# Analysis of breakeven conditions under price changes - Prices and pricing

## Analysis of breakeven conditions with price changes

Turning to the procedure for analyzing the incremental break-even, we focus our attention only on changes in profitability as a result of price decisions. Accordingly, the starting point for managers in conducting such an analysis is data on current or projected sales volumes and profitability levels under the current (or previously defined) price. And then the question is posed: "Can the price change improve the situation?".

Otherwise, this question can be formulated as follows:

How much sales should increase to offset the loss of revenue due to lower prices?

To what extent can the sales volumes decrease so that the profit growth provided by the price increase does not disappear?

The answers to these kinds of questions depend on the size of the relative gain, and we'll look at the procedure for finding such answers using the example of the conditional firm "Plastikon", which produces plastic garbage containers.

For the company Plastics the following monthly performance indicators are characteristic (Table 6.1).

Table 6.1

Performance of the company Plasticon

 The name of the indicator Monthly data Sales, pcs. 6000 Selling price, thousand rubles. 12 Revenues from sales, mln rubles. 72 Variable costs, thousand rubles/pcs. 6 Constant costs, million rubles. 20

Managers of the company are dissatisfied with the volume of its sales and consider the desirability of reducing the price by 10% for the sake of

its increase. It is assumed that such growth in sales (and, accordingly, output) can be achieved without increasing fixed costs. But how much should the sales volume actually increase in order to compensate for the 10% price reduction?

To answer this question, you need to calculate the break-even sales change. For the variant of price reduction, it will represent the minimal increase in sales, which is necessary, so that the price decrease leads to an increase in relative gains relative to the reference point.

To make this idea easier to understand, we illustrate it with the help of the economic results of the company's work "Plastikon" at different price levels.

With the previous level of the price of 12 000 rubles. Plastics sold 6000 units of goods per month. This provided the firm with a sales volume of 72 million rubles.

Of this revenue, the company Plastikon covered variable costs (variable cost, VC) in the amount of 6000 rubles. per unit of goods or 36 million rubles. for the entire monthly release. Therefore, before the price change, the win of the Plasticon from the sale of products amounted to 36 million rubles. (72 million - 36 million).

From here we can make the first conclusion: that the price reduction justified itself, the gain after the price reduction should be per month more than 36 million rubles.

Let's see now how the results of the firm's work will be formed after the expected price reduction by 10%, i.e. from 12,000 to 10,800 rubles. (/ & gt ;,). Based on the previous production volume, the reduction in the win of "Plasticon" will be 7.2 million rubles. ((12 000 rubles/piece - 10 800 rubles./Piece) x 6000 pcs.). And then, with the previous volume of production (sales), the firm's profit will be only 28.8 million rubles. (36 million - 7.2 million).

The situation of the change (in this case, reduction) in the company's gain from the sale of the previous volume of output when the price is changed is called the price effect.

But since we are dealing with a normal commodity (the amount of demand for which increases with a decrease in its price), it is fair to expect that the cheapening of goods sold by "Plastikon" will lead to an increase in the volumes of their sale. However, we do not know the amount of winnings that a firm will receive as a result of such a change in the situation (it is usually called the volume effect).

The only thing we can say for now is that a firm will benefit from a price reduction if the gain obtained as a result of the effect of scale will exceed the loss of the prize as a result of the effect of the price. In other words, the change in price will justify itself for the firm in the event that the additional gain, obtained due to the change in sales, will exceed the reduction in winnings based on the previous sales volume due to the price reduction. If the price increases, the firm will achieve better results if the additional gain from the sale of products at a higher price exceeds the reduction in the winnings due to a drop in sales volumes.

In this situation, the problem of breakeven analysis is to determine the minimum increase in sales that must be achieved so that the effect of the volume effect balances the effect of the price effect. If, however, the magnitude of the gain in the gain as a result of the effect of the volume is greater than the value of the reduction in the gain as a result of the effect of the price, then the price reduction will indeed lead to an increase in the firm's profit.

How to determine the break-even sales growth?

We have already established that the reduction in the winnings of the firm "Plastikon" as a result of the price reduction will amount to 7.2 million rubles. Accordingly, and the amount of the win as a result of the manifestation of the effect of volume should amount to the same amount.

It is not difficult to calculate that after a price reduction, the win of "Plasticon" with each container sold will be 4800 rubles. (10 800 - 6000). This means that the total gain from the increase in sales volume is equal to the loss of profit as a result of the price reduction, the company "Plastikon" should sell an additional 1500 containers (7.2 million rubles: 4,800 rubles./pcs.).

The amount of the minimum sales increase necessary to maintain the previous total amount of the prize after the price change can be calculated arithmetically using the following formula:

(6.5)

where BSC p - break-even sales growth as a result of price changes ( break-even sales change ),%; A P - change in price (indicated with the sign: + when the price increases and - when the price decreases); CM - specific payoff.

In this equation, the values ​​of changes in prices and winnings can be expressed in any, but in the same way (in absolute values, in percentages or decimals).

In the end, we still get a percentage of how much needs to change the number of products sold to and after the price change in the total amount of the winning firms remained unchanged.

The sign in the numerator of this equation reminds us of the alternative with which the price change is connected: an increase in price leads not only to a reduction in the number of products sold, but also to a reduction in the number of products that need to be sold in order to achieve the desired level of profitability. On the contrary, price reduction leads not only to an increase in the number of products sold, but also to an increase in the number of products that must be able to sell in order to achieve the desired level of profitability.

The larger the scale of price reduction, the more it is essential to increase the number of products sold, in order to maintain at least the previous total amount of the firm's profit from the sale of such goods.

Let's return to explain this thought to the situation in question, and suppose that the company's planned "Plastic" a price reduction of 10% will not entail an increase in variable and fixed costs for it. Then, using the formula (6.3) to calculate the specific gain and conducting the calculation in absolute values, we get the value of the specific winnings CM of this firm before the price decrease:

SM about = 12,000 rubles. - 6000 rub. = 6000 rubles.

On this basis, we can now easily calculate the increment in the number of containers that we need to achieve "Plasticon" in order to justify a price reduction of 10%:

BSC p = (- (- 1200 rubles.)): (6000 rubles. + (- 1200 rubles.)) * 100 = 25%; or in relative terms:

BSC p = (- (- 10%)): (50% + (-10%)) х ЮО = 25%.

Thus, a 10% reduction in the price will pay off for Plasticon Only if the number of containers sold increases by 25% (which corresponds to the result we already obtained - an increase of 1500 units is just 25% of the previous sales volume of 6,000 units).

The break-even increase in sales (in absolute terms) can be found by using the formula

(6.6)

where BSC a , BSC - break-even sales growth when prices change, in absolute and in percentage terms; S o - the volume of sales before the price change, units

In our example it will be: 0,25 х 6000 rub. = 1500 pcs.

Accordingly, if the real increase in sales exceeds the break-even gain, the firm not only loses nothing as a result of price changes, but even gets additional profit. And this logic can significantly influence the formation of the company's commercial policy.

Say, if the management of the company Plastic At this stage it is mainly interested in seizing a larger market share, rather than in increasing the mass of profit, it can go for a price cut even if the increase in the number of containers sold does not exceed the breakeven number (in our case, 1500 units). On the contrary, if the main task of the firm in this period is to maximize profits, then it can go for such a price reduction only if there are good reasons to expect the growth in the number of containers sold by more than 25%.

Evaluation of the impact of changes in sales volumes on the amount of the company's gain can be made very simply. To do this, we only need to multiply the difference between the real gain achieved after the price change by the sales volume and the break-even sales volume by the new value of the specific payoff (ie, the value that will be formed after the price change).

Returning to our example, suppose that after a price change, the sales volume of "Plasticon" will increase by 1700 pcs. As for the new value of the specific gain, according to formula (6.3) it will be equal to 4800 rubles. (10 800-6000).

Then the profit growth of this firm will be:

(1,700 pieces - 1500 pcs.) x (10,800 rubles - 6,000 rubles.) = 960,000 rubles.

Exactly the same logic is used in the analysis of the expected price increase.

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