Accomodative Monetary Policy Effects on Corporate Capital Structure

Accomodative Monetary Policy Effects on Corporate Capital Structure

Jasper Bergwerff

Abstract

Upon the start of the financial crisis in 2008 the FED has undergone an

accommodative monetary policy, dropping interest rates to unforeseen low levels. As a result,

the risk free rates dropped, decreasing the required returns on debt and equity. This paper

aims to provide an understanding to how the capital structure is affected by interest rate

changes of the Federal Reserve. The capital structure of a firm should be determined such that

the weighted average cost of capital is minimized and firm value is maximized. Theory shows

that returns on debt and equity fall as a result of lower interest rates. In turn, the lower returns

on debt and equity enter the WACC method such that the WACC decreases, but

disproportionally decreases more with equity than with debt. A panel data regression reveals

that the capital structure is determined by both US Treasury bill rates and the Federal funds

rate, among other factors. These other factors entail the pretax income, the tax shield, asset

values, US GDP growth rate, the expected future interest rate and the debt to capital ratio of

the preceding quarter. It is found that cash and short term investments, deferred income taxes,

income of the preceding quarter, and volatility of income are not sufficiently statistically

significant to explain the debt to capital structure.

Table of Contents

I.

Introduction

(3)

II.

Literature Review FFR

(4-5)

III. Derivation R

D

WACC

(5-6)

IV.

Literature Review WACC

(6-8)

V.

Methodology

(8-10)

VI.

Data

(10-16)

a. Official interest rate

b. Motivation for Large Market Capitalization

c. Other Explanatory variables

d. Composition of the Dependent Variable

VII. Results

(16-21)

a. Summary Descriptive Statistics

b. Beta Coefficient Results

VIII. Concluding Remarks

(21-23)

a. Conclusion

b. Limitations

c. Suggestions for Further Research

IX.

References

(24-25)

X.

Appendix

(26-33)

I.

Historical Credit Spreads

II.

Net Debt/Enterprise Value

III. Trade-off Theory

IV.

Elaborate Beta Coefficient Results

I.

Introduction

End 2007, early signals of a potential market downturn became evident and a time period arose which would eventually be termed the Great Recession. In order to combat the recession and stimulate the economy during the Great Recession, monetary policy has been very accommodative. While interest rates started from high levels before the recession at 5% on 3 and 6 month treasury bills in 2007, due to the accommodative policy of the Fed, interest rates plummeted to below the 1% level in an 18 month time span to boost the economy (Blinder, 2010). By the end of 2008, the Federal Reserve had lowered the federal funds rate target to zero (Mishkin, Matthews, and Giuliodori, 2013). This accommodative policy still holds until today and interest rates have dropped further since end 2008 (Blinder, 2010). The accommodative policy did not only affect yields on government bonds, but also corporate bonds. Not only government bonds of Germany and the Netherlands experience negative yields, several corporations now experience negative interest rates as well.

In this thesis an investigation will be done on whether the current and the past interest rate environment caused by the central bank influences the capital structure, debt to capital, of firms. To be more specific, this thesis will look at the effect of interest rate changes performed by the Federal Reserve from 2003 to 2013 for 416 of the largest 500 US firms. It is argued by Leland (1994) and Goldstein et. al (2001) in Ju, Ou-Yang (2006) that the capital structure of a firm is affected by deviations in the interest rate. A demonstration will be made to show how the change in the interest rate affects the weighted average cost of capital used in valuation, on which firms decide their capital structure. Although the weighted average cost of capital is used for capital budgeting, goal setting, performance measurement and regulation, among other things as stated by Cooper and Davydenko, this thesis will only use the weighted average cost of capital and its argumentation for firm valuation as this determines the decision of the capital structure (2001).

This paper is organized as follows: In section two a literature review of the Federal Funds rate, the risk-free Treasury bond and the return on debt is made. Following this, section 3 proceeds with a derivation of the return on debt. This derivation demonstrates how the adjustment of the interest rates at the central bank affect the return on debt included in the weighted average cost of capital. Section 4 demonstrates the assumptions and empirics concerning the weighted average cost of capital which will be used in this research. Section five proceeds with the methodology. Section six proceeds with the data of this research where the assumptions for the research are mentioned. Section seven

demonstrates the results of the research. Section eight provides concluding remarks concerning the research, as well as limitation and possible additional research subjects. Following this, section nine lists the references to the works used in this thesis. Lastly, section ten is the appendix, providing additional figures and concludes this paper with the findings and additional figures and the list of company tickers used in this research.

II.

Literature Review FFR

To begin, there must first be a clear connection in how the interest rate policy of a central bank affects the required return on debt that investors demand to invest in corporations, and thus how it influences the capital structure of a firm. The Central Bank manipulates the lending and deposit rate in order to affect the official interest rate, known as the Federal Funds rate in the United States (Mishkin et al., 2013). The federal funds rate is also known as the official interest rate: the interest rate set by the central bank in order to perform its policy (Mishkin et al., 2013). As specified by Cook and Hahn, market interest rates in turn depend on the level of the Federal Funds rate set by the FED (1989). This argument is supported by Bernanke and Blinder who claim that the federal funds rate is the interest rate on which all other interest rates depend (1992). Cook and Hahn, go on to argue that the amplitude of changes in the federal funds rate have a constant and similar effect on the change of the three, six, or twelve month treasury bill (1989). In other words, deviations in the federal funds rate trigger a change of similar magnitude in the same direction on these treasury instruments (Cook and Hahn, 1989). So far we have therefore concluded that the FED can directly control the federal funds rate by adjusting the deposit rate and lending rate. In short then, by changing the deposit and lending rates, the central bank affects the federal funds rate, triggering a similar movement in the yields of US treasury bills.

The US treasury bills are highly liquid short term debt instruments. In addition they are regarded as default-free investments due to their low probability of default (Mishkin et al, 2013). Mishkin et al. continue by stating that the issuer of treasury bills is the national government, the face value of the bond can therefore always be repaid simply by raising taxes in order to appropriate the funds for the debt payoff (Mishkin et al, 2013). Bonds like the US treasury bills are therefore

considered default-free bond, therefore offer the risk-free interest rate (Duffee, 1998). It is mentioned by Mishkin et al. that corporate bonds carry default risk however and therefore contain a risk

premium. These risk premia depend on the credit ratings corporations receive from credit rating agencies such as Moody’s Investor Service, Standard & Poor’s Corporation and Fitch Ratings

(Mishkin et al., 2013). This implies that the interest rate paid by a firm on debt is higher than from the risk free market interest rate because of the risk premium (Ting, 2012). To elaborate, corporate bonds, regardless of whether they have an investment grade or a junk bond status, will have a yield spread compared to the treasury bonds. This yield difference is referred to a credit spread, which increases as the bond ratings decrease (Berk, DeMarzo, 2011). Credit ratings historically assign spreads which are provided in the appendix, section X.I.

Corporations therefore receive ratings depending on the risk exposure to the business. The riskier the business, the higher the probability of default and thus the higher credit spread with the risk-free US Treasury bond. The size of the positive yield spread together with the yield on the treasury bills therefore determine the return on corporate debt (Blinder, 2010). This return on debt is

the cost of debt financing to a firm and plays a vital role in firm valuation. The information mentioned above can also be shown by a derivation, which will be demonstrated in the following section.

III. Derivation R

D

WACC

The interest rate offered with the federal funds rate directly influences the cost of debt in the weighted average cost of capital formula. A derivation of the return on debt is shown in the derivation below.

A. The federal funds rate depends on the lending and deposit rate. (Mishkin et al., 2013)

Step 1: Central bank changes the lending and deposit rate to adjust the federal funds rate. Lending rate is lowered such that Lending rate at t=1 < Federal Funds rate at t=0. The lending rate is here-on after termed iL, the deposit rate is termed iD,, the Federal Funds rate iFFR

Lending rate (iL) > Federal Funds rate (iF ) > Deposit rate (iD)

iL↓ > iFFR↓ > iD↓ (1)

B. The risk-free treasury bill rate depends on the federal funds rate (Mishkin et al., 2013)

Step 2: The return on the federal funds rate is the return on the treasury rate minus a constant factor α (where α is a positive rate to ensure that iFFR < rf). A change in the federal funds rate causes a change

of similar amplitude to the treasury bill rate, here-on after termed the risk free rate, rf.

iFFR = rf - α

rf↓ = iFFR↓ + α (2)

C. The return on debt depends on the risk free rate (Blinder, 2010)

Step 3: With corporate bond spreads held constant per rating grade, corporate bond yields (rd) depend

on the treasury bill rates, and β, where β is the number of basis points of the rating grade (Cantor and Packer, 1994).

rd = rf+ β(1%)

rd = iFFR+ α + β(1%)

Keeping all else equal, ceteris paribus,

If federal funds rate decreases, return on debt decreases

By no arbitrage argumentation, a lower return on debt also results in a lower return on equity. In effect then a drop in the risk-free rate caused by a decrease in the FFR will not only lower the return on debt, but also has to lower the return on equity. Immediately upon announcement of lower Treasury bill rates, interest rates will drop and equity prices will rise, implying a lower return on equity by the inverse relation between price and return on such securities. As a result, the weighted average cost of capital will drop as both return inputs are now lower as shown below.

a. WACC = rWACC = � 𝐷𝐷

𝐷𝐷+𝐸𝐸𝑟𝑟𝑑𝑑(1 − 𝑡𝑡)� + � 𝐸𝐸

𝐷𝐷+𝐸𝐸𝑟𝑟𝑒𝑒� (Cooper and Nyborg, 2004) (4)

A lower 𝑟𝑟_𝑑𝑑 and 𝑟𝑟_𝑒𝑒 lowers the wacc.

We see however that there is an effect that results in equity becoming disproportionally cheaper than debt. Assuming the firm is 50% levered and 50% financed by equity, if the return on equity

(𝑟𝑟_𝑒𝑒) changes by 1, the WACC decreases by 0.5%. On the contrary, if the return on debt decreases by 1%, the wacc will decrease by 0.5(1-t) %. As shown, in order to minimize the WACC, there should be a change in the capital structure upon a change in the risk free rate.

IV.

Literature Review WACC

Corporate finance theory supports contradictory assumptions of the optimal capital structure during a time when there is a downturn in business environment such as the recent recession (i.e. 2007-2009). In order to elaborate on the idea of optimal capital structure, this paper first defines the motive for a firm to alter the capital structure. To begin, the main goal of a corporation is to maximize shareholder value. Therefore, since shareholders are the owner of a firm, the goal of the corporation is to maximize firm value (Berk and DeMarzo, 2011). This argument is in agreement with Ting who states that finance assumes value maximization is the main goal of a firm (2012). Firm value is in turn affected by the capital structure a firm uses to finance its business. For instance, Brennan and Schwartz confirm that the value of the firm may increase or decrease according to the amount of debt in the capital structure (1978). An essential assumption and condition for this to hold true is the idea that the corporations are not active not a tax-free environment, i.e. there are taxes. In reality this holds true, in fact numerous nations in the words maintain a policy whereby the interest expenditures on debt can be deducted from their income prior to being taxed on this income (Cooper and Nyborg, 2004). In effect then, as Cooper and Nyborg proceed, adding debt to the capital structure allows for a tax shield as the taxable income is then reduced. This feature to debt leads to proof that the value of a levered firm is equal to unlevered firm value plus a tax shield (Cooper and Nyborg, 2004). Debt also brings about

financial distress costs however, and hence a fully levered capital structure is not optimal and seen in practice.

In order to reach determine firm value, we must obtain the free cash flows of a firm. Free cash flows are cash flows after which all investments, operating and other expenses have been paid for. These free cash flows are in turn discounted to the present in order to generate a firm value.

Maximization of firm value is done by maximizing the present value of the future free cash flows to the firm (Berk, DeMarzo, 2011). Assuming, that free cash flows are held constant, the other portion relevant for maximizing the present value of the future cash flows is the discount factor by which cash flows are discounted. This discount rate is termed the weighted average cost of capital, which can be manipulated by a different capital structure (Brennan and Schwartz, 1978). It is therefore via the weighted average cost of capital: the weighted cost of the funds a firm needs to finance its investment and operations, that manipulations in capital structure alter the firm value (Koziol, 2014). More specifically, the capital structure is chosen such that the weighted average cost of capital will be minimized, thereby maximizing firm value, ceteris paribus.1

𝑉𝑉𝑡𝑡 = �

_{(1 + 𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊)}

𝑬𝑬

𝒕𝒕

(𝑋𝑋

𝑡𝑡+𝑠𝑠

)

_𝑠𝑠 𝑡𝑡

𝑠𝑠=1

The value of the firm is shown above, where Vt is the firm value, X the cash flow t, current time, s time periods in the future and WACC the weighted average cost of capital (Koziol, 2014).

This weighted average cost of capital is then the weight of the sources of financing, whether debt or equity, multiplied times the required returns investors demand on debt and equity financing into a company, respectively (Cooper and Davydenko, 2001). Since firms also get to deduct interest expenses from their income before taxation, including the tax shield the WACC can be written as (Cooper and Nyborg, 2004):

b. WACC = rWACC = � 𝐷𝐷

𝐷𝐷+𝐸𝐸𝑟𝑟𝑑𝑑(1 − 𝑡𝑡)� + � 𝐸𝐸

𝐷𝐷+𝐸𝐸𝑟𝑟𝑒𝑒� (Cooper and Nyborg, 2004) In 1963, Modigliani and Miller made the assumption that corporate taxes result in a

dominating strategy for capital structure, namely fully levering the company to 100% debt (Schnabel, 1984). Furthermore the perfect capital market assumption with no taxes of Modigliani and Miller state that in the case of bankruptcy, equity holders lose ownership and give this to the debt holders of the firm. According to the above shown equation for the weighted average cost of capital, debt financing seems to dominate equity financing. In reality however companies are not 100% leveraged (Berk and 1. For the sake of this thesis we assume that the free cash flows are constant, the derivation is beyond the scope of this thesis. This is not a strong assumption as we assume that the capital structure of a firm does not alter the firm’s operations or investment activity (Cooper and Nyborg, 2004). As a result, the cash flows of a firm should be unchanged by its financing choice.

DeMarzo, 2011). This becomes evident by the chart from Berk and DeMarzo (2011) included in the appendix as under X.II. This argument is further supported in the papers of Wrightsman (1978) and Brennan and Schwartz (1978), demonstrating that the optimal capital structure is composed of both debt and equity as opposed to purely debt. In addition, value is not simply transferred when a firm goes bankrupt but several costs are incurred (Berk and Demarzo, 2011). What Modigliani and Miller fail to account for in their 1963 paper is that higher leverage will increase the financial distress costs and thus raise the return on debt, 𝑟𝑟_𝑑𝑑.

In order to give a representation of the real world, a deviation is made to demonstrate the tradeoff between debt and equity from the historical Modigliani Miller assumptions. As a result, as shown above in the derivation of the return on debt, this thesis will incorporate the assumption that high debt levels in the capital structure increase distress costs, mitigating firm value. Credit rating agencies assign credit spreads on top of the risk free rate in order to arrive at a required return on debt for a specific company. As leverage increases, lower credit ratings are assigned to firms since

fundamental ratios such as debt/assets increase, leading to a higher basis point spread and triggering more expensive debt financing (Berk and DeMarzo, 2011). Thus the model used throughout this thesis is a slight modification to the “Trade-off Theory” which is shown in the appendix, section X.III. The “Trade-off Theory” states:

“The total value of a levered firm equals the value of the firm without leverage plus the present value of the tax savings from debt, less the present value of financial distress costs.” (Berk and DeMarzo, 2011).

The benefit of the tax shield increases as the debt to capital ratio increases, meanwhile financial distress costs increase as well. The modification to this trade theory in this thesis is that that the cost of financial distress will be incorporated into the return on debt, therefore eliminating the need to account for financial distress costs directly. Still, with this deviation, the same assumptions hold as in trade-off theory: the value of the levered firm increases with debt due to the tax shield, lowering the WACC. Meanwhile, increased leverage can in turn also increase the WACC by increasing the financial distress costs, thereby decreasing the value of the firm (Davydenko, 2012).

V.

Methodology

In order to analyze if the capital structure changes upon interest rate changes by the FED, 416 of the 500 largest US companies by 2015 market cap size will be investigated. Quarterly data is obtained for these companies starting from 2003 until 2013, including the long term debt, short term (current) debt and market value of equity. In this research, a panel data regression is run in order to investigate whether the dependent variable, debt to capital is related to certain variables. Each panel subject of this

regression refers to a different company, resulting in a total of 416 different companies, or panels. The time period used for this regression is from the first quarter of 2003 to the fourth quarter of 2013, encompassing a total of 44 quarters, or time periods per company, or panel. This results in a total of (i*t=n), 416*44 = 18304 observations, sufficient for a strong statistical power. A panel data regression is run in order to see the relation of variables moving over time and between companies. As a result, a longitudinal regression, which can account for changes in t and i, is necessary for the regression instead of a simple linear regression which can account only for t. All variables are tested with a two sided 95% confidence interval test with an H0 hypothesis test against zero. An explanation for the model to be tested and motivations for the variables are provided below.

The model is based on a number of variables with an economic interpretation that will be

regressed on the dependent variable, debt to capital structure. To elaborate further, five types of panel data regressions are run which are demonstrated below. In the event that significant results are obtained for the coefficient of both the interest rate and deferred variables, a follow-up regression is run to see if the interaction term of the respective interest rate and the deferred tax is significant. Firms may decide to issue more debt if the interest rate drops when they have deferred income taxes. This is in spite of the fact that the derivation in section III demonstrates that equity issuance is superior. The motivation is that firms can offset losses against profits, making the interest tax shield unnecessary. All profits can be shielded from taxation due to the deferred income tax. This regression would look similar to regression six.

(1) 𝐷𝐷 𝐷𝐷+𝐸𝐸 = 𝛼𝛼+ 𝛽𝛽1�𝑟𝑟𝑓𝑓6 𝑚𝑚𝑚𝑚𝑚𝑚𝑡𝑡ℎ∗ 𝐷𝐷� + 𝛽𝛽2�� 𝐷𝐷 𝐷𝐷+𝐸𝐸�_𝑡𝑡−1� + 𝛽𝛽3�𝐸𝐸�𝑟𝑟𝑓𝑓6𝑚𝑚𝑚𝑚𝑚𝑚𝑡𝑡ℎ𝑡𝑡+2�� + 𝛽𝛽4(𝑊𝑊 + 𝑆𝑆𝑆𝑆𝑆𝑆) + 𝛽𝛽5�𝑆𝑆𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼(𝑡𝑡−1)� + 𝛽𝛽6�_{𝐴𝐴𝑠𝑠𝑠𝑠𝑒𝑒𝑡𝑡}𝐷𝐷𝑒𝑒𝐷𝐷𝑡𝑡� + 𝛽𝛽7(𝑆𝑆𝐷𝐷𝑚𝑚𝑒𝑒𝑡𝑡 𝑖𝑖𝑚𝑚𝑖𝑖𝑚𝑚𝑚𝑚𝑒𝑒) + 𝛽𝛽8(𝑈𝑈𝑆𝑆𝑈𝑈𝐷𝐷𝑈𝑈%) + 𝛽𝛽9(𝐷𝐷𝐼𝐼𝐷𝐷𝐼𝐼𝑟𝑟𝑟𝑟𝐼𝐼𝐷𝐷) + 𝛽𝛽10(𝑈𝑈𝑟𝑟𝐼𝐼𝑡𝑡𝑃𝑃𝑃𝑃 𝑖𝑖𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼) + ε𝑡𝑡 (2) 𝐷𝐷 𝐷𝐷+𝐸𝐸 = 𝛼𝛼+ 𝛽𝛽1�𝑟𝑟𝑓𝑓6 𝑚𝑚𝑚𝑚𝑚𝑚𝑡𝑡ℎ∗ 𝐷𝐷� + 𝛽𝛽2�� 𝐷𝐷 𝐷𝐷+𝐸𝐸�_𝑡𝑡−1� + 𝛽𝛽3�𝐸𝐸�𝑟𝑟𝑓𝑓6𝑚𝑚𝑚𝑚𝑚𝑚𝑡𝑡ℎ𝑡𝑡+2�� + 𝛽𝛽4(𝑊𝑊 + 𝑆𝑆𝑆𝑆𝑆𝑆) + 𝛽𝛽5�𝑆𝑆𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼(𝑡𝑡−1)� + 𝛽𝛽6(𝑊𝑊𝑠𝑠𝑠𝑠𝐼𝐼𝑡𝑡𝑠𝑠) + 𝛽𝛽7(𝑆𝑆𝐷𝐷𝑚𝑚𝑒𝑒𝑡𝑡 𝑖𝑖𝑚𝑚𝑖𝑖𝑚𝑚𝑚𝑚𝑒𝑒) + 𝛽𝛽8(𝑈𝑈𝑆𝑆𝑈𝑈𝐷𝐷𝑈𝑈%) + 𝛽𝛽9(𝐷𝐷𝐼𝐼𝐷𝐷𝐼𝐼𝑟𝑟𝑟𝑟𝐼𝐼𝐷𝐷) + 𝛽𝛽10(𝑈𝑈𝑟𝑟𝐼𝐼𝑡𝑡𝑃𝑃𝑃𝑃 𝑖𝑖𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼) + 𝛽𝛽11�𝑟𝑟𝑓𝑓6 𝑚𝑚𝑚𝑚𝑚𝑚𝑡𝑡ℎ� + ε𝑡𝑡 (3) 𝐷𝐷 𝐷𝐷+𝐸𝐸 = 𝛼𝛼+ 𝛽𝛽1�𝑟𝑟𝑓𝑓6 𝑚𝑚𝑚𝑚𝑚𝑚𝑡𝑡ℎ∗ 𝐷𝐷� + 𝛽𝛽2�� 𝐷𝐷 𝐷𝐷+𝐸𝐸�_𝑡𝑡−1� + 𝛽𝛽3�𝐸𝐸�𝑟𝑟𝑓𝑓6𝑚𝑚𝑚𝑚𝑚𝑚𝑡𝑡ℎ𝑡𝑡+2�� + 𝛽𝛽4(𝑊𝑊 + 𝑆𝑆𝑆𝑆𝑆𝑆) + 𝛽𝛽5�𝑆𝑆𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼(𝑡𝑡−1)� + 𝛽𝛽6(𝑊𝑊𝑠𝑠𝑠𝑠𝐼𝐼𝑡𝑡𝑠𝑠) + 𝛽𝛽7(𝑆𝑆𝐷𝐷𝑚𝑚𝑒𝑒𝑡𝑡 𝑖𝑖𝑚𝑚𝑖𝑖𝑚𝑚𝑚𝑚𝑒𝑒) + 𝛽𝛽8(𝑈𝑈𝑆𝑆𝑈𝑈𝐷𝐷𝑈𝑈%) + 𝛽𝛽9(𝐷𝐷𝐼𝐼𝐷𝐷𝐼𝐼𝑟𝑟𝑟𝑟𝐼𝐼𝐷𝐷) + 𝛽𝛽10(𝑈𝑈𝑟𝑟𝐼𝐼𝑡𝑡𝑃𝑃𝑃𝑃 𝑖𝑖𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼) + 𝛽𝛽11�𝑟𝑟1𝑦𝑦𝑒𝑒𝑦𝑦𝑦𝑦� + ε𝑡𝑡 (4) 𝐷𝐷 𝐷𝐷+𝐸𝐸 = 𝛼𝛼+ 𝛽𝛽1�𝑟𝑟𝑓𝑓6 𝑚𝑚𝑚𝑚𝑚𝑚𝑡𝑡ℎ∗ 𝐷𝐷� + 𝛽𝛽2�� 𝐷𝐷 𝐷𝐷+𝐸𝐸�_𝑡𝑡−1� + 𝛽𝛽3�𝐸𝐸�𝑟𝑟𝑓𝑓6𝑚𝑚𝑚𝑚𝑚𝑚𝑡𝑡ℎ𝑡𝑡+2�� + 𝛽𝛽4(𝑊𝑊 + 𝑆𝑆𝑆𝑆𝑆𝑆) + 𝛽𝛽5�𝑆𝑆𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼(𝑡𝑡−1)� + 𝛽𝛽6(𝑊𝑊𝑠𝑠𝑠𝑠𝐼𝐼𝑡𝑡𝑠𝑠) + 𝛽𝛽7(𝑆𝑆𝐷𝐷𝑚𝑚𝑒𝑒𝑡𝑡 𝑖𝑖𝑚𝑚𝑖𝑖𝑚𝑚𝑚𝑚𝑒𝑒) + 𝛽𝛽8(𝑈𝑈𝑆𝑆𝑈𝑈𝐷𝐷𝑈𝑈%) + 𝛽𝛽9(𝐷𝐷𝐼𝐼𝐷𝐷𝐼𝐼𝑟𝑟𝑟𝑟𝐼𝐼𝐷𝐷) + 𝛽𝛽10(𝑈𝑈𝑟𝑟𝐼𝐼𝑡𝑡𝑃𝑃𝑃𝑃 𝑖𝑖𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼) + 𝛽𝛽11�𝑟𝑟𝑓𝑓5𝑦𝑦𝑒𝑒𝑦𝑦𝑦𝑦� + ε𝑡𝑡 (5) 𝐷𝐷 𝐷𝐷+𝐸𝐸 = 𝛼𝛼+ 𝛽𝛽1�𝑟𝑟𝑓𝑓6 𝑚𝑚𝑚𝑚𝑚𝑚𝑡𝑡ℎ∗ 𝐷𝐷� + 𝛽𝛽2�� 𝐷𝐷 𝐷𝐷+𝐸𝐸�_𝑡𝑡−1� + 𝛽𝛽3�𝐸𝐸�𝑟𝑟𝑓𝑓6𝑚𝑚𝑚𝑚𝑚𝑚𝑡𝑡ℎ𝑡𝑡+2�� + 𝛽𝛽4(𝑊𝑊 + 𝑆𝑆𝑆𝑆𝑆𝑆) + 𝛽𝛽5�𝑆𝑆𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼(𝑡𝑡−1)� + 𝛽𝛽6(𝑊𝑊𝑠𝑠𝑠𝑠𝐼𝐼𝑡𝑡𝑠𝑠) + 𝛽𝛽7(𝑆𝑆𝐷𝐷𝑚𝑚𝑒𝑒𝑡𝑡 𝑖𝑖𝑚𝑚𝑖𝑖𝑚𝑚𝑚𝑚𝑒𝑒) + 𝛽𝛽8(𝑈𝑈𝑆𝑆𝑈𝑈𝐷𝐷𝑈𝑈%) + 𝛽𝛽9(𝐷𝐷𝐼𝐼𝐷𝐷𝐼𝐼𝑟𝑟𝑟𝑟𝐼𝐼𝐷𝐷) + 𝛽𝛽10(𝑈𝑈𝑟𝑟𝐼𝐼𝑡𝑡𝑃𝑃𝑃𝑃 𝑖𝑖𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼) + 𝛽𝛽11(𝐹𝐹𝐹𝐹𝐹𝐹) + ε𝑡𝑡

(6) 𝐷𝐷 𝐷𝐷+𝐸𝐸 = 𝛼𝛼+ 𝛽𝛽1�𝑟𝑟𝑓𝑓6 𝑚𝑚𝑚𝑚𝑚𝑚𝑡𝑡ℎ∗ 𝐷𝐷� + 𝛽𝛽2�� 𝐷𝐷 𝐷𝐷+𝐸𝐸�_𝑡𝑡−1� + 𝛽𝛽3�𝐸𝐸�𝑟𝑟𝑓𝑓6𝑚𝑚𝑚𝑚𝑚𝑚𝑡𝑡ℎ𝑡𝑡+2�� + 𝛽𝛽4(𝑊𝑊 + 𝑆𝑆𝑆𝑆𝑆𝑆) + 𝛽𝛽5�𝑆𝑆𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼(𝑡𝑡−1)� + 𝛽𝛽6(𝑊𝑊𝑠𝑠𝑠𝑠𝐼𝐼𝑡𝑡𝑠𝑠) + 𝛽𝛽7(𝑆𝑆𝐷𝐷𝑚𝑚𝑒𝑒𝑡𝑡 𝑖𝑖𝑚𝑚𝑖𝑖𝑚𝑚𝑚𝑚𝑒𝑒) + 𝛽𝛽8(𝑈𝑈𝑆𝑆𝑈𝑈𝐷𝐷𝑈𝑈%) + 𝛽𝛽9(𝐷𝐷𝐼𝐼𝐷𝐷𝐼𝐼𝑟𝑟𝑟𝑟𝐼𝐼𝐷𝐷) + 𝛽𝛽10(𝑈𝑈𝑟𝑟𝐼𝐼𝑡𝑡𝑃𝑃𝑃𝑃 𝑖𝑖𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼) + 𝛽𝛽11(𝑠𝑠𝑖𝑖𝑠𝑠. 𝑖𝑖𝐼𝐼𝑡𝑡. 𝑟𝑟𝑃𝑃𝑡𝑡𝐼𝐼) + 𝛽𝛽12(𝑠𝑠𝑖𝑖𝑠𝑠. 𝑖𝑖𝐼𝐼𝑡𝑡. 𝑟𝑟𝑃𝑃𝑡𝑡𝐼𝐼 ∗ 𝐷𝐷𝐼𝐼𝐷𝐷𝐼𝐼𝑟𝑟𝑟𝑟𝐼𝐼𝐷𝐷)+ ε𝑡𝑡 Independent Variable Coefficient

Hypothesis about coefficient

Intercept, 𝜶𝜶 𝛼𝛼 Alpha is zero

𝒓𝒓𝒇𝒇𝒇𝒇 𝒎𝒎𝒎𝒎𝒎𝒎𝒕𝒕𝒎𝒎∗ 𝑫𝑫 𝛽𝛽1 Positive � 𝑫𝑫 𝑫𝑫 + 𝑬𝑬�𝒕𝒕−𝟏𝟏 𝛽𝛽2 _Positive 𝑬𝑬�𝒓𝒓𝒇𝒇𝒇𝒇𝒎𝒎𝒎𝒎𝒎𝒎𝒕𝒕𝒎𝒎𝒕𝒕+𝟐𝟐� 𝛽𝛽3 Positive 𝑪𝑪 + 𝑺𝑺𝑺𝑺𝑺𝑺 𝛽𝛽4 Positive 𝑺𝑺𝒎𝒎𝑰𝑰𝒎𝒎𝒎𝒎𝑰𝑰(𝒕𝒕−𝟏𝟏) 𝛽𝛽5 Positive 𝑨𝑨𝑨𝑨𝑨𝑨𝑰𝑰𝒕𝒕s 𝛽𝛽6 Positive 𝑺𝑺𝑫𝑫𝒎𝒎𝑰𝑰𝒕𝒕 𝒊𝒊𝒎𝒎𝑰𝑰𝒎𝒎𝒎𝒎𝑰𝑰 𝛽𝛽7 Negative 𝑼𝑼𝑺𝑺𝑼𝑼𝑫𝑫𝑼𝑼% 𝛽𝛽8 Positive 𝑫𝑫𝑰𝑰𝒇𝒇𝑰𝑰𝒓𝒓𝒓𝒓𝑰𝑰𝑫𝑫 𝛽𝛽9 Positive 𝑼𝑼𝒓𝒓𝑰𝑰𝒕𝒕𝑷𝑷𝑷𝑷 𝒊𝒊𝒎𝒎𝑰𝑰𝒎𝒎𝒎𝒎𝑰𝑰 𝛽𝛽10 Positive 𝒓𝒓𝒇𝒇𝒇𝒇 𝒎𝒎𝒎𝒎𝒎𝒎𝒕𝒕𝒎𝒎 𝛽𝛽11 (2) Positive 𝒓𝒓𝒇𝒇𝟏𝟏𝒇𝒇𝑰𝑰𝑷𝑷𝒓𝒓 𝛽𝛽11 (3) Positive 𝒓𝒓𝒇𝒇𝒇𝒇 𝒇𝒇𝑰𝑰𝑷𝑷𝒓𝒓 𝛽𝛽11 (4) Positive 𝑭𝑭𝑭𝑭𝑭𝑭 𝛽𝛽11 (5) Positive 𝑨𝑨𝒊𝒊𝒔𝒔. 𝒊𝒊𝒎𝒎𝒕𝒕. 𝒓𝒓𝑷𝑷𝒕𝒕𝑰𝑰 ∗ 𝑫𝑫𝑰𝑰𝒇𝒇𝑰𝑰𝒓𝒓𝒓𝒓𝑰𝑰𝑫𝑫 2 𝛽𝛽12 (6) _Positive

VI.

Data

a. Official interest rate

First of all, the choice for the official interest rate used in this research is the federal funds rate of the US Central bank. The purpose for this is that the FED uses an aggressive accommodative monetary policy whereas other banks such as the ECB choose to be slightly more conservative and gradually ease into more accommodative policy (Mishkin et al., 2013). The Federal Reserve has changed its main refinancing rate more frequently than the sixteen times the ECB has changed the main rate since its introduction in 1999 (Sahuc and Smets, 2008). Sahuc and Smets elaborate this idea further by stating that the magnitude of the interest rate deviations are smaller for the ECB than for the Federal Reserve (2008). In addition, a stronger correlation exists with the stock returns of the data set in this research paper, the S&P500, and the US economy which the FED looks at for her monetary policy. Since the S&P 500 is composed out of the largest 500 US firms, the debt to capital structures should be closely affected by the US treasury interest rates, which are in turn affected by the federal funds rate.

2.. A regression on the significant interest rate * deferred is only run in the event that both the interest rate and the coefficient for deferred are statistically significant, otherwise regression 6 can be ignored.

Due to the reasons listed above, a panel-data regression is run on three US treasury rates, each holding a different maturity, as well as a regression with the federal funds rate (FFR). The different interests rates are the 𝒓𝒓_{𝒇𝒇𝒇𝒇 𝒎𝒎𝒎𝒎𝒎𝒎𝒕𝒕𝒎𝒎}, 𝒓𝒓_{𝒇𝒇𝟏𝟏𝒇𝒇𝑰𝑰𝑷𝑷𝒓𝒓}, 𝒓𝒓_{𝒇𝒇𝒇𝒇 𝒇𝒇𝑰𝑰𝑷𝑷𝒓𝒓}, and the 𝑭𝑭𝑭𝑭𝑭𝑭, for which the coefficients of all four are expected to be positive. This hypothesis originates from the derivation of the return on debt equation by plugging equation (3) into equation (4). This derivation demonstrates that the dominant strategy for a company is to lever up, i.e. increase the debt to capital ratio, when the risk free rate or federal funds rate increases, ceteris paribus3. Even though, according to the WACC theory firms should alter their capital structure when the return on debt changes, theory also states debt is not likely to change significantly from one quarter to the next, but rather takes a longer time period (Welch, 2002). This implies that the capital structure at time t depends positively on the debt to capital ratio of time t-1. As a result, a variable � 𝑫𝑫

𝑫𝑫+𝑬𝑬�_{𝒕𝒕−𝟏𝟏} for which a positive coefficient is expected is included in the model. Another argument originates from the management entrenchment theory. This entails that managers see debt as a measure of discipline and refrain from incurring debt for job safety because of the minimal chance of firm default (Berk and DeMarzo, 2011). As a result, the debt to capital structure is likely to depend on the debt to capital theory experienced at time t-1.

b. Motivation for Large Market Capitalization

This dataset is composed out of 416 of the largest 500 US companies by market capitalization. These 416 companies were all part of the 2015 S&P 500, an index composed of the largest 500 US

companies in 2015, meanwhile also being active since the first quarter of 2003. Reasons for including the largest firms by market capitalization are mentioned hereafter.

First of all, Welch claims that large US corporations have negligible transaction costs whereas small companies experience high costs (2004). Since large US corporations have negligible

transaction costs, this paper can refrain from incorporating transaction costs in the research. Secondly, financial distress costs are greater for firms that experience more volatile, or risky cash flows (Brennan and Schwartz, 1978). This would imply that additional leverage in the capital structure increases the financial distress costs greatly and would therefore be undesirable (Welch, 2004). This could lead to a one sided research thesis since prior to the analysis, we can conclude that there is a large aversion to increasing leverage. For this reason Miao states that industries with risky technology, are industries with higher bankruptcy costs and thus have lower debt to capital ratios (2005). In other words, firms with more volatile cash flows tend to be smaller and have a bias to including lower debt to capital 3.. An essential criteria is that all other variables in this model are held constant, otherwise the debt to capital ratio need not increase. For example, the growth rate of the US economy as well as the asset value may be altered in such a way that the debt to capital ratio will actually move the opposite direction as was argued. To analyze the sole impact of the risk free rate, the other variables must be held constant.

ratios. This finding is supported by Welch who states that firms with growth opportunities in the future are less inclined to increase debt for a small tax benefit now, because these firms risk large bankruptcy costs (2004). For example, firms with income that is more volatile are more conservative, and include lower debt ratios regardless of the market movement (Welch, 2002). This finding is visible in the appendix, section X.II where an industry such as computer hardware has lower debt in the capital structure. As a result, this thesis includes a standard deviation of the net income variable, depicted by 𝑺𝑺𝑫𝑫𝒎𝒎𝑰𝑰𝒕𝒕 𝒊𝒊𝒎𝒎𝑰𝑰𝒎𝒎𝒎𝒎𝑰𝑰 in the regression. The negative relation as predicted in the methodology is derived from the idea that a higher volatility implies larger fluctuations in earnings. In other words, a company may experience large positive earnings while the subsequent period only a small profit is realized or even a large negative net result. This would increase the riskiness of the cash flows and increase the chance interest payments can’t be met.

The cash flows of these companies depend for a large part on the state of the economy as well. During growth periods, companies with riskier cash flows tend to outperform the market, whereas market downturns result in underperformances. Hence, another regressor used in this research is the US GDP growth rate, shown by 𝑼𝑼𝑺𝑺𝑼𝑼𝑫𝑫𝑼𝑼% in the model. According to theory in Berk and DeMarzo, the S&P 500 index is considered a market index and therefore carries a beta of one. As a result, the performance of the S&P500 depends on the performance of the overall economy (2011). When the US economy grows, demand for goods and services increase and debt issuances should increase because the total market earnings increase and allow for easier debt repayment, leading to a positive expected coefficient for the US growth rate. The inclusion of only the largest companies in this paper also allows for the exclusion of smaller, more volatile companies which have riskier technology. This ensures that smaller companies in the growth phase of a business cycle do not drive the results and yield biased outcomes (Welch, 2002).

Accumulation of debt also has a negative influence on firm value however, as was argued earlier. Miao continues by elaborating that buildup of debt, or leverage, also brings about increased bankruptcy costs (2005). An argument for including large sized firms is that large firms experience lower financial distress costs due to higher asset values and a developed source of income (Welch, 2004). Put differently, Leland and Toft (1996) argue that bankruptcy occurs when firms have lower asset values. The justification to including large market capitalization companies is that the companies in the data set have larger asset values. As a result Assets is included in the regression since this can serve as collateral to issue new, or repay old debt. Hence a positive coefficient is expected for this variable. This implies lower bankruptcy costs and therefore less aversion in firms to accumulate debt. This allows the debt to capital results to move freely in both directions, i.e. increase, decrease. Still, to include relevant variables, a cash and short term investment position is included in the model, represented by the variable 𝑪𝑪 + 𝑺𝑺𝑺𝑺𝑺𝑺. The underlying theory to include this variable is that cash and short term investments are liquid assets that can be used to repay debt obligations and principal in case the company has negative EBIT. Intuitively, a positive coefficient is then expected. As was argued

earlier, this thesis includes the idea of financial distress costs through the credit ratings assigned to corporations. Cash and short term investments, as well as assets are used by credit rating agencies to determine credit rating levels (Berk and DeMarzo, 2011). The higher the cash + STI and the higher the assets of a firm, the superior the credit rating of a company, and the cheaper debt financing is to a firm. Low cash and asset levels imply that the firm has a thin margin for entering financial distress. This holds even when business results are poor only for a short time period (Cantor and Packer, 1994). This idea is elaborated by Davydenko, who claims that a firm can enter financial distress even when the business and business strategy is successful, simply because of a short term decline in cash flow (2012). To see whether the previous short term cash flow is relevant for the capital structure, a variable 𝑺𝑺𝒎𝒎𝑰𝑰𝒎𝒎𝒎𝒎𝑰𝑰(𝒕𝒕−𝟏𝟏) is included. This variable represents the net income of a corporation realized in the previous period. A positive relation is expected since the net income incurred in the previous period demonstrates the results the company can expect with the current environment and business activity. The more net income was experienced last quarter, the higher the safety net to meet debt repayments and interest expenditures, instigating a company to issue more debt. A similar argument holds for the inclusion of the term 𝑼𝑼𝒓𝒓𝑰𝑰𝒕𝒕𝑷𝑷𝑷𝑷 𝒊𝒊𝒎𝒎𝑰𝑰𝒎𝒎𝒎𝒎𝑰𝑰 since a high value for pretax income indicates that after interest payments on debt, a positive value remains for taxation. This allows a company to have room to reduce the effective taxable income by incurring more debt and shielding taxes through a higher interest expenditure. Furthermore it informs the company of the magnitude of excess income the company has to meet interest payments on the debt. A positive coefficient is expected for this value since a higher value for pretax income can trigger a company to incur more debt for tax shielding purposes while it also provides the corporation with a higher safety margin to meet debt interest payments.

Various research papers incorrectly make the assumption that the risk premium to debt is zero (Cooper and Davydenko, 2001). The result of ignoring the default risks of the firm in the WACC however will lead to an underestimated discount rate and therby an incorrectly high firm value (Koziol, 2014). To solve this problem, this paper accounts for a risk premium as there is still a chance of default which increases as more debt is accumulated. As stated above, the financial distress costs in this paper will be included in the return on debt. Credit rating agencies will assign lower ratings for the companies according to the chance of bankruptcy (Cantor and Packer, 1984). Not only does this ensure that this research takes the default risk of a firm into account, it also ensures that firms with higher default risk receive lower ratings. This causes an increasing spread as the debt to capital ratio increases that would trigger an increase WACC, similar to how the financial distress costs increase the WACC. This further enforces our argument of including a return on debt that contains financial distress costs in the form of a credit spread.

To summarize, the inclusion of large companies imply negligible transaction costs, which can be kept out of this model. In addition, the data is composed of larger sized companies since the returns for these large capitalization companies are less volatile and since these firms have a higher value, the

likelihood of bankruptcy with large market capitalization firms are smaller, leading to diminished expected bankruptcy costs. As a result, financial distress costs are excluded from the model directly but these are still incorporated in the model in the sense that the return on debt is dependent on the credit rating a company receives. This allows us to perform a more thorough empirical analysis as the numerical data can be extracted for all the other criteria while there is no existence of a value for financial distress costs available.

c. Other Explanatory Variables

This thesis includes several other factors in the regression in order to account for all the factors that influence the capital structure, in the hope to prevent a biased conclusion. Several authors argue that the amount of debt is affected by a number of factors. First of all, as stated in Miao, interest payments on debt are tax deductible and therefore incentivize the accumulation of debt in the firm (2005). This is in agreement with Cooper and Nyborg who claim that various nations in the words maintain a policy whereby the interest expenditures on debt can be deducted from their income prior to being taxed (2004). This motivates the inclusion of the variable 𝒓𝒓_{𝒇𝒇𝒇𝒇 𝒎𝒎𝒎𝒎𝒎𝒎𝒕𝒕𝒎𝒎}∗ 𝑫𝑫 in the panel data regression model. This variable shows the interaction of the risk free rate and the debt, symbolizing a proxy to the value of the tax shield. Several authors, as stated above, recognize the value and benefit of the tax shield. This thesis expects that there is a positive relation between the debt to capital structure and the tax shield. A lower tax shield would signify that the benefits to debt are lower and would trigger a lower debt to equity ratio. Similarly the expected future 6-month risk-free interest rate at t+2 is included, represented in the model by the variable 𝑬𝑬(𝒓𝒓_{𝒇𝒇𝒇𝒇𝒎𝒎𝒎𝒎𝒎𝒎𝒕𝒕𝒎𝒎𝒕𝒕+𝟐𝟐)}. A positive relation is expected since the higher the expected future interest rate, the more tax shield benefits are expected in the future and the more beneficial it is to accumulate debt in the capital structure.

Another variable incorporated into the panel data regression model is 𝑫𝑫𝑰𝑰𝒇𝒇𝑰𝑰𝒓𝒓𝒓𝒓𝑰𝑰𝑫𝑫. This variable concerns the level of deferred income taxes, or income taxes that can be carried forward or redeemed due to losses in the past. This variable is included in the model because several countries in the world maintain a policy whereby the losses of a company can be carried forward to offset future profits (Ju and Ou-Yang, 2006). The effect of this accounting rule is that the taxable income of the corporation is reduced. In time, the right to offset past losses against future profits may expire however because there is a time limit to the extent that losses are allowed to offset profits. To elaborate, the Generally

Accepted Accouting Principles (GAAP) specify that losses can be used up to a maximum of seven years after the loss is incurred to offset profits (Marshall, McManus, and Viele, 2012).

The input variables to the WACC model as mentioned in the theory are incorporated into a weighted cost of capital which is shown below.

a. WACC = rWACC = �

𝐷𝐷

𝐷𝐷+𝐸𝐸𝑟𝑟𝑑𝑑(1 − 𝑡𝑡)� + � 𝐸𝐸 𝐷𝐷+𝐸𝐸𝑟𝑟𝑒𝑒�

D = The book value of debt, composed of debt in current liabilities and long term debt E = The market value of equity, also referred to as the Market Capitalization

t = The corporate tax rate, the US corporate tax rate is 40% (Corporate, 2015).

rd = Return on debt. The return investors in corporate fixed income securities and corporate loans

demand for lending to a corporation. The specific derivation is shown above under Section II:

rd = Federal funds rate + α + β(1%)

re = return on equity. The return investors in common shares of a corporation demand for investing in

a corporation, this return will always exceed rd

The debt which returns in the WACC formula above is the sum of the total long term debt (Compustat item 9) and the total current debt (Compustat item 34). Welch uses the actual corporate debt ratio ADR as a measure of debt to capital structure in his paper for the National Bureau of Economic research (Welch 2002), as well as his later paper “capital structure and stock returns” (2004). In this research, the exact same components are used, however, rather than referring to this as the ADR, this is referred to as the debt to capital ratio of a firm. To be more explicit, the debt to capital structure is therefore the book value of debt divided by the sum of the book value of debt and market equity value. This ratio, representing the dependent variable of this research paper, informs about composition of debt in the capital structure. In other words, it is the portion of the total firm capital raised by debt issuance that has to be repaid upon maturity.

The equity values retrieved are composed of the market value of equity, namely the quarterly price close multiplied times the number of outstanding common shares, also obtained from Compustat. The motivation to include market value of equity as opposed to book value is that book value is an accounting term (Welch 2002). According to Welch (2002), “Book value of equity is a plug number used to balance the right-hand and left-hand sides of the balance sheet” (p. 6). He continues by claiming book value is based on the lagged accounting variables whereas market capitalization has a true economic value. This argument is further explicated based on observations for companies such as Sky Broadcasting which carried negative book value of equity of 1.2 billion dollars in 1995, while the market capitalization was a positive 495 million (Welch 2002). This demonstrates that the use of book

value of equity is inappropriate since it can provide negative values of equity and hence nonsensical results.

VII. Results

This section will provide the outcome and elaborate on the results to the model constructed in the previous section. While the previous section explicitly presented the theoretical interpretation and conjectures for the coefficients of each variable in determining the capital structure, a numerical analysis needs to be performed to determine whether variables are significant and how they influence the debt to capital ratio in case the variables are significant. The elaborate numerical results for each regression are reported in the appendix table with the same number corresponding to the regression. For instance, the results to the first regression as shown in the previous section can be found in the table named Table 1 in section X.IV. A summary of all the beta coefficient regression results are also included in the beta coefficient section below.

a. Summary Descriptive Statistics

Prior to mentioning the beta coefficients of the regression, some summary statistics must be pointed out. Table A reports the summary statistics of all the variables used in the regression. For instance, it becomes evident that the data set contains minimal debt values near zero for the variables current debt and long term debt (debt is denoted in millions of dollars). This implies that certain companies in the data set are practically unlevered. Having a closer look, companies that can be found in this category are represented by tech sector corporations such as Google, Apple and Facebook. According to the theory by Welch, 2002, as was mentioned earlier in this thesis, it is plausible that there is no debt in the capital structure of these firms since technological firms tend to have more volatile cash flows and are more averse to building up debt. To proceed, minimum statistics values for variables such as stock price close of the quarter and common shares (in millions) equity are uncommon. One reason for this is that some companies present in the dataset started to trade publicly not long before the first quarter of 2003, which is the time period used in this data set. Another reason is that some companies were near bankruptcy in the financial crisis, causing share prices to plummet. As a result, low equity values (in millions), determined by quarter stock price close multiplied by the total number of common shares, date from either the early period of the data set, or during the financial crisis. Again, due to near-zero debt levels of corporations like Google, Apple and Facebook, debt to capital shows 1.09e-07 for the minimum value. Still, companies such as American Airlines are highly levered and responsible for the maximum observed debt to capital ratio. Furthermore, it must be noted that the numerical values listed for the USGDP growth rates and interest rates for mean minimum and maximum are denoted in percent. Pretax income and net income t-1 are denoted in hundred-thousands. Lastly, values

for assets are denoted in millions, cash and STI values are denoted in hundred-thousands while deferred income is denoted in ten-thousands.

TABLE A

Variable

Obs

Mean

Std. Dev.

Min

Max

Dcurrent 18304 5661.08 37036.04 0 56285.7 Dlongterm 18304 9137.275 32139.03 0.01 55883.0 Price close Quarter 18304 49.6690 0.2700 0.27 1162.4 # of Common shares 18304 628.0365 1285.335 6.947 29206.44 Equity 18304 24439.28 43530.50 100 626550.4 �_{𝑫𝑫 + 𝑬𝑬�}𝑫𝑫 18304 0.2452 0.2068 1.09e-07 0.993393 𝒓𝒓𝒇𝒇𝒇𝒇 𝒎𝒎𝒎𝒎𝒎𝒎𝒕𝒕𝒎𝒎∗ 𝑫𝑫 18304 195.4403 1306.624 4.00e-08 3813.774 �_{𝑫𝑫 + 𝑬𝑬�}𝑫𝑫 𝒕𝒕−𝟏𝟏 18304 0.2454402 0.207366 1.09e-07 0.993393 𝑬𝑬�𝒓𝒓𝒇𝒇𝒇𝒇𝒎𝒎𝒎𝒎𝒎𝒎𝒕𝒕𝒎𝒎𝒕𝒕+𝟐𝟐� 18304 1.837877 1.765813 .13001 5.277654 𝑪𝑪 + 𝑺𝑺𝑺𝑺𝑺𝑺 18304 6319.77 31825.56 10 638025 𝑺𝑺𝒎𝒎𝑰𝑰𝒎𝒎𝒎𝒎𝑰𝑰(𝒕𝒕−𝟏𝟏) 18304 911.7464 2825.594 -99289 108260 Assets 18304 52909.26 183632.5 39.673 2463309 𝑺𝑺𝑫𝑫𝒎𝒎𝑰𝑰𝒕𝒕 𝒊𝒊𝒎𝒎𝑰𝑰𝒎𝒎𝒎𝒎𝑰𝑰 18304 302.3191 898.9045 0.3943095 29351.52 𝑼𝑼𝑺𝑺𝑼𝑼𝑫𝑫𝑼𝑼% 18304 4.038636 3.119104 -7.7 9.3 Deferred 18304 14.45273 1092.676 -35561 36977 𝑼𝑼𝒓𝒓𝑰𝑰𝒕𝒕𝑷𝑷𝑷𝑷 𝒊𝒊𝒎𝒎𝑰𝑰𝒎𝒎𝒎𝒎𝑰𝑰 18304 1347.876 3900.549 -108761 107127 𝒓𝒓𝒇𝒇𝒇𝒇 𝒎𝒎𝒎𝒎𝒎𝒎𝒕𝒕𝒎𝒎 18304 1.633864 1.789067 0.04 5.24 𝒓𝒓𝒇𝒇𝟏𝟏𝒇𝒇𝑰𝑰𝑷𝑷𝒓𝒓 18304 1.7356282 1.769341 0.1 5.21 𝒓𝒓𝒇𝒇𝒇𝒇 𝒇𝒇𝑰𝑰𝑷𝑷𝒓𝒓 18304 2.708182 1.329427 0.62 5.10 𝑭𝑭𝑭𝑭𝑭𝑭 18304 1.644545 1.87516 0.05 5.34

b. Beta coefficient results

Table 1 in Appendix of section X.IV conveys the elaborate coefficient results for explanatory variables listed in the model of the first regression. This table does not incorporate an interest rate in the model, apart from the interaction term of the 6-month US treasury and the level of debt, which serves as a proxy variable of the tax shield. It becomes evident that the model receives a very high value for the Chi^2 test, which is significant at the 1% level. This suggests that a model with only an intercept significantly reduces the fit of the model. Furthermore, the r^2 demonstrates that the variance in the dependent variable is for 92.76% explained by variance in the independent variables. These results together convey that the model is complete and includes several statistically important factors in determining the debt to capital ratio. Several conclusions can be deducted these results. At a first glance the coefficients appear small, however, it should be noted that the dependent variable, debt to capital carries a numerical value between zero and one.

First of all, it becomes evident that the debt to capital ratio of t-1 is the most significant explanatory variable. The coefficient to this variable is 0.947, indicating that calculations to the regression find that the debt to capital structure depends greatly on the debt to capital ratio of the preceding quarter. The economic interpretation is found in Welch, 2002, where it is explicated that large firms are inert on changing their capital structure from one period to the next. In the event that large firms do decide to manipulate their capital structure, it also requires more than one time period to see significant changes because the long term debt position does not change every quarter (Ju and Ou-Yang, 2006). Ting corroborates this idea by confirming that capital of a firm is flexible in the long run (2012). The results confirm our hypothesis that the capital ratio depends positively on the debt to capital ratio of the previous period.

While the capital structure t-1 is a strong determinant of the capital structure of t=1, other factors can still greatly influence the capital structure. The growth rate of the US economy per quarter is another explanatory variable significant at the 1 % level. Of the values provided in the table 1 for this variable, we see that coefficient is 0.0024863, with an average value from the summary statistics of 3.1, this variable does not seem to have a strong influence in the capital structure. As stated earlier however, the debt to capital ratio carries a value between zero and one. If we use a growth rate of say 5% we see that the debt to capital ratio is expected to change more than 0.01 due to this factor. This implies that a five percent growth rate, results in a one percent of the maximum amount of debt to capital increase from the US growth rate, which is not limited to 5% per quarter. In combination with the coefficient for assets for instance, 2.50e-08 multiplied by some of the higher values, say two million in asset value, the capital structure will increase by 0.05, resulting in 5% of the maximum debt to capital ratio possible. An increase in debt to capital of 0.06 points in one quarter can greatly affect the weighted average cost of capital and thus the valuation. The positive coefficient for US GDP

growth and for assets confirm the hypotheses made in the previous section. The greater the growth of the economy, the more demand for goods and services, the greater asset values become, leading to a lower chance of bankruptcy (Leland and Toft, 1996).

Still there is a group of significant variables for which the statistics demonstrate statistical significance though the coefficients are so small that the influence on the debt to capital structure remains negligible. The tax shield proxy, 𝑟𝑟_{𝑓𝑓6 𝑚𝑚𝑚𝑚𝑚𝑚𝑡𝑡ℎ}∗ 𝐷𝐷, is another significant variable at the 1% level. Various papers argue that the tax shield a motivation for a firm to increase leverage. For instance, Koziol claims that the tax shield can greatly attribute to firm value (2013). The outcome therefore confirms the conjecture that there is a positive relation between the debt to capital ratio and the size of the tax shield proxy. The coefficient seems very small however, especially when noting, based on the summary statistics that the average value for this variable is 195.44, meaning the debt to capital ratio will only change 5.5e-04. Perhaps this is due to the fact that the proxy in this model does not correctly portray a true tax shield. In addition, the time period of one quarter may be too short to show the value of the tax shield in firm valuation. As stated above, To explicate, the expectation of the future interest rate is significant at the 5% level. There is a positive relation as this thesis expected in the previous section. The theory is then supported that firms look forward and anticipate the future value of the tax shield by looking at the expected future interest rate. As a result, an increase in the future interest rate of 1% increases the debt to capital ratio by 0.0006333. This coefficient still remains small, especially when compared to other explanatory variables such assets or the debt to capital ratio t-1. In addition, it should be noted that the future 6 month treasury rate in the 21st century has seldom exceeded the 5%, so the influence on the capital structure is limited. The last significant variable is the negative coefficient to the pretax income. This variable has a coefficient of -6e-07, with an average value of 1347.88. On average this results in a negligible influence on the debt to capital structure. Still, the coefficient is negative, opposite to the conjecture made in the methodology portion of this thesis. Berk and DeMarzo do mention theory concerning the effect that disappointing earnings as perceived by the public can have. They argue that this drops stock prices making equity issuances rare. On the contrary, high stock value make it more attractive to issue equity which can explicate why debt to equity

decreases when earnings are high (2011).

Lastly, the variables cash + short term investments, income t-1, volatility of the income and deferred income tax are insignificant. To elaborate further, there is not sufficient statistical evidence that the cash and short term investments, net income realized in the previous quarter, volatility of the income and the value of the deferred income tax influence the debt to capital ratio of a firm. The coefficient for the constant is significant and positive. Berk and DeMarzo provide an economic interpretation of the constant by claiming that most companies have a combination of both debt and equity (2011). The constant implies that regardless of other explanatory variables, there is at least some debt in the company, ceteris paribus.

Following the first regression are the regressions two through five, each including the explanatory variables of table one, as well as a differing interest rate. The regression results convey that the interest rate, regardless of the maturity and regardless of whether it is a US Treasury rate or the Federal Funds rate is significant. The 6 month risk free and the 1 year treasury rate are both significant at the 5% level and carry a positive coefficient, as was predicted earlier. The coefficient for the federal funds rate from table 5 is also positive and significant at the 1% level. Interestingly

however, table four shows a negative coefficient for the 5 year US treasury rate. At first glance this seems contradictory as the interest rate results of table two, three and five all show positive significant coefficients. However, it can be noted that the addition of an interest rates relative to the first

regression also changes the coefficient of the expected future interest rate. To elaborate, the coefficient to the future interest rate is 0.000633 for regression three, whereas this coefficient is significant and negative at the 5% level for regression three and five and negative at the 10% level for regression two. To interpret this phenomenon, companies seem to incur more debt as the risk free rate increases due to the dominant strategy of debt issuance, as shown in the derivation of the return on debt. In addition, for regressions two, three and five, debt to capital is negatively related to the expected future interest rate. If the future interest rate is expected to be lower in the future, the debt to capital ratio increases. Monetary theory assumes that low future interest rates convey that the market will be stimulated and demand for goods and services will increase again, implying that business will prosper and debt repayments will be met (Mishkin et al, 2013). This aspect of future prosperity mitigates the aversion to debt issuance. It was noted that the five year interest rate carried a negative coefficient but this

triggered the expected future interest rate to become positive. Though this seems contradictory, the same argument may be used. To expatiate on this claim, the five year interest rate yield has a far longer maturity than the interest rates in the second, third and fifth regression. This implies that the five-year interest rate carries assumptions and predictions about the future expected interest rates. The date of expiration of a five year maturity bond lies further in the future than a 6 month treasury rate, six months from now. As a result, the signs have changed here, where the five year bond interest rate is seen as the future expected interest rate and the forward 6 month interest rate resembles the more recent interest rate. To summarize, the movement of the interest rate with an expiration date that lies farther in the future is negatively to the debt to capital structure whereas the interest rate that expires earlier is positively related to the interest rate. These variables all carry a positive coefficient, therefore the underlying reasoning as explained in the methodology holds. The derivation of the return on debt by plugging equation (3) into equation (4) showed that debt issuance is a dominant strategy when the risk free rate increases since it also increases the the value of the tax shield.

Looking beyond the interest rate, it becomes evident that the introduction of the variables slightly changes the coefficients for the variables, however these, with the exception of the expected risk free rate at time t+2, still carry the same coefficients and are still significant. Insignificant variables from regression 1 remain insignificant in all other regressions.

(1) (2) (3) (4) (5) Constant .0207917*** (.0009573) .021203*** (.0009718) 0.212005*** (.0009717) .0297021*** (.0015427) .0214386*** (.0009778) 𝒓𝒓𝒇𝒇𝒇𝒇 𝒎𝒎𝒎𝒎𝒎𝒎𝒕𝒕𝒎𝒎∗ 𝑫𝑫 2.83e-06*** _(3.83e-07) 2.79e-06*** _(3.83e-07) 2.79e-06*** _(3.83e-07) 2.84e-06*** _(3.82e-07) 2.79e-06*** _(3.83e-07)

� 𝑫𝑫 𝑫𝑫 + 𝑬𝑬�𝒕𝒕−𝟏𝟏 .9471023*** (.002176) .9473064*** (0021773) .9473055*** (.0021773) .9475562*** (.0021737) .9473637*** (.0021769) 𝑬𝑬�𝒓𝒓𝒇𝒇𝒇𝒇𝒎𝒎𝒎𝒎𝒎𝒎𝒕𝒕𝒎𝒎𝒕𝒕+𝟐𝟐� .0006333** _(.0002517) -.0023861* _(.0012597) -.0053676** _(.0024733) .0052589*** _(.0006769) -.0026449** _(.0010463) 𝑪𝑪 + 𝑺𝑺𝑺𝑺𝑺𝑺 -4.13e-07 (3.09e08) -4.16e-08 (3.08e-08) -4.16e-08 (3.08e-08) -4.46e-08 (3.08e-08) -4.14e-08 (3.08e-08) 𝑺𝑺𝒎𝒎𝑰𝑰𝒎𝒎𝒎𝒎𝑰𝑰(𝒕𝒕−𝟏𝟏) -1,99e-07 (1.97e-07) -2.14e-07 (1.97e-07) -2.14e-07 (1.97e-07) -1.98e-07 (1.97e-07) -2.26e-07 (1.97e-07)

Assets

2.50e-08*** (5.98e-09) 2.51e-08*** (5.98e-09) 2.51e-08*** (5.98e-09) 2.53e-08*** (5.97e-09) 2.51e-08*** (5.98e-09) 𝑺𝑺𝑫𝑫𝒎𝒎𝑰𝑰𝒕𝒕 𝒊𝒊𝒎𝒎𝑰𝑰𝒎𝒎𝒎𝒎𝑰𝑰 _(5.13e-07)4.45e-07 _(5.13e-07) 4.23e-07 4.23e-07 _{5.13e-07 (5.12e07)} 4.37e-07 _(5.13e-07) 4.20e-07

𝑼𝑼𝑺𝑺𝑼𝑼𝑫𝑫𝑼𝑼% .0024863*** (.0001392) .002443*** (.0001403) .0024432*** (.0001402) .0023469*** (.0001402) .0024515*** (.0001395) 𝑫𝑫𝑰𝑰𝒇𝒇𝑰𝑰𝒓𝒓𝒓𝒓𝑰𝑰𝑫𝑫 2.77e-07 (3.86e-07) 2.73e-07 (3.86e-07) 2.73e-07 (3.86e-07) 3.13e-07 (3.86e-07) 2.71e-07 (3.86e-07) 𝑼𝑼𝒓𝒓𝑰𝑰𝒕𝒕𝑷𝑷𝑷𝑷 𝒊𝒊𝒎𝒎𝑰𝑰𝒎𝒎𝒎𝒎𝑰𝑰 -6.00e-07*** (1.46e-07) -5.95e-07*** (1.46e-07) -5.95e-07*** (1.46e-07) -.647e-07*** (1.46e-07) -5.87e-07*** (1.46e-07) 𝒓𝒓𝒇𝒇𝒇𝒇𝒎𝒎𝒎𝒎𝒎𝒎𝒕𝒕𝒎𝒎 _- .0030168** (.0012333) - - - 𝒓𝒓𝒇𝒇𝟏𝟏𝒇𝒇𝑰𝑰𝑷𝑷𝒓𝒓 _{- -} .005999** (.0024597) - - 𝒓𝒓𝒇𝒇𝒇𝒇𝒇𝒇𝑰𝑰𝑷𝑷𝒓𝒓 _{- - -} -.0066532*** (.0009041) - 𝑭𝑭𝑭𝑭𝑭𝑭 _{- - - -} .0031572*** (.0009781) R2 _(overall) 0.9277 0.9277 0.9277 0.9279 0.9277 Prob > Chi2 0.0000 0.0000 0.0000 0.0000 0.0000

NOTE.— Each column number indicates the regression number. Due to the insignificance of the coefficient for the variable for deferred, a sixth regression, containing the interaction term between the respective significant interest rate and the deferred variable is not run. *** indicates significance at the 1% level, ** indicates significance at the 5% level, * indicates significance at the 10% level

VIII. Concluding remarks

a. Conclusion

In conclusion, an extensive panel data regression of 18,304 observations on 416 of the S&P 500 companies reveals that the debt to capital structure of firms depend on the interest rate. Regressions two through five all showed statistically significant coefficients for the interest rate used in the

or 60 month maturity or the federal funds rate, the interest rate affects the capital structure. Movements in the six and twelve month treasury yields as well as the federal funds rate positively relate to the debt to capital structure. On the contrary, the 60-month US treasury yield is negatively related to the debt to capital structure, signifying that 5 year treasury yield decreases trigger an increase the debt to capital ratio. The results seem contradictory, but the explanation derives from the fact that the introduction of the 5 year treasury yield changed the sign of the significant coefficient for the future interest rate. In all regressions, apart from the fourth regression with the 5 year treasury rate, the coefficient for future 6 month interest rate is negative. Since the 5 year treasury yield included in regression four contains predictions of the future path of interest rates beyond the expectation for the future (t+2) 6 month interest, the interest rate with a later expiration date now receives the negative coefficient. The economic theory remains unchanged, namely that there is a positive coefficient for the current interest rate as debt is a dominant strategy when interest rates rise, while the coefficient for more forward looking interest rate is negative. Mishkin et al. elaborate on this issue by affirming that a low future interest rate is representative of an accommodative policy to boost the economy and

demand for goods, making business prosper, and increasing the probability that debt repayments will be made (2013).

Other conclusions that can be drawn from the panel data regression is that the pretax income, tax shield, asset value, US GDP growth rate and the debt to capital ratio of the preceding quarter are all statistically significant positively related explanatory variables for the debt to capital ratio. To explicate further, the debt to capital structure of the preceding quarter is the most significant variable and suggests that the debt to capital structure of time t is not flexible after one quarter and carries the same characteristics as the debt to capital in the preceding quarter. On the contrary, cash and short term investments, deferred income taxes, income of the preceding quarter and volatility of income are not sufficiently significant in explaining the debt to capital structure.

b. Limitiations

Still this paper has some limitations which can influence the results. First of all, this thesis is based on a panel data regression, where the panel is the debt to capital ratio and where time is measured in quarters. Due to the fact that this paper assumes the book value of debt which is composed of both short (current) and long term debt, debt does not change much from quarter to quarter. To specify, long term debt typically has a maturity of around 5 years, implying that it may take a similar time period before the funds are earned such that it can be repaid. This suggests that the debt might not change significantly from one quarter to the next and thus nor will the debt to capital ratio. This can also explain why the debt to capital t-1 variable is so significant. This was a necessary trade-off between an efficiently large sample size to ensure statistical power and more flexibility of the capital structure due to lengthier time periods t. Furthermore, the original dataset of the 500 S&P companies

was not compatible for the analysis of this paper. The reason for this was the fact that the data set contained a number of companies which entered the S&P 500 during the Great Recession as a result of financial distress for companies as Fanny Mae and Freddy Mac, as well as bankruptcies for companies such as Lehmann Brothers. Several of these companies that entered the S&P during the Great

Recession therefore had no data in the years prior to the recession. The exclusion of these companies may have resulted in a In addition, this model ignored default costs directly and rather included them through the credit rating a company receives. No account was made in this thesis, as it would further complicate the analysis, of how increases in debt would at some point cause a corporation to receive a lower credit rating. Still however, Koziol explains that traditional WACC models without the default risk is sufficient since most analyses contain firms with credit ratings of A or higher, thus bankruptcy costs are not severe (2013). In this thesis, due to the selection of the 416 large-cap companies in the S&P 500, the credit ratings of all companies are high investment grade, as supported in Leland and Toft (1996).

c. Suggestions for further research

An interesting alternative study is whether the coefficients to the variables in the regression differ for smaller firms. In this thesis the sample size was composed of 416 companies, all a part of the 2015 S&P 500. An extension to the research may be whether the capital structure is also affected by firms in the Russel 3000 index as the companies in this index altogether compose 98% of the US equity market. Alternatively an analysis may also be done on small cap firms since this would ensure that the sample does not contain companies that are also present in the S&P 500, as was used in this thesis. It was argued earlier in this thesis that large corporations experience negligible transaction costs. Since transaction costs play a larger role for small-cap firms, the capital structure of these companies might be influenced differently by the variables included in this model. Another interesting alternative study is to investigate whether the extent to which debt to capital ratio depends on the US Treasury rates differs between sectors or industries. Perhaps the coefficient for US treasury rates for the financial industry is significantly larger than for consumer goods sector, implying that the debt to capital structure of the financial industry depends significantly more on the US treasury rates than the consumer good industry.