8 COST-VOLUME-PROFIT - Waikato Management · PDF fileChapter 8: Cost-Volume-Profit 141 -...

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8 COST-VOLUME-PROFIT

IntroductionCost-Volume-Profit AnalysisBreakeven Analysis

- Selling Price Changes- Volume Changes- Variable Cost Changes- Fixed Cost Changes

Cost-Volume-Profit with Stepped Costs - ‘Option II’Multiple Changes Involving Fixed and Variable

Costs - ‘Option III’Multiple Breakeven Points - A Special CaseSpreadsheet ApplicationProfitability and Breakeven Analysis through Contribution MarginMargin of SafetyCost-Volume-Profit AssumptionsSummary

IntroductionThis chapter explores breakeven analysis and the manner in which fixed andvariable costs interact, as well as discussing the use of these concepts formanagement operating decisions. Such decisions involve the interaction of all thebasic operating elements, including:

- sales volume and price- production volume- variable and fixed production costs.

Cost-volume-profit relations provide management with the means to makestatements about the likely profitability of a venture or particular product line. Therelationship between sales price, variable costs, fixed costs and volume allowmanagement to massage the relative levels of these factors to achieve managementobjectives of profitability, risk aversion, and breakeven point. Thus, the purpose ofthis chapter is to present the variables in such a way that the reader may betterunderstand their contribution to management operating decisions.

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140 Financial Management and Decision Making

Cost-Volume-Profit AnalysisThe clearest way to present cost-volume-profit analysis is with the use of graphs.Exhibit 8.1 shows the typical representation of the cost- volume-profitrelationship and includes the breakeven point. The key elements of this graphinclude:

Fixed Costs: costs that do not vary with respect to output/quantity andinclude rates, insurance and many other overhead charges.Variable Costs: these costs vary in direct relationship to output/quantity andinclude direct labour and direct materials.Sales: the cumulative sales for the total period in question.

Assumptions of the model will be discussed in detail later. However, it can beassumed that costs, in particular, can be discretely divided between fixed andvariable components, and that sales revenue remains constant on a per unitbasis.

Exhibit 8.1 Cost-volume-profit Graph for Mousetrap Production

Dollars(100,000s)

BreakevenVolume

Volume in Units (100,000)

Fixed Costs

Total Costs(Fixed andVariable)

SalesRevenue

1 2 3 4 5 6 7 8 9 10

5

4

3

2

1

RelevantRange

In this example the firm produces mousetraps. The fixed costs are estimated to be$100,000 per year with variable costs per unit estimated to be 30c. It is expectedthat the mousetraps will be able to be sold for 50c and the marketing department hasestimated total sales to be between 500,000 and 700,000 units per year throughoutAustralasia and South East Asia with likely sales of 600,000 units. The graph wasproduced by initially entering the fixed cost at the $100,000 mark and the variablecosts were plotted on top of this at 30c per unit. The sum of these two elementsproduces the Total Cost line. The Revenue line starts at the origin (the first unitsold earns 50c and so on) and continues through the breakeven point into a zone ofprofitability. Clearly all points above the Breakeven Volume are profitable andthose below are not. To the graph is added the constraint of the ‘relevant range’which indicates the upper and lower limits of feasible activity. Several inputs willhelp define the relevant range and these will typically include:

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Chapter 8: Cost-Volume-Profit 141

- production ceiling for the given production facility and minimum productionlevel where it is simply not worthwhile operating the system,

- marketing information which may dictate a ceiling on sales in perhaps theshort-run and which might also indicate a minimum sales figure under whichit is simply not economic to sell the good when considering distribution andpromotion expenditure, and

- the size of the organisation may be such that an output of less than a certainamount is not viable when viewed alongside the volume of other activities inthe enterprise.

Based on company information the relevant range is estimated to extend from300,000 units to 900,000 units.

The relevant range is often said to cover that range of production when all theparameters are constant; however, we shall see later that one can legitimately relaxassumptions especially in the area of fixed costs.

From the above information we can determine the profitability at certain levels. Forexample, what would the position be at a volume of 600,000 units? By consultingExhibit 8.1 we can see that the 600,000 volume produces revenue of $300,000 andcosts of $280,000 resulting in an expected income or profitability of $20,000.

The position of the firm (whether a loss or profit) can be determined using theabove approach for any volume level. Also, the information may be deducedwithout the use of a graph. The above information may be represented in equationform.

The general Net Income situation is:

Net Income = Sales - Total Costs

We know from the earlier discussion that:

Total Costs = Fixed Costs + Variable Costs

Therefore:

Net Income = Sales - Fixed Costs - Variable Costs

Two of these items, sales and variable costs, are based on per unit value multipliedby volume. Therefore, we can represent the above formula as:

I = Sx - F - Vx

whereS = selling price per unitx = number of units soldF = total fixed costs

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V = variable cost per unitI = total net income

The position at the 600,000 volume level would be:

I = Sx - F - Vx= (0.50 x 600,000) - 100,000 - (0.30 x 600,000)= $20,000

Thus, the Mousetrap Manufacturing Company can work out its profitability at anylevel, say at 750,000 units, via the following:

I = Sx - F - Vx= x(S - V) - F= 750,000(.50 - .30) - 100,000= 150,000 - 100,000= $50,000

This basic approach is fundamental to all the cost-volume-profit, breakeven analysisand contribution approaches that are used for management decision making. Nomatter what the size of the organisation and no matter how detailed and complicatedthe particular problem, any question of production may be handled using these basicelements.

To summarise, any cost-volume-profit graph will generally look like Exhibit 8.2.By the time you have finished this chapter you should be familiar with the conceptsimplicit in this.

Exhibit 8.2Dollars

BreakevenVolume

Volume

Fixed Costs


SalesRevenue

RelevantRange

Loss Profitability

Breakeven AnalysisBreakeven analysis is used to give an indication of the robustness of a project or

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production operation. It gives an indication of what level of negative information(whether this be decrease in sales volume, decrease in sales price, increase in fixedcosts or an increase in variable production costs) can be sustained before the firmruns into a loss situation. The breakeven point may be calculated using the earlierequation and letting the net income be zero.

Using the information from Mousetrap Manufacturing and letting the net income bezero gives:

Sx = F + Vxx(S - V) = F

x = F/(S - V)x = 100,000/(.50 -.30)

= 500,000 units

This figure is the breakeven volume for the given information. Above this volumelevel the project will be profitable, and below, it will be in a loss situation.

What is generally calculated is how the project reacts to changes in the input figuresand thus we arrive at some measure of sensitivity or, as mentioned earlier, therobustness of the operation. Sensitivity analysis answers a series of ‘what if’questions, and helps define a likely operating region as well as worst and best casealternatives. Below we consider a series of changes to the initial information. It isnormal to initially consider each change as discrete and later to compound them.

Selling PriceChanges

Although 50c a unit is the expected selling price, sales staff feel that the market maydictate any price between 40c and 60c especially when exchange rate fluctuationsare taken into account. How profitable will the project be under each of thesealternatives?

Sales Price: 40c per unitI = Sx - F - Vx

= x(S - V) - F= 600,000(.40 - .30) - 100,000= $(40,000)

Sales Price: 60c per unitI = x(S - V) - F

= 600,000(.60 - .30) - 100,000= $80,000

Thus, at the three sales prices we have different profit and loss performances givena sales volume of 600,000 units.

Sales Price Profit/(Loss)40c (40,000)50c 20,00060c 80,000

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VolumeChanges

As discussed in the initial data, the marketing department has only broad indicationsabout likely sales volume, ranging from 500,000 through 700,000. We know theprofitability at the 600,000 output is $20,000, what is it at the others?

Volume: 500,000 unitsI = x(S - V) - F

= 500,000(.50 - .30) - 100,000= 0

Volume: 700,000 unitsI = x(S - V) - F

= 700,000(.50 - .30) - 100,000= $40,000

Thus, over the likely volume range the project should be profitable.

Volume Profit/(Loss)500,000 0600,000 20,000700,000 40,000

Variable CostChanges

Initial research indicated that the variable costs - including direct labour andmaterials - would amount to 30c per unit. The cost accountant feels that the costcould range from 25c to 40c per unit under actual production conditions.

Variable Costs: 25c per unitI = x(S - V) - F

= 600,000(.50 - .25) - 100,000= $50,000

Variable Costs: 40c per unitI = x(S - V) - F

= 600,000(.50 - .40) - 100,000= $(40,000)

Therefore, over the likely variable cost range the income fluctuates as below:

Variable Cost per Unit Profit/(Loss)25c 50,00030c 20,00040c (40,000)

The fourth area covered by the cost-volume-profit relationships is fixed cost.

Fixed CostChanges

It had been estimated that the fixed costs would amount to $100,000. However, alarge component is imported and therefore subject to exchange rate changes. After

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discussions with the International Manager at the bank it was felt that in the short tomedium term the exchange rate (against a basket of currencies) would be volatilebut tend to stay around its current position, also that the source country for the plantwould tend to devalue against our currency. Thus, likely fluctuations in the fixedcost might well be downwards. Two figures were selected for fixed costs, thesebeing $85,000 and $110,000.

Fixed Costs: $85,000

I = x(S - V) - F= 600,000(.50 - .30) - 85,000= $35,000

Fixed Costs: $110,000I = x(S - V) - F

= 600,000(.50 - .30) - 110,000= $10,000

The effects of differing fixed costs are:

Fixed Costs ($)Profit/(Loss)85,000 35,000

100,000 20,000110,000 10,000

After considering each discrete alternative it is important to combine alternativesinto one which is feasible in order to obtain some ‘feel’ for the robustness of theproject - remembering that the initial information was considered the most likelysingle point outcome. Two examples of combinations follow.

Generally unfavourable performanceSales volume 500,000Variable costs 40c per unitSales price 50c per unitFixed costs $110,000

I = x(S - V) - F= 500,000(.50 - .40) - 110,000= $(60,000)

Mixed performanceSales volume 700,000Sales price 40c per unitVariable costs 30c per unitFixed costs $110,000

I = x(S - V) - F= 700,000(.40 - .30) - 110,000= $(40,000)

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In both of these scenarios a loss situation develops, and it appears that the criticalelement in the analysis is the difference between the unit selling price (S) andvariable cost (V). This difference is the unit contribution margin. The use ofcontribution margin techniques is central to most segmental or departmentalanalysis as well as in deciding to add, drop or modify product lines. This area willbe looked at in detail in a later chapter.

Before turning to profitability and breakeven analysis through contribution margin,the cost-volume-profit example covered before should be extended to coverchanges to fixed costs, that is, stepped fixed costs.

Cost-Volume-Profit with Stepped Costs - ‘Option II’In the earlier example the Mousetrap Manufacturing Company was offered a singlepiece of plant that could produce up to 900,000 units. Following further discussionwith the suppliers, it is found that they can offer a staged multi-level modular plantsuch that Stage I can produce up to 600,000 units costing $75,000 and Stage II willadd 350,000 units and cost an extra $30,000. This is called ‘Option II’. The fixedcosts are shown in Exhibit 8.3.

Exhibit 8.3 Fixed Costs Option II

Dollars

Stage I

Stage II

600,000 950,000

The cost-volume-profit graph for this scenario is shown in Exhibit 8.4.

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Exhibit 8.4 Cost-volume-profit graph Option II

Dollars(100,000s)


Fixed Costs


SalesRevenue

1 2 3 4 5 6 7 8 9 10

5

4

3

2

1

RelevantRange

Stage IStage II

BreakevenPoint

This production alternative introduces some important alternatives. The breakevenvolume point becomes:

x = F/(S -V)= 75,000/(.50 - .30)= 375,000 units

which is 125,000 units less than before.

Is there a second breakeven point above the 600,000 unit level? Using the sum ofthe fixed costs (Stage I plus Stage II, or $75,000 + $30,000):

x = F/(S - V)= 105,000/(.50 - .30)= 525,000 units

This is less than 600,000 units where Stage II is introduced and since only the StageI development is in place, it is a fictitious result. However, if the firm had alsopurchased Stage II (and presumably could not sell it back to the supplier) then525,000 units would be the breakeven point.

From the preceding graph the area of profitability is shaded in Exhibit 8.5.

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Exhibit 8.5 Dollars(100,000s)


Fixed Costs


SalesRevenue

1 2 3 4 5 6 7 8 9 10

5

4

3

2

1

RelevantRange

Stage IStage II

BreakevenPoint

If the company has some control over its sales, what is the most economicproduction level? Initially the maximum income levels, immediately below thefixed cost step (599,999 units) and at the top of the relevant range (900,000 units)are calculated.

Note that the relevant range sets the higher income level not the feasible productionrange of 950,000 units.

599,999 unit levelI = x(S - V) - F

= 599,999(.50 - .30) - 75,000= $45,000

900,000 unit levelI = x(S - V) - F

= 900,000(.50 - .30) - 105,000= $75,000

At the 599,999 level the profit is greater than under the initial proposal (599,999unit = $20,000); at the 900,000 unit level, profit is less than under the initialproposal (900,000 unit = $80,000). However, from 600,000 units upwards the firstproposal will always be more profitable due to the higher fixed cost figure($100,000 compared with $105,000). Thus, if management feels cautious about theventure it should adopt the second proposal and use only Stage I. This would alsoallow the company to expand into Stage II if strong extra demand occurred althoughthe profitability would be less than with the first proposal. If management feels thatit is highly likely that sales will be over the 600,000 unit level then the companyshould opt for the first proposal.

The critical area for comparison is in the 500,000-700,000 unit range where themarketing department feels that sales will fall. This area should be looked at inmore detail rather then the extremes of the relevant range.

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A graphic representation of the relative profitability over this range is shown inExhibit 8.6.

Exhibit 8.6

50

40

30

20

10

0

5 6 7

DollarsProfitability

(1000s)

Initial Proposal

Option II

Units (100,000s)

25

45

15

35

40

It can be clearly seen that Option II is substantially better than the initial proposalover the 500,000-599,999 unit range and only moderately worse over the600,000-700,000 unit range ($5,000 less profit at all points). The final point to bemade about this illustration is that the breakeven point for Option II is 375,000units. Thus, the downside risk is much less.

All things being equal in a situation like the above, management would opt forOption II due to:

- substantially better profitability over half the expected sales range and onlymarginally worse over the other half (upper); and

- a lower breakeven point, down from 500,000 units to 375,000 units.

Multiple Changes Involving Fixed and Variable Costs - ‘Option III’This section extends the earlier example whereby, instead of an alternative steppedfixed cost proposal, the firm is offered a lower fixed cost proposal that wouldinvolve a more labour intensive process and hence higher variable costs. Thisscenario, labelled ‘Option III’, is fairly typical of the sorts of alternatives facingbusiness people. Typically, a higher fixed cost alternative will go hand in handwith lower variable costs and vice versa; for example, robotised car assemblycompared with older manual assembly line or manual work group situations. It isimportant to make sure that underlying comparability of proposals is still

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Exhibit 8.7

maintained since, for example, the automation alternative will often result in adifferent scale of operation.In this third option the fixed costs would be reduced to $35,000 over the entirerelevant range but the variable costs would increase by 10c to 40c per unit due toan increase in labour usage. Management must now reappraise the alternatives. The cost-volume-profit graph is shown in Exhibit 8.7.

3

2

1

1 2 3 4 5 6 7 8

Dollars(100,000s)

Breakeven Point

SalesRevenue


Fixed Costs

Volume

(100,000)

It can be seen that the total cost curve, although starting at a lower level ($35,000)than in the previous proposal, increases at a faster rate due to the higher ratio of unitvariable costs to unit sales price. This typically has two results. Firstly, that thebreakeven point is, ceteris paribus, lower than under a more capital intensive option(the initial proposal and Option II earlier). Secondly, that both profits and lossesaccrue at a slower rate than under more capital intensive approaches. This isbecause the fixed costs are covered more quickly due to being lower, but that onceprofitable, the profits accrue at a slower rate due to the lower contribution margin.

A comparison of the three options shows their various performances.

Breakeven Profit level at:Option Point 500,000 600,000 700,000

(units)I Initial 500,000 0 20,000 40,000II Multi Stage 375,000 25,000 15,000 35,000III Low Fixed Cost 350,000 15,000 25,000 35,000 It can be seen that the third option is a profitable performer, and in times ofdownturn will generally be less exposed than higher fixed cost options. However, asthe other options become more profitable they overhaul Option III until from700,000 units they are both more profitable.

Two general comments should be made concerning the issues raised above. A fewyears ago high fixed cost capital investment ventures normally implied inflexibleproduction, ‘assembly-line’ type operations in which the introduction of even

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relatively minor changes often involved substantial retooling and breaks inproduction. Thus, many companies in developing economies that could not beguaranteed large markets, tended to stay with lower fixed costs and relatively highlabour contents. This was a ‘Catch 22’ situation, for as the large scale operationsbecame more efficient their absolute profitability increased. This allowed them toreduce margins, sell more and squeeze the smaller producers out. We are now in anera of programmable, much more sophisticated capital equipment that can produce awide range of alternate items (within a family bounded by similar parameters butwithin which wide variations exist) with minimal or no delay to the production line. The result of this is that where previously producers could claim a market niche dueto their smaller size and often ‘craftsperson’ approach, large scale productionfacilities are now achieving the ability to produce smaller-run, specialist productswhile still maintaining their ‘high volume’ cost characteristics. The implications forsmaller business is in many cases fundamental as they either move into moresophisticated production and higher fixed cost facilities or they must close down. This question is currently facing many small to medium sized firms in the Pacific. The question is whether or not they can assemble the capital necessary to make thejump to a higher plane of equipment investment, and whether they are prepared toaccept the risk that goes with this.

The second point is that cost-volume-profit exists within the matrix of society and allof the political, economic and social factors of the society will impinge on anydecision made. Thus, from a management perspective it is critical to be aware of thewider ramifications of a ‘production’ decision and to keep in mind the wider issuesof the day. Too often one becomes myopic when faced with day to day decisionsand loses sight of the wider perspective.

Multiple Breakeven Points - A Special CaseIt is possible to end up with multiple breakeven points when the fixed costs changein a step fashion although this would be a special case. While in practice it seldomoccurs, this can be seen by modifying Option II in the earlier MousetrapManufacturing Company example. In that case the fixed costs were $75,000 forStage I and an extra $30,000 for Stage II that produced above 600,000 units. IfStage II had cost $50,000 or more then additional breakeven points would havebeen introduced. For example, if Stage II cost $60,000 then there would bebreakeven points at:

x = F/(S - V)= 75,000/(.50 - .30)= 375,000 units

andx = F/(S - V)

= 135,000/(.50 - .30)= 675,000 units

There would also be a breakeven point at the 600,000 unit level where the increasein fixed costs through Stage II occurs.

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This is shown graphically in Exhibit 8.8.

Exhibit 8.8 Option II with Modified Stage II

Dollars(100,000s)

Volume (100,000) 1 2 3 4 5 6 7 8

4

3

2

1

BreakevenPoints

Loss

Profit

If this were an actual case then the company would be unlikely to proceed due tothe second loss area in the centre of the relevant range. A result like this wouldtypically lead to a re-examination of the entire project. The project package (thatis, the mix of marketing, production, finance etc) would be reassessed to formulatea more acceptable proposition, or dropped entirely.

Spreadsheet ApplicationThis method of analysis is tailor-made for spreadsheets, and any good spreadsheetpackage will enable you to run ‘what if’ games with the data and so develop anappreciation of how a project would respond to changing parameters.

Profitability and Breakeven Analysis through Contribution MarginThe fundamental approach in finance and management decision making is an‘incremental’ or ‘discretionary’ one. This can also be called a ‘contribution margin’approach. These terms all have similar meanings, although you may find them definedspecifically in particular texts. However, the underlying principle of the contributionmargin and the incremental approach is fundamentally the same. It is different,however, from that found in a traditional financial Income Statement since in thecontribution margin approach the variable revenues and costs are grouped together soas to provide a contribution margin from which the fixed costs are then deducted. Thecontribution margin per unit will stay the same for all levels of output in the relevant

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range; thus, the percentage contribution margin to sales price will also remain thesame. Thus, the difference between total revenue and total variable costs, defined astotal contribution margin, will be directly proportional to the production/sales volume. This can be seen for the Mousetrap Manufacturing Company where the contributionmargin under the initial proposal was:

Units Sold Contribution Margin150,000 $30,000300,000 $60,000600,000 $120,000

From the total contribution margin we must deduct the fixed costs to arrive at the netincome. The breakeven point is typically calculated in terms of units and in terms ofdollars and simple formulae to derive these are shown below and in Exhibit 8.9.

Exhibit 8.9

FixedCosts

Dollars

3.75 6.75

Contribution Margin

Volume

Breakeven Sales

Total Costs

Variable Costs

Break-even in dollarsFrom the original cost-volume-profit equation and remembering that at thebreakeven point Income equals zero, then:

Sx = F + VxSx - Vx = Fx(S - V) = F

x = F/(S - V)

Multiplying both sides by S gives:

Sx = FS/(S - V)

and dividing numerator and denominator by S:

Sx = F/(1 - V/S)

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orSx = F / Contribution Margin Ratio

where Sx is the breakeven point in dollars (unit sales price x unit volume).Break-even in units

Sx = F + VxSx - Vx = Fx(S - V) = F

x = F/(S - V)or

x = F / Contribution Margin Per Unit

where x is the breakeven point in units.

Each of these equations can be modified to produce units or dollars of sales necessaryfor a required net income, simply by adding the targeted net income to the fixed costs. In each equation the top line then becomes fixed costs plus net income.

Required sales dollars (Sx) to obtain desired net income (I):

Sx = (F + I)/(1 - V/S)

Required sales volume (x) to obtain desired net income (I):

x = (F + I)/(S - V)

Option I, Mousetrap Manufacturing Company discussed earlier can be used toillustrate these formulae.

BEP100,000

1 .30/.50

100,000.40

$250,000

$ =−

=

=

BEP100,000.50 .30

500,000 units

$ =−

=

If a net income of $55,000 was required, the desired sales in dollars and units wouldbe:

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Sales100,000 55,000

1 .30/.50

$387,500

$ = +−

=

Sales100,000 55,000

.50 .30

775,000 units

units = +−

=

Although one would normally use the formulae to calculate specific outcomes, thepresentation of the data in graph form often provides for a better appreciation of theoverall situation, and should be utilised wherever appropriate, for example, inpresentations to staff or management.

Margin of SafetyMargin of safety is the level of sales decline that may take place before a losssituation occurs. This is commonly expressed in terms of percentage decline in salesor decline in units. This measure gives a useful guide as to how robust the product isand may be calculated after the ‘what if’ alternatives have been developed. UsingOption I as an example, the margin of safety at sales of 700,000 units is 200,000 units(700,000 units - breakeven units of 500,000) or 29%. Thus, a 29% downturn in salesmay take place before a loss will develop.

Cost-Volume-Profit AssumptionsIt is important to realise that cost-volume-profit is only a model of the real world.Although the model is particularly useful and is frequently used in business, one mustnevertheless still be aware of its assumptions and limitations. These include:

1. That variable costs and revenue are both linear throughout the relevant range.

This implies that there are no cost savings through purchasing large quantities ofraw materials nor are there any returns to scale or learning curve effects. Also onthe revenue side, no discount is given for large sales and the last item sold returnsas much as the first.

2. That fixed costs are constant across the relevant range. This assumption may be relaxed to incorporate a step in fixed costs within the

relevant range. However, the fixed costs are nevertheless fixed across each level,that is between each step.

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3. That a single volume measure may be used for both the costs and revenues. This implies that all production is sold and that there are no changes in inventory

levels. With increasing recognition currently that inventory holding is a majorcost and the consequent move towards substantially reduced inventory levels, thisassumption is reasonably fair. One can look to several industries that use the‘just-in-time’ approach whereby inventory holding is kept to a minimum andsometimes virtually nothing.

4. That fixed and variable costs can be meaningfully separated into their individual

elements. In real life some costs are clearly variable and some are clearly fixed. However,

there can be a wide range of items which fall somewhere between; in other words,they have both fixed and variable cost components. Cost-volume-profit analysisassumes that items are either fixed or variable.

5. That the analysis takes place over a particular time or production period (whether

it be a day, a week, or a year) and over that period no significant changes occur inproduction methods, management practice, price levels or any exogenous factors.

6. That the analysis is based on a single product or a group of products that are sold

in a fixed ratio to each other.

Cost-volume-profit analysis also assumes a relevant range of activity in which the aboverelationships or assumptions hold. However, it is not assumed that the aboverelationships hold from the first unit produced to the nth unit produced, since this wouldclearly be unreasonable and naive. The concept of the relevant range is that withincertain bounds, typically defined by production and marketing information, the cost andrevenue relationships approximate the assumptions discussed above. The realrelationship is shown in Exhibit 8.10 which introduces the various economic or realbusiness world elements into the analysis.

Exhibit 8.10

RelevantRange

Total Costs

Total RevenueDollarsSales

Volume in units

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The fundamental relationships of the cost and revenue structures remain the samealthough with some major differences.

Looking firstly at the revenue side, the total revenue starts out per unit at arelatively high level and as production increases the unit return gradually reducesas the firm is forced to reduce price in order to increase sales penetration. This canbe seen from a static analysis of demand and supply in which consumer demand isinitially relatively low but the price that the consumer is willing to pay is quite high. As one moves down the demand curve the price will fall but the volume willincrease.

Thus, the relationship shown in Exhibit 8.11 is reflected in the total revenue curve. Obviously there will be wide variations in the sorts of relationships one may finddepending on the competitive nature of the particular market place and theparticular factors which are impacting on it when the analysis is carried out.

Exhibit 8.11

Price

Initial Sales atHigh Price

Large Volume at Lower Price

Quantity

Turning to the cost side, the cost of producing the first unit will be fairly high due to lackof experience and operating inefficiencies. As production increases, a period ofincreasing efficiency and decreasing costs on a per unit basis occurs. The result ofdecreasing costs on a per unit basis is that the total cost curve increases at a slower rate. At high production levels inefficiencies begin to occur and at this stage the cost per unitwill typically begin to increase. The result of this is an increasing rate of increment inthe total cost curve. This produces the typical ‘S’ shaped total cost curve, shown inExhibit 8.12

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Exhibit 8.12

Cost

Volume

Cumulative orTotal Costs

Cost Per Unit

When the cost and revenue curves are brought together one expects to have adiagram as in Exhibit 8.10. The level of output that maximises profitability occurswhere there is the greatest vertical distance between the total cost curve and totalrevenue curve - it is not the place where the area between the curves to the left of theoutput level, is maximised. By moving a production process to the quantity levelwhere the total cost curve approaches the total revenue curve, the level of maximumsustainable output at a profitable level is approached. At this level, output wouldnormally be reduced and the firm would move back towards a more optimalsituation. However, many firms will operate between the area of maximum profitand maximum feasible output and take a less profitable situation. At the same time agreater market share (due to the greater output) can be obtained and other operatorsmay be discouraged from entering the field. To explain, if an industry is seen to behighly profitable then other producers will look to move in, the net effect being toreduce the available profits, due to greater competition and lowered margins. If theexisting enterprise moves to a level of higher output leading to less revenue per unit,the income available to new entrants in the field will be less and hence willdiscourage them. Obviously a number of questions must be raised when anenterprise finds itself in this situation. These include questions of life of the product,change in the nature of the market, whether the product is in an innovative or maturephase of the product cycle, etc. Thus, it is important that when considering thesequestions an in-depth industry and product analysis be undertaken. Too oftenbusiness people do not have either the time or the resources to adequately researchand evaluate the position of their product and their firm in a market place. This areais clearly one where the argument for an integrated business approach bringingtogether the elements of finance, production and marketing has considerable merit.

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SummaryA comment should be made concerning the assumptions of cost-volume-profit andthe relevance of the model. The relationships described in this section must be seenas approximations, or generalisations that have been found to work in the main, andwhich can typically help in better management decisions. However, at all times youmust be wary about changing factors which may negate the applicability orrelevance of a particular model, no matter what area you may be working in.

In many cases, especially in relatively short run situations the model is an extremelyuseful tool for making production decisions. Clearly when facing longer termdecisions, various parameters may change to such an extent that the model is nolonger valid. However, forms of the model incorporating sensitivity analysis as wellas strategic changes to various parameters can easily be constructed and make avaluable tool in business production planning. Thus, the cost-volume-profit model,while on the face of it relatively simplistic, is an extremely important toolembodying concepts fundamental to any real production situation.

Glossary ofKey Terms

Breakeven PointThe output level, measured in terms of sales dollars or units, where the total costsequal sales revenue.

Contribution MarginUnit contribution margin is the difference between selling price and variableproduction costs.

Production contribution margin is the revenue less the variable production costsby product line.

Product contribution margin is the total production contribution margin by productline, less the non-production variable costs of that product line.

Relevant RangeThe range of output over which the variables are constant.

Margin of SafetyThe amount by which sales may decline before a loss is incurred, typically expressedas a percentage of sales.

Sensitivity AnalysisA series of ‘what if’ alternatives that test how a project reacts to changes in keyvariables.

Product MarginThe product contribution margin less traceable or discretionary fixed costs.

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