Cost-Volume-Profit (CVP) Analysis
In marginal costing, marginal cost varies directly with the volume of production or output. On the other hand, fixed cost remains unaltered within the relevant range. Thus, if volume is changed, variable cost will vary in proportion to the volume. In this case, selling price remains fixed, fixed cost remains fixed which translates to a change in profit.
Managers constantly strive to relate these elements in order to achieve maximum profit. Apart from profit projection, the concept of Cost-Volume-Profit (CVP) is relevant to virtually all decision- making areas, particularly in the short run.
The relationship among cost, revenue and profit at different levels of output may be expressed in graphs such as break-even charts, profit volume graphs, or in various statement forms.
Profit depends on a large number of factors, most important of which are the cost of manufacturing and the volume of sales. Both these factors are interdependent. Volume of sales depends upon the volume of production and market forces which in turn is related to costs. Management has no control over market. In order to achieve certain level of profitability, it has to exercise control and management of costs, mainly variable cost. This is because fixed cost is a non-controllable cost and is irrelevant for decision making where it is not changed by the course of action taken.
But then, cost is determined by various factors which include:
• Material prices, wage rates and overhead costs may all change because of the impact
• Material usage may change where scrap is expected to fall because of improved
methods, better trained workers or better material quality.
• Labor efficiency may change where improved training programs or a reduction in labour turn over is expected to occur.
• Internal efficiency and the productivity of the factors of production; Overhead expenses may fall due to more efficient placement of order with suppliers who offer best terms
• Product volume of production or size of batches.
• Product mix may change either as part of overall company strategy or due to increased
• Methods of production and technology.
• Size of plant.
Thus, one can say that cost-volume-profit analysis furnishes the complete picture of the profit structure. This enables management to distinguish among the effect of sales, fluctuations in volume and the results of changes in price of product/services.
In other words, CVP is a management accounting tool that expresses relationship among sale volume, cost and profit. CVP can be used in the form of a graph or an equation. Cost-volume-profit analysis can answer a number of analytical questions. Some of the questions are as follows:
a) What is the break-even revenue of an organization?
b) How much revenue does an organization need to achieve a budgeted profit?
c) What level of price change affects the achievement of budgeted profit?
d) What is the effect of cost changes on the profitability of an operation?
Cost-volume-profit analysis can also answer many other “what if” type of questions. Cost-volume- profit analysis is one of the important techniques of cost and management accounting. It provides an answer to “what if” theme by telling the volume required to produce. Cost and revenues will change as well as sales revenue due to a number of factors. These are:
a) Increased competition may require selling price discounts in order to stimulate demand
b) Material prices, wage rates and overhead costs may all change because of the impact
c) Material usage may change where scrap is expected to fall because of improved methods, better trained workers or better material quality
d) Labour efficiency may change where improved training programs or a reduction in
labour turn over is expected to occur
e) Overhead expenses may fall due to more efficient placement of order with suppliers
who offer best terms
f) Product mix may change either as part of overall company strategy or due to increased competition
Following are the three approaches to a CVP analysis:
• Cost and revenue equations
• Contribution margin
• Profit graph
a) In order to forecast profits accurately, it is essential to ascertain the relationship between cost and profit on one hand and volume on the other.
b) Cost-volume-profit analysis is helpful in setting up flexible budget which indicates cost at various levels of activities.
c) Cost-volume-profit analysis assists in evaluating performance for the purpose of control thus enabling management to take corrective actions where necessary and in good time.
d) Such analysis may assist management in formulating pricing policies by projecting the
effect of different price structures on cost and profit.
Assumptions and Terminology
CVP is based on various assumptions as listed below:
1. Volume is the only factor affecting sales and expenses The changes in the level of various revenue and costs arise only because of the changes in the volume of output produced and sold, e.g., bales of flour produced by Unga Ltd. The number of output (units) to be sold is the only revenue and cost driver.
2. Total costs can be divided into fixed and variable components. Variable component will vary directly with level of output. Direct materials, direct labour and direct chargeable expenses form the direct variable costs while variable part of factory overheads, administration overheads and selling and distribution overheads form the variable overheads.
3. There is linear relationship between revenue and cost.
4. The behavior of both sales revenue and expenses is linear throughout the entire relevant
range of activity. Graphically, it assumes a linear equation of the form Y=mX + C
5. The unit selling price, unit variable costs and fixed costs are constant.
6. The theory of CVP is based upon the production of a single product. However, of late, management accountants are functioning to give a theoretical and a practical approach to multi-product CVP analysis.
7. There is only one product or service or a constant Sales Mix. The analysis either covers a single product or assumes that the sales mix sold in case of multiple products will remain constant as the level of total units sold changes.
8. All revenue and cost can be added and compared without taking into account the time
value of money.
9. The theory of CVP is based on the technology that remains constant.
10. The theory of price elasticity is not taken into consideration.
11. Inventories do not change significantly from period to period:
Many companies, and divisions and sub-divisions of companies in various industries have found the simple CVP relationships to be helpful in Strategic and long-range planning decisions and product features and pricing decisions
In real life, the assumptions described above may not hold. The theory of CVP can be tailored for individual industries depending upon the nature and peculiarities of the same.
For example, predicting total revenue and total cost may require multiple revenue drivers and
multiple cost drivers. Some of the multiple revenue drivers are as follows:
• Number of output units
• Number of customer visits made for sales
• Number of advertisements placed
Some of the multiple cost drivers are as follows:
• Number of units produced
Managers and management accountants, however, should always assess whether the simplified CVP relationships generate sufficiently accurate information for predictions of how total revenue and total cost would behave. However, one may come across different complex situations to which the theory of CVP would rightly be applicable in order to help managers to take appropriate decisions under different situations.
Limitations of Cost-Volume Profit Analysis
The CVP analysis is generally made under certain limitations and with certain assumed conditions, some of which may not occur in practice. Following are the main limitations and assumptions in the cost-volume-profit analysis:
1. It is assumed that the production facilities anticipated for the purpose of cost-volume- profit analysis do not undergo any change. Such analysis gives misleading results if expansion or reduction of capacity takes place, which in most cases does.
2. In case a variety of products with varying margins of profit are manufactured, it is difficult to forecast with reasonable accuracy the volume of sales mix which would optimize the profit.
3. It assumes that input price and selling price remain fairly constant which in reality is not the case. Thus, if cost or selling price changes, the relationship between cost and profit will not be accurately depicted.
4. It assumes that variable costs are perfectly and completely variable at all levels of activity and fixed cost remains constant throughout the relevant range. However, this situation is not a practical one.
5. It is assumed that inventories do not change significantly from period to period. However, in reality, opening inventory and closing inventory are never the same and in most cases they vary significantly.
6. Inventories are valued at variable cost and fixed cost is treated as period cost. Therefore, closing stock carried over to the next financial year does not contain any component of fixed cost. Inventory should be valued at full cost in reality because such costs were incurred to bring the inventory into existence..
The limitations of CVP analysis are actually its assumptions, which do not hold outside the
Approaches to CVP
Rearranging the equation above to make profit the subject of the formula one will get
Graphical Illustration between Cost and Revenue Behavior
The contribution sales ratio is affected by any change in selling price and or variable cost per unit. This ratio is a measure of the rate at which profit is being earned and its size illustrated by the steepness of the slope of the profit volume graph
In the figure above graph -FP2 shows the existing profit curve for a company with a fixed cost OF, Break-even point B2, margin of safety M2. An increase in the selling price and/or decrease in the variable cost per unit will increase the contribution margin ratio. This translates to a higher profit. The graph line derived shall be steeper than the original one. In our chart above, the profit line
-FP1 illustrates such a situation.
A decrease in selling price and/or an increase in variable cost per unit will reduce contribution margin ratio thus translating to a lower profit. The profit graph obtained shall be gentler than the initial one. In the chart above, the profit line -FP3 illustrates such situation.
Margin of safety (MOS)
This is the excess of budgeted sales over the break-even volume in sales. It states the extent to which sales can drop before losses begin to be incurred in a firm.
MOS is calculates as:
MOS = Total budgeted sales – Break-even sales
MOS may also be expressed as a percentage of sales. The higher the percentage, the better positioned a firm is in its operations.
Margin of safety is a tool designed to point out a problem but not to solve it. To rectify the problem of a low MOS, management must direct its efforts towards either reducing the break-even point or increasing the overall level of sales.
In the chart above, the margin of safety in the three situations analyzed equals M2, M1 and M3 respectively
Change in fixed cost
In figure on the previous page graph -F2P2 shows the existing profit curve for a company with a fixed cost 0F2, Break-even point B2, margin of safety M2. Assuming constant production and sales volume, an increase in the fixed costs (F3 -F2) will translate to an increase in the break-even point (B3 -B2), a decrease in the Margin of safety (M2 –M3) and a decrease in profits. The profit graph line will have the same gradient as the initial one since a change in fixed costs does not affect the contribution to sales ratio. The line will shift downwards by a vertical distance equivalent to the increase in the fixed costs (F3 -F2)
The profit line – F3P3 illustrates the situation above.
On the other hand, a decrease in the fixed costs (F2 –F1) will translate to a decrease in the break- even point; (B2 –B1), an increase in the margin of safety (M1 –M2) and an increase in the profits. The profit graph line will have the same gradient as the initial one. The line will shift downwards by a vertical distance equivalent to the decrease in the fixed costs (F2 –F1). The profit line – F1P1 best illustrates the situation.
Change in production or sales mix
One of the key assumptions of break-even analysis is that there is only one product or service or a constant Sales Mix. Sales mix refers to the relative combination in which a company’s products are sold. Managers strive to achieve an optimal sales mix which yields the greatest amounts of profits. Profits will be greater if high margin items make up a relative large proportion of sales and less if sales consist of low margin items.
Determining the constituents of the sales Mix
T-Bug plc produces and sells 2 products T and B. The following is the budget for the coming year.
a) Compute the company’s break-even point
b) Determine the constituents of the sales mix i.e. quantities of T and B
Let b be the number of units of B sold and 3b be the number of units of T sold.
Using the fundamental marginal cost equation (Sales – variable cost) – fixed costs = Profit Contribution – Fixed costs = Profit
But at break-even point, profit is equal to zero. Therefore,
Therefore the break-even point of T-Bug plc is 105,264 units comprising of 78,948 units of T and
26,316 units of B.
A change in sales mix without a change in the total output will no doubt give different results. This is because the individual products in the mix have different contributions thus giving a different weighted contribution sales ratio. This will cause a change in the overall profit curve.
The summary of results of Donlon Ltd are as follows;
1. Prepare a profit volume graph which shows the overall results for Donlon Ltd
2. Prepare an amended profit curve where the market forces have led to a switch of Shs.200,000 of sales from product A to Product C.
3. Prepare a summary which shows the value of each of the following for both the original results and the amended results.
Margin of safety
Overall contribution sales ratio
The above profit volume graph shows the existing and amended cost curves for Donlon Ltd. The amended data which shows the switch of Shs.200,000 of sales from product A to Product C may be summarized as follows:
Note that the variable costs for Product A are reduced proportionally while those of product C are increased proportionally to the change in sales value according to the variable cost sales ratio (VCR) for each product.