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LIBRARY

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|

Michigan State f
University ‘

 

This is to certify that the

thesis entitled w__.-
THE EFFECTS OF INFLAT'T‘OM‘

THE DEGREE OF LEVERAGING,
AND ACCOUNTING PRACTICES UPON COMMON STOCK PRICES

presented by
Duncan Cameron Bryan
has been accepted towards fulfillment

of the requirements for

PhoDI degree in FINANCE

     

[JI‘ {‘é;;£4’\

Major professor

Date April 30. 1975

0-7639

amozg "3:
1 o MIG l

 

 

 

 

i

ABSTRACT

THE DEGREE OF LEVERAGING,

d
.W)\;j? THE EFFECTS OF INFLATION,
\

AND ACCOUNTING PRACTICES UPON COMMON STOCK PRICES

BY

Duncan Cameron Bryan

 

This thesis analyzes the response of investors to
the differential impact of inflation upon firms having
differing degrees of leveraging and differing accounting
practices. Investor reaponse is measured by the relation-
ship of common stock prices to historical-dollar earnings
from which inflation-induced earnings have been abstracted.

In order to pursue this research. a model for true
after-tax net nominal earnings (TANNE) was develOped°
TANNE are equal to historical-dollar earnings adjusted
for earnings resulting from: a net-monetary debtor position9
FIFO inventory valuation. and the underdepreciation of
fixed assets when general price—level adjusted accounting
is contrasted with historical-dollar accounting.

TANNE were incorporated within the framework of a new
common stock valuation model, which includes not only
characteristics of the individual firm, but also charact-

eristics of the market as a whole. This model is an

 

l—'Em"u

extension of the works of John B. Williams and David
Durand. The explanatory variables in the model include:
the firm's current dividend, the firm's expected dividend
growth rate, the firm's risk premium, the market's dividend
yield, the market's expected dividend growth rate. and the
market's risk premium.

In order to capture the impact of inflation tests were
run on 1965 and 1972 data. 1965 was the final year of a
six year period of relative price stability. while 1972
came at the end of a six year period in which the average
annual rate of inflation was twice that of the prior period.

The major findings of this research are as follows.

The coefficients of the relative dividend payout
ratio were negative in both of the test years, but signifi-
cant only for 1972. These results indicate that investors
prefer a lower relative dividend payout ratio or a higher
relative earnings retention rate, in an inflationary
period.

The coefficients for the FIFO inventory valuation
holding gains were significant in both of the test years.
However. in the relatively low inflation period the sign
of the coefficient was positive and in the relatively
high inflation period it was negative. These results
indicate that in a period of relatively low inflation
investors look favorably upon such gains. but in an in-

flationary period such gains are discounted by investors.

 

The coefficients of the net-monetary debtor leverage
position were negative in both years. and significant
only in the 1972 inflationary period. These results
indicate that investors tended to ignore a net-monetary
debtor position in a period of relative price stability.
However, in an inflationary period, specifically 1972.
investors viewed a net-monetary debtor leverage position
as not enhancing the relative value of the firm’s common

stock. These results appear to be at variance with those

 

of Professors R. Kessel and A. Alchian. but may be ex-
plained by the four-fold increase in the cost of servicing
net-monetary debt per dollar of earnings.

The coefficients of the relative historical-dollar
accounting earnings were positive and significant in both
test years, indicating that investors look favorably upon
a relative increase in historical-dollar earnings.

The coefficients of the proxy for the underdepreciation
of fixed assets when general price-level adjusted accounting
and historical—dollar accounting are contrasted were
significant in the period of low inflation and not signifi-
cant in the inflationary period. The individual values of
the lagged coefficients were positive and significant for
the most recent three years in both test periods. It
would appear that investors looked favorably upon the
underdepreciation of fixed assets. This apparent anomaly

may have been caused by the inability to specify the

 

replacement variable in the regression model. Thus these
findings. rather than revealing investor perception of
underdepreciation. may indicate that investors look
favorably upon the most recent three year's general price-
level adjusted capital spending.

The empirical results lend support to the hypothesis
that investors were intuitively adjusting historical-
dollar accounting earnings for the impact of inflation
even before the artificiality of some of these earnings
had been brought to general attention. In this way these

findings support the efficiency of capital markets.

THE EFFECTS OF INFLATION,
THE DEGREE OF LEVERAGING.
AND ACCOUNTING PRACTICES UPON COIION STOCK PRICES

By

Duncan Cameron Bryan

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Accounting and Finance

1975

 

 

 

ACKNOWLEDGEMENTS

I wish to thank those who have provided me with the
inspiration and support necessary for the completion of
this thesis.

I am grateful to Professor Roland I. Robinson for
agreeing to serve as Chairman of my Thesis Committee, and
for his insightful comments and advice on my work.
Professor Harold Sollenberger. as well as serving on my
committee, was a source of literary and professionsl help
throughout this thesis. I am especially grateful to
Professor Robert Rasche without whose enthusiasm and
knowledge, my work would not have been completed.

I am indebted to Professor William Barnett who
undertook to read this thesis. and whose comments were
invaluable.

To my wife whose faith and editorial ability during
a period of ever increasing adversity was a source of
constant inspiration.

I humbly acknowledge that my wife and daughters gave
several years of their husband and father to this work.

Finally I would thank Christine. Harvey and Mermum

and all those others who have believed in the X factor.

ii

 

 

CHAPTER I
CHAPTER II

CHAPTER I I I

TABLE OF CONTENTS

INTRODUCTION
A REVIEW OF PAST STUDIES
INFLATIQNNAND A NQNETARY DEBTQN
POSITION
ENE ACCUNACY OF INFLATIONARY
ANTICIPATION
ENE ADAPTIVE EXPECTATIONS MODEL
INFLATION AND DEPRECIATIQN
INFLATION AND FINANCIAL ACCOUNELNQ
SUMMARY
ANALYTICAL FRAMEWORK
TRUE AFTER-TAX NET NOMINAL
EARNINGS MODEL
Model of a World Without
Inflation
Model of a World With Inflation
Common Stock Valuation Model
Based Upon Historical-Dollar

Accounting Earnings
SUMMARY

Page

Page

Page

Page
Page
Page
Page
Page

Page

Page

Page

Page

Page

Page

1
L.

7

24

25

 

CHAPTER IV REGRESSION MODEL BASED UPON TRUE
AFTER-TAX NET NOMINAL EARNINGS
REGRESSION MODEL DEVELOPMENT
SUMMARY
CHAPTER V TESTING THE PRICE RELATIVE
REGRESSION MODEL
SOURCE AND SELECTION OF DATA
PROCEEDURE
RESULTS OF ENE STUDY
Ngglysis of the Coefficients
of the Individual Variables
INTERPNETATION OF THE RESULTS
The Relative Dividend Payout Ratio
The Relative Historiggl-Dollar
Accounting Earnings
The Differegge Between HiStQEEEEI‘

Dollar and General-Price Level

Adjusted Depreciation

The Inventory Holding Gain
The Net-Monetary Debtor Leverage

3N9 ExpectgggDivigggg,Growth Ratgg
The Relative Risk Premium
SUMMARY OF FINDINGS
APPENDIX DEFINITION OF VARIABLES
THE BIBLIOGRAPHY

iv

Page
Page

Page

Page
Page
Page

Page

Page
Page

Page

Page

Page
Page
Page
Page
Page
Page
Page
Page

87
93

95

95
9?

100
100
102
105
108

Table

Table

Table

Table

Table

Table

Table

LIST OF TABLES

Page

Page

Page

Page

Page

Page

Page

91

91

93

CHAPTER I

INTRODUCTION

A decade of accelerating inflation has made financial
analysts deeply conscious of how the shrinking value of
money effects the calculus of economic decision making.
Investors are particularily sensitive to this problem
because they must make a trade-off between certain consump-
tion today and uncertain consumption in the future.
Inflation has a variety of influences upon the value of
corporate equities; some would appear to be favorable,
while others appear to be unfavorable.

This study is an effort to sort out these presumptive
influences and to bring to bear the powerful tools of
statistical research upon these influences. and to give
some quantitative measure of their relative importance.

This research was stimulated by still one more
consideration. Security analysis depends in a large
measure upon the financial reports prepared by accountants.
During the past decade the accounting profession has been
in an unusual period of flux as "generally accepted

accounting principles" have been revised, disputed. and

revised again. Investors have become more sensitive to
the fact that accounting is not an exact science and
presumably wish to look more deeply into the impact of
inflation upon the 'quality of earnings" as reported by
the accountants.

This research will investigate investor perceptions
of certain financial variaoles as determanents of common
stock valuation during an inflationary period.

The primary area where inflation might be expected
to affect this perception would be in current earnings
relative to the previous year's earnings; a focus stimu—
lated by investor emphasis upon growth in earnings per
share. In addition, investor discrimination between the
current dividend payout ratio as compared to the previous
year's ratio deserves testing.

A second area where inflation might be expected to
affect investor perception, is in the difference between
real economic and accounting depreciation of fixed assets.

Another area where inflation might be expected to
affect investor perception, is the earnings attributable
to the first-in-first-out (FIFO) inventory valuation
method.

Still another area where inflation might be expected
to affect investor perception, is the degree to which a
firm is a net-monetary debtor.

Still other areas where inflation might be expected

 

to affect investor perception are the riskiness of the
firm and its expected dividend growth rate.

In order that firm-size may not be a source of possible
distortion. financial data for individual firms will be
standardized by dividing these data by the previous year's
earnings.

This study will require models for inventory holding
gains. and for the underdepreciation of fixed assets when
historical-dollar accounting is contrasted with general
price-level adjusted accounting. Further. it will deveIOp
and Specify a common stock valuation model that incorporates
the firm's current dividend, the dividend yield for the
market as a whole. the expected dividend growth rate of the
firm relative to that of the market. and the risk premium

of the firm relative to that of the market as a whole.

 

CHAPTER II

A REVIEW OF PAST STUDIES

The economic literature and more recently the finance
and accounting literature have dealt with the potential
wealth redistribution due to unanticipated inflation.

Economists have Speculated that business firms gain
from inflation. Kessel has summarized the three basic
transmission hypotheses.1

First, based upon the hypothesis that debtors gain
from inflation, and the assumption that business firms
are debtors, then wealth will be transferred from creditors
to debtor firms if the creditor's inflationary expectations
are less than the actual rate of inflation. Firms contract
to pay fixed sums of money in the form of debt instruments;
inflation will cause a depreciation in the real value of
money, i.e. its command over real resources. If this
depreciation in the real value of money were not fully

anticipated by creditors. when the nominal interest rate

1 Reuben Kessel, "Inflation Caused Wealth Redistribution:
A test of a Hypothesis." American Economic Review. vol.
66 (March 1956), pp. 128-I5I.

on the debt was established, creditors would lose and
debtor firms would gain.2 Fisher took the position that
wealth redistribution clearly took place through this
debtor-creditor mechanism: "When prices are rising, the
rate of interest tends to be high but not so high as it
should be to compensate for the rise; and when prices are
falling, the rate of interest tends to be low, but not so
low as it should be to compensate for the fall".3

Second, based upon the assumption that nominal wages
lag behind prices during an inflationary period, worker's
real wages decline while business firms are in a position
to raise prices. Thus firm's earnings would be relatively
higher during periods of inflation and wealth would be
transferred from wage earners to business firms.“ However,
serious doubt has been cast upon the validity of this

hypothesis by the empirical studies of Alchian and Kessel,5

2 J.M. Keynes, Tract on Monetary Reform, London: MacMillan
Co., 1923, p. 18.

 

3 I. Fisher, The Purchasing Power of Money, New York:
MacMillan Co., 1920, pp. 58-73, 190-191.

 

4 E.J. Hamilton, "Prices as a Factor in Business Growth,"
Journal of Economic History, vol. XII. (Fall, 1962),
pp' 325-31‘90

5 Armen Alchian, Reuben Kessel. "The Meaning and Validity
of Inflation - Induced Lag of Real Wages Behind Prices,"
American Economic Review, vol. 50 (March, 1960), pp.
U3-66.

 

 

Bach and Ando,6 and Felix.7

Third, firms may increase real profits in an
inflationary period due to inventory holding gains.

This hypothesis assumes that inventories are sold at prices
that reflect a mark-up based upon current prices rather
than based upon historical costs.6 However, there is no
real gain or loss in terms of real resources as a
consequence of inflation. As Kessel stated:

"Reported business profits may appear larger . . . .
However, this is purely an artifact of the original cost
accounting."9

The proposed study will not pursue the wage-lag
hypothesis, but will concentrate on the debtor-creditor

hypothesis and the apparent increase in nominal income

due to inventory holding gains in an inflationary period.

6 G.L. Bach, A. Ando, "The Redistributional Effects of
Inflation," Review of Economics and Statistics, vol. 37
(February, 1957), pp. 1-13.

7 D.E. FEliX. ”Profit Inflation and Industrial Growth,"

Quarterly Journal of Economics, vol. 70 (August, 1956),
pp. EEILU63.

 

8 J.M. Keynes, gp.cit., pp. 18-19.
9 R. Kessel. gp.cit., p. 129.

INFLATION AND A MONETARY DEBTOR POSITION

10 and Graham,11 found that the real

Bresciani-Turroni,
value of bank stocks declined during inflations, and that
stock price indexes rose at most only about as much as the

12 attempted to evaluate the

rise in price indexes. Kessel
Keynes-Fisher hypothesis, that monetary debtors gain from
inflation, in terms of stock price movements and to ration-
alize his findings with those of Bresciani-Turroni and
Graham. Kessel used four random samples of industrial

firms, each from those listed on the New York Stock Exchange,
and one non-random sample of 16 firms in the banking
industry. He classified firms as either net-monetary
debtors or net-monetary creditors based upon whether their
monetary liabilities were greater than their monetary

assets. Monetary assets were defined as an asset whose
market value is unaffected by changes in the level of

prices. He included in monetary assets: cash, marketable
securities, accounts receivable, tax refund receivable,

notes receivable, prepaid insurance and gold. Marketable

securities required the determination of the net-monetary

position of each of the firms these securities represented.

10 Bresciani-Turroni, Economics of Inflation, London:
MacMillan Co., 1937, pp. 253, 29 .

11 F.D. Graham, Exchange Prices and Production in Hyper-
Inflation: Germany 1920-23, Princeton, 1930, pp. 7h, 177.

12 R. Kessel, gp.cit.

In view of these difficulties he assumed that prior to
1930 these securities represented monetary assets and that
after 1930 they were monetarily ”neutral" - neither
monetary assets nor monetary liabilities. Direct invest-
ments in other firms were considered monetarily ”neutral".
Monetary liabilities were defined as liabilities whose
amount would be independent of changes in the level of
prices. Monetary liabilities included: accounts payable,
notes payable, tax liability reserves, bonds and preferred
stock. Convertible and participating preferred stocks,
while income dependent to some degree, were included as
part of the monetary liabilities.

Using beginning of the period balance sheet data,
Kessel found that the increase in the market price of the
common stock of net-monetary debtor firms was greater than
the increase in common stock price of net-monetary creditors
in two overlapping inflationary periods: 1939-1948 and 1942-
19h8. Using the Mann and Whitney test for differences in
random variables Kessel found an indicated difference at a
level of significance of less than .0025.13 Rank correla-
tion testing was also used and yielded results which were
significant at the .002 level (R2 = .47). An additional
test during a deflationary period 1929-1933 was made and

as hypothesized, the market price of net—monetary creditor

13 Ibid., p. 135.

 

 

firms outperformed that of net-monetary debtor firms at
significance levels of .05“ and .03.1u

The 16 banking firms were tested using rank correlation
based upon the relative net-monetary creditor status, as all
firms were found to be net creditors during the 1942-1948
period, and the relative percent increase in each firm's
stock price. "Roughly 23 percent of the observed variation
was explained by the debtor-creditor hypothesis.”15

Kessel concluded that net-monetary debtor or creditor
position had a significant impact upon stock prices in
periods of both inflation and deflation. but Kessel
questioned the Keynesian assumption that industrial firms
were net-monetary debtors. He further concluded that
since many industrial firms were not monetary debtors that
any stock market index would be composed of both monetary
debtors and creditors. The performance of the stock
market index as compared to the price index would be a
function of the percentage of net—monetary debtors compris-
ing the stock market index, and thus, it might not reflect
the change in price levels, thereby confirming the findings

of Bresciani-Turroni and Graham.

1n Ibid., p. 137.
15 Ibid., p. 132.

10

De Alessi,16 using data from a study by Alchian and

15 found that in

Kessel,17 and from a work by Broussalian,
1915 94 percent of the firms studied were net-monetary
debtors: by 1934 this percentage had dropped to 54 percent
and by 1952 the percentage was 57 percent. De Alessi's
conclusion was that:

”Like any other economic unit, a business firm will
gain from any unanticipated inflation only in preportion
to its net debtor position and the evidence indicates

"19

that all business firms are not net debtors.

Bach and Ando20

analyzed a random sample of 52 firms
over the 1939-1952 inflationary period. They performed
rank correlation testing using net-monetary debtor or
creditor rank and the increase in stock prices over three
sub periods. Their highest rank correlation coefficient
was .26 and Bach and Ando concluded that:

"These results do not confirm the prediction that

debtor companies will gain more during inflation than

16 Louis de Alessi, "Do Businesses Gain From Inflation,"
Journal of Business, vol. 37 (April, 1964), pp. 159-166.

 

17 Armen A. Alchian, Reuben Kessel. "Redistribution of
Wealth Through Inflation," Science, vol. 130 (Sept. 4,
1959): pp° 535‘539-

18 V.A. Broussalian, "Unanticipated Inflation: A Test of
the Debtor-Creditor Hypothesis," Unpublished Ph.D. ’
dissertation, University of California. Los Angeles, 1961.

19 De Alessi, gp.cit., p. 166.

20 Each, Ando, gp.cit., p. 9.

 

11

will creditors, for any of the sub periods shown, the
results are mixed, and over all show no very significant

differences.”21

Alchian and Kessel22

made a more comprehensive study
of all industrial firms whose common stock was traded on
the New York Stock Exchange at any time between 1914 and
1952. They incorporated in their study a new measure of
net-monetary debtor or creditor status - the ratio of
net-monetary debt to the market value of the firms' common
stock. They employed a t test for differences between

the means of the relative market value of debtor and
creditor firms, adjusted for stock Splits and dividends

and assumed that all cash dividends were continuously
reinvested in the firm. Their tests for various sub
periods which included both inflation and deflation
constitute in their words ”overwhelming evidence in support
of the Keynes-Fisher reasoning about the bias in interest
rates during inflation."23
THE ACCURACY OF INFLATIONARY ANTICIPATION

24

De Alessi constructed a model which is designed to

measure the degree of accuracy with which inflation is

21 1.12.1.2” p. 10
22 Alchian, Kessel. 22-213}: p- 535-
23 Ibid.. p- 539-

2# Louis de Alessi, “The Redistribution of Wealth by
Inflation: An Empirical Test With U.K. data,” Southern
Economic Review, vol. 3 (October, 1963), pp. 113-127.

 

12

anticipated. The firm's monetary debtor position was

established in a manner similiar to that of Kessel.25

Mt E MLt - MAt Mt = Net monetary debtor position.
MLt ‘ Monetary liabilities.
MAt = Monetary assets.

He then defined net non-monetary position as the
difference between non-monetary assets (land, buildings,
inventory) and non-monetary liabilities (depreciation and

maintenance).

R ' NMA

t _ - NML R

Net non-monetary position,

t t

i.e. net real assets.

NMAt = Net non—monetary assets.

NMLt Net non-monetary

liabilities.

Nominal wealth, wt, was then defined as the difference
between net non-monetary position (net real assets) and
net-monetary debtor position.

W 5 R

t - M

t t

De Alessi then excludes all other wealth-affecting
factors except "normal income under conditions of static
equilibrium” so that net real assets, Rt’ grow at some

normal income rate, r, which is termed the real rate of

interest. Net monetary liabilities, Mt' grow at the

25 R. Kessel, gp.cit., p. 114.

 

13

contractually specified interest rate, m.26
De Alessi assumes that m = r.
Thus:
wt+1 ' "t ’ r<Rt) ' “(Mt)
If all prices increase at some rate, K, per period
then net real assets will grow at a rate of r+K per period
and net-monetary liabilities will grow at a rate of m+Ka.
where Ka was the anticipated rate of inflation at the time
the monetary debts were contracted.
Then:

wt+1 - wt . (r+K)(Rt)-(m+Ka)(Mt)

Through algebraic manipulation and substitution:

w - wt s (r+K)wt + B(K)(Mt) + U

t+1 t

Where:

 

K U 3 an error term.

t
B = a variable denoting how well
inflation has been
anticipated.
B is restricted by de Alessi to be:
o<B-<1.27

26 De Alessi, 22.cit.. p. 114.
27 Ibid., p. 116.

 

14

If:
0<1B411 Inflation has been partially anticipated.
B ' 0 Inflation has been perfectly anticipated.
B = 1 There has been no anticipation of
inflation.
De Alessi then makes his crucial assumption:

”The debtor-creditor hypothesis does not deny that
factors other than inflation may effect wealth positions
of firms or individuals during inflation. It does assert
that, in a sample in which such factors are randomly
distributed with respect to net-monetary position, a
positive correlation will be found to exist during
inflation between the net-monetary position of firms and
relative changes in wealth."25

Thus all other phenomena that may effect wealth
over time are assumed to be independent of net-monetary
debtor status and are included in an error term, Ut'
Dividing through by, wt, de Alessi obtains

I I

wt+1

 

 

I
w ‘r+ f+1+B(_Ei_1—;£)W£+Ut
t t t t
I ‘ An index of prices.
The variables are converted to units relative to
I
a M Mt
their value at t = O and —T is an estimate of W— over
w t

the period.

15

o to t is substituted in the model.

 

w I I -I '
w .
WE‘HEIWW O)L'-+Ut
o o o N
th
As an estimate of 7~ de Alessi uses the relative
0

price changes in the market price per share of a firm's
it . . . . \

common stock :- adjusted for cash diVidends and changes
‘0

in the number of shares outstanding.

De Alessi’s final regression model is:

 

De Alessi evaluated the null hypothesis, using United
Kingdom data, that inflation was perfectly anticipated,
(i.e. B = 0). His tests for levels of significance at
which the null hypothesis could be rejected yielded mixed
results. In only three out of 36 tests was the level of
significance less than .05. 29

While his other tests did not yield much more
conclusive results de Alessi concluded:

"This study corroborates the results obtained by
Professors Alchian and Kessel in the United States, and
provides evidence to support the general applicability of

the debtor-creditor hypothesis."30

 

 

16

De Alessis' construction of a formal model was a

contribution: however, it appears to have been incompletely

specified. Further, he attributes the lack of decisiveness

to the possibility that his sample size may have been
insufficient and that 40 percent of his sample population
could have been affected by a non inflationary event that
was not randomly distributed among the total sample p0p-
ulation. The latter possibility was caused by the fact
that 40 percent of his sample was restricted to firms in
the breweries and distilleries industry (BD), and in his
words, "a change in the relative price of beer would
clearly affect the wealth of firms in the BD sample".31

In the next section a more complete model will be
Specified and the sample pOpulation of this study will
not be as heavily concentrated in any one industry.
THE ADAPTIVE EXPECTATIONS MODEL

Prichard32 built on the work of de Alessi. Prichard
incorporated an adaptive expectations model for the
expected rates of inflation into de Alessi's original

model, which Prichard then called ”the adaptive eXpecta-

tions—wealth redistribution model".33 Using his model,

31 Ibid., p. 123.

32 Woodward C. Prichard, “Inflation, Expectations and

Wealth Redistribution," Unpublished Ph.D. dissertation,

Michigan State University, East Lansing, 1970.
33 Ibid., p. 86.

._4.b-‘~D o

 

1?

Prichard attempted to predict periods when wealth redis-
tribution would or would not take place. In discussing
his results Prichard stated, "these results do not support
the predictive accuracy of the adaptive expectations-
wealth redistribution mocel . . . the . . . model did not
appear to be a good predictor of the periods in which
significant wealth redistribution could be found".34

In reviewing the inconclusiveness of his results

 

Prichard concludes that, "the rates of price level change
may not have been great enough for wealth redistribution
to show up in the testing”. The period covered by his
tests was 1949-1967. Finally Prichard states, "the wealth
redistribution model itself may be inadequate. It may be
necessary to use a complete multivariate model of changes
in wealth. This would be a very large undertaking."35
INFLATION AND DEPRECIATION
36

Bach and Stephenson in a recent journal article
building upon the work of Kessel37 classified firms as to

their net debtor, creditor status. Their results indicate

3“ Ibide ' p. 92
35 Ibid., p. 95
36 G.L. Bach and James B. Stephenson, “Inflation and the

Redistribution of Wealth," The Review of Economics and
Statistics, vol. LVI (Feb., 1974), pp. 1-13.

 

37 Kessel, gp.cit.

 

lb

that for two inflationary sub periods, 1955-1957, and
1965-1970, the ratio of the increase in stock value for
net creditor firms divided by the increase in stock value
for net debtor firms was a standoff. The increase in
median stock value for net creditor firms was only 63
percent of that for net debtor firms in the first sub
period, while in the second sub period net creditor's
median stock value was 191 percent of that of net

debtors. In the third sub period of relative price

 

stability, 1956-1964, as Bach and Stephenson expected, net
creditors outperformed net debtors by 193 percent in median
stock value.35

Bach and Stephenson incorporated a measure of the
eXposure to the loss a firm might undergo in a period of
unanticipated inflation: this measure was the sum of the
erosion of its net creditor position due to the actual
inflation eXperienced during the period plus, "the monetary
asset equivilent of the future tax savings resulting from
39

depreciation deductions”.

The exposure to erosion on net creditor account, ENCA:

ENCA = (MA-ML)K MA ’ Monetary assets.

ML Monetary liabilities.

K The actual rate of inflation.

38 Bach, Stephenson, gp.cit., p. 9.

39 lb;§.. p. 9.

19

The eXposure on depreciation account, EDA:

EDA ‘ FX(t)K FX = Net fixed assets.

H

t The tax rate.

ll

K The actual inflation.
Net fixed assets times the tax rate is the future tax

savings from future depreciation deductions. When multi-

plied by the rate of inflation a measure of the erosion of

future tax savings due to inflation can be deveIOped.

 

I

Total exposure ' ENCA + EDA

(MA’ML)K + FX(t)K

Bach and Stephenson define a positive exposure as one
in which the firm's net creditor exposure is greater than
its exposure on depreciation account. A negative exposure
as one in which the net debtor eXposure is greater than
the exposure on depreciation account.

Positive exposure means: (MA-ML + FX(t))K>O

Negative eXposure means: (MA-ML + FX(t))K<O or,

Negative exposure means: (ML-MA)>FX(t)
As measured by the median increase in stock values positive
exposure firms did 23 percent and 111 percent better than
the negative exposure firms in the 1955-1957 and 1965-1970
inflationary periods, while in the 1958-1964 period of
price stability positive exposure firms outperformed
negative exposure firms by 148 percent using median stock
values. While these values indicate a weak confirmation

of the debtor-creditor hypothesis, it is believed that

20

the stringency of the negative exposure criterion elimin-
ated all but the strongest net debtor firms, and reclassi-
fied the less strong net debtor firms as positive exposure
firms.”O
INFLATION AND FINANCIAL ACCUUNTING

The inclusion of depreciation in a wealth redistrib-

ution model is significant because George Terborgh has

estimated that 20 percent of reported corporate profits

 

since World War II were "paper" profits due to under-

depreciation of fixed assets in inflationary periods.“1

Bach and Stephenson recognized "the overstatement of
real profits because of inflation-induced increases in

stated inventories", but did not include them "because

satisfactory data were unavailable for individual firms".l+2

“3

Rosenfeld reviewed a field test in which 18 U.S.

companies restated their financial reports for 1966 and

40 If a tax rate of 50 percent is assumed, to qualify as a
negative eXposure firm the firm's net monetary debtor
position must be at least 50 percent of the firm's net
fixed assets. This criterion would lead one to expect a
substantial reduction in the impact of net debtor firms
in any test. While 89 percent of the firms were net
debtor firms in their initial tests, only 30 percent of
the firms analyzed by positive and negative eXposure
were negative, i.e. very strongly net debtor.

41 George Terborgh, Essays in Inflation, Washington,
Machinery and Alli3d Products Institute, 1971, pp. 53-54.

42 Bach, Stephenson, gp.cit., p. 7.

43 Paul Rosenfeld, "Accounting For Inflation: A Field
Test," Journal of Accountancy, (June, 1969), pp. 45-50.

,7i,fl___.___________‘_ _ F..- 7.. _, ____.,

21

1967 on the basis of "general price level accounting”.

The impetus for this test may be found in the minutes of
the Accounting Principles Board, April 28, 1961: "the
assumption in accounting that fluctuations in the value of
the dollar may be ignored is unrealistic". Further,

ARS #6 maintained that "general price-level financial
statements should provide a basis for a more intelligent,
better informed allocation of resources".uu Rosenfeld
states that general price-level financial statements:

"are based on the same generally accepted accounting
principles as conventional ("historical-dollar") financial
statements except that changes in general purchasing power
are recognized. All items in the restatements are given in
a unit of measure which represents the same amount of
general purchasing power. . . . Assets are restated at cost
not at current value in general price level balance sheets.
Cost is restated for changes in the general purchasing
power of the dollar, but not for changes in specific prices
of assets." 45

Rosenfeld singles out three areas that are eSpecially
prone to historical-dollar distortion during inflationary
periods:

Inventory holding gains as a result of using first-
in-first-out inventory valuation. Underdepreciation of
assets based upon historical-dollar costs. General price
gains and losses, which result from holding monetary assets

and liabilities, that are not reported in historical-

dollar accounting financial statements.

44 "Reporting the Effect of Price Level Changes," Accounting
Research Study #6, American Institute of Certified Public
Accountants, New York, 1963, p. 16.

45 Rosenfeld, gp.cit., p. 45.

22

SUMMARY

While these previous studies made a valuable contrib-
ution to the body of knowledge concerned with wealth redis-
tribution during periods of inflation, they indicated areas
that require further analysis.

This study, building upon the foundation of this
previous work, will focus on net-monetary debt per dollar
of earnings, the relative dividend payout ratio, under-
depreciation of fixed assets when general price-level
adjusted and historical-dollar accounting earnings are

contrasted, and on the effects of FIFO inventory valuation.

CHAPTER Ill

ANALYTICAL FRAMEWUKK

In this chapter a mocel Will be formulated for true
after-tax net nominal earnings, TANNE. This model will
incorporate the inflationary effects upon historical-
dollar earnings of: general price—level adjusted accounting
depreciation, inventory holding gains and a net-monetary
debtor position.

Further, a common stock valuation model will be
formulated that incorporates: the firm's current dividend,
the dividend yield of the market as a whole, the expected
dividend growth rate of the firm relative to that of the
market as a whole, and the risk premium of the firm rel-

ative to that of the market.

23

an

TRUE AFTER-TAX NET NUMINAL EARNINGS MODEL
Given the following balance sheet:
Cash (C) Total Current Liabiliities (C/L)
Marketable Securities (MS) Long Term Debt (LT)
Accounts Receivable (A/R) Preferred Stock (PF)
Inventories (IN) Boox Value Equity (8)
Total Current Assets (C/A)
Net Fixed Assets (FX)
Total Assets (PA) Total Liabilities a Equity (TLE)

TLE = TA

C/L + LT + PF + s = C/A + &x
Add and subtract IN from the right hand side.
C/L + LT + p? + b = C/A - IN + FX + IN
B = (C/A - IN) - (C/L + LT + PF) + (FX + IN)
The first term on the right hand side represents the
firm's Monetary Assets (MA).
The second term on the right hand side represents the
firm's Monetary Liabilities (ML).
The third term on the right hand side represents the
firm's Real Assets (RA).
B 3 MA - ML + FX + IN
B = FX + IN - (ML - MA)
Let Net-Monetary Liabilities, M = ML - MA
B = FX + IN - M
at time: t = 0

Bo ‘ FXO + INO - MO

 

25

Model of a World Without Inflation

Under conditions of static equilibrium, in a world
without risk, the real assets of the firm will grow at
some normal real rate of return, r. The firm's net-
monetary liabilities will grow at a real rate of
interest, m, which is contractually Specified. In a
Wicksellian equilibrium m = r, because if m<:r the firm
would continue to expand (contract) its stock of capital
until the marginal revenue equals the marginal cost.

The normal gross real income for the firm, Y1, in
period 1, will be the difference between real asset
growth and net monetary liability growth.

Y1 = r(FXo +INO) - m(MO)

In a world with risk, the real assets of the firm

will grow at some risk adjusted nominal rate of return,

r = r + w w = a risk premium.

The net-monetary liabilities of the firm will also
grow at some risk adjusted nominal rate of return, mr.

m=m+w
I‘

0
Thus gross nominal income, Y1, will be:

Y1 = rr(FXO + INO) - mr(MO)
In addition, there is a depreciation accounting

(affect which will decrease the gross nominal income.

26

The depreciation accounting effect would be some
function of the gross fixed real assets, a-(GFXI).
Where a 3 g(L.DM)

L = The average life of depreciable real assets. The
longer the average life of the depreciable real assets,
the lower will be the depreciation charge per period
and the higher will be the nominal income per period.

DM = The accounting depreciation method adOpted by the firm.
The straight line method, in lieu of the accelerated
methods, will result in a lower initial depreciation
charge and thus higher nominal income for the period
if the installation of real assets has been at a

constant or increasing rate in the past.

The actual depreciation rate, DR, will reflect the

combined effects of both L and DM.

Thus:
a = DR1 DR1 = The depreciation rate in
period 1.
But:
DP
2 1 z . . .
DRl EFYl DP1 The depre01ation charge in
period 1.
SO:
DP1
a " GFx1
And:
IJPl

27

Thus the depreciation adjusted gross nominal income,
I.
Y1 . will be!
0.
Y1 = rr(FXO+INO) - DP1 - mr(MO)

In a world with government, there will be taxes, 61'

which Will reduce the depreciation adjusted gross nominal

income, Y1 .

.0:
Y1 * rr(FXO+INO) - 0P1 - mr(Mo) - 01

Model of a World With Inflation
Assume that all prices increase at some rate K1 the
next period.

I - I
Where K1 = —l———- I = An appropriate price

index.
Then, in equilibrium, the real assets of the firm

must grow at a nominal rate r = rr + K1.

The value of the real assets.

Let F
rr = The risk adjusted nominal rate of return
in a period of no inflation.
X = The normal real return on real assets.
rr(F) = X
Assume that the normal income stream grows at
1 + K1 in order to maintain the real return on real assets,

and that the real assets grow at 1 + K1 in order to main-

tain their real value. Then the nominal rate of growth of

28

0
real assets, r , is:

. (1+K1)X + (1+K1)F — F
2 I.“

 

I‘

(1+K1)X

=—-—-F1—-——+1+K1-1

Substitute: rr(F) = X

: (1+K1)rr(f")

r " F +K1

 

(1+Kl)rr + K1

 

= rr + Klrr + K1

but Klrr’Y 0 if both K and rr take on small values.

Thus the rate of return on FXO+INO must grow at a

D
nominal rate r = r + K1 while the book value of the net-

r
monetary liabilities would not be affected by the price
increase of K1 per period. However, the embedded money
rate of interest, mp, is the sum of the risk adjusted real
rate of interest rr plus the creditor's previous expect-
ations about the then rate of anticipated inflation, KP.

mp = rr + Kp

Given inflation, the nominal earnings, T1, would be:
/\ -

Y1 = (rr+K1)(FXO+INO) - DPl - mp(MO) - G1

It is further hypothesized that the depreciation

accounting effect upon the nominal earnings will be

modified by the rate of inflation, K1.

— Vifiw———__—_.-H.—¢- ,4", _ .._.__ m. _._,-_.. .,-.~

29

The nominal earnings under conventional historical—
dollar accounting are greater than they would be under
general price-level adjusted accounting. This overstatement
of nominal earnings results from the fact that the deprecia-
tion charge is understated as compared to the depreciation
charge under general price-level adjusted accounting.

Rosenfeld“6 has indicated that to capture the full
impact of this underdepreciation, assets should be restated
under general price-level accounting to reflect the actual
inflation since their acquisition.

Under general price-level accounting:

Let: GFXl

N

The general price-level adjusted '
gross fixed assets at the end of
period 1.

CS. = The capital Spending, to acquire

th

fixed assets, in the i period.

x?

j i = The general price-level adjusted
fixed assets acquired in period j,
that are retired in period i.

j i = The percentage of fixed assets
acquired in period j that are re-

tired in period i.

46 Paul Rosenfeld, gp.cit., p. 45.

30
At the end of period 1.

1 cs .75
GFX]: z: 11 E _l .. Ll)

=-OO(
1 I1 Ii
Sci Lb It Lb ,1:
- , l ' i l 1
—I(=_°o:—-1—>+(—-—>
1 l Il Ii 11 11
O . ”.V
' '—l 0;). ;K‘
= __i _ 4.1—1
GFXO Io izzgphi 11)

o I :
AGFX = GI‘Xl '- GFXO

=-00(
o l i I1
0 “V
(35- -R-
l I] l ‘ "’
z (11 ‘ 10)). =-00(I - I, )+ (’bl - R1
1. 1

Under historical-dollar accounting:

Let: GFX1 = The historical-dollar gross fixed assets
at the end of period 1.
CS.l = The capital Spending to acquire fixed
assets in the ith period.
jRi = The assets that were acquired in period
j that are retired during period i.
in = The percentage of fixed assets acquired

in period j that are retired in period 1.

31

1
= Z: \-‘ _
Where 1
R. a -E: - CS.
J 1 J ="OOJXI ( J)
a
. _ L . _ __
9—.
fl = 24 ..
ero i =..,Q(tsl 3R1)
[)GFX = CFXI - GFXO

Historical-dollar accounting, compared to general
price-level accounting, understates the change in gross

fixed assets in period 1 by:

O ’V
n Cb ”R v
.. W. = .. __l .— -l]———l ‘ .-
O 'V
—n CS -R-
z _ 2... __1. _ .1; _
(11 IO) 1 :-wD<I I- ) + R1 R1
1 l
0 i
' _ Z 0b 05
acpx 4:ch - (1l - 10)1 =_ (I.._1 .. jgwxl (I. ))
1 J
1 1
"n CS
+ .Z . ~. .24 .

32

I .
Multiplying the 2nd term R.H.S. by f%

L:

o 1 i ‘d’j i Ij
1 1
CS. CS.
__J - __J
'1" J --oOIj J31(Ij) 11 J =fioon1-(Ij)
o
L.)
— _ a '2: __1
(11 10) i ="J31.
i
o i
'fi Cb
_ Z L _.1
(11 ' Io)i =~ooj° reef/$13 )
1 1
CS CS
__J ._J
CS. CS.
To deveIOp the coefficients of the If; and the f—J
l 3'

terms.

 

P.
N

2. o o

2. o 0

3:0!

3 ' O:

J

33

-1
-1, -2

'1: ‘2' '3
-1

-1, -2

‘1: '20 '3

 

 

18t Term Right Hand Side
0
CS
(1 - I )-—‘-’-
1 0 IO
cs_1
(11 ' Io) I_l
CS
-2
(11 ' Io) I__2
CS
(11 - lo) _I—2
‘3
nd

 

 

O
’ (11 ’ 10) 0X0 BBQ
0
(_lxo + _13,1>
- (I1 10>(C:::>

34

 

 

 

 

 

Let: 3rd Term Right Hand Side
. _ . cs
I1
_ _ CSO
1 — 0 j — 0 10 031 “"
IO
cs
1 = -1 j = o, -1 I X -1
cs
1 = -2 j = o, -1, -2 I . X -2
-2 -2 1 I_2
1 “ 3 J ’ o 1 2 3 3 EE—3
_ ’ "' o " v ' 9 ' I C
- - 1 I
, 3 3 _3
N 4th Term Right Hand Side
cs
1 z 3 a 1 ‘ I1 131 “3
I1
_ cs
1 ‘ 0 J ' ° ‘ I1 031 f‘9
O
l = -1 j = o, -1 - 11 1X1 8E1;
_ 1-1
cs
1 = —2 J = o, -1, -2 - I X '2
1 _.
2 1 1_2
_ cs
1 - -3 J = o, -1, -2, -3 - 11 _3X1 “1:2
-3

2. o o

35

Then when:

i=1, AGFX' -AGFX - o
. CS0 CS0

i=0. AGFX -ACFX - (I1 - Io)(I——)(1 "030*(11 - 10531-3—
O 0

CS

i= -1.zchx' qAGFX - (I1 - Io)‘i:%(1'-138 - _IBLI)
cs
”(11 ' I-i)-131 1-:
, cs_2
i- -2,1iGFx -AGFX = (11 - IO)—f—;(1-_2Xo - _2811 - _2812)
cs_2
’(Ii ’ 1—2)-251 “1‘;
U CS—
1- -3. AGFX -AGFX x (I1 - lo) I 3 (13315”o - _3X_ - _3312
cs
- _ - __13
_3X_3> “1 I-3’ -3X1 1-3

Let:

OX0 =-1X n-ZX-Z x-jX-B 80...: X .8

0X1 8 -1X0 = -

25:1 . 43-2 " 4:3 3 """ 3 3 B1

4&1 ‘ -2Xo g -3b:1 ' -4g-2 z ~5513 -n-2X-n 3 B2
Where Bh is the percentage of the period's capital

Spending that is replaced h periods later.

Then when:

i=1, AGFX' - AGFX -= o

. CS0 CS0
120: AGFX " AGFX 3 (I1 " IO)(1 " 80)”?- “(Il - IO)B1T
O O
i- -1.liGFx -zchx = (11 - 10)(1 - Bl - Boy—f—'
-1

cs_1

- (11 - I-1)B2 “T:I

30

 

 

cs
._ ' .. = _ \ _ . _ -2
1- 4’2:ch use“ (11 101(1 :52 51 so) 1-2
cs_2
‘ (11 ‘ 1-2)B3 I_2
'
1: -3) AGFX 4;de =(I1 - IO)(1 - 53 - 82 - B1 - BO)
(L5 . (35
'5 _ - __:l
‘1’; (11 I-flbu I_3

In the generalized form this reduces to:

. __...‘ (lsJ‘ i
. . w _ 1
AQFX ‘AGFA - 2. T:— (ll-loHl-hizo:bn)-bl_i(ll-Ii)]

i=0

Substituting K1

. "“3 CS1 i
AGFX - AGFX 2 Z ‘I— (K110)(l-hz Bh)-Bl_i(IO(1+Kl)-Ii)-]
1:0 1 =0

The change in gross fixed assets is understated in
9
period 1 by ZIGFX - [iCFX, and thus the depreciation in
period 1 will be undercharged by:

ADP/1 = i)R1(AGFX -AGFX)

Then:

0 U
let K1(1)}'1) = 11k1(AG£~‘x - AGFX)
o . A

Thus the nominal earnings, Y1, are overstated by

0 A:
K1(DP1). Net nominal earnings, Y1, would be:
A' ‘ ' -
Y1 - (rr+K1)(PAO+INO) - 0P1 - K1(DP1) - mp(MO) - G1

In a period of inflation there may be an increase in

the net nominal earnings due to an historical-dollar

37

inventory accounting effect. This inventory accounting

effect would be due to the differential impact of inflation

upon the cost of goods sold. If the last-in first-out

(LIFO) method of inventory valuation is adopted the major

portion of the inflationary impact will be reflected in the

cost of gooas 8010. However, if the first-in-first-out

(FIFO) valuation methOd is adopted a much smaller portion

of the inflationary impact will be embodied in the cost of

goods sold. It is this differential effect of historical-
dollar valuation upon net nominal earnings in a period of
inflation that we would like to examine.

It is hypothesized that this differential accounting
effect is some function of the real inventory, C(FXO).
Where:

c = V1(j"(T1.K1))

V1 = The inventory valuation method. If the firm is on
LIFO there will be no differential accounting effect
upon net nominal earnings. 1f the firm is on FIFO
there will be an increase in net nominal earnings.

Thus V1 is a dummy variable such that:

V1 0 if ldfl)

II

VI 1. if FIFT)
T1 = The inventory turnover rate, the cost of goods sold
divided by the initial inventory, will effect the

differential net nominal earnings. As the inventory

38

turnover increases the change in net nominal earnings
per inventory turnover will decrease. However, as the
inventory turnover increases the change in differential
net nominal earnings will increase at a decreasing
rate.

K1 = The rate of inflation, the greater the rate, the
greater will be the increase in differential net
nominal earnings.

The differential net nominal earnings effect due to

the inventory valuation method would be develOped as

follows:
Let: YF = Nominal income with FIFO inventory valuation.
YL ' Nominal income with LIFO inventory valuation.

= Sales for the period.

S
C = The cost of goods sold using FIFO valuation.
C

L = The cost of goods sold using LIFO valuation.

YF = S - CF
YL = S - CL
YF-YL=AY=s-L -S+CL

II
0

[iY L - LF
To approximate the functional relationship between
K1 and T1, we assume the following:

a. That production and sales are deveIOped at an even

rate within the period.

39

b. That the rate of inflation, K1, is constant within
the period.

Assume an inventory turnover rate, T1 8 1

 

 

 

 

End End
Period 0 Period 1
I Q
' 3
_ - _ II- Klpo
Fig. 1
INo I IEPO
q0 q0
COGSF ‘ INo
COGSL a I + II (see Fig. 1)
K
cocs - p q + F q (—1)
L o o o o 2
K1
3 P0q0(1 4 2—)
K1
3 INO(1 + 5—)
[XY ' COGSL - COGSF
K1
‘ INO(1 + 5—) - INO
K1
8 INO(1 + 2_ - 1)

40

Now assume an inventory turnover rate, T1 = 2

 

 

 

 

End End
Period 0 Period 1
. l
I
IV K P
————————— 1 o .
Fig. 2

INO I 1 III 3P0
qo qo qo

COGS = INo + I + II (see Fig. 2)

IN + P + P (i) Ei
o oqo oqo 2 2

ll

K1
3‘ ZINo + INO(E_)

K1
' INO(2 + IT)

COGS - I + II + III + IV (see Fig. 2)
= I + III + (II + IV)

1
poqo + Poqo + Po(2qo)(2)K1
' 2Poqo + Poqo (K1)
3 INO(2+K1)

K
[32' = IN0(2+K1) - INO(2 + 5;)

z IN0(£ K1)

41

Thus:

. .1.

1

c x v1(x1(1 - ETI))

1

C(INO) a V1(K1(1 ’ ETI))(INO)

Where V1 = 0 if LIFO

V1 1 if FIFO

Thus earnings for the period would be increased by
this differential historical-dollar inventory accounting
effect during an inflationary period. However, to obtain
adjusted net nominal earnings, $1., this differential
historical-dollar inventory accounting effect must be
subtracted. To accommodate the effect of taxation, later
in this study, the differential historical-dollar inventory
accounting effect will be both added and subtracted from
the adjusted net nominal earnings.
Thus:
A" ' 1
Y1 = (rr+K1)(FXo+INO)-DP1-K1(DP1)+V1(K1)(1 - 2T;>INO

- V1(K1)(1 - §%—)INo-m (M ) - G1

1 P °

Substituting hp = rr + Kp in the 6th term R.H.S.

fun 0
3 1
11 (rr+K1)(FX0+INo)-DP1—K1(DP1)+V1(K1)(1 - ETI)IN0

1 -

42

Au: 0
Y1 * rr(FXo+INO)+K1(FXO+INO)-DP1-K1(DPI)

+V1(K1)(1 - 5%?)INO-V1(Kl)(1 - 2%?)INo-rr(mo)

-Kp(MO) - 01
Combining terms:
‘Ii' = rr(FXO+INO-MO)+K1(FXO+INO)-DP1-K1(DP;)
+V1(K1)(1 - 5%73IN0-V1(K1)(1 — f)_%I.—-)INO-K (Mo) - c1
1 1 p

But FXO+INO-MO = s substituting in the 1St term R.H.S.

0

A0: - w ; I ..-' 1
- v (K )(1 - —$—)IN -K (M ) - G
1 1 2T1 o p o 1
But FXO+INO = BO+MO substituting in the 2nd term R.H.S.
A00 .— P . ' I 1 .
Y1 = rr(bo)+K1(50+M0)-UP1-hl(UPl)+v1(Kl)(1 ' ETI)INO
1 -
- V1(K1)(1 - 2T;>INO-Kp(MO) - G1
/\00 _ ' 1
Y1 “ rr(BO)+K1(BO)+K1(M0)“DP1’K1(DP1)+V1(K1)(1 - ETI)INO
- v (K )(1 - -l—)IN -K (M ) - G
1 1 2T1 O p o 1
Combining terms:
A00 - . _ t 1

1 - .
- V1(K1)(1 ‘ ETI)INO+K1(MO)-KP(MO) ' 01

“3

But KP 8 ap - rr substituting in the 7th term R.H.S.
A00 - 0 1
1 ' -
_ V1(K1)(1 - 2T?)INO+K1(M0)-(mp-rr)Mo - G1

Combining terms:

A. U _ v ’ . O 1

1 . . -
’ "1(K1)(1 ’ ETI)I“OI(rr*‘1)Mo‘mp(Mo) ‘ G1

The taxes, 61' are a function of historical-dollar
accounting nominal earnings, and not a function of
adjusted net nominal earnings.

Thus:

1

_ - 1 —* . ‘
cl - t1[(rr+k1)BO-Dpl+vl(kl)(1 - ETI)INo-mp(LTO)J

Where:

m; = The embedded cost of debt.

LT0 = The amount of debt outstanding in period 0.

Thus:
_._co C_F.dh i 'do
mp LTD 0 ixe c arges n perio .
PDQ = Preferred Dividend in

. d .
And: perio O
- Co + PDo PFC = Preferred stock at redem-
m _

 

p - LTo + PFO tion value in period 0.

44

Divide numerator and denominator of each term R.H.S.

 

 

 

 

by LTO.
$1532 Eo_+§32
a : LTO L O : LTO LTO
p TO + Pro 1 + PFO
LTO LTO LTO
But:
-‘I'_CO
mp LTD
00!
PD
'7" +-—TO'
a = p ”0
p PFO
1 *T
h 0
Or:
PF PD
- o - o
m (1 + ———) = m 7——
P LTO p LTO
PF PD
-*=_ 0‘ 0
mp mp(1 + __.LTO/ LT

Multiply through by LTO:

_* _ PFC PDQ .
mp(LTO) = mp(1 + 15;)(LT0) - IT; (LTO)

= mp(LTO) + mp(PFO) - PDO

45

NOW:

M0 = MLO - MAO

= LT + CLO + PFC - (CAO - INC)

0
MLO = Monetary liabilities.
MAO = Monetary assets.
CLO = Current liabilities.
CAO = Current assets.
30:
. z . _‘. _-p , - ,
uTO MO (4.140 {'1 0+(CAO 1N0)
And:
.4? _ 1‘ . '_‘ .. .1 - ‘
mp(LTO) - mpiNO-(buo+rfo-CAO+INO)Jtmp(PPO) FDO
= mp(MO)-mp(CLO+PFO-CAO+INO-PFO)-PDO
= mp(MO)-mp(CLO-CAO+INO)-PDO
Then:

I:

.. . . 1 ..

_ . 1 -

+mp(CLO-CAO+INO)+PDOJ

46

Substituting for G1:

AI. _ , ' 1

Y1 - (rr+K1)BO-UP1-K1(UP1)+V1(K1)(1 “ ETI>INO
v 1 —l—‘ y M ' (M ‘ t r( k '
- 1(K1)( - 2T1)I‘o+(rr+K1) o-mp ‘0)‘ 1L rr+ 1)bo

 

—DP1+V1(Kl/kl - 2T )INO-mpkMO)tmp(ULO*CAO+INO)+PUO{j

‘tl(mp)(ChO‘CAO+lNO)‘tl(PU )‘K1(DP1)
—v (y )(1 - —l—)IN +(r +K )M
1 ‘1 2T1 o r 1 o
In order to develOp true after-tax net nominal earnings
available to common stock holders 81' preferred dividends in
period 1, PDI, must be subtracted from adjusted net nominal
AI:
earnings, Y1 .
.' _ t .t 1
E1 - [(1-t1)(rr+Kl)BO-(1-tl)Dll+(1-t1)(V1)(K1)(1 - ETI)INO
-(1-tl)(mp) MO-t1(mp)(CLO-CAO+INO)-thDO-FDq

.
_ - _ _ 1
K1(“P1) "1(K1)(1 2T;)IN0+(rr*K1)Mo

1+7

Thai Jterm on the R.H.S. is historical-dollar

accounting earnings available to common stockholders, E1.

80 that:
O

_ a U l,' U ~U : 1 a . .
“I — “Inr‘l(‘)‘/1)""1(r‘1M1 - 2Tl’l”e+(rr+K1)Mo

Substituting back for the 2nd term R.H.S.:

 

. f“ lea}? i_
K1(DP1) -DR1 i‘ r—llHKlloHl - 2: sh)
—o 1 J); h—o
-1‘
wind (mg-1 ’i)
Then:
/ ..
. "’0 (ids. - '1 ‘1
a = , _.. <fl 1 . _ s. , _. _ .
Ll JRl , iI \(xlI )(1 a. sh) B1_i(IO(1+Kl) I.)

   

E ‘ _ ;
1 i=o<: i L_ O h=o l 3

R 1 .
“VIMIM1 - 2T?)1No+(rr+Kl)Mo
Thus we have formulated a model of true after-tax net
nominal earnings, or TANNE.
The economic significance of each of the terms is:
El: Represents the increase in TANNE due to historical-
dollar accounting earnings.
”'43 13:51 I"

i -
-DR " —— K I 1 - "‘ B -s . I 1 K -I- :
1 5&0 Ii i( l o)( Méb h) 1-1( 0( + 1) 1%

4b

Represents the decrease in TANNE due to the under
depreciation of gross fixed assets in an inflationary
period caused by the difference between historical-

dollar and general price-level adjusted depreciation.

‘ , 1 t . . . ,i
-/ (K )(1 - s——)IN : Represents the decrease in TANNE due
1 1 2T1 o
to inflation caused in.entory holding gains.
(rr+K1)MO: Represents the increase in TANNE due to a net-

monetary center position in an inflationary periOd.

Common Stock Valuation Model eased Upon Historical-Dollar

 

Accountinggnarnings

 

Let us assume that:

1. The firm will generate a constant dividend stream
forever.

2. The annual dividend is eXpected to grow at a constant
rate of, g, per periou.

3. The cost of equity capital to the firm is defined as
the market rate of discount, keo in period 0.

4. k ‘g.

5. DO is the common stock dividend in period 0.

117

Then for the continuous case:

47 John Burr Williams, Theory of Investment Value, Harvard
University Press, (1938). Also: David Durand, "Growth
Stocks and Petersburg Paradox," Journal of Finance,
vol. XII, (Sept., 1957), pp. 348-363.

 

 

x

O‘-

l t“
Joe e

11:0

 

 

p =
O keo-‘g’o
D
. 0
Let b e ——
0 50
And
boEo
keo _ P + go
0
But:
ke0 3 k0 + wo
Or:
ko : keo ' W0
0 E
k = o o
o -o

“9

_keot
dt

'I‘l'nere D
O

The dividend payout ratio

in period 0.

The riskless market rate of

discount in period 0.

The risk premium on the firm's

equity capital in period 0.

50

Let the superscript m denote the stock market.

 

 

 

 

Then:
m m
b E
km = o o + {m
eo Pm o
0
And.
}(m = km _ wm
o eo o
30:
7m
km = bIT: O + {In _- Wm
o o Pm -o o
0
But.
a m
ko ko
30:
E:o m E: m m
b —— + g - w = b —— + I - w
o P o o o .m #0 o
O I)
0
E0 m 32 m m
bo P— _ 0o —m + (g0 - g0) - (wo I WO)
0 I
o
m m m
- - .. w \
E2 = b0 E0 + (20 go) (w 0)
Po bo PE b0

03
S

 

51

Inverting both sides:

 

 

 

-m
:9 1 be *“o
E m m ‘m m m _
0 b0 Eo + 10((g0 " g0) - (W0 W0))
Multiplying both sides by E0:
a 1m
P = t’obo‘flo
o m 1m m m m
bO no + PO((so - so) - (WO - wo))
This can be simplified by substituting DO = bOEO and
m m 1m . . . .
D0 = bO so, and d1v1d1ng the numerator and the denominator
of the R.H.;. by PE.
80 that:
LJo
P0 = m
Do m m
‘E t (go " so) - (W0 - W0)
po

Thus we have developed a common stock valuation model
based upon the historical-dollar dividend per Share, the
dividend yield for the market as a whole, the expected
dividend growth rate for the firm relative to that of the
market, and the risk premium for the firm relative to that
of the market as a whole.

The economic significance of each of the terms is as
follows:

D : If the dividend per share increases, then

0

the market price per share increases.

t It)
<35<DS

SUMMARY

52

If the dividend yield for the market as a
whole decreases, then the price per Share
increases. This reflects the fact that

when the dividend yield for the market falls
it is because investors are willing to pay a
higher price for a dollar of dividends, and
some portion of this multiple should apply
to the firm's price per share.

If the expected dividend growth rate for the
firm increases relative to that of the market
as a Whole, the price per share increases.
If the risk premium for the firm increases
relative to that of the market, the price

per share decreases.

Models have been formulated for true after-tax net

nominal earnings, TANNE, and for common stock valuation

based upon historical-dollar accounting. In the next

chapter a regression model will be develOped incorporating

true after-tax net nominal earnings within the framework

of the common stock valuation model.

CHAPTER IV

RECHESJIUN MUDhl :ASEU UPON

Thea AFTER-TAX NET NOMINAL EARNINGS

In this chapter the common stock valuation model will
be extended to incorporate true after-tax net nominal
earnings. Using this extended model, a price relative
model will be constructed. Finally, the price relative
model will be converted to a regression model for testing
in Chapter V.

Regression analysis was chosen for the following
reasons:

1. We will be examining a single pre-screened

population of manufacturing firms.

2. The price relative theoretical model has clearly
indicated those variables which Should be import-
ant in the determination of relative share prices.

3. Discriminant analysis was considered, but it is
not applicable to a single pOpulation because its
power lies in examining characteristics (variables)

of the individual elements in the sample to

53

54

determine if the element was drawn from one or
another of the underlying pOpulations.

4. Cluster analysis was rejected because in this
study we are not attempting to determine the
variables that determine relative share prices,
rather we have develOped these and wish to test
them.

REGRESSIQN MouhL DEVELOPMENT

Let us assume that:

 

1. The firm will generate a constant dividend
stream forever.

2. The annual dividend is eXpected to grow at a
constant rate of g', per period.

3. The cost of equity capital to the firm is

defined as the market rate of discount, keo'
O

4. keo> g.
C
5. The common stock dividend in period 0, Do' is

based upon the true after-tax net nominal

 

earnings.

Then for the continuous case:

00

O
, , g t - keot , .
P = D e e dt P = The price per share
0 t=o o o
of common stock based
00 I
_ _ upon TANNE.
z j/fD. t(keo g )
oe dt

t=o

55

Integrating the R.H.S.

, U
_ o
keo-go

Based upon the premise that the market is efficient
the market price per share, PO, will have discounted

historical-dollar earnings so that:

D .

b = —$ Where bO = The dividend payout
E

0 ratio based upon

Then: TANNE.

 

56
O
Multiplying both sides by keo—gO and dividing both sides

by P0:

 

 

 

c o o
keo PC + go

But:

ke0 5 k0 + w; k0 = The riskless rate of

Or: discount in period 0.

. w; = The risk premium on the
ko : keo - wo firm's equity capital in
Substituting for keo: period 0, based upon

TANNE.
b.E. . .
k0 = :00 + g0 ' wo

Let the superscript m denote the stockmarket as a whole:

E m
0 O 0
km 2 b m o + g m _ w m
o o m ,0 0
p0

But the riskless rate of discount for the firm must
be equal to the riskless rate of discount for the market

as a whole in period 0. So:

 

57

 

Then:
I I Im

bE o e u E 0 0
o o + g _ w = b m o + g m _ w m
P o o o m o o
0 PO

I I
Subtract g0 - wO from both sides:

 

 

 

 

 

 

I I Im
b0E0 : b'm Eo + ,‘m _ ' _ w'm _ w.)
P o m ‘50 go) i o o
o P
0
Divide both sides by b0:
I I I I I I I
a mu m . m _ _ m _
o _ b0 “0 (go go) (wo we)
a" ‘ *T-——a + .
o b P b
o o o
m
. nd - Po
Multiply 2 term R.H.S. by —E:
P
o
I I Im m Im I Im I
F‘ - .. ...
:2 g bomso + Po((€o so) (w0 w0))
P ' -m
0 b0 P0
Inverting both sides:
I
m
33 = bo pc
I Tm m Im I Fm I
Eo bomEo + P0((go - go) - (wo - wo))
I
Multiplying both sides E0:
I I
b E Pm
P ‘7' 1 o : O OI : o
o m m m m
bomao + Po<<€o — so) - (we - we):

58

Dividing numerator and denominator R.H.S. by PS:

 

 

 

 

 

P = bo E0
0 1 1m
bomEo 'm ' 'm '
m + (so - so) - (wO - “0)
P
0
Likewise:
p: b1351
II
1 mem . . . .
1 1 +< m- )-<w‘“-w>
m g1 E1 1 1
p1
Dividing both sides of the above equation by P0:
P1 I n l 1
P_ : b1 E1 'm 1m P
O blhl I I O
m + ($1 ’ El) (WI ' W1)
P1
bo Eo
Multiply R.H.S. by 57—i—
0
Where:
bO = Historical-dollar accounting earnings dividend
payout ratio.
E0 = Historical-dollar accounting earnings.
II
P1 _ b1 E1 1 boEO
—’ " I I
po bo Eo blmElm . , , PC

+ (glm ‘ gi) “ (wlm ' WI)

59

 

 

 

 

 

 

 

 

 

 

But:
m m
b E b E
o o = o o m _ - m _
Po Pm + (go go) ("0 WO)
0
. m m _ m
On the R.H.s. bO E0 - DO
SO that:
b0E0 0? m m
P0 = P5 + (£0 - so) - (wO - WO)
0
b0 3
Substituting for P in the last term R.H.S.:
o
T 7
Um
_ m
. Ѥ+(aԤ-ao)- (vac-we)
P E P
_1 z 1 1 o
I I
PO bO E0 b m E m . ' .
1 1 +( m-r)-<w’“-w)
m g1 Pl 1 1
p1
Also:
'm _ m 'm
Substituting in the denominator of the and term R.H.S.:
Tum ‘
o m
p b: E: “55+ (go-g0) " (WC-WC)
1 _ 1 1 o
“_ * ‘1
P0 boEo Dim .m . .m .
;5_ + ($1 ’ g1) ‘ (W1 ‘ WI)
L1 -J

 

 

60

Now let:

X=P§+(m )

o m g0 - g0 - (w ' we)
P
o
I

I Dlm I I I

X1 8 m + (g1 ‘ g1) - (WI - WI)
P1

Then:

:ILEEL'EAOX—(‘Z

Po bc 1“0 X1

Taking logs of both sides:

I I
lnPl-lnPo = lnb1 lnb0+lnsl-lnEO-(-lnxo+lnX1)

But:
P -PO P -P 45
.. Y
lnP1 lnPO P for small P

O O

O

 

 

48 H. Thiel, Applied Economic Forcasting, Rand-McNally,

 

 

 

 

 

 

 

P P P -P P P -P
1 1 1 o 1 1 o
.__ _ 1+(__ -1) - 1+( ) ln(-) = ln(l+( ))
P0 P0 P0 P0 P0
. . P1430
HlnPl-lnP0 = ln(1+( Po ))
Using a Taylor series expansion the R.H.S. becomes:

P -P P -P P -P

1 o 1 o 1 1 o 2
ln(1+(-+--)) = - -( - ) + - - . -

P0 P0 2 Po

P -P
For all: 1 °\(1
po

 

Truncating after the first term R.H.S., because the
higher order terms approach zero.

P -P
Then: A, 1 o

61

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

And:
I I
o b -b b -b
lnb - lnb “I 1 ° for small 1 °
1 o b b
o o
I
. E"E E“E
lnEl - lnE 3' i O for small 1 O
O E E
o o
I I
o X -X X -X
-(lnX — lnx )’3 - i O for small i O
1 o X A
o 0
Thus:
I I
Pl-PO‘: bl-bo + r’1"r‘o _ Xl-Xo
Po bo no ‘0
Or:
' ‘.\
P1-Po _ b1'bo EzlmF‘o xl-xo
P ‘b +s “x *e
o o o 0
And:
I I 0
P b E X
51 - 1 = bi - 1 + Ei - 1 - Y1 + 1 + e
o o o o
I I I
Po bo E:0 ‘0
I
Substituting back for X1 and X0:
f“. ..
- m
U
1 I I I I
0 o “a" + (g1m_g1) “ (wlm—Wl)
P b E P
1 g 1 1 1 +
‘p‘ aw"... e
o o 0 DO m m
_m + (g0 -g0) - (wo - wo)
P
..0 l

 

 

62

'm .m
U D .
. . 1 o m m
In cross section analysxs: ——— . -— . gl , and g are
pm Pm o
1 0

all constant.

In order to develOp a polynomial expression for the

d

I I I
3r term R.H.6. in the variables (wlm-wl), g1, g0, and
(WE-wo), we shall use a Maclaurin series eXpansion.

rd

Therefore the 3 term H.H.$. can be rewritten with

constant terms in[ J8.

 

 

 

(“um T
1 Im I Im I
gfi’ * g1 ‘ €1‘(w1 ‘“1)
3rd term H H 5 =‘ 1 A
O O O rum 1 m
o m _
£5 + go - g0 -(wo wo)
L 0 J
Let:
m
k = 29 + m
0 pm go
o
I
m
k - Ei— + .m
1 pm g1
1
And:
A0 2 go B0 = (w 'wo)
I Im I

 

 

 

 

 

 

 

Then:
1: -A --B
rd o = . = 1 1 1
3 term R.H.o. f(Ao. A1. 80' bl) m
o o o
f(AO.A1.BO,B1) A =0 = f(o,o,o,o) +~é>£ (0.0.0.0)AO
o 9 o
A =0
1
50:0
bl‘o
+ 1:91:— (0.0.0.0).111
1
+ 3f (0.0.0.0)8
(3‘30 0
31“
+ 98 (0.0.0.0)51
2
1 f
+59 2 (o,o,o.o)A(2D
9 A0
2
1 9 r
+ :2 2 (0.0.0.0)AE
2 A1
2
1 / f 2
+ E D 2 (o.o.o,o)B
:9 5 °
0
2
+ %‘1"f‘2‘ (0.0.0.0)83 + . .
a bl
k -A -B
1 1 1 __ . -1
ko-Ao-BO ’ (k1'A1’51)(ko'Ao“Bo)
k
_, 1
f(0) *1;-

 

 

614

 

 

 

 

 

 

 

 

 

 

2r _ 1(
9%-- -1)(k -A -B ‘2 k
0 o o) (kl-Al'Bl) * 1
0:0)2
9 r
...—... = (-1 .. ’ - _.—
9A1 )(ko Ao-bo) 1 = - 1
k
0
9f - +1(
.. k .. _' '2 ‘
980 0 A0 :50) (k -i—. —B ) ' K1
1 1 1 2
(k0)
fi = _1(k -1
9131 o-Ao-bo) 8 — —1_
R
o
f(A .A k
0 l’Bo'Bl) A =0 2 El + k1 Al x
o 2 A - — + 1 b
_ o (k 0 k - l
A * ) 2 B _—
1 O o o (X) o k
B =0 0 O
o
8 =0
1
DIm I
1 + g'm (Dlm '
T rd m '1 + m
hen 3 term R.H.S. = P1 PT g1 )g0 '
Dm + m - g1
—% + gm (Do m 2 Dm
P o 73 + g) —0 m
0 Po 0 (pm + go)
o
'm
(8}. + 'm m
m g1 )(w “w)
pl 0 o 'm '
+ (wl 'w)
om - 1
_2 m 2 m
(Pm + go) D—o m
o m + g
P o
o

65

 

 

 

 

 

 

 

Thus:
'm 'm
01 'm 01 'm
0 : (T+gl) (T'gl) o
P b E P P g
_l:._1.+._.- 1 - 1 g+ 1
Po bo E0 Um Dm , o Dm
(—9 +g'“) (—9- +gW (—9—+ m)
“m o Pm o Pym go
r0 0 o
I
m
D
1 ’m m
(ffi— + $1 ) (WC-WC) cm a
P1 w1 “"1
- m + m + e
D U
0 m 2 o m
(E5 + £0) (Efi + go)
o 0
But:
m
111 D0 111
keo z Pm + go
0
Likewise:
I
m
km = 01 + g'm
e1 J1
PT
'm m
D D
Substituting for —%— + gim and —% + g3:
P P
1 o
' ' m m ' m
P1 _ b1 E1 ke1 (kel) g1 ke1 m
5; i B; + E; _ (km )- (km )2 go + km - (km )2 (wo-wo)
eo eo e0 90
I I
w -w
+ 1m 1 + e
(k )

66

 

 

 

m
k
Multiplying the 5th and 7th term R.H.S. by —§9:
keo
' ' m m m ' m m
51 = E1 + E1 _ ke1 _ (Rel) g keogl _ (ke1)(wo-wo)
P E .m m 2 o m 2 m 2
o o o Keo (keo) (keo) (keo)
km (w.m-w.)
+ co 1 1 + e
(km )2
eo
Combining terms:
p b. E. km km km '
_1 = _1 + _1 _ e1 _ elgo eogl
po bo Eo kzo (k20)2
m m m 'm
_ ke1(wo-wo) - keo(w1 -W1) + e
m 2
(km)

The economic significance of each of these terms is as

follows:
I
b1
3_ 2 If the ratio of the current period TANNE dividend
o
payout ratio increases relative to the previous
period's historical-dollar accounting dividend
payout ratio then the relative price per share
increases.
I
E1
E" : If the ratio of TANNE per share to historical-
0

dollar accounting earnings per share increases

3‘
<33

...;

3'
a>5

O

k

67

then the relative price per share increases.

: If the relative cost of equity capital for the

market as a whole increases then the relative

price per share decreases.

m _km '
elgo eogl

 

m 2 :
(keo)

This is an interactive term. For a

constant eXpected dividend growth rate

for the firm, i.e. g1 = g .

 

0
Then:
m m
_g' (kel'keo)
1 m 2
(Rec)

50 that if the cost of equity capital
for the market as a whole increases the
relative price per share decreases, not
only by the amount of the increase in

m

kel' but also by a factor of:

Similarily for a constant cost of equity

capital for the market as a whole, i.e.
m m

 

ke1 = keo'
Then:
km( - I) — I
_ so g0 g1 = _ g0 g1
(km )2 km

so 60

m m m
ke1(wo‘wo)'keo(w1

68

So that if the eXpected dividend growth
rate increases, the relative price per
share increases not only by the amount
of the increase in the expected rate of

dividend growth, but also by a factor of:

It should be noted that an increase in
the cost of equity capital will have a
greater effect on the relative price per
share than an increase in the eXpected

dividend growth rate because:

 

1 1 . m
(k20)2> (REC) Since keo<1.0.

I I
m_w1)

 

(k

m )2

80

: This is an interactive term.
For a constant relative risk
premium for the firm to the
risk premium for the market as

. m 'm '
w . . w -w = w -w
a hole, 1 e o o 1 1

Then:
(w'm w'>(km ~km >
1 ‘ 1 e1 e0
m 2
(1:80)

 

69

So that if the cost of equity
capital for the market as a
whole increases the relative
price per share decreases, not
only by the amount of the
increase in kgl. but also by a

factor of:
_1____

m 2
(keo)

Similarily for a constant cost

of equity capital for the market
. . m - m
as a wnole, i.e. ke1 ~ ke0

Then:

kid (”‘3‘“0 >~<W1m*‘"1 > >
- m 2
e0)

 

(k

So that if the risk premium for
the firm relative to the risk
premium for the market as a
whole increases the relative
price per share decreases not
only by the amount of the in-
crease in the risk premium of
the firm relative to the risk
premium of the market as a

whole, but also by a factor of:

70

In order to specify the model, substitute:

 

 

 

 

 

m
Do m _ m
— + g - 1!
P11: 0 eo
o
I
Dlm fin
— * g1 " ke1
PT
Im Im
D1 'm 01 'm
o : ("I—n" + $1 ) (—51 + g1 ) 0
p1 b1 E1 P1 P1 g1
—— z —— + —— - - g +
P b E m m o m
o o o D D D
o m o m 2 ( o m
(*5 + go) (“a + go) *5 + g0)
P P P
o o o
I
m
D
1 'm
(T + g1 )(W ’wO) :m :
P1 (w1 -w1)
- + + e
(E: "52 (B: + m)
Pm g0 pm go
o o
I
Substituting for E1 from Chapter III:
~d)

1

71

 

 

 

 

Then:
I
3.1.. 2 b1 1 E}.
Po 5—0 E0
DR ‘90 :3. i
' “ET—1“ 2’ 1—3L “(110”l ‘ 2 En)"
o 1=o i h=o
IN M
. 1 o 0
’ V1(K1)(1 ' ET?) E;— * (FrtK1) E;
0"" 0""
1 'm 1 'm
‘5‘ + g1 ) (—5- + g1 ) .
P1 P1 g1
.. .. g +
_m m o m
Do m Do m 2 Do
1 + so) (—m + so) (—In +
P P P
o o o
I
m
D .
-1- + g m) . .
PT 1 (W1"1 - wl)
— m (w - w ) + m
D . D
(—°— + gmf (—0 + gm)
Pm 0 Pm o
o o

r = rr + K1

And:

m = r + K
P r P

72

 

Then:

=' -K
rr p p
80 that:

. . -

= + -
r mp K1 Kp
Thus:

M M M

<r+x )-—°=fi:<.°>+(K-K)—2
r 1 E0 p so 1 p 30

Thus we postulate the following:

P
1 -
T7'* (90+181

O

r
I I

b E
BL +32 El
0 O

 

3 E .

0 i=0 I'

i h=o

 

 

 

 

 

 

 

 

 

‘ IN M
i __1_ __9 8 - _0
-05 V1(K1)(1 - 2T1) E20 +. 6[mp(EO)J + 7
'm - f 'm W
(D .m 01 .m l
-- + s (-- + g )
Pm 1 pm 1
-8 1 -8 1 g .8
8 Dm 9 Dm o 10 Dm
o m o m 2 0
P5 + 60 (P5 + go) PE
.0 J 1 0 j _0
r- u ‘1
m
DI om F 1
(T + g1 ) cm 0
p1 W1 - W1
-6 wm-w)-M3
11 Dm o o 12 Dm
o m 2 o m
(—— + g ) -— + s
m o m o
P P
o o
— J » l

 

 

 

 

rDR “if CS- 1
..(? .——l 2:: [——£ (KIIO)(1‘ :5: Eh)" B1—1(Io(1+K1)-Ii)

B (kl-RP)E—‘:

 

73

b

nd term R.H.S. multiply by Si
1

In the 2

b1 {3 b1 D1
=. ( )( )
1 b0 1 b1 b0

(3

Then let:

I I
. b b
[?1 =/§;(Bl) where —l-is a scaling constant.
1 1

In the at“

term k.H.S.
In order to evaluate the proxy for the underdeprecia-
tion of real fixed assets when historical—dollar accounting

and general price-level accounting depreciation are com-

pared, we have employed a Lagrangian interpolation tech—

nique to estimate the lagged coefficients for this term.“9
In:
DR "00 cs 1
E_l.§E: I—l K110 (1- E3 Eh) - Bl_i(10(1+K1)—Ii)
0 i=0 i h=o

1
Let 3,-1 = (1- 52% sh) - Bl_i(IO(1+K1)—Ii)

49 S. Almon, "The Distributional Lag Between Capital
Appropriations and Expenditures,“ Econometrica,
(Jan. 1965), pp. 178-196.

 

7::

 

Then:
DR —oo 1
1 —
E ii: [TK1I0)(1- :§:'Bh)- Bl_i(Io(1+Kl)-Iifl _
0 =0 h 0
~00
Z 5/ . C31 0R1
i=0 -1 I:— [Kllo] E;—

Assuming 5 i = O: for all i< -10

Construct 2nd Degree pagrangian interpolation polynomials:

g (-igj) Where: i = O, 000. -10

Such that:

5’-1 =’Gg fl (—i.1) +/?u fl (-1,2)

Then:
__ A) .-
DR1 cs. 10
E /93 ‘fl (- -i, 1)
0 i= 0

 

1.

C81 DR
+3 :6 (-1. 2)]l:(_1c>)(K11)('E_’1‘)
O

The R. H. S. can be rewritten:
~10

DRl
83 120 :6 (- -1, Inf—Q— 11 )(x110)(E——0 )
-10

S DR
+(3u 2:: fl ( i 2) (f:$)(KIIO)(E—$)

i=0 0

75

Let:
3;; fl ( 1><Csi)< )(DR1>
Z = -i. ———’ K I -—-
1 i=0 Ii 1 0 E0
and
-10 .
‘8. 0R
2 = Z (-i.2>(—l—) K 1 ) _1:
2 i=0 g 1.1 ( 1 0 (E0 ’

21 and 22 are the variables which are entered into
the regression equation. The fl (-i,j) are constructed

50

according to formula in Almon, and the other elements
in 21 and 22 are available from our data sources.

In the 8th term R.H.5., if we assume homogeneity of
investor expectations about KP, the previously anticipated
future rate of inflation, then in cross section analysis
Kl-K will be a constant.

P
Then let:

B7 = 37(K1-Kp)

th
In the 9th, 10th, 11th 12th and 13 terms.

D2 m D1m 'm
_E + go and "5’ + g1 will be constants in cross section
P P

o 1

analysis.

 

 

 

 

 

 

Then let
2
0"“
0' (7:— + .
u- = P m
8 8 1 g1 )
m
_9.
m + m
p0 g0)
01""
(—
9 i 1 )
Di
(.9.
m + m 2
6). p0 g0)
10 -3
10 1
Dm
<-9 +
m m
Po go)
b'm
f2' 6’ 1
11 = m + .m
11 P1 81 )
Dm
(.2
I}; + g2)?-
[3 O
12 ‘01
2
Dm
(—°+
m m
p0 go)

76

H‘
u—
._‘.

77

Then:
F 1
p1 ° b1 E1 -10 DR1 I
-p— =8 +01 b—o +82 E— J33 Z 2! <-1.1)(-f——:110)<x1 >(——>
O 0 EO
_ J
-10
DR
#3.. Z ¢(-1.2)(-::—iix)(1<110)(§—i)

i=0 0

 

 

IN M . M
J35 vlmlm - ——1—>(E—09) +36 ‘p<E—°) +87 13:2

2Tl
-Bé[1]-6’9 [go *810[g1] B11[“’m " wo]*81.2[‘”1m ’ “’1 + e

We have no a priori reasons to believe that the basic

 

assumptions underlying ordinary least squares regressions

are not satisfied.
1. That the disturbance term ei is normally

distributed.

2. That the eXpected value of e. is equal to zero.

1

3. That every ei has the same variance.

a. That ei and ej(ifj) are not correlated.
E(ei

5. That the values for the Xi are fully predictable.

.83) = 0

SUMMARY

A price relative regression model has been formulated
which will isolate the effects of a firm's: relative

dividend payout ratio, relative historical-dollar earnings,

78

underdepreciation of fixed assets when historical-dollar
accounting is contrasted with general price-level adjusted
accounting per dollar of earnings, inventory holding gains
per dollar of earnings, net-monetary debtor position per
dollar of earnings, eXpected dividend growth rate. risk
premium relative to that of the market as a whole.

In Chapter V, ordinary least squares multiple
regression will be employed to estimate the coefficients

of the model.

 

CHAPTEK V

TESTING THi PmiCi kirATIVL hinbdsIUh mouEl
SOURCE AND silsCTioN c? pATA

The standard and Eoor's Annual Primary Industrial
File, COMPUJTAT tape was the source for all financial
data for individual firms, except for risk and share
price information. These data items were obtained from
THE VALUE LINE INVEdTMENT dUHVEY. "Summary of Advices
and Index”. The inflation rate is based upon the Consumer
Price Index for "all items for city wage earners and
clerical workers"; published by the U.5. Department of
Labor, Bureau of Labor Statistics.

The years chosen for this study were 1905 and l972.
1965 had an inflation rate of 1.07 percent based upon the
Consumer Price Index (C.P.l.). and relative stock market
increase of e.us percent based upon the Standard and Poors
425 Industrial Index (0&P-425). This year represents the
last year of a period of relative price stability. The
mean annual change in the C.P.I. for the six previous
years was less than 1.19 percent.

1972 represents the most recent year for which the

79

60

complete CJMPUJTAT tape was available. In this year. the
inflation rate was 3.20 percent based upon the C.}.I. and
the stock market increased 12.u percent based upon the
3&P-h25. Further. 1972 came at the end of a six year
period in which the mean annual rate of change in the
3.P.I. exceeded b.32 percent. and tnus investors nau
eXperienced a considerable periou of time over which to
readjust their expectations of Stock price appreciation
based upon a significantly higher rate of inflation.

The firms in this study consisted of unregulated
manufacturing firms. Thus the following industries were
eliminated from the study: government regulated or de-
pendant (i.e. Aerospace), service and entertainment,
financial, building. publishing, agricultural, and

wholesale and retail trade. The Value Line Investment

 

Survey had risk class and share price data on 935 firms
for 1965. When these firms were matched to the individual
firm data on COMPUSTAT the number of firms was reduced to
393. Further screens were employed on these firms so that
the computed inputs to the regression equation would be

both meaningful and stay within the range of computation.

 

bl

The following screens were employed to eliminate firms:

béo tzl r7131
0 1 p
bléo 1530 E
o .
E_ out of range

0
t$o aéo T>5
1 ”o 1 '

As a result of these criteria 240 firms were used in
the 1965 regressions, while 21h firms were used in the
1972 tests.

PROCEEUURE

 

The regression equation to be estimated is:

 

 

r ' ~10 ,
“ b E _ C5. Us
1 _ ' 1 :7 __1; f) ‘7-1 _. l ~ 1
.3" -[}o+'/))1'b_ +/)2 s “”3 .44 fl(1'1HI. )(KIIOME )
O O 0 1‘0 1 O
r
8 l.:_'3 L101 0K1
" u[ :4 g ('lv2)(l )(K110)(E )
1‘0 1
C IN M M-
. 1 o - o ' o 1
-‘[{5{V1(K1)(1 - 5T1”)?- BC) mp(EO) +/)7 E; _/)51

0 J. O O m 0 Um Q
-09[gOJ+/)10’L51 -/))11 [W0 - WO‘]+/212[wl - W1 + 8
Since the net—monetary debtor leverage variables

M

) and E2 are highly colinear, we were forced to
o

:11]:
0

E:
p(

O

drOp one of these two variables in order to estimate

 

82

the regressions. It was decided to retain ap<E9) since
0

this variable includes ap. the embedded money rate of
interest.

0
In cross section analysiS/delll will be incorporated

into the constant term of the regression, so it too was
drOpped from the analysis.

The expected dividend growth rate. as perceived the
previous year. go, was proxied by the actual dividend
growth rate eXperienced over the last five years ending
with the previous year. similarily. the eXpected dividend
growth rate, as perceived during the current year, gi, was
proxied by the actual dividend growth rate eXperienced
over the last five years ending with the current year.
Since these are overlapping moving averages, the simple
correlation coefficient between g0 and g; should be high.
In fact in 1965 it was .674 and in 1972 it was .735. Thus,
it is highly likely under this condition that either one
or both of the estimated coefficients of these variables
will not be significant.

The relative risk of the firm to that of the market

as a whole for the previous year, w? - we, and that for

m ' . . .
the current year, wl — wl, were prox1ed uSing Value Lines's
five risk class estimates. In accordance with Value Line's
classification each firm was assigned a rating of 1, 2, 3,

u, 5. Thus the proxy was measured by the deviation of the

 

53

firm’s assigned risk rating from 3. the risk rating
assigned to the market as a whole.

Thus the equation upon which the regressions were

 

 

 

 

run is:
r
P /7 /7'ibli /1 rm1 /> -19 V” ”“1 i
__.— =: _—| ) I J .. ‘ ‘-
P ')o +’/1[QIT /i: + j) ‘: fl ( lol)il. )(h110)\r II
0 OJ o 1—0 1 o
1
-10 C. J“ 1
_., Ui‘ , l
+/;1 :1: fl (‘1:4)(ff")(nllo)(E—“)
i=0 1 o
' m ’ .- M
/ 1 O [2 " O / .
+ . - H—— <—- +1) :- + '
/{5 llUllm1 2T1 h mp(s ) I)9 go
o o
/." '6 r ' m ,/h 'm '
+5310 g1 +1fill wo - w +/)12 w1 — w1 + e
PO: krice per share of common stock for the previous
year.
P1: Brice per share of common stock for the current year.

b x The dividend payout ratio for the previous year,

 

1)
based upon historical-dollar accounting bO = no.
L‘O
b1: The dividend payout ratio for the current year,
“1
based upon historical—dollar accounting b1 = E—°
1
E z The historical-dollar accounting earnings in the

previous year.

 

at:

El: The historical-dollar accounting earnings in the
current year.
m : The embedded money rate of interest.

K1: The actual inflation rate in the current period.

I : The C.P.I. value in the previous period.
0
. , . .tn .
1.: The C.r.I. value in the 1 period.
1
obi: The capital spending in the l periOd.
0R1: The depreciation rate in the current period, based

upon historical-dbllar accounting.

V1: A dummy variable such that V1 0 if sIEO

V1 1 if FIFO

 

T1: Inventory turnover rate.

INC: The dollar amount of inventories for the previous
period.

MO: Net monetary debtor position for the previous period.

go: The expected dividend growth rate as perceived during

the previous year.
g1: The eXpected dividend growth rate as perceived during
the current year.
wE—w : The relative risk of the firm to that of the
market as a whole as perceived during the previous
year, where: w: represents the risk of the market
and wO represents the risk of the individual firm.
The relative risk of the firm to that of the

market as a whole as perceived during the current

year.

 

05

RESULTS UP THE dTbbY

The most significant regression results are reported
in Table l.

The Hz values, while low, are not unusually low for
cross section analysis. The IUll regression moeel, Eq. VI.
has an kg = .sto for 1905 and an a2 = .5950 for 1972.

In 1905 Lq. I, wnicn represents the relationship
between the relative stocx prices and the relative
historical-dollar accountinr dividend payout ratios plus
the relative nintariCal~ddllar accounting earnings, has
an H2 = .1930. sq. VI, which is the full model, has an
R = .3u00. Thus the relative dividend payout ratios
plus relative historical-dollar accounting earnings are
reSponsible for 57 percent of the total explained variance
in relative stock prices during 1905.

In 1972 hi. I has an kg = .1135, as compared to Eq. VI
which has an H2 = .2950, was responsible for only 30 percent
of the total explained variance in relative stock prices
that year.

From a different point of view the additional
explanatory variables of sq. VI, as compared to Eq. I.
were responsible for only “3 percent of the explained
variance in relative stock prices during 1965, while in
a period of relatively high inflation, 1972, these
additional variables were reSponsible for 62 percent of

the eXplained variance in relative stock prices.

 

 

..
On '.
s. ‘
. .J
. .
.. ,.
.. .
P!
-o
. ..
v
,.
. ‘
-|
...
.. 1
' ‘4
'v ' .
n ‘ I.
’ 1. .‘
- .
v
c
.
nu .
“.
1 4|
‘.
’ I
.-
. .
‘ I
..
c
.1 z, - .
‘ I
,.
c
. .
a r. . .
‘ I
.
4
u‘ " o ,.
‘11
, .
,-
v
n.
.. . .

..J
.....

n
.‘- ;
.1 '1‘
.0 j
. .-1
. ‘.
3.
.. «I
"~ :1. Y
- .ll 1 l
« .:| -. r
’1 -# o

...l

:"I

A ' I;

I I - v 4 U
‘ ' v

or. n’ I

.
..
V ?
4 ul
:)
. .
A 3
. .4
’ t
' )
' I
. .
{’1
‘ .
'1 a
(J
,_ ,.
. .
| .4
I
I) (V
l) 4':
w .a
.1 i)
. .
| .4
I
‘1.
{I
I,
.c
’I
O

0‘
I!)

 

.4,
A ' 1 \
‘ --~ ... \
' .‘ . a
. . ‘ . . '
. . .
x' y 5 .
. ..
Q C : ‘
.’
. . _ . .
.
I
4
o . I
.. . v
v’ ‘ ‘
- . .o
t .4 .
4
v' .3 . - ' -- f '
? ‘ -4 7
I 5 ‘ ' .o
- . . . . . . . .
4 ’ ~~4
' .l o
.. .4 .. o ..
. l I s I n 1
l -' l
‘ < l ' . i . l-
, .
. . j a f .4
.. _0 .. .‘ . ‘ r ‘, I r‘
l . . . . . . . . . .
1 l I v I r | r. l ..
I 1
. x -a r r ' v,- '. :. ' 1 l
. r , y 1 r ? .a ‘ u -)
‘1 ', . ‘ _, . .' .s v .
. . 1 .. . Q ' ,.
. . . . . . . . . . . . .
.- 1 V .4 I
. . .. : v. I: . ,. 1.) I .4 ' . "
1 y ‘. 1: '. 5 #1 u {1 1 I
I. . K‘ ‘ .4 7c (,. ’V f I» ‘
x . a . - J \1 '- ‘ ‘ 3 ' -4
. . . . . . . . . . . . . .
I l P I . 1 I .4 .. I A J
I I , I I
v f 11 '1 , ( ’ ) ’ I: .d g) .a ' I)
‘ Ir I) ' I) .1 ' " ‘x -‘ ' J a 3 I
I) ' I) .‘ ‘ ( “ I I) .. .o .. U ‘
v r ' : ‘ ’\ 1‘“. .4 '. 1 D .4 t "\
. . . . . . ~ . o n o . o . .
J l: J I "‘ I ‘\
l' " U '1 ' l) l) ‘l\ '- -f\ .l -l '-J '1 1‘
x, .4 r“ J .: ' .—o r) n I": I I" J ‘ I)
1; f l ( l1 - p .- y -) I) t y .4 (
.a f ’1 .0 .0 7 ’ H .4 ) V) l‘ .4 l1 '
. . . . . . . o . . . . . .
. ,.. ‘ v. ‘ I Q ,4 Q "\ I .l l I I
l l 1 I l l I
.z . .
« u ') H Y I) l l) (' 7 'V I" 1‘ u-4
'7‘) I: P nt ’ I "\ ' 'I f “3 v0 ’1 .4 ()
,‘ , r :1 .1 H 1' ‘7. I"\ f) ) -'\ :\) \I\ :‘\
’l H I t 'l ‘1‘ .4 “J 'I "\ .I 7 ‘ J .4
. . . . . . . - - . . . . .
(‘1 I .1 'l I v-4 - I .4 l
- | l O
r) V\ ,1 \l\ n: It\ a) If\
f‘ 0 f l“) {-2 L') f‘- D
n r) 1 t) (Y 1% (7 (7\
r‘ .c .d .4 v4 .4 F4 .—4
pa
ii .’
:4 ... :-

fj‘ rj‘
(II (I) (I)

 

U‘
..J
.‘
:3

.:

(
v

.1

 

87

Analysis of the Coefficients of the Individual Variables

 

The constant term,/30, is consistently negative in
the 1965 regressions and is statistically significant at
the 5 percent level in only one of the six regressions.
While in the 1972 regressions the constant term is
consistently positive and significant at the 5 percent
level in three of the six regressions.

I
6?1. the coefficient of the relative historical-dollar
D/E.
accountin aiout ratio 1 l is consistentl ne ative
g P J : 5375;: y g

for both years. In 1905 it is significant at the 5 percent
level in only two of the six regressions, while in 1972 it

is significant in all six regressions.

/32, the coefficient of the relative historical-dollar

. . E1. ..
accounting earnings, 5—, is pOSitive and Significant at
o

the 5 percent level in both years for all regressions.
Linear combinations of (93 and Z2; generate the g{_i's,
the proxy variables for the difference between historical-

dollar accounting and general price-level adjusted

accounting depreciation, Thus,

:E:.¢ (“1:1)(Tf—)(KIIO)(E——) and
i=0 1 O

-10 C31 DRl

2 fl (‘192)('I'_)(K110)(E_')o
i=0 1 0

must be treated as a joint addition to the regression.

 

88

The hypothesis that they are jointly equal to zero was
investigated, because if we are unable to reject the
hypothesis that /?3 =/?L = 0 then we cannot reject the
hypothesis that 5/-i = O for i = O,..., 10.

Since the 1965 test statistic falls in the rejection
region there is sufficient evidence to indicate that the
joint addition of the proxies for the difference between
historical-dollar accounting and general price-level
adjusted depreciation contribute significantly, at the 5
percent level, to the regressions.

Since the 1972 test statistic does not fall in the
rejection region there is no evidence to indicate that the
joint addition of the proxies for the difference between
historical-dollar accounting and general price-level
adjusted depreciation contribute significantly. at the 5
percent level, to the regressions.

Table 2

ANALYSIS OF VARIANCE

 

Test of the hypothesis that,[?3 = [94 = O for 1965

 

Sum of Degrees of Mean F
Squares Freedom Squares
Total
(Restricted) 26.766168 232 .123992
Regression
(Unrestricted) 26.019979 230 .116609
Error 1.946189 2 .973095 6.344935
F 04

2.230 y3'

 

09

TABLE 3

ANALYSIS OF VARIANCE

 

Test of the hypothesis that /33 = A?“ = O for 1972

 

Sum of Degrees of Mean F
squares Freedom Squares
Total A
(Restricted) 10.051306 200 .0u0793
Regression '
(Unrestricted) 9,9061U1 209 .040952
Error .005245 2 .032023 .000410
F2,2ou ‘ 3'0“

 

/G;, the coefficient of the proxy for inventory

IN
gains, V1(K1)(1 — —i~)———, is consistently positive and

2T1 E0
significant at the 5 percent level in all of the 1905
regressions. While in 1972 the coefficient is negative

and significant at the 5 percent level for all regressions.

[26’ the coefficient of the proxy for net-monetary

M
debtor leveraging of earnings, mp(E9), is negative in
o

1965 and not significant at the 5 percent level. While,
in 1972, it is negative but significant at the 5 percent
level.

[2;, the coefficient of the proxy for the previous
year's expectations about the future dividend growth rate,
go, has mixed signs and lacks significance at the 5 percent
level in all of the 1965 regressions. In 1972 the

coefficient is consistently positive, but it is only

90

significant at the 5 percent level in one of the six
regressions.

(9io, the coefficient of the proxy for the current
year's expectations about the future dividend growth rate,
gi, has mixed signs and lacks significance at the 5 percent
level in the 1905 regressions. While in 1972 it is
consistently negative and it also lacks significance at

the 5 percent level. These data bear out the previously

expressed concern about these overlapping moving averages.

 

Since the estimated coefficients of the proxies, go
and gi, for the expected future dividend growth rate are
not significant at the 5 percent level, the hypothesis
that these coefficients are jointly equal to zero was
investigated. The results of these tests are tabulated
in Tables 9 and 5. Both the 1965 and 1972 test statistics
do not fall in the rejection region, thus there is no
evidence to indicate that the joint addition of go and

.

g1 contribute significantly, at the 5 percent level, to

the regressions.

 

91

TABLE u
ANALYSIS OF VARIANCE

I I
Test of the hypothesis that [39 = (310 = O for 1965

 

Sum of Degrees of Mean F
Squares Freedom Squares
Total . .
(Restricted) 29.050193 236 .125070
Regression
(Unrestricted) 29.507000 23h .120357
Error .090593 2 .045297 .350900
2? 1
F2'23u 3.0+
TABLE 5

ANALYSIS OF VARIANCE

I 0
Test of the hypothesis that,/?9 = (910 = O for 1972

 

Sum of Degrees of Mean F
Squares Freedom Squares
Total
(Restricted) 11.301119 210 .059196
Regression
(Unrestricted) 11.336787 200 .054504
Error .044332 2 .022106 .900000
F2,205 ‘ 3'0“

fl3£1, the coefficient of the proxy for the previous
year's relative risk of the firm to that of the market as
a whole, w? - wo, is consistently negative and significant
at the 5 percent level in all of the 1965 regressions. In
the 1972 regressions it was consistently negative, but

without significance at the 5 percent level.

 

92

[312' the coefficient of the proxy for the current year's

relative risk of the firm to that of the market as a whole,

w; - wi, is consistently positive and not significant at

the 5 percent level in both the 1905 and 1972 regressions.
Since the estimated coefficients of the proxies,

m '3 '
w - w and w ‘- w

o o 1 1' are of mixed significance the hypo-
thesis that these coefficients are jointly equal to zero
was investigated. The results of these tests are tabulated
in Tables 6 and 7 . Both the 1905 and 1972 test statistics

fall in the rejection region. Thus there is sufficient

evidence to indicate that the joint addition of w: — WC

and wlm- w1 contribute significantly. at the 5 percent
level, to the regressions.
TAbLE 0

ANALYSIS OF VARIANCE

 

I I
Test of the hypothesis/211 =16?12 = O for 1905

 

Sum of Degrees of Mean F
Sguares Freedom squares
Total .
(Restricted) 29.507000 234 .120357
Regression
(Unrestricted) 20.700100 232 .123992
Error .001432 2 .u00710 3.231709
F2'232'— 3.0M

 

 

93

TABLE 7

ANALYSIS OF VARIANCE

 

I I
Test of the hypothesis /?11 ==K312 = o for 1972

 

Sum of Degrees of Mean F
dguares Freedom Sguares
Total
(Restricted) 11.330707 200 .05450u
Regression .
(Unrestricted) 10.051300 200 .0U0793
Error 1.255401 2 .042701 13.171902
a 'y r)
1‘2,206 1'0“

INTERPRETATION OF THE RESULTS

 

The constant term,/3;, is without consistent signifi-
cance and thus does not lend itself to interpretation.

The relative Dividend Payout Ratio

 

The coefficient of the relative dividend payout ratio,
[;£, is consistently negative. but is significant at the
5 percent level in only one third of the regressions in
the relatively low inflation year 1905. While in the high
inflation year 1972 it is consistently negative and
significant at the 5 percent level.

These results indicate that an increase in the
relative dividend payout ratio will cause a decrease in
the price per share of a firm's common stock, ceteris
paribus. Thus investors act as if they believe that
when a firm retains a lower percentage of its earnings

relative to the previous year's retention rate that the

 

 

9“

price per share of its common stock will decrease
relative to the previous year’s share price, because
the future earnings potential has been reduced by the
relatively lower retention rate.

A second interpretation which is consistent with
these results is that for a given total return on a share
of common stock, dividends plus price appreciation, if a
firm increases its dividend relative to the previous
year's dividend then the price per share does not have to
increase relative to the previous year's share price in
order to maintain the given total return.

It should be noted from Table 1, that in the 1905
regressions where the coefficient is statistically
significant the value of the coefficient is approximately
one-half the value of the 1972 coefficient. This indicates
that in a period of relatively high inflation, ceteris
paribus, a unit change in the earnings retention rate will
cause almost twice the change in relative prices as com-
pared to a unit change during periods of relatively low
inflation. Further, if a firm wants to increase the
relative price per share it should increase its retention
rate, i.e. reduce its current dividend payout ratio, and
this is even more important in a period of relatively
high inflation. That firms may have employed this

strategy appears to be borne out by the fact that the

 

95

mean value of the 1972 relative dividend Dl/Do is only
91.5 percent of the mean value of the 1905 relative
dividend ratio.

The Relative Historical-Dollar Accounting Earnings

 

The coefficient of relative historical—dollar earnings,
[92, is consistently positive and statistically significant
in both years indicating that investors appear to like a

relative increase in earnings per share. It should be

 

noted from Table 1 that in the period of relatively high
inflation, 1972, the values of the coefficient are
approximately one-half those found in the period of a
relatively low inflation, 1905. Thus in a period of
relatively high inflation, ceteris paribus. investors
appear to discount relative increases in historical-dollar
earnings by approximately 50 percent, as compared to
relative earnings in a period of low inflation. This may
be an indication that investors may perceive a "quality of
earnings" problem in relative historical-dollar accounting
earnings in a period of relatively high inflation.

The Difference Between Historical~Dollar and General-

 

Price Level Adjusted Depreciation

 

The coefficients of the Lagrangian polynomial proxies
for the difference between historical-dollar accounting
and general price-level adjusted depreciation,(3/_i,
which are generated by linear combinations of /93 and/(fa,

are significant at the 5 percent level in the 1905

90

regression. and not significant in the 1972 regression.
In evaluating the individual values of the lagged
coefficients developed by means of the Lagrangian poly-
nomial it was found that the proxies for the most recent
four years were all positive and significant at the 5
percent level in the 1905 regressions. In the 1972
regression, the coefficients of the proxies for the most
recent three years were positive and significant at the
5 percent level. and in addition the coefficient of the
most distant lagged proxy was negative and significant.
All other coefficients were not significant at the 5
percent level in either year.

These results are at variance with those predicted
in the full model. except for the most distant lagged
year of the 1972 regressions. This anomaly may be caused
by our inability to specify the replacement variable Bh'
the percentage of this period's capital Spending that is
replaced h periods later. Thus, the chosen proxy repre-
sents general price-level adjusted capital spending with
no provision for the replacement or the retirement of
fixed assets. In this more restricted context the signs
of the significant coefficients of the lagged proxies
have economic meaning. In a period of relatively low
inflation, 1965, investors looked favorably upon capital

spending during the most recent four years. While in a

period of relatively higher rate of inflation, 1972,

 

97

investors only looked with favor on the most recent three

year's capital Spending, while capital spending in the 10th
previous year was looked upon as being deleterious to

stock prices.

The Inventory Holding Gain

 

The coefficient of the inventory holding gain proxy,
/?5, is consistently significant at the 5 percent level
for both 1905 and 1972.

We therefore would like to investigate the following

 

hypotheses:

Hypothesis I: In periods of continuing inflationary
expectations the sign of the coeff-
icient should be significant and
negative, and in periods when there
are no expectations of continuing
inflation the sign should not be
significant or negative.

Hypothesis II: In periods when there are no expect-
ations of continuing inflation and
firms eXperience inventory holding
gains the coefficient should be
significant and positive.

In 1905 the sign of the coefficient is consistently

 

positive indicating that, in that year of relatively low
inflation, investors looked favorably upon such gains.

Using mean values of the 1905 data series, the average

90

proxied holding gain represented only 5.9 percent of the
increase in earnings for that year. Also, 1905 was the
final year in a seven year period of relative price
stability, when the inflation rate averaged less that 1.3
percent per year so that firms could look forward to
replacing inventories at approximately the same cost.
Thus investors might well perceive such holding gains as
enhancing the relative price per share of a firm's common
stock in a period of price stability.

In 1972 the sign of the coefficient is consistently
negative, indicating that, in that year of relatively
high inflation, investors looked with disfavor upon such
gains. Using mean values of the 1972 data series, the
average holding gain proxy represented 19.2 percent of
the increase in earnings for the year. 1972 was the final
year in a seven year period of relatively high inflation
when the average annual rate of inflation exceeded 4.1
percent. Investors recognizing that inventory holding
gains represented almost one-fifth of the increase in
earnings for the year, and if their expectations were for
an increasing rate of inflation this could mean inventory
replacement at substantially higher costs leading to
uncertainty about future earnings.

The coefficients for 1905 and 1972 regressions are
consistent with hypothesis I, and the coefficient for the

1965 regression is consistent with hypothesis II.

 

99

The uncertainty about the true worth of inventory
holding gains in a period of relatively high inflation
may cause investors to perceive such gains as having a
deletarious effect upon the relative price per share.

The Net-Monetary Debtor Leverage

 

The coefficient of the net-monetary debtor leverage
proxy,/?6, was negative in both years and significant
at the 5 percent level only in 1972. The coefficient's
lack of significance in 1905 indicates that investors
tended to ignore a firm's net-monetary debtor leverage
position in valuing its common stock. That investors
appear to have ignored a firm's net-monetary debtor
leverage position may be attributable to two facts: in
1905 the mean value of the net-monetary debtor position
proxy per dollar of earnings was only $1.31 and the mean
value of the embedded cost of net-monetary debt was only
3.90 percent that year, for a mean total cost of servicing
net-monetary debt of $.O50 per dollar of current earnings.

In a period of relatively high inflation, such as
1972, the model and previous studies indicate that a
net-monetary debtor leverage position should enhance the
value of a firm's common stock. However, the results of
these regressions indicate that investors appear to dis-
count the value of a highly leveraged firm's common stock

even in a period of relatively high inflation. This

 

100

apparant anomaly may be explained by two facts: in 1972
the mean net—monetary debtor position per dollar of earn-
ings was over three times that of 1905 at $4.20 and the
mean embedded cost of net-monetary debt had increased
fifty-five percent to 0.15 percent for a mean total cost
of servicing net-monetary debt of $.259 per dollar of
current earnings. The fact that the degree of net-monetary
debt leveraging had increased over three times while the
embedded cost of net-monetary debt had increased by one-
half resulting in over a four-fold increase in the cost
of servicing net—monetary debt may have overcome the
beneficial effects of a net-monetary debtor position in a
period of relatively high inflation.

The Expected Dividend Growth Rates

 

The coefficients of the expected dividend growth
I I
rate proxies, (29 and K? 10 are of mixed signs and lack
consistent statistical significance in both 1905 and 1972.
The joint addition of these two variables likewise does

not contribute significantly to the regression.

The Relative Risk Premium

 

The coefficients of the relative risk premium proxies,
I I
/?.11 and/(312 are individually of the predicted sign in
both 1905 and 1972, but only the 1905 coefficients for
the previous year's relative risk premium are significant
at the 5 percent level. However, the joint addition of

the relative risk premium proxies are significant at the

 

101

5 percent level in both 1905 and in 1972. These results
indicate that proxies based upon the Value Line Investment
Survey risk-rankings when incorporated in the valuation
model deveIOped in this research perform as predicted.

The average value of the risk premium proxies in 1905

were close to the risk premium for the market as a whole,
which is 3.0. The mean value for the previous year's risk
premium proxy was 2.05 decreasing slightly to 2.74 for the
current year's risk premium proxy in 1905. In 1972 the
mean values of the previous year and the current year risk
premium proxies are identical at 2.24 indicating a further
decrease in the risk level for the firms studied in this
research.

This decrease in risk may be attributable to Value
Line's more generous use of the higher "safety" classifi-
cations in 1972 as compared to its 1905 rankings, or to
an inaccurate perception of risk in a period of relatively

high inflation.

 

 

102

SUMMARY OF FINDINGS

 

Investors appear to have learned that in an inflat-
ionary period a relatively high dividend payout ratio, or
a relatively low earnings retention rate, reduces future
earnings potential. This is reflected, of course, in
relatively lower prices per snare for a given level of
dividends. This finding appears to be at variance with

51

the works of frofessors Gordon and Arditti. However, it
should be pointed out that their empirical studies covered
periOds of relative price stability and were based upon
historical—dollar accounting data.

Investors have detected the inventory profit illusion.
Thus FIFU-caused inventory holding gains in a period of
relatively high inflation do not help the relative price
per share.

Investors appear to discount an increase in relative
historical-dollar accounting earnings in a period of high
inflation by approximately 50 percent as compared to the
same increase in relative historical—dollar accounting

earnings in a period of low inflation. Thus investors

appear to perceive a "quality of earnings" problem in

51 Myron J. Gordon, "Dividends, Earnings and Stock Prices,"
The Review of Economics and Statistics, vol. 41, no. 2,

(May. 1959). pp. 99-105.

 

Fred D. Arditti. "Risk and the Required Rate of Return
on Equity," The Journal of Finance, vol. 22, (March,
1907), pp. 19-36.

 

 

103

relative historical-dollar accounting earnings during an
inflationary period.

Investors were not sensitive to a firm's net-monetary
debtor leverage position in a period of price stability.
This finding is in accord with previous studies. Also,
previous studies indicate that a net-monetary debtor
position should enhance relative common stock prices in a
periOd of relatively high inflation. The results of this
study indicate just the Opposite effect - that investors
look with disfavor upon a net-monetary debtor position.
These results may be due to investor fears that the debt
burden is excessive in view of the higher costs of servic-
ing that debt and the increased uncertainties about the
"quality" and variability of future earningso By incor-
porating the cost of servicing a net-monetary debtor pos-
ition in this study we have included not only the benefits,
but also the costs attributable to such a position. Thus
these results may not be at variance with previous studies,
but represent an extension of Professors Alchian, Kessel
and others.

Investors appear to be indifferent to the under-
depreciation of fixed assets caused by the use of
historical-dollar accounting in comparison to general
price-level adjusted accounting. This may be attributable

to our inability to Specify the replacement variable in

 

104

the model, or it may indicate that investors are insens-
itive to the more distant lagged capital spending in
periods of relatively high inflation.

The study failed to get a clear reading on both
expected dividend growth rates and the effect of risk

upon stock valuation.

 

 

 

APPENDIX

APPENDIX

DEFINITION OF VARIABLES

 

A. Source: VALUE LINE INVESTMENT SURVEY, "Summary of
Advices and Index".

P The average of weekly closing prices for December

 

of the current year.
The relative risk of the firm to that of the
market as a whole as perceived in the second
week of the December prior to the current year.
Risk was proxied using VALUE LINE'S five risk
class estimates. The firm was assigned a
rating of 1 - 5, with risk classification 1
representing the least risky classification.
The market as a whole was assigned the median
risk classification 3.
wg—w : The relative risk of the firm to that of the
market as a whole as perceived in the second
week of the December prior to the previous year.
Risk was proxied using VALUE LINE'S five risk
class estimates. The firm was assigned a

rating of 1 - 5, with risk classification 1

105

100

representing the least risky classification.
The market as a whole was assigned the median
risk classification 3.
Source: Standard and Poor's Annual Primary Industrial
File, COMPUSTAT tape. (Data Item shall be
referred to as DI)

The historical-dollar accounting earnings in the

II]

 

previous year.
00 = Available for Common (DI 20)
D1: The common stock dividend per share (DI 20)
bl: The dividend payout ratio for the current year.
01 = DI
Available for common (DI 20)
Common shares outstanding (DI 25)
mp: The embedded money rate of interest.

Fixed charges (DI 15)
= + Preferred dividends (D1 19;

p Long term debt (DI 97—
+ Debt in current liabilities (DI 34)

 

 

Preferred at redemption value (DI 50)
CS.: The capital expenditures (DI 30)
0R1: The depreciation rate in the current period.

= Depreciation and amortization (D1 14)

UR1 Gross plant and equipment (D1 7)

V A dummy variable such that V1 = 0 if LIEU

13

V1 1 if FIFO

V1 z Inventory valuation method (U1 59)

 

107

T1: Inventory turnover rate.

_ Cost of goods sold (DI 41)

T1 fl Inventories TDI 3)

 

INO: Inventories (DI 3)

MO: The net-monetary debtor position for the previous
period.
MO = Current liabilities (DI 5)

+ Long term debt (DI 9)

+ Preferred stock at redemption value
(DI 5o)

- (Current assets (DI 4)

- Inventories (DI 3))

g1: The eXpected dividend growth rate as perceived

during the current year

I
(D

‘31

Dt = Dividends per share (DI 20)

Ii: The C.P.I. value for the current period.

10: The C.P.I. value for the previous period.

K1: The inflation rate for the current period.

 

THE BI BLI OGRAPHY

 

THE BIBLIOGRAPHY

Alchian, Armen, and Kessel, Reuben. "The Meaning and
Validity of Inflation — Induced Lag of Real Wages
behind Prices.” American Economic Review, vol. 50
(March, 1900), pp. 43-00.

 

 

Alchian, Armen, and Kessel, Reuben. "The Redistribution
of Wealth Through Inflation." Sciencg, vol. 130
(September 4, 1959): Pp- 535-539.

 

Almon, S. ”The distributional Lag Between Capital
ApprOpriations and Expenditures." Econometrica,
(January, 1905), pp. 170-190.

 

Arditti. Fred D. “Risk and the Required Rate of Return
on Equity.“ The Journal of Finance, vol. 22 (March,
1907)! pp- 139-36-

 

Bach, G.L., and Ando, A. "The Redistributional Effects of
Inflation." Review of Economics and Statistics,

vol. 37, (February, 1957), pp. 1-13.

 

Bach, G.L., and Stephenson, James B. "Inflation and the
Redistribution of Wealth." The Review of Economics
and Statistics, vol. LVI (February, 1974), pp. 1-13.

 

 

Bresciani~Turroni, Economics of Inflation, London:
MacMillan Co., 1937, pp. 253,298.

 

Broussalian, V.A. "Unanticipated Inflation: A Test of
the Debtor—Creditor Hypothesis." Unpublished Ph.D.
Dissertation, University of California, Los Angeles,

1901.

De Alessi, Louis. "The Redistribution of Wealth by
Inflation: An Empirical Test With U.K. data."
Southern Economic Review, vol. 3 (October, 1903),
pp. 113-127.

 

100

 

 

109

De Alessi, Louis. "Do Businesses Gain From Inflation."
Journal of Business, vol. 37 (April, 1969),
pp. 159-166.

 

Durand, David. "Growth Stocks and Petersburg Paradox."
Journal of Finance, vol. XII (September, 1957),

 

Felix, D.E. "Profit Inflation and Industrial Growth.”

Quarterly Journal of Economics, vol. 70 (August,
1956). PP: uni—“6?.

 

Fisher, 1. The Purchasing Power of Money. New York:
MacMillan Co., 1920, pp. 58¥73, 190-191,

 

Gordon, Myron J. "Dividends, Earnings and Stock Prices.“
The Review of Economics and Statistics, vol. 41,
no. 2. (May. 1959). pp- 99-105.

 

Graham, F.D. Exchange Prices and Production in Hyper-
Inflation: Germany 1920-2}. Princeton: Princeton
University Press, 1930, pp. 74, 177.

 

 

Hamilton, E.J. "Prices as a Factor in Business Growth."
Journal of Economic History, vol. XII (Fall, 1962),

pp' 325’ Bug-

 

Kessel, Reuban. "Inflation Caused Wealth Redistribution:
A Test of a Hypothesis." American Economic Review,
vol. 66 (March, 1956), pp. 128-191.

 

Keynes, J.M. Tract on Monetary Reform. London: MacMillan
Co., 1923, pp. 18—19.

 

Prichard, Woodward 0. "Inflation, Expectations and Wealth
Redistribution.” Unpublished Ph.D. Dissertation,
Michigan State University, East Lansing, Michigan,

1970.

"Reporting the Effect of Price Level Changes." Accounting
Research Study #6, American Institute of Certified
Public Accountants, New York, 1963, p. 16.

 

 

Rosenfeld, Paul, "Accounting For Inflation: A Field Test."
Journal of Accountancy, (June, 1969), pp. U5-50.

 

Terborgh, George. Essays in Inflation. Washington,
Machinery and Allied Products Institute, 1971,
pp. 53—5“.

 

 

110

Thiel, H. Applied Economic Forcasting. Chicago:
Rand-McNally, 1966, pp. U7-“9.

 

Williams, John Burr. Theory of Investment Value.
Cambridge: Harvard University Press, 1938.

 

 

 

 

 

 

   

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