ks - it is return on investments in equity;

T - it is marginal corporate income tax rate.

In the formula (1) company's debt consists of the sum of its short-term and long-term debts. The value of equity was taken from the initial database `Intellectual capital of Russian companies'.

In the formula (1) the required creditors' profitability was calculated by the following formula:

, (2)

where: spread - it is the default spread of a company;

krf - it is risk-free profitability (rate of return);

country_premium - it is premium for the risk of investing in emerging markets;

In the formula (2) the credit spread was taken from the Damodaran statistic database. It was determined for each company individually depending on its value of interest coverage ratio (ICR), which was computed by the following formula:

, (3)



where: EBIT - it is earnings before interest and taxes.

In the formula (3) all values ??were taken from the initial database `Intellectual capital of Russian companies'.

In the formula (2) a risk-free rate of return was computed as the average yield of ten-year US treasury bonds for a fifty-year period (for 2010 the period was from 1960 to 2010, for 2011 the period was from 1961 to 2011, for 2012 the period was from 1962 to 2012, for 2013 the period was from 1963 to 2013, for 2014 the period was from 1964 to 2014). The Treasury bond yield was taken from the Damodaran statistic database.

The value of the Russian country risk was taken separately for each year from the Damodaran statistic database.

In the formula (1) the return on investments in equity or the cost of equity was calculated by means of the CAPM model (Capital Asset Pricing Model):

, (4)

where: km - it is the market portfolio yield of securities;

вl - it is beta coefficient (leverage beta) measuring the level of the relevant risk of individual stocks (“the amount of risk” which is added to the market portfolio by a single stock).

In the formula (4) the market portfolio yield of securities was assessed as the average value of the yield as it was estimated by the S&P 500. There was taken a fifty-year period and calculations were made in the same way as it was done with the risk-free rate of return. The data was also taken from the Damodaran statistical database.

However, it should be built on the premise that a risk level increases simultaneously with a growth of the share of borrowed funds in company's capital structure. In turn, rise of the risk level leads to a change of the cost of equity.

This interrelation can be estimated by the means of the Hamada equation, which allows to determine an effect of share of a borrowed capital change (and, consequently, a change of a financial leverage ratio) on a company's beta coefficient. Thus, the leverage beta was calculated by the formula of the Hamada equation:

, (5)

where: вul - it is a beta coefficient or non-leverage beta which has the same economic meaning as leverage beta, but provided that a company does not use borrowed funds.

In the formula (5) the value of the non-leverage beta was taken from the Damodaran statistical database for Europe individually for each particular industry and for each particular year.

Due to the fact that initial data in the sample is in euro while km and krf are interest rates, which are measured in dollars, these two interest rates were transferred into euro by using the following formula of Interest Rate Parity:

where: - rate of inflation in the EU or US respectively.

The current weighted average cost of capital was calculated for each company in the sample taking into account its real capital structure in each year.

A standard financial leverage coefficient was chosen as a quantitative indicator of a capital structure. It was calculated by the following formula:

, (6)

where: fin_lev - it is a financial leverage ratio;

debt - it is a long-term company's liabilities;

loans - it is a short-term company's liabilities;

funds - it is company's equity

In the formula (6) the total amount of all company's borrowed funds is in term of a fraction. Thus, a financial leverage index is the ratio of company's borrowed funds to its own funds and, subsequently, represents the structure of company's capital.

After that, there was found an optimal capital structure for each company with the help of the WACC method. The procedure of searching an optimum consisted of several steps.

First of all, various ratios of equity and borrowed funds in the capital structure of each particular company were paste in the WACC formula (10% of equity - 90% of debt, 20% of equity - 80% of debt and so on). For each ratio cost of debt and equity were recomputed. Concerning the required creditors' profitability, it changed each time because of the value of spread which depends on the ICR. In turn, the ICR took various values owing to change of interests payable (in the denominator) which rose and fell with the increase and decrease of company's possible debt. Regarding the return on investments in equity, it changed its value because beta coefficient (leverage beta) is calculated by means of the Hamada equation. Thereby, as this equitation allows to consider an increase of risk level which takes place when a share of borrowed funds in company's capital structure grows, beta coefficient changed its value with the changed of a debt-equity ratio. Finally, a new value of WACC was obtained each time.

After that, the minimum value of the weighted average total cost of capital was found among all enumerated possible variants of a capital structure. This scheme was applied to each particular company in each year from the observed period. As a result, the ratio which gave the minimum WACC value was taken as the optimum point of a capital structure for each company. Finally, a quantitative indicator of a capital structure was calculated by using the formula (6) for a company.

It is worth mentioning that the option with 100% of borrowed funds and 0% of own ones was not taken into consideration. It is due to the fact that according to the Russian Legislation each company must have an authorized capital. So, a totally debt financing is an impossible option for Russian companies.

It was necessary to determine an average credit interest for all debts of each particular company in order to calculate a credit interest which would be paid by a company in case of another share of borrowed funds in its capital structure. All these calculations were necessary for computing the minimum WACC. So, the amount of real interest payments was divided by the real value of borrowed capital:

, (7)

This is a rather rough method of calculating average company's debt interest. However, since almost no company from the sample disclosed notes to its financial statements this approach has become the only possible one, although it feasible gives a skewed estimation.

3.2 Method of calculation of an optimal capital structure by using regression equation approach

The second method of calculation of an optimal capital structure was a regression equation. It has a number of significant advantages. It allows to examine a number of determinants at once, consider their joint effect, and take into account some peculiarities of a particular country or industry and even nonlinear relations of variables with a capital structure. Moreover, this method is one of the most widespread approaches among foreign scholars (Rajan and Zingales, 1995; Bevan and Danbolt, 2002; Bauer, 2004; Chen, 2004; Deesomsak et. al. 2004; Beattie et al., 2006; Fraser et al., 2006; Delcoure, 2007; Chakraborty, 2010; Qui and La, 2010; Cйspedes et al., 2010; Kedzior, 2012; Kouki, 2012; Mokhova and Zinecker, 2013).

The made literature review has revealed the tremendous abundance of researches investigated relations of various determinants with company's capital structure. It is worth noticing, that a group of determinants significantly differs depending on a level of a country's economic development - country with developed or developing financial market. This condition provides serious peculiarities of functioning of the whole economic system. In order to systemize the acquired results the Table 1 was created.

Table 1 Determinants of an optimal capital structure

Determinant	Researches
	Developed financial markets	Developing financial markets
Profitability	Campbell, Graham, 2001;Bauer, 2004; Bevan, Danbolt, 2004; Chen, 2004; Loof, 2004; Beattie, 2006; Dudley, 2007; Qiu, La, 2010; Leary, Roberts, 2010; Dang, 2012; Ke?dzior, 2012; Kouki, 2012; Mokhova, Zinecker, 2013;Antill, Grenadier, 2019; Cappa et al., 2019;	Deesomsak et al., 2004; Fraser et al., 2006; Delcoure, 2007; Chakraborty, 2010; Cйspedes et al., 2010; Thippayana, 2014; Sohrabi, Movaghari, 2019
Liquidity	Campbell, Graham, 2001; Cappa et al., 2019	Deesomsak et al., 2004
The share of intangible assets in the total assets of the company	Rajan, Zingale, 1995; Bauer, 2004; Bevan, Danbolt, 2004; Chen, 2004; Loof, 2004; Dudley, 2007; Qiu, La, 2010; Leary, Roberts, 2010; Kouki, 2012; Mokhova, Zinecker, 2013	Deesomsak et al., 2004; Fraser et al., 2006; Chakraborty, 2010; Cйspedes et al., 2010; Sohrabi, Movaghari, 2019
Company' value (Market to Book ratio)	Loof, 2004; Qiu, La, 2010; Leary, Roberts, 2010; Antill, Grenadier, 2019	Fraser et al., 2006; Sohrabi, Movaghari, 2019
Size (natural logarithm of assets)	Scott, 1976; Rajan, Zingale, 1995; Campbell, Graham, 2001;Bauer, 2004; Bevan, Danbolt, 2004; Chen, 2004; Loof, 2004; Beattie, 2006; Qiu, La, 2010; Dang, 2012; Ke?dzior, 2012; Kouki, 2012; Mokhova, Zinecker, 2013; Antill, Grenadier, 2019; Cappa et al., 2019	Deesomsak et al., 2004; Fraser et al., 2006; Delcoure, 2007; Chakraborty, 2010; Cйspedes et al., 2010; Thippayana, 2014; Sohrabi, Movaghari, 2019

For the present research were chosen the five most common determinants of an optimal capital structure: profitability, tangibility of assets, liquidity, company's value and size. Thus, the following econometric model was created for calculation of an optimal capital structure:



, (8)

where: opt_cs - an optimal capital structure;

prof - profitability;

liq - liquidity;

tang - share of intangible assets in the total assets of the company;

value - company's value;

size - company size;

Y_2010 - a dummy-variable conforming to the 2010 year of the observation;

Y_2012 - a dummy-variable conforming to the 2012 year of the observation;

Y_2013 - a dummy-variable conforming to the 2013 year of the observation;

Y_2014 - a dummy-variable conforming to the 2014 year of the observation;

The biggest number of observations in each sector was in 2011 (see Appendix 1). So the variable Y_2011 was taken as base and excluded from the model.

This regression model is additive because it is presumed that company's capital structure should be deduced as the sum of individual effects of the explanatory variables.

As for the variables of the model:

1) Profitability was calculated by the formula of the return on assets (ROA) as the ratio of EBIT to its total assets by the following formula:

, (9)



where: EBIT - earnings before interest and tax.

Due to information asymmetry between company's managers and a market, the former tend to prefer internal financing. Moreover, for fear of potential dilution of ownership they do not increase external equity. From this point of view, it is presumed to find a negative relation between profitability and financial leverage.

On the other hand, some scholars obtained empirical evidences of the positive relation (Frank and Goyal, 2003; La Rocca et al., 2009; Frank and Goyal, 2009). They assume that companies with a higher profitability rate are tend to use more borrowed fund owing to opportunity to use tax shield benefits in terms of the Trade-off Theory.

2) Liquidity was calculated by the following formula:

. (10)

Considering liquidity, in terms of the Pecking Order Theory when firms prefer internal funding a negative relation is projected. In such situation liquidity coefficient rises while financial leverage identifies a downward trend.

3) Tangibility of company's assets was calculated by the following formula:

. (11)

The Agency Theory suggests that tangible assets can be used as a collateral which provides lower interest rates on banks loans. At the same time, taking into account the Trade-Off Theory companies are presumed to prefer debts for financing their activity due to tax shield benefits, so a deliberate increase of a financial leverage may involve rise of tangible assets. Consequently, there might be a positive relation between tangibility of companies' assets and its debt-equity ratio.

4) Company's value.

Market-to-Book ratio was chosen as an indicator of company's value due to several reasons. Firstly, in all analyzed researches scholars took this coefficient (see Table 1). Secondly, this ratio allows to estimate the efficacy of company's activity without taking into account its size. Market-to-Book ratio was calculated by the following formula:

, (12)

where: Market Capitalization - it is the total market value of the company;

Equity - it is the total book value of a company.

In conformity with a number of previously observed studies it is relevant to presume that there is a reverse relation between Market-to-Book ratio and financial leverage. It is relevant because an increase of equity simultaneously leads to a rise of Market-to-Book ratio and decline of a financial leverage.

5) Company's size was measured as the natural logarithm of company's assets.

In regard with the Trade-Off Theory level of bankruptcy risk and corresponding bankruptcy cost diminish as companies assets (it size) increase. As a result, there will be a positive relation between company's size and financial leverage.

In order to obtain accurate results, firstly, the initial sample was divided into five sub-samples by industry of companies inside them (manufacturing, construction, energy, services and trade companies). After that, the created regression equation was implied to each of the five subsamples separately. As a result, five various equations with different coefficients were acquired. Such approach allows to identify an optimal capital structure for a particular company from a particular sector of Russian economy.

Owing to the fact that some companies did not disclose some information which is necessary for calculation of the variables missing data will emerged, and, thus, endogeneity problem. That makes it impossible to compile a balanced panel data, therefore, there was used pooled regression and it was assessed by the least squares method (OLS).

3.3 Methodology of analysis of an influence of capital structure deviations from optimal levels on companies' value

In order to assess an influence of capital structure deviations from an optimal level on company's value in the present study was used multiple regression equation (Gill, Obradovich, 2012; Ayako, Wamalwa, 2015; Saono, San Martin, 2016; Vo, Ellis, 2017; Fatemia et al., 2018; Luo, Wang, 2018; Sheikh, 2018). This model is one of the most frequently used in such studies. However, multiple non-linear regression provides an assessment of a strength and direction of impact of chosen independent variables on a main (dependable) variable of a study. Moreover, since in this study a pooled regression is used, this type of model is the most suitable and does not sophisticated the work. In that case, the ordinary least squares method (OLS) is relevant because it ensures effectiveness of the acquired estimates of the regression coefficients.

Market-to-Book ratio was taken as the dependent variable (Vo, Ellis, 2017). It was measured as it had been done for the regression devoted to an optimal capital structure in the previous section.

The main factor, which is in the focus of this work, is a capital structure deviation. It was calculated by the following formula:

, (13)

where: fin_levi - it is a financial leverage coefficient of each individual company;

fin_levoptimal - it is a financial leverage ratio for the optimal capital structure of each individual company.

It is important to notice, that a deviation for each company in each year was computed twice. For the first time, the optimum was found with the help of the minimum WACC method (section 3.1.). For the second time, the optimum was found by the regression equation approach (section 3.2.).

In this study three variables describing a capital structure deviation were included: a module of a capital structure deviation itself; a dummy-variable which indicated if a certain deviation was negative or positive (if the current financial leverage was greater or less than the optimal one respectively); a module of a capital structure deviation multiplied by a dummy-variable in order to find their joint impact. This approach allows to evade difficulties with the interpretation of the results and misunderstanding which may appear in case of including only an absolute value of a deviation into the model. Moreover, it is also presumed to examine an influence of a deviation more accurately and identify a quadratic dependency without problems engendered because of turning a value of a negative deviation into a positive one. All these peculiarities will be discussed in more detail in the Chapter 4.

The basic regression model was additive because company's value was the sum of individual effects of the explanatory variables. However, a module of a capital structure deviation variable and a dummy-variable indicating a sign of a deviation were dependable. That is why, introduction of their interaction term (expressed as a multiplication) was not to clarify a separate effect of each of these variables but their joint influence on company's value.

Made literature review revealed a great variety of factors which expose influence of company's value. However, for the present study the most significant were added as control variables.

1) Firm size was measured as the natural logarithm of company's assets.

In a number of researches (Gill, Obradovich, 2012; Ayako, Wamalwa, 2015; Firk et al., 2016; Saono, San Martin, 2016; Vo, Ellis, 2017; Fatemia et al., 2018; Luo, Wang, 2018; Sheikh, 2018; Firk et al., 2019) firm size is included into models examining determinants of company's value because it is one of the basic independent variables for such models. It is presumed that firm's expansion facilitates value decrease owing to diversification of its activity (Lang and Stulz, 1994).

2) There was also included the Return on assets coefficient (Gill, Obradovich, 2012; Ayako, Wamalwa, 2015; Saono, San Martin, 2016; Fatemia et al., 2018; Luo, Wang, 2018; Sheikh, 2018; Firk et al., 2019). It was calculated as it had been done in the previous section for an optimal capital structure regression.

This indicator allows to assess company's ability to operate efficiently or to generate profit which is the main aim of any entrepreneurship. So, it is anticipated that a positive relation between company's value and its Return on assets will be found because more profitable companies are more attractive for investors than companies with operating losses.

3) The ratio of company capital expenditures to its assets (Sheikh, 2018).

This coefficient identifies amount of company's capital expenditure is allocated on increase of its assets by one unit. The indicator is important, since a rise of assets may by a sign of production expansion, which, in turn, a positive trend for company's development. Consequently, company's value has to increase.

It worth noticing that in the initial database the “CAPEX” indicator was calculated by the following formula:

. (15)

Thus, there are observations with the negative value of this variable because fixed assets of some companies decreased in comparison with the previous year.

4) Company's sector (Gill, Obradovich, 2012; Fatemia et al., 2018; Sheikh, 2018).

It is a dummy variable, where:

· construction - companies from construction sector;

· manufacturing - companies from manufacturing sector;

· energy - companies from energy industry;

· services - service companies;

· trade - trading companies.

Based on the analysis of the sample it was found that the majority of companies in the sample belong to the manufacturing sector (see Appendix 2). Therefore, this particular variable was taken as the base one and excluded from the further regression equation in order to avoid multicollinearity.

5) Share of intangible assets in the total assets of a company (Ayako, Wamalwa, 2015; Firk et al., 2016).

This variable was calculated by the following formula:

. (16)

If a company has intangible assets it means that it adheres to an innovative development strategy. In turn, it is often a factor increasing investing attractiveness at a start-up stage as well as at the time when a company produces an innovative product. In both cases, a large share of intangible assets has to lead to a rise of company's value.

6) Board members qualification (Firk et al., 2016; Sheikh, 2018; Firk et al., 2019).

This variable was introduced into regression in a following way:

· if more than one third of directors had a master's degree and more than 5 years of experience of work in a particular industry, a company got 2 points;

· if more than one third of the directors had a master's degree or more than 5 years of experience of work in a particular industry, a company got 1 point.

A company's management has to be well prepared and highly qualified in order to be capable of efficaciously implementing the VBM concept. Thus, it is assumed that the better qualification and more considerable experience company executives have, the higher company's value will be.

7) Share of owners in a company's board of directors (Cornett et al., 2007; Firk et al., 2016; Sheikh, 2018; Firk et al., 2019).

It is business owner who is most interested in a growth of company's value. Consequently, owners dominance in a board of directors should lead to an increase of company's value.

Russian government is not an ineffective manager because its goals are disparate with the business ones. The obsolete concept of rising firm's revenue, rather than its value, is still the pillar management approach from the governmental point of view. In practice, an increase of revenue and rise of value are the opposite aims. In this regard, if Russian government is involved in a company as a member of its board of directors it will lead to a decrease of enterprise's value.

8) Government involvement in a company as a member of a board of directors (Cornett et al., 2007; Firk et al., 2016; Firk et al., 2019).

This variable was introduced into regression as a dummy. If Russian government (or some affiliated structures) was firm's owners, company got 1 point, otherwise - 0.

9) Year of a certain observation (Firk et al., 2016; Fatemia et al., 2018; Firk et al., 2019).

It is a dummy variable, where:

· Y_2010 - observation from 2010 year;

· Y_2011 - observation from 2011 year;

· Y_2013 - observation from 2013 year;

· Y_2014 - observation from 2014 year.

To summarize, in the present study in order to investigate the influence of a company's capital structure deviation on its value a multiple regression equation was used. The relevant econometric model is:

, (17)

where: p_pb - Market-to-Book ratio (company's value);

|lev_dev| - module of deviation of company's capital structure from its optimal level;

dev_sign - dummy variable indicating the sign (plus or minus) of company's capital structure deviation (1 - negative deviation, 0 - positive);

Controls - control variables.

The biggest number of observations was over 2011 year and in the manufacturing industry (see Appendix 2). Thereby, the dummy-variables identifying 2012 year of observation and a manufacturing sector were taken as base and excluded from the model.

As it has been noticed in the previous section, in the case of the first regression model there also will be some companies which did not disclose some necessary information. This will engender endogeneity owing to missing data. Moreover, in this regression there are variables (company's sector and government involvement) which value does not change in time. Due to these reasons it does not seem possible to utilize a panel data, that is why, a pooled regression will be implied.

3.4 Sample description

For conducting the empirical part of the present study it was necessary to create a representative sample of Russian companies in order to calculate their current capital structure, as well as to calculate its optimal value. All necessary information about companies' financial performance was taken from the database of the International Laboratory of Intangible-driven Economy of the Higher School of Economics - Perm `Intellectual Capital of Russian Companies'.

For the sample, members of the International Laboratory of Intangible-driven Economy of the Higher School of Economics - Perm collected data which consisted of various annual indicators of companies' financial performance. For this work was taken data only for the period from 2010 to 2014. This time frame was chosen because Russian economy suffered from recession caused by the global financial crisis during the period from 2008 to 2010.

The sample comprised companies from five different sectors of the economy: manufacturing, construction, energy, services and trade.

Companies from financial sector (banks, investment companies and others) were not included in the sample due to the distinctive features of their economic activity which provide specific principles of choosing a debt-equity ratio for such firms.

All data from financial statements of companies are measured in euro, ratios are expressed in fractions.

The initial sample for the study included 5000 observations. However, there were some companies which did not disclosed information about their financial state. Thus, such observations (a particular company from a particular year) with missing data were excluded from the sample. Therefore, in each sector the number of observations (companies) in one year does not coincide with the number of observations in this sector in another year. Moreover, owing to various variables used in the WACC procedure, the first and the second regressions the total number of observations differs in these samples. It happens owing to a various amount of information (which is necessary for calculation of a particular indicator) disclosed by one company in different years.

The created initial sample is quite representative in term of a distribution of companies by sectors. As presented in the Figure 1 (Russian Federal State Statistics Service, 2019), the greatest sector of Russian economy is the Manufacturing one. Construction and Energy has approximately the same significance for our country as well as Service and Trade ones, however, the former are slightly large.

Concerning the sample utilized, in accordance with the Figure 2, the majority of companies are from the Manufacturing economic sector while the least number of observations were recorded in the Trade one, which conforms to the priority of sectors of Russian economy.



Figure 1. Structure of Russian GDP (aggregated; 2018)

Figure 2. Distribution of observations by sectors

Also, it can be noticed from the Figure 3 that only 12% of all companies had a government representatives in their board of directors. So, it identifies that during the observed period Russian economic sector was quite independent of the state.

Figure 3. Distribution of observations by governmental involvement



Regarding board members' qualification, based on the data presented in the Figure 4, it can be concluded that only 20% of Russian companies had a highly qualified board members with a master's degree and more than a 5 years work experience while approximately a third of firms had managers with a proper qualification. Therefore, the majority of Russian firms were managed by a staff with a sufficient level of education.

Figure 4. Board members' qualification



4. Empirical results

4.1 WACC calculation results

At the interim stage of calculations descriptive statistics of the acquired current and optimal values of cost of debt, equity and weighted average cost of capital were computed and presented in Table 2.

Table 2 Descriptive statistics for WACC method calculations

	Min	Max	Mean
kd current	0.106	0.166	0.136
ks current	0.031	0.792	0.228
WACC current	0.106	0.167	0.132
kd optimal	0.03	0.094	0.07
ks optimal	0.177	0.385	0.265
WACC optimal	0.093	0.126	0.109

Current values of these three key variables of the WACC method were analyzed in order to check the accuracy of the obtained results. On average, for all Russian companies the cost of debt was 13.6% throughout the observed period. It means that in Russia borrowed funds are a quite expensive source of business financing. However, the cost of equity was 22.8% and it still was higher than the average cost of debt. Consequently, internal funds were more expensive source of financing. This finding reconciles with the theoretical premise of the minimum WACC method according to which borrowed funds should be cheaper than the own ones. Thus, this conclusion allows to assume that Russian companies might follow the VBM approach of capital structure formation during the period from 2010 to 2014 and makes it possible and rational to use the minimum WACC method in assessment of their current and optimal capital structure.

As for the weighted average cost of capital its real average value was 13.2% over the period under observation. It is less than both the cost of debt and equity which also proves the relevance of the minimum WACC method use in the present study.

After that the comparison with the vales of cost of debt, equity and weighted average cost of capital calculated for an optimal level were made. The average optimal debt cost was 7% for all companies from the sample over the whole period. It is two times less than the real one. At the same time, the average optimal equity cost was by 3.7% higher than the real rate (26.5%). The average optimal WACC amounted to 10.9%. It is less than the real average WACC by 2.3%. The figures obtained allow to conclude that if Russian companies had had the optimal structure of their capital, they would have been able to pay on average by 2.3% less for all sources of financing.

4.2 First regression results

For the regression of an optimal capital structure, firstly, all missing data were excluded from the initial sample. Then, it was segregated into five various sub-samples depending on the industrial attribution of each company. After that, each sub-sample was scrutinized with the help of descriptive statistics, Quantile-Quantile graphs and box diagrams. Also, there were used the Cook's distance method. As a result some statistical outliers were found and excluded from each sub-sample.

The analysis of descriptive statistics (see Appendix 3) of each of sub-samples revealed that the most profitable industry in Russia is the Energy one while companies from the Construction, Service and Trade sectors are equally profitable. Moreover, the Energy sector is also a leading one by the fraction of fixed assets in its total assets. What is more extraordinary is that liquidity of construction companies is around 60 times higher than that of others. It means that firms from the Construction sector have the best level of solvency. Their financial risk is minimal, however, such a value may be an indicator of an irrational capital structure. Regarding value and size of all companies from the sample, these indicators do not significantly differ among industries.

Based on the sub-samples created five various regression equations for defining an optimal capital structure for companies from each of the five economic sectors were obtained. It is worth mentioning, that according to the Appendix 1 the majority of observations were over the 2011 year in each industry, that is why, the dummy-variable identifying this year was taken as a base (among five dummy-variables identifying a year of an observation) and excluded from all the regressions.

All the models acquired are statistically significant at a 1% significance level. Regarding equations for companies from the Manufacturing and Energy sectors, robust standard errors were calculated for them because of the heteroscedasticity problem (see Appendix 5 and Appendix 6 respectively). Their explanatory power amounts to 36% and 38.4% respectively. As for three other industries - Construction, Service and Trade - their explanatory power is 44.5%, 22.8% and 38.5% respectively (see Appendix 4, Appendix 7 and Appendix 8 respectively). Such high values of adjusted R square together with a statistical significance of the models suggest that these equations are relevant and can be used for the further calculation of an optimal capital structure.

Subsequently, an optimal debt-equity ratio was computed for each company from the initial sample (for companies which had disclosed enough information for making necessary calculations). As the result, there were some companies for which this method gave a negative value of an optimal financial leverage indicator. Such companies were considered as statistical outliers and removed from the sample used at the next step of the research.

4.3 Second regression results

For the second regression all missing data were excluded from the initial sample too. Then, it was examined in order to filter it and exclude statistical outliers. There were conducted analysis of descriptive statistics, Quantile-Quantile graphs and box diagrams. Also, there was used the Cook's distance method. As a result, some statistical outliers were identified and, consequently, removed. Thus, the final sample entailed 973 observations.

For the acquired sample descriptive statistics of variables for the second regression model were calculated. They are presented in Table 3.

Table 3 Descriptive statistics for the 2nd step of the study (estimation of an influence of a capital structure deviation on company's value)

Variable	Mean	Median	Std. Dev.	Min	Max
Company's value	1.12	0.65	1.43	0.00	10.99
Ln of assets (size)	5.60	5.41	1.89	0.82	12.62
ROA	0.09	0.08	0.11	-0.63	0.87
Ratio of company capital expenditures to its assets	0.01	0.02	0.37	-10.01	3.99
Share of intangible assets	0.02	0.00	0.06	0.00	0.74
Government is in a board of directors	0.20
Board members qualification	0.96	1.00	0.70	0.00	2.00
Share of owners in a company's board of directors	0.17	0.11	0.21	0.00	1.00

As for the dependent variable `Company's value' its mean amounted to 1.12. It means that on average stocks of Russian companies were overestimated during the observed period. However, this value is close to 1, thus, it is possible to assume that stocks of Russian companies were close to their real value. Since the range between maximum and minimum value is quite large, the sample is heterogeneous by this variable.

It can be claimed that on average Russian companies did not work at a loss during the period from 2010 to 2014 because the average value of ROA is 0.09. However, this value is quite close to zero that is pointed out that Russian companies worked not very efficiently owing to a low profitability. In addition, by the minimum value of the variable it can be concluded that there were companies with even a negative value of their EBIT.

A relatively low value of the ratio of a company's capital expenditures to its assets suggests that, on average, Russian companies did not spend large amounts of money on equipment revamp and overhaul. Also, there minimum value is even negative because there were firms which shortened their fixed assets (in relation to the previous year). This is not a positive trend since it can lead to a retardation of Russian companies from Western ones in terms of goods quality and production technologies development.

With regard to the board of directors' qualification, its average value is close to 1. That is why it can be assumed that, on average, more than one third of directors in a board of directors of Russian companies had a master's degree or work in a particular industry for more than 5 years.

The average value of the share of owners in a board of directors is only 0.17. It means that, on average, there were only 17 owners per 100 directors of a company in its board. It suggests that in Russia it is not a widely spread practice when company's directors are its owners at the same time.

Table 4 Correlation matrix (2nd step)

	Company's size	ROA	Ratio of company capital expenditures to its assets	Share of intangible assets	Board members qualification	Share of owners in a company's board of directors
Company's size	1	0.08**	0.11***	0.18***	0.09***	-0.04
ROA	0.08**	1	0.14***	0.02	0.01	0.04
Ratio of company capital expenditures to its assets	0.11***	0.14***	1	0.02	-0.00	-0.02
Share of intangible assets	0.18***	0.02	0.02	1	0.01	-0.01
Board members qualification	0.09***	0.01	-0.00	0.01	1	-0.01
Share of owners in a company's board of directors	-0.04	0.04	-0.02	-0.01	-0.01	1

*p<0.1; **p<0.05; ***p<0.01

Analysis of the correlation matrix, which is presented in Table 4, revealed that chosen variables are not strongly correlated. It stems from the fact that there is no correlation coefficient which is greater than 0.5 and for the majority of variables this coefficient is slightly lower than 0.1 and is not significant at all. For some variables it is significant at 10%, 5% and 1% significance levels. Thus, it can be concluded that there is no multicollinearity between variables.

Before proceeding to the results of the second regression, the comparison of values of a capital structure deviation module and a dummy identifying a sign of a deviation (which were acquired at the previous stages by means of the minimum WACC and first regression equation methods) was made. The figures are presented in the Table 5.

Table 5 Comparison of results acquired by minimum WACC and first regression equation methods

	Mean	Median	Std. Dev.	Min	Max
Optimal capital structure (WACC)	4,69	4	4,33	0	9
Module of a capital structure deviation (WACC)	6.19	6.74	8.637	0.00	121.52
Optimal capital structure (regression)	2,03	1,49	2,1	0,01	22,19
Module of a capital structure deviation (regression)	2.44	0.97	7.98	0.00	119.16

Table 6 Comparison of results acquired by minimum WACC and first regression equation methods (dummy-variable)

	Number of observations with a negative deviation	Number of observations with a positive deviation
Minimum WACC	584	389
Regression equation	658	315

The Table 5 has revealed that an average optimal debt-equity ratio is slightly more than two times greater if it was computed by the WACC approach as well as a maximum value. So, it can be concluded that if a Russian company choose the WACC method it will get an optimal capital structure with a larger proportion of debt than in the case of using a regression equation method. What is more interesting is that the mean of a deviation module is two-and-a-half times higher in a case of the minimum WACC method application. However, there are companies with an optimal capital structure in both cases as well as companies with a significant deviation which is approximately the same in both cases.

Also, with accordance to the Table 6, the majority of companies had a negative capital structure deviation regardless the optimum calculation method. It means that value of a defined optimum greater is than a current financial leverage ratio.

Finally, these values were consistently introduced into the second regression equation. It is worth noticing, that the errors of both models are not subjected to the Normal distribution. Moreover, due to the heteroscedasticity problem, robust standard errors were computed for both models. The results are presented in the Table 7.



Table 7 Regression model results (2nd step, OLS model, robust)

Variable	Coefficients (WACC method)	Coefficients (regression method)
Module of a capital structure deviation	0.033** (0.016)	0.027* (0.015)
Sign of a deviation	-0.242* (0.137)	-0.783*** (0.107)
Interaction term	-0.051** (0.021)	0.476*** (0.040)
Company's size	0.079*** (0.026)	0.088*** (0.022)
ROA	2.699*** (0.793)	2.051*** (0.561)
Ratio of company capital expenditures to its assets	-0.221 (0.246)	0.141** (0.063)
Share of intangible assets	0.933 (0.867)	0.774 (0.749)
Government is in a board of directors	-0.039 (0.118)	-0.110 (0.117)
Board members qualification	-0.044 (0.067)	0.014 (0.058)
Share of owners in a company's board of directors	0.059 (0.192)	0.151 (0.178)
Controls on a year	Included
Controls on an industry	Included
Constant	0.703*** (0.241)	0.315 (0.196)
Observations	974	974
R2	0.131	0.317
Adjusted R2	0.115	0.304
Residual Std. Error	1.345 (df=955)	1.196 (df=955)
F statistic	8.026*** (df=18; 955)	24.633*** (df=18; 955)
*p<0.1; **p<0.05; ***p<0.01

First of all, both models are statistically significant at a 1% significance level. The regression with the WACC method results explains 11.6% of the dependent variable variance, while the second regression's explanatory power is higher - 30.4%.

The obtained results are quite unexpected in terms of significance and signs of the main regressors. As for the first model, such variables as module of a capital structure deviation and an interaction term of a module and sign of a deviation turned to be statistically significant at a 5% significance level, while a sign of a deviation itself is statistically significant at 10% level. On the contrary, in the second regression interaction term and a sign of a deviation are statistically significant at a 1% significance level. Regarding a module of a deviation it is statistically significant at a 10% significance level in both models. Concerning control variables (including all dummy-variables and a constant), in the first model 6 variables out of 20 are statistically significant whereas in the second - 8.

4.4 Interpretation of the final results

In order to interpret the values of all three variables identifying an effect of a deviation on company's value correctly the calculations, which presented in the Appendix 9, were made. The main conclusion is that a capital structure deviation affects value of Russian companies regardless the method of computing an optimum.

However, before moving to the more detailed discussion of the acquired results it worth considering the meaning of introduction of three variables, describing a capital structure deviation, into the second step regression. For better understanding the other regression model with only an absolute value of a deviation was provided for the sample with a deviation acquired by means of the regression equation (Appendix 10). The econometric model made was:

, (17)

where: p_pb - Market-to-Book ratio (company's value);

lev_dev - absolute value of a deviation of company's capital structure from its optimal level;

Controls - control variables.

First of all, if we assume that an absolute value of a deviation is statistically significant we will make an attempt to interpret it. This variable has a positive sign which means that an increase of a deviation leads to a rise of firm's value which contradicts the Theory. However, it is a correct conclusion only for a positive deviation because if we add some value to a positive deviation we will acquire a greater positive value of a deviation and, consequently, a higher value of a company. On the contrary, in a case of a negative deviation if we add some value to it we will obtain a smaller value a deviation but a greater company's value. Thereby, an increase of a negative deviation is a consequence of a subtraction and of this operation leads to a decrease of firm's value.

Secondly, introduction of the three variables describing a deviation allows to identify a quadratic dependency between a deviation and company's value what will be discussed further and be clearly seen in the Figure 7. In case the equation contains an absolute value of a deviation and its square the latter variable would turn a negative deviation into a positive value what will subsequently lead to the same problem described in the previous example.

Therefore, based on the example it has become obvious that in case when only an absolute value of a deviation is introduced into the equation interpretation may be confusing and vague, also it requires more attentive consideration. In this regard, the model with three variables describing a deviation, which seems to be more complicated at a first glance, makes it easier to understand and, consequently, use the results.

Moreover, the model used in both cases (with any method of optimum calculation) has a much greater explanatory power (by the value of R adjusted coefficient).

Additionally, it is worth noticing, that in the model with an absolute value of a deviation this variable turned to be insignificant. That means that there are not any relations between value and a deviation. In turn, it is possible to assume that such a simple approach to considering a deviations does not describe interrelations between capital structure deviation and company's value correctly because in both models with three variables, describing a deviation, all of them are statistically significant.

With regard to the first model (based on the WACC method), if a deviation is positive it will lead to an increase of company's value, expressed as a Market-to-Book ratio, by 0.033 units multiplied by a value of a deviation module of a certain company and this finding totally contradicts the premise of the Capital Structure Theory. On the contrary, if a deviation is negative, a rise of a deviation module will occur simultaneously with a decrease of company's value, expressed as a Market-to-Book ratio, by 0.242 units minus 0.018 units multiplied by a value of a deviation module of a certain company.

As for the second regression, in the area of a positive deviation the same relations were found: an increase of a deviation module will lead to a growth of company's value, expressed as a Market-to-Book ratio, by 0.027 units multiplied by a value of a deviation module of a certain company. In contrast, in the area of a negative deviation company's value will plunge till a deviation module becomes by 1.56 units smaller that the optimal point of a particular company. In turn, after that value till the optimum itself value will rise. The common value of the effect is (-0.783) units plus 0.503 units multiplied by a value of a deviation module of a certain company.

Therefore, these results demonstrate not only the opposite to the Capital Structure Theory effect of a capital structure deviation on value of Russian companies but rather complex interrelations between the examined notions.

In accordance with the Capital Structure Theory an optimal capital structure ought to provide maximum company's value as presented in the Figure 4. So, any debt-equity ratio fluctuations lead to a decrease of value of a business, thereby, there should be a strong negative correlation between company's value and capital structure devotion regardless its sign (a positive or negative deviation).



Figure 4. Interrelations between company's capital structure and its value in accordance with the Capital Structure Theory

Concerning the first model, where the minimum WACC approach results were used, in theory this method ought to identify an optimal ratio of borrowed and own funds which, consequently, leads to a maximum company's value (see Figure 5). Thus, any deviation from a WACC method also ought to cause a company's value drop.

Figure 5. Interrelations between company's capital structure, WACC and its value in accordance with the Capital Structure Theory

However, results acquired witnessed that a growth of a positive debt-equity ratio deviation provides a rise of value of Russian companies. In other word, if a Russian company raises a fraction of its equity, it will facilitate an infinite increase of value. On the contrary, a negative deviation which means a gradual increase of company's debt is accompanied by a decrease of value in accordance with the Theory. This correlation is demonstrated in the Figure 6.

Figure 6. Interrelations between company's capital structure and its value in accordance with the first model results

The results of the second model are similar to the first one in terms of a positive deviation. In case of a negative one there were identified a threshold (1.56) before which company's value demonstrate a downward trend (in contradiction to the Theory) but after which there is a small area where the Theory works and value rises (see Figure 7).

Figure 7. Interrelations between company's capital structure and its value in accordance with the second model results



Thereby, for Russian companies an optimal capital structure (calculated by means of two methods used) does not provide a maximum value. With regard to the WACC method there cannot be defined an optimal level because this approach demonstrate a straight linear correlation, so the larger a proportion of debt in a company's capital structure becomes, the higher company's value soars. Concerning the industrially-specified regression, it allows to find a minimum company's value which conforms a debt-equity which is by 1.54 smaller than a computed optimum. Therefore, in case of this method the results are absolutely opposite to the Theory and any deviation will foster rise of value of Russian companies. The main conclusion is that even if company's debt-equity ratio becomes closer to its optimal level it does not always allow to increase firm's value.

Such astonishing conclusions point out the fact that for Russian companies the concept of Value Based Management with the use of the WACC and industrially specified regression equation methods of calculation of an optimal capital structure works in the wrong way and the results are distorted. This happens owing to the violation of the Capital Structure Theory in case of using both methods of defining an optimal capital structure. So, it can be assumed, that in modern Russian economic conditions, these procedures cannot be used by companies for selection of their optimal debt-equity ratio (if an optimal capital structure is considered as a debt-equity ratio which provides maximum company's value) . As a consequence, it can be concluded that the hypothesis propound has not been confirmed and capital structure deviations of Russian companies from their optimal levels do not negatively affect their value.

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