Determining the optimal output volume. How to calculate the optimal production volume

The optimal volume of production is understood as such a volume that ensures the fulfillment of concluded contracts and obligations for the production of products (performance of work) in deadlines with minimum costs and maximum possible efficiency.

The most common methods for determining optimal production volume include:

method of comparison of gross indicators;

method of comparison of limit indicators.

The following assumptions apply when using these methods:

the enterprise produces and sells only one product;

the goal of the enterprise is to maximize profits during the period under review;

only price and production volume are optimized (it is assumed that all other parameters of the enterprise’s activities remain unchanged);

the volume of production in the period under review is equal to the volume of sales.

The above assumptions may seem quite strict, but if we take into account that it is the price of the product and the volume of its production and sales that, as a rule, have the greatest impact on the economy of the enterprise, the use of these methods significantly increases the likelihood that the right decisions will be made .

Let us consider the essence of the proposed methods using the example of a hypothetical enterprise operating in a free competition market (initial data are given in Table 1).

Table 1. Product sales volume and production costs.

Sales volume, thousand pcs.	Fixed costs, thousand rubles.	Variable costs, thousand rubles.	Gross costs, thousand rubles.
	1200		1200
	1200		1400
	1200		1560
	1200		1690
	1200		1810
	1200		1960
	1200		2160
	1200	1220	2420
	1200	1550	2750
	1200	1980	3180
	1200	2560	3760

Gross Compilation Method involves calculating the profit of the enterprise at various volumes production and sales of products. The calculation sequence is as follows:

the value of the production volume at which zero profit is achieved is determined;

the volume of production with maximum profit is determined (Table 2).

Table 2. Sales volume of products with maximum profit.

Sales volume, thousand pcs.	price, rub.	Gross revenue, thousand rubles.	Gross costs, thousand rubles.	Profit, thousand rubles
			1200	1200
			1400
			1560
		1440	1690
		1920	1810
		2400	1960
		2880	2160
		3360	2420
		3840	2750	1090
		4320	3180	1140
		4800	3760	1040

In our example, zero profit is achieved with a production and sales volume in the range of 30-40 thousand units. products, which corresponds to the value of gross revenue and costs, respectively, in the intervals of 1440-1920 and 1690-1810 thousand rubles.

With an increase in production volumes, gross revenue begins to exceed costs and profit appears, the maximum value of which is 1140 thousand rubles. is achieved with a production and sales volume of 90 thousand units. This is what is in in this case optimal production volume.

The method of comparing limit indicators makes it possible to establish to what extent it is profitable to increase production and sales. It is based on a comparison of marginal cost and marginal revenue. If the marginal revenue per unit of output exceeds the marginal cost per unit of output, then increasing production and sales will be profitable.

Let us illustrate this based on the data given in table. 3.

Table 3. Calculation of the optimal volume of product sales using the method of comparing limit indicators.

Sales volume, thousand pcs.	Marginal income, thousand rubles.	Marginal costs, thousand rubles.	Gross profit, thousand rubles.

In this case, the marginal revenue per unit of output is essentially market price unit of product equal to 48 rubles, and marginal costs are calculated as the difference between subsequent total costs and previous ones, divided by production volume.

Marginal profit is calculated as the difference between marginal revenue and marginal cost.

From the data in the table it is clear that as long as marginal revenue exceeds marginal costs, increasing production volumes is effective, i.e. expansion of production to 90 thousand units. cost-effective. With a further increase in production volume, the amount of additional costs will exceed the amount of additional income per unit of production, which will lead to a decrease in gross profit.

A sign of production optimization is the achievement of the most profitable output at the lowest possible costs. The result of an optimal production process depends on the influence of external and internal factors.

The optimal volume of output is achieved as a result of the interconnection of technological and management problems being solved, based on analysis and a mathematical approach.

Ensuring the manufacturer’s ultimate goal – making a profit – requires analysis:

The consumer market in terms of product categories and characteristics.
Composition of fixed and variable costs.
The impact of changes in the cost structure on optimal production output.
The minimum acceptable product price at the break-even point.
Determination of relationships between factors influencing output volume.

Research is aimed at a specific type of product unit, which allows you to obtain accurate analysis data.

Balance of consumer demand and supply

The dynamics of changes in market demand for products affects the company's product release strategy. decreases:

Enterprises independently determine the composition of costs and establish the structure in their accounting policies. For operational analysis, costs are calculated by item.

The impact of cost composition on the pricing mechanism

With a constant selling price of products, a decrease in costs per unit of goods leads to an increase in part of the profit. One form of optimization is changing the balance between fixed and variable costs. An increase in production volume affects an increase in variable costs, permanent species costs remain unchanged. By adjusting the quantitative composition of shares, an optimal balance of costs is achieved.

The structure of fixed and variable costs differs when calculating parameters:

Planned output, in which the value of each component is clearly defined. Actual data is used for calculations.
Additional release, the basis for which is market need.

With additional production, a reduction in product prices is achieved. The share of fixed costs in the additional batch of products is absent (covered by planned production) and the resulting difference goes into the profit category. As a result, a reserve of the minimum acceptable price is ensured, which allows for competitive discounts and seasonal sales of goods.

Determination of break-even production level

The optimal level of production volume is located within the boundaries of the minimum acceptable and maximum possible output levels. To plan the quantity of production, it is important to determine the minimum level - the lower break-even limit.

Calculation of the break-even point (TB) is carried out by attributing indicators of variables, fixed costs to the volume of output (quantity of goods) and the price of a unit of production. The critical point is calculated graphically.

Determining the critical release level allows you to:

Maintain the minimum permissible output during periods unfavorable for product sales. The need may arise in conditions of seasonality or high competitive market supply.
Reveal weak spots And possible problems quantitative output of products. The indicator makes it possible to vary the parameters of costs and volume.
Eliminate products with unprofitable performance from production.

An accurate indicator and the use of calculated data can only be used if the data is unchanged in a certain unit of time. If the structure of goods produced, the selling price or the amount of costs changes, a new calculation will need to be made.

The challenge in the production process is to get the most out of capacity and human resources. On technical economic indicators influenced by external and internal factors. Non-production causes arise when:

Changes in the raw materials and consumer markets;
increasing transport costs.

Internal factors are based on:

The technical level of equipment of the enterprise;
ensuring warehousing materials and finished products;
management system and labor organization.

To determine the optimal level of production, it is not enough to determine the total break-even volume of revenue and costs. In practice, an important indicator is the optimal batch size. The following costs are taken into account:

Required for the implementation of the order;
necessary for the safety of stocks and products.

For example, you can determine the impact of capacity utilization on variable costs. The value of the share of costs decreases in total value with fuller utilization of capacity and increases with a decrease in productivity, which, in turn, affects. In turn, an increase in output will require the use of large areas for storing inventories.

Searching for relationships between indicators allows us to develop the degree of influence on optimal output. A common option for searching for the interaction of factors is a combination of labor automation and capital investment. The selection of options is carried out for similar units of goods. Comparative analysis carried out in quantitative or cost assessment.

To make things easier to understand, analysts use materials in the form of tables or diagrams. Most visual way is achieved using graphs and curved lines - isoquants. Graphical method allows you to obtain information about possible substitution when the original data changes.

The practical benefit of obtaining information on substitution allows us to consider, for example, the possibility of increasing automation and mechanization of labor in comparison with the use of costs handmade. In a common version, the method is used when selecting raw materials or materials as a share of variable costs in the cost of finished products.

Basis for determining the optimal level of production output

The enterprise strategy to achieve the optimal level of production comes down to the relationship of factors influencing the process. Using aggregated assessment and analysis data, the following is achieved:

Determining the volume of output at which financial stability. The indicator is based on calculating the break-even point.
Obtaining data on the feasibility of releasing a number of types of products. The assortment policy is determined based on the ratio of average costs to unit production costs.
Search internal and external factors influencing pricing.
Determination of business risk as a result of studying market demand.

A combination of factors allows us to obtain the optimal level of production of assortment units and the enterprise as a whole.

The value of the optimal production level determines the profit of the enterprise. Obtaining data on optimization is achieved by calculation, in which indicators of revenue volume, costs, demand, and other interrelated parameters are compared. By analyzing external and internal influencing factors, maximum output volumes are achieved at minimum costs.

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ACADEMY OF LABOR AND SOCIAL RELATIONS

ALTAI INSTITUTE OF LABOR AND LAW

FACULTY OF FINANCIAL AND ECONOMIC

Course work

in the discipline: "Company Economics"

on the topic: "Determination of the optimal volume of production at an enterprise"

Completed by: 2nd year student, 472 groups

Ryabtsev E.K.

Scientific adviser:

academic degree, title

Shutova N.A.

"_____"______________200_g.

Grade_________________

Barnaul 2008

Introduction

Conclusion

Bibliography

Introduction

For successful entrepreneurial activity of enterprises in market conditions, it is necessary to establish the patterns of supply and demand, as well as determine the target setting: what to produce, in what quantity, at what costs and at what prices.

Relevance of the topic course work thing is great importance in product output management, there is an assessment of actual output and sales within production capacity, i.e. within the boundaries of "minimum - maximum" production volume. Comparison with the minimum, break-even volume allows you to assess the degree or zone of “safety” of the organization and, if the “safety” value is negative, remove certain types of products from production, change production conditions, and thereby reduce costs or stop production.

Comparing the achieved output volume with the maximum volume determined by the production potential of the enterprise allows us to assess the possibilities of profit growth with an increase in production volumes if demand or the organization’s market share increases.

In economic management important has a long-term analysis that allows you to justify and optimize the plan for production and sales of products. A long-term analysis of product output is carried out in parallel with an analysis of market conditions and the enterprise's needs for production resources.

Break-even analysis, or cost-volume-profit analysis (marginal analysis, CVP analysis), is one of the most effective means of planning and forecasting the activities of an enterprise. It allows the management of the enterprise to identify the optimal proportions between variable and fixed costs, between price and sales volume, to identify the most profitable types of products, which will optimize the volume of production and sales, and minimize business risk.

The purpose of the course work is to determine the optimal production volume based on the results of a break-even analysis of a commercial organization.

To achieve this goal, it is necessary to solve the following tasks:

explore the role and classification of costs for the purpose of determining the optimal volume of production and sales;

generalize the methodology for calculating break-even sales and safety zones as a basis for making management decisions in terms of optimizing production volume;

carry out calculations of the break-even volume of production and sales of products at a specific commercial enterprise;

Based on the information received, develop management decisions to optimize production volume and maximize profits.

The object of the study is the production activities of Uyut LLC, which produces furniture. The subject of study is the decision-making process to determine the optimal production volume in an organization for 2004-2006.

The course work consists of an introduction, two chapters, a conclusion and a list of references. The introduction substantiates the relevance of the topic, sets the goal and outlines the tasks for its successful implementation.

The first chapter of the work examines the theoretical aspects of the methodology for determining the optimal volume of production and sales, in particular, it examines the role and classification of costs for the purpose of determining the optimal volume of production and sales, and also discusses methods for calculating the break-even volume of production. In the second chapter of the work, a brief description of the organization under study is given and the break-even volume of production is calculated. In the third chapter of the work, management decisions are developed to optimize production volume based on the results of a break-even analysis. In conclusion, a brief summary of the work is provided.

The work will consider methods for analyzing break-even by such authors as G.V. Savitskaya, N.P. Lyubushina, S.A. Boronenkova, M.A. Vakhrushina, V.P. Gruzinova T. P. Karpovoy et al.

1. Theoretical aspects of the methodology for determining the optimal production volume

1.1 The role and classification of costs for the purpose of determining the optimal volume of production and sales

One of the main goals of an enterprise conducting its economic activities in market conditions is to obtain the maximum possible profit. The ability to achieve this strategic goal is limited by production and sales costs, as well as market demand for the enterprise's products. Costs are thus a factor that determines the quantity supplied and profit margins. Therefore, making management decisions about optimal volume production is impossible without analyzing the current costs of production and sales of products and the costs that will arise during the implementation of newly developed projects and business plans.

As noted by A.D. Sheremet, effective management costs at different levels is ensured by the use of methodological unity, which presupposes uniform requirements for information support, planning, accounting, cost analysis in the enterprise. This is provided by a management accounting system that connects all these elements in a single methodological and methodological space and acts as a comprehensive, systematic study of production costs.

All costs that form the cost of products (works, services) are not the same not only in their composition, but also in their significance in the manufacture of the product, performance of work and services. Some costs are directly related to the manufacture and release of products (costs of raw materials, materials, wages of workers, etc.), others - to the management and maintenance of production (costs of maintaining the management apparatus, providing the production process with the necessary resources, maintaining fixed assets in working condition, etc.), and still others, not being directly related to production, are still included in production costs according to current legislation (contributions for the reproduction of the mineral resource base, social needs of the population, etc.). In addition, part of the costs is directly included in the cost of specific types finished products, and the other part, in connection with the production of several types of products - indirectly.

According to G.V. Savitskaya, marginal analysis plays a large role in justifying management decisions and business, the methodology of which is based on studying the relationship between three groups of the most important economic indicators: costs, production volume and profit and predicting the value of each of these indicators at a given value of the others. This method of management calculations is also called break-even analysis or calculation assistance. Developed in 1930 by American engineer Walter Rautenstrauch as a planning method known as the critical output schedule.

The methodology is based on the division of production and sales costs depending on changes in production volume into variable and constant and the use of the category of marginal income.

Variable costs are costs whose total amount changes in direct proportion to changes in production volume. These costs per unit of output decrease (increase) as production volume increases (decreases). They characterize the dynamics of costs depending on fluctuations in production volume and are used to draw up estimates for the coming period.

Both production and non-production costs can be variable. Production costs include direct material costs, direct labor costs, costs of auxiliary materials and purchased semi-finished products.

Fixed costs are part of the costs for a certain period, the total amount of which does not change when production volume changes. An example here is the cost of raw materials and fixed materials as variable costs and depreciation charges as fixed costs. There is also a group of cost items that do not change in direct proportion to changes in production volume. These costs are usually called conditionally constant (or conditionally variable); for ease of calculation, they are often combined with fixed or variable costs, respectively.

Unlike variables, fixed costs are not so easy to reduce in the event of a decline in production and a decrease in revenue from product sales. And during these periods, the enterprise must accrue depreciation in the same amounts (if the equipment is not sold), pay interest on previously received loans, and pay wages, since the mass dismissal of an excess number of workers is a very difficult matter.

It is more profitable for an enterprise if there is a smaller amount per unit of production fixed costs, which is possible when the maximum volume of production and sales of products for which these costs were determined is reached. If, during a decline in production, variable costs are reduced proportionally, then the amount of fixed costs does not change, which leads to an increase in production costs and a decrease in the amount of profit. Therefore, writing off fixed costs in foreign practice is considered as one of the areas of cost distribution.

There are costs that certain situation can be constant, and in another - variable. The answer to the question of whether these costs should be considered fixed or variable depends on two factors: the length of the period considered for making the decision and divisibility production factors. It is enough to give an example of labor costs: with piecework payment these are variable costs, with a fixed salary of workers these are constant costs.

Over a long period of time, all costs become variable. Fixed costs may arise as a result of legal or contractual relationships (leasing agreements, employment agreements, etc.).

Therefore, it is useless to divide expenses into fixed and variable according to their essence. Western management accounting argues that the nature of behavior depends on the relevant production situation in which decisions are made. Another reason for the occurrence of fixed costs is the insufficient divisibility of production factors. The consequence is that many costs do not increase gradually with increasing load, but in an abrupt manner. These costs are constant for a certain capacity utilization interval, then they increase sharply and again remain unchanged over a certain interval. The shorter the loading intervals become, the closer the costs are to variable in nature.

Fixed costs arising from the indivisibility of production factors consist of “idle” costs not used in the production process and useful costs. The problem of dividing fixed costs into useful and useless is especially acute when production is equipped with special automatic machines. When production volumes decrease, interest payments on invested capital and depreciation continue to be charged in the same amounts. Thus, an important provision of the theory of cost classification is the conditionality of this classification. There are no costs that can essentially be classified as either fixed or variable. The division of costs into fixed and variable is largely determined by the specific situation or decision-making problem.

As a result, the total amount of costs of the main activity of the enterprise is divided into two sets: fixed and variable costs, depending on their behavior in relation to the volume of production or sales in previous reporting periods.

Thus, the methodology for determining the optimal volume of production and sales is based on dividing all costs into constant and variable.

Variables are costs, the size of which depends on the level (volume) of production activity, constants are costs, the value of which does not depend on changes in the volume of output. In practice, in addition to those considered, costs are divided into conditionally constant and conditionally variable.

1.2 Calculation of break-even sales and safety zone as a basis for making management decisions in terms of optimizing production volume

According to V.P. Gruzinova, even having a good production base and producing high quality products, the enterprise may not receive the desired amount of profit due to insufficiently efficient organization of the work of commercial and financial services. Indeed, the inability to create its own consumer and find highly effective sales channels leads the enterprise to a loss of profit.

The starting point in solving these problems is to determine the break-even conditions for work, after the creation of which we can talk about making a profit. In other words, this is nothing more than determining the cost of product sales at which the enterprise covers its costs of production and sales of products without making a profit or loss.

The problem of reducing costs makes it urgent to more often turn to well-known brands different names in foreign practice, methods for studying various aspects of the “cost-volume-profit” relationship (“cost-volume-profit - “cvp”), or “direct costing”, or analysis of the break-even operation of enterprises (marginal analysis) , or operational analysis.

Margin analysis is one of the most powerful tools available to managers. It helps them understand the relationships among product price, volume or production level, direct unit costs, total fixed costs, mixed costs, and profit. It is a key factor in the process of making many management decisions. The purpose of marginal analysis is to determine what will happen to financial results if a certain level of productivity or output changes. This information is of significant importance to management because one of the most important variables affecting total sales revenue, total costs and profits is output or production volume. For this reason, product output is given Special attention, since knowledge of this dependence allows us to determine critical levels of output, for example, at which there will be neither profit nor loss (that is, the break-even point).

The key elements of such an analysis are: break-even point, profitability threshold, margin of financial strength.

According to V.A. Chernov, “these elements should be supplemented with marginal income, since its use makes it possible to evaluate operational forecasts based on the ratio of fixed and variable costs, which determine the strength of the operating leverage.”

If break-even analysis allows you to determine and study the break-even point (profitability threshold, critical sales volume), the margin of financial strength (security index), and analyze the sensitivity of critical break-even ratios, then the wider use of the marginal approach in the analysis also allows you to form an optimal range of production and determine the price , volume of production and sales to obtain the planned profit, take into account restrictions on resources, financial capabilities when choosing products, determine which goods are more profitable to produce and which to buy, justify the choice of equipment, production technologies, etc.

As for critical ratios, marginal analysis reveals not only the critical sales volume corresponding to the break-even point, but also the sales volume that justifies the “make or buy” decisions, the choice of machinery and equipment, and the analysis of the effectiveness of technologies when planning and forecasting production. This sales volume should also be considered critical (threshold) in relation to the choice of decisions that depend on it (exceeding the critical volume causes a positive decision, and a value below the critical one inclines to a negative choice.

T.P. Karpova points out that “in order to study the relationship between changes in production volume, total sales income, expenses and net profit, a break-even analysis of production is carried out. In this case, special attention is paid to the analysis of product output, which allows management to determine the critical (“dead”) points of production volume "The critical point in sales volume is considered to be the point at which the enterprise has costs equal to the revenue from the sale of all products. In this system there is neither profit nor loss." .

There are several ways to calculate break-even sales volume.

The equation method is based on calculating net profit in the following way: revenue from sales of products - variable costs for the same volume of production - fixed costs in total amount= net profit from sales.

The equation method can be used to analyze the impact of structural changes. Sales are considered as a set of relative shares of products in the total amount of sales revenue. If the structure changes, then the revenue volume may reach a given value, but the profit may be less. The impact on profit will depend on whether the assortment has changed towards low-margin or high-margin products.

Gross margin (profit) method. Gross margin is the sum of profit and fixed expenses. The use of this category is based on the fact that the complete absorption of all fixed costs involves writing off their full amount to the current costs of the enterprise and are considered as one of the areas of profit distribution.

First of all, marginal income is necessary to cover fixed costs, and then to make a profit for the enterprise. This value in Western and domestic practice is often also called the result of sales after reimbursement of variable costs, the amount of coverage or contribution, or gross margin or marginal income.

Gross margin (marginal income) is defined as the difference between sales revenue and variable costs for the same volume of production. Then the critical point is equal to the ratio of total fixed costs to marginal income per unit of output.

With the marginal approach, the manager receives information: about fixed costs - whether they are reimbursed by the total margin or not; on the amount of marginal income from each type of product; about the marginality of each product. Product margin is the marginal income per unit of product, expressed as a percentage of revenue (price).

Marginal income underlies management decisions related to the revision of prices, changes in the range and volume of products, establishing the size of bonuses that stimulate the sale of products, carrying out advertising campaign and other marketing operations.

The graphical method reveals the theoretical dependence of total income on sales, costs and profits on production volume based on the construction of graphs of economic and accounting break-even models.

The break-even chart in its various modifications is widely used in modern economics. The undoubted advantage of this method is that with its help you can quickly obtain a fairly accurate forecast of the main performance indicators of an enterprise when market conditions change.

Mathematical model The relationship between profit, costs and volume is based on dividing cost into fixed and variable costs, the essence of which was discussed in the previous paragraph.

The connection between profit, sales volume and cost lies in the fact that profit depends not only on the quantity sold, but also on the share of fixed costs that fall on a unit of production, i.e. There is a real opportunity to save semi-fixed costs. In search of maximum profit, opportunities to reduce the level of fixed costs are carefully studied. Therefore, estimates called budgets are drawn up for variable and, especially, fixed costs. The optimal project estimate is one that allows you to reduce the share of fixed costs in the price per unit of production.

However, despite the great possibilities of marginal analysis, as noted by Yu.D. Zemlyakov, and, despite a large number of translated literature, and publications of domestic authors, the distribution of this method is quite limited, and the use of its capabilities is significantly narrowed for the following reason: analysis of the break-even operation of an enterprise is purely internal matter, additional work for economic and financial services and burdensome to the extent that the analytical capabilities of the cost-volume-profit relationship are not used.

Thus, marginal analysis allows you to find the most favorable relationship between variable costs, fixed costs, price and production volume.

The results of marginal analysis play an important role in determining the sales structure (product mix) in conditions of limited resources, which means determining the most profitable combination of products or services in the case where an organization produces several types of products. The marginal approach is successfully used to make decisions in these situations. Having completed this stage of analysis, management must study the market for this type of product in order to determine the upper limits of demand for this most profitable product, and then make the final management decision.

2. Optimization of production volume using the example of Uyut LLC

2.1 Brief description of the organization

LLC "Uyut" was created in accordance with the law Russian Federation March 12, 2003 in the city of Karasuk, is commercial organization and specializes in the production of upholstered furniture for home and office.

The enterprise is a legal entity, has an independent balance sheet, a bank account, round stamp with its name. The company is a commercial organization, in its activities it is guided by the Civil Code and current legislation

The target function of the enterprise is to satisfy public needs in the results of its activities and profit.

The company manufactures the following types products:

a set of upholstered furniture;

The company Uyut LLC is a commercial organization that in its activities is guided by the Civil Code and the current legislation of the Russian Federation. The authorized capital of the LLC is 120 thousand rubles. rubles divided between participants into shares certain sizes. Participants bear so-called limited liability for the activities of the company, i.e. are not liable for its obligations and bear the risk of losses associated with the activities of the company, within the limits of the value of the contributions they made. The constituent documents of the Company are the Charter and the Memorandum of Association. The memorandum of association, concluded by the founders in accordance with the Law on Limited Liability Companies and valid along with the charter, determines legal status society, on the one hand, and on the other, contains the features of an agreement on joint activities to create legal entity.

Supreme body management of the Company is General meeting participants. The company's property is formed from contributions to authorized capital, as well as from other sources provided for by the current legislation of the Russian Federation.

The market for goods and services is the city of Karasuk. Let's consider the main economic indicators of the organization under study for 2004-2006.

Table 2.1

Technical and economic indicators of the activities of Uyut LLC for 2004-2006.

Index	Analysis period	Changes, +,-	Growth rate,%




Sales revenue, thousand rubles.
Cost of products sold, thousand rubles.
Profit from sales, thousand rubles.
Profit from sales, thousand rubles.
Average annual cost of OPF, thousand rubles.


Average annual number of employees, people.
Average annual labor productivity, thousand rubles.
Average monthly salary per employee, thousand rubles.
Capital productivity, rub.
Return on sales,%

According to the table, we can conclude that for the entire period under study, the indicators characterizing the financial and economic activities of Uyut LLC are somewhat ambiguous: sales revenue building materials increased in 2005 compared to last year by 405 thousand rubles, in 2006 compared to 2005 by 569 thousand rubles; The cost of products sold increased in 2004-2005. by 563 thousand rubles, in 2006 - by 585 thousand rubles. compared to the previous year.

However, the revenue growth rate for the entire period was 11.68 and 113.56%, respectively, and the cost growth rate in 2005 was 116.43%, in 2006 - 114.66%, which characterizes the inefficient use of resources in the organization .

Sales profit for 2004-2005 decreased by 158 thousand rubles, and in 2006 there was a decrease in profit compared to the previous year by 16 thousand rubles. or by 7.73%.

Return on sales for 2004-2005 decreased by 4.69%, and in 2006 compared to the previous period - by 0.92%, which is a consequence of the fact that the cost of production in the organization is growing at a faster rate than revenue.

A positive aspect of the organization’s activities is the fact that the average annual output of one operating enterprise tends to grow, since in 2005 compared to 2004 its growth amounted to 0.28 thousand rubles, or 0.14%, and in 2006 compared to 2005 - 27.10 thousand rubles, or 13.56%. The average annual salary per employee also tends to grow, however, the rate of growth of wages is lower than the rate of growth of labor productivity, which shows an increase in the efficiency of labor use at Uyut LLC.

2.2 Estimation of break-even production at Uyut LLC

To calculate break-even production and determine the optimal sales volume, at the first stage we will group costs by economic elements.

Table 2.2

Structure of production costs by economic elements of Uyut LLC for 2004-2006.

Expenditures	Cost level, thousand rubles.	Absolute deviation, thousand rubles.	Share in cost,%	Absolute deviation,%
Expenditures

Salary
Contributions to the fund social insurance
Material costs
Depreciation
Other costs
Full cost
Including:
Variable costs
Fixed costs

So, the data presented in the table shows that the total amount of costs in 2005 compared to the previous year increased by 563 thousand rubles. This change was positively influenced by all factors: an increase in wages and contributions to state extra-budgetary funds, an increase in the amount of material costs, and the amount of other costs.

However, despite the increase in the absolute amount of costs for material resources, their share in the cost of production decreased by 4.05%, with an increase in the share of wages and contributions to extra-budgetary funds. In addition, in 2005 there was a decrease in the share of variable expenses and the share of fixed expenses, which is primarily due to an increase in salaries of administrative and managerial personnel and an increase in utility costs.

In 2006, the total amount of costs increased by 585 thousand rubles compared to the previous year. In the year under study, a similar situation is observed as in the previous period: a decrease in the share of material costs in their total amount, and, consequently, an increase in the share of labor costs. Expenses related to depreciation and other expenses did not change significantly. In 2006, the share of variable costs increased, which was associated with a sharp jump in purchase prices for materials, especially wood. The share of fixed costs decreased by 2.59%. Let us carry out a break-even analysis, which allows us to determine the minimum required volume of product sales at which the enterprise covers its costs and operates break-even, without making a profit, but also without incurring losses. On next stage work, we will calculate the break-even sales volume using the data presented in table 2.3

Table 2.3

Initial data for calculating the break-even sales volume of Uyut LLC for 2004-2006.

Index	Set of upholstered furniture (B)	Bed (G)


Sales volume, pcs.
Price for 1 piece, rub.



Marginal income, thousand rubles.
Fixed expenses, thousand rubles.
Net profit, thousand rubles.

Sales volume, pcs.
Price for 1 piece, rub.
Sales revenue, thousand rubles.
Variable costs per 1 piece, rub.
Variable expenses for the entire sales volume, thousand rubles.
Marginal income, thousand rubles.
Fixed expenses, thousand rubles.
Net profit, thousand rubles.

Sales volume, pcs.
Price for 1 piece, rub.
Sales revenue, thousand rubles.
Variable costs per 1 piece, rub.
Variable expenses for the entire sales volume, thousand rubles.
Marginal income, thousand rubles.
Fixed expenses, thousand rubles.
Net profit, thousand rubles.

Based on the information presented in Table 2.3, we calculate the break-even sales volume for 2005-2006. for each type of product using the equation method.

In 2005, sales of unit A (sofa) accounted for 0.53 units. products B (sofa), 0.58 products B (upholstered furniture) and 1.06 products G (bed).

(5.2x+0.53*5.9+0.5x*12.8+1.06x*5.6) -

(2.9x+0.53x*4.6+0.58x*9.9+1.06x*4.2) - 983.4

x = 160 pcs. product A (sofa)

160*0.53 = 80 pcs. products B (sofa)

160*0.58 = 93 pcs. products B (upholstered furniture)

160*1.06 = 170 pcs. products G (bed)

Let us carry out similar calculations for 2006.

In 2006, sales of unit A (sofa) accounted for 0.5 units. products B (sofa), 0.72 products B (upholstered furniture) and 1.56 products G (bed). Further, let us conditionally assume that the critical point is reached by x products A, 0.53x products B, 0.58x products C and 1.06x products D. Then we obtain the following equation:

(5.8x+0.5x*6.5+0.72x*13.5+1.56x*5.7) –

(3.5x+0.5x*4.9+0.72x*10.3+1.56x*4.7) - 1010

x = 145 pcs. product A (sofa)

145*0.5 = 72 pcs. products B (sofa)

145*0.72 = 104 pcs. products B (upholstered furniture)

145*1.56=226 pcs. products G (bed)

Comparing the result obtained in 2006 with the previous year, we note that the critical point for “sofa” products decreased by 15 products; for “sofa” products decreased by 8 pieces. products; for the product “set of upholstered furniture”) decreased by 11 products, for the product “bed” the break-even sales volume in physical terms decreased by 56 pieces of products.

At the next stage of analysis, we will calculate the threshold revenue.

Threshold revenue (PV) = break-even sales volume * price (2.1)

PV (sofa) = 160 * 5.2 = 832 thousand rubles.

PV (sofa) = 80 * 5.9 = 472 thousand rubles.

PV (set of upholstered furniture) = 93 * 12.8 = 1190 thousand rubles.

PV (bed) = 170 * 5.6 = 952 thousand rubles.

Total: 832+472+1190+952=3446 thousand rubles.

Consequently, with revenue from sales of all types of products equal to 3446 thousand rubles. the organization will not yet make a profit, but it will not have losses on sales.

PV (sofa) = 145 * 5.8 = 841 thousand rubles.

PV (sofa) = 72 * 6.5 = 468 thousand rubles.

PV (set of upholstered furniture) = 104 * 13.5 = 1404 thousand rubles.

PV (bed) = 226 * 5.7 = 1288.2 thousand rubles.

Total: 841+468+1404+1062.2=4001.2 thousand rubles.

Thus, with revenue from sales of all types of products equal to 4001.2 thousand rubles. Uyut LLC will not yet make a profit, but it will not have losses from sales.

Marginal margin of safety (MSP),% = (actual revenue - threshold revenue): actual revenue*100 (2.2)

Operating leverage = contribution margin: profit (2.3)

Minimum wage 2005 = (4197-3446) /4197*100 = 17.9%

Minimum wage 2006 = (4764.7-4001.2) /4764.7*100 = 16.02%

Production leverage 2005 = 1194.9/208 = 5.7

Production leverage 2006 = 1199.6/189.6 = 6.3

Let us summarize the calculation results in Table 2.4 and summarize the results of the marginal analysis.

Table 2.4

Results of calculations of break-even sales volume by type of product at Uyut LLC for 2005-2006.

Index	Set of upholstered furniture (B)	Bed (G)



Threshold revenue, thousand rubles.
Security zone, thousand rubles.



Production leverage

Break-even sales volume, pcs.
Threshold revenue, thousand rubles.
Security zone, thousand rubles.
Product profitability,%, (marginal income per unit/unit price)
Break-even selling price, rub. (threshold revenue/production volume)
Marginal safety margin,%
Production leverage

So, according to the calculated data presented in the table, we see that with this combination of break-even sales volume in physical terms, the break-even point in value terms in 2005 was 3,446 thousand rubles, and in 2006 - 4,001 thousand rubles . The safety zone during the study period decreased by 11.4 thousand rubles. (3660-3230); there is also a decrease in the marginal safety margin from 17.9% to 16.02%, the Safety Zone shows that in 2005 revenue can be reduced by 752.1 thousand rubles, without incurring losses, in 2006 - by 763.5 thousand rub. The margin of safety shows that in 2005 the actual sales volume was 17.9%, and in 2006 - 16.02% higher than the critical one. Production leverage calculated for 2005 is 5.7, and in 2006 - 6.3. This means that with an increase in revenue by 1%, sales profit will increase by 5.7% in 2005 and by 6.3% in 2006. It should be noted that the economic activity of the enterprise is in 2003-2004. profitable, the profitability threshold has been crossed, however, in 2006 there was a decrease in the margin of financial strength of the enterprise due to a decrease in sales volumes, therefore, the management of the company should think about the reasons for the deterioration in the financial condition of the enterprise and take specific measures to optimize the volume of production and sales of products in order to increase revenues, reduce costs and profit maximization.

3. Ways to improve the efficiency of decision making to optimize production volume and maximize profits

Management decisions made by the manager of Uyut LLC in terms of costs and selection of the optimal assortment option in some cases are purely intuitive in nature, i.e. these decisions are not based on economic calculations. .

As a result, as noted above, the organization is experiencing a decrease in profits and a deterioration in financial indicators. economic activity.

Let's look at specific examples of business situations that arose in the organization for the period 2004-2006, and can also arise when managing costs in different situations.

To analyze management decision making, we will use the data from tables 2.2, 2.3 and 2.4

An important source of increasing the amount of profit is the optimization of the structure of commercial products, i.e. increasing the share of those products that bring greater profit to the enterprise. Let's consider the possibility of increasing the amount of profit based on the data presented in table 3.1

Table 3.1

Change in the product structure in 2007 at Uyut LLC in 2007

Product type	Selling price, units	Variable costs per unit, thousand rubles.	Specific gravity,%
Product type	Selling price, units	Variable costs per unit, thousand rubles.	first version (2006)	second version (2007)



Set of upholstered furniture

Fixed costs for the year for the first option (2006) are 1010 thousand rubles. If the product structure changes, fixed costs, according to the calculations of the economist at Uyut LLC, will increase by 97 thousand rubles. and will amount to 1107 thousand rubles. Revenue in 2006 amounted to 4,766 thousand rubles. If the sales structure changes in 2007, revenue will be 5,290 thousand rubles.

Calculation of revenue when the sales structure changes, but at unchanged prices: sofa - 30% of sales volume at a price of 5.8 thousand rubles. per unit of production

651 units * 0.3*5.8 = 1132 thousand rubles.

Sofa - 7% of sales volume at a price of 6.5 thousand rubles.

651 units * 0.07*6.5 = 296 thousand rubles.

A set of upholstered furniture 30% of sales volume at a price of 13.5 thousand rubles.

651 units * 0.3*13.5 = 2637 thousand rubles.

Bed 33% in sales volume at a price of 5.7 thousand rubles.

651 units *0.33*5.7 = 1225 thousand rubles.

Let's analyze this situation using marginal income.

First option (2006) Second option (2007)

(5,8-3,5) /5,8*0,21 = 0,083 (5,8-3,5) /5,8*0,3 = 0,119

(6,5-4,9) /6,5*0,118= 0,029 (6,5-4,9) /6,5*0,07= 0,017

(13,5-10,3) /13,5*0,351 = 0,083 (13,5-10,3) /13,5*0,3 = 0,071

(5,7-4,7) /5,7*0,321=0,056 (5,7-4,7) /5,7*0,33=0,058

Total 0.251 Total 0.265

We calculate profit using formula 3.1:

Revenue * share of marginal income in sales revenue - fixed costs (3.1)

P 2006 = 4766*0.251-1010=191 thousand rubles.

P2007 = 5290*0.265-1107 = 247 thousand rubles.

Thus, the second option allows you to increase the absolute amount of profit by 56 thousand rubles, therefore, it should be given preference.

Using the marginal approach, you can set a critical level not only for sales volume, but also for the amount of fixed costs.

The critical level of fixed costs at a given level of marginal income and sales volume is calculated using formula 3.2

N = V*Dn (3.2)

Where B is sales revenue

Du - the share of marginal income in revenue from product sales

The point of this calculation is to determine the maximum allowable amount of fixed costs, which is covered by marginal income for a given sales volume, price and level of variable costs per unit of production.

Since the enterprise under study is experiencing a systematic increase in fixed costs, such a calculation is necessary due to the fact that if fixed costs exceed the acceptable level, the enterprise’s activities will be unprofitable.

Table 3.1

Calculation of the critical amount of fixed expenses for 2004-2006. LLC "Uyut"

Index	Analysis period	Changes, +,-	Growth rate,%




Sales revenue, thousand rubles.
Marginal income, thousand rubles.
Share of marginal income in revenue
Amount of fixed expenses, thousand rubles.
Critical amount of fixed expenses, thousand rubles.

Thus, the calculations presented in the table show that in 2004 the critical amount of fixed costs was 336 thousand rubles. higher than the actual amount; in 2005 - by 191 thousand rubles, and in 2006 - only by 182 thousand rubles. Consequently, due to the fact that the gap between the actual and the critical amount of fixed costs is decreasing from year to year, the enterprise under study needs to either increase production and sales volumes, or reduce the share of fixed costs. Otherwise, the amount of fixed costs may be higher than the critical amount, which will lead to losses.

Let's consider the process of making management decisions about accepting an additional order at a price below the cost of production. Since the organization under study has had a competitor in the city of Karasuk for the production of furniture over the past year, in addition, the share of imported furniture from Novosibirsk has increased, the need to accept an additional order at a price below the cost of production may arise during a decline in production, if the enterprise fails to form a portfolio, but its production capacity is not fully used.

Despite the fact that in 2006 the sales volume for the product “set of upholstered furniture” increased, however, such a situation may arise in relation to this type of product, since the business plan for 2007 plans to produce only 110 units of this type of product, i.e. 88% of the previous year’s volume due to a decrease in demand for upholstered furniture.

To avoid losses and not discontinue production of this type of product, the organization must look for a way out of this situation. And if at this time an offer is received from the customer for the production of products that require a slightly different technology (different sizes, model, etc.), then the administration of the organization can accept such an order even at prices below cost.

Let's say a wholesale customer agrees to buy at this year 15 sets at a price of 13.0 thousand rubles, which is lower than its planned cost. In this case, the enterprise must additionally spend 35 thousand rubles on technological re-equipment of the line for the production of this batch. We will carry out a feasibility study for solving an additional order on such terms and answer the question of whether this is beneficial for the enterprise under study.

Table 3.3

Justification for an additional order of “sofa” products at a lower selling price

INDEX	1 option (100% of the order package)	Option 2 (88% of the order package)	Option 3
INDEX	1 option (100% of the order package)	Option 2 (88% of the order package)	88% of the order package	additional order 15 units

Sales volume, pcs.
Unit price, rub.
Sales revenue, thousand rubles.
Variable costs per unit of production, rub.
Amount of variable costs for the entire volume, thousand rubles.
Amount of fixed costs for the entire volume, thousand rubles.
Cost of the entire issue, thousand rubles.
Cost per unit of production, rub.
Profit (loss), thousand rubles.

So, the proceeds from the sale of an additional batch of the order will be 195 thousand rubles, variable costs will increase by 154.5 thousand rubles, and fixed costs - by 35 thousand rubles. .

Consequently, additional revenue covers all variable costs, technological costs for changing the form of products and part of the fixed costs in the amount of 5.5 thousand rubles. (195-154.5-35). As a result, the company will receive not a loss of 2.7 thousand rubles, but a profit of 2.8 thousand rubles.

This proves that even under such unfavorable conditions, accepting an additional order is economically justified. An additional order allows you to reduce the cost per unit of production by increasing production volumes and make a profit instead of a loss.

And on last stage analysis, we will consider the rationale for the option for new products, since important factor, on which the profit of the enterprise depends, is the level of prices for products.

In August 2007, the enterprise under study mastered the production of a new product - a children's sofa "frog". The price of competitors for a similar product is 5 thousand rubles. To conquer the market, the company needs to provide either high quality sofas or sell this type of product at a lower price. Fixed costs associated with the production and sale of this type of product amount to 48 thousand rubles. Variable costs - 3.8 thousand rubles. If you improve the quality of the product (for example, use better material for upholstery), then the sofa can be sold for 5.5 thousand rubles, but fixed costs will increase by 20% and variable costs will also increase by 20% and amount to 4.56 thousand roubles. To analyze this situation, we will calculate the profit and break-even point for the production and sale of a “frog” sofa using two options.

Table 3.4

Justification of the selling price for the new kind products sofa "frog"

Index	First option	Second option
1. Sales price, thousand rubles.
2. Variable costs per unit of production, thousand rubles.
3. Fixed costs, thousand rubles.
4. Marginal income per unit of production, thousand rubles. (page 1-page 2)
5. Critical sales volume, pcs. (page 3/page 4)
6. Enterprise capacity, pcs.
7. Amount of profit, thousand rubles. (p.4*p.6-p.3)

As can be seen from the table, the second option is more profitable for the enterprise, i.e. selling a sofa at a lower price because it provides a higher amount of profit and a lower profitability threshold.

Thus, the results of the analysis in this chapter allow us to conclude that through the marginal approach, the enterprise will be able to plan a break-even volume of production and sales, determine the critical amount of fixed costs and the critical level of the selling price, and analytically evaluate decisions on accepting an additional order at a price below cost products, justify the product structure and price option for a new product.

Conclusion

One of the powerful tools for solving a large class of marketing problems is calculating the break-even point of production. Using this calculation, you can determine the break-even point, plan the target production volume, set prices for products, select the most efficient production technologies, and develop optimal production plans. As you know, there are two models of break-even analysis: economic and accounting.

Knowledge of break-even levels allows you to determine the minimum sales volumes for each type of product and build a portfolio of orders so that production is always profitable.

The purpose of the course work was to study the process of determining the optimal volume of production and sales.

The object of the study was the production activities of Uyut LLC. The subject of the study was the calculation of the optimal production volume and the development of management decisions based on the cost-volume-profit analysis.

The calculation results allowed us to establish the following.

In 2005, the share of variable costs in total costs decreased, and the share of fixed costs increased, which is explained by an increase in the amount of salaries of administrative and management personnel and an increase in utility costs.

In 2006, the share of variable costs increased due to rising prices for materials used in production. Respectively. the share of fixed costs has decreased.

Using the equation method, critical points were calculated in physical terms for all types of products, as well as the break-even sales volume in value terms equal to 3,446 thousand rubles in 2005, and 4,001 thousand rubles in 2006.

Consequently, as a result of the calculations, it was revealed that at Uyut LLC the actual production volume is above the critical point, i.e. break-even point and the company made a profit for the entire study period.

Safety zone for 2005-2006. decreased by 11.4 thousand rubles; The marginal safety margin also decreased from 17.9% to 16.02%,

Production lever in 2005 is 5.7, and in 2006 - 6.3, which indicates that with an increase in revenue by 1%, sales profit will increase by 5.7% in 2005 and by 6.3% in 2006

As a result of the work carried out, on the basis of calculating the break-even sales volume, some proposals were developed to improve the efficiency of management decisions made:

a methodology for selecting the most cost-effective types of products for production and sale is outlined;

options for setting prices for a new type of product are justified;

the critical amount of fixed costs and the critical price level have been determined;

The decision to accept an additional order at a price below the unit cost of production was assessed.

These recommendations will allow the organization to stay within the critical volume of not only sales, but also the amount of fixed costs, and changing the product structure will allow the company to receive additional income and profit from sales, which will improve financial condition enterprises.

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Under optimal production volume production is understood to be such a volume that ensures the fulfillment of concluded contracts and obligations for the production of products (performance of work) on time with a minimum of costs and the highest possible efficiency.

The most common methods for determining optimal production volume include:

Gross comparison method;

Method of comparison of limit indicators.

The following assumptions apply when using these methods:

The company produces and sells only one product;

The goal of the enterprise is to maximize profits during the period under review;

Only price and production volume are optimized (it is assumed that all other parameters of the enterprise’s activities remain unchanged);

The volume of production in the period under review is equal to the volume of sales.

The above assumptions may seem quite “rigid”, however, if we take into account that it is the price of the product produced and the volume of its production and sales that, as a rule, have the greatest impact on the economy of the enterprise, the use of these methods significantly increases the likelihood that they will be accepted right decisions.

Let us consider the essence of the proposed methods using the example of a hypothetical enterprise operating in a free competition market (initial data are given in Table. 11.1).

Table 11.1 Product sales volume and production costs

	Permanent	Variables
implementation,	costs,	costs,	costs,

Gross Compilation Method involves calculating the profit of an enterprise at various volumes of production and sales of products. The calculation sequence is as follows:

The value of the production volume at which zero profit is achieved is determined;

The volume of production with maximum profit is determined (Table 11.2).

Table 11.2 Volume of product sales with maximum profit

			Profit, thousand rubles
implementation,	price, rub.	costs,

Rice. 11.1. Comparison of gross revenues and costs

Line BB shows the change in gross revenue, and curve VI shows the corresponding gross costs. Rice. 11.1 shows that sales of products in the amount of up to 37 thousand units. it is unprofitable for the enterprise, since the gross cost curve is located above the gross revenue line; at the point where production is 37 thousand units, profit is zero, and gross revenue is approximately 1850 thousand rubles. With an increase in production volumes after 37 thousand units. gross revenue begins to exceed costs and profit (AC) appears, the maximum value of which is 1140 thousand rubles. is achieved with a production and sales volume of 90 thousand units. This is the optimal production volume in this case.

Limit comparison method allows you to establish to what extent it is profitable to increase production and sales. It is based on a comparison of marginal cost and marginal revenue. If the marginal revenue per unit of output exceeds the marginal cost per unit of output, then increasing production and sales will be profitable.

Let us illustrate this based on the data given in table. 11.3.

Table 11.3

Calculation of the optimal volume of product sales using the method of comparing limit indicators

Volume of sales,	Limit	Limit	Limit
	income, rub.	costs, rub.	profit, rub.

In this case, the marginal revenue per unit of production is essentially the market price of a unit of product, equal to 48 rubles, and marginal costs (IPR) are calculated as the difference between subsequent total costs and the previous ones, divided by the volume of production.

Marginal profit is calculated as the difference between marginal revenue and marginal cost.

A visual representation of this method is given in Fig. 11.2.

Rice. 11.2. Comparison of marginal revenue and marginal cost

Graph Fig. 11.2 shows that as long as the marginal revenue curve is located above the marginal cost curve, increasing production volumes is effective, i.e. expansion of production to 90 thousand units. cost-effective. With a further increase in production volume, the amount of additional costs will exceed the amount of additional income per unit of production, which will lead to a decrease in gross profit.

In both cases, it was assumed that the market price per unit of the product was 48 rubles, but what would happen if the price decreased? In this case, the company will incur losses and may go bankrupt. Let's say that the price has decreased from 48 to 30 rubles. for 1 piece, i.e. the marginal income per unit of production for any production volume will be 30 rubles, and the optimal production volume will be 70 thousand units.

Let's calculate average variables and average gross costs (Table 11.4).

Table 11.4 Product sales volume and average costs

Volume of sales,	Average variables	Average gross
	costs, rub.	costs, rub.

From the table 11.4 it follows that the optimal volume of production expansion lies within 70 thousand units. and its further expansion will lead to the fact that the enterprise will begin to operate at a loss.

It should be noted that the average gross costs are 34.57 rubles, i.e. exceed the price set at 30 rubles. However, since the price is higher than average variable costs (RUB 17.43), the average coverage amount will be RUB 12.57. (30.00-17.43), which corresponds to a gross value of 879,000 rubles. (12.57 70,000). This value does not compensate for fixed costs equal to RUB 1,200,000. In other words, the company will have a loss of 320,100 rubles. (1,200,000 - 879,000). If the management of the enterprise stops production, the company will suffer a loss in the amount of 1,200,000 rubles, i.e. in the amount of fixed costs.

Thus, under these conditions, as forced measure a decision must be made to continue production. But, if the price per unit of production is set at 30 rubles. and will remain unchanged for a long time, production should be discontinued.

The goal of the company is to maximize profits. Profit(P) is the difference between revenue (TR) and the firm’s total costs (TC):

Since in the revenue function (TR = P × Q) the market price is completely uncontrollable competitive firm, the latter's task is to determine the output at which its profit will be maximum.

Firm maximizes profit at such an output when its marginal revenue becomes equal to its marginal cost:

Mr = mc

wherein optimal production volume

According to the rule of profit maximization, a firm producing products in volumes at which MR = MC receives the maximum possible profit at given prices, i.e. optimal production volume is the volume at which marginal cost (MC) and marginal revenue (MR) are equal.

The equality of MR and MC is condition for profit maximization for any firm, regardless of the market structure in which it operates (perfect or imperfect competition).

Equality MR = MC as a condition for maximizing profit can be justified logically. Each additional unit of output brings some additional income (marginal revenue), but also requires additional costs (marginal cost). As long as marginal revenue exceeds marginal cost, an additional unit of output increases profit.

Accordingly, at the moment when marginal cost equals marginal revenue, profit reaches maximum. A further increase in output, at which marginal costs exceed marginal revenue, will lead to a decrease in profit.

In its decisions, the company strives to achieve best results– get maximum profits at minimum costs. In this case, the company is said to be in a position equilibrium .

The equilibrium condition of the firm is the equality of marginal costs, marginal revenue and factor price:

The point at which the market price intersects the marginal cost curve determines the equilibrium position.

To the left of point E (Fig. 2) MC > MR, it is profitable for the company to increase production, because on each unit of production it receives more than it expends. Having produced less output than at point E, the firm incurs losses from underproduction.

Figure 2. Firm's equilibrium in production

To the right of point E MC > MR. For each additional unit of production, the company incurs losses, because its costs exceed its income. Increasing production to the right of point E is unprofitable. Hence, optimal production volume is Q 0 .

Thus, with production volume Q 0, the firm achieves maximum profit.

Hence. To achieve maximum profit, the firm must produce this volume of output. at which marginal revenue equals marginal cost.

The equality of marginal revenue and marginal costs characterizes the equilibrium of the firm in any market structure and is used to maximize profit. minimizing losses and obtaining zero economic profit.

Conclusions on question 3

The volume of production at which marginal revenue equals marginal cost (optimal production volume) ensures maximum profit. If the actual output volume is lower than optimal, then the company should expand production - profits will increase; If output is greater than optimal, then to increase profits the firm should reduce production.

4. Theory of optimal production volume

1. Determination of the optimal volume of production and sales of products by comparing gross indicators.

An enterprise, as a rule, strives to obtain maximum profit.

All other things being equal, the greatest influence on profit maximization is exerted by the volume of production (sales) of products and the price of the product produced. Having passed the production volume corresponding to the break-even point, the enterprise will subsequently receive a certain profit with an increase in production volume. The optimization method is a method of comparing gross indicators. Its use requires a number of assumptions:

1) the enterprise produces and sells only one product;

2) the goal of the enterprise is to maximize profits during the period under review;

3) only price and production volume are optimized.

The essence of this method, when the manufacturer does not have any influence on price formation, comes down to determining the quantity of goods that he can offer to customers at the prevailing market price.

The method of comparing gross indicators involves calculating profit at different meanings volume of production and sales of products by deducting the amount of gross costs from gross revenue.

Gross costs are determined by multiplying the cost per unit of production by its quantity. Gross revenue is calculated by multiplying the price by the same quantity.

2. Determination of the optimal volume of production and sales of products by comparing limit indicators.

Along with determining the optimal volume of production and sales of products by comparing gross indicators, the method of comparing marginal indicators is used for the same purposes.

When optimizing production volumes using this method, the concepts of “marginal revenue”, “marginal costs” and “marginal profit” are used.

Marginal Revenue– the average amount of decrease (increase) in revenue per unit of goods as a result of a change in the volume of production and sales of products by more than one unit. It is defined as the quotient of dividing the difference between subsequent and previous revenue by the corresponding difference in sales volumes in physical measurements.

Marginal cost– the average value of the cost of increase (reduction) per unit of production, which arose as a result of a change in the volume of production (sales) of products by more than one unit. They are determined by the ratio of the difference between subsequent and previous gross costs to the difference in the corresponding volumes of output.

Marginal profit– the average amount of increase (decrease) in profit per unit of production resulting from a change in production volumes by more than one unit.

Marginal profit– the difference between marginal revenue and marginal cost.

The starting point of the method of comparing marginal indicators is that increasing production volume is profitable as long as the value of marginal revenue exceeds the value of marginal costs.

In order to plan production volumes, it is necessary to know the indicators of worker productivity. Labor productivity characterizes the efficiency of an employee in a broad sense - this is the ability of a particular employee to produce products or provide services.

Labor productivity can be individual (for one worker, measured by the amount of material goods produced by one worker per unit of time) and social (determined by the costs of not only living, but also materialized labor).

Labor efficiency indicators are used for various purposes - planning, comparison, standardization, etc. Therefore, they can have different forms of measurement, which are determined by the purpose and purpose of determining the indicator.

Natural indicators characterize the production of products in kind per unit of working time and are expressed in physical form, for example, tons, kilograms, liters, meters, etc.

They are absolute in nature and have limited application. They are mainly used in comparing performance indicators of teams, units, workers, as well as in determining production standards and the level of their implementation.

To analyze the actual expenditure of working time and determine the intensity of labor, a natural indicator of the labor intensity of work is used (an indicator inversely proportional to production output), which is defined as the ratio of the total amount of working time spent on the entire volume of work to the number of completed works (standard time).

However, cost indicators of labor productivity are characterized by greater efficiency, feasibility and ease of use. They have become more widespread in industrial enterprises and are distinguished by great versatility.

Their use makes it possible to take into account and compare various types of work by bringing them to a single meter (cost).

Labor indicators characterize the ratio of standard costs to actual working hours. Such indicators are used to determine the efficiency of the use of workers' labor in comparison with standards. Such indicators are convenient to use when rationing labor and determining optimal labor standards for workers.

Depending on the purpose of planning, various methods for measuring labor productivity are used. After all, labor productivity has a great influence on the level of competitiveness of the enterprise and its financial results.

Any planning cannot do without taking into account the productivity of labor, both individual and social. Production planning is inseparable from rationing the labor of workers and from taking into account their compliance with labor standards.

In practice, in general accounting, cost accounting indicators have become widespread, since they are general and universal for production planning purposes. An enterprise should strive to increase labor productivity as a guarantee of future prosperity.

2. Determining the optimal production volume in the short term

The market mechanism operates most effectively under conditions of pure, or perfect, competition. One of the first to give the concept of perfect competition was A. Smith in his work “An Inquiry into the Nature and Causes of the Wealth of Nations.” Perfect or pure competition occurs when certain conditions and as an economic phenomenon in real life it is quite rare.

The demand for the product of an individual firm under conditions of perfect competition is perfectly elastic. If the price of its products is R 0, then graphically the demand curve D can be represented as horizontal line, showing that any quantity of products offered will be sold at a price R 0 (Fig. 22).

In contrast, the market demand schedule for a product D– an inclined line reflecting the willingness of consumers to purchase different quantities of products (Fig. 23). Price R 0 is formed in the industry as a result of the interaction of demand D and suggestions S and it is precisely this that is installed on the products of an individual company.

Since the price of a company’s products is set by the market and does not depend on the volume of production, the total (gross) revenue (income) of the company TR will be equal to the product of price R per quantity Q products, and marginal revenue M.R.(increase in income from the release of each additional unit of production) – product price R:

M.R.= P.

Average revenue AR(gross revenue divided by the number of goods sold) of a firm under perfect competition will also be equal to price R:

AR= P.

For example, we sold 100 kg of apples on the market at a market price of 50 rubles. for 1 kg. The total gross revenue was 5,000 rubles. (100 × 50), and the average and maximum are 50 rubles. In our example, selling 101 kg of apples would also increase gross revenue by 50 rubles. In Fig. 24 it is clear that the lines of the average AR, limit M.R. revenue and demand D for the products of an individual company are the same.

In order to determine what volume of production must be achieved in order to provide the company with maximum profit, it is necessary to consider its activities in time intervals: in the short and long term.

TO short term period- one that is insufficient for new producers to enter or exit the industry. There are two ways to determine the volume of production.

First, the company chooses the option when the difference between gross income and gross costs is maximum; in other words, when the maximum amount of profit is achieved at Q 0 (Fig. 25). In this case, she compares the gross income she receives at different volumes of output TR with gross costs TS, corresponding to each of the possible volumes.

The second way - comparing marginal revenue and marginal costs - is used more often. The company will expand production as long as it ensures an increase in income compared to the increase in costs. When additional production requires more costs than expected income, the firm will stop expanding production.

The turning point will be the moment when marginal income equality is achieved. M.R. and marginal costs M.C.: M.R.= M.C.. The volume of production at which marginal revenue equals marginal cost is called optimal release(Fig. 26), at which the company receives maximum profit.

Using either the first approach (comparing gross revenue TR with gross costs TC), or the second (comparison of marginal revenue M.R. at marginal cost M.C.), the firm can choose the volume of production Q 0, which will provide maximum profit. Any production volume from Q 1 to Q 2 will bring profit to the company (see Fig. 25). However, the profit will be maximum only at the point Q 0 . This is where marginal revenue will be equal to marginal cost (see Fig. 26). Location on Q 1 Q 0 the company will receive less potential profit, and in the interim Q 0 Q 2 marginal costs will exceed marginal revenue and efficiency will decrease. As soon as the increase in costs begins to exceed the increase in revenue, the company will stop producing additional products. production.

By producing products in quantity Q 0, at which equality of price (marginal revenue) and marginal costs is ensured, the firm receives maximum profit, since the prevailing price in the market P 0 exceeds average gross costs (Fig. 27). The shaded rectangle shows the profit margin.

In the short term, if the market price decreases, the company may face losses. The behavior of the company in this case can be twofold: either it will continue production despite losses, or it will cease its activities. Closing is a highly undesirable option. However, the following situations are also possible here.

If the market price of a product has fallen and is below average gross costs, but above average variable costs, then the firm continues production. In this case, the optimal production volume (at R = MS) allows you to minimize incurred losses and partially compensate for fixed costs.

If the price falls below average variable costs, the firm will not be able to recover even part of its fixed costs and will then be forced to stop production.

The relationship between market conditions (product prices) and the firm's response to them (the quantity of goods produced and sold) is determined by the supply curve. To construct an industry supply curve, you must first find the supply curves of individual firms and then sum them up.

Individual firm supply curve shows how much of a good a firm is willing to produce and offer on the market at each price. As you know, the company will begin production at a price not lower than average variable costs AVC. If the price of the product falls below this level, the company will not be able to offer a single unit of the product on the market. For all the same prices R 1 , R 2 , R 3 (Fig. 28) above level AVC the firm will produce this quantity of goods each time Q 1 , Q 2 , Q 3, at which the price of the product equals the marginal cost. Therefore, under perfect competition, an individual firm's short-run supply curve coincides with its marginal cost curve above the curve. AVC.

Rice. 28. Supply curve of a perfectly competitive firm

In Fig. 28 intersection points MS with price lines indicate the volume of supply of the company that, at a given price, ensures maximum profit or minimizes possible losses: at a price R 1 this Q 1, at a price P 2 – Q 2, at a price P 3 – Q 3. Thus, the volume of supply of a firm seeking to maximize profit when the price of a product changes shows that the marginal cost curve establishes the dependence of the volume of supply on price, i.e., it is also the firm’s supply curve.

Manufacturing program. Determining the optimal volume of production and sales (sales) of products

Determining the optimal volume of production and sales (sales) of products

Topic 6. PRODUCTION AND SALES OF PRODUCTS

The task of a small manufacturer (seller) is to determine the optimal volume of production and sales of products (goods). The optimal volume of production and sales of products is understood as the volume at which the best economic results of the enterprise are achieved, for example, profit.

The most common methods for determining optimal production volume are:

· method of comparison of gross indicators;

· method of comparison of limit indicators.

Let us consider the essence of the proposed methods using the example of a hypothetical enterprise operating in a free competition market (initial data are given in Table 1).

Table 1

Product sales volume and corresponding production costs

Gross matching method indicators involves calculating the profit of an enterprise at various volumes of production and sales of products. Calculation sequence:

· the volume of production at which zero profit is achieved is determined;

· the volume of production with maximum profit is determined (see Table 2).

Zero profit in our example is achieved with a production and sales volume in the range of 30 – 40 thousand units. products, which corresponds to the value of gross revenue and costs, respectively, in the intervals of 1440 - 1920 thousand rubles. and 1690 – 1810 thousand rubles. The exact value of production and sales volume corresponding to zero profit can be obtained by interpolation.

table 2

The volume of product sales that maximizes the profit of the enterprise

In Fig. 5 provides a more visual graphical explanation of this method. With a certain degree of assumption, the maximum profit (1140 thousand rubles) is achieved with a volume of production and sales of products of 90 thousand units.

Limit comparison method is based on the use of the concepts of marginal cost and marginal revenue. Marginal revenue refers to the additional revenue for each subsequent unit of output. Marginal cost is the additional cost for each subsequent unit of output.

Table 3

Calculation of the optimal volume of product sales using the method of comparing limit indicators

In table 3 shows the calculation of the limit values for income, costs and profits. For a perfectly competitive market, marginal revenue is equal to the price of products that are formed in the market. In our example, 48 rubles/piece.

For a more complete presentation of this method, we provide a graphical interpretation (see Fig. 6).

The main thesis of the method of comparing marginal indicators: as long as the value of marginal income exceeds the value of marginal costs, increasing production and sales of products is profitable. In Fig. Figure 6 shows a graphical interpretation of this provision.

Any commodity producer determines for itself the minimum acceptable selling price of a product. Moreover, this issue must be resolved in a competitive market environment. Let's assume that the market price of a product has fallen for some reason. What does the company need to do? The company will not be able to survive if it incurs losses for a long time, therefore:

· in the long term, the selling price of manufactured products cannot be lower than the average gross costs;

· in the short term, an enterprise is often forced to incur losses even if sales of products are completely stopped.

In the event that the price of a product temporarily decreases on the market, the minimum acceptable price for the seller (manufacturer) must not be lower than average variable costs for the following reasons:

· fixed costs occur under any circumstances;

· When prices and variable costs are equal, losses are minimized.

Let's consider a specific situation: the market price for products has decreased to 30 rubles/piece, therefore, the marginal income will be 30 rubles. Based on the data in table. 3, the optimal sales volume (marginal revenue equals marginal costs) will be in the range between 70 and 80 thousand units. products sold. To simplify the calculation, we will conventionally assume the value of the optimal volume – 70 thousand pieces. products. According to the table 4 we find the value of average variable costs - 17.43 rubles, which are equal to the minimum price of products.

Table 4

Product sales volume and average costs

Sales volume, thousand pcs.	Average variable costs, rub. / PC.	Average gross costs, rub. / PC.
	–
	20,00	140,00
	18,00	78,00
	16,33	56,33
	15,25	46,25
	15,20	39,20
	16,00	36,00
	17,43	34,57
	19,38	34,38
	22,00	35,33
	25,60	37,60

Under these conditions, the enterprise incurs losses in the following amount:

1,200,000 – (30.0 – 17.43) × 70,000 = 320,100 rub. However, if the company stops selling products altogether, then the losses will be equal to fixed costs– 1,200,000 rub.

Under production program enterprise is understood as a scientifically based plan for the volume, nomenclature, range and quality of products, developed on the basis of concluded contracts and approved at the enterprise by the relevant body.

The production program consists of the following sections:

I. Planned target for volume, nomenclature and range of products.

P. Planned target for the quality of products.

III. Plan for specialization and cooperation.

During development production program The following principles must be observed:

· scientific basis use of production capacities, material, labor and financial resources;

· systematic updating of the nomenclature and range of products and improving their quality;

· consistency of the enterprise’s production program with the production programs of other enterprises closely related through cooperation;

· the most complete and rational use of all available resources in the enterprise;

· continuous increase in production and sales of products if there is demand for it.

The basis for developing a production program is the results marketing research, order portfolio, availability of production capacity and resources at the enterprise.

The production program is characterized by the following indicators: quantitative and qualitative, natural and cost.

Quantitative (volume) indicators: sales volume, volume of commodity, gross and net products.

Volume of products sold according to plan ( V r) can be determined by the formula

V r = V t + V np1 – V np2 ,

Where V t– volume of marketable products according to plan;

V np1, V np2– balances of unsold products at the beginning and end of the planning period.

Commodity products are finished products, intended for external sales, as well as to satisfy one’s own needs of both production and non-production nature. Volume of gross output ( V in) includes the volume of marketable products and the difference in work in progress, semi-finished products and tools of its production at the beginning and end of the planning period.

Volume of net production ( V chp) can be determined from the expression

V chp = V t – MZ – A ,

Where MOH– material costs;

A– depreciation.

Qualitative indicators: grade, brand, content of useful components, share of products that meet international standards and exceed them, share of export products, the most important technical parameters of manufactured products.

Natural and cost indicators: planned production. In the production program, this indicator is indicated both in value and in physical terms. Natural meters depend on the specifics of the product being manufactured, so it can be indicated in linear meters, m3, pieces, kg, t, sections and other units, as well as in conventional units. The volume of sold and marketable products is shown in current wholesale prices enterprises, in comparable prices and in wholesale prices of the reporting period.

Products sent for export are shown in convertible currency with subsequent conversion into rubles in accordance with the current exchange rate. Such a cost estimate is necessary not only for planning a production program, but also for analyzing its implementation.