000

503.23 10

3,000

503.23 10

1,600

= 2.52 = 1.68 = 10.06

Power 1.08 6 1.08 3 1.08 2

= 6.48 = 3.24 = 2.16

Material handling 0.70 4 0.70 6 0.70 3

= 2.80 = 4.20 = 2.10



Direct labour 1.60 4.00 8.00

Material receipt costs 2.52 1.68 10.06

Power costs 6.48 3.24 2.16

Material handling costs 2.80 4.20 2.10

19.40 18.12 31.32




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Question 3

(a) Number of machine hours = D 1,500 3 = 4,500= E 2,500 2 = 5,000

= F 14,000 6 = 84,000

= 93,500

Overhead absorption rate935,000

=93,500

= 10 per machine hour

Cost per unit D E F

Material 18 10 20

Labour 8 24 16

Overhead 30 20 60

56 54 96

(b) Total number of set-ups = 90 + 138 + 576

= 804

Absorption rate per set-up327,250

=804

= 407.03 per set-up

Total number of issues = 16 + 28 + 116

= 160

Absorption rate per issue187,000

=160

= 1,168.75

Absorption rate per machine hour140,250

=

93,500= 1.50

Total number of inspections = 180 + 216 + 804

= 1,200

Absorption rate per inspection280,500

=1,200

= 233.75




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Overheads per unit D E F

Set-up 90 407.031,500 138 407.03

2,500 576 407.03

14,000

= 24.42 = 22.47 = 16.75

Issue16 1,168.75

1,500

28 1,168.75

2,500

116 1,168.75

14,000

= 12.47 = 13.09 = 9.68

Machining 3 1.50 2 1.50 6 1.50

= 4.50 = 3 = 9

Inspection180 233.75

1,500

216 233.75

2,500

804 233.75

1,400

= 28.05 = 20.20 = 13.42

Total cost per unit D E F

Material 18.00 10.00 20.00

Labour 8.00 24.00 16.00

Set-up costs 24.42 22.47 16.75

Handling costs 12.47 13.09 9.68

Machine costs 4.50 3.00 9.00

Inspection costs 28.05 20.20 13.42

95.44 92.76 84.85




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Question 4

(a) Total labour hours = P 4 15,000 = 60,000Q 6 10,000 = 60,000

R 3 4,000 = 12,000

132,000

Total overheads = 1,834,000

Total absorption rate1,834,000

132,000

= 13.89

Cost per unit P Q R


Direct labour 40.00 60.00 30.00

Production overheads 55.56 83.34 41.67

115.56 158.34 81.67

(b) Cost driver absorption rates

Machining684,000

114,000

= 6.00 per machine hour

Set-up costs60,000

(6 + 14 + 40)

= 1,000 per production run

Receiving costs240,000

(12 + 28 + 80)

= 2,000 per receipt

Packing costs300,000

(30 + 20 + 50)

= 3,000 per order delivered

Engineering costs450,000

(45 + 30 + 75)

= 3,000 per production order




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Overhead cost per unit P Q R

Machining 6.00 4 6.00 3 6.00 6

= 24.00 = 18.00 = 36.00

Set-up costs6 1,000

15,000

14 1,000

10,000

40 1,000

4,000

= 0.40 = 1.40 = 10

Receiving costs12 2,000

15,000

28 2,000

10,000

80 2,000

4,000

= 1.60 = 5.60 = 40

Packing costs30 3,000

15,000

20 3,000

10,000

50 3,000

4,000

= 6 = 6 = 37.50

Engineering costs45 3,000

15,000

30 3,000

10,000

75 3,000

4,000

= 9 = 9 = 56.25



Direct labour 40.00 60.00 30.00

Machining 24.00 18.00 36.00

Set-up 0.40 1.40 10.00

Receiving 1.60 5.60 40.00

Packing 6.00 6.00 37.50

Engineering 9.00 9.00 56.25

101.00 115.00 219.75




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Question 5

(i) Total Factory Overheads = 90,000135,000

105,000

120,000

150,000

600,000

Total machine hours = 75,000

Absorption rate600,000

75,000

= 8 per machine hour

Cost per unit X Y

Material 5.00 8.00

Labour 8.00 12.00

Overheads 24.00 16.00

37.00 36.00

(ii) Cost Driver Absorption Rates

Quality control90,000

450= 200 per inspection

Process set-up135,000

450= 300 per set-up

Purchasing105,000

1,000= 105 per order

Order processing 120,0002,000

= 60 per order

Occupancy costs150,000

75,000= 2 per machine hour




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Overhead cost per unit X Y

Quality control 150 20010,000 210 200

6,000

= 3 =7

Process set-up150 300

10,000

210 300

6,000

= 4.50 = 10.50

Purchasing500 105

10,000

300 105

6,000

= 5.25 = 5.25

Order processing1,000 60

10,000

800 60

6,000

= 6 = 8

Occupancy 6 4

Cost per unit X Y

Material 5.00 8.00

Labour 8.00 12.00

Quality control 3.00 7.00

Set-up 4.50 10.50

Purchasing 5.25 5.25

Order processing 6.00 8.00

Occupancy 6.00 4.00

37.75 54.75




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MULTI-PRODUCT BREAK-EVEN ANALYSIS

Section 2

Multi-Product Break-Even Analysis

You will recall from your studies of Break-Even Analysis in Higher

Accounting that the basis of this technique was the ability to classify all costs

in an enterprise as either fixed or variable.

That is not to say that all costs are either totally fixed or totally variable.

Indeed there will be very few costs in the long run which could be said to fall

into either of these categories. However, the assumption that is made is that

all costs will be made up of a variable component and a fixed component, and

that these can be separated. Thus we could add all the variable components

together to arrive at a total variable cost per unit, and all the fixed

components to arrive at total fixed costs, e.g. if we consider a cost like

machine maintenance it can be argued that there would be a minimum amount

of maintenance required even if production was zero. That then would

constitute the fixed component of machine maintenance. Then, of course, as

output builds up the machines will be subject to more wear and tear and

breakdowns, and thus require more and more maintenance. This would

constitute the variable component of machine maintenance.

However, in your past studies the behaviour of costs (i.e. how costs change as

output changes) was kept relatively simple (e.g. direct costs like material and

wages were often assumed to be perfectly variable and costs like rent

assumed to be perfectly fixed).

In fact there were a number of assumptions made in break-even analysis

which had the effect of keeping things relatively simple e.g. the relationshipbetween sales revenue and volume was based on the assumption that the

selling price was constant at all levels of output and variable costs per unit

were also assumed to stay constant.

As far as this section of notes is concerned there was one further assumption

which simplified matters and which we are now going to relax, i.e. we

assumed that we were dealing with a single product model or perhaps, if there

were more than one product, we assumed a constant sales mix.




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Therefore what we are now going to consider is the effect of several products

on the calculations of break-even and profit and loss and the effect of changes

in product or sales mix.

Basic Concepts of Break-Even Analysis

It is perhaps worth revising the basic relationships which Break-Even

Analysis depends on.

As already stated the starting point is

Total Costs = Fixed Costs + Variable Costs

Since, by definition, fixed costs have no relationship with output/sales no

attempt is made to arrive at a total cost per unit.

The next step is to find what is left over out of sales revenue once the

variable costs have been met. This is called the contribution.

Contribution = Sales Variable Costs

It is so called because it is the contribution towards paying the fixed costs. If

there is sufficient contribution to pay the fixed costs and have something left

over then that will be profit (since all costs have now been met). If there isinsufficient contribution to cover the fixed costs then a loss will be made

(since the total costs have exceeded sales revenue).

In between these two situations there must be a point where there is just

sufficient contribution to pay the fixed costs and thus neither a profit nor a

loss is made.

This is known as Break-Even Point and is where

Contribution = Fixed Costs

Remember as we said above

Contribution Fixed Costs = Profit (if positive)

= Loss (if negative)

The key to calculating the profit or loss in any situation is therefore

contribution, and profit/loss can only be found by two steps, i.e.

find contribution by comparing sales and variable costs

deduct fixed costs from contribution to determine profit or loss.




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Break-Even Point is important, because it marks the output level where a

business moves from loss into profit ; therefore there is an important formula

which allows us to calculate it, i.e.

Break-Even Point (units) =Fixed Costs

Contribution per unit

To convert this into Break-Even Sales we only need to multiply the break-

even units by the selling price per unit.

Break-Even Point () = B/E units Selling Price per unit

There is one other relationship which is important in break-even analysis andthat is the relationship between contribution and sales value. This is

calculated as contribution/sales and is sometimes referred to as the

Profit/Volume Ratio, although it can be referred to simply as the

contribution/sales ratio.

The important thing about this ratio is that it will remain constant at all levels

of output. This is because all the constituent parts of the ratio are by

definition variable, i.e. sales, variable costs and consequently contribution. It

must be remembered, however, that this ratio will only remain constant as

long as the basic assumptions mentioned earlier hold true, i.e. a constant

selling price per unit and a constant variable cost per unit.

The advantage of this ratio is that once calculated you can apply it at any

level of output and thus determine the contribution earned from a particular

level of sales or the sales necessary for a particular level of contribution and

hence profit.




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Multi-Product Break-Even

The problem with calculating the break-even point for a business with morethan one product is that another variable has been added, i.e. the product mix.

Product mix means the relative percentage or share of total sales which each

product represents.

If each product earns a different contribution per unit then any change in the

relative volume of sales of each product will cause difficulties.

The way round this is to calculate a weighted average contribution per unit to

apply when calculating the break-even point.

Example

CMA plc produce a range of three products to which the following details

relate:

Product Basic Special Deluxe

Selling Price p.u. 205 250 350

Variable Costs p.u. 130 145 200

Fixed costs for CMA plc total 600,000

Let us take each product in turn and calculate what the break-even point

would be if only that product were produced and sold.

Basic

Contribution per unit = 205 130

= 75

Break-Even Point (units) =600,000

75

= 8,000




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Special

Contribution per unit = 250 145= 105


105

= 5,715 (approx.)

Deluxe

Contribution per unit = 350 200

= 150


150

= 4,000

The two extreme outcomes for break-even are 8,000 units if all sales were the

basic model and 4,000 units if all sales were deluxe.

Therefore any sales mix will be bound to produce a break-even point which

lies somewhere between these two levels.

Given a sales mix the break-even point can be found using the familiarformula but using a weighted average contribution per unit.

Using the figures from the above example let us calculate the break-even

point if sales were spli t evenly between the three products.

Weighted Average Contribution per unit = (1/3 75) + (1/3 105)

+ (1/3 150)

= 25 + 35 + 50

= 110


110

= 5454.5

= 5455




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We can prove that this is correct by working out the relevant figures.

Basic Special DeluxeSales (units) 1,818 1,818 1,818

Sales () 372,690 454,500 636,300

Variable Costs 236,340 263,610 363,600

Contribution 136,350 190,890 272,700

Total Contribution 599,940

Fixed Costs 600,000

60 (caused by rounding units)

Now let us see what happens when the sales mix changes.

Suppose the product mix is 3:2:1 for Basic/Special/Deluxe.

Total sales are then represented by

Basic 3/6 = 1/2

Special 2/6 = 1/3

Deluxe 1/6

Weighted Average Contribution per unit =

(1/2 75) + (1/3 105) + (1/6 150)

= 37.50 + 35 + 25

= 97.50


97.50

= 6154 (nearest unit)

The answer is greater than the previous answer and that makes sense because

we have moved to a s ituation where we are selling most of the product which

has the lowest contribution per unit and we are selling fewest of the one with

the highest contribution per unit.




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Once again we can prove that this is the correct answer by multiplying out the

figures.

Total Units = 6,154

Split as follows: Basic 3077 (1/2)

Special 2051 (1/3)

Deluxe 1026 (1/6)

Basic Special Deluxe

Sales () 630,785 512,750 359,100

Variable Costs 400,010 297,395 205,200

Contribution 230,775 215,355 153,900


Fixed Costs 600,000

30 (due to rounding)

This approach can then be used to answer the typical range of questions

which you associate with basic break-even problems, i.e. calculating the level

of sales required to earn a specified profit.

For example, using the sales mix of 3:2:1 above calculate the sales in units of

each product which would produce a profit of 100,000.

Remember in marginal or break-even problems there is no direct connection

between units and profit , and therefore we must convert profit into

contribution.

Contribution = Fixed Costs + Profit

= 600,000 + 100,000

= 700,000

Total No. of Units Required =

700,000

97.50

= 7,180 (approx)

Units of Basic = 1/2 7,180

= 3,590

Units of Special = 1/3 7,180

= 2,393

Units of Deluxe = 1/6 7,180

= 1,197




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Let us just prove that this is the correct solution.


Sales () 735,950 598,250 418,950

Variable Costs 466,700 346,985 239,400

Contribution 269,250 251,265 179,550


Less: Fixed Costs 600,000

Profit 100,065 (due to rounding)

If we now consider the opposite type of problem:

How much profit will be made from sales of 9,000 units, also assuming a

ratio of 3:2:1 between sales of the three products?

Once again we must convert the units into contribution before we can

calculate profit.

Contribution from 9,000 units = 9,000 97.50

= 877,500

Less: Fixed Costs 600,000Profit 277,500

Once again we can prove the result:

Sales Mix Basic 1/2 9,000 = 4,500

Special 1/3 9,000 = 3,000

Deluxe 1/6 9,000 = 1,500


Sales () 922,500 750,000 525,000

Variable Costs 585,000 435,000 300,000

Contribution 337,500 315,000 225,000


Fixed Costs 600,000

277,500

Here are some questions to try.




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Question 1

Clear Picture Ltd produce two models of t elevision sets, Brilliant and SuperBright to which the following details relate for the current year.

Brilliant Super Bright

Selling price per set 250 350

Variable cost per set 125 190

Current sales (units) 5,000 2,500

Fixed costs 600,000

(a) Calculate the profit which Clear Picture would earn from the above

situation.

(b) Calculate the total number of sets which require to be sold to break

even if the above sales mix applies.

(c) Prepare a detailed Profit Statement to show the full figures for each

product at break-even point.

(d) What would the break-even point be if the sales mix changed to three

Brilliant sets for every Super Bright set?

(e) Explain why the increase/decrease in break-even point was predictable.




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Question 2

MPV plc manufactures and sells three products with the following sellingprices and variable costs:

Basic Superior Supreme

Unit selling price 3.00 3.75 5.00

Unit variable cost 2.10 1.50 3.25

Current sales (units) 500,000 230,000 190,000

Existing fixed costs amount to 1,000,000.

(a) Calculate the total number of units MPV plc will require to sell in order

to break even if the current sales mix persists.

(b) Prepare a Profit Statement showing the relevant figures for the three

products to prove your answer to (a).




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Question 3

Easylearn Ltd provide expert tutoring on a range of subjects. Next yearsbudget shows the following expected figures:

Accounting Maths English French

Expected hours of work 2,500 3,000 3,500 1,000

Charge per hour 40 50 45 35

Variable cost per hour 10 15 9 10

Fixed costs for the year are expected to be 198,600.

(a) Calculate the total number of hours Easylearn Ltd will have to work to

break even, assuming the above mix of tutoring hours.

(b) Calculate the contribution from each subject and in total at break-even

point.

(c) Using the same mix as above prepare a Profit Statement for Easylearn

plc to earn a profit of 100,000.

(d) The actual hours provided during the year turned out to be:

Accounting 1,500Maths 1,000

English 4,500

French 3,000

Calculate the break-even number of hours.




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Solutions

Question 1

(a) Brilliant Super Bright

Contribution p.u. 125 160

Total Contribution 5,000 125 2,500 160

= 625,000 = 400,000

Total Contribution for company 1,025,000

less: Fixed Costs 600,000

Profit 425,000

(b) Sales (units) Brilliant 5,000 67%

Super Bright 2,500 33%

7,500 100%

Weighted Average Contribution p.u.= (125 67%)+(160 33%)

= 83.75 + 52.80

= 136.55

B/E Point (units) =600,000

136.55

= 4,394 (nearest unit)

(c) Brilliant Super Bright

Sales (units) 4394 67% 4394 33%

2944 1450

Profit Statement for Year Brilliant Super Bright

Sales 736,000 507,500

Variable Costs 368,000 275,500

Contribution 368,000 232,000






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(d) Weighted Average Contribution p.u. = (125 75%)+(160 25%)

= 93.75 + 40

= 133.75

B/E point (units) =600,000

133.75

= 4,486

(e) Since they were selling more of the product with the lower contribution

per unit , it was inevitable that the break-even point would increase.




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Question 2

(a) Sales (units) Basic 500,000 0.5435 or 54.35%Superior 230,000 0.25 or 25%

Supreme 190,000 0.2065 or 20.65%

920,000 1.0 100%

Contribution per unit Basic = 0.90

Superior = 2.25

Supreme = 1.75

Weighted Average Contribution p.u. = (0.90x0.5435)+(2.25 x

0.25) + (1.75 0.2065)

= 48.915p + 56.25p + 36.138p

= 141.303p

B/E point (units) =1,000,000

1.413

= 707,714

(b) Total Sales (units) = 707,714

Basic = 707,714 0.5435 = 384,643Superior = 707,714 0.25 = 176,928

Supreme = 707,714 0.2065 = 146,143

MPV Profit Statement

Basic Superior Supreme Total

Sales 1,153,929 663,480 730,715 2,548,124

Variable Costs 807,750 265,392 474,965 1 ,548,107

Contribution 346,179 398,088 255,750 1,000,017

Fixed Costs 1,000,000

17




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Question 3

(a) Tutoring hours: Accounting 2,500 25%Maths 3,000 30%

English 3,500 35%

French 1,000 10%

10,000 100%

Contribution per hour Accounting 30

Maths 35

English 36

French 25

Weighted Average Contribution per hour

= (30 25%) + (35 30%) + (36 35%) + (25 10%)

= 7.50 + 10.50 + 12.60 + 2.50

= 33.10

B/E Point (hours ) =198,600

33.10

= 6,000

(b) Accounting Maths English French Total

Hours of 1,500 1,800 2,100 600 6,000

Tutoring

Contribution 1,500 1,800 2,100 600

30 35 36 25

45,000 63,000 75,600 15,000 198,600




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(c) Contribution required = 198,600 + 100,000

= 298,600

Number of hours required =298,600

33.10

= 9,021 (nearest hour)

Hours per subject: Accounting 25% 2,255

Maths 30% 2,706

English 35% 3,158

French 10% 902

Profit Statement for Easylearn Ltd

Accounting Maths English French Total

Sales 90,200 135,300 142,110 31,570 399,180

Variable Costs 22,550 40,590 28,422 9,020 100,582

Contribution 67,650 94,710 113,688 22,550 298,598


Profit 99,998

(d) Accounting 1,500 15%

Maths 1,000 10%

English 4,500 45%

French 3,000 30%

10,000 100%

Weighted Average Contribution per unit

= (15% 30) + (10% 35) + (45% 36) + (30% 25)

= 4.50 + 3.50 + 16.20 + 7.50

= 31.70

B/E Point (hours ) =198,600

31.70

= 6,265




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CONTRACT COSTING STATEMENTS

Section 3

Contract Costing Statements

A long-term contract is defined as:

A contract entered into for the design, manufacture or construction of a single

substantial asset or the provision of a service where the time taken to complete thecontract is such that the contract activity falls into different accounting periods.

So a contract is really an example of job costing with the following important

features:

it usually takes a long time to complete

it is usually completed at a particular site which is not the contractors

workplace.

Therefore contracts are common in most types of building and construction work,

civil engineering, shipbuilding, etc.

These contracts pose a particular problem for the accountant, i.e. when should any

profit on the contract be recognised in the accounts?

The problem arises because there is a conflict between two fundamental

accounting concepts or principles, i.e. matching and prudence.

The matching or accruals concept states that income and expenditure should be

matched against one another and placed in the accounting period to which they

relate.

Clearly in the case of long-term contracts the costs and indeed the revenues will

overlap more than one accounting period. Because a contractor cannot wait until

the end of a contract before he receives any income from it, the work is valued at

regular intervals by architects who certify the value of the work at selling price.

When this is compared with the costs incurred to date it may well indicate a profit

on the contract.




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However, the prudence concept states that profits should not be anticipated and

therefore recording profit on an incomplete contract could be construed as

breaching that concept.

As with many problems where basic principles conflict, the resolution of the

problem is something of a compromise. It would clearly be unacceptable only to

recognise contract profit at the end of the contract. This would mean that in any

accounting period the profits would simply relate to those contracts which had

finished during the period, irrespective of the length of period of the contracts.

It seems that recognition of profit on a contract would be acceptable as long as the

concept of prudence is not ignored.

Statement of Standard Accounting Practice Number 9 (SSAP 9) gives guidance on

this matter.

It states that profits should only be recognised on a contract when its outcome can

be assessed with reasonable certainty. The profit to be included should be

calculated prudently and should reflect the amount of work completed at the

accounting date. On the other hand if losses are anticipated they must be

recognised in full.

The standard does not give unequivocal guidance on a formula to be applied in

recognising profit on a contract, and several methods have been developed whichmeet the underlying principles outlined above.

One approach is to determine the expected profit at the conclusion of the contract

and recognise a proportion of this figure based on the percentage completion of

the contract at the appropriate date.




48/59


Consider the following example:

At 31 December Year 4 the figures relating to an incomplete contract are asfollows:

Costs to date 3m

Estimated costs to complete 1m

Value of certified work 4m

Contract price 5m

We can calculate the expected outcome of the contract as follows:

Cost of work completed 3m

Add: estimated costs to complete 1m

estimated total costs 4m

contract price 5m

estimated profit 1m

Profi t Recognised =Estimated Profit Value of Certified Work

Contract Price

=1m 4m

5m

= 800,000

However, if a contract is not close to completion the forecast of expected profits

may be deemed to be too unreliable to adopt as a basis for profit recognition.

In these circumstances the fraction may be based on the notional profit at that

point in the li fe of the contract rather than on the estimated profit at the end of the

contract, i.e.

Profit recognised =Work Certified

Notional ProfitContract Price

What is important is that whichever formula is used takes into account the degree

of completion of the contract, which both of the formulae above do.




49/59


Preparing Contract Accounts

ExampleA builder is currently working on two major contracts, both of which are

incomplete at the end of his financial year on 31st March Year 7.

The details of the contracts are as follows:

Contract A Contract B

000s 000s

Opening Balances at 1st April Year 6

Completed Work 1,620

Materials on Site 80

Plant & Machinery (written down value) 300

Wages Accrued 20

Costs Incurred During Year to 31st March Year 7

Materials Delivered to Site 340 880

Wages Paid 180 400

Salaries 60 160

Value of Plant Delivered 800 140

Head Office/Establishment Charges Apportioned 40 80

Closing Balances at 31st March Year 7Materials on Site 80

Value of Plant on Site 600 80

Wages Accrued 20 40

Other Details

Value of Work Certified at year end 800 3,200

Contract Price 1,200 5,800

Profit is recognised using the following formula:

Work CertifiedNotional Profit

Contract Price

Prepare accounts for each of the contracts showing clearly the calculations of any

profit to be taken for the period.




50/59


Solution

Contract A a/cMaterials 340 Balances c/d

material 80

Wages Paid 180 plant 600

add: accrued 20 200 Cost of contract to date 758

Salaries 60

Plant & Machinery 800

Head Office costs 38

1,438 1,438

Cost of Contract 758 Work Certified 800

Profit & Loss a/c (Profit Taken) 28

Profit not Taken 12

800 800

Balances b/d: material 80 Balances b/d wages 20

plant 600

Working

Notional Profit = Value of Work Certified less cost of contract to date

= 800 758= 42

Profi t Recognised =800 42

1,200

= 28

The first step is to charge or debit the Contract a/c with all the costs incurred

during the year to date, including any accruals, e.g. in this case wages accrued.

However, not all of these costs have been used up in the course of the year so any

remaining unused, i.e. material and plant and machinery are carried down asbalances to start the next period.

This allows the cost of the contract to date to be calculated as the sum of the debit

entries less the credit balances being carried forward.

The working for the notional profit and the part of it which is going to be

recognised can now be done, using whichever formula the question suggests.

The profit taken is then debited to the account as it will go to the credit of the

Profit & Loss a/c.




51/59


Contract B a/c

Balances b/d Balance b/d: Wages 20

Completed Work 1,620 Balances c/d: Plant 80Material 80 Cost of Contract to date 3,600


Materials Delivered 880

Wages Paid 400

add accrued 40 440

Salaries 160


Head Office Costs 80

3,700 3,700

Cost of Contract 3,600 Work Certified 3,200

Profit & Loss

(Loss written off) 400

3,600 3,600

Balances b/d: plant 80 Balances b/d wages 40

There are a number of differences to be accounted for with Contract B.

Firstly, this is a contract which was already under way at the start of the year and

therefore has opening balances which must be entered in the account to start with.

Thereafter the procedure is the same, but when we attempt to calculate thenotional profit we discover that in fact the contract is showing a loss at this point

in time. When that happens we have to write off the whole of the loss (there is no

division into part recognised and part not recognised) to comply with the prudence

concept.

The above question illustrated a number of basic principles of accounting for long-

term contracts:

how to deal with opening balances

how to calculate notional profit

how to apply formulae for recognising profit

how to treat anticipated losses.

The following questions give you the opportunity to test your understanding of

these principles. Some of the questions are based on previous Higher Accounting

or Higher Accounting and Finance paper questions.




52/59


Question 1(based on Higher Paper II 1997 Q7)

JBC plc, a construction company, undertook a 2-year contract with Factory Outlets

Ltd for a fixed price of 1m.

Work began in September of Year 5 and on 1 January Year 6 the following

information was available.

Direct materials on site 10,000

Plant at cost on site 90,000

At 31 December Year 6 the following information was available.

Direct materials sent to site 350,000

Materials requisitioned from stores 5,000

Materials returned to stores 2,000

Direct wages paid 337,000

Direct expenses 20,000

Sub-contracting costs 28,000

Architects fees 2,000

Insurance 1,000Hire of special equipment 6,000

Plant maintenance 2,000

Value of plant on site at 31 Dec Year 6 78,000

Value of work certified by architect 850,000

Cost of work not yet certified at 31 Dec Year 6 15,000

Direct wages due at 31 Dec Year 6 3,000

Direct materials on site at 31 Dec Year 6 3,000

Overheads are charged at 10% of Direct Wages cost.

JBC plc recognises profit using the formula


Contract Price

Prepare the Contract Account at 31 December Year 6 showing clearly the profit

recognised.




53/59


Question 2(based on Higher 1993 Paper II Q2)

Appin Builders plc started work on a 3-year contract on 1 April Year 2 at a

contract price of 5m. On 31 March Year 3 the following information was

available.

000s

Plant sent to site 75

Materials sent to site 375

Materials delivered from store 50

Sub-contracting costs 48

Direct wages 250

Direct expenses 85

Hire of scaffolding 20

Work certified by architect 1,000

Cost of work not yet certified 150

Value of plant at 31 March Year 3 50

Material unused on site at 31 March Year 3 23

Accrued wages 10

Overheads are recognised at 10% of Direct Material costs (including sub-contract

costs).

Appin Builders plc recognise profit using the formula


Contract Price

Prepare the Contract Account for year ended 31 March Year 3.




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Question 3(based on Higher 1992 Paper II Q4(a))

Contract Builders plc undertook a 3-year contract in January Year 4 for a fixed

price of 4,800,000.

On 31 December Year 4 the following information was available relating to the

first year of the contract.

000s

Materials sent to site 535

Direct wages paid 380

Direct expenses 180

Overhead charged 200

Plant hire 110

At 31 Dec Year 4

Material on site 10

Wages accrued 20

Value of work certified 1,000

Cost of work completed but not certified 165

Prepare the Contract Account for the year ended 31 December Year 4.




55/59


Question 4

The following information relates to Contract 654 of Builders plc at 31 DecemberYear 5.

Materials sent to site 108,400

Materials delivered from store 1,320

Materials transferred to other contracts 3,100

Direct wages 84,310

Plant purchased 25,500

Plant transferred from other contracts 10,000

Sub-contract costs 40,137

Site expenses 10,172

At 31 December Year 5

Materials on site 36,680

Value of plant on site 29,500

Accrued wages 1,840

Site expenses prepaid 1,014

Value of work certified 420,000

Contract price 560,000

Overheads are charged at 10% of wages cost.

Profits are recognised using the formula


Contract Price

Prepare the Contract 654 Account for year ended 31 December Year 5.




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Solutions

Question 1

Material b/f 10,000 Material returned to 2,000

stores

Plant b/f 90,000 Material c/d 3,000

Material sent to site 350,000 Plant c/d 78,000

Materials taken from stores 5,000 Cost of contract 805,000

Direct wages paid 337,000

add: accrued 3,000

Direct expenses 20,000


Architects fees 2,000

Insurance 1,000

Hire of equipment 6,000

Plant maintenance 2,000

Overheads 34,000 .

888,000 888,000

Cost of contract 805,000 Value of work certified 850,000

Profit taken 51,000 Cost of work not 15,000

certifiedProfit not taken 9,000 .

865,000 865,000

Notional profit = 850,000 (805,000 15,000)

= 850,000 790,000

= 60,000

Profit taken =850,000

60,0001,000,000

= 51,000




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Question 2

Contract a/c

000s 000sMaterial sent to site 375 Material c/d 23

Material from store 50 Plant c/d 50

Sub-contract costs 48 Cost of contract 885

Plant sent to site 75

Direct wages 250

Add: accrued 10 260

Direct expenses 85

Hire of scaffolding 20

Overheads (10% 450) 45

958 958

Cost of contract 885 Value of work certified 1,000

Profit taken 53 Cost of work not certified 150

Profit not taken 212

1,150 1,150

Notional Profit = 1,000 (885 150)

= 1,000 735

= 265

Profit Taken = 1,000 2655,000

= 53




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Question 3

Contract a/c000s 000s

Material 535 Material c/d 10

Wages 380 Cost of contract 1,415

add: accrued 20 400

Direct expenses 180

Plant hire 110

Overheads 200

1,425 1,425

Cost of contract 1,415 Value of work certified 1,000

Value of work no t cert if ied 165

Loss on contract 250

1,415 1,415

Profit/loss on contract = 1,000 (1,415 165)

= 1,000 1,250

Loss = 250




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Question 4

Contract 654 a/c

Material sent to site 108,400 Material transferred 3,100

Material from store 1,320 Material c/d 36,680

Direct wages 84,310 Plant c/d 29,500

add: accrued 1,840 86,150 Cost of contract 220,000

Plant purchased 25,500

Plant transferred 10,000


Site expenses 10,172

less: prepaid 1,014 9,158

Overheads 8,615

289,280 289,280

Cost of contract 220,000 Work certified 420,000

Profit taken 150,000

Profit not taken 50,000

420,000 420,000

Notional profit = 420,000 220,000

= 200,000

Profit taken =420,000

200,000560,000

= 150,000

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