cvp assumpitions

8/9/2019 CVP ASSUMPITIONS

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1 All costs can be analysed into their fixed and variable elements.

When we talk about fixed and variable costs, we usually assume that it ispossible to take alook at individual or total costs and split them into their fixed and variable elements.

However, if we look at any organisation of a reasonably large size we will quickly appreciate

that not only might there be several hundred costs comprising total cost but also there aremany forces acting on those costs (cost drivers in activity based costing

parlance). Consequently, it cannot be a simple matter of a few minutes' analysis and the

fixed and variable split has been fully explained.

Splitting out fixed and variable costs can be a long, time consuming process; and techniques

such as the inspection of accounts method really are not suitable if the analysis is to be

realistic. At the very least, some kind of statistical or mathematical analysis will have to be

undertaken. I have undertaken this kind of an exercise in a wide variety of companies and

industries; and it takes many man hours to research the organisation, set up and work a

spreadsheet, analyse the results and then present my findings.

This is not to suggest that the splitting of fixed and variable costs is too difficult for theaverage student or practitioner. Consider diagram one below (which we can assume for the

sake of the discussion is the regression line derived from an analysis of a business's totalcosts) and suggest the level of fixed costs and hence calculate a variable cost per unit:

The graph is suggesting a regression equation of:

y = a + bx = 1,000 + 3x

Which, in the present context, will be interpreted as: the fixed cost for the business is 1,000;and the variable cost per unit is 3.

It should be remembered that this graph refers to the whole business and, as we have already

agreed, a reasonably large business is complex: consequently, although a statistical analysis

can be carried out, its results will not always be as simple to interpret as the assumptions on

which CVP analysis, and the example surrounding diagram one, would have us believe.


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Imagine the problems which must be faced by the analyst trying to cope with the kind of costportrayed in diagram five: no longer a straight line at all; and such cost profiles are likely to

be the normal: as opposed to straight lines, that is.

More than all of this, though: it is frequently the case that even the people working in an

organisation will have little or no idea

a) of their fixed/variable cost split; andb) b) how to split their total costs into their fixed and variable components if asked!

It is these two aspects that often cause management accountants to assume linearity and/or

spend many hours analysing total costs.

Assessing the fixed and variable cost split can be fraught with difficulties and can be

time consuming.

2 Fixed costs remain fixed even over a wide range of activity.

Another simplifying assumption which helps to keep the arithmetic of CVP analysis simplebut which does not help those of us who wish to apply the techniques.

The common view of fixed costs is given in diagram two:

However, the major error contained in such charts is that it ignores (or merely assumes away)

the importance of the relevantrange.

The relevant range is the range of levels of activity over which the business has direct

experience. That is, it has probably produced at or over that range of outputs; or it has

studied such levels of output carefully. Hence, no business will know with certainty what itsfixed costs will be outside its relevant range; and there is no guarantee that fixed costs willremain fixed if the business produces at a level of output outside its relevant range: whether

through expansion or contraction. Diagram three illustrates a more realistic scenario: where afixed cost can change as a result of a change in output level to a level outside the relevant

range. The relevant range in diagram three is represented as 401 units to 800 units.

The reasons why fixed costs will change in such a way include, for a reduction in

output: managers and supervisors being laid off as no longer required at reduced levels of


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output; machinery sold; buildings sold or not rented any more. A similar analysis applies toan increase in output and fixed costs.

Fixed costs behaving in this step cost fashion is another cause for concern over glibly trying

to apply CVP analysis. We may not, in fact, know how our fixed costs will behave outsideour relevant range unless and until we carry out detailed cost analysis of extra relevant range

scenarios.

3 Variable costs always vary directly with activity.

It is possible for a cost to be truly variable and behave in a perfectly linear way: think ofexamples such as making one standard design of wooden tables and chairs. However, it is

still useful to explore here the more likely exceptions to that behaviour.

Diagram four demonstrates how a perfectly variable cost behaves:

In reality, of course, a whole host of forces can act upon a cost which is deemed to be

variable. For example, once a business grows beyond a certain size it can then enjoy the

benefits of greater volume: such benefits are known as economies of scale and include being

awarded trade discounts, being offered cash discounts now that it can obtain credit; and

quantity discounts because it can now buy in greater bulk. Consequently, even though the


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quantity of components in a product remains standard and fixed, their cost per unit can fall asa result of these economies of scale.

These changes to the basic assumption of linearity mean that when diagram four shows a

perfectly straight line, reality could be more like diagram five where we can easily be dealing

with a situation where variable costs are essentially variable but which are not perfectly

variable. In the case of diagram five, we see a true curve; and any analysis of an estimationof a precise relationship between variable cost and output will yield a solution but not a linear

one. Again, since any reasonably large business will have many such costs, isolating the

variability of all such costs can be a major task.

There are many variations on the possible shapes which a variable cost curve might

assume. For example, it might be the case that at higher levels of output a variable cost curve

starts to slopes upwards again, having initially behaved like the curve in diagram five: such a

situation would hold when diseconomies of scale or increasing import tariffs were being

imposed.

4 Selling prices are constant per unit.

A very similar series of arguments holds for selling prices as held for variable costs. There is

no reason why any business needs to sell to all of its customers at the same price for allproducts. We could easily demonstrate that different prices are offered for different levels of

purchasing: for example, discounts for bulk buying. The hypothesis of supply and demandalso dictates that the higher the price the fewer will be sold; and the lower the price the more

will be sold. Diagram six combines the basic assumed sales curve and a more realistic sales

curve based on the arguments just put forward:

Again, when we consider the realistic side of total sales a true curve emerges; and again, thismeans that any analysis of sales immediately becomes more difficult than the basic

assumptions of CVP analysis would have us believe.


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As with the variable cost curve, there are potentially many shapes which the sales curve couldtake on: diagram six gives only one variation from the usually assumed straight line.

5 Only levels of activity affect costs and revenues

This, to some extent, is the worst of all of the assumptions from the point of view of a

realistic application of CVP analysis. It is the worst because it denies there being such things

as labour efficiency and changes to labour efficiency: the learning effect is ignored, or

assumed away, by this assumption, of course.

Along with all of the discussion so far, there are many reasons why a total cost or a cost per

unit might change; and changes in the level of output is only one. Consider your own

environment: why might any one of the costs with which you are associated change?

In the case of a manufacturer, costs might change because someone has improved the way an

operation is performed. A friend of mine, John, has a good eye for helping people to workmore efficiently. One day he hoticed that an operative in a factory was working on makingcomponents for a Poly Tunnel (greenhouse type thing!) and was working on a bench but

keeping his metal rods on the floor. John brought a stand around to where the operative wasworking and put the metal rods on there the operative then completed his jobs in half the

time it used to take! The consequences of this relate to time, productivity, possibly betterquality output and the cost per unit will have improved. None of the reason for this change in

cost is due to the restrictive assumption of output being the only determinant of cost.

6 usually only one product can be effectively dealt with

One product business

The reason for this assumption rests on the mathematics involved if more than one product is

assumed to be made. Although it is not the purpose of this paper to go too deeply into such

issues, we should be aware that trying to model a multi product business in terms of CVP

analysis can become very frustrating indeed. Consider diagram seven, which represents a ten

product business: all products have different characteristics, as we can see from the three

products included in the graph.


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Within this multiproduct business, there are six prices, all of which are subject to varying

levels of variability.

The purpose of the graph is to demonstrate that simply by analysing the total sales curve, and

ignoring its constituent parts, is likely to lead to serious errors of judgement or decisionmaking: the total sales curve is almost a straight line, but any one of the individual sales

curves for any product can be significantly different to a straight line; as is the case,

especially, with products three and ten.

Anysimplistic attempt at unravelling this business is destined to fail. The mathematical

model even for this relatively simple ten product business could run to several complete lines

across an A4 page. Such a model is not too unmanageable for most of us, but it is unwieldy

and cannot be readily simplified just for the sake of argument; and the same arguments would

apply equally well to the variable and fixed costs (although they have been excluded fromdiagram seven).

Sales mix issues

The sales mix argument is a straightforward one and it deals with the contribution to sales

ratio (the C/S ratio). If a business makes two products: one with a C/S ratio of 80% and theother with a C/S ratio of 70%, the average C/S ratio will notbe 75% (which would be

thesimple average of the two C/S ratios). The average C/S ratio has to be based on

the weighted average of the two; and the value of this weighted average varies as the sales

mix varies.

Consider the weighted averages in each of the following cases for the business just

introduced:


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Sales mix (i) Product 1 Product 2Sales (units) 100,000 200,000Sales () 500,000 300,000

C/S ratio (as given above) 80% 70%

The weighted average C/S ratio is:

Total Contribution= (500,000 x 80%) + (300,000 x 70%)Total Sales 500,000 + 300,000

= 76.25%

Sales mix (ii) Product 1 Product 2Sales (units) 300,000 350,000Sales () 1,500,000 525,000C/S ratio 80% 70%

The weighted average C/S ratio is:

Total Contribution=

(1,500,000 x 80%) + (525,000 x 70%)Total Sales 1,500,000 + 525,000

= 77.41%

By changing the sales mix, in a situation where the values of the C/S ratio change fromproduct to product, the weighted average value of all C/S ratios also changes; and unless this

point is appreciated, the results of any CVP analysis could easily be invalidated.

7 Uncertainty does not exist.

The final assumption underlying CVP analysis is that there is no such thing as

uncertainty. Everything is known and knowable to 100% certainty levels. Prices are sure;

variability of cost is certain; and there is nothing so certain as the level of fixed cost!

It should be clear that the only certainty about certainty is that it is certain not to

exist! Indeed, as has been said and widely quoted many times, the only things certain in this

world are death and taxes: CVP analysis was not included on that list!

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