AN EMPIRICAL STUDY OF THE
RELATIONSHIPS BETWEEN FINANCIAL
LEVERAGE AND CAPITAL COSTS
FOR ELECTRIC UTILITIES
BY
LOUIS CHARLES GAPENSKI
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1987
ACKNOWLEDGEMENT
I would like to thank the members of my committee,
Eugene F. Brigham, Sanford V. Berg, and Arnold A. Heggestad,
for their assistance and encouragement throughout this
dissertation. Also, Dana Aberwald provided considerable
econometric support as well as helpful comments. Of course,
any dissertation requires a good typist, and I was lucky
enough to have three: Carol Stanton, Steve Ambrose, and Bob
Karp. Finally, I would like to thank the Public Utility
Research Center, College of Business, University of Florida,
for its generous financial support.
TABLE OF CONTENTS
ACKNOWLEDGEMENT . . . . ... . . . . .. ii
ABSTRACT . . . . . . . . . . .
CHAPTERS
I INTRODUCTION . . . . . . . . . 1
The Regulatory Process . . . . . .. 1
Rate of Return Regulation . . . . . . 3
Relevance of the Study . . . . . . 5
Study Objectives . . . . . . . . 6
Basic Methodology . . . . . .. . 7
Summary of Results . . . . . .. . 8
Report Organization . . . . . .. . 9
Notes . . . . . . . . . . . 10
II REVIEW OF PRIOR STUDIES . . . . . .. 11
Theoretical Studies . . . . . . .. 11
Empirical Studies . . . . . . . . 17
Notes . . . . . . . . . . 22
III THE ECONOMETRIC MODEL . . . . . .. 23
Model Overview . . . . . . . . 23
Dependent Variable Measures . . . . .. 24
Leverage Measures . . . . . . . .. 26
Other Independent Variables . . . . . 28
Notes . . . . . . . . . . 44
IV REGRESSION RESULTS . . . . . . .. 46
Data Sample . . . . . . . . . 46
Regression Specifications . . . . . .. 46
A Priori Expectations about Coefficient Signs .48
Input Data Summary . . . . . . .. 49
Dependent Variable Measure Correlations . .. 50
Equity Regression Results . . . . .. 51
Debt Regression Results . . . . . .. 65
Notes . . . . . . . . . 72
V THE BOND RATING GUIDELINES MODEL . . . . 73
Model Overview . . . . . . . . 73
Bond Ratings . . . . . . . . . 74
Bond Rating Guidelines . . . . . .. 75
Bond Yield Spreads . . . . . . .. 76
Model Results . . . . . . . . 77
Notes . . . . . . . . . . 79
iii
VI SUMMARY AND CONCLUSIONS . . . . .
The Choice of Leverage Measure . . .
Leverage/Capital Cost Relationships . .
Nonlinearities . . . . . . .
Business Risk Factors . . . . . .
Conclusions . . . . . . . .
Notes . . . . . . . . . .
APPENDICES . . . . . . . . . .
A SAMPLE SET . . . . . . .
B GLOSSARY OF SYMBOLS . . . . .
C EQUITY RECESSION RESULTS . . . .
D INDEPENDENT VARIABLE CORRELATION MATRIX
E DEBT REGRESSION RESULTS . . . .
BIBLIOGRAPHY . . . . . . . . .
BIOGRAPHICAL SKETCH . . . . . . . .
. . 80
. . 80
. . 82
. . 84
. . 85
. . 86
. . 87
. . 88
. . 88
. . 90
. . 92
. . 96
. . 98
. . 102
. . 109
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of
the Requirements for the Degree of Doctor of Philosophy
AN EMPIRICAL STUDY OF THE
RELATIONSHIPS BETWEEN FINANCIAL
LEVERAGE AND CAPITAL COSTS
FOR ELECTRIC UTILITIES
By
Louis Charles Gapenski
May 1987
Chairman: Eugene F. Brigham
Major Department: Finance
A major element in utility regulation is the setting of
just and reasonable allowed rates of return. This rate is a
weighted average of the costs of the types of capital
employed by the firm, and the weights should reflect the
firm's target capital structure. The information required
to set the target, or optimal, capital structure includes
the relationships between the component costs of capital and
the amount of financial leverage used. The primary
objective of this study is to empirically estimate the
relationships between financial leverage and the costs of
common equity and debt for electric utilities.
Two different approaches were used to estimate these
relationships. First, an econometric model was developed
with the component cost as the dependent variable and
leverage as the independent variable. Other factors were
included as independent variables to account for nonconstant
business risk. Second, a model was developed using the bond
rating guidelines and bond yields reported by Standard &
Poor's Corporation. The data set consisted of about 70
electric utilities for 1983 and 1984.
The results indicated a strong positive relationship
between financial leverage and the costs of debt and equity.
Several leverage measures were used, and the relationship
was strongest when leverage was measured by market value
debttoequity ratios. The relationships were stronger than
reported in previous studies, and there was no indication
that the relationships were nonlinear when leverage was
measured by debttoequity ratios. Further, the two most
important business risk factors to both debt and equity
investors were nuclear construction programs and reserve
margins. Somewhat surprisingly, regulatory climate did not
affect debt or equity costs.
CHAPTER I
INTRODUCTION
The Regulatory Process
Electric utilities are suppliers of an essential and
indispensable service to society, and hence they are
typically required to serve all customers in their market
area at reasonable rates and without undue price
discrimination. Further, for many years economies of scale
in production and distribution made it possible for a single
firm to provide lower cost service than several smaller
firms. Thus, electric utilities are to a large extent
natural monopoly providers of an essential service. This
fact prompted governmental regulation at a very early stage
in the development of the electric utility industry, with
the primary purpose of regulation being to replicate the
results that would have occurred under a competitive market
system.1 In a competitive market, the forces of competition
hold prices down to the cost of production and distribution,
including a return on invested capital. Over the long run,
the return on capital will reflect the riskiness of the
industrythe greater the risks confronted by the industry,
the greater the required rate of return. Under regulation,
regulators act as a substitute for the competitive market
system by setting output prices and controlling entry and
service standards.
Regulation of output prices involves two major tasks.
First, regulators must determine the total revenues required
to cover all operating expenses, including a fair rate of
return on invested capital. Second, regulators must
apportion this revenue requirement among the different
customer classes and categories of service. (The latter
task, often called rate design, is not relevant to this
study, although rate structures certainly affect the
volatility of sales and hence returns, capacity investment
decisions, and incentives for customers to alter consumption
patterns.) Overall revenue requirements for a firm are
determined in the following manner:
R = O + (R O I)T + rB, (11)
where
R = total revenue requirements,
O = total operating expenses including depreciation,
I = embedded interest expense, or the interest on
outstanding debt,
T = tax rate,
r = allowed rate of return, determined as a weighted
average of the costs of debt and equity, and
B = rate base.
Total revenue requirements are thus set to cover all
operating costs, including depreciation and taxes, plus
provide a return to the firm's investors. The last term in
Equation 11, the allowed rate of return multiplied by the
rate base, provides this return to investors. Normally, the
rate base, B, is approximately equal to the net book value
of that part of the firm's plant considered "used and
useful" in providing service, plus an allowance for working
capital requirements. The allowed rate of return, r, is
calculated on the basis of the required rates of return of
the investors providing the capital needed to acquire the
assets used to provide service to consumers.
Rate of Return Regulation
A major element in utility regulation is the setting of
just and reasonable allowed rates of return. The allowed
rate of return is a blend, or weighted average, of the costs
of the three types of capital used: debt, preferred stock,
and common stock. It is estimated by the following
equation:
r = wdkd + pkp + wsks,
where
wd = proportion of debt in the capital structure,
kd = embedded cost of debt,
p = proportion of preferred stock,
kp = embedded cost of preferred stock,
ws = proportion of common stock, and
ks = marginal cost of common equity.
The embedded costs of debt and preferred stock are
relatively easy to estimate, whereas the appropriate
weights, wi, and the marginal cost of common stock, ks,
present a much larger estimation problem.2
The weights should represent the proportions of debt,
preferred stock, and common stock in the firm's target, or
optimal, capital structure, which is that mix of capital
components that minimizes the firm's marginal weighted
average cost of capital. The estimation of a firm's target
capital structure is complicated by the fact that the
component costs (kd, kp, and ks) are related to the amount
of financial leverage, or fixed cost (debt and preferred
stock) financing, used.3 Further, the costs of debt and
preferred stock are less than the cost of common stock.
The more financial leverage that is used, the higher
the proportion of lower cost components, but at the same
time, the higher the cost of each component. Thus,
selecting the optimal amount of financial leverage (the
optimal capital structure), like virtually all finance
decisions, involves a risk/return tradeoff. The
information required to set the optimal capital structure
includes the relationships between the component costs of
capital (debt, preferred stock, and common stock) and the
amount of financial leverage used. None of these
relationships are easy to estimate, but establishing the
relationship between financial leverage and common equity
cost is especially difficult.
5
Relevance of the Study
Until recently, the optimal capital structure played a
minor role in electric utility management and regulation.
The industry was under great stress during the 1970s and
early 1980s as a result of record inflation, huge oil price
increases which necessitated conversion from oil generating
plants to coal or nuclear fuel, escalating costs and
regulatory delays for nuclear plants, and, for some
companies, dramatic growth in their service areas. These
factors combined to depress profits and drive down stock and
bond prices at the very time that the industry needed to
raise huge amounts of cash to finance construction programs.
Under such conditions, not much attention could be given to
financing according to an optimal capital structurefirms
had to raise capital any way they could, and that normally
meant using first mortgage bonds to a very large extent. As
a result, the financial leverage of most firms, measured in
either book or market values, rose to alltime highs.
Concurrently, regulatory agencies did not pay much attention
to optimal capital structure in rate cases: The companies
financed as best they could, and the allowed rate of return
was generally based on the actual capital structure at the
time the rate case was decided.
This lack of attention to capital structure issues also
created little incentive for capital structure research.
Thus, no conclusive empirical work has been conducted using
data beyond the early 1970s.
Today, however, many companies have significantly
improved their financial positionsprofits are higher,
capital expenditures are down sharply, and large
depreciation cash flows are coming in from newly completed
plants. These changes are giving companies the flexibility
to adjust their capital structures, so the question of
optimal capital structure, and the related question of the
effect of capital structure on capital costs, is becoming a
major issue for both regulators and managers.
Study Objectives
The primary objective of this study is to estimate
empirically the relationships between financial leverage and
the costs of common equity and debt. The study has two
secondary objectives: (1) To determine if the relationships
between leverage and the costs of debt and equity are
affected by the financial leverage measure used, and (2) to
determine if the empirical relationships between capital
costs and financial leverage exhibit significant
nonlinearities. Finally, there is one tertiary objective:
to identify the business risk factors which influence an
electric utility's cost of capital.
Preferred stock typically plays only a minor role in
the capital structure of electric utilities, and hence the
preferred stock/leverage relationship will not be addressed
in this study.
Basic Methodology
The empirical portion of the study consisted of two
models. First, an econometric model based on multiple
regression techniques was used to estimate the relationships
between leverage and capital (debt and common equity) costs:
ks or kd = b0 + bl(Leverage) + b2F2 + ... + bnFn + e.
Here either the cost of common equity or the cost of debt is
the dependent variable, and financial leverage is one of the
independent variables. Additional independent variables
(the Fi's) are included in the regression to account for
other factors which might affect ks or kd and which may be
correlated with financial leverage. The econometric model
was also used to (1) assess the impact of the leverage
measure used, and (2) test for nonlinear relationships.
Second, a bond rating guidelines model was developed to
estimate the relationship between debt cost and financial
leverage. This model uses Standard & Poor's Corporation
(S&P) published guidelines, along with yields on bonds with
different ratings, to estimate the leverage/debt cost
relationship. To illustrate, S&P might state that a 43.5
percent debt ratio is average for AArated electric
utilities, while a 49.0 percent debt ratio is representative
of firms rated single A. Thus, a debt ratio difference of
5.5 percentage points leads to a full step difference in
ratings. The yields on issues with different ratings can
also be estimated, and the leverage differential and yield
differential was then used to estimate the cost of
debt/leverage relationship.
Summary of Results
The results show strong positive relationships between
financial leverage and both debt and equity costs. Table
11 summarizes these relationships. The results indicate
Table 11
Summary of Results
Basis Point Change Basis Point Change
in Debt Cost in Equity Cost
Rating Rating
Change in Econometric Guidelines Econometric Guidelines
Debt Ratio Model Model Model Model
40% to 50% 28 56 74 111
50% to 60% 42 120 113 240
a much stronger relationship between financial leverage and
equity costs than reported in previous studies. Further,
the capital costs/leverage relationship was strongest when
leverage is measured by market value debttoequity
ratiosbook value ratios were inferior measures of
financial leverage for estimating its impact on capital
costs. There was no evidence that the leverage/capital
costs relationships were nonlinear when leverage is measured
by debttoequity ratios.
The two dominant risk business factors, to both debt
and equity investors, were nuclear construction programs and
reserve margins. In contrast to previous studies,
regulatory climate did not affect equity or debt costs
during the study period.
Report Organization
The remainder of this study is divided into five parts.
Chapter II contains a review of the relevant literature.
Both theoretical and empirical work are discussed. Chapter
III describes the econometric model and provides the
rationale for the particular specifications selected, while
Chapter IV contains the results of the regression runs.
Chapter V then describes the bond rating guidelines model
and results, and, finally, Chapter VI summarizes and
compares the results of the two models and presents the
final conclusions.
Notes
1For an indepth discussion of the regulatory process,
including rate of return regulation, see Phillips (1984).
2The costs of debt and preferred stock consist primarily of
the fixed historic costs of the securities already issued,
which are known at the time the allowed rate of return is
set. The costs of debt and preferred stock anticipated to
be issued during the effective period of the rate decision
may also be included. These marginal costs are somewhat
more difficult to estimate, but they represent only a small
fraction of the total debt and preferred stock outstanding.
3Finance theorists hypothesize a positive relationship
between financial leverage and component coststhe higher
the proportion of debt and preferred stock in the capital
structure, the higher the costs of debt, preferred stock,
and common equity. Empirical studies have tended to support
this relationship, although the exact form of the
relationship has not been established. Chapter II discusses
the supporting theoretical and empirical studies in detail.
CHAPTER II
REVIEW OF PRIOR STUDIES
A number of theoretical studies have set forth
hypothesized relationships between financial leverage and
the cost of various types of capital. Further, several
empirical studies have been conducted to estimate these
relationships for electric utilities. This chapter
summarizes these studies.
Theoretical Studies
Cost of Equity Studies
The theoretical studies addressing the cost of
equity/leverage relationship fall into three broad classifi
cations: (1) the classics, (2) extensions of the classics,
and (3) studies which incorporate in the impact of
regulation. The studies are discussed in that order.
The classics. The theoretical relationships between a
firm's use of financial leverage and its equity cost have
evolved from the classic articles by Modigliani and Miller
(MM) (1958 and 1963). They prove, under a wellknown set of
restrictive assumptions, that a levered firm's cost of
common equity, ks, is related to financial leverage in the
following way:1
ks = ku + (ku kRF)(1 T)( ), (21)
where
ku = cost of common equity to an unlevered firm with
the same business risk as the levered firm,
kRF = cost of riskfree debt,
T = tax rate of the levered firm,
D = market value of the levered firm's debt, and
S = market value of the levered firm's common equity.
In their original work, MM assumed that corporate debt is
risk free. Under this assumption, the cost of equity is
linearly related to the market value debttoequity ratio.
Extensions to the classics. Finance theorists and
practitioners alike doubt that Equation 21 holds when MM's
restrictive assumptions are relaxed. Stiglitz (1969) and
Rubinstein (1973) went on to show that the introduction of
risky corporate debt does not alter the basic MM
relationship, which can be rewritten as
D
ks = ku + (ku kd)(1 T) () (22)
where kd is the levered firm's cost of risky debt. Equation
22 again shows that common equity costs increase with the
use of financial leverage. However, the addition of risky
debt results in kd being a function of financial leverage,
and hence the cost of equity is no longer linearly related
to the market value debttoequity ratio.
Perhaps the two most important of MM's restrictive
assumptions are (1) the absence of personal taxes and (2)
the absence of financial distress and agency costs. Miller
(1977) and DeAngelo and Masulis (1980) argued that the
addition of personal taxes increases the levered firm's cost
of common equity above that given by Equation 22. Under
Miller's assumptions, the addition of personal taxes results
in this relationship:
D
ks = ku + (ku (1 T)kd)j. (23)
Under Miller, the leverage risk premium (the last term in
Equation 23) is larger than hypothesized by MM and hence
leverage has a greater impact on equity cost.
The biggest criticism of both the MM and Miller models
stems from the assumption of a zero cost for financial
distress. In bankruptcy, the value of the firm is reduced
by payments made to third parties. Fees paid to trustees,
lawyers, accountants, appraisers, and so on, reduce the
value of the firm's assets, and hence the funds available
for distribution to bondholders and stockholders. These are
the direct costs of bankruptcy. Additionally, firms in
financial distress may suffer indirect costs such as lost
customers, managerial inefficiency due to pressing financial
problems, job security demands, and so on. Warner (1977),
in examining 11 railroad bankruptcies, concluded that direct
bankruptcy costs are small, averaging about 2.5 percent of
the market value of the firm 3 years prior to the
bankruptcy. On the other hand, Altman (1984) estimated both
direct and indirect bankruptcy costs for 26 firms, and he
found these combined costs to average about 15 percent of
total firm value. The results are mixed, but there is
evidence to suggest that expected bankruptcy costs can be
sufficiently high to influence the cost of common
equity/leverage relationship.
In addition to bankruptcy costs, Jensen and Meckling
(1976) and Barnea, Haugen, and Senbet (1985) argued that the
use of leverage imposes costs associated with the restric
tive covenants and monitoring actions that creditors take to
protect themselves against unfavorable managerial actions.
These costs, called agency costs, may increase as leverage
increases. It is commonly argued (see Chen and Kim (1979)
and Kim (1982)) that leveragerelated agency and financial
distress costs invalidate the theoretical relationships
developed by MM and by Miller. With these costs added, the
relationship becomes much more complex, and it is possible
that the relationships between common equity cost and
financial leverage expressed in Equations 22 and 23
require additional terms. For example, see Patterson
(1984).
The impact of regulation. The process of regulation
may affect the theoretical relationships between common
equity costs and financial leverage. MM and Miller, in
deriving Equations 22 and 23, assumed that the firm's
earnings before interest and taxes (EBIT) is independent of
financial leverage. However, the regulatory process seems
to invalidate this assumption. Gordon (1967) and Gordon and
McCallum (1972), argued that, for regulated firms, earnings
before interest but after taxes, rather than EBIT, is the
cash flow variable that is independent of leverage. They
further argued that, under the remaining MM assumptions, the
correct relationship between common equity costs and
financial leverage for regulated firms is that prescribed by
MM in a zerotax world:
ks = ku + (ku kd)D. (24)
Elton and Gruber (1971) made the same cash flow
independency argument as Gordon and McCallum, but reached
different conclusions. They argued that the proper leverage
relationship for regulated firms is the same as for
unregulated firms given by MM when corporate taxes are
considered:
D
ks = ku + (ku kd)(1 T)S. (22)
Elton and Gruber (1972) then demonstrated that either
Equation 22 or Equation 24 can be correct, depending upon
what further assumptions are made about regulatory behavior.
Equation 24 is correct if the allowed rate of return is
uncertain over time, but once set the allowed rate is
realized in each period. On the other hand, Equation 22 is
correct if the allowed rate of return is fixed over time,
but the earned rate of return may vary across periods. Of
course, neither description of the process is correct since
both allowed and realized rates of return are uncertain over
time.
Finally, Jaffe and Mandelker (1976) argued that the
relationship between leverage and equity cost for a
regulated firm cannot be derived without specifying its
supply and demand curves, because the regulated price is a
function of financial leverage. Further, Equation 22 or
Equation 24 can only be correct for special cases of supply
and demand conditions that are not likely to hold for
regulated firms. Instead, they argued that under more
traditional demand assumptions, the cost of equity rises
even less with leverage than indicated by Equation 22.
In summary, finance theory provides many different
models of the relationship between equity cost and leverage.
The exact specification of the relationship depends on the
underlying assumptions, and it is virtually impossible a
priori to choose among the hypothesized relationships.
Cost of Debt Studies
The theoretical cost of debt/financial leverage
relationship has not received as much attention as the cost
of equity/financial leverage relationship. However, it is
generally held that, like common equity, debt costs are
positively related to the use of financial leveragethe
greater the use of debt financing, the higher the cost of
debt. This is because higher debt usage increases the fixed
claims against a firm's earnings stream, and hence (1)
increases the probability of financial distress and (2)
increases the dollar value of claims against any liquidation
proceeds.
Hsia (1981) combined the Option Pricing Model (OPM),
the Capital Asset Pricing Model (CAPM), and the MM zero tax
model to demonstrate consistency among the models. In this
work, Hsia developed the following expression for the
relationship between the cost of debt and financial
leverage:
V
kd = kRF + (ku kRF)(1 N(dl))D. (25)
Here N(dl) is the cumulative probability for a unit normal
variable, and hence must fall between 0 and 1, and V = D +
S.2 Thus, Equation 25 shows that the cost of debt is equal
to the riskfree rate, kRF, plus a risk premium that
increases with financial leverage. If a firm used all debt
financing, then N(dl) = 0 and V/D = 1, and hence the cost of
debt would equal the cost of equity to an unlevered firm.
Note, though, that Hsia's result is based on the assumption
that bankruptcy costs are zero.
Empirical Studies
Cost of Equity Studies
The number of theoretical models proposed supports
the need for empirical studies which attempt to estimate the
relationship between an electric utility's financial
leverage and its cost of common equity. Numerous such
studies have been conducted, and even more studies have
examined the relationship for unregulated firms. In the
following paragraphs, only the more prominent electric
utility studies are discussed.
Virtually all empirical work has used the following
specification:
ks = b0 + bl(Leverage) + b2F2 + ... bnFn + e.
Here the firm's cost of common equity is the dependent
variable, leverage is one of the independent variables, and
other independent variables are included to account for
crosssectional differences in k not attributable to
leverage. All studies of this nature have three major
problems: (1) It is very difficult to estimate the
dependent variable, and hence the early studies used proxies
such as dividend yield in place of a direct estimate of the
cost of common equity. (2) The specification must include
all other risk factors that are correlated with financial
leverage to avoid biasing the leverage coefficient.3 (3)
All of the variables in the specification should be measured
in terms of investors' expectations, not historic data, and
this presents a serious measurement problem.
The first major study to incorporate modern financial
and statistical concepts was conducted by Brigham and Gordon
(1968). They used the following model:
Dividend yield = b0 + bl(Growth rate)
+ b2(Book value debt/equity ratio)
+ b3(Earnings instability)
+ b4(Corporate size)
+ b (Proportion of sales from
electricity) + e.
Their sample consisted of 69 electric utilities during
the years 1958 to 1962. They found, on average, that a
unitary increase in the book debttoequity ratio raised the
dividend yield by about 0.33 percentage points.4
Gordon (1974) expanded both the model and the sample
used in the Brigham and Gordon study. Gordon used the
following model:
Dividend yield = b0 + bl(Market value debt/equity ratio)
+ b2(Growth rate) + b3(Proportion of
sales from electricity)
+ b4(Earnings quality) + e,
and he found that over the 19581968 period, the coefficient
of the leverage variable averaged about 0.5 when leverage
was measured by the market value debttoequity ratio.5
Robichek, Higgins, and Kinsman (1973) carried out a study
over the 19621969 period, using the following model:
ks = bo + bl((Debt + preferred)/equity ratio)
+ b2(Flowthrough dummy) + e.
They estimated ks using several different discounted
cash flow (DCF) models, and used both book and market value
leverage ratios. They found that the effect of leverage on
common equity costs was about 0.9 percentage points for each
unit change in leverage as measured by the book value debt
toequity ratio. Their results using market value debtto
equity ratios were inconclusive.
Mehta et al. (1980) carried out a study based on 55
electrics during the 19681972 period using the following
model:
Dividend yield = b0 + bl(Growth rate) + b2(Book value
preferred/market value common equity
ratio) + b3(Book value debt/market value
common equity ratio) + e.
They found that dividend yield changed on average by
about 1.01 percentage points for a unitary change in the
preferred stock leverage variable, and by about 0.74
percentage points for a unitary change in the debt leverage
variable. Mehta et al. also reached these related
conclusions: First, the effect of preferred stock leverage
on common equity costs is the same as the effect of debt
leverage, except for the tax deductibility of interest
expense. Second, if the leverage variable is defined as
preferred leverage plus debt leverage multiplied by (1 Tax
rate), then a unitary increase in this combined leverage
variable increases common equity costs by about 1.25
percentage points. If the combined leverage variable is
measured merely by preferred leverage plus debt leverage,
the effect of a unitary change is a 0.75 percentage point
change in equity costs.
Finally, Patterson (1984) used a quadratic relationship
between the cost of common equity and leverage, based on an
assumed quadratic function for the value/leverage relation
ship. Although his study focused on the relationship
between financial leverage and the value of the firm, using
a sample of 114 utilities for the years 1975 to 1979, he did
draw some conclusions about the effect of leverage on equity
costs. He concluded that the relationship between leverage,
as measured by the market value debt/equity ratio, and
common equity costs is a nonlinear function whose slope
rises as leverage increases. However, he did not attempt to
attach numerical significance to the relationship.
It is very difficult to compare and contrast the
results of the five studies just cited. The studies differ
in model specification, variable measurement, and sample
size, content, and period. However, the five studies are
consistent with the theoretical hypothesis that equity costs
increase with leverage.
Cost of Debt Studies
As with theoretical studies, there are few works which
empirically estimate the relationship between financial
leverage and debt cost. There has been little motivation in
the electric utility industry to conduct such research,
because the important variable in rate case work is the
firm's embedded cost of debt, which can easily be measured.
The relationship between debt costs and financial leverage
only becomes important when capital structure is an issue.
However, Gordon (1974) did estimate the cost of
debt/leverage relationship using 1963 and 1968 data. He
found that an increase in the book value debttoequity
ratio from 1.0 to 2.0 increased the cost of debt by 0.93
percentage points using 1963 data, and by 1.14 percentage
points using 1968 data.
Notes
1Equation 21 is the final result of the MM work when
corporate taxes are considered. MM's first article (1958)
focused on a zerotax world.
2N(dl) and di stem from the BlackScholes Option Pricing
Model. See Black and Scholes (1972).
3If all of the factors affecting common equity costs were
statistically independent, then the omission of independent
variables would lower the R of the regression but would not
bias the coefficients. However, the omission of variables
correlated with the leverage variable would result in a
leverage coefficient that is too large and a standard error
that is too small.
4The average coefficient over the five years of the study is
0.33. A unitary change in the book debttoequity ratio is
when the ratio changes by plus or minus 1.0. For example, a
change from 0.5 to 1.5 is a unitary change, and such a
change would increase common equity costs by 0.33 percentage
points. Finally, Brigham and Gordon argued that since
market/book ratios were about 2 to 2.5 over the period, the
coefficient for the leverage variable measured in market
value terms would be approximately 0.8.
5The coefficient values ranged from 0.4 to 0.7, and were
statistically significant in only 5 of the 11 years. The
values of the market value debttoequity ratio ranged from
0.59 to 0.88.
CHAPTER III
THE ECONOMETRIC MODEL
Model Overview
In general, a firm's capital costs are a function of
the riskfree rate, the firm's business risk, its financial
risk, and possible other factors such as its dividend
policy. Thus,
ks or kd = f(kRF, business risk, financial risk,
other factors).
The specific relationships can be estimated using the
classical linear multiple regression model, which takes this
form:
ks or kd = bo + bl(Leverage) + b2F2 +...+ bnFn + e,
where F2...Fn are business risk factors which influence ks
and kd and which may be correlated with firms' financial
leverage.
The multiple regression model is based on the following
assumptions:
1. The relationships between the dependent variable
(ks or kd) and the independent variables (Leverage
and Fi) are linear and correctly specified.
2. The independent variables (Leverage and Fi) are
statistically independent.
3. The error term, e,
a. has a normal distribution with a mean of zero.
b. has a constant variance across observations.
c. is independent across observations.
Violation of any of these assumptions can have a significant
impact on the validity of the results. Tests for
assumptional violations are discussed in Chapter IV.
To use the multiple regression model, two important
steps are required: First, the business risk factors, the
Fi's, must be selected. Then, measures must be chosen for
each variable which appears in the model. The remainder of
this chapter provides the rationale for the selection of the
other risk factors and describes the measures selected for
all the variables.
Dependent Variable Measures
Cost of Equity Measures
The cost of equity was measured in two ways, by a
direct DCF estimate and indirectly by the inverse of the
market/book (M/B) ratio. In the direct DCF model,
D1
ks PO + g'
the dividend yield is found by dividing D1, next year's
expected dividend as reported by Value Line, by PO, the end
ofyear stock price reported by Compustat. The growth rate,
g, is the 5year median expected growth rate in earnings as
reported by Institutional Brokers Estimate System (IBES).1
The second measure recognizes that M/B ratios are
functionally related to equity capital costs, and hence that
the M/B ratio can serve as a proxy for the cost of equity.
Rather than use the M/B ratio, that ratio's reciprocal, the
B/M ratio was used; this facilitates the interpretation of
the independent variable coefficients.2 The DCF ks, al
though a direct measure of equity costs, probably has
significant measurement error because (1) it assumes
constant growth whereas very few firms are actually expected
to grow at a constant rate over a prolonged period, and (2)
there is no assurance that the IBES median growth rate is
the rate used by investors to value the stock. Conversely,
the B/M ratio has less measurement error, but as a proxy for
ks, it may introduce specification error.
Cost of Debt Measures
Two measures were also used for the cost of debt, kd.
The first measure used the Standard & Poor's (S&P)
Corporation bond rating as the dependent variable and thus
as a proxy for kd. The S&P letter ratings were converted
into a numerical rating system with 2 = AAA, 4 = AA+, 5 =
AA, 6 = AA, 7 = A+, and so on (there is no number 1 or 3).
This measure recognizes that a direct relationship exists
between a company's bond rating and its cost of new debt.
The second measure also uses reported bond ratings, but
converted to their matching S&P yields. However, since S&P
only reports yields on the primary rating groups, that is,
on the letter classification without modifiers, all double A
bonds (AA+, AA, and AA) were assigned the yield reported
for AA bonds, and so on.
The first measure, which uses bond ratings as a proxy
for kd, provides more detailed information, but (1) its
independent variable coefficients measure the impact on
rating rather than on kd and (2) it assumes that at the
analysis date the yield differentials between each rating
category are equal (for example, that the yield differential
between AA and AA is equal to that between A and BBB+), a
condition that usually does not hold.
Leverage Measures
The independent variable of primary interest is
financial leverage, which can be measured in many ways.
This section provides the rationale for the leverage
measures used in the multiple regression model.
Equity Regressions
Debt leverage can be measured in terms of either debt
toassets or debttoequity. However, the theoretical
studies discussed in Chapter II show that, under the
ModiglianiMiller assumptions, equity cost is linearly
related to the debttoequity ratio rather than the debtto
assets ratio. For this reason, debt leverage was measured
in terms of debttoequity.
Finance theory also suggests that financial leverage
should be measured on a market value basis. Conversely,
practicing financial managers and Wall Street analysts tend
to focus on book value leverage measures. To further
complicate matters, investors are more concerned with the
amount of financial leverage a firm will use in the future
(its target leverage) than with the current level.
Theoretically, the best measure would be the expected market
value debttoequity ratio. However, all measures are
subject to measurement error, and a priori, it is impossible
to state categorically that one measure will give better
results than another, and hence four different leverage
measures were used: (1) the market value debttoequity
ratio (MVDE), (2) the book value debttoequity ratio
(BVDE), (3) the expected book value debttoequity ratio
(EXBVDE), and (4) the expected market value debttoequity
ratio (EXMVDE).3 Debt is defined in all leverage measures
as shortterm interest bearing debt plus longterm debt.
Market values were estimated as follows: (1) Book
value was used for shortterm debt. (2) The market value of
longterm debt was estimated on the basis of embedded
interest payments and the yield required on similarly rated
bonds, assuming an average maturity of 20 years.4 (3) The
market value of common stock was calculated by multiplying
yearend closing stock price times the yearend number of
common shares outstanding. All data required for the book
value and market value debttoequity ratios were obtained
from Compustat. The expected book value debttoequity
ratio was taken from Value Line's forecasted common equity
ratio 35 years hence.5 The expected market value debtto
equity ratio was based on the expected book value measure,
scaled to reflect current book/market relationships.
Debt Regressions
As described in Chapter 2, Hsia (1981) derives a
theoretical relationship which indicates that the cost of
debt is related to the valuetodebt ratio, and trial runs
were conducted using this as the leverage measure. However,
the explanatory power of the leverage variable was higher
when debttoequity ratios were used as the leverage
measure, and hence the final specifications for the debt
regressions used the same leverage measures as the equity
regressions.
Other Independent Variables
In addition to financial leverage, seven factors are
often cited by security analysts as having an influence on
an electric utility's cost of capital: (1) its regulatory
climate, (2) its electric/gas sales mix, (3) its fuel mix,
(4) the size of its construction program in relation to
operating assets, (5) its nuclear construction program, (6)
its reserve margin situation, and (7) its dividend policy.
More factors could, of course, be added to the list, but a
review of prior studies, the general literature, and utility
analysts' reports suggests that the ones listed are the most
important.6 This section discusses the rationale for
including these variables in the regression model along with
the measures used.
Regulatory Climate7
Rationale. Risk is inherent in the utility industry
due to the inability to forecast perfectly input prices,
demand growth, construction costs, and so on. However, the
regulatory agency, to some extent, can dictate the
allocation of this risk between investors and ratepayers.
Additionally, there are actions that regulators can take
which systematically affect realized returns. For example,
long regulatory lag times in periods of increasing input
prices, coupled with the use of historic test periods,
result in a bias towards realized returns that are less than
those required. Further, regulators can purposely set
allowed rates below required rates, or not allow a company
to earn a return on all of its invested capital. Thus, the
regulators themselves have considerable influence over
equity riskiness.
It is possible to review the past and potential future
actions of regulatory bodies, and then rank these agencies
on the basis of their impact on realized rates of return.
Currently, over twenty investment and research firms provide
such rankings. According to Dubin and Navarro (1983), the
ranking methodology is generally based on six objective
criteria:
1. Allowed rate of return.
2. Average regulatory lag and the use of interim
rates.
3. Test year used, historical or future.
4. Treatment of construction work in process (CWIP)
and allowance for funds used during construction
(AFUDC).
5. Treatment of tax benefits from investment tax
credits and accelerated depreciation.
6. Inclusion of fuel adjustment clauses.
In today's operating environment, two more criteria should
be added:
7. Phasein of completed plants.
8. Recovery of costs of cancelled plants.
Together, these eight criteria significantly may affect the
level and predictability, and hence "quality," of earnings.
From the investors' standpoint, a favorable regulatory
climate in today's operating environment would include most
or all of the following: a relatively high allowed rate of
return, minimal regulatory lag and/or interim rate
provisions, the use of a future test year, CWIP in the rate
base, normalization of tax benefits, a full automatic fuel
adjustment clause, a full cash return on plants as soon as
they go into service, and full recovery of prudently
incurred costs of cancelled plants. Conversely, an
unfavorable regulatory climate would include the following:
a relatively lower allowed rate of return, lengthy
regulatory lag and no interim rate provisions, the use of an
historical test year, AFUDC accounting for construction work
in process, flowthrough of tax benefits, restrictive or no
fuel adjustment clauses, phaseins of completed plants, and
only partial recovery of cancelled plant costs. To the
extent that unfavorable regulatory climates increase firms'
riskiness, while favorable regulatory climates decrease
firms' riskiness, investors should price this risk dif
ferential in their required returns.
Several recent studies have confirmed that the more
unfavorable the regulatory climate, as measured by
commission rankings, the higher the cost of equity. Dubin
and Navarro (1983) conducted the most comprehensive study of
the effects of regulatory environment to date. They used
1978 data with markettobook ratio as a proxy for equity
cost, and regulatory ranking, the rate of return on book
equity, expected rate of return, dividend payout ratio, and
fuel cost as a proportion of total costs as the independent
variables. They concluded that, for an average utility, the
change from a favorable ranking to an average/unfavorable
ranking results in an equity cost increase of 2.28
percentage points. Trout (1979) in a study using 1976 data,
concluded that moving from a veryfavorable to an
unfavorable regulatory environment raised equity costs by
1.97 percentage points. However, Fanara and Gorman (1986),
in a recent study, found that the effect of regulatory
climate on equity cost was considerably stronger in the
early 1970s than in 1980.
Several studies have also examined the regulatory
climate/debt cost relationship. For example, Dubin and
Navarro (1983) and Archer (1981) concluded that regulatory
climate also affects debt costthe lower the regulatory
ranking, the higher the cost. Dubin and Navarro found that,
for an average utility, a change from a very favorable
climate to an average or unfavorable climate (they used
three categories for regulatory ranking) resulted in a drop
in bond rating roughly equivalent to an S&P rating change
from AA to A.
Measure. Regulatory climate (REGRANK) was measured by
the Salomon Brothers' regulatory ratings. These ratings,
which can range from A+ to E, where A+ is the most
favorable climate and E is the least favorable, were
converted into a numerical scale as follows:8
Letter Numerical
Rating Rating
A+ to A 1
B+ to B 2
C+ to C 3
D+ to D 4
E+ to E 5
Gas/Electric Sales Mix
Rationale. Many utilities (the combination companies)
provide both gas and electric services, and there is some
evidence suggesting that gas operations might be riskier
than electric operations. For example, Joskow (1972) made
an intensive study of the regulatory decisionmaking process
in New York State. He found that gas departments of
combination companies made an upward adjustment in their
requests relative to the calculated cost of capital, which
reflected the belief that gas sales were riskier than
electric sales. However, Joskow did not present any
economic justification to support his observation, and he
noted that the commission typically allowed a higher equity
return on gas operations than on electric operations, but
the premium was normally less than that requested. On the
other hand, Dubin and Navarro (1983) concluded that there is
no risk differential between gas and electric operations.
Brigham, Vinson, and Shome (1983), and Brigham, Tapley,
and Aberwald (1984) conducted multiple regression analyses
in which cost of equity measures were the dependent
variable, and various risk measures, including percentage of
gas revenues to total utility revenues, were used as the
independent variables. They concluded (1) that gas
operations were (at least in 1983) slightly riskier than
electric operations, (2) that the differential riskiness of
gas and electric operations varies over time depending on
the relative prices of gas and fuel oil, and (3) that
differences across companies depend on other factors such as
customer mix.9
Measure. The gas/electric sales mix was measured by
the percentage of gas revenues to total gas plus electric
revenues as reported by Compustat (PCTGASREV).
Fuel Mix
Rationale. Little work has been done which attempts to
relate a firm's electric generation fuel mix to its capital
costs. However, fuel expense accounts for about onehalf of
total operating expenses, and hence the variability of fuel
prices has a significant impact on input price variability,
which affects a firm's business risk.
Fuel price uncertainty is shaped by the underlying
uncertainties in supply and demand. To complicate matters,
the relative price uncertainties among the fuel sources
change over time. In addition to price uncertainty, the
fuels have different accident risk. For example, nuclear
operating plant accidents can be much more disastrous than
accidents in other types of plants. Also, nuclear plants
are probably shut down more quickly, and stay down longer,
than other types of plants. This is important, because (1)
the variable costs associated with nuclear generation are
lower than for other types of plants, so costs shoot up when
a nuclear plant goes out of service, and (2) regulators may
not allow the company to pass these costs on to consumers.
This problem is exacerbated if the loss of a base load plant
requires the utility to use speaker units. Further, the
fuels have different environmental impact risk. To illus
trate, the imposition of legislation further restricting the
emission of sulfur and nitrogen oxides could significantly
increase the costs of building and operating coalfired
plants. Finally, the fuels have different impacts on the
firm's operating leverage. Nuclear plants have relatively
high fixed costs, while fossilfueled plants have relatively
high variable costs. For all these reasons, there is a
sound basis for believing that the five basic fuels
nuclear, coal, oil, gas, and hydrogenerationhave different
inherent riskiness.
It is important to recognize that this inherent
riskiness is not necessarily borne by the firm's capital
suppliers, and hence does not necessarily affect capital
costs. Regulators can effectively allocate much of the fuel
mix risk to the firm's customers by such actions as
automatic fuel adjustment clauses and full recovery of
accident costs through rate increases. However, different
regulatory agencies utilize different procedures, and hence
allocate fuel mix risk differently. All of this complicates
and perhaps obscures the relationship between fuel mix and
the riskiness of the utility's securities.
Measure. Fuel mix was measured by three separate
variables: (1) the percentage of nuclear generating
capacity to total capacity (PCTNUC), (2) the percentage of
coal generating capacity to total capacity (PCTCOAL), and
(3) the percentage of oil generating capacity to total
capacity (PCTOIL). Generating capacity data were obtained
from Compustat. Gas generation and hydrogeneration were not
included because these fuels represent a relatively small
contribution to industry capacity.
Construction Program
Rationale. Large construction programs could be
considered risky for several reasons. First, in an
inflationary environment new plant is much more costly than
old plant, both in terms of construction costs and capital
carrying costs. Commissions can deem that the company was
"imprudent" either in deciding to build the plant or in the
way the construction was carried out, and disallow a portion
of the plant's total cost from rate bases. If the costs are
not fully allocated to the ratepayers, then the construction
program will have a direct impact on investors' returns.
Second, large construction programs often require new equity
financing. If the firm's stock is selling below book value
at the time of sale, the current stockholders' equity
position is diluted, and hence value is lost.
Third, there is the risk that the plant will be
cancelled and investors will be forced to bear the costs of
cancellation. And fourth, there is significant risk when
the plant is actually available for service. Electric
utilities must plan their new construction programs well in
advance of the time that the capacity will actually be
needed. If demand growth turns out to be less than was
expected, then the capacity of the plant may not actually be
required, and the risk exists that the regulators will not
place the plant in the rate base. Under these
circumstances, the carrying cost of the plant must be borne
by the investors rather than the customers. Further, even
if the capacity of the new plant is needed, regulators, to
avoid "rate shock," may not grant a full and immediate cash
return on the plant, choosing instead to phase the plant
into the rate base and hence to delay the return.
Measure. The firms' construction programs were
measured by the percentage of total construction
expenditures forecasted for the next three years to total
current gross plant (PCTCON). The data were provided by
Salomon Brothers.
Nuclear Construction Program
Rationale. Over the past 10 years, changing
regulatory, legislative, financial, and legal environments
have had a significant adverse impact on nuclear
construction costs. For example, the safetyrelated
retrofits mandated after the Three Mile Island incident in
March 1979 have, by themselves, added between $27 and $100
million to the cost of each reactor unit, nationwide.
Further, it is estimated that electricity produced by
reactors completed in the 1980s will cost 3 times as much as
that produced by plants completed in the late 1970s, and 5
times more than plants completed in the early 1970s.
The effect of this substantial increase in nuclear
plant costs, coupled with decreased demand growth, has been
profound.10 Over 100 nuclear units have been cancelled over
the last 12 years. It is estimated that the cancellation
costs in 1983 alone totalled $3 billion, and that the cost
of future cancellations could easily top $20 billion.
Two main conclusions can be drawn: (1) The cost of
placing nuclear reactors into service has escalated
significantly since the first one was placed into service in
1956. (2) There is considerable risk that many of the units
currently under construction will never see service. Thus,
the utilities today having unfinished nuclear units face
significant riskinesseither from cancellation or from
placing units into service which are significantly more
costly than those currently in service. Further, the
slowing in demand growth has, in some cases, created excess
capacity, and additional units merely add to the reserve.
The riskiness inherent in unfinished nuclear units is
further compounded by the uncertainties of regulatory
response. When a plant is cancelled, or is placed into
service without a corresponding demand for its output,
someone must bear a loss. The question then becomes: How
will regulators allocate this loss?11 At one extreme, the
entire cost could be passed on to the firm's customers. In
this case, the presence of unfinished nuclear units poses
little risk to the firm's capital suppliers. At the other
extreme, regulators could impose the entire cost on the
utility's investors. Here, the possibility of abandoned or
excess nuclear plant would have the greatest impact on
security risk. Further, as in the case of nonnuclear
plants, even needed capacity may not be given a full and
immediate cash return upon completion in order to avoid
"rate shock."
Measure. Nuclear construction was measured by the
firm's total dollar investment in uncompleted nuclear plants
expressed as a percentage of current gross plant (NUCCON).
This measure was obtained from Salomon Brothers and
Compustat data, and the amount of investment includes both
costs incurred to date and estimated completion costs.
Reserve Margin
Rationale. A high reserve margin tends to reduce the
need for new construction, and in this sense it might reduce
investors' perceptions about a firm's riskiness. Also, a
high reserve margin reduces the risk of outages or hookup
delays, both of which can lead to consumer complaints, to
resistance to rate increases, and to a loss of regulatory
goodwill. Conversely, a high reserve margin could indicate
excess capacity, higherthannecessary costs, and the
possibility of regulatory penalties. A high reserve margin
is especially troublesome for a company with a large
construction program, for many of the problems associated
with construction are exacerbated if new plant is not really
needed.
Note, though, that it is often difficult to interpret
reserve margins across firms. For example, a reserve margin
of 40 percent might not be bad if most of the offline plant
consists of old, inefficient, highoperatingcost equipment
which has been largely depreciated. However, the same 40
percent margin would be bad if the excess plant had a high
cost and was as efficient as the plant being used to
generate power. Also, high reserve margins are much worse
for slowly growing utilities than for rapidly growing
companies, whose growth can quickly eliminate high reserve
margins.
Measure. Reserve margin was measured by the percentage
of unused generating capacity to total peak requirement
(RESMAR). Here total peak requirement is the higher of
summer and winter peaks. This measure was taken from
Compustat data.
Dividend Policy
Rationale. One of the most debated issues in finance
is whether a firm's dividend policy affects its required
return on equity. Miller and Modigliani (MM) (1961) argued
that a firm's cost of common equity is unaffected by its
dividend policy. They presented a welldeveloped proof, but
that proof hinged upon some restrictive assumptions,
including zero taxes and transactions costs. Basically, MM
showed that a dollar of dividends is the same as a dollar of
capital gains, and that dividend policy merely alters the
dividend/capital gain mix that equity investors receive.
The introduction of corporate taxes does not change MM's
basic conclusions (but, as noted below, the introduction of
personal taxes does).
Conversely, Gordon (1959) argued that dividends
represent certain cash in the hand while retained earnings
lead to uncertain capital gains and hence uncertain future
cash flows, and thus investors require a higher return on
low dividend payout stocks to account for their increased
riskiness. Brennan (1971) questioned Gordon's argument,
stating that Gordon was really talking about changes in
investment policy, and not dividend policy.
The theories discussed above were all based on the
assumption of a world with only corporate taxes. The
introduction of personal taxes could affect the conclusions
of earlier models, because capital gains are taxed at lower
rates than dividends.12 Farrar and Selwyn (1967) and
Brennan (1970) argued that investors value aftertax
returns. Thus, if two firms have equal risk, investors
would require the same aftertax return, but the beforetax
returns would depend on each firm's dividend yield/capital
gains mix. The firm with the higher dividend yield would
have a higher beforetax required return than the firm with
the lower dividend yield, and hence the higher capital gain.
Thus, they argued that a firm's cost of common equity is
directly related to its dividend payout ratiothe higher
the dividend payout, the higher the equity costs. This
relationship is exactly opposite of that proposed by Gordon.
Miller and Scholes (1978) went on to argue that investors
have the ability to postpone the tax on dividends, or even
to transform dividend income into capital gains income. If
this is the case, then the tax differential can be
effectively neutralized, and dividend policy again becomes
irrelevant. Black and Scholes (1974) also supported
dividend policy irrelevance, but they offered a different
argument. They argued that firms' dividend policies attract
particular investor clienteles, with high payout firms
attracting low tax bracket investors and low payout firms
attracting high tax bracket investors. If the clienteles
are satisfied, then an individual firm can appeal to either
clientele with no effect on its equity costs.
Rozeff (1981) suggested that dividend policy may be
tied to agency costs. Shareholders recognize that managers
may increase their personal wealth at the expense of outside
shareholders, and this risk is taken into consideration in
setting required rates of return. Dividend payments may
serve as a way of monitoring management performance, since
the requirement for external financing forces careful
scrutiny of the firm, and a higher payout leads to a greater
requirement for external financing. Thus, a higher payout
could lead to reduced monitoring costs, and hence a lower
cost of equity.
As with the financial leverage relationship, finance
theory presents contradictory arguments concerning the
relationship between dividend policy and equity costs. In
fact, the dividend policy situation is even more confusing,
for virtually all financial leverage theories posit a direct
relationship between leverage and equity costs, but with
dividend policy, theory provides three conflicting
relationships: (1) a direct relationship, (2) an inverse
relationship, and (3) independence.
Many empirical studies have been undertaken in attempts
to shed light on the true effects of dividend policy. For
example, Black and Scholes (1974) presented empirical
evidence to support the dividend irrelevance theory. On the
other hand, Litzenberger and Ramaswamy (1979) found a
positive relationship between dividend yield and required
return, which supported Brennan's theoretical position.
Both studies used empirical forms of the Capital Asset
Pricing Model with an added dividend yield term.13
Allinall, the empirical results, like the underlying
theories, reach conflicting conclusions, so it is difficult
to say that the existing empirical evidence supports one
side or the other.
Measure. Dividend policy is measured by a firm's
payout ratio (PAYOUT). However, realized payout ratios can
vary significantly from target payout ratios, and hence
Value Line's forecasted average payout ratio in 35 years
was used as the dividend policy measure in this study.
Notes
IIBES compiles the forecasts of leading Wall Street and
Regional brokerage firms. For electric utilities, the
growth rate data reflects the estimates of some 10 to 30
analysts, depending on the company.
2For example, companies with higher leverage would be
expected to have higher equity costs, other things held
constant, so the regression coefficient between ks and
leverage should be positive. However, leverage would be
expected to be inversely correlated with the M/B ratiothe
higher a company's debt ratio, the lower its M/B ratio,
other things held constant. To make the signs of the
independent variables consistent in the DCF k and M/B
specifications, the M/B ratio was inverted and B/M was used.
3Leverage can also be measured by coverage ratios, which
show the amount of earnings or cash flow available to cover
a firm's interest payments. Several coverage measures were
used in preliminary specifications, but their explanatory
power was considerably less than debttoequity measures,
and hence coverage measures were dropped.
4Average longterm debt maturity for a random sample of 10
companies was found to be 19.9 years. The minimum maturity
was 16.3 years, while the maximum was 22.9 years. Errors in
average maturity of plus or minus 5 years do not have a
significant effect on estimated market values.
5Value Line estimates the average common equity ratio during
a future threeyear period. For example, in 1986, it
reports the expected average equity ratio during the years
19881990. Thus, for all intents and purposes, the Value
Line forecast represents the equity ratio expected three
years into the future.
6There should perhaps also be variables which measure a
company's costs relative to other companies in its region on
the grounds that a highcost company is more exposed to load
loss from cogeneration and/or industrial plant relocations,
and also a variable that measures a company's operating
efficiency on the grounds that operating inefficiencies will
lead to high costs, hence to possible load loss and/or
regulatory penalties. However, no one has, thus far, been
able to develop quantitative measures for these variables,
and hence they are not included in the regression models.
To the extent that they (1) are important and (2) are not
already captured in the included variables, their omission
will result in larger error terms and lower R2 values.
However, their omission will not affect the leverage
variable's coefficient unless cost and efficiency, on a
companybycompany basis, are correlated with leverage.
The term "regulatory climate" encompasses public service
commission actions, legislative actions, and court actions.
The terms "regulators" and "regulatory agencies" include all
of these bodies, not just commissions.
8Various combinations of dummy variables were also used to
measure regulatory climate. The results were similar, so
the dummy variable specification was dropped.
Various measures of customer mix were included in early
specifications, but these did not affect explanatory power
and were not statistically significant, and hence they were
dropped.
10Electricity demand grew by about 7 percent per year up
until the 1973 oil embargo. Recently, demand has been
growing at an annual rate of less than 3 percent.
11For an excellent discussion of loss allocation, see
Robinson (1981).
120nly 40 percent of capital gains were taxed under laws in
effect during the study period. The Tax Reform Act of 1986
eliminated the preferential treatment of capital gains, but
capital gains still retain a slight tax advantage due to
deferral of taxes.
13For example, Litzenberger and Ramaswamy used this model:
ki kRF = aI + a2bi + a3(di kRF),
where
ki = expected rate of return on Firm i,
krf = riskfree rate,
bi = the beta coefficient of Firm i,
di = the dividend yield on Firm i, and
al, a2, a3 = regression coefficients.
A statistically positive a3 would mean that equity costs and
dividend yield are positively related.
CHAPTER IV
REGRESSION RESULTS
Chapter III described the variables chosen for
inclusion in the regression model and the specific measures
selected for those variables. Now, Chapter IV provides
additional information on the regression model and then
presents the results of the regression runs.
Data Sample
The data set consisted of those electric utilities that
were followed by Institutional Brokers Estimate System
(IBES), Value Line, Salomon Brothers, and Standard & Poor's
(Compustat). However, companies which had lowered or
omitted their common dividends were excluded on the grounds
that those firms clearly violated the constant growth
assumption needed to estimate the DCF ks. Two years of data
were used, 1983 and 1984.1 After applying these data
restrictions, the sample consisted of 70 companies for 1983
and 66 for 1984. Appendix A contains a listing of the
companies included in the sample set.
Regression Specifications
Two measures were used for both equity cost and debt
cost, and four measures were used for leverage. Thus, there
were eight different equity model specifications and eight
different debt model specifications for each year. Table 41
summarizes the regression model specifications. In total,
32 separate model specifications constitute the primary
regression runs. Additionally, other specifications were
used to investigate side issues that arose during the study.
These secondary specifications will be discussed as
appropriate throughout the remainder of the study.
Table 41
Regression Model Specifications
Specification
Designation
DCF3BV
DCF3MV
DCF3EXBV
DCF3EXMV
B/M3BV
B/M3MV
B/M3EXBV
B/M3EXMV
DCF4BV
DCF4MV
DCF4EXBV
DCF4EXMV
B/M4BV
B/M4MV
B/M4EXBV
B/M4EXMV
YLD3BV
YLD3MV
YLD3EXBV
YLD3EXMV
RAT3BV
RAT3MV
RAT3EXBV
RAT3EXMV
YLD4BV
YLD4MV
YLD4EXBV
YLD4EXMV
RAT4BV
RAT4MV
RAT4EXBV
RAT4EXMV
Year
1983
1983
1983
1983
1983
1983
1983
1983
1984
1984
1984
1984
1984
1984
1984
1984
1983
1983
1983
1983
1983
1983
1983
1983
1984
1984
1984
1984
1984
1984
1984
1984
Type
Equity
Equity
Equity
Equity
Equity
Equity
Equity
Equity
Equity
Equity
Equity
Equity
Equity
Equity
Equity
Equity
Debt
Debt
Debt
Debt
Debt
Debt
Debt
Debt
Debt
Debt
Debt
Debt
Debt
Debt
Debt
Debt
Dependent
Variable
DCF k
DCF k
DCF k
DCF k
B/M ratio
B/M ratio
B/M ratio
B/M ratio
DCF k
DCF k
DCF k
DCF k
B/M ratio
B/M ratio
B/M ratio
B/M ratio
S&P k
S&P k
S&P k
S&P k
Bond rating
Bond rating
Bond rating
Bond rating
S&P k
S&P k
S&P k
S&P k
Bond rating
Bond rating
Bond rating
Bond rating
Leverage
Measure
BVDE
MVDE
EXBVDE
EXMVDE
BVDE
MVDE
EXBVDE
EXMVDE
BVDE
MVDE
EXBVDE
EXMVDE
BVDE
MVDE
EXBVDE
EXMVDE
BVDE
MVDE
EXBVDE
EXMVDE
BVDE
MVDE
EXBVDE
EXMVDE
BVDE
MVDE
EXBVDE
EXMVDE
BVDE
MVDE
EXBVDE
EXMVDE
A Priori Expectations about Coefficient Signs
Table 42 contains the a priori estimates of the
coefficients' signs based on the previous empirical and
theoretical studies discussed in Chapter II. (Note that
Appendix B contains a glossary of the variable measure
symbols.) Regulatory environment, both regular and nuclear
construction, and all of the leverage variables should have
positive coefficients, indicating that an increase in the
variable's value raises ks and kd. However, there are no
strong logical arguments as to what the signs should be for
the sales mix, fuel mix, reserve margin, or payout ratio
variables.
Table 42
A Priori Coefficient Estimates
Factor
Financial leverage
Regulatory environment
C
Measure
BVDE
MVDE
EXBVDE
EXMVDE
REGRANK (1 = best,
5 = worst)
Estimated
'oefficient
Sign
+
+
+
+
+
Gas/electric sales mix
Fuel mix
Construction program
Nuclear construction program
Reserve margin
Dividend policy
PCTGASREV
PCTNUC
PCTCOAL
PCTOIL
PCTCON
NUCCON
RESMAR
PAYOUT
Input Data Summary
Table 43 contains a summary of the input data. For
the most part, the table is selfexplanatory, but two points
deserve clarification. First, the S&P bond ratings range
from 4 = AA+ to 12 = BBB, and the means for 1983 and 1984
indicate that the average company has an A rating. Second,
the reserve margin, RESMAR, is negative for some utilities
because they purchase a significant amount of the power they
sell from other utilities. Note too that the means reflect
unweighted rather than weighted averages.
Table 43
Input Data Summary
1983
Minimum Maximum
e Value Value Mean
12.8% 19.0% 15.8%
io 0.61 1.35 1.04
12.6% 13.6% 13.0%
ting 5 14 7.9
2 4 2.8
0.68 1.86 1.27
0.44 1.91 0.96
0.77 1.70 1.29
0.48 1.63 0.97
1EV 0.0% 53.9% 13.7%
0.0% 83.0% 13.3%
0.0% 100.0% 65.4%
0.0% 100.0% 9.1%
9.0% 175.0% 36.5%
0.0% 99.8% 17.9%
68.0% 54.5% 18.3%
57.7% 94.7% 73.3%
Based on yearend data.
Minimum
Value
12.9%
0.60
12.1%
4
2
0.62
0.36
0.83
0.53
0.0%
0.0%
0.0%
0.0%
10.0%
0.0%
51.5%
52.9%
1984
Maximum
Value
17.3%
1.44
12.9%
13
5
1.83
2.02
1.94
1.79
66.2%
68.6%
100.0%
100.0%
161.0%
94.8%
56.2%
94.6%
Variabl
ks
B/M Rat
kd
Bond Ra
REGRANK
BVDE
MVDE
EXBVDE
EXMVDE
PCTGASR
PCTNUC
PCTCOAL
PCTOIL
PCTCON
NUCCON
RESMAR
PAYOUT
Note:
Mean
14.8%
0.98
12.5%
7.5
2.8
1.22
0.94
1.24
0.93
13.4%
13.6%
63.6%
7.9%
33.5%
14.6%
18.8%
72.0%
Dependent Variable Measure Correlations
Since two measures are being used for both debt and
equity costs, and because one would expect a strong positive
relationship between debt and equity costs, the first step
in the analysis was to determine the correlations among the
dependent variable measures. Table 44 contains these values.
Table 44
Dependent Variable Correlation Coefficients
1983 1984
B/M Bond B/M Bond
DCF ks Ratio S&P kd Rating DCF ks Ratio S&P kd Rating
DCF ks 1.00 0.74 0.59 0.64 1.00 0.58 0.47 0.49
B/M Ratio 1.00 0.58 0.63 1.00 0.61 0.69
S&P kd 1.00 0.94 1.00 0.95
Bond Rating 1.00 1.00
There are three major points to note: (1) There was
extremely high correlation between the two cost of debt
measures in both years. This was expected, since each
firm's S&P cost of debt is derived from the firm's S&P bond
rating. (2) There was, in general, a strong positive
correlation (from 0.47 to 0.69) between a firm's cost of
debt measures and its cost of equity measures. This was
also expected since the same underlying risk factors should
affect the riskiness of a firm's securities, and hence its
costs of debt and equity. (3) The correlations between the
DCF ks and the other dependent variable measures were
stronger in 1983 than in 1984, but correlations among the
other variables were not materially stronger in one year
than the other. This could mean that the DCF ks contains
more measurement error in 1984 than in 1983.
The high correlation between a firm's bond rating and
its DCF ks suggests that this relationship be examined more
closely. Thus, two new specifications were created with DCF
ks as the dependent variable in both specifications and (1)
S&P bond rating as the independent variable and (2) S&P kd
as the independent variable. The results of these
specifications are contained in Table 45.
Table 45
Relationship between DCF ks and Debt Cost
S&P kd S&P Bond Rating
1983 1984 1983 1984
Coefficient 1.99 1.59 0.36 0.22
tstatistic (6.07) (4.22) (6.93) (4.55)
Adjusted R2 0.34 0.21 0.41 0.23
The average coefficient for S&P kd was 1.79 over 1983 and
1984. This implies that a one percentage point increase in
a firm's cost of debt would lead to a 1.79 percentage point
increase in its cost of equity.
The average coefficient for bond rating was 0.29.
Thus, a decrease in a firm's S&P bond rating from, say A+ to
A, would increase its cost of equity by 29 basis points. A
change by one full rating, say from AA to A, would increase
a firm's equity cost by 87 basis points.
Equity Regression Results
Appendix C contains the regression results
(coefficients and tstatistics) for the cost of equity
regressions: Table Cl reports the results using book value
debttoequity as the leverage measure, Table C2 contains
the market value debttoequity results, Table C3 contains
the results using the expected book value debttoequity
ratio as the leverage measure, and Table C4 reports the
results using the expected market value debttoequity
ratio.
The Leverage/Cost of Equity Relationship
To begin, examine the adjusted R2 (the explanatory
power) of the equity regressions. First, the explanatory
power of the DCF ks specifications was significantly greater
in 1983 than in 1984. This, in part, could reflect the
smaller sample size in 1984, but this appeared to have
minimal impact on the adjusted R2 of the regressions using
the B/M ratio as the dependent variable. The difference in
explanatory power could also be caused by increased
measurement error in the 1984 DCF ks estimates. This
explanation is consistent with the dependent variable
correlation results discussed previously.
Second, the two specifications using market value debt
toequity as the leverage measure had greater explanatory
power than the two book value specifications. Further, the
market value debttoequity ratios had considerably higher
tstatistics than the corresponding book value measures.
Thus, variations in equity costs among firms are more
closely related to market value leverage measures, and hence
equity investors appear to judge the financial risk of a
firm in market value terms rather than book value terms.
This conclusion is consistent with the theoretical rela
tionships discussed in Chapter II. Further, this result
supports the findings of Gordon (1974) and Mehta et al.
(1980), who found that equity cost is positively related to
market value leverage measures, but refutes the study of
Robicheck, Higgins, and Kinsman (1973), which had
inconclusive results when leverage was measured in market
value terms.
Finally, the explanatory power of the specifications
using expected debttoequity ratios was generally higher
than those using current debttoequity ratios. Further,
the leverage measure tstatistics were generally higher for
the expected measures. This could indicate that
expectational leverage measures more closely parallel
investors perceptions of financial risk than do current
measures. This supports the argument that firms' capital
structures vary from optimal over time, but that investors
recognize this and demand financial risk premiums based on
longrun target capital structures rather than current
structures.
One of the primary goals of this study is to estimate
the cost of equity/leverage relationship. As just
discussed, this relationship is strongest when leverage is
measured in expected market value terms. Table 46 contains
extracts from Table C4 in Appendix C. The relationship
between a firm's expected market value debttoequity ratio
and its cost of equity was positive and statistically
significant in both years for both measures of the cost of
equity.
Table 46
Expected Market Value DebttoEquity
Coefficients and tstatistics
Dependent Variable
DCF ks B/M Ratio
1983 1984 1983 1984
2.25 1.59 0.36 0.36
(4.25) (3.21) (7.30) (7.89)
The DCF ks specification permits an easy interpretation
of the impact of financial leverage on the cost of equity.
The leverage coefficient averaged 1.92 over the two years.
However, as previously discussed, there appears to be more
measurement error in DCF ks in 1984 than in 1983. Further,
note that the coefficient when the B/M ratio is used as the
cost of equity measure was the same in both years. Rather
than average the coefficients, it seems that the 1983
estimate, 2.25, is a better estimate of the true, but
unknown, relationship. Using this estimate, within the
range of expected market value debttoequity ratios found
in the sample (0.48 to 1.79 as reported in Table 43), a
unitary increase in the expected market value debttoequity
ratio increased equity cost, on average, by 2.25 percentage
points. (A unitary increase means an increase in the debt
toequity ratio from, say, 0.4 to 1.4 or from 1.0 to 2.0.)
Most practitioners think of financial leverage in terms
of the debt (debttovalue) ratio, so it would be useful to
express the results in these terms. Table 47 illustrates
the impact of leverage changes on equity cost in terms of
both debttoequity and debttovalue ratios. For example,
an increase in a firm's market value debt ratio from 40 to
50 percent would increase its cost of equity by 1.28 0.54
= 0.74 percentage points, or by 74 basis points. Note that
the relationship between equity cost and financial leverage
is nonlinear when leverage is measured by the debt ratio.
Thus, while an increase in the debt ratio from 40 to 50
percent increases equity cost by 74 basis points, an
increase in the debt ratio from 50 to 60 percent increases
the cost of equity by 1.13 percentage points.
Table 47
Impact of Leverage on Equity Cost
Expected Expected Increase in Financial
Market Value Market Value Risk Premium from Base
Debt Ratio DebttoEquity Ratio Level Debt Ratio of 30%
30% 0.43
40 0.67 +0.54
50 1.00 +1.28
60 1.50 +2.41
Table 48
Results Comparison
Average
DebttoEquity
Coefficient
Study Book Market Study
Value Value Period
Brigham and Gordon (1968) 0.33  1958 1962
Robichek et al. (1973) 0.9  1962 1969
Gordon (1974)  0.5 1958 1968
Mehta et al. (1980)  0.74 1968 1972
Gapenski (1986) (DCF k) 1.41 1.92 1983 1984
Gapenski (1986) (Div. Yld.) 2.01 2.94 1983 1984
Table 48 compares the results of this study with
previous work. Of course, there are definitional
differences among the studies, so a precise comparison is
impossible. For example, only Robichek et al. and Gapenski
used a direct measure of ks as the dependent variable, all
other studies used the dividend yield. To provide a better
comparison, the cost of equity regressions were rerun using
a dividend yield specification. That is, dividend yield was
used as the dependent variable and dividend growth rate was
added as an independent variable.2 These runs resulted in
an average EXMVDE coefficient and tstatistic of 2.94 (6.72)
and 2.01 (3.35) for EXBVDE. Thus, this study finds leverage
to have a much greater impact on electric utility equity
costs than previously reported. However, capital costs have
generally risen over the period of the studies, so one would
expect the leverage coefficients to increase over time.
Nevertheless, the market value coefficients reported here
have increased much more dramatically than have capital
costs.
To test for possible nonlinearities, each equity
regression specification was rerun with an additional
independent variable, the leverage measure squared. The
coefficients of the second order terms were all
statistically insignificant, and hence there was no indica
tion that a quadratic relationship existed between equity
cost and leverage over the range of observations.
Other Risk Factors
Perhaps the most startling result with regard to the
other risk factors was the failure of regulatory climate to
consistently affect a firm's equity cost. The regulatory
rank variable was statistically significant in only 2 of 16
regression runs, and regulatory rank was not significant at
all when leverage was measured by market value debtto
equity ratios, although these leverage measures produced the
highest explanatory power (R2). Further, the sign of the
regulatory rank coefficient was inconsistent.3
The dominant business risk factor was nuclear
construction programs. The average coefficient of the
nuclear construction variable over 1983 and 1984 (DCF ks
with expected market value debttoequity specification) was
0.018, which indicates that a firm with no incompleted
nuclear plant would have a zero nuclear construction risk
premium, a firm with a 20 percent nuclear construction to
current gross plant ratio would have a 36 basis point
nuclear construction risk premium, and a firm with an 80
percent nuclear construction ratio would have a 144 basis
point risk premium. Of course, these premiums reflect the
riskiness of "average" nuclear construction programs, but
extremely high cost plants with significant regulatory
opposition are clearly much riskier than incomplete nuclear
plants that are on schedule, have relatively low costs, and
are expected to be placed into service with full cost
recovery. Thus, although the regression analysis confirms
that equity investors view nuclear construction as having
significant risk, it is probably not appropriate to apply
the numerical results to particular firms.
There was also some evidence that investors considered
reserve margin to be a risk factor for electric utilities.
The reserve margin coefficient was statistically significant
in 9 out of 16 runs, including 4 out of 8 runs using market
value debttoequity leverage measures.4 On average, a
higher reserve margin decreases the riskiness of a firm's
equity. However, the coefficient averaged only 0.012 in
1983 and 1984 in the DCF ks specifications with market value
leverage, so an average reserve margin of about 18.5 percent
only reduced equity costs by 22 basis points, while a high
margin of 50 percent would reduce ks by 60 basis points
compared to a firm with a zero reserve margin. As with
nuclear construction, it is probably nonsensical to attempt
to apply the reserve margin results to a particular utility,
for as discussed in Chapter III, the impact of reserve
margin is highly dependent upon the firm's particular
situation.
Finally, there was some evidence that gas revenues are
riskier than electric revenues and that nuclear operating
plant is riskier than coal or oil generation. However, the
results in this regard are not conclusive.5 There was no
indication that conventional construction programs or
dividend policy affects the equity cost of electric
utilities.
In Chapter III, several potential interactions were
discussed. Specifically, it is possible that nuclear
construction programs or nuclear operating plants could have
a greater impact on equity cost if the utility were
operating in a poor regulatory climate. Also, reserve
margin could be viewed as unfavorable if the firm has large
ongoing construction or nuclear construction programs. To
test for possible interactions, the equity regressions were
rerun with the following interaction terms added:
REGRANK*NUCCON, REGRANK*PCTNUC, RESMAR*PCTCON. The
coefficients of the interaction terms were mixed in sign and
statistically insignificant. Thus, there was no evidence
that the hypothesized interaction relationships affected
equity cost.
Statistical Problems
Three major statistical problems often occur in
multiple regression crosssectional analyses: (1)
heteroscedasticity, (2) multicollinearity, and (3)
measurement error.
Heteroscedasticity. One of the assumptions of the
classical normal linear regression model is that the error
term has a constant variance across observations. This
assumption is violated if the error term exhibits
heteroscedasticity, or nonconstant variance. If
heteroscedasticity occurs, the least squares parameter
estimates (coefficients) remain unbiased, but the parameter
variances will be biased, and hence the standard statistical
tests (tstatistics and adjusted R2) will be incorrect.
The statistical software used to conduct the regression
analysis (SAS Version 5) can automatically adjust the
covariance matrix to correct for heteroscedasticity. This
option was used on all regressions. However, preliminary
examination of corrected and uncorrected regressions
indicated that heteroscedasticity was not a problem in this
analysis; that is, the significance of the independent
variables was unaffected by the heteroscedasticity
adjustment.
Multicollinearity. Multicollinearity occurs when two
or more independent variables are correlated with one
another. In extreme cases, when there is a perfect linear
relationship between two or more independent variables, it
is impossible to calculate the leastsquares parameters.
This situation is easy to correctmerely delete one of the
collinear variables. However, the problem becomes more
difficult when two independent variables are highly, but not
perfectly, correlated. In this situation, the coefficient
estimates remain unbiased in the statistical sense, but (1)
the estimated parameter standard errors are too large, and
hence the tstatistics are biased downward, and (2) it is
difficult to give proper interpretation to the coefficients,
because standard interpretation requires that all other
independent variables remain constant, a condition which
cannot hold when independent variables are correlated.
Unfortunately, there is no accepted measure for
defining when multicollinearity becomes a serious problem.
Pindyck and Rubinfeld (1981) state a rule of thumb that is
commonly used: Multicollinearity is likely to be a problem
if the simple correlation between two variables is larger
than the correlation of either or both variables with the
dependent variable. However, they also state that this rule
may be quite unreliable if there are more than two
independent variables.
Appendix D contains the independent variable
correlation matrix. The leverage measures are obviously
highly correlated, but only one of these measures is used in
each specification. However, there are relatively high
correlations (defined here as greater than 0.30) between (1)
the leverage variables and nuclear construction, and (2) the
fuel mix variables. There is no accepted correction
procedure for multicollinearity, but it is possible to
examine the impact of the multicollinear variables on each
others coefficients and tstatistics. This was accomplished
by conducting a stepwise regression. Since the primary
leverage variable of interest is the expected market value
debttoequity ratio, the stepwise regression used this
specification. The results are contained in Table 49.
Two major conclusions can be drawn from the stepwise
regressions. First, a utility's equity costs are affected
most by leverage and nuclear construction programs. These
two variables had the most explanatory power in both years,
although in 1983 leverage appeared to dominate, while in
1984 nuclear construction dominated. (Note that in the B/M
stepwise regressions which are not reported here, the
dominant variable was leverage in both years.) Further, the
Table 49
Stepwise Regression Results
(DCF ks with Expected Market Value DebttoEquity)
1983
Variables Added Coefficient tstatistic R2
EXMVDE 3.3433 8.57 0.52
EXMVDE 2.3693 5.46 0.61
NUCCON 0.0211 3.90
EXMVDE 2.2154 5.11 0.63
NUCCON 0.0230 4.25
RESMAR 0.0102 1.88
EXMVDE 2.1432 4.98 0.64
NUCCON 0.0228 4.33
RESMAR 0.0118 2.17
PCTCOAL 0.0050 1.67
1984
Variables Added Coefficient tstatistic R2
NUCCON 0.0304 5.37 0.31
NUCCON 0.0210 3.49 0.41
EXMVDE 1.3726 3.30
EXMVDE 1.8908 4.18 0.46
NUCCON 0.0179 3.03
REGRANK 0.4335 2.47
EXMVDE 1.7019 3.73 0.49
NUCCON 0.0198 3.35
REGRANK 0.3864 2.22
RESMAR 0.0104 1.77
collinearity between these variables had a large impact on
the coefficient of the leverage variable (EXMVDE), which is
the major variable of interest in this study. The
coefficient of EXMVDE was 3.34 in 1983 when nuclear
construction was not considered, but it fell to 2.37 with
the addition of the nuclear construction variable. When all
variables are included, the coefficient was 2.25, so only
nuclear construction had a major impact on the coefficient
of the leverage variable. A separate regression was
conducted for 1984 in which the only independent variable
was EXMVDE. Its coefficient was 2.07 with a tstatistic of
5.21. Note in Table 49 that the addition of the nuclear
construction variable lowered the EXMVDE coefficient to
1.37. In each year, the leverage coefficient (as measured
by EXMVDE) was reduced by about 30 percent by the inclusion
of the nuclear construction variable. Over the two years,
the coefficient of EXMVDE averaged 2.71 when the collinear
nuclear construction variable was dropped from the
regression. This compares with a coefficient of 1.92 when
nuclear construction is included in the specification. When
considering only 1983 because of possible measurement error
in the 1984 DCF k variable, the EXMVDE variable fell from
3.34 to 2.25. Table 410 illustrates the impact of leverage
changes on equity cost when the collinearity is removed, and
a coefficient of 3.34 is used. (See Table 47 for
comparison.) Now, an increase in a firm's market value debt
ratio from 40 to 50 percent would increase its cost of
equity by 110 basis points, and an increase in the debt
ratio from 50 to 60 percent would increase a firm's equity
cost by 1.67 percentage points.
Table 410
Impact of Leverage on Equity Cost
(Collinearity Removed)
Expected Expected Increase in Financial
Market Value Market Value Risk Premium from Base
Debt Ratio DebttoEquity Ratio Level Debt Ratio of 30%
30% 0.43
40 0.67 +0.80
50 1.00 +1.90
60 1.50 +3.57
The second conclusion that can be drawn from the
stepwise regression is that regulatory climate did not
appear to be a major risk factor for electric utilities
equity investors in 1983 and 1984. In 1983, the regulatory
climate variable (REGRANK) did not appear in the stepwise
results, and in 1984 it appeared, but with the wrong sign.
These results tend to confirm the earlier results using the
full specifications, which support and extend the results of
Fanara and Gorman (1986), who concluded that regulatory
climate was a significant equity risk factor in the early
1970s, but that its influence diminished over time.
Measurement error. The classical linear regression
model requires that all variables in the model be measured
without error. In practice this is generally not the case.
In this study, the dependent variables are merely proxies
for investors' required rates of return, and hence
measurement error exists. Measurement error in the
dependent variable affects the intercept term, but the
coefficients of the independent variables remain unbiased
(see Pindyck and Rubinfeld (1981)).
However, measurement error in the independent
variables, or in both the dependent and independent
variables, has more serious consequences. Here, measurement
error typically leads to coefficient estimates that are
biased downward, and hence understate the true
relationships. Again, there is every reason to believe that
measurement error exists in the financial leverage measures,
since they are all proxies for investors' views on firms'
target capital structures. Thus, there is reason to suspect
that the coefficients reported earlier understate the true,
but unobservable, relationships. This point will be
discussed in more detail in Chapter VI.
Debt Regression Results
The coefficients and tstatistics for the cost of debt
regressions are presented in Appendix E: Table El reports
the results using book value debttoequity as the leverage
measure, Table E2 contains the market value debttoequity
results, Table E3 contains the results using the expected
book value debttoequity ratio as the leverage measure, and
Table E4 reports the results using expected market value
debttoequity as the leverage measure.
The Leverage/Cost of Debt Relationship
The first point to note is that the leverage measure
used had considerably less impact on the debt regression
results than on the equity regression resultsthe leverage
coefficients and explanatory power (adjusted R2) were much
less sensitive across leverage measures. Further, unlike
the equity results, the explanatory power was greater in
1984 than in 1983 for all specifications.
The current market value debttoequity measure had the
highest explanatory power and tstatistics by a slim margin.
Table 411 contains extracts from Table E2 in Appendix E.
Table 411
Market Value DebttoEquity
Coefficients and tstatistics
Dependent Variable
S&P kd S&P Bond Rating
1983 1984 1983 1984
0.84 0.52 4.51 4.06
(5.34) (4.51) (5.45) (5.53)
The relationship between a firm's market value debtto
equity and its cost of debt was positive and statistically
significant for both years and both debt cost measures.
Focusing on the S&P kd specification, the average
coefficient value was 0.68, which means that a unitary
change in a firm's market value debttoequity ratio (within
the sample range) would increase its cost of debt by 68
basis points. However, to be consistent in reporting both
the debt and equity results, the impact of leverage on debt
costs will be measured by the 1983 coefficient, 0.84.5
Table 412 illustrates the impact of leverage changes on
debt cost. For example, a change in a firm's market value
debt ratio from 40 to 50 percent increases its cost of debt
by 28 basis points, while an increase in debt utilization
from 50 to 60 percent increases a firm's cost of debt by 42
basis points.
Table 412
Impact of Leverage on Debt Cost
Change in Financial
Market Value Market Value Risk Premium from Base
Debt Ratio DebttoEquity Ratio Level Debt Ratio of 30%
30% 0.43
40 0.67 +0.20
50 1.00 +0.48
60 1.50 +0.90
Note that the coefficient average over 1983 and 1984
was 0.69 using book value debttoequity, 0.65 using
expected book value debttoequity, and 0.61 using expected
market value debttoequity. Thus, the effect of leverage
on the cost of debt was relatively invarient to the leverage
measure used.
Second order leverage terms were also added to the debt
specifications to test for nonlinear leverage relationships.
These second order terms neither enhanced the explanatory
power of the specifications nor proved to be statistically
significant. Thus, there was no evidence that the
leverage/debt cost relationship is quadratic when leverage
is measured by debttoequity ratios.
Other Risk Factors
In general, the results of the debt regressions
parallel those of the equity regressions. Other than
financial leverage, the two factors which were consistently
statistically significant were nuclear construction programs
and reserve margins. Using the market value leverage
specifications over both years, the average coefficient for
nuclear construction was 0.0055 and for reserve margin, 
0.0049. Thus, a firm with a 50 percent nuclear
constructiontocurrent gross assets ratio would pay 27.5
basis points more in debt cost than a utility with no
nuclear construction. Similarly, a firm with a 40 percent
reserve margin would pay about 9.8 basis points less than a
firm with a 20 percent reserve margin. Although nuclear
construction programs and reserve margins have high
statistical significance, their impact on debt costs is not
very large. Further, these risk factors, as well as
financial leverage, appear to have a much greater impact on
equity cost than on debt cost. This could be due to two
factors: (1) Utility debt is typically in the form of
mortgage bonds, and hence debtholders have a claim against
specific assets in the event of financial distress. (2)
Perhaps more important, no major utility has defaulted on
its first mortgage bonds in several decades, and debt
investors could view the impact of such factors as nuclear
construction and reserve margin as minimal as long as the
regulatory agencies allow the utilities to earn enough to
service the debt.
The debt regressions, like the equity regressions, were
rerun with interaction terms added: specifically
REGRANK*NUCCON, REGRANK*PCTNUC, and RESMAR*PCTCON. There
was no consistent evidence that the hypothesized interaction
relationships affected debt cost.
Statistical Problems
The debt regressions exhibited the same potential
statistical problems as the equity regressions.
Heteroscedasticity. Corrections for heteroscedasticity
were automatically performed by the software, although
preliminary analysis did not indicate that a problem
existed.
Multicollinearity. The procedures to assess the impact
of multicollinearity that were used on the equity
regressions were also used on the debt regressions. Table
413 contains the results of the stepwise regressions using
the market value debttoequity ratio as the leverage
variable. Note that a firm's financial leverage had the
greatest impact on debt cost. In both years, MVDE was the
first variable selected, and the explanatory power of the
specification was improved only slightly by the addition of
other variables.
As in the equity regressions, the addition of the
nuclear construction variable had a considerable impact on
the magnitude of the leverage coefficient. In 1983, the
coefficient of MVDE was 0.9563 with leverage as the sole
independent variable (see Table 413), but the coefficient
dropped to 0.8400 when all explanatory variables were
included (see Table E2 in Appendix E). Similarly, in 1984
the coefficient dropped from 0.7299 to 0.5170.
Table 413
Stepwise Regression Results
(S&P kd with Market Value DebttoEquity)
1983
Variables Added
MVDE
MVDE
PCTCOAL
MVDE
PCTCOAL
RESMAR
MVDE
PCTCOAL
RESMAR
NUCCON
MVDE
PCTCOAL
RESMAR
NUCCON
PCTOIL
Coefficient
0.9563
1.0031
0.0027
0.9876
0.0023
0.0033
0.8518
0.0023
0.0037
0.0030
0.8647
0.0037
0.0035
0.0042
0.0039
tstatistics
7.91
8.57
2.68
8.56
2.39
1.85
6.26
2.46
2.11
1.80
6.43
2.95
2.08
2.39
1.67
1984
Variables Added
MVDE
MVDE
RESMAR
MVDE
RESMAR
NUCCON
MVDE
RESMAR
NUCCON
PCTCON
Coefficient
0.7299
0.7259
0.0045
0.6058
0.0048
0.0033
0.5990
0.0054
0.0075
0.0047
tstatistics
8.13
8.59
3.03
6.07
3.30
2.02
6.23
3.78
3.26
2.41
R2
0.48
0.53
0.55
0.57
0.59
R2
0.51
0.57
0.60
0.63
Also, note that the stepwise regression did not select
the regulatory climate variable. Thus, as with the cost of
equity, regulatory climate did not appear to be a major risk
factor to electric utility debt investors in 1983 and 1984.
Measurement error. The same problems discussed in
regard to the equity regressions apply to the debt
regressions. The implications of measurement error will be
discussed fully in Chapter VI.
This chapter discussed in detail the results of the
regression model, which was used to estimate both the
leverage/debt cost and leverage/equity cost relationships.
In Chapter V, a second approach is used to estimate the
leverage/debt cost relationship, the bond rating guidelines
model.
Notes
1It was apparent that a major risk factor for electric
utilities in recent years was nuclear construction programs.
Thus, the inclusion of this variable was considered
mandatory. Nuclear construction program data first became
available in usable form in 1983, and hence this variable
dictated the number of years used in the study.
2Dividend yield was measured by dividing Value Line's
forecast of next year's dividend by the endofyear stock
price reported by Compustat. Dividend growth was estimated
by the 5year IBES median growth rate in earnings.
3The dividend yield specifications produced similar results.
Regulatory climate was not statistically significant in any
of the eight dividend yield specifications (four leverage
measures over two years).
4Reserve margin was statistically significant in six of the
eight dividend yield specifications.
5Alternative specifications with percent hydrogeneration and
percent gas generation in lieu of percent coal generation
and percent oil generation were also run. The results were
similar to those reportedfuel mix did not appear to affect
capital costs in 1983 and 1984.
6Unlike the equity regressions, there is no indication that
the 1983 results are any better than the 1984 results for
the debt regressions. However, in Chapter VI the debt and
equity results will be compared, and using the 1983 debt
regressions, allows comparison of like sample sets and
economic conditions.
CHAPTER V
THE BOND RATING GUIDELINES MODEL
Model Overview
Firms' bonds are rated for quality by many rating
agencies. These agencies assign ratings, such as AAA, AA,
A, BBB, which reflect the agency's judgment of the default
risk of the issue. Also, these same firms provide data on
bond yields for the various ratings. Recently, one of these
agencies, Standard & Poor's (S&P) Corporation, made public
its rating guidelines for financial leverage for several
industries. For example, S&P might state that, other things
held constant, a debt ratio of 48 percent plus or minus 5
percent is required for an AA rating, while a ratio of 42.5
percent plus or minus 5 percent would result in an A rating.
(Some overlaps occur, and in these cases "other things"
determine the actual bond rating.) With the bond yields for
each rating, and the rating guidelines known, it is possible
to estimate the effect of financial leverage on debt costs.
For example, if the yield on AArated bonds was 12.6
percent, and the yield on Arated bonds was 12.9 percent,
then a one percentage point change in the debt ratio would
be associated with a (12.9 12.6)/(48.0 42.5) = 0.055
percentage point change in the cost of debt. In this
chapter, such a relationship is used to estimate the finan
cial leverage/debt cost relationships for 1983 and 1984.
Bond Ratings
Standard & Poor's assigns bond ratings to electric
utilities based on both nonfinancial and financial criteria.
The nonfinancial criteria include (1) service territory, (2)
fuel mix, (3) operating efficiency, (4) regulatory
treatment, (5) management, and (6) competition/monopoly
balance. The financial criteria include (1) construction
risk, (2) earnings protection, (3) financial leverage, (4)
cash flow adequacy, (5) financial flexibility/capital
attraction, and (6) accounting quality.1 Table 51 contains
a breakdown of the sample set by Standard & Poor's bond
rating. The ratings ranged from AA to BB in 1983 and from
AA+ to BB+ in 1984, with the vast majority (over 98 percent)
of companies being rated from AA+ to BBB.
Table 51
Sample Set Bond Ratings
Number of Companies
Rating 1983 1984
AA+ 0 5
AA 16 16
AA 8 4
A+ 9 13
A 10 5
A 5 4
BBB+ 7 8
BBB 6 5
BBB 8 5
BB+ 0 1
BB 1 0
70 66
Bond Rating Guidelines
Standard & Poor's provides explicit guidelines for the
leverage ratios associated with its bond ratings; those
guidelines for the electric utility industry are contained
in Table 52. It should be noted that S&P, in its
discussion of guidelines, states that a strong (or weak)
leverage ratio could be offset by some other factor such as
coverage. Also, S&P is very interested in a firm's
trends, so a company with a debt ratio of 50 percent, but
with a target debt ratio of 45 percent and a trend which
indicates that it is moving towards the target, might be
rated on the basis of the 45 percent target ratio rather
than the 50 percent current figure. Thus, companies' actual
ratings will not always be consistent with the guidelines
contained in Table 52.
Table 52
Standard & Poor's Rating Guidelines for Electric Utilities
Leverage Guidelines
Rating 1982 1985 Average Midpoint
AAA Debt Under 45% Debt Under 41% Under 43.0%
AA 42 47 39 46 43.5
A 45 55 44 52 49.0
BBB Over 53 50 58 54.0
BB  Over 56 Over 56.0
Sources: (1) Standard & Poor's Corporation, Credit Overview
(New York, 1982), 40.
(2) Standard & Poor's Corporation, Credit Week
(New York, February 18, 1985), 2244.
Nevertheless, the rating guidelines do provide the
range of typical debt ratios. Since the data sample (1983
and 1984) falls between the published guidelines (1982 and
1985), an average of the two guidelines is used to estimate
the guideline midpoints. The midpoint for an AA rating is a
43.5 percent debt ratio; for an A rating, 49.0 percent; and
for a BBB rating, 54.0 percent.
Bond Yield Spreads
Standard & Poor's Corporation also reports yields by
rating on several different types of bonds, including public
utilities (electric, gas, and telephone). Table 53
contains the December average yields on the S&P public
utility index for 1983 and 1984. The data in Table 53 can
easily be converted to yield spreads. In 1983, the spread
between double A and single A issues was 0.26 percentage
points, and between single A and triple B issues, 0.71
Table 53
S&P Public Utility Index Yields
Yield to Maturity
Rating 1983 1984 Average
AAA 12.62%  
AA 12.64 12.11% 12.38%
A 12.90 12.43 12.67
BBB 13.61 12.93 13.27
Source: Standard & Poor's Corporation, Security Price Index
Record (New York, 1986), 224227.
Notes: (1) Yields are averages for the month of December.
(2) S&P discontinued its AAA utility index on
January 1, 1984.
percentage points. In 1984, the spread was 0.32 percentage
points between AA and A ratings and 0.50 percentage points
between A and BBB rating. Over the twoyear period, the
average spread was 0.29 percentage points between double A
and single A utility bonds and 0.61 percentage points
between single A and triple B bonds.
Model Results
The rating guidelines and yield spreads presented in
the previous two sections can be combined to estimate the
relationship between financial leverage and debt cost. This
analysis is summarized in Table 54. Over the range in
ratings which encompasses the bulk of the sample (AA to
BBB), on average a one percentage point increase in the debt
ratio, say from 48 to 49 percent, increases the cost of debt
by 0.087 percentage points, or by 8.7 basis points.
Table 54
Financial Leverage/Cost of Debt Relationships
Bond Rating AA A BBB
Average Yield 12.38% 12.67% 13.27%
Yield Spread 0.29 0.60
Midpoint Debt Ratio 43.5% 49.0% 54.0%
Leverage Spread 5.50 5.00
Change in kd per
Percentage Point
Change in Debt Ratio 0.053 0.120
Average Change in kd
per Percentage Point
Change in Debt Ratio
0.087
These data can be used to estimate the impact of a
change in leverage from, say, a 40 percent debt ratio to a
50 percent debt ratio. Table 55 illustrates the results.
Table 55
Impact of Leverage on Debt Cost
Change in Financial
Risk Premium from
Book Value Book Value Base Level Debt
Debt Ratio DebttoEquity Ratio Ratio of 40%
40% 0.67
50 1.00 +0.56
60 1.50 +1.76
Table 55 was constructed by assuming (from Table 54) that
each percentage point change in debt ratio from 40 to 49
percent will increase debt costs by 5.3 basis points, while
each percentage point change from 49 to 60 percent will
increase debt costs by 12 basis points.
Thus, the bond rating guidelines model indicates that
an increase in the debt ratio from 40 to 50 percent
increases a firm's cost of debt by 56 basis points, while an
increase from 50 to 60 percent debt increases a firm's debt
cost by 1.76 0.56 = 1.2 percentage points.
In this chapter, the bond rating guidelines model was
used to estimate the cost of debt/leverage relationship. In
prior chapters, an econometric model was presented which
estimated the same relationship. In Chapter VI, the results
of both models will be summarized and compared, and final
conclusions will be presented.
79
Notes
1For a more complete discussion of Standard & Poor's bond
rating process, see Standard & Poor's (1982).
CHAPTER VI
SUMMARY AND CONCLUSIONS
Chapter III discussed the econometric model, and
Chapter IV presented the empirical results. Chapter V
introduced the bond ratings guidelines model and presented
its results. Now, in Chapter V, the results are summarized
and compared, and final conclusions are drawn.
In Chapter I, the objectives of the study were stated
as follows: (1) to estimate empirically the relationships
between financial leverage and the costs of debt and equity,
(2) to determine if the relationships between leverage and
capital costs are affected by the leverage measure chosen,
(3) to determine if the empirical relationships between
leverage and capital costs exhibit any nonlinearities, and
(4) to identify those business risk factors which influence
an electric utility's capital costs. The summary and
conclusions here are structured to address those objectives.
The Choice of Leverage Measure
The econometric model included two measures of both
debt cost and equity cost, and four measures of financial
leverage: (1) current book value debttoequity ratio
(BVDE), (2) current market value debttoequity ratio
(MVDE), (3) book value debttoequity ratio expected 35
years hence (EXBVDE), and (4) market value debttoequity
ratio expected 35 years hence. Note that all four primary
measures express leverage as the ratio of debttoequity,
because theoretical studies suggest that the relationship
between equity cost and leverage is linear when leverage is
measured by the debttoequity ratio.1
Equity cost relationship. In the equity regressions,
the tstatistics and adjusted R2 were higher using market
value measures than with book value measures. Also, the
expected market value measure had higher (in three of four
specifications) tstatistics and adjusted R2 than the
current market value measure. This leads to two
conclusions: (1) equity costs are more closely related to
market value measures than to book value measures, and (2)
equity costs are more closely related to future capital
structures than to current structures.
These two findings, which have not been reported in the
previous empirical studies, support two hypotheses about the
financial leverage/equity cost relationship. First, as
theory indicates, the relationship is based upon market
value leverage rather than book value leverage. Second,
current leverage measures have less impact on equity cost
than expectational measures. Apparently, investors believe
that firms stray from target capital structures, and a
firm's perceived financial risk is related more to target
structures than to current structures.
Debt cost relationship. The choice of leverage measure
had much less impact in the debt regressions than in the
equity regressions. Like the equity case, market value
measures did have slightly higher explanatory power and t
statistics than did book value measures. However, current
leverage measures were more closely related to debt costs
than were expectational measures. Since debt costs are
highly related to bond ratings, this could mean that rating
agencies (particularly Standard & Poor's) are more
influenced by current capital structure than by expectations
of capital structure changes.
Leverage/Capital Cost Relationships
The primary objective of this study is to estimate the
relationships between financial leverage and the costs of
debt and equity. Since some of the equity results are tied
to the debt results, the discussion begins with the
leverage/debt cost relationship.
Leverage/debt cost relationship. Table 61 summarizes
the results presented in Chapters IV and V. Both the
Table 61
Impact of Leverage on Debt Cost
Basis Point Change in Debt Cost
Econometric Rating Guidelines
Change in Debt Ratio Model Model
40% to 50% 28 56
50% to 60% 42 120
econometric approach and the rating guidelines approach
support the contention that financial leverage increases
debt costs. However, as is vividly shown by Table 61, the
rating guidelines model shows this relationship to be much
stronger than indicated by the econometric model.
There are three possible explanations for this
difference. First, those firms with the highest cost of
debt (those rated below BBB) were mostly dropped from the
sample set because those firms had recently cut or omitted
their common dividends. Thus, the highest debt cost firms
were systematically excluded from the sample. Second, as
discussed in Chapter IV, measurement error can cause a
downward bias in the coefficient estimate. Third, the
rating guidelines provided by S&P assume that all other
factors are held constant at industry average values. As
shown earlier, there is a positive correlation between
financial leverage and several of the business risk factors.
Thus, the rating guidelines model tends to remove the
collinearity that is known to exist.2 These three factors
could explain the differences in the results of the two
models.
Leverage/equity cost relationship. This study suggests
two methods for estimating the relationship between a firm's
financial leverage and its cost of equity. First, the
relationship was estimated directly using the econometric
model. Second, an econometric model was used to estimate
the relationship between a firm's cost of equity and its
cost of debt, and this relationship was combined with the
rating guidelines model. The results of these two
approaches are presented in Table 92.2 As with debt cost,
the direct econometric estimation of the equity
cost/leverage relationship is substantially lower than the
estimation based on the bond guidelines model. Again, this
could be caused by the three factors previously discussed.3
Table 92
Impact of Leverage on Equity Cost
Basis Point Change in Equity Cost
Change in Debt Ratio Direct Estimation Debt Cost Comparison
40% to 50% 74 111
50% to 60% 113 240
Both estimates, however, are substantially higher than
those reported previously by Brigham and Gordon (1968),
Robichek, Higgins, and Kinsman (1973), Gordon (1974), and
Mehta et al. (1980). Although some of this difference can
be attributed to specification differences and generally
rising capital costs, the impact of financial leverage was
clearly greater than previous studies have indicated.
Nonlinearities
Both the debt and equity regression specifications were
modified to include second order terms. That is, the
leverage term squared was added. The addition of these
second order terms neither enhanced the explanatory power of
the specification nor produced statistically significant
coefficients. Thus, within the range of observations, there
was no indication that the leverage/capital costs
relationships are quadratic when leverage is measured by
some form of the debttoequity ratio.
Business Risk Factors
Since the econometric model included other independent
variables to account for nonconstant business risk, some
judgements can be made concerning business risk factors.
Equity risk factors. The dominant equity business risk
factor in 1983 and 1984 was nuclear construction programs.
A firm with a 20 percent nuclear construction to current
gross plant ratio was estimated to have a 36 basis point
nuclear construction risk premium, while an 80 percent
nuclear construction ratio leads to a 144 basis point
premium. These premiums reflect "average" nuclear
construction programs, which perhaps do not exist.
There is some evidence that equity investors considered
reserve margins to be a business risk factor for electric
utilities. An average reserve margin of about 18.5 percent
reduced equity costs by 22 basis points, while a high margin
of 50 percent reduced equity costs by 60 basis points, when
compared to a firm with a zero reserve margin.
There is also some indication that gas revenues were
riskier than electric revenues, and that nuclear operating
plant was riskier than coal or oil generation, but the
results are not conclusive.
Perhaps the most striking result is that regulatory
climate did not appear to affect equity cost in 1983 and
1984. This supports the results of Fanara and Gorman
(1986), who concluded that regulatory climate was a
significant risk factor in the early 1970s, but that its
influence diminished over time.
Debt risk factors. In general, the results of the debt
regressions parallel those of the equity regressions. The
two business risk factors that affected debt costs were
nuclear construction programs and reserve margins. A firm
with a 50 percent nuclear construction ratio would pay 27.5
basis points more in debt cost than a firm with no nuclear
construction program. A firm with a 40 percent reserve
margin would pay about 9.8 basis points less than a firm
with a 20 percent reserve margin. No other business risk
factors, including regulatory climate, consistently affected
debt costs.
Conclusions
The primary objective of this study is to estimate the
financial leverage/capital costs relationships for electric
utilities. The results indicate strong positive
relationships between financial leverage and both debt and
equity costs. Although the two methods used did not produce
identical results, there is strong evidence that the impact
of financial leverage on the cost of equity is much greater
than reported in previous studies.
NOTES
1Several coverage ratios as well as debttovalue measures
were also used, but those leverage measures had less
explanatory power and lower statistical significance than
the debttoequity measures.
2The debt cost comparison estimation was calculated as
follows: (1) According to the rating guidelines model, an
increase in debt ratio from 40 to 50 percent increases debt
cost by 56 basis points, while an increase in leverage from
50 to 60 percent increases debt cost by 120 basis points.
(2) From Table 45, equity costs change by 1.99 basis points
for every basis point change in debt cost (the 1.99
coefficient is the 1983 estimate). (3) Thus, a 56 basis
point change in debt costs is estimated to have a 56(1.99) =
111 basis point change in equity costs, and so on.
3Note that the 1983 EXMVDE coefficient was 3.34 when the
collinearity was removed. When the only independent
variable is financial leverage, an increase in a firm's debt
ratio from 40 to 50 percent leads to a 110 basis point
increase in its cost of equity, and an increase from 50 to
60 percent increases equity costs by 167 basis points.
These values are much closer to those reported in Table 92
for the debt cost comparison model.
APPENDIX A
SAMPLE SET
Allegheny Power System
American Electric Power
AZP Group (Arizona Public Service)
Atlantic City Electric*
Baltimore Gas & Electric
Boston Edison
Carolina Power & Light*
Central & Southwest
Central Illinois Public Service
Cleveland Electric Illuminating
Commonwealth Edison
Consolidated Edison of New York
Delmarva Power & Light
Detroit Edison
Dominion Resources
Duke Power
El Paso Electric
FPL Group
Florida Progress
Gulf States Utilities
Hawaiian Electric
Houston Industries (Houston Light and Power)
Idaho Power
Illinois Power
Iowa Electric Light & Power
IowaIllinois Gas & Electric
Iowa Resources
Ipalco Enterprises (Indianapolis Power and Light)*
Kansas City Power & Light
Kansas Power & Light
Kentucky Utilities
Louisville Gas & Electric
Middle South Utilities
Minnesota Power & Light
Montana Power
Nevada Power
New England Electric System
New York State Electric & Gas
Niagara Mohawk Power
Northeast Utilities
Northern Indiana Public Service
Northern States Power
Ohio Edison
Oklahoma Gas & Electric
Orange & Rockland Utilities
Pacific Gas & Electric
Pacificorp (Pacific Power and Light)
Pennsylvania Power & Light
Philadelphia Electric
Portland General Electric
Potomac Electric Power
Public Service of Colorado
Public Service of New Mexico
Public Service Electric & Gas
Puget Sound Power & Light
San Diego Gas & Electric
SCANA (South Carolina Electricity and Gas)
Southern California Edison
Southern
Southern Indiana Gas & Electric
Southwestern Public Service
Teco Energy
Toledo Edison
Tucson Electric Power
Union Electric
Utah Power & Light
Washington Water Power*
Wisconsin Electric Power
Wisconsin Power & Light
Wisconsin Public Service
Notes: (1) Utilities with recent organizational changes
have their former designations in parentheses.
(2) An asterisk following the company name
indicates 1983 data only.
APPENDIX B
GLOSSARY OF SYMBOLS
Definition
B/M
Booktomarket
ratio
BVDE
DCF k
EXBVDE
EXMVDE
MVDE
NUCCON
PAYOUT
PCTCOAL
PCTCON
PCTGASREV
PCTNUC
PCTOIL
Book value debt
toequity ratio
Cost of equity
Expected book
value debtto
equity ratio
Expected market
value debtto
equity ratio
Market value debt
toequity ratio
Nuclear
construction
program
Payout ratio
Coalfueled
generation
capacity
New construction
program
Gas/electric sales
mix
Nuclearfueled
generation
capacity
Oilfueled genera
tion capacity
Book value of equity
divided by market value
of equity
Book value of debt divided
by book value of equity
Discounted cash flow
estimate of ks
Book value debttoequity
ratio expected 3years
hence
Market value debttoequity
ratio expected 3years
hence
Market value of debt divided
by market value of equity
Dollar value of uncompleted
nuclear construction
divided by current gross
plant (%)
Common dividend divided by
net income (%)
Coal generation capacity
divided by total capacity
(%)
Dollar value of total con
struction program divided
by current gross plant (%)
Gas revenues divided by
total utility revenues (%)
Nuclear generation capacity
divided by total capacity
(%)
Oil generation capacity
divided by total capacity
(%)
Symbol
Measure
Regulatory climate
Reserve margin
Cost of debt
Regulatory ranking as repor
ted by Salomon Brothers
Capacity in excess of peak
load divided by capacity
(%)
Bond yield by rating
reported by S&P
REGRANK
RESMAR
S&P k
APPENDIX C
EQUITY REGRESSION RESULTS
Table C1
Coefficients Using Book Value DebttoEquity
(tstatistics in parentheses)
DCF ks
1983 1984
Variable
B/M Ratio
1983 1984
BVDE
REGRANK
PCTGASREV
PCTNUC
PCTCOAL
PCTOIL
PCTCON
NUCCON
RESMAR
PAYOUT
INTERCEPT
Adjusted R2
1.0669
(1.79)
0.1769
(0.78)
0.0047
(0.67)
0.0012
(0.17)
0.0126
(2.24)
0.0088
(0.95)
0.0020
(0.25)
0.0324
(4.17)
0.0148
(2.33)
0.0372
(2.03)
11.6474
(7.26)
0.51
1.2818
(2.44)
0.1232
(0.66)
0.0108
(1.54)
0.0025
(0.38)
0.0063
(1.33)
0.0117
(1.41)
0.0083
(0.84)
0.0173
(1.71)
0.0150
(2.37)
0.0124
(0.86)
12.7830
(10.25)
0.40
0.0614
(0.90)
0.0488
(1.89)
0.0008
(1.01)
0.0023
(2.77)
0.0007
(1.06)
0.0002
(0.15)
0.0014
(1.52)
0.0047
(5.24)
0.0021
(2.88)
0.0022
(1.06)
0.6757
(3.68)
0.52
0.1405
(2.15)
0.0745
(3.22)
0.0022
(2.56)
0.0009
(1.11)
0.0002
(0.36)
0.0006
(0.59)
0.0000
(0.04)
0.0038
(3.00)
0.0011
(1.40)
0.0009
(0.51)
0.4747
(3.05)
0.50
Table C2
Coefficients Using Market Value DebttoEquity
(tstatistics in parentheses)
DCF ks
Variable
MVDE
REGRANK
PCTGASREV
PCTNUC
PCTCOAL
PCTOIL
PCTCON
NUCCON
RESMAR
PAYOUT
INTERCEPT
Adjusted R2
1983
2.0042
(4.06)
0.0179
(0.08)
0.0054
(0.85)
0.0039
(0.59)
0.0078
(1.50)
0.0036
(0.39)
0.0040
(0.54)
0.0221
(2.90)
0.0122
(2.10)
0.0253
(1.52)
12.2114
(9.16)
1984
1.5428
(3.27)
0.3147
(1.59)
0.0082
(1.25)
0.0027
(0.41)
0.0040
(0.86)
0.0078
(1.00)
0.0055
(0.57)
0.0135
(1.35)
0.0143
(2.34)
0.0061
(0.44)
13.8894
(11.9)
B/M Ratio
1983 1984
0.2941
(5.90)
0.0085
(0.40)
0.0012
(1.86)
0.0019
(2.80)
0.0000
(0.05)
0.0006
(0.71)
0.0011
(1.51)
0.0029
(3.76)
0.0017
(2.87)
0.0008
(0.47)
0.6520
(4.85)
0.69 0.69
0.3089
(6.42)
0.0241
(1.19)
0.0021
(3.10)
0.0008
(1.18)
0.0002
(0.44)
0.0001
(0.16)
0.0008
(0.83)
0.0026
(2.59)
0.0009
(1.39)
0.0007
(0.47)
0.6260
(5.26)
0.59 0.44
Table C3
Coefficients Using Expected Book Value DebttoEquity
(tstatistics in parentheses)
DCF ks
Variable
EXBVDE
REGRANK
PCTGASREV
PCTNUC
PCTCOAL
PCTOIL
PCTCON
NUCCON
RESMAR
PAYOUT
INTERCEPT
Adjusted R2
1983
1.2859
(1.94)
0.1789
(0.80)
0.0060
(0.83)
0.0018
(0.24)
0.0127
(2.28)
0.0095
(1.03)
0.0017
(0.21)
0.0313
(3.98)
0.0137
(2.15)
0.0286
(1.56)
11.9815
(7.89)
1984
1.5318
(2.41)
0.1138
(0.62)
0.0084
(1.23)
0.0039
(0.58)
0.0073
(1.52)
0.0103
(1.26)
0.0035
(0.34)
0.0233
(2.33)
0.0114
(1.73)
0.0068
(0.46)
12.9038
(10.42)
B/M Ratio
1983 1984
0.1350
(1.80)
0.0427
(1.70)
0.0011
(1.34)
0.0022
(2.72)
0.0007
(1.15)
0.0003
(0.24)
0.0015
(1.59)
0.0044
(4.97)
0.0020
(2.73)
0.0015
(0.72)
0.6541
(3.81)
0.52 0.40
0.2017
(2.59)
0.0728
(3.22)
0.0020
(2.40)
0.0011
(1.31)
0.0004
(0.61)
0.0005
(0.50)
0.0007
(0.58)
0.0045
(3.66)
0.0006
(0.75)
0.0001
(0.05)
0.4735
(3.12)
0.54 0.52
