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Managing Costs and FinanceMA2FIA

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MA2 Managing Costs and Finance1. Management Information 3

2. Cost Accounting Systems and Cost Recording 17

3. Cost Classification 33

4. Accounting for Material Costs And Inventory Management 45

5. Accounting for Labour 61

6. Accounting for Overheads – Marginal Costing and Total Absorption Costing 71

7. Job, Batch and Process Costing 83

8. Cost-Volume-Profit (CVP) Analysis 93

9. Short Term Decision Making 105

10. Capital Investment Appraisal 121

11. Cash Management 137

12. Information for comparison 157

Answers to Examples 163

Answers to Questions 181

FIA MA2 Managing Costs and Finance (2019 Exams) 1




Chapter 1MANAGEMENT INFORMATION

1. Introduction

This chapter looks at management information: its purpose, sources, categories, desirable qualities and potential problems. It finishes by considering the role of a trainee accountant in a cost and management accounting system

2. The purpose of management information

Management information is used by managers to

๏ Plan the future of the business. For example, future cash flows and whether borrowing will need to be arranged or whether more employees need to be recruited.

๏ Control the progress of the business. For example whether budgets set in the planning stage will be met.

๏ Decision making. For example, what to produce or which branch to close.

Obviously, managers of different departments will usually require different information. However, managers at different levels within a department will also need different information. For example, senior managers will often require more summarised information to see ‘the whole picture’, whereas more junior managers often need more details.

3. Data and informationThe following diagram is often used to represent a computerised accounting system was shown:

Input ofdata

Processing data Output of information

Files

In fact, the diagram can apply to the processing of any information whether manually or by computer. A person (or machine) received data, processes it in some way (perhaps by using it to make a decision or to produce a report) and outputs or passes on that information to the next stage in the whole process. Often files (collections of data) have to be accessed.



For example, on receiving a customer order (input), the customer’s receivables record and the inventory price files would be accessed so that a decision could be made (process) about whether or not the order should be approved. The decision is then passed on within the organisation or sent to the customer (output).

Nothing in that description has said whether this is a computerised or a manual process.

Note that a distinction has been made between data and information. Data is ‘raw fact’; information is data with meaning. For example, a record of the height of everyone living in a certain city would be data (not much use). Once that data is processed and, for example summarised into average heights of men, women etc, then the data becomes more interesting and useful.

Similarly a list of all unpaid invoices is data which only become meaningful i.e. informative once sorted by customer to show what each owes and also, perhaps, then presented in descending order so that the customers owing most are shown at the top of any list.

However, computerised accounting systems will normally produce information:

๏ More cheaply (because fewer people need to be employed)

๏ More accurate (fewer arithmetic errors – though incorrect programs will repeatedly report incorrect information)

๏ Faster (because the processing is automated and computers work very quickly)

๏ More specific (because computers can scan through vast amounts of data and report on the note-worthy events).

๏ More complex such as analysis of sales trends

๏ Wider access because a terminal on everyone’s desk potential gives all access to information needed.

The importance of the last two qualities cannot be over-emphasised: if you are going to exercise management control you must have your attention quickly drawn to events that need you attention. Control will be poor if you have to search through vast quantities of data that is provided a month late.

Question 1 What are the three purposes, described above, for which managers use management information?

A Estimating, investigating and planning

B Planning, controlling and decision-making

C Controlling, buying and selling

D Accounting, manufacturing and auditing



Question 2 Which of the following is information rather than simply data?

1. A random list of the wages of all employees

2. A list of all stock items that haven’t sold at all in the last three months

3. A report showing where expenses are 10% or more over budget

4. A list of all invoices that have to be paid by the company

A 1 and 4 only

B 2, 3 and 4 only

C 2 and 3 only

D All items are information rather than just data

4. The features of useful management information

The features of good management information are often described and remembered using the word ‘ACCURATE’.

Accurate. Certainly accurate enough for managers to use confidently. Some managers need information accurate to the last cent whilst other are happy with accuracy to the nearest $1,000.

Complete. Missing information can be very serious. For example, omitting a cash outflow that will happen next month could be fatal for a business.

Cost-beneficial There is little point having information which costs more to provide than any benefit that arises from it.

User-targeted The information should be what users need. For example, senior managers often have to be planning for the future so need forward-looking information.

Relevant Too much information causes information overload and might mean that important matters are overlooked.

Authoritative What is the information’s source and reliability? Just because you find something by ‘Googling’ the internet does not mean the information is correct.

Timely The information should be received quickly enough to be of use to the decision-maker. Real-time on-line systems can speed up the supply of information.

Easy-to-use The information should be well-set out and described.



5. Sources and categories of informationThe main sources of information are:๏ Internal information

๏ External information

Example 1

List examples of internal and external information Internal External

In addition to internal/external, information can be categorised as:๏ Financial/non-financial

๏ Quantitative/non-quantitative

๏ Historical/future estimates

๏ Routine/ad hoc (as and when needed)

๏ Numerical/graphical

You are undertaking accountancy training and this is likely to affect your view of how important financial and non-financial information are. It is important to emphasise now the importance of non-financial information. For example, financial information can show you that sales have increased, but that might not explain why sales have increased. The cause of the improvement might be better customer service, more innovative products, or more reliable products, and none of threes is a financial measure.

Indeed financial measures are often described as lagging indicators because the information they contains often lags behind non-financial indicators. For example, customer satisfaction will rise before sales rise.



Example 2

List examples of information from each of the above category pairsFinancial/non-financial

Quantitative/non-quantitative

Historical/future estimates

Routine/ad-hoc

Numerical/graphical

Example 3

Suggest why the provision of non-financial, non-quantitative information might be important

6. Cost centres, profit centres and investment centres

A manager who is in charge of a cost centre is responsible for costs only and therefore the information that will be useful will be solely related to costs. For example, cost budgets compared to actual costs.

A cost centre could be:

๏ A subsidiary company

๏ A division

๏ A department

๏ A team

๏ A person

๏ A production line

๏ A project

๏ A machine

Examples of cost centres can include: the IT department, quality control department, the accounting department, the manufacturing facility.

A manager who is in charge of a profit centre is responsible for costs and revenues, so will be interested in information about both costs and sales.



As above, a profit centre could be:


๏ A division

๏ A department

๏ A team

๏ A person

๏ A production line

๏ A project

๏ A machine

The difference is that here, besides being responsible for costs, the head of a profit centre will also be responsible for revenues.

The revenues could be sales to outside organisations or they could be internal sales to elsewhere in the organisation. For example, an IT department could be turned from a cost centre into a profit centre if it were to be allowed to charge IT users for the services supplied.

Being head of a profit centre is usually more interesting and demanding than being just the head of a cost centre. Many people don’t get great satisfaction from ensuring that costs do not exceed budget (a cost centre managers’ responsibility), but would get much satisfaction from beating a profit budget (a profit centre manager’s responsibility).

A manager who is in charge of an investment centre is responsible for costs, revenues and the use made of the funds invested in that subsidiary or division. In addition to keeping a close eye on costs and revenues, the manager will also have to have information available about, for example, the rate of return or net present value (see a later chapter) that that division is generating.

Because costs, revenue and capital expenditure all have to be identified separately an investment centre would normally be:


๏ A division

Whether dealing with a cost, profit or investment centre, it is important that the information that is provided to managers is tailored to their needs.

Question 3

In a garage, costs are associated with each car that comes in for repair.

Cars are therefore:

A Cost centres

B Cost units

C Profit centres

D Investment units



Question 4 If a manager is in charge of an investment centre, which of the following would he or she be responsible for:

1. Costs

2. Revenue

3. Investment

4. Profit

A 1 and 2 only

B 2 and 3 only

C 1, 2 and 4 only

D 1, 2, 3 and 4

7. The limitations of cost and management accounting information

The limitations of cost and management accounting information are:๏ Potentially all the matters covered by ACCURATE (Accurate, Complete, Cost-beneficial, User-

targeted, Relevant, Authoritative, Timely, Easy-to-use.)

๏ Difficulty making future estimates.

๏ Often quantitative and financial only, but undoubtedly matters such as quality and customer service levels will be important.

๏ Can be difficult for manager with no financial training to understand.

๏ Often too inward-looking. For example, perhaps it does not give information about competitors’ selling prices.

8. The role of a trainee accountant in a cost and management accounting system.

A trainee accountant is likely to have the following roles in a cost and management system:๏ Recording transactions. For example, making posting to the ledgers.

๏ Extracting information and presenting it for management use. For example, a comparison of budget and actual figures for a period.

๏ Investigating financial matters. For example, looking into an overrun in a cost.

๏ Helping with budget preparation.

๏ Helping and supervising more junior staff.

Note that a trainee accountant will generally not be closely involved in decision-making and planning as these functions will normally be carried out by more senior staff.



9. Methods of analysing, presenting and communicating information

Example 4

Suggest ten communications media and formats

10. Suitable formats for communicating management information

For all the variety of methods suggested in Example 1, communication tends to be of three possible types:

๏ Oral/spoken

๏ Written

๏ Graphical

They have their own strengths and weaknesses:

Oral/spoken

Strength/advantage Weakness/disadvantageCan be instant Might be poorly expressed or ambiguousAllows interaction eg questions to be asked. Instant feedback.

Not good where a lot of detail has to be communicated

More personal Often no record of what was saidInformal (could also be a weakness) Informal (could also be a strength)Allows body language to be observed Message might alter over time

Written

Strength/advantage Weakness/disadvantagePrecise communication possible Takes time to produceGood for supplying detail No immediate interaction. no instant feedbackImpersonal (could be a weakness) Often no record of what was saidFormal (could also be a weakness) Formal (could also be a strength)Uniform message to all recipients. Does not allow body language to be observed.

Graphical

Strength/advantage Weakness/disadvantageEye-catching Can be open to distortion



Strength/advantage Weakness/disadvantageMemorable Can be expensive to produceCan be easy to interpret and see trends

More efficient for some purposes

Typical formats of written communication are as follows๏ Letters

Name and address of recipient

References

Date

Dear Sir

About:_______________

Body of letter ________________________________________________________________________________________________________________________________________________________________________________________________________________________

Your faithfully

Signature

Name and address of sender

‘Dear Sir’: pairs with ‘Yours faithfully’. ‘Dear Mr Smith’ pairs with ‘Yours sincerely’



๏ Email

From! _____________________________To! _____________________________CC ! _____________________________

Subject ____________________________

Note that emails are:

- Less formal than letters.

- Can easily be sent to the wrong person (with potentially embarrassing results).

- Can be composed and sent quickly without sufficient thought or care.

๏ Reports

REPORT TITLE

To:From:AboutDate

1. Introduction and terms of reference2. Paragraph 1 title3. Paragraph 2 title4. Paragraph 3 title5.6.7.8.

12. Conclusions/recommendations

Appendices

The appendices contain detailed information that is referred to elsewhere in the report.



๏ Memoranda

MEMORANDUM

To:From:AboutDate

Paragraph 1 titleParagraph 2 titleParagraph 3 titleetc

Memoranda do not have Dear Sir/Yours faithfully

Short memoranda might not have numbered, titled paragraphs.

Question 5

Your company has just investigated the possibility of opening abroad.

What would be the most suitable format in which to set out the findings?

A Report

B Letter

C Email

D Conversation

11. Distribution of reportsThere is little point in producing information and reports if these are not reliably distributed to the people who need them. Similarly, it is not satisfactory for information and reports to be distributed to the wrong people. Not only will this probably waste their time, but many reports contain confidential information which needs to be restricted. Examples of confidential information would include employees’ salary details and company performance data.

It is also important that information is produced at the right time and at the right frequency. For example, management accounts every month and by the 6th of the following month, sales analyses every Monday for the previous week.

Methods to ensure the proper distribution of information include:

๏ Circulation lists. A list of people who should each receive a copy or a list that is marked off as a copy is passed round.

๏ Calendars/spreadsheets/timetables to show employees in advance the dates by which information has to be provided and by when it should be available.



๏ Email groups. Many reposts are nowadays distributed by email. It is extremely easy when addressing an email to leave of a person who should be included or to pick the wrong email address. Email systems allow groups to be set up so that instead of listing the addresses each time you simply pick a distribution list, such as “Accounts team” and this will then ensure that the document will be sent to the email addresses of all on the team.

๏ Encryption. Very sensitive data can be encrypted before transmission. The information can only be read by recipients who know the password.

๏ Access rights. When you sign into a corporate network, your sign-in details can be used to restrict your ability to see or change information. You are given access only to information which you have been granted access rights.

๏ Envelopes. Old fashioned, but sealed envelopes are a way in which information can be kept from prying eyes. For example, in the UK several government ministers have been photographed going into government meetings carrying official papers. Unfortunately, after the photographs were enlarged, the top copies of the papers could be easily read along with hand written comments made by the ministers. A simple envelop or folder would have prevented this embarrassment.

12. Charts and graphsCharts and graphs can make information much more memorable and easier to understand

Bar chart

The graph below is a column chart:

The chart below is a bar chart of the same data:



Line chart

Scattergraph



Pie chart

Area graph

Often like a line chart, but with filled in areas:



Chapter 2COST ACCOUNTING SYSTEMS AND COST RECORDING

1. Introduction

This chapter looks at how the financial accounting system and the management accounting system interrelate. It also considers coding systems and computerised processing.

2. Cost and management accounting compared with external financial reporting

There are two sets of accounting information in many organisations:

Financial reporting information: for example, the amounts paid for purchases and wages. These are the amounts that appear in the financial statements published by businesses every year.

Cost and management accounting information: For example, how much materials and wages go into each item produced. This information is used internally by the company.

The main differences between these are:

Cost and management accounting External financial reporting

Usually produced monthly Produced annually

Reports both historical information (results so far) and future information (budgets for the next periods)

Reports historical information only (typically: statement of financial position, income statement, cash flow statement, notes)

Can be any format management finds useful Format is strictly controlled by law and accounting reporting standards

Does not have to be audited Usually audited (independently checked)

Produced for management Produced for shareholders (or other owners)

However, when wages (and many other transactions) are paid this will affect both the external financial statements and the internal cost and management accounts. The same transactions often therefore have to be dealt with in two different ways: once for the accounting information and then again for the cost accounting information. There are two approaches to these requirements:

An integrated accounting system. Here, information is recorded once for the two separate purposes. This can save time and effort at the recording stage but might increase effort at the presentation stage.



An interlocking accounting system: here separate ledger systems are maintained for the financial information and the costing information. This increases the recording effort but can be more efficient later when presenting information.

Whether integrated or interlocking, both systems rely on a flow of documentation to generate the accounting data. The flow of documentation should be planned, consistent, and subject to controls and checks otherwise the information provided will be unreliable.

3. The material control cycleThe material cycle can be depicted as:

Purchase requisition

Order goods

Receive goods

Store raw materials Issue materials to production

Manufacture products

Sell products

At each stage there should be documents or other procedures that allow control to be exercised.

Purchase requisition: there will normally be a purchase requisition note showing:๏ Sequential document number

๏ Date of requisition

๏ Stock code

๏ Quantity needed

๏ Supplier

๏ Supplier’s product code

๏ Signatures authorising the requisition

The purchase requisition notes are passed to the purchasing department where they will be examined and approved or queried. Sometimes, despite the supplier being entered on the purchase requisition, the purchasing department might ask several suppliers for quotations.



A purchase order is then raised (created). This will typically show:

๏ Our name, address and contact details

๏ Purchase order number

๏ Date

๏ Supplier’s name and address

๏ Details of goods required: product codes, description, unit price and total price.

๏ Authorisation

The order will have at least two copies: one for the supplier one for the stores to inform them that a delivery is expected.

When goods are received, they will usually be accompanied by a delivery note. This will show the information that is on the purchase order, except for the value of the goods. Goods should not be accepted before checking to a copy of the order that they have, in fact, been ordered. One copy of the delivery note is signed and kept by the supplier. Usually the receiving company will create a standard goods received note from the delivery note. The goods will be stored in the warehouse and stock records on bin cards (see below) will be updated from the goods received note.

A purchase invoice showing the payment due will be received from the supplier, and before this is approved for crediting to the suppliers account and subsequent payment, it should be matched to the order and goods received note to ensure that the correct goods have been received.

When materials are needed for production a materials requisition note should be created requesting the release of material from the stores: part/material code, quantity, job number and so on. This should be signed by the person requesting the goods. Stock records will be updated as goods are issued.

There might be production order setting out goods and labour needed for the production of the goods ordered by customers.

As goods are produced they will be transferred from the production line to the finished goods store. Stock records there should be updated with goods description, quantities and costs.

Customer orders will initiate sales. From those, despatch (or delivery notes) will be produced. These can be used as the basis for taking goods from stores, updating the bin card (see below) packing the goods and despatching them. There will usually be three copies of the delivery note: two go with the goods and of those one stays with the customer and one is signed by the customer and returned as proof of delivery receipt. One copy will stay in the despatch department in case of later queries.

Central to the material control cycle is the recording of the amount of inventory as this will determine when goods need to be ordered and will also record the receipt and issue of goods.



In manual accounting systems bin cards are used (a bin is where a specific item of inventory is stored). The equivalent records are now usually held in computer systems. A typical bin card would look as follows:

Part number A 1234 Bin number/location A1284Description 30cm bracketsPart number A 1234 Bin number/location A1284Description 30cm bracketsPart number A 1234 Bin number/location A1284Description 30cm bracketsPart number A 1234 Bin number/location A1284Description 30cm bracketsPart number A 1234 Bin number/location A1284Description 30cm bracketsPart number A 1234 Bin number/location A1284Description 30cm bracketsPart number A 1234 Bin number/location A1284Description 30cm bracketsReceiptsReceiptsReceipts IssuesIssuesIssues BalanceDate Goods

received note number

Quantity Date Requisition number

Quantity

b/f 10015/1/2013 1235 200 300

29/1/2013 1929 140 1603/2/2013 1955 120 20

10/2/2013 1384 500 520

This allows a continuous recording of stock quantities.

Question 1 What document shows the amount due to a supplier for goods bought?

A Purchase invoice

B Purchase requisition

C Goods received note

D Purchase order

Question 2 Which of the following sets out the sequence of steps in a purchases transaction

A Purchase order; purchase requisition; goods received note; purchase invoice

B Purchase order; purchase requisition; purchase invoice; goods received note

C Purchase requisition; purchase order; goods received note; purchase invoice

D Purchase requisition; purchase order; purchase invoice; goods received note

Question 3 When goods are needed for production from stores, what document is used?

A Materials requisition note


C Purchase order

D Materials order



Question 4 When goods are received, what is the name given to the document that is raised (created) at that stage.

A Delivery note



D Purchase invoice

4. The procedures and documentation to ensure the correct authorisation, analysis and recording of direct and indirect material costs

Direct materials are those which can be specifically traced to a unit of production.

Indirect materials cannot be specifically traced to a unit of production. For example, paint being used in the construction of a product will be not be identified as going to a specific product.

Direct materials will be subject to formal requisition requests. Indirect material might simply be made available. For example, it is hardly likely to be cost-beneficial to account for individual screws or the use of drops of adhesive.

The costs of materials can be traced to production: the cost of direct material can be linked to specific items but the cost of indirect materials is likely to be allocated on an average basis.

Question 5 In a factory making chairs, there are four types of material:

1. Wood

2. Glue

3. Polish

4. Fabric for covering the chair

Which would be classified as direct and indirect material?

A Direct: 1 and 2; indirect 3 and 4

B Direct: 1 and 4; indirect 2 and 3

C Direct: 2 and 3; indirect 1 and 4

D Direct: 1 and 3; indirect 2 and 4



5. The procedures and documentation needed to ensure the correct authorisation, coding, analysis and recording of direct and indirect labour and expenses.

Direct labour is labour that can be directly identified with a unit of production. A mechanic repairing a car would be an example of direct labour.

Indirect labour cannot be identified with specific units of production. For example a supervisor’s time is spread amongst all workers.

Labour time can be recorded using clock cards, time sheets, or by an assumption that everyone works a standard day. The clock card system is where the employee swipes a card through a reader when getting to work and again when leaving (“clocking-in and clocking-out”. The time working (or at least the time at work) can be calculated and wages calculated from that). The clocking-in and clocking-out processes should be supervised to ensure that employees do not clock in/out for friends.

Time sheets should be reviewed to ensure that time is recorded accurately against the jobs involved. For example, when an audit assistant spends time on a specific audit, an account code (or job code) will placed against that time on the time sheet. This code will enable the total time spent on each job by each employee to be accumulated.

Any overtime worked should be authorised by supervisors.

Employee wage rates should have been approved by the human resources department.

Question 6

In a factory there are four types of job:

1. Machine operators

2. Supervisors

3. Maintenance engineers

4. Quality control checkers

Which would be classified as direct and indirect labour?



C Direct: 1 and 3; indirect 2 and 4




6. The procedures and documentation to ensure the correct analysis and recording of sales.

Sales transactions will normally be initiated by receiving an order from a customer. It is important that orders are recorded as soon as possible, for example by entering them in a register (book).

The customer’s account will be checked to ensure that the customer is paying for previous orders satisfactorily and will remain within any credit limit if the new order is approved.

As outlined above, from the order a multi-set delivery note or despatch notes will be raised so that the goods can be packed and despatched to customers. It is, of course vital that all despatched goods are invoiced otherwise the company will effectively be giving goods away. One way of doing this is to enter invoice numbers against the original register of orders. This should mean that all orders received have been despatched and invoiced.

In a manual system, the invoices will be listed in the sales day book. Sometime, the sales day book can have several columns for the sales of different categories of goods. The sum of these lists will be the total of sales made in each category.

Example 1

List three examples documents that are related to each of purchases, sales and inventory (three for each category).

Purchases

Sales

Inventory



7. The use of codes in categorising and processing transactions

It is universal practice in accounting systems to use coding systems to refer to customers, suppliers, accounts and employees. Codes are used because they are concise and precise, and can be subject to computer checking

Concise: instead of referring to a product as a “50cm, high resolution LED monitor”, the product is given a code such as 50HRL. This is much quicker to write or type.

Precise: there might be several makes of 50cm high resolution LED monitors and information might be confusing and ambiguous if the manufacturer (Sony, Panasonic, Samsung, LG etc) wasn’t specified. A code number can therefore be used to ensure that products and people are referred to uniquely eg 50HRLLG.

Checking: if all inventory codes are 7 digits long then forms and input screens can be designed for this. Computers can check that all 7 digits are present; sometime more sophisticated checks can be carried out on the structure off the code. This reduces the chance of errors.

Processing: Codes can also help in processing transactions. For example if all income-related accounts have the structure 1xxxx, all expense-related accounts have the structure 2xxxx, all asset-related accounts 3xxxx and all liability accounts 4xxxx, then this will help the production of the income statement (all 1xxxx amounts less all 2xxxx amounts) and the statement of financial position (3xxxx as asset amounts and 4xxxx amounts as liabilities). This is particularly needed in computerised accounting systems because the computer cannot understand that, say, rent is an expense, but doesn’t need this understanding so long as rent is coded, say 21892. Because it starts with ‘2’ it will be treated as an expense.



8. Different methods of codingThere are several methods of coding. Codes should be:๏ Simple to use

๏ Understandable

๏ Concise

๏ Precise

๏ Expandable

As we will see, these requirements can be in conflict.

Sequential codes

In this method products or customer are simply allocated numbers in sequence:

0001! ! Abrahams0002! ! Adkins0003 ! ! Ahmad...

It is simple and concise, but as constructed might have some faults:

1. There is no relationship at all between the code and the item/person being encoded.

2. Expansion might be difficult once you have over 9999 customer if documents and computer files can hold only four digits. Additionally, if someone called Affleck becomes a customer, he will have to be tagged onto the end of the sequence ie not reflecting alphabetical order. To avoid this problem, often sequence codes proceed as 0010, 0020, 0030…etc so that gaps are built in for future use.



Hierarchical (or significant digit) codes

Here, are you progress through the code, information become increasingly specific. Many libraries use this system to code their books using the Dewey Decimal System

500 Natural sciences mathematics ..510 Mathematics520 Astronomy & allied sciences530 Physics540 Chemistry & allied sciences550 Earth sciences560 Paleontology, paleozoology570 Life sciences580 Botanical sciences590 Zoological sciences..555 Earth sciences of Asia

In a business, hierarchical codes could be used to code the accounts in the general ledger. For example a code such as 3112 could be interpreted as the Machinery Cost Account, using the following system.

3 1 1 21 = expenses2 = income3 = assets4 = liabilities

1 = non-current assets2 = current assets

1 = cost2 = accumulated depreciation

1 = property2 = machinery3 = office equipment4 = motor vehicles

The great advantage of this type of code is that its structure provides information both to human users and to computers. For example, it would be easy to program the compute to work out the total cost of all fixed assets: simply add up all accounts starting 311.

Block codes

These lie somewhere between simple sequence codes and the full, detailed hierarchical code. They start off giving some information but then lose enthusiasm. So for general ledger codes you might have

1xxx = expenses2xxx = income3xxx = assets4xxx = liabilities



Faceted codes

These are an improvement of block codes and provide more information but lack a logical hierarchical structure. The code is broken down into sections or groups of digits and each group codes for a particular attribute.

For example and employee code could be:

Facet 1 Sex of employee:! ! ! 1 = male; 2 = female

Facet 2 Department:! ! ! ! 01 = accounts; 02 = sales; 03 = IT etc

Facet 4 Full or part time! ! ! 1 = full time; 2 = part time

Facet 5 Weekly or monthly paid:!! ! 01 = weekly; 02 = monthly

Mnemonic

All the codes illustrated do far have been purely numerical. Mnemonic codes contain letters to help humans to learn what the codes mean. The hierarchical code above:





could then become

A N C ME = expensesI = incomeA = assetsL = liabilities

N = non-current assetsC = current assets

C = costA = accumulated depreciation

P = propertyM = machineryO = office equipmentM = motor vehicles

It is not common to have full mnemonic codes and often just the first character will be mnemonic and the rest will follow another system.



Question 7 A company uses the following hierarchical system:





Which of the following correctly codes for the accumulated depreciation on cars?

A 1212

B 4124

C 3124

D 2133

Question 8 A company uses a block code with the following structure:

1xxx = expenses

2xxx = income

3xxx = assets

4xxx = liabilities

Which on of the following accounts should not appear in the statement of financial position?

A 4321

B 3214

C 2234

D 3123

Question 9

What is the name given to a code in which the level of detail increases in a logical way as you work through the code?

A Sequence

B Hierarchical

C Faceted

D Block



Example 2

List three advantages of using coding systems

Example 3

List the desirable attributes of a coding system

9. Computer systemsMany, if not most, cost accounting systems are now computerised. As mentioned earlier this brings advantages relating to cost, speed, accuracy, more complex processing, and wider availability of information. Computer systems can be depicted by the following diagram:

Input ofdata

Processing data Output of information

Computer files

There follows a brief description of input, storage, processing and output technology found in modern systems.



Input methods

Keyboard Flexible, but slow and error proneBar-code scanning Inflexible, but fast and accurateCharacter recognition Flexible, fast and accurate, but characters have to

be well-writtenRFID tags ‘Radio frequency identification tags’ Commonly used in inventory tracking where

each unit has a unique tag. Cheat, accurate but inflexible

Mouse (or other pointing device, such as touch screens)

Best for making choices and selections.

Voice input Accuracy is Improving rapidlySmart cards/magnetic strip cards Eg a credit card with information embedded on a

chip. Quick, accurate, but inflexibleOptical mark readers Used for specialist applications such as multiple

choice exam answer sheetsCameras For example, face recognition as used for security

and some social networking sites.

Output methods

Printers Ink-jet or laser. A great range of speed is available. Can be colour or black and white. These are used to produce hard output.

VDU (visual display unit)/monitor/screen Fast. Used for temporary output and there is no cost of consumables. Can be used in conjunction with touch screen input.

Voice output Not widely used but becoming more common. For example, Apple’s Siri application.

3D printers An emerging technology in which physical products are built up layer by layer. The process is known as additive manufacturing, and can allow complex items to be made much more cheaply than conventional manufacturing.



File storage

Hard discs Most personal computers have an internal hard drive where most of their data is stored. These are usually mechanical spinning discs, but laptops now often come with an option to have solid state storage. These have no moving parts and can be more robust. So far, solid state drives are more expensive than the older mechanical drives.

It is also possible to have external drives. These can be very useful for the transfer or backing-up of data.

USB sticks/memory sticks Interchangeable solid state memory. Excellent for data transfer and small backups.

‘The cloud’ Instead of holding data locally, it can be uploaded to ‘the cloud’. The data is then stored on third party file-servers at a remote location.

CDs and DVDs Becoming less common, though can still be used to transfer data and to back-up data. Often they are write-once only, meaning that data once written cannot be changed. This is useful for archive purposes.

Tapes Rare now, but still used for back-up of data.

Processing

Personal computers and laptops Small computers. They can be joined together to form a network and this allows data sharing.

There are two main operating system technologies: Microsoft and Apple. Microsoft uses Windows and Apple uses OS X. Both use graphical user interfaces consisting of WIMPs: windows, icons, mouse, pull-down (or pop-up) menus.

Mainframe Mainframe computers are computers primarily used by large companies and governments for bulk processing.





Chapter 3COST CLASSIFICATION

1. Introduction

This chapter looks at how costs can be classified and how profit statements can be prepared using both marginal cost and total absorption costing approaches.

2. The nature and types of cost classificationCosts can be classified in a number of different ways:๏ By their behaviour. Do they increase as an organisation gets busier or do they tend to stay the

same? This is important when it comes to budgeting as it is essential to be able to predict how costs are likely to change.

๏ By their location. Where in the organisation are they incurred? For example, costs incurred in the factory are relevant to working out the cost of production. However, costs incurred in storing and delivering finished goods are not relevant to production.

๏ By their function. For example costs related to research and development, marketing, training, manufacturing.

๏ By the person responsible for their control. All costs need to be controlled and there should be a clearly identified person who is responsible for the control of each cost. For example, the managers of a branch might be held responsible for the costs incurred there.

๏ By their type. For example, material, labour, other production expenses, such as the cost of running machinery.

๏ By their traceability. Are they direct or indirect? Direct costs are closely related and traceable to each item produced. Indirect costs are not so easy to relate and trace to each unit of production.



3. Variable, fixed, semi-variable and stepped fixed costs

These terms relate to how costs behave as the activity level of an organisation changes.

Variable costs: these are directly proportional to the level of activity.

If the number of units produced doubles, then variable production costs will double also. An example would be the cost of material used to produce units.

If the number of units sold increases by 20% then variable selling and distribution costs would increase by 20% also.

On a graph, variable costs would look like:

Total cost ($)

Activity level ($)

Fixed costs: constant over a wide range of activity

An example would be the factory rent. It does no matter how many units are made, the rent is fixed.

On a graph, fixed costs would appear as:

Total cost ($)

Activity level ($)

Note that the cost per unit will decrease as the activity level decreases. For example, say that the rent was $10,000 and 1,000 units were made. Then you could argue that it takes $10 rent to make a unit ($10,000/1,000).



If, however, 10,000 units were made, the rental cost per unit would be only $1 ($10,000/10,000). Higher production volumes are making better use of the fixed resource.

Semi-variable costs have a fixed element and a variable element.

An example would be a telephone bill. Usually there is a fixed cost for the line rental then each minute of telephone calls causes an additional cost.

On a graph, fixed costs would appear as:

Total cost ($)

Activity level ($)

Fixed element

Variableelement

Stepped fixed costs: constant over a range of activity then a sudden increase, then constant again

An example would be the salary of supervisors. One supervisor for up to six workers, two for up to 12 workers, etc.

On a graph, stepped fixed costs would appear as:

Total cost ($)

Activity level ($)



Question 1 A mail order company distributes sales items by post. All other communication is by email or the internet. Are postage costs likely to be:

A Fixed

B Variable

C Semi-variable

D Stepped fixed

Question 2

A company rents a factory that will allow production of up to 10,000 units per month.

If the company is considering a new order that would push production to 15,000 units, rental costs will be:

A Fixed

B Variable

C Semi-variable

D Stepped fixed

Question 3 A company pays its staff a basis wage plus a bonus based on production.

Wage costs are likely to be:

A Fixed

B Variable

C Semi-variable

D Stepped fixed



4. Analysing semi-variable costs using the high-low (or range) method.

When trying to draw up budgets, which are really just plans quantifying sales and costs, it is essential to understand how costs will behave so that reasonable predictions can be made.

Variable costs are easy as they vary in direct proportion to output. Fixed costs are relatively easy as they stay fixed within a range of activity. At some point there might be a step, but that is not usually difficult to build into a budget. However, semi-variable costs need to be split into their fixed and variable parts so that each component can be handled appropriately.

Assume that the fixed part of a semi-variable cost = F, and that the variable part of the semi-variable cost is V per unit. Then:

At a high production level P2: Total semi-variable cost = F + V P2

At a low production level P1: Total semi-variable cost = F + V P1

Subtracting:

P2 – P1 = VP2 – VP1

So the increase in units (P2 – P1) has caused the increase in total variable costs

Therefore, the variable cost per unit will be the increase in total costs divided by the increase in the units.

Example 1

A company has obtained the following results from a year of trading:

Quarter Volume of production

Total cost $

1 10,000 220,0002 20,000 340.0003 25,000 370,0004 18,000 320,000

How can you tell that these costs are not purely variable?

Using the high-low (range) method, estimate the fixed cost and the variable cost per unit

How accurate are these estimates?



Example 2

A company has obtained the following results from four years of trading:

Year Volume ofproduction

Total cost $

2009 10,000 220,0002010 20,000 340.0002011 40,000 430,0002012 18,000 320,000

When production volumes are above 30,000 units fixed costs rise by 50%.

What will predicted costs be at output of (a) 25,000 units (b) 35,000 units?

Question 4

A company has measured production volume and costs over five days. Results are:

Day Volume Cost ($)Monday 2,000 5,300Tuesday 3,000 7,000Wednesday 4,000 9,000Thursday 2,000 5,400Friday 1,000 3,000

Using the high-low method, what will total costs be on a day where production is 3,500 units?

A $8,750

B $7,000

C $8,000

D $8,167



Question 5

A company has measured production volume and costs over three periods. Results are:

Period Volume Cost1 4,000 9,7002 3,000 7,0003 1,000 3,400

Because overtime rates have to be paid, variable costs increase by 50% for each unit made in excess of 3,000 units.

Using the high-low method, what will total costs be on a day where production is 3,500 units?

A $7,900

B $11,050

C $8,650

D $8,350

5. The effect of activity levels on unit costs

Total pure variable costs increase in direct proportion to units produced. If output doubles then total variable costs double. However, in simple cases the variable cost per unit will stay constant. Variable cost per unit might change at high levels of production where overtime has to be paid or more expensive supplies of raw material have to be used.

Total pure fixed costs are constant over a given range of production. However, the fixed cost per unit will decrease because the constant fixed costs are being spread over more items. Better use is being made of fixed costs are more units are made.

Look at this example

Variable cost per unit = $5

Fixed costs = $1,000

Volume of production

Variable costs ($5 x

production)

Fixed costs Total costs Total costs Per unit

10 50 1,000 1,050 10550 250 1,000 1,250 25

100 500 1,000 1,500 15200 1,000 1,000 2,000 10600 3,000 1,000 4,000 6.7800 4,000 1,000 5,000 6.25

1,000 5,000 1,000 6,000 6.0



Question 6

When a company makes 5,000 units in a period, the total absorption per unit is $20, of which $12 is the variable cost.

What will the total absorption cost per unit be if production is 8,000 units?

A $20.0

B $17.0

C $15.5

D $12.50

Question 7

When a company makes 10,000 units in a period, the total absorption per unit is $50, of which $30 is the variable cost.

If the company wants to reduce the total cost per unit to $46, how many units will it need to produce?

A 12,500

B 10,870

C 40,000

D 11,538



6. Direct and indirect expenses

There are three types of production expenses:

๏ Material

๏ Labour

๏ Expenses (often known as overheads)

Each can be direct or indirect

๏ Direct material means material traceable to units of production (for example, tracing wood into furniture)

๏ Indirect material means material that is not traceable into specific units (for example, tracing sand paper in sanding machinery.

๏ Direct labour means labour directly involved in making units.

๏ Indirect labour. Not directly involved with specific units. For example maintenance engineers.

๏ Direct expenses. Rare, but an example would be a royalty that had to be paid for each unit of production.

๏ Indirect expenses. For example, the rent and heating expenses for the factory.

Direct expenses are usually also variable costs.

Indirect expenses are usually fixed or stepped-fixed.

Businesses also have non-production overheads. These are costs which have nothing to do with production such as the accounting department, advertising, distribution, head office costs.

Question 4

Lubricating oil poured over a drilling machine to reduce friction and to keep it cool would be classified as a

A Direct material cost

B Indirect material cost

C Direct expense

D Indirect expense



7. Capital and revenue expenditure

Capital expenditure is expenditure on acquiring or upgrading non-current assets. Such expenditure will enhance the scope of an operation’s activities. Non-current assets will provide benefits for more than one accounting period.

Examples are: buying additional production machinery, extending the office, upgrading the memory in a computer.

Revenue expenditure is incurred for the purposes of trading or for maintaining the earning capacity of non-current assets.

Examples are: rent, electricity, advertising and the repair and maintenance of machinery.

Revenue expenditure will appear as an expense on the income statement. Sometimes a payment will relate to a single accounting period; sometimes if might span more than one. For example, if rent of $18,000 is paid for the year ended 30 September 2014, then 3/12 of that ($4,500) will relate to the accounting year ended 31/12/2013 and 9/12 ($13,500) will relate to the accounting period ending 31/12/2014.

In contrast, several periods will always benefit from capital expenditure. For example, a machine bought for $72,000 might be expected to last for 6 years. At the end of that period it might be worth nothing, so it would be fair to charge each of the 6 years with $72,000/6 = $12,000 to match, as fairly as possible the income of each year with the cost of the machine.

The $12,000 cost per year is known as depreciation.

There are four approaches to calculating depreciation:

๏ Straight line

๏ Reducing balance

๏ Machine hours

๏ Product unit

All aim to write off (ie gradually expense) the asset over its estimated useful life.

Straight line

This is the easiest approach: the asset is written down from cost to residual value over its estimated useful life.

Example 3

Cost = $24,000; scrap (residual) value at end of life $4,000; estimated useful life = 5 years.



Reducing balance method

Each year’s depreciation is based on the brought forward written down value

Example 2

Cost = $24,000 to be depreciated at 25% pa on the written down basis.

Machine hours method

Each year’s depreciation is based on the hours worked that year divided by the machines initial total estimated working hours

Example 5

Cost = $24,000; scrap (residual) value at end of life $4,000; estimated total machine hours 60,000. Hours worked in the year = 10,000

Product unit method

Each year’s depreciation is based on units produces in that year divided by estimated total units the machine could make over its life.

Example 6

Cost = $24,000; scrap (residual) value at end of life $4,000; estimated total production = 200,000 units. Units made in the year = 25,000





Chapter 4ACCOUNTING FOR MATERIAL COSTS AND INVENTORY MANAGEMENT

1. Introduction

This chapter looks at how material costs are accounted for and how inventory can be valued.

2. Material cost classification

Raw materials are purchased and then undergo further processing or are incorporated into products. Raw materials can be basic materials such as chemicals, flour, or lengths of wood. Or raw materials can be items which have been manufactured by the supplier, such as components and parts for use in production.

Work in progress refers to partly made products. They have progressed from the bought in stage (raw materials) but are not yet complete.

Finished goods are complete and are ready for sale.

Direct materials are those that can be easily identified with or traced to a unit of production. For example, microprocessor chips being incorporated into laptop computers.

Indirect materials are not easy to trace to a unit of production. For example, the solder used to secure electronic components in circuits, or the adhesive used to join components.

Question 1 In a factory making chairs, there are four types of material:

1 Wood

2 Glue

3 Polish

4 Fabric for covering the chair

Which would be classifies as direct and indirect material?







3. Accounting for material costs

Materials progress through a factory as follows:

Raw materials Work-in-progress Finished goodsSupplier Customer

Movement of the material between each stage has to be accounted for in a series of ‘T’ accounts.

As material moves into a department or category, the T account is debited with the cost.

As material moves out of a department or category, the T account is credited with the cost.

Raw materials Work-in-progress Finished goods

Supplier Customer

It can be useful to record units of material as well as value.



Illustration

Assume there is no opening inventory at any stage.

1,000 units of raw material are bought for $5 per unit800 are issued to production where labour worth $2 per unit and production expenses of $1 per unit are added. 700 of the units are transferred out to Finished goods at the end of the period. Although finished, 100 units are still in work in progress at the end of the period.

500 units finished units are sold.

Raw materialsRaw materialsRaw materialsRaw materialsRaw materialsRaw materialsUnits $ Units $

Payables 1,000 5,000 To WiP 800 4,000

C/f Closing inventory 200 1,000

1,000 5,000 1,000 5,000

Work-in ProgressWork-in ProgressWork-in ProgressWork-in ProgressWork-in ProgressWork-in ProgressUnits $ Units $

From raw materials 800 4,000 To Finished goods 700 5,600

Labour 1,600

Overheads 800 C/f Closing inventory 100 800

800 6,400 800 6,400

Finished goodsFinished goodsFinished goodsFinished goodsFinished goodsFinished goodsUnits $ Units $

From WIP 700 5,600 Cost of sales 500 4,000

C/f Closing inventory 200 1,600

700 5,600 700 5,600

Note: finished goods and closing inventory are values at:Material $5 + Labour $2 + Overheads $1 = 8 per unit

Question 2 Which double entry records the movement of raw material to work-in-progress?

A Cr WIP; Dr Raw material

B Dr Purchases; WIP

C Dr WIP; Cr Raw material

D Cr Raw material; Dr Finished goods



4. Material requirements making allowance for sales and product/material inventory changes

Raw materials that have to be purchased are not necessarily the same as the raw materials that will be used in production. This is because there might be changes in raw material inventory. It would, for example be possible to use raw materials in a period without having to purchase any if there were already enough raw materials in inventory.

The adjustments needed are:

Raw material purchased = Raw material

used + Closing stock – Opening

stock

The company has to buy enough to cover usage and to provide enough for closing inventory, but it gets a ‘head start’ because there is already some in opening inventory.

Similarly:

Units produced = Units sold + Closing stock (finished goods) – Opening stock

(finished goods)

Question 3 Opening inventory = 20,000 units.

Units to be sold = 90,000

Closing inventory to be 10,000 units.

How many units must be bought or produced?

A 80,000

B 100,000

C 90,000

D 120,000

Question 4 Opening inventory of raw material = 1,000 kg

Units to be made = 5,000 (each takes 3kg of material)

Closing inventory of raw materials to be 1,500 kg

How many kilograms of raw material must be bought?

A 5,500

B 14,500

C 15,500

D 4,500



The calculation of the amount of material needed for production can be complicated if there is wastage. For example, to produce 80kg of good output, it might be necessary to input 100kg. The loss of $10 does not necessarily mean that someone has been careless; a loss might be an inevitable part of the production process (for example, evaporation or removing impurities).

Obtaining 80kg from 100kg can be called a yield of 80%; alternatively, it can be defined as having a wastage rate of 20%. So:

Input – Wastage = Output100 – 20 = 80

The wastage id 20% of input but 25% (20/80) of output.

If the required output is top be 1,000kg, the input can be worked out using the above model:


1,250 – 250 = 1,000

Question 5 Opening inventory of raw material = 1,000 kg

Units to be made = 5,000 (each weights 3kg)

Closing inventory of raw materials to be 1,500 kg

The yield is 75% by weight

How many kilograms of raw material must be bought?

A 20,500

B 19,500

C 11,750

D 10,750

5. Inventory purchase, use and sale

The purchasing process will normally start with a purchase requisition note that will normally show the following:

๏ Sequential document number

๏ Date of requisition

๏ Our stock code

๏ Quantity needed

๏ Supplier

๏ Supplier’s product/stock code

๏ Signatures authorising the requisition



The purchase requisition notes are passed to the purchasing department where they will be examined and approved or queried. Sometimes, despite the supplier being entered on the purchase requisition, the purchasing department might ask several suppliers for quotations.

A purchase order is then raised (created). This will typically show:

๏ Our name, address and contact details

๏ Purchase order number

๏ Date

๏ Details of goods required: product codes, description, unit price and total price.

๏ Authorisation

The order will have at least two copies: one for the supplier one for the stores to inform them that a delivery is expected.

When goods are received, they will usually be accompanied by a delivery note. This will show the information that is on the purchase order, except for the value of the goods. Goods should not be accepted before checking to a copy of the order that they have, in fact, been ordered. One copy of the delivery note is signed and kept by the supplier. Usually the receiving company will create a standard goods received note from the delivery note. The goods will be stored in the warehouse and stock records on bin cards (see below) will be updated from the goods received note.

A purchase invoice showing the payment due will be received from the supplier, and before this is approved for crediting to the suppliers account and subsequent payment, it should be matched to the order and goods received note to ensure that the correct goods have been received.

When materials are needed for production a materials requisition note should be created requesting the release of material from the stores: part/material code, quantity, job number and so on. This should be signed by the person requesting the goods. Stock records will be updated as goods are issued.

There might be production order setting out goods and labour needed for the production of the goods ordered by customers.

As goods are produced they will be transferred from the production line to the finished goods store. Stock records there should be updated with goods description, quantities and costs.

As goods are sold, customer orders will be received and from those, despatch (or delivery notes) produced. These can be used as the basis for taking goods from stores, updating the bin card (see below) packing and despatching them. There will usually be three copies of the delivery note: two go with the goods and of those one stays with the customer and one is signed by the customer and returned as proof of delivery receipt. One copy will stay in the despatch department in case of later queries.

Central to the material control cycle is the recording of the amount of inventory as this will determine when goods need to be ordered and will also record the receipt and issue of goods.

In manual accounting systems bin cards were used (a bin is where a specific item of inventory is stored). The equivalent records are now usually held in computer systems. A typical bin card would look as follows:



Part number A 1234 Bin number/location A1284Description 30cm bracketsPart number A 1234 Bin number/location A1284Description 30cm bracketsPart number A 1234 Bin number/location A1284Description 30cm bracketsPart number A 1234 Bin number/location A1284Description 30cm bracketsPart number A 1234 Bin number/location A1284Description 30cm bracketsPart number A 1234 Bin number/location A1284Description 30cm bracketsPart number A 1234 Bin number/location A1284Description 30cm bracketsReceiptsReceiptsReceipts IssuesIssuesIssues BalanceDate Goods

received note number

Quantity Date Requisition number

Quantity

b/f 10015/1/2013 1235 200 300

29/1/2013 1929 140 1603/2/2013 1955 120 20

10/2/2013 1384 500 520

This allows a continuous recording of stock quantities.

A particularly important figure to calculate is free inventory. This is

Free inventory = Quantity on hand plus units ordered less units allocated for use

The calculation of free inventory has the advantage of anticipating stock movements so that receipts and issues that are known about are taken into account when assessing the need to order.

To ensure that the inventory as recorded on the bin cards is accurate, companies should carry out periodic stock counts (sometimes called cycle counts) and correct the amounts on the bin cards. Some companies carry out one only stock count per year.

Question 6 What document shows the amount due to a supplier for goods bought?

A Purchase invoice



D Purchase order



Question 7 Which of the following sets out the sequence of steps in a purchases transaction?

A Purchase order; purchase requisition; goods received note; purchase invoice

B Purchase order; purchase requisition; purchase invoice; goods received note

C Purchase requisition; purchase order; goods received note; purchase invoice

D Purchase requisition; purchase order; purchase invoice; goods received note

Question 8 When goods are needed for production from stores, what document is used?

A Materials requisition note


C Purchase order

D Materials order

Question 9

There are currently 120 units of an item in inventory. There are material requisitions amounting to 40 units that have not yet been acted on and there are 90 units on order.

What is the free inventory?

A 70

B 170

C 120

D 250

Question 10 When goods are received, what is the name given to the document that is raised (created) at that stage.

A Delivery note



D Purchase invoice



6. Different methods used to price materials issued from inventory and to value closing inventory

Consider the following:

12 March 20X4: buy 1000 units at $5 each21 March 20X4: buy 500 units at $6 each31 March 20x4: sell 800 units at $12 each.

Clearly revenue will be 800 x $12 = $9,600, but what is the cost of the units sold? Which have been sold? What is their value and the value of the inventory left?

You have to know four approaches:๏ FIFO

๏ LIFO

๏ Cumulative weighted average

๏ Periodic weighted average

FIFO (First-in, first out)

This method assumes that the goods that arrive first are the first to be used. It is only an assumption: apart from their price all goods of a given type are identical and therefore you don’t know, or care, how they are physically used.

So, in the above case, all 800 units sold would be assumed to be those delivered on 12 March. They would have a cost of 800 x $5 = $4,000 and the value of the inventory remaining would be 200 x $5 + 500 x $6 = $4,000.

Note that receipts and sales are handled on a strict time basis.

LIFO (Last-in, first out)

This method assumes that the goods that arrive last are the first to be used. As before It is only an assumption: apart from their price all goods of a given type are identical and therefore you don’t know, or care, how they are physically used.

So, in the above case, the 800 units sold would be assumed to be all 500 of those delivered on 21 March plus 300 from the March 12 delivery. They would have a cost of 500 x $6 plus 300 x $5 = $4,500, and the value of the inventory remaining would be 700 x $5 = $3,500.

Note that receipts and sales are handled on a strict time basis.



Cumulative weighted average

Every time units are added, a new average price is calculated. Any time goods are removed they are removed at the prevailing average.

12 March 20X4: buy 1000 units at $5 each21 March 20X4: buy 500 units at $6 each31 March 20x4: sell 800 units at $12 each.

$12 March 20X4 1000 @ $5 5,00021 March 20X4 500 @ $6 3,000$5.33 = average cost 1,500 @ $5.33 8,00031 March 20X4 (800) @ $5.33 (4,267)Closing inventory 700 @ $5.33 4,733

Note:

Sales do not alter the average cost.

Receipts and sales are handled on a strict time basis.

Periodic weighted average

Here, a new inventory value is calculated at the end of a set period. The cost of goods used is given by:

Cost of opening inventory + cost of purchases in the periodUnits in opening inventory + units purchased in the period

So, all units used in the period will have the same cost.

In the above simple example this method would give the same result as the cumulative weighted average approach.



Example 1

Recent results of a division are:

Date Units Unit price

1 April Opening inventory 1,000 5.005 April Purchased 500 6.009 April Sold 200 N/a14 April Purchased 600 5.5021 April Sold 1,200 N/a

Calculate the cost of inventory used each time and the cost of the inventory remaining at the end of the period using:(a) FIFO(b) LIFO(c) Average cumulative cost(d) Periodic average cost

Advantages and disadvantages of the methods:

Advantages Disadvantages

FIFO • Permitted by accounting standards as an acceptable approach to inventory valuation

• Closing inventory has a value close to its replacement value

• Might reflect physical use of stock

• Requires care to get it right

LIFO • Inventory is issued at close to its current cost (significant if there is high inflation of volatile stock prices)

• Might reflect physical use of stock

• Not permitted as a stock valuation method under financial reporting standards

• Requires care to get it right

Average stock values

• Averages out stock price fluctuations

• Relatively easy to work out.

• Permitted by Financial Reporting Standards



7. The need for inventory

Inventory is held for the following reasons:

๏ To cope with erratic demand

๏ To deal with unreliable supplies

๏ Because raw material is seasonal and must be bought when available.

๏ Because demand is seasonal. Manufacturing at a constant rate and storing in inventory might be cheaper than paying employees overtime during busy periods.

๏ To qualify for bulk discounts, large volumes must be purchased

๏ Because prices are volatile and large quantities are bought when prices seem low.

๏ The production process requires time. For example, Scotch whisky matures for many years.

๏ To provide flexibility in case of machine breakdown

Some businesses attempt just-in-time inventory management (JIT), where the aim is to have no inventory at all. When a customer order is received, material is ordered for production and the goods produced and despatched.

JIT requires very good management information systems and integrated systems to ensure that everything works like clockwork. Suppliers must be very reliable and need to be physically close if goods have to transferred by road or sea. You cannot really organise JIT if it takes goods two months to arrive from suppliers.

Although costs are saved because no inventory has to be held, JIT has dangers. If a suppliers doesn’t supply on time or a machine breaks down then production will soon stop, wasting huge amounts of money 9as employees will usually still have to be paid) and damaging the company’s reputation with its customers.

8. The managing inventory

When inventory is held, there are two main amounts that have to be determined;

๏ The reorder level When orders should be placed. How low should inventory be allowed to fall before an order is placed?

๏ The reorder quantity How much should be ordered?

These are independent quantities.

If the usage rate of inventory and the lead time (the delay between placing the order and receiving the goods) were constant, the reorder level would be easy to work out.

Reorder level = Daily usage rate x lead time (days)

So, if 120 units were used per day, and the lead time is 4 days, reorder level (ROL) = 4 x 120 = 480 units.

However, both usage and lead times can vary. It is usually very important to businesses not to run out of stock (a ‘stock out’) because that will be expensive and cause ill-will with customers. Therefore, when usage and lead times vary the reorder level is set to;



Reorder level = maximum usage rate x maximum lead time

This should prevent stock outs.

The minimum stock level will be:

Minimum stock level = Reorder level – average usage x average lead time

This is not the absolute minimum to which inventory can fall; it is the average minimum stock level.

The maximum stock level will be

Maximum stock level = Reorder

level + reorder quantity –

(minimum usage x

minimum lead time)

Example 2

Inventory statistics are:

Maximum usage/day 20Minimum usage/day 12Average usage per day 15Maximum lead time 11 daysMinimum lead time 4 daysAverage lead time 6 daysReorder quantity 1,000 units

Calculate the (a) Reorder level(b) Minimum stock(c) Maximum stock



9. The economic order quantity

The economic order quantity (EOQ) is the order quantity which minimised stockholding costs. There are two sets of costs relevant;

The holding cost. This is made up of costs such as financing the inventory, storing it, and the risks of the stock being damaged, deteriorating or becoming out-of-date.

The reorder cost. This is the administration cost of raising requisitions and orders, receiving the stock and processing the invoices.

For example:

Annual demand for inventory 20,000 units

Order quantity is 1,000 units per order

Ordering costs = $50/order

Holding cost = $5 per unit per year.

Holding costs: the maximum inventory is assumed to be 1,000 units ie the reorder quantity. That is then used up steadily and just as the last unit is used, another 1,000 units will be received.

Stock level 1,000

Average stock level 500

Time

The average stock level will be 500 (order quantity/2)

So the annual holding cost will be 500 x $5 = $2,500.

Ordering costs: if annual demand = 20,000 units and order quantity = 1,000 units, there will be 20 orders per year. Each costs $50, so the annual cost of ordering is $50 x 20 = $1,000.

The total cost of holding and ordering is therefore $2,500 + $1,000 = $3,500



Example 3

Work out the annual holding, ordering and total costs at the following reorder quantities:Reorder quantity

Holding cost½ ROQ x $5

Ordering Occasions

20,000/ROQ

Ordering Cost (orders x $50)

Total cost

100200500

1,0002,0004,000

Reorder quantity


Ordering Occasions

20,000/ROQ


Total cost

100 250 200 10,000 10,250200 500 100 5,000 5,500500 1,250 40 2,000 3,250

1,000 2,500 20 1,000 3,5002,000 5,000 10 500 5,5004,000 10,000 5 250 10,250

As the reorder quantity increases, the holding costs increase and the ordering costs decrease. The total costs fall to a minimum, then rise. The minimum costs are at the economic order quantity (EOQ). Here, EOQ is probably a little above 500.

The precise EOQ can be found using a formula



EOQ = 2CoD

CH

2

CO = cost of placing an order

CH = cost of holding one unit for one year

D = annual demand

So for this example:

EOQ=

2x50x20,0005

2 = 632 units

Question 11 Monthly demand = 3,000 units

Annual ordering costs = $600

Order quantity = 6,000

Holding cost = $6 per unit per year.

CO = cost of placing an orderCH = cost of holding one unit for one yearD = annual demand

EOQ = 2CoDCH

2

What is the economic order quantity?

A 1,095

B 775

C 346

D 1,897

Question 12 A company uses the formula

CO = cost of placing an orderCH = cost of holding one unit for one yearD = annual demand

EOQ = 2CoDCH

2

to determine its economic order quantity

If the cost of placing an order increases what will happen the EOQ and the annual stock-holding cost?

A EOQ: Higher; Stockholding cost: No effect

B EOQ: Higher; Stockholding cost: Higher

C EOQ: Lower; Stockholding cost: Lower

D EOQ: Lower; Stockholding cost: No effect



Chapter 5ACCOUNTING FOR LABOUR

1. Introduction

This chapter looks at how remuneration is calculated and accounted for, and also how certain labour-related ratios can be calculated.

2. Remuneration methods

Labour costs can arise from:

๏ Basic wage or salary

๏ Overtime premiums

๏ Bonuses

๏ Holiday pay

๏ Sick Pay

๏ Payroll taxes

Many countries pay wages and salaries under a ‘pay as you earn scheme’ which means that the employer deducts the employees’ income tax form the gross wage and pays that over directly to the tax authority. Only the net amount after tax is then paid to the employee.

Employee remuneration can be based on the following approaches:

1. A constant weekly or monthly amount

This is easy to calculate:

Labour cost = remuneration per period x number of periods

2. An amount based on hours worked (basis plus overtime)

Illustration

52 hours are worked in a week. Basic week is 40 hours, the basic rate of pay = $10, and overtime is paid at time and one half.

Basic pay: hours worked @ basic rate 52 x $10 = 520Overtime premium: (52 – 40) x $10 x 50% = 60Total pay US$580



3. An amount based on units produced: piecework

Often there is a guaranteed minimum amount of pay so as to comply with minimum wage rate legislation.

Illustration

Minimum pay/week = $250Piece rate = $3/unit

If 100 units are made in a week then the pay will be $3 x 100 = $300If 80 units are made in a week then the pay will by $250 (because the piece rate amount would be only $240.

4. An amount based on productivity

There are many different types of bonus scheme and any question would have to set out the precise rules.

Illustration

Basic pay = $9/hour for a 40 hour week. Normal production in that time = 120 unitsBonus = 50% of the time saved on production paid at time and a third

What will be the total wage in a week in which 150 units are made in 40 hours?

Answer$

Basic pay = 45 x $9 405150 units should take 50 hours150 units did take 40 hoursHours saved 10 hours

Bonus = 50% x 10 x 9 x 1 ⅓ 60

Total pay 465

5. An initial amount plus a bonus

Here, for example, the bonus could be part of a profit share. Full instructions would have to be supplied as to how to calculate the amounts.

Example 1

Employees are paid $6/hour for a standard 40 hour week. Overtime is paid at time and one third.

The employee is expected to make at least 80 units in a week, and to encourage productivity, each unit in excess of 80 will be generate an additional payment of $5 less any overtime premium that would relate to the time the additional unit would normally take.

What is an employee’s wages in a week in which 90 units are made and the employee works 44 hours?



6. The effect of changes in remuneration methods and changes in productivity on unit labour costs

To increase competitiveness, employers will try to reduce unit costs and will often attempt to do this by offering employees productivity payments. Employers need to look at the before and after costs.

Illustration

Current scheme: $7/hour, 40 hour week. Overtime premium = time and a half. Usually 400 units are produced in 50 hours

Weekly wages = 50 x $7 + 10 x $3.5 = $385Cost per unit = $385/400 = 0.9625

Proposed scheme: rates as above, but in addition the overtime premium is paid on any hours saved. Assume that 50 units are now made in 44 hours

Possible results:

Hours saved = 50 – 44 = 6Weekly wages = 44 x $7 +4 x $3.5 + 6 x $3.5 = 343Cost per unit = 343/400 = 0.8575

7. Gross and net earnings๏ Gross pay: the total amount earned by the employee

๏ Net pay: the amount paid to the employee after the employer makes deduction for income tax and certain statutory amounts.

๏ Total labour cost to employer: employees’ gross pay plus any additional payroll taxes (and perhaps pension costs) that the employer has to bear.

Example 2

An employee is paid at the rate of $10/hour.

Tax and other deductions amount to 25% for weekly income in excess of $100

Employer payroll taxes = 10% gross wages

If an employee works 38 hours in a week, what are the employee’s gross pay, net pay and the total amounts that have to be paid by the employer to the tax authorities?



8. Accounting for labour costs

In addition to being paid whilst working (basic, overtime premiums, productivity bonuses, employees are often also paid when:

๏ on holidays

๏ ill

๏ idle (because, say of machine breakdown)

The labour costs are classified as direct or indirect depending on what caused those costs:

Direct labour costs: all hours worked x normal hourly rate

Indirect labour costs: overtime premium, idle time, sick pay, holiday pay.

In double entry, the system is as follows:

Dr Work-in-progress with the gross wagesCr Wages control account with the gross wages

Dr Work-in progress with the employer’s payroll taxCr Wages control account with the employer’s contributions to payroll tax

Dr Wages control accountCR Cash as employee paid the net amountCR Cash as the revenue authorities are paid employee deductions and employer

contributions.

Example 3

Show the following transactions in wages control account(a) 31 March, gross wages calculated as $36,000; deductions for employees taxes = $8,000(b) 31 March, employer’s payroll tax calculated as $4,000(c) 1 April, employees paid amounts due(d) 15 April, tax authorities paid amounts due



Question 1 Which of the following is the correct treatment?

A Direct labour: standard hours at basic rate. Indirect labour: overtime hours at overtime rate

B Direct labour: total hours worked at actual rates. Indirect labour: idle hours at standard rate

C Direct labour: standard and idle hours at basic rate. Indirect labour: overtime hours at overtime premium

D Direct labour: total hours worked at basic rate. Indirect labour: overtime hours at overtime premium

Question 2 Under most systems of tax, what do employers pay to employees?

A Gross wages

B Gross wages less employees’ deductions less employers’ payroll tax

C Gross wages less employees’ deductions

D Gross wages less employers’ payroll tax

9. The relationship between payroll and productionIt is common for manufacturing companied to pay on the basis of time worked, so clock cards showing total hours worked per week can be used as the basis of simple pay calculations. If the factory always produces the same product, then it is easy to trace the labour cost into the production cost.

Labour cost/unit = Total labour costs/total units produced.

If the factory produces several different types of unit (perhaps different units are made on different days), or makes individual products for customers (job or contract costing), then the factory will have to keep more detailed time records, showing exactly how long each person spend on each type of production.

The factory will also have to record separately details of production.

Example 4

In a week 80 employees each spend 40 hours working and their labour cost is $15/hour.

2 days are spend on making 200 units of Product 1

2 days are spent on making 500 units of Product 2

1 day is spent making 4 units of Product 3

Work out the company’s total wage cost and the labour content of each produce.



10. Utilisation, production volume and idle time ratios

When setting a labour budget it is normal to specify how long it should take to produce each item (standard hours/unit), how many units will be made and therefore how many hours the employees and the factory is expected to work.

For example, if each unit should take 2 hours to make and output is planned to be 5,000 units in a period, then the planned labour hours will be 10,000. This is also how long the factory should be working. Here, 10,000 is said to be the capacity of the factory ie what was expected to work.

A number of things can happen to these plans:

1. The units output might not take the standard hours per unit. This will give an assessment of efficiency.

2. More or fewer hours might be worked in the factory than originally expected. This will give an assessment of capacity.

3. More or fewer units might be produced than budgeted. This will give an assessment of production volume.

4. Although employees are being paid, they might be idle for a time (for example, if a machine broke down). IT will be useful to quantify idle time.



IllustrationStandard hours per unit = 2Planned production = 5,000 units

Actual production = 5,200 unitsActual hours worked = 10,800Actual hours paid 11,000.

Efficiency ratio5,200 units should take 10,400 hours (2 hours per unit)5,200 units did take 10,800 hours

Production has been therefore been inefficient.

Efficiency ratio = standard hours for production achieved

x 100 =10,400

x 100 = 96%Efficiency ratio = actual hours

x 100 =10,800

x 100 = 96%

Efficiency is below what was expected.

Capacity utilisation ratioPlanned factory hours were 10,000 (2 hours x 5,000 units)Hours worked = 10,800

More work has been squeezed out of the factory than expected because people are working longer.

Capacity utilisation ratio =actual hours worked

x 100 =10,800

x 100 = 108%Capacity utilisation ratio =budgeted hours

x 100 =10,000

x 100 = 108%

Production volume ratioPlanned production = 5,000 units (or 10,000 hours)Actual production = 5,200 units or (10,400 hours)

Production has been higher than expected.

Production/volume ratio =actual production

x 100 =5,200

x 100 = 104%Production/volume ratio = planned production

x 100 =5,000

x 100 = 104%

[Note this could be also worked out using planned and actual hours 100 x 10,400/10,000)].

Idle time ratioIf 11,000 hours were paid for but only 10,800 were worked, the workforce must have been idle for 200 hours. The idle time ratio is:

Idle time ratio (or per cent) =Idle hours

x 100 =200

= 1.8%Idle time ratio (or per cent) =Total hours

x 100 =11,000

= 1.8%



Question 3 Does an efficiency percentage of 110% indicate efficient or inefficient production?

A Efficient

B Inefficient

Question 4 Does a capacity ratio of 90% indicate that better than expected or worse than expected use has been made of the factory facilities?

A Better

B Worse

Question 5 What does a production volume ratio of 120% say about the efficiency of workers?

A Better than expected

B Worse than expected

C No conclusion can be drawn about worker efficiency

5. Labour turnover

Labour turnover measures the rate at which employees leave the company.

Generally, this rate should be kept low because:

๏ Cost of recruitment is high

๏ Cost of training is high

๏ Labour efficiency is likely to be low because new workers will usually not work as quickly as more experienced ones.

๏ Quality and customer satisfaction might be adversely affected.

๏ Work might have to be turned away because there isn’t enough staff

Of course, some businesses encourage a certain amount of labour turnover because new recruits are usually paid at a lower rate than more experienced ones.



It’s not hard to understand possible reasons for labour turnover. For example:

๏ Illness

๏ Employees want to move to get a variety of experience

๏ Dismissal

๏ Poor wages and conditions

๏ Too much stress

๏ Anti-social hours

๏ Poor opportunities for promotion

๏ Oppressive, unpleasant management

๏ Horrible job

๏ Broken promises

The labour turnover ratio is defined as:

labour turnover ratio =Number of replacement staff

x 100labour turnover ratio =Average employees in period

x 100

Question 6

A company had 1,000 employees at the beginning of the accounting period. It wanted to down size to 800, but when offered voluntary redundancy 300 staff left. The resultant shortfall in employee numbers was immediately made good by recruitment.

What is the labour turnover ratio?

A 22.2%

B 33.3%

C 11.1%

D 5.6%





Chapter 6ACCOUNTING FOR OVERHEADS – MARGINAL COSTING AND TOTAL ABSORPTION COSTING

1. Introduction

This is a key chapter as it looks at two approaches to calculating profits: marginal costing and total absorption costing. Marginal costing account for only variable costs in the cost of production. Total absorption cost tries to take all production costs into account.

Different profits are likely to be calculated under each method.

2. Profit statements and their preparation in absorption and marginal costing formats

Some definitions:

Marginal cost (MC): the additional cost caused when one more unit is made. Marginal cost will be the sum of all variable costs per unit.

Total absorption cost (TAC): the total cost of manufacturing a unit. This is the sum of the marginal cost and a fair share of the fixed production costs.

Fixed overhead absorption rate: budgeted fixed production costs divided by budgeted output in units.

Profit per unit: selling price per unit less total absorption cost per unit ie less marginal costs and all fixed production costs.

Contribution per unit: selling price per unit less marginal cost per unit



Here is a cost card showing selling price and costs per unit:

$ $

Selling price 100

Material 20

Labour 15

Variable overheads 5

Marginal cost (40)

Contribution 60

Fixed overhead per unit (based on budgeted costs of $25,000 divided by budgeted output of 1,000 units)

(25)

Profit 35

Note:

Total absorption cost per unit = $65 ($40 marginal cost + $25 fixed cost per unit)

Let us say that in a month, 1000 units were made and 900 of those were sold. This means that there must be 100 items left in inventory. The profit can be calculated in two ways.

Marginal cost (MC) approach

$ $

Sales revenue 100 x 900 90,000

Marginal cost of production 40 x 1,000 40,000

Less: closing inventory 40 x 100 (4,000)

Marginal cost of sales 36,000

Contribution 54,000

Less Fixed overheads (25,000)

Profit 29,000

Note:

1. Under marginal costing closing inventory is valued at its marginal cost

2. All fixed costs are deducted as a lump sum, sometimes referred to as a period cost.



Total absorption cost (TAC) approach

$ $

Sales revenue 100 x 900 90,000

Total absorption cost of production 65 x 1,000 65,000

Less: closing inventory 65 x 100 (6,500)

Total absorption cost of sales 58,500

Profit 31,500

Note:

1. Under TAC closing inventory is valued at its total absorption cost

Fixed costs are accounted for in the total absorption cost of sales.

Question 1 Contribution per unit is;

A Selling price less total absorption cost per unit

B TAC – MC

C Selling price less marginal cost

D MC +overhead absorption rate per unit

Question 2 Profit can be calculated as:

A Revenue less marginal cost

B Revenue less marginal cost plus fixed production costs

C Revenue less marginal cost less fixed production costs

D Revenue less total absorption costs less fixed costs



Example 1

What is the contribution and profit if 500 units are made and sold where the selling price is $20 per unit and the marginal cost is $8 per unit? Fixed overheads are expected to be $4,000 for the period.

Commentary on the two methods of calculating profits

You will see that the two profits are different, with TAC profits of $31,500 and MC profits of 29,000, i.e. TAC profits are $1,500 greater.

This difference can be reconciled to the difference in closing inventory valuation. In TAC, the closing inventory of $6,500 contains some fixed costs ($6,500 = 100 x ($40 + $25)). These will be accounted for in the next period when those items are sold. In the MC approach all fixed costs are deducted in the period.

Both methods are correct. It’s simply if inventories are valued differently then profits will be different.

Commentary on the two methods of calculating the cost of production

Marginal cost: each unit causes $40 additional costs and when sold will generate $100 additional revenue. The contribution of $40 means that each unit makes the company $40 richer. It would even be worthwhile making for $40 MC and selling as low as $41 as that would generate a small contribution. Marginal cost is therefore good for decision making.

However, because MC does not take into account all production costs, it can be argued that the cost of production and the value of inventory is understated.

Total absorption cost: each unit costs $65 to produce, but each unit does not cause an extra $65 as fixed costs are fixed. Despite a TAC of $65 is would still be worth selling units at $50, so TAC can be bad for decision making.

However, all production costs are taken into account and arguable TAC is better for stock valuation.

Either methods can be used in internal cost accounting, but for external reporting in the financial statements TAC has to be used for stock valuation.

Question 3 Which of the following statements is true?

A Stock valuation using marginal cost is acceptable for external reporting; using TAC is not acceptable for external reporting.

B Both MC and MC are acceptable for external reporting

C TAC is better for decision-making

D Stock valuation using TAC is acceptable for external reporting; using MC is not acceptable for external reporting.



3. Cost allocation and cost apportionment

Marginal costs are relatively easy to account for because the cost caused by each additional unit can be measured. However, fixed costs to not increase with each extra unit made. The best that can be done to take these production costs into account is to spread them, as fairly as possible into the cost per unit.

The simplest way to work out an absorption rate is to calculate:

Budgeted fixed production costsBudgeted production in units

Typically as units are produced they pass through a number of departments such as component manufacturing, assembly, finishing and testing. The first challenge is to calculate the fixed production costs relating to each production department.

There are two general ways in which costs can be traced to or identified with production departments:

Cost allocation: where the whole of a cost can be traced to a single department.

Cost apportionment: where a cost has to be divided over several departments.

Cost allocation occurs when it is obvious that all of the cost relates to a single department. For example, assembly might take place in a building which receives a separate rent invoice; all of the rent would be allocated to assembly.

Cost apportionment would have to be carried out if a rent invoice were received for the whole business, so relating to all manufacturing departments. Apportionments (dividing-up the total cost) are done on a common sense basis. For example:

Heating costs apportioned on the basis of floor area

Insurance of machines apportioned on the basis of machine value

Rent apportioned on the basis of floor area

Canteen costs apportioned on the basis of the number of people employed.

Question 4 Which of the following would be the most suitable way of apportioning depreciation of plant and machinery?

A Power consumption of the machinery

B Number of workers using the machinery

C Floor area occupied by the machinery

D Cost of the machinery



Question 5 Which of the following could be suitable ways of apportioning maintenance of plant and machinery?

1. Number of hours the machinery runs for

2. Number of machines

3. Book value of the machinery

4. Cost of the machinery

A Any of the above

B 1 or 2 only

C 1, 2, or 3

D 1, 2, or 4

Question 6 If an entire cost can be related to a department, then the cost is said to be:

A apportioned to that department

B allocated to that department

C absorbed by that department

D allotted to that department

Example 2

A factory has two production departments: preparation and assembly, and one canteen for the labour force.

Statistics about the departments are:

Preparation Assembly CanteenFloor area 400 m2 500 m2 100m2

Machine value $94,000 $80,000 $6,000Employees 8 6 2Power consumption 75% 20% 5%

Fixed overhead costs are: rent $45,000, insurance $5,400, canteen costs $12,000, electricity $40,000

Show how the costs would be apportioned to each department.



Once the amounts are apportioned the cost in each department will be:

Cost Basis of apportionment Total Preparation Assembly CanteenRent Floor area 4:5:1 45,000 18,000 22,500 4,500Insurance Machine value 94:80:6 5,400 2,820 2,400 180Canteen Employees 8:6:2 12,000 6,000 4,500 1,500Power consumption 75%,20%,5% 40,000 30,000 8,000 2,000

Total 102,400 56,820 37,400 8,180

4. Secondary apportionment

The canteen is a production-related cost because it is used to provide meals to the workforce. It is known as a service department. However, units being produced spend time only in the preparation and assembly departments. Therefore, to account for canteen costs they must be re-apportioned into the preparation and assembly departments (secondary apportionment).

This will be done on the basis of the number of employees in each of those departments ie 8:6

Cost Basis of apportionment Total Preparation Assembly CanteenRent Floor area 4:5:1 45,000 18,000 22,500 4,500Insurance Machine value 94:80:6 5,400 2,820 2,400 180Canteen Employees 8:6:2 12,000 6,000 4,500 1,500Power consumption 75%,20%,5% 40,000 30,000 8,000 2,000

Total 102,400 56,820 37,400 8,180Reapportionment of service department costs

8:6 4,674 3,506 (8,180)

Final apportionment 102,400 61,494 40,906 –

5. Absorption rates

The costs now have to be traced into (or charged) to items being produced. If there is only one type of item being produced then the costs per item would simply be the total costs spread over the items. This would be known as a fixed overhead absorption rate per unit.

However, often a mix of items is produced, and the normal approach is to charge overheads on the basis of the amount of time that the items spend in each department. It is assumed that there is a correlation between spending time in a department and benefitting form what goes on there.



The time can be estimated using:๏ Labour hours: this will give a fixed overhead absorption rate per labour hour

๏ Machine hours: this will give a fixed overhead absorption rate per machine hour

๏ Assume the following;

Preparation departmentPreparation department Assembly departmentAssembly departmentProduct Budgeted

volumeMachine hours

per unitLabour hours

unitMachine hours

per unitLabour hours

unitProduct A 10,000 units 2 2.5 1 3Product B 6,000 units 3 1 1 4

Machine hours basis

Budgeted machine hours in the preparation department

10,000 x 2 + 6,000 x 3 = 38,000

Budgeted machine hours in the assembly department

10,000 x 1 + 6,000 x 1 = 16,000

Fixed overhead absorption rate per machine hour in the preparation department

= 61,494 [the apportioned costs]/38,000 = $1.62/hour

Fixed overhead absorption rate per machine hour in the assembly department

= 40,906 [the apportioned costs]/16,000 = $2.56/hour

Fixed overheads charged to Product A:

Preparation 2 x 1.62 + Assembly 1 x 2.56 = $5.80

Fixed overheads charged to Product B

Preparation 3 x 1.62 + Assembly 1 x 2.56 = $7.42

Example 3

Re-calculate the overhead absorption rates and amount to be charged to each product using a labour hour basis.

The required information is below;

Costs apportioned into preparation department = $61,494

Costs apportioned into assembly department = $40,906


volumeMachine

hours per unitLabour hours

unitMachine

hours per unitLabour hours

unitProduct A 10,000 units 2 2.5 1 3Product B 6,000 units 3 1 1 4



6. More on service department costs: reciprocal services

It can happen that one service department provides services for another service department as well as for production departments. For example, the factory canteen will provide meals to maintenance department staff as well as to production department workers. Also, the maintenance department might spend some time servicing and repairing machinery in the canteen.

There are a number of ways of dealing with these reciprocal service costs, but you need to know only two for this syllabus:

Direct apportionment: this approach completely ignores inter-service department costs transfers. Because inter-service relationships are usually relatively minor and there are some arbitrary choices to make on initial apportionment (heating could be apportioned on floor area, volume of buildings or the number of radiators), this rough and ready approach is almost certainly good enough.

Step down method: this approach starts with one service department and apportions its costs to production departments and other service departments. Another service department is then reapportioned to production departments and remaining service departments: no costs will ever be apportioned back into a service centre once it has been cleared out of costs.

Example 4

Production department

1

Production department

2

Maintenance department

Canteen

Overhead costs after initial allocation and apportionment $ 150,000 160,000 72,000 35,100Percentage of maintenance department time spent on other departments 40 50 - 10Number of employees receiving meal 25 40 5

(1) Reapportion the two service department costs using the direct method(2) Reapportion the two service department costs using the step-down method, starting with

the maintenance department



7. More on the process of cost absorption for indirect costs The illustrations above showed how:

1. Fixed overheads are allocated or apportioned into production departments

2. An overhead absorption rate is calculated (usually per labour hour or per machine hour)

3. Overheads will be charged back to production using the same basis as used to work out the absorption rate.

It is important to understand that overhead absorption rates are calculated in advance on the basis of budgeted costs and budgeted output because a rate is needed from the very start of the period and only budgeted amounts will be known then.

The predetermined absorption rate is then never adjusted retrospectively.

This will usually mean that the actual fixed costs are not properly accounted for and that a final adjustment is needed in respect of:

๏ Under-absorption where not enough fixed costs have been accounted for.

๏ Over-absorption where too many fixed costs have been accounted for.

Illustration

Budgeted fixed costs = $100,000Budgeted output = 50,000 units

Therefore, fixed overhead absorption rate per unit = $2

Actual fixed costs = $120,000Actual production = 53,000 units.

Here, the 53,000 units produced will each absorb (account for) $2, so, £2 x 53,000 = $106,000 fixed costs will be accounted for in the cost of production. However, actual fixed costs are $120,000, so the costs have been under-absorbed by $14,000 and a deduction of this amount has to be made from profits.

If results had been:Actual fixed costs = $95,000Actual production = 49,000 units.

Here, the 49,000 units produced will each absorb (account for) $2, so, £2 x 49,000 = $98,000 fixed costs will be accounted for in the cost of production. However, actual fixed costs are $95,000, so the costs have been over-absorbed by $3,000 and $3,000 has to be added back to profits



Question 7

Budgeted overheads = $12,000; budgeted production = 2,000 units

Actual overheads = $13,000; actual production = 1,900 units.

Which of the following is correct?

A Overheads under-absorbed = $1,000

B Overheads under-absorbed = $1,600

C Overheads over-absorbed = $1,600

D Overheads over-absorbed = $1,000

Question 8

Budgeted overheads = $50,000; budgeted production = 20,000 units

Actual overheads = $46,000; actual production = 19,000 units.

Which of the following is correct?

A Overheads under-absorbed = $2,000

B Overheads under-absorbed = $1,500

C Overheads over-absorbed = $1,500

D Overheads over-absorbed = $2,000





Chapter 7JOB, BATCH AND PROCESS COSTING

1. Introduction

This chapter looks at how products are costed, depending on whether they are unique products or one of many identical products.

2. Job costing

Job costing is where a unique item is being made and costs can be specifically traced into that item.

The job could be large (such as building a house or a ship) or small (such as constructing a set of shelving for a room).

Often jobs are given identifying numbers, such as contract numbers or simply job numbers.

All relevant costs are labelled with that number and the total costs can be accumulated.

๏ Material costs: either invoices for specially bought material or requisitions from stores can be labelled with the job number so that material costs can be accounted for.

๏ Labour costs: times sheets can be filled in using the job number to track time spent on the job.

๏ Other expenses: if direct, then the job number will be noted against that cost; if indirect then expenses are often charged to a job on the basis of time and an overhead absorption rate.

Example 1

Job 666 required 20 kgs of a material in stores which cost $15/kg, and also a special component had to be bought at a cost of $150.

30 hours labour were spent on the job where the employees were paid at $9/hour. In addition 3 hours was spent by a supervisor who is paid at $15/hour. Overheads are absorbed at the rate of $4/labour hour.

Calculate the total absorption cost of the job.



3. Batch costing

In batch costing several identical items are produced as a batch. Each batch will be given a number so that costs can be traced into the batch. The batch costs can be averaged over the units produced.

Example 2

Batch 7777 used 2000 kgs of a material in stores which cost $10/kg, and also 500 kgs of special material that was bought in at $4/kg.

90 hours labour were spent in Department A where the employees were paid at $12/hour, and 40 hours were spent in department B where employees are paid at 10/hour. Overheads are absorbed at the rate of $3/labour hour.

900 units were produced

Calculate the total absorption cost of the batch and each unit produced.

4. Process costing - introduction

Process costing deals with manufacturing that takes place as a continuous process.

Examples of industries using process costing are:

๏ Oil refining

๏ Chemical works

Because work carries on continuously, there are no batches as creating a batch implies that you know when it starts and stops, and therefore what costs have gone into it.

In process costing, costs are worked out for periods: measure the costs that are used in a period and the output produced in the period and you have a way of working out the cost per unit.



IllustrationCosts for July:• Material costs = 100,000 units costing $20,000• Labour costs = $10,000• Overheads = $5,000• Output produced in July = 100,000 units

Cost per unit = ($20,000 + $10,000 + $5,000)/100,000 = $0.35/unitIn a process account this would be

Process accountProcess accountProcess accountUnits $ Units $

Material 100,000 20,000 To finished goods

100,000 @

$ 0.35

35,000

Labour 10,000Overheads 5,000

100,000 35,000 100,000 35,000

5. Process costing – with normal lossesMany processes incur losses which are inevitable. For example, liquids evaporate or solids are filtered out. Therefore, the units of good output are often not the same as the units input.

If you can’t make units without some losses, then the cost of that loss is spread over (or absorbed) into the good units produced. The loss is just another cost on the way to good production.

Cost/unit = costs for the period

Cost/unit = expected good output for the period

Illustration

1000 kgs at $3.60/kg were input to a process and there was a 10% loss due to evaporation.

900 good units should result and their cost per unit would be:

1000 x $3.60/900 = $4/unit.

Sometimes the ‘lost’ material can be sold as scrap. For example, in a saw-mill, sawdust can be sold for various uses.



Illustration

For example: 1,000 kgs at $4.00/kg were input to a process and there was a 20% loss due to filtration. The materials filtered out could be sold for $0.50kg.

800 good units should result and their cost per unit would be:

1,000 x 4 – 200 x 0.50= $4.875/unit

800= $4.875/unit

So, if the good units can’t be made without making some losses, it is reasonable to say that the initial cost will always be reduced by what the scrapped/lost units can be sold for.

In a ‘T’ account this would be shown as:

Process accountProcess accountProcess accountUnits $ Units $

Material 1,000 4,000 Normal loss 200 @ $0.50

100

To finished goods 800 @$4.875

3,900

1,000 4,000 1,000 4,000

Question 1

3,000 kg are input to a process and total costs amount to $9,000. 100 units are expected to be lost and can be sold for $1 each.

What is the cost per unit of good output?

A £2.97

B $3.00

C $3.10

D $3.07

Example 3

In August 2000 kgs of a material were introduced to a process at a cost of $5/kg, and

200 hours labour were spent at a cost of $12/hour. Overheads are absorbed at the rate of $3/labour hour.

Normal losses are incurred at the rate of 5% of input and lost units can be sold for $0.8 per kilogram 1,900 units were produced

Calculate the total absorption cost of the good output and also show the process account.



6. Process costing – with abnormal losses and gains

Illustration

Let’s look again at the example where 1,000 kgs at $4.00/kg were input to a process, there was a 20% loss due to filtration and the materials filtered out could be sold for $0.50kg.800 good units should result and their cost per unit would be:

1,000 x 4 – 200 x 0.50= $4.875/unit

800= $4.875/unit

Now let’s say that only 750 goods units were produced. The missing 50 units are an abnormal loss. Just about the only thing you have to understand is that each unit abnormally lost costs the same to produce good units would cost. In fact, you could simulate the abnormal loss by removing 50 good units from output and throwing them away (or selling them for scrap.

Similarly, if 850 units had resulted there would be an abnormal gain. The extra 50 units would be identical to the normal good units and must be valued the same way.

The basis principles of process costing cannot be emphasised enough:

๏ Good units are valued according to the expected output

๏ Abnormally lost or gained units are valued in the same way as expected units.

Example 4

In August 2000 kgs of a material were introduced to a process at a cost of $6/kg, and

200 hours labour were spent at a cost of $15/hour. Overheads are absorbed at the rate of $4/labour hour.

Normal losses are incurred at the rate of 5% of input and lost units can be sold for $0.9 per kilogram

1,800 kgs were produced

Calculate the total absorption cost of the good output, the treatment of any abnormally lost or gained units, and also show the process account and loss account



Example 5

In May 5000 kgs of a material were introduced to a process at a cost of $9/kg, and labour and overheads amounting to $25,000 were also contributed.

Normal losses are incurred at the rate of 10% of input and lost units can be sold for $1 per kilogram

4,700 kgs were produced

Calculate the total absorption cost of the good output, the treatment of any abnormally lost or gained units, and also show the process account and loss account

Question 2

Input costs to a process amount to $120,000. It is expected that 1,000 units of good output will be produced and that normal losses will be 200 units. In fact, only 900 units of good output were produced. All losses, whether normal or abnormal can be sold for $5/unit.

What is the cost per unit of good output and what is its inventory value?

A Cost per unit = $131.67; inventory value = $118,500

B Cost per unit = $132.22; inventory value = $118,000

C Cost per unit = $119; inventory value = $107,100

D Cost per unit = $100; inventory value = $90,000

Question 3 Which on of the following statements is true?

A The number of units abnormally lost does not affect inventory value

B The number of units abnormally lost or gained does not affect the cost per unit of good inventory.

C The number of units abnormally lost or gained does affect the cost per unit of good inventory.

D Abnormally gained production is values at scrap value.



Question 4

Normal losses are 10% of input.

400 units are produced.

There are 50 abnormally lost units

Lost units have no sales value.

Input costs = $120 per unit input

What is the cost per unit produced?

A $150.00

B $120.00

C $133.33

D $118.52

7. Joint and by-products

There are some manufacturing processes in which it is inevitable that more than one product is made. For example, an oil refinery buys crude oil and this is then split (‘cracked’) into kerosene, diesel, petroleum and many other chemicals. Or a dairy buys milk and this is separated into skimmed milk and cream.

If the various products that are made are of comparable value or are material, then they are called joint products.

Any unimportant products of small value are called by-products.

The process can be shown as:

Joint or common or pre-separation costs

Joint product A

Split-off or separation point

Separate costs

Separate costs Joint product B

By-product



To be able to value inventory, it is necessary to take all costs into account that were responsible in getting the product to its present location and condition. So, to value Product A, its separate costs plus a share of the joint (common) costs have to be used. There is no problem with the separate costs as they are clearly only to do with specific products, but the joint costs have to be split in some way.

There is no single correct way to split joint costs, but common approaches are:

๏ Physical (weight/volume)

๏ Net realisable value of the final product (sales value less separate costs)

๏ Equal profit margins

๏ Sales value of the final product

This syllabus asks you to deal with only the first two methods.

Example 6

A production process has joint costs of $12,000 for the input of 1,000 kgs of material. Two products are produces from this:

Product A: 600 kgs. Selling price = $25/unit. Separate costs = $4,000

Product B: 400 kgs. Selling price = $40/unit. Separate costs = $7,000

Calculate the inventory value of the production using(a) Weigh to apportion the joint costs(b) Net realisable value to apportion the joint costs

Note that the costs of the products change under the two methods. This does not mean that the company’s overall profit changes: whatever way the joint costs are split and apportioned to products they are still the same total costs to the business.

Joint products are important and material to a business’s results, so care is taken to work out their costs. By-products are not material and are a bit of a nuisance. Joint costs are never apportioned into by-products; nor are sales of by products separately accounted for. Instead, the sales proceeds are deducted from the joint costs and the net amount split over the joint products. In effect, by-products are being treated in the same way as normal losses in process costing where sales revenue from sale of scrap was credited to the process account.

Example 7

A production process has joint costs of $12,000 for the input of 1,000 kgs of material. Two products are produces from this:

Product A: 500 kgs. Selling price = $25/unit. Separate costs = $4,000

Product B: 400 kgs. Selling price = $40/unit. Separate costs = $7,000

By product: 100 kgs. Selling price = $2/kg

Calculate the inventory value of the production of the joint products using(a) Weigh to apportion the joint costs(b) Net realisable value to apportion the joint costs



8. Further processing decisions

Look at these results:

Product A Product BSales revenue 100,000 150,000Post separation/own costs 40,000 90,000Joint costs (split) 40,000 70,000Total costs 80,000 160,000Profit/(loss) 20,000 (10,000)

Note that this does not mean that Product B should be discontinued because it seems to make a loss. If a different basis were used to apportion the joint costs so that they, for example, were split equally between the two products, then both products would show a profit:

Profit for A: 100,000 – 40,000 – 55,000 = 5,000

Profit for B: 150,000 – 90,000 – 55,000 = 5,000

Overall the total profit is unchanged at $10,000.

If the business wants to make product A it has to incur all of the joint costs. There can be a choice, however, as to whether to incur the post separation costs. For example, instead of incurring $40,000 to complete Product A it might be possible to sell its pre-cursor just after split off.

Example 8

Look at the following:

Product A Product BSales revenue of final product 100,000 150,000Sales revenue at split-off 45,000 45,000

Post separation/own costs 40,000 90,000Joint costs (split) 40,000 70,000Total costs 80,000 160,000Profit/(loss) 20,000 (10,000)

Should Product A and Product B be processed from split off to completion?



Question 5 Joint costs allocated to Product A are $10,000; post-separation costs are $16,000

Sales value at split-off is $6,000. Final sales value = $23,000.

Joint costs allocated to Product B are $8,000; post-separation costs are $12,000

Final sales value = $25,000.

Which of the following statement is true?

A All production should be closed down

B We cannot decide on whether production should be closed until we know the joint costs allocated to product B

C It is worth processing Product A to completion

D It is not worth processing product A to completion

9. Service costing

This looks at costing services, such as providing transport or haulage.

A particular characteristic of service costing is that it often requires the use of composite cost units. For example, if costing a bus service you would be interested in the cost per passenger kilometre; if costing haulage you would be interested in cost per tonne kilometre. Composite units are essential because if you wanted to estimate, say a haulage cost that should be charged, it will depend on both weight and distance.

Example 9

Total annual cost of running a lorry fleet = $80,000

Jobs:

Job Weight (KG)

Distance (KM)

1 5,000 2002 10,000 5003 7,000 4004 12,000 600

Total

What is the cost per kg km of transport?



Chapter 8COST-VOLUME-PROFIT (CVP) ANALYSIS

1. Introduction

This chapter looks at how analysing costs and contribution can be used for decision making.

2. RecapSome definitions:

Marginal cost (MC): the additional cost caused when one more unit is made. Marginal cost will be the sum of all variable costs per unit.

Total absorption cost (TAC): the total cost of manufacturing a unit. This is the sum of the marginal cost and a fair share of the fixed production costs.

Fixed overhead absorption rate: budgeted fixed production costs divided by budgeted output in units.

Profit per unit: selling price per unit less total absorption cost per unit ie less marginal costs and all fixed production costs.

Contribution per unit: selling price per unit less marginal cost per unit

Here is a cost card showing selling price and costs per unit:

$ $

Selling price 100

Material 20

Labour 15

Variable overheads 5

Marginal cost (40)

Contribution 60Fixed overhead per unit (based on budgeted costs of $30,000 divided by budgeted output of 1,200 units)

(25)

Profit 35

Remember, the volume of items made will not alter the total fixed costs.

The contribution is always fundamental to decision-making; profit is usually irrelevant.



3. Breakeven calculations

In the above example, if no units are made and sold, fixed costs of $30,000 are still expected to be incurred and this will result in the business making a loss of $30,000.

If one unit is made and sold, there will be extra costs of $40 incurred (the marginal cost) and revenue of $100 will be earned, so the business will be richer by $100 - $40 = $60. The initial loss of $30,000 will be reduced by $60 to $29,940.

Gradually, as each additional item is made and sold, the loss will become smaller by $60/unit. So, to eliminate the initial loss of $30,000 (caused by the fixed costs) the business will have to make and sell:

$30,000/$60 = 500 units.

Check: Total contribution = 500 units x 60 = $30,000

Fixed costs that have to be covered = $30,000

At an output of 500 units, there will be zero profit (fixed costs = contribution) and the business is at break-even point.

The following diagram shows what’s going on:

When no units are made and sold, there is a loss of $30,000. The organisation can ‘climb’ out of that position by making and selling units. Each unit lifts the organisation by $60, the contribution.

The number of steps needed to just break even will be 30,000/60 = 500.

The break even revenue = 500 x 100 = $50,000



Question 1

Fixed costs are $120,000; selling price per unit = $150; total absorption costs per unit = $90; marginal cost per unit = $70.

What is the break-even point in units (to the nearest whole unit)?

A 1,500

B 2,000

C 800

D 1,333

Question 2

Selling price per unit = $190; total absorption costs per unit = $120; marginal cost per unit = $90. Budgeted production = 2,000 units.

What is the break-even point in units (to the nearest whole unit)?

A 2,400

B 857

C 600

D 500

Question 3

Selling price per unit = $90; total absorption costs per unit = $70; marginal cost per unit = $50. Budgeted production = 2,000 units.

What is the profit or loss if 1,500 units are made and sold?

A $60,000 profit

B $20,000 loss

C $40,000 profit

D $20,000 profit



4. Margin of safety

The margin of safety is a measure of how much budgeted sales can fall by before the break even point is reached. It is usually expressed as the percentage fall from budgeted production that can be tolerated before falling in a loss.

Example 1

A company has budgeted fixed costs of $240,000 and budgeted output of 50,000 units. Each unit makes a contribution of $8.

What is the break even point and the margin of safety?

Question 4

Selling price per unit = $60; total absorption costs per unit = $50; marginal cost per unit = $40. Budgeted production = 1,500 units

What is the margin of safety?

A 1,000 units; 50%

B 1,000 units; 33.3%

C 500 units; 50%

D 500 units; 33.3%



5. Break even charts and P/V charts.

These charts display revenue, costs, profits and contribution in various formats.

For all of the following examples, the following information will be used:

Selling price = $20. Variable (marginal) cost per unit = $12. Fixed costs = $16,000

Budgeted output and sales = 3,000

The basic break even chart

Steps in drawing a break even chart:

1. Work out the break even point. Here, 16,000/(20 – 12) = 2,000 units

2. Draw the fixed cost line – horizontal at $16,000.

3. Draw the revenue line. This starts the origin.

4. Draw the total cost line. This starts at Units = 0 and Total cost = Fixed cost.

5. Note that the revenue line rises more quickly ($20 for each extra unit) than the total cost line ($12 for each extra unit).



The budgeted profit is the difference between revenue and total costs at the budgeted volume of sales.

To the left of the breakeven point, total costs exceed total revenue so a loss is made.

The margin of safety (in units) is the distance between the budgeted volume and the breakeven volume.

Contribution break even chart

You can see that at the break even point, the contribution (revenue less variable costs) is equal to the fixed costs.



The profit volume graph

This graph allows you to immediately see the profit at any level of sales. It is not very helpful in identifying the break even point (which you would calculate before drawing the graph).

6. Contribution to sales ratioThe contribution to sales ratio is: contribution per unit/sales price per unit.

It allows you to calculate how much contribution is generated per $ of sales.

Contribution = Sales x C/S ratio

Example 2

A product sells for $24, has total absorption costs of $18 and marginal costs of $15.

What is the C/S ratio as a percentage?

If fixed costs are $20,000, what contribution and profit will be made when revenue is $60,000?



The C/S ratio can also be used to work out the break even point in terms of sales revenue.

We know that breakeven point occurs when the contribution just matches the fixed costs.

At break-even point Sales x C/S ratio = Fixed costs

Break-even sales Sales =Fixed costs

Break-even sales Sales =C/S ratio

Example 3

A product sells for $24, and has a C/S ratio of 37.5%. Fixed costs are $20,000.

What is the breakeven point in revenue and in sales units?

Question 5

A product has a C/S ratio of 30%.

If contribution is $75/unit what is the variable cost per unit?

A $225

B $250

C $175

D $150

Question 6

Break even sales units = 1000. Selling price per unit = $60. C/S ratio = 60%.

What are the fixed costs?

A $40,000

B $60,000

C $24,000

D $36,000



7. Achieving target profits

Remember what was said near the start of this chapter: contribution is always fundamental to decision-making; profit is usually irrelevant.

So, if you are asked to work out what volume of product needs to be made and sold to achieve a target profit, work out what target contribution is needed and calculate how many units need to me made to achieve that.

Target contribution = Target profit + fixed costs

The contribution has to be enough to first cover the fixed costs then it will start contributing towards profits.

Example 4

Selling price/unit = $50, marginal cost = $20 and total absorption cost = $30

Budgeted output = 2,000 units.

How many units need to be sold to make a profit of $70,000?

Question 7

A product makes a profit of $50 per unit and a contribution of $80 per unit. Fixed costs are $220,000.

How many units will need to be made and sold to make a profit of $100,000?

A 2,000

B 4,000

C 6,400

D 4,750



8. The effects of changing selling prices and costs

Businesses often have the option to change selling prices and costs – but usually these changes affect other amounts as well.

For example, if selling prices are lowered, sales volume is likely to increase. Or, if new machinery is installed, fixed costs might rise but the variable cost of manufacturing might fall because the machines are more efficient.

As always, concentrate on working out the new contribution. The new profit can then be calculated easily.

Example 5

Existing situation: selling price/unit = $50, marginal cost = $20. Expected sales = 40,000 units and fixed costs = $100,000.

New situation: a new machine is introduced that makes better quality products at a lower marginal cost per unit. Selling price/unit = $55, marginal cost = $18. Fixed costs = $160,000. The same volume will be sold.

What volume will have to be sold to keep profits the same?

Question 8

Currently a product has marginal costs of $40 and a selling price of $60. Fixed costs are $120,000 and 10,000 units are sold. Inflation will increase both marginal costs and fixed costs by 10%, but competition means that the selling price can be increased by 5% only.

What volume will have to be sold if the same profits are to be earned?

A 6,000

B 11,000

C 10,526

D 11,158



Question 9

Currently a product has marginal costs of $45 and a selling price of $70. 200,000 units are sold and fixed costs are $3 million.

If the selling price were reduced by $5, by how many units would the volume sold have to increase to earn the same profit?

A 50,000

B 250,000

C 15,385

D 40,000

Question 10 Where is profit on the following diagram?

A Line A

B Line B

C Line C

D Line D



Question 11 Where is the margin of safety on the following diagram?

A Line A

B Line B

C Line C

D Line D



Chapter 9SHORT TERM DECISION MAKING

1. Introduction

The previous chapter looked at the importance of contribution when working out break even points and deciding what quantities had to be made and sold to make target profits. This chapter looks at other decisions that contribution analysis can be used for. It also introduces the concept of relevant costs.

2. Limiting factors

Limiting factors are also sometime known as key factors or restricted resources.

A limiting factor is whatever restricts an organisation’s activities. It could be a limitation on the amount of materials, labour or machine time available. It might be that no more units can be sold because all demand has been met. Occasionally, there might be production quotas restricting output.

Usually in questions the limiting factor is whatever first prevents more profits being made.

Look at this example:

Product A Product B

Maximum demand 12,000 units

10,000 units

$ $Selling price 30 40

Material 10 16Labour 8 8Variable overhead 6 8Fixed overhead 4 5

Total absorption cost 28 37Profit 2 3

Both products use the same material, of which there is only $200,000 available

Step 1 – identify the limiting factor

Here, if the maximum units demanded were made, the material needed would be;

12,000 x 10 + 10,000 x 16 = $280,000.

Only $200,000 is available, so material is a limiting factor.

Step 2 – calculate the contribution per unit of limiting factor used



We have identified material as the limiting factor. This means that material is particularly precious and we have to take care when deciding how to use it: each unit of material be used in the way that will earn most.

As in all decision-making, profits are usually irrelevant 9because the fixed costs are fixed) and what we need to concentrate on are the contributions.

Product A Product B


10,000 units

$ $Selling price 30 40

Material 10 16Labour 8 8Variable overhead 6 8Marginal cost 24 32Contribution 6 8

So, every unit of Product A made and sold makes the company $6 richer and every unit of Product B made and sold makes the company $8 richer.

However, this does not mean that Product B should be made in preference to Product A. Different amounts of material are needed for each and we need to make sure that each precious unit of material is used wherever it earns most. That can be found by working out:

Contribution per unit/Material needed per unit

or more generally:

Contribution per unit of limiting resource

The higher this is the better: it gives an earning rate per unit of the restricted resources used

Product A Product B


10,000 units

$ $Material 10 16

Contribution 6 8Contribution/$ of material needed 6/10 = 0.6 8/16 = 0.5

Ranking 1 2

Therefore, make Product A in preference, then turn to Product B and make as much of that as possible with any material left.



Step 3 – calculate the production plan

The production plan would be:

Material used $

Units made Contribution made

Product A120,000

(12,000 x $10)

@ $10/unit

12,000(maximum

demand)

72,000(12,000 x $6)

Product B80,000

(balance of material)

@ $16/unit 5,000 40,000

(5,000 x $8)

Maximum material 200,000

Total contribution 112,000

Fixed costs4 x 12,000 +

5 x 10,000 (98,000)

Profit 14,000

Note: the fixed costs are based on the absorption rates in the original budget.

Example 1

Material available = 1200 kgs

Product A: contribution/unit = $24; uses 10 kg/unit; maximum demand = 80 units

Product B: contribution/unit = $15; uses 5 kg/unit; maximum demand = 200 units

What is the production plan that would maximise contribution and what is that contribution?

Question 1

A company makes three products, X, Y and Z,

Their contributions per unit are: X $25; Y $45; Z $30

The manufacturing hours for each are: X 5; Y 10; Z 4

If manufacturing hours are a limiting resource, in what order of preference should the units be made?

A X, Y, Z

B Y, Z, X

C Z, X, Y

D Y, X, Z



Question 2

A company makes two products, P and Q

Their contributions per unit are: P $25; Q $45. The materials needed for each are P $5; Q $10. A contract means that a minimum of 1,000 units of Q have to be made. Maximum demands are P: 2,000 units and Q: 3,000.

Material available = $16,000

How many units of Q will be made if contribution is to be maximised?

A 1,000

B 3,000

C 1,600

D 2,000

Question 3

A company makes two products, R and S. The products use the same material, which is limited to 3,900 kgs.

Details are as follows:

Product R Product SSelling price per unit $60 $32Variable cost per unit $45 $20Material used per unit 6 kgs 3 kgsMaximum demand 500 1,200

How many units of R and S should be made to maximise contribution?

A 500 R and 300 S

B 1,200 S and 50 R

C 1,200 units of S and 500 units of R

D 500 units of R and 150 of S



3. Limiting factors with make-buy decisions

If production capacity is limited then it is sometime possible to buy in some of what’s needed so that higher sales levels can be achieved. For example:

Material available = 1200 kgs

Product A: manufacturing cost/unit = $20; buy-in cost /unit = $25; uses material at the rate of 10 kg/unit; maximum demand = 80 units

Product B: manufacturing cost/unit = $25; buy-in cost = $35; uses material at the rate of 5 kg/unit; maximum demand = 200 units

Step 1 identify the limiting factor

If maximum demand for each product were manufactured then the material used would be:

80 x 10 + 200 x 5 = 1,800 kgs.

As only 1,200 are available, material is a limiting resource.

Step 2 identify which product should be bought in by calculating the extra cost of buying over making per unit of scarce resource

Product A: buying for $25 rather than making for $20 costs $5 per unit

Product B: buying for $35 rather than making for $25 costs $10 per unit.

However, buying a unit of A instead of making it saves 10kg material

and buying a unit of B instead of making it saves 5kg material

Additional cost per kg of material saved:

Product A: 5/10 = 0.5 Product B: $10/5 = 2.0

Therefore, make Product B in preference as that is a much more expensive way of saving material.



Step 3 The production plan

The production plan would be:

Material used kg

Units made Costs

Product B 1,000 @ 5 kgs/unit 200(maximum

demand)

5,000(200 x$25)

Product A 200(balance of

material)

@ 10 kgs/unit

20 400(20 x $20)

Maximum material 1,200

Product A to be bought in

Product A to be bought in

60(to make up to

maximum demand)

1,500 (60 x 25)

Total costs 6,900



Example 2

The availability of Material M is limited to 32,000 kg

Product Azed ByozDemand (units) 5,000 7,000Variable cost to make ($ per unit) 22 30Buy-in price ($ per unit) 38 34Kg of X required per unit 4 2

Calculate how much of each product should be bought and how much should be bought in.

Question 4

A company makes 10,000 units of a component for a variable cost of $25,000. This takes all of the 6,000 production hours available.

The components (essential for other production) could be bought for $55,000 and the machine hours released could then be spent on making:

Product Unit contribution Maximum demand (units)

Machine hours per unit

P 18 500 6Q 48 250 12

Contribution will be maximised if the company:

A Buys 10,000 units and makes P

B Buys 10,000 units and makes Q

C Buys 10,000 units and makes P and Q

D Manufactures 10,000 units



4. Discontinuing operations

Sometimes a company might want to look at the effect of discontinuing a product or a whole division. What is must compare is the revenue lost and the costs saved from the closure.

Illustration$ Division A Division B

Sales 250,000 600,000

Variable costs (120,000) (350,000)

Fixed costs (150,000) (200,000)

Divisional profit (20,000) 50,000

The company is worried about Division A, which reports a loss of $20,000, and is considering closing down that division.

Fixed costs of only $100,000 would be saved if A were closed.

Advise the company on whether Division A should be closed.

Solution:If A is closed down, revenue will fall be $250,000 and costs of $220,000 will be saved ($120,000 + $100,000 = $220,000).Revenue falls more than costs, so closing the division will make the company worse off.Therefore do not close down Division A

Example 3

Trio Ltd operates three divisions. The latest profit statements and is concerned that division Gamma is making a loss.

Advise Gamma whether or not to close down division C.Division Alpha Beta Gamma

(000s) (000s) (000s)Sales 150 120 60Variable costs 90 75 45Fixed costs 30 30 20Profit/(loss) 30 15 (5)

You are also informed that 50% of the fixed costs are division specific. The rest of the fixed costs are allocated arbitrarily to the divisions from head office.

Should division Gamma be shut down?



Question 5

A company division makes two products. Details are as follows:

Product A Product BSales revenue 200,000 300,000Variable costs 170,000 150,000Divisional fixed costs 100,000 100,000Profit (70,000) 50,000

The divisional fixed costs are arbitrarily split (equally) between the products. These costs can be avoided if the division is shut down. No fixed costs are avoided by discontinuing one product.

The action needed to maximise profits is:

A Discontinue product A

B Discontinue product B

C Keep production as it is at present

D Shut down the whole division.

5. Relevant costsThe costs relevant to decision making are those which are:

๏ Affected by the decision. Therefore they are future incremental costs.

๏ Cash flows

Some examples should make these points clear.

Illustration 1A company has spent $100,000 acquiring patent rights to manufacture a product. It hopes to sell 30,000 units at a selling price of $10 each and the variable costs of production will be $7 per unit. Should the company proceed with production?

Solution$100,000 is known as a past cost or a sunk cost. That money is gone and what the company has to do is to concentrate on future cash flows. The future cash flows will generate a contribution of:

30,000 x ($10 - $7) = $90,000

Therefore, proceeding with production will increase the company’s wealth, so it should proceed.

[Note: The incorrect approach would be to look at all costs: 30,000 ($10 - $7) - $100,000 = -$10,000. This incorrect because the business has no control over the past cost of $100,000. The company has to make the best of what can be done in the future.]



Illustration 2A company rents a factory for $100,000 per year. Half of the factory is already occupied by a machine. The company is considering installing an additional machine which would produce 20,000 units for a variable cost of $5 per unit. These units would sell for $7 each. Half of the factory rent would be apportioned to the new machine.

Should the company purchase new machine?

SolutionThe factory rent of $100,000 will be paid irrespective of whether the factory is empty, has one machine or two machines. It is a fixed cost, is non-incremental and is therefore irrelevant to the decision.

The new machine will generate a contribution of 20,000 x ($7 - $5) = $40,000

The new machine should therefore be purchased.

Illustration 3A company is considering installing a machine which would produce 20,000 units for a variable cost of $5 per unit. These units would sell for $7 each. Additional space would have to be rented at a cost of $50,000.

Should the company take on this project?

SolutionHere the rent of $50,000 is an incremental cost and is therefore relevant to the decision.

The new machine will generate a contribution of 20,000 x ($7 - $5) - $50,000 = - $10,000.

Therefore, the project should not be taken on.



Illustration 4A company has some inventory that was bought for $10,000.It could be sold for $4,000 or used to make a product that would sell for $15,000. There is no other use for the inventory. Additional costs needed to convert the inventory into the product are £9,000. The material could be bought now for $8,000

What should the company do?

SolutionThe $10,000 cost of the inventory is irrelevant: it is a sunk or past cost.

The $8,000 current price is irrelevant because the company has no use for the material so would not buy more.

The $4,000 resale value of the inventory is relevant as the company could receive that cash by selling the inventory. Therefore, $4,000 is a future incremental cash flow. If the company keeps the inventory and produces the product $4,000 will not be obtained and the $4,000 is known as an opportunity cost.

If the company proceeds with the new product, the incremental cash flows will be:$

Sales revenue 15,000Conversion costs (9,000)Opportunity cost of not selling the material (4,000)Contribution 2,000



Illustration 4A company has some inventory that was bought for $10,000. The inventory is used on a day to day basis for normal production. It could be sold for $4,000 or used to make a special product that would sell for $15,000. Additional costs needed to convert the inventory into the product are £9,000. The material could be bought now for $11,000

What should the company do?

SolutionThe $10,000 cost of the inventory is irrelevant: it is a sunk or past cost.

The $11,000 current price is relevant because the company uses the material every day. If some of the material is used to make the special product, it will have to be replaced, at a cost of $11,000, to allow ordinary production to be carried on.

The $4,000 is irrelevant as the company would not sell material for $4,000 only to have to replace it for $11,000.

If the company proceeds with the special product, the incremental cash flows will be:$

Sales revenue 15,000Conversion costs (9,000)Opportunity cost of the material (11,000)Negative contribution (5,000)

Therefore, the special product should not be made.



Illustration 6A company can make 1,000 units of a product for $12 material per unit and $15 per unit for labour costs. The product sells for $20 per unit.

There is enough spare (currently idle) labour capacity to make the 1,000 units. These employees are paid but are not working on any product.

Should the product be made?

SolutionThe labour cost is irrelevant: these employees are being paid anyhow and all the new product does is to require them now to work for their wages.

$Sales revenue 1,000 x $20 20,000Material costs 1,000 x $12 (12,000)Contribution 8,000

Therefore the product should be made.



Illustration 7A company can make 1,000 units of a product for $12 material per unit and 2 hours per unit for labour. The product sells for $22 per unit.

Employees are paid at $15 per hour and are currently employed on the production of another product that takes 3 hours of labour and which generates a contribution of $12/unit. Extra employees cannot be recruited and would have to be transferred from current work.

Should the new product be made?

SolutionNote: this quite a difficult problem

If employees are transferred from current work to the new product, each 2 hours needed to make the new product will mean that 2/3 of an existing product cannot be made. This will cause a contribution loss of $12 x 2/3 = $8 new unit made.

You will be tempted to set out the effect of the new product as:

$Sales revenue 1,000 x $22 22,000Material costs 1,000 x $12 (12,000)Contribution forgone 1,000 x $8 (8,000)Contribution 2,000

However, this would be incorrect.

The problem is that the contribution that is being given up on existing production $12/unit (or $4/hour) implies that sales revenue is lost and that material and labour costs are saved (contribution is revenue less costs). If they simply sacked employees from the existing production the company would lose $12/unit of old production no longer manufactured. But here, the employees are still employed and are still being paid at $15/hour.

Therefore, the correct calculation is:$

Sales revenue 1,000 x $20 22,000Material costs 1,000 x $12 (12,000)Contribution forgone 1,000 x $8 (8,000) [if employees no longer employed]Labour costs 1,000 x 2 x $15 (30,000)Contribution (28,000)

The new product should not be made.



Example 4

A company will make a new product that takes 2,000 kg of material. 1,200 kg is already in inventory, bought some time ago for $3,600 and with a sales value of £1,600.

The current purchase price of the material is $1.20/kg.

The company has no use for this material other than making the new product, which uses 2kg/unit.

Market research of $1,500 has already been carried out and this indicates that the product would sell for $4/unit. Fixed costs of $4,000 will be apportioned to the new product.

Should production commence?

Question 6

To make a product a business needs to use two materials, G and H. These materials are in inventory. G is used on a day-to-day basis in the business; H has no uses other than in the new product.

Information about the two materials is as follows:

Material Quantity neededper unit of thenew product

(kg)

Original cost($/kg)

Current purchase price

($/kg)

Sale price($/kg)

G 6 3.00 4.00 2.00

H 9 2.00 3.50 0.60

What cost should be included for materials per unit of the new product?

A $55.50

B $29.40

C $43.50

D $36.00



Question 7

Gizmo Incorporated needs to work out the cost of a new contract. The contract requires two sorts of employee:

Programmers: time needed = 2,000 hours @$30/hour

Analysts: time needed = 900 hours @ $50/hour

There is currently a shortage of analysts and if this contract is accepted, analysts will have to be moved from other work where they generate a contribution of $80/hour, after charging their salaries.

There is sufficient idle time amongst programmers to provide the time needed for this project. Because programmers are skilled and scarce, the company has no intention of removing programmers from the workforce.

What is the incremental and opportunity costs of labour that should be assigned to this contract?

A 117,000

B 72,000

C 177,000

D 132,000



Chapter 10CAPITAL INVESTMENT APPRAISAL

1. Introduction

‘Capital investment’ refers to the purchase of non-current assets. These purchases are often known as capital expenditure. Non-current assets are used by the business to make profits over a number of accounting periods. Examples include: factories, machinery, office equipment and motor vehicles.

Capital investment therefore typically involves spending now to enjoy increased income in the future. Income and expenditure are therefore not matched in a profit and loss account and it is important to have techniques that help businesses to decide if the expenditure is justified.

2. introduction to discounted cash flow

As stated above, a key feature of capital expenditure is that expenditure occurs now and income is in the future. The cash outflows (expenditure) and inflows (income) occur in different time periods and so cannot be directly compared.

For example, here is a simple choice. Would you rather have:

1. $1,000 now, or

2. $1,000 in one year’s time?

Most people would prefer option 1 because it is:

๏ Safer

๏ Gives immediate enjoyment

๏ Even if you do not need it now, you can invest it for a year.

The value of investment can be evaluated by looking at interest rates. If the money could be placed on deposit at 6% for a year, then the two options really are:

1. $1,000 x 1.06 = $1,060 in 1 year, or

2. $1,000 in one year.

So earlier flows are worth more than later ones.

Instead of projecting amounts into the future (which calculates the terminal values), it is more normal to bring all amounts back to the present. So, for option 2, we want to find out how much would need to be received now to become (be identical to) $1,000 in one year.



So, if p is received now and invested at 6% to become $1,000, the following must be true:

p x 1.06 = 1,000

p = 1,000/1.06 = 943.40.

$943.40 is known as the present value of receiving $1,000 in 1 year at a discount rate of 6%.

This means $943.40 is equivalent to receiving $1,000 in 1 year if interest rates are 6%. [Check $943.30 invested at 6% becomes $943.40 x 1.06 = $1,000]

So the two original options can be rephrased as:

Would you rather have:

1. $1,000 now, or

2. $943.30 now?

Obviously, option 1 is preferable.

Example 1

By working out the present values of the options, indicate which of the following options is preferable.1. $3,000 received now or

2. $4,000 received in 4 years

Interest rate = 7%

By working out the present values of the options, indicate which of the following options is preferable.1. $3,000 received in 2 years or

2. $3,800 received in 5 years

Interest rate = 10%



3. Discounted cash flow tables

The above examples should help you to realise that:

Present value =

Cash flow ×1(1+r)n or [or Cash flow x (1 + r)-n

where:

r = discount rate as a decimal

and

n = number of years in the future the flow occurs.

You can see this in previous example 1 where the present value of $4,000 received in 4 years at an interest rate (discount rate) of 7% is:

PV = 4,000 ×1

(1+ 0.07)4 = 4,000 × 0.736 = 3,052

0.763 is known as the discount factor for 4 years at 7%.

Instead of having to work this out manually, discount tables are routinely provided. They are at the start of this set of notes, but here is an excerpt:

You will see that with a discount rate of 7% and a period of 4 years, the discount factor is as was previously calculated, 0.763.

It is common in investment appraisal to have a number of years with equal flows: this would be termed an ‘annuity’. For example, the same rent might have to be paid for several years.



So, if a payment of $1,500 had to be made after one, two, and three years, with a discount rate of 9%, the calculation could be set out as:

Time Cash flow $ Discount factor(see table above)

Discounted cash flow $

1 1,500 0.917 1,375.50

2 1,500 0.842 1,263.00

3 1,500 0.772 1,158.00

Total 3,796.50

However, a faster way of working this out would be to add up the discount factors and multiply their total by $1,500:



1 1,500 0.917

2 1,500 0.842

3 1,500 0.772

1,500 2.531 3,796.50

This would normally be written out as:



1 - 3 1,500 2.531 3,796.50

Once again, this type of calculation is made easier by the use of tables known as Annuity Tables or Cumulative Discount Tables. Here’s an excerpt:



You will see that at a discount rate of 9% and for three periods (n = 3), the annuity discount factor from this table is 2.531, as was calculated above.

It is important to realise that if you are using discount factors straight from annuity tables, then the cash flows must start after 1 year and occur every year up to the stated number off periods.

Therefore, if any other pattern of flows occurs the discount factor will have to be adjusted.

So, if $200 is to be received in years 4 – 10 with a 5% discount rate, the required calculation would be:

Cumulative discount factor years 1 – 10 7.722less: cumulative discount factor years 1 – 3 2.723Cumulative discount factor years 4 – 10 4.999

Therefore, the present value of the cash received is $200 x 4.999 = $999.8

Note: the cumulative factor for years 1 – 3 has to be removed to leave 4 – 10. The commonest error made is to remove the cumulative factor for 1 – 4, but that would only leave a factor for years 5 –10.

Example 2

What is the present value if $100 is to be received in years 6 – 9?

Discount rate = 5%

What is the present value if $100 is to be received in years 3 – 10 except year 5?

Discount rate = 4%

What is the present value if $200 is to be received in years 0 – 5? Discount rate = 10%

Question 1

A business has five annual cash inflows of $1,500 pa starting at time 3.

What is the present value of these flows at a discount rate of 7%?

A 6,245

B 5,372

C 4,148

D 5,021



Question 2

A business has cash inflows of $400 pa for times 0 – 8, except time 5.

What is the present value of these flows at a discount rate of 10%?

A 2,534

B 1,018

C 1,886

D 2,286

4. The cumulative discount factor formula and perpetuities

You will see a formula at the top of the annuity tables:

Annuity factor = 1− (1+ r)−n

r

Some people prefer to write this as:

Annuity factor = 1

r1− 1

(1+ r)n⎡⎣⎢

⎤⎦⎥

This will give the figures in the tables (a pointless exercise in itself!) but might need to be used if the discount rate or the number of periods is no on the tables.

Example 3

Work out the cumulative discount factor for n = 7 and the discount rate = 8% (ie r = 0.08), and check to the figure in the tables.

Work out the cumulative discount factor for n = 12 and the discount rate = 5.5% (ie r = 0.055).

As annuity is an annual cash flow. As the annuity becomes longer (ie more years of flow) the annuity becomes close to a perpetuity, which is an equal cash flow for ever ie in perpetuity. Obviously no set of flows is for ever, but after 20 years or so, at moderate discount rates, discount factors are so small that further flows can be ignored (for example, the 20 year 10% factor is 0.149) and for convenience the flows can be treated as a perpetuity.



Notice what happens the annuity factor formula as n, the number of years of flow, becomes very large

Annuity factor = 1

r1− 1

(1+ r)n⎡⎣⎢

⎤⎦⎥

An n becomes large this term becomes very small and the formula can be simplified to

Perpetuity factor =

1Perpetuity factor = r

So, the present value of receiving $1,000 from time 1 to infinity at a discount rate of 10% is:

PV = 1,000 =$10,000PV = 0.1 =$10,000

Note that as with annuities, perpetuities start at time 1 and occur every year. So, if the pattern is something else, the perpetuity factor will have to be adjusted.

Question 3

A business will receive rent of $10,000 pa on a 500 year lease.

What is the present value of the rental receipts if the discount rate is 5%?

A $200,000

B $100 million

C $1 million

D $5 million

Question 4 A business will receive rent of $10,000 pa on a 999 year lease, starting at year 3.

What is the present value of the rental receipts if the discount rate is 5%?

A $200,000

B $172,770

C $181,410

D $185,900



Question 5

A business will receive rent of $10,000 pa on a 999 year lease, starting at year 0. At time 2 the business will also receive $1,000 to cover the legal fees involved in setting up the lease.

What is the present value of the receipts if the discount rate is 7%?

A $153,730

B $152,857

C $143,730

D $142,857

5. Using present values in investment appraisal – net present value approach.

It was shown above that flows of cash occurring at different times cannot be directly compared. For comparison all flows are discounted to their present values.

For investment appraisal the cash outflows (usually the initial investment) and inflows (usually the future income and sale of the non-current asset at the end of its life) are all discounted to their present values. Outflows are negative, inflows are positive and when added up the net total is known as the net present value (NPV).

If the NPV > 0 the present value of the inflows exceeds the present value of the outflows, so the business would be richer. The investment would be worthwhile and should be accepted.

If the NPV< 0 the present value of the outflows exceeds the present value of the inflows and this means that the business would be poorer if it invested. The investment should be rejected



IllustrationFor example: an investment in new machinery would cost $25,000 and would produce additional cash inflows of:Year 1 $8,000Year 2 $15,000Year 3 $10,000.The machinery could be sold for $2,000 at time 3.Is the project worthwhile if the discount rate is 8%?

SolutionTime Flow Amount $ Factor@ 8% Discounted

cash flow $0 Initial investment (25,000) 1 (25,000)1 Additional income 8,000 0.926 7,4082 Additional income 15,000 0.857 12,8553 Additional income 10,000 0.794 7,9403 Scrap proceeds 2,000 0.794 1,588

Net present value (NPV)Net present value (NPV) 4,791

As the NPV is positive, the project should be accepted

Example 4

An investment requires expenditure of $10,000 now and $12,000 at time 1. Income will be $5,000, $15,000 and $7,000 in years 2, 3 and 4. There are no scrap proceeds.

Is the investment worthwhile when evaluated at a 9% discount rate?

Example 5

An investment requires expenditure of $18,000 now will yield income of $8,000 pa for times 2 - 5




6. Net present value approach – care needed

To carry out NPV you have to identify relevant cash flows. The rules are similar to what you met earlier with relevant costing. Look for cash flows that are future incremental costs or income caused by the investment decision.

In particular:

๏ Cash flows are what you need, so look at income before depreciation.

๏ Reapportionment of existing fixed costs is irrelevant.

๏ Sunk or past costs are irrelevant.

๏ Opportunity costs are relevant ie cash flows forgone because of a decision

๏ Ignore all interest and other finance flows. These are taken account of by discounting.

Example 6

An investment requires expenditure of $15,000 now will yield income of $5,000 pa after depreciation for times 1 – 3 then $4,000 after depreciation of year 4. The machine can be sold for $3,000 in year 4. Research expenditure of $5,000 has been incurred on the new product that would be made by the machine.


Question 6

A business is considering implementing solar heating throughout its factories. This will cost $900,000 after one year and the savings are estimated to be $400,000 two years from now and $600,000 three years from now.

The savings figures are after time from existing managers has been charged to the project at $30,000 per year.

Discount rate = 10%

What is the NPV of the project?

A 111,710

B 37,100

C +37,100

D –37,510



Question 7

A business owns some land that could be sold for $1 million and which cost $800,000 two years ago. Alternatively, the land could have apartments build on it for a present cost of $5 million. The apartments would bring in rent of $550,000 pa in perpetuity from time 1 onwards.

Discount rate = 10%

What is the NPV of the project?

A 4,700,000

B 5,500,000

C 4,500,000

D 6,500,000

7. Discounted cash flow – internal rate of return (IRR)

The internal rate of return (IRR) is defined as:

IRR = discount rate where NPV = 0

It is sometimes referred to as a breakeven discount rate.

If the discount rate to be used is greater than the IRR, then the project is not worthwhile. That would be like borrowing at 10% and investing in a project which generated 5%: obviously you would lose out.

If the discount rate to be used is less than the IRR, then the project is worthwhile. That would be like borrowing at 5% and investing in a project which generated 10%: obviously you would make money.

The IRR will tell you nothing about accepting/rejecting a project that the NPV has not already told you.

Estimating the IRR requires you to work out the NPV of the project at two discount rates. There is nothing special about the two rates chosen, but many people try 10% and 15%, or 5% and 15% or 10% and 20%.

For example:

NPV at 5% = $1,000

NPV at 15% = -$1.300

These results can be shown on a graph:



At a low discount rate the future positive cash flows stay relatively large after discounting so the NPV is likely to be positive.

At a high discount rate the future positive cash flows are considerably reduced after discounting so the NPV is likely to be negative

The IRR must be between 5% and 15% and this has to be estimated. However, the line joining the two discount rates and NPVs is usually curved and this makes estimation more difficult. To simplify matters it is assumed that the line is straight and this will result in an estimation of the IRR rather than a precise figure.



Simplifying, and drawing some triangles:

Our aim is to work out the distance BF as the IRR will then be estimated as 5+BF

The triangles ABF and ACD are similar, meaning that they have the same proportions. Therefore, for each, the base/height must be equal:

BF/AB = CD/AC

BF = AB x CD/AC

= 1000 x (15 – 5) /(1,000 + 1,300) = 4.3

Therefore, point F must be 5 + 4.3 = 9.4%, and this is the estimate of the IRR.

Note that if someone had calculated the IRR using the NPVs at, say, 4% and 16%, the IRR estimate would be slightly different.

Some people are happy sketching diagrams such as those above. Others prefer to use a formula (not given in the exam):

IRR = A%+ NA

(NA −NB)(B%− A%)

Where

A% = lower discount rate tried

B% = higher discount rate tried

NA = NPV at A%

NB = NPV at B%

So, in the above example

A% = 5, B% = 15, NA = 1,000, NB = -1,300

IRR = 5%+ 1,000

(1,000 − (1,300))(15− 5) = 5+ 1,000

2,300×10 = 9.4%



Note the bottom line carefully: NA – NB;

NA = 1,000 and NB = –1,300.

So, NA – NB = (1,000 – (- 1,300)) = 2,300 [the two negative signs make a plus]

Question 8 At 10% NPV = $1,200

At 20% NPV = $-500

What is the estimated IRR?

A 17%

B 27%

C 19%

D 20%

Question 9 At 8% NPV = $1,200

At 12% NPV = $500

What is the estimated IRR?

A 18.9%

B 10.8%

C 14.9%

D 17.3%



Question 10

Mr A Chancer is thinking of investing $20,000 on 31 December 2013 to receive on repayment of $25,000 on 1 January 2016.

What is the IRR on his investment?

A 12.5%

B 8%

C 5.7%

D 25%

Question 11

A project with conventional cash flows (cash out now, received in the future) has an IRR of 12%. The discount rate is 9%.

This means that;

A The NPV will be positive, but the project should be rejected

B The NPV will be negative, but the project should be accepted

C The NPV will be negative and the project should be accepted

D The NOV will be positive and the project should be accepted.

8. Pay back periodThe payback period measures how long it takes for a business to recoup its cash outlay.

It uses the same figures as an NPV calculation.

IllustrationFor example: initial outlay = $12,000, cash inflows Year 1 = $4,000, Year 2 = $5,000, Year 3 = $6,000, Year 4 =$4,000.

Pay back can be estimated by:Cost = $12,000 Inflow

$Cumulative inflow

$Year 1 4,000 4,000Year 2 5,000 9,000Year 3 6,000 15,000Year 4 4,000 19,000

The initial cost is recouped after year 2 and by the end of year 3. If cash is earned evenly over the period, then payback will be at 2 years 6 months (6 month of year 3 earnings will be $3,000, bringing cumulative earnings up to $12,000 = $9,000 + $3,000)



Companies set pay back targets and if the actual payback period I shorter than the target, the project will be accepted; if longer than the target, payback will be rejected.

The main faults with payback are:

๏ No account is taken of the time value of money: flows from each year are simply added together.

๏ Payback loses interest after the target has either been met or missed. So if the payback target in the above example had been 2 years the project would be rejected. That decision would be the same even if, say, the inflow in year 3 was forecast to be $150,000, not $15,000. Obviously, payback can’t be used just on its own.

9. Discounted payback

Here, future inflows are discounted to their present values. So, if the discount rate were 10%, the above illustration would be:

Cost = $12,000 Inflow$

10%factor

Discounted Inflow

$

Cumulative discounted

inflow $

Year 1 4,000 0.909 3,636 3,636

Year 2 5,000 0.826 4,130 7,766

Year 3 6,000 0.751 4,506 12,272

Year 4 4,000 0.683 2,732 15,004

You can see here that the discounted payback period is almost 3 years

(strictly 2 + 4,234/4,506 = 2.94 years)

Question 12

A company has an investment costing $20,000 and will hope to receive inflows as follows:

Year 1 = $7,000;

Year 2 = $8,000,

Year 3 = $10,000,

Year 4 = $8,000.

The company uses a discount rate of 8% and has looks for a payback of 4 years and a discounted payback of 5 years.

Cash flows arise evenly throughout the year.

A Payback = 2 years; discounted payback = 2 years

B Payback = 3 years; discounted payback = 3 years

C Payback = 2.5 years; discounted payback = 2.3 years

D Payback = 2.5 years; discounted payback = 2.8 years



Chapter 11CASH MANAGEMENT

1. Introduction

You might have come across the saying ‘Cash is King’, and in business, it is. Organisations can exist for a long time even if they make losses. If they can raise capital from a bank, or from investors in shares, or the government, or by selling assets, they will survive. But businesses that are long-term unprofitable will eventually find it impossible to raise more capital and they will run out of cash. Once the organisation cannot pay its employees, its suppliers, its landlord, its interest or its tax it will have to stop trading.

2. Profit v cash

Profits are usually calculated using the accruals basis. So, a sale will count as income as soon as it is made even though the customer might not pay for a month or so.

Cash movements are not necessarily caused by profit and loss account items. For example, buying non-current assets, paying dividends and repaying loans are not expenses to be deducted from the profit and loss account, but they do deplete cash.

Unfortunately it is often relatively inexperienced but successful businesses that run out of cash. They might be expanding rapidly by buying equipment (cash spent), and fail to budget properly for future cash needs. A business can be profitable but can have net negative cash flows.

3. Cash flow budgetsCash flow budgets (or forecasts) are essential for successful cash management. The secret is to get the timing correct.



Example 1

Here are actual figures for November and December 2013 and budgeted figures for 2014:

$ November 2013

December 2013

January2014

February 2014

March 2014

April2014

Sales 12,000 14,000 9,000 8,000 10,000 12,000Purchases 10,000 10,000 4,000 4,000 5,000 8,000Other expenses 3,000 5,000 3,000 3,000 3,000 4,000Purchase of non-current assets 20,000Tax 10,000

You are told that 60% of customers pay after one month and 40% after two months. Suppliers are always paid after one month. Expenses are paid in the month incurred.

Cash at 1 January 2014 = $20,000

Draft the cash flow budget for the first four months of 2014.

$ January2014

February 2014

March 2014

April2014

Cash from customers

Total

Cash paid to suppliers

Other expensesPurchase of non-current assetsTaxTotal cash expenditureNet cash flowCash b/fCash c/f

You will see that the company needs to arrange borrowing of $4,400 (or to raise cash in some other way) for March and $2,600 for April. Instead of raising cash the company might be able to:

1. Postpone or reduce the capital expenditure of $20,000 in February,

2. Delay paying its suppliers – though this can ultimately lead to suppliers refusing to supply goods or suppliers asking the court to wind up the company.

3. Accelerate receipts form customers. 40% of them take a leisurely two months to pay.



Question 1

Erasmus Ltd made cash sales of $10,000, $8,000 and $12,000 in its first three months of business. 35% of its sales are for cash. The remaining sales are on credit and amounts are received as follows:

Received in month of sale: 15% of total sales (after a 5% settlement discount).

Received in the 2nd month: 30% of total sales

Received in the 3rd month: 20% of total sales.

What will Erasmus receive in its third month of business?

A $12,000

B $10,100

C $10,400

D $10,310

Question 2

At the start of a month, Spinoza has cash at the bank of $20,000, receivables of $42,000 and payables of $65,000. The company will sell goods in the month for $120,000 that cost $80,000.

50% of amounts due from sales are collected in the month and 50% in the following month. Purchases are paid for in the following month. Inventory is constant and other expenses, paid in the month are $90,000.

What will the company’s bank balance be at the end of the month?

A $54,000 overdrawn

B $33,000 overdrawn

C $48,000 overdrawn

D $69,000 overdrawn

Question 3 A company budgets sales as follows:

Month 1 3,000 units

Month 2 3,600 units

It also wants to increase finished goods levels by 500 units in Month 1 and 1000 units in Month 2. Material costs $5/kg and each unit takes 2 kg. The company keeps no stocks of raw material.

50% of purchases are paid for in the month of purchase and 50% in the following month.

How much cash will be paid to suppliers in Month 2?

A $46,000

B $33,000

C $40,500

D $25,500



4. The working capital cycle

Some of what you see in the cash flow forecast is the working capital cycle. This can be depicted as:

Goods are sold

Customers pay

Suppliers are paid

Material is bought. Raw material becomes

work-in-progress, which becomes finished goods

Cash is tied up in inventory and (raw material, work-in-progress, and finished goods). It is then tied up for a period in receivables. After some time, cash has to be paid to suppliers. The cycle repeats.

The cycle length can be calculated as:

Days of inventory + Receivables collection period – Payables payable period.

Example 2 What is the working capital cycle length for the following information?

Raw material days (ie how many days’ supply of raw material there is). Sometimes known as raw material turnover period. 20Work-in-progress turnover period. 2Finished goods turnover period 25Payables days 34Receivables collection period 45



The longer the working capital cycle, the more working capital the organisation needs to be able to trade. Organisations differ greatly in this regard. For example:

Supermarkets: the days of inventory will be low as food is perishable. Therefore cash is not tied up in inventory very long – perhaps 5 days on average. There are no credit customers, so cash is received immediately for sales. Receivables collection = 0. Supermarkets will take 30 – 60 days credit (say) from suppliers.

Working capital cycle = 5 + 0 – 30 = -25. So supermarket’s working capital is self-funding as they get cash in before they have to pay it out.

Engineering company: assume days of inventory = 90; receivables collect ion period = 40 days and suppliers have to be paid after 30 days.

Working capital cycle = 90 + 40 – 30 = 100 days

So, engineering firms are ‘out of pocket’ for 100 days and this has to be funded by raising capital.

Anything a company can do to reduce its working capital cycle length will improve its position. So they should concentrate on reducing inventory, negotiating better terms form suppliers and encouraging customers to pay more quickly.

Question 4

A company holds raw material for 50 days and finished goods for 12 days.

It takes 45 days credit from suppliers and customers pay after 50 days.

What is the length of its working capital cycle?

A 45 days

B 57 days

C 55 days

D 67 days



5. Treasury management

Treasury management can be defined as:

“The management of an organisation’s investments and cash flows, its banking, money market and capital market transactions; the control of the risks associated with those activities, and the pursuit of optimum returns consistent with those risks”.

Some terms need to be expanded on here:

Money market: where money can be placed on deposit or borrowed from. The main participants are banks but other organisations such as insurance companies and local councils can be involved also.

Capital market: for example, the stock exchange. Shares can be issued here to raise cash.

Risks and returns: these go hand in hand. If money is put into a risky investment then the depositor would expect a higher return. Generally, the longer the term of a deposit, the higher the interest rate that will be obtained. The borrower knows that the cash doesn’t have to be repaid for some time (so will pay more) but the lender is locked in for a longer time so will demand higher interest in exchange for flexibility and the risk that the money will be needed earlier.

The aims of treasury management are to try to ensure that

๏ no cash is lost through poor investments

๏ investments are timed to prevent the need for short term, emergency borrowing

๏ borrowing is planned and taken at the best time and only for as long as necessary

๏ the most efficient use is made of surplus cash



6. Raising capital

There are two main sources of capital: share capital and loan capital. This syllabus does not deal with share capital.

Most businesses will raise loan capital from a bank and this is typically divided into four types of capital:

๏ Overdrafts: repayable on demand and short term loans : usually < 1 year

๏ Medium term loans: typically 1 – 5 years

๏ Long term loans: typically >5 years

Generally companies are advised to raise loans that match the life of the asset being bought or funded by the loan. This is similar to what happens in personal finance:

If you were buying an apartment a long term loan (‘mortgage’) of around 25 years would be used.

If you were buying a car, a medium term loan of about 4 years might be arranged

If you wanted to finance a holiday trip, you might use a credit card (effectively a short term loan)

Overdrafts do not have a fixed repayment schedule and banks regard them as relatively risky. They usually have relatively high interest rates, but they can be repaid whenever the lender wants to so that gives the lender flexibility. The bank can demand immediate repayment – which can be somewhat precarious for the borrower. Overdrafts are very suitable for short term, temporary needs such as dealing with seasonal stock increases that need temporary funding. They are not advised for long-term financing.

Long term capital will be used to fund assets such as premises and machinery.

Medium term finance is suitable for office equipment and motor vehicles.

Loans can be:

๏ Fixed rates interest; or

๏ Variable rate interest

The former gives certainty about payments but the company loses out if interest rates fall.

Loans can be:

๏ Unsecured

๏ Secured

A secured loan means that the lender has the right to seize a specific asset or assets of the borrower if the loan repayment terms are breached. For example, a loan might be secured on the company’s office building (the building is said to be ‘charged’). If the company defaults on repayments, the lender can ‘seize’ the building and sell it to recover amounts owing.

A fixed charge relates to a specific asset off the company that can be seized and sold.

A floating charge relates to all the assets of the company at the time the charge is exercised.



7. Investing surplus finds

It is important that surplus funds do not simply stay in a bank deposit account earning nothing. There are three reasons for having cash available:

๏ Transactions motive: the cash needed for day-to-day operations and the purchase of new equipment.

๏ Precautionary motive: the cash needed to see the business through emergencies

๏ The speculative motive: cash needed in case a good opportunity arises eg the take over of another company.

The cash flow budget looks primarily at analysing the transactions need for cash. However, the company should have cash (or cash available) to cover the other reasons. It might have amounts on deposit in case of need, or it might have lines of credit set up (ie a pre-agreed right to borrow).

This is similar to our private lives: your current account will hold the money for day-to-day living. However, you might like to have some cash in a deposit account in case of a financial emergency. Additionally, you might have a credit card with a relatively high, but unused, borrowing limit. So, if the engine on your car suddenly blows up you have the precautionary motive resources to fix it by dipping into savings or charging it to your credit card.

The cash flow budget will be able to when surplus funds might arise and for how long. These can then be invested in a number of ways:

๏ Bank deposits. Many bank deposit accounts are linked to current accounts allowing the instant transfer from one to the other. Some deposit accounts have terms associated with them (for example, the bank must be given 1 month’s notice for repayment, or the minimum deposit length must be 3 months)

๏ Money-market deposits. These are either fixed term or with a given notice period. They are used for larger amounts, typically over $50,000.

๏ Certificates of deposits. CDs are documents showing that an amount of money has been deposited with a bank for a given period (typically 6 months). The key feature of a CD is that it can be bought and sold. Whoever owns it at the end of the borrowing term is repaid the money. This means that CDs are ‘liquid’. So, if a company deposits $50,000 with a bank for 6 months and receives a CD to that effect, but needs the money after 2 months, the CD can be sold to realise the investment.



๏ Government stock (gilts). These are very safe insofar as almost certainly the interest will be repaid and they will be repaid upon maturity. However, their value can fluctuate as will be demonstrated below. They can be for between 1 and, say 50 years (though some are undated and never repaid). They can be bought and sold very readily on the stock exchange. Their value fluctuates with market interest rates. For example, look at this government stock:

$20 is the par or nominal value

5 ¼ % is the coupon rate

2017 is the repayment date

Whoever owns this stock will receive $20 x 5 ¼ % = $1.05 interest every year.

If market interest rates fell to 3%, the owner of the stock would still receive $1.05. If

the stock were to be sold, the new owner would receive $1.05. If the bond still cost that person $20 then they would be getting a very high rate of interest (5 ¼ %) compared to the market rate of interest. Therefore, the value of the bond increases until it effectively pays 3%.

3% = 100 x $1.05/market value

Market value = $1.05/0.03 = $35

[Check 1.05/35 = 3%]

๏ Local authority stocks. To all intents and purposes these have identical characteristics to central government stocks. There will be slightly more risk as it is more likely that a local authority will default than a country will default.



Question 5 Which of the following statements is true?

A Government stocks can be traded; certificates of deposit cannot be traded

B Both Government stocks and certificates of deposit can be traded

C Neither Government stocks and certificates of deposit can be traded

D Government stocks cannot be traded; certificates of deposit can be traded

Question 6 What would be the market value of $100 nominal of 4.2% Government Stock if the current interest rate in the economy is 6%?

A $143

B $100

C $42

D $70

8. Interest rate calculationsInterest rate calculations apply to both borrowing and lending. You have to be aware of the meanings of the following terms.

Simple interest

Interest is always calculated with respect to the original amounts deposited (the principal).

Example 3

$12,000 is deposited at 4% simple interest for 3 years.

How much will there be on deposit at the end of that time?



Compound interest

Interest is always calculated on both the principal and the interest earned so far.

IllustrationFor example $1,200 on deposit at 10% compound.After 1 year: $1,200 x 1.1 = $1,320After 2 years: $1,320 x 1.1 = $1,452and so on.

The general formula is:

Final amount invested = Principal x (1 + r)n

where: r = interest rate as a decimal;

n = number of years.

Example 4

$2,000 is deposited at 6% for 8 years.


$5,000 is deposited at 5.5% for 5 years.




Nominal interest rates

The word ‘nominal’ means ‘not real’. So the nominal head of a country is a figurehead and not where the real power lies. Similarly, ‘nominal interest rate’ means that the figure is not the real interest rate. The discrepancy arises because although interest is often paid several times a year (for example monthly), the interest rate is expressed in annual, nominal terms.

To work out the interest that will actually be charged or earned it is necessary to work out the effective annual interest rate.

IllustrationA bank deposit account quotes a nominal rate of 9%, but interest is paid quarterly. The effective rate will be greater than 9% because interest will be paid on the interest credited each quarter.This nominal rate means that the bank pays 2.25% every quarter.

The effective interest rate is given by:

Effective interest rate = (1 + r)12/n – 1

where: r = rate of interest for each time period

n = number of months in the period

In the example above,

Effective interest rate = (1 + 0.0225)12/3 – 1 = 0.0931 or 9.31%

After a year, if $1,000 had been placed on deposit, there would be $1,093.10in the account.

Question 7 How much will an investor end up with if $5,000 is deposited at 5% compound interest, for 6 years, where interest is paid annually?

A $6,700

B $6,500

C $5,250

D $6,691



Question 8

A bank quotes an interest rate of 8%. Interest is credited quarterly to the account.

If $2,000 is deposited for 3 years, how much interest will be earned?

A $519

B $536

C $480

D $466

Question 9 Interest is credited each month to an account.

If the effective annual interest rate is 6%, what is the nominal annual interest rate?

A 5.84%

B 6.16%

C 4.87%

D 5.00%

9. Types of payment from the bankPayments can be made from a bank account in four main ways:

๏ Cheques: see later

๏ Internet transfer: now very common. It is vitally important that account log-on details are kept secure. In addition to user-known passwords, some banks now issue devices that generate unique use-once codes. Access to the bank account is then possible only by someone who both knows the password and who possesses the device.

๏ Direct debit. Here the person receiving the funds has the right to extract them from the bank account. This is often used by institutions like insurance companies to collect insurance premiums from clients. The process can be completely automated.

๏ Standing order Here the person paying instructs their bank to pay a regular amount to the recipient. This is often used to pay regular amounts like rent. The process can be completely automated.

All payments should be properly authorised and approved.

In addition, banks can remove funds from accounts for interest and bank charges.



10. Cheques and the clearing system

Cheques are unconditional orders in writing given to a bank (the drawee) by the person paying out of his or her bank account (the drawer of the cheque) to pay an amount to the payee (the person receiving the money).

Here is a typical UK cheque

Counterfoil Cheque

HSBC is the bank (the drawee ie the institution on whom the cheque is drawn and the order to pay given).

Mr J Tar is the drawer (the person paying the money)

40-07-05 and 21745175 are numbers that identify the bank branch and the bank account

202546 is the cheque number (for identification)

The numbers printed at the top right are reproduced in special machine-readable characters at the bottom of the cheque and these allow automatic processing of the cheque.

The cheque can be torn out of the cheque book leaving a counterfoil onto which details should also be entered.



When completed, the cheque would look like:

ABC Co Ltd

One thousand five hundredpounds only

ABC Company Ltd--------------15 January 2013

15 /1/2013

1500.00

1,500 - 00

The ABC Company Ltd is the payee (the person who will receive the funds.

Cheque books must be kept securely as the signature of the authorised person (J Tar) could be forged (falsified) and cheques made out improperly to steal funds.

Note that the payee is written as “ABC Company Ltd-------------------“ and the amount as “One thousand five hundred pounds only”. The line after Ltd and the word ‘only’ are to prevent changes being made.

All cheques should be accounted for, even those which are made out incorrectly and scrapped: the cheque should be marked “VOID” in large letters and kept in the cheque book.

When ABC Company receives the cheque it must be promptly paid into the company’s bank. Any delay means that there is a delay in the company being able to use that money and also it increases the risk that cash or cheques go astray or are stolen.

Paying in is done using a paying-in slip.

ABC will list cheque details on the reverse of the slip, and the total on the front.

The total will appear in ABC’s bank account at the end of the day, but that does not mean that funds have been safely transferred: the amount is only provisional. The cheque from J Tar has to be sent back to his bank to see if there is enough money in the account. If there is, then Tar’s bank will send the money to ABC’s bank and the funds are transferred at that point.

This process is known as ‘clearing the cheque’ and it takes around three days (Internet transfers are usually completed in a couple of hours).



If Tar did not have enough funds to pay the money, then the cheque is sent back to ABC’s bank and then on to ABC marked ‘Refer to Drawer’. ABC then has to pursue the matter with Tar and the funds that had provisionally appeared in ABC’s account are removed.

11. Cash flow forecasting

Cash flow forecasting can be complicated by:

๏ Inflation

๏ Seasonal fluctuations and trends in operations.

Inflation and index numbers

Price inflation is typically measured by an index, in general calculated as:

Price of commodity nowPrice of commodity in the base year

The base year is an arbitrary date from which price rises are measured.

The index is usually expressed as points (Which are essentially which start at a value of 100.

So:

Price of commodity, now (2013) $45 =100

Price of commodity in the base year (2013) $45 =100

If the price in 2015 is $54, then in 2015 the index will be $54/$45 = 120.

This means that the price has risen 20% from the base year.

Although individual commodities can have an index calculated as above, often companies (and certainly individuals) are buying a collection, or basket, of items and economies are therefore subject to general inflation based on the mix of items bought. From time to time the mix of goods in the ‘basket’ is changed to keep it up to date. For example, 25 years ago or so, mobile phone costs would not have been very important o most people, but now they are material and should be taken into account.

In the UK the measure of general inflation in the economy is the Retail Price Index (RPI). Other countries have similar measures and these will often be used as a starting point for wage negotiation and other price adjustment.



Question 10

A price index over a period of 3 years is 125. If goods cost $5,000 now.

What did they cost in the base year of the index?

A 1,000

B 3,750

C 4,000

D 1,250

Seasonal fluctuations and trends in operations

If you were to plot, say sales, against time, it is common to find a pattern such as:

Sales

Time

Clearly there is an underlying increase in sales but that there are also regular variations.

๏ The underlying increase is called the trend

๏ The regular variations repeating in less than a year are called seasonal variations

So, a holiday company’s sales are generally increasing but superimposed on that increase are busy periods (such as summer) and slack periods (such as winter)

It is very important to take the seasonal variations into account when working out cash flows. Although over a year the company might be cash positive, it might have several months where it is cash negative and it has to have enough cash available to cover the hard times before business picks up again.

There are two other types of variation which are not used in predictions:

๏ Random (such as the effect of a strike on revenues). By definition these cannot be predicted but some precautionary cash should be available to handle disappointments.

๏ Cyclical. These are regular but with a very long repeat period. For example the economic cycle seems to go in a cycle length of about 12 years.



The trend and seasonal variations over time are estimating using the technique of moving averages

Look at this series of sales results. The raw results are listed in column 3, and you will see that the sales figures follow a reasonably regular pattern. For example in all of the first quarter’s sales seem to be particularly high, and in all of the second quarters seem to be particularly low.

To smooth these out averages of each set of four quarters are calculated (the 4-part moving average). So

1350 = (2,000 + 900 + 1,000 + 1,500)/4

1,400 = (900 + 1,000 + 1,500 + 2,200)/4

ie, for the calculation, move down one quarter at a time.

Year Quarter Sales (units)

4-part moving average

8 – part centred moving average:

trend

Seasonal variation (additive)

Seasonal variation

(multiplicative)1.00 1.00 2,000.00

2.00 900.00

1,350.00

3.00 1,000.00 1,375.00 (375.00) 0.73

1,400.00

4.00 1,500.00 1,413.00 88.00 1.06

1,425.00

2.00 1.00 2,200.00 1,456.00 744.00 1.51

1,488.00

2.00 1,000.00 1,513.00 (513.00) 0.66

1,538.00

3.00 1,250.00 1,575.00 (325.00) 0.79

1,613.00

4.00 1,700.00 1,635.00 65.00 1.04

1,658.00

3.00 1.00 2,500.00 1,689.00 811.00 1.48

1,720.00

2.00 1,180.00 1,726.00 (546.00) 0.68

1,733.00

3.00 1,500.00

4.00 1,750.00

These averages are not ‘opposite’ any season, so the process is repeated to obtain the 8-part centres moving average: 1,375 = (1,350 + 1,400) 2; 1,413 = (1,400 + 1,425) etc.

This is the trend, and you will see that these figures rise constantly and that the seasonal variations have been smoothed out. The increase per quarter can be calculated by saying that sales have increased by 351 (from 1,375 to 1,726) in 7 increments (there are 8 trend figures and 7 increases). The trend per quarter is there fore 351/7 = 50



Seasonal variations

The seasonal variations are the differences between the initial sales figure and the trend figures (additive model) or the ratio of actual sales compared to trend (multiplicative model). These can be collected together and averaged:

Seasonal variations additive model:

Qtr 1 Qtr 2 Qtr 3 Qtr 4

744.00 (513.00) (375.00) 88.00

811.00 (546.00) (325.00) 65.00

1,555.00 (1,059.00) (700.00) 153.00

778.00 (530.00) (350.00) 77.00

Seasonal variations multiplicative model:

Qtr 1 Qtr 2 Qtr 3 Qtr 4

151.00 66.00 73.00 106.00

148.00 68.00 79.00 104.00

1.50 0.67 0.76 1.05

Predictions

These results can now be used for predictions. For example, the sales figure for season 3, year 4 would be predicted by;

Trend: This season is 5 seasons further on (count from Yr 3 season 2, the last trend figure, to 3.3, 3.4, 4.1, 4.2, 4.3) so the trend figure will be;

1,726 + 5 x 50 = 1,976

Then adjust for the season 3 seasonal effect using the additive adjustment (- 700) or the multiplicative adjustment, and the predictions will be:

1,976 – 350 = 1,626

or

1,976 x 76% = 1,502

You should not expect the additive and multiplicative models to give the same estimates off future sales.



Question 11

The trend of sales is an increase of $1,000 per quarter. The trend figure for year 4 season 2 was $12,000.

What is the predicted sales figure for year 5 season 4 if the seasonal adjustment is 75% for season 2 and 110% for season 4

A $17,273

B $20,900

C $16,364

D $19,800

Question 12

The trend figure for year 3 season 2 is $14,000

The prediction for year 4 season 1 is $16,200

Trend = $500/season

What is the seasonal adjustment for season 1 using the additive model?

A +700

B -700

C +200

D -200



Chapter 12

INFORMATION FOR COMPARISON

1. Introduction

Presenting a piece of information on its own is of little value. You would not know, for example, whether or not sales of $5 million or a gross profit of 20% is good or bad. To make a judgement you have to compare figures to ‘get a feel’ for performance.

2. Basis of comparison

The normal bases of comparison are:

1. Previous period information

For example, compare revenue and expenses of this year so far to last year’s revenue and expenses. This has the advantage that the last period’s information is usually readily available, but has the disadvantage that the period lengths will normally not match. For example, comparing the results of the current three months with the last 12 months.

2. Corresponding period information

Here you would, for example, compare the result of 1/1/2015 – 31/3/2015 to those of 1/1/2014 – 31/3/2014. This has the advantage of taking into account any seasonal factors that might be relevant.

3. Forecast/budget information

Forecasts and budgets are often used to set targets and comparing the current actual information with budget information will gave a feel for whether or not the organisation is on target to meet its budget.

4. Other organisations

This needs care as there is little point in comparing a supermarket’s results to those of an airline. However, large chains of supermarkets keep a careful eye on each other to judge their performance: market share, gross profit, overhead costs. Even within one business sector, such as supermarkets some care is needed to ensure comparisons are valid as different companies might target different sectors or have within them a degree of diversification. For example, in the UK some of our supermarkets also run banks and credit card operations whereas others specialise in food.



5. The forecasting and budgeting process

Most budgets are created by looking at last year’s budget and updating for price changes, changes in product lines and so on. This approach is known as incremental budgeting and it is relatively quick and easy to carry out. However, it is often criticised because the operations of the company are not necessarily examined and challenged during the budgeting process. Just because last year IT cost $3 million and inflation is running at 10%, there is no need to assume that next year IT should cost $3.3 million. Technological advances or eliminating surplus reports and processing could allow savings to be made. Alternatively, improving the web-site dramatically could cause expenditure to be much higher in the next period. Some companies attempt zero-based budgeting which implies starting from scratch and building up the budget, justifying each $ spent.

Forecasting sales for a budget is particularly difficult as this will depend on prices, the economy, competitor action, the success of new products, the continuing popularity of old products and the effectiveness of advertising. Statistical approaches might be of some use. For example, it should be possible to predict future seasonality of sales from the patterns in previous years.

6. Feedback and feed forward control

Once budgets and forecasts have been established, then feedback control and feed forward control become possible.

Feedback control: for example, budget costs $1/unit, actual costs $1.5/unit. It appears that costs are running out of control and action should be taken to try to bring the costs back into line. This would be negative feedback control as it attempts to reduce the deviation from budget. In feedback control the problem or deviation has already happened. If sales were running ahead of budget, then there would be positive feedback control to try to keep or increase the deviation.

Feed forward control: this is where a problem in the future is anticipated and action is taken to avert that occurring. For example, if the cash flow budget is suggesting that, because of poorer than expected sales, the company will be short of cash in six months, then action could be taken now to avoid the problem. That action could be to increase the amount of borrowing that’s available, or to cut back on discretionary expenditure to maximise cash.

7. Flexible budgetsOften budgets are drawn up for only one level of activity, such as assuming production and sales will be 10,000 units. This is known as a fixed budget.

However, fixed budgets are of limited comparative value if actual production and sales are very different to the budget. Therefore, some companies draw up in advance flexible budgets. These are budgets produced at a number of different activity levels. For example, at production levels of 6,000, 8,000, 10,000 and 12,000 units. Having a range of possible forecasts will make comparisons to actual results more meaningful and also facilitates creating additional budgets between two existing flexible budgets.



8. Variances

A variance is the difference between actual and budgeted expenditure or income. Some care is needed to ensure that the comparison is valid.

If actual expenditure is higher than it should be, the variance is described as being ‘unfavourable’ (or ‘adverse’); if actual expenditure is lower than it should be then the variance is described as being ‘favourable’.

For example, assume that the raw material budget for a period is $100,000, but that actual expenditure is $110,000. Because expenditure is $10,000 above the budget it might look as though the production manager had been careless in the use of material.

However, this might be an invalid conclusion. What if you were told that the budget assumed that production would be 10,000 units but that because of extra demand actual production was increased to 12,000 units? Increasing production by 20% implies that raw material costs should increase 20% to $120,000. Viewed in that light, it can be argued that the production manager has actually saved $10,000 ($120,000 - $110,000). This would be a $10,000 favourable variance.

Adjusting the budget in line for the units produced is known as ‘flexing the budget’ and the result is a ‘flexed’ budget. Note this is different to a flexible budget as described above.

Amounts that need to be flexed are those which vary with production volume, typically:

๏ Raw material

๏ Variable labour

๏ Variable overheads (machine costs)

Example 1

A company has budgeted to produce 8,000 units in a month. Variable labour costs relating to this production are budgeted to be $96,000. Because of a fall-off in demand the company made only 7,000 units and the actual labour cost was $89,000.

What is the labour cost variance and indicate whether it is favourable or adverse?



Example 2

A company has budgeted to produce 10,000 units in a period. Material costs relating to this production are budgeted to be $150,000. The company actually produced 10,500 units for a material cost of $155,000.

What is the material cost variance and indicate whether it is favourable or adverse?

Example 3

A company has budgeted to produce 10,000 units in a period. Fixed overheads are budgeted to be $200,000. 11,000 units were produced and actual fixed costs were $230,000

What is the fixed overhead variance and indicate whether it is favourable or adverse?

Sales figures can also show variance ie revenue can be greater or less than budgeted for each line of inventory.

Some amounts do not need to be flexed in line with output because they are not variable ie they do not depend on production volumes. These are the company’s fixed costs. Examples include:

๏ Rent

๏ Depreciation

๏ Administrative salaries

Therefore, if the actual rent is $15,000 above budget this will be an adverse variance no matter what production is.



9. Causes of variances

Identifying the amount and sign of a variance is only the first step. Unless the cause of the variance is investigated and understood, knowing what the size of the variance is rather useless. Only once its cause has been discovered can steps be taken to try to eliminate it (in the case of an adverse variance) or to repeat it (in the case of a favourable variance).

Typical causes of variances are

Material cost Material price being higher or lower than expected.

Different amounts of material being used per unit that had been budgeted for.

Might be caused by commodity process changing or by good/bad negotiations over purchase price.

More careful or more careless workers; better/worse quality material so that wastage rates are altered.

Labour cost Wage rates being different to what was budgeted.

Staff being more efficient/inefficient than expected.

Staff allowed to be idle

Negotiations with employee representatives

Good/bad supervision and training.

Poor supervision.

Variable overhead costs

Machines being more or less expensive to run per hour.

Machines being used efficiently/inefficiently

Changes in power costs; maintenance.

Good/bad supervision and training/maintenance.

Fixed overhead variances

Expenditure different to budgeted Unanticipated price changes. Good/bas negotiation. More expenses taken on for expansion, but not budgeted for.

Sales variances Different prices to those that were budgeted

Different volumes sold compared to volumes budgeted.

Competitor pressure, economic changes, sales drives (ie deliberate price reduction to stimulate demand).

Change in market taste, competitor action production problems.

Note that many variances can be interdependent. So, if sale prices are reduced then sales volumes are likely to increase. If more money is spent on training (potentially an overhead variance) then labour and material costs are likely to decrease because the workforce is more efficient and wastes less material. If cheap material is bought then you might expect more to be used because it is of poor quality. It follows that an adverse variance will not always mean that a wrong decision has been made or that performance is poor. Certainly, large adverse variances would probably be investigated, but spending more than expected on training might be repaid many times over in lower expenditure on materials and labour.



10. Exception reporting

Exception reporting is the idea that if a business is producing results in line with a budget or forecast, then not much management action will be needed. If however there are substantial deviations from a plan then this needs to be investigated and management attention is required. For example, if sales are below budget, then management might have to think about increasing advertising spend, or decreasing prices. If wages and salaries are too high, management might consider a recruitment freeze of limiting pay rises.

In other words, management should be particularly interested where unusual or exceptional events occur. Variance analysis is of great help here as, in general, large variances imply unusual, exceptional that are worthy of management attention. Generally management would set control limits for each variance and if a variance went over that then an explanation would be required.

11. Investigation of variances

The following are the main influences on whether or not to investigate a variance.

๏ Cost v benefit. Variance investigation takes employee time and this has costs attached. Variances are only worth investigating if the cost of the investigation is less than the benefit likely to arise. There is little point in spending $1,000 investigating a cost overrun of $10.

๏ Size of the variance. Larger implies that the investigation is more worthwhile. In most cases using the percentage deviation will be more appropriate than the absolute variance. IN a small business $10,000 might be very material, but in a large multi-national business $10,000 will be trivial.

๏ Sign of the variance. Most people will be keener to investigate the cause of an adverse variance than a favourable variance. There is a feeling that the adverse variance implies something going wrong and that we want to ‘stop the rot’, or at least be able to explain to our boss what the cause is.

๏ Likelihood that the variance can be controlled. If heating costs were above average, but the weather had been particularly cold, then there is little management can do to stop the additional expenditure.

๏ Natural variability. Some amounts will vary quite a lot from month to month (eg direct labour overtime payments will depend on orders and production that month) whereas other amounts will be much more stable (eg admin salary costs). It is likely to be more useful investigating a 5% overrun on admin costs than a 10% variation on overtime.



ANSWERS TO EXAMPLES

Chapter 1

Example 1

Suggestions:

Examples of internal information: sales, purchases, wages and other expenses, inventory held, cost of producing an item, profitability of an item, amounts owing to and from the company, cash in the bank.

Examples of external information: competitors’ prices, interest rates, exchange rates, details about competing products, technological developments, market size and growth rate, customers’ assessment of us, forthcoming price changes.

Example 2

Suggestions:

Financial/non-financial: Value of sales/number of products sold to customers which needed maintenance.

Quantitative/non-quantitative: Market share as a % /customers’ opinions of us

Historical/future estimates: Costs for the first three months/costs for the next nine months

Routine/ad-hoc: Monthly management accounts/special report on a customer who went into liquidation

Numerical/graphical A table showing sales per country/a pie chart showing sales in each European country.

Example 3

The provision of non-financial, non-quantitative information is important because financial information does not capture everything that is of significance. For example, financial information might show that sales have declined but that will not explain why they have fallen. The cause might be that our goods have gained a reputation for poor quality. Financial information often records the results not the causes.

Example 4

Written - reportWritten – memorandumWritten – letterWritten – emailOral – address an audienceOral – discussion in a groupOral – one-to-one interviewsOral – pod-cast



Graphics – videoGraphics – graphs and diagramsMixture – internet site

Chapter 2

Example 1

(Any three for each category)Purchases: purchase requisitions, purchase orders, goods received notes, purchase

invoicesSales: sales orders, delivery/despatch notes, sales invoicesInventory: goods received notes, materials requisition notes, bin cards, despatch notes

Example 2

PreciseConciseEnables automatic processingChecking for errors/preventing errors.

Example 3

Simple to useUnderstandableConcisePreciseExpandable

Chapter 3

Example 1

Output doubles between quarters 1 and 2, but costs do not double, so they cannot be purely variable.

High = 25,000 units and $370,000 costsLow = 10,000 units and $220,000 costsDifference = 15,000 units and 150,000 costsTherefore, variable cost per unit = $10Fixed cost = 220,000 - $10 x 10,000 = $120,000 [or $370,000 - £10 x 25,000 = $120,000]

If these are used to predict costs at 20,000 units and 18,000 units, the results would be:

20,000: Costs = 20,000 x $10 + $120,000 = $320,000 [Actual costs = $340,000]

18,000: Costs = 18,000 x $10 + $120,000 = $300,000 [Actual costs = $320,000]

High low takes only two pieces of data and assumes that variable costs are only dependent on output and that fixed costs are constant. In practice, these strict assumptions are unlikely to be met. For example, heating costs would also depend on the weather.



Example 2

The high-low approach cannot use production of 10,000 and 40,000 because fixed costs step up at 30,000.

Therefore take 10,000 and 20,000

Low: output = 10,000, costs = $220,000High output = 20,000, costs = $340,000Difference = 10,000 and $120,000, so variable costs are $12/unit

Fixed costs below 30,000 units are therefore:

220,000 - $12 x 10,000 = $100,000 [or $340,000 - $12 x 20,000 = $100,000]

Fixed costs above 30,000 units will be $150,000.

At output of 25,000: costs = $100,000 + $12 x 25,000 = $400,000

At output of $35,000: costs = $150,000 + $12 x 35,000 = $570,000

Example 3

Straight lineCost = $24,000; scrap (residual) value at end of life $4,000; estimated useful life = 5 years.($24,000 - $4,000)/5 = $4,000 per year

Example 4

Reducing balance methodCost = $24,000; scrap (residual) value at end of life $4,000; estimated useful life = 5 years.

Year Cost/written down value

24,0001 25% 6,000

18,0002 25% 4,500

13,5003 25% 3,375

10,125Etc

.

.

.

This method never gets to zero.



Example 5

Machine hours method

Cost = $24,000; scrap (residual) value at end of life $4,000; estimated total machine hours 60,000. Hours worked in the year = 10,000

10,000 x $(24,000 – 4,000)/60,000 = 3,333

Example 4

Product unit method

Cost = $24,000; scrap (residual) value at end of life $4,000; estimated total production = 200,000 units. Units made in the year = 25,000

25,000 x $(24,000 – 4,000)/200,000 = $2,500

Chapter 4Example 1

Date Units Unit price1 April Opening inventory 1,000 5.005 April Purchased 500 6.009 April Sold 200 N/a14 April Purchased 600 5.5021 April Sold 1,200 N/a

FIFO

Sale of 200 on 9 April: assumed to be units from opening inventory: 200 @ $5 = $1,000

Sale of 1,200 on 21 April: assumed to be the 800 remaining from opening stock plus 400 from the purchase on 5 April: 800 @ $5 + 400 @ $6 = $6,400

Closing inventory will be all the 600 purchased on 14 April plus 100 left from the 5 April purchase = 600 @ $5.50 + 100 @ $6.00 = 3,900.

LIFO

Sale of 200 on 9 April: assumed to be units purchased on 5 April: 200 @ $6 = $1,200

Sale of 1,200 on 21 April: assumed to be the 600 from the purchase on 14 April (600 x 5.5 = $3,300) plus 300 remaining from the purchase on 5 April: 300 @ $6 = $1,800, plus 300 from opening stock @$5 = $1,500. Total cost of those sales = $6,600

Closing inventory will be all from opening stock: 700 @ $5.00 = $3,500



Cumulative weighted averageDate Units Unit price Cumulative weighted

average1 April Opening

inventory1,000 5.00 5,000

5 April Purchased 500 6.00 3,000

1,500 @5.333 [8.000/1,500 = 5.3333] 8,000

9 April Sold (200) @5.333 (1,067)

1,300 @5.333 6,933

14 April Purchased 600 5.50 3,300

1,900 @5.386 10,233

21 April Sold (1,200) @5.386 (6,463)

Closing stock 700 @5.386 3,770

Cost of sales = $1,067 + $6,463 = 7,530Closing inventory = $3,770Periodic weighted averageValue of purchases plus opening stock = $5,000 + $3,000 + $3,300 = $11,300Units purchased plus in opening stock = 1,000 + 500 + 600 = 2,100Periodic average = 11,300/2,100 = 5.381Cost of sales = (200 + 1,200) x 5.381 = 7,533Value of inventory = 700 x 5.381 = 3,767

Example 2

Inventory statistics are:Maximum usage/day 20Minimum usage/day 12Average usage per day 15Maximum lead time 11 daysMinimum lead time 4 daysAverage lead time 6 daysReorder quantity 1,000 units

Reorder level = maximum usage rate x maximum lead time = 20 x 11 = 220 units

Minimum stock level = Reorder level – average usage x average lead time = 220 – 15 x 6 = 130 units.

Maximum stock = Reorder level + reorder quantity–(minimum usage x minimum lead time) = 220 + 1,000 – 12 x 4 = 1,172



Example 3

Work out the annual holding, ordering and total costs at the following reorder quantities:

Reorder quantity


Ordering Occasions

20,000/ROQ


Total cost

100 250 200 10,000 10,250200 500 100 5,000 5,500500 1,250 40 2,000 3,250

1,000 2,500 20 1,000 3,5002,000 5,000 10 500 5,5004,000 10,000 5 250 10,250

Chapter 5

Example 1

Note: each unit is expected to take 40/80 = 0.5 hoursBasic wages for 44 hours = 44 x $6 = US$264

Overtime premium 4 x $6 x ⅓ = 8

Extra units 10 x $5 = 50Overtime premium that could be associated with the extra units

10 x 0.5 x $6 x ⅓ (10)312

Example 2

Gross wages 38 x $10 = US$380Tax and other deductions 25% x (380 – 100) = $70)Net pay $310

Payroll taxes $380 x 10% $38Total payments by employer to tax authorities = $70 + $38 = $108

Example 3

Wages control accountWages control accountWages control accountWages control account31/3 Work in progress account 36,00031/3 Work-in-progress account 4,000

1/4 Cash (paid to employees) 28,00015/5 Cash (paid to tax authorities) 12,000

40,000 40,000



Example 4

In a week 80 employees each spend 40 hours working and their labour cost is $15/hour.

Total wage cost = 80 x 40 x $15 = $48,000This will be $48,000/5 = $9,600 per day

Product Days Cost Units Cost/unit1 2 19,200 200 $96.002 2 19,200 500 $38.403 1 9,600 4 $2,400

Chapter 6Example 1

500 (20 – 8) – 4,000 = $2,000

Example 2

Cost Basis of apportionment Total Preparation Assembly CanteenRent Floor area 4:5:1 45,000 18,000 22,500 4,500Insurance Machine value 94:80:6 5,400 2,820 2,400 180Canteen Employees 8:6:2 12,000 6,000 4,500 1,500Power consumption

75%,20%,5% 40,000 30,000 8,000 2,000

Total 102,400 56,820 37,400 8,180

Example 3

Costs apportioned into preparation department = $61,494Costs apportioned into assembly department = $40,906


volumeMachine

hours per unit

Labour hours unit

Machine hours per

unit

Labour hours unit

Product A 10,000 units 2 2.5 1 3Product B 6,000 units 3 1 1 4

Total budgeted labour hours in preparation department = 31,000

Overhead absorption rate/labour hour in preparation = 61,494/31,000 = $1.98

Total budgeted labour hours in assembly department = 54,000

Overhead absorption rate/labour hour in preparation = 40,906/54,000 = $0.76

Product A overheads: 2.5 x 1.98 + 3 x 0.76 = 7.23Product B overheads: 1.0 x 1.98 + 4 x 0.76 = 5.02



Example 4

Direct apportionmentProduction

department 1Production

department 2Maintenance

departmentCanteen

Overhead costs after initial allocation and apportionment $ 150,000 160,000 72,000 35,100Maintenance 40:50 32,000 40,000 (72,000) –Canteen 25:40 13,500 21,600 – (35,100)Total overhead costs for production departments 195,500 221,600 – –

Step-downProduction

department 1Production

department 2Maintenance

departmentCanteen

Overhead costs after initial allocation and apportionment $ 150,000 160,000 72,000 35,100Maintenance 40:50:10 28,800 36,000 (72,000) 7,200

42,300Canteen 25:40 16,269 26,031 (42,300)Total overhead costs for production departments 195,069 221,031 – –

Chapter 7Example 1

Job 666 Quantity Unit price $$

Material – stores 20 15 300 – special 1 150 150Labour – basic 30 9 270 – supervisor 3 15 45Overheads 33 4 132Total 897



Example 2

Batch 7777 Quantity Unit price $$

Material – stores 2000 10 20,000 – special 500 4 2,000Labour – Dept A 90 12 1080 – Dept B 40 10 400Overheads 130 3 390Total for the batch 23,870

Cost per unit made in batch 7777 = 23870/900 = $26.52

Example 3

Input costs less sale of normal loss = 2,000 x $5 + 200 x $12 + 200 x 3 – 100 x 0.8 = 12,920

Expected output = 2,000 x 0.95 = 1,900

Cost per unit = $6.80

Process accountProcess accountProcess accountProcess accountProcess accountProcess accountUnits $ Units $

Material 2,000 10,000 To finished goods 1,900 @ 6.80

12,920

Labour 2,400 Sale of scrap (cash) 100@ 0.8

80

Overheads 6002,000 13,000 2,000 13,000



Example 4

Input costs less sale of normal loss = 2,000 x $6 + 200 x $15 + 200 x 4 – 100 x 0.9 = 15,710

Expected output = 2,000 x 0.95 = 1,900 (actual output = 1,800; abnormal loss = 100).

Cost per unit = $15,710/1,900 = $8.2684



14,883

Labour 3,000 Normal loss: sale of scrap

100 @ 0.9

90

Overheads 800 Abnormal loss [email protected]

827

2,000 15,800 2,000 15,800

Normal loss accountNormal loss accountNormal loss accountNormal loss accountNormal loss accountNormal loss accountUnits $ Units $

Process account 100 90 Cash 100 90100 90 100 90

Abnormal loss accountAbnormal loss accountAbnormal loss accountAbnormal loss accountAbnormal loss accountAbnormal loss accountUnits $ Units $

Process account 100 827 Cash 100 90Income statement 737

100 827 100 827

The net cost of the abnormally lost units is $737.



Example 5

Input costs less sale of normal loss = 5,000 x $9 + $25,000 – 500 x 1 = 69,500

Expected output = 5,000 x 0.9 = 4,500 (actual output = 4,700; abnormal gain = 200).

Cost per unit = $69,500/4,500 = $15.4444



72,589

Labour and overheads

25,000 Normal loss: sale of scrap

500 @ 1

500

Abnormal gain [email protected]

3,089

5,200 73,089 5,200 73,089

Normal loss accountNormal loss accountNormal loss accountNormal loss accountNormal loss accountNormal loss accountUnits $ Units $

Process account 500 500 Cash 300 300To abnormal gain account

200 200

100 90 100 90

Abnormal gain accountAbnormal gain accountAbnormal gain accountAbnormal gain accountAbnormal gain accountAbnormal gain accountUnits $ Units $

Normal loss account 200 200 Process account 200 3,089Income statement 2,889

100 3,089 100 3,089

The net gain on the abnormally gained units is $2,889. The extra and unexpected 200 units represents a gain in good inventory value of 3,089, but to create these good units, fewer normally lost units actually occurred, and 200 amounts of expected scrap proceeds @$1 per unit could not be sold. Net gain = $3,089 - $200 - £2,889



Example 6

(a) Joint costs apportioned using weight

Product A (600 kg)

Product B (400 kg)

Separate costs 4,000 7,000Pre-separation costs 60:40 $12,000 7,200 4,800Total costs 11,200 11,800

(b) Joint costs apportioned using net realisable value

Product A Product B Sales value 15,000 16,000Post separation/own costs (4,000) (7,000)Net realisable value 11,000 9,000

Separate costs 4,000 7,000Pre-separation costs 11/20 and 9/20 of $12,000 6,600 5,400Total costs 10,600 12,400

Example 7

(a) Joint costs apportioned using weight

Sales of the by-product will produce revenue of $200, so the joint cost is reduced to $11,800

Product A (500 kg)

Product B (400 kg)

Separate costs 4,000 7,000Pre-separation costs 50:40 of $11,800 6,555 5,245Total costs 10,555 12,245

(b) Joint costs apportioned using net realisable value

Product A Product B Sales value 500 x 25; $400 x $40 12,500 16,000Post separation/own costs (4,000) (7,000)Net realisable value 8,500 9,000

Separate costs 4,000 7,000Pre-separation costs 8.5/17.5 and 9/17.5 of $11,800 5,731 6,069Total costs 9,731 13,069



Example 8

Product A Product BSales revenue of final product 100,000 150,000Sales revenue at split-off 65,000 45,000

Post separation/own costs 40,000 90,000Joint costs (split) 40,000 70,000Total costs 80,000 160,000Profit/(loss) 20,000 (10,000)

Product A: As this moves from split-off to final product, revenue increases by 100,000 – 65,000 = $35,000. This is the marginal revenue of completing the product.

The marginal cost of completing the product = post separation costs = $40,000

MC>MR, so it would be better to sell the product pre-cursor at split-off

Product B: As this moves from split-off to final product, revenue increases by 150,000 – 45,000 = $105,000. This is the marginal revenue of completing the product.

The marginal cost of completing the product = post separation costs = $90,000

MR>MC, so it would be better complete product B

Example 9

Total annual cost of running a lorry fleet = $80,000

Jobs:Job Weight

(KG)Distance

(KM)KG x KM

1 5,000 200 1,000,0002 10,000 500 5,000,0003 7,000 400 2,800,0004 12,000 600 7,200,000

Total16,000,00

0

Cost per kg km = 800,000/16,000,000 = $0.0058



Chapter 8

Example 1

Break even point = Fixed costs/contribution per unit = $240,000/$8 = 30,000 units

Budgeted output = 50,000 units. Therefore, sales could fall by 20,000 units to 30,000 units to just break even.

Margin of safety = 20,000 units or 100 x 20,000/50,000 = 40%

Example 2

C/S ratio = ($24 - $15)/24 = 0.375 or 37.5%

If revenue is $60,000 the contribution will be 60,000 x 0.375 = 22,500

Profit = $22,500 – 20,000 = $2,500.

Example 3

Either:

Break-even sales Sales =20,000

= $53,333Break-even sales Sales =0.375

= $53,333

In units this would be: 53,333/24 = 2222

OR

Contribution per unit = $24 x 0.375 = $9

Break even point = 20,000/9 = 2,222 in units

In revenue this would be 2,222 x $24 = $53,333.

Example 4

Contribution per unit = $50 - $20 = $30

Fixed cost per unit = TAC – MC = $30 - $20 = £10

If budgeted output is 2,000, budgeted fixed costs must be 2,000 x $10 = $20,000

If profits are to be $60,000, contribution will have be $70,000 + $20,000 = $90,000 to cover the fixed costs and to make the profit.

Therefore, required number of units to be sold = $90,000/30 = 3,000

Example 5

Current profits = ($50 - $20) x 40,000 – 100,000 = 1,100,000

New profits = $1,100,000 also

Therefore new required contribution must be $1,100,000 + $160,000 [new fixed costs] = $1,260,000.

($55 - $18) x Quantity = 1,260,000



Quantity = 34,054 units

Chapter 9

Example 1

Product A: contribution/kg = 24/20 = 2.4Product B: contribution/kg = 15/5 = 3Therefore make B in preference.

200 units (maximum demand) of B will consume 1000kg and generate $3,000 200 kgs of material left, which is enough to allow 20 units. These will generate $480.Therefore, total maximum contribution = $3,480

Example 2

Azed ByozBuy-in price 38 34Cost to make 22 30Saving per unit of making rather than buying 16 4

Kg of scarce resource M used/unit 4 2Saving per Kg of scarce resource made by making rather then buying 4 2Ranking 1 2

Make as much as possible of the products with the higher rank:

Product Azed: make 5,000 units, consuming 20,000 kgsProduct Byoz: make 6,000 units, consuming 12,000 kgs (Balance)

32,000 kgsBuy in the remaining 1,000 units of Byoz

Example 3

If Gamma is closed:๏ Revenue will decrease by $60,000

๏ Costs will decrease by $45,000 + $10,000 x 50% = $50,000

Therefore the division should not be closed. If it were, contribution would be reduced.

Example 4

Incremental revenue = $4 x 2,000/2 = 4,000Incremental costs 800 kg bought @1.20 (960)Opportunity cost of not selling existing inventory (1,600)Increase in contribution = 1,440

[Note irrelevant: $3,600 = sunk; $1,500 market research = sunk/past; $4,000 not incremental, merely reapportioned.]



Chapter 10

Example 1

Option 1: Present value = $3,000Option 2: Present value = 4,000 x 0.763 = $3,052

Option 2 is therefore preferable.

Option 1: Present value = 3,000 x 0.826 = $2,478Option 2: Present value = 3,800 x 0.621 = $2,360

Option 1 is therefore preferable

Example 2

1 – 9 5% annuity factor = 7.108

1 – 5 5% annuity factor = (4.329)

6 – 9 5% annuity factor 2.779

zPV = $100 x 2.779 = $278


1 – 2 4% annuity factor (1.886)

year 5 4% annuity factor (0.822)5.403

PV = $100 x 5.403 = $540


0 10% annuity factor 1.000

0 – 5 4.791

PV = $200 x 4.791 = $958

Example 3

Annuity factor = 1

r1− 1

(1+ r )n⎡⎣⎢

⎤⎦⎥= 1

0.081− 1

(1.08)7⎡⎣⎢

⎤⎦⎥= 5.206

Annuity factor = 1

r1− 1

(1+ r )n⎡⎣⎢

⎤⎦⎥= 1

0.0551− 1

(1.055)12⎡⎣⎢

⎤⎦⎥= 8.619

Example 4

Time Flow $ Factor Discounted cash flow

0 Investment (10,000) 1.000 (10,000)1 Investment (12,000) 0.917 (11,004)



2 Income 5,000 0.842 4,2103 Income 15,000 0.772 11,5804 Income 7,000 0.708 4,956

Net present valueNet present value -258So, marginally, the investment is not worthwhile.

Example 5

Required discount factor = 3.791 – 0.909 = 2.882PV of inflows = 2.882 x 8,000 = $23,056PV of outflow = $18,000NPV = $5,056

So, project is worthwhile.

Example 6

Depreciation charged = (15,000 – 3,000)/4 = 3,000Time Flow $ 6% Factor Discounted

cash flow1 Investment (15,000) 1.000 (15,000)2 investment 5,000 + 3,000 = 8,000 2.673 21,384

4 Income before depreciation 4,000 + 3,000 = 7,000 0.792 5,544

4 Scrap 3,000 0.792 2,367Net present valueNet present value 14,295

Therefore the project is worthwhile

Chapter 11

Example 1

$ January2014

February 2014

March 2014

April2014

Cash from customers– previous month 8,400 5,400 4,800 6,000– two months ago 4,800 5,600 3,600 4,800Total 13,200 11,000 8,400 10,800

Cash paid to suppliers 10,000 4,000 4,000 5,000

Other expenses 3,000 3,000 3,000 4,000Purchase of non-current assets 20,000Tax 10,000Total cash expenditure 13,000 27,000 17,000 9,000Net cash flow 200 (16,000) (8,600) 1,800Cash b/f 20,000 20,200 4,200 (4,400)Cash c/f 20,200 4,200 (4,400) (2,600)



Example 2

The cycle length can be calculated as:

Days of inventory + Receivables collection period – Payables payable period.

Raw material days (ie how many days’ supply of raw material there is). Sometimes known as raw material turnover period. 20

Work-in-progress turnover period. 2Finished goods turnover period 25Payables days (34)Receivables collection period 45Working capital cycle 58

Example 3

$12,000 is deposited at 4% simple interest for 3 years.

$12,000 x 4% x 3 = $1,480

So $13,480 will be on deposit

Example 4

$2,000 x (1.06)8 = $3,188$5,000 x (1.055)5 = $6,535

Chapter 12Example 1

Flexed budget = $96,000 x 7,000/8,000 = $84,000Actual cost = $89,000

Variance = $5,000 adverse/unfavourable.

Example 2

Flexed budget = $150,000 x 10,500/10,000 = $157,500Actual cost = $155,000

Variance = $2,500 favourable

Example 3

Fixed costs are fixed and do not depend on production levels. Therefore, these should not be flexed.

The variance is simply $230,000 - $200,000 = $30,000 adverse/unfavourable.



ANSWERS TO QUESTIONS

Chapter 1

Question 1

B The three purposes of information that were described were planning, controlling and decision-making

Question 2

C 2 and 3 will be particularly meaningful as they draw attention to matters that might need attention. Lists of all items are certainly data but are often not very meaningful or helpful.

Question 3

B Each car is a cost unit

Question 4

D Sales – costs = profit, so the manager is responsible for all or these plus investment.

Question 5

D

Chapter 2Question 1

A

Question 2

C

Question 3

A

Question 4

C

Question 5

B Glue and polish would be indirect and not traced to each product individually.

Question 6

D

Question 7

C Asset, non-current, accumulated depreciation, motor vehicles

Question 8

C Income is not part of the statement of financial position



Question 9

B This is a hierarchical code

Chapter 3

Question 1

B Postage will increase with business activity

Question 2

D Rent will be constant until the new factory has to be taken on

Question 3

C Fixed element = basic wage. Variable element = bonus

Question 4

C Low = 1,000 units, $3,000 cost; high = 4,000 units, $9,000 cost

Difference = 3,000 units, $6,000 cost

So variable cost = $2/unit

Fixed cost = $3,000 - $2 x 1,000 = $1,000 [or $9,000 - $2 x 4,000 = $1,000]

At output of 3,500, total costs = $1,000 + $2 x 3,500 = $8,000.

Question 5

D You have to take two outputs where the variable cost per unit is constant, so 1,000 to 3,000.

Increase in output = 3,000 – 1,000 = 2,000; increase in costs = $3,600.

Therefore, variable cost per unit = $1.80 (for output up to 3,000)

Fixed costs = $3,400 – 1,000x 1.80 = 1,600.

At 3,500 units: variable costs = 3,000 x $1.80 + 500 x $2.70 = $6,750.

Total costs = $6,750 + 1,600 = $8,350

Question 6

B Total fixed cost = $(20 – 12) x 5,000 = $40,000

At 8,000 units, fixed cost per unit = 40,000/8,000 = $5

TAC = $5 + $12 = $17

Question 7

A Total fixed cost = ($50 - $30) x 10,000 = $200,000

The fixed cost per unit must be no more then $46 - $30 = $16

Therefore units to be made = $200,000/$16 = 12,500



Chapter 4

Question 1

B Glue and polish would be indirect and not traced to each product individually.

Question 2

C Remove from raw material and introduce to WIP

Question 3

A Purchases/produced = Sold + closing inventory – opening inventory

= 90,000 + 10,000 – 20,000 = 80,000

Question 4

C Purchases = Used + closing inventory – opening inventory

= 15,000 + 1,500 – 1,000 = 15,500

Question 4


= 15,000 + 1,500 – 1,000 = 15,500

Question 5

C Output weight = 15,000 and this is after a 25% loss. Therefore input weight must be 20,000. Or


20,000 – 5,000 = 15,000

Must buy enough to deal with 20,000 being used in production and to increase inventory by 500 kg. So 20,500 must be bought

Question 6

A

Question 7

C

Question 8

A

Question 9

B (120 – 40 + 90 = 170)

Question 10

C



Question 11

A EOQ=

2CoDCH

2 =2x100x3,000x12

62 =1.095

Note D = annual demand = 12 x 3,000 = 36,000

If order quantity = 6,000 there will be 6 orders per year.

If annual ordering costs = $600, cost per order = 600/6 = $100

Question 12

B If CO increases EOQ must increase also. If EOQ rises the average stock level will rise so holding costs must rise.

Chapter 5Question 1

D Basic and overtime hours at the basic rate are direct labour costs. The overtime premium is indirect.

Question 2

C Employer’s payroll taxes are not a deduction from employees’ wages.

Question 3

A The efficiency ratio is: standard hours for production achieved/actual hours. Therefore a ratio of 110% implies efficiency as actual hours would be less than standard

Question 4

B The capacity utilisation ratio is: actual hours worked/budgeted hours. If this ratio is only 90% fewer hours were worked than expected implying poor use of the factory.

Question 5

C 100 x 100 replaced/(1,000 + 800)/2 average = 11.1%

Chapter 6

Question 1

C

Question 2

C

Question 3

D

Question 4

D Depreciation is usually related to cost.



Question 5

D Maintenance could depend on how long machines run for, the number of machines that have to be serviced and the cost (size and complexity) of the machines. Apportioning according to net book value runs the risk of apportioning least to the oldest (most depreciated) machines but presumably old machines would require more maintenance.

Question 6

B By definition

Question 7

B Actual costs = 13,000. Absorbed = 1,900 x 12,000/2,000 = 11,400. So $1,600 under-absorbed

Question 8

C Actual costs = 46,000. Absorbed = 19,000 x 50,000/20,000 = 47,500. So $1,500 over-absorbed

Chapter 7Question 1

D Net cost = $9,000 - $100 = $8,900

Good output expected = 2,900

Cost per unit = $8,900/2,900 = 3.07

Question 2

B Net cost of expected good production = $120,000 – 200 x $5 = 119,000

So cost per unit = 119,000/1,000 = $119

Good inventory = 900 units and at $119 per unit, its value will be $107,100

Question 3

B Cost per unit is calculated on expected results so the number of abnormally lost units has not effect.

Question 4

A If output was produced as expected there would have been 450 units (expected output after normal loss) and this represents 90% of input. Therefore 500 units would have been input at a cost of $120 each, so $60,000

Cost per unit = costs/expected output = 60,000/450 = $133.33

Question 5

C Total profit = 23,000 + 25,000 – 10,000 – 8,000 – 16,000 – 12,000 = 2,000 so production is worthwhile.

For Product A incremental revenues from processing to completion = $23,000 – $6,000 = 17,000.

Incremental costs = $16,000 so it is worth completing this product.



Chapter 8

Question 1

A Contribution/unit = 150 – 70 = $80; BEP = 120,000/80 = 1,500

Question 2

C Fixed overhead per unit = 120 – 90 = $30.

Budgeted fixed costs = £30 x 2,000 = $60,000. BEP = 60,000/(190 – 90) = 600

Question 3

A Fixed overhead per unit = 70 – 50 = 20.

Budgeted fixed overheads = $20 x 2,000 = $40,000.

If 1,500 units are made, contribution = 1,500 x (90 – 50) = $60,000.

Therefore a profit of $20,000 = $60,000 - $40,000 is expected

Question 4

D Contribution per unit = $60 - $40 = $20.

Fixed costs per unit = $50 - $40 = $10. Budgeted fixed costs = $10 x 2,000 = $20,000.

BEP = 20,000/20 = 1,000 units.

So, output could fall from budgeted 1,500 to 1,000 and just break even.

Margin of safety = 500/1,500 = 33.3%

Question 5

C C/S = 0.30 = 75/Selling price; Selling price = 75/0.3 = 250.

[Check C/S = 75/250 = 0.3].

If selling price if $250 and contribution is $75, the variable cost must be 250 – 75 = $175.

Question 6

D Contribution = 60% x $60 = $36.

If BEP = 1,000, contribution must equal the fixed costs at that point.

So fixed costs must be 1,000 x $36 - $36,000

Question 7

B Total required contribution = $220,000 + $100,000 = $320,000.

Therefore, 320,000/80 = 4,000 units must be made and sold



Question 8

D Current profits = (60 – 40) x 10,000 – 120,000 = $80,000.

If the same profits are t be made, the new contribution must be $80,000 + $120,000 x 1.10 = $212,000.

New contribution per unit = 60 x 1.05 – 40 x 1.1 = 19

Required volume = 212,000/19 = 11,158

Question 9

B Current contribution = final contribution = ($70 - $45) x 200,000 = 5,000,000

New contribution per unit= $65 - $45 = $20

Required sales = $5,000,000/20 = 250,000

Question 10

C Profit = revenue – total costs

Question 11

D Margin of safety is how far budgeted volume can fall before break-even is reached.

Chapter 9Question 1

C X 25/5 = 5; Y 45/10 = 4.5; Z 30/4 = 7.5. Therefore order = Z, X, Y

Question 2

A P 25/5 = 5; 45/10 = 4.5. 1000 units of Q consume $10,000 material. Then use the remaining $6,000 material to make 6,000/5 = 1,200 P. No material left to make more than 1,000 units of Q

Question 3

B Contribution/kg: R = (60 – 45)/6 = 2.5; S (32 – 20) = 3 = 4

Make S in preference, so 1,200 units (max demand) S. This consumes 1,200 x 3 = $3,600 material, leaving $300 material which is enough for 50 of R

Question 4

D Contribution per machine hour of making not buying the component = (55.000 – 25,000)/6,000 = $5

Contribution per machine hour from P = 18/6 = $3

Contribution per machine hour from Q = 48/12 = $4

So the best use of machine hours is to make all of the component needed.

Question 5

D Total revenues – total costs = 500,000 – 320,000 – 200,000 = (20,000). This loss is avoided if the division is shut down. Discontinuing either product will simply deprive the company of that product’s contribution and no fixed costs will be saved.



Question 6

B G relevant cost = current purchase price = $4.00/kg

H relevant cost = sale value = $0.60 per unit.

Material cost = 6 x 4 + 9 x 0.6 = $29.40

Question 7

A Programmers: $Nil as no incremental cost

Analysts: 900 (50 + 80) = 117,000 [The labour rate has to be added in as the $80 lost contribution takes into account a labour saving]

Chapter 10

Question 1

B We need the 3 – 7 for the five flows. 1 – 7: annuity factor = 5.389; 1 – 2: annuity factor = 1.808. Factor for 3 – 7 = 5.389 – 1.808 = 3.581. PV = 3.581 x $1,500 = 5,372

Question 2

D 1 – 8 except time 5 = 5.335 – 0.621 = 4.714

0 – 8 = 1 + 4.714 = 5.714

PV = $400 x 5.714 = 2,286

Question 3

A 10,000/0.05 = 200,000

Question 4

D 1 – infinity: 1/0.05 = 20

1 – 2 5% factor = 1.859

3– infinity = 18.141

PV = 18.141 x 10,000 = $181,410

Question 5

D Rent PV factor (time 0 – infinity) = 1/.07 +1 [for time 0] = 15.2857

Rent PV = 15.2857 x 10,000 = 152,857.

Other time 2 receipt = 1,000 x 0.873 = $873

Total PV = $873 + $152,857 = $153,730.

Question 6

B NPV = - 900,000 x 0.909 + 400,000 x 0.826 + 600,000 x 0.751 = -37,100



Question 7

C Opportunity cost = $1 million; PV of rental income = $550,000/0.1 = $5,500,000

NPV = $4,500,000

Question 8

A IRR = 10 + 1,200 x (20 – 10)/(1,200 + 500) = 17%

Question 9

C IRR = 8 + 1,200 x (12 – 8)/(1,200 - 500) =14.9%

Question 10

B IRR occurs when NPV = 0

NPV = -20,000 + 25,000 x 1/(1 +r)3 [Income arises 36 months or 3 years after expenditure]

When NPV = 0

20,000 = 25,000 x 1/(1 +r)3

(1 +r)3 = 25,000/20,000 = 1.25

1+ r = 1.08

So r = 8%

Question 11

D If IRR > D/c rate, NPV will be positive and the project should be accepted.

Question 12

D Payback: Cost = $20,000

Year Flow Cumulative inflow1 7,000 7,0002 8,000 15,0003 10,000 25,0004 8,000 33,000

So, payback = 2.5 years

Discounted pay back

Year Flow Factor Discounted flow

Cumulative inflow

1 7,000 0.926 6,482 6,4822 8,000 0.857 6,856 13,3383 10,000 0.794 7,940 21,2784 8,000 0.735 5,880 27,158

So discounted payback almost 2.8 years. [2 + (20,000 – 13,338)/7,940]



Chapter 11

Question 1

D 12,000 x 35% +12,000 x 15% x 95% + 8,000 x 30% + 10,000 x 20%

Question 2

B

Cash balance b/f 20,000Received from debtors 42,000Received in month of sale $120,000/2 60,000Paid to suppliers (65,000)Other expenses (90,000)Cash balance c/f (33,000)

Question 3

C Month 1: 3,000 sold, 3,500 produced costing $5 x 2kg each = $35,000

Month 2: 3,600 sold, 4,600 produced costing $5 x 2kg each = $46,000

Payments = 50% x $35,000 + 50% x $46,000 = $40,500

Question 4

D 50 + 12 - 45 + 50 = 67

Question 4


= 15,000 + 1,500 – 1,000 = 15,500

Question 5

B

Question 6

D Investment in $100 nominal will give $4.2 per year and this must be equivalent to a 6% return on investment. Therefore the market value must be $100 x 4.2/6 = $70. [Check receiving $4.2 on investing $70 is a 6% return]

Question 7

A 5,000 (1.05)6 = 6,700

Question 8

B 8% = Nominal. Effective rate for each year (1.02)12/3 – 1= 0.0824.

2000 invested at 8.24% compound results in $2,536. So interest = $536



Question 9

A (1 + Monthly nominal)12 – 1 = 0.06

(1 + Monthly nominal) = 12√1.06 = 1.004868

Monthly nominal = 0.004878 or 0.4868%

Annual nominal = 12 x 0.4868 = 5.84%

Question 10

C 125 = current price/base year price

Base year price = $5,000/1.25 = 4,000

Question 11

D The required season is 6 increments away, so that would increase the trend by $6,000 to $18,000. This has to be adjusted up by 110% = 19,800.

Question 12

A Year 3 season 2 to year 4 season 1 is 3 increments at $500/season. That would produce a prediction of $14,000 + 3 x $500 = $15,500

The actual prediction is $16,200, so the seasonal adjustment must be +700




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