Evaluation of the cost of capital and the discount rate based on the Russian financial statistics Текст научной статьи по специальности «Экономика и бизнес»

DOI: 10.29141/2658-5081-2023-24-1-3 EDN: OJNEWT JEL classification: C82, G31, O16

Dmitry S. Voronov Technical University of UMMC, Verkhnyaya Pyshma,

Sverdlovsk oblast, Russia

Lyudmila A. Ramenskaya Ural State University of Economics, Ekaterinburg, Russia

Evaluation of the cost of capital and the discount rate based on the Russian financial statistics

Abstract. The cost of capital and the discount rate calculated on its basis are the key parameters in the financial modelling and assessment of investment projects' economic efficiency. Therefore, the method for their evaluation is always a relevant issue for economists and financiers all over the globe. In conditions of unprecedent sanctions pressure this problem has gained special significance for Russian investors, for whom the assets denominated in 'unfriendly' currencies have ceased to be risk-free. The study aims to develop an algorithm for evaluating the cost of capital and calculating the discount rate based on ruble-denominated risk-free assets and Russian financial statistics. The methodological basis of the research is the theories of corporate finance and investment project design, as well as the portfolio theory. The statistics of the Russian stock market for 2003-2022 are studied using general scientific (systems analysis and synthesis) and econometric methods, as well as by adopting the Capital Asset Pricing Model (CAPM) and weighted average cost of capital (WACC). The paper suggests and tests a step-by-step algorithm for collecting and processing the Russian financial statistics to calculate the cost of capital and risk premiums to it. The findings prove that unsystematic risks should be assessed separately, rather than within the weighted average cost of capital, as well as propose a determined mechanism for this. The developed method allows avoiding the prohibitively high values of the cost of capital that arise during the use of foreign sources of information.

Keywords: Capital Asset Pricing Model (CAPM); weighted average cost of capital (WACC); discount rate; investment project; risk-free asset; risk assessment.

For citation: Voronov D. S., Ramenskaya L. A. (2023). Evaluation of the cost of capital and the discount rate based on the Russian financial statistics. Journal of New Economy, vol. 24, no. 1, pp. 50-80. DOI: 10.29141/2658-5081-2023-24-1-3. EDN: OJNEWT. Article info: received November 11, 2022; received in revised form December 15, 2022; accepted December 30, 2022

Introduction

In order to determine the discount rates of investment projects and the weighted average cost of capital (WACC), the Capital Asset Pricing Model (CAPM) is widely applied; it is built on the principle that the risk-free rate of return should be increased by a number of risk premiums. At the same time, the return on the 'most risk-free asset' - long-term US government bonds, is usually taken as the risk-free rate, and risk premiums are determined using American financial statistics.

However, after Russian foreign exchange reserves and US debt securities owned by Russian residents were blocked in the spring of 2022, it became clear that US government bonds are no longer a risk-free asset for Russian investors. Therefore, for the conditions of the Russian Federation, assessing the cost of capital by 'unfriendly' currencies has lost its relevance.

On the one hand, the problem of a risk-free asset is easily solved by replacing US government bonds with Russian government bonds. On the other hand, in this case, the American financial statistics used to determine risk premiums also require replacement.

Thus, in the current geopolitical situation, the traditional methods of estimating the cost of equity, which have been used in domestic practice until recently, need to be revised both in terms of the basis, a risk-free asset, and in terms of the superstructure, sources of information for determining risk premiums.

We propose the 'import substitution' algorithm for estimating the cost of capital and, for this purpose, we have developed methods for calculating the CAPM, WACC and discount rates based solely on Russian financial assets and information sources.

Literature review

The concept of weighted average cost of capital was proposed by Modigliani and Miller [1963] in 1963. The definition of WACC involves assessing the imputed cost of equity as well as the cost of raising debt financing.

In its turn, the Capital Asset Pricing Model is usually used to justify the cost of equity. Markowitz's works on modern portfolio theory were the prerequisites for the emergence of this model [Markowitz, 1952].

Markowitz's model describes an investor's choice of a portfolio, where the rate of return in the subsequent period is described stochastically. This model is based on the assumption that investors are efficient, risk-averse, and utility-maximising. Therefore, the choice of a portfolio depends on the return and risk (dispersion of return) determined for one investment period. Consequently, investors choose a portfolio that either minimises dispersion for a given level of return, or maximises return for a given level of risk, focusing on the 'efficient frontier' of possible portfolios. The procedure for identifying specific portfolios from an efficient set was developed by Tobin [1958].

The Capital Asset Pricing Model itself, proposed by Sharpe [1964] and Lintner [1965], is based on the relationship between the expected rate of return on asset and the measure of its systematic risk (the model's mathematical framework will be discussed in more detail below).

When developing the CAPM model, the authors added some assumptions to the Markowitz model about the existence of the same risk-free interest rate for all investors, as well as equal investor expectations regarding the rate of return, which leads to an identical assessment of the probability distributions of return on assets.

Numerous testing of the CAPM model [Miller, Scholes, 1972; Miles, Timmermann, 1996 and others] showed a strong relationship between the return on assets and their risk measure, which confirmed the reliability of the model. Due to this, the CAPM remains one of the most popular tools for determining the cost of capital of a company and the rate of return on investments today.

At the same time, some researchers noted errors in the application of this model, since in some cases it predicted the return on assets poorly [Basu, 1977; Davis, 1994; Ramenskaya, 2015]. The model has been criticised for the unrealistic assumptions, the instability of risk ratios over time, and also for being fundamentally unprovable due to the impossibility of monitoring the market portfolio as a whole [Black, 1972; Roll, 1977; Faff, Brooks, 1998]. This made it possible to question the applicability of the model in its original form.

Researchers have proposed numerous modifications of the CAPM model. The first versions of these modifications partially weakened the model's assumptions. Subsequently, the method for determining the risk ratios was subjected to adjustment, and the number of factors in the model increased.

Thus, based on a large-scale study of companies' shares traded on the New York Stock Exchange, Fama and French [1993] proposed the so-called three-factor model, adding indicators of a premium for a small company size, as well as a premium for value, defined as the ratio of the book and market value of a firm.

Subsequently, other multifactorial models appeared, for example, the four-factor model of Carhart [1997]. In 2015, Fama and French, based on the results of empirical studies, expanded their model to a five-factor model, including indicators of return on equity and investment in firm assets.

In developing capital markets, the application of the Systematic Risk-Based Downside Capital Asset Pricing Model (D-CAPM), developed by Estrada [2002], is being studied. Teplova and Selivanova [2007] justified the use of this model in the Russian market.

The studies of Russian scientists are generally in line with the global trend - they are aimed at testing various modifications of the CAPM model in the Russian market [Sidorenko, Sidorenko, Termosesov, 2022] and considering the possibility of using

it to calculate the discount rate for projects of domestic companies [Dorofeev et al., 2015; Lisovskaya, Mamedov, 2016; Okulov, Khafizova, 2018].

Thus, the Capital Asset Pricing Model in its modified form remains the most widely used tool for estimating the cost of equity.

Methods (research procedure)

The discount rate of an investment project is a rate of return that reflects the market assessment of the temporal cost of capital and risks inherent in this project. The discount rate is one of the key parameters for assessing the economic efficiency of investment projects, since it helps to bring future cash flows to the current point in time.

To determine the discount rate for an investment project, the world financial practice, as a rule, uses the weighted average cost of capital, which characterises the imputed cost of an investor's capital, taking into account the project financing structure [Damodaran, 2021]:

WACC project = Re x we + Rd x (1 - T) x wd, (1)

where WACC project is the weighted average cost of capital for a project, %; Re is the expected return (cost) of equity, %; we is the share of equity in project financing; Rd is the cost of borrowed capital, %; T is income tax rate, share; wd is the share of borrowed capital in project financing.

The cost of equity (Re) is determined by increasing the return of a risk-free asset by a number of risk premiums. As shown above, the modified CAPM is used for this, which can be represented as follows [Pereiro, 2002]:

Re = Rf + p x ERP + C + S1 + S2, (2)

where Re is the expected return (cost) of equity, %; Rf is the expected return on a risk-free asset, %; p is a coefficient characterising the measure of an asset market risk, units; ERP is an equity (corporate) risk premium, %; C is a country risk premium, %; S: is a company size premium, %; S2 is a company's specific risk premium, %.

Further, we propose ways to build CAPM and WACC models based solely on Russian publicly available financial statistics. In order to demonstrate the practical feasibility of the proposed algorithms, we will accompany the methodological theses at each step with a running example of calculating the cost of capital and the discount rate.

The expected return on a risk-free asset (Rf) is the starting point of the CAPM model. Until recently, it was believed that US government bonds were the most risk-free asset, so their return was considered as risk-free.

After the financial infrastructure of 'unfriendly' countries became toxic to Russian investors in 2022, US government bonds lost their status as a reliable tool for

investing capital. Therefore, in the conditions of the domestic financial market, it is necessary to consider Russian government bonds as a risk-free asset.

To determine their expected return, one can use the values of the zero-coupon yield curve published by the Central Bank of the Russian Federation (CBR)1. At the same time, the maturity of bonds must be taken depending on the planning horizon.

Suppose that in our example, the estimated period of an investment project is 10 years. Therefore, we choose the return on 10-year federal loan bonds (OFZs) as a risk-free return, the expected yield for them was 10.31 % per annum as of December 30, 2022. Thus we take Rf = 10.31 %.

Equity Risk Premium (ERP) can be defined as an additional return above the risk-free rate, which compensates for the additional risks associated with investing in corporate capital. In some works, it is also referred to as the systematic risk premium. This premium is defined as the difference (spread) between the return on a broad stock market portfolio and a risk-free rate:

ERP = Rm - Rh, (3)

where ERP is equity (corporate) risk premium, %; Rm is historical return on a broad stock market portfolio, %; Rfh is historical return on a risk-free asset, %.

The equity risk premium is calculated with historical data by finding the difference between the geometric average annual returns on a broad stock market portfolio and a risk-free asset [Damodaran, 2021]. We pay attention to the fact that the historical (past) return on a risk-free asset (Rfh), determined on the basis of stock market statistics, should not be confused with its expected (future) return (Rf), determined using the OFZ zero-coupon yield curve.

If a risk-free asset is US government bonds, the equity risk premium will be the difference (spread) between the average annual yield of a broad market portfolio of US stocks (S&P500 index) and long-term US government bonds. Further, to consider country risks (C), an adjustment is made based on default ratings assigned by specialised agencies (Standard & Poor's, Moody's, Fitch). In this case, an excellent source of information is the constantly updated database of the world-famous Professor Da-modaran, which allows you to quickly get the necessary indicators of the US stock markets since 19282.

Financiers around the world are so accustomed to using this database that, when changing the jurisdiction of a risk-free asset, they continue to use US financial statistics to determine the equity risk premium (and other premiums). This is probably

1 Bank of Russia. Russian Government Bond Zero Coupon Yield Curve, Values (% per annum). https://cbr.ru/ hd_base/zcyc_params/

2 Damodaran online. Data: Current. https://pages.stern.nyu.edu/~adamodar/New_Home_Page/datacurrent. html.

why available options for building the CAPM model using Russian government bonds [Suvorova, Suvorova, Kuklina, 2016; Galevskiy, 2019] in the calculations risk premiums are used based on the statistics of the US stock markets.

There arises a question: is such an 'eclectic' approach correct, when the risk premiums of the US stock market are applied to risk-free assets of other jurisdictions? From a methodological viewpoint, the discrepancy between the jurisdictions of a risk-free asset (Rf) and the equity risk premium (ERP) causes an error due to the geopolitical, legal, currency and other specifics of stock markets in different jurisdictions. On the contrary, the consistency of the CAPM model elements will only be achieved if they all belong to the same jurisdiction.

Therefore, the 'eclectic' approach is incorrect, whereby the jurisdiction of risk premiums should correspond to the jurisdiction of a risk-free asset. If Russian government bonds are chosen as this asset, the risk premiums must also be Russian. Therefore, our further objective is to propose an algorithm for calculating risk premiums based on the statistics of domestic stock markets, without using information sources from 'unfriendly' jurisdictions.

In accordance with the expression (3), in order to determine the equity (corporate) risk premium, we need to find the historical returns on a risk-free asset (Rfh) and a broad stock market portfolio (Rm).

Since long-term OFZs are taken as a risk-free asset, their yield can best be characterised using the Moscow Exchange Russia Government Bond Total Return index (RGBITR1). This index includes the most liquid OFZs with a duration of more than one year. The index is calculated using the total return method (i.e., it reflects the dynamics of the bonds value, taking into account the accumulated coupon rate).

As an indicator of a broad market portfolio of Russian stocks, we take the Moscow Exchange Gross Total Return Index (MCFTR2), which includes about 50 of the most liquid stocks of the largest and fastest growing Russian companies, weighted by market capitalisation (cap). The index is calculated using the total return method (i.e., it reflects the dynamics of stock price, taking into account dividend payments).

The values of both indices have been available on the Moscow Exchange website since 2003. This makes it possible to form a sample for 20 years, which can be considered a representative period. Information about the yield of the Russian portfolio of shares and bonds is presented in Table 1.

Based on the data presented in Table 1, we can determine that in the period of 2003-2022, the average annual growth rate of the stock index (MCFTR) was 14.21 % per annum (calculated using the geometric mean method), and the average annual

1 Moscow Exchange. Russia Government Bond Total Return index. https://www.moex.com/ru/index/RGBITR.

2 Moscow Exchange. Gross Total Return Index. https://www.moex.com/ru/index/totalreturn/MCFTR.

Table 1. Russian stock and bond indices, 2002-2022

Year Stock Index (MCFTR) Bond Index (RGBITR)

Close Change, % Close Change, %

2002 318.91 - 100.00 -

2003 514.71 61.40 127.73 27.73

2004 552.22 7.29 141.64 10.89

2005 1,020.91 84.87 158.13 11.64

2006 1,733.52 69.80 169.10 6.94

2007 1,952.83 12.65 181.50 7.33

2008 652.08 -66.61 171.42 -5.55

2009 1,474.41 126.11 231.98 35.33

2010 1,847.21 25.28 257.84 11.15

2011 1,580.19 -14.46 272.78 5.79

2012 1,718.76 8.77 312.73 14.65

2013 1,827.30 6.32 324.62 3.80

2014 1,793.60 -1.84 278.02 -14.36

2015 2,372.49 32.28 360.19 29.56

2016 3,150.20 32.78 413.58 14.82

2017 3,144.34 -0.19 466.49 12.79

2018 3,744.45 19.09 476.39 2.12

2019 5,184.22 38.45 571.63 19.99

2020 5,952.77 14.82 620.45 8.54

2021 7,250.04 21.79 589.78 -4.94

2022 4,548.82 -37.26 611.72 3.72

2003-2022 (average annual change) 14.21 - 9.48

Note: Tables 1 and 2 are based on the data of the Moscow Exchange. https://www.moex.com/.

growth rate of the bond index (RGBITR) was 9.48 %. Consequently, the return spread (difference) of these indices for 20 years amounted to 4.73 %.

Figure 1 shows the accumulated average annual returns of Russian stock and bond indices for 2003-2022, as well as the spread of accumulated returns.

15

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Fig. 1. Cumulative returns of the MCFTR and RGBITR indices, 2003-2022

m m vo tN 00 ON O i—i CN CO LO VO 00 <J\ O i—i CN

o o o o O O o i-H i-H Ï-H ï—1 i—i f—i 1—1 »-H 1-H Ï-H CN CN CN

o o o o o o o O o O O O O o o o O O O O

CS CS CN CN (N CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN

Analysis of the presented data allows us to make a conclusion that in the first 10 years of observations, the index yield spread was subject to significant fluctuations (from 3 to 38 %), which were due to the extremely high volatility of the equity index (MCFTR). This volatility can be explained by the period of the Russian stock market formation, as well as by the crisis of 2008.

Since 2012, the returns of both indices have stabilised, and their spread has been steady in the range of 6-8 %. This confirms the representativeness of the selected settlement period.

We note that in 2022, the cumulative average annual return of the Russian equity index decreased. As a result the yield spread between MCFTR and RGBITR narrowed from 8.08 % to 4.73 %. On the one hand, such a low spread value is atypical for the last 10 years of observations. On the other hand, it quite objectively reflects the 'atypical' strengthening of the ruble exchange rate (and the currency valuation of Russian government bonds) in 2022 due to external sanctions pressure.

Having determined the historical spread of returns on a broad stock market portfolio (Rm) and a risk-free asset (Rfh), we found a measure of corporate risk for the Russian market as a whole: ERP = 4.73 %. At the same time, the return on shares of individual companies may differ significantly depending on industry risks and debt load. To account for these factors, the equity risk premium rate must be adjusted by a correction factor showing the company's (industry's) exposure to market risk.

fi (beta) coefficient characterises the degree of industry and financial risk inherent in an analysed company (industry) and reflects the amplitude of fluctuations in its yield relative to the market as a whole. It can be argued that p coefficient shows by how many percents the shares quotes of the analysed company will change if the stock market as a whole changes by 1 %.

Mathematically, p is the regression coefficient in the correlation equation for the dependence betwen the return on the analysed stocks and the return on the stock index for the period under study. The coefficient value is calculated using the following formula [Sharpe, 1964]:

COM (4)

° (Rm)

where p is a coefficient characterising the measure of the asset market risk, units; COV(Ri, Rm) is covariance between the return on the asset R) and the return in the market as a whole (Rm) for the period under study; a2 (Rm) is the dispersion of market returns in general for the period under study.

Calculation of p for a public company is performed by regression analysis of the return on its shares relative to the stock index. For a non-public company (which

shares are not traded in the stock market), 0 is defined as the weighted average of 0 coefficients of comparable companies in the same industry (type of activity).

The choice of the calculation period for determining 0 depends on the planning horizon: the longer it is, the greater should be the depth of retrospective statistics for regression analysis. Most researchers agree that five years of data analysis is optimal for long-term planning. For short-term forecasting, it is sufficient to analyse statistics for 1-2 years.

At the same time, different companies in the industry may have significantly different debt burden (financial leverage), which leads to different financial risks of companies. The value of 0 coefficient obtained in the course of the regression analysis takes into account the actual indicators of the financial leverage of comparable companies (the so-called levered 0). It needs to be 'cleared' of the debt burden factor through Hamada's formula [Hamada, 1972] and get 'unlevered' 0:

Pcompar

Pu =-£-, (5)

K [1 + (1 - T) x (D/EfH

where 0C°mpar is the unlevered 0 of comparable companies; 0L°mpar is levered 0 of comparable companies; T is income tax rate, share; D/E)compar is the debt-to-equity ratio of comparable companies.

The debt-to-equity ratio (D/E) characterises a company's financial leverage. In the case when 0 is determined by several comparable companies, the value (D/E)compar is taken as an average value.

At the same time, debt (D) should include only the 'paid' part of the company's debt, on which interest payments are made [Damodaran, 2022]. On a balance sheet, debt is generally shown as loans and borrowings (short-term and long-term). Conversely, the composition of the debt in this case should not include current accounts payable and other interest-free obligations.

After calculating the unlevered 0 according to the expression (5), it is necessary to evaluate the debt-to-equity ratio of an analysed company (D/E)analysis, and then recalculate 0 to levered using the new value of the financial leverage:

0 analysis = 0 corner x [1 + (1 - j) x (D/E)-alysis], (6)

where 0Lnalysis is the levered 0 of an analysed company; 0compar is the unlevered 0 of comparable companies; T is income tax rate, share; (D/E)analysis is the debt-to-equity ratio of an analysed company.

We note that when calculating 0, the debt-to-equity ratio (D/E)analysis is determined in general for a company (according to its balance sheet) and therefore, it may not coincide with the financing structure of an individual investment project (expression (1)).

Continuing our example, we determine p coefficient for a non-public Russian iron and steel company. Due to the fact that this company's shares are not traded on the stock exchange, we will determine the ratio for comparable public companies.

As comparable companies, we take Novolipetsk Steel Company (NLMK), Severstal and Magnitogorsk Iron and Steel Works (MMK). Since the stock quotes that we will use to determine the returns of these companies do not reflect dividends to assess the returns in the stock market as a whole, we choose the Moscow Exchange Index without dividend payments - IMOEX1 (not to be confused with the previously used MCFTR index, which takes into account dividend payments).

In our example, a long planning horizon (10 years) is chosen. Therefore, we perform regression analysis for comparable companies for 5 years with a monthly calculation step. Comparable company returns and stock index statistics are given in Appendix 1.

The task of calculating p coefficients is easily solved in any statistical program, as well as using standard spreadsheets (SLOPE function). As a result of the calculations, we obtain the following values of the coefficients for comparable companies (rounded): NLMK is 0.57; Severstal is 0.49; MMK is 0.88. The average value of p coefficient (with equal weights of comparable companies) is 0.64.

Further, we determine the financial leverage of comparable companies. The source of information for this is the financial statements posted on the websites of the issuers. It is recommended to use IFRS (International Financial Reporting Standards) reporting, although in its absence it is permissible to use RAS (Russian Accounting Standards) reporting.

The average debt-to-equity ratio at the beginning of each calendar year out of five reporting years is (rounded): NLMK is 0.48; Severstal is 0.66; MMK is 0.15. The average financial leverage of comparable companies is 0.43.

We find the unlevered p of comparable companies:

_=-064-= QA8

[1 + (1 - 0.2) x 0.43]

We assume that the debt-to-equity ratio (D/E) of an analysed company is 0.74.

Then the levered p of the analysed company will be:

panalysis = 0.48 X [1 + (1 - 0.2) X 0.74] = 0.76.

The obtained value of p coefficient can be used to calculate the cost of equity in accordance with the expression (2).

1 Moscow Exchange. Moscow Exchange Index. https://www.moex.com/ru/index/IMOEX.

In the investment analysis, there are some situations when the structure of a company's liabilities is unknown, which makes it difficult to assess its financial leverage (D/E). This happens if a company does not disclose its financial statements, or a new enterprise is created to implement an investment project, the future capital structure of which has not yet been determined.

In this case, it is allowed to accept the financial leverage at the level of comparable companies. Mathematically, this means that (D/E)analysis = (D/E)compar. Then it is easy to prove that ^fnalysis = ^¿ompar, that is, the levered p of an analysed company will be equal to the levered p of comparable companies. Therefore, recalculation of the levered p into the unlevered one (expression (5)) and vice versa (expression (6)) is not required.

On the one hand, this approach results in some decrease in the accuracy of the results obtained. On the other hand, the complexity of the calculations and the collection of initial data is significantly reduced (because then it is not necessary to obtain information on the capital structure and calculate the financial leverage of every comparable companies).

In addition, in this case, p coefficient of comparable companies can be calculated on the basis of sectoral indices of the Moscow Exchange, reflecting the stock quotes of leading Russian companies whose economic activity belongs to the corresponding sectors of the national economy. Currently, 10 sectoral indices are distinguished, which cover the main sectoral groups of the domestic economy (from transport to information technology)1.

Thus, the Moscow Metal and Mining Exchange Index currently includes 13 largest Russian companies in ferrous and non-ferrous metals production, gold mining, etc. Consequently, sectoral indices ensure a more representative sample, which increases the accuracy of statistics.

These indices have another indisputable advantage: they are calculated taking into account dividend payments, which allows us to perform a regression analysis with respect to the Moscow Exchange Total Return Index including dividend payments (MCFTR), which we took as a base when estimating the yield spread of stocks and government bonds. This greatly increases the methodological consistency of the elements of the CAPM model.

Thus, if an analyst does not have a task of forming a unique sample of comparable companies or an analysed company is not characterised by an anomalous structure of liabilities, the determination of p coefficient is quite acceptable using a regression analysis of a corresponding Moscow Exchange Sectoral Index.

The described approach (we will refer to it as industrial one) is of particular relevance at the present time, when many public companies have ceased to publish their

1 Moscow Exchange indices. https://www.moex.com/ru/indices.

financial statements due to geopolitical tensions. Under these conditions, obtaining information on the capital structure of comparable companies and recalculating the beta taking into account the debt burden turns out to be fundamentally impossible. It follows that during the period of the moratorium on the publication of financial statements, the only possible option for determining ft coefficient is the regression analysis of a corresponding Moscow Exchange Sectoral Index.

The return statistics of Moscow Exchange Sectoral Indices for 2017-2022 (for 5 years) with a monthly calculation step are presented in Appendix 2. The values of 0 coefficients for each sectoral index are also given, which, with the industry approach, are taken as the levered 0 of an analysed company. The lowest value of 0 is observed in the "Chemistry and petrochemistry" sector (0.53), and the highest - in the "Information technologies" sector (1.39). The "Oil and Gas" sector has a beta of 1.00, which is due to its high share in the Russian economy. In the event that for some reason the CAPM model is calculated without industry reference (for the Russian market in general), then the beta of the Moscow Exchange index, which by definition is equal to 1.00, should be taken.

Now we will return to our example and calculate 0 coefficient for a metals company according to the 'industry' scheme. In Appendix 2 we find the "Metals and Mining" sector and determine that for it the value of this coefficient is 0.70. No additional calculations are required. It is fast and efficient! At the same time, "sectoral" 0 coefficients will remain relevant until at least 2024.

We note that the obtained "industry" beta value is very close to the value calculated by the classical algorithm for comparable companies, taking into account the financial leverage (0.76), which indicates the correctness of the "industry" approach.

As a result, we were able to propose and test two methods for calculating 0 coefficients based on Russian financial statistics.

The country risk premium (C) in the case of an 'unfriendly' risk-free asset is determined as the difference between the yields of US government bonds and government bonds of the assessed country or on the basis of default ratings assigned to countries by specialised rating agencies (Standard & Poor's, Moody's, Fitch, etc.).

Since Russian government bonds are a risk-free asset in our case, their yield includes all national geopolitical, currency and other risks. Therefore, no additional country risk premium is required (C = 0).

We should stress that it would be wrong to interpret a zero country risk premium as ignoring it. It is already included in the statistics of the Russian stock market, and therefore, an additional premium would lead to its re-registration.

For the same reason, there will be no need for inflationary adjustment, which is required when converting foreign currency cash flows into Russian rubles.

The company size premium (SJ reflects the additional premium for investing in non-public and small companies with higher risks. The studies by American economists conducted in the early 1980s found that small firms were more profitable than large firms. This pattern was first discovered by Banz [1981]. Fama and French [2012] made a great contribution to the study of the company size premium, proving that small cap ensures that stock returns exceed the forecast given by the CAPM model.

Since then, the including a size premium (for small cap) in the Capital Asset Pricing Model has become a common practice. This premium is usually based on data from consulting companies (e.g., Duff&Phelps or Morningstar) and ranges 1-4 % depending on the size of the company.

At the same time, not all economists agree with the application of the small size company premium. In particular, Horowitz, Loughran and Savin [2000] have shown that studies based on more recent data show different results. They divided the statistical sample into two parts: from 1963 to 1981 and from 1982 to 1997. For the first sample, the result was predictable: the premium was approximately 1.1 %. However, in the second sample, small firms performed worse than large firms, and the premium for small size was negative. Based on this, the researchers concluded that the size premium should not be applied in the pricing of capital assets.

Damodaran is also skeptical about the use of a risk premium for the size of the company. In his works, he points out that the additional returns of small and medium-sized firms was statistically observed only until the 1980s, after which the size premium lost its relevance [Damodaran, 2015]. He believes that if additional risks exist for small companies, they are already accounted for in p coefficients, whereby the application of a separate size premium will entail these risks re-counting. Therefore, Damodaran does not use the small company size premium in his cost of capital models.

The applicability of the size premium to Russian companies is a more debatable issue. Obviously, the hypotheses formulated during the study of the American stock market require verification when used in other markets. At the same time, it has not yet been possible to obtain statistical confirmation of the size premium on the Russian stock market. In particular, Fomkina [2016], Bogatyrev et al. [2013] and a number of other researchers point out to this fact.

In order to answer the question about the existence of a size premium in the domestic stock market, we, in our turn, propose comparing the return of the main Moscow Exchange Total Return Index including dividend payments (MCFTR), which includes only the largest Russian companies, with the return of the Moscow Exchange Medium and Small Cap Total Return Index including dividend payouts (MESMTR1).

1 Moscow Exchange Medium and Small Cap Total Return Index. https://www.moex.com/ru/index/totalreturn/ MESMTR/archive.

Statistics on the medium and small cap index has been maintained by the exchange since 2013, so the analysed period is limited to the specified time period. The initial data for the calculations are given in Table 2, their results are presented in Figure 2.

Table 2. Moscow Exchange Index and the Moscow Exchange Medium and Small Cap Index,

2013-2022

Year Moscow Exchange Index (MCFTR, large companies) Medium and Small Cap Index (MESMTR)

Close Change, % Close Change, %

2013 1,827.30 - 896.03 -

2014 1,793.60 -1.8 951.35 6.2

2015 2,372.49 32.3 1,378.95 44.9

2016 3,150.20 32.8 2,193.32 59.1

2017 3,144.34 -0.2 2,053.14 -6,4

2018 3,744.45 19.1 1,853.75 -9.7

2019 5,184.22 38.5 2,235.61 20.6

2020 5,952.77 14.8 2,733.64 22.3

2021 7,250.04 21.8 2,975.26 8.8

2022 4,548.82 -37.3 1,842.06 -38.1

2013-2022 (average annual change) 10.7 - 8.3

2014

2015

2016

2017

2018

2019

2020

2021

2022

Moscow Exchange Index (MCFTR, large companies) Medium and Small Cap Index (MESMTR)

Fig. 2. Return of MCFTR and MESMTR indices, 2014-2022

An analysis of the presented data allows us to state that in the period 2014-2016, medium and small cap companies had higher returns than large companies. However, since 2017, large companies have consistently shown higher returns.

In general, during 2014-2022, MESMTR grew by 105.6 %, having demonstrated an average annual (geometric average) yield of 8.3 % per annum over 9 years. During the same period, MCFTR increased by 148.9 %, and its average annual (geometric average) yield was 10.7 % per annum.

Consequently, the growth rates of large companies in the Russian stock market over the past 9 years have been higher than those of medium and small cap companies (both in recent years and in general over the analysed period). Thus, the hypothesis about the presence of a small size company premium in the Russian market was not confirmed.

Undoubtedly, 9 years is not a long period for the formation of a representative array of statistics. At the same time, taking into account the lack of confirmation of the company size premium in developed stock markets (which we have discussed above), we believe that there are not any statistical grounds for applying this risk premium to Russian companies. Therefore, no additional company size premium in the Russian market is required (Si = 0).

The company-specific risk premium (S2) reflects unsystematic risks to which a company is exposed. Such risks include low diversification of suppliers or buyers, remote location and poor infrastructure, specifics of local authorities and increased regulatory requirements, as well as a number of other adverse factors that increase the risks of economic activity.

As a rule, to assess the unsystematic risks premium, expert and rating assessments are used. Thus, Deloitte & Touche applies a method that involves studying the company's activities in ten different areas (from product price fluctuations to management competence), after which each of the areas is assessed with a risk premium of up to 1 % [Shepeleva, Nikitushkina, 2016]. It is easy to calculate that the total risk premium using this method can be up to 10 %.

Imagine that an analyst has performed a huge amount of research and based on the analysis of a long-term array of financial statistics has deduced to the nearest hundredth that the cost of equity before this step was 13.92 %. And he/she is asked to expertly add another 10-15 % to this value as a specific risk premium.

Obviously, this approach seems to be overly enlarged and highly subjective. In addition, it requires the involvement of subspecialists for peer review, which is sometimes more complicated than analysing long-term arrays of financial statistics. Therefore, we regret to state that an acceptable method for quantitative assessment of a company's specific risks has not yet been proposed; as a result most researchers do not apply this premium (including Damodaran).

On the one hand, the authors are convinced that ignoring specific risks is wrong, since it leads to an underestimation of the discount rate. On the other hand, the inclusion of specific risks in the cost of equity entails two important conflicts of methods.

Firstly, when calculating WACC, the cost of equity is taken into account in proportion to its share in financing sources (expression (1)). Then, with a share of own funds of 20-30 % (a typical financing structure for domestic investment lending),

the 'contribution' of specific risks to the discount rate is reduced by 3-5 times, which leads to their underestimation.

Secondly, if the specific risk premium is included in the cost of equity, the discount rate for all projects of a company with a similar financing structure will be the same. It contradicts the requirements of risk management, since different projects have different risk levels.

Therefore, recognising the need to consider specific risks, we believe that their assessment should be carried out outside the framework of the CAPM and WACC models. Thus, the consideration of specific risks at this stage is not required (S2 = 0). We will definitely return to them later.

After evaluating all the elements of the CAPM model, we can calculate a company's cost of equity. Taking into account our conclusions and assumptions, the expression (2) is presented below:

Re = Rf + 0 X ERP, (7)

where Re is the expected return (cost) of equity, %; Rf is the expected return on a risk-free asset, %; 0 is a coefficient characterising the measure of the market risk of an asset, units; ERP is equity risk premium, %.

It may seem that we have simply removed risk premiums from the expression (2). We should note again that this is not the case. We have included country risks (C) in the return of a risk-free asset, a company size premium (S1) is not observed in the domestic market, and we take specific risks (S2) out of the cost of equity.

Therefore, the apparent removal of some risk premiums does not mean they are ignored, but proceeds from the specifics of applying the CAPM model based on Russian financial statistics. At the same time, the model has become much more convenient to use and returned to its original form suggested by Sharpe in the mid-1960s [Sharpe, 1964]. We note that Damodaran, who is deservedly considered an unquestioned authority in investment appraisal, also calculates the cost of equity precisely according to the canonical Sharpe model (without premiums for company size and specific risks).

Let us return to the example of estimating the cost of equity of a Russian metals company. Previously, we determined that the risk-free return (Rf) amounts to 10.31 %, the equity risk premium (ERP) equals 4.73 %. We also calculated two options for 0 coefficient: 1) 'classical' (taking into account the financial leverage of an analysed company) is 0.76; 2) 'industrial' (taking into account the average industry financial leverage) is 0.70.

Then the 'classical' cost of equity is:

Re = 10.31 + 0.76 X 4.73 = 13.9 %.

'Industrial' option for calculating the cost of equity is:

Re = 10.31 + 0.70 X 4.73 = 13.6 %.

We note that the proposed 'sectoral' approach makes it possible to calculate the cost of equity by sectors of the Russian economy (Table 3).

Table 3. Cost of equity by groups of industries in Russian economy as of January 2023

Group of industries Rf, % ERP, % ß Re, %

Metals and mining 0.70 13.6

Chemistry and petrochemistry 0.53 12.8

Oil and gas 1.00 15.1

Power industry 0.76 13.9

Telecommunications 0.61 13.2

Finance 10.31 4.73 1.17 15.8

Consumer sector 0.95 14.8

Information technology 1.39 16.9

Construction 1.04 15.2

Transport 1.06 15.3

Mid and small cap 0.92 14.7

Whole-economy average 1.00 15.0

If a company is diversified, then the cost of equity should be taken as a weighted average of several industries, taking into account their share in revenue. If the assessment is carried out without sectoral reference (for the Russian market in general), the average indicators for the economy (15.0 %) should be taken.

The presented results are of high practical value. Suppose that an investment project is financed only with its own funds. Then it follows from the WACC formula (expression (1)) that WACC = Re. If we also assume that the project is low-risk and the specific risk premium is close to zero, the discount rate will tend to the cost of equity (a Re). Consequently, the calculated sectoral values of equity (Re) make it possible to promptly assess the level of sectoral discount rates without debt financing.

Since the p coefficients values and ERP value are relatively stable over time, they require recalculation no more than once a year (usually at the end of the calendar year). Therefore, they can be used by Russian analysts to build financial models until at least 2024 without adjustments.

The only variable in the CAPM model that can change significantly in the short term is the expected yield of Russian government bonds (Rf). At the same time, its update does not require additional calculations: one just needs to go to the website of the Central Bank of the Russian Federation1 and get the current yield. Further, in

1 Bank of Russia. Russian Government Bond Zero Coupon Yield Curve, values (% per annum). https://cbr.ru/ hd_base/zcyc_params/.

accordance with the expression (7), we can easily determine the new value of the cost of equity.

Having estimated the cost of equity, we move on to other elements of the WACC model.

The cost of borrowed capital (Rd) and the shares of project financing sources (we, wd) are determined based on the planned structure of project financing.

It should be noted that the cost and share of borrowed capital for an individual investment project may differ from similar indicators for a company as a whole.

To implement the project, a loan can be attracted on purpose, and then the share of borrowed funds in project financing will be greater than the average amount of borrowed capital in the structure of the company's liabilities. Or vice versa, for the implementation of the project, the owners can plan most of their own funds, and then their share in project financing will exceed the average amount of equity in the company's liabilities.

Therefore, one should distinguish between the WACC of a company in general and the WACC of an investment project.

If WACC is calculated for the company as a whole and there is a reason to believe that the cost and structure of its loan portfolio will not change significantly (for a mature business, such an assumption is quite acceptable), then the cost of borrowed capital (Rd) can be determined as the weighted average rate on existing loans and company loans. Then the shares of equity and borrowed capital (we, wd) will be determined by the formulas (8) and (9), respectively:

W<=DTir (8)

<9>

where we is the share of equity in project financing; wd is the share of borrowed capital in project financing; E is the value of the company's equity capital, rubles; D is the amount of borrowed capital of the company, rubles.

If WACC is calculated for a separate project, then the cost of borrowed capital (Rd) and the structure of funding sources (we, wd) should be taken based on the terms of loan agreements planned to be concluded as part of an investment project.

If information on the lending rate for the project is not available, the cost of borrowed capital can be taken based on the average rates on loans for non-financial organisations according to information published by the Central Bank of the Russian Federation 1.

1 Interest rates and structure of loans in rubles. https://cbr.ru/statistics/bank_sector/int_rat/LoansDB/.

Thus, according to data as of October 2022, the average rate on loans over 3 years was 9.1 % per annum. Since the key rate has remained unchanged since then, it can be assumed that the lending conditions have not changed substantially during this time, and in further calculations we can assume the cost of borrowing at the indicated level.

The cost of borrowed capital in the WACC model (expression (1)) is adjusted for the so-called tax shield effect (1-T), which reflects the reduction in the tax base for income tax by the amount of interest on loans and borrowings.

Continuing our running example, we assume that to finance an investment project a metals company plans to attract a bank loan on 30/70 terms (30 % is funds of a project initiator (we); 70 % is a bank loan (wd)). The income tax rate is 20 %, the estimated lending rate (Rd) is 9.10 % per annum (according to the Central Bank of the Russian Federation). The cost of equity (Re) was previously estimated by us according to the classical algorithm at 13.9 % per annum. Then, in accordance with the expression (1), we obtain the following:

WACC project = 13.9 X 0.30 + 9.10 X (1 - 0.2) X 0.70 = 9.3 %.

We have calculated the weighted average cost of capital (WACC) of the investment project. We note that in many works the discount rate is identified with the WACC indicator. However, if we assume that the discount rate is taken in the amount of WACC, then for all projects of a company with a similar financing structure, this rate will be the same. Obviously, this is wrong - different investment projects have different levels of risk.

Consequently, it is time to return to the issue of assessing the specific risks of a project. As we stated above, due to the imperfection of existing methods, the specific risk premium is applied extremely rarely. And if, when calculating the WACC for the company as a whole, it can be acceptable to refuse to take into account specific risks, then ignoring them when determining the discount rate of an investment project may lead to the underestimation of its risks.

Therefore, when evaluating the economic efficiency of a single investment project, the discount rate should be determined as the weighted average cost of capital, increased by the specific risks of a project. At the same time, it is important that the method for assessing specific risks should ensure the proportionality of the risk premium relative to the cost of capital and minimise subjectivity.

For example, the official current Guidelines for evaluating the efficiency of investment projects1 at an average level of risk require the use of a risk premium of 8-10 %

1 Guidelines for evaluating the efficiency of investment projects no. VK 477, approved by the Ministry of Economy of the Russian Federation, the Ministry of Finance of the Russian Federation and the State Construction Committee of the Russian Federation on June 21, 1999.

(clause 11.2 of this document). At the same time, in an environment where the WACC is only 9.3 %, the risk premium of 8-10 % makes the discount rate too high.

The reason for this disparity is the fixed nature of risk premiums, while the cost of capital changes following the dynamics of inflation and the key rate of the regulator. Therefore, to ensure proportionality, the specific risk premium should not be set absolutely, but relatively, through a multiplying coefficient to the cost of capital. Then you can write the following formula for calculating the discount rate of the investment project:

a = WACC project x KS, (10)

where a is the discount rate of an investment project, %; WACC project is the weighted average cost of capital for a project, %; KS is the risk ratio of a project.

The risk ratio (KS) reflects the level of specific (unsystematic) risks characteristic of the investment project under consideration, which makes it possible to differentiate projects by risk level. In order to minimise the subjective factor, the risk ratio should be determined deterministically, without the use of expert and other subjective assessments.

Based on this, we propose to set the project risk ratio (KS) depending on the strategic goals of its implementation (Table 4).

Table 4. Target classification of investment projects

Project's strategic goal Expected effect Risk level* Ks

Supporting projects (forced investments) Losses prevention due to the failure of fixed assets or the entry into force of regulatory requirements Low 1.00

Improving existing technology Cost reduction by optimising existing technology Moderate 1.25

Expanding production (growth projects) Growth in sales of already mastered types of products Average 1.50

Growth in sales due to the development of new types of products High 1.75

Innovation projects Growth in sales or cost reduction due to the development of new technologies Extremely high 2.00

Note: * If a project can be classified into several categories, the risk coefficient is taken at the maximum level.

Let us complete the calculations using our running example of determining the discount rate for an investment project of a metals company. Previously, we found that the WACC project = 9.3 %. Suppose that the goal of an investment project is to reduce costs by optimising existing technology. In accordance with the data in Table 4,

we determine that this project has a moderate level of risk (KS = 1.25). Then, in accordance with the expression (10), we obtain the following calculation:

a = 9.3 X 1.25 = 11.6 %.

Thus, we have assessed the specific risks of a project; taking them into account the discount rate amounts to 11.6 %.

Results and discussion

The main steps in calculating the discount rate are shown in Table 5, which summarises the results of all the previously described calculations.

Table 5. The main steps in calculating the discount rate

Indicator Value

Company and project parameters

Equity share in project financing (we) 0.30

The share of borrowed capital in project financing (wd) 0.70

Cost of borrowed capital (Re), % 9.10

Income tax rate, % 20.0

Macroeconomic yield parameters

Expected risk-free yield (10-year OFZs),% 10.31

Historical yield on a risk-free asset (RGBITR), % 9.48

Historical stock portfolio yield (MCFTR), % 14.21

Equity risk premium (ERP), % 4.73

P coefficient Classical Industrial

P coefficient unlevered (Pu) 0.48

Company debt/equity ratio (D/E) 0.74

P coefficient levered (Pi) 0.76

P coefficient industry levered (PJ - 0.70

Company equity cost (Re) 13.9 13.6

Weighted average cost of capital (WACC) 9.3 9.2

Project risk ratio (KS) 1.25

Nominal project discount rate (a), % 11.6 11.5

Expected (imputed) inflation, % 7.19

Real project discount rate (ar), % 4.1 4.0

Thus, we were able to estimate the cost of equity (according to the CAPM model), the weighted average cost of capital (according to the WACC model) and the discount rate of an investment project solely on the basis of Russian financial statistics.

For the colleagues' convenience, all the initial data and calculation models of our study are stored in spreadsheet format for public access and use on the website of our research group and are available at http://vds1234.ru/wacc/49.

We have already noted that Damodaran uses Sharpe's canonical model to determine the cost of equity (expression (7)). Here, our method coincides with the approach of

the American financier. Therefore, in order to verify the results obtained, we propose to compare the cost of equity, calculated by us, with a similar indicator calculated using the database of Damodaran1.

As of January 6, 2023, the expected yield on 10-year US government bonds (Rf) was 3.74 %. The historical yield spread for US stocks and bonds was 5.06 %, while the equity risk premium for the Russian Federation (based on 'unfriendly' default ratings) has now increased to 12.94 %. We take ft coefficient = 1.00 (for the market as a whole) and using the expression (7) we obtain the dollar cost of equity of 21.74 %. Adjusting it for the parity of inflation rates in the Russian Federation and the United States, we obtain the ruble cost of equity (Re) of about 25 %.

Obviously, such a high cost of capital is prohibitive for any investment. Probably, from the viewpoint of 'unfriendly' countries, the risks of investing in Russia in the current situation are really high (let us recall significant losses of many Western companies as a result of an emergency exit from the Russian Federation), which is why Damodaran's calculations make certain economic sense for them.

However, from the viewpoint of a Russian investor, the situation is quite different. Russia is our home, and we are not going to leave it. Therefore, the risks of an emergency winding down of business are irrelevant for us. Therefore, we are convinced that the cost of equity (Re) for the Russian market, equal to 15.0 % (Table 3), is much closer to the reality than the defensive hostile default ratings.

Consequently, the proposed method for assessing the cost of capital not only gives reliable results, but also becomes an uncontested option in the face of sanctions pressure on the Russian economy. This once again confirms the relevance of conducting economic research based on Russian financial statistics.

Conclusion

In our research, we proposed a method for calculating the cost of equity (according to the CAPM model), the weighted average cost of capital (according to the WACC model) and the discount rate of an investment project solely on the basis of Russian financial statistics.

In the course of the research, the hypothesis about the presence of a small company size premium in the Russian market was not confirmed, which is why the application of this risk premium in relation to Russian companies is not required. We substantiated the need to analyse unsystematic risks beyond the assessment of the cost of capital, and also propose a mechanism that minimises subjectivity and disparity in risk premiums for specific risks.

1 Damodaran online. Data: Current. https://pages.stern.nyu.edu/~adamodar/New_Home_Page/datacurrent.

html.

The proposed approach allows avoiding the high values of the cost of capital that arise when using 'unfriendly' sources of information. Moreover, the developed calculation algorithm adapts internationally recognised financial methods to the domestic information database. This makes it possible to ensure methodological continuity and, at the same time, to obtain an assessment of the cost of capital that is relevant to the domestic stock market, thereby contributing to an increase in the competitiveness of Russian companies [Belyaeva, Voronov, Erypalov, 2017; Voronov, 2019].

The directions for further research include studying the possibility of using financial leverage indicators while pursuing the sectoral approach to calculating 0 coefficient, as well as improving the mechanism for taking into account the specific risks of an investment project.

Appendix 1. Initial data for calculating ß coefficient, 2017-2022

Period MOEX Index NLMK Severstal MMK

Value Change, %. Value Change, %. Value Change, %. Value Change, %.

December 2017 2,109.74 - 147.22 - 887.40 - 41.86 -

January 2018 2,289.99 8.5 147.00 -0.1 919.10 3.6 45.61 9.0

February 2018 2,296.80 0.3 146.10 -0.6 918.40 -0.1 47.68 4.5

March 2018 2,270.98 -1.1 143.50 -1.8 872.40 -5.0 44.13 -7.4

April 2018 2,307.02 1.6 161.16 12.3 1,011.90 16.0 48.68 10.3

May 2018 2,302.88 -0.2 163.15 1.2 1,002.80 -0.9 49.09 0.8

June 2018 2,295.95 -0.3 151.84 -6.9 930.10 -7.2 42.55 -13.3

July 2018 2,321.11 1.1 162.40 7.0 1,020.30 9.7 46.26 8.7

August 2018 2,345.85 1.1 165.66 2.0 1,086.10 6.4 48.44 4.7

September 2018 2,475.36 5.5 177.90 7.4 1,091.30 0.5 52.19 7.7

October 2018 2,352.71 -5.0 160.42 -9.8 1,030.00 -5.6 47.94 -8.1

November 2018 2,392.50 1.7 158.36 -1.3 1,002.70 -2.7 46.81 -2.4

December 2018 2,369.33 -1.0 157.42 -0.6 942.90 -6.0 43.04 -8.1

January 2019 2,521.10 6.4 152.02 -3.4 998.50 5.9 43.30 0.6

February 2019 2,485.27 -1.4 158.44 4.2 1,028.80 3.0 44.50 2.8

Match 2019 2,497.10 0.5 170.50 7.6 1,028.00 -0.1 45.90 3.1

April 2019 2,559.32 2.5 171.10 0.4 1,045.20 1.7 44.20 -3.7

May 2019 2,665.33 4.1 172.32 0.7 1,036.40 -0.8 44.65 1.0

June 2019 2,765.85 3.8 159.70 -7.3 1,067.60 3.0 44.99 0.8

July 2019 2,739.50 -1.0 150.90 -5.5 1,028.80 -3.6 42.88 -4.7

August 2019 2,740.04 0.0 148.84 -1.4 1,002.80 -2.5 41.84 -2.4

September 2019 2,747.18 0.3 142.22 -4.4 933.20 -6.9 39.15 -6.4

October 2019 2,893.98 5.3 125.04 -12.1 882.20 -5.5 36.53 -6.7

November 2019 2,935.37 1.4 129.42 3.5 908.00 2.9 38.99 6.7

December 2019 3,045.87 3.8 143.72 11.0 937.60 3.3 41.95 7.6

January 2020 3,076.65 1.0 138.00 -4.0 911.40 -2.8 44.91 7.1

February 2020 2,785.08 -9.5 124.94 -9.5 814.60 -10.6 39.99 -11.0

March 2020 2,508.81 -9.9 124.00 -0.8 866.60 6.4 38.50 -3.7

April 2020 2,650.56 5.7 128.34 3.5 889.60 2.7 40.26 4.6

May 2020 2,734.83 3.2 137.76 7.3 934.60 5.1 40.44 0.4

Appendix 1 (concluded)

MOEX Index NLMK Severstal MMK

Period Value Change, Value Change, Value Change, Value Change,

%. %. %. %.

June 2020 2,743.20 0.3 140.88 2.3 864.00 -7.6 36.99 -8.5

July 2020 2,911.57 6.1 145.72 3.4 912.60 5.6 39.96 8.0

August 2020 2,966.20 1.9 154.48 6.0 931.00 2.0 37.85 -5.3

September 2020 2,905.81 -2.0 172.00 11.3 992.00 6.6 38.63 2.1

October 2020 2,690.59 -7.4 185.10 7.6 1,085.00 9.4 37.19 -3.7

November 2020 3,107.58 15.5 192.62 4.1 1,131.80 4.3 43.48 16.9

December 2020 3,289.02 5.8 208.84 8.4 1,323.20 16.9 55.83 28.4

January 2021 3,277.08 -0.4 210.42 0.8 1,262,80 -4.6 51.90 -7.0

February 2021 3,346.64 2.1 222.12 5.6 1,343.60 6.4 54.21 4.5

March 2021 3,541.72 5.8 242.16 9.0 1,534.60 14.2 60.88 12.3

April 2021 3,544.00 0.1 264.68 9.3 1,774.00 15.6 65.26 7.2

May 2021 3,721.63 5.0 261.88 -1.1 1,686.00 -5.0 63.17 -3.2

June 2021 3,841.85 3.2 230.74 -11.9 1,577.40 -6.4 60.58 -4.1

July 2021 3,771.58 -1.8 258.50 12.0 1,799.40 14.1 68.79 13.6

August 2021 3,918.96 3.9 247.60 -4.2 1,722.40 -4.3 73.85 7.4

September 2021 4,103.52 4.7 216.62 -12.5 1,520.00 -11.8 68.38 -7.4

October 2021 4,150.00 1.1 223.60 3.2 1,614.20 6.2 65.93 -3.6

November 2021 3,890.59 -6.3 217.08 -2.9 1,564.60 -3.1 59.66 -9.5

December 2021 3,787.26 -2.7 217.04 0.0 1,604.20 2.5 69.65 16.7

January 2022 3,530.38 -6.8 213.34 -1.7 1,511.00 -5.8 61.65 -11.5

February 2022 2,470.48 -30.0 177.50 -16.8 1,315.00 -13.0 47.67 -22.7

March 2022 2,703.51 9.4 171.90 -3.2 1,100.00 -16.3 43.90 -7.9

April 2022 2,445.17 -9.6 158.60 -7.7 1,095.00 -0.5 44.93 2.3

May 2022 2,355.75 -3.7 144.30 -9.0 974.80 -11.0 35.71 -20.5

June 2022 2,204.85 -6.4 133.40 -7.6 830.00 -14.9 32.10 -10.1

July 2022 2,213.81 0.4 130.00 -2.5 733.80 -11.6 26.47 -17.5

August 2022 2,400.08 8.4 120.66 -7.2 754.80 2.9 29.22 10.4

September 2022 1,957.31 -18.4 84.90 -29.6 622.00 -17.6 24.24 -17.0

October 2022 2,166.61 10.7 103.08 21.4 786.8 26.5 31.17 28.6

November 2022 2,174.53 0.4 106.48 3.3 790.8 0.5 31.57 1.3

December 2022 2,154.12 -0.9 117.76 10.6 904.00 14.3 32.87 4.1

$ coefficient - 0.57 - 0.49 - 0.88

Note: Appendices 1, 2 are based on the data of the Moscow Exchange. https://www.moex.com/.

Appendix 2. Sectoral indices of Moscow Exchange, 2017-2022

Period MOEX Index (MCFTR) Metals and mining (MEMMTR) Chemistry and petrochemistry (MECHTR) Oil and gas(MEOGTR)

Value Change, % Value Change, % Value Change, % Value Change, %

December 2017 3,144.34 - 7,383.78 - 17,647.62 - 6,266.93 -

January 2018 3,414.71 8.6 7,655.93 3.7 17,666.39 0.1 6,918.39 10.4

February 2018 3,424.86 0.3 7,587.18 -0.9 17,162.01 -2.9 6,931.20 0.2

March 2018 3,386.59 -1.1 7,379.96 -2.7 16,795.17 -2.1 6,978.62 0.7

April 2018 3,440.33 1.6 7,577.62 2.7 17,962.15 6.9 7,457.61 6.9

Appendix 2 (continued)

MOEX Index Metals and mining Chemistry and Oil and

Period (MCFTR) (MEMMTR) petrochemistry (MECHTR) gas(MEOGTR)

Value Change, Value Change, Value Change, Value Change,

% % % %

May 2018 3,441.38 0.0 7,441.20 -1.8 16,963.42 -5.6 7,551.78 1.3

June 2018 3,478.67 1.1 7,536.69 1.3 17,004.67 0.2 7,659.25 1.4

July 2018 3,598.97 3.5 7,870.91 4.4 17,414.77 2.4 8,137.50 6.2

August 2018 3,644.40 1.3 8,016.32 1.8 19,223.31 10.4 8,672.04 6.6

September 2018 3,862.51 6.0 8,465.81 5.6 18,841.25 -2.0 9,282.34 7.0

October 2018 3,698.66 -4.2 8,334.52 -1.6 18,716.36 -0.7 8,941.58 -3.7

November 2018 3,761.21 1.7 8,688.66 4.2 19,454.57 3.9 8,864.94 -0.9

December 2018 3,744.45 -0.4 8,865.11 2.0 19,376.31 -0.4 8,915.95 0.6

January 2019 3,994.97 6.7 9,044.30 2.0 19,588.07 1.1 9,251.78 3.8

February 2019 3,939.07 -1.4 9,259.09 2.4 19,862.65 1.4 9 040,80 -2.3

March 2019 3,957.82 0.5 9,124.82 -1.5 19,757.50 -0.5 9,092.41 0.6

April 2019 4,056.44 2,5 9,067.28 -0.6 19,423.82 -1.7 9,311.85 2.4

May 2019 4,247.64 4.7 9,036.62 -0.3 20,052.40 3.2 9,839.79 5.7

June 2019 4,490.16 5.7 9,582.23 6.0 21,010.77 4.8 10,154.99 3.2

July 2019 4,567.84 1.7 9,575.41 -0.1 20,900.30 -0.5 10,328.99 1.7

August 2019 4,568.74 0.0 9,987.79 4.3 22,189.15 6.2 10,224.03 -1.0

September 2019 4,596.98 0.6 9,856.28 -1.3 22,086.19 -0.5 10,594.59 3.6

October 2019 4,883.16 6.2 10,158.69 3.1 22,053.31 -0.1 11,568.00 9.2

November 2019 4,953.00 1.4 10,003.16 -1.5 21,959.54 -0.4 11,570.30 0.0

December 2019 5,184.22 4.7 10,779.80 7.8 22,202.79 1.1 12,014.46 3.8

January 2020 5,245.60 1.2 11,376.64 5.5 23,377.10 5.3 11,698.29 -2.6

February 2020 4,750.17 -9.4 10,755.55 -5.5 22,031.41 -5.8 10,194.15 -12.9

March 2020 4,284.51 -9.8 11,343.75 5.5 23,683.73 7.5 8,898.05 -12.7

April 2020 4,526.59 5.7 12,083.49 6.5 24,745.97 4.5 9,270.65 4.2

May 2020 4,702.49 3.9 12,324.81 2.0 25,632.65 3.6 9,612.60 3.7

June 2020 4,737.97 0.8 11,956.33 -3.0 24,943.48 -2.7 9,613.18 0.0

July 2020 5,146.69 8.6 13,873.84 16.0 25,843.12 3.6 9,806.03 2.0

August 2020 5,248.26 2.0 14,275.08 2.9 26,194.04 1.4 9,812.44 0.1

September 2020 5,146.23 -1.9 14,148.84 -0.9 26,325.62 0.5 9,336.26 -4.9

October 2020 4,845.13 -5.9 14,159.09 0.1 25,574.93 -2.9 8,569.14 -8.2

November 2020 5,596.76 15.5 15,130.42 6.9 27,121.22 6.0 10,201.62 19.1

December 2020 5,952.77 6.4 16,930.16 11.9 28,336.26 4.5 10,598.57 3.9

January 2021 5,938.74 -0.2 16,643.35 -1.7 31,125.22 9.8 10,698.91 0.9

February 2021 6,064.80 2.1 16,643.69 0.0 32,763.28 5.3 11,028.46 3.1

March 2021 6,419.07 5.8 17,548.84 5.4 33,098.61 1.0 12,044.15 9.2

April 2021 6,424.44 0.1 18,654.99 6.3 35,586.42 7.5 11,311.40 -6.1

May 2021 6,865.79 6.9 19,985.48 7.1 37,136.15 4.4 11,874.19 5.0

June 2021 7,103.76 3.5 19,014.43 -4.9 38,345.21 3.3 12,858.69 8.3

July 2021 7,096.15 -0.1 19,972.29 5.0 39,107.80 2.0 12,561.35 -2.3

August 2021 7,373.45 3.9 19,773.54 -1.0 43,532.18 11.3 12,834.83 2.2

September 2021 7,743.94 5.0 18,707.49 -5.4 45,203.36 3.8 14,258.82 11.1

October 2021 7,865.13 1.6 19,772.69 5.7 47,960.11 6.1 14,258.74 0.0

November 2021 7,373.48 -6.3 19,691.85 -0.4 49,285.83 2.8 13,258.43 -7.0

Appendix 2 (continued)

Period MOEX Index (MCFTR) Metals and mining (MEMMTR) Chemistry and petrochemistry (MECHTR) Oil and gas(MEOGTR)

Value Change, % Value Change, % Value Change, % Value Change, %

December 2021 7,250.04 -1.7 19,883.26 1.0 51,446.13 4.4 13,922.20 5.0

January 2022 6,794.02 -6.3 18,620.76 -6.3 49,112.70 -4.5 13,532.46 -2.8

February 2022 4,754.32 -30.0 16,045.91 -13.8 44,488.53 -9.4 9,880.29 -27.0

March 2022 5,202.78 9.4 16,474.73 2.7 65,851.24 48.0 10,881.31 10.1

April 2022 4,705.62 -9.6 15,746.81 -4.4 56,212.09 -14.6 9,758.14 -10.3

May 2022 4,544.33 -3.4 13,934.26 -11.5 55,347.36 -1.5 9,663.31 -1.0

June 2022 4,256.30 -6.3 11,837.91 -15.0 59,840.83 8.1 9,586.71 -0.8

July 2022 4,323.46 1.6 10,893.89 -8.0 57,451.74 -4.0 9,784.27 2.1

August 2022 4,687.26 8.4 11,315.71 3.9 62,866.20 9.4 10,428.54 6.6

September 2022 3,832.96 -18.2 8,264.86 -27.0 53,989.06 -14.1 8,385.78 -19.6

October 2022 4,429.18 15.6 9,769.22 18,2 57,195.25 5.9 9,947.36 18.6

November 2022 4,445.38 0.4 10,203.00 4.4 58,685.79 2.6 9,628.50 -3.2

December 2022 4,548.82 2.3 10,858.81 6.4 60,436.37 3.0 9,826.60 2.1

¡5 coefficient 1.00 - 0.70 - 0,53 - 1.00

Period Power industry (MEEUTR) Telecommunications (METLTR) Finance (MEFNTR) Transport (METNTR)

Value Change, % Value Change, % Value Change, % Value Change, %

December 2017 2,170.35 - 2,490.24 - 8,076.17 - 2,193.86 -

January 2018 2,303.43 6.1 2,727.42 9.5 8,640.87 7.0 2,225.58 1.4

February 2018 2,325.72 1.0 2,754.73 1.0 8,787.38 1.7 2,270.88 2.0

March 2018 2,329.80 0.2 2,660.55 -3.4 8,678.32 -1.2 2,380.60 4.8

April 2018 2,320.94 -0.4 2,608.09 -2.0 8,490.76 -2.2 2,187.79 -8.1

May 2018 2,301.47 -0.8 2,528.45 -3.1 8,303.19 -2.2 2,134.34 -2.4

June 2018 2,285.71 -0.7 2,572.90 1.8 8,364.89 0.7 2,101.23 -1.6

July 2018 2,293.26 0.3 2,708.39 5.3 8,254.37 -1.3 2,047.25 -2.6

August 2018 2,142.44 -6.6 2,748.22 1.5 7,614.38 -7.8 1,926.89 -5.9

September 2018 2,205.31 2.9 2,849.51 3.7 7,694.30 1.0 1,892.16 -1.8

October 2018 2,079.33 -5.7 2,749.48 -3.5 7,072.68 -8.1 1,768.44 -6.5

November 2018 2,085.19 0.3 2,675.91 -2.7 7,214.60 2.0 2,028.48 14.7

December 2018 2,042.60 -2.0 2,612.93 -2.4 6,768.15 -6.2 1,869.21 -7.9

January 2019 2,193.47 7.4 2,821.88 8.0 7,516.88 11.1 1,989.82 6.5

February 2019 2,162.66 -1.4 2,761.81 -2.1 7,257.46 -3.5 1,864.83 -6.3

March 2019 2,141.42 -1.0 2,754.24 -0.3 7,369.86 1.5 1,876.95 0.6

April 2019 2,235.14 4.4 2,790.49 1.3 7,431.59 0.8 1,864.76 -0.6

May 2019 2,330.75 4.3 2,821.94 1.1 7,649.10 2.9 1,841.51 -1.2

June 2019 2,602.47 11.7 3,098.45 9.8 8,232.39 7.6 1,983.46 7.7

July 2019 2,547.82 -2.1 3,127.69 0.9 8,391.24 1.9 2,088.48 5.3

August 2019 2,506.99 -1.6 3,126.07 -0.1 8,206.04 -2.2 2,146.95 2.8

September 2019 2,544.13 1.5 3,095.49 -1.0 8,344.94 1.7 2,077.48 -3.2

Appendix 2 (continued)

Period Power industry (MEEUTR) Telecommunications (METLTR) Finance (MEFNTR) Transport (METNTR)

Value Change, % Value Change, % Value Change, % Value Change, %

October 2019 2,498.44 -1.8 3,355.29 8.4 8,427.72 1.0 2,140.43 3.0

November 2019 2,589.92 3.7 3,549.62 5.8 8,842.75 4.9 2,105.52 -1.6

December 2019 2,727.68 5.3 3,677.05 3.6 9,072.40 2.6 2,190.47 4.0

January 2020 3,056.85 12.1 3,955.74 7.6 9,360.50 3.2 2,249.73 2.7

February 2020 2,901.14 -5.1 3,885.98 -1.8 8,806.67 -5.9 1,987.10 -11.7

March 2020 2,497.87 -13.9 3,564.85 -8.3 7,017.88 -20.3 1,616.57 -18.6

April 2020 2,683.69 7.4 3,839.13 7.7 7,755.88 10.5 1,739.96 7.6

May 2020 2,940.38 9.6 3,841.66 0.1 8,196.61 5.7 1,831.80 5.3

June 2020 3,006.21 2.2 3,986.32 3.8 8,515.13 3.9 1,940.48 5.9

July 2020 3,188.29 6.1 4,162.00 4.4 9,886.97 16.1 1,960.98 1.1

August 2020 3,040.37 -4.6 4,393.76 5.6 9,956.52 0.7 1,928.55 -1.7

September 2020 3,122.64 2.7 4,417.93 0.6 10,232.87 2.8 1,850.58 -4.0

October 2020 2,984.39 -4.4 4,155.44 -5.9 9,576.67 -6.4 1,568.81 -15.2

November 2020 3,189.04 6.9 4,298.58 3.4 11,335.35 18.4 1,859.32 18.5

December 2020 3,312.36 3.9 4,394.66 2.2 11,623.09 2.5 1,844.02 -0.8

January 2021 3,266.36 -1.4 4,444.87 1.1 12,263.49 5.5 1,899.72 3.0

February 2021 3,261.39 -0.2 4,373.79 -1.6 13,719.22 11.9 1,876.85 -1.2

March 2021 3,261.45 0.0 4,378.32 0.1 14,992.10 9.3 1,861.83 -0.8

April 2021 3,209.84 -1.6 4,376.76 0.0 15,620.20 4.2 1,825.21 -2.0

May 2021 3,305.75 3.0 4,529.36 3.5 16,933.30 8.4 1,915.94 5.0

June 2021 3,241.16 -2.0 4,553.78 0.5 17,516.85 3.4 1,950.52 1.8

July 2021 3,190.59 -1.6 4,484.03 -1.5 17,473.62 -0.2 2,017.08 3.4

August 2021 3,283.27 2.9 4,645.29 3.6 18,663.05 6.8 2,132.10 5.7

September 2021 3,210.84 -2.2 4,600,52 -1.0 18,655.94 0.0 2,181.21 2.3

October 2021 3,277.11 2.1 4,540,51 -1.3 19,436.09 4.2 2,198.68 0.8

November 2021 3,021.28 -7.8 4,238,60 -6.6 17,965.25 -7.6 1,962.81 -10.7

December 2021 2,951.36 -2.3 4,325,77 2.1 16,886.66 -6.0 2,043.74 4.1

January 2022 2,769.11 -6.2 4,033,56 -6.8 15,462.45 -8.4 1,905.54 -6.8

February 2022 2,073.86 -25.1 3,424.86 -15.1 8,965.01 -42.0 1,257.13 -34.0

March 2022 2,150.35 3.7 3,423.57 0.0 9,251.74 3.2 1,417.85 12.8

April 2022 2,114.35 -1.7 3,033.09 -11.4 8,369.20 -9.5 1,366.21 -3.6

May 2022 2,230.71 5.5 3,469.36 14.4 7,667.84 -8.4 1,298.47 -5.0

June 2022 2,292.32 2.8 3,736.86 7.7 7,439.76 -3.0 1,184.83 -8.8

July 2022 2,373.20 3.5 3,800.82 1.7 7,716.12 3.7 1,147.19 -3.2

August 2022 2,308.09 -2.7 3,721.77 -2.1 8,732.84 13.2 1,274.79 11.1

September 2022 1,877.31 -18.7 3,017.06 -18.9 7,301.41 -16.4 1,019.07 -20.1

October 2022 2,235.66 19.1 3,552.81 17.8 8,326.29 14.0 1,203.63 18.1

November 2022 2,261.84 1.2 3,657.79 3.0 8,584.06 3.1 1,189.19 -1.2

December 2022 2,290.38 1.3 3,642.85 -0.4 8,772.88 2.2 1,129.83 -5.0

¡5 coefficient 0.76 - 0.61 - 1.17 - 1.06

Appendix 2 (continued)

Period Consumer sector (MECNTR) Information Technology (MEITTR)* Construction companies (MERETR)* Medium and small cap (MESMTR)

Value Change, % Value Change, % Value Change, % Value Change, %

December 2017 7,398.79 - - - - - 2,053.14 -

January 2018 7,460.59 0.8 - - - - 2,135.35 4.0

February 2018 7,491.05 0.4 - - - - 2,142.08 0.3

March 2018 7,385.89 -1.4 - - - - 2,110.80 -1.5

April 2018 7,305.03 -1.1 - - - - 2,057.95 -2.5

May 2018 7,343.77 0.5 - - - - 2,051.28 -0.3

June 2018 7,160.52 -2.5 - - - - 2,040.98 -0.5

July 2018 6,908.21 -3.5 - - - - 1,989.72 -2.5

August 2018 6,938.73 0.4 - - - - 1,941.45 -2.4

September 2018 6,647.93 -4.2 - - - - 1,923.17 -0.9

October 2018 6,413.96 -3.5 - - - - 1,845.14 -4.1

November 2018 6,646.99 3.6 - - - - 1,897.52 2.8

December 2018 6,641.46 -0.1 - - - - 1,853.75 -2.3

January 2019 7,015.41 5.6 - - - - 1,947.01 5.0

February 2019 6,822.83 -2.7 - - - - 1,937.18 -0.5

March 2019 6,807.73 -0.2 - - - - 1,915.45 -1.1

April 2019 7,150.20 5.0 - - - - 1,955.03 2.1

May 2019 7,204.22 0.8 - - - - 1,989.73 1.8

June 2019 7,302.11 1.4 - - - - 2,095.61 5.3

July 2019 7,399.31 1.3 - - - - 2,171.36 3.6

August 2019 7,537.07 1.9 - - - - 2,129.32 -1.9

September 2019 7,252.20 -3.8 - - - - 2,116.79 -0.6

October 2019 7,028.35 -3.1 - - - - 2,107.98 -0.4

November 2019 7,319.57 4.1 - - - - 2,165.04 2.7

December 2019 7,538.71 3.0 - - - - 2,235.61 3.3

January 2020 8,064.24 7.0 - - - - 2,445.60 9.4

February 2020 7,291.36 -9.6 - - - - 2,264.10 -7.4

March 2020 6,976.33 -4.3 - - 5,440.21 - 1,913.08 -15.5

April 2020 7,303.32 4.7 - - 5,198.21 -4.4 2,029.53 6.1

May 2020 7,429.70 1.7 - - 5,200.24 0.0 2,109.69 3.9

June 2020 8,243.52 11.0 - - 5,896.57 13.4 2,245.77 6.5

July 2020 9,422.84 14.3 - - 6,539.01 10.9 2,419.64 7.7

August 2020 9,835.13 4.4 - - 6,865.35 5.0 2,477.27 2.4

September 2020 10,276.11 4.5 - - 7,568.81 10.2 2,504.92 1.1

October 2020 9,808.04 -4.6 - - 7,817.15 3.3 2,418.59 -3.4

November 2020 10,605.97 8.1 - - 8,092.19 3.5 2,682.03 10.9

December 2020 11,329.69 6.8 5,086.88 - 8,012.32 -.,0 2,733.64 1.9

January 2021 11,298.25 -0.3 4,832.47 -5.0 9,126.72 1.,9 2,822.85 3.3

February 2021 11,520.40 2.0 4,920.39 1.8 9,428.16 3.3 2,871.21 1.7

Marc 2021 11,984.27 4.0 4,916.21 -0.1 10,226.88 8.5 2,898.07 0.9

April 2021 11,816.65 -1.4 5,008.19 1.9 10,183.05 -0.4 2,888.30 -0.3

May2021 12,344.50 4.5 4,909.70 -2.0 11,301.52 11.0 3,012.53 4.3

June 2021 12,513.01 1.4 5,146.82 4.8 11,714.48 3.7 3,024.94 0.4

Appendix 2 (concluded)

Period Consumer sector (MECNTR) Information Technology (MEITTR)* Construction companies (MERETR)* Medium and small cap (MESMTR)

Value Change, % Value Change, % Value Change, % Value Change, %

July 2021 12,192.06 -2.6 4,902.77 -4.7 12,538.58 7.0 3,009.12 -0.5

August 2021 12,970.59 6.4 5,416.51 10.5 14,367.39 14.6 3,189.42 6.0

September 2021 12,753.36 -1.7 5,548.22 2.4 15,230.35 6.0 3,128.35 -1.9

October 2021 13,206.18 3.6 5,533.38 -0.3 13,506.83 -11.3 3,252.84 4.0

November 2021 12,552.81 -4.9 5,123.56 -7.4 12,654.14 -6.3 3,078.75 -5.4

December 2021 11,915.91 -5.1 4,247.08 -17.1 12,484.33 -1.3 2,975.26 -3.4

January 2022 10,629.83 -10.8 3,378.20 -20.5 11,277.67 -9.7 2,670.00 -10.3

February 2022 7,644.97 -2.,1 1,806.90 -46.5 6,467.46 -42.7 1,996.23 -25.2

March 2022 9,324.43 22.0 2,228.21 23.3 7,595.63 17.4 2,309.88 15.7

April 2022 7,960.78 -14.6 1,706.00 -23.4 6,988.59 -8.0 2,055.37 -11.0

May 2022 7,209.09 -9.4 1,483.62 -13.0 6,689.42 -4.3 1,963.34 -4.5

June 2022 7,003.73 -2.8 1,475.57 -0.5 8,486.73 26.9 1,915.22 -2.5

July 2022 8,092.87 15.6 1,863.94 26.3 8,950.93 5.5 2,031.79 6.1

August 2022 8,804.71 8.8 2,057.29 10.4 9,083.96 1.5 2,115.27 4.1

September 2022 6,945.40 -21.1 1,702.88 -17.2 6,354.28 -30.0 1,584.85 -25.1

October 2022 8,496.58 22.3 1,979.30 16.2 7,316.54 15.1 1,897.79 19.7

November 2022 8,031.62 -5.5 1,918.41 -3.1 7,170.38 -2.0 1,902.86 0.3

December 2022 7,592.45 -5.5 1,770.62 -7.7 7,074.10 -1.3 1,842.06 -3.2

¡5 coefficient 0.95 - 1.39 - 1.04 - 0.92

Note: * Until 2020, the sectoral index was not calculated.

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Information about the authors

Dmitry S. Voronov, Dr. Sc. (Econ.), Associate Prof., Head of Applied Economics Dept. Technical University of UMMC, Verkhnyaya Pyshma, Sverdlovsk oblast, Russia. E-mail: vds1234@yandex.ru

Lyudmila A. Ramenskaya, Cand. Sc. (Econ.), Associate Prof. of Corporate Economics and Business Maganement Dept. Ural State University of Economics, Ekaterinburg, Russia. E-mail: ramen_lu@mail.ru

© Voronov D. S., Ramenskaya L. A., 2023