Management & Cost Accountingdocshare01.docshare.tips/files/18670/186704103.pdf · Management & Cost...

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INTRODUCTION TO MANAGEMENTACCOUNTING

1. Definition of accounting

• The process of identifying, measuring and communicatingeconomic information to permit informed judgements anddecisions by users of the information.

2. Users of accounting information can be dividedinto two categories:

(i) External parties outside the organization (financialaccounting).

(ii) Internal parties within the organization (managementaccounting).

3. Major differences between financial andmanagement accounting:

• Statutory requirement for public companies to produceannual financial accounts, whereas there is no legalrequirement for management accounting.

• Financial accounting reports describe the whole of theorganization, whereas management accounting focuses onreporting information for different parts of the business.

• Financial accounting reports must be prepared inaccordance with generally accepted accounting principles(e.g. SSAPs).

• Financial accounting reports historical information,whereas management accounting places greater emphasison reporting estimated future costs and revenues.

• Management accounting reports are produced at morefrequent intervals.

Management and Cost Accounting, 5th edition.© 2000 Colin Drury1.1


The Changing Business Environment

1. Organizations have faced dramatic changes in theirbusiness environment.

• Move from protected markets to highly competitiveglobal markets.

• Deregulation.

• Declining product life-cycles.

2. To compete successfully in today’s environment companiesare:

• Making customer satisfaction an overriding priority.

• Adopting new management approaches.

• Changing their manufacturing systems.

• Investing in AMT’s.

3. Above changes are having a significant impact on the MAS.



Focus on Customer Satisfaction


Key success factors• Cost efficiency• Quality• Time• Innovation

Total value chainanalysis

Continuousimprovement

Employeeempowerment

Customersatisfaction


Focus on Customer Satisfaction and NewManagement Approaches

1. Key success factors

• Cost efficiency – increased emphasis on accurateproduct costs and cost management.

• Quality – TQM, quality measures.

• Time – reduced cycle time, focus on non-value-addedactivities.

• Innovation – responsiveness in meeting customerrequirements.Product comparisons.Feedback on customer satisfaction.

2. Continuous improvement

• Static historical standards no longer appropriate.

• Benchmarking.

3. Employee empowerment

• Delegate more responsibility to people closest tooperating processes and customers.

4. Value chain analysis

• Suppliers, R & D, design, production, marketing,distribution, customer service, customers.

• Internal customer perspective.

5. Social responsibility and corporate ethics



Primary Functions of Cost/ManagementAccounting Systems

1. Inventory valuation for internal and external profitmeasurement

• Allocate costs between products sold and fully andpartly completed products that are unsold.

2. Provide relevant information to help managers make betterdecisions

• Profitability analysis

• Product pricing

• Make or buy (Outsourcing)

• Product mix and discontinuation

3. Provide information for planning, control andperformance measurement

• Long-term and short-term planning (budgeting)

• Periodic performance reports for feedback control

• Performance reports also widely used to evaluatemanagerial performance

Note that costs should be assembled in different ways to meetthe above three requirements.



Inventory Valuation and Profit Measurement

1. Consider a situation where a company has produced threeproducts (A, B and C) during the period. The total costs forthe period are £40 000. Product A has been sold for £20 000,product B has been completed but is in finished goodsstock, and product C is partly completed. Costs must betraced to products to value stocks and cost of goods sold.

£ £

Sales 20 000

Production cost 40 000

Less Closing stocks

(B = £18 000, C = £8 000) 26 000

Cost of goods sold (A = £14 000) 14 000

Profit 6 000

2. Approximate but inaccurate individual product costs may beappropriate for profit measurement for financialaccounting.

Example

Production expenses for the period = £10mCosts of products sold = £7mCost of products not sold = £3m

Note focus is on aggregate figures for financial accounting.



Cost Information for Providing Guidance forDecision-Making

In theory cost information computed for stock valuation oughtnot to be used for decision-making.

Example: Short-term decision

A company is negotiating with a customer for the sale of XYZ.The cost recorded for stock valuation purposes is:

£

Direct materials 200

Direct labour 150

Fixed overheads 300

650

The maximum selling price that can be negotiated is £500 perunit for an order of 100 units over the next three months.Should the company accept the order?

Spare capacity

Additional relevant costs (100 × £200) £20 000

Additional sales revenue £50 000

Contribution to profits £30 000



Operational Control and PerformanceMeasurement

The allocation of costs to products is not particularly useful forcost control purposes. Instead, costs should be traced toresponsibility/cost centres to the person who is accountable forcontrolling the costs.

Example

Budgeted costs per unit:

Product 1 Product 2 Product 3 Total£ £ £ £

Cost centre A 10 40 70 120

Cost centre B 20 50 80 150

Cost centre C 30 60 90 180

60 150 240 450

Budgeted andactual production(units) 1 000 1 000 1 000



Operational control and performance measurement

Comparison of actual with budgeted costs by products

Product 1 Product 2 Product 3 Total£000 £000 £000 £000

Budgeted cost 60 150 240 450(1,000×£60)

Actual cost 70 170 270 510Variance 10A 20 A 30A 60A

The variances are not identified to responsibility (cost centres)

Comparison of actual with budgeted costs by cost centres

Cost centre Cost centre Cost centreA B C Total

£000 £000 £000 £000

Budgeted cost 120 150 180(1,000×£120)

Actual costs 130 150 230Variance 10A – 50A 60A

Notes

1. Performance reports analysed in far more detail for costcentre managers.

2. Should not be used as a punitive device (identify areaswhere managers need to focus their attention).

3. Non-financial critical success factors are also of vitalimportance and should be included on the performancereports.


COST TERMS AND CONCEPTS

Cost Objects

• A cost object is any activity for which a separatemeasurement of cost is required (e.g. cost of making aproduct or providing a service).

• A cost collection system normally accounts for costs in twobroad stages:

1. Accumulates costs by classifying them into certaincategories (e.g. labour, materials and overheads).

2. Assigns costs to cost objects.

Direct and Indirect Costs

• Direct costs can be specifically and exclusively identifiedwith a given cost object.

• Indirect costs cannot be specifically and exclusivelyidentified with a given cost object.

• Indirect costs (i.e. overheads) are assigned to cost objects onthe basis of cost allocations.

• Cost allocations = process of assigning costs to cost objectsthat involve the use of surrogate, rather than directmeasures.

• The distinction between direct and indirect costs dependson what is identified as the cost object.



Categories of Manufacturing Costs

• Traditional cost systems accumulate product costs asfollows:

Direct materials xxxDirect labour xxxPrime cost xxxManufacturing overhead xxxTotal manufacturing cost xxxNon-manufacturing overheads xxxTotal cost xxx

Period and Product Costs

• Product costs are those that are attached to the productsand included in the stock (inventory valuation).

• Period costs are not attached to the product and included inthe inventory valuation.

Example

Product costs = £100,000Period costs = £80,00050% of the output for the period is sold and there are noopening inventories.

Production cost (product costs) 100,000

Less closing stock (50%) 50,000

Cost of goods sold (50%) 50,000

Period costs (100%) 80,000

Total costs recorded as an expense for the period 130,000


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• Important to predict costs and revenues at different activitylevels for many decisions.

• Variable costs vary in direct proportion with activity.

• Fixed costs remain constant over wide ranges of activity.

• Semi-fixed costs are fixed within specified activity levels,but they eventually increase or decrease by some constantamount at critical activity levels.

• Semi-variable costs include both a fixed and a variablecomponent (e.g. telephone charges).

Note that the classification of costs depends on the time periodinvolved. In the short term some costs are fixed, but in the longterm all costs are variable.



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Avoidable and unavoidable costs

• Avoidable costs are those costs that can be saved by notadopting a given alternative, whereas unavoidable costscannot be saved.

• Avoidable/unavoidable costs are alternative termssometimes used to describe relevant/irrelevant costs.

Relevant and irrelevant costs and revenues

• Relevant costs and revenues are those future costs andrevenues that will be changed by a decision, whereasirrelevant costs and revenues will not be changed by adecision.

Example

Materials previously purchased for £100 have no alternative useother than being converted for sale at a cost of £200. The saleproceeds after conversion would be £250.

Do notConvert Convert

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Conversion costs – 200 Relevant

Revenue – (250) Relevant

Net cost 100 50

Note that in the short term not all costs may be relevant fordecision-making.



Sunk costs

• Sunk costs are the costs of resources already acquired andare unaffected by the choice between the variousalternatives (e.g. depreciation).

• Sunk costs are irrelevant for decision-making.

Opportunity costs

• A cost that measures the opportunity that is lost orsacrificed when the choice of one course of action requiresthat an alternative course of action be given up.

Example

To produce product X requires that an order that yields £1 000contribution to profits is rejected. The lost contribution of £1 000 represents the opportunity cost of producing product X.

Marginal and incremental costs/revenues

• Incremental costs and revenues are the additionalcosts/revenues from the production or sale of a group ofadditional units.

• Marginal cost/revenue represents the additionalcost/revenue of one additional unit of output.



Job and process costing systems

• There are two types of costing systems that companies canadopt – job and process costing systems.

• Job costing applies where each unit or batch of output ofproduct or service is unique so that the cost of each unitmust be calculated separately.

• Process costing relates to those situations where masses ofidentical units are produced so that it is unnecessary toassign costs to individual units of output.

• Cost per unit is assumed to be the average cost per unit ofoutput.

• In practice these two systems represent extreme ends of acontinuum.

Maintaining a cost database

• A cost and management accounting system shouldgenerate information for meeting the followingrequirements:

1. Inventory valuation for internal and external profitmeasurement

2. Provide relevant information to help managers makebetter decisions

3. Provide information for planning, control andperformance measurement

• A database should be maintained, with costs appropriatelycoded and classified, so that relevant information can beextracted to meet each of the above requirements.


COST ASSIGNMENT

Assignment of direct and indirect costs

• Direct costs can be specifically and exclusively identifiedwith a given cost object – Hence they can be accuratelytraced to cost objects.

• Indirect costs cannot be directly traced to a cost object –∴ assigned to cost objects using cost allocations.

• Cost allocations = process of assigning costs to cost objectsthat involve the use of surrogate rather than directmeasures.

• Surrogates known as allocation bases or cost drivers.

• For accurate cost assignment, allocation bases should besignificant determinants of the costs (i.e. cause-and-effectallocations).

• Allocation bases that are not significant determinants ofthe costs are called arbitrary allocations (∴ result ininaccurate cost assignment).

• Traditional costing systems use arbitrary allocations to asignificant extent whereas more recent (ABC) systems relymainly on cause-and-effect allocations (see Fig. 3.1 on sheet 3).


COST ASSIGNMENT

Different costs for different purposes

• Manufacturing organizations assign costs to products for:

1. Inventory valuation and profit measurement.2. Providing information for decision-making.

• For inventory valuation and profit measurement the aim isto allocate costs between cost of goods sold (COGS) andinventories:

1. Accurate individual product costs are not required –only an accurate allocation at the aggregate levelbetween inventories and COGS.

• For decision-making more accurate product costs arerequired.

• Different cost information is required for inventoryvaluation and decision-making but most companies use asingle database and extract different costs for differentpurposes.

• Companies can choose to maintain their database usingcosting systems that vary on a continuum from simplisticto sophisticated (The choice should be based on costsversus benefits criteria – See Figure 3.2 on sheet 3).


COST ASSIGNMENT

Figure 3.1: Cost allocations and cost tracing

Figure 3.2: Costing systems (Varying levels of sophistication forcost assignment)


Directcosts

Indirectcosts

Traditionalcostingsystems

ABCsystems

Costobjects

Cost tracing

Cost allocations

Simplistic systems Highly sophisticated systems

Level of sophistication

• Inexpensive to operate• Extensive use of arbitrary

cost allocations• Low levels of accuracy• High cost of errors

• Expensive to operate• Extensive use of cause-

and-effect cost allocations• High levels of accuracy• Low cost of errors

COST ASSIGNMENT

Assigning indirect costs using blanket overheadrates

• Some firms use a single overhead rate (i.e. blanket or plant-wide) for the organization as a whole.

Example

Total overheads = £900 000Direct labour (or machine hours) = 60 000Overhead rate = £15 per hour

• Assume that the company has 3 separate departments andcosts and hours are analysed as follows:

Dept. A Dept. B Dept. C TotalOverheads £200 000 £600 000 £100 000 £900 000Direct labour hours 20 000 20 000 20 000 60 000Overhead rate per DLH £10 £30 £5 £15

• Product Z requires 20 hours (all in department C)

Blanket overhead rate charge = £300 (20 hrs × £15)Separate departmental overhead rate charge = £100 (20 hrs × £5)Separate departmental rates should be used since product Zonly consumes overheads in department C.

• A blanket overhead rate can only be justified if all productsconsume departmental overheads in approximately thesame proportions:

Product X spends 1 hour in each department and product Yspends 5 hours in each department (Both blanket anddepartmental rates would allocate £45 to X and £225 to Y).

• If a diverse range of products are produced consumingdepartmental resources in different proportions separatedepartmental (or cost centre) rates should be established.


COST ASSIGNMENT

Cost centre overhead rates

• Where a department contains a number of different centres(each with significant overhead costs) and productsconsume overhead costs for each centre in differentproportions, separate overhead rates should also beestablished for each centre within a department.

• See example on page 51 of text for an illustration.

• The terms cost centres or cost pools are used to describe alocation to which overhead costs are initially assigned.

• Frequently cost centres/cost pools will consist ofdepartments but they can also consist of smaller segmentswithin departments.


COST ASSIGNMENT

The two-stage allocation process

• To establish departmental or cost centre ovehead rates atwo-stage allocation procedure is required: Stage 1 – Assign overheads initially to cost centres.Stage 2 – Allocate cost centre overheads to cost objects

(e.g.products) using second stage allocation bases/cost drivers.

Figure 3.3 (a) An illustration of the two-stage allocation processfor traditional costing systems


Overhead cost accounts(for each individual category of expenses

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COST ASSIGNMENT

An illustration of the two-stage process for atraditional costing system

• Applying the two-stage allocation process requires thefollowing 4 steps:

1. Assigning all manufacturing overheads to productionand service cost centres.

2. Reallocating the costs assigned to service cost centres toproduction cost centres.

3. Computing separate overhead rates for each productioncost centre.

4. Assigning cost centre overheads to products or otherchosen cost objects.

• Steps 1 and 2 comprise stage one and steps 3 and 4 relate tothe second stage of the two-stage allocation process.

• Note that in the third stage above traditional costingsystems mostly use either direct labour hours or machinehours as the allocation bases.


COST ASSIGNMENT

The annual overhead costs for a company which has threeproduction centres and two service centres (Materialsprocurement and General factory support) are as follows:

(£) (£)Indirect wages and supervision

Machine centres: X 1 000 000Y 1 000 000

Assembly 1 500 000Materials procurement 1 100 000General factory support 1 480 000 6 080 000

Indirect materialsMachine centres: X 500 000

Y 805 000Assembly 105 000Materials procurement 0General factory support 10 000 1 420 000

Lighting and heating 500 000Property taxes 1 000 000Insurance of machinery 150 000Depreciation of machinery 1 500 000Insurance of buildings 250 000Salaries of works management 800 000 4 200 000

11 700 000The following information is also available:

Book Area Number Directvalue of occupied of labour Machinemachinery (sq. mtrs) employees hours hours(£)

Machine shop: X 8 000 000 10 000 300 1 000 000 2 000 000Y 5 000 000 5 000 200 1 000 000 1 000 000

Assembly 1 000 000 15 000 300 2 000 000Stores 500 000 15 000 100Maintenance 500 000 5 000 100

15 000 000 50 000 1000

Details of total materials issues (i.e. direct and indirect materials) to the production centres areas follows:

£Machine shop X 4 000 000Machine shop Y 3 000 000Assembly 1 000 000

8 000 000

To allocate the overheads listed above to the production and service centres wemust prepare an overhead analysis sheet.


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COST ASSIGNMENT

Budgeted overhead rates

• Actual overhead rates are not used because of:

1. Delay in product costs if actual annual rates are used.

2. Fluctuating overhead rates that will occur if actualmonthly rates are used.

Example

Estimated annual fixed overheads = £24 millionEstimated annual activity = 2.4 million hoursActivity varies throughout the year as indicated below:

Month Month Month Month Annual1 2 3 4 Total

Fixed overheads £2m £2m £2m £2m £24mActivity (hours) 0.2m 0.1m 0.4m 0.3m 2.4mHourly overhead £10 £20 £5 £6.67 £10

rate

• An estimated normal product cost based on average long-runactivity is required rather than an actual product cost(which is affected by month-to-month fluctuations inactivity).

• ∴ use estimates of overhead costs and activity over a long-run period (typically one year) to compute overhead rates(i.e. £10 per hour in the above example).


COST ASSIGNMENT

Under-and over recovery of overheads

• If actual activity or overhead spending is different fromthat used to compute the estimated overhead rates therewill be an under or over recovery of fixed overheads.

Example

Estimated fixed overheads = £2 millionEstimated activity = 1 million direct

labour hoursOverhead rate = £2 per DLH

• Assume actual activity is 900 000 DLH’s and actualoverheads are £2 million:

Overhead allocated to products = £1.8 million (900 000 × £2)

Under-recovery = £200 000

• Assume actual overheads are £1 950 000 and actual activityis 1 million DLH’s:

Overhead allocated to products = £2 million (1 million × £2)

Over-recovery = £200 000

• External financial accounting principles (GAAP) requirethat under/over recoveries are treated as period costs.


COST ASSIGNMENT

Non-manufacturing overheads

• Financial accounting regulations specify that onlymanufacturing overheads should be allocated to products.

• Non-manufacturing costs should be assigned to productsfor decision-making (Particularly cost-plus pricing).

• Simplistic methods, such as using direct labour hours, or apercentage of total manufacturing cost, are frequently usedas allocation bases with traditional systems.

Example

Manufacturing cost = £1 million Non-manufacturing overheads = £500 000Overhead rate = 50% of manufacturing

cost

• Simplistic methods do not provide a reliable measure of thenon-manufacturing overheads consumed by products.

• ABC is advocated for providing a more accurate measure ofresources consumed by products.

ACCOUNTING ENTRIES FOR A JOB COSTINGSYSTEM

Pricing the issue of raw materials

1. The issue of raw materials involves:• reducing the value of raw material stocks

• recording the cost of the materials issued to theappropriate job or overhead account.

2. Difficulty arises in determining which costs should beassigned to material issues.

Example

1 February : 1000 units purchased at £1 per unit1 March : 1000 units purchased at £2 per unit30 March : 1000 units sold at £4 per unit

Three alternative issue prices:

First-in, first-out (FIFO) = £1.00 per unitLast in, first out (LIFO) = £2.00 per unitAverage cost = £1.50 per unit

A summary of the transactions

Raw materials GrossSales Cost of sales closing stock profit

£ £ £ £FIFO 4000 1000 × £1.00 = 1000 1000 × £2.00 = 2000 3000LIFO 4000 1000 × £2.00 = 2000 1000 × £1.00 = 1000 2000Average cost 4000 1000 × £1.50 = 1500 1000 × £1.50 = 1500 2500


ACCOUNTING ENTRIES FOR ANINTEGRATED ACCOUNTING SYSTEM

Example

The following are the transactions of AB Ltd for the month of April.

1. Raw materials of £182 000 were purchased on credit.2. Raw materials of £2 000 were returned to the supplier because of

defects.3. The total of stores requisitions for direct materials issued for the

period was £165 000.4. The total issues for indirect materials during the period was

£10 000.5. Gross wages of £185 000 were incurred during the period

consisting of:Wages paid to employees £105 000PAYE due to Inland Revenue £60 000National insurance contributions due £20 000

6. All the amounts due in transaction 5 were settled by cash duringthe period.

7. The allocation of the gross wages for the period was as follows:Direct wages £145 000Indirect wages £40 000

8. The employer’s contribution for national insurance deductions was£25 000.

9. Indirect factory expenses of £41 000 were incurred during theperiod.

10. Depreciation of factory machinery was £30 000.11. Overhead expenses charged to jobs by means of factory overhead

absorption rates was £140 000 for the period.12. Non-manufacturing overhead incurred during the period was

£40 000.13. The cost of jobs completed and transferred to finished goods stock

was £300 000.14. The sales value of goods withdrawn from stock and delivered to

customers was £400 000 for the period.15. The cost of goods withdrawn from stock and delivered to

customers was £240 000 for the period.Management and Cost Accounting, 5th edition.

© 2000 Colin Drury4.2


Example

1. Purchase of raw materials

Dr Stores ledger control account 182 000Cr Creditors control account 182 000

2. Return of raw materials

Dr Creditors control account 2 000Cr Stores ledger control account 2 000

3. Issue of direct materials

Dr Work in progress control account 165 000Cr Stores ledger control account 165 000

4. Issue of indirect materials

Dr Factory overhead control account 10 000Cr Stores ledger control account 10 000

Stores ledger control account

1. Creditors a/c 182 000 2. Creditors a/c 2 0003. Work in progress a/c 165 0004. Factory overhead a/c 10 000

Balance c/d 5 000

182 000 182 000

Balance b/d 5 000



1. Recording labour costs payable

Dr Wages control account 185 000Cr Inland Revenue account 60 000Cr National insurance contribution account 20 000Cr Wages accrued account 105 000

Note the above accounts will be cleared by crediting cashand debiting each of the accounts.

2. Recording the allocation of labour costs

Dr Work in progress account 145 000Dr Factory overhead control account 40 000

Cr Wages control account 185 000

3. Recording the employer’s national insurance contribution

Dr Factory overhead control account 25 000Cr cash/bank 25 000

Wages control account

5. Wages accrued a/c 105 000 7. Work in progress a/c 145 0005. PAYE tax a/c 60 000 7. Factory overhead a/c 40 0005. National Insurance

a/c 20 000

185 000 185 000



1. Recording the overheads incurred

Dr Factory overhead control account 71 000Cr Expense creditors control account 41 000Cr Provision for depreciation 30 000

2. Recording the allocation of overheads to production

Dr Work in progress control account 140 000Cr Factory overhead control account 140 000

Note that the balance of the factory overhead control accountrepresents the under or over recovery of overhead that istransferred to costing profit and loss account.

Factory overhead control account

4. Stores ledger control a/c 10 000 11. Work in progress

7. Wages control a/c 40 000 control a/c 140 000

8. Employer’s national Balance – under recoveryins contributions a/c 25 000 of overhead transferred

to costing profit and9. Expense creditors a/c 41 000 loss a/c 6 000

10. Provision fordepreciation a/c 30 000

146 000 146 000



1. Recording non-manufacturing overheads incurred

Dr Non-manufacturing overheads account 40 000Cr Expense creditors 40 000

Dr Profit and loss account 40 000Cr Non-manufacturing overheads account 40 000

2. Production completed during the period

Dr Finished goods stock account 300 000Cr Work in progress control account 300 000

3. Recording sales and cost of goods sold

Dr Debtors control account 400 000Cr Sales account 400 000

Dr Cost of sales account 240 000Cr Finished goods stock account 240 000


BACKFLUSH COSTING

Illustration

Purchase of raw materials £1 515 000Conversion costs £1 010 000Finished goods manufactured 100 000 unitsSales for the period 98 000 unitsNo opening stocksStandard unit cost is £25 (£15 materials and £10 conversioncost)Zero material variances

Method 1

Trigger point 1 = Purchase of raw materials and componentsTrigger point 2 = Manufacture of finished goods

Raw materials inventory

1. Creditors £1 515 000 3. Finished goods £1 500 000

Finished goods inventory

3. Raw materials £1 500 000 4. COGS £2 450 0003. Conversion cost £1 000 000

Conversion costs

2. £1 010 000 3. Finished goods £1 000 000

Cost of goods sold (COGS)

4. £2 450 000The end of month inventory balances are:

Raw materials £15 000Finished goods £50 000

£65 000


BACKFLUSH COSTING

Method 2

1. Only one trigger point = Manufacture of finished product

2. Conversion costs are debited as the actual costs areincurred.

3. Dr Finished goods inventory (100 000 × £25) 2 500 000

Cr Creditors 1 500 000Cr Conversion costs 1 000 000

Dr Cost of goods sold 2 450 000Cr Finished goods inventory 2 450 000


CONTRACT COSTING

1. Contract costing is applied to relatively large cost unitswhich take a long time to complete (e.g. civil engineeringprojects).

2. A separate account is maintained for each contract.

• The first section is used to determine cost of sales.• In the second section cost of sales is compared with

sales to derive the profit to date.• The third section records future expenses and accrued

expenses.

3. Guidelines for determining profit to date on contracts.

• No profit is taken if the contract is at an early stage.• Prudence concept applied and losses recorded as

incurred or anticipated.• If the contract is near completion a proportion of the

profit should be recognized based on the followingformula:

× Estimated profit

• Within the 35–85% stage of completion, the followingformula is recommended to determine profit to date:

�23

� × Notional profit* ×

*Notional profit = Value of work certified – Cost of work certified

Cash received��Value of work certified

Cash received to date��

Contract price


CONTRACT COSTING EXAMPLE

A construction company is currently undertaking threeseparate contracts and information relating to these contractsfor the previous year, together with other relevant data, areshown below.

Contract A Contract B Contract C£000 £000 £000

Contract price 1 760 1 485 2 420Balances b/f at beginning of year:

Material on site – 20 30Written down value of plant and machinery – 77 374Wages accrued – 5 10

Transactions during previous year:Profit previously transferred to P & L A/C – – 35Cost of work certified (cost of sales) – 418 814

Transactions during current year:Materials delivered to sites 88 220 396Wages paid 45 100 220Salaries and other costs 15 40 50WDV of plant issued to sites 190 35 –HO expenses apportioned during year 10 20 50

Balances c/f at the end of the year:Material on site 20 – –WDV of plant and machinery 150 20 230Wages accrued 5 10 15

Value of work certified at end of year 200 860 2 100Cost of work not certified at end of year – – 55

The agreed retention rate is 10% of the value of work certified bythe contractees’ architects. Contract C is scheduled for handingover to the contractee in the near future, and the site engineerestimates that the extra costs required to complete the contract,in addition to those tabulated above, will total £305 000. Thisamount includes an allowance for plant depreciation,construction services, and for contingencies.

You are required to prepare a cost account for each of the threecontracts and recommend how much profit or loss should betaken up for the year.


CONTRACT COSTING EXAMPLE

Contract accounts

aProfit taken plus cost of sales for the current period, or cost of sales less loss to date.


A B C£000 £000 £000

Materials on site b/f – 20 30Plant on site b/f – 77 374Materials control a/c 88 220 396Wages control a/c 45 100 220Salaries 15 40 50Plant control a/c 190 35 –Apportionment of

head office exps 10 20 50Wages accrued c/f 5 10 15

353 522 1 135

Cost of sales b/f 183 497 840Profit taken this period – – 282

183 497 1 122

Cost of work not – – –certified b/f 55

Materials on site b/f 20 – –Plant on site b/f 150 20 230

A B C£000 £000 £000

Wages accrued b/f – 5 10

Materials on site c/f 20 – –Plant on site c/f 150 20 230Cost of work not

certified c/f – – 55Cost of sales

– current period(balance) c/f 183 497 840

353 522 1 135

Attributable salesrevenuea

(current period) 183 442 1 122Loss taken – 55 –

183 497 1 122

Wages accrued b/f 5 10 15

CONTRACT COSTING – BALANCE SHEET ENTRIES


Stocks:

Total costs incurred to date 183 860 1 709 (814 + 840 + 55)

Included in cost of sales 183 860 1 654

Included in long-termcontract balances 0 0 55

Debtors

Cumulative sales turnover 183 860 1 971Less Cumulative

progress payments 180 774 1 890

Amounts recoverableon contracts 3 86 81

Debtors accounts (debit entries)


Previous period –Attributable sales – 418 849

Current period –Attributable sales 183 442 1 122

183 860 1 971


PROCESS COSTING

1. Job costing assigns costs to each individual unit of outputbecause each unit consumes different quantities ofresources.

2. Process costing does not assign costs to each unit of outputbecause each unit is identical. Instead, average unit costsare computed.


PROCESS COSTING

A comparison of job and process costing


Work in progress stock

Work in progress stock

Job A Job B

Direct costs and factory overheadsare allocated toof production

individual units

Job C

Process A Process B Process C

Finished goods stock

Finished goods stock

Consists of stock ofunlike units

Completedproduction

Consists of stock ofvalued at

average unit cost ofproduction

like units

Input Input InputOutput

No attempt is made to allocate costs to individual units ofproduction. Direct costs and factory overhead costs are allocatedto process A, process B, and so on.When units are completed, theyare transferrred to finished goods stock at costaverage unit

Output Output

Process costing

Job costing

PROCESS COSTING

Normal and abnormal losses

• Normal losses cannot be avoided – Cost is absorbed by goodproduction.

• Abnormal losses are avoidable – Cost is recorded separatelyand treated as a period cost.

Example

Input =1 200 litres at a cost of £1 200

Normal loss = �16

� of input

Actual output = 900 litres

CPU = £1 200/Expectedoutput (1 000 litres) =1.20

Cost of completedproduction =£1 080 (900 × £1.20)

Cost of abnormal loss =£120 (100 × £1.20)

Process account

Unit UnitUnits cost £ Units cost £

Input costs 1 200 1.00 1 200 Normal loss 200 – –Abnormal loss 100 1.20 120Outputtransferred tonext process 900 1.20 1 080

1 200 1 200


PROCESS COSTING

Sale proceeds from normal losses

Example 1

Input = 1 200 litres at a cost of £1 200

Output = 1 000 litres

Normal loss = �16

� of input

Scrap value of losses in process = £0.50 per litre

CPU =

= £1 100 / 1 000 = £1.10 per litre

Process account


Input costs 1 200 1.00 1 200 Normal loss 200 – 100Output transferredto next process 1 000 1.10 1 100

1 200 1 200

Cost of production less scrap value of normal loss��

Expected output


PROCESS COSTING

Sale proceeds (normal and abnormal losses)

Example 2

As example 1 but output = 900 litres (abnormal loss = 100 litres)

CPU as example 1 = £1.10 per litre

The sales value of the abnormal loss should be offset against thecost of the abnormal loss.

Process account


Input costs 1 200 1.00 1 200 Normal loss 200 – 100Abnormalloss 100 1.10 110Outputtransferred tonext process 900 1.10 990

1 200 1 200

Abnormal loss account

Process account 110 Cash salefor unitsscrapped 50Balancetransferred to profitand loss a/c 60

110 110


PROCESS COSTING

Abnormal gains

Example

Input = 1 200 litres at a cost of £1 200Output = 1 100 litresNormal loss = �

16

� of inputScrap value = £0.50 per litre

CPU =

= £1 100 / 1 000 = £1.10 per litreProcess account


Input costs 1 200 1.00 1 200 Normal loss 200 – 100

Abnormal gain 100 1.10 110 Transferred to

next process 1 100 1.10 1 210

1 310 1 310

Abnormal gain account

Normal loss account 50 Process account 110Profit and loss

account 60

110 110

Normal loss account (income due)

Process account 100 Abnormal gain account 50Cash from scrap sold

(100 × £0.50) 50

100 100

Cost of production less scrap value of normal loss��

Expected output


PROCESS COSTING

Equivalent production and closing WIP

Partly completed units are expressed as fully completedequivalent units in order to compute CPU (e.g. 1 000 units 50%complete equals 500 equivalent production).

Example

Opening WIP NilUnits introduced into the process 14 000Units completed and transferred to next process 10 000Closing WIP (50% complete) 4 000Materials cost (introduced at start) £70 000Conversion cost £48 000

Note materials are 100% complete.

Total WIP Total CostCost cost Completed equiv. equiv. per unitelement £ units units units £

Materials 70 000 10 000 4 000 14 000 5.00Conversion

cost 48 000 10 000 2 000 12 000 4.00

118 000 9.00

Value of work in progress: £ £Materials (4 000 units at £5) 20 000Conversion cost (2 000 units at £4) 8 000 28 000

Completed units (10 000 units at £9) 90 000

118 000


PROCESS COSTING

Equivalent production and closing WIP

Process A account

Materials 70 000 Completed unitsConversion cost 48 000 transferred to

process B 90 000Closing WIP c/f 28 000

118 000 118 000

Opening WIP b/f 28 000


PROCESS COSTING

Previous process cost

Costs transferred from a previous process are treated as aseparate element of cost (100% complete).

Example

Opening WIP NilUnits transferred 10 000Closing WIP (50% complete) 1 000Completed units transferred to finished goods stock 9 000Previous process cost £90 000Conversion costs £57 000Materials (introduced at end of process) £36 000Note materials are zero complete and previous process cost 100% complete.

Total WIP Total CostCost cost Completed equiv. equiv. per unitelement £ units units units £

Previous process cost 90 000 9 000 1 000 10 000 9.00

Materials 36 000 9 000 – 9 000 4.00

Conversioncost 57 000 9 000 500 9 500 6.00

183 000 19.00

Value of work in progress: £ £Previous process cost(1 000 units at £9) 9 000Materials nilConversion cost (500 units at £6) 3 000 12 000

Completed units (9 000 units at £19) 171 000

183 000


PROCESS COSTING


Process B account

Previous process cost 90 000 Completed production Materials 36 000 transferred to

finished stock 171 000Conversion cost 57 000 Closing WIP c/f 12 000

183 000 183 000

Opening WIP b/f 12 000


PROCESS COSTING

Example to illustrate weighted average and FIFO

Process X Process YOpening WIP (units): 6 000 2 000

(60% complete) (80% complete)

Materials £24 000 £4 000

Conversion cost £15 300 £12 800

Previous processcost – £30 600

Added costs:Materials £64 000 £20 000

Conversion cost £75 000 £86 400

Closing WIP (units) 4 000 8 000(75% complete) (50% complete)

Completed units 18 000 12 000

Materials are introduced at the start for process X and at the 70% stagefor process Y.


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Opening WIP – FIFO method

The FIFO method assumes opening WIP is the first group ofunits to be completed. Therefore, opening WIP is chargedseparately to completed production and the CPU is based oncurrent period costs.

Process X

Completed Closing Current CostCost Current units less WIP total perelement period opening WIP equiv. equiv. u n i t

costs £ equiv. units units units £

Materials 64 000 12 000 (18 000 – 6 000) 4 000 16 000 4.00

Conversioncost 75 000 14 400 (18 000 – 3 600) 3 000 17 400 4.31

139 000 8.31

Completed production: £ £

Opening WIP 39 300

Materials (12 000 units at £4) 48 000

Conversion cost (14 400 units at £4.31) 62 069 149 369

Work in progress:


Conversion cost (3 000 units at £4.31) 12 931 28 931

178 300


PROCESS COSTING

Opening WIP – FIFO method

Process Y

Completed Closing Current CostCost Current units less WIP total perelement period opening WIP equiv. equiv. unit

costs £ equiv. units units units £

Previousprocess cost 149 369 10 000 8 000 18 000 8.2983

Materials 20 000 10 000 nil 10 000 2.0

Conversioncost 86 400 10 400 4 000 14 400 6.0

255 769 16.2983

Cost of completed production: £ £

Opening WIP 47 400


(10 000 units at £8.2983) 82 983


Conversion cost (10 400 units at £6) 62 400 212 783

Cost of closing work in progress:


(8 000 units at £8.2983) 66 386

Materials nil

Conversion cost (4 000 units at £6) 24 000 90 386

303 169

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JOINT AND BY-PRODUCT COSTING

Example of joint cost apportionments

Joint costs for the period £60 000

Output and salesX = 4 000 units at £7.50Y = 2 000 units at £25Z = 6 000 units at £3.33

There are no further processing costs after split-off point.

Physical measures method

Apportioned ProfitOutput costs Sales (loss)(units) £ £

Product X 4 000 (�13

�) 20 000 30 000 10 000

Product Y 2 000 (�16

�) 10 000 50 000 40 000

Product Z 6 000 (�12

�) 30 000 20 000 (10 000)

12 000 60 000 100 000 40 000

Sales value method

Apportioned ProfitSales costs (loss)

£ £

Product X 30 000 (30%) 18 000 12 000

Product Y 50 000 (50%) 30 000 20 000

Product Z 20 000 (20%) 12 000 8 000

100 000 60 000 40 000



Net realizable value (NRV) method

• Where further processing costs are incurred sales values atsplit-off point may not be available.

• Further processing costs are deducted from sales value toestimate NRV at split-off point.

Example

Further % Jointprocess cost

Sales costs NRV allocated£ £ £

Product A 36 000 8 000 28 000 28%

Product B 60 000 10 000 50 000 50%

Product C 24 000 2 000 22 000 22%

120 000 20 000 100 000



Constant gross profit percentage method

• Based on the assumption that the gross profit should beidentical for each product.

• Joint costs are therefore allocated so that the gross profits atsplit-off point are identical for each product.

• Using the example on sheet 3 and assuming that joint costsare £60 000 the gross profit is £40 000 (£120 000 sales less£80 000 total costs) – ∴ the total gross profit is 33.33%.

Product Product Product TotalA B C£ £ £ £

Sales value 36 000 60 000 24 000 120 000

Gross profit (33.33%) 12 000 20 000 8 000 40 000

Cost of goods sold 24 000 40 000 16 000 80 000

Less further processingcosts 8 000 10 000 2 000 20 000

Allocated joint costs(balance) 16 000 30 000 14 000 60 000



Comparison of methods

• Cause-and-effect criterion cannot be applied so allocationshould be based on benefits received.

• If benefits received cannot be measured allocation shouldbe based on the principle of equity or fairness.

• Literature tends to advocate the net realizable method.

• Also note that with the physical units method the jointcost allocation bears no relationship to the revenueproducing power of the individual products.

Accounting for by-products

• The major objective is to produce the joint products.Therefore the joint costs should be charged only to thejoint products.

• Further processing costs should be charged to the by-product.

• Net revenues from the sale of the by-product should bededucted from the cost of the joint process.



Example

Joint product costs £3 020 000Output of the joint products A – 30 000 kgs

B – 50 000 kgsC – 5 000 kgs

By-product C requires further processing at a cost of £1 per kgafter which it can be sold for £5 per kg.

• The accounting entries are:

Dr. By-product stock (5 000 × £4) 20 000Cr. Joint process WIP account 20 000

With the net revenue due from the production of the by-product

Dr. By-product stock 5 000Cr. Cash 5 000

With the separable manufacturing costs incurred

Dr. Cash 25 000Cr. By-product stock 25 000

With the value of the by-product sales for the period



Relevant costs for decision-making

Joint cost allocations are necessary for financial accounting, butthey should not be used for decision-making.

Example

Joint product costs £100 000

Sales value at split-off point:

Product X (5 000 units at £16) £80 000

Product Y (5 000 units at £8) £40 000

If additional costs of £6 000 are incurred on product Y it can beconverted into product Z and sold for £10 per unit.

• Note that the joint costs are irrelevant for this decisionsince they will be incurred irrespective of which decision istaken.

• The decision should be based on a comparison of relevantcosts with relevant revenues:

£Relevant revenues (additional revenues of 5 000 × £2) 10 000

Relevant costs (additional costs of processing) 6 000

Additional profit from conversion 4 000


INCOME EFFECTS OF ALTERNATIVE COSTACCUMULATION SYSTEMS

Absorption and variable costing

1. Absorption costing (also known as full costing) traces allmanufacturing costs to products and treats non-manufacturing overheads as a period cost.

2. Variable costing (also known as direct or marginal costing)traces all variable costs to products and treats fixedmanufacturing overheads and non-manufacturingoverheads as a period cost.

3. Therefore, variable and absorption costing differ in thetreatment of fixed manufacturing costs.


Variable costs

Variable costs

Fixed costs

Fixed costs

Products

Products

Stocks

Stocks

P & L a/c

P & L a/c

Absorption costing

Variable costing


Example

The following information is available for periods 1–6 for acompany that produces a single product:

£

Unit selling price 10

Unit variable cost 6

Fixed costs for each period 300 000

Normal activity is expected to be 150 000 units per period, andproduction and sales for each period are as follows:

Period Period Period Period Period Period1 2 3 4 5 6

Units sold (000’s) 150 120 180 150 140 160Units produced (000’s) 150 150 150 150 170 140

There were no opening stocks at the start of period 1, and theactual manufacturing fixed overhead incurred was £300 000 perperiod. Assume that non-manufacturing overheads are £100 000per period.



Variable costing statements


£000’s £000’s £000’s £000’s £000’s £000’s

Opening stock – – 180 – – 180

Production cost 900 900 900 900 1 020 840

Closing stock – (180) – – (180) (60)

Cost of sales 900 720 1 080 900 840 960

Fixed costs 300 300 300 300 300 300

Total costs 1 200 1 020 1 380 1 200 1 140 1 260

Sales 1 500 1 200 1 800 1 500 1 400 1 600

Gross profit 300 180 420 300 260 340

Less Non-manufacturing costs 100 100 100 100 100 100

Net profit 200 80 320 200 160 240




Absorption costing statements


£000’s £000’s £000’s £000’s £000’s £000’s

Opening stock – – 240 – – 240

Production cost 1 200 1 200 1 200 1 200 1 360 1 120

Closing stock – (240) – – (240) (80)

Cost of sales 1 200 960 1 440 1 200 1 120 1 280

Adjustment forunder/(over)recovery ofoverhead – – – – (40) 20

Total costs 1 200 960 1 440 1 200 1 080 1 300

Sales 1 500 1 200 1 800 1 500 1 400 1 600

Gross profit 300 240 360 300 320 300

Less Non-manufacturing costs 100 100 100 100 100 100

Net profit 200 140 260 200 220 200


Profit comparisons (variable and absorptioncosting)

• Profits are the same for both methods when productionequals sales (no changes in stock levels) in periods 1 and 4.

• Where production exceeds sales (increasing stock levels)the absorption costing system produces higher profits inperiods 2 and 5.

• Where sales exceed production (declining stock levels) thevariable costing system produces higher profits in periods 3and 6.

• With an absorption costing system profits can declinewhen sales volume increases and costs remain unchanged(e.g. period 6).

Some arguments in support of variable costing

• Variable costing provides more useful information fordecision-making.

• Variable costing removes from profit the effect of stockchanges.

• Variable costing avoids fixed overheads being capitalized inunsaleable stocks.

Some arguments in support of absorption costing

• Absorption Costing does not understate the importance offixed costs.

• Absorption costing avoids fictitious losses being reported(e.g stocks accumulated for seasonal sales).

• Absorption costing is theoretically superior to variablecosting. (Note cost obviation concept favours variablecosting, whereas revenue production concept favoursabsorption costing.)



Conclusion

1. Choice depends on the circumstances.

• Volatile sales and changing stock levels favour variablecosting for internal monthly or quarterly profitmeasurement.

• Seasonal sales where stocks are built up in advancefavours absorption costing.

2. Debate only applies to internal reporting – SSAP 9 requiresthat absorption costing is used for external reporting.

3. Debate only applies when historical cost accounting is used.


INCOME EFFECTS OF ALTERNATIVECOSTING SYSTEMS

Alternative denominator level measures

• Absorption costing systems require the computation ofestimated fixed overhead rates.

• The fixed overhead rate will be significantly influenced bythe choice of the denominator level.

Example

Annual budgeted fixed overheads for a machine cost centre £192 000

The cost centre operates 3 shifts of 8 hours for 5 days per week for 50 weeks 6 000 hours

Practical operating capacity to allow for preventative maintenance 5 000 hours

Requirements based on average sales demand for next 3 years 4 800 hours

Budgeted usage for the coming year 4 000 hours

• Four different denominator levels can be used

1. Theoretical maximum capacity of 6 000 hours = £32 perhour (£192 000/6 000 hours)

2. Practical capacity of 5 000 hours = £38.40 per hour (£192 000/5 000 hours)

3. Normal average long-run activity of 4 800 hours = £40 perhour (£192 000/4 800 hours)

4. Budgeted activity of 4 000 hours = £48 per hour (£192 000/4 000 hours)


INCOME EFFECTS OF ALTERNATIVECOSTING SYSTEMS

• Assuming actual activity and spending is the same asbudget the annual costs will be allocated as follows:

Allocated to Volume variance Totalproducts (cost of unused (£)

capacity)Practical £153 600 £38 400 192 000capacity (4 000 hrs × £38.40) (1 000 hrs × £38.40) Normal £160 000 £32 000 192 000activity (4 000 hrs × £40) (800 hrs × £40)Budgeted £192 000 Nil 192 000activity (4 000 hrs × £48)

• The choice of an appropriate activity level can have asignificant effect on the inventory valuation and profitcomputation.

• Assuming 90% of output is sold and no openingsinventories the above costs will be allocated as follows:

Allocated to Allocated tocost of sales inventories Total

£ £ £Practical capacity 176 640 15 360 192 000

Normal activity 176 000 16 000 192 000

Budgeted activity 172 800 19 200 192 000

• For many organizations the allocation of costs between costof sales and inventories is not an issue.

• Note the theoretical disadvantages of using budgetedactivity.


COST–VOLUME–PROFIT ANALYSIS

Economist’s cost-volume graph

1. Curvilinear graph results in two break-even points.

2. Note the shape of the total cost function:

• initial steep rise, levels off, followed by a further steeprise.

3. The total revenue line initially rises steeply, then levels offand declines.


Cos

ts a

nd r

even

ue

£Total cost

D

CB

0

A

Total revenue

Volume

Units of production and sales


Economist’s variable cost function

1. Output levels between 0 and Q1 = Increasing returns to scale

2. Output levels between Q1 and Q2 = Constant returns to scale

3. Output levels beyond Q2 = Decreasing returns to scale


£

Ave

rage

uni

t va

riab

leco

st

0Volume

Q1 Q2


The accountant’s cost–volume–profit model

1. Constant variable cost and selling price is assumed.2. Only one break-even point, and profit increases as volume

increases.3. The diagram is not intended to provide an accurate

representation for all levels of output. The objective is toprovide an accurate representation of cost and revenuebehaviour only within the relevant range of output.


Break-evenpoint

Accountant’sfixed cost

Accountant’stotal cost

Accountant’stotal revenue

Economist’stotal cost

Units of production and sales0 YX

£

Tota

l cos

ts a

nd r

even

ue

Relevant range


Accountant’s fixed cost function

1. Within the short term the firm anticipates that it willoperate between output levels Q2 and Q3 and commitsitself to fixed costs of 0A.

2. Costs are fixed in the short term, but can be changed in thelonger term.


£

Cos

t

0

A

Relevant rangeB

Q1 Q2 Q3

Units of production and sales


Changes in fixed costs

1. At the planning stage the firm must decide on how muchproductive capacity should be provided and, therefore, thelevel of fixed costs.

2. If maximum sales levels are 0Q1, 0Q2 and 0Q3, then profitsare maximized at output level 0Q2.

3. The firm will choose to provide capacity of 0Q2 and willoperate on total cost line AB during the next period.


£

Cos

t an

d re

venu

es

0

A

C

Q1 Y

D

B

ETotal cost

Units produced and sold

Total revenue

Q2 Q3


Changes in selling price

1. At the planning stage prior to setting selling prices for theforthcoming period, the firm is considering whether toreduce the selling price in order to increase demand.

2. The potential revenue functions are 0A and 0C.

3. If anticipated demand is 0Q2 at the lower selling price and0Q1 at the higher selling price, then the lower price will beselected and the firm will be committed to a revenuefunction of 0C during the next period.


B

A

£

Sales revenueand costs

0

C

Total revenue

Total cost

Fixed cost

Units produced and soldQ2Q3Q1

Prof

it


CVP analysis: non-graphical computations

1. Example 1Fixed costs per annum £60 000Unit selling price £20Unit variable cost £10Relevant range 4 000–12 000 units

2. Break-even point

= = 6 000 units

3. Units to be sold to obtain a £30 000 profit

= = = 9 000 units

4. If unit costs and revenues are not given, the break-evenpoint (expressed in sales values) can be calculated asfollows:

× Total sales

5. Profit volume ratio = �SC

aolen

str

riebvuetnio

une

� × 100

6. Percentage margin of safety = Expected sales – Break-even sales��

Expected sales

Total fixed costs��Total contribution

£90 000�

£10Fixed costs + desired profit��

Contribution per unit

60 000�

£10Fixed costs

��Contribution per unit



Break-even chart for example 1


Profit area

280

260

240

220

200

180

160

140

120

100

80

60

40

20

0 1 2 3 4 5 6

Units of production and sales (000)

7 8 9 10 11 12 13 14 15

Loss area

Poun

ds p

er y

ear

(£00

0)

Break-evenpoint

Salesrevenue

Totalcosts

Relevant range

Total variablecosts

Total fixedcosts


Contribution chart for example 1


Profit area

280

260

240

220

200

180

160

140

120

100

80

60

40

20

0 1 2 3 4 5 6

Units of production and sales (000)7 8 9 10 11 12 13 14 15

Loss area

Poun

ds p

er y

ear

(£00

0)

Break-evenpoint

Salesrevenue

Totalcosts

Con

trib

utio

n

Variable cost li

ne

Relevant range

Fixedcosts

Variablecosts


Profit-volume graph for example 1


Profit area

90

80

70

60

50

40

30

20

10

0

10

20

30

40

50

60

1 2 3 5 6

Units of production and sales (000)7 8 9 10 11 13 14 15

Loss area

Break-evenpoint

Relevant range

Lo

sses

(£00

0)P

rofit

s(£0

00)

4 12

COST–VOLUME PROFIT ANALYSIS

CVP analysis assumptions

1. All other variables remain constant• e.g. sales mix, production efficiency, price levels,

production methods.

2. Complexity-related fixed costs do not change.• If the range of items produced increases but volume

remains unchanged, then it is assumed fixed costs willnot alter.

3. Profits are calculated on a variable costing basis.

4. Unit variable cost and selling price are constant per unit ofoutput.

5. The analysis applies over the relevant range only.

6. Costs can be accurately divided into their fixed and variableelements.

7. Single product or constant sales mix.

Example

Product X Product Y

Unit contribution £12 £8

Budgeted sales mix 50% 50%

Actual sales mix 25% 75%

Fixed costs are £180 000

Budgeted BEP = £180 000 / £10a = £18 000 units

Actual BEP = £180 000 / £9b = 20 000 unitsa (50% × £12) + (50% × £8)b (25% × £12) + (75% × £8)


MEASURING RELEVANT COSTS ANDREVENUES FOR DECISION-MAKING

Relevant costs and revenues

• The relevant financial inputs for decision-making are futurecash flows that will differ between the various alternativesbeing considered.

• Therefore only relevant (incremental/differential) cashflows should be considered.

• Relevant costs and revenues are required for special studiessuch as:

1. Special selling price decisions.2. Product-mix decisions when capacity constraints exist3. Decisions on replacement of equipment.4. Outsourcing (Make or buy) decisions.5. Discontinuation decisions.

• Decisions should not be based only on items that can beexpressed in quantitative terms — Qualitative factors mustalso be considered.



Special pricing decisions

• Special pricing decisions are typically one-time only ordersand/or orders below the prevailing market price.

Example 1 (A short-term order)

Monthly capacity for a department within a company = 50 000 units

Expected monthly production and sales for next quarter at normal selling price of £40 = 35 000 units

Estimated costs and revenues (for 35 000 units):

£ £Direct labour 420 000 12Variable costs 350 000 10Manufacturing non-variable overheads 280 000 8Marketing and distribution costs 105 000 3Total costs 1 155 000 33Sales 1 400 000 40Profit 245 000 7

The excess capacity is temporary and a company has offered tobuy 3 000 each month for the next three months at a price of£20 per unit. Extra selling costs for the order would be £1 perunit.



• Evaluation of the order (£’s monthly costs and revenues)

(1) (2) (3)Do not Accept Difference

accept order order (Relevant costs)

Direct labour 420 000 420 000Variable costs 350 000 380 000 30 000Manufacturing non-

variable overheads 280 000 280 000Extra selling costs 3 000 3 000Marketing /dist. costs 105 000 105 000Total costs 1 155 000 1 188 000 33 000Sales 1 400 000 1 460 000 60 000Profit 245 000 272 000 27 000

• Only variable costs, the extra selling costs and salesrevenues differ between alternatives and are relevantcosts/revenues.

• Two approaches to presenting relevant costs — Present onlycolumns 1 and 2 or just column 3.

• Since relevant revenues exceed relevant costs the order isacceptable subject to the following assumptions: 1. Normal selling price of £40 will not be affected.2. No better opportunities will be available during the

period.3. The resources have no alternative uses.4. The fixed costs are unavoidable for the period under

consideration.• Note that the identification of relevant costs depends on

the circumstances.



Example 1 (A longer-term order)

• Assume now spare capacity in the foreseeable future(Capacity = 50 000 units and demand = 35 000 units) andthat an opportunity for a contract of 15 000 units permonth at £25 SP emerges involving £1 per unit specialselling costs.

• No other opportunities exist so if the contract is notaccepted direct labour will be reduced by 30%,manufacturing non-variable costs by £70 000 per monthand marketing by £20 000. Unutilised facilities can berented out at £25 000 per month.



• Evaluation of the order (£’s monthly costs and revenues):

(1) (2) (3)Do not accept Accept the Difference

orders orders (Relevant costs)

Units sold 35 000 50 000 15 000£ £ £

Direct labour 294 000 420 000 126 000Variable costs 350 000 500 000 150 000Manufacturing non-

variable overheads 210 000 280 000 70 000Extra selling costs 15 000 15 000Marketing/dist. costs 85 000 105 000 20 000 Total costs 939 000 1 320 000 381 000Revenues-facilities rental 25 000 25 000Sales revenues 1 400 000 1 775 000 (375 000)Profit 486 000 455 000 31 000

• Company will be better off by £31 000 per month if itreduces capacity (assuming there are no qualitative factors).

• You can present only columns 1 and 2 or just column 3(note the opportunity cost shown in column 3).

• In the longer-term all of the above costs and revenues arerelevant.



Product mix decisions with capacity constraints

• Limiting or scarce factors are factors that restrict output.• The objective is to concentrate on those products/services

that yield the largest contribution per limiting factor.

Example

Components X Y Z

Contribution per unit £12 £10 £6Machine hours per unit 6 2 1Estimated sales demand (units) 2 000 2 000 2 000Required machine hours 12 000 4 000 2 000 Contribution per machine hour £2 £5 £6Ranking per machine hour 3 2 1Capacity for the period is restricted to 12 000 machine hours.

• Profits are maximized by allocating scarce capacityaccording to ranking per machine hour as follows:

Machine hours Balance of machineProduction used hours available

2 000 units of Z 2 000 10 0002 000 units of Y 4 000 6 0001 000 units of X 6 000 –

The production programme will result in the following: 2 000 units of Z at £6 per unit contribution 12 0002 000 units of Y at £10 per unit contribution 20 0001 000 units of X at £12 per unit contribution 12 000

Total contribution 44 000

• Note that qualitative factors should be taken into account.



Decisions on replacement of equipment

• The original purchase cost of the old machine, its writtendown value and depreciation are irrelevant for decision-making.

Example

WDV of existing machine (remaining life of 3 years) £90 000Cost of new machine (expected life of 3years and zero scrap value) £70 000Operating costs (£3 per unit old machine)

(£2 per unit new machine)Output of both machines is 20 000 units per annumDisposal value of old machine now £40 000Disposal value of new and old machines (3 years time) Zero



• Total costs over a 3 year period are as follows:

(1) (2) (3)Retain Buy Difference

£ £ £

Variable operating costs: 20 000 units at £3 per unit (3 yrs) 180 00020 000 units at £2 per unit (3 yrs) 120 000 (60 000)

Old machine book value: 3-year annual depreciation charge 90 000Lump sum write-off 90 000

Old machine disposal value (40 000) (40 000)Initial purch. price of new machine 70 000 70 000

Total cost 270 000 240 000 30 000

• Note that the depreciation charge is not a relevant cost.• Columns 1 and 2 or just column 3 can be presented but it is

more meaningful to restate column 3 as follows:

Savings on variable operating costs (3 years) 60 000

Sale proceeds of existing machine 40 000

100 000

Less purchase cost of replacement machine 70 000

Savings on purchasing replacement machine 30 000



Outsourcing (make or buy decisions)

• Involves obtaining goods or services from outside suppliersinstead of from within the organization.

Example

A division currently manufactures 10 000 components perannum. The costs are as follows:

Total (£) Per unit (£)Direct materials 120 000 12Direct labour 100 000 10Variable manufacturing overhead costs 10 000 1Fixed manufacturing overhead costs 80 000 8Share of non-manufacturing overheads 50 000 5

Total costs 360 000 36

A supplier has offered to supply 10 000 components per annumat a price of £30 per unit for a minimum of three years. If thecomponents are outsourced the direct labour will be maderedundant. Direct materials and variable overheads areavoidable and fixed manufacturing overhead would be reducedby £10 000 per annum but non-manufacturing costs wouldremain unchanged. The capacity has no alternative uses.



• Assuming there is no alternative use of the released internalcapacity arising from outsourcing annual costs will be asfollows:

(1) (2) (3)Make Buy Difference

(£) (£) (£)Direct materials 120 000 120 000Direct labour 100 000 100 000Variable manufacturing overhead 10 000 10 000Fixed manufacturing overheads 80 000 70 000 10 000Non-manufacturing costs 50 000 50 000Outside purchase cost incurred/

(saved) 300 000 (300 000)

Total costs incurred/(saved) 360 000 420 000 (60 000)

• Columns 1 and 2 can be presented or just column 3 whichshows that the relevant costs of making are £240 000compared with £300 000 from outsourcing (buying).

• Where the released internal capacity arising fromoutsourcing can be used to generate rental income or aprofit contribution the lost income or profit contributionrepresents an opportunity cost associated with making thecomponents.

• Assume that the released capacity from outsourcingenables a profit contribution of £90 000 to be generated.The relevant costs of making will now be: Relevant costs (described above) £240 000Opportunity cost (Lost profit contribution) 90 000

Total relevant costs of making 330 000

Outsourcing is now the cheaper alternative.



Discontinuation decisions

• Routine periodic profitability analysis by cost objectsprovides attention-directing information that highlightsthose potential unprofitable activities that require moredetailed (special studies).

• Assume the periodic profitability analysis of sales territoriesreports the following:

Southern Northern Central Total£000 £000 £000 £000

Sales 900 1 000 900 2 800Variable costs (466) (528) (598) (1 592)Fixed costs (266) (318) (358) (942)

Profit/(Loss) 168 154 (56) 266

• Assume that special study indicates that £250 000 ofCentral fixed costs and all variable costs are avoidable and£108 000 fixed costs are unavoidable if the territory isdiscontinued.

• The relevant financial information is as follows: Keep Central Discontinue Difference

open Central£000 £000 £000

Variable costs 1 592 994 598Fixed costs 942 692 250

Total costs to be assigned 2 534 1 686 848Reported profit 266 214 52

Sales 2 800 1 900 900

• Columns 1 and 2 can be presented or just column 3 whichshows that the relevant revenues arising from keeping theterritory open are £900 000 and the relevant (incremental)costs are £848 000. Therefore Central provides acontribution of £52 000 towards fixed costs and profits.



Generating relevant cost information

• There are 3 main reasons why a cost accumulation systemis required to generate relevant cost information:

1. Many indirect costs are relevant for decision-making:

• The cost of many joint resources (e.g. support functioncosts) fluctuate according to the demand for them.

• Product introduction, discontinuation, redesigndecisions determine the demand for support functionresources and thus future costs.

• Costs of support functions are difficult to trace directlyto cost objects.

2. An attention directing system is required to identifypotentially unprofitable products that require moredetailed special studies:

• It is not feasible to periodically undertake special studiesfor all products or combination of product mixes.

3. Many product-related decisions are not independent:

• Focusing only on individual products ignores impactthat the culmination of many decisions will have onthose joint resources that fluctuate according to thedemand for them.



Types of cost systems

• Direct costing systems:

1. Indirect costs are not assigned to cost objects so thatonly contributions to indirect costs are reported.

2. Appropriate where the majority of costs are direct.3. Require that indirect costs are incorporated at the

special study stage.

• Traditional costing systems:

1. Use unsophisticated methods to allocate indirect coststo cost objects.

• ABC systems:

1. Use sophisticated methods to allocate indirect costs tocost objects.



A comparison of traditional and ABC systems

• Both systems use the two-stage allocation process.

• In the first stage traditional systems tend to allocate costs todepartments whereas ABC systems allocate costs toactivities:

(∴ ABC systems tend to have more cost centres/cost pools)

• In the second stage traditional systems rely on a smallnumber of volume-based cost drivers (typically directlabour or machine hours) whereas ABC systems use manysecond stage cost drivers.

• ABC systems seek to use only cause-and-effect cost driverswhereas traditional systems often rely on arbitraryallocation bases.

• ABC systems tend to establish separate cost driver rates forsupport departments whereas traditional systems mergesupport and production centre costs.



The two-stage allocation process (traditionalcosting system)


Overhead cost accounts(for each individual category of expenses e.g. property taxes, depreciation etc.)

Costcentre

1(normally

departments)

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The emergence of ABC systems

• Traditional systems were appropriate when:

1. Direct costs were the dominant costs

2. Indirect costs were relatively small

3. Information costs were high

4. There was a lack of intense global competition

5. A limited range of products was produced.



Errors from relying on misleading product costs

• Traditional costing systems use volume-based (e.g. directlabour and machine hours) second stage drivers but ifvolume bases are not the cause of indirect costs reportedcosts will be misleading.

Example

Products HV (a high volume product) and LV (a low volumeproduct) are two of several products produced by a company.HV is made in large batches and LV is made in small batches. HVconsumes 30% of DLH’s and LV consumes 5% but each productconsumes 15% of the batch-related indirect costs. Thetraditional system uses DLH’s as the cost driver and the ABCsystem uses the number of batches processed. All overheads(total = £1m) are batch-related .

• Reported product costs:

Traditional system ABC systemProduct HV Product LV Product HV Product LV

£ £ £ £Direct costs 310 000 40 000 310 000 40 000Overheads 300 000 50 000 150 000 150 000allocated (30%) (5%) (15%) (15%)profits/(losses) (10 000) 60 000 140 000 (40 000)Sales 600 000 150 000 600 000 150 000

• Traditional system reports misleading information — Inthe longer term overheads will not decline by £300 000 ifHV is discontinued.

• ABC allocates on a cause-and-effect basis and shows highlevel of resources consumed by LV — The 2 costing systemsreport different messages (Traditional = Drop HV ABC = Drop LV).

• Traditional system motivates the wrong strategy.



Designing ABC systems

1. Identify the major activities that take place in anorganization:

• The activities chosen should be at a reasonable level ofaggregation based on cost/benefit criteria.

• Choice of activities influenced by the total cost of theactivity centre and the ability of a single cost driver toprovide a satisfactory determinant of the cost of theactivity.

2. Assign costs to cost pools / cost centre for each activity:

• Costs assigned to activity cost pools will include directand indirect costs.

• Resource cost drivers used to assign indirect costs.• Reliability of cost information will be reduced if

arbitrary allocations are used to assign a significantproportion of costs to activities.

3. Determine the cost driver for each major activity:

• Drivers at this stage called activity drivers. They should: (a) provide a good explanation of costs of each

activity pool. (b) be easily measurable(c) the data should be easy to obtain and

identifiable with the product.• Activity cost drivers consist of three types (Transaction,

duration and intensity drivers).

4. Assign the cost of activities to products:

• The cost driver must be measurable so that it can beidentified with individual products.



Classification of activities

• Unit-level activities

1. Performed each time a unit of the product or service isproduced.

2. Resources are consumed in proportion to the number ofunits produced or sold.

3. Examples — Direct materials and labour, energy costsand expenses consumed in proportion to machineprocessing time.

• Batch-related activities:

1. Performed each time a batch of goods is produced.2. Costs vary with the number of batches made.3. Examples include set-ups, purchase ordering and first-

item inspection activities.

• Product/service sustaining activities:

1. Performed to enable the production of individualproducts or services.

2. Examples include activities related to maintaining anaccurate bill of materials, preparing engineering changenotices.

• Facility-sustaining (or business-sustaining) activities:

1. Performed to support the organization as a whole.2. Examples include plant management, property costs

and salaries of general administrative staff.3. Common to all products and services – ∴ not allocated

to products/services.



Activity-based profitability analysis

• Applies ABC hierarchical activity classification toprofitability analysis.

• Used for attention directing — claimed provides moreaccurate information.

• Hierarchical approach can be applied to different costobjects (e.g. products/services, customers, locations.)

• See sheet 11 for an illustration of the ABC hierarchicalprofitability analysis.

• Aim is to assign all organizational expenses to a particularhierarchical level where cause-and-effect cost assignmentscan be established.

• The approach helps to identify the impact of resourceconsumption of adding or dropping items at each level ofthe hierarchy.


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• ABC systems measure the cost of using resources and notthe cost of supplying resources:

Cost of resources = Cost of resources + Cost of unusedSupplied used capacity

• Periodic financial statements measure the cost of resourcessupplied (i.e. 15 000 orders at a cost of £300 000 in Example10.2).

• ABC systems measure the cost of resources used (i.e. 13 000 orders at a cost of £20 per order in Example10.2).

• The difference between the cost of resources supplied andthe cost of resources used represents the cost of unusedcapacity(i.e. 2 000 orders at £20 per order = £40 000)

• Unused capacity arises with committed resources becausethey must be acquired in discrete amounts in advance ofusage.

• With flexible resources supply can be continually adjustedto match exactly the usage of resources.

• Managers make decisions that will result in a change ofactivity usage(e.g. discontinuation decisions reduce cost of resourcesused and increase the cost of unused capacity).

• Cash flow consequences will only arise if action is taken toremove unused capacity by reducing spending on thesupply of resources.

• The periodic reporting of unused capacity signals the needfor a change in the spending on the supply of resources.



Example 10.2

(1) Resources supplied10 staff at £30 000 per year = £300 000 annual activity costCost driver = Number of orders processedAnnual quantity of cost driversupplied: (1 500 orders per employee) = 15 000 purchase ordersEstimated cost driver rate = £20 per purchase order

(£300 000/15 000 orders)

(2) Resources usedEstimated annual number oforders to be processed = 13 000Estimated cost of resources used assigned to parts/materials = £260 000 (13 000*£20)

(3) Cost of unused capacityResources supplied (15 000)– Resources used (13 000) at £20 per order = £40 000 (2 000*£20)



Selecting the cost driver denominator level

• The correct denominator activity level to use is the level ofcapacity supplied (practical capacity) and not theanticipated usage.

• Using anticipated usage in Example 10.2 would result in acost driver rate of £23.08 (£300 000/13 000) so that the costof unused capacity will be hidden in the cost driver raterather than being separately reported.

• Using anticipated usage would result in high cost driverrates in periods of low sales demand.

The ABC data base

• Ideally maintained at estimated standard costs andperiodically reviewed.

• In addition a cost and profitability audit of a firm’sproducts, customers and sales outlets should beperiodically undertaken.



ABC cost management applications

• ABC can be used for a range of cost managementapplications besides product costing.

Criticisms of ABC

• ABC unit costs must be used with care — They can suggestan inappropriate degree of variability.

• The concept of unused capacity within the resourceconsumption model is questionable for physical resources.

• Reported costs may not significantly differ from a lesscostly traditional system if indirect costs are a lowproportion of total costs.


PerformanceMeasures

Activities

Resources

Cost Objects

Cost Drivers

Process View

Cost Assignment View

PRICING DECISIONS AND PROFITABILITYANALYSIS

Economic theory

The optimum selling price is the price at which marginalrevenue equals marginal cost.


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Demand and output

Profit


Problems with applying economic theory

1. Difficult and costly to derive reasonably accurate estimatesof demand.

2. Difficult to estimate cost functions to determine marginalcost at different output levels for many different products.

3. Demand is influenced by other factors besides price.

4. Profit maximization assumed – firms may pursue othergoals.



Role of cost information in pricing decisions

• Price takers are those firms that have little control over theprices of their products or services.

• For price takers cost information is of vital importance indeciding on the output and mix of products and services.

• Price setters are those firms that have some discretion overthe setting of selling prices for their products or services.

• Cost information is of vital importance to price setters inmaking pricing decisions.

• Firms may be price setters for some of their products/services and price takers for others.

• Four situations will be considered:

1. A price setting firm facing a short-run pricing decision2. A price setting firm facing a long-run pricing decision3. A price taker firm facing a short-run product-mix

decision4. A price taker firm facing a long-run product-mix

decision



A price setting firm facing short-run pricingdecisions

• Applies where companies are faced with the opportunity ofbidding for one time special orders in competition withother suppliers.

• In this situation only the incremental cost of undertakingthe order should be taken into account.

• Given the short-term one-off nature of the opportunitymany costs will be non-incremental.

• Bids should be made at prices that exceed the incrementalcost and must meet the following conditions:

1. Sufficient capacity must be available to meet the order.

2. The bid price should not effect future selling prices andthe customer should not expect repeat business atshort-term incremental cost.

3. The order will utilize unused capacity for only a shortperiod and capacity will be released for use on moreprofitable opportunities.



A price setting firm facing long-run pricingdecisions

• Three scenarios considered:

1. Pricing customized products using cost-plus pricing.2. Pricing non-customized products using cost-plus

pricing or demand estimates.3. Pricing non-customized products using target costing.

• In the long-term a firm can adjust the supply of resourcesthat are committed to it – ∴ a product or service should bepriced to cover all of the resources that are committed to it.

• Price setters have stronger grounds for adopting ABC.

• Pricing customized products using cost-plus pricing:

1. An accurate costing system is required sinceundercosting will result in acceptance of unprofitablebusiness and overcosting in the loss of profitablebusiness.

2. To determine the selling price a full cost/long-run costshould be calculated and a mark-up added (i.e. a cost-plus selling price is determined — see sheets 11.11 and11.12 for a more detailed explanation).

3. Cost assignment for pricing should be based on directcost tracing or cause-and-effect assignments — Arbitraryallocations (e.g. some business/facility-sustaining costs)should be allocated using behavioural drivers or coveredwithin the mark-up.

4. ABC provides a better understanding of cost behaviourfor negotiating with customers the price and size of theorders.



A price setting firm facing long-run pricingdecisions (cont.)

• Pricing non-customized products (Cost-plus pricing):

1. Pricing decision involves large volumes to manycustomers of a single product/service.

2. Cost-plus pricing requires an estimate of sales volume todetermine unit cost in order to derive the cost-plusprice.

3. Recommended that cost-plus prices are estimated for arange of potential sales volumes (see Example 11.3(a) onsheet 11.7).

• Pricing non-customized products (Using demandestimates):

1. If approximations of demand can be derived they maybe preferable to using the cost-plus pricing approach.

(‘Crude estimates of demand may serve instead ofcareful estimates of demand but cost gives remarkablylittle insight into demand.’ — Baxter and Oxendfelt).

2. See Example 11.3(b) on sheet 11.7 for an illustration ofthe approach (Note that profits are maximized at a SP of£80 and how the information can be used for showingthe effects of other pricing policies).


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A price setting firm facing long-run pricingdecisions (cont.)

• Pricing non-customized products (Target costing):

1. Target costing is the reverse of cost-plus pricing — Thetarget selling price is the starting point.

2. Four stages are involved:

Stage 1: Determine the target price which customerswill be prepared to pay for the product.

Stage 2: Deduct a target profit margin from the targetprice to determine the target cost.

Stage 3: Estimate the actual cost of the product.Stage 4: If estimated actual cost exceeds the target cost

investigate ways of driving down the actualcost to the target cost.

3. Marketing factors and customer research provide thebasis for determining selling price (Not cost).

4. Emphasizes a team approach to achieving the targetcost.

5. Most suited to high sales volume products.



A price taker firm facing short-run product-mixdecisions

• Applies where opportunities exist for taking on short-termbusiness at a market determined selling price.

• Cost information required and the same conditions applyas those specified for a price setter facing short-term pricingdecisions.

• If short-term capacity constraints apply the product mixshould be based on maximizing contribution per limitingfactor (see Chapter 9).

A price taker firm facing long-run product-mixdecisions

• In the long-term a firm can adjust the supply of resourcesthat are committed to it – ∴ The sales revenue from aproduct or service should be sufficient to cover all of theresources that are committed to it.

• Periodic profitability analysis is required to ensure thatonly profitable products/services are marketed.

• Profitability analysis should be used as an attention-directing mechanism.

• Ideally ABC hierarchical profitability analysis should beused (see sheet 11.10).


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Cost-plus pricing

• Different cost bases and mark-ups can be used to determinethe cost-plus selling price:

Cost base Mark-up Cost-plus(£) % selling price

(£)(1) Direct variable costs 200 250 500(2) Direct non-variable costs 100(3) Total direct costs 300 70 510(4) Indirect costs 80(5) Total cost (excluding higher

level sustaining costs) 380 40 532(6) Higher level sustaining costs 60(7) Total cost 440 20 528

• Target mark-ups seek to provide a contribution to non-assigned costs and profit.

• Target mark-ups are also adjusted to reflect demand, typesof products, industry norms, competitive position, etc.

• Criticisms of cost-plus pricing:

1. Ignores demand2. Does not necessarily ensure that total sales revenue will

exceed total cost.3. Can lead to wrong decisions if budgeted activity is used

to unitize costs.4. Circular reasoning — Volume estimates are required to

estimate unit fixed costs and ultimately price.



Cost-plus pricing (cont.)

• Reasons for using cost-plus pricing:

1. May encourage price stability

2. Demand can be taken into account by adjusting thetarget mark-ups.

3. Simplicity

4. Difficulty in applying sophisticated procedures where afirm markets hundreds of products/services.

5. Used as a guidance to setting the price but other factorsare also taken into account.

6. Applied to only the relatively minor revenue items.

Pricing policies

• Price-skimming

• Penetration pricing

• Pricing policies may vary depending on the different stagesof a product’s life cycle.


RISK AND UNCERTAINTY

1. The decision-making model involves the following stages:

(i) Identify objectives.(ii) Search for possible courses of action.(iii) Identify potential events or states of nature.(iv) List possible outcomes for each state of nature applying

to each alternative course of action.(v) Measure the pay-off for each alternative course of

action.(vi) Select course of action.

2. Probabilities are used to measure the likelihood that anevent or stature will occur.

3. A probability distribution lists all possible outcomes for anevent and the probability that each will occur:

Student A Student Bprobability probability

Outcome:Pass examination 0.9 0.6Do not pass 0.1 0.4

1.0 1.0

4. Probability distributions provide more meaningfulinformation than stating the most likely outcome (i.e. bothstudents will pass).



1. Instead of presenting probability distributions for eachalternative, two summary measures are often used:

(i) expected value.(ii) standard deviation.

2. The expected value is the weighted average of the possibleoutcomes. It represents the long-run average outcome ifthe decision were to be repeated many times.

Example

Product A probability distribution

(1) (2) (3)Estimated Weighted (col. 1

Outcome probability amount × col. 2)£

Profits of £6 000 0.10 600

Profits of £7 000 0.20 1 400

Profits of £8 000 0.40 3 200

Profits of £9 000 0.20 1 800

Profits of £10 000 0.10 1 000

1.00 8 000 Expected value



Product B probability distribution

(1) (2) (3)Estimated Weighted (col. 1

Outcome probability amount × col. 2)£

Profits of £4 000 0.05 200

Profits of £6 000 0.10 600

Profits of £8 000 0.40 3 200

Profits of £10 000 0.25 2 500

Profits of £12 000 0.20 2 400

1.00 8 900 Expected value

Which product should the company make?



1. Product C probability distribution

Estimated ExpectedOutcome probability value (EV)

£

Loss of £4 000 0.5 (2 000)Profit of £22 000 0.5 11 000

9 000

2. Product C has a higher EV than either products B or C, butit is subject to greater uncertainty.

3. The standard deviation is often used to measure thedispersion of the possible outcomes:

• SD of A = £1 096• SD of B = £2 142• SD of C = £13 000

4. The standard deviation measures dispersion around theexpected value, but does not measure downside risk. TheSD would increase if product C was replaced with £122 000instead of £22 000, but does this make the product morerisky?

5. The coefficient of variation V is a relative measure of risk:

V =

For example, a SD of 200 with an EV of 2 000 has the samerelative variation as a SD of 2 000 with an EV of 20 000.

6. Where possible, it is preferable to focus on probabilitydistributions rather than summary measures of EV and SD.

Standard deviation��

Expected value



Attitudes towards risk

1. The selection of an alternative is influenced by anindividual’s attitude towards risk.

Example

Possible outcomes A B

Recession 90 0

Normal 100 100

Boom 110 200

Expected value 100 100

The probability of each outcome is �13

�.

2. The two alternatives have the same EV but different levelsof risk.

3. • A risk-seeker will prefer B.

• A risk-averter will prefer A.

• A risk-neutral individual will be indifferent between A and B.



Decision trees

Decision trees are useful for clarifying alternative courses ofaction and their potential outcomes.

Example

A company is considering whether to develop and market a newproduct. Development costs are estimated to be £180 000, andthere is a 0.75 probability that the development effort will besuccessful and a 0.25 probability that the development effortwill be unsuccessful. If the development is successful, theproduct will be marketed, and it is estimated that:

(i) If the product is very successful, profits will be £540 000.

(ii) If the product is moderately successful, profits will be£100 000.

(iii) If the product is a failure, there will be a loss of £400 000.

Each of the above profit and loss calculations is after taking intoaccount the development costs of £180 000. The estimatedprobabilities of each of the above events are as follows:

(i) Very successful 0.4

(ii) Moderately successful 0.3

(iii) Failure 0.3


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men

t

Do

not d

evel

oppr

oduc

t


Maximin, maximax and regret criteria

1. Can be applied where it is not possible to assignmeaningful probabilities to alternative courses of action.

ExampleLow High

demand demand

Machine A £100 000 £160 000Machine B £10 000 £200 000

2. With the maximin technique the largest payoff is selectedbased on the assumption that the worst possible outcomewill occur.Machine A = £100 000Machine B = £10 000Decision = Choose product A

3. With the maximax technique the largest payoff is selectedassuming the best possible outcome will occur.Machine A = £160 000Machine B = £200 000Decision = Choose product B

4. The aim of the regret criterion is to minimize themaximum possible regret.

Regret tableLow High

demand demandoccurs occurs

Choose machine A 0 £40 000Choose machine B £90 000 0

The maximum regret is £40 000 for A and £90 000 for B.Therefore, choose A.



Portfolio approach

1. Alternatives should not be considered in isolation. Accountshould be taken of how they interact with existingactivities and other alternatives.

Example

States of nature Umbrella Ice-cream Combinedmanufacturing manufacturing activities

£ £ £

Sunshine –40 000 +60 000 +20 000

Rain +60 000 –40 000 +20 000

Assume there are only two possible states of nature.

2. Each activity is risky on its own, but when the activities arecombined risk is eliminated.


CAPITAL INVESTMENT DECISIONS

1. The objective is to accept all those investments whosereturns are in excess of the cost of capital.

2. A firm should invest in capital projects only if they yield areturn in excess of the opportunity cost of an investment(also known as the minimum rate of return, cost of capital,discount/hurdle rate).


%

5

5 7 13 18 21 24

1012

15

20A

B C D

E

F

MCC(cost of capital)

25

Investment projects (£m)


3. Opportunity cost of investment = returns available toshareholders in financial markets from investments withthe same risk as the project.


Expe

cted

ret

urn

on in

vest

men

t

10

15

RiskCompany X


Compounding and discounting

1. Compounding expresses today’s cash flows in future values.

FVn = V0 (1 + K)n

TotalEnd of year Interest earned investment

£ £

0 100 0000.10 × 100 000 10 000

1 110 0000.10 × 110 000 11 000

2 121 0000.10 × 121 000 12 100

3 133 1000.10 × 133 100 13 310

4 146 410

2. Discounting is the process of converting future cash flowsinto a value at the present time.

Present value (V0) =

3. £121 000 receivable in year 2 has a PV of:

= £100 000£121 000��(1 + 0.10)2

FVn�(1 + K)n



The concept of net present value (NPV)

1. By using DCF techniques and calculating PVs we cancompare the return on capital projects with an alternativeequal risk investment in securities traded in the financialmarket.

2. The four projects shown below are identical to the risk-freesecurity illustrated on sheet 13.3. Therefore, they have aNPV of zero.

A B C D£ £ £ £

Project investment outlay 100 000 100 000 100 000 100 000

End of year cash flows:

Year 1 110 000 0 0 0

Year 2 0 121 000 0 0

Year 3 0 0 133 100 0

Year 4 0 0 0 146 410

Present value = 110 000 121 000 133 100 146 410

1.10 (1.10)2 (1.10)3 (1.10)4

= 100 000 = 100 000 = 100 000= 100 000

3. NPV = PV – Investment cost

4. The decision rule is to accept only those projects withpositive NPVs (e.g. if the investment costs above were lessthan £100 000 then the projects would be preferable toinvesting in financial securities and they would havepositive NPVs).



Calculating NPVs

1. NPV = �(1

F+V1

K)� + �

(1F+V

K2

)2� + �(1

F+V

K3

)3� + �(1

F+V

Kn

)n� – I0

2. Example (£000’s)

NPV = �£13.010

0� + �£

(11

.01

00

0)2� + �

(£14.10

00

)3� – £1 000 = + £399.7

or use the discount tables (appendix A):

DiscountYear £000’s factor PV (£000)

1 300 0.9091 272.7302 1 000 0.8264 826.4003 400 0.7513 300.520

1 399.650

Less investment cost 1 000.000

NPV 399.650

3. If annual cash flows are constant, the cumulative discounttables can be used (appendix B):

Example (000’s)

Cash flows are £600 p.a. for three years, the discount rate is 10%and the investment outlay is £1 000.

NPV = (£600 × 2.487) – £1 000 = £492.2



Internal rate of return (IRR)

1. IRR is the discount rate that will cause the NPV to be zero.

NPV = �1 +

FVIR

1

R� + �

(1 +FV

IR2

R)2� + �(1 +

FVIR

n

R)n� – I0 = 0

Example (£000’s)

NPV = �1

£+300.031

� + �(1

£+1

00

.03

01)2� + �

(1£+

400.30

1)3� – £1 000 = 0

2. IRR is approximately 31%. The decision rule is to accept theproject if IRR is greater than the cost of capital.

3. ExampleNPV at 25% = + £84.8 (say 85)

NPV at 35% = –£66.53 (say 67)

Using interpolation:

IRR = 25% + �18552

� × (35% – 25%) = 30.59%



The calculation of IRR


NPV

(£)

+400

+300

+200

+100

05 10 15 20 25 30 35 40

–100

NPV = +85

NPV = –130

Discount rate

NPV = –67

Line A

Line B


Comparison of NPV and IRR

1. NPV is preferred to IRR because:

• IRR can incorrectly rank mutually exclusive projects.

IRR NPV% £

Project A 22 1 530Project B 18 1 728

• IRR is expressed in percentage terms:

Investment Y yields a return of 50% (I0 = 100) = £50Investment Z yields a return of 25% (I0 = £1 000) = £250If the remaining £900 from Y only yields £100 then Z ispreferable.

• IRR assumes internal cash flows are reinvested at the IRR,whereas NPV assumes they are invested at the cost ofcapital.

• Unconventional cash flows (–, +, –) can result in multiplerates of return.



Payback method

1. Measures the length of time that is required for a stream ofcash flows from an investment to recover the original cashoutlay required by the investment.

Year Year Year Year0 1 2 3 Payback NPV at 10%

£000’s £000’s £000’s £000’s

A –400 +400 1 year –36.364B –400 +200 +200 +1000 2 years +698.422

The payback method suggests A but B has the higher NPV.

2. Limitations

• Ignores time value of money.

• Ignores cash flows after the payback period.

3. Widely used

• Simple to understand.

• Appropriate where liquidity constraints exist and a fastpayback is required.

• Appropriate for risky investments in uncertain markets.

• Often used as an initial screening device.



Accounting rate of return

1. Calculated by dividing the average annual profits from aproject into the average investment cost.

Project X

Years0 1 2 3

£000’s £000’s £000’s £000’s

Book value 24 16 8 0Cash flow 12 11 10Depreciation (8) (8) (8)Profit 4 3 2

Average return = = 25%

2. Project YYears

0 1 2 3£000’s £000’s £000’s £000’s

Book value 24 16 8 0Cash flow 10 11 12Depreciation (8) (8) (8)Profit 2 3 4

Average return = �132� = 25%

3. Project Y also has a 25% return, but the cash flows arereceived later and NPV is less than X.

Average profit (3)��Average investment (12)



The effect of performance measurement

• In the diagram below the cash flows and (profits) are shownfor projects J and K (initial cost for both projects = £5m)

• Project J is preferable but if the manager focuses on the short-term profit measure he or she may be motivated to acceptproject K


Year 1

+£2m (+£1m)

+£0.5m (–£0.5m)

Year 2

+£1.5m (+£0.5m)

+£0.5m (–£0.5m)

Year 3

+£0.5m (–£0.5m)

+£2m (+£1m)

Year 4

+£0.5m (–£0.5m)

+£3m (+£2m)

Year 5

+£0.5m (–£0.5m)

+£5m (+£4m)

Project J (+NPV)

Project K (–NPV)


The effect of performance measurement

There is a danger that managers will be motivated to choose theinvestment that maximizes their performance measure ratherthan maximizing NPV.

NPV calculations (decision model)

X Y X£000’s £000’s £000’s

Machine cost initial outlay (time zero) 861 861 861Estimated net cash flow (year 1) 250 390 50Estimated net cash flow (year 2) 370 250 50Estimated net cash flow (year 3) 540 330 1 100Estimated NPV at 10% cost of capital 77 (52) 52Ranking 1 3 2

Performance measurement criteria

Profits X Y Z£000’s £000’s £000’s

Year 1 (37) 103 (237)Year 2 83 (37) (237)Year 3 253 43 813

Total profits 299 109 339

Return on investments X Y Z% % %

Year 1 (4.3) 11.9 (27.5)Year 2 14.5 (6.4) (41.3)Year 3 88.1 15.0 283.2Average 32.8 6.8 71.5



Capital investments with unequal lives

• Machines A and B are two mutually exclusive machinesA’s life = 3 years and B’s life = 2 years

• Can we base the decision on the NPV or IRR’s of eachmachine?

(Only if the task for which they are required ceases atthe end of the project lives).

• What if the task for which the machines are required is formany years (say > 6 years)?

We are faced with a replacement chain problem and aslong as the common denominator for the project lives isless than the task life we can use either the lowestcommon multiple method or the equivalent annualcash flow method.

• Lowest common denominator method: Lowest common multiple = 6 years (2 replacements ofmachine A and 3 of B)

Cash outflows (£000’s) for a sequence of type A machines:

Year 0 1 2 3 4 5 6Initial outlay 1 200 1 200Operating costs 240 240 240 240 240 240PV at 10% = 3 146.8

Cash outflows (£000’s) for a sequence of type B machines:

Year 0 1 2 3 4 5 6Initial outlay 600 600 600Operating costs 360 360 360 360 360 360PV at 10% = 3 077.1

Decision = Choose sequence of type B machines (lowest PV ofcash outflows).



• Equivalent annual cost (cash flow) method:

1. The costs are made comparable by converting the cashflows to an equivalent annual cost (EAC).

2. EAC = PV of costs / Annuity factor for n years at R%

3. EAC for A =£1 796.8/2.4869 (Based on years 0–3) or

£3 146.8/4.3553 (Based on years 0–6)

=£722.5 for both time periods

4. EAC for B =£705.7 (calculated as above)

5. The cash flow stream of A is equivalent in PV terms to anannual cash flow of £722.5 (£705.7 for B) – ∴ Choose B

• Assume the task life < lowest common denominator

Task life = 10 years

Machine X life = 6 years

Machine Y life = 8 years

Lowest common multiple is 24 years

Suggest use a 10 year horizon with each machine beingreplaced once and incorporate an estimate machinerealisable values at the end of year 10.



Single period capital rationing

1. Refers to a situation where investment funds are restrictedand it is not possible to accept all positive NPV projects.

2. Where capital rationing exists, ranking in terms of NPVswill normally result in an incorrect allocation of scarcecapital.

3. The correct approach is to rank by profitability index (PI):

PI =

4. Example

Project NPV PII0 PV NPV PI ranking ranking£ £ £

A 25 000 32 500 7 500 1.30 6 2B 100 000 108 250 8 250 1.08 5 6C 50 000 75 750 25 750 1.51 1 1D 100 000 123 500 23 500 1.23 2 3E 125 000 133 500 8 500 1.07 4 7F 25 000 30 000 5 000 1.20 7 4G 50 000 59 000 9 000 1.18 3 5

Funds available for investment are restricted to £200 000.

5. NPV ranking leads to acceptance of C, D and G (NPV = £58 250).

PI ranking leads to acceptance of C, A, D and F (NPV = £61 750).

PV��Investment outlay



Taxation and investment decisons

1. Taxation legislation specifies that net cash inflows ofcompanies are subject to taxes, and capital allowances(writing down allowances) are available on capitalexpenditure.

ExampleI0 = £100 000, cash inflows = £50 000 for four yearsEstimated sale proceeds = Tax WDV at end of year 4Capital allowances = 25% on a reducing balance basisCorporate tax rate = 35%

2. Calculation of capital allowances

AnnualYear WDAs WDV

£0 0 100 0001 25 000 (25% × 100 000) 75 0002 18 750 (25% × 75 000) 56 2503 14 063 (25% × 56 250) 42 1874 10 547 (25% × 42 187) 31 640

3. Calculation of incremental taxes arising from the project:

Year Year Year Year1 2 3 4£ £ £ £

Incremental profits 50 000 50 000 50 000 50 000WDAs 25 000 18 750 14 063 10 547Taxable profits 25 000 31 250 35 937 39 453Taxes at 35% 8 750 10 937 12 578 13 809



Taxation and investment decisions

4. If the estimated sale proceeds exceeded the WDV (say,£45 000) there would also be an additional balancingcharge of £13 360 (£45 000 – £31 640) to deduct from theWDAs in year 4 (taxable profits would equal £52 813).

5. If the estimated sale proceeds were less than the WDV (say£25 000) there would be an additional balancing allowanceof £6 640 (£31 640 – £25 000) to add to the WDAs in year 4.



Dealing with inflation

• Inflation affects both future cash flows and interest rates(i.e. RRR /discount rate)

Impact on Cash Flows

• Assume no inflation and estimated cash flows of £100 attime 1 and you can buy a basket of goods for £1 at time 0

∴ Your cash flow has the potential of buying 100 baskets attime 0 or time 1.

• Assume now estimated inflation is 10%

Estimated cash flows at time 1 = £110

The cash flows have increased but your purchasing power isunchanged ( You still have the potential to purchase 100baskets i.e. £110 / £1.10)

• Cash flows can be expressed in monetary units at the timethey are received (i.e. nominal cash flows = £110 at time 1)

or

they can be expressed in today’s (time zero) purchasingpower (i.e. real cash flows = £110 / £1.10 = £100)

∴ £110 nominal cash flows is equivalent to £100 in realcash flows.

• Nominal CF’s = Real CF’s × (1 + inflation rate)n

= £100 (1.10)1 = £110

• Real CF’s = = £110 / 1.101 = £100

REAL CASH FLOWS ARE WHAT THE CASH FLOWS WOULD BEIN A WORLD OF NO INFLATION

Nominal CF’s��(1 + inflation rate) n



Impact of inflation on interest rates (also discount rates)

• Assume the interest rate is 2% in a world of no inflation

∴ You require £102 for an investment of £100 (providespurchasing power to purchase 102 baskets)

• Now assume the anticipated rate of inflation is 10%

You require a NOMINAL return of 12.2% to maintain yourpurchasing power (£112.20 / £1.10 = 102 baskets)

• REAL RATE OF INTEREST RATE = WHAT THE INTERESTRATE WOULD BE IN A WORLD OF NO INFLATION

1 + Nominal rate= (1 + Real rate) × (1 + Est. inflation rate)= (1 + 0.02) × (1 + 0.10) = 1.122 = 12.2%

1 + Real rate = (1 + Nominal rate) / (1 + Est. inflation rate)= (1 + 0.122) / (1 + 0.10) = 1.02 = 2%

• Approximations may suffice 2% real rate + 10% inflationrate = 12% approximation

• Note that interest rates and RRR’s on securities are derivedfrom current financial market data (∴ they will already beexpressed in nominal terms)



Investment appraisal and inflation

• Two correct approaches: 1. Discount nominal cash flows at a nominal discount rate2. Discount real cash flows at the real discount rate

Example

A company is appraising a project with an investment outlay of£200,000 with estimated annual cash inflows of £100,000 perannum for years 1, 2 and 3. The cost of capital is 9% and theexpected rate of inflation is zero.

NPV = 100 / (1.09) + 100 / (1.09)2 + 100 / (1.09)3 – 200 = 53.1

NOW ASSUME ANTICIPATED RATE OF INFLATION = 10%

1. Discount nominal cash flows at the nominal discount rate

NPV = + + – 200 = 53.1

2. Discount real cash flows at the real discount rate

NPV = 100 / (1.09) + 100 / (1.09)2 + 100 / (1.09)3 – 200 = 53.1

• We have assumed that current price cash flows are equivalentto real cash flows but this only applies if all company cashflows are subject to the general rate of inflation.

WHAT IF THE CASH FLOWS ARE SUBJECT TO A SPECIFICRATE OF INFLATION OF 8% AND THE GENERAL RATEFOR THE ECONOMY IS 10%?

We must calculate real cash flows as follows:

Year 1 = 100 (1.08) / 1.10 ; Year 2 = 100 (1.08)2 / (1.10)2

In these circumstances it is easier to discount nominal cashflows at a nominal discount rate.

100 (1.10)3

��(1.09)3 (1.10)3

100 (1.10)2

��(1.09)2 (1.10)2

100 (1.10)��(1.09) (1.10)



Calculating risk adjusted discount rates

1. The returns which shareholders require from investing inrisky securities = Risk free rate + Risk premium.

2. The greater the risk, the greater the return required byinvestors.

3. The market portfolio is used as a benchmark fordetermining risk/return relationships. The risk of aninvestment relative to the market portfolio is measured bybeta:

• An investment with identical risk to the marketportfolio will have a beta of 1.

• An investment half as risky as the market portfolio willhave a beta of 0.5.

• An investment twice as risky as the market portfolio willhave a beta of 2.

4. The return that shareholders require (i.e. the opportunitycost of an investment) is:

• Risk free rate + (Risk premium × Beta) = CAPM formula

5. The past average risk premium of 8% (defined as the returnon the market portfolio less the risk free rate) is normallyused. If the risk free rate is 9% then the following returnswill be required:

• Security A (Beta of 1) = 9% + (8% × 1) = 17%• Security B (Beta of 0.5) = 9% + (8% × 0.5) = 13%• Security C (Beta of 2) = 9% + (8% × 2) = 25%

6. Note the risk premium = (Return on the market – risk freerate)



The capital asset pricing model

Required return on a security = Rf + (Rm – Rf) × Beta


25

17

13

Security B

Security Aand marketportfolio

Security market line

Security C

9

0 0.5 1.0

Risk (beta)

Expe

cted

ret

urn

(%)

2.0

Rf


Weighted average cost of capital (WACC)

1. The CAPM is used to calculate the cost of equity finance.

2. Most firms use a combination of debt and equity financeand both sources of finance should be taken into accountwhen calculating the discount rate.

3. Where combinations of debt and equity are used, theWACC is used to discount project cash flows.

Example

Cost of equity capital = 18%

Cost of debt capital = 10%

Projects financed by 50% debt and 50% equity

WACC = (0.5 × 18%) + (0.5 × 10%) = 14%

4. The WACC represents the firm’s overall cost of capitalbased on the average risk of all the firm’s projects. If therisk of a project differs from average firm risk the WACCwill not reflect the correct risk-adjusted discount rate.



Traditional methods of measuring risk

1. Standard deviations and probability distributions2. Simulation 3. Sensitivity analysis

Standard deviations and probability distributions

Year 1 Year 2 Year 3Potential Probabil’y Cash Probabil’y Cash Probabil’y Cashstates of flows flows flowsnature (£m) (£m) (£m)A 0.10 10 0.10 –5 0.10 –10B 0.25 15 0.25 0 0.25 –5C 0.30 20 0.30 5 0.30 0D 0.25 25 0.25 10 0.25 5E 0.10 30 0.10 15 0.10 10

Expected value 20 5 0

• Expected NPV at 10% discount rate

= �(1

2.10

0)� + �

(1.510)2� + 0 – 20 = £2.314m

• Standard deviation of NPV = £8.21m

• There is no guidance as to whether a NPV of £2.314m issufficient to compensate for the risk involved (SD of£8.21m)

• Consider an alternative mutually exclusive investment thathas an expected NPV of £3m and a SD of £10m.

We cannot determine whether this is preferable to theabove investment

• To avoid prejudging risk CF’s should be discounted at therisk free rate



Simulation analysis

1. Where several variables (e.g. sales, costs, etc.) are uncertain,it may be appropriate to develop a simulation model.

Simplified example

Cash flows Cash flowsYear 1 Probabilities Year 2 Probabilities

£ £

10 000 0.10 –5 000 0.1015 000 0.25 0 0.2520 000 0.30 5 000 0.3025 000 0.25 10 000 0.2530 000 0.10 15 000 0.10

2. Numbers are assigned to the cash flows so that they exactlymatch their respective probabilities:

Year 1 Assigned Year 2 Assignedcash flows numbers cash flows numbers

£ £

10 000 1–10 –5 000 1–1015 000 11–35 0 11–3520 000 36–65 5 000 36–6525 000 66–90 10 000 66–9030 000 91–100 15 000 91–100

3. Numbers from 1 to 100 selected at random using computerruns, e.g. if 36 and 8 selected cash flows of £20 000 (year 1)and –£5 000 (year 2) will be selected and NPV calculated.

4. The process continues with many computer runs, whichare used to derive a probability distribution of NPVs. (Noterisk-free rate used as the discount rate.)



Sensitivity analysis

1. Shows how sensitive NPV is to a change in the assumptionsrelating to the variables used to compute it (e.g. pessimistic,most likely or optimistic estimates). Can also be used toindicate the extent to which variables may change beforeNPV becomes negative.

ExampleYear Year Year1 (£) 2 (£) 3 (£)

Cash inflows (10 000 × £30) 300 000 300 000 300 000VC 200 000 200 000 200 000

Net cash flows 100 000 100 000 100 000

I0 = £200 000, cost of capital = 15%, NPV = £28 300

2. Sales volume

• NPV = 0 when net cash flows are £87 600 (£200 000 /2.283)

• Total net cash flows can decline by £12 400 p.a. beforeNPV becomes negative

• Total sales can fall by £37 200 p.a. (i.e. 12.4%) or 1240units

• Note net cash flows are one-third of sales.

3. Selling price

• Total sales revenue can fall to £287 600 (£300 000 – £12400) before NPV becomes negative = £28.76 per unit (i.e.4.1% decline)

4. Variable costs

• Can increase by £12 400 p.a. (£1.24 per unit) = 6.2%decline.

5. Initial outlay

• Can increase by £28 300 (14.15%).



Sensitivity analysis (cont.)

6. Cost of capital

• IRR = 23% (cost of capital can increase by 53%).

7. Highlights those variables that are most sensitive so thattheir estimates can be thoroughly reviewed.

8. Limitations

• Considers variables in isolation.

• Ignores probabilities



Classification of risk measurement techniques

1. CAPM approach• Risk is compared relative to the variability with the

market portfolio.• Risk is divided into two categories:

(i) Specific (diversifiable) risk(ii)Market (non-diversifiable) risk

• CAPM assumes specific risk can be avoided and it is notrewarded.

• CAPM assumes market rewards only non-diversifiablerisk.

2. Stand-alone risk measurement approach• Does not distinguish between specific and non-

diversifiable risk.• Does not provide a basis for determining the rates of

return required for different levels of risk.

3. Corporate portfolio risk measurement approach• Focuses on incremental total risk arising from a project.• Recognizes that incremental risk may not be the same

as the total risk of the project.

Example

SD of project X = £10 000SD of existing projects = £60 000SD of existing projects plus project X = £65 000Incremental risk of project X = £5 000 (not £10 000)

• Does not distinguish between specific and non-diversifiablerisk.

• Difficult practical problems in measuring risk of existingprojects


THE BUDGETING PROCESS

An overview of the planning process

1. Identify the objectives of the organization.

2. Identify potential strategies.

3. Evaluate alternative strategic options.

4. Select course of action.

5. Implement the long-term plan in the form of the annualbudget.

6. Monitor actual results.

7. Respond to divergencies from plan.


1. Identify objectives

6. Monitor actual results

2. Identify potentialcourses of action (i.e. strategies)

3. Evaluate alternativestrategic options

4. Select alternative coursesof action

5. Implement long-term plan inthe form of the annual budget

7. Respond todivergencies from plan

Long-termplanningprocess

Annualbudgetingprocess


Why do we produce budgets?

1. To aid the planning of actual operations:

• by forcing managers to consider how conditions mightchange and what steps should be taken now.

• by encouraging managers to consider problems beforethey arise.

2. To co-ordinate the activities of the organization:

• by compelling managers to examine relationshipsbetween their own operation and those of otherdepartments.

3. To communicate plans to various responsibility centremanagers:

• everyone in the organization should have a clearunderstanding of the part they are expected to play inachieving the annual budget.

• by ensuring appropriate individuals are madeaccountable for implementing the budget.

4. To motivate managers to strive to achieve the budget goals:

• by focusing on participation

• by providing a challenge/target.

5. To control activities:

• by comparison of actual with budget (attentiondirecting/management by exception).

6. To evaluate the performance of managers:• by providing a means of informing managers of how

well they are performing in meeting targets they havepreviously set.



Stages in the budgeting process

1. Communicate details of budget policy and guidelines tothose people responsible for preparing the budget.

2. Determine the factor that restricts output.

3. Preparation of the sales budget.

4. Initial preparation of budgets.

5. Negotiation of budgets with higher management.(See figure on sheet 15.4)

6. Co-ordination and review of budgets.

7. Final acceptance of budgets.

8. Ongoing review of the budgets.



An illustration of budgets moving up theorganization hierarchy


762

Manager of plant 1 Manager of plant 2

Production manager

3 4 51 8

Dept A Dept B Dept C Dept D


Activity-based budgeting (ABB)

• Conventional budgeting is inappropriate for thoseactivities where the consumption of resources does notvary proportionately with the volume of the final output ofproducts or services.

• For support activities conventional incremental budgetsmerely serve as authorization levels for certain levels ofspending.

• Incremental budgeting results in the cost of non-unit levelactivities becoming fixed.

• ABB aims to authorize only the supply of those resourcesthat are needed to perform activities required to meetbudgeted production and sales volumes.

• The ABB process is the reverse of the ABC process:

Budgeted output of cost objects

Determine the necessary activities

Determine the resources required for the budget period



• ABB involves the following stages:

1. Estimate the production and sales volume by individualproducts and customers.

2. Estimate the demand for organizational activities.(e.g. Process 5,000 customers’ orders for thecustomer order processing activity)

3. Determine the resources that are required to performorganizational activities.

(e.g. 0.5 hours per order = 5,000 × 0.5 hours =2,500 labour hours for the customer processingactivity must be supplied)

4. Estimate for each resource the quantity that must besupplied to meet the demand.

(e.g. Assume a step cost function with eachperson employed contracted to work 1,500 hoursper year so that quantity of resources required =2,500/1,500 = 1.67 persons meaning that 2persons must be employed)

5. Take action to adjust the capacity of resources to matchthe projected supply.

(e.g If 3 persons are presently employed on theactivity resources must be reduced, or redeployed,by one person)



• Periodically actual results should be compared with anadjusted (flexible) budget.

Example

Budgeted activity for processing orders = 2,800 ordersOrders processed per person = 600Resources required = 4.67 personsResources supplied (practical capacity for 3,000 orders) = 5 personsEmployment costs (£25,000 per person per year) = £125,000Cost driver rate (£125,000/3,000 orders) = £41.67Actual orders processed for the period = 2,500 orders

Performance report: Flexed budget (2,500 × £41.67) = £104,175Budgeted unused capacity (3,000 — 2,800) × £41.67 = 8,334Unplanned unused capacity (2,800–2,500) × £41.67 = 12,491

125,000

• Above represent committed resources but for flexibleresources (e.g. office supplies) resources supplied can bematched exactly to resources demanded.

• See sheet 8 for an illustration of an activity-based budget foran order processing activity.


TH

E B

UD

GET

ING

PR

OC

ESS

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MANAGEMENT CONTROL SYSTEMS

Different types of controls

• Action (or behavioural) controls

• Personnel and cultural (or clan and social) controls

• Results (or output controls)

Action (or behavioural) controls

• Consist of: • Behavioural constraints

• Preaction reviews

• Action accountability

• Focus should be on prevention rather than detectioncontrols.

Social, personnel and cultural controls

• Social controls involve selection of people who have beensocialized into adopting particular norms of behaviour.

• Personnel controls build on employees natural tendenciesto control themselves (Emphasis is on selection, trainingand job design).

• Cultural controls represent a set of values, social norms andbeliefs that are shared by members of an organization andthat influence their actions.

• In recent years there has been a greater emphasis oncultural controls in the form of employee empowerment.



Results or output controls

• The focus is on reporting information about the outcomesof work effort.

• Results controls involve the following stages:

1. Establishing performance measures that minimizeundesirable behaviour.

2. Establishing performance targets.

3. Measuring performance.

4. Providing rewards or punishments.

Cybernetic control systems

• Results controls resemble a cybernetic (mechanical) controlsystem.

• Cybernetic systems involve feedback controls (actions afterthe events) but ideally control should be based on controlactions before the events.

A cybernetic control system


Input Process

Feedback FeedbackAutomaticregulator

Output


Harmful side-effects of controls

1. Occurs when controls motivate employees to engage inbehaviour that is not organizationally desirable (i.e. systemleads to a lack of goal congruence).

2. Results controls:

• Encourages individuals to focus only on what ismeasured, regardless of whether it is organizationallydesirable (see sheet 16.4)

• Focuses mainly on quantifiable and easily measurableitems.

• Subject to data manipulation.

• Can lead to negative attitudes towards the controlsystem.

3. Action controls:

• May discourage creativity

4. Cultural controls:

• Lack of goal congruence where group goals do notcoincide with firm goals



Fig. 16.2 — The measurement reward process with imperfectmeasures


System oforganizational

rewards

Organizationalgoals

Formal performancemeasurement

system

Individualmanager’s

goals

A Behaviour necessary to achieve organizational goalsB Behaviour actually engaged in by an individual managerC Behaviour formally measured by control systems

A

B

C

Source: Otley (1987)


Advantages and disadvantages of different typesof controls

• Personnel/cultural controls:

• Few harmful side-effects

• Inexpensive to operate

• Appropriate only in certain circumstances

• Action controls:

• Direct link between control mechanism and the action.

• Measurement problems do not apply.

• Not feasible where cause-and-effect relationships are notwell understood or easily observable.

• Best suited to stable situations.

• Results controls:

• Can be applied where knowledge of what actions aredesirable is lacking.

• Focus is on outcomes (individual autonomy is notrestricted).

• Subject to limitations described on sheet 16.3.



Management accounting control systems (MACS)

• Tend to be the predominant controls in most organizationsbecause:

• Monetary measure provides a means of aggregatingresults from dissimilar activities.

• Profitability and liquidity are essential for companysurvival.

• Financial measures enable a common decision rule tobe applied.

• Measuring results in financial terms enables managersto be given more autonomy.

Responsibility accounting

• Responsibility accounting is a fundamental part of theMACS.

• Four types of responsibility centres:

1. Cost or expense centres (Two types: standard costcentres and discretionary cost centres).

2. Revenue centres

3. Profit centres

4. Investment centres



The nature of MACS

• Two core elements:

1. Formal planning processes (e.g. budgeting and long-term planning) for establishing performanceexpectations.

2. Responsibility accounting

• Responsibility accounting assigns differences from theperformance target to the individual who is accountable forthe responsibility centre.

• Process involves:

1. Setting performance targets.2. Measuring performance.3. Comparing performance against target.4. Analysing variances and taking remedial actions.

• Responsibility accounting is implemented by issuingperformance reports similar to that on sheet 16.8.

• Issues that must be addressed by responsibility accountinginclude:

1. Distinguishing between controllable and non-controllable items (i.e. the controllability principle).

2. Determining how challenging the targets should be.3. Determining how much influence managers should

have in the setting of targets.



A typical performance report

Performance report to Managing director

Budget Variance F(A)Current Year to This Year tomonth date month date

£ £ £ £

Factory A 453 900 6 386 640 (80 000) (98 000)Factory B X X X XFactory C X X X XAdministration costs X X X XSelling costs X X X XDistribution costs X X X X

2 500 000 30 000 000 (400 000) (600 000)

Performance report to production manager of factory A

Works manager’s office X X X XMachining department 1 165 600 717 600 (32 760) (89 180)Machining department 2 X X X XAssembly department X X X XFinishing department X X X X

453 900 6 386 640 (80 000) (98 000)

Performance report to head of machining department 1

Direct materials X X X XDirect labour X X X XIndirect labour X X X XIndirect materials X X X XPower X X X XMaintenance X X X XIdle time X X X XOther X X X X

165 600 717 600 (32 760) (89 180)



The controllability principle

• Principle advocates that it is appropriate to charge to aresponsibility centre only those costs that can beinfluenced by the manager of the responsibility centre.

• Implemented by either eliminating uncontrollables orreporting controllable and uncontrollable items separately.

• Types of uncontrollable factors:

1. Economic and competitive factors (Because managerscan respond to some of these changes most MACS donot shield managers completely from them).

2. Acts of nature (Managers normally protected from them).3. Interdependencies where outcomes are affected by

other units within the organization:

• Pooled interdependencies• Sequential interdependencies• Reciprocal interdependencies

• Adjustments for the distorting effects of uncontrollablescan be made either before or after the measurement period.

• Adjustments before the measurement period:

1. Specify which budget line items are uncontrollable(eliminate or report separately in performance report).

2. Insurance

• Adjustments after the measurement period:

1. Variance analysis2. Flexible performance standards (e.g. flexible budgeting

and ex post budget adjustments)3. Relative performance evaluations4. Subjective performance evaluations



An example of flexible budgeting

Budgeted activity = 20,000 units Actual activity = 24,000 unitsBudgeted unit variable cost = £5 Actual variable costs = £105,000

Original fixed budget Flexible budget Actual Reportedcost variance

20,000 × £5 = £100,000 24,000 × £5 = £120,000 £105,000 £15,000F

• Ensures that managers are accountable for the conditions applyingduring the period and not those envisaged when the budget wasset.



Guidelines for applying the controllabilityprinciple

• Price and quantity of service controllable = Controllableexpense

• Quantity controllable but not price = Manager accountablefor difference between (actual quantity × budgeted price)and (budgeted quantity × budgeted price)

• Quantity and price not controllable = Non-controllableexpense

• General principle = Hold managers accountable forperformance areas you want them to pay attention to.

Determining how challenging the targets shouldbe

• A clearly defined quantitative goal is likely to motivatehigher levels of performance.

• Level of budget difficulty should be related to taskuncertainty.

• Targets must be accepted to motivate managers to achievehigher levels of performance.

• Literature identifies a theoretical relationship betweenbudget difficulty, aspiration levels and performance (seesheet 16.12).

• Hypothesized relationships suggest that budget level thatmotivates best performance is unlikely to be achieved mostof the time (∴ do not adopt a punitive approach for adversevariances)




Perf

orm

ance

Expectationsbudget

Optimalperformance budget

Adverse budgetvarience

Budgetlevel

Actualperformance

Budget difficultyEasy Difficult

Case

Expe

nse

leve

ls

1 2

(alternative budget levelsfrom very loose to very tight)

3

N N

b

b

b

bb

ar

ar

bar

b budget levela aspiration levelr result

ar

a

r

r

4 5 6

The effect of budget difficulty on performance (Source: Otley (1987))

The effect of budget levels on aspiration and performance (Source: Hofstede (1968))


Arguments in favour of setting highly achievablebudgets

• Conflict between planning and motivational purposes.• Psychological benefits (e.g. achievement and self-esteem).• Shields managers from adverse impact of environmental

changes.• Alleviates harmful side-effects of controls.

Determining how much influence managersshould have in setting standards

• Advantages of participation in the setting of performancestandards:

1. Targets more likely to be accepted2. Reduces the information asymmetry gap3. Reduces negative attitudes and dysfunctional behaviour

• Empirical studies provide conflicting evidence on theeffectiveness of participation.

• Factors influencing the effectiveness of participation:

1. Personality variables: • Authoritarianism • Locus of control

2. Work situation3. Job difficulty

• Limitations on the positive effects of participation:

1. Budgetee has the opportunity to negotiate lower targets.2. Depends on personality traits and work situation.3. A top down approach may be preferable where a large

number of similar units exist.



Side-effects arising from using accountinginformation for performance evaluation

• Hopwood observed three different styles of managerial useof accounting information for performance evaluation:

1. A budget-constrained style2. A profit-conscious style3. A non-accounting style

• Hopwood’s findings

Style of evaluationBudget- Profit- Non-

constrained conscious accounting

Involvement with costs High High LowJob-related tension High Medium MediumManipulation of

accounting information Extensive Little LittleRelations with superior Poor Good GoodRelations with colleagues Poor Good Good

• Otley replicated Hopwood’s study and found no significantdifferences in terms of budget-constrained and profit-conscious styles in terms of undesirable behaviour.

• Conflict in findings attributed to differences in managerialinterdependency and task uncertainty.


CONTINGENCY THEORY ANDORGANIZATIONAL ASPECTS OF MA

Contingency theory approach

• Advocates that there is no one best design of a managementaccounting control system (MACS) and that it all depends onthe situational (contingent) factors.

• The contingency theory literature has two strands —theoretical and empirical.

• Contingent factors can be grouped by major categories such as:

1. The external environment• Uncertain and certain• Static and dynamic• Simple and complex• Turbulent and calm

2. Competitive strategy and strategic mission• Low cost and differentiation• Defender and prospector• Product life cycle (Build, hold, harvest and divest)

3. Technology• Small batch, large batch, process production, mass

production• Interdependence (pooled, sequential, reciprocal)

4. Business unit, firm and industry variables• Firm size• Firm diversification (single product, related diversified

and unrelated diversified)• Organizational structure• Industry variables

5. Knowledge and observability factors• Knowledge of the transformation process• Outcome (output) observability• Behaviour (effort) observability



1. The external environment

• Evidence to suggest that business units that face higherenvironmental uncertainty use a more subjectiveperformance appraisal approach.

• The greater the perceived environmental uncertainty thegreater the need for more sophisticated accountinginformation that has a broad scope.

2. Competitive strategy and strategic mission

• Advocated that defenders (Miles and Snow) and businessunits pursuing a low cost strategy (Porter) should adoptresults measures that emphasize cost reductions and budgetachievement.

• Business units competing on the basis of differentiation(Porter) or those prospecting new markets should:

1. Have a more participative decision-making environment 2. Emphasize rewards based on non-financial factors (e.g.

product innovation, market development) besidessecondary financial measures.

• Evidence to suggest that:

1. Business units following a defender strategy place agreater emphasis on the use of financial measures forrewarding managers.

2. Non-financial measures for determining executives’bonuses increases with the extent to which firms followprospector strategies.

3. Businesses following a build strategy rely more on non-financial measures of performance for determiningmanagers’ bonuses.



3. Firm technology and interdependence

• The nature of the production process determines the typeof costing system (Job or process costing).

• Pooled, sequential and reciprocal interdependencies createthe need for recharging costs to user centres.

4. Firm size, diversification, structure andindustry type

• Positive relationship between firm size and thesophistication of the management accounting system.

• Related diversification:

1. Elaborate planning and budgeting systems tocoordinate activities.

2. Rewards based on group performance

• Unrelated diversification

1. Decentralization and the creation of profit andinvestment centres.

2. Greater reliance on financial results controls.

• Structure — Interdependence that exists betweenresponsibility centres determines style of budgetevaluation.

• Industry type influences type of control system employed.



5. Knowledge and observability factors

Four areas examined:

A. Knowledge of the transformation process and the ability tomeasure output.

B. Appropriate type of performance assessment in relation tocause-and-effect relationships.

C. Influence of programmability of decisions on the type ofcontrols that should be used.

D. Relationship between accounting information anduncertainty about objectives and uncertainty about cause-and-effect relationships.

A. Knowledge of the transformation process and the ability tomeasure output

• Above framework draws attention to those conditionswhere accounting-based control systems are inappropriateand places MACS within a broader framework of otherorganizational control systems.


Knowledge of the transformation process

Ability tomeasure output

Perfect

HighBehavioural and/oroutput measurement

Behaviouralmeasurement

“clan” control

Output measurement

1 2

3 4

Imperfect

Low

Uncertainty situations and control measurements(Source: Onchi, 1979)


B. Appropriate type of performance assessment in relation to cause-and-effect relationships.

• Efficiency is concerned with achieving a given result with aminimum use of resources (or achieving maximum outputfrom a given level of input resources).

• Measures of effectiveness focus on whether or not theaction resulted in the desired goal (i.e. Instrumental tests).

C. Influence of programmability of decisions on the type of controlsthat should be used

• A programmed decision is one where the decision issufficiently well understood for a reliable prediction of thedecision outcome to be made: 1. Equivalent to cell 1 in the two previous diagrams2. Behavioral and output controls are appropriate

• A non-programmed decision is where one has to rely onthe judgement of managers because there is no formalmechanism for predicting likely outcomes: 1. Equivalent to cells 2 and 4 in the two previous

diagrams. Management and Cost Accounting, 5th edition.


Task instrumentality(beliefs about cause/effect knowledge)

Goal (ends)

Complete

Efficienty testsClear andunambiguous

Ambiguous

Outputmeasurement

Social testsSocial tests

1 2

3 4

Incomplete

Assessment situations and appropriate tests


D. Relationship between accounting information and uncertaintyabout objectives and uncertainty about cause-and-effectrelationships

Figure 17.3 Uncertainty, decision-making and ideal informationsystems (Source: Earl and Hopwood, 1981)

• Answer machines – AIS is used to provide solutions toproblems (e.g. DCF, LP and EOQ models).

• Dialogue machines – AIS is used to encourage explorationand debate rather than providing answers.

• Learning machines – AIS is used to explore problems, askquestions, investigate the analysable parts of decisions andfinally resort to judgement (e.g. sensitivity analysis).

• Idea machines – AIS used to stimulate and trigger creativity.

• Actual uses:– Ammunition machines used instead of dialogue

machines (cell 2).– Answer machines used instead of learning machines

(cell 3).– Rationalisation machines used instead of ideas

machines (cell 4).17.6

Uncertainty about ojectives

Uncertainty ofcause and effect

Low

Low- Decision bycompromise

- Dialogue machines

- Decision bycomputation

- Answer machines

- Decision byjudgement

- Learning machines

- Decision byinspiration

- Idea machines

1 2

3 4

High

High

Management and Cost Accounting, 5th edition.© 2000 Colin Drury


Purposes of management accounting

1. A rational/instrumental purpose:

• Assumes that the role of management accounting is toaid rational economic decision making.

• This role is appropriate when task instrumentality iswell understood and objectives are well understood.

2. A symbolic purpose:

• Accounting information is used to signal to othersinside and outside the organization that decisions arebeing taken rationally and that managers in theorganization are accountable.

• Managers can find value in AIS for symbolic purposeseven when the information has little or no relation todecision-making.

3. A political/bargaining purpose:

• Accounting information is used to achieve politicalpower or a bargaining advantage.

4. A legitimating/retrospective rationalizing purpose:

• Accounting information is used to justify and legitimiseactions that have already been decided upon (i.e. endowpast actions and decisions with legitimacy).

5. A repressive/dominating/ideological purpose:

• Adopts a Marxist perspective and assumes that MASplay a crucial role in preserving capitalistic and class-based systems of domination.


STANDARD COSTING AND VARIANCEANALYSIS

Definition

1. Standard costs are target costs for each operation that canbe built up to produce a product standard cost.

2. A budget relates to the cost for the total activity, whereasstandard relates to a cost per unit of activity.

Operation of a standard costing system (see figure on sheet 18.2 foran overview)

1. Most suited to a series of common or repetitiveorganizations (this can result in the production of manydifferent products).

Operationno. and Total

Respons- standard Products standardibility cost cost Actualcentre No. £ 100 101 102 103 104 105 106 £ cost

A 1 20 ✓ ✓ ✓ ✓ ✓ ✓ 120

B 2 30 ✓ ✓ ✓ 90

C 3 40 ✓ ✓ ✓ 120

D 4 50 ✓ ✓ ✓ ✓ 200

Standardproduct cost £110 £100 £90 £50 £60 £50 £70 530

2. Variances are traced to responsibility centres (notproducts).

3. Actual product costs are not required.4. Comparisons after the event provide information for

corrective action or highlight the need to revise thestandards.



An overview of a standard costing system


Standard cost of actualoutput recorded for each

responsibility centre

Standard and actual costs comparedand variances analysed and reported

Variances investigated andcorrective action taken

Standards monitored and adjusted toreflect changes in standard

usage and/or prices

Actual costs traced toeach responsibility centre


Establishing cost standards

1. Two approaches:(i) past historical records(ii) engineering studies

2. Engineering studiesA detailed study of each operation is undertaken:• direct material standards (standard quantity × standard

prices)• direct labour standards (standard quantity × standard

prices)• overhead standards:

• cannot be directly observed and studied and tracedto units of output;

• analyse fixed and variable elements;• fixed tend not to be controllable in the short term.

Standard hours produced

1. Used to measure output where more than one product isproduced.

Example

Standard (target) times: X = 5 hours, Y = 2 hours, Z = 3 hoursOutput = 100 units of X, 200 units of Y, 300 units of ZStandard hours produced = (100 × 5 hours) + (200 × 2 hours) +(300 × 3 hours) = 1 800

2. If actual DLH are less than 1 800 the department will beefficient, whereas if hours exceed 1 800 the department willbe inefficient.Note: Different activity measures and other factors (besidesactivity) will influence cost behaviour.



Purposes of standard costing

1. To provide a prediction of future costs that can be used fordecision-making.

2. To provide a challenging target that individuals aremotivated to achieve.

3. To assist in setting budgets and evaluating performance.4. To act as a control device by highlighting those activities

that do not conform to plan.5. To simplify the task of tracing costs to products for

inventory valuation.

Figure 18.2 Standard costs for inventory valuation and profitmeasurement


Standardcosts InventoriesProducts

Actualcosts

Period cost

Profit and loss statement

Cost of goods sold

VariancesVariances


Direct material variances

1. Can be analysed by price and quantity.

2. Material price variance• (SP – AP) × AQ• Possible causes• Should AQ be quantity purchased or quantity used?

Example

Price variance = 10 000 units purchased in period 1 at £1 over SP2 000 units per period usedShould £10 000 variance be reported in period 1 or £2 000 perperiod?

3. Material usage variance• (SQ – AQ) × SP• Possible causes• Speedy reporting required

4. Joint price/usage variance• It could be argued that SQ used to compute price

variance and that (SP – AP) × (AQ – SQ) is reported as ajoint price/usage variance.

5. Total material variance = SC – AC



Direct labour and overhead variances

1. Can also be analysed into price and quantity.

2. Wage rate variance• (SR – AR) × AH• Possible causes

3. Labour efficiency variance• (SH – AH) × SR• Possible causes

4. Variable overhead expenditure variance• Flexed budget allowance (AH × SR) – Actual cost• Possible causes

5. Variable overhead efficiency variance• (SH – AH) × SR• Possible causes (note similarity to labour efficiency)

6. Fixed overhead expenditure (spending) variance• BFO – AFO



Sales variances

1. Variances should be computed in terms of contributionprofit margins rather than sales revenues.

2. Example

Budgeted sales = 10 000 units × £11 = £110 000Standard and actual cost

per unit = £7Actual sales = 12 000 units × £10 = £120 000Variance in terms of sales

value = £10 000FVariance in terms of contribution margin = £4 000A(Budgeted contribution margin = 10 000 × £4 = £40 000Actual contribution margin = 12 000 × £3 = £36 000)

3. Objective is to maximize profits (not sales value).

4. Total sales margin variance

Example 18.1

Actual contributionActual sales (9 000 × £90) = £810 000Standard VC of sales (9 000 × £68) = £612 000

£198 000

Budgeted contribution margin: 10 000 × £20 £200 000

Variance = £2 000 A



Sales variances (cont.)

5. Total sales contribution variance can be analysed further:

Sales margin price = (AP – BP) × AQ

or (AM – BM) × AQ

Sales margin volume = (AQ – BQ) × SM

Therefore,Sales margin price = (£90 – £88) × 9 000 = £18 000 FSales margin volume = (9 000 – 10 000) × £20 = £20 000 A

£2 000 A

Reconciliation of budgeted and actual profit (see sheet 18.9).



Reconciliation of budgeted and actual profit

£ £ £

Budgeted net profit 80 000

Sales variances:Sales margin price 18 000 FSales margin volume 20 000 A 2 000 A

Direct cost variances:

Material: Price 8 900 AUsage 26 500 A 35 400 A

Labour: Rate 17 100 AEfficiency 13 500 A 30 600 A

Manufacturing overhead variances:

Fixed overhead expenditure 4 000 FVariable overhead expenditure 5 000 FVariable overhead efficiency 3 000 A 6 000 F 62 000 A

Actual profit 18 000



Standard absorption costing

1. For financial accounting (stock valuation) fixed overheads must beallocated to products. This results in a volume variance.

2. Fixed overhead rate = = £12 per unit

or £120 000 / 30 000 hours = £4 per standard hour = £12 per unit (3 × £4).

3. If actual production is different from budgeted production, avolume variance will arise:

Actual production = 9 000 units or 27 000 SHPBudgeted production = 10 000 units or 30 000 SHPVolume variance = 1 000 units × £12 or (3 000 SHP × £4) = £12 000AVolume variance = (AP – BP) × SR

4. Volume variances are not useful for cost control since FC are sunkcosts.

5. Sometimes analysed into two subvariances (capacity andefficiency):

(A) Budgeted hours of input and output = 30 000(B) Actual hours of input = 28 500(C) Actual hours of output = 27 000

Volume variance = A – C = 3 000 hours (£12 000)Capacity variance = A – B = 1 500 hours (£6 000)Efficiency variance = B – C = 1 500 hours (£6 000)

Budgeted fixed overhead (£120 000)��

Budgeted activity (10 000 units)



Reconciliation of budgeted and actual profit(absorption costing)

To reconcile the budget and actual profit with an absorptioncosting system, the sales volume margin variance is measured atthe standard profit margin (and not the contribution margin),i.e. 1 000 units × £8 = £8 000.

£ £ £ £Budgeted net profit 80 000Sales variances

Sales margin price 18 000 FSales margin volume 8 000 A 10 000 F

Direct cost varianceMaterial – Price: Material A 19 000 A

Material B 10 100 F 8 900 A

– Usage: Material A 10 000 AMaterial B 16 500 A 26 500 A 35 400 A

Labour – Rate 17 100 A– Efficiency 13 500 A 30 600 A

Manufacturing overhead variancesFixed – Expenditure 4 000 F

– Volume capacity 6 000 A– Volume efficiency 6 000 A 8 000 A

Variable – Expenditure 5 000 F– Efficiency 3 000 A 2 000 F 6 000 A 62 000 A

Actual profit 18 000



Mix variance

1. A mix variance arises when the actual mix differs from thepredetermined standard mix.

Example

Standard mix to produce 9 litres of output:

5 litres of X at £7 per litre = £353 litres of Y at £5 per litre = £152 litres of Z at £2 per litre = £4

£54

Standard loss = 10% of input. Actual output = 92 700 litres

Actual inputs: £53 000 litres of X at £7 = 371 00028 000 litres of Y at £5.30 = 148 40019 000 litres of Z at £2.20 = 41 800

100 000 561 200

2. Mix variance = (AQ in standard mix – AQ) × SP

AQ in standard mix × SP £ AQ × SP £X = 100 000 × 5/10 × £7 350 000 53 000 × £7 371 000Y = 100 000 × 3/10 × £5 150 000 28 000 × £5 140 000Z = 100 000 × 2/10 × £2 40 000 19 000 × £2 38 000

540 000 549 000

Mix variance = £9 000 A



Yield variance

1. Yield variance is the difference between the standardoutput for a given level of inputs and the actual output:

= (Actual yield – Standard yield from actual input)× SC per unit of output

= (92 700 – 90 000) × £54/9 = £16 200 F

2. Possible causes

3. Mix and yield variances are interrelated and should not beinterpreted in isolation.

Summary

Total variance = SC (92 700 × £6) – AC (561 200) = £5 000 A

Price variances £12 200 A+ Mix variance £9 000 A+ Yield variance £16 200 F

£5 000 A



Sales mix and quantity variances

1. Where a company sells several different products that havedifferent profit margins, it is possible to divide the salesvolume variance into a quantity and mix variance.

Example

Budgeted sales£

X = 8 000 units at £20 contribution = 160 000Y = 7 000 units at £12 contribution = 84 000Z = 5 000 units at £9 contribution = 45 000

20 000 289 000

Actual sales£

X = 6 000 units at £20 contribution = 120 000Y = 7 000 units at £12 contribution = 84 000Z = 9 000 units at £9 contribution = 81 000

22 000 285 000

2. Mix variance = (AQ – AQ in budgeted proportions) ×Standard margin

AQ – AQ in budgeted proportions Standard marginX 6 000 – 8 800 (40%) × £20 = £56 000 AY 7 000 – 7 700 (35%) × £12 = £8 400 AZ 9 000 – 5 500 (25%) × £9 = £31 500 F

22 000 £32 900 A



Sales mix and quantity variances (cont.)

3. Quantity variance = (AQ in budgetedproportions – BQ) × SM

X = (8 800 – 8 000) × £20 =£16 000 FY = (7 700 – 7 000) × £12 = £8 400 FZ = (5 500 – 5 000) × £9 = £4 500 F

£28 900 F

4. If planned mix had been achieved the sales volumevariance would have been £28 900 F.



Recording Standards Costs in the Accounts

1. Purchase of materials (Material A)

Dr Stores ledger control account (AQ × SP) 190 000Dr Materials price variance 19 000

Cr Creditors control 209 000

2. Issue of materials (Material A)

Dr Work in progress (SQ × SP) 180 000Dr Material usage variance 10 000

Cr Stores ledger control account (AQ × SP) 190 000

3. Recording of wages due

Dr Wages control account (actual cost) 273 600Cr Wages accrued account 273 600

The wages control account is cleared as follows:

Dr Work in Progress (SQ × SP) 243 000Cr Wages control account 243 000

Dr Wage rate variance 17 100Dr Labour efficiency variance 13 500

Cr Wages control account 30 600



Recording Standard Costs in the Accounts (cont.)

4. Manufacturing overhead cost incurred

Dr Factory variable overhead control account 52 000

Dr Factory fixed overhead control account 116 000Cr Expense creditors 168 000

5. Absorption of fixed manufacturing overhead

Dr Work in progress (SQ × SP) 108 000Dr Volume variance 12 000

Cr Factory fixed overhead control account 120 000

Dr Factory fixed overhead control account 4 000Cr Fixed overhead expenditure variance 4 000

6. Variable manufacturing overhead

Dr Work in progress (SQ × SP) 54 000Dr Variable overhead efficiency variance 3 000

Cr Factory variable overhead control account 57 000

Dr Factory variable overhead control account 5 000

Cr Variable overhead expenditure variance account 5 000

7. Completion of productionDr Finished stock account 720 000

Cr Work in progress 720 000

Note that the variances are transferred to the profit and lossaccount at the end of the period.



Ex post variance analysis

1. A major criticism is that actual performance is compared with astandard based on the environment that was anticipated when thestandard was set.

2. It is argued that an ex post variance analysis approach should beadopted that distinguishes between planning and operatingvariances.

3. A Original standardB Ex post standard given the benefit of hindsightC Actual outcome

Planning variance = A – BOperating variance = B – C

4. ExampleSP = £5 per unit, market price at time of purchase = £5.20Actual purchases = 10 000 units at £5.18Conventional variance analysis = 10 000 × £0.18 = £1 800 AEx post analysis:

Purchase planning variance = (£5 –£5.20) × 10 000 = £2 000 A

Purchase efficiency variance = (£5.20 – £5.18) × 10 000 = £200 F

£1 800 A5. Sales variances

Assume:Budgeted sales = 10% market share (10% × 1m units)Actual sales = 110 000 unitsActual industry sales volume = 1.2m unitsBudgeted and actual contribution = £100Ex post standard = 120 000 units (10% × 1.2m)

Conventional sales variance = £1m favourable (10 000 × £100)

Ex post analysis: Planning variance = 2m favourable (20 000 × £100)Appraisal variance = £1m adverse (10 000 × £100)



Investigation of variance

1. Variance investigation models can be classified into thefollowing categories:

• Simple rule of thumb models.

• Statistical models that do not incorporate costs andbenefits of investigation.

• Statistical decision models that take into account thecost and benefits of investigation.

2. Reasons for variances

• Measurement errors.

• Out-of-date standards.

• Out-of-control operations.

• Random or uncontrollable factors.

3. Investigation will indicate that variance is due to:

• Random uncontrollable factors when the operation isunder control.

• Assignable causes, but the cost of investigation exceedsbenefits.

• Assignable causes, but the benefits of investigationexceed the cost.

Note: The aim is to investigate only those variances in the finalcategory.



Statistical investigation models not incorporatingcost and benefits

1. Assume actual observations when under control indicate amean usage of 10 kg per unit with a SD of 1 kg (normallydistributed).

2. Actual usage is 12 000 kg for an output of 1 000 units.Therefore, average usage = 12 kg per unit.

3. Z = = 2.0

4. Normal distribution table indicates that an observation2SDs from the mean has a probability of 2.275%.

5. Thus the probability of actual average material usage perunit of output being 12 kg or more when the operation isunder control is 2.275%. It is very unlikely that materialusage comes from ‘in control distribution’.

6. Statistical control charts, which rely on the aboveprinciples, can be used to monitor resources usage and theprobability that operations are out of control. (See figure onsheet 19.10.)

Actual usage (12 kg) – Expected usage (10 kg)��

SD (1 kg)


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Variance investigation decision models

1. Bierman et al model assumes two mutually exclusive statesexist:

(i) System in control and variance due to random factors.

(ii) System out of control and corrective action can be takento remedy the situation.

2. If the process is out of control there is a benefit (B)associated with returning it to its in-control state (i.e. costsavings from avoiding variances in future periods). AssumeB = £400.

3. Let C = cost of investigation (assume C = £100).

Let P = probability that the process is out of control.

4. Expected benefit = PB

5. Investigate if PB > C, or P > C/B

6. P > 100 / 400 = 0.25

7. P (Process is in control) = 0.02275 (see sheet 19.9)

8. P (Process out of control) = 1 – 0.02275 = 0.97725

9. Decision = Investigate the variance

10. Note the difficulty in estimating C and B.



Criticisms of standard costing

• The usefulness of standard costing has been questioned,and its demise predicted, because of the following:

1. The changing cost structure

2. Inconsistency with modern management approaches

3. Over-emphasis on the importance of direct labour

4. Delay in feedback reporting

The future role of standard costing

• Standard costs and variance analysis required for manyother purposes besides cost control and performanceevaluation:

(e.g. tracking costs for inventory valuation andmaintaining a database for decision-making)

• Variance analysis adapted to report on items that arecompany specific.

• Shift from treating the variances as the foundations for costcontrol and performance evaluation to being one among abroader set of measures.

• Empirical evidence suggests that practitioners still regardvariance analysis as being important for cost control.

• Can still play a useful role within ABC systems particularlyin relation to controlling unit-level and batch-levelactivities.



The future role of standard costing (cont.)

• ABC and variance analysis:

1. Most appropriate for controlling the costs of unit-levelactivities.

2. Can also provide meaningful information forcontrolling those costs that are fixed in the short-termbut variable in the longer-term provided suitable costdrivers can be established.

Example

Costs of set-up activity: Budget Actual

Activity level (1 600 set-ups) Total FC (£70 000)Practical capacity supplied (2 000 set- Total VC (£39 000)ups)Total fixed costs (£80 000)Total variable costs (£40 000)Cost driver rates:

Variable (£25 per set-up)Fixed (£40 per set-up)

Variance analysis for fixed set-up expenses:

£Set-up expenses charged to products (1 500 × £40) 60 000Budgeted unused capacity variance (400 × £40) 16 000 ACapacity utilization variance (100 × £40) 4 000 AExpenditure variance 10 000 F

Total actual expenses 70 000



The future role of standard costing (Cont.)

• ABC and variance analysis:Variance analysis for variable set-up expenses:

£Variable set-up expenses charged to products

(1 500 × £25) 37 500Variable overhead variance (Flexed budget —

Actual cost) 1 500 A

Total actual expenses 39 000


DIVISIONAL FINANCIAL PERFORMANCEMEASURES

Functional and divisionalized organizationstructures

• In a functional structure only the organization as a whole isan investment centre (IC) and below this level a functionalstructure applies throughout.

• A functional structure is where all activities of a similartype are placed under the control of a departmental head.

• In a divisionalized structure the organization is dividedinto separate investment or profit centres (PC’s) and afunctional structure applies below this level.

• Diagram on sheet 20.2 indicates that:

1. In a functional structure all centres below the chiefexecutive or corporate level are cost centres (CC’s) orrevenue centres.

2. In a divisionalized structure divisions tend to be eitherIC’s or PC’s but within each division there are multiplecost and revenue centres.

• Divisionalized structures generally lead to adecentralization of the decision-making process whereasmanagers in a functional structure will tend to have lessindependence.




ChiefExecutive

(IC)

ChiefExecutive

(IC)

(a) Functional organizational structure

(b) Divisionalized organizational structure

IC = Investment centres, CC = Cost centres, RC = Revenue centres

Financial andadministration

manager(CC)

ProductYDivisionalmanager

(IC)

Product ZDivisionalmanager

(IC)

Product XDivisionalmanager

(IC)

Otherfunctionalmanagers

(CCs)


(CCs)


(CCs)


(CCs)

Research anddevelopment

manager(CC)

Purchasingmanager

(CC)

Productionmanager

(CC)

Marketingmanager

(RC)

Figure 20.1:


Advantages of divisionalization

• Improved quality of decisions

• Speedier decisions

• Increases managerial motivation

• Enables top management to devote more time to strategicissues

Disadvantages of divisionalization

• Suboptimization and may promote a lack of goalcongruence.

• More costly to operate a divisionalized structure.

• Loss of control by top management.

Prerequisites for successful divisionalization

• More appropriate for companies with diversified activities.

• Relations between divisions regulated so that no division,by seeking to increase its own profit, can reduce theprofitability of the company as a whole.



Measuring divisional profits

• There are strong arguments for producing two measures ofdivisional profitability — one to evaluate managerialperformance and the other to evaluate the economicperformance of the division.

• Alternative divisional profit measuresSales to outside customers xxxTransfers to other divisions xxxTotal sales revenue xxxLess variable costs xxx1. Variable short-run contribution margin xxx

Less controllable fixed costs xxx2. Controllable contribution xxx

Less non-controllable avoidable costs xxx3. Divisional contribution xxx

Less allocated corporate expenses xxx4. Divisional net profit before taxes xxx

• Controllable contribution is the most appropriate measureof a divisional manager’s performance (should be measuredrelative to budget performance).

• Divisional contribution and divisional net profits beforetax are appropriate measures of economic performance: 1. Divisional contribution = Incremental short-term

contribution2. Net profit before taxes = Estimate of longer-term

contribution

• Empirical evidence indicates that divisional net profit iswidely used to evaluate both divisional and managerialperformance.



Measuring divisional profitability

• Ideally focus should be on relative measures (profitability)rather than absolute measures of profit.

• Relative profitability measures:

1. Return on investment (ROI)2. Residual income (RI)3. Economic value added (EVA™)



Return on investment

Division A Division BProfit £1m £2mInvestment £4m £20mROI 25% 10%

• Division B earns higher profits but A is more profitable

• ROI is a relative measure of performance that can becompared with other investments. It also provides a usefulsummary measure of the ex post return on capitalemployed.

• A major disadvantage of ROI is that managers may bemotivated to make decisions that make the company worseoff.

Division X Division Y

Investment project available £10 million £10 million

Controllable contribution £2 million £1.3 million

Return on the proposed project 20% 13%

ROI of divisions at present 25% 9%

The overall cost of capital for the company is 15%

The manager of X would be motivated not to invest and themanager of Y would be motivated to invest.

• ROI may also motivate managers to make incorrect assetdisposal decisions.



Residual income

• Controllable residual income = Controllable profit less acost of capital charge on the investment controllable by themanager.

• It is claimed that RI is more likely to encourage goalcongruence

Division X (£m) Division Y (£m)Proposed investment 10 10Controllable profit 2 1.3Cost of capital charge(15%) 1.5 1.5Residual income + 0.5 – 0.2

• The manager of division X is motivated to invest and themanager of division Y is motivated not to invest.

• RI also enables different cost of capital percentages to beapplied to different investments that have different levels ofrisk.

• If RI is used it should be compared with budgeted/targetlevels which reflect the size of the divisional investment.

• Empirical evidence indicates that RI is not widely used.



Economic value added (EVA™)

• During the 1990’s RI was refined and renamed EVA™

• EVA™ = Conventional divisional profit based on GAAP± Accounting adjustments– Cost of capital charge on divisional assets

• Conventional divisional profit based on principles outlinedfor measuring divisional managerial and/or economicprofits.

• Adjustments intended to convert historic accounting profitto an approximation of economic profit.

• Adjustments typically include capitalization ofdiscretionary expenses.

Assets to be included in the investment base

• Assets to be included must be specified for ROI, RI andEVA™

• To measure the managerial performance only controllableassets should be included in the investment base.

• To measure economic performance all assets, and possiblyan allocation of some corporate assets, should be included.


MEASURING DIVISIONAL FINANCIALPERFORMANCE

The impact of depreciation

1. Assume investment cost = £1m, Cost of capital = 10%, NPV = £326 850

1 2 3 4 5£ £ £ £ £

Net cash flow 350 000 350 000 350 000 350 000 350 000Depreciation 200 000 200 000 200 000 200 000 200 000

Profit 150 000 150 000 150 000 150 000 150 000Cost of capital(10% of WDV) 100 000 80 000 60 000 40 000 20 000

RI/EVA 50 000 70 000 90 000 110 000 130 000Opening WDVof the asset 1 000 000 800 000 600 000 400 000 200 000

ROI 15% 18.75% 25% 37.5% 75%

2. If original cost is used to compute ROI and RI

• ROI = 15% p.a. for years 1–5• RI/EVA = £50 000 p.a. for years 1–5• May motivate managers to replace existing assets with

new assets that have negative NPVs.

3. If WDV is used to compute ROI and RI/EVA

• Both RI/EVA and ROI increase steadily over five years.• Managers can attain higher performance measures by

retaining old assets (i.e. not motivated to replace).

4. To overcome the above problems assets should be valued attheir economic cost (or replacement cost as anapproximation).



The effect of performance measurement oncapital investment decisions

1. NPV calculations for three mutually exclusive projects:

X Y Z£000 £000 £000

Machine cost initial outlay (time zero) 861 861 861Estimated net cash flow (year 1) 250 390 50Estimated net cash flow (year 2) 370 250 50Estimated net cash flow (year 3) 540 330 1 100Estimated net present value

at 10% cost of capital 77 (52) 52Ranking on the basis of NPV 1 3 2

2. Estimated ROI and RI/EVA

Profits X Y Z£000 £000 £000

Year 1 (37) 103 (237)Year 2 83 (37) (237)Year 3 253 43 813

Total profits 299 109 339

PV of future profits 225 96 199

ROI X Y Z% % %

Year 1 (4.3) 11.9 (27.5)Year 2 14.5 (6.4) (41.3)Year 3 88.1 15.0 283.2

Average 32.8 6.8 71.5



The effect of performance measurement oncapital investment decisions (cont.)

3. RI/EVA for project X

Year 1 Year 2 Year 3 Total£000 £000 £000 £000

Profit before interest (37) 83 253

10% interest on openingwritten down value 86 57 29

RI/EVA (123) 26 224

PV of RI/EVA (112) 21 168 77

4. There is no guarantee that the short-run RI/EVA measurewill be consistent with the long-term measure.

X Y Z

RI/EVA (year 1) –£123 17 –£323

5. To ensure that the short-term performance measure isconsistent with NPV decision model the literature suggeststhat alternative depreciation models should be used basedon accrual accounting or actual cash flows should becompared with the budgeted cash flows (see appendix toChapter 20).



Addressing the dysfunctional consequences ofshort-term financial performance measures

• Financial performance measures can encourage managersto become short-term oriented and seek to boost short-term profits at the expense of long-term profits.

• Approaches for reducing the short-term orientation:

1. Divisional performance evaluated on the basis ofeconomic income (PV of future cash flows).

2. Adopt EVA™ incorporating many accountingadjustments.

3. Lengthen the measurement period.

4. Do not rely excessively on financial measures andincorporate non-financial measures that measure thosefactors that are critical to the long-term success of theorganization.

(i.e. adopt a Balanced Scorecard Approach)


TRANSFER PRICING

Purposes of transfer pricing

1. To provide information that motivates divisional managers tomake good economic decisions.

2. To provide information that is useful for evaluating themanagerial and economic performance of the divisions.

3. To intentionally move profits between divisions or locations.4. To ensure that divisional autonomy is not undermined.

Information for making good decisions

• Intermediate products = Goods transferred from the supplyingto receiving division.

• Final products = Products sold by the receiving division to theoutside world

• ExampleIncremental cost of making intermediate product = £100Incremental further processing costs in receiving division = £60Market price of final product = £200No external market for the intermediate product and sparecapacityCost-plus 50% transfer price =£150Business will be rejected if TP set at £150

EVALUATING MANAGERIAL PERFORMANCE

• TP of £60 incremental cost of supplying division wouldmotivate correct decision but it does not form a basis formeasuring the performance of the supplying division.

• A conflict of objectives exists which can be difficult to resolve.


TRANSFER PRICING

Alternative transfer pricing methods

1. Market-based2. Marginal cost3. Full cost4. Cost-plus a mark-up5. Negotiated transfer prices

Market-based transfer prices

• Where there is a perfectly competitive market for theintermediate product, the current market price is the mostsuitable basis for setting the transfer prices.

• TP’s will motivate sound decisions and form a suitable basisfor performance evaluation (see Exhibit 21.2 and Figure21A.1)

Marginal cost transfer prices

• Economic theory indicates TP based on the MC ofproducing the intermediate product at the optimumoutput level for the company as a whole will encouragetotal organizational optimality (see Figure 21.1).

• Adopting a short-run perspective to derive MC results inMC = VC and the assumption that MC is constant per unitthroughout the relevant output range.

• MC not widely used:

1. Provides poor information for performance evaluation2. MC may not be constant over entire range of output3. Measuring MC beyond short-term is difficult4. Managers reject short-term perspective


TRANSFER PRICING

Figure 21.1: An illustration of cost-based transfer prices


£ pe

r un

it

Transfer price at marginal costplus fixed costs (or a mark-up)

Transfer price at marginal costof production (MC =VC)

Net marginal revenue of finalproduct

Units producedQ1 Q2

TRANSFER PRICING

Full cost transfer prices

• Widely used because managers require an estimate of long-run marginal cost for decision-making.

• Traditional costing systems tend to provide poor estimatesof long-run MC.

• Does not enable supplying division to report a profit ongoods transferred.

Cost-plus a mark-up transfer prices

• Attempts to meet the performance evaluation purpose oftransfer pricing (profit allocated to the supplying division)

• Results in non-optimal decisions (See Figure 21.1) becauseTP exceeds short-run or long-run MC.

• Enormous mark-ups can result when goods/services aretransferred between several divisions.

Negotiated transfer prices

• Most appropriate where there are market imperfections forthe intermediate product and managers have equalbargaining power.

• To be effective managers must understand how to use costand revenue information.

• Claimed behavioural advantages.• Limitations:

1. Can lead to sub-optimal decisions2. Time-consuming3. Divisional profitability may be strongly influenced by

the bargaining skills and powers of the divisionalmanagers.

4. Inappropriate in certain circumstances (e.g. no marketfor the intermediate product or an imperfect marketexists).


TRANSFER PRICING

Example

Oslo = Supplying division (No external market for theintermediate product)

Bergen = Receiving division (converts intermediate to finalproduct)

Expected sales of the final product:

Net selling price Quantity sold(£) Units100 1 00090 2 00080 3 00070 4 00060 5 00050 6 000

The costs of each division are:

Oslo Bergen(£) (£)

Variable cost per unit 11 7Fixed costs attributable to the

products 60 000 90 000

The transfer price of the intermediate product has been set at£35 based on a full cost plus a mark-up.


TRANSFER PRICING

Whole company profit computations

Output level Total Company Company Company(units) revenues variable costs fixed costs profit/(loss)1 000 100 000 18 000 150 000 (68 000)2 000 180 000 36 000 150 000 (6 000)3 000 240 000 54 000 150 000 36 0004 000 280 000 72 000 150 000 58 0005 000* 300 000 90 000 150 000 60 000*6 000 300 000 108 000 150 000 42 000

Oslo Division (Supplying division)

Output level Transfer price Variable Fixed Total(units) revenues costs costs profit/(loss)1 000 35 000 11 000 60 000 (36 000)2 000 70 000 22 000 60 000 (12 000)3 000 105 000 33 000 60 000 12 0004 000 140 000 44 000 60 000 36 0005 000 175 000 55 000 60 000 60 0006 000* 210 000 66 000 60 000 84 000*

Bergen Division (Receiving division)

Output level Total Variable Total cost Fixed Total(units) revenues costs of transfers costs profit/

(loss)1 000 100 000 7 000 35 000 90 000 (32 000)2 000 180 000 14 000 70 000 90 000 6 0003 000* 240 000 21 000 105 000 90 000 24 000*4 000 280 000 28 000 140 000 90 000 22 0005 000 300 000 35 000 175 000 90 000 06 000 300 000 42 000 210 000 90 000 (42 000)


TRANSFER PRICING

• TP does not motivate optimum output level for thecompany as a whole.

• To ensure overall company optimality the TP must be set atMC of the intermediate product (i.e VC of £11 per unit or£11,000 per batch of 1,000 units).

• The receiving division will face the following net marginalrevenue (NMR) schedule:

Units net marginal revenue(£)1 000 93 000 (100 000 – 7000)2 000 73 000 (80 000 – 7 000)3 000 53 000 (60 000 – 7 000)4 000 33 000 (40 000 – 7 000)5 000 13 000 (20 000 – 7 000)6 000 –7 000 (0 – 7 000)

• At £11 TP receiving division will choose to expand outputto 5,000 units.

• Consider a full cost TP without a mark-up (£23 if thedenominator level to compute unit fixed costs is 5,000units)

The receiving division manager will choose to produce4,000 units

• Negotiation:

1. No external market so supplying division manager haslittle bargaining power.

2. Could avoid £60,000 fixed costs so would look for a TPof at least £23.


TRANSFER PRICING

Resolving transfer pricing conflicts

• Two approaches advocated: 1. Adopt a dual rate TP system2. Transfer at MC plus a lump sum fee

Dual rate TP system

• Uses two transfer prices1. Supplying division may receive full cost plus a mark-up

so that it makes a profit on inter-divisional transfers (e.gOslo TP > £23).

2. Receiving division charged at MC of transfers thusmotivating managers to operate at the optimum outputlevel for the company as a whole.

3. Profit on inter-group trading removed by an accountingadjustment.

• Not widely used because: 1. Use of two TP’s causes confusion2. Seen as artificial3. Divisions protected from competition4. Reported inter-divisional profits can be misleading

Marginal cost plus a lump sum fee

• Intended to motivate receiving division to equate MC oftransfers with its net marginal revenue to determineoptimum company profit maximizing output level.

• Enables supplying division to cover its fixed costs and earna profit on inter-divisional transfers through the fixed feecharged for the period.

• Motivates receiving division to consider full cost ofproviding intermediate products/services (∴ TP =£11MCplus £60,000 lump sum plus a profit contribution in theexample).


TRANSFER PRICING

Domestic TP conclusions/recommendations

• Competitive market for the intermediate product — Usemarket prices.

• No market for the intermediate product or an imperfectmarket — Transfer at MC plus a lump sum or negotiationmay be appropriate in certain circumstances.

• Use standard costs for cost-based TP’s

International transfer pricing

• Where divisions are located in different countries taxationimplications become important and TP has the potential toensure that most of the profits on inter-divisional transfersare allocated to the low taxation country.

Example

Supplying division in country A (Tax rate = 25%)

Receiving division in country B (Tax rate = 40%)

Motivation is to use highest possible TP so receivingdivision will have high costs and low profits whereassupplying division will have high revenues and highprofits.

• Taxation authorities in most countries are wise tocompanies using TP to manipulate profits and seek to applyOECD guidelines based on arm’s length pricing principles.

• TP can also have an impact on import duties and dividendrepatriations.


ECONOMIC THEORY OF TRANSFER PRICING

No market for the intermediate product

1. Correct TP is MC of producing the intermediate product atthe optimal output level for the company as a whole.

2. The optimal output for the company as a whole is where:

• MC of supplying division + MC of receiving division =MR of receiving division

• MC of supplying division = MR of receiving division –MC of receiving division

• MC of supplying division = NMR of receiving division

Supplying division Receiving division(1) (2) (3) (4) (5) (6) (7

OverallTotal Net company

Units Total Marginal Units net marginal profitpro- cost cost pro- revenuea revenue (loss)

duced £ £ duced £ £ (5)–(2) £1 000 4 000 4 000 1 000 10 000 10 000 6 0002 000 7 000 3 000 2 000 19 000 9 000 12 0003 000 10 000 3 000 3 000 27 000 8 000 17 0004 000 11 000 1 000 4 000 34 000 7 000 23 0005 000 13 000 2 000 5 000 40 000 6 000 27 0006 000 15 000 2 000 6 000 45 000 5 000 30 0007 000 19 000 4 000 7 000 49 000 4 000 30 0008 000 24 000 5 000 8 000 52 000 3 000 28 0009 000 31 000 7 000 9 000 54 000 2 000 23 000

10 000 39 000 8 000 10 000 55 000 1 000 16 00011 000 48 000 9 000 11 000 55 000 0 7 00012 000 58 000 10 000 12 000 54 000 –1 000 (4 000)

aNet revenue is defined as total revenue from the sale of the finalproduct less the conversion costs incurred. It does not includethe transfer price.



No market for the intermediate product (cont.)

3. Optimal output = 7 000 units

4. MC at 7 000 units = £4 000 (TP = £4 000 per 1 000 batch)

5. At £4 000 TP the supplying division is motivated to transfer7 000 units and the receiving division is motivated to buy 7 000 units.

6. Note: optimum TP = VC where MC = VC.


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Imperfect market for the intermediate product

Optimum transfer price for an imperfect intermediate market

Supplying division Receiving division(1) (2) (3) (4) (5) (6)

Mar- NetUnits Total ginal Marginal Units Marginal

pro- cost cost revenue pro- revenueduced £ £ £ duced £

1 19 19 40 (1) 1 35.00 (3)2 37 18 37 (2) 2 33.50 (5)3 54 17 34 (4) 3 32.00 (6)4 69 15 31 (7) 4 30.50 (8)5 83 14 28 (10) 5 29.00 (9)6 98 15 25 (13) 6 27.50 (11)7 114 16 22 7 26.00 (12)8 132 18 19 8 24.509 152 20 16 9 23.00

10 175 23 13 10 21.5011 202 27 10 11 20.0012 234 32 7 12 18.5013 271 37 4 13 17.00



Imperfect market for the intermediate product(cont.)

Allocation of output of supplying division betweenintermediate and external market

(1) (2) (3) (4)marginal cost Allocation per Marginal revenue /

Output of supplying ranking in net marginal(units) division (£) Sheet 21.13 revenue (£)

1 19 Intermediate market 40.002 18 Intermediate market 37.003 17 Final market 35.004 15 Intermediate market 34.005 14 Final market 33.506 15 Final market 32.007 16 Intermediate market 31.008 18 Final market 30.509 20 Final market 29.00

10 23 Intermediate market 28.0011 27 Final market 27.5012 32 No allocation 26.00




1. Correct TP is the MC of producing the intermediateproduct at the optimal output level (see tables on sheets21.13 and 21.14).

2. To determine the optimum output level allocate theintermediate product according to its most profitable use(see table on sheet 21.14).




3. Optimal output = 11 units (MC at this level = £27)

4. To be more precise, the optimal TP is where MCs andMR/NMR intersect between £27 and £27.50.

5. At a TP of £27.01 to £27.49

• the supplying division will choose to sell five unitsexternally and transfer six units internally

• the manager of the receiving division will choose to sellsix units of the final product.

6. If MC = VC the optimum TP = VC

7. Note the TP of £27.01 to 27.49 is only optimal where thereare no capacity constraints. If capacity constraints exist, theanalysis must be modified to reflect the constraint.


Output

MR/NMR

MC

£27.50

£27

£


Perfect external market for the intermediateproduct

• NMR for company as a whole = BCDE

• MC for company as a whole = ADE

• Optimal output is where MC and NMR for the company asa whole intersect (point D at Q2)

• TP = OP

• At a TP of OP the receiving division will require OQ1 andthe supplying division will wish to sell OQ2 (Q1Q2

externally if it supplies OQ1 internally).


CP

A

0 Q1 Q2

B

D

MCs

E

NMR=MR –MCR R

Intermediatemarket price

MRs=P

Rev

enue

/cos

t pe

r un

it

Output


No external market for the intermediate productand a perfect market for the final product

• Optimal output for the company as a whole is where MCs +MCR equals the MR for the company as a whole (MRR) atOQ.

• MC of supplying division at the optimal output level is OPand this is the optimum TP.

• Supplying division will wish to produce OQ at a TP of OPand the receiving division will wish to produce OQ at thisTP.


C

P

0 Q

A

B

D

E

F

Rev

enue

/cos

t pe

r un

it

Output

NMR=MR –MCR R

MC +MCS R

Price of finalproduct =AR =MRR R

MCS

MCR


Imperfect market for the intermediate product

• The MC and MR schedules for the company as a whole areMCs and MRs + NMR.

• Optimal output is OQ3 and the MC at this output level isOPT.

Therefore, optimal TP is OPT.

• At this TP the receiving division will wish to purchase OQ2

(where TP = NMR).

• The supplying division faces a MR schedule of BED and willsell OQ1 externally and Q1Q3 internally giving a totaloutput of OQ3. (Note Q2Q3 = OQ1.)


C

PE

PT

0 Q1 Q2 Q3

A

B

DE

F

Rev

enue

/cos

t pe

r un

it

Output

MR +NMRS

NMR

MCS

MRS

ARS

COST MANAGEMENT

• Traditional management accounting control techniquestend to focus on cost containment whereas costmanagement concentrates on cost reduction.

• Traditional management accounting control techniquesare routinely applied on a continuous basis whereas costmanagement tends to be applied on an ad hoc basis.

• Many of the approaches that fall within the area of costmanagement do not rely exclusively on accountingtechniques.

Life-cycle costing (LCC)

• Traditional management accounting procedures havefocused primarily on the manufacturing stage of aproduct’s life cycle.

• LCC focuses on costs over the product’s entire life cycle todetermine whether profits earned during themanufacturing phase will cover the costs incurred duringthe pre- and post-manufacturing stages.

• A large proportion of a product’s costs can be committedor ‘locked in’ during the planning and design stage (seeFigure 22.1).

• Cost management can be most effectively exercised duringthe planning and design stage.


COST MANAGEMENT

Fig. 22.1: Cost committed and incurred during a product’s lifecycle


Perc

enta

ge o

f cos

ts c

omm

itted

or

incu

rred

Costs committed

Product planningand design phase

Product manufacturingand sales phase

Costs incurred

Post salesservice andabandonmentphase

Product life-cycle phase

100%

80%

60%

40%

20%

COST MANAGEMENT

Target costing

• Focuses on managing costs during a product/service’splanning and design phase.

• Involves the following stages:

1. Determine the target price which customers will beprepared to pay for the product.

2. Deduct a target profit margin from the target price todetermine the target cost.

3. Estimate the actual cost of the product.4. If estimated actual cost exceeds the target cost

investigate ways of driving down the actual cost to thetarget cost.

• Iterative process involving:

1. Tear-down analysis2. Value analysis and functional anaysis

• It is important that target costing is supported by anaccurate costing system using appropriate cause-and-effectcost drivers.

Kaizen Costing

• Kaizen costing is applied during manufacturing stagewhereas target costing is during planning stage.

• Kaizen costing focuses on production processes whereastarget costing focuses on the product.

• Kaizen costing aims to reduce costs of processes by a pre-specified amount relying on employee empowerment.


COST MANAGEMENT

An example of target costing

Projected lifetime sales volume 300 000 unitsTarget selling price of the product £800Target profit margin (30% of selling price) £240Target cost (£800 – £240) £560Projected cost £700

Analysis of the projected cost before and after the target costing:

Before AfterManufacturing cost £ £ £ £Direct materials (bought in parts) 390 325Direct labour 100 80Direct machining costs 20 20Ordering and receiving 8 2 Quality assurance 60 50Rework 15 6Engineering and design 10 603 8 491Non-manufacturing costsMarketing 40 25Distribution 30 20After-sales service and warranty costs 27 97 19 64Total cost 700 555


COST MANAGEMENT

Activity-based management (ABM)

• Involves the following stages:

1. Identifying the major activities that take place in anorganization.

2. Assigning costs to cost pools/cost centres for each activity.3. Determining the cost driver for each activity.

• Omits the fourth stage required for product costing ABC.

• ABM focuses on managing the business on the basis of theactivities that make up the organization — by managing theactivities costs are managed in the long term.

• Traditional control reports analyse costs by types of expensesfor each responsibility centre whereas ABM analyses costs byactivities (See sheet 22.6 for an illustration).

• Knowing the cost of activities is a catalyst for triggering actionto become competitive.

• Activity cost information is useful for prioritizing thoseactivities that need to be studied more closely. Activities can beclassified:

1. As value-added or non-value-added.2. According to a scale similar to that advocated by Kaplan

and Cooper.

• Activity-based systems can also be used to manage costs at thedesign stage using behavioural drivers.

• Surveys also suggest that many organizations use cost driverrates as measures of cost efficiency

Example

Cost of purchasing activity = £100,000 Orders processed = 10,000Cost per order = £10 (Used for relative, trend and budgetcomparisons).


COST MANAGEMENT

Example

Customer order processing activity

Traditional analysis (customer order processingdepartment) £000’sSalaries 320Stationery 40Travel 140Telephone 40Depreciation of equipment 40

580

ABM analysis

Preparing quotations 120Receiving customer orders 190Assessing the credit-worthiness of customers 100Expediting 80Resolving customer problems 90

580


COST MANAGEMENT

Business process re-engineering (BPR)

• A business process consists of a collection of activities thatare linked together in a co-ordinated manner to achieve aspecific objective.

• BPR involves examining business processes and makingsubstantial changes to how the organization operates byfocusing on:

1. Cost reduction2. Simplification3. Improved quality and enhanced customer satisfaction.

Cost of quality

• Quality is now one of the key competitive variables.

• Management accountants are now placing greateremphasis on the provision of information relating to thecost of quality.

• Cost of quality reports prepared periodically:

1. Prevention costs2. Appraisal costs3. Internal failure costs4. External failure costs

• Increasing attention is also being given to continuousimprovement with the aim of zero defects.

• Non-financial measures and statistical quality control toolsalso play a key role in improving quality and reducinginternal and external failure costs.


COST MANAGEMENT

Cost of quality report% of sales

Prevention costs: (£000’s) (£50 million)Quality training 1 000Supplier reviews 300Quality engineering 400Preventive maintenance 500

2 200 4.4Appraisal costs: Inspection of materials received 500Inspection of WIP and completedunits 1 000Testing equipment 300Quality audits 800

2 600 5.2Internal failure costs: Scrap 800Rework 1 000Downtime due to quality problems 600Retesting 400 2 800 5.6

External failure costs: Returns 2 000Recalls 1 000Warranty repairs 800Handling customer complaints 500Forgone contribution from lost sales 3000

7 300 14.6

14 900 29.8


COST MANAGEMENT

Cost management and the value chain

• The value chain (see Fig.22.3) is the linked set of value-creating activities from supplier to customer.

• Objective is to perform value chain activities moreefficiently and at a lower cost than the competitors.

• Focus on each link in the chain from the customer’sperspective.

• Critics claim that traditional management accountingstarts too late and finishes too soon in terms of the valuechain.

Figure 22.3 The value chain


Suppliers Organization Customers

Researchand

developmentDesign Production Marketing

Strategy and administration

DistributionCustomer

service

COST MANAGEMENT

Benchmarking

• Objective is to improve key activities/processes.

• Compares key activities/processes with world-class bestpractices.

Management audits

Management audits investigate the entire management controlsystem and focus on:

1. The nature and functioning of the organization’smanagerial systems and procedures.

2. The economy and efficiency with which the organization’sservices are provided.

3. The effectiveness of the organization’s performance inachieving its objectives.


COST MANAGEMENT

Just-in-time systems

JIT seeks to achieve the following goals:

• Elimination of non-value added activities

1. Many activities add cost but no value to the product2. The aim of JIT is to convert raw materials to finished

products with a lead time equal to processing time.

• Zero inventory

• Zero defects

1. Emphasis on preventative maintenance and doing thejob right first time.

• Batch sizes of one

The aim is to reduce set-up times, batch sizes andthroughput times, thus minimizing inventories.

• Zero breakdowns

• A 100% on-time delivery service

• JIT also involves a change in factory layout:

1. Move from batch production to cellular flowlines ofdissimilar machines (with products grouped intofamilies of similar products or components)

2. Pull systems (instead of a push system) used andmaterial movements minimized.

3. Considered more beneficial to add to short-run idletime rather than adding to inventory.

• JIT purchasing arrangements:

1. More frequent deliveries of materials that immediatelyprecede their use.


STRATEGIC MANAGEMENT ACCOUNTING

What is strategic management accounting (SMA)

• The provision of information to support strategic decisionsin organizations (Innes, 1998).

• Review of literature by Lord (1996) identified the followingstrands:

1. Extension from internal focus of managementaccounting (MA) to include external information aboutcompetitors.

2. The relationship between the strategic position chosenby the firm and the expected emphasis on MA.

3. Gaining competitive advantage through exploitinglinkages in the value chain.

• Target costing is also identified as falling within thedomain of SMA.

• Strategic role of MA emphasized in formulating andsupporting the overall strategy of an organization bydeveloping an integrated framework of performancemeasurement.



External information about competitors

• MA should help firm evaluate its competitive positionrelative to the rest of the industry.

• Managers require information that indicates by whom andby how much they are gaining or being beaten.

Accounting in relation to strategic positioning

• Advocates that firms should place more emphasis onparticular techniques depending upon the strategicposition they adopt.

• Evidence to suggest that:

1. Business units following a defender strategy place agreater emphasis on the use of financial measures forrewarding managers.

2. Non-financial measures for determining executives’bonuses increases with the extent to which firms followprospector strategies.

3. Businesses following a build strategy rely more on non-financial measures of performance for determiningmanagers’ bonuses.

• Advocated that defenders (Miles and Snow) and businessunits pursuing a low cost strategy (Porter) should adoptresults measures that emphasize cost reductions and budgetachievement.

• Business units competing on the basis of differentiation(Porter) or those prospecting new markets should requiremore information than a cost leader about new productinnovations, design cycle times and research anddevelopment.



Gaining competitive advantage throughexploiting linkages in the value chain

• Focuses on each link in the chain from the customer’sperspective.

• Claimed that traditional management accounting startstoo late and finishes too soon in terms of the value chain.

• Porter advocates identifying the value chain and operationof cost drivers of competitors in order to understandrelative competitiveness.



The balanced scorecard

• Traditionally MA focused mainly on financial performancemeasures.

• Greater emphasis now being given to incorporating non-financial measures into the formal reporting system.

• Result was a proliferation of performance measures.

• To integrate financial and non-financial measures theBalanced Scorecard (BS) emerged.

• BS seeks to link performance measures to an organization’sstrategy — Should be used to clarify, communicate andmanage strategy.

• BS Advocates looking at the business from four differentperspectives by seeking to provide answers to the followingfour basic questions:

1. How do customers see us? (customer perspective)2. What must we excel at? (internal business process

perspective)3. Can we continue to improve and create value? ( learning

and growth perspective)4. How do we look to shareholders? (financial perspective)



Figure 23.1: The Balanced Scorecard (Source: Kaplan andNorton, 1996b)


Goals

Goals

Goals

GoalsVisionand

strategy

Measures

How do we look to shareholders?

Can we continue to improveand create value?

How docustomers

see us?

Whatmust weexcel at?

Measures

Measures

Measures

Financial perspective

Customer perspective Internal business processperspective

Learning and growth perspective


The financial perspective

• Typical measures include ROI, RI and EVATM.• Besides targets for the above, other objectives include

revenue growth, cost reduction and asset utilization.• Argued by some that by focusing on other perspectives

financial measures will take care of themselves.

The customer perspective

• Typical generic measures include: 1. Market share2. Customer retention and loyalty3. Customer acquisition4. Customer satisfaction5. Customer profitability

The internal business perspective

• Critical internal processes for which the organization mustexcel (e.g. innovation, operation and post-service salesprocesses).

• Typical innovation measures include: 1. Percentage of sales from new products.2. New product introduction versus competitors.3. Product development break-even time.

• Typical operation process measures include: 1. Cycle time 2. Quality 3. Activity and process costs

• Post-sales service processes: 1. Develop appropriate time, quality and process

measurements.Management and Cost Accounting, 5th edition.



The learning and growth perspective

• Focuses on the infrastructure that the business must buildto create long-term growth and improvement.

• Three principal categories identified:

1. Employee capabilities

2. Information system capabilities

3. Motivation, empowerment and alignment


COST ESTIMATION AND COST BEHAVIOUR

General principles

• A regression equation (or cost function) measures pastrelationships between a dependent variable (total cost) andpotential independent variables (i.e. cost drivers/activitymeasures).

• Simple regression y = a + bxWhere y = Total cost

a = Total fixed cost for the periodb = Average unit variable costx = Volume of activity or cost driver for the period

• Multiple regression y = a + b1 x1 + b2 x2

• Resulting cost functions must make sense and beeconomically plausible.

Cost estimation methods

1. Engineering methods2. Inspection of accounts method3. Graphical or scattergraph method4. High-low method5. Least squares method.



Engineering methods

• Analysis based on direct observations of physical quantitiesrequired for an activity and then converted into costestimates.

• Useful for estimating the costs of repetitive processes whereinput-output relationships are clearly defined.

• Appropriate for estimating the costs associated with directlabour, materials and machine time.

Inspection of accounts

• Departmental manager and accountant inspect each itemof expenditure within the accounts for a particular periodand classify each item as fixed, variable or semi-variable.



Graphical or scattergraph method

• Past observations are plotted on a graph and a line of bestfit is drawn.

• Unit VC = = = £2 per hour

• Y = £240 + £2x

£720–£560��240 hours – 160 hours

Difference in cost��Difference in activity


1280120011201040960880800720640560480 3

67

10

2 9

5

1

48

480

x (hours)

Mai

nten

ance

cos

t(£

)y

400

400

320

320

240

240

160

160

80

800


High – low method

• Involves selecting the periods of highest and lowest activitylevels and comparing changes in costs that result from thetwo levels.

Example

Lowest activity 5,000 units £22,000Highest activity 10,000 units £32,000Cost per unit = £10,000/5,000 units = £2 per unitFixed costs = £22,000 – (5,000 × £2) = £12,000

• Major limitation = Reliance on two extreme observations

Figure 24.2 High–low method.


Tota

l cos

ts (

£)

TC2

TC1

30 000

20000

10000

0

Units of output

A5000

B10000


The least squares method

MaintenanceHours x cost y £ x2 xy

90 1 500 8 100 135 000150 1 950 22 500 292 500

60 900 3 600 54 00030 900 900 27 000

180 2 700 32 400 486 000150 2 250 22 500 337 500120 1 950 14 400 234 000180 2 100 32 400 378 000

90 1 350 8 100 121 50030 1 050 900 31 500

120 1 800 14 400 216 00060 1 350 3 600 81 000

�x = 1 260 �y = 19 800 �x2 = 163 800 �xy = 2 394 000

Simple regression equation y = a + bx can be found from thefollowing two equations and solving for a and b:

�y = Na + b�x

�xy = a�x + b�x2

19 800 = 12a + 1 260b

2 394 000 = 1 260a +163 800b

Solving the above simultaneous equations:

b = 0.10 and a = 600

so that y = 600 + 10x

The above equation can be used to predict costs at differentactivity levels.



Multiple regression analysis

1. With simple regression analysis it is assumed that total costis determined by only one activity-based variable.

2. With multiple regression several factors (rather than one)are assumed to determine total cost.

For example, y = a + b1 x1 + b2 x2

where x1 and x2 are different activity variables.

3. Assume x1 = Number of machine hours

x2 = Number of days in period in which temperature < 15degrees

Assuming that y = 20 + 4x1 + 12x2

estimate the total cost for 1 000 machine hours and aperiod of 30 days with a temperature of less than 15degrees.

4. Total cost (y) = 20 + (4 × 1 000) + (12 × 30) = £4 380

5. Multicollinearity exists when the independent variables arehighly correlated with each other, resulting in it beingimpossible to separate the effect of each of these variableson the dependent variable.

6. The existence of multicollinearity does not affect thevalidity of the prediction of total cost but it does affect thevalidity of the individual coefficient estimates.



Factors to be considered when using past data toestimate cost functions

• Identify the potential activity bases (i.e. Cost drivers)

1. The objective is to find the cost driver that has thegreatest effect on cost.

• Ensure that the cost data and activity measures relate to thesame period.

1. Some costs lag behind the associated activity measures(e.g. wages paid for the output of a previous period).

• Ensure that a sufficient number of observations areobtained.

• Ensure that accounting policies do not lead to distortedcost functions.

• Adjust for past changes so that all data relates to thecircumstances of the planning horizon.

1. Adjust for inflation, technological changes andobservations based on abnormal situations.



Summary

1. Select the dependent variable (y) to be predicted.

2. Select the potential cost drivers.

3. Plot the observations on a graph.

• Be aware of the dangers of predicting costs outside therelevant range.

4. Estimate the cost function.

5. Test the reliability of the cost function.


Activity level x

0

A

C

B

x1 x2

Tota

l cos

t


Tests of reliability

1. Coefficient of determination (r2)

• See Exhibits 24A.1 (page 979) and 24A.2 (page 979) forthe calculation of r2 of 0.8861.

• r2 of 0.8861 indicates that 88.61% of the variation intotal cost is explained by variations in the activity baseand the remaining 11.39% is explained by eitherrandom variation or the effect of other (omitted)variables on total cost.

2. Standard error of the estimate

• Gives an indication of the absolute size of the probabledeviations from the line.

• For example, in Exhibit 24A.1 on page 979 there is a0.90 probability that the true cost for an activity of 180hours will fall within the range:

£2 400 ±1.812 (201.25) = £2 035 to £2 765.

3. Standard error of the coefficient

• Focuses on the regression coefficient b (i.e. variablecost).

• In Exhibit 24A.1 there is a 0.90 probability that the truevariable cost lies within the range £7.95 to £12.05.



An illustration of an 80% learning curve

Number of units Cumulative hours Hours for each order(1) (2) (3) (4) (5) (6) (7)

Order Per Cumulative Per Total Total Perno. order production unit unit

(3) × (4) (6) ÷ (2)

1 1 1 2 000 2 000 2 000 2 0002 1 2 1 600 3 200 1 200 1 2003 2 4 1 280 5 120 1 920 9604 4 8 1 024 8 192 3 072 7685 8 16 819 13 104 4 912 6146 16 32 655 20 960 7 856 491


5 10 15 20 25 30 35

Cumulative quantity (units)

Ave

rage

hou

rs p

er u

nit

of c

umul

ativ

e pr

oduc

tion 2000

1600

1200

800

400

00

1280

1024953

819762 709 669 655 637 Steady state

1600


Mathematical method

1. Yx = axb

Yx = Cumulative average time to produce x unitsa = Time required to produce the first unit of outputb = Ratio of the log of the learning curve improvement ratedivided by log of 2.

2. For an 80% learning curve

b = �lolo

gg02.8

� = �–00..62923311

� = – 0.322

3. Y10 = 2 000 × 10–0.322

= 2 000 × 0.476431= 953

4. Y20 = 2 000 × 20–0.322

= 2 000 × 0.381126= 762

5. Assume the company has completed four units cumulativeproduction.To calculate incremental hours for six more units:

Total hours for 10 units (10 × 953 hours) 9 530Total hours for 4 units (4 × 1 280 hours) 5 120

4 410

6. Note learning effect only applies to direct labour-relatedvariable costs.

7. Learning curve applications• Pricing decisions• Work scheduling• Standard setting


PLANNING AND CONTROL OF STOCKS

1. Reasons for holding stocks

• Transaction motive• Precautionary motive• Speculative motive

2. Relevant costs required for determining EOQ

• Holding costs• Ordering costs

3. Holding costs

• Opportunity cost of investment in stocks• Incremental insurance costs• Incremental warehouse and storage costs• Incremental material handling costs• Costs of deterioration and obsolete stocks

4. Ordering costs

• Incremental clerical costs of preparing a purchase order,receiving deliveries and paying invoices.



Determining the EOQ

1. Assume holding cost = £1 per unit, Ordering costs = £2 perorder

Annual demand = 40 000 units

2. EOQ = 400 units

Tabulation method

Order quantity 100 200 300 400 500 600 800 10 000Average stock

in units 50 100 150 200 250 300 400 5 000Number of

purchase orders 400 200 133 100 80 67 50 4Annual holding

cost £50 £100 £150 £200 £250 £300 £400 £5 000Annual ordering

cost £800 £400 £266 £200 £160 £134 £100 £8Total relevantcost £850 £500 £416 £400 £410 £434 £500 £5 008


PLA

NN

ING

AN

D C

ON

TR

OL

OF

STO

CK

S

Eco

no

mic

ord

er q

uan

tity

gra

ph

25.3

700

600

100

200

200

800

600

400

Ord

er q

uant

ity

Ave

rage

sto

ck le

vels

100

400

300

200

300

400

Annual costs (£)

500 0

Tota

lco

sts

Hol

ding

cost

s

Ord

erin

gco

sts

Ma

na

gem

ent

an

d C

ost

Acc

ou

nti

ng,

5th

ed

itio

n.

© 2

00

0 C

oli

n D

rury


EOQ formula

1. Q = ��2�D

H�O��

where D = total demand for the periodO = cost per orderH = holding cost per unit

2. Q = ��2� ×� 4�0� 10�0�0� ×� 2�� = 400 units

3. Assume H and O are constant per unit and stock isconsumed evenly throughout the planning period.

4. Total cost curve tends not to be significantly affected ifsome of the underlying functions are violated.

Determining the length of a production run

1. EOQ formula can be adopted to determine the optimumlength of a production run when a set-up cost is incurredonly once for each batch produced.

2. Assume sales demand (D) = 9 000 units, Cost per set-up =£90, H = £2 per unit.

Q = ��2�H

D�S�� = ��2� ×� 9� 0�2

0�0� ×� 9�0�� = 900

3. With demand of 9 000 units the optimum production runis 900 units (10 batches × 900 units).



Quantity discounts

1. Assume purchase cost = £7 per unit

Demand = 9 000 unitsHolding cost = £4 per unitCost per order = £5A quantity discount of 3% is available for orders in excess of1 000 units.

2. EOQ = ��2� ×� 9� 04�0�0� ×� 5�� = 150 units

The savings available from purchases in batches of 1 000units (instead of 150) are:

£Savings in purchase price (3% × £63 000) 1 890Savings in ordering cost (9 × £5) – (6 × £5) 15

Total savings 1 905

The additional holding cost if the larger quantity ispurchased is:

�(Qd –

2Q)H� = = £1 700

It is therefore cheaper to purchase in batches of 1 000 units.

(1 000 – 150) × £4��

2



Determining when to place the order

1. Assume: EOQ = 600 units; Lead time = 2 wks; Usage per wk =120 units

2. Re-order point = 2 weeks × 120 units = 240 unitsWith an EOQ of 600 units orders will be placed at five-weeklyintervals.

Uncertain demand

1. If weekly demand exceeds 120 units there will be a stockout.

2. Therefore safety stocks are maintained and re-order point is:(Average usage during average lead time) + (Safety stocks)

Example

Probability distribution of possible usage over a two-week lead time;

Usage (units) 60 120 180 240 300 360 420Probability 0.07 0.08 0.20 0.30 0.20 0.08 0.07

Re- Stockout Total ex-Average safety order Stock cost Expected Holding pected

usage stock point -out (£5 per Prob- stockout costa cost(units) (units) (units) (units) unit) ability cost £ £

240 180 420 0 0 0 0 180 180240 120 360 60 300 0.07 21 120 141240 60 300 120 600 0.07 42

60 300 0.08 24

66 60 126

240 0 240 180 900 0.07 63120 600 0.08 48

60 300 0.20 60171 0 171

aTo simplify the analysis, it is assumed that a safety stock is maintainedthroughout the period. The average safety stock will therefore be equal to the totalof the safety stock.


LINEAR PROGRAMMING

Example

LP is a manufacturing company that currently makes twoproducts. The standards per unit of product are as follows:

£ £ £ £Product Y Product ZStandard selling price 110 Standard selling price 118

Less Standard cost: Less Standard cost:

Materials 32 Materials 16(8 units at £4) (4 units at £4)

Labour (6 hours at £10) 60 Labour (8 hours at £10) 80

Variable overhead Variable overhead(4 machine hours at £1) 4 (6 machine hours at £1) 6

96 102

Contribution 14 Contribution 16

During the next accounting period, the availability of resourcesare expected to be subject to the following limitations:

Labour 2 880 hoursMaterials 3 440 unitsMachine capacity 2 760 hours

The marketing manager estimates that the maximum salespotential for product Y is limited to 420 units.

LP model:

Maximize C = 14Y + 16Z (subject to)8Y + 4Z � 3 440 (material constraint)6Y + 8Z � 2 880 (labour constraint)4Y + 6Z � 2 760 (machine capacity constraint)0 � Y � 420 (maximum and minimum sales constraint)Z � 0 (minimum sales limitation)


LINEAR PROGRAMMING

Materials constraint (8Y + 4Z � 3 440)

WhenY = 0, Z = 860Z = 0, Y = 430


200

Feasibleproductioncombination

400 600 800

8 +4 < 3440

YZ

1000

Qua

ntity

ofY

pro

duce

d an

d so

ld

Quantity of Z produced and sold

800

200

400

600

0

LINEAR PROGRAMMING

Labour constraint (6Y = 8Z � 2 880)

WhenZ = 0, Y = 480Y = 0, Z = 360


200

Feasibleproduction

combinations

400 600 800

6+8

<2880

YZ

1000

Qua

ntity

ofY

pro

duce

d an

d so

ld


800

200

400

600

0

LINEAR PROGRAMMING

Machine capacity constraint (4Y + 6Z � 2 760)

WhenZ = 0, Y = 690Y = 0, Z = 460


200

Feasibleproductioncombination

400 600 800

4+6

<2760

YZ

1000

Qua

ntity

ofY

pro

duce

d an

d so

ld


800

200

400

600

0

LINEAR PROGRAMMING

Sales limitation Y � 420


200 400 600 800

Y < 420

1000

Qua

ntity

ofY

pro

duce

d an

d so

ld


800

200

400

600

0

LINEAR PROGRAMMING

Optimum solution

Feasible production combination = Area ABCDE


8 +4 < 3440 (materials)

YZ

4+6

<2760

YZ

6+8

<2880

(labour)

YZ

C=2240

Y < 420

Qua

ntity

of Y

pro

duce

d an

d so

ld


690

600

400

200

160

140 200 400 600 800 860

GD

0

E

AB

F

C

LINEAR PROGRAMMING

Optimum solution

1. The optimum output can be determined by solving thesimultaneous equations that intersect at point C:

8Y + 4Z = 3 440 6Y + 8Z = 2 880 so that Y = 400 and Z = 60

2. The materials and labour constraints are binding andtherefore have opportunity costs. The marginalcontribution from obtaining one extra unit of materialscan be calculated by solving the following equations:

8Y + 4Z = 3 441 (revised materials constraint)6Y + 8Z = 2 880 (unchanged labour constraint)Y = 400.2 units, Z = 59.85 units

Therefore the planned output of Y would be increased by0.2 units and Z reduced by 0.15 units and contribution willincrease by £0.40 (the opportunity cost).

3. The marginal contribution from obtaining one extra labourhour can be found in a similar way:

8Y + 4Z = 3 440 (unchanged materials constraint)6Y + 8Z = 2 881 (revised labour constraint)Y = 399.9 and Z = 60.2Marginal contribution = £1.80


LINEAR PROGRAMMING

Simplex method

1. The first stage is to introduce slack variables:

Maximize C = 14Y + 16Z (subject to)8Y + 4Z + S1 = 3 440 (materials constraint)6Y + 8Z + S2 = 2 880 (labour constraint)4Y + 6Z + S3 = 2 760 (machine capacity constraint)1Y + S4 = 420 (sales constraint for product Y)

First matrix

Quantity Y ZS1 = 3 440 –8 –4 MaterialsS2 = 2 880 –6 –8 LabourS3 = 2 760 –4 –6 Machine hoursS4 = 420 –1 0 Sales

C = 0 +14 +16 Contribution

1. Choose product Z but output restricted by:

Materials (S1) = 860 units (3 440 / 4)Labour (S2) = 360 units (2 880 / 8)Machine hours (S3) = 460 units (2 760 / 6)

2. Rearrange the equation that results in the constraint (S2) interms of the product chosen. Therefore S2 becomes:

S2= 2 880 – 6Y – 8Z8Z = 2 880 – 6Y – S2

Z = 360 – 3 / 4Y – 1 / 8S2

We now substitute this value for Z into each of the aboveequations. The revised equations are listed in the second matrix(sheet 26.9).


LINEAR PROGRAMMING

Simplex method (Cont.)

Second matrix

Quantity Y S2

S1 = 2 000 –5 + �12

� (1) (Material constraint)

Z = 360 – �34

� – �18

� (2)

S3 = 600 + �12

� + �34

� (3) (machine hours constraint)

S4 = 420 –1 0 (4) (sales constraint)

C = 5 760 + 2 – 2 (5)

1. Choose product Y (substitute 1 unit of Y for �34

� units of Z),but substitute process restricted by:

S1 materials = 400 units (2 000 / 5)Z (substitution of Z) = 480 units (360 / �

34

�)S4 (maximum sales of Y) = 420 units (420 / 1)

2. Rearrange the equation, which results in the constraint (S1)in terms of the chosen product (Y) and substitute therevised values of Y in each of the equations shown in thesecond matrix. The revised values are listed in the thirdmatrix. (See sheet 26.10).


LINEAR PROGRAMMING

Simplex method (cont.)

Third matrix

Quantity S1 S2

Y = 400 – �15

� + �110� (1)

Z = 60 + �230� – �

15

� (2)

S3 = 800 – �110� + �

45

� (3)

S4 = 20 + �15

� – �110� (4)

C = 6 560 – �25

� – 1 �45

� (5)

1. The contribution row contains only negative items, whichsignifies that the optimum solution has been reached.

2. Interpretation of final matrix

• Produce 400 units of Y and 60 units of Z.

• Unused resources = 800 machine hours and 20 unitsunused sales potential of Y.

• Materials and labour hours are fully utilized.

• Maximum contribution = £6 560

• Opportunity costs = £0.40 for materials and £1.80 forlabour hours.


LINEAR PROGRAMMING

Simplex method (Cont.)

Third matrix (Cont.)

3. To release 1 unit of materials from the optimum productionprogramme we should increase the output of Z by �

230� of a unit

and decrease Y by �15

� of a unit.

4. S3 S4 S1 S2

Machine Salescapacity of Y Materials Labour Contribution

Increase product Zby �

230� of a unit – �

190� (�

230� × 6) — – �

35

� (�230� × 4) – 1 �

15

� (�230� × 8) + 2 �

25

� (�230� × 16)

Decrease product Yby �

15

� of a unit + �45

� (�15

� × 4) + �15

� + 1 �35

� (�15

� × 8) + 1 �15

� (�15

� × 6) – 2 �45

� (�15

� × 14)

Net effect – �110� + �

15

� + 1 Nil – �25

�

5. If additional scarce resources are obtained, all of the signs inthe final matrix and the table in (4) above should be reversed(e.g. increase Y by �

15

� of a unit and decrease Z by �230� of a unit and

contribution will increase by £0.40).

6. Relevant costs = Acquisition cost + Opportunity costs

7. Potential uses• Costing alternative uses of scarce resources by different

products.• Determining the minimum payment for additional

resources.• Variance analysis for bottleneck operations.• Transfer pricing.

8. The marginal rates of substitution and opportunity costs onlyapply within a certain range for each scarce resource:

Materials: 1 440 (3 440 – 2 000) to 3 540 units (3 440 + 100)Labour hours: 2 680 to 3 480 hours


LINEAR PROGRAMMING

Capital rationing

Present value Present value Present value NetInvestment of outlay in of outlay in of outlay in present value

project period 1 period 2 period 3 of investment£000 £000 £000 £000

1 12 3 5 142 54 10 4 303 6 6 6 174 6 2 5 155 30 35 10 406 6 10 4 6

The present value of the outlays for the budget constraints foreach of periods 1–3 are as follows:

£000Period 1 35Period 2 20Period 3 20

You are required to formulate the linear programming modelthat will maximize net present value.

Initial model

12X1 + 54X2 + 6X3 + 6X4 + 30X5 + 6X6 + S1 = 35 (period 1 constraint)3X1 + 10X2 + 6X3 + 2X4 + 35X5 + 10X6 + S2 = 20 (period 2 constraint)5X1 + 4X2 + 6X3 + 5X4 + 10X5 + 4X6 + S3 = 20 (period 3 constraint)0 � Xj � 1 (j = 1, …, 6)

Output of the model

X1 = 1.0 X2 = 0.07 X3 = 1.0 X4 = 1.0 X5 = 0.235 X6 = 0.0S1 = 0.408 S2 = 0.792 S3 = 0.0 Objective function = £57.50


LINEAR PROGRAMMING

Capital rationing (cont.)

1. Decision = Accept projects 1, 3, 4, and 7% of project 2

2. Slack variable indicates NPV can be expected to increase by£0.408 if investment funds are increased by £1.

3. Above model assumes that budgeted capital constraintscannot be removed by project-generated cash inflows.

4. If project-generated cash inflows are available forinvestment the revised model will be:

3X1 + 10X2 + 6X3 + 2X4 + 35X5 + S2

= 20 + 5X1 + 6X2 + 7X3 + 8X4 + 9X5 + 10X6

assuming cash inflows in period 2 are £5 000, £6 000, £7 000, £8 000, £9 000 and £10 000.


LINEAR PROGRAMMING

Assumptions underlying LP

1. Linearity

2. Divisibility of products

3. Divisibility of resources

4. All of the available opportunities can be included in themodel

5. Assumed fixed costs are constant for the period


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