How the break-even point level is calculated. Determining the break-even point

Determining the break-even point is the cornerstone of the effective functioning of any enterprise. The calculation of this indicator is of paramount importance not only for the owners of the enterprise, but also for its investors. If the former should be aware of when the release of products becomes payback, then the latter should be aware of the value of this indicator to make an informed decision on the provision of funding.

What is a break-even point and what does it show

This indicator helps to understand when the company stops incurring losses, but at the same time is not yet able to earn a profit. Moreover, the production and sale of any additional unit of production entails the formation of profit. Thus, the break-even point is a certain starting point from which the enterprise can begin to develop effectively. Those. this indicator is a kind of indicator that the company is moving on the right path.

This indicator is called differently the threshold of profitability or simply BEP (from english break-evenpoint). It characterizes the volume of output of a product at which the proceeds from its sale will be equal to the cost of its production.

What is the economic sense of determining the value of this indicator? The profitability threshold shows the exit of the enterprise to the recoupment of its costs.

The emergence of a break-even point is said when expenses are covered by income. The company fixes profit when this indicator is exceeded. If this indicator is not reached, then the firm incurs losses.

So, the break-even point shows:

• the level above which the company begins to fix profits;
• the minimum permissible level of revenue, upon falling below which the production of products ceases to pay off;
• the minimum permissible level of pricing, below which one cannot fall.

In addition, the definition of this indicator allows:

• identify problems that are associated with the change in the break-even point over time;
• identify how to make it possible to change the volume of output of a product or its production when prices vary;
• calculate how expedient it is to reduce revenue so as not to incur losses.

Determining the threshold of profitability helps investors determine whether a given project is worth financing if it pays off for a given volume of sales.

Video - break-even point analysis:

Thus, most management decisions are made only after the break-even point has been calculated. This indicator helps in calculating the critical value of sales volume at which the company's costs become equal to the proceeds from the sale of goods. Even a slight decrease in this indicator will indicate the beginning bankruptcy of the company.

Important! When the company crosses the break-even point, it will start taking profits. Until then, it works at a loss.

Calculation formulas

The profitability threshold can be measured in kind or in monetary terms.

In both cases, it is important to first calculate the costs of the enterprise to determine the profitability threshold. For this, we introduce the concept of fixed and variable costs.

Fixed costs do not change over time, and do not have a direct relationship to sales. However, they can also change under the influence of, for example, the following factors:

• changes in company performance;
• expansion of production;
• changes in the cost of rent;
• changes in general economic conditions, etc.

It is customary to include the following costs to them:

• payment of administrative expenses;
• rental fees;
• depreciation deductions.

Variable costs are a more unstable quantity that depends on changes in the volume of production. This type of cost includes:

• payment of wages and other deductions to workers;
• costs for raw materials and for the purchase of necessary materials;
• purchase of components and semi-finished products;
• energy payment.

Accordingly, the amount of variable costs will be the higher, the greater the volume of production and the amount of sales.

Variable costs per unit of manufactured goods do not change when the volume of its production changes! They are conditionally permanent.

Having decided on the concept and types of costs, we will find out how to calculate the break-even point (BEP) in kind... For this we use the following formula:

BEP (in kind) \u003d Fixed Cost / (Unit Selling Price - Variable Cost Per Unit)

It is advisable to use this formula when the company is engaged only in the production of products of one type. However, this is extremely rare. If an enterprise manufactures a wide range of products, then the indicators for each of its types are calculated separately according to a special extended formula.

When calculating the break-even point in monetary terms another formula is used:

BEP (monetary) \u003d (fixed costs / profit margin) * revenue from product sales

For correct calculation, we use factual data on costs and revenues for the analyzed period. In this case, you should use indicators that relate to the same analysis interval.

However, the use of this formula is correct when determining the BEP with a positive profit margin. If it is negative, then the BEP is defined as the sum of the costs of the fixed and the variables that are relevant to the period.

Video - about the importance of determining the threshold of profitability in business:

Or you can use another formula for calculating the profitability threshold:

BEP (in monetary terms) \u003d Fixed costs / KMD,

where KMD is the margin profit ratio.

In this case, the CMR can be determined by dividing the MD (marginal income) by revenue or by price. In turn, the MD is obtained using one of the following formulas:

MD \u003d V - PZO,

where B is the revenue,

PZO - variable costs for sales.

MD \u003d C - PZE,

where C is the price,

PZE - variable costs per unit of goods.

Calculation examples

For greater clarity, consider examples of calculating the break-even point using the example of an enterprise and a store.

For an industrial enterprise

Suppose the following conditions are given. The enterprise is engaged in the production of products of one type. At the same time, the unit cost is 50,000 rubles. Price - 100,000 rubles. Fixed costs - 200,000 rubles. It is necessary to calculate the minimum volume of manufactured goods at which the enterprise will reach the threshold of profitability. Those. we need to calculate the BEP in kind. Let's use the above formula and get:

BEP (in kind) \u003d 200000 / (100000-50000) \u003d 40 (product units).

Conclusion: thus, with the release of at least 40 units of products, the enterprise will reach the break-even point. An increase in the volume of products manufactured by the enterprise will lead to profit.

For shop

In the following example, we will calculate the break-even point for a store. Let's say that the store is a grocery store and has the following fixed costs (in rubles):

• rent of space - 80,000;
• salaries of managers - 60,000;
• insurance premiums - 18,000;
• utility bills - 10,000.

Total: 168,000 (rubles).

The conditions also give the values \u200b\u200bof the costs of the variables:

• energy payment - 5,000;
• raw material costs - 10,000.
• Total: 15,000 (rubles).

Let's say that the amount of revenue is 800,000 rubles. Let's define the BEP in terms of value. First, let's calculate the margin profit. To do this, subtract variable costs from the proceeds and get 800,000 - 15,000 \u003d 785,000. Then KMD will be 785,000 / 800,000 \u003d 0.98.

Then the break-even point will be equal to the fixed costs divided by the resulting coefficient, or 168,000 / 0.98 \u003d 171,429 rubles.

Conclusion: Thus, the store must sell goods in the amount of 171,429 rubles so that the income is greater than the expenses. All subsequent sales will bring the store a net profit.

Schedule

In order to find the threshold of profitability, you can use the graphical method for calculating this indicator. To do this, we will reflect on the graph the fixed and variable costs, as well as the total (gross) costs. The break-even point graphically corresponds to the intersection of the gross revenue and total cost curves.

Let's look at an example.

The following conditions are given (in rubles):

• the amount of revenue - 100,000;
• production output - 100 (pieces);
• fixed costs - 25,000;
• variable costs - 30,000.

Marking these data on the graph, we get the following conclusion: the company will be at the break-even point when it receives income in the amount of 35,700 rubles. Thus, if an enterprise sells more than 35 items of goods, then it will take profit.

Calculating a break-even point using formulas in Excel

It is very easy and convenient to calculate the profitability threshold using Excel - for this you just need to enter the initial data in the corresponding table, after which, using the programmed formulas, we will get the value of the profitability threshold for our case, both in monetary and physical terms.

You can download the calculation of the break-even point in Excel for a manufacturing enterprise specializing in the production of parts in the engineering industry by.

The graph and formula for calculating the break-even point in Excel for the general case are given

It is known that the release of a product implies an investment in its production and sale. Each entrepreneur, intending to create a benefit, pursues the goal of making a profit from the sale of goods / services. The break-even chart helps to see in value and physical terms the revenue and volume of production, at which the profit is zero, but all costs have already been covered. Accordingly, having crossed the break-even point, each subsequent unit of goods sold begins to bring profit to the enterprise.

Data for the graph

To draw up sequential actions and get an answer to the question: "How to build a break-even chart?" an understanding of all the ingredients required to create a functional dependency is required.

All costs of the company for the sale of products are gross costs. Dividing costs into fixed and variable costs allows you to plan profit and is the basis for determining the critical volume.

Premises lease, insurance premiums, equipment depreciation, labor remuneration, management are components of fixed costs. They are united by one condition: all the listed expenses are paid regardless of the volume of production.

The purchase of raw materials, transportation costs, labor remuneration of production personnel are elements of variable costs, the size of which is determined by the volume of the produced good.

Revenue is also the initial information for finding the break-even point and is expressed by the product of sales volume by price.

Analytical method

There are several ways to determine the critical volume. Using the analytical method, that is, through the formula, the break-even point can also be found. A schedule is not required in this case.

Profit \u003d Revenue - (Fixed Costs + Variable Costs * Volume)

The determination of break-even is carried out on the condition that the profit is zero. Revenue is the product of sales volume and price. A new expression is obtained:

0 \u003d Volume * Price - (Fixed costs + Variables * Volume),

After elementary mathematical procedures, the output is the formula:

Volume \u003d Fixed Cost / (Price - Variable Cost).

After substituting the initial data into the resulting expression, the volume is determined that covers all the costs of the goods being sold. You can go from the opposite, setting the profit not zero, but the target, that is, the one that the entrepreneur plans to receive and find the volume of production.

Graphical method

An economic instrument such as a break-even chart is capable of predicting the main performance indicators of an enterprise, taking into account unchanging market conditions. Basic steps:

1. The dependence of sales volumes on proceeds and costs is plotted, where the X-axis reflects data on volume in physical terms, and on the Y-axis - revenue, costs in monetary terms.
2. Constructed in the resulting system is a straight line parallel to the X-axis and corresponding to fixed costs.
3. Coordinates corresponding to variable costs are postponed. The straight line goes up and starts from scratch.
4. A straight line of gross costs is plotted. It is parallel to the variables and originates on the ordinate axis from the point from which the construction of fixed costs began.
5. Construction in the system (X, Y) of a straight line characterizing the revenue of the analyzed period. Revenue is calculated on the condition that the price of the product does not change during this period and the release is made evenly.

The intersection of direct revenue and gross expenses, projected on the X-axis, is the desired value - the break-even point. An example graph will be discussed below.

Example: how to build a break-even chart?

An example of building a functional dependence of sales volumes on revenues and costs will be produced using the Excel program.

The first thing to do is to bring the data on revenue, costs and sales into a single table.

Next, you should call the function "Chart with markers" through the toolbar using the "Insert" tab. An empty window will appear, right-click to select a data range that includes the cells of the entire table. The X-axis label is changed through the selection of data related to the output volume. After that, in the left column of the "Select data source" window, you can delete the issue volume, since it coincides with the X-axis.

If we project the intersection point of direct revenue and gross costs on the abscissa axis, then the volume of about 400 units is clearly determined, which characterizes the breakeven of the enterprise. That is, having sold over 400 units of products, the company begins to work in a plus, receiving revenue.

Example by formula

The initial data of the task is taken from the table in Excel. It is known that the production of products is cyclical and amounts to 150 units. The issue corresponds to: fixed costs - 20,000 monetary units; variable expenses - 6,000 den. units; revenue - 13,500 den. units It is necessary to make a break-even calculation.

1. Determination of variable costs for the release of one unit: 6000/150 \u003d 40 den. units
2. The price of one sold good: 13,500 / 150 \u003d 90 den. units
3. In physical terms, the critical volume: 20,000 / (90 - 40) \u003d 400 units.
4. In value terms, or revenue with this volume: 400 * 90 \u003d 36,000 den. units

The break-even chart and the formula led to a single solution to the task - to determine the minimum production volume that covers the cost of production. Answer: 400 units must be produced in order to cover all costs, while the revenue will be 36,000.00 den. units

Constraints and conditions of construction

The ease of estimating the level of sales at which the cost of selling the product is recovered is achieved through a number of assumptions made for the availability of the model. It is believed that production and market conditions are ideal (and this is far from reality). The following conditions are accepted:

• Linear relationship between output and cost.
• The entire volume produced is equal to the realizable one. There are no stocks of finished products.
• The prices of goods do not change, as do variable costs.
• No capital costs associated with the purchase of equipment and the start of production.
• A specific time period is taken, during which the size of fixed costs does not change.

Due to the listed conditions, the break-even point, the example of which was considered, is considered a theoretical value in the projection of the classical model. In practice, calculations for multi-product production are much more complicated.

Disadvantages of the model

1. The volume of sales is equal to the volume of production and both values \u200b\u200bvary linearly. Not taken into account: behavior of buyers, new competitors, seasonality of release, that is, all conditions affecting demand. New technologies, equipment, innovations and other things are also not taken into account when calculating the volume of output.
2. Finding a break-even position is applicable for markets with strong demand and low levels of competition.
3. Inflation, which may affect the cost of raw materials, rent, is not taken into account when setting one product price for the period of the break-even analysis.
4. The model is inappropriate when applied by small businesses, where product sales are unstable.

Practical use of the break-even point

After the company's specialists, economists and analysts have made calculations and built a break-even schedule, external and internal users draw information to make a decision on the further development of the company and investment.

The main purposes of using the model:

• Calculation of the price of products.
• Determination of the volume of output that ensures the profitability of the enterprise.
• Determination of the level of solvency and financial reliability. The farther the output is from the break-even point, the higher the margin of financial strength.
• Investors and lenders - an assessment of the development efficiency and solvency of the company.

The breakeven point is the critical volume of production. When the break-even point is reached, the profit, as well as the losses of the organization, are equal to zero.

The break-even point is an important value in determining the financial position of an enterprise. The excess of production and sales volumes over the break-even point determines the financial stability of the enterprise.

The break-even model relies on a number of initial assumptions:

• the behavior of costs and revenues can be described by a linear function of one variable - the volume of output;
• variable costs and prices remain unchanged throughout the planning period;
• the structure of products does not change during the planning period;
• the behavior of fixed and variable costs can be accurately measured;
• at the end of the analyzed period, the enterprise does not have stocks of finished products (or they are insignificant), i.e. sales volume corresponds to production volume.

Using the algebraic method, the zero profit point (break-even point formula) is calculated based on the following relationship:

I \u003d S - V - F \u003d (p * Q) - (v * Q) - F \u003d 0

Where, I is the amount of profit;

S - revenue;

V is the total variable costs;

F is the total fixed costs;

Q is the volume of production in physical terms;

v - variable costs per unit of output;

p - unit price (selling price).

The break-even point determines how much sales should be in order for the company to cover all its expenses without making a profit. In turn, how profit grows with changes in revenue (shows operating leverage (operating leverage)).

When determining the break-even point, you need to divide the costs into two components:

- Variable costs - increase in proportion to the increase in production (volume of sales of goods);

Fixed costs - do not depend on the amount of products produced (goods sold) and on whether the volume of transactions increases or decreases.

The break-even point is of great importance to the lender, as he is interested in the question of the viability of the company and its ability to pay interest on the loan and the principal amount. So, the degree of excess of sales volumes over the break-even point determines the stability margin (safety margin) of the enterprise.

Let's introduce the notation:

B - sales proceeds.

Рн - sales volume in kind.

Zper - variable costs.

Zpost - fixed costs.

P - price per piece.

ЗСпр - average variable costs (per unit of production).

Tbd - break-even point in monetary terms.

Tbn is a break-even point in kind.

Break-even point formula in monetary terms:

TBd \u003d B * Zpost / (B - Zper)

The formula for the break-even point in kind (in pieces of products or goods):

Tbn \u003d Zpost / (C - ZSper)

How far is the enterprise from the break-even point margin of safety.

The formula for the safety factor in monetary terms:

ZPd \u003d (B -Tbd) / B * 100%

Safety factor formula in physical terms:

ZPn \u003d (Rn-Tbn) / Rn * 100%

The safety factor shows how much revenue or sales volume must decrease in order for the enterprise to be at the break-even point.

The safety factor is a more objective characteristic than the break-even point. For example, break-even points small shop and a large supermarket can differ thousands of times, and only a margin of safety will show which of the enterprises is more stable.

Financial safety margin shows the excess of actual sales proceeds over the profitability threshold. The larger this value, the more financially stable the p / p is. Financial safety margin shows how much you can reduce the sale (production) of products without incurring losses.

The excess of real production over the threshold of profitability is a margin of the company's financial strength:

Financial safety margin \u003d Revenue - Profitability threshold.

The financial strength of an enterprise is the most important indicator of the degree of financial stability. The calculation of this indicator makes it possible to assess the possibility of an additional reduction in proceeds from the sale of products within the boundaries of the break-even point.

In practice, three situations are possible, which will be reflected in different ways on the amount of profit and the margin of financial strength of the enterprise:

1) the volume of sales coincides with the volume of production;

2) the volume of sales is less than the volume of production;

3) sales volume is greater than production volume.

Both the profit and the margin of financial strength obtained with a surplus of manufactured products are less than when sales volumes correspond to production volumes. Therefore, an enterprise interested in improving both its financial stability and financial results should strengthen control over the planning of production volumes. In most cases, an increase in the inventory of an enterprise indicates an excess of production.

An increase in stocks in terms of finished products directly testifies to its excess, indirectly - an increase in stocks of raw materials and raw materials, since the enterprise bears the costs for them already upon their purchase. A sharp increase in inventory may indicate an increase in production in the near future, which also needs to be subjected to a rigorous business case.

Thus, when an increase in the company's inventories is detected in the reporting period, it can be concluded that it has an impact on the size of the financial result and the level of financial stability. Therefore, in order to reliably measure the value of the margin of financial strength, it is necessary to correct the indicator of revenue from sales by the amount of the increase in the company's inventory for the reporting period.

Cost-volume-profit analysis is sometimes referred to in practice as break-even analysis. This point is also called "critical" or "dead" or "equilibrium" point. In the literature, you can often find the designation of this point as BEP (abbreviation "breakeven point"), i.e. point, or threshold, profitability.

Three methods are used to calculate the break-even point (profitability threshold): graphic, equations and profit margins.

When graphic method finding a break-even point (profitability threshold) is reduced to the construction of a complex schedule "costs - volume - profit". The break-even point on the chart is the intersection of the straight lines plotted based on the value of total costs and gross revenue. At the break-even point, the revenue received by the enterprise is equal to its total costs, while the profit is zero. The amount of profit or loss is shaded. If the company sells products less than the threshold sales volume, then it suffers losses, if more, it makes a profit.

The revenue corresponding to the break-even point is called threshold revenue ... The volume of production (sales), at the break-even point is called production threshold (sales), if the company sells products less than the threshold sales volume, then it suffers losses, if more, it makes a profit.

Figure 1 - Break-even point

Equation method based on the calculation of the company's profit according to the formula:

Revenue - Variable Cost - Fixed Cost \u003d Profit

Detailing the procedure for calculating the indicators of the formula, it can be represented in the following form:

(Unit price × Number of units) - (Variable cost per unit × Number of units) - Fixed cost \u003d Profit.

The equation method can also be used to analyze the impact of structural changes in a product range. In this case, sales are considered as a set of relative shares of products in the total amount of sales proceeds. If the structure changes, then the volume of proceeds can reach a given value, and the profit can be less. In these conditions, the effect of the change in the structure on profit will depend on how the assortment changed - towards low-profit or high-profit products.

A variation of the method of equations is the method of marginal income, in which the break-even point (profitability threshold) is determined by the following formula:

Breakeven point \u003d Composition and content of financial statements: Balance sheet, Gains and losses report. Purpose of financial documents and the possibility of their use in the management system.

The main sources of information for the Finn analysis and adoption of SD is accounting (Form 1 - Form 5).

Bukh reporting should provide an objective and complete picture of the financial position of the company at a specific date. Information compiled on the basis of the rules established by regulatory enactments on accounting is reliable and complete. When generating accounting reports, it is necessary to ensure the neutrality of information, that is, exclusively one-sided satisfaction of the interests of some user groups over others.

Boo balance allows you to get a clear and unbiased idea of \u200b\u200bthe property and Finnish position of the enterprise. It reflects the state of the enterprise's funds in monetary terms as of a certain date in 2 sections.

Balance:

1. Property:

By the composition of investments:

Non-turnover assets (basic assets and intangible assets);

Circulating assets (stocks, money, assets, accounts receivable).

2. Finn resources :

By sources of formation:

Equity capital (section 3 "capital and reserves");

Borrowed funds (sections 4 and 5).

2 interconnected interpretations of balance have become widespread:

1. Subject-material - the asset of the balance sheet shows the composition and location of property, the presence of which is confirmed by the inventory

2. Cost-effective - the balance sheet asset expresses the amount of the enterprise's costs resulting from previous economic operations and financial transactions and the costs incurred by it for the sake of possible future income; the liability reflects the liabilities arising in the process of attracting funds, its interpretation is of a legal nature

All obligations are ranked in accordance with the legislation according to the obligation and priority of satisfaction (primarily short-term debt). The economic significance of the balance sheet liability lies in the fact that it reflects the sources of property formation. One of the purposes of the balance sheet is to characterize the change in the financial state of the enterprise for the reporting period.

Balance classification:

1) According to information sources: inventory, book (based on the General Ledger), general (based on the statement);

2) By the time of compilation: introductory, current, liquidation, separation (if there are divisions), unification (if merger);

3) By the amount of information: single (1 structural subsection), consolidated;

4) By type of activity: commercial organization, investment fund, bank balance sheet, organization fear balance, budget organization balance sheet;

5) By the nature of the activity: the balance of the main activities, the balance of the non-main activities;

6) By forms of ownership: state (municipal) enterprise, private enterprise (society, partnership), organization with foreign investment;

7) Degree of cleaning the balance sheet from unnecessary indicators: gross, net (net).

In form 2 "Profit and loss statement" -data on income, expenses and financial results are presented on an accrual basis from the beginning of the year to the reporting date. Here you can find information about the Finn result, both for the reporting period and for the previous one.

The types of profit are reflected here:

Gross (the difference between sales and sales proceeds);

From sales (difference between gross and commercial expenses);

Before taxation (from sales + balance from other income and expenses);

Net (after taxation, i.e. before taxation-income tax).

Form 3 "Statement of capital flows»- contains information about the amount of capital at the beginning of the period, its receipt and use during the year and reflects the carrying balance at the beginning of the year.

Form 4 "Statement of cash flows" - contains information about cash flows, their receipt, taking into account their balance at the beginning of activities in the context of current, investment and financial activities.

Bukh data. reporting allow you to identify fin. the position of the enterprise, its solvency and profitability.

1 - Bukh. reporting provides an opportunity to look more deeply into the internal and external relations of households. subject and enterprise, to assess its ability to timely and fully calculate the obligations.

2 - External users bukh. information on the reporting data are able to assess the feasibility of acquiring the property of an enterprise, to avoid issuing loans to unreliable clients, to build relationships with existing customers correctly, and also to assess the financial resources. position of potential partners.

3 - According to the reporting data, the head of the enterprise reports to the founders and other management and control structures. A thorough analysis of the reporting allows you to reveal the reasons for shortcomings in the work of the enterprise, to identify reserves and outline ways to improve its activities. T. about. the importance of reporting is great.

Andrey MitskevichCandidate of Economic Sciences, Associate Professor of the Graduate School of Financial Management of the Academy of National Economy under the Government of the Russian Federation, Head of the Consulting Bureau of the Institute for Economic Strategies

Break-even analysis

The management of the company has to make various management decisions regarding, for example, the sale prices of goods, planning sales volumes, opening new outlets, increase or, conversely, savings for certain types of costs. In order to understand and evaluate the consequences of the decisions made, an analysis of the ratio of costs, volume and profit is required.

The break-even analysis shows what will happen to the profit when the volume of production, price and basic cost parameters change. The English name for the break-even analysis is CVP-analysis (cost - volume - profit, that is, "costs - output - profit") or Break - even - point (breakpoint, break-even point in this case).

Who does not know this? However, only a few companies use the classics in their life. Why? Maybe "professorial economics" is so out of touch with life? Let's try to understand what CVP analysis is and why its fate is ambiguous. At least in our country.

CVP Analysis Assumptions

The break-even analysis is performed in the short term, subject to the following conditions in a certain range of production volumes, called the acceptable range:

• costs and output are in the first approximation expressed as a linear relationship;
• performance does not change within the considered output changes;
• prices remain stable;
• stocks of finished goods are insignificant.

Academician and our only compatriot - laureate of the Nobel Prize in Economics for 1975 L.V. Kantorovich said: “economists-mathematicians begin all their work with“ suppose that ... ”. So this cannot be assumed. " Perhaps, in our case, the professors stepped on the same rake?

The answer to this question pleases: working hypotheses, tested by practice

management accounting. If they are violated, it is not difficult to make changes to the model.

The acceptable range of production volumes (area of \u200b\u200brelevance) is determined by the cost linearity hypothesis. If the hypothesis is not in doubt, the range is taken as the constraints of the CVP model. Basic classical relations:

1.AVC ≈ const, i.e. average variable costs are relatively constant.

2. FC are unchanged, i.e. there is no threshold effect.

Then the total cost of producing a product is determined by the ratio

TC \u003d FC + VC \u003d FC + a × Q, where Q is the output volume.

A single-product problem lives on in textbooks, and a multi-product problem lives on in practice.

• Single-product problems answer questions from the field of break-even analysis in the form of the amount of product produced ((2). Most often, CVP analysis in theory boils down to determining the classic break-even point, which shows how many units of product need to be produced to cover all fixed costs. as a rule, it also applies to the target profit, i.e. it comes down to determining the volume of output that provides a given profit.
• Multi-product tasks answer the same questions in the form of revenue (TC). In this case, it is assumed that its structure remains unchanged, at least in the sense of the constancy of the share of the marginal profit in the proceeds.

Accounting methods affect the applicability of CVP analysis. Break-even analysis is carried out using Variable Costing, since Direct Costing and even more so Absorption Costing give errors. If the company does not apply at least Direct Costing, then there will be a break-even analysis, therefore one of the reasons for the unpopularity of CVP analysis in Russia is the dominance of Absorption Costing.

Break-even points

1) The classic break-even point in terms of the number of units of production assumes a payback of total costs (TC \u003d TC). Critical is the amount of sales at which the company has costs equal to the proceeds from the sale of all products (i.e., where there is no profit or loss).

In the single-product version, the value of the break-even point (Q b) is directly derived from this ratio:

This formula dominates the literature and, in fact, has earned the name of the classic break-even point (see Fig. 1).

Figure: 1. Classic CVP analysis of the behavior of costs, profits and sales

An example of calculating the classic break-even point by the number of product units

The Corporation decides to open several mini-wholesale stores. Their characteristics:

• narrow specialization (office paper, mainly A4)
• small trading area (premises up to 20 sq.m., or a portable point of sale);
• minimum sales staff (up to two people);
• the form of sales is mainly small wholesale.

Table 1

• Marginal profit per unit of production: 224 -180 \u003d 44 rubles. We calculate the critical point using the formula:
• Break Even Point \u003d Fixed Costs / Profit Margin Per Unit
  We get: 10000: 44 \u003d 227.27.

To reach critical point the store needs to sell 228 reams of paper (10 reams per day) within a month, with six working days a week.

2) Multi-product break-even analysis. Until now, we have assumed that there is one product, but in real life this is an insignificant special case. Paradoxically, the multi-product case is less in demand in the literature, and even more so in practice. The fact is that in this case the result of the break-even analysis is difficult to interpret. For a practitioner, it is not specific, since it gives hundreds of answer options instead of a clear guideline for assessment.

Consider the mathematics of this case. It is clear that the revenue should cover the total costs. In this case, we get not one break-even point, but a plane in the N-dimensional space, where N is the number of types of products. If we make a fairly correct and accepted in classical management accounting assumption about the constancy of AVC i \u003d V i, we get a linear equation:

Logically, these points are very similar to the points of the margin I variable of breakeven. Unfortunately, the remaining inseparable fixed costs cannot be distributed between products one by one and balanced bases. If all products are cash cows, the base could be a notional margin (revenue minus variable costs and minus own fixed costs for each product). But since the issue is unknown in the issue of the break-even point, neither the notional margin nor the revenue works.

The second step will have to distribute the remaining costs:

NFC \u003d FC - ΣMFC i

Options:

a) equally, if there is no reason to prefer any one product;

b) in proportion to the planned revenue, if the sales plan is drawn up. Only the total fixed costs are naturally divided;

c) if you have a plan, you can return to a balanced base (for example, marginal profit), but already without part of the product
attributed to covering own costs (МРС i).

An example of calculating break-even points based on developed Direct Costing.

Let's say a firm produces two types of products: "Alpha" and "Beta", which are sold at prices of 9 and 20 thousand dollars apiece, respectively. Average variable costs (AVC) are projected at $ 4,000 and $ 10,000, respectively.

Individual fixed costs for Alpha were $ 2,000 for the planned quarter and for Beta $ 8,000. The remaining fixed costs (NFC) were found to be $ 10,000.

a) when dividing the non-divided fixed costs equally (5000 per product type), we get:

Let's try to determine the break-even points with different options. First, let's calculate the coverage of our own fixed costs:

b) when dividing in proportion to the plan, you need to know this plan: 2900 and 2175, for example, in pieces. As the distribution base, we take the revenue minus the coverage of our own fixed costs:

22,500 thousand dollars \u003d 2,900 x 9 - 400 x 9 for Alpha;

$ 27,500,000 \u003d 2,175 x 20 - 800 x 20 for Beta.

c) the base of the profit margin assumes that the planned output is reduced by the amount of its own coverage (in pieces):

2900 — 400 = 2500 2175 — 800 = 1375

Conclusion: deviations in the calculations are small, so you can use any of the proposed methods in the case of an approximate equality of product volumes. Otherwise, it is better to use methods B and C:

B - for growing markets and products;

B - for "dairy cows".

3) The classic revenue break-even point is the most common approximate solution to a multi-product problem. It is assumed that the structure of revenue changes slightly. The problem is posed as follows: find such a value of revenue at which the profit is zeroed. For this, the economist is required to have a coefficient ( to), showing the share of variable costs in revenue. It is not difficult to find it, knowing the share of variable costs in total costs and profit in revenue. As a result, we get the equation:

For example:

• share of variable costs in revenue \u003d 9742/16800 \u003d 58%;
• fixed costs \u003d 5816 thousand rubles;
• break-even point \u003d 5816 / (1-0.58) \u003d 13848 thousand rubles of revenue

Unlike the classic break-even point in terms of the number of product units, here you should make a reservation regarding the accuracy of the results:

• formula (7) is probably correct with an unchanged output structure;
• however, a less stringent condition can be formulated: the invariability of the coefficient k, i.e. share of variable costs in revenue.
• Break-even point based on descending margin ordering. The break-even point shifts to the left when using the ordering of products in descending order of the profit margin.

Let's consider this interesting and rarely described effect with an example. So, the firm has fixed costs equal to $ 16,000 and produces 4 products with different shares of marginal profit in the revenue (see table. 2).

Table 2. Initial data for calculating the break-even point based on marginal ordering

Let's calculate the break-even point for revenue based on formula (7):

Let's define it taking into account the fact that we will first produce the most profitable products: A and B. They are just enough to cover the fixed costs: μπ (A) + μπ (B) \u003d 12000 + 4000 \u003d 16000 \u003d FС. Thus, we get an optimistic estimate of the break-even point:

20000 + 8000 = 28000.

The break-even point based on ascending margin ordering gives a pessimistic estimate. Let's use the same example for illustration. Products D, C, B are only enough to cover $ 12,000, and the remaining fixed costs of $ 4,000 are one third of the release of product A. That is, a pessimistic estimate of the break-even point:

The break-even points based on the descending and ascending marginal ordering together give the range of possible break-even points.

4) Point 1. LCC-breakeven. Life Cycle Costing's cost-benefit approach defines a break-even point as an output that pays for the full cost over the life of the item. The LCC approach encroaches on the prerogative of investment design. In addition to fixed costs, he insists on covering investment costs.

Example LCC Analysis

Let's say a consortium of Russian firms has invested $ 500 million in research and development (R&D) of a new aircraft.

Fixed costs are made up of $ 700 million in R&D (one-off costs in a given year) and $ 50 million in annual fixed costs. Variable costs per plane - $ 10 million. It is expected that 25 aircraft will be produced a year, and they can be sold on the market for a maximum of $ 16 million. How many planes should be sold to compensate for all costs without taking into account the time factor (this is also a break-even point, but taking into account what?) And how many years will it take?

Solution: Let's denote the unknown number of years as Y. Fixed costs will depend on the number of years the break-even point is reached: 700 + 50 x Y. Let's equate the total costs and revenues for Y years:

700 + 50 x Y + 25 x 10 x Y \u003d 25 x 16 x Y.

Hence Y \u003d 7 years, during which 175 aircraft will be produced and sold.

5) The point of marginal break-even (payback point of an additional unit of production). With modern complex production, the marginal costs (for the production of an additional unit of production) do not immediately become lower than the price. Release,

providing break-even for an additional unit of production, is determined by the ratio:

Q bm: P \u003d MC (Q bm) (8)

This point shows the moment (release) when the company starts to work "in plus", i.e. when with the release of another unit of production, profits begin to grow.

Unfortunately, there is no more detailed formula. This ratio

6) Break-even point of variable costs (point of coverage of variable costs):

TR \u003d VC or P \u003d AVC. (nine)

It shows that the process of recouping fixed costs is about to begin. This is an important indicator both for managers who "started" a new product and for owners. However, even here there is no more intelligible formula for calculations. The reason is the same: the ratio

(9) is always individual.

Target profit points

They show the output of a single product (or revenue - in the case of multi-product production) that provides a given mass or rate of return.

1. Target profit point for the number of product units.

The traditional indicator is the output that provides the target profit. Similar calculations are performed in many firms. Suppose the required profit is π, that is

This formula is easily modified in the case of target profit after tax. Here's a simplified calculation. If the target profit after tax should be equal to z, then (TR - ТС) × (1 - t) \u003d z, where t is the income tax rate. Therefore, (P - AVC) x Q x (1 - t) \u003d z + FC × (1 - t) or

2. The target profit point for revenue is easily calculated by analogy with the formula (7):

In the multi-product case, it is subject to the same restrictions on the invariability of the coefficient k, i.e. share of variable costs in revenue.

Sensitivity analysis is based on the use of the technique "what happens if one or more factors affecting the amount of sales, costs or profits change". Based on the analysis, you can get data on the final result for a given change in certain parameters. Sensitivity analysis is based on safety edges.

Safety edges (sometimes translated as safety margin or safety margin) show the safety margin, business break-even in percent or natural units, or in rubles of revenue. The representation in percentage is more visual and, most importantly, allows you to normalize this important indicator. Although these norms are extremely approximate, they are useful. Mathematicians speak about such numbers and formulas with disdain: "managerial indicators". But this "engineering approach" cannot be avoided.

The classic safety edge in terms of the number of products:

It shows how much the revenue can decrease in case of non-loss production. An indicator less than 30% is a sign of high risk.

Classic safety edge by revenue:

Both of these safety margins are good for the business in general, as the fixed costs are understandable, but not very useful for business segments. However, the "head-on" use of variables or marginal costs, as you remember, requires non-linearity of their functions. Classical management accounting does not study these functions and therefore has to consider them linear. Does this mean that there are no other safety edges besides the classic ones? The answer will be no.

The price safety edge shows how much the price needs to be reduced in order for the profit to turn to zero. This will be at a critical price P k \u003d AC. Then the safety edge will be as a percentage of the current price:

The safety edge for variable costs shows how much you need to increase the unit variable costs in order for the profit to go to zero. The critical value of AVC is achieved when AVC \u003d P - AFC. because

The security edge at fixed costs in absolute terms is equal to profit, and in relative terms:

Note that in formulas (15-17) the issue remains unchanged.

Problems in determining break-even points

If a firm is facing semi-fixed costs, there may be several break-even points. The break-even chart (see Fig. 2) shows three break-even points, and profit and loss zones replace each other as the volume of activity increases.

Figure: 2. The multiplicity of classical break-even points in the case of semi-fixed costs.

A similar breeding applies to non-classical break-even points.

Difficulties in conducting a break-even analysis can be associated with the following reasons:

• with a high level of supply, it may be necessary to reduce the unit price. Consequently, a new break-even point will appear, lying to the right;
• “Large” buyers are likely to be eligible for bulk discounts. The breakeven point moves to the right again;
• if the amount of demand exceeds supply, then it may be advisable to increase the price. This will move the break-even point to the left;
• the cost of raw materials and materials per unit of production may decrease with large volumes of purchases or increase with supply interruptions;
• the unit cost of wages of production workers is likely to decrease with a large volume of production;
• both fixed and variable costs tend to increase over time;
• costs cannot always be accurately divided into fixed and variable;
• the structure of sales can change quite significantly.

All these elementary analytical calculations are simply ignored by primitive business plans.

Nevertheless, it is believed that break-even analysis is carried out everywhere and its significance is great. My observations do not confirm this. Like any model, the CVP has its own "battlefield" and it is fragmented. Many firms conduct CVP analysis only for new projects. Regular work with the profitability of products and segments in our country, unfortunately, is not enough yet.

Case with solutions

So, two companies: ZAO Staromekhanicheskiy Zavod (hereinafter referred to as SMZ) and OAO Zarubezhny Automation (hereinafter referred to as ZAM) operate in the Little Russian market and manufacture a part used in car repairs. Today, these two companies have divided the Russian market - each holding 50%. The parts produced are of the same quality and price. The production facilities of both companies are located in the vicinity of Mariupol.

However, companies differ radically in their cost structures. Foreign Automation has a fully automated and highly capital-intensive production facility. And the "Staromekhanicheskiy Zavod" is a non-automated production with a large share of manual labor. The companies' monthly profit and loss statements are as follows (see table 1).

Table 1. Initial situation (in USD)

Both companies are looking at ways to increase profits. One is to start selling your products to a sizable but relatively low-income (or thrifty) segment of buyers who are currently not served. The potential capacity of this segment is 2000 pieces per month. Thus, the company that has captured this segment will have sales in physical terms by 40%. The only problem is that in this segment, consumers will buy parts for no more than 8.50 USD. i.e. per piece, i.e. 15% lower than the market price and 1 cu. That is, below the full cost of production at the moment. "How can you sell at a price below cost?" - the head of the PEO with many years of experience at the "Staromekhanichesky Zavod" is outraged.

Question 1: Let's say both companies can segment the market without additional costs (that is, start selling parts to the economy segment at a 15% discount, while not undermining their sales at full price to wealthy buyers). How much will each company be able to increase profits if it increases sales (in pieces): a) by 20%, that is, capturing half of the economy segment?

b) by 40%, capturing the entire economy segment?

Should companies (one or both) use this opportunity to increase profits?

Conclusion: Both companies will be happy to "grab" even half of the economy segment, not to mention the happiness of taking over it entirely.

Question 2: What to do if neither SMZ nor ZAM can effectively segment the market, and both firms are forced to set a single price for all buyers (i.e. $ 8.50 for both the economy segment and wealthy buyers ).

a. Calculate BOP (Break Even Sales) for each of

companies, if the price is reduced to 8.50 USD. e.

b. How much will the profits of each company grow if its sales

increase by 40% (in pieces)?

Attention: BOP (break-even sales) in this case assumes that the company should receive the previous, not zero, profits.

Break-even sales are more common in practice than the classic CVP analysis. It is found in life, but not always in textbooks. This is a variant of the target profit point in dynamics: when the factors change, the profit remains at the same level. The break-even sales volume assumes that the company should receive the previous profits in case of changes, and not zero. For example, an old machine has been replaced with a more efficient and expensive one. Naturally, the question arises, how much should the output be increased in order to “recoup costs”?

This is what we call the competitiveness of the cost structure with lower average variable costs. "Foreign Automation" will withstand the decline in prices, but "Old Mechanical Plant" will not. Dumping (the game of lowering prices) is the lot of firms with low variable costs. Fixed costs have nothing to do with it.

Question 3: While the companies were thinking, their market was invaded by a strong competitor - the Automobile Plant. He easily took over half the market, trading the same parts for $ 9. We will have to return to the initial situation and analyze the reliability of the LPS and ZAM. Both firms lost half of their sales (in pieces). The results are presented in table. 2.

Table 2. Situation after the invasion of the "adversary" (in USD)

Of course, both companies are at a loss, but transferring them is probably easier for "Staromekhanicheskiy Zavod". This is what we call robust cost structure with lower fixed costs.

Question 4: Morning. The invasion of the Automobile Plant turned out to be a nightmare. Assuming no company can segment the market, what advice would you give each company about this opportunity?

Answer: “Foreign Automation” should reduce the price, but “Staromekhanicheskiy Zavod” should not. ZAM has every chance of winning the price competition due to its lower variable costs.

After analyzing the situation, ZAM decided to take the opportunity to sell parts to a new segment and cut prices by 15%. Its sales rose to 7,000 units a month at a price of $ 8.50. e. Belatedly, SMZ was also forced to lower prices to retain its customers. SMZ management believes that if they had not reduced their prices, they would have lost 60% of sales. Unfortunately, after the price reduction, SMZ is operating at a loss.

Question 5: Was the decision of "Staromekhanichesky Zavod" to cut prices financially justified? For example, if the SMZ decides to completely withdraw from this market, it will be able to cut fixed costs in half. For example, refuse to rent premises, land and other expenses. The remaining 50% of fixed costs are servicing a bank loan for the purchase of equipment with zero liquidation value. Calculate and compare profits for different options.

Position after price decline:

μπ (up to) \u003d 4.5x5000 \u003d 22500

μπ (after) \u003d 3x5000 \u003d 15000

FC \u003d 20,000, π \u003d -5000.

Alternative option: do not reduce the price, but lose part of the market:

μπ (up to) \u003d 4.5x5000 \u003d 22500

μπ (after) \u003d 4.5x2000 \u003d 9000

FC \u003d 20,000, π \u003d -11,000.

Therefore, price reduction is beneficial in the short term.

When leaving the market π \u003d -10000. Therefore, one should stay and reduce the price, although production will be unprofitable: FC \u003d 20,000, π \u003d 15,000 - 20,000 \u003d -5,000.

Fortunately, the managers of the Old Mechanical Plant read the book Competitive Advantages by Michael Porter and decided to analyze how the entire value chain works. As a result of market analysis, they found that at least 3,500 parts are bought monthly by drivers, who then have to rework the part on their own so that it better fits their car brand: namely, the Volga. Thus, there is an opportunity on the market to produce a specialized version of the part for this category of drivers. And although production costs at the SMZ will rise, the additional costs will still be less than what drivers currently spend on reworking the part.

For the production of specialized parts, the SMZ will have to invest additional capital, the payment for which will be 3000 USD. per month.

Question # 6: In order to produce specialized parts, the SMZ will have to buy new equipment and a new building, which will cost 23,000 USD. fixed costs per month instead of $ 20,000 e. per month. The plant management is convinced that they will be able to sell specialized parts for $ 6 more than conventional parts (i.e. at $ 16), but the unit variable costs will rise by $ 3.00. e. per month. Will it be profitable for SMZ to focus on the production of only specialized parts?

Answer: FС \u003d 23000, π \u003d (1b-8.5) х3500 - 23000 \u003d 3250. Yes, the production of only specialized parts is profitable, since the profit will increase by 3250 - 2500 \u003d 750 USD. e.

Question # 7: What is the minimum number of custom parts a LMP must sell per month to exceed the profits it currently earns as a generic parts manufacturer? Remember? We called this break-even sales.

Answer: FC \u003d 23000, π \u003d (16-8.5) xQ - 23000 \u003d 2500. Q \u003d 3400.

Question # 8: How much will the profits of "Staromekhanichesky Zavod" grow as a manufacturer of specialized parts, if it sells 3,500 pieces per month at a price of $ 16 per piece? ?

Answer: 3250 — 2500 = 750.

"Unfamiliar options for break-even analysis"

There are other options for analyzing break-even. For most, they will be unexpected. We call them the “three break-even points”:

The first and the fastest attainable - the point of marginal break-even - shows at what output the price will start to recoup the additional costs of producing another unit of production (P\u003e MC - in conditions of perfect competition or MR\u003e MC - in conditions of imperfect competition). The first condition (P\u003e MC) corresponds to the spirit of management accounting and is quite worthy of use. The second (MR\u003e MC) is suitable only for pure economic theory, although it would be presumptuous to deny the possibility of its practical use.

The second point - the break-even point of variable costs - shows the output at which it will be possible to cover all variable costs (TR\u003e VC). Naturally, this formulation of the problem is typical for Variable Costing. In the case of using Direct Costing, a similar point will be called the direct cost break-even point (TR\u003e DC).

The third point - the classic one - sets the release at which it will be possible to cover all costs (TR\u003e TC). It has filled all textbooks, so most students and professionals think that the classic break-even point is CVP analysis. This is a clear exaggeration, or rather an understatement of the role and capabilities of CVP analysis.

Example. Evaluating the operation of company stores and posting general administrative costs

At the beginning of the year, a large Moscow company set an ambitious goal: to open 200 new brand stores throughout the country in a couple of years. The head office economist asked how to spread head office costs between stores? The answer, surprisingly enough, relies on "three break-even points":

1. A newly opened store must first recoup its current content. This is the first and specific task for management. It is not necessary to post costs to such stores. This is also a break-even point, not for groceries, but for stores. All other things being equal, the collective that passes the first stage faster "will win the capitalist competition." Nobody canceled moral incentives.

2. Once the store contributes to coverage, another stage of development will begin. Here it is required to recoup the accumulated current losses of the previous stage. This is also a kind of break-even point of variable costs, only not for products, but for stores.

3. Only at the next, third stage it is necessary to fight for the classical payback. And only here you can spread the costs of the central office between stores. Advanced Direct Costing welcomes this solution, but does not provide advice on which overhead posting base to use.

It is on such a decision that the business plan of each store or branch, representative office, business line, and so on should be aimed.

When starting any business, you need to be prepared for the fact that the profit of the enterprise will appear, most likely, not immediately. To understand at what point all losses will be covered and income will begin to exceed expenses, you need to calculate the break-even point in advance. We will talk about this indicator in our article.

Enterprise breakeven point

The break-even point (or profitability threshold) can be defined as the volume of production (sales) at which the income from the business covers all the costs of it, that is, the company goes to "zero" - still without profit, but already without loss, and the next sales will begin bring long-awaited profit. In monetary terms, this is the size of the proceeds received, and in quantitative terms, the volume of products produced.

The break-even point indicator is not constant, it can rise or fall, depending on the dynamics of the enterprise, price changes, etc.

Why is it necessary to determine the break-even point? For example, in order to:

• find out when the funds invested in the business can pay off, how effective this business project is,
• determine how the company is financially stable,
• understand how justified the planned expansion of production, sales market, branch network, etc. will be,
• identify the minimum level of production or the amount of revenue, below which the company's activities will become unprofitable

Break-even point: how to calculate?

To calculate the break-even point, you need to deal with costs, separating from them fixed and variable costs:

• permanent - salary and deductions from it for administrative and managerial personnel, depreciation, office rent, etc. These expenses of the enterprise do not directly depend on the volume of production and sales, but they are influenced by changes in the rent, opening or closing of divisions, workshops, etc.
• variable costs depend on the volumes of products produced (sales made) and change with them, increasing in proportion to the increase in production, or sales volumes - this is the piecework salary of workers and deductions from it, the cost of raw materials and materials, spare parts, etc., transportation costs, Fuels and lubricants, electricity, etc.

Having distributed all your costs to fixed and variable, you can start calculating.

Break-even point: calculation formula

Depending on the specifics of the business, it is possible to calculate the break-even point both in monetary and in kind. So, for production it will be more convenient to use the "natural" method, and for sellers of goods or services - money.

The formula for calculating the break-even point in monetary terms (TBden).

Let's calculate margin ratio (KMD), for which we first calculate marginal income (MD):

• MD \u003d B - Zperm,
• where B - revenue, and Zperm - variable costs for the volume of products (goods, services),

then we find the coefficient itself, dividing the marginal income by the revenue:

• KMD \u003d MD / V

The amount of revenue at which the profit will be "zero", it is also the break-even point, is equal to:

• TBden \u003d Zpost / KMD,
• where Zpost is a fixed cost.

An example of calculating a break-even point for a store

The break-even point is the calculation formula in kind (TBnat).

• TBnat \u003d Zpost / (C - Zperm unit),
• where C is the price of a unit of production, goods, or services,
• We change units - variable costs per unit of output.

Let's calculate the break-even point.

Example for a manufacturing plant

Suppose the price of one product manufactured by an enterprise (C) is 450 rubles.

Fixed costs (Zpost) are 305,000 rubles. and include:

• salary of administrative and management personnel with deductions - 110,000 rubles,
• utility bills - 25,000 rubles,
• depreciation - 100,000 rubles,
• other fixed costs - 70,000 rubles.

Variable costs, with a production volume of 1000 pieces, are allocated as follows:

Let's make a calculation using the formula:

TBnat \u003d Zpost / (C - Zperm unit) \u003d 305,000 rubles. / (450 rubles - 350 rubles) \u003d 3,050 pcs., Such a quantity of products produced will cover the costs, and everything produced above the break-even point is profit.

What to consider when calculating the break-even point

The examples given by us are conditional and assume the invariability of the initial data. But when calculating a break-even point for an operating business, you need to take into account a number of the following factors that can affect the reliability of the result:

• the price of products, services, goods in reality does not "stand still", but can change for various reasons,
• if the volume of production or sales grows, then the costs of the company also grow, and not only variable, but also fixed costs can grow,
• the calculation of the break-even point is done for many types of products (goods), and not for one, which requires calculating the share of costs for each of them,
• purchased goods, or manufactured products are far from always sold in full - unrealized balances remain in the company's warehouse.