The effect of the interest rate on the capital structure
of U.S. firms.
Abstract:
This study analyses the effect of the interest rate on the capital structure of U.S. firms. Capital structure theories provide clear predictions on how the leverage of a firm and the interest rate are related. We test these predictions by constructing a fixed effects model in which we regress the leverage on the interest rate. The dataset used is obtained from the Wharton Research Data Services and contains yearly firm specific data for all publicly listed U.S. firms over a 54-year time period from 1962 to 2015. Overall, we find a positive
relationship between leverage and the interest rate indicating that firms issue more debt when interest rates decrease. We, however, find a negative relationship between leverage and the interest spread suggesting that firms issue more equity in periods of economic growth.
Widmer van der Wal - s2058588
Study Program: MSc Finance Supervisor: Dr. Lammertjan Dam
Field Key Words: Interest rate, Capital structure Words: 10197
2 1. Introduction
The discussion of capital structure goes all the way back to Modigliani and Miller (1958) who first derived that in a world with frictionless markets the capital structure of a firm should be irrelevant for its value. While their model is based on assumptions that would not hold in imperfect markets, it did lay the basis for future capital structure research. In the decades to follow, the attention for capital structure grew and it arguably became the core of modern corporate finance research (Drobetz and Wanzenried, 2006). Nowadays, literature provides us with an extensive list of theories and factors influencing capital structure. However, research on the relationship between the interest rate and the capital structure remains limited. In this study, we attempt contribute to the debate by researching the effect of the interest rate on the leverage ratio of a firm.
The study of the effect of the interest rates is especially relevant in the present time as over the last decade, interest rates have decreased to historically low levels thereby, providing firms access to cheap capital. According to the neoclassical theory of investment, a decrease in the cost of capital results in an increase in investment spending (Baker et al. 2008). How firms finance the increase in investments influences their capital structure. In line with the neoclassical theory of investment, after a decrease in the cost of capital, capital structure theories predict an increase in investment. However, capital structure theories differ in their predictions on how firms finance these investments and therefore, how the investments influence a firm’s capital structure. As the literature does not provide us with a clear prediction on the relationship between the interest rate and the leverage of a firm, analyzing the relationship from an academic perspective provides an relevant topic for a thesis.
To be able to analyze the effect of the interest rate on the leverage of a firm we construct a fixed effects model in which we regress the leverage ratio on the yearly interest rates. In this model we control for firm size, tangibility of assets, profitability and the market-to-book ratio of a firm. Furthermore, to provide a robust analysis we construct three different measures of leverage for both book and market values.
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predictions based on the dominant theories in the field of capital structure. These theories, further described in the literature section, are the trade off theory and the market timing theory.
We find a significant positive relationship between leverage and the interest rate, as predicted by the trade off theory. The positive relationship indicates that in periods of high (low) interest rates firms prefer debt (equity) financing. Moreover, we find that the interest spread, a measure of the state of the economy, is negatively related to the leverage of a firm. This contradicts our previous findings as interest rates are expected to increase in periods of economic growth. Furthermore, in line with both theories, we find that both the tangibility of assets and the size of a firm are positively related to leverage. The profitability and the market-to-book ratio of a firm are negatively related to a firm’s leverage. Only the market timing theory correctly predicts the relationship of leverage with all control four factors. However, the market timing theory predicts a negative relationship between leverage and the interest rate which contradicts our findings.
Our results provide insight on how firms adjust their capital structure with regard to the interest rate. In periods of high (low) interest rates, firms finance their investments with relatively much debt (equity). As neither of the theories are capable of fully explaining our results, we believe a combination of the theories is the next step in capital structure research. The rest of this paper will continue as follows. Section two provides a summary of the theoretical literature and discuss the relevant theories. Section three describes the collected data and provides an overview of the modifications made to the data as well as the descriptive statistics. The methods used in the analysis of this study are discussed in Section four. Thereafter, Section five presents the results of this analysis. Finally, Section six provides an overall conclusion of the study.
2. Literature
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literature presented, we state the goal and relevance of this study and the main research question.
As mentioned before, Modigliani and Miller (1958) derived that, in a world with frictionless markets, the value of a firm does not depend on its capital structure. Research, however, shows us that firms are able to enhance their value by utilizing frictions like taxes, interest rates and market timings. The literature presents several theories on how firms adjust their leverage ratio’s to utilize market frictions. In this study, we focus on the two most relevant theories, the market timing theory and the trade off theory. As these theories are chosen as they predict a clear relationship between leverage and the interest rate.
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markets the market timing theory predicts a negative relationship between leverage and the interest rate.
The second theory is the trade off theory. According to the trade off theory, debt enhances firm value as the interest payments on debt are tax deductible (Modigliani and Miller, 1963). However, debt financing also increases the bankruptcy costs of a firm through a higher probability of default (Scott, 1976). The trade off theory states that firms have an optimal capital structure in which they balance the benefits of debts against its costs (Kraus and Litzenberger, 1973).
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Size
Size is one of the main determinants the leverage of a firm. Larger firms tend to be more diversified and therefore face lower default risks (Titman and Wessels, 1988). A lower default risks influences the leverage in two ways, first it increases the access to capital and allows firms to borrow at a lower rate (Feri and Jones, 1979). Secondly it reduces the bankruptcy costs of the firm which, according to the tradeoff theory, shifts the optimal capital structure towards to be more debt oriented. In line with this reasoning Ozkan (1996) finds that smaller firms are more likely to be liquidated when they are in financial distress and therefore have lower leverage ratios. Therefore, we expect size to be positively related to leverage.
Tangibility
Previous studies by Titman and Wessels (1988), Rajan and Zingales (1995) and Fama and French (2002) find that the tangibility of assets and leverage are closely related. As tangible assets, such as property, plant, and equipment are easier to value than intangible assets the financial distress costs of firms with a relatively high amount of tangible assets are expected to be lower than firms with mainly intangible assets. This is the case because the tangible assets act as collateral for bondholders the thereby increase the chance of repayment in bad states (Drobetz and Wanzenried, 2006). As tangible assets act as a form of collateral more tangible firms are able to borrow at lower rates. Tangibility is therefore, positively related to leverage.
Profitability
The effect of profitability on leverage is ambiguous. Trade-off theory states that profitable firms are pushed towards higher leverage through bankruptcy costs, taxes and agency costs (Drobetz and Wanzenried, 2006). Profitable firms are expected to have lower bankruptcy costs and therefore, have a more levered optimal capital structure. The increase in leverage will increase firm value due to the deductibility of corporate interest payments making debt more attractive. Finally, high leverage ratios help mitigate agency costs as it limits the amount managers are able to spend on perks.
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sense that if a firm becomes more profitable its value of equity increases and its leverage decreases. Titman and Wessels (1988), Rajan and Zingales (1995) and Wald (1999), all find a strong negative relationship between leverage ratios and past profitability. Wald (1999) even indicates that profitability is the largest determinant of a firm’s leverage ratio.
Market-to-book ratio
Literature often uses the market-to-book ratio as a proxy for the growth opportunities of a firm. Growth firms have a high market-to-book ratio indicating that they have more investment opportunities than value firms. Titman and Wessels (1988) argue that even though growth opportunities add firm value when undertaken they generate no current income and cannot be collateralized. They are therefore, of a similar nature as intangible assets in such a way that as long as a firm is alive its growth opportunities are valuable. However, if a firm faces bankruptcy they are unlikely to invest in their growth opportunities decreasing their value. Similar to the tangibility of assets, literature suggests that firms with more growth opportunities have higher expected bankruptcy costs and are therefore, negatively related to a firm’s leverage (Harris and Raviv, 1990).
Research question
Based on the existing literature it is clear that the interest rate is related to the leverage of a firm. However, theories differ in their prediction on how they are related. The trade off theory predicts firms to increase their leverage when interest rates increase while the market timing theory predicts managers to focus on the equity market in such a situation. As, to date there has been no study that explicitly focusses on this relationship, we pose the following research question; ‘What is the relationship between the interest rate and the leverage of a firm?’ In the remainder of this thesis, we will try to answer this question by empirically testing the theoretical predictions of the capital structure theories.
3. Data
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the for the interest rate. Finally, we provide an overview of the descriptive statistics of the main variables used in our analysis.
We obtain the data for this study from the Wharton Research Data Services database. Firm specific data is gathered from the Compustat database, specifically Compustat North America, for a 54-year period from 1962 to 2015. For this period, we gather annual firm specific data resulting in a panel data set containing 492,651 observations for 36,379 U.S. firms over 54 years. Data regarding the one and ten year U.S. Treasury rates is obtained through the Federal Reserve Bank reports. As the Federal Reserve reports these rates monthly, we take the observation on December 31 of each year to make sure it coincides with our annual firm specific data.
To optimize the data for analysis we make several modifications. First all observations with a negative book value are removed to avoid a negative market-to-book ratio. This, however, can still occur if the minority interest (MIB) is negative and exceeds the book value (SEQ) of a firm. Secondly, from the raw data, we compute the following control variables, as defined in the Literature section: Size, Tangibility, Profitability and Market-to-Book ratio. Furthermore, all control variables are winsorized at a 0.50 per cent level at both tails of the distribution to reduce the effect of outliers. Finally, we lag all independent variables by one year to mitigate simultaneity concerns.
Previous literature does not provide one universal definition of leverage. Most studies use the financial-debt-to-asset ratio (FD/AT), where financial debt is the sum of long-term debt (DLTT) and debt in current liabilities (DLC). Welch (2011), however, argues that this measure is wrong as its converse includes non-financial liabilities. Therefore, changes in the non-financial liabilities also influence the financial-debt-to-asset ratio of a firm. Even though there is no universal correct measure of leverage Welch provides the following two alternatives to the financial-debt-to-asset ratio:
- Balance sheet leverage, defined as total-liabilities-to-assets (LT/AT). This measure treats financial and non-financial liabilities the same.
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Welch (2011) argues that these measures are appropriate as they both have an equity-based measure as converse and therefore, neither declines with an increase in the non-financial liabilities. In this paper, we focus on the leverage ratios defined by Welch (2011). As a robustness check, we include the financial-debt-to-asset ratio resulting in a total of three leverage ratios. These measures differ whether market or book values are used. In total, we study the following six definitions of leverage:
- Total-debt-to-book value of assets (FD/AT) - Total-debt-to-book value of capital (FD/BCP) - Total-liabilities-to-book value of assets (LT/AT) - Total-debt-to-market value of assets (FD/MAT) - Total-debt-to-market value of capital (FD/MCP) - Total-liabilities-to-market value of assets (LT/MAT)
The book value of capital (BCP) is defined as the financial debt plus the book value of equity (SEQ + MIB). Similarly, the market value of capital is the financial debt plus the market value of equity (CSHO∙PRCCF). Furthermore, to derive the market value of assets we subtract book value of equity (SEQ + MIB) and then add the market value of equity (CSHO∙PRCCF).
We use the U.S. Treasury rates as a measure for the interest rate. To be able to provide a robust analysis both the one and ten year Treasury rates are gathered. Furthermore, we also construct the interest spread by deducting the one year from the ten year Treasury rate. As the interested spread is generally accepted as a predictor of economic prospects (Drobetz and Wanzenried, 2006) this gives us an understanding of how firms rebalance when they expect future economic growth or an economic downturn.
Descriptive Statistics
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which makes sense, as it is common that the market value of assets is higher than the book value, this is can also be seen by looking at the market to book ratio.
Table 1: Descriptive statistics for publicly traded U.S. companies and Treasury rates, 1962-2015 The table provides and overview of the descriptive statistics for six different leverage measures, four independent variables, two Treasury rates and the interest spread. All statistics are
computed with annual data. All variables, except for the treasury rates, are winsorized at a 0.50% level at both tails of the distribution. Reported are the mean, standard deviation,
minimum, maximum and amount of observations for each factor. All values are recorded at the 31st of December.
Variable Mean
Standard
Deviation Minimum Maximum Observations Leverage measures Book value FD/AT 0.275 0.189 0.000 0.805 287,074 FD/BCP 0.369 0.239 0.000 0.943 268,318 LT/AT 0.485 0.229 0.015 0.966 336,182 Market value FD/MAT 0.220 0.182 0.000 0.764 215,635 FD/MCP 0.288 0.236 0.000 0.910 230,910 LT/MAT 0.374 0.250 0.005 0.942 255,901 Factors Size 4.621 2.455 -6.908 14.517 310,568 Tangibility 0.563 0.390 0.000 1.907 294,063 Profitability -0.013 0.203 -1.608 0.342 304,154 Market-to-Book ratio 1.818 1.597 0.449 14.469 241,663 Treasury rates Treasury rate, one
year 5.028 3.375 0.120 14.880 358,940
Treasury rate, ten
year 6.156 2.763 1.720 13.720 358,940
Interest Spread 1.128 1.218 -2.040 3.220 358,940
All the descriptive statistics presented above are end of the year values recorded at December
31st. When looking at independent variables it is surprising that, the mean of profitability is
negative meaning that over our entire sample the average net income is negative. A logical explanation for this is that the possibility for losses is much larger, for example a firm going bankrupt, than the possibility for gains. This can also been seen when comparing the minimum and maximum of profitability.
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volatile which follows from its higher standard deviation. As the interest spread is constructed by deducting the one year Treasury rate from the ten year Treasury rates it follows that its mean can be found by deducting the one year mean from the ten year mean. Furthermore, it has a lower volatility than the one and ten year Treasury rates which is also expected.
4. Methodology
The focus of this study is to analyze the effect of the interest rate on the capital structure of U.S. public firms. To do so, we construct a fixed effects model with leverage as dependent variable and interest rate as independent variable. However, as leverage is not solely determined by the interest rate we have to include several control variables mentioned in the literature section. This section will start by stating how we measure these control variables, next we will discuss the use of fixed or random effects and robust standard errors, and finally we construct the fixed effects model.
Control Variables
In this study, we control for the following variables: firm size, tangibility of assets, profitability and the market-to-book ratio of a firm. To measure these control variables, we follow Welch (2011) which uses the follow proxies:
- Size is measured by taking the natural logarithm of total assets (Log (AT)).
- Tangibility is measured by the ratio of property, plant and, equipment over total assets (PPEGT/AT).
- Profitability is measured by the ratio of net income over total assets (NI/AT).
- Market-to-book value is measured by the market value of equity over the book value of equity (MAT/AT).
Fixed Effects Model vs. Random Effects Model
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all leverage ratios, with a 0.000 chi-square probability the null hypothesis and therefore, the use of random effects is rejected. The complete Hausman test is reported in appendix A.1. Arguing from a theoretical point of view if the effect of unobservable factors on our dependent and independent variables is assumed time-invariant the use of fixed effects helps us reduce the omitted variable bias (Alisson, 2009). As we have no reason to assume that the effect of unobservable factors on our variables changes over time a fixed effects model is used in our analysis.
Constructing the Fixed effects model
To construct the fixed effects model used for our analysis we start with the following standard linear regression model (Verbeek, 2012):
𝑦𝑖𝑡 = 𝑎𝑖 + 𝑋′𝑖𝑡𝛽 + 𝜀𝑖𝑡 𝑤𝑖𝑡ℎ 𝑡 = 1, 2, … , 𝑇 𝑎𝑛𝑑 𝑖 = 1, 2, … , 𝐼 (1)
With 𝑦𝑖𝑡 being the dependent variable, leverage, observed for firm 𝑖 at time 𝑡. Moreover, 𝑋′𝑖𝑡
represents the independent variables, the interest rate, and several control variables,
observed for firm 𝑖 at time 𝑡, 𝜀𝑖𝑡 being the error term, and 𝑎𝑖 being the unobserved
time-invariant effect. Finally 𝛽 represents the coefficients of the interest rate and the control
variables used in our analysis. As 𝑎𝑖 is unobservable we cannot directly control for it. A fixed
effects model takes care of this issue by demeaning the variables using a within transformation. The within transformation calculates the average value of each variable and subtracts this from the observed values, as shown in the following equation:
𝑦𝑖𝑡− 𝑦̅𝑖 = (𝑋𝑖𝑡− 𝑋̅𝑖)′𝛽 + (𝑎𝑖− 𝑎̅𝑖) + (𝜀𝑖𝑡 − 𝜀̅𝑖) (2)
Since 𝑎𝑖 is assumed time-invariant it is a constant so 𝑎̅𝑖 is equal to 𝑎𝑖. Therefore, demeaning
removes 𝑎𝑖 from the equation completely. This transformation mitigates the omitted variable
bias in our analysis. This results in the following model: 𝑦̈𝑖𝑡 = 𝑋̈𝑖𝑡
′
𝛽 + 𝜀̈𝑖𝑡 (3)
Where 𝑦̈𝑖𝑡, 𝑋̈𝑖𝑡 and, 𝜀̈𝑖𝑡 represent the demeaned dependent variable, demeaned independent
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To be able to provide a thorough analysis we construct five models each adding an extra independent variable. Model one starts by regressing leverage on the interest rate. Model two to five each add an extra control variable starting with size, secondly tangibility is added, then profitability and finally the market-to-book ratio is added. The models are presented below:
Model 1: 𝐿𝑒𝑣̈ 𝑖𝑡 = 𝛽1𝐼𝑛𝑡̈ 𝑡+ 𝜀̈𝑖𝑡
Model 2: 𝐿𝑒𝑣̈ 𝑖𝑡 = 𝛽1𝐼𝑛𝑡̈ 𝑡+ 𝛽2𝑆𝑖𝑧𝑒̈ 𝑖𝑡+ 𝜀̈𝑖𝑡
Model 3: 𝐿𝑒𝑣̈ 𝑖𝑡 = 𝛽1𝐼𝑛𝑡̈ 𝑡+ 𝛽2𝑆𝑖𝑧𝑒̈ 𝑖𝑡+ 𝛽3𝑇𝑎𝑛𝑔̈ 𝑖𝑡+ 𝜀̈𝑖𝑡
Model 4: 𝐿𝑒𝑣̈ 𝑖𝑡 = 𝛽1𝐼𝑛𝑡̈ 𝑡+ 𝛽2𝑆𝑖𝑧𝑒̈ 𝑖𝑡+ 𝛽3𝑇𝑎𝑛𝑔̈ 𝑖𝑡+ 𝛽4𝑃𝑟𝑜𝑓̈ 𝑖𝑡+ 𝜀̈𝑖𝑡
Model 5: 𝐿𝑒𝑣̈ 𝑖𝑡 = 𝛽1𝐼𝑛𝑡̈ 𝑡+ 𝛽2𝑆𝑖𝑧𝑒̈ 𝑖𝑡+ 𝛽3𝑇𝑎𝑛𝑔̈ 𝑖𝑡+ 𝛽4𝑃𝑟𝑜𝑓̈ 𝑖𝑡+ 𝛽5𝑀𝑘𝑡𝑏𝑘̈ 𝑖𝑡 + 𝜀̈𝑖𝑡
In the models above 𝐿𝑒𝑣̈ 𝑖𝑡 represents the leverage of firm 𝑖 at time 𝑡, 𝐼𝑛𝑡̈ 𝑡 represents the
interest rate at time t, 𝑆𝑖𝑧𝑒̈ 𝑖𝑡 represents the size of firm 𝑖 at time 𝑡, 𝑇𝑎𝑛𝑔̈ 𝑖𝑡 represents the
tangibility of assets of firm 𝑖 at time 𝑡, 𝑃𝑟𝑜𝑓̈ 𝑖𝑡 represents the profitability of firm 𝑖 at time 𝑡,
and 𝑀𝑘𝑡𝑏𝑘̈ 𝑖𝑡 represents the market-to-book ratio of firm 𝑖 at time 𝑡. All variables are
demeaned using the within transformation described earlier. Furthermore, in all models the independent variables are lagged by one year to mitigate simultaneity concerns.
5. Results
This chapter will discuss the results obtained after estimating the specified regression model using the data described in the data section. For the convenience of the readers, we repeat the simple version of the fixed effects model:
𝑦̈𝑖𝑡 = 𝛽𝑋̈𝑖𝑡′+ 𝜀̈𝑖𝑡 (3)
The betas are the coefficients for the interest rate, size, tangibility, profitability, and market-to-book factors. Our findings are robust for all the leverage definitions therefore, we will only present the results of the book value of capital and the financial-debt-to-market value of capital measures in this section. The other results can be found in the appendix. This paper studies the effect of the interest rate on the leverage ratio therefore, we are mainly interested in the sign, value, and significance of the coefficient of the interest rate,
𝛽1. As the dataset is very large, we find the coefficients to be significant at a one per cent level
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soundness of our results. Table 2, 3 and 4 show the regressions results of the financial-debt-to-book value of capital:
Table 2: Effect one-year interest rates on Financial-Debt-to-Capital ratio, Book value. The table provides the results of the fixed effects model regressing the financial-debt-to-book value of capital ratio on the one-year treasury rate. All data is recorded annually on December 31. For a detailed description of the variables see Methodology section. All independent variables are lagged by one year to mitigate simultaneity concerns. (1), (2), (3), (4), and (5) denote models one to five as described in the methodology section. *, **, and *** denote significance at a 10, 5 and 1 per cent level respectively.
Variable (1) (2) (3) (4) (5)
Constant 0.371*** 0.254*** 0.223*** 0.223*** 0.229***
(253.70) (55.13) (38.88) (38.51) (30.33) Treasury rate, one year -0.001*** 0.001*** 0.002*** 0.002*** 0.002*** (-2.84) (4.93) (6.36) (8.50) (7.32) Size 0.022*** 0.022*** 0.024*** 0.023*** (23.92) (23.36) (24.61) (19.81) Tangibility 0.041*** 0.023*** 0.026*** (8.85) (4.82) (4.84) Profitability -0.185*** -0.189*** (-36.86) (-34.13) Market-to-Book value -0.010*** (-14.60) R2 0.003 0.040 0.051 0.045 0.067 Observations 249,784 243,334 232,243 229,474 182,707
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more on equity financing and is in line with previous findings from Titman and Wessels (1988), Rajan and Zingales (1995) and Wald (1999).
In line with both the trade off theory and the market theory we find a negative relationship between leverage and the market-to-book ratio. Theory offers two explanations for the negative coefficient. According to Baker and Wurgler (2002) the negative coefficient is the result of managers attempting to exploit equity mispricing by issuing equity when its value is high. Trade off theory, however, states that the negative coefficient is caused by an increase in bankruptcy costs associated with growth firms. Overall, as predicted by Wald(1999), we find that the profitability of a firm has the largest impact on a firms leverage followed by size and tangibility. Even though the coefficient for the market-to-book ratio and the interest rate is significant it’s impact in minor when compared to the other factors.
Table 3: Effect ten-year interest rate on Financial-Debt-to-Capital ratio, Book value.
The table provides the results of the fixed effects model regressing the financial-debt-to-book value of capital ratio on the ten-year treasury rate. All data is recorded annually on December 31. For a detailed description of the variables see Methodology section. All independent variables are lagged by one year to mitigate simultaneity concerns. (1), (2), (3), (4), and (5) denote models one to five as described in the methodology section. *, **, and *** denote significance at a 10, 5 and 1 per cent level respectively.
Variable (1) (2) (3) (4) (5)
Constant 0.377*** 0.261*** 0.230*** 0.232*** 0.240***
(160.37) (52.48) (38.04) (38.05) (30.37) Treasury rate, ten year -0.002*** 0.000 0.001*** 0.001*** 0.001*** (-4.39) (1.30) (2.63) (3.80) (2.80) Size 0.021*** 0.021*** 0.023*** 0.022*** (23.13) (22.54) (23.59) (18.71) Tangibility 0.040*** 0.021*** 0.024*** (8.55) (4.46) (4.46) Profitability -0.184*** -0.187*** (-36.60) (-33.84) Market-to-Book value -0.010*** (-14.66) R2 0.003 0.038 0.049 0.041 0.064 Observations 249,784 243,334 232,243 229,474 182,707
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Furthermore, model one shows a negative relationship between leverage and the interest rate, however, when we expand the model the coefficient for the interest rate changes.
Table 4: Effect interest spread on Financial-Debt-to-Capital ratio, Book value.
The table provides the results of the fixed effects model regressing the financial-debt-to-book value of capital ratio on the interest spread. All data is recorded annually on December 31. For a detailed description of the variables see Methodology section. All independent variables are lagged by one year to mitigate simultaneity concerns. (1), (2), (3), (4), and (5) denote models one to five as described in the methodology section. *, **, and *** denote significance at a 10, 5 and 1 per cent level respectively. Variable (1) (2) (3) (4) (5) Constant 0.368*** 0.265*** 0.237*** 0.243*** 0.251*** (910.36) (59.18) (43.13) (43.45) (34.18) Interest Spread -0.001*** -0.005*** -0.005*** -0.006*** -0.006*** (-3.150) (-13.03) (-13.85) (-17.88) (-16.47) Size 0.020*** 0.022*** 0.023*** 0.022*** (23.720) (22.94) (24.09) (18.98) Tangibility 0.041*** 0.023*** 0.026*** (8.88) (4.77) (4.76) Profitability -0.187*** -0.190*** (-37.03) (-34.26) Market-to-Book value -0.010*** (-14.94) R2 0.001 0.039 0.049 0.042 0.064 Observations 249,784 243,334 232,243 229,474 182,707
The results of estimating the regression with the interest spread instead of the interest rate are reported in Table 4. Similar to the previous results all coefficients are highly significant at a one per cent level indicating that all variables influence the leverage. Moreover, the signs of coefficients of the control variables remain the same. The coefficient for the interest spread, however, differs in sign from the coefficient found when using the one and ten-year treasury rate. Table 4 shows that the coefficient for the interest spread is negative for all models indicating that leverage decreases if the interest spread increases. As stated in the literature, the interest spread is generally accepted as an indicator of economic prospects. The negative relationship between leverage and the interest spread therefore, implies that in a good (bad) economic state, firms issue more equity (debt). These results are in line with Chen et al. (2013) who find a similar relationship in Taiwan.
17 Table 5: Effect one-year interest rate on Financial-Debt-to-Capital ratio, Market value.
The table provides the results of the fixed effects model regressing the financial-debt-to-market value of capital ratio on the one-year treasury rate. All data is recorded annually on December 31. For a detailed description of the variables see Methodology section. All independent variables are lagged by one year to mitigate simultaneity concerns. (1), (2), (3), (4), and (5) denote models one to five as described in the methodology section. *, **, and *** denote significance at a 10, 5 and 1 per cent level respectively.
Variable (1) (2) (3) (4) (5)
Constant 0.276*** 0.099*** 0.050*** 0.052*** 0.183***
(182.83) (19.37) (7.91) (8.05) (25.31) Treasury rate, one year 0.003*** 0.007*** 0.007*** 0.008*** 0.007*** (10.44) (24.02) (26.22) (28.46) (26.08) Size 0.032*** 0.033*** 0.034*** 0.023*** (33.23) (32.78) (33.29) (21.94) Tangibility 0.066*** 0.049*** 0.025*** (13.63) (9.79) (5.01) Profitability -0.167*** -0.160*** (-35.97) (-34.72) Market-to-Book value -0.034*** (-50.53) R2 0.018 0.038 0.056 0.046 0.163 Observations 221,869 219,857 211,049 208,801 192,974
Similar to Table 2, Table 5 presents the results of the regression estimation using the one-year treasury rate. The most striking difference between the use of market and book value of capital is the effect of the interest rate on leverage. When using market values the coefficient of the interest rate has a positive effect on leverage throughout all models and does not exhibit a sign change any more. Moreover, the effect of the interest rate increases from a maximum of 0.002 when using book values to 0.008 using market values indicating that the interest rate has a larger effect on market values of leverage than the book values present. Although the coefficient increases substantially when using market values the effect remains small. When comparing the test statistic of the market-to-book value in Table 5 to the test statistic for the markettobook value in Table 2 we find an unusual increase, from 14.60 to -50.53. We expect that this could be the results of an indirect relationship between leverage and the book ratio as the market value of equity is included in both the market-to-book ratio as well as in the leverage measure.
18
and a decreased effect for profitability, -0.185 to -0.167. Furthermore, the constant is substantially lower decreasing from 0.223 to 0.052 when changing from book to market values. The value changes in the coefficients suggest a stronger effect of the control variables on leverage. Nonetheless, when in model five the market-to-book ratio is added the values for the constant and the coefficients for size and tangibility revert to values similar to the book value estimation, 0.183, 0.023 and 0.025 respectively. The effect of the market-to-book value on leverage appears to increase from -0.010 when using book values to -0.034 when using market values. Although, in model one to four, the value of the coefficients increases when using market values the implications remain the same as when using book values.
Table 6: Effect ten-year interest rate on Financial-Debt-to-Capital ratio, Market value.
The table provides the results of the fixed effects model regressing the financial-debt-to-market value of capital ratio on the ten-year treasury rate. All data is recorded annually on December 31. For a detailed description of the variables see Methodology section. All independent variables are lagged by one year to mitigate simultaneity concerns. (1), (2), (3), (4), and (5) denote models one to five as described in the methodology section. *, **, and *** denote significance at a 10, 5 and 1 per cent level respectively.
Variable (1) (2) (3) (4) (5)
Constant 0.275*** 0.097*** 0.050*** 0.053*** 0.190***
(113.12) (17.40) (7.36) (7.77) (24.60) Treasury rate, ten year 0.003*** 0.007*** 0.007*** 0.008*** 0.007*** (7.05) (18.03) (19.90) (21.20) (17.88) Size 0.031*** 0.031*** 0.032*** 0.021*** (31.66) (31.13) (31.42) (19.91) Tangibility 0.063*** 0.045*** 0.021*** (12.94) (9.10) (4.28) Profitability -0.163*** -0.156*** (-35.38) (-33.99) Market-to-Book value -0.034*** (-50.25) R2 0.015 0.035 0.052 0.041 0.160 Observations 221,869 219,857 211,049 208,801 192,974
19
0.021 to 0.045 respectively. Furthermore, the coefficient for profitability decreases from -0.184 to -0.163. When in model five the market-to-book value is controlled for, we see that the values for the coefficients of the other control variables revert to the values found in the estimation using the book value of capital. Identical to the one-year treasury rate estimation in Table 5 the effect of the market-to-book value on leverage increases from -0.010 to -0.034 when using the market value of capital.
Table 7: Effect interest spread on Financial-Debt-to-Capital ratio, Market value.
The table provides the results of the fixed effects model regressing the financial-debt-to-market value of capital ratio on the interest spread. All data is recorded annually on December 31. For a detailed description of the variables see Methodology section. All independent variables are lagged by one year to mitigate simultaneity concerns. (1), (2), (3), (4), and (5) denote models one to five as described in the methodology section. *, **, and *** denote significance at a 10, 5 and 1 per cent level respectively. Variable (1) (2) (3) (4) (5) Constant 0.299*** 0.160*** 0.122*** 0.129*** 0.258*** (677.96) (32.61) (20.19) (21.00) (37.56) Interest Spread -0.006*** -0.010*** -0.011*** -0.012*** -0.012*** (-14.88) (-26.72) (-28.16) (-31.67) (-33.39) Size 0.029*** 0.029*** 0.030*** 0.019*** (29.42) (8.76) (29.13) (18.27) Tangibility 0.061*** 0.043*** 0.020*** (12.42) (8.59) (3.96) Profitability -0.165*** -0.159*** (-35.50) (-34.27) Market-to-Book value -0.035*** (-50.68) R2 0.009 0.028 0.043 0.032 0.153 Observations 221,869 219,857 211,049 208,801 192,974
20
Although our findings provide evidence that there is a significant relationship between leverage, the interest rate and the control variables the R-squared of your models is limited. In our analysis, the highest adjusted R-squared achieves a mere 0.067 for book values of leverage and 0.163 for market values of leverage. The low R-squared suggests that there might be other factors, not incorporated in the models, that influence the leverage ratio. Furthermore, the adjusted R-squared decreases when we add profitability in model four. This is surprising as the coefficients for profitability are highly significant for both book and market values of leverage. When the market-to-book ratio is added in model five the adjusted R-squared increases substantially for market values of leverage, indicating a possible endogeneity problem.
7. Conclusion
This paper studies the effect of the interest rate on the capital structure of U.S. firms. The market timing theory and the trade off theory provide a theoretical framework for our analysis. Each of these theories predicts a specific relationship between a firms capital structure and the interest rate. We test these predictions by constructing a fixed effects model in which we regress leverage on the interest rate. Furthermore, in the model we control for firm size, tangibility of assets, profitability and the market-to-book ratio. To strengthen the analysis, we use six different definitions of leverage, three for both the book and the market value of leverage. We use the one and ten-year U.S. treasury rate as a proxy for the interest rate as well as the interest spread. The dataset used is obtained from the Wharton Research Data Services and consists of panel data including yearly firm specific data for all publicly listed U.S. companies and annual treasury rates over a 54-year period from 1962 to 2015.
We find a positive relationship between leverage and the interest rate and a negative relationship between leverage and the interest spread. Thereby, we answer our research question; ‘What is the relationship between the interest rate and the leverage of a firm?’ Although these findings are significant and robust for all definitions of leverage as well as the different treasury rates the effect we find is small. This indicates that the interest rate only explains leverage to a small extent.
21
However, theory states that leverage and the interest rate might be indirectly related through interest tax shields or a change in costs of capital. Moreover, the changes in the cost of capital and the interest tax shields are not solely determined by the interest rate and are influenced by other factors that are not included in the model.
We also find that our control variables have a significant impact on leverage. As stated by the theory firm size and tangibility of assets are positively related to leverage while profitabilitya nd the market-to-book ratio are negatively related. These findings are relevant for our ssesment of both capital structure theories.
This study provides evidence for the validity of both capital structure theories, the trade off theory and the market timing theory. With respect to the trade off theory we find a small but positive relationship between the interest rate and the leverage of a firm, indicating that firms issue more debt when interest rates are high. This supports the trade off theory as it suggests that the value of the interest tax shield increases when the interest rate increases. However, these findings are contradicted by the negative relationship between leverage and the interest spread which suggests that firms issue more equity in periods of economic growth and debt in periods of economic downturn. Our findings therefore, support as well as contradict the predictions of the trade off theory.
The negative relationship between leverage and the interest rate, however, is predicted by the market timing theory and is in line with previous findings by Chen et al. (2013). Furthermore, the market timing theory correctly predicts the signs of the control variables namely, a postive effect of size and tangibility and a negative effect of profitability and the market-to-book ratio. The market timing theory, however, is unable to explain the positive relationship between interest and the leverage. As for the the trade off theory we conclude that the market timing theory is supported as well as contradicted by our findings.
22 8. References
Allison, P. D., 2009. Fixed effects regression models (Vol. 160). SAGE publications.
Brounen, D., De Jong, A., & Koedijk, K., 2004. Corporate finance in Europe: Confronting theory with practice. Financial management, 71-101.
Chen, D. H., Chen, C. D., Chen, J., & Huang, Y. F., 2013. Panel data analyses of the pecking order theory and the market timing theory of capital structure in Taiwan. International Review of Economics & Finance, 27, 1-13.
Drobetz, W., & Wanzenried, G., 2006. What determines the speed of adjustment to the target capital structure?. Applied Financial Economics, 16(13), 941-958.
Ferri, M. G., & Jones, W. H., 1979. Determinants of financial structure: A new methodological approach. The Journal of Finance, 34(3), 631-644.
Frank, M. Z., & Goyal, V. K. 2004. The effect of market conditions on capital structure adjustment. Finance Research Letters, 1(1), 47-55.
Frank, M. Z., & Goyal, V. K., 2007. Trade-off and pecking order theories of debt. Handbook of empirical corporate finance, 2, 135-202.
Frank, M. Z., & Goyal, V. K., 2009. Capital structure decisions: which factors are reliably important?. Financial management, 38(1), 1-37.
Graham, J. R., & Harvey, C. R., 2001. The theory and practice of corporate finance: Evidence from the field. Journal of financial economics, 60(2-3), 187-243.Harris and Raviv, 1990
Kraus, A., & Litzenberger, R. H., 1973. A state‐preference model of optimal financial leverage. The journal of finance, 28(4), 911-922.
Modigliani, F., & Miller, M. H., 1958. The cost of capital, corporation finance and the theory of investment. The American economic review, 48(3), 261-297.
Modigliani, F., & Miller, M. H., 1963. Corporate income taxes and the cost of capital: a correction. The American economic review, 53(3), 433-443.
Myers, S. C., 1984. The capital structure puzzle. The journal of finance, 39(3), 574-592.
Rajan, R. G., & Zingales, L., 1995. What do we know about capital structure? Some evidence from international data. The journal of Finance, 50(5), 1421-1460.
Titman, S., & Wessels, R., 1988. The determinants of capital structure choice. The Journal of finance, 43(1), 1-19.
23
Verbeek, M., 2012. A Guide to Modern Econometrics. Wiley, Chichester
24 9. Appendices
Appendix A
Table A.1: Hausman test
The table provides the results of the Hausman test for the financial-debt-to-book value of total assets on the one-year treasury rate.
Variable Fixed (b) Random (B) Difference (b-B) Square root standard error
Treasury rate, one year 0.002 0.003 -0.001 0.000
Size 0.027 0.027 -0.001 0.000 Tangibility 0.056 0.053 0.002 0.001 Profitability -0.182 -0.168 -0.014 0.001 Market-to-book ratio -0.009 -0.010 0.002 0.000 Chi-square 2361.8 Probability 0.000 Appendix B
Table B.1: Effect one-year interest rate on Financial-Debt-to-Total Assets ratio, Book value. The table provides the results of the fixed effects model regressing the financial-debt-to-book value of total assets on the one-year treasury rate. All data is recorded annually on December 31. For a detailed description of the variables see Methodology section. All independent variables are lagged by one year to mitigate simultaneity concerns. (1), (2), (3), (4), and (5) denote models one to five as described in the methodology section. *, **, and *** denote significance at a 10, 5 and 1 per cent level respectively.
Variable (1) (2) (3) (4) (5)
Constant 0.270*** 0.207*** 0.186*** 0.188*** 0.201***
25 Table B.2: Effect ten-year interest rate on Financial-Debt-to-Total Assets ratio, Book value. The table provides the results of the fixed effects model regressing the financial-debt-to-book value of total assets on the ten year treasury rate. All data is recorded annually on December 31. For a detailed description of the variables see Methodology section. All independent variables are lagged by one year to mitigate simultaneity concerns. (1), (2), (3), (4), and (5) denote models one to five as described in the methodology section. *, **, and *** denote significance at a 10, 5 and 1 per cent level respectively.
Variable (1) (2) (3) (4) (5)
Constant 0.274*** 0.213*** 0.193*** 0.196*** 0.214***
(153.17) (53.31) (40.47) (40.68) (34.23) Treasury rate, ten year 0.000 0.001*** 0.001*** 0.002*** 0.001*** (0.36) (3.96) (5.11) (5.94) (3.61) Size 0.011*** 0.011*** 0.012*** 0.010*** (15.21) (14.85) (15.34) (10.94) Tangibility 0.026*** 0.014*** 0.013*** (7.15) (3.84) (3.01) Profitability -0.114*** -0.112*** (-31.30) (-28.21) Market-to-Book value -0.008*** (-16.35) R2 0.004 0.020 0.036 0.024 0.047 Observations 266,704 260,063 249,094 246,231 194,981
Table B.3: Effect interest spread on Financial-Debt-to-Total Assets ratio, Book value.
The table provides the results of the fixed effects model regressing the financial-debt-to-book value of total assets on the interest spread. All data is recorded annually on December 31. For a detailed description of the variables see Methodology section. All independent variables are lagged by one year to mitigate simultaneity concerns. (1), (2), (3), (4), and (5) denote models one to five as described in the methodology section. *, **, and *** denote significance at a 10, 5 and 1 per cent level respectively.
26 Table B.4: Effect one-year interest rate on Total-Liabilities-to-Total Assets ratio, Book value. The table provides the results of the fixed effects model regressing the total-liabilities-to-book value of total assets on the one year treasury rate. All data is recorded annually on December 31. For a detailed description of the variables see Methodology section. All independent variables are lagged by one year to mitigate simultaneity concerns. (1), (2), (3), (4), and (5) denote models one to five as described in the methodology section. *, **, and *** denote significance at a 10, 5 and 1 per cent level respectively.
Variable (1) (2) (3) (4) (5)
Constant 0.490*** 0.356*** 0.314*** 0.310*** 0.322***
(410.30) (99.80) (71.44) (69.45) (54.60) Treasury rate, one year -0.001*** 0.001*** 0.002*** 0.002*** 0.002*** (-5.38) (4.95) (7.64) (10.45) (8.16) Size 0.026*** 0.026*** 0.029*** 0.027*** (35.76) (34.71) (37.02) (28.45) Tangibility 0.068*** 0.049*** 0.056*** (17.48) (12.31) (12.49) Profitability -0.173*** -0.182*** (-46.22) (-44.59) Market-to-Book value -0.009*** (-17.95) R2 0.010 0.096 0.095 0.087 0.111 Observations 311,391 303,154 287,262 282,771 224,031
Table B.5: Effect ten-year interest rate on Total-Liabilities-to-Total Assets ratio, Book value. The table provides the results of the fixed effects model regressing the total-liabilities-to-book value of total assets on the ten year treasury rate. All data is recorded annually on December 31. For a detailed description of the variables see Methodology section. All independent variables are lagged by one year to mitigate simultaneity concerns. (1), (2), (3), (4), and (5) denote models one to five as described in the methodology section. *, **, and *** denote significance at a 10, 5 and 1 per cent level respectively.
Variable (1) (2) (3) (4) (5)
Constant 0.492*** 0.355*** 0.312*** 0.310*** 0.325***
27 Table B.6: Effect interest spread on Total-Liabilities-to-Total Assets ratio, Book value.
The table provides the results of the fixed effects model regressing the total-liabilities-to-book value of total assets on the interest spread. All data is recorded annually on December 31. For a detailed description of the variables see Methodology section. All independent variables are lagged by one year to mitigate simultaneity concerns. (1), (2), (3), (4), and (5) denote models one to five as described in the methodology section. *, **, and *** denote significance at a 10, 5 and 1 per cent level respectively.
Variable (1) (2) (3) (4) (5) Constant 0.482*** 0.365*** 0.328*** 0.330*** 0.343*** (1415.35) (104.71) (76.77) (75.51) (58.54) Interest Spread 0.002*** -0.002*** -0.002*** -0.004*** -0.004*** (6.73) (-5.48) (-7.41) (-12.71) (-12.20) Size 0.026*** 0.026*** 0.028*** 0.026*** (34.73) (33.20) (35.28) (26.60) Tangibility 0.067*** 0.047*** 0.055*** (17.21) (12.00) (12.26) Profitability -0.172*** -0.182*** (-46.14) (-44.46) Market-to-Book value -0.009*** (-18.21) R2 0.002 0.092 0.090 0.080 0.104 Observations 311,391 303,154 287,262 282,771 224,031
Table B.7: Effect one-year interest rate on Financial-Debt-to-Total Assets ratio, Market value. The table provides the results of the fixed effects model regressing the financial-debt-to-market value of total assets on the one year treasury rate. All data is recorded annually on December 31. For a detailed description of the variables see Methodology section. All independent variables are lagged by one year to mitigate simultaneity concerns. (1), (2), (3), (4), and (5) denote models one to five as described in the methodology section. *, **, and *** denote significance at a 10, 5 and 1 per cent level respectively.
Variable (1) (2) (3) (4) (5)
Constant 0.212*** 0.099*** 0.063*** 0.064*** 0.156***
28 Table B.8: Effect ten-year interest rate on Financial-Debt-to-Total Assets ratio, Market value. The table provides the results of the fixed effects model regressing the financial-debt-to-market value of total assets on the ten year treasury rate. All data is recorded annually on December 31. For a detailed description of the variables see Methodology section. All independent variables are lagged by one year to mitigate simultaneity concerns. (1), (2), (3), (4), and (5) denote models one to five as described in the methodology section. *, **, and *** denote significance at a 10, 5 and 1 per cent level respectively.
Variable (1) (2) (3) (4) (5)
Constant 0.213*** 0.102*** 0.067*** 0.069*** 0.164***
(111.08) (22.49) (12.25) (12.55) (26.67) Treasury rate, ten year 0.002*** 0.004*** 0.005*** 0.005*** 0.004*** (5.42) (14.55) (16.30) (17.25) (15.14) Size 0.020*** 0.020*** 0.020*** 0.013*** (24.47) (24.38) (24.53) (14.34) Tangibility 0.046*** 0.034*** 0.018*** (11.99) (8.65) (4.40) Profitability -0.102*** -0.098*** (-30.28) (-28.58) Market-to-Book value -0.024*** (-47.94) R2 0.013 0.031 0.057 0.043 0.152 Observations 207,132 205,159 197,097 194,922 181,531
Table B.9: Effect interest spread on Financial-Debt-to-Total Assets ratio, Market value.
The table provides the results of the fixed effects model regressing the financial-debt-to-market value of total assets on the interest spread. All data is recorded annually on December 31. For a detailed description of the variables see Methodology section. All independent variables are lagged by one year to mitigate simultaneity concerns. (1), (2), (3), (4), and (5) denote models one to five as described in the methodology section. *, **, and *** denote significance at a 10, 5 and 1 per cent level respectively.
29 Table B.10: Effect one-year interest rate on Total-Liabilities-to-Total Assets ratio, Market value. The table provides the results of the fixed effects model regressing the total-liabilities-to-market value of total assets on the one year treasury rate. All data is recorded annually on December 31. For a detailed description of the variables see Methodology section. All independent variables are lagged by one year to mitigate simultaneity concerns. (1), (2), (3), (4), and (5) denote models one to five as described in the methodology section. *, **, and *** denote significance at a 10, 5 and 1 per cent level respectively.
LT/MAT (1) (2) (3) (4) (5)
Constant 0.374*** 0.160*** 0.093*** 0.087*** 0.233***
(265.66) (35.59) (16.31) (14.84) (36.89) Treasury rate, one year 0.001*** 0.006*** 0.007*** 0.008*** 0.007*** (3.87) (21.76) (25.92) (29.02) (29.51) Size 0.041*** 0.042*** 0.044*** 0.032*** (45.34) (44.31) (45.37) (32.56) Tangibility 0.102*** 0.084*** 0.056*** (23.16) (18.49) (12.75) Profitability -0.162*** -0.160*** (-40.19) (-41.14) Market-to-Book value -0.036*** (-63.65) R2 0.034 0.091 0.107 0.090 0.246 Observations 244,994 242,247 229,875 226,383 209,989
Table B.11: Effect ten-year interest rate on Total-Liabilities-to-Total Assets ratio, Market value. The table provides the results of the fixed effects model regressing the total-liabilities-to-market value of total assets on the ten year treasury rate. All data is recorded annually on December 31. For a detailed description of the variables see Methodology section. All independent variables are lagged by one year to mitigate simultaneity concerns. (1), (2), (3), (4), and (5) denote models one to five as described in the methodology section. *, **, and *** denote significance at a 10, 5 and 1 per cent level respectively.
Variable (1) (2) (3) (4) (5)
Constant 0.373*** 0.151*** 0.083*** 0.078*** 0.229***
30 Table B.12: Effect interest spread on Total-Liabilities-to-Total Assets ratio, Market value.
The table provides the results of the fixed effects model regressing the total-liabilities-to-market value of total assets on the interest spread. All data is recorded annually on December 31. For a detailed description of the variables see Methodology section. All independent variables are lagged by one year to mitigate simultaneity concerns. (1), (2), (3), (4), and (5) denote models one to five as described in the methodology section. *, **, and *** denote significance at a 10, 5 and 1 per cent level respectively.
