Capital structure variables and the adjustment to a target:
UK empirical evidence
J.E.R. ter Veer* Master’s Thesis Finance University of Groningen
Supervisor: dr. N. Brunia, ing
January 2014
Abstract
This study finds evidence that firms in the United Kingdom adjust debt levels to a target capital structure in the period 1993-2012. Mixed results are documented. The firm characteristics collateral, non-debt tax-shield, growth, profitability, firm size and earnings volatility partly explain the existence of an optimal or target capital structure. However, the inclusion of a one year lagged capital structure in a fixed effects regression model shows a large positive relationship between current and past debt levels. This result confirms existing UK empirical evidence in a new time frame that firms adjust to a value maximizing capital structure.
Keywords: capital structure, debt, firm characteristics, leverage
JEL classification: G32, G33, G34
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1. Introduction
Corporate valuation practitioners use the cost of capital to measure the present value of a company. The cost of capital represents the opportunity cost that investors face for investing in one particular company instead of other investments with identical risk. One way to measure the cost of capital of debt and equity is to use the Weighted Average Cost of Capital (WACC). The WACC uses the target capital structure and the market beta to measure the total costs of capital.
To determine the WACC of a company, Koller, Goedhart and Wessels (2010) use a peer group comparison on which the target capital structure and market beta are based. The peer group exists of firms from the same industry with similar business risks and operating characteristics such as profitability, growth, asset specificity and firm size. Koller et al. (2010) claim that the target capital structure should be based on the median capital structure of the peer group.
The proposed way of Koller et al. (2010) in setting the target capital structure does not fully take into account the specific level of the operating characteristics. For example, a firm is valued and the target capital structure that is used for the WACC calculation is determined on median values of the operating characteristics of comparable firms. However, if this valued firm is highly profitable, a larger tax-shield could be available. This tax-shield could be used to profit from the benefits of debt, which is the deductibility of the costs of debt from a firm’s taxable income. If the used debt in the chosen target capital structure is lower than the available tax-shield, a part of the firm’s value is left on the table.
Korteweg (2010) applies the trade-off theory (Kraus and Litzenberger, 1973) to estimate the benefits of debt and concludes the existence of a trade-off between the use of debt and equity. The benefits of leverage are up to 5.5% for a median, optimal leveraged firm. Firms adjust their debt levels if they are suboptimal. However, firms only adjust if the benefits of adjusting outweigh the adjustment costs (e.g. transaction costs due to issuance of new debt). Korteweg finds that the firm’s collateral and profitability are positively related to optimal leverage, where growth opportunities, non-debt tax-shield and earnings volatility are negatively related to optimal leverage. Mixed results are documented for the effect of firm size on net debt leverage.
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market debt values of the UK firms are unavailable; therefore, book values of debt are used. Two debt ratios are used, the net debt ratio and the long-term debt ratio. If this study finds similar relationships for UK firms, the method of determining a target capital structure proposed by Koller et al. (2010) can be improved in terms of firm value for UK firms. A regression model based on the firm characteristics of UK companies could be used to determine the target capital structure instead of, or in combination with, a median target capital structure from a peer group.
Besides the existence of relationships for the firm characteristics to leverage, Korteweg (2010) also finds that firms adjust their leverage to the optimum if the costs of adjustment are lower than the benefits. If this conclusion also holds for UK firms, firm’s current leverage ratios should be substantially related to its past leverage ratio. Because Korteweg finds that firms adjust their leverage quickly, a one year lagged leverage ratio is included in a fixed effect regression model to capture this possible effect. If a relationship is found, which implies that UK firms current capital structure is highly related to the past current capital structure, the conclusion of Korteweg (2010) is confirmed for the UK market.
This study finds evidence that an optimal capital structure exists for UK firms. The results of the regression which test the relationship between the firm characteristics and the leverage ratios show mixed results. The firm characteristics collateral, non-debt tax-shield and growth are in line with the results of Korteweg (2010). Collateral shows a positive relationship, while depreciation and growth display a negative relationship. The effect of volatility is positive, where a negative relationship is expected. However, it is not completely clear how Korteweg calculates the volatility of earnings. The results could differ due to calculations differences. Korteweg finds mixed results for the firm size characteristic, whereas the results of this study show a positive relationship. This study finds no evidence for a positive relationship between leverage and profitability, which contradicts the trade-off theory. The results show a negative relationship in line with the pecking order theory (Myers and Majluf, 1984). Although some of the relationships of the firm characteristics are not in line with the trade-off theory and with the results of Korteweg, the results are in line with UK empirical evidence (see e.g. Rajan and Zingales, 1995; Charalambakis and Psychoyios, 2012). Possible differences might be explained by the use of book debt levels instead of market debt.
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outcomes of these two leverage ratios confirm that firms in the UK use an target capital structure in line with the trade-off theory and the empirical results of Korteweg (2010). A formal test shows that including a one year lagged leverage in the regression model better explains the current capital structure of UK Firms than the six firm characteristics solely. A robustness check shows that the inclusion of the one year leverage capital structure better explains the current capital structure than the inclusion of other period past capital structures.
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2. Literature review
This section discusses the literature and empirical evidence that are relevant for this study. First, the relationship between the firm characteristics and leverage is discussed. A table is presented which shows the different relationships that relevant empirical research finds. Next, the trade-off theory and the theoretical relationships of the individual variables collateral, depreciation, growth, profitability, firm size and volatility are described.
Empirical research
Table 1 presents an overview of the relevant empirical research on UK firms. The first column shows the relationships find by Korteweg (2010) between the firm characteristics (or variables) collateral, non-debt tax-shield, growth, profitability, firm size and earnings volatility and the net debt market leverage ratio. Korteweg finds mixed results regarding the effect of firm size on the net debt leverage ratio. The other five variables show a clear significant relationship. The second column shows the relationships find by Rajan and Zingales (1995), who examined the relationship between the variables and adjusted market leverage (debt adjusted for excess cash and short-term investments). The relationships of the collateral and growth variables are similar to the results of Korteweg. Growth is negatively related to leverage, whereas firm size is positively related to leverage. Charalambakis and Psychoyios (2012) finds similar results as Rajan and Zingales for long-term debt leverage and adjusted leverage. Both papers do not investigate the non-debt tax-shield and volatility variables.
Table 1: overview results relevant UK empirical research
This table presents the results of existing UK empirical research. The type of relationships between six firm characteristics and the leverage ratios are illustrated with a positive (+) or negative (-) sign. The abbreviation NR means that the specific variable is not researched in the related research. *** denotes 1% significance level.
Korteweg (2010)
5 Trade-off theory
According to the Modigliani and Miller (1958) capital structure irrelevance proposition firm value is not influenced by the way a firm is financed. This holds only under the assumptions of no taxes, transaction costs and perfect markets. However, in the real world transaction costs and taxes exist. In 1963 Modigliani and Miller came up with a theory which assumes that the firm value is influenced by the tax-shield; the cost of debt, interest, is tax deductible which creates a tax-shield. The tax-shield represents value. This possibility to add value by financing with debt should create a preference for managers to use debt to financing the firm’s activities because debt adds value for shareholders. Based on the findings of Modigliani and Miller (1958, 1963) firms should maximize their debt to a certain level to maximize the value of the tax-shield. The trade-off theory (Kraus and Litzenberger, 1973) sets limits to debt financing. According to Kraus and Litzenberger too much debt could lead to financial distress. Financial distress has a negative influence on the firms stakeholders which are less willing to do business or demand better conditions. Therefore, changes in the capital structure affect not only the financial position of a firm, but also its operational performance. Furthermore, the possibility of reinvesting in positive investments is limited due to the high levels of debt. The trade-off theory states that firms should find the optimum between benefiting from the tax-shield and the costs of financial distress.
Collateral
This study expects to find a positive relationship between leverage and collateral. Firms with a large amount of tangible (fixed) assets can use more debt: Fixed assets can be used as collateral. If lenders provide secured debt, they are insured of the collateral in case of bankruptcy or financial distress. This lowers the risk of the lender and increases management discipline (Charalambakis and Psychoyios, 2012). If the promised payments are not provided to the lender he could claim the collateral (Tirole, 2006). Firms with more intangible assets have higher agency costs because they are difficult to monitor. This reduces the amount of debt that a lender is willing to provide to these firms. Empirical evidence from Korteweg (2010) and Rajan and Zingales (1995) finds that the amount of collateral is indeed positively related to leverage.
Non-debt tax-shield
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(2010) use depreciation to measure the non-debt tax-shield. Depreciation could be a large part of the total costs of firms. Firms with high depreciation have smaller available tax-shield for debt, which makes debt less attractive (DeAngelo and Masulis, 1980). Depreciation is a substitute for interest expense because both are deductible from the corporate tax (Ozkan, 2001). Therefore, a negative relationship between leverage and depreciation is expected. Korteweg and Titman and Wessels empirically test this relationship; Titman and Wessels don’t find a relationship, whereas Korteweg finds a significant negative relationship between depreciation and leverage.
Growth
A firm’s growth opportunities are the extent to which a firm is expected to grow in the future. Based on the theoretical conclusions of Myers (1977), a negative relationship between a firm’s growth opportunities and leverage ratio is expected in this study. Firms with growth opportunities need financial freedom to make investments without the restrictions of debt to maximize the potential profit. The restrictions of debt could lead firms to pass up valuable investments. Titman and Wessels (1988) argue that growth opportunities are assets of a firm which add value, but cannot be collateralized; they are intangible. These intangibles do not generate income (yet). If the expected growth opportunities do not pay off, a firm’s residual value in case of bankruptcy is expected to be much lower than the residual value of mature firms. Tangible assets can be collateralized and have a higher expected value in the event of a bankruptcy. Consequently, the expected bankruptcy costs of growth firms are higher than for mature firms (see e.g., Williamson, 1988; Harris and Raviv, 1990).
Empirical evidence finds mixed results. For example, Lasfer (1995), Rajan and Zinagles (1995) and Charalambakis and Psychoyios, (2012) find a negative relationship between growth and leverage for UK Firms. However, Kester (1986) does not find evidence that leverage is negatively related to growth.
Profitability
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Empirical evidence by Charalambakis and Psychoyios (2012) and Rajan and Zingales (1995) confirms this theory. Both papers find a negative relationship between leverage and profitability for UK and US firms. Korteweg (2010) finds a positive relationship between profitability and optimal leverage ratios, which is in line with the trade-off theory. Therefore, this study expects to find a positive relation between leverage and profitability.
Firm size
Theoretical evidence claims that leverage is positively related to size. Warner (1977) and Ang, Chua and McConnel (1982) state that the direct costs of bankruptcy to a firm’s value declines if the firm’s value is higher. This statement implies that bankruptcy costs are less relevant for large firms in the process of attracting debt. According to Koller et al. (2010) and Lev (1983) large firms have more leverage because the operations of large firms are more diversified. This makes the profit and cash flows of large firms more stable, which decreases the possible risk of bankruptcy. Furthermore, large firms have easier access to capital markets, because these companies are more likely to have a credit rating (Bevan and Danbolt, 2002). The access to capital markets is also positive for the cost of debt. Through the large supply of debt on capital markets, large firms can use more and cheaper debt. Ozkan (1996) argues that small firms are more likely to liquidate in a situation of financial distress than larger firms and that this results in lower debt levels for small firms. Rajan and Zingales (1995) and Bennett and Donnelly (1993) empirically test the relationship of firm size on leverage and indeed find a positive relationship for UK firms. Based on this theoretical and empirical evidence this study expects to find a similar relationship in my dataset: large firms use more leverage.
Earnings volatility
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credit rating, firms could increase their earnings or lower their cost of debt. This would imply that firms with high earnings volatility have indeed lower debt levels. Therefore, a negative expect relationship between earnings volatility and leverage is expected. Korteweg (2010) confirms this by finding a significant negative relationship between leverage and volatility. However, Titman and Wessels (1988) do not find a relationship between volatility and leverage.
Last year capital structure
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3. Data and Methodology
This chapter discusses the data and the methodology that is used in this study. First, the dataset characteristics are described. Next, the description of the used variables are presented. Finally, the methodology is discussed.
Data sample
This study uses a sample of companies that were active in the United Kingdom during the period 1993 - 2012. In total, the initial sample consists of 4,490 companies which were listed in the UK in the period 1964 -2012. Data is obtained from Thomson Reuters Datastream. However, not all firms have (sufficient) data available; other firms are double listed in Datastream. Firms with less than ten observations per independent variable in the sample period are deleted from the sample. Furthermore, firms in the financial and insurance industry are removed from the sample because of differences in capital structure and because financial firms are subjected to minimum capital requirements. These differences could distort the samples capital structure compared to non-financial firms. Based on these criteria, 905 listed companies are available that are suitable for the sample. Table 2 presents the construction of the sample.
Table 2: Overview of the sample
This table presents the selection of firms based on the original firm data in Thomason Reuters Datastream. Banks, financial and insurance firms are excluded. Furthermore, firms are removed that are double listed or with less than ten observations per independent variable in Datastream within the sample period. The final sample contains 905 firms.
UK Sample selection Number of firms
Total UK companies in Datastream 4,490
Industries removed
Banks 24
Financial services 388
Insurance 102
Total 514
Firms double in Datastream 113
No data available 509
Less than 10 year data per variable available 2,449
10 Variables
Table 3 presents an overview of the data that is collected form the companies in the sample to calculate the regression variables (see Table 4). Furthermore, Table 3 shows the symbols and the Datastream field numbers.
Table 3: Description and source of data
This table presents an overview and description of the data that is obtained from Datastream. This raw input is used in calculating the variables that are defined in Table 4.
Symbol Name Explanation Source
BVE Book value equity Common and preferred equity Field 03995
DEPRE Depreciation Depreciation of property, plant and
equipment.
Field 04049
DLT Long-term debt Book value of long-term debt. Field 02731
DNet Net debt Debt minus excess cash (book value) Field 18199
EBITDA Earnings before interest, taxes,
depreciation & amortization.
Field 18198
MVE Market value common equity Outstanding shares multiplied by
value of shares
Field MVE
PPE Property, Plant & Equipment All the firm’s assets that could be
used as collateral. (book value)
Field 02501
SALES Net sales Sales netted for allowances, returns
and discounts.
Field 01001
TA Total assets Book value of total assets Field 02999
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equipment by total assets (COL). The non-debt tax-shield is measured by dividing depreciation with total assets (DEPR). Growth opportunities are proxied by the market-to-book ratio, which is calculated by dividing the market value of equity with the book value of equity (MTB). Profitability is calculated as earnings before interest, amortization, depreciation and tax divided by net sales (PROF). Firm size is defined as a natural logarithm of total assets (SIZE). The volatility of earnings is measured by taking the standard deviation of the relative differences in earnings over the current and last four years (VOL). Korteweg describes the calculation of volatility as the standard deviation from the differences in earnings. However, it is unclear how many years are used in this calculation.
Table 4: Overview of calculated variables
This table presents the calculations of the variables that are used in this study. The variables are calculated based on the data of Table 3.
Symbol Name Calculation
COL Collateralizable assets
DEPR Depreciation MTB Market-to-book PROF Profitability
SIZE Firm size (natural logarithm of total assets)
VOL Volatility of earnings The standard deviation of the
current en last four years relative differences in earnings.
LTDR Long-term market leverage ratio
NDR Net debt market leverage ratio
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Korteweg (2010) uses net debt; this is justified as it also includes the short-term debt obligations of a firm. Short-term debt is debt with an approximate maturity between zero and one year. Firms with excess cash (non-operating cash) can easily use this cash to reduce short-term debt liabilities. Therefore, net debt includes both long-term and short-term debt netted with excess cash. Because of the inclusion of short-term debt and excess cash, the net debt leverage ratio is more volatile. The long-term debt ratio includes debt with a maturity longer than one year and is therefore less volatile. This debt ratio with lower volatility could possibly show better results. Therefore, both leverage ratios are tested in this study and are based on the market value of equity. The net debt leverage ratio is constructed as follows: net book debt divided by net book debt plus the market value of equity (NDR). The leverage ratio based on long-term debt is based on the book value of long-term debt divided by the sum of long-term book debt and the market value of equity (LTDR).
3Outliers
Extreme positive or negative data could bias the results of the regressions, thus the dataset of this research is treated for outliers. Market-to-book, profitability, size, volatility and the net debt leverage ratio are winsorized at the upper and lower 0.5% tails based on the application of Charalambakis and Psychoyios (2012). The outliers for collateral, depreciation and the long-term debt leverage ratio are also removed as well as all values of this variables above one. These three variables do not have any extreme negative outliers, since they all have a minimum value of zero or higher.
Methodology
The following section describes the methodology that is used for this study. First, the descriptive statistics and correlation matrix are presented. Next, the regression model and method are discussed.
Descriptive statistics
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The net debt leverage ratio also has negative values. Negative leverage values below zero are caused by the use of net debt, which is below zero when firms have more cash than debt.
Table 5: Descriptive statistics
This table presents the descriptive statistics of the common sample used in this study. Firm years with missing data are excluded. The sample contains 905 firms with 97,728 yearly observations from 1993 to 2012. The variables market-to-book, profitability, size, volatility and net debt leverage are winsorized at the upper and lower 0.5 percent tails. The values above one are removed for: collateral, depreciation and long-term market leverage. The calculation of the variables are made in Table 4.
Mean Median Std. Dev. Minimum Maximum
COL 0.344 0.289 0.267 0 0.963 DEPR 0.034 0.029 0.029 0 0.286 MTB 2.359 1.614 2.390 0.016 18.750 PROF 0.120 0.113 0.444 -4.894 4.129 SIZE 11.793 11.548 2.140 6.019 19.206 VOL 1.651 0.423 3.862 0.021 45.087 LTDR 0.164 0.097 0.190 0 0.988 NDR 0.110 0.108 0.300 -0.912 0.949
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Table 6: Correlation matrix
This table presents the correlations between the dependent and the independent variables. All the correlations are significantly different from zero on a 1% level, except the correlation between volatility (VOL) and the lagged net debt ratio (NDR LAG). The calculation of the variables are made in table 4. The related t-values, which are the results of a spearman correlation test, are documented in Appendix A. + denotes insignificant based on a 10% level.
COL DEPR MTB PROF SIZE VOL LTDR NDR LTDR LAG
DEPR 0.346 1 MTB -0.180 0.216 1 PROF 0.334 -0.077 0.026 1 SIZE 0.253 -0.049 0.058 0.335 1 VOL -0.226 -0.113 -0.147 -0.344 -0.342 1 LTDR 0.384 -0.046 -0.281 0.166 0.443 -0.081 1 NDR 0.363 -0.062 -0.348 0.075 0.279 -0.025 0.761 1 LTDR LAG 0.368 -0.031 -0.237 0.180 0.433 -0.071 0.832 0.680 1 NDR LAG 0.346 -0.049 -0.316 0.101 0.264 -0.010+ 0.692 0.839 0.762
Research model and method
In order to test if the variables have a significant effect on a firms capital structure a fixed effects regression is used. The regression analysis is applied on two models. The first model is based on the following variables:
! " # $ % & (1)
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coefficients and t-values for error terms that do not have a constant variance. The error term contains unexplained part of the regression model.
The second model is based on the first model. However, one variable is added to test the conclusions of Korteweg (2010):
'(). ∝ ! " # $ (2)
% ,- &
Korteweg finds that firms rebalance their capital structure if the benefits outweigh the cost. This rebalancing, which is based on the cost and benefits of optimal leverage, implies that capital structure decisions concern not only the firm’s characteristics but also the current debt-equity levels. To capture this possible effect, a variable is added to the second regression model: the one period lagged leverage ratio (- ). The current leverage implies the firm’s characteristics and the leverage ratio of the previous
period.
Regression method
This study uses panel data to test the effect of multiple variables on leverage. According to Brooks (2010), the use of panel data is preferred. Panel data has a few major advantages. It can capture both time effects and firm effects at once. This increases the degrees of freedom, which in turn increases the power of the test. Furthermore, panel data helps avoiding multicollinearity problems and can deal with omitted variables.
The panel used in this research includes firms with at least 10 years of data so not all firms have equal years. Therefore, unbalanced panel data is used. The software package that is used to gather the results automatically accounts for the missing observations.
Several techniques to test panel data are available. Brooks (2010) recommends using the fixed or random effects model. To determine if the random effects or fixed effects model is required, the Hausman (1978) test needs to be executed. The results of the Hausman test show no evidence that the random effects model is appropriate. Therefore, all the results in this study are based on the fixed effects model.
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are fixed. Second, it can be used to test fixed time-series effects. This method does the opposite; the intercept is allowed to vary over time, but fixed across sections. Finally cross-section and time series could both be fixed. The effects are measured by adding time and cross-sectional dummies. The time dummies are represented by: . . The cross firm effects dummies are represented by: / . This study test
on fixed firm and time effects in one model. The regression model based on Eq. (1) and (2):
17 4. Results
This section contains the results of the tests that are executed on the dataset. First, some trends are illustrated using graphs. Next, the results of the regression analyses are discussed.
Leverage development
Fig. 1 shows the development of net market leverage and long-term market leverage during the sample period.
Fig. 1: Leverage development 1993 - 2012
This figure presents the development of market leverage in the period 1993 - 2012. Both median leverage ratios of every year are shown in the figure; the solid line illustrates the development of the net debt leverage ratio, the dotted line shows the development of the long-term debt ratio. The y-axis contains the amount of leverage and the x-axis contains the dates by year. Observations equal to or below zero are excluded.
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Fig. 2: Relation leverage and UK FTSE ALL-Share index between 1993 and 2012.
This figure presents the development of leverage in the period 1993 - 2012 and the development of the UK FTSE ALL-Share index in this period. The solid line illustrates the development of the net debt leverage ratio. The dotted line shows the development of the long-term debt ratio and the broken line illustrates the development of the FTSE ALL-Share index. The x-axis contains the dates by year.
Fig. 2 shows part of the underlying movements of the market leverage ratios. Fig. 2 is similar to Fig. 1, but additionally the movement of the UK FTSE ALL-Share index is included (the broken line). The FTSE ALL-Share index includes approximately the largest 600 UK firms. The two leverage ratios show an opposite trend compared to the FTSE ALL-Share index, which seems a logical consequence. If the value of equities is high, leverage ratios are relatively low. During the sample period two worldwide economic crises occurred. The first crisis, the dot com bubble, occurred at the end of 2000. The figure shows a sharp downward movement of the FTSE ALL-Share index and upward movement of the leverage ratios. The second crisis occurred in 2008. The financial crisis is clearly visible in both leverage ratios and in the FTSE ALL-Share index. When markets decreased sharply, leverage ratios raised around 8% and recovered to the pre-crisis level between 2009 and 2011.
Individual relationships variables
To get a better understanding of the relationship between the independent regression variables and the dependent variables, a table with six individual relationships is presented below in Table 7. The individual relationships of the six variables (COL, DEPR, MTB, PROF, SIZE, VOL) with the market net and long-term debt leverage are presented before the results of the regressions are discussed. The six variables are divided in six groups and sorted from low to high. Thereafter, the six groups are divided in
93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12
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Table 7: Relationships between leverage and variables
This table presents the relationship between the variables collateral (COL), depreciation (DEPR), market-to-book (MTB), profitability (PROF), size (SIZE) and volatility (VOL) with the two leverage ratios; long-term debt (LTDR) and net debt ratio (NDR). The data represents the median values of the UK sample between the 1993 and 2012 divided in ten groups. The sample is divided based on every single variable and sorted from low to high. The median net debt and long-term leverage ratio of every group is presented. Calculations of the variables are made in Table 4.
COL 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% LTDR 0.00 0.01 0.02 0.05 0.05 0.08 0.10 0.12 0.19 0.36 NDR 0.00 0.01 0.02 0.04 0.05 0.07 0.12 0.14 0.20 0.39 DEPR 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% LTDR 0.24 0.02 0.04 0.09 0.08 0.09 0.08 0.07 0.07 0.08 NDR 0.26 0.04 0.05 0.08 0.09 0.10 0.09 0.09 0.09 0.10 MTB 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% LTDR 0.24 0.21 0.16 0.11 0.10 0.10 0.08 0.06 0.03 0.01 NDR 0.43 0.31 0.22 0.15 0.12 0.10 0.07 0.05 0.02 0.00 PROF 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% LTDR 0.01 0.06 0.09 0.08 0.08 0.09 0.07 0.09 0.10 0.29 NDR 0.01 0.16 0.14 0.11 0.08 0.08 0.07 0.08 0.10 0.30 SIZE 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% LTDR 0.00 0.01 0.02 0.03 0.05 0.05 0.12 0.16 0.23 0.22 NDR 0.01 0.02 0.04 0.04 0.08 0.06 0.12 0.17 0.19 0.20 VOL 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% LTDR 0.09 0.10 0.10 0.13 0.11 0.09 0.07 0.07 0.04 0.03 NDR 0.10 0.10 0.11 0.14 0.11 0.10 0.11 0.11 0.07 0.09
ten groups from 10% to 100%. The median net debt and long-term debt ratio of every group are presented in Table 7. For example, firms in the group of 10% profitability are in the lowest decile of firms of the total sample that have the lowest profitability; firms in the group of 100% profitability are the highest decile of firms in the sample with the highest profitability, etc.
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negative, where the long-term debt ratio is stable for the firms with a market-to-book ratio between 40% and 60% of the total sample. Profitability does not show a clear relationship with leverage; however, it is clear that the least profitable firms have the lowest leverage ratios and very profitable firms have the highest leverage ratios. The remaining median values of profitability do not show a clear relationship with leverage. Firm size is in line with the theoretical expectations: Large firms use more debt, whereas small firms use almost no debt. The relationship between volatility and leverage is not what would be expected based on current literature. The long-term debt ratio shows a negative relationship for the six groups with the most volatility. A similar relationship is not visible for the net debt ratio.
Fixed effects regression results
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Table 8: Results regression firm characteristics
This table contains the coefficients from a fixed effects regression on UK panel data. The long-term debt and net debt market ratios are explained by the variables collateral (COL), depreciation (DEPR), growth (MTB), profitability (PROF), volatility (VOL) and firm size (SIZE). The regression results are based on Eq. (1). The total sample contains 905 UK firms between 1993 and 2012. Calculations of the variables are made in Table 4. The values between brackets represent the t-values adjusted for heteroscedastic errors with a White test. *** denotes 1% significance level, ** denotes 5% significance level. LTDR NDR C -0.253 *** -0.743 *** (-9.176) (-14.648) COL 0.162 *** 0.372 *** (10.916) (16.389) DEPR -0.154 ** -0.075 (-1.94) (-0.514) MTB -0.007 *** -0.004 *** (-12.14) (-4.31) PROF -0.013 *** -0.032 *** (-4.587) (-5.385) SIZE 0.032 *** 0.061 *** (14.184) (14.655) VOL 0.001 *** 0.003 *** (3.195) (4.871) N 12,747 12,216 R-squared 0.68 0.63 Adjusted R-squared 0.65 0.60 Durbin-Watson 1.95 1.97
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Based on the results of Table 9, the conclusion of Korteweg (2010) are confirmed for firms in the United Kingdom during the period of 1993 until 2012. Korteweg finds that firms adjust the leverage ratio to the optimum when the costs of adjusting are lower than the benefits of using debt. The conclusion for US firms indicates a relationship between current leverage ratios and the previous period leverage ratios. The results show that leverage has a large positive relationship with the past leverage ratio for the net debt ratio and long-term debt ratio. UK firms indeed adjust their leverage relatively fast to some target capital structure. The change in leverage depends largely on this movement to a target capital structure and less on the change in the six firm characteristics.
Table 9: Results regression firm characteristics and last year leverage
This table contains the coefficients from a fixed effects regression on UK panel data. The long-term debt and net debt market ratios are explained by the variables collateral (COL), depreciation (DEPR), growth (MTB), profitability (PROF), volatility (VOL), firm size (SIZE) and the one period lagged long-term or net debt ratio (DR LAG). The regression results are based on Eq. (2). The total sample contains 905 UK firms between 1993 and 2012. Calculations of the variables are made in Table 4. The values between brackets represent the t-values adjusted for heteroscedastic errors with a White test.*** denotes 1% significance level, ** denotes 5% significance level.
23 Selecting the correct model
This study tests two regression models. The first model includes the six variables and the second model includes the last year leverage ratio. Based on the results of Table 9, this study concluded that the previous leverage ratio has a large positive influence on the current leverage ratio. In order to determine which of the two regression models has the best fit a likelihood-ratio test (Keller, 2008) is used. Table 10 presents the results. The log likelihood ratios of both regression models are used in this test for both debt ratios.
Table 10: Results for likelihood ratio test
This table shows the results of the likelihood ratio test. The log likelihood ratio of the regression results are used to calculate the test statistic. The null-hypothesis is based on the regression model of Eq. (1). The alternative hypothesis is based on the regression model of Eq. (2). The degrees of freedom (df) are determined by subtracting the amount of coefficients from regression model (2) with regression model (1). The critical value is significant above the value 10.83. *** denotes 1% significance.
LTDR NDR
Log likelihood Log likelihood
H0 10,376 3,437
H1 11,972 5,458
Test statistic (χ2) 3,193 *** 4,044 ***
df1 1 1
1. Eq. (1) contains seven coefficients, where Eq. (2) contains eight coefficients. The degrees of freedom are therefore calculated as 8 - 7 = 1.
The null-hypothesis contains the log likelihood ratio from the regression results of the model without the previous period capital structure, Eq. (1). The null-hypothesis contains the log likelihood ratio from the regression results of the model with the previous period capital structure, Eq. (2). The degrees of freedom are determined by subtracting the amount of coefficients from Eq. (2) with the Eq. (1). If the test statistic (χ2) is above 10.83, the null-hypothesis is rejected with 1% significance level and the alternative hypothesis is accepted. The results show that the test statistics are far above 10.83 for both ratios. This means that the model based on Eq. (1) is rejected. The model based on Eq. (2), which includes the previous year leverage ratio, has a better fit.
Robustness check
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influenced by firms with zero or negative leverage, firms that do not have long-term debt or have negative leverage due to excess cash are excluded. The new sample contains 634 firms with long-term debt and 599 firms with positive net debt (for descriptive statistics, see appendix B). Table 11 shows the results of the regressions for firms with (positive) leverage.
Table 11: Results for robustness of positive leveraged firms
This table contains the coefficients from a fixed effects regression on panel data. The market debt ratios based on long-term debt and net debt are explained with collateral (COL), Depreciation (DEPR), growth (MTB), profitability (PROF), volatility (VOL) and firm size (SIZE) and the one period lagged long-term or net debt ratio (DR LAG). The regression results are based on Eq. (1) and Eq. (2). The total sample contains 905 UK firms between 1993 and 2012. Calculations of the variables are made in Table 4. The values between brackets represent the t-values adjusted for heteroscedastic errors with a White test.*** denotes 1% significance level, ** denotes 5% significance level, *** denotes 10% significance.
LTDR NDR LTDR NDR C -0.063 -0.270 *** -0.113 *** -0.223 *** (-1.539) (-4.675) (-2.804) (-4.440) COL 0.185 *** 0.315 *** 0.125 *** 0.231 *** (9.986) (13.031) (7.556) (11.024) DEPR -0.325 *** -0.309 ** -0.438 *** -0.671 *** (-3.27) (-2.147) (-4.496) (-4.847) MTB -0.013 *** -0.007 *** -0.010 *** -0.004 *** (-12.423) (-5.134) (-10.127) (-4.023) PROF -0.017 *** -0.035 *** -0.019 *** -0.034 *** (-3.928) (-5.083) (-4.144) (-5.155) SIZE 0.021 *** 0.031 *** 0.018 *** 0.023 *** (6.539) (6.872) (5.686) (5.855) VOL 0.002 *** 0.003 *** 0.001 * 0.001 * (3.623) (4.318) (1.815) (1.638) DR LAG 0.500 *** 0.504 *** (33.71) (32.609) N 8,917 9,454 7,814 8,342 R-squared 0.66 0.60 0.77 0.72 Adjusted R-squared 0.63 0.56 0.74 0.69 Durbin-Watson 1.96 1.89 1.95 1.82
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could benefit more from available tax-shields, than firms with no leverage. The available tax-shield for the cost of debt decreases if the costs of depreciation are higher, which increases the effect of depreciation in this result. The results of the two regressions with the last year leverage variable included are similar to the results presented in Table 9. Again, the magnitude of depreciation is higher. Furthermore the magnitude of the previous year lagged leverage term is also slightly higher, around 50%.
Based on the results of Table 11 it can be concluded that the results of Table 8 and Table 9 are robust. Removing firms with no or negative leverage do not change the results.
The next robustness test is based on Eq. (2), which is the regression model with the six variables and the last year leverage ratio and the original sample. The results in Table 9 show that leverage is highly related to the last year leverage ratio. To see if this effect increases or decreases over time, different periods are used in the regression model. In an optimal scenario the relationships between current and previous leverage ratios would be tested on a 3 month basis. However, this is not taken into account in this study as only the annual book debt data is unavailable. Table 12 shows the results of the coefficient of the lagged variables for 1 to 5 years. The complete results are documented in appendix C.
Table 12: Robustness lagged leverage
This table shows the leverage based on Eq. (2). The lagged leverage ratios from 1 to 5 years are used. The complete results are documented in appendix C, table C1 and C2. Calculations of the variables are made in Table 4. The total sample contains 905 UK firms between 1993 and 2012. The values between brackets represent the t-values adjusted for heteroscedastic errors with a White test. *** denotes 1% significance level, * denotes 10% significance level.
1 2 3 4 5
LTDR LAG 0.498 *** 0.277 *** 0.081 *** -0.016 -0.023 *
(35.012) (19.454) (3.066) (-1.282) (-1.725)
NDR LAG 0.487 *** 0.248 *** -0.001 -0.059 *** -0.058 ***
(39.308) (19.691) (-0.072) (-4.504) (-4.386)
26
5. Conclusion
This study tests the relationships of six firm characteristics with leverage ratios in the United Kingdom during the period 1993 - 2012 for 905 firms. This research attempts to find the same relationships as Korteweg (2010), who finds the existence of an optimal capital structure based on the trade-off theory (Kraus and Litzenberger, 1973). The firm characteristics that are tested are collateral, non-debt tax-shield, growth, profitability, firm size and volatility of earnings. The results show positive significant relationships for collateral, firm-size and volatility of earnings and negative significant relationships for non-debt tax-shield, growth and profitability. The results are in line with existing UK empirical evidence (Rajan and Zingales, 1995; Charalambakis and Psychoyios, 2012) who also tested the relationships of firm characteristics, except for depreciation and volatility. However, the relationships of profitability, firm size and volatility differ from the results of Korteweg. The results of profitability could alternatively be explained by the pecking order theory (Myers and Majluf, 1984) instead of the trade-off theory. Furthermore, the results for the volatility variable could possibly be explained by differences in measurement of earnings volatility. The relationships that this study finds between leverage and firm characteristics do not fully support the conclusions of Korteweg for the UK. That is, the existence of some optimal capital structure that can be profitable for corporate valuation practitioners in determining a value maximizing target capital structure. Therefore, this study does not provide sufficient evidence to improve the method of Koller et al. (2010) in determining a target capital structure in the Weighted Average Cost of Capital to measure the value of a company.
Although not all relationships are similar to Korteweg (2010), the conclusion that firms adjust their capital structure to an optimum or target is supported for the UK market. The results show that the current leverage net debt and long-term debt ratios are positively related to the one year lagged leverage ratio. The long-term debt ratio is 50% related to the lagged leverage ratio, while the net debt ratio is almost 49% related to the past leverage ratio. A formal test to determine the best way to capture the determinants of leverage shows that the inclusion of this one year lagged variable is the best model to explain the leverage ratios of firms. The UK firms leverage ratios are largely determined by the firm’s movement to a target capital structure and in a less extent to the firm characteristics collateral, non-debt tax-shield, growth, profitability, firm size and volatility of earnings. The robustness check shows that including the one year leverage term explains most of the current leverage ratio.
27
28 Appendix
Appendix A: Correlation matrix with t-values
Table A1: Correlation matrix
This table contains the correlations between the variables that are used in this study. The significance of the variables are tested with a Spearman correlations test. All the variables are significantly different form zero on a 1% level, except the correlation between volatility (VOL) and the net debt lagged leverage ratio (NDR LAG). Calculations of the variables are made in Table 4. + denotes insignificant based on a 10% level.
COL DEPR MTB PROF SIZE VOL LTDR NDR LTDR LAG
29 Appendix B: Descriptive statistics
Table B1: Descriptive statistics (positive) leverage sample
This table presents the descriptive statistics of the common sample used in this study. Firm years with missing data are excluded. The sample contains 634 firms with long-term debt and 599 firms with positive net debt from 1993 to 2012.The calculation of the variables are made in Table 4.
Mean Median Std. Dev. Minimum Maximum
30 Appendix C: Complete results robustness check
Table C1: Results for multiple periods of lagged long-term debt leverage
This table contains the coefficients from a fixed effects regression on panel data. The long-term market debt ratios are explained by the variables collateral (COL), depreciation (DEPR), growth (MTB), profitability (PROF), volatility (VOL), firm size (SIZE) and the lagged long-term debt ratio (LTDR LAG) from 1 – 5 years. The regression results are based on Eq. (2). The total sample contains 905 UK firms between 1993 and 2012. Calculations of the variables are made in Table 4. The values between brackets represent the t-values adjusted for heteroscedastic errors with a White test.*** denotes 1% significance level, ** denotes 5% significance level, *** denotes 10% significance.
31
Table C2: Results for multiple periods of lagged net debt leverage
This table contains the coefficients from a fixed effects regression on panel data. The market net debt ratios are explained by the variables collateral (COL), depreciation (DEPR), growth (MTB), profitability (PROF), volatility (VOL), firm size (SIZE) and the lagged net debt ratio (NDR LAG) from 1 – 5 years. The regression results are based on Eq. (2). The total sample contains 905 UK firms between 1993 and 2012. Calculations of the variables are made in Table 4. The values between brackets represent the t-values adjusted for heteroscedastic errors with a White test.*** denotes 1% significance level, ** denotes 5% significance level, *** denotes 10% significance.
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