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MA2 Managing Costs and Finance
1
MA2 Managing Costs and Finance
1.
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
91
9.
Short Term Decision Making
103
10.
Capital Investment Appraisal
119
11.
Cash Management
135
12.
Information for comparison
155
Answers to Examples
161
Answers to Questions
179
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3
Chapter 1
MANAGEMENT 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 information
The following diagram is often used to represent a computerised accounting system was shown:
Input of
data
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.
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4
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
๏
More accurate (fewer arithmetic errors – though incorrect programs will repeatedly report
incorrect information)
๏
Faster
๏
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
needed.
because a terminal on everyone’s desk potential gives all access to information
(because fewer people need to be employed)
(because the processing is automated and computers work very quickly)
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
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5
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 forwardlooking 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.
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6
5. Sources and categories of information
The 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 nonfinancial 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.
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Example 2
List examples of information from each of the above category pairs
Financial/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.
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As above, a profit centre could be:
๏
A subsidiary company
๏
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 subsidiary company
๏
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
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9
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, Usertargeted, 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.
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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/disadvantage
Can be instant
Might be poorly expressed or ambiguous
Allows 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 said
Informal (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/disadvantage
Precise communication possible
Takes time to produce
Good for supplying detail
No immediate interaction. no instant feedback
Impersonal (could be a weakness)
Often no record of what was said
Formal (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/disadvantage
Eye-catching
Can be open to distortion
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Strength/advantage
Weakness/disadvantage
Memorable
Can be expensive to produce
Can 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
Name and
address of
sender
Date
Dear Sir
About:_______________
Body of letter ______________________________________
____________________________________________________
____________________________________________________
____________________________________________________
______________________
Your faithfully
Signature
‘Dear Sir’: pairs with ‘Yours faithfully’. ‘Dear Mr Smith’ pairs with ‘Yours sincerely’
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๏
12
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:
About
Date
1.
2.
3.
4.
5.
6.
7.
8.
Introduction and terms of reference
Paragraph 1 title
Paragraph 2 title
Paragraph 3 title
12. Conclusions/recommendations
Appendices
The appendices contain detailed information that is referred to elsewhere in the report.
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๏
13
Memoranda
MEMORANDUM
To:
From:
About
Date
Paragraph 1 title
Paragraph 2 title
Paragraph 3 title
etc
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 reports
There 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.
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๏
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.
14
12. Charts and graphs
Charts 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:
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Line chart
Scattergraph
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Pie chart
Area graph
Often like a line chart, but with filled in areas:
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Chapter 2
COST 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.
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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 cycle
The material cycle can be depicted as:
Purchase requisition
Sell products
Manufacture products
Issue materials
to production
Order goods
Receive goods
Store raw materials
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.
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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.
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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
Description
Receipts
Date
A 1234
30cm brackets
Bin number/location A1284
Issues
Goods
Quantity
received
note number
Date
Balance
Requisition
number
Quantity
b/f 100
15/1/2013
10/2/2013
1235
1384
200
300
29/1/2013
1929
140
160
3/2/2013
1955
120
20
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
B
Purchase requisition
C
Purchase order
D
Materials order
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Question 4
When goods are received, what is the name given to the document that is raised (created) at
that stage.
A
Delivery note
B
Purchase requisition
C
Goods received 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
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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?
A
Direct: 1 and 2; indirect 3 and 4
B
Direct: 2 and 3; indirect 1 and 4
C
Direct: 1 and 3; indirect 2 and 4
D
Direct: 1 and 4; indirect 2 and 3
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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
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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 assetrelated 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.
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8. Different methods of coding
There 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! !
0002! !
0003 ! !
.
.
.
Abrahams
Adkins
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.
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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 Mathematics
520 Astronomy & allied sciences
530 Physics
540 Chemistry & allied sciences
550 Earth sciences
560 Paleontology, paleozoology
570 Life sciences
580 Botanical sciences
590 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 = expenses
2 = income
3 = assets
4 = liabilities
1
1 = non-current assets
2 = current assets
1
1 = cost
2 = accumulated
depreciation
2
1 = property
2 = machinery
3 = office equipment
4 = 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 = expenses
2xxx = income
3xxx = assets
4xxx = liabilities
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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:
3
1 = expenses
2 = income
3 = assets
4 = liabilities
1
1 = non-current
assets
2 = current assets
1
1 = cost
2 = accumulated
depreciation
2
1 = property
2 = machinery
3 = office equipment
4 = motor vehicles
C
C = cost
A = accumulated
depreciation
M
P = property
M = machinery
O = office equipment
M = motor vehicles
could then become
A
E = expenses
I = income
A = assets
L = liabilities
N
N = non-current
assets
C = current assets
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.
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Question 7
A company uses the following hierarchical system:
3
1 = expenses
2 = income
3 = assets
4 = liabilities
1
1
2
1 = non-current assets 1 = cost
1 = property
2 = current assets
2 = accumulated depreciation 2 = machinery
3 = office equipment
4 = motor vehicles
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
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Example 2
List three advantages of using coding systems
Example 3
List the desirable attributes of a coding system
9. Computer systems
Many, 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 of
data
Processing data
Output of
information
Computer files
There follows a brief description of input, storage, processing and output technology found in
modern systems.
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Input methods
Keyboard
Flexible, but slow and error prone
Bar-code scanning
Inflexible, but fast and accurate
Character recognition
Flexible, fast and accurate, but characters have to
be well-written
RFID 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 rapidly
Smart cards/magnetic strip cards
Eg a credit card with information embedded on a
chip. Quick, accurate, but inflexible
Optical mark readers
Used for specialist applications such as multiple
choice exam answer sheets
Cameras
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.
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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, pulldown (or pop-up) menus.
Mainframe
Mainframe computers are computers primarily used
by large companies and governments for bulk
processing.
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Chapter 3
COST 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 classification
Costs 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.
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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).
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If, however, 10,000 units were made, the rental cost per unit would be only $1 ($10,000/10,000).
Higher production volumes are making better use of the fixed resource.
Semi-variable costs have a fixed element and a variable element.
An example would be a telephone bill. Usually there is a fixed cost for the line rental then each minute
of telephone calls causes an additional cost.
On a graph, fixed costs would appear as:
Total cost
($)
Variable
element
Fixed
element
Activity level ($)
Stepped fixed costs: constant over a range of activity then a sudden increase, then constant
again
An example would be the salary of supervisors. One supervisor for up to six workers, two for up to 12
workers, etc.
On a graph, stepped fixed costs would appear as:
Total cost ($)
Activity level ($)
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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
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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
1
2
3
4
Volume of
production
10,000
20,000
25,000
18,000
Total cost
$
220,000
340.000
370,000
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?
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Example 2
A company has obtained the following results from four years of trading:
Year
2009
2010
2011
2012
Volume of
production
10,000
20,000
40,000
18,000
Total cost
$
220,000
340.000
430,000
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
Monday
Tuesday
Wednesday
Thursday
Friday
Volume
2,000
3,000
4,000
2,000
1,000
Cost ($)
5,300
7,000
9,000
5,400
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
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Question 5
A company has measured production volume and costs over three periods. Results are:
Period
1
2
3
Volume
4,000
3,000
1,000
Cost
9,700
7,000
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
Fixed costs
Total costs
Total costs
Per unit
10
Variable costs
($5 x
production)
50
1,000
1,050
105
50
250
1,000
1,250
25
100
500
1,000
1,500
15
200
1,000
1,000
2,000
10
600
3,000
1,000
4,000
6.7
800
4,000
1,000
5,000
6.25
1,000
5,000
1,000
6,000
6.0
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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
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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
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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.
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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
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Chapter 4
ACCOUNTING 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?
A
Direct: 1 and 2; indirect 3 and 4
B
Direct: 1 and 4; indirect 2 and 3
B
Direct: 2 and 3; indirect 1 and 4
D
Direct: 1 and 3; indirect 2 and 4
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3. Accounting for material costs
Materials progress through a factory as follows:
Supplier
Raw materials
Work-in-progress
Finished goods
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.
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Illustration
Assume there is no opening inventory at any stage.
1,000 units of raw material are bought for $5 per unit
800 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 materials
Payables
Units
$
Units
1,000
5,000 To WiP
C/f Closing inventory
1,000
5,000
$
800
4,000
200
1,000
1,000
5,000
Units
$
Work-in Progress
Units
From raw materials
800
Labour
$
4,000 To Finished goods
700
5,600
100
800
800
6,400
1,600
Overheads
800 C/f Closing inventory
800
6,400
Note: finished goods and closing inventory are values at:
Material $5 + Labour $2 + Overheads $1 = 8 per unit
Finished goods
Units
From WIP
700
$
Units
5,600 Cost of sales
C/f Closing inventory
700
5,600
$
500
4,000
200
1,600
700
5,600
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
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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
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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
100
–
–
Wastage
20
=
=
Output
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:
Input
100
1,250
–
–
–
Wastage
20
250
=
=
=
Output
80
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
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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:
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Part number
Description
Receipts
Date
51
A 1234
30cm brackets
Bin number/location A1284
Issues
Goods
Quantity
received
note number
Date
Balance
Requisition
number
Quantity
b/f 100
15/1/2013
10/2/2013
1235
1384
200
300
29/1/2013
1929
140
160
3/2/2013
1955
120
20
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
B
Purchase requisition
C
Goods received note
D
Purchase order
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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
B
Purchase requisition
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
B
Purchase requisition
C
Goods received note
D
Purchase invoice
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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 each
21 March 20X4: buy 500 units at $6 each
31 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.
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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 each
21 March 20X4: buy 500 units at $6 each
31 March 20x4: sell 800 units at $12 each.
12 March 20X4
21 March 20X4
$5.33 = average cost
31 March 20X4
Closing inventory
1000 @ $5
500 @ $6
1,500 @ $5.33
(800) @ $5.33
700 @ $5.33
$
5,000
3,000
8,000
(4,267)
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 period
Units 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.
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Example 1
Recent results of a division are:
Date
Units
1 April Opening inventory
5 April Purchased
9 April Sold
14 April Purchased
21 April Sold
1,000
500
200
600
1,200
Unit
price
5.00
6.00
N/a
5.50
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
FIFO
Disadvantages
• Permitted by accounting standards as • Requires care to get it right
an acceptable approach to inventory
valuation
• Closing inventory has a value close to
its replacement value
• Might reflect physical use of stock
LIFO
Average stock
values
• Inventory is issued at close to its
current cost (significant if there is
high inflation of volatile stock prices)
• Not permitted as a stock valuation
method under financial reporting
standards
• Might reflect physical use of stock
• Requires care to get it right
• Averages out stock price fluctuations
• Relatively easy to work out.
• Permitted by Financial Reporting
Standards
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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;
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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
Minimum usage/day
Average usage per day
Maximum lead time
Minimum lead time
Average lead time
Reorder quantity
20
12
15
11 days
4 days
6 days
1,000 units
Calculate the
(a) Reorder level
(b) Minimum stock
(c) Maximum stock
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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
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Example 3
Work out the annual holding, ordering and total costs at the following reorder quantities:
Reorder
Holding cost
Ordering
Ordering Cost
Total cost
quantity
½ ROQ x $5
Occasions
(orders x $50)
20,000/ROQ
100
200
500
1,000
2,000
4,000
Reorder
quantity
Holding cost
½ ROQ x $5
100
200
500
1,000
2,000
4,000
250
500
1,250
2,500
5,000
10,000
Ordering
Occasions
20,000/ROQ
200
100
40
20
10
5
Ordering Cost
(orders x $50)
Total cost
10,000
5,000
2,000
1,000
500
250
10,250
5,500
3,250
3,500
5,500
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
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EOQ = 2
60
2C o D
CH
CO = cost of placing an order
CH = cost of holding one unit for one year
D = annual demand
So for this example:
EOQ= 2
2x50x20,000
= 632 units
5
Question 11
Monthly demand = 3,000 units
Annual ordering costs = $600
Order quantity = 6,000
Holding cost = $6 per unit per year.
EOQ = 2
2CoD
CH
CO = cost of placing an order
CH = cost of holding one unit for one year
D = annual demand
What is the economic order quantity?
A
1,095
B
775
C
346
D
1,897
Question 12
A company uses the formula
EOQ = 2
2CoD
CH
CO = cost of placing an order
CH = cost of holding one unit for one year
D = annual demand
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
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Chapter 5
ACCOUNTING FOR LABOUR
1. Introduction
This chapter looks at how remuneration is calculated and accounted for, and also how certain labourrelated 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 =
Overtime premium:
(52 – 40) x $10 x 50% =
Total pay
520
60
US$580
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62
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 = $250
Piece rate = $3/unit
If 100 units are made in a week then the pay will be $3 x 100 = $300
If 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 units
Bonus = 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
150 units should take
150 units did take
Hours saved
Bonus = 50% x 10 x 9 x 1 ⅓
Total pay
5.
$
405
50 hours
40 hours
10 hours
60
465
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?
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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 = $385
Cost 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 = 6
Weekly wages = 44 x $7 +4 x $3.5 + 6 x $3.5 = 343
Cost 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?
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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
Cr
Work-in-progress with the gross wages
Wages control account with the gross wages
Dr
Cr
Work-in progress with the employer’s payroll tax
Wages control account with the employer’s contributions to payroll tax
Dr Wages control account
CR Cash as employee paid the net amount
CR 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
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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 production
It 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.
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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.
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Illustration
Standard hours per unit = 2
Planned production = 5,000 units
Actual production = 5,200 units
Actual hours worked = 10,800
Actual hours paid 11,000.
Efficiency ratio
5,200 units should take 10,400 hours (2 hours per unit)
5,200 units did take 10,800 hours
Production has been therefore been inefficient.
standard hours for production achieved
10,400
Efficiency ratio =
x 100 =
x 100 = 96%
actual hours
10,800
Efficiency is below what was expected.
Capacity utilisation ratio
Planned 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
budgeted hours
x 100 =
10,800
10,000
x 100 = 108%
Production volume ratio
Planned 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
5,200
x
100
=
x 100 = 104%
planned
5,000
production
[Note this could be also worked out using planned and actual hours 100 x 10,400/10,000)].
Idle time ratio
If 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
Total hours
x 100 =
200
11,000
= 1.8%
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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.
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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
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%
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Chapter 6
ACCOUNTING 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
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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.
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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
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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.
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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 costs
Budgeted 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
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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:
Floor area
Machine value
Employees
Power consumption
Preparation
Assembly
Canteen
400 m2
500 m2
$94,000
8
75%
$80,000
6
20%
100m2
$6,000
2
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.
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Once the amounts are apportioned the cost in each department will be:
Cost
Rent
Insurance
Canteen
Power consumption
Basis of apportionment
Total Preparation Assembly Canteen
Floor area 4:5:1
45,000
18,000
22,500
4,500
Machine value 94:80:6
5,400
2,820
2,400
180
Employees 8:6:2
12,000
6,000
4,500
1,500
75%,20%,5%
40,000
30,000
8,000
2,000
102,400
56,820
37,400
8,180
Total
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
Rent
Insurance
Canteen
Power consumption
Reapportionment of service
department costs
Basis of apportionment Total Preparation Assembly Canteen
Floor area 4:5:1
45,000
18,000
22,500
4,500
Machine value 94:80:6
5,400
2,820
2,400
180
Employees 8:6:2
12,000
6,000
4,500
1,500
75%,20%,5%
40,000
30,000
8,000
2,000
Total
102,400
56,820
37,400
8,180
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.
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The time can be estimated using:
๏
Labour hours:
๏
Machine hours: this will give a fixed overhead absorption rate per machine hour
๏
Assume the following;
Product
Product A
Product B
this will give a fixed overhead absorption rate per labour hour
Preparation department
Assembly department
Budgeted
Machine
Labour hours
Machine
Labour hours
volume
hours per unit
unit
hours per unit
unit
2
2.5
1
3
10,000 units
3
1
1
4
6,000 units
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
Product
Product A
Product B
Preparation department
Assembly department
Budgeted
Machine
Labour hours
Machine
Labour hours
volume
hours per unit
unit
hours per unit
unit
2
2.5
1
3
10,000 units
3
1
1
4
6,000 units
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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 Production Maintenance Canteen
department department department
1
2
Overhead costs after initial allocation and
apportionment $
Percentage of maintenance department time
spent on other departments
Number of employees receiving meal
(1)
(2)
150,000
160,000
72,000
35,100
40
25
50
40
5
10
Reapportion the two service department costs using the direct method
Reapportion the two service department costs using the step-down method, starting with
the maintenance department
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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 = $100,000
Budgeted output = 50,000 units
Therefore, fixed overhead absorption rate per unit = $2
Actual fixed costs = $120,000
Actual 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 = $95,000
Actual 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
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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
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Chapter 7
JOB, 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.
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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.
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Illustration
Costs 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/unit
In a process account this would be
Material
Labour
Overheads
Process account
Units
$
100,000 20,000 To finished
goods
10,000
5,000
100,000 35,000
Units
100,000
@
$ 0.35
$
35,000
100,000 35,000
5. 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:
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Joint product A
Separate
costs
Joint or common or
pre-separation costs
Separate
costs
Joint product B
Split-off or
separation point
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 3
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
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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 4
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
6. Further processing decisions
Look at these results:
Sales revenue
Post separation/own costs
Joint costs (split)
Total costs
Profit/(loss)
Product A Product B
100,000
150,000
40,000
90,000
40,000
70,000
80,000
160,000
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.
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Example 5
Look at the following:
Sales revenue of final product
Sales revenue at split-off
Product A Product B
100,000
150,000
65,000
45,000
Post separation/own costs
Joint costs (split)
Total costs
Profit/(loss)
40,000
40,000
80,000
20,000
90,000
70,000
160,000
(10,000)
Should Product A and Product B be processed from split off to completion?
Question 1
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
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7. 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 6
Total annual cost of running a lorry fleet = $80,000
Jobs:
Job
1
2
3
4
Weight
(KG)
5,000
10,000
7,000
12,000
Distance
(KM)
200
500
400
600
Total
What is the cost per kg km of transport?
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Chapter 8
COST-VOLUME-PROFIT (CVP) ANALYSIS
1. Introduction
This chapter looks at how analysing costs and contribution can be used for decision making.
2. Recap
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
$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.
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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
Fixed costs that have to be covered
= $30,000
= $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
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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
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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%
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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).
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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.
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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 ratio
The 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?
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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
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
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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
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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
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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
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Question 11
Where is the margin of safety on the following diagram?
A
Line A
B
Line B
C
Line C
D
Line D
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Chapter 9
SHORT 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:
Maximum demand
Selling price
Material
Labour
Variable overhead
Fixed overhead
Product A
12,000
units
$
30
Product B
10,000
units
$
40
10
8
6
4
16
8
8
5
28
2
37
3
Total absorption cost
Profit
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
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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.
Maximum demand
Selling price
Material
Labour
Variable overhead
Marginal cost
Contribution
Product A
12,000
units
$
30
Product B
10,000
units
$
40
10
8
6
24
6
16
8
8
32
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 $8 richer.
However, this does not mean that Product B should be made in preference to Product A. Different
amounts of material are needed for each and we need to make sure that each precious unit of
material is used wherever it earns most. That can be found by working out:
Contribution per unit/Material needed per unit
or more generally:
Contribution per unit of limiting resource
The higher this is the better: it gives an earning rate per unit of the restricted resources used
Maximum demand
Material
Contribution
Contribution/$ of material
needed
Ranking
Product A
12,000
units
$
10
Product B
10,000
units
$
16
6
8
6/10 = 0.6
8/16 = 0.5
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.
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Step 3 – calculate the production plan
The production plan would be:
Product A
Product B
Maximum
material
Material
used $
120,000
(12,000 x
$10)
80,000
(balance of
material)
Units made
Contribution
made
@ $10/
unit
12,000
(maximum
demand)
72,000
(12,000 x $6)
@ $16/
unit
5,000
40,000
(5,000 x $8)
200,000
Total
contribution
Fixed costs
4 x 12,000 +
5 x 10,000
(98,000)
Profit
14,000
112,000
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
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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:
Selling price per unit
Variable cost per unit
Material used per unit
Maximum demand
Product R Product S
$60
$32
$45
$20
6 kgs
3 kgs
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
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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.
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108
The production plan
The production plan would be:
Product B
Product A
Maximum
material
Product A to be
bought in
Material used
kg
1,000 @ 5 kgs/unit
200
(balance of
material)
@ 10 kgs/
unit
Units made
200
(maximum
demand)
20
Costs
5,000
(200 x$25)
400
(20 x $20)
1,200
Product A to
be bought in
60
(to make up to
maximum
demand)
1,500
(60 x 25)
Total costs
6,900
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Example 2
The availability of Material M is limited to 32,000 kg
Product
Demand (units)
Variable cost to make ($ per unit)
Buy-in price ($ per unit)
Kg of X required per unit
Azed
Byoz
5,000
22
38
4
7,000
30
34
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
Q
18
48
500
250
6
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
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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)
(20,000)
50,000
Divisional profit
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
Sales
Variable costs
Fixed costs
Profit/(loss)
Alpha
Beta
Gamma
(000s)
(000s)
(000s)
150
90
30
30
120
75
30
15
60
45
20
(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?
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Question 5
A company division makes two products. Details are as follows:
Product A Product B
Sales revenue
Variable costs
Divisional fixed costs
Profit
200,000
170,000
100,000
300,000
150,000
100,000
(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 costs
The 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 1
A 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.]
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Illustration 2
A 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?
Solution
The 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 3
A 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?
Solution
Here 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.
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Illustration 4
A 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?
Solution
The $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
$
15,000
Conversion costs
(9,000)
Opportunity cost of not selling the material
(4,000)
Contribution
2,000
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Illustration 4
A 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?
Solution
The $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
$
15,000
Conversion costs
(9,000)
Opportunity cost of the material
(11,000)
Negative contribution
(5,000)
Therefore, the special product should not be made.
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Illustration 6
A 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?
Solution
The 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
$
20,000
Material costs
1,000 x $12
(12,000)
Contribution
8,000
Therefore the product should be made.
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Illustration 7
A 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?
Solution
Note: 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
$
22,000
Material 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
22,000
Material costs
1,000 x $12
(12,000)
Contribution forgone
1,000 x $8
(8,000)
Labour costs
1,000 x 2 x $15
(30,000)
Contribution
[if employees no longer employed]
(28,000)
The new product should not be made.
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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 $4,000 will be apportioned to the new product.
Should production commence?
Question 6
To make a product a business needs to use two materials, G and H. These materials are in inventory. G
is used on a day-to-day basis in the business; H has no uses other than in the new product.
Information about the two materials is as follows:
Material Quantity needed
per unit of the
new product
(kg)
Original cost
($/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
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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
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Chapter 10
CAPITAL 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.
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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%
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3. Discounted cash flow tables
The above examples should help you to realise that:
Present value =
Cash flow ×1
or [or Cash flow x (1 + r)-n
(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
= 4,000 × 0.736 = 3,052
(1+ 0.07)4
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.
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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:
Time
Cash flow $
Discount factor
(see table above)
1
1,500
0.917
2
1,500
0.842
3
1,500
0.772
1,500
2.531
Discounted cash flow
$
3,796.50
This would normally be written out as:
Time
Cash flow $
Discount factor
(see table above)
Discounted cash flow
$
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:
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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
less: cumulative discount factor years 1 – 3
Cumulative discount factor years 4 – 10
7.722
2.723
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
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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:
1⎡
1 ⎤
Annuity factor = ⎢1−
r ⎣ (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.
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Notice what happens the annuity factor formula as n, the number of years of flow, becomes very
large
1⎡
1 ⎤
Annuity factor = ⎢1−
r ⎣ (1+ r )n ⎥⎦
An n becomes large this term becomes very small and the formula can be simplified to
Perpetuity factor
=
1
r
So, the present value of receiving $1,000 from time 1 to infinity at a discount rate of 10% is:
PV =
1,000
=$10,000
0.1
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
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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
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Illustration
For example: an investment in new machinery would cost $25,000 and would
produce additional cash inflows of:
Year 1
$8,000
Year 2
$15,000
Year 3
$10,000.
The machinery could be sold for $2,000 at time 3.
Is the project worthwhile if the discount rate is 8%?
Solution
Time
Flow
0
1
2
3
3
Initial investment
Additional income
Additional income
Additional income
Scrap proceeds
Amount $
Factor@ 8% Discounted
cash flow $
(25,000)
1
(25,000)
8,000
0.926
7,408
15,000
0.857
12,855
10,000
0.794
7,940
2,000
0.794
1,588
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
Is the investment worthwhile when evaluated at a 10% discount rate?
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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.
Is the investment worthwhile when evaluated at a 6% discount rate?
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
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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
-$200,000
B
$5,500,000
C
-$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:
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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.
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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
BF
= CD/AC
= 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
(B % − A%)
(N A − NB )
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
(15 − 5) = 5 +
× 10 = 9.4%
(1,000 − (1,300))
2,300
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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%
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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 period
The payback period measures how long it takes for a business to recoup its cash outlay.
It uses the same figures as an NPV calculation.
Illustration
For 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
Year 1
Year 2
Year 3
Year 4
Inflow
$
4,000
5,000
6,000
4,000
Cumulative inflow
$
4,000
9,000
15,000
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)
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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
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Chapter 11
CASH 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 budgets
Cash flow budgets (or forecasts) are essential for successful cash management. The secret is to get the
timing correct.
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Example 1
Here are actual figures for November and December 2013 and budgeted figures for 2014:
$
Sales
Novembe December January February
r 2013
2013
2014
2014
12,000
14,000
9,000
8,000
March
2014
10,000
April
2014
12,000
Purchases
10,000
10,000
4,000
4,000
5,000
8,000
Other expenses
Purchase of noncurrent assets
Tax
3,000
5,000
3,000
3,000
3,000
4,000
20,000
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.
$
January
2014
February
2014
March
2014
April
2014
Cash from customers
Total
Cash paid to suppliers
Other expenses
Purchase of non-current assets
Tax
Total cash expenditure
Net cash flow
Cash b/f
Cash 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.
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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
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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:
Material is bought.
Raw material becomes
work-in-progress, which
becomes finished goods
Suppliers are paid
Goods are sold
Customers pay
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.
Work-in-progress turnover period.
Finished goods turnover period
Payables days
Receivables collection period
20
2
25
34
45
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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
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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
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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:
๏
Long term loans: typically >5 years
typically 1 – 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.
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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:
another company.
cash needed in case a good opportunity arises eg the take over of
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.
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๏
143
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.
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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 calculations
Interest 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?
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Compound interest
Interest is always calculated on both the principal and the interest earned so far.
Illustration
For example $1,200 on deposit at 10% compound.
After 1 year: $1,200 x 1.1 = $1,320
After 2 years: $1,320 x 1.1 = $1,452
and 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.
How much will there be on deposit at the end of that time?
$5,000 is deposited at 5.5% for 5 years.
How much will there be on deposit at the end of that time?
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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.
Illustration
A 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
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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 bank
Payments can be made from a bank account in four main ways:
๏
Cheques:
๏
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.
see later
All payments should be properly authorised and approved.
In addition, banks can remove funds from accounts for interest and bank charges.
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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.
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When completed, the cheque would look like:
15 /1/2013
ABC Co Ltd
1500.00
15 January 2013
ABC Company Ltd-------------One thousand five hundred
pounds only
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).
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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 now
Price 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
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.
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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.
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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)
1.00
1.00
2,000.00
2.00
900.00
4-part
moving
average
8 – part centred Seasonal
moving average: variation
trend
(additive)
Seasonal
variation
(multiplicative)
1,350.00
3.00
1,000.00
1,375.00
(375.00)
0.73
1,413.00
88.00
1.06
1,456.00
744.00
1.51
1,513.00
(513.00)
0.66
1,575.00
(325.00)
0.79
1,635.00
65.00
1.04
1,689.00
811.00
1.48
1,726.00
(546.00)
0.68
1,400.00
4.00
1,500.00
1,425.00
2.00
1.00
2,200.00
1,488.00
2.00
1,000.00
1,538.00
3.00
1,250.00
1,613.00
4.00
1,700.00
1,658.00
3.00
1.00
2,500.00
1,720.00
2.00
1,180.00
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
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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.
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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
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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.
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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 budgets
Often 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.
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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?
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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.
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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
Labour cost
Material price being higher or lower than Might be caused by commodity process
expected.
changing or by good/bad negotiations
over purchase price.
Different amounts of material being used More careful or more careless workers;
per unit that had been budgeted for.
better/worse quality material so that
wastage rates are altered.
Wage rates being different to what was Negotiations with employee
budgeted.
representatives
Staff being more efficient/inefficient than Good/bad supervision and training.
expected.
Poor supervision.
Staff allowed to be idle
Variable
Machines being more or less expensive Changes in power costs; maintenance.
overhead costs to run per hour.
Good/bad supervision and training/
Machines being used efficiently/
maintenance.
inefficiently
Fixed overhead Expenditure different to budgeted
Unanticipated price changes. Good/bas
variances
negotiation. More expenses taken on for
expansion, but not budgeted for.
Sales variances Different prices to those that were
Competitor pressure, economic changes,
budgeted
sales drives (ie deliberate price reduction
to stimulate demand).
Different volumes sold compared to
volumes budgeted.
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.
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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.
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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 - report
Written – memorandum
Written – letter
Written – email
Oral – address an audience
Oral – discussion in a group
Oral – one-to-one interviews
Oral – pod-cast
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Graphics – video
Graphics – graphs and diagrams
Mixture – internet site
Chapter 2
Example 1
(Any three for each category)
Purchases:
purchase requisitions, purchase orders, goods received notes, purchase
invoices
Sales:
sales orders, delivery/despatch notes, sales invoices
Inventory:
goods received notes, materials requisition notes, bin cards, despatch notes
Example 2
Precise
Concise
Enables automatic processing
Checking for errors/preventing errors.
Example 3
Simple to use
Understandable
Concise
Precise
Expandable
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 costs
Low = 10,000 units and $220,000 costs
Difference = 15,000 units and 150,000 costs
Therefore, variable cost per unit = $10
Fixed 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.
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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 = $220,000
High output = 20,000, costs = $340,000
Difference = 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 line
Cost = $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 method
Cost = $24,000; scrap (residual) value at end of life $4,000; estimated useful life = 5 years.
Year
1
25%
2
25%
3
25%
Cost/written
down value
24,000
6,000
18,000
4,500
13,500
3,375
10,125
Etc
.
.
.
This method never gets to zero.
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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 4
Example 1
Date
Units
Unit price
1,000
500
5.00
6.00
1 April
5 April
Opening inventory
Purchased
9 April
Sold
200
N/a
14 April
Purchased
600
5.50
21 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
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Cumulative weighted average
Date
1 April
5 April
9 April
14 April
21 April
Opening
inventory
Purchased
Sold
Purchased
Sold
Closing stock
Units
Unit price
1,000
5.00
Cumulative weighted
average
5,000
500
6.00
3,000
1,500
@5.333
(200)
@5.333
[8.000/1,500 = 5.3333]
8,000
(1,067)
1,300
@5.333
6,933
600
5.50
3,300
1,900
@5.386
10,233
(1,200)
@5.386
(6,463)
700
@5.386
3,770
Cost of sales = $1,067 + $6,463 = 7,530
Closing inventory = $3,770
Periodic weighted average
Value of purchases plus opening stock = $5,000 + $3,000 + $3,300 = $11,300
Units purchased plus in opening stock = 1,000 + 500 + 600 = 2,100
Periodic average = 11,300/2,100 = 5.381
Cost of sales = (200 + 1,200) x 5.381 = 7,533
Value of inventory = 700 x 5.381 = 3,767
Example 2
Inventory statistics are:
Maximum usage/day
Minimum usage/day
Average usage per day
Maximum lead time
Minimum lead time
Average lead time
Reorder quantity
20
12
15
11 days
4 days
6 days
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
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Example 3
Work out the annual holding, ordering and total costs at the following reorder quantities:
Reorder
quantity
Holding cost
½ ROQ x $5
100
200
500
1,000
2,000
4,000
250
500
1,250
2,500
5,000
10,000
Ordering
Occasions
20,000/ROQ
200
100
40
20
10
5
Ordering Cost
(orders x $50)
Total cost
10,000
5,000
2,000
1,000
500
250
10,250
5,500
3,250
3,500
5,500
10,250
Chapter 5
Example 1
Note: each unit is expected to take 40/80 =
0.5 hours
Basic wages for 44 hours = 44 x $6 =
US$264
8
Overtime premium 4 x $6 x ⅓ =
Extra units 10 x $5 =
50
Overtime premium that could be associated with the extra units
(10)
10 x 0.5 x $6 x ⅓
312
Example 2
Gross wages
Tax and other deductions
Net pay
38 x $10 = US$380
25% x (380 – 100) = $70)
$310
Payroll taxes $380 x 10%
Total payments by employer to tax authorities
$38
= $70 + $38 = $108
Example 3
Wages control account
31/3 Work in progress account
36,000
31/3 Work-in-progress account
4,000
1/4 Cash (paid to employees)
28,000
15/5 Cash (paid to tax authorities)
12,000
40,000
40,000
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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 = $48,000
This will be $48,000/5 = $9,600 per day
Product
Days
Cost
1
2
19,200
2
2
19,200
3
1
9,600
Units
200
500
4
Cost/unit
$96.00
$38.40
$2,400
Chapter 6
Example 1
500 (20 – 8) – 4,000 = $2,000
Example 2
Rent
Insurance
Canteen
Power
consumption
Cost Basis of apportionment
Floor area 4:5:1
Machine value 94:80:6
Employees 8:6:2
75%,20%,5%
Total
Total Preparation Assembly
45,000
18,000
22,500
5,400
2,820
2,400
12,000
6,000
4,500
40,000
30,000
8,000
102,400
56,820
37,400
Canteen
4,500
180
1,500
2,000
8,180
Example 3
Costs apportioned into preparation department = $61,494
Costs apportioned into assembly department = $40,906
Product
Budgeted
volume
Product A
Product B
10,000 units
6,000 units
Preparation department
Machine
Labour hours
hours per
unit
unit
2
2.5
3
1
Assembly department
Machine
Labour hours
hours per
unit
unit
1
3
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 = 7.23
Product B overheads: 1.0 x 1.98 + 4 x 0.76 = 5.02
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Example 4
Direct apportionment
Overhead costs after initial allocation
and apportionment $
Maintenance 40:50
Canteen 25:40
Total overhead costs for production
departments
Production
department 1
Production
department 2
Maintenance
department
Canteen
150,000
32,000
13,500
160,000
40,000
21,600
72,000
(72,000)
–
35,100
–
(35,100)
195,500
221,600
–
–
Production
department 1
Production
department 2
Maintenance
department
Canteen
150,000
28,800
160,000
36,000
72,000
(72,000)
35,100
7,200
Step-down
Overhead costs after initial allocation
and apportionment $
Maintenance 40:50:10
Canteen 25:40
Total overhead costs for production
departments
16,269
26,031
195,069
221,031
42,300
(42,300)
–
–
Chapter 7
Example 1
Job 666
Material
Labour
Overheads
Total
– stores
– special
– basic
– supervisor
Quantity Unit price
$
20
15
1
150
30
9
3
15
33
4
$
300
150
270
45
132
897
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Example 2
Batch 7777
Material
Labour
– stores
– special
– Dept A
– Dept B
Overheads
Total for the batch
Quantity Unit price
$
2000
10
500
4
90
12
40
10
130
3
$
20,000
2,000
1080
400
390
23,870
Cost per unit made in batch 7777 = 23870/900 = $26.52
Example 3
(a)
Joint costs apportioned using weight
Separate costs
Pre-separation costs 60:40 $12,000
Total costs
(b)
Product A
(600 kg)
4,000
7,200
11,200
Product B
(400 kg)
7,000
4,800
11,800
Joint costs apportioned using net realisable value
Sales value
Post separation/own costs
Net realisable value
Separate costs
Pre-separation costs 11/20 and 9/20 of $12,000
Total costs
Product A
15,000
(4,000)
11,000
Product B
16,000
(7,000)
9,000
4,000
6,600
10,600
7,000
5,400
12,400
Example 4
(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
Separate costs
Pre-separation costs 50:40 of $11,800
Total costs
Product A
(500 kg)
4,000
6,555
10,555
Product B
(400 kg)
7,000
5,245
12,245
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Joint costs apportioned using net realisable value
Sales value 500 x 25; $400 x $40
Post separation/own costs
Net realisable value
Separate costs
Pre-separation costs 8.5/17.5 and 9/17.5 of
$11,800
Total costs
Product A
12,500
(4,000)
8,500
Product B
16,000
(7,000)
9,000
4,000
7,000
5,731
9,731
6,069
13,069
Product A
100,000
65,000
Product B
150,000
45,000
40,000
40,000
80,000
20,000
90,000
70,000
160,000
(10,000)
Example 5
Sales revenue of final product
Sales revenue at split-off
Post separation/own costs
Joint costs (split)
Total costs
Profit/(loss)
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
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Example 6
Total annual cost of running a lorry fleet = $80,000
Jobs:
Job
1
Weight
(KG)
5,000
Distance
(KM)
200
KG x KM
1,000,000
2
10,000
500
5,000,000
3
7,000
400
2,800,000
4
12,000
600
7,200,000
16,000,00
Total
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
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.
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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 = 2.4
Product B: contribution/kg = 15/5 = 3
Therefore 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
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Example 2
Buy-in price
Azed
38
Byoz
34
Cost to make
22
30
Saving per unit of making rather than buying
16
4
Kg of scarce resource M used/unit
4
2
Saving per Kg of scarce resource made by making rather then buying
4
2
Ranking
1
2
20,000 kgs
12,000 kgs
32,000 kgs
(Balance)
Make as much as possible of the products with the higher rank:
Product Azed: make 5,000 units, consuming
Product Byoz: make 6,000 units, consuming
Buy 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
Incremental costs
Opportunity cost of not selling existing inventory
Increase in contribution =
= $4 x 2,000/2 =
800 kg bought @1.20
4,000
(960)
(1,600)
1,440
[Note irrelevant: $3,600 = sunk; $1,500 market research = sunk/past; $4,000 not incremental, merely
reapportioned.]
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Chapter 10
Example 1
Option 1: Present value = $3,000
Option 2: Present value = 4,000 x 0.763 = $3,052
Option 2 is therefore preferable.
Option 1: Present value = 3,000 x 0.826 = $2,478
Option 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
z
PV = $100 x 2.779 = $278
1 – 10
4% annuity factor
8.111
1–2
4% annuity factor
(1.886)
year 5
4% annuity factor
(0.822)
5.403
PV = $100 x 5.403 = $540
1–5
10% annuity factor
3.791
0
10% annuity factor
1.000
0–5
4.791
PV = $200 x 4.791 = $958
Example 3
1⎡
1 ⎤
1 ⎡
1 ⎤
Annuity factor = ⎢1−
=
1−
= 5.206
n ⎥
⎢
r ⎣ (1+ r) ⎦ 0.08 ⎣ (1.08)7 ⎥⎦
1⎡
1 ⎤
1 ⎡
1
⎤
Annuity factor = ⎢1−
=
1−
= 8.619
n ⎥
12 ⎥
⎢
r ⎣ (1+ r) ⎦ 0.055 ⎣ (1.055) ⎦
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Example 4
Time
Flow
$
Factor
Investment
(10,000)
1.000
Discounted
cash flow
(10,000)
0
1
Investment
(12,000)
0.917
(11,004)
2
3
4
Income
Income
Income
5,000
15,000
7,000
0.842
0.772
0.708
Net present value
So, marginally, the investment is not worthwhile.
4,210
11,580
4,956
-258
Example 5
Required discount factor = 3.791 – 0.909 = 2.882
PV of inflows = 2.882 x 8,000 = $23,056
PV of outflow = $18,000
NPV = $5,056
So, project is worthwhile.
Example 6
Depreciation charged = (15,000 – 3,000)/4 = 3,000
Time Flow
$
1
Investment
2
investment
Income before
depreciation
Scrap
4
4
6% Factor
(15,000)
1.000
Discounted
cash flow
(15,000)
5,000 + 3,000 = 8,000
2.673
21,384
4,000 + 3,000 = 7,000
0.792
5,544
3,000
0.792
Net present value
2,367
14,295
Therefore the project is worthwhile
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Chapter 11
Example 1
$
January
2014
February
2014
March
2014
April
2014
Cash from customers
– previous month
8,400
5,400
4,800
6,000
– two months ago
Total
4,800
13,200
5,600
11,000
3,600
8,400
4,800
10,800
Cash paid to suppliers
10,000
4,000
4,000
5,000
Other expenses
3,000
3,000
3,000
4,000
10,000
17,000
(8,600)
4,200
(4,400)
9,000
1,800
(4,400)
(2,600)
Purchase of non-current assets
Tax
Total cash expenditure
Net cash flow
Cash b/f
Cash c/f
20,000
13,000
200
20,000
20,200
27,000
(16,000)
20,200
4,200
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.
Work-in-progress turnover period.
Finished goods turnover period
Payables days
2
25
(34)
Receivables collection period
45
Working capital cycle
58
20
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
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Chapter 12
Example 1
Flexed budget = $96,000 x 7,000/8,000 = $84,000
Actual cost = $89,000
Variance = $5,000 adverse/unfavourable.
Example 2
Flexed budget = $150,000 x 10,500/10,000 = $157,500
Actual 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.
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ANSWERS TO QUESTIONS
Chapter 1
Question 1
B
The three purposes of information that were described were planning, controlling and decisionmaking
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
A
Chapter 2
Question 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
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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
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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
C
Purchases
= Used + closing inventory – opening inventory
= 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
Input
100
20,000
–
–
–
Wastage
25
5,000
=
=
=
Output
75
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
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Question 11
EOQ= 2
A
2CoD 2 2x100x3,000x12
=
=1.095
CH
6
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 5
Question 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.
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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 7
Question 1
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.
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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.
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Chapter 9
Question 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
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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 = $5.5m; cost of the building
$5m
NPV = -$1m - $5m + $5.5m = -$0.5m
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%
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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
1
2
3
4
Flow
7,000
8,000
10,000
8,000
Cumulative inflow
7,000
15,000
25,000
33,000
So, payback = 2.5 years
Discounted pay back
Year
Flow
Factor
1
2
3
4
7,000
8,000
10,000
8,000
0.926
0.857
0.794
0.735
Discounted
flow
6,482
6,856
7,940
5,880
Cumulative inflow
6,482
13,338
21,278
27,158
So discounted payback almost 2.8 years. [2 + (20,000 – 13,338)/7,940]
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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
Received from debtors
Received in month of sale $120,000/2
Paid to suppliers
Other expenses
Cash balance c/f
20,000
42,000
60,000
(65,000)
(90,000)
(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
C
Purchases = Used + closing inventory – opening inventory
= 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
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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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