Factor analysis factor analysis. Factor analysis: an example of composition and its features

All phenomena and processes of economic activity of enterprises are interconnected and interdependent. Some of them are directly related to each other, others indirectly. Hence, an important methodological issue in economic analysis is the study and measurement of the influence of factors on the value of the studied economic indicators.

Under economic factor analysis is understood as a gradual transition from the initial factor system to the final factor system, the disclosure of a full set of direct, quantitatively measurable factors that influence the change in the performance indicator.

Based on the nature of the relationship between indicators, methods of deterministic and stochastic factor analysis are distinguished.

Deterministic factor analysis is a methodology for studying the influence of factors whose connection with the performance indicator is functional in nature.

The main properties of the deterministic approach to analysis:

building a deterministic model through logical analysis;

the presence of a complete (hard) connection between indicators;

the impossibility of separating the results of the influence of simultaneously acting factors that cannot be combined in one model;

studying relationships in the short term.

There are four types of deterministic models:

Additive Models represent an algebraic sum of indicators and have the form

Such models, for example, include cost indicators in relation to elements of production costs and cost items; an indicator of the volume of production in its relationship with the volume of output of individual products or the volume of output in individual departments.

Multiplicative models in generalized form can be represented by the formula

An example of a multiplicative model is a two-factor model of sales volume

Where H - average number workers;

C.B.- average output per employee.

Multiple models:

An example of a multiple model is the indicator of the turnover period of goods (in days). T O.T. :

Where Z T- average stock of goods; ABOUT R- one-day sales volume.

Mixed models are a combination of the above models and can be described using special expressions:

Examples of such models are cost indicators per 1 ruble. commercial products, profitability indicators, etc.

To study the relationship between indicators and quantitatively measure the many factors that influenced the effective indicator, we present general model transformation rules in order to include new factor indicators.

To detail the generalizing factor indicator into its components, which are of interest for analytical calculations, the technique of lengthening the factor system is used.

If the original factor model is , a , then the model will take the form .

To identify a certain number of new factors and construct the factor indicators necessary for calculations, the technique of expanding factor models is used. In this case, the numerator and denominator are multiplied by the same number:

To construct new factor indicators, the technique of reducing factor models is used. When using this technique, the numerator and denominator are divided by the same number.

The detail of factor analysis is largely determined by the number of factors whose influence can be quantitatively assessed, therefore multifactorial multiplicative models are of great importance in the analysis. Their construction is based on the following principles:

the place of each factor in the model must correspond to its role in the formation of the effective indicator;

the model should be built from a two-factor full model by sequentially dividing factors, usually qualitative, into components;

When writing a formula for a multifactor model, factors should be arranged from left to right in the order in which they are replaced.

Building a factor model is the first stage of deterministic analysis. Next, determine the method for assessing the influence of factors.

Chain substitution method consists in determining a number of intermediate values of the generalizing indicator by sequentially replacing the basic values of the factors with the reporting ones. This method based on elimination. Eliminate- means to eliminate, exclude the influence of all factors on the value of the effective indicator, except one. Moreover, based on the fact that all factors change independently of each other, i.e. First, one factor changes, and all the others remain unchanged. then two change while the others remain unchanged, etc.

In general, the application of the chain production method can be described as follows:

where a 0, b 0, c 0 are the basic values of factors influencing the general indicator y;

a 1, b 1, c 1 - actual values of factors;

y a, y b, are intermediate changes in the resulting indicator associated with changes in factors a, b, respectively.

The total change ∆ y=y 1 –y 0 consists of the sum of changes in the resulting indicator due to changes in each factor with fixed values of the remaining factors:

Let's look at an example:

Table 2 – Initial data for factor analysis

Indicators	Legend	Basic values	Actual values	Change
Indicators	Legend	Basic values	Actual values	Absolute (+,-)	Relative (%)
Volume of commercial products, thousand rubles.
Number of employees, people
Output per worker, thousand rubles

We will analyze the impact of the number of workers and their output on the volume of marketable output using the method described above based on the data in Table 2. The dependence of the volume of commercial products on these factors can be described using a multiplicative model:

Then the effect of a change in the number of employees on the general indicator can be calculated using the formula:

Thus, the change in the volume of marketable products was positively influenced by a change in the number of employees by 5 people, which caused an increase in production volume by 730 thousand rubles. and a negative impact was had by a decrease in output by 10 thousand rubles, which caused a decrease in volume by 250 thousand rubles. The combined influence of two factors led to an increase in production volume by 480 thousand rubles.

The advantages of this method: versatility of application, ease of calculations.

The disadvantage of the method is that, depending on the chosen order of factor replacement, the results of factor decomposition have different meanings. This is due to the fact that as a result of applying this method, a certain indecomposable residue is formed, which is added to the magnitude of the influence of the last factor. In practice, the accuracy of factor assessment is neglected, highlighting the relative importance of the influence of one or another factor. However, there are certain rules that determine the substitution sequence:

if there are quantitative and qualitative indicators in the factor model, the change in quantitative factors is considered first;

if the model is represented by several quantitative and qualitative indicators, the substitution sequence is determined by logical analysis.

Under quantitative factors in analysis they understand those that express the quantitative certainty of phenomena and can be obtained by direct accounting (number of workers, machines, raw materials, etc.).

Qualitative factors determine the internal qualities, signs and characteristics of the phenomena being studied (labor productivity, product quality, average working hours, etc.).

Way absolute differences is a modification of the chain substitution method. The change in the effective indicator due to each factor using the method of differences is defined as the product of the deviation of the factor being studied by the basic or reporting value of another factor, depending on the selected substitution sequence:

Relative difference method used to measure the influence of factors on the growth of a performance indicator in multiplicative and mixed models of the form y = (a – c) . With. It is used in cases where the source data contains previously determined relative deviations of factor indicators in percentages.

For multiplicative models like y = a . V . The analysis technique is as follows:

find relative deviation each factor indicator:

determine the deviation of the performance indicator at due to each factor

Example. Using the data in table. 2, we will analyze using the method of relative differences. The relative deviations of the factors under consideration will be:

Let's calculate the impact of each factor on the volume of commercial output:

The calculation results are the same as when using the previous method.

Integral method allows you to avoid the disadvantages inherent in the chain substitution method, and does not require the use of techniques for distributing the indecomposable remainder among factors, because it has a logarithmic law of redistribution of factor loads. The integral method makes it possible to achieve a complete decomposition of the effective indicator into factors and is universal in nature, i.e. applicable to multiplicative, multiple and mixed models. The operation of calculating a definite integral is solved using a PC and is reduced to constructing integrand expressions that depend on the type of function or model of the factor system.

You can also use already formed working formulas given in the specialized literature ∆ 4∆:

1. Model view:

2. View model :

3. View model:

4. View model:

Let's consider the possibility of using the main methods of deterministic analysis, summarizing the above in the form of a matrix (Table 3).

Table 3 – Matrix of application of deterministic factor analysis methods

	Multiplicative	Additive	Mixed

Chain substitution
Absolute differences
Relative differences
Integral

Questions for self-control

What management problems are solved through economic analysis?

Describe the subject of economic analysis.

Which distinctive features characterize the method of economic analysis?

What principles underlie the classification of techniques and methods of analysis?

What role does the method of comparison play in economic analysis?

Explain how to construct deterministic factor models.

Describe the algorithm for using the simplest methods of deterministic factor analysis: the method of chain substitutions, the method of differences.

Describe the advantages and describe the algorithm for using the integral method.

Give examples of problems and factor models to which each of the methods of deterministic factor analysis is applied.

Factor analysis profit allows you to evaluate the impact of each factor separately on the financial result as a whole. Read how to do it, and also download the methodology.

The essence of factor analysis

The essence of the factorial method is to determine the influence of each factor separately on the result as a whole. This is quite difficult to do, since the factors influence each other, and if the factor is not quantitative (for example, service), then its weight is assessed by experts, which leaves the imprint of subjectivity on the entire analysis. In addition, when there are too many factors influencing the result, the data cannot be processed and calculated without special mathematical modeling programs.

One of the most important financial indicators of an enterprise is profit. As part of factor analysis, it is better to analyze marginal profit, where there are no fixed costs, or profit from sales.

Factor analysis by chain substitution method

In factor analysis, economists usually use the chain substitution method, but mathematically this method is incorrect and produces highly skewed results that vary significantly depending on which variables are substituted first and which ones later (for example, in Table 1).

Table 1. Analysis of revenue depending on the price and quantity of products sold

	Base year		Current year		Revenue growth
		Revenue B 0		Revenue B 0	Due to prices In p	Due to quantity In q
Option 1					P 1 Q 0 -P 0 Q 0	P 1 Q 1 -P 1 Q 0	B 1 -B 0
Option 1
Option 2					P 1 Q 1 -P 0 Q 1	P 0 Q 1 -P 0 Q 0	B 1 -B 0
Option 2

In the first option, revenue due to price increased by 500 rubles, and in the second by 600 rubles; revenue due to quantity in the first increased by 300 rubles, and in the second by only 200 rubles. Thus, the results vary significantly depending on the order of substitution. .

It is possible to more correctly distribute the factors influencing the final result depending on the markup (Nat) and the number of sales (Kol) (see Figure 1).

Figure 1

Formula for profit growth due to markup: P nat = ∆ Nat * (Count (current) + Quantity (base)) / 2

Formula for profit growth due to quantity: P count = ∆ Quantity * (Nat (current) + Nat (base)) / 2

Example of two-factor analysis

Let's look at an example in Table 2.

Table 2. Example of two-factor revenue analysis

	Base year		Current year		Revenue growth
		Revenue B 0		Revenue B 0	Due to markup In p	quantities In q
					∆ P(Q 1 +Q 0)/2	∆Q(P 1 +P 0)/2	B 1 -B 0
Product "A"

The results were averaged values between the variants of chain substitutions (see Table 1).

Excel model for factor analysis of revenue

Download the finished model in Excel, it will calculate how revenue changed in the reporting period compared to the previous period or plan. The model will help you evaluate how sales volume, price and sales structure affected revenue.

Three-factor model for profit analysis

The three-factor model is much more complex than the two-factor model (Figure 2).

Figure 2

The formula that determines the influence of each factor in a 3-factor model (for example, markup, quantity, nomenclature) on overall result similar to the two-factor formula, but more complicated.

P nat = ∆Nat * ((Kol (tek) * Nom (tek) + Kol (base) * Nom (base)) / 2 - ∆Kol * ∆Nom / 6)

P count = ∆Kol * ((Nat (tek) * Nom (tek) + Nat (base) * Nom (base)) / 2 - ∆Nat * ∆Nom / 6)

P nom = ∆Nom * ((Nat (tek) * Kol (tek) + Nat (base) * Kol (base)) / 2 - ∆Nat * ∆Kol / 6)

Analysis example

In the table we have given an example of using a three-factor model.

Table 3. An example of calculating revenue using a three-factor model

Last year	Current year	Revenue factors
				Nomenclature
		∆ Q((N 1 P 1 + N 0 P 0) / 2 - - ∆ N ∆ P/6)	∆ P((N 1 Q 1 + N 0 Q 0) / 2 - - ∆ N ∆ Q/6)	∆ N ((Q 1 P 1 + Q 0 P 0) / 2 - - ∆ Q ∆ P/6)

If you look at the results of revenue analysis using the factor method, the largest increase in revenue occurred due to price increases. Prices increased by (15 / 10 - 1) * 100% = 50%, the next most important was the increase in product range from 3 to 4 units - growth rate (4 / 3 - 1) * 100% = 33% and in last place " quantity”, which increased by only (120/100-1)*100% = 20%. Thus, factors affect profits in proportion to the growth rate.

Four-factor model

Unfortunately, for a function of the form Pr = Kol av * Nom * (Price - Ceb), there are no simple formulas for calculating the influence of each individual factor on the indicator.

Pr – profit;

Kol av – average quantity per unit of item;

Nom – number of nomenclature items;

Price – price;

There is a calculation method based on Lagrange's finite increment theorem, using differential and integral calculus, but it is so complex and time-consuming that it is practically not applicable in real life.

Therefore, to isolate each individual factor, more general factors are first calculated using the usual two-factor model, and then their components are calculated in the same way.

General profit formula: Pr = Quantity * Nat (Nat – markup on unit of production). Accordingly, we determine the influence of two factors: quantity and markup. In turn, the quantity of products sold depends on the item and the number of sales per unit of item on average.

We get Kol = Kol avg * Nom. And the markup depends on the price and cost, i.e. Nat = Price – Seb. In turn, the impact of cost on changes in profit depends on the quantity of products sold and on changes in cost itself.

Thus, we need to separately determine the influence of 4 factors on the change in profit: Quantity, Price, Seb, Nom, using 4 equations:

Pr = Col * Nat
Kol = Kol avg * Nom
Cost = Qty * Seb.
Vyr = Quantity * Price

Example of analysis using a four-factor model

Let's look at this with an example. Initial data and calculations in the table

Table 4. An example of profit analysis using a 4-factor model

Last year
		Col (wed) Q (avg 0)				Profit P 0
						Q 0 *(P 0 -C 0)




			∑Q 0 P 0 / ∑Q 0	∑Q 0 P 0 / ∑Q 0

Current year
		Col (wed) Q (avg 1)
						Q 1 *(P 1 -C 1)



Totals and weighted averages
			∑Q 1 P 1 /∑Q 1	∑Q 1 P 1 /∑Q 1

Influence of the factor on the change in profit
Nome N∆	Number Q ∆	Col (wed) Q (avg)∆	Prices P∆		Nat N ∆
∆N * (Q (avg 0) +Q (avg 1)) / 2 * (H 1 + H 0) / 2	∆Q*(H 1 + H 0) / 2	∆Q (avg) * (N 1 + N 0) / 2 * (H 1 + H 0) / 2	∆P * (Q 1 + Q 0) / 2	∆C * (Q 1 + Q 0) / 2	∆H * (Q 1 +Q 0)/2



Totals and weighted averages

Note: numbers in Excel spreadsheet may differ by several units from what is given in the text description, because in the table they are rounded to tenths.

1. First, using the two-factor model (described at the very beginning), we decompose the change in profit into a quantitative factor and a markup factor. These are first order factors.

Pr = Col * Nat

Column ∆ = ∆Q * (H 1 + H 0) / 2 = (220 - 180) * (3.9 + 4.7) / 2 = 172

Nat ∆ = ∆H * (Q 1 + Q 0) / 2 = (4.7 - 3.9) * (220 + 180) / 2 = 168

Check: ∆R = Col ∆ + Nat ∆ = 172+168 = 340

2. We calculate the dependence on the cost parameter. To do this, we decompose costs into quantity and cost using the same formula, but with a minus sign, since cost reduces profit.

Cost = Count * Seb

Seb∆ = - ∆С*(Q1+Q0) / 2 = -(7.2 - 6.4) * (180 + 220) / 2 = -147

3. We calculate the dependence on price. To do this, we decompose revenue into quantity and price using the same formula.

Exp = Quantity*Price

Price∆ = ∆P * (Q1 + Q0) / 2 = (11.9 - 10.3) * (220 + 180) / 2 = 315

Check: Nat∆ = Price∆ - Seb∆ = 315 - 147 = 168

4. We calculate the impact of the product on profit. To do this, we decompose the quantity of products sold into the number of units in the assortment and the average quantity per one unit of the product range. This way we will determine the ratio of the quantity factor and the nomenclature in physical terms. After this, we multiply the obtained data by the average annual markup and convert it into rubles.

Quantity = Nom * Quantity (avg)

Nom ∆ = ∆N * (Q (avg 0) + Q (avg 1)) / 2 * (H 1 + H 0) / 2 = (3 - 2) (73 + 90) / 2 * (4.7 + 3.9) = 352

Col (avg) = ∆Q (avg) *(N 1 + N 0) / 2 * (H 1 + H 0) / 2 = (73 - 90) * (2 + 3) / 2 * (4.7 + 3.9) = -180

Check: Quantity ∆ = Nom ∆ + Quantity (avg) = 352-180 = 172

The above four-factor analysis showed that profit increased compared to last year due to:

price increases by 315 thousand rubles;
changes in nomenclature by 352 thousand rubles.

And decreased due to:

increase in cost by 147 thousand rubles;
a drop in sales by 180 thousand rubles.

It would seem like a paradox: the total number of units sold this year compared to the previous year increased by 40 units, but at the same time the quantity factor shows negative result. This is because sales growth occurred due to an increase in product units. If last year there were only 2 of them, then this year one more has been added. At the same time, in terms of quantity, product “B” was sold by 20 units in the reporting year. less than the previous one.

This suggests that product “C”, introduced in the new year, partially replaced product “B”, but attracted new buyers that product “B” did not have. If next year product “B” continues to lose its position, then it can be removed from the assortment.

As for prices, their increase by (11.9/10.3 – 1)*100% = 15.5% did not greatly affect sales in general. Judging by product “A”, which was not affected by structural changes in the assortment, then its sales increased by 20%, despite a price increase of 33%. This means that price increases are not critical for the company.

Everything is clear about the cost: it has increased and profits have decreased.

Factor analysis of sales profit

Evgeniy Shagin, Financial Director of Management Company "RusCherMet"

To conduct factor analysis, you must:

choose the basis for analysis - sales revenue, profit;
select factors whose influence needs to be assessed. Depending on the chosen analysis base, they can be: sales volume, cost, operating expenses, non-operating income, interest on loans, taxes;
evaluate the influence of each factor on the final indicator. In the basic calculation for the previous period, substitute the value of the selected factor from the reporting period and adjust the final indicator taking into account these changes;
determine the influence of the factor. Subtract its actual value for the previous period from the resulting intermediate value of the estimated indicator. If the number is positive, the change in the factor had a positive impact; if the number is negative, it has a negative impact.

Example of factor analysis of sales profit

Let's look at an example. In the financial results report of the Alpha company for the previous period, we will substitute the sales volume for the current period (RUB 571,513,512 instead of RUB 488,473,087), all other indicators will remain the same (see Table 5). As a result, net profit increased by RUB 83,040,425. (RUB 116,049,828 – RUB 33,009,403). This means that if in the previous period the company had managed to sell products for the same amount as in this period, then its net profit would have increased by exactly these 83,040,425 rubles.

Table 5. Factor analysis of profit by sales volume

Indicator	Previous period, rub.
Indicator		with substitution values factor from current period
Sales volume

Gross profit
Operating expenses

Operating profit
Interest on loan
Profit before tax

Net profit
1 Sales volume for the current period. 2 The indicator has been recalculated taking into account the adjustment of sales volume.

Using a similar scheme, you can evaluate the influence of each factor and recalculate net profit, and summarize the final results in one table (see Table 6).

Table 6. Impact of factors on profit, rub.


Sales volume
Cost of products sold, services
Operating expenses
Non-operating income/expenses
Interest on loan

Total	32 244 671

As can be seen from Table 6, the greatest impact in the analyzed period was exerted by sales growth (RUB 83,040,425). The sum of the influence of all factors coincides with the actual change in profit over the past period. From this we can conclude that the analysis results are correct.

Conclusion

In conclusion, I would like to understand: what should profit be compared with in factor analysis? With last year, with the base year, with competitors, with the plan? How to understand whether an enterprise has performed well this year or not? For example, a company doubled its profit for the current year, it would seem that this excellent result! But at this time, competitors carried out technical re-equipment of the enterprise and next year will drive the lucky ones out of the market. And if compared with competitors, their income is lower, because... Instead of, say, advertising or expanding the range, they invested money in modernization. Thus, everything depends on the goals and plans of the enterprise. From which it follows that actual profit must be compared, first of all, with planned profit.

The functioning of any socio-economic system (which includes an operating enterprise) occurs in conditions of complex interaction of a complex of internal and external factors. Factor- this is the reason driving force any process or phenomenon that determines its character or one of its main features.

Under factor analysis understands the methodology for a comprehensive and systematic study and measurement of the impact of factors on the value of performance indicators.

In general, the following main ones can be distinguished: stages (tasks) factor analysis:

Setting the purpose of the analysis.

Selection of factors that determine the performance indicators under study.

Classification and systematization of factors in order to provide an integrated and systematic approach to the study of their influence on the results of economic activity.

Determination of the form of dependence between factors and the performance indicator.

Modeling the relationships between performance and factor indicators.

Calculation of the influence of factors and assessment of the role of each of them in changing the value of the performance indicator.

Working with the factor model (its practical use for managing economic processes).

In other words, method task- transition from real large number signs or reasons that determine the observed variability in a small number of the most important variables (factors) with minimal loss of information (methods that are similar in essence, but not in mathematical terms - component analysis, canonical analysis, etc.).

The method arose and was initially developed in problems of psychology and anthropology (at the turn of the 19th and 20th centuries), but now the scope of its application is much wider.

Purpose of factor analysis

Factor analysis- determining the influence of factors on the result - is one of the strongest methodological solutions in analyzing the economic activities of companies for decision making. For managers - an additional argument, an additional “angle of view”.

The feasibility of using factor analysis

As you know, you can analyze everything ad infinitum. It is advisable to implement deviation analysis at the first stage, and where necessary and justified, apply factor method analysis. In many cases, a simple analysis of deviations is enough to understand that the deviation is “critical”, and when it is not at all necessary to know the degree of its influence.

Factors are divided into internal and external, depending on whether the activities of a given enterprise affect them or not. The analysis focuses on internal factors that the enterprise can influence.

Factors are divided into objective, independent of the will and desires of people, and subjective, influenced by the activities of legal entities and individuals.

According to the degree of prevalence, factors are divided into general and specific. Common factors operate in all sectors of the economy. Specific factors operate within a particular industry or a specific enterprise.

Types of factor analysis

The following types of factor analysis exist:

1) Deterministic (functional) - the effective indicator is presented in the form of a product, quotient or algebraic sum of factors.

2) Stochastic (correlation) - the relationship between the effective and factor indicators is incomplete or probabilistic.

3) Direct (deductive) – from the general to the specific.

4) Reverse (inductive) – from the particular to the general.

5) Single-stage and multi-stage.

6) Static and dynamic.

7) Retrospective and prospective.

Depending on the type of factor model, there are two main types of factor analysis - deterministic and stochastic.

Deterministic factor analysis is a technique for studying the influence of factors whose connection with the effective indicator is functional in nature, that is, when the effective indicator of the factor model is presented in the form of a product, quotient or algebraic sum of factors.

This type of factor analysis is the most common, since, being quite simple to use (compared to stochastic analysis), it allows you to understand the logic of the action of the main factors of enterprise development, quantify their influence, understand which factors and in what proportion it is possible and advisable to change to increase production efficiency.

Deterministic factor analysis has a fairly strict sequence of procedures:

1.construction of an economically sound deterministic factor model;

2. choosing a method of factor analysis and preparing conditions for its implementation;

3.implementation of counting procedures for model analysis;

Basic methods of deterministic factor analysis

Chain substitution method; Absolute difference method; Relative difference method; Integral method; Logarithm method.

Stochastic analysis is a methodology for studying factors whose connection with an effective indicator, unlike a functional one, is incomplete, probabilistic (correlation). The essence of the stochastic method is to measure the influence of stochastic dependencies with uncertain and approximate factors. Stochastic method It is advisable to use for economic research with incomplete (probabilistic) correlation: for example, for marketing problems. If with a functional (complete) dependence with a change in the argument there is always a corresponding change in the function, then with a correlation connection a change in the argument can give several values of the increase in the function depending on the combination of other factors that determine this indicator. For example, labor productivity at the same level of capital-labor ratio may be different at different enterprises. This depends on the optimal combination of other factors affecting this indicator.

Stochastic modeling is, to a certain extent, a complement and deepening of deterministic factor analysis. In factor analysis, these models are used according to three main reasons:

It is necessary to study the influence of factors for which it is impossible to build a strictly determined factor model (for example, the level of financial leverage);

It is necessary to study the influence of complex factors that cannot be combined in the same strictly deterministic model;

It is necessary to study the influence of complex factors that cannot be expressed in one quantitative indicator (for example, the level of scientific and technological progress).

It is also necessary to distinguish static And dynamic factor analysis. The first type is used when studying the influence of factors on performance indicators on the corresponding date. Another type is a technique for studying cause-and-effect relationships in dynamics.

Finally, factor analysis can be retrospective, which studies the reasons for the increase in performance indicators over past periods, and promising, which examines the behavior of factors and performance indicators in perspective.

Factor analysis can be single-stage or multi-stage. The first type is used to study factors of only one level (one level) of subordination without detailing them into their component parts. For example, . In multi-stage factor analysis, factors a and b are detailed into constituent elements in order to study their behavior. The detailing of factors can be continued further. In this case, the influence of factors at different levels of subordination is studied.

It is also necessary to distinguish between static and dynamic factor analysis. The first type is used when studying the influence of factors on performance indicators on the corresponding date. Another type is a technique for studying cause-and-effect relationships in dynamics.

All processes occurring in business are interconnected. There is both a direct and indirect connection between them. Various economic parameters change under the influence of various factors. Factor analysis (FA) allows you to identify these indicators, analyze them, and study the degree of influence.

The concept of factor analysis

Factor analysis is a multidimensional technique that allows you to study the relationships between the parameters of variables. In the process, the structure of covariance or correlation matrices is studied. Factor analysis is used in a variety of sciences: psychometrics, psychology, economics. The basics of this method were developed by psychologist F. Galton.

Objectives of the

To receive reliable results a person needs to compare indicators on several scales. In the process, the correlation of the obtained values, their similarities and differences is determined. Let's consider the basic tasks of factor analysis:

Detection of existing values.
Selection of parameters for a complete analysis of values.
Classification of indicators for system work.
Detection of relationships between resultant and factor values.
Determining the degree of influence of each factor.
Analysis of the role of each value.
Application of the factor model.

Every parameter that affects the final value must be examined.

Factor analysis techniques

FA methods can be used both in combination and separately.

Deterministic Analysis

Deterministic analysis is used most often. This is due to the fact that it is quite simple. Allows you to identify the logic of the impact of the company’s main factors and analyze their impact in quantitative terms. As a result of the DA, you can understand what factors should be changed to improve the company's performance. Advantages of the method: versatility, ease of use.

Stochastic Analysis

Stochastic analysis allows you to analyze existing indirect relationships. That is, there is a study of indirect factors. The method is used if it is impossible to find direct connections. Stochastic analysis is considered complementary. It is only used in certain cases.

What is meant by indirect connections? With a direct connection, when the argument changes, the value of the factor will also change. An indirect connection involves a change in the argument followed by a change in several indicators at once. The method is considered auxiliary. This is due to the fact that experts recommend studying direct connections first. They allow you to create a more objective picture.

Stages and features of factor analysis

Analysis for each factor gives objective results. However, it is used extremely rarely. This is due to the fact that in the process complex calculations. To carry them out you will need special software.

Let's consider the stages of FA:

Establishing the purpose of the calculations.
Selection of values that directly or indirectly affect end result.
Classification of factors for complex research.
Detecting the relationship between the selected parameters and the final indicator.
Modeling of mutual relationships between the result and the factors influencing it.
Determining the degree of impact of the values and assessing the role of each parameter.
Use of the generated factor table in the activities of the enterprise.

NOTE! Factor analysis involves very complex calculations. Therefore, it is better to entrust it to a professional.

IMPORTANT! When carrying out calculations, it is extremely important to correctly select factors that influence the results of the enterprise’s activities. The selection of factors depends on the specific area.

Factor analysis of profitability

A profitability analysis is carried out to analyze the rationality of resource allocation. As a result, it is possible to determine which factors most influence the final result. As a result, we can retain only those factors that in the best possible way affect efficiency. Based on the data obtained, you can change pricing policy companies. The following factors may influence the cost of production:

fixed costs;
variable costs;
profit.

Reducing costs provokes an increase in profits. In this case, the cost does not change. We can conclude that profitability is affected by existing costs, as well as the volume of products sold. Factor analysis allows us to determine the degree of influence of these parameters. When does it make sense to do it? The main reason for this is to reduce or increase profitability.

Factor analysis is carried out using the following formula:

Rв= ((W-SB -KRB-URB)/W) - (WB-SB-KRB-URB)/WB, Where:

VT – revenue for the current period;

SB – cost price for the current period;

KRB – commercial expenses for the current period;

URB – management expenses for the previous period;

VB – revenue for the previous period;

KRB – commercial expenses for the previous period.

Other formulas

Let's consider the formula for calculating the degree of impact of cost on profitability:

Rс= ((W-SBot -KRB-URB)/W) - (W-SB-KRB-URB)/W,

CBO is the cost of production for the current period.

Formula for calculating the impact of management expenses:

Rur= ((W-SB -KRB-URot)/W) - (W-SB-KRB-URB)/W,

URot is management expenses.

The formula for calculating the impact of business costs is:

Rк= ((W-SB -KRo-URB)/W) - (W-SB-KRB-URB)/W,

CR is commercial expenses for the previous time.

The total impact of all factors is calculated using the following formula:

Rob=Rv+Rс+Rur+Rk.

IMPORTANT! When making calculations, it makes sense to calculate the influence of each factor separately. Overall PA results are of little value.

Example

Let's consider the organization's indicators for two months (for two periods, in rubles). In July, the organization's income amounted to 10 thousand, production costs - 5 thousand, administrative expenses - 2 thousand, commercial expenses - 1 thousand. In August, the company's income amounted to 12 thousand, production costs - 5.5 thousand, administrative expenses - 1.5 thousand, commercial expenses - 1 thousand. The following calculations are carried out:

R=((12 thousand-5.5 thousand-1 thousand-2 thousand)/12 thousand)-((10 thousand-5.5 thousand-1 thousand-2 thousand)/10 thousand)=0.29-0, 15=0.14

From these calculations we can conclude that the organization’s profit increased by 14%.

Factor analysis of profit

P = RR + RF + RVN, where:

P – profit or loss;

РР – profit from sales;

RF – results of financial activities;

RVN is the balance of income and expenses from non-operating activities.

Then you need to determine the result from the sale of goods:

PP = N – S1 – S2, where:

N – revenue from the sale of goods at selling prices;

S1 – cost of products sold;

S2 – commercial and administrative expenses.

The key factor in calculating profit is the turnover of the company for the sale of the company.

NOTE! Factor analysis is extremely difficult to perform manually. You can use special programs for it. The simplest program for calculations and automatic analysis - Microsoft Excel. It has tools for analysis.

Factor analysis is understood as a method of complex and systematic study and measurement of factors for the value of effective indicators.

The following types of factor analysis are distinguished: deterministic (functional)

stochastic (probabilistic)

Deterministic factor analysis is a technique for assessing the influence of factors whose connection with the performance indicator is functional in nature, i.e. the effective indicator can be presented as a product, quotient or algebraic sum of factors.

Methods of deterministic factor analysis:

chain substitution method

index

integral

absolute differences

relative differences, etc.

Stochastic Analysis – a methodology for studying factors whose connection with an effective indicator, unlike a functional indicator, is incomplete, probabilistic.

Methods of stochastic factor analysis:

correlation analysis

regression analysis

dispersive

component

modern multivariate factor analysis

discriminant

Basic methods of deterministic factor analysis

THE CHAIN SUBSTITUTION METHOD is the most universal; it is used to calculate the influence of factors in all types of factor models: addition, multiplication, division and mixed.

This method allows you to determine the influence of individual factors on changes in the value of the performance indicator by replacing the base value of each factor indicator with the actual value in the reporting period. For this purpose, a number of conditional values of the performance indicator are determined, which take into account the change in one, then two, three, etc. factors, assuming that the rest do not change.

Comparing the value of an effective indicator before and after changing the level of one or another factor allows us to eliminate the influence of all factors except one and determine its impact on the increase in the effective indicator.

The algebraic sum of the influence of factors must necessarily be equal to the total increase in the effective indicator. The absence of such equality indicates mistakes have been made.

INDEX METHOD is based on relative indicators of dynamics, spatial comparisons, plan implementation (indices), which are defined as the ratio of the level of the analyzed indicator in the reporting period to its level in the base period (or to the planned or other object).

Using indices, you can identify the influence of various factors on changes in performance indicators in multiplication and division models.

The INTEGRAL METHOD is a further logical development of the considered methods, which have a significant drawback: when using them, they assume that the factors change independently of each other. In fact, they change together, are interconnected, and from this interaction an additional increase in the effective indicator is obtained, which is added to one of the factors, usually the last one. In this regard, the magnitude of the influence of factors on the change in the performance indicator changes depending on the place in which one or another factor is placed in the model under study.

When using the INTEGRAL method, the error in calculating the influence of factors is distributed equally between them, and the order of substitution does not matter. The error distribution is carried out using special models.

Types of finite factor systems, the most frequently encountered in the analysis of economic activity:

additive models

multiplicative models

;

multiple models

;
;
;,

Where y– effective indicator (initial factor system);

x i– factors (factor indicators).

In relation to the class of deterministic factor systems, the following are distinguished: basic modeling techniques.

those. multiplicative model of the form
.

3. Factor system reduction method. Initial factor system
. If we divide both the numerator and 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
.

Thus, the complex process of forming the level of the studied indicator of economic activity can be decomposed using various techniques into its components (factors) and is presented in the form of a model of a deterministic factor system.

Modeling the return on capital indicator of an enterprise ensures the creation of a five-factor profitability model, which includes all indicators of intensification of the use of production resources.

We will conduct a profitability analysis using the data in the table.

CALCULATION OF KEY INDICATORS FOR THE ENTERPRISE FOR TWO YEARS

Indicators	Legend	First (base) year (0)	Second (reporting) year (1)	Deviation, %
1. Products (sales at selling prices without indirect taxes), thousand rubles.
2. a) Production staff, Human
b) Remuneration with accruals, thousand rubles.
3. Material costs, thousand rubles.
4. Depreciation, thousand rubles.
5. Fixed production assets, thousand rubles.
6. Working capital in inventory, thousand rubles.	E 3
7. a) Labor productivity (page 1:page 2a), rub.	λ R
b) Products worth 1 rub. wages (line 1: line 2b), rub.	λ U
8. Material productivity (page 1: page 3), rub.	λ M
9. Depreciation return (page 1: page 4), rub.	λ A
10. Capital productivity (page 1: page 5), rub.	λ F
11. Turnover working capital(page 1:page 6), speed	λ E
12. Cost of sales (line 2b+line 3+line 4), thousand rubles.	S P
13. Profit from sales (page 1 + page 12), thousand rubles.	P P

Based on the basic indicators, we will calculate the indicators of intensification of production resources (rub.)

Indicators	Legend	First (base) year (0)	Second (reporting) year (1)
1. Payment intensity (labor intensity) of products
2. Material consumption of products
3 Depreciation capacity of products
4. Capital intensity of production
5. Working capital consolidation ratio

Five-factor model of return on assets (advanced capital)

We will illustrate the methodology for analyzing the five-factor model of return on assets using the method of chain substitutions.

First, let's find the profitability value for the base and reporting years.

For base year:

For the reporting year:

The difference in the profitability ratios of the reporting and base years was 0.005821, and as a percentage - 0.58%.

Let's look at how the five factors mentioned above contributed to this increase in profitability.

In conclusion, we will compile a summary of the influence of factors on the deviation of profitability of the 2nd year compared to the 1st (base) year.

Total deviation, % 0.58

Including due to the influence of:

labor intensity +0.31

material consumption +0.28

depreciation capacity 0

Total cost: +0.59

capital intensity −0.07

working capital turnover +0.06

Total advance payment −0.01