Economic analysis. Methods of economic analysis of an enterprise - theoretical aspects Analysis of equipment use
The method of economic analysis is a method of systematic, comprehensive study, measurement and generalization of the influence of individual factors on the results of financial economic activity enterprises, carried out by processing with special techniques the sources available to the analyst economic information.
The features of the method of economic analysis result in a number of special methods and techniques used in conducting complex economic analysis.
When conducting economic analysis, they use various ways and techniques. In the literature one can find various classifications of methods of economic analysis. The simplest of these is the division of techniques used in analytical research into two main categories:
1) Classical techniques of economic analysis;
2) Models used in economic analysis developed within other sciences.
The first group includes: comparison, balance method, factor analysis, chain substitution method and absolute differences etc. The main methods borrowed by economic analysis from other sciences include statistical and economic-mathematical methods. Statistical methods include methods of average and relative values, groupings, index method, etc. Economic and mathematical methods include: correlation analysis, regression analysis, optimization methods (simplex method, game theory, etc.), etc. Let's take a closer look at the analysis methods most often used in the analysis of financial statements.
Comparison- the earliest and most common method of analysis is the earliest and most common method of analysis. The comparison method is based on a comparison of phenomena, through which their common features and differences are revealed. In economic analysis, the method of comparison is considered one of the most important, and the analysis begins with it. There are several forms of comparison: comparison with planned and standard values of indicators, comparison of actual data with data from previous years, comparison of the performance indicators of the enterprise under study with industry average data and with data from the best enterprises, comparison of performance results before and after changing any factor with the purpose of determining the influence of factors and calculating reserves. In economic analysis, the following types of comparative analysis are distinguished: horizontal, vertical, trend. Horizontal analysis is used to determine absolute and relative deviations of the actual value of the analyzed indicators from their basic value. Using vertical analysis, the structure of the object under study is studied. By determining the specific gravity of its components, identifying their changes under the influence of various factors and the impact of these changes on the level of the performance indicator. Trend analysis is used to study the relative rates of growth and increase in indicators over a number of years to the level of the base indicator; in essence, it is the study of a particular indicator in dynamics. One of the most significant disadvantages of the comparison method and its indispensable condition is comparability in the content and structure of the analyzed indicators. To ensure comparability, estimated adjustments to planned indicators are allowed. In particular, it is necessary to recalculate the planned amount of costs for cost items that depend on the volume of products produced and sold for the actual output of products. Comparison with historical data is also widely used in economic analysis. It manifests itself in a comparison of economic indicators of the current day, decade, month, quarter, year with similar indicators of the previous period. Carrying out such an analysis is made difficult by violating the condition of data comparability. Comparison with best results, best practices, etc. can be carried out both within the enterprise itself and outside it. Within the enterprise, the basis for comparison is the performance indicators of the best workshops, sections, and employees; outside the enterprise - performance indicators of the best enterprises in the industry operating in approximately the same conditions. In economic analysis, the performance indicators of an enterprise are often compared with average indicators, for example, for the industry, but here, too, certain conditions and requirements must be met. If a consolidated link combines enterprises with different production profiles, then the average indicators should be calculated for each homogeneous group of enterprises.
Balance sheet method– The balance sheet method is widely used in accounting, statistics and planning. It is also used in the economic activities of enterprises. The balance sheet method owes its name to the balance sheet, which was one of the first historical examples of linking a large number of economic indicators with two equal amounts results. The use of the method is especially widespread in analyzing the correct placement and use of economic assets and the sources of their formation. On industrial enterprises, for example, using this method, the use of working time, machine tools and production equipment, the movement of raw materials, semi-finished products, finished products etc. Let us demonstrate the application of the balance method using the example of a commodity (raw material) balance, which is compiled at enterprises in almost all industries. Its formula is:
Zo + P = P + B - Z1, where
Zo, Z1 - stock of goods at the beginning and end of the reporting period,
P - receipt of goods for the reporting period,
P - sales of goods in the reporting period,
B - other disposal of goods in the reporting period (natural loss, markdown, etc.)
Each of the listed quantities can be represented as an algebraic sum of the others. The commodity balance itself allows one to draw important analytical conclusions, especially if it is compiled not only as a whole, but also for individual groups of raw materials.
The balance sheet method is widely used in economic analysis and as an auxiliary method. In particular, this method is used to check the correctness of determining the influence of various factors on changes in the value of the effective indicator. In this case, its use is based on the fact that in deterministic analysis the algebraic sum of the magnitudes of the influence of individual factors must be equal to the magnitude of the change in the effective indicator. In some cases, the balance sheet method can be used to determine the magnitude of the influence of individual factors on changes in the value of the performance indicator. This approach is possible, for example, in the case when the combined influence on the value of the performance indicator of two factors and the influence of one of them is known. In this case, the influence of the second factor is determined by subtracting the known magnitude of the influence of one of them from the sum of the combined influence of two factors. This method is also called balance method.
Factor analysis– The results of the economic activities of any enterprise are influenced by certain causes or factors. Some of them directly affect the change in value, others only indirectly. For example volume change industrial products(resultative indicator) directly depends on changes in factors such as labor productivity and number of workers. Other factors. For example, such as changes in the wage fund, energy and mechanical equipment of production and labor, etc. influence changes in the volume of industrial production only indirectly. In economic research, a factor is understood as a set of conditions and causes necessary for the implementation of an economic process and obtaining a given result. Factors affecting the results of economic activities can be classified according to various criteria. However, the most important from the point of view of economic analysis are production and economic factors. The determination of factors whose influence on the change in the analyzed indicator is studied during the analytical study is based on theoretical and practical knowledge acquired in a particular industry. An interconnected study of the influence of factors on the value of performance indicators is achieved through their systematization. At the next stage of factor analysis, the form of dependence that exists between the factors and the resulting indicator is determined. For example, direct or inverse, functional or stochastic, etc. The next stage involves the construction of a factor model, with the help of which the influence of changes in each factor on changes in the performance indicator is studied. To solve this problem, economic analysis uses a number of specific methods (techniques) of analysis, based on the principle of elimination (from English - exception). Elimination is a logical technique with the help of which the influence on the performance indicator of all factors except one, the influence of which is being established at the moment, is mentally excluded. The most common methods in the practice of economic analysis based on the principle of elimination are the method of chain substitutions and absolute differences.
Chain substitution method- Chain substitutions are used to calculate the influence of individual factors on the corresponding aggregate indicator. Chain substitution is widely used in analyzing the performance of individual enterprises and associations. This method analysis is used in cases where the relationship between the phenomena being studied is strictly functional in nature, when it is presented in the form of a direct or inversely proportional relationship. In these cases, the analyzed aggregate (resultative) indicator must be presented in the form of an algebraic sum, product or quotient of dividing one indicator by another. The method of chain substitutions consists of sequentially replacing the basic value of one of the algebraic terms or one of the factors with its actual value, all other indicators are considered unchanged. The calculation algorithm using this method can be presented as follows:
A = X x Y x Z, where A is a generalizing (effective) indicator; X,Y,Z - factors under the influence of which the effective indicator changes; A′, A′′, A′′′ - the results of sequential replacement of factors.
Ao = Ho x Uo x Zo;
А′ = Х1 x Уо x Zo; DA(X) = A′ - Ao
А′′= Х1 x У1 x Zo; DA(U) = A′′ - A′
A′′′ = X1 x Y1 x Z1; DA(Z) = A′′′ - A′′
When calculating using the chain substitution method It is very important to ensure a strict sequence of factor replacement. In the practice of analysis, the influence of quantitative indicators is first identified, and then qualitative ones. For example, if it is necessary to determine the degree of influence of the number of employees and labor productivity on the volume of industrial output, then first determine the influence of the number of employees, and then labor productivity. In the event that the influence of a factor has not yet been determined, the basic value of the corresponding factor indicator is taken into account, but if the influence of a factor has already been determined, its actual value is taken into account. A characteristic feature of the method there is mandatory equality between the total influence of all factors and the deviation of the performance indicator from the base The above-mentioned features of the method of chain substitutions fully apply to the method of absolute differences.
Absolute difference method is based on finding the difference between the actual and basic values of partial indicators with the subsequent determination of the value thus found for the change in the general indicator. The calculation algorithm and the sequence of replacing partial indicators are similar to the method of chain substitutions, but the influence of a particular indicator on the resultant one is calculated immediately. All indicators preceding the calculated change in a particular indicator are taken in their actual value. Subsequent indicators are basic. The calculation algorithm is as follows:
A = X x Y x Z, where A is a generalizing (effective) indicator; X,Y,Z - factors under the influence of which the performance indicator changes.
Ao = Ho x Uo x Zo;
DA(X) = (X1 - Xo) x Uo x Zo;
DA(U) = X1 x (U1 - Uo) x Zo;
DA(Z) = X1 x Y1 x (Z1 - Zо);
DA = A1 - Ao = DA(X) + DA(Y) + DA(Z).
When analyzing using the method of absolute differences, special attention should be paid to signs. For example, an increase in the amount of other disposals of goods had a negative impact on sales volume (-), although the mathematical sign is defined as positive (+), since a smaller one is subtracted from a larger value. When performing calculations using the chain substitution method, the deviation values (more, less) coincide with their mathematical expression (+ or -). Therefore, signs have to be placed based on economic sense.
Methods of average and relative values– The economic activities of an enterprise and its results are usually presented in the form of indicators having quantitative and cost significance, which can be expressed in the form of absolute and relative values. The absolute value of an enterprise’s economic activity indicators reflects their quantitative characteristics, presented in units of volume, weight, cost, etc. regardless of other indicators. Accordingly, the analysis of absolute changes in a particular indicator comes down to identifying the deviation of its actual value from the planned, calculated, etc. Unlike absolute relative indicators, they reflect the change in one or another indicator of economic activity in relation to another (other) indicators taken as the basis of comparison. Analysis using relative values allows you to determine the influence of one of the factors of the enterprise’s economic activity on the value of the performance indicator depending on changes in the other (other) factors. For example, the impact on changes in the volume of output of workers' labor productivity (i.e., the change in the products produced by workers in relation to the time required for its production). In practice economic work along with absolute and relative values, average values are often used. They are used to generalize the quantitative characteristics of a set of homogeneous phenomena according to some characteristic. For example, average cost main production assets, average wage workers, etc. Using averages, you can compare different sets of objects, for example, enterprises in terms of wages, countries in terms of living standards, etc. In economic analysis, the following types of averages are most often used: arithmetic averages (simple and weighted) and chronological averages. One of the advantages and at the same time disadvantages of the method is that average values provide a generalized characteristic of a phenomenon, smoothing out the degree of influence of the best and worst components of it.
Grouping method- Grouping is an integral part of almost any economic research. It allows you to study certain economic phenomena in their interrelation and interdependence, identify the influence of the most significant factors, and discover certain patterns and trends inherent in these phenomena and processes. Grouping presupposes a certain classification of phenomena and processes, as well as the causes and factors that determine them. Grouping as a method of analysis can be widely used in concerns, joint stock companies, limited liability partnerships, etc. In this case, the object of study can be both the enterprises themselves and their internal divisions and individual business transactions. Structural groupings are used, as their name implies, when studying the composition of the enterprises themselves, as well as the structure of the products they produce. Analytical groupings are intended to identify the relationship, interdependence and interaction between the phenomena, objects, and indicators being studied. When constructing an analytical grouping of two interrelated indicators, one is considered as a factor influencing the other, and the second as a result of the influence of the first. The general population of objects of the same type or a sample population serves as the information basis for the grouping. In the first case, as a rule, materials from national or regional censuses are used, in the second - a typological sample.
Index method- The index method is based on relative indicators, expressing the ratio of the actual level of the phenomenon being studied to its level in the base period or to the level of a similar phenomenon taken as the base. Any index is calculated by comparing the measured (reported) value with the base one. Indices that express the ratio of directly comparable quantities are called individual (simple). For example, i = p1/q1. Indices that characterize the characteristic under study in relation to other characteristics are called group or aggregate. For example, I = Σp1q1 / Σp0q1. Such an index always consists of two parts: an index feature p, the dynamics of which is studied, and a weight feature q. Using the weight indicator, the dynamics of a complex economic phenomenon, individual elements of which are incommensurable, are measured. Simple and aggregate indexes complement each other.
The most frequently used economic and mathematical methods in economic analysis include the following: the method of correlation and regression analysis, linear programming methods, game theory, matrix analysis methods, dynamic programming methods, etc. Their detailed consideration is beyond the scope of this textbook and is considered as part of the relevant training courses.
Methods of economic analysis- divided into general scientific and specifically scientific. The first are the methods used by all sciences. This:
- observation,
- comparison,
- detailing,
- abstraction,
- modeling,
- experiment.
Analysis and synthesis also belong to general scientific methods. Specifically, scientific methods are formed within the framework of individual sciences; they detail and concretize general scientific methods of cognition.
Comparison
Comparison is the earliest and most common method of analysis. Comparison begins with the relationship between phenomena, i.e. from the synthetic act through which phenomena are analyzed, what is common and different is highlighted in them. The generality found as a result of analysis synthesizes generalizable phenomena.
In economic analysis, the method of comparison is considered one of the most important: the analysis begins with it. There are several forms of comparison:
- with a plan
- with the past
- with the best
- with average data.
An important condition for comparing indicators is comparability. The following is used as a basis for comparison:
- indicators of previous years;
- business planning and regulatory values;
- achievements of science and advanced experience;
- performance levels of closest competitors;
- average indicators of research objects in a territorial context;
- options for management decisions;
- theoretically the maximum possible, potential and predicted indicators.
Educational vertical comparisons, making it possible to study the structure of phenomena and processes and trends in their change.
Interesting multivariate comparisons in analysis, when a wide range of indicators are compared for several objects. Multidimensional comparisons are used for a comprehensive assessment of performance in competitive comparisons to establish financial risks. For such comparisons, special algorithms have been developed and used in practice.
The role of comparisons in economic analysis is determined by the fact that this method allows you to achieve a number of targets, for example, assessing:
- progress in implementing current and future business plans,
- ways to save resources,
- selection of optimal solution options,
- assessment of the degree of business risks.
Average values
Average values are important in economic analysis. Their “analytical power” lies in the generalization of the corresponding array of typical, homogeneous indicators, phenomena, processes:
- they allow one to move from the individual to the general, from the random to the natural;
- without them, it is impossible to compare the studied characteristic across different populations, and it is impossible to characterize changes in a varying indicator over time;
- they make it possible to abstract from the randomness of individual values and fluctuations.
In analytical calculations, the following forms of averages are used, based on necessity:
- arithmetic mean,
- weighted harmonic mean,
- average chronological moment series,
- fashion,
- median.
With the help of average values (group and general), calculated on the basis of mass data on qualitatively homogeneous phenomena, it is possible, as mentioned above, to determine general trends and patterns in the development of economic processes.
Grouping method
Groups systematize the material, identify characteristic and typical relationships between processes, and suppress random deviations. The following types of groupings are used in the analysis:
- typological (for example, grouping organizations by type of ownership);
- structural - to assess the internal structure of indicators (for example, to study personnel by length of service, by profession, etc.);
- analytical groupings - to study the relationship between factor and performance indicators (for example, the dependence of the amount of a loan issued by a bank on the interest rate).
The grouping method is the main one among the ordering methods. It involves dividing the studied set of objects into qualitatively homogeneous groups according to relevant characteristics. In analysis, grouping is used to identify the relationship between individual phenomena in order to study the composition, structure and dynamics of development, and determine average values.
Grouping involves both the classification of phenomena and processes, as well as the causes and factors that determine them. Groupings combine qualitatively homogeneous phenomena that are similar in economic or social nature. Using the grouping method involves the following steps:
- classification of objects, phenomena (processes) selected as a defining feature;
- determination of derived characteristics and their meanings;
- presentation of results in the form of tables;
- identifying the influence of each of the derived characteristics.
A general population of similar objects or a sample population is used as the information basis for grouping. In the first case, systematically accumulated information fund data, in the second - typological samples. Economically sound grouping makes it possible to study the relationship between indicators and systematize analytical data.
Grouping - allows you to study certain economic phenomena in interrelation and interdependence, identify the influence of significant factors, discover certain patterns and trends inherent in these phenomena and processes. Grouping involves the classification of phenomena and processes, as well as the causes and factors that determine them.
Balance sheet method
TO traditional ways processing and verification of source information includes balance sheet. It is also used to measure the influence of additively related factors on a performance indicator. In the additive form of dependence, the generalizing indicator is an algebraic sum of the quotients. Based on the balance sheet method, a method of proportional division, or equity participation, has been developed.
The balance sheet method has found application in the analysis of an organization's provision with labor, material and financial resources and the completeness of their use, in the study of the compliance of means of payment with payment obligations, etc. As a technical technique, the balance sheet method is used to verify the correctness of analytical calculations by compiling a balance of deviations.
Linear programming method
The linear programming method is used to solve experimental problems when searching for the maximum or minimum values of certain functions of variables. The value of using this method is that best option choose from a large number alternative options. It is not possible to solve such problems using other methods. When using the linear programming method you should:
- present solution alternatives in the form of mathematical variables;
- identify constraints and represent them in the form of mathematical expressions;
- solve problems using a graphical or algebraic approach.
Graphic method
The graphical method is widely used to study production processes, organizational structures, programming processes, etc. For example, to analyze the efficiency of using production equipment, calculation graphs are constructed, including graphs of multiple factors.
Network diagrams occupy a special place in mathematical analysis, planning and management. They provide an economic effect during the construction and installation of industrial and other enterprises.
Method of correlation and regression (stochastic) analysis
Correlation analysis sets the task of measuring the closeness of the relationship between varying variables and assessing the factors that have the greatest influence on the resulting characteristic.
Regression analysis is intended to select the form of connection, the type of model, to determine the calculated values of the dependent variable (resultative characteristic).
Methods of correlation and regression analysis are used in combination. Methods of correlation and regression analysis are used in combination. Pairwise correlation is the most developed in theory and used in practice. Here we study the relationship between the effective characteristic and one factor characteristic. This is a one-way correlation and regression analysis.
Game theory
Game theory studies the optimality of strategy in gaming situations. Formalizing conflict situations mathematically, they are represented as a game of two, three, etc. players, each of whom pursues the goal of maximizing their own benefit, winning at the expense of others.
Solving such problems requires certainty in formulating the conditions for establishing the number of players, the rules of the game, identifying possible player strategies, and possible winnings.
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In contrast to the method of economic analysis as a general approach to the study of phenomena, there are methodology economic analysis as a set of special techniques (methods) used to process economic information. The methods of economic analysis are divided into general and specific. General The methodology is a set of methods of analytical work in any sector of the national economy, in any type of economic activity. Private the methodology specifies the general methodology in relation to economic processes occurring in a certain sector of the national economy, to a certain type of production. The degree of specification of private methods may vary.
Traditional and economic-mathematical methods of economic analysis. The most important methods of processing economic information used in economic analysis are statistical methods: summary and grouping; absolute and relative values; average values; dynamics series; indexes; method of chain substitutions; elimination; balance sheet links; selective and continuous observations; comparisons; graphic methods.
The initial basis for economic analysis is accounting and reporting data, the analytical review of which should restore all the main aspects of economic activity and completed transactions in a generalized form, i.e. with the degree of aggregation necessary for analysis.
The practice of analysis has developed the main methods for reading financial statements. Among them are the following standard techniques, which will be discussed in special chapters of the textbook:
- analysis of absolute data;
- horizontal analysis;
- vertical analysis;
- trend analysis;
- method of financial ratios.
In the practice of economic analysis, various quantitative methods are actively used, which are divided into statistical, accounting and economic-mathematical.
Mathematics, as defined by F. Engels, is the science of quantitative relations and spatial forms of the real world. In economic analysis, great importance is attached to mathematical methods, models, formulas, but these methods, models and formulas cannot replace and replace the theoretical analysis of the essence of economic phenomena and processes. As the English naturalist T.G. pointed out. Hekeli, mathematics, like a millstone, grinds the grain that is poured into it, and just as by pouring in quinoa you will not get wheat flour, so by writing whole pages with formulas you will not get truth from false premises.
The penetration of mathematics and computers into economic analysis is an objective process. Economic analysis is being enriched. The mathematical methods used in the analysis of economic activity can be systematized according to various criteria. The most appropriate classification of economic and mathematical methods seems to be according to the content of the method, i.e. belonging to a certain section of modern mathematics (Fig. 13.1).
Economic and mathematical modeling. The application of mathematics in economics takes the form of economic-mathematical modeling. Using an economic-mathematical model, one or another actual economic process is depicted. Such a model can only be constructed on the basis of a deep theoretical study of the economic essence of the process. Only in this case will the mathematical model be adequate to the actual economic process, will objectively reflect it.
Rice. 13.1.
Economic analysis mainly uses mathematical models that describe the phenomenon or process being studied using equations, inequalities, functions and other mathematical tools. There are mathematical models with quantitative characteristics, written in the form of formulas; numerical models with specific numerical characteristics; logical, written using logical expressions, and graphic, expressed in graphic images. Models implemented using computers are called electronic or computer models.
Thus, economic and mathematical modeling of the operation of an enterprise should be based on an analysis of its activities and enrich this analysis with the results and conclusions obtained after solving the relevant problems.
Of particular importance in the analysis of economic activity is the grouping of tasks into balance and factor ones.
Balance problems (methods)- this is an analysis of structure, proportions, relationships (analysis financial situation according to the balance sheet, analysis cash flows, analysis of the balance of material resources, etc.).
Largest specific gravity problems of economic analysis are solved using methods factorial analysis (approximately 90% of tasks fall on factor analysis and only 10% on balance analysis).
Under economic factor analysis refers to the gradual transition from the initial factor model (resultative indicator) to the final factor model (or vice versa), the disclosure of the full set of quantitatively measurable factors influencing the change in the effective indicator.
The construction, or modeling, of the final factor system for the analyzed economic indicator of economic activity can be carried out as formal, so and heuristic through a qualitative analysis of the essence of the economic phenomenon reflected through this effective indicator. Modeling of the factor system is based on the following economic criteria for identifying factors as elements of the factor system: causality, sufficient specificity, independence of existence, accounting possibility. From a formal point of view, the factors included in the factor system must be quantitatively measurable.
IN deterministic modeling factor systems, we can distinguish a small number of types of finite factor systems, most often found in the analysis of economic activity, where X is the sum, P is the product of factors:
Additive Models
Multiplicative models
Multiple models
Where y - effective indicator (initial factor system); x j And Xj- factors (factor indicators).
In relation to the class of deterministic factor systems, the following basic modeling techniques are distinguished.
1. Method of lengthening the factor system. Initial factor system y = a x /a g If A presented as a sum of individual factor terms, then
finite factor system of the form
2. Factor system expansion method. Initial factor system at = a x /a 2. If both the numerator and the denominator of the fraction are “expanded” by multiplying by the same number, we get a new factor system:
those. multiplicative model of the form
3. Factor system reduction method. Initial factor system y = a x /a 2. If we divide both the numerator and the denominator of the fraction by the same number, we get a new factor system (in this case, of course, the rules for selecting factors must be followed):
In this case we have a finite factor system of the form Y = x x / x 2.
Thus, the complex process of forming the level of the studied indicator of economic activity can be decomposed using various techniques into components (factors) and presented in the form of a model of a deterministic factor system.
The basis of deterministic modeling of a factor system is the possibility of constructing an identical transformation for the original formula of an economic indicator based on the theoretically assumed direct connections of the latter with others indicators-factors. Deterministic modeling of factor systems is a simple and effective means of formalizing the relationship of economic indicators; it serves as the basis for quantitative assessment of the role of individual factors in the dynamics of changes in the general indicator.
Deterministic modeling of factor systems is limited by the length of the factor field of direct connections. With an insufficient level of knowledge about the nature of direct connections of a particular indicator of economic activity, a different approach to understanding objective reality is often necessary. The scope of quantitative changes in economic indicators can only be determined stochastic modeling methods massive empirical data.
Stochastic analysis is aimed at studying indirect relationships, i.e. indirect factors (if it is impossible to determine a continuous chain of direct communication). From this follows an important conclusion about the relationship between deterministic and stochastic analysis: since direct connections must be studied first, stochastic analysis is of an auxiliary nature. Stochastic analysis acts as a tool for deepening the deterministic analysis of factors for which it is impossible to build a deterministic model.
Correlation and regression analysis - classic method stochastic modeling of economic activity. He studies the relationships between indicators of economic activity when the relationship between them is not strictly functional and is distorted by the influence of extraneous, random factors. When conducting correlation and regression analysis, various correlation and regression models of economic activity are built. In these models, factor and performance indicators (traits) are distinguished. Depending on the number of indicators studied, there are doubles And multifactor models correlation and regression analysis.
The main task of correlation and regression analysis is to clarify the form and closeness of the relationship between the effective and factor indicators. The form of connection is understood as the type of analytical formula that expresses the dependence of the effective indicator on changes in the factor indicator. There is a direct connection when, with an increase (decrease) in the values of the factor indicator, there is a tendency for an increase (decrease) in the values of the effective indicator. Otherwise, there is an inverse relationship between the indicators. The form of the connection can be rectilinear (it corresponds to the equation of a straight line), when there is a tendency for a uniform increase or decrease in the effective indicator, otherwise the form of the connection is called curvilinear (it corresponds to the equation of a parabola, hyperbola, etc.).
Basic models of correlation analysis: pair correlation coefficient, partial correlation coefficient, multiple correlation coefficient, determination coefficient.
Modern factor analysis- a direction of multivariate statistical analysis that allows us to identify internal, directly unmeasurable variables (factors) between correlating indicators of economic activity. There are two main methods of modern factor analysis: principal component method And classical factor analysis.
The mathematical apparatus for solving stochastic modeling problems is described in sufficient detail in textbooks on statistical theory.
Methods of deterministic factor analysis. In the analysis of economic activity, which is sometimes called accounting, methods of deterministic modeling of factor systems predominate, which provide an accurate (and not with some probability characteristic of stochastic modeling) balanced description of the influence of factors on changes in the performance indicator. But this balance is achieved by different methods. Let's consider the main methods of deterministic factor analysis.
Differential calculus method is theoretical basis for quantitative assessment of the role of individual factors in the dynamics of the resulting (generalizing) indicator.
The differential calculus method is based on the total differential formula. For a function of two variables z=/(x, U) we have the full increment of the function Az:
Where Ah, oh- factor increments of the corresponding variables; - partial derivatives; -
an infinitesimal quantity of a higher order than . This value is discarded in calculations (it is often denoted as e).
Thus, the influence of the factor X to the general indicator is determined by the formula
and the influence of the factor y - according to the formula
In the method of differential calculus, it is assumed that the total increment of functions (resulting indicator) is decomposed into terms, and the value of each of them is determined as the product of the corresponding flexible derivative and the increment of the variable (factor) by which this derivative is calculated. In this method, the so-called irreducible remainder, which is interpreted as a logical error in the differentiation method, is simply discarded. This is the “inconvenience” of differentiation for economic (especially accounting) calculations, in which, as a rule, an exact balance of changes in the effective indicator and the algebraic sum of the influence of all factors is required.
Index method for determining the influence of factors on a general indicator used in statistics, planning and analysis of economic activities as a basis for quantitative assessment of the role of individual factors in the dynamics of changes in general indicators.
Thus, when studying the dependence of the volume of output at an enterprise on changes in the number of employees and their labor productivity, you can use the following system of interrelated indices:
![](https://i1.wp.com/studref.com/htm/img/6/6593/78.png)
Where I N - general index of changes in product sales volume; I I- individual (factorial) index of changes in the number of employees; /* - factor index of changes in labor productivity of workers; R Q , R ( - average annual number of personnel in the base and reporting periods, respectively; A, 0, - average annual product sales per
one employee, respectively, in the base and reporting periods.
The above formulas show that the overall relative change in production volume is formed as the product of relative changes in two factors - the number of workers and their labor productivity. The formulas reflect the practice accepted in statistics for constructing factor indices, the essence of which can be formulated as follows.
If a general economic indicator is the product of a quantitative (volumetric) and qualitative indicators-factors, then when determining the influence of a quantitative factor qualitative indicator is fixed at the basic level, and when determining the influence of a qualitative factor, the quantitative indicator is fixed at the level of the reporting period.
The index method makes it possible to decompose into factors not only relative, but also absolute deviations of the generalizing indicator.
In our example, formula (13.1) allows us to calculate the absolute deviation (increase) of the general indicator - sales volume of the enterprise’s products:
Where AN- absolute increase in product sales in the analyzed period.
This deviation was formed under the influence of changes in the number of workers and their labor productivity. In order to determine what part of the total change in product sales volume was achieved due to changes in each of the factors separately, it is necessary to eliminate the influence of the other factor when calculating the influence of one of them.
Formula (13.2) corresponds to this condition: in the first factor the influence of labor productivity is eliminated, in the second - the number of employees. Consequently, the increase in production volume due to a change in the number of employees is defined as the difference between the numerator and denominator of the first factor:
The increase in output due to changes in labor productivity of workers is determined similarly using the second factor:
This principle of decomposing the absolute increase (deviation) of a generalizing indicator into factors is suitable for the case when the number of factors is equal to two (one of them is quantitative, the other is qualitative), and the analyzed indicator is presented as their product.
Index theory does not provide a general method for decomposing the absolute deviations of a generalizing indicator into factors if there are more than two factors and if their relationship is not multiplicative.
Chain substitution method consists in obtaining a number of intermediate values of a generalizing indicator by sequentially replacing the basic values of factors with actual ones. The difference between two intermediate values of a generalizing indicator in a chain of substitutions is equal to the change in the generalizing indicator caused by a change in the corresponding factor.
IN general view We have the following calculation system using the chain substitution method:
The total absolute deviation of the generalizing indicator is determined by the formula
The general deviation of the generalizing indicator is decomposed into factors:
By changing the factor A:
By changing the factor b:
The chain substitution method, like the index method, has disadvantages. Firstly, the calculation results depend on the sequence of factor replacement; secondly, the active role in changing the general indicator is unreasonably often attributed to the influence of changes in the qualitative factor.
For example, if the indicator under study z has the form of a function Z=/(x, y) = hu, then its change over the period At = t l - t Q expressed by the formula
Where Az- increment of the general indicator; Ah, Au - factor increment; x 0, y 0- basic values of factors; /0, t ( - respectively basic and reporting periods time.
By grouping the last term in this formula with one of the first, we obtain two different variants of chain substitutions:
first option
second option
In practice, the first option is usually used, provided that X - quantitative factor, and y - qualitative.
This formula reveals the influence of the qualitative factor on the change in the general indicator, i.e. the expression (x 0 + Dx)Dy is more active, since its value is established by multiplying the increment of the qualitative factor by the reported value of the quantitative factor. Thus, the entire increase in the general indicator due to the joint change in factors (e) is attributed to the influence of only the qualitative factor. Thus, the task precise definition The role of each factor in changing the general indicator is not resolved by the usual method of chain substitutions.
Integral method of factor analysis is based on the summation of increments of a function, defined as the partial derivative multiplied by the increment of the argument on infinitesimal intervals.
The integral method gives the most general approach to solving problems of factor analysis to decompose the total increase in an indicator into factor increments. The basis of the integral method is the Euler-Lagrange integral, which establishes the connection between the increment of a function and the increment of factor characteristics. For the function g =/(x, y) we have following formulas calculation of factor influences:
by differentiation method
- factor influence X,
where /" is the partial derivative function with respect to X;
-
factor influence y,
where /" is the partial derivative function with respect to y;
according to the integral method
- influence of factor x;
- factor influence u.
The integral method gives accurate estimates of factor influences. The calculation results do not depend on the sequence of substitutions and the sequence of calculation of factor influences. The method is applicable for all types of continuously differentiable functions; does not require prior knowledge of which factors are quantitative and which are qualitative.
To apply the integral method, knowledge of the basics of differential calculus, integration techniques, and the ability to find derivatives of various functions are required. At the same time, in the theory of business analysis, for practical applications, final working formulas of the integral method have been developed for the most common types of factor dependencies, which makes this method accessible to every analyst. Let's list some of them.
1. Factor model type
2. Factor model type
3. Factor model type
4. Factor model type
In Fig. 13.2 shows an example of using the main methods of factor analysis based on enterprise indicators for two years (see Appendix 4, to the data of which we add: the number of personnel in the 1st year - 381 people, in the 2nd year - 382 people). A two-factor multiplicative model is considered N = RxX, Where N- sales of products; R- production personnel; X- labor productivity. First year sales amounted to N 0 = R Q x X 0, those. 79,700 thousand rubles. = 381 x 209 186. Sale of the second year - accordingly, N l =R l xX v those. 83,610 thousand rubles. = 382 x 218,874. The deviation of the sales of the second year from the first year was A N= TV, - 7V 0, i.e. 3910 thousand rubles. = 83,610 - 79,700. The task is to decompose this deviation depending on the influence of the two factors under consideration. The diagram and calculations of the main methods of economic factor analysis are given below.
Rectangle A in the diagram means first year products (N q = R q X 0 = 79,700 thousand rubles); large rectangle IN - second year products ( N j = R ] X ] = 83,610 thousand rubles); rectangle C - increase in production due to the number of personnel factor, calculated by the method of differential calculus (AN R = AR Q = = 209.2 thousand rubles); rectangle D- increase in production due to the labor productivity factor, also calculated by the differential calculus method (AN X = AXR 0 = 3691.1 thousand rubles),
![](https://i0.wp.com/studref.com/htm/img/6/6593/101.png)
Rice. 13.2. Illustration of factor analysis methods rectangle E - g, those. infinitesimal value upon differentiation (e = ARAX = 9.7 thousand rubles). Thus, the production of the second year exceeds the production of the first year by three amounts: B-A = C + D + E, a B = A + C+D + E.
The method of differential calculus decomposes the increase in production into three elements: AN = C + D + E. The index method decomposes the increase in production into two elements: AN = (D + E) + C. The method of chain substitutions decomposes the increase in production into two elements, but when considering a two-factor multiplicative model, two calculation options are possible: AN = (D + E) + C or AN = D + (C + E) - depending on the order of substitutions. When considering a three-factor function, six possible results are already possible, etc. (those. P outcome options). The integral method always gives an unambiguous result, in in this example AN=(C + E/2) + (D + E/2).
- See Sheremet A.D. Theory of economic analysis: Textbook. - 3rd ed. - M.: INFRA-M, 2009. P. 28-34.
- For a brief description of the methods, see Sheremet A.D. Theory of economic analysis: Textbook. - 3rd ed. - M.: INFRA-M, 2009. P. 38-41.
- See: Sheremet A.D. Theory of economic analysis: Textbook. 2nd ed., additional M.: INFRA-M, 2005. P. 316-326.
TO economic methods analysis includes comparison, grouping, balance sheet and graphical methods.
Statistical methods include the use of averages and relative values, the index method, correlation and regression analysis, etc.
Mathematical methods can be divided into three groups:
- - economic (matrix methods, theory of production functions, theory of input-output balance);
- - methods of economic cybernetics and optimal programming (linear, nonlinear, dynamic programming);
- - methods of operations research and decision making (graph theory, game theory, queuing theory).
Characteristics of the basic techniques and methods of economic analysis
Comparison is a comparison of the data being studied and the facts of economic life. There are:
- - horizontal comparative analysis, which is used to determine absolute and relative deviations of the actual level of the studied indicators from the base;
- - vertical comparative analysis used to study the structure of economic phenomena;
- - trend analysis used in studying the relative rates of growth and increase in indicators over a number of years to the level of the base year, i.e. when studying time series.
Average values are calculated on the basis of mass data on qualitatively homogeneous phenomena. They help determine general patterns and trends in the development of economic processes.
Groupings - are used to study dependencies in complex phenomena, the characteristics of which are reflected by homogeneous indicators and different values (characteristics of the equipment fleet by commissioning time, by place of operation, by shift ratio, etc.)
The balance method consists of comparing and measuring two sets of indicators tending to a certain balance. It allows us to identify a new analytical (balancing) indicator as a result.
When applied to the object of study, the method of economic analysis has a number of characteristic features, namely:
- 1) The system of economic indicators is studied, with the help of which a quantitative assessment of individual aspects of the economic activity of an enterprise is given. Each economic phenomenon or process is described, as a rule, not by one indicator, but by a set of economic indicators. The results of the analysis depend on how fully and accurately the indicators reflect the essence of the phenomena being studied.
- 2) The system of indicators is studied in their relationship, interdependence, and interdependence. Studying the relationship requires identifying the subordination of indicators, identifying the aggregate, effective indicator and the factors influencing it.
- 3) A quantitative measurement of the influence of factors on the aggregate indicator is made using a number of special methods and techniques.
This makes the analysis accurate and its conclusions justified.
Thus, a precondition, a prerequisite for correct analysis is an economically sound classification of the causes affecting economic activity and its results. One of the characteristic principles of the analysis method is the need to make constant comparisons, which are widely used in the analysis of the actual results of economic activity with indicators of past periods of time, with plan indicators and the results of achievements of other enterprises, etc.
Economic analysis methods:
Graphic method. Graphs are a large-scale representation of indicators and their relationships using geometric shapes. The graphical method has no independent significance in the analysis, but is used to illustrate measurements.
The index method is based on relative indicators expressing the ratio of the level this phenomenon to its level taken as a basis of comparison. Statistics names several types of indices that are used in analysis: aggregate, arithmetic, harmonic, etc. By using index recalculations and constructing a time series characterizing, for example, the output of industrial products in value terms, it is possible to skillfully analyze dynamic phenomena.
The method of correlation and regression (stochastic) analysis is widely used to determine the closeness of the relationship between indicators that are not functionally dependent, i.e. the connection is not manifested in each individual case, but in a certain dependence. With the help of correlation, two main problems are solved:
- - a model of operating factors is compiled (regression equation);
- - a quantitative assessment of the closeness of connections is given (correlation coefficient). economic correlation regression
Matrix models are a schematic representation of an economic phenomenon or process using scientific abstraction. The most widely used method here is the “input-output” analysis, which is built according to a checkerboard pattern and makes it possible to present the relationship between costs and production results in the most compact form.
Mathematical programming is the main means of solving problems to optimize production and economic activities.
The operations research method aims to study economic systems, including the production and economic activities of enterprises, in order to determine such a combination of structural interconnected elements of systems that will best allow us to determine the best economic indicator from a number of possible ones.
Game theory, as a branch of operations research, is the theory of mathematical models for making optimal decisions under conditions of uncertainty or conflict of several parties with different interests. In this case, general methods of cognition are used: induction and deduction.
Induction provides the possibility of moving from single facts to general provisions, i.e. research from specific to general. In real knowledge, it is inextricably linked with deduction, i.e. the process of cognition in the direction from the general to the specific.
The use of a systems approach in the analysis determines the detailing of the studied phenomena and processes into parts, as well as their systematization and generalization.
Detailing is used to identify the main, most significant in the object of study, and is determined by the given object and the purpose of the study. analysis. Based on the relationship, interdependence and interaction, the elements of phenomena and processes are systematized, which makes it possible to determine an approximate model of the object under study and identify its main elements and functions.
As a result of studying all sides economic activity enterprises need to summarize all the information received by using the “synthesis” (generalization) method.
Concept of economic analysis
Definition 1
Economic analysis is understood as one of the methods of understanding the financial and economic processes of an economic entity, based on dividing it as a whole into its constituent elements and studying each of these elements separately and in relation to each other.
In the course of economic analysis, analytical methods are used to study various financial and economic documents in order to identify significant connections and patterns in them in order to transform economic indicators into analytical information.
Comprehensive economic analysis as an element of the management system as a whole is used as:
- Options for constructing forecasts and plans during the assessment of an investment project
- One of the forecasting tools
- Ways to identify problems in production management and reserves for eliminating them
- A method for assessing the overall financial condition of a company
Types of economic analysis of an enterprise
Note 1
To ensure the most complete and effective application of economic analysis, one should properly know its types, the content of these types and the features of their application.
According to the period of coverage, the analysis is distinguished:
- Operational in nature (used for operational and short-term management)
- Current nature (applied currently and for the medium term)
- Forward-looking (aimed at long-term planning and management)
Depending on the nature and scale of application, the analysis is distinguished:
- On-farm (the activities of a specific enterprise, production site, workshop are analyzed)
- Sectoral (a sector of the national economy is analyzed, for example, food or textile)
- Intersectoral (analysis of enterprises in different industries, but geographically located within the same territory)
- National economic (complete analysis of the country's economy as a whole)
In addition, the economic analysis itself includes the following subsystems:
Note 2
So, economic analysis itself and its subsystem - financial analysis - serve as an integral element economic management and planning at the enterprise. Users of economic information at any level apply analysis methods in the process of making and optimizing management decisions.
Methods in economic analysis
The method of economic analysis is a method, an approach to the study of a particular indicator or process, one might say a specific point of view. Among the methods of economic analysis, the following categories are distinguished:
- Classic methods
- Factor analysis
- Economic-mathematical method
- Methods using graphs
Classical methods of economic analysis involve the use of methods:
- Absolute differences
- Relative values
- Comparison
- Grouping indicators
- Analytical tables
Such methods make it possible to produce quite accurately necessary calculations, identify the dependence of indicators on each other.
Factor analysis methods include:
- Index
- Elimination
- Balance sheet method
The essence of factor methods is to assess the impact of a change in one factor on the financial performance of an enterprise.
Economic and mathematical methods involve the use of:
- Correlation and Regression Analysis
- Cluster analysis
- Econometrics
- Mathematical programming
- Wilson model
The peculiarity of economic-mathematical methods is that they allow one to identify the essential factors influencing the economic result of an activity, while discarding details and values that are not essential for the analysis.
Graphical methods allow you to visually depict the analyzed data on graphs through geometric shapes, lines and points. Usually the most visual types of graphs are used - these are diagrams and cartograms. In charts, data is represented by geometric shapes and lines, and in cartograms - columns, sectors, and curly diagrams.
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