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M £33. can” - ‘1’:u~‘u :8: "y 4%er :3": -m. ‘1‘?” J. “3:35 m an n IllU/l/ll/I/l/ Hwy/81w /////I/ I/ W! {—— \ lLlllflUlllY’ Michigan State University k I This is to certify that the dissertation entitled AN EMPIRICAL INVESTIGATION OF DEBT AND TAXES IN A MULTIPERIOD FRAMEWORK presented by Jamshed Yunas Uppal has been accepted towards fulfillment of the requirements for Ph.D. degree in Bus . Adm. ,, ' A a ‘ 7 212/9,“ ”(j (I; AzL/kmta L ’3" Major professor 11/3/89 Date MSU it an Affirmative Action/Equal Opportunity Institution 0- 12771 PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or More date due. DATE DUE DATE DUE DATE DUE E__J[::JL_J i-l ' VT i ll MSU Is An Affirmative Action/Equal Opportunity Institution chJ-DJ AN EMPIRICAL INVESTIGATION OF DEBT AND TAXES IN A HULTIPERIOD FRAMEWORK BY Jamshed Yunas Uppal A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Finance and Insurance 1989 GO 1 I L. 0043' ABSTRACT AN EMPIRICAL INVESTIGATION OF DEBT AND TAXES IN A MULTIPERIOD FRAMEWORK BY Jamshed Yunas Uppal This study develops a multiperiod model of capital structure choice when firms are faced with uncertain cash flows. The value implications of tax shields provided by debt as well as non-debt deductions are considered. Our analysis shows that the value generated by the debt tax shield for a growing firm and a non-growing firm differs in a fundamental manner. This difference is sufficient to produce a negative relationship between growth and financial leverage. The model also indicates substitutability between debt and non-debt tax shields in a multiperiod framework. We obtain empirical hypotheses similar to those derived earlier by Barnea, Talmor and Haugen1 using a more restrictive set of assumptions. First, the direction of the relationship (positive or negative) between financial leverage and operating risk is shown to depend upon the personal and corporate tax rates. Second, non-growth firms with high operating earnings to market value ratio are predicted to employ relatively more debt than growth firms. Third, the ratio of yields on taxable and non-taxable bonds is predicted to follow a cyclical pattern lagging the business cycle. The study provides empirical evidence on the hypotheses derived from our multi-period model. OLS regressions, using a pooled sample of 19 years of time series and cross sectional data on 431 companies were employed. The results of the study largely support the hypotheses following from our model and tend to indicate that taxes systematically affect capital structure policies and bond market equilibrium. Tests using pooled sample data indicated no significant relationship between growth and financial leverage. However, cross-sectional and direct tests which controlled for firm size by including firm value as a separate regressor supported the hypothesized negative relationship. The study also presents evidence that factors other than taxes, such as asymmetric information, agency costs also affect the financial leverage choice. This suggests that different capital structure theories may complement rather than compete with each other. 1. Barnea, A; Talmor, E; Haugen, R. A. "Debt and Taxes: A Multiperiod Investigation." Journal of flanking and Finance 11(1987) 79-97. This dissertation is dedicated to the memory of my beloved father, Dr. Mohammad Yunas Uppal. iv ACKNOWLEDGEMENTS I gratefully acknowledge the help, support and inspiration from the members of my guidance committee in completion of this dissertation. In particular I wish to express my gratitude to Dr. Richard R. Simonds for providing insights and guidance through the course of this study. I am specially grateful to Dr. John L. O'Donnell for his continued encouragement and inspiration. I am also indebted to Dr. Kirt C. Butler for his valuable comments and ideas at every stage. This dissertation would not have been possible without the constant support, love and forbearance on the part of my family, in particular on the part of my wife, Nasreen. TABLE OF CONTENTS LIST OF TABLES O O O O O O O O O O O O O O O O O O 0 LIST OF FIGURES O O O O O O O O O O O O O O O 0 O 0 LIST OF APPENDICES . . . . . . . . . . . . . . . . . Chapter I. F’HFJF’HTJ OiU'lakle-J INTRODUGION I O O O O O O O O O O O O O O O O 0 Background . . . . . . . Objectives of the Study. . . . . An Extended Multiperiod Model. . Empirical Hypotheses . . . . . . Importance of the study . . . . Organization of the Dissertation II. LITERATURE REVIEW 2.1 Single Period Models . . . . . . . . . . . . . 2.2 2.3 2.4 1. Perfect Capital Market Models . . . 2. Static Trade-off Models and Bankruptcy Costs. 3. Agency Cost . . . . . . . . . . . . . . . . 4. Asymmetric Information. . . . . . . . . . . 5. Pecking Order . . . . . . . . . . . . . . . Treatment of Cash Flows in Bankruptcy . . . . Multiperiod Models . . . . . . . . . . . . . . Multiperiod Model of Barnea, Talmor and Haugen 1. Assumptions . . . . . . . . . . . . . . . . 2. Numerical Illustration. . . . . . . . . . . 3. Empirical Hypotheses. . . . . . . . . . . . III. A MULTIPERIOD 'DEBT AND TAXES' MODEL 3 3 3 3 1 2 3 4 Incorporating Risky Debt . . . . . Numerical Simulations . . . Incorporating Non-Debt Tax Shields Conclusions . . . . . . . . . . . vi Page ix xii xiii p oxooomUH-a 13 13 15 18 19 19 20 23 27 27 31 37 41 41 54 61 63 vii IV. THEORETICAL CONSIDERATIONS AND EMPIRICAL EVIDENCE 68 4.1 Operating Risk and Financial Leverage. . . . . . 68 4.2 Growth and Financial Leverage . . . . . . . . . 80 4.3 Time Series Behavior of Implied Marginal Tax Rates . . . . . . . . . . . . . . 86 V. RESEARCH METHODOLOGY AND PROXY VARIABLES 96 5.1 Methodology . . . . . . . . . . . . . 96 5.2 Hypothesis 1: Operating Risk and Financial Leverage . . . . . . . . . . . . . . 100 5.3 Empirical Proxies . . . . . . . . . . . . . . . 103 1. Financial Leverage. . . . . . . . . . . . . . 103 2. Operating Risk. . . . . . . . . . . . . . . 108 3. Implied Marginal Tax Rate . . . . . . . . . . 111 5.4 Growth and Financial Leverage . . . . . 114 1. Hypothesis 2: Operating Earnings-Value Ratio and Debt Ratio . . . . . . . . . . . . . . 114 2. Hypothesis 2a: Operating Earnings-Value Ratio and Interest Ratio. . . . . . . . . . . . . 116 3. Pooled and Cross-Sectional Tests. . . . . . . 117 4. Spurious Correlation. . . . . . . . . . . . . 117 5. Direct Tests. . . . . . . . . . . . . 121 5.5 Hypothesis 3: Time Series Behavior of Implied Marginal Tax Rates. . . . . . . . . . . . . 122 1. Dependent Variable. . . . . . . . . . . . . . 124 2. Independent Variable. . . . . . . . . . . . . 125 5.6 Expanded Model - Other Variables . . . . . . . . 128 1. Non-Debt Tax Shields. . . . . . . . . . . . . 128 2. Assets Composition. . . . . . . . . . . . . . 129 3. Firm Size . . . . . . . . . . . . . . . . . . 130 5.7 Sample . . . . . . . . . . . . . . . . . . . . . 130 5.8 Data Source . . . . . . . . . . . . . . . . . . 130 5.9 Time Period . . . . . . . . . . . . . . . . . . 131 VI. RESULTS OF EMPIRICAL TESTS 132 6.1 Hypothesis 1: Operating Risk and Financial Leverage . . . . . . . . . . . 132 6. 2 Hypothesis 2: Growth and Debt Ratio . . . . . . 144 1. Pooled Sample Tests . . . . . . . . . . . 144 2. Cross-sectional Tests of Hypothesis 2 . . . . 151 3. Direct Tests. . . . . . . . . . . . . . 157 6. 3 Hypothesis 2a: Growth and Interest Ratio . . . . 169 6. 4 Hypothesis 3: Time Series Behavior of Implied Marginal Tax Rates . . . . . . . . . . . . . 181 viii VII. SUMMARY AND CONCLUSIONS 197 7.1 Summary of Results of Theoretical Analysis . . 197 7.2 Summary of Results of Empirical Tests . . . . . 200 1. Operating Risk and Financial Leverage . . . . 200 2. Debt Ratio and Growth . . . . . . . . . . . . 201 3. Interest Ratio and Growth . . . . . . . . 202 4. Results of Tests of Expanded Model. . . . . . 203 5. Time Series Behavior of Implied Tax Rates . . 204 7.3 Conclusions . . . . . . . . . . . . . . . . . . 205 7.4 Suggestions for Future Research . . . . . . . 207 BI BLIOGMPHY O O O C O O O O C O O O O O O O O O O O O 2 o 9 APPENDIX I: Yield Series Used For Calculation of Implied Marginal Tax Rates . . . . . . . 220 APPENDIX II: Description of Business Cycle Indicators. 226 APPENDIX III: Business Cycles Indicators 1967-1985 . . 228 LIST OF TABLES Numerical Illustration of the BTH Model . . . . Firm Value for Different Levels of Debt . . . . Table Comparing Empirical Hypotheses from the BTH Model and the Extended Model. . . . . . List of Proxy Variables . . . . . . . . . . . . Formulas Used for Calculation of Ratios . . . . Results of Test of Hypothesis 1: Financial Leverage & Operating Risk . . . . . Results of Test of Hypothesis 1: Financial Leverage, Operating Risk, and Gamma Results of Test of Hypothesis 1: Expanded Model . . . . . . . . . . . . . . . . Results of Test of Hypothesis 2: Debt Ratio and Earnings Value Ratio: . . . . . Results of Test of Hypothesis 2: Debt Ratio and Growth in Firm Value:. . . . . . Results of Test of Hypothesis 2 - Expanded Model: Debt Ratio and Earnings-Value Ratio:. . Results of Test of Hypothesis 2-Expanded Model: Debt Ratio and Growth in Firm Value . . . . . . Results of Cross-Sectional Tests: Long-term Debt Ratio and Earnings-Value Ratio. Results of Cross-Sectional Tests: Total Debt Ratio and Earnings-Value Ratio . . Results of Cross-Sectional Tests: Long-term Debt Ratio and Value Growth . . . . . ix Page 33 34 98 133 134 136 138 141 146 147 149 150 153 154 155 6.2.10 6.2.11 6.2.12 6.2.13 6.2.14 6.2.15 6.2.16 6.2.17 6.2.18 X Results of Cross-Sectional Tests: Total Debt Ratio and Value Growth . . . . . . Results of Direct Tests of Hypothesis 2: Long-term Debt and Expected Income. . . . . . Results of Direct Tests of Hypothesis 2: Total Debt and Expected Income . . . . . . . Results of Direct Tests of Hypothesis 2: Long-term Debt and Expected Value . . . . . . Results of Direct Tests of Hypothesis 2: Total Debt and Expected Value . . . . . . . . Results of Test of Hypothesis 2a: Interest Ratio and Growth . . . . . . . . . . Results of Test of Hypothesis 2a - Expanded Model: Financial Leverage and Growth . . . . Results of Cross-Sectional Tests: Interest Ratio and Earnings-Value Ratio. . . . Results of Cross—Sectional Tests Interest Ratio and Value Growth . . . . . . . Results of Direct Tests of Hypothesis 2: Interest Expense and Expected Income. . . . . Results of Direct Tests of Hypothesis 2: Interest Expense and Expected Value . . . . . Results of Test of Hypothesis 3: GAMMA & XBUS Almon's Lag Scheme AR(l) . . . . . . . . . . Results of Test of Hypothesis 3: GAMMA & XDCEM Almon's Lag Scheme AR(1). . . . . . . . . . . Results of Test of Hypothesis 3: GAMMA & XDCEMXT Almon's Lag Scheme AR(1). . . . . . . . . . . Results of Test of Hypothesis 3: GAMMA & XDCOIN Almon's Lag Scheme AR(1). . . . . . . . . . . Results of Test of Hypothesis 3: GAMMA & XDLEAD Almon's Lag Scheme AR(1). . . . . . . . . . . Results of Test of Hypothesis 3: GAMMA & XDLEAP Almon's Lag Scheme AR(1). . . . . . . . . . . 156 161 163 165 167 171 173 174 175 177 179 183 184 185 186 187 188 6.3.10 6.3.11 6.3.12 6.3.13 Results Almon's Results Almon's Results Almon's Results Almon's Results Almon's Results of Test of Lag Scheme of Test of Lag Scheme of Test of Lag Scheme of Test of Lag Scheme of Test of Lag Scheme of Test of xi Hypothesis AR(1). . . Hypothesis AR(1). O O Hypothesis AR(1). . . Hypothesis AR(1). . . Hypothesis AR(1). . . Hypothesis OLS Regression Estimates. . . Results of Test of Hypothesis Yule-Walker Estimates . . . . 3: 3: 3: 3: 3: GAMMA & XDLEM GAMMA & XDLEMXG GAMMA & XINC GAMMA & XIPMFG GAMMA & XIPX 189 190 191 192 193 195 196 LIST OF FIGURES Figure 2.1 Capital Structure Theories . . . . . . . . Firm Value Against Total Debt Under the BTH Model. Value of Debt Shield Under the BTH Model . Two Period Model: Analytical Framework . . Model Comparison: BTH and Extended Model . Firm Value vs Debt Level For Different Interest Rates . . . . . . Firm Value vs Debt Level For Different Values of V1 . . . . . . . Firm Value vs Debt Level For Different Levels of Operating Risk - Low Interest Rates. Firm Value vs Debt Level For Different Levels of Operating Risk - High Interest Rates Relationship Between Operating Risk and Leverage Bond Market Equilibrium: Effects of Economic Expansion. . . . . . Value of Gamma and the Composite Index of 12 Leading Indicators . . . . . . . . xii Page 12 36 44 52 55 56 58 59 70 88 127 LIST OF APPENDICES Appendix Page I. Yield Series Used For Calculation of Implied Marginal Tax Rates . . . . . . . . . . . . 220 II. Description of Business Cycle Indicators . . . . . 226 III. Business Cycles Indicators 1967-1985 . . . . . . . 228 xiii INTRODUCTION 1.1 Background: Thirty years after the publication of the seminal paper by Modigliani and Miller [MM, 1958] the search for the optimal capital structure remainsl, in the words of Myers [1984], "as elusive as search for Truth or Wisdom." MM had first shown that in a perfect capital market a firm's financial decisions have no impact on it's value. Since then a persistent issue in the financial literature has been how far market imperfections materially alter MM's irrelevancy proposition and provide incentives for firms to issue securities in an optimal manner. One major source of imperfection in the capital market is the system of corporate and personal taxes. Under the current taxation system, deductibility of interest provides an incentive for firms to minimize their tax liability by issuing debt and, thereby, increasing 1 Testimony to the continuing debate are recent issues of Financial Management [Summer, 1989] and the Journal of Economic Perspectives [Fall, 1988]: see Durand [1989], Gordon [1989], Weston [1989], Miller [1988], Modigliani [1988] and Stiglitz {1988]. 2 cashflow available for distribution to the security holders. However, the tax code also provides for taxes on individual incomes, and gives a preferential treatment to returns on equity securities relative to debt securities by taxing capital gains only when realized. A firm attempting to minimize its tax liability by issuing more debt would increase the personal tax liability of its bond holders. Therefore, a firm seeking to maximize the combined value of its securities should attempt to minimize the net tax liability resulting from the interaction of personal and corporate taxes. Miller [1977] incorporated corporate and personal taxes in an equilibrium model for aggregate debt and showed that in equilibrium the tax advantage of debt at the corporate level is offset by tax disadvantage at the personal level and, thus, results in an indifferent financial policy at the firm level. Miller's model, however, is based on assumptions which are considered restrictive and unrealistic. There have been numerous studies which have attempted to generalize Miller's equilibrium by relaxing its restrictive assumptions, particularly its assumption that the corporate tax subsidy is riskless. When debt is risky the firms may not realize the full amount of the tax subsidy in some states of nature. In the DeAngelo and Masulis' [DM, 1980] model there exists an interior optimal capital structure and debt is issued until the marginal corporate tax subsidy equals the marginal tax disadvantage. 3 Other studies have sought to explain optimal leverage by off-setting the benefits of debt as a tax shield with the 'costs' associated with risky debt (e.g., Scott [1976,1977] and Kim [1978]). Besides the tax-subsidy bankruptcy-costs static trade-off models, efforts to explain cross-sectional capital structures have lead to the development of models based on assumptions of asymmetric information (Ross [1977]), agency problems (Jensen and Meckling [1976]), and 'pecking-order' financing behavior (Myers and Majluf [1984]). Other writers have emphasized the interaction between the investment and financial decisions (Hite [1977], Dammon and Senbet [1988]). The capital structure issue, however, remains largely a 'puzzle' in empirical work as well as in financial theory. Most of the early capital structure models were one period models. Others have relied on an assumption of perpetual cash flows to construct simple models from which generalizations have been made about the dynamics of the capital structure problem (e.g., Modigliani and Miller [1963], Miller [1977], DeAngelo and Masulis [1980], Kim [1978], Kraus and Litzenberger [1973]). This simplification remains valid when debt is taken to be perpetual and riskless. As Talmor, Haugen and Barnea [1985] point out, when debt is risky the equivalence between single period and multiperiod models breaks down since future cash flows are truncated in bankruptcy. Therefore, explicit multiperiod models are needed to analyze risky debt, carry-overs, and 4 interactions between real and financial decisions. Scott [1976, 1977] developed a multiperiod model of firm valuation when debt is risky and the secondary market for assets is imperfect implying a cost to bankruptcy. However, he assumed the same distribution of the operating cash flows for all periods and the major thrust of his paper was to show that issuance of secured debt can increase the total value of the firm. Ross [1985] examined the effects of uncertainty and progressive taxation in a multiperiod setting. His model utilizes a continuous time framework but essentially retains the limitations of a single period model, since payments to the security holders occur at the horizon date. Recently Barnea, Talmor and Haugen [BTH, 1987] have explicitly dealt with the issue of debt and taxes in a multiperiod context. BTH derive the various implications of introducing inter-temporal dependencies in the financial structure decision while staying close to the original Miller [1977] model. The BTH model also assumes an absence of non-debt tax shields and debt is default free in a special sense. It assumes that in the event that the firm's operating cash flow is not adequate to meet its debt obligations at the end of a period the firm's next period value is sufficiently large so that the shareholders find it worthwhile to meet the deficiency and avoid bankruptcy. Following this setup, in the event cash flow falls short of debt obligations the debt holders still get paid off and are 5 liable for personal taxes, but the firm loses the value of the corporate tax shield. This asymmetry in the tax effects produces a tradeoff between the expected benefits of the corporate tax shield and the personal tax liability of the debt holders with a possible optimal debt level. 1.2 Objectives Qf the Study: The main focus of this study is an examination of the capital structure choice in a world with personal and corporate taxes where firms can have risky debt as well as non-debt tax shields. We are interested in empirically testing the equilibrium implications of introducing inter- temporal dependencies in the firm's choice of capital structure. The two objectives of the present study are to: 1) build a multiperiod model of firm's capital structure choice with uncertain future cash flows allowing for the possibility of default on debt and the existence of non-debt tax shields; ii) Develop empirically testable hypotheses from such a model and conduct empirical tests of these hypotheses. In this dissertation we extend and generalize the work of BTH by introducing risky debt and allowing for firms to have non-debt tax shields such as depreciation. We then proceed to empirically test the hypotheses emerging from such a model. If the empirical testing fails to reject these 6 hypotheses then we would infer support for a theoretical explanation of capital structure based on tradeoffs of tax shields and costs. If the hypotheses are rejected then we would tend to conclude that the tax arguments may not be sufficient to explain cross-sectional differences in the firms' observed capital structures. 1.3 An Extended Multiperiod Model: In the BTH model operating cash flow can fall short of the debt obligations for the period. Debt is "riskless" in the sense that the firm's next period value (V1) is assumed to be always greater than any possible shortfall. Shareholders, therefore, find it in their interest to meet such shortfall by contributing fresh equity. Our extension of the BTH model shows that when the value of the firm at time t=1 is greater than the possible deficiency in meeting the debt obligation (debt is riskless in period one), an interior optimal is indicated as in the BTH model even when debt is risky in period two. In case V1 is not sufficiently high, our extension of the model shows that a corner solution with 100% debt may obtain instead. In this case existence of other imperfections such as bankruptcy costs may be necessary in order to indicate an interior optimum for most firms. It follows from our model that the higher growth firms would tend to have a lower financial leverage than non-growth firms or negative growth firms. 7 This implication of the extended model suggests that there would be a negative relationship between growth and financial leverage. This produces an hypothesis similar to the relationship between growth and financial leverage predicted by the BTH model. However, our result stems from a different form of the value function for growing companies and a different functional form for non-growing companies. In the BTH model, the ratio of interest expense to the expected cash flow is, however, not expected to be different for firms with different growth rates. Under the extended model the interest to operating cash flow ratio will be higher for non-growing firms. We may be able to empirically test for this difference in the relationship predicted by the BTH and the extended models. It is conceivable that the BTH constraint on the possible cash flow deficiency is operative for most firms in which case firms would tend to obtain an interior optimum. However, it remains to be seen whether empirical research supports the hypotheses derived by BTH. When we extend the model to include the presence of non- debt tax shields our model shows that the existence of non- debt tax shields is relevant to the debt policy in a multi- period context. Our results conform to DeAngelo and Masulis' [1980] prediction that firms with higher non-debt tax shields would tend to carry relatively less debt. ’1‘ '1 1.4 Empirical Hypotheses: Analysis following our generalized multiperiod capital structure model shows that as long as the marginal firm in the economy is a non-growing firm, the hypotheses derived by BTH with respect to cross-sectional debt ratios and bond market equilibrium should still be empirically observable. The following empirical hypotheses were derived by BTH: First, the relationship between a firm's level of operating risk and its degree of financial leverage can be positive or negative. Operating risk (or business risk is defined as the variance of operating cash flows. The direction of this relationship depends upon the difference between yields of taxable and non-taxable bonds. This yield differential has been regarded as an indicator of the tax rate faced by the marginal investor. In periods when such an implicit marginal tax rate is close to the statutory tax rate, firms with a higher degree of operating risk would be inclined to employ less debt. When the implicit marginal tax rate is low compared to the statutory rate the relationship between the operating risk and financial leverage is positive, i.e., risky firms employ larger amounts of debt. In finance theory both positive and negative relationships are predicted under different assumptions. Second, non-growth firms with high earnings to value ratios are predicted to employ greater amounts of debt relative to the firm value than growth firms. Our model suggests that the interest ratios for non-growth firms are 9 also likely to be relatively higher than for growth firms. Similar predictions are derived from models based on the existence of growth opportunities (Myers [1977]) and asymmetry in information (Ross [1977]). Third, the implicit marginal tax rate would follow a cycle lagging the economic cycle, increasing with an improving economy when the supply of corporate debt is higher but investors' demand is lower, and decreasing in a recessionary economy when bond market conditions reverse. Another explanation of varying marginal tax rates is based on the institutional arbitrage argument (Fama [1977]). 1.5 Importanee e: the study: The study will contribute towards our understanding of the role of taxes in the determination of the optimal capital structure. Past empirical studies have failed to provide clear evidence that taxes impact debt policy in a systematic manner. One explanation of a lack of evidence is provided by the models which explicitly take into account the interdependence between debt levels and expected future cash flows. The multiperiod treatment of the capital structure issue leads to conclusions that are quite different from those derived in earlier single-period models. The multiperiod line of inquiry may also help to explain why most of the empirical studies fail to reject the irrelevancy proposition in cross-sectional studies. The hypotheses emerging from the BTH model and our extended 10 models have important implications for the characteristics of debt market equilibrium and for the financial policies of firms cross-sectionally as well as over time which are different from those following both from single period models and from competing theories of capital structure. The empirical hypotheses following from the multiperiod models have not been tested before and it is important to test such a model empirically. 1.6 Organizatien e; the Dissertation: Chapter 2 reviews the relevant theoretical literature and develops some related issues. Chapter 3 develops a multiperiod model of capital structure by incorporating risky debt and non-debt tax shields. It is shown that the conclusions of the BTH model are not valid for non-growing companies. Chapter 4 examines the empirical hypotheses from the BTH model and relates these to alternative capital structure theories. A literature survey of the relevant existing empirical evidence is also provided. Chapter 5 develops empirically testable hypotheses from the extended model and examines various proxies to be used in the empirical testing. Chapter 6 summarizes the empirical results and the final Chapter 7, presents a summary and conclusion of the study with suggestions for_future research. CHAPTER II LITERATURE REVIEW The literature on theories of capital structure is extensive. We may categorize these theories into two groups: (1) theories predicting irrelevance of capital structure for maximization of firm's value and (ii) theories showing its relevance to the firm's value. The first group of theories relies on an assumption of perfect capital markets while the second group relies on the presence of various imperfections in the capital markets. We present in Figure 2.1 a schematic overview of the development of various theoretical papers in the evolution of capital structure theories and briefly discuss each line of theoretical development in section 1. Models discussed first are largely single period models. A particular problem relating to these models relates to the treatment of the distribution of cash flows in bankruptcy. This is discussed in section 2. Section 3 describes multi- period models and section 4 explains the BTH model in detail. 11 IRRELEVNCY . m G WITH. m I ' I I per-rectum] IsmicTI-utOffHIdtlumfinkmtI r l l I I III/IO! W I I 1 r J l I I l | I r ‘ l I | No Taxes | I |Modigtiani a. | . l [Miller 1958 | | l J - r I I F I l | In: Shield | Ll Maggy Costs | . IModigliaIi & | |Baxter 1%? | , {Miller Correctiml IKras 8. Litml I . um I H1975. I | . l J | |Kim1978 | r ‘ l - I ‘ 1 ' I m l - I I INemI-al Matias] . I r———‘——-. |Miller 1977 I - I IN! I I I . I | Scott 1976 | I . I l_______.l l I I I I r ' r I - I MEL—‘3 I } {Mule 8r Haulisl I - I‘m l | |TBH 1% I | l J I | . | . I - r l I - | WI L 1' BTH 1%? | . | Z 8. s 1%? | . | Lads 1% | . | Sd'rerr 1%? | I r-—"—'I - l'"'——l | Wei | . | We | | muiu| . | [Nu-timl I__.I.__l , I__r__I l - I I . I l - l I . I I l j ' I Imam I - I |ooretdccn1961| . | |__.'_.__J . I I - I I - I I I I l | I l - | I - | I I l 1 fl r—J—I | MS I - tum! IJa'ea'Illhcklirul . |Ross1976| | 1976 | . gj—J l I J . | I - I r ' 1 - | IWI . l | Wities | . | I "1831977 I I I F l . I r ' I - I IN I - I |muujlur§ . | 198‘ I - Fim 2.1 : Flow of “martial Daelqmmt l l 13 2.1 §ingle-period Models: 2.1.1 Perfect Capital Market Models: Modigliani and Miller [1958] showed that given unfettered arbitrage opportunities, no bankruptcy possibilities, and no corporate taxes, the total market value of the firm is unaffected by the amount of debt issued. The Modigliani- Miller [1963] 'correction', which assumed that (a) equity returns were taxed at the same rate as personal interest income, and (b) the tax savings from the use of debt could be regarded as a perpetual riskless flow, arrived at the conclusion that debt should add to the value of the firm by a fractional multiple equal to the corporate tax rate. The debate over the optimal capital structure was, therefore, intensified since their analysis resulted in a corner solution with 100% debt, which is counter to both observed leverage levels and common sense. Indeed, even Modigliani and Miller recognized that a number of considerations outside their model would make such a corner solution unacceptable. In order to illustrate the main features of the capital structure theories based on the role of taxation, it is helpful here to construct a simple model. We use the following definitions: V1 5 value of a levered firm Vu 8 value of an unlevered firm D 5 value of debt r a return on debt before personal tax 14 X a cash flow from operations before tax Tc 5 corporate tax rate prE personal tax rate on interest income Ipss personal tax rate on equity income Then the total cash flows to the security holders (TCF) can be expressed as: TCF = (X - rD)(1-1c)(l-Tps) + rD(1-1pb) (2.1) The first product denotes after-tax cash flow to the shareholders and the second denotes after-tax cash flow to the bondholders. Simplifying: TCF = X(1-1C)(1-1ps) + rD[(1-1pb) - (l-Tc)(l-Tps)] (2.2) Discounting the first term by the cost of capital for an unlevered firm and the second by the after-tax cost of debt we obtain: V1 = Vu + D[1 - (l-Ic)(1-1ps)/(1-1pb)] (2.3) In a world without taxes the second term, value of debt tax shield, is zero as in MM [1958]. MM [1963] consider the effect of corporate taxes but ignore differences in personal tax rates i.e., Tps=7pb° Under these conditions, the equation reduces to V1=Vu + 1CD. Here, the value of the tax- shield is always positive leading to a 100% debt solution. In Miller's [1977] model, individual investors face a constant personal tax rate but different investors have different tax rates. This progressivity in personal taxes gives an upward sloping demand curve for debt, as before-tax interest rates on corporate debt have to be higher and 15 higher in order to induce investors in higher tax brackets to hold more and more bonds and realize the same after-tax returns. As the before-tax interest rate increases with larger amounts of debt, the advantage to the firm disappears in equilibrium at which point (l-Tc)(1-Tps)=(1-pr). Assuming Tps=0, for simplification, in equilibrium 7c=7pb and firms are indifferent as to their capital structure. 2.1.2 t t' rade- f od d os 5° Research focusing on the supply-side of debt analyze the adverse effects of leverage in a number of ways. Firstly, dead-weight costs associated with bankruptcy and reorganization were introduced as major avenues of investigation. Following this line, Baxter [1967], Bierman and Thomas [1972], Kraus and Litzenberger [1973], and Robichek and Myers [1966] have argued that debt policy can be relevant and an interior optimal capital structure can exist. Scott [1976,1977] analyzed the question of capital structure when debt is secured. His line of analysis is important because he shows that even in the absence of taxes the issuance of secured debt can enhance the total value of a firm. He assumes, however, that the value of the firm's assets in bankruptcy is less than their value in use. For this conclusion he has to assume an imperfect market for assets which amounts to introducing bankruptcy costs in another form. Smith and Warner [1979] argue that Scott's 16 results depend critically on the assumption that the firm's customers and unsecured creditors would not adjust their behavior to reflect the firm's current level of secured debt. They point out that secured debt can reduce the administrative and enforcement costs to the creditors. Scott [1979] further remarks that the timing of such an adjustment on the part of the unsecured creditors would be crucial. Kim [1978] developed the bankruptcy model further by incorporating it into a rigorous mean-variance framework. Turnbull [1979] developed an option model and showed that, in the presence of bankruptcy costs, the market value of debt as promised interest payments are increased reaches a maximum and then declines. The maximum value of the debt is termed the debt capacity. The firm's optimal capital structure always occurs before its debt capacity. Connected with this bankruptcy cost argument is the controversial issue about whether or not the bankruptcy process has any significant costs. Miller [1977] argues that the expected bankruptcy costs are relatively insignificant compared to the tax effects, hence the "rabbit and horse stew" parallel. Haugen and Senbet [1978] argue that these costs are related to the decision to liquidate and are independent of the event of bankruptcy. Warner [1977] showed that the direct costs associated with bankruptcy are relatively small and decrease with firm size though there is doubt as to how far his results can be generalized. Altman [1984] reported that the direct plus the indirect costs of 17 bankruptcy are substantial for large industrial firms. Masulis [1988] concludes that "this evidence is inconsistent with Miller's irrelevance theory, which assumes that these costs are insignificant." Another line of theory first developed by Brennen and Schwartz [1978] rests on the increasing probability of loss of tax shields as debt is increased. The theory was further developed by DeAngelo and Masulis [DM, 1980] by taking into account other non-debt related items, like depreciation and tax credits, which may also serve to shelter income from taxes. DM [1980] show that, with the presence of non-debt tax shields together with an asymmetric taxation system which does not rebate losses, the MM irrelevancy proposition is overturned. Their model predicts a negative relationship between the amount of non-debt tax shield and financial leverage. Dotan and Ravid [1985] endogenize the capital structure and production decisions of the firm incorporating bankruptcy costs and corporate but not personal taxes in their model. They keep the level of output fixed and find that the optimal investment level and depreciation tax shield are negatively related to the level of debt, supporting the prediction of DM [1980]. Dammon and Senbet [1988] extend the work of Bite [1977] and DM [1980] and analyze the effect of corporate and personal taxes on the firm's optimal investment and financing decision under uncertainty. Hite [1977] had 18 extended the MM [1963] model by taking into account the effect of leverage on the firm's optimal production decision. In his model an increase in a firm's leverage reduces the 'user cost of capital' leading to an increase in the optimal output of the firm. Dammon and Senbet [1988], by incorporating investment decision in their model, show that the optimal level of non—debt tax shields is determined endogenously allowing for an "income effect" on the level of debt-shield, compared to the "substitution effect" as in DM [1980]. They conclude that the net effect of higher investment-related tax shields on leverage could be positive or negative in cross-sectional comparisons depending upon the production technology. 2.1.3 Aggggy QQSE: A second avenue of research focuses on the agency costs resulting from the divergent interests of owners, creditors and management. The resulting costs of enforcing and monitoring agreements needed to protect the creditors prescribe an optimal level of debt where the agency costs are minimized.(see Jensen and Meckling [1976], Chen and Kim [1979]). Myers [1977] points out the possibilities of foregoing valuable opportunities when debt levels become high. He utilizes the composition of assets for a rationale for a trade-off between the cost and benefits of debt. Hypothesizing that a firm can be viewed as owning 'assets in place' and 'growth opportunities', Myers showed that issuing 19 risky debt can induce a firm to take suboptimal investment decisions and, hence, reduce its market value. 2.1.4 Asymmetric Information; Thirdly, another line of research focuses on the asymmetry of information and managerial incentives and has been advanced by Ross [1977] who suggests that changes in capital structure could be used to alter the market's perception of the firm's future returns stream. Managers having superior information about the firm's expected cash flows will convey unambiguous signals to the market provided they have proper incentives to do so. The managers choose real variables, such as capital structure changes or dividend policy, to signal since these signals can not be falsely mimicked by other firms. Leland and Pyle [1977] argue that equity investment by entrepreneurs conveys information about the future prospects to the market since it is in the owners' interest to invest a greater fraction of his or her wealth in a successful project. 2-1-5 EQQBiDQ_QIQ§£L Finally, a different perspective on the capital structure is given by the observed behavior of managers, first noted by Donaldson [1961], who appear to prefer using internal equity to issuing external equity and issuing debt rather than equity. The proponents of 'managerial capitalism' explain this 'pecking order' behavior by pointing to the 20 agency relationship between managers and owners of the firm. According to this theory managers avoid using external financing because doing so would subject them to the discipline of the market. Another explanation of the 'pecking-order' behavior is offered by Myers and Majluf [1984] who have shown that asymmetry of information between management and investors can lead to firms foregoing investment opportunities when forced to seek external financing. Managers would tend to offer securities when the market overprices these securities based on the superior information of managers. Since the market is aware of this tendency, it places a higher risk premium on new offerings. Myers and Majluf's conclusion is driven by an underpricing of securities by the market rather than a trade-off of tax shields and bankruptcy costs. 2.2. Treatment of Cash Flows in Bankruptcy: The effect of debt on the market value of the levered firm has been studied in the financial literature by formulating a tax subsidy function that shows the effect of debt on the expected tax savings at the corporate level. An assumption usually made in these studies is that both principal and interest are tax deductible. This assumption produces the same value of the tax shield in a single period framework as the one produced when debt is perpetual and riskless. DeAngelo and Masulis [1980] worked with this assumption and showed that, in the presence of non-debt 21 related tax shields, the probability of redundancy of tax shields increases with higher levels of risky debt and thereby generates an interior optimal capital structure. Talmor, Haugen and Barnea (THB) [1985], have suggested that the principal deductibility assumption is weak on two grounds. Firstly, consideration of non-debt tax shields such as depreciation simultaneously with the deductibility of principal is inconsistent under income tax as well as wealth tax systems. Secondly, in the case of risky debt, future cash flows are terminated in the event of bankruptcy. Therefore, deduction of principal in the single period framework is no longer equivalent to deduction of interest in perpetuity. TBH proceed to analyze the tax subsidy function under the assumption that only interest is deductible. In the event of bankruptcy, partial payments to bondholders are treated as a return of principal first (the 'principal first' doctrine) and payments over the principal are considered deductible for the firm. The amount of principal is determined to be the market value of the debt at the time of issue. Their analysis indicates that the marginal value of the tax subsidy increases with the increase in the amount of debt. The intuitive explanation for their result is that as debt levels increase the amount of promised payments to the bondholders must increase relative to the initial market value to compensate for the increased riskiness of the debt. As a result, the expected cash flows to the owners increase 22 with higher expected amounts of interest deduction. This effect dominates the reduction in the value of expected cash flows as the probability of default increases. The net effect is to produce a tax subsidy function which not only is generally positively sloped but has an increasing slope at the margin. Following their analysis, there is no optimal capital structure at the firm level and a firm would adopt a corner solution depending upon the firm-specific values of the available non-debt tax shields. The exact shape of the function is, however, not determinable analytically and the authors have resorted to numerical simulation to arrive at their conclusion. Though the 'principal first' doctrine assumed by Talmor et al. [1985] conforms to the US tax code, Park and Williams [1985] have argued that the actual pattern of payments in bankruptcy may be closer to an 'interest first' doctrine in which partial payments in bankruptcy are treated as interest first. Interest payments are made semi-annually and part of the annual interest claim effectively precedes the repayment of principal. Also, in the case of secured debt, interest payments to secured debt holders precede the repayment of principal to the unsecured debt holders. Lewis [1986] argues that in the event of bankruptcy the current bankruptcy law allows for either reorganization (Chapter 11) or liquidation (Chapter 7). In liquidation the 'principal first' doctrine holds but in reorganization the firm is permitted a degree of flexibility in allocating bond 23 payments between accrued interest and principal. He shows that the availability of this "interest option" produces the same qualitative features as the 'interest first' doctrine. Proceeding on similar lines to TBH, Zechner and Swoboda [1987] analyze the capital structure issue under both the 'principal first' and 'interest first' doctrines regarding the priority of partial payments in bankruptcy. Whereas Talmor et al. [1985] work directly with the shape of the tax subsidy function, Zechner and Swoboda focus on the implicit tax rate that makes a firm marginally indifferent between debt and equity when debt-related tax savings are uncertain. They conclude that higher non-debt—related tax shields tend to decrease the optimal amount of debt only under the 'interest first' doctrine. However, under the 'principal first' doctrine, they may have a decreasing or increasing effect on leverage. Under both doctrines, pure tax arguments do not produce interior optimal structures for all firms. 2.3 u t'- o o e ° Most of the analytical models of bond market equilibrium and capital structure are single period models (e.g., Modigliani and Miller [1963], Miller [1977], DeAngelo and Masulis [1980], Kim [1978], Kraus and Litzenberger [1973]). When debt is taken to be perpetual and riskless the conclusions of the single period models can be generalized to a multi-period setting. For risky debt the equivalence between single period and multi-period models breaks down 24 since future cash flows are truncated in bankruptcy. One particular feature of the multi-period models, for example, is that in a single-period model bankruptcy occurs when the firm's cash flows are less than their debt obligations. In a multi-period model it is possible for the firm to remain solvent even though the firm's current cash flow may be less than its debt obligations. If the value of shareholders' claims to the future cash flows are more than the deficiency in meeting the current obligation, rational shareholders will avoid bankruptcy by raising more equity or borrowing more debt to meet their obligation to the debt holders. Therefore, explicit multi-period models are needed to analyze risky debt, carry-overs, and interactions between real and financial decisions. Inter-temporal dependencies in financial decisions arise in Barnea, Talmor and Haugen's [1987] model as the optimal level of debt becomes dependent on future cash flows. Multi-period models of capital structure have to address the issue of how a firm meets losses. Scott [1981] makes a distinction between "gambler's ruin models" (e.g., Wilcox [1976]) and perfect access models (e.g., Scott [1976] or Barnea et a1. [1987]). The former type of model assumes that a firm meets losses by selling assets, and the 'ultimate' bankruptcy depends upon the liquidation value of the shareholder's equity. The latter type of model assumes that the firm can also sell debt and/or equity in an efficient, frictionless securities market. 25 In Scott's [1976,1977] models a firm has a potentially infinite life and meets losses by selling new equity. It remains solvent as long as stockholder's wealth, in terms of market value, remains positive. Scott [1981] developed a model for determining bankruptcy probabilities assuming perfect as well as imperfect access to the capital markets. However, his main concern was to relate theoretical predictors of bankruptcy with the predictors found significant in empirical research. Flath and Knoeber [1980] construct measures of the tax advantage and cost of failure for 38 major industries and relate these variables to cross-sectional and temporal variations in industry capital structure. In their model, default implies a "failure" and encompasses a range of possible settlements between insolvent firms and their creditors. However, the firm never liquidates and default, while costly, does not lead to liquidation of assets and termination of the earnings stream. Their empirical results suggest that failure costs are substantial and are correlated with the size of the firm. other researchers have constructed explicit multi-period models to analyze the interaction between financing and investment decisions (e.g., Cooper and Frank [1983] ). Green and Talmor [1985,1986] employ a muliperiod model to analyze the effects of asymmetries in taxation on the overall scale and nature of investment. In their 1985 paper they show that asymmetry in taxes makes the tax liabilities of a firm 26 similar to a short position in a call option. Thus the firm has incentives to under-invest in risky projects and to engage in conglomerate mergers. Their 1986 paper relates the scale of firms' investments to the type of tax deductions. When the deductions are related to the level of investment (such as depreciation) the optimal investment decreases. When deductions are debt-related (interest) the reverse is true. This produces the same kind of conflict between bondholders and stockholders as noted by Myers [1977]. Scherr [1987] developed a multi-period model and allowed for the firm's cash flows to fluctuate over time and for the firm to issue new debt. He assumed two types of bankruptcy costs depending upon the outcome of negotiations between the firm and its creditors. If the negotiations with creditors are successful the firm continues but the resulting agency cost is borne by the shareholders. He prices risk using Sharpe-Lintner's Capital Asset Pricing Model and his simulation results are consistent with the CAPM and the tax- shield bankruptcy-cost hypothesis. Lewis [1986] examined capital structure and debt maturity structure in a multi-period model considering corporate as well as personal taxes as market imperfections. His model results in an interior capital structure solution. The capital structure decision is relevant but the debt maturity structure decision is not relevant. Capital structure becomes relevant due to the interaction of the uncertain corporate tax subsidy and the personal tax disadvantage. 27 Optimal capital structure, however, does not imply a unique debt/asset ratio since there exists a set of debt/asset ratios that are consistent with firm value maximization. Irrelevancy of debt maturity structure appears since aggregate interest expenses are tax deductible and it does not matter whether interest deductions are generated by short-term or by long-term debt. 2.4 Multi-period Model 9f Barneal Talmor and Haugen: 2.4.1 Assumptions: Barnea, Talmor and Haugen [1987] examine corporate debt policy and bond market equilibrium in a multi-period context by looking at differential utilization of debt over time as a (costly) tax shelter. In their model the current level of debt is a function of the (optimal) level of debt in each future period via the tax-sheltering property of the tax expenses. The analysis is conducted within the original Miller [1977] equilibrium framework assuming in particular absence of transaction costs of changing capital structure, no non-debt tax shields, risk neutral investors,and riskless corporate debt. They assume an imperfect market for tax shelters in the sense that redundant interest deductions can not be traded or deferred to the next period. Debt is risk- less in the sense that any shortfall of cash flow in one period is financed by the original shareholders, which implies that the next periods' firm value is greater than the maximum shortfall of cash flow from the contractual 28 payments under the debt covenant. The authors initially construct their model in a single period context and introduce a second period to demonstrate the effect on the firm value and debt policy. The model is then generalized to a multi-period framework. In the one- period case the authors arrive at the following relationship: v1 = v1“ + D1 [r0 - (1-6)r]/(1+r0) (2.4) Where: Vt = value of firm at time t Vt“ = value of an otherwise identical unlevered firm Dt = value of debt issued at time t 6 = corporate tax rate r0 = risk-free rate of return on tax exempt securities r = risk-free (taxable) interest rate on corporate bonds. In a one-period setting the expression gives the same results as in Miller [1977] where in equilibrium r = ro/(l-e), so that the firm is indifferent as to its capital structure. This capital structure irrelevance disappears when a second period is introduced. The authors treat the debt as riskless over the entire life of the debt. At the end of the first period Operating earnings may not be adequate to cover interest charges. The firm's value at the end of the first period is assumed to be greater than the shortfall in the first year's cash flows and the shareholders are assumed to be willing to provide the difference by raising fresh equity. 29 In a two-period setting the value of the firm is shown to be: v0 = v0u + Do [r0 - r(1 - 62)]/(l+ro) (2.5) Here, 2 is the expected proportion of the interest tax shield used. As more debt is issued the marginal value of the expected tax shield diminishes. Now the value of 2 would depend upon the cash flow distribution specific to each firm, since Z is firm-specific, implying an optimal debt level for each individual firm. It is then shown that at optimality : 1 - (1+ro) F(a*) = (r - r0)/6r (2.6) Here a = rDt is the interest payment on debt and F(a*) is the cumulative distribution function at Xt = a adjusted for the time value of money. The optimality condition requires that the certainty equivalent probability that the interest payment on the marginal unit of debt will serve as a non-redundant tax deduction (left side of optimality condition) be equal to the fraction of the corporate tax that is reflected in the equilibrium differential rate on corporate debt (right side of the optimality condition). Equilibrium in the bond market is arrived at in the following manner. The demand curve for bonds is upward sloping due to the assumption that individuals' interest income is taxed proportionately at different rates. The supply curve is now downward sloping instead of horizontal as in Miller [1977]. The firms will supply no debt when r> rO/(l-e) , but firms are exclusively debt financed when 30 r <= r0 . Between these two extremes the supply of debt is monotonically decreasing in r. The bond market equilibrium has the following characteristics: a) An interior optimal capital structure exists for most of the firms. This is due to the tax asymmetry in the treatment of interest payments. When operating income does not Cover interest, the debt shield is irretrievably lost at the corporate level but interest is still paid by the investors since the shortfall was met by the shareholders. b) The optimal level of debt depends upon the distribution of future periods' cash flows. This implies that otherwise similar firms may have different levels of financial leverage depending upon their future cash flow distributions. c) It is optimal for firms to issue sufficient debt to make the generated tax shelters risky. d) Firms earn a financier's surplus on all units of debt issued prior to the marginal unit. e) It may be possible to generate financial synergies by merging two firms if the combined variance of their operating cash flows decreases after merger. 31 2.4.2 Numerical Illustration: In order to convey a better understanding of how the BTH model can result in an interior solution we present a numerical illustration. In the BTH model, debt is riskless as shareholders are assumed to meet any deficiency in the operating cash flows based on next period's value. There are, however, states where the firm can not deduct interest payments in full and consequently loses the debt tax shield. In these states the bondholders are still subject to personal taxes. Here, the value of the debt tax shield consists of two components, (see endnote 1): debt tax shield = rD[6 - ¢].k - 6.Ea(rD - x) (2.7) The first expression represents the value of the debt tax shield when default does not occur. The second expression represents the value of expected loss of the debt tax shields in states where operating income (X) does not cover the interest charges (rD). Firms gain in value by issuing debt as long as the corporate tax rate is higher than the implied personal tax rate i.e., e>¢. However, with an increase in the probability of default the expected value of loss of the debt tax shield reduces the net value of the debt tax shield. We illustrate how the BTH model can result in an interior solution to the capital structure problem with an example. We consider three cases with debt levels 200, 400, and 600, respectively. The required return on debt is ten percent for 32 all three cases. Operating cash flow (X) can take three values (20, 40 and 60) with equal probability. The values assumed for other variables used in the illustration are described in Table 2.1. For the debt level of 200 (case 2), the operating cash flows are always greater than the interest charges. Here the value of the debt tax shield is 3.74 and expected loss of the debt tax shield is zero. This, along with the value of the unlevered firm of 953.27, gives a total value of 957.01. When the debt level is raised to 400, there is 1/3 probability of loss of the debt tax shield results in an expected loss of 3.12 which reduces the 'gross' value of the debt shield yet gives a higher firm value of 957.63. A debt level of 600 (Case 3) results in a lower total value than with debt of 400. Hence, firm value is maximized at debt=400. Table 2.2 illustrates the effect of successively higher debt levels on the 'gross debt tax shield', the expected loss of the debt tax shield and the total value of the firm. In this example, the firm obtains a maximum value when debt = 400. Figures 2.2 and 2.3 convey the same relationship showing firm value at various debt levels. 33 Table 2.1 Nume ica lust at'on o T ode PARAMETERS Tax-free interest rate (r0) - 0.07 Corporate tax rate - 0.5 Taxable interest rate (r) - 0.10 t1 Firm Value (V1) - 1000 X Prob X*p(x) Tax CFd CFs CFs*p Ba(1-x/a) 20 0.33 6.67 0 220 800 266.67 0.0000 40 0.33 13.33 10 220 810 270.00 0.0000 60 0.33 20.00 20 220 820 273.33 0.0000 1.00 40.00 810.00 0.0000 Value of Stock: 757.01 Value of Unlevered Firm - 953.27 Value of Debt: 200.00 Corporate Debt Advantage = 3.74 Total Value 957.01 Personal Tax Disadvantage= 0.00 Net Debt Shield 3.74 Value of Levered Firm 957 01 X Prob X*p(x) Tax CFd CFs CFs*p £a(1-x/a) 20 0.33 6.67 0 440 580 193.33 0.1558 40 0.33 13.33 0 440 600 200.00 0.0000 60 0.33 20.00 10 440 610 203.33 0.0000 1.00 40.00 596.67 0 1558 Value of Stock: $57.63 Value of Unlevered Firm 8 953.27 Value of Debt: 400.00 Corporate Debt Advantage: 7.48 Total Value 957.63 Personal Tax Disadvantage -3.12 Net Debt Shield 4.36 Value of Levered Firm 957.63 0 3 e 3 X Prob X*p(x) Tax CFd CFs CFs*p Ea(1-x/a) 20 0.33 6.67 0 660 360 120.00 0.2077 40 0.33 13.33 0 660 380 126.67 0.1010 60 0.33 20.00 0 660 400 133.33 0.0000 1.00 40.00 380.00 0.3087 Value of Stock: 355.14 Value of Unlevered Firm - 953.27 Value of Debt: 600.00 Corporate Debt Advantage- 11.21 Total Value 955.14 Personal Tax Disadvantage —9.26 Net Debt Shield Value of Levered Firm 34 Table 2.2 'rm Valu Fo if e vels Of lilustration of the 513 Mode; Debt Firm Corporate Personal Net Debt Vu + Net Level Value Debt Shield Taxes Shield Debt Shield 0 953.27 0.00 0.00 0.00 953.27 100 955.14 1.87 0.00 1.87 955.14 200 957.01 3.74 0.00 3.74 957.01 300 957.32 5.61 1.56 4.05 957.32 400 957.63 7.48 3.12 4.36 957.63 500 956.39 9.35 6.23 3.12 956.39 600 955.14 11.21 9.35 1.87 955.14 700 952.34 13.08 14.02 -0.93 952.34 800 949.53 14.95 18.69 -3.74 949.53 900 946.73 16.82 23.36 -6.54 946.73 TOTAL VALUE 958 35 FIRM VALUE AGAINST TOTAL DEBT UNDER THE BTHIKIIfl. 857 - 856 — 955 J S46 I I 200 400 600 800 TOTAL DEBT Figure 2.2 'rm V ue ainst ota Under the BTH Model ADDED VALUE 36 VALUE OF DEBT TAX SHIELD UNDER TEE BTH MODEL -4 _ -5 _ > '8 T I T I I I I T 0 200 400 600 800 TOTAL DEBT Corp 05 + Personal Tax Disadv 0 Net 05 Figure 2-3 W de e H od 1 37 2.4.3 Empirical Hypotheses: Three hypotheses with empirical significance follow from the equilibrium conditions given by the BTH model: 1) Operating Risk and Eipapcial Leverage: The relationship between a firm's level of operating risk and its degree of financial leverage depends upon the ratio of the marginal tax rate implicit in the price differential between taxable and non-taxable bonds and the statutory tax rate. In periods when the implicit marginal tax rate is close to the statutory rate, firms with higher degrees of operating risk are inclined to employ less debt. When the implicit marginal tax rate is low compared to the statutory rate the relationship between the operating risk and financial leverage is positive, i.e., risky firms employ larger amounts of debt. In the capital structure literature both positive and negative relationships have been predicted under different assumptions. 2) Earnings-Vaiue Ratio and Financiai Lgvgrage: Non- growth firms with high earnings to value ratios are predicted to employ greater amounts of debt than growth firms. Similar predictions are arrived at from models based on different assumptions (e.g., Myers [1977] and Ross [1977]). 38 3) Time Ser' s e vior o l'c' Ma ax R es: The implicit marginal tax rate follows a cycle lagging the economic cycle, increasing with an improving economy and vice versa. Another explanation of varying marginal tax rates is based on an institutional arbitrage argument (Fama [1977]). These hypotheses are examined in detail in Chapter 4 along with competing theories of capital structure. Barnea, Talmor and Haugen then proceed to develop an explicit multi-period model in order to explore the inter— temporal nature of the capital structure decision and to bring out the effects of time variability in cash flows. They consider two cases. First, they assume that the periodic operating earnings are independently distributed and follow a uniform distribution. They next develop a closed form valuation expression for the case of certainty. The main conclusion from the multi-period valuation formulation assuming a uniform distribution is that the market value of each periodic cash flow depends upon the expected magnitudes of the subsequent cash flows via their ability to shelter taxable profits. Thus the current leverage ratios (Do/V0) may not reflect the value of the tax subsidy as the tax savings associated with future debt utilizations would depend upon time variability in the expected earnings. Hence, leverage measures may not accurately represent the tax effect of debt financing throughout the life of the firm. Cross-sectional studies of 39 financial leverage and firm values would ,therefore, be potentially biased. The next chapter extends the theoretical model by allowing for risky debt and for non-debt (e.g., depreciation) tax shields. The empirical hypothesis are discussed in detail in chapter 4. n We use ro k 40 o e to C te : the same notation as employed by BTH: = risk-free rate of return on tax exempt securities. 1/(1+ro)= one-period discount factor. interest rate on corporate bonds (taxable). state-contingent operating cash flow at time t, t=l,2. the value of debt issued at t. the value of common stock at t. = the value at time t of net cash flows generated by the firm at time t+1 and beyond. = personal tax rate on interest income, such that r0 = r(1-¢): or ¢ = 1-ro/r. Let rDt = a, and Ea(.) = one period certainty-equivalent operator ranging from 'a' to the upper limit of Xt [a superscript_denotes an upper limit]. Then, CF 5 X1 - 6(X1- rDo) - (1+r)Do : X > rD X1 - (l+r)DO ; X < rD and CFd = (1+r)Do - ¢rDo in all states. The total value of the equity and debt is: V = - - a - - Ea[X1 9(x1roo) (1+r)Do] + E [xi(1+r)no] + ”0 + v1 - a- E(1 e)x1+ 6E x + EaerDo+ k[rO-r]Do + v 1 1 vu + E[6rD 1 + k[r -r]D - Ea[9rD 1 + 933x 0 o o o o 1 u o a - v + rno[e -(1 ro/r)].k - 9E [roo- x 1} u a ' , . _ _ VO + rDo[e o].k 6E [rD0 X1] , Since ¢ — 1 ro/r CHAPTER III A.MULEIPERIOD 'DEBT AND TAXES' MODEL In this chapter we generalize the BTH model by extending it to situations where debt is risky and where firms also have non-debt tax shields (depreciation). 3.1 Incorporating Risky ert: First, we extend the multiperiod BTH model to incorporate risky debt. The analysis is conducted within the framework of their original two—period model staying as close to their assumptions as possible. These assumptions include : l. The investment decision of the firm is predetermined and the firm generates periodic stochastic cash flows with a specified distribution. 2. All debt is of a pure discount variety with one period until maturity. 3. Redundant interest deductions cannot be traded and tax losses cannot be carried forward. 4. There are no debt-related (agency or bankruptcy) costs and no non-debt-related tax shields (e.g., depreciation) exist. 41 42 Each period all net income is paid out to the shareholders. If cash flow at the end of a period is insufficient to cover the debt payments, the original shareholders have the option of supplying the cash shortfall in order to keep the firm operating for an additional period. Corporate tax rate (6) is constant. Individual interest income is taxed proportionately at different rates. The highest personal tax rate exceeds 9. Interest (but not the principal) payments on debt are taxable at the individual level and deductible at the corporate level. Following the 'interest first' doctrine, in bankruptcy partial payments to bond holders are treated as interest for tax purposes. Income from equity securities is tax exempt. Capital markets are complete and spanned, and tax arbitrage (e.g., in Miller and Scholes [1978]) is not allowed. 8. We utilize the state preference framework and assume We use 1‘0 r = risk neutrality. the same notation as employed by BTH: risk-free rate of return on tax exempt securities. 1/(1+ro)= one-period risk-free (tax exempt) discount factor. interest rate on corporate bonds (taxable). Xt(¢t)= state-contingent operating cash flow at time t(t=1,2) over the states ¢t° 43 fT(Y) = f1<¢t3xt = Y) = price at time 1 (1=1,2) of one dollar delivered at time t (t>1) in all states ¢tt for which Xt(¢t)=Y. By definition, I f1(Y)dy = kt'T F(Y) = one-period certainty-equivalent cumulative 'distribution' function at Xt=Y. Formally, w F(Y) = I fT (xt) dXt ; w = (xt:xt 5 Y ). ET(g(Xt)) = I g(Xt )f.r (Xt) dXt = valuation operator at time 1 for time t cash flows. Dt = the value of debt issued at time t and due with interest at time t+l. St = the value of common stock at t. Vt = the value at time t of net cash flows generated by the firm at time t+1 and beyond. c = cost of financial distress as a fraction of the end of period cash flow (Xt). This is introduced to generalize the analysis and will be dropped later without any loss of generality of conclusions. ¢ = personal tax rate on interest income, such that r0 = r(1-¢) e = corporate tax rate. Figure 3.1 depicts the two-period state preference framework in which this analysis is conducted. The firm generates operating cash flows X1 and X2 at the end of 44 TWO PERIDD MDDEL Analytical Framework Ho Default No Default X1+ U1)=(1+r)na 32)=(1+l")o1 Default Default 81+ U1< “+1000 1! 2 <(1+r)D1 t=fl t=1 t=2 Figure 3.1 Tyo Period Model: Apaiytical Epamewopk 45 period one and two, respectively. At time t=0, the firm issues debt Do with the intention of maximizing shareholders wealth. At the end of period one, shareholders must decide whether to liquidate the firm or pay off period one debt- holders in the amount (1+r)Do and continue to operate the firm. This decision depends primarily on the realized cash flow X1 and on the distribution of period two cash flows X2. If X1>=(l+r)Do, shareholders exercise their call option to pay off period one debt-holders at time t=1. Shareholders then issue a new value maximizing level of debt D1 and continue to operate the firm. If the period one cash flow is insufficient to meet the promised payments (i.e., X1<(1+r)DO) shareholders still choose to pay off debt- holders if X1+V12(1+r)D0. Any additional cash is assumed to come from the original shareholders. This will be the case if the present value of period two operating cash flow exceeds the period one shortfall (l+r)Do-X1. If X1+V1<(1+r)Do , the shareholders allow the firm to default. The model terminates at the end of period two and default occurs at that time if X2<(1+r)D1. To solve for the value of the firm at time t=0, we first specify cash flows to the equity (CFS) and bond holders (CFd) at time t=2 . The cash flow to the equity holders is: - = [: x2 - 9(x2 -rDl) - (1+r)D1 ; x2 2 (1+r)D1 0 CF (3-1) NU) : otherwise Where X2 - rDl is period two taxable income and (1+r)Do is 46 the payment to period two bondholders. Period two after tax cash flow to the debt-holders is: (1+r)D1 - ¢rD1 : X2 2 (1+r)Dl - d - - . . = _ - - - - < < CF2 X2 6(X2 rDl) ¢rD1 ch . rD1_~X2- (1+r)D1 (3.2) __X2 - ¢X2 - ch I X1 < rD1 When X22 (l+r)D1, the total cash flows (CF) to the security holders are: ” _ “ s ‘ d _ ' ' _ CF2 — CF2 +~CF2 — x1 e(x r01) (1+r)D1 +(1+r)D1 ¢rD1 CF2 ~ = (1-e)x2 + erD1 - «pro1 = u - CF2 + (e ¢)rol (3.3) Where CF§=(1-6)X2 denotes cash flow from an unlevered but otherwise identical firm at t=2. When rD S X S (1+r)D the total cash flows are: l 2 1 CFZ = X2 - 6(X2 - rDl) - orDl- ch = (1-9)X2 + erD1 - ¢rD1 - CXZ = ch + (e-¢)rD1 - ciz (3.4) When X2 < rD1 the total cash flows are: .12 = 12 - .12- .12 = (1-6)X2 + eXz- ¢X2- ch = (1-e)x2 + (e-¢)x2 - ciz (3.5) Let rDt = a, (1+r)Dt = b, and Ea(-) = one-period certainty- equivalent operator ranging from 'a' to the upper limit of Xt (a superscript will denote an upper limit). Then the value of the firm at time one (V1= S + D1) is : 1 V1= E(CFu) + Eb(e-¢)rD1 + E:[(6-¢)rD1 - cX 2] + a - - E [(9-¢)X2 " 0X2] 47 a b ' + Ea(6-¢)rD1 + E (6-¢)X2 - E (CXZ) + (e-¢)E-(e-¢)Ea(rnl)+ (l+r)DO - V1 Let d = X at which after tax cash flow just equal debt obligation Do(1 + r), then at d: Xl- 6(X1- rDO) = (1+r)DO or d = D0[l/(l-6) + r]. Then, X1 - 9(X1- rDo) (1+r)Do ; X1 > d s = _ _ _ _ ' CF1 X1 6(X1 rDo) (1+r)Do I rDo< X1< d (3.8) __ X1 - (1+r)Do : X1 < rDo and CF? = (1+r)Do - ¢rDo in all states. Note that the value Of CFl at t=0 is Do. Then V0 = So + Do. Vo Ed[X1:e(X1-rDO)-(1+r)DO]+Eg[X1-9(X1-rDo)-(l+r)D0] + O + E(V1) Ea[X1- (1+r)Do] + D Ed[(1-9)X1+erDO]+Eg[(1-6)X1+erDOJ+Ea(X1)+E(V1) - O E(1+r)Do + D (l-e)Ed(X1)+6Ed(rDo)+(1-e)E2(X1)+6E:(rDo)+Ea(X1)+E(V1)+ [- (1+r )Do+ (1+ro)Do]k (3.9) Adding and Subtracting 923(x1) v0 = (1-6)E(X1)+9Ea(rDo)+eEa(X1)+E(V1)+[r0- erok (3.10) 49 Noting that V: = (1-e)s(x1) + 2(v1) = v3 + 6E(rDo) - 6Ea(rDo) + eEa(x1) + [r0 - rJDOk = V; + erD0.k - 6rD0.Ea[l - i /rDo] + [r0 - rJDOk = V: + 00(r0: r + 9: (1 - (1+ro)Ea[1 - i /rDo]))k = v3 + Do[r0 - r(1-OZ)].k (3.11) Where 2 = 1 - (1+rO)Ea(l - (ii/a), The resulting equation (3.11) is exactly the same as equation (13) in BTH (page 85). As in the original BTH model Z represents the expected proportion of the interest tax shield used. As the amount of debt used is increased the marginal value of the expected tax shield diminishes (dZ/da < 0). The value of Z depends upon the cash flow distribution of an individual firm and, therefore, is firm-specific implying capital structure optimality at the firm level. Consequently, all of BTH's hypotheses logically follow if debt is risky in period 2 but not risky in period 1 based on the value of the firm at the end of period one. Qutcome i 2: Here, the value of the firm at t=1 is not higher than the deficiency in cash flow and shareholders choose to default. The value of the firm at time t=0 is then given by an expression similar to equation (3.1): V0— V + Do(ro r(1 6))Z.k cE (X1) (3.12) which without bankruptcy costs reduces to: — u - — v0- v0 + 00(1-O r(1 8))Zk (3.13) In this case the bondholders also receive V1, so that 50 v3 = (1-e)x1+ E(V1) . Now, let w = x1 > (1+r)D0 - v1 and p(Xl) be the probability density function of X1. Note that p(x) = (1+r0)f(x). Then the value of the firm at time t=0 is given from (3.2) and (3.4) by : m v0= Jw(vg+ Do[ro- r(1-62)]k}p(X1)dx w u + J0{VO+Do(rO-r(1-6))Zk) p(x1)dx m w = V3+J30[rO-r(l-OZ)]f(X1)dx + J30(ro-r(1-e))2f(xl)dx ..... (3.14) Where m denotes the maximum value of X1. Equation (14) can be further simplified as follows: V = V W 0 + Ew{Do[ro- r(1-OZ)]} + E {Do[rO-r(1-6)]Z) CJCCDfi v + E{Do[ro-r(l-6Z)]} - Ew(Do[ro-r(1-OZ)]} + EW{DO [ro- r(1-6)]Z} = vo+ DO[rO-r(l-9Z)]k - Ew{Do[ro-r(l-BZ)]- Do[rO-r(l-e)]Z} - Vo+ D0[rO r(1 OZ)]k E {Do[ro r +rez roZ + rZ r621} _ u _ _ _ W _ _ — vo+ Do[ro r(1 OZ)]k E {00(r0 r)(1 2)) = vg+ Do[ro-r(l-OZ)]k + Ew{Do(r - r0)(1-Z)} (3.15) It can be observed from (3.14) that the value function has two segments. For debt levels Do(1+r) < X1 + V1, the value function is the same as given by the BTH model. Over this first segment the value of the firm increases to a maximum point and then declines and the firm obtains an optimum debt level. Over the second segment where default is possible { D0(1+r) > X1 + V1}, the slope of the value 51 function (see end note 2) is : dVo/dDo [r0 - r(1-6)](l-F(a)).k = r(9-¢) (l-FIaH which is positive as long as r0 > r(1-9) or e > ¢. For 6>¢ this gives a corner solution with 100% debt and is consistent with single period capital structure models without considerations for any imperfections such as bankruptcy costs or the existence of non-debt tax shields. The nature of the value function defined by equations (3.14) or (3.15) is depicted by Figure 3.2. The segment a-b of the figure shows firm value where D0(1+r)X1+V1 for all values of X1 , or D0(1+r)>max(X1)+V1. This corresponds to the extension of the BTH model. The middle segment b-c depicts firm value when min(X1)+V1ro (end note 2). This implies that the firm will not be at the optimal debt level over segment a-b as prescribed by the BTH model but will obtain a corner solution at point e. This would be the case as long as point d defining the total value constraint on the level of debt (Do S V0) comes about before the BTH condition becomes operative at point b. To see the conditions under which this might happen note that the BTH constraint implies that at b, Do(l+r) S min(X1) + V1. In the case where min(X1)=0 , Dosvl/(1+r). For line d-e to lie before point b the condition is V0 5 DO = Vl/(1+r). It follows from the above analysis that firms with Vo<=V1/(1+r) will follow a debt policy described by the BTH model and will obtain an optimum over the segment a-d. Firms with V0>V1/(1+r) will follow the BTH path a-d up to the point b, but would be over the segment b-c-e after the BTH constraint obtaining the maximum value at corner with 100% debt. Firms in the first group, i.e., with Vo<=V1/(1+r), can be thought of as growing firms and those in the second group, i.e., with V0>V1/(1+r), may be considered as non-growth firms. The first group, growing firms, would follow the BTH model and obtain an interior optimum, while the second group, non-growing firms, would maximize their value at 100 percent debt following the extended model. Since the slope 54 of the extended segment a-c-e is non—negative and greater than the curve a-b-d, the value of the debt subsidy is higher at the margin for non-growing firms than for the growing firms. It follows that the non-growing firms would employ relatively higher financial leverage than the growing firms. The condition for the BTH model to be operative is that V0 5 D0 = Vl/(1+r). It may be easily met for firms with modest growth and BTH's predicted hypotheses may be relevant for a large number of firms in empirical samples making it still worthwhile to empirically test BTH's hypotheses. 3.2 ume 'c l imu at o s: The first-order condition following from (3.5) above does not yield a closed form solution and we resort to numerical simulation of the model described by equation (3.5) to get an understanding of the comparative statics. The model was simulated with respect to three important variables. These were (1) rate of interest (r) on taxable bonds (ii) value of the firm at t=1, V1 and (iii) operating risk, represented by the standard deviation of the distribution of operating cash flow at t=1, X1. Figure 3.3 shows the results of numerical simulation of the extended model for various interest rates. The distribution of X1 was assumed to be uniform with X1 taking 20 equally likely values between 2.5 and 100. V1 is kept constant at 1000, 6=50% and r0 = 7%. The interest rate on I" I DH VAN]: 983 570 ”I 'II I) 'n M Q 55 FIRM VALUE VS DEBT LEVEL Fm DIFFSBJT INTEREST RATES _ : 2 If A 4 4, > 455‘: ‘ I ~ \A\ v f fl T 1 Y 1 r v v W T f * f V f I .00 200.00 400.00 600.00 835.00 1000.00 BET LEVEL ~89. 4 r #103. o r #129; A r -15% Figure 3.3 Eirm Value VS Debt Level For Different Interest Rates I’v II'H ‘JM '1‘. 56 FIRM VALUE VS DEBT LEVEL FDR DIFFERENT VALUES OF V3 1 02 % 1. .1 C E 1 I 1.01: _.! I I ,. I 2.0'“ fl 1.57: — | l / ”.C J //y a 0:- -1 :35 4 I I ’1 IQ.‘ ._ ' K 1 01:: — / , I xI/ Ix" ‘ V T Ti fl 7 I T C 200 400 600 EETLBEL o '1-4CZ A v4-500 x v1-600 V v4-7OO Figure 3.4 Firm Value VS Debt Level For Differept Values of v1 57 taxable bonds (r) takes values of 8%,10%,12%, and 15%. It can be seen from Figure 3.3 that when r is such that r 2 ro/(l-e) (i.e., 15% in our example) the value of the debt tax shield is negative and the firm loses value by raising debt before the BTH constraint is reached (i.e., Do(1+r)(1+r)Do-X1). At time t=1 the firm has a given amount of depreciation expense (I) which is tax deductible. There is no tax deductible depreciation at t=2 Cash flows at t=1 to the bond and share holders are: or: = %1- 9011 - r00 — I) - (1+r)Do ; x1 > rDo + I x1 - (1+r)D0 ; x1 < r00 + I ... (3.16) DP? = (1+r)D0 in all states. Let c = rDo + I ; then: so = Ec[x1-e(x1-rDo-I) - (1+r)Do] + E°[xl-(1+r)no] + E(v1) and D0= E(1+r)Do . Then, Vo = So + DD v0 =EC[X1-6(X1-rDo-I) - (1+r)Do 1 + 2°[i1- (1+r)D 01+D0+E(Vl) = (1-e)E c(x1) + eEc (r00 +1) - EC (1+r)Do + EC (x1) - EC (1+r)Do + k.Do(1+r) + E(V1) ' (3.17) Adding and subtracting 6EC(X1) and simplifying : v0 = (1-6)E(X1)+E(V1)+9EC (X1)+GEC (c) -E(1+r)Do+kDo(1+ro) Value of an unlevered firm at t=0 is V‘1 o=(1-6)E(x1) + E(V1) 62 Substituting and simplifying: v0 = v3 + eE°(x1) + 6E(c) - eE°(c) + D0[ro - r]k = V: + 00(1-O - r)k + 9[EC(X1) + k.c - c.F(c)] = v3 + 00(r0 -r)k + 9c[1 + (1+ro)Ec(X /c)~- (1+ro)F(c)]k = v3 + Do(ro - r)k + ec[1 - (1+ro)E°(1 - Xl/c)]k (3.18) Let 21 = 1 - (1+ro)Ec(1 - X /c) : then u V0 = V0 + Do[ro - r]k + GCZIk (3.19) The first order condition for maximizing (19) with respect to Do is: dVo = 8V0 + 5V0 dZI dDo SDO SZI dDo 229 c ' 2 dDo =(ro -r)k + GrZIk + 6ck[-(1+ro)E (Xi/C ).r] =0 (3.20) _ _ a ' 2 Where, dZI/dD0 - (1+rO)E (XI/c ).r simplifying (3.19) the optimality condition becomes: r - r + er{zI - (1+ro)E°(x1/c)} = o 0 Substituting 2 = l-(1+ro)Ec(1-X1/c), and simplifying: I (r0 - r) + 9r[1 - (1+r0)F(c)] = 0 By rearranging at optimality: F(c*) = [r0 - r(1-6)] / er(1+ro) (3.21) Or, 1 - (1+ro)F(c*) = (r - ro)/8r (3.22) From (3.9) we have: c* =F-1[ro -r(1-6)]/[er(1+ro)] (3.23) We observe from equations (3.20), (3.21) and (3.22) that these expressions are similar to the optimality conditions derived in BTH. Comparing these with expressions (18), (18a) and (19) {page 86, BTH} the only difference is that (a=rD) 63 is replaced here by (c=rD + I). Therefore, the conclusions of the model do not change substantially by the introduction of depreciation expense. 21 can now be interpreted as the expected proportion of the total tax shield (rD + I) used. We note that dZI/dI = -[(1+r0)EC(X1)/a2 < O, which implies that the marginal value of the total tax shield diminishes with higher depreciation expense. Also from (3.11): * * -1 (rD0+ I) = c = F [ro - r(1-e)]/[9r(1+ro)] It is clear that for the optimality condition to hold rDO must be smaller by the same amount depreciation (I) is increased. This result conforms to DeAngelo and Masulis' [1980] prediction that firms with higher non-debt tax shields (depreciation) would tend to carry relatively less debt. 3.4 Conclusions; It has been shown analytically that when the value of the firm at t=1 is greater than the possible deficiency in meeting the debt obligation (debt is riskless in period one), the conclusions of BTH are confirmed even when debt is risky in period two. In case V1 is not sufficiently high our extension of the model shows that the existence of other imperfections may be necessary in order to indicate an interior optimum for most firms. It follows from our extension of the BTH model that the higher growth firms would tend to have a lower financial leverage than non- growth firms or negative growth firms. This implication of 64 the extended model produces a hypothesis similar to BTH's H2, namely, that there would be a negative relationship between growth and financial leverage. However, our hypothesis stems from a different form of the value function for growing companies and a different functional form for non-growing companies. The BTH hypothesis follows from the tendency on the part of firms to seek tax shelter for their current income. In their model optimal debt level is a function of operating cash flows and not of V1. Since V0 depends upon V1 and the optimum level of debt is given, the debt ratio (Do/V0) varies inversely with the next period value (V1). The ratio of debt to the expected cash flow is, however, not expected to be different for firms with different growth rates. In the extended model the negative relationship between growth and financial leverage is driven by a higher value of debt subsidy at the margin and, therefore, is a function of both the current operating cash flow and next period firm value. Under the extended model, the debt to operating cash flow ratio will be higher for non-growing firms. We may be able to empirically test for this difference in the relationship predicted by the BTH and in the extended models. It is conceivable that the BTH constraint, Do(1+r)r0 From BTH model we have : V0=V0U + Do[ro-r(1-GZ).k and dVo/dDo = [ro-r+er(1-(1+ro)F(a))].k .........(i) For the extended model where default is possible the firm value is given by: v0 = VOU + Do[ro-r(1-e)]z.k and the slope is: dVo/dDo = [ro-r(1-6)][1-(1+r0)F(a)] ...... (ii) Subtracting (i) from (ii) and letting n=1-(1+ro)F(a) k.{[r0-r(1-9)]n - r0 + r - era} = k.{(ro-r)n + r60 - r0 + r - ern} k.(ro-r)(n-1) k.(ro-r)[1-(1+ro)F(a) ' l] k.(ro-r)[-(1+ro)F(a)] = (r-ro)F(a) which is positive for r > r0. CHAPTER IV THEORETICAL CONSIDERATIONS AND EMPIRICAL EVIDENCE The main empirical hypotheses to be examined in this study were stated in Chapters II and III. In this chapter these hypotheses are examined in detail. Theoretical considerations which relate to these hypotheses are discussed, along with a review of the present empirical evidence and its bearing on various theories of capital structure. 4.1 eratin isk and F'nanc a v ra e: BTH derive the following hypothesis from their model: H1: "A systematic relationship between operational (sic) risk and financial leverage should exist, and its direction and slope should depend upon the fraction of the corporate tax rate that is reflected in the tax induced differential between corporate debt and equity." As explained in Chapter II the optimality condition in the BTH model is given by the relationship: 1 - (1+r0) F(a*) = (r - ro)/er (4.1) Where, a*=rDt is the interest payment on debt and F(a*) is the cumulative distribution function evaluated at Xt=a*. The condition states that firms will employ debt up to the 68 69 point where the probability of having redundant tax shields (left hand side) is equal to the ratio between implied marginal tax rate {(r-ro)/r} and the statutory tax rate (6) (right hand side). This optimality condition is depicted in Figure 4.1. It shows the complements of the cumulative distributions of the operating cash flows of two firms: firm A has low operating risk and firm B has higher operating risk. When the implied tax rate, (r-ro)/r, is higher reflecting higher bond interest rate (r1), the less risky firm A employs more debt than B. With lower bond interest rate (r2), firm B with higher operating risk employs more debt. Therefore, the relationship between operating risk and financial leverage would be positive in times of low bond interest rates and negative in times of higher interest rates. It has long been accepted in financial theory that risky firms should tend to borrow less, other things being equal (see Stiglitz [1972], Lintner [1977], Leland and Pyle [1977], Ross[1977], Bradley, Jarrell and Kim [1984]). However, the "evidence on risk and debt policy is not extensive enough to be totally convincing" (Myers [1984]). Financial theories based on bankruptcy costs predict a negative relationship between operating risk and financial leverage since probability of bankruptcy is increased with larger amounts of debt. Contrary to this a positive relationship between operating risk and financial leverage is postulated under various theoretical scenarios. 70 Operating Risk and Financial Leverage Probabilitu of _ Soluency=1-(1+ra)F(a) 1 r1 \ B n .5 n B l"2 a o 0 EU!) I‘ D I r r r nterest 1 B 1 n 1 2 n 2 Expense F = - 1 (n' fin)lfln' F2 = (r2 -r.)/8r2 Figpre 4.; Relationship Between Operating Risk and Leverage 71 Myers [1977] notes that the impact of risky debt on the market value of the firm is less for firms holding investment options on assets that are risky relative to the firm's present 'in place' assets. An increase in the variance of market value is favorable in the sense that it reduces the value transferable to bond-holders following discretionary investment and thus reduces sub-optimal investment choices. In this sense, risky firms may end up borrowing more than safe ones. Castanias [1983] has pointed out that the existence of bankruptcy cost is not a sufficient condition for an inverse relationship between operating risk and financial leverage. He demonstrates that an inverse relationship would obtain in firms for which earnings are normally distributed and for which default costs are sufficiently high. Castanias [1983] studied the relationship between probability of failure and leverage. The financial data used was drawn from Robert Morris Associates' Annual Statement Studies organized according to 306 lines of business and firm size, and Dun and Bradstreet Failure Reports. His results are consistent with the tax-shelter/bankruptcy-cost model in that firms in lines of business with high historical failure rates also tend to have less debt. Ex ante default costs appear to have a substantial impact on the capital structure policy of firms. Bradley, Jarrell and Kim [1984] developed a one-period theoretical model of optimal capital structure which 72 synthesized various theories incorporating personal and corporate taxes, non-debt tax shields, costs of financial distress and risky debt. The model's comparative statics show that the variability of the firms' end-of-period value can be either positively or negatively related to the optimal leverage. They note that when the underlying distribution of the end-of-period value is normal the cross- partial derivative of its standard deviation with respect to the optimal value is of ambiguous sign (Also noted by Scott [1976] and Castanias [1983]). Their simulation results show that firm leverage ratios will be negatively related to the volatility of earnings if the costs of financial distress are non-trivial. When a firm has no leverage-related costs it receives only the positive advantage of debt. In their empirical work they find that leverage ratios are inversely related to earnings volatility at the industry level. They find that an average firm's leverage ratio is strongly related to the industrial classification indicating support for a long-run optimal target capital structure. An inverse relationship is also predicted if there is asymmetric information about the variance rate but not about the firm's value. This line of argument has been developed further by Shah and Thakor [1987]. They examine optimal capital structure in the context of project financing assuming that each firm knows its own expected return as well as risk but that the creditors know only the expected return and are a priori uninformed about the risk. Their 73 analysis shows that riskier firms acquire more debt, pay higher interest rates, and have higher value in equilibrium. The intuition behind their results is as follows. The high risk firms have an incentive to understate their risk levels and thus to obtain lower interest rates. Creditors offset this incentive by offering them higher levels of debt as a 'reward' for reporting higher risk. The less risky firms are offered low interest rates as a reward for foregoing higher financial leverage. The riskier firms have a greater probability of realizing higher incomes, and the high- debt/high-interest-rate combination permits greater tax shields. Shah and Thakor [1987] postulate that this direct relationship will be more pronounced in larger firms. Their model assumes risk neutrality and in larger firms entrepreneurial risk preferences are likely to be relatively unimportant. They infer that in smaller firms where risk aversion assumes greater importance an inverse relationship between leverage and risk is more likely to prevail. Castanias [1983] points out that firm size may be indirectly related to operating risk and bankruptcy costs. A larger firm size may lead to less operating risk per dollar of investment or different marginal tax rates due to the diversification effect or lower bankruptcy costs per dollar invested. The direction of the risk-leverage relationship has been observed to be positive in most empirical research which is 74 discussed below. However, its direction has not been tested in small vs large firms. Such an investigation would shed light on the hypothesis put forth by Shah and Thakor [1987]. Various studies have hypothesized that if financial structure is relevant to the valuation of the firm then firms in various industry groups would have recognized this fact and developed capital structures suited to their particular operating risk. This approach attempts to show that an appropriate range of leverage exists for a particular industry and that the firms seek this target ratio over time. This approach is a surrogate for the direct method of testing for the effects of leverage on firm value. Schwartz and Aaronson [1967] provide empirical evidence that financial structures measured by book values do not vary significantly within an industry but do vary significantly among industries over the two years studied. Scott [1972] expanded on the work of Schwartz and Aaronson [1967] by examining financial structures in 12 industries over a period of ten years (1959-1968). He also conducted pair-wise tests of differences in equity ratios for each individual year under study and found that financial structures over industries do cluster significantly in a majority of the industry groups. Scott and Martin [1975] study the relationship between industry classification and financial structures. Data covered the period 1967-72 for 12 industry classes chosen on an a priori basis. Parametric and non-parametric analysis of 7S variance indicated that industry class is indeed a determinant of financial structure for each of the years in the sample. They also considered if differences in firm size had any effect on the use of financial leverage. The sample firms were divided into three sizes according to their ranking by total assets. They found significant differences in leverage use by size group: smaller equity ratios were generally associated with larger companies. Flath and Knoeber [1983] calculate the implied relative failure cost for 38 business lines by combining estimates of the tax advantage of capital structure with failure rates from Dun and Bradstreet Failure Reports. Financial leverage is regressed on the estimated failure costs along with the estimated tax advantage, the operating risk proxy, and a dummy variable for regulated industries. They report that the cross-sectional variation in capital structure is best explained by differences in operating risk: the relationship being significantly negative. Ferri and Jones [1979] test four hypotheses; the relationship of financial leverage to industrial class- ification, firm size, operating risk and operating leverage. They group firms using a clustering technique into six groups according to financial leverage. They employ multi- variate discriminate analysis and find that the relationship between operating risk and leverage is significantly negative for firms in their 1976 sample. However, they observe that this relationship may have been induced by 76 different within group variance of the lowest group. They also report that firm size has a significant effect on leverage. Their results differ for expansionary and recessionary periods and suggest that the ability of small firms to access debt is influenced by the state of the economy. Bowen, Daley and Huber [1982] conclude that there are statistically significant differences between mean industry financial structures using both parametric and non- parametric tests. The ranking of the mean industry ratios exhibits stability over the entire period. Moreover, firms show a tendency to converge towards their industry mean leverage ratios over the long run. They provide evidence consistent with the DeAngelo and Masulis hypothesis that the level of non—debt tax shelters should be negatively correlated with the use of debt. Their evidence is on the industry level using industry averages of depreciation, ITC, and operating loss carry forwards divided by total revenues. Boquist and Moore [1984] performed an analysis of variance study of leverage ratios in the several industry groupings. They found that while total debt varies significantly across industry groupings, the use of interest bearing debt does not. They conclude that it is the current liabilities that vary across industries and not long-term debt. Marsh [1982] conducted an empirical study of security issues by UK companies over 1959-1974 period. His results indicate that companies are heavily influenced by market 77 conditions and the past history of security prices in their choice between debt and equity. The study provides evidence that the companies appear to make their choices as though they had target levels for both long-term debt ratios and the ratio of short-term to total debt. The empirical evidence suggests that the target ratios are themselves a function of company size, bankruptcy risk and asset composition: smaller companies with fewer fixed assets and those with greater bankruptcy risk are more likely to issue equity. Sorenson and Kim [1986] empirically test the relationship of agency costs (proxied by a lower inside ownership) to the debt policies of the corporation. They find that firms with higher inside ownership have greater debt ratios than firms with lower inside ownership. This relationship may be explainable by the influence of agency cost of debt and/or of equity. They also find that high growth firms use less debt, and high operating risk firms use more debt rather than less debt. They conclude that their regression results support Myers' [1977] hypothesized relationship. A study by Kester [1986] comparing the capital structures of Japanese and 0.8. firms indicates that when leverage is measured on a market value basis and adjusted for liquid assets, there is no significant country difference which cannot be explained by differences in growth, profitability, risk, size and industrial classification. 78 The results of Auerbach [1985] appear to contradict most existing theories and empirical evidence and are hence inconclusive. The measured effects of a firm's growth rate on the level of debt are inconsistent with the model of Myers [1977]. The rate of capital depreciation exerts a positive effect. The variance of earnings has a positive coefficient. Only the variance of value has the predicted sign but it is not significant. Long and Malitz [1985] used capital expenditure, operating cash flow, the firm's systematic risk or beta, and firm-specific risk as proxies for tangible assets, availability of internal funds, operating risk and the probability of bankruptcy, respectively, in a cross- sectional regression study of capital structure. They found that the total risk measured by unsystematic, firm-specific residual variance of the firms' stock return standardized by the market variance has a significantly positive association with financial leverage. Also, firms' total variance of stock returns unlevered to remove the effect of debt is significantly positively related to financial leverage. They find that firms with higher systematic risk have lower financial leverage. Long and Malitz [1985] conclude that the probability of bankruptcy does not exert a significant influence on the debt ratios. Mikkelson [1984] suggests that conflicting empirical evidence on the relationship between operating risk and financial leverage may be due to the lack of a properly 79 specified functional form. Kale, Noe and Ramirez [1988] have shown theoretically that the operating risk and financial leverage relationship is roughly U-shaped which is supported by their empirical analysis. In addition, they report empirical support for DeAngelo and Masulis' [1980] hypothesis on the substitutability of non-debt and debt tax shields. The hypothesis advanced by Barnea, Talmor and Haugen [1987] relates the direction and slope of the risk-leverage relationship to the magnitude of the differential return between corporate debt and tax exempt bonds. This differential is regarded as a measure of the marginal tax rate, and has been observed to differ across firms as well as over time. In periods when the implicit marginal tax rate is close to the statutory rate, firms with higher degrees of operating risk would be inclined to employ more debt. When the implicit marginal tax rate is low compared to the statutory rate the relationship between the operating risk and financial leverage is positive i.e., risky firms employ larger amounts of debt. In finance theory either a positive or a negative relationship may be predicted under different assumptions. Both agency and option theory suggest that shareholders are likely to shift investment into high risk projects. Hence firms with more risky projects are less likely to under- invest. BankruptCy theory on the other hand suggests that higher variance firms would have lower debt levels. Which 80 consideration would weigh more is an empirical question. Our theoretical model (Chapter III) supports the BTH hypothesis which relates the direction of the relationship between operating risk and financial leverage to the ratio of marginal tax rate implied in the yield differential to the statutory tax rate. This study constructs and conducts empirical tests of the operating-risk/financial-leverage relationship by studying cross-sectional samples for time periods with higher and lower marginal/statutory tax ratios. 4.2 growph epg Eipepciei Leverage; BTH arrive at the following hypothesis regarding the relationship of the earnings-value ratio to financial leverage: H2: "A direct cross-sectional relationship should exist between an individual firm's (operating) earnings- value ratio and the degree of its financial leverage." This hypothesis implies that growth firms with small earnings-value ratios should employ relatively less financial leverage than more mature firms with larger earnings-value ratios. A low (expected) earnings to value ratio implies that a large portion of the current value is attributable to the future value of the firm rather than its next period's earnings. This would be the case for a high growth firm. Such a firm would need to employ relatively less leverage to shield its current income. 81 A negative relationship between growth and debt level is also predicted by DeAngelo and Masulis [1980], Myers [1977], and Myers and Majluf [1984]. Growth firms are more likely to have higher investment levels and, therefore, higher amounts of non-debt tax shields such as higher depreciation, investment tax credits and R&D expenditure. In DeAngelo and Masulis' [1980] model the presence of non-debt related tax shields increases the probable loss of tax shields causing firms to employ lower debt levels. Firms with higher investments and consequently enjoying greater growth would, therefore, employ lower levels of debt. Growth firms also are likely to derive a large part of their value from 'growth opportunities' rather than from 'assets in place'. In Myers and Majluf's [1984] model firms with higher growth opportunities relative to the value of their tangible assets would borrow less. This financing behavior follows from their assumption of asymmetric information between firm management and the investors. Bowen, Daley and Huber [1982] conducted an analysis of variance study of two leverage measures across nine SIC industrial groupings. They confirmed that leverage does differ across these industrial groups but found generally negative rank correlation coefficients between industry leverage ratios and industry average tax shelter ratios. The latter was defined as the reported depreciation plus reported investment tax credits plus remaining operating tax loss carry forwards divided by total revenues. They conclude 82 that the DeAngelo and Masulis hypothesis is supported at the industry level. Boquist and Moore [1984] used operating income (as opposed to total revenues used by Bowen, Daley and Huber [1982]) to standardize non-debt tax shields in an attempt to better capture the thrust of the DeAngelo and Masulis model. Boquist and Moore's [1984] results indicate that the tax shelters and leverage ratios are not negatively correlated at the firm level and hence do not support the DeAngelo and Masulis hypothesis. Bradley, Jarrell and Kim [1984] report a positive association between financial leverage and non-debt tax shields which they proxied by depreciation and investment tax credits. They interpret these results as raising doubts as to the validity of DeAngelo and Masulis' [1980] argument and as consistent with Scott's [1976] "secured debt" hypothesis. Non-debt tax shields could be an instrumental variable for the securability of the firm's assets with more securable assets leading to higher leverage ratios. Davis [1987] conducted an empirical study of effective tax rates as determinants of capital structure for a sample of Canadian companies. Since the effective tax rate is reduced both by the amount of non-debt tax shields (via DeAngelo and Masulis model) as well as the amount of debt, an 'unlevered effective tax rate' was imputed by adding the tax shields from interest (the statutory tax rate times the interest expense: T‘1 = T + t*I) to focus on the relationship 83 of the effective tax rate to capital structure. Davis' cross-sectional tests provide only weak support for the DeAngelo and Masulis hypothesis that firms subject to lower corporate tax rates will employ less debt in their capital structure. Long and Malitz [1986] similarly report a positive correlation between leverage and non-debt shields. They computed these shields as depreciation expenses times the corporate marginal tax rate plus the changes in deferred taxes plus investment tax credits. They conclude that the possibility of a tax effect cannot be excluded. However, when they included advertising and R&D expenditure which too provides non-debt tax shields the correlation of the expanded tax shields with leverage was significantly negative. They report that 35-41% of the variation in financial leverage is explained by investment type. Firms with discretionary investments have lower financial leverage than those facing tangible investments. Hence, they conclude that there is some evidence that non-debt shields (when R&D and advertising expenditure is also included as a tax shield) can influence the amount of corporate debt as predicted by DeAngelo and Masulis. Long and Malitz [1985] also investigate the effect of the size of a firm's operating cash flows on its debt policy. Donaldson [1961] pointed out that firms prefer to use internally generated funds to minimize the cost and constraints of external financing. Long and Malitz [1985] 84 argue that the firm's operating cash flows may be a proxy for the type of investment opportunities they face. When investment opportunities are firm-specific (e.g., unique products or processes) or intangible, they are more likely to enjoy higher cash flows. Under either explanation the relationship of operating cash flows to financial leverage is negative. Their empirical evidence confirms this negative relationship. However, since firms with higher systematic risk are expected to have higher cash flows their results are inconclusive. Moreover, when they neutralize risk by forming equal beta portfolios the importance of both R&D and advertisement variables is reduced below statistical significance but the cash flow coefficient remains statistically negative. They conclude that their study cannot empirically distinguish among alternative explanations for this result due to different possible relationships between cash flows, R&D and advertising expenditures. Myers [1984] infers support for the 'pecking order' hypothesis from the evidence provided by Long and Malitz and also by Williamson (quoted in Myers [1984]). Myers interprets the level of R&D and advertising expenditures as a proxy for the value of growth opportunities and intangible assets. Williamson [1981] had used the difference between the value of the firm's debt and equity securities and the replacement value of its assets as a proxy for intangible assets. However, replacement costs may also be related to an 85 assets' value as collateral and its inclusion may affect the debt levels via Scott's "secured debt" hypothesis. Moore [1986] presents an extension of the DeAngelo- Masulis model which allows for interaction between securability and depreciablity of assets. The interaction between tax shields and asset composition renders ambiguous the cross-sectional relationship between financial leverage and non-debt shields making untestable the DeAngelo-Masulis hypothesis. Titman and Wessels [1988] use a factor-analytical technique to analyze the explanatory power of different theories of optimal capital structure. Their results suggest that firms with unique or specialized products have relatively low debt ratios. They find no evidence that debt ratios are related to a firm's expected growth, non-debt tax shields, volatility, or the collateral value of its assets. It appears that the relationship of growth to leverage needs to be examined more closely. By formulating empirical tests which include the ratio of operating earnings to firm value as an explanatory variable we may be able to shed light on the competing theories. 86 4.3 T'me-se es e av'o m 'e ' : The BTH model predicts the following time-series behavior of marginal tax rates: H3: "There should be a cyclical pattern in the fraction of the corporate tax rate embodied in the tax induced differential return on debt. The fraction should increase when an improving economy in the next period is expected and decrease if the opposite is true." The fraction of the corporate tax rate embodied in the tax induced differential return on debt is defined as P=(r - r0)/re. The spread between corporate and municipal bond yields, divided by the yield on corporate bonds i.e., (r- ro)/r, has conventionally been treated as a measure of the marginal tax rate on corporations implied in the prices of taxable and non-taxable securities as explained below. For an investor to be indifferent between taxable securities and tax-free securities, after-tax return should be the same: or r0 = (1 - pr)*r (4.2) where: r0 = tax free return r = taxable return 7pb= personal tax rate on interest income. In Miller [1977], the progressive individual tax structure results in an upward sloping demand curve which ensures that in equilibrium the personal marginal tax rate on bonds (pr) equals the corporate tax rate (9). As a result the marginal value of the tax shield to an individual 87 firm would be zero. The relationship advanced by Miller is: e = pr = (r - ro)/r (4.3) which is equal to the marginal tax rate on corporate debt. In Figure 4.2, Miller's equilibrium with 9 = pr occurs at point e. In the presence of risky debt ,for instance, in the DeAngelo-Masulis model, the supply curve for corporate debt is downward sloping and equilibrium occurs when the personal tax rate on bond income is below the corporate tax rate at point f in Figure 4.2. The higher the level of default risk the greater is the departure from Miller's equilibrium and the larger is the difference between the corporate tax rate (9) and the implied marginal tax rate (r-ro)/r. In the BTH model F = (r - r0)/re measures the ratio of the implied marginal tax rate and the statutory corporate tax rate and represents the extent of departure from Miller's equilibrium. The rationale behind BTH's third hypothesis can be explained as follows. Operating earnings tend to follow the business cycle. The average ratio of operating earnings to firm value will follow this cycle. When the economy is expected to improve, for example, firms would attempt to shield their higher expected earnings by issuing more debt and the supply of corporate debt should increase. On the other hand, since the aggregate realized income of the investors also increases with a business upturn, the demand curve for corporate debt shifts upwards (less is demanded). 88 BOND MGRKET EQUILIBRIUM Effect of Economic Expansion Interest Rate D D' aggregate Debt Figure 4.2 Bond Market Egpilibrium Effects of Economie Expapsiop 89 These two effects combine to produce a cycle in the fraction of the corporate tax rate reflected in the tax-induced differential return. Figure 4.2 shows how supply and demand would shift with an upturn in the economy. The sold lines SS and DD represent supply and demand curve for corporate debt defining an equilibrium rate of interest of r. With an improving economy the new supply and demand curves (dotted SS' and DD' curves) give in equilibrium a new and higher interest rate level r'. With a constant statutory corporate tax rate, if r' > r then (r'-r'o)/re > (r-ro)/re. With a downturn in the economy the reverse applies. Empirically, there is no evidence of a single tax rate equating yields on corporate bonds with yields on tax exempt municipal bonds of similar risk and maturity. Studies based on long-term yield ratios have reported implied tax rates as being lower than the statutory rate (e.g., Trzcinka [1982]) with estimates varying over time. One explanation of this variation over time in the implied tax rates has been the cyclical demand and short term maturity preference of the commercial banks. According to this segmentation theory, an extra inducement has to be offered to attract lower tax- bracket investors to buy municipal bonds. Jordon and Pettway [1985] point out that this line of reasoning ignores supply side adjustments by corporations who would find it advantageous to offer long-term debt. Skelton [1983] examines alternative mechanisms for obtaining equilibrium in yield ratios of taxable and non- 9O taxable bonds. Fama [1977] suggests that it is tax arbitrage by the commercial banks which determines the relative pricing of short term tax exempt bonds and, therefore, reflects the marginal tax bracket of the commercial banks. In Miller's model it is the debt financing decisions of the corporations which provide an equilibrium mechanism. Skelton tests the alternative explanations by comparing the relative pricing of short term bonds over periods when the short term taxable rate exceeded the Regulation Q ceiling on interest thereby inhibiting tax arbitrage by the banks and over periods when banks were not thus inhibited. He finds that when arbitrage by banks is inhibited the mean marginal tax bracket is significantly lower than the statutory corporate or bank tax rate. When banks are relatively free the implied tax rate is close to the statutory rate. He concludes that the ability of the commercial banks to perform tax arbitrage at the short end maturities is an important factor in the relative pricing of short term taxable and tax exempt bonds and, therefore, suggests support for Fama's explanation and a rejection of Miller's model in its original form. He also points out that it may be inappropriate to infer marginal tax brackets directly from long term yield ratios since these ratios may reflect the expectations of lower marginal tax brackets or other differences between taxable and non- taxable bonds which are unrelated to the tax bracket of the marginal holder. Kim and Booth [1985] investigate the relationship of 91 yield ratios between non-taxable and taxable bonds to default risk. They test the hypothesis that higher empirical yield ratios at a given time should be associated with higher risk of loss of tax shield with default. This default risk is measured by the failure rate of firms for different years. In other studies (e.g., Trzcinka [1982]) the yield ratio of similar risk class taxable and tax-exempt bonds defines the riskless equilibrium conditions since these studies assume that the risk premium of taxable bonds cancels the risk premium of non-taxable bonds. Their results show that under conditions of no risk Miller's [1977] proposition holds i.e., the yield ratio equals one minus the marginal corporate income tax rate. When risk is introduced the implied tax rate is less than the statutory rate indicating the influence of default and agency related costs. Kim and Booth [1985] report that the yield ratio is positively related to the failure rate, a surrogate for the general riskiness of the economy. They suggest that the yield ratio may be used as an indicator of the general economic condition of the economy. It is, however, possible that their observation is similar to the observed increase in the spread between high grade and low grade bonds as economic conditions worsen. Hence, this result could also obtain if the total risk of municipals is greater than that of utilities. Jordon and Pettway [1985] compare taxable and tax-free 92 money market fund weekly rates over February 1982 to July 1985 in order to avoid difficulties in controlling for risk premium and term structure effects in long term bonds. They report results supporting Miller's hypothesis observing that "returns on taxable and non-taxable investments imply a rate almost exactly equal to the corporate rate." They, however, note that their results obtained from short-term rates can be generalized to long-term debt only if the pure expectation theory of the term structure holds. Different tax brackets may prevail for different maturities if the municipal and corporate bond markets are segmented. Trzcinka [1982] argues that bond ratings may not capture risks other than default risk. Allowing for the possibility of municipal bonds having higher default risks than corporate bonds, he uses a random intercept model to control for the relative risk. His results show that the yield ratio of municipal to corporate bonds is close to 52% as per the Miller model but estimated equilibrium tax rates vary from 38% to 57%. Van Horne [1982] reports that implicit tax rates vary over time as the supply of bonds changes (see also Trczinka [1982]). He derives implied tax rates from yields for a discount Treasury bond and a similar bond trading near par. The implied tax rate is found to vary inversely with the level of interest rates. As interest rates rise and the supply of discount bonds increases, investors in lower tax brackets must be attracted by higher yields. His results are 93 consistent with the view that the demand for discount bonds is segmented and that discount bonds are sold at a lower yield due to the capital gains potential subject to a lower tax rate. Cordes and Sheffrin [1983] present estimates of the marginal effective tax advantage to debt financing. They simulate the impact of a change in interest deductions using the Treasury Corporate Tax Model. They conclude that the statutory and the effective tax rates differ considerably and that there are significant variations in the after-tax marginal cost of debt faced by different industries and firms. Davis [1987] investigated whether the effective tax rate and leverage ratios are stable over time . His tests indicate that while at the aggregate level the two variables show stability, they exhibit stability at the firm level only in a few cases. Moreover, the effective tax rate was not stable over the test period for the majority of the firms. Park and Williams' [1985] explain cross-sectional differences in implicit tax rates by the existence of different bondholder clienteles in different tax brackets. In their model, firms with higher cash flows can promise higher coupons and still deduct all interest from taxable income, and thus have a comparative advantage in issuing bonds with higher coupons. These bonds attract investors in lower tax brackets. As a result such bonds are priced in 94 equilibrium at lower rates. In their model only interest and not principal is tax deductible (as opposed to DeAngelo and Masulis [1980]) and in bankruptcy interest precedes principal (as opposed to Talmor, Haugen and Barnea [1985]). Because of this distinct treatment of interest, bonds with different coupons are no longer perfect substitutes as in Miller [1977]. This results in clienteles of firms categorized by their capacity to deduct interest payments, facing clienteles of investors categorized by their tax rates. Effects of inflation on the aggregate financing pattern have been analyzed by Taggart [1985]. In the tax- saving/bankruptcy model an increase in expected inflation leads to an upward shift in the demand curve equal to 8i. The supply curve on the other hand shifts by 8i/(1-t) . Hence, the equilibrium amount of corporate debt must increase. In Miller's [1977] model the increase in expected inflation causes the demand curve to shift upward by the same amount as the supply curve, leaving the level of corporate debt unchanged. When Miller's [1977] model is combined with agency costs (or with bankruptcy costs as in Gordon and Malkiel [1981]) the debt supply curve is imparted a negative slope which is shifted upward due to an increase in expected inflation. The positively sloped demand curve is also shifted upward. The resulting equilibrium is achieved at an increased level of debt. This finding is consistent with Modigliani's [1982] analysis. 95 Time series variation in the implied marginal tax rates has been attributed to the arbitrage activities of the commercial banks (Fama [1977]). BTH's model predicts a similar behavior in implied tax rate series. However, with the institutional arbitrage argument banks react to the yield differential between taxable and non-taxable bonds. In the BTH model firms adjust their leverage in anticipation of changes in the operating earnings and hence contribute to this yield differential. Empirical tests suggested in Chapter V may shed some light on the two competing perspectives regarding observed differences in the implicit marginal tax rates. CHAPTER V RESEARCH METHODOLOGY AND PROXY VARIABLES In this chapter empirically testable models are developed and variables to be used are described. Possible proxies for these variables are discussed in turn. 5.1 Methodology: The BTH model and its extension in Chapter III derive relationships between financial leverage, operating risk, earnings-value ratios, and implied tax rates. We first develop testable hypotheses of the form suggested by the BTH model and its extension. Later we include other variables suggested by competing theories of capital structure, including those related to agency costs and asymmetric information, in order to examine their comparative explanatory power as well as to minimize possible mis- specification error due to omitted variables. In the BTH model debt is riskless in a special sense. At the end of period one the firm's cash flows can fall short of its debt obligations but the firm's end of period one value is assumed to be always greater than any possible 96 97 shortfall and, therefore, any short fall is met by fresh equity brought in by the shareholders. In chapter III we relaxed this restriction on the firm value and extended the model to situations where firm's value is not thus constrained. One implication of relaxing this restriction is that an interior optimal capital structure does not unambiguously obtain for all firms. Firms with end of period one value less than the possible shortfall in debt obligations, characterized as non-growth firms, obtain a corner solution with 100% debt. For growing firms, however, an interior optimal is achieved as in the BTH model. Implications of our extension for the market equilibrium and empirical hypotheses derived by BTH are summarized in Figure 5.1 and are discussed below. The first hypothesis (H1) relating operating risk to financial leverage is derived from the equilibrium condition for an individual firm given by equation 4.1 1 - (1+r)F(a*) = (r-ro)/r (5.1) This equilibrium condition does not hold in the extended model for non-growth firms i.e., with V0 2 Vl/(1+r), which achieve optimality at 100% debt ratio. No relationship between operating risk and financial leverage is predicted by the model for such firms. For a sample of both growth and non-growth firms, however, hypothesis 1 may still be empirically observable if the sample is dominated by growth firms. 98 Table 5.1: Iabie gpppazing Empizieal Hypptneses From t e od Empirical Hypotheses BTH EXTENDED MODEL MODEL 1. Operating Risk & 8(Do/Vo) > Financial Leverage H1: -—-——- - 0 holds holds 8Var(X1) < Sign depends on P 2. Growth and 5(Do/Vo) Financial Leverage H2: -—-——-——-> 0 holds holds 8(X1/Vo) 5(rDo/X1) H2a: > 0 - holds 5(X1/V0) 3. Implied Tax Rate & Business Cycle H3: 5F/81 > 0 holds holds P 2 (r-ro)/er : implied tax rate in the yield differential between taxable and tax exempt bonds, divided by statutory tax rate, 6. I a business cycle indicator. 99 In Chapter III it was shown that it follows from the extended model that the growth firms would tend to have lower financial leverage than non-growth firms. This implies a negative relationship between growth and financial leverage similar to BTH's hypothesis 2, which predicts a positive relationship between the debt ratio (Do/V0) and earnings to value ratio (Xl/V0)- The extended model predicts this same relationship but also predicts that the ratio of interest to cash flow (rDo/Xl) is positively related to the ratio of earnings to value (Xl/Vo) . This hypothesis is labeled H2a in Table 5.1 and is separately tested. The third hypothesis following from the BTH model predicts a positive relationship between the implied interest rates and expansion or contraction in the economy. This relationship is also derived from the interior equilibrium condition given by equation 5.1 which leads to a downward supply curve for corporate debt. In the extended model 100% debt is optimum for non-growth firms implying a horizontal supply curve for corporate bonds. However, for a bond market in which both growth and non-growth companies are present, supply curve would still be downward sloping at the margin. It follows that the extended model implies the same relationship between implied tax rates and business cycle as predicted by the BTH model. When non-debt tax shields are included in the analysis the expanded model suggests that these affect the financial structure choice in a systematic manner. The non-debt tax 100 shields, such as depreciation, and the debt related tax shields (interest on debt) do appear to be substitutes and therefore predict a negative relationship between non-debt tax shields and debt ratios. This hypothesized relationship is empirically tested with an expanded set of explanatory variables. 5.2 Hypothesis i: Qperepipg Risk end Eipepeiai Leverage: Hypothesis 1 states that there should be a systematic relationship between operating risk and financial leverage and its sign and slope should depend upon the fraction of the corporate tax rate that is reflected in the tax induced differential between corporate debt and tax exempt rates, P=(r-ro)/er. Thus financial leverage will be positively related to operating risk when P is greater than a critical value, and financial leverage will be negatively related when P is less than the critical value. If the distribution of the firm's operating cash flows is symmetric then the critical value of P will be 0.5. The distribution of the operating cash flows is most likely not symmetric. Moreover, the slope of this relationship is neither constant nor has the same sign, but depends upon the value of r. 101 The empirical test of the hypothesis (H1) is based on the following model: FLit = a + bt * Sit (5.2) Where: FLit 5 Financial leverage for ith company at time t Sit 2 Operating risk for ith company at time t bt a slope coefficient of Sit at time t i=1, . . . , p ; p number of firms in the sample number of time periods for each firm t=1, . . . , m : m It is further hypothesized that: bt = k * (r* - rt) F* a the critical value of F=(r - ro)/er at which coefficient ht would change sign Ft 5 the observed value of F at time t By substitution we have: FLit = a + k(r* - rt) Sit a + (kF*)Sit - kIFtSit) (5.3) Here a, k and (F*) are parameters to be estimated, i refers to an individual firm and t is a time subscript. The expected sign for the coefficient kr* is positive, and negative for the coefficient k. Equation 5.3 specifies a model where observations are available on the financial structure of a "panel" of firms at a number of successive time periods. The common way of 102 organizing the pooled sample is by decision units (firms). The data is organized in the following way: 1 1 1 Y = X = u = P P P Here Yi and xi are vectors of observation on each firm m- w: x-o x on a: and “i is the vector of error terms. The model may be expressed as: a y=[ix][:l + 11 (5-4) B The model postulates a common intercept and a common set of slope coefficients for all units at all times periods. If the assumption regarding the disturbance term is that “it - iid(0,o'u) for all i, t then the appropriate estimation method is OLS. If “it are assumed to be normally distributed the usual finite sample tests are appropriate. The financial time series data, however, are likely to be highly auto-correlated in which case the disturbance terms will not be independent over time and the usual inference procedures are not appropriate 1. In order to overcome this problem the first differences of all variables are used in OLS regressions. 1 OLS regression applied to estimate coefficients for models on the pattern of equation 6.1 using financial variables without differencing yielded a Durbin-Watson statistic around 0.3 indicating a high degree of autocorrelation in the error terms. 103 5.3 Em iri ox e : In order to test the first hypothesis three proxy variables are required (i) financial leverage (ii) operating risk (iii) fraction of corporate tax rate that is reflected in the tax induced differential between corporate debt and tax exempt bonds. The dependent and independent variables are operationalized as described in the following section. 5.3.1 Financial Leverage: In hypothesis 1, the probability that the interest payments on the marginal unit of debt will serve as a non- redundant tax shield depends upon the distribution of the operating cash flows (X) and the periodic interest payments (rD). The model suggests that the proxy for financial leverage should be interest paid relative to operating earnings. Therefore, a logical proxy for financial leverage would be the ratio of operating cash flow to interest expense, the former being defined as earnings before interest and taxes plus depreciation. Debt ratios have been used as proxies for financial leverage by other researchers and are theoretically justified. The financial leverage variable will be measured in the following alternative ways: 1) total interest expense / (EBIT + depreciation) 2) long-term debt / (book debt + market value of equity) 3) (long-term debt + short term debt) /(book debt + market value of equity) 104 The interest ratio is calculated by dividing interest expense (Compustat item #15) by operating income before depreciation (Compustat item #13). Two debt ratios are used: first, total long-term debt (Compustat item #9) divided by firm value measured as the sum of the book value of long- term debt and the market value of equity which is calculated by multiplying number of common shares outstanding (Compustat item #25) by the average of highest and lowest .share price for the year. Second, debt ratio includes short- term debt (Compustat item #34) and long-term debt in the numerator and firm value in the denominator. (We examine here some other traditional proxies used for financial leverage in previous empirical work in order to provide a perspective to our choice of variables. Scott and Martin [1975] proxied financial structure by the ratio of common equity to total assets calculated at book values. Bowen, Daley and Huber [1982] used two alternative leverage ratios, the debt-to-assets and equity- to-assets ratios, both employing total debt including spontaneous liabilities such as accounts payables, accrued wages and taxes payable. It is argued that such spontaneous liabilities also generate tax deductions because of their embedded interest cost. Since it is not clear who bears these costs and also since the IRS considers only explicit interest as tax deductible, it appears appropriate to include only interest bearing debt (see Boquist and Moore [1984]). Therefore, we propose to include only interest 105 bearing debt (defined as long-term debt plus the current portion of long-term debt and notes payable). Bowen, Daley and Huber [1982] use two leverage ratios. The first one is common equity divided by total assets [also used by Schwartz and Aaronson [1967], Scott [1975], and Scott and Martin [1975]). The second ratio used was long- term plus short-term debt divided by total assets (also used by Remmers, Stonehill, Wright and Beckhuisen [1974]). Bowen, Daley and Huber [1982] point out that the two ratios may assess leverage very differently. The debt ratio may understate leverage by excluding non-capitalized leases, deferred credits and preferred stock. The equity ratio may overstate leverage by excluding non-capitalized leases from the denominator. Their results, however, lead them to conclude that the debt ratio dominates the equity ratio in so far as industrial classes are more significantly related to debt ratios rather than equity ratios. Marsh [1982] also includes preferred stock for calculation of debt ratios, since, it has been argued, companies view preferred stock as similar to debt. The debt ratio is then long-term debt plus preferred stock divided by the capital employed. He also experiments with ratios of long-term debt plus preferred to both total assets and fixed assets but finds that the results are not much different. Bradley, Jarrell and Kim [1984] use a sample of 821 firms for the 1962-1981 period. Their leverage measure is the ratio of mean book value of long-term debt to the mean sum 106 of the market value of equity and the book value of long- term debt. Sorensen and Kim [1984] also tested for other determinants of the debt level. They include firm size, operating risk, growth, depreciation and effective tax rate. Sorensen and Kim [1984] measure leverage as long-term debt divided by total capitalization in book values. Growth is measured as the geometric mean annual growth in earnings before interest and taxes over the preceding ten years period. Two proxies of operating risk are used (i) coeff- icient of variation in earnings before interest and taxes over ten years (ii) coefficient of variation of equity over ten years. Shrieves and Pashley [1984] studied changes in capital structure following mergers. They use three ratios for measuring financial leverage (1) the ratio of long-term debt to total assets (2) the ratio of long-term debt plus debt portions in current liabilities to the total assets and (3) the ratio of interest expense to earnings before depreciation , interest and taxes. Shrieves and Pashley [1984] argue that non-parametric tests are more appropriate for the following reasons (i) debt ratios are restricted to the 0-1 interval and, therefore, are not normally distributed (ii) the interest ratio may also follow a non- normal distribution as the denominator may be zero or negative. Kester [1986] uses book value ratios as well as market 107 value ratios. Debt is defined to include all notes payables, short-term debt, bonds and other types of long-term debt including convertible debt and capitalized leases. Book equity includes preferred stock, common stock and retained earnings. He also adjusts debt-equity ratios by subtracting cash and marketable securities from total debt. A fully adjusted 'debt ratio' is also calculated for the Japanese firms by subtracting notes receivables from the net debt. Long and Malitz [1985], however, argue against inclusion of convertible debt and leases since these can be used to circumvent agency problems. Davis [1987] employs a book value debt ratio i.e., debt divided by the total assets. Only interest bearing debt was used in the leverage measure. The theory of capital structure suggests that debt ratios should be measured in market value terms. Marsh argues that since the corporate treasurers tend to think in terms of book ratios rather than market value ratios and various restrictive covenants are expressed in book rather than market value ratios, use of book values can be justified in a model explaining corporate decisions. Following Myers [1977] there may be some theoretical justification for their use since book values may be more closely related to the value of assets in place. 108 5-3-2 QEQIQLiDQ.Bi§KL Since the hypothesis being tested relates to time series relationship between operating risk and financial leverage we need a proxy for operating risk which can capture changes over time. In our theoretical model, financial leverage depends upon the variance of the operating cash flows denoted as the operating risk. We proxy it by calculating for each year the variance of a firm's equity return using a seven trading-day period. The variance of equity returns thus calculated is then adjusted to unlever it by multiplying it through by the square of E/(D+E) i.e., varu = {E/(D+E))2var1, on the lines suggested by Hamada [1972]. It would be useful here to briefly examine various variables used by other researchers to represent operating risk in some of the earlier empirical work. Ferri and Jones [1979] used four variables to measure operating risk (a) the coefficient of variation in sales (b) the coefficient of variation in pre-tax cash flows (c) the standard deviation of the standardized growth in sales (d) the standard deviation of standardized growth in cash flow. Standardized growth in X (sales or cash flow) is (Xt-Xt-1)/u(X). Marsh [1982] experiments with four different measures of risk. The first measure is of bankruptcy risk and is defined as fixed charges minus earnings before tax divided by the estimated standard deviation of the past ten years' earnings. The second is the standard deviation of the scaled earnings (EBIT) changes, where the scaling factor is total 109 assets. The third measure is beta or systematic risk of a company's equity. The fourth measure is the standard deviation of the returns on the company's shares. Only the second proxy purports to measure operating risk per se, since all other measures are influenced by leverage. In their final model they dropped three out of four variables, only bankruptcy risk was retained. Flath and Knoeber's [1983] measure of operating risk is one minus the coefficient of determination (1 - R2) of EBIT on a log linear time series. Their definition of capital structure is interest divided by annual expected income averaged over an eight year period. The data are drawn from IRS Statistics of Income and Corporate Income Tax Returns. Bradley, Jarrell and Kim [1984] use the standard deviation of first differences in annual earnings divided by the average value of total assets over the whole period for a volatility proxy of the end-of-period value. Taggart [1985] uses the standard deviation of stock returns multiplied by one minus the market-debt-to-value ratio as a proxy for the standard deviation of returns on total assets. Following Hamada [1972], he suggests this is a good measure of operating risk or the standard deviation of unlevered asset returns if (i) debt is risk-less, (ii) preferred stock is negligible, and (iii) leverage has no effect on the value of the firm. Auerbach [1985] empirically studies the importance of different firm characteristics in influencing debt policies. 110 His study covers the period 1958-79. Balance sheet and income statement data on long-term debt, capital, inventories and earnings was corrected to market values and then all variables were deflated to be expressed in constant dollars rather than current dollars. Each firm's earnings growth rate was estimated by fitting a quadratic trend for its corrected earnings before interest but after taxes. The variance of the earnings was estimated by the sample variance around this trend normalized by the squared mean trend value. Beta of each firm was estimated by using a three index market model and using observations for every tenth trading day over the period of the study. To estimate variance in the value of each firm, variance of the percentage capital gains was multiplied by the sample ratio of equity to debt plus equity for each firm. (Gordon [1985] notes that such an adjustment creates endogeneity and bias). Long and Malitz [1985] argue that since firms do not instantaneously adjust their financing mix to reflect changes in the underlying characteristics the average stock of debt outstanding at any period should provide a better indication of the firm's target capital structure. Their ratios are averaged over three years. They consider only the long term funded debt. They include measures of risk to isolate the effect of investment opportunities. Risk is proxied by equity beta unlevered by the relationship suggested by Hamada [1972]. This method assumes riskless corporate debt and may result in biased estimates of 111 systematic risk for high levered companies (e.g., see Conine and Tamarkin [1985] and Butler, Mohr and Simonds [1989]). To neutralize the effect of risk Long and Malitz also formed equal beta portfolios in another regression. Kester [1986] calculates a simple OLS prediction of return on assets using observations from the preceding five years. The sum of squared residuals from such regressions is used as a proxy for the volatility or risk of return on assets. The growth variable is defined as the compound average annual rate of growth in revenues over a five year period. 5.3.3 Implied Marginal Tax Rare: The relative difference in the yields on taxable bonds (r) and on tax exempt bonds (r0) has been considered in the finance literature as an indicator of the marginal investor's tax rate. Under hypothesis 1 the direction of the relationship between financial leverage and operating risk is explained by the ratio of the implied marginal tax rate (r-ro)/r to the statutory tax rate. The proxy for the explanatory variable, the ratio of the tax induced differential on bonds to the corporate tax rate {F = (r - ro)/6r) is constructed by estimating the implied tax rate over the study period along the lines followed by Skelton [1983]. To proxy tax exempt rates (r0), we use monthly observations on new issue yields for one year, prime, 112 general obligation bonds collected from Salomon Brothers Analytical Record of Yields and Yield Spreads for January 1967 through December 1986 (Table III-1). In order to represent taxable rates (r), yields for one-year certificates of deposits are used for the period beginning 1973. Prior to 1973, CD's were subject to Regulation Q and do not truly reflect the taxable rate. For the period 1967- 73, therefore, rates on banker's acceptances are used instead of CD rates. Banker's acceptances are, however, quoted with six month maturities. Following Skelton [1983] these rates were adjusted by adding or subtracting the difference in yield between one-year and six-month government bonds. The rates on banker's acceptances and government bonds are also obtained from Salomon Brothers. The yield series are given in Appendix I. The ratio of implied to statutory tax rate (r) is then obtained by the expression F =(r - ro)/er, where e = 52% for the period 1967 through 1978 and e = 46% for the later period. In most empirical studies the implied marginal tax rates are calculated by comparing yield indices of taxable corporate bonds and non-taxable municipal bonds. There are two potential problems with this methodology: (1) Trzcinka [1982] points out that municipal and corporate bonds of the same rating may not be of the same risk (2) Skelton [1983] points out a potential yield to maturity bias associated with discount bonds. 113 Ang et al. [1985] employ an alternative procedure for calculating implied marginal tax rates to avoid the problem of differential risk and potential yield to maturity bias for discount bonds. They calculate implied tax rates from pairs of newly issued corporate bonds, each pair consisting of one non-taxable corporate bond (a tax-exempt industrial development or pollution control bond) and one taxable corporate bond. The matched pairs are selected so as to control for rating class, issue date, utility vs non-utility class, issue price, maturity and coupon rate. Their results indicate that the marginal personal tax rate on interest is less than the statutory corporate rate. Their bonds, however, have maturities exceeding five years and the implied tax rates thus calculated may not exhibit enough time variability to be useful in testing the hypothesis. Moreover, inferred marginal tax rates from long-term bonds are subject to biases as noted by Skelton. Skelton [1983] argues that the municipal and corporate bonds which are approximately identical are short-term, high quality tax-exempt and taxable notes. These bonds are nearly default free, are not callable, and are invariably held to maturity. Therefore, the yield ratio of these bonds should reflect only the difference in the taxability of the coupon. He uses monthly observations on new issue yields for one year, prime, general obligation bonds collected from Salomon Brothers Analytical Record of Yields and Yield Spreads for 1954 through 1978. 114 Trzcinka [1982] argues that studies which use bond ratings to control for the risk of the corporate and municipal bonds may be flawed as these ratings at best indicate only default risk and do not imply that the bonds have equivalent risk. He controls for the relative risk by employing a random intercept model and finds that the implied marginal rate is very close to Miller's prediction. The data used was obtained from Solomon Brothers' Analytical Record of Yields and Yield Spreads. The interest rates are new issue, monthly averages of yields with various grades and maturities of ten, twenty and thirty years. Kim and Booth [1985] use Salomon Brothers' "Analytical Record of Yields and Yields Spreads" for the period September 1970 to December 1981. MUnicipal bond yields and utility bond yields are used as proxies for non-taxable and taxable bond yields. The monthly failure rates are taken from the Survey of Current Businesses. 5.4 Growrh and Financial Leverege: 5.4.1 Hyporhesis 2: Qperaripg Eernipgs-Veipe Berio Wig; Hypothesis 2 states that a direct cross-sectional relationship should exist between an individual firm's (operating) earnings to value ratio and the degree of its financial leverage. 115 This hypothesis can be tested in two forms: (i) the firm's financial leverage as measured by Do*/VO(DO*), the ratio of optimal debt to the total market value of the firm, is positively related to E(X1)/VO(DO*), the ratio of next period's expected operating cash flows to the total value of the firm (ii) The financial leverage Do*/VO(DO*) is negatively related to the ratio of the firm's value in the next period to its current value, i.e., E(V1)/V0(Do*). If managers and the market form expectations rationally and unbiasedly then expectations for next period's earnings and values may be replaced by historical values, or E(X1)=X1 and E(V1)=V1. Then two regression models may be employed : (i) (Do/VOIit = a1 + b1 (Xi,t+1/Vit) (5-5) (ii) (DO/V0)it = a2 + b2 (Vit+1/Vit) (5-5) The expected sign of b1 is positive and that of b2 is negative. Here: Xit = cash flow from operations for company i, at time t; cash flow being earnings before interest and taxes plus depreciation, (Do/VOIit = Debt ratio of company i at time t, proxied as in the above section, Vit = total value of the firm : total debt at book value plus market value of equity. 116 5-4-2 flYe2shesis_2ai_Q2eratins_Earnings:Yalus_Batie end IDEQIQSE Betio: It follows from our extension of the BTH model (Chapter III) that the higher growth firms would tend to have a lower financial leverage than non-growth firms or negative growth firms. In the BTH model the ratio of debt to expected cash flow is, however, not expected to be different for firms with different growth rates. In the extended model the debt to operating cash flow ratio will be higher for non-growing firms. We may be able to empirically test for this difference in relationship predicted by the BTH and the extended models by comparing the explanatory power of the growth indicators in explaining financial leverage proxied by the interest coverage ratio and debt value ratio. The hypothesis is tested in two forms: (1) rDO/xit = a1 + b1 (xi,t+l/Vit) (5.7) (ii) rDO/Xit = a2 + b2 (Vit+1/Vit) (5.8) The expected sign of b1 is positive and that of b2 is negative. Here: Kit I cash flow from operations for company i, at time t: cash flow being earnings before interest and taxes plus depreciation, Vit I total value of the firm : total debt at book value plus market value of equity, rD0 5 interest expense. 117 5.4.3 Pooled eng Crpss-Seetipnel Ieereg Ratios employed in the test of Hypotheses 2 and 2a will be in the form of first differences to avoid possible auto- correlation in the residuals. Differencing, however, could impart different attributes to the ratios than intended. Therefore, tests will first be conducted using pooled data as described in section 5.1 and second, using cross- sectional data. The tests using pooled data are in the following form: Yit = 30 + 51*Xit (5-9) Where i=1....n, n=no of firms, and t=1....T, T=no of years. The models are tested assuming a common intercept and slope. The tests are then repeated on cross-sectional samples for each year in the following form: Yit = Bat + 51t*xit (5.10) Where i=1....n, =no of firms, and t=1....T, T=no of years. The models are tested assuming a different intercept and slope for each year in the study period and the ratios are used without differencing. 5.4.4 Spurious Correiepions: When relationships under study are in the form of ratios as in the above section there is a possibility of inducing "spurious" correlations. Karl Pearson [1897] examined the effect on the correlation coefficient of ratios having a common deflator and made the point that correlation between ratios can be larger than the simple correlation between the 118 numerator series. He used the first two terms of a series expansion to relate correlation of the ratios to the moments of the original series and derived the following result: 2 - - + P = rxyvxvy rxflfi rjgvyvzt V; i ( 5 1 1 ) 2 2 i 2 2 ° (Vx + Vz erzvx Vz) (Vy + Vz 2rszsz) Where: P a correlation between X/z and Y/Z: X, Y E the variables to be deflated by variable Z: V V V I coefficient of variation for X, Y, and z x' y' z ryz‘ simple correlation coefficients. Generalizing from Pearson's results, Kuh and Meyer [1955] showed that the ratio correlation may just as well be spuriously low as spuriously high. They conclude that "if primary interest centers on the simple correlation between the numerator series, it would usually be appropriate to proceed in a straight forward manner by relating these variables to one another." They go on to derive necessary and sufficient conditions for the correlation between two series with a common denominator to equal the partial correlation between the numerator series with the deflating variable's influence held constant. The two conditions are (1) that Vz be small so that the series expansion yields a good approximation of P; and (2) that the variables deflated, X and Y, be linear homogeneous functions of the deflator, Z. The concern over spurious correlation is relevant only when the inference about sample or partial correlations between numerator variables is drawn on the basis of ratio 119 correlations. Kuh and Meyer note that "the question of spurious correlation quite obviously does not arise when the hypothesis to be tested has initially been formulated in terms of ratios." Briggs [1962] also concludes that "The correlation between the ratios can in no sense be regarded as spurious when it is to this correlation that interest attaches. The division by the common deflating variable is in this case part of the mechanism by which the correlation is created." In much empirical work in finance, ratios are used to control for size or when errors are heteroskedastic. For example, Weston [1963] regressed weighted average cost of capital of the firm, measured by the ratio of after tax "total earnings" divided by the market value of all its securities, on the ratio of the market value of senior securities divided by the market value of all securities, along with book value of total assets and growth rate of EPS. Miller and Modigliani [1966] in their cost of capital study divided values of equity, earnings and asset growth by total assets. Their structural equation is: (V-ID) = a + a1X (1-1) + a28A + U (5.12) 0 Here: V, D, and X are total value of firm, debt and expected earnings, respectively. 1 is the marginal tax rate and 8A, change in assets, is an indicator of growth. They control for heteroskedasticity by weighing each observation in inverse proportion to the size of the firm, assuming errors are multiplicative and the standard deviation of the 120 error term is approximately proportional to the size of the firm. The fitted equation is of the form V-TD _ 1 X (1-1) 8A __—A___ - ao -A— + a1 A + a2 _A_ + u (5.13) Miller and Modigliani as such used ratios to remove heterskedasticity from the effect of size on the error variance. Lev and Sunder [1979] investigated conditions under which the use of ratios can adequately control for the firm size. These conditions are derived from the strict proportionality condition between the numerator series and the deflating series and are not met when: (a) There is an error term in the relationship, yan+e. If the error term 6 is, however, heteroskedastic of the form oe=k.z', deflation by z will lead to homoskedasticity in the OLS residuals and therefore improve estimation. (b) Presence of an intercept in the relationship between the numerator series will lead to a bias in the series deflated by another variable. (c) when the numerator series depends upon variables other than the deflating variable or when there are non-linearities in the relationship, use of ratios can result in bias. In case where ratios can not provide for adequate control for size, Lev and Sunder have suggested, "The size effect, for example, can be often accounted for by adding a relevant 121 variable to the regression equation." Other researchers, for example, Johnston [1960], Lev [1974], Whittington [1980], Barnes [1982, 1987], have suggested using regression to control for the size effect. 5.4.5 Direct Tests: As discussed in section 5.4.4 in case of a possibility of inducing spurious correlation when using ratios in regression studies direct tests are indicated where numerator variables are used in the regression model and the size effect is controlled by including it as another explanatory variable. The following models will be used to supplement evidence on hypotheses 2 and 2a from pooled and cross-sectional tests. i) FLit = dot + alt*Xi’t+1 + 02t*FVit (5.14) ii) FLit = not + alt*xi,t+l + a2t*5Fvit + 03t*FVit (5.15) where: FLit I Financial leverage for ith company at time t, Xit I cash flow from operations for company i, at time t: cash flow being earnings before interest and taxes plus depreciation, FVit = total value of the firm : total debt at book value plus market value of equity, and i=1....n, n=no of firms, and t=1....T, T=no of years, assuming different intercepts and slopes for each years. 122 5.5 H othesis ' 'me 8 'es e v' f m We; Hypothesis 3 postulates a cyclical pattern in the r (fraction of corporate tax rate implied in the tax induced differential return on debt) which would follow business cycles. The fraction P is predicted to increase when an improving economy is expected in the next year and decline if the economy is expected to worsen. Since the expectation of aggregate economic activity affects expectations of firms' future cash flows and individuals' incomes and thereby supply and demand for corporate bonds, the explanatory variables are indicators of business cycles. Therefore, a regression model of the following general form is tested: rt = a + bi.Yi't+1 (5.16) where Yi represents an indicator of the business cycle. Under the BTH hypothesis the expected sign of the coefficient bi is positive. However, the independent variables are trend variables and it would be more proper to use changes in the indicators as explanatory variables. Moreover, the effect of explanatory variables is likely to be transmitted with lags distributed over several periods in the following form : Ft = ai + b11*8Yi't+1 + ... + bsi*5Yi,t+s (5.17) where s is an appropriate lead period and 8Y1 represents 123 percentage change in the value of business cycle indicator, used to proxy expansion or contraction in economic activity. No particular lead time is suggested by theory. Moreover, the regressors are likely to be autocorrelated at various lags indicating a collinearity problem. Therefore, an Almon distributed lag scheme is employed to estimate coefficients of the lagged regressors. Under the Almon scheme, coefficients (bi) of the lagged variables are approximated by a polynomial function of a suitable degree. Orthogonal reparametrization of the independent variable is achieved by setting b = Wq.c, where b is the vector of coefficients of regressors and Wq is defined as a matrix of coefficients as: 1 o o . . . o 1 1 1 . . . 1 wq = 1 2 4 . . . zq (5.13) 1552...Sq where subscript q indicates the degree of the approximating polynomial. Thus, new regressors Ci are formed as linear combinations of the lagged independent variables. The regression of the dependent variable on these new variables yields estimates of the c's, which in turn yield estimates of the b's.2 The dependent variable gamma (F) is highly auto- correlated and therefore error terms in the OLS regression are not independent over time. When autocorrelation is present, the OLS parameter estimates are not efficient and 2 See Johnston pp. 352-358 124 the standard error estimates are biased. A variation of the Cochrane-Orcutt process, the Yule-Walker method, is employed to control for autocorrelation in the residuals. It is a two-step full transform generalized least square method using OLS residuals to estimate the covariances across observations. For a first-order AR(1) process it is equivalent to the Prais-Winsten estimation method.3 5.5.1 Dependent Variable; The dependent variable for this hypothesis is the ratio of the tax induced differential between tax exempt and taxable bonds to the corporate tax rate (r=(r - ro)/6r}. The method to derive a proxy for this variable was discussed in the section above. The same measure as used for tests of hypothesis 1 is employed here. In estimation of gamma P, we have used new issue yields for one year, prime, general obligation bonds and yields on CD's. Yields on short term maturities were used to minimize any risk premium between municipal bond yields and the CD yields. Earlier studies (for example, Benson and Rogowski [1978], Jaffee [1975] and Tezel [1978]) have shown that municipal bond risk premiums vary inversely with the business cycle. If there remains a risk premium in the municipal bond yields used here to proxy non-taxable rates over the CD yields implying that CD are less risky than 3 For a description of the method see SAS/ETS User's Guide Version 5 Edition. SAS Institute Inc., 1984 Cary NC. 125 municipal bonds 4' gamma could be rewritten as: r0+ p r = {1- —-—r }/9 (5°19) If the risk premium (p) moves counter cyclically, then P will move cyclically. This risk premium effect could reinforce the positive relationship postulated by BTH. On the other hand, it is possible that the arbitrage activities of institutional investors work to offset changes in the tax differential induced by the supply and demand of corporate bonds. As such, these activities may work against detection of the positive relationship predicted by the theoretical model. 5.5.2 independenr Verieble: In order to study the cyclical behavior of the ratio of implied to statutory tax rates (r), the following indicators of the business cycle were obtained from the Citibank database (described in Appendix II) and are used in separate regression models as explanatory variables: 1. BUS 5 Index of Net Business Formation 2. DCEM 5 Coincident Index of Employment, Including Trend 3. DCEMXT I Coincident Index of Employment, Excluding Trend 4. DCOINC I Composite Index of 4 Roughly Coincident 4 Trczinka [1982] showed that municipal bonds have higher risk than corporate bonds of the same ratings. 126 Indicators 5. DLEAD 5 Composite Index of 12 Leading Indicators 6. DLEAP 2 Composite Index of Profitability 7. DLEM 5 Leading Index of Employment, Including Trend 8. DLEMXG a Leading Index of Employment, Excluding Trend 9. INC I Number of New Business Incorporations 10. IPMFG I Industrial Production: Manufacturing 11. IPX I Capacity Utilization Rate: Total Industry Indicators 1,5, 6, a 9 (BDC series 5) are generally considered by NBER as leading at peaks, trough and at business cycle turns while indicator 4 (BDC series) coincides with the business cycle. Leading and coincident indices of employment are constructed by the Center for International Business Cycle Research. The Capacity utilization rate is considered as leading at peaks and coincident at turns while industrial production is a coincident index. Figure 5.1 shows a plot of the value of gamma (F) and the composite index of leading indicators (DLEAD) over the 1967- 86 period. The shaded areas indicate periods of recessions bounded by reference peaks (P) and reference troughs (T) as designated by NBER. From the plot the value of gamma (F) appears to be generally moving together with the index 5 Business Conditions Digest, U.S. Department of Commerce, Bureau of Economic Analysis. (For complete description see Handbook of Cyclical Indicators) 127 GANIM\ & EM_EAEJZ COHKMDSII. Hmdex Of 12 Leadlng Indicators P T 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 66 D QEAD + MA Figure 5.1 Value of Gamma and pne Composite Index of adin Indi rs 128 except for the period 1985-86 when gamma values are quite low. The lower value of gamma in this period may be reflecting the lower statutory tax rate under the Tax Reform Act of 1986 with anticipation of its passage built up much earlier than its effective date. 5.6 x and d de - t e V ' e ' The expanded testable models will include indicators for firm attributes suggested by earlier theories of capital structure which are predicted to affect financial leverage decisions. These include non-debt tax shields, composition of assets, and firm size. 5.6.1 Non-Debt Tax Shieigs: Our multi-period model in Chapter III shows that the existence of tax deductions other than interest on debt is a relevant determinant in capital structure. Firms with relatively higher non-debt tax shields are expected to employ relatively less debt. This relationship was earlier predicted by DeAngelo and Masulis [1980] in a single-period context. Two proxies of non-debt tax shields (NDTS) are employed: 1. ratio of investment tax credits plus depreciation to total assets ; NDTSa = (ITC + Depreciation)/Total Assets 2. a direct indicator of non-debt tax shields (suggested by Titman and Wessels [1988]), calculated 129 from the reported taxes paid (T), operating income (OI), interest payments (rD), and the corporate tax rate (9): NDTSb = 01 - rD - T/e (5.20) 5.6.2 Assets Composition: Three variables are used to reflect the influence of asset composition on capital structure: 1. We proxy for collateral value of assets with the reported value of inventory plus gross plant and equipment (PPE) divided by total assets. Collateral Value = (Closing Inventory + PPE)/Total Assets 2. To capture the effects of agency costs suggested by Myers and Majluf [1984], we include the ratio of intangible assets to total assets and the ratio of advertising and research and development expense to sales: AGENCYa = Intangible Assets/Total Assets AGENCYb = (Advertising + R&D Expenses)/sales 3. The informational asymmetry regarding assets in place is captured by the ending inventory to total assets ratio: INVTOASS = Closing Inventory/Total Assets 130 5.6.3 Firm Sire: Large capitalization firms are expected to be able to carry relatively larger amounts of debt having a better access to capital markets and lower expected bankruptcy costs through the coinsurance effect. Firm size is represented here by the natural log of the firm's sales. SIZE = loge(Net Sales) 5 . 7 Sampie: The sample consists of all manufacturing companies represented on COMPUSTAT as well as on CRSP tapes for the sample period 1968-1986. We excluded utilities and companies engaged in agricultural or extractive industries, banking, insurance and real estate (SIC code less than 2000 and greater than 4799 were excluded). We included only those firms with complete historical data for the sample period. Since many of the indicator variables are scaled by total assets, sales, or operating income, firms with missing values for these items were also excluded. These requirements may have biased our sample selection toward relatively large firms. In all 431, firms were included in the sample which consists of 19 years of financial data. 5.8 pata Sonree: The financial data on the sample companies is obtained from the standard version of the 1988 Annual COMPUSTAT tape. The variances of stock returns were computed from the CRSP 131 daily return tape. The data on yields of non-taxable municipal, and taxable corporate bonds was obtained from "Salomon Brothers' Analytical Record of Yields and Yields Spreads." 5.9 Time Perigd: The time period chosen for the study is from 1-1-68 to 12-31-86. The nineteen year period is selected to cover a number of economic cycles as well as periods of different statutory corporate tax rates. Data for 1987 available on the 1988 COMPUSTAT tape are not used to exclude the influences of the 1986 Tax Reform Act. CHAPTER VI RESULTS OF EMPIRICAL TESTS This chapter reports the results of the empirical tests conducted on the four hypotheses formulated in Chapter V. The tests are carried out first by using the variables suggested by the BTH model and its extension and, second, by using an expanded set of variables to take into account other factors suggested in the finance literature as relevant to financial policy. The proxies used for the empirical tests were discussed in Chapter V. Tables 6.1.1 and Table 6.1.2 summarize the source of each variable and the formulas used to calculated various financial ratios. Statistical significance is determined at 5 percent level. 6.1 Hypothesis l: Operating Risk and Financial Leverage: Hypothesis 1 predicts that the relationship between operating risk and financial leverage should be positive (negative) when the ratio of implied marginal tax rate to the statutory rate is low (high). The empirical tests are based on equation 5.3 and the proxies as explained in section 5.3. 132 133 Table 6-1-1 LI§I_QE_EBQKX_EABIA§LE§ Name Compustat Description Data # INV 3 Inventories TASS 6 Assets-Total PPE 7 Property, Plant & Equipment-Total (Gross) LTD 9 Long-term Debt - Total SALES 12 Sales (Net) OINC 13 Operating Income Before Depreciation DEPR 14 Depreciation and Amortization INTEREST 15 Interest Expense ITAX 16 Income Taxes - Total INCBEX 18 Income Before Extraordinary Items PRHI 22 Price - High PRLO 23 Price - Low SHARES 25 Common Shares Outstanding INTAN 33 Intangibles CLDEBT 34 Debt in Current Liabilities ADVER 45 Advertising Expense RND 46 Research & Development Expense ITC 51 Income Tax Credit (Income Account) VR 5 Variance of the common stock seven-trading-day-return for the year. 134 Table 6.1.2 o E F R o s FVALUEA = LTD + SHARES*(PRHI+PRLO)/2 FVALUEB = FVALUEA + CLDEBT LDRAT = LTD/FVALUEA TDRAT = (LTD + CLDEBT)/FVALUEB INTRAT = INTEREST/OINC EVRAT = OINC/LAG(FVALUEA) NDTSA = (ITC + DEPR)/TASS NDTSB = (OINC — INTEREST - ITAX/THETA)/TASS IF YEAR <= 78 THEN THETA=.52 ELSE THETA=.46 COLLAT = (INV + PPE)/TASS AGENCYA = INTAN/TASS AGENCYB = (ADVER + RND)/SALES INVTOASS= INV/TASS SIZE = LOG(SALES) BRISK = VR*(l-LDRAT)**2 BRGAMMA = BRISK*YRGAMMA VlVO = FVALUEA/LAG(FVALUEA)-1 135 The first set of tests examine the relationship between operating risk and financial leverage which is generally considered to be negative in the finance literature. The three measures of financial leverage were regressed on a measure of operating risk as proxied by unlevered variance of common stock returns. OLS regressions on the first differences (denoted by 8) of the dependent and independent variables were run assuming the following relationships. MODEL #1: 8LDRAT = Bo + 81*SBRISK MODEL #2: 5TDRAT = 30 + 81*SBRISK MODEL #3: slNTRAT = 30 + 81*SBRISK The regressions are run on pooled data as explained above. The regression is of the following form: Yit = 30 + 31*Xit (5-1) where i=1....n, =no of firms, and t=1....T, =no of years. The models are tested assuming a common intercept and slope for the study period. Each variable pertains to a firm i and a year t. The subscripted (it) is omitted in this section for clarity. The results of OLS regression are reported in Table 6.1.3. The coefficients 81's for these first three models are negative and highly significant (p-value = .0001) indicating an inverse relationship between financial leverage and operating risk. The coefficient of operating risk regressed on interest ratio (INTRAT) is, however, not statistically significant at five percent level. 136 Table 6.1.3 Resulrs of Test pf fiypprneeie l; E1DaEsial_Lexerass_§_QPerating_Bisk MODEL #1: 8LDRAT = 80 + 81*SBRISK MODEL #2: 5TDRAT = 80 + 81*58RISK MODEL #3: SINTRAT = 80 + 61*SBRISK PARAMETER ESTIMATES INDEPENDENT MODEL #1 MODEL #2 MODEL #3 VARIABLES COEFF T-STAT COEFF. -STAT COEFF. T-STAT INTERCEPT 0.005 4.531* .005 5.109* 0.180 0.779 sBRISK -0.943 -lO.276* -.858 -9.l98* 15.479 0.746 F - VALUE 105.604 84.598 0.556 PROB > F 0.0001 0.0001 0.4559 R - SQUARE 0.0134 0.0108 0.0001 ADJ R-SQ 0.0133 .0107 -0.0001 DURBIN-WATSON D 2.067 .960 2.694 * Significant at 0.0001 level 137 The second set of regressions is based on the BTH hypothesis 1 in which the relationship between financial leverage and operating risk is predicted to depend on the magnitude of gamma (P) and the ratio of the implied marginal tax rate to the statutory tax rate. The operational form of the hypothesis follows equation 5.3: FLit = a + (kr*)sit - k.(rt.sit) (6.2) The expected sign of the coefficient kF* is positive, and of the coefficient k is negative. OLS regression was applied to the following models: MODEL #4: 8LDRAT = po + 81*5BRISK + 82*53RGAMMA MODEL #5: 5TDRAT = so + 61*SBRISK + 82*SBRGAMMA MODEL #6: slNTRAT = so + 81*5BRISK + 82*5BRGAMMA Table 6.1.4 shows the results of OLS regression for models 4 to 6. As can be seen from the table, the coefficients of BRISK (Sit) and BRGAMMA (rt-Sit) are both significant and of the expected sign for model 4 and 5. For model 6 (dependent variable is interest ratio) the coefficients are not significant (p-values z 0.12). The relative gain in the explanatory power of the model including BRGAMMA can be judged by constructing an F-test based on the squared errors of the restricted and unrestricted regressions. (SSEr -SSEur)/s F = - F(s,n-k) SSEur/(n-k) The computed F-statistics are 82.88 and 19.79 for models 4 and 6, respectively, which are significant at the 1% 138 Table 6.1-4-- ResulIs_ef_Ts§I_2f_HYPeIhesis_1i Finaneial Leverage, Qperaring risk and gamma MODEL #4: 5LDRAT = so + 51*58RISK + 62*SBRGAMMA MODEL #5: 5TDRAT = so + 81*5BRISK + 82*58RGAMMA MODEL #6: sINTRAT = so + 81*88RISR + 82*8ERGAMMA PARAMETER ESTIMATES INDEPENDENT MODEL #4 MODEL #5 MODEL #6 VARIABLES COEFF. T-STAT COEFF. T-STAT COEFF. T-STAT INTERCEPT 0.005 4.499* 0.005 5.088* 0.179 0.772 ssRISK 26.240 8.784* 12.697 4.165* 870.980 1.283 58ROAMMA -29.562 -9.104* -l4.74l -4.449* -930.348 -l.260 P-VALUE 94.801 52.297 1.072 PROB > P 0.0001 0.0001 0.3423 R - SQUARE 0.0239 0.0133 0.0003 ADJ-RSQ 0.0236 0.0131 0.0000 DURBIN-WATSON D 2.059 1.962 2.694 * Significant at 0.0001 level 139 level indicating that BRGAMMA has additional explanatory power over models containing just the indicator of Operating risk (BRISK).1 Using equation 6.2, we can compute F*, the critical value of F=(r - ro)/er, at which the slope of the financial- leverage-business-risk relationship changes sign. From the coefficients of BRISK and BRGAMMA, this critical value (r*) works out to be 0.89 and 0.86 for models 4 and 5, respectively. The theoretical value of r* under assumption of a symmetrical distribution of operating cash flows is 0.5. It appears that BRISK and BRGAMMA are be highly collinear since the yearly average of gamma does not show much variation from year to year. Therefore, it is difficult to estimate their coefficients with much precision. Consequently we can not put much confidence in the estimate of F*. The third set of tests used expanded models 7-9 which include an expanded set of variables suggested by other theories of capital structure. In addition to operating risk and gamma (F) suggested by the BTH model, we include proxies for non-debt tax shields, collateral assets value, asymmetric information, and agency costs. 1 F.01(l,1000) = 6.66 140 The tested models are: MODEL #7: 8LDRAT = BO + 81*SBRISK + 82*SBRGAMMA + 83*8NDTSA + B4*5NDTSB + 85*5COLLAT + 66*8AGENCYA + 87*8AGENCYB + 88*SINVTOASS + 89*SSIZE MODEL #8: STDRAT = 80 + 01*SBRISK + 62*SBRGAMMA + 83*8NDTSA + 84*8NDTSB + 85*8COLLAT + 86*8AGENCYA + 87*8AGENCYB + 88*SINVTOASS + 89*SSIZE MODEL #9: SINTRAT = 60 + 81*SBRISK + 62*SBRGAMMA + 83*5NDTSA + 64*5NDTSB + 65*5COLLAT + 86*5AGENCYA + 87*8AGENCYB + 08*SINVTOASS + B9*SSIZE Table 6.1.5 presents the results of OLS regression for the three models 7-9. The coefficients of BRISK and BRGAMMA are significant and of the predicted signs when the dependent variables are the long-term debt ratio (LDRAT) or the total debt ratio (TDRAT) as was found earlier (models 4-6). As before, coefficient for BRISK and BRGAMMA are not significant when the interest ratio (INTRAT) is the dependent variable. The model uses two proxies for non-debt tax shields. The first, based on investment tax credit and depreciation expense, NDTSA = (ITC + DEPR)/TASS, has the expected negative coefficient for the two models (7 8 8) using debt ratios as measures Of financial leverage. The coefficient of NDTSA in model 9 where the dependent variable is the 141 Table 6.1-5 Bess1Is_2f_TesI_2f_HxP2Inesis_li_ExPensed_Megsl MODEL #7: 5LDRAT = so + 81*58RISK + 82*88RGAMMA + 83*8NDTSA + 54*5NDTSB + 85*8COLLAT + 86*8AGENCYA + B7*8AGENCYB + 58*SINVTOASS + 89*OSIZE MODEL #8: STDRAT = 60 + 81*SBRISK + 62*SBRGAMMA + 83*8NDTSA + B4*5NDTSB + 35*8COLLAT + 86*5AGENCYA + 57*8AGENCYB + 88*SINVTOASS + 89*OSIZE MODEL #9: SINTRAT = 80 + 81*SBRISK + 82*OBRGAMMA + 83*5NDTSA + B4*5NDTSB +85*5COLLAT + 86*8AGENCYA + B7*5AGENCYB + 38*SINVTOASS + B9*SSIZE PARAMETER ESTIMATES INDEPENDENT MODEL #7 MODEL #8 MODEL #9 VARIABLES COEFF. T-STAT COEFF. T-STAT COEFF. T-STAT INTERCEPT 0.002 1.316 0.004 3.6020 1.542 6.153* 8BRISK 25.808 8.663* 13.833 4.565* 503.434 0.753 SBRGAMMA -29.078 -8.980* -15.964 -4.847* -533.179 -0.734 5NDTSA -0.560 -3.576@ -0.923 -5.801* 116.816 3.328# 8NDTSB -0.039 -0.905 0.064 1.475 4.932 0.516 SCOLLAT 0.036 2.145 -0.010 -0.594 4.429 1.173 SAGENCYA 0.433 8.590* 0.452 8.807* 1.062 0.094 SAGENCYB 0.081 0.975 -0.0079 -0.093 121.626 6.541* SINVTASS -0.078 -2.508 0.143 4.544* 5.835 0.840 SSIZE 0.032 6.107* 0.019 3.4709 19.045 -16.091* F-VALUE 36.740 33.037 39.335 PROB > F 0.0001 0.0001 0.0001 R - SQUARE 0.0409 0.0370 0.0437 ADJ-RSQ 0.0398 0.0358 0.0426 DURBIN-WATSON D 2.052 1.951 2.694 * Significant at 0.0001 level @ Significant at 0.0005 level # Significant at 0.0010 level 142 interest ratio (INTRAT = INTEREST/OINC ) is unexpectedly positive and significant (p-value = .0007). The second proxy for non-debt tax shields, (NDTSB = (OINC - INTEREST - ITAX/THETA)/TASS), is insignificant in all regressions. The indicator variable for the collateral value of the assets of the firm, COLLAT = (INV + PPE)/TASS, is marginally significant (p-value = 0.0451) as an explanatory variable for long-term debt ratio (LDRAT), but in other models the coefficient is not statistically significant. This result could be driven by the gross value of property, plant and equipment included in the numerator of the ratio which are considered more suitable as collateral for long-term debt than short term debt. The explanatory variable, AGENCYA = INTAN/TASS, meant to capture the effect of collateral value of the assets, has a positive and highly significant coefficient with positive sign instead of the expected negative sign. This is true for all regression models. It appears that the proxy is reflecting the value of higher future cash generating possibilities recorded on financial statements rather than the value of growth opportunities in the Myer and Majluf sense. A firm records an intangible assets only when the expected future benefits have a high probability of being realized as cash flows. Viewed as such, increases in intangible assets are more likely to be associated with increased leverage as observed here. The ratio of advertisement plus research and development 143 expenses to net sales, AGENCYB = (ADVER + RND)/SALES, has insignificant coefficients in the first two models (7 and 8) but is a highly significant explanatory variable of the interest ratio and has positive sign. The indicator is considered a measure of the uniqueness of products and also of non-debt tax shields. In either case, the variable is expected to be negatively related to financial leverage. It is possible, however, that increases in advertisement and R&D expense may also be associated with higher cash flows resulting in an ambiguous net effect. The ratio of inventory to total assets, INVTOASS = INV/TASS, has been used as an indicator of asymmetrical information regarding the value of assets and is expected to have a positive sign. The regression coefficient is, however, positive and highly significant for total debt ratio, negative and marginally significant for the long-term debt ratio and not significant for the interest ratio. It appears that this ratio is representing the collateral value of current assets which have a stronger positive relationship with short-term debt and hence with the total debt ratio. The coefficient of firm size indicator, SIZE = LOG(SALES), is significant and positive for models using debt ratios as the dependent variables. It appears to support the notion that larger firms are able to support higher levels of debt, having either lower bankruptcy costs or a better access to the capital markets. 144 6.2 Rypophesis 2: Groyrn and rhe Rep; Ratio; The BTH model predicts that the Operating earnings-value ratio and the debt ratio will exhibit a direct (positive) relationship. Firms with high earnings-value ratios are likely to be low growth firms. Therefore, we employ a direct indicator of growth, i.e., Vl/Vo- The form of test and the proxies employed were discussed in section 5.4. The hypothesis were operationalized by running OLS regressions on the following models: Earnings Velpe Ratio eng Deb; Rerip: MODEL #10 : ELDRATit = $0 + 81*5EVRATit MODEL #11 : 8TDRATit = so + 81*8EVRATit growth in Eirn yelue and Dept Rarip: MODEL #12 : 5LDRATit = so + 51*sv1v01t MODEL #13 : STDRATit = 60 + 31*8V1V0it 6.2.1 Pooled Sanple Teens: The models were tested using first differences of ratios and pooled data as described in section 5.4 in the following form: RYit = 50 + 51*Xit (6.2) Where i=1....n, n=no of firms, and t=1....T, T=no of years. The models are tested assuming a common intercept and slope. In this section the subscripts are omitted for simplicity. In the first set of models 10-11 the expected earnings to firm value ratio is measured by EVRAT = OINC/LAG(FVALUEA). 145 The second set of models 13-15 relates firms' financial leverage to growth in firm value measured by V1V0 = FVALUEA/LAG(FVALUEA)-1. Tables 6.2.1 and 6.2.2 present the results of OLS regressions for models 10 and 11. In Table 6.2.1, the sign of the coefficient on EVRAT is positive as expected and highly significant for model 11 employing total debt as the dependent variable. The sign of the coefficient for EVRAT in model 10 is negative, contrary to that predicted by the theoretical model. It appears that increases/decreases in the earnings-value ratio are indicating increases/decreases in the internally generated cash flows. Given a tendency on the part of firms to rely on internally generated funds to finance investment opportunities, higher operating cash flows may lead to lower debt ratios. Table 6.2.2 shows the results of OLS regression of financial leverage measures on the value ratio given by models 12 and 13. The coefficients of V1V0 are significant for the two regressions but the sign is unexpectedly positive for the total debt ratio regression and is negative, as expected, for the long-term debt ratio regression. Increases/decreases in the growth ratio may also indicate higher/lower expected cash flows and render the empirical relationship ambiguous. 146 Table 6.2.1 BesulIs_2f_TesI_2f_Hxnetne§i§_21_ pebr Retip eng Eernings Velue Retip: MODEL #10 . 8LDRAT = $0 + 81*8EVRAT MODEL #11 . 5TDRAT = so + 81*8EVRAT PARAMETER ESTIMATES VARIABLE MODEL #10 MODEL #11 COEFF. T-STAT COEFF. T-STAT INTERCEPT 0.005 4.900* 0.0053 5.062* SEVRAT -0.016 -1.971@ 0.0740 9.136* F - VALUE 3.886 83.467 PROB > P 0.0487 0.0001 R-SQUARE 0.0005 0.0113 ADJ-RSQ 0.0004 0.0111 DURBIN-WATSON D 2.023 1.927 * Significant at 0.0001 level @ Significant at 0.0500 level 147 Table 6.2.2 Resnlrs of Tesr or Rypornesis 2: DebI_BaIi2_aDQ_§I2EIh_iD_Eirm_EEIUEI MODEL #12 . 8LDRAT 50 + 81*5v1v0 MODEL #13 : 5TDRAT so + 81*8V1V0 PARAMETER ESTIMATES VARIABLE MODEL #12 MODEL #13 COEFF. T-STAT COEFF. T-STAT INTERCEPT 0.005 5.148* 0.005 5.120* 8V1V0 -0.021 -11.805* 0.009 4.867* F - VALUE 14.522 23.690 PROB > P 0.0001 0.0001 R-SQUARE 0.0020 0.0032 ADJ-RSQ 0.0018 0.0031 DURBIN-WATSON D 2.670 1.928 * Significant at 0.0001 level 148 Further tests of hypothesis 2 were conducted by using an expanded set of explanatory variables suggested by other theories of capital structure. The following models were tested. MODEL #14: sLDRAT = so + s1*5EVRAT + 32*8NDTSA +B3*8NDTSB + 84*5COLLAT + s5*5AGENCYA + so*5AGENCYB + s7*5INVTOASS + so*5SIZE MODEL #15: STDRAT = so + 81*8EVRAT + 62*8NDTSA +s3*5NDTSB + s4*5COLLAT + s5*5ASENCYA + 55*8AGENCYB + s7*5INVTOASS + 68*SSIZE MODEL #16: DLDRAT = so + 61*5V1V0 + 82*8NDTSA +B3*6NDTSB + s4*5c0LLAT + 65*8AGENCYA + so*5AGENCYB + s7*5INVTOASS + 68*SSIZE MODEL #17: 5TDRAT = so + s1*5VIv0 + 82*8NDTSA +B3*8NDTSB + s4*500LLAT + s5*5AGENCYA + so*5AGENCYB + 37*8INVTOASS + 88*SSIZE The results of OLS regression for the models 14-15 and models 16-17 are given in Tables 6.2.3 and 6.2.4, respectively. From comparing these tables with Tables 6.2.1 and 6.2.2 it is seen that the signs of the earnings-value ratio (EVRAT) and of the value ratio (V1V0) are unchanged Table 6.2.3 Ode ° MODEL #14: 8LDRAT = so Results of 149 st of Ra - E ande + 31*5EVRAT + 32*5NDTSA +B3*8NDTSB + s4*5OOLLAT + 05*8AGENCYA + 66*5AGENCYB + s7*5INVTOASS + 88*SI2E MODEL #15: 5TDRAT = so + 81*8EVRAT + 52*8NDTSA +B3*5NDTSB + B4*5COLLAT + 85*8AGENCYA + 86*8AGENCYB + 87*SINVTOASS + 88*SIZE PARAMETER ESTIMATES VARIABLE MODEL #14 MODEL #15 COEFF. T-STAT COEFF. T-STAT INTERCEPT 0.003 2.532$ 0.004 3.7226 SEVRAT -0.010 -1.287 0.084 10.429* 8NDTSA -0.541 -3.146# -1.020 -5.876* 8NDTSB -0.066 -l.405 0.017 0.365 SCOLLAT 0.044 2.479$ -0.003 0.145 8AGENCYA 0.479 8.171* 0.517 8.740* SAGENCYB 0.024 0.277 -0.004 -0.052 SINVTASS -0.109 -3.455# 0.143 4.462* OSIZE 0.023 4.100* 0.019 3.405# F - VALUE 14.013 34.060 PROB > F 0.0001 0.0001 R-SQUARE 0.0151 0.0359 ADJ-RSQ 0.0140 0.0348 DURBIN-WATSON D 2.014 1.912 * Significant at 0.0001 level 6 Significant at 0.0005 level # Significant at 0.0010 level & Significant at 0.0050 level $ Significant at 0.0100 level I Significant at 0.0500 level 150 Table 6.2.4 Results of Ieet of Rypotnesis z-Erpenged upgel: Debt Retio ang Grpyrn in Rirn Velpe: MODEL #16: 5LDRAT = so + s1*5v1v0 + 82*5NDTSA +B3*8NDTSB + 84*8COLLAT + s5*5AOENcYA + so*5AOENCYB + s7*5INVTOAss + s8*5SIZE MODEL #17: 5TDRAT = so + s1*5v1v0 + 82*5NDTSA +B3*8NDTSB + 84*8COLLAT + 85*5AGENCYA + 86*5AGENCYB + s7*51NVTOAss + so*5SI2E PARAMETER ESTIMATES VARIABLE MODEL #16 MODEL #17 COEFF. T-STAT COEFF. T-STAT INTERCEPT 0.004 3.386# 0.005 3.849* 8V1V0 -0.020 -10.868* 0.012 6.464* 8NDTSA -0.469 -2.749$ -1.012 -5.797* 5NDTSB -0.061 -l.312 0.015 0.321 8COLLAT 0.050 2.857& 0.005 0.276 SAGENCYA 0.459 7.882* 0.526 8.840* SAGENCYB -0.006 -0.073 -0.007 -0.082 SINVTASS -0.113 -3.605@ 0.135 4.214* SSIZE 0.014 2.581$ 0.018 3.129& F - VALUE’ 28.789 25.504 PROB > F 0.0001 0.0001 R-SQUARE 0.0305 0.0271 ADJ-RSQ 0.0295 0.0261 DURBIN-WATSON D 1.992 1.915 * Significant at 0.0001 level 9 Significant at 0.0005 level # Significant at 0.0010 level & Significant at 0.0050 level $ Significant at 0.0100 level I Significant at 0.0500 level 151 and their significance levels are not materially affected when the models are extended. The conclusions reached from the simple regression models are not altered. A comparison of coefficients for the expanded set of variables from tables 6.1.4 and 6.1.5 with those reported in tables 6.2.3 and 6.2.4 shows that signs and significance levels of these explanatory variables are also not materially changed. It appears that the expanded set of variables represent attributes which are independent of the explanatory variables suggested by the BTH model. 6.2.2 Cross-sectipnel 195:5 of Rypornesis g: In the pooled sample test on models 10-17, possible auto-correlation in errors was avoided by working with the first differences of the ratios. The differenced ratios, however, could measure a different attribute and thereby change the nature of the test being conducted. For example, change in the earnings-value ratio, an indicator of growth, may indicate change in profitability, a different attribute than growth, introducing ambiguity as to its effects. In order to forestall any such unintended effects, models 10-15 were tested using cross-sectional samples for each year. s e 'o b ' ° MODEL #18 : LDRATit = Bot + Blt*EVRATit MODEL #19 : TDRATit = 50t + Blt*EVRATit 152 growth in Firn Velue eng ert Regio: MODEL #20 : LDRATit = 50t + 61t*V1V01t MODEL #21 : TDRATit = BOt + s1t*v1voit The regression is of the following form: Yit = Bot + Blt*Xit where i=1....n, =no of firms, and t=1....T, T=no of years. The models are tested assuming a different intercept and slope for each year in the study period and the ratios are used without differencing. The results of cross-sectional tests for models 18-21 are shown in Tables 6.2.5 through Table 6.2.8. Table 6.2.5 reports results of regression of LTD on EVRAT. The coefficient of EVRAT is positive as expected and significant for 6 years out of 18 years in the period. These coefficients are, however, negative and significant for four of the years. For the rest of the years, the coefficients are not significant. A similar pattern is depicted in Table 6.2.6 where the total debt ratio is regressed on the earnings-value ratio. Nine out of 18 coefficients are of the expected sign (positive) and significant while 3 coefficients are negative and significant. Table 6.2.7 gives results of the OLS regression of LTDRAT on the growth ratio (V1V0). The sign of V1V0 is negative and significant for most of the years as predicted. For four years (1969, 1973, 1976 and 1983) the coefficient is positive and significant. For the same years, coefficients 153 Table 6.2-5 EesulIs_2f.§r9§s:§estieanl_12§I§i LeDgIerm_DebI_Bati2_aDQ_EaInins§:YelnelsuaIz Intercept Independent Variable Yea Coe i. - t t - u - - 1968 0.102 7.112 0.0001 0.312 3.255 0.0012 1969 0.134 9.852 0.0001 0.202 2.142 0.0328 1970 0.191 11.802 0.0001 0.167 1.861 0.0635 1971 0.160 9.360 0.0001 0.302 3.146 0.0018 1972 0.130 7.443 0.0001 0.449 5.081 0.0001 1973 0.201 12.970 0.0001 0.214 4.084 0.0001 1974 0.312 16.114 0.0001 0.013 0.210 0.8338 1975 0.335 16.366 0.0001 -0.066 -1.127 0.2605 1976 0.274 15.035 0.0001 -0.005 -0.083 0.9338 1977 0.246 10.611 0.0001 0.084 1.091 0.2760 1978 0.266 11.988 0.0001 0.007 0.093 0.9260 1979 0.303 14.760 0.0001 -0.l33 -1.853 0.0646 1980 0.255 13.206 0.0001 0.006 0.085 0.9321 1981 0.293 19.143 0.0001 -0.213 -3.167 0.0017 1982 0.294 18.364 0.0001 -0.130 -2.069 0.0391 1983 0.219 13.279 0.0001 -0.009 -0.130 0.8964 1984 0.257 16.851 0.0001 -0.l67 -2.370 0.0182 1985 0.244 17.607 0.0001 -0.082 -l.374 0.1701 154 Table 6.2.6 Resnlts pg Qrpse-Sepripnel Teere: Tota ebt d a 'n -V ue t' Intercept Independent Variable Year Coefgi, r-eret R-velpe Qpeffi, r-erer R-valne 1968 0.124 7.766 0.0001 0.432 4.036 0.0001 1969 0.163 10.623 0.0001 0.350 3.308 0.0010 1970 0.232 12.925 0.0001 0.278 2.784 0.0056 1971 0.197 10.358 0.0001 0.380 3.571 0.0004 1972 0.156 8.323 0.0001 0.542 5.719 0.0001 1973 0.260 15.697 0.0001 0.210 3.731 0.0002 1974 0.360 18.056 0.0001 0.101 1.645 0.1008 1975 0.351 16.653 0.0001 0.046 0.773 0.4402 1976 0.279 14.665 0.0001 0.141 2.344 0.0195 1977 0.275 11.333 0.0001 0.136 1.705 0.0889 1978 0.296 12.819 0.0001 0.060 0.817 0.4143 1979 0.338 16.125 0.0001 -0.097 -1.315 0.1893 1980 0.288 14.543 0.0001 0.052 0.701 0.4836 1981 0.329 20.273 0.0001 -0.155 -2.181 0.0297 1982 0.311 18.428 0.0001 0.004 0.062 0.9503 1983 0.246 14.197 0.0001 0.025 0.328 0.7433 1984 0.303 18.933 0.0001 -0.179 -2.423 0.0158 1985 0.295 20.159 0.0001 -0.108 -1.716 0.0869 155 Table 6.2.7 esu t o C sts: n te t t d V owth Intercept Independent Variable Year Coef f i - t-stat P—Mw 1968 0.145 22.314 0.0001 -0.019 -0.760 0.4479 1969 0.172 21.413 0.0001 0.085 2.989 0.0030 1970 0.236 24.840 0.0001 -0.119 -4.117 0.0001 1971 0.228 25.451 0.0001 -0.150 -5.009 0.0001 1972 0.209 22.421 0.0001 0.015 0.355 0.7230 1973 0.284 24.616 0.0001 0.232 4.951 0.0001 1974 0.326 28.234 0.0001 -0.107 -2.419 0.0160 1975 0.347 26.278 0.0001 -0.l41 -4.050 0.0001 1976 0.269 27.388 0.0001 0.023 2.632 0.0088 1977 0.270 25.176 0.0001 -0.004 -0.130 0.8969 1978 0.278 26.578 0.0001 -0.072 -2.055 0.0405 1979 0.293 28.313 0.0001 -0.116 -4.794 0.0001 1980 0.279 26.398 0.0001 -0.159 -4.335 0.0001 1981 0.256 28.206 0.0001 -0.082 -2.793 0.0055 1982 0.296 24.770 0.0001 -0.077 -3.939 0.0001 1983 0.215 24.458 0.0001 0.069 1.839 0.0665 1984 0.243 26.014 0.0001 -0.108 -4.508 0.0001 1985 0.250 24.596 0.0001 -0.088 -4.133 0.0001 156 Table 6.2.8 Reeulps pr Qroes-Seepionel 195:8: Iotel Debt Rario eng yelpe Qrpgrh Intercept Independent Variable ear . - t -va e f - -v 1968 0.184 25.211 0.0001 -0.030 -1.054 0.2923 1969 0.214 23.405 0.0001 0.054 1.672 0.0952 1970 0.293 27.418 0.0001 -0.109 -3.350 0.0009 1971 0.280 28.194 0.0001 -0.175 -5.285 0.0001 1972 0.247 24.533 0.0001 -0.030 -0.663 0.5076 1973 0.351 28.943 0.0001 0.298 6.042 0.0001 1974 0.393 32.817 0.0001 -0.058 -1.281 0.2010 1975 0.384 27.937 0.0001 -0.087 -2.392 0.0172 1976 0.309 30.539 0.0001 0.042 4.740 0.0001 1977 0.306 27.320 0.0001 0.046 1.442 0.1499 1978 0.319 29.189 0.0001 -0.041 -1.125 0.2610 1979 0.337 31.823 0.0001 -0.112 -4.535 0.0001 1980 0.324 29.937 0.0001 -0.169 -4.502 0.0001 1981 0.302 31.395 0.0001 -0.059 -1.879 0.0609 1982 0.314 24.651 0.0001 -0.005 -0.245 0.8063 1983 0.248 26.907 0.0001 0.094 2.370 0.0183 1984 0.283 28.693 0.0001 -0.088 -3.448 0.0006 1985 0.296 27.273 0.0001 -0.081 -3.577 0.0004 157 are also positive and significant in the regression of the total debt ratio on value growth V1V0 (Table 6.2.8). The problem of inducing a spurious correlation when variables are in form of ratios was discussed in Chapter V. The ratios used to test hypothesis 2 were examined to see if these meet the Kuh-Meyer conditions under which deflation by a common denominator would correctly control for size differences among units in cross-sectional study. In models 10-21 the numerator series have been deflated by the firm value in order to control for size of the firm. Each individual numerator series (EOINC, 8FVALUE, LTD, and Total debt) was regressed on the deflating series, FVALUE, for each year over 1968-1985 period. The regression indicated that the homogeneity condition of Kuh and Meyer does not hold, i.e., for each of the relationships between a numerator series and the deflator there is a significant and large (in relation to the mean of the dependent variable) intercept. Moreover, the coefficient of variation Of the deflating series, FVALUE, was found to be large (2.5 to 3). Hence the Kuh and Meyers conditions are not met by the data. 6.2—3 121W In the BTH model the hypotheses have initially been stated in the form of ratios. Hypothesis 2, for example, states that a direct cross-sectional relationship should exist between an individual firm's operating earnings-value ratio and the degree Of its financial leverage. While the 158 results of cross-sectional regressions reported earlier may not be plagued by spurious correlation, we form alternative models to supplement the empirical evidence on hypothesis 2 in the cross-sectional models 18-21 using ratios. The following direct models were tested. Model #22: LTDit = sot + Blt*OINCit+1 + 62t*FVALUEAit Model #23: TOTDEBTit = sot + Blt*OINCit+1 + 02t*FVALUEAit where i=1....n, n=no of firms, and t=1....T, T=no of years, assuming different intercepts and slopes for each years. Here, TOTDEBT= long-term debt plus short-term debt. Firm value (FVALUEA) is included to control for the size effect as an explanatory variable rather than as a deflator. Similarly, models employing growth in value are: Model #24: LTDit = sot + Blt*8FVALUEAit + 62t*FVALUEAit Model #25: TOTDEBTit = sot + Blt*8FVALUEAit + th*FVALUEAit where: 8FAVLUEAt = FVALUEAt+1 - FVALUEAt and i=1....n, n=no of firms, and t=1....T, T=no of years. Two problems may arise in estimation of models #22-25. First, near multi-collinearity may exists as the regressors are correlated among themselves. When independent variables are collinear the OLS estimates are still best linear unbiased estimates but the sampling variances of the estimates increase with rising collinearity. In order to check for multi-collinearity, tests were carried out on 159 selected years following the detection procedure recommended by Belsley, Kuh and Welsch [1980]2. Such tests indicated that the problems of multi-collinearity may not be severe. The second problem relates to heteroskedasticity in the error term. The basic assumption underlying the OLS estimation method is that the disturbance variance is constant at each observation and that the disturbances are pair-wise uncorrelated. In the OLS regressions of models #28-33, residuals were examined for the presence of hetero- skedasticity. For the majority of tests the null hypothesis of constant residual variance was rejected. When the assumption of a constant variance is violated, the OLS estimators are still unbiased, but the conventional formulas for computing sampling variances of the estimators are not applicable and the usual inference procedures are invalid. In case the process generating differing variances is known on a priori grounds or can be determined by empirical methods, feasible generalized least square procedures can be employed. For these models, there is no strong a priori basis to postulate a certain model generating the error variance. The alternative to employing GLS is suggested by White [1980] who derives a covariance matrix of the estimators which is consistent even in the 2 The procedure involves computing a condition index, k(X)=./gmax/./gmin from the eigenvalues of X'X matrix and examining the proportion Of the sampling variance of each coefficient associated with the condition index. Condition indices in the range of 20-30 are considered 'dangerous'. Computed condition indices were in the range of 5-10. 160 presence of heteroskedasticity. The advantage Of employing White's method is that this estimator does not depend upon a formal model of the structure of the heteroskedasticity and allows testing of linear hypothesis by conducting a chi- square test similar to the familiar t-test. Tables 6.2.9 through 6.2.12 contain the results of OLS regression for direct tests of hypothesis 2. Values of the estimators of the coefficients are given along with White's chi-square statistics, the achieved level of significance, (p-value), and the partial correlation (squared) between the regressor and the dependent variable. Table 6.2.9 reports results of the model #22: LTDit = sot + Blt*OINCit+1 + BZt*FVALUEAit The coefficient of Operating income is positive and significant for all but two years supporting the theoretical hypothesis. The firm value has a coefficient which is mostly negative and insignificant. A similar picture is emerges in Table 6.2.10 when we regress total debt on operating income and firm value using model #23: TOTDEBTit = sot + Blt*OINCit+1 + $2t*FVALUEAit Comparing Table 6.2.9 with 6.2.10,the partial correlation between total debt and expected income is generally higher than it is between long-term debt and expected income suggesting that the firms may be responding to the expectations of higher incomes by increasing short-term debt to a greater degree than long term debt. 161 Table 6.2.9 Resulrs pf Direer Tesre pf Hypprneeis 2: WW: Dependent Variable: Long-term debt Independent Variable: 1. Operating Income t+1, EOINC 2. Firm value, FVALUEA Year Coefficient CHI-SQR p-value Partial Corr. 1968 INTERCEPT 39.1306 26.5540 0.0001 EOINC 0.8834 10.2848 0.0013 0.3240 FVALUEA -0.0405 1.8505 0.1737 0.0732 1969 INTERCEPT 52.2261 46.3645 0.0001 EOINC 0.8522 15.1889 0.0001 0.3199 FVALUEA -0.0375 2.0971 0.1476 0.0617 1970 INTERCEPT 64.9986 60.6071 0.0001 EOINC 0.7535 30.1693 0.0001 0.3457 FVALUEA -0.0347 2.3558 0.1248 0.0485 1971 INTERCEPT 68.7261 57.9350 0.0001 EOINC 0.7288 39.5714 0.0001 0.3827 FVALUEA -0.0347 2.8691 0.0903 0.0560 1972 INTERCEPT 76.9775 61.7101 0.0001 EOINC 0.5264 26.4977 0.0001 0.4411 FVALUEA -0.0205 2.0360 0.1536 0.0381 1973 INTERCEPT 89.7049 67.5065 0.0001 EOINC 0.2872 24.8253 0.0001 0.3764 FVALUEA -0.0001 0.0002 0.9889 .0000 1974 INTERCEPT 101.4542 33.0642 0.0001 EOINC 0.3690 11.4286 0.0007 0.2789 FVALUEA -0.0008 0.0006 0.9807 0.0000 1975 INTERCEPT 104.8745 21.2936 0.0001 EOINC 0.5312 23.0259 0.0001 0.2789 FVALUEA -0.0234 0.2280 0.6330 0.0093 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 INTERCEPT EOINC FVALUEA INTERCEPT EOINC FVALUEA INTERCEPT EOINC FVALUEA INTERCEPT EOINC FVALUEA INTERCEPT EOINC FVALUEA INTERCEPT EOINC FVALUEA INTERCEPT EOINC FVALUEA INTERCEPT EOINC FVALUEA INTERCEPT EOINC FVALUEA INTERCEPT EOINC FVALUEA 162 105.3016 0.5546 -0.0260 103.9102 0.6799 -0.0609 120.4542 0.5333 113.6814 0.5668 -0.0301 97.1226 0.3517 0.0560 84.8118 0.1422 0.1359 154.6039 0.4186 0.0436 173.8938 0.6641 -0.0517 151.9836 0.8077 -0.0495 165.9428 0.7768 -0.0180 Table 6.2.9 (Cont'd.) 18.1817 17.0449 0.2561 15.5622 8.5187 0.5793 16.7127 7.8632 0.3599 19.0798 12.3576 0.2561 9.2342 1.6798 0.4726 7.8079 0.1972 3.3794 6.7529 3.6044 0.2642 14.9109 13.2197 0.8187 5.8273 6.7938 0.3142 14.8783 8.0520 0.1057 0.0001 0.0001 0.6128 0.0001 0.0035 0.4466 0.0001 0.0050 0.5485 0.0001 0.0004 0.6128 0.0024 0.1950 0.4918 0.0052 0.6570 0.0660 0.0094 0.0576 0.6073 0.0001 0.0003 0.3656 0.0158 0.0091 0.5751 0.0001 0.0045 0.7451 0.2822 0.0135 0.2679 0.0373 0.3564 0.0210 0.3376 0.0120 0.0425 0.0140 0.0078 0.0833 0.0856 0.0097 0.2763 0.0292 0.2106 0.0127 0.2102 0.0034 163 Table 6. 2. 10 Results pf Direct 125:8 of Rypprnes ie 2: To a e e In 0 Dependent Variable: Total Debt Independent Variables: 1. Operating Income t+1, EOINC 2. Firm value, FVALUEA Year Coefficient CHI-SQR p-value Partial Corr. 1968 INTERCEPT 45.5091 21.5345 0.0001 EOINC 1.2751 13.6268 0.0002 0.4204 FVALUEA -0.0650 3.0062 0.0829 0.1287 1969 INTERCEPT 66.7428 48.6478 0.0001 EOINC 1.3062 23.5591 0.0001 0.4230 FVALUEA -0.0665 4.1893 0.0407 0.1208 1970 INTERCEPT 81.5116 62.2504 0.0001 EOINC 1.1720 48.7956 0.0001 0.4548 FVALUEA -0.0597 4.4354 0.0352 0.0894 1971 INTERCEPT 84.0246 57.3002 0.0001 EOINC 1.0968 55.7874 0.0001 0.4901 FVALUEA -0.0588 5.1323 0.0235 0.1044 1972 INTERCEPT 90.7059 51.7115 0.0001 EOINC 0.7874 32.5606 0.0001 0.5566 FVALUEA -0.0372 3.7017 0.0544 0.0847 1973 INTERCEPT 113.0803 62.7311 0.0001 EOINC 0.4054 33.3106 0.0001 0.4200 FVALUEA -0.0015 0.0069 0.9336 0.0001 1974 INTERCEPT 134.7415 30.1185 0.0001 EOINC 0.5461 15.3744 0.0001 0.2887 FVALUEA -0.0017 0.0011 0.9736 0.0000 1975 INTERCEPT 123.1884 18.7109 0.0001 EOINC 0.7430 29.5008 0.0001 0.3233 FVALUEA -0.0384 0.3770 0.5392 0.0158 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 164 (Table 6.2.10 Cont') INTERCEPT EOINC FVALUEA INTERCEPT EOINC FVALUEA INTERCEPT EOINC FVALUEA INTERCEPT EOINC FVALUEA INTERCEPT EOINC FVALUEA INTERCEPT EOINC FVALUEA INTERCEPT EOINC FVALUEA INTERCEPT EOINC FVALUEA INTERCEPT EOINC FVALUEA INTERCEPT EOINC FVALUEA 119.7534 0.7737 -0.0432 120.4979 0.9005 -0.0853 141.9957 0.6830 -0.0518 133.5180 0.7112 -0.0275 127.3310 0.6488 0.0253 115.4127 0.4546 0.1162 201.8645 0.7873 -0.0135 210.6865 0.8052 -0.0613 205.7861 1.0175 ~0.0691 198.1307 1.0849 -0.0345 15.2475 25.0754 0.4480 14.5741 10.5411 0.7868 16.7225 9.0667 0.4326 18.6016 12.0962 0.1364 9.1729 2.5355 0.0496 8.3352 1.1566 1.6161 6.7850 8.0569 0.0165 14.1849 11.5199 0.7176 7.9768 8.3643 0.4608 16.0743 12.0381 0.2746 0.0001 0.0001 0.5033 0.0001 0.0012 0.3751 0.0001 0.0026 0.5107 0.0001 0.0005 0.7119 0.0025 0.1113 0.8238 0.0039 0.2822 0.2036 0.0092 0.0045 0.8977 0.0002 0.0007 0.3969 0.0047 0.0038 0.4972 0.0001 0.0005 0.6002 0.3416 0.0249 0.3107 0.0507 0.4030 0.0264 0.3471 0.00670 0.0733 0.00152 0.0435 0.0359 0.1886 0.00067 0.2945 0.0305 0.2681 0.0212 0.3012 0.0104 165 Table 6.2.11 Resulrs of Direcr Teere pf flypprhesie z: n -te b nd ed V Dependent Variable:Longterm Debt Independent Variables: 1. Value Change, 2. Firm value, DFVALUEA FVALUEA Year Coefficient CHI-SQR p-value Partial Corr. 1968 INTERCEPT 58.1764 13.9587 0.0002 DFVALUEA -14.9982 0.8479 0.3572 0.0004 FVALUEA 0.0500 5.1558 0.0232 0.3143 1969 INTERCEPT 70.8575 13.0909 0.0003 DFVALUEA 32.2602 1.5031 0.2202 0.0015 FVALUEA 0.0519 4.9182 0.0266 0.2983 1970 INTERCEPT 91.2755 22.1432 0.0001 DFVALUEA -76.4461 9.7408 0.0018 0.0098 FVALUEA 0.0615 4.5014 0.0339 0.2867 1971 INTERCEPT 93.5612 23.2882 0.0001 DFVALUEA -105.2789 16.4653 0.0001 0.0144 FVALUEA 0.0629 5.8558 0.0155 0.3271 1972 INTERCEPT 108.9648 22.6263 0.0001 DFVALUEA 176.7152 8.4621 0.0036 0.0199 FVALUEA 0.0498 5.9174 0.0150 0.2568 1973 INTERCEPT 124.9181 34.4631 0.0001 DFVALUEA 204.1030 12.6613 0.0004 0.0240 FVALUEA 0.0528 6.4167 0.0113 0.2842 1974 INTERCEPT 96.8694 14.2290 0.0002 DFVALUEA -0.4401 0.0002 0.9886 0.0000 FVALUEA 0.0874 6.9185 0.0085 0.3499 1975 INTERCEPT 107.1791 10.0807 0.0015 DFVALUEA -22.4673 0.6120 0.4341 0.0004 FVALUEA 0.1084 7.8413 0.0051 0.3977 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 INTERCEPT DFVALUEA FVALUEA INTERCEPT DFVALUEA FVALUEA INTERCEPT DFVALUEA FVALUEA INTERCEPT DFVALUEA FVALUEA INTERCEPT DFVALUEA FVALUEA INTERCEPT DFVALUEA FVALUEA INTERCEPT DFVALUEA FVALUEA INTERCEPT DFVALUEA FVALUEA INTERCEPT DFVALUEA FVALUEA INTERCEPT DFVALUEA FVALUEA 166 109.5356 -5.9465 0.0971 120.8420 -88.0219 0.1119 110.7293 -8.5822 0.1352 94.8414 7.9051 0.1468 104.9175 -140.3353 0.1508 77.1504 -133.6640 0.1738 170.0504 -137.7259 0.1659 145.7218 121.1673 0.1163 162.0696 -340.3194 0.1585 236.1982 -182.2169 0.1232 (Table 6.2.11 Cont'd) 9.2761 1.3029 6.0429 6.1367 2.4641 5.5199 3.7935 0.0318 5.2470 4.3128 0.0704 9.4999 9.3440 8.2164 28.8837 4.6476 4.0417 33.2387 4.9605 4.6197 12.7275 4.6156 1.9787 7.1872 2.8553 7.0832 6.9180 7.7918 9.7536 7.1918 0.0023 0.2537 0.0140 0.0132 0.1165 0.0188 0.0515 0.8585 0.0220 0.0378 0.7907 0.0021 0.0022 0.0042 0.0001 0.0311 0.0444 0.0001 0.0259 0.0316 0.0004 0.0317 0.1595 0.0073 0.0911 0.0078 0.0085 0.0052 0.0018 0.0073 0.0003 0.3854 0.0052 0.4123 0.0000 0.3935 0.0000 0.5205 0.0066 0.6240 0.0067 0.6321 0.0108 0.4847 0.0016 0.3972 0.0168 0.4236 0.0069 0.3918 167 Table 6.2.12 Results 9: Direcr Teers of Rypornesis 2: Total DeDr end Erpeepeg Velpe Dependent Variable: Total Debt Independent Variables: 1. Value Change, DFVALUEA 2. Firm value, FVALUEA Year Coefficient CHI-SQR p-value Partial Corr 1968 INTERCEPT 72.7427 11.5275 0.0007 DFVALUEA -15.5570 0.6003 0.4385 0.0003 FVALUEA 0.0656 4.4654 0.0346 0.3297 1969 INTERCEPT 93.3245 11.1661 0.0008 DFVALUEA 36.7870 1.0843 0.2977 0.0011 FVALUEA 0.0706 4.2651 0.0389 0.3068 1970 INTERCEPT 116.1862 18.1364 0.0001 DFVALUEA -80.5266 6.8500 0.0089 0.0059 FVALUEA 0.0899 4.4447 0.0350 0.3178 1971 INTERCEPT 116.6786 19.3378 0.0001 DFVALUEA -122.1433 13.5444 0.0002 0.0110 FVALUEA 0.0880 5.6853 0.0171 0.3486 1972 INTERCEPT 130.7644 16.4509 0.0001 DFVALUEA 189.3928 5.4223 0.0199 0.0129 FVALUEA 0.0690 5.2456 0.0220 0.2707 1973 INTERCEPT 151.2889 30.0344 0.0001 DFVALUEA‘ 203.5703 8.7598 0.0031 0.0133 FVALUEA 0.0729 6.1671 0.0130 0.2952 1974 INTERCEPT 128.1527 11.8683 0.0006 DFVALUEA -2.5352 0.0036 0.9523 0.0000 FVALUEA 0.1290 7.0328 0.0080 0.3564 1975 INTERCEPT 123.5294 7.7340 0.0054 DFVALUEA -18.8653 0.2693 0.6038 0.0002 FVALUEA 0.1460 8.0295 0.0046 0.4150 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 INTERCEPT DFVALUEA FVALUEA INTERCEPT DFVALUEA FVALUEA INTERCEPT DFVALUEA FVALUEA INTERCEPT DFVALUEA FVALUEA INTERCEPT DFVALUEA FVALUEA INTERCEPT DFVALUEA FVALUEA INTERCEPT DFVALUEA FVALUEA INTERCEPT DFVALUEA FVALUEA INTERCEPT DFVALUEA FVALUEA INTERCEPT DFVALUEA FVALUEA (Table 6.2.12 Cont'd) 124.2372 -0.8554 0.1288 138.6630 -89.6055 0.1439 130.0546 -14.6064 0.1722 113.4759 -6.8428 0.1944 126.8168 -161.1278 0.2010 80.4087 -153.3207 0.2383 182.4644 -131.9758 0.2186 177.1980 123.6080 0.1424 207.5545 -352.5453 0.1930 278.6002 -183.2909 0.1629 6.7928 0.0111 5.9587 5.0946 1.6952 5.7113 3.4052 0.0635 5.5325 4.0282 0.0344 10.7679 7.2446 5.7206 24.3942 2.5625 3.3320 30.2501 3.0703 2.6032 11.6326 4.5016 1.6312 7.1186 3.2625 7.0794 7.4491 6.4868 8.1706 7.5048 0.0092 0.9162 0.0146 0.0240 0.1929 0.0169 0.0650 0.8011 0.0187 0.0447 0.8529 0.0010 0.0071 0.0168 0.0001 0.1094 0.0679 0.0001 0.0797 0.1066 0.0006 0.0339 0.2015 0.0076 0.0709 0.0078 0.0063 0.0109 0.0043 0.0062 0.0000 0.4068 0.0036 0.4337 0.0000 0.4204 0.0000 0.5542 0.0044 0.5981 0.0047 0.6354 0.0062 0.5029 0.0012 0.4175 0.0145 0.4660 0.0051 0.4522 169 Table 6.2.11 reports the results of testing model #24: LTDit = sot + Blt*8FVALUEAit + 62t*FVALUEAit The coefficient of change in firm value (8FVALUEA) is negative and significant for a majority of the years as predicted by the model. For two years (1972 and 1973), however, the coefficient is positive and significant. For model #25: TOTDEBTit = sot + Blt*5FVALUEAit + th*FVALUEAit the regression results are reported in Table 6.2.12. Here, the coefficient on 8FVLAUEA is of the expected negative sign for most of the years. 6.3 Hypothesis 2e: Grpyrn and the lnrerest Rerio; In the extended model, higher growth firms are likely to have lower interest ratios than lower growth firms. Similar to the tests for hypothesis 2, hypothesis 2a was tested by (i) using a pooled sample and working with first differences of ratios, (ii) using cross-sectional samples to test the relationship for each separate year (iii) employing a direct test. (i) In the pooled sample the following models were tested: MODEL #26 : SINTRATit = so + 81*8EVRATit MODEL #27 : 8INTRATitI so + s1*5v1voit Results of the OLS regressions applied to models 26 and 27 are presented in Table 6.2.13. The coefficient for the explanatory variables is highly significant for both of the 170 models. The sign of the coefficient of EVRAT is positive as predicted by the model. But the sign of the coefficient V1V0, growth ratio, is also positive contrary to the prediction. Again it appears that the differencing of the ratio is imparting an ambiguity in the meaning of this proxy and precludes drawing any conclusions. The models were expanded to include proxy variables for non-debt tax shields, asymmetric information, asset composition and firm size. The following models were tested: MODEL #28: SINTRAT = so + 51*8EVRAT + s2*5NDTSA +B3*5NDTSB + 84*8COLLAT + s5*5AOENCYA + 86*8AGENCYB + 87*51NVTOASS + 63*SSIZE MODEL #29: SINTRAT = so + s1*5v1v0 + 82*8NDTSA +B3*5NDTSB + 84*5COLLAT + 65*8AGENCYA + 86*8AGENCYB + 67*5INVTOASS + 88*OSIZE Results of models 28 and 29 are reported in Table 6.2.14. The results shows a similar pattern as reported in section 6.2. The sign and significance of coefficients for ERAT, V1V0 and the expanded set of variables is not materially affected compared to models 18 and 19 and as reported earlier in Tables 6.2.3 and 6.2.4. 171 Table 6.2.13 Resnlrs Test p: Rypotnesis 2e: IDseress_8asie_and_sresthl MODEL #26 :OINTRAT = 60 + 61*8EVRAT MODEL #27 : sINTRAT = so + s1*5V1v0 PARAMETER ESTIMATES VARIABLE MODEL #26 MODEL #27 COEFF. T-STAT COEFF. T-STAT INTERCEPT 0.2208 0.943 0.2453 1.042 SEVRAT 16.8853 9.329* 5V1V0 1.5621 3.811* F - VALUE 87.026 14.522 PROB > F 0.0001 0.0001 R-SQUARE 0.0117 0.0020 ADJ-RSQ 0.0116 0.0018 DURBIN-WATSON 2.608 2.670 * Significant at 0.0001 level 172 (ii) cross-sectional tests for hypothesis 2a used models 30 and 31. MODEL #30 :INTRATit = Bot + Blt*EVRATit MODEL #31 :_INTRATit= Bot + 51t*V1V°it Table 6.2.15 shows results of regression of the interest ratio on the earnings-value ratio. The coefficients of INTRAT are negative and highly significant for all but three years. The results are thus contrary to those expected under hypothesis 2a. When interest ratio is the dependent variable, in Table 6.2.16, value growth has a negative sign for most of the years as expected under H2a. However, only one coefficient out of the six positive coefficients is significant. The overall evidence from the cross-sectional tests is not conclusive and somewhat contradictory. (iii) Direct tests on hypothesis 2a employed the following models: Model #32: INTERESTit+1 = sot + Blt*OINCit+1 + 82t*FVALUEAit Model #33: INTERESTit+1 = sot + Blt*OINCit+1 + 62t*8FVALUEAit + B3t*FVALUEit . Model #32 is in a slightly different form than its counterpart model #30 in the earlier section where the interest ratio, INTRAT=INTEREST/OINC, was regressed on the 173 Table 6.2.14 Results o: Test of Rypornesis 2e - Erpended Model: Rinenciel Leyerege and Qrpyrn: MODEL #28: 8NTRAT = so + s1*5EVRAT + 82*8NDTSA +B3*8NDTSB + 64*8COLLAT + 5*8AGENCYA + 66*8AGENCYB + s7*5INVT0ASS + s8*SI2E MODEL #29: 8INTRAT = so + s1*sv1v0 + s2*5NDTSA +B3*5NDTSB + 64*5COLLAT + s5*5AGENCYA + so*5AOENCYB + s7*5INVTOASS + s8*5SIZE PARAMETER ESTIMATES VARIABLE MODEL #28 MODEL #29 COEFF. T-STAT COEFF. T-STAT INTERCEPT 1.5327 5.937* 1.6369 6.310* SEVRAT 13.0826 7.279* 5V1V0 0.4142 1.012 8NDTSA 117.6642 3.0518 124.7786 3.222# 8NDTSB -0.1939 -0.019 -0.1422 -0.014 SCOLLAT 7.1848 1.819 8.0698 2.036! SAGENCYA -0.5548 -0.042 -0.7533 -0.057 SAGENCYB 112.0805 5.931* 109.3235 5.763* OINVTASS 3.5707 0.503 2.0581 0.289 5SIZE -17.6309 -14.173* -18.5274 -14.770* F - VALUE 46.854 40.076 PROB > F 0.0001 0.0001 R-SQUARE 0.0487 0.0420 ADJ-RSQ 0.0477 0.0409 DURBIN-WATSON 2.616 2.661 Significant at 0.0001 level Significant at 0.0005 level Significant at 0.0010 level Significant at 0.0050 level Significant at 0.0100 level Significant at 0.0500 level "(09‘3th 1' Table 6. 2. 15 Resglts or Dro ee- Seetipa anl Tests: 174 te est at o a -V t o Intercept Independent Variable Coef t-st -v ue - -v 1968 8.316 5.149 0.0001 -43.952 -4.071 0.0001 1969 3.771 4.152 0.0001 -21.391 -3.411 0.0007 1970 13.728 8.215 0.0001 -63.746 -6.868 0.0001 1971 16.913 9.153 0.0001 -8l.339 -7.848 0.0001 1972 5.165 3.813 0.0002 -18.215 -2.656 0.0082 1973 5.741 6.506 0.0001 -18.066 -6.044 0.0001 1974 5.175 4.493 0.0001 -11.649 -3.286 0.0011 1975 3.505 2.340 0.0197 -1.711 -.401 0.6889 1976 6.582 4.947 0.0001 -15.369 -3.653 0.0003 1977 4.281 2.776 0.0057 -7.961 -1.564 0.1187 1978 10.433 6.597 0.0001 -28.648 -5.715 0.0001 1979 11.541 10.118 0.0001 -38.908 -9.740 0.0001 1980 15.168 9.291 0.0001 -49.737 -8.173 0.0001 1981 13.143 9.229 0.0001 -50.281 -8.024 0.0001 1982 19.209 9.915 0.0001 -56.467 -7.484 0.0001 1983 22.486 8.212 0.0001 -76.156 -6.324 0.0001 1984 12.211 7.904 0.0001 -45.340 -6.362 0.0001 1985 9.008 4.880 0.0001 -11.881 -1.495 0.1356 175 Table 6.2.16 Resulpe pr Qrese-Seeripnal Teete; lnteresp Ratio and Velne grgyrn Intercept Independent Variable Tear Coeffi. t-stat P-va ue oef . 1968 2.686 3.673 0.0003 -6.540 -2.313 0.0212 1969 0.467 0.861 0.3897 -4.194 -2.180 0.0298 1970 6.306 6.155 0.0001 -14.731 -4.704 0.0001 1971 5.889 5.693 0.0001 -12.900 -3.734 0.0002 1972 1.386 1.966 0.0500 -6.840 -2.195 0.0287 1973 2.027 2.945 0.0034 3.491 1.249 0.2125 1974 2.599 3.738 0.0002 -5.890 -2.218 0.0271 1975 2.270 2.311 0.0213 3.239 1.250 0.2119 1976 1.904 2.687 0.0075 3.492 5.579 0.0001 1977 2.203 3.091 0.0021 -0.765 -0.377 0.7065 1978 3.024 3.917 0.0001 -5.759 -2.230 0.0262 1979 1.898 2.921 0.0037 -1.327 -0.875 0.3822 1980 3.123 3.186 0.0015 2.798 0.823 0.4108 1981 4.108 4.566 0.0001 -6.297 -2.159 0.0314 1982 9.145 5.905 0.0001 -3.944 -l.547 0.1227 1983 7.803 5.090 0.0001 0.317 0.048 0.9615 1984 4.115 4.094 0.0001 0.647 0.250 0.8025 1985 8.656 6.292 0.0001 -7.256 -2.514 0.0123 176 earnings-value ratio, EVRAT=OINC/FVALUEA, leading to the possibility of a negative spurious correlation. Interest and operating income (OINC) are cotemporaneous since the leverage decision at time t, which is predicted to depend upon expected income at time t+1, will affect interest expense at time t+l. A positive relationship is indicated, as predicted by the theory, by the results of the regression reported in Table 6.2.17 using interest as the dependent variable, i.e., Model #32: INTERESTit+1 = sot + Blt*OINCit+1 + 82t*FVALUEAit Table 6.2.18 shows that when we regress interest expense on expected income and change in firm value (Model #33) the coefficient of 5FAVLUEA is mostly insignificant but that of expected income is highly significant and of the expected positive sign. It appears the expectations of income play a more significant role in leverage policy than change in the market value of the firm. The results of direct tests therefore provide evidence in support of hypothesis 2a predicting a positive relationship between interest expenses and expected income in the next period. 177 Table 6.2.17 W W t . e e Dependent Variable: Interest Expense Independent Variables: 1. Operating Income (t), OINC 2. Firm value (t-l), LAGFVA Year Coefficient CHI-SQR p-value Partial Corr. 1968 INTERCEPT 3.4150 24.7286 0.0001 OINC 0.0876 15.7399 0.0001 0.4114 LAGFVA -0.0047 3.9201 0.0477 0.1369 1969 INTERCEPT 5.1875 60.6998 0.0001 OINC 0.0953 41.7370 0.0001 0.4311 LAGFVA -0.0049 6.7711 0.0093 0.1282 1970 INTERCEPT 5.2831 63.5105 0.0001 OINC 0.0811 70.4321 0.0001 0.4785 LAGFVA -0.0039 5.0545 0.0246 0.0885 1971 INTERCEPT 5.2294 57.0300 0.0001 OINC 0.0760 76.9047 0.0001 0.5197 LAGFVA -0.0038 6.2028 0.0128 0.1069 1972 INTERCEPT 7.0026 55.3212 0.0001 OINC 0.0567 36.8337 0.0001 0.4800 LAGFVA -0.0019 1.8025 0.1794 0.0343 1973 INTERCEPT 11.3581 56.4078 0.0001 OINC 0.0377 42.4593 0.0001 0.3476 LAGFVA 0.0000 0.0011 0.9730 0.0000 1974 INTERCEPT 12.1812 28.6675 0.0001 OINC 0.0482 17.9994 0.0001 0.2460 LAGFVA 0.0004 0.0098 0.9210 0.0003 1975 INTERCEPT 10.4555 15.8567 0.0001 OINC 0.0743 42.6794 0.0001 0.3336 LAGFVA -0.0048 0.7172 0.3971 0.0257 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 INTERCEPT OINC LAGFVA INTERCEPT OINC LAGFVA INTERCEPT OINC LAGFVA INTERCEPT OINC LAGFVA INTERCEPT OINC LAGFVA INTERCEPT OINC LAGFVA INTERCEPT OINC LAGFVA INTERCEPT OINC LAGFVA INTERCEPT OINC LAGFVA INTERCEPT OINC LAGFVA 178 11.8629 0.0710 -0.0040 12.6294 0.1033 -0.0113 15.7449 0.0636 -0.0027 17.6572 0.0792 -0.0008 18.7787 0.1161 -0.0021 18.5995 0.0535 0.0161 21.9132 0.0839 0.0016 28.0817 0.1251 -0.0106 26.8690 0.1313 -0.0098 23.1309 0.1277 -0.0034 (Table 6.2.17 Cont'd) 16.8098 20.1239 0.4627 13.6099 6.0646 1.1025 21.0819 7.2745 0.1302 17.4423 7.6865 0.0070 12.2593 5.3885 0.0225 11.1797 1.1015 1.9368 5.6725 11.0935 0.0192 11.6856 8.9016 0.8704 10.1914 13.1371 0.7593 13.7178 13.8867 0.1715 0.0001 0.0001 0.4964 0.0002 0.0138 0.2937 0.0001 0.0070 0.7182 0.0001 0.0056 0.9332 0.0005 0.0203 0.8807 0.0008 0.2939 0.1640 0.0172 0.0009 0.8898 0.0006 0.0028 0.3508 0.0014 0.0003 0.3836 0.0002 0.0002 0.6788 0.2791 0.0193 0.2370 0.0471 0.3139 0.0059 0.2252 0.0002 0.0974 0.0004 0.0265 0.0301 0.1605 0.0006 0.2958 0.0379 0.3633 0.0396 0.3243 0.0082 Table 6.2.18 esu s nte est 179 s s o ec ed V ue ens n Dependent Variable: Interest Independent Variables: 1. Operating Income (t), OINC 2. Change in Firm Value, DFVALUEA 3. Firm value (t-l), LAGFVA t es's 2 Year Coefficient CHI-SQR p-value Partial Corr. 1968 INTERCEPT 3.3561 25.0371 0.0001 OINC 0.0880 16.2972 0.0001 0.4122 DFVALUEA 0.0022 4.0790 0.0434 0.0018 LAGFVA -0.0047 0.1677 0.6821 0.1385 1969 INTERCEPT 5.1273 63.7470 0.0001 OINC 0.0944 44.0317 0.0001 0.4264 DFVALUEA -0.0074 9.7046 0.0018 0.0082 LAGFVA -0.0054 1.0689 0.3012 0.1303 1970 INTERCEPT 5.3767 61.3361 0.0001 OINC 0.0835 75.7143 0.0001 0.4694 DFVALUEA -0.0051 2.4887 0.1147 0.0074 LAGFVA -0.0035 0.3971 0.5286 0.0639 1971 INTERCEPT 5.3220 50.4311 0.0001 OINC 0.0673 36.2177 0.0001 0.3987 DFVALUEA -0.0107 0.1114 0.7385 0.0413 LAGFVA -0.0008 6.0024 0.0143 0.0022 1972 INTERCEPT 6.7484 48.1159 0.0001 OINC 0.0614 77.2285 0.0001 0.5173 DFVALUEA -0.0181 2.0012 0.1572 0.0718 LAGFVA -0.0021 3.3617 0.0667 0.0433 1973 INTERCEPT 9.8278 51.3133 0.0001 OINC 0.0311 30.0441 0.0001 0.2106 DFVALUEA 0.0197 7.9367 0.0048 0.0403 LAGFVA 0.0063 5.6133 0.0178 0.0352 1974 INTERCEPT 10.7677 30.6742 0.0001 OINC 0.0419 15.0132 0.0001 0.1826 DFVALUEA 0.0302 0.2766 0.5989 0.0375 LAGFVA 0.0022 3.8903 0.0486 0.0072 1975 INTERCEPT 9.6554 33.3395 0.0001 OINC 0.0783 29.8988 0.0001 0.3535 DFVALUEA -0.0178 0.3808 0.5372 0.0300 LAGFVA -0.0015 1.0784 0.2991 0.0018 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 INTERCEPT OINC DFVALUEA LAGFVA INTERCEPT OINC DFVALUEA LAGFVA INTERCEPT OINC DFVALUEA LAGFVA INTERCEPT OINC DFVALUEA LAGFVA INTERCEPT OINC DFVALUEA LAGFVA INTERCEPT OINC DFVALUEA LAGFVA INTERCEPT OINC DFVALUEA LAGFVA INTERCEPT OINC DFVALUEA LAGFVA INTERCEPT OINC DFVALUEA LAGFVA INTERCEPT OINC DFVALUEA LAGFVA 11.6635 0.0589 0.0200 -0.0010 9.7557 0.0907 0.0775 -0.0082 15.7569 0.0641 -0.0013 -0.0027 16.8516 0.0719 0.0061 0.0007 18.0094 0.1133 0.0069 -0.0015 19.6680 0.0604 -0.0186 0.0138 16.6366 0.0741 -0.0572 0.0190 28.2016 0.0893 0.0611 -0.0044 24.7112 0.1079 -0.0564 0.0034 23.6851 0.1293 -0.0023 -0.0034 180 (Table 6.2.18 Cont'd) 11.7479 4.2932 0.0108 0.5720 5.4374 7.6330 0.5283 3.6923 21.3694 4.7090 0.1293 0.0020 22.7029 3.7759 0.0048 0.1228 11.5398 4.6750 0.0102 0.2268 12.9617 1.8237 1.5449 0.5376 22.1638 8.6471 3.7512 16.2222 12.1272 5.2263 0.1689 17.0631 22.6311 16.6083 0.2226 18.9277 19.2858 13.8720 0.1811 0.0203 0.0006 0.0383 0.9174 0.4495 0.0197 0.0057 0.4673 0.0547 0.0001 0.0300 0.7192 0.9646 0.0001 0.0520 0.9449 0.7260 0.0007 0.0306 0.9194 0.6339 0.0003 0.1769 0.2139 0.4634 0.0001 0.0033 0.0528 0.0001 0.0005 0.0222 0.6811 0.0001 0.0001 0.0001 0.6371 0.0001 0.0001 0.0002 0.6704 0.8866 0.1594 0.0256 0.0009 0.2269 0.2015 0.0312 0.2229 0.0000 0.0059 0.1151 0.0028 0.0001 0.0910 0.0021 0.0002 0.0339 0.0266 0.0224 0.1629 0.2424 0.0864 0.1767 0.1695 0.0077 0.3311 0.2705 0.0054 0.2920 0.0003 0.0084 181 6.4 H othesis 3: T e 'me e ’ v ’e MW; Hypothesis 3 postulates that the ratio of the implied marginal tax rate to the statutory tax rate, I, will lag business cycles. The fraction is predicted to increase in an expanding economy and decrease in a recession. As discussed in the earlier section 5.5, Almon's distributed lag scheme with correction for an auto- regressive error term was applied for estimation of coefficients of regression of gamma (P) on the percent changes in values of indicators of business cycle. Lags from 3 to 24 months with up to 4 polynomial degrees and a second degree auto-regressive process were tried in order to identify the model. The results of these exercises were similar to the one reported here (Tables 6.3.1 through 6.3.11) for lags up to 12 periods and AR(1). The form of the regression model reported here is: _ 2 F — a + 8:0 b + v t i,s5Yi,t+s it Where: 8Y1 5 percent change in indicator i Vit follows AR(1) i.e., Vit = Git - ai-Vi,t-1 bi,s were re-parameterized by a polynomial of degree one3. The results reported in Tables 6.3.1 through 6.3.11 show that each model obtains a very high F-value indicating that 3 An Almon scheme of up to 4 polynomial degrees was investigated but a simple lag structure was found more appropriate. A test that an n degree rather than an n+1 degree polynomial is appropriate is given by the t-value and the probability associated with (n+1)th degree. 182 the model as a whole significantly explains the variations in the dependent variable. However, the individual t-values are very low implying that none of the regressors significantly explains the variation in gamma (F). This is true of the transformed variables as well as the individual lagged variables. The indices are highly auto-correlated and it appears that a high degree of multi-collinearity exists which is resulting in high values of the standard errors of the estimators making it difficult to draw inferences regarding the true value of the coefficients. Hypothesis 3 was therefore tested employing a simpler model and disregarding lagged effects of indices on gamma (F). The model tested is of the following form: rt = ai + b1i*5Yi,t where 8Y1 represent percentage change in the value of ith indicator of business cycle. An autoregressive process followed by the dependent variable was incorporated by Yule- Walker procedure explained earlier. Results of the OLS regression without correction for the auto-regressive process are reported in Tables 6.3.12. Table 6.3.13 reports results after correcting for the first-order auto-regressive process. It can be seen from Table 6.3.13 that except for XBUS and XINC all other indices have positive coefficients as expected under hypothesis #3. Coefficients of XDLEAD, XDLEM and XDLEMXG are, however, not significant. In the absence of an a prior notion of the lag involved in the relationship and the cyclical nature of the 183 Table 6.3.1 Results pf Test of Rypptneeie 3: DARRR & RDUS Almon's Leg Senene AR(l) DEPENDENT VARIABLE: GAMMA Lag(12) INDEPENDENT VARIABLE XBUS, LAG 0-12 F VALUE = 254.485 PROB>F = 0.0001 R-SQUARE = 0.6953 ADJ R-SQ = 0.6926 mo P e S ‘ PARAMETER STANDARD T FOR H0: VARIABLE ESTIMATE ERROR PARAM=0 PROB>|T| INTERCEPT 0.9479 0.0215 44.180 0.0001 XBUS**0 -l.0831 0.6843 -1.583 0.1149 XBUS**1 0.1422 0.4580 0.311 0.7565 La9990.25ramser_zssimaies_ PARAMETER STANDARD T FOR H0: VARIABLE ESTIMATE ERROR PARAM=O PROB>|T| XBUS(O) -0.3636 0.2779 -l.309 0.1920 XBUS(1) -0.3531 0.2542 -1.389 0.1661 XBUS(2) -0.3426 0.2330 -1.470 0.1429 XBUS(3) -0.3320 0.2151 -1.544 0.1241 XBUS(4) '-0.3215 0.2013 -1.597 0.1118 XBUS(5) -0.3109 0.1927 -1.614 0.1080 XBUS(6) -0.3004 0.1898 -l.583 0.1149 XBUS(7) -0.2899 0.1929 -1.502 0.1344 XBUS(8) -0.2793 0.2018 -1.384 0.1677 XBUS(9) -0.2688 0.2157 -l.246 0.2141 XBUS(10) -0.2582 0.2338 -l.105 0.2705 XBUS(ll) -0.2477 0.2551 -0.971 0.3325 XBUS(12) -0.2372 0.2789 -0.850 0.3960 184 Table 6.3.2 Resulre pf Tess e: Rypgtnesis 3; gauge & RDQRM Almenls_Las_§sheme_ABlll DEPENDENT VARIABLE: GAMMA Lag(12) INDEPENDENT VARIABLE XDCEM, LAG 0-12 F VALUE = 251.710 PROB>F = 0.0001 R-SQUARE = 0.6930 ADJ R-SQ = 0.6903 Almons Paremerer Esrimteeg PARAMETER STANDARD T FOR H0: VARIABLE ESTIMATE ERROR PARAM=0 PROB>|T| INTERCEPT 0.9387 0.0258 36.435 0.0001 XDCEM**0 0.4844 0.9647 0.502 0.6161 XDCEM**1 0.1315 0.8273 0.159 0.8739 ed Para te t a s PARAMETER STANDARD T FOR H0: VARIABLE ESTIMATE ERROR PARAM=O PROB>|T| XDCEM(0) 0.0759 0.4557 0.167 0.8679 XDCEM(1) 0.0856 0.4076 0.210 0.8338 XDCEM(2) 0.0954 0.3636 0.262 0.7933 XDCEM(3) 0.1051 0.3252 0.323 0.7468 XDCEM(4) 0.1149 0.2947 0.390 0.6971 XDCEM(5) 0.1246 0.2747 0.454 0.6505 XDCEM(6) 0.1344 0.2676 0.502 0.6161 XDCEM(7) 0.1441 0.2743 0.525 0.5999 XDCEM(8) 0.1538 0.2939 0.523 0.6012 XDCEM(9) 0.1636 0.3242 0.505 0.6143 XDCEM(10) 0.1733 0.3623 0.478 0.6329 XDCEM(11) 0.1831 0.4062 0.451 0.6527 XDCEM(12) 0.1928 0.4542 0.425 0.6716 185 Table 6.3-3 BesUlIs_2:_IesI_ef_HxPeshesi§_zi§AMMA_§_XD§EMIT _Almenis_Lag_§shsme_A8111 DEPENDENT VARIABLE: GAMMA Lag(12) INDEPENDENT VARIABLE XDCEMXT, LAG 0-12 F VALUE = 251.650 PROB>F = 0.0001 R-SQUARE = 0.6930 ADJ R-SQ = 0.6902 s P a t ' : PARAMETER STANDARD T FOR H0: VARIABLE ESTIMATE ERROR PARAMETER=0 INTERCEPT 0.9389 0.0258 36.351 XDCEMXT**0 0.4539 0.9634 0.471 XDCEMXT**1 0.1114 0.8243 0.135 a ed Pa t s a es PARAMETER STANDARD T FOR H0: VARIABLE ESTIMATE ERROR PARAM=0 XDCEMXT(O) 0.0764 0.4544 0.168 XDCEMXT(1) 0.0846 0.4066 0.208 XDCEMXT(Z) 0.0929 0.3628 0.256 XDCEMXT(3) 0.1011 0.3246 0.312 XDCEMXT(4) 0.1094 0.2942 0.372 XDCEMXT(S) 0.1176 0.2743 0.429 XDCEMXT(G) 0.1259 0.2672 0.471 XDCEMXT(7) 0.1342 0.2739 0.490 XDCEMXT(B) 0.1424 0.2934 0.485 XDCEMXT(9) 0.1507 0.3235 0.466 XDCEMXT(10) 0.1589 0.3614 0.440 XDCEMXT(11) 0.1672 0.4051 0.413 XDCEMXT(12) 0.1754 0.4528 0.387 PROB>|T| 0.0001 0.6380 0.8926 PROB > |T| 0.8667 0.8353 0.7982 0.7556 0.7104 0.6684 0.6380 0.6247 0.6279 0.6418 0.6606 0.6803 0.6988 186 Table 6.3-4 BesElts_2f_Iest_2f_flYD2&hseie.11§AMMA_§_XD§QIH Alnon's Leg Denene AR(l) F VALUE = 251.805 PROB>F = 0.0001 DEPENDENT VARIABLE: GAMMA Lag(12) INDEPENDENT VARIABLE XDCOIN LAG 0-12 R-SQUARE = 0.6931 ADJ R-SQ 8 0.6904 elnons Reremeter Espintes; VARIABLE INTERCEPT XDCOIN**0 XDCOIN**1 VARIABLE XDCOIN(O) XDCOIN(1) XDCOIN(2) XDCOIN(3) XDCOIN(4) XDCOIN(5) XDCOIN(6) XDCOIN(7) XDCOIN(8) XDCOIN(9) XDCOIN(10) XDCOIN(11) XDCOIN(12) PARAMETER ESTIMATE 0.9457 -0.2593 0.5612 ed PARAMETER ESTIMATE -0.3215 -0.2799 -0.2383 -0.1967 -0.1551 -0.1135 -0.0719 -0.0303 0.0113 0.0529 0.0945 ‘0.1361 0.1777 STANDARD T FOR H0: ERROR PARAM=0 0.0247 38.361 1.0296 -0.252 0.9143 0.614 am st' ates STANDARD T FOR H0: ERROR PARAM=0 0.4968 -0.647 0.4431 -0.632 0.3937 -0.605 0.3505 -0.561 0.3161 -0.491 0.2935 -0.387 0.2856 -0.252 0.2935 -0.103 0.3162 0.036 0.3506 0.151 0.3938 0.240 0.4432 0.307 0.4970 0.358 PROB>|T| 0.0001 0.8014 0.5399 PROB>|T| 0.5181 0.5281 0.5455 0.5751 0.6240 0.6992 0.8014 0.9178 0.9716 0.8803 0.8106 0.7591 0.7210 187 Table 6-3-5 BesUlIs_2f_TesI_ef_flYPesnesi§_11§AMMA_£_DLEAD ._AlmenL§_Lag_§sheme_ABill DEPENDENT VARIABLE: GAMMA Lag(12) INDEPENDENT VARIABLE XDLEAD, LAG 0-12 F VALUE = 253.935 PROB>F = 0.0001 R-SQUARE = 0.6949 ADJ R-SQ = 0.6922 0 ame m ' PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAM=0 PROB>|T| INTERCEPT 0.9516 0.0246 38.697 0.0001 XDLEAD**0 -0.7982 0.7818 -l.021 0.3083 XDLEAD**1 -0.5432 0.6589 -0.824 0.4106 Lassed.£aram§er.£s§ima§ee_ PARAMETER STANDARD T FOR H0: VARIABLE ESTIMATE ERROR PARAM=0 PROB>|T| XDLEAD(0) 0.0202 0.3642 0.056 0.9558 XDLEAD(1) -0.0200 0.3263 -0.061 0.9511 XDLEAD(2) -0.0603 0.2916 -0.207 0.8363 XDLEAD(3) -0.1006 0.2615 -0.385 0.7008 XDLEAD(4) -0.1408 0.2376 -0.593 0.5540 XDLEAD(5) -0.1811 0.2222 -0.815 0.4158 XDLEAD(6) -0.2214 0.2168 -1.021 0.3083 XDLEAD(7) -0.2617 0.2224 -l.l77 0.2406 XDLEAD(8) -0.3019 0.2380 -1.269 0.2059 XDLEAD(9) -0.3422 0.2619 -1.306 0.1928 XDLEAD(10) -0.3825 0.2922 -1.309 0.1919 XDLEAD(11) -0.4227 0.3269 -1.293 0.1973 XDLEAD(12) -0.4630 0.3649 -l.269 0.2058 188 Table 6.3.6 Reeulre of Teet of Hypprneeis 3:GAMMR & RDLEAP Almon's Leg Senene AR(1) F VALUE VARIABLE INTERCEPT XDLEAP**0 XDLEAP**1 VARIABLE XDLEAP(O) XDLEAP(1) XDLEAP(2) XDLEAP(3) XDLEAP(4) XDLEAP(5) XDLEAP(6) XDLEAP(7) XDLEAP(8) XDLEAP(9) XDLEAP(10) XDLEAP(11) XDLEAP(12) DEPENDENT VARIABLE: GAMMA Lag(12) INDEPENDENT VARIABLE XDLEAP, = 252.663 PROB>F = 0.0001 R-SQUARE = 0.6938 ADJ R-SQ = 0.6911 runs a et s PARAMETER STANDARD ESTIMATE 0.9414 0.5399 0.4755 ed PARAMETER ESTIMATE -0.0617 -0.0265 0.0087 0.0440 0.0793 0.1145 0.1498 0.1850 0.2202 0.2555 0.2907 0.3260 0.3612 ERROR 0.0244 0.8847 0.6896 te STANDARD ERROR 0.3914 0.3530 0.3183 0.2884 0.2651 0.2503 0.2454 0.2510 0.2665 0.2903 0.3205 0.3556 0.3942 T FOR H0: PARAM=0 38.646 0.610 0.690 T FOR H0: PARAM=0 -0.158 -0.075 0.028 0.153 0.299 0.457 0.610 0.737 0.826 0.880 0.907 0.917 0.916 LAG 0-12 PROB>|T| 0.0001 0.5423 0.4912 PROB>|T| 0.8748 0.9403 0.9781 0.8789 0.7653 0.6478 0.5423 0.4619 0.4094 0.3797 0.3653 0.3602 0.3604 189 Table 6.3.7 R est O es's 3: GAMMA & GAMMA & U on's c e DEPENDENT VARIABLE: GAMMA Lag(12) INDEPENDENT VARIABLE XDLEM, LAG 0-12 F VALUE = 252.177 PROB>F = 0.0001 R-SQUARE = 0.6934 ADJ R-SQ = 0.6907 Almons Parameter Estimtes: PARAMETER STANDARD T FOR H0: VARIABLE ESTIMATE ERROR PARAM=0 PROB>|T| INTERCEPT 0.9436 0.0256 36.834 0.0001 XDLEM**0 -0.0302 1.0083 -0.030 0.9761 XDLEM**1 -0.4860 0.6406 -0.759 0.4489 Lesssd.22ramter_fissimases_ PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAM=0 PROB>|T| XDLEM(0) 0.2078 0.4019 0.517 0.6057 XDLEM(1) 0.1717 0.3692 0.465 0.6423 XDLEM(2) 0.1357 0.3401 0.399 0.6903 XDLEM(3) 0.0997 0.3155 0.316 0.7523 XDLEM(4) 0.0637 0.2965 0.215 0.8302 XDLEM(5) 0.0276 0.2843 0.097 0.9226 XDLEM(6) -0.0084 0.2797 -0.030 0.9761 XDLEM(7) -0.0444 0.2830 -0.157 0.8755 XDLEM(8) -0.0804 0.2941 -0.273 0.7848 XDLEM(9) -0.1165 0.3122 -0.373 0.7095 XDLEM(10) -0.1525 0.3360 -0.454 0.6504 XDLEM(ll) -0.1885 0.3644 -0.517 0.6055 XDLEM(12) -0.2245 0.3966 -0.566 0.5719 190 Table 6.3.8 Results o: Test p: Rypprnesis D:§LRRA & RDLRMXG GAMMA & US ' c DEPENDENT VARIABLE: GAMMA Lag(12) INDEPENDENT VARIABLE XDLEMXG, LAG 0-12 F VALUE = 252.313 PROB>F = 0.0001 R-SQUARE = 0.6935 ADJ R-SQ = 0.6908 A s P m te ' tes: PARAMETER STANDARD T FOR H0: VARIABLE ESTIMATE ERROR PARAM=0 PROB>|T| INTERCEPT 0.9433 0.0239 39.526 0.0001 XDLEMXG**O -0.0216 1.0093 -0.021 0.9829 XDLEMXG**1 -0.5237 0.6449 -0.812 0.4176 ed te ' at s PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAM=0 PROB>|T| XDLEMXG(O) 0.2269 0.4034 0.563 0.5743 XDLEMXG(1) 0.1881 0.3704 0.508 0.6121 XDLEMXG(2) 0.1493 0.3410 0.438 0.6620 XDLEMXG(3) 0.1105 0.3162 0.349 0.7272 XDLEMXG(4) 0.0716 0.2970 0.241 0.8096 XDLEMXG(5) 0.0328 0.2846 0.115 0.9083 XDLEMXG(6) -0.0060 0.2799 -0.021 0.9829 XDLEMXG(7) -0.0448 0.2834 -0.158 0.8745 XDLEMXG(8) -0.0836 0.2946 -0.284 0.7768 XDLEMXG(9) -0.1225 0.3129 -0.391 0.6959 XDLEMXG(10) -0.1613 0.3369 -0.479 0.6327 XDLEMXG(11) -0.2000 0.3657 -0.547 0.5848 XDLEMXG(12) -0.2389 0.3982 -0.600 0.5491 191 Table 6.3.9 Results Oi Tee; pf Rypprneeis 3: DARE; & RTNC Almenls_Lds_§sheme_ABill DEPENDENT VARIABLE: GAMMA Lag(12) INDEPENDENT VARIABLE XINC, LAG 0-12 F VALUE = 255.295 PROB>F = 0.0001 R-SQUARE = 0.6960 ADJ R-SQ = 0.6933 Almens.£arame£er_fisi11:251. PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAM=0 PROB>|T| INTERCEPT 0.9547 0.0242 39.374 0.0001 XINC**0 -0.5045 0.3153 -l.600 0.1111 XINC**1 0.0114 0.1823 0.063 0.9499 d a amte s es PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAM=0 PROB>|T| XINC(O) -0.l450 0.1189 -l.220 0.2239 XINC(1) -0.l442 0.1102 -1.308 0.1922 XINC(2) -0.l433 0.1025 -1.398 0.1636 XINC(3) -0.1425 0.0962 -l.481 0.1400 XINC(4) -o.1416 0.0914 -1.550 0.1226 XINC(5) -0.1408 0.0884 -1.592 0.1128 XINC(6) -0.1399 0.0874 -1.600 0.1111 XINC(7) -O.l39l 0.0887 -1.570 0.1178 XINC(B) -0.1382 0.0917 -1.507 0.1332 XINC(9) -0.1374 0.0966 -l.422 0.1565 XINC(lO) -0.l365 0.1031 -1.324 0.1868 XINC(11) -0.1357 0.1109 -l.224 0.2223 XINC(12) -0.l348 0.1196 -l.127 0.2610 192 Table 6.3.10 Be5ulIs__f_TesI_2f_HxPeIhesi§_lixI£ME§ o . Almenls_Les_§sheme_AElll DEPENDENT VARIABLE: GAMMA Lag(12) INDEPENDENT VARIABLE XBUS, LAG 0-12 F VALUE = 252.373 PROB>F = 0.0001 R-SQUARE = 0.6936 ADJ R-SQ = 0.6908 Almons Parameter Estimtes: PARAMETER STANDARD T FOR H0: VARIABLE ESTIMATE ERROR PARAM=0 INTERCEPT 0.9389 0.0250 37.545 XIPMFG**O 0.5059 0.8472 0.597 XIPMFG**1 0.3825 0.6542 0.585 Legged Reramter Rsrimeree PARAMETER STANDARD T FOR H0: VARIABLE ESTIMATE ERROR PARAM=0 XIPMFG(O) -0.0298 0.3759 -0.079 XIPMFG(l) -0.0014 0.3394 -0.004 XIPMFG(Z) 0.0269 0.3062 0.088 XIPMFG(3) 0.0553 0.2776 0.199 XIPMFG(4) 0.0836 0.2551 0.328 XIPMFG(S) 0.1120 0.2404 0.466 XIPMFG(6) 0.1403 0.2350 0.597 XIPMFG(7) 0.1687 0.2394 0.705 XIPMFG(B) 0.1970 0.2533 0.778 XIPMFG(9) 0.2254 0.2751 0.819 XIPMFG(lO) 0.2537 0.3031 0.837 XIPMFG(ll) 0.2821 0.3358 0.840 XIPMFG(lZ) 0.3104 0.3720 0.834 PROB>|T| 0.0001 0.5510 0.5594 PROB>|T| 0.9369 0.9966 0.9300 0.8424 0.7434 0.6418 0.5510 0.4818 0.4374 0.4134 0.4034 0.4019 0.4050 193 Table 6.3-11 WW 81mgnL§_ng_§gn§m§_83111 DEPENDENT VARIABLE: GAMMA Lag(12) INDEPENDENT VARIABLE XBUS, LAG 0-12 F VALUE = 252.645 PROB>F = 0.0001 R-SQUARE = 0.6938 ADJ R-SQ = 0.6911 A o 5 Pa mete st 5: PARAMETER STANDARD T FOR H0: VARIABLE ESTIMATE ERROR PARAM=0 PROB>|T| INTERCEPT 0.9439 0.0242 39.043 0.0001 XIPX**0 0.2178 0.9183 0.237 0.8128 XIPX**1 0.6429 0.7308 0.880 0.3800 ngged Eggamte; Estimates PARAMETER STANDARD T FOR H0: VARIABLE ESTIMATE ERROR PARAM=0 PROB>|T| XIPX(0) -0.2255 0.4159 -0.542 0.5881 XIPX(1) -0.1779 0.3745 -0.475 0.6353 XIPX(2) -0.1302 0.3368 -0.387 0.6994 XIPX(3) -0.0826 0.3041 -0.271 0.7863 XIPX(4) -0.0349 0.2782 -0.125 0.9003 XIPX(5) 0.0127 0.2612 0.049 0.9611 XIPX(6) 0.0604 0.2547 0.237 0.8128 XIPX(7) 0.1081 0.2596 0.416 0.6777 XIPX(8) 0.1557 0.2753 0.566 0.5722 XIPX(9) 0.2034 0.3001 0.678 0.4987 XIPX(10) 0.2510 0.3319 0.756 0.4503 XIPX(11) 0.2987 0.3690 0.809 0.4192 XIPX(12) 0.3463 0.4100 0.845 0.3991 194 indices, it is not possible reach any conclusion regarding the hypothesized relationship for these indices. Overall evidence, however, bears support in favor of a cyclical pattern in the time series of gamma (P) which seems to lag business cycle indices. 195 Table 6.3.12 0 1 a th si ressionE in tes Dependent Variable: Gamma Independent Variables: Business Cycle Indicators Index Intercept I-Ratio p-value Coeff. 1-Rati0 p-value R-Sqr D-H XBUS 0.9399 121.735 0.0001 -0.7720 -1.440 0.1512 0.0087 0.3480 XDCEM 0.9367 115.412 0.0001 0.8735 0.938 0.3491 0.0037 0.3245 XDCEMXT 0.9367 115.230 0.0001 0.8501 0.915 0.3610 0.0035 0.3249 XDCOIN 0.9394 116.963 0.0001 -0.1435 -0.146 0.8838 0.0001 0.3314 XDLEAD 0.9429 118.678 0.0001 -1.3879 -1.880 0.0614 0.0147 0.3505 XDLEAP 0.9386 121.081 0.0001 0.5217 0.638 0.5241 0.0017 0.3262 XDLEM 0.9398 117.776 0.0001 -0.2986 -0.384 0.7015 0.0006 0.3323 XDLEMXG 0.9390 121.439 0.0001 -0.3106 -0.397 0.6914 0.0007 0.3324 XINC 0.9400 119.872 0.0001 -0.1404 -0.666 0.5059 0.0019 0.3322 XIPMFG 0.9372 118.016 0.0001 0.7431 0.986 0.3253 0.0041 0.3201 XIPX 0.9395 121.748 0.0001 0.9970 1.219 0.2242 0.0062 0.3215 196 Table 6.3.13 Results of Test of H othesis : Yule-walker Estimates Dependent Variable: Gamma Independent Variables: Business Cycle Indicators Index Intercept T-Ratio p-value Coeff. T~Ratio p-value REG RSO TOT Ron XBUS .9352 37.445 0.0001 -0.0192 -0.078 0.9376 0.0000 0.6964 XDCEM .9318 36.920 0.0001 1.2274 2.221 0.0273 0.0205 0.7027 XDCEMXT .9319 36.946 0.0001 1.1815 2.142 0.0332 0.0191 0.7022 XDCOIN .9329 36.839 0.0001 0.9721 1.675 0.0952 0.0118 0.7000 XDLEAD .9350 37.324 0.0001 0.0528 0.113 0.9101 0.0001 0.6965 XDLEAP .9341 37.032 0.0001 1.1019 2.005 0.0461 0.0167 0.7015 XDLEM .9348 37.360 0.0001 0.1247 0.363 0.7170 0.0006 0.6966 XDLEMXG .9352 37.394 0.0001 0.1172 0.340 0.7345 0.0005 0.6966 XINC .9356 37.425 0.0001 -0.0509 -0.652 0.5149 0.0018 0.6970 XIPMFG .9319 36.481 0.0001 1.3278 3.100 0.0022 0.0391 0.7083 XIPX .9359 36.972 0.0001 1.3234 2.777 0.0059 0.0316 0.7061 CHAPTER.VII SUMMARY AND CONCLUSIONS The focus of this study has been an examination of the implications of introducing temporal dependencies in the firm's cash flows for bond market equilibrium and choice of the capital structure. The theoretical analysis in this study has been confined to a scenario where the only source of imperfection is the system of corporate and personal taxes. In this world, firms faced with uncertain cash flows make capital structure choices considering the value implications of tax shields provided by debt as well as by non-debt tax deductions. The study provides empirical evidence on the hypotheses derived from such a multiperiod model of capital structure. 7.1 ngmary e: Besulte 9: the Ineeregieel Agelyeis; This study builds a multiperiod model of capital structure choice by firms faced with uncertain future cash flows and having debt and non-debt related risky tax- shields. We generalize the work of Barnea, Talmor and Haugen [BTH, 1987] who had examined corporate debt policy 197 198 and bond market equilibrium in a multiperiod model assuming perfect markets and riskless debt but disallowing tax carry- backs or carry-forwards. In their model, debt is riskless in the sense that any shortfall of cash flow at the end of a period is met by the original shareholders, following their assumption that the firm's end of period value is always greater than any possible shortfall in the debt obligations. We expand the BTH framework by removing this restrictive assumption regarding the firm's future value and allowing for the possibility of default, and also by introducing non- debt related tax shields. Our model indicates that there is a marked difference between the capital structure choice of a growing firm and a non-growing firm stemming from a structural difference in the functional form of value generated by the debt tax shields. While the growing firm obtains a concave value function giving an interior optimum debt level, non-growing firms maximize their value by maximizing debt i.e., a corner solution with 100% debt. The difference in the functional form alone is sufficient to observe a negative relationship between growth and financial leverage for a sample of companies comprised both of growing as well as non-growing companies. Though such a negative relationship has been predicted by theories based on asymmetric information, for example by Myers and Majluf [1984], our model has provided a purely taxed-based explanation. When non-debt related tax shields are introduced in the 199 model our analysis indicates substitutability between debt and non-debt tax shields implying that firms with relatively high non-debt tax shields would employ less debt. Our analysis thus confirms DeAngelo and Masulis' [1980] results in a multiperiod framework. The following empirical hypotheses are derived from the multiperiod model. First, financial leverage is systematically related to the operating risk but the direction of relationship (positive or negative) depends upon the marginal tax rate implied in the yield differential between taxable and non-taxable bonds. Second, non-growth firms with a high operating earnings to value ratio are predicted to employ relatively more debt than growth firms. Our model predicts both the interest ratio and the debt ratio to be lower for growing firms while only debt ratio is expected to be high in the BTH model. Third, the implied tax rate is predicted to follow a cyclical pattern lagging the business cycle. Though our generalized multi-period capital structure model produces empirical hypothesis similar to those given by the BTH model, our model is not restricted by a particular assumption regarding the firm's end of period value. 200 7.2 Summar of R s ' ° ' This study presents results of the tests of empirical hypotheses derived from the extended multi-period capital structure model. The tests are conducted by first using the variables suggested by the BTH model and its extension. Later, the empirical models are expanded to take into account factors suggested by other theories of capital structure. These factors included proxies for non-debt tax shields, asymmetric information, agency costs and firm size. 7.2.1 Opegating Risk end Eigeneiel Legerege; Three measures of financial leverage, long-term debt ratio, total debt ratio and interest to operating cash flow ratio, were separately regressed on operating risk as proxied by the unlevered variance of common stock. OLS regressions on the first differences of the dependent and explanatory variables were run using a pooled sample of 19 years of time series and cross-sectional data on 431 companies. The regression results indicate a statistically significant negative relationship, at one percent level, between operating risk and financial leverage using long- term debt and total debt ratios as the dependent variables. The coefficient of operating risk regressed on the interest ratio was, however, not significant at five percent level. When implied marginal tax rates were included in the model as an explanatory variables, the OLS coefficients were statistically significant and of the predicted sign 201 indicating empirical support for the hypothesis that the direction of the relationship between operating risk and financial leverage is affected by the ratio of implied marginal tax rates to the statutory tax rates. 7.2.2 ert Betio end Ggewgh: The relationship of debt ratios to growth was first tested by using the earnings-to-value ratio and the value growth ratio on a pooled sample comprised of time series as well as cross-sectional data. The regression results provided no conclusive evidence on the growth and debt ratio relationships. It is possible that a regression on first differences of the dependent and independent variables used to control for serial correlation in the residuals may have rendered the ratios ambiguous as proxy variables. Therefore, the empirical hypotheses were also tested using cross- sectional data for each of 19 years under study. In the cross-sectional tests the coefficients on the earnings-value ratio and the value growth ratio are statistically significant and of the predicted sign for the majority of the years under study. In empirical research, when relationships under study are in form of ratios as in this case, there is a possibility that use of a common deflator may induce "spurious" correlation. Though the question of spurious correlation is not relevant when a hypothesis has initially been formulated in terms of ratios, it was considered proper to supplement 202 the evidence from cross-sectional tests by conducting "direct tests" on hypothesis relating debt ratios to growth. These tests involved controlling for firm size by including firm value as a separate regressor rather than as a deflator of both the dependent and the independent variables. When long-term and total debt are regressed on operating income and firm value in direct tests, the coefficients are significant and positive as predicted by the model for all but two out of nineteen years. Similar results supporting a negative relationship between growth and the debt ratio are obtained when the value growth ratio is used as an explanatory variable. 7.2.3 The Intezesg Retio egg firefigh; Our model suggests that growing firms would tend to have a higher ratio of interest expense to operating cash flows. This hypothesis was tested with a pooled sample as well as with cross-sectional sample both in ratio and direct forms. Empirical tests showed the interest ratios to be positively related to both the earnings to value ratio, as expected, and the value growth ratios, contrary to expectations. The cross-sectional tests were similarly inconclusive. Direct tests, however, tend to support the hypothesis of a negative relationship between the interest ratio and growth. A positive and significant relationship between interest expense and expected operating cash flows was found for almost all years after controlling for the size effect. The 203 relationship between interest and next period's expected firm value was found to be mostly insignificant. 7.2.4 Results of Tests gt Expeegeg Model; Including variables suggested by other theories in the regression model relating debt ratios to operating risk did not affect the significance of operating risk or the implied tax rate proxies as explanatory variables confirming the supporting evidence from the simpler model. Tests on the expanded model also shed some light on competing theories of capital structure. There is some evidence that non-debt tax shields bear a negative relationship to the debt ratios in line with the prediction of our model and that of DeAngelo and Masulis' [1980]. The results also appear to support the notion that larger firms carry relatively greater debt, having either lower expected bankruptcy costs through the coinsurance effect or better access to the capital markets. The evidence on capital structure theories based on agency costs and asymmetric information is, however, mixed and seems neither to refute nor support these theories. When tests on hypotheses relating debt and interest ratios to growth were expanded by including proxies for non- debt tax shields, asymmetric information, agency costs and firm size, the coefficients and significance levels on the explanatory variables used in the restricted model, earnings value ratio and growth ratio, were not materially affected. Evidence on the influence of the competing theories was 204 similar to the one reported in the paragraph above. It appears that different theories of capital structure bring out factors which affect the firm's behavior independent of each other. Different theories may complement rather than compete with each other in explaining corporate capital structure policies. 7.2.5 The Time Series Behavio; of Implied Tax Rates; Hypothesis 3 postulates a cyclical pattern in the marginal tax rates implied in the yield differential between taxable and non-taxable bonds which will lag business cycles. This implied tax rate was calculated from an observed bond yield series and was regressed on 12 series of business indicators. Since the model does not suggest a specific time lag in the postulated relationship an Almon's distributed lag scheme was employed to estimate the hypothesized relationship. Though the distributed lag model as a whole significantly explained the variations in the dependent series, it was not possible to detect a specific lag structure. A simpler model disregarding lagged effects of indices was tested. All 12 indices except two were found to have positive coefficients as predicted by the theoretical model. 205 7.3 Cenclusions: Analysis of the capital structure problem in a multi- period framework in this study has underscored the importance of dependencies in the financial decision variables. As multi-period models show, debt policies depend not only on the expected cash flows in the current period but also on the time pattern of cash flows in future periods. It also brings out the inevitable interaction between investment and financing decisions. The contribution of our theoretical model lies in its formulation of the capital structure problem in a more generalized framework. By considering risky debt as well as the existence of non- debt tax shields, the analytical setting is rendered more realistic. The model brings new theoretical support to the empirical hypotheses put forth earlier by Barnea, Talmor and Haugen [1987] using a more restrictive set of assumptions. Our model throws fresh light on the relationship between debt policies and growth. The empirical hypotheses examined in this study are derived using only features of the taxation system and compete with the predictions of other non-tax based theories prevalent in the finance literature. We find empirical evidence that taxes systematically affect capital structure policies and bond market equilibrium. The results of the study show that business risk systematically affects financial leverage. This relationship has not been observed before at the individual firm level. Earlier studies used industry averages and 206 portfolios and the overall evidence has been inconclusive or differed from study to study. Our research also supports the tax-shielding motivation underlying the choice of capital structure and offers an explanation of why in a cross- sectional sample we would observe a negative relationship between growth and financial leverage. We find empirical support for the hypothesis predicting a cyclical pattern in the implied tax rates and trace its temporal movements in relation to the business cycle. Earlier cyclical movements in implied tax rates were observed but traced to changes in the risk premium over time rather than changes in the supply and demand for corporate debt. This research is however not conclusive regarding the comparative merits of various theories of capital structure. It presents fresh evidence without refuting or confirming the empirical validity of any particular theoretical model to the exclusion another. We do find some support for the hypothesis that non-debt shields are negatively and firm size is positively related to debt ratios. The variables suggested by the multiperiod model were found to explain only a small fraction of the variations in debt levels in cross-sectional samples. It appears that many factors including corporate and personal tax rates affect capital structure choice. 207 7.4 u est' 5 o Fut e ese c : A number of suggestions can be made for further theoretical as well as empirical research in this area. Considerable progress can be made in furthering the theoretical multiperiod framework for the analysis of firms' financial and capital structure policies. For example, the model can be extended to explicitly deal with the interaction of financial and investment decisions, problems related to tax losses carried back and forward, and bankruptcy costs. The analysis here has been conducted assuming risk neutrality. It would be of interest to examine the implications of relaxing this assumption in a world where risk is priced, for example, according to the Capital Asset Pricing Model. Another theoretical extension can be made by incorporating growth patterns in the expected operating cash flows which may shed light on the question of the maturity structure of debt. 0n the empirical side, an immediate extension could be made by using monthly or quarterly financial data instead of annual data which would be more appropriate for observing the response of firms to changes in the implied tax rates as well as exploring the dynamics of equilibria in the bond market. Possible differences in the debt policies of growing and non-growing firms need to be examined more closely. Such differences may have eluded this study due to the fact that the sample used has been unavoidably biased in favor of growing firms. The problems of 'spurious' correlation which 208 may arise when ratios are used in regression studies is another challenge for the future researcher. 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One year maturity D: Cert of Deposit-one year (Table III-5) E: Bankers Acceptance 6 months (Table IV-l ) F & G: US T-Bill 6 months and 1 year (Table I-l) H: One year taxable yield, H = D + E - F + G I: Implied Marginal Tax Rate, I = 1 - C/H 68 10 0.3794 0.4376 0.4380 0.3764 0.4627 0.4469 0.4220 0.3942 0.4112 0.4079 0.4069 0.3474 0.3879 0.3948 0.3931 0.4176 0.4262 0.3781 0.4098 0.4705 0.4690 0.4849 0.4881 0.4732 70 71 FJP’H tar-H hJF‘OlOalflchUIhlJADHBOP‘OloaidChUlb(QAJH \OQOUl-b-wNH 0.4023 0.3711 0.3967 0.3675 0.4334 0.4048 0.4172 0.3850 0.3682 0.4104 0.3773 0.3867 0.4007 0.4125 0.4526 0.4274 0.4200 0.3835 0.4386 0.4366 0.4413 0.4350 0.4453 0.5345 0.4352 0.4456 0.3878 0.4565 0.4522 0.4144 0.4515 0.4590 0.4968 0.4836 0.4611 0.4269 0.4787 0.3649 0.4050 0.4922 0.4286 0.4845 0.4917 0.4707 0.4867 0.4665 0.4681 0.4918 \I .b. \l Ul H14»: F’Hld IOF‘O\OG>fiChUTbl053HBOF'OloGJQCAUIhlak’H qumthNl-J 0.5082 0.5185 0.5000 0.4800 0.4730 0.4839 0.5030 0.5000 0.5158 0.5059 0.4875 0.4909 0.5000 0.4667 0.4933 0.4707 0.5000 0.5025 0.5091 0.5000 0.4909 0.5047 0.4368 0.5278 0.4706 0.4571 0.4412 0.4718 0.4839 0.4222 0.4621 0.5000 0.5092 0.5030 0.4865 0.5172 0.5000 0.5200 0.5077 0.5276 0.5397 0.4714 0.4745 0.5039 0.5122 0.5041 0.4643 0.5534 YR MON C D E F G H I 77 1 2.40 5.10 5.10 0.5294 2 2.75 5.88 5.88 0.5323 3 2.90 5.75 5.75 0.4957 4 3.00 5.80 5.80 0.4828 5 2.75 5.70 5.70 0.5175 6 2.90 6.20 6.20 0.5323 7 2.90 6.05 6.05 0.5207 8 2.90 6.35 6.35 0.5433 9 3.00 6.63 6.63 0.5475 10 3.10 7.00 7.00 0.5571 11 3.25 7.38 7.38 0.5596 12 3.10 7.13 7.13 0.5652 78 1 3.50 7.30 7.30 0.5205 2 3.70 7.65 7.65 0.5163 3 3.60 7.60 7.60 0.5263 4 3.75 7.55 7.55 0.5033 5 4.00 7.95 7.95 0.4969 6 4.30 8.40 8.40 0.4881 7 4.30 8.75 8.75 0.5086 8 4.25 8.75 8.75 0.5143 9 4.30 8.85 8.85 0.5141 10 4.20 9.30 9.30 0.5484 11 4.75 10.25 10.25 0.5366 12 5.20 10.60 10.60 0.5094 79 1 5.40 10.80 10.80 0.5000 2 5.00 10.75 10.75 0.5349 3 5.25 10.80 10.80 0.5139 4 5.10 10.50 10.50 0.5143 5 5.15 10.65 10.65 0.5164 6 5.10 10.17 10.17 0.4985 7 4.80 9.89 9.89 0.5147 8 4.90 10.20 10.20 0.5196 9 5.25 11.35 11.35 0.5374 10 5.40 11.85 11.85 0.5443 11 6.20 13.25 13.25 0.5321 12 6.00 12.50 12.50 0.5200 80 1 5.90 12.63 12.63 0.5329 2 6.00 13.13 13.13 0.5430 3 7.10 15.75 15.75 0.5492 4 8.25 17.30 17.30 0.5231 5 6.10 12.00 12.00 0.4917 6 5.00 9.35 9.35 0.4652 7 5.00 9.13 9.13 0.4524 8 5.10 9.75 9.75 0.4769 9 5.70 11.80 11.80 0.5169 10 6.10 12.75 12.75 0.5216 11 6.25 14.10 14.10 0.5567 12 7.20 15.13 15.13 0.5241 (D N 83 84 Hr-F’ F‘Hl- tor-cloaaqch01el0A>He0haO\oa1qcnUielasiH \DmflmUlnbh-JNH 10 0.4737 0.5410 0.5359 0.4885 0.5385 0.5079 0.5238 0.5397 0.4568 0.4743 0.4355 0.3852 0.4107 0.4915 0.4692 0.4667 0.4784 0.4526 0.4745 0.4340 0.4748 0.4444 0.4472 0.4403 0.4324 0.4936 0.4753 0.4475 0.4565 0.4211 0.4416 0.4762 0.4575 0.4289 0.4241 0.4359 0.4417 0.4192 0.4787 0.4775 0.4825 0.4767 0.4924 0.4862 0.4575 0.4530 0.4340 0.4472 86 0.4211 0.4444 0.4732 0.4500 0.4444 0.4012 0.4444 0.4412 0.4012 0.4012 0.3990 0.3873 0.3185 0.3704 0.3926 0.3889 0.3567 0.3986 0.3869 0.3252 0.2629 0.3443 0.3622 0.3866 Appendix II Description of Business Cycle Indicators CITIBASE : Citibank Economic Database [machine-readable magnetic data file] 1946- New York, Citibank, N.A. 1978. BUS: Index of Net Business Formation (BCD-12) DLEAD : Composite Index of 12 Leading Indicators (BCD- 910) DCOIN : Composite Index of 4 Roughly Coincident Indicators (BCD-920) DLEAP : Composite Index of Profitability (ECU-916) Source : U.S. Department of Commerce, Bureau of Economic Analysis Document : Business Conditions Digest Units : 1967=100, seasonally adjusted INC: Number of New Business Incorporation (BCD-13) Source : Dun & Bradstreet, Inc. Document : New Business Incorporation Units : Number, seasonally adjusted IPMFG: Industrial Production Index (Manufacturing) Source : U.S. Department of Commerce, Bureau of Economic Analysis Survey of Current Business 1977=100, seasonally adjusted Document Units IPX : Capacity Utilization Source :The Board of Governors of the Federal Reserve System Document :Capacity Utilization: Manufacturing, Mining, Utilities and Industrial Materials - Statistical Release G3 Units : Percent of Capacity, seasonally adjusted 226 10. 11. DLEM : 227 Leading Employment Index - With Trend Factor DLEMXG: Leading Employment Index - Omitting Trend Factor DCEM : DCEMXT Source Units Coincident Employment Index - With Trend Factor Coincident Employment Index - Omitting Trend Factor Center for International Business Cycle Research 1967=100, seasonally adjusted Rain-s cycle Irdicatora 167-6 (For éfiniticm aae [matrix 11) WW YR 8.5 064 new MIDI: DLEM m “.31 m 10$ 11$ 12$ 16.4 101 .1 101 .1 16.1 16.8 101 .9 16.0 103.5 104.3 16.0 16.3 16.6 16.0 16.8 107.4 107.8 16.5 16.8 16.6 110.3 110.7 111.1 111.7 111.7 112.4 112.1 112.5 112.5 112.9 6.2 16.3 16.4 16.3 16.0 16.3 16.8 16.5 104.0 104.4 16.2 16.0 16.6 16.8 107.1 107.7 16.5 16.9 16.1 16.9 110.5 110.8 110.8 111.4 112.1 112.5 112.6 112.9 111.9 112.0 16.1 101 .9 16.3 16.5 16.2 104.4 104.4 16.5 16.7 104.7 16.4 16.0 16.9 16.5 16.1 110.3 110.8 111.5 112.2 112.1 111.7 112.7 112.2 111.2 110.2 110.3 110.8 110.7 16.5 16.1 16.1 16.5 101 .0 101 .2 16.9 16.9 16.3 6.0 6.0 16.4 101 .0 101 .3 101 .2 16.7 16.8 16.8 16.6 16.4 6.5 6.0 6.1 97.9 97.8 6.5 6.4 6.9 6.0 93.2 6.4 6.6 16.760 17.627 17.76 16.3!) 17.674 17.818 17.64 17.68 18.88 18.61 18.041 18.R 18.66 18.75 18.86 19.407 19.947 6.56 21 .M 6.“ 6.619 21 .364 6.16 6.- 8.62 23.118 23.46 8.36 6.61 6.5% 6.65 3.16 6.46 73.1 73.7 75.0 75.8 75.6 76.0 76.1 76.1 77.1 77.3 ".0 77.4 77.5 77.9 79.1 79.1 79.5 6.2 6.8 6.5 6.1 6.6 81 .2 81 .3 81 .2 81 .3 6.4 6.0 6.1 6.4 6.3 6.8 6.4 6 .3 6.3 6 .1 6.7 6.7 6.2 6 .2 6.0 6.8 6.8 6.0 6.5 6.9 6.2 6.7 6.8 6.7 6.4 6.1 6.9 6.4 0.8115 0.7844 0.7“ 0.6681 0.7460 0.7592 0.7560 0.8151 0.8197 0.7271 0.761 0.9048 0.6 0.936 0.9% 0.9101 0.7736 0.7136 0.766 0.767 mm 0.7784 0.6 0.746 0.7m 0.762 0.766 0.7436 170 270 370 470 570 670 770 870 970 1070 1170 1270 171 271 371 471 571 671 771 871 971 1071 1171 1271 16 26 36 46 56 66 76 86 96 106 116 126 173 273 373 473 573 673 773 873 973 1073 1173 1273 174 274 374 474 574 674 114.9 114.6 111.8 110.9 16.1 107.5 16.1 16.5 16.7 16.7 107.0 16.8 16.4 16.4 16.3 16.6 110.1 111.8 113.2 113.4 112.0 114.1 114.4 115.4 116.1 116.0 117.2 118.9 118.7 118.8 119.4 119.0 121.0 16.3 121.7 16.6 121.4 121.6 16.0 121.2 120.1 119.5 119.3 118.6 116.8 116.4 117.3 115.3 114.1 113.5 113.2 116.8 116.3 115.7 111.5 111.0 111.0 16.9 16.4 107.8 16.0 107.3 16.2 16.3 104.4 16.0 16.8 16.5 16.2 16.8 16.2 16.0 16.4 16.4 16.9 107.1 16.2 16.9 110.6 111.2 111.8 112.7 113.1 113.9 113.7 115.0 115.7 116.4 118.1 118.8 120.1 121.5. 16.8 18.1 18.5 124.4 124.8 124.9 18.6 18.5 127.2 127.2 18.4 18.6 18.7 18.8 127.2 18.6 111.7 111.2 111.2 110.1 16.6 16.0 16.2 107.5 16.4 16.5 104.6 16.2 16.0 16.7 16.5 16.1 16.5 16.3 16.7 16.7 107.2 107.4 16.5 16.2 110.9 111.5 112.1 113.0 113.5 114.3 114.1 115.4 116.1 116.8 118.5 119.2 16.5 121 .9 18.2 18.5 124.0 124.9 18.3 18.4 18.1 127.0 127.7 127.7 18.9 127.1 127 .2 18.3 127.7 127.2 110.8 110.8 110.8 110.5 110.1 16.7 16.8 16.3 16.0 16.7 16.8 107.6 16.6 16.5 16.8 16.1 16.6 16.8 16.6 16.3 110.1 110.2 111 .0 112.2 114.0 114.4 115.6 116.6 117.2 116.9 117.8 119.3 119.9 121 .8 18.2 124.5 18.5 127 .0 127.4 127 .2 127 .5 127.8 18.7 127.8 18.7 129.7 16.7 129.8 18.7 18.0 127.8 127 .6 18.2 18.3 107.5 16.6 16.5 104.5 16.1 16.5 18.8 104.7 18.9 18.4 16.0 107.3 16.6 110.2 111.9 112.9 113.7 113.5 113.3 113.7 114.6 115.5 116.5 118.0 119.2 18.7 16.2 18.0 16.9 18.3 124.4 18.0 127.5 129.4 130.3 131.4 16.4 134.1 134.2 18.4 18.5 18.1 16.7 131.5 16.9 131.0 131.1 18.7 18.7 18.0 127.8 18.1 18.5 18.8 6.5 6.0 6.9 6.1 6.0 6.7 6.4 6.6 6.9 6.7 6.2 6.4 91 .2 6.0 93.3 93.8 93.5 93.7 6.1 6.3 6.9 6.8 6.3 6.4 6.1 6.4 6.8 97.0 6.9 97.1 97.2 97.8 6.0 6.5 6.6 16.0 16.2 6.7 6.5 97.3 6.0 6.2 6.9 6.2 6.6 6.4 6.5 6.3 91 .4 6.9 6.9 6.7 6.7 6.3 16.4 16.2 107.7 16.3 16.5 16.7 16.4 16.3 18.7 104.1 16.1 18.6 16.3 16.5 107 .1 107 .3 16.4 16.7 16.2 16.0 16.6 16.9 110.0 111 .5 112.4 114.2 114.3 115.3 115.4 114.6 115.1 116.2 117.4 118.0 119.5 18.2 121 .2 16.1 16.3 16.7 16.2 121 .4 121 .8 121 .4 18.2 18.8 18.7 16.5 121 .6 16.6 121 .9 119.8 16.5 16.0 16.5 6.1 6.4 6.9 6.8 6.6 6.1 6.7 6.0 6.2 93.0 93.2 6.4 6.3 6.6 6.5 6.2 6.1 6.4 6.1 6.3 6.2 6.0 6.0 6.5 97.8 97.6 6.2 6.0 97.1 97.2 97.9 6.8 6.8 16.1 16.7 101 .1 101 .0 101 .1 16.4 6.4 6.5 6.9 16.1 16.3 6.9 6.7 97.7 6.6 6.4 6.4 6.6 6.16 6.68 21 .346 21 .69 21 .64 21 .76 21 .614 21 .76 6.181 21 .712 6.217 6.26 6.58 21 .84 6.. 6.814 8.” 8.481 8.677 8.012 8.68 8.86 8.510 8.84 8.270 8.64 8.81 8.66 8.270 8.175 8.76 8.365 27.168 27.529 8.84 27.66 27.76 8.752 8.64 8.56 8.3 27.69 27.477 8.66 8.80 8.69 8.718 8.61 8.511 27.66 8.458 29.071 27.562 8.78 78.3 78.3 78.1 77.8 77.6 77.4 77.6 77.1 76.5 74.8 74.3 76.3 76.9 76.9 76.8 77.2 77.7 6.9 78.0 6.1 78.7 79.8 6.1 6.9 6.8 8.4 84.1 8.5 8.3 8.6 8.6 6.8 6.6 6.0 6.1 91 .1 91 .3 6.6 6.8 6.1 93.4 6.1 6.6 6.7 6.2 6.8 6.0 6.2 93.1 6.7 6.8 6.9 6.2 8.5 8.1 6.7 6.2 81 .8 81 .3 81 .2 6.7 79.9 78.0 77.3 78.8 79.2 78.8 78.5 78.8 78.9 79.1 78.6 78.0 79.1 79.4 79.6 6.3 81 .9 6.2 6.7 8.8 8.4 8.4 8.1 84.0 8.7 8.7 6.5 6.1 6.9 6.9 6.6 87.6 6.7 6.1 6.4 6.1 6.5 6.6 6.3 6.7 8.2 8.7 8.8 8.4 8.2 8.2 0.776 0.7% 0.66 0.- 0.677 0.7375 0.88 0.37 0.86 0.866 0.88 1.678 0.869 0.870 0.7457 0.679 0.66 0.7970 0.68 0.6 0.653 0.9301 mm 0.66 0.935 0.7017 0.776 0.665 0.642 0.618 0.655 0.9052 0.9360 0.66 0.9002 0.658 0.9773 0.66 0.615 0.m1 0.9096 0.935 0.674 0.615 0.619 0.9729 0.9375 0.641 0.615 0.674 0.66 0.652 0.615 0.68 774 874 974 1074 1174 1274 175 275 375 475 575 675 775 875 975 1075 1175 1275 176 276 376 476 576 676 776 876 976 1076 1176 1276 177 277 377 477 577 677 777 877 977 1077 1177 1277 178 278 378 478 578 678 778 878 978 1078 1178 1278 118.8 117.5 113.8 107 .3 15.9 15.8 15.8 101.9 15.9 15.7 15.1 110.3 115.2 114.7 115.4 114.4 114.4 117.6 118.3 118.1 119.7 119.0 117.4 121.0 121 .1 119.7 120.1 121 .9 18.8 124.8 13.8 127.3 13.3 127.3 13.1 15.7 131.9 15.2 132.3 134.5 134.4 15.0 15.0 136.8 136.6 15.9 137.2 15.4 140.0 15.0 15.3 140.4 139.7 15.2 13.6 13.3 13.5 13.1 121 .7 118.1 115.1 113.1 111.1 110.3 110.3 110.7 112.1 114.1 114.6 115.5 116.6 118.1 120.6 121 .5 12.1 12.4 18.7 12.9 18.6 18.8 13.2 13.1 124.9 13.0 13.4 127 .8 129.3 15.9 15.6 15.1 134.5 15.0 136.3 137.1 15.2 15.7 140.0 141.1 142.7 145.7 147.1 148.7 148.2 149.2 149.9 151.6 152.6 152.7 127 .2 13.9 13.1 13.7 12.3 118.6 115.6 113.6 111.6 110.8 110.8 111.2 112.7 114.7 115.2 116.1 117.2 118.7 121 .2 12.2 12.8 18.1 13.4 18.6 13.3 13.5 13.9 13.8 13.6 13.7 127 .1 13.6 15.1 131.7 15.4 15.9 15.3 15.8 137.2 15.0 15.1 140.9 142.0 143.6 146.7 148.1 149.7 149.2 150.2 150.9 152.7 153.7 153.8 13.2 127.3 13.5 13.2 12.2 118.4 116.2 114.6 113.0 113.3 114.1 114.9 115.6 117.3 118.1 118.5 118.9 119.5 121 .4 12.9 18.6 13.3 13.6 124.8 13.3 13.5 13.6 13.3 13.8 127 .8 13.3 129.2 15.9 131 .6 15.5 134.3 134.6 15.8 136.6 137.2 15.1 137.1 15.3 140.0 143.0 143.1 144.2 145.0 145.9 146.1 147.4 148.4 149.7 18.5 13.3 116.5 113.5 111 .2 15.2 107.7 107.6 107.8 111 .0 113.4 115.8 118.2 119.0 13.6 12.0 12.4 12.8 13.1 13.0 13.8 129.3 15.5 131 .6 15.2 131 .9 15.4 15.2 15.5 134.5 134.5 136.5 15.4 15.5 15.9 15.8 15.5 140.5 141 .1 141 .9 141 .6 142.4 141.0 142.8 144.9 146.3 5.7 81.0 5.1 5.7 81 .6 81 .5 5.2 3.3 87.3 91 .0 ”.7 ”.0 ”.1 ”.1 ”.9 ”.2 ”.4 97.0 97 .9 97.5 97.1 ”.5 ”.4 ”.6 ”.2 ”.3 ”.6 ”.2 ”.4 97.0 97.2 ”.1 ”.8 ”.6 15.4 101 .2 101 .5 15.3 ”.9 ”.0 97.4 ”.2 ”.4 ”.3 97.9 ”.6 ”.6 ”.5 15.5 15.6 15.1 ”.2 ”.6 12.5 121 .2 119.5 118.9 115.2 113.9 111.6 111.8 111.2 112.6 112.7 115.0 117.3 118.8 118.7 119.3 121 .3 12.9 124.5 13.2 13.7 12.6 13.6 13.1 13.8 13.6 13.1 13.5 13.6 127.0 127.7 127.1 129.6 131.6 131.5 131.2 131.7 15.4 15.0 134.1 134.8 15.7 134.7 15.6 137.1 15.7 15.2 15.6 15.4 15.8 140.2 140.7 141.0 140.9 ”.8 ”.5 ”.9 ”.1 ”.0 3.7 3.7 3.6 5.9 3.7 3.6 3.1 5.6 ”.5 ”.2 5.4 91 .6 92.6 ”.5 ”.8 ”.9 91 .3 ”.3 ”.4 ”.9 ”.5 91 .9 91 .9 ”.5 ”.5 ”.8 92.1 ”.6 ”.8 ”.5 ”.0 ”.1 ”.3 ”.5 ”.0 ”.2 ”.6 ”.6 ”.0 ”.8 97.3 ”.0 ”.0 ”.6 ”.6 ”.3 ”.4 ”.3 ”.0 27 .7” 3.4” 3.313 3.404 3.555 3.55 24.” 3.”1 3.076 3.75 3.& 3.57 3.55 27.810 3.59 29.079 3.54 29.252 29.613 29.72 31 .0” 5.” 3.784 31 .420 31 .57 31 .51 31 .921 5.15 5.15 5.13 34.311 5.844 5.018 34.529 5.36 36.694 36.874 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