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Fundamentals of Management

AccountingBA2Ce

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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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FORMULAE


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Standard normal distribution table

0·00 0·01 0·02 0·03 0·04 0·05 0·06 0·07 0·08 0·09

0·0 0·0000 0·0040 0·0080 0·0120 0·0160 0·0199 0·0239 0·0279 0·0319 0·0359

0·1 0·0398 0·0438 0·0478 0·0517 0·0557 0·0596 0·0636 0·0675 0·0714 0·0753

0·2 0·0793 0·0832 0·0871 0·0910 0·0948 0·0987 0·1026 0·1064 0·1103 0·1141

0·3 0·1179 0·1217 0·1255 0·1293 0·1331 0·1368 0·1406 0·1443 0·1480 0·1517

0·4 0·1554 0·1591 0·1628 0·1664 0·1700 0·1736 0·1772 0·1808 0·1844 0·1879

0·5 0·1915 0·1950 0·1985 0·2019 0·2054 0·2088 0·2123 0·2157 0·2190 0·2224

0·6 0·2257 0·2291 0·2324 0·2357 0·2389 0·2422 0·2454 0·2486 0·2517 0·2549

0·7 0·2580 0·2611 0·2642 0·2673 0·2704 0·2734 0·2764 0·2794 0·2823 0·2852

0·8 0·2881 0·2910 0·2939 0·2967 0·2995 0·3023 0·3051 0·3078 0·3106 0·3133

0·9 0·3159 0·3186 0·3212 0·3238 0·3264 0·3289 0·3315 0·3340 0·3365 0·3389

1·0 0·3413 0·3438 0·3461 0·3485 0·3508 0·3531 0·3554 0·3577 0·3599 0·3621

1·1 0·3643 0·3665 0·3686 0·3708 0·3729 0·3749 0·3770 0·3790 0·3810 0·3830

1·2 0·3849 0·3869 0·3888 0·3907 0·3925 0·3944 0·3962 0·3980 0·3997 0·4015

1·3 0·4032 0·4049 0·4066 0·4082 0·4099 0·4115 0·4131 0·4147 0·4162 0·4177

1·4 0·4192 0·4207 0·4222 0·4236 0·4251 0·4265 0·4279 0·4292 0·4306 0·4319

1·5 0·4332 0·4345 0·4357 0·4370 0·4382 0·4394 0·4406 0·4418 0·4429 0·4441

1·6 0·4452 0·4463 0·4474 0·4484 0·4495 0·4505 0·4515 0·4525 0·4535 0·4545

1·7 0·4554 0·4564 0·4573 0·4582 0·4591 0·4599 0·4608 0·4616 0·4625 0·4633

1·8 0·4641 0·4649 0·4656 0·4664 0·4671 0·4678 0·4686 0·4693 0·4699 0·4706

1·9 0·4713 0·4719 0·4726 0·4732 0·4738 0·4744 0·4750 0·4756 0·4761 0·4767

2·0 0·4772 0·4778 0·4783 0·4788 0·4793 0·4798 0·4803 0·4808 0·4812 0·4817

2·1 0·4821 0·4826 0·4830 0·4834 0·4838 0·4842 0·4846 0·4850 0·4854 0·4857

2·2 0·4861 0·4864 0·4868 0·4871 0·4875 0·4878 0·4881 0·4884 0·4887 0·4890

2·3 0·4893 0·4896 0·4898 0·4901 0·4904 0·4906 0·4909 0·4911 0·4913 0·4916

2·4 0·4918 0·4920 0·4922 0·4925 0·4927 0·4929 0·4931 0·4932 0·4934 0·4936

2·5 0·4938 0·4940 0·4941 0·4943 0·4945 0·4946 0·4948 0·4949 0·4951 0·4952

2·6 0·4953 0·4955 0·4956 0·4957 0·4959 0·4960 0·4961 0·4962 0·4963 0·4964

2·7 0·4965 0·4966 0·4967 0·4968 0·4969 0·4970 0·4971 0·4972 0·4973 0·4974

2·8 0·4974 0·4975 0·4976 0·4977 0·4977 0·4978 0·4979 0·4979 0·4980 0·4981

2·9 0·4981 0·4982 0·4982 0·4983 0·4984 0·4984 0·4985 0·4985 0·4986 0·4986

3·0 0·4987 0·4987 0·4987 0·4988 0·4988 0·4989 0·4989 0·4989 0·4990 0·4990




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 for-profit 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





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





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





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





Types of expenses

$

Production/manufacturing costs X

Administration costs X

Selling and distribution costs X

TOTAL EXPENSES 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





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 √ √





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 Total Costs

(units) ($’000)

200 30

1,000 110

(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) 3.00

- Direct labour (3 hrs @ $4/hr) 12.00

Prime cost 15.00

Indirect costs

- Variable overheads 2.00

- Fixed overheads 3.00

Full product cost 20.00





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:

Units produced Cost ($)

January 340 2,260

February 300 2,160

March 380 2,320

April 420 2,400

May 400 2,300

June 360 2,266

Calculate the fixed and variable costs using the high-low method.





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∑∑∑

n x 2∑ − x∑( )

2

a = y∑

n−

b x∑n

Example 2

The following table shows the number of units produced each month and the total cost incurred:

Units Cost($ ‘000)

January 100 40

February 400 65

March 200 45

April 700 80

May 600 70

June 500 70

July 300 50

Calculate the regression line, y = a + bx





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 2

∑ − x∑( )2( ) n y 2

∑ − y∑( )2( )

Example 3

Using the data in example 2, calculate the correlation coefficient





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.





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.





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.





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.





A fuller example of allocating and apportioning overheads:

Example 4

Production overhead costs for the period

$

Factory rent 20,000

Factory heat 5,000

Processing Dept – supervisor 15,000

Packing Dept – supervisor 10,000

Depreciation of equipment 7,000

Factory canteen expenses 18,000

Welfare costs of factory employees 5,000

80,000

Processing Dept Packing Dept Canteen

Cubic space 50,000 m3 25,000 m3 5,000 m3

NBV equipment $300,000 $300,000 $100,000

No. of employees 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 - these make the cost units.

SERVICE COST CENTRES - 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).





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 DeptsProduction Depts Service CentresService CentresX Y Stores Maintenance$ $ $ $

Allocated and apportioned overheads 70,000 30,000 20,000 15,000

Estimated work done by the service centres for other departments:Estimated work done by the service centres for other departments:Estimated work done by the service centres for other departments:Estimated work done by the service centres for other departments:Estimated work done by the service centres for other departments:

Stores 50% 30% - 20%Maintenance 45% 40% 15% -

Reapportion service department costs to departments using:

(a) repeated distribution method; and(b) algebraic method.





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





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:

January February

Production 11,000 units 9,500 units

Sales 9,000 units 11,500 units

(a) Prepare a cost card using absorption costing

(b) 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





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 X

Direct labour X

Variable production overheads X

Marginal cost of a unit 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:Selling price: X

Less: Variable production costs X

Variable non-production costs X (X)

ContributionContribution X X

Note: Contribution takes account of all variable costs. Marginal cost takes account of variable production costs only and inventory is valued at marginal cost.





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 February

Production 11,000 units 9,500 units

Sales 9,000 units 11,500 units

All other results were as budgeted.

(a) Prepare a cost card using marginal costing

(b) 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





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:

$ per

unit

Materials 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





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 5,000

Labour 6,000

Variable overheads 4,000

Fixed overheads 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:

$ per

unit

Materials 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.





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.





3. Benefits of budgeting

Planning

Controlling

Co-ordination

Authorising and delegating

Evaluation of performance

Communicating and motivating





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.





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

Wood(kg per unit)

Varnish

(litres per unit)Product X 5 2

Product Y 3 2

Product Z 2 1

Standard cost of raw materialStandard cost of raw material $8 $4

Inventories of finished goods

X Y Z

Opening 500u 800u 700u

Closing 600u 1,000u 800u

Inventories of raw materials

Wood(kg)

Varnish (litres)

Opening 21,000 10,000

Closing 18,000 9,000

Labour

X Y Z

Standard hours per unit 4 6 8

Labour is paid at the rate of $3 per hourLabour is paid at the rate of $3 per hour

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)





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





Example 2

A company has prepared the following fixed budget for the coming year.

Sales 10,000 units10,000 units

Production 10,000 units10,000 units

$

Direct materials 50,000

Direct labour 25,000



$97,500

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 60,000

Direct labour 28,500



$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.





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.

NovX1 DecX1 JanX2 FebX2 MarX2

$ $ $ $ $

Sales 80,000 100,000 110,000 130,000 140,000

Purchases 40,000 60,000 80,000 90,000 110,000

Wages 10,000 12,000 16,000 20,000 24,000

Overheads 10,000 10,000 15,000 15,000 15,000

Dividends 20,000

Capital expenditure 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.





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.





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:

$ per unit$ per unit

Materials (4 kg at $4.50 per kg) 18

Labour (5 hrs at $5 per hr) 25

Variable overheads (5 hrs at $2 per hr) 10

$53

Fixed overheads have been budgeted at $130,500Fixed overheads have been budgeted at $130,500

Budgeted selling price $75 per unit.

Budgeted production 8,700 units

Budgeted sales 8,000 units

There is no opening inventory

The actual results are as follows:

Sales: 8,400 units for $613,200

Production: 8,900 units with the following costs:

Materials (35,464 kg) 163,455

Labour (Paid 45,400hrs; worked 44,100 hrs) 224,515



Prepare a flexed budget and calculate the total variances





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.





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.





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).





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..





3. Worked example

Example 1

Statements of Financial Position as at 31 December

20072007 20062006

$ $ $ $

ASSETS

Non-current assets 1,341 826

Current assets

Inventory 1,006 871

Receivables 948 708

Cash 360 100

2,314 1,679

3,655 2,505

EQUITY AND LIABILITIES

Share capital and reserves 2,190 1,401

Non-current liabilities 500 400

Current liabilities 965 704

3,655 2,505

Income statement for the year ended 31 December

2007 2006

$ $

Revenue 7,180 5,435

Cost of sales 5,385 4,212

Gross profit 1,795 1,223

Distribution costs 335 254

Administrative expenses 670 507

Profit from operations 790 462

Finance costs 50 52

Profit before taxation 740 410

Company tax expense 262 144

Profit after taxation 478 266

You are required to calculate the profitability ratios.





Return on capital employed =Profit before interest and tax

Return on capital employed =Total long term capital

(= capital + reserves + long-term liabilities)

Net profit margin =Profit before interest and tax

Net profit margin =Revenue

Asset turnover =Revenue

Asset turnover =Total long term capital

NB: ROCE = asset turnover × net profit margin

Gross profit margin =Gross profit

Gross profit margin =Revenue





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.





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





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 timeTo reduce staff turnover

Learning and growth perspective To increase the proportion of revenue from new mealsTo increase the % of training time for staff

Financial perspective To increase the spend per customerTo increase the gross profit margin

The following information is also available for the year just ended and for the previous year:

2016 2017

Total customers 27,800 29,000

- of which are new customers 6,500 8,200

- of which are returning customers 21,300 20,800

Customer complaints 820 1,050

Waiting time for order to arrive 15 minutes 25 minutes

% staff turnover 15% 30%

% of time that staff spend training 4% 2%

Revenue $252,000 $302,000

- revenue from new meals $26,000 $64,000

- revenue from existing meals $226,000 $238,000

Gross profit $51,000 $64,000

Calculate appropriate measures, and comment on whether or not MacWendys have achieved

their goals.





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





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





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





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.





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.





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





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.





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?





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 Probability400 0.2500 0.3700 0.4900 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.

(a) Calculate all possible profits that could result

(b) Determine for what quantity John should sign the contract, using expected values.

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.





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

Frequency

0 12

1 16

2 20

3 4

52





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



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





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





Example 3

A company has recorded the total amount paid to employees each week over the last year, and has



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





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





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.





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).





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.

Breakeven volume =Fixed costs

Breakeven volume =Contribution per unit

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%Margin of safety =Budgeted sales

× 100%

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





4. Contribution to sales ratio

The contribution to sales ratio (or C/S ratio) is calculated as follows:

C/S ratio =Contribution in $

C/S ratio =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

Output (units)

Cost and

revenue

($)





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

Sales units)

Profit ($)

Loss ($)





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 B

Selling price 25 28

Materials 8 20

Labour 5 2

Other variable costs 7 2

Fixed costs 3 2

23 26

Profit $2 $2

Machine hours p.u. 2 hrs 1 hr

Maximum demand 20,000 units 10,000 units

The total hours available are 48,000.

Calculate the optimum production plan and the maximum profit using conventional limited

factor analysis





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

Variable cost to make ($ per unit) 10 12 14Buy-in price ($ per unit) 13 17 16

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?





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.





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)





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

However tables are provided in the examination which give the discount factors

1

(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%?





6. Annuities

An annuity is regular payment of the same amount each year.

The present value of an annuity is given by the formula:

P =

A 1−1

(1+r)n

⎛⎝⎜

⎞⎠⎟

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.?





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

P = 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?





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 20,000Year 2 30,000Year 3 40,000Year 4 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.





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.





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) Calculate the payback period

(b) Calculate the discounted payback period





ANSWERS TO EXAMPLES

Chapter 1

No examples

Chapter 2

Example 6

units cost

High 1,000 110,000

Low 200 30,000

Difference 800 80,000

Therefore, variable cost =80,000

= $100 per unitTherefore, variable cost =800

= $100 per unit

Using in ‘high’, total cost = $110,000

variable cost

(1,000 × $100) $100,000

Therefore, fixed cost = $10,000

Therefore, y = 100x +10,000

Chapter 3

Examples 2 & 3

× y xy x2 y2

1 40 40 1 1,600

4 65 260 16 4,225

2 45 90 4 2,025

7 80 560 49 6,400

6 70 420 36 4,900

5 70 350 25 4,900

3 50 150 9 2,500

28 420 1,870 140 26,550

b =nΣxy − ΣxΣy

nΣx 2− Σx( )

2=

(7×1,870)− (28× 420)

(7×140)− (28×28)=

1,330

196= 6.7857

a =Σy

n−

bΣx

n=

420

7−

6.7857×28

7= 60−27.1428 = 32.8572

y = 32.86 + 6.79x

or: y = 32,857 + 67.9x





(if × and y are actual units and $’s)

Coefficient of correlation:

r =nΣxy −ΣxΣy

nΣx 2 − Σx( )2

( ) nΣy 2− Σy( )2⎛

⎝⎜⎞⎠⎟

=7×1,870−28× 420

(7×140−282)(7×26,550− 420

2)

=+1330

196×9, 450= +0.98

Chapter 4

Chapter 4

Example 1

$ p.u.

Material (3kg × $4) 12

Labour (4hrs × $2) 8

Overheads ($700,000 ÷ 50,000) 14

$34

Example 2

Total overheads $700,000

Total labour hours

Desks (30,000 × 4hr) 120,000

Chairs (20,000 × 1 hr) 20,000

140,000hrs

Overhead absorption rate:$700,000

= $5 per hourOverhead absorption rate:140,000 hr

= $5 per hour

Costs cards:

Desks Chairs

Materials (3kg × $4) 12 (2kg × $4) 8

Labour (4hrs × $2) 8 (1hr × $2) 2

Overheads (4kg × $5) 20 (1hr × $5) 5

$40 $15





Example 3

Total overheads: Total Assembly Finishing

Supervisors 100,000 60,000 40,000

Other 600,000 240,000 360,000

(40:60)

$700,000 $300,000 $400,000

Total hours:

Desks (30,000 × 3 hr; 30,000 × 1 hr) 90,000 30,000

Chairs (20,000 × ½ hr; 20,000 × ½ hr) 10,000 10,000

100,000 hrs 40,000 hrs

O.A.R $3 per hr $10 per hr

Cost cards:

desk chair

Materials 12 8

Labour 8 2

Overheads:

Assembly 9 1.50

Finishing 10 5.00

19 6.50

$39 $16.50

Example 4

Total Processing Packing Canteen

Factory rent 20,000 12,500 6,250 1,250

(cubic space)

Factory Heat 5,000 3,125 1,563 312

(cubic space)

Supervisors 25,000 15,000 10,000 –

Depreciation 7,000 3,000 3,000 1,000

(NBV equipment)

Canteen 18,000 – – 18,000

Welfare 5,000 2,500 2,000 500

(No of employees)

$80,000 $36,125 $22,813 $21,062

Example 5

Processing Packing Canteen

Already apportioned 36,125 22,813 21,062

Recharge canteen 11,701 9,361 (21,062)

(no. of employees)

$47,826 $32,174 –





Example 6

Repeated distribution method

X Y Stores Maintenance

Already allocated 70,000 30,000 20,000 15,000

Recharge stores 10,000 6,000 (20,000) 4,000

– 19,000

Recharge maintenance 8,550 7,600 2,850 (19,000)

–

Recharge stores 1,425 855 (2,850) 570

–

Recharge maintenance 257 228 85 (570)

–

Recharge stores 43 25 (85) 17

–

Recharge maintenance 8 7 2 (17)

–

Recharge stores 1 1 (2)

$90,284 $44,716 –

Algebraic methodStores: S = 20,000 + 0.15M (1)Maintenance M = 15,000 + 0.20S (2)Replace M in (1): S = 20,000 + 2,250 + 0.03S 0.97S = 22,250 S = 22,250/0.97 = $22,938Replace S in (2): M = 15,000 + 0.20 × 22,938 M = $19,588

X Y Stores Maintenance

Already allocated 70,000 30,000 20,000 15,000

Recharge stores:

($22,938) 11,469 6,881 (22,938) 4,588

Recharge maintenance:

($19,588) 8,815 7,835 2,938 (19,588)

$90,284 $44,716 – –





Chapter 5

Example 1

(a) Cost cards:

$ p.u

Materials (4kg × $3) 12


Var. overheads 5

Fixed overheads

($20,000/10,000) 2

$27p.u

Selling price $35p.u

Standard profit $8p.u

(b) Income Statements

January February

Sales (9,000 × $35) 315,000 (11,500 × $35) 402,500

Cost of sales:

Opening inventory – (2,000 × $27) 54,000

Materials (11,000 × $12) 132,000 (9,500 × $12) 114,000

Labour (11,000 × $8) 88,000 (9,500 × $8) 76,000

Variable o/h (11,000 × $5) 55,000 (9,500 × $5) 47,500

Fixed o/h (11,000 × $2) 22,000 (9,500 × $2) 19,000

297,000 310,500

Less: Closing inventory (2,000 × $27) (54,000) –

243,000 310,500

Standard Gross Profit (9,000 × $8) 72,000 (11,500 × $8) 92,000

Adjustment for over/(under) absorption of fixed overheads

2,000(1,000)

Actual fixed o/h’s: 20,000 Actual: 20,000

Absorbed: 22,000 Absorbed: 19,000

Actual Gross Profit 74,000 91,000

Less: selling costs

Variable (9,000 × $1) (9,000) (11,500 × $1) (11,500)

Fixed (2,000) (2,000)

Actual Net Profit $63,000 $77,500





Example 2

(a) Overhead absorption rate = 320,000

=$4 per hour(a) Overhead absorption rate = 80,000

=$4 per hour

(b) Amount absorbed =78,000 × $4 = $312,000 Actual overheads = $315,500 Amount under absorbed = 315,500 – 312,000 = $3,500

Chapter 6

Example 1

(a) Cost card

$ p.u

Materials (4kg × $3) 12


Var. overheads 5

Marginal cost $25p.u

Selling price $35p.u

Marginal cost (25)

Variable selling cost (1)

Standard profit $9p.u

(b) Income Statements

January February

Sales (9,000 × $35) 315,000 (11,500 × $35) 402,500

Less: Cost of sales:

Opening inventory – (2,000 × $25) 50,000

Materials (11,000 × $12) 132,000 (9,500 × $12) 114,000

Labour (11,000 × $8) 88,000 (9,500 × $8) 76,000

Variable o/h (11,000 × $5) 55,000 (9,500 × $5) 47,500

275,000 287,500

Less: Closing inventory (2,000 × $25) (50,000) –

225,000 287,500

90,000 115,000

Less: Variable selling costs (9,000 × $1) (9,000) (11,500 × $1) (11,500)

Contribution 81,000 103,500

Less: Fixed costs

Production (20,000) (20,000)

Selling (2,000) (2,000)

Actual Net Profit $59,000 $81,500





Example 2

January February

Absorption costing 63,000 77,500

Marginal costing 59,000 81,500

Difference 4,000 (4,000)

Fixed overheads in inventory value:

Opening inventory (2,000 × $2) – (4,000)

Closing inventory (2,000 × $2) 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





Chapter 9

Example 1

Original Fixed Budget

Flexed Budget

Actual Variances

$ $ $

Sales (units) 8,000 8,400 8,400

Production (units) 8,700 8,900 8,900

Sales 600,000 630,000 613,200 16,800 (A)

Materials 156,600 160,200 163,455 3,255 (A)

Labour 217,500 222,500 224,515 2,015 (A)

Variable o/h 87,000 89,000 87,348 1,652 (F)

461,100 471,700 475,318

Closing inventory (37,100) (26,500) (26,500)

424,000 445,200 448,818

Contribution 176,000 184,800 164,382

Fixed overheads 130,500 130,500 134,074 3,574 (A)

Profit $45,500 $54,300 $30,308 23,992 (A)

Example 2

Materials Expense variance

Actual purchases at actual cost 163,455

35,464kg

at standard cost

($4.50) 159,588

$3,867 (A)

Usage variance

kg

Actual usage 35,464

Standard usage for actual production

(8,900 u × 4kg) 35,600

136kg

at standard cost ($4.50) = $612 (F)Labour Rate of Pay variance

Actual hours paid at actual cost 224,515

45,400 hours at standard cost ($5) 227,000

$2,485 (F)

Idle Time Variance

Actual hours paid 45,400

Actual hours worked 44,100

1,300 hrs

at standard cost ($5) = $6,500 (A)





Efficiency variance


Standard hours for actual production

(8,900 u × 5hrs) 44,500

400 hrs

at standard cost ($5) = $2,000 (F)

Variable overheads Expenditure variance

Actual hours worked at actual cost 87,348

44,100 at standard cost 88,200

$852 (F)

Efficiency variance


Standard hours for actual production

(8,900u × 5hrs) 44,500

400 hrs

at standard cost ($2) = $800 (F)

Example 3

Sales price variance

$

Actual sales at actual selling price 613,200

Actual sales at standard selling price (8,400u × $75) 630,000

$16,800(A)

Sales volume variance

units

actual sales 8,400

budgeted sales 8,000

400 u × $22 = $8,800(F)

(Standard contribution per unit)(Standard contribution per unit)





Example 4

Operating Statement

Budgeted profit 45,500

Sales volume variance 8,800 (F)

Sales price variance 16,800 (A)

37,500

Materials price variance 3,867 (A)

Materials usage variance 612 (F)

Labour rate of pay variance 2,485 (F)

Labour idle time variance 6,500 (A)

Labour efficiency variance 2,000 (F)

Variable overheads expenditure variance 852 (F)

Variable overheads efficiency variance 800 (F)

Fixed overheads expenditure variance 3,574 (A)

Actual profit $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





Chapter 13

Answer to ALL examples

MaterialsMaterials LabourLabour

Cash 77,000 Cost of Sales 77,000 Cash 35,000 Overheads 5,000

Cost of Sales 30,000

35,000 35,000

OverheadsOverheads SalesSales

Cash 10,000 Cost of Sales 15,000 SOPL 200,000 Cash 200,000

Labour 5,000

15,000 15,000

CashCash Cost of SalesCost of Sales

Sales 200,000 Materials 77,000 Materials 77,000SOPL(1000x$120)

120,000

Labour 35,000 Labour 30,000

Overheads 10,000 Overheads 15,000Mats usage variance

7,500

Balance 78,000Mats usage variance

5,500

200,000 200,000

127,500 127,500

Statement of Profit or LossStatement of Profit or LossStatement of Profit or LossStatement of Profit or Loss

Cost of Sales 120,000 Sales 200,000

Std profit 80,000

200,000 200,000

Std profit 80,000

Mats usage variances

7,500Mats price variances

5,500

Actual Profit 78,000

85,500 85,500





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) 1/6(b) 2/6 ( = 1/3)(c) 3/6 (= 1/2)

Example 2

(a) 1/52(b) 4/52 ( = 1/13)(c) 13/52 ( = 1/4)(d) 16/52

Example 3

20/52 ( = 5/13)

Example 4

(a) 50/200 = 1/4 (0.25 or 25%)(b)

For A Not for A Total

Male 60 90 150

Female 25 25 50

Total 85 115 200

85/200

(c) 25/85





Example 5

(a) 4/52 x 4/52 = 1/169(b) 13/52 x 13/52 = 1/16(c) 8/52 x 4/52 = 2/169

Example 6

(a) 4/52 x 3/51(b) 13/52 x 12/51(c) 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

(a) 400u 500u 700u 900u

300u 2,900 3,400 4,400 5,400

500u 3,500 4,000 5,000 5,000

700u 4,100 4,600 4,600 4,600

800u 4,400 4,400 4,400 4,400

DemandContract size

(b) Expected value if contract size =

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





Chapter 15

Example 1

(a)

(b)

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

$0 - $500 $500 - $1,000 $1000 - $1,500$1,500 - $2,000 $2,000 - $2,500 $2,500 - $3,000

12%

27%

37%

15%

8%2%





(c)

(d)

Example 2

Number of

complaints

x

Frequency

f

fx

0 1 0

1 6 6

2 4 8

3 2 6

13 20

(a) arithmetic mean = 20/12 = 1.54(b) median = value of 7th observation = 1(c) mode = most frequently occurring observation = 1

0

5

10

15

20

$0 - $500 $1,500 - $2,000

0

15

30

45

60

$500 $1,500 $2,500





Example 3

Total paid ($) Mid-point

x

Frequency

f

fx

0 - under $500 250 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) arithmetic mean = 94,500 / 52 = $1,817(b) median = value of the 25.5th item, which is in the range $1,500 to $2,000 (watch lecture for more)(c) modal class = $1,500 to $2,000

Example 4

Number of

complaints

X

Frequency

f

fX X-x̄ (X-x̄)2 f(X-x̄)2

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

(a) Range = 3 - 0 = 3(b) Variance = 9.21 / 13 = 0.71(c) Standard deviation = √0.71 = 0.84(d) Coefficient of variation = 0.84 / 1.54 = 0.55





Example 5

Total paid ($) Mid-pointx

Frequencyf

fX X-x ̄ (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 17514428

(a) Range = 3,000 = 0 = 3,000(b) Variance = 17514428/52 = 336816(c) Standard deviation = √336816 = 580(d) Coefficient of variation = 580/1817 = 0.32

Chapter 16

Example 1

(a)

(b) 35/150 = 0.23(c) 55/150 = 0.37

0

10

20

30

40

0 - 1000 2000 - 3000





Example 2

(a) 0.5 (50%)(b) z = 0.4/0.2 = 2 Proportion = 0.4772 (47.72%)(c) z = 0.2/0.2 = 1 Proportion = 0.5 - 0.3414 = 0.1587 (15.87%

Example 3

z = 1.64Length = 10 - (1.64 x 0.2) = 9.672 cms

Chapter 17

Example 1

$

Selling price 6

Variable costs 2

Contribution 4

(a) $

Total contribution (300u × $4) 1,200

Fixed costs (1,000)

Profit $200

(b) Breakeven =Fixed costs

=1,000

= 250 units(b) Breakeven =Contribution p.u

=4

= 250 units

(c) Breakeven revenue = 250 u × $6p.u. = $1,500

(d) $

Target profit 300

Fixed costs 1,000

Target contribution $1,300

Number of units =Target contribution

=1,300

= 325 unitsNumber of units =Contribution p.u

=4

= 325 units

Example 2

Budgeted sales = 300 units

Breakeven = 250 units

Margin of safety =300 – 250

× 100 = 16.67%Margin of safety =300

× 100 = 16.67%





Example 3

C/S ratio =Contribution

=4

= 0.67C/S ratio =Sales

=6

= 0.67

$Target profit 320Fixed overheads 1,000

Target contribution $1,320

Sales revenue required = Target contribution ÷ C/S ratio = 1320 ÷ 4/6 = $1,980

Example 4

output (units)

Cost & revenue($)

0

3,000

2,000

1,000

Total cost

Total

revenue

500250

breakeven

}variable

cost

fixed cost}





Example 5

Profit($)

0

1,000

1,000

500

breakeven

(250 units)

Sales (units)





Chapter 18

Example 1

A B

Selling price 25 28

Materials 8 20

Other variable 12 4

20 24

Contribution p.u. 5 4

Machine hrs p.u. 2 1

Contribution per hour $2.50 $4

Production

units hours

B: 10,000 × 1 hr = 10,000

A: 19,000 × 2hrs = 38,000

48,000hours

Profit

$

A: 19,000 × $5 95,000

B: 10,000 × $4 40,000

135,000less Fixed costs:

[A: 20,000 × $3

B: 10,000 × $2] 80,000

Profit $55,000





Example 2

X Y Z

Buy-in price 13 17 16

Cost to make 10 12 14

Saving (p.u.) $3 $5 $2

Kg of B 3 2 1

Saving per kg $1 $2.50 $2

RANKING 3 1 2

UnitsMaterial B

(kg)

Y MAKE 2,500 5,000

Z MAKE 3,000 3,000

8,000 kg

Z BUY 1,000

X BUY 2,000

Chapter 19

Example 1

Capital Account

Interest Account

Payment – 1 Jan year 1 200

Interest – 31 Dec year 1 30


400



600



800


800 300

Total Total $1,100$1,100





Example 2

$

Now payment 500

Year 1 interest 50

550

Year 2 interest 55

605

Year 3 interest 60.5

$665.50

(or $500 × (1.1)3 =  $665.50)

Example 3

A = P (1 + r)n

= 800 × (1.06)5 = $1070.58

Example 4

Amount owed after 12 months = P (1 + r)n

= 100 (1.02)12

= $126.82

APR = actual interest over the year = 26.82 × 10%

× 100% = 26.82%APR = actual interest over the year = 100

× 100% = 26.82%

Example 5

$x now will become $x(1.10)4 in 4 years

Therefore x (1.10)4= 800

x =800

(1.10)4

= £546.41

Example 6

P.V. = 1,200 ×1

(1.13)12=£277

or using tables,P.V. = 1,200 × 0.231 = $277

Example 7

Present value = 500 × 4·968 = $2,484





Example 8

Discount factor at 8%

1-12 7·536

less: 1-3 (2·577)

4-12 4·959

Present value = 1,000 × 4·959 = $4,959

Example 9

Present value = A

r

=5,000

0.12

= $41,667

Chapter 20

Example 1

d.f. @ 10% P.V.

0 (80,000) 1.000 (80,000)

1 20,000 0.909 18,180

2 30,000 0.826 24,780

3 40,000 0.751 30,040

4 20,000 0.683 13,660

N.P.V. 6,660

The net present value is positive and therefore we should invest in the project.

Example 2

d.f. @ 15% P.V.

0 (80,000) 1.000 (80,000)

1 20,000 0.870 17,400

2 30,000 0.756 22,680

3 40,000 0.658 26,320

4 20,000 0.572 11,440

N.P.V. (2,160)

I.R.R. = 10% + 6,660

× 5% = 13.78%I.R.R. = 10% + 6,660 + 2,160

× 5% = 13.78%





Example 3

Cash inflow

Cumulative Cash inflow

Discounted cash inflow

Cumulative discounted cash inflow

1 20,000 20,000 18,180 18,180

2 30,000 50,000 24,780 42,960

3 40,000 90,000 30,040 73,000

4 20,000 140,000 34,150 107,150

5 30,000 170,000 18,630 125,780

Payback period = 3 +10,000

= 3.2 years (or within 4)Payback period = 3 +50,000

= 3.2 years (or within 4)

Discounted payback period = 3 +27,000

= 3.79 years (or within 4)Discounted payback period = 3 +34,150

= 3.79 years (or within 4)




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