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ACCA Paper F5
Performance
Management
Class Notes
June 2011
© The Accountancy College Ltd, February 2011
All rights reserved. No part of this publication may be reproduced, stored in a
retrieval system, or transmitted, in any form or by any means, electronic,
mechanical, photocopying, recording or otherwise, without the prior written
permission of The Accountancy College Ltd.
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Contents
PAGE
INTRODUCTION TO THE PAPER
5
FORMULAE PROVIDED IN THE EXAMINATION PAPER
7
CHAPTER 1:
COST ACCOUNTING AND NEW DEVELOPMENTS
9
CHAPTER 2:
DECISION MAKING AND LINEAR PROGRAMMING
31
CHAPTER 3:
PRICING
57
CHAPTER 4:
DECISION MAKING UNDER UNCERTAINTY
71
CHAPTER 5:
BUDGETING TYPES
85
CHAPTER 6:
BUDGETARY CONTROL
93
CHAPTER 7:
QUANTITATIVE AIDS TO BUDGETING
105
CHAPTER 8:
STANDARD COSTING AND VARIANCE ANALYSIS
123
CHAPTER 9:
ADVANCED VARIANCE ANALYSIS
141
CHAPTER 10: PERFORMANCE EVALUATION
155
CHAPTER 11: TRANSFER PRICING
177
APPENDIX:
185
SOLUTIONS TO EXERCISES AND EXAMPLES
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Introduction to the
paper
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IN TR O DUC T IO N T O T H E PA P ER
AIM OF THE PAPER
To develop knowledge and skills in the application of management accounting
techniques to quantitative and qualitative information for planning, decisionmaking, performance evaluation and control.
OUTLINE OF THE SYLLABUS
1.
Cost accounting techniques.
2.
Decision-making techniques including risk and uncertainty.
3.
Budgeting techniques and methods.
4.
Standard costing systems.
5.
Performance appraisal including financial and non-financial measures.
FORMAT OF THE EXAM PAPER
The syllabus is assessed by a three hour paper-based examination.
The examination consists of 5 questions of 20 marks each.
compulsory.
All questions are
FAQs
How has the exam format changed and what impact will that
have on the paper?
The paper has moved to having five 20 mark questions rather than four 25 mark
questions. This move has been, it appears, to improve pass rates. Initial evidence
would suggest that this will be the case. The questions will become less complex
and there will be less emphasis on the discursive elements of answers and more
emphasis on computation. The downside for students is that there will be more
time pressure due to the fact that five separate scenarios must be understood
during the limited time of the exam. On balance this is a good thing for students in
future diets.
What is the skills set that a student must bring to the paper?
As a student approaching this paper the basic requirement is an ability to
understand and compute the differing techniques and methods in the syllabus. In
addition there is a need to understand the scenario and critically be able to write in
relation to the scenario and whatever the numbers you have already calculated.
What impact will there be of having a new examiner on this
paper?
There should be little or no impact of having a new examiner on the well prepared
student. The style and content of the questions will change to some degree but the
new examiner is given the same remit as the previous examiner.
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Formulae provided in
the examination paper
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F OR MU LA E & T AB L E S PR OV ID E D IN T H E EXA M INA T IO N P AP E R
FORMULAE SHEET
Learning curve
Y = ax b
Where:
y = average cost per batch
a = cost of first batch
x = total number of batches produced
b = learning factor (log LR/log 2)
LR = the learning rate as a decimal
Regression analysis
y = a + bx
b=
n∑ xy − ∑ x∑ y
2
n∑ x 2 − (∑ x )
a=
∑ y b∑ x
−
n
n
n∑ xy − ∑ x∑ y
r =
2
(
2
n∑ x 2 − (∑ x ) n∑ y 2 − (∑ y )
)
Demand curve
P = a − bQ
b=
change in price
change in quantity
a = price when Q = 0
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Chapter 1
Cost accounting and
new developments
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CH AP T ER 1 – C O ST ACC O UN T IN G A ND N E W D EV E L O PM E N TS
CHAPTER CONTENT DIAGRAM
Costing methods
Absorption
costing
Activity
based costing
Other costing
methods
●
Full cost per unit
●
●
Issue:
Arbitrary
cost allocation
Accurate
costs
●
Solution: Activity
based costing
Swap cost units
with cost pools
●
Swap OARs with
cost driver rates
●
product
Throughput
accounting
10
●
Life cycle costing
●
Target costing
Environmental
Accounting
●
Return per factory hour
●
Costing methods
●
Cost per factory hour
●
Reasons for use
●
Throughput accounting
ratio (TPAR)
●
Decision making
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CHAPTER 1 – COST ACCOUNTING AND NEW DEVELOPMENTS
CHAPTER CONTENTS
ABSORPTION COSTING ------------------------------------------------- 12
ABSORPTION COSTING – A REMINDER
12
TRADITIONAL OVERHEAD ANALYSIS
12
STEPS USING ABSORPTION COSTING
12
CRITICISMS OF ABSORPTION COSTING:
13
RECENT CHANGES IN MANUFACTURING
13
A REVISED ANALYSIS – ABC
14
STEPS USING ABC
14
CONDITIONS UNDER WHICH ABC IS MOST APPROPRIATE
16
BENEFITS AND LIMITATIONS
16
ACTIVITY BASED BUDGETING (ABB) ---------------------------------- 18
THROUGHPUT ACCOUNTING ------------------------------------------- 19
BASICS
19
RATIONALE
19
KEY TERMINOLOGY
19
CONCEPTS UNDERPINNING THROUGHPUT ACCOUNTING
20
FACTORS AFFECTING THE VALUE OF THROUGH ACCOUNTING PUT
20
STEPS IN THROUGHPUT ACCOUNTING
20
LIMITATIONS OF THROUGHPUT ACCOUNTING
21
TARGET COSTING -------------------------------------------------------- 22
TRADITIONAL COSTING SYSTEMS
22
TARGET COSTING STEPS
22
CLOSING A TARGET COST GAP
23
IMPLICATIONS OF USING TARGET COSTING
24
LIFE CYCLE COSTING ---------------------------------------------------- 25
COMPARISON OF LIFE CYCLE COSTING AND TRADITIONAL MANAGEMENT ACCOUNTING
25
ENVIRONMENTAL ACCOUNTING --------------------------------------- 27
INTRODUCTION
27
TYPES OF ENVIRONMENTAL COSTS
27
MANAGING ENVIRONMENTAL COSTS
28
ENVIRONMENTAL COSTS STRATEGIES
28
METHODS FOR ACCOUNTING OF ENVIRONMENTAL COSTS
28
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CH AP T ER 1 – C O ST ACC O UN T IN G A ND N E W D EV E L O PM E N TS
ABSORPTION COSTING
Absorption costing – a reminder
The linking of all production costs to the cost unit to prepare a full cost per unit.
Uses
1.
Stock Valuation
2.
Pricing decisions
3.
Budgeting
Traditional overhead analysis
Cost
Centres
Overhead
cost item
Cost Item
Cost
Units
Steps using absorption costing
The steps using absorption costing are:
1
Overhead costs are collected in various cost centres
Allocation: Specific overhead costs directly relating to individual cost centres,
for example, supervision, indirect materials.
Apportionment: General or common overhead costs like rent, heating,
electricity are incurred as a whole item by the company and therefore have to
be distributed to cost centres on some sharing bases like floor area, machine
hours, number of staff etc
2
Overhead absorption is achieved by means of a predetermined Overhead
Absorption Rate.
a.
Overhead Absorption Rate =
Budgeted Overheads
Budgeted Level of Activity *
* Activity levels generally used by examiners are number of units,
labour hours or machine hours, which means overheads are
charged to units on these bases.
b.
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Number of Units:
Single product environment
Labour Hours:
Manual manufacturing operations
Machine Hours:
Mechanical manufacturing operations
Absorbed overheads
=
OAR x Actual Activity
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CHAPTER 1 – COST ACCOUNTING AND NEW DEVELOPMENTS
Example 1 2P2D Ltd
2P2D Ltd produces 2 products in 2 departments. Relevant product information is:
Direct material cost (£)
Direct labour cost in Department X (£)
Time per unit in Department X (Hours)
Direct labour cost in Department Y (£)
Time per unit in Department Y (Hours)
Budgeted number of units
Product A
20
20
4
25
5
2,000
Product B
35
30
6
35
7
1,000
The labour rate is £5 per hour in each department.
The Budgeted Departmental Overheads are:
Department X
Department Y
£18,000
£6,500
Required:
Calculate the cost/unit using:
(a)
Separate OARs for each department, based on labour hours.
(b)
An overall OAR, based on labour hours.
(c)
Discuss the differences.
Criticisms of absorption costing
Criticisms of absorption costing are:
●
A big amount of guess work in relating overhead costs to the products.
●
Inappropriate bases to link overheads to products
●
Can only work in single product and simple manufacturing environments
Recent changes in manufacturing
The reason for the increasing inaccuracy of absorption costing is due to two basic
issues:
1.
Increased production complexity.
2.
Increased proportion of overhead costs.
Production complexity
A wide variety of production processes have become more complex in recent years
in a number of ways:
1.
Flexible manufacturing systems allow for a number of widely differing
products to be produced on the same machinery. Absorbing overhead on a
simple volume base is unlikely to reflect the differing overhead costs incurred
by each product.
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CH AP T ER 1 – C O ST ACC O UN T IN G A ND N E W D EV E L O PM E N TS
2.
Fast product development may mean that a number of differing iterations
of the same product may be produced in quick order. With such products
having differing production volumes again a volume base is unlikely to work.
3.
Wider product ranges lead to a more complex cost analysis.
Increased proportion of overhead costs
Overheads have increased in importance as a percentage of total costs due to both
the substitution of direct labour with indirect labour as companies mechanise to a
greater degree. Also the increased production complexity outlined above has given
rise to increased costs for such disciplines as production planning and logistics.
Increased proportion of support services’ costs
Activity based costing also introduces the important aspect that cost are incurred in
selling and distributing a product and the cost of servicing customers are often
more important than production therefore an accurate cause effect relationship
should be established as to what generates the cost and what is the real impact of
this cost on the volume of units sold.
A revised analysis – ABC
Overhead
Cost Item
Cost
Pool
Cost
Unit
Steps using ABC
The steps involved in ABC are:
1.
Identify an organisation’s activities.
2.
Collect the cost of each activity into what is called cost pool (equivalent to
cost centre under traditional costing).
3.
Identify the factors which determine the size of the costs of an activity. These
are called cost drivers.
Activity
Ordering
Material handling
Production scheduling
Despatching
4.
Possible Cost Drivers
number of orders
number of production run
number of production run
number of despatches
Assign the cost of activities to products according to the product’s demand for
activities.
Cost Pool is an activity that consumes resources and for which overhead
costs are identified and allocated. For each cost pool there should be a cost
driver.
Cost Driver is any factor which causes a change in the cost of an activity.
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CHAPTER 1 – COST ACCOUNTING AND NEW DEVELOPMENTS
Example 2 Hensau Ltd
Hensau Ltd has a single production process for which the following costs have
been estimated for the period ending 31 December 2010:
£
Material receipt and inspection costs
Power costs
Material handling costs
15,600
19,500
13,650
Three products - X, Y, and Z are produced by workers who perform a number of
operations on material blanks using hand held electrically powered drills. The
workers are paid £4 per hour.
The following budgeted information has been obtained for the period ending 31
December 2009:
Production quantity (units)
Batches of Material
Data per product unit:
Direct material (square metres)
Direct material cost (£)
Direct labour (minutes)
No. of power drill operations
Product X
Product Y
Product Z
2,000
10
1,500
5
800
16
4
5
24
6
6
3
40
3
3
6
60
2
Overhead costs for material receipt and inspection, process power and material
handling are presently each absorbed by product units using rates per direct
labour hour.
An activity based costing investigation has revealed that the cost drivers for the
overhead costs are as follows:
Material receipt and inspection:
Process power:
Material handling:
Number of batches of material
Number of power drill operations
Quantity of material (square metres)
handled
Required
(a)
(b)
Prepare a summary which shows the budgeted product cost per unit
for each product of X, Y, and Z for the period ending 31 December
2010 detailing the unit costs for each cost element using:
(i)
the existing method for the absorption of overhead costs and
(ii)
an approach which recognises the cost drivers revealed in the
activity based costing investigation.
(13 marks)
Explain the relevance of cost drivers in activity based costing. Make
use of figures from the summary statement prepared in (a) to
illustrate your answer.
(7 marks)
(20 marks)
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CH AP T ER 1 – C O ST ACC O UN T IN G A ND N E W D EV E L O PM E N TS
Conditions under which ABC is most appropriate
The usefulness of ABC techniques will depend on the characteristics of the
organisation, in particular the following:
(1)
Cost structure
(2)
Product mix or diversity
(3)
Information
(4)
Environment.
Benefits and limitations
Benefits
1.
More accurate product costing.
2.
Is flexible enough to analyse costs by activity providing more useful costing
data.
3.
Provides a reliable indication of long-run variable product cost.
4.
Helps understanding of cost.
5.
Provides a more logical basis for costing of overhead.
Limitations
1.
Cost vs benefit.
2.
ABC information is historic and internally.
3.
Difficult to apply in practice.
4.
Focuses on the allocation of cost rather than minimizing the cost incurred.
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CHAPTER 1 – COST ACCOUNTING AND NEW DEVELOPMENTS
Example 3 Brunti plc
The following budgeted information relates to Brunti plc for the forthcoming period.
Products
XYI
(000s)
YZT
(000s)
ABW
(000s)
50
40
30
£
£
£
45
32
95
84
73
65
Hours
Hours
Hours
2
7
5
3
4
2
Sales and production (units)
Selling Price (per unit)
Prime cost (per units)
Machine department (machine hours per unit)
Assembly department (direct labour hours per
unit)
Overheads allocated and apportioned to production departments (including service
cost centre costs) were to be recovered in product costs as follows.
●
Machine department at £1.20 per machine hour
●
Assembly department at £0.825 per direct labour hour
You ascertain that the above overheads could be re-analysed into 'cost pools' as
follows:
Cost pool
£000
Machining services
Assembly services
357
318
Set-up costs
Order processing
Purchasing
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156
84
941
Cost driver
Machine hours
Direct labour
hours
Set-ups
Customer orders
Suppliers' orders
Quantity for the
period
420,000
530,000
520
32,000
11,200
You have also been provided with the following estimates for the period:
Number of set-ups
Customer orders
Suppliers' orders
XYI
Products
YZT
ABW
120
8,000
3,000
200
8,000
4,000
200
16,000
4,200
Required:
(a)
(b)
Prepare and present profit statements using:
(i)
conventional absorption costing, and
(5 marks)
(ii)
activity based costing.
(9 marks)
Comment on why activity based costing is considered to present a
fairer valuation of the product cost per unit.
(6 marks)
(20 marks)
ACCA June 1995 Amended
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CH AP T ER 1 – C O ST ACC O UN T IN G A ND N E W D EV E L O PM E N TS
ACTIVITY BASED BUDGETING (ABB)
●
Activity based budgeting extends the use of ABC from individual product
costing, for pricing and output decisions, to the overall planning and control
systems of the business.
●
The basic principle of ABB is that the work of each department for which a
budget is to be prepared is analysed by its major activities, for which cost
drivers may be identified. The budgeted cost of resources used by each
activity is determined (from recent historical data) and, where appropriate,
cost per unit of activity is calculated.
●
Future cost can then be budgeted by deciding on future activity levels and
working back to the required resource input.
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CHAPTER 1 – COST ACCOUNTING AND NEW DEVELOPMENTS
THROUGHPUT ACCOUNTING
Basics
Throughput accounting is a method of accounting that focuses on throughput, and
relates costs of production to throughput. Throughput accounting applies the
theory of constraints as advocated by Goldratt and Cox.
Rationale
Profitability of a product is determined by the rate at which it contributes money
and the rate at which the factory spends money. To increase profitability, Goldratt
and Cox advocated that managers should aim to increase throughput while
simultaneously reducing inventory and operational expenses. However, the scope
of reducing operational expenses is limited as they are to be maintained at some
minimum level for production to take place.
Throughput is calculated as the difference between sales and material cost.
Throughput (contribution) = sale – material cost.
Key terminology
(Please note the similarity to marginal costing terminology that you already know)
Marginal costing
Throughput accounting
Variable Cost
=
Direct Material Cost
Fixed Cost
=
Total Factory Cost
(Including labour cost)
Contribution
(Sales – Variable Cost)
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=
Throughput
(Sales – Direct Material Cost)
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CH AP T ER 1 – C O ST ACC O UN T IN G A ND N E W D EV E L O PM E N TS
Concepts underpinning throughput accounting
Throughput accounting is based on following concepts:
1.
Cost Behaviour
In the short-term all manufacturing cost with the exception of material cost
are fixed.
2.
Inventory
Holding and producing stocks do not add to the value of products (no value
addition).
The longer it takes to output, the lower the profitability.
Throughput is created when the finished output is sold. If items are produced
and put into finished goods stock, no throughput is created. Therefore
managers should aim to increase throughput whilst simultaneously reducing
inventory and operational expenses.
Factors affecting the value of throughput accounting
●
The selling price of the item sold
●
The purchase cost of direct materials
●
Efficiency in the usage of direct materials
●
The volume of the throughput.
Bottleneck is any limitation or restraint in the production process which
limits the production managers to fully utilise some of their resources.
Machine capacities (can we insert these 3 into circles?)
Human resources
Materials in scarcity
In order to maximise throughput, managers should focus attention on any
bottlenecks and remove them. If this is not possible they should ensure that the
bottlenecks are fully utilised at all times.
Steps in throughput accounting
1.
Identify the system bottlenecks. These are the constraints that restrict output
from being increased
2.
Concentrate on each bottleneck in turn to ensure that they are being fully and
efficiently utilised.
3.
Scale down the throughput of non-bottleneck activities to match what can be
dealt with by the bottleneck.
4.
Remove the bottlenecks if possible.
5.
Since throughput accounting is a continues improvement process, return to
step 1 and re-evaluate the system now that bottlenecks have been removed.
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CHAPTER 1 – COST ACCOUNTING AND NEW DEVELOPMENTS
Formulae to remember:
Return per Factory Hour
=
Throughput per unit
Factory hours per unit
Cost per Factory Hour
=
Total factory cost *
Total factory hours
Throughput Accounting Ratio (TPAR)
=
Return per factory hour
Cost per factory hour
* total factory cost includes direct labour and production overheads.
Example 4 3P3M Ltd
3P3M Ltd produces three products using three different machines.
The following information is available for a product for a period:
Product
Sales (£)
Direct materials (£)
Direct labour (£)
Overheads (£)
Estimated sale demand (unit)
Machine
Machine
Machine
Machine
Machine
X
20
8
5
2
200
Y
15
5
3
1
200
Z
10
4
2
1
200
hours required per unit:
1
6
2
1
2
9
3
1.5
3
3
1
0.5
capacity is limited to 1,600 hours for each machine.
Required:
Calculate throughput accounting ratio and rank the products.
Limitations of throughput accounting
●
Selling price could be uncompetitive
●
Material suppliers may not be reliable
●
Product quality is low
●
Need to deliver on time
●
Very little attention is paid to overhead costs.
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CH AP T ER 1 – C O ST ACC O UN T IN G A ND N E W D EV E L O PM E N TS
TARGET COSTING
Traditional costing systems
Traditional costing systems:
1.
Calculate unit cost.
2.
Add profit margin.
3.
Equals Selling price.
Problems:
●
No consideration of market
●
Costs are not challenged
Target costing steps
Target costing steps:
1. Determine possible selling price – with reference to the market/customer and
taking into consideration the specification of the product.
2. Establish the required profit margin – this is based upon the overall required
return of the business and the level of perceived risk of the product
3. Calculate the target cost – ie the cost that the company must produce at in
order to be able to achieve the required profit level (Selling price – profit
margin)
4. Close the gap – reduce the cost from the original expected cost to the target
cost.
Example 5 CMC Ltd
CMC Ltd, a car manufacturing company, wants to calculate a target cost for a new
car. The price will be set at £20,000. CMC Ltd requires a 10% profit margin.
Required:
What is the target cost?
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CHAPTER 1 – COST ACCOUNTING AND NEW DEVELOPMENTS
Example 6 Fantata Ltd
Fantata Ltd makes and sells a product H which is manufactured through two
consecutive processes; assembly and finishing. Raw material is input at the
commencement of the assembly process. An activity-based costing approach is
used in the absorption of product specific conversion cost.
The following estimated information is available for the period.
Production/ sales units
Selling price per unit
Direct material cost per unit
ABC variable conversion cost per unit:
Assembly
Finishing
Product specific fixed costs
Company fixed costs
Product A
12,000
£75
£20
£20
£12
£170,000
£50,000
Fantata Ltd uses a minimum contribution to sale ratio target of 25% when
assessing the viability of a product. In addition, management wish to achieve an
overall net profit margin of 12% on sales in this period in order to meet return on
capital target.
Required:
(a)
Calculate target cost.
(b)
Calculate the cost gap.
(c)
Suggest specific areas of investigation.
Closing a target cost gap
The designed specification for each product and the production methods should be
examined for potential areas of cost reduction that will not compromise the quality
of the products.
For example:
1.
2.
Reduced component count
●
Reducing the number of components
●
Using standard components wherever possible
●
Using different materials.
Reduce production complexity
●
Acquiring new, more efficient technology
●
Cutting out non-value added activities.
3.
Revise production process
4.
Revise specification
Note: Remember that these above points should not be implemented if
they would compromise quality.
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CH AP T ER 1 – C O ST ACC O UN T IN G A ND N E W D EV E L O PM E N TS
Implications of using target costing
Target costing requires managers to change the way they think about the
relationship between cost, price and profit.
Key advantages:
●
Reduction and control
Possible elimination of non value added elements and activities in production
process.
●
Market based costing
Selling price considers what customer might want to pay for the product.
●
Customers
Customer requirements for quality, cost and time are incorporated into
product and process decisions.
The value of product features to the
customers must be greater than the cost of providing them.
●
Design
Cost control is emphasised at the design stage so any engineering changes
must happen before production starts.
●
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Cost
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CHAPTER 1 – COST ACCOUNTING AND NEW DEVELOPMENTS
LIFE CYCLE COSTING
Cradle to grave
The term life-cycle costing is used to describe a system that tracks and
accumulates the actual costs and revenues attributable to each product from
inception to abandonment.
In life-cycle costing the profitability of each product can therefore be determined
right from design stage through development to market launch, production and
sales, and finally to its eventual withdrawal from the market.
Life cost per unit
=
Total life costs for product
Total expected life volumes
The component elements of a product’s cost over its life cycle could therefore
include the following:
1.
Research and development costs
●
Design
●
Testing
●
Production process and equipment.
2.
The cost of purchasing and any technical data required.
3.
Training costs (including initial operator training and skills updating).
4.
Manufacturing or production costs.
5.
Marketing costs
6.
●
Customer service
●
Field maintenance
●
Brand promotion.
Distribution cost (including transportation and handling costs).
Comparison of life cycle
management accounting
costing
and
traditional
●
Traditional MA merely report on a periodic basis, and product profits are not
monitored over their life cycle. Such a practice does not, therefore, assess a
product’s profitability over the entire life but rather on a periodic basis. Costs
tend to be accumulated according to function; research, design, development
and customer service costs incurred on all products during a period are
totalled and recorded as period expense.
●
LCC involves tracing costs and revenues on product-by-product basis over
several calendar periods throughout their entire life cycle. Costs and revenue
can be analysed by time periods, but the emphasis is on costs and revenue
accumulation over the entire life cycle for each product.
●
Recognition of the commitment needed over the entire life cycle of a product
will generally lead to more effective resource allocation than the traditional
annual budgeting system.
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CH AP T ER 1 – C O ST ACC O UN T IN G A ND N E W D EV E L O PM E N TS
Key issues:
●
Failure to trace all costs to products over their life cycles hinders
management’s understanding of product line profitability, because a product’s
actual life-cycle profit is unknown.
●
Inadequate feedback information is available on the company’s success or
failure in developing new products.
●
The control function of life cycle costing lies in the comparison of actual and
budgeted life cycle costs for a product.
●
The application of life cycle costing will ensure that cost control and cost
reduction will be carried out at the early stages, as well as during the
production stages.
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CHAPTER 1 – COST ACCOUNTING AND NEW DEVELOPMENTS
ENVIRONMENTAL ACCOUNTING
Introduction
Due to rapid growth in world population and mass scale consumption of global
resources, the amount of wasteful and hazardous output has increased
tremendously. It has become such an important issue that business and political
leaders have come to talk of the greener and safer environment.
Many
organisations worldwide like Greenpeace, Environmental Protection Agency, Kyoto
Protocol are seeking to reduce emissions of greenhouse gases which are believed to
be causing global warming.
In order to comply with different local and global requirements, businesses and
governments spend huge amounts of money protecting environment in the name of
environmental costs, eg improving production process to reduce or eliminate
pollutants and cleaning up contaminations in soil and water resources.
Types of environmental costs
1.
Public sector costs (social sector costs)
●
Costs borne by taxpayers.
●
Include staffing costs of the public sector organisations involved, reduce or
eliminate pollution from society, natural resources.
●
Health and Medicare costs caused due to pollutants.
2.
Private sector costs
●
Business investments in environment related costs.
●
Incurred to comply with local and global environmental requirements.
●
Include, for example: costs of cleaning water resources due to pollutants such
as toxic wastes from production and chemical processes; compensation on a
social level such as investing in parks, public gardens, schools, forestry; and
Medicare projects.
Identifiable and non-identifiable costs
Some of the above costs are clearly identified and known as attached to
environment protection, such as environmental organisations’ staffing costs, costs
of cleaning up a polluted lake or a river etc.
Some environment costs are hidden as they are not directly tied to environment
but are caused by environmental issues. Such costs are borne by individuals,
insurance companies, or even governments, examples include medicare costs (due
to cancer or other illnesses caused by environmental pollutants).
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CH AP T ER 1 – C O ST ACC O UN T IN G A ND N E W D EV E L O PM E N TS
Managing environmental costs
Private sector focus
1.
Monitoring costs.
2.
Prevention costs.
3.
Clean-up costs:
●
On-site costs.
●
Off-site costs.
Environmental costs strategies
1.
End-of-pipe strategy
This strategy focuses on cleaning up pollutant and toxic waste before it is
released into environment.
2.
Process improvement strategy
The focus is on products and process modification to reduce or eliminate
pollutants.
3.
Prevention strategy
The focus is to design the production process in such a way which does not
create any pollutant in the first place.
Methods of accounting for environmental costs
The following methods are generally in practice to deal with reporting of
environmental costs.
1.
Input / output method
This method records material inflows, and balances these with outflows on the
same basis. The simple idea is that what comes in should go out.
2.
Material flow cost accounting
Under this method the material inflows are divided into three categories based on
physical quantities involved, their costs and value:
●
Material
●
System and delivery
●
Disposal.
The values and costs of each of these three flows are then calculated.
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CHAPTER 1 – COST ACCOUNTING AND NEW DEVELOPMENTS
3.
Activity based costing (ABC)
ABC clearly distinguishes between environment related costs which can be charged
to joint cost centres and environment driven costs hidden in general overheads. It
provides an allocation of internal costs to cost centres and cost drivers on the basis
of activities that give rise to the costs.
4.
Life cycle costing
This method focuses on adding environment related costs, such as cost of waste
disposal, energy emissions etc into total cost of products over entire life cycle. The
main aim is to reduce total cost with environment friendly options in all stages of
the cycle.
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CH AP T ER 1 – C O ST ACC O UN T IN G A ND N E W D EV E L O PM E N TS
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Chapter 2
Decision making and
linear programming
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CH AP T ER 2 – D E C IS IO N M AK IN G AN D L I N EAR PR O GR A MM IN G
CHAPTER CONTENT DIAGRAM
DECISION MAKING
Contribution
analysis
CVP
analysis
Relevant cost
analysis
Sensitivity
analysis
Limitations & constraints
LINEAR PROGRAMMING
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C H A P T E R 2 – D E C I S IO N M A K IN G A N D L IN E A R P R O G R A M M I N G
CHAPTER CONTENTS
INTRODUCTION TO DECISION MAKING------------------------------- 34
CONTRIBUTION ANALYSIS --------------------------------------------- 35
MAKE OR BUY DECISION
35
SHUTDOWN (DISCONTINUANCE) DECISIONS
36
LIMITING FACTOR DECISION
38
FURTHER PROCESSING DECISIONS
39
CVP ANALYSIS (BREAKEVEN ANALYSIS) ----------------------------- 41
WHAT IS CVP (BREAK-EVEN) ANALYSIS?
41
HOW IS THE BREAK-EVEN POINT CALCULATED?
41
LIMITATIONS OF BREAK-EVEN ANALYSIS
43
MARGIN OF SAFETY
43
CONTRIBUTION / SALES RATIO
43
RELEVANT COST ANALYSIS --------------------------------------------- 45
OPPORTUNITY COST
45
AVOIDABLE COSTS
45
VARIABLE COSTS
46
INCREMENTAL COSTS
46
ACCEPTING OR REJECTING ORDERS ---------------------------------- 47
LINEAR PROGRAMMING – MULTI LIMITING FACTORS -------------- 51
SENSITIVITY ANALYSIS ------------------------------------------------ 54
ASSUMPTIONS AND LIMITATIONS OF LINEAR PROGRAMMING
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CH AP T ER 2 – D E C IS IO N M AK IN G AN D L I N EAR PR O GR A MM IN G
INTRODUCTION TO DECISION MAKING
The choice between two or more alternatives, decision making normally considers
only the short term consideration of maximising profitability.
We base our
decisions on relevant costs and revenues.
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C H A P T E R 2 – D E C I S IO N M A K IN G A N D L IN E A R P R O G R A M M I N G
CONTRIBUTION ANALYSIS
One aspect of decision making is closely linked to the impact of a change in the
level of activity. In these situations the decision is based upon the variable costs or
contributions generated. Fixed costs are not affected by activity and hence can be
ignored.
Make or buy decision
The decision to make a component or product ‘in-house’ or to buy from an outside
supplier. The underlying assumption of this decision is that all fixed costs of
manufacture are general to the organisation as a whole and hence only the
marginal cost of making the component is relevant.
Decision criteria: Compare marginal cost of making to the purchase price
(the marginal cost of buying).
Example 1 Clemence Ltd
Clemence Ltd produces a number of components, two of which it is considering
buying in, components X and Y.
Cost of making (£)
Variable
Fixed
X
14
4
Y
28
4
Total
18
32
Purchase price (from outside supplier)
17
25
Required:
Should Clemence Ltd make or buy in?
Example 2 PCO Ltd
PCO Ltd is considering the alternatives of either purchasing a component from an
outside supplier or producing the component itself. The estimated costs to the
company of producing a component are as follows:
Direct labour
Direct materials
Variable overheads
Fixed overheads
100
300
50
200
650
The outside supplier has quoted a price of £400 for supplying the component.
Required:
Should PCO Ltd produce or buy the component from the supplier?
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CH AP T ER 2 – D E C IS IO N M AK IN G AN D L I N EAR PR O GR A MM IN G
Example 3 Central Ltd
Central Ltd makes four components, W, X, Y and Z, for which costs in the coming
year are expected to be as follows:
W
1,000
£
4
8
2
14
Production units
Unit marginal costs
Direct materials
Direct labour
Variable production overheads
X
2,000
£
5
9
3
17
Y
4,000
£
2
4
1
7
Z
3,000
£
4
6
2
12
Direct attributable fixed costs per annum and committed fixed costs are:
incurred as a direct consequence
incurred as a direct consequence
incurred as a direct consequence
incurred as a direct consequence
other fixed costs (committed)
of
of
of
of
making
making
making
making
W
X
Y
Z
1,000
5,000
6,000
8,000
30,000
50,000
A sub-contractor has offered to supply units of W, X, Y and Z for £12, £21, £10,
and £14 respectively.
Required:
Should the company make or buy the component?
Other important factors to consider
1.
If the components are sub-contracted, the company will have spare capacity.
How should that spare capacity be profitably used, that is, are there hidden
benefits to be obtained from sub-contracting?
2.
Would the sub-contractor be reliable with supply and delivery time?
3.
Would the sub-contractor supply the same or improved quality components as
the one produced internally?
4.
Does the company wish to be flexible and maintain better control over
operations by making everything itself?
5.
The going concern of the sub-contractor should also be considered.
Shutdown (discontinuance) decisions
The decision whether to shut down a part or segment of a business. The focus of
the question is the impact of the shutdown on the cost base. Revenue will be
foregone but which costs will be affected.
The avoidable costs include variable costs and specific fixed costs. Specific fixed
costs are those costs specific to the part or segment of the business to be
shutdown. General fixed costs will not be relevant.
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C H A P T E R 2 – D E C I S IO N M A K IN G A N D L IN E A R P R O G R A M M I N G
The simplest way to consider such a problem is to re-draft any information in the
form of a marginal costing profit statement.
Any product that produces a positive contribution is worth undertaking as it will
contribute to profit, unless
●
The company can use the capacity used by this product to produce another
new product with a higher contribution than that of this first product.
●
The capacity used by this product can be used to produce more of the other
existing product with higher contribution.
Example 4 Jones Ltd
Jones Ltd operates three divisions within a larger company. The CEO has been
shown the latest profit statements and is concerned that division C is losing
money.
You are required to advise her whether or not to close down division C.
Division
Sales
Variable costs
Fixed costs
Profit/(loss)
A
(000s)
100
60
20
20
B
(000s)
80
50
20
10
C
(000s)
40
30
20
(10)
You are also informed that 40% of the fixed cost is product specific, the remainder
being allocated arbitrarily to the divisions from head office.
Required:
Should division C be shut down?
Example 5 Fantum Ltd
Fantum Ltd has three operating divisions. The expected financial results of each
division next year are as follows:
Sales
Variable costs
Specific fixed cost
Apportioned head office costs
Profit or loss
Division A
£
50,000
(30,000)
(12,000)
(5,000)
3,000
Division B
£
30,000
(18,000
(10,000)
(4000)
(2000)
Division C
£
40,000
(20,000)
(10,000)
(5000)
5000
Required:
Taking only the financial results next year into consideration, recommend
whether or not division Y should be closed down.
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CH AP T ER 2 – D E C IS IO N M AK IN G AN D L I N EAR PR O GR A MM IN G
Limiting factor decision
Where there is a factor of production that is limited in some way by:
1.
Scarce raw materials.
2.
Shortage of skilled labour.
3.
Limited machine capacity.
4.
Finance (see capital rationing in FM).
Aim: Maximise the contribution per unit of limiting factor
Steps:
1.
Contribution per unit of sale.
2.
Contribution per unit of scarce resource.
3.
Rank in order of 2 - highest first.
4.
Use up the resource in order of the ranking.
Assumption:
●
Fixed cost is assumed to be the same whatever the production mix is
selected, so that the only relevant cost is the variable cost.
●
The unit variable cost is constant at all levels of production and sales
●
The estimates of sales demand for each product are known with certainty
Example 6 (a) Neal Ltd
Neal Ltd produces two products using the same machinery. The hours available on
this machine are limited to 5000. Information regarding the two products is
detailed below:
Products (per unit data)
Selling price (£)
Variable cost (£)
Fixed cost (£)
Profit (£)
M
40
16
10
14
N
30
15
8
7
8
3
600
500
Machine hours
Bud. sales (units)
Required:
Calculate the maximum profit that may be earned.
Example 6 (b) Neal Ltd
Using the previous example, Neal Ltd is now able to buy in the products at the
following costs
Products (per unit data)
Purchase price(£)
M
24
N
21
Required:
What is the revised production schedule and the maximum profit earned?
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C H A P T E R 2 – D E C I S IO N M A K IN G A N D L IN E A R P R O G R A M M I N G
Example 7 WXYZ Ltd
WXYZ Ltd makes four products W, X, Y and Z for which costs and sales in the next
year are expected to be as follows:
Sales units
Direct materials
Direct labour
Sales price
Contribution
W
2,000
£
10
7
17
29
12
X
4,000
£
5
2
7
11
4
Y
3,000
£
7.5
4.5
12
18
6
Z
1,000
£
12.5
6.5
19
39
20
The company is having difficulty of obtaining the materials. Each product uses the
same material, and only one type of material is used in manufacture. The
expected available materials next year are 11,000 kilos. The material cost £5 per
kilo.
An overseas manufacturer is willing to supply the items to the company at the
following costs per unit including delivery.
Cost to buy
W
20.00
X
11.00
Y
15.75
Z
21.50
Required:
Which items should the company make internally, and which should it buy
from the external manufacturer?
Further processing decisions
A further processing decision may arise in a manufacturing company that produces
an item in a process or a sequence of processes. The output from a process might
have a market value, and a selling price. However, there might also be an
opportunity to further process the output to produce a finished item with a higher
selling price.
The decision is whether to sell the item in its part-finished form, or whether to
process it further and sell the finished item.
The relevant cash flows are:
●
The extra revenue obtained by further processing the item (incremental
revenues), and
●
The incremental costs of further processing.
The financial decision should be to further process the item if the extra revenue
exceed the incremental costs.
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CH AP T ER 2 – D E C IS IO N M AK IN G AN D L I N EAR PR O GR A MM IN G
Example 8 CF Ltd
CF Ltd manufactures two cleaning fluids, X and Y. The two fluids are manufactured
in a joint process. Every 8,000 litres of materials input to the joint process
produces 4,000 litre of X and 3,200 of Y. The costs of processing are as follows:
Direct material
Direct labour
Variable production overheads
Fixed production overheads
£
1,600
200
300
2,000
Product X sells for £1.10 per litre and product Y for £0.75 per litre.
CF Ltd could put product X through another production process, where there is
spare production capacity. The further processing would produce another cleaning
product, Zplus. Every one litre of input to the further process will produce 0.90
litres of Zplus.
The costs of further processing would be:
Product X: 4,000 litres
Additional materials
Direct labour
Variable overheads
Fixed production overheads
400
40
80
400
920
Zplus would sell for £1.40 per litre
Required:
Using financial reasons only to justify the decision, should the company
sell product X or should it further process the product to make Z plus?
Assume for the purpose of the analysis that direct labour is a variable
cost.
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C H A P T E R 2 – D E C I S IO N M A K IN G A N D L IN E A R P R O G R A M M I N G
CVP ANALYSIS (BREAKEVEN ANALYSIS)
What is CVP (break-even) analysis?
An understanding of the relationship between the level of activity and costs and
revenues.
CVP analysis is a technique which uses cost behaviour to identify the level of
activity at which we have no profit or loss (break-even point).
It can also be used to predict the profits or losses to be earned at varying activity
levels (using the assumed linearity of costs and revenues).
CVP analysis assumes that selling prices and variable costs are constant per unit
regardless of the level of activity and that fixed costs are just that – fixed.
In order to calculate these levels we need to consider the contribution provided by
each unit of production. Contribution is the term given to the difference between
the selling price and the variable costs which contributes first towards paying the
fixed costs and then towards providing profit.
How is the break-even point calculated?
If we are to calculate the break-even point let us first imagine that the fixed costs
are a large hole in the ground. What we need to find out is how many contributions
it takes to fill that hole.
Similarly the profit we require is the pile on top of the hole. How many
contributions does it take to reach the required height?
Formulae required (not given in exam):
1
Unit contribution
=
Selling price per unit – Variable cost per unit
2
Total contribution
=
Unit contribution x volume
3
Break-even point (units)
=
Fixed costs
Unit contributi on
4
Contribution target
=
Fixed costs + Target profit
5
Volume target
=
Contribtio n target
Unit contributi on
We can use these formulae to calculate our break-even point. Alternatively we can
use either a traditional break-even chart or a profit/volume chart.
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C H A P T ER 2 – D E C I S I O N M A K I N G A N D L I N EA R P R O GR A M M I N G
Break-even chart
Costs and
revenues
Sales revenue
Total costs
Profit
Fixed costs
Margin of safety
Sales activity
Break-even point
Profit/volume chart
A break-even chart shows the costs and revenues at a number of activity levels. It
does not however, show the amount of profit or loss at these levels. This is shown
on the profit/volume chart.
Profit
Total profit
Break-even point
Loss
Fixed costs (total loss)
From this chart we can read off the amount of profit or loss for any level of activity.
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C H A P T E R 2 – D E C I S IO N M A K IN G A N D L IN E A R P R O G R A M M I N G
1.
The x axis represents sales (units or values)
2.
The y axis shows profits above the x axis and losses below.
3.
When sales = zero, the net loss is equal to the fixed costs.
4.
If variable cost per unit and total fixed costs are constant throughout the
relevant range, the profit/volume chart is shown as a straight line.
5.
If there are\changes in either of these costs at various levels of activity, it will
be necessary to calculate the profit or loss at each point where the cost
structure alters before plotting the points onto the chart.
Limitations of break-even analysis
●
Once costs and revenues have been determined, it is usually assumed that
they will have a linear relationship.
●
Fixed costs will be constant over the relevant range
●
Variable costs will vary in direct proportion to volume
●
Selling price will remain unchanged
●
The efficiency and productivity of the workforce remain constant.
The analysis covers either a single product or a mix of products at which it is
assumed that the proportion of each product will remain the same as volume
increases or decreases.
In constructing a break-even chart, the sales and costs are likely to be valid only in
a particular range of activity. This is referred to as THE RELEVANT RANGE. Outside
this range the same cost and revenue relationships are unlikely to exist. E.g. An
alteration in volume could affect the level of fixed costs (stepped) or the rate of
variable costs or selling prices (economies of scale).
Margin of safety
The margin of safety is the area between the break-even point and the maximum
sales. This is the area that the company can operate in and be certain of making a
profit. It is usually classed as the amount of sales that a company can afford to
lose before it gets into a loss making situation.
It is usually expressed as a percentage (%) of sales.
It can be calculated as:
Margin of safety =
Maximum sales - break-even point
× 100 %
Maximum sales
Note: Maximum sales are alternatively described as budgeted sales revenues.
Contribution / sales ratio
The above calculations are useful in calculating the break-even point of one unit of
production. If a company makes more than one product it may be better to
calculate the C/S ratio.
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C H A P T ER 2 – D E C I S I O N M A K I N G A N D L I N EA R P R O GR A M M I N G
Weighted average C/S ratio
C/S ratio
=
Unit contribution
Unit sales price
or
Total contributi on
Total sales
Example 9 Beauty Co
Beauty Co makes two products, nail polish and lipsticks. Nail polish sales make up
30% of total sales and their variable costs are 45% as a percentage of sales value.
Lipsticks sales are 70% of the total sales and their variable costs are 40% as a
percentage of sales value.
Total fixed costs are $400,000 for the company.
Required:
What is break-even level of sales revenues for the company?
Group task
Given the following information, calculate the breakeven point and the
level of activity at which profits are £20,000.
Hughes
Smith
Variable cost per unit
£20
£300
Selling price
£40
£350
£10,000
£5,000
8,000
250
Fixed cost
Budgeted units
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C H A P T E R 2 – D E C I S IO N M A K IN G A N D L IN E A R P R O G R A M M I N G
RELEVANT COST ANALYSIS
There are 3 components to a relevant cost:
1.
Future
2.
Cash flow
3.
Arising as a direct result of the decision
Relevant costs
Non-relevant costs
Opportunity cost
Sunk cost
Incremental cost
Committed cost
Variable cost
Fixed O/H absorbed
Avoidable cost
Depreciation (non cash flows)
Opportunity cost
The benefit foregone by choosing one alternative in preference to the next best
alternative.
Example 10 a lecturer
A lecturer is being timetabled for the coming year. She has expressed a desire to
teach in London. The courses she alone can do, in a specific week, generate the
following contributions:
London
Croatia
Moscow
£
1,200
1,500
2,100
Required:
What is the opportunity cost of working in:
(a)
London?
(b)
Croatia?
(c)
Moscow?
Avoidable costs
Costs attached to a part or segment of a business which could be avoided if that
part or segment ceased to exist. Variable costs are normally considered avoidable,
fixed costs normally not. Fixed costs may be considered avoidable if arise within
the single part or segment of the business that is relevant. They are particularly
applicable in shutdown decisions.
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C H A P T ER 2 – D E C I S I O N M A K I N G A N D L I N EA R P R O GR A M M I N G
Variable costs
Those costs which vary proportionately with the level of activity. As seen above the
variable nature of the cost often makes it more likely to be relevant. We should
already know that the variable cost is useful for break-even analysis or any other
form of contribution analysis.
Incremental costs
Those additional costs (or revenues) which arise as a result of the decision. This
classification is particularly useful for further processing decisions, but may be used
as a basis for tackling any relevant cost analysis.
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C H A P T E R 2 – D E C I S IO N M A K IN G A N D L IN E A R P R O G R A M M I N G
ACCEPTING OR REJECTING ORDERS
Another type of decision is a decision whether or not to accept an order.
comparison here should be between:
The
●
The relevant costs of the order, including any opportunity cost of other
opportunities forgone as a consequence; and
●
The incremental revenue from the order.
Other factors to consider
●
Is there an alternative more profitable way of utilising spare capacity?
●
Will fixed cost be unchanged if the order is accepted?
●
Will accepting one order at below normal selling price lead other customers to
ask for price cuts?
Material costs flow chart
YES
Is the
material in
stock?
Purchase price is
relevant
Next question
YES
Is the material in
constant use?
Replacement cost
is relevant
YES
Opportunity cost
is relevant
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NO
NO
Next question
Is the material
scarce?
NO
Nil value with
possible disposal
cost
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C H A P T ER 2 – D E C I S I O N M A K I N G A N D L I N EA R P R O GR A M M I N G
Labour costs flow chart
YES
Is the labour
in permanent
employment?
Hourly rate is
relevant
Next question
YES
NO
Is the labour fully
utilised?
NO
Nil value
Next question
YES
Overtime rate is
relevant
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Overtime
possible?
NO
Opportunity cost
is relevant
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C H A P T E R 2 – D E C I S IO N M A K IN G A N D L IN E A R P R O G R A M M I N G
Example 11 Pantum
Pantum Ltd is considering whether or not to undertake an order from a customer.
It is trying to establish the relevant costs of the order.
The order would require 3,000 kilos of material W. There are over 3,000 kilos
already held in inventory. Material W is no longer in regular use by the company
and could be sold for scrap at £1.5 per kilo. It could also be used as a substitute
for material Z, which is in regular use for making another product. Material Z can
be purchased for £4 per kilo. To use material W as a substitute for material Z,
conversion costs of £1.6 per kilo would have to be spent on the material W. One
kilo of material W, after conversion, would be a substitute for one kilo of material Z
Skilled labour needed to fulfil the order would be specifically recruited for £50,000.
Unskilled labour needed to fulfil the order would be transferred from another
department. The cost of the labour time (3000 hours) would be £30,000 in wages.
However, 1,500 of these hours would be idle time if the order is not undertaken.
The other 1,500 would be spent on work that would provide a contribution of
£5,000.
Required:
Identify the relevant costs of material and labour for this customer order.
Example 12 Tricks
You are the management accountant of Tricks, an organisation which has been
asked to quote for the production of a pamphlet for an event. The work could be
carried out in addition to the normal work of the company. Due to existing
commitments, some overtime working would be required to complete the printing
of the pamphlet. A trainee has produced the following cost estimate based upon
the resources required as specified by the operations manager:
£
Direct materials:
Direct labour:
- paper (book value)
- inks (purchase price
4,000
2,400
- highly skilled 250 hours @ £4.00
- semi-skilled 100 hours @ £3.50
1,000
350
Variable overhead
Printing press depreciation
Fixed production costs
Estimating department costs
350 hours @ £4.00
200 hours @ £2.50
350 hours @ £6.00
1,400
500
2,100
400
______
12,150
You are aware that considerable publicity could be obtained for the company if you
are able to win this order and the price quoted must be very competitive.
The following notes are relevant to the cost estimate above:
(1)
The paper to be used is currently in stock at a value of £5,000. It is of an
unusual specification (texture and weight) and has not been used for some
time. The replacement price of the paper is £9,000, whilst the scrap value of
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C H A P T ER 2 – D E C I S I O N M A K I N G A N D L I N EA R P R O GR A M M I N G
that in stock is £2,500. The stores manager does not foresee any alternative
use for the paper if it is not used on the pamphlet.
(2)
The inks required are presently not held in stock. They would have to be
purchased in bulk at a cost of £3,000. 80% of the ink purchased would be
used in producing the pamphlet. There is no foreseeable alternative use for
the remaining unused ink.
(3)
Highly skilled direct labour is in short supply, and the factory labour is already
being utilised at full capacity, therefore, to accommodate the production of
the pamphlet, 50% of the time required would be worked at weekends for
which a premium of 25% above the normal hourly rate is paid. The normal
hourly rate is £4.00 per hour.
(4)
Semi-skilled labour is presently under-utilised, and 200 hours per week are
currently recorded as idle time. If the printing work is carried out, 25
unskilled hours would have to occur during the weekend, but the employees
concerned would be given two hours time off during the week in lieu of each
hour worked at the weekend.
(5)
Variable overhead represents the cost of operating the printing press and
binding machines.
(6)
When not being used by the company, the printing press is hired to outside
companies for £6.00 per hour. This earns a contribution of £3.00 per hour.
There is unlimited demand for this facility.
(7)
Fixed production costs are those incurred by and absorbed into production,
using an hourly rate based on budgeted activity.
(8)
The cost of the estimating department represents time spent in discussions
with the organisation concerning the printing of its pamphlet.
Required:
Prepare a revised cost estimate using the opportunity cost approach,
showing clearly the minimum price that the company should accept for the
order. Give reasons for each resource valuation in your cost estimate.
(20 marks)
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C H A P T E R 2 – D E C I S IO N M A K IN G A N D L IN E A R P R O G R A M M I N G
LINEAR PROGRAMMING – MULTI LIMITING FACTORS
The aim of decision making is to maximise profit, assuming that the fixed cost does
not change, this would mean that we must maximise contribution. Alternatively the
aim may be minimise cost to subsequently maximise profit.
Linear programming involves the construction of a mathematical model to
represent the decision problem where the activities of the problem constitute
variables.
Steps
1.
Define the problem (unknowns or variables)
2.
Objective function
3.
Constraints
4.
Graph
5.
Optimal solution
6.
Shadow prices
Example 13
A company makes two products (R and S), within three departments (X, Y and Z).
Production times per unit, contribution per unit and the hours available in each
department are shown below:
Contribution/unit
Product R
£4
Product S
£8
Department X
Department Y
Department Z
Hours/unit8
8
4
12
Hours/unit
10
10
6
Capacity (hours)
11,000
9,000
12,000
Required:
What is the optimum production plan in order to maximise contribution?
1.
Define the problem
Let x = number of units of R produced
Let y = number of units of S produced
2.
Objective Function – maximise contribution = Z
Z = 4x + 8y
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C H A P T ER 2 – D E C I S I O N M A K I N G A N D L I N EA R P R O GR A M M I N G
3.
Subject to – constraints
(Dept A hrs)
8x + 10y ≤ 11000
(Dept B hrs)
4x + 10y ≤ 9000
(Dept C hrs)
12x + 6y ≤ 12000
(non-negativity) x, y ≥0
4.
Plotting the graph
If we know the constraints we are able to plot the limitations on a graph identifying
feasible and non-feasible regions. The linearity of the problem means that we need
only identify two points on each constraint boundary or line. The easiest to identify
will be the intersections with the x and y-axes.
For example:
Dept A hrs – equating the formula 8x + 10y
=
11,000
If x
=
0
then y
=
-1,100
Co-ordinates (0, 11,00)
If y
=
0
then x
=
1,375
(1,375, 0)
Dept B hrs – 4x + 10y
=
9,000
(0, 900)
(2,250, 0)
Dept C hrs – 12x + 6y
=
12,000
(0, 2,000)
(1,000, 0)
And hence:
By plotting the individual constraints we build up an area of what is possible within
all the constraints ie the FEASIBLE REGION.
5.
Identifying the optimal solution
1.
The Iso-contribution (IC line) line is plotted identifying points of equal
contribution. The linear nature of the problem means that this line will be a
straight line identifying an inverse relationship between the two products.
The IC line is of importance because the relationship of the contribution
earned by each product is constant (ie £4 for R against £8 for S). This means
that the gradient of the line will remain constant as the total contribution
figure gets larger or smaller.
If we ‘push out’ the IC line to the point where it leaves the feasible region,
that point will be the point of maximum contribution.
Steps
(i)
Choose an arbitrary contribution figure (preferably one that can be
easily plotted on the graph just drawn).
Example
(ii)
contribution =
Z
=
£3,200
What are the objective function values?
4x + 8y = 3,200
(iii)
Translate those values into co-ordinates for plotting on the graph
Co-ordinates (0, 400) and (800, 0)
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C H A P T E R 2 – D E C I S IO N M A K IN G A N D L IN E A R P R O G R A M M I N G
2.
The optimal solution can now be found by interrogating the point at which the
IC line leaves the feasible region to identify the co-ordinates and hence the
product mix and maximum contribution.
The intersection or VERTEX identified is where two constraints meet, those
constraints can be solved simultaneously to identify the product mix.
a
8x + 10y
= 11,000
b
4x + 10y
=
9,000
4x
=
2,000
x
=
500
y
=
700
(a – b)
Therefore the optimal product mix is to make and sell 500 units of X and 700 units
of Y. The maximum contribution is (500 x 4 + 700 x 8) = £7,600.
This can be checked by seeing how much of the constraints are used up:
Dept
hours used
hours available
A
500 x 8 + 700 x 10 = 11,000 hours
11,000 hours
B
500 x 4 + 700 x 10 = 9,000 hours
9,000 hours
B
500 x 12 + 700 x 6 = 10,200 hours
12,000 hours
Slack and surplus
Departments A and B are fully utilised or what are termed binding constraints (ie
they bind the decision or output). Department C has 1,800 hours un-utilised and is
not binding on the decision, it is called a slack constraint.
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C H A P T ER 2 – D E C I S I O N M A K I N G A N D L I N EA R P R O GR A M M I N G
SENSITIVITY ANALYSIS – SHADOW PRICE
An investigation to identify how the optimum solution will change with changes to
individual variables.
The SHADOW PRICE or dual price is the amount by which the total optimal
contribution would rise if an additional unit of input (hour) was made available.
Department X – shadow price of one hour
If one more hour was available (ie 11,001 hours now), the constraint of department
A will relax outward slightly which should improve the overall optimum solution.
Solve the new constraint equations:
Dept X
8x + 10y = 11,001
Dept Y
4x + 10y =
9,000
Revised solution
Revised contribution
Shadow price
Effects – As A increases by 1:
1.
x
2.
y
3.
Contribution
4.
Dept Z
Department Y – shadow price of one hour
If one more hour was available (ie 9,001 hours now), the constraint of department
B will relax outward slightly which should improve the overall optimum solution.
Solve the new constraint equations:
Dept X
8x + 10y
=
11,000
Dept Y
4x + 10y
=
9,001
4x + 0
=
1,999
Revised solution
x = 499.75,
y = 700.2
Revised contribution
499.75 x 4 + 700.2 x 8 = £7600.6
Shadow price
£7,600.6 - £7,600.0 = £0.6/hour of dept Y
Effects – As Y increases by 1:
1
x decreases by 0.25
2
y increases by 0.2
3
Contribution increases by £0.6
Dept Z slack actually increases by 1.8 hours.
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Department Z – shadow price of one hour
Department Z already has spare capacity, extra hours would not increase the
contribution generated by the optimum solution (they would not change the
solution). They have no shadow price.
Assumptions and limitations of linear programming
●
Linear programming may be used when relationships are assumed to be linear
and where an optimum solution does in fact exist.
●
Assumes contribution per unit for each product is constant irrespective of the
total quantities produced and sold
●
Assumes utilisation of resource per unit for each product is constant
irrespective of the total quantities produced and sold
●
Assumes that units produced and resources allocated are infinitely divisible.
●
When there are a number of variables, it becomes too complex to solve
manually and a computer is required.
Example 14 Cantata
Cantata operates a small machine shop. Next month he plans to manufacture two
products, A and B upon which the unit contribution is estimated to be £50 and £70
respectively.
For their manufacture both products require inputs of machine processing time, raw
materials and labour.
Each unit of product A requires 3 hours of machine
processing time, 16 units of raw materials and 6 hours of labour.
The
corresponding per unit requirements for product B are 10, 4 and 6 respectively.
Cantata forecasts that next month he can make available 330 hours of machine
processing time, 400 units of raw materials and 240 labour hours. The technology
of the manufacturing process is such that at least 12 units of product B must be
made in any given time.
Required:
How many units of product A and B should be produced in order to
maximise contribution?
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Example 15 Tronto
Tronto is a family-operated business that manufactures fertilisers. One of its
products is a liquid plant feed into which certain additives are put to improve
effectiveness. Every 10,000 litres of this feed must contain at least 480g of
additive A, 800g of additive B and 640g of additive C. Tronto can purchase two
ingredients (X and Y) that contain these three additives. The information, together
with the cost of each ingredient, is given as follows:
Additive A
Additive B
Additive C
Cost per litre
ingredient X
2g
5g
10g
£25
ingredient Y
8g
10g
4g
£50
Both ingredients require specialist storage facilities and as such no more than 120
litres each can be held in stock at any one time.
Tronto’s objective is to determine how many litres of each ingredient should be
added to every 10,000 litres of plant feed so as to minimise cost.
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Chapter 3
Pricing
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C H A P T ER 3 – P R I C I N G
CHAPTER CONTENTS
INTRODUCTION TO PRICING ------------------------------------------- 59
FACTORS AFFECTING PRICING DECISIONS
59
WAYS OF CALCULATING THE PRICE
59
COST-PLUS PRICING ---------------------------------------------------- 60
1.
FULL COST-PLUS PRICING
60
2.
MARGINAL COST-PLUS PRICING
61
MARKETING APPROACHES---------------------------------------------- 62
PRODUCT LIFE CYCLE
62
PRICING STRATEGIES
63
FOR NEW MARKETS – MONOPOLY POSITION
63
EXISTING MARKET – NO MONOPOLY POSITION
64
DEMAND BASED PRICING----------------------------------------------- 66
DERIVING THE DEMAND CURVE
66
FACTORS INFLUENCING DEMAND
66
PRICE ELASTICITY OF DEMAND
67
PROFIT MAXIMISING PRICE AND QUANTITY------------------------- 69
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INTRODUCTION TO PRICING
The pricing of products or services is one of the more difficult and more important
decisions for the organisation. The prices adopted by a company will have an
immediate effect on the profitability of an organisation and longer term implications
on the marketing of the product.
Factors affecting pricing decisions
Factors underlying pricing decisions
There are several factors underlying all pricing decisions, including the following:
1.
Organizational goals
2.
Price and demand relationship
3.
Competitors
4.
Cost
5.
Product mix
6.
Quality
7.
Inflation
8.
Product life cycle
Ways of calculating the price
There are three ways in which we may calculate the price of the product:
1.
Cost-plus pricing – marginal cost or full cost as a base.
2.
Marketing based pricing – the aim to generate profit maximisation in the
longer term.
3.
Demand based pricing – the application of economic theory to maximise
profit in the short-term.
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C H A P T ER 3 – P R I C I N G
COST-PLUS PRICING
The simplest form of pricing, it is still widely used particularly in the retail industry
and in specific / job order situations. The price is based on the cost plus a margin.
Cost-plus pricing may be based on:
1.
full cost (calculated using absorption costing) or
2.
marginal / variable cost.
The rationale behind this method is that if the price is greater than the cost then a
profit must be made (providing that the expected volumes are achieved).
1. Full cost-plus pricing
Advantages of full cost-plus pricing strategy:
●
Easy to use.
●
Ensures that all costs are covered.
●
Ensures that firm can generate profits and survive in the future.
●
Avoids costs of collecting market information on demand and competitor
activity.
●
It is believed to establish stable prices.
Disadvantages of full cost-plus pricing strategy:
●
It does not consider the demand pattern of the product.
●
The absorption of overheads is a guess work therefore the strategy will
produce different selling prices using different bases.
●
Takes no account of market conditions since its focus is entirely internal.
●
By using a fixed mark up it does not permit the company to respond to the
pricing decisions of its competitors.
●
It is not appropriate for making special decisions involving use of spare
capacity.
An example of typical total cost plus price calculation is as follows
£
Direct materials
Direct labour
Prime cost
Factory overheads:
Fixed
Variable
Total manufacturing cost
Non manufacturing costs:
Fixed
Variable
Total cost
Add profit (20% x 50)
Selling price
60
10
5
10
0
£
10
15
25
15
40
10
50
10
60
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CHAPTER 3 – PRICING
Manufacturing Cost-Plus Method
Total manufacturing cost
Add profit (50% x 40)
Selling price
40
20
60
2. Marginal cost-plus pricing
Pricing strategy in which a profit margin is added to the budgeted marginal or
variable cost of the product.
Advantages
●
This strategy ensures that fixed costs are covered.
●
The size of the mark up can be adjusted to reflect demand.
●
Maximum capacity utilisation.
●
Efficient and most economic use of scarce resources.
Disadvantages
●
Ignore profit maximisation.
●
Ignores fixed overheads. The price may not be high enough to ensure that a
profit is made after fixed overheads are covered.
●
Lack of consideration of overall market and customers.
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C H A P T ER 3 – P R I C I N G
MARKETING APPROACHES
The aim is to maximise the profit over the length of the product’s life.
Product life cycle
Decline
Growth
Level of
activity
Maturity
Introduction
Time
Example 1
What are the implications on profitability, cash flow and strategy of each stage in
the product life cycle?
Phase
Introduction
Growth
Maturity
Decline
Profitability
Cash flow
Strategy
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Pricing strategies
For new markets – monopoly position
Market skimming
The price is set at a high level to generate maximum return per unit in the early
units. The aim is to sell to only that small part of the market which is not price
sensitive. For market skimming to be effective the company must have a barrier to
entry in the form of a patent, brand, technological innovation or other.
Features
1
Low volume, high price
2
Low initial investment in production capacity
3
Low risk, if strategy fails price can be dropped.
Limitations of market skimming strategy
●
It is only effective when the firm is facing an inelastic demand curve (market
is not price sensitive).
●
Price changes by any one firm will be matched by other firms resulting in a
rapid growth in industry volume.
●
Skimming encourages the entry of competitors.
●
Skimming results in a slow rate of diffusion and adaptation. This results in a
high level of untapped demand. This gives competitors time to either imitate
the product or leap frog it with a new innovation.
Market penetration pricing
The price is set at a level which should generate demand from the whole market
and by so doing encourage an acceleration of the life cycle quickly into growth and
maturity phases. Necessary if the market skimming approach is not possible
because of a lack of barriers to entry or high initial development costs.
Features
1
Low price, mass market.
2
Substantial investment required.
3
High risk, the low price is used to deter other competitors.
Penetration pricing strategy is appropriate when:
●
Product demand is highly price elastic so that demand responds to price
changes.
●
Substantial economies of scale are available.
●
The product is suitable for a mass market and there is sufficient demand.
●
The product will face competition soon after introduction.
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C H A P T ER 3 – P R I C I N G
Existing market – no monopoly position
Penetration pricing - see above
May also be used in an existing market.
Going rate pricing or average pricing
Where the product is a leading brand (in market share terms) and any change in
price made that company will lead to a change by other competitors. Competition
will continue in other forms.
Example 2
Identify three industries/companies which use going rate pricing.
Intel, Unilever, and Procter and Gamble.
Premium pricing
The product is able to command a premium due to specific and identifiable features
of the product. The premium may be payable for a number of differing reasons
such as:
1.
Prestige
2.
Reliability
3.
Longevity
4.
Technology
5.
Style.
Example 3
Identify the car manufacturers which use each feature to command a
premium for their product.
Discount pricing (loss leaders)
The product is sold at a discount to encourage higher sales. This often has the
effect of reducing the image of the product because customers equate price with
quality.
Example 4
Identify three industries/companies that use discount pricing.
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CHAPTER 3 – PRICING
Complementary product pricing
Complementary products are products that are goods that tend to be bought and
used together. For example: computers and software. If sales of one increase,
demand for the other will also increase. Also referred to as joint demand.
Captive product pricing
Where products have complements, companies will charge a premium price where
the consumer is captured (family of brands).
Product line pricing
A product line is a group of products that are related to each other.
Product line pricing strategies include setting prices that are proportional to full or
marginal cost with the same profit margin for all products in the product line.
Alternatively, prices can be set to reflect demand relationships between products in
the line so that an overall return is achieved.
Volume discounting
A volume discount is a reduction in price given for purchases of large volume. The
objective is to increase sales from large customers. The discount differentiates
between wholesale and retail customers. The reduced cost of a large order will
compensate for the loss of revenues from offering the discount.
Price discrimination
This is the practice of selling the same product at different prices to different
customers. Examples: off peak travel bargains; theatre tickets sold at different
prices based on location so that customers pay different prices for the same
performance.
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C H A P T ER 3 – P R I C I N G
DEMAND BASED PRICING
The preparation of a price in relation to the demand for a product.
This technique considers the demand for a product at a given price by developing a
demand curve.
Deriving the demand curve
Formula sheet extract
Demand curve
P = a − bQ
b=
change in price
change in quantity
a = price when Q = 0
Example 5 Biscan
A product sells 500 units at a price of £25 and 700 units at a price of £20.
Required:
Assuming a unitary demand curve, what is the formula for the demand
curve?
Example 6 Mellor
A company presently sells 20,000 units at £12.50 each. The managing director
believes that they will be more profitable if they sell 20% more unit at a price of
£11 each.
Required:
(a)
Derive the demand curve.
(b)
Calculate the total revenue in each circumstance.
Is the managing director necessarily correct in her assumption?
Factors influencing demand
The demand for a particular company’s goods will be influenced by 3 main factors:
1.
The Product Life Cycle (PLC).
adopted.
2.
Quality of the product. High quality of product can support a high price.
3.
Marketing (Price is one of the 4 P’s). Can capture a higher market share by
adopting a particular pricing strategy.
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If life cycle is short, a high price strategy is
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CHAPTER 3 – PRICING
Price elasticity of demand
Price elasticity of demand is the measure of the extent of change in market demand
for a good in response to a change in its price. When a small change in price
results in more than a proportionate change in demand, the product is said to be
elastic, where a change in price results in less than proportionate change in
demand, we have price inelastic (e.g. salt). However, where a change in price
results in an equal change in demand, we have unitary elastic demand.
Elasticity of demand (PED) =
% change in demand of good X
% change in price of good X
Price elasticity of demand
(Q2 − Q1) ÷ Q1
(P2 − P1) ÷ P1
=
If the PED is greater than one, the good is price elastic. Demand is responsive to
a change in price. If for example a 15% fall in price leads to a 30% increase in
quantity demanded, the price elasticity = 2.0.
If the PED is less than one, the good is inelastic. Demand is not very responsive
to changes in price. If for example a 20% increase in price leads to a 5% fall in
quantity demanded, the price elasticity = 0.25.
If the PED is equal to one, the good has unit elasticity. The percentage change in
quantity demanded is equal to the percentage change in price. Demand changes
proportionately to a price change.
If the PED is equal to zero, the good is perfectly inelastic. A change in price will
have no influence on quantity demanded. The demand curve for such a product
will be vertical.
If the PED is infinity, the good is perfectly elastic. Any change in price will see
quantity demanded fall to zero. This demand curve is associated with firms
operating in perfectly competitive markets.
Other factors affecting elasticity
●
Availability of substitutes.
●
Complementary products.
●
Disposable income.
●
Necessities.
●
Tastes and fashions.
●
Advertising and Marketing.
●
Price.
●
Local laws.
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C H A P T ER 3 – P R I C I N G
Example 7
The price of a good is £1.20 per unit and the annual demand is 800,000 units.
Market research indicates that an increase in price of 10pence per unit will result in
a fall in annual demand of 75,000 units.
Required:
What is the price elasticity of demand?
Advantages of demand based pricing
1.
A consideration of the market.
2.
It considers only incremental costs.
3.
Relationship between Price and Demand.
Limitations of demand based pricing
1.
Degree of accuracy to determine price and demand relationship.
2.
Accuracy to determine true variable / marginal cost.
3.
Many companies aim to achieve a target profit, rather than the theoretical
maximum profit.
4.
Less focus on other factors such as quality, advertising, packaging, credit
facilities and after sales services also affect the quantity demanded of a
product, not just the Price.
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CHAPTER 3 – PRICING
PROFIT MAXIMISING PRICE AND QUANTITY
It is important to understand cost behaviour in many business decisions. The rate
of increase in total cost as a consequence of increase in volume may increase or
decline due to price changes, inflation, and discount factors etc.
The same principle applies to the rate of increase in revenues as a result of
increase in volume.
Profit maximising price and quantity can be determined by using the idea of
marginal revenue and marginal cost.
It can be determined by plotting marginal revenue and marginal cost curves and
equating them on the graph paper, the point of intersection shows the profit
maximising price and quantity.
Hence, the profit maximising price and quantity will be at a point where:
Marginal revenue (MR)
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=
marginal cost (MC)
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C H A P T ER 3 – P R I C I N G
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Chapter 4
Decision making under
uncertainty
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CHAPTER CONTENTS
INTRODUCTION ---------------------------------------------------------- 73
WHAT IS RISK AND UNCERTAINTY? ----------------------------------- 74
UNCERTAINTY
74
RISK
74
WORST, MOST LIKELY, AND BEST OUTCOME ESTIMATES
74
DECISION CRITERIA
75
EXPECTED VALUE -------------------------------------------------------- 76
PROBABILITY
76
EXPECTED VALUES
76
SENSITIVITY ANALYSIS ------------------------------------------------ 79
INTRODUCTION
79
IMPLEMENTING SENSITIVITY ANALYSIS
79
SIMULATION ------------------------------------------------------------- 81
VALUE OF PERFECT INFORMATION (VPI) ----------------------------- 82
MARKET RESEARCH------------------------------------------------------ 83
DECISION TREE ANALYSIS --------------------------------------------- 84
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INTRODUCTION
Decision making, particularly long-term decisions, has to be taken under the
conditions of risk and uncertainty.
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C H A P T E R 4 – D E C I S IO N M A K IN G U N D E R U N C E R T A IN T Y
WHAT IS RISK AND UNCERTAINTY?
Uncertainty
Uncertainty simply reflects that there is more than one possible outcome for a
given event but there is little previous statistical evidence to enable the possible
outcomes to be predicted.
Risk
Risk is where that uncertainty can be quantified in some way.
It is normal to quantify the risk in terms of a probability distribution, generally
derived from statistical data in the past.
Risk attitudes
Risk preference describes the attitude of a decision-maker toward risk – as there is
a relationship between risk and reward.
●
Risk averse – a risk averse decision-maker considers risk in making decision,
and will not select a course of action that is more risky unless the expected
return is higher and so justifies the extra risk.
●
Risk seeker – a risk seeker decision-maker also considers risk in making a
decision.
A risk seeker, unlike a risk averse decision-maker, will take extra risks in the
hope of earning a higher return.
●
Risk neutral – a risk neutral decision-maker ignores risk in making a
decision.
A risk neutral decision-maker will select the course of action with the highest
expected return, regardless of risk
Worst, most likely, and best outcome estimates
The choice between two or more alternative courses of action might be based on
the worst, most likely or best expected outcomes from each course of action.
This choice will show the full range of possible outcomes from a decision, and might
help managers to reject certain alternatives because the worst possible outcome
might involve an unacceptable amount of loss.
This requires the presentation of a pay-off table.
Pay-off table (or matrix)
The pay-off matrix is a tabular layout specifying the result (pay-off) of each
combination of decision and the state of the world over which the decision maker
has no control.
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C H A P T E R 4 – D E C I S IO N M A K IN G U N D E R U N C E R T A IN T Y
Example 1 Won Ltd
Won Ltd is trying to decide the selling price for a product. Three prices are under
consideration and expected sales volume and costs are as follows:
Price per unit
Expected sale volume (unit)
Best possible
Most likely
Worst possible
£4
16,000
14,000
10,000
£4.30
£4.40
14,000
12,500
8,000
12,500
12,000
6,000
Fixed costs are £20,000 and variable cost is £2 per unit.
Required:
Which price should be chosen?
Decision criteria
Choosing between mutually exclusive courses of action on the basis of worst, most
likely or best possible outcome can be stated as decision rules.
The choice may be based on a maximax, maximin, or a minimax regret decision
rule, and expected value.
Maximax
The decision maker will select the course of action with the highest possible payoff
(the best of the best).
The maximax decision rule is the decision rule for the risk seeker.
Maximin decision rule
The decision maker will select the course of action with the highest expected return
under the worst possible conditions. This decision rule might be associated with a
risk averse decision maker.
Minimax regret decision rule
The decision maker selects the course of action with the lowest possible regret. It
aims at minimising the regret from making the wrong decision.
Regret is the opportunity cost of having made the wrong decision, giving the actual
conditions that apply in the future.
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EXPECTED VALUE
The expected value ignores the degree of risk and focuses solely on the average
return of the event given repetition of the event.
Example 2 Too Ltd
Too Ltd is trying to decide which of the three mutually exclusive projects to
undertake. The company has constructed the following payoff table or matrix.
Net profit if outcome turns out to be
Project A
Project B
Project C
Worst
50
70
90
Most likely
85
75
100
Best
130
140
110
Required:
State which project would be selected using each of the:
(a)
maxmin;
(b)
maximax criteria; and
(c)
minimax regret rule.
Probability
The measurement of the outcomes in terms of their estimated likelihood of
occurring.
Overall probability of an event must sum to 1.0 (or if you wish 100%). For
example, if you toss a coin there is a 0.5 (50%) probability of a head or a tail.
Adding both outcomes total 1.0 (100%).
Expected values
A weighted average value of all the possible outcomes. It does not reflect the
degree of risk, but simply what the average outcome would be if the event were
repeated a number of times.
A decision rule is to select the course of action with the highest expected value of
profit or the lowest expected value of cost.
Expected value formula
76
EV
=
Σpx
P
=
probability of an outcome
x
=
value of an outcome
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C H A P T E R 4 – D E C I S IO N M A K IN G U N D E R U N C E R T A IN T Y
Example 3 3D Ltd
3D Ltd expects the following monthly profits:
Monthly profit
£50,000
£35,000
Probability
0.6
0.4
Required:
Calculate the expected value of monthly profit.
Example 4 For Ltd
Consider the following sales and probabilities.
Sale
£
20,000
25,000
30,000
35,000
probabilities
%
25
40
15
20
Required:
What will be the expected value?
Advantages of expected values
1.
EV considers all the different possible outcomes and the probability that each
will occur.
2.
It recognises risk in decision, based on the probabilities of different possible
results or outcomes.
3.
It expresses risk as a single figure.
Limitations of expected values
1.
The EV shows a long term average, so that the EV will not be reached in the
short term and is therefore not very suitable for one-off decisions.
2.
The accuracy of the results depends on the accuracy of the probability
distribution used.
3.
EV takes no account of the risk associated with a decision.
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Example 5 Mr Fyvestall
Mr Fyvestall runs a market stall selling vegetables and fruit. He buys a product for
£20 per case. He can sell the product for £40 per case on his stall. The product is
perishable and it is not possible to store it, instead any cases unsold at the end of
the day can be sold off as scrap for £2 per case.
Purchase orders must be made before the number of sales is known. He has kept
records of demand over the last 150 days.
Demand / day
10
20
30
Number of days
45
75
30
Required:
(a)
Prepare a summary of possible net daily margins using a payoff table.
(b)
Advise Mr Fyvestall:
(i)
How many cases to purchase if he uses expected values.
(ii)
How many cases to purchase if he uses maximin / maximax.
(iii) How many cases to purchase if he uses minimax regret.
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SENSITIVITY ANALYSIS
Introduction
Sensitivity analysis is a method of risk or uncertainty analysis in which the effect on
the expected outcome of the change in values of key variables or key factors is
tested. For example, in budget planning, the effect on budgeted profit might be
tested for changes in the budgeted sales volume, or the budgeted sale price,
material and labour costs, and so on.
There are several ways of using sensitivity analysis including:
●
To estimate by how much costs and revenues would need to differ from their
estimated values before the decision would change.
●
To estimate whether a decision would change if estimated sales were A%
lower than estimated, or estimated costs were B% higher than estimated.
This is called ‘what if’ analysis. For example: what if the sales volume is 5%
less than the expected volume?
Implementing sensitivity analysis
The starting point of sensitivity analysis is the original plan or estimate, giving an
expected profit or value.
Key variables that determine the profit or value are identified. Such variables
include: sale price, sales volume, completion time, material and labour costs, and
so on.
The values of these key variables are altered to determine how much they would
differ from their estimated values before the decision would change.
In this way, the sensitivity of a decision or plan to changes in the value of the key
variables can be measured.
Example 6 VI Ltd
VI Ltd has estimated the following sales and profit for a product which it may
launch onto the market.
£
Sales (2,000 units)
Variable costs:
Materials
Labour
£
4,000
2,000
1,000
Contribution
Incremental fixed costs
Profit
3,000
1,000
800
200
Required:
(a)
Analyse the sensitivity of the product.
(b)
Determine which of the variables is the product most sensitive.
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C H A P T E R 4 – D E C I S IO N M A K IN G U N D E R U N C E R T A IN T Y
Advantages
1.
It is not a complicated theory to understand
2.
It forces managers to identify the underlying variables, indicate where
additional information would be most useful, and helps to expose confused
and inappropriate forecasts
3.
An indication is provided of those variables to which profitability or value is
most sensitive. And the extent to which those variables may change before
the investment break-even.
4.
It provides an indication of why a project might fail. Once these critical
variables have been identified, management should review them to assess
whether or not there is a strong possibility of events occurring which will lead
to a negative NPV.
5.
It serves as an aid in the preparation of contingency plans, should key
parameters show unfavourable variations ex-post.
Disadvantages
1.
The method requires that changes in each key variable are isolated. But
management is more interested in the combination of the effects of changes
in two or more variables. Looking at factors in isolation is unrealistic since
they are often inter-dependent.
2.
It does not examine the probability that any particular variation in cost or
revenue might occur.
3.
It is not in itself a decision rule. Management must weigh the information
provided by the analysis in deciding whether the investment is worthwhile.
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SIMULATION
Simulation is a quantitative technique that uses IT based computerised packages
with built in mathematical models for decision making under conditions of
uncertainty.
It evaluates various courses of action based upon facts and
assumptions.
Monte Carlo is a widely used method of simulation, where complex problem is
solved by simulating the original data with random number generators.
Usefulness of simulation:
●
Medical diagnosis
●
Gambling
●
Air force trainings
●
Traffic scheduling.
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VALUE OF PERFECT INFORMATION (VPI)
If perfect information about the future were available, it would be very easy to
make a decision as the uncertainty and risk associated with it would be minimum.
Therefore knowledge about cost of obtaining the perfect information is very
important for management point of view.
The price that one would be willing to pay in order to gain access to perfect
information of an uncertain outcome in decision making is known as Value of
Perfect Information.
Mathematically VPI is the difference between the payoff under certainty and the
payoff under risk.
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MARKET RESEARCH
Market research is a process of systematically and objectively gathering, recording
and analysing information. This information may relate to:
●
customers;
●
general trends in the market;
●
competitors;
●
government regulations;
●
economic trends;
●
technological advancements; and
●
any other factors that constitute the business environment.
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DECISION TREE ANALYSIS
A decision tree is a diagram showing several possible courses of action and possible
events and the potential outcomes for each course of action.
Each alternative course of action is represented by a branch, which leads to
subsidiary branches for further course of action or possible events.
Decision tree analysis is designed to illustrate the full range of alternatives that can
occur, under all possible given conditions.
Example 7 Seven Trees Ltd
The following information relates to Seven Trees Ltd, a company which is
considering whether to develop and market a product.
Probability
Development
Being successful
Being unsuccessful
0.75
0.25
Estimated development costs would be $180,000
If successful, the product will be marketed with following probabilities:
Being very successful
Being moderately successful
Being failure
Probability
0.4
0.3
0.3
Profits / (Loss)
$540,000
$100,000
($400,000)
The above profits / losses figures include the effect of the development costs.
Required:
Draw a decision tree to illustrate the above problem, and recommend the
best course of action.
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Chapter 5
Budgeting types
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CHAPTER CONTENTS
WHAT IS A BUDGET? ---------------------------------------------------- 87
FUNCTIONS OF BUDGETING
87
BUDGET PERIOD
87
ADMINISTRATION OF A BUDGET
88
BUDGET PREPARATION ------------------------------------------------- 89
TYPES OF BUDGET ------------------------------------------------------- 90
86
1.
ZERO BASED BUDGETING
90
2.
CONTINUOUS BUDGETING
91
3.
NON-PARTICIPATORY BUDGETING
92
4.
ACTIVITY BASED BUDGETING
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WHAT IS A BUDGET?
A quantitative plan prepared for specific time period.
financial terms and prepared for one year.
Functions of budgeting
It is normally expressed in
(PCCCEMA)
We can identify the aims of a budget in seven ways:
1.
Planning
2.
3.
Communication
4.
7.
Control
Co-ordination
5.
Evaluation
6.
Motivation
Authorisation & Delegation
Budget period
The budget period is the period of time for which the budget is prepared and over
which the control aspect takes place. Except for capital expenditure budgets, the
budget period is usually the accounting year, sub divided into 12 or 13 control
periods.
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Administration of a budget
It is important that suitable administration procedures are introduced to ensure that
the budget process works efficiently.
(a)
Budget Committee
The budget committee should consist of high-level executives who represent the
major segments of the business. It typically includes the chief executive, the
corporate or management accountant (acting as budget officer) and functional
heads. Their main task is to ensure that budgets are realistically established and
that they are coordinated satisfactory.
The functions of the committee are:
●
agree policy with regards to budgets
●
coordinate budgets
●
suggest amendments to budgets, example, because they are not adequate
●
approve budgets after amendments, as necessary
●
examine comparison of actual and budget and recommend corrective actions.
The accountant and his team will normally assist managers in the preparation of
their budgets. They will circulate and advise on the instructions about budget
preparation, provide past information that may be useful for preparing the present
budget, and ensure that managers submit their budgets on time. The accounting
staff does not determine the content of the various budgets, but they do provide
valuable advisory and clerical services for the line managers.
(b)
Budget Manual
A budget manual describes the objectives and procedures involved in the budgeting
process and will provide a useful reference source for managers responsible for the
budget preparation. In addition, the manual may include a timetable specifying the
order in which the budgets should be prepared and the dates when they should be
presented to the budget committee. The manual should be circulated to all those
who are responsible for preparing budgets.
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BUDGET PREPARATION
Steps
1.
Budget aims
Strategic aims.
Key assumptions.
2.
Identify the principal budget factor
1.
Sales demand for production environment.
2.
Cash resource for non profit making organisation.
3.
Prepare the sales budget
Start with the principal budget factor:
1.
Marketing department function.
2.
Price/volume relationship.
4.
Prepare all other functional budgets
Prepare each functional budget separately.
Participatory process
1.
Local knowledge.
2.
Promotes ownership.
5.
Negotiation
Meeting between junior management and senior managers to ensure that the
budget is a realistic target. In particular the aim is to eliminate budgetary slack.
6.
Review
Bring all individual functional budgets together to form a master budget, an overall
budget for the whole organization.
Budget assessed for:
1.
Feasibility
2.
Acceptability
Once completed budgeted financial statements and cash flow statements can be
prepared.
7.
Acceptance
Acceptance means that the budget becomes a formal authorisation for all levels of
management to take action for and on behalf of the company.
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TYPES OF BUDGET
When looking at differing types of budgeting we are concerned with the benefits or
otherwise to the more traditional budget techniques. We would normally expect a
budget to be:
1.
Incremental
2.
Periodic
3.
Participatory
(Bottom – Up)
In comparison to this we will look at four alternative budgeting types:
1.
Zero based budgeting (ZBB)
2.
Continuous (or rolling) budgets
3.
Non-participatory budgets
4.
Activity based budgeting
1. Zero based budgeting
A simple idea of preparing a budget from a ‘zero base’ each time, ie as though
there is no expectation of current activities to continue from one period to the next.
ZBB is normally found in service industries where costs are more likely to be
discretionary. A form of ZBB is used in local government. There are four basic
steps to follow:
1.
Prepare decision packages
Identify all possible services (and levels of service) that may be provided
and then cost each service or level of service, these are known individually
as decision packages.
2.
Rank
Rank the decision packages in order of importance, starting with the
mandatory requirements of a department. This forces the management to
consider carefully what their aims are for the coming year.
3.
Funding
Identify the level of funding that will be allocated to the department.
4.
Utilise
Use up the funds in order of the ranking until exhausted.
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Advantages (as opposed to incremental budgeting)
1.
Emphasis on future need not past actions.
2.
Eliminates past errors that may be perpetuated in an incremental analysis.
3.
A positive disincentive for management to introduce slack into their budget.
4.
A considered allocation of resources.
5.
Encourages cost reduction.
Disadvantages
1.
Can be costly and time consuming.
2.
May lead to increased stress for management.
3.
Only really applicable to a service environment.
4.
May ‘re-invent’ the wheel each year.
5.
May lead to lost continuity of action and short term planning.
2. Continuous budgeting
In a periodic budgeting system the budget is normally prepared for one year, a
totally separate budget will then be prepared for the following year. In continuous
budgeting the budget from one period is ‘rolled on’ from one year to the next.
Typically the budget is prepared for one year, only the first quarter in detail, the
remainder in outline. After the first quarter is revised for the following three
quarters based on the actual results and a further quarter is budgeted for.
This means that the budget will again be prepared for 12 months in advance. This
process is repeated each quarter (or month or half year).
Advantages (as opposed to periodic budgeting)
1.
The budgeting process should be more accurate.
2.
Much better information upon which to appraise the performance of
management.
3.
The budget will be much more ‘relevant’ by the end of the traditional
budgeting period.
4.
It forces management to take the budgeting process more seriously.
Disadvantages
1.
More costly and time consuming.
2.
An increase in budgeting work may lead to less control of the actual results.
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3. Non-participatory budgeting (top-down budgets)
Some organisations do not require junior management to participate in the
budgetary process.
This may be because of security or more likely due to
centralised nature of the company.
Advantages
1.
Saves time and money.
2.
Individual wishes of senior management will not be diluted by others’ plans.
3.
Reduces the likelihood of information ‘leaking’ from the company.
4. Activity based budgeting
Use of activity based costing principles to provide better overhead cost data for
budgeting purposes. The advantages of using such a technique accrue from better
cost allocation.
Exam questions will be closely related to the ABC questions we looked at earlier on
in the course.
Applicability of ABB
Used in an environment with the following criteria:
1.
Complex manufacturing environment.
2.
Wide range of products.
3.
High proportion of overhead costs.
4.
Competitive market.
Benefits of ABB
1.
Better understanding of overhead costs.
2.
Identifies the accurate relationship between product and activity.
3.
Each activity more accurately describes where costs are incurred.
Each and every benefit allows for better control of costs together with the
opportunity to reduce the costs using other management accounting techniques.
Key point
Whenever discussing ABB in an exam context a balance must be drawn between
the better information that is provided against the high cost of implementation and
maintaining an ABB system.
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Chapter 6
Budgetary control
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CHAPTER CONTENTS
INTRODUCTION ---------------------------------------------------------- 95
FIXED BUDGET ----------------------------------------------------------- 96
FLEXIBLE BUDGET ------------------------------------------------------- 97
STEPS IN FLEXIBLE BUDGETING
97
SEPARATING FIXED AND VARIABLE COST
97
INTRODUCTION TO BUDGETARY CONTROL --------------------------- 98
PLANNING AND CONTROL CYCLE -------------------------------------- 99
PLANNING PROCESS:
99
BUDGETING PROCESS:
100
FEEDBACK AND FEED-FORWARD CONTROL
100
BEHAVIOURAL ASPECTS OF BUDGETING ---------------------------- 102
94
PARTICIPATION
102
BUDGET BIAS OR BUDGET SLACK
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CHAPTER 6 – BUDGETARY CONTROL
INTRODUCTION
The use of budgeted data for control purposes. The budget is used as the
comparator against which the actual results may be compared. Any differences can
then be investigated and appropriate action taken. Budgetary control may also be
called responsibility accounting because it gives individual managers the
responsibility to achieve results.
Receive
actual results
Compare to
budget
Analyse the
differences
Revise the
budget
Revise the
actual
Take action
Example 1 Ogrisovic
Ogrisovic plc has the following budgeted and actual information:
Units
Cost
Budget
1,000
£20,000
Actual
1,200
£22,500
Required:
Has the company done better or worse than expected?
If we are now told that £10,000 of budgeted costs are variable, the remainder
being fixed: are we able to tell whether the company has done better or worse than
expected?
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FIXED BUDGET
A budget prepared at a single (budgeted) level of activity.
The term fixed budget means the following
1.
that, the budget is prepared on the basis of an estimated volume of
production and sales, but no plans are made for the event that actual
volume of production and sales may differ from budgeted volume
2.
when actual volume of production and sales during a control period are
achieved, a fixed budget is not adjusted to the new levels of activity.
Advantage:
A fixed budget is likely to be useful in circumstances where the organisational
environment is relatively stable and can be predicted with a reasonable degree of
certainty.
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FLEXIBLE BUDGET
A budget prepared with the costs classified as either fixed or variable. The budget
may be prepared at any activity level and can be ‘flexed’ or changed to the actual
level of activity for budgetary control purposes.
Flexible budget recognises the difference in behaviour between fixed and variable
cost in relation to fluctuations in output, turnover or other variable factors and is
designed to change appropriately with such fluctuations.
Steps in flexible budgeting
1.
A fixed budget is set at the beginning of the period based on estimated
production. This is the original budget.
2.
This is then flexed to correspond with actual level of activity.
3.
The result is compared with actual cost and differences (variances) are
reported to the managers responsible.
Separating fixed and variable cost
One problem normally faced in examinations is how to divide cost into its fixed and
variable elements. One possible way of separating fixed and variable cost is
through the use of high-low method.
Example 2 ABC Ltd
ABC Ltd expects production and sales during the next year to be 90% of the
company’s output capacity, which is 9000 units of a single product. Cost estimates
will be made using the high/low technique and the ff historic records of cost were
provided.
Units of output/sales
9,800
7,700
cost of sale
£44,400
£38,100
The sales price per unit has been fixed at £5.
Required:
The company’s management is not certain that the estimate of sales is correct, and
has asked for flexible budget to be prepared at output and sales levels of 8,000 and
10,000 units.
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INTRODUCTION TO BUDGETARY CONTROL
Budgetary control involves
1.
setting targets or performance standards for individuals (budget holders)
2.
comparing actual performance against the budget (variances)
3.
expecting the budget holder to use this information to take action where
necessary to make sure that the budget is achieved
4.
where necessary, changing the budget targets or performance standards.
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PLANNING AND CONTROL CYCLE
The key stages in the planning process that links long-term objectives and
budgetary control can be divided between long-term planning and the budgeting
process.
Long-term planning involves:
1.
Identifying objectives;
2.
Identifying, evaluating and selecting alternative courses of action.
Budgeting Process involves:
1.
Implementing the long-term plan in the annual budget;
2.
Monitoring actual results;
3.
Responding to divergences from plan.
Planning process:
Identifying objectives
The planning process cannot take place unless organisational objectives are
identified, since these determine what the organisation is seeking to accomplish
through its operations and activities.
These objectives will be long-term or
strategic in nature and will give direction to the organisation’s operational activities.
Identifying alternative courses of action
Once organisational objectives have been identified, alternative courses of action
that may lead to achieving those objectives can be identified.
Strategic analysis of the organisation and its environment can indicate potential
courses of action. For example, a company may look at its existing products and
markets, its potential markets, the threat posed by its competitors, the impact of
changes in technology on its products and production processes, and so on, and
decide that a key objective is the development of new products to replace existing
products in existing markets that are reaching the end of their product life cycle.
Evaluating alternative courses of action
At this stage the various alternative courses of action are considered from the point
of view of suitability, feasibility and acceptability. In order for this to be done,
detailed information about each alternative course of action needs to be gathered
and analysed.
Selecting alternative courses of action
Once the most appropriate alternative courses of action have been selected, longterm plans to implement them are formulated. Because these plans are long-term
in nature, they will of necessity be less detailed than short-term plans, and will
need to allow a degree of flexibility in responding to the changing organisational
environment.
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Budgeting process:
Preparing and implementing the budget
A budget is a short-term plan formulated in financial terms and will show in detail
the short-term actions the organisation will take in working towards its long-term
objectives. Once the budget has been formulated, finalised and agreed it can be
implemented.
Monitoring actual results
In order to achieve the long-term objectives that are reflected in the budget, the
organisation must ensure that actual performance is proceeding according to plan.
It will therefore need to monitor actual performance and results.
Responding to divergences from plan
Divergences from planned activity, as measured by variances from budget, can lead
to action if they are deemed to be significant. This action may be corrective in
nature, in order to bring actual activity back into line with planned activity, or may
entail revision of the budget if one of its underlying assumptions is seen as being in
error.
Feedback and feed-forward control
Feedback control
Feedback control is defined as the measurement of differences between planned
outputs and actual outputs achieved, and the modification of subsequent action
and/or plans to achieve future required results. (CIMA).
Control through feedback is where actual result (output) are compared with those
which were planned for the budget period. Likewise, the input (cost) are compared
with the budget, taking account of the actual level of outputs. This comparison of
actual with plan takes place after the event. The intention is to learn for the future
so that future deviations of actuals and plans are avoided or minimised. Feedback
is a reactive process.
Budgetary control systems are feedback control systems.
Feed-forward control
Feed-forward control is an alternative approach to control using feedback.
Feed-forward control is defined as the forecasting of differences between the actual
and planned outcomes and the implementation of actions before the event, to
prevent such differences. (CIMA).
Control through feed-forward is where prediction is made of what output and inputs
are expected for some budget period. If these predictions are different from what
was planned, then control actions are taken which attempts to minimise the
differences. The aim is for control to occur before the deviation is reported hence
feed-forward control is more proactive. Budget generation is a form of fed-forward
in that various outcomes are considered before one is selected.
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Example 3
You have been provided with the following operating statement, which represents
an attempt to compare the actual performance for the quarter that has just ended
with the budget.
Number of units sold (000)
Cost of sales (all variable)
Materials
Labour
Overheads
Fixed Labour cost
Selling and distribution costs
Fixed
Variable
Administration costs
Fixed
Variable
Total Costs
Sales
Net Profit
Budget
640
Actual
720
Variance
80
£000
£000
£000
168
240
32
440
144
288
36
468
24
(48)
(4)
(28)
100
94
72
144
83
153
(11)
(9)
184
48
548
988
1,024
36
176
54
560
1,028
1,071
43
8
(6)
(12)
(40)
47
7
6
Required:
(a)
Using a flexible budgeting approach, redraft the operating statement so as to
provide a more realistic indication of the variances, and comment briefly on
the possible reasons (other than inflation) why they have occurred.
(10 marks)
(b)
Explain why the
management.
original
operating
statement
was
of
little
use
to
(2 marks)
(c)
(i)
Discuss the problems associated with the forecasting of figures which
are to be used in flexible budgeting.
(4 marks)
(ii)
Further analysis has indicated that the 'variable' overheads for cost of
sales are, in fact, only semi-variable. Whilst the budgeted overheads
for 640,000 units is indicated to be £32,000, it is felt that the budget
for 760,000 units would be £37,000. Included in this later cost is
£1,000 incurred when the activity reached 750,000 units due to extra
hiring capacity.
Produce a revised flexed budget for the overheads contained in cost of
sales for an activity level of 720,000 units.
(4 marks)
(20 marks)
(ACCA)
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C H A P T ER 6 – B U D G E TA R Y C O N T R OL
BEHAVIOURAL ASPECTS OF BUDGETING
It is very easy for the budgetary process to cause dysfunctional activity. For
example, if junior management believe that a budget imposed upon them is
unattainable, their aim may well be to ensure that the budget is not achieved,
thereby proving themselves to be correct.
Otley Illustration
Bud. Cont. System
Dysfunctional
behaviour
Organisation’s
aims
Manager’s aims
Task:
Identify as many examples of dysfunctional behaviour as you can in the time
provided.
Participation
Behaviour studies
performance
have
shown
relationships
between
budget
levels
and
Top-down budgeting
A budget that is set without allowing the ultimate budget holder to have the
opportunity to participate in the budgeting process. Also called “imposed” budget,
or non-participative.
Bottom-up budgeting
A system of budgeting in which budget holders have the opportunity to participate
in setting their own budgets. Also called participative budgeting.
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CHAPTER 6 – BUDGETARY CONTROL
Advantages of participation
Disadvantages of participation
1
Increased motivation to the
budget holder(ownership of
budget)
1
Senior managers may not be able to
give up control
2
Should contain better
information, due to local
knowledge
2
Poor decision making due to
inexperience
3
Increases managers’
understanding
3
Lack of goal congruence
4
Better communication forced
upon the company
4
Budget preparation is slower and may
lead to conflict
5
Senior managers can concentrate
on strategic matters
5
Junior managers may introduce
budgetary slack
6 Participation may not really occur as
senior managers revise data receive
to their own ends
Budget bias or budget slack
Budget holders who are involved in the process from which the budget standards
are set are more likely to accept them as legitimate.
However, they may also be tempted to seize the opportunity to manipulate the
desired performance standard in the favour.
That is, they may make the
performance easier to achieve and hence be able to satisfy personal goals rather
than organisational goals. This is referred to as incorporating a slack into the
budget. In this case there may be a relationship between the degree of emphasis
placed on the budget and tendency of the budget users to bias the budget content
or circumvent its control.
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C H A P T ER 6 – B U D G E TA R Y C O N T R OL
104
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Chapter 7
Quantitative aids to
budgeting
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C H A P T ER 7 – QU A N T I TA T I V E A I D S T O B U D G E T I N G
CHAPTER CONTENTS DIAGRAM
Quantitative Aids to Budgeting
Regression
Analysis
106
Time
Series
Learning
curve
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C H A P T E R 7 – Q U A N T I T A T IV E A ID S T O B U D G E T IN G
CHAPTER CONTENTS
INTRODUCTION --------------------------------------------------------- 108
REGRESSION ANALYSIS ----------------------------------------------- 109
CORRELATION COEFFICIENT
111
COEFFICIENT OF DETERMINATION
112
TIME SERIES ANALYSIS ----------------------------------------------- 113
THE ANALYSIS
113
IDENTIFYING THE TREND LINE
114
EVALUATING THE SEASONAL VARIATION
115
FORECASTING
116
LEARNING CURVE ------------------------------------------------------ 118
MATHEMATICAL ILLUSTRATION
118
USING THE FORMULA
118
GENERAL USE OF LEARNING CURVE
121
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C H A P T ER 7 – QU A N T I TA T I V E A I D S T O B U D G E T I N G
INTRODUCTION
Budgeting requires the prediction, or forecasting, of the volume of output and
sales, sales revenue and costs. Forecasts in budgeting process are to establish
realistic assumptions for planning.
Forecasts might be prepared using a number of forecasting models, methods or
techniques.
The two main areas of consideration are the prediction of costs, mainly based upon
the assumption of a linear relationship between costs and activity level, and time
series analysis, commonly used for forecasting sales.
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C H A P T E R 7 – Q U A N T I T A T IV E A ID S T O B U D G E T IN G
REGRESSION ANALYSIS
Linear regression analysis can be used to make forecast or estimate wherever a
linear relation is assumed between two variables, and historical data is available for
the analysis.
Linear regression analysis is a statistical technique for identifying a “line of best fit”
from a set of data.
If it is assumed that there is a linear relationship between two variables, the
technique can be used to quantify this relationship using historical data. The
relationship is expressed as:
y = a + bx
This is the same as equation of a line.
Where:
y
x
a
b
=
=
=
=
the value of the dependent variable
the value of the independent variable
intercept
gradient
a and b are values obtained from a statistical analysis of historical data for values
of X and Y.
This can be deduced from a scatter diagram as follows:
Y
----- line of best fit
b
a
X
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C H A P T ER 7 – QU A N T I TA T I V E A I D S T O B U D G E T I N G
Key formulae (given in the exam)
a = y – bx
b=
∑ ∑x∑y
n∑x − (∑x )
n xy −
a=
2
2
∑y − b ∑x
n
n
Example 1
A company has recorded expenditure on advertising and resulting sales for 6
months as follows:
Marketing spend
(£000)
Sales
(£000)
x
y
July
40
680
August
80
960
September
100
1,040
October
120
1,200
November
60
880
December
80
1,000
Month
Required:
(a)
Plot the data on a scatter diagram and comment.
(b)
Calculate the line of best fit through the data, and interpret your values of a
and b.
(c)
Forecast sales when advertising expenditure is:
(i)
£100,000
(ii)
£250,000
and comment on your answers.
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C H A P T E R 7 – Q U A N T I T A T IV E A ID S T O B U D G E T IN G
Weaknesses of linear regression analysis
The analysis is based on the following assumptions
1.
there is a linear relationship between the two variables represented by X and
Y
2.
the relationship in the future can be predicted from the relationship in the
past.
Correlation coefficient
In the previous example, having found the equation of the line of best fit, we used
this to forecast the total cost for a given level of activity.
The validity of such forecasts will depend upon two main factors
1.
Whether there is sufficient correlation between the variables to support a
linear relationship within the range of the data used.
2.
Whether the forecast represents an interpolation or an extrapolation.
The correlation coefficient (r) measures the strength of a linear relationship
between 2 variables. Its range of values is –1 through 0 to +1. It shows how well
the data supports the line of best fit.
Negative correlation (r = -1)
Indicates an inverse relationship. This means that the line will be downwards
sloping. For example the relationship between price and volume. The coefficient
will be negative.
Positive correlation (r = +1)
A direct relationship. This means that the line will be upward sloping. For example
the relationship between a team winning and sales of its merchandise. The
coefficient will be positive.
Calculating the correlation coefficient
r=
∑ ∑x∑y
(n∑x − (∑x) )(n∑y −(∑y) )
n xy −
2
2
2
2
Example 2
Calculate the correlation coefficient in example 1 above, and interpret your answer.
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C H A P T ER 7 – QU A N T ITA T IV E A ID S T O B U D G E T IN G
Coefficient of determination
The coefficient of correlation squared (r2). The coefficient of determination shows
the amount of the change in the dependent variable that is due to the independent
variable.
For example, if ice cream sales show a coefficient of determination of 0.6 or 60% in
relation to daily maximum temperature, this would mean that ice cream sales were
determined 60% and 40% due to other factors.
Example 3
The following information shows the units of a good produced and the total costs
incurred.
Month
Jan
Feb
Mar
Apr
May
Units produced
100
120
140
110
70
total costs (£000)
144
163
176
157
115
Required:
Calculate the correlation coefficient.
Example 4
Calculate the coefficient of determination from Example 3 above, and interpret your
answer.
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C H A P T E R 7 – Q U A N T I T A T IV E A ID S T O B U D G E T IN G
TIME SERIES ANALYSIS
A time series is a set of observations or measures taken at equal intervals of time.
The observation could be taken hourly, daily, weekly, monthly, quarterly or yearly.
Examples of time series might include the following:
●
daily production output over a month
●
quarterly sales revenue over five years
●
annual overhead costs over six years.
Activity
Time period
There are four components
1.
The Trend
2.
Seasonal Variation
3.
Cyclical Variation
4.
Residual Variation
The analysis
This is performed by carrying out two distinct steps:
1.
To find the trend.
2.
To find the seasonal variation.
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C H A P T ER 7 – QU A N T ITA T IV E A ID S T O B U D G E T IN G
Identifying the trend line
This is the way in which the time series appears to be moving over a long interval
of time. It is the prevailing direction, upwards or a downwards or flat. For example,
sales might be on an upward or a downward trend over time.
There are two methods of evaluating the trend.
(i)
Fit the line by eye on the graph.
(ii)
Moving averages.
Moving averages
Illustration
Year
Quarter
Sales
1
Q1
18
Q2
20
Q3
34
Q4
44
2
Q1
22
Q2
20
Q3
3
Moving
Total
Moving
average
116
29
29.5
120
30
120
30
30.0
30.5
124
31
128
32
124
31
31.5
38
Q4
48
Q1
18
Q2
20
Q3
42
Q4
56
31.5
31.0
124
31
128
32
31.5
33.0
136
114
Centred
moving
average
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C H A P T E R 7 – Q U A N T I T A T IV E A ID S T O B U D G E T IN G
Evaluating the seasonal variation
There are two models:
1.
The additive model
This is based upon the idea that each actual result is made up of two influences.
The magnitude of the seasonal variation is not affected by the change in the trend
line.
Actual
=
Trend
+
Seasonal Variation
The seasonal variation (SV) will be expressed in absolute terms.
2.
The multiplicative model
The magnitude of the seasonal variation is in direct proportion to the change in the
trend.
Actual
=
Trend
x Seasonal Variation factor
The seasonal variation (SV) will be expressed in proportional terms.
For example, if, in one particular period the underlying trend was known to be
£10,000 and the seasonal variation in this period was given as +12%, then the
actual result could be forecast as:
£10,000 x
112
100
= £11,200.
The additive model - an example
Year
Quarter
Sales
1
Q1
Q2
Q3
Q4
Q1
Q2
Q3
Q4
Q1
Q2
Q3
Q4
18
20
34
44
22
20
38
48
18
20
42
56
2
3
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Centred moving
average
29.5
30.0
30.5
31.5
31.5
31.0
31.5
33.0
Seasonal
variation
4.5
14.0
-8.5
-11.5
6.5
17.0
-13.5
-13.0
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C H A P T ER 7 – QU A N T ITA T IV E A ID S T O B U D G E T IN G
Now calculate the average ‘Actual – Trend’ for each quarter. This is a task that
should be carried out by drawing up a second working table (see below).
Quarter
Year
Q1
Q2
1
2
- 8.50
- 11.50
3
- 13.50
- 13.00
Average Seasonal
Variations
- 11
- 12
Q3
Q4
4.50
14.00
6.50
17.00
6
16
(rounded)
The multiplicative model – an example
The multiplicative seasonal variations are calculated in a similar manner, but the
variations are proportions. Instead of finding A – T, we find A/T, then average the
results as above. For example, for quarter 1, A/T is 22/30.5 = 0.71 in year 2, and
18/31.5 = 0.55 in year 3. The average of these is 0.6; the variations below have
been rounded to one decimal place for simplicity, so that the seasonal variations
are approximately:
Quarter 1:
0.6
Quarter 2:
0.6
Quarter 3:
1.2
Quarter 4:
1.6
Forecasting
The model used in the analysis of the historical numbers should be used to perform
the forecast.
Additive Model
= Forecast of Trend + Seasonal Var.
Multiplicative Model = Forecast of Trend x SV proportion
The trend may be forecast by extrapolating the trend line on the time series graph.
Forecasting the quarterly sales in Year 4, using both the additive and then the
multiplicative model
Exercise 5
Required:
Forecast the trend value and the actual predicted result in year 5 quarter 2 using:
(a)
The additive model.
(b)
The multiplicative model.
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C H A P T E R 7 – Q U A N T I T A T IV E A ID S T O B U D G E T IN G
Disadvantages of forecasting with time series
1.
There is an assumption that what has happened in the past is a reliable guide
to the future.
2.
There is assumption that a straight line trend exit.
3.
There is assumption that seasonal variations are constant.
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C H A P T ER 7 – QU A N T ITA T IV E A ID S T O B U D G E T IN G
LEARNING CURVE
A statistical relationship establishes this fact that labour time per unit falls as a
complex task is repeated. As workers become more familiar with the production of
a new product or task, average time (and average cost) will decline and exhibit a
statistical relationship. It can be stated as follows:
“As cumulative production doubles from the first unit, the cumulative
average time per unit falls by a constant percentage”
Mathematical illustration
Example 6
If the first unit requires 100 hours and the learning curve rate is 80%, calculate
the following cumulative and incremental data.
Cumulative
units
Average
time per
unit
Cum
total
time
Incremental
units
Incremental
total time
Average
time per
unit
1 unit
2 units
4 units
8 units
As cumulative output doubles, the cumulative average time per unit falls to a fixed
percentage of the previous average time.
Using the formula
The geometric formula can be used to establish the average time (or average cost)
per unit.
y = axb
where:
118
y
=
average time (or average cost) per unit
a
=
time (or cost) for first unit
b
=
slope =
x
=
cumulative output
log r
(r = rate of learning)
log 2
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C H A P T E R 7 – Q U A N T I T A T IV E A ID S T O B U D G E T IN G
Example 7
Required:
Using the above example calculate the incremental time taken by the 2nd, 3rd and
4th units.
Applying the learning curve theory
The application of the learning curve is important and can be found in questions
involving:
●
pricing
●
budgeting
●
standard costing
●
decision making.
The following illustration shows its use in the preparation of budgets.
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C H A P T ER 7 – QU A N T ITA T IV E A ID S T O B U D G E T IN G
Example 8 Limitation plc
Limitation plc commenced the manufacture and sale of a new product in the fourth
quarter of 1991. In order to facilitate the budgeting process for quarters 1 and 2 of
1992, the following information has been collected.
(a)
Forecast production/sales (batches of product) is as follows:
Quarter 4, 1991
Quarter 1, 1992
Quarter 2, 1992
(b)
30 batches
45 batches
45 batches
It is estimated that direct labour is subject to a learning curve effect of 90%.
The labour cost of batch 1 of quarter 4, 1991 was £600 (at £5 per hour). The
labour output rates from the commencement of production of the product,
after adjusting for learning effects, are as follows:
Total batches produced
Overall average time per batch
Batches
15
30
45
60
75
90
105
120
Hours
79.51
71.56
67.28
64.40
62.25
60.55
59.15
57.96
Labour hours worked and paid for will be adjusted to eliminate spare capacity
during each quarter. All time will be paid for at £5 per hour.
(c)
Variable overhead is estimated at 150% of direct labour cost during 1992.
(d)
All units produced will be sold in the quarter of production at £1,200 per
batch.
Required:
(a)
Calculate the labour hours requirement for the second batch and the sum of
the labour hours for the third and fourth batches produced in quarter 4, 1991.
(3 marks)
(b)
Prepare a budget for each of quarters 1 and 2, 1992 showing the contribution
earned from the product. Show all relevant workings.
(12 marks)
(c)
Limitation plc wishes to prepare a quotation for 12 batches of the product to
be produced at the start of quarter 3, 1992.
Calculate the cost of the labour and labour related costs incurred as a result of
the additional batches produced.
(5 marks)
(20 marks)
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C H A P T E R 7 – Q U A N T I T A T IV E A ID S T O B U D G E T IN G
General use of learning curve
Learning curve provides useful information to management accountant since it
helps with
●
setting realistic labour standards
●
planning manpower needs
●
formulating budgets
●
interpretation of variances
●
calculation of incentive rates in bonus wages
●
setting delivery date
●
pricing for successive units, where prices are established, or quotations are
made, on a cost plus basis
●
for cost control in general.
Limitations of learning curve
●
It is only applicable in labour intensive operations which are repetitive and
reasonably skilled.
●
It assumes that employees are motivated to learn
●
It assumes that there is a stable labour mix with a negligible turnover
●
Difficulty in determining the learning curve effect accurately
●
Difficulty in determining the level of production where the curve will be flat
and no further learning takes place.
●
Breaks between production runs must be short or learning will be forgotten.
Example 9 BG
BG has recently developed a new product. The nature of their work repetitive, and
it is usual for there to be 80% learning curve effect when a new product is
developed. The time taken for the first unit was 22 minutes. Assuming that an
80% learning effect applies:
Required:
What is the time to be taken for the fourth unit?
Example 10 Martina Ltd
Martina Ltd has received an order to make 8 units of product sampa. The time to
produce the first unit is estimated to be 80 hours and an 80% learning curve is
expected. The rate of pay is £7.50 for each hour.
The direct material cost for each unit is £4000 and fixed costs associated with the
order are £6400.
Required:
Calculate the average cost for each unit for this order.
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C H A P T ER 7 – QU A N T ITA T IV E A ID S T O B U D G E T IN G
122
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Chapter 8
Standard costing and
variance analysis
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C H A P T ER 8 – S TA ND A R D C O S T IN G A ND V A R IA N C E A N A L YS I S
CHAPTER CONTENTS DIAGRAM
Standard Costing
Basic Variances
Material
cost
variances
124
Labour
cost
variances
Sales
cost
variances
Overheads
cost
variances
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C H A P T E R 8 – S T A N D A R D C O S T I N G A N D V A R I A N C E A N A L Y S IS
CHAPTER CONTENTS
STANDARD COSTING --------------------------------------------------- 126
TYPES OF STANDARDS
126
PREPARATION OF STANDARD COSTS
127
USES OF STANDARD COSTS
127
PROBLEMS IN SETTING STANDARDS
127
VARIANCE ANALYSIS -------------------------------------------------- 129
MATERIAL VARIANCES
130
LABOUR VARIANCES
131
VARIABLE OVERHEAD VARIANCES
132
FIXED OVERHEAD VARIANCES ---------------------------------------- 133
ABSORPTION COSTING PRINCIPLES
133
SALES VARIANCES------------------------------------------------------ 136
RECONCILIATION OF PROFIT STATEMENTS
136
BACKWARDS STANDARD COSTING ----------------------------------- 139
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C H A P T ER 8 – S TA ND A R D C O S T IN G A ND V A R IA N C E A N A L YS I S
STANDARD COSTING
●
A standard is ‘a benchmark measurement of resource usage, set in defined
conditions’.
●
Standard costing is a system of accounting based on pre-determined costs
and revenue per unit, which are used as a benchmark to compare actual
performance, and therefore provide useful feedback information to
management.
●
Variance analysis is performed by comparing the actual cost and the standard
cost to ascertain the difference.
●
Standard costs can be prepared using either absorption costing or marginal
costing.
Types of standards
Ideal standard
●
A standard that assumes perfect working conditions and does not make
allowance for any losses, waste and machine breakdown.
●
It can be used as a long-term organisational goal and is particularly applicable
in total quality management environments.
●
The variances can only be adverse and it may have an adverse motivational
impact.
Attainable standard
●
It is based upon efficient (but not perfect) levels of operation but will include
allowances for normal material losses, realistic allowances for fatigue,
machine breakdowns, etc.
●
Attainable standards must be based on a tough but realistic performance level
so that its achievement is possible, but has to be worked for.
●
They are used for budgeting and budgetary control.
Basic standard
●
These are long-term standards which remain unchanged over a period of
years. Their sole use is to show trends over time for such items as material
prices, labour rates and efficiency and the effect of changing methods.
●
They cannot be used to highlight current efficiency because they are out-ofdate.
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C H A P T E R 8 – S T A N D A R D C O S T I N G A N D V A R I A N C E A N A L Y S IS
Preparation of standard costs
Standard costing is directly linked to the budgeting process. Individual standards
are prepared for each component of cost. From these a standard cost may be
prepared for each product produced (or service provided).
Material
Usage x Price
Labour
Hours x Rate
Var. O/H
Hours x rate
Build the variable costs up
to the unit cost
Standard cost
per unit
Break the total fixed costs down
using the budgeted level of
activity
Fixed O/H
Budgeted fixed
cost
÷
Budgeted number
of units
Uses of standard costs
●
Preparation of budgets
●
Stock valuation
●
Budgetary control and variance analysis
•
Decision making (pricing)
•
Performance monitoring and evaluation
Problems in setting standards
1.
Deciding how to incorporate inflation into planned unit costs.
2.
The cost of setting up and maintaining a system of establishing standards.
3.
Possible behavioural problems.
4.
Deciding on the quality of materials and grade of labour to be used.
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C H A P T ER 8 – S TA ND A R D C O S T IN G A ND V A R IA N C E A N A L YS I S
Example 1 Jojo Ltd
Jojo Ltd manufactures and sells a range of products one of which is the jojo. The
following data relates to the expected costs of production and sales of the jojo.
Budgeted production for the year is 11,400 units.
Standard details for one unit are:
Direct materials
Direct labour:
Dept P
Dept Q
30 metres @ £6.1
40 hours @ £2.2 per hour
36 hours @ £2.5 per hour
Budgeted cost and hours per annum:
Variable production overheads
Dept P £525,000 : 700,000hrs
Dept Q £300,000 : 600,000hrs
Fixed overheads to be absorbed:
Production
Administration
Marketing
£1,083,000, absorbed on direct labour hour basis
£125,400, absorbed on a unit basis
£285,000, absorbed on unit basis
The company’s policy is to make a standard profit of 10% of the sales price.
Required:
Calculate the selling price of one jojo detailing all costs information, step by step.
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VARIANCE ANALYSIS
The main application of standard costing is for budgetary control purposes. The
standard is compared to the actual result the difference being the variance. The
analysis provides the following information:
1.
Cost control.
2.
Reconciliation between Budgeted and Actual Profit (or Contribution or cost).
3.
Variances may quantify the value of a known difference.
4.
Performance Appraisal.
Example 2 Owen Ltd
Owen Ltd uses a standard costing system. The standard cost card for one product
is shown below:
Direct Material
Direct Labour
Variable Overhead
Total Variable Cost
Fixed Overhead
Total Product Cost
Standard Selling Price
Standard Profit Margin
4 kg at £5 per kg
2 hours at £8 per hour
2 hours at £3.5 per hour
2 hours at £7 per hour
£
20
16
7
43
14
57
70
13
The budgeted output and sales was 1,000 units. Actual output for the period was
1,300 units and actual sales for the period was 1,250 units.
Actual cost and revenue were as follows:
Direct Material
Direct Labour
Variable Overhead
Fixed Overhead
Sales Revenue
5,000 kg, costing
2,850 hours, costing
1,250 units at £68 per unit
£
22,700
21,500
7,800
14,600
85,000
Required:
Calculate all possible variances.
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C H A P T ER 8 – S TA ND A R D C O S T IN G A ND V A R IA N C E A N A L YS I S
Material variances
Standard Cost
Direct Material
4 kg at £5 per kg
Actual Results
Actual output
Materials Purchased and used
1,300 units
£22,700
5,000 Kg, costing
Key pro forma
SQSP
Usage
AQSP
Price
AQAP
Possible reasons
Price Variance
Usage Variance
1.
Wrong budgeting
1.
Wrong budgeting
2.
Lower/higher quality material
2.
Lower/higher quality of material
3.
Good/poor purchasing
3.
Lower/higher quality of labour
4.
External factors (inflation, exchange
rates etc)
4.
Theft
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C H A P T E R 8 – S T A N D A R D C O S T I N G A N D V A R I A N C E A N A L Y S IS
Labour variances
Standard Cost
Direct Labour
2 hours at £8 per hour
Actual Results
Actual output
Hours paid and worked
Labour Cost
1,300 units
2,850
£21,500
Key pro forma
SHSR
Efficiency
AHSR
Rate
AHAR
Idle time variance
Idle time may be caused by:
1.
machine break downs
2.
not having work to give to employees due to bottleneck in production and
shortage of order from customers
Idle time variance: Time (hours) lost x SR
Possible reasons
Rate Variance
Efficiency Variance
1.
Wrong budgeting
1.
Wrong budgeting
2.
Wage inflation
2.
Lower/higher morale
3.
Lower/higher skilled employees
3.
Lower/higher skilled employees
4.
Unplanned overtime or bonuses
4.
Lower/higher quality of material
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C H A P T ER 8 – S TA ND A R D C O S T IN G A ND V A R IA N C E A N A L YS I S
Example 3 Dido
Product Dido has a standard direct labour cost as follows:
97hrs @ £4 per hr
£388
During the period 530 units of product Dido were produced. Total hours paid for
were 51,380 hours of labour at a cost of £200,382, but hours actually worked were
51,000 hours.
Required:
Calculate direct labour cost variance analysing into labour rate, labour efficiency
and idle time variances.
Variable overhead variances
Standard Cost
Variable overhead
2 hours at £3.5 per hour
Actual Results
Actual output
Hours worked (from above)
Variable overhead Cost
1,300 units
2,850
£7,800
Key pro forma
SHSR
Efficiency
AHSR
Expenditure
AHAR
Possible reasons
Efficiency Variance
As per labour efficiency.
Expenditure (rate) Variance
Variable overheads are made up of many different overhead cost elements; to
identify reasons for the variance we would need to analyse all elements separately.
●
Unexpected price changes for overhead items
●
Incorrect split between fixed and variable overheads.
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C H A P T E R 8 – S T A N D A R D C O S T I N G A N D V A R I A N C E A N A L Y S IS
FIXED OVERHEAD VARIANCES
Fixed costs are a constant in total terms, hence total cost is our starting point. The
analysis of variances will be dependent on the costing methodology. Do we use
absorption costing or marginal costing? Either is potentially applicable.
Absorption costing principles
Using absorption costing the fixed cost is charged or absorbed to the cost unit or
product. The total fixed overhead variance will be similar to the under/ over
absorption of overhead.
The total variance may be sub-analysed into two:
1.
Volume variance – if the company produces more or less units and hence
absorb more or less overhead than budgeted.
2.
Expenditure variance – if the company spends more or less fixed overhead
than budgeted.
Question extract
Standard and Budgeted Cost
The fixed cost is (£7/hour for 2 hours) £14 per unit
The budgeted number of units is 1,000
Budgeted fixed overheads is therefore £14,000
Actual Results
Actual output
Hours worked (from above)
Fixed overhead Cost
1,300 units
2,850
£14,600
Key pro forma
Std fixed OH cost (of actual output)
Volume variance
Budgeted fixed OH cost
Expenditure variance
Actual fixed OH cost
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C H A P T ER 8 – S TA ND A R D C O S T IN G A ND V A R IA N C E A N A L YS I S
Further analysis of fixed overheads
It is also possible to further analyse fixed overheads by considering actual hours in
relation to the actual and budgeted units produced. To be comparable the output
measures must be measures in terms of standard hours.
Key pro forma
SHSR
Efficiency
AHSR
Capacity
BHSR
Expenditure
AHAR
Possible reasons
Efficiency
As per labour efficiency.
Capacity
If adverse
1.
Machine breakdown.
2.
Poor sales demand.
3.
Strike.
Expenditure
Must be analysed further, fixed overheads are made up of many individual costs all
of which would have to analysed individually.
●
Changes in prices relating to fixed overhead items. For example an increase
in rent.
●
Seasonal effect. For example, heat/light in winter.
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Standard Cost Card
£
Direct Material
Direct Labour
Variable Overhead
Total Variable Cost
Fixed Overhead
Total Product Cost
Standard Selling Price
Standard Profit Margin
Budgeted production & sales units
4 kg at £5 per kg
2 hours at £8 per hour
2 hours at £3.5 per
hour
20
16
7
43
14
57
70
13
1,000
Actual Results
Sales (units)
Selling Price
1,250
£68
Production units
1,300
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C H A P T ER 8 – S TA ND A R D C O S T IN G A ND V A R IA N C E A N A L YS I S
SALES VARIANCES
The sales variances identify any change between the selling price and the standard
cost.
Key formulae
Volume variance
(AS - BS) x SPM
Price variance
(AP - SP) x AS
Reconciliation of profit statements
Absorption costing
Example 2 (cont) Owen Ltd
Required:
Prepare an absorption costing operating statement for Owen Ltd.
Key pro forma
Budgeted Profit
X
Sales volume variance
X
Standard profit
X
Sales price variance
X
Sub-total
X
Cost variances
X
Actual profit
X
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C H A P T E R 8 – S T A N D A R D C O S T I N G A N D V A R I A N C E A N A L Y S IS
Marginal costing
Variances that remains the
same
Variances that change
All variable cost variances
Sales price variance
Sales volume variance now valued
at standard contribution margin
Fixed overhead expenditure
Fixed overhead volume (and hence
capacity and efficiency) disappear
Revised sales volume variance
(AS – BS) x SCM
Example 2 (cont) Owen Ltd
Required:
Prepare a marginal costing operating statement for Owen Ltd.
Key pro forma
Budgeted contribution
X
Sales variances
X
Sub-total
X
Variable cost variances
X
Actual contribution
X
Budgeted fixed cost
X
Fixed o/h variances
X
X
Actual profit
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X
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C H A P T ER 8 – S TA ND A R D C O S T IN G A ND V A R IA N C E A N A L YS I S
Exercise 4 Barnes
The standard cost and price for one unit being as follows:
£
104
30
36
60
___
230
50
___
280
Direct material A - 8 Kilograms at £13 per Kg
Direct material B - 5 Kilograms at £6 per Kg
Direct wages - 6 hours at £6 per hour
Fixed production overhead – 6 hours at £10 per hour
Total Standard Cost
Standard gross profit
Standard Selling price
The fixed production overhead included in the standard cost is based on an
expected monthly output of 800 units. Overheads are absorbed using direct labour
hours.
During March this year the actual results were as follows:
£
Sales
780 units @ £300
Direct Materials:
A:
B:
Direct Wages
Fixed production overhead
Gross Profit
7,500 Kg
3,500 Kg
3,400 hours
£
234,000
91,500
20,300
27,880
37,320
177,000
47,000
Required:
Reconcile budgeted profit with actual profit for March, calculating the following
variances:
Selling price, sales volume, material price, material usage, labour rate, labour
efficiency, fixed overhead expenditure, fixed overhead capacity and fixed overhead
efficiency.
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BACKWARDS STANDARD COSTING
Exercise 5 CRV Ltd
CRV Limited makes and sells a single product and operates a standard costing
system. During a period, production was 40,000 units and actual labour costs were
£480,000. The standard labour time per unit is 2 hours. Materials actually used
were 2.9 kgs per unit and the standard price per kg is £12.50.
At the end of the period, the following variances were reported to management:
Labour variances:
Rate
Efficiency
Material variances:
Price
Usage
16,800
3,200
Favourable
Adverse
71,050
43,750
Adverse
Favourable
There was no movement in opening and closing stocks in the period.
Required:
Calculate
(i)
the standard labour rate per hour,
(ii)
the actual hours worked,
(iii)
the actual expenditure on materials,
(iv)
the standard material allowance in kgs per unit.
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Chapter 9
Advanced variance
analysis
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C H A P T ER 9 – A D V A N C ED V A R IA N C E A NA LY S IS
CHAPTER CONTENTS
INTRODUCTION --------------------------------------------------------- 143
ADVANCED VARIANCES ------------------------------------------------ 144
PLANNING AND OPERATIONAL VARIANCES
144
MIX AND YIELD VARIANCES
146
IDLE TIME
147
EXCESS IDLE TIME
148
INVESTIGATION AND INTERPRETATION ---------------------------- 150
SALES MIX VARIANCE
150
SALES QUANTITY VARIANCE
150
MARKET SIZE AND MARKET SHARE VARIANCES
151
INVESTIGATION AND INTERPRETATION ---------------------------- 152
142
TREND
152
MATERIALITY
152
STATISTICAL SIGNIFICANCE
153
CONTROLLABILITY
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CHAPTER 9 – ADVANCED VARIANCE ANALYSIS
INTRODUCTION
Variance analysis is used to separate costs and revenues into controllable elements
(eg material, labour etc) in order that we can compare expected (standard)
performance with actual results. Advanced areas simply increase the degree to
which the variances may be sub-analysed into
1.
Planning and operational variances.
2.
Excess idle time variances.
3.
Investigation and interpretation of variances.
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ADVANCED VARIANCES
Planning and operational variances
Traditionally, when comparing standards to actual results the comparison has
suffered from the time delay between setting the standard and the incurrence of
actual results.
The standard is set as part of the budgeting process which occurs before the period
to which it relates, this means that the difference between standard and actual may
arise solely due to an unrealistic budget and not due to operational factors.
Normal
analysis
Original
Standard
Revised
Standard
Actual
result
Planning
variance
Operational
variance
Planning error
Operational
factors
Changes over
time
Reconciling item
Management
action
Controllable
Uncontrollable
Example 1 Liddell
A company expects to use 4kg per unit at a standard price of £5/kg. During the
period it used 4,000 kilos at a total cost of £25,000.
After closer consideration of the market for the raw material it has been found that
the general market price of the material has risen by 50% due to exchange rate
movements.
Required:
(a)
Based on normal variance analysis, has the purchasing manager done a good
or bad job?
(b)
Is your conclusion changed as a result of sub-analysing the variance into
planning and operational elements?
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CHAPTER 9 – ADVANCED VARIANCE ANALYSIS
Pro Forma (using materials variances)
Basic pro forma
Planning
Operational
(substitute actual with
(substitute standard with
revised standard)
revised standard)
SQSP
SQSP
RSQRSP
RSQSP
AQRSP
RSQRSP
AQAP
Usage
AQSP
Price
AQAP
Advantages
●
Variances are more relevant, especially in an unpredictable environment.
●
The operational variances give fair reflection of the actual results achieved in
the actual conditions that existed.
●
Managers are more likely to accept and be motivated by the variances
reported which provide a better measure of their performance.
●
It emphasises the importance of planning and the relationship between
planning and control and a better guide for cost control.
Disadvantages
●
The establishment of the revised standard is very difficult
●
There is a considerable amount of administrative work
●
It may become too easy to justify all variances as being due to bad planning,
so no operational variances will be highlighted.
Example 2
Standards
3kg/unit for £5/kg
Actual
Output
12,500 units
Usage
38,000 kg
Cost
£195,500
Required:
Prepare the variances using basic variance analysis and assess whether the
purchasing manager and production manager individually have done a good or bad
job.
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Example 2 (cont)
After further consideration the standards have been revised to reflect changes that
have occurred over time. The standard usage is now expected to be 3.1kg due to a
poor harvest leading poorer quality material inputs. In addition due to adverse
movements in the exchange rate the material costs have changed. It is now
expected that each kg will cost £5.15.
Required:
Prepare an analysis of variances into both planning and operational elements and
assess the performance of the purchasing manager and the production manager
individually.
Mix and yield variances
A sub-analysis of the material usage variance into a mix and a yield
component.
Applicable in a manufacturing environment where:
1.
2 or material inputs go into to making the product (a mix)
2.
The material inputs are inter-changeable to some degree (process costing
environment).
Key pro forma
SQSP
Yield
AQ(SM)SP
Mix
AQSP
Price
AQAP
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Example 3 Dalglish
Dalglish manufactures a fertiliser by mixing three chemicals, A, B and C, and the
following standards apply:
Standard proportions
%
70
20
10
A
B
C
Standard cost per tonne
£
20
30
50
During the process of mixing, a process loss of 10% is regarded as the standard.
In week 17, 855 tonnes of the fertiliser were produced and inputs were as follows:
Actual inputs
tonnes
660
210
130
_____
A
B
C
Actual prices
£ per tonne
21
32
47
1,000
_____
Actual cost
£
13,860
6,720
6,110
______
£26,690
______
Required:
Calculate the material price, mix and yield variances.
Idle time
The use of variance analysis where idle time is expected to occur and hence
budgeted. This has the effect of differentiating between the hours paid (gross
hours) and hours worked (net or productive hours).
Example 4 Carragher
Labour standards
£6/hour x 3 hours/unit = £18/unit
Actual results
Output
Hours worked
Hours paid
Labour cost
1,300 units
4,200 hrs
5,500 hrs
£32,000
Required:
All normal labour variances.
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C H A P T ER 9 – A D V A N C ED V A R IA N C E A NA LY S IS
Pro forma
SHSR
Efficiency
AHw SR
Excess Idle Time
AHp SR
Rate
AH AR
Excess idle time
The variances have to be revised if idle time is expected or budgeted. The
standards will have to be revised to reflect the additional costs associated with
incurring idle time.
When looking at the variances we need to make a distinction between the paid and
worked hours and the appropriate rates per hour (see pro forma).
Example 5 Hansen
A company budgets to pay 10,000 hours of labour during the year. Due to
seasonal and other factors the labour force is expected to stand idle 20% of the
time.
Required:
What are the budgeted hours worked?
Idea
If the hours worked differ from the hours paid then we must ensure that the total
labour cost is ‘absorbed’ or recovered over those hours worked.
Standard Rate /Hour Worked
=
Standard Rate Paid
(1 - Idle Time %age)
Example 6
Continuing from Example 5 the company pays £5 per hour.
Required:
Standard rate per hour worked.
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Example 7
As per example 6 but we reflect the expected idle time by introducing a budgeted
idle time equal to 20% of total hours paid.
Required:
Calculate all variances including excess idle time.
revised pro forma
SHwSRw
Efficiency
AHwSRw
Excess Idle Time
AHpSRp
Rate
AHpARp
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SALES MIX AND QUANTITY VARIANCES
Sales mix variance
Sales mix variance refers to the proportion of different products in total sales.
It is the difference between planned mix of various products and actual mix or
proportion of those products.
Also called as margin variance, it determines the impact of change in the mix on
profits.
Sales Mix Variance
=
budgeted contribution per unit x (actual sales at actual mix – actual sales at
budgeted mix)
Sales quantity variance
It determines the effect on profit of selling a different total quantity from the
budgeted total quantity.
Sales Quantity Variance
=
budgeted contribution margin per unit x (actual sales at budgeted mix – standard
sales at budgeted mix)
Example 8
A
B
Budgeted Sales
800
1,200
Actual Sales
500
1,500
Budgeted contribution per unit
$5
$8
Required:
Calculate Sales mix variance.
Example 9
ABC company budgeted sales of 10,000 units and the budgeted sales mix was 2:3
for products A and B respectively. The actual sales of X and Y were 3,000 units and
10,000 units respectively. Sales prices were $5 and $9 respectively. The variable
costs are 50% of the sales prices.
Required:
Calculate Sales Quantity variance.
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Market size and market share variances
The sales quantity variances can further be analysed into a component due to
changes in market size and a component due to changes in market share, provided
published industry sales statistics are readily available.
Market size variance:
Budgeted market share % x (budgeted industry sales volume – actual industry
sales volume) x budgeted contribution per unit
Market share variance:
(Budgeted market share % - actual market share %) x (actual industry sales
volume x budgeted average contribution margin per unit)
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INVESTIGATION AND INTERPRETATION
The preparation of variances is only to provide an indicator of what is actually
happening in relation to some control standard. The analysis does not stop with
the calculation of the variance; this is simply a figure upon which to base further
analysis or investigation. We work on the assumption that the standard is the
optimum, or at least acceptable, level of performance. If we achieve the standard
then no control action need be taken and a variance prompts some control action.
This is simplistic: in reality we would be concerned with the following factors when
considering whether to investigate or not:
1.
Trend.
2.
Materiality.
3.
Controllability.
Trend
A budget or standard is normally set for one year, and hence is an average value
for that period. If we have one anomalous variance arising in an individual month,
whereas the other values are all within acceptable limits, this would suggest a
problem that is non-controllable or arising in the reporting system for that month,
rather than a structural problem that needs addressing with control actions.
The underlying movement of variances in relation to the control standard is of vital
importance to the control of the system. We would normally consider calculating
individual monthly variances together with an annual running total. We are then
able to see the movement in trend and the total impact over the year.
Materiality
When assessing whether to investigate a variance we can consider how significant
the variance is in three ways:
1.
Total value.
2.
As a percentage to the budgeted (or standard) value.
3.
Statistical significance.
Total value
It is normal to investigate the largest variances first to eliminate the greater
amount of value initially. It is important to note however that such an approach
leads to assessing the same few areas of the organisation every period as the size
of variance is normally strongly correlated to the amount of a resource being used.
As a percentage
Used in addition to the above technique where key anomalies arise.
The
percentage reflects better than overall value the degree to which the variance is out
of control (distance from the standard value).
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Statistical significance
Theoretically the best basis upon which to select a variance for investigation. If we
have reliable historic data regarding the likelihood that a process was under control
we can establish effective rules as to when we should and should not investigate
variances. In practice, it is difficult to identify the appropriate standard deviations
required.
It is expected that almost all elements will give variances of some value each
month due to the difficulties of easily segmenting results into individual periods and
the average nature of the standard. We need to only investigate those variances
that most warrant the cost of the investigation.
Controllability
Once the variance has been investigated then if a poor result was achieved we
would look to improve the results in the future (negative feedback). This is only
possible if all aspects of the following situation are present:
1.
The variance is investigated.
2.
The reason for poor performance is identified.
3.
The poor performance is expected to continue in the future.
4.
Control action is possible to change the present situation.
5.
Control action is successful.
If just one of the above is not present, we are unable to control the future costs or
revenues.
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154
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Chapter 10
Performance
evaluation
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C H A P T ER 1 0 – P ER F OR M A NC E EV A L U A T IO N
CHAPTER CONTENTS DIAGRAM
PERFORMANCE
EVALUATION
Responsibility
Accounting
Cost
centres
Performance
Measurement
Profit
centres
Investment
centres
Financial
analysis
Nonfinancial
analysis
CHAPTER CONTENTS
RESPONSIBILITY ACCOUNTING -------------------------------------- 158
RESPONSIBILITY CENTRES
158
DIVISIONALISATION (DECENTRALISATION)
158
REPORTING RESPONSIBILITY CENTRE RESULTS ------------------- 160
156
COST CENTRE REPORTING
160
PROFIT CENTRE REPORTING
161
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PERFORMANCE EVALUATION MEASURES ---------------------------- 162
RETURN ON CAPITAL EMPLOYED (ROCE) OR (ROI)
162
RESIDUAL INCOME (RI)
163
KEY ISSUES ------------------------------------------------------------- 164
GOAL CONGRUENT DECISION MAKING
164
SHORT-TERMISM AND DEPRECIATION OF ASSETS
165
MANAGEMENT FRAUD
165
TRANSFER PRICING
165
RATIO ANALYSIS ------------------------------------------------------- 166
PROFITABILITY RATIOS
166
LIQUIDITY RATIOS
166
EFFICIENCY RATIOS
166
GEARING RATIO
166
PERFORMANCE EVALUATION – NON FINANCIAL MEASURES ------ 167
THE BALANCED SCORECARD------------------------------------------- 168
CUSTOMER PERSPECTIVE
168
INTERNAL BUSINESS PERSPECTIVE
168
INNOVATION AND LEARNING PERSPECTIVE
169
FINANCIAL PERSPECTIVE
169
SERVICE INDUSTRIES
169
THE BUILDING BLOCK MODEL----------------------------------------- 170
1.
STANDARDS
170
2.
REWARDS
170
3.
DIMENSIONS
171
PERFORMANCE MEASUREMENT IN A NOT FOR PROFIT
ORGANISATION AND THE PUBLIC SECTOR -------------------- 173
OBJECTIVES OF A NOT FOR PROFIT ENTITY
173
PROBLEMS OF PERFORMANCE MEASUREMENT OF A NOT FOR PROFIT ENTITY
173
PERFORMANCE MEASUREMENT
174
VALUE FOR MONEY (VFM) --------------------------------------------- 175
THE KEY TO VFM
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C H A P T ER 1 0 – P ER F OR M A NC E EV A L U A T IO N
RESPONSIBILITY ACCOUNTING
Responsibility accounting segregates revenue and cost information into areas of
personal responsibility to assess the performance achieved by relevant persons to
whom authority has been designated.
This system recognise various decision centres throughout the organisation and
trace costs, revenue, assets and liabilities, to the individual managers who are
primarily responsible for making decisions about the costs, revenue, etc in
question.
Responsibility centres
Cost centre
●
a unit of a business where the manager is made accountable for all the cost.
Revenue centre
●
a unit of an organisation where the manager is accountable for the sales
earned in the unit.
Profit centre
●
where the manager is responsible for the profitability of the unit.
Investment centre
●
where the manger is responsible for both the profitability and the capital
investment of the unit.
Note that variance analysis alone will not work particularly well in the last two
situations.
Divisionalisation (decentralisation)
Delegating responsibilities to divisional managers or unit heads.
Advantages
●
It increases motivation of the divisional managers as they feel involved in the
decision making of the organisation.
●
It is a form of training for the divisional managers and it easy for them to rise
through the ranks to strategic positions.
●
It should promote goal congruence (see later), as all decisions been taken are
all geared towards achieving the objectives of the whole organisation.
●
It drastically reduces the time taken to make decisions.
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Disadvantages
●
Divisional managers may make dysfunctional decisions (decisions that are not
in the best interests of the organisation).
●
There is a need for a performance appraisal system to assess the performance
of individual managers.
●
Top management may lose control by delegating decision making to divisional
managers, since they are not aware of what is going on in the whole
organisation.
●
Lack of economies of scale. For example, efficient cash management can be
achieved much more effectively if all cash balances are centrally controlled.
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C H A P T ER 1 0 – P ER F OR M A NC E EV A L U A T IO N
REPORTING RESPONSIBILITY CENTRE RESULTS
Cost centre reporting
Performance and control reporting for cost centre focus on the costs of the centre,
by comparing actual costs with the expected costs for a given level of activity.
Performance reporting should recognise both variability of costs and controllability
of costs.
Variability of costs – cost should be analysed into their fixed and variable cost
elements, and the expected costs for the period should be based on a flexed
budget.
Controllability of costs - Responsibility accounting is based on the principle that
it is appropriate to charge to an area of responsibility only those costs that are
significantly influenced by the manager of that responsible centre.
Controllable costs are costs which can be directly influenced by a given manager
within a given time span.
As a general rule, controllable costs are both variable costs and some or all of the
fixed costs that are directly attributable to the centre.
Cost centre report
Expected (flexed budget)
actual
variance
£
£
£
Variable costs
Material cost
Labour cost
Other variable cost
Controllable fixed cost
Labour
Others
Uncontrollable fixed cost
Apportioned central cost
Total costs
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C H A P T E R 1 0 – P E R F O R M A N C E E V A L U A T IO N
Profit centre reporting
The profitability of profit and investment centres should be prepared on the basis of
marginal costing, that is, to identify the contribution to profit from the centre in
each reporting period.
Controllable fixed cost is then deducted to get the
controllable profit for the centre. The uncontrollable fixed cost is then deducted to
obtain the net profit.
Profit and investment centre report
Expected (flexed budget)
actual
variance
£
£
£
Sales
Variable costs
Material cost
Labour cost
Other variable cost
Contribution
Controllable fixed cost
Labour
Others
Controllable profit
Uncontrollable fixed cost
Apportioned central cost
Net profit
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PERFORMANCE EVALUATION – FINANCIAL MEASURES
The basic measure of performance is profit. The measure of profit that is used is
normally related to operating profit or PBIT this being the measure that is within
the control of operational management.
When assessing performance of a manager it is important to only assess the
manager on a profit measure that is within the control of the manager. This means
that any costs or revenues that are outside the control of the manager should be
excluded.
In practice the obvious uncontrollable cost for a division would be apportioned head
office costs on the basis that the incurrence of cost is controllable by head office
and is charged in an arbitrary manner to the division.
When looking at an investment centre the manager is able to control the amount of
investment in the division. It is normal to assess the performance of profit in
relation to investment made by head office in the division using either return on
investment (ROI) or residual income (RI)
Return on capital employed (ROCE) or (ROI)
ROCE = profit before interest and tax x 100
capital employed
Advantages of ROCE
1.
It is easy to understand and easy to calculate.
2.
ROCE is still the commonest way in which business unit performance is
measured and evaluated, and is certainly the most visible to shareholders.
3.
Managers may be happy in expressing project attractiveness in the same
terms in which their performance will be reported to shareholders, and
according to which they will be evaluated and rewarded.
4.
The continuing use of the ROCE method can be explained largely by its
utilisation of balance sheet and income statement magnitudes familiar to
managers, namely profit and capital employed.
Criticisms of ROCE
1.
It fails to take account of the project life or the timing of cash flows and time
value of money within that life.
2.
When assets are valued at net book value, reported performance improves
with time as the assets get old. In this case there is a disincentive to invest
in new assets.
3.
It uses accounting profit and capital employed, hence subject to manipulation
due to various accounting conventions.
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4.
Performance measurement based on ROCE encourages short-termism in
decision making. Failure to invest in new assets could be harmful to the longterm interest of the division and the organisation as a whole.
5.
It is difficult to assess the significance of ROI. There is no definite investment
signal. The decision to invest or not remains subjective in view of the lack of
objectively set target ROI
6.
ROI is sometime confused with internal rate of return (IRR)
Residual income (RI)
RI
=
profit – (capital employed x the cost of capital)
Advantages of residual income
Residual income overcomes many of the problems of ROI:
●
It encourage investment centre managers to undertake new investments if
they add to residual income.
●
As a consequence it is more consistent with the objective of maximising the
total profitability of the company.
●
It is possible to use different rates of interest for different types of asset.
Disadvantages of residual income
●
Like ROI, residual income is also based on accounting profit and capital
employed which can be manipulated.
●
It encourage investment centres managers to think in the short-term about
how to increase next year’s residual income for the centre, hence does not
encourage decision making for long-term.
●
Residual income is not as widely used as the ROI despite overcoming some of
the problems in ROI.
Example 1 Tata
Tata is a division of Tatan group. Its manager has the authority to invest in new
capital expenditure, within limit set by head office. The senior management team
of the division is considering an investment of £4.2 million. This would have a
residual value of zero after four years. Net cash flows from the investment would
be £1.4 million for each of the next four years.
The cost of capital for the Tata division is 10%. It is the group’s policy to use
straight-line depreciation when measuring divisional profit.
For measuring purpose and reporting purposes, capital is defined as the opening
net book value at the start of each year.
Required:
(a)
Calculate residual income each year.
(b)
Calculate the return on investment each year.
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KEY ISSUES
●
Goal congruent decision making
●
Short-termism
●
Management fraud
●
Transfer pricing
Goal congruent decision making
In decision making, managers should not use measures like ROI and RI. However,
generally the aforementioned measures are used in performance measurement;
therefore managers tend to include these in their assessments of new projects.
Example 2
There are two divisions with the following performance for the current year
Division
X
y
Investment ($m)
10
30
Controllable Profit
2
3
Required rate of return
15%
Required:
Calculate the performance of each division based using:
(a)
ROI
(b)
RI
Which division has superior performance?
Example 3
Continuing from the previous example each division has the opportunity to invest in
a new project.
Division
Investment ($000s)
Controllable Profit
X
500
80
y
1,000
120
Required rate of return is 15%.
Required:
Using the measures of performance above assess the decisions that would be made
by:
(a)
The divisional managers;
(b)
Head office;
(c)
Whether the decisions are congruent with each other.
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Short-termism and depreciation of assets
However the performance is appraised, it is normal to appraise divisional managers
over one year. When using ROI and RI the investment will fall in value over time
as a result of depreciation.
This has the impact of increasing the reported
performance for each year that investment is not made within the division.
A cynical manager could improve their perceived performance simply as a result of
deferring investment and using increasingly outdated assets. This could well have
adverse consequences to the business including:
1.
Poorer quality output due to worn out machines
2.
Higher risk of machine breakdown
3.
using outdated technology.
Management fraud
Having a single profit measure or relatively few related measures of performance
appraisal allows managers to manipulate the figures underpinning these measures.
In simple terms the manager only needs to overstated profits in a period or
understate the investment.
Simple ways to overstate of profits
1.
Phasing of apportioned costs to charge fewer costs during the period.
2.
Revenue recognition of sales in previous periods or future periods.
3.
Ignoring part of the cost base.
4.
Incorporate sales from other divisions.
5.
Double count sales.
To reduce the opportunity for fraud a range of performance measures should be
used that are inter-linked. They will make it more difficult for managers to
manipulate the figures for personal gain.
Transfer pricing
The sale of goods between one division and another within the same organisation.
The setting of the transfer price will have no direct impact on the overall
performance of the company but a very real impact on individual divisional
performance.
The setting of transfer prices will therefore be highly political. The manager can
improve his own reported performance more easily by arguing for a better transfer
price than in any other way.
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RATIO ANALYSIS
Any financial ratios could be required by the examiner. Please note that it is
unlikely that a wide range of ratios will be required in a single question, instead the
focus will be on 3 or 4 ratios at most normally focussing in profit measures.
Profitability ratios
Return on Capital Employed
gross profit
capital employed
gross profit
sales
Profit margin =
sales
capital employed
=
Asset Turnover
=
Liquidity ratios
Current ratio
current assets
current liabilitie s
=
current assets − inventory
current liabilitie s
=
Quick (acid test) ratio
Efficiency ratios
=
Inventory days
=
Receivable days
=
Payable days
inventory × 365
cost of sales
receivable s × 365
revenue
payables × 365
cost of sales
Gearing ratio
Gearing
166
=
equity
debt + equity
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PERFORMANCE
MEASURES
EVALUATION
–
NON
FINANCIAL
Non-financial measure of performance should focus on critical success factors of a
non-financial nature. The measures include market share, capacity utilisation,
labour turnover, etc.
Below are some examples of non-financial measures:
AREA
POSSIBLE CRITERIA
COMPETITIVENESS
●
sale growth by product or service
●
measures of customer base
●
relative market share and position
●
sales units
●
labour hours
●
machine hours
●
number of
serviced
●
number of accounts reconciled
●
efficiency
measurements
of
resources planned against those
consumed
●
production per person
●
production per hour
●
production per shift
●
number of customer complaints
●
rejections as a percentage
production or sales
●
number of account lost or gained
●
days absence
●
labour turnover
●
overtime
●
measures of job satisfaction
●
proportion of new products and
services to old ones
●
new product or service sales level
●
speed
need
●
informal listening by calling a
certain number of customers each
week
●
number of customer visit to the
factory or workplace
●
number of
customers
ACTIVITY
PRODUCTIVITY
QUALITY OF SERVICE/PRODUCT
QUALITY OF WORKING LIFE
INNOVATION
CUSTOMER SATISFACTION
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of
material
response
requisitions
to
managers
of
customer
visit
to
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THE BALANCED SCORECARD
The balanced scorecard forces managers to look at the business from four
important perspectives.
It links performance measures by requiring firms to address four basic questions:
1.
How do customers see us? – Customer perspective.
2.
What must we excel at? – Internal perspective.
3.
Can we continue to improve and create value? – Innovation & learning
perspective.
4.
How do we look to shareholders? – Financial perspective.
The justifications of balanced scorecard over the traditional measures are that:
●
accounting figures are easily manipulated and as such unreliable
●
changes in the business and market environment do not show in the financial
results of a company until much later.
Factors other than financial
performance must therefore be targeted.
Customer perspective
●
How do customers perceive the firm?
●
This focuses on the analysis of different types of customers, their degree of
satisfaction and the processes used to deliver products and services to
customers.
●
Particular areas of focus would include:
o
Customer service.
o
New products.
o
New markets.
o
Customer retention.
o
Customer satisfaction.
Internal business perspective
●
How well the business is performing.
●
Whether the products and services offered meet customer expectations.
●
Activities in which the firm excels?
●
And in what must it excel in the future?
●
Quality performance.
●
Quality.
●
Motivated workforce.
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Innovation and learning perspective
●
Can we continue to improve and create value?
●
In which areas must the organisation improve?
●
Product diversification.
●
% sales from new products.
●
Amount of training.
●
Number of employee suggestions.
●
Extent of employee empowerment.
Financial perspective
●
This is concerned with the shareholders view of performance.
●
Shareholders are concerned with many aspects of financial performance.
●
Amongst the measures of success are:
o
Market share.
o
Profit ratio.
o
Return on investment.
o
Economic value added.
o
Return on capital employed.
o
Cash flow.
o
Share price.
Service industries
In general services differ from manufacturing since they are:
●
Intangible.
●
Simultaneous.
●
Perishable.
●
Heterogeneous.
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THE BUILDING BLOCK MODEL
This model is particularly suited to service industries.
Fitzgerald and Moon divide performance measurement into three areas:
1.
Standards.
2.
Rewards.
3.
Dimensions.
●
●
●
●
●
●
Dimensions
Financial performance
Competitiveness
Quality
Flexibility
Resource utilisation
Innovation
Standards
●
●
●
Ownership
Achievability
Equity
Rewards
●
●
●
Clarity
Motivation
Controllability
1. Standards
This refers to the targets that are set within the organisation. These should be:
●
High enough to motivate.
●
Be owned by the employees (through participation in target-setting).
●
Be seen to be equitable.
2. Rewards
This refers to what the organisation (and the employee) is trying to achieve.
●
The organisation’s objectives should be clearly understood.
●
Employees should be motivated to work towards these objectives.
●
Employees should be able to control areas over which they will be held
responsible.
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3. Dimensions
This refers to how performance will be measured. The areas are:
●
Financial
●
Competitive performance
●
Quality of service
●
Flexibility
●
Resource Utilisation
●
Innovation.
Example 4 Scotia Health Consultants Ltd
Scotia Health Consultants Ltd provides advice to clients in medical, dietary and
fitness matters by offering consultation with specialist staff.
The budget information for the year ended 31 May 2010 is as follows.
(i)
Quantitative data as per Appendix 1.
(ii)
Clients are charged a fee per consultation at the rate of: medical £75;
dietary £50 and fitness £50.
(iii)
Health foods are recommended and provided only to dietary clients at an
average cost to the company of £10 per consultation. Clients are
charged for such health foods at cost plus 100% mark-up.
(iv)
Each customer enquiry incurs a variable cost of £3, whether or not it is
converted into a consultation.
(v)
Consultants are each paid a fixed annual salary as follows: medical
£40,000; dietary £28,000; fitness £25,000.
(vi)
Sundry other fixed cost: £300,000.
Actual results for the year to 31 May 2010 incorporate the following additional
information.
(i)
Medical salary costs were altered through dispensing with the services of
two full-time consultants and sub-contracting outside specialists as
required. A total of 1,900 consultations were sub-contracted to outside
specialists who were paid £50 per consultation.
(ii)
Fitness costs were increased by £80,000 through the hire of equipment
to allow sophisticated cardio-vascular testing of clients.
(iii)
New computer software has been installed to provide detailed records
and scheduling of all client enquiries and consultations. This software
has an annual operating cost (including depreciation) of £50,000.
Required:
(a)
Prepare a statement showing the financial results for the year to 31 May 2019
in tabular format.
This should show the budget gross margin for each type of consultation and
for the company. (Expenditure for each expense heading should be shown as
relevant.)
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(b)
Suggest ways in which each of the undernoted performance measures (1 to 5)
could be used to supplement the financial results calculated in (a). You
should include relevant quantitative analysis from Appendix 1 for each
performance measure.
1.
Competitiveness.
2.
Flexibility.
3.
Resource utilisation.
4.
Quality.
5.
Innovation.
Appendix 1
Statistics relating to the year ended 31 May 2010
Budget
Actual
50,000
30,000
80,000
20,000
15,000
12,000
20,000
10,000
6,000
12,000
9,000
5,500 (note)
10,000
14,500
6
12
9
4 (note)
12
12
270
600
Total client enquiries
−
−
new business
repeat business
Number of client consultations
−
−
new business
repeat business
Mix of client consultations
−
−
−
medical
dietary
fitness
Number of consultants employed
−
−
medical
dietary
fitness
Number of client complaints
Note Client consultations includes those carried out by outside specialists. There
are now 4 full-time consultants carrying out the remainder of client consultations.
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PERFORMANCE MEASUREMENT IN A NOT FOR PROFIT
ORGANISATION AND THE PUBLIC SECTOR
In simple terms the basic objective of a not for profit is to provide a service without
making a loss, a profit or surplus simply being either a timing issue or a means to
an end.
The wider issue is that the organisation is providing a service of social or moral
worth. We can attempt to measure this service.
Objectives of a not for profit entity
The objective for such an organisation will differ widely from one organisation to
another. They may include one or more of the following:
●
Client satisfaction
●
Employee satisfaction (particularly when volunteers are a substantial part of
the workforce)
●
Maximisation of surplus (perhaps to assist in growth or protect against loss of
future funding)
●
Growth
●
Usage of facilities (for example library services)
●
Maintenance of capability (for example a fire service or army).
The key to remember in the exam is that for every not for profit organisation there
will be multiple objectives that have to be addressed as opposed to a profit making
organisation where profit is the key aim in relation to satisfying the owners or
shareholders.
Problems of performance measurement of a not for profit
entity
1.
Multiple objectives
As seen above most organisations will have competing objectives. The
difficulty arises when attempting to identify the relative importance of the
objectives.
2.
Measurement of services provided
The nature of many services is that they are more qualitative than
quantitative. When measuring such outputs it is often very difficult to get
meaningful aggregate measures of performance.
3.
No profit motive
Measures such as ROI and RI cannot be used to gain an overall measure of
performance.
4.
Identification of cost unit
The cost unit is likely to be relatively complex and there is likely to be more
than one cost unit. For example what is a cost unit for a hospital/ there are
likely to be multiple such cost units being used by a single patient.
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5.
Key constraint
For most organisations the key constraint is the level of finance available. A
charity is limited to its donations and a government department is limited to
its allocation from the finance department. This constraint is separate in most
organisations to their end objective.
6.
Political intervention
Unlike commercial entities not for profit entities are far more likely to be
affected by political influence, either directly in the form of elected official or
indirectly by public sentiment.
7.
Legal considerations
It is likely that adherence to restrictive legal rules are going to impact on a
not for profit entity because of the nature of the organisation or the links to
government at a local or national level.
Performance measurement
In order to establish meaningful measures within such an environment we can
employ the following solutions:
1.
Input measurement
In the absence of easily measured output then more consideration can be put
into the costs and resourcing of an organisation.
2.
Independent scrutiny and target setting
There is need for fine judgement when setting qualitative targets. By use of
independent experts then measures can be set that reflect performance levels
appropriate without introducing bias.
3.
External comparison
A powerful assessment of the performance of an organisation is to benchmark
that performance in relation to similar organisations. This allows for both
historical results to be used but also best practice measures to be developed.
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VALUE FOR MONEY (VFM)
Value for money is a framework by which not for profit organisations can be
measured. It separates the performance of the business into three areas – the
three E’s:
1.
1.
Effectiveness
2.
Efficiency
3.
Economy
Effectiveness (an output measure)
This may be described as how well the organisation meets its objectives. Perhaps
an easier way of understanding it would be to see how well the output of services
match the client need.
2.
Efficiency (the relationship between input and output)
This describes how well resources are utilised; it measures the output of services
for a given level of resource or input.
3.
Economy (an input measure)
This considers the cost of sourcing the input resources. The aim being to minimise
the costs of the input for a given standard and level of resource.
The key to VFM
The key to VFM is to understand that performing in a single area is not sufficient,
instead the organisation must achieve in relation to all three aspects in order to
provide value for money.
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Chapter 11
Transfer pricing
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CHAPTER CONTENTS DIAGRAM
TRANSFER
PRICING
Transfer pricing
methods
Dimensions of
transfer pricing
Cost
based
178
Market
based
Other
approaches
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CHAPTER CONTENTS
INTRODUCTION --------------------------------------------------------- 180
OBJECTIVES
180
SUBSIDIARY OBJECTIVES
181
DECISION-MAKING
181
PERFORMANCE MEASUREMENT
181
DIVISIONAL AUTONOMY
181
BASES FOR SETTING TRANSFER PRICES ----------------------------- 182
1.
COST BASED TRANSFER PRICE
182
2.
MARKET-BASED TRANSFER PRICE
183
3.
NEGOTIATED TRANSFER PRICE
184
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INTRODUCTION
Supplying
Division
Buying
Division
When an organization is structured into profit centres or investment centres,
authority is delegated to the profit or investment centre managers.
The
performance of these managers will be assessed and rewarded, on the basis of the
results of their centres. Profit centre managers will therefore be motivated to
optimise the result of their own division, regardless of other profit centres and
regardless of the organization as a whole.
Transfer pricing is used when divisions of an organization need to charge other
divisions of the same organization for goods or services they provide to them.
Objectives
Goal congruent decision making
Any decision by the management to improve the performance of either of the
divisions must also improve the performance of the company as a whole.
“Fair” performance measurement
The transfer price used will normally have a substantial effect on the distribution of
profit between divisions, it is important that this distribution is seen to be equitable
to all parties.
Maintaining divisional autonomy
A key purpose of decentralisation is to provide greater autonomy at divisional level,
there is little point in granting autonomy and then imposing transfer prices that will
materially affect the profitability of those supposedly autonomous divisions.
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Subsidiary objectives
Minimising global tax liability
If transactions occur within one tax regime little can be gained by manipulating
transfer prices. A multinational organisation can and will use transfer pricing to
move profits “round the world” either to a low tax regime or alternatively to the
country of the holding company.
Recording the movement of goods and services
An important function of transfer pricing is simply to record movement of goods
and services in financial terms.
Decision-making
In order to promote goal congruence we must ensure that the transfer price
encourages the divisions to trade with each other only when it is appropriate for the
larger organisation. In order for this to take place we follow a simple rule:
GENERAL RULE - All goods and services should be transferred at
opportunity cost.
Performance measurement
The aim is to set a transfer price that will give a “fair” measure of performance in
each division, ie profit. There is no formula for ensuring this and the result will
always be an arbitrary allocation between the divisions involved. We will see
however that in some circumstances this will give a “better” result than others.
How do the transfer prices we have already calculated measure up?
Divisional autonomy
Should the transfer prices be imposed on the divisions by Head Office, or should the
divisions negotiate the transfer price between themselves? The negotiation route
seems more consistent with divisional autonomy. There are however significant
disadvantages:
1.
Negotiation is time-consuming.
2.
It leads to conflict between divisions.
3.
Negotiated transfer prices are unlikely to reflect rational factors.
4.
They will reflect Personality/Skill/Status/Training.
5.
Senior management will need to spend substantial time overseeing the
process.
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BASES FOR SETTING TRANSFER PRICES
There are three main bases for setting transfer price:
1.
Cost-based prices.
2.
Market-based prices.
3.
Negotiated prices.
1. Cost based transfer price
Non-existent market
Where there is no external market for the transferred product, the ideal transfer
price should be based on cost.
A cost based transfer price could take the following forms:
●
transfer at full cost to the selling division of producing the product or services
with or without profit mark-up
●
transfer at marginal cost to the selling division of producing the product or
services with or without profit mark-up.
Example 1
The following relates to two divisions of a company:
Selling price
Variable production cost per unit
Fixed cost
Division A
5
40,000
Division B
20
3
80,000
The budgeted unit for division B are 20,000 units transferred from division A.
There is no external market for the product from division A.
division A are required to produce product of division B.
The products of
Required:
Determine the ideal transfer price.
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Example 2
The following relates to a selling division:
External market price
30
Variable cost of production 15
Total capacity of the division is 20,000 units.
The market demand for this product is 15,000.
A buying division requires 2000 unit of this product.
Required:
Determine the ideal transfer price.
2. Market-based transfer price
Market-base transfer price might be used when there is an intermediate market for
transferred goods or services. An intermediate market is the external market for
the goods or services of the selling division.
The market based transfer price could take the following forms:
●
the transfer price is the price of the item in the external market, or
●
the transfer price is at a discount to the external market price to allow for a
saving in selling cost by selling internally.
Example 3
Division A of a company produces sigma which is needed as a component by
division B of the same company. Division B converts the sigma to form alpha
which is sold externally.
The following is relevant:
Selling price
Marginal cost of production
Further marginal cost
Fixed costs
Division A
30
20
300,000
Division B
50
25
400,000
Required:
Determine the ideal transfer price, if there is a perfect market for sigma.
Example 4
Assuming the same facts as in example above and that division A can sell in the
external market at a marginal selling cost of £4 per unit.
Required:
What will be the ideal transfer price?
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3. Negotiated transfer price
In some cases transfer price might be negotiated. If divisional managers are
allowed to negotiate transfer prices with each other, the agreed transfer price may
be finalized from a combination of accounting arithmetic, negotiation and
compromise.
The difficulties encountered in establishing a sound system of transfer pricing have
led to suggestions that negotiated transfer prices should be used. Negotiated
transfer prices are most appropriate in situations where some market imperfections
exist for the transfer product, particularly when there are different selling costs for
internal and external sales, or where there exist different market prices.
In order to solve these problems other negotiating transfer price techniques can be
used. These are the dual transfer price and the two-part tariff arrangement.
Dual transfer price
Dual transfer price is applied where the buying division pays one transfer price for
unit purchased from the selling division and the selling division receives a different,
higher transfer price for each unit that it transfers to the receiving division. The
difference in the two transfer prices (the buying price and the selling price) is
subsidized by the head office, which charges the loss to head office costs.
The advantage for having dual prices should be to motivate the divisional managers
to produce and sell the quantities that will maximize the profit of the company.
One major problem with dual price is that it removes the decision-making authority
from the profit centres, since the head office decides what the transfer prices
should be as they have to absorb the loss.
Two-part tariff arrangement
Two-part tariff arrangement is where the receiving division pays the selling division
a fixed price per unit transferred which is equal to the variable cost of the selling
division and a fixed fee as a lump sum payment to the selling division, representing
an allowance for the fixed cost of the selling division.
The advantage of this approach is that the transfers will be made at the variable or
marginal cost of the selling division, and both divisions should be able to report
profit from inter-divisional trading. This approach ensures that the selling division
would not make loss, and would make profit if its actual costs are less than the
agreed transfer fixed fee and unit rate.
Also the receiving division is made aware of the full cost of obtaining products from
other divisions.
The problems of this approach are that:
●
the measurement of performance of the selling division would not be fair
●
it does not provide motivation to the selling division manager, since it earns
no profit on the transaction made during the period if actual is equal to the
agreed figures.
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Appendix
Solutions to exercises
and examples
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A PP E N D IX – S O LU T I O NS T O EX E R C IS ES A N D E X A M P L ES
CHAPTER 1
Example 1 2P2D Ltd
(a)
Direct material
Direct labour
X
Y
Prime Costs
Production Overheads:
(W-1)
X
Y
A
B
20
20
25
65
35
30
25
90
7.74
2.66
100.4
5.2
1.9
72.1
Total Costs
W-1
Overhead Absorption Rates: per hour
X
Y
£18,000/14000
£6,500 / 17000
=
=
1.29 per hour
0.38
W-2
Calculation of Labour hours
X
Y
A
B
4 x 2,000 = 8,000
5 x 2,000 = 10,000
6 x 1,000 = 6,000
7 x 1,000 = 7,000
(b)
A
Prime Costs
Overheads
65
7.1
------72.1
B
90
10.27
------100.27
Overheads Absorption Rate: £24,500/ 31,000 = 0.79 per hour.
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Example 2 Hensau Ltd
(a)
(i)
Cost per Unit
X
5
1.6
-----6.6
7.5
-----14.1
Direct materials
Direct labour
Production Overheads
Total Cost per unit
(a)
Y
3
2.7
----5.7
12.5
------18.2
Z
6
4
-----10
18.75
-------28.75
(ii)
Cost Drivers Calculation:
Number of batches
X
10
Y
5
Z
16
Total
31
Number of drill operations:
X
2,000 x 6
=
Y
1,500 x 3
=
Z
800 x 2
=
Total
12,000
4,500
1,600
18,100
Quantity of materials:
X
2,000 x 4
Y
1,500 x 6
Z
800 x 3
Total
8,000
9,000
2,400
19,400
=
=
=
Cost Driver rate Calculation:
Material receipts and inspections
Power
Material Handling
£15,600 / 31
£19500 / 18100
£13,650 / 19400
£503.23 / batch
£1.08 / drill ops
£0.70 / sq. Meter
Cost Per Unit
Prime Costs
Overheads:
Material receipts
Power
Material Handling
Cost per unit
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X
6.6
Y
5.7
2.52
6.48
2.8
------18.4
1.68
3.24
4.20
------14.82
Z
10
10.06
2.16
2.10
-------24.32
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OR
Drivers
Drivers
Batches of material
Drill operations
Material Handing
Cost Pool
Material receipts and
inspections
Power
Material handling
Total
Divide by units
X
Y
Z
10
5
16
(2000 x 6)
12,000
(2,000 x 4)
8,000
(1,500 x 3)
4,500
(1,500 x 6)
9,000
(800 x 2)
1,600
(800 x 3)
2,400
X
(10/31 x 15,600)
5,032
(12,000/18,100 x
19,500)
12,928
(8,000/19,400 x
13,560)
5,592
23,552
(23,552/2,000)
11.78
Y
Z
TOTAL
31
18,100
19,400
TOTAL
2,516
8,052
£15,600
4,848
1,724
£19,500
6,290
13,654
1,678
11,454
£13,560
(13,654/1,500)
9.10
(11454/800)
14.32
48,750
Cost Per Unit
Prime Costs
Overheads
Cost per unit
X
6.6
11.78
------18.38
Y
5.7
9.10
------14.80
Z
10
14.32
-------24.32
(b)
See class discussion.
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Example 3 Brunti plc
(a)
(i)
Profit statement using Absorption costing
Sales
Less cost of sales:
Prime costs
Production Overheads
Machining dept
Assembly dept
Profits for the period
(a)
(ii)
XYI
2,250,000
YZT
3,800,000
ABW
2,190,000
1,600,000
3,360,000
1,950,000
120,000
288,750
241,250
240,000
99,000
101,000
144,000
49,500
46,500
XYI
2,250,000
YZT
3,800,000
ABW
2,190,000
1,600,000
3,360,000
1,950,000
85,000
210,000
6,000
39,000
22,500
170,000
72,000
10,000
39,000
30,000
102,000
36,000
10,000
78,000
31,500
287,500
119,000
(17,500)
Profit statement using ABC
Sales
Less cost of sales:
Prime costs
Production Overheads
Machining services
Assembly services
Set up costs
Order processing
Purchasing
Total profit for each
product
Workings:
Cost driver rates:
Machining services
357,000 / 420,000
0.85 per hour
Assembly services
318,000 / 530,000
0.6 per hour
Set up costs
26,000 / 520
50 per set up
Order processing
156,000 / 32,000
4.875 / customer order
Purchasing
84,000 / 11,200
7.5 per supplier order
(b)
See class discussion.
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Example 4 3P3M Ltd
Total machine hours required for each product
X
200
Sales demand
Y
200
Z
200
Required machine hours:
Machine 1
Machine 2
Machine 3
(6, 2, 1)
(9, 3, 1.5)
(3, 1, 0.5)
1,200
1,800
600
+
+
+
400
600
200
+
+
+
200
300
100
=
=
=
1,800
2,700
900
Required hours as a percentage of hours available
Machine 1
Machine 2
Machine 3
1800/1600
2700/1600
900/1600
=
=
=
112%
169%
56%
Machine 2 represents the bottleneck activity because it has the highest machine
utilization.
Calculation of return per factory hour
Sales - direct material cost
Usage in hours of bottleneck resource
X
20
8
12
9
1.333
Sales
Direct materials
Throughput
Usage in hours of bottleneck
Return per factory hour
Y
15
5
10
3
3.333
Z
10
4
6
1.5
4
Cost per factory hour
Total factory cost
bottleneck resource hours available
Total factory cost (labour and overheads)
Factory cost per unit (5+2), (3+1), (2+1)
Units
Total factory cost
Cost per factory hour
Cost per factory hour =
£2,800/ 1600 =
=
X
7
200
1,400
1.75
Y
4
200
800
1.75
Z
3
200
600
1.75
= 2,800
1.75
Throughput accounting ratio
Return per factory hour
Cost per factory hour
Return per factory hour
Cost per factory hour
Throughput accounting ratio
Ranking
190
X
1.33
1.75
0.76
3
Y
3.33
1.75
1.90
2
Z
4.00
1.75
2.29
1
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A P P E N D I X – S O L U T IO N S T O E X E R C IS E S A N D E X A M P L E S
Therefore the allocation of the 1,600 hours of the bottleneck activity is:
Production
200 units of Z
200 units of Y
77 units of X
Machine hours
300
600
700
balance of hours available
1,300
700
-
Following the five steps theory of constraints outlined earlier, action should be
taken to remove the constraint.
Let us assume that a financial analysis indicates that the purchase of a second
machine 2 is justified. Machine capacity will now be increased by 1,600 hours to
3,200 hours and machine two will no longer be a constraint. In this case machine 1
would now be the bottleneck. The above process must be repeated to determine
the optimum output for machine 1.
Example 5 CMC Ltd
Target Cost
Target selling Price
20,000
Target Profit @ 10%
(2,000)
Target cost
18,000
Example 6 Fantata Ltd
(a)
Target Cost
Target selling price
Target profit margin @ 12%
Target Cost
75
(9)
66
(b)
Expected current cost per unit:
Direct materials
ABC conversion cost
Assembly
Finishing
Product specific fixed cost
Company fixed cost
20
12
14.17
4.17
Total expected current cost per unit
70.34
Cost Gap (70.34 – 66)
20
4.34
(c)
The company is falling considerably short of its 12% net profit margin target. If
sales quantities and prices are to remain unchanged, costs must be reduced if the
required return is to be reached.
Product B is falling short of the C/S ratio target. Cost reduction methods exercise
must be concentrated particularly on this product if its production is to continue to
be seen to be worthwhile.
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The designed specification for each product and the production methods should be
examined for potential areas of cost reduction that will not compromise the quality
of the products. For example:
●
Can any materials be eliminated, eg cut down on packing materials?
●
Can a cheaper material be substituted without affecting quality?
●
Can part assembled components be bought in to save on assembly time?
●
Can the incidence of the cost drivers be reduced, in particular for product Y?
●
Is there some degree of overlap between the product-related fixed costs that
could be eliminated by combining service departments or resources?
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CHAPTER 2
Example 1 Clemence Ltd
Using marginal costing principles:
X
14
17
Y
28
25
Make
Buy
Variable cost of making
Purchase price offered
Decision:
Example 2 PCO Ltd
The decision rule is which alternative is cheaper.
The cost of buying the component from the supplier is £400
The relevant cost of producing the component is the incremental cost which
includes:
Direct labour
Direct materials
Variable overheads
Relevant cost
100
300
50
450
If fixed cost is assumed to be constant, then it will be cheaper to buy, because
there will be net savings of £50.
Example 3 Central Ltd
The relevant costs are the differential costs between making and buying, and they
consist of differences in unit variable costs plus the differences in directly
attributable fixed costs. Sub-contracting will result in some fixed cost savings.
Unit variable cost of making
Annual required units
Total variable cost
Direct attributable fixed cost
Relevant cost of making
W
£
14
1,000
14,000
1,000
15,000
X
£
17
2,000
34,000
5,000
39,000
Y
£
7
4,000
28,000
6,000
34,000
Z
£
12
3,000
36,000
8,000
44,000
Unit Variable cost of buying
Annual required units
Total variable cost of buying
Attributable Fixed cost of
buying
Relevant cost of buying
W
12
1,000
12,000
0
X
21
2,000
42,000
0
Y
10
4,000
40,000
0
Z
14
3,000
42,000
0
12,000
42,000
40,000
42,000
Differences in relevant cost
3,000
(3,000)
(6,000)
2,000
The company would save £3,000 and £2,000 per annum for buying components W
and Z respectively. Therefore component W and Z should be purchased from the
subcontractor and components X and Y should be produced internally.
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A PP E N D IX – S O LU T I O NS T O EX E R C IS ES A N D E X A M P L ES
Example 4 Jones Ltd
If Division C is shut down as per the CEO’s concerns, the following would be the
financial impact on the company.
Loss of Sale from closure
Savings in variable cost
Fall in contribution
Saving in Division specific fixed cost
(40,000)
30,000
(10,000)
8,000
Fall in divisional / company profits
(2,000)
Decision: Division C should not be closed down.
Example 5 Fantum Ltd
Loss of sale from closure
Saving in variable costs
Fall in contribution from closure
Savings in specific fixed cost
Net loss from closure
(30,000)
18,000
(12,000)
10,000
(2,000)
On the basis of this information, Division Y should remain open as it will make a net
additional to profit next year of £2,000.
This assumes that the specific fixed costs will be saved if the division closes but
there will be no savings in head office costs – this being a general fixed cost.
Example 6 (a) Neal Ltd
Step 1: Calculate the extent of Limiting factor (shortage)
Product M
600 units x 8 hours/unit
Product N
500 units x 3 hours/unit
Total hours required
Hours available
Shortage
=
=
=
=
=
4,800 hours
1,500 hours
6,300
5,000
1,300 hours
That explains that hours at present are not sufficient to fulfil demand for both
products so we will have to develop the optimal production plan using 5,000 hours
which maximises the profit.
M
N
24
15
Step 3: Calculate contribution per hour
3/hour
5/hour
Ranking
2
1
Step 2: Calculate contribution per unit
Step 4: Develop optimal (most profitable) production plan using 5,000 hours
Product 1 (N)
500 units x 3 hours per unit
=
1,500 hours
Leaving 3,500 remaining hours to be allocated to product 2 (M)
3,500 hours / 8 per unit
194
=
437 units
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Step 5: Total contribution from M and N
M
437 unit x 24 per unit
N
500 units x 15 per unit
10,488
7,500
Total contribution
17,988
Less fixed cost
10,000*
Total profit
7,988
*Fixed cost (M =10 x 600 + N = 8 x 500)
Example 6 (b) Neal Ltd
M
N
Variable cost to make
16
15
External purchase price
24
21
Make
Make
Based on the above comparison both products should be made internally, but due
to limited plant capacity only 437 units can be produced as per 6 (a), therefore in
order to fulfil the demand of M, remaining 163 units will have to be bought in.
Revised Contribution
M
on first 437 units x 24 per unit
on the purchased units(163 units x 16 per unit)
10,488
2,608
N (as per 6(a))
Total contribution
Less: fixed cost
7,500
20,596
10,000
Revised Profit
10,596
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Example 7 WXYZ Ltd
Are the materials a limiting factor?
Units
Materials (kilos) per unit
W
2,000
2
4,000
X
4,000
1
4,000
Y
3,000
1.5
4,500
Z
1,000
2.5
2,500
Available
Shortage
=
=
=
15,000
11,000
4,000
Therefore materials are a limiting factor.
Variable cost per unit to make
Cost of buying
Extra cost of buying
W
£
17
20
3
X
£
7
11
4
Y
£
12
15.75
3.75
Z
£
19
21.5
2.5
Materials per unit
Extra cost of buying per kilo
Ranking
2
1.5
3rd
1
4
1st
1.5
2.5
2nd
2.5
1
4th
The make or buy decision should be as follows, to maximise contribution and profit.
Products
Units
Materials(Kilos)
Contribution/unit
£
Make
X
Y
W(balance)
Buy
W(balance)
Z
Total
contribution
196
4,000
3,000
1,250
750
1,000
4,000
4,500
2,500
11,000
Total
contribution
£
4
6
12
16,000
18,000
15,000
49,000
9
9
6,750
17,500
73,250
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Example 8 CF Ltd
The joint processing costs are irrelevant to the decision. They will be incurred
whether product X is sold for £1.10 per litre or is processed further to make Zplus.
The analysis of relevant cash flow is as follows:
Every 4,000 litres of product X can be further processed to make 3,600 litres of
Zplus.
£
Revenue from sale of 3,600 litres of Zplus @ £1.4
Revenue from sale of 4,000 litres of X @ £1.1
Incremental revenue from further processing
Incremental cost of further processing
Added materials
Direct labour
Variable production overheads
£
5,040
4,400
640
400
40
80
Incremental gain from further processing
520
120
This analysis assumes that there would be no additional fixed costs from further
processing, and that no capital expenditure would be required to make further
processing possible.
Example 9 Beauty Co
The formula needed for a multi product break-even point is:
Break-even point
Total fixed costs
Weighted average C/S ratio
=
Weighted average C/S ratio in this case:
Nail polish C/S ratio is 55% and proportion of its sales is 30%, therefore
proportionate C/S ratio would be 55% x 30% = 16.5%
Lipstick C/S ratio is 60% and proportion of its sales is 70%, therefore proportionate
C/S ratio would be 60% x 70% = 42%
The combined weighted average C/S ratio, therefore will be: 16.5% + 42% =
58.5%
Break-even sales
=
=
$400,000
-----------58.5%
$683,761
(to the nearest dollar)
Example 10 a lecturer
(a)
Moscow
(b)
Moscow
(c)
Croatia
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Example 11 Pantum
●
The relevant cost of material W is the benefit that would be obtained from the
most profitable alternative use. The alternatives from using material W are
o
to sell for scrap and earn £1.5 per kilo
o
to use as a substitute for material Z, and save £2.4 per kilo (4-1.6)
o
therefore the relevant cost of material W is £2.4 per kilo.
●
The full £50,000 will be the relevant cost of the skilled labour as all represent
incremental cost.
●
The relevant cost of the unskilled labour, which will be paid wages of £30,000
anyway, is the loss of cash flow from having to move the labour from other
work. Contribution is calculated after deducting labour cost as a variable cost,
therefore 50% of the labour cost--£15,000 must be included in the relevant
cost
●
Relevant cost
Material W (3000 kilos x2.4)
Skilled labour
Unskilled labour:
7,200
50,000
Use of idle time
Use of other time (50% x 30,000) + 5000
0
15,000
77,200
Example 12 Tricks
Revised estimate:
Direct materials- paper (opportunity cost)
Inks(full purchase value)
2,500
3,000
Direct Labour:
1,125
0
Highly skilled (125 x 4 + 125 x 5)
Semi skilled (idle capacity)
Variable overheads (as per original
Printing press(200 hours x 3.00
Fixed production costs (not relevant)
Estimating department costs (not relevant)
Total relevant cost (minimum price)
1,400
600
0
0
8,625
Example 13
The optimum production plan is to make and sell 500 units of X and 700 units of Y.
The maximum contribution is (500 x 4 + 700 x 8) = £7,600.
Please see page 51 for step-by-step answer.
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Example 14 Cantata
Step 1
Let a =
the number of units of product A produced next month.
Let b =
the number of units of product B produced next month.
Let z =
total contribution earned from the manufacture of products A and B next
month.
Step 2
The objective is to maximise contribution, so the objective function can be
expressed as:
Z = 50a + 70b
Step 3
The constraints here are machine hours, material quantities, and labour hours;
hence the constraint functions can be expressed as follows:
Machine time
3a + 10b ≤ 330
material
16a + 4b ≤ 400
labour
6a + 6b ≤ 240
Step 4
Non-negative constraints
a ≥0
b ≥ 12.
The full linear programming model can be summarised as follows:
Maximise: z = 50a + 70b
Subject to:
3a + 10b ≤ 330
16a + 4b ≤ 400
6a + 6b ≤ 240
a≥0
b ≥ 12.
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Step 5
Constraint
a
b
1
0
60
1
240
0
2
0
80
2
160
0
3
0
160
3
64
0
4
120
0
4
120
160
5
0
120
5
240
120
OF
0
30
OF
60
0
160
140
120
100
80
60
40
20
0
0
50
100
150
200
250
The feasible region is indicated by the shaded region on the graph. The points are
MNOPQ
Point M
a = 22; b = 12.
Z 50(22) + 70(12) = 1,940
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Point N a = 20; b = 20
Z = 50(20) + 70(20) = 2,400
Point O a = 10; b = 30
Z = 50(10) + 70(30) = 2,600
Point P a = 0; b = 33
Z = 50(0) + 70(33) = 2,310
Point Q a = 0; b = 12
Z = 50(0) + 70(12) = 840
Conclusion
The combination of products A and B that maximise contribution is obtained at the
point O, hence 10 units of product A and 30 units of B should be produced to
maximise contribution.
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Example 15 Tronto
Let
a = the number of ingredient X purchased
b = the number of ingredient Y purchased
z = total cost of additive for every 10,000 litres of plant feed
Minimise
Subject to
z = 25a + 50b
2a + 8b ≥ 480
5a + 10b ≥800
10a + 4b ≥ 640
a ≤120
b ≤ 120
a, b ≥ 0
Values of a and b on or within the shaded area RSTUV will satisfy all the constraints
of the model and thus this area constitutes the feasible region. [See class
discussion for shaded optimal solution area].
Point
Point
Point
Point
Point
Ra
Sa
Ta
Ua
Va
=
=
=
=
=
120, b
120, b
16, b
40, b
80 b
=
=
=
=
=
30,
120,
120,
60
40
Z
Z
Z
Z
Z
=
=
=
=
=
25(120) + 50(30) = 4,500
9,000
6,400
4,000
4,000
As the objective is one of minimisation then the optimum solution is given by the
values of a and b that results in the least value of Z. This can be achieved at the
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points U and V. In this case multiple solutions is said to exist because there is
more than one solution.
Therefore Tronto should purchase either 40 litres of ingredient X and 60 litres of
ingredient Y, or 80 litres of ingredient X and 40 litres of ingredient Y to achieve a
minimum cost of £4,000.
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CHAPTER 3
Example 1
Phase
Introduction
Growth
Maturity
Decline
Profitability
Low but will
depend on
pricing
strategy.
Steady and
rising profit
levels
Profits begin
to fall,
boosted by
product
relaunched
with
variations on
the original eg
different
colours
Profits falling
and may fall
faster if
decommissioning
of product
necessary
Cashflow
Steadily
increasing
Accelerating
to max point
Cash ‘cow’
Cashflow falling
accelerated by
need to cover
fixed costs until
they step as
product sales
fall.
Strategy
Price
Skimming –
profit level
occurs faster.
Launch to
different
geographic
areas, variety
of sizes
versions to
boost sales
Product
relaunch
market drive
to hold sales
levels
Deliberate
replacement of
product
Price
Penetration –
if successful
volumes
causes profit
faster
Example 2
Intel, Unilever, and Procter and Gamble.
Example 3
BMW, Bentleys.
Example 4
Supermarket economy range, Lidl, 99p shops.
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Example 5 Biscan
25
=
a – (b x 500)
b
=
5/200
25
=
a – (0.025 x 500)
A
=
37.50
=
37.50 – 025Q
=
0.025
So:
P
Example 6 Mellor
(a)
12.50
=
a – (b x 20,000)
b
=
1.50/(20,000 x 20%)
12.50
=
a – (0.000375 x 20000)
a
=
5
=
5 – 0.000375Q
=
0.000375
So:
P
(b)
PxQ=
If price = £12.50
12.50 x 20,000 = £250,000
If price = £11
11.00 x (20,000 x 1.2) = £264,000
Example 7
% change Q
% change P
Annual demand at £1.20 = 800,000 units
Annual demand at £1.30 = 725,000 units
Elasticity of demand
 725,000


× 100 
 800,000

 0.10

× 100 

1
.
20


=
-1.125
Ignoring the negative sign, the elasticity of demand is 1.125.
The demand will therefore be elastic, because the price elasticity of demand is
greater than 1.
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A PP E N D IX – S O LU T I O NS T O EX E R C IS ES A N D E XA M P L ES
CHAPTER 4
Example 1
TABLE IN £
DECIDE
£4
£4.30
£4.40
*3 32,200
30,000
To price
OUTCOME
Sales volume
Best
*1 32,000
Most likely
*2 28,000
28,750
28,800
20,000
18,400
14,400
Worst
Fixed costs ignored as asked for price not profit and can make decision on
contribution.
Contribution
per unit if VC
£2
£4
£4.30
£4.40
2
2.30
2.40
*1 – 16,000 x 2 =32,000
*2 – 14,000 x 2 = 28,000
*3 – 14,000 x 2.30 = 32,200
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A P P E N D I X – S O L U T IO N S T O E X E R C IS E S A N D E X A M P L E S
Example 2
DECIDE:
A
B
C
Worst
50
70
90
Likely
85
75
100
Best
130
140
110
(a) Min
50
70
90
OUTCOME:
Pick C
pick max
(b) Max
130
pick max
(a)
140
110
Pick B
maximin decision rule
This is the decision criterion that management should play safe and either
minimises their losses or costs, or else go for the decision which gives the
highest minimum profits.
If the company selects:
Project A the worst result is a net profit of 50.
Project B 70
Project C 90.
The best worst outcome is 90 and project C would be selected.
(b)
Maximax decision rule
This is the decision to select the best possible result, by maximising the
maximum result (profit). The best possible outcomes are as follows:
Project A = 130
Project B = 140
Project C = 110.
As 140 is the highest of these three figures, project B would be selected using
the maximax criterion.
(c)
minimax regret decision rule
The minimax regret decision rule aims to minimise the maximum regret from
making the wrong decision.
A table of regret can be compiled, as follows, showing the amount of profit
that might be forgone for each project, depending on whether the outcome is
worst, most likely or best.
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A PP E N D IX – S O LU T I O NS T O EX E R C IS ES A N D E XA M P L ES
DECIDE:
A
B
C
Worst
40
20
0
Likely
15
25
0
Best
10
0
30
Max regret
40
25
30
OUTCOME:
Pick B
Pick min
Workings
0 = no regret rest of the row numbers are compared to this and are all
opportunity losses.
The maximum regret for each decision is 40, 25 and 30 for projects A,B and C
respectively.
The lowest of the maximum regrets is 25 with project B, and so project B would
be selected if minimax regret rule is used.
Example 3 3D Ltd
Monthly profit x
Probability p
EV = px
50,000
0.6
30,000
35,000
0.4
14,000
∑44,000
EV monthly profit is £44,000
Example 4 For Ltd
Sale (x)
Prob (p)
EV = (px)
20,000
0.25
5,000
25,000
0.4
10,000
30,000
.15
4,500
35,000
.2
7,000
∑26,500
EV of sales is £26,500.
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A P P E N D I X – S O L U T IO N S T O E X E R C IS E S A N D E X A M P L E S
Example 5 Mr Fyvestall
(a)
Payoff Table
Workings – Probability of demand
Number of Days
Probability
45
45/150 = 0.3
75
75/150 = 0.5
30
30/150 = 0.2
Total 150
TABLE IN £
DECIDE
10
20
30
10
*1 200
*4 20
(160)
20
*2 200
*5 400
220
30
*3 200
*6 400
600
To Buy
PROBABLE
OUTCOME
Demand
COLUMN FOR
PROBABILITY
*1 - Buy 10 sell 10,
10 x (40-20) = 100
*2, *3 - only bought 10 so maximum
*4– Buy 20 only sell 10 and scrap 10
Income (10 x £40) + (10 x £2)
=
Costs (20 x £20)
420
(400)
£20
*5, *6
Income (20 x £40)
=
800
Costs (20 x £20)
=
(400)
£400
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Add probability:
TABLE IN £
DECIDE
10
20
30
To Buy
PROBABLE
OUTCOME
Demand
COLUMN FOR
PROBABILITY
10
0.3
200
20
(160)
20
0.5
200
400
220
30
0.2
200
400
600
200
286
182
Expected
Values
(b)
(i)
0.3
x
200
200
0,5
x
200
200
0.2
x
200
200
∑200
0.3
x
20
6
0,5
x
400
600
0.2
x
200
80
∑286
0.3
x
(160)
(48)
0,5
x
220
110
0.2
x
600
120
∑182
(c)
EV = £286 per day so buy 20
(b)
(ii)
Maximin buy 10, Maximax buy 30
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A P P E N D I X – S O L U T IO N S T O E X E R C IS E S A N D E X A M P L E S
(b)
(iii) Minimax Regret
TABLE IN £
DECIDE
10
20
30
10
0
180
360
20
200
0
180
30
400
200
0
Max
400
200
360
To Buy
PROBABLE
OUTCOME
Demand
Minimax regret buy 20
Example 6 VI Ltd
(a)
(b)
Sales fall by
200/4,000 x 100
=
5%
Costs rise by
200/3,800 x 100
=
5.3%
Materials rise by
200/2,000 x 100
=
10%
Labour rise by
200/1,000 x 100
=
20%
Fixed costs rise by
200/800 x 100
=
25%
Sales need to fall by least % so is most sensitive.
Example 7 Seven Trees Ltd
Step 1:
Draw the tree from left to right showing appropriate decisions and
events/outcomes.
Symbols to use:
A square is used to represent a Decision point. At a decision
point the decision maker has a choice of which course of
action he wishes to undertake.
A circle is used at a chance Outcome point.
from here are always subject to probabilities.
The branches
Label the tree and relevant cash inflows/outflows (discounted to present
values) and probabilities associated with outcomes.
Step 2:
Step 3:
Evaluate the tree from right to left carrying out these two actions:
1.
Calculate an EV at each Outcome Point.
2.
Choose the best option at each Decision Point.
Recommend a course of action to management.
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3 (0.4)
2 (0.75)
1
4 (0.3)
5 (0.3)
6 (0.25)
7
1.
Develop product
2.
Development succeeds
3.
Very successful
4.
Moderately successful
5.
Failure
6.
Development fails
7.
Do not develop the product
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A P P E N D I X – S O L U T IO N S T O E X E R C IS E S A N D E X A M P L E S
Calculation of EV of each outcome:
Decision
Outcome
Outcome
Develop
product
successful
very successful
0.75 x
0.4 = 0.3
x $540,000
successful
moderately succ
profits
0.75 x
0.3 = 0.225
x $100,000
successful
failure
loss
EV
0.75 x
0.3 = 0.225
x ($400,000) =
($90,000)
Development
fails
loss
EV
0.25
($180,000)
($45,000)
Develop
product
Develop
product
Develop
product
Overall result
Do not Develop product
Profits
EV
=
$162,000
EV
=
$22,500
$49,500
EV
0
Thus, based on expected values developed from the decision tree, the company
should develop the product as it is giving a positive sum of profits.
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CHAPTER 6
Example 1 Ogrisovic
Based on traditional analysis, the company has overspent $2,500 (difference
between budgeted cost and actual cost), whereas we will have to use flexible
budgeting style to analyse information further into variable and fixed components
for a fair conclusion.
Flexed variable cost for 1,200 units ($10 per unit x 1,200 units)
$12,000
Flexed fixed cost for 1,200 units
$10,000
Total flexed costs
$22,000
Actual costs for the period
$22,500
There is still an adverse variance of $500 but it is better than original analysis
where results were $2,500 adverse and it could have led to a de-motivational
situation for the concerned managers.
Example 2 ABC Ltd
Difference
Total cost
44,400
38,100
6,300
Variable cost per unit
Unit produced
9,800
7,700
2,100
6,300
2,100
=
£3
The fixed and flexible budget can be prepared as:
sales (£5)
variable cost (3)
contribution
fixed cost
profit
214
Fixed budget
9,000 unit
Flexible budget
8,000 unit
Flexible budget
10,000 unit
45,000
27,000
18,000
15,000
3,000
40,000
24,000
16,000
5,000
1,000
50,000
30,000
20,000
15,000
5,000
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Example 3
(a)
Flexible budget Operating statement flexed at actual units of 720,000
Flexed Budget
$000
Actual
$000
Cost of sales: (all variable)
Materials
Labour
Overheads
189
270
36
144
288
36
45 F
18 A
0
Variable S&D costs
Variable admin costs
162
54
153
54
9F
0
Total variable costs
711
675
36 F
Fixed costs:
Labour
Selling & Distribution
Administration
100
72
184
94
83
176
6F
11 A
8F
Total fixed costs
356
353
3F
1,152
441
85
1,071
396
43
81 A
45 A
42 A
Sales
Contribution
Net Profit
Variance
$000
(b)
The original operating statement was prepared on the basis of fixed budgeting
basis, and is of little use to management due to following reasons:
1.
Out of date budgeted figures were compared with actual results – which were
a year later.
2.
Market fluctuations were not considered and updated into the original budget
in order to give better ideas to management, thus providing less meaningful
variance analysis.
3.
The original budgeted statement was produced on the basis of original
budgeted output, whereas actual results were drafted on actual output
achieved – which was significantly different from the budget.
4.
Variable costs should have been flexed on the basis of actual output to
provide reasonable comparison. For example, the material costs original
budget was produced on the basis of 640,000 units whereas 720,000 units
were actually produced: therefore the flexed costs for materials should have
been calculated to compare with actual material costs – thus providing more
meaningful variance.
5.
The original statement was misleading in terms of providing more meaningful
feedback for various operations.
It therefore might de-motivate some
managers since their performance would be monitored on wrong basis.
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(c)
(i)
The following are the main problems associated with forecasting of figures used in
flexible budgeting:
1.
Accurate identification of different cost behaviours, in their variable and fixed
components, may be complicated in complex manufacturing environments.
2.
Determination of linear relationship of variable costs based on their activity
levels such as output. Some costs may directly depend on volume of units
and some costs may depend on other factors like labour hours, machine
hours.
3.
Accurate understanding of activity levels (cost drivers) affecting various costs
may be difficult to determine.
4.
Use of different forecasting models may produce different results which may
create a misleading effect.
5.
Cost bases used in original budgets may be different as to the flexible budgets
due to change in cost behaviours and market patterns. Furthermore, they
may be significantly different from actual spending patterns.
6.
Currency fluctuations and inflation adjustment can be complicated to be
incorporated on exact and accurate basis.
(c)
(ii)
Using High Low method
Variable cost per unit $4,000 / 120,000 units
= $0.0333 per unit
Fixed cost will be
= $10,667
Step-up cost above 750,000 units
= $1,000
Flexed budget for 720,000 units (720,000 x $.0333) + $10.667 = $25,000
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CHAPTER 7
Example 1
(a)
Graph
Marketing Spend Effect on Sales
1400
1200
sales
1000
800
Sales £000
600
400
200
0
0
20
40
60
80
100
120
140
m arketing
There is a relationship between the amount spent on marketing and resultant
sales revenue, however it is not perfectly linear.
(b)
Calculate using regression formula and get a and b from regression formulae,
b first as you need b to get a:
X
£000
40
80
100
120
60
80
∑480
∑X
Y
£000
680
960
1,040
1,200
880
1,000
∑5,760
∑Y
XY
27,200
76,800
104,000
144,000
52,800
80,000
∑484,800
∑XY
X2
1,600
6,400
10,000
14,400
3,600
6,400
∑42,400
∑X2
Y2
462,400
921,600
1,081,600
1,440,000
774,400
1,000,000
∑5,680,000
∑Y2
b = 144,000/24,000 = 6
a = 960 -480 = 480
y = 480 + 6x
a represents what would be sold even if there were no advertising.
b represents the effect of each £1,000 marketing spend on sales, ie spend
£1,000 on marketing stimulates £6,000 sales income.
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A PP E N D IX – S O LU T I O NS T O EX E R C IS ES A N D E XA M P L ES
(c)
(i)
sales = 480 + (6 x 100) = £1,080,000 sales are forecast.
(ii)
sales = 480 + (6 x 250) = £1,980,000 sales are forecast.
Comments on forecast sales using regression based formula:
●
Figures are accurate re information given about marketing and sales no
unusual circumstances.
●
Future can be predicted from the past results of marketing and sales.
●
The only factor affecting sales is marketing.
●
There is a linear relation between marketing and sales.
Example 2
(6 × 484,800) − (480 × 5,760)
((6 × 42,400) − (480 2 )) × ((6 × 5,680,000) − (5,760 2 ))
2,908,800 − 2,764,800
=
(254,400 − 230,400) × (34,080,000 − 33,177,600)
144,000
=
24,000 × 902,400
=
144,000
147,165
r
=
0.978
r²
=
0.9565 95.65% of the shift in y is caused by changes in x
There is a fairly linear relationship between marketing expenditure and sales.
Example 3
X
Units
100
120
140
110
70
Y
£000
144
163
176
157
115
∑540
∑X
r
=
=
218
∑755
∑Y
XY
X2
Y2
14,400
19,560
24,640
17,270
8,050
10,000
14,400
19,600
12,100
4,900
20,736
26,569
30,976
24,649
13,225
∑83,920
∑XY
∑61,000
∑X2
∑116,155
∑Y2
(5 × 83,920) − (540 × 755)
((5 × 61,000) − 540 2 ) × ((5 × 116,155) − 7552 )
419,600 − 407,700
(13,400 × 10,750)
=
11,900
12,002
=
0.992
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Example 4
0.992² = 0.98 or 98%
98% of the changes in y so changes in total costs are caused by changes in x ie
units produced.
Exercise 5
(a)
Additive
Forecast trend = 33 in Q2 year 3 move forward the Q2 yr 5 = 8 moves and
Q2 SV = (12)
So:
(b)
33 + ((33-29.5)/7 x 8) – 12 = 25
Multiplicative
Forecast trend = 33 in Q2 year 3 move forward the Q2 yr 5 = 8 moves and
Q2 SV = x0.6
So:
(33 + ((33-29.5)/7 x 8)) x 0.6 = 22.2
Example 6
Average
time per
unit
Cum
total
time
Incremental
units
Incremental
total time
1 unit
100
100
1
100
2 units
80
160
2nd
60
4 units
64
256
3rd and 4th
96
8 units
51.2
409.6
5th to 8th
153.60
Cumulative
units
Example 7
2nd = 60 hours
3rd and 4th – can’t do using this as you can get time of next 2 so 2 take 96 hours
but not actual time of 3rd and 4th
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A PP E N D IX – S O LU T I O NS T O EX E R C IS ES A N D E XA M P L ES
Example 8 Limitation plc
(a)
Time for second batch, sum of third and fourth together
Average
time per
unit
Cum
total
time
Incremental
units
Incremental
total time
1 unit
120
120
1
120
2 units
108
216
2nd
96
4 units
97.2
388.8
3rd and 4th
172.8
Cumulative
units
(b)
Quarter 1
Quarter2
£
£
54,000
54,000
Labour *1
12,610
11,432
Variable Overheads (150% labour)
18,915
17,148
Total variable costs
31,525
28,580
CONTRIBUTION
22,475
25,420
Sales (£1,200 per batch)
Variable costs:
Material
*1 Cumulative total to end Q1 = 75 batches
75 batches – first 30 batches in Q4 = Q1 45 batches
For 75 in total (y = axb) x 75 = (120 (75 -0.152)) x 75 = 62.25 x 75 =
4,668.75hours (note 62.25 hours was given too)
For first 30 in total = (120 (30 -0.152)) x 30 = 71.56 x 30 = 2,146.8hours
(note 71.56 hours was given too)
4,668.75hours
(2,146.8hours)
2,521.95 hours
@£5 = £12,610
Cumulative total to end Q2 = 120 batches
120 batches – first 70 batches in Q4 and Q1
For 120 in total = (120 (120 -0.152)) x 120 = 57.96 x 120 = 6,955.2hours
(note 57.96 hours was given too)
For 75 in total (y = axb) x 75 = (120 (75 -0.15 )) x 75 = 62.25 x 75 =
4,668.75hours (note 62.25 hours was given too)
6,955.2hours
(4,668.75hours)
2,286.45 hours
220
@£5 = £11,432.25
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(c)
Cumulative total to end Q3 = 132 batches
132 batches – first 120 batches in Q4, Q1 and Q2
For 132 in total (y = axb) x 132 = (120 (132 -0.152)) x 132 = 57.13x 132 =
7,541hours
For 120 in total = (120 (120 -0.152)) x 120 = 57.96 x 120 =6,955.2hours
(note 57.96 hours was given too)
7,541.16 hours
(6,955.2hours)
585.96 hours
@£5 = £2,929.80 are the labour costs
And variable overhead would be = £4,394.70
Example 9 BG
b = log 0.8/log 2 = -0.3219
Total time of 4
(22 (4-0.3219)) x 4 = 14.08 x 4 =
56.32 minutes
Total time of 3
(22 (3-0.3219)) x 3 = 15.45 x 3 =
46.34 minutes
Time of 4th
9.98 minutes
Example 10 Martina Ltd
Direct Material (£4,000 x 8)
Direct Labour average *1
Fixed cost
Total for 8
£32,000
£2,458
£6,400
£40,858
Average per unit £40,858/8 = £5,107
*1
b = log 0.8/log 2 = -0.3219
Time to make 8 = (80 x (8-0.3219)) x 8 = 40.96 hours x 8 = 327.7 hours x £7.50 =
£2,458
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CHAPTER 8
Example 1 Jojo Ltd
Standard cost sheet for jojo
£
Direct material 30 x 6.1
Direct labour:
Dept P 40 x 2.20
Dept Q 36 x 2.5
Variable production overhead:
Dept P (525,000/700,000) x 40
Dept Q (300,000/600,000) x 36
Fixed overheads:
Production:
Dept P (40x1.25)
Dept Q (36x1.25)
Administration (125,400/11,400)
Marketing
285,000/11,400
Full cost
Profit
(1/9) x 540
Selling price
£
183
88
90
178
30
18
48
50
45
11
25
131
540
60
600
Total direct lab hrs = (40 + 36)x 11,400= 866,400
Production o/h rate = 1,083,000/ 866,400 = £1.25
Example 2 Owen Ltd
Direct Materials:
Total Variance
=
Standard material cost for actual output – actual material cost
(£20 x 1,300) – £22,700 = £3,300 F
Price Variance
=
(SP – AP) x AQ
(£5 – 4.54) x 5,000 = 2,300 F
Usage Variance =
(SQ – AQ) x SP
(5,200kg – 5,000kg) x £5 = £1,000 F
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Direct Labour Variances:
Total Variance
=
Standard labour cost for actual output - actual labour
cost
(£16 x 1300) - £21,500 = £700 A
Rate variance
=
(SR – AR) x AH paid for
(£8 - £7.543) x 2850 = £1,300 F
Efficiency variance
=
(SH – AH) x SR
(2,600 – 2,850) x £8 = £2,000 A
Variable overheads variances:
Total variance
=
Standard variable overheads cost for actual output actual cost
(£7 x 1,300) - £7,800 =£1,300 F
Expenditure variance =
(SR – AR) x AH
(£3.50 - £2.736) x 2850 = £2,175 F
Efficiency Variance
=
(SH – AH) x SR
(2,600 – 2,850) x £3.50 =£875 A
Fixed Overheads variances:
Total variance
=
Standard fixed overheads cost for actual output actual cost
(£14 x 1,300) – £14,600 =£3,600 F
Expenditure Variance =
Budgeted fixed cost – actual fixed cost
(£14 x 1,000) – £14,600 = £600 A
Volume Variance
=
(BV – AV) x OAR
(1,000 – 1,300) x £14 = £4,200 F
Sales variances:
Price variance
=
(SP – AP) actual units sold
(£70 x 1,250) – 78,000 =£9,500 A
Volume Variance
=
(SV – AV) x Standard profit per unit
(1,000 – 1,250) x £13 = £3,250 F
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Example 3 Dido
Direct Labour cost variance:
Standard labour cost for actual units - Actual labour cost for actual units
(388 per unit x 530 units) =
(200,382)
Total cost variance
=
5,258 Favourable
Labour Rate Variance
=
(SR – AR) x Actual Hours paid (AH)
=
(4 – 3.9) x 51,380 hours
=
5,138 F
=
(SH – AH worked) x SR
=
(51,410 – 51,000) x 4
=
1,640 F
=
Idle Hours x SR
=
380 x 4
=
1,520 Adverse
Labour efficiency variance
Labour Idle time variance
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Example 2 (cont) Owen Ltd
Operating Statement
£
£
Budgeted Profit
(1,000x 13)
Sales Volume
Flexed Budget Profit
(1,250 x 13)
Sales Price
COST VARIANCES:
Direct Materials:
Price variance
Use variance
Direct Labour:
Rate variance
Efficiency variance
Variable Overheads:
Expenditure variance
Efficiency variance
Fixed Overheads:
Expenditure variance
Capacity variance
Efficiency variance
Total cost variances
£
13,000
3,250
16,250
(9,500)
Favourable
Adverse
2,300
1,000
1,300
2,000
2,175
875
600
5,950
1,750
12,725
5,225
Actual Gross Profit
7,500
£14,250
Actual profit proof:
£
Sales
Cost of Sales
Opening stock
Production:
Materials
Labour
Variable Overheads
Fixed Overheads
£
78,000
0
22,700
21,500
7,800
14,600
66,600
Closing Stock
(1,300-1,250) x 57
(2,850)
63,750
£14,250
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Example 2 (cont) Owen Ltd
Operating Statement
£
£
Budgeted Contribution:
(1,000x 27)
Sales Volume
6,750
Flexed Budget Contribution
(1,250 x 27)
Sales Price
VARIABLE COST VARIANCES:
Direct Materials:
Price variance
Use variance
Direct Labour:
Rate variance
Efficiency variance
Variable Overheads:
Expenditure variance
Efficiency variance
Total variable cost variances
£
27,000
33,750
(9,500)
Favourable
Adverse
2,300
1,000
1,300
2,000
2,175
875
6,775
2,875
Fixed Overheads:
Budget Fixed cost
Expenditure variance
14,000
600
Actual Fixed costs
14,600
Actual Gross Profit
(Inventory value of fixed
overhead = 50 x 13 = £650
AC £650 higher than MC profit)
3,900
(14,600)
£13,550
Sales Volume:
●
Should sell 1,000
●
Did sell
1,250
250 units at contribution of £27 = £6,750 favourable
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Exercise 4 Barnes
Operating Statement
£
£
Budgeted Profit
(800 x 50)
Sales Volume
Flexed Budget Profit
(780 x 50)
Sales Price
COST VARIANCES:
Direct Materials:
Price variance A
Price variance B
Use variance A
Use variance B
Direct Labour:
Rate variance
Efficiency variance
Fixed Overheads:
Expenditure variance
Capacity variance
Efficiency variance
Total cost variances
Actual Gross Profit
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£
40,000
(1,000)
39,000
15,600
Favourable
Adverse
6,000
700
16,380
2,400
7,480
7,680
10,680
14,000
12,800
40,260
37,860
2,400
£57,000
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Exercise 5 CRV Ltd
(i)
Standard Labour Rate
Total Labour Variance = £16,800 F - £3,200 A = £13,200
Total variance = Standard labour cost for actual units – actual labour cost
£13,200
=
X - £480,000
X = £480,000 + £13,200
= £493,200
For one unit = £493200 / 40,000 = £12.33 per unit
Standard rate per unit = £12.33 / 2 hours = £6.165 per hour
(ii)
Actual Hours worked (AH)
Efficiency Variance = (SH – AH) x SR
3,200 A = (80,000 – AH) x 6.165
3200 /6.165 = 80,000 – AH
519 = 80,000 – AH
AH = 80,000 +519
AH = 80,519
(iii) Actual material expenditure
Actual Quantity = 40,000 units x 2.9 kgs = 116,000 kgs
Standard cost = 116,000 x £12.50 = £1,450,000
Actual cost = 31,450,000 + £71,050 = £1,521,050
(iv) Standard material allowance
Usage Variance
=
(SQ – AQ) – SP
£43,750
=
( Xkgs -116,000kg) x £12.50
£43,750 / £12.50
=
( Xkgs – 116,000kg)
3,500 kgs
= Xkgs – 116,000
X = 116,000 + 3500 = 119,500
Per unit = 119,500 / 40,000 = 2.9875 per kgs
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CHAPTER 9
Example 1 Liddell
(a)
Material Price
Should pay
£
20,000
(4,000kg x 5)
Did pay
25,000
£5,000
Adv
Purchasing manager has done a bad job as it is adverse.
(b)
Planning
Initial standards
£
20,000
(4,000kg x 5)
Revised standards
30,000
4,000 x (£5 +50%)
£10,000
Adv
Standards were incorrect.
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Operations
£
Revised standards
30,000
4,000 x (£5 +50%)
Did Pay
25,000
£5,000
Fav
Purchasing manager did a good job.
Example 2
Material Price
£
Should pay
190,000
(38,000kg x 5)
Did pay
195,500
£5,500
Adv
Purchasing manager has done a bad job as it is adverse
Material Use
Should use
Kg
£
37,500
(12,500 x 3)
Did use
38,000
500
x £5
£2,500
Adv
Production manager has done a bad job.
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Example 2 (cont)
Planning
£
Initial budget flexed
187,500
(12,500 x 3 x 5)
Revised budget flexed
199,562.50
(12,500 x 3.1 x 5.15)
£12,062.50
Adv
Standards were incorrect.
Planning - use
Initial budget flexed
kg
£
37,500
Should use
(12,500 x 3)
Revised budget flexed
38,750
Now will use
(12,500 x 3.1)
1,250
X £5
£6,250
Adv
Standards were incorrect for use.
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Planning - price
Initial budget flexed
£
193,750
Should pay
(12,500 x 3.1 x 5)
Revised budget flexed
199,562.50
Now will pay
(12,500 x 3.1 x 5.15)
£5,812.50
Adv
Standards were incorrect for price.
Operations
£
Material Price
Should pay Revised
standards
195,700
38,000 x 5.15
Did Pay
195,500
£200
Fav
Purchasing manager did a good job.
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Operations
Material Use
Should use Revised
standards
£
Kg
38,750
(12,500 x 3.1)
Did use
38,000
750
x £5.15
£3,862.50
Adv
Production manager has done a good job.
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Example 3 Dalglish
PRICE
SHOULD PAY
DID PAY
VARIANCE
£
A
13,200
13,860
660 ADV
B
6,300
6,720
420 ADV
C
6,500
6,110
390 ADV
26,000
26,690
690 ADV
MIX
SHOULD MIX
DID MIX
DIFFERENCE
STANDARD
VARIANCE
KG
KG
KG
COST £
£
A
70
%
700
660
40
20
800 FAV
B
20
%
200
210
(10)
30
300 ADV
C
10
%
100
130
(30)
50
1,500 ADV
1,000
1,000
0
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YIELD – IN TOTAL
UNITS
ACTUAL INPUT SHOULD YIELD
900
(1,000 X 90%)
DID YIELD
855
45
X STANDARD COST INCLUDING LOSS
GROSSED UP
20 X 70% = 14
30 X 20% = 6
50 X 10% = 5
25/0.9 = £27.77
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£1,250 ADV
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Example 4 Carragher
LABOUR Rate
£
Should pay
33,000
(5,500 x 6)
Did pay
32,000
£1,000
Fav
LABOUR IDLE
£
Hours
Was paid
5,500
Worked
4,200
1,300
x £6
£(7,800)
Adv
LABOUR Efficiency
Should work
Kg
£
3,900
(1,300 x 3)
Did work
4,200
300
x £6
£1,800
Adv
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Example 5 Hansen
Budgeted Hours worked:
10,000 x 80% = 8,000 hours.
Example 6
10,000 hours x £5 = £50,000 / 8,000 hours = £6.25 per hour.
Example 7
Total labour cost variance is now:
●
Should have paid at gross hours
1,300 x 3 7.50
£29,250
●
Did pay
£32,000
●
Total labour cost variance
£2,750
Now the rate, excess idle time, and efficiency variances can be illustrated as
follows:
LABOUR Rate
£
Should pay
33,000
(5,500 x 6)
Did pay
32,000
£1,000
Fav
LABOUR IDLE excess
Should have had idle
£
Hours
1,100
5,500 x 205
Did have idle
1,300
5,500-4,200
200
x £6/0.8 = 7.50
£1,500
Adv
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LABOUR Efficiency
Kg
Should work
£
3,900
(1,300 x 3)
Did work
4,200
300
x £7.50
£2,250
Adv
Example 8
Sales mix variance:
Budgeted contribution per unit x (actual sales at actual mix – actual sales at
budgeted mix)
Budgeted sales mix
=
800 units + 1,200 units
=
2:3
=
2,000 units
Therefore budgeted mix for actual sales of A should be:
=
(500 + 1,500) x 2/5
=
800 units;
and budgeted mix for actual sales of B should be:
=
(500 + 1,500) x 3/5
=
1,200 units;
but actual sales were 500 units of A and 1,500 units of B;
so the sales mix variance will be:
A
$5
x
(800 – 500)
=
$1,500 A
B
$8
x
(1,500 – 1,200)
=
$2,400 F
=
$900 F
Total sales mix variance
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Example 9
Sales Quantity variance:
Budgeted contribution per unit x (Standard sales at budgeted mix – Actual
sales at budgeted mix)
Budgeted sales 10,000 units, so the standard mix of these budgeted sales will be:
A
10,000 x 2/5
=
4,000 units
B
10,000 x 3/5
=
6,000 units.
Actual sales 13,000 units, the actual sales at budgeted mix will be:
A
13,000 x 2/5
=
5,200 units
B
13,000 x 3/5
=
7,800 units.
Sales quantity variance:
A
$2.50 x (4,000 – 5,200)
=
$3,000 F
B
$4.50 x (6,000 – 7,800)
=
$8,100 F
=
$11,100 F
Total sales quantity variance
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CHAPTER 10
Example 1 Tata
(a)
YEAR
Profit
1
2
3
4
0.35
0.35
0.35
0.35
3.15
2.1
1.05
0
11.11%
16.67%
33.33%
∞
1
2
3
4
0.35
0.35
0.35
0.35
0.315
0.21
0.105
0
0.035
0.14
0.245
0.35
(1.4-1.05)
Asset
Costaccumulated
depreciation
ROI
(b)
YEAR
Profit
(1.4-1.05)
Imputed
interest
Costaccumulated
depreciation x
cost of capital
RI
Example 2
(a)
ROI
X
Y
=
=
$2 m / $10 m
$3m / $30m
=
=
20%
10%
(b)
RI = NOPAT – internal cost of capital
X
Y
$2m - $1.5m =
$3m - $4.5m =
$0.5m
-$1.5m
Hence division A has performed better currently on both yardsticks.
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Example 3
X
ROI
RI
=
=
$80,000/$500,000
$80,000 - $75,000
=
=
16%
$5,000
Y
ROI
RI
=
=
$120,000/$1,000,000
$120,000 - $150,000
=
=
12%
-$30,000
(a)
X would accept the project on the basis of both measures. Y can accept the
project on the basis of ROI as it is higher than current one, but overall they
would resist as it still not meeting the requirements of the head office.
(b)
Head office should go for both projects. Clearly X is acceptable. But Y can
also be accepted on the basis of ROI as it will improve the results, and may
motivate the managers of Y in the long run.
Example 4 Scotia Health Consultants Ltd
(a)
Operating statement for the year ended 31 May 19X7
Medical
£000
Dietary
£000
Fitness
£000
Total
£000
450.0
600.0
450.0
1,500.0
Budget
Client fees
Health food mark-up (cost x 100%)
Salaries
(i)
Budget gross margin
120.0
120.0
(240.0)
(336.0)
(225.0)
(801.0)
210.0
384.0
225.0
819.0
(100.0)
275.0
137.5
Variances
Fee income gain/(loss)
(37.5)
Health food mark-up loss
(30.0)
Salaries increase (TN 1)
(15.0)
Extra fitness equipment
(ii)
Actual gross margin
Less
157.5
254.0
(30.0)
(75.0)
(90.0)
(80.0)
(80.0)
345.0
756.5
Company costs
Enquiry costs − budget
(240.0)
(60.0)
−
Variance
General fixed costs
(300.0)
Software systems cost
(50.0)
(iii)
Actual net profit
106.5
(iv)
Budget margin per consultation (£)
35.00
32.00
25.00
(v)
Actual margin per consultation (£)
28.64
25.40
23.79
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(b)
Competitiveness may be measured in terms of the relative success/failure in
obtaining business from enquiries from customers.
The percentages are as follows:
Uptake from enquiries
New business
Repeat business
Budget
Actual
30%
40%
25%
50%
Repeat business suggests customer loyalty.
The new business figures are
disappointing, being below the budgeted level of uptake.
In absolute terms, however, new business is 5,000 consultations ABOVE budget
whereas repeat business is 2,000 consultations BELOW budget.
There are variations within the types of consultation. Medical and dietary are
DOWN on budget by approximately 8% and 16% respectively. Fitness is UP on
budget by approximately 60%.
Flexibility may relate to the company being able to cope with flexibility of volume,
delivery speed and job specification. Examples of each may be taken from the
information in Appendix 1.
Additional fitness staff have been employed to cope with the extra volume of clients
in this area of business.
Medical staff levels have been reorganised to include the use of external specialists.
This provides flexibility where the type of advice required (the job specification) is
wider than expected and may improve delivery speed in arranging a consultation
more quickly for a client.
Dietary staff numbers are unchanged even though the number of consultations has
fallen by 16% from budget. This may indicate a lack of flexibility. It may be
argued that the fall in consultations would warrant a reduction in consultant
numbers from 12 to 11. This could cause future flexibility problems, however, if
there was an upturn in this aspect of the business.
Resource utilisation measures the ratio of output achieved from input resources. In
this case the average consultations per consultant may be used as a guide.
Medical (full-time only)
Dietary
Fitness
Average consultations per
consultant
Budget
Actual
1,000
900
1,000
833
1,000
1,208
Rise (+) or fall (−) %
−10%
−16.7%
+20.8%
These figures show that:
(1)
Medical consultants are being under-utilised. Could this be due to a lack of
administrative control? Are too many cases being referred to the outside
specialists? This may, however, be viewed as a consequence of flexibility − in
the use of specialists as required.
(2)
Dietary consultants are being under-utilised. Perhaps there should be a
reduction in the number of consultants from 12 to 11 as suggested above.
(3)
Fitness consultants are carrying out considerably more consultations
(+20.8%) than budgeted. There are potential problems if the quality if
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decreasing. Overall complaints from clients are up by 120%. How many
relate to fitness clients? It may be, however, that the new cardio-vascular
testing equipment is helping both throughput rates and the overall level of
business from fitness clients.
Quality of service is the totality of features and characteristics of the service
package that bear upon its ability to satisfy client needs. Flexibility and innovation
in service provision may be key quality factors.
The high level of complaints from clients (up from 1% to 2% of all clients) indicates
quality problems which should be investigated.
Quality of service may be improving. For example the new cardio-vascular testing
equipment may be attracting extra clients because of the quality of information
which it provides. Quality may also be aided through better management of client
appointments and records following the introduction of the new software systems.
Innovation may be viewed in terms of the performance of a specific innovation. For
example, whether the new computer software improved the quality of appointment
scheduling and hence resource utilisation; improved competitiveness in following up
enquiries and hence financial performance; improved flexibility in allowing better
forward planning of consultant/client matching.
Innovation may also be viewed in terms of the effectiveness of the process itself.
Are staff adequately trained in its use? Does the new software provide the data
analysis which is required?
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CHAPTER 11
Example 1
Variable cost
$5
Fixed costs ($40,000 / 20,000 units)
$2
Total cost per unit for Division A
$7
As there is no external market price, therefore the ideal transfer price should be
based on cost based approach ($7) with or without any profit margins depending
upon policy of the division / organisation.
Example 2
We have to see here that the division has extra capacity to produce and sell 2,000
units to the buying division, therefore the selling division will not have to incur any
additional fixed costs for this manufacture, but also have to note a point that the
division has an external market for this product.
So the ideal transfer may range from the variable costs per unit to the external
selling price.
Transfer price ranges
$15
------ $30
Example 3
There is a perfect external market for the product Sigma, therefore external market
price ($30) should be an ideal price for the selling division to maximise its
profitability and hence its performance.
Example 4
In this situation selling division can deduct selling cost from the external selling
price to revise its internal transfer price for the buying division and it could be
reduced to $26.
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