William L. (William Leo) White.

The debt-equity ratio, the dividend payout ratio, growth and the rate at which earnings are capitalized: an empirical study online

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SCHOOL OF INDUSTRIAL MANAGEMENT



COPY I

The Debt-Equity Ratio, the Dividend Payout Ratio,
Growth and the Rate at Which Earnings Are
Capitalized: An Empirical Study
52-64
William L. White




MASSACHUSETTS

INSTITUTE OF TECHNOLOGY

50 MEMORIAL DRIVE

CAMBRIDGE 39, MASSACHUSETTS



MASS. m)^
NOV 10 1"P4



This working paper is one of a set of publications by the School
of Industrial Management at M.I.T. reporting on the research currently
being pursued by its staff. This investigation was originally sub-
mitted as a thesis as partial fulfillment of the requirements for the
degree of Ph.D. in Industrial Management at M.I.T. Since it will form
a continuing part of the research of the author, who is now an Assistant
Professor of Finance , these first results are being published with the
hope of stimulating comments and suggestions.



COPY I

The Debt-Equity Ratio, the Dividend Payout Ratio,
Growth and the Rate at Which Earnings Are
Capitalized: An Empirical Study r
52-6U
William L. White



MflSS.



INST. TZCK.

W0V19 ic"-'

DEWEY USff/lRy



Most grateful thanks are extended to the Harold Stonier Foundation
and the American Bankers Association as well as to the Ford Foundation's
grant to M.I.T, 's School of Industrial Management for Research in Bus-
iness Finance for the generous support which made this work possible.
Professors Eli Shapiro, Edwin Kuh, and Daniel M. Holland also deserve
thanks for their guidance and assistance.



• f



>L^' i";^-^^




nhfi4ty



CHAPTER 1
INTRODUCTION

One of the most important problems facing a financial manager is that
of choosing from all the available investment projects that set whose
acquisition will enhance the value of the firm. That is, he must select
that set of proposals whose elements have income streams with a capitalized
value greater than their cost. Conversely, his problem is to choose those
projects whose cash flows, when discounted at that capitalization rate,
have a positive present value.

This problem can be separated into two parts - the determination of
the cash flow associated with each project and the discount or capitaliza-
tion rate to be used in computing the present value of these cash flows.
The major concern of this thesis is not with the former but with the
latter. Its purpose is to identify the factors determining the capitaliza-
tion rate and, more specifically, to separate these factors into those
associated with the physical assets in which the firm invests and the in-
come streams they generate, and those having their origin in the method
used to finance those assets.

If it would be possible to ascertain what forces influenced the rate
at which income streams to a specific firm were capitalized and the
mechanisms through which these forces acted, a major step would have been
taken toward the solution of the capital budgeting problem. Thus, this
thesis has as its focus the capitalization rate. It is meant to be both
a theoretical and empirical study, drawing on the relevant parts of



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economic analysis to construct a logical and (hopefully) relevant model,
and relying on statistical tests to determine its real world validity.

Much has been written concerning the manner in which firms oupht to
make investment decisions. While there is some difference of opinion as
to how the problem is to be formulated, there is widespread agreement on
the need for a required or cut-off rate of return. Thus, although the
linear programming approach to the capital budgeting problem was developed
primarily to deal with multiperiod outlays and the analysis of sets of
investments, and the straightforward computation of present values
usually considers investments as individual ventures, both formulations
of the problem require a rate of return as an input.—

This required rate of return or cut-off return for investment
projects is the weighted average cost of the debt and equity funds employed
to finance the project. Clearly, if the project generates a rate of re-
turn in excess of the cost of funds to finance its purchase, the value of
the firm will be increased. Projects yielding less than their cost have
the opposite effect. Therefore, the implementation of capital budgeting



i/see Weingartner, Martin, Mathematical Programming and the Analysis
of Capital Budgeting Decisions , Prentice-Hail, 1963; ~, Chames , A.,
iTal., ''Application of Linear Programming to Financial Budgeting and the
Costing of Funds," Jo urnal of Business , January, 1959, for a presentation
of the linear programming vITw ; the discussion in The Capital Budgeting
Decision by H, Bierman, Jr.. ^nd S. Smidt, Macmillan, 1960, is represent-
ative of the analysis of independent projects with single period outlays.



- 3 -

theory requires a knowledge of how this weighted average cost is
determined and what its magnitude is. For the individual firm, the
crucial problem is isolating the effects on the capitalization rate of
actions and variables it can control. Specifically, the important ques-
tion is whether the financial mix employed affects the weighted average
cost of capital, or whether this average is independent of the mix and
solely determined by the kind of physical assets in which the firm in-
vests. That is, given the type of assets in which the firm invests, is
it possible for the management of a firm to make a set of financial
decisions which will influence the weighted average costs of the debt
and equity funds employed by them? Restated in even another way, is
there any such thing as an optimal debt-equity ratio or an optimal
dividend payout policy? These are the questions to which this thesis
is addressed.

Several studies have already been undertaken with these questions
in mind. They have been both empirical and theoretical. The theoret-
ical work of Modigliani and Miller^^ has shown that in a world with risk-
less debt, no growth, and no taxes, the financial managers cannot in-
fluence the weighted average cost of capital by altering their debt-equity
ratio. The average cost of capital in their model is independent of
financial structure. In this thesis, the assumption of riskless debt is
rejected in favor of a debt instrument which has associated with it some



>)



i/Modigliani, Franco, and Merton H. Miller. "The Cost of Capital,
Corporation Finance and the Theory of Investment," American Economic
Review. Vol. XXVIII. June, 1958, pp. 261-297.



/•



risk for both issuer and acceptor. These risks are developed in
Chapter II. The introduction of these risks creates a model in which
there is an optimal debt-equity ratio in that there is now a debt-equity
ratio which minimizes the weighted average cost of debt and equity.

As soon as the phenomenon of growth is introduced, there is another
financial decision which may influence the value of the firm. It is the

portion of earnings paid as dividends. Two views have been advanced con-

. 3/
ceming the importance of this variable. Miller and Modigliani— have

presented a model in which the value of a finii is independent of the

dividend payout rate chosen. This may be alternately stated as showing

that the dividend payout ratio does not influence the rate at which

earnings are capitalized. Others, notably, Gordon— and Lintner,— have

expressed a quite different view - one which does involve a relation

between dividend payout ratios and the value of the firm. For reasons

developed in Chapter II, this latter view is adopted in this thesis. In

addition to hypothesizing that the dividend payout affects the capitaliza- ^^j

tion rate, a variable is introduced in an attempt to account for the effect

of the difference between the personal income tax and the capital gains tax.



I'^Miller, Merton H., and F. Modigliani, "Dividend Policy, Growth and
the Valuation of Shares," Journal of Business , Vol. XLIX, September, 1959.

I'^Gordon, Myron J., "The Investment, Financing and Valuation of the
Corporation," Homewood, Illinois: R. D. Irwin, 1962.

l^Untner. John, "Dividends, Earnings, Leverage, Stock Prices and the
Supply of Capital to Corporations," 72ie_ Review of Economics and Statistics.
Vol. XLIV, August, 1962, pp. 2U3-269.



- 5 -

With these variables we construct a model for the capitalization rate for
earnings having three terms which, taken together, imply an optimal divi-
dend policy.

Thus, our interest in the rate at which the earnings of a firm are
capitalized arises from the desire to be able to implement the theory of
capital budgeting. We are interested both in the magnitude of the
capitalization rate and the extent to which it can be influenced by
financial decisions. With these goals in mind, a model is constructed
which specifically incorporates the influences of the risks which are
thought to be associated with debt as well as the advantages and dis-
advantages of dividend payments.

Once the model is developed, statistical tests are undertaken to
assist in assessing the validity of the model as well as to provide
estimates of the values of the parameters. These estimates are then
to be used in the determination of optimal policies for debt and divi-
dends. The first of these tests is a cross sectional analysis of the
firms in five different industries in each of the fifteen years between
19U6 and 1960 inclusive. In these tests the equation specified by the
model is estimated for each industry in each of the years. These tests
show the model "fits" the data well but indicate the colinearity in
part of the data makes it impossible to split the influences of debt and
dividends into the separate parts necessary for the determination of
optimal policies for these variables.



- 6 -

That is, as originally formulated, the total influence of debt is
composed of one element which causes the capitalization rate to fall as
the debt-equity ratio is increased and one which makes it rise. At low
debt-equity ratios the first influence is thought to be the more important
while at higher debt-equity ratios, the force of the second influence pre-
dominates. This means that at some intermediate debt-equity ratio the
combination of the two forces has its minimum. As it turned out to be
statistically impossible with the chosen formulation to split the total
force into its two components, it was also impossible to determine em-
pirically optimal strategies under the assumption that both forces ex-
isted in reality. That is, the inability to partition the total force
into the hypothesized components was thought to be derived from problems
with the data (strong colinearity) and perhaps from the exact way the
equation had been specified but was not taken as necessarily implying
that the separate forces did not exist.

However, it was possible to estimate equations containing only one
term for debt and one term for dividends instead of the two hypothesized
in the initial structure. While the estimates from these latter re-
gressions are of little use in determining optimal debt and dividend
policies if the originally hypothesized influences are thought to exist,
they still are of some interest. They can be used to test whether the
capitalization rate is at all influenced by the debt-equity ratio or the
dividend payout ratio chosen by a firm. A statistically significant re-
lation between the capitalization rate and either of these variables
would imply that capitalization rates were at least not independent of
debt or dividend policy.



'-.•■>



- 7 -

When these equations containing only one term each for the influence of debt
and dividends were estimated it was found that in only a minority of cases
did these two variables significantly influence the capitalization rate. It
was also found that a variable introduced to estimate the influence of the
differential between the income tax and the capital gains tax did not have
a constantly significant slope coefficient. Most of the explanatory power
of the model came from a growth variable which was originally introduced as
part of an attempt to adjust short-run expectations to long-run expectations.
It was also found that rapidly growing firms had higher capitalization rates
than slowly growing firms. According to the original hypothesis, the cap-
italization rate, defined to be the ratio of dividends per share to price per
share plus the growth rate of dividends, was independent of the magnitude of
the growth rate. It was hypothesized that higher growth rates would imply
share prices enough higher to assure that the ratio of dividends per share
to price per share plus the growth rate of dividends was the same for firms
equivalent in all other respects. These cross section regressions indicated
that as growth rates increased, prices did not increase enough to keep the
capitalization rate constant, and seemed to imply that rapidly growing firms
had higher capitalization rates - lower prices - than the original model
predicted.

Summarizing the results of both of the sets of cross section regressions,
it was found that the managerial implications which had motivated the thesis
could not be extracted from the data, that there was little influence on the
capitalization rate for any debt and dividend terms and that growth seemed the
most important variable determining capitalization rates.



- 8 -

Having been unsuccessful with the estimation of the parameters of the
original model, but suspicious of the lack of results, it seemed wise to
examine the statistical properties of the model more closely. The residuals
computed from the estimated equations were the object of immediate interest.
Autccorrelated residuals, the plague of time series analysis, have their
counterpart in cross section analysis. In cross section analysis the problem
is that each firm being studied may have associated with it a particular
unexplained effect which is present each time a cross section is estimated
using that firm as a data point. This means that the error variances in
each of the cross sections have common components arising from these firm
effects. These effects when present and not specifically estimated, create,
among other things, biased slope coefficients. A tentative test showed ev-
idence of such influences associated with most of the firms which were
included in the study.

Considerable theoretical interest has been shown in the estimation of
equations containing firm effects, but due to computational difficulty,
little empirical work has been possible, A method of specifically estimating
firm effects which eliminates the biases introduced when they are ignored
has been developed by A, H, Carter.— He has shown that an adaptation of
the original hypothesis which includes the "firm effects" by introducing
dummy variables, one for each firm, will lead to unbiased estimates of
slope coefficients and error variances. The availability of these relatively



—'^Carter, A. H, , "The Estimation and Comparison of Residuals Regressions
Where There are Two or More Related Sets of Observations," Biometrika ,
Vol, 36, 1949, pp. 26-46,



- 9 -

new and untried statistical techniques together with the computational ability
of the IBM 7090, and the evidence of the potential usefulness of such an
analysis in this study, lead to the adaptation of the original cross section
hypothesis and to a test which pooled the annual cross sections for an
industry into a single regression estimating the influences of debt, dividends,
and growth along with a new set of variables, the firm effects.

As there was no reason to believe that the effects of the colinearity
encountered earlier would be diminished by the introduction of firm effects,
the analysis included only one term each for debt and dividends. This meant
that although the equation had better statistical properties than the original
cross sections, it was like the second set of cross section regressions in
that it would produce few managerial implications for debt and dividend
policy. This failing of the new formulation was not considered critical
as there was more concern that the earlier cross sections had shown no
influence of debt and dividends at all, than that it had been impossible to
split these influences into two parts. Hopefully, this new approach would
imply at least some influence of debt and dividend policies on equity
prices. This hope, and the implementation of an interesting statistical
tool, created the interest in the pooled regressions.

Initially three hypotheses were to be tested. First, were there
significant firm effects and did their inclusion alter the earlier slope
coefficients; second, was growth per se still important; and, finally, could
debt and dividend policy be found to influence the rate at which earnings
were capitalized?



- 10 -

Significant firm effects were found. The significance was far beyond
the ,001 level. Also, the slope coefficient for growth was reversed - it had
been positive and significant in the cross sections and it was now negative
and significant in four of the five industries examined. The positive sign
had implied that the original model had overstated the influence of growth on
equity prices. In the cross section regressions, as growth rates increased,
prices seemed not to rise as much as the model predicted. The negative sign
in the pooled regression implied just the opposite, however. In this
statistically more correct adaptation of the hypothesis, as growth rates
increased, prices increased faster than the original model had predicted.
Although the debt term still proved either to be insignificant or to have the
wrong sign, the dividend term was significant with higher dividend payout
ratios implying higher equity prices. Thus these pooled regressions had
proved most successful. They made it clear that the cross section analysis
had presented a misleading influence for growth and also restored the
dividend payout ratio to a place of importance in determining capitalization
rates.

At the time the pooled regressions were to be run, notice was taken of
another hypothesis concerning the behavior of equity prices. It had been
conjectured that the equity prices of rapidly growing firms might be reduced
by the payment of dividends while the share prices of less rapidly growing
firms would be little influenced by such an effect. Noting that both growth
rates and dividend payout rates were important in the hypothesis being tested
in this thesis, the question was raised as to whether it would be possible to
test the validity of the conjecture. That is, if the hypothesis tested in this



't',.



- 11 -

thesis showed growth and dividends to be important, could it find any
statistical verification for an interaction between the two? A rather neat
test was possible and the hypothesized interaction was found to be signif-
cant. As will be explained more fully in Chapter VI, the elasticity of
equity price with respect to changes in the growth rate is cut approximately
in half by the introduction of this interaction. In addition to being
significant in the sense that it significantly reduced residual variance,
this interaction also improved the stability of the coefficient of the
dividend payout ratio taken alone. This was taken as further evidence of
the validity of the interaction.

Thus, although no specific conclusions directly relevant to a firm's
financial policy were possible, two inferences of a managerial sort could be
made. First, the original model of the capitalization rate understated the
influence of growth on equity prices and second, there was substantiation of
a significant interaction in the way that the dividend payout and growth
rates affected the capitalization rate. The first inference means that, as
the growth rate increases, share prices rise more than enough to keep the
ratio of dividends to price plus the growth rate constant - the capitalization
rate falls as the growth rate i-ises. The second inference is that the
dividend payout rate ought not to be chosen without consideration of the
growth rate - higher growth rates should be accompanied by lower payout rates.

The major statistical or methodological conclusion was that the original
cross section analysis was inappropriate and had led to serious bias in the
estimation of slope coefficients. In addition it was concluded that the in-
ability to estimate an influence for debt arose from the fact that the method



- 12 -

of allowing for risk was inadequate. Each industry had been hypothesized
to contain firms with identical risk associated with the streams of in-
come arising from their physical assets. While this assumption may have
been valid enough to measure the influences of growth and dividend policy
on capitalization rates, it does not seem to have been valid enough to
estimate the influences of debt. This can be seen by noting that debt
was thought to influence the capitalization rate by adding some financial
risk to the existing risk associated with the physical assets. If the
asset risk were not strictly homogeneous within the industries, differ-
ences in risk between firms would not result solely from differences in
debt-equity ratios. This mixing of different asset risk and different
financial risk would make it difficult to isolate the influence of debt
alone on financial risk. The reliability of the coefficients of the
growth and dividend terms is also diminished by this heterogeneity of
risk within industries. However, as the growth and dividend influences
do not depend so crucially on homogeneous asset risk, the slope co-
efficients are not likely to be so seriously affected as in the case of
debt. This a priori belief is reinforced by the stability of the
coefficient of the growth term and by the favorable results of the test
for the influence of an interaction of dividend policy and growth. Thus,
with respect to the assumption that the industry classification chosen
contained firms with homogeneous asset risk, it is concluded that it is
a valid enough risk characterization for the estimation of the influences
of growth and dividends but not a valid enough characterization to esti-
mate the influence of debt. To specifically deal with debt, some better
way has to be found to standardize for risks other than those arising from
the debt itself.



CHAPTER II
The Variables Influencing the Capitalizaticfo Rate

This chapter develops the variables thought to influence the
rate at which the earnings of a firm are capitalized. In order to
clarify the issues and to construct a framework for evaluating the
model once constructed, it is useful first to comment upon several
other studies concerned with the general problem of valuation.

Much of the empirical research to date on the problem of the
valuation of the firm has been primarily concerned with attempts to
explain the price at which the equity of a firm is sold. This is
usually done by arrying those variables which are thought to affect
price on the right hand side of a regression equation and proceeding
with a least squares estimate of the slope coefficients. Thus
M, J. Gordon— has models of the form:

P r/1 w^Y^°'l br c°3 ^ W °5
-= a[(l-b)-] a^ S a,^ L



where



p

— is year end price/book value per share
W

Y

— is income/book value per share
W

b is the retention rate, (income - dividends) /in come



i^Gordon, Myron J., The Investment. Financi ng and Valuation of
the Corporation, Homewood, Illinois: Irwin, 196'^,



■o '•■'iiv:



• '.<



- l«t -



r is the return on net worth

S is a size index

w is an uncertainty index

L is the debt -equity ratio

Here, s, w, and r measure the influences of the composition and
the total of the firm's assets, while b and L are concerned with the
financial mix employed to finance them.

2/
Again concentrating on price, Durand— estimates

log P = K + b log B + d log D + e log E

where P is price, B is book value (or capital per share), D is divi-
dends per share, and E is earnings per share. He also states "... a
number of others were tried in the course of the study, and these
included: total capital as a measure of size ..., several ratios of
assets to capital, a lagged variable consisting of average past divi-
dends, and some variables relating to the growth and stability of
earnings. None of these additional variables, however, significantly
reduced the residual variance..."

However, several attempts have been made along another track.
In these studies, earnings or dividends are explicitly capitalized
to obtain price. Thus Durand^'' uses a capitalization process and



1/ Durand, David, "Bank Stocks and the Analysis of Covariance,"


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Online LibraryWilliam L. (William Leo) WhiteThe debt-equity ratio, the dividend payout ratio, growth and the rate at which earnings are capitalized: an empirical study → online text (page 1 of 8)