This is one of the modifications of the chain substitution method, it is used to calculate the influence of factors in multiplicative and mixed models of the type: Y = (a - b)*c and Y = a*(b - c). Its use is especially effective when the initial data already contain absolute deviations in terms of factor indicators.

The calculation algorithm for a multiplicative factorial model of the type Y = a * b * c * d is as follows. There are planned and actual values ​​for each factor indicator, as well as their absolute deviations:

a = af - apl; b = bf - bpl; c \u003d cph - cpl; d = df - dpl

The determination of the change in the value of the effective indicator due to each factor is carried out as follows:

Ya = a * bpl * cpl * dpl;

Yb \u003d af * b * cpl * dpl;

Yc = aph * bf * c * dpl;

Yc = aph * bph * cf * d.

Thus, the magnitude of the influence of factors is calculated by multiplying the absolute increase in the factor under study by the base (planned) value of the factors that are to the right of it, and by the actual value of the factors located to the left of it in the model.

Relative difference method

The scope of its application is the same as that of the previous one. It is especially effective when the initial data contain already defined relative deviations of factorial indicators in percentages and coefficients.

The methodology for calculating the influence of factors in this way for multiplicative models of the type Y = a * b * c is as follows. First, you need to calculate the relative deviations of factor indicators:

Then the deviation of the effective indicator due to each factor is determined as follows:

According to this rule, to calculate the influence of the first factor, it is necessary to multiply the base (planned) value of the effective indicator by the relative growth of the first factor, expressed as a percentage, and divide the result by 100.

To calculate the influence of the second factor, you need to add the change due to the first factor to the planned value of the effective indicator and then multiply the resulting amount by the relative increase in the second factor in percent and divide the result by 100, etc.

A variation of this method is prem percentage differences. The methodology for calculating the influence of factors with its help can be considered using the example of a multiplicative model of the scope of work:

O \u003d H * I * n * B,

where O is the amount of work, rub.;

I - the average number of days of work of one worker per year;

n is the number of worked man-hours. an average of one worker per day;

B - average hourly output of a worker, rub.

The advantage of this method is that when using it, it is not necessary to calculate the level of factor indicators. It is enough to have data on the percentage of the implementation of the plan in terms of the amount of work (O%), the number of workers (H%) and the number of days they worked (D%) and hours (t%) for the analyzed period.

Then the deviation of the amount of work due to each factor is determined as follows:

The index method is based on relative indicators dynamics, spatial comparisons, implementation of the plan, expressing the ratio of the actual level of the analyzed indicator in reporting period to its level in the base period or to the planned or other object.

With the help of aggregate indices, it is possible to identify the influence of various factors on the change in the level of performance indicators in multiplicative and multiple models.

For example, let's take the CMP volume index.

It reflects the change in the number of workers (H) and their average annual output (B) and is equal to the product of these indices:

To establish how the volume of construction and installation works has changed due to a change in the number of workers and due to a change in their average annual output, it is necessary to calculate the headcount index JH and the output index JB:

If we subtract the denominator from the numerator of the above formulas, then we will get the absolute increases in the volume of construction and installation works as a whole and due to each factor separately (they will be equal to the results calculated using the chain substitution method).

Types of deterministic models that use the chain substitution method. Essence and rules of its application. Algorithms for calculating the influence of factors by this method in various types of models.

One of the most important methodological issues in AHD is to determine the magnitude of the influence of individual factors on the growth of performance indicators. In deterministic factor analysis (DFA), the following methods are used for this: chain substitution, index, absolute differences, relative differences, proportional division, integral, logarithms, etc.

The first four methods are based on the elimination method. To eliminate means to eliminate, reject, exclude the influence of all factors on the value of the effective indicator, except for one. This method proceeds from the fact that all factors change independently of each other: first one changes, and all others remain unchanged, then two change, then three, etc., while the rest remain unchanged. This allows you to determine the influence of each factor on the value of the studied indicator separately.

The most versatile of these is chain substitution method. It is used to calculate the influence of factors in all types of deterministic factor models: additive, multiplicative, multiple and mixed (combined). This method allows you to determine the influence of individual factors on the change in the value of the effective indicator by gradually replacing the base value of each factor indicator in the volume of the effective indicator with the actual value in the reporting period. For this purpose, a number of conditional values ​​​​of the effective indicator are determined, which take into account the change in one, then two, three, etc. factors, assuming that the others do not change. Comparing the value of the effective indicator before and after changing the level of one or another factor allows you to eliminate the influence of all factors except one, and determine the impact of the latter on the growth of the effective indicator.

The procedure for applying this method will be considered in the following example (Table 6.1).

As we already know, the volume of gross output ( VP) depends on two main factors of the first level: the number of workers (CR) and average annual output (GV). We have a two-factor multiplicative model: VP = Czech Republic X GV.

The algorithm for calculating by the method of chain substitution for this model:

As you can see, the second indicator of gross output differs from the first one in that when calculating it, the actual number of workers was taken instead of the planned one. The average annual production by one worker in both cases is planned. This means that due to the increase in the number of workers, output increased by 32,000 million rubles. (192,000 - 160,000).

The third indicator differs from the second one in that when calculating its value, the output of workers is taken at the actual level instead of the planned one. The number of employees in both cases is actual. Hence, due to the increase in labor productivity, the volume of gross output increased by 48,000 million rubles. (240,000 - 192,000).

Thus, the overfulfillment of the plan in terms of gross output was the result of the influence of the following factors:

a) increase in the number of workers + 32,000 million rubles.

b) increasing the level of labor productivity + 48,000 million rubles.

Total +80,000 million rubles

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 errors in the calculations.

For clarity, the results of the analysis are given in table. 6.2.

If it is required to determine the influence of three factors, then in this case not one, but two conditional additional indicators are calculated, i.e. the number of conditional indicators is one less than the number of factors. Let's illustrate this on a four-factor model of gross output:

The initial data for solving the problem are given in Table 6.1:

The plan for the production of products as a whole was overfulfilled by 80,000 million rubles. (240,000 - 160,000), including by changing:

a) the number of workers

Using the chain substitution method, it is recommended to adhere to a certain sequence of calculations: first of all, you need to take into account the change in quantitative, and then qualitative indicators. If there are several quantitative and several qualitative indicators, then first you should change the value of the factors of the first level of subordination, and then the lower one. In the above example, the volume of production depends on four factors: the number of workers, the number of days worked by one worker, the length of the working day and the average hourly output. According to Scheme 5.2, the number of workers in this case is the factor of the first level of subordination, the number of days worked is the second level, the length of the working day and the average hourly output are factors of the third level. This determined the sequence of placement of factors in the model and, accordingly, the sequence of their study.

Thus, the application of the method of chain substitution requires knowledge of the relationship of factors, their subordination, the ability to correctly classify and systematize them.

We considered an example of calculating the influence of factors on the growth of the effective indicator in multiplicative models.

In multiple models the algorithm for calculating factors for the value of the studied indicators is as follows:

where FD- return on assets; VP- gross output; OPF - average annual cost of fixed production assets.

Method for calculating the influence of factors in mixed models:

a) Multiplicatively-additive type P = VPP (C - WITH)

where P- the amount of profit from the sale of products; VPP - the volume of sales of products; C - selling price; C - unit cost of production;

In a similar way, the influence of factors is calculated for other deterministic mixed-type models.

Separately, it is necessary to dwell on the methodology for determining the influence structural factor on the increase in the effective indicator using this method. For example, sales revenue (V) depends not only on the price (C) and quantity of products sold (VPN), but also from its structure (UDi). If the share of products increases the highest category quality, which is sold at higher prices, the revenue due to this will increase, and vice versa. The factorial model of this indicator can be written as follows:

In the process of analysis, it is necessary to eliminate the influence of all factors, except for the structure of the product. To do this, we compare the following revenue indicators:

The difference between these indicators takes into account the change in revenue from the sale of products due to changes in its structure (Table 6.3.).

The table shows that due to the increase in the share of second-class products in the total volume of its sales, revenue decreased by 10 million rubles. (655 - 665). This is the unused reserve of the enterprise.

6.2. Index method

The essence and purpose of the index method. Algorithm for calculating the influence of factors by this method for different models.

The index method is based on relative indicators of dynamics, spatial comparisons, plan implementation, expressing the ratio of the actual level of the analyzed indicator in the reporting period to its level in the base period (or to the planned or other object).

With the help of aggregate indices, it is possible to identify the influence of various factors on the change in the level of performance indicators in multiplicative and multiple models.

For example, let's take the index of the cost of marketable products:

It reflects the change in the physical volume of marketable products (q) and prices (R) and is equal to the product of these indices:

To establish how the cost of marketable products has changed due to the quantity of manufactured products and due to prices, it is necessary to calculate the index of physical volume Iq and price index 1 p:

In our example, the volume of gross output can be represented as the product of the number of workers and their average annual output. Therefore, the index of gross output 1ch will be equal to the product of the index of the number of workers lchr and index of average annual output 1gv:

If we subtract the denominator from the numerator of the above formulas, then we will obtain the absolute growth of gross output as a whole and due to each factor separately, i.e. the same results as the chain substitution method.

6.3. Absolute difference method

Essence, purpose and scope of the method of absolute differences. The procedure and algorithms for calculating the influence of factors in this way

Way absolute differences is one of the elimination modifications. Like the chain substitution method, it is used to calculate the influence of factors on the growth of the effective indicator in deterministic analysis, but only in multiplicative and multiplicative-additive models: Y= (a -b)With and Y = a(b- With). And although its use is limited, but due to its simplicity, it has been widely used in AHD. This method is especially effective if the initial data already contains absolute deviations in factorial indicators.

When using it, the value of the influence of factors is calculated by multiplying the absolute increase in the factor under study by the base (planned) value of the factors that are to the right of it, and by the actual value of the factors located to the left of it in the model.

Consider the calculation algorithm for multiplicative factor model of the type Y= a x b x c x d. There are planned and actual values ​​for each factor indicator, as well as their absolute deviations:

We determine the change in the value of the effective indicator due to each factor:

As can be seen from the above diagram, the calculation is based on the successive replacement of the planned values ​​of factor indicators with their deviations, and then with the actual level of these indicators.

Consider the methodology for calculating the influence of factors in this way for a four-factor multiplicative model of gross output:

Thus, the absolute difference method gives the same results as the chain substitution method. Here it is also necessary to ensure that the algebraic sum of the increase in the effective indicator due to individual factors is equal to its total increase.

Consider the algorithm for calculating factors in this way in mixed models type V = (a - b)With. For example, let's take the factorial model of profit from the sale of products, which was already used in the previous paragraph:

P = VRP(C - WITH).

The increase in the amount of profit due to changes in the volume of sales of products:

selling prices:

production cost:

Calculation of the influence of the structural factor using this method is carried out as follows:

As can be seen from Table. 6.4, due to the change in the structure of sales, the average price for 1 ton of milk decreased by 40 thousand rubles, and for the entire actual volume of sales of products, the profit was received less by 10 million rubles. (40 thousand rubles x 250 tons).

6.4. Relative difference method

The essence and purpose of the method of relative differences. Scope of its application. Algorithm for calculating the influence of factors in this way.

Relative difference method, like the previous one, it is used to measure the influence of factors on the growth of the effective indicator only in multiplicative and additive-multiplicative models of the type V= (a - b)c. It is much simpler than chain substitutions, which makes it very efficient under certain circumstances. This primarily applies to those cases where the initial data contain previously determined relative increases in factor indicators in percentages or coefficients.

Consider the methodology for calculating the influence of factors in this way for multiplicative models of the type V = A X V X WITH. First, you need to calculate the relative deviations of factor indicators:

Then the change in the effective indicator due to each factor is determined as follows:

According to this rule, to calculate the influence of the first factor, it is necessary to multiply the base (planned) value of the effective indicator by the relative growth of the first factor, expressed as a percentage, and divide the result by 100.

To calculate the influence of the second factor, you need to add the change due to the first factor to the planned value of the effective indicator and then multiply the resulting amount by the relative increase in the second factor in percent and divide the result by 100.

The influence of the third factor is determined in a similar way: it is necessary to add its growth due to the first and second factors to the planned value of the effective indicator and multiply the resulting amount by the relative growth of the third factor, etc.

Let's fix the considered technique on the example given in tab. 6.1:

As you can see, the calculation results are the same as when using the previous methods.

The method of relative differences is convenient to use in cases where it is required to calculate the influence of a large complex of factors (8-10 or more). Unlike the previous methods, the number of calculations is significantly reduced.

A variation of this method is acceptance of percentage differences. We will consider the methodology for calculating the influence of factors with its help using the same example (Table 6.1).

In order to establish how much the volume of gross output has changed due to the number of workers, it is necessary to multiply its planned value by the percentage of overfulfillment of the plan by the number of workers CR%:

To calculate the influence of the second factor, it is necessary to multiply the planned volume of gross output by the difference between the percentage of the plan fulfilled by total days worked by all workers D% and the percentage of completion of the plan for average headcount workers CR%:

The absolute increase in gross output due to a change in the average length of the working day (intra-shift downtime) is established by multiplying the planned volume of gross output by the difference between the percentage of the plan fulfilled by the total number of hours worked by all workers t% and the total number of days they worked D%:

To calculate the impact of average hourly output on the change in the volume of gross output, the difference between the percentage of the implementation of the plan for gross output VP% and the percentage of plan fulfillment by the total number of hours worked by all workers t% multiply by the planned volume of gross output VPpl:

The advantage of this method is that when it is applied, it is not necessary to calculate the level of factor indicators. It is sufficient to have data on the percentage of fulfillment of the plan in terms of gross output, the number of workers and the number of days and hours worked by them for the analyzed period.

6.5. Method of proportional division and equity participation

Essence, purpose and scope of the method of proportional division. The procedure and algorithms for calculating the influence of factors in this way.

In some cases, to determine the magnitude of the influence of factors on the growth of the effective indicator, one can use proportional division method. This applies to those cases when we are dealing with additive models of the type V = Xi and multiply additive type

In the first case, when we have a single-level model of type V= a + b+ p. calculation is carried out as follows:

For example, the level of profitability decreased by 8% due to an increase in the company's capital by 200 million rubles. At the same time, the value of fixed capital increased by 250 million rubles, while the value of circulating capital decreased by 50 million rubles. So, due to the first factor, the level of profitability decreased, and due to the second - increased:

The calculation procedure for mixed models is somewhat more complicated. The relationship of factors in the combined model is shown in fig. 6.1.

When known Vd, Vp and W, as well as Yb, then to determine Yd, Y n, Ym you can use the method of proportional division, which is based on the proportional distribution of the increase in the effective indicator Y due to a change in the factor V between second level factors D, N and M according to their growth. The proportionality of this distribution is achieved by determining a coefficient constant for all factors, which shows the amount of change in the effective indicator Y due to a change in the factor V per unit.

Coefficient value (TO) is defined as follows:

Multiplying this coefficient by the absolute deviation V due to the corresponding factor, we find the change in the effective indicator:

For example, the cost of 1 tkm increased by 180 rubles due to a decrease in the average annual output of a car. At the same time, it is known that the average annual production of a car has decreased due to:

a) overscheduled downtime of machines -5000 tkm

b) overplanned idle runs -4000 tkm

c) incomplete use of load capacity -3000 tkm

Total-12000 tkm

From here you can determine the change in cost under the influence of factors of the second level:

To solve this type of problem, you can also use the method of equity participation. First, the share of each factor in the total amount of their growth is determined, which is then multiplied by the total growth of the effective indicator (Table 6.5):

There are a lot of similar examples of the application of this method in AHD, as you can see in the process of studying the industry course of analysis. economic activity enterprises.

6.6. Integral method in the analysis of economic activity

The main disadvantages of the elimination method. The problem of decomposition of additional growth from the interaction of factors between them. The essence of the integral method and the scope of its application. Algorithms for calculating the influence of factors in different models in an integral way.

Elimination as a way of deterministic factor analysis has a significant drawback. When using it, it is assumed that the factors change independently of each other. In fact, they change together, interconnectedly, and this interaction results in an additional increase in the effective indicator, which, when applying elimination methods, is added to one of the factors, usually the latter. In this regard, the magnitude of the influence of factors on the change in the effective indicator varies depending on the place on which this or that factor is placed in the deterministic model.

Let's consider it on an example which is given in tab. 6.1. According to the data given in it, the number of workers at the enterprise increased by 20%, labor productivity - by 25%, and the volume of gross output - by 50%. This means that 5% (50 - 20 - 25), or 8,000 million rubles. gross output is an additional increase from the interaction of both factors.

When we calculate the conditional volume of gross output, based on the actual number of workers and the planned level of labor productivity, then the entire additional increase from the interaction of two factors refers to a qualitative factor - a change in labor productivity:

If, however, when calculating the conditional volume of gross output, we take the planned number of workers and the actual level of labor productivity, then the entire additional increase in gross output refers to the quantitative factor, which we change secondarily:

We will show a graphical solution to the problem in different versions (Fig. 6.2).

In the first version of the calculation, the conditional indicator has the form: VP cond. = ChRf X GV pl, in the second - VP conv = CH pl X GVf.

Accordingly, deviations due to each factor in the first case

in the second

On the graphs, these deviations correspond to different rectangles, since with different substitution options, the value of the additional increase in the effective indicator, equal to the rectangle ABCD, relates in the first case to the magnitude of the influence of annual output, and in the second case, to the magnitude of the influence of the number of workers. As a result, the magnitude of the influence of one factor is exaggerated, while the other is underestimated, which causes ambiguity in assessing the influence of factors, especially in cases where the additional increase is quite significant, as in our example.

To overcome this shortcoming, deterministic factor analysis uses integral method, which is used to measure the influence of factors in multiplicative, multiple and mixed models of a multiple-additive type

Using this method allows you to get more accurate results of calculating the influence of factors compared to the methods of chain substitution, absolute and relative differences and avoid an ambiguous assessment of the influence of factors because in this case the results do not depend on the location of the factors in the model, and an additional increase in the effective indicator, which formed from the interaction of factors, is decomposed between them equally.

At first glance, it may seem that in order to distribute an additional increase, it is enough to take half of it or a part corresponding to the number of factors. But this is most often difficult to do, since factors can act in different directions. Therefore, certain formulas are used in the integral method. Here are the main ones for different models.

The logarithm method is used to measure the influence of factors in multiplicative models. In this case, the result of the calculation, as in the case of integration, does not depend on the location of the factors in the model, and in comparison with the integral method, an even higher accuracy of calculations is provided. If, when integrating, the additional gain from the interaction of factors is distributed equally between them, then using the logarithm, the result of the combined action of the factors is distributed in proportion to the share of the isolated influence of each factor on the level of the effective indicator. This is its advantage, and the disadvantage is its limited scope.

Unlike the integral method, the logarithm uses not absolute increases in indicators, but indices of their growth (decrease).

Mathematically, this method is described as follows. Suppose that the performance indicator can be represented as a product of three factors: f = xz. Taking the logarithm of both sides of the equation, we get

Considering that the same dependence remains between the indexes of change in indicators as between the indicators themselves, we will replace their absolute values ​​with indices:

It follows from the formulas that the overall increase in the effective indicator is distributed among the factors in proportion to the ratio of the logarithms of the factor indices to the logarithm of the index of the effective indicator. And it doesn't matter which logarithm is used - natural or decimal.

Using the data in Table. 6.1, we calculate the increase in gross output due to the number of workers (CR), number of days worked by one worker per year (D) and average daily output (DV) according to the factor model:

Comparing the results of calculating the influence of factors different ways according to this factorial model, one can be convinced of the advantage of the logarithm method. This is expressed in the relative simplicity of calculations and an increase in the accuracy of calculations.

Having considered the main methods of deterministic factor analysis and the scope of their application, the results can be systematized in the form of the following matrix:

Knowledge of the essence of these techniques, their scope, calculation procedures - necessary condition qualified quantitative research.

The method of relative differences is used to measure the influence of factors on the growth of the effective indicator only in multiplicative models. Here, relative increases in factor indicators are used, expressed as coefficients or percentages. Consider the methodology for calculating the influence of factors in this way for multiplicative models of the type Y=abc.

The change in the performance indicator is determined as follows:

Δy a = y 0 * Δa%,

Δy b \u003d (y 0 + Δy a) ​​* Δb%,

Δy c \u003d (y 0 + Δy a + Δy b) * Δc%,

Δa% \u003d (a 1 -a 0) / a 0,

Δb% \u003d (b 1 -b 0) / b 0,

Δc% \u003d (c 1 -c 0) / c 0,

To calculate the influence of the first factor, it is necessary to multiply the base (planned) value of the effective indicator by the relative growth of the first factor, expressed as a decimal fraction.

To calculate the influence of the second factor, you need to add the change due to the first factor to the base (planned) value of the effective indicator and then multiply the resulting amount by the relative increase in the second factor.

The influence of the third factor is determined in a similar way: it is necessary to add its increase due to the first and second factors to the base (planned) value of the effective indicator and multiply the resulting amount by the relative increase of the third factor, etc.

Let's fix the considered technique on the example given in tab. one:

ΔVPchr = VPpl * ΔChR/ChRpl = 400*20/100 = +80 million rubles;

ΔVPd \u003d (VPpl + ΔVPchr) * ΔD / Dpl \u003d (400 + 80) * 8.33 / 200 \u003d +20 million rubles.

ΔVPp = (VPpl + ΔVPchr + ΔVPd)* ΔP/Ppl = (400 + 80 + 20)* - 0.5/8 = - 31.25 million rubles

ΔVPcv = (VPpl + ΔVPchr + ΔVPd + ΔVPp)* ΔChV / ChVpl = (400 + 80 + 20 - 31.25) * 0.7 / 2.5 = 131.25 million rubles.

The method of relative differences is convenient to use in cases where it is required to calculate the influence of a large complex of factors (8-10 or more). Unlike the previous methods, the number of computational procedures is significantly reduced here, which makes it rarely used.

Index method

The index method is based on relative indicators expressing the ratio of the level of a given phenomenon to its level in the past or to the level of a similar phenomenon taken as a base. Any index is calculated by comparing the measured (reporting) value with the base value. Indexes expressing the ratio of directly commensurable quantities are called individual, and characterizing the ratio of complex phenomena - group.

The index method can reveal the effect on the studied cumulative rate various factors. Statistics names several forms of indices that are used in analytical work (aggregate, arithmetic, harmonic, etc.)

An important constituent element of the index is its weight or the coefficient of reduction of parts of a heterogeneous population to a single indicator. It must preserve the model of the structure of the phenomenon under study in dynamics.

It is customary to use prices (p o) as a weight when calculating volume indices, and volumes (q 1) when calculating quality indices.

The main form of the economic index is aggregate characterizing the change in the level of development of the entire complex population.

With the help of aggregate indices, it is possible to identify the influence of various factors on the change in the level of performance indicators in multiplicative and multiple models.

The aggregate index is calculated by the formulas:

Volume index:

I q = ∑q 1 p 0,

Quality index I р = ∑q 1 p 1, (prices)

Revolution index I o \u003d ∑q 1 p 1= I q * I p

where p 1, p 0 - the price of the reporting and base period

q 1 , q 0 - quantity in the reporting and base period.

The essence of factor analysis in economics

Definition 1

Factor analysis is a type of economic analysis that studies the influence of specific factors on economic performance. The main types of factor analysis: deterministic and stochastic analysis.

The basis of deterministic analysis is the methodology for studying the influence of those factors that have a functional relationship with a generalizing indicator.

In stochastic factor analysis, the influence of those factors that have a probabilistic relationship with a generalizing indicator, i.e. correlation.

Many factors influence the performance of an enterprise. They can be classified into internal, which depend on the activities of this firm, and external, independent of this enterprise.

The methods used in factor analysis can also be different. Deterministic factor analysis uses:

• Chain substitution method;
• Method of absolute and relative differences;
• index method;
• balance method;
• Integral method;
• Logarithmic method, etc.

Stochastic analysis uses:

• Correlation method;
• Regression method;
• Cluster analysis method;
• Dispersion method, etc.

The greatest completeness and depth of analytical research, the greatest accuracy of the results is ensured through the use of economic and mathematical methods. These methods have a great advantage over statistical and traditional methods, since they allow more accurate and detailed calculation of the influence of individual factors on the value economic indicators, as well as some analytical problems are solved with their help.

Relative difference method

Remark 1

The relative difference method is used in deterministic factor analysis to assess the impact of a particular factor on the growth of performance indicators. The main advantage of this method is its simplicity. However, it can only be used in multiplicative and multiplicative-additive factorial models.

The basis of this method is the method of elimination. Elimination is understood as the elimination of the influence of other factors, i.e. all other factors become static. main idea way is an independent change of all factors. First, the base value is changed to the reporting one for one factor, while the other factors are static, and then the second, third, etc. change.

To calculate the impact of the first factor on the effective one, multiply the base value of the effective indicator by the relative growth of the first factor in % and divide by 100. To calculate the degree of impact of the second factor, add the base value of the effective indicator and its increase from the first factor, and multiply the amount by the relative growth of the next factor, etc.

When using this method, the order of factors in the model and, consequently, the sequence of changing their values ​​is of great importance, since this determines the quantitative assessment of the influence of each individual factor.

The use of the method of relative differences involves the use of a correctly constructed deterministic factor model, the observance of a certain order in the arrangement of factors.

Factors can be both quantitative and qualitative. Qualitative factors reflect the internal properties, features and characteristics of the objects under study. For example, labor productivity, milk fat content, product quality. Quantitative factors characterize the quantitative certainty of the phenomenon. Quantitative factors have both cost and natural expression. Quantitative factors can characterize the volumes of production and sale of goods, and the value of such factors can be expressed both in money and pieces, etc.

If during the analysis there are several quantitative and qualitative indicators, then the value of the factors that are at the first level of subordination changes first, and then at the lower one.

The factors of the first level are the factors that have a direct impact on the performance indicator, and the factors that indirectly affect the performance indicator are at a lower level (second, third, etc.)

The algorithm for calculating the relative difference method is shown in Figure 1.

The sum of the quantities $∆X_A$, $∆X_B$ must be identical to the difference between $X_1$ and $X_0$.

An example of using the relative difference method

Consider the use of the relative difference method on a specific example. The volume of production for the year depends on the average annual number of workers (H) and the average annual output per worker (B). A two-factor multiplicative model is built, in which the number of workers is a quantitative factor, so it is in the first place, and output is a qualitative factor, and is located behind the quantitative one.

$OP = H B$

All data that will be used is presented in the table (Figure 2).

At the first step, the relative growth of factors is calculated (Figure 3).

Figure 3. Calculation of the relative growth of factors. Author24 - online exchange of student papers

At the second step, the degree of influence of the first factor on the performance indicator is determined (Fig. 4)

Figure 4. Calculation of the degree of influence of the factor. Author24 - online exchange of student papers

It follows from the data obtained that with an increase in the average annual number of employees by 2 people, the volume of production will increase by 400 thousand rubles.

At the third step, the sequential consideration of the factors of the model continues (Fig. 5)

According to the data obtained, it can be concluded that by increasing the average annual output of one worker, the volume of production increased by 810 thousand rubles.

At the fourth step, the calculations are verified (Fig. 6).

Thus, the calculations performed are correct.

The result of deterministic factor analysis is the decomposition of the increase in the effective indicator, due to the general influence or change in factor characteristics, into the sum of partial increases in the effective indicator, which are due to a change in only one factor. To do this, in addition to the index, specially developed methods, which are sometimes called techniques, are used in economic analysis. The main ones are the method of differences and the method of identifying the isolated influence of factors. In turn, the method of differences includes methods of chain substitutions, absolute (arithmetic) differences and relative (percentage) differences.

The method of chain substitutions is considered to be the main method of elimination. It is used in the study of functional dependencies and is intended to measure the impact of a change in factor characteristics on a change in the effective indicator with a constant (fixed) value of others.

To do this, the basic values ​​​​of each factor (planned, last period) are successively replaced by its actual data (reporting). The results of the successive replacement of each factor-indicator are compared. The difference between each subsequent and previous indicators characterize the influence of the factor, subject to the elimination of the influence of all other factors.

Based on the above, the method of chain substitutions is often called the method of sequential, gradual isolation of factors.

When applying the method of chain substitutions, one should adhere to a clear order for replacing factors:

First of all, volumetric (quantitative) indicators are replaced;

In the second - structural;

Third, quality.

In cases where there are several quantitative or qualitative indicators in the analytical model, the order is established among them - first they replace the main, primary (general) indicators, and then the secondary, derivative (partial) ones (Fig. 11.2).

Rice. 11.2. The sequence of replacing indicators when applying the method of chain substitutions

We will consider the general scheme for receiving chain substitutions using the example of a chotirox-factor multiplicative model:

where T - effective indicator;

a, b, c, d - factor indicators, and a - a qualitative indicator; v - structural indicator; c, d - volumetric (quantitative) indicators and indicator d is primary relative to indicator c.

Let's compare the actual values ​​of indicators (index "1") with the planned ones (index "0"). The total deviation of the T indicator from the plan will be:

.

For further calculations, we will rebuild our analytical model in the order necessary for the replacement of indicators. Then:

;.

Let us determine the variation of the effective indicator due to the change in all factors and each separately:

General impact of factors;

Influence of factor d;

Influence of factor c;

Influence of factor b;

Influence of factor a;

In this way:

Example. According to the data in the table, calculate the influence of factors on the deviation of the cost of output in the reporting year compared to the previous one (Table 11.5).

1. Define the total change in output:

(thousand UAH).

2. Calculate the influence of individual factors as a change in output:

a) the impact of a change in the number of workers on a change in output:

b) the impact of a change in the number of days worked by one worker on a change in output:

c) the impact of changes in the average shift duration on the dynamics of output:

d) the impact of changes in labor productivity on changes in output:

Deviation balance:

Thus, in the reporting year compared to the previous year, the output increased by 429.3 thousand UAH. It was influenced the following factors: change in the number of workers, the number of days worked, the duration of the work shift and the average hourly output (labor productivity).

Thus, due to the increase in the number of workers, output increased by 269.5 thousand UAH. Due to the reduction in the number of days worked, the output decreased by UAH 64.68 thousand. The increase in the duration of the shift led to an increase in output by 34.16 thousand UAH, and an increase in labor productivity - by 190.32 thousand UAH.

The reception of absolute (arithmetic) differences by the reception of relative differences is a modification of the reception of chain substitutions. It can be used in determining the influence of factor indicators on the resultant one in multiplicative and mixed models. It is better to use the method of absolute differences when the original data already contain absolute deviations in terms of factor indicators. However, this method is inappropriate to use for multiple models.

Consider the algorithm for calculating the influence of factors using the method of absolute differences using the example of a chotirox factor multiplicative model, which was used above in the method of chain substitutions:

There are absolute deviations of the actual values ​​of each factor indicator from the base ones:

;

;

;

.

As a result:

According to the above example (Table 11.5), we determine the influence of factors on the change in output using the reception of absolute differences.

1. Total change in output:

(thousand UAH).

2. The impact of changes in individual factors on the dynamics of output, namely:

a) number of employees:

(thousand UAH);

b) the number of days worked by one worker:

(thousand UAH);

c) average shift duration:

(thousand UAH);

d) labor productivity:

(thousand UAH).

Deviation balance:

It can be seen from the example that the method of absolute differences gives the same results of the influence of factors as the method of chain substitutions.

The reception of relative (percentage) differences is a kind of chain substitutions reception, which is used in multiplicative models, when the initial data are presented in relative terms. Determining the influence of factors using the reception of relative differences involves the following sequential actions:

To determine the influence of the first factor, the basic value of the effective indicator should be multiplied by the relative deviation (growth rate) of the first indicator, taken as a percentage, and divided by 100;

To calculate the influence of the second and subsequent factors, it is necessary to multiply the sum of the base value of the effective indicator and the magnitude of the influence of the previous factors by the relative deviation of the indicator factor in question, expressed as a percentage, and divide by 100.

For instance,. Then:

Deviation balance:

According to the above example, we determine the influence of factors on the change in output using the reception of relative differences, first calculating the percentage deviation (growth rate) of the indicators of the reporting year from the previous year (column 5 of Table 11.5):

1. General change in output.

(thousand UAH).

2. Change in output due to changes in the number of employees:

(thousand UAH).

3. Change in output due to a change in the number of days worked:

(thousand UAH).

4. Change in output under the influence of the dynamics of shift duration:

5. Influence of average hourly output on output:

Deviation balance:

As you can see, we got the same results using the methods of chain substitutions and relative differences.

It should be noted that it is advisable to use the reception of relative differences when the initial data for the analysis are presented in the form of relative values ​​(for example, the percentage of the plan completed).

Thus, the difference method can be used in studying the deviations of the actual values ​​of economic indicators from the planned ones, as well as in studying the dynamics of indicators. Its advantage is simplicity and versatility of application.

However, this method also has certain disadvantages. Thus, the result of the decomposition of the influence of factors on the effective indicator depends on the observance of the order (sequence) of their replacement. In addition, this method is non-additive in time, that is, the results of the work done, for example, for the year of analysis do not coincide with the corresponding data obtained by months or quarters.