One of the problems with the conventional or basic breakeven chart is that it is not pos- sible to read contribution directly from the chart. A contribution breakeven chart is based on the same principles but it shows the variable cost line instead of the fi xed cost line ( Figure 3.2 ). The same lines for total cost and sales revenue are shown so the breakeven point and profi t can be read off in the same way as with a conventional chart. However, it is also possible to read the contribution for any level of activity.
Using the same basic example as for the conventional chart, the total variable cost for an output of 1,700 units is 1,700 £30 £51,000. This point can be joined to the origin since the variable cost is nil at zero activity.
The contribution can be read as the difference between the sales revenue line and the variable cost line.
This form of presentation might be used when it is desirable to highlight the impor- tance of contribution and to focus attention on the variable costs.
Fixed cost
Contribution
Variable cost 90
80 70 60 50 40 30 20 10 0
0 400 800 1,200 1,600
Number of units Breakeven point
Total cost Sales revenue PROFIT
LOSS
£000
Figure 3.2 Contribution breakeven chart
Your own graph should be considerably larger than this: a full A4 graph-ruled sheet is recommended to facilitate ease of interpretation. Your graph should also have a clear title.
3.7 The profit–volume chart
Another form of breakeven chart is the profi t–volume chart. This chart plots a single line depicting the profi t or loss at each level of activity. The breakeven point is where this line cuts the horizontal axis. A profi t–volume chart for our example will look like Figure 3.3 .
The vertical axis shows profi ts and losses and the horizontal axis is drawn at zero profi t or loss.
At zero activity the loss is equal to £ 20,000, that is, the amount of fi xed costs. The sec- ond point used to draw the line could be the calculated breakeven point or the calculated profi t for sales of 1,700 units.
The profi t–volume chart is also called a profi t graph or a contribution-volume graph.
BREAKEVEN ANALYSIS
Exercise
Make sure that you are clear about the extremes of the chart axes. Practise drawing this chart to scale on a piece of graph paper.
3.7.1 The advantage of the profit–volume chart
The main advantage of the profi t–volume chart is that it is capable of depicting clearly the effect on profi t and breakeven point of any changes in the variables. An example will show how this can be done.
Example
A company manufactures a single product which incurs fi xed costs of £30,000 per annum. Annual sales are budgeted to be 70,000 units at a sales price of £30 per unit. Variable costs are £28.50 per unit.
(a) Draw a profi t–volume chart, and use it to determine the breakeven point.
The company is now considering improving the quality of the product and increasing the selling price to £ 35 per unit. Sales volume will be unaffected, but fi xed costs will increase to £45,000 per annum and vari- able costs to £33 per unit.
(b) Draw, on the same graph as for part (a), a second profi t–volume chart and comment on the results.
Profit PROFIT
Loss
LOSS
400 800 1,200
15 10 5 0 5 10 15 20
1,600 Breakeven
point
Number of units
£000
Figure 3.3 Profit–volume chart
Situation (a) Situation (b)
Breakeven point (a)
£000100 90 80 70
70 60
60 50
50 40
40 30
30 20
20 10
10 0
10 20 30 40 50
Breakeven point (b)
Number of units (000)
Profit Loss
Figure 3.4 Showing changes with a profit–volume chart
BREAKEVEN ANALYSIS Solution
The profi t–volume chart is shown in Figure 3.4 . The two lines have been drawn as follows:
● Situation ( a ). The profi t for sales of 70,000 units is £75,000.
£000
Contribution 70,000 £(30 28.50) 105
Fixed costs (30)
Profi t 75
This point is joined to the loss at zero activity, £30,000, that is, the fi xed costs.
● Situation ( b ). The profi t for sales of 70,000 units is £95,000.
£000
Contribution 70,000 £(35 33) 140
Fixed costs 45
Profi t 95
This point is joined to the loss at zero activity, £45,000, that is, the fi xed costs.
Comment on the results
The chart depicts clearly the larger profi ts available from option (b). It also shows that the breakeven point increases from 20,000 units to 22,500 units but that this is not a large increase when viewed in the context of the projected sales volume. It is also possible to see that for sales volumes above 30,000 units the profi t achieved will be higher with option (b). For sales volumes below 30,000 units option (a) will yield higher profi ts (or lower losses).
The profi t–volume chart is the clearest way of presenting information like this. If we attempted to draw two con- ventional breakeven charts on one set of axes the result would be a jumble that would be very diffi cult to interpret.
3.8 The limitations of breakeven (or CVP) analysis
The limitations of the practical applicability of breakeven analysis and breakeven charts stem mostly from the assumptions that underlie the analysis:
(a) Costs are assumed to behave in a linear fashion. Unit variable costs are assumed to remain constant and fi xed costs are assumed to be unaffected by changes in activity levels. The charts can in fact be adjusted to cope with non-linear variable costs or steps in fi xed costs, but too many changes in behaviour patterns can make the charts very cluttered and diffi cult to use.
(b) Sales revenues are assumed to be constant for each unit sold. This may be unrealistic because of the necessity to reduce the selling price to achieve higher sales volumes.
Once again, the analysis can be adapted for some changes in selling price but too many changes can make the charts unwieldy.
(c) There is assumed to be no change in inventory. Reported profi ts can vary if absorption costing is used and there are changes in inventory levels.
(d) It is assumed that activity is the only factor affecting costs, and factors such as infl ation are ignored. This is one of the reasons why the analysis is limited to being essentially a short-term decision aid.
(e) Apart from the unrealistic situation of a constant product mix where a range of products are sold but always in the same ratio to one another, the charts can only be applied to a single product or service. Not many organisations have a single product or
BREAKEVEN ANALYSIS
service, and if there is more than one then the apportionment of fi xed costs between them becomes arbitrary.
(f ) The analysis seems to suggest that as long as the activity level is above the breakeven point, then a profi t will be achieved. In reality certain changes in the cost and revenue patterns may result in a second breakeven point after which losses are made. This situ- ation will be depicted in the next section of this chapter.
3.9 The economist’s breakeven chart
An economist would probably depict a breakeven chart as shown in Figure 3.5 .
The total cost line is not a straight line that climbs steadily as in the accountant’s chart.
Instead it begins to reduce initially as output increases because of the effect of economies of scale. Later it begins to climb upwards according to the law of diminishing returns.
The revenue line is not a straight line as in the accountant’s chart. The line becomes less steep to depict the need to give discounts to achieve higher sales volumes.
However, you will see that within the middle range the economist’s chart does look very similar to the accountant’s breakeven chart. This area is marked as the relevant range in Figure 3.5 .
For this reason it is unreliable to assume that the cost–volume–profi t relationships depicted in breakeven analysis are relevant across a wide range of activity. In particular, Figure 3.5 shows that the constant cost and price assumptions are likely to be unreliable at very high or very low levels of activity. Managers should therefore ensure that they work within the rel- evant range for the available data, that is, within the range over which the depicted cost and revenue relationships are more reliable.
£000
Activity level Breakeven
point (1)
Relevant range
Total cost Revenue Breakeven
point (2)
Figure 3.5 The economist’s breakeven chart
3.10 Using costs for decision-making
Most management decisions involve a change in the level, method or mix of activities in order to maximise profi ts. The only costs that should be considered in decision-making are those that will be altered as a result of the decision. Those costs that will be affected by the decision may be referred to as relevant costs, while others are non-relevant and should be ignored in the analysis.
BREAKEVEN ANALYSIS It is often the case that variable costs are relevant whereas fi xed costs are not, unless the decision affects the cost structure of the organisation. Thus, information for decision- making should always be based on marginal costing principles, since marginal costing focuses on the variable costs and is not concerned with arbitrary apportionment of fi xed costs that will be incurred anyway.
3.10.1 Short-term decision-making
An important point that you should appreciate for all of the decision-making techniques that you learn about in this chapter is that they are usually most relevant to short-term, one-off decisions. Furthermore, as you will see with the example of the minimum-price quotation, the analysis provides only a starting point for management decisions. The fi nan- cial fi gures are only part of the information needed for a fully informed decision. It is also important to consider the non-fi nancial factors which might be relevant to the decision.
You must get into the habit of considering non-fi nancial and qualitative fac- tors in any decision. Many exam questions will specifi cally ask you to do so.
3.11 Evaluating proposals
As an introduction to using cost information to evaluate proposals, use your understand- ing of breakeven analysis and cost behaviour patterns to evaluate the proposals in the fol- lowing exercise.
Exercise
A summary of a manufacturing company’s budgeted profi t statement for its next fi nancial year, when it expects to be operating at 75 per cent of capacity, is given below.
£ £
Sales 9,000 units at £32 288,000
Less:
direct materials 54,000
direct wages 72,000
production overhead – fi xed 42,000
– variable 18,000
186,000
Gross profi t 102,000
Less: admin., selling and dist’n costs:
– fi xed 36,000
– varying with sales volume 27,000
63,000
Net profi t 39,000
It has been estimated that:
(i) if the selling price per unit were reduced to £28, the increased demand would utilise 90 per cent of the company’s capacity without any additional advertising expenditure;
(ii) to attract suffi cient demand to utilise full capacity would require a 15 per cent reduc- tion in the current selling price and a £5,000 special advertising campaign.
BREAKEVEN ANALYSIS
You are required to:
(a) calculate the breakeven point in units, based on the original budget;
(b) calculate the profi ts and breakeven points which would result from each of the two alternatives and compare them with the original budget.
Solution
(a) First calculate the current contribution per unit.
£000 £000
Sales revenue 288
Direct materials 54
Direct wages 72
Variable production overhead 18
Variable administration, etc. 27
171
Contribution 117
Contribution per unit ( 9,000 units) £13
Now you can use the formula to calculate the breakeven point.
Breakeven point Fixed costs Contribution per unit
£ ,42 000£336 000
13 , 6 000
£ , units
(b) Alternative (i)
Budgeted contribution per unit £13
Reduction in selling price (£32 £28) £4
Revised contribution per unit £9
Revised breakeven point£ ,
£ 78 000
9 8,667 units
Revised sales volume9 00090
, 75 10,800 units
Revised contribution 10,800 £9 £97,200
Less fi xed costs £78,000
Revised profi t £19,200
Alternative ( ii )
Budgeted contribution per unit £13.00
Reduction in selling price (15% £32) £4.80
Revised contribution per unit £8.20
Revised breakeven point£ , £ ,
£ .
78 000 5 000
8 20 10,122 units
Revised sales volume9 000 units100
, 75 12,000 units
Revised contribution 12,000 £8.20 £98,400
Less fi xed costs £83,000
Revised profi t £15,400
Neither of the two alternative proposals is worthwhile. They both result in lower fore- cast profi ts. In addition, they will both increase the breakeven point and will therefore increase the risk associated with the company’s operations. This exercise has shown you how an understanding of cost behaviour patterns and the manipulation of contribution
BREAKEVEN ANALYSIS can enable the rapid evaluation of the fi nancial effects of a proposal. We can now expand it to demonstrate another aspect of the application of marginal costing techniques to short- term decision-making.
Exercise
The manufacturing company decided to proceed with the original budget and has asked you to determine how many units must be sold to achieve a profi t of £ 45,500.
Solution
Once again, the key is the required contribution. This time the contribution must be suf- fi cient to cover both the fi xed costs and the required profi t. If we then divide this amount by the contribution earned from each unit, we can determine the required sales volume.
Required sales Fixed costs required profit Contribution per
unit
units (£ , £ , )£ ,
£ ,
42 000 36 000 45 500
13 9 500
3.12 The impact of risk and uncertainty on cost–volume–profit analysis
Cost–volume–profi t analysis can be used by a decision-maker to determine the effect of changes in variables such as fi xed costs, variable costs and sales price on future profi ts.
However, the specifi c profi t earned will depend on actual levels of revenue, cost, etc.
In practice, all such decisions are based on forecasts, which cannot be predicted with certainty.
If even the likely outcomes cannot be predicted with confi dence, the decision-maker is said to be subject to uncertainty. However, where the forecaster knows the various poten- tial outcomes and can predict with some accuracy the probability of each outcome occur- ring, the decision is described as one subject to risk.
By using techniques such as probability and normal distributions, the element of risk associated with breakeven analysis can be accounted for.
3.12.1 Normal distribution and CVP
This technique can be used where the decision-maker can produce estimates for:
● the average or mean fi gure for a variable;
● the standard deviation or the likely variability of the variable.
Example
A sales manager has identifi ed fi xed costs for a new product of £1,200,000. The product is to be sold for
£6 and has associated variable costs of £3.50. She predicts that the mean sales for the coming year would be 500,000 units. She also believes that the sales volume is normally distributed with a standard deviation of 16,000 units. What is the probability of at least breaking-even?
BREAKEVEN ANALYSIS Solution
The breakeven point in units is calculated as:
£ , ,
£ .1 200 000£ . , 6 00 3 50 480 000
units
Since sales are normally distributed, they can be represented on the following curve:
500,000
480,0001.25 Sales units
The z value for the shaded area in the above diagram can be found using the formula:
z x
= μ σ
z 480 000500 000
16 000 1 25
, ,
, .
From the tables, the shaded area therefore has a probability of 0.3944. Since the area above the mean has a probability of 0.5, the overall probability of at least breaking-even is:
0.5 0.3944 0.8944 or 89.44%
With this information, the sales manager may well decide that production should go ahead.
Example
A second product has associated fi xed costs of £2,300,000. The selling price will be £12 and the associ- ated variable costs are £8.75. The sales manager predicts that the mean sales for the coming year would be 600,000 units. She also believes that the sales volume is normally distributed and that there is a 60% chance that sales will be within 200,000 units of the average. What is the probability that profi ts will be at least
£230,000?
Solution
The breakeven point is:
£ , ,
£ 2 300 000. £ . , 14 50 8 75 400 000
units
BREAKEVEN ANALYSIS The shaded area in the diagram below represents the chance that sales will be below average but within 200,000 units of it. If there is a 60% chance that sales could be 200,000 units above or below the average, then the shaded area has an associated probability of 0.6/2 0.3
600,000 400,000
p=0.3
From the tables, the z value below the mean at p 0.3 is 0.845 Using the formula for standard deviation:
z x μ
σ
The standard deviation can be calculated as:
0 845 400 000 600 000 0 845 200 000
236 687
. , ,
. ,
, σ σ
σ = units
There is now suffi cient data to fi nd the probability that profi ts would be at least £230,000:
To earn £230,000 profi t, a further
£ ,
£ .230 000£ . , 14 50 8 75 40 000
units
above the breakeven fi gure of 400,000 must be sold.
The probability of selling at least 440,000 units has a z value of:
z440 000600 000
236 687 0 68
, ,
, .
From the tables, the probability associated with a z value of 0.68 is 0.2518.
So the probability of selling at least 440,000 units is 0.2518 0.5 0.7518 or 75.18%.
3.13 Multi-product CVP analysis
The basic breakeven model can be used satisfactorily for a business operation with only one product. The model has to be adapted somewhat when one is considering a business operation with several products.
A simple example can be developed to illustrate the various model adaptations that are possible.
BREAKEVEN ANALYSIS
Example
A business operation produces three products, the X, the Y and the Z. Relevant details are:
X Y Z
Normal sales mix (units) 2 : 2 : 1
£ £ £
Selling price per unit 9 7 5
Variable cost per unit 6 5 1
Contribution per unit 3 2 4
Forecast unit sales 400 400 200
Fixed costs are £2,000 per period, not attributable to individual products.
A budget for the forecast is as follows:
X Y Z Total
£ £ £ £
Sales revenue 3,600 2,800 1,000 7,400
Variable costs 2,400 2,000 200 4,600
Contribution 1,200 800 800 2,800
Fixed costs 2,000
Profi t 800
The objective is to construct a CVP chart for the business operation. Several alternative approaches are possible and three are now considered.
0 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000
200 400 600
Units (400X, then 400Y, then 200Z) 800 1000
costs revenues
£
Figure 3.6 CVP chart – X, Y and Z in sequence
1. Consider the products in sequence, X then Y then Z ( Figure 3.6 )
In this case it can be seen that breakeven occurs at 800 units of sales (400X plus 400Y) and the margin of safety is 200 units of Z.
2. Consider output in terms of £ sales and assume a constant product mix (2X:2Y:1Z) ( Figure 3.7 )
Inspection of the budget (above) shows that £1 sales is associated with £0.6216 variable costs (that is, £ 4,600 variable costs ÷ £ 7,400 sales). The contribution per £1 sales is £0.3784 (i.e. £1 £ 0.6216).
So, if the fi xed costs are £2,000 then the breakeven point is £5,285 sales (£2,000÷£0.3784) and the margin of safety is £2,115 (i.e. £7,400 forecast sales £ 5,285).
BREAKEVEN ANALYSIS
The general point of the foregoing discussion is that output can be viewed in several dif- ferent ways. Cost–volume–profi t analysis exercises can adopt any of these different ways.
3.14 Using the C/S ratio – an example
Decisions about a company’s cost structure will affect its risk profi le. The cost structure of a company is made up of fi xed and variable costs. The proportion of each depends on business strategy – for example, companies that
0 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000
2000 4000 6000
£ Sales revenue 8000
costs revenues
£ Sales revenue
Figure 3.7 CVP chart – sales with constant product mix
3. Consider output in terms of percentage of forecast sales and a constant product mix ( Figure 3.8 )
Inspection of the budget ( Figure 3.8 ) shows that 1 per cent of forecast sales is associated with a contribu- tion of £28.00 (i.e. £2,800 total contribution ÷ 100 per cent). So, if fi xed costs are £2,000 it follows that the breakeven point is 71.43 per cent and the margin of safety is 28.57 per cent.
0%
0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000
20% 40% 60%
% Forecast sales 80% 100%
costs revenues
£
Figure 3.8 CVP chart – percentage of forecast sales
BREAKEVEN ANALYSIS manufacture their own products are likely to have a higher proportion of fi xed to variable costs than those that buy in products for resale. The proportion of fi xed to variable costs in a company is known as its operating gear- ing (or operating leverage).
A simple method of determining operating gearing is to consider the level of contribution earned in relation to sales i.e. the contribution to sales ratio (C/S ratio). A high C/S ratio suggests that a company has a high proportion of fi xed costs compared to variable (i.e. high operating gearing). A low C/S ratio suggests that a company has a low proportion of fi xed costs compared to variable (low operating gearing). The importance of the distinction is shown in the following example.
Table 1 contains data in respect of two companies that operate in the same business sector, sell similar products, are of equivalent size and have similar fi nancial gearing ratios. The key difference between the companies is their differing cost structures. Company A has a high level of fi xed costs since it manufactures its products. Company B has a high level of variable costs since it purchases its products from another manufacturer. The C/S ratios calcu- lated for Company A (80%) and Company B (40%) confi rm this key difference between these companies.
The data in Table 2 is based on three levels of sales and assumes that the C/S ratio and fi xed costs remain constant across this range of activity. (In practice, these fi gures may not remain constant due to the impact of economies of scale, learning effect and semi-fi xed costs.) The profi t volume graph in Table 3 , based on the data in Table 2 , demonstrates the signifi cance of the differing C/S ratios for the two companies. Each company has a different profi t profi le across a range of sales. Company A has higher losses than Company B when sales are below breakeven but higher profi ts when sales are above breakeven.
Why does this occur ?
Company A has a higher level of fi xed costs than Company B and these fi xed costs will be incurred irrespective of the level of sales achieved. However, when sales are above break-even, Company A reaps the reward of having a higher C/S ratio since it earns more for every product sold compared to Company B.
So which company has the better operating gearing ratio?
Company A, which is highly geared, or Company B, which has a low gearing ratio? Risk takers will prefer Company A since it offers higher levels of return if the company is successful. Risk takers are more concerned with the upside of an investment. However, the risk-averse will prefer Company B, as it would produce lower losses if there is downturn in trading conditions. The risk-averse are more concerned with the downside of an investment.
Table 1 Comparative cost data
Company A Company B
£1.00 Variable costs per unit £3.00
Contribution per unit £4.00 Contribution per unit £2.00 Contribution to sales ratio 80% Contribution to sales ratio 40%
Fixed costs £20,000 Fixed costs £10,000
Table 2 Comparative profi tability
Company A
Sales (£) 0 25,000 50,000
Contribution (£) 0 20,000 40,000
Fixed costs (£) 20,000 20,000 20,000
Profi t/-Loss (£) 20,000 0 20,000
Company B
Sales (£) 0 25,000 50,000
Contribution (£) 0 10,000 20,000
Fixed costs (£) 10,000 10,000 10,000
Profi t/Loss (£) 10,000 0 10,000