my. .. .gd :‘IALV fivg. n5 ~ Lu E '5"- ‘I ‘ ‘Stc a“.r ”x \ .\ 1n- ”'4‘! ‘4? "s gihé v‘ 331%“ “S < {fit ‘ ‘1‘ v‘::‘ sub 0 a k s ". ‘.‘:r a ‘II Nye ABSTRACT THE EFFECTS OF CORPORATE FINANCIAL POLICY ON STOCKHOLDER EXPECTATIONS BY Richard Gene Walter Two areas of theoretical controversy in business finance remain unresolved because of inadequate empirical techniques. Repeated attempts to isolate the effects of capital structure and dividend policy on the coSt of equity capital have been unsuccessful because the methods used to measure stockholder expectations of return lacked objectivity. The purpose of this study was to examine the potential of a new approach to this measurement problem and attempt to resolve the empirical questions noted above through its use. Research in business finance relies heavily on market prices of securities. In theory the market price of a given equity share represents stockholder expec- tations of future cash flows to be obtained by holding that share, discounted at a rate appropriate to the risk class of that firm. A change in stock price reflects either a change in cash flow expectations or a change in the rate of discount or both. One problem with previous 22:3. lques 1 earnings as need not e1 method 33U5ing t} . u... «=5 and t I C - V .V. ‘5‘ " "*9 rate Th: 1:5 assoc: CCZmOn 113.535 if". .. "I .‘A ug‘a tion u‘ “l‘Jest‘ :vi,‘ .‘.\_es Of we16m n. \ y' g 1 &lq:n a? \ "a; i‘ ‘;Sc""‘1+ Vi“ ‘ I ;‘.‘1“,. it"! “‘ato‘ \‘ angel] \ Richard Gene Walter techniques is that they rely in some way on accounting earnings as a measure of expected future cash flows. We need not elaborate on the ways in which accounting earn- ings fall short of an ideal measure in this instance but merely note that any departure from true expectations will be reflected as error in the discount rate so obtained. The method employed in this study avoids this shortcoming by using the relationship of two closely related securi- ties and their respective market prices to obtain estimates of the rate of discount. The relationship of a stock purchase warrant to its associated common stock is the basis for this method. The commonality of interests of stockholders and warrant holders in the future cash flows of the firm permits the isolation of changes in the discount rate of either type 0f investor from relative or absolute changes in the prices of these related securities. Using the theoretical Structure and empirically determined investor preference function developed by Ayresl which links these rates of discount, the magnitude of the discount rate for each may be determined assuming that both securities are in equi- librium at the time of observation. This method was used to determine the stockholder <fi£count rate, which is also the cost of equity capital, lflmediately following annual reporting dates for all firms \fluch have had warrants actively traded on the American nil, “a"! r ‘r-vnl - qr...- lilfll L 1 3:33." Excite. iisccun-t ra :eztion rat .1: results 5 Kat! $23: 0; I 1‘ . A r -.: “IO: Fax Richard Gene Walter Stock Exchange for at least five consecutive years. These discount rates were regressed on the debt/equity and re- tention ratios for each of the sixteen qualifying firms. The results were rather disappointing and inconclusive. Many of the observations failed to yield estimates of the discount rate because of apparently short investment hori- zons on the part of warrant holders. Those observations which were obtained showed a positive relationship between leverage and the discount rate as would be expected but the error in these estimates was so great as to hide any relationship to payout. This error resulted from measure— nmnt error in the model parameters and therefore severely limits the usefulness of the method. Improved techniques for measuring the model parameters might well redeem this method. The recent increase in the number of warrants in the market broadens considerably the range of firms to which the method might be applied in the future. Unless such an improvement in technique is found, however, the method does not merit further research effort. Herbert Frazer Ayres, "Risk Aversion in the Warrant Markets" (unpublished Master's thesis, Massachu— ifituslhstitute of Technology, 1963), and an article with Eisame title and derived from that thesis, published in £EE§¢rial Management Review, V, No. 1 (Fall, 1963), 45-53. P. Wu ml in pa] THE EFFECTS OF CORPORATE FINANCIAL POLICY ON STOCKHOLDER EXPECTATIONS BY Richard Gene Walter A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Accounting and Financial Administration 1970 n I l 1 A H :1 \r 1"“ ce, enCO' b." u I as.- «3 A a ,_ \r - 0-9- BAA o my 0 k c0131tte y ‘ h a to Pro u-i V «1.. Q U nu . ‘3 .4 C p i- .. .«uvd» ~§ . ..._, ‘Ifi‘fl ell C s «£43! 0 i‘.‘ ‘1 \ $.10: ACKNOWLEDGMENTS When I look back over the individuals, organi— zations, and institutions to which I am indebted for assistance, encouragement, and support, it amazes me that this dissertation did not write itself. I am most deeply indebted to Professor Roland I. Robinson who, in addition to being one of the greatest men I have ever known, served as my committee chairman. I also wish to express my grati— tude to my other committee members, Professors Alden C. Olson, and Richard F. Gonzalez, for their assistance. Professors Myles S. Delano and Adolph E. Grunewald and a number of fellow students also deserve credit for their comments and suggestions at the time I conceived this study. Without the financial assistance of the American Bankers Association in the form of the Harold Stonier Fellowship, I could not have given my full attention to my research. Without the modern computer facilities of the Michigan State University Computer Laboratory the project would have been impossible. Without the en- couragement and assistance of my good friend, buddy, and wife, Carol, I would never have started the doctoral pro- gram much less this dissertation. ii ‘ t *0 ’\ \‘&. O TABLE OF CONTENTS Page INTRODUCTION . . . . . . . . . . . . . 1 Chapter I. MEASURING STOCKHOLDER EXPECTATIONS OF RETURN O O O O I O O O O C O O O 5 A. Relationship Between a Warrant and Its Associated Stock. . . . . . . 6 B. The Model . . . . . . . . . . l4 1. Warrant Price at the Time of Exercising. . . . l4 2. Expected Present Value of the Warrant. . . . . . . . . . 15 3. Distribution of Future Stock Prices . . . . . . . . . . l6 4. Investor Preferences . . . . . 20 5. The Complete Model . . . . . . 30 C. Solution Procedure . . . . . . . 31 D. Sensitivity Analysis. . . . . . . 37 E. Measuring the Model Parameters . . . 42 l. Coefficient of Risk Aversion. . . 44 2. Market Prices. . . . . . . . 49 3. Leverage . . . . . . . . . 50 4. Variance . . . . . . . . 55 5. Dividend Yield . . . . . . . 56 II. THE EFFECT OF CAPITAL STRUCTURE ON THE COST OF EQUITY CAPITAL . . . . . . . . . 57 III. THE EFFECT OF DIVIDEND POLICY ON THE COST OF EQUITY CAPITAL . . . . . . . . . 65 iii . R .- n‘n Dr vv 0 Sui-3 "'f f? TESTING ‘ A. ReSt; For: B. Meas C. Stat. PESULTS ; A. 8616; 3- Resul Chapter IV. TESTING THE HYPOTHESES . . . . . . . A. Restatement of Hypotheses in Testable Form. . . . . . . . . . . . B. Measuring the Sample Variables . . . C. Statistical Testing. . . . . . . V. RESULTS OF THE STUDY. . . . . . . . A. Selection of the Sample . . . . . B. Results. . . . . . . . . . . uthNF-J 5. 6. 7. 8. 9. 10. ll. 12. 13. 14. 15. 16. ACF-Brill Motors . . . . . . Armour & Company . . . . . . GAC Corporation. . . . . . Jefferson Lake Petrochemicals of Canada, Limited. . . . . . . Mack Trucks, Incorporated . . . Martin Marietta. . . . . . . McCrory Corporation . . . . . Molybdenum Corporation of America. National General Corporation . . Pacific Petroleums. . . . . . Sperry Rand . . . . . . . . Textron . . . . . . . . . Trans World Airlines . . . . . Uris Buildings Corporation . . . Van Norman Industries, Incorporated Ward Baking Company . . . . . VI. CONCLUSIONS 0 O O O O O O C O O C BIBLIOGRAPHY. iv Page 74 75 77 79 84 84 87 9O 93 97 104 107 111 115 120 123 126 129 129 134 138 142 146 150 153 2 Jo Corporatio ACE-Brill Arm-Our 5, c LIST OF TABLES Table Page 1. Corporations Satisfying Original Criteria . 86 2. ACF-Brill Motors . . . . . . . . . 92 3. Armour & Co. . . . . . . . . . . 95 4. GAC Corporation. . . . . . . . . . 101 5. Jefferson Lake Petrochemicals of Canada, Ltd. . . . . . . . . . . . . 105 6. Mack Trucks, Inc. . . . . . . . . . 109 7. Martin Marietta. . . . . . . . . . 113 8. McCrory Corporation . . . . . . . . 117 9. Molybdenum Corporation of America. . . . 122 10. National General Corporation . . . . . 125 11. Pacific Petroleums, Ltd. . . . . . . 128 12. Sperry Rand . . . . . . . . . . . 131 13. Textron . . . . . . . . . . . . 133 14. Trans World Airlines . . . . . . . . 136 15. Uris Buildings Corporation . . . . . . 140 16. Van Norman Industries. . . . . . . . 144 17. Ward Baking . . . . . . . . . . . 148 3...”.3 ..".V 1 '._n o s‘ «to Relation Stock 1 Equilihr Computes DEtermin ‘ aha ; \- COmParis s an: a. MOBCI Figure l. 10. 11. 12. 13. LIST OF FIGURES Page Relation of Warrant Price to Associated Stock Price . . . . . . . . . . . 7 Equilibrium in Indifference . . . . . . 27 Computed Warrant Price as a Function of a. . 33 Determination of Expected Holding Period and Maximum Return 8 . . . . . . . . 36 Comparison of Ayres' Published Scatter Diagrams with Revised Scatter Diagram . . 45 CALCOMP PLOT of Ln Warrant Price versus Ln Stock Price . . . . . . . . . . . 53 Warrant Price Versus Stock Price, ACF-Brill Motors. . . . . . . . . . . . . 91 Warrant Price Versus Stock Price, Armour & CO. 0 O O O O O C I O O I O 94 Required Return Versus Debt/Equity Ratio for Armour & Co. . . . . . . . . . 96 Warrant Price Versus Stock Price, General Acceptance Corp. (Old) . . . . . . . 99 Warrant Price Versus Stock Price, General Acceptance Corp. (New) . . . . . . . 100 Required Return Versus Debt/Equity Ratio for GAC Corporation . . . . . . . . 102 Warrant Price Versus Stock Price, Jefferson Lake Petro. . . . . . . . . . . 106 vi Ox-) ol 3 0's.) fx.) (.1 v (7‘) Ix.’ t-‘J r»..; (1,7 Warrani Truc} Requir L' Warrar Mari Requi- for 3U Figure Page 14. Warrant Price Versus Stock Price, Mack TrUCks I O O O O O O O O O O O 108 15. Required Return Versus Debt/Equity Ratio for Mack Trucks, Inc. . . . . . . . 110 16. Warrant Price Versus Stock Price, Martin Marietta Corp. . . . . . . . . . 112 17. Required Return Versus Debt/Equity Ratio for Martin Marietta. . . . . . . . 114 18. Warrant Price Versus Stock Price, McCrory Corp. (Old) . . . . . . . . . . 116 19. Required Return Versus Debt/Equity Ratio for McCrory Corp. . . . . . . . . 118 20. Warrant Price Versus Stock Price, Molybdenum of America . . . . . . . 121 21. Warrant Price Versus Stock Price, National General Corp. . . . . . . 124 22. Warrant Price Versus Stock Price, Pacific Petroleums, Ltd. . . . . . . . . 127 23. Warrant Price Versus Stock Price, Sperry Rand. O I O I O O I O O O O O 130 24. Warrant Price Versus Stock Price Textron, Inc. C O O O O O O O O O I O 132 25. Warrant Price Versus Stock Price, Trans World Airlines . . . . . . . . . 135 26. Required Return Versus Debt/Equity Ratio for Trans World Airlines . . . . . . 137 27. Warrant Price Versus Stock Price, Uris Buildings Corp. . . . . . . . . 139 28. Required Return Versus Debt/Equity Ratio for Uris Building Corp. . . . . . . 141 vii .'-' m 1.3-4. 4 N n. Warrant 2 Norman 1. Warrant P Baking. D. Required for War Figure 29. 30. 31. 32. Warrant Price Versus Stock Price, Van Norman Industries . . . Required Return Versus Debt/Equity Ratio for Van Norman Industries Warrant Price Versus Stock Price, Baking. . . . . . . Required Return Versus Debt/Equity Ratio for Ward Baking Company . viii Ward Page 143 145 147 149 In dis L‘e present VF: constantly COI reason for th. manly acce value of the seats the dis aired by 1101 ékpected retx iXpected retx rerun neces is also the 535546 in st 3‘1r93ted fut Ant Y capit The vale Ft enect c Bu INTRODUCTION In discharging his duty of attempting to maximize the present value of his firm, the financial manager is constantly concerned about stockholder expectations. The reason for this is quite simple: market price is the most commonly accepted surrogate for maximization of present value of the firm. To be more specific, stock price repre- sents the discounted expected future cashflows to be ob— tained by holding that stock. The rate of discount is the expected return. When the market is in equilibrium the expected return of the marginal investor is the required return necessary to support the current stock price. It is also the cost of equity capital. Thus we see that any Change in stock price may reflect either a change in eXpected future cashflows or a change in the cost of equity capital or both. The purpose of this dissertation is to determine the effect of corporate financial policy on the cost of equity capital. Clearly it is necessary to separate the effects of changes in cashflow expectations from changes in the discount rate in order to accomplish this. It is . n \ 3:33.195 have t In the Modigliani and The P0 approach h results ha this line is largely effect of and of 110‘" The"; proceeded aiequate theor :arket valuati results entire statistical ar capital was $1 the market val :‘ie reciprocal iismptions a: the cost of e WE. Stock 51518 are as Qt yea c “fittings for atcckholders ' l EitapitaFrar it " in separating and measuring these two factors that previous studies have been inadequate. In the introduction to their now legendary paper, Modigliani and Miller wrote: The potential advantages of the market-value approach have long been appreciated; yet analytical results have been meager. What appears to be keeping this line of develOpment from achieving its promise is largely the lack of an adequate theory of the effect of financial structure on market valuations, and of how these effects can be inferred from ob- jective market data.1 [Italics mine.] They proceeded to develop a very clever and, perhaps, even adequate theory of the effect of financial structure on market valuation. They did not, however, infer these results entirely from objective market data. In their statistical analyses the measure of the cost of equity capital was stockholder net income after taxes divided by the market value of common stock which is equivalent to the reciprocal of the PE ratio. A number of implicit assumptions are made in identifying this statistic with the cost of equity capital, but one is of crucial impor- tance. Stockholders' expectations of annual future cash— flows are assumed equal to accounting earnings for the Past year. Clearly there are many cases where accounting earnings for the past year may not adequately represent Stockholders' expectations for the current year let alone \ 1Franco Modigliani and Merton H. Miller, "The Cost of Capital, Corporation Finance, and the Theory of Invest- gggtp" American Economic Review, XLVIII, No. 3 (June, 1958), :5. perpetuity - I iuction meth0¢ trier of othe ngs as a meas C121! historic lodiqliani and tier measures earnings have ' Eactors have in gated from his replied is a capital at a : 'v'rjective ma “St 0f equit 'P’CliCies are :1" 1“ ilcies on t A ne'. L 1 are “VJ‘ersl 4. e)?“ htJ‘ U"- H". 3 dissert :14 we between - “on S to C If to perpetuity. Acquisition or sale of assets, new pro- duction methods, new products, an invention or any of a number of other events could invalidate accounting earn- ings as a measure of expected cashflows on the basis of their historical nature alone. Additional tests of Modigliani and Miller's theory have been made based upon other measures of the cost of equity capital. Accounting earnings have been averaged, "normalized," and growth factors have been added, the growth factors being com- puted from historical accounting data. What is, indeed, required is a method of measuring the cost of equity capital at a specified point in the time on the basis of "objective market data." Given this, one may observe the cost of equity capital at times when different financial policies are in effect and infer the effects of these policies on the cost of equity capital. A new method for separating and measuring stock— holders' expectations regarding rate of return is used in this dissertation. The method relies upon the relation- Ship between a stock purchase warrant and its associated Common stock. Because of the commonality of interests on the part of warrant holders and stockholders in the future caShflows from the enterprise, we may infer expectations regarding rate of return from the relative market prices of the related securities. Changes in the relationship of these market prices signify changes in expectations regarding rate cost of equity ieternined frc: securities at ‘ A com- exists between and of the met; :i;ital from t‘: The second and effect of capi tirely on the lave-ted to dev ce effects of net of equity Company in the aid Chapter VI regarding rate of return. By using this relationship the cost of equity capital at a given point in time can be determined from the prevailing market prices of these securities at that time. A complete explanation of the relationship which exists between a warrant and its associated common stock and of the method used to measure the cost of equity capital from that relationship may be found in Chapter I. The second and third chapters review the theory of the effect of capital structure and dividend policy respec- tively on the cost of equity capital. Chapter IV is devoted to developing the tests of hypotheses regarding the effects of these two areas of financial policy on the cost of equity capital. The results of the study for each company in the corporate sample are presented in Chapter V and Chapter VI is devoted to conclusions. CHAPTER I MEASURING STOCKHOLDER EXPECTATIONS OF RETURN The major emphasis of this dissertation is on investigating a new method for determining stockholders' expectations regarding future rates of return on their investment. The purpose of this chapter is to acquaint the reader with the method by which these expectations are determined. The method, as noted in the Introduction, relies on the relationship between a stock purchase war— rant and its associated common stock. In the first section of this chapter this relationship is presented in general to provide the reader with an intuitive under— standing. In the second section a specific mathematical mOdel of the relationship is developed. The third section Provides an iterative solution procedure for the equations developed in the second section. The fourth section is devoted to a sensitivity analysis of the model. The final SeCtion is directed toward the problems and procedures anOlved in measuring the model parameters. In a sense, 33;“ I is t. which follow C financial POli A stOC rant, provides related seCL‘e‘fi price until 6? exercising Prj warrant or maj- fied in the w against dil‘at aresult of t exercising pr Chapter I is the heart of this dissertation. The chapters which follow concern the search for relationships between stockholders' expectations and two areas of corporate financial policy. A. Relationship Between a Warrant and Its Associated Stock A stock purchase warrant, hereafter termed a war- rant, provides its holder with the Option to purchase the related security, usually common stock, at a specified price until expiration. This price, properly called the exercising price, may be constant over the life of the warrant or may increase one or more times on dates speci- fied in the warrant contract. Most warrants are protected against dilution by the terms of the warrant contract. As a result of this protection, the number of shares and the exercising price per share may change, but in a way such that an equivalent share of the organization may be ob- tained according to the stated terms. Warrant holders do not receive dividends. Figure 1 illustrates the relationship between war— rant price, W, and its primary determinant, the price of its associated common stock, 8. At times relatively diStant from the expiration date, the warrant price versus StOCk price relationship falls along a path such as AB, approaching CD at the higher ranges of stock price. 0CD is the minimum bound for warrant price. No justification (A . 1 u latich WARRANT PRICE W D A E PREMIUM 45° “\sz } 0 Tc #8 e STOCK PRICE Figure 1 Relation of Warrant Price to Associated Stock Price is needed for are clearly U7 j‘fi for stock her] high ““3 :bserved t0 f5 explained belc to arbitrage C and sell the 5 errant price he purchased. “homdary” on ted frequentlh Having relationship 1 the premium, . exceeds the n has found e111: tent of thi Price to exer “QIdiVidend The . “cg fl ISt thr is needed for the segment OC since negative warrant prices are clearly unreasonable. The segment CD traces the mini- mum for stock prices above the exercising price, Pe' For very high ranges of stock price, warrant prices have been observed to fall below this level for reasons which are explained below, but only far enough to make it attractive to arbitrage operators who buy the warrant, exercise it, and sell the stock at a profit. OE is the upper limit on warrant price since at this price the stock, itself, could be purchased. Shelton placed a more restrictive upper "boundary" on warrant prices, but it is empirically based and frequently violated. Having established the limits between which the Ixalationship must fall, let us turn to an examination of tflme premium, i.e., the amount by which the warrant price e>nzeeds the minimum bound for a given stock price. Shelton iNiS found empirically that several factors determine the anIOunt of this premium, among them the relation of stock Prfiice to exercising price, length of Option period remain- inSJp dividend yield, and marketability considerations. Thfii first three of these factors is intuitively related tolthe premium in the discussion below. Since marketability \ W 2John P. Shelton, "The Relation of the Price of a arifiant to the Price of Its Associated Stock," Financial £23££fi§ts Journal, (May—June, 1967), 144. Wa 3John P. Shelton, "The Relation of the Price of a rrftnt to the Price of Its Associated Stock," Ibid., (“half-August, 1967), p. 94. is not a ques Sections, and siiered in th 31 the Americ. ations are of Consir :‘ie exercisim this range deh value," i.e., grehium is not Price will (let ;aid because prices above warrant. The the price wil3 ation, but he t'htion regard: 38:. 2e v Q 0 Probe EXE:CJ ~ ‘Slng pr; .LL‘um. The is not a question of theory, but results from market imper— fections, and further, since the sample of warrants con- sidered in this dissertation was drawn from those listed on the American Stock Exchange, marketability consider- ations are of no concern. Consider a warrant whose stock is selling below the exercising price. The warrant sells at a premium in this range despite the fact that it has no "intrinsic value," i.e., the minimum bound is zero. Clearly that premium is not paid based on the expectation that stock price will decrease or remain the same. The premium is paid because of the expectation of the existence of stock Irrices above the exercising price before expiration of the ‘marrant. The warrant holder generally is not certain that tflie price will get above the exercising price before expir- ai:ion, but he must have a subjective probability distri— lDution regarding future stock prices in which there is a ncnn~zero probability of stock prices greater than the eJ'Cercising price or he would not be willing to pay the Prfnnium. The more of this distribution that falls above thfi exercising price, the greater the premium he is will- inEJ to pay. It seems reasonable to assume that expec- ta”ti-ions of future stock prices are tied to the current prjdze and that an increase in the current price would Shift the subjective distribution of future prices upward. This, as stoc helow, the pr The e expectation < range of sto. shorter by 1 fiction of st am, Thu: premium is j 10 Thus, as stock prices approach the exercising price from below, the premium increases. The argument that the premium depends upon the expectation of higher stock prices is valid over the entire range of stock price. The effect of the option period re- maining tends to constrain the premium as it becomes shorter by limiting the spread of the subjective distri- bution of stock prices that could prevail before expir- ation. Thus, on the last day of the option period, the premium is forced to zero because there is zero proba- bility of higher stock prices prevailing before expiration. Let us now consider the third factor, dividend jyield, and the constraining effect it has on the premium at: higher ranges of stock price. In the process the inqportant concept of leverage between the warrant and CCnnmon stock will be introduced. The fact that a warrant has a limited life, and thirt a range of stock prices exists for which it has no Value, are factors which increase the risk of the warrant rel-<‘ative to the stock for most investors. The higher risk leads warrant holders to expect a higher return. Let B rePIE‘Esent the annual expected return to warrant holders. SlnCe this entire return must come in the form of price lncreases , B = All (I-l) where W is t. next year. TL has two addit capital gains price increas Where :5 is t 3914*» year. 5 :93 reasons c 4 2\ If ‘5: n ' U'fEK'tatlon L . ‘ the . :Jbect d E:- J-‘Qt‘ l the die 50: t3 8.. JldEm Crib» LOCK-101' m4 ‘- d 11 where AW is the warrant price increase expected over the next year. The expected return to stockholders, however, has two additive components, the dividend yield, 5, and a capital gains return, a, resulting from expected future price increases.4 We may express a as a = ——- (I-2) where AS is the eXpected stock price increase over the next year. Since warrant holders expect a higher return for reasons given above, B Z O. + O (I-3) or" AW AS ‘w— 1 s + 5 (1-4) L - _ AW AS . . €3t us define L — V? 13' Then we may rewrite Inequality (1‘4) as 6 L > 1 + — (I-S) — a \ ex: 41f the reader is tempted to claim that a general EN3ctation of rising stock price could not exist, i.e., that the current price would be bid up to eliminate this exF’fiicrted increase, he should reconsider the effects of dis- :OtuTting for the time value of money and risk. Whenever e (iividend yield, 6, falls short of the required return Co Stockholders, the future price of the stock will be dis- anunted by the difference, in this case or, thus providing to eMpected annual price increase of or per cent relative e current stock price. The reader wi . , I pnce Wlth re factor betwee: Tron the righl Est always b values as the 1% stockholde Harv hant is 5 .i t ‘u'dII ant “Ow 12 The reader will recognize L as the elasticity of warrant price with respect to stock price. This is the leverage factor between a warrant and its associated common stock. From the right side of Inequality (I-5), we see that L must always be greater than unity and must take on higher values as the dividend yield increases in order for the return to warrant holders to be at least as great as that to stockholders. An extreme example is in order at this point, both to demonstrate the existence of this leverage factor and to show how it varies with the premium. Assume that we can buy a warrant whose associated stock is selling for, say; 20. Assume further that the exercising price of the vwarrant is $20.00 and the premium is zero. Assume now tfliat stock price increases by 10 per cent to 22. The “warrant now has an intrinsic value of $2.00 which is an iJlfinite return on an investment of zero; so L = w in this Case. We have already established the existence of pre— milnns, however, so let us assume that the warrant sold at a Exremium of $1.00 before and after the change in stock Prince. .A little computation shows L to have a value of 20 .in this case. Let us assume now that stock price in- creases another 10 per cent to 24%. Assuming the dollar prEHnium remains, L would have a value of approximately 7.3. It ca iatcnstrated that L decree dLstance of s graciously de 7.1-3) places faction of t not very resi :ising price higher range to zero as s satisfy Inec arbitrage Q; the warrant 3.888 Operad rat-Ilium) fre 13 It can be shown mathematically that the results demonstrated by the example are generally valid, i.e., that L decreases with increases in the premium and with distance of stock price from exercising price. Along the previously defined upper limit OE, L = 1. Inequality (I—S) places a new upper limit on the premium which is a function of the dividend yield. This new upper limit is not very restrictive for low stock prices (below exer- cising price), but it forces the premium to zero at the higher ranges. It can be shown that the premium must go to zero as stock price approaches Pe(l + %) in order to satisfy Inequality (I-S). For higher stock prices, artdtrage Operators will move in and begin to exercise idle warrant as its price falls below CD. The action of tflmese Operators will prevent any large discount (negative Premium) from occurring. At this point the reader should have an intuitive fetaling for the relationship between a warrant and its assuociated common stock and the role played by the three facrtors in determining that relationship. The remainder of ‘this chapter provides a description of a model in which all_ Of the effects assumed in the previous intuitive justification are made explicit and put into symbolic form. The n‘. aspects wi th being one of was to neasur 35 risk avers research whic “Ported in 1 i. 'idl'rant . ‘31 exercisin \ As 1 there is no 33:15 8611 1; 53‘, aSsume l V the ac 5k 5 H16 Effo i“: "t thCk I: in: “MS may b VFW, E 1:”‘tts n 1 1363‘ I ‘ J ' 45:: 14 B. The Model The model presented below is identical in all aspects with that developed by Ayres,5 the difference lxaing one of application. The purpose of Ayres' research hmas to measure investor preferences for warrant holders. Spencifically, his purpose was to measure the coefficient of :risk aversion as defined below. The results of his research which are relevant to this dissertation are repnorted in the last section of this chapter. 1;_ Warrant_price at the time 9:13 exercising As long as the warrant is selling at a premium, tfluare is no reason for its holder to exercise it since he coulxi sell the warrant and buy the stock for less. We may iassume then that warrants will be exercised only when their premium is zero or negative, i.e., selling at a discxount. Since this discount will always be small due tO‘theeefforts of arbitrage operators, let us assume it to be zero for practical purposes. We know, therefore, that the warrant price at the time of exercising, te, must lie along the minimum bound and is, thus, a function of the stock price prevailing at that time. Symbolically this may be expressed as 5Herbert F. Ayres, "Risk Aversion in the Warrant fiarkets," Industrial Management Review, V, NO. 1 (Fall, Ther premium will :5 very sbor intersection yield With t 35139 on t? 15 wte = MAX(O,S - pe) (I-6) There are only two conditions under which the prendum will go to zero: (1) the remaining option period ix; very short, and (2) the stock is selling above the iJItersection of the upper bound imposed by the dividend yixald with the lower bound. Expectations of early exer- cijsing on the part of warrant holders for the second renason are predictable from the results of the sensitivity arualysis. This question is covered in the section con- cxarning the solution procedure. 2. Expected present value of the warrant We now have an expression relating warrant price at £1 future date to stock price on that date. Unfortu- nately'we do not know future stock prices precisely. Assume» however, that we know f(S), the expected proba- bility density function of stock prices as of the exer- CiSing date. We may then determine the expectation of Warrant price as of the exercising date by integrating. oo E[Wt 1 = f MAX(O,S-Pe) f(S) dS (I-7) e —00 Pe m = f MAX(O,S-Pe) f(S) dS+f MAX(O,S-Pe) f(S) dS -m p e (I-8) Obviously t}: the S-P ter: e expected war am the pres future EXpec required by The Un Edit, gix‘rep‘ Berra» t may 16 Obviously the first integral is zero since zero dominates the S-Pe term for all values of S less than Pe’ The expected warrant price, then, reduces to E[Wt ] = g (S-Pe) f(S) dS (I-9) e e and the present value is obtained by discounting this future eXpected value at the rate 8, the rate of return required by warrant holders. -81: co PV(E[wt 1) = e 8! (S-Pe) f(S) dS (1-10) e P e The reader should satisfy himself at this point that, given f(S) and B, the expected present value of the Vfiirrant may be computed. The probability density function (If stock prices as of the expiration date, f(S), will now be developed . 3- Distribution of future Elizsfifprices It has been noted that the investor is assumed to haVTe a "subjective" probability distribution of future Stc>Ck.prices. We do not know the precise shape of that dist:ribution, but presumably it is based upon the in- veStI-or's observation of security price action. If he has ¢Observed carefully then he probably has come to the c . . . °n<3lus10n that succe551ve stock price changes are uncorrelated tide of wee}: fashion but quite stable assumption, distribution limit theore. 3133988 over ”lm - "“5: If our aCtion' he I: l7 uncorrelated. He probably has also noted that the magni- tude of weekly stock price changes behaves in a random fashion but that the distribution of those changes remains quite stable over time. If we merely add one technical assumption, i.e., that the first two moments of that distribution of price changes exists, then by the central limit theorem, the distribution of the sum of these changes over time will approach a normal distribution. Thus, if our investor has correctly observed market price action, he must accept the random walk hypothesis. The only question remaining is whether the normal or log- normal distribution best approximates our investor's "subjective" distribution. The two most promising approxi- Imating distributions, the normal and lognormal, are pre- sented below. To provide a basis for selecting one of tfluese distributions, it is necessary to show how they (havelop from assumptions concerning price series which fCXLlow a random walk. The following closely parallels the development in Sprenkel. The notion of a random walk is really quite simple. Hawking observed stock price S0 at time zero, let us observe 51 Eat t = 1. In general the prices will not be equal; the priJBe will have taken a "step" from S0 to 51' The size of is a random variable. As time passes, that step, 8 -s \ l 0’ of 6Case M. Sprenkle, "Warrant Prices as Indicators I I31x:pectations and Preferences," Yale Economic Essays, ' No. 2 (1961), 191-97. a series of farm a rando specified, w time in the Let distributed ST : 30+S . that their 'k‘y this ad ‘ I . ~ll'St, the: c 3‘. ST’ Clea One Point 18 a series of random length steps linked one to the next form a random walk. Once the distribution of St-St—l is specified, we may derive the distribution of St for any time in the future from the chain prOperty of the series. Let us first assume that the "steps" are normally T distributed. Let S = Z (Xt-S 1). Clearly then, t=l t" 2 ST = SO+S. If the steps are N(u,o ), it can be shown that their sum, S, is N(Tu,T02). There are two reasons why this additive random walk model is inappropriate. First, there is a positive probability of negative values of S clearly not in conformance with conventional notions TI Concerning stock prices. Secondly, the size of each step is independent of St-l' Thus the implication is that a (nae point step is as likely for the stock when it is sell- iJng at low prices as when it is selling at high prices. Both of these problems may be overcome by using a nurltiplicative random walk. Assume that steps in the lckgarithms of stock prices, i.e., lnSt-lnSt_l, are normally di - = . ._ stmibuted. Let St St-lSt-l where Xt-l is the multi PliJSative step factor. Taking logarithms and rearranging, ln _ - ' ' 2 - St: lnSt-l — lnXt-l which is N(u,0 ) by assumption. We kncny, then, that the sum, X, will be N(Tu,T02). It can . S eaS-‘J—ly be shown that ln-é3 = X. Knowing the form of the o normmal probability density function, we obtain Ike problem 0 Further, equa steps are eqt lation. This If to :tdom walk that EISt] in Expressic if growth 01 the stockho' Ser failed C “ha-2' a 3‘:U J) 7 ST 2 (Ins—- " T) _ O 202T S _ ___:!.'__. u— ._J (1-11) 0 /2ng T The problem of negative values of ST is eliminated. Further, equal percentage steps rather than equal dollar steps are equally likely, a much more reasonable formu— lation. This model is called a lognormal random walk. If we assume that lnX is N(O,02), but that the Inandom walk is superimposed upon a growth process such at ST _ ST tdiat E[S ] = S e , then ln——— dT - ln—— - aT. Thus, a t 0 See So irl Expression (I-ll) may be interpreted as the annual rate ch growth of stock price or the capital gain portion of the stockholder's return. Serial correlation tests on stock price series hirve failed to disprove the random walk hypothesis. Cer- taLin evidence exists, however, than an unbounded random ‘VEle may be inapprOpriate as a model of future stock Prices. Cootner7 champions random walks bounded by :rEBflective barriers and the spectral analysis work of Granger and Morgenstern indicates that significantly \ 7Paul H. Cootner, "Stock Prices: Random vs. SYstematic Changes," Industrial Management Review, III, N0. 2 (Spring, 1962), 211-213. 8C. W. J. Granger and O. Morgenstern, "Spectral Al'lalysis of New York Stock Market Prices," Kyklos, XVI (1963), 1—27. greater valu ties and Exc for low fret fitted by tl ings, the r. of future p eblurring for use in 1 \ J lit)” re St. 20 greater values of the power spectrum of the weekly Securi- ties and Exchange Commission composite price index exist for low frequency (long period) bands than would be pre- dicted by the random walk hypothesis. Despite these find- ings, the random walk utilizing a lognormal distribution of future prices has enjoyed cOnsiderable success in explaining warrant and option prices and has been adopted for use in the proposed study. 4. Investor preferences In order to complete the model it is necessary to define explicitly the relationship between the expected return on the warrant, B, and that on stock, d+6. In the first section of this chapter it was argued that the limited life of the warrant coupled with the higher proba- bility, relative to the stock, of losing the entire in- Vestment, rendered the warrant inherently riskier than the Stock and justified the expectation of higher returns. ‘3ne point not mentioned earlier is that the leverage factor between the warrant and its associated stock multiplies not only the expected return, but also the Standard deviation of return of the former relative to the latter. Ever since Markowitz associated the variance of returns with risk, this measure has played a central role in security research as it does in determining the relative return relationship required here. This is not to say that it is an ideal indicator. Much to the contrary, it The two reas of the warre Fortunately measured . lllfiltéd dow the distrib skewed, i.e 3i(El-ificant "’19“ POSiti ‘IxeaSUred b: Set those risk of tin C °« return. rim-“ 1 21 contrary, it provides a measure of only one type of risk. The two reasons originally given for the greater riskiness of the warrant are not covered at all by this measure. Fortunately there is one factor which tends to offset this unmeasured additional riskiness. Because of the more limited downside risk resulting from the exercising price, the distribution of expected warrant returns is positively skewed, i.e., the third moment of the distribution is significantly positive. Investors have been found to View positive skewness with favor9 and since it is not measured by the variance of return either, it helps off- set those factors previously mentioned which increased the risk of the warrant, but were not measured by the variance of return. Ayres did not use the variance of return as his Ineasure of risk, but rather the standard deviation of annual stock price steps. This may seem odd to the reader at.first glance, but, in fact, if we assume a random walk, ‘the distribution of expected annual stock price steps 'translates directly into a distribution of expected Inaturns with the exception of a shift in the distribution 'Ikisulting from the dividend yield. The distribution of eJ‘Cpected annual warrant price steps translates directly lrrto a distribution of returns assuming a random walk for \ 91. N. Fisher and G. R. Hull, "Risk and Corporate Rates of Return," Quarterly Journal of Economics, LXXXIII, NS). 1 (February, 1969), 86. stock price, skewed as n deviation 0 assumed to leverage rat question of seers little Estimate of ex98(2th re efiect of u 22 stock price, except that the distribution is positively skewed as noted above. The relationship of the standard deviation of warrant price to that for stock price is assumed to be multiplicative with the factor being L, the leverage ratio as previously defined. Aside from the question of scale, which is eliminated by the ratio, there seems little cause to doubt that L is a reasonably good estimate of the ratio between the standard deviation of expected return for the related securities. Thus the effect of using standard deviation of annual price changes is not very different from using the standard deviation of expected return as a measure of risk. The purpose of Ayres' work was to determine in- vestor preferences for warrant holders. His work was an extension of that done by Farrarlo who studied investor 'preferences for other groups of investors. Using a Farrar Ohdective function, Ayres was able to determine a coef- ficient of risk aversion for warrant investors which fell .in a region along the efficient frontier of investment oPportunities at a place where one would expect to find it:. Despite certain shortcomings, Ayres deserves a gCNDd deal of credit for ingenuity in the argument he makes irl establishing the functional form of the relationship \ loDonald Eugene Farrar, The Investment Decision lg£5235;gncertainty, "The Ford Foundation Dissertation leries (Englewood Cliffs, N.J.: Prentice-Hall, Inc., (52) between the stock. The theneceSsi1 thewarrant apportllnity purposes of regards the eggposlte i AYI and two inf stated bY ; There 6 1, The in 2. Th se‘ 3. Ma: af. ri. The in 1. Th ce 2. Th in me A Wan ~~~es is i Al 1 based r 11 efe48\ 23 between the expected return on the warrant and that on stock. The beauty of his argument is that it eliminates the necessity of considering the complex covariance of the warrant with all other members of the investment opportunity set. The basic idea, which is assumed for purposes of the argument, isthat the warrant investor regards the warrant and its associated common stock as a composite investment Opportunity. Ayres' derivation proceeds from three assumptions and two inferences. The assumptions and inferences as Stated by Ayres are as follows. There are three assumptions: 1. The market price of a warrant is dominated by investors with a Farrar objective function. 22. The common stock is a member of the opportunity set of the warrant investor. 33. Market action of the warrant investors does not affect the position of the common stock in the risk-return, o-R plane. The inferences are: 1.. The warrant may be regarded as having 100 per cent positive correlation with its common stock. 13. The warrant investor regards the measure of risk in the stock as being 0, and he regards the measure of risk in the warrant as being Lo where L = d(an) 11 dZInSOS A brief discussion of the assumptions and infer- Shoes; is in order, not because the result will stand or fallbased upon the premises, but rather to clarify their \ ll 19 Ayres, "Risk Aversion in the Warrant Markets," P- 48-49. content. Li its predicti stands firm: The The first 1 group of lIl seeing the taking the rating grO‘ part of tin has a Farr tom of ti:- s'ltere U re 4. . be warm :v. ' o’er sion, 24 content. Like any other theory, its value depends upon its predictive power and, in this respect, Ayres' theory stands firmly. The first assumption really entails two assumptions. The first is that the warrant market is dominated by a group of investors each having the same preference function, seeing the same facts at the same time, and simultaneously making the same decisions. Ayres likens this market domi- nating group to Cootner's professional group.12 The second part of the first assumption, that this group of investors has a Farrar-type objective function, simply defines the form of the relationship as U = R-A02 (I-12) where U represents utility, R is expected return, 02 is the variance of return, and A is the coefficient of risk aversion, the value of which Ayres determined. Farrar deve10ped Equation (I—12) as an approxi— mation to an investor's utility function from the aSsumption that (1) An investor's utility of money function is ‘positively $10ped and concave downward, and (2) His investment strategy is the maximization 9f expected utility.13 \ 12Cootner, "Stock Prices: Random vs. Systematic Changes I u p. 27 . 13 pp. 19-20. Farrar, The Investment Decision Under Uncertainty, He concludes Equation (1- I :u-. do under :cted t‘nat ” equivalence sought and r sion increas lS , k“, “ w‘ne . MM “.K‘ 25 He concludes that a quadratic approximation such as Equation (I-lZ) is both the best and the worst that we can do under the preceding set of assumptions.14 He also noted that "all the properties so common to a certainty equivalence model are met; that is, expected return is sought and risk avoided, while one's degree of risk aver- sion increases with the amount of risk already being 15 borne." The second assumption is basic to the argument, hunt there is no evidence or precedent for it. The assnnmption merely states that the common stock associated Witfli the warrant in question is also a member of the QPEHDrtunity set of our composite investor and that under Cexrtain conditions he may choose to buy it in preference to the warrant. A rationale for the third assumption is that the PCHSjgtion of the common stock in the risk-return plane is thSE :result of an equilibrium in the stock market which is established by investors who have greater funds at their disposal than the warrant investors, but who, because of tfln€354r higher aversion to risk, do not enter the warrant market. The effect of the dominating groups' buying and Se:I-ling on the risk-return position of the common stock is thus negligible. \ 14 15Ibid., p. 25. Ibid., p. 20. The observation certainly i. he explaine< distorting ¢ has been d i i 26 The first inference, which is based upon empirical observation, is clearly only approximately true. There certainly is some variance of warrant price which cannot be explained by stock price, but it is very small and its distorting effects are negligible. The second inference has been discussed above. It should be noted that (I-l3) I ”45H; These are alternate forms of writing the elasticity of warrant price with respect to stock price. Having laid the groundwork, let us proceed with Ayres' covariance eliminating argument. Observe Figure 2, a Plot of hypothetical investor iso-utility curves in the risk-return plane. The common stock may be found at point P with risk 0 and return n+6. The warrant has risk LG by Ayres' Inference 2. The risk-return characteristics of colnbinations of these securities lie along a straight line connecting the two points by Inference 1. Assume iso- utility curve U2 passes through point P, the location of the common stock in the risk-return plane. Suppose initially that the expected return on the Warrant is r3. The dominating investor group would begin 1; . 0 buy warrants to adjust their combined portfolio of s toCk and warrants to point C which has higher utility f or them. According to Ayres this is impossible "because 27 2 U1 C y P l ' U I 3 l ' I a+6 Figure 2 Equilibrium in Indifference isere are r. :arket—domi *mderlying enected re attractive higher aver; ‘50 they, t Piaference 1 daninators 1 t‘eY must The warrant in Price ha. 28 there are not enough warrants available when all the market-dominators want to buy."16 While this is true, the underlying reason for the scarcity is concealed. When the expected return on the warrant is r3, it is also an attractive investment opportunity to investors with higher aversion to risk than the market—dominating group and they, too, wish to hold some of the warrants in preference to the common stock. In order for the market dominators to satisfy their desire to buy the warrant, they must bid up the price, hence forcing down the return. The warrant will then be sold by those investors with higher risk aversion. This will continue until increases in price have driven the return down to r2. If the expected warrant return were less than r2 initially, say r1, the market-dominating investors would Prefer the common stock to the warrant and they might even Sell the warrant short. Only investors whose risk aversion is less than that of the market-dominating group would now prefer the warrant to the stock. But, as Ayres points Cnltl, "there must be a scarcity of funds controlled by SuCh peOple compared to the peOple with risk aversion A. :[15 'that were not the case, they would have taken the war- rant out of the opportunity set of the peOple with risk a“’ersion A before now." The effect will be for expected .‘~_‘~‘__ l6Ayres, "Risk Aversion in the Warrant Markets," p. 50. l7Ibid. return to ri reaches r2- At 3 :eristiCS Cf mgent to i zarket domir‘ in the warra utility. Ir- disposal to warrants in nating group equilibrium reader will investments , strange at a willing to t are warrant 29 return to rise as warrant price falls until the return reaches r2. At r2 the line representing the risk-return charac— teristics of combinations of the stock and warrant, PB, is tangent to iso—utility curve U2 at point P. None of the market dominators will take either a long or short position in the warrant since to do so would be to lower their total utility. Instead, they will be applying the funds at their disposal to bringing about an equilibrium price for other warrants in the market. The fact that the market domi- nating group has no position in the warrants at the equlilibrium point may seem strange at first. If the reader will consider the fundamentalist approach to inVestments, he will realize that this behavior is not Strange at all. A fundamentalist would be just as un- willing to take a position in a correctly priced issue as the warrant market dominators are. Having established r2 as the equilibrium return, we may set 8 equal to r2. From the figure it is easy to See that the slope of the line PB must be -——-5 mm The total derivative of U is zero along any iso- u - . tlllty curve, so along U2 we know dU = dR-ZAodo = 0 (I-lS) Specifical. is Since p13 isl with the ri obtain Thi .. The MC \ Lima; ‘iOn (: 30 Specifically at point P, the point of tangency, the lepe is do _ l at: — “~on ”‘16) Since PB is tangent to U2, we may equate Expression (I-l4) ‘with the right side of Equation (I-l6) and, after reducing, obtain a = d+6+A(L-l)202 (1-17) This is the necessary relationship between a+5 and The amount by which 8 must exceed the total expected 8. 2 . which may be Ifrturn to stockholders depends upon L and o ITleaasured empirically, and A, the coefficient of risk aver— Sixon measured by Ayres. .§;;~_;The complete model If we now assume that the warrant and stock prices aJTEB in equilibrium at the time of observation, we may equate the price of the warrant with PV(E[Wt ]) from e Ekqllation (I-lO) and we have .8t 00 2 w = e ef (S-PC) f(S,SO,o ,te)dS (I—l8) O P e We now have two Equations, (I-l7) and (I-18) , in two un- knOVVIIS, 0L and B. All of the other variables are either 8 tated in the option contract, determined by the market cr measure; in obtaini: (1'17) and in Equatic: fraction 0: The value c are seachip 5065 not e in order tc The prSce’iure 5 There are a The first 5 flat t . e ml! altions. 1nitial so h. .ng ear 1y t 5 he Correc Amu- yrocedure 31 or measured empirically. Since we are primarily interested in obtaining the value of a from the solution of Equations (I-l7) and (I-l8), we may substitute Equation (I-l7) for B in Equation (I-l8) and obtain an expression which is a function of a alone. -(a+6+A(L-l)202)t m 2 ef (S—Pc)f(s,so,o ,te)dS (1-19) 0 P c (Dhe value of a for which Equation (I—l9) holds is what we aare seaching for. Unfortunately, an analytical solution dcxes not exist for a. We must turn to numerical methods ir1 order to find it. C. Solution Procedure The purpose of this section is to explain the Exr<>cedure adOpted to find a solution to Equation (I-l9). There are actually two steps to searching for this solution. TQIGE first step is to find a solution for a assuming that te 143 'the time to expiration. It was noted above, however, tllért te might be less than that period under certain con- ditions. We may determine from the sensitivity of the 'lrlistial solution to te whether warrant holders are plan- ning early exercising. If early exercising is planned, t o o o . 11GB <:orrected time to exerCiSing and a new solution value of 0‘ must be determined. The second step involves the prOCedure for accomplishing this. F0 Equation (l a fraction 1 for whic': Ithh we a: in visuali: “0 Versus : January 30‘ a; 3‘ “(1) am CV1. , “~Y he he 32 For convenience let us define the right side of Equation (I-l9) as W(a), keeping in mind that it is really a function of all the model parameters. Then the value of a for which W(a) = W0 is a*, the initial solution for which we are searching. In order to assist the reader in visualizing the solution, Figure 3, a plot of W(a) and versus a, has been included for Armour & Company as of W O .Ianuary 30, 1961. The solution lies at the intersection caf W(a) and W0. In order to find this solution numeri- <:ally we need a routine to evaluate W(a) and a routine hfliich will adjust a in a way such that this intersection “wry be found for a minimal number of computations of W(a). Evaluating W(d) may be accomplished either by in- Cllnding a table of the normal distribution function and interpolating between the values or integrating numerically. 111E: latter method was adopted although on the basis of hindsight the first probably would have been more efficient. One of Cotes' formulas for numerical integration was Sfiiliected.18 This formula provided acceptable accuracy fCNE‘ an interval of integration equal to one—tenth of lrlifitial stock price. The search procedure ad0pted is very similar to Newton's method for solving equations. This method was \ 18Bernard Dimsdale, "Interpolation, Curve Fitting, D - lfferentiation, and Integration," Handbook of Automation, and Control, ed. by Eugene M. Grabbe, Simon (2 Rim utation, Irimnc>, and Dean E. Wooldridge (New York: John Wiley & Sons, c, . 1958), I, pp, 14—11. 3O 25 Warrant Price (Dollars) 3O 25 20 33 . W(a) I I I 1 I I | j 0 10 20 3O 40 a* Expected Rate of Increase of Stock Price (Per Cent) Figure 3 Computed Warrant Price as a Function of a. chosen bec sate valueI to: is CC: required f1 next sectiC evaluated 6 above is CC Basie based sill”) deV abtaifled at from W0 by difference basis of t} the prOCeSf which is w is normall‘ Ha te is the that assum canpllting is covered COD slat Part1 would net 34 chosen because of its efficiency and because the approxi- mate value of the partial derivative of W(a) with respect to on is computed routinely. This partial derivative is required for the sensitivity analysis as explained in the next section. Briefly, the method requires that W(a) be evaluated at two points. The partial derivative noted above is computed and an estimate of the intersection is made based upon the value of this derivative and the value Of W(a) deviating least from W0. A value of W(a) is then Obtained at the approximated intersection. If it deviates from Wo by less than one cent is is accepted. If the difference is greater, a new approximation is made on the baSis of the two values of W(0L) which are closest to W0 and the process repeated until a value of W(0L) is obtained Which is within one cent of WO. An acceptable solution is normally obtained in three to five iterations. Having obtained one initial solution assuming that te is the time to expiration, we must now test to see if that assumption is justified. Since the mechanics of computing the partial derivative of a* with respect to te i . . . S c=<>vered in the next section, they Will not be repeated ere . ConSider the implication of a negative value for t hat partial derivative. A shorter expected holding period w ould net the warrant holder a higher expected return. 'I‘ hue . as long as 30L*/3te is zero or positive, the initial 3 Glution is accepted. Whenever it is negative, however, w . e 1"(lust go on to step two. Before explaining the precedure cf the way Pi cardition. :bta'ned f: Prices for in StOCk p} is legarit‘: 71335 stock 128 frOm 5 the SlOpe < aid paSSim 3311 the R Price at t‘ Starch pro such that {33*5 £ sagase t ‘C'Uln . I‘Q‘ 35 procedure adopted to handle this condition, an explanation of the way in which it arises is in order. Figure 4 is a graphic presentation of this condition. The curve labeled E[Wt ] represents values obtained from Expression (I-9), i.:., future expected prices for the warrant based upon an expected growth rate in stock price of a. Note that since the ordinate scale is logarithmic we may draw growth curves as straight lines. Thus stock price is assumed to grow over time along the line from S0 to C, the slope of which is a. Similarly, the slope of the discounting line extending from WO to B and passing through point D has a slope of B. The point D on the E[Wt ] curve represents the eXpected warrant price at the :ime of expiration. The purpose of the search procedure presented above was to find a value of a such that a line of slope 8 would intersect the ordinate at W0. We see from Figure 4 that the warrant holder could increase the SlOpe of his discount line, and hence his expected return by planning to sell earlier. In fact, he would maximize his expected return by discounting the exPeCted price of the warrant from time te . If the max time of expiration had been to the left of te , say at max F, this condition would not arise since the warrant holder does not have the rational choice of holding the warrant past expiration. In fact, the curve E[Wt ] drops dis- conti - - e - nuously to zero at the time of expiration, but this is not Shown here because the diagram is designed to show e and E[Wt ] on Warrant Price, 2 Stock Price, Logarithmic Scale U) 0 O l { 36 Slope a Slope B B C A // E[Wt ] / e ID I I I I I I I I l I I I I I l I I I I I - I ' L t time to t e . . e max expiration time to exercising Figure 4 Determination of EXpected Holding Period and Maximum Return 8 37 that as te becomes large the slope of this curve approaches a from above. Since we have already argued that Bid in the intuitive presentation above, the reader should see that the warrant must be exercised when an acceptable return can no longer be obtained by holding it. The procedure for maximizing a* with respect to time involves a second Optimization procedure whenever 8a*/3te is negative for te equal to the time of expiration. A simple binary search procedure was adopted for use in this case. Upper and lower bounds are established on te such that the partial derivative just mentioned is negative and positive respectively at these points. Half of the interval is eliminated as not containing the maximum at each step and the procedure is stopped when there is a period of approximately two weeks left between the bounds. This provides acceptable accuracy for our purposes. D. Sensitivity Analysis Even if the model set forth above were a perfect description of reality, the value of a* obtained as its SOIution would be in error. This error results from the measurement errors made in obtaining estimates of the ImOdel parameters. One of the reasons for performing a Sensitivity analysis is to determine an estimate of the are reproduced in Figure 5. The Experimental Results Application of the theory developed above was tested on a sample of 31 warrants. The theory applied very well to 24 of them and not at all to four. (See Appendix 1 of the reference.) Two warrants were re- moved from the sample because the market action at the time of interest was too turbulent to permit an esti- mation of leverage. One warrant was arbitrarily re- moved because it was a companion to one of the four warrants to which the theory does not apply. The results cited here are for the group of 24. It is often stated that there is a strong tendency in the world of investments for higher expected return to be accompanied by higher risk. This idea is ex- amined first to provide a setting for the test of the hypothesis. The first-order correlation coefficient Ibetween the expected return r and the measure of risk ILs, where s is the estimator of c and L is the lever— age, was found to be 0.61. Therefore, a regression (of r on Ls would result in a reduction in variance of ‘about 37 per cent over the hypothesis that r equals r ayerage in this sample. A scatter diagram of r vs Ls is shown in Figure 3. 45 Emnmmwn kuumom ommfl>wm nufl3 mEMHmMHQ Hmuumom Umnmflansm .mmH>< mo cemflummsoo zmm «m m AWWV To md . 1‘0 T 6.0 m mnsmflm 30h > £3539 .3525 Q 0.52“. t + E + .nN: I J7< 6.0 v.0 Nd u d‘ u 0 N6 #6 a6 3 :o t .0 523m 9 0501 ed v.0 Nd _ _ H q u — O I N6 1 Q6 1 6.6 1 0.0 46 It is interesting to note that this result is quite comparable to results found in the stock market. Yohn . . . found that the correlation coefficient between expected return and risk was 0.59 in a random sample of 45 stocks. The hypothesis of equation (8) proves far superior to the hypothesis that r is a linear function of L0. It was found that v(r) = .021 and V = 0.0030. A* was found to be 0.868. In short, the hypothesis of equation (8) together with the assumption that A is a constant for all war- rants results in a reduction of variance by a factor of seven. If the theory is completely false and the right and left halves of equation V-S are in fact uncorrelated, and if both halves are uniformly distributed between the observed rmax and rmin of the sample, the observed results have less than one chance in 2 x 107 of occur- ring. A visual presentation of these results is con- tained in Figure 4, where a scatter diagram of r vs. A*(L-l)282+m+d is displayed. 20 Figure 4 is to be compared with Figure 3. 1\ reduction in variance by a factor of seven is very im- Exressive. Such a reduction would indicate great eXplana- tKDry power for Ayres' theory. The decision to utilize AYres' model was based upon two factors, the reduction in VTiriance being primary and the fact that the estimated ‘VEilue of A fell where one might expect it based upon the ‘VCJrk of Farrar being secondary. Farrar found that the rYinge of A for growth stocks was 2.5 < A‘: 4.75, for stock 3fllnds 4.75 < A 5 13.5, and for balanced funds 13.5 < A i 24. 21 Thus a value of .868 for A places it at the high risk end of the spectrum as we might eXpect. \ 20Ayres, "Risk Aversion in the Warrant Markets," EDE>~ 50-51. 2x 21Ayres mistakenly reported that "Farrar found Q: ~— 5 correSponded to the least-risk-averting investment C3nmpany." (Ayres, "Risk Aversion in the Warrant Markets," ‘ w, 5;. .. I" . I ' 47 As the research reported herein progressed, it became clear that there was a tremendous amount of un- eXplainable error in the estimates of a obtained. One of the steps taken in searching for the source of that error was to review Ayres‘ analysis of his results using the data from his thesis. Ayres' equation (8), referred to in the quote above, was given as follows r = u+d+A(L—1)202 This is the same as Equation (I-l7) since r = B, u = a, and.d = 6. Ayres proposed to fit this model to his twenty- ftnar observations of r,:m, d, L, and 52 where m.is the eEstimator of u and 52 is the estimator of o and then com- ENare the sum of squares remaining with the variance of r. TIlat sum of squares, V, is defined by Ayres as 2 [ri-mi-di-A(Li-l)2512] (I—3l) l V=MINl~ n Htflb i C:learly, Ayres intends V to be the mean square error term :ECJr what he calls a "special case of multiple regression." fiei then compares V with v(r) and claims to have obtained a Sexlenfold reduction in variance. \ I;'- 52.) Farrar actually found that -U" > 5 for the least- :iidsk-averting investment company. (Farrar, p. 72.) Since == -U"/2, (Farrar, p. 21), the least-risk-averting growth :i11c3ck fund actually had a coefficient of risk aversion t:11£Ly slightly greater than 2.5. The limits given in the eBantt are correct. 'QEWW 48 There are a number of problems in this approach. First, V, as defined by Ayres, implies a regression of the following form. ri-mi-di = A(Li-1)25i2+ei (1-32) where ei is the error term. Viewed in this light, V be- comes an estimate of the variance of e and must be compared to the variance v(r-m—d) rather than v(r) for purposes of —l—-for V to be testing. Secondly, fi-must be replaced by n-l an unbiased estimator. Ayres raw data was obtained from his thesis and the aPpr0priate statistics were computed. Since the values pre- Sennted were rounded, some variation in the statistics is to b6! expected. For example, the value obtained for A was = .00853 and V = .00344. Thus 0«872. The variance v(r-m—d) Abfires hypothesis provided a reduction in variance of 59.6 pefir cent. This is a far cry from a sevenfold reduction. The reader should compare the Revised Scatter Dia- glfianxin Figure 5 with the Scatter of r on Ls. Clearly t'here is much less reduction of scatter than Ayres would h'a-Ve us believe. The reason for the tremendous reduction “111 'variance for Scatter Diagram, V Test is that m and r are highly correlated . All this is not to say that Ayres' work is without Inealritn Clearly, his model has predictive power, but it is IICDt: so great as his reader might believe from the presen- t'5‘1Zion. 49 2. Market prices The assumption has been made that the warrant and stock prices measured at a point in time are in equilibrium within the market and relative to one another.” It is im- possible to tell whether the securities are out of equilibrium with their markets, but it is possible to observe the relationship between them and make sure that any deviation from the established pattern reflects the infusion of new information by observing the price move- ment in the following weeks. Initially there was a question of whether to use \narrant low against stock low, high against high, or the xveekly close for each. The reason this was considered follows from the notion that warrant price is determined lalmost entirely by stock price and that the extremes might loe more likely to represent equilibrium points between the ssecurities than would weekly close. To check on this, Vvarrant price versus stock price was plotted for several (iifferent warrants on the basis of low versus low, high ‘Iersus high, and warrant close versus stock close. Except IECm a shift along the underlying relationship, there was 110 apparent difference in the plots. The scatter of the Emoints around the real relationship was comparable for the iihree plots in each case. As a result, closing prices were cIhosen since to consistently choose the high or low re- ldationship might bias the results in terms of equilibrium ‘“Nithin the market. The weekly close refers to the Friday 50 closing price. Whereas a Wednesday closing price might have been better because of the higher volumes generally traded on that day, it would have involved considerably more effort to collect Wednesday closing prices before 1962, and the possible benefit did not seem to justify the additional effort. Actual selection of the prices to be used was made as follows. The date on which annual reports were mailed was obtained for each year of the study from the companies in question. Twelve of the companies supplied this infor— mation upon request. Data for the rest of the companies in the final sample was obtained from the records of the New York Stock Exchange where the stocks were listed. A mini- mum period of three weeks was allowed for diffusion of information contained in the annual report. If the prices seemed stable at this time, they were used. If there was turbulence or a marked shift in level or relation between the securities, prices were taken for a later date when the disturbance had subsided. This paragraph may make more sense to the reader after reading the part of Chapter IV regarding the measurement of independent variables. §;5 Leverage The reader will recall that L, the leverage factor between the warrant and its associated common stock, was defined as d(an) L=—— d(lnSO) “I a. ) (I-33) ‘32-. 51 or equivalently as t" ll 04' Q: U32 (I-34) Elm It is fortunate that these two alternate forms exist since they provide two methods of measuring L. This tends to reduce the measurement error somewhat. Initial plans called for fitting a straight line to an versus lnS using the method of least squares, the lepe being a measure of L. Ayres noted in his thesis that he had estimated L by visually faring a line through a plot of W versus S and multiplying the lepe of that line by So/wo' They were "drawn by eye to minimize de- parture not departure squared. . . . Least squares would place too much emphasis on short term transients."22 A little experience showed that least squares estimation was undesirable, not only for the reason Ayres gave, but for a number of others as well. In addition to stray points, the relationship be— tween warrant price and stock price often changes just prior to the time at which we wish to measure L. This is not to say that this change, which usually takes the form of an increase or decrease in the premium, is undesirable. Indeed, changes are expected as a result of the information g 22Herbert Frazer Ayres, "Risk Aversion in the War- rant Markets" (unpublished Master's thesis, Massachusetts 'Institute of Technology, 1963), p. 103. ‘97 ',)_W 52 provided by the annual reports. This change does, however, present a problem if we are trying to fit a line to a plot of an versus lnS. As an example, Figure 6 shows the type of plot prepared by the CALCOMP plotter for each company for each observation. This particular plot is for Martin Marietta 31‘ from 4/9/65 to 4/8/66. There are clearly two groups of points here, group B which starts on 4/9/65 and runs wnvwwrv through ll/l9/65, and group A which runs from ll/26/65 through 4/8/66. Clearly, fitting a straight line by either least squares or visual methods to all of the points at once would give a poor estimate of L. This case was easy to spot since the shift occurred roughly halfway through the period being considered, the two groups of points were clearly separated, and a relationship was obvious for each group. When the change occurs very near to the end of the period or if there is a gradual shift in the relationship, these conditions may not hold and it is very difficult to determine whether a shift has occurred. The result is that L may be badly overstated (as it would be if a line were fitted to all of the points in Figure 6), or understated if the lower premium were associated with the higher stock prices. Only experience and intensive individual scrutiny 0f each of these plots can reduce the error in estimating L from this type of plot. It was noted earlier that L could be computed from E:Xpression (I—34) as well as from Expression (I—33). This 53 L slit..-) ... gr. GUHHQ MUOHHW Cd” mSmHm> mUflHm “CMHHMS SQ MO BOQQ @SOU‘HANU m mnsmflm amuHEO yuOHmC 24 x coma.m . meamm>rn ng-m -1 oh mn-n -1 gown ammo «ppm and: 2Hem4: .L NV £1“ch .J N"! id \ \ [JD] ' 54 is the method used by Ayres. Its use has helped to catch shifts in the relationships which would otherwise have been overlooked. Expression (I-34) has also been used to com- pute L whenever there was so much scatter in the data that it could not be estimated from the an versus lnS plots. The scatter can result from shifts in the relationship, a very narrow range of stock price during the period plotted, or very low warrant prices in which case a movement of one- ._ - ‘ _ “ A12"; V9,. . t”! ‘3‘. tin“ ‘n‘ Q r: eighth of a point is large on the scale used. Measuring the variables on the right side of Ex- pression (I-34) separately has distinct advantages over measuring L as a slope in most of the foregoing problem situations, especially for a shift in the premium. Values for S and W may be obtained directly from the market data as of the day on which L is to be estimated. The deriva— tive of warrant price with respect to stock price, 3%, may be obtained as a slope from a plot of warrant price versus stock price. The real advantage is this: When there is a shift in premium, W and 3 change, but dW/dS remains very nearly constant. Since W and S are easily and precisely measurable as of a specific point in time, a much more reliable measure of L may be obtained. Since dW/dS has both an upper and lower limit, whereas L has only a lower limit, Expression (I—34) is eSpecially useful for the higher ranges of stock price. ‘COnsidering the advantages of the latter method the reader Inay wonder why L was estimated from plots of an versus 55 lnS at all. The most important reason for this is that this relationship is more nearly linear than that between W and S for most of the range under consideration. As a result, dW/dS must be measured as a tangent when Expression (I-34) is used, introducing the possibility of additional error. When possible, both methods have been used to check for agreement. In cases of discrepancy, the value for the method believed to provide the more accurate value under the circumstances was accepted. 4. Variance Having selected the lognormal random walk as the model which most nearly reflects stockholder expectations regarding the distribution of future stock prices, it is necessary to obtain an estimate of the variance of loga— rithms of the ratios of weekly closing stock prices for the preceding year for each observation. It is assumed that the most recent market price activity, i.e., the immediately preceding year, would weigh most heavily in determining stockholders' expectations regarding this variable. This variance had to be computed on the basis of weekly closing prices since the interval between the prices used to compute the ratio had to be constant. Since the Variance used in the model was an annual figure, the vari- ance computed on a weekly basis must be multiplied by lEifty-two for use in the model. 56 One very serious problem was encountered in measur- ing this variance. What we wish to measure is this vari- ance over periods when the market is in equilibrium, and no disturbances in the form of new information are experi- enced. Such periods are rare and impossible to recognize. As a result we must settle for variances computed during periods in which new infusions of information cause the market to revalue the stock. The effect of this is to overstate the magnitude of this variance, sometimes seriously. No objective method could be found to elimi— nate the effect of this overstatement in the cases where it was serious or, for that matter, where it was not. 5. Dividend yield It was assumed that the dividends paid during the previous year divided by the current price of the stock provided the best estimate of expectations regarding that portion of the return received through dividends. Clearly, there were cases where dividend announcements for the cur— rent year had changed these expectations, but the change was generally of small magnitude. CHAPTER II THE EFFECT OF CAPITAL STRUCTURE L. ON THE COST OF EQUITY CAPITAL There is a long—standing tradition in the field of . business finance which still stands firmly in many quarters. At the base of this tradition is the notion that because the rate of interest on bonds is lower than the rate of return required by stockholders, the use of debt to finance a part of the firm's assets is "cheaper" than the use of equity capital alone. Thus for moderate amounts of debt the weighted average cost of capital, hereafter simply called cost of capital, would be reduced according to traditionalists. If the firm should take on debt in excess of some "conventional debt limit," the stockholders would require higher returns to compensate for the added risk of default. The rising cost of equity capital would eventu- ally make the cost of capital turn upward. The belief that the cost of capital first decreases, then, after hitting a minimum, begins to increase, led the tradition- alists to search for the Optimum capital structure. What amount of debt would minimize the firm's cost of capital? 57 58 In 1958 Professors Franco Modigliani and Merton H. Miller suggested that everyone should stOp asking that question and give up the search for the Optimal capital structure.1 According to them there is no optimal capital structure, at least in the sense of a minimum cost of capital, since the cost of capital is independent of capital structure. They based their conclusion regarding the independence of the cost of capital and capital struc- ture on a market equilibrium argument and the results of cross-sectional statistical analyses. Modigliani and Miller, hereafter M & M, concluded that the cost of equity capital would begin to increase immediately with the addition of debt. Furthermore, it would increase just enough to precisely offset the lower cost of debt so that the cost of capital would remain constant. "We conclude therefore that levered companies cannot command a premium over unlevered companies because investors have the opportunity of putting the equivalent leverage into their portfolio directly by borrowing on personal account."2 There were those who disagreed, claiming that personal debt could not produce "equivalent leverage" for any of a number of reasons. Criticism of the premises and the argument served only to uncover an 1Modigliani and Miller, "The Cost of Capital, ggiporation Finance, and the Theory of Investment," pp. -97 0 2Ibid., p. 270. 59 error in the treatment of the effect of the favored tax treatment of interest on debt for which a correction was published.3 Attacking the premises of a deductive argu- ment is futile, however, when the conclusion is supported by empirical evidence. This was recognized, and criticism of M & M's statistical results issued forth. Let us look first at their results, then review some of the criticism leveled against them, and finally look at the conflicting results obtained by others. The empirical evidence reported by M & M was aimed at supporting their first two propositions. Those propositions were stated by M & M as follows. Proposition I The average cost of capital to any firm is independent of its capital structure and is equal to the capitali- zation rate of a pure equity stream of its class. Proposition II The expected yield total return of a stock is equal to the appropriate capitalization rate for a pure equity stream in the class, plus a premium related to financial risk equal to the debt-to-equity ratio times the spread between pk and r.5 3Franco Modigliani and Merton H. Miller, "Corpor- ate Income Taxes and the Cost of Capital: A Correction," American Economic Review, LIII, No. 3 (June, 1963), 433-43- 4Modigliani and Miller, "The Cost of Capital, gorporation Finance, and the Theory of Investment," p. 68. 51bid., p. 271. Symbolically tively as and where r: 60 Propositions I and II may be stated respec- 3?. V1 = pk for any firm j, in class k (II-l) j '4. ll j pk + (pk-r)D%j (II-2) expected return on assets before interest (dollars) total market value of common stock (dollars) total market value of senior securities (dollars) total market value of all securities (dollars) rate of return expected on pure equity stream (dimensionless) rate of return expected on levered earnings stream (dimensionless) interest rate on debt (dimensionless) and the subscripts j and k stand for the firm and equiva- lent return class respectively. M & M assume that "firms can be divided into 'equivalent return' classes such that the return on the shares issued by any firm in any given class is proportional to (and hence, perfectly correlated 61 with) the return on the shares issued by any other firm in the same class."6 In order to test PrOposition I, the cost of capital, computed as total earnings after taxes divided by market value of all securities, was regressed on financial struc— ture. Financial structure was computed as Dj/V.. A nega- tive correlation between these variables would support the traditional position. A correlation not significantly different from zero would support the M & M position. In cross—sectional samples involving forty-three electric utilities and forty-two oil companies, both correlations were slightly positive, but not significantly different from zero, thus tending to support M & M. The test for PrOposition II, "yield on common stock," computed as stockholders' net income after taxes divided by total market value of common stock, was re— gressed on leverage, defined as Dj/Sj‘ A near zero corre- lation and slope for this regression would support the traditional position, whereas a positive correlation with a slope of the magnitude of (pi-r), where T signifies an after tax expectation, would tend to support M & M's theory. The regression was run for the samples mentioned above and it was found that the correlations were signifi- cantly positive and that the slopes were in fair accord with theory. The estimated regression equations were 61bid., p. 266. 62 6.6 + .Ol7h r .53 Electric utilities Z Oil companies Z = 8.9 + .OSlh r .53 M & M made an error in their derivation of the tax effect. In the published correction it was concluded that the effect of taxes would be to produce a U—shaped cost of capital curve. Proposition II on an after tax basis could be symbolically stated —T %; = oT+<1-r>[pT—r13/; (II-3) where the symbols are as defined above, except that the subscripts have been dropped, T is the marginal tax rate on corporate earnings, and FT is expected net profits after taxes.7 The effect of this error on the favorable inter- pretation of the regression results was minimal. The first regressions still accord more closely with M & M's theory than with the traditional view. The effect on the second set of regressions, since the slope should now be (l-T)[pT-r], was to bring the regression for electric utilities more nearly into accord, but at the expense of that for oil companies. M & M's empirical evidence was criticized mainly on the basis of their assumption that firms in the 7Modigliani and Miller, "Corporate Income Taxes and the Cost of Capital: A Correction," p. 439. 63 industries chosen were sufficiently similar to form an equivalent risk class. The second most serious criticism was that the use of current earnings might not closely approximate expected future earnings, especially in the case of oil companies. Other criticisms, with the ex- ception of the one regarding a bias introduced by the use of the same variables in the denominator of the ratios on .both axes, generally pertained to the sample. For example, We! 1‘" Barges notes that "the data have been criticized on the grounds that there are insufficient observations over certain ranges of capital structure to justify drawing inferences about the shape of the relations over the entire range."8 He goes on to note that "the problems encountered by M & M in their tests will in all probability appear in other similar studies, and to a certain extent they appear in the tests to be presented at a later point in this paper."9 For Barges, Weston,10 and others excepting this dissertation, the two most serious criticisms noted above remain unanswered. The use of the method presented 8Alexander Barges, The Effect of Capital Structure on the Cost of Capital, "The Ford Foundation DiSsertation Series?r (Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1963), pp. 21-22. 9Ibid., p. 22. . 10J. Fred Weston, "A Test of Cost of Capital Propo- 51tions," The Southern Economic Journal, XXX, No. 2 (OCtober, 1963), 105:12. 64 in Chapter I to measure stockholder expectations of return from objective market data answers the criticism that cur- rent earnings may not closely approximate expected future earnings. Furthermore, the ability to measure the cost of equity capital at a point in time allows us to study the effect of changes in the debt—to—equity ratio on it for a single firm over time, eliminating the need for the equiva- lent return class assumption. The use of time-series rather than cross—sectional data introduces the possibility of changes in the firm other than capital structure which would change the return required by stockholders, but this is the price that must be paid. The null hypothesis, stated in accordance with the M & M theory as amended by the effect of income tax, may be stated H1: The only reduction in the cost of capital resulting from leverage lS attributable to the deductability of interest as an expense for tax purposes. CHAPTER III THE EFFECT OF DIVIDEND POLICY ON THE COST OF EQUITY CAPITAL The reader is familiar by now with the notion that ‘ Mm-‘flFV r . the return to stockholders has two components, the dividend yield and the capital gains return resulting from price appreciation of the security. The total return to any shareholder is determined competitively in the market on the basis of risk and whatever other factors affect the investment decision. Thus, if the dividend is nil, the security will be priced such that the investor may expect it to appreciate at a rate equal to the total return. If, on the other hand, the dividend were equal to the total return, the investor should expect no price appreciation. In fact, the rate of price appreciation which a share- holder ought to expect is the difference between the total return and the dividend yield. The real question is whether the sum of these two return components, the total return, is constant or a function of the dividend rate. That is to say, is dividend policy one of those "other factors" which affect investment decisions and, hence, the 65 66 total return as determined by the market. Professor Gordon clearly concurred when he wrote The issue, therefore, is whether the behavior of in- vestors under uncertainty is correctly represented by a model in which the discount rate that equates a dividend expectation with its price is a function of the dividend rate. If all of the participants in the great debate on dividend policy had so clearly perceived the issue, it might have been more productive. As it was, most of the participants passed over, assumed away, or, in one case, dismissed as irrational, the real issue. The resulting conflicts be— tween theory and observation could in all cases be ex- plained by a dependence between dividend policy and the required return. The major problem again seems to have been the lack of an adequate method of separating expectations regarding return from those regarding future cashflow. In choosing to examine the effect of dividend policy on stock price, they picked a variable which is affected by changes in either type of expectation. Although stock price was selected for lack of a measurable alternative, the selection was natural. Graham and Dodd had maintained for years that a dollar of divi— dends should be valued more highly than a dollar of 1Myron J. Gordon, "Optimal Investment and Financ- ing Policy," Journal of Finance, XVIII, No. 2 (May, 1963), 267. \“W_mm—ER IF 67 retained earnings.2 They supported their view with examples of comparable companies, one of which had a higher payout policy and sold at a higher earnings multi- ple. In fact, statistical analyses generally showed high payout to be associated with higher earnings multiples for the stock. Since from the point of view of financial L management, dividend policy is understood to mean the L relationship of cash dividends to retained earnings, it a seemed natural that if Graham and Dodd's valuation formula i were correct, management could increase stock price by paying out a larger portion of earnings in the form of dividends and retaining less for reinvestment in the firm. There were those who found it difficult to accept this conclusion, especially considering the favored tax treat— ment of capital gains return relative to dividend income. Not only is the tax rate on capital gains only one-half the marginal rate on current income, which includes dividend income, but payment of the tax is postponed until the gain is realized. Enter now two battle—tested veterans, Miller and O O O 3 I Modigliani. The names are reversed in order, but no one 2Benjamin Graham and David L. Dodd, Securit Anal sis (lst ed.; New York: McGraw-Hill Book Company, , p. 327. 3Merton H. Miller and Franco Modigliani, "Dividend Policy, Growth, and the Valuation of Shares," Journal of Business, XXXIV, No. 4 (October, 1961), 411-33. 68 doubted their identity for a moment and their old nick— name, M & M, still fit. After assuming away the issue under the assumption of "rational behavior," M & M went on to show that stock price could not be affected by dividend policy, given investment policy. They note that while the market imperfection resulting from the favored tax treatment of capital gains would tend to make stock- holders prefer higher retention of earnings, War-u..- .‘ '15."?— . 1.0-. a I . . . the "standard View" is not that low-payment companies command a premium; but that, in general, they will sell at a discount! If such indeed were the case . . . there would be only one way to account for it; namely, as the result of systematic irration- ality on the part of the investing public.4 The reader might be tempted to believe that the last sentence was meant as a criticism of the investing public, especially since M & M go on to warn that investors may learn from their article and mend their ways. In fact, M & M were merely suggesting to the reader, perhaps un— consciously, where to look for the flaw in their argument. Systematic irrationality would violate M & M's rational behavior assumption. Rational behavior, according to M & M "means that investors always prefer more wealth to less and are in: different as to whether a given increment to their wealth takes the form of cash payments or an increase in the market value of their holding ." [Italics mine.]5 We 41bid., p. 432. SIbid., p. 412. see t at tt a t r\ «flu in G» W; Cr. why; ya u :1.» OH 5 u .1» 'il' . u 69 see that M & M have assumed away the real issue in arriving at their irrelevance theorem. Accepted doctrine identifies wealth with utility and risk with disutility for the stockholder. If instead of assuming that investors maximize wealth it were assumed that they maximized utility, M & M might have brought their theory into accord with the "standard View" by adopting the position that future cash receipts are inherently riskier than current cash receipts. Hence, the shift from current to future cashflows resulting from increased retention would necessitate a higher return for the investor to derive the same utility. Stock prices would fall and the stock would sell at a discount. This is, in fact, the road taken by Gordon. He made two assumptions: "(1) Investors have an aversion to risk or uncertainty, and (2) given the riskiness of a cor— poration, the uncertainty of a dividend it is expected to pay increases with the time in the future of the dividend." These assumptions lead to a theory which supports the notion that the discount rate increases with retention, or that a dollar of dividends is worth more than a dollar of retained earnings. Regarding his empirical results, Gordon reports that "although the results compare 6Gordon, "Optimal Investment and Financing Policy," p0 2690 6 70 favorably with earlier work, they are not good enough to settle the question."7 Irwin Friend and Marshall Puckett tried to provide some empirical evidence, but like M & M they failed to address themselves to the real issue. Their results, to the extent that they are improvements over earlier work, tend to supply additional evidence that there is, indeed, a preference for dividends over capital gains return. Friend and Puckett set forth three conditions, at least one of which is necessary to account for earlier statistical results. This lower valuation (on retained earnings) could exist if any one of the following situations is pre- sent: (1) the average holder of common stock possesses, at the margin of his portfolio, a very strong prefer- ence for current income over future income; . . . (2) the expected increase in earnings arising from in- creased per share investment is viewed as involving a much higher degree of risk than that attaching to earnings on existing corporate assets; (3) the profitability of incremental corporate investment, as viewed by shareholders, is extremely low relative to the competitive yield prevailing in the stock market.8 The first two conditions are dismissed because: . . . neither of these assumptions is consistent with observed behavior of the market. . . . we do not normally witness perceptible drops in the market price level when the aggregate supply of corporate stock is increased by new issues, requiring for their absorption the substitution of current for future income and potentially raising the risk premium demanded by 7Ibid., p. 269. 8Irwin Friend and Marshall Puckett, "Dividends and Stock Prices," American Economic Review, LIV, No. 5 (September, 1964), 658. In‘“ 173*" L 71 investors; nor do we typically witness sharp drops in per share price when the supply of an individual com— pany's shares is increased. They also question the third assumption noting that "marginal profit rates in a substantial number of 10 Their conclusion industries appear to be quite high." is that at least for some industries, i.e., growth in- dustries, none of these three conditions holds and earlier statistical results must, therefore, be in error. After QmaVWmvw~«1——— (considerable criticism of earlier statistical procedures, 'they carried out their own statistical tests which did :show that growth companies with low payout tend to sell at a premium. This result says virtually nothing about the real :issue. Since "the essence of 'growth' . . . is not ex- pansion, but the existence of opportunities to invest Significant quantities of funds at higher than 'normal' rates of return,"11 the result they obtain can be ex— plained as the consequence of investment policy which results in higher expectations of future cashflows. The real evidence in the study may be taken from those industries for which it was shown that dividends were still more highly valued. Friend and Puckett should have held that the third condition does not hold for any listed ¥ 9 10 Ibid., p. 659. Ibid. 11Miller and Modigliani, "Dividend Policy, Growth, and the Valuation of Shares," p. 417. 72 firm. If the stockholder is willing to hold a stock, he must be satisfied with its return based on the current market price. Since the firm that issued that stock al— ways has the option of reacquiring it at the prevailing price, the reinvestment rate should never fall below the "competitive yield prevailing in the stock market." Thus we must reconsider whether both of the first tnno conditions can be dismissed. As for the reasoning on xvhich they were dismissed by Friend and Puckett, it must loe said that it is flimsy at best. Why should we expect Exerceptible drops in the market price level to result from ianerceptible additions to the aggregate supply of cor— Exorate stock? In the case of a large issue by a single firnn the substitution effect would spread the addition so tflninly over the entire market that no price drop should be exPected. There is one very simple reason for dismissing the first condition. Any stockholder who is dissatisfied With his current income from dividends is perfectly free to sell a portion of his portfolio to augment it. Thus we are left with the second condition which, if we accept Gordon's hypothesis that the uncertainty of a dividend increases with its remoteness in time, might be imagined to hold. The real question is whether the required return is a function of the dividend rate. Statistical analyses and those who believe in them claim that it is an increas- ing function of retention. Investor surveys and the HEEW l II E . Emmi 17 when th 11 that t mi new: IVE 73 favored tax treatment of capital gains have convinced others that investors must really prefer capital gains :50 that the required return must be a decreasing function (of retention. Since there is such clearly contradictory opinion suirrounding the topic, the null hypothesis is stated as H2: The expected return is independent of dividend policy. Vke will attempt to reject H2 and, if successful, additional lrypotheses will be formulated. ‘ mfg“?! an 4 JV ‘— CHAPTER IV TESTING THE HYPOTHESES The purpose of this chapter is to specify the Errocedure to be followed in testing the hypotheses set fkorth in Chapters II and III. These hypotheses regard tile effect on required return of capital structure and (iividend policy respectively. They are restated here ftbr the reader's convenience. H1: The only reduction in the cost of capital resulting from leverage is attributable to the deductibility of interest as an expense for tax purposes. H2: The expected return is independent of dividend policy. Tfliere are three major steps to be taken in testing these I‘IIYpotheses. First, the hypotheses must be restated in t6estable form. This entails the construction of a sta- 'tistical model in which the rate of return expected by Stockholders is functionally related to variables which are indicative of the two areas of financial policy under Consideration. Secondly, these independent variables must be measured. And finally, a series of regression 74 “F - 1441310113 sections 75 :models must be fit to this data and accept or reject «decisions made regarding the hypotheses. The three sections of this chapter correspond to these three areas. A. Restatement of Hypotheses in Testable Form Since H1 is stated in terms of M & M's theory as aunended for the favored tax treatment of interest, we may lise the modified symbolic statement of their Proposition III expressed in Equation (II-3). Let us define ke as the cxost of equity capital. Then, we may write ke = pT+[pT-r](l-T)D/S (Iv—1) “fliere the symbols have the same meaning assigned in CHIapter II, but for the reader's convenience, pT = after tax rate of return expected on pure equity stream r = interest rate on corporate debt I = marginal corporate income tax rate debt-to-equity ratio based on market values D/S Each of these variables and ke is dimensionless. Adding a term to reflect H2 is really quite simple Since we are merely searching for an effect at this point. Thus, including a term for dividend policy effect, we may rewrite Equation (IV-l) dk _ T T_ _ __g. _ ke — p +[p r](l T)D/S+db b (IV 2) ‘fi h 76 where b is the earnings retention rate and dke/db is the derivative of the cost of equity capital with respect to ‘the retention rate. Since the data to which the final regression enquation will be fit are time—series extending over periods xyhen there was considerable change in the interest rate, aan.allowance must be made to nullify this factor. Let us eassume, as is often done, that pT has two components, the irisk-free interest rate plus a risk premium 0, i.e., pT = i+¢ (IV—3) Shibstitution (IV-3) into (IV-2), we obtain dk ke—i = +[—(r-i)] (l—T)D/S + T59 b (IV-4) For reasons to be noted in the next section, book 111ther than market values of debt were used to compute I3/S. Because of the upward trend of interest rates over tile period studied, this would effectively overstate D/S Vfliich would understate the slope of the regression. If Vfle assume that r = i, it will help offset the effect of this bias on the estimate to be obtained for the second 4 in Equation (IV—4) and simplify the testing considerably. If this assumption is made, Equation (IV-4) may be written dk - — _ __£ - ke-l — ¢+¢(l T)D/S +- db 1) (IV 5) 77 Using a+6 obtained from the warrant—stock relationship as an estimate of ke' the full regression equation may be written d+6—i = al+a2(l-T)D/S+a3b+e (IV-6) xvhere e is the error term. To reject Hl we must show that al # a2. Rejection c>f H2 requires that we show that a3 # 0. Actual testing [procedures must await the third section. ' B. Measuring the Sample Variables It has been mentioned above that the model stated iJa Equation (IV—6) would be fitted to each of the com- ;xanies in the corporate sample using time-series data for teach company. Unfortunately, statistics necessary to com— ENJte ratio, D/S, and the earnings retention ratio, b, are Gully available once a year in the annual report to stock— rHolders. Since we are trying to assess the impact of these Ifiactors on the cost of equity capital, we are limited in lflle frequency of observation of the sample variables. |The chabt-to-equity ratio and earnings retention rate were com- ‘Puted from information provided in the annual report. As eXplained in Chapter I, after an interval of time to allow for dissemination of the information in the report, decision-making on the basis of that information, and market adjustment, warrant price and stock price were observed and an estimate of the required return was 78 computed. In all cases, the value of the risk-free interest rate, 1, was assumed to be the rate prevailing for long-term government bonds at the time warrant and stock prices were observed. The marginal corporate income ‘tax was also that which prevailed at the time of that observation. It was noted above that the book value of senior ssecurities was used in computing the debt-to—equity ratio xvhereas the market value of equity was used. The market \Lalue of debt was not used since for most of the firms in tflne sample only a small part of the debt was subject to Inarket evaluation. The majority was in the form of nuortgages or notes for which there was no way of system- ertically computing the market value. Since in most cases tflae market value of debt would have been below book value, tJIiS introduces a bias. The assumption that the interest Irate on debt equals the risk-free rate helps offset this llias however. The market value of equity was computed by Huiltiplying the number of shares outstanding as of the end <3f the reporting period times the stock price at the time Of observation. The retention rate was computed as that fraction Of total earnings for the preceding year which was retained for reinvestment in the business. No attempt was made to Obtain an average figure. It was assumed that the most recent evidence would weigh most heavily in the eyes of the investor. i g 79 C. Statistical Testing In order that the reader may more easily understand 'the statistical tests to be applied, they are developed in terms of the "fitting-the—models" argument.l For our pur- pxoses, this argument states that the resulting reduction in 'the sum of squares observed in passing from a model in xvhich the hypothesis is constrained to hold to one in which tfliis constraint is relaxed, provides us with a decision xlariable for accepting or rejecting the hypothesis. The series of models presented below will be fitted suc- cxessively and F statistics computed from the resulting rteduction in the sum of squares. The models to be fitted Eire x. = a l+Z . +e. IV-7 J l< 1]) J ( ) xj = al+a2le+ej (IV—8) xj = al+a2le+a3Z2j+ej (IV—9) where x. = d+6—i J le = (l-T)D/S sz = b 1D. A. S. Fraser, Statistics: An Introduction (New York: John Wiley & Sons, Inc., 1958), pp. 255-66- ‘Ifi' 80 In the first model the slope and intercept of x versus Z are constrained to be equal and dividend policy is assumed to have no effect. In the second model the «constraint on the slope and intercept is relaxed, but ciividend policy is still excluded. Finally, the effect 1 (of dividend policy is allowed to enter in the third model. For each company an analysis of variance table :such as that presented below will be prepared. ANALYSIS OF VARIANCE TABLE Sum of Source Squares DF Reduction in SS resulting from Fitting Equation (IV-7) ZMflditional reduction resulting from Fitting Equation (IV-8) Zkiditional reduction resulting from Fitting Equation (IV—9) Error Total ml©® @ 9 “Hie second and third models may be fitted using a canned S'tatistical routine and the last three entires in the sum of squares column obtained directly from the output. Un- fortunately, the first model cannot be fit using the Standard procedures of the canned routines. In order to Obtain the first entry in the sum of squares column, and hence, the second since it is computed as the difference between the first entry and the total "eXplained" by 81 Equation (IV-8), it will be necessary to make a few simple computations. Standard regression procedure calls for fitting a mean to the data and then proceeding to fit terms of higher degree. In the case of the first model, both the slope and intercept are fitted initially. What we are searching for is the ray emanating from the point -1 on the Z axis for ‘which the sum of squared deviations from the data is xEW" "I? Ininimized. For the sake of completeness and because the (derivation is short, the formulas for obtaining the first eantry in the sum of squares column are derived below. Define Yj = (1+Zij) so that the model we wish to fit is X. = a Y.+e. (IV—10) J J Yj]2 (IV-ll) It) ndnimize Q, set the first derivative with respect to al 'to zero. 2 .- . - . - [XJ ale][ Y3] (IV 12) 0.. 10 II II MU n = 2 Z [a Yj -X.Y.] = 0 (IV-l3) 82 Solving for the value of al, which minimizes O, we get XX.Y. a1 = (IV-l4) BY. 3 Substituting this value of al into Equation (IV-ll) and reducing, we get the minimized sum of squared derivatives P as 2 (ZXo-Yo)2 ...] Q = 2x. — J 23 (IV-15) .; 3 XY. y 3 Tune first term is the total sum of squares and the second 1J5 the reduction in the sum of squares resulting from iiitting Equation (IV—7). Resubstituting for Yj' we get 2 [2X3 (1 zljfl (IV—16) Z(l+le) aes the first entry in the sum of squares column of the analysis of variance table. Returning to the question of testing the hypotheses, F satatistics are computed from the ratios of mean squares and! tested for significance. The hypothesis must be tested in Ineverse order since if the dividend hypothesis is ac- Cepted the error term must be pooled with the third entry in the sum of squares column. Turning there to the test of H2, the test sta- tistic may be computed as 2 7:3— (IV-17’ Rejection of H2 at the .05 level of significance requires that F1 ’ Fl,n-2,.05' The test for the capital structure hypothesis, H1, depends upon whether H2 is accepted or rejected. Assuming acceptance, the error would be pooled and the test sta— tistic computed as F :=CD,/C9-+QD n-2 l (IV—18) Itejection of H1, assuming acceptance of H at the .05 2 lxevel of significance requires that F -F l 1,1'1-2, .05. If, on the other hand, H2 was rejected, the second and third entries in the sum of squares column must be snammed and the F statistic computed as __CD-+CD GD Fl — 2 n_3 (IV 19) FHEjection of H1, assuming rejection of H2, then requires at; the .05 level of significance that F - F 1 2,n-3,.05’ “'§.7.;..rln“ : "I Err—’7 7F CHAPTER V RESULTS OF THE STUDY This chapter is divided into two sections. The <3riteria used to select the corporate sample are explained ‘E-rmtama - c .p k 111 the first section. In the second section the results (If the study for each of the selected companies are pre- sented . A. Selection of the Sample Originally there were four criteria which any ccnnpany had to satisfy in order to be eligible for con- s ideration . They were: 1. The corporation must have issued stock pur- chase warrants. 2. These warrants must be actively traded on the American Stock Exchange. 3. These warrants must have a limited exercis- ing period. 4. The above criteria must be satisfied for a minimum of five years. 84 85 The requirement that a corporation have stock pur- chase warrants outstanding limits the study to several hundred firms. When the requirement that these warrants be traded on the American Stock Exchange is added, the number falls to sixty-odd corporations.~ The second re- quirement is necessary because of the importance of marketability considerations to the equilibrium assumption. Since until recently the New York Stock Exchange refused to aallow warrant trading, those warrants listed on the Ameri- <1an.Stock Exchange account for a large fraction of the dc>llar value of all warrants traded. The final two criteria were included for technical rtaasons. The first of these, i.e., that the warrants have a. limited life, is used to obtain an initial solution. Tume last criterion is to assure an adequate number of cfloservations of the independent variables in the sta- tistical tests. The eighteen companies listed in Table l satisfied all. of these criteria. As the study proceeded it became Cleaur that several of these were unsuitable, however. Hiltxon Hotels gave up control of its international divi- siorl in.exchange for TWA stock. This precipitated a PrOblem in terms of the option since the Hilton warrant holder was entitled to a fractional share of TWA upon exercising. For this reason Hilton warrants were dropped frOHl't11e study. Realty Equities Corporation of New York 86 TABLE l.--Corporations satisfying original criteria. Corporations Number of Corporations Dismissed Possible From Sample Observations ACF-Brill Motors 8 Armour & Co. 10 GAC Corp. 12 Hilton Hotels Corp. X Jefferson Lake Petrochemicals 7 Mack Trucks, Inc. 9 Martin Marietta Corp. 6 McCrory Corp. 9 Molybdenum Corp. of America 5 National General Corp. 6 Pacific Petroleums Ltd. 8 Realty Equities Corp. of N.Y. X Sperry Rand Corp. 8 Textron, Inc. 10 Trans World Airlines 9 Uris Buildings Corp. 7 Van Norman 6 Ward Baking Co. 8 ‘p-fi-r'F—‘u-—-r—_ 87 was dropped because adequate financial information and annual statement issue dates could not be obtained. The company did not reply to requests for this information. Finally, the new Universal American warrant was drOpped from consideration because at the time Van Norman (the issuer of the "old" Universal American warrant) was merged into Universal American, a combination of common stock and the "new" warrant became the package to be obtained upon exercising. Such combinations, as in the case of Hilton, invalidate the model. As a result, only the old Universal American warrant was used. Since this was really the Van Norman warrant, it will be referred to as such in the dis- cussion of the results. Thus we are left with sixteen companies. B. Results The rest of this chapter is devoted to the results of the method described above as applied to the sixteen companies finally selected for study. If each observation had yielded an acceptable solution, an analysis of variance table would be included for each company. As it turned out, statistical testing proved impossible for all com— panies except GAC Corporation and McCrory Corporation. In each of the other cases too few acceptable observations were obtained to allow the regression equation to be fitted. chap ‘QZT"“ 88 The reader probably is wondering what constitutes_ an acceptable solution and why so many of the observations yielded unacceptable values for required return. In order to understand the problem it will be necessary to return to the method used to obtain the estimates of required return. The reader should refer to Figure 4 throughout the following explanation. Recall that it was determined that warrant holders might purchase the warrant without planning to hold it to expiration. In fact, he would plan to hold it only over the period which would maximize his expected return. In Figure 4 that period would be the time up to temax. Note that this period is determined by the tangency between the line emanating from W0 and the function E[W ]. There is nothing to prevent t te max from being less than one year from the observation date. The problem is that for short holding periods, the solution value of required return becomes extremely sensitive to the holding period. Thus it was decided to drop all obser- vations for which the expected holding period, as deter— mined by the model, was less than one year. The result of this decision was that a majority of the observations were drOpped. The question remains as to whether warrant holder's expected holding periods are generally short or the model is providing misleading results. One factor which could cause the model to give abnormally short expected holding periods is that relating to stock price 89 variance. It has been noted that this statistic is systematically overstated but that there is no way of removing the bias. The format for presenting the results will be as follows. A brief description of the company, its warrant, and the price behavior of the warrant and its associated common stock is followed with a table of rele- vant statistics required for the study. When there is more than one "acceptable" observation for a company, a plot of required return versus the debt equity ratio is included. In the case of GAC and McCrory, analysis of Variance tables and tests of hypotheses are presented. Before presenting the results, one final point Should be made. The American Stock Exchange prefers to haVe each warrant traded exercisable for one common share to avoid confusion. The reader will note that many war- rants are exercisable for a number of common shares. In these cases, the quoted price must be multiplied by this fac tor to determine the actual price of one warrant. W1'15— le this is practicable for warrants exercisable for an integral number of common shares, the effects of stock splits and stock dividends often alter the terms signifi- cantly and the trading is no longer on the basis pre— fe“Tired by the American Stock Exchange. Determining the terms following a split is really quite simple. For a S"30(3): dividend of, say 10 per cent, there are now 1.10 new shares outstanding for each old share. Thus the “Q o L. _ arm). 9O warrant, if it is protected against dilution, will now be exercisable into 1.10 new shares at a price per share equal to the old price per share divided by 1.10. 1. ACF—Brill Motors The merger of ACF with Brill Motors on August 1, 1944 , provided for the issuance of 280,138 warrants to purchase a like number of shares at $12.50 per share until January 1, 1950, and at $15.00 thereafter until January 1, 1955 - The company, principally engaged in the production Of motorized transit equipment and engines for buses, trucks, marine, industrial, and other purposes, was con- trOlled by AVCO Manufacturing Corporation until June 11, 1951. On that date AVCO sold its holdings in the company iI'7lC‘:IL1:1ding 48.6 per cent of the common stock and more than half of the outstanding warrants. The reader should note from Figure 7 that stock priCe did exceed exercising price during the life of the WanTili‘ants. In the early years, stock price was consider— ab 11’ above the exercising price, but by the end of 1947 it had fallen below and never again rose above exercising price. Only 140 warrants were ever exercised. From Table 2 the reader can see that all but one of tlie eight observations were eliminated because the Warrant investor's horizon was determined to be less than one Year. The error limits are wide for the one acceptable 0 bservation. Only leverage and the coefficient of risk .a‘fiT \‘ u- .u‘ 1-x..- b5 mmlmlv ou mvlhla Eoum mHODOZ HHHHmImufi moanm xooum momHm> woeum ucouumz n wusmflm mmm ha¢044 .Hmma mso one» mmoa :oNauos Houmw>cH4 92 o.H mam.a ~m\am\ma 4 mmmoo. ma.~ mm HH mm\p\4 o.a osa.H Hm\Hm\~H 4 ammoo. ap.a mp 6H ~m\a\a o.H mos.a om\Hm\mH 4 mamoo. am.H 64 as Hm\~\4 o.H omm.~ ma\am\~a 4 ommoo. aa.a Hm NH om\m\a o.H Hmm.m ma\am\ma 4 smaoo. aa.a pm as ma\a\v o.H soo.a ss\am\ma 4 memos. mH.H am pm ms\m\4 o.H pmm.o ma\am\~a . 4 ommoo. mH.H m as sa\a\v o.H mm~.o m4\am\mfl ma~.+ amo. ammoo. 44.H ems om ma\fl\a 38 HQ SH 13V 33 AS 1 d8 dM 00 ea 98 up. 114d 33 21. e 11. In. 0.9 11 10. GT. de 4b 10 A to TI 83 1.3 1.3. an. 1.01 nn 1.0 a 30 01 as on O/ ....u 1.10 11. 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N~.~ bas mm sm\mm\m o~.o oo.s mm\sm\~s omo.» sos. mmooo. os.~ mms oo om\o~\m o~.o oh.o om\sm\ms ooo.+ hos. omooo. ~m.m oms oo mm\o~\m as as so new as so 4 so no mo 1s+ s+a. 8.L m Isa «3b 110 A 7.0 4:: ss+ 1.8 1.1. 89 1.01 nn 1.0 8 00 01 88 on O/ ....u 310 11. ex. 1 8x. 88 1 .... 3 0 s x U1 u E u A0 1. .0 G8 ... 1. 8 0d 5 1. PI. 0 n 8 ... m D. 81 8 .... u I. 1 e t. I. .... 8 1. 0 O 4A 8 8 .u moanmaum> unoccmmwocH manusum> useccmomo can mumumEMHmm .GOflHMHOQHOU 040ll .v wsm 5, we have grounds for rejecting H1, the 1 F1,5,.0 Cap-i tal structure hypothesis. Acceptance of H2 should not be surprising. It Could easily occur because the error involved is too great to C1etect any dividend effect. The rejection of H1 is more Significant, however. The fact that a2 in Model (IV‘B) is negative makes one question the results rather seve rely. It would seem to indicate that some other file th has not been controlled in the observations. 104 Actually, when one considers the growth and changes in the asset structure of GAC over the period considered, it is quite likely that the lower estimates of required return in the later years were caused by other factors. 4. Jefferson Lake Petrochemicals of Canada Limited The Jefferson Lake warrant was attached to their secured sinking fund debenture 6 1/2 5 due 1981. {The warrants attached to that issue, dated May 1, 1961, vvere exercisable after September 1, 1961. Each warrant (entitled the holder to purchase fifty common shares at the fkallowing price per share until June 1 of the years shown: JJBGS, $7.00; 1966, $8.00; 1967, $9.00; 1968, $10.00; 1969, $141.00; 1970, $12.00; 1971, $13.00. A 4 per cent stock djnvidend in 1966 changed the terms. The company, controlled by Occidental Petroleum Ccncporation, produces sulphur from purchased natural gas. It..also produces commercial pipeline gas, liquefiable Petzrcdeum.gases, and natural gasoline. While the product line: has remained virtually unchanged over time, the 9r0Vrth.in sales has been significant. Total assets nearily'doubled during the period of study. In 1968 the warrant was delisted from the American Stocl<-1Exchange so only seven observations were possible. Of tdfirose, all but one were unacceptable because of the From sh . . . Olrtl investor horizon as can be seen in Table 5. F' ' lgure 13 it is obvious that the stock was selling at very ' r . I d.“ l ,...~..»4'JJ .cusumu omnflsku “0m mGOHusHom manmummoom Hem magmaflm>m Maco«* .Hmmh moo swap mmma :oNHuon Houmm>cH« 105 mm.o oa.o sm\am\ma . momoo. mm.a mos ovm mm\m\m vs.o qH.o mm\am\ma . maaoo. m~.H «mm owm sm\m\m mm.o H~.o mm\Hm\~H . momoo. mm.H vsm oma om\m\m mm.o vH.o ¢o\am\ma . msmoo. sm.a sea HHH mm\s\m ms.o w~.o mm\am\ma - . smmoo. H¢.H mm mm vm\a\m oo.a H¢.o ~m\am\ma Hmm.+ mom. mmmoo. H5.H om mu mm\m\m oo.H sm.o Hm\am\ma . moaoo. NQ.H hm mm mwxvxm 33 HQ SH 13V HE AS ni dS dM OG 28 98 "we Tld as 91. e 11. In. 0.9 11 4Q 3T mid 1b 10 A To T1 31 1.8 .....1. an. 1.01 mm To a 00 01 as on. O/ ....u 1.10 IT. EH. I 83. an. I .... 3 o S x u: u e u A0 I. ..D 09 x. T. 3 0d 5 1. El. 0 n 9 x. m P 81 a 1. u I. 3 e I. I. 1. a 1. 3 O ..A a a u moanmwum> ucmpcmmmUcH magmaum> pampcmmmo can mumumfimnmm .6uq .mwmcmo mo mamoflsmsoouumm mxmq cemumummuuu.m mamma 1116 . law L1»... m1 . n rail. pi v3.14“. 4‘ fl mmlmlm Op Nolmlm Eoum .oupmm mxmq c0mumwmmb woflum xooum mamum> mofium ucmuumz ma musmflm pmm moflnm ucmunmz 4H musmflm .m:¢tixsem ‘.J..J.vl “1.! A; 4,, .2 - 49.4 ,1. .9 CD (Lg imu (L mu.” 11m (7 (L LP r P p b p P r L LI F p F1 .1. fig m . _ _ v . . 0 m 0 0 4 0 Afifiygifi 0 so fl —|’ I... . . .. ... L. t... ‘4 a9 T‘fi 1 . 5 <0 my” .. V g ’ ¢1o ...... Q 0 T. 6“. I 9 ¢ 1 of O ‘1 ‘ «V o ‘ fit?“ o v V a. «+3 49 M: f .7 N o 9+ $ 4 r fied ...Wotr+ 1.0-- . h 9+? .¢¢ 1 o «4.. +1 ” .0) H o 1. Ia. ion”; .4 ‘r‘ . . A M3 0. ‘0, «.th 0V4. r. TT'fiMv on” 0 Q . .. b m T.. I T. 0 ‘V . .. .+7 r _v C o o, .r « ... . ... . SH m _ . m z. m i. NVbUY/m I 7.71 ha i 1 'J deV "I”iCUJ 109 .cndpmn pmnfldwmu How mGOHMDHOm manmummoom How magmaflm>m >HQO44 .Hmm> moo cusp meH GONfiHOS HO¥m®>GH¥ 0.4 mm.o mm\am\ma 4 mmaoo. ms.a vmv «mm mm\-\4 vm.o- mm.o 46\Hm\ma 4 mamoo. ~4.H ~04 «ma mm\ma\4 sm.o mm.o mm\flm\~4 . 4 Hoaoo. mo.~ 044 mom vm\a\m mm.o mm.o ~m\am\ma >4~.+ msm. mmaoo. oo.~ vmv mmm mm\ma\4 44.4- Hm.o Hm\Hm\~H 4 mmaoo. 4~.H oaq omm ~m\ma\q mm.o mm.o om\Hm\~H . 4 smaoo. mv.H mow vom Hw\sfl\¢ mm.o mv.o mm\am\~a mam.” smm. mmfloo. sm.a one mvm om\ma\¢ as.o om.o mm\am\ma mom.+ omm. mmooo. mm.a mos mmm mm\om\v mm.o mo.a hm\Hm\~H 4 msaoo. H~.H mew mm mm\a~\w 00 E. 3 3. new 3 44 a ”A... .3 2 44+ law e.L m4id in” 410 A 4L0 1;; s.+ Ila t;+ .ce 740.1 nun TAU e o.s no: .ae on O/ ....u 1.10 It. 2.x. 1 8H. 89 I 3 3 a s x u.i u e u Auo T: b 03 x. T: 9 3d 5 1. ET: 0 n 2 ¥ m P 9.4 a 1 u 4. 4 w. m. m. h. e a a u mmHQMHHm> ucmpcmmmch magmaum> ucmpcmmmo tam mnmqumuwm .UGH 4mxosha xom2|l.m mqmdfi 110 GD 6 a 30%« H 3 .LJ (1) a: ,0 ca 3 -H 20%4 5 U‘ (D m 10%- 4 J». J. T I I 0.4 0.8 1.2 Debt/Equity Ratio (Market) Figure 15 Required Return versus Debt/Equity Ratio for Mack Trucks, Inc. F _n KL__ . lll warrant. Stock price declined precipitously just before expiration of the warrant to the point where the warrant became valueless. Of the nine observations, three yielded acceptable solutions. These are plotted versus debt equity ratio in Figure 15. The slope of the line drawn Uirough the points is positive as we would expect, but the: overall level of expected returns seems entirely too high. The error limits are quite broad. Three of the F; painameters contributed to this error, leverage, stock perse variance, and the coefficient of risk aversion. The: last factor was responsible for the major fraction of that error . E; Martin Marietta The Martin Marietta warrant was originally attxached to a debt issue of the Martin Company before its Inerger in 1961 with American Marietta Company. Each MarWLin Company sinking fund debenture 5 1/2 5 due 1968 was :issued with ten warrants. Each warrant entitled the h01d£xr to purchase one common share at $40.00 per share to I\TO'vember l, 1963 and $45.00 thereafter until November 1' 13968. Since the merger was made on the basis of 2.73 Martin Marietta shares for each Martin Company share, the terms of the warrant changed accordingly. This acchInts for the steep slope of the warrant price versus 3 . . . . . tock price relationship in Figure 16. ~m¢<44001 clud‘ . Hy . L mmnmtv ou Hmtmloa Eoum .QHOU muuoflumz sauna: moflum Roonm mamnm> mowum ucmuumz 112 SH musmflm muamc yumem cm 01 am Om OH » P p p r r p p _ 94 4f. 4:4. Max I. on o. . w. 44 4“ .41 L}... +4 g 4.1,. ...... ...: ‘14 M U 1Q ‘,~ C . f. .?d i.- 4d. ‘ . 9.49 .5 o f . 4 5-..- __ (Z? 1.71):ch J NV'QHVT“. 7D I Vii.“ "CJ .-\ ‘ 113 .cusuwu Umuflsvmu 40m macauSHOm magnummuom How mHQMH0m>m >4c044 .400» 0:0 can» mmma neuwuos Houmw>cH4 00.0 04.0 00\40\04 - 4 00000. 00.4 040 000 00\0\0 00.0 04.0 00\40\04 004.+ 000.0 00000. 00.4 000 000 00\0\0 40.0 44.0 00\40\04 4 00000. 40.4 040 000 00\0\0 00.0 04.0 00\40\04 - 4 04400. 00.4 004 004 00\04\0 40.0 04.0 00\40\04 000.+ 000.0 00000. 40.4 040 000 00\0\0 00.0 04.0 40\40\04 4 00400. 00.4 000 040 00\0\0 00 00 00 000 00 00 0 40 00 00 14+ 00a. a_L m4id 03b 440 A 0.0 741 3.4 1.8 1.1. an. 1.01 mm 1.0 a 30 31 as on O/ ....u 1.10 11. EN. 1 ex. 89 I 1. 3 o S X u: u e u A0 1. .b 08 ... 1. a 0d 6 1. PI. 0 n p. x. m P 81 a 1. u I. 1 e I. I. 1. a .... O O 4A e a u moanmwum> usmoammmch manmflum> pampcmmmo tam mumumEmumm E .00004402 04040:--.0 44000 Required Return 114 4 O % '1 TT G) 30%0 G) 20%4 1 10%“ V I I 0.1 0.2 Debt/Equity Ratio (Market) Figure 17 Required Return versus Debt/Equity Ratio for Martin Marietta 115 The merger combined a technology oriented firm engaged in design development and production of guided missiles, military aircraft, and electronic systems with a cyclical construction materials firm. The observations included in Table 7 are for the merged company only. Two of the observations yielded acceptable solutions. These are plotted in Figure 17. While the level of these is high, the error is also very large so little confidence should be placed in them. The coef- ficient of risk aversion accounts for a large fraction of this error. 7. McCrory Corporation McCrory has had two warrants outstanding, but only the "old" warrant, issued in an exchange with the share- holders of Lerner Stores, qualifies for study. That war- rant, issued on June 21, 1961, had a fixed exercising Prbce of $20.00 until expiration on March 15, 1976. Lerner was not the only acquisition, however. SinCEE 1959 McCrory has expanded almost continually through acquiSitions including McLellan, Green, Otasco-Economy Auto £3tores, S. Klein Department Stores, and Best & Com— pany. McCrory, itself controlled by Rapid American Cor- poratxion, also has controlling interest in Glen Alden Corptxtation. To say that the McCrory asset structure has Chan€¥ed over the life of the warrant is an understatement. 116 outmim 0» Hmtamth 804m 46400 .muoo >404002 mOHHm xooum msmnm> moaum ucmuumz m4 94:04.4 4mQ mco can» mmma sesame: Houmm>cH4 .cusumu Umuflsku 40m mcofluSHOm manmummoom How mannafim>m >H:O«4 00.0 00.4 00\40\4 004. m 00.0 40400. 00.4 004 00 00\44\0 00.0 00.0 00\40\4 000. 4 00.0 00400. 00.4 000 444 00\00\0 00.0 00.0 00\40\4 000. H 00.0 00400. 00.4 400 404 00\40\0 00.0 00.0 00\40\4 400. H 04.0 00000. 00.4 004 00 00\04\0 00.0 00.0 00\40\4 004.04 00.0 04400. 00.0 004 00 00\00\0 00.0 40.0 00\40\4 004. + 04.0 00400. 40.4 004 00 00\00\0 04.0- 00.0 00\40\4 4 00000. 40.0 444 00 00\04\0 00.0- 00.0 00\40\04 4 04000. 04.0 004 00 00\0\0 00.0- 00.0 40\40\04 4 00400. 00.4 400 00 00\00\0 00 00 00 0.0.0 00 00 0 00 00 0.0 43 3Q at mid 3b 10 A to I: 304 1.8 1.1. 88 1.01 nn 1.0 8 00 81 88 on o/ 1.u 1.10 11. ex. 1 8X. 88 I 1. 3 o S x u: u 8 u A0 1. b 08 ... 1. 8 0d 5 1. 81.. O n e ... m P 81 8 1. u I 3 9 I. T 1. 8 1. O O 4A 8 8 u moanmflum> ucmpcmmmch man00um> ucmpcmmmo can mumumEmumm / .GOflumuomuoo 0404002 I m mqmdfi Required Return 118 400 0* A L- 3020 G) GED 2090 CD 61? J4 10% ‘ I T fl 1.0 2.0 3. 0 Debt/Equity Ratio (Market) Figure 19 Required Return versus Debt/Equity Ratio for McCrory Corp. 119 From Figure 18 it is clear that stock price has been above exercising price during much of the Option period. The shifts in the relationship are due to a number of factors including significant changes in the dividend yield. Table 8 shows that six of the nine origi- nal observations were acceptable. The 1966 observation was discarded for testing purposes because of the ex- tremely broad error limits. Error in the McCrory obser- vations was due to three of the parameters, the coef- ficient of risk aversion generally accounting for more than half and the remainder being divided between lever- age and stock price variance. The five acceptable observations were used to test the hypotheses. The analysis of variance table resulting from successively fitting models IV—7, IV—8, and IV-9 is as follows. Sum of Degrees of Source Squares Freedom Reduction in SS resulting from Fitting Equation (Iv-7) .16189682 1 Additional reduction resulting from Fitting Equation (IV-8) .00007426 1 Additional reduction resulting from Fitting Equation (IV-9) .00510964 1 Error .00124065 2 Total .16832137 5 I I." ‘ \v. H - 120 Let us test the dividend hypothesis first. F2 = 8.237037 Fl,2,.05 = 18.513 Since F2 < F1,2,. H2 at the .05 level of significance so we must accept the 05, we do not have grounds for rejecting dividend hypothesis. Having accepted H2, we may pool the error and test H1. Fl = .035081862 Fl,3,.05 = 10.128 Again we do not have ground for rejecting the hypothesis so we must also accept H1, the capital struc- ture hypothesis. The reader must keep in mind that acceptance of a hypothesis does not imply that it is true, but simply that there is inadequate evidence to disprove it. 8. Molybdenum Corporation of America Molybdenum Corporation of America is engaged in mining, refining, and distribution of molybdenum, tungs— ten, boron—rare earths, and columbium. The company gave stockholders of record September 27, 1957 the right to subscribe to a package of one common share and one six- year warrant at $21.25 a unit for each share held. The warrant entitled the holder to purchase one common share at $30.00 until October 18, 1963. From Figure 20 it is 121 0004054 mo Escmpnwaoz mOHHm xooum msmum> moflum ucmuumz 00 04:04.0 4mmm m4c044 .400» 0:0 cmsu mmma 2000403 Houmm>cH4 0.4 00.0 40\40\04 4 00000. 00.4 000 000 00\00\0 0.4 40.0 00\40\04 4 00000. 00.4 000 400 40\00\0 . 0.4 00.0 00\40\04 4 00000. 00.4 400 000 00\00\0 00.4- 00.0 00\40\04 4 00000. 04.4 000 000 00\0\0 04.0- 40.0 00\40\04 4 00000. 04.0 000 00 00\00\0 00. 0.0 .000. 0.0.0. 0.0. mm 0. .00.. mm mm 14+ 00c. 40T. m4id 300 010 A 4.0 IL; 544 1.8 1.1. 88 1.01 nn 1.0 8 00 01 88 on O/ 1.u 1.10 11. W04. 1 8X. 88 1 4.0 3 0 S X HI 8 u A0 I. .b 0.0 4 I. a o d .b 4+ 2.0 o n 8 t m P 40: 8 1 u I. 1 e I. I. .4 8 1. 0 O ..A 8 8 ..u mmanmflum> ucmcdmdmch manmwum> usmocmmmo 8cm mnmumfimumm .moaumfi¢ mo coaumuomuoo Edcmpn>HOZIl.m mamda 123 clear that stock price exceeded exercising price for a good portion of the life of the warrant. In fact, stock prices were quite high relative to the exercising price and investor horizons were short. The result is that none of the original observations yielded acceptable solutions. 9. National General Corporation Until 1967, National General Corporation was a holding company whose subsidiaries were primarily in- volved in movie theatres and the production of motion pictures although among the subsidiaries were a manu- facturer of modular buildings and a savings and loan association. To say that the company has expanded through acquisition since then is an extreme understate- ment. Total assets increased from $31 million to $178 million from 1967 to 1968 alone. For the purpose of this study we are only inter- ested in the National General warrant attached to the subordinated debenture 5 5 due 1984. The warrants entitle the holder to purchase one common share for $15.00 prior to May 15, 1974. From Figure 21 it is obvious that stock price greatly exceeded the exercising price during the life of the warrant. Only two of the six observations yielded accept- able solutions. These have not been plotted against debt equity ratio since one was obtained before the great 124 onlmum oa 0010:44 804m .muoo Hmnmcmw Hmcoflumz moflum xooum m9m40> moanm ucmunmz 40 049040 10001100. 00000 00000 . . Oh on on 03 0m 0m 00 o r 4 0 h p 0 0 4 0 0 4 0 . 0 .mxer . a» .44 . “V a 0 Jon . +. . 41fl0.\11 1 OH § d fi .444 if?“ $.«.. 1 f.44 - .0 10¢ .4 0 3.0 4 Crl 0... M. .9 O c. «4 f 4. 9 4 1.00 .4“ . ... D. 4. ‘. .l .4 4, 4. 1 OT. 3315c; iNV‘cj‘dV’fl : ‘- LIV—173(1) r\ I L 125 .ummm mco ems» mmmH cenauos Houmm>cH4 .cnsumu vmuwswmu How mcoHuSHOm mHQmummoom Mom m4an4m>m >4c044 mo.on 4o.m mw\m~\m . 4 mmmoo. mm.4 444 mm o~\m4\m mm.o o4.~ mm\4~\m mo4.m+ 444. om4oo. 44.4 444 omm mox4m\4 4m.o 04.0 44\4~\m . 4 mnmoo. 44.4 444 444 mm\m\m 4m.o 4m.4 mo\4~\m mm4.+ 444. 44moo. ~4.4 044 44 44\m4\4 cm.o 44.0 m4\mm\m 4 44400. 44.4 044 m4 mo\44\4 mm.o 4m.o 4m\m~\m 4 444cc. 44.4 o44 N4 mo\m4\4 mm. mm 44.44 mg .44. mm .4 mm mm mm 14+ 440. a.L m44d «In 440 A 4.0 1.1 3.4 453 T44 4c? 7:0.4 man 453 8 «go 0.4 4u9 Gnu O,/ 14H 1440 14} p.X 44 84% 442 I 1 4a a s X u.4 u e u A40 I. .D 044 ¥ T. e 3 d 40 1 P.& o n 9 ¥ m P 944 a 3 u I. 4 E I. I. 3 a 3 3 O K a e u mmHQMHHm> ucmncmmmvcH manmwnm> ucmvcmmwa 6cm muwumEmumm .GOHfiMHOQHOU HMHmGGU HMCOHUMZII.OH Wflm¢9 126 expansion in assets and one after, and are thus not com— parable. The 1969 required return is very high but the error range is also very large. Measurement errors in leverage and the coefficient of risk aversion each account for roughly half of that error. 10. Pacific Petroleums Pacific Petroleums is engaged in producing, pro— cessing, and selling crude petroleum, natural gas, and related products. The company is also involved in exploration and development work. Phillips Petroleum effectively controls Pacific Petroleums. The Pacific Petroleum warrant was attached to the debenture 5 1/2 5 due 1973. Each warrant entitled the holder to purchase twenty common shares at $19.00 per share from November 1, 1958 through March 31, 1968. Although no stock dividend or split was given, the terms of the warrant were changed so that after September 27, 1963 each warrant holder could obtain twenty-two shares at $19.00 per 1.1 shares. During the life of the warrant, stock price rarely exceeded the exercising price as can be seen in Figure 22. None of the observations yielded an accept- able solution. :r :5 4 holmmlv Ou mmlmalma Eonm .wuq .masm4oupwm 0444omm ooflum xooum momum> moaum ucmuumz mm musmHm 4mm<4409 gamma .1qu Q. on Om OT. am Ca 0 4 _ 4 p 4 4 r 4 — w — b L fig 127 I D N '93} Ho lNV €1an \av1”3ql ~F ‘1 L .cusumu omnflswmn How mcoHuSHOm magnummoom How magmaflm>m hHCO44 .Hmmm moo swap mmma aoNflHon Houmm>cH4 128 0.4 4m.o mm\4m\~4 4 O4moo. 4m.4 N44 mm 44\m4\m o.4 mm.o 4o\4m\m4 4 mo4oo. mm.4 4O4 mo m4\44\4 o.4 om.o m4\4m\m4 4 mm4oo. mm.4 o44 4m 4m\44\4 o.4 44.0 ~m\4m\~4 4 mm4oo. mo.4 om4 44 mm\m4\4 0.4 44.0 4o\4m\~4 4 m44oo. 04.4 444 mm ~o\o~\4 o.4 m~.o 4o\m~\~ 4 mm4oo. mm.4 o~4 4m 4m\mm\4 0.4 4m.o om\m~\~ 4 momoo. 44.4 mm mm o4\om\m 0.4 44.o mm\mm\m 4 44400. «4.4 444 44 mm\4\4 88 HQ 88 THV 38 AS T as am 00 98 Be v.9 ....Id 88 E4... 8 1.... In. 0.9 14+ 14% 94L m44d 134 440 A 7:0 7:1 4.1 ....e ....1. 8“ 1.01 nn 1.0 a so 01 as on O/ 4... 1.10 1.... EX. 1 ex. 844. I 4... 3 o S x u: ..u e u A0 I. b 08 ... I. a 3d 6 4... PI. 0 n e 4 m P 844 e 1 u 1. 4+ 9 I. 1. 4+ 8 1. o O 4A 8 a u moanmfinm> ucmocmmmocH mHQMHHm> vamocmmma can mnmumsmnmm .ouq 4mEdmaonuwm UHMHommII.HH mqmfla 129 11. 4§per§y Rand The Sperry Rand warrant was attached to the sink— ing fund debenture 5 1/2 s due 1982, dated September 1, 1957. Each warrant entitled its holder to purchase twenty shares of common stock at $25.00 per share to September 16, 1963 and thereafter at $28.00 per share until September 15, 1967. Stock dividends in 1961 and 1962 altered these terms. The reader should note from Figure 23 that stock price never got significantly above exercising price dur- ing the life of the warrant. In this case it is diffi- cult to understand why acceptable solutions were not ob- tained for some of the observations. 12. Textron The Textron warrants were originally attached to their subordinated debenture 5 5 dated May 1, 1959. The exercising price was $25.00 until May 1, 1964 but then it increased by five dollars on May 1 of every fifth year thereafter until May 1, 1984 when it expires. The reader may be somewhat confused by the odd Patterns in Figure 24. There is a very simple explanation. On December 17, 1965 and again on August 11, 1967, the OOmmany split its stock two for one. The effect of each Split.on the terms of the warrant was to double the number of shares which may be purchased and halve the exercising Price per share. Since the American Stock Exchange 130 molvmlo ou mmlvmlm Eoum ocmm muummm woflum xooum msmum> moflum gamuumz mm 0.44.44.44.44 mwmm >42044 .Hmm» mco swan mama acnwuos Houmm>cH4 131 00.4 04.0 00\4m\m 4 00400. 44.4 044 404 00\44\0 00.4 00.0 00\4m\0 4 44400. 44.4 444 40 00\04\0 00.4 00.0 40\4m\m 4 04400. 04.4 044 00 40\04\0 00.4 40.0 m0\4m\m 4 40400. 44.4 404 00 m0\44\0 00.4 04.0 40\4m\m 4 44400. 04.4 444 00 40\04\0 04.0 44.0 40\4m\m 4 00400. 04.4 044 004 40\04\0 04.0 44.0 00\4m\m 4 44400. 40.4 044 404 00\m4\0 44.0 44.0 00\4m\m 4 00400. 04.4 004 044 00\44\0 “qua G E. .44... 04 4.4.4.4 .44 40 .4. .444 .04 mm 144 44a. e.L m44d any 140 A T40 4&1 34+ ....3 ....1. 89 .....01 mm 1.3 e 33 31 88 CW OW 1w $4.1m. NH. W44 m 8.44. 40% M o t. b . o n W40 n m m. an“ % 4 W44 U "”4... “la... n. m. T. 4 a 4 0 meQM4Hm> unmocmmmocH manmwnm> unwocmmmo ocm mnmumemumm .0cmm muummmuu.44 wands 132 9 . . -U'I.VV 4 4 b H‘- owlmlm Ou omlmmlma Eoum .ocH4couuxmB mOHHm xooum msmum> GUAHQ ucmuumz 44 045040 494248 ...UH E 605.. Q. On. 8 0: 4M ON DA — F P b! r h b b P h b P b o '0' 99 v 09 0% f 4.. .4 ' ' 94¢ on O Q ”’ Q 9 o v 900 o v 4 o 9' 99 9 v 9’9 0 4: 00 Q C O . ' 99 9? v'v 9 v 9 .~.. .44 00 9 do & ‘ a fl. 0 v0 9 Q ' ’0 C O V 0 0’9 9 C 90" 4’ K. 0 2 Q Q 9‘ ‘ O h 9 V 40 I .04 3 1 331 Ho .LNV LUV!“ {W'lml an... 5.1.... .....l‘n ... . W.ii!a:.hflllll§ .cuoumu omnflsvmu How mcofluSHOm mHQmumwoom 40m mHQmHHm>m >4c044 ..Hmmxn 0G0 GMQU mmmH GONHHOS HoummwaHi 133 00.0 44.0 04\0\4 440.0m 00. 40400. 04.4 444 004 04\0\4 04.0 04.0 00\04\44 000.4 00. 40400. 04.4 400 404 00\4\4 04.0 00.0 40\0m\44 4 40400. 04.4 004 400 00\44\4 04.0 40.0 00\40\44 4 44400. 04.4 400 040 40\4\4 00.0 04.0 00\4\4 4 40400. 40.4 404 000 00\4\4 40.0 04.0 00\4\4 4 40000. 00.4 400 440 00\4\4 00.0 04.0 00\04\44 4 44400. 40.4 004 044 40\0\4 00.0 04.0 40\04\44 4 40400. 40.4 040 404 00\0\4 00.0 00.0 40\00\44 4 40400. 00.4 004 044 40\0\4 40.0 40.0 00\00\44 4 00400. 04.4 004 404 40\04\4 38 HO SH 13V 38 AS 1 d8 dM 00 Pa 98 We 1.140 98 9.... a 1.... IE 0.9 ......4. ....O. 8T. mid ......D 10 A To ....1 8.... 7:8 7...... an. 1.01 mm 1.0 e 30 01 38 Cu O/ ....u ....10 14... EX. 1 8H. 39 1 1. 3 o S X H... u p. u A0 T. .D 040 ¥ T. a O.d 5 1 2.9 o n e 4 m o. e 1 a 3 u I. 1 e I. I. 4... e .... D O ..A a a u mmHQmHHm> usmocmmmoCH mannaum> usmoawmmo pom mumumfimumm .couuxmaln.m4 mamfia 134 requires warrant prices to be on the basis of one for one (except for small stock dividend effects and in the case of the Martin Marietta warrant) the $10pes remain equal but the intercept shifts with the exercising price. In one case in Figure 24 the trading terms of the warrant were not changed at the time of the split, so there was also a change in slope until the trading terms were changed. Since the stock sold at fairly high multiples of the exercising price during nearly the entire period under consideration, it should not surprise the reader that warrant investor's horizons were quite short. In fact, only two of the ten observations yielded acceptable solutions and the error limits on those were so great as to be absurd. 13. Trans World Airlines The TWA warrant was attached to the subordinate income debenture 6 1/2 5 due June 1, 1978 and dated June 8, 1961. The warrants allowed for the purchase of a common share at $20.00 from November 1, 1961 to June 1, 1965 and at $22.00 thereafter until December 1, 1973. It goes without saying that TWA common sold well above the exercising period during the life of the option. The reader may confirm this by referring to Figure 25. The fact that the warrants were not all exercised should not surprise the reader once he notes from Table 14 that 135 8a owlmlm ow Holmlaa Eonm mwcflauflfl UHAOB mCMHB moflum xooum msmum> moflum ucmuumz mm mudmflm a; HUME gm 9 8 On on R O: QM ON OH O p b F > 0 b n > h b b r n r p r by r o 5‘ . o. O 9‘\ .. .2 .oo ‘0’. o 4 o O O .09.? on v 9 .... . .. ...... 00. 0'99 9 ..0. .ON O O 90*. f o 9 9 O. 0.99.9... .13 ‘4” .4» I .Q a.» 24.. 0R 00b"?! “.09 o 0"” 9 9 $.. 0 0 o ‘0 l3 . .. o.. .07 ...... .4 r .... o .Qu .u r o ‘ . .. r. .I I .. h .. _ . w 7t. 8 :MTTID 1315:! MW .cusumu ponflsvmu HON mcofluSHOm magnummoom How mHQmH0m>m >.c04« .Hmmm mco swap mmma £00000: Houmm>cH4 136 00.0 00.0 00\.0\0. 4 00000. 00.. 00. 00. 00\0\0 00.0 00.. 00\.0\0. 4 00000. 00.. 000 000 00\0\0 00.0 00.. 00\.0\0. . 4 00.00. .0.. 0.0 000 00\0\0 00.0 00.0 00\.0\0. 00.. 00. 00000. 00.. 000 000 00\0\0 00.. 00.0 00\.0\0. 00.. .0.- 00000. 00.. 000 000 00\0\0 00.. 00.0 00\.0\0. 00.. 0.. 00000. 00.. 000 000 00\0\0 00.. 00.. 00\.0\0. 00.4 0..: 00000. 00.. 000 000 00\0.\0 00.. .0.0 00\.0\0. 4 .0000. 0... 00. .0 00\0\0 00.. .0.0 .0\.0\0. 4 00.00. 00.. 0.. .0 00\0\0 ..1 d O 0 0. 0. .0 .0 0 0. m0. 0 0. m m a m .... 0 m m. .. 3.1. .40. 9.... mid 3b 10 A To 7...... 8.... 1:3 7...... an. 1.0.... nn To a DD 07. ea 0 u 0 / .... u .... .... O 1 .... E N. ... e v... a e 1 .... 3 3 S X H ... u 9 u A o I. .b 0.0 4 r. e 3.0 .b 3 2.0 O n E ... m D. a .... a .... u I. 1 e I. I. .... a .... D O ..A .0 a u mmHQMHHm> quUGmeUCH GHQMHHM> Ufimficmmmfl UGM muwflwfimumm .mmcflanwm vauoz mammall.v. mqmda Required Return 137 40%1 A 30%< 20%. T 10%- 0%0 C) -lO%— *20% I r 0.4 0.8 1.2 Debt/Equity Ratio (Market) Figure 26 Required Return versus Debt/Equity Ratio for Trans World Airlines 138 there was full retention of earnings in the early years. Thus capital gains made up the entire return for stock- holders as well as warrant holders. There were four acceptable solutions, but two of these were negative, probably as a result of measurement error. The error bounds were quite broad and resulted primarily from errors in measuring leverage. Only about 40 per cent of the error could be attributed to the coef- ficient of risk aversion. l4. Uris Buildings Corporation Uris Buildings Corporation is engaged in building and operating commercial structures, primarily office buildings, in New York and other major eastern cities. Their warrants were attached to their sinking fund debenture 6 1/2 5 dated May 26, 1960. The warrants were detachable after August 16, 1960 and exercisable at $12.50 per share on or before May 1, 1975. Stock dividends of 3 per cent in 1961 and 1962 and a two for one split in 1969 have changed the terms considerably. The high plot in Figure 27 results from a failure to adjust the trading terms of the warrant after the split. All but one of the observations yielded acceptable solutions but the error limits were extremely large so the statistical tests were not performed. Again, the error could be accounted for by errors in the measurement of leverage, stock price variance and the coefficient of 139 J- a. \L ‘bmlw: ...(r M. mi. 4”“: “hi. All II. IL ohlmal. Op mmIOMIm Eoum .muoo mmCHUHMDm mans moaum xooum msmum> moaum vacuum: 00 0.00.. 0.2.80. 0030.690 Om. » 0.3 F a.“ 03 R Ow OH O F b h { p P L v? 0 V .00 .n... . Q. in. . . 0m 4... o i i Q r ..w v 4.: fi 9 fl 1 B o .09 Q9. +9 N9 r 0 our. 9 v Q: t u 4.4 . 0. .... . . .cnsumu 60005000 How mcoHuSHOm magnummoom How mHQMH0m>m >Hco40 .Hmmm mco cmnu mmma GONHHOS Houmm>cH4 140 .0.0 00.. 00\00\0 00.0w 00. 0.000. 00.. 00. 000 00\00\. 00.0 00.. 00\00\0 0.. H 00.-. .0000. 00.. 000 000 00\.0\. .0.0 00.. 00\00\0 .0.0. 00. 00000. 00.. 000 000 00\0\0 00.0- 00.0 00\00\0 00. + 00. 00000. 0..0 00. 00 00\00\. 00.0: 00.. 00\00\0 . 4 00.00. 00.0 00. 00 00\0\0 00.0 0..0 00\00\0 .0.0. 00. 00000. .0.0 00. .0 00\00\. 00.0 00.. 00\00\0 0..0+ 00. 00.00. 00.. 00. 00 00\0.\. HH HG SH 13V. 88 AS 0.. d8 dM 00 Be 98 We ....Jd ea 21. 8 1.1. 1.9 0.... ...... no. .0... 0.1... ...b ..o A to ...... s... ....a ....1. 32 ....O... nn ....0 8 DD 31 88 on O/ 1.0 1....0 1.... 9...). I ex. 89 ... 1. H o s x u... u E 0 A0 .... b 0.0 ... T. 9 ad 5 .... 9.... O n E ... m D. a... a .... u .... .... P .... .... .... a .... o O .A e e u mmHQmwum> unmocmmmch mHQMHHm> unmocmmmo cam mumumEmHmm .GOHumnomuou mmaflnawsm mHHDII.mH mqmda Required Return 141 4 O %“L (L 30%1 20%- 10%- 0%d -lO% Debt/Equity Ratio (Market) Figure 28 Required Return versus Debt/Equity Ratio for Uris Building Corp. ...—s. 142 risk aversion. The relative importance of each of these measurement errors varied from one observation to the next. This was unusual in that in most cases the error could be traced primarily to one parameter for all obser- vations. 15. Van Norman Industries, Incorporated Van Norman Industries was primarily a manufacturer of tools, especially universal milling machines for general production work and die, pattern and tool work. Through subsidiaries they also produced a full line of precision and carbide-tipped cutting tools. The Van Norman warrant was issued in connection with their corporate acquisition activities in 1955. The warrant entitled the holder to purchase one common share on or before March 31, 1965. Before expiration, Van Norman was itself acquired by Universal American Corpor- ation. Thus the period of study was limited to issue through 1961. From Figure 29 it is clear that the warrant generally sold below exercising price. It was extremely difficult to estimate values of leverage for Van Norman because of the limited price range and price disturbances Which affected the stock. Of the six observations only two yielded acceptable solutions and the error limits on these are surprisingly narrow. Two points are slight 143 3‘...th i _. .mlqmlv 0» mmlmmlm Eoum mmwuumSUGH cmEuoz cm> moaum MOOpm msmum> @0000 “cmuumz 00 0000.0 0004.00. 00.00 y0000 : . 00 00 cm 0. 00 00 _ :. 0 . .0. 40am: .mnw.ammw U Om. 3318a lNVBHVfl l§BVWWOUJ 144 .cnsuwu pmuflsvmu .Hmmm mco cmnu mmm. coNHHoc Houmm>cH« MOM mc00uSHOm wanmumwoom you mHQmHflm>m >HGO40 0.. 00.0 00\.0\0. 4 00.00. 00.. 00. 00 .0\00\0 0.. 00.0 00\.0\0. 4 00.00. 00.. .0. 00 00\00\0 0.. .0.0 00\.0\0. 4 00000. .0.. 00. 00 00\00\0 00.0 00.. 00\.0\0. . 4 00000. 00.. 00 00 00\00\0 .0.0 .0.. 00\.0\0. 0..0 00. 00.00. 00.. 00 .0 00\00\0 00.0 00.0 00\.0\0. 0..+ .0. ...00. 00.. 00. .0 00\00\0 00. 00.. 00 ...00.... 0..... m... m. 0.... am mm 4.+ 0+0. 8.1 m.xa. .+b 7.0 A 7.0 TL. 8.4 +58 T.+ .09 7:00. nun T00 a .00 0.4 8.0 on O/ 1...... 1.7.0 7..... EX. 7. .00.. an. 7. 4 .0 O 8 x 0.. u E u Auo I. .D 0.0 4 I. a 0.4 5 0+ 9.9 o n e x m P 0.. e 3 u .... 1. E 7.. .... 1 a 3 O O K .0 .0 u moanmflum> pampcmmmUCH manuaum> pampcmmmo paw mumumamumm .mmHHHWSUGH GMEHOZ Gm>ll.mfl mgmflB Required Return 145 40% T A 69 30%~ 1r 20%~ CD J4. l 10%- o.4 0.8 1.2 1.6 Debt/Equity Ratio (Market) Figure 30 Required Return versus Debt/Equity Ratio for Van Norman Industries ———.u .1“ 3 .U‘v. v ...—*‘0 i‘ u.“ ”CL 146 evidence, but the line determined by the two values of required return does SIOpe upward when plotted against the debt equity ratio in Figure 30. 16. Ward Baking Company The Ward Baking Company, since 1964 Ward Foods, Incorporated, issued its first warrant in 1945 and has just recently issued another. The company has diversi- fied its product line somewhat since 1945 when it was involved principally in the production and distribution of bread and cake. It now produces and distributes frozen pies, cooked meats, and allied products and processes coffee and tea. The Ward Baking warrant was issued in connection vvith a recapitalization plan approved on September 26, £1945. The warrants entitled the holder to purchase com— nnon shares at $12.50 from April 1, 1947 to March 31, 1951 21nd thereafter until April 1, 1956 at $15.00 per share. From Figure 31 it is clear that stock price was aabove exercising price during most of the Option period, kNJt did not go too far above it. Of the eight original Cflbservations only three were unacceptable because of short iJrvestor horizons. Unfortunately, of the remaining five, two estimates were ridiculously high and their error lilnits very broad. These results are plotted against thee debt equity ratio in Figure 32, but the statistical tests were not performed. 147 (ll - whiny)?! ‘00h004rh‘ . ... 00.xmm 0.03 woflum xooum mzmum> moflum ucmuumz .0 mn:m.m _mH444050 mu.uu yumbm on Om 0: mm ON 0 b P p P » :13] Ba 1 i’w’Vb‘dVFl (Sti'V—l 10G) 148 .cndumu omufldwmu How mcoflusHOm manmummoom 00w mannaflm>m mac044 .000» 020 can» mmm. c000uos Houmm>cH4 0..0- 00.0 00\00\0. I 4 00000. 00.0 0.0 00 00\0\0 00.0 00.0 00\00\0. 00. H 00. 00000. 00.0 000 .0 00\0\0 0..0 00.0 .0\00\0. 00. 0 00. 00000. 00.0 00. .0 00\0\0 0..0 00.0 00\00\0. 0.. H 00. 00.00. 00.. 00. 00 .0\0\0 00.0 00.0 00\.0\0. 00.0+ 00. 00.00. 00.. 00. 00 00\0\0 00.0 .0.0 00\00\0. : 4 00.00. 00.0 00. 00 00\0\0 00.0 00.0 00\00\0. 000.0+ 00. 00000. .0.. 00. 00 00\0.\0 00.0 00.0 00\00\0. 4 00000. 00.. 00. .0 00\0\0 83 HQ SH 013V 38 AS .... dS dM 00 .0.0 .0.0 0.? 1.7.40 .00 E1. .0 11. In. 0.0. 44 4Q 01 mxd 1b 10 A To T1 33 .....0 7:1. .0.0 7:01 nn .....0 .0 00 0... .0.0 0H 0/ ....u 1.10 7.7.. Eva. ... .00... .02 7. .4 3 o 8 x 07. u p. 0 A0 7.. b 0.0 ... 7.. .0 0d 5 .... 0..... 0 n p. ... m D. .01 .0 .... u I. 1 e I. I. .... a 1. 0 0 ..A .0 .0 u mmHQMHHm> uchcmmmch magmaum> pcmocmmmo 0cm mumuwfimumm .mcwxmm 00034:.0H mumqa Required Return 149 40%1 A G I? 30%- 1r- 6] 20%~ CD I J. 10%— 0.2 0.4 0.6 Debt/Equity Ratio (Market) Figure 32 Required Return versus Debt/Equity Ratio for Ward Baking Company I v ')\‘!’ x,“ CHAPTER VI CONCLUSIONS There were two major objectives for the research reported in this dissertation. The first related to the development and exploration of an entirely new approach to the problem of measuring the cost of equity capital. The second involved the application of that technique to a sample of firms with the hope of resolving two signifi- cant empirical questions in the field of business finance. That hope has now been laid to rest but the value of the technique itself is still alive. The model, as currently formulated, has definite limitations which were brought out in Chapter V. The large error resulting from imprecise measurement of the model parameters tends to limit the usefulness of the method. The apparently short investment horizon of war- rant holders tends to reduce its value still further. However, it is possible that these problems are related and that a more satisfactory method of obtaining estimates of the variance of the logarithm of weekly closing stock 150 151 price relatives could increase the usefulness of the method significantly. The reader will recall that in discussing the measurement of this variance it was noted that we wished to measure it in periods during which no new information regarding the security was released. Unfortunately, it is impossible to use only such periods for examinations for we do not even know when new information is being recognized. The use of all time periods tends to reduce the weighting of those periods during which new information is injected but our estimate is destined to be overstated. The effect of this overstatement is to overstate the magnitude of E[Wt ] at any time in the future. This e effectively shortens the expected holding period as com- puted from the model and may have been partially responsi- ble for so many of the observations being discarded be- cause of short holding periods. Thus in addition to the prOpagated error resulting from the measurement of this variance, its overstatement may be the source of this major difficulty. If we were to work further into the model for an answer to its shortcomings, we should examine the use of the random walk model to obtain a distribution of future stock prices. This is not to say that Ayres' model of the relationship of expected warrant return to expected return on the associated common stock is without fault. We have already seen that his model suffers more in its 152 predictive ability than Ayres realized or, perhaps, cared to admit. The reader must recall that Ayres tested his theory with data based upon the same random walk assumption. If we actually knew the shape of stockholders' subjective probability distributions of future stock prices, the author feels confident that Ayres' empirical results would be improved considerably and the method used herein might prove to be fruitful. Current work in portfolio theory utilizing the two parameter model may well improve the state of the art of measurement techniques or provide an alternative for the random walk model. Since the model used is perfectly consistent with the most recent developments along these lines, this is a distinct possibility. In addition, an increasing number of warrants are being actively traded on our securities exchanges so the usefulness of the method, should a breakthrough in measurement techniques occur, could have more general applicability. In conclusion, the author would like to discourage others from attempting to salvage this model until some such breakthrough does occur. The use of this model has been explored in depth and it is the author's opinion that the value of additional research would yield a low marginal return. fl In.....l.Mfl|Il.. .Ft kh.lanilillléld4lnlldfl‘fw M W", Allan-hid] . r BIBLIOGRAPHY BIBLIOGRAPHY Ayres, Herbert Frazer. "Risk Aversion in the Warrant Markets." Unpublished Master's thesis, Massachusetts Insitute of Technology, 1963. . "Risk Aversion in the Warrant Markets.“ Industrial Management Review, V, No. 1 (Fall, 1963), 45-53. Barges, Alexander. The Effect of Capital Structure on the Cost of Capital. frThe Ford Foundation DISser- tation Series." Englewood Cliffs, N.J.: Prentice- Hall, Inc., 1963. Cootner, Paul H. "Stock Prices: Random vs. Systematic Changes." Industrial Management Review, III, No. 2 (Spring, 1962), 24-45. Farrar, Donald Eugene. The Investment Decision Under Uncertainty. "The Ford Foundation Dissertation Series." Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1962. Fisher, I. N., and Hull, G. R. "Risk and Corporate Rates of Return.“ Quarterly Journal ofJEconomics, LXXXIII, No. 1 (February, 1969), 79—92. Friend, Irwin, and Puckett, Marshall. “Dividends and Stock Prices." American Economic Review, LIV, No. 5 (September, 1964), 656-82. Gordon, Myron J. "Optimal Investment and Financing Policy." Journal of Finance, XVIII, No. 2 (May, 1963), 264-72. Graham, Benjamin, and Dodd, David L. Security Analysis. lst ed. New York: McGraw—Hill Book Company, 1934. 153 154 Granger, C. W. J., and Morgenstern, O. “Spectral Analysis of New York Stock Market Prices." Kyklos, XVI Miller, Merton H., and Modigliani, Franco. “Dividend Policy, Growth, and the Valuation of Shares." Journal of Business, XXXIV, No. 4 (October, 1961), 411-33. Modigliani, Franco, and Miller, Merton H. “The Cost of Capital, Corporation Finance, and the Theory of Investment." American Ecgnomic Review, XLVIII, No. 3 (June, 1958), 261—97. . "Corporate Income Taxes and the Cost of Capital: A Correction." American Economic Review, LIII, No. 3 (June, 1963), 433-43. Shelton, John P. "The Relation of the Price of a Warrant to the Price of its Associated Stock." Financial Analystsfigournal. An article in two parts (May- June, 1967), 143-50 and (July-August, 1967), 88- 104. Sprenkle, Case M. "Warrant Prices as Indicators of Expec- tations and Preferences." Yale Economic Essays, I, No. 2 (1961), 178-231. Weston, J. Fred. "A Test of Cost of Capital Propositions." The Southern Economic Journal, XXX, No. 2 (October, 1963), 105-12. .,~ g; l E“ N "“mm!I‘M@7177ng