THE RELATIONSHIP BETWEEN tlAIJET PRICE AiDi BOOK
VALUE FOR REGULATED UTILITIES
THOtMAS ARTHUR BANKSTON
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLTIEIJT OF THE REOUIREHEINTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
To Dr. Eugene F. Brigham, who was my advisor and counselor during
the conception, research, and writing of this dissertation, I owe my
deepest gratitude. I am also grateful to Dr. Sanford V. Berg and
Dr. H. Russell Fogler for their criticism and guidance in the preparation
of this dissertation. A special word of appreciation is extended to
Dr. C. Arnold Matthews, Dr. John B. McFerrin, and Dr. Robert E.. Nelson
for their assistance and encouragement throughout my studies at the Uni-
versity of Florida.
I am indebted to numerous colleagues for their suggestions and
assistance, but, in particular to Dr. Abdul-Karim T. Sadik,
Dr. Surendra P. Agrawal, Mr. John H. Pinkerton, and Mr. Paul Vanderheiden
for specific contributions.
Any errors which remain are, of course, my sole responsibility.
I thank the Public Utility Research Center at the University of
Florida for their financial support of this project.
I appreciate the efforts of Dr. Dollie M. Clover, whose editing
helped put this work in presentable form. I also thank Miss Barbara Brown
and Mrs. Edith Schmitt for typing and retyping from the early drafts to
the final version.
Finally, I wish to express my sincerest gratitude to my wife, Joan,
not only for tolerating the entire procedure but also for encouraging me
in this endeavor.
TABLE OF CONTENTS
ACKHIOWL EDGME'NTS ii
LIST OF TABLES v
LIST OF FIGURES vi
1: INTRODUCTION TO THE ECOIO11ICS OF REGULATION 1
2: A MODEL OF MARKET/BOOK RATIOS 11
Rates of Return 11
Basic Mlarket/Book Relationships 13
larket/Book Ratios with External Equity Financing 19
Other Market/Book Models 32
3: EMPIRICAL TESTS 40
The Independent Variables 41
Ex Post Variables 64
Selection of the Sample 72
Least-Squares Regression Analysis 74
Empirical Tests with the Model 79
4: TOWARD A "FAIR" M1ARKET/BOOK RATIO 84
Competitive Market I/Bs 85
Capital Attraction 89
Market/Book Ratios Under Inflation 96
Market/Book Ratios in Regulation 119
5: SU LIMARY 128
APPENDIX A: NOTATION 132
APPENDIX B: DIFFERENTIATION OF 11/B 135
APPENDIX C: TIE APPROPRIATE USE OF THE EARNINGS/PRICE RATIO
AS THE COST OF EQUITY CAPITAL 141
TALE OF CONTENTS continued
APPENDIX I :
DERIVATION OF THE M/B EQUATION WIlEIl STOCK IS SOLD
DERIVATION OF THE M1/3 EQUATIOiN WHEN FLOTATION
COSTS ARE INCURRED
DIFFERENTIATION OF THE 11/B MODEL WITH SALE OF
STOCK AND FLOTATION COSTS
COMPANIES III THE SAIIPLE OF ORIGINAL COST,
NORbMALIZED DEPRECIATIOII-TAX-SAVINGS ELECTRIC
ACTUAL DATA, NORMALIZED VALUES, ArD RESIDUALS FOR
ACTUAL RATE OF RETURII, RETENTION PATE, AND TOTAL
ASSET GROWTH FOR FLORIDA POWER CORPORATION DURING
THE YEARS 1954 1972
REGRESSION STATISTICS FOR 23 ORIGINAL-COST,
IIORIALIZED-DEPRECIATIOII ELECTRIC UTILITIES
DURING THE PERIOD 1954 1972, USING TREND-
IIORMALIZED DATA FOR RATE OF RETURN, r, RETENTION
RATE, b, AND GROWTII RATE. G. Iil EQUATION FORM:
Il/B = B + Br + Blb + B3g + B4(D/A) + C
CORRELATION MA\TRICES FOR DEPENDENT MAD INDEPEN-
DENT VARIABLES FOR 23 ORIGINAL-COST, NOR-
IL\LIZEI DEPRECIATION ELECTRIC UTILITIES
DURING THE PERIOD 1954 1972
ILARKET/BOOK RATIOS CALCULATED FRO[ LQUATLION
(25) COMPARED TO ACTUAL VALUES DURING 1972
1MARKET/BOOK RATIOS CALCULATED FROII EQUATION
(25) COMPARED TO ACTUAL VALUES DURING 1970
CALCULATION OF INVESTORS' REQUIRED RATE OF RE-
TURN FROM THE MI/B EQUATION
INFLATION PREI11 UMS
SAMlPLE CALCULATIONS FOR CURRENT-DOLLAR VALUE
OF EQUITY FOR ALLEGHIENY POWER SYSTEM .
ILLUSTRATIONS OF ACCOUNTING METHODS WITH 10
PERCEIIT INFLATION MID O10 OTHER TRANSACTIONS
LIST OF TABLES
1: THE RELATIVE STABILITY OF RETENTION RATES AND DOLLAR
AllOUNTS OF DIVIDENDS PER SHARE FOR SELECTED ELECTRIC
POWER FIRMS 24
2: YIELDS-TO-MIATURITY FOR MOODY'S AAA UTILITY BONDS AND
AAA INDUSTRIAL BONDS DURING TIIE PERIOD 1954 1972 63
3: EQUATIONS USED TO CALCULATE E: POST VALUES OF THE
VARIABLES IN EQUATION 14 DIRECTLY FROM THE
COlPUSTAT AiNNUAL; UTILITY TAPE 67
4: EA1M-fPLE OF HOW INFLATION AFFECTS THE tBARKET/BOOK
5: HMARKET/BOOK RATIOS AND INFLATION 106
6: Mb\RKET/BOOK RATIOS AND CURRENT-DOLLAR MT\RKET/BOOK
RATIOS IN 1965 and 1972 113
LIST OF FIGURES
1: ILARKET/BOOK RATIOS OF SELECTED FLORIDA UTILITIES 6
2: IIARPJET/BOOK RATIOS OF SELECTED UTILITIES 7
3: GENERAL RELATIONSHIP BETWEEN MARKET/BOOK RATIOS
AIJD ALLOIIED RATES OF RETURN 17
4: .MARKET[/BOOK RATIOS UITIi CONSTANT GROWTH 20
5: IMARKET/BOOK RATIOS WITH SALE OF STOCK 28
6: tLMARKET/BOOK RATIOS WITH SALE OF STOCK AIJD FLOTATION
7: ACTUAL ANID NOPRIALIZED RATES OF RETURN FOR TAIPA
ELECTRIC COIIPANJY 45
8: HYPOTHETICAL PATTERN OF RATES OF RETURII FOR A
REGULATED UTILITY 47
9: RATES OF RETURN FOR TAMIPA ELECTRIC CO.IMPAtJNY AND
REGIONAL AIJD NATIONAL AVERAGES 48
10: HYPOTHESIZED SHIFTS III THE CAPITAL MARKET LINE 60
11: ELECTRIC UTILITY INDUSTRY AVERAGE RATIO OF TOTAL
DEBT TO TOTAL ASSETS 61
12: COMPARISON OF IIORItALIZED AID ACTUAL DATA FOR
FLORIDA POWER CORPORATION 70
13: MILARKET/BOOK RATIOS APPROXIMATING LINEARITY 76
1-: REVENUE :'lD COST CURVES FOR A "IJATURAL" MONOiPOLY 88
15: TP.ENDS IN I\ARKET/BOOK RATIOS 110
16: TRENDS INI CURRENTI-DOLLAR IMARKET/BOOK RATIOS 112
LIST OF FIGURES continued
17: JAl APPROACH TO SETTING FAIR RATES OF RETURN 124
18: ?LAPJET/BOOK PATIO AS A FUN]CTI'OI OF ALLOWED
RATE OF RETUPI 138
19: FIRST PARTIAL DERIVATIVE OF THE [tAPRET/BOOK RATIO
AS A FLUICTIOII OF THE RETENITION RATE 140
Abstract of Dissertation Presented to the
Graduate Council of the University of Florida in Partial
Fulfillment of the Requirements for the Degree of
Doctor of Philosophy
THE RELATIONSHIP BETWEEN MARKET PRICE AND BOOK
VALUE FOR REGULATED UTILITIES
Thomas Arthur Bankston
Chairman: Eugene F. Brigham
Major Department: Finance, Insurance, Real Estate and
Urban Land Studies
Today the great majority of regulated public utilities find their
market prices below their book values. Many utilities are faced with the
need for heavy capital expenditures. However, if these firms sell new
common stock to meet their financing requirements, this very action re-
duces allowable earnings per share and this is detrimental to the exis-
ting stockholders. In this dissertation, the theoretical and practical
aspects of this dilemma are discussed, and the implications of these con-
siderations for rate-of-return regulation are given special emphasis.
First, a mathematical model is developed to describe the relation-
ships among the financial variables. The market value/book value ratio
is treated as the dependent variable, and the model examines the effects
of changes in the allowed rate of return, g-owth in assets., and other
factors on this variable.
Empirical tests are then undertaken to test the extent to which the
theoretical relationships among the variables actually exist. The find-
ings are generally consistent with the model, but this statistical con-
firmation is not strong. Clearly, factors not incorporated into the
model are also at work, or the data (which consists to some extent of
proxies for investors' expectations) contain inaccuracies, or both.
It has been suggested in the literature that the 1r.arket/book ratio
can be used as an indicator of the regulatory agency's fairness to
equity investors. Under ideal economic conditions of perfect competition,
instantaneous regulation, no flotation costs, and no inflation, a
market/book racio of 1.0 would result when the firm earns d fair return.
In a more realistic economic setting, this research suggests chat a
market/book ratio somewhat greater than unity is required both in fair-
ness to investors and to enable the company to attract capital over the
long pull. fhe model developed in the thesis can be used to help regula-
tors specify the rate of return on the rate base necessary to maintain
the market/book ratio at any predetermined level.
INTRODUCTION TO THE ECONOMICS OF REGULATION
Of 106 utilities listed on the NYSE, only eight
were selling at above book value on September 6, 1974.
One was at book value and the rest were selling below.
This means that each time those utilities selling
below book value are forced to sell common stock, they
dilute the book value of existing stockholders. Be-
cause of the exigencies of rate regulations, this re-
duces the earnings base of the existing stockholder.
The result is a downward spiral.
In order to break this cycle, it is necessary
that the price of the stock equal or exceed book value.
This cannot happen until the rate of return on equity
equals or exceeds approximately 16%.'
This statement by a telephone company executive illustrates the
nature and seriousness of one problem faced by regulated public utilities
in the United States today. The statement not only recognizes the depen-
dence of market price on the rate of return on equity, but also indicates
a specific rate of return necessary for utility companies to achieve a
market price equal to book value per share, that is, a market/book ratio
equal to unity. Because of the increasing recognition of the market/bcok
relationship by industry spokesmen and in regulatory proceedings, this
thesis probes the theoretical determinants of the market/book ratio in an
attempt to define the functional form of the market/book model when new
stock is sold by the firm. The practical problems involved in using theo-
retical relationships as an input to the process of rate determination are
then explored by empirical testing.
Theodore F. Brophy, "A Plan for Action by Independents", Telephony,
November 11, 1974, p. 35.
The need for regulation arises when government views the competitive
pricing mechanism as being unable to function properly. The responsibility
for nonmarket regulation specifically falls upon some state or federal
agency. The agency's problem is to allow equity owners a sufficient re-
turn to maintain a going enterprise but not to allow extraction of monop-
olistic profits from the consuming public.
Two situations often used to justify regulation are those of "natural
monopolies" and "infrastructure." A natural monopoly exists when declin-
ing long-run average costs allow one firm to supply an entire market more
efficiently than could several competing firms. The other case sometimes
used to justify regulation involves an industry or firm which is part of
the foundation or infrastructure of economic society.2 Power and commu-
nication utilities often fall into both categories and are subject to
The most prominent forms of regulation in these instances are re-
stricting entry, regulating prices, requiring certain quality standards,
and obligating the firm to serve all applicants. This thesis focuses
upon price and regulation designed to restrict the rate of return on in-
vested capital. In order to isolate several problems involved in rate-
of-return regulation, it considers only established firms, so the question
of entry is moot. It also assumes that all applicants are served with an
adequate quality of service.
The determination of total dollar return on invested capital involves
establishing the rate of return and specifying the aggregate investment
/Alfred E. Kahn, The Economics of Regulation: Principles and Insti-
tutions, I (New York: John Wiley & Sons, Inc., 1970), p. 11.
or "rate base" to which the rate will be applied. In 1898 the Supreme
Court of the United States in Smyth v. Ames established that the "fair
value" of the property should be considered by regulatory commissions in
rate determination. Among the matters deemed appropriate for consider-
ation in the fair value were "the original cost of construction, ...the
amount and market value of its bonds and stock, the present as compared
with the original cost of construction, the probable earning capacity of
the property...and...operating expenses...."' The Court, therefore,
set a precedent for considering both the book value and the market value
of the firm as well as inflation (through replacement costs) and probable
earnings. These are still central elements of controversy 75 years later.
The legitimate expenses were expanded to include the cost of capital
in the Bluefield case in 1923.5 Financial integrity, capital attraction,
and compensation for risk were specified as valid tests for rate fairness
in the Hope case in 1944.6 The search still continues for generally ap-
plicable guidelines which will assist regulatory commissions in their job
of intervening where the competitive market system cannot or does not
The ratio of market value to book value of equity has been discussed
in several recent rate cases as one possible criterion of fairness that
has been largely overlooked in much past regulation. David Kosh's comment,
relative to his proposal to allow a rate of return slightly in excess of
Kahn, pp. 35-36.
'Smvth v. Ames, 169 U.S. 466, 546-547 (1898), cited by Alfred E. Kahn,
The Economics of Regulation: Principles and Institutions, I (New York:
John Wiley & Sons, Inc., 1970).
SBluefield Water Works & Improve. Co. v. Public Service Commission
of West Virginia, 262 U.S. 679, 693 (1923).
Federal Power Commission v. Hope Natural Gas Co., 320 U.S. 591
his estimate of the cost of capital for South Central Bell in a 1972 rate
case in an example: "This rate would, in my opinion, keep the market
price of South Central's stock if traded more than sufficiently above book
value so as to allow for equity financing without dilution. As such it
will maintain the credit of the company.7
Rhoads Foster, in a similar vein, stated in a Southern Bell rate
hearing that "It may be agreed that financial integrity means, at a mini-
mum, the maintenance of stock market values somewhere above book value.
The crucial issue is: How much higher than book value?"8 Foster's tes-
timony included an exhibit comparing market/book ratios of AT&T to those
of samples of electric utilities, industrials, food processors, and an-
other exhibit showing the capital of Southern Bell in current dollars as
compared with the book value. An analytical approach to using comparative
market/book ratios as a means of determining a fair rate of return was
presented by Peter Gutmann in two rate cases involving Consolidated Edison
Company and Brooklyn Union Gas.o1 In still another instance, rebuttal
testimony of Alexander Robichek recalled that Kosh has stated that a mar-
ket/book ratio in the range of 1.1 to 1.5 was desirable for Pacific North-
west Bell. Robichek disagreed with Kosh as to what allowed rate of return
would be necessary for the firm to achieve a market/book ratio within
David A. Kosh, Testimony of, re Fair Pate of Return. before the
Public Service Commission of the State of Tennessee in re South Central
Bell Telephone Company, Docket U-5571, March 1972, p. 54.
J. Rhoads Foster, Testimony before the Florida Public Service
Commission, Fair Rate of Return to Southern Bell Telephone & Telegraph
Company, February 1973, p. 52.
9Foster, pp. 27 and 58 of exhibits.
1oPeter M. Gutmann. "The Fair Rate of Return: A New Approach,"
Public Utilities Fortnightlv, Vol. 87, No. 5 (March 4, 1971), p. 41.
The subject of market/book ratios, therefore, has been receiving
some discussion but without general agreement as to the approach to be
taken, the level to be sought, or even the usefulness thereof. As Robichek
expressed it,'"In my opinion, the desirable market-to-book ratio should
reflect more than one's own feelings about the subject. In particular, I
believe that the desirable range for this ratio should be justifiable on
economic grounds."12 The purpose of this thesis is to explore the ques-
tions involved, to clarify the issues and, hopefully, to develop useful
input for the regulatory decision process.
The urgency attached to this task may be emphasized by considering
historic trends in public utilities' market/book ratios, which have been
falling rapidly during recent years. The severe declines shown for sev-
eral Florida companies in Figure 1 pervade the electricity utility indus-
try. The market/book ratio for each firm at the end of 1973 was very near
or below 1.0. The implications of a firm's common stock selling below book
value (i.e., market/book ratio less than 1.0) are discussed at length in
the chapters to follow. Let it suffice here to mention that where capital
expansion requires the sale of new common stock at a time when the market/
book ratio is below 1.0, the previously existing stockholders suffer a
Consider the plight of Consolidated Edison of New York, whose market/
book ratio has been below 1.0 since 1969, as shown in Figure 2. The
l'Alexander A. Robichek, Testimony of, Washington Utilities and
Transportation Commission v. Pacific Northwest Bell Telephone Company,
Cause llo. U-71-5-TR, September 27, 1971, pp. 1493-1680.
12Robichek, pp. 1567-68.
SI I I I I I
1966 1970 197-
Florida Power & Light Company
0 I I I l lIll
1966 1970 1974
Florida Power Corporation
0 I I I I I I I
1966 1970 1974
Tampa Electric Company
Figure 1: Harket/Book Ratios of Selected Florida Utilities.
Source: Calculated from Compustat Annual Utility Tape and Standard &
Poor's Stock Guide, October 1974.
1966 1970 1974
Consolidated Edison of Ilew York
1966 1970 1974
Detroit Edison Company
Figure 2: Market/Book Ratios of Selected Utilities.
Source: Calculated from Compustat Annual Utility Tape and Standard &
Poor's Stock Guide, October 1974.
company has been suffering a severe cash shortage, both as a result of
rising operating costs and a need to expand plant facilities. The seri-
ousness of Consolidated Edison's situation was recently highlighted when
the Board of Directors passed a regular quarterly dividend payment. Be-
cause this firm has paid some dividends in each year since 1885 and has
long been considered a stronghold within the electric power industry, the
gravity of this decision was felt throughout the financial community.
The Dow Jones Utility Average, in fact, responded by tumbling 4.16 points
(4.93 percent) on April 23, 1974, the day of Consolidated Edison's divi-
dend announcement. 3
Another firm with current financing woes is Detroit Edison Company,
whose bonds were downgraded in April 1974, from AA to A by Standard and
Poor's. Their action raised interest rates paid by the firm, since the
lower rating indicated a higher risk. The utility is now having so much
trouble attracting capital at a reasonable cost to finance construction
that in Mlay it announced an 18 percent cut in its five-year capital-
spending plan. The company realized that this curtailment of expansion
might affect service within a few years.14 Detroit Edison's market/book
ratio was only slightly above 1.0 from 1969 through 1972; then in 1973 it
dropped below, as indicated in Figure 2.
The problems illustrated by these firms are not isolated instances;
rather, they are widespread. Irving Trust Company predicted that $75
billion will have to be raised by electric utilities in the period
"The Value Line Investment Survey, Edition 5 (May 10, 1974),
4"Detroit Edison Cuts Its Spending Plans 18% Due To Financing
Woes," The Wall Street Journal, May 24, 1974.
1974 197S.1" With this magnitude of capital needed, other companies
will almost certainly be facing financing problems similar to those of
Consolidated Edison and Detroit Edison. An approach to these problems
through an understanding of the relationships among the market/book ratio,
the firm's financial decisions, the regulatory agency's actions, and the
effects on both owners and consumers is sought in the pages that follow.
The discounted cash flow valuation model presented by Robichek,16
among others, relates the market/book ratio to the rate of return allowed
by the regulatory commission, the rate of return required by investors
in the securities markets, and the retention rate of the firm's earnings.
This basic model is developed in detail in Chapter 2 to reveal the as-
sumptions and implications within testimony such as that cited above.
The assumptions in the model are then relaxed to accommodate sale of new
equity with allowance for flotation costs and to restructure the assump-
tions concerning total asset growth. Implications of the expanded model
for regulatory purposes are considered in light of current practices.
The market/book model uses expectations to explain investor behavior
in relation to other economic forces. Historical data are a record of
financial events as they actually occurred, not a record of investors'
expectations. Empirical evidence can be used as a guide to judging ex-
pectations as explained in Chapter 3. Market/book ratios were calcu-
lated and compared to actual values to test the predictive power of the
model. Least-squares regression was also performed as an alternative
method for predicting market/book ratios.
Value Line, p. 703.
1Robichek, Exhibit 106, pp. 1-6.
Chapter 4 deals with the elusive problem of fairness in race regu-
lation. An economic basis for a competitive, and presumably fair, rate
of return is developed and related to the market/book model. Certain
assumptions regarding the value of assets make application of the economic
theory difficult. An approach to reconciling economic theory and account-
ing conventions is suggested in hopes of providing a practical and econom-
ically sound input for the rate determination process.
A IIODEL OF rIARKET/BOOK RATIOS
This chapter develops a mathematical model relating the firm's mar-
ket/book ratio to other financial variables, including the rate of return
allowed on equity. The first section distinguishes among several rate of
return concepts discussed in the financial literature. The second section
examines in detail the expected rate of return as determined by the dis-
counted cash flow (DCF) technique, which has been widely cited in utility
rate regulation proceedings. The assumptions going into the DCF approach,
the implications arising out of its usage, and its limitations are dis-
cussed for a better understanding of past and current rate regulation.
One limiting assumption in many DCF models is that retention of earnings
supplied all equity financing; this assumption is relaxed in the third
section, where the model is expanded to allow for equity financing through
the sale of new stock. The expanded model includes flotation costs, and
it is this new model that should be used in utility rate regulation.
A discussion of several other market/book models concludes the
chapter, and few relevant, but lengthy, points are developed in the
appendices to this chapter.
Rates of Return
The term rate of return refers to rate of return on equity capital
throughout this thesis. The rate of return required by investors on the
ith company's stock, k*i, consists of a risk-free rate of return, RF, plus
a risk premium, pi' suitable to the riskiness of the stock. In equation
form, this required rate of return is defined as follows:
k*. = RF + '.. (1)
1 F C
The average investor requires a return of k*. to induce him to buy or hold
Any particular asset, say the common stock of a regulated utility,
has associated with it an expected rate of return, k. For common equity
the expected rate of return often used in rate regulation cases is
k p + g, (2)
where D1 is the cash dividend expected during the year, P is the current
price of the stock, and g is the expected constant growth rate in earnings,
dividends, and stock price.1 This equation is the discounted cash flow
(DCF) cost of equity capital formula. When investors expect asset i to
earn the rate that they require for its level of risk, the capital market
is in equilibrium; that is, equilibrium exists when k = kV.. Henceforward,
we shall assume that the capital market is in equilibrium, so that the
required and expected rates of return are the same at any point in time.
Subsequent model developments use k in the context of Equation (2) while
sometimes referring to it as the required rate of return because of market
One aspect of utility regulation is the control of profits by setting
lMyron Gordon, The Investment, Financing, and Valuation of the Cor-
poration (Homewood, Illinois: Irwin, 1962).
a maximum overall rate of return on the rate base. This allowed rate of
return is given the symbol r in the following equations. (Further, for
convenience, we assume that the rate base is equal to total capital.)
The regulatory agency is required by legal precedent to allow a rate of
return that is "fair" to the equity owners. Thus r is also the fair rate
of return. The allowed and fair rates of return are ex ante concepts.
If, indeed, the utility achieves a level of earnings sufficient for the
allowed rate to be realized, then the actual rate of return, in the ex
post sense, is equivalent to the allowed rate. Because of regulatory lag
or other problems, the actual rate of return may be quite different from
the commission-determined fair and, therefore, allowed return. For the
following equation derivations, we shall assume that the fair, the allowed,
and the actual rates of return are equal. Later on, where regulatory lag
is discussed, this equality assumption is relaxed.
Basic Market/Book Relationships
The DCF approach to the cost of equity capital is based on expected
and required market returns; it relates the price investors pay for a
stock to the return these investors require and expect to receive on that
investment. Regulation, on the other hand, generally focuses on book
value, and regulators prescribe rates of return on the book value of equity.
If regulation is to be fair and effective, the interrelationships between
market value, book value, and rate of return must be recognized and taken
into account in the regulatory process. Here we show the basic relation-
ships in algebraic form.
The Gordon model2 for constant growth, Equation 2, which is used
frequently in financial and regulatory analysis, can be rewritten as
P = D1 (3)
Recognizing capital market equilibrium, k, the expected rate of re-
turn, must equal k*., the required rate of return. Dividends are depen-
dent on earnings per share, Et, and the percentage of earnings paid out.
If a constant percentage of earnings, b, is retained, then the dividend
payout ratio is (1 b), and dividends per share for a period t are
Dt = (1 b)Et. (4)
Earnings per share is equal to the allowed rate of return, r, times the
book value per share at the beginning of the period, Bt l:
E = rB (5)
t t -1
Substituting Equation 5 into Equation 4 we see that the dividend expected
during period c is
Dt = (I b)rBt I. (6)
The growth rate in earnings, dividends, and share prices is
g = br, (7)
in the very limited situation that assumes (1) k, b, and r are constant
and (2) that all growth is from internally generated funds. Letting
t = 1 and substituting Equations 6 and 7 into Equation 3 gives
P = (8)
o k- br
One can now solve for the market value/book value ratio, M/B:
/B = (1 b)r
M/B = (9)
B k br
This H/B relationship is basic to much of the discussion throughout
this thesis. It is expanded later in this chapter in order to take into
account the effects of selling new stock. We shall return to it in
Chapter 4 in order to scudy the effects of inflation on the utility. Thus
it is important that we understand the nature of the equation and the
underlying assumptions. Consequently we shall now look carefully at the
characteristics of the function.
Characteristics of the Function
Further examination of Equation 9 reveals that the signs of the
first and second derivatives with respect to r are positive for relevant
ranges of the constants, namely, k > 0, 1 > b 0, and k > br. If b = 1,
then both derivatives are zero. Setting the first derivative equal to
zero and solving for r, one finds chat r = k/b. These mathematics indi-
cate that the market/book ratio is an increasing function as r approaches
k/b for positive values of H/B.
If one recognizes b, the retention rate, as a variable, also, he can
determine the second order partial derivative of H/B with respect to r
and b. The sign of this derivative depends not only on r and b but also
on k. For values of k > 0, 1 > b > 0, k > br, and r > 0 the sign will be
positive, which indicates that the M/B ratio increases with both r and b.
Details of these derivatives are presented in Appendix B.
Some illustrative M/B ratios are calculated with Equation 9 and plotted
in Figure 3. The significant features of this exhibit may be summarized
1. For any given b and k, the higher the value of r,
as r approaches k/b, the higher the M/B ratio.
For r greater than k/b, M/B is undefined.
2. If b is zero--i.e., if the firm pays all its
earnings out as dividends--then the M/B ratio
rises linearly with r without limit. Other-
wise the relationship between N/B and r is not
3. For any specified r and b, the H1/B ratio is
higher for lower values of k.
4. Over most of the ranges of the curves, the
higher the value of b, the steeper the slope
of the curve relating rI/B to r; i.e., ri/B is
most sensitive to changes in r for high values
5. When r = k, I/B = 1.0 regardless of the level
of b. If r > k, then M/B > 1.0, and conversely
if r < k. The relative levels of r and k are
important to the question of fairness as dis-
cussed in Chapter 4.
6. If r > k, then the higher the level of b, the
larger the value of M/B, and conversely if
r < k.
The Special Case When r = k
With this basic relationship one can predict what will happen if a
regulatory agency sets the allowed rate of return, r, equal to the DCF
required (and expected) rate of return, k. Substituting r = k into
Equation 9 gives
o (1 b)k
B k bk
General Relationship Between Market/Book Ratios and Allowed
Rates of Return.
M/B = (1 b)r/(k br).
which can be rewritten
P = B .
This equality shows that by using the DCF cost of equity capital as the
allowed rate of return, a utility commission will be forcing the market
price of the stock to equal its book value.
Although a slight digression, it is interesting to note that when
the market/book ratio equals 1.0, the required rate of return, k, equals
the earnings/price ratio.4 In this case the earnings/price ratio is an
appropriate measure of the cost of equity capital. The derivation of
this result is presented in Appendix C.
The Asset Growth Rate
In the calculations used to construct Figure 3, the growth rate in
total assets, g, was assumed to increase with r, i.e., g = br, with b con-
stant. Thus, increase in the allowed rate of return implies a faster rate
of growth in total assets. Is this assumption that g increases with r
reasonable? Probably not--ordinarily, for most utilities, g is probably
independent of r. The demand for many utility services, including elec-
tricity, appeared to be relatively inelastic in the short run over observed
narrow ranges of prices, at least prior to the recent escalation in prices.
More recently, there has been a reduction in power usage, apparently dem-
onstrating some price elasticity, but perhaps reflecting a desire to
J. C. Van Horne, Financial Management and Policy, 2nd ed. (Engle-
wood Cliffs: Prentice-Hall, Inc.), pp. 115-117.
conserve waning energy supplies as well as price elasticity. If elastic-
ity is low, the price changes necessitated by changes in r probably will
not greatly affect the amount demanded in the short run. Since growth in
demand is the primary determinant of the asset growth rate, g would seem
to be relatively independent of r. Accordingly, it would seem preferable
to evaluate Equation 9 under the assumption that g is a constant rather
than to assume that g changes proportionately to r.
If we assume that g is a constant, then increases in r must be off-
set by decreases in b to keep the product br = g constant. In other words,
if g is to be held constant, the higher earnings resulting from an increase
in r must be paid out as dividends, which results in a reduction of b.
Under these conditions, the H/B ratio is a linear function of r, as illus-
trated by the examples plotted in Figure 4. As was true with an increasing
g, the M/B ratio still equals 1.0 where r equals k. However, we now have
an X-axis intercept at the point where r = g. If r is less than g, nega-
tive M/B ratios, which are nonsense, arise, while positive M/Bs occur
whenever r is greater than g. The higher the growth rate, the more sensi-
tive is M/B to changes in r (i.e., the greater the slope) for any given
value of k.
These points hold if all new equity financing is expected to come
from retained earnings. They also hold if new equity is sold at book
value. Since these conditions do not hold for all utilities, it is nec-
essary to broaden the analysis to permit the sale of stock, and at prices
different from book values.
Market/Book Ratios With External Equity Financing
In the no-external-equity model, earnings growth occurs only through
reinvestment of retained earnings. If, however, equity is raised externally,
g = O.o
k = 8S
g = S
k = 8.
k = 10.5%
g = Y5
k = 10.5.
5 10 15
Market/Book Ratios With Constant Growth.
I/B = (1 b)r/(k br).
g = br = constant.
an additional element of earnings growth will occur if the stock is sold
at prices above its book value, and earnings growth will be retarded if
the sales price is below the book value. The earnings of a utility are
dependent upon its book equity, and if stock is sold at prices different
from book value, the difference between price and book value accrues to
the old stockholders.
Book value, earnings per share, dividends, and stock prices will all
grow if stock is sold at prices above book value, and they will all fall
if it is sold below. In this section we extend the II/B ratio equation to
encompass the sale of common stock.
The Retention Rate
In a Miller-Modigliani world, investors are indifferent to dividends
and retention of earnings, which will be reinvested and result in capital
gains. Since :.-I- assume that investors do not distinguish between divi-
dends and retained earnings, the cost of equity capital to the firm is
independent of the retention rate; that is, neither k nor the value of the
firm is a function of b, according to H-H.
A contrary argument suggests that in a world with taxes and brokerage
costs, certain investors might prefer capital gains to dividends; capital
gains tax ratios are lower, and capital gains taxes can be deferred until
some point in the future. Other investors may prefer current dividends
to future capital gains: uncertainty increases as one projects farther
into the future, so potential long-term capital gains may be regarded as
If a rights offering is used, then the stock split effect of under-
pricing must be taken into account. The relevant book value is B after
adjusting for this stock split effect.
6F. Modigliani and M. H. Miller, "The Cost of Capital, Corporation
Finance, and the Theory of Investment", Anerican Economic Review, June
1958; and "Correction", American Economic Review, June 1963.
more risky than current dividends, causing investors to discount expected
dividends at a lower rate than expected capital gains. That is, the cost
of capital for a firm paying out a high proportion of its earnings as div-
idends might be lower than one retaining a relatively high proportion of
its earnings, ceterus paribus. Both lines of reasoning disagree with the
Hiller-Hodigliani assumption that investors are indifferent concerning
dividends or capital gains, and both suggest that the cost of equity capi-
tal is indeed dependent on the retention rate, i.e., that k is a function
of b. (Ml-I argue that the two forces are offsetting, with the result
being an empirically observed independence of k on b.)
If this functional relationship were definitely known to exist, and
if the function were defined, then this information could be incorporated
into the M/B model. Since the question is still open to discussion, this
M/B model opts for the Hiller-Hlodigliani position that the cost of equity
capital is independent of the retention rate. This choice seems superior
to defining, perhaps erroneously, a function relating k to b.
One is also faced with the possibility that management could change
the retention rate every dividend period. Indeed, one observes small,
periodic retention rate fluctuations in many utility companies. A general
practice is to maintain constant dollar-amount dividends per share through
time with occasional increases, as permanently increased earnings per
share permit. A stable dividend per share reduces risk in the investor's
eyes. Firms take pride in a long record of uninterrupted dividend pay-
ments. Earnings per share seldom exhibit the stability of dividends per
'Richard Schramm and Roger Sherman, "Profit Risk Management and the
Theory of the Firm", Southern Economic Journal, Vol. 40, No. 3 (January
1974), pp. 353-363.
share. Earnings fluctuate as dividends are held constant; consequently,
the retention rate varies from period to period. This point is confirmed
in Table 1 by data from a few illustrative firms. Although these reten-
tion rates do vary from year to year, they are usually of the same general
magnitude as the long-term average for a particular company. Year-to-year
changes result largely from variations in earnings rather than from changes
in retention-rate policy.
Although the firm's managmeent could make major and frequent alter-
ations in its retention rate by changing the dollar amount of dividends
paid out, this procedure is not generally accepted behavior in the busi-
ness community. In a study by Brigham and Pettway,9 a majority of finan-
cial managers questioned indicated that they would not be willing to change
their dividend policy significantly under normal circumstances. The re-
tention rate seems to be regarded as a constant by management, and probably
also by investors, at least in an expectational sense. Since investors
seem to expect a reasonably stable retention race, in a H/B model built ;.n
expectations for the future, a constant retention rate is a plausible
The retention rate has an important bearing on the growth rate of
earnings of the firm; this relationship is shown in the next section.
The Two Components of Growth
Tlere are two elements of growth of earnings for a utility: (1) growth
from retention of earnings, gl, and (2) growth from sale of new stock, g,.
Our previously discussed growth variable, g, is a combination of these two
E. F. Brigham and R. II. Pettway, "Capital Budgeting By Utilities",
Financial Management, Vol. 2, No. 3 (Autumn 1973), pp. 20-21.
THE RELATIVE STABILITY OF RETENTION PATES 1AJD
DOLLAR AMOUNTS OF DIVIDENDS PER SHAPE FOP
SELECTED ELECTRIC POWEP FIPRIS
g = gl + g2
Here g is equivalent to the g defined in Equation 7, where retention of
earnings was the only source of growth (i.e., g2 = 0),
g8 = br,
while the growth from sale of new stock is described by Equation 10, which
is derived in Appendix D:
P (1 + s)
S- 1. (10)
2 P + sB
Here s is the rate of growth in total equity from the sale of new common
stock; P is the market price per share; and B is the book value per
In the case where M/B = 1.0 (i.e., P = B ), go will equal zero; this
can be seen by substituting B_ for Po in Equation 10. If, however,
M/B > 1.0, then the larger the value of s, the greater will be the value
of g,; that is, old stockholders will enjoy larger growth rates in divi-
dends and earnings per share as larger amounts of new stock are sold,
provided the market price is above book value. On the other hand if
M/B L 1.0, then g, is negative, and the larger the value of s, the smaller
will be g2, and the greater the dilution of dividend earnings when new
stock is sold. At some combination of low M/B and high s, the resultant
negative-g2 will offset a positive gl, causing total earnings per share
growth to be negative even for a company that plows back some of its
How that we have established the two components of earnings growth,
through internal and external equity financing, we can use these to develop
a modofied model of market/book ratios.
The Modified Market/Book Equations
Equation 11, which is similar to Equation 9 except that it is modi-
fied to show the effects of stock sales on the 1/B ratio, is derived in
i/B = r(l b)(l + s) s(l + k br) (1)
k br s
This equation shows that the M/B ratio is dependent upon the allowed rate
of return, r; the retention rate, b; the extent to which outside equity
financing is used, s; and the DCF cost of capital, k.
Equation 11 also depends upon the asset growth rate, G. With a con-
stant debt ratio and a constant asset growth rate, the rate of external
equity financing is a residual equal to the rate needed to make up the
difference between the asset growth rate and the growth supplied by re-
tention of earnings; that is, s = G br. Consequently, for an', given b
and r, s varies with G. Alternatively, we can express the assumed con-
stant growth rate as the sum of its parts:
G = br + s. (12)
We can now substitute Equation 12 in the denominator of Equation 11 to
obtain Equation 13:
Sr(l b)(l + s) s(l + k br) (13)
In evaluating Equation 13, we are primarily interested in the
relationship between M/B and r, since r is a major parameter upon which
both utility companies and their regulators focus. Accordingly, we hold
constant the values of the other variables and analyze M/B as r changes.
As with the no-outside-equity-financing case, however, we still have the
choice of holding G constant or letting G = br + s increase with increases
in r. This is an important consideration, as M/B rises exponentially with
r if G is permitted to vary, but H/B is approximately linear if G is held
As explained earlier in this chapter, it is probably more realistic
to hold G constant than to let it vary, at least within a "reasonable"
range of values for r. Under the assumption that G is constant, Figure 5
shows how M/B varies with r at different asset growth rates. The main
features of the figure may be summarized as follows:
1. The relationship between H/B and r is approximately
linear for relevant ranges of r when G is constant.
2. When r = k, M/B = 1.0 regardless of the asset growth
rate, the retention rate, or the outside equity fin-
3. Whenever r > k, H/B is larger for higher values of
C, and conversely if r < k. That is, given two firms
with the same allowed rate of return, retention rate,
and cost of equity capital, but with different asset
growth rates, the firm with the higher growth will
have the higher M/B ratio if the allowed return is
greater than the cost of capital, but a lower H/B
ratio if less than the cost of capital.
I. The M/B ratio is most sensitive to changes in r if
the asset growth rate is large. For instance, with
G = 10 percent, a small change in r produces a sub-
stantial change in M/B, whereas, with G = 0 percent,
the same small change in r produces a much smaller
change in H/B.
The third and fourth points above are particularly interesting. If
a utility is in a rapidly growing service area, a value of r only slightly
less than k will produce a very low M/B ratio; conversely, if r is even
5 10 15
Figure 5: Market/Book Ratios With Sale of Stock.
Equation: IM/B = r(1 b)(l + s) s(l + k br)
k br s
Conditions: G = br + s = constant
b = 40.0%
k = 10. 5
G = 10C
G = 81
G = 0
slightly greater than k, the M/B ratio will be relatively high. Thus,
utilities in high growth areas are likely to exhibit a relatively high
degree of stock price instability in periods when realized rates of return
An additional factor affecting the market/book ratio is the cost in-
volved in floating a new stock issue. Thus far we have implicitly assumed
that flotation costs are zero, i.e., that new stock can be sold to net the
company the current market price. Clearly this is not a realistic assump-
tion; as a result, the model must be further expanded to allow for flots-
There are actually two types of flotation costs: (1) the specific
costs associated with underwriting an issue, including whatever under-
pricing might be necessary to sell the issue, and (2) the more subtle
impact of a continual increase in the supply of a given stock. The spe-
cific costs associated with a given flotation, as a percentage of the
funds raised, is designated by the term F. Assume first that a stock is
selling at $50 per share before a new financing is announced, that selling
efforts enable the underwriters to market the stock at $50, and that under-
writing costs are $2 per share. In this case, the seller will net $48 per
share, and F = $2/$50 = 4 percent. If, however, market pressure caused
the stock to decline so that it was sold to the public at $45 to net the
seller $43, then F = ($50 $43)/$50 = $7/$50 = 14 percent.
If the issue were a "one-time-shot", or at least if issues occurred
only every four or five years, the market price would probably rebound to
the original $50 price, assuming the firm earned its cost of capital. If,
however, the firm were forced to go to the market every year or two, and
investors expected this situation to continue, then the continuous pressure
cf new shares being put on the market might hold the stock price down in-
definitely. Whenever supply increases faster than demand, there will be a
tendency for price to decline. Of course, if M/B > 1.0, and the sale of
stock can be expected to boost earnings (i.e., to increase g2), then this
pressure should not be great.
The percentage flotation cost, F, associated with an individual stock
issue is incorporated into Equation 14, which is derived in Appendix E:
i/B = r(l b)(l + s)(l F) s(l + k br) (14)
(k br s)(l F)
If F = 0, then Equation 14 reduces to Equation 13; but if F > 0, I/B is
lower than it would otherwise be. If F = 0 and G = br, then Equation 14
reduces to Equation 9, the basic M/B relationship presented in an earlier
section of this chapter.
Figure 6 shows how the M/B ratio varies with r, assuming different
values for F. Some interesting features of the figure include the
I. If r = k, then M/B = 1 only if F = 0 or if s = 0.
In the figure, H/B = 1 where r k 10.5 percent
only on the line with F = 0. In other examples
depicted, H/B < 1 where r = 10.5 percent.9 Flo-
tation costs do not affect the M/B if no new stock
is sold, i.e., if s = 0.
2. The higher the value of F, the larger is the value
of r needed to attain a specified H/B ratio.
'Where F > 0, the cost of capital obtained by selling new stock is
greater than k, the DCF required rate of return on the common stock. This
point, which is discussed in detail in Weston & Brigham's Managerial Fi-
nance, 4th ed., pp. 306-307, explains why the H/B ratio is less than 1.0
if r is set equal to 10.5. The true DCF cost of capital is greater than
10.5 percent if the firm incurs flotation costs; setting r = 10.5 implies
r < k, which leads to M/B < 1.0.
5 10 15 20
Figure 6: Market/Book Ratios With Sale of Stock and Flotation Costs.
./B r(l b)(1 + s)(l F) s(1 + k br)
(k br s)(1 F)
Conditions: G = br + s = constant = 6.07
b = 40.0%
k = 10.5%
F = 0%
F = 10o
F = 20 ,
3. At the point where r = 15 percent, the firm can fi-
nance its 6 percent growth rate through internal
equity only. Here the Hl/B ratio is independent of
flotation costs. That is, G = br and s = 0 at this
4. When a firm finds it necessary to sell stock in
order to achieve a particular rate of asset growth,
flotation costs decrease the amount of incoming
funds, as reflected in the factor (1 F). In
the case where retained earnings, given a speci-
fied level for b, exceed the amount needed to fi-
nance asset growth, stock may be purchased to re-
duce the expansion of equity capital. Flotation
costs are really brokerage costs, and they increase
the amount of outgoing funds, so the correction
factor is (1 + F). In this example, the lines bend
down past r = 15 because, if G, b, and the debt ratio
are all to remain constant, then the firm must re-
purchase and retire stock, and F becomes a broker-
age rather than a flotation cost.
Equation 14 is probably the best, or most realistic, model relating
1/B ratios to allowed rates of return. If the author were called upon to
recommend to a utility commission the allowed rate of return needed to
attain a specific M/B ratio, he would use Equation 14 as the basis for the
recommendation. The model, however, is subject to several faults which
might cause the actual M/B to deviate from the one predicted. As we shall
see in Chapter 3, the model is extremely sensitive to both required and
allowed rates of return. Thus, when investor expectations are not met,
actual M/Bs may vary widely from those calculated using expected values
in the model.
Other Market/Book Models
Among the studies concerning the importance of the market value/
book value relationship in public utility rate regulation are those of
Gordon, Thompson and Thatcher, Morton, Carleton, Myers, and Davis.
Mortonic considers the proper level of the tl/B; Carleton concerns himself
with the economic impact of rate decisions under inflation; Davis delves
into the impact of regulation on capital budgeting; and the other studies
deal with the theoretical relationships among the various financial para-
The groundwork for developing a theoretical relationship between the
market price and book value was laid by Gordon.11 His DCF cost-of-capital
model (k = D /P + g) provides the basis from which more complex models
have been developed. Gordon assumed that expected dividend yield and ex-
pected dividend growth through retention of earnings are the quantifiable
determinants of the cost of capital. The model assumes no new financing
through sale of stock or bonds. Furthermore, the expected dividend growth,
which is the product of the retention rate and the allowed rate of return,
is assumed to be constant over tine.
This basic model was used by Stewart flyers'2 to demonstrate that the
market price will equal the book value per share if the allowed (and
actual) rate of return is set equal to the cost of equity capital, i.e.,
if r = k, then P = B or M/B = 1.0. Essentially, Myers expressed the
market/book ratio as a function of the allowed rate of return, the required
rate of return, and the rate of earnings retention, i.e., M/B = f(r, k, b).
Gordon later generalized his own model to include circumstances of
growth through external funding as well as through retained earnings.13
lW. A. Morton, "Risk and Return: Instability of Earnings as a
Measure of Risk", Land Economics (lay 1969), pp. 229-61.
12S. C. Myers, "The Application of Finance Theory to Public Utility
Rate Cases", The Bell Journal of Economics and Management Science, Vol. 1,
No. 2 (Autumn 1970), pp. 245-270.
'3M1. J. Gordon, "The Cost of Capital for a Public Utility", Unpub-
lished paper, February 1973, University of Toronto.
Thompson and Thatcher14 built a model relating the allowed rate of
return on equity capital and the rate of growth of shares via the market/
book mechanism. They asserted that the rate of earnings on equity capital,
not just the rate of dividends, should be reflected in the cost of equity
capital. T & T assume that a utility's growth rate in total assets is de-
termined by growth of consumer demand, and that asset growth is independent
of the retention ratio. Further, they assume a stable capital structure,
so the rate of growth of assets is also the rate of growth of equity.
The Thompson and Thatcher net-asset rate of growth, "I, is equivalent
in concept to our asset growth rate, C. This equivalency can be shown as
follows. First, our LS is equivalent to their h:
LS o = growth in total book equity = change in number of
(1 F)P price after flotation costs shares outstanding.
h =S sS0 s o rate of growth in
S (1 F)P S (1 F)P number of shares.
Second, they write the asset growth equation as follows:
y = (i p)r + P(t)fh E-t)
y = asset growth rate
P(t) = market price of a share at time t
S(t) = number of shares outstanding at time t
E(t) = book value of equity at time t
p = dividend payout ratio
h = growth rate of shares of common stock
f = ratio of net proceeds to market price
r = allowed rate of return.
H. E. Thompson and L. W. Thatcher, "Required Rate of Return for
Equity Capital Under Conditions of Growth and Consideration of Regulatory
Lag", Land Economics, Vol. 49, No. 2 (May 1973), pp. 148-162.
Substituting the symbols used in our Equation 14 into Thompson and Thatcher's
equation, we obtain
G = br + P (1 F) o 0 1
(1 F)P B
= br + s,
which is our Equation 12.
Thompson and Thatcher expressed the M/B ratio as a function of the
allowed rate of return, the required rate of return, growth in equity
capital from all sources, the dividend payout ratio, and the rate of
growth of shares. Their equation is, with cx = lI/B, as follows:
L = pr
p (y h)
Substituting our smybols from Equation 14 into their equation gives the
o (1 b)r
( F)P BsB
C(1 F)P sB
K (1 F)P
(1 b)r(l F)P
k(] F)P G(l F)P- + sB
(1 b)(l F)P r
(1 F)(k G)P + sB
Multiplying both sides of the equation by (1 F)( O)P + sB gives
(1 b)(l F)P r
(1 F)(k G)P 2 + sB P= ( b)(l F)P B r.
Dividing through by P B results in
(1 F)(k G) + s = (1 b)(l F)r
o 0 (1 b)(I F)r s
B (1 F)(k G)
Substituting C = br + s, we obtain
H/B (1 b)(l F)r s
(1 F)(k br s)
Their equation, although somewhat different than our Equation 14, leads
to the same conclusion, namely, that market price will equal book value
per share if r = k and there are no flotation costs, but, I/B will be
less than unity if there are positive flotation costs whenever r = k and
growth is positive.
Thompson and Thatcher rewrite both the growth equation and the H/B
equation to express r in terms of net asset growth and in terms of the
H/B. Given a set of values, including an H/B value, they solve these
equations simultaneously for r and h. This system finds the allowed rate
of return and the rate of growth of shares necessary to produce the given
Carletonis argues that the cost of equity capital responds to monetary
changes and that these changes were not adequately considered by Thompson
and Thatcher. He addresses the problems of inflation and regulatory lag
and proposes a partial solution by an alternative method for calculating
the equity base; however, he then notes there is a legal precedent16
against his suggestion to allow after-the-fact for return on equity in
constructing the rate base.
Davis' study7 concerns the relation of growth, allowed rates of re-
turn, and capital attraction to capital budgeting. He addresses the prob-
lem of how to account for these three factors in the capital budgeting
process. His assumptions are largely consistent with ours, as are his
conclusions. He concludes that in order to insure consistent growth at
a constant rate over the planning horizon, the allowed rate of return
should be set at the investor discount rate, corrected for flotation costs,
plus the growth rate, also corrected for flotation costs and any imper-
fection in the capital market response.
The market/book valuation models illustrate that the market price
can be expected to be lower than book value per share if the allowed (or
actual) rate of return is less than the stockholders' required rate of
return, i.e., M/B < 1.0 when r < k. If new stock is sold under these
circumstances, the original stockholders' claim to earnings is reduced,
'U. T. Carleton, "Rate of Return, Rate Base and Regulatory Lag Under
Conditions of Changing Capital Costs", Land Economics.
16Galveston Electric Co. v. City of Galveston, et al., 258 U.S. 388
17Blaine E. Davis, "Investment and Rate of Return for the Regulated
Firm", The Bell Journal of Economics and Management Science, Vol. 1,
No. 2 (Autumn 1970), pp. 245-270.
relative to the claims of the new stockholders. Repeated offerings of
new stock to the public at prices below book value causes the deteriora-
tion of an early owner's portion of earnings over time. Consequently, the
financial community recognizes that the sale of new stock at a price be-
low book value is undesirable. Graham, Dodd and Cottle recognized this
sentiment when they stated, "If a utility company's earnings were re-
stricted to a level that supported common stock prices at say, not more
than 10 percent above book value, then utility equities would lose a major
part of their investment appeal...." l
This chapter examined DCF rate of return models previously used in
regulatory proceedings, then developed a new model suitable for such use.
In all of the models, the market/book ratio is forced to unity (M/B = 1.0)
if the regulatory body allows a return exactly equal to the cost of equity
capital (r = k). If flotation costs were zero, then with an Hl/B = 1.0,
equity financing would leave old stockholders' financial position unchanged,
whereas their position would be improved if H/B > 1.0 or worsened if
M/B < 1.0. In reality, problems will arise if a company must sell new
stock at a time when its M/B is exactly equal to unity. Flotation costs,
including fees to investment bankers and downward stock price pressure
from the increased supply of the firm's securities, would promptly drive
the M/B below unity, causing the old investors a loss on stock price.
To allow for the sale of new equity, various expert witnesses have
suggested that market/book ratio should be somewhat above unity. In an
B. Grahnm, D. C. Dodd, and S. Cottle, Security Analysis, 4th ed.
(New York: :IcGraw-Hill Book Company, 1962), p. 598.
attempt to understand these proposals and to define more clearly the re-
lationships involved, this chapter developed a relatively complete market/
book model. With this expanded model, we see that a generally linear re-
lationship exists between H/B and the allowed rate of return. Given a
combination of variables, we can use the model to determine the rate of
return on book equity necessary to achieve a target II/B ratio. At this
point, however, the question of an appropriate target H/B ratio is still
open. The question is addressed in Chapter 4, but first, in Chapter 3,
we test the H/B model to see just how well it actually explains empirical
The model developed in the preceding chapter is based on a number
of assumptions; to the extent that the assumptions are not realistic, then
relationships predicted by the model will not hold in the real world, and
the model will not be useful for regulatory purposes. Accordingly, it is
necessary to test to see whether or not the postulated relationships hold.
The major test involves generating data on such factors as the expected
rate of return on book equity, the expected asset growth rate, flotation
costs, and the required rate of return; inserting these values into the
M/B model; and comparing the predicted M/B ratios for a sample of companies
with their actual I/B ratios. To the extent that the model is an accurate
representation of reality, and that we can develop reasonable proxies for
investors' expectations regarding the independent variables, a close re-
lationship will exist between the "calculated" or predicted M/B values
and the actual M/B ratios.
The first section of the chapter delineates the factors that are
taken into account by potential investors and security analysts in the
process of forming expectations about the future financial performance of
individual firms: (1) the required rate of return on equity (k), (2) rate
of return on book equity (r) investors expect the Commission to permit,
(3) the expected retention rate (b), (4) the expected rate of growth in
total book value from the sale of common stock (g2), (5) the expected
growth rate in assets (C), and (6) expected flotation costs (F). Since
all of these variables represent expectations of future events, they can-
not be measured directly, but, rather, must be proxied in some manner on
the basis of existing ex post data.
Given the basic input data, in subsequent sections we go on to de-
velop calculated or predicted M/B ratios for a sample of electric utilities,
co compare these predicted ratios with the companies' actual M/B ratios,
and to test the statistical significance of the findings. The results do
turn out to be statistically significant, although some companies' actual
M/B ratios are quite different from the predicted values. A careful anal-
ysis of these cases reveals that the model is quite sensitive to certain
ones of the input variables, and slight errors in the variables can lead
to large errors in the calculated M/B ratios. This sensitivity suggests
both the critical importance good input data and also the need for ex-
treme care in using the model for regulatory purposes.
Tie Independent Variables
The model is built on expectations about the future. The market
price of a stock depends upon the cash flow stream (dividends and capital
gains) the investor expects, and the rate at which he capitalizes that
income stream. Both dividends and capital gains depend upon the firm's
earning ability and the proportion of earnings that are retained. Growth
in earnings and dividends is determined by the rate of return earned on
common equity, the rate of earnings retention, and the sale of new stock.
Since all of these variables relate to future occurrences, ex ante values
are the proper ones to use in testing the model.
Equation 15, which we regard as the most realistic model and which
is the primary one used for the empirical tests, is repeated here for
/B = 'r(l b)(l + s)(l F) s(l + k br)
(k br s)(l F)
Ex ante values are needed for each of the independent variables in Equa-
tion 15: r, the expected rate of return; b, the retention rate; s, the
growth rate in total book value from sale of common stock; k, the investors'
required rate of return; and F, the flotation costs expressed as a percent-
age of the funds raised.
The dependent variable, which is the market/book ratio, M/B, is a
known quantity at any particular time t, and it is determined by values
which investors expect the independent variables to assume in the future.
Although we know investors do not expect the independent variables to re-
main constant over time, we believe that investors do expect these vari-
ables to fluctuate within a fairly narrow range, and that the mean of this
range is used when evaluating the value of the stock. For example, in-
vestors will expect the retention rate to vary somewhat due to changes in
earnings, but in investment decisions they analyze the stock with a spe-
cific value of b in mind. Our task is to determine the value of this fu-
ture value of b as estimated by investors. Clearly, past values of b will
be a major determinant of the expected future b, but just as clearly, the
average value of b in the past is not necessarily the value investors pro-
ject for the future.
Some variables may be expected to change in the future; for example,
a particular company's asset growth rate, G, might be expected to remain
high for a few years, then to decline. If we know the time path of this
expected growth rate, we can calculate an average growth rate--a single
value--for use in fitting the model. In any event, the task is to deter-
mine from ex post data, ex ante values of the independent variables.
Having done so, we can use these values in Equation 15 to calculate the
H/B ratio. If the model is a good representation of the market valuation
process, and if we have proxied the expectations reasonably well, the cal-
culated II/B ratios will be close to the actual ratios.
The Allowed Rate of Return on Book Equity (r)
Since the allowed rate of return, r, is a key determinant of price
in this valuation model, we must determine what values are in investors'
minds at present concerning future values of r. Investors consider many
factors in reaching this judgment, including (1) the past returns actually
achieved by the company, (2) the relation of these past returns to the re-
turns explicitly allowed by the regulatory agency in rate findings, (3)
the average returns earned by the industry, (4) the relation of the firm's
rate of return to the industry average, (5) the rate of return on bonds
and other alternative investments, (6) the riskiness of the stock, and
k7) coverage ratios.
An investor or security analyst would be interested in past rates
of return for a firm, since this is solid evidence of past achievements.
Also, the trend of past rates over time might offer a first clue to future
rates. But earnings and rates of return cannot necessarily be expected
to continue on an established course of growth or decline; other factors
must also be considered. In the case of utilities, particularly electric
utilities, demand and asset growth over the long run has been demonstrated
to be closely related to population growch,1 although recent experience
during and following the energy crisis of 1973 suggests a certain degree
J. B. Cohen and E. D. Zinbarg, Investment Analysis and Portfolio
Management (Homewood, Illinois: Dow-Jones-Irwin, Inc., 1967), pp. 253-254.
of price elasticity not heretofore thought to be important. Here, then,
are two exogenous factors affecting demand which are certainly considered
Normalized rates of return
The earnings of any business are affected by random economic factors
that cause revenues and expenses to fluctuate from year to year. Investors,
however, cannot anticipate each random fluctuation when forming earnings
expectations. Instead, they project a rate of return that is either con-
stant or steadily changing, while recognizing that random events will
occur and will affect future net income. Hence, when they compare past
predictions to actual returns, they find that the two seldom, if ever,
One method used to smooth out past random fluctuations and thus
better predict future trends is least-squares regression. Applying least-
squares regression to past rates of return minimizes the expected value
of the squared error in prediction, forcing all predicted values to lie
on one curve or line. Investors might accept the regression equation de-
rived from past data as a fair approximation of predicted rates of return.
Realized rates of return, r, are regressed as the dependent variable
against time, t, (years), using a linear equation of the form r = B Bt,
where B is a constant and B is the regression coefficient. We use both
the "normalized" values from the regression line, as illustrated in Fig-
ure 7, as well as individual annual values in the empirical tests of the
"Zone of reasonableness"
The regulatory climate is also quite important to the utility
Figure 7: Actual and Normalized Rates of Return for Tampa Electric
Source: Calculated from the Compustat Annual Utility Tape.
I I I I I I- ,IIII l l i I
because the maximum rate allowed is determined by a regulatory commission.
The relationship of the company's recent returns to generally allowed re-
turns for the jurisdiction would be of significance to the analyst. Regu-
latory commissions often think in terms of a range within which the rate
of return is reasonable or "fair." If this range were rising gradually
over time, perhaps because of inflation and a rising debt ratio, a regu-
lated firm's return pattern might be something like that depicted in
Figure 8. When a rate increase is granted, the utility's race might jump
co the target rate of return. The firm might maintain this rate of return,
or the rate might fall under inflationary pressures or rise if conditions
of increasing productivity existed. If the commission perceives that the
zone of reasonableness is rising faster than the company's return, the
firm will soon find itself at the bottom of the range. At this time, the
regulators will presumably grant another rate increase that will put the
firm back near the target. This repeated action could cause a sawtooth
earnings pattern such as that shown in Figure 8. The astute investor
would recognize this phenomenon and be aware of impending rate cases and
potential rate adjustments. He would then look at past returns with an
eye to the future, and anticipate that past races might be adjusted.
The average returns earned by the industry in general, and in par-
ticular by those companies within the same regulatory jurisdiction as the
firm in question, would also offer insights into the expected rate of re-
turn on equity. Over the period from 1954 through 1972, the average rate
of return for three Florida companies exceeded the national average by
from one to two percentage points; see Figure 9.2 The same figure also
'One could argue that this premium indicates a lenient commission,
that is reflects a higher cost of capital caused by risk differentials,
Figure 8: Hypothetical Pattern of Rates of Return for a Pegulated
SI I I . I p I I I p I
Pates of Return for
Tampa Electric Company and Regional and
Tampa Electric Company data are normalized by least-squares
The Florida average is the arithmetic average of data for
three electric utilities.
The national average is the arithmetic average of 23 elec-
tric utilities from throughout the nation.
Source: Calculated from the Compustat Annual Utility Tape.
r (. )
shows that Tampa Electric Company's rate of return has historically fluc-
tuated about the Florida average, sometimes higher and sometimes lower.
One would expect that any individual firm would tend to follow the juris-
dictional average rate rather closely, perhaps with some adjustment for
relative riskiness as reflected in the debt ratio, so if the individual
firm's return were to diverge from the jurisdictional average, the regu-
lating body could be expected to take steps to bring the company back into
The debt-to-total asset ratio is another factor that influences the
level of rates of return. Higher debt ratios imply higher risk because
of higher fixed interest payments, and lower coverage ratios. Thus, a
firm with higher than average debt could be expected to have a consistently
higher than industry or jurisdictional average rate of return, and con-
versely for a firm uith a lower than average debt ratio.
Putting the factors together to estimate r
Many factors have been mentioned as having an influence on the for-
mation of investors' expectations. The investor, trying to assess future
earnings prospects for a given firm, would presumably look at all of these
factors, pull them together in some fashion by assigning weights to each
reflecting their relative importance, and reach a projected value for the
rate of return, r. This process might be formalized, rigorous, and con-
sistent, or it might be quite informal and impressionistic. Institutional
that it is a necessary premium needed to attract capital to companies
growing more rapidly than the national average, that it reflects low "qual-
ity" earnings representing in large part an allowance for funds used during
construction, or all of these factors. We have not analyzed why the dif-
investors are likely to make relative formal estimates, individual inves-
tors to make informal judgment (although individuals could base purchase
decisions on analysts' recommendations, which might, in turn, be based on
formal analysis.) If we knew the factors and weights used in the aggre-
gate by investors at any given point in time, then we could incorporate
these factors into a model to estimate r, which could then be used in the
market/book model for one particular year. If these aggregate assessments
and weights were known to be stable from year to year, the same evaluation
procedure could be used annually. Correspondingly, they could be altered
to reflect known shifts in the estimation parameters. Unfortunately,
neither the variables nor the weights are known for sure, so our estimated
values for expected r could differ markedly from those of investors. Such
differences would cause the calculated and actual 11/B ratio to differ.
The Retention Rate
As with r, we are really concerned with future retention rates, but
lacking clairvoyance, we can only form expectations and estimates of future
values. Investors presumably begin with past retention rates and, as a
first approximation, assume that similar levels and trends will continue
in the future. Upon closer examination, they may discover that b appears
to be a direct function of the rate of return, that is, b = f(r). This
is a reasonable expectation in view of the fact that many companies tend
to maintain a reasonably stable dollar dividends per share over time,
with occasional increase, while trying to avoid decreases. Thus, in a year
when the rate of return rises, yet dollar dividends stay the same, the re-
tention rate would rise, and conversely when the rate of return falls. A
firm with wide fluctuations in earnings would generally pay out a low pro-
portion of earnings to be sure that its dividends are protected from having
to be reduced in years when earnings are low. Consequently, firms with
unstable earnings often have higher retention rates than those with more
stable earnings. This factor would be reflected in past data and could
be expected to continue into the future, barring drastic changes in the
nature of the firm or its product market. Since the retention rate is
subject to random fluctuations, the least-squares technique can be used
to normalize retention rates; thus, past retention rates were regressed
against time, and the normalized values were used as proxies for investors'
expectations of the effective rate.
The past and expected future growth of the firm's demand should also
be taken into consideration when determining expected values for b. If,
for example, a firm has been experiencing rapid growth for some period,
and had a had a high retention rate during this time, it apparently was
using a large portion of its earnings to finance the expansion. If a
slower growth rate is forecast for the future because demand is leveling
off, then the company's financing needs would probably diminish, allowing
a higher portion of earnings to be paid out as dividends. Under such cir-
cumstances an investor might reasonably anticipate lower retention rates
to accompany lower growth rates.
The debt-to-total asset ratio may affect the retention rates of dif-
ferent companies. A firm with a higher debt ratio than another would have
a lower borrowing capacity, ceterus paribus, and it might be forced to fi-
nance a higher proportion of its capital needs through equity, and specif-
ically by retaining earnings. Thus, a firm with a high debt ratio might
also be expected to have a relatively high retention rate.
Growth Due to Sale of Stock
When a firm finds that .retained earnings plus new debt are
insufficient to meet its financial requirements, it must turn to external
equity financing. Utility companies faced with a high growth in service
demand and a capital intensive production process, are often in this situ-
ation, so outside equity financing does affect investors' expectations re-
The variable s is defined as the growth rate in total book equity
resulting from the sale of common stock. When funds are needed and sale
of common stock is the method of financing decided upon, the number of
new shares can be found by dividing the total dollars needed by the ex-
pected sales price of the stock. Let S be the total number of shares out-
standing before the new stock is sold, and let BO be the pre-sale book
value per share. The total book value before the stock sale is then SBo,
and the amount raised by the sale is sSB The number of shares that must
be sold at price Po, after a flotation cost of F percent, is:
AS = sSB /Po(1 F).
We can rearrange this equation to show s is a function of the market/book
ratio, P /B and the percentage change in the number of shares outstanding,
ASP (1 F) AS P
s (1 F).
SB S B
If, for example, shares were increased 10 percent, with a market/book
ratio of 2.0 and a flotation cost of 10 percent, then s would be 18 percent
(.10 x 2.0 x .9 = .18). If the H/B was 1.0, then s would be nine percent
(.10 x 1.0 x .9 = .09).3
If the rate of return and the retention rate are both high, so that
much expansion is being financed through earnings retention, then s may
be small, perhaps even zero. Further, companies tend to sell stock peri-
odically, using changes in their debt ratios to take up the slack between
equity issues so at times s will be zero for a few years, and then, in a
year when common stock financing is undertaken, have a substantial value.
Security analysts recognize this periodic equity financing, so they tend
to use a smoothed or average annual s, rather than the actual values. In
the M/B model, we need a long-run annual expected value for s rather than
the on-again, off-again values actually observed.
Several alternative smoothing techniques might be used. First, we
could use a least-squares regression to get a trend line over time, then
use the predicted value for each year as the expected value of s. But,
this procedure might not capture long-run expectations if there were long
periods with no stock sales and occasional years with large stock sales.
A second alternative involves assuming that the target proportion
of equity in the firm's total capitalization is a constant, or, as is more
often stated, that the debt-to-total asset ratio is constant. With this
assumption, the rate of growth of equity is the same as the rate of growth
of debt, and. therefore, the same as the rate of growth of total assets.
Since the total growth in equity comes from both earnings retention, br,
and sale of stock, s, this rate is the sum of the two parts, br = s.
Note, however, that the relationship is not causative: s is not
determined by the H/B; rather, s is determined by the amount of financing
needed. Thus, s is specified exogenously in the derivation of AS and
survives further derivations to play an important role in the final M/B
Given the assumption of a constant debt-to-total asset ratio, total asset
growth, G, equals the equity growth rate. That is, G = br + s. Hence,
s can be calculated as s = G br, where G is the change in total assets
during period t divided by the asset value at the beginning of the period,
and h and r are determined as previously described.
Under the second procedure, s is a residual dependent upon the total
asset growth, the retention rate, and the rate of return; given values for
these variables, s is automatically determined. The really critical
issue is the asset growth rate, G. Consider an electric utility. Its
demand depends primarily upon population growth, industrial use, intro-
duction of new, electricity-consuming appliances and equipment such as
air conditioning, upon the general health of the economy, and upon the
price of electricity. Electricity has historically been thought of as
rather price inelastic. However, the recent energy crisis has led to a
reconsideration of the elasticity question. Usage of electricity has
declined, perhaps because of rising prices but also perhaps because of a
patriotic desire to conserve energy.
If price elasticity is low, then we can conclude that factors exo-
genous to the model determine utility demand, i.e., that finding s as a
residual is valid. Since utilities have a responsibility to serve all
demands presented to them, their total asset growth is an exogenous vari-
able, determined by growth in demand. Plant expansion must occur at a
rate which will enable the companies to meet the public's demand. Total
asset growth, G, is not limited to growth that can be financed through
earnings retention, br; if G exceeds br, then retained earnings must he
supplemented by sale of debt equity. Although new bonds and new common
stock are not always issued simultaneously, compaines try to maintain a
fairly consistent debt-equity relationship over time. Hence, it does not
seem unreasonable to assume a constant debt-to-total asset ratio and to
calculate s = G br. We must, of course, have reasonably good values
for G, b, and r if our estimate of s is to be a good one.
Actual values for G vary from year to year, since large plant addi-
tions occur in certain years while lesser growth takes place in others.
Accordingly, most security analysts use an average growth rate in their
projections. This average growth rate can be proxied, for each utility,
by running a least-squares regression of G against time. The predicted
value from the regression equation is a good first-approximation estimate
of the long-term asset growth rate. Trends are not always continued,
however, and analysts might recognize that during any given period of time
even normalized values of G could differ from the long-run growth rate
needed in a model such as Equation 15. Suppose, for example, that during
a sample period a particular company's G is 25 percent. Nio analyst would
project such a high growth rate; rather, he would constrain G to a more
reasonable (lower) level.
Flotation costs are represented in Equation 15 as the variable F,
which includes all costs associated with a new issue of common stock ex-
pressed as a percentage of the equity capital thus raised. The percentage
flotation costs associated with issuing new stock affect the M/B ratio
because a portion of the new dollars invested in the firm is absorbed as
an issue cost, thus is not available for the purchase of productive assets.
Flotation costs depend upon a number of factors. First, the larger the
size of the issue, the lower the percentage flotation cost other things
the same. Thus, very large firms generally lower percentage costs than
smaller companies simply because their stock issues are larger. The rep-
utation of the company and the strength of the stock at the time of the
issue also affect flotation cost. A temporary depression in stock price
resulting from the pressure of a new issue in the marketplace is consid-
ered a part of the flotation cost. This element of cost may not exist if
the firm is in favor with the investment community so that the demand for
the stock is sufficient to offset the increase in supply caused by the new
issue. Such intangible elements of cost are difficult to ascertain on
either an ex ante or an ex post basis. The security analyst, nonetheless,
may anticipate a temporary price depression in forming expectations about
the future value of a stock.
Another type of price depression is possible from the issue of new
stock: there may be a gradual price decline due to a gradually increasing
supply of stock brought about by frequent trips to the market. This cost
is not a flotation cost in the sense intended in Equation 15, because it
is not associated with one particular issue. Instead, the investor would
recognize this erosion of earnings as an additional risk and would, accord-
ingly, require a higher rate return in order to be induced to invest in
or to maintain a position in a given equity security.
The total costs of flotation expected to accompany future stock
issues, as seen by the potential investor, would be the proper value to
use in calculating the percentage flotation costs, F, for use in Equation
15. With this variable now defined, one may turn to the remaining vari-
able in the model, the investors' required rate of return.
The Required Rate of Return
The rate of return required to attract capital plays an important
role in the determination of the market/book ratio. This required rate
of return is expressed as follows:
k* = RF + P.. (16)
k F 1
Here k*. is the required rate of return; R is the risk-free rate of re-
turn, and P. is a risk premium.
Long-term government bond yields are used as the risk-free rate.
Government bonds are risk free in the sense of being free from default risk.
If one buys a long-term government bond and holds it to maturity, he knows
exactly what his cash flow will be over the life of the investment. Since
he knows these cash flows with certainty, there is no risk involved.
Several factors influence the risk premium. First, the general na-
ture of the business in which the firm is engaged would be considered.
Since we are dealing with regulated utilities, an analyst would narrow
the field further to the specific type utility, for example an electric
power company. Closer examination would reveal that the processes by
which some firms operate are different from those of others and may affect
their riskiness. A firm that uses nuclear power to generate electricity
may face a different level of risks than one which, for example, generates
electric power in fossil fuel.
Political risk is particularly important to regulated utilities.
Each company is limited in its freedom to increase prices, in the services
is offers, and the territory it serves. In many instances the regulatory
officials are publicly elected, a situation which causes direct political
pressure to enter into the regulatory process. In addition to the risks
inherent in regulated businesses, political risks are brought to bear
through external groups organized to support such causes as environmental
Once the levels of business and political risks have been determined,
the analyst will consider the firm's financial risk. Financial authorities
agree that a company's cost of equity capital is functionally related to
the level of debt in its capital structure. The exact nature of the func-
tion has been the subject of considerable discussion during recent years."
One may generalize that increased debt in the capital structure accentuates
the variance of earnings, thus causing increased risk to the owners of
the firm. To compensate for the increased risk brought about by the use
of financial leverage, investors require higher returns from more highly
levered firms, ceterus paribus. An analyst would consider a firm's debt/
total asset ratio as a guide to the individual company's risk vis-a-vis
other firms in the same industry with the same business and political risks.
He would then presumably adjust his required rate of return upward if the
firm's debt ratio were above industry average and downward if it were
below industry average. The precise amount of the adjustment would be
largely a matter of judgment. The potential investor might receive assist-
ance or at least gain assurance from the bond ratings published by bloody's
Investors Services, Inc. and Standard and Poor's Corporation. The risk
classifications reflected in the bond ratings could be extended to encom-
pass the risk of returns to common equity.
Having considered the above risks, the analyst will decide upon a
risk premium. The sum of the riskless rate and the risk premium is the
required rate of return. If investors can reasonably expect to receive
this required rate, they will commit funds to the firm; othenrise, they
will not. Equation 1 states this proposition symbolically and is referred
See J. F. Weston and E. F. Brigham, Managerial Finance, 4th ed.
(New York: Holt, Rinehart and Winston, Inc., 1972), Appendix A to Chapter
11, pp. 337-40, for a discussion of "The Leverage Controversy."
to as the capital market line (CHL). From year to year (or period to
period) the capital market line may shift vertically and may change slope,
as illustrated in Figure 10.5 If the riskless rate, RF, rises, while the
risk premium, Pi, remains unchanged, then the required rate of return,
k*i, will rise by the same amount as the risk-free rate. The risk pre-
mium for any class of risky assets, however, need not remain constant over
time, and it can change the slope of the capital market line whether or
not RF changes. Alternatively, an individual security can change from
one risk class to another as economic conditions and financial factors
within the company change.
Suppose, for example, that in 1954 investors were willing to accept
2.53 percent riskless return and required an additional premium of 0.40
percentage points for utility company bonds rated AAA by Iloody's. The
required rate on AAA utility bonds would be 2.93 percent, corresponding
to the point located by k*1954 and AAA1 in Figure 10. Using these tuo
points, we can construct the capital market line CHL1954. The rate of
return required on the common stock of a utility with AAA rating would be
somewhat above the rate required on the firm's bonds.
Between 1954 and 1965, the average utility's debt ratio fell from
66 percent to 61 percent; see Figure 11. This reduction in financial
leverage was largely responsible for a reduction in risk premiums on AAA
utility bonds: the average risk premium was down to only 0.29 percentage
points in 1965. The slope of the capital market line was correspondingly
tIn this dissertation, we do not treat explicitly that body of theory
known as the Capital Asset Pricing Model. No attempt is made herein to
measure risk by beta coefficients; rather, more traditional measures of
risk are employed.
C"FL 196 5
CMLI 9 5
C 4L1 ^
AAA AAA ,
Figure 10: Hypothesized Shifts in the Capital Market Line.
1955 1960 1965 1970
Figure 11: Electric Utility Industry Average Ratio of Total Debt to
Conditions: Total debt includes preferred stock.
The industry average consists of data from 23 electric
Source: Calculated from the Compustat Annual Utility Tape.
less steep during that period. The risk-free rate, however, had increased
to 4.21 percent by 1965 so that the total return on AAA utility bonds was
4.50 percent. Accordingly one can see that the capital market line in-
dicated by these figures shifted upward and decreased in slope between
1954 and 1965 to a position like CIIL1965.
By 1972 the riskless rate had risen to 5.63 percent and the risk
premium on AAA utility bonds to 1.83 percentage points, producing a total
required return of 7.46 percent. Assuming the designation AAA represented
the same level of risk in 1972 as in 1965, these data indicate that the
capital market line shifted upward and increased in slope between 1965 and
1972. The industry average debt ratio also increased to 67 percent during
this period, resulting in bond downgradings; both factors suggest that the
industry, on average, was being perceived as increasing in risk, i.e.,
moving out the horizontal axis and up the CML of Figure 10.
The degree of riskiness attributed to AAA utility bonds vis-a-vis
alternative investment opportunities probably increased to a position
such as AAAn in Figure 10. During 1965 AAA utility bonds yielded 0.05
percentage points more than AAA corporate bonds, whereas by 1972 the yield
spread had increased to 0.49 percentage points as shown in Table 2. This
change might indicate that the risk differential between utility bonds
and corporate bonds increased between 1965 and 1972; alternatively, it
might simply reflect the fact that utilities were, during this period,
borrowing much more heavily than industrials, and an excess supply of
utility bond in an imperfect market might account for tle difference.
Although the exact interchange of risk and return between these
classes of securities is unknown, it is reasonably certain that the aver-
age utility security moved outward to a higher risk level by 1972. A
YIELDS-TO-MATURITY FOR MOODY'S AAA UTILITY
BONDS MAD AAA INDUSTRIAL BONDS DURING
THE PERIOD 1954 1972.
Average Percentage Yields-To-flaturity
AAA Utility Bonds
4. 3 7
AAA Industrial Bonds
Source: bloody's Bond Survey (September 30, 1974), and loody's Industrial
Manual (1970), (Newt York: Moody's Investors Service, Inc.).
combination of chree factors--an increase in the riskless rate, an in-
crease in the slope of the capital market line, and an outward shift of
utilities as a risk class--consequently caused investors to require higher
returns from utility securities than in previous years. All of these
factors would enter a potential investor's analysis of the securities
markets and would affect his expectations about future returns and
return requirements. The solution finally reached would be used for
the required rate k* and, assuming capital market equilibrium, for the
expected rate of return k in Equation 15; thus, these factors would affect
Ex Post Variables
The preceding discussion has centered on the ex ante variables which
should be used in Equation 15 to predict market/book ratios. Because of
the nature of the variables, all of which are based on investors' expecta-
tions about the future, they cannot be determined exactly from ex post
data. Still, expectations are based in part on historical data, so we
need to find out what data are available and how they may be used to
approximate the desired ex ante values.
One cannot look backwards to a past year and determine exactly wht
investors' expectations for the future were at that time. Financial
records, however, reveal the occurrences which did take place, namely,
the income statements and balance sheets for public utilities are avail-
able. A large amount of data has been accumulated by Standard and Poor's
Corporation in the Compustat Annual Utility Tape for use with computerized
analysis. The tape provides annual income statement data and year-end
balance sheet data. Using the available data, we may approximate the
needed variables as closely as possible.
Each value needs to be calculated as of some point in time. Consid-
ering which point in time to use--for example, end-of-year, middle-of-
year, or beginning-of-year values--brings up the fact that certain vari-
ables are flow variables, whereas others are stock variables. Earnings
(a flow variable), for instance, are generated over the course of a year;
whereas book value (a stock variable), is measured as of a particular
date. Should the rate of return on book value be calculated on the basis
of the book value as of the first day of the year or as of the last day
of the year when the earnings were produced from assets all during the
year? Should the market/book ratio be calculated with data representing
only one point in time? This association of flow and scock variables may
generally be acceptable, but in an instance where, for example, a firm
doubles its asset holdings in one year, perhaps through purchase of another
company, the earnings flow is not actually generated from the asset base
as measured exclusively at either the beginning or the ending of the year.
Misleading values could emerge under such conditions. In anticipation of
this problem, the set of test values was calculated using averages of
beginning and end of year data. The market price for any given year, for
example, is taken as the sum of the closing price of the prior year and
the closing price of the current year divided by two. Average book values
and average total asset values are calculated similarly. Although the
Compustat data bank includes 20 years of data, 1953 through 1972, the above
averaging procedure reduced the number of observations for each variable
to 19, covering years 1954 through 1972.
The market/book ratio is calculated as the average price for the
year divided by the average book value per share for the year. The book
value per share is calculated by dividing the total book value by the
number of shares of common stock outstanding. This calculation and the
others which follow are summarized in equation form in Table 3. Since
averages of year-end per share data are used in this ratio, the values
must be adjusted for any stock splits or stock dividends which took
place during the year, because sensible averages could not be obtained
The actual rate of return on book equity is calculated as the earn-
ings available for common stockholders during the current year divided
by the average book value for the year.
Dividends and earnings are available on the tape and are used to
calculate the retention rate. The dividend payout rate is calculated
by dividing the dividends for the year by the earnings for the year. The
retention rate is then found by subtracting the dividend payout rate from
The rate of growth in total assets is found by dividing the change
in total asset value from the beginning of the year to the end of the year
by the beginning asset value. The rate of growth in total book value from
the sale of stock is the growth rate in total assets minus the product of
the retention rate times the realized rate of return.
The debt-to-total asset ratio is calculated as the sum of annual
average long-term debt, short-term debt, and preferred stock divided by
their sum plus the book value of common equity. The sum of year-end
figures for each component is divided by two to get the average value for
each year; however, since this division occurs in both the numerator and
the denominator, the twos cancel out and would be redundant in the equa-
tion given in Table 2.
The ex post variables must be further refined after they are taken
from the tape but before being used for empirical testing. To better
approximate the ex ante variables described earlier, one needs to estimate
EQUATIONS USED TO CALCULATE EX POST VALUES OF THE
VARIABLES IlI EQUATION 14 DIRECTLY FPOM
THE COIIPUSTAT AIINUAL UTILITY TAPE.
Definitions of Symbols
M/B = market/book ratio
P = price per share of common stock
BV = total book value of equity
S = number of shares of common stock outstanding
r = actual rate of return on book equity
b = retention rate
E = total earnings available for common shareholders
D = total dividends paid
C = rate of growth of total assets
s = rate of growth of total book equity from sale of stock
A = total asset value
D/A = ratio of total debt, including preferred stock, to total assets
LTD = value of long-term debt
STD = value of short-term debt
PFD = value of preferred stock
t = time period (year) t.
The Market/Book Ratio
M/Bt = (P-,1 + Pt)/(BVt_I/St-_ EVt/St).
The Actual Rate of Return on Book Equity
r, = E,/[(BVty + BVt)/2].
The Retention Rate
b, = 1 D/!E,.
The Rate of Growth in Total Book Value From Sale of Stock
G = (At At-1)/At-1 and
st = Gt btr.
TABLE 3, continued
The Debt/Total Asset Ratio
LTDt- + LTDt + STDt + STDt + PFDt- + FJDt
. = ITD + LTDt + STDC_- + STD + PFDt_- + PFDt + BVt_1 + BVt
an expected value or trend line value for the realized rate of return on
equity, the retention rate, and the total asset growth rate. The annual
values for each of these variables were regressed over time (years) using
the least-squares technique with the equation form y = a + bx in the Re-
gression Analysis Program for Economists. The actual values and the nor-
malized or predicted values are illustrated in Figure 12 and enumerated
in Appendix H for Florida Power Corporation. The normalized values rep-
resented by the straight line are the values used in subsequent testing
for the realized rate of return and the retention rate. The total asset
growth rate appears to need additional constraining before it is relied
upon as a long-term estimate of growth for the utility firm.
Although certain companies such as Florida Power Corporation en-
countered total asset growth rates in the range of 10 to 15 percent, nor-
malized, it seems unrealistic to assume that such growth will continue
indefinitely, or that investors expected a continuation of such rates of
growth. In all likelihood their ex ante expectations should be more
closely aligned with longer term growth rates of population, gross national
product, or electric power production. A total asset growth rate of six
percent per annum was judged to be a reasonable long-term growth expecta-
tation for the "average" firm in the electric power industry. In order to
recognize individual differences among companies, a functional relationship
was hypothesized in form of Equation 17.
bWilliam J. Raduchel, Regression Analysis Program for Economists:
Version 2.7 (Harvard University, February 22, 1972).
'Calculated from data presented in Cohen and Zinbarg, p. 254. Clearly,
the asset growth rate, measured in dollars, is dependent upon the rate of
inflation in utility plant construction costs. During most of the period
studied, construction costs were not going up rapidly, and the inflation
that was taking place was being offset to a degree by economies of scale
that served to keep capital costs per unit of service reasonably constant.
I i I i i !
Cn C n 0-
I I .I I I I
i i i
G = GI + a(Gi C). (17)
Here G is the growth rate used to approximate the ex ante rate from the
determined long-run industry growth rate, GI, and adjusted for the indiv-
idual firm's actual growth rate, Gi. If the company's growth is greater
than the projected long-term industry growth, then the estimated G is in-
creased by a proportion, a, of the difference, and decreased if the in-
dividual firm's rate is less than the average. The proportion of the
difference used in subsequent calculations is 60 percent; that is a =
0.60. The resulting C is then used to calculate the growth rate in
total book equity due to sale of stock, s.
The final variable that needs to be estimated before values can be
substituted into Equation 15 is the required rate of return, k*. As
shown in Figure 10, the required rate is composed of a risk-free return
plus a risk premium associated with the individual firm. The yield on
AA, utility bonds represents the minimum yield acceptable to investors
for the level of risk faced by the least risky utility bonds. This yield,
averaged for each year, is available in Moody's bond survey and is used
as a proxy for the riskless rate in subsequent calculations.8 To this
AAA bond yield a risk premium must be added to approximate the return
required to the "average" firm's common stock. Then, since each firm
represents a separate set of risks, each must have an individual risk
premium that may be more or less than the industry average. Perhaps the
key distinguishing feature in risk determination during the 1950s and
bEven AAA corporate bonds are not riskless, so the risk premium used
for equity in the subsequent analysis is somewhat lower than it would
be had U.S. Treasury securities been used to represent the riskless rate.
1960s was the debt ratio. In order to take into account this important
variable, the model used to generate risk premiums adjusts the "average"
risk premium according to the firm's debt ratio. This is accomplished
by determining the industry average debt ratio and multiplying the assigned
industry premium, PI, by the ratio of the firm's debt ratio to the indus-
try's debt ratio, as indicated in Equation 18:
k*. = RAAA + PI j (18)
This adjustment has the effect of increasing a firm's risk premium if
its debt ratio is above industry average and decreasing the premium if
the ratio is below the industry average.
With the data needs outlined above, the next step is to choose a
sample of firms with the necessary data.
Selection of the Sample
Some regulatory jurisdictions require that rate base valuation be
based on original cost, while others allow "fair" value in rate base
determination.9 Only firms in regulatory jurisdictions using original-
cost valuation of assets for rate purposes are used in the sample. Inter-
company differences in earnings and prices arising from rate base valu-
ation differences are likely to be minimized by using only original cost
companies. Further, many electric utility firms use accelerated depre-
ciation methods for tax purposes, but the reporting of depreciation ex-
penses to the public is not uniform throughout the industry. The
Alfred E. Kahn, The Economic of Regulation, Vol. I: Economic Prin-
ciples (Hew York: John Uiley & Sons, Inc., 1970), pp. 32-35.
regulatory commission must decide whether tax savings from accelerated
depreciation are to be "flowed through" to investors or "normalized" over
the life of the investment. With normalization, the tax savings are level
from year to year, while under flow through the tax savings are larger
during the early years of the investment's life and smaller during later
years. A firm with relatively new assets would flow through greater tax
savings than a firm with relatively old assets, whereas the same two firms
would report similar tax savings if the effects were normalized. For the
sake of comparability, only firms using normalized depreciation tax savings
are included in the sample.
A third criterion for company selection relates to the fiscal year
used. Compatibility of fiscal years among companies in the sample is
desirable in order to eliminate seasonal differences which might occur.
Fiscal years ending on December 31 tie in with the Compustat market value
data because all annual closing prices are calendar year end prices, not
fiscal year end prices. Only firms with fiscal years ending December 31
were included in the sample of utilities.
The Compustat Annual Utility Tape has the electric utilities separ-
ated into two groups according to whether they use normalized or flow
through depreciation tax reporting. The group using normalized data was
screened for those companies with fiscal years ending December 31. These
firms were then checked to be sure that all the necessary data was avail-
able before being included in the sample. The firms in the resulting
sample were checked by hand against the Public Utility Reports to find
those with original cost valuation of the rate base. This final screen-
ing process left a sample of 23 electric power firms to be used in the
ensuing empirical tests. The firms in this sample are listed in Appendix G.
LeasL-Squares Regression Analysis
This section explains the use of least-squares regression analysis
to establish whether or not statistically significant relationships exist
among the variables estimated ex post for use in Equation 15. Results of
this analysis are summarized in the text, and the regression statistics
are presented in detail in Appendix I.
The Regression Equation and Results
A least-squares regression using historical, cross-sectional data
assigns weights (coefficients) to each independent variable considered.
The resulting t-values indicate whether or not each independent variable
is statistically significant in determining the dependent variable, the
market/book ratio in this case. A least-squares regression minimizes the
expected value of the squared error in prediction, and all predictions
are forced to be on the resultant equation line. The regression coeffi-
cients serve to correct systematic measurement errors in the independent
variable. For example, if there were a systematic downward bias in esti-
mating the values of the growth variables, the net contribution of growth
in determining M/B ratios would not be diminished; instead, the value of
the regression coefficient would be increased enough to offset the mea-
The coefficient of determination, R2, for the regression equation
shows the amoiJnt of variation in the dependent variable which is "ex-
plained" by the independent variables in the sample. However, R2 is
known to be a positively biased estimate of the true coefficient of
determination for the underlying population. "...(T)he bias in R2 is no
greater than the ratio of the number of independent variables to the
number of observations in the sample.10 For the sample of 23 electric
utilities, the maximum bias would be 4/23 or 0.1793. The Barton coefficient
of determination, R2, is corrected for this bias and presents a more reli-
able estimate of the explained variation.11
In order to determine an appropriate mathematical form for the equa-
tion to be used in the market/book problem, one may examine the theoret-
ical relationships within a relevant range of values. Given hypotheti-
cal, but reasonable, values, Equation 15 approximates linearity as
depicted in Figure 13. Constant asset growth is assumed in order to
obtain this result. In view of this relationship, the following re-
gression equation form was chosen:
M/B = B0 + Blr + B2b + B3G + B4(D/A) + E (19)
The dependent and independent variables are identified in the previous
section of this chapter as ex post approximations of the desired, but
unobtainable, ex ante variables. The intercept term, B0, and the co-
efficients, B1, B2, B3, and B4, are to be determined from the data through
the least-squares regression, and E is an error term. This equation is
reminiscent of several stock price models tested by Gordon, Friend and
Puckett, and Bower and Bower,12 in that they also considered price or
price used in a ratio as the dependent variable and various measures of
earnings, dividends, leverage, and growth as the independent variables.
'D). B. Montgomery and D. G. Morrison, "A Note on Adjusting R ",
The Journal of Finance, Vol. 28, No. 4 (September, 1973), p. 1011.
''A. P. Barton, "Note on Unbiased Estimation of the Squared Mulri-
ple Correlation Coefficient", Statistica Neerlandica, Vol. 16, No. 2
(1962), pp. 151-63.
12H. Russell Fogler, Analyzing the Stock Market: A Quantitative
Approach (Columbus, Ohio: Grid, Ind.), 1973, pp. 179-92.
0 5 10 15 20 r()
Figure 13: MarkeE/Book Ratios ADproximating Linearity.
r(I b)(1 + s)(1 F) s(1 + k br)
Equation: M/B -
(k br s)(1 F)
Conditions: k = 10.5'
b = 40.0'.
C = 6.0
F = 10.0L
The data tested in Equation 19 are taken from the Compustat Annual
Utility Tape in the form illustrated earlier in Figure 7. The market/
book ratio, M/B, and the debt ratio, D/A, are used as extracted from
the data bank. The realized rate of return, r, is normalized over the 19-
year test period, as are the total asset growth rate, G, and the retention
rate, b, before being used in the regression. The process of normalization
by least-squares regression of the variable against time was explained
previously in this chapter.
A cross-sectional regression was performed on the data for 23 com-
panies during each of the 19 years in the period 1953 through 1972, in-
clusive, using the Regression Analysis Program for Economists.13 The
resultant Barton's coefficients of determination ranged from 0.5836 in
1972 to 0.7614 in 1964, indicating that the independent variables ex-
plained between 53.36 percent and 76.14 percent of the variation in the
market/book ratio in all years. In 12 out of the 19 years, 70 percent or
more of the variation was explained by the independent variables, as in-
dicated by the regression statistics presented in Appendix I.
T-values indicate the significance of each independent variable in
predicting the dependent variable, assuming that the multicollinearity
between variables is insignificant. The t-values in Appendix I show
that the normalized rate of return, r, is a significant determinant of the
market/book ratio, M/B, in each of the 19 years at the 0.10 level. The
retention rate, h, and the debt ratio, D/A, are significant in only six
'JWilliam J. Raduchel, Regression Analysis Program for Economists,
Version 2.7 (Harvard University, February 22, 1972).
'IThe correlation coefficients among the independent variables were
found to be generally insignificant as shown in Appendix N, so multicol-
linearity does not present a problem in the regression analysis.
years and two years, respectively. Apparently b and D/A are less impor-
tant in investors' analyses and evaluations of stock prices than is r.
The total asset growth rate, C, was significant and positively re-
lated to the M/B ratio from 1953 through 1968. The maximum t-value for
G occurs in 1961, after which time its magnitude decreases gradually until
it becomes insignificant in 1969 and 1970, and then the coefficient turns
negative during 1971 and 1972. Reference to Figure 16 in Chapter 4 shows
that the average market/book ratios for electric utilities declined stead-
ily from 1965 through 1972. As the I/B fell, the contribution of G to the
regression fell, and it finally became negative. This finding supports
the theoretical position that growth is desirable and exerts a positive
pressure on price when a firm's M/B is greater than unity, and is undesir-
able, having a negative effect on price when a firm's M/B is less than
Potential Problems in Regression Analysis
The results of a regression analysis can be invalid if the data do
not meet certain requirements. One of these requirements is that multi-
collinearity does not exist among the independent variables. Fortunately,
the simple correlation coefficients among the independent variables indi-
cate that multicollinearity is not a significant problem in this study.
(See Appendix J.) Another potential problem is spurious correlation.
The fact that both the dependent variable, M/B, and the independent
variable, r, have the book value per share as the denominator could cause
spurious correlation; that is, the reported correlation between M/B and
r might be unduly influenced by their common denominator. In the case
under consideration, one would expect a high degree of correlation between
price and earnings per share, the numerators of M/B and r. The correlation
between M/B and r consequently cannot be attributed to the division by
book value, and the potential problem of spurious correlation appears not
to be an issue in this case.
Empirical Tests with the Model
In this section market/book ratios are calculated using the H/B
model, and these predicted values are compared to the actual values by
regressing the latter against the former. The results are summarized
in the text, while the detailed tables are presented in Appendices 0 and
P. The sensitivity of the model to variations in the data is discussed
in order to show the importance of careful data specification.
Market/Book Ratio Calculations
By now one realizes that Equation 15 is a model based on ex ante, or
expected, data. It is impossible to look to historical data to determine
exactly the values that investors were expecting for a particular period
of time. One is able to observe the values of the rate of return earned
on stockholders' equity and the retention rate for a given year in the
past. Normalization of these variables over the 19-year test period in
order to approximate investors' expectations was discussed previously.
The firm's asset growth rate was normalized over the test period, but it
was tempered with the estimated long-run growth for the industry of six
percent while allowing for individual company growth rates according to
The rate of return required by investors, k*, was determined by
Equation 16, using Moody's AAA utility bond rate as the "risk free" rate.
An average risk premium for the industry was assigned each year, and the
individual company's premium was above or below the industry average
according to whether its debt ratio was above or below the industry
average for the period. The industry average risk premium was chosen
as described below. Flotation costs were assumed to be ten percent of the
issue price to allow for both underwriting charges and underpricing "pres-
sure" when common stock is issued.
Calculations were performed with data from the sample of 23 companies,
and these predicted Il/B values are compared to actual values for 1972 in
Appendix K and for 1970 in Appendix L. Moody's AAA\ utility bond rate,
which averaged 7.46 percent during 1972, was used as the risk free rate
of return in determining k. The risk premium was varied from approximately
3.0 percent to 4.6 percent, causing the industry average required rate of
return to vary from 10.5 percent to 12.1 percent. The predicted ri/Bs were
sometimes quite close to the actual I/Bs, but sometimes they were not. Re-
gressing the predicted tI/B values against the actual values gave Barton's
coefficients of determination that ranged from 0.5828 to 0.6000. The
highest R" occurred when the risk premium was set at 4.28 percent; assuming
the M/B model expressed in Equation 15 is a valid representation of the
way ri/B ratios are determined, the average risk premium for the sample
companies' common stock in 1972 was about 4.28 percent.
Using Iloody's AAA utility bond rate of 8.31 percent for 1970 and
varying the risk premium as in 1972 caused the industry average required
rate of return to vary from 11.3 percent to 12.9 percent. The resultant
Il/Bs are compared to the actual Il/Bs in Appendix L, where one finds that
Barton's RP ranged from 0.4761 to 0.5057. In this set of calculations the
R s increased as the risk premium decreased, so that the highest R' re-
sulted from the lowest premium.
The fact that higher coefficients of determination occurred with
higher risk premiums in 1972 than in 1970 suggests that the slope of the
capital market line increased from 1970 to 1972, that the risk of the
industry increased, or both. In reality, both events probably occurred.
Sensitivity of the Model
Equation 15 is extremely sensitive to small changes in the values
of the variables, particularly r, C, and k. Since the denominator contains
the term (k br s) and since G is assumed to equal br + s, the M/B
can become extremely large as G approaches k; it can be undefined if C
equals k; or it can become negative if C exceeds k. Constraining C to
a long-term expected value relieves the problem but does not do away with
it entirely. The model is also sensitive to changes in b and F, but to
a lesser degree.
As an illustration of the intricacies involved, consider the follow-
ing example: Letting r = 11.9 percent, b = 33.7 percent, k = 10.0 percent,
s = 4.5 percent, and F = 10.0 percent, results in I/B = 1.99, as calculated
from the model. Reducing k by one percentage point to 9.0 percent causes
M/B to increase to 6.15. Holding k at 10.0 percent while increasing s to
5.5 percent causes M/B to increase to 3.77. One can see that the correct
specification of variables is of utmost importance when attempting to use
this model. Because of the relationship between k and C, the model was
more prone to produce abnormal M/B ratios for firms with unusually high
growth rates than for firms with lower growth rates.
Cost of Capital Calculations
Discounted cash flow techniques are often used in regulatory pro-
ceedings as a method of determining the cost of equity capital for the
firm. Although the calculations in the prior section were directed at
specifying the market/book ratio, Equation 15 could be used to calculate
the cost of equity capital, k, as shown in Appendix N. To accomplish this
end, the observed market/book ratio would be used as input data to the
equation, and k would be calculated. This procedure is potentially useful,
but since the M/B model does not predict actual M/B ratios very well--the
R2 values were in the range of .47 to .60--ulich is not sufficient for
one to place a great deal of reliance on the outcome of either M/B or k.
This chapter discusses the theoretical ex ante variables upon which
the discounted cash flow valuation model is based. Since investors' ex-
pectations, per se, are not observable historically, this chapter presents
data which the potential investor might consider in forming his expecta-
tions about the future. As with all DCF models, the specification of
expected future values requires a substantial degree of judgment. The
judgments presented in this chapter are, of course, open to both criticism
Data was gathered for a sample of electric utilities normalizing de-
preciation tax savings and operating in original-cost rate base juris-
dictions. The data was fitted to regression Equation 19, and M/B ratios
were calculated using Equation 15. The predictive power of the regression
equation was superior to that of the M/B model as evidenced by the co-
efficients of determination. The linear multiple regression equation ex-
plained between 58 percent and 76 percent of the variation in M/B ratios,
but calculations using Equation 15 explained only some 48 percent to 60
percent of the variation.
Both equations point to the fact that the allowed (or actual) rate
of return and the asset growth rate are the most significant determinants
of the H/B ratios. The most serious problem encountered in the use of
either equation is that of data specification; whereas the potential
dangers of multicollinearity and spurious correlation appear to be minor
with this sample. Equation 15 is highly sensitive to small variations
in input data, so anyone attempting to calculate market/book ratios,
allowed rates of return, or costs of capital with it or a similar model,
as might be done in rate cases, should use caution and judgment.
TOWARD A "FAIR" MARKET/BOOK RATIO
Economic theory suggests that unity is a fair M/B arising from the
return to capital achieved by a firm operating under pure competition in
a noninflationary setting. However, since inflation is a fact of life,
this conclusion is of limited value in an uncertain, oligopolistic, in-
flationary world. The ability of a utility to attract new capital in
an uncertain economic environment without unduly harming its existing
stockholders is a critical consideration in fairness to consumers as well
as to owners and is one of the criteria for fairness established in the
Hope case.} The ratio of the market price of a firm's stock to its book
value offers some practical guidance toward fairness, and the M/B ratio
is widely recognized in the financial community as being a significant
This chapter examines the competitive market approach to regulating
a natural monopoly, i.e., one with decreasing long-run average costs, and
we suggest a similar application of the principle in the increasing-cost
case. The problem of capital attraction is then discussed in terms of
consumers versus investors. The difficult problem of inflation and how
it may be dealt with through accounting practices are then aired. Finally,
a practical approach to using an M/B model in the regulatory process is
presented along with an acknowledgement of certain problems which may be
FPC v. Hope Natural Gas Company, 320 U.S. 591 (1944).
encountered in its use in a rapidly changing economic environment.
Competitive Market M/Bs
This section first examines the studies of Myers2 and Leland3 re-
lating the economic model for natural monopolies (decreasing long-run
average costs) to the competitive, and therefore fair, rate of return in
utility regulation. Later in the section we delve into the competitive
market approach to regulation of monopolies facing increasing costs.
The rate of return that would exist in a competitive market is pro-
posed as "fair" by Stewart C. Myers," and ideal regulation would eliminate
monopoly profits and force the firm to accept the competitive return.
Regulation may, however, eliminate monopoly profits without reaching the
competitive solution of investment, output, or prices. Nonetheless, if
the aim of regulation is to eliminate monopoly profits, then "Regulation
should assure that the average expected rate of return on desired new in-
vestment is equal to the utility's cost of capital."5 This principle
follows from defining "fair return" in terms of the competitive model
since the equilibrium return to capital is precisely the amount required
to attract capital to that industry or firm. Myers specifies that this
principle is strictly an ex ante concept and that the existence of a com-
petitive market does not require expectations to be realized for any asset.
To implement this concept of fair return, the regulatory authority
S. C. Myers, "The Application of Finance Theory To Public Utility
Rate Cases", The Bell Journal of Economics and Management Science, Vol.
3, No. 1 (Spring 1972), pp. 58-97.
3H. E. Leland, "Regulation of Natural Monopolies and the Fair Rate
of Return", The Bell Journal of Economics and Management Science, Vol.
5, No. 1 (Spring 1974), pp. 3-15,
LMy:ers, pp. 79-80.
5IMyers, p. 80.
would, with no lag, set prices so that total expected revenue equals the
sum of expected operating costs and depreciation, plus a fair return to
capital. The return to capital would be the product of the firm's cost
of capital measured at the beginning of the period times the rate base
at the start of the period. The rate base would have to represent the
competitive market value of the firm's assets, that is, the value of the
assets in long-run equilibrium in a competitive market. The competitive
market value is the original cost of the assets less economic depreciation,
whereas book value is original cost less accounting depreciation. A fair
solution will not result using the accounting book value unless it equals
the competitive market value. In practice, rate base valuation remains
a thorny problem.
Using the competitive market return as the fair return has the ad-
vantages of (1) allowing a low cost of capital, since investor-borne risk
is small, and (2) ease of administration. Rate cases would be frequent
but routine. Disadvantages are (1) that all uncertainty about operating
costs is borne by consumers even though this allocation of risk may not
be optional, and (2) that little incentive is provided for efficiency in
operating or capital budgeting procedures. Conscious use of regulatory
lag, however, could provide the needed incentive for efficiency with this
approach to regulation.
A similar approach was taken by H. E. Leland when he proposed the
A "fair return" to capital is a pattern of profits
across states of nature just sufficient to attract
capital to its present use, which is equivalent to
the stock market value of the firm, V, equalling the
value of the firm's assets, K .6
'Leland, p. 7.
He frames his presentation in terms of a naturally monopolistic industry,
that is, one which has long-run decreasing average and marginal costs,
as shown in Figure 14. Although monopolies often achieve an efficient
use of inputs, given a level of outputs, they often do not achieve an
efficient level of output. From the viewpoint of social welfare they
produce too little, q,,, and charge too much, pm, as determined by the
intersection of the marginal cost and marginal revenue curves. The regu-
lators would choose to limit the firm's price to p* and force it to produce
quantity q*, as determined by the intersection of the average cost and
In a competitive environment under long-run equilibrium the return
to suppliers of capital is exactly the amount needed to keep capital in
the industry. If r* were the competitive return and Ko were the total
book value of the firm, then the corresponding "fair" return r would be
r = P*/K. The total market value of the firm, V, could be determined by
V = n*/r. Thus the market value equals book value in the competitive,
long-run equilibrium model. If the unregulated monopoly earns excess
profits of irm then its market, m /r, is greater than the competitive (and
book) value, i*/r, since Tm > n*.
Leland develops the argument that although this solution is from a
certainty model, similar results obtain under uncertainty. If the expected
competitive profit pattern were c(,*), then the expected fair rate of
return would be r* = c(n*)/K. Risk aversion on the part of investors
will require a higher expected profit from a riskier firm co generate the
same market value as a less risky firm. Leland states that a regulatory
agency "would be ill-advised" to limit expected returns to r*, for the
results would be neither technical efficiency nor maximal output. Allowing
q q.' Quantity
Figure 14: Revenue and Cost Curves for a "flatural" Monopoly.
Source: H. E. Leland, "Regulation of Natural Monopolies and the Fair
Rate of Return," The Bell Journal of Economics and Management
Science, Vol. 5, NJo. 1 (Spring 1974), p. 8.
some rate of excess profits greater than r*, which also allows market value
to exceed book value during regulatory lags, may be an effective incentive
for introduction of new technology. An admitted problem in the implemen-
tation of competitive market regulation is specifying competitive market
values of assets.
In summary, both Myers and Leland used economic models for natural
monopoly and pure competition, imposing the profit level of the latter on
the former as a means of determining the fair return; that is, they say
the monopoly is earning a fair return if all "ex:cess" profits have been
eliminated by regulation. Using the profits, thus determined, along with
the competitive market value of the firm's assets, they determine the
fair rate of return long sought by regulatory agencies. The market value
of the utility's assets will necessarily equal their competitive market
value. Both authors recognize that determination of the competitive market
value of assets is a major, unsolved problem faced in rate cases. The
rate base (asset value) usually accepted is an accounting-determined value,
sometimes with an ad hoc adjustment intended to bring it nearer a replace-
ment value. Practically speaking, this proposal would force the H/B to
unity. Myers and Leland also recognize additional problems involving un-
certainty and incentives for efficiency.
In order to consider the capital attraction standard set forth in the
Hope case, it may be useful to discuss the economic interdependence between
consumers of utility services and suppliers of capital, and their mutual
dependence upon regulatory commission. Carleton pointed out a wealth
distribution problem in applying a price-determined allowed rate of return
to an accounting-determined book value of equity. The discounted cash
flow (DCF) procedure used in many rate decisions today estimates a cost
of equity capital, k, that is constant over time because this assumption
is in the estimation procedure. If this k is then taken as the allowed
rate of return (k.e., r = k), and if expectations are realized over time
so that r does, indeed, equal, then the market price would equal the book
value per share at any time as long as all asset growth is financed through
retention of earnings.
Fluctuations in investor expectations may occur throughout time and
cause fluctuations in the M/B. If these fluctuations in k (the cost of
equity capital or the required rate of return) are small and around the
assumed "constant" value of k, then the accompanying fluctuations in H/B
would be transitory. The regulatory body would not try to correct short-
term inequalities between price and book value by adjusting the allowed
rate of return to fulfill temporarily changed expectations. A problem of
circularity would emerge rapidly if r were adjusted to equal k on a short-
term basis, for the capital market's valuation of the firm's risk could
be altered by the regulatory decision. A change in risk class would
change the rate of return, k, required to induce investors to furnish
capital to the utility. If the regulating body again adjusted r to meet
the new k, one could only expect another movement in k, followed by a
compensating adjustment in r, and so forch.
With the assumptions of a constant k and expectations that are realized,
one could calculate a pro form book value, Bt, for any time, t, given the
information r, Bt 1 and Dr, as Bt = Bt 1(1 + r) Dt. This one-period
'W. T. Carleton, "Rate of Return, Rate Base and Regulatory Lag Under
Conditions of Changing Capital Costs", Land Economics (July 1974).
model can be generalized to
Bt = B0( = r)t D1(l + r) D2(l + r)t Dt -
This procedure determines a rate base, Bt, founded on investors' expecta-
tions rather than on accounting values. Bt would seem to be an appropri-
ate base for use with a rate of return determined from investor expectations.
Actually, both the rate of return required by equity investors and the
rate base are determined jointly over time. Regulatory practice determines
each separately. In rate cases, k and r are regularly updated to market
conditions, while the rate base is left at book value.
The procedure for calculating both the allowed rate of return and the
rate base from market values has economic appeal but conflicts with legal
precedent set in the Galveston case. The most prominent argument against
after-the-fact allowance for k in constructing the rate base is that it
capitalizes "'earnings deficiencies'," which reduces risk to owners
(stockholders) and reduces managerial incentives for efficiency. Suppose,
for example, that the mean value of k shifts permanently to some value k,
and there is a one-period lag before r is adjusted to equal k (i.e., r
does not equal k for one period); then the market price, P does not equal
book value per share, B for one period. The market price will be less
than or greater than book value according to whether r is less than or
greater than k. The resultant "effects through earnings retention and
reinvestment in rate base assets will be permanently capitalized into Bt
from period 2 onward."10 If the change in k is an increase, as in the
uGalveston Electric Co. v. City of Galveston, et al., 258 U.S. 388
9Carleton, p. 5.
1oCarleton, p. 6.