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Monday, September 25, 2000



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Cost-volume-profit analysis

N. R. Parasuraman

ONE issue of paramount interest to management is the impact of costs and volume on profits. If a linear relationship could be established among costs, volume and profits, it would help decision-makers to figure out the right volu me, the right cost and consequently the right profit.

That profit is the difference between sales turnover (in value) and cost is common knowledge. Sales turnover equals sale price per unit multiplied by the number of units. This means that sales turnover goes up with higher volume and comes down with lower volume. One also knows intuitively that total cost rises with higher volume and falls with lower volume, but the extent of this movement is not known. Under the cost-volume-profit analysis (CVP analysis), given the cost pattern, the impact of costs on p rofits for various volumes, as also of volumes on profits, is studied.

The analysis would be easier if the cost can be segregated into fixed and variable. In fact, the basic tenet of CVP analysis is to split the cost into variable, which varies with volume, and fixed, which remains constant regardless of the volume. Let us assume that such a division of costs is easily possible. And it may be noted that even when such an absolute segregation is not possible, there are statistical tools which enable the analyst to do so with a fairly high degree of accuracy.

Consider the following example:

A firm sells its products at Rs 10 per unit. The variable cost per unit is Rs 6. And regardless of the volume, the firm has to spend Rs 50,000 on other expenses (fixed expenses). In this case, the profit chart of the firm for various volumes can be analy sed as follows:

Sale price per unit - Rs 10

Variable cost per unit - Rs 6

Contribution per unit - Rs 4 (Rs 10 - Rs 6)

No. of units required to meet fixed costs - Rs. 50,000/Rs 4 = 12,500 units

Here, the difference between the sales price per unit and the variable cost per unit is called the contribution per unit. This means that for every unit sold, Rs 4 comes in as a contribution to meet fixed expenses. How many such units will be needed to m eet the fixed expenses completely? This can easily be computed as 12,500. So, in terms of units, 12,500 units are required to meet both the variable and the fixed costs. This is called the break-even point (BEP) in units.

The relationship between contribution and sales can also be expressed as a ratio, which is called contribution margin. In the example, the contribution margin is 4/10 or 0.4. The BEP in rupees can be found by dividing the fixed cost with the contribution margin. This will be Rs 50,000/0.4 = Rs 1,25,000.

Understanding the BEP concept enables one to take a number of strategic decisions. The following is an illustrative list of the uses of CVP and BEP analyses:

* Deciding on a level of sales to achieve a targeted profit: At the BEP of sales, there is neither profit nor loss. It means that the contribution (sales minus variable expenses) has just about covered the fixed expenses. This suggest s that for sales beyond this point, the entire contribution will be profits because there is no more fixed expenses to meet. So, if a profit of, say, Rs 1,00,000 is targeted in the illustration, all that is to be done is to sell additional un its that will make the incremental contribution beyond meeting the fixed expenses as Rs 1,00,000.

In other words, the new volume is targeted to cover not only the fixed expenses of Rs 50,000, but also the profit of Rs 1,00,000. So, dividing Rs 1,50,000 by the contribution per unit of Rs 4 gives us 37,500 units. Thus, 37,500 units will have to be manu factured to achieve a profit of Rs 1,00,000.

The number of units to be manufactured to achieve target profit = target profit plus fixed expenses divided by contribution per unit.

* Determining the profit at a targeted level of sales: Similarly, if the management has targeted a level of sales on the basis of its market survey or otherwise, the profits that will emerge from that level of sales can be determined using CVP an alysis. The contribution margin per unit multiplied by the number of units produced over and above the BEP gives us this figure. Of course, profits can always be computed as the difference between sales and total cost. But what CVP analysis achi eves is that incremental profits from selling additional units can be easily calculated on the basis of the established relationship between cost and volume.

* Determining the impact of additional fixed costs: If the fixed costs go up, the revised BEP can be computed. A no-profit, no-loss situation comes up only at the increased point now, consequent to the increased fixed costs. The entire structure o f relationship between cost and volume will undergo a change consequent to this increase in fixed cost.

In real life, it may be difficult to segregate cost strictly into its fixed and variable elements. What can be attempted is to bring about as close a split as possible. The advantages of CVP analysis would far outweigh whatever difficulties one might fac e in segregation.

CVP analysis for multiple products

So far, CVP analysis was made based on the assumption that the unit produces only one product. CVP analysis is useful even when more than one product is produced. In that case, the ratio of production of the products will have to be determined in advance . This ratio has to be assumed to be rigid for the analysis to be precise. Thus, if a firm manufactures two products `A' and `B', whose cost structure is shown in the Table, and if the fixed expenses are Rs 2,00,000, the BEP can be computed as follows:

Take one whole unit to be three units of Product A and one unit of Product B. The combined contribution of the two units, which is the contribution of the whole unit, is Rs 15. The combined fixed cost is Rs 2,00,000. The BEP is (2,00,000/15) = 13333.34 u nits.

Since each whole unit consists of three units of Product A and one unit of Product B, it can be taken to mean 40,000 units of Product A and 13,333 units of Product B. Having found the level at which the break-even position will be achieved, all the other calculations can be carried out as in the case of a single product.

Margin of safety: The safety margin or the margin of safety of a firm is the difference between the budgeted sales revenue and the break-even sales revenue. The margin of safety is a quick-fire method of knowing how close the firm is to its level of brea k-even. If the margin of safety is low, it means that the firm is only just-about managing to cover the break-even level.

Limitations of CVP analysis: While appreciating the major benefits of CVP analysis, one has to keep in mind the limitations of the model, which arise from its assumptions. For the analysis to be accurate, the behaviour of sales and the variable portion o f the costs has to be linear, that is, greater the volume, higher the revenue and cost in the same proportion. It is assumed that the total cost can be successfully segregated into its fixed and variable elements. Also, in a multiple product set-up, the mix of the products is taken to remain the same throughout the analysis.

Also assumed is that the inventory levels at the beginning and the closing of the relevant periods remain the same. Each of these assumptions is far-fetched and may not happen in real life. But then, one is not looking for an arithmetically accurate tool . An indicative figure would suffice so long as it enables one to take better decisions. All things considered, the principles of CVP analysis provide a useful tool for managerial decision-making.

Concept check

i) Suppose there is a change in the variable cost component, how do we revise our CVP postulates?

ii) When we make the division of costs into fixed and variable heads, does it mean that overhead expenditure will always be fixed? Conversely, will there be any direct expenditure which is fixed?

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