“Cost Volume Profit Analysis is not appropriate in an environment where companies produce many diverse products”.
Cost volume profit analysis is the study of the effects of output volume on revenue, costs and profit (Horngren, Sundem and Stratton). The most common use of cost volume profit analysis is to find break-even point in terms of number of units sold. In its simplest form cost volume profit analysis works for single product companies. But most of the companies produce more than one product. Sales mix is the relative proportion of quantities of different products that comprise total sales. When sales mix changes, break-even point changes and so does the profit.

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Like any model, cost volume profit analysis is based on certain assumptions. This paper looks at the applicability of the assumptions, especially for a company producing more than one product. Most of the assumptions in cost volume profit model are based on the linearity of cost and sales with units. Major elements impacting cost are sudden increase in fixed costs, gain in worker efficiency and higher bargaining power of the company. Similarly revenues are non-linear because companies give varying discounts to different customers.
Assumptions made in cost volume profit analysis:
Unit selling price remains constant. This implies that the price of the product or service will not change as sales volume varies. In reality the situation is different as reduced selling prices are normally associated with increased sales volume and this supports the supply-demand hypothesis which states that lowering of price will result in higher sales and vice-versa. It is a common practice in the business world to offer different discounts to different customers based on the volume of purchase and the strategic importance of sale. Companies offer bulk discounts to larger customers. Managers often reduce prices as volume increases to attract more customers. Also stiff competition means selling product at discounts during lean periods or during festive times. Bigger companies producing more than one product have often more than one sales manager and they have their own targets. Each sales manager would adjust his sales volume and price to maximize his products profits and this may not result in ideal sales mix for the whole company. Hence the assumption of constant sales price is rarely applicable in today’s dynamic world.
The realistic sales-output relationship is more like a curve than a straight line. And when a company is selling more than one product, the analysis of break-even point under multiple non-linear relationships becomes more difficult.
The behavior of costs is linear (straight line) over the relevant range. This implies the following assumptions:

Costs can be categorised as fixed or variable. In a large organisation with multi-product it becomes very difficult to organize costs into fixed and variable. Not only there are a large number of costs involved but also there are a large number of cost drivers acting on those costs. Under such circumstances segregating costs into fixed and variable is a very tedious and time consuming job.
Unit variable costs are fixed and constant. It is possible that unit variable costs remain fixed under circumstances like where a company produces just one standard product. Most businesses enjoy benefits of economics of scale as their production increases in terms of

Higher trade discounts;
Better credit and financing terms.

The above benefits result in reduction of variable cost per unit with increase in number of units. The assumption of linear variable costs doesn’t hold true in reality and will result in a situation where the relationship between variable cost and output is a non-linear relation (Williamson).
Also when a company sells many products, unit variable costs can’t be identified properly and hence not known. It is hard to classify variable cost to each product. As an example, a superstore sells thousands of products at different prices. Calculating break-even point in terms of number of units sold would be meaningless. In such scenarios, companies can use total sales and total variable costs to calculate variable costs as a percentage of total sales.
Fixed costs remain fixed over a wide range of activity. Companies, based on their experience and studies, can analyse fixed cost over a range of activity. But it would be improper to assume that fixed costs would remain constant over a wide range of activity. In a multi-product company, different products will take different unit time of various production facilities. A change in sales mix may not be met by existing fixed capacity and involve setting up of further facilities resulting in higher fixed costs. Many times fixed cost has a step change and a particular fixed cost is applicable for a range of production only. Because of sudden change in fixed costs, unit costs can vary a lot just near the step change point. In case of multi product companies, because of change in sales mix, it becomes difficult to access which product has caused the change in fixed costs.
The efficiency and productivity of the production process and workers remain constant. Under economics of scale, efficiency of production processes increases with increase in production of units. Higher production levels should result in lower variable cost due to higher productivity. This means that assumption of constant unit variable costs doesn’t hold true when there is a change in productivity and efficiency. It is easier to calculate efficiency gains in a single product business. But for a company involved in multiple products, it becomes difficult to track efficiency gains in each process.
In multi-product organizations, the sales mix remains constant over the relevant range. It is hardly a scenario where all products perform as per budget expectations in terms of number of units sold. Let’s first examine the scenario where sales-output relationship is a straight line. If products have different contribution percentages, change in sales mix would change overall contribution. A change in sales mix is now basically a question of working out new contribution to sales ratio which is a weighted average based on the number and contribution percentage of each product sold. Change in sales mix would change the contribution ratio and hence the break-even point.
If now sales-output relationship is a non-linear one, it becomes much more difficult to calculate contribution percentage at different sales mix. The use of computer programming has made the task of calculations much easier but managers can miss the learning by just focusing on overall break-even point and profits.
Fearon (1960) reasoned that the problem of maintaining a constant product-mix in a multi-product company may not be that serious because of the following main points:

Break-even analysis is not just to give exact answer, it is more to throw light on the problem areas for management;
Break-even point should be used as approximation and as an area rather than a point;
Over time, multi-product companies reach a stable product mix which changes slowly. Hence constant product mix could be a good approximation for such scenarios; and
Also if company uses constant margin over the cost for all products, then it is much simpler to use cost volume analysis. For companies adopting this pricing strategy, sales mix is not a complex issue.

Ignores the time value of money. Cost volume profit analysis doesn’t take into account the time value of money. All cash flows are taken at face value. In real world, there are differences in timing of cash inflows and outflows. Companies have to pay for buying stock, workers salary, marketing and distribution before they can realize sales. Companies pay interest on any money borrowed to finance their working capital. Companies operating in high margin products can still manage to ignore the time value of money but companies with low-margin products have to take into account interest charges.
There is no change in inventory levels at the beginning and end of the period. This is hardly the case as most of the companies have work in progress at the beginning and end of a period. It can be a coincidence that the inventory levels are same at the beginning and end, but very rarely a company would plan inventory levels in such a way so that there is no net change in inventory during a period. The task of managing inventory with multiple products is even more difficult.
This is not a major issue as companies do stock taking at the end of a period for financial records. But the change in prices over the period and interest on working capital should be taken into account for proper cost volume profit calculations.
Fearon (1960) suggested some techniques to incorporate the product mix in a multi-product company for cost volume profit analysis. Though he suggested five different ways of adopting simple cost volume profit analysis in a multi-product company, he himself wasn’t fully satisfied with any of those solutions. But he mentioned that the sales mix could be approximated to benefit from the cost volume profit analysis.
With all its shortcomings and assumptions, cost volume profit analysis can be used to look at the profitability levels. Companies producing multiple products in today’s dynamic world should carry on the analysis with a view to look at the results as an approximation and not the definite answer. Management should use the results to highlight problem areas.
CONCLUSION
Cost volume profit analysis is a common tool used to find break-even point in terms of number of units sold. Assumptions used in cost volume profit analysis are debatable because of linearity of cost and sales price. In real world, both cost and sales price remain fixed only over a narrow range and are impacted by elements like improvement in worker efficiency, bulk discounts both in purchasing and being offered to clients and competition.
When a company produces more than one product, a change in the relative proportion of quantities of different products changes the break-even point and profit. Because of the non-linearity and change in sales mix, cost volume profit analysis will not give a correct answer but could be a good approximation of what levels of production should a company target to break-even or to make certain level of profits. Management should use the analysis to look more at the problem areas and profitability of products rather than finding exact profit numbers.
BIBLIOGRAPHY
Fearon, H. E. (1960). “Constant product mix – A limiting assumption in B-E analysis”, National Association of Accountants, NAA Bulletin, July 1960, Pg. 61
Horngren, C.T., G.L. Sundem and W.O. Stratton. “Introduction to management accounting”. Prentice Hall International, Eleventh edition.
Williamson, D. “Cost Volume Profit Analysis: Its assumptions and their pitfalls”, (http://business.fortunecity.com/discount/29/cvpass.htm), date 21 January 2007