NON-LINEAR EFFECT OF DEBT ON FIRM VALUE: DYNAMIC PANEL THRESHOLD EVIDENCE

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1 The Global Journal of Finance and Economics, Vol. 11, No. 1, (2014) : NON-LINEAR EFFECT OF DEBT ON FIRM VALUE: DYNAMIC PANEL THRESHOLD EVIDENCE Matemilola B.T a, Mohammad Karimi b, Bany-Ariffin, A. N. c and Carl B. McGowan d* ABSTRACT At moderate levels, debt increases firm value in the real world, where firms can take advantage of tax savings from debt financing. However, higher levels of debt financingmay lead to financial distress. This paper explores whether there is a threshold level of debt in the debt-value relationship. The paper applies dynamic panel-threshold regression to determinethe optimal debt ratio beyond which further increases in the debt level decreases firm value. We find a threshold effect of % between the debt ratio and firm value, using Tobin s Q as a proxy for firm value. When the debt ratio is less than %, a one percent increase in the debt ratio increases firm value by 0.236%. However when the debt ratio is greater than %, a one percent increase in debt ratio decreases firm value by 0.325%. The paper concludes that there is an optimal debt ratio of % at which point further increases in the debt ratio decreases firm value. These empirical results are consistent with the trade-off theory, which suggests that there is an optimum debt level that maximizes firm value where the marginal benefits of debt equate to the marginal costs of debt. Keywords: Firm value, Debt ratio, Trade-off theory, Dynamic panel-threshold analysis, South Africa. JEL code: G32, G30, G33 1. INTRODUCTION At moderate levels, debt increases firm value in the real world, where firms can take advantage of the debtinterest tax-shield. However, higher debtmay lead to financial distress. Specifically, in South Africa, there are cases of firms going bankrupt due to excessive debt (EzeohaandBotha, 2012). Firms financial distressis explainable within the framework of the trade-off theory of capital structure. Thus, testing the trade-off theory in South Africa would provide more empirical evidence for one of the main theories of capital structure as well as add clarity to the ongoing capital structure debate from a South African perspective. a,b b c d Department of Economics, Universiti Putra Malaysia, Malaysia Department of Economics, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran Department of Accounting and Finance, Universiti Putra Malaysia Norfolk State University, USA.

2 40 Matemilola B. T., Mohammad Karimi, Bany-Ariffin, A. N. and Carl B. McGowan Debt or capital structure decisionshave generated intense debate in the field of financial economics for over 50 years, but available theoretical and empirical evidence remains inconclusive. Besides, past empirical studies assume that the relationship between firm value and debt is linear. However, the actual relation between firm value and debt is non-linear (Ahmad and Abdullah, 2013; Li and Chang, 2011). Ahmad and Abdullah (2013) and Li and Chang (2011) apply Hansen (1999) static panel threshold to investigate the effect of debt on firm value. Unlike previous studies, this paper applies Kremer et al. s (2013) dynamic panel approach, which is an extension of Hansen s (1999) static panel threshold to endogenous regressors. This paper is unaware of any study that applies the dynamic panel threshold method to analyze the non-linear relationship between debt and firm value. The relationship between debt and value is dynamic in nature(johnson et al., 2011).Therefore, the dynamic panel threshold model is more appropriate than the static panel threshold model commonly used in the literature. Theoretical and empirical debate on the debt-value relationship remains inconclusive, suggesting that more studies need to be conducted in order to add clarity to the theoretical and empirical debate. Most of the theoretical and empirical debates on the debt-value relationshipare from developed countries, with very few contributions from Africa. It is interesting to make a contribution to this debate using data for firms fromsouth Africa, becausemost of the predictions about capital structure theories are testable in South Africa, where some degree of market imperfection such as bankruptcy costs exists. The rest of the paper is organized as follows: Section 2 reviews the relevant literature. Section 3 describes the methodology and data. Section 4 discusses the results while section 5 concludes the paper. 2. LITERATURE REVIEW Following the capital structure irrelevance theory proposed by Modigliani and Miller in 1958, numerous studies have been conducted to explain various conditions under which capital structureor debt become relevant. This has led to the development of five major theories (e.g. trade-off theory, pecking order theory, agency theory, market timing theoryand signaling theory) of which the trade-off theory emerges as one of the best possible explanations of how firms finance themselves in the real world (Bessler et al., 2011; Frank and Goyal, 2008; Bradley et al., 1984; Myers, 1984). The trade-off theory is one of the main theories of capital structure that explain how firms make capital structure decisions in the real world. Trade-off theory argues that there exists an optimal capital structure that maximizes firm value at a point where the tax-shield benefits of debt equate to the costs of debt. Despite various criticisms in the literature, the trade-off theory is supported by both empirical and theoretical studies (Ahmad and Abdullah, 2013; Oztekin and Flannery, 2012 Nunkoo and Boateng, 2010). Thus, the trade-off theory remains one of the dominant theories of corporate capital structure.the trade-off theory made some important predictions that are intuitively reasonable. Firstly, increases in the costs of financial distress reduce the optimal debt level. Secondly, an increase in the tax shield increases the optimal debt level. Third, at the optimal capital structure, an increase in the marginal bondholder tax rate decreases the optimal debt level. The dynamic trade-off theory improves on the limitation of

3 Non-linear Effect of Debt on Firm Value: Dynamic Panel Threshold Evidence 41 the static trade-off theory by allowing for possible deviations from the optimal debt level in the short run as well allowing for mean reversion back to the long-run optimal debt level (Matemilola et al., 2013; Oztekin and Flannery, 2012; Nunkoo and Boateng, 2010). However, the main challenge of the trade-off theory is that the optimal capital structure or optimal debt level is unobservable and a proxy is needed (Frank and Goyal, 2008). Earlier studies used the historical mean of the actual debt ratio for a firm (e.g. Shyam-Sunder and Myers, 1999). The use of the historical mean of debt has the advantage of minimizing the effects of temporal variations over time due to business cycles, floatation costs, and the firm s lagged adjustment towards their target debt level. Subsequent studies employ alternative specifications such as a rolling target debt ratio for each firm using only historical information and an adjustment process with lags of more than one year(frank and Goyal, 2008). Recent studies improve on the limitation of subsequent measures of target debt ratio by allowing for a time dependent target debt ratio which is assumed to be mean reverting (e.g.oztekin and Flannery, 2012; Nunkoo and Boateng, 2012). However, the panel threshold regression applied in this study is able to estimate the optimal debt level that maximizes firm value, which has receivedinadequate attention in the capital structure literature. The Modigliani and Miller (1958;1963) theoretical model with taxes establishes a positive relationship between debt and firm value. Extending the M-M (1958; 1963) theoretical model, Bhandari (1988) documents a positive relationship between debt returns. The Bhandari (1988) argues that the debt-equity ratio is a natural proxy for financial risk and the debt-equity ratio should have a positive relationship with equity risk and returns. Bhandari s (1988) empirical results show that debt is positively related to returns, after including firm size as a control variable. Recent empirical studies that investigate how debt relates to returns or firm value report mixed results. Ahmad et al. (2012) examines the effect of debt on firm value. The authors findings indicate that debt is positively related to firm value for Malaysian listed firms. Similarly, Matemilola et al. (2012) tests the impact of debt onshareholder required returns. The authors empirical results indicate that long-term debt and total debt are positively related to shareholderrequired returns for South African listed firms. Ahmad et al. (2013) also analyze the co-determinants of debt and stock returns. The authors results indicate that both debt and returns affect each other but that debt has a dominant effect on stock returns. The results illustrate that profits, growth, and liquidity are significant determinants of debt and returns. Specifically, profits negatively affect debt and positively affect stock returns. Moreover, growth has a positive effect on debt and returns while size does not have any significant effect on either debt or stock returns. Conversely, Dimitrov and Jain (2008) find that debt has a negative relationship with returns. They study changes in debt levels and show that debt is negatively related with current and future adjusted returns. Similarly, Penman et al. (2007) examine book-to-price effect on returns by accounting for debt. They decompose the book to price component into the enterprise bookto-price which reflects the operating risk and a debt component which reflects the financing risk. Penman et al. (2007) find that debt component has a negative effect on returns. This outcome holds in firms with both high and low book-to-price ratio.

4 42 Matemilola B. T., Mohammad Karimi, Bany-Ariffin, A. N. and Carl B. McGowan The fact that some authors find a positive effect of debt on value or returns while other authors report a negative effect of debt on value or returns suggests that there should be an optimal capital structure that maximizes firm value. One issue has received inadequate attention in the capital structure literature. What is the optimal debt level that maximizes firm value? This issue is resolved by applying Kremer et al. s (2013) dynamic panel threshold regression analysis to test whether there is a threshold effect ( ) at which point further increasesin debt decrease firm value. Kremer et al. (2013) investigate inflation thresholds for long-term economic growth using macro data. Conversely, our paper applies their dynamic panel threshold to explore whether there is a threshold level of debt in the debt-value relationshipusing firm-level data. 3. METHODOLOGY AND DATA 3.1. Threshold Model This section adopts a dynamic panel threshold model of Kremer et al. (2013). Q µ Q Z I( D ) I( D ) Z I( D ) Model (1) it i it 1 1 it 1 it 2 it it it Debt is the independent variable as well as the threshold variable. is the threshold level. u i is the firm-specific effect, 1 is the regime intercept, and it is the error-term which is independently and identically distributed with zero mean and constant variance, I( ) is the indicator function that indicate the regime defined by the threshold variable (Debt). Z it is a vector of explanatory variables that may include lagged values of the dependent variable and other endogenous variables. The paper divides the explanatory variables into two components Z 1 it which are exogenous variables which are uncorrelated with the error-term ( it ) and Z 2it which are endogenous variables which are correlated with the error-term ( it ). The exogenous variables are size, growth, and the taxrate. The explanatory variables may also include lagged values of the dependent variable and other endogenous variables. In addition to the structural equation (1), the model requires a suitable set of k m instrumental variables, x it and Z 1it. Tobin s Q it-1 is the endogenous variable and Generalized Method of Moments (GMM) type estimators are implemented to resolve endogeneity problem Estimation In dynamic model (1), the standard within transformation applied by Hansen (1999) leads to inconsistent estimates because the lagged dependent variable is correlated with the individual error-term. Applying a first differencing technique to eliminate the firm-specific effect implies negative serial correlation of the error-term and it is not possible to apply the distributional theory for panel data developed by Hansen (1999). In order to resolve this problem, the study used forward orthogonal deviations transformation as in Kremer et al. (2013) and Arellano and Bover (1995) to eliminate the fixed effects. The forward orthogonal deviations transformation subtracts the average of all future observations of a variable and this technique avoids serial correlation of the transformed error term. Therefore, for the error-term, the forward orthogonal deviations transformation is stated below: * T t 1 ( 1)... it T t 1 it T t i t it

5 Non-linear Effect of Debt on Firm Value: Dynamic Panel Threshold Evidence 43 The main advantage of these forward orthogonal deviations transformations is that the process ensures that the explanatory variables are not correlated with the error-term. Consequently, the estimation procedure allows for the application of the Cancer and Hansen (2004) cross-sectional model to the dynamic panel model (Kremer et al., 2013). Following Kremer (2013), this paper estimates a reduced form regression for the endogenous variable (Z 2it ), as a function of the instruments, x it. Then, the endogenous variables are replaced in the structural equation by their predicted values ( Z ˆ 2it ). In the second step, we estimate model (1) and model (2) via least squares for a fixed threshold, where the endogenous variables are replaced by their predicted values from the first-step regression. The sum of squared residuals obtained from the second-step regression is represented by S ( ). The step is repeated for a strict subset of the threshold variable (debt). Then, in the third step, we select an estimator of the threshold value of that has the smallest residuals (i.e. ˆ argmin ( ). The critical values to determine the 95% confidence interval of the threshold variable is stated below: = { : LR( ) C( )} Where C( ) is the 95% percentile of the asymptotic distribution of the likelihood ratio statistics LR ( ). The underlying likelihood ratio is adjusted in order to account for the number of time period for each cross section. After the threshold value ( ) is estimated, the slope coefficients is estimated by the Generalized Method of Moments for the previously used instruments and previous estimated threshold ˆ ( ) Data Data are obtained from Bloomberg. Specifically, the study uses the top 100 listed firms on the Johannesburg Stock Exchange from 2004 to Financial firms are excluded because their financial statement differs significantly from those of non-financial listed firms. Also, regulated firms will be excluded because their debt ratios are regulated to be higher than other nonfinancial firms.listed firms are chosen because valuation is available for listed firm stocks. Similar to Lin and Chang (2011), valueis defined as the ratio of market value of equity plus book value of total debt divided by book value of its total assets (Tobin s Q). Unlike accountingbased measures, Tobin s Q takes risk into account. Total debt (TD) is the ratio of total debt to total assets.total debt is a broader measure that encompasses the total of all liabilities and ownership claims on a firm. Debt is either measured in book-value debt or market-value debt(tchuigoua, 2014; Matemilola et al., 2013).Similar toahmad and Abdullah (2013) and Lin and Chang (2011), size is the logarithm of total assets. Growth is the annual percentage change in total assets. Tax (effective tax rate) is the ratio of tax liability to taxable income.moreover, the traditional variables use as independent variables are proxy commonly use in the literature and they are believed to be good predictor of firm value. S n

6 44 Matemilola B. T., Mohammad Karimi, Bany-Ariffin, A. N. and Carl B. McGowan 4. EMPIRICAL RESULTS The descriptive statistics and correlation results are presented in Table 1. Correlations between the variables affect the efficiency of the estimated coefficients. The correlation coefficients between the independent variables are generally less than 0.4. The low correlation between variables shows little risk of multicollinearity problem in the data.model 1 uses Tobin s Q as a proxy for firm value. Table 1 Descriptive Statistics TOBIN Q TD SIZE GROWTH TAX Mean Median Maximum Minimum Std. Dev Observation TOBIN Q TD SIZE GROWTH TAX TOBIN Q TD 0.114** SIZE 0.531*** 0.057** GROWTH * ** TAX ** ** *** ** a Tobin s Qis the ratio of market value of equity plus book value of total debt divided by book value of its total assets.debt is the ratio of total debt to total assets. Size is log of total assets. Growth is annual percentage in total assets. Tax is the ratio of tax liability to taxable income. d***, ** and *indicatecoefficientsaresignificantat1, 5and10percentlevels respectively. The panel threshold estimation results are presented in Table 2. The parameter ( ) splits the observation into two regimes based on whether the threshold variable debt is smaller or greater than the threshold value ( ). The regime one and regime two are separated by different slope estimates which are and respectively. In regime one where the debt ratio is less or equal to , the estimated coefficient of is and it is significant at 1% level. This empirical 1 result shows that Tobin s Q increases by 0.236% as debt ratio increases by 1%. In regime two where the debt ratio is greater than %, the estimated coefficient of is and it is 2 significant at 1% level. This result indicates that Tobin s Q increases by 0.032% as the debt ratio increases by 1%. The slope coefficient of the panel threshold does not have a fixed value in the two regimes. The estimated coefficient of the debt ratio (0.236) in regime one is larger than the estimated coefficient of the debt ratio (0.0325) in regime two. Thus, the results reveal that the relationship between debt and Tobin s Q (proxy for firm value) varies according to different changes in debt structure and a decreasing trend is found. The empirical results of this paper show that there is an optimal debt ratio of % at which point further increases in the debt ratio decrease firm value. These empirical results are consistent with the trade-off theory which suggests that an optimum debt level exists that maximizes firm value. An optimal debt level exists where the marginal benefits of debt and the marginal costs of debt are equal.

7 Non-linear Effect of Debt on Firm Value: Dynamic Panel Threshold Evidence 45 Theseempirical results are consistent with Ahmad and Abdullah (2013) and Lin and Chang (2011) who find the thresholddebt level that maximizes firm value in Taiwan and Malaysia, respectively using Hansen s (1999) static panel threshold regression. Table 2 Debt Threshold and Firm Value Model 1 (Tobin s Q) Threshold estimates % confidence interval Impact of Debt 0.236*** (3.746) 1 [0.063] *** (4.714) [0.007] Impact of independent variables Size 0.024*** (3.429) [0.007] Growth (0.255) [0.353] Tax *** (-2.200) [0.010] ˆ 1 (Constant) * (-1.946) [0.573] Observation 600 a Tobin s Qis the ratio of market value of equity plus book value of total debt divided by book value of its total assets.debt is the ratio of total debt to total assets. Size is log of total assets. Growth is annual percentage in total assets. Tax is the ratio of tax liability to taxable income.industry dummy is a dummy variable equal to 1 if a firm belongs to a particular industry and zero otherwise. b Thenumbersinparenthesesaretest statistics. c Thenumbersinbracketsarestandard errors. d ***, *indicatecoefficientsaresignificantat1and 10 percentlevels respectively. e Estimation code source: Table 3 presents the percentage of firms that fall within each of the two regimes, every year. The number of firms in the low-debt category is less than that of firms in the high-debt regime. As control variables, the size coefficient is statistically significant and positively related to Tobin s Q because bigger firms are more stable and less likely to go bankrupt. The tax rate coefficient is statistically significant and negatively related to firm value because taxes are expenses to firms which should lower returns. Growth is positively related to Tobin s Q but not statistically significant. Table 3 Number [percentage] of Firms in each Regime by Year for Model 1 (Tobin Q) Firm class Debt < Debt

8 46 Matemilola B. T., Mohammad Karimi, Bany-Ariffin, A. N. and Carl B. McGowan As arobustness check, the study uses dynamic system generalized method of moments (GMM) estimators developed by Arellano and Bover (1995) and Blundell and Bond (1998), where we include the square term of debt in the model specification. Despite the limitation of adding the squared term, the paper estimates the results to confirm the non-linear relationship between debt and firm value. As shown in Table 4, both the coefficients of the debt and squared debt are statistically significant in all three models, with positive and negative signs, respectively. These empirical results imply that debt and firm value havean inverted U-shape relationships. Theseempirical results are similar to the results reported in Table 2 that uses dynamic panel threshold analysis. The results of the post estimation tests suggest that the models are relatively well specified. Independent variable Table 4 Dynamic Panel Generalized Method of Moment (Two-step) Model 3 (Tobin Q Tobin Q it ** (42.92) Debt 0.079*** (12.94) Debt *** (-4.20) Size 0.153*** (94.07) Growth 0.024** (14.98) Tax ** (18.43) 2 nd order serial correlation (p-value) Difference Sargan Test (p-values) Notes: a Tobin s Qis the ratio of market value of equity plus book value of total debt divided by book value of its total assets. Debt is the ratio of total debt to total assets. Size is log of total assets. Growth is annual percentage change in total assets. Tax is the ratio of tax liability to taxable income. Industry dummy is a dummy variable equal to 1 if a firm belongs to a particular industry and zero otherwise. b The numbers in parentheses are test statistics. c The model estimated using Dynamic panel program of by Blundell and Bond (1998). d **and*** indicate coefficients are significant at 5 and 1 percent levels respectively. e Second order correlation that has N(0,1) distribution, but null uncorrelated with errors. f Standarderrors are robust system GMM results. g Differenced Sargan (1958) overidentificationtestandnullthatinstrumentsarevalid, but it runs if the errors are GMM type. N = 100, T = 6. Number of instruments are 68. TD it-2, Size it-2, Growth it-2 are used as instruments. CONCLUSIONS The paper applies panel-threshold regression toexplore whether there is a threshold level of debt in the debt-value relationship. The paper finds a threshold effect of % between debt ratio and Tobin s Q (proxy for firm value). When the debt ratio is less than %, a one percent increase in the debt ratio increases Tobin s Q by 0.236%. But when the debt ratio is greater than %, a one percent increase inthe debt ratio decreases Tobin s Q by 0.325%. The empirical results for this study indicate that there is an optimal debt ratio of % at which point further increases in the debt ratio decrease firm value. These empirical results are consistent with the trade-off theory which suggests that an optimum debtlevel exists that maximizes firm value. An optimal debt exists where the marginal benefits of debt equal the marginal costs of debt. The implications of these empirical results are that financial managers should take steps to increase the debt level if they are below the threshold debt level - that is when the debt level is

9 Non-linear Effect of Debt on Firm Value: Dynamic Panel Threshold Evidence 47 less than ( ), in order to maximize the firm value. However, financial managers should take steps to reduce their debt level if they are above the threshold debt level ( ) - that is when the debt level exceeds ( ) in order to avoid financial distress. Furthermore, investors should make an effort to investigate the firm s debt level by computing relevant debt ratios to avoid investing in firms with a debt ratio above the required threshold debt level.moreover,policy makers should encourage firms to maintain a sustainable level of debt (the threshold debt level) which will prevent the firm from possible bankruptcy. Unlike previous studies that specify a static panel model to investigate the relationship between debt and firm value, this paper applies Kremer et al. s (2013) dynamic panel approach. Moreover, Kremer et al. (2013) investigate inflation thresholds for long-term economic growth using macroeconomic data. Conversely, our paper applies the dynamic panel threshold model to investigate the effect of debt on firm value using firm-level data. Future researchers are encouraged to apply the non-linear dynamic panel to investigate the relationship among financial economic variables, especially where non-linear relationship is suspected. References Ahmad, A. H. and Abdullah, A.H. (2013), Investigation of optimal capital structure in Malaysia: panel threshold estimation. Studies in Economics and Finance, 30(2): Ahmad, Z., N.M.H. AbdullahandS. Roslan, (2012), Capital structure effect on firms performance: focusing on consumers and industrials sector on Malaysian firms, International Review of Business Research Papers, 8 (5): Ahmad, H., B.A. FidaandM. Zakaria, (2013), The co-determinants of capital structure and stock returns: evidence from the Karachi Stock Exchange. The Lahore Journal of Economics, 18(1): Arellano, M. and O. Bover, (1995), Another look at the instrumental-variable estimation of error components models. Journal of Econometrics, 68(2): Bhandari, L.M., (1988), Debt and equity ratio and expected common stock returns: empirical evidence. Journal of Finance, 43(2): Blundell, R., and S. Bond, (1998), Initial condition and moment restriction in dynamic panel data models. Journal of Econometrics, 87: Bessler, W., W. Drobetz and M.C. Gruninger, (2011), Information asymmetry and financing decisions. International Review of Finance. 11(1): 123:154. Bradley, M., G. Jarrell and E. Kim, On the existence of an optimal capital structure: theory and evidence. Journal of Finance. 39(3): 857:78. Cancer, M. and B.E. Hansen, (2004), Instrumental variable estimation of a threshold model. Economic Theory, 20: Dimitrov, V. and P.C. Jain, (2008), Value relevance of changes in financial leverage beyond growth in assets and GAPP earnings. Journal of Accounting and Finance, 23: Ezeoha, A. and F. Botha, (2012), Firmage, collateralvalue, andaccess to debt financing in an emergingeconomy: Evidence from South Africa, South Africa. Journal of Economics and Management Sciences, 15 (1): Frank, M. Z. and K.V. Goya, (2008), Trade-off and pecking order theories of debt. Handbook of Corporate Finance: Empirical Corporate Finance. 2: 1-82.

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