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BA2
Ex
am
s
Fundamentals
of Management
Accounting
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2020 Examinations
Watch free CIMA BA2 lectures 1
BA2 Fundamentals of Management Accounting
Formulae
3
1.
Accounting for Management
7
2.
Cost Classification and Behaviour
11
3.
Semi-Variable Costs
15
4.
Accounting for Overheads
19
5.
The Management Accountant’s Profit Statement – Absorption Costing
25
6.
The Management Accountant’s Profit Statement – Marginal Costing
27
7.
Cost–Plus Pricing
29
8.
Budgeting
31
9.
Variance Analysis
39
10.
Performance Measurement Overview
41
11.
Financial Performance Measurement
43
12.
Non-Financial Performance Measurement
47
13.
Integrated Cost Accounting
51
14.
Probability
55
15.
Measures of Average and of Dispersion
59
16.
The Normal distribution
65
17.
Breakeven Analysis
67
18.
Limited Factor Analysis and Make or Buy Decisions
71
19.
Interest
73
20.
Investment Appraisal
79
Answers to Examples
83
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2020 Examinations
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2
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2020 Examinations
FORMULAE
FORMULAE SHEET
Regression analysis
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4
Watch free CIMA BA2 lectures
2020 Examinations
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2020 Examinations
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6
Standard normal distribution table
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0·2
0·3
0·4
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0·0000
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0·0793
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0·1554
0·01
0·0040
0·0438
0·0832
0·1217
0·1591
0·02
0·0080
0·0478
0·0871
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0·1628
0·03
0·0120
0·0517
0·0910
0·1293
0·1664
0·04
0·0160
0·0557
0·0948
0·1331
0·1700
0·05
0·0199
0·0596
0·0987
0·1368
0·1736
0·06
0·0239
0·0636
0·1026
0·1406
0·1772
0·07
0·0279
0·0675
0·1064
0·1443
0·1808
0·08
0·0319
0·0714
0·1103
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0·1844
0·09
0·0359
0·0753
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0·1517
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0·5
0·6
0·7
0·8
0·9
0·1915
0·2257
0·2580
0·2881
0·3159
0·1950
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0·2611
0·2910
0·3186
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0·4826
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0·4868
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0·4922
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0·4871
0·4901
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0·4838
0·4875
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0·4927
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0·4803
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0·4965
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0·4969
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0·4984
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0·4960
0·4970
0·4978
0·4984
0·4948
0·4961
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0·4979
0·4985
0·4949
0·4962
0·4972
0·4979
0·4985
0·4951
0·4963
0·4973
0·4980
0·4986
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0·4964
0·4974
0·4981
0·4986
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0·4987
0·4987
0·4988
0·4988
0·4989
0·4989
0·4989
0·4990
0·4990
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Chapter 1
ACCOUNTING FOR MANAGEMENT
1. Introduction
The purpose of management accounting is to assist management in running the business in ways
that will improve the performance of the business.
2. The definition of management accounting
CIMA defines management accounting as “the application of the principles of accounting and
financial management to create, protect, preserve and increase value for the stakeholders of forprofit and not-for-profit enterprises in the public and private sectors”.
3. The Global Management Accounting Principles
The purpose of the Principles is to help organisations to improve their management accounting
systems in order to be able to make better decisions and to respond appropriately to the risks that
they face.
There are four Principles:
Communication provides insight that is influential
By communicating information well, the organisation can make better decisions
Information is relevant
Organisations need to be helped in planning the information needed for the decisions they are
making
Stewardship brings trust
The assets, reputation and value of the organisation need protecting
Impact on value is analysed
It is necessary to consider different possible scenarios in order to be in a position to make better
decisions
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8
4. Data and information
One way of assisting management is to provide them with good information to help them with
their decisions.
The information can be provided to them in different ways, but is usually in the form of reports. For
example, a report analysing costs of producing each of several products may assist management in
deciding which products to produce.
It is the management accountant who will be expected to provide the information, and in order to
do so he/she needs to collect data.
Data consists of the facts that are gathered and stored. Data has no clear meaning until it is
processed – analysed and sorted – into information.
5. What makes good information?
Good quality information should:
๏
be Accurate
๏
be Complete (but not excessive)
๏
be Cost effective (should cost less than the savings to be made)
๏
be Understandable (to whoever is using it)
๏
be Relevant (to the decision being made)
๏
be Authoritative (be able to be trusted by the users)
๏
be Timely
๏
be Easy to use
6. The main managerial processes
The main areas of management accounting are:
๏
Costing
Cost accounting is identifying the cost of producing an item (or providing a service) in order
to, for example, assist in deciding on a selling price.
๏
Planning
e.g. plan how many staff will be required in the factory next year
๏
Decision making
e.g. decide on what selling price to charge for a new product
๏
Control
e.g. check month-by-month whether the company is over or under spending on wages
๏
Performance evaluation
Comparing the performance of mangers or departments against budgets or targets
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7. The different levels of planning
๏
strategic planning
long-term plans (e.g. 5 to 10 years) for the business
e.g. what new offices to open? / what new products to launch?
๏
tactical planning
medium-term, more detailed, plans – usually involving producing budgets for the next year
e.g. how many staff to employ next year?
๏
operational planning
short-term planning and decisions
e.g. which supplier to choose for a purchase next week
8. Comparison of Management Accounting with Financial
Accounting
Financial accounting
Management accounting
Prepare reports, generally
based on past performance;
in line with reporting
requirements
Collate information such as revenue, cashflow and
outstanding debts to produce timely trend reports
and statistics to inform important, day-to-day
management and business decisions
Produce the required
financial information for use
by other functions within the
business, for example
department managers.
Combine financial information with non financial
information data to paint a complete picture of the
business. They use this to drive business success.
9. CIMA’s Professional Standards
CIMA has a code of ethics which all members and students are required to comply with in order to
maintain the highest ethical and professional standards.
There are five fundamental principles:
๏
Integrity
๏
Objectivity
๏
Professional competence and due care
๏
Confidentiality
๏
Professional behaviour
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Chapter 2
COST CLASSIFICATION AND
BEHAVIOUR
1. Cost classification
Cost classification is the arrangement of cost items into logical groups. For example: by their nature
(materials, wages etc.); or function (administration, production etc.).
The eventual aim of costing is to determine the cost of producing a product/service; for profitability
analysis, selling price determination and stock valuation purposes.
Cost unit
A cost unit is a unit of product or service in relation to which costs may be ascertained.
The cost unit should be appropriate to the type of business, for example:
Example 1
Suggest appropriate cost units for the following businesses
Solution
Business
Appropriate cost unit
Car manufacturer
Cigarette manufacturer
Builder
Audit company
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Types of expenses
$
Production/manufacturing costs
Administration costs
Selling and distribution costs
TOTAL EXPENSES
X
X
X
X
Only the production costs will be relevant in costing.
Direct costs
Direct costs are those costs which can be identified with and allocated to a particular cost unit.
TOTAL DIRECT COSTS = PRIME COST
Example 2
Direct costs
Indirect production costs (overheads)
Indirect production costs (known as production overheads) are those costs which are incurred in
the course of making a product/service but which cannot be identified with a particular cost unit.
Example 3
Indirect production costs
TOTAL PRODUCTION COST = PRIME COST + PRODUCTION OVERHEADS
Non-production costs
Other costs required to run the business.
Example 4
Non-manufacturing/production costs
TOTAL COSTS = PRODUCTION COSTS + NON-PRODUCTION COSTS
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2. Cost behaviour
It is expected that costs will increase as production increases (i.e. as output increases) but the exact
way in which costs behave with output may differ.
Example 5
Types of behaviour
(a)
Variable cost
(b)
Fixed cost
(c)
Stepped fixed cost
(d)
Semi variable/fixed cost
Linear assumption
For this examination we will assume that total variable costs vary linearly with the level of
production (or that the variable cost per unit remains constant). In practice this may not be the
case, but we will not consider the effect of this until later examinations.
Behaviour of manufacturing costs
With the linear assumption all costs can be categorised as either fixed or variable. This fits together
with previous definitions:
Direct costs
By their nature direct costs will be variable costs.
Indirect costs/overheads
Overheads can be fixed or variable
Fixed
Variable
Direct costs
X
√
Production overheads
Non-manufacturing costs
√
√
√
√
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Semi-variable costs
It is necessary to determine the fixed and variable elements of semi-variable costs. A method
known as ‘High-Low’ can be used to establish the fixed and variable elements. This technique is
best illustrated by the use of an example.
Example 6
The total costs of a business for differing levels of output are as follows:
Output
(units)
200
1,000
Total Costs
($’000)
30
110
(a)
What are the fixed and variable elements of the total cost using the High-Low method?
(b)
Describe the relationship between the output and costs in the form of a linear equation.
A better approximation of the fixed and variable elements can be obtained using Regression
Analysis. This will be considered in the next chapter of these notes.
Typical cost card for a cost unit
$/unit
Direct costs:
- Direct materials
(2kg @ $1.50/kg)
- Direct labour
(3 hrs @ $4/hr)
Prime cost
Indirect costs
- Variable overheads
- Fixed overheads
Full product cost
3.00
12.00
15.00
2.00
3.00
20.00
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Chapter 3
SEMI-VARIABLE COSTS
1. Introduction
The chapter relates to semi-variable costs i.e. part fixed and part variable. It may be necessary for
you in the examination to identify the fixed and variable elements and in this chapter we will revise
the ‘high-low’ method and also explain Regression Analysis.
2. High-Low Method
This is a quick and easy approach that estimates fixed and variable costs by comparing the highest
and lowest activity levels.
Example 1
Electricity costs for the first 6 months of the year are as follows:
January
February
March
April
May
June
Units produced
340
300
380
420
400
360
Cost ($)
2,260
2,160
2,320
2,400
2,300
2,266
Calculate the fixed and variable costs using the high-low method.
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3. Problems with the high-low approach
4. Regression
If there is a reasonable degree of linear correlation between two variables, we can use regression
analysis to calculate the equation of the best fit for the data.
This is known as least squares linear regression.
If the equation relating two variables, × and y, is
y = a + bx
then the values of a and b may be calculated using the following formulae (which are given in the
examination)
b=
n∑ xy − ∑ x ∑ y
2
n∑ x 2 −(∑ x )
a=
∑ y − b∑ x
n
n
Example 2
The following table shows the number of units produced each month and the total cost incurred:
Units
January
February
March
April
May
June
July
100
400
200
700
600
500
300
Cost
($ ‘000)
40
65
45
80
70
70
50
Calculate the regression line, y = a + bx
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5. Problems with regression analysis
6. The correlation coefficient
Pearson’s correlation coefficient is a measure of how linear the relationship between variables is.
A correlation coefficient of +1 indicates perfect positive linear correlation, whereas -1 indicates
perfect negative linear correlation.
The further away from + or – 1, the less linear correlation exists.
The correlation coefficient may be calculated using the following formula (which is given to you in
the examination)
r=
n∑ xy − ∑ x ∑ y
(n∑ x −(∑ x ) )(n∑ y −(∑ y ) )
2
2
2
2
Example 3
Using the data in example 2, calculate the correlation coefficient
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7. Coefficient of determination
The coefficient of determination is the square of the coefficient of correlation (r2).
It is a measure of how much of the variation in the dependent variable is ‘explained’ by the
variation of the independent variable.
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Chapter 4
ACCOUNTING FOR OVERHEADS
1. Introduction
A business needs to know the cost per unit of goods or services that they produce for many
reasons.
E.g. to value stock
to fix a selling price
to analyse profitability
In principle, the unit cost of materials and of labour should not be a problem, because they can be
measured. It is the overheads that present the real difficulty – in particular the fixed overheads.
E.g. if the factory costs $100,000 p.a. to rent, then how much should be included in the cost of
each unit?
2. Absorption of overheads
To show our approach to solving the problem referred to above, consider the following example:
Example 1
X plc produces desks.
Each desk uses 3 kg of wood at a cost of $4 per kg, and takes 4 hours to produce.
Labour is paid at the rate of $2 per hour.
Fixed costs of production are estimated to be $700,000 p.a..
The company expects to produce 50,000 desks p.a..
Calculate the cost per desk.
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This method of arriving at an overhead cost p.u. (dividing total overheads by total production) is
known as the absorbing of overheads.
(Note that because we need the cost p.u. for things like fixing a selling price, we will usually absorb
the overheads based on estimated total cost and estimated production. This can lead to problems
later because obviously our estimates may not be correct. We will deal with this problem in the
next chapter.)
Although the basic approach to absorbing overheads is not difficult, there are two extra problems
that can occur and that you can be asked to deal with.
We will consider each of these problems in turn, and then look at a full example.
3. First problem – more than one product produced in the same
factory
In this situation we have to decide on a basis for absorption first.
There are many bases for absorption that could be used (e.g. per unit, per labour hour, per machine
hour etc.)
Example 2
X plc produces desks and chairs in the same factory.
Each desk uses 3 kg of wood at a cost of $4 per kg, and takes 4 hours to produce.
Each chair uses 2 kg of wood at a cost of $4 per kg., and takes 1 hour to produce.
Labour is paid at the rate of $2 per hour.
Fixed costs of production are estimated to be $700,000 p.a..
The company expect to produce 30,000 desks and 20,000 chairs p.a.
(Overheads are to be absorbed on a labour hour basis)
Calculate the cost per unit for desks and chairs
In practice it would be up to the Management Accountant to decide on the most appropriate basis.
In examinations it will be made obvious to you which basis to use, but read the question carefully.
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4. Second problem – more than one department in the factory.
In this situation we need first to allocate and apportion the overheads between each department.
We can then absorb the overheads in each department separately in the same way as before.
Example 3
X plc produces desks and chairs in the same factory. The factory has two departments, assembly
and finishing.
Each desk uses 3 kg of wood at a cost of $4 per kg., and takes 4 hours to produce – 3 hours in
assembly and 1 hour in finishing.
Each chair uses 2 kg of wood at a cost of $4 per kg, and takes 1 hour to produce – ½ hour in
assembly and ½ hour in finishing.
All labour is paid at the rate of $2 per hour.
Fixed costs of production are estimated to be $700,000 p.a.. Of this total, $100,000 is the salary of
the supervisors – $60,000 to Assembly supervisor, and $40,000 to Finishing supervisor.
The remaining overheads are to be split 40% to Assembly and 60% to Finishing.
The company expects to produce 30,000 desks and 20,000 chairs.
(Overheads to be absorbed on a labour hour basis)
Calculate the cost per unit for desks and for chairs
The charging of supervisors’ salaries to the relevant department is known as allocation of
overheads.
The splitting or sharing of overheads between departments (as in the remaining $600,000 in our
example) is known as the apportionment of overheads.
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A fuller example of allocating and apportioning overheads:
Example 4
Production overhead costs for the period
$
20,000
5,000
15,000
10,000
7,000
18,000
5,000
80,000
Factory rent
Factory heat
Processing Dept – supervisor
Packing Dept – supervisor
Depreciation of equipment
Factory canteen expenses
Welfare costs of factory employees
Cubic space
NBV equipment
No. of employees
Processing Dept
Packing Dept
Canteen
50,000 m3
25,000 m3
5,000 m3
$300,000
$300,000
$100,000
50
40
10
Allocate and apportion production overhead costs amongst the three departments using a
suitable basis.
5. Reapportionment of service cost centre overheads
Factory cost centres can be broken down into two types:
PRODUCTION COST CENTRES
SERVICE COST CENTRES
- these make the cost units.
- these do work for the production cost centres and one another.
We therefore need to transfer all service cost centre overheads to the production centres so that all
production overheads for the period are shared between the production cost centres alone - as it is
through these cost centres that cost units flow.
No Inter Service Work Done
If there is just one service department, or if there is more than one service department but there is
no work done by one service department for another, then reapportionment is done using a
suitable basis (e.g. canteen costs by the number of employees).
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Example 5
Reapportion the canteen costs in Example 4 to the production cost centres.
Inter-Service Work Done
The problem is a little more complicated if there is more than one service cost centre and where
they do work for one another. The way to deal with this is the reciprocal method.
The reciprocal method can be carried out in one of two ways:
๏
either the continuous or repeated distribution (tabular) method; or
๏
the algebraic method.
Example 6
Production Depts
X
Y
$
$
Allocated and apportioned overheads
70,000
30,000
Service Centres
Stores Maintenance
$
$
20,000
15,000
15%
20%
-
Estimated work done by the service centres for other departments:
Stores
Maintenance
50%
45%
30%
40%
Reapportion service department costs to departments using:
(a) repeated distribution method; and
(b) algebraic method.
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Chapter 5
THE MANAGEMENT ACCOUNTANT’S
PROFIT STATEMENT – ABSORPTION
COSTING
1. Introduction
In the previous chapter we stated that the cost per unit is normally calculated in advance using
estimated or budgeted figures. This is for several reasons. For instance, we need an estimate of the
cost before we can fix a selling price. In addition, the estimated cost per unit provides a benchmark
for control purposes. The Management Accountant can check regularly whether or not units are
costing more or less than estimated and attempt to take corrective action if necessary.
As a result, the Management Accountant’s Profit Statement (or Operating Statement) takes a
different form than that of the Financial Accountant’s Income Statement
The statement is usually prepared monthly, and its objective is to show whether the profit is higher
or lower than that expected, and to list the reasons for any differences.
The statement starts with the profit that should have been made if all the costs had been the same
as on the standard cost card.
It then lists all the reasons for any differences in profit (or variances) to end with the actual profit.
However, in calculating the budgeted profit for individual months, absorption costing causes a
problem when the expected production in a month differs from that used to absorb fixed
overheads for the cost card.
This problem is illustrated in the following example
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2. Illustration
Example 1
X plc produces one product – desks.
Each desk is budgeted to require 4 kg of wood at $3 per kg, 4 hours of labour at $2 per hour, and
variable production overheads of $5 per unit.
Fixed production overheads are budgeted at $20,000 per month and average production is
estimated to be 10,000 units per month.
The selling price is fixed at $35 per unit.
There is also a variable selling cost of $1 per unit and fixed selling cost of $2,000 per month.
During the first two months X plc expects the following levels of activity:
Production
Sales
(a)
(b)
January
11,000 units
9,000 units
February
9,500 units
11,500 units
Prepare a cost card using absorption costing
Set out budget Profit Statements for the months of January and February.
3. Hourly absorption rates
The previous example assumed that fixed overheads were absorbed on a unit basis. A popular
question in the exam is to be asked to calculate the amount of any over or under - absorption when
fixed overheads are absorbed on an hourly basis
Example 2
Y plc budgets on working 80,000 hours per month and having fixed overheads of $320,000. During
April, the actual hours worked are 78,000 and the actual fixed overheads are $315,500.
Calculate:
(a) the overhead absorption rate per hour.
(b) the amount of any over or under-absorption of fixed overheads in April
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Chapter 6
THE MANAGEMENT ACCOUNTANT’S
PROFIT STATEMENT – MARGINAL
COSTING
1. Overview
Some businesses only want to know the variable cost of the units they make, regarding fixed costs
as period costs. The variable cost is the extra cost each time a unit is made, fixed costs being
effectively incurred before any production is started.
The variable production cost of a unit is made up of:
Direct materials
Direct labour
Variable production overheads
Marginal cost of a unit
$
X
X
X
X
Marginal costing
Variable production costs are included in cost per unit (i.e. treated as a product cost).
Fixed costs are deducted as a period cost in the profit statement.
2. Contribution
Contribution is an important concept in marginal costing. Contribution is an abbreviation of
“contribution towards fixed costs and profit”.
It is the difference between selling price and all variable costs (including non-production variable
costs), usually expressed on a per unit basis.
$
Selling price:
Less: Variable production costs
Variable non-production costs
Contribution
Note:
X
X
X
$
X
(X)
X
Contribution takes account of all variable costs. Marginal cost takes account of
variable production costs only and inventory is valued at marginal cost.
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Example 1
X plc produces one product – desks.
Each desk is budgeted to require 4 kg of wood at $3 per kg, 4 hours of labour at $2 per hour, and
variable production overheads of $5 per unit.
Fixed production overheads are budgeted at $20,000 per month and average production is
estimated to be 10,000 units per month.
The selling price is fixed at $35 per unit.
There is also a variable selling cost of $1 per unit and fixed selling cost of $2,000 per month.
During the first two months, X plc expects the following levels of activity:
January
Production
February
11,000 units
9,500 units
9,000 units
11,500 units
Sales
All other results were as budgeted.
(a)
(b)
Prepare a cost card using marginal costing
Set out Profit Statements for the months of January and February.
Example 2
Prepare a reconciliation of absorption and marginal costing profits
January
February
$
$
Absorption costing
Marginal costing
Difference
The difference in profit arises from the different inventory valuations which are the result of the
difference in treatment of the fixed production overheads.
Effects
The delay in charging some production overheads under absorption costing leads to the following
situations.
Example 3
Compare profits under marginal and absorption costing for the following situations
(a) Production > Sales
(b) Production < Sales
(c) Production = Sales
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Chapter 7
COST–PLUS PRICING
1. Introduction
An important decision for the management accountant is that of fixing a selling price.
Clearly, in order to be profitable, the selling price will be higher than the cost, and in this
chapter we will look at several ways in which they may choose to decide on a selling price.
2. Full cost-plus pricing
With full (or absorption) cost pricing, we determine the selling price by adding a profit to the
absorption cost of the product.
The profit is calculated using either a mark-up or a margin.
When the profit is calculated as a percentage of costs is is known as a mark-up.
Example 1
Peter has prepared a cost card for a product as follows:
Materials
$ per
unit
10.00
Labour
5.00
Variable overheads
2.00
Fixed overheads
3.00
$20.00
He arrives at selling prices by adding a mark-up of 20% to the full product cost.
Calculate the selling price per unit
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When the profit is calculated as a percentage of selling price, it is known as a margin.
Example 2
Paul has prepared the following costing for a new job:
Materials
Labour
Variable overheads
Fixed overheads
$
5,000
6,000
4,000
3,000
$18,000
Paul requires a margin of 20% on sales revenue.
Calculate the selling price for this new job.
3. Marginal cost plus pricing
With marginal cost plus pricing, we apply a mark-up to the marginal cost of the product.
Although this is less complicated than full cost pricing (because fixed overheads do not need to be
absorbed) there is the problem of deciding what mark-up needs to be added to the variable cost in
order to ensure that fixed overheads are covered and that a profit is made.
Marginal cost plus pricing is especially useful for one-off price decisions where production of the
product in question will not change the total existing fixed overheads of the organisation.
Example 3
Mary has prepared a cost card for a product as follows:
Materials
$ per
unit
8.00
Labour
5.00
Variable overheads
3.00
Marginal cost
$16.00
He arrives at selling prices by adding a mark-up of 40% to the marginal cost.
Calculate the selling price for this new product.
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Chapter 8
BUDGETING
1. Introduction
Budgeting is an essential tool for management accounting for both planning and controlling future
activity. In this chapter we will discuss the benefits of budgeting, the types of budget, and the
preparation of budgets.
2. What is budgeting
Most companies prepare budgets – generally once a year they budget for the coming year.
Although this usually includes a forecast Profit Statement for the year, the budget is actually a set
of plans.
For example, a manufacturing company needs to plan their material and labour requirements for
the coming year. In order to do this they will generally have to forecast their expected sales units
for the year i.e. a sales budget. Then they will be in position to budget their production units for the
year i.e. a production budget. Once they have budgeted how many units to produce they are in a
position to estimate how much material and how much labour they will require i.e. a materials
usage budget and a labour budget.
None of the budgets so far mentioned will be in money terms – they will be expressed in units of
production, or kg of material, or hours of labour – but they each represent a plan for the year.
When all the individual budgets (or functional budgets) have been prepared, then it will be
possible to cost them out in money terms and prepare a forecast Profit Statement.
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3. Benefits of budgeting
Planning
Controlling
Co-ordination
Authorising and delegating
Evaluation of performance
Communicating and motivating
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4. Principal budget factor
As previously discussed, the budget needs to be prepared in stages – for example we normally will
need to know the budget production (in units) before we can budget how much material will be
needed (in kg).
The first thing that the person in charge of the budget process must do is decide where to start! For
most companies the starting point will be a sales budget. Once it has been decided how many
units the company expects to sell it is then possible to produce a production budget and so on.
However, this will not always be the starting point. Suppose, for example, that the company is a
manufacturer of desks for which wood is the main material. Suppose also that during the coming
year there is expected to be only a limited supply of wood available. In this situation the starting
point will be to budget the amount of wood available, then budget how many units the company
is capable of producing (a production budget) and then how many they expect to sell (a sales
budget).
In general terms, the first budget to be prepared should be whatever factor it is that limits the
growth of the company – it may be the level of demand (so a sales budget will be prepared first) or,
as for the example in the previous paragraph, it may be the availability of raw material (so a
material budget will be prepared first).
The factor that limits the company is known as the principal budget factor. The management
accountant needs to identify the principal budget factor and it is this factor that will be budgeted
first.
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5. The preparation of budgets
Example 1
The XYZ company produces three products, X, Y, and Z. For the coming accounting period budgets
are to be prepared using the following information:
Budgeted sales
Product X 2,000 units at $100 each
Product Y 4,000 units at $130 each
Product Z 3,000 units at $150 each
Standard usage of raw material
Product X
Product Y
Product Z
Standard cost of raw material
Wood
(kg per unit)
5
3
2
$8
Varnish
(litres per unit)
2
2
1
$4
Inventories of finished goods
X
Y
500u
800u
600u 1,000u
Opening
Closing
Z
700u
800u
Inventories of raw materials
Opening
Closing
Varnish
(litres)
10,000
9,000
Wood
(kg)
21,000
18,000
Labour
Standard hours per unit
Labour is paid at the rate of $3 per hour
X
4
Y
6
Z
8
Prepare the following budgets:
(a) Sales budget (quantity and value)
(b) Production budget (units)
(c) Material usage budget (quantities)
(d) Material purchases budget (quantities and value)
(e) Labour budget (hours and value)
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6. The Master Budget
After all the functional budgets have been prepared, they are summarised into a master budget for
submission to the senior management. This will normally comprise a budgeted statement of profit
or loss, a budgeted statement of financial position, a cash budget, and a capital expenditure
budget.
7. Type of budgets
Fixed budget
Flexed budget
Flexible budget
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Example 2
A company has prepared the following fixed budget for the coming year.
Sales
Production
10,000 units
10,000 units
$
50,000
25,000
12,500
10,000
$97,500
Direct materials
Direct labour
Variable overheads
Fixed overheads
Budgeted selling price $10 per unit.
At the end of the year, the following costs had been incurred for the actual production of 12,000
units.
Direct materials
Direct labour
Variable overheads
Fixed overheads
$
60,000
28,500
15,000
11,000
$114,500
The actual sales were 12,000 units for $122,000
(a)
Prepare a flexed budget for the actual activity for the year
(b)
Calculate the variances between actual and flexed budget, and summarise in a form
suitable for management.
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8. The Cash Budget
One of the most important budgets for future planning is the cash budget. It is usually prepared on
a month-by-month basis showing all the planned receipts and payments of cash each month. It is
then possible to see in which months there is likely to be surplus cash and in which months there is
likely to be a deficit.
In months where the cash balance is expected to be in surplus, the organisation can plan ahead as
to where to invest the money in the short-term. In months where the cash balance is expected to
be in deficit they can plan ahead as to how to deal with it - for example, they may need to arrange
with the bank to be allowed to go overdrawn, or they may decide to defer planned expenditure on
new machines etc..
Example 3
You are presented with the following flow forecasted cash flow data for your organisation for the
period November 20X1 to Mar 20X2. It has been extracted from functional flow forecasts that have
already been prepared.
Sales
Purchases
Wages
Overheads
Dividends
Capital expenditure
NovX1 DecX1 JanX2 FebX2 MarX2
$
$
$
$
$
80,000 100,000 110,000 130,000 140,000
40,000 60,000 80,000 90,000 110,000
10,000 12,000 16,000 20,000 24,000
10,000 10,000 15,000 15,000 15,000
20,000
30,000
You are also told the following.
(a) Sales are 40% cash 60% credit. Credit sales are paid two months after the month of sale.
(b) Purchases are paid the month following purchase.
(c) 75% of wages are paid in the current month and 25% the following month.
(d) Overheads are paid the month after they are incurred.
(e) Dividends are paid three months after they are declared.
(f)
Capital expenditure is paid two months after it is incurred.
(g) The opening cash balance is $15,000.
Prepare a monthly cash budget for the three months from January to March 20X2.
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9. Participation in the preparation of budgets
There are two basic approaches to the way budgets are prepared:
(1)
one approach is for top management to prepare the budgets and then to impose them
on their managers. This is known as top-down budgeting
(2)
the alternative approach is to get the managers to prepare their own budgets and for
top management to then approve them (after obviously due discussion). This is known
as bottom-up budgeting.
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Chapter 9
VARIANCE ANALYSIS
1. Introduction
In the previous chapter we prepared a flexed budget and calculated the total variances. In this
chapter we are going to analyse these variances in order to provide more useful information.
2. Total variances
Example 1
A company has prepared the following standard cost card:
Materials (4 kg at $4.50 per kg)
Labour (5 hrs at $5 per hr)
Variable overheads (5 hrs at $2 per hr)
$ per unit
18
25
10
$53
Fixed overheads have been budgeted at $130,500
Budgeted selling price $75 per unit.
Budgeted production
Budgeted sales
There is no opening inventory
8,700 units
8,000 units
The actual results are as follows:
Sales:
Production:
8,400 units for $613,200
8,900 units with the following costs:
Materials (35,464 kg)
Labour (Paid 45,400hrs; worked 44,100 hrs)
Variable overheads
Fixed overheads
163,455
224,515
87,348
134,074
Prepare a flexed budget and calculate the total variances
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3. Analysis of cost variances
The total variance that we have calculated for materials indicates that the actual expenditure on
materials was not $18 per unit. However, this could be either because we used the wrong amount
of materials (which should have been 4 kg per unit) or that we paid the wrong price (which should
have been $4.50 per kg). More likely of course, it would be a combination of the two.
We will therefore analyse this and the other variances in as much detail as possible.
Example 2
Using the data from example 1, analyse each of the cost variances.
(a) Materials
(b)
Labour
(c)
Variable Overheads
4. Sales variances
Although we have already calculated the sales variances in example 1, you may be asked to
calculate them independently.
Example 3
Using data from example 1, calculate the Sales price variance and the Sales volume variance
5. The operating statement
The operating statement is a statement that reconciles the actual profit with the budgeted profit.
Example 4
Using the previously calculated variances, prepare an operating statement for the company
6. The interpretation of variances
Example 5
In the previous example there was a materials price variance.
Suggest possible reasons for its occurrence.
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Chapter 10
PERFORMANCE MEASUREMENT
OVERVIEW
1. Introduction
This chapter introduces the idea of performance measurement and its importance for the
management accountant.
2. The Mission Statement
This statement expresses the overall purpose of the organisation.
It will generally contain four elements:
๏
a purpose
why the company exists
๏
a strategy
the range of activities in which the business intends to compete,
and how it intends to compete
๏
policies and standards
guidelines which help staff decide what to do to carry out the
strategy
๏
values
the beliefs and moral principles which lie behind the firm’s
culture
Here is an example of an actual mission statement:
“McDonalds’ vision is to be the world’s best quick service restaurant experience. Being the best
means providing outstanding quality, service, cleanliness, and value, so that we make every
customer in every restaurant smile”
3. Goals and Objectives
Having decided on the company’s mission, it is then necessary to have goals and objectives.
Goals are statements of general intentions, whereas objectives are more specific.
An example of a goal is:
to improve profits
An example of an objective is:
to increase the profit by 20% within 2 years.
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4. Critical Success Factors and Key Performance Indicators
Having decided on the objectives of the business, it is important that we measure how well they
are achieving these objectives.
There are two parts to this. First they must decide what are the critical success factors (CSF’s) – the
performance requirements that are most fundamental to being successful.
For example, two of McDonalds’ CSF’s could be quality, and speed of service.
Secondly, they must then decide how they are going to measure their performance in these areas.
For this they need key performance indicators (KPI’s) – aspects to which they can actually put
numbers to, that indicate whether they are doing better or worse.
For example, McDonalds might decide to measure quality by asking customers to complete a form
scoring the quality between 1 to 5, and then recording the average score. They could decide to
measure speed of service by keeping records of the time taken to serve each customer and
recording the average service time in minutes.
๏
As you will see in the following chapters, it is important that a company has a range of KPI’s –
both financial (measuring, for example, profitability) and non-financial (measuring, for
example, quality).
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Chapter 11
FINANCIAL PERFORMANCE
MEASUREMENT
1. Introduction
Financial statements are prepared to assist users in making decisions. They therefore need
interpreting, and the calculation of various ratios makes it easier to compare the state of a company
with previous years and with other companies.
In this chapter we will look at the various ratios that you should learn for the examination.
2. The main areas
When attempting to analyse the financial statements of a company, the main area that we need to
look at is that of profitability.
We will work through an example to illustrate the various ratios that you should learn..
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3. Worked example
Example 1
Statements of Financial Position as at 31 December
2007
$
ASSETS
Non-current assets
$
2006
$
1,341
Current assets
Inventory
Receivables
Cash
1,006
948
360
$
826
871
708
100
EQUITY AND LIABILITIES
Share capital and reserves
2,314
3,655
1,679
2,505
2,190
1,401
500
400
965
3,655
704
2,505
Non-current liabilities
Current liabilities
Income statement for the year ended 31 December
Revenue
Cost of sales
Gross profit
Distribution costs
Administrative expenses
Profit from operations
Finance costs
Profit before taxation
Company tax expense
Profit after taxation
2007
$
7,180
5,385
2006
$
5,435
4,212
1,795
335
670
1,223
254
507
790
50
462
52
740
262
478
410
144
266
You are required to calculate the profitability ratios.
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Return on capital employed
Profit before interest and tax
=
Total long term capital
(= capital + reserves + long-term liabilities)
Net profit margin
Asset turnover
Profit before interest and tax
=
Revenue
=
Revenue
Total long term capital
NB: ROCE = asset turnover × net profit margin
Gross profit margin
=
Gross profit
Revenue
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4. Limitations of only looking at financial performance
Clearly any business wishes to improve its profitability, but there are dangers involved in only
looking at the financial performance:
Short-termism
Performance measures are often used as targets for the managers and they are often rewarded as
to how well they achieve or ‘beat’ the targets. As a result there is a danger that managers will be
focussed on doing well in the short-term rather than making decisions that will benefit the
business in the long-term.
Manipulation of the profits
In order to meet their targets in the current period, managers may be tempted to make the results
better by, for example, wrongly including revenue this year that should really be included next
year.
Historic measures
Financial measures only measure the performance of the business in the previous period. For the
business to grow in the future we need also to look at factors that will improve the business in the
future, such as the quality of the goods or services that the business is providing. However well we
performa financially this year, if the quality is suffering then we are likely to lose business and
therefore be less profitable in the future.
For this reason it is important that we also consider non-financial performance measures.
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Chapter 12
NON-FINANCIAL PERFORMANCE
MEASUREMENT
1. Introduction
In the previous chapter we looked at various measures of financial performance. However it is
important to have a range of performance measures considering non-financial and well as financial
matters. This is particularly important in the case of service businesses where such things as quality
are of vital importance if the business is to grow in the long-term.
In this chapter we will consider the various areas where performance measures are likely to be
needed.
Various authors have summarised the areas in different ways – the best known one is Kaplan and
Nortons Balance Scorecard. You will not be tested specifically on Kaplan and Norton, but you
should be aware of the areas that they consider important and be able to suggest performance
indicators under the various headings.
2. Kaplan and Nortons Balance Scorecard
Kaplan and Norton stated the importance of having a range of performance measures and forming
a balance between them. They grouped them under the following headings, which they called
perspectives:
๏
Customer satisfaction perspective
๏
Process efficiency (or internal business) perspective
๏
Growth (or innovation and learning) perspective
๏
Financial perspective
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Example 1
MacWendys is an Indian restaurant that wishes to implement a balanced scorecard approach and
has established the following goals for each of the balances scorecard perspectives:
Perspective
Goals
Customer perspective
To increase the number of new and returning customers
Process efficiency perspective
To reduce the customer waiting time
To reduce staff turnover
Learning and growth perspective
To increase the proportion of revenue from new meals
To increase the % of training time for staff
Financial perspective
To increase the spend per customer
To increase the gross profit margin
The following information is also available for the year just ended and for the previous year:
Total customers
- of which are new customers
- of which are returning customers
Customer complaints
Waiting time for order to arrive
% staff turnover
% of time that staff spend training
Revenue
- revenue from new meals
- revenue from existing meals
Gross profit
2016
2017
27,800
29,000
6,500
8,200
21,300
20,800
820
1,050
15 minutes
25 minutes
15%
30%
4%
2%
$252,000
$302,000
$26,000
$64,000
$226,000
$238,000
$51,000
$64,000
Calculate appropriate measures, and comment on whether or not MacWendys have achieved
their goals.
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3. Service versus manufacturing businesses
Although the same perspectives and approach for measuring performance can be used for both
service and manufacturing industries, there are more difficulties involved in both the costing and
the performance measurement for service industries.
There are four main features of service industries that make them different from manufacturing
industries:
Intangibility
Variability
Simultaneity
Perishability
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Chapter 13
INTEGRATED COST ACCOUNTING
1. Introduction
Transactions of a business need recording, both for the financial accounts and for the management
accounts. Some businesses keep completely separate sets of records, but this clearly involves
duplication which is why it is common to have one set of records for both purposes - this is known
as integrated cost accounting. In this chapter we will work through an example in order to show
how the records are maintained.
2. Labour
Before we work through a full example, it is important to appreciate that labour can be either a
direct cost or an indirect cost (or overhead).
All costs of indirect workers (i.e. those not directly involved in making products, such as
maintenance staff and supervisors) are indirect costs.
For workers directly involved in making products:
๏
Direct costs are their basic pay, and any overtime premium (i.e. the extra that is paid over and
above their basic pay) paid for a specific job at the customer’s request.
๏
Indirect costs are general overtime premiums, bonus payments, idle time, and sick pay
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3. The accounting entries
To explain the accounting entries, we will work through an example step-by-step.
First, we record the actual costs by entering them on the debit (left-hand) side of accounts for each
of materials, direct labour, and overheads. At the same time we enter the amounts on the credit
(right-hand) side of cash (in respect of costs paid in cash) or on the credit side of payables (in
respect of anything bought on credit).
We also record the sales revenue by entering it on the credit side of a sales account, and at the
same time entering it on the debit side of cash (if the sales were for cash) or on the debit side of
receivables (if the sales were made on credit).
Example 1
ABC produces and sells product X.
The standard cost card for product X is as follows:
$
Materials (5kg at $15 per kg)
75
Direct labour (10 hours at $3 per hour)
30
Variable production overheads
15
Standard marginal cost
120
The standard selling price is $200 per unit.
During January, they produced and sold 1,000 units and the actual results were as follows:
$
Sales, all for cash (1,000 units at $200)
200,000
Materials (5,500 kg)
77,000
Labour
35,000
Other variable overheads
10,000
There were no opening inventories, and all expenses were paid in cash.
(Note: $5,000 of the labour cost was for indirect labour. Also, direct labour worked for 10,000
hours.)
Enter the actual results into the relevant accounts
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Next, we will transfer any indirect labour from the labour account to the overheads account.
Example 2
Transfer the indirect labour to the overheads account.
Next, we put all the production costs together in order to get the total cost of production , by
transferring each of them to a Cost of Sales account. In each case, we credit the cost account and
debit the Cost of Sales account.
Example 3
Transfer each of the production costs to the Cost of Sales account
Now, we transfer the total standard cost of the goods sold to the Statement of Profit or Loss
account - we credit the Cost of Sales account and debit the SOPL account, with the standard cost of
the goods sold.
Example 4
Transfer the standard cost of the goods sold to the SOPL account
You will notice that the total on the debit side of the cost of sales account does not equal the total
on the credit side.
The reason is that we have debited with what was actually spent, but credited with the standard
cost.
If you look back, then for direct labour and overheads, the amount actually spent is the same as the
standard costs for the production. However, in respect of materials, the total actually spent of
$77,000 was not equal to the standard cost of materials of $75,000 (1,000 units at $75 per unit).
As a result we have variances, and we need to analyse into the price variance and the usage
variance.
When we have done this, we transfer the variances from the cost of sales account to the SOPL
account.
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Example 5
Calculate the materials price variance and the materials usage variance, and transfer to the
SOPL account.
We have now almost finished!
To complete the exercise we will transfer the figure on the sales account to the SOPL account. The
balancing figure on the SOPL account will be the profit for the month and we can then re-write the
figures in the account in the form of a statement to present to management (the operating
statement).
Example 6
Complete the exercise as described above.
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Chapter 14
PROBABILITY
1. Introduction
In this chapter we will explain what we mean by probabilities, and look at a range of different
calculations of probabilities that could be required of you in the exam.
2. Simple probabilities
The probability of an event occurring is the likelihood or the change that it will occur.
So, for example, if we toss a coin then their are two possible outcomes - that it falls as a head or as a
tail - and both outcomes have an equal chance of occurring. Therefore the probability of it being a
head - one of the two outcomes - is 1 in 2, which can be expressed at a probability of 1/2, or as 0.5,
or as 50%.
Example 1
If we toss a 6-sided die, what is the probability of getting:
(a) a six
(b)
a one or a two
(c)
a number greater than 3
Example 2
If we pick one card from a pack of 52 playing cards, what is the probability of that card being:
(a) the ace of diamonds
(b)
an ace
(c)
a heart
(d)
an ace or a diamond
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Example 3
A company has recorded the number of complaints received per week over the last year, and has
produced the following table:
Number of
complaints
Frequency
0
12
1
16
2
20
3
4
52
What is the probability that in one particular week there are 2 complaints?
Example 4
In a group of 200 potential voters, 150 are male and 50 are female.
60 of the male voters will vote for Party A. 25 of the female votes will not vote for Party A.
If one voter is picked at random:
(a) What is the probability that they are female
(b)
What is the probability that they will vote for Party A
(c)
If the voter picked will be voting for Party A, then what is the probability that they are
female?
3. Joint probabilities
If we want to know the probability of two or more events occurring, then we can calculate it by
multiplying the individual probabilities together.
For example, if we toss a die two times, then there are 36 possible outcomes - a 1 and a 1, a 1 and a
2, a 1 and a 3, and so on. So the probability of getting two 6’s is 1/36 because two 6’s is just one of
the 36 possible outcomes. However, we could have got the same answer by saying that the
probability of getting a 6 on the first toss is 1/6; the probability of getting a 6 on the second toss is
1/6; and therefore the probability of getting two 6’s is 1/6 x 1/6 = 1/36.
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Example 5
A card is picked at random from a pack of 52 playing cards. It is replaced, and then a second card is
picked at random from the same pack.
What is the probability of having picked:
(a) two Kings
(b)
two hearts
(c)
an Ace and a King
In example 4, we replaced the playing card after the first pick. and therefore there were 52 cards to
pick from on both picks. However, if the first card had not been replaced, then it would change the
probabilities for the second card.
Example 6
A card is picked at random from a pack of 52 playing cards. It is NOT replaced, and then a second
card is picked at random from the same pack.
What is the probability of having picked:
(a) two Kings
(b)
two hearts
(c)
an Ace and a King
4. Expected values
Probabilities can be useful in a business situation where there are various possible results that
could occur for which we know the probabilities. We can use the probabilities to arrive at an
‘average’ result, which we call the expected value.
Example 7
A company is considering launching a new product. The demand for the new product is uncertain,
but the company has estimated that if demand is high then the revenue will be $500,000 a year; if
the demand is medium then the revenue will be $300,000 a year; and if the demand is low then the
revenue will be $200,000 a year.
The probabilities of high, medium, and low are 0.2, 0.5 and 0.3 respectively.
What is the expected revenue?
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Expected values can be used to help make decisions, in which case it is common to need to
produce a table first showing the possible outcomes and their probabilities.
Example 8
John has a factory capacity of 1,200 units per month.
Units cost him $6 each to make and his normal selling price is $11 each. However, the demand per
month is uncertain and is as follows:
Demand
Probability
400
0.2
500
0.3
700
0.4
900
0.1
He has been approached by a customer who is prepared to contract to a fixed quantity per month
at a price of $9 per unit. The customer is prepared to sign a contract to purchase 300, 500, 700 or
800 units per month.
The company can vary production levels during the month up to the maximum capacity, but
cannot carry forward any unsold units in inventory.
Calculate all possible profits that could result
(a)
Determine for what quantity John should sign the contract, using expected values.
(b)
5. The limitations of expected values
There are two main limitations as to the use of expected values in decision making:
๏
it is unlikely that the probabilities can be determined with accuracy, and should the
probabilities turn out to be different then the wrong decision may have been made.
๏
for a ‘one-off’ decision, the actual outcome is unlikely to coincide with the expected outcome
- it may turn out to be better or it may turn out to be worse.
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Chapter 15
MEASURES OF AVERAGE AND OF
DISPERSION
1. Introduction
It is often of interest to be know the average of a set of data. For example we may have asked a
sample of people what their wages are, and want to know what the average wage is. In this chapter
we will look at different ways we can calculate an average. Additionally, even if we have calculated
the average wage, it might be on interest to know whether all of the sample had a wage close to
the average or whether some earned a lot more and some a lot less than the average. This is known
as the dispersion and we will look at different ways of measuring this.
2. Frequency distributions
A frequency distribution is a table showing the number of observations of each variable. They may
be discrete variables which can only consist of certain values, or continuous variables where we
group the variables.
Discrete variables:
A company has recorded the number of complaints received per week over the last year, and has
produced the following table:
Number of
complaints
0
1
2
3
Frequency
12
16
20
4
52
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Continuous variables:
A company has recorded the total amount paid to employees each week over the last year, and has
produced the following table:
Total paid ($)
Frequency
0 - under $500
1
500 - under 1,000
4
1,000 - under 1,500
8
1,500 - under 2,000
19
2,000 - under 2,500
14
2,500 - under 3,000
6
52
3. Ways of presenting data
In many cases, management do not need to see the actual numbers (and indeed the actual
numbers may confuse them). Often a chart or graph can present the information more clearly.
Example 1
A company has recorded the total amount paid to employees each week over the last year, and has
produced the following table:
Total paid ($)
Frequency
0 - under $500
1
500 - under 1,000
4
1,000 - under 1,500
8
1,500 - under 2,000
19
2,000 - under 2,500
14
2,500 - under 3,000
6
52
Present the above table in the form of
(a) a bar chart
(b)
a pie chart
(c)
a histogram
(d)
an ogive
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4. Measures of average
You need to be aware of the following different measures of determining the average of a set of
observations:
Arithmetic mean
This is calculated by adding up all of the observations and dividing by the number of observations
Median
This is the centrally occurring observation when all of the observations are arranged in order of
magnitude
Mode
This is the most frequently occurring observation
Example 2
A company has recorded the number of complaints received per week over the past thirteen
weeks, and has produced the following table:
Number of complaints
Frequency
0
1
1
6
2
4
3
2
13
Calculate:
(a) the arithmetic mean
(b)
the median
(c)
the mode
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Example 3
A company has recorded the total amount paid to employees each week over the last year, and has
produced the following table:
Total paid ($)
Frequency
0 - under $500
1
500 - under 1,000
4
1,000 - under 1,500
8
1,500 - under 2,000
19
2,000 - under 2,500
14
2,500 - under 3,000
6
52
Calculate:
(a) the arithmetic mean
(b)
the median
(c)
the mode
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5. Measures of dispersion
Dispersion is looking at the spread of the observations.
You need to be aware of the following measures of dispersion:
Range
This is simply the difference between the highest and the lowest of the observations
Variance
Here we measure the differences between the observations and the arithmetic mean, square the
differences, and then take the average of these squared differences.
Standard deviation
This is the square root of the variance
Coefficient of variation
The standard deviation divided by the arithmetic mean
Example 4
For the information in example 2, calculate:
(a)
the range
(b)
the variance
(c)
the standard deviation
(d)
the coefficient of variation
Example 5
For the information in example 3, calculate:
(a)
the range
(b)
the variance
(c)
the standard deviation
(d)
the coefficient of variation
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Chapter 16
THE NORMAL DISTRIBUTION
1. Introduction
We discussed probabilities in a previous chapter. In this chapter we will see how tables make me
used to calculate probabilities for certain frequency distribution.
2. The histogram revisited
You should remember from the last chapter what the histogram is, and how it is drawn.
Importantly, it is the area of the bars that is proportional to the frequency.
Example 1
The following table shows the annual salaries earned by 150 workers.
Salary
Frequency
$0 - $1,000
25
$1,000 - $2,000
35
$2,000 - $3,000
40
$3,000 - $5,000
50
150
(a)
Show this frequency table in the form of a histogram
(b)
Calculate the probability of a worker earning between $1,000 and $2,000
(c)
Calculate the probability of a worker earning more than $2,000
We can easily calculate the probabilities from the frequency table. However, if we were presented
an accurately drawn histogram, then even without the original table we could still calculate the
probability of a worked earning within a specific range.
The area of all the bars is proportional to the total number of workers, and the area of the bars
representing any specific range is proportional to the number of workers earning within that range.
We could calculate the probability by dividing the area of the bar(s) representing the specific range
by the total area of all the bars.
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3. The normal distribution
The normal distribution is effectively a ‘smoothed-out’ histogram with a very specific shape.
The main features of a normal distribution are:
๏
it is symmetrical about the mean
๏
it is continuous
๏
the mean concides with the mode
๏
it is ‘bell-shaped’
๏
For a distribution that is shaped normally, we can calculate the areas under the curve as a
proportion of the total area (and therefore the probabilities) by using normal distribution
tables (which you will be provided with in the exam).
๏
The normal distribution tables give us the area under the curve between the mean and some
other point above or below the mean.
๏
The size of the areas we are at for will depend on how great or small the spread of the
distribution is, and therefore when we use the tables we look at the number of standard
deviations we are from the arithmetic mean.
๏
We call this distance the z-score.
Example 2
A company produces units with an average length of 10 cm, and a standard deviation of
0.2 cm
What proportion of the units will have a length of:
(a)
more that 10 cms
(b)
between 10 and 10.4 cms
(c)
less than 9.8 cms
It is also possible to use the normal distribution tables ‘backwards’.
Example 3
For the same information as in Example 2, there is a 0.95 (or 95%) probability that the length will be
more than X cms.
Calculate a value for X (remember that there is a 0.5 (or 50%) probability of the length being more
than the average of 10 cms, because the normal distribution is symmetrical).
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Chapter 17
BREAKEVEN ANALYSIS
1. Introduction
Breakeven analysis considers how profits change with changes in the level of activity of a business,
and calculates how what sales are needed in order for the business to be profitable.
2. Breakeven
Breakeven is the level of activity which gives rise to zero profit. Since profit is the difference
between total contribution and fixed costs, breakeven is where the total contribution equals
total fixed costs.
Fixed costs
Contribution per unit
Breakeven volume =
Example 1
Product X has variable costs of $2 per unit, and selling price of $6 per unit.
The fixed costs are $1,000 per year
(a) If budgeted sales and production are 300 units, what is the budgeted profit (or loss) for
the year?
(b) What is the breakeven point (in units)?
(c) What is the breakeven revenue?
(d) How many units need to be sold to achieve a target profit of $300 per year?
3. Margin of safety
The Margin of Safety measures the %’age fall in budgeted sales that can be allowed before
breakeven is reached.
Margin of safety =
Budgeted sales - breakeven
× 100%
Budgeted sales
It is useful in identifying how big a problem any inaccuracy in the budgeted sales is likely to
be.
Example 2
Calculate the margin of safety for example 1
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4. Contribution to sales ratio
The contribution to sales ratio (or C/S ratio) is calculated as follows:
C/S ratio =
Contribution in $
Sales in $
Since the contribution and the sales revenue both vary linearly with the volume, the C/S ratio
will remain constant.
[Note: the C/S ratio is sometimes called the profit to volume (or P/V ratio)].
Example 3
Calculate the C/S ratio for example 1
What sales revenue is needed to generate a target profit of $320?
5. Breakeven chart
The breakeven chart plots total costs and total revenues at different levels of volume, and
shows the activity level at which breakeven is achieved.
Example 4
Draw a breakeven chart for example 1
Cost and
revenue
($)
Output (units)
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6. Profit-volume chart
The profit volume chart shows the net profit or loss at any level of activity
Example 5
Draw a profit-volume chart for example 1
Profit ($)
Sales units)
Loss ($)
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Chapter 18
LIMITED FACTOR ANALYSIS AND MAKE
OR BUY DECISIONS
1. Introduction
In this chapter we will look at how a business should decide what to produce when they have
limited resources available. We will also look at how to apply the same technique to the making of
decisions as to whether to make products ourself or buy from others - again, when resources are
limited.
2. Limited factor analysis
In a situation where we are manufacturing several products, all of which use the same limited
resource, then we need to decide on how best to use the limited resource in production.
The standard key factor approach is to rank the products on the basis of the contribution earned
per unit of the limited resource.
Example 1
A
Selling price
Materials
Labour
Other variable costs
Fixed costs
Profit
Machine hours p.u.
Maximum demand
The total hours available are 48,000.
B
25
28
8
20
5
2
7
2
3
2
23
26
$2
$2
2 hrs
1 hr
20,000 units 10,000 units
Calculate the optimum production plan and the maximum profit using conventional limited
factor analysis
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3. Make or Buy decisions
In order to overcome problems of limited resources, a firm may buy in a product instead of
making it itself.
Where incremental costs of manufacture are less than those of buying in, the firm should
make – assuming that there are not limited resources.
Where resources are limited, the firm should concentrate on making those products which
give the greatest saving (over buying in) per unit of the scarce resource.
To decide which products should be made and which should be bought, we calculate the
saving per unit of scarce resource from making the product rather than buying it in.
Example 2
The availability of Material B is limited to 8,000 kg
Product
X
Y
Z
Demand (units)
2,000
2,500
4,000
10
13
12
17
14
16
Variable cost to make ($ per unit)
Buy-in price ($ per unit)
Kg of B required per unit
3
2
1
(included in variable cost)
How many units of each product should the company make and how many should it buy?
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Chapter 19
INTEREST
1. Introduction
The purpose of this chapter and the next chapter is to consider a key area for management
accountants – the appraisal of capital investments.
In this chapter we will look at interest on capital and continue in the next chapter with the use of
these techniques in investment appraisal.
2. Simple interest
A sum of money invested or borrowed is known as the principal.
When money is invested it earns interest; similarly when money is borrowed, interest is payable.
With simple interest, the interest is receivable or payable each year, but is not added to the
principal.
Example 1
A man invests $200 on 1 January each year. On 31 December each year simple interest is credited
at 15% but this interest is put in a separate account and does not itself earn interest.
Find the total amount standing to his credit on 31 December following his fourth payment of
$200.
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3. Compound interest
With compound interest the interest is added each year to the principal and in the following year
the interest is calculated on the total.
Example 2
A man invests $500 now for 3 years with interest at 10% p.a.
How much will be in his account after 3 years?
The amount (A) at the end of the n’th year is given by:
A = P(1+r)n
This is also known as the future value (or terminal value)
Example 3
A man invests $800 at 6%p.a. for 5 years.
How much will be in his account at the end of 5 years?
4. Effective Rate
For simplicity, the previous compound interest examples have assumed that interest is calculated
only once a year.
However in practice interest may be calculated on a monthly or even daily basis. The same formula
can still be used, but we need to distinguish between the nominal and annual percentage rates.
There are usually two rates quoted by financial institutions. The first is the nominal rate and the
other, the rate actually earned, is known as the effective or the annual percentage rate (APR).
Example 4
A credit card company charges a nominal rate of 2% per month.
If a customer has purchased $100 worth of goods on his credit, calculate the amount she will
owe after one year, and also the annual percentage rate (APR)
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5. Discounting
In the previous example we calculated the future value of cash flows by adding on (or
compounding) the interest.
We can do the same exercise in reverse to calculate the amount now that is equivalent to future
flows, by removing interest.
This exercise is known as discounting and the equivalent amount is known as the present value.
Example 5
What amount now is equivalent to $800 in 4 years time, with interest at 10% p.a.?
The formula for this is
P=
A
(1+r)n
⎛ 1 ⎞
However tables are provided in the examination which give the discount factors ⎜
⎝ (1+r)n ⎟⎠
at different rates of interest for different numbers of years.
Example 6
What is the present value of 1,200 receivables in 12 years time, with interest at 13%?
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6. Annuities
An annuity is regular payment of the same amount each year.
The present value of an annuity is given by the formula:
1 ⎞
⎛
A ⎜ 1−
⎝ (1+r)n ⎟⎠
P=
r
but again, tables are provided for this in the examination.
Example 7
Interest rate is 12% p.a.
What is the present value of $500 receivable in 1 years time and thereafter every year for a
total of 8 receipts?
Example 8
A man expects to receive $1,000 in each of 9 years, with the first receipt being in 4 years time.
What is the present value of the receipts if interest is 8% p.a.?
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7. Perpetuities
Perpetuity is an annuity that is expected to continue for an indefinitely long period of time.
The present value of a perpetuity is given by the formula:
P=
A
r
Example 9
Interest rate is 12% p.a.
What is the present value of $5,000 receivable in 1 years time and thereafter in perpetuity?
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Chapter 20
INVESTMENT APPRAISAL
1. Introduction
In this chapter we will apply the discounting techniques covered in the previous chapter to the
appraisal of capital investments.
2. Net Present Value
Under this approach to investment appraisal we look at all the expected cash flows that will arise
from an investment.
If overall the investment generates a cash surplus then we will accept and invest; if however there
is an overall cash deficit then we will reject the investment.
However, we also need to take into account interest on the investment in the project. This is either
because we have needed to borrow money and therefore be paying interest, or because we are
using money that could otherwise have been invested and be earning interest.
In either case, we account for the interest by discounting the future cash flows to get the present
value. The overall surplus or deficit is known as the Net Present Value.
Example 1
A new project will cost $80,000 and is expected to last 4 years. At the end of 4 years it is expected to
have a scrap value of $10,000.
The project is expected to generate operating cash flows each year as follows:
Year 1
Year 2
Year 3
Year 4
20,000
30,000
40,000
10,000
Assume that all operating cash flows occur at the ends of years.
If interest is 10% p.a., calculate the Net Present Value of the project and state your decision
as to whether or not we should invest.
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3. Internal Rate of Return
One problem in practice with basing our decision on the Net Present Value is that it will usually be
impossible for a company to determine their cost of capital (or interest cost) accurately.
In these circumstances, it is therefore often useful to calculate a ‘breakeven’ interest rate of the
project.
This is known as the Internal Rate of Return (IRR) and is the rate of interest at which the project
gives a NPV of zero.
Example 2
For the project detailed in Example 1.
Calculate the net present value at interest of 15% and hence estimate the Internal Rate of
Return of the project.
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4. Payback Period
One problem with basing decisions on the net present value of a project is that the cash flows are
only estimates, and if the estimates are wrong then the decision could be wrong.
It is likely to be the earlier cash flows that are the most certain whereas the further into the future
that we are estimating the more uncertain the cash flows are likely to be.
The payback period is the number of years it takes to get back the original investment in cash
terms. The shorter the payback period, the more certain we are that the project will actually pay for
itself.
The discounted payback period is exactly the same except that it takes into account the time
value of money by measuring how many years it takes to get back the original investment looking
at the discounted cash flow each year.
Example 3
A new project will cost $100,000 and will last for 5 years with no scrap value.
The project is expected to generate operating cash flows each year as follows:
Year 1
20,000
Year 2
30,000
Year 3
40,000
Year 4
50,000
Year 5
30,000
The cost of capital is 10%
(a)
(b)
Calculate the payback period
Calculate the discounted payback period
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ANSWERS TO EXAMPLES
Chapter 1
No examples
Chapter 2
Example 6
units
1,000
200
800
High
Low
Difference
80,000
= $100 per unit
800
Therefore, variable cost =
Using in ‘high’,
cost
110,000
30,000
80,000
total cost
variable cost
(1,000 × $100)
fixed cost
y = 100x +10,000
Therefore,
Therefore,
=
$110,000
=
$100,000
$10,000
Chapter 3
Examples 2 & 3
×
1
4
2
7
6
5
3
28
b=
a=
or:
y
40
65
45
80
70
70
50
420
xy
40
260
90
560
420
350
150
1,870
x2
1
16
4
49
36
25
9
140
y2
1,600
4,225
2,025
6,400
4,900
4,900
2,500
26,550
nΣxy − ΣxΣy (7 ×1,870) − (28 × 420) 1,330
=
= 6.7857
2 =
(7 ×140) − (28 × 28)
196
nΣx 2 − ( Σx )
Σy bΣx 420 6.7857 × 28
−
=
−
= 60 − 27.1428 = 32.8572
n
n
7
7
y = 32.86 + 6.79x
y = 32,857 + 67.9x
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(if × and y are actual units and $’s)
Coefficient of correlation:
r=
=
nΣxy − Σx Σy
(
nΣx 2 −
( Σx ) )⎛⎜⎝ nΣy
2
− ( Σy ) ⎞⎟⎠
2
2
=
7 ×1,870 − 28 × 420
(7 ×140 − 282 )(7 × 26,550 − 4202 )
Chapter 4
+1330
= +0.98
196 × 9, 450
Chapter 4
Example 1
$ p.u.
12
8
14
$34
Material (3kg × $4)
Labour (4hrs × $2)
Overheads ($700,000 ÷ 50,000)
Example 2
Total overheads
Total labour hours
Desks (30,000 × 4hr)
Chairs (20,000 × 1 hr)
Overhead absorption rate:
$700,000
120,000
20,000
140,000hrs
$700,000
140,000 hr
= $5 per hour
Costs cards:
Materials (3kg × $4)
Labour (4hrs × $2)
Overheads (4kg × $5)
Desks
12
8
20
$40
Chairs
(2kg × $4)
8
(1hr × $2)
2
(1hr × $5)
5
$15
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Example 3
Total overheads:
Supervisors
Other
(40:60)
Total
100,000
600,000
Assembly
60,000
240,000
Finishing
40,000
360,000
$700,000
$300,000
$400,000
Total hours:
Desks (30,000 × 3 hr; 30,000 × 1 hr)
Chairs (20,000 × ½ hr; 20,000 × ½ hr)
90,000
30,000
10,000
10,000
100,000 hrs
40,000 hrs
$3 per hr
$10 per hr
O.A.R
Cost cards:
desk
12
8
Materials
Labour
Overheads:
Assembly
Finishing
chair
8
2
9
10
1.50
5.00
19
$39
6.50
$16.50
Example 4
Factory rent
(cubic space)
Factory Heat
(cubic space)
Supervisors
Depreciation
(NBV equipment)
Canteen
Welfare
(No of employees)
Total
20,000
Processing
12,500
Packing
6,250
Canteen
1,250
5,000
3,125
1,563
312
25,000
7,000
15,000
3,000
10,000
3,000
–
1,000
18,000
5,000
–
2,500
–
2,000
18,000
500
$80,000
$36,125
$22,813
$21,062
Example 5
Already apportioned
Recharge canteen
(no. of employees)
Processing
36,125
11,701
Packing
22,813
9,361
$47,826
$32,174
Canteen
21,062
(21,062)
–
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86
Example 6
Repeated distribution method
X
70,000
10,000
Y
30,000
6,000
Recharge maintenance
8,550
7,600
Recharge stores
1,425
855
257
228
43
25
8
7
(85)
–
2
1
$90,284
1
$44,716
(2)
–
Already allocated
Recharge stores
Recharge maintenance
Recharge stores
Recharge maintenance
Recharge stores
Algebraic method
Stores:
Maintenance
Replace M in (1):
Replace S in (2):
Already allocated
Recharge stores:
($22,938)
Recharge maintenance:
($19,588)
Stores
20,000
(20,000)
–
2,850
(2,850)
–
85
Maintenance
15,000
4,000
19,000
(19,000)
–
570
(570)
–
17
(17)
–
S = 20,000 + 0.15M
(1)
M = 15,000 + 0.20S
(2)
S = 20,000 + 2,250 + 0.03S
0.97S = 22,250
S = 22,250/0.97 = $22,938
M = 15,000 + 0.20 × 22,938
M = $19,588
X
70,000
Y
30,000
Stores
20,000
Maintenance
15,000
11,469
6,881
(22,938)
4,588
8,815
$90,284
7,835
$44,716
2,938
–
(19,588)
–
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Chapter 5
Example 1
(a)
Cost cards:
$ p.u
12
8
5
Materials (4kg × $3)
Labour (4hrs × $2)
Var. overheads
Fixed overheads
($20,000/10,000)
2
$27p.u
$35p.u
$8p.u
Selling price
Standard profit
(b)
Income Statements
Sales
Cost of sales:
Opening inventory
Materials
Labour
Variable o/h
Fixed o/h
(9,000 × $35)
Less: Closing inventory
(2,000 × $27)
(11,000 × $12)
(11,000 × $8)
(11,000 × $5)
(11,000 × $2)
Standard Gross Profit
(9,000 × $8)
Adjustment for over/
(under)
absorption of fixed
overheads
Actual fixed o/h’s: 20,000
Absorbed: 22,000
Actual Gross Profit
Less: selling costs
Variable
Fixed
Actual Net Profit
(9,000 × $1)
January
315,000
–
132,000
88,000
55,000
22,000
297,000
(54,000)
243,000
72,000
(11,500 × $35)
(2,000 × $27)
(9,500 ×$12)
(9,500 × $8)
(9,500 × $5)
(9,500 × $2)
(11,500 × $8)
February
402,500
54,000
114,000
76,000
47,500
19,000
310,500
–
310,500
92,000
(1,000)
2,000
Actual: 20,000
Absorbed: 19,000
74,000
(9,000)
(2,000)
$63,000
91,000
(11,500 × $1)
(11,500)
(2,000)
$77,500
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88
Example 2
320,000
(a)
Overhead absorption rate =
(b)
Amount absorbed =78,000 × $4 = $312,000
Actual overheads = $315,500
Amount under absorbed = 315,500 – 312,000 = $3,500
80,000
=$4 per hour
Chapter 6
Example 1
(a)
(b)
Cost card
Materials (4kg × $3)
Labour (4hrs × $2)
Var. overheads
Marginal cost
$ p.u
12
8
5
$25p.u
Selling price
Marginal cost
Variable selling cost
Standard profit
$35p.u
(25)
(1)
$9p.u
Income Statements
Sales
Less: Cost of sales:
Opening inventory
Materials
Labour
Variable o/h
Less: Closing inventory
Less: Variable selling costs
Contribution
Less: Fixed costs
Production
Selling
Actual Net Profit
(9,000 × $35)
(11,000 × $12)
(11,000 × $8)
(11,000 × $5)
(2,000 × $25)
(9,000 × $1)
January
315,000
–
132,000
88,000
55,000
275,000
(50,000)
225,000
90,000
(9,000)
81,000
February
(11,500 × $35) 402,500
(2,000 × $25)
(9,500 ×$12)
(9,500 × $8)
(9,500 × $5)
(11,500 × $1)
50,000
114,000
76,000
47,500
287,500
–
287,500
115,000
(11,500)
103,500
(20,000)
(2,000)
(20,000)
(2,000)
$59,000
$81,500
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Example 2
Absorption costing
Marginal costing
Difference
Fixed overheads in inventory value:
Opening inventory (2,000 × $2)
Closing inventory (2,000 × $2)
January
63,000
59,000
4,000
–
4,000
4,000
February
77,500
81,500
(4,000)
(4,000)
–
(4,000)
Chapter 7
Example 1
Selling price = $20 + (20% x $20) = $24.00
Example 2
Selling price = 100/80 x $18,000 = $22,500
Example 3
Selling price = $16 + (40% x $16) = $22.40
Chapter 8
No answers
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90
Chapter 9
Example 1
Sales (units)
Production (units)
Original
Fixed Budget
$
8,000
8,700
Flexed
Budget
$
8,400
8,900
Actual
600,000
156,600
217,500
87,000
461,100
(37,100)
424,000
176,000
130,500
$45,500
630,000
160,200
222,500
89,000
471,700
(26,500)
445,200
184,800
130,500
$54,300
613,200
163,455
224,515
87,348
475,318
(26,500)
448,818
164,382
134,074
$30,308
Sales
Materials
Labour
Variable o/h
Closing inventory
Contribution
Fixed overheads
Profit
Variances
$
8,400
8,900
16,800
3,255
2,015
1,652
(A)
(A)
(A)
(F)
3,574 (A)
23,992 (A)
Example 2
Materials
Expense variance
Actual purchases
at actual cost
35,464kg
at standard cost
($4.50)
163,455
159,588
$3,867 (A)
Usage variance
Actual usage
Standard usage for actual production
(8,900 u × 4kg)
kg
35,464
35,600
136kg
at standard cost ($4.50) = $612 (F)
Labour
Rate of Pay variance
Actual hours paid at actual cost
45,400 hours at standard cost ($5)
224,515
227,000
$2,485
(F)
Idle Time Variance
Actual hours paid
Actual hours worked
45,400
44,100
1,300
at standard cost ($5) = $6,500 (A)
hrs
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Efficiency variance
Actual hours worked
Standard hours for actual production
(8,900 u × 5hrs)
44,100
44,500
400 hrs
at standard cost ($5) = $2,000 (F)
Variable overheads
Expenditure variance
Actual hours worked
44,100
at actual cost
at standard cost
Efficiency variance
Actual hours worked
Standard hours for actual production
(8,900u × 5hrs)
87,348
88,200
$852 (F)
44,100
44,500
400 hrs
at standard cost ($2) = $800 (F)
Example 3
Sales price variance
Actual sales at actual selling price
Actual sales at standard selling price (8,400u × $75)
$
613,200
630,000
$16,800(A)
Sales volume variance
actual sales
budgeted sales
units
8,400
8,000
400 u × $22
= $8,800(F)
(Standard contribution per unit)
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92
Example 4
Operating Statement
Budgeted profit
Sales volume variance
Sales price variance
Materials price variance
Materials usage variance
Labour rate of pay variance
Labour idle time variance
Labour efficiency variance
Variable overheads expenditure variance
Variable overheads efficiency variance
Fixed overheads expenditure variance
Actual profit
45,500
8,800 (F)
16,800 (A)
37,500
3,867
612
2,485
6,500
2,000
852
800
3,574
(A)
(F)
(F)
(A)
(F)
(F)
(F)
(A)
$30,308
Chapter 10
No examples
Chapter 11
Example 1
2007
2006
Net profit margin
(
790
)
7,180
11%
8.5%
Gross profit margin
(
1,795
)
7,180
25%
22.5%
Return on capital
(
790
)
2,690
29.4%
25.7%
Asset turnover
(
7,180
)
2,690
2.67
3.02
Chapter 12
No answers
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Chapter 13
Answer to ALL examples
Materials
Cash
77,000 Cost of Sales
Labour
77,000
Cash
35,000 Overheads
Cost of Sales
35,000
Overheads
Cash
Labour
10,000 Cost of Sales
5,000
15,000
15,000
15,000
SOPL
Cash
Sales
200,000 Materials
77,000
Materials
Labour
35,000
Labour
Overheads
10,000
Overheads
Balance
78,000
Mats usage
variance
200,000
Sales
200,000 Cash
Cost of Sales
SOPL
77,000
(1000x$120)
30,000
Mats usage
15,000
variance
5,000
30,000
35,000
200,000
120,000
7,500
5,500
200,000
127,500
127,500
Statement of Profit or Loss
Cost of Sales
Std profit
Mats usage
variances
Actual Profit
120,000 Sales
80,000
200,000
200,000
200,000
7,500
78,000
85,500
Std profit
80,000
Mats price
variances
5,500
85,500
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Variances
Materials Price Variance
Actual Purchase at actual cost
77,000
Actual Purchase at standard cost
82,500
$5,500 (F)
Materials usage variance
Actual usage
5,500
Standard
5,000
500 kg x$15
= $7,500
(A)
Chapter 14
Example 1
(a)
(b)
(c)
1/6
2/6 ( = 1/3)
3/6 (= 1/2)
Example 2
(a)
(b)
(c)
(d)
1/52
4/52 ( = 1/13)
13/52 ( = 1/4)
16/52
Example 3
20/52 ( = 5/13)
Example 4
(a)
(b)
50/200 = 1/4 (0.25 or 25%)
For A
Not for A
Total
Male
60
90
150
Female
25
25
50
Total
85
115
200
85/200
(c)
25/85
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Example 5
(a)
(b)
(c)
4/52 x 4/52 = 1/169
13/52 x 13/52 = 1/16
8/52 x 4/52 = 2/169
Example 6
(a)
(b)
(c)
4/52 x 3/51
13/52 x 12/51
8/52 x 4/51
Example 7
($500,000 x 0.2) + ($300,000 x 0.5) + (200,000 x 0.3) = $310,000
Example 8
Demand
(a)
Contract size
300u
500u
700u
800u
(b)
Expected value if contract size =
400u
2,900
3,500
4,100
4,400
500u
3,400
4,000
4,600
4,400
700u
4,400
5,000
4,600
4,400
900u
5,400
5,000
4,600
4,400
300 units = (0.2×2,900) + (0.3 × 3,400) + (0.4 × 4,400) + (0.1 × 5,400) = $3,900
500 units = (0.2 × 3,500) + (0.3 × 4,000) + (0.5 × 5,000) = $4,400
700 units = (0.2 × 4,100) + (0.8 × 4,600) = $4,500
900 units = $4,400
Sign contract for 700 units
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96
Chapter 15
Example 1
(a)
Frequency
$0 - $500
$500 - $1,000
$1000 - $1,500
$1,500 - $2,000
$2,000 - $2,500
$2,500 - $3,000
0
5
10
15
20
(b)
$0 - $500
$1,500 - $2,000
$500 - $1,000
$2,000 - $2,500
$1000 - $1,500
$2,500 - $3,000
12% 2%8%
15%
27%
37%
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(c)
20
15
10
5
0
$0 - $500 $1,500 - $2,000
(d)
60
45
30
15
0
$500
$1,500
$2,500
Example 2
Number of
complaints
x
0
1
2
3
(a)
(b)
(c)
Frequency
fx
f
1
6
4
2
0
6
8
6
13
20
arithmetic mean = 20/12 = 1.54
median = value of 7th observation = 1
mode = most frequently occurring observation = 1
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Example 3
Total paid ($)
Mid-point
Frequency
fx
0 - under $500
x
250
f
1
250
500 - under 1,000
750
4
3000
1,000 - under 1,500
1250
8
10000
1,500 - under 2,000
1750
19
33250
2,000 - under 2,500
2250
14
31500
2,500 - under 3,000
2750
6
16500
52
94500
(a)
(b)
(c)
arithmetic mean = 94,500 / 52 = $1,817
median = value of the 25.5th item, which is in the range $1,500 to $2,000
(watch lecture for more)
modal class = $1,500 to $2,000
Example 4
Number of
complaints
Frequency
fX
X-x̄
(X-x̄)2
f(X-x̄)2
f
X
(a)
(b)
(c)
(d)
0
1
0
-1.54
2.37
2.37
1
6
6
-0.54
0.29
1.74
2
4
8
+0.46
0.21
0.84
3
2
6
+1.46
2.13
4.26
13
20
9.21
Range = 3 - 0 = 3
Variance = 9.21 / 13 = 0.71
Standard deviation = √0.71 = 0.84
Coefficient of variation = 0.84 / 1.54 = 0.55
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Example 5
Total paid ($)
Mid-point Frequency
x
f
fX
X-x̄
(X-x̄)2
f(X-x̄)2
0 - under $500
250
1
250
-1567
2455489
2455489
500 - under 1,000
750
4
3000
-1067
1138489
4553956
1,000 - under 1,500
1250
8
10000
-567
321489
2571912
1,500 - under 2,000
1750
19
33250
-67
4489
85291
2,000 - under 2,500
2250
14
31500
+433
187489
2624846
2,500 - under 3,000
2750
6
16500
+933
870489
5222934
52
94500
(a)
(b)
(c)
(d)
17514428
Range = 3,000 = 0 = 3,000
Variance = 17514428/52 = 336816
Standard deviation = √336816 = 580
Coefficient of variation = 580/1817 = 0.32
Chapter 16
Example 1
(a)
40
30
20
10
0
(b)
(c)
0 - 1000
2000 - 3000
35/150 = 0.23
55/150 = 0.37
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Example 2
(a)
(b)
(c)
0.5 (50%)
z = 0.4/0.2 = 2
Proportion = 0.4772 (47.72%)
z = 0.2/0.2 = 1
Proportion = 0.5 - 0.3414 = 0.1587 (15.87%
Example 3
z = 1.64
Length = 10 - (1.64 x 0.2) = 9.672 cms
Chapter 17
Example 1
$
6
2
4
Selling price
Variable costs
Contribution
(a)
$
1,200
(1,000)
$200
Total contribution (300u × $4)
Fixed costs
Profit
Fixed costs
Contribution p.u
=
1,000
= 250 units
4
(b)
Breakeven =
(c)
Breakeven revenue = 250 u × $6p.u. = $1,500
(d)
$
300
1,000
$1,300
Target profit
Fixed costs
Target contribution
Number of units
=
Target contribution
Contribution p.u
=
1,300
= 325 units
4
Example 2
Budgeted sales
Breakeven
Margin of safety =
=
=
300 units
250 units
300 – 250
300
× 100
= 16.67%
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Example 3
Contribution
4
=
= 0.67
Sales
6
C/S ratio =
$
320
1,000
$1,320
Target profit
Fixed overheads
Target contribution
Sales revenue required = Target contribution ÷ C/S ratio = 1320 ÷ 4/6 = $1,980
Example 4
Cost & revenue
($)
3,000
Total
revenue
Total cost
2,000
}
}
1,000
0
250
500
variable
cost
fixed cost
output
(units)
breakeven
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102
Example 5
Profit
($)
1,000
0
500
Sales (units)
breakeven
(250 units)
1,000
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Chapter 18
Example 1
A
25
8
12
20
5
2
B
28
20
4
24
4
1
$2.50
$4
Selling price
Materials
Other variable
Contribution p.u.
Machine hrs p.u.
Contribution per hour
Production
B:
A:
units
10,000 × 1 hr =
19,000 × 2hrs =
hours
10,000
38,000
48,000hours
Profit
A:
B:
19,000 × $5
10,000 × $4
less
Fixed costs:
[A: 20,000 × $3
B: 10,000 × $2]
$
95,000
40,000
135,000
Profit
80,000
$55,000
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104
Example 2
Buy-in price
Cost to make
Saving (p.u.)
Kg of B
Saving per kg
RANKING
X
13
10
$3
Y
17
12
$5
Z
16
14
$2
3
2
1
$1
3
Units
Y
Z
MAKE
MAKE
2,500
3,000
Z
X
BUY
BUY
1,000
2,000
$2.50
1
Material B
(kg)
5,000
3,000
8,000 kg
$2
2
Chapter 19
Example 1
Payment
Interest
Payment
–
–
–
1 Jan year 1
31 Dec year 1
1 Jan year 2
Interest
Payment
–
–
31 Dec year 2
1 Jan year 3
Interest
Payment
–
–
31 Dec year 3
1 Jan year 4
Interest
–
31 Dec year 4
Capital
Account
200
Interest
Account
30
200
400
60
200
600
90
200
800
800
120
300
Total $1,100
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Example 2
$
500
50
550
55
605
60.5
$665.50
Now payment
Year 1 interest
Year 2 interest
Year 3 interest
(or $500 × (1.1)3 =$665.50)
Example 3
A
= P (1 + r)n
= 800 × (1.06)5
= $1070.58
Example 4
= P (1 + r)n
= 100 (1.02)12
= $126.82
26.82 × 10%
APR = actual interest over the year =
100
Amount owed after 12 months
× 100% = 26.82%
Example 5
$x now will become $x(1.10)4 in 4 years
Therefore x (1.10)4 = 800
800
(1.10)4
= £546.41
x=
Example 6
1
= £277
(1.13)12
or using tables,
P.V. = 1,200 × 0.231 = $277
P.V. = 1,200 ×
Example 7
Present value = 500 ×4·968 = $2,484
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Example 8
Discount factor at 8%
1-12
7·536
less: 1-3
(2·577)
4·959
4-12
Present value = 1,000 × 4·959 = $4,959
Example 9
A
r
5,000
=
0.12
= $41, 667
Present value =
Chapter 20
Example 1
d.f. @ 10%
1.000
0.909
0.826
0.751
0.683
P.V.
0
(80,000)
(80,000)
1
20,000
18,180
2
30,000
24,780
3
40,000
30,040
4
20,000
13,660
N.P.V.
6,660
The net present value is positive and therefore we should invest in the project.
Example 2
0
1
2
3
4
(80,000)
20,000
30,000
40,000
20,000
I.R.R. = 10% +
d.f. @ 15%
1.000
0.870
0.756
0.658
0.572
6,660
6,660 + 2,160
P.V.
(80,000)
17,400
22,680
26,320
11,440
N.P.V. (2,160)
× 5% = 13.78%
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2020 Examinations
Example 3
1
2
3
4
5
Cash
inflow
Cumulative
Cash inflow
Discounted
cash inflow
20,000
30,000
40,000
20,000
30,000
20,000
50,000
90,000
140,000
170,000
18,180
24,780
30,040
34,150
18,630
Cumulative
discounted
cash inflow
18,180
42,960
73,000
107,150
125,780
Payback period =
3+
10,000
= 3.2 years
50,000
(or within 4)
Discounted payback period =
3+
27,000
= 3.79 years
34,150
(or within 4)
Only on OpenTuition you can find: Free CIMA notes • Free CIMA lectures • Free CIMA tests • Free tutor support • StudyBuddies • CIMA forums
2020 Examinations
Watch free CIMA BA2 lectures
108
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