tonne. If the business were to dispose of the material, it could sell any quantity but only for £36 a tonne; it does not have the contacts or reputation to command a higher price. Processing this material may be undertaken to develop either Product A or Product X. No weight loss occurs with the processing, that is, one tonne of material will make one tonne of A or X. For Product A, there is an additional cost of £60 a tonne, after which it will sell for £105 a tonne. The marketing department estimates that 500 tonnes could be sold in this way. With Product X, the business incurs additional costs of £80 a tonne for processing. A market price for X is not known and no minimum price has been agreed. The management is currently engaged in discussions over the minimum price that may be charged for Product X in the cur- rent circumstances. Management wants to know the relevant cost per tonne for Product X so as to provide a basis for negotiating a profitable selling price for the product. Required: Identify the relevant cost per tonne for Product X, given sales volumes of X of: (a) up to 1,500 tonnes (b) over 1,500 tonnes, up to 2,000 tonnes (c) over 2,000 tonnes. Explain your answer. A local education authority is faced with a predicted decline in the demand for school places in its area. It is believed that some schools will have to close in order to remove up to 800 places from current capacity levels. The schools that may face closure are referenced as A, B, C and D. Their details are as follows: l School A (capacity 200) was built 15 years ago at a cost of £1.2 million. It is situated in a ‘socially disadvantaged’ community area. The authority has been offered £14 million for the site by a property developer. l School B (capacity 500) was built 20 years ago and cost £1 million. It was renovated only two years ago at a cost of £3 million to improve its facilities. An offer of £8 million has been made for the site by a business planning a shopping complex in this affluent part of the area. l School C (capacity 600) cost £5 million to build five years ago. The land for this school is rented from a local business for an annual cost of £300,000. The land rented for School C is on a 100-year lease. If the school closes, the property reverts immediately to the owner. If School C is not closed, it will require a £3 million investment to improve safety at the school. l School D (capacity 800) cost £7 million to build eight years ago; last year £1.5 million was spent on an extension. It has a considerable amount of grounds, currently used for sporting events. This factor makes it popular with developers, who have recently offered £9 million for the site. If School D is closed, it will be necessary to pay £1.8 million to adapt facilities at other schools to accommodate the change. In the accounting system, the local authority depreciates non-current assets based on 2 per cent a year on the original cost. It also differentiates between one-off, large items of capital expenditure or revenue, and annually recurring items. The local authority has a central staff, which includes administrators for each school costing £200,000 a year for each school, and a chief education officer costing £80,000 a year in total. Required: (a) Prepare a summary of the relevant cash flows (costs and revenues, relative to not making any closures) under the following options: (i) closure of D only (ii) closure of A and B (iii) closure of A and C. Show separately the one-off effects and annually recurring items, rank the options open to the local authority, and briefly interpret your answer. Note: Various approaches are acceptable provided that they are logical. 2.6 CHAPTER 2 RELEVANT COSTS FOR DECISION MAKING 52 M02_ATRI3622_06_SE_C02.QXD 5/29/09 10:34 AM Page 52 (b) Identify and comment on any two different types of irrelevant cost contained in the infor- mation given in the question. (c) Discuss other factors that might have a bearing on the decision. Rob Otics Ltd, a small business that specialises in building electronic-control equipment, has just received an order from a customer for eight identical robotic units. These will be completed using Rob Otics’s own labour force and factory capacity. The product specification prepared by the estimating department shows the following material and labour requirements for each robotic unit: Component X 2 per unit Component Y 1 per unit Component Z 4 per unit Other miscellaneous items see below Assembly labour 25 hours per unit (but see below) Inspection labour 6 hours per unit As part of the costing exercise, the business has collected the following information: l Component X. This item is normally held by the business as it is in constant demand. The 10 units currently held were invoiced to Rob Otics at £150 a unit, but the sole supplier has announced a price rise of 20 per cent effective immediately. Rob Otics has not yet paid for the items currently held. l Component Y. 25 units are currently held. This component is not normally used by Rob Otics but the units currently held are because of a cancelled order following the bankruptcy of a customer. The units originally cost the business £4,000 in total, although Rob Otics has recouped £1,500 from the liquidator of the bankrupt business. As Rob Otics can see no use for these units (apart from the possible use of some of them in the order now being consid- ered), the finance director proposes to scrap all 25 units (zero proceeds). l Component Z. This is in regular use by Rob Otics. There is none in inventories but an order is about to be sent to a supplier for 75 units, irrespective of this new proposal. The supplier charges £25 a unit on small orders but will reduce the price to £20 a unit for all units on any order over 100 units. l Other miscellaneous items. These are expected to cost £250 in total. Assembly labour is currently in short supply in the area and is paid at £10 an hour. If the order is accepted, all necessary labour will have to be transferred from existing work, and other orders will be lost. It is estimated that for each hour transferred to this contract £38 will be lost (calcu- lated as lost sales revenue £60, less materials £12 and labour £10). The production director suggests that, owing to a learning process, the time taken to make each unit will reduce, from 25 hours to make the first one, by one hour a unit made. Inspection labour can be provided by paying existing personnel overtime which is at a pre- mium of 50 per cent over the standard rate of £12 an hour. When the business is working out its contract prices, it normally adds an amount equal to £20 for each assembly hour to cover its general costs (such as rent and electricity). To the resulting total, 40 per cent is normally added as a profit mark-up. Required: (a) Prepare an estimate of the minimum price that you would recommend Rob Otics Ltd to charge for the proposed contract such that it would be neither better nor worse off as a result. Provide explanations for any items included. (b) Identify any other factors that you would consider before fixing the final price. A business places substantial emphasis on customer satisfaction and, to this end, delivers its product in special protective containers. These containers have been made in a department 2.8 2.7 EXERCISES 53 M02_ATRI3622_06_SE_C02.QXD 5/29/09 10:34 AM Page 53 within the business. Management has recently become concerned that this internal supply of containers is very expensive. As a result, outside suppliers have been invited to submit tenders for the provision of these containers. A quote of £250,000 a year has been received for a vol- ume that compares with current internal supply. An investigation into the internal costs of container manufacture has been undertaken and the following emerges: (a) The annual cost of material is £120,000, according to the stores records maintained, at actual historic cost. Three-quarters (by cost) of this represents material that is regularly stocked and replenished. The remaining 25 per cent of the material cost is a special foam- ing chemical that is not used for any other purpose. There are 40 tonnes of this chemical currently held. It was bought in bulk for £750 a tonne. Today’s replacement price for this material is £1,050 a tonne but it is unlikely that the business could realise more than £600 a tonne if it had to be disposed of owing to the high handling costs and special transport facilities required. (b) The annual labour cost is £80,000 for this department; however, most workers in the depart- ment are casual employees or recent starters, and so, if an outside quote was accepted, little redundancy would be payable. There are, however, two long-serving employees who would each accept as a salary £15,000 a year until they reached retirement age in two years’ time. (c) The department manager has a salary of £30,000 a year. The closure of this department would release him to take over another department for which a vacancy is about to be advertised. The salary, status and prospects are similar. (d) A rental charge of £9,750 a year, based on floor area, is allocated to the containers depart- ment. If the department were closed, the floor space released would be used for ware- housing and, as a result, the business would give up the tenancy of an existing warehouse for which it is paying £15,750 a year. (e) The plant cost £162,000 when it was bought five years ago. Its market value now is £28,000 and it could continue for another two years, at which time its market value would have fallen to zero. (The plant depreciates evenly over time.) (f) Annual plant maintenance costs are £9,900 and allocated general administrative costs £33,750 for the coming year. Required: Calculate the annual cost of manufacturing containers for comparison with the quote using relevant figures for establishing the cost or benefit of accepting the quote. Indicate any assump- tions or qualifications you wish to make. CHAPTER 2 RELEVANT COSTS FOR DECISION MAKING 54 M02_ATRI3622_06_SE_C02.QXD 5/29/09 10:34 AM Page 54 Cost–volume–profit analysis LEARNING OUTCOMES This chapter is concerned with the relationship between volume of activity, cost and profit. Broadly, cost can be analysed between that element that is fixed, relative to the volume of activity, and that element that varies according to the volume of activity. We shall consider how we can use knowledge of this relationship to make decisions and to assess risk, particularly in the context of short-term decisions. This will help the business to work towards its strategic objectives. This continues the theme of Chapter 2, but in this chapter we shall be looking at situations where a whole class of cost – fixed cost – can be treated as being irrelevant for decision- making purposes. INTRODUCTION 3 When you have completed this chapter, you should be able to: l Distinguish between fixed cost and variable cost and use this distinction to explain the relationship between cost, volume and profit. l Prepare a break-even chart and deduce the break-even point for some activity. l Discuss the weaknesses of break-even analysis. l Demonstrate the way in which marginal analysis can be used when making short-term decisions. M03_ATRI3622_06_SE_C03.QXD 5/29/09 3:30 PM Page 55 We saw in the previous chapter that cost represents the resources that have to be sacrificed to achieve a business objective. The objective may be to make a particular product, to provide a particular service, to operate an IT department and so on. The costs incurred by a business may be classified in various ways and one important way is according to how they behave in relation to changes in the volume of activity. Costs may be classified according to whether they l remain constant (fixed) when changes occur to the volume of activity, or l vary according to the volume of activity. These are known as fixed cost and variable cost respectively. Thus, for example, in the case of a restaurant, the manager’s salary would normally be a fixed cost while the unprepared food would be a variable cost. As we shall see, knowing how much of each type of cost is associated with a par- ticular activity can be of great value to the decision maker. The way in which fixed cost behaves can be shown by preparing a graph that plots the fixed cost of a business against the level of activity, as in Figure 3.1. The distance 0F represents the amount of fixed cost, and this stays the same irrespective of the volume of activity. Fixed cost Cost behaviour CHAPTER 3 COST–VOLUME–PROFIT ANALYSIS 56 ‘ Graph of fixed cost against the volume of activity Figure 3.1 As the volume of output increases, the fixed cost stays exactly the same (0F). M03_ATRI3622_06_SE_C03.QXD 5/29/09 3:30 PM Page 56 Staff salaries (or wages) are often assumed to be a variable cost but in practice they tend to be fixed. Members of staff are not normally paid according to volume of out- put and it is unusual to dismiss staff when there is a short-term downturn in activity. Where there is a long-term downturn, or at least it seems that way to management, redundancies may occur, with fixed-cost savings. This, however, is true of all types of fixed cost. For example, management may also decide to close some branches to make rental cost savings. There are circumstances in which the labour cost is variable (for example, where staff are paid according to how much output they produce), but this is unusual. Whether labour cost is fixed or variable depends on the circumstances in the particular case concerned. It is important to be clear that ‘fixed’, in this context, means only that the cost is unaffected by changes in the volume of activity. Fixed cost is likely to be affected by inflation. If rent (a typical fixed cost) goes up because of inflation, a fixed cost will have increased, but not because of a change in the volume of activity. Similarly, the level of fixed cost does not stay the same irrespective of the time period involved. Fixed cost elements are almost always time-based: that is, they vary with the length of time concerned. The rental charge for two months is normally twice that for one month. Thus, fixed cost normally varies with time, but (of course) not with the volume of output. This means that when we talk of fixed cost being, say, £1,000, we must add the period concerned, say, £1,000 a month. FIXED COST 57 Can you give some examples of items of cost that are likely to be fixed for a hairdress- ing business? We came up with the following: l rent l insurance l cleaning cost l staff salaries. These items of cost are likely to be the same irrespective of the number of customers hav- ing their hair cut or styled. Activity 3.1 Does fixed cost stay the same irrespective of the volume of output, even where there is a massive rise in that volume? Think in terms of the rent cost for the hairdressing business. In fact, the rent is only fixed over a particular range (known as the ‘relevant’ range). If the number of people wanting to have their hair cut by the business increased, and the busi- ness wished to meet this increased demand, it would eventually have to expand its phys- ical size. This might be achieved by opening an additional branch, or perhaps by moving the existing business to larger premises nearby. It may be possible to cope with relatively minor increases in activity by using existing space more efficiently, or by having longer opening hours. If activity continued to expand, however, increased rent charges would seem inevitable. Activity 3.2 M03_ATRI3622_06_SE_C03.QXD 5/29/09 3:30 PM Page 57 At lower volumes of activity, the rent cost shown in Figure 3.2 would be 0R. As the volume of activity expands, the accommodation becomes inadequate and further expansion requires an increase in premises and, therefore, cost. This higher level of accommodation provision will enable further expansion to take place. Eventually, additional cost will need to be incurred if further expansion is to occur. Elements of fixed cost that behave in this way are often referred to as stepped fixed cost. We saw earlier that variable cost varies with the volume of activity. In a manufactur- ing business, for example, this would include the cost of raw materials used. Variable cost can be represented graphically as in Figure 3.3. At zero volume of activ- ity, the variable cost is zero. It then increases in a straight line as activity increases. Variable cost CHAPTER 3 COST–VOLUME–PROFIT ANALYSIS 58 ‘ Graph of rent cost against the volume of activity Figure 3.2 As the volume of activity increases from zero, the rent (a fixed cost) is unaffected. At a particu- lar point, the volume of activity cannot increase further without additional space being rented. The cost of renting the additional space will cause a ‘step’ in the rent cost. The higher rent cost will continue unaffected if volume rises further until eventually another step point is reached. Can you think of some examples of cost that are likely to be variable for a hairdressing business? We can think of a couple: l lotions, sprays and other materials used; l laundry cost to wash towels used to dry customers’ hair. As with many types of business activity, variable cost incurred by hairdressers tends to be low in comparison with fixed cost: that is, fixed cost tends to make up the bulk of total cost. Activity 3.3 In practice, the situation described in Activity 3.2 would look something like Figure 3.2. M03_ATRI3622_06_SE_C03.QXD 5/29/09 3:30 PM Page 58 The straight line for variable cost on Figure 3.3 implies that this type of cost will be the same per unit of activity, irrespective of the volume of activity. We shall consider the practicality of this assumption a little later in this chapter. In some cases, cost has an element of both fixed and variable cost. It can then be described as semi-fixed (semi-variable) cost. An example might be the electri- city cost for the hairdressing business. Some of this will be for heating and lighting, and this part is probably fixed, at least until the volume of activity expands to a point where longer opening hours or larger premises are necessary. The other part of the cost will vary with the volume of activity. An example would be power for hairdryers. Semi-fixed (semi-variable) cost SEMI-FIXED (SEMI-VARIABLE) COST 59 ‘ Graph of variable cost against the volume of activity Figure 3.3 At zero activity, there is no variable cost. However, as the volume of activity increases, so does the variable cost. Can you suggest another cost for a hairdressing business that is likely to be semi-fixed (semi-variable)? We thought of telephone charges for landlines. These tend to have a rental element, which is fixed, and there may also be certain calls that have to be made irrespective of the vol- ume of activity involved. However, increased business would be likely to lead to the need to make more telephone calls and so to increased call charges. Activity 3.4 M03_ATRI3622_06_SE_C03.QXD 5/29/09 3:30 PM Page 59 From the graph we can say that the fixed element of the electricity cost is the amount represented by the vertical distance from the origin at zero (bottom left-hand corner) to the point where the line of best fit crosses the vertical axis of the graph. The variable cost per unit is the amount that the graph rises for each increase in the vol- ume of activity. By breaking down semi-fixed cost into its fixed and variable elements in this way, we are left with just two types of cost: fixed cost and variable cost. Armed with knowledge of how much each element of cost represents for a particu- lar product or service, it is possible to make predictions regarding total and per-unit cost at various projected levels of output. Such predictive information can be very use- ful to decision makers, and much of the rest of this chapter will be devoted to seeing how, starting with break-even analysis. Estimating semi-fixed (semi-variable) cost Often, it is not obvious how much of each element a particular cost contains. However, past experience may provide some guidance. Let us again take the example of electricity. If we have data on what the electricity cost has been for various volumes of activity, say the relevant data over several three-month periods (electricity is usually billed by the quarter), we can estimate the fixed and variable portions. This may be done graphic- ally, as shown in Figure 3.4. We tend to use past data here purely because they provide us with an estimate of future cost; past cost is not, of course, relevant for its own sake. Each of the dots in Figure 3.4 is the electricity charge for a particular quarter plotted against the volume of activity (probably measured in terms of sales revenue) for the same quarter. The diagonal line on the graph is the line of best fit. This means that this was the line that best seemed (to us, at least) to represent the data. A better estimate can usually be made using a statistical technique (least squares regression), which does not involve drawing graphs and making estimates. In practice, though, it probably makes little difference which approach is taken. CHAPTER 3 COST–VOLUME–PROFIT ANALYSIS 60 ‘ Graph of electricity cost against the volume of activity Figure 3.4 Here the electricity bill for a time period (for example, three months) is plotted against the vol- ume of activity for that same period. This is done for a series of periods. A line is then drawn that best ‘fits’ the various points on the graph. From this line we can then deduce both the cost at zero activity (the fixed element) and the slope of the line (the variable element). M03_ATRI3622_06_SE_C03.QXD 5/29/09 3:30 PM Page 60 If, for a particular product or service, we know the fixed cost for a period and the vari- able cost per unit, we can produce a graph like the one shown in Figure 3.5. This graph reveals the total cost over the possible range of volume of activity. Finding the break-even point The bottom part of Figure 3.5 shows the fixed-cost area. Added to this is the variable cost, the wedge-shaped portion at the top of the graph. The uppermost line represents the total cost over a range of volume of activity. For any particular volume, the total cost can be measured by the vertical distance between the graph’s horizontal axis and the relevant point on the uppermost line. Logically, the total cost at zero activity is the amount of the fixed cost. This is because, even where there is nothing going on, the business will still be paying rent, salaries and so on, at least in the short term. As the volume of activity increases from zero, the fixed cost is augmented by the relevant variable cost to give the total cost. If we take this total cost graph in Figure 3.5, and superimpose on it a line represent- ing total revenue over the range of volume of activity, we obtain the break-even chart. This is shown in Figure 3.6. Note in Figure 3.6 that, at zero volume of activity (zero sales), there is zero sales rev- enue. The profit (loss), which is the difference between total sales revenue and total cost, for a particular volume of activity is the vertical distance between the total sales revenue line and the total cost line at that volume of activity. Where there is no ver- tical distance between these two lines (total sales revenue equals total cost) the volume of activity is at break-even point (BEP). At this point there is neither profit nor loss: that is, the activity breaks even. Where the volume of activity is below BEP, a loss will be incurred because total cost exceeds total sales revenue. Where the business operates at a volume of activity above BEP, there will be a profit because total sales revenue will FINDING THE BREAK-EVEN POINT 61 ‘ ‘ Graph of total cost against volume of activity Figure 3.5 The bottom part of the graph represents the fixed cost element. To this is added the wedge- shaped top portion, which represents the variable cost. The two parts together represent total cost. At zero activity, the variable cost is zero, so total cost equals fixed cost. As activity increases so does total cost, but only because variable cost increases. We are assuming that there are no steps in the fixed cost. M03_ATRI3622_06_SE_C03.QXD 5/29/09 3:30 PM Page 61 [...]... Survey of Management Accounting, Ernst and Young, 2003 Using contribution to make decisions – marginal analysis If we cast our minds back to Chapter 2, where we discussed relevant costs for decision making, we should recall that when we are trying to decide between two or more possible courses of action, only costs that vary with the decision should be included in the decision analysis For many decisions... costs of operating the workshop for a month total £500 Each basket requires materials that cost £2 Each basket takes one hour to make, and the business pays the basket makers £10 an hour The basket makers are all on contracts such that if they do not work for any reason, they are not paid The baskets are sold to a wholesaler for £14 each What is the BEP for basket making for the business? Solution The... books: Drury, C., Management and Cost Accounting, 7th edn, Cengage Learning, 2007, chapter 8 Hilton, R., Managerial Accounting, 6th edn McGraw-Hill Irwin, 2005, chapter 8 Horngren, C., Foster, G., Datar, S., Rajan, M and Ittner, C., Cost Accounting: A Managerial Emphasis, 13th edn, Prentice Hall International, 2008, chapter 3 McWatters, C., Zimmerman, J and Morse, D., Management Accounting: Analysis... less risk of things going wrong Closing or continuation decisions It is quite common for businesses to produce separate financial statements for each department or section, to try to assess their relative performance Example 3.3 below considers how marginal analysis can help decide how to respond where it is found that a particular department underperforms Example 3.3 Goodsports Ltd is a retail shop that... is subcontracted For example, the producer may have a component for the appliance made by another manufacturer In principle, there is hardly any limit to the scope of make-or-buy decisions Virtually any part, component or service that is required in production of the main product or service, or the main product or service itself, could be the subject of a make-or-buy decision So, for example, the personnel... Marginal analysis may be used in four key areas of decision making: l accepting/rejecting special contracts; l determining the most efficient use of scarce resources; l make-or-buy decisions; l closing or continuation decisions We shall now consider each of these areas in turn Accepting/rejecting special contracts To understand how marginal analysis may be used in decisions as to whether to accept or reject... (12) 11 4 £2.75 3rd Therefore produce: 20 units of product B17 using 22 units of product B14 using 60 hours 88 hours 148 hours This leaves unsatisfied the market demand for a further 3 units of product B14 and 30 units of product B22 Activity 3.14 What steps could be taken that might lead to a higher level of contribution for the business in Activity 3.13? The possibilities for improving matters that... fears’, Financial Times, 28 February 2008 Real World 3.7 provides a more formal insight into the extent to which managers in practice use break-even analysis M03_ATRI3622_06_SE_C03.QXD 5/29/09 3:30 PM Page 77 USING CONTRIBUTION TO MAKE DECISIONS – MARGINAL ANALYSIS REAL WORLD 3.7 Break-even analysis in practice A survey of management accounting practice in the United States was conducted in 2003 Nearly... equation for calculating b looks perfectly logical Though the BEP can be calculated quickly and simply without resorting to graphs, this does not mean that the break-even chart is without value The chart shows the relationship between cost, volume and profit over a range of activity and in a form that can easily be understood by non-financial managers The break-even chart can therefore be a useful device for. .. the decision, because it will be the same irrespective of the decision made This is because either l fixed cost elements tend to be impossible to alter in the short term or l managers are reluctant to alter them in the short term Activity 3.11 Ali plc owns premises from which it provides a PC repair and maintenance service There is a downturn in demand for the service, and it would be possible for Ali . machine With the machine ££££ Sales revenue (500 × 14 ) 7,000 7,000 Materials (500 × £2) (1, 000) (1, 000) Labour (500 × 1 × 10 ) (5,000) (500 × 1 /2 × 10 ) (2,500) Fixed cost (500 ) (3,000) ( 6,500. 429 Difference (margin of safety): Number of baskets 250 71 Percentage of estimated volume of sales 50% 14 % Margin of safety 14 − 7 14 14 − 12 14 Contribution Sales revenue MARGIN OF SAFETY 67 ‘ ‘ What. (number 500 1, 000 1, 500 500 1, 000 1, 500 of baskets) ££££££ Contribution* 1, 000 2,000 3,000 3,500 7,000 10 ,500 Fixed cost (500 ) (500 ) (500 ) ( 3,000 ) ( 3,000 ) (3,000 ) Profit 500 1, 500 2,500