Capital Market-Based Calculation of the Cost of Equity

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Capital Market-Based Calculation of the Cost of Equity
Chapter 2
Capital Market-Based Calculation
of the Cost of Equity
2.1
Introduction
To conduct cash flow-based business valuations, the projection of future cash flow
is necessary. The future cash flow is to be evaluated by means of an appropriate
discount interest calculation.
For regulated companies, determining an appropriate interest rate has effects on
the rate of the discount interest calculation and on the volume of the projected
future cash flow. This double meaning from determining the interest rate is the
peculiarity for companies whose prices are regulated compared with companies that
are active in competitive markets.
For planning future profits in price-regulated companies, interest costs for
borrowed funds and equity must be considered. As a part of the cash flow-based
business valuation, it depends on the valuation model applied whether a return on
equity (return required by the investor) or a weighted average cost of capital
(WACC) is used as the discount interest calculation.
Common to all cash flow-based procedures is that the rate of return is contained
in the discount interest calculation. To calculate the return on equity, the capital
asset pricing model (CAPM) will be explained more carefully in Sect. 2.2 and the
advantages and disadvantages are portrayed.
In Sect. 2.3 a normative statement is provided as to how operating costs and capital
costs should be made for projecting future cash flow within the scope of a regulatory
system, in order to do justice to business requirements. This should enable a founded
projection of future cash flow. Section 2.4 serves as the summary of this chapter.
2.2
Capital Market-Based Calculation of the Cost of Equity
By applying capital market-based models to calculate equity costs, risk premiums,
which investors require for taking on risks, are derived from capital market data and
are not the result of a subjective estimate. For this purpose, reference is most often
M. Hierzenberger, Price Regulation and Risk,
Lecture Notes in Economics and Mathematical Systems 641,
DOI 10.1007/978-3-642-12047-3_2, # Springer-Verlag Berlin Heidelberg 2010
5
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2 Capital Market-Based Calculation of the Cost of Equity
made to CAPM in practice, which is a so-called one-factor model. CAPM defines
the investor’s return requirements on the basis of a risk-free interest rate, which is
increased according to a risk premium. This risk premium is determined by multiplying the market risk premium with the so-called beta factor, as a measurement for
the systematic risk of a security.
The Arbitrage Pricing Theory (APT) developed by Ross1 is classified as a multifactor model. With APT, risk premium is established by several factors. APT
assumes, in contrast to CAPM, that the risk of a security is contingent on an
unknown amount of factors in a linear fashion. These factors can be, e.g., exchange
rates, interest levels and index trends in various stock exchanges.2
An exceptional form of APT is presented in the FF3F model by Fama and
French. This model defines the investor’s return requirements on the basis of 3
factors and hence is classified among the group of multi-factor models.3
In the following, CAPM is explained, on which basis the consideration of risk
factors for assessing a risk premium is presented in detail.
2.2.1
Capital Asset Pricing Model (CAPM)
Building on the portfolio theory from Markowitz4 and the separation theory from
Tobin,5 the CAPM was developed primarily by Sharpe (1964).6,7
CAPM defines the investor’s return requirements as follows:8
EðRi Þ ¼ Rf þ bi ½EðRm Þ Rf with:
EðRi Þ
Rf
bi
EðRm Þ
1
Expected returns from the risky security i
Returns from a risk-free capital investment (risk-free interest rate)
Measurement for the systematic risk of security i (beta factor)
Expected return from the market portfolios
cf. Ross (1976).
cf. Mandl and Rabel (1997), p. 310; Buckley et al. (2000), p. 283 ff.
3
cf. Fama and French (1992).
4
cf. Markowitz (1952).
5
cf. Tobin (1957).
6
cf. Sharpe (1964); along with Sharpe, CAPM goes back to Lintner, Treynor and Mossin as well.
7
cf. Damodaran (2001), p. 164 f.
8
cf. Mandl and Rabel (1997), p. 290; Copeland et al. (2002), p. 265; Fischer (2002), p. 74;
Drukarczyk (2001), p. 354.
2
2.2 Capital Market-Based Calculation of the Cost of Equity
7
Security Market Line (SML)
17.5%
15.0%
Rendite
12.5%
m
10.0%
7.5%
5.0%
2.5%
0.0%
0
0.5
1
Beta
1.5
2
Fig. 2.1 Security market line. “m” in the figure represents the situation of the market portfolios,
which intrinsically has a beta factor of 1
This linear interrelationship between expected volume of the investor’s return
requirement and the systematic risk is depicted graphically as the Security Market
Line in Fig. 2.1.9
When determining risk premium, CAPM assumes the entire risk of a precarious
security decomposes into a systematic and an unsystematic part. The unsystematic
risk is not influenced by the capital market, rather it is influenced from factors that
are evaluated as specific to a security. These could be, e.g., certain characteristics of
the management or the client structure. These factors can be diversified through
portfolio formation, which is why the capital market does not compensate for
unsystematic risk components.10
Systematic risk components cannot be avoided through diversification, which is
why they are compensated from the capital market.11 Systematic components are
generally e.g., tax policy measures, economic and interest trends.12
Moreover, the original form of CAPM is based on further restrictive premises:13
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The planning horizon is one period.
All investors are unwilling to take risks (risk aversion).
cf. among others Fischer (2002), p. 75; Mandl and Rabel (1997), p. 290; Spremann (2006), p. 310;
Copeland et al. (2002), p. 265; Franke and Hax (2004), p. 353.
10
cf. Mandl and Rabel (1997), p. 290; Fischer (2002), p. 74, 103; Copeland et al. (2002), p. 265;
Damodaran (2001), p. 155 ff.
11
cf. Spremann (2006), p. 314 f.
12
cf. Mandl and Rabel (1997), p. 290 f.; Purtscher (2006), p. 108.
13
cf. Mandl and Rabel (1997), p. 291; Ballwieser (2002), p. 738; Fischer (2002), p. 71 f.;
Damodaran (2001), p. 164.
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2 Capital Market-Based Calculation of the Cost of Equity
l
All investors have homogeneous expectations.
All risky securities are traded on the capital market and can be divided in any
way.
Funds can be received or invested without restriction at a risk-free interest rate.
There are no limitations, transaction costs or taxes.
All information is available to the investor at no charge (information efficiency).
The prices of risky securities are not influenced by an investor’s purchase or
sales activities.
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Further developments in the original CAPM have nullified several of these
premises (partially).14 The original form of CAPM is the basis of the investigations
in this work.
The planning horizon of one period is especially a problematic assumption for
determining capital costs for a business valuation because business valuations very
often imply an infinite planning horizon. However, if the cost of equity rate
determined in accordance with CAPM is applied for a longer period of time,
stationary conditions are implied. The parameters defining returns are to be
assumed as constant for the entire period under consideration.15
How individual parameters from CAPM are determined for defining the cost of
equity rate is shown in the following.
2.2.1.1
Risk-Free Interest Rate
The risk-free interest rate can only be determined approximately. In practice, long
term, fixed-interest bearing securities are offered by debtors with very good solvency (e.g., long term state debentures), for which equivalence in the term and in
the planning horizons between the company’s expected holdings and the interest
maturity are of special importance for reasons of comparison.16 An orientation to
actual rate of return on state bonds with a term of 10–30 years is often recommended, whereas for Austrian securities with a very long term, infrequent disbursement, low liquidity and the increased sensitivity to inflation rates thwart the
advantage of the approximated matching maturities. A practicable alternative is
to draw on the approx. 10-year government bonds and to apply the returns to long
term government bonds, published monthly from the Austrian National Bank.17
Fixing the risk-free interest rate should essentially occur on the basis of the
future. Consequently, the historical interest rates would be discarded. However,
since estimating future interest rates is only possible with great uncertainty, the
14
cf. Brennan (1971); Black (1972); Merton (1973); Rubinstein (1976); Lucas (1978); Breeden
(1979); Hansen and Richard (1987); Overviews on this by: Rudolph (1979) and Copeland and
Weston (1988), among others.
15
cf. Fama (1977), p. 7 ff.
16
cf. Ballwieser (2002), p. 737; Purtscher (2006), p. 109.
17
cf. Purtscher (2006), p. 109.
2.2 Capital Market-Based Calculation of the Cost of Equity
9
alternative also exists to use current rates from government bonds. For this, it is
assumed that the current returns on these types of securities are the best estimates
for future returns.18
Government bonds must provide evidence for cash in any currency that was
implemented for the calculation of the expected cash flow of the company to be
valuated. Otherwise, there would be a currency exchange risk, which would
complicate the comparison of profit with cash flow from alternative transactions.19
Implementation of the above is recommended for small return differences
between short and long term, risk-free securities. However, should the yield
curve, which displays the interrelation between rate of return and maturity, not
show a flat structure, period-specific interest rates can also be applied as an
alternative to applying a uniform, risk-free interest rate. This indeed increases the
calculation effort for the costs of equity, but it leads to more consistent results.20
2.2.1.2
Market Risk Premium
Market risk premium is calculated as the difference between return from the market
portfolio and the risk-free interest rate, on the basis of historical return. The amount
of this premium is dependent upon the risk-free interest rate chosen as well as the
calculation period; both the risk-free interest rate and the return from the market
portfolio are not constant throughout the time period. To avoid inconsistencies
when determining market risk premium, the risk-free interest rates that must be
used are those that were fixed for the interest of risk-free alternative investments in
CAPM.21
Further, it is important to take note that the determination of market risk
premium, as the difference between return from the market portfolio and the riskfree interest rate, can only be approximated by applying the appropriate market
indices.
The decision for or against the use of arithmetic or geometric averages has a
significant influence on the rate of the market risk premium determined, bearing in
mind that arithmetic averages for return fluctuations end up higher than geometric
averages.22 Copeland, Koller and Murrin assume that the actual market risk premiums lies between the geometric and the arithmetic mean.23
Subsequently, the market risk premium is to be checked as to whether the
expected future market trends can be described as plausible from this. Provided
18
cf. Ballwieser (2002), p. 738; Busse and Colbe (2002), p. 7; Copeland et al. (2002), p. 266.
cf. Ballwieser (2002), p. 737.
20
cf. Daske and Gebhardt (2006), p. 531; Mandl and Rabel (2006), p. 104 f.
21
cf. Purtscher (2006), p. 109.
22
cf. Ballwieser (2002), p. 739; Purtscher (2006), p. 109.
23
cf. Copeland et al. (2002), p. 271.
19
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2 Capital Market-Based Calculation of the Cost of Equity
that this is not the case, the historical returns thus do not give the best estimate for
future trends; an appropriate adjustment of the market risk premium is to be made.24
2.2.1.3
Beta Factor
In CAPM, consideration of company-specific or project-specific systematic risk for
defining the required rate of return on equity occurs via the beta factor. This factor
measures the change of the (historical) individual rate of return from the security
with the change of the (historical) market rate of return.25 The beta factor represents
the quotient of the covariance between the rate of return of the security i and the rate
of return on the market portfolio m and the variance of the rate of return of the
market portfolio:26
bi ¼
with:
bi
CovðRi ; Rm Þ
s2m
CovðRi ; Rm Þ
s2m
Beta factor from company i
Covariance of security return i and market return m
Variance in the market return m
A beta factor of 1, determined according to its structure and in accordance with
the method of the least square estimate, means that the rate of return of the security
develops proportionally to the market rate of return. A beta factor of >1 means that
the rate of return of the security strongly reacts disproportionately to market
fluctuations in relationship to the market rate of return, and thus displays stronger
price fluctuations than the market portfolio and for this reason, a higher rate of
return on equity is required in this scenario as a compensation for taking on an
increased risk. Conversely, if the beta factor is less than 1, this leads to a reduction
of the required rate of return on equity because price fluctuations for this security
are lower in comparison with the market portfolio and thus this security presents a
lower risk. A beta factor of 0 presents a risk-free assessment, for which reason the
risk-free interest rate corresponds to the return on equity requirements in this
scenario.27
24
cf. Maier (2001), p. 299; Daske and Gebhardt (2006), p. 531; It must be especially noted that the
data used does not include events such as wars or currency reforms, as long as these events are not
expected in the future.
25
When using historical returns to calculate the beta factor, one is bound by the following
assumption: ex-ante probability distribution ¼ ex-post probability distribution, stochastically
independent of the realization of returns, stationary process of returns generation within one
period; cf. among others, Maier (2001), p. 300.
26
cf. Mandl and Rabel (1997), p. 297; Fischer (2002), p. 75.
27
cf. Fischer (2002), p. 74; Mandl and Rabel (1997), p. 297.
2.2 Capital Market-Based Calculation of the Cost of Equity
11
As noted above, measuring the beta factor most often takes place on the basis of
historical rate of return. However, since business valuation is oriented toward the
future, the representativeness of a beta factor determined on the basis of historical
market trends should be reviewed for the future.28
Systematic risk can be decomposed into two fundamental component parts:29
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Operating Risk
Financial Risk
On the basis of this type of fundamental decomposition of the beta factor based
on historical data and only statistically presented, it should be possible to increase
the future reference of the beta factor by means of an effective hypothesis.
2.2.1.3.1
Operating Risk
Operating risk contains any systematic risk factors that are shaped predominantly
through the industry in which the respective company is active.30
The profit cycle of a company is defined by its belonging to an industry. This
cycle can be strongly or less strongly shaped and can correspond to the general
market cycle or exhibit an acyclical trend compared with the market index. The
amount of the beta factor is influenced by the strength of the cyclicality. Here the
company with a stronger cyclicality tends to exhibit a higher beta factor than
does a company with a lower cyclicality.31 However, substantial, expected
changes of the operating risk can only be taken into account in a simplified
manner.32
2.2.1.3.2
Financial Risk
The financial risk is contingent upon the level of debt of the company in question
because it is assumed that the risk for the investor increases with increased
financing from borrowed funds.33 This effect is weakened from the tax-related
28
cf. Mandl and Rabel (1997), p. 306; Purtscher (2006), p. 111; Knieps (2003), p. 1000; Maier
(2001), p. 299.
29
cf. Mandl and Rabel (1997), p. 299.
30
cf. Mandl and Rabel (1997), p. 299.
31
cf. Buckley et al. (2000), p. 311; Spremann (2006), p. 344 f.; Born (1995), p. 151 f.; Nielsen
(1992), p. 228 ff.; Mandl and Rabel (1997), p. 306.
32
cf. Mandl and Rabel (1997), p. 306.
33
cf. Fischer (2002), p. 129 f.; Buckley et al. (2000), p. 313 ff.; Drukarczyk (2001), p. 357.
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2 Capital Market-Based Calculation of the Cost of Equity
consideration of interest on borrowed funds. The interrelation between the level of
debt and the indebted or debt-free beta factor is presented formally as follows:34
h
i
bv ¼ bu 1 þ ð1 sÞ FK bf ð1 sÞ FK EK
EK
with:
bv
bu
s
FK EK bf
Beta factor from the indebted company
Beta factor from the debt-free company
Corporate tax rate
Market value of the borrowed funds
Market value of the equity
Beta factor of the borrowed funds
Provided that the investor’s rate of return requirement (rðFKÞ) does not correspond to the risk-free interest rate (Rf ), and hence the beta factor of the borrowed
funds is greater than 0, then the beta factor for the borrowed funds can be
determined from the following equation with an appropriate conversion:35
rðFKÞ ¼ Rf þ bf ½EðRm Þ ir 2.2.1.3.3
Other Influencing Factors
Besides the influence of operating and financial risks on the beta factor, other
potential influencing factors are to be accounted.36
The highly condensed information on the effect of influencing factors listed in
Table 2.1 can only be understood as a very rough directional indicator because the
basic, underlying empirical studies have produced different results and an unequivocal
cause-effect interrelation is not demonstrable.
Table 2.1 Influencing factors on the beta factor level
Influencing factor
Characterized by
Disbursement behavior
High disbursement rates
Growth
Large growth
Company size
Bigger company
Degree of diversification
High degree of diversification
Market power
Significant market power
Liquidity
High liquidity
a
BF beta factor.
34
cf. Mandl and Rabel (1997), p. 299 f.; Fischer (2002), p. 126.
cf. Mandl and Rabel (1997), p. 300.
36
cf. Hachmeister (2000), p. 217 ff.
35
Effecta
Index for lower BF
Index for higher BF
Index for lower BF
–
Index for lower BF
Index for lower BF
2.2 Capital Market-Based Calculation of the Cost of Equity
2.2.1.4
13
A CAPM Evaluation
In the following, difficulties with defining model parameters necessary for CAPM
are discussed and possible problems when implementing CAPM in empirical
papers are explained.
2.2.1.4.1
Efficiency and Definition of Market Portfolio
As outlined above, the market portfolio is formed by a market index, as the sum of
all risk-laden investment possibilities. As for the validity of the assumption of a
linear relationship between the systematic risk of a security and the average rate of
return from the market, the choice of the market portfolio is of utmost importance
for an empirical review.37 Roll (1977) and Roll and Ross (1994) have demonstrated
that the linear interrelation between systematic risk and the average market rate of
return is not a given, if the market portfolio chosen is inefficiently diversified in
comparison with a theoretically ascertainable, overall “investment universe”.38
Stambaugh (1982) points out how sensitively CAPM tests react to different definitions of the market portfolio. Oertmann and Zimmermann (1996) examined the
effects of different specifications of the market portfolio on the level of the betas
determined for stock from credit institutions. They arrived at the following result,
which underscores the leverage of the choice of the market portfolio, as shown
in Table 2.2.39
Spremann (2006) adds to the reasons why empirical reviews of CAPM evaluate
this as inaccurate by including the possibility that investors make irrational
Table 2.2 Sensitivity of the
beta factor with change in the
market portfolio specification
37
Country
Switzerland
Switzerland
Switzerland
Germany
Germany
Germany
French
French
French
England
England
England
Enterprise
Beta
MSCI-country
UBS
1.095
SBC
0.863
CS
1.279
Deutsche Bank
0.901
Dresdner Bank
0.751
Commerzbank
0.895
Paribas
1.451
Societe Generale 0.999
BNP
0.946
Barclays
1.316
Nat West
1.386
Lloyds Bank
1.125
Beta
MSCI-world
0.889
0.703
0.944
0.535
0.479
0.572
1.034
0.751
0.717
0.925
0.972
0.688
cf. Laux (2003), p. 208.
The theoretical validity of CAPM for additional consideration of an investment possibility not
yet contained in the market index is shown by Spremann (2006), p. 324 ff.
39
cf. Oertmann and Zimmermann (1996), p. 276.
38
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2 Capital Market-Based Calculation of the Cost of Equity
decisions. He grounds this in the restricted possibility of acting rationally or in the
fact that investors make portfolios from more complex investment decisions than
those assumed by Markowitz’s portfolio theory.40
2.2.1.4.2
Anomalies
Already in the 1980s empirical investigations came to the conclusion that expectations of the rate of return on the basis of CAPM systematically deviate from the
actual, observable expectations of the rate of return.
Investigations on the interrelationship of company growth potential, measured
for instance by price earning ratios and their rate of return on equity, showed that
securities with low growth potential exhibit a positive, risk-adjusted rate of return.
This effect has been coined as the “value effect” and was recognized by Basu
(1977).41
The “book to market effect” was recognized by Stattmann (1980). This anomaly
describes the interrelation between the ratios of equity book values to equity market
value with equity returns. As long as the ratio between book value and market value
of equity is high, a higher rate of return is expected.42
Banz (1981) recognized that small companies exhibit a positive, risk-adjusted rate
of return. This effect of market capitalization of a security is called “size effect”.43
Empirical studies also came to the conclusion that temporary anomalies exist.
Stocks in January and on certain weekdays, show significant, positive, risk-adjusted
rate of returns, as Fama (1991) shows, among others.44
Fama and French have especially examined “size effect” and “value effect” in a
detailed manner. For the period between 1963 and 1990, Fama and French established the average monthly rate of return for approx. 1,000 US stocks on the basis of
ten categories for company size and ten categories for the beta value determined.
The result from Fama and French’s investigation is summarized in Table 2.3.45
As Table 2.3 shows, the average rate of return for companies with similar market
capitalization hardly changes on the different beta levels. On the basis of the
assumption of CAPM, this could not be the case because CAPM assumes a linear
interrelation between rate of return on equity and the beta factor. However, the
average rate of return for companies with identical beta factors on their market
capitalization changes in a way that the average rate of return drops with increased
40
cf. Spremann (2006), p. 334 ff.; Spremann (2007), p. 456 f.
cf. Basu (1977); Reinganum (1981); Sharpe et al. (1993).
42
cf. Spremann (2007), p. 461.
43
cf. among others Hung et al. (2004), p. 89; Spremann (2007), p. 459.
44
An overview on works confirming this effect is given by Spremann (2006), p. 338 f.
45
cf. Fama and French (1992), p. 434; an overview on the works from Fama/French in the 1990s is
given by, among others: Spremann (2007), pp 462–464; Spremann (2006), p. 341 ff.; Franke and
Hax (2004), p. 357; Ziegler et al. (2007), p. 359 ff.; Wallmeier (2000), p. 32 ff.
41
2.2 Capital Market-Based Calculation of the Cost of Equity
Table 2.3 Beta factors according to size categories
Average Beta-low
2
3
4
Average
1.3
1.3
1.3 1.4 1.3
Small
1.5
1.7
1.6 1.8 1.6
2
1.3
1.3
1.4 1.4 1.4
3
1.2
1.1
1.3 1.2 1.7
4
1.3
1.3
1.1 1.5 1.1
5
1.3
1.3
1.4 1.4 1.5
6
1.2
1.1
1.5 1.3 1.2
7
1.1
1.0
1.2 1.3 1.1
8
1.1
1.1
1.1 1.4 1.2
9
1.0
1.0
0.9 1.0 1.1
Big
0.9
1.0
0.9 1.1 0.9
5
1.3
1.5
1.7
1.3
1.3
1.4
1.2
1.2
1.3
1.1
0.9
15
6
1.3
1.5
1.6
1.1
1.1
1.2
1.2
1.1
1.0
1.2
0.9
7
1.2
1.4
1.4
1.3
1.4
1.1
1.2
1.2
1.2
0.9
1.0
8
1.2
1.6
1.3
1.4
1.2
1.3
1.0
0.6
1.0
0.8
0.7
9
1.3
1.5
1.3
1.3
1.4
1.2
1.1
1.3
1.0
0.9
0.7
Beta-high
1.1
1.4
1.1
0.8
1.0
1.1
1.0
0.8
0.9
0.6
0.6
market capitalization. It can be derived from this that the beta factor does not
provide an explanation for the average rate of return, however, market capitalization appears to have a significant influence on this.
The findings from Fama and French were refuted by several authors.46 The basic
question, as is formulated by Roll (1977), is whether the validity of CAPM is even
possible because the market portfolio can only be approximated for this by implementing a market index as a proxy variable and any empirical CAPM test can only
be a test for the market index, regardless of whether this corresponds to the market
portfolio.47 However, this point of criticism overlooks the empirically fixed, systematic interrelation between rate of return deviations and certain figures, as
presented by Fama and French.48
2.2.1.4.3
Estimate and Specification Problems When Determining Beta
When determining the beta factor based on historical market data, various problems
arise which reduce the quality of the beta factor. Determining the beta factor
essentially is based on a linear equation, which is also described as a market model:
Rit ¼ ai þ bi Rmt þ uit
with:
Rit Security returns in period t
Rmt Returns from the market portfolios in period t
ai
The constant from the regression line
bi
Slope of the regression line (beta factor)
uit Confounding variable from the regression model for security i in period t
46
cf. Damodaran (2001), p. 173 f.
cf. Roll (1977); Damodaran (2001), p. 172; Spremann (2006), p. 331 ff.; Wallmeier (2000), p. 34.
48
cf. Wallmeier (2000), p. 34.
47
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2 Capital Market-Based Calculation of the Cost of Equity
This market model is based on four premises:
1. The expected value of the confounding variable is 0.
2. The variance of the confounding variable is constant over time.
3. The confounding variables from two periods that follow each other are not
correlated.
4. The confounding variable has a normal distribution.
Violating one or more of these premises as well as additional peculiarities and
specification problems can adversely effect the quality of a beta factor determined
according to the method presented above. These causes are explained as follows:
Heteroscedasticity
The property that the variances of a confounding variable change over time is called
heteroscedasticity. This can be evoked by a falsely assumed linear interrelationship
or be based on strong time-related trends of the variable.49 The implication is that
the beta factor determined is no longer efficient because the regression line determined no longer minimizes the confounding variable.50
Autocorrelation of the Confounding Variable
Autocorrelation of the confounding variable is present if the previously observed
values of the confounding variable exert a systematic influence on the following
observation values. A systematic trend of this type can be caused by not considering
a significant parameter in the regression line or can be based on a falsely assumed
linear interrelation.51 Additionally, in the case of autocorrelation from observation
values from the confounding variable, the beta factor determined is no longer
efficient.
Autocorrelation of Security Returns
Provided that the security returns to be estimated themselves exhibit the effect of
autocorrelation, the estimate of a beta factor according to the OLS method52 leads
to a distorted and inconsistent value determination.53
49
cf. Zimmermann (1997), p. 62.
cf. Ulschmid (1994), p. 210.
51
cf. Becker (2000), p. 39.
52
The form known in German as the “method of least squares” for determining regression lines is
described as an “OLS method”.
53
cf. Becker (2000), p. 41; Hachmeister (2000), p. 194.
50
2.2 Capital Market-Based Calculation of the Cost of Equity
17
Measurement Errors
If securities possess low liquidity or do not react synchronously with the market
index to new information relevant to market value, by which the assumption of an
efficient capital market is violated, this leads to a distorted and inconsistent beta
factor.54
Choice of Market Index
The beta factor portrays the upward slope of the regression line, in relationship to
the market index used. By choosing the market index, against which the security
returns should be recovered according to the OLS method, the amount of the beta
factor is influenced. Reference is made here to the explanations at Sect. 2.2.1.4.1.
Estimate Period Lengths
Beta factors are not constant over time. If the interval of time for determining beta is
extended, this leads to a higher quality of the regression lines. However, this causes
an allowance of anachronistic market data for determining beta and contradicts the
basic future orientation.55
It has been substantiated empirically that the beta factor sinks when extending
the estimate period because strong, short term fluctuations can balance out this
factor.56 In practice, an interval of 1 year is defined for determining the beta factor.
For cyclical values, at least one cycle should be completely incorporated into the
interval.57
Definition of Return Interval
The definition of a return interval is also important for determining the beta factor.
The return interval defines any period on which the calculation of a security return
is based. In a normal scenario, this could be daily, weekly or monthly returns.
Frantzmann and Pfennig, among others, substantiated this empirically on the
German stock market. On the basis of their investigations, they came to the conclusion that the extent of the return interval has an increasing influence on the beta
factor.58
54
cf. Becker (2000), p. 42 f.
cf. Mandl and Rabel (1997), p. 297 f.
56
cf. Hachmeister (2000), p. 197.
57
cf. Timmreck (2002), p. 302; Becker (2000), p. 51.
58
cf. Frantzmann (1990), p. 71; Pfennig (1993), p. 17.
55
18
2 Capital Market-Based Calculation of the Cost of Equity
2.2.1.4.4
Determining Adjusted Beta Factors
As portrayed in Sect. 2.2.1.4.3, beta factors determined on the basis of historical
market data might not meet the theoretical requirements for various reasons.
Furthermore, a beta factor determined by the OLS method was exclusively
determined by historical data and thus brackets the future orientation. However,
should the cost of equity be determined for the future, the beta factor must be
reviewed in a continuous manner as to whether or not the data basis can be used as
the best estimate for future trends.59
These deficiencies should be corrected by adjusting the historical beta factor.
Different procedures can be applied for this type of adjustment, of which the
following are explained:60
l
l
l
l
Mean value method
The blume procedure
The MLPFS procedure
Vasicek procedure
Mean Value Method
Any adjustment procedure is identified as a mean value method when the procedure
is applied to large data providers such as Barra or Bloomberg. This method assumes
that beta factors have the intrinsic tendency during the time lapse to converge on the
beta factor of the market portfolio, which is 1. For this reason, the following
adjustment is made in the mean value method, in order to minimize the effect of
underestimation and overestimation:
badj ¼
with:
badj
bhist
bM
2
1
b þ bM
3 hist 3
Adjusted beta factor following the mean value method
Historical beta factor before adjustment
Beta factor from the market portfolios ¼ 1
Pedell (2007) writes about this: “. . . When estimating beta factors, gearing towards past data is
particularly problematic because significant structural breaks regarding risk can result for
companies whose fees are regulated, precisely from changes in regulation itself. The estimated
beta factors are thus to be interpreted carefully and adjusted, if necessary, especially for changes
in the regulation mechanism. These type of adjustments require a foundation from theoretical and
empirical knowledge about the determination of the risk in regulated comanies. . . .”, Pedell
(2007), p. 47. Please note, that this is a translation (German).
60
It is noted in advance that there are no plausible reasons for the inherent preference of one of
these procedures compared with other procedures in general. cf. Pfennig (1993), p. 23.
59
2.2 Capital Market-Based Calculation of the Cost of Equity
19
The Blume Procedure
The procedure developed by Blume accounts for the determination of the beta
factor for one period, whose value arises from the previous period:61
bit ¼ at þ bt bi;t1
with:
bit
bi;t1
Realized beta factor from security i in period t
Realized beta factor from security i in period t 1
The values determined for a and b on the basis of this equation are assumed to be
constant. However, this assumption cannot be substantiated empirically.62 Nevertheless, the estimate precision can be increased on the basis of this method.63
The MLPFS Procedure
This procedure developed by the investment bank Merril Lynch Pierce Fenner and
Smith accounts for the interrelation of the beta factor from two periods by means of
the correlation coefficient of the time-dependent beta factor as follows:64
bit ¼ 1 þ rt ðbi;t1 1Þ
with:
bit
bi;t1
rt
Realized beta factor from security i in period t
Realized beta factor from security i in period t 1
Correlation coefficient betweenbi;t and bi;t1
If the correlation coefficient takes on a value of 0, this means that there is no
interrelation between the beta factor from the time period t and t 1. The best
estimate for the beta factor for t is thus displayed in the beta factor from the market
portfolio, which is 1. Otherwise, if the correlation coefficient takes on a value
unequal to 0, this shows the interrelation between the beta factor of previous periods
and the current periods.
The Vasicek Procedure
This procedure defined by Vasicek on the basis of the Bayes theorem accounts
for the degree of imprecision of the beta estimate from previous periods for
determining the most efficient beta estimate from the current period. This transpires
61
cf. Blume (1971).
cf. Zimmermann (1997), p. 246.
63
cf. Ulschmid (1994), p. 248.
64
cf. Hachmeister (2000), p. 187.
62
20
2 Capital Market-Based Calculation of the Cost of Equity
by considering the security-specific beta factor and the average beta factor as
follows:65
bi;tþ1 ¼
with:
bi;tþ1
bm;t
bi;t
Varðbi;t Þ
Varðbt Þ
Varðbi;t Þ
Varðbt Þ
bm;t þ
bi;t
Varðbi;t Þ þ Varðbt Þ
Varðbi;t Þ þ Varðbt Þ
Estimated value of the beta factor for security i in period t þ 1
Average beta factor in period t
Realized beta factor in period t
Security-specific variance of the beta factor in period t
Variance of all beta factor in period t
By weighing the security-specific beta factor and the average beta factor with
the respective variance of the factor to be weighted, the estimate precision is
improved.66 In accordance with the above equation, security-specific beta factor
estimates that are relatively reliable in the previous periods are considered stronger
in the weighted average than the average beta factor and vice versa.
2.2.2
Conclusion
The capital market-based calculation of the cost of equity by means of CAPM is
convincing because of the model’s plain intelligibility as well as because of the
theoretical foundation of the interrelation between the expected rate of return and
systematic risk. The theoretical foundation, however, is based on restrictive premises, which would essentially limit the possible applications of this model in
practice.
CAPM’s parameters are only definable empirically by applying the proxy variables. How sensitive the results from CAPM react to the application of various
indices as proxy for the market portfolio was demonstrated above.
In practice, CAPM is used readily, not least because of its (apparent) simple,
didactic usability. Empirical studies prove that the prognosis quality of capital
market rate of returns is low with CAPM. By adjusting the beta factor, one can
attempt to increase the prognosis quality. In whatever form this type of adjustment
should be made, it is not formulated in general terms, however, and this type of
adjustment often lacks a theoretical point of reference. Any adjustments are to be
substantiated on an individual basis.
65
cf. Hachmeister (2000), p. 187 f.; Ulschmid (1994), p. 252.
cf. Schultz and Zimmermann (1989), p. 201; Zimmermann (1997), p. 249.
66
2.3 Rate of Return on Equity as a Regulatory Parameter
2.3
2.3.1
21
Rate of Return on Equity as a Regulatory Parameter
Introduction
In market-based systems, attempts are essentially made to arrive at price formations
by means of the effects of supply and demand in markets. For certain goods,
however, this type of price formation mechanism is not possible or is only hardly
possible, for which reason official regulatory measures become necessary. Besides
public goods such as national defense, included in this are goods that have an
enormous investment cost, which leads to their being no appeal for companies to
become active in that type of market. These type of natural monopolies are, e.g.,
electric, gas and water networks as well as railway and road infrastructures.67
In the following, possible goals from official regulatory measures are presented,
in order to emphasize price regulation related to them. The following shows how
fair prices are determined in regulated industries and what meaning that has for the
cost of equity in regulated companies. By considering these economical principles,
it should be possible to produce a grounded prognosis regarding future revenue
for price-regulated companies, in order to derive the necessary cash flow volume
within the scope of a cash flow-based business valuation convincingly.
2.3.2
Goals in Regulation
The legislator, i.e., the regulatory agency wants to achieve certain goals by regulating industries. These can be (1) control of market power and guidelines for (2)
quality and the extent of the provision of goods and also certain (3) social goals. The
first group of goals includes the prevention of abuse from monopoly power and anticompetitive behavior. The second group. Is directly oriented toward the consumer.
A basic, sufficient provision of goods should be ensured and minimum qualities of
service provision are defined. The third group attempts to protect the interests of
socially weaker people (e.g., retirees, the handicapped and the sick) or certain
groups (e.g., agricultural communities).68
2.3.3
Defining Fair Prices
In order to avoid overloading the state’s budget, it can be assumed as a rule
that price-regulated companies have prices, i.e., profits approved that ensure the
67
cf. K€upper (2002), p. 31; König and Benz (1997), p. 70 ff.; Geradin et al. (2005), p. 25 ff.
cf. K€upper (2002), p. 32 f.; taken from: Broomwich and Vass (Broomwich and Vass (2002)),
Sp. 1678.
68
22
2 Capital Market-Based Calculation of the Cost of Equity
self-financing of the company in question. In order to attain this, the company must
have prices approved that can cover both the operating costs as well as the financing
costs.69 Operating costs are to be understood as the variable costs (e.g., material
costs, external services etc.). Due to capital consumption, financing costs are
effected in the form of depreciation and the cost of interest.
2.3.3.1
Operating Costs
Accounting for operating costs as a prognosis parameter for fair prices, i.e., profits
can take place by using actual costs or budget costs. Whereas actual costs can be
verified to a great extent upon application, this is not the case for budget costs,
which can be verified upon application only to a lesser extent compared with actual
costs. Bearing in mind the requirement of legality when setting fair prices, applying
actual costs seems to be expedient. However, in addition to legality, the aspect of
efficiently providing a service is considered, in which the consideration of objectives in the form of budget costs and target costs seem to be expedient. Much
attention must be given to the generally unattainable operationalization of the
efficiency concept to attain an equilibrium between legality and efficiency orientation when defining fair prices.70
2.3.3.2
Financing Costs
Due to capital consumption, financing costs are effected in the form of depreciation
and the cost of interest.71 The cost of interest can be subdivided into the costs for
borrowed funds and the costs for equity.
Swoboda defines three principles that should apply for defining fair financing
costs:72
Principle 1. “The investor’s expected rate of return from the EVU should be fair for
the capital market and it should also correspond to the special risk of the investor”.
Principle 2. “The costs should be distributed fairly across the consumer’s
various periods”.
Principle 3. “The costs that underlie pricing are to be determined in such a way
that negative incentives can be avoided”.
Principle 1 is derived from the goals in regulation presented above. In order to
prevent companies from attaining a monopoly income, the basic principles of
pricing in markets with full competition must be considered when setting fair prices.
For this reason, investors must be entitled to a rate of return on invested equity
69
cf. K€upper (2002), p. 34; taken from: Broomwich and Vass (2002), Sp. 1679.
cf. K€upper (2002), p. 33 f.
71
cf. Knieps (2003), p. 994; Seicht (2001), p. 105 ff. and 115 ff.
72
Swoboda (1990), p. 66 ff. Please note that this is a translation (German).
70
2.3 Rate of Return on Equity as a Regulatory Parameter
23
appropriate to the risk. Setting a higher or lower rate of return should be avoided
within the scope of setting prices.73
Principle 2 is justified by the relatively long life of investments in the network
infrastructures, compared with other branches of the economy, and the possibility
of a very different periodization of cash flow. Besides the life of the investment, the
consideration of future expenditures in the form of accruals has a significant
influence on the setting of fair prices (e.g., accruals for pension).74
Principle 3 contains the requirement that fair prices should not be set on the basis
of (historical) actual costs because this does not provide an incentive for the
management of a regulated company to organize service provision in an efficient
manner.75 As has already be portrayed above on setting fair operating costs, the
consideration of budget costs instead of actual costs is a possibility for providing an
incentive to provide services efficiently. As a part of setting fair financing costs, this
principle can be realized, for instance, by checking the investment costs for large
projects if the investment costs that are classified as too high may not be passed on
to the customer as financing costs.76
2.3.3.2.1
Depreciation
When determining fair depreciation, the depreciation period applied and the depreciation method applied must be reviewed. Before this, it must be defined whether
historical and initial costs, production costs, current price or the projected replacement costs should be applied for setting the depreciation to be accounted for.77
Historical Costs and Current Prices or Replacement Costs
Answering the question about the economically correct accounting of capital
consumption in the form of depreciation can only be answered when bearing in
mind the set of questions about the fair rate of return for companies that have an
intrinsic right of monopoly. This question is answered by means of the target
definition for the regulatory system, especially by means of the definition in
which form the costs to be approved must be determined. In the 1990s in Austria,
the basic objectives of price regulation in the electricity industry were based in
finding “economically justified prices”.78 Whether setting “economically justified
prices” is to be understood in the sense of the lowest prices possible or whether
there is interpretive leeway for considering “actual” profits (excess returns), is
73
cf. Swoboda (1990), p. 67.
cf. Swoboda (1990), p. 67 f.; Swoboda (1992), p. 84.
75
cf. Swoboda (1990), p. 68.
76
cf. Swoboda (1990), p. 68.
77
cf. Swoboda (1990), p. 69.
78
cf. Seicht (1996), p. 345; Mayer (2002), p. 197.
74
24
2 Capital Market-Based Calculation of the Cost of Equity
ultimately a political question. It must be noted with certainty, however, that excess
returns are not attainable in markets with full competition, but rather the investors
only receive interest appropriate to the risk for the capital invested. In this respect,
an orientation to pricing premises with full competition seems to be the only correct
basis for further investigations.79
Swoboda, representing an orientation to historical costs and production costs,
argues his position as follows:80
. . .Investments can be self-financed, externally financed or a combination of both. To the
extent that they are externally financed, obvious depreciation of the cost price and of
the nominal interest calculated from the respective book values are sufficient to satisfy
the claims of the lender. Depreciation of more than 100% of the investment or a higher
interest settlement would end in profits for the lender, for which no initial investment
accounts. This would stand in contrast to a competition situation. Analogously, this is also
valid for the self-financed part of the investment. Investors expect a return from their assets
that is appropriate to the risk. This type of expected return is enabled by means of pricing, in
which the calculation incorporates depreciation of cost price (which could be used for
repayment of principal) and interest, including an appropriate risk premium from each of
the book values. That depreciation and a part of the targeted return on equity are not
disbursed cannot be used as a counter argument. The depreciation compensated as well as
the retained profit can be invested in assets that again justify a fair return. . . .
However, Swoboda grants that under the following condition the application of
replacement prices would lead to the same result as does the orientation to historical
costs:81
. . .The inflation rate, toward which the nominal interest rate is adjusted, must be exactly the
same in the increase of the replacement price, in order to maintain the real interest rate. . . .
If this condition postulated by Swoboda is not fulfilled, an orientation to
replacement prices would lead to positive or negative excess returns.
To qualify this, it must be mentioned that real capital maintenance is not possible
if taxation of collected compensation due to inflation is involved. Nevertheless, this
is the case if nominal capital costs are passed on to the customer on the basis of the
book value of historical costs and production costs.82
On the contrary, Seicht argues that sheer orientation to replacement price can
guarantee the regulated company a long-term maintenance of asset value. He bases
this postulate of asset value maintenance on the company’s mandate to supply a
good, which he interprets as a service duty. This mandate to supply a good precludes a change of industry or the liquidation of a price-regulated company, for
which reason the assurance of asset value maintenance must be the highest goal.83
79
Even the ordinance on charges for system use stipulates for prices to be allowed that these
“. . . are to be determined based on costs . . .”, cf. Mayer (2002), p. 197.
80
Swoboda (1996), p. 365. Please note that this is a translation (German).
81
Swoboda (1996), p. 364. Please note that this is a translation (German).
82
cf. Swoboda (1992), p. 83; Swoboda (1996), p. 366.
83
cf. Seicht (1996), p. 351 ff.
2.3 Rate of Return on Equity as a Regulatory Parameter
25
Seicht grants, however, that only a real interest rate is to be used to calculate
financing costs when orienting to replacement prices.84
Depreciation Period
Principle 2 presented above requires the application of the service life when
calculating depreciation, which in the ideal situation corresponds to the technical
service life of the fixed assets. Since the technical service life does not only depend
on the demands of the assets, but also on the maintenance and replacement policies,
applying the service life defined outside of operation seems to be hardly possible.85 It
must be ensured that 100% of the depreciation must be passed on to the customer
even if the technical and operational service lives differ from each other.86
Depreciation Method
Besides linear methods of depreciation, digressive or progressive procedures can
also be applied. Bearing in mind Swoboda’s principle 2 presented above, the
straight-line methods appear to correspond to this, although the financing costs
exhibit a digressive trend and hence the sum total of the capital costs are lower over
time because the book value decreases as the basis for setting financing costs. On an
international level, straight-line depreciation has prevailed.87
2.3.3.2.2
Financing Costs
To calculate fair financing costs, a calculatory approach can be implemented, which
reflects the subjective view, or a market-based approach, which reflects the view of
the capital market. Both approaches together provide the answer to specific detailed
questions, which are presented in the following.
A Basis for Calculating Interest
The basis for determining financing costs is formed by means of a balance sheet
view of the assets or capital, corrected for certain adjustments. These adjustments
relate on one hand to the assets that are necessary for operation because, in general,
only assets that are necessary for operation are considered as a basis for financing
costs. A further criterion is formed by whether the assets are interest-bearing.
84
cf. Seicht (1996), p. 355.
cf. Swoboda (1990), p. 70.
86
cf. Swoboda (1990), p. 70; Swoboda (1996), p. 372 ff.
87
cf. Swoboda (1990), p. 71.
85
26
2 Capital Market-Based Calculation of the Cost of Equity
Assets that are necessary for operation form the basis for interest calculation
only to the extent that no interest-bearing equity items account for them. Noninterest related equity items are understood as contributions to building costs and
government grants, for instance.88
Concerning accruals for pension, it is important to consider whether the interest
claims from employees eligible for benefits are designated in personnel expenditures or in financial income. As long as these claims are designated in personnel
expenditures and hence are a component part of operating costs, accruals for
pension may not be calculated into the basis of calculation for interest because
this would mean a double calculation of these interest claims. If the latter is the
case, the accruals for pension are described as borrowed funds that are eligible for
interest.89
For supplier’s accounts payable, interest settlement can arise in the form of
guaranteed discounts. As long as services including discounts are activated and
flow into the price calculation in the form of depreciation, including supplier’s
accounts payable in the basis of interest would mean a double charge of interest
from the interest expenditure to the customer.90
The question about applying historical cost items or daily prices when determining depreciation also has effects when defining the basis of calculation for interest.
As long as historical costs are used to calculate depreciation, it only seems consistent to apply the balance sheet book value to calculate the capital employed on the
basis of historical costs. The same applies in an analogous form for applying current
prices or future replacement prices when calculating depreciation.
Calculating Interest Rates – The Calculatory Approach
The calculatory approach denotes the concept of determining an appropriate rate of
capital costs as summarized in cost accounting under the concept calculatory
interest. Methodologically this is reached by raising a risk-free interest rate to a
subjectively guaranteed risk surcharge. When using nominal interest rates, the basis
for calculating interest is the continued historical costs and production costs. As
long as real interest rates are used, the basis for calculating interest is formed by the
balance sheet assets evaluated at the replacement price minus the interest-free
borrowed funds.91
The basic problem of the calculatory approach, the subjective establishment of a
risk surcharge, should be overcome by the capital market-based approach.92
88
cf. Swoboda (1990), p. 71.
cf. Busse and Colbe (2002), p. 9.
90
cf. Busse and Colbe (2002), p. 9.
91
cf. Busse and Colbe (2002), p. 4.
92
cf. Swoboda (1996), p. 376.
89
2.3 Rate of Return on Equity as a Regulatory Parameter
27
Calculating Interest Rates – The Capital Market-Based Approach
The capital market-based approach defines the interest rate when determining
financing costs by taking account of the return requirements from the self-financiers
and external investors. The risk-free interest rates serve as the basis for both the
return requirements from the self-financier as well as for those of the external
investor. These interest rates are increased for specific risk surcharges that are
determined on the basis of capital market models. Besides CAPM, as the capital
model used most often, there are also other models available.93 Reference is made
here to the explanations in Sect. 2.2 of this work.
2.3.4
Conclusion
For projecting future cash flow surplus in price-regulated companies, the regulatory
system defining profit or price must be considered. From this, a range can be
determined for the amounts of future cash flows.
The expected profits from regulated companies correspond with the allowed
costs that account for them. These costs can be separated into operating costs and
capital costs. Whereas for the operating costs specific assumptions must be made
regarding their acceptance in the regulatory system applied, budgeting of the capital
costs is possible on the basis of basic economical reflection, as long as it can be
expected that the regulatory agencies also are oriented to these principles.
The following can be maintained for incoming payments that correspond to
capital costs:
1. Depreciation
To calculate future cash flow, which serves as the cover for capital consumption
in the form of depreciation, it must be taken into consideration whether the
depreciation is calculated assuming historical costs or on the basis of replacement
values. Allocating compensation due to inflation either to depreciation or to
financing costs must be considered when calculating financing costs.
The service life underlying the depreciation determination as well as the depreciation method used (straight-line, progressive, digressive) must comply with the
principle of “fair distribution to the generations”, unless the regulatory agencies
themselves deviate from this principle.
2. Financing costs
Interest-bearing assets that are necessary for operation minus non-interest bearing capital items available should apply as the capital basis to calculate financing
costs. The rate of capital costs related to this capital basis should be calculated by
93
cf. Swoboda (1996), p. 376 f.
28
2 Capital Market-Based Calculation of the Cost of Equity
applying a capital market model. The calculatory derivation of a rate of capital costs
does not have to be performed.
A rate determined for financing costs must include a risk surcharge, for which
the amount depends on “. . . what risks a price regulation leaves to the power supply
company”.94
2.4
Conclusion
In Sect. 2.2 CAPM and the set of problems related to a basic orientation to the past
were presented. By adjusting parameters in the model, attempts can be made to
impute a higher-value future orientation to the cost of equity rates determined.
However, these adjustments take place most often without the theoretical or
empirical foundation required by them.
The analysis of which economical principles should be considered regarding the
projection of future cash flow in regulated companies was presented in Sect. 2.3.
This analysis showed that “fair” operating costs and appropriately determined
capital costs, which contain a fair risk premium, are to be acknowledged by the
regulatory agency and should be significant for regulating “fair” prices.
94
Swoboda (1996), p. 377.
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