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DETERMINANTS OF CAPITAL STRUCTURE AN EMPIRICAL STUDY OF AMERICAN COMPANIES Supervisor: Author: Dr Cormac Mac Fhionnlaoich Nguyen Thi Dieu Hong August 31st 2016 Abstract This study investigates the factors that potentially have impact on capital structure decisions of American firms, and identify the key determinants of the capital structures of these firms The paper also explores the capital structure theories and how they explain capital structure decisions of firms worldwide and in the U.S The sample of includes 1.500 U.S firms, which covers 90% publicly-traded companies in the U.S during post-financial crisis time, from 2010 to 2016 Using panel data techniques with fixed-effects model and random-effects model, firms ‘characteristics are tested if they explain for leverage ratios The explanatory variables represent the factors that potentially determine capital structure: business risk, profitability, firm size, growth opportunities, tangibility of assets, non-debt tax shields This study finds that the most reliable and important factors that determine the use of debt by American listed firms are firm size (+), tangibility of assets (+), profitability (–) Besides, the moderately influential factors of leverage includes: business risk (+/–), non-debt tax shield (+/–) and growth opportunities (+/–) The study finds evidences which are consistent with pecking-order theory’ prediction of a positive relationship between asset tangibility and financial leverage and a negative relationship between profitability and financial leverage The finding moderately supports trade-off theory’s prediction of negative relationship between non-debt tax shield and leverage, business risk and leverage The trade-off suggestion of a positive relationship between asset tangibility and financial leverage are also confirmed by this study Finally, agency’s prediction of a negative relationship between growth opportunities and leverage is moderately supported by a negative and insignificant relationship found in this study Acknowledgement In the last three months, I have been lucky to receive great support from many people who have helped to make this study possible At first, I would like to extend the most sincere gratitude to Dr.Cormac Mac Fhionnlaoich, UCD Michael Smurfit Graduate Business School, for providing supporting during the process of conducting this research Dr.Cormac Mac Fhionnlaoich has shown great support in guiding me through this project, providing detailed comments and thoughtful suggestions in my completion of the project Furthermore, I would like to send my appreciation to Irish Aid, The UCD Michael Smurfit Graduate Business School staff and lectures, and ICOS for giving the scholarship and support me during my academic year in Ireland I also would like to place on the record my sincere gratitude to my IDEAS Fellows, in particular, Pham Khanh Linh, for his guide on data solving and Nguyen Thi Phuong Thao for her company and encouragement Last but not least, I would like to show my great appreciation family and friends for their support and constant care for me on the way to my completion of the master program Contents o INTRODUCTION LITERATURE REVIEWS 2.1 Modigliani-Miller theorem 2.2 Tradeoff theory 2.3 Pecking order theory 2.5 Determinants of capital structure 2.5.1 Size 2.5.2 Tangible assets 2.5.3 Profitability 10 2.5.4 Growth 10 2.5.5 Non-debt taxed shield 11 2.5.6 Risk 12 DATA AND METHOLOGY 15 3.1 Data Description 15 3.2 Panel data regression model 15 3.2.1 Panel data 15 3.2.2 Definition of variables 17 3.2.3 Model 20 RESULT 21 4.1 Data descriptive 21 4.2 Correlation Test 22 4.3 Test of determinants of capital structure 24 CONCLUSION, LIMITATION AND SUGGESTED FUTURE WORKS 34 5.1 Conclusion 34 5.2 Limitation 35 5.3 Suggestions for future research 37 REFERENCES 38 List of tables Table 1: Predicted effects on leverage based on capital structure theories 13 Table 2: Determinants of capital structure in previous researches 14 Table 3: Measures of leverage 17 Table 4: Measures of capital structures determinants 19 Table 5: Descriptive statistics of the sample 21 Table 6: Correlation of variables 22 Table 7: Fixed-effects regression results 24 Table 8: Random effects regression results 25 Table 9: Hausman test results 25 Table 10: Regression with selected factors 27 Table 11: Modified Wald test results for heteroskedasticity 27 Table 12: Wooldridge test results for autocorrelation 28 Table 13: Fixed-effects regression with Driscoll-Kraay standard errors 29 INTRODUCTION Capital structure is one of the most important decisions of every company A false decision in capital structure can lead a firm to severe difficulties Managers always want to find a suitable capital structure policy to meet their goals Researchers, from another aspect, are curious to know how firms choose of sources of financing, they have target structure and what factors affect firms’ decisions That is the reason makes the capital structure to become one of the most important fields of corporate finance Modern corporate capital structure theory originated by Modigliani and Miller’s (1985) with irrelevance theorem The idea of the theory is that in an efficient market with the absence of taxes, agency costs, bankruptcy, and asymmetric information, how a firm is financed does not affect its value Since the value of the company depends neither on its dividend policy nor its source of capital, the Modigliani, and Miller theorem is often called capital irrelevance principle This theory is considered to lay stones for many followers to study capital structure However, it is clear that Modigliani and Miller’s assumptions are unrealistic and hard to happen in the real market Following Modigliani and Miller (1958), several other theories have been developed on the topic of capital structure The trade-off theory states that companies choose an amount of debt finance and equity finance base on the balance of benefit and financial cost The pecking order theory focusses on asymmetric information with considering that the cost of finance increases with asymmetric Therefore, firms will choose to internal financing as the first priority, then debt and equity as a ‘’last resort’’ Another stream of research was initiated by Ross (1977) on how the choice of a firm’s capital structure can signal information to outside investors about the company, i.e issuing large debt levels is a signal of higher quality of the firm With regards to empirical work, many studies were done to find an answer to the capital structure puzzle Concerning to U.S firms, one of the earliest attempts to extend empirical study on capital structure was conducted by Titman and Wessels (1988) A large set of data of U.S companies between 1974 and 1982 was used to examine theoretical determinants of capital structure Following this, Rajan and Zingales (1995) investigated the determinants of capital structure decisions on a broader scope in G-7 countries with more focus on U.S firms It can be clearly seen that both theoretical and empirical work has made progress in investigating which factors influence capital structure decisions Yet, Titman and Wessels (1988), Rajan and Zingales (1995), and Harris and Raviv (1991) agreed on the fact that, while progress has been made from the initial work of Modigliani and Miller in 1958, the empirical work was lagging behind and doing very little to identify empirical findings of capital structure in practice While theoretical work had identified a large number of potential determinants of capital structure, empirical studies have not frequently considered various contexts outside the G-7 countries In recent years, empirical studies on capital structure determinants have been largely extended to different developed and developing countries including Malaisia, (Pandey, 2001), India (Joy Pathak, 2010), Portugal (Vergas, Cerqueira, Brandão 2015), Sweden (Han-Suck Song, 2005) They pointed out both similarities and discrepancies in what factors influence firm financing decisions across different contexts By updating data, applying the methodology used for the panel data that has been improved upon and updated with a thorough analysis of different models and using four kinds of leverage ratios, the study wants to find out which factors are important in the capital structure decisions of U.S in recent time, especially after the financial crisis time 2 LITERATURE REVIEWS 2.1 Modigliani-Miller theorem Fifty-eight years ago (1958), two economists Franco Modigliani and Merton Miller proposed Modigliani-Miller theorem on the capital structure which plays an essential role in modern corporate finance Before them, no widelyaccepted theory of capital structure has existed The theorem states that in a perfect market without taxes, asymmetric information, bankruptcy cost, and agency costs, the way in which a firm raise its capital makes no influence on its value This suggests that the valuation of a firm is irrelevant to its capital structure, so the theorem is also called capital structure irrelevance principle The assumptions of the theory are based on an efficient market First, there are no taxes Second, there is no transactions costs and bankruptcy costs Third, the information is symmetric, all investors are rational and have the same access to information Fourth, the costs of debt are the same for everyone and last, debt financing not affect firms The fact is that it is very hard to find a perfect market In reality, corporations business in a market containing transaction costs, borrowings costs, taxes, asymmetric information and agency costs By relaxing some assumption in Modigliani-Miller theory, some alternative theories were proposed to address these imperfections 2.2 Tradeoff theory The Static tradeoff theory The basic idea of trade-off theory is that that firms follow an optimal capital structure to maximize value by offsetting the cost of the additional unit of debt by its benefit Baxter (1967) and Kraus and Litzenberger (1973) stated that a taxable corporation should consider an increase in its debt level until there is a balance between the marginal value of tax shield and the present value of any financial distress costs occurred Trade-off model with bankruptcy costs When firms borrow, they get a tax advantage as interest is deductible for income tax Besides, firms have to incur bankruptcy cost of debt Companies using leverage need to pay interest on their borrowings This changes companies’ earnings and cash flow The more firms borrow, the higher probability of bankruptcy increases The trade-off theory predicts that firms choose an optimal capital structure to balance tax benefits and cost of debt Companies substitute debt with equity or versus while maximizing the company’s value Trade-off model with agency costs Jensen and Meckling (1976) notice that debt had been used widely before the appearance of subsidies tax on interest payment, given that there must be other important factors of capital structure that have not been recognized Two kinds of agency costs were suggested that is the gap between shareholders and managers and conflict between shareholders and creditors Agency cost between shareholders and managers: This type of agency costs appear when there is a separation between ownership and management When shareholders lose control, sometimes managers have opportunities to put their benefits above shareholders Instead of always making decisions to maximize the market value of the firms, managers may make the inefficient allocation of capital For example, managers may pursue growth and size at the expense of profitability and value by investing in unprofitable projects Some managers prefer managing a bigger, and more influential firms have less incentive to act for benefits of shareholders If increasing using debt, firms have to pay interest payment and by that reduce free cash flow within the firms As a result, there is a deterioration of liquidity that allows managers to take part in projects that the profit maximization (Jensen, 1986) Agency cost between shareholders and creditors: The shareholder's attempt to engage in new projects that generate more benefits for shareholder while posing higher risks to the firm’s creditors If the risky capital investment project is successful, shareholders will gain more rate of return Lender’s benefit does not change because the interest rate is fixed If the project fails, the creditors are forced to share in the loss The reduction in value of debt due to risky projects is called agency cost of debt financing Jensen and Meckling (1976) suggested that firms can find optimal capital structure point where the total cost of agency is minimized Dynamic Trade-off theory There are abundant studies supports this static trade-off theory such as Myers (1993); Andrade and Kaplan (1998); Graham (2000); Hovakimian, Kayhan, and Titman (2012) Graham and Harvey (2001) find that 81% of CFOs model for measuring SDB The table also only keeps statistically variables in the models Table 10: Regression with selected factors FACTORS ROA SIZE TDB TDM LDB SDB -0.00317* -0.0190*** -0.00304* (-2.09) (-15.07) (-2.38) 0.128*** 0.136*** 0.123*** 0.00713*** (4.10) (5.29) (4.71) (6.65) GROWTH TANG 0.276*** -0.0140** (3.78) (-2.87) NDTS -0.725** (-2.95) RISK _CONS R-sq – -.6761197* -.8005491*** -.6919881** (-2.50) (-3.57) (-3.04) 0.0067 0.0687 0.0074 0.0076 0.0006 0.0000 0.0000 0.0000 overall Prob > F Test for heteroskedasticity The modified Wald test (Greene, 2000) is the used to test for heteroskedasticity of the sample This test helps detect whether the errors are uncorrelated and normally distributed, and that their variances are constant and not vary with the effects modelled H0: sigma(i)^2 = sigma^2 for all i Table 11: Modified Wald test results for heteroskedasticity TDB TDC LDB LDB chi2 (1286) 8.7e+37 5.3e+35 1.4e+38 1.7e+38 Prob > chi2 0.0000 0.0000 0.0000 0.0000 27 It can be seen from table 11 that p-value is equals 0.0000 for all four leverage models The test indicates a strong evidence to rejects the null hypothesis Heteroskedasticity clearly exists in the estimation The presence of such heteroskedasticity can invalidate the significance of the statistical model To deal with this violation, the regression with Driscoll and Kraay standard errors will be used Test for autocorrelation The Wooldridge test is used to test for autocorrelation (Wooldridge, 2002) following the regression results above Assume that there is no correlation between a time-series with its own past and future values; this test determines if such a correlation exists H0: no first order autocorrelation Table 12: Wooldridge test results for autocorrelation F (1,827) Prob > F TDB TDM LDB LDB 209.350 0.0000 2109.411 0.0000 107.850 0.0000 8.521 0.0036 Since ther p-value equals 0.0000 and one p-value is small, the Wooldridge test rejects the null hypothesis of no autocorrelation The test indicates a strong evidence to rejects the null hypothesis Autocorrelation exists in the estimation To deal with this violation, the regression with Driscoll and Kraay standard errors will be used Dealing with the violations The Driscoll and Kraay (1998) standard errors for coefficients are calculated to avoid estimation biases caused by heteroskedasticity, autocorrelation The following are results of regression models for the respective leverage measures 28 Table 133: Fixed-effects regression with Driscoll-Kraay standard errors FACTORS TDB TDM LDB SDB -0.00317 -0.0190*** -0.00304* -0.000140 (-2.09) (-6.46) (-2.39) (-0.49) 0.128*** 0.136*** 0.123*** 0.00415 (4.85) (3.99) (5.48) (0.90) 0.000249 -0.0226** -0.00291 0.00295* (0.05) (-3.29) (-0.58) (2.53) 0.00333 0.276*** 0.0226 -0.0202 (0.06) (6.30) (0.47) (-1.66) 1.170** 3.108** 1.356** -0.155 (3.20) (3.09) (3.60) (-1.63) 000179 00138 000624 -.000477 (0.07) (0.30) (0.32) (-0.73) -0.676** -0.801* -0.692*** (-3.37) 2.8) (-4.06) N 20118 19993 20082 19527 R-sq – within 0.0013 0.0206 0.0017 0.0184 Prob > F 0.0006 0.0000 0.0000 0.0000 ROA SIZE GROWTH TANG NDTS RISK _CONS 0.0207 (0.55) Profitability It can be seen from the regression results that profitability, which is measured as return on assets, has a negative relationship with all of the measures of debt including total debt ratios, long-term debt ratios, short-term debt ratios The relationship is highly significant for Total Debt to Book value of capital and Long-term debt ratios and moderately significant for Total Debt to Market value of capital This indicates that when firms are profitable, they tend to borrow less except short-term debt This result agrees with pecking-order theory, as proposed by Myers and Majluf (1984) which states that firms make profit prefer retained earnings as a source of capital to external financing This result agrees with Rajan and Zingales (1995) They also found a negative influence of profitability on 29 leverage U.S firms during 1987-1991 Moreover, not only in the US, the study found that during this time the other G-7 countries except Germany also experienced the same relationship of profitability Tugba, Gulnur, and Kate when studying samples of 25 emerging market countries from different regions also found an inverse impact of profitability on leverage The negative relationship between profitability and leverage is also found in a various empirical study such as Frank and Goyal (1995), Nelson, Antonio and Elisio (2015), Titman and Wessels (1988), Joy Pathak (2010) and Han-suck Song (2005) Size The result reveals that firm size of the U.S firms moves in the same direction with their debt ratios The relationship of firm size measured as the log of total assets had significantly positive relationship with all types of leverage All the β are significant at a level of percent In general, larger firms will use more debt, both in term of the total debt, short-term debt and long-term debt Moreover, whether debt ratios base on book value or market value of capital, there is strong evidence of a statistically significant relationship between firm size and leverage Growth Growths of firms, as measured by growth in sales, is found to have an insignificant relationship with all measurement of capital structures The relationship of growth and Total Debt to Book value of capital, Short-term Debt to Book value of capital is positive The relationship of growth and Total Debt to Market value of capital, Long-term Debt to Book value of capital is negative However, all the β are insignificant This finding does not support that growth is a determinant of capital structure This study has found the result different with many studies Frank and Goyal (2009) while studying publicly traded American firms from 1950 to 2003 found that firms with high market-to-book ratio tend to have low levels of 30 leverage Rajan and Zingales (1995) in another study of G-7 countries, also found a negative relationship when using market-to-book ratio as the proxy for growth opportunities Titman and Wessels (1988), who also used realized value of growth as this study, while examining 469 U.S firms from 1974 to 1982 found a negative relationship between growth and leverage However, results of this study share the same finding that is an ambiguous relationship between growth and leverage such as Han-Suck Song (2005), Cassar and Holmes (2000) Many studies which also use a change in sales as the proxy of growth also found an insignificant relationship between growth and leverage such as Hall, Hutchinson and Michaelas (2000), Cassar and Holmes (2000), Klapper, Sarria-Allende and Zaidi (2006) and Hall, Hutchinson, and Michaelas (2004) It can be inferred that choosing different measurement of factors can lead to different results Here, many studies using growth as changes in sales find no significant relationship between leverage and growth while others many studies measuring growth in other ways such as changes in total assets find a significant relationship Tangibility Tangibility, as measured by the percentage of tangible assets on total assets, in general, moves in the same direction with leverage It can be seen from regression table that tangibility has a positive relationship with Total debt to Book value of the capital structure, Total Debt to Market value of the capital structure, Long-term debt to Book value of capital Especially, the relationship is significant at percent between tangibility and Total Debt to Market value of the capital structure This can be explained by trade-off theory, as firms can borrow at lower costs by using tangible assets as collaterals in debt financing – reducing the financial distress costs This result also agrees with agency theory, since high tangibility helps reduce agency problems by preventing asset substitution Tangibility has a positive relationship with long-term debt but has a rather significant negative relationship (at percent) with short-term debt These findings is similar to recent studies’ findings such as Bas et al (2009) 31 which studied small and private firms from 25 developing countries, Koksal et al (2013) which examined the determinant of Turkish firms and Martina Harc (2015) which investigated determinant of Croatian firms They both found that tangibility appears to be the key determinants of long-term leverage (positive relationship) but not important for short-term leverage (negative relationship) This finding can be explained by maturity matching principle which states that firms use long-term debt to financing long-term assets and short-term funds to finance short-term assets Non-debt tax shield The impact of non-debt tax shield on leverage found in this study is ambiguous Non-debt tax shield moves in the same direction with Total debt to Book value of the capital structure, Total Debt to Market value of the capital structure, Long-term debt to Book value of capital However, only the relationship of Total Debt to Market value and non-debt tax shield is significant This finding, however, still supports DeAngelo and Masulis ‘s model which states that firms with large non-debt tax shield borrow more borrow more Risk This study reveals that business risk has a positive influence on the leverage of American listed firms The higher the business risk firms have, the more debt is used in firms’ capital structure This finding does not follow the prediction provided by trade-off theory that firms with more risky earnings should have less debt as they face higher financial distress costs from fixed commitments to debt holders and benefit less from tax shields Instead, the result confirms the principle of pecking order theory that firms with more risky earnings have higher levels of information asymmetry and therefore have more debt The time from 2010 to 2015 is the period follows the financial crisis, the business risk for companies as well as the whole country is very high In response to this, American firms have increased debt financing Empirically, this study disagrees with Titman and Wessel (1988), Joy Pathak (2010), Frank and Goyal (2009) about the direction of the relationship between leverage and business risk of U.S companies These two studies 32 concluded that business risk inversely affects leverage However, the findings of this study agree with Huang and Song (2002), and especially, Pandey (2001) on the positive relationship between leverage and business risk 33 CONCLUSION, LIMITATION AND SUGGESTED FUTURE WORKS 5.1 Conclusion This study investigates publicly traded American firms over the period 2010 to 2015 to find the influence of six firms’ characteristics on leverage The sample consists 1.500 firms of S&P Composite 1500 index which covers 90% of the market capitalization of U.S public stock The study uses four leverage measures and six potential capital structure determinants to measure the impacts these factors have on firm leverage The study finds that the most reliable and influential factors + Assets structure plays an important role in the capital structure The larger portion of tangible assets firms have, the more leveraged they are However, assets structure have a different impact on long-term debt and shortterm debt Firms tend to use more long-term debt when they have larger tangible assets and use less short-term debt when they have larger tangible assets This finding agrees with maturity matching principle which states that firms use long-term debt to financing long-term assets and short-term funds to finance short-term assets This finding supports trade-off and agency theory which predicts a positive relationship between tangibility and leverage It also follows pecking-order theory which predicts both positive and negative relationship of leverage and tangibility + Firms that make profit tend to be less leveraged, in term of total debt to market value and book value of capital, long-term debt to book value of the capital structure This supports pecking order theory because firms rather use retained earnings as a source of investment than use outside funds However, profitability does not have much influence on short-term debt decision + Larger firms tend to be more leveraged The larger firms have better access to debt markets such as bank loan and corporate bond issuance Larger firms tend to borrow more debt whether it is long-term debt or shortterm debt This is consistent with both trade-off theory and pecking order theory 34 + In contrast with others studies which find a relationship of business risk and leverage The relationship of risk and leverage found in this study is insignificant It can be concluded from this study that risk not have a large influence on capital structure decisions + Non-debt tax shield has ambiguous impact on the capital structure The relationship of non-debt tax shield is positive and insignificant This finding moderately supported DeAngelo and Masulis ‘s model which states that firms with large non-debt tax shield borrow more + Firms growth has a negative relationship with capital structure However, the relationship is insignificant Therefore, it can be concluded from this study that firms growth, as measure by the change of sales, is not a determinant of capital structure decisions The study finds evidences which are consistent with pecking-order theory’ prediction of a positive relationship between asset tangibility and financial leverage and a negative relationship between profitability and financial leverage The finding moderately supports trade-off theory’s prediction of negative relationship between non-debt tax shield and leverage, business risk and leverage The trade-off suggestion of a positive relationship between asset tangibility and financial leverage are also confirmed by this study Finally, agency’s prediction of a negative relationship between growth opportunities and leverage is moderately supported by a negative and insignificant relationship found in this study 5.2 Limitation First, the study just focuses on the six most popular and important factors recommended by vast literature It does not include some relevant firms’ characteristics that are recommended from others empirical studies such as R&D activities, manager behaviors, and state ownership Besides lacking some firms’ characteristics, other factors from the economy can be included such industry average growth rate, inflation rate, interest rate The reason this study does not contain such factors is due to limited availability of databases and the long process involved in collecting data from diverse and un-unified 35 sources for data such as in the case of state ownership and manager behaviors Secondly, although the five-year period with 24 quarter provides an enough long time to the research, this is still a short period of the credible studies worldwide, such as Frank and Goyal (2009) who study spans over a 50-year horizon The time from 2010 to 2015 is a special period It is the time the economy recovers from the financial crisis There are many changes in this time affects companies’ decision, especially on capital structure Therefore, the result may have some differences with a study conducted in a different period or a longer period Thirdly, the study just includes listed U.S companies The result of the study cannot be correct to all others private and not publicly traded companies United Stated is a developed financial market Therefore, the result also cannot be correct to others developing markets Tugba, Gulnur, Kate (2009) investigating companies in developing countries and Pandey (2014) studying capital structure in some emerging markets both found some differences results with this study Next, choosing proxies for factors are also needed to be carefully considered For example, to examine the influence of growth, many studies use already realized value such as changes in sales, assets while many others use growth opportunity such as market-to-book ratios Those study using market-to-book ratio often find a negative relationship between capital structure and growth Many other studies such as this one using changes in sales as the proxy for growth find an ambiguous relationship between leverage and growth The method and analysis of capital structure theories need to be improved The study has not examined deeper the influence of each determinant and not included the relation of capital structure decisions to tradeoff theories, agency theory, free cash flow theory, pecking order theory, and market timing theory 36 5.3 Suggestions for future research First, it is necessary to include a complete set of factors from both firms and the economy As mention above, those factors can be inflation rate, interest rate, industry average rate, R&D activities, firms’ uniqueness, state ownership and manager behaviors Second, the time horizon should be expanded longer Collecting a broader range of date in a longer period can lead to more generality of the result Third, the sample of the study is also should be broadened Further studies can examine more about private and not publicly traded companies Further studies on undeveloped and emerging market should be done Moreover, it is important to find a right proxy for each factor The measurement of leverage also needs to be carefully chosen Last but not least, it is important to study the capital structure determinants for specific industries separately to understand the capital structure behaviors about each industry and to remove the industry difference that may provide biased results 37 REFERENCES Armen Hovakimian, Tim Opler and Sheridan Titman (2002).The capital structure choice: new evidence for a dynamic tradeoff model, 15(1), 24-30 Baker, M., Wurgler, J (2002) Market timing and capital structure The journal of finance, 57(1), 1-32 Barry, C.B., Mann, S.C., Mihov, V., Rodriguez, M (2008) Corporate debt issuance and the historical level 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Table 2: Determinants of capital structure in previous researches Study Titman and Wessel (1988) Pandey(2001) Joy Pathak (2010) Vergas, Cerqueira, Brandão (2015) Frank and Goyal (2009) Rajan and Zingales(1995)... Modigliani and Miller (1958), several other theories have been developed on the topic of capital structure The trade-off theory states that companies choose an amount of debt finance and equity finance... more demand of funds and also retain more earnings When examining the determinants of capital structure of Malaysian during 1994 to 1999, Pandey found a significant relation between growth and all