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    ACCA Paper F2Management Accounting

    For exams in 2010

    theexpgroup.com

    Notes

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    ExPress NotesACCA F2 Management Accounting

    Page | 2 2010 This material is the copyright of the ExP Group. Individuals may reproduce this material if it is for their ownprivate use. It is illegal for any individuals to reproduce this for commercial use or for companies to reproduce thismaterial partially and/or in full by any means, be it printed, photocopied, on electronic devices or any other means ofreproduction. All examples presented in these course materials are for information and educational purposes only andshould not be applied to a specific real life situation without prior advice. Given the nature of information presented inthese materials, and given that legislation may change at any time, The ExP Group will not be held liable for anyinformation presented in these materials as to its application to any specific cases.

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    Contents

    About ExPress Notes 3

    1. The Nature and Purpose of Cost andManagement Accounting

    7

    2. Cost Classification, Behaviour and Purpose 103. Business Mathematics and Computer

    Spreadsheets12

    4. Cost Accounting Techniques 145. Budgeting and Standard Costing 236. Short-term decision-making techniques 35

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    ExPress NotesACCA F2 Management Accounting

    Page | 3 2010 This material is the copyright of the ExP Group. Individuals may reproduce this material if it is for their ownprivate use. It is illegal for any individuals to reproduce this for commercial use or for companies to reproduce thismaterial partially and/or in full by any means, be it printed, photocopied, on electronic devices or any other means ofreproduction. All examples presented in these course materials are for information and educational purposes only andshould not be applied to a specific real life situation without prior advice. Given the nature of information presented inthese materials, and given that legislation may change at any time, The ExP Group will not be held liable for anyinformation presented in these materials as to its application to any specific cases.

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    STARTAbout ExPress Notes

    We are very pleased that you have downloaded a copy of our ExPress notes for this paper.

    We expect that you are keen to get on with the job in hand, so we will keep the introduction

    brief.

    First, we would like to draw your attention to the terms and conditions of usage. Its a

    condition of printing these notes that you agree to the terms and conditions of usage.

    These are available to view at www.theexpgroup.com. Essentially, we want to help people

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    You will however need to get our written permission in advance if you want to use these

    notes as part of a training programme that you are delivering.

    WARNING! These notes are not designed to cover everything in the syllabus!

    They are designed to help you assimilate and understand the most important areas for the

    exam as quickly as possible. If you study from these notes only, you will not have covered

    everything that is in the ACCA syllabus and study guide for this paper.

    Components of an effective study system

    On ExP classroom courses, we provide people with the following learning materials:

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    an invaluable resource. You can find links to the most useful pages of the ACCA database

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    How to get the most from these ExPress notes

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    Your stage instudy for eachpaper

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    START

    About The ExP Group

    Born with a desire to be the leading supplier of business training services, the ExP Group

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    Chapter 1

    The Nature and Purpose of Cost andManagement Accounting

    The Characteristics of Good Information

    The qualities of good information can be summarized in the word ACCURATE:

    Accurate, Complete, Cost-beneficial, User-targeted, Relevant, Authoritative, Timely and Easy to use

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    Responsibility centres

    Cost centres: Responsible for current expenses only

    Revenue centres: Responsible for revenues, but not current expenses other than marketingexpenses

    Profit centres: Responsible for revenues and current expenses

    Investment centres: Responsible for revenues, current expenses and capital expenditure

    KEY KNOWLEDGE

    Management Accounting

    The process of identification, measurement, accumulation, analysis, preparation,interpretation and reporting of information used by management to set targets, planresource allocation, evaluate investment choices and monitor/control the operatingperformance and the orderly conduct of the business.

    Differences in purpose and scope, compared to Financial Accounting

    Aimed at internal users (as opposed to financial accounting, which is aimed atexternal stakeholders)

    Focused on present and future performance (as opposed to financial accounting,which reports past performance)

    Not required by law and not regulated by accounting frameworks (as opposed tofinancial accounting, which is a legal requirement and is regulated by accountingframeworks)

    Cost Centres Profit Centres Investment CentresRevenue Centres

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    Focused on specific areas or activities (as opposed to financial accounting, whichprovides a holistic view of companys performance)

    Employs non-financial indicators as well financial, while financial accounting usesonly financial measures.

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    Chapter 2

    Cost Classification, Behaviour andPurpose

    In financial accounting, it is a convention to break down costs into:

    KEY KNOWLEDGEProduction vs. Non-Production costs

    Production costs: These are costs (both direct and indirect, also variable and fixed) which

    relate to the production of goods; this is also referred to as manufacturing or factory cost. It

    is these costs, accumulated, which provide the value at which goods are placed in inventory

    (prior to sale) and form the cost of goods value when sold.

    Non-production costs: These are expenses that are incurred independent of production and

    include administrative, selling, distribution and finance costs. These costs can have thecharacter of period costs, as they relate to the period of time in which they occur.

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    KEY KNOWLEDGE

    Direct vs. Indirect costs

    Direct costs: are costs that can be directly attributable to a product.

    Indirect costs: these are costs that cannot be directly attributable to a product.

    KEY KNOWLEDGE

    Fixed vs. Variable costs

    Fixed costs: are costs that remain constant regardless of the volume of production. A variety

    of indirect costs are fixed.

    Variable costs: vary in proportion with the volume produced. Direct costs are by their nature

    variable in behaviour.

    Although a variable cost increases with the level of activity, the variable cost per unit

    remains fixed, while a fixed cost per unit falls with a rise in the level of activity.

    Other types of costs:

    Mixed costs: these are costs that contain a fixed and a variable element.

    Step costs: costs that remain fixed within a defined range of production, but at a certain

    level of output increase in a significant way to a new (fixed) level.

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    Chapter 3

    Business Mathematics and

    Computer Spreadsheets

    Expected Value

    This is the average of possible outcomes weighted by the probability of each outcome.

    Profit/(Loss) ProbabilityExpectedValue

    340 10% 34.0

    766 20% 153.2

    278 50% 139.0

    450 18% 81.0

    -230 2% -4.6

    100% 402.6

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    ExPress NotesACCA F2 Management Accounting

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    Chapter 4

    Cost Accounting Techniques

    Materials

    The ordering, receiving and issuing of materials from inventory must be controlled according

    to procedures and documented at all stages with forms appropriate to the purpose.

    The controls and procedures are designed to monitor inventory movements so as to

    minimise discrepancies and losses and theft.

    Economic Order Quantity

    This is a method which seeks to minimize the costs associated with holding inventory.

    To determine the total costs, the following data is required:

    Q = order quantity

    D = quantity of product demanded annually

    P = purchase cost for one unit

    C = fixed cost per order (not incl. the purchase price)

    H = cost of holding one unit for one year

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    The total cost function is as follows:

    Total cost = Purchase cost + Ordering cost + Holding cost

    which can be expressed algebraically as follows:

    TC = P x D + C x D/Q + H x Q/2

    It is this total cost function which must be minimized.

    Recognizing that:

    PD does not vary; Ordering costs rise the more frequently one places (during the year); and Holding costs rise the fewer times one places orders (due to larger quantities being

    ordered each time),

    It follows that there is a trade-off between the Ordering and the Holding costs.

    The optimal order quantity (Q*) is found where the Ordering and Holding costs equal each

    other, i.e.

    C x D/Q = H x Q/2

    Rearranging the above and solving for Q results in

    Labour

    Direct labour refers to work which is directly involved in the manufacture of a product.

    Indirect labour (e.g. the supervisors salary or that of a security guard) forms part ofoverhead costs.

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    Absorption Costing

    This is one method which seeks to make the link between overheads and (product) cost

    units. The diagram below provides a useful roadmap.

    Total Production Costs

    Direct Costs Indirect costs (overheads)

    2. Allocate/Apportion to Cost Centers

    Production A Production B Service C

    1. Allocate

    3. Reapportion fromService to Production

    Production A Production B

    4. Absorb

    Cost Unit

    The focus (above) is production. Overhead costs that are not incurred at the time of

    production do not find their way into inventory.

    It is useful to think of production costs as being those that end up as part of the inventory

    (valuation) while other (non-production) costs are incurred outside, and normally after the

    product leaves inventory.

    Contribution

    Contribution is defined as the difference between Sales revenue and the marginal cost of

    sales, or

    Contribution = Sales Variable costs (both production and non-production)

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    Marginal costing

    A marginal approach to costing focuses on the variable (marginal) costs generated in a

    business and considers fixed costs as period costs. This allows the company to be able toquantify the amount by which its costs rise, if it produces/sells an additional unit of output.

    Example

    Below is data on a manufacturing company.

    Selling price (per unit): 120

    Cost card (per unit):

    Direct materials 45Direct labour 18 Variable production O/Hs 9Total variable costs 72

    There is a variable selling cost of $2 per unit

    Year 1 Year 2(units) (units)

    Budget (normal) production 1,100 1,100

    Actual Production 1,000 1,100 Actual Sales 950 1,150

    Actual fixed production O/Hs $16,500 $16,500 Actual SGA costs $ 7,000 $ 7,000

    Based on the above data, a profit and loss statement for the Years 1 and 2 is shown on the

    next page.

    Assume that the beginning inventory is zero.

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    Profit/Loss (Marginal costing)

    Year 1 Year 2

    $ $

    Sales (950/1,150 units) 114,000 138,000

    Less: Variable cost of sales

    Opening inventory 0 3,600

    Production costs:

    o Variable(1,000 x $72) 72,000(1,100 X $72) 79,200

    Less: closing inventory(50 x $72) (3,600) 0

    (68,400) (82,800)Less: Variable selling costs

    (950 x $2) (1,900)(1,150 x $2) (2,300)

    Contribution 43,700 52,900

    Less: Fixed production O/Hs (16,500) (16,500)Less: SGA costs (7,000) (7,000)

    Profit 20,200 29,400

    Inventory is valued at variable production costs.

    Absorption Costing

    This method argues that focusing on marginal costs is potentially misleading in the longer

    run because fixed production costs have also to be covered. Accounting conventions require

    that fixed production costs be reflected in each unit produced.

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    Revised cost card (Absorption costing)

    Cost card (per unit):

    Direct materials 45Direct labour 18 Variable production O/Hs 9Fixed production O/Hs 15

    Total production costs 87

    Profit/Loss (Absorption costing)

    Year 1 Year 2$ $

    Sales (950/1,150 units) 114,000 138,000

    Less: Variable cost of sales

    Opening inventory 0 4,350

    Production costs:

    o Variable(1,000 x $72) 72,000(1,100 X $72) 79,200

    o Fixed(1,000 x $15) 15,000(1,100 X $15) 16,500

    Less: closing inventory(50 x $87) (4,350) 0

    Over/(under) absorption 1,500 0(84,150) (100,050)

    Gross Profit 29,850 37,950

    Less: Variable selling costs(950 x $2) 1,900(1,150 x $2) 2,300

    Less: SGA costs 7,000 (8,900) 7,000 (9,300)

    Profit 20,950 28,650

    Inventory is valued at the full production costs.

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    Summary of Absorption costing and Marginal costing formats

    Absorption Costing Marginal Costing

    Revenue

    Less: Cost of Sales

    Variable/Fixed Variable production/

    production costs non-productioncosts

    Gross profit Contribution

    Less: Expenses

    Variable/Fixed Fixed production/

    non-production costs non-productioncosts

    Net Profit

    Job costing / Batch costing

    This refers to the calculation of costs associated with a specific job or customer order. Thisis appropriate in situations where each product or service is distinct, and possibly unique, inits delivery.

    Batch costing is similar to job costing; the distinction lies in the identification of costs withspecific batches, which are numbered (separately identified) for this purpose.

    Process Costing

    Process costing is a technique that applies to the mass production of a large number ofidentical products, moving through a series of processing stages. The accumulated costs of

    production can be averaged over the number of items produced.

    The average cost is determined by the following formula:

    Average cost per unit = Total cost of inputs Scrap value of rejected unitsNo. of units of input Normal loss

    The total cost of inputs refers to labour, materials and overhead costs of production. Iflosses occur along the way that necessitate the scrapping of defective units, then to the

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    extent that these items fetch a scrap value, then that (scrap) value will reduce the totalcosts.

    Similarly, an accounting is made of the number of units introduced into a process with theexpectation that a normal loss will be incurred. The number of good units emerging from aprocess will therefore be the number of units entering it, minus the expected number lost inprocessing.

    Abnormal gains and losses are accounted for as an adjustment to the accounts using thesame value as the good output (deducted in the case of loss and added in the case ofgains).

    Equivalent units (EU)

    This refers to the way in which partially-completed output (work-in-progress or WIP) isexpressed. If an unfinished unit of product contains 35% of the labour and materials costsof a complete unit, then the unit has a degree of completion of 35% in terms of value. It istherefore considered to have an EU of 35%, which is normally expressed in monetary terms.

    Weighted average method

    The weighted average method makes no distinction between units that were started (butnot finished) in a previous process and those started in the current process. Since all theunits, when completed, are visually identical, processing costs are averaged over all theunits.

    First-In-First-Out (FIFO) method

    The FIFO method does make a distinction between units that were started in a previousprocess and those begun in a current process. FIFO costing separates the costs that wereincurred in the previous period from costs of the current period.

    Joint products / By-products

    Joint products are two or more products that share a common processing path until the

    point of separation. Until they go their own (separate) ways, the costs of production duringthe joint processing cannot be physically distinguished.

    There are different methods used to apportion common costs to such products at the pointof separation:

    Market value (based on expected sales price) Number of units (litres, tons, or some other objective physical measurement) Net realizable value = Final sales value Incremental processing costs

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    By-products are goods which are incidental to the production process and which generatecash from sales, though the amount is modest in comparison to the overall revenues of thefirm. The cash received for by-products can be viewed as a bonus that reduces productioncosts.

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    Chapter 5

    Budgeting and Standard Costing

    Budgeting: definition and purpose

    Quantitative plan for the future, used to:

    The master budget process

    Annual frequency, preferably revised on a regular basis (rolling budget) Based on organizations objectives, expressed in financial, quantitative and

    qualitative measures

    b) Motivate

    Employees

    b) Evaluate

    Performance

    b) Control

    Activities

    a) Communicate

    Objectives

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    The operating budget sequence

    Sales budget Production budget Ending inventory budget Direct materials budget, Direct labour budget, Factory overhead budget Cost of Sales budget R&D budget, Marketing budget, Distribution budget, Customer service budget, Admin

    budget

    Pro-forma income statement

    The financial budget sequence

    Capital budget Cash budget Pro-forma balance-sheet and pro-forma statement of cash-flows

    Operating budgets

    These are budgets that quantify the revenues and costs relating to a companys activities ata disaggregated level, meaning that there is direct input from department and functional

    levels. They require both volume (e.g. units of output, quantities, hours, etc.) and price

    specifications. Operating budgets are modelled on what will emerge as the companys

    income statement. Examples include:

    Sales budget Production budget Direct material usage Direct material purchases Direct labour budget Factory overhead budget Selling & distribution budget

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    Administrative expenses budgetThe disaggregation of budgets referred to above allows the practice of responsibilityaccounting.

    Principal budget factor

    When a budget is prepared, management must identify any factors that will prevent thecompany from surpassing a certain level of activity.

    A bank, for example, may be constrained from developing an extensive branch networkowing to the scarcity of suitably-skilled professional staff; or production may be constrainedby the built capacity of the plant or by the level of demand for a companys products. In

    each of these cases, there is a limiting factor at work.

    Fixed vs. flexible budgets

    Traditional budgets tended to be rigid, i.e. they were not subject to modification during the

    period to which they referred.

    Example

    A producer of office equipment has a budget for the coming year:

    Output: 1,000 units

    Costs:

    Materials 75,000

    Labour 200,000

    Fixed O/Hs 100,000

    Total 375,000

    After 3 months, the company observes that sales are running ca. 20% higher than originally

    projected and it has therefore increased its production by a similar amount. In order to lookback at what its budget would have been had the actual (higher) level of activity been

    anticipated, management can prepare a flexed budget; this is effectively a re-calibration of

    the original budget. It allows management to re-focus their efforts without losing time

    tracking artificial spending excesses according to the original budget.

    Output: 1,200 units

    Costs:

    Materials 90,000

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    Labour 225,000

    Fixed O/Hs 100,000

    Total 415,000

    Prepare a flexed budget for an output level of 1,075 units.

    Based on the data (below), the

    variable cost of labour is $125 per unit, and the fixed cost of labour is $75,000

    Output: 1000 1200

    Mats 75,000 90,000

    Labour 200,000 225,000

    Fix 100,000 100,000

    Total 375,000 415,000

    Therefore the cost of labour at output of 1,075 units is $209,375.

    Absorption Costing

    This method argues that focusing on marginal costs is potentially misleading in the longer

    run because fixed production costs have also to be covered. Accounting conventions require

    that fixed production costs be reflected in each unit produced.

    Fixed Overhead Absorption Rate (FOAR) = Budgeted production O/HBudgeted level of production

    Year 1 Year 2

    (units) (units)Budget (normal) production 1,100 1,100

    Actual fixed production O/Hs $16,500 $16,500

    Fixed Overhead Absorption Rate (FOAR) = $15 ($16,500/1,100)

    Cost card (Absorption costing)

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    Cost card (per unit):Direct materials 45Direct labour 18

    Variable production O/Hs 9Fixed production O/Hs 15Total production costs 87

    Having established the OAR, we now have a basis on which the production department can

    keep track of the fixed overheads being generated as the manufacturing process proceeds.

    Actual output (units) x OAR = Fixed O/H absorbed

    Basic variance analysis

    The following data is from a manufacturing company

    BudgetProduction: 1,100 unitsSales: 1,000 unitsSales Price: $120 / unit

    Actual resultsProduction: 1,000 unitsSales: 950 unitsMaterials: 4,900 kg, $45,025Labour: 3,100 hrs, $19,050Variable O/Hs: $9,250Fixed O/Hs: $17,000Sales price: $115 / unit

    Cost card (per unit)

    Materials (5kgs x $9 per kg) 45Labour (3hrs x $6 per hr) 18 Variable O/Hs (3 hrs x $3 per hr) 9Fixed O/Hs (3 hrs x $5 per hr) 15

    87

    Variance calculations

    Sales volume variance (Absorption costing)

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    Budgeted sales volume 1,000 Actual sales volume 950

    Sales volume variance 50 (A)@ standard margin ($120-$87) $1,650 (A)

    Sales volume variance (Marginal costing)

    Budgeted sales volume 1,000 Actual sales volume 950

    Sales volume variance 50 (A)@ standard contribution ($120-$72) $2,400 (A)

    Sales price variance

    950 units should have sold @$120 114,000 Actual revenues (950 units x $115) 109,250

    Sales price variance 4,750 (A)

    Material variances

    (i) Material price variance Materials used (4,900 kg) should have cost @ $9 44,100 Materials (4,900 kg) did cost 45,025

    Materials price variance $925 (A)

    (ii) Material usage variance 1,000 units should have used @ 5 kg 5,000 kg

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    1,000 units did use 4,900 kgMaterials usage variance 100 kg (F)

    @ standard $9 $900 (F)

    Materials total variance: $ 25 (A)

    Labour variances

    (i) Labour rate variance Labour (3,100 hrs) should have cost @ $6 18,600 Labour (3,100 hrs) did cost 19,050

    Labour rate variance $450 (A)

    (ii) Labour efficiency variance 1,000 units should have taken @ 3 hrs 3,000 hrs 1,000 units did take 3,100 hrs

    Labour efficiency variance 100 hrs (A)@ standard $6 $600 (A)

    Labor total variance: $ 1,050 (A)

    Variable O/H variances

    (i) Variable O/H expenditure variance 3,100 hrs should have cost @ $3 9,300 3,100 hrs did cost 9,250

    Variable O/H expenditure variance 50 (F)

    (ii) Variable O/H efficiency variance 1,000 units should have taken @ 3 hrs 3,000 hrs 1,000 units did take 3,100 hrs

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    Variable O/H efficiency variance 100 hrs (A)@ standard $3 $300 (A)

    Variable O/H total variance: $ 250 (A)

    Fixed O/H total variance (Absorption costing)

    Overhead actually incurred $17,000 Overhead absorbed (1,000 units x $15) $15,000

    Fixed O/H total variance $ 2,000 (A)

    This can be broken down into two components:

    (i) Fixed O/H expenditure variance Budgeted O/H should have cost (1,100 units x $15) 16,500 Actual O/H cost 17,000

    Fixed O/H expenditure variance $500 (A)

    (ii) Fixed O/H volume variance (Absorption Costing) Budgeted production 1,100 units Actual production 1,000 units

    Fixed O/H volume variance 100 units (A)

    @ standard $15 $1,500 (A)

    Interpreting variances

    Material price

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    Favourable: Unanticipated discounts received, better purchasing/negotiation,cheaper (substandard) materials

    Adverse: Price inflation, poor purchasing, better quality materials

    Material usage

    Favourable: Better quality materials, more efficient processing

    Adverse: Substandard material, waste, poor quality control, theft

    Labour rate

    Favourable: Low pay rates, cheap workers

    Adverse: Wage inflation

    Labour efficiency

    Favourable: More efficient production, motivated/better trained workers, bettermaterials and/or equipment

    Adverse: Poorly trained workers, deficient work organization, materials orequipment

    Overhead expenditure

    Favourable: Cost savings, more efficient use of ancillary services

    Adverse: Poor cost disciplines, complexity and bureaucracy

    Overhead volume

    Favourable: Using production capacities beyond the level budgeted

    Adverse: Under-utilization of production capacities

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    Inter-connections among variances

    As can be seen above, a factor causing a favourable variance may at the same time be the

    cause of an adverse variance in another part of the companys operations.

    It is managements responsibility to understand these relationships and to be able toanticipate, and if possible quantify, the impact of their actions on overall performance.

    At the same time, management needs to review standards for their relevance andusefulness, as well as apply common sense to the materiality and controllability of specificvariances.

    Reconciliation of budgeted profit and actual profit

    Operating statement

    Prepare a reconciliation between the profit budgeted and that realized.

    Budgeted profit (Absorption costing) 33,000

    Sales volume variance 1,650 (A)

    Sales price variance 4,750 (A)

    26,600

    Cost variances:

    Materials F A

    Price 925

    Usage 900

    Labour

    Rate 450

    Efficiency 600

    Variable

    Expenditure 50

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    Efficiency 300

    Fixed

    Expenditure 500

    Volume 1,500950 4,275 3,325 (A)

    Actual profit 23,275

    Note: Closing inventory is valued at standard cost

    Operating Statement based on Marginal costing

    Budgeted contribution (Marginal costing) 48,000

    Sales volume variance 2,400 (A)

    Sales price variance 4,750 (A)

    40,850

    Cost variances:

    Materials F A

    Price 925

    Usage 900

    Labour

    Rate 450

    Efficiency 600

    Variable

    Expenditure 50

    Efficiency 300950 2,275 1,325 (A)

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    Actual contribution 39,525

    Fixed O/Hs Budgeted 16,500Fixed O/Hs Expenditure variance 500 (17,000)

    Actual profit 22,525

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    Chapter 6

    Short-term decision-makingtechniques

    Cost-Volume-Profit (CVP) Analysis

    The breakeven formula

    Total Costs = Fixed Costs + Unit Variable Cost x Number of Units

    Total Revenue = Sales Price x Number of Units

    If

    TC = Total Costs,

    FC = Fixed Costs,

    V = Unit Variable Cost,

    X = Number of Units,

    TR = Total Revenue,

    SP = Selling Price,

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    C = SP V = Unit Contribution and

    CM%= C/SP = Contribution Margin,

    Then the break-even point(the output level at which TR=TC) is:

    In units sold: X = FC/C In dollar sales: TR = FC/CM%

    Safety Margin = Budgeted Sales Break-even point (units/dollars) C is an important indicator, as it shows the contribution of each unit sold towards

    covering fixed costs. Therefore, in the short run, the firm may prefer to produce/sell

    below break-even in order to recover some of its fixed costs.

    Relevant costs, incremental analysis and linear programming

    Relevant costs are costs expected to vary with the action takeno Past (sunk) costs are irrelevanto Fixed costs are irrelevant if there is idle capacityo Variable (marginal) costs are relevanto Opportunity costs (foregone benefits) are relevant

    Incremental analysis uses relevant costs in order to quantify the short-term effects ofbusiness decisions taken.

    Applying incremental analysis in business decision-making

    Accept or reject a special ordero Accept if selling price exceeds variable production cost and there is spare

    capacity

    Make (in-sourcing) or buy (out-sourcing)

    http://en.wikipedia.org/wiki/File:CVP-TC-FC-VC-Sales-Contrib-VC-PL-compat.s
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    o Outsource least efficient activities if full capacity reached Capital budgeting

    o Invest if marginal cost of investing is below marginal cost of not investing(marginal benefit foregone)

    Disinvestmento Divest if (marginal revenue generated + cost of resulting idle capacity +

    severance payments + restoration costs) fall below marginal cost ofproduction + salvage value of assets

    Determining optimal mix of products where there are limiting factors

    It addresses the problem of maximizing or minimizing a linear function subject to linearconstraints. The constraints may be equalities or inequalities.

    (end of ExPress Notes)