Andrei Mitskevich PhD in Economics, Associate Professor of the Higher 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 of Economic Strategies

Break even analysis

The company's management has to make various management decisions regarding, for example, the price of selling goods, planning sales volumes, opening new outlets, increasing or, conversely, saving on certain types of expenses. In order to understand and evaluate the consequences of the decisions made, it is necessary to analyze the ratios of costs, volume and profit.

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

Who doesn't know this? However, only a few use the classics in the life of firms. Why? Maybe "professional 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.

Assumptions made in the CVP analysis

Break-even analysis is performed in the short run under the following conditions in a certain range of production volumes, called the acceptable range:

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

Academician and our only compatriot - Nobel Prize winner in economics for 1975 L.V. Kantorovich said: “Mathematical economists 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: the hypotheses are working, 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 (relevance area) is determined by the cost linearity hypothesis. If the hypothesis is not in doubt, the range is accepted as the constraints of the CVP model. Basic classical ratios:

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 relation

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

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

• Single-product tasks 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 comes down to determining the classical break-even point, which shows how many units of production need to be produced to cover all fixed costs. How 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). At the same time, its structure is assumed to be unchanged, at least in the sense of the constancy of the share of marginal profit in revenue.

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 a company does not use 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 classical break-even point in terms of the number of units of production assumes the payback of total costs (TC = TC). The critical value is considered to be such a value of sales at which the company has costs equal to the proceeds from the sale of all products (ie, where there is neither profit nor loss).

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

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

Rice. 1. Classical CVP-analysis of the behavior of costs, profits and sales volume

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

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

• narrow specialization (office paper, mainly A4 format)
• small retail space (premises up to 20 sq.m., or a remote outlet);
• minimum sales staff (up to two people);
• form of sales - mostly 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 = Fixed Costs / Profit Margin Per Unit
  We get: 10000: 44 = 227.27.

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

2) Multi-product break-even analysis. So far, we have assumed that there is one product, but in real life this is a minor special case. Paradoxically, the multicommodity 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 answers instead of a clear guideline for evaluation.

Let's consider the mathematics of this case. It is clear that the revenue must cover the total costs. In this case, we obtain 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 = V i , we get a linear equation:

These points, by the logic of reasoning, are very similar to the points of the marginal I breakeven variable. Unfortunately, the remaining inseparable fixed costs cannot be distributed between products on the same and balanced bases. If all products are cash cows, such a base could be the notional contribution margin (revenue minus variable costs minus each product's own fixed costs). But since output is unknown in the break-even point question, neither the notional contribution margin nor the revenue work.

In the second step, you will have to allocate the remaining costs:

NFC = 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. Naturally, only the total fixed costs are shared;

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

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

Suppose a firm produces two types of products: "Alpha" and "Beta", sold at a price of 9 and 20 thousand dollars apiece, respectively. Average Variable Costs (AVC) are planned at $4,000 and $10,000 respectively.

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

a) when dividing undivided fixed costs equally (5000 per type of product), we get:

Let's try to determine the break-even points in different ways. First, we 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 proceeds minus the coverage of own fixed costs:

22500 thousand dollars \u003d 2900 x 9 - 400 x 9 for Alpha;

$27,500 = 2175 x 20 - 800 x 20 for Beta.

c) the marginal profit base assumes that the planned output is reduced by the amount of own coverage (in units):

2900 — 400 = 2500 2175 — 800 = 1375

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

B - for growing markets and products;

B - for "cash cows".

3) The classical break-even point in terms of revenue is the most common approximate solution to a multi-product problem. It is assumed that the revenue structure changes insignificantly. The task is set as follows: to find such a value of revenue at which profit is zeroed. To do this, the economist requires 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 = 9742/16800 = 58%;
• fixed costs = 5816 thousand rubles;
• break-even point \u003d 5816 / (1-0.58) \u003d 13848 thousand rubles of revenue

In contrast to the classical break-even point in terms of the number of units of production, here it is necessary to make a reservation regarding the accuracy of the results:

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

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 revenue (see Table 2).

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

Product		Revenue (TK) Doll.	Marginal profit (/OT), USD	Share of contribution margin in revenue

Calculate the break-even point for revenue based on formula (7):

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

20000 + 8000 = 28000.

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

Break-even points based on marginal descending and ascending ordering together give an interval of possible break-even points.

4) Point 1. LCC break even. The Life Cycle Costing approach to the problem of cost and profit defines the break-even point as an output that pays for the full costs, taking into account the entire life of the product. The LCC approach encroaches on the prerogatives of investment design. In addition to fixed costs, he also insists on covering investment costs.

An example of an LCC analysis

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

Fixed costs consist of $700 million in R&D (a one-off cost in a given year) plus $50 million in annual fixed costs. Variable cost per aircraft - $10 million. It is expected that 25 aircraft will be produced per year, and they can be sold on the market for a maximum of $16 million. How many planes need to be sold to offset 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. Equate the total costs and revenue for Y years:

700 + 50 x Y + 25 x 10 x Y = 25 x 16 x Y.

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

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

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

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

This point shows the moment (output) when the company starts to work "in plus", i.e. when with the release of one more 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 = VC or P = AVC. (nine)

It shows that the process of recoupment of fixed costs will soon begin. This is an important indicator both for managers who “started” a new product, and for owners. However, there is no more intelligible formula for calculations here either. The reason is the same: the ratio

(9) always individually.

Target profit points

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

1. Target profit point by the number of units of production.

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 a target after-tax profit. Here are the simplified calculations. If the target profit after tax should be equal to z, then (TR - TC) × (1 - t) = z, where t is the income tax rate. Therefore, (P - AVC) x Q x (1 - t) = z + FC × (1 - t) or

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

In the multicommodity case, it is subject to the same restrictions on the invariance of the coefficient k, i.e. share of variable costs in revenue.

Sensitivity analysis is based on the use of the “what happens if one or more factors that affect the amount of sales, costs or profits” change. Based on the analysis, you can get data about the final result with a given change in certain parameters. The sensitivity analysis is based on safety edges.

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

Classic safety edge by number of units:

It shows how much percentage revenue can decrease with break-even production. Less than 30% is a sign of high risk.

Classic Safety Edge by Revenue:

Both of these safety margins are good for the business as a whole, as fixed costs are understandable, but not very useful for business segments. However, the "frontal" application of variable or marginal costs, as you remember, requires the non-linearity of their functions. Classical management accounting does not study these functions and therefore is forced to consider them linear. Does this mean that there are no other safety edges than the classic ones? The answer will be negative.

The price safety margin shows how much price needs to be lowered in order for the profit to become zero. This will be at the critical price P k = AC. Then the margin of safety will be as a percentage of the existing price:

The variable cost safety margin shows how much the unit variable costs need to increase in order for the profit to go to zero. The critical value of AVC is reached at AVC = P - AFC. That's why

The margin of safety for fixed costs in absolute terms is equal to profit, and in relative terms:

Please note that in formulas (15-17) the output remains unchanged.

Problems in determining break-even points

If a firm faces semi-fixed costs, there may be multiple break-even points. The break-even chart (see Figure 2) shows three break-even points, and profit and loss zones follow each other as the volume of activity increases.

Rice. 2. Multiplicity of classical break-even points in the case of semi-fixed costs.

Similar reproduction also applies to non-classical break-even points.

Difficulties in conducting a break-even analysis may be due to the following reasons:

• if supply is high, the unit price may have to be lowered. Consequently, a new break-even point will appear, lying to the right;
• "Large" buyers are likely to be eligible for volume discounts. The break-even point shifts to the right again;
• if demand exceeds supply, it may be appropriate 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 can not always be accurately divided into fixed and variable;
• the structure of sales can change quite significantly.

Primitive business plans simply ignore all these elementary analytical calculations.

However, it is believed that break-even analysis is carried out everywhere and its value is great. My observations do not support this. Like any model, the CVP has its own “battlefield”, and it is fragmented. Many firms conduct CVP analysis only for new projects. Unfortunately, regular work with the profitability of products and segments in our country is still not enough.

Case with solutions

So, two firms: CJSC "Staromehanicheskij Zavod" (hereinafter - SMZ) and OJSC "Foreign Automation" (hereinafter - ZAM) work in the Little Russian market and manufacture a part used in car repairs. Today, these two companies have divided the Russian market - each holds 50%. Manufactured parts have 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 structure. "Foreign Automation" has a fully automated and very capital-intensive production. And the "Old Mechanical Plant" is a non-automated production with a large share of manual labor. Monthly profit and loss statements of companies are as follows (see table 1).

Table 1. Initial situation (in c.u.)

Indicators	"Foreign Automation"	"Old Mechanical Plant"
Sales, pcs.
Price for one
Unit Variable Costs
Unit fixed costs
Total unit cost
Full costs	9.5x5000 = 47500	9.5x5000 = 47500
	50000 — 47500 = 2500	50000 — 47500 = 2500

Both companies are looking at ways to increase profits. One is to start selling your products to a sizable but relatively low-income (or frugal) segment of customers who are currently not being served. The potential capacity of this segment is 2000 pieces per month. Thus, the company that has captured this segment, sales in physical terms will increase by 40%. The only problem is that in this segment, consumers will buy parts at a price no higher than 8.50 USD. e. per piece, i.e. 15% lower than the market price and 1 c.u. That is, below the total cost of production at the moment. How can you sell below cost? - the head of the FEO with many years of experience at the "Old Mechanical Plant" is indignant.

Question 1: Let's say both companies can cost-free segment the market (i.e. start selling parts to the economy segment at a 15% discount without undermining their full-price sales to wealthy customers). To what extent can each company increase profits if it increases sales (in units): a) by 20%, that is, by 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?

Question	Response Logic	"Foreign Automation"	"Old Mechanical Plant"
	Profit increment (Δπ) is calculated through the marginal profit per unit of production in an additional batch (αμπ)	αμπ \u003d 8.5 - 2.5 \u003d 6 Δπ \u003d 6x1000 \u003d 6000	αμπ \u003d 8.5 - 5.5 \u003d 3 Δπ \u003d 3x1000 \u003d 3000
		αμπ \u003d 8.5 - 2.5 \u003d 6 Δπ \u003d 6x 2000 \u003d 12000	αμπ \u003d 8.5 - 5.5 \u003d 3 Δπ \u003d 3x2000 \u003d 6000

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

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

but. Calculate the BOP (break even sales volume) for each

companies, if the price is reduced to 8.50 c.u. e.

b. How much would each company's profits increase if its sales

increase by 40% (in pieces)?

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

Breakeven sales volume is more common in practice than the classic CVP analysis. In life, it is found, in textbooks - not always. This is a variant of the target profit point in dynamics: when factors change, the profit remains at the same level. The break-even volume of sales assumes that the company should receive the same profits during 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 output be increased in order to “recoup costs”?

Question	Response Logic	"Foreign Automation"	"Old Mechanical Plant"
	Calculated through the equality of marginal profits before and after changes	μπ (up to) \u003d 7.5x5000 \u003d 37500 \u003d μπ (after) = 6xQ μπ (after) = 7.5x5000 =37500	μπ (up to) \u003d 4.5x5000 \u003d 22500 \u003d μπ (after) = 3xQ
b. Output growth by 40%	Profit growth (Δπ) is calculated as the difference between marginal profits before and after changes	μπ (after) \u003d 6x7000 \u003d 42000 μπ \u003d 42000 - 37500 \u003d 4500	μπ (after) = 4.5x5000 = 22500

This is what we call cost structure competitiveness with lower average variable costs. Foreign Automation will survive the price cuts, but Old Mechanical Plant will not. Dumping (the game to lower prices) is the lot of firms with low variable costs. There are no fixed costs here.

Question 3: While the companies were thinking, their market was invaded by a strong competitor - "Avtomobilny Zavod". He easily captured half the market, trading the same parts for $9. We will have to return to the original situation and analyze the reliability of the SMZ and ZAM. Both firms lost half of their sales (in units). The results are presented in table. 2.

Table 2. The situation after the invasion of the "adversary" (in c.u.)

Indicators	"Foreign Automation"	"Old Mechanical Plant"
Sales, pcs.
Price per piece e.
Specific
variables
costs
Fixed costs (per month)
Specific
permanent	14 = 35000: 2500
costs
Total unit cost
Full costs	16.5x2500 = 41250	13.5x2500 = 33750
	22500 — 41250 = -18750	22500 — 33750 = -11250

Of course, both companies are at a loss, but it is perhaps easier to transfer them to the Staromehanicheskoy Zavod. This is what we call cost structure reliability with lower fixed costs.

Question 4: Morning. The invasion of the "Automobile Factory" turned out to be a nightmare. Given that no single company can segment the market, what advice would you give each company on this opportunity?

Answer: "Foreign Automation" should lower the price, but "Old Mechanical Plant" - no. ZAM has every chance to win price competition due to lower variable costs.

After analyzing the situation, ZAM decided to take the opportunity to sell parts to a new segment and reduced prices by 15%. Its sales rose to 7,000 units per month at a price of $8.50. e. Belatedly, SMZ was also forced to cut prices to keep 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 operates at a loss.

Question 5: Was Staromekhanichesky Zavod's decision to cut prices financially sound? For example, if SMZ decides to leave this market entirely, it can cut its fixed costs in half. For example, refuse to rent premises, land and other expenses. The remaining 50% of fixed costs is servicing a bank loan for the purchase of equipment that has a zero salvage value. Calculate and compare profits for different options.

Position after price reduction:

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

μπ (after) = 3x5000 = 15000

FC = 20000, π = -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 = 20000, π = -11000.

Therefore, price reduction is beneficial in the short run.

When leaving the market, π = -10000. Therefore, one should stay and reduce the price, although production will be unprofitable: FC = 20000, π = 15000 - 20000 = -5000.

Fortunately, the managers of the Old Machine Factory read Michael Porter's book Competitive Advantage 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 remake this part on their own so that it better suits their brand of car: 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 the cost of production at the LMP will increase, the additional costs will still be less than what drivers currently spend on reworking the part.

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

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

Answer: FC \u003d 23000, π \u003d (1b-8.5) x3500 - 23000 \u003d 3250. Yes, the manufacture of only specialized parts is profitable, since the profit will increase by 3250 - 2500 \u003d 750 c.u. e.

Question #7: What is the minimum number of custom parts that SMZ must sell per month to exceed the profits it currently earns as a generic parts manufacturer? Remember? This is what we call break-even sales volume.

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

Question No. 8: How much will Staromekhanichesky Zavod's profits increase as a manufacturer of specialized parts if it sells 3,500 pieces per month at a price of 16 USD per piece. ?

Answer: 3250 — 2500 = 750.

"Unfamiliar options for break-even analysis"

There are other options for break-even analysis. For most, they will be unexpected. We call them "three break-even points":

The first and fastest achievable - the marginal break-even point - shows at what output the price will begin to recoup the additional costs of producing one more unit of output (P > MC - in conditions of perfect competition or MR > MC - in conditions of imperfect competition). The first condition (P > MC) corresponds to the spirit of management accounting and is quite worthy to use. The second (MR > 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, such a statement of the problem is typical for Variable Costing. In the case of using Direct Costing, a similar point will be called the break-even point of direct costs (TR> DC).

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

Example. Evaluation of the work of company stores and allocation of general administrative costs

At the beginning of the year, a large Moscow company set an ambitious goal: to open 200 new branded stores across the country in a couple of years. The central office economist asked how to allocate the costs of the central office between stores? The answer, surprisingly, relies on the “three break-even points”:

1. A newly opened store must first recoup its current upkeep. This is the first and concrete task for management. It is not necessary to post costs to such stores. This is also a marginal break-even point, but not for products, but for stores. Ceteris paribus, the team that gets through the first stage faster will “win the capitalist competition.” Moral incentives have not been canceled.

2. As soon as the store contributes to the 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 for variable costs, but not for products, but for stores.

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

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

What is the operational analysis of the enterprise? What is it used for? What allows you to know?

general information

Operational analysis is aimed at identifying the dependence of the financial results of enterprises on sales volumes and costs. It uses the cost/volume/profit ratio. Thanks to this, it is possible to determine the relationship between existing costs and incomes at different volumes of production. Operational analysis aims to discover the most beneficial combination of variables. This approach is considered one of the most effective means of planning and forecasting the company's activities. As an alternative, the phrase "CVP analysis" is also often used to denote it. This is most often found in foreign literature. The analysis has the following categories:

1. Manufacturing lever.
2. Break even.
3. Stock of financial strength.
4. Marginal income.

Manufacturing Lever

This indicator gives an idea of ​​how profit will change if sales revenue changes by one percent. Production leverage is defined as the ratio of gross margin to profit. The greater the share of fixed costs, the more power it has. It should be noted that operational analysis and provide not only the calculation of coefficients, but also their correct interpretation. That is, conclusions should be drawn that will improve the situation in the future. Based on the coefficients obtained, it is necessary to develop probable scenarios for the development of the enterprise, where the final results will be calculated for a certain time period. To do this, you should look for the most favorable ratio between variable and fixed costs, production volume and product price. Also, on the basis of the coefficients, it is possible to draw a conclusion about which direction of the enterprise's activity should be expanded and which should be curtailed. Also, CVP-analysis gives an idea of ​​the state of affairs, which is why its results are often referred to as a trade secret of enterprises.

Break even

This is the revenue or quantity of production that allows for full coverage of all existing costs and when there is a zero profit. Can be found both analytically and graphically. Any change will result in a loss or profit. This is especially evident when using the graphical method. The analytical approach is more convenient in terms of finding the value and in terms of the labor involved. The break-even point can be calculated not only for the entire enterprise, but also for certain types of services and products. As soon as the actual revenue begins to exceed the threshold, the company makes a profit. The higher this indicator, the more profitable the company. And all this allows us to define operational analysis.

Margin of financial strength

This parameter indicates how much the actual revenue is above the profitability threshold. A search for the difference between the actual and the threshold can also be carried out. This allows you to talk about how much the company needs to sell products in order to maintain its work at the current level, and also find out how much its cost can be reduced if it is necessary to compete. To determine this coefficient, the following formula is used:

margin of financial strength = the company's revenue - the threshold of profitability (necessarily in monetary terms).

In a market economy, the answer to the question of how much an enterprise will prosper depends on the amount of profit it receives. Therefore, it is necessary to make reasonable and balanced strategic and tactical decisions. The margin of financial strength will allow you to find out what kind of insurance cushion the company has in case of an error.

Marginal income

Now let's look at the last category. In this case, we are interested in the gross margin ratio. It is defined as the difference between revenue and variable costs. This coefficient is needed to characterize the change in the volume of gross sales made in the current period in relation to the past. It can be used to judge how effectively the team of managers and analysts is working. Additionally, production cost factors for products sold and general and administrative costs can be calculated on the basis of marginal income.

Additional useful information

Operational analysis allows you to get a wide range of indicators, on the basis of which you can effectively influence the final performance of the company. Among them it should be noted:

1. The most profitable assortment in terms of implementation with a limited amount of resources.
2. Breakeven sales volume.
3. minimum selling price.
4. Possibility of lowering the price while increasing the volume of sales of products.
5. The ability to trace how structural shifts in the assortment affect the profit of the enterprise.
6. Solving problems by the type of purchase / production of parts and / or semi-finished products.

Also, the use of operational analysis allows you to judge the minimum values ​​of orders, which should be taken under certain circumstances.

What can you pay attention to?

For starters, we can recommend the book by I. Eremeev “Operational Analysis as a Basic Element of the CVP Model Management Process”. Here it is very well considered how this approach allows you to evaluate the performance of the organization, as well as develop recommendations for improving performance. This is not the only work that can be recommended to read. We should also mention A. Brown's book "Operational Analysis as an Approach to Pricing". Familiarization with this literature will allow you to understand, if not all, then at least the vast majority of aspects and nuances of using operational analysis. The authors pay the most important role to the indicator of marginal income. Then the break-even point value is calculated, a safety margin is searched for and calculated. The more correct the decision made by the management, the more the enterprise will receive. With the help of operational analysis, you can identify reserves, ensure their objective assessment and degree of use, get acquainted with the potential or real shortage or abundance of resources in warehouses, and so on. This approach is operational and internal in nature, thanks to which it is possible to assess the real state of affairs.

Conclusion

An integral part of operational analysis is a careful consideration and study of the cost structure of the enterprise. It is not possible to give specific recommendations here (even if we consider not the entire economy, but only one industry). To optimize the ratio, the operating conditions, the influencing factors, the long-term trend and many other variables must be taken into account. For the best result, the analysis is divided into separate stages, at each of which the specialist studies certain questions and provides answers to them. At the same time, one should observe the edge of reason and not work them out extremely scrupulously, because this will not ultimately give the desired result, but will require a lot of resources.

Budgeting and cost control: theory and practice Krasova Olga Sergeevna

2.3. CVP analysis: "costs - output - profit"

This analysis, together with data on the dynamics of costs, helps in solving many analytical problems. The subject of this analysis is the study of the dependence of profits on fixed and variable costs, sales prices, production volume and sales structure. CVP analysis is based on the calculation of marginal profit and is consistent with costing according to the "direct costing" system. In various economic publications devoted to this issue, this analysis has various names: “operational analysis”, “marginal analysis”, “dead point method”, but it can be more accurately defined as “break-even analysis”. The essence of the break-even analysis is to determine the volume of output to ensure the positive activity of the enterprise, taking into account the available reserves and costs incurred, that is, the definition of the so-called "break-even point".

The main methods for conducting CVP analysis include the equation method and the graphical method.

Equation method. The break-even point is the volume of products sold that will cover all costs, that is, there are no losses or profits. The equation method is based on the calculation of net profit, which is determined by the formula:

Where IN- the company's revenue for the period, determined by the formula: Cr*Or (CR- the selling price of a unit of production, Or– volume of sales in natural terms),

PZ- total fixed costs

PrZ - variable costs over the same period of time,

PrZ unit- variable costs per unit of output.

Therefore, the break-even point can be determined by the following formula:

Let's define the break-even point using a specific example:

The company "Phoenix" is engaged in the production of cutlets. When developing the planned costs for the month, it was found that for 1 kg of finished products, variable costs will amount to 25 rubles (PrZed). Fixed costs per month are determined in the amount of 210,000 rubles (PZ). Selling price for 1 kg. cutlets are planned in the amount of 55 rubles (Tsr). The budget for the month is planned to produce 8000 kg. product and make a profit of 40,000 rubles. It is required to conduct a break-even analysis in the production and sale of this product.

Q= 210,000/ 55–25= 7,000 kg. - with such a volume of production, the enterprise will cover all costs and reach zero profit. If the volume is less than 7000 kg, the company will suffer losses.

Considering that a profit of 40,000 rubles is planned, it is necessary to calculate what volume of production will provide the desired result:

But according to the plan, the company expects to produce 8,000 kg. products. With this amount of production, the profit will be:

Thus, we find that with the planned production volume, the enterprise will not be able to get the desired profit, and as a result, it becomes necessary to revise the planned indicators, taking into account these calculations.

In the break-even analysis, an indicator such as safety threshold. It expresses the value upon reaching which a decrease in the volume of sales proceeds may begin and losses occur, and is determined as a fraction of the expected sales volume according to the formula:

The higher the volume of production, the less painfully the enterprise will endure fluctuations in market conditions.

Returning to our example, let's calculate the security indicator for the enterprise:

We considered the calculation of the break-even point on the example of an enterprise that produces one type of product, but in most cases enterprises specialize in the production of many types of goods. In this case, the break-even analysis will be much more complicated both in form and content. The leaders of such industries face the problem of not only how to achieve the desired profit, but also to make the best choice between the types of products produced, taking into account many restrictions. Consider the analysis of the break-even production of an economic entity using a specific example:

The Phoenix enterprise expanded its production and began to produce, in addition to cutlets (A), ravioli (B) and khinkali (C). To develop a plan for the next month, it is necessary to analyze the indicators for the previous period with a view to its possible further change, taking into account the results obtained. All indicators are presented in the table.

In this case, the break-even point is calculated using the following formula:

where the average contribution is:

i= A, B, C, a P– share in the total volume of sales.

Thus the value of the average contribution per 1 kg. products with the received sales volumes will be:

Average contribution = (30*612,000+ 36*507,000+ 37*258,000)/ 612,000+ 507,000+ 258,000= 33.5%.

The production volumes that allow covering all costs and reaching the zero level for each type of product will be:

Qa \u003d 173,000 * 0.50 / 33.5 \u003d 2582 kg.

Qb \u003d 173,000 * 0.33 / 33.5 \u003d 1704 kg.

Qc \u003d 173,000 * 0.17 / 33.5 \u003d 878 kg.

Having calculated the break-even level for all types of goods, we see that it lies below the prevailing production volumes. This is a positive moment for the enterprise and, as a result, management has ample opportunity to vary the total volume of output, as well as the share of its individual types in its total output.

Graphic method. Another way to present information on costs and profits (losses) is a graphical method.

The graph is constructed by adding at each point the graphs of variable and fixed costs. Below the breakeven point is loss zone and if the values ​​of the total costs are in its area, this means that with the received volumes of output, the company cannot cover all its losses. Break even - is the intersection of total cost and revenue curves. profit zone located above the intersection point, its values ​​show that the company makes a profit and covers all costs, but with an increase in output, the divergence of the straight lines will increase.

The relationship between variable costs and revenues from the volume of production, displayed on the graph, is conditionally proportional. The study of real dependencies shows their non-linear nature and this is understandable. The area of ​​income cannot be infinite - when a certain volume of output is reached, its further increase may be unprofitable. With an increase in production, it is necessary to increase the amount of consumed resources, and since they are limited, an attempt to purchase them additionally leads to an increase in material costs.

Another feature of this method is the relationship between the concepts of "output" and "profit". In the formulation of the break-even analysis, a parallel is drawn between profit and production volume: it is assumed that the amount of profit is formed with changes in the amount of the product produced, which is erroneous. The goods produced until the moment of sale are incoming costs (subsequently it may also be part of illiquid stocks) and has nothing to do with profit. In the practice of contractual relations, the pace of implementation often does not coincide with the pace of receipt of funds. Therefore, the results of this analysis can be recognized provided that the volumes of production and sales volumes coincide with each other.

The calculation of the CVP analysis, considered up to this point, was carried out on the condition that all the variable costs of the company were known to us. When considering the types of budgets (Chapter 1, § 1.3), attention was drawn to such a fact as the uncertainty of the business environment (changes in external and internal factors). Given this point, it seems risky to conduct a break-even analysis with a possible change in variable costs for this scheme. Further analysis is required to evaluate alternative contingency plan development options. One of the ways to solve the problem of uncertainty is statistical (probabilistic) model breakeven calculation.

Assume that some uncertainty exists in the sales volume planning process. When using the statistical method, it is possible to determine the impact of this uncertainty on the amount of net (marginal) profit and the probability of maintaining breakeven.

Net income (P) is affected by any uncertainty about sales volume. In this case, the value of the expected profit (OzhP) will be equal to the product of the specific marginal profit (MP units) and the expected sales volume (OzhOr) minus fixed costs:

Therefore, the value of the expected profit also becomes uncertain.

To answer the question about the probability of maintaining breakeven, the value of the standard deviation from the expected profit is needed, which is determined by the product of the specific marginal profit and the standard deviation from the sales volume:

Let's carry out the analysis of break-even in the conditions of uncertainty on a concrete example.

In the Frost trading company, fixed costs are 1,300,000 rubles, and variable costs are 28 rubles. per unit of production. The selling price of a unit of goods is a constant value and amounts to 64 rubles, however, the annual sales volume is uncertain. The average expected sales volume is 60,000 units. The standard deviation is equal to 31038 units. it is necessary to determine the expected profit and the probability of maintaining break-even.

The expected profit will be:

The standard deviation from the expected profit will be:

To determine the probability of maintaining breakeven, it is necessary to calculate the value of the standard deviation of a random variable (F).

According to the normal distribution table, the probability of obtaining an F value equal to -0.80 is 0.2119 (1–0.7881), which means 21.19% of the probability that the company will incur losses and 78.81% of the probability of breaking even.

Using this method, when checking the impact of uncertainty on profit, both fixed and variable costs, as well as the selling price of goods, can act as random variables. However, if all these indicators become random variables at the same time, the analysis procedure becomes much more complicated and it is necessary to use in-depth statistical calculations for its implementation.

Practical tasks

Task 1.

A detailed income statement is given in terms of costs (thousand rubles):

It is also known that 11,963 units were produced at a cost of 193 rubles/unit; spent on the production of 380,000 hours with an actual payment of 11 rubles per hour. The standard price per unit of direct materials was 200 rubles, and the standard price of direct labor was 10.5 rubles per hour. Variable overhead costs were budgeted at 2 rubles per hour, 800,000 = 400,000 hours * 2 rubles.

You need to calculate flex budget variances, as well as price and quantity variances for direct materials, direct labor, and general production costs.

Solution.

1. Determine the deviations from the flexible budget for all items of expenditure.

H - unfavorable deviation,

B - favorable deviation.

The overall deviation from the flexible budget is unfavorable due to an increase in the total amount of both variable and fixed costs.

2. Determination of deviations by materials:

a) we calculate price deviations according to the formula: (actual cost - budgeted cost) * actual volume of purchases:

(193.1 rubles - 200 rubles) * 11963 units. = - 82 thousand rubles.

b) deviations in quantity are defined as the difference between the actual and budgeted volume of purchases, multiplied by the budgeted cost of materials:

(11963 units - 10000 units) * 200 rubles = 392 rubles.

The final deviation for materials is: 392 + (- 82) = 310 thousand rubles, which is an unfavorable value.

3. Labor deviations:

a) price variances are determined similarly to direct cost variances:

(11 rubles / hour - 10.5 rubles / hour) * 380,000 hours \u003d 190 thousand rubles.

b) efficiency deviation:

(380,000 hours - 400,000 hours) * 10.5 rubles. = -210 thousand rubles.

The favorable deviation in labor costs eventually amounted to 20 thousand rubles.

4. Deviations for general production costs:

The first step is to calculate the standard cost allocation rate.

For fixed expenses: 1,200 thousand rubles / 400,000 hours \u003d 3 rubles.

For variable expenses: 800 thousand rubles. / 400,000 hours = 2 rubles

- for fixed costs: 380,000 * 3 \u003d 1140 thousand rubles.

- for variable expenses: 380,000 * 2 = 760 thousand rubles.

According to these results, the deviation of the actual costs will be:

- for permanent: 1230 thousand rubles. - 1140 thousand rubles. = 90 thousand rubles.

- for variables: 900 thousand rubles. - 760 thousand rubles. = 140 thousand rubles.

These deviations are formed under the influence of the following factors:

1) due to deviations in the volume of production:

- for fixed costs: (400,000–380,000) * 3 \u003d 60 thousand rubles.

- for variable costs: (400,000–380,000) * 2 = 40 thousand rubles.

2) due to deviations of actual expenses from budget ones:

- for fixed costs: 1230 thousand rubles. - 1200 thousand rubles. = 30 thousand rubles.

- for variable costs: 900 thousand rubles. - 800 thousand rubles. = 100 thousand rubles.

Task 2.

The company produces two types of products (A and B) and is characterized by the following data:

It is conditionally assumed that up to the critical point - X units of production A and 2X units of production B.

The administration of the enterprise decides to change the structure of products sold as follows:

It is necessary to determine the marginal income for each type of product and from the total volume of products sold. Determine the amount of net profit before and after the change in product range. Calculate critical points (break-even points) before and after changing the product mix. To analyze, using the equation method, the impact of changes in the structure of products on the value of marginal income.

Solution.

Marginal income is defined as the difference between revenue and its partial cost:

We calculate the marginal income for each type of product before and after changing the structure of goods sold as follows:

Option 1.

Option 2.

Based on the calculations obtained, we determine the amount of net profit, which is equal to the difference between marginal profit and the amount of fixed costs:

Option 1.

Option 2.

2. Using the equation method, we determine the impact of changes in the structure of sold products on the marginal profit.

Before the assortment change, there were 2 units of product B for 1 unit of product A.

We calculate the critical points (break-even points) of the sales volume for each type and for the total volume.

2000X + (4000 * 2X) - 1200X - (2900 * 2X) - 100,000 \u003d 0

10,000X - 7000X - 100,000 = 0

3000X = 100,000

X \u003d 33 units. - product A.

33*2 = 66 units - product B.

For the total volume - 33 + 66 = 99 units.

Thus, the value of the break-even point for the total volume is 99 units, of which 33 units. product A and 66 units. goods B.

After changing the structure of sold products, 1 unit of product B began to account for 1.14 units of product A, that is, the share of product A increased in the total volume. Let us determine the value of the critical point in the modified version:

(2000 * 1.14X) + 4000X - (1200 * 1.14X) - 2900X - 100,000 \u003d 0

6280X - 4268X - 100,000 = 0

2012X = 100,000

X = 49.70 units - product B.

49.70 * 1.14 \u003d 56.67 units. - Product A.

For the total volume - 49.70 + 56.67 = 106.37 units.

As a result of the calculations, we got that the value of the break-even point was 106.37 units, of which 56.67 units. for product A and 49.70 units. for product B.

Compared to the original plan, the break-even point has increased by about 10 units.

3. When comparing the structure of products, it becomes obvious that the change led to a decrease in marginal profit and, as a result, the amount of net profit.

Despite the decrease in total variable costs and the unchanged volume of sales, revenue decreased by 60,000 rubles.

By changing the assortment with an increase in the production of product A, the enterprise reduced its profitability and increased the value of the critical point, which means an increase in the share of risk in further production.

If we carry out further analysis and assume that management decides to change the structure of manufactured products relative to the original version in the direction of increasing the production of product B (suppose product A - 30pcs, and B - 120pcs, with the volume unchanged), we get the following picture:

Option 3.

That is, the share of products with high marginal income increases and, as a result, net profit increases.

At the same time, if we calculate the value of the break-even point, we will get a significant decrease in its value compared to the first calculation option and, it should be specially noted, with the second option too:

Head. – product A, 4Head. - item B.

2000X + (4000*4X) - 1200X - (2900*4X) - 100,000 = 0

18,000X - 12800X - 100,000 = 0

5200X = 100,000

X = 19.23 units - Product A.

19.23 * 4 \u003d 79.9 units. - Product B.

The total value of the break-even point = 96.13 units.

Based on the analysis, certain conclusions can be drawn. When changing the assortment in favor of product A, the company reduced profitability on savings in variable costs, thereby increasing the break-even point. This indicates problems with the enterprise with the availability of additional resources or their likely high price. Product B is more resource-intensive, but at the same time it brings more additional income. Management needs to revise the planned indicators, taking into account the results of the analysis, and possibly develop a different strategy for the development of the enterprise.

Task 3.

A trading company sells a permanent range of products. In a simplified form, the assortment of goods consists of bolts, nuts and washers of a certain size. Acceptable sales range (scale base) - from 2 to 6 tons.

The company's turnover is subject to seasonal fluctuations.

Initial information about the costs and income of the organization in the off-season period is presented in the table:

2) evaluate the contribution of each type of goods to the formation of the total profit of the enterprise;

A sharp increase in sales is expected in the coming month. Seasonal demand will increase sales to 6.5 tons, which will require the lease of additional storage space. Fixed costs (rent) will increase by 1000 rubles, variable costs for each item - by 5%. The price of washers will increase by 10% due to its partial sale in packaged form through stores. Structural changes will take place in the direction of a more profitable type of product, as a result of which the range of products sold will look like this: bolts - 4000 kg, nuts - 1750 kg, washers - 750 kg.

2) determine the profit of the enterprise in the new conditions.

Solution.

1. According to the conditions of the problem, first we calculate the profit of the enterprise in the off-season period:

2. The next task is to determine the "contribution" of each type of goods in the formation of the total profit. To do this, the profitability of each type of product is determined at full cost.

Distribution of fixed costs for each type of goods, taking into account their share in the total sales volume:

Bolts - 6000 * 0.7 / 3500 \u003d 1.2

Nuts - 6000 * 0.2 / 1000 \u003d 1.2

Washers - 6000 * 0.1 / 500 = 1.2

According to the results of the calculations, nuts are the most cost-effective product.

3. Using the equation method, we determine the break-even point for each type of product.

According to the sales volumes, 1 washer has 2 nuts and 7 bolts, therefore: W - X, D - 2X, B - 7X.

(9.5x7X) + (13x2X) + 14X - (7.5x7X) - (9.5x2X) - 12X - 6000 = 0

106.5X - 83.5X - 6000 = 0

X = 261 kg. - washers.

Nuts - 261x2 = 522 kg.

Bolts - 261x7 = 1827 kg.

The total value of the break-even point is: 261+522+1827 = 2610 kg.

4. According to the changes in the seasonal period, we will compile a table of final indicators:

Let's determine the profit of the enterprise under the changed conditions:

When calculating the break-even point in the seasonal period, the ratio in the sale of goods will be: per 1 kg. washers: 2.33 kg. nuts, 5.33 kg. bolts.

The equation will look like this:

(9.5 x 5.33X) + (13 x 2.33X) + 15.4X - (7.88 x 5.33X) - (9.98 x 2.33X) - 12.6X - 7000 \u003d 0

96.325X - 77.8538X - 7000 = 0

18.4712X = 7000

X = 379 kg. - washers

Nuts - 379 x 2.33 = 883 kg.

Bolts - 379 x 5.33 = 2020 kg.

The total break-even point is 3282 kg.

Having obtained the value of the critical point of the total sales volume, we calculate the value of the break-even threshold in conditions of increased seasonal demand:

PB \u003d (Or - Q) / Or x 100%

PB \u003d (6500–3282) / 6500 x 100% \u003d 49.5%.

This text is an introductory piece. From the book Finance and Credit author Shevchuk Denis Alexandrovich

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Analysis "Cost - Volume - Profit" - "Costs - Volume - Profit" (CVP analysis)

One of the fairly simple and at the same time effective methods of analysis for the purpose of operational and strategic planning and management of the financial and economic activities of an enterprise is operational analysis, also called cost-volume-profit analysis, or CVP analysis. This method allows you to identify the dependence of financial performance on changes in costs, prices, volumes. "CVP"-analysis allows you to identify the optimal proportions between fixed and variable costs, the proportion between price and sales volume, as well as to minimize business risk.

The main role in choosing an enterprise behavior strategy belongs to the indicator of marginal income.

CVP-analysis - analysis of cost behavior, which is based on the relationship of costs, revenue (income), production volume and profit. It is a management planning and control tool, i.e. these relationships form the basic model of financial activity and allow the analysis results to be used for short-term planning and evaluation of alternative solutions.

Its main tasks are:

• 1. calculation of the volume of sales, which provides full coverage of costs - the break-even point (profitability threshold);
• 2. Calculation of the volume of sales, providing, ceteris paribus, obtaining the required amount of profit;
• 3. analytical assessment of the volume of sales, in which the company can be competitive (margin of financial strength);
• 4. determining the price of products, allowing to ensure demand and profit at the planned level;
• 5. selection of the most efficient production technologies;
• 6. implementation of the adoption of the optimal production plan.

CVP Analysis Assumptions:

• - costs should reasonably be divided into fixed and variable parts;
• - fixed costs remain unchanged depending on the production volumes within the studied production range;
• - Variable costs within the specified limits are directly proportional to the volume of production. Relevant levels - levels of business activity, i.e. the volumes of production with which the organization is likely to expect to work. This is usually the normal production capacity;
• - there are constant prices for sold products - on the one hand, and prices for consumed production resources - on the other hand;
• - the range of products is constant;
• - the volume of production is approximately equal to the volume of sales;
• - received revenue is directly proportional to the volume of production;
• - the efficiency of the enterprise remains unchanged.

The main indicators of the analysis "costs - volume - profit":

• 1. Revenue = costs (cost) + Profit;
• 2. Revenue = fixed costs + variable costs + profit;
• 3. Revenue = fixed costs + variable costs per unit * quantity + profit.

CVP analysis is an enterprise management system that integrates various subsystems and management methods and subordinates them to the achievement of a single goal. Analysis is a link between various management functions, it is a tool that provides a scientific approach to production management.

The assignment of CVP analysis to management functions is due to a number of obligations:

• - the analysis is carried out at all levels of management and in all divisions of an economic entity;
• - the analysis is based on a single methodological basis, which makes it possible to develop common approaches to organizing and conducting analysis in various industries, regions and other structural communities of economic units;
• - analysis of financial and economic activity is a necessary element in the system of enterprise management functions, since without it many other functions, primarily related to managerial decision-making, cannot be implemented. The cost structure affects the financial condition of an enterprise and can increase operational and financial risks.

Example. The enterprise (table 6) has information on two periods of the enterprise's operation - for January and February. Revenue, total costs, profit did not change over the period. But the cost structure of the enterprise has changed - constants have increased and variables have decreased. How will this affect the economic condition of the enterprise?

Table 6

Let's calculate all indicators of CVP-analysis (Table 7).

Reducing variable costs by 10% with a fixed amount of total costs led in this example to an increase in the break-even level by 3.5%. Now the company will need to produce products for a large amount to cover all costs. An increase in the break-even level (profitability threshold) is considered a negative factor for the dynamics of development. Accordingly, the margin of financial strength is reduced by 15%, which also negatively affects the activity.

The same change gives an increase in the level of operating leverage by 17.8%, that is, a significant increase in production risk.

In the new version, the profit received by the enterprise becomes more sensitive to changes in production and sales volumes.

With an increase in the share of fixed costs, even with a decrease in variable costs, the control of sales volumes becomes very significant: a possible decrease in sales can lead to a greater decrease in profits than in the first option, and vice versa.

An increase in the share of fixed costs, even with a decrease in variable costs per unit of production, always leads to the need to choose a strategy aimed at increasing sales volumes.

Table 7

Thus, all negative changes, i.e. the increase in the profitability threshold, the reduction in the margin of financial safety and the increase in operating leverage occurred due to an increase in fixed costs in the cost structure (but the total cost did not change). This problem seems to be very important for cost management in the enterprise, because without a special analysis, managers do not see these negative changes.

What are the goals of introducing CVP-analysis in the enterprise?

• 1) it allows you to choose the best of the alternative options for the production and sale of products without a detailed calculation of the cost (without distributing fixed costs);
• 2) with an uncertain market situation, several scenarios can be calculated quite quickly: - optimistic, pessimistic, more realistic (based on the principle of what will happen if ...);
• 3) it is possible to determine the volume of sales required for the break-even operation of the enterprise when one of the parameters is changed;
• 4) allows you to build relations between the production units of the enterprise in a different way;
• 5) allows for multi-product production and market pricing to determine the most profitable goods (services) and, accordingly, make decisions on the assortment shift of production and sales of products.
• 6) makes it possible to apply the "Rule of 50%". It is as follows:

all types of products manufactured by the enterprise are divided into two groups depending on the share of variable costs in the total amount of sales proceeds.

• more than 50%, then for these types of products it is more profitable to work on cost reduction in order to increase the share of marginal profit.
• if the share of variable costs less than 50%, then it is better for the enterprise to focus on increase in sales volumes, since this will give a greater increase in marginal profit

Production costs are the starting point for setting the price for the products produced by the enterprise. All the necessary information about the costs of production and sales of products is fully available at the enterprise, so cost management is becoming one of the most accessible strategic tools when making decisions in the field of enterprise pricing policy.

The change in the volume of production has a different impact on the amount of total costs. Since part of the costs remains relatively unchanged (fixed costs), and the other part changes proportionally with the change in production volume (variable costs).

Establishing the relationship between sales volume, fixed, variable costs and profit is carried out using CVP-analysis (from the English. Costs - Volume - Profit) - analysis of the ratio "costs - volume - profit". This method in international practice is called marginal income due to the indicator of marginal income, which is the main one within the framework of this approach.

Marginal income (coverage amount) is the difference between sales revenue and cost calculated at variable costs. It is determined both for a unit of production and for the entire volume of production (sales). Calculated per unit, this indicator is called specific income or marginal income rate.

The advantage of marginal analysis is that it allows you to compare different options for product prices and choose those that bring the maximum profit, as well as to find the most favorable relationship between variable, fixed costs, price and volume of production.

The main prerequisite for using the analytical capabilities of marginal income is the division of costs with a high degree of accuracy into fixed and variable.

When using this method, the following assumptions on which the CVP analysis is based must be taken into account:

total costs and sales revenue are linearly dependent on the level of business activity (production);

fixed costs do not change with changes in the volume of production;

variable costs are directly proportional to the volume of production;

during the period under review, variable costs per unit of output (specific variable costs) are fixed;

the selling price of a unit of production does not change;

prices for materials and services used in production do not change;

labor productivity does not change;

the volume of production is the only factor affecting changes in the costs and income of the enterprise;

the volume of sales is equal to the volume of production (i.e., during the period under review, there are no changes in inventory levels);

the product range of an enterprise that produces a number of different goods or provides several types of services is unchanged. The variable costs and unit selling price used in the analysis are a weighted average of the costs of the various units of production and the prices of the related goods and services.

CVP analysis is also often referred to as determining the break-even point. It helps to determine the amount of sales needed to cover costs and achieve the desired profit. CVP analysis also allows you to determine how profit will be affected by changes in sales price, variable and fixed costs, and income.

Determining the breakeven point is one of the most important CVP analysis procedures. Finding it is the initial stage of the analysis and serves to make a number of management decisions, incl. - in the field of pricing policy. The break-even point corresponds to such a sales volume at which the costs are equal to the proceeds from the sale of all products, i.e. there is no profit or loss.

To calculate it, you can use three methods: equations, marginal profit and graphical representation.

Equation method based on the calculation of profit (meaning the economic concept of profit).

The following ratio of revenue, costs and profit is taken as the initial equation for analysis:

Revenue - variable costs - fixed costs = profit.

The task is to determine the critical volume of output that is necessary to achieve the "threshold" of profit at a given price, as well as the volume of output, which corresponds to a given (target) amount of profit.

The "threshold" of profit is reached when the total costs are equal to the gross revenue, i.e.:

FC+VC×q=p×q, (1)

Whence the critical volume at which the “threshold” of profit is reached (profit is zero) is equal to:

q crit = . (2)

The volume of output, which corresponds to a given amount of profit, is determined on the basis of the fact that:

FC+VC×q+δ = pq, whence (3)

where q, q crit - the volume of output;

p is the given price;

FC - fixed costs;

VC - variable costs;

δ is a given amount of profit.

Based on the above formulas, it is possible to derive relationships between price changes, changes in sales volumes and profit mass:

δ = (p-Δp)×(q-Δq) - VC×(q-Δq) – FC, (5)

where Δp is the price change;

Δq is the change in sales volume.

Having equalized the equations, we obtain the dependences of the change in price and sales volume, which make it possible to ensure the preservation of the existing profit:

Δq = (p - VC) / (p - Δp - VC); (6)

Δp = (p - VC) - [(p - VC) / Δq]. (7)

Thus, not every price reduction brings an increase in profits due to an increase in sales volume. In order to maintain the existing profit when the price changes, it is necessary to increase the volume of sales accordingly at a rate that will depend on the ratio of variable and fixed costs. Moreover, the greater the share of variable costs in the cost, the correspondingly greater the need for an increase in sales to maintain the existing profit while reducing the price. Conversely, when deciding to increase sales, you can calculate how much you can reduce the price to maintain the existing profit margin.

The relationship "cost-volume-profit" can be expressed graphically. Break-even charts show the volume of total fixed costs, total variable costs, total costs (the sum of total fixed and total variable costs), and total revenue for all levels of activity (sales volumes) of the enterprise at a given sales price. If unit price, cost, efficiency, or other conditions change, then the model must be revised.

Figure 1.1 - Analysis of the behavior of costs, profits and sales volume

On the chart, the break-even point is defined as the point of intersection of direct total costs and direct sales revenue.

For management, the break-even point is an important benchmark in the analysis, as it shows the level of sales below which the company will incur losses. For this reason, it can be considered as the minimum acceptable level of sales of products or services.

When justifying pricing policy, the break-even method can be successfully used to determine prices based on the amount marginal profit (coverage amount). Since fixed costs within the planning period are not decisive, they do not affect actual pricing decisions. In doing so, the following steps are distinguished:

a possible price is set;

the amount of coverage per unit of production is determined;

the critical volume of production is determined by dividing fixed costs by the amount of coverage;

the possibility of achieving it at a given price is estimated.

If the actual volume exceeds the critical value, the product makes a profit, if not, then there will be losses.

The search for a price based on this method begins with an estimate of the expected sales volume at each possible price. Of all the price-sales combinations, the one that provides the greatest amount of coverage is selected.

The coverage amount is a good means of estimating the relationship between output, revenue and price, which is necessary to establish a “threshold” of profit in the event of a price change. For this, the following indicators are used: DR and TR critical. :

where DR is the share of the coverage amount in the price.

The critical amount of revenue (TR critical), which corresponds to the "threshold" of profit (profit at the previous price):

TR critical = . (nine)

Determining prices based on the calculation of marginal income has a number of advantages, because. the method is based on more reliable information about direct (variable) costs and contributes to the determination of the optimal price in a competitive environment. Variable costs within the framework of this method are considered as the lower limit of the price, or, otherwise, as the minimum price, below which the production of products is impossible.

Thus, the division of enterprise costs into fixed and variable provides opportunities for financial analysis of its activities. Information about costs (fixed and variable) allows us to assess their impact on the final financial results and, on this basis, choose the alternative that provides the maximum possible profit in this situation, as well as develop a set of measures aimed at further increasing profits from product sales.

The use of the CVP-analysis methodology to justify pricing decisions has shown its practical significance and effectiveness compared to traditional management methods. The implementation of marginal income in the enterprise requires close cooperation between sales or marketing specialists, who provide information about the change in the state of demand in response to price changes, and analytical department specialists, who have information about the costs of production and sale of products. As a result of such joint work, the probable revenue, costs are estimated and the expected financial result of the activity is revealed, showing the effectiveness or inefficiency of decision-making on prices.