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FACULTY iraRKBTG PAPERS College of Conmerce and Business Administration University of Illinois at Urbana-Champaiga June 11, 1979

TIIE EFFECTS OF COIIPLEX CAPITAL STP^UCTURE Oil TIIE l-IATJCET VALUES OF FIPJIS

Thrmas J. Frecka, Assistant Professor, Department of Accountancy

//579

Summary:

'■ In this study, the familiar llodigliani and lliller risk class model provided the ba; to test for a difference in value between simple and complex capital structure groups oJ firms in the same risk class. Cluster analysis, using market risk measures and debt-eq» ratios as inputs, provided the method for obtaining the required risk class sample of firms. Cross sectional tests at the end of 1972, 1973, and 1974, for the sample of 26 complex capital structure firms, indicated that capital structure v/as a highly signific; effect. For all periods examined, the complex capital structure firms were valued lovjei than the simple capital structure firms. One explanation for the results is that most ( tl^e convertible securities for the complex capital structure group were overhanging issi during the test period.

Ackno\/ledy;ment :

•t

The author gratefully acknowleges the help of George H. Frankfurter, xrho helped formulate the research question, and chaired the dissertation on \;hich this study is ba;

The Effects of Complex Capital Structure on the Market Values of Firms

Thomas J. Frecka*

I. Introduction

Spurred by the seminal work of Modlgliani and Miller [19], an issue of continuing concern and controversy in the field of finance has been the effect of the financing decision on firm market values. Despite the persistance of controversy, progress has been made at both theoretical and empirical levels. At the theoretical level, the MM arbitrage proofs have been extended and illustrated to hold in a variety of contexts

1 ' '

by numerous authors. And those theorists who continue to believe that

capital structure matters have turned from ad hoc rationalization to more explicit consideration of the effects of certain market imperfec- tions. At the empirical level, the main progress stems from the use of

increasingly sophisticated econometric techniques to deal with a variety

2 of measurement problems. As a minimum, the result of continuing

research during the last twenty years has been to raise the discussion

to a higher plane.

Despite the plethora of research dealing with capital structure and

value relationships, neither the theory nor empirical tests of the MM

risk class model have explicitly considered the Impact of convertible.

securities and warrants on firm market values. This is somewhat surpris-

4 ing given the continuing interest in these forms of financing and the

sometimes confusing reasons given for their issuance, as explained below.

*llniversity of Illinois, Champaign-Urbana. This paper is a summary of my dissertation, completed at Syracuse University in 1978. Grateful acknowledgement is given to George M. Frankfurter, who served as chair- man, and helped formulate the research question.

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A major purpose of this study Is to investigate empirically the effects of complex capital structure on firm market values. This is accomplished by testing for a difference in value between simple and complex capital structure groups of firms in the same risk class.

Despite the variety of analytic proofs showing that the existance of security types simply results in a fragmentation of the firm's total earnings stream among various security holders, suggestions that coiq>lez capital structure may impact on firm values are prevalent. These sug- gestions are evaluated in Part II. Related to this point, arbitrage proofs for the complex capital structure case within the two period risk class model are shown in Appendix 1.

An important assumption of the MM theory is that firms can be

assigned to equivalent risk classes. Part III discusses limitations of

previous risk class approaches and suggests the use of a new procedure

based on cluster analysis,

* ,- Part IV discusses sanpie selection procedures, measurement pro-

■••■■-■■-■■ ■" ■-: y'lr.' ... .. jr=.: .::<.v

cedures, statistical tests, and results.

r -> ;■ -■ j~» »

A summary is provided in Part V, including limitations and sug-

gestions for future research.

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II. Reasons Coiaplex Capitrl Structure May Inpact on Firm Values

The traditional view concerning the effect of convertible securities

■' ■■■■ • ■' : ■• ■:■-■: ■■' ■■■"■ : ■ ■ - ,:, ,:_,_2 ■^•i^fk-^, ^:^

on value is expressed by Johnson [15, p. 403] as follows.

But the dilution of earnings per share is not neces- sarily equivalent to the dilution of price per share. Although conversion brings a drop of earnings per ' T" share ...» it does not follow that the market value

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of comQDn stock will decline by the same percentage. Given the smaller financial risk attributable to the common stock because of the reduction of financial leverage, the price-earnings ratio may rise to off- set in part the decline in earnings.

The above statement suggests that current shareholders react to a com- bined dilution and leverage effect associated with convertible securities. But the main concern is with dilution.

Dilution represents an expropriation of value without appropriate compensation. In a perfect market, it is assumed that security holders protect themselves from dilution by a variety of "me first" rules. With respect to convertible securities, while the firm and current shareholders do suffer an opportunity loss upon conversion, this loss is not without . compensation. For in a perfect market, this opportunity loss should be exactly offset by the present value of accumulated savings in interest due to originally issuing the convertible security instead of straight debt. But even if dilution in the above sense is possible, this only

means that classes of security holders may not be indifferent to capital

8 structure. Total firm value should be unaffected.

Another set of arguments Is based on the belief that management can more accurately estimate the firm's growth opportunities than the market. These arguments are based on the empirical fact that, on average, com- panies experience much higher stock price appreciation before issuing complex securities than occurs after the securities are issued.

It has been shown that investors are willing to pay a premium for

9 past growth indicating their optimism that It will continue. The

in5)licatlon is that managers believe they can successfully "fool the '

market" regarding growth, thus resulting in overvalued complex securities

and firms.

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A sooewhat contrary explanation of how management might act If it perceived the market was unable to impound growth opportunities is as follows. If management believed its firm's common stock to be under- priced, perhaps due to nondisclosure of a recently developed growth opportunity or the market's failure to impound a disclosed growth oppor- tunity in current stock prices, convertible securities could be issued to finance such opportunities. When the investment resulted in Increased iearnings, conversion would occur. The implication is that management seeks to ptotect current shareholders from the effects (if any) of current earnings dilution by issiiing the convertible security rather than currently issuing stock. -xv-' ■ c»'>

Although the difficulty of defining, measuring, and forecasting growth is admitted, it seems unlikely that the market is unable to make unbiased estimates of growth based on the information set available. ;. The substantial empirical evidence concerning market efficiency in a variety of contexts might lead us to suspect that the market is also efficient regarding growth. But empirical tests will, hopefully, con- firm or deny this suspicion. ...

A final suggestion as to why complex capital structure might affect market value Is based on the leverage preferences of "gamblers." Al- „ though equity and debt markets are dominated by risk averse investors, this is, less likely to be true in markets for convertible securities, warrants, and options. Given the well-known leverage opportunities associated with these latter securities, risk loving investors may bid up the price of these securities and firms in periods of high growth. Presumably the opposite effect would occur if anticipated growth was not forthcoming, e.g., the overhanging issue case. .,. -._^^

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Despite the above arguments to the contrary, the crux of capital structure theory, given perfect market assumptions, stresses the inde- pendence of total firm value and capital structure. Fama and l-Iiller [9] analyze the issue first in a general equilibrium setting and then present the well-known arbitrage arguments using partial equilibrium ^r. ■ states of the world and risk class approaches. Hamada [12, 13] has pro-^ vided the analytic link between the risk class model and the capital ,. • asset pricing model. Finally, Merton [17] has provided the analytic link between the Black and Scholes [3] option pricing model and the risk class model. ■ ■ . . u:^: = ^;^m ,:iT^..::

Iheory suggests that the separation principle should continue to hold for the complex capital structure case. While a strict indepen- dehce will not hold given imperfections such as taxes and assuming ... risky debt, these considerations are no more or less present for simple or complex capital structiires and should not affect test results. , Arbitrage proofs using a two period risk class model are Illustrated for the complex capital structure case in Appendix 1. . ■■ i ;.■■--::;::.•

III. The Risk Class Assumption I' " ■-

4 • • . 1 -

i" ' ■' • • -.."-■ . ' . ; • .' ^

The nxill hypothesis examined in this study is that there la no difference in value between groups of simple versus complex capital structure firms in the same risk class. Before explaining the procedure used to obtain a risk class sample in this study, it would be useful to examine the nature and objectives of the risk class assumption.

In a theoretical sense, MM define a risk class as a group of firms whose net cash earnings before interest are perfectly correlated, and

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hence differ only by a scale factor. "In periods before t, earnings and Investments at t are uncertain; but for two firms to be in the same class, investors must agree that whatever values earnings and investment outlays take in any period, for these two firms they are always pro- portional by the factor ^, and hence perfectly correlated," [9, p. 161] However, the concept is an ex ante one and risk classes are not directly observable. • . , ■

In a more pragcatic sense, the risk class assumption refers to ,^; c,- firms with equivalent business or operating (as opposed to financial) ■ risk. The objective is to hold operating risk constant so that the . ..v;^ effects of financial risk can be observed. But in this study, it is desirable to hold both operating risk and leverage, as defined, in the usual sense, constant to determine if complex capital structure impacts on value. , ■i.-f-'- •> - ^f

On a third level, the important objective is to obtain a sample that is homogeneous in a statistical sense. The need for sample homo— ■■. geneity is summarized by Elton and Gruber [6, 7] who note three reasons for grouping in empirical studies:

(1) To isolate units that should in some sense act alike;

(2) To hold the effect of one or more omitted variable constant; .; .;.:or , .. . ... ^ . .-s:^ 3:.:

(3) To obtain a homogeneous relationship between the variables included in the model. [6, p. 81]

All three of these objectives are necessary in a valuation study. But

particularly the second objective is critical. Elton and Grubar show

that the failure to hold business risk constant may result in (1) biased

regression coefficients, (2) biased correlation coefficients, and (3)

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results that are extremely sample sensitive. The direction of the biases depends on the relationship between the omitted variable(s) and those in- cluded in the regression equation.

Previous researchers including MM [19, 21] and Barges [1] have used Industry samples in an attempt to achieve homogeneity. But an Industry approach is not possible in this study since no single industry or group of industries provides a large enough sample of simple and complex capital structure firms. Furthermore, several studies, including those of Wippem [30], Gonedes [11], Elton and Gruber [6], and more recently by Boness and Frankfurter [4] Indicate that industry groups are hetero- genebus with respect to business risk. The latter results are particu- larly striking in that firms in the assumed homogeneous electric utility industry do not pass statistical tests for homogeneity, Boness and Frankfurter conclude that more parsimonious methods should be used to obtain a risk class sample. „ . •:

Due to limitations of the industry risk class approach, an alternate method of obtaining a sample is required. Tne objective of the sampling procedure is to select a sufficiently large and homogeneous group of firms from a piopulatlon that is heterogeneous with respect to business risk. The set of algorithms connnonly referred to as cluster analysis techniques seem particularly well suited to this purpose and are used ifi this study. Although several different clustering algorithms are Available, the common objective of most methods is to separate a set of data into groups or clusters that can be viewed as contiguous elements of a statistical population. The hierarchical methods, a subset of cluster analytic techniques, combine objects into larger and larger

=8-

groups by minimally increasing some generalized distance function. The Euclidean metric is frequently employed, where the distance between points 1 and j, d . is defined as:

P 1/9

' ^irK\ ^ik" V^ ^'^ [8. p. 563

where X., and X,, are the scores of objects 1 and j on variable k, with the summation over p variables. An algorithm that utilizes this Euclidean metric is used in this study. .'.s-.'ii<iP'.

Although cluster analysis provides a method for obtaining a risk-, class sample, it is not without problems. Issues such as variable ; selection, measurement procedures, and criteria for judging the results of clustering remain. v-

With respect to grouping variables, accounting risk measures, market risk measures, and combinations of accounting and market risk measures are possible choices. Accounting risk measures (financial ratios) have long been used by analysts in the security selection and evaluation process. In the present study, the objective is to use accounting measures to capture the basic risk characteristics of com- panies which should "behave alike" in the MM partial equilibrium frame- work. The main advantage of grouping based on accounting risk measures is that the approach focuses on company characteristics evaluated by the market in establishing relative security prices. To the extent variables can be selected that result in a homogeneous risk class, our knowledge of the risk determination process is enhanced. ,.

But there are several limitations to the use of accounting risk measures. First, differences in accounting methods across industries

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and Individual firms may affect the conpar ability of riBk measures and result In inappropriate groupings. Second, there ia a lack of theory concerning exactly vhat accounting measures to include. While a generally agreed upon list of risk measures could be obtained from research done in this area, there is always the danger that factors considered Important by the market were not considered. A third dis- advantage is that accounting measures lack certain desirable statistical properties. - r . . ^. ,; ,;.. . _ .;,

■i.i.A currently popular method of obtaining a risk class is to select firms with similar market risk measures. Typically, capital asset . . '• pricing theory is invoked which assumes that only systematic risk (beta) affects security prices since nonsystematic risk can be diversified away.. Under the assumption that financial risk affects the systsnatic component of risk, Hamada [13] develops a method of unlevering security - returns. While Hamada's approach is widely supported by theory [2, 16, 28], empirical results are mixed. . ^i . r .■.-^r^..

,.-<;.. An appealing approach in this study is to cluster based on beta and similar debt-equity ratios. The approach, while equivalent to Eamada's "and only slightly more restrictive, avoids an assumption concerning the financial risk and systematic risk relationship. To the extent non- '■ systematic risk is deemed Important, it can be included as another grouping variable.

Regardless of what set of variables is employed, the distance metric employed in this study weights all sources of variation equally in com- puting a single distance index between groups. To the extent that some values are larger and fluctuate more than others due to scale differences.

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greater consideration will be given to them. However, standardization may result in dampening sources of variation that are particularly good discriminators. A more appropriate method of dealing with the weighting question may be to use factor analysis to account for correlations ^mnng variables. While the classification of firms into groups may be extremely sensitive to data, this is not considered a problem in this study since a unique risk class is not being sought; all that is sought is a sample that can be accepted as reasonably homogeneous. ,-:.i.c.-; ts ;t;:i-:

.: In evaluating the success of a particular grouping procedure, the primary test concerns how xj'ell the sample satisfies the assumptions of ' the MM risk class model. Certain statistical tests for homogeneity can '

be done; but to be valid, the tests should be applied to the valxiation '^--

12 model directly. Clearly, the determination of a normative procedure

'for selecting risk classes would require the testing of all proposed '" -' methods in the valuation model. Such tests are beyond the scope of this study. An initial concern is the ability of a given set of variables to interact with the clustering algorithm so as to obtain relatively large groups with little within group variation. If several sets of grouping variables satisfy this requirement, then a choice will be made on theo- retical grounds. .-j.TriaxT;

'X.ji' ; '-. 'i.'/ iy-- ■^■^'■■■•' ' ■ ' - .. - -

IV. Empirical Tests

. >.. ;,-.vi. ,■ v'i-

Sample Selection • .■•!■■.'■ «■;..: I. »:;:i-i

The population consisted of 515 calendar year-end industrial com- ■ panics for which: (1) monthly returns could be calculated from the quarterly COMPUSTAT file for the period February 19S7 through December

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1972, and (2) required financial statement data was available from the annual CCfMFUSTAT file for use in the MM model and in clustering routines.

The grouping algorithm for t:iis population was then applied to

13 various sets of accounting and market risk measures. The most Impor- tant result was that all sets of variables examined in conjunction with the grouping algorithm resulted in some large clusters of firms while maintaining relatively little variation within groups. While there was little correspondence of groups based on different sets of variables, this result was not unexpected. ' - • -. ,--■-

'. ' Somewhat aritrarily, three market risk measures and a leverage -.-:■. variable were finally selected as grouping variables. To obtain the market risk measures, monthly rates of return were computed for the Standard and Poor's Industrial Index for the 1967-1972 period and used as regressors in the equation: ,■ _^ , ■.,-.;

^it -= ^i -^ Vnt •*■ ^it l"]' 2, .... 515' (2)

where: . ■ •. '. .r?-. : -i

r, is the rate of return of company i in period t, ••-::••:■■.;',

a. and b. are constants, -•"■

r is the index ret-urn in period t, • . , -.-. ■. -

and e. is a random disturbance. "■.;.->

The resulting parameter estimates and mean square error (nonsy sterna tic risk) were used as the market risk measures. The leverage variable was computed as the ratio: (Current Liabilities + Long-term Debt + Preferred Stock) t Common Equity, using the average of annual observa- tions for 1963 through 1972, and is denoted LEV-3. In order to deter- mine the dilution potential for the population, the ratio: shares

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reserved for conversion v shares outatanding was also computed. The average values and standard deviations of the market risk measures, ..:

the above leverage variable plus two additional leverage variables,

14 and dilution potential are shown in Table I. . -

In 1972, the average dilution potential for the population averaged about ten percent. Table II further details the potential dilution from 1963 through 1975. The dilution ratio was generally increasing through 1970 and has remained fairly constant since that time. The fact that many companies had high dilution potential while others had relatively low dilution potential provides hope that a risk class sample containing both high and low dilution companies can be fonaed. ,:. ;■ -.'.v'^ i::- :<

In order to avoid overweighting particular sources of variation and to account for corrections f_3iong the risk measures, factor scores from the a., b,, KSE, and LEV-3 measures were used as input to the clustering routine. Table III shows the factor analysis results. Three factors account for about 75 percent of the variability.

Using the first three factor scores as Inputs, the clustering algorithm was run and then observed at the point where the 515 firms had been coabined into 15 groups. Groups sizes ranged from 2 to lOA firms at this point. l>'hlle several large clusters were evident, total variation within groups was only 14.613 as compared with total variation of 254.396 for the population based on the factor scores. , .■-!.;.^.;: •■{■.•.■:>

A group containing 82 firms was chosen as the cluster from which the sample was obtained. The firms were then classified into simple, . _- intermediate, and complex categories as follows: . ■ . : . i.V:JL -i: ■,;:.:■;

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(1) simple: dilution potential < 6%

(2) intermediate: dilution potential 6% >_ d. <^ 11%

(3) complex: dilution potential > 11%.

Klne intermediate firas were discarded, leaving 36 complex and 37 , simple firms.

: .• . An additional requirement was the availability of market values of convertible securities and warrants in published sources. Ten complex firms failed to satisfy this requirement, thus reducing the usable complex sample to 26 firms. Finally, 26 simple firms were randomly orl selected in obtaining a total sample of 52 firms. Due to the many restrictions placed on the population and on the sample, a caveat Is in order when generalizing from the results of tests.

Table IV details the market risk leverage, dilution, and size characteristics of the simple and complex groups. There is no signifi- cant difference in the market risk measures for the two groups. , .■^•.•'• However, the attempt to obtain a sample that was equally levered for the two groups was not successful. The complex group's debt to equity ratio of 1.06 was significantly higher than the simple group's ratio 'of .902. This result may indicate that complex capital structure firms are in general more highly levered than simple capital structure firms. The importance of this difference in leverage must be judged when evalutlng the test results.

The most Important result of the sample selection process was that a substantial difference in dilution potential was achieved. The com- plex group's dilution potential averaged about 25% compared with only 3% for the simple group.

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One difference betveen the two groupa is average firm size, as measured by total assets in 1972. The simple group's average total assets of $1,002 billion is about fifty percent larger than the complex group's average of $.667 billion. Further consideration is given to the effects of size later.

Comparing Table IV with Table I, note that the average risk measures for the sample are close to the population values. However, the vari- ability of the sample risk neasurea is substantially less than that of ,^ ,. the population. This provides evidence of the homogeneity resulting .., from the clustering procedure. * ..- • -j f^.

Model Selection

The familiar MM valuation model expresses total market value as:

-. .n:T;V. V =-ix(l-T) + tD + l<^a-r)f^fx^lT (3) [21. p. 344]

where: ^■'•■■■^^■■■■■' i-:; ■;.•■■? • -' =.--■. ^ ■ . ^ ., ■ ^ j^.^.

V - total market value of the firm , .-.

— ■»= the appropriate capitalization rate for uncertain pure _ equity earning streams for the risk class * c v.j at; s

X = expected average annual earnings before interest and tax X = the marginal tax rate . .. ; , r.j;is~

D = the market value of debt

k = the earnings growth rate ' ".'-'O?"', "?:•-»

p* = the rate of retvurn on growth opportunities C = the cost of capital, and i , r .; , • =--•«•-- ^.-r-j^^-

T = the duration of growth.

Econometric analogs of model (3) provided the basis for the 1966 MM

tests and are also used in this study for testing hypotheses concerning

the effects of complex capital structure on value. The following three

models are employed:

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V-xD = a^ + a^x""^ + a^G + u (A) [21, p. 348]

T^ = «1 ■*• -0 v4d ^ V=?D -^ - <^> t21, p. 349]

^=^0X-^^1?^^2!^- (6) [21, p. 350]

All three codels are now expressed in the form of first order, normal error, multiple regression models. Model (A) is the econometric analog of model (3), with the growth tern G simplified. Model (5) is the "yield" formulation of model (A), where a| =• p. tSodel (6) is the deflated ver- sion of model (A), where A is the book value of assets. The model was ..^^ suggested as a means of implementing the weighted least squares approach, under the assumption that the source of heteroscedasticity is firm size.

Dates of Tests

An objective was to test hypotheses at various points in the busi- ness cycle. Conmon stock prices were generally increasing in the early 1970*s and reached a peak in December- January 1972-1973. Stock prices generally fell after 1973 and reached low levels at the end of 197A. In contrast, long-term bond prices were relatively flat in the early 1970's but then started to fall rapidly in 1973, reaching a low in the third quarter of 197A.

The test dates were chosen as January 31, 1973, 197A, and 1975 to reflect stock price peaks, midpoints, and troughs respectively. The January 31st dates were chosen to avoid any possible year-end price aberations and so that the previous year's earnings number would be

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better known by the market. D&tes close to year-ends were chosen to avoid measureaient errors resulting from poet year-end capital structure

changes.

Variable Definition

The details of Che capital structures of the 52 firms comprising the sample were obtained as of 1972, 1973, and 1974 year-ends. The variables in model (4) were then operationally measured as follows: '•"-V. represents the total market value of firm i at the time t and consists of the market value of all securities and other claims against the assets of the firm. Market prices of common stock, warrants,

most convertible securities and preferred stock issues were obtained

19 , from published sources.

,£,.!'- Based on a pilot study on a smaller sample of 28 firms, it was

determined that all non-convertible long-term debt could be measured

20

at book value without significantly affecting the results. Conver- tible securities and warrants were measured at market values. All other liabilities, primarily current liabilities and deferred taxes, were included at their book values.

The expected cash savings due to the tax deductibility of interest payments, tD, was computed at 48% of the book value of long-term debt. It should be noted that to the extent the market views the issuance of a convertible security as an expectation that the firm will unlever, the operational definition of the tax savings is upward biased for the

complex group.

—1 The tax-adjusted earnings term, X , was computed from CQMPUSTAT

data as operating earnings less taxes (COJIPUSTAT variable numbers (13-14)

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-16). The current year's earnings was used under the assumption that the process generating the annual accounting earnings number approxi- mates a randon walk [32, 33].

Finally the growth term, G, was measured as in the 1966 MM study using the 4-year linear growth rate of assets times the current year's assets. While this operational definition is not a good proxy for

growth in the true sense, the election was made to follow MM due to

21 -.<='■ ■' -.<.:• lack of a better measure. ; . '

HycothesiH Testing

Using models C4) , (5) , and (6) a variety of approaches are available for testing for differences in value between the simple and complex groups. One approach is to add a dummy variable or series of dummy variables representing complex capital structure to the models and test the coefficient (s) for significance. A second approach is to run sep- arate regressions for the simple and complex groups and test for differ- ences in regression lines. A third approach is to test for differences in the average residuals of the two groups using an analysis of variance •approach. Essentially, these techniques ere equivalent and will be ' subject to the same econometric problems. " ..•.-• ...

. ' Due to its ability to examine several effects simultaneously, and because of its relative parsimony with respect to theory, an analysis of variance model, using residuals from the two groups as data, was preferred in this study.

Consider the following niodel:

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\jk = VJ-- + «! + Pj + (ag)^^ + e^j,^ (7) [25, p. 568]

1 » 1, 2, 3

J = 1, 2

k— 1, 2, •••( 26

where:

y.. is an overall constant

a is the time effect (years 1972, 1973, and 1974)

0. is the capital structure effect (simple or complex)

(ttg) is the interaction effect

k is the number of replicates.

I_ U..i:lJ.

The Y, , ^s are residuals from the regressions and are assumed indepen- dent N(u.. + a^ + B + (a8)^.)a^ [25, p. 569].^^

Using model (7), it is possible to test for differences in value between the simple and complex groups by examining the following oper- ational hypotheses:

H^ Hiere is no difference in average residuals over the three - ., year period .

Kj There is no difference in the average residuals of the simple versus complex groups.

-?:./. 1 "•-

H There is no interaction between time and capital structure

effects. Note that the use of least squares estimators in models (A), (5), and (6) rules out rejecting K. since the residuals must sxim to zero In any one time period. But the use of the two-way design provides a con- venient accuracy check on the data, and more Importantly, allows for testing Interactions. .. ..

Results

Table V summarizes the estimates obtained using model (4) for the combined 52-flrm san^le. The earnings and growth coefficients are significant in all three years while the constant is not significantly

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dlfferent from zero. The values of the coefficients seem reasonably consistent with the underlying theory.

Plots of residuals on the estimated values of the dependent vari- able appear in Table VI. The plots show evidence of heteroscedastlclty, but there is little evidence that a linear regression function is not appropriate. A possible concern is the presence of some outliers. Standardizing residuals in terms of the residual standard deviation (mTsTET) " from model (A), and treating deviations in excess of 2,5 standard deviations as outliers, several outliers are noted each year. In 1972 and 1973, Phillips Petroleum (44 s.d.), Texas Instruments ' - C+3 s.d.) and Goodyear (-2,5 s.d.) are outliers. In 1974, Phillips Petroleum and Texas Instruments again appear, along vrith Bristol Myers and Union Carbide. The outliers all belong to the simple group and are some of the larger firms in the sample. '^ " .' ' ' *"■ ' '•■•''■■'■-

To assure that a few large firms were not influencing the results*' model (4) was rerun, using a reduced sample of the twenty smallest companies from each of the two groups. This procedure had the added "• advantage of eliminating the previous noted average size difference -''* of the two groups. The regression results are shown in Table VII. It. is evident that the estimates are not unduly influenced by the large • firms. The earnings and growth coefficients are consistent with the ' '"' previous results. But the fit is somewhat better as evidenced by smaller standard deviations, generally higher T-statistics and higher R values. ^

Models (5) and (6) were suggested variance- stabilizing transfor- mations of the basic valuation model. Estimates for these models are sho^m in Tables VIII and IX respectively.

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Model (5) Is the "yield" formulation of model (4), where the con- stant al provides the estimate of p. The reciprocal of the constant

^ ■•.-•..' "j

term is equivalent to the estimated earnings capitalization rate in model (A) . Compared with Tables V and VII, the reciprocal valxies are all higher, but the direction of change over time is consistent with the previous re- suits. As in the MM study, the explanatory power of model (5) applied to this sample is much lower than for the non-deflated model.

The residual plots for model (5) are presented in Table X. The— ^ . residuals appear particularly well-behaved with an apparent random distribution about zero and no evidence of heteroscedasticity. Only one outlier is noted. Stone Container, in 1974. , .. , : ^ ,

. ., Hbdel (6) is the deflated form of model (4), where the deflatex is book value of assets. The explanatory power of this model when employed by tM, using a utility sample, was relatively high.. Uut this is not the case in the present study and there is other evidence of model mlsspeclfication. This is clear from the residual plots, shown in Table XI. There is a noticeable doimward drift in the residuals for higher values of the dependent variable. This effect is especially noticeable in the 1974 plot and may indicate a violation of the lin-. .• earity assumption, the effect of an omitted variable, or some other mlsspeclfication. , , .,„

The following conclusions seem warranted concerning the adequacy of the sample and models examined. It seems that a relatively homo- geneous sample has been obtained using the clustering procedure. This is evidenced by high explanatory power of model (4), coefficients that are consistent with the theory, and evidence that the estimators are not

' ' ' ' ■ ■ i.i -y

-21-

very sample sensitive. Sample homogeneity implies that the average results of the cross-sectional tests are due to the entire sample, rather than due to the influence of just a few firms.

A concern was the average size difference between the simple and complex firms. In the presence of heteroscedasticity, the size differ- ence la Important, since It could lead to rejecting the null hypothesis for thi.s reason alone. The use of the reduced sample for model (4) and the deflated model (5) have apparently purged the results of the effect of size differences, but model C6) inay be oisspecified. --.■..;. .-i;...^, '*"■ The results of hypothesis testing using the analysis of variance

i^del (7) appear in Tables XII vand XIII. Note that time is not a slg-

24 nlf leant effect and that there is no significant interaction. However,

for all models tested, capital structure is a highly significant effect. Note the direction of the difference between groups. Except for the deflator, models (4) and (6) are equivalent. The residuals using these models are consistently negative for the complex group and positive for the simple group. In other ^«3rds, the observed market values for the compilex firms consistently fell below the estimated value and the simple , firms above. The results from model (5) are consistent with the other models. Since model C^) is the yield formulation of model (4), consis- tency requires that complex firms sell at higher yields (lower values)

25 than the simple firms, as the results indicate. ..,..,

Discussion

The test results indicating that complex capital structure firms were valued lower by the market than risk equivalent simple capital structure firms was a surprising result and one that is contrary to the

-22-

underlying theory and conventional wisdom. For this reason, a variety of additional steps vere taken to assure that the results were not due to using different measurement procedures for the two groups or due to perceived risk differences.

In regard to possible neasuremant differences, the following steps were taken. Off balance sheet financing (leases) were valued and in- cluded in measuring the dependent variable. Four simple and five coa- -

plex firms had substantial amounts of leases. Another concern was a

26 possible overstatement of the tax savings from convertible debt. .. ■ >..

The dependent variable was recalculated for the complex group under the assumption that the tax savings from convertible debt was zero. Finally, convertible debt was originally computed at market value, while all other debt was computed at book value. Kow measuring convertible debt at book Value, and along with the other changes, the models were rerun. Conclusions based on the revised measures were unchanged.

A second concern was the procedure used to calculate the market risk measures. These were calculated using historical return series under the assumption of stationarity. Perhaps the risk characteristics ■ of the simple and complex groups differed en an ex post basis which woxild account for the observed difference in value. To investigate this possibility,' the market risk measures were recalculated at the end of 1973, 1974, and 1975 using the seventy-one most recent monthly obser- vations prior to the respective year-ends. Although there were a few anomalies in the results, a geaer.\l conclusion is that the two groups

did not differ significantly in terms of market risk measures for the

' L 4 J 27 ex post periods.

-23-

There are several possible explanations for the difference in value. One conclusion is that the difference is evidence of market inefficiency. Based on test resxilts, investors should have sold their portion of the more highly valued simple capital structure firms, reinvesting in com- plex capital structure firms, to obtain the same expected earnings stream at a lower cost. But while market inefficiency is a possible ex- planation, it seems unlikely that such large and significant differences In value could have persisted over the three year period observed.

To assist in providing an alternate explanation. Tables XIV and XV summarize, as of January 31, 1973, valuation data for convertible bonds and convertible preferred stock included in the sample. Although January 31, 1973 was near a stock market peak, few of the convertible seciflrities were selling at premiums. In fact, most of the convertible debt issues x;ere selling below book values. Although not shown, this disparity betv;een book values and market values became much greater in 1973 as Interest rates continued to rise.

Analysis of the issue dates of the complex securities indicated that a high majority were issued in the middle to late 1960*8. Empir- ically, it is known tliat conversion generally occurs within five to seven years fro^i issue date, or not at all. By the end of 1973, or perhaps earlier, it became obvious that any hoped for conversion was not forthcoming. Thus, for the test period, the market generally viewfed the complex securities as overhanging issues. . ......

To the extent there is a cost to the firm associated with over- hanging Issues, this cost would explain the observed difference in value. The complex firms were already more highly levered than the simple firms

-24-

and may seek a lower debt/equity ratio in the future. If equity is issued in an atteapt to nove toward a lower target debt level, the issue may only be marketable at a relatively high cost to the firm. If the target is achieved by calling the convertible securities, the cost of the required funds nay also be high. la sunmary, there are real costs associated with the loss of financing flexibility due to overhanging Issues, The market is not ignoring these costs.

Another anomaly in the results is the leverage difference between groups without a corresponding difference in market risk measures. This relationship is inconsistent with Hamada's argument that beta is a func- tion of leverage. The difference in leverage tended to increase from 1973 to 1975. As an explanation of the difference in value, the higher levered complex firms may offer a higher risk of bankruptcy. But this suggestion is not appealing, since ex ante bankruptcy costs are believed

to be small US]- " . i;.-.;c::.

In concluding this section, a statement seems necessary concerning possible measurement error in the independent variables. Since observa- tions on true earnings and growth are not available, it is known that ' parameter estimates for the valuation equations are biased and the :-:- measurement error will be impounded in the residuals. However, para- meter estimation was not a primary objective in this study. Unless there is a difference in bias between the simple and complex groups, and there is no reason to expect this to occur, the test results should be unaffected by the presence of measurement error. . ^

-25-

V. Conclusion

This study has attenipted to extand previous tests of the risk class model by examining the effects of complex capital structure. The major research finding was that, within a risk class sample, a group of complex capital structure companies was valued lower than a group of simple cap- ital structure companies. This occurred over a three-year cross sec- tional test period when there was little expectation that complex secur- ities would be converted.

Assiuning the theory is correct, the sample can be accepted as a "■■ homogeneous risk class, and assuming that the always present danger of measurement errors did not affect the results, two possible explanations for the results were suggested. One explanation, market inef ficiencyj is unlikely to have persisted over the test period. The other explana- tion, future coats associated with correcting capital structure to a lower target debt/equity ratio for the complex group, is a more likely explanation.

A limitation of the study is that convertible securities were eval- uated in a period when conversion was not expected. It would be inter- esting to repeat the tests in periods when convertible securities are selling at substantial premiums.

Methodologically, cluster analysis seems to provide a useful pro- cedure for obtaining a homogeneous risk class sample. The method pro- vides a useful alternative to the well-known industry and beta adjustment approaches.

M/B/151

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-27-

TABLE II

Shares Reserved for Conversion As a Per Cent of Outstanding Shares

515 Industrial Firms

>50% >40% >30% >20% >10% TOTAL

1963

1964

195 5

1966

1957

1963

1969

1970

1971

1972

1973

1974

1975

Nun±)er Per Cent of Total	1 .02	6 1.1	7 1.4	17 3.3	49 8.0	515
NuirjDer Per Cent of Total	1 .02	6 1.2	8 1.6	16 3.1	51 9.9	515
Number Per Cent of Total	2 .04	6 1.2	8 1.6	20 3.9	50 9.7	515
Number Per Cent of Total	3 .06	9 1.7	11 2.1	24 4.7	57 11.1	515
Hinrber Per Cent of Total	5 1.0	15 2.9	22 4.3	43 8.3	90 17.5	515
Nunber Per Cent of Total	8 1.6	18 3.5	29 5.6	53 10.3	112 21.7	515
Number Per Cent of Total	8 . 1-5	17 3.3	28 5.4	57 11.6	127 24.7	515 .
Number Per Cent of Total	12 2.3	21 4.1	44 8.5	83 16.2	162 31.5	515
Number Per Cent of Total	14 2.7	22 4.3	39 7.6	75 14.9	172 33.4	515
Nuirber Per Cent of Total	9 1.7	22 4.3	*3B 7.4	75 14.6	167 32.4	515
Number Per Cent of Total	9 1.7	20 3.9	39 7.6	78 15.1	175 34.0	515
Niimber Per Cent of Total	9 1,7	20 3.9	36 7.0	32 15.9	170 33.1	515
Number Per Cent of Total	9 1.7	21 4.1	34 6.6	74 14.4	171 33.2	515

-28-

TABLE III

SiOTinary Factor Analysis Statistic^ Alpha, Beta, M.S.E., and LEV-3

Correlation Matrix

	ALPHA	BETA	M.S.E.	LEV-3
	1	2	3	4
1	1.00000			-
2	-0.35347	1.00000
3	0.01813	0.40780	1.00000
4	-0.12980	0.30450	0.18031	1.00000

1.44159

0.82411

Eigenvalues .0.70545

0.00114

0.36040

Cumulative Proportion of Total Variance 0,56642 0.74279 0.74307

VARIABLE

1

• 2

3

4

ESTIMATED COMMUKALITY

0-823072

0.404411

; ,- - 0.762258

0.982558

FINAL COMMUNALITY

0.822933 0.40 3622 0.762050 0.982537

-29-

TABLE IV Market Risk and Other Characteristics of Sanqple

COMPLEX GROUP

GROUPING VARIABLES

FIRM NW-IE	^i	H	MSE 38.8	LEV-3 .883	' DIL. ? .13	: SIZE*
Amax	-.025	.711	1408
Greyhound	-.281	1.136	28.4	1.069	.35	1444
National Distillers	-.377	.703	30.3	.951	.12	966
Cluett Peabody	-,324	1.246	47,2	1.190	.15	316
Wayne Go s sard	-.273	1.119	63.3	1.180	.57	40
Fibreboard	-.029	1.194	73.8	1.450	.51	182
Monsanto	-.216	1.126	31.9	.750	.13	2236
Stauffer Chemical	-.275	1.210	35.3	.660	.14	578
Witco Chemical	-.389	1.636	48.2	1.253	.25	229
Lone Star Industries	-.072	1.640	55.9	.747	.18	449
Medusa Corp.	.085	1.369	51.6	.640	.17	143
Interpace Corp.	-.504	1.402	53.8	1.340	.37	158
Annco Steel	-.349	.987	30.5	.720	.15	2082
Crane Co.	-.208	1.234	44.2	1.540	.41	573
Cooper Industries	.007	1.511	80.7	1.160	.43	214
Otis Elevator	-.112	.691	29.8	.740	.18	572
' Scovill Mft.	-.191	1.488	44.3	1.160	.43	318
Singer	-.003	1.123	28.3	1.520	.26	1608
Fruehauf	-.118	1.255	48.7	1.150	.19	556
Eaton	-.078	1.549	40.3	.810	.13	947
Ainfac	.715	1.294	57.9	1.280	.20	560
Host International	.399	1.445	64.1	1.080	.15	82
GAF Corp.	-.544	1.223	63.5	1.202	.50	610
Copperweld Corp.	-.036	1.109	64.2	.718	.12	83
Interstate Brands	-.069	.524	68.8	.937	.14	98
GATX	.004	1.023	76.5	1.468	.11	864
Average	-.126	1.191	50.5	1.06	.25	667
Standard Deviation	.264	.291	15.96	.282	.14 •	620

* Book value of total assets for 1972.

-30-

TASLS IV Market Risk and Other Characteristics of Sample

SE-IPLE GROUP

GROUPING ^/ARIABLES

FIRM NAME	-^	1.428	MSE 84.8	LEV-3 1.415	OIL. % .03	SIZE *
Eastern Gas	,014	482
Sante Fe International	.525	1.885	83.4	1.189	.04	185
Domtrir Ltd-	.016	1.057	57.7	.376	.00	503
Stone Container	.192	.880	69.4	.649	.00	73 .
Union Carbide	-.432	1.073	16.9	.763	.00	3718
Koppers Co.	.080	1-028	44.1	.832	.01	470
Bristol Myers	-.175	.948	29.3	1.241	.05	2560
Ansul Co.	.310	1.054	97.8	1.061	.06	48
Marathon Oil	■ -.220	1.243	46.9	.655	.02	1514
Phillips Petroleum	.503	1.141	62.0	.647	.00	3269
Robertson <• .	-.174	1-050	75.4	.915	.03	133
Goodyear	.080	1.066	28. 3	.953	.03	3980
American Can	-.541	.714	25.6	.831	.05	1491
Continental Can	-.186	-830	34.5	.702	.05	1574
Carborundum	.102	1.188	52.8	.565	.06	308
Owens Corning	-.001	1.107	45.3	.588	.04	533
Hoadaille •. -■--	-.007	1-448	52.8	.993	.02	159
Honeywell	-.199	1-932	152.7	1.259	.06	2240
Texas Instr^jments	.037	1.240	41.6	.741	.06	534
A. 0. Smith	.335	1.314	41.7	.700	.06	302
ACF Industries	.182	.692	78.8	1.015	.03	179
Pullman	-.190	.917	35.1	.855	.03	509
H. K. Porter	-.340	.588	42.6	1.245	.00	151
G. C. Murphy ^ .	-.088	1.035	45.7	-464	.02	188
Kroger	-.349	1.062	43.4	1.117	.00	811
Servisco	.301	.834	102.4	1.172	.03	36

Average

Standard Deviation

-.009 1.108 57.346 .902 .03 1002

.273 .313 29.629 .253 .02 1191

* Book value of total assets for 1972-

-31-

ThHLF. V

Estiniates From Model f4) 52-Firm Combined Sample

Year a_

1972 64.073

Standard deviation 78.116

T statistic .82

R'^ .85

^1	^2
16.138*	1.477*
1.273	.577
12.67	2.56

1973		76.801	12.269*	1.616^
	Standard deviation	98.911	1.285	.815
	T statistic R	.45	9.54	1.98
	.78
1974		68.933	7.685*	2.695*
	Standard deviation	54.666	.581	.623
	T statistic	1.26	13.21	4.32
	r2	.92

* significant at <_ .05

-32-

TABLE VI

Kodal (4) Plot Jtaolduals 7S. SatXaAtmA ?

Petroieur

, Brisfol Myers

l?72

Qsady*

till ;oo Lcog

I t I I I

I I J I I I

l*)0 woo nV> 3MO 330d *0OO 4300

t

Pefroitfum

200«t
isool
1000 1
SO»E
01		T	♦ T f» f » f
1

Xn3^rt*rf»enfa

T f

I'? 73

303 1000

CacfAv^

f

Onto** Corbxle

£ I 1

1,300 ^000 1300 iflOO K30 4000 4300 30OO

% •^

^

Pafroleum

i?7¥i

6i\ r o (^

Car b«d«

JT * 1 : Ko ^c-'^j 3;co »■»■>*

Year

-33-

TABLL VII

Estimates From Model ' (4) Reduced 40-Finr. Sample

1972

1973

1974

	19.160	15.671*	.986*
standard deviation	24.179	.878	.451
T statistic	.79	17.83	2.19
. r2	.93
	-17.370	12.536*	2.381*
standard deviation	33.477	1.088	. 1.026
■ T statistic	.52	11.52	2.32
r2	.91
	-22.654	7.807*	3.437*
standard deviation	29.228	.677	.581
T statistic	.78	11.53	5.91
r2	.93

* significant at < .05

-34-

TABLE VIII

Estimates From Model {5) CoirJjined 52-Firm Sample Dependent Variable: (x'^/V-tD)

Coefficients of

Constant Size Growth Reciprocal

Year a'-=p '^'o" ~^o'' ^'2^ "^2*^ °^ Constemt

* significant at < .05

1972 .049* 1.006* .045 20.408

std. dev. .004 .339 .033

T Stat. 12.36 2.97 1.35 R^ .169

1973 .069* 1.105* - .003 14.493

std. dev. .008 .435 .075

T Stat. 9.09 2.54 - .04

R^ . 117 . . • ..

1974 .088* .749 .046 . 11.363

std. dev. .010 .484 .076

T Stat. 8.73 1.55 .60 r2 .049

\

-35-

TABLS IX

Estimates From Model (6) Combined 52-Fim Sair^ile

Year

1972

standard deviation T statistic

^0	^1	^2
306	11.693*	1.285
247	3.966	.942
24	2.95	1.36

	r2	.188
1973		.244	8.836*	1.609
	' standard deviation	.228	3.245	1.041
	T statistic R^	1.07	2.72	1.55
	.179		1
1974		.398*	4.533*	1.138
	standard deviation	.135	1.384	.804
	T statistic	2.94	3.28	1.42
	r2	.204

* significant at < .05

-36-

TAELE X

Modal (5) Plot lUsLdua^j vs. Ssdeatad Y

/17Z

\

/

I 1 1 I !•• I ( < I I I I I t I )

O.'JiU C.O'.*^ J.usO O.ia*. O.ii.-O 0.073 O.^dO O.iJi)'

m3

t 1 1 Q.oe O.J/	1 1 1 O.lO	1 1 1 0.11 o.i:
■•-	\'=]l'i

-36-

TAELE A

Wximl (5)

1111

C.J*.:, O,«i0 O.ia*

) I I I ) )

t I I I I r

O. 13 0.11 0, IZ

[mT

-27

TABLE XI

»iod*l (6) Plot RaalduaLs vm, gsf Irjitad Y

Teta^

/f72 I

>■ • .

O.JI .

A - • -

tC .••

' ♦

ms

_Inst rumen Is

I I r I t

i.o 1.: t.'

« Tr«o3 .rii'.lriunriit'^ ' ' ' '

■ y'S?..

• % .•*'-lS».i

/?7^

6rl^fol My»rC'

frlf.-t^on

)l .< f'ofle,

GlolK"

5. J

-38-

TABLE XII

Test for Difference in Mean Residuals Model (A) - 52 Finos

Source	Suia
of	of
Variation	Squares
Time	cO
Capital Structure	910,586.6
Interaction	41,304.1
Error	2,680,720.5

D.F.

2

1

2

150

Mean Square

.0

910,586.6

20,652.1

178,714.7

h:

iC

F* 2,150 F* 1,150 F* 2,150

Probability of F* 0 .9999

5.095 .116

.0241** .8909

Mean Residuals

Simple 76.403 Complex -76.399

Test for Difference in Mean Residuals Model (4) - 40 Firms

Source of Variation

Time

Capital Striicture

Interaction

Error

Sum

of Squares

.0

113,114.2

2,853.6

1,525,467.2

D.F.

2

1

2

114

Mean Square

.0

113,114.2

1,426.8

13,381.3

H'

H

H"

F* 2,114

F* 1,114 F* 2,114

Probability of F* 0 .9999

8.453 .107

.0045** .8987

Mean Residuals

Simple 30.702 Complex -30.702

** Significant at £ .05

Ul.

-39-

TABLE XIII

Test for Difference in Mean Residuals Model (5) - 52 Firms

Source of Variation		Sum of Squares	D.F.	•	Mean Sqiiare
Time Capital Structure Interaction Error		.0006 .0063 .0010 .1508	2 1 2 150		»0003 . .0063 .0005 .0010	'■.■•-
		■	Probability of F*	Mean Residtials
*	-t	F* 2,150		.7210		. ■• ■ •-■
	-\	F* 1,150 -	6.3	.0128**	Simple Complex	-.007 .005
	Hi	F* 2,150		.6253

Test for Difference in Mean Residuals Model (6) - 52 Firms

Source of Variation

Tine

Capital Structure

Interaction

Error

■4

1 2

1

H

h:

Sum of Squares

.0

1.705

.116

23.308

F* 2,150 F* 1,150 F* 2,150

D.F.

2

1

2

150

Mean Square

.0

1.705 ,058 .155

Probability of F* .9999

10.0

.0013** .6936

Mean Residuals

Simple .105 Complex -.105

** Significant at <. .05 *** Yield formulation

-40-

TSBLE xrv

Convertible Debt

Bcok Market Conversion Value* Value*. Price

Common Price

Conversion

Value*

Greyhound

6 1/2 's ld90 ■

Nat' 1 Distillers 4 1/2 's 1992

Fibreboard

4 3/4 's . i993

••;' ' 'V !,-. i...

Stauffer Chemical 4 1/2 's 1991

Witco Chemical 4 1/2 's 1993

Lone Star
5 1/8 's	1993
Medusa
5 3/4 's	1998
Crane Co.
5's	1993
5's	1994
Otis Elevator
5 1/2' s	1995
Fruehauf
5 1/2' s	1994
Amfac,.-.-. >••,	". '• -1 ' •
■5's '■'"■■	1989
5 1/4's	1994

$68.1 $68.6 $18,375 $17 $^3.0

$60.1 $45.2 $25.02

$19.7	$14.6	$31.25
$35.2	$32.4	$53,50
$15.0	$14.0	:• '^ ' ' ' $50.00 . ...I -^
$28.7	$28.4	$26.00

$ 4.9 - $ 4.9 $35.00

$18.1 $16.8 $25.00

$34.8 $32.3 $28.75

$50.0 $52.5 $46.50

$60.0 $49.9 $46.25

$15.75 $37.8,-:::vi

i ■-

$17,375 $11.0 :

$44,125 $29.0

$22.75 $ 6.8

$20,875 $23.0

$33.50 $ 4.7

$15.1 $35.0

$13.1 $30.5

$35.7143 $43.67

$20.50	$14.8
$20.50	$24.tf
$42.50	•fj';/'.-., ■ $45.7
■ ■*■.	;::J:; Ii: 'i
$31.25	• $4Qi.-5
$26,625	$11.3
$26,625	$21.3

* Millions of dollars

■r^.i .

-41-

TABLE 3C7

Convertible Preferred Stock (Millions of dollars) Total Market

Conversion Veilue

Amax $1 preferred

Cluett Peabody $1 preferred

Wayne Gossard

Monsanto

Stauffer Chemical $1.80 preferred

Witco Chemical $2.65 preferred

Interpace 5% preferred

Lone Star $14.50 preferred

Armco Steel $2.10 preferred

Cooper Ind. $5 preferred

$2.50 preferred

Scovill

Eaton

Amfac $1.00 B preferred GAF $1.20 preferred GATX $2.50 preferred

$ 73.2	$	58.9
$ 21.8	$	14.2
$ 7.3	$	7.0	,
$ 140 . 2	$128.1	: •-*' ' ■■ '-. \
$ 17.2	$	17.3	■' ■ -.
$ 15.6	$	15.5	:^:V-K.r -•;
$ 23-3	$	15.7	J.- .. •" ,w
$ 13.6	$	12.0	—•"■■■- ■' ■ ■ •
$123.6	$	79-5
$ 16.8 $ 27.7	$ $	14.6 ^2.2	■; • . ."'■■ i:
$ 59.2	$	60.1	\- ■■ - •
$30.1	$30.5	•>
. $ 17.7	$	14.7	. .' ■": r - :
$ 74.1	$	69.4	'.' *' -, '•: ■
$ 38.7	$36.9

-42- Footnotes

1. For example, see Kanada (12, 13), Stiglitz (27), Rubinstein (24), Merton (17), and tliller (18).

2. For instance, see Boness and Frankfurter (4).

3. MM explain in both (19, fnt. 37) and in (21, p. 357) that this issue was avoided in their empirical tests since they had few convertible issues in their samples.

4. Soldofsky (26) estimated $12.4 billion of convertible bonds and $17,8 billion of convertible preferred stock was outstanding in 1969. From 1970 to 1977 new issues of convertible bonds ranged from a high of $3.7 billion in 1971 to a low of $.5 billion in 1974. New issues of nonconvertible bonds ranged from a low of $20.1 billion in 1973 to a high of $40.4 billion in 1975. New issues of preferred and common stock ranged from lows of $1.4 billion

and $4.0 billion in 1970 and 1974 respectively and highs of $3-7 billion and $10.7 billion in 1971 and 1972 respectively. Standard and Poor's Trade and Securities, Statistics, Banking and Finance, July, 1978, p. 27.

5. For a good discussion of the concept, see Hubbard (14).

6. Following Fama and Miller (9, Chp. 4), a frictionless market is assumed in terms of infinitely divisible securities, costless information, the absence of transaction costs and taxes. Further, all financial arrangements are equally available to individuals and firms; individuals and firms are price takers. Finally, investors are assumed to protect themselves from dilution (expro- priation without compensation) by means of subordination rules, pre-emptive issues, and other "me first" rules.

7. This tradeoff is explained by Onsi and Frankfurter (22) who also develop a

new method of calculating earnings per share based on the opportunity loss ' concept.

8. This point is discussed using the states of the world model in (9, pp. 178-181).

9. See Poensgen (23, pp. 91-94) for these empirical results.

10. Modigliani and Idler (19, p. 291) and Soldofsky (26, p. 61) offer this explanation.

11. The tax, savings from interest on convertible debt \-rLll be lower than that from interest on straight debt.

12. An example of a direct test is that of Boness and Frankfurter (4), where the vector of disturbances for each firm is tested for homogeneity.

13. The market risk measures are explained below. The nineteen accounting variables listed in Appendix 2 were used. Both raw scores and factor scores were examined. Further details concerning the clustering procedures can be found in (10).

14. On average, the 515 firms are more risky than firms included In the Standard and Poor's index, as evidenced by an average beta of 1.194, but the average monthly return is also higher than the index. In regard to leverage, the most prevalent feature is the importance of current liabilities as a contributor to total debt, a fact noted by MM in (21) .

15. The model used is of the form:

Zj = ajiFi 4- aj2F2 + . . . + ajm^m + djVj (j = 1, 2, . . . , n)

where each of the n variables is described linearly in terms of m common factors and a unique factor. See Harman (31, p. 15).

16. Test for differences in means were done using the ANOVA model at the 1% significance level.

17. However, if convertible securities are excluded from debt, the difference is not significant. .- . - • *

18. Test dates are subsequently referred to as 1972, 1973, and 1974. The 52-firm sample had no major capital structure changes during January for the three- year test period.

19. Sources of price data included:

Moody's Bond Record, Moody's Investors Service, Inc. Bond Guide, Standard and Poor's Corporation " Stock Guide, Standard and Poor's Corporation Barron's, Dow Jones and Company, and Daily Stock Price Record, Standard and Poor's Corporation

Financial s'tatement data was obtained from:

Microfiche, by Disclosure, Inc.

Moody's Industrial Manual, Moody's Investors Services, Inc.

Moody's Transportation Manual, Moody's Investors Services, Inc., and '

CO>£PUSTAT.

20. This was true for several reasons. First, current liabilities comprise a sub- stantial portion of total firm debt. Second, about one-half of all debt issues are privately placed and are not traded in the market. Third, the market prices of most debt issues did not deviate greatly from par during the test period.

21. A summary of the calculations is provided in (10), Exhibit 4-26.

22. Of the independence, normality and constant variance assumptions, the most important. is independence. Given this design it is known that the test for differences in means is relatively robust to departures from normality and equal variance assumptions (25). In regard to independence, as possible con- cern is that residuals for the same firm observed at three points in time are correlated. To the extent this is true, the two-way design has the effect of artifically increasing the sample and the probability of Type-I error. Vfhlle a more elegant design could be used to exploit any expected correlations, in- stead, simple one-way analyses for individual years will be used to supplement the two-way analysis. If inconsistencies result, alternate designs can be explored.

-44-

23. Residual plots for the reduced sample showed a reduction in the severity of both the heteroscedasticity and outlier problems. Only two possible outliers remained, Pullman (+3 s.d.) in 1972 and Amfac (-3.5 s.d.) in 1974.

24. The absence of interactions implies that the main effects are meaningful measures of the differences between groups.

25. One-way analyses were also run on residuals from model (4). For the 52-firm sample, capital structure was significant at 5% to 15% levels in the three years. For the 40-firm sample, significance level were from .5% to 5%. This provides evidence that the results of the two-way analysis are not greatly influenced by any correlations among a specific firm's residuals over time.

26. Miller (18) has suggested that the previously assumed tax savings'" from debt may be substantially overstated. This should not affect the results of the present study as long as there is no differential bias in the calculations for the simple versus complex groups.

27. The anomalies were significant bo differences for 1973 and 1974, and a dif- ference in b-, that was significant at the 9.3 percent level for 1973.

-45-

Appendlx 1.

Arbltraga iqi the Two Period Risk Claas Model Complez Capital Structtire Case

In the two period tnodel,* the flrti makes production declaions at period - 1 that will yield probability distributions of net cash eam«> . Ings at period - 2 to be paid to security holders at that tine* 'The role of the capital market is to establish prices for such securities at period - 1. Let us consider the icarket values of three f IrmB— one unlevered, a second with straight debt as part of its ca|>lt«X. struer'>: turef and a third whose debt can be converted into a specif 1«1 percent-;- age y of the number of coomon shares Issued at. period - 1 at . the option of the holder at period - 2. It is presisaed that the market at period - 1 anticipates. the sans period - 2 net cash earnings for the "^"'

three firms such that X ^^v " ^f?-) " ^ f2") " ^(.T\* *^®^® '^® subscripts mean complex, levered and tmlevered respectively. In the ensuing dls- cusslon, the following notation is used, with subscripts as above: '-

'i-rV ■ total niarket value of the firm at period - 1« -■ ■.^■;'- ;'.i-;''-^'/ ^ S ■• total market value of coaaaon shares at period - 1, /^;! . B - total market value of debt at period - 1. . _ -/.■■■ ""•:.' f-'-'R "total pajraentes to debtholders at period - 2.\ •:.l,;,,;.'j.^^.a

Let us now consider the market value of a percent investments in eacb-y-;,

.firm. .•■•..

The market value of an a percent investment in the unlevered firm

«Vi)""'u(i) -::-m

•;^

< -

i^i:

!^^...

'.■■^■i <i/-.;:0-

' '*The example asstuoea a perfect market (see footnote 6.) and no taxes. Notation follows Fana and Miller [9, Chp. A] . - . ., ' ' -- '

-46-

asd the period - 2 return Is:

^ «\(2) "«^2) <9>

■''■'''"■ ■ " •'-■; ■■ • - ■'" u

An Investor could obtain the same return by purchasing a percent of

. ■ , r *, ?-..

the stocks and bonds of the levered fins. In this case, ignoring taxes,'

■ -^ S'.i:zy;,i/ ;iv, nj;

the market value of the Investment would be

v-^.U/-

»•- Sj

and the period - 2 return would be

^''"'- «fX(2) " \(2)3 -^ °^(2) - « ^(2) ' -> ^^ - --^^ -.XU). ,^

■ - ■ . ', , .- , J. .

Similarly, an investor in the complex firm could obtain the same return

''■*''■ ■ ' „ . - s. - ...

by purchasing a percent of that firm's stock and convertible bonds, and the period - 2 return will not depend on conversion.* The market value

of this investment would be

■"'""■ '" " ■ ■■ '* ■" '■ ""' " "" ' ^i ::::',:. ..ire

^■- - -■■- ■'■ ■■-"■' v-Wl,' .;: ,-ri;:J.- >••-::':-;;....• -^\ ^.{- ^n^s^..

If conversion does not occur, the period - 2 return will be computed as in Cll) above and would be -'■■ j./ ■ ^;v . -\ - -.; ::r\.-^ ,vnij ???•; ^'r -i

^n . ,«I^2 - \(2)^ -^ " \C2) -- ° ^(2) . , . . ^ , .^ ^ ^^^ . , ^"^ If conversion does occur, the investor will receive

*Conversion will occur, if, after equilibrium prices are established, the price associated with the "option" portion of the security is such that the expected return from holding the "right" in the original form, rather than common stock form, vanishes. :,:

-47-

• V .°iX(2) - y ^(2)^ + " y ^C2) " ° ^(2) ^^*>

The two components of the left side of (14) refer to the return appli-: r

cable to the old shares plus the return applicable to shares received . : .

from conversion. .' ":' iL.l.t j^

Kov consider investor actions if the market value of the unlevered

firm is higher than the other firms such that V > V. " V . In this -vt;

u D c

case, it is clear that no investor would want to hold shares in the tin- levered firm because the same return could be obtained at less cost hy:. ». purchasing a combination of debt and shares in either of the other firms. Thus, arbitrage opportunities would prevent the unlevered fixna f r on- ;:. ,>;.>!' selling at a higher price than the other firms. \^,.:i - »^ Vl ; The siore important arbitrage arguments have centered around actions

of o S. shareholders in the levered firm where V, > V . The share- ;„'i b b u

holder's period - 2 return will be -.; a ■■ .ra? j;.;.v.i

°t^2)-\(2)^ . i^^^

■ • ■ •■ -■ .. : .;-. : ,->, -.oirj

In this case, the shareholder owning a S, has the opportunity to tin- do the leverage by selling his shares and purchasing a shares in the unlevered firm. The purchase would be made with funds obtained from the sale of the levered shares and personal borrowing. Since the capi- tal market is perfect, the Investor must be able to borrow a B, ,,v on personal account, by promising to pay lenders o times the levered firm's bond payments at period - 2. The period - 2 return will be ^^"^(2^ ~ ^(2^^* ^^® same as (15) above. But since V, > V , the return from a V can be obtained at less cost, and no investor would choose to own S, .

D

-A8-

Now consider the case of V > V, > V for an a S shareholder In

c b u c

the complex firm. A variety of options to achieve the same return at a

lover cost are available to this Investor; we will consider Just one

at this time. ....;;

.V One possible action for th^ complex firm's shareholder would be to

sell his a S o-,7nershlp and buy a S ^ »= a V o^marshlp in the unlevered ,

firm, financing part of the purchase vith personal borrowing. Again,

since markets are perfect, the inv>istor must be able to borrow a B ,^k ,.

on<piersonal account, promising to rep^y a R .„•, or o y X^„v at period 7-. 2,

depending on conr/srsion. The net period - 1 cost to the investor is

<»[V /,x ~ B ,,v), and his return on V will be afX,_. - R ,_.] or .... "■ uCl) c(l) ' u ' (2) c(2)'' .-jx-.ti :

o[X^_i::^- y'X>.2\]» depending on coni'ersion. This is the same return that would be achieved by holding a S ,.,.. But since V < V ..this re- . turn can be achieved at a lower cost by investing in V . Thus, the In-

U ": i

dependence of capital structure and value continues to hold for the com- plex capital structure case. Vs-'^

•*n'i* ' i"*,'} y V c*; ".'"' ' c*7'"c h''i^ v"

,vii.=5^ ^.tdi .^;I

an:; -fi. s:::.cvla -: ^.;^.ecf!.-i"i ;i:.f tv;^.!; •".■... ^ y-: ^ :'r-^vvii ^^j ..!>

■?■ .-i

-A9-

Appendix 2«

Accounting Risk Measures Used in Clustering Routines

Satloa

Ccilculation*

1. Dividend payout Z DATA (21, I) / E DATA (20, I)

2. Capital expenditures/Total Assets Z DATA (30, 1) / I DATA (6, I)

3. Capital fexpenditures/Net Income I DATA (30, I) / Z DATA (18, I)

4. Average asset turnover

5. Average profit margin

6. Senior d^t/Tot2d Assets

7. Long term debt/Conanon Equity

8. Retiirh on Common Equity

9. Return on Invested Capital

10. Current Ratio

Z DATA (12, I) / E DATA (6, I) „;■-

Z DATA (18, I) / Z DATA (12, 1)

Z (DATA (9, I) + DATA (10, I)) / Z DATA (6, I)

Z DATA (9, I) / Z DATA (11, I)

Z DATA (20, 1) / Z DATA (11, I)

Z (DATA (18, I) + DATA (15, I)) /

Z (DATA (9, I) + DATA (10, 1) -f DATA (11, I)) -

Z DATA (4, I) / Z DATA (5, I) . '

ferbwth Rates**

11. Total Assets

12. Operating Earnings

13. Met Income

14* Earnings Per Share (Primary)

15. Operating Earnings Per Share

16. Capital Expenditxires

17. Retvurn on Comnion Equity

18. Retxim on Invested Capital

19. Dividends Per Share

Variable Numbers

6
13 -	14
18				«
58
13 -	14 / 25
30
20 /	11
18 +	15 / 9 ■»■	10	+	11
26

* Nvcabers refer to COMPUSTAT variable numbers ** Geometric growth rates were calculated as follows:

. - n -^

gmg » emtilog Z log (1 + g^) = t=>l

- 1

n

-50-

REFEPvSNCES

1. Barges, Alexander. The Effect of Capital Structure on the Cost of Capital, Prentice-Hall, 1963.

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3. Black, Fischer andMyron Schol^.s. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, May-June 1973, pp. 637-654. - ..'.

4. Boness, James A. and George !I- Frankfurter. "Evidende of Non-Homogeneity ■; of Capital Costs Within 'Risk Classes'," Journal of Finance, June 1977,

pp. 775-788. •-:■ ; _ .;, .'....r; vA ,i.

5. Chen, Andrew "fl. Y:.'"A Model 6f Warrant Pricing in a DjTiamic Market," .-.v' 5 Journal of Finance, December 1970.

^-.T-j;-.^ /.' ■"••;^ '•-!.' ;:■ "oi:/;-^.-, .^

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15. Johnson, Robert W. Financial Management, Fourth Edition, Allyn and Bacon,... 1971.

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-51-

17. Herton, Robert C. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, May 1974, pp. 449-470.

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nOUNDf

t\^.

3-9-'' ,