Analyze the Linear and Curvature Relationship of Financing by Debt and Firms Performance and Moderator Role of Firm Size
Abstract:
Achieve to optimal financial leverage for achieving to maximum profitable, value and minimum capital are important topics of research that studies by financial experts. Economic researchers found that capital structure and firms performance are affiliated with each other but the relationship between them according to financial operations in international affairs is not the same and according to country type depends on financial structure and economic conditions. The aim of the present article is to evaluate the mutual relationship between financial leverage and firm performance concerning the moderating role of the firm size. Given that, the financial information of 108 listed companies in Tehran Stock Exchange were used during the financial period from 2005 to 2014. Multivariable regression model was employed for hypotheses testing. The results indicated that there is a positive and significant relationship between financial leverage and firm performance and the firm size has no moderating effect on the relationship between the two variables. Moreover, there is a negative and significant relationship between financial leverage and the changes of firm performance and the firm size has no moderating impact on these relationships. On the other hand, there is a negative and significant relationship between firm performance and the changes of financial leverage. Similarly, the moderating effect of the firm size was not significant in these relationships.
1. Introduction
Capital structure has been mentioned as the most important parameter affecting on companies structure and to prevent them in capital markets. Now changing environment also calculation of company’s ion terms of credit has been affiliated to their capital structure. This has a close relation with their strategic planning to select of effective resources with aim to the maximization of shareholder wealth.
Fluid variables and factors affecting on capital structure can affect on companies performance and efficiency covering the goal of the agency theory and pecking order theory. it is clear that financial decision markers in compliance with matching principle when financing the funds is considered a effective approach in modifying these decisions with respect to requirements of the economic environment and also is a suitable model for increasing the efficacy dominant thinking on companies performance. (sinayi and rezaian, 2006).
The main problem with the capital structure is that according to differences between stocks and debt that with having a suitable performance, how much stock and debt should be in the capital structure so that company is not at risk of bankruptcy and also it pay less costs? Ultimately, the question arises that does the financial leverage affect on the companies performance? (Nikbakht and Pykani, 2010).
Maximizing the value of companies requires to the implementation of profitable projects. in today’s world, duo to the competition market situation, it is necessary to determine the appropriate financing methods to increasing the profitable and continuing the life of the companies. shareholders also with respect to separation of ownership from management, requires to vast financial recourses in companies and also fans of financial resources use their financial resources to increasing the wealth to analyze the companies performance and their capital structures so that they can get to the right investment.
In field of the relationship between financing decisions and companies profitability mainly from four Miller and Modiglian theories is mentioned the agency theory, static balance theory and pecking order theory. financial economy researchers found that capital structure and performance depends on together but relationship between them according to financial operations of stock companies internationally is not the same and according to country type is depend to financial structures and economic conditions. therefore, researchers according to the country type are analyze the relationship between capital structures and performance that of course the results obtained in this regard is different from each other. several factors such as nature of activity, assets and economic conditions governing on society can effect on financing the companies and, consequently, on the profitable that identify the results of these economic activities by using the efficient and dynamic analytical methods can provide a knowledge – based decision making tool by governors, managers and investors. (shahedani et.al, 2013).
Financial leverage has the ability to change efficiency and companies risks. So capital structure in each company has a close relationship with its financial leverage. Therefore, using of the companies from different financing methods is depend to existence of conditions and effect of contingency variables that sometimes occurs according to position and to prevent of the companies in markets and also their assessment by credit institutions. but the need to pay attention to the agency theory is that conflict of stock holders, ownerships, managers as well as bond owners effect on the capital financing decision and investment.
Hensen &Mecking(1976), Myers(1977) also say that amount of debt is create by tax deduction paid interest, bankruptcy costs and agency costs which is effects in the schedule investment decisions and company’s value.
Modigliani &Miller (1963) are stated that company’s value and capital structure is affiliated together till constituent elements of capital structure has the ability to complete the replacement.
Currently, the identification of contributing factors on performance is one of the major concerns in entrepreneurship research studies. According to the report of American Small Business Administration (SBA), more than 50% of small businesses will fail in their first year and 90% collapse within the first five years. However, the rank of business setting index in the U.S. was two times higher in 2006. This indicates that the environmental factors could affect the business failure, but 90% of failure is derived from some internal factors, which have dramatic effects on the downfall of a business firm.
Since financial limitations could hinder the growth opportunities, bank financing is a way to alleviate some of the restrictions and consequently to boost firm growth, entrepreneurship, and performance. Entrepreneurship and small businesses are always faced with lack of investment opportunities in developing countries. Most research studies from macroeconomics viewpoint are concerned with the effect of financial development on firm growth. This topic could best describe the relationship between financial development and economic growth in all countries (Levine). Due to availability of loan facility, most corporates are inclined toward bank resources to supply the required properties and this could be a reason why the financial risk of such firms elevated. There is always the rationale that the incremental growth of bank debts could lower the inverse effect of the increase of financial leverage. This means that the longterm performance of firms with higher bank finance is less than those corporates that benefited from nonbank debts, such that companies that used bank resources for financing were faced with abnormal negative return of share price during a threeyear period (Duchin, et al. 2010).
Corporate debt, by assuming that the growth opportunities are available, could have a mutual role in firm value, which could be elaborated by two approaches of investment deduction and additional investment. Investment deduction approach first introduced by Myers (1997) expressing that high range of debts has a negative effect on firm value, and could cause the inclination of managers toward profitable investment projects.
Therefore, by assuming the existence of growth opportunities, we could expect a negative relationship between debts and firm value. Debt financing could support the value of the participant and moderate the inefficiency of managers by restricting their access to free cash flows. In other words, according to this approach, in cases that no growth opportunity is available, a positive relationship between debts and firm value is expected (Singh and Faircloth, 2005). Regarding the abovementioned topics, the aim of the present study is to investigate the mutual relationship between financial leverage and firm performance and to discover the moderating impact of firm size on these relationships.
2. Review of Literature
Gunny et al. (2008) investigated the data of Chinese companies from 1994 to 2006 in 12 different industries and found that there is a nonlinear relationship between capital structure and competitive market of a product based on the type of industry, size, and growth opportunities and Chinese companies try to moderate their capital structure, over time.
Nikolas et al. (2007) within a research, entitled “how the firm properties could affect the capital structure of Greece Market?” indicated that quick ratio, interest coverage ratio, and expected growth have negative relationship with capital structure and there is a positive relationship between firm size and capital structure.
Ogundipe et al. (2012) studied the effect of working capital management on performance and value of companies listed on Nigerian Stock Exchange from 1995 to 2009. Their results illustrated that there is a negative and significant relationship between cash conversion cycle, market value, and firm performance. In addition, their findings showed that debt ratio has a positive and negative relationship with market value and with firm performance, respectively.
Vithessonthi and Tongurai (2014) argued that financial leverage has a positive and significant impact on firm performance in small businesses. In addition, the financial leveragehas a negative and significant effect on firm performance of large corporates. The negative effect of the financial leverage is more severe on extremely small businesses than the larger ones. Moreover, the positive effect of financial leverage on firm performance in extremely large corporates is stronger. Besides, results indicated that there is a nonlinear and curved relationship between financial leverage and firm performance at various levels of firm sizes.
Multy and Manage (2014) evaluated the effect of firm size on the relationship of financial leverage with firm performance from 2007 to 2009 in companies listed on Thailand Stock Exchange. Their resultsindicated that financial leverage has negative impact on performance in corporate with various sizes and this effect is significant in corporates with large and small sizes.
Namazi and Shirzadeh (2005) investigated the relationship between capital structure and profitability. They also assessed the relationship between mean debt ratio and return of assets. However, such relationship is statistically less strong. The relationship between capital structure and profitability depends on the type of industry, as well. The capital structure could be established in various industries and the relationship between capital structure and profitability depends on how profitability is defined.
Faramarzi (2005) examined the relationship between capital structure and profitability. According to the results of the experiments carried out on all companies, we could substantiate the direct relationship between variables, which are indicative of type of capital structure applied in companies, and asset return ratio, which is an index for describing corporate profitability. Results showed that the higher the proportion of equity than debts in companies, the higher is the profitability. Actually, profitability is a function of equity ratio to debts.
Badri and Imenifar (2011) showed that drawing a conclusion from capital structure analyses depends on financial leverage on the one hand, and is affected by defected measurements of the scholar on the other hand. Moreover, their results indicated that the level of leverage has an inverse relationship with the variables of growth opportunities and profitability and a direct relationship with the firm size, but is in no relationship with asset structure.
3. Research Hypotheses
With regard to the proposed theoretical principles, research hypotheses will be put forward as follows:
There is a meaningful relationship Between financial leverage with firm performance, financial leverage changes with company’s performance changes and financial leverage changes with company’s performance and firm size has a moderator effect in this field.
Therefore, the main hypothesis in the form of 7 sub hypotheses is expressed as follows:
Hypothesis 1: there is a significant relationship between financial leverage and firm performance.
Hypothesis 2: firm size has a moderating effect on the relationship between financial leverage and firm performance.
Hypothesis 3: there is a nonlinear (curved) relationship between financial leverage and firm performance.
Hypothesis 4: there is a significant relationship between the changes of financial leverage and firm performance.
Hypothesis 5: firm size has a moderating effect on the relationship between the changes of financial leverage and firm performance.
Hypothesis 6: there is a significant relationship between firm performance and the changes of financial leverage.
Hypothesis 7: firm size has a moderating effect on the relationship between firm performance and the changes of financial leverage.
4. Methodology
The statistical population is the listed companies on Tehran Stock Exchange from 2005 to 2011. The final sample is selected randomly among the companies listed on Tehran Stock Exchange prior to 2005, their end of fiscal year was on March 19th, had no changes or stop in their financial period, were not affiliated with banks, financial institutions (investment companies, intermediaries, holdings, leasing), and their data were available. The required data were extracted, by defining the dependent and independent variables, from reliable sources, including RahAvarNovin database and Tehran Stock Exchange publisher system (CODAL). After data collection and establishing the model, data were initially placed as the panel data and EviewsSoftware was used for hypothesis testing.
Table 1 displays the variables used in this research for hypothesis testing along with their specific calculation method, separately.
Several agents have been used by scholars for measuring performance, among which we could refer to corporate profitability, and asset return. Tobin's Q ratio has been used in this research for computing performance.
To calculate the financial leverage, two ratios of office leverage (the proportion of total book value of debt to total asset book value) and marker leverage (the proportion of long term debt book value to total asset book value) were used.
The total assets natural logarithm was used for calculating the firm size.
To control other contributing factors on explanatory power of the relationship between variables, a number of control variables were inserted to control the potential effect of firm performance.
Symbol  Name 
 Calculation method 
Firm Performance i; t  Tobin’s Ratio  Q  market value of total assets = book debt value + common stock market value total assets book value common stock market value = Tobin′s Q Ratio 
LEV i; t  Financial leverage  totaldebtbookvalue long − termdebtsbookvalue total assets book value ﻭ total assets book valueﮐﻞ  
ΔLEV i; t  Changes of financial leverage  Financial leverage of end of the year  Financial leverage of the previous year  
Size Dummy  Artificial variable of the firm size  Is equal to 1, should the firm size is more than the mean of total firms. Is equal to 0, should the firm size is less than the mean of total firms  
INT t  Interest rate  Average interest rate for 12 months  
GDP t  Gross domestic product growth  The growth rate of gross domestic product compared with the previous year  
AGE i; t  Firm age  Natural logarithm of years passed from the year of establishment  
SIZE i; t  Firm size  Natural logarithm of assets book value  
EBIT i; t  Earnings before interest and taxes  Firm’s earnings before interest and taxes  
ε i; t  Residual or component error 
5. Data analysis
Before research hypotheses test, firstly examined the stationary of variables used in this research, because the variables’ nonsense in case of the time series data and panel data are caused the false regression. But in addition to what is customary in case of the time series data, in case of the panel data not can used from Foler Diky test for monotony but it is necessary tests the variables collective monotony which for this purpose should use from Hadri tests.
The stationary of variables used in this research were evaluated prior to the hypotheses testing. The results are illustrated in table 2. According to the results, the null hypothesis, that is a unit root variables or their nonstationary is rejected at 0.05 confidence level and all research variables are stationary. Thus, we could estimate the pattern of the present study without being concerned of unit root variables.
Symbol  Name  Haderi Test  Stationary state  

 test of significance  Test of statistic 

Firm Performance i; t  Asset return  ***0.0000  11.0309 
Stationary 
Tobin’s Q Ratio  ***0.0000  11.5890  
Modified economic value added  ***0.0000  15.4573  
LEV i; t  Financial leverage  ***0.0000  13.6107  Stationary 
ΔLEV i; t  Changes of financial leverage  ***0.0000  10.9851  Stationary 
LEV2 i; t  Square of financial leverage  ***0.0000  17.0123  Stationary 
Size Dummy  Artificial variable of the firm size  ***0.0000  12.2704  Stationary 
INT t  Interest rate  ***0.0000  16.4059  Stationary 
GDP t  Gross domestic product growth  ***0.0000  18.4062  Stationary 
AGE i; t  Firm age  ***0.0000  19.5645  Stationary 
SIZE i; t  Firm size  ***0.0000  19.1752  Stationary 
EBIT i; t  Earnings before interest and taxes  ***0.0000  14.7012  Stationary 
ΔQ TOBIN i; t  Changes of firm performance  ***0.0000  11.2433  Stationary 
The following regression pattern is estimated to evaluate the relationship between financial leverage and firm performance:
$\begin{aligned} & \text { Firm Performance }{ }_{i t}=\beta_0+\beta_1 I N T_t+\beta_2 G D P_t+\beta_3 A G E_{i, t}+\beta_4 \text { SIZE }_{i, t}+\beta_5 E B I T_{i, t} \\ & \quad+\beta_6 L E V_{i, t}+v_i+\varepsilon_{i, t},\end{aligned}$
The results depicted in table 3 indicate that the financial leverage (LEV variable) at the significance level of 0.0000 has a positive and significant relationship with firm performance (Tobin’s Q ratio). The descriptive power (modified coefficient of determination) of this model is 84.91%. The result shows a positive and significant relationship between financial leverage and firm performance (Tobin’s Q ratio) in companies listed on Tehran Stock Exchange. Accordingly, the first hypothesis is accepted.
Descriptive variable 
Coefficient 
Standard error 
T statistic 
Prob 
INT t  0.023761  0.007869  3.019506  ***0.0026 
GDP t  0.111262  0.056150  1.981523  **0.0479 
AGE i; t  0.389422  0.251929  1.545763  0.1225 
SIZE i; t  0.127615  0.044515  2.866815  ***0.0042 
EBIT i; t  1.79E08  8.38E09  2.135694  **0.0330 
LEV i; t  0.888632  0.033205  26.76201  ***0.0000 
ε i;t  1.793969  0.672477  2.667703  ***0.0078 
Model test statistics  
F statistic (significance of total regression) 
Coefficient of determination R2  Modified coefficient of determination ADJ R2 
Durbin Watson statistic  
F statistic  Prob  
48.73875  0.0000  0.866910  0.849124  2.115190 
Panel tests  
Detection tests  Statistic test  Significance  Result  
Generalized F test  8.546407  0.0000  Emphasis on use of FE against PLS  
Hausman Test  31.996739  0.0000  Emphasis on use of FE against RE  
Final result  Emphasis on use of FE against PLS and RE  
FE: fixed effects model. RE: random effect model. PLS: integrative data model. ***: significance level of 99%, **: significance level of 95%, *: significance level of 90%. 
The following model is used for testing the second hypothesis:
$\begin{aligned} \text { Firm Performance }_{i t} & \beta_0+\beta_1 I N T_t+\beta_2 G D P_t+\beta_3 A G E_{i, t}+\beta_4 \text { SIZE }_{i, t}+\beta_5 E B I T_{i, t} \\ & +\beta_6 L E V_{i, t}+\beta_7 L E V_{i, t} \times \text { Size Dummy }+v_i+\varepsilon_{i, t} .\end{aligned}$
Regarding the variable of Size Dummy, which is indicative of artificial variable of the firm size, the relationship between financial leverage and firm performance in large corporates (the size of which is larger than the mean of all companies and the Size Dummy variable of these companies is equal to 1) is examined via (β6+ β7).
Similarly, the relationship between financial leverage and firm performance in small companies (the size of which is smaller than the mean of all companies and the Size Dummy variable of these companies is equal to 0) is merely considered as β6. Finally, the equation (β6+β7 ≠ β6) should be satisfied for the acceptance of the second hypothesis.
Therefore, by simplifying the above equation, it is only required that the equation (β7 ≠ 0) be balanced and its respective variable be significant, so the second hypothesis is accepted.
The results of table 4 indicates that the artificial variable of firm size (LEV i; t * Size Dummy) at the significance level of 0.1835 has a negative and nonsignificant relationship with firm performance index (Tobin’s Q ratio).
The descriptive power (modified coefficient of determination) of this model is 82.56% and this means that 82.56% of changes in dependent variables are expressed by the independent variables. Therefore, since (β7 ≠ 0) is a nonsignificant coefficient, the result of the second hypothesis is rejected and this is indicative of no modifying effect of the firm size on the relationship between financial leverage and the firm performance (from Tobin’s Q ratio) in companies listed on Tehran Stock Exchange.
Descriptive variable  Coefficient  Standard error  T statistic  Prob 
INT t  0.023824  0.008036  2.964571  ***0.0031 
GDP t  0.112685  0.056718  1.986762  **0.0473 
AGE i; t  0.346844  0.241834  1.434222  0.1519 
SIZE i; t  0.118380  0.047831  2.474970  **0.0135 
EBIT i; t  1.65E08  7.72E09  2.138031  **0.0328 
LEV i; t  0.880744  0.038337  22.97356  ***0.0000 
LEV i; t * Size Dummy  0.012810  0.009624  1.331127  0.1835 
Model test statistics  
F statistic (significance of total regression) 
Coefficient of determination R2  Modified coefficient of determination ADJ R2 
Durbin Watson statistic  
F statistic  Prob  
40.82612  0.0000  0.846404  0.825672  2.113055 
Panel tests  
Detection tests  Statistic test  Significance  Result  
Generalized F test  8.337106  0.0000  Emphasis on use of FE against PLS  
Hausman Test  29.716696  0.0000  Emphasis on use of FE against RE  
Final result  Emphasis on use of FE against PLS and RE  
FE: fixed effects model. RE: random effect model. PLS: integrative data model. ***: significance level of 99%, **: significance level of 95%, *: significance level of 90%. 
Following hypothesis is used for testing the third hypothesis:
$\begin{aligned} & \text { Firm Performance }_{i t}=\beta_0+\beta_1 I N T_t+\beta_2 G D P_t+\beta_3 A G E_{i, t}+\beta_4 S I Z E_{i, t}+\beta_5 E B I T_{i, t} \\ & +\beta_6 L E V_{i, t}+\beta_7 L E V_{i, t}^2+v_i+\varepsilon_{i, t} . \\ & \end{aligned}$
The result of table 5 illustrates that the index of financial leverage square (LEV2 variable), at the significance level of 0.0000, has a positive and significant relationship with firm performance.
The descriptive power (modified coefficient of determination) of this model is 73.71% and this means that 73.71% of changes in dependent variables are expressed by the independent variables. The result of the third hypothesis substantiates a nonlinear (curved) relationship between financial leverage and firm performance (Tobin’s Q ratio) in companies listed on Tehran Stock Exchange.
Descriptive variable  Coefficient  Standard error  T statistic  Prob 
INT t  0.030586  0.006054  5.052229  ***0.0000 
GDP t  0.017252  0.015340  1.124590  0.2610 
AGE i; t  0.002385  0.088447  0.026968  0.9785 
SIZE i; t  0.087382  0.035735  2.445285  **0.0147 
EBIT i; t  1.97E08  7.09E09  2.783679  ***0.0055 
LEV i; t  0.495932  0.040974  12.10361  ***0.0000 
LEV 2 i;  0.109176  0.015071  7.244138  ***0.0000 
Model test statistics  
F statistic (significance of total regression)  Coefficient of determination R2  Modified coefficient of determination ADJ R2  Durbin Watson statistic  
F statistic  Prob  
27.45124  0.0000  0.765062  0.737192  1.533405 
Panel tests  
Detection tests  Statistic test  Significance  Result  
Generalized F test  7.351662  0.0000  Emphasis on use of FE against PLS  
Hausman Test  34.646700  0.0045  Emphasis on use of FE against RE  
Final result  Emphasis on use of FE against PLS and RE  
FE: fixed effects model. RE: random effect model. PLS: integrative data model. ***: significance level of 99%, **: significance level of 95%, *: significance level of 90%. 
Following hypothesis is used for testing the third hypothesis:
$\begin{aligned} \Delta \text { Firm Performance }_{i t} & =\beta_0+\beta_1 A G E_{i, t1}+\beta_2 \text { SIZE }_{i, t1}+\beta_3 E^2 I T_{i, t1}+\beta_4 R_{i, t} \\ & +\beta_5 L E V_{i, t1}+\beta_6 \Delta L E V_{i, t}+v_i+\varepsilon_{i, t},\end{aligned}$
The result of table 6 displays that the index of financial leverage changes (ΔLEV variable), at the significance level of 0.0000, has a negative and significant relationship with the changes of firm performance (changes of Tobin’s Q ratio).
The descriptive power (modified coefficient of determination) of this model is 75.22% and this means that 75.22% of changes in dependent variables are expressed by the independent variables. The result is the rejection of H_{0} hypothesis and this means that there is a negative and significant relationship between the changes of financial leverage and firm performance (change of Tobin’s Q ratio) in companies listed on Tehran Stock Exchange. Accordingly, the fourth hypothesis is accepted.
Descriptive variable  Coefficient  Standard error  T statistic  Prob 
AGE i; t  0.097580  0.079145  1.232921  0.2179 
SIZE i; t  0.004136  0.006262  0.660545  0.5090 
EBIT i; t  1.42E09  5.89E09  0.240308  0.8101 
ROA i; t  1.508302  0.287426  5.247624  ***0.0000 
LEV i; t1  0.549267  0.041065  13.37543  ***0.0000 
ΔLEV i; t  1.241840  0.108410  11.45505  ***0.0000 
ε i;t  0.347920  0.093507  3.720801  ***0.0002 
Model test statistics  
F statistic (significance of total regression) 
Coefficient of determination R2  Modified coefficient of determination ADJ R2 
Durbin Watson statistic  
F statistic  prob  
544.9661  0.0000  0.753618  0.752235  2.106824 
Panel tests  
Detection tests  Statistic test  Significance  Result  
Generalized F test  0.993849  0.5017  Emphasis on use of PLS against FE  
Hausman Test  30.308760  0.0000  Emphasis on use of FE against RE  
Final result  Emphasis on use PLS of against FE and RE  
FE: fixed effects model. RE: random effect model. PLS: integrative data model. ***: significance level of 99%, **: significance level of 95%, *: significance level of 90%. 
The fifth hypothesis is concerned about the evaluation of modifying effect of the firm size on the relationship between changes of financial leverage and firm performance.
To test the hypothesis, companies were classified initially based on the first quarter, middle, and third quarter of firm size index, such that a quarter of the firm size is placed in each group of companies. Then, the fourth hypothesis model is tested in each group, separately. Finally, the acceptance or rejection of hypotheses was studied by comparing the coefficient of changes of financial leverage index and variable significance level.
Therefore, the statistical hypothesis for the test of fifth hypothesis is as follows:
The regression coefficient between the variable of financial leverage changes and performance changes should increase or decrease constantly along with the increase of firm size level. The increase of firm size level means moving from the first quarter of the firm size to the fourth quarter.
The result of table 7 shows that the index of financial leverage (ΔLEV variable), at the significance level of 0.060 and coefficient of 0.5480, has a positive and significant relationship with the changes of firm performance (changes of Tobin’s Q ratio) in the first quarter of the firm size. The descriptive power (modified coefficient of determination) of this model is 09.97%.
Descriptive variable  Coefficient  Standard error  T statistic  Prob  
AGE i; t  0.081662  0.126891  1.276208  0.2030  
SIZE i; t  4.16E06  0.083083  0.982895  0.3266  
EBIT i; t  0.620907  3.77E06  1.105310  0.2700  
ROA i; t  0.257640  0.786809  0.789145  0.4307  
LEV i; t1  0.548004  0.141108  1.825832  *0.0690  
ΔLEV i; t  0.668191  0.297968  1.839140  *0.0670  
ε i;t  0.081662  0.991463  0.673944  0.5009  
Model test statistics  
F statistic (significance of total regression)  Coefficient of determination R2  Modified coefficient of determination ADJ R2  Durbin statistic  Watson  
F statistic  Prob  
5.969994  0.000007  0.119871  0.099792  1.947772  
***: significance level of 99%, **: significance level of 95%, *: significance level of 90%. 
The result of table 8 shows that the index of financial leverage (ΔLEV variable), at the significance level of 0.0009 and coefficient of 0.9792, has a positive and significant relationship with the changes of firm performance (changes of Tobin’s Q ratio) in the second quarter of the firm size. The descriptive power (modified coefficient of determination) of this model is 06.85%.
Descriptive variable  Coefficient  Standard error  T statistic  Prob 
AGE i; t  0.415728  0.200139  2.077199  **0.0388 
SIZE i; t  0.245596  0.218061  1.126273  0.2611 
EBIT i; t  3.01E06  2.65E06  1.136042  0.2570 
ROA i; t  1.607551  1.220979  1.316608  0.1891 
LEV i; t1  0.293701  0.157896  1.860094  *0.0640 
ΔLEV i; t  0.979207  0.292268  3.350368  ***0.0009 
ε i;t  2.514883  2.819219  0.892050  0.3732 
Model test statistics  
F statistic (significance of total regression)  Coefficient of determination R2  Modified coefficient of determination ADJ R2  Durbin Watson statistic  
F statistic  Prob  
4.286671  0.000385  0.089393  0.068539  1.773540 
***: significance level of 99%, **: significance level of 95%, *: significance level of 90%. 
Descriptive variable  Coefficient  Standard error  T statistic  Prob 
AGE i; t  0.153130  0.148994  1.027758  0.3050 
SIZE i; t  0.198550  0.211755  0.937638  0.3493 
EBIT i; t  9.31E07  1.17E06  0.798389  0.4254 
ROA i; t  1.139499  1.159105  0.983085  0.3265 
LEV i; t1  0.001559  0.286409  0.005443  0.9957 
ΔLEV i; t  0.792528  0.306246  2.587883  **0.0102 
ε i;t  2.501795  2.850615  0.877634  0.3810 
Model test statistics  
F statistic (significance of total regression)  Coefficient of determination R2  Modified coefficient of determination ADJ R2  Durbin Watson statistic  
F statistic  Prob  
3.061789  0.006523  0.065994  0.044440  2.153846 
***: significance level of 99%, **: significance level of 95%, *: significance level of 90%. 
Descriptive variable  Coefficient  Standard error  T statistic  Prob 
AGE i; t  0.431564  0.174194  2.477485  **0.0139 
SIZE i; t  0.056510  0.030229  1.869416  *0.0627 
EBIT i; t  3.79E08  2.09E08  1.812348  *0.0711 
ROA i; t  0.353039  0.329759  1.070597  0.2853 
LEV i; t1  0.586906  0.149470  3.926572  ***0.0001 
ΔLEV i; t  1.305475  0.140808  9.271312  ***0.0000 
ε i;t  0.836869  0.551874  1.516414  0.1306 
Model test statistics  
F statistic (significance of total regression)  Coefficient of determination R2  Modified coefficient of determination ADJ R2  Durbin Watson statistic  
F statistic  Prob  
2470.987  0.000000  0.982570  0.982172  1.881552 
***: significance level of 99%, **: significance level of 95%, *: significance level of 90%. 
The result of table 9 indicates that the index of financial leverage (ΔLEV variable), at the significance level of 0.102 and coefficient of 0.7925, has a positive and significant relationship with the changes of firm performance (changes of Tobin’s Q ratio) in the third quarter of the firm size. The descriptive power (modified coefficient of determination) of this model is 04.44%.
The result of table 10 shows that the index of financial leverage (ΔLEV variable), at the significance level of 0.0000 and coefficient of 1.3054, has a positive and significant relationship with the changes of firm performance (changes of Tobin’s Q ratio) in the fourth quarter of firm size. The descriptive power (modified coefficient of determination) of this model is 98.21%.
The regression coefficient between the changes of financial leverage index and changes of performance does not increase or decrease constantly along with the increase of the firm size level (moving from first quarter group of firm size toward the fourth quarter group of firm size). Hence, the results indicates that firm size has no modifying effect on the relationship between changes of financial leverage and changes of performance in companies listed on Tehran Stock Exchange. So, the fifth hypothesis is rejected.
The following model is used for testing the sixth hypothesis:
$\begin{aligned} \Delta L E V_{i, t}= & \beta_0+\beta_1 A G E_{i, t1}+\beta_2 \text { SIZE }_{i, t1}+\beta_3 E B I T_{i, t1}+\beta_4 \text { Firm Performance } \\ & +\beta_5 L E V_{i, t1}+v_i+\varepsilon_{i, t},\end{aligned}$
The result of table 11 displays that the index of firm performance (Tobin’s Q ratio), at the significance level of 0.0000, has a negative and significant relationship with the changes financial leverage.
The descriptive power (modified coefficient of determination) of this model is 76.36% and this means that 76.36% of changes in dependent variables are expressed by the independent variables. The result is the rejection of H_{0} hypothesis and this means that there is a negative and significant relationship between firm performance (Tobin’s Q ratio) and changes offinancial leveragein companies listed on Tehran Stock Exchange. Accordingly, the sixth hypothesis is accepted.
Descriptive variable  Coefficient  Standard error  T statistic  Prob 
AGE i; t  0.118626  0.049716  2.386084  **0.0172 
SIZE i; t  0.045289  0.011912  3.801881  ***0.0002 
EBIT i; t  3.50E09  5.30E09  0.659582  0.5097 
Firm Performancei; t  0.054529  0.009943  5.483955  ***0.0000 
LEV i; t1  0.897947  0.106580  8.425092  ***0.0000 
ε i;t  1.022324  0.217106  4.708883  ***0.0000 
Model test statistics  
F statistic (significance of total regression)  Coefficient of determination R2  Modified coefficient of determination ADJ R2  Durbin Watson statistic  
F statistic  Prob  
32.01704  0.0000  0.788301  0.763680  1.749706 
Panel tests  
Detection tests  Statistic test  Significance  Result  
Generalized F test  5.119117  0.0000  Emphasis on use of PLS against FE  
Hausman Test  62.790285  0.0000  Emphasis on use of FE against RE  
Final result  Emphasis on use PLS of against FE and RE  
FE: fixed effects model. RE: random effect model. PLS: integrative data model. ***: significance level of 99%, **: significance level of 95%, *: significance level of 90%. 
Similar to the fifth hypothesis, companies were initially classified based on the first, middle, and third quarter of firm size index, such that there is a quarter of firm size in each group of companies. Then, the model of the sixth hypothesis is tested in each group, separately. Finally, we study the acceptance or rejection of hypothesis in 4 groups by comparing the coefficient of firm performance index and significance level of the variable. Thus, the statistical hypothesis of seventh hypothesis testing is expressed as follows:
The regression coefficient between the variables of firm performance and changes of financial leverage should be increased or decreased constantly along with the increase of firm size level. The increase of firm size level means moving from first firm size quarter group toward the fourth.
The result of table 12 shows that the index of firm performance (Tobin’s Q ratio), at the significance level of 0.0000 and coefficient of 0.0776, has a positive and significant relationship with the changes financial leverage) in the first quarter of the firm size. The descriptive power (modified coefficient of determination) of this model is 48.96%.
Descriptive variable  Coefficient  Standard error  T statistic  Prob 
AGE i; t  0.072520  0.031368  2.311893  **0.0216 
SIZE i; t  0.004118  0.019564  0.210506  0.8334 
EBIT i; t  3.27E06  4.09E07  8.002478  ***0.0000 
Firm Performancei; t  0.077612  0.011377  6.821618  ***0.0000 
LEV i; t1  0.181499  0.033201  5.466683  ***0.0000 
ε i;t  0.176353  0.226451  0.778766  0.4368 
Model test statistics  
F statistic (significance of total regression)  Coefficient of determination R2  Modified coefficient of determination ADJ R2  Durbin Watson statistic  
F statistic  Prob  
52.62275  0.000000  0.499159  0.489674  1.807513 
***: significance level of 99%, **: significance level of 95%, *: significance level of 90%. 
The result of table 13 indicates that the index of firm performance (Tobin’s Q ratio), at the significance level of 0.0004 and coefficient of 0.0472, has a positive and significant relationship with the changes financial leverage) in the second quarter of the firm size. The descriptive power (modified coefficient of determination) of this model is 21.11%.
Descriptive variable  Coefficient  Standard error  T statistic  Prob 
AGE i; t  0.037898  0.046594  0.813369  0.4167 
SIZE i; t  0.018912  0.042216  0.447974  0.6545 
EBIT i; t  1.68E06  1.99E07  8.468277  ***0.0000 
Firm Performancei; t  0.047216  0.013246  3.564574  ***0.0004 
LEV i; t1  0.174407  0.035125  4.965395  ***0.0000 
ε i;t  0.075323  0.539163  0.139703  0.8890 
Model test statistics  
F statistic (significance of total regression)  Coefficient of determination R2  Modified coefficient of determination ADJ R2  Durbin Watson statistic  
F statistic  Prob  
15.34937  0.000000  0.225894  0.211177  2.015936 
***: significance level of 99%, **: significance level of 95%, *: significance level of 90%. 
The result of table 14 reveals that the index of firm performance (Tobin’s Q ratio), at the significance level of 0.0004 and coefficient of 0.0746, has a positive and significant relationship with the changes financial leverage) in the third quarter of the firm size. The descriptive power (modified coefficient of determination) of this model is 60.58%.
Descriptive variable  Coefficient  Standard error  T statistic  Prob 
AGE i; t  0.034617  0.028678  1.207079  0.2285 
SIZE i; t  0.194482  0.031261  6.221282  ***0.0000 
EBIT i; t  8.49E07  7.95E08  10.67755  ***0.0000 
Firm Performancei; t  0.074664  0.014000  5.333216  ***0.0000 
LEV i; t1  0.747152  0.037216  20.07622  ***0.0000 
ε i;t  2.152424  0.424795  5.066967  ***0.0000 
Model test statistics  
F statistic (significance of total regression)  Coefficient of determination R2  Modified coefficient of determination ADJ R2  Durbin Watson statistic  
F statistic  prob  
82.77323  0.000000  0.613257  0.605848  1.971656 
***: significance level of 99%, **: significance level of 95%, *: significance level of 90%. 
The result of table 15 shows that the index of firm performance (Tobin’s Q ratio), at the significance level of 0.0057 and coefficient of 0.0766, has a positive and significant relationship with the changes financial leverage) in the fourth quarter of the firm size. The descriptive power (modified coefficient of determination) of this model is 98.68%.
Descriptive variable  Coefficient  Standard error  T statistic  Prob 
AGE i; t  0.101360  0.077946  1.300383  0.1946 
SIZE i; t  0.048484  0.012487  3.882799  ***0.0001 
EBIT i; t  3.80E08  6.92E09  5.492960  ***0.0000 
Firm Performancei; t  0.076638  0.027509  2.785874  ***0.0057 
LEV i; t1  1.052876  0.007439  141.5262  ***0.0000 
ε i;t  0.011295  0.231426  0.048806  0.9611 
Model test statistics  
F statistic (significance of total regression)  Coefficient of determination R2  Modified coefficient of determination ADJ R2  Durbin Watson statistic  
F statistic  prob  
4047.488  0.000000  0.987123  0.986879  1.987878 
***: significance level of 99%, **: significance level of 95%, *: significance level of 90%. 
The regression coefficient between the variable of firm performance (Tobin’s Q ratio) and changes of financial leverage does not increase or decrease constantly along with the increase of the firm size level (moving from first quarter group of firm size toward the fourth quarter group). Hence, the results indicates that firm size has no modifying effect on the relationship between firm performance (Tobin’s Q ratio) and changes of financial leverage in companies listed on Tehran Stock Exchange. So, the seventh hypothesis is rejected.
6. Conclusion
Results of this research in case of the first hypothesis is based on the meaningful relationship between financial leverage and firm performance according in accordance with Jamal Zubairi (2009 Rajan, G, r, and Zingales L ) Badri Far and Emen Far (1390), Faramarzi (1384) results. Also present research results is inconsistent with Namazi and Shirzadeh (1384), Malek Pour Gharbi (1375).
Zobairi Jamal research results (2009) show that financial leverage has a negative effect on the profitable (ROE). But its relationship with ROA has been at a significant level of %90.
Rajan and Zenghals (1995) in their research showed that financial leverage in each of these countries has a negative relationship with corporate profit and has a positive relationship with the evidence fixed assets value and firm size.
Badri and Emeni Far (1390) also in their research showed that conclusion of capital structure analysis in one hand is depend on leverage definition and in the other hand influenced by researchers incomplete measurements. also, leverage level has a reverse relationship with growth opportunity variables and profitable and has a direct relationship with firm size but there is no relationship between assets structures with leverage.
In according to Faramarzi test results (1384) obtained on total firms is proven that there is a direct relationship between variables which are indicted type of the used capital structure in firms and asset return ratio which is as a index to express profitability in firm. results show that if equity is more in firms, it is expected that more be profitable in firms and in fact, profitable is a function from shareholders equity ration than to debt.
The obtained results in Namazi and Shiezadeh(1384) stating that in general, there is a meaningful relationship between capital structure and firms profitable but this relationship from statistical point of view is weak. relationship between capital structure and profitable also is depend on type of the industry and capital structure can be determined in various industries and relationship between capital structure and profitable in different industries also depends on the profitable definition.
Malek Pour Gharbi (1375) concluded that use of the financial leverage did not affect on firms profitable. Also, firms could not increase each share by using profitable leverage. Comparison of equity standard deviation of return and assets of returns represents a reduction in the risk of financial leverage during years under investigation.
Results of this research in case of the second hypothesis based on lack of the moderator effect of firm size on relationship between financial leverage and firms performance is inconsistent with Vithessonthi & Tongurai(2014) results.
Vithessonthi & Tongurai(2014) showed that financial leverage has a effect meaningful and positive on the small firms performance. Also, financial leverage has a negative and meaningful effect on the great firm’s performance. Negative effect of financial leverage on very small firm’s performance is more intense than to small firms. also results indicate the existence of non –linear and curvature relationship between financial leverage and firm performance in the different levels of firm size. present research result in case of the third hypothesis based on existence of non linear (curvature ) relationship between financial leverage and firm performance is in line with Vithessonthi & Tongurai results (2014).
Vithessonthi & Tongurai (2014) and Coricelli et al. (2012) showed that financial leverage has a non linear and curvature relationship with firm performance. They described this relationship U form.
One of the reasons that some researches merely have been achieved to a negative or positive relationship between financial leverage and firm performance is that such researches have been examined this relationship before or after financial leverage of optimal point. In this circumstances, this relationship merely will be reported the linear. while in fact, relationship between financial leverage and performance is nonlinear and curvature. result of this research in case of the fourth hypothesis based on the existence of negative and meaningful relationship between financial leverage changes is in line with firm performance changes based on Vithessonthi & Tongurai results (2014) and Giroud et al. (2012).
Vithessonthi & Tongurai(2014) showed that in all firms with different sizes there is a meaningful relationship between financial leverage changes with firm performance changes. According to their results, the last year financial leverage has a meaningful and negative with firm performance. Also, incremental changes in financial leverage reduce the performance in firm.
According to Giroud et al. (2012) financial leverage reduction improves the firm performance.
Research results in case of the fifth hypothesis impaling the lake of the existence moderator effect of firm size on the relationship between financial leverage changes and performance changes is inconsistent with Vithessonthi & Tongurai results (2014).
Vithessonthi & Tongurai(2014) showed that firm size has a reducing effect on relationship between financial leverage changes and firm performance changes so that greater firms have a more weak and negative relationship between financial leverage and firm performance changes than to smaller firms.
The present research results about sixth hypothesis based on the existent of negative and meaningful relationship between firm performance and financial leverage changes is in line with Vithessonthi & Tongurai(2014) and Bris et al. (2004) and XU ( 2012). They reported the negative relationship between firm performance and financial leverage changes and stated that in the very great firms or very small there is this negative relationship because the small firms is not able to receive the financial facility, therefore, firm performance will not have any effect on receiving the facilities and financial leverage changes. But with increasing firm size increase the performance effect on the financial leverage changes . this theme shows that small firms and average have the financial constraints and the severity of financial constraints is less in the greater firms.
The present research results about seventh hypothesis based on lack of the existent of moderator effect of firm size on relationship between firm performance and financial leverage changes is inconsistent with Vithessonthi & Tongurai(2014) and Mehrotra et al. (2003).
They showed that with increasing firm size increase the performance effect on the financial leverage changes. this theme shows that small firms and average have the financial constraints and the severity of financial constraints is less in the greater firms. Small firms than to great firms have lesser features to receive the loan and bank facilities and they have more financial constraints.
The results of hypothesis testing revealed that the relationship between financial leverage, asset return, and modified economic value added, as the firm performance indexes, is negative and significant. However, the relationship between financial leverage and Tobin's Q ratio, as a firm performance index, is positive and significant. Since a significant relationship is reported in all items, the first hypothesis is accepted by all three indexes of performance. The second hypothesis is constructed using all three indexes of firm performance (asset return, Tobin’s Q ratio, and modified economic value added), such that firm size has no modifying effect on the relationship between financial leverage and firm performance in companies listed on Tehran Stock Exchange and these results are in contrast with that of the Vithessonthi&Tonguari (2014). The result of the third hypothesis indicates a nonlinear (curved) relationship between financial leverage and firm performance (modified economic value added) in companies listed on Tehran Stock Exchange, which is line with the results of Vithessonthi&Tonguari (2014) and Coricelli et al. (2012). The result of the fourth hypothesis showed a negative and significant relationship between the changes of financial leverage and firm performance (the change of Tobin’s Q ratio), which are in accordance with the results of Vithessonthi&Tonguari (2014) and Giroud et al. (2012). The results illustrated no modifying effect of firm size on the relationship between the change of financial leverage and performance changes. Therefore, the result is the rejection of the fifth hypothesis that is in contrast with that of the Vithessonthi&Tonguari (2014). The result of sixth hypothesis indicated a negative and significant relationship between firm performance (Tobin’s Q ratio) and changes of financial leverage in companies listed on Tehran Stock Exchnage. These results led to the acceptance of the sixth hypothesis and are in line with that of the Vithessonthi&Tonguari (2014), Bris et al. (2004), and Xu (2012). Furthermore, results revealed no modifying effect of firm size on the relationship between firm performance (Tobin’s Q ratio) and change of financial leverage. The result is the rejection of the seventh hypothesis that is in contrast with that of the Vithessonthi&Tonguari (2014) and Mehrotra et al. (2003).
7. Discussion
Based on the obtained results of research are provided the following suggestions:
It is suggested to the Stock Exchange that in accepting and measuring the small firms are considered the firm performance ration in such companies and are apply relevant disclosure requirements for these firms.
Past information can be a suitable base for future decisions. it is suggested to financial statements user such investors that before making any decision based on that to invest in which company are analyze the financial leverage ration and performance in the past years by introduced ration in this research.
Securities and stock exchange organization can publish the more comprehensive information in regard of the financial leverage and firm performance for stockholders with respect to results of this research and similar researches.
It is better that active financial analyzers in capital market, investment advisers on the stock exchange along with theirs usual analyzes and techniques analyzes the firm performance than to financial leverage optimal ratios and firms financial constraints with respect to accounting standards.
In decisions related to select of the capital structure ratio not only is pay attention to its short term consequences but such decisions in long term increase the firm value an finally increasing the stockholders wealth and improving the firm performance, also it is necessary that prompting the level of knowledge of managers to true decision making about capital structure ration and financial leverage.
With respect to results of based on financial constraints in small firms and duo to these firms are less able to receive banking facilities it is suggested to authorities to improving business apace and firms economic leakage provides some condition to receiving facilities by small firms.
With respect to non linear and curvature relationship between financial leverage and firm performance it is suggested to managers that identify the financial leverage optimal point having the best function and stockholders will be have the most wealth. it is necessary that managers and decision makers in their planning considered the financial leverage optimal point about firms capital structure.
 We recommend the Securities and Stock Exchange Organization of Tehran to consider the proportions of firms’ performance in the process of acceptance and evaluation of small firms and to set out more appropriate disclosure requirements for these companies.
 We recommend the users of financial statements, especially investors, to analyze and compare the previous financial leverage and performance ratios of companies prior to any decision making regarding the investment and selection of companies using the defined ratio of this research.
 We recommend the senior managers not to pay attention to shortterm consequences through the process of optimal capital structure establishment, in that the impact of such decisions will affect the longterm results of performance, corporate value, and finally the shareholders’ wealth.
 Concerning the financial limitation of small and mediumsized companies in supplying bank finance, we recommend banking practitioners to provide conditions for the improvement of competitive business settingto shorten the process of receiving facilities for these companies.
 We recommend the financial managers to be fully acquainted with the optimum point of leverageto be able to yield the maximum performance of the company, because in this point of financial leverage, the company has the best performance and shareholders would benefit from the highest wealth.
8. Suggestions for Future Research
It is suggested that in future researches is consider other variable such as firm risk and inflation as control variable.
With respect to changing effective factors in performance such as economical, social and political conditions, theme of this research can be study in future time by researchers and compare with present research results.
It is suggested to strengthen results in future researches are examined the financial leverage relationship and firms performance monthly and seasonal by using firms midterm information.
It is suggested that desirable accounting regulations evaluated by long terms changes test in visible criteria of firms performance after and before regulating the important provisions.