ACCA F5

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. 2

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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.

.

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 ew examiner is given the same remit as the previous examiner.

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Formulae provided in the examination paper

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FOR 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∑ 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

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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

26 156 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 GRA 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 GRA 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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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 GRA 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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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 ew 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 GRA 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 GRA 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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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 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 PR 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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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 PR 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 PR 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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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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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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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 PR 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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LINEAR PROGRAMMING – MULTI LIMITING FACTORS The aim of decision making is to maximise profit, assuming that the fixed cost does ot 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

. 6.

Optimal solution 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 PR 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.

. 1.

Identifying the optimal solution 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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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 ot binding on the decision, it is called a slack constraint.

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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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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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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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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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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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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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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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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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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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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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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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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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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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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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C H A P T ER 5 – B U D G E T I N G T YP E S

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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C H A P T E R 5 – B U D G E T IN G T Y P E S

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.

.

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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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 ecessary 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 eed 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 ature, 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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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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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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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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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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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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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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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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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

34

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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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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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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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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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Chapter 8

Standard costing and variance analysis

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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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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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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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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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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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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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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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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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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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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

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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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

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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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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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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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

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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Chapter 10

Performance evaluation

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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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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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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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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 ormally 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 et 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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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

PERFORMANCE MEASURES

EVALUATION

–

NON

FINANCIAL

Non-financial measure of performance should focus on critical success factors of a on-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 ot 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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C H A P T E R 1 1 – T R A N S F E R P R I C IN G

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

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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 o 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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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

5.2 1.9 72.1

Total Costs

7.74 2.66 100.4

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

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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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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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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 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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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

200

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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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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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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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APP E N D IX – S O LU T I O NS T O EX E R C IS ES AN D E XAM 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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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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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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(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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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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APP E N D IX – S O LU T I O NS T O EX E R C IS ES AN D E XAM P L ES

(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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APP E N D IX – S O LU T I O NS T O EX E R C IS ES AN D E XAM 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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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

234

£1,000 ADV

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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 umbers 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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