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COST–VOLUME–PROFIT ANALYSIS 45

Shown below is a typical cost–volume–profit chart:

Required:(a) Explain to a colleague who is not an accountant the reasons for the change in

result on this cost–volume–profit chart from a loss at point (a) to a profit atpoint (b). (3 marks)

(b) Identify and critically examine the underlying assumptions of this type ofcost–volume–profit analysis and consider whether such analyses are useful tothe management of an organization. (14 marks)

(Total 17 marks)ACCA Level 1 Costing

The graphs shown below show cost–volume–profit relationships as they are typi-cally represented in (i) management accounting and (ii) economic theory. In eachgraph TR=total revenue, TC=total cost, and P=profit. You are required to comparethese different representations of cost–volume–profit relationships, identifying,explaining and commenting on points of similarity and also differences. (15 marks)

ICAEW Management Accounting

Question IM 8.1Intermediate


Cost–volume–profit analysis

£+

0

£–

Volume

P

TC

TR £+

0

£–

Volume

P

TC

TR

Total revenue

Total costs

Variable costs

(b)(a) Volume

£

‘A break-even chart must be interpreted in the light of the limitations of its underly-ing assumptions…’ (From Cost Accounting: A Managerial Emphasis, by C.T. Horngren.)

Required:(a) Discuss the extent to which the above statement is valid and both describe and

briefly appraise the reasons for five of the most important underlyingassumptions of break-even analysis. (c. 14 marks)

(b) For any three of the underlying assumptions provided in answer to (a) above,give an example of circumstances in which that assumption is violated.Indicate the nature of the violation and the extent to which the break-evenchart can be adapted to allow for this violation. (c. 6 marks)

(Total 20 marks)ACCA P2 Management Accounting

The accountant’s approach to cost–volume–profit analysis has been criticized inthat, among other matters, it does not deal with the following:(a) situations where sales volume differs radically from production volume;(b) situations where the sales revenue and the total cost functions are markedly

non-linear;(c) changes in product mix;(d) risk and uncertainty.

Explain these objections to the accountant’s conventional cost–volume–profitmodel and suggest how they can be overcome or ameliorated. (17 marks)

ACCA Level 2 Management Accounting

JK Limited has prepared a budget for the next twelve months when it intends tomake and sell four products, details of which are shown below:

Sales in units Selling price Variable costProduct (thousands) per unit (£) per unit (£)

J 10 20 14.00K 10 40 8.00L 50 4 4.20M 20 10 7.00

Budgeted fixed costs are £240 000 per annum and total assets employed are £570 000.

You are required(a) to calculate the total contribution earned by each product and their combined

total contributions; (2 marks)(b) to plot the data of your answer to (a) above in the form of a contribution to

sales graph (sometimes referred to as a profit–volume graph) on the graph paperprovided; (6 marks)

(c) to explain your graph to management, to comment on the results shown andto state the break-even point; (4 marks)

(d) to describe briefly three ways in which the overall contribution to sales ratiocould be improved. (3 marks)

(Total 15 marks)CIMA Stage 2 Cost Accounting

(a) Identify and discuss briefly five assumptions underlying cost–volume–profitanalysis. (10 marks)

(b) A local authority, whose area includes a holiday resort situated on the eastcoast, operates, for 30 weeks each year, a holiday home which is let to visitingparties of children in care from other authorities. The children areaccompanied by their own house mothers who supervise them throughout


Question IM 8.4Advanced

Question IM 8.5Intermediate:Multi-productprofit–volumegraph

Question IM 8.6Intermediate:Break-even chartwith increases infixed costs

46 COST–VOLUME–PROFIT ANALYSIS

their holiday. From six to fifteen guests are accepted on terms of £100 perperson per week. No differential charges exist for adults and children.

Weekly costs incurred by the host authority are:

(£ per guest)

Food 25Electricity for heating and cooking 3Domestic (laundry, cleaning etc.) expenses 5Use of minibus 10

Seasonal staff supervise and carry out the necessary duties at the home at a cost of£11 000 for the 30-week period. This provides staffing sufficient for six to ten guestsper week but if eleven or more guests are to be accommodated, additional staff at atotal cost of £200 per week are engaged for the whole of the 30-week period.

Rent, including rates for the property, is £4000 per annum and the garden of thehome is maintained by the council’s recreation department which charges a nomi-nal fee of £1000 per annum.

You are required to:(i) tabulate the appropriate figures in such a way as to show the break-even

point(s) and to comment on your figures; (8 marks)(ii) draw, on the graph paper provided, a chart to illustrate your answer to (b)(i)

above. (7 marks)(Total 25 marks)

CIMA Cost Accounting Stage 2

(a) ‘The analysis of total cost into its behavioural elements is essential for effectivecost and management accounting.’

RequiredComment on the statement above, illustrating your answer with examples of costbehaviour patterns. (5 marks)(b) The total costs incurred at various output levels, for a process operation in a

factory, have been measured as follows:

Output (units) Total cost (£)

11 500 102 47612 000 104 73012 500 106 26313 000 108 02113 500 110 72714 000 113 201

Required:Using the high–low method, analyse the costs of the process operation into fixedand variable components. (4 marks)(c) Calculate, and comment upon, the break-even output level of the process

operation in (b) above, based upon the fixed and variable costs identified andassuming a selling price of £10.60 per unit. (5 marks)

(Total 14 marks)ACCA Foundation Paper 3

Question IM 8.7Intermediate:Analysis of costsinto fixed andvariable elementsand break-evenpoint calculation


Video Technology Plc was established in 1987 to assemble video cassette recorders(VCRs). There is now increased competition in its markets and the companyexpects to find it difficult to make an acceptable profit next year. You have beenappointed as an accounting technician at the company, and have been given acopy of the draft budget for the next financial year.

Draft budget for 12 months to 30 November 2001

(£m) (£m)

Sales income 960.0Cost of sales:

Variable assembly materials 374.4Variable labour 192.0Factory overheads – variable 172.8Factory overheads – fixed 043.0 (782.2)

177.8Gross profit

Selling overheads – commission 38.4Selling overheads – fixed 108.0

Administration overheads – fixed 020.0 (166.4)Net profit 0011.4

The following information is also supplied to you by the company’s financial con-troller, Edward Davies:1 planned sales for the draft budget in the year to 30 November 2001 are

expected to be 25% less than the total of 3.2 million VCR units sold in the yearto 30 November 2000;

2 the company operates a Just-In-Time stock control system, which means itholds no stocks of any kind;

3 if more than 3 million VCR units are made and sold, the unit cost of materialfalls by £4 per unit;

4 sales commission is based on the number of units sold and not on turnover;5 the draft budget assumes that the factory will only be working at two-thirds of

maximum capacity;6 sales above maximum capacity are not possible.

Edward Davies explains that the Board is not happy with the profit projected inthe draft budget, and that the sales director, Anne Williams, has produced threeproposals to try and improve matters.1 Proposal A involves launching an aggressive marketing campaign:

(i) this would involve a single additional fixed cost of £14 million for advertising;(ii) there would be a revised commission payment of £18 per unit sold;

(iii) sales volume would be expected to increase by 10% above the level pro-jected in the draft budget, with no change in the unit selling price.

2 Proposal B involves a 5% reduction in the unit selling price:(i) this is estimated to bring the sales volume back to the level in the year to

30 November 2000.3 Proposal C involves a 10% reduction in the unit selling price:

(i) fixed selling overheads would also be reduced by £45 million;(ii) if proposal C is accepted, the sales director believes sales volume will be 3.8

million units.

Task 1(a) For each of the three proposals, calculate the:

(i) change in profits compared with the draft budget;(ii) break-even point in units and turnover.

(b) Recommend which proposal, if any, should be accepted on financial grounds.

Question IM 8.8Intermediate:Non-graphicalCVP analysis andthe acceptance ofa special order


(c) Identify three non-financial issues to be considered before a final decision ismade.

Edward Davies now tells you that the company is considering a new export orderwith a proposed selling price of £3 million. He provides you with the followinginformation:1 The order will require two types of material:

(i) material A is in regular use by the company.The amount in stock originallycost £0.85 million, but its standard cost is £0.9 million. The amount in stockis sufficient for the order. The current market price of material A to be usedin the order is £0.8 million;

(ii) material B is no longer used by the company and cannot be used elsewhereif not used on the order. The amount in stock originally cost £0.2 millionalthough its current purchase price is £0.3 million. The amount of materialB in stock is only half the amount required on the order. If not used on theorder, the amount in stock could be sold for £0.1 million;

2 direct labour of £1.0 million will be charged to the order. This includes £0.2million for idle time, as a result of insufficient orders to keep the workforcefully employed. The company has a policy of no redundancies, and spreads theresulting cost of idle time across all orders;

3 variable factory overheads are expected to be £0.9 million;4 fixed factory overheads are apportioned against the order at the rate of 50% of

variable factory overheads;5 no sales commission will be paid.

Task 2Prepare a memo for Edward Davies:(a) showing whether or not the order should be accepted at the proposed selling

price;(b) identifying the technique(s) you have used in reaching this conclusion.

AAT Technicians Stage

PE Limited produces and sells two products, P and E. Budgets prepared for thenext six months give the following information:

Product P per unit Product E per unit£ £

Selling price 10.00 12.00Variable costs: production and selling 5.00 10.00Common fixed costs:

production and selling for six months £561 600

(a) You are required, in respect of the forthcoming six months,(i) to state what the break-even point in £s will be and the number of each

product this figure represents if the two products are sold in the ratio 4Pto 3E; (3 marks)

(ii) to state the break-even point in £s and the number of products this figurerepresents if the sales mix changes to 4P to 4E (ignore fractions of products);

(3 marks)(iii) to advise the sales manager which product mix should be better, that in (a)

(i) above or that in (a) (ii) above, and why; (2 marks)(iv) to advise the sales manager which of the two products should be concen-

trated on and the reason(s) for your recommendation assume that what-ever can be made can be sold, that both products go through a machiningprocess and that there are only 32 000 machine hours available, with prod-uct P requiring 0.40 hour per unit and product E requiring 0.10 hour perunit. (2 marks)

Question IM 8.9Intermediate:Calculation ofbreak-even pointsbased on differentproduct mixassumptions


(b) You are required to compare and contrast the usefulness of a conventionalbreak-even chart with a contribution break-even chart. Your explanationshould include illustrative diagrams drawn within your answer book and noton graph paper. (5 marks)

(Total 15 marks)CIMA Stage 2 Cost Accounting

York plc was formed three years ago by a group of research scientists to market anew medicine that they had invented. The technology involved in the medicine’smanufacture is both complex and expensive. Because of this, the company is facedwith a high level of fixed costs.

This is of particular concern to Dr Harper, the company’s chief executive. Sherecently arranged a conference of all management staff to discuss company prof-itability. Dr Harper showed the managers how average unit cost fell as productionvolume increased and explained that this was due to the company’s heavy fixedcost base. ‘It is clear,’ she said, ‘that as we produce closer to the plant’s maximumcapacity of 70 000 packs the average cost per pack falls. Producing and selling asclose to that limit as possible must be good for company profitability.’ The data sheused are reproduced below:

Production volume (packs) 40 000 50 000 60 000 70 000Average cost per unita £430 £388 £360 £340Current sales and production

volume: 65 000 packsSelling price per pack: £420aDefined as the total of fixed and variable costs, divided by the production volume

You are a member of York plc’s management accounting team and shortly after theconference you are called to a meeting with Ben Cooper, the company’s marketingdirector. He is interested in knowing how profitability changes with production.

Task 1Ben Cooper asks you to calculate:(a) the amount of York plc’s fixed costs;(b) the profit of the company at its current sales volume of 65 000 packs;(c) the break-even point in units;(d) the margin of safety expressed as a percentage.

Ben Cooper now tells you of a discussion he has recently had with Dr Harper. DrHarper had once more emphasized the need to produce as close as possible to themaximum capacity of 70 000 packs. Ben Cooper has the possibility of obtaining anexport order for an extra 5000 packs but, because the competition is strong, the sell-ing price would only be £330. Dr Harper has suggested that this order should berejected as it is below cost and so will reduce company profitability. However, shewould be prepared, on this occasion, to sell the packs on a cost basis for £340 each,provided the order was increased to 15 000 packs.

Task 2Write a memo to Ben Cooper. Your memo should:(a) calculate the change in profits from accepting the order for 5000 packs at £330;(b) calculate the change in profits from accepting an order for 15 000 packs at £340;(c) briefly explain and justify which proposal, if either, should be accepted;(d) identify two non-financial factors which should be taken into account before

making a final decision.AAT Technicians Stage

Question IM 8.10Intermediate:Decision-makingand non-graphicalCVP analysis


A company has two products with the following unit costs for a period:

Product A Product B(£/unit) (£/unit)

Direct materials 1.20 2.03Direct labour 1.40 1.50Variable production overheads 0.70 0.80Fixed production overheads 1.10 1.10Variable other overheads 0.15 0.20Fixed other overheads 0.50 0.50

Production and sales of the two products for the period were:

Product A Product B(000 units) (000 units)

Production 250 100Sales 225 110

Production was at normal levels. Unit costs in opening stock were the same asthose for the period listed above.

Required:(a) State whether, and why, absorption or marginal costing would show a higher

company profit for the period, and calculate the difference in profit dependingupon which method is used. (4 marks)

(b) Calculate the break-even sales revenue for the period (to the nearest £000)based on the above mix of sales. The selling prices of products A and B were£5.70 and £6.90 per unit, respectively. (7 marks)

(Total 11 marks)ACCA Foundation Stage Paper 3

A local government authority owns and operates a leisure centre with numeroussporting facilities, residential accommodation, a cafeteria and a sports shop. Thesummer season lasts for 20 weeks including a peak period of 6 weeks correspond-ing to the school holidays. The following budgets have been prepared for the nextsummer season:

Accommodation60 single rooms let on a daily basis.35 double rooms let on a daily basis at 160% of the single room rate.Fixed costs £29 900Variable costs £4 per single room per day and £6.40 per double room per day.

Sports CentreResidential guests each pay £2 per day and casual visitors £3 per day for the use offacilities.Fixed costs £15 500

Sports ShopEstimated contribution £1 per person per day.Fixed costs £8250

CafeteriaEstimated contribution £1.50 per person per day.Fixed costs £12 750

During the summer season the centre is open 7 days a week and the followingactivity levels are anticipated:Double rooms fully booked for the whole season.

Question IM 8.11Intermediate:Marginal costingand absorptioncosting profitcomputations andcalculation ofbreak-even pointfor a given salesmix

Question IM 8.12Advanced: CVPanalysis based oncapacity usage ina leisure centre


Single rooms fully booked for the peak period but at only 80% of capacity duringthe rest of the season.30 casual visitors per day on average.

You are required to(a) calculate the charges for single and double rooms assuming that the authority

wishes to make a £10 000 profit on accommodation; (6 marks)(b) calculate the anticipated total profit for the leisure centre as a whole for the

season; (10 marks)(c) advise the authority whether an offer of £250 000 from a private leisure

company to operate the centre for five years is worthwhile, assuming that theauthority uses a 10% cost of capital and operations continue as outlined above.

(4 marks)(Total 20 marks)

CIMA Stage 3 Management Accounting Techniques


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