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Market imperfections call into question the suitability of the CAPM for deriving the cost of capital. The valuation by incomplete replication introduces a valuation concept that takes capital market imperfections into account and derives the risk-adjusted cost of capital (or risk discounts) on the basis of corporate or investment planning and risk analysis. The risk measure is derived consistently (using risk analysis and Monte Carlo simulation) from the cash flows to be valued, that is, the earning risk. Historical stock returns of the valuation object are therefore not necessary. It can be shown that the valuation result of the CAPM can be derived using the approach of imperfect replication as a special case for perfect capital markets.
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Company valuation as result of risk analysis:
replication approach as an alternative to the
Werner Gleißner* - Dietmar Ernst**
Market imperfections call into question the suitability of the CAPM for deriving the cost of capital. The
valuation by incomplete replication introduces a valuation concept that takes capital market imperfections
into account and derives the risk-adjusted cost of capital (or risk discounts) on the basis of corporate or
investment planning and risk analysis. The risk measure is derived consistently (using risk analysis and
Monte Carlo simulation) from the cash flows to be valued, that is, the earning risk. Historical stock returns
of the valuation object are therefore not necessary. It can be shown that the valuation result of the CAPM
can be derived using the approach of imperfect replication as a special case for perfect capital markets.
1. Introduction and overview
The idea of a capital market-oriented
company va-
luation has to be questioned due to many imperfec-
of the capital market
. Especially the CAPM
does not meet the challenges of a company valuation
on imperfect capital markets due to the assumption of
perfect and complete capital markets
. An improve-
ment in the valuation results (e.g. as a basis for deci-
sion-making on the purchase of companies) if com-
pany-related factors (such as growth
, return on equity
or company-specific risks) are taken into account in
the valuation models
. This leads to a replacement of
capital market-oriented valuation approaches with
procedures that - in the tradition of investment theo-
retical valuation approaches
- deal with earnings risks
and not primarily with share price fluctuations; these
are the semi-investment theoretical valuation methods
described in this article, which are based on an analysis
of business risks and the method of imperfect replica-
tion. The central advantage of the valuation approach
is that it is based on only two low restrictive assump-
tions and, in particular, does not make any restrictive
assumptions about the characteristics of the valuation
subject or the capital market. In particular, there is no
need to assume a perfect or complete or arbitrage-free
capital market (the central assumption is simply the
following: two payments at the same time have the
same value if they match the expected value and the
risk measure chosen by the valuation subject). Also
rating and financing restrictions and insolvency costs
are possible. Overall, an ‘‘idealized market calculus’’, as
explained by Ballwieser (2010), is therefore not re-
quired for deriving the valuation equations
. So the
actual approach presents an alternative to CAPM and
implied cost of capital (Bini, 2018) to derive cost of
capital. But it is not necessary to assume that the value
is the market price. The valuation always takes place
consistently from the perspective of the respective va-
luation subject (so that, for example, the degree of
diversification of its assets achieved by this valuation
subject always prevails, and not the diversification pos-
sibilities of other valuation subjects on the capital mar-
In contrast to pure investment theoretical methods
the valuation (and the derivation of the cost of capi-
tal) takes place without the necessity of considering
and simultaneously optimizing all investment and fi-
nancing possibilities of the valuation subject (espe-
* FutureValue Group AG (Executive), Technische Universita
Dresden (Faculty of Business and Economics).
** School of International Finance (SIF) - Hochschule fu¨r
Wirtschaft und Umwelt (HfWU) Nu¨ rtingen-Geislingen - Chair “Inter-
na-tional Finance”.
I.e. financial theoretical.
See the overview of empirical studies at Gleißner, 2014.
Hering 2014.
See Bini, 2018, pp. 8-11; Dempsey 2013a and b; Fernandez 2013
and 2017; Rossi, 2016; the empirical studies (and alternative models) at
Fama/French, 2015; Blitz/Hanauer/Vidojevic/van Vliet, 2018; Kaserer/Ha-
nauer, 2017; Ang et al 2006 and 2009; De Bondt/Thaler, 1985 and 1987;
Jegadeesh/Titman, 2011.
Esp. of assets (see Chen/Novy-Marx/Zhang, 2011 and Fama/French,
See Ang et al 2006 and 2009; the empirical studies (and alternative
models) at Fama/French, 2015; Kaserer/Hanauer, 2017; Walksha
2013; Zhang, 2009.
See Matschke/Bro
¨sel, 2013 and Hering, 2014.
The explained semi-investment-theoretical valuation approach is
new due to the lack of need for an idealized capital market or the
existence of a utility function. It is not included in the survey of
Ballwieser, 2010.
See i.e.Hering, 2014; Matschke/Bro
¨sel, 2013; Toll/Kintzel, 2018.
Business Valuation OIV Journal Spring 2019 3
Company valuation as result of risk analysis
Volume 1 - Issue 1
cially by means of a simplex algorithm)
. In the tradi-
tion of risk-value models
, valuation is performed by
comparing the expected value of cash flows and their
risks, expressed by a selected risk measure, with the
risk-return profile of alternative investment opportu-
nities (e.g. government bonds and equity indices avail-
able on the capital market). In accordance with the
idea of ‘‘imperfect replication’’, the risky cash flow to
be valued is thus expressed only in terms of the ex-
pected value and risk measure (R). It is only necessary
to know the relevant information about two alterna-
tive investment opportunities (and not about the
whole investment program)
. Accordingly, the valua-
tion is based on a (m,R)-preference function that in-
cludes the well-known (m,s)-preference function of the
Capital Asset Pricing Model (CAPM) as a special case.
In contrast to the utility theoretical evaluation, knowl-
edge of utility functions is also not required
. The
great advantage of the valuation approach is that no
(historical) capital market information about a com-
pany to be valued is required and the derivation of the
cost of capital and company value from the analysis of
the opportunities and risks of the company is possible.
Risk analysis and Monte Carlo simulation for the ag-
gregation of individual risks with reference to corpo-
rate planning provide the valuation-relevant informa-
tion. Due to the consistent reference to the future and
the consideration of future risks, the valuation ap-
proach outlined in this article is suitable for valuing
existing options for action in the preparation of busi-
ness decisions (e.g. in the context of a strategy assess-
ment). This also explains the great importance of the
valuation approaches presented here for financial cor-
porate management (controlling). The central busi-
ness task is a well-founded weighing of expected re-
turns and risks in important decisions. The preparation
of business decisions requires a well-founded strategy,
operational planning based on it, an analysis of oppor-
tunities and threats and a risk-adequate evaluation of
the options for action.
In this article we first discuss the challenges of a
modern company valuation. We then analyse how a
risk adjustment is made using the risk premium meth-
od and the certainty equivalence method. We then
apply the certainty equivalence method to the CAPM.
In the next section, we derive the valuation equation
and the cost of capital using incomplete replication as
an alternative to CAPM. Insolvency risk and rating
are also taken into account.
The article is structured as follows. Section 2 ad-
dresses some of the key challenges of adequately cap-
turing risks in the valuation of companies, such as the
fact that business risks generally affect (1) the expected
value of cash flows and (2) the cost of capital. Chapter
3 discusses the two ways in which business risk is ac-
counted for in the valuation: the calculation of risk-
adjusted cost of capital or of certainty equivalents.
Section 4 shows how to derive valuation equations
and cost of capital without assuming a perfect capital
market (as in the case of the CAPM). In particular,
the above-mentioned method makes it possible to de-
rive risk-appropriate cost of capital directly from the
results of the analysis of the company’s risks. Special
attention is also paid to the significance of the insol-
vency risk as well as the often existing rating and
financing restrictions for the shareholder value (sec-
tion 5). Section 6 explains the method by means of a
simple case study before a short summary of the key
2. Effects of risk on company value
When determining the value of a company as a fu-
ture success value, it is necessary to observe certain
equivalence principles
. It must be ensured that the
‘‘numerator’’ and the ‘‘denominator’’ of the valuation
equation(s) are consistent with each other, especially
with regard to risk assessment. This applies regardless
of whether the risk adjustment of the cash flows is ‘‘in
the denominator’’
(in the case of the risk premium
method) or ‘‘in the numerator’’ (in the case of the risk
discount method)
It should be noted that risks potentially affect (1) the
expected value of the cash flow Eð
CF ) and (2) the
cost of capital
at the same time. The effect of a risk R
is simplistically shown in graph 1.
The evaluation is understood as a comparison procedure and not
as an optimization procedure.
See Sarin/Weber, 1993.
This is why the term ‘‘semi-investment theory approach’’ is also
used here, see Gleißner, 2011.
See Bamberg/Dorfleitner/Krapp, 2006 and the overview at Schosser/
Grottke, 2013.
See Moxter, 1983 and Dehmel/Hommel, 2017.
Which is not recommended (see Spremann, 2004).
See especially how to deal with insolvency risks that lead to a
termination of the cash flow to the owner, Gleißner, 2017c.
By means of a risk discount in the numerator or a risk premium r
in the interest rate in the denominator.
4Business Valuation OIV Journal Spring 2019
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Company valuation as result of risk analysis
Graph 1: Impact of risk of a company on its valuation components
This article deals with the methods of adequately
recording risks in company valuation and shows in
particular that the impact of risks on the expected
value of cash flows (the numerator) and the discount
rate (the denominator) can be derived consistently
from a risk analysis of cash flows. An independent
model for determining the discount rate - e.g. for de-
riving the CAPM beta based on fluctuations in equity
returns or via a peer group - is not necessary
. The
unrealistic assumptions of a perfect (or complete) ca-
pital market, as in financial theory valuation methods,
are not required
In addition, risks also affect the probability of default
(the rating) and, via it, the level of cost of debt and
the development over time of the expected value of
the cash flows (a special case of the expected value
effects explained above, see section 5).
In the following, ‘‘semi-investment’’ theoretical va-
luation methods are presented that take capital market
imperfections into account and consistently calculate
risk-adjusted cost of capital (or risk discounts) on the
basis of corporate or investment planning. The infor-
mation from risk analysis, financing restrictions, and
insolvency risks are taken into account. The proce-
dures can also be used if no capital market data is
available for non-listed companies because the valua-
tion is consistently derived from the uncertain cash
flows themselves (business plan).
3. Fundamentals of risk adjustment in the evaluation
of series of cash flows
The company valuation is based on the discounted
cash flow method (DCF). Under the DCF method, the
value of a company is determined on the basis of ex-
pected future cash flows
. These expected cash flows
are derived from an integrated planning calculation.
To determine the company value, the cash flows are
discounted to the valuation date using a suitable capi-
talization interest rate (cost of capital).
The risk of future cash flows (
CF ), i.e. the extent of
possible deviations from the expected value ðEð
can be considered in the following two ways
using the risk premium method, i.e. the calcula-
tion of the cost of capital
or using the certainty equivalence method (risk
discount variant).
3.1 Cost of capital: the risk premium method
With the risk premium method, a risk premium (r
is added to the risk-free interest rate (r
). This results in
a discount rate (c) (approximately the cost of capital)
for discounting the expected future cash flows
. The
formula for the discount rate is as follows:
is usually determined as a function of equity yield
risks, e.g. expressed by the beta factor of the CAPM.
The extent to which this reflects the actual risks of the
company, e.g. the volatility of cash flows ð
CF ) is,
however, open. And only under specific additional
assumptions, especially with regard to perfect capital
market, the risks of the cash flows of the company are
adequately recorded in r
The value of a risky cash flow (
CF1) at time t = 0 is
obtained by discounting the expected value Eð
with the cost of capital c:
The risk premium method is often used in company
valuation practice. However, it leads to valuation er-
rors when a uniform risk premium is applied to both
positive and negative cash flows
. This can be ex-
plained as follows. The basic idea behind discounting
And generally not consistent with the valuation-relevant risk
scope of the cash flow.
See Ballwieser, 2008; see also the criticism at Dempsey, 2013;
Gleißner, 2014; Hering, 2014 and Ferna
´ndez, 2013 und 2017.
I.e. free cash flows or flows to equity.
This approach is usually applied in business valuation practice.
But it is necessary to know the market price and to assume that
the value is the price (see Black, 1986 and Shleifer/Vishny, 1992 und
1997 for some problems with this assumption).
See Spremann, 2004, p. 253.
Business Valuation OIV Journal Spring 2019 5
Company valuation as result of risk analysis
Volume 1 - Issue 1
uncertain cash flows is that due to risk aversion, un-
certain cash flows are assigned a lower value by dis-
counting than certain cash flows. However, this is
precisely not achieved by discounting negative cash
flows: discounting negative cash flows increases the
value because it becomes less negative
. It is therefore
advisable to use the certainty equivalence method,
which provides correct valuations
3.2 Certainty equivalence method
The certainty equivalence method is based on the
following equation:
CE stands for the ‘‘market price of risk’’. This term
expresses what additional return per unit for addition-
ally accepted risk (measured in the selected risk mea-
sure Rð
CF )
for the alternative investment opportu-
nity under consideration, e.g. the capital market) is to
be expected. The scope of risk of a cash flow is re-
corded with a deduction in the numerator. A clear
distinction is made between risk preference in the nu-
merator and time preference (risk-free interest rate) in
the denominator (Ballwieser, 1981).
The risk analysis of the cash flows to be valued leads
to risk-adjusted risk measures that are not derived from
historical stock returns. Suitable risk measures, such as
value-at-risk, can take into account not only the stan-
dard deviation used in the beta factor but also the
skewness and kurtosis of the distribution or a larger
data density.
3.3 CAPM based on certainty equivalent and risk
analysis as a special case
Even if an appraiser wishes to follow the traditional
CAPM valuation approach, he or she should aggregate
the valuation-relevant information on the risks of un-
certain cash flows
CF to an appropriate risk measure.
This is made possible by the ‘‘risk discount variant’’ of
CAPM, whose risk measure is based on the correlation
between future cash flows and the market return. The
‘‘risk discount variant’’ of the CAPM is also applicable
in the case of unlisted companies, there are no
historical share price returns to calculate the beta
factor, or
historical returns cannot be regarded as represen-
tative for the future, for example, due to capital
market imperfections or a strategic decision, like
change in the business model.
The risk discount variant or certainty equivalence
variant of the CAPM is as follows:
with as correlation coefficient of the uncertain
cash flow and the uncertain return of the market
CF ) as standard deviation of the expected cash
flows (scope of risk expressed in monetary units) and
rm) as expected return of the market port-
folio (see Robichek/Myers, 1966; Rubinstein, 1973 and
Gleißner/Wolfrum, 2009).
A future-oriented calculation of the correlation is
possible either through a so-called ‘‘risk factor ap-
proach’’, which models joint influencing factors on
CF1and the uncertain return of the market e
(e.g., economic situation, exchange rate, and oil price)
or through a statistical analysis of historical data. It
cannot be assumed that historical stock returns, which
may also be influenced by psychological factors or mo-
mentum trading strategies, show the valuation-rele-
vant risk of the cash flows to be valued (Dirrigl, 2009).
In contrast to the traditional CAPM return equa-
tion, the variant shown is also applicable to negative
cash flows. For communication purposes, the valuation
result can also be converted into a cost of capital rate
(or an implicit beta factor).
The valuation equation for the risk discount variant
of the CAPM can be derived using a robust replication
approach even without the restrictive assumptions of
the CAPM (see Gleißner/Wolfrum, 2009 and Dorfleit-
ner/Gleißner, 2018).
4. Deriving the valuation equation and cost of capital
from a risk analysis using incomplete replication
4.1 Deriving the valuation equation using incomplete
In the following, a so-called incomplete replication
approach (‘‘duplication’’) is used to show how concrete
valuation equations (and thus the market price of the
risk CE can be derived)
. Later in 4.2 we will derive
the cost of capital.
It is of fundamental importance - and a key advan-
tage - that the following valuation methodology, and
the cost of capital derived later in section 4.2, are
This is only correct in context of the market approach for a well-
diversified shareholder and for cash flows with a negative correlation to
the market returns.
For derivation see Gleißner/Wolfrum, 2009.
It is worth to mention that a risk measure Rð
CF Þe.g. ð
CF Þis
not necessary if it is intended to get implied cost of capital (Bini, 2018).
Gleißner, 2011 and Dorfleitner/Gleißner, 2018.
6Business Valuation OIV Journal Spring 2019
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Company valuation as result of risk analysis
based on only a few, and less restrictive, assumptions
that open up a broad field of application:
First assumption:
Two cash flows at the same time have the same
value for the valuation subject if they match the ex-
pected value and the risk measure chosen by the va-
luation subject.
Second assumption:
For the subject of the valuation, a
risk-free invest-
ment with an interest rate r
and a risk-bearing invest-
ment option with an uncertain return e
rM(e.g. a broad
empirical market portfolio) are available as alternative
investment opportunities.
That’s all. In particular, no further assumptions about
the capital market are required (this does not have to be
arbitrage-free or complete). Further assumptions about
the subject of the valuation are required. It does not
need to be perfectly rational nor perfectly diversified
(due to ancillary assumptions, such as in CAPM).
In particular, no utility function of the evaluation
subject must be known because its risk preference only
manifests itself in the choice of the risk measure
(which, incidentally, is similar in this respect to the
CAPM), which specifically underlays a ð; Þi.e. a
special case of the here generally accepted (; R)
In order to determine the value of an uncertain cash
CFAof an investment Ain a one-period model,
an (incomplete) replication that is in line with expec-
tations and is risk-adequate is carried out. Two invest-
ment options should be available for this purpose:
- the (empirical) market portfolio
with an uncer-
tain return e
- a risk-free investment with the interest rate r
It is important to note that in contrast to CAPM or
valuation methods based on the assumption of an ar-
bitrage-free capital market
this valuation approach
does not require any customary, restrictive (and less
realistic) assumptions about the capital market. This is
a significant advantage of the method explained here.
With regard to the capital market, it is only assumed
that there is a
risk-free investment opportunity and a
risky investment opportunity (for example, the ability
to invest in a broad market index, such as the MSCI All
Country). In particular, it is not necessary to assume
that the capital market is perfect, complete or arbit-
. No assumptions are required regarding e.g.
the absence of taxes or transaction costs. The risky in-
vestment opportunity, which can be understood as an
‘‘empirical market portfolio’’, need not have any other
condition than that considered by the valuation subject
as an investment opportunity
The market portfolio in this context is nothing more
than a portfolio of uncertain assets that exist (and can
be invested) in the real world.
It is a fundamental advantage of the methodology
proposed here that it does not require any restrictive
assumptions about (1) the capital market or (2) the
behavior of the valuation subject (as explained above,
the latter is not necessarily the - in reality non-existent
– homo economicus, who, however, chooses operatio-
nalized optimal behavior, acts only according to the
central assumption 1 above).
Unrealistic and restrictive assumptions are not re-
quired for deriving the valuation equations. In parti-
cular, the application of the valuation method also
allows for constellations in which no sale of the com-
pany is envisaged at all (as discussed in the introduc-
tion situation of a strategy assessment).
In contrast, e.g. there are no assumptions for the
CAPM that would imply that
Value and price are basically the same,
The valuation subjects would have perfectly diver-
sified portfolios (and therefore would only bear
systematic risks, as in the CAPM).
Value and price can differ so very well in the as-
sumption system made here and valuation subjects -
as in reality – are free to have diversified portfolios or
not. Due to the lack of the need to use restrictive
assumptions, it is possible in particular to cover exist-
ing constellations for the valuation which otherwise
cannot be assessed (e.g. the evaluation of strategic op-
tions for action of an entrepreneur as a valuation sub-
ject who owns all his assets in his own company and
thus carries company-specific risks).
It is easy to calculate the value (CF) = x+y. The
amount of capital xinvested in the market portfolio
and the amount of capital yinvested in the risk-free
investment is exactly enough that the risk of this port-
folio corresponds to the risk of the uncertain cash flow
CFA. The risk is measured by a suitable risk measure
CFAÞ, such as standard deviation, value-at-risk or
conditional value-at-risk. The risk measure can gener-
ally be selected by the valuation subject and is an
expression of the risk perception. In addition to the
risk measure of the standard deviation which is usual
in capital market-oriented valuation (especially the
At least, so to speak.
This is an ‘‘empirical’’ market portfolio (like a stock market in-
dex). Not necessarily the theoretical market portfolio based on the
No-arbitrage conditions.
At least, so to speak.
See for an explanation of the terms and their relationship,
Friedrich, 2015, pp. 13.
It is therefore a ‘‘real’’ investment opportunity and not a model
construct, such as the market portfolio at Markowitz (1952) or within
the framework of the CAPM. The assumption that the (empirical)
market portfolio can be invested corresponds to the idea of ‘‘availabil-
ity’’ in Richter, 2005, p. 22.
Business Valuation OIV Journal Spring 2019 7
Company valuation as result of risk analysis
Volume 1 - Issue 1
CAPM), downside risk measures can also be used.
With these downside risk measures, risk is expressed
as ‘‘possible loss’’ or the utilization of a risk coverage
potential (equity and liquidity reserve) that is scarce in
reality. The risk measure should be homogeneous and
translation- or position-invariant
The expected value of the repayment of the invest-
ment in the market portfolio and the risk-free invest-
ment should correspond to the expected value
The value of the risky cash flow
CFAcorresponds to
the sum of the two investments xand y. The same risk
and the same expected value imply the same value.
The replication equation can be derived from equa-
tions (6) and (7)
If the risk measure is known, this equation can be
solved and thus evaluated. It is important to know
whether this is a position-dependent risk measure
(such as the value-at-risk or the conditional value-at-
risk) or a position-independent risk measure (such as
the standard deviation or the deviation value-at-risk).
The deviation value-at-risk or relative value-at-risk is
defined as DV aRð
with a as confidence level (e.g. a=99%).
Since cash flows often cannot be described by nor-
mal or log-normal distributions (e.g., because of fat
tails), downside risk measures are gaining in impor-
In the following, only position-independent risk
measures such as standard deviationare considered
more closely, since they are seen as a measure of plan-
ning reliability or the extent of possible plan devia-
tions (from the expected value)
. This applies to
these (see Rockafellar/Uryasev/Zabarankin, 2002):
With equation (9) equation (8) simplifies to
For the value one obtains by transformations (and by
neglecting a time index)
A special variant of equation (3) has thus been de-
. The market price of the risk shows how
much more return per unit of risk can be expected
for the alternative investments under consideration.
In the simplest case, the risk discount corresponds to
the product of the risk premium and the risk volume
(e.g. ‘‘equity requirement’’ as a risk measure based on
Now assume the risk measure Rð
CF Þis the standard
deviation and so Rðaþb
the following equation shows how is the value of the
cash flow
The cost of capital (c) is thus implicitly the ratio of
the cost of Eð
CFAÞto V alue0ð
CFAÞwhich will be
discussed later in section 4.2.
Until now, it has been assumed that the cash flow
from investment Aand the market portfolio is fully
correlated, i.e., that the correlation coefficient
AM ¼1or investment Ais the only asset.
As a rule, however, this assumption will not be ful-
filled and thus diversification possibilities will be avail-
able so that only the non-diversifiable portion of the
risk (the systematic risk) of the cash flow is relevant for
the valuation.
This reduces the valuation-relevant risk of the cash
flow by multiplying the standard deviation by
AM ¼ð
CF ; e
rMÞ, so that the following equation re-
Equation (14) corresponds to the certain equiva-
lence equation of the CAPM (3)
. The following
conditions apply:
Position-independent. See Dorfleitner/Gleißner, 2018.
See Dorfleitner/Gleißner, 2018.
See Dorfleitner/Gleißner, 2018 for translation- invariant risk mea-
CF ¼
CF1is considered to be the cash flow of period 1. Period 1
is between time t=0 and t=1. Valuation date is t=0.
See Gleißner/Wolfrum, 2009.
See Robichek/Myers, 1966; Rubinstein, 1973.
8Business Valuation OIV Journal Spring 2019
Volume 1 - Issue 1
Company valuation as result of risk analysis
the risk measure is the standard deviation,
only non-diversifiable, systematic risks are as-
sessed, and
there are homogeneous expectations, i.e., the cash
flow is valued by the capital market according to
the planning ðð
It should be noted that the replication equations do
not conflict with CAPM if the same assumptions are
made as in CAPM and in this case the risk measure
(‘‘capital requirement’’, CVaR or VaR) contains ex-
actly the same information as the standard deviation
and the beta factor (see Mai, 2006, on the relationship
with the traditional CAPM return equation, specifi-
cally on the assumption of proportionality of cash flow
and value fluctuations).
The replication methodology can also be extended
to multi-period cash flows
4.2 Deriving the cost of capital from the valuation
equation using incomplete replication
The procedures described in section 4.1 allow the
risk-adjusted measurement of uncertain cash flows
(in one or more periods). However, valuation using a
risk discount in the numerator, i.e., the calculation of
certainty equivalents, is unusual in valuation practice.
The previously explained (semi-investment theoreti-
cal) valuation based on ‘‘incomplete replication’’ can,
however, also be directly linked to the discounted cash
flow (DCF) methods known in practice. For this pur-
pose, it is necessary to determine the cost of capital
(discount rate) of the DCF methods using the methods
explained in section 4.1.
The bridge from the aggregated total risk, e.g. ex-
pressed by the standard deviation of the cash flow
CF Þ, to the company value, is precisely the cost
of capital (or certainty equivalents). In contrast to
the traditional ‘‘capital market-oriented’’ valuation,
the cost of capital in a risk simulation can be derived
directly from the earnings risk and not from historical
stock return fluctuations (as is usually the case with the
beta factor of the CAPM; see Gleißner, 2011 and
2014). The results of a risk analysis are used, on the
one hand, to obtain expected cash flow values and, on
the other hand, to derive the cost of capital rates con-
sistently (the consistency between the expected value
of the cash flows in the numerator and the cost of
capital rates in the denominator is a notable advantage
of the methodology explained). Such a discount rate,
which is often assumed to be constant, can be derived
as a risk measure from the standard deviation of the
cash flow, for example. It obviously applies:
If one resolves this equation with equation (14) for
the value Vafter c, one obtains the risk-adequate cost
of capital. If
CF is the operating free cash flow
(oFCF), cis the weighted cost of capital (WACC));
CF is the flow to equity (FtE), cis the cost of equity.
Based on the risk-free interest rate, the following
equation for the risk-adequate capitalization rate (cost
of capital) is obtained
The ratio of cash flow risk ð
CFAÞto expected cash
flow Eð
CFAÞis the coefficient of variation V. The
variable shows the excess return per unit of risk
(Sharpe Ratio).
is dependent on the expected return of the market
index, its standard deviation and the risk-free rate of
return and expresses the risk/return profile of the alter-
native investments: to value means to compare (Mox-
ter, 1983). As the owners do not necessarily bear all
the risks of the company, the risk diversification factor
dmust also be taken into account. It shows the pro-
portion of risks of a company that the owner has to
bear in equation (16)
An estimate of the degree of risk diversification d
can be derived by the correlation of the (trend-ad-
justed) earnings (or earnings growth) of the company
to the earnings of all companies in the market index.
The risk diversification factor dimplicitly follows from
the simulation-based risk aggregation if exogenous risk
factors are considered independently to record the sys-
tematic, cross-company risk
. Under the special as-
sumptions of the CAPM, dconforms to a correlation
with the return on the market portfolio.
Equation (16) can be used for different definitions
of cash flows
flow, the cost of equity is obtained. If the operating
free cash flow is used, the weighted average cost of
capital (WACC) is obtained. The WACC results
See Dorfleitner/Gleißner, 2018.
It is the proportion of Rð
CF Þto additional (‘‘incremental’’) risk
in the portfolio of the owner caused by the company (see Gleißner,
2011 and Tasche/Tibiletti, 2003).
‘‘Risk factor model’’; see Gleißner, 2017a, pp. 261-263.
Business Valuation OIV Journal Spring 2019 9
Company valuation as result of risk analysis
Volume 1 - Issue 1
‘‘directly’’, without first having to calculate cost of
equity and cost of debt and weight them appropri-
ately. The total extent of the risks determines the
total cost of capital (only in a second step are the
total risks divided between equity and debt capital
providers, which determine the cost of equity and
cost of debt). Determining the total cost of capital
(WACC) in this way is comparatively simple and
there is no need for leveraging or deleveraging when
calculating the cost of equity.
It should be noted that it is not necessary to calcu-
late the cost of capital only for a representative period
and to assume it to be constant for all periods for the
sake of simplicity. Of course, it is also possible to cal-
culate periodic cost of capital. In addition to periodic
cost of capital, it is also possible, and useful in many
valuation cases, to calculate two different cost of capi-
tal: a cost of capital c
for the detailed planning period
and a cost of capital c
for the continuation period.
This is particularly appropriate if, in the detailed plan-
ning period, the risk-return profile of the company,
and thus the coefficient of variation V, still differ sig-
nificantly from that in the continuation period. This is
particularly the case if, for example, a young company
has significantly higher risks at the beginning of its
existence than later when it is established (i.e. in the
continuation period).
4.3 Risk analysis and risk aggregation using Monte
Carlo simulation
The identification and quantification of the compa-
ny’s risks (opportunities and threats) must be the basis
for the risk-appropriate evaluation of a company.
As a result, the risk analysis and risk aggregation - as
shown above - leads to cost of capital that express the
risk-adjusted requirement for the return on a project,
business unit or company (e.g., for the calculation of
a discounted cash flow DCF or Economic Value
Added EVA). In addition to the risk measure of the
standard deviation, which is based on a normal dis-
tribution and is used in CAPM, there are other risk
measures. These risk measures are often better suited
to describe the actual risk in the company. In order to
determine suitable risk measures for company valua-
tion, the actual risks in the company must be deter-
mined. This is done with the help of a risk analysis.
Then it has to be examined how the risks are related
to each other and how they affect the cash flows and
thus the company value. This is done on the basis of a
Monte Carlo simulation. The results of the Monte
Carlo simulation can be used to calculate suitable risk
measures. These risk measures are then incorporated
into the company valuation using the certainty
equivalence method and are expressed by the variable
4.3.1 Risk analysis of corporate risks
The first step in risk analysis is the identification of
risks, which can be structured as follows:
(1) Strategy and strategic risks
Strategic risks are the risks arising from the threat to
the company’s most significant potential for success.
(2) Controlling, operational planning and budgeting
In controlling, business planning or budgeting, cer-
tain assumptions are made (for example, with regard to
the growth rate of the economy, exchange rates and
successes in sales activities). All uncertain planning
assumptions show a risk because plan deviations can
occur. The causes of plan deviations show the effects
of existing risks.
(3) Risk workshops (risk assessment) on performance
Certain types of risk are best identified in a workshop
through critical discussions. These include, in particu-
lar, operational risks, legal risks, political risks, and
risks arising from support services (e.g., IT).
For the quantitative description of a risk, a probabil-
ity distribution can be used that describes the effects of
a risk on earnings in a period (e.g., year). A more
differentiated consideration is possible if a risk is de-
scribed by (1) a probability distribution for the fre-
quency of the occurrence of the risk in a period and
(2) a probability distribution for the amount of damage
per occurred risk event.
4.3.2 Risk aggregation using Monte Carlo simulation
It is not individual risks but the aggregated overall
risk scope that is decisive for assessing a company’s
(free) risk-bearing capacity and the degree of threat
to its continued existence. Aggregation across all in-
dividual risks and over time is therefore necessary.
Since only quantified risks can be aggregated, all rele-
vant risks must be quantified. By aggregating the quan-
tified risks in the context of planning, it is examined
what effects these have on future earnings, future cash
flows, the key financial indicators, credit agreements
(covenants), the rating, and thus on the enterprise
value. For example, it is necessary to calculate the
probability that risks (e.g., an economic downturn in
connection with a failed investment project) could
cause the company’s future rating to fall below a level
(B rating) necessary for the company’s ability to ser-
vice its debt.
The aggregation of risks in the context of corporate
planning requires the use of simulation methods
(Monte Carlo simulation) because risks - unlike costs
- cannot be added together, at least if special cases
(normal distributions) are excluded. Furthermore, risks
in an integrated planning model must also be aggre-
gated over several years to identify serious crises over
10 Business Valuation OIV Journal Spring 2019
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Company valuation as result of risk analysis
time. Simulation methods are the further development
of the well-known scenario analysis techniques
Monte Carlo simulation is used to analyze a large re-
presentative number of risk-related possible future sce-
narios (planning scenarios) in risk aggregation. In this
way, a frequency distribution and thus a realistic range
of future cash flows and returns are shown, i.e., the
planning reliability or extent of possible negative de-
viations from the plan.
4.3.3 Risk measures
In addition to the quantitative description of risks,
the calculation of risk measures (R) is another sub-task
in risk quantification
. The term risk measure is a
collective term for statistical measures that make it
possible to describe the uncertainty of an event quan-
titatively. A risk measure maps a frequency or prob-
ability distribution to a real number. A risk measure
expresses the scope of risk of a distribution in a number
that can then be used for further economic and appli-
cation-oriented calculations. Risk measures are neces-
sary to enable simple ‘‘calculating with risks’’ (as shown
in section 4). They thus serve to transform risk or
A distinction is made between position-dependent
(position-invariant) and position-independent risk
measures. Position-dependent risk measures, such as
the value at risk, are dependent on the expected value.
If a position-dependent risk measure is not applied to a
random variable
X, but to a centered random variable
XÞ, the result is a position-independent risk
. Position-independent risk measures (such
as the standard deviation or deviation value at risk
(DVaR)) describe the extent of plan deviations and
are therefore also referred to as deviation measures.
Furthermore, a distinction is made between one-
sided and two-sided risk measures. Two-sided risk mea-
sures measure deviations from the planned or expected
value in both directions, i.e., opportunities and risks.
The one-sided risk measures consider only possible
deviations in one direction, mostly possible negative
plan deviations.
For the derivation of the evaluation equations, it is
assumed, as explained above, that the risk measure (a)
is homogeneous and (b) is either translational or posi-
tion-invariant, and therefore the following applies ac-
positive homogeneity (PH) is defined by
translation invariance (TI) is defined by
position invariance (PI) is defined by
5. Insolvency risk and rating
Previously, this section explained how the risks (op-
portunities and threats) affect the expected value of
cash flows and the cost of capital. In real, incomplete
capital markets with rating and financing restrictions,
there is a further impact of risks that is discussed below.
A particularly unfavorable combination of individual
risks can arise scenarios that lead to the insolvency of
the company and thus to the interruption of the cash
flow of the (previous) owners. This risk of insolvency
has so far received little attention in valuation prac-
tice, although it can have considerable effects on the
value of the company.
It should be noted that the insolvency risk, especially
the probability of insolvency p, influences the ex-
pected value of the cash flows and their development
over time
In the detailed planning phase, the probability of
insolvency must be taken into account directly when
determining the expected values (as a scenario with, as
a rule, no return to the owners). In general, it is ad-
visable to map insolvency scenarios in detail in a sto-
chastic event space or in the paths of a simulation
model even in the continuation phase.
In addition to considering the insolvency scenario in
the detailed planning, it should be noted that insol-
vency can occur in any year of the continuation phase.
An approach that is partly implemented in valuation
practice is the evaluation of an insolvency scenario for
the expected result. Even if this may already sensitize
to the possibility of insolvency, considerable problems
remain: On the one hand, the estimated probability of
insolvency is usually not rating and planning consis-
tent, on the other hand, it is often ignored that insol-
vency is possible every year, so that there are many
insolvency scenarios - and in the long term, insolvency
is a scenario with a high probability.
If it is assumed for the continuation phase when
determining the terminal value that the probability
of insolvency - corresponding to the steady state in
the terminal value formula - remains constant, it leads
(under otherwise identical conditions) over time to
continuously declining expected cash flows.
See Grisar/Meyer, 2015 and 2016 on significance.
See cf. Gleißner, 2017a and Artzner et al., 1999, Pedersen/Satchell,
1998, Albrecht/Maurer, 2005 and Brandtner, 2012.
See Pedersen/Satchell, 1998.
See Gleißner, 2010 and Friedrich, 2015 and 2016 and Lahmann/
Schreiter/Schwetzler, 2018.
Business Valuation OIV Journal Spring 2019 11
Company valuation as result of risk analysis
Volume 1 - Issue 1
Graph 2: Implications of a probability of defaults (p=2%)
In the long term - in the continuation phase – phas
the effect of a negative growth rate
(see graph 2),
which must be taken into account when calculating
the terminal value (TV)
. This applies here:
This also applies if cost of capital or discount rates
(c) are calculated according to the CAPM.
With a growth rate
(g), the (conditional) expected
values of the cash flows Eð
and a discount rate
(c), the following equation results for the company
value (Value) in the continuation phase (terminal va-
lue) as a function of the insolvency probability (p)
The value of a company (or its terminal value) with
g= 0 is then:
When determining an infinite series (Gordon Shapiro
model), the insolvency probability (just like the growth
rate) actually appears in the numerator in each indivi-
dual period (see equation (17)). However, the dissolu-
tion of the series leads to the fact that the probability of
insolvency (as well as the growth rate) mathematically
‘‘migrates’’ into the denominator. This does not mean,
however, that double counting would occur or that the
probability of insolvency would become a component of
the discount rate. In the continuation phase, the prob-
ability of insolvency thus largely acts like a ‘‘negative
growth rate’’ - but is not part of the cost of capital.
Anyone who accepts the recording of a growth rate in
the terminal value must also accept the consideration of
the probability of insolvency derived from the same
assumption system. The above-mentioned ‘‘pragmatic’
recording of the possibility of insolvency within the
framework of the usual (deterministic) ‘‘terminal value
formula’’ is not without alternatives. A more precise
recording of the risks and stochastic dependencies, also
between the individual periods, can be achieved e.g. by
binomial models (Friedrich, 2015)
and especially by
flexible stochastic planning models and Monte Carlo
simulation. When calculating the expected values in
the simulation, the insolvency scenarios are recorded
and a closed ‘terminal value formula’’ is practically un-
necessary if one simulates many years of the future.
Nevertheless, as explained above, pragmatic solutions
certainly also have practical advantages.
See Shaffer, 2006, Gleißner, 2010; Knabe, 2012; Saha/Malkiel,
2012; Ihlau/Duscha, 2019.
See Gleißner, 2017c, Knabe,2012andSaha/Malkiel, 2012 and
Lahmann/Schreiter/Schwetzler, 2018.
On the relationship between wand cin inflation-, accumulation-
and tax-indexed (endogenous) growth see Tscho
sen, 2010.
Without insolvency (conditional expected value) and period-in-
variant probability of insolvency (here for T, i.e. after detailed planning
CF Þis the expected value of growth and probability of insol-
vency. If Eð
CF Þis interpreted as cash flow before probability of in-
solvency, (1 + g) is omitted.
In addition, one can immediately see with binomial models by
Friedrich, 2015, that, as is usual with such (simple) binomial models, no
negative free cash flows can occur, which is unrealistic. Insolvencies
naturally occur especially with negative free cash flows. The impossi-
bility of depicting negative cash flows in the simple binomial model
results from the fact that in the binomial tree the last cash flow is
multiplied by 1.4 (up scenario) with a previously given probability
(e.g. p= 60%) or by 0.8 (down scenario) with a probability of (1 - p).
12 Business Valuation OIV Journal Spring 2019
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Company valuation as result of risk analysis
6. Case study: From CAPM to risk-adequate assess-
6.1 Introduction
The explanations above will be illustrated in the
following with a small example. The transition from
‘‘traditional’’ planning, which here is based on the
assumption of (ambitious) planned values of the com-
pany and discount rates calculated using CAPM, takes
place in three steps.
1. The systematic analysis of existing risks allows a
transparent reconciliation of the usual planned values
with the expected values relevant to valuation, which
will be realised ‘‘on average’’. This creates transparency
with regard to the essential, even uncertain planning
assumptions and an adequate consideration of a risk
2. The probability of insolvency expressed by the
rating can be assessed by means of a key financial
figures rating and the evaluation of combined effects
of risks (Monte Carlo simulation). The often ignored
value driver ‘‘probability of insolvency (insolvency
risk)’’ is taken into account in the implications for
the company value and thus takes into account the
fact that, contrary to the usual assumption, companies
do not exist forever (see section 5).
3. The transparency created by risk analysis and risk
simulation (risk aggregation) with regard to planning
security and thus the aggregated cash flow risk (cash
flow volatility) makes it possible to derive risk-adjusted
cost of capital. Expected values of cash flows (‘‘nu-
merator’’) and discount interest rate (‘‘denominator’’)
are thus determined consistently and the problems of
the low informative capacity of CAPM cost of capital
(due to capital market imperfections) are avoided.
This enables a risk-adjusted valuation, i.e. a calcula-
tion taking into account the risks of a company’s future
earnings and cash flows.
6.2 Initial Situation: CAPM and planning values
(corporate planning)
The valuation of the company is based on a two-year
detailed planning period (t = 1,2) whereby the second
period is regarded as representative for the future
The enterprise has planned the cash flow to equity
to be discounted. The long-term growth rate is as-
sumed to be g= 0 and insolvency risks are neglected.
The following assumptions are made about the para-
meters of the environment:
= 3% (for all periods)
m¼5% (market risk premium)
ß= 0.75 (calculated with a market price of the risk
From the information provided, the following time-
invariant cost of capital results.
The following applies to the value
Table 1: Company valuation based on planned values and
T 1 2 TV NPV of
the cash
and TV
Cash flow
10 15 (15 ...)
c (CAPM, Beta) 6.75% 6.75% 6.75%
Value 9.37 13.16 195.01
On the basis of the cash flows and terminal value
shown in table 1, the company value is calculated as
6.3 First step: Transfer from plan values to expected
The discounted cash flow methods are based on ex-
pected cash flows. In order to calculate these, the re-
sults of the analysis of chances and risks of the com-
pany are used. In particular, uncertain planning as-
sumptions, which form the basis for the cash flow fore-
cast in table 1, are considered and described using
appropriate probability distributions. Without further
explanation of details, it is assumed that risk analysis
and risk aggregation (Monte Carlo simulation) result
in a threats overhang and thus lower expected values
compared with the planned values.
All other information is unchanged, i.e. the cost of
capital rate c= 6.75% derived from CAPM is still
used. The Monte Carlo simulation also produces a
quantification of the cash flow risk, in the example
here a coefficient of variation of V= 0.35, which,
however, is not (yet) included in the valuation (see
step 3 in 6.5).
For t = 3, 4, ..., 8.
It shall apply to company i: c¼rfþiwith ias the
standard deviation of the stock return of i.
The present value in t = 0 of the TV in t = 2 is 195.01 = 15 /
((0.0675)(1 + 0,0675)
Business Valuation OIV Journal Spring 2019 13
Company valuation as result of risk analysis
Volume 1 - Issue 1
Table 2: Company valuation based on expected values and
T 1 2 TV NPV of
the cash
and TV
Cash flow
10 15 15
Cash flow
c(CAPM, Beta) 6.75% 6.75% 6.75%
Value 8.43 11.41 169.01 188.85
Taking into account the effects of the opportunities
and threats on the expected value of the cash flows,
the resulting value is now Value
= 188.85
6.4 Second step: Consideration of the effects of
insolvency risk
In step 1, the company’s earnings risks were taken
into account. However, no account was taken of the
fact that risk-related future scenarios could arise for
the company, which could lead to insolvency and
thus to the discontinuation of the cash flows for
the owners (as the valuation subject). Now it is ta-
ken into account that insolvency risks influence
both the expected value of the cash flows in each
period of the detailed planning phase and the ex-
pected value in the continuation phase (t > 2).
Further effects of the insolvency risk, e.g. on the
tax shield, are neglected. It is also assumed that
the implications of the probability of insolvency p
expressed by the rating are already included in the
interest rates and thus in the cost of debt (and thus
in the expected values of the cash flows). In general,
it is also necessary to adjust interest rates and cost of
debt to the rating.
In the case study, the probability of insolvency pis
estimated based on financial ratios, i.e. equity ratio
25% and return on capital employed 10%. (The
Monte Carlo simulation carried out for risk aggrega-
tion serves to check the plausibility of the probability
of insolvency). Furthermore, an insolvency probability
of p= 1.55% is assumed
This results in the following company valuation:
Table 3: Company valuation based on expected values,
CAPM, and insolvency risk
T 1 2 TV NPV of
the cash
and TV
Cash flow
10 15 15
Cash flow
of survival
98.45% 96.92% 95.42% sinking
with p
Cash flow
(expected, incl.
insolvency risk)
8.86 12.60 12.40
c (CAPM, Beta) 6.75% 6.75% 6.75%
Value 8.43 11.41 131.15 150.51
The company value is reduced to Value
= 150.51
Euro due to the consideration of insolvency risk.
6.5 Third step: Calculation of cost of capital based on
earnings risk (coefficient of variation of earnings)
As already mentioned, the coefficient of variation of
the returns is - according to the simulation - V= 35%.
The risk diversification factor here is d= 0.5, which
corresponds precisely to the correlation between the
return on the shares of the valuation object and the
return on the market portfolio.
With the results from risk analysis and risk simula-
tion in step 1, the coefficient of variation of the returns
was calculated in addition to the adjustment of the
planned values, but has not yet been taken into ac-
count. The coefficient of variation is a measure of the
overall scope of risk (extent of possible deviations from
the plan) With equation (15) explained above, infor-
mation about the risks of the company - instead of
information about the risks of the company’s shares -
is now used as the basis for deriving the discount rate.
The following applies accordingly
In this third step, the company value is now deter-
mined with a cost of capital ccorresponding to the
earnings risks.
It is based on an empirically determined simple formula for esti-
mating the probability of insolvency
(see Gleißner, 2017a, pp. 336-
338 with reference to the basic research projects).
14 Business Valuation OIV Journal Spring 2019
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Company valuation as result of risk analysis
Table 4: The final valuation
T 1 2 TV NPV of
the cash
and TV
Cash flow
10 15 15
Cash flow
of survival
98.45% 96.92% 95.42% sinking
with p
Cash flow
(expected, incl.
insolvency risk)
8.86 12.60 12.40
c(earnings risks
7.71% 7.71% 7.71%
Value 8.23 10.86 115.47 134.56
The resulting value is now Value
= 134.56 Euros.
Now the information on the risk profile of the com-
pany as a whole is adequately taken into account in
the company valuation. It should be mentioned that
the adjustment according to steps 1 and 2 is also ne-
cessary if the valuation of perfect capital markets and
in particular the validity of the assumptions of the
CAPM are assumed.
In the example, in comparison to the initial situa-
tion, the enterprise value decreases with every further
step. This is not necessarily the case. Thus, there are
constellations in which existing opportunities out-
weigh existing dangers and thus the expected value
is higher than a (conservative) plan value. The con-
sideration of the probability of insolvency (p), contrary
to the first impression, does not necessarily lead to a
lower enterprise value. This is because, in valuation
practice, the growth rate g applied in view of economic
growth for a company’s long-term profit growth (in the
continuation phase) is implicitly offset by a ‘typed’
probability of default ðp
Empirical studies
show typical growth rates in the
order of 0 to 0.5% in the continuation phase. This is
much less than the inflation rate alone (excluding real
economic growth) and can only be explained by as-
suming it as an ‘‘insolvency-risk-adjusted’’ growth rate
with a typical probability of insolvency (of, for exam-
ple, 1%) already deducted. The implication for the
valuation of different companies is clear: if implicit
(and non-transparent) is valued with a medium prob-
ability of default, which is offset against the growth
rate, it leads to advantages and disadvantages for cer-
tain companies: companies with a below-average prob-
ability of default have a higher value compared with
the traditional approach. The approach tends to be too
low, while those with an increased probability of de-
fault are too high. Campbell,Hilscher and Szilagyi
(2008) show, for example, that companies with a very
good rating on the stock exchange generate above-
average returns that can be explained if one assumes
that the probability of default is ignored, especially in
the valuation calculus of most capital market partici-
pants, and thus ‘‘quality companies’’ with a very good
rating tend to be undervalued and accordingly gener-
ate above-average risk-adjusted returns).
7. Summary and outlook
In practice, there are many problems with the valua-
tion of companies, for example due to the often un-
justified assumption of perfect capital markets. With
risk analysis, Monte Carlo simulation and the method
of incomplete replication, instruments exist that take
account of the imperfections of the capital market and
can also be applied to companies that are not listed on
the stock exchange. The valuation-relevant risks are
derived by means of risk analysis and risk aggregation,
and planning consistency - e.g. via standard deviation
or VaR as risk measure - is recorded in the valuation,
whereby financing restrictions of the creditors can be
taken into account. The detour of obtaining risk in-
formation from historical stock returns - instead of
from the company itself - is avoided.
Even if CAPM-based valuation is to be applied, the
‘‘risk discount variant of CAPM’’ and the information
provided by the risk analysis can be used to ensure that
the appraiser is not dependent on historical stock re-
turns that are often missing or not representative for
the future. In this respect, the valuation approach also
contributes to a new (more accurate) interpretation of
the paradigm of value orientation (value based man-
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owners, but use of the best available information -
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18 Business Valuation OIV Journal Spring 2019
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Company valuation as result of risk analysis
... Dorfleitner, Gleißner (2018) Introducing theoretical basis and formal framework (incomplete replication approach) for simulation-based valuation Gleißner, Ernst (2019) The mentioned literature agrees on the flaws of traditional valuation models and on the necessity to develop better valuation models. Dorfleitner and Gleißner (2018) set the theoretical framework of a new valuation approach where risky cashflows can be valued without the restrictions from the CAPM. ...
... Dorfleitner and Gleißner (2018) set the theoretical framework of a new valuation approach where risky cashflows can be valued without the restrictions from the CAPM. Gleißner and Ernst (2019) show a first practical example and explain the difference to traditional models. Gleißner (2020) includes insolvency risk and Dorfleitner (2020) develops the framework to calculate the terminal value. ...
... Valuation practitioners are used to display the risks within the capital costs. Gleißner and Ernst (2019) and Ernst (2022) show how to derive the risk premium method, which then gives the same result as the certainty equivalent approach. The capital costs then are, contrary to the CAPM, not solely market oriented. ...
... Simulation-based business valuations have been in discussion for some time as an alternative to the CAPM-based business valuation (see Gleißner and Ernst 2019 for an English summary of the research and the literature cited there). The simulation-based business valuation has the advantage of capturing the company-specific risk position by means of an unbiased planning (Gleißner 2021). ...
... Due to the increasing imperfections in capital markets and the growing influence of risk management in companies, some valuation approaches have burgeoned in the recent years that, on the one hand, derive the risk scope of companies through risk analysis, and on the other hand, take into account the imperfections of real markets. These approaches include investment-theoretical valuation theory (Smith 1998;Hazen 2009 for extensive references) and simulation-based valuation theory (Gleißner and Ernst 2019 and the literature cited there). The investment-theoretical valuation theory assumes that the preferences of a decision-maker can be described as a neoclassical decision function. ...
... It has not yet been shown how the connection to the DCF models used in the valuation practice can be established. Gleißner and Ernst (2019) describe important basics of the simulation-based valuation and demonstrate them with a simple example, which, however, does not answer questions of implementation in a concrete valuation example. Furthermore, they do not discuss which formulas are used in the certainty equivalent method and the risk premium method to arrive at identical company values. ...
Full-text available
The simulation-based company valuation values a company on the basis of the risks actually present in the company without having to derive them from the capital market data. The simulation-based company valuation takes into account the market imperfections, such as the probability of insolvency or the lack of diversification, and fulfils the legal requirements and auditing standards for a company valuation. The simulation-based company valuation is an alternative to the CAPM-based company valuation, which, under the assumption of perfect capital markets, derives the risks through capital market comparisons. A simulation-based business valuation has many advantages and is particularly suitable for valuing medium-sized companies, start-ups, companies in a crisis, and for integrating country-specific risks into business valuations. Due to the internationally widespread use of the CAPM, a simulation-based company valuation is still rarely used in practice. This article shows which valuation formulas are necessary for the application of a simulation-based company valuation. These are used for both the certainty equivalent method and for the risk premium method. In a concrete and valuation example, the simulation-based business planning and company valuation is carried out, and the derived valuation formulas are applied in a way that allows a transfer to concrete valuation cases in practice. It is shown that the certainty equivalent method and the risk premium method lead to identical company values.
... A company basically has several different options for conducting the risk assessment process. The risk of a company can either be derived from an outsideoriented risk analysis on the capital market or determined internally with respect to the specific risks actually carried by the company (Gleißner and Ernst, 2019;Ernst, 2022bErnst, , 2023. The last approach in particular is attracting increasing interest, especially in Europe, and the approaches are being increasingly refined and implemented in tools for corporate planning (Ernst and Gleißner, 2022b). ...
... The basic idea for the latter is to model the tail region with the GPD, see Appendix B, and then derive statements about the risk. Key risk indicators in corporate planning are usually known: value-at-risk, conditional value-at-risk, risk coverage potential, risk bearing capacity, and risk tolerance (Gleißner and Ernst, 2019;Ernst, 2022bErnst, , 2023. Many of the risk indicators mentioned can be derived from quantiles, so we will focus on the calculation of quantiles and briefly distinguish three methods for determining quantiles and assessing tail risks. ...
Recently, simulation-based methods for assessing company-specific risks have become increasingly popular. This is because modern capital market theory, with its assumptions of perfect and complete capital markets, cannot satisfactorily explain the risk situation in companies and its effects on entrepreneurial success. Through simulation, the individual risks of a company can be aggregated and the risk effect on a target variable can be shown. The aim of this article is to investigate which statistical methods can best assess tail risks in the overall distribution of the target variables. By doing so, the article investigates whether extreme value theory is suitable to model tail risks in a business plan independent of company-specific data. For this purpose, the simulated cash flows of a medium-sized company are analyzed. Different statistical ratios, statistical tests, calibrations, and extreme value theory are applied. The findings indicate that the overall distribution of the simulated cash flows is not unimodal in many cases. In the example studied, the potential loss side of the cash flow exhibits a superimposed, well-delimitable second distribution. This tail distribution is analyzed extensively through calibration and the application of extreme value theory. Using the example studied, it is shown that similar tail risk distributions can be modeled both by calibrating the simulation data in the tail and by using extreme value theory to describe the tail. This creates the possibility to work with tail risks even if they have not been explicitly modeled by simulation. Thus, this approach contributes to systematically combining risk management and corporate finance and to significantly improving corporate risk management. Based on these findings, further analyses can be performed in terms of risk coverage potential and rating to improve the risk situation in a company.
... The simulation-based approach has been presented and discussed in the literature (Dorfleitner and Gleißner (2018), Ernst (2022), Gleißner (2011Gleißner ( , 2017Gleißner ( , 2019Gleißner ( , 2021, Ernst and Gleißner (2022a), Gleißner and Ernst (2019)). The approach, which was initially developed in Germany, is now also receiving increased international recognition and attention (see Ernst (2022), Ernst and Gleißner (2022a) and Ernst and Gleißner (2022b)); for a classification of the contribution by Ernst (2022) in the international state of research, see Sinnadurai (2022). ...
... Initially, a simulation-based valuation does not imply a commitment to a specific theoretical framework for valuation. If one chooses, as is common practice, a semi-investmenttheoretic valuation uses "imperfect replication" (Dorfleitner and Gleißner 2018;Gleißner 2011Gleißner , 2019; then, all market constellations resulting from a high degree of market imperfection can be modeled as perfect and complete capital markets (including the CAPM as a special case) (Gleißner and Ernst 2019). Accordingly, different degrees of diversification can also be modeled. ...
Full-text available
Simulation-based company valuations are based on an analysis of the risks in the company to be valued. This means that risk analysis is decisively important in a simulation-based business valuation. The link between risk measures, risk conception and risk axiom systems has not yet been sufficiently elaborated for simulation-based business valuations. The aim of this study was to determine which understanding of risk underlies simulation-based business valuations and how this can be implemented via suitable risk measures in simulation-based business valuations. The contribution of this study is providing guidance for the methodologically correct selection of appropriate risk measures. This will help with avoiding valuation errors. To this end, the findings were combined from risk axiom systems with the valuation equations of simulation-based business valuations. Only position-invariant risk measures are suitable for simulation-based business valuations.
... Currently, CAPM-based company valuations have come under increasing criticism from practitioners, academics, and courts. The reason for is that they do not offer any decision-making support in a world of imperfect markets and transformations (Ernst 2022;Gleißner and Ernst 2019). The world of business valuation is undergoing a period of upheaval. ...
... The derivation of the valuation equation is based on the idea of risk-value models (Sarin and Weber 1993;Spremann 2004) and the method of "imperfect replication" (Dorfleitner 2020; Dorfleitner and Gleißner 2018;Gleißner 2011Gleißner , 2019Gleißner and Ernst 2019). A central assumption is made here: the same risk measure (R) and the same expected value of payments at the same time imply an identical value. ...
Full-text available
In the capital market and financing theory, we are currently observing major upheavals. For decades, the neoclassical paradigm has dominated in science and practice. Triggered by economic and political crises, transformations, the COVID-19 pandemic, and political instabilities, a paradigm shift is currently occurring in finance. This paradigm shift leads to models and theories that can explain imperfections in capital markets and provide decision support for managers. The aim of this article is to analyse the paradigm shift and to demonstrate it using an example of business valuation theory. We draw on the insights of the philosopher Thomas Samuel Kuhn. He vividly explains the paradigm shift in science in his major work “The Structure of Scientific Revolutions”. A paradigm shift in science always encounters resistance. The reasons for this include the strong neoclassical school in finance and the dependence on research funds. Funders expect the use of established methods and the simplicity and dissemination of the models that have prevailed so far. On the other hand, the neoclassical models are unsuitable to explain the transformation processes on financial markets. This fact has been empirically proven. We show a variety of arguments that speak clearly about this paradigm shift. Their importance clearly outweighs the reasons to continue subscribing to the old paradigm. Accordingly, new theories and models have been developed to better explain the changes in the markets. With the simulation-based business valuation, an approach has been developed that considers different degrees of market imperfections. The simulation-based valuation can also depict the special case of the neoclassical paradigm, so that all market constellations can be covered.
... See Gleißner, 2010 and2015;Saha/Malkiel, 2012 as well as Franken/Gleißner/Schulte, 2020 14 See for the derivation from the risk aggregationGleißner, 2019. 15 See alternatives to a simulation-based assessment Gleißner/Ernst, 2019;Ernst 2022 and Gleißner, 2017. 16 SeeGleißner/Follert, 2022 andDorfleitner/Gleißner, 2018 to the theoretical basis of the valuation. ...
Full-text available
Simple DCF analysis based on the CAPM lead to strongly distorted, often significantly inflated, company values. A proper valuation requires more than the application of the usual simple "recipes". For example, a systematic identification, quantification and aggregation of risks is necessary in order to be able to map the effects of existing opportunities and threats on the expected value of cash flows and earnings. The discount rates should reflect the riskiness of the cash flows relevant to the valuation. And the insolvency risks, which leads to a finite life expectancy of a company, must be considered in the valuation. All these aspects are considered in a simulation-based valuation.
... Gleißner, 2011Gleißner, und 2019Dorfleitner/Gleißner, 2018), können alle Marktkonstellationen von einem hohen Grad an Marktunvollkommenheit bis zu einem vollkommenen und vollständigen Kapitalmarkt (auch das CAPM als Spezialfall) modelliert werden (vgl. Gleißner/Ernst, 2019). Die aus der Monte-Carlo-Simulation resultierenden Häufigkeitsverteilungen werden bei der simulationsbasierten Bewertung jeweils auf den Erwartungswert verdichtet und das Risiko der Cashflows durch ein Risikomaß, wie Standardabweichung oder Value-at-Risk, ausgedrückt. ...
Full-text available
Die simulationsbasierte Unternehmensbewertung ist eine Alternative zur CAPM-basierten Unternehmensbewertung. Sie bewertet ein Unternehmen aus Basis der im Unternehmen tatsächlich vorhandenen Risiken, ohne diese über Kapitalmarktdaten ableiten zu müssen. Die simulationsbasierte Unternehmensbewertung kann Marktunvollkommenheiten wie die Insolvenzwahrscheinlichkeit oder mangelnde Diversifikation berücksichtigen und erfüllt die gesetzlichen Anforderungen (z.B. StaRUG) und Prüfungsstandards (z.B. IDW PS 340) an eine Unternehmensbewertung.
Objective – This paper aims to examine the theoretical and practical aspects of the widely used discounted cash flow (DCF) valuation method. Methodology – The proposed method is probably the most widely used approach in the valuation of unlisted companies. It involves estimating the future cash flows that the company is expected to generate and discounting them to their present value using a discount rate. The study was conducted on Spanish olive oil companies between 2005 and 2020. Findings – Our results show that there are two values for valuing companies: static and dynamic values. Both values are calculated based on the sum of the updated cash value plus the remaining value. The static value provides only one value, while the dynamic value provides a range of values, resulting in a more accurate understanding of a company's value and a better comprehension of the risks associated with that value. Therefore, the company is considered a cash flow generator, and the value of the company is found by calculating the present value of these flows using an appropriate discount rate. Novelty – Despite this method being a powerful tool for evaluating companies, even in complex situations, the DCF method is subject to a significant assumption bias, and even slight changes in the underlying assumptions of the analysis can greatly alter the evaluation results. Type of Paper: Empirical JEL Classification: G12, G31, M21 Keywords: Cash flow; Unlisted companies; Valuation methods; Discounted Cash flow Reference to this paper should be made as follows: DRISSI, R. (2023). Empirical Analysis of Unlisted Companies' Valuation Using Discounted Cash Flow Methods, J. Fin. Bank. Review, 8(1), 73 – 84.
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Taking into account expected return characteristics like firm size and book-to-market in the selection of winners and losers helps to ex ante separate stocks with momentum from those that exhibit reversal in international equity markets. A strategy that buys small value winners and sells large growth losers generates significantly larger momentum profits than a standard momentum strategy, is robust to common return controls, and does not suffer from return reversals for holding periods up to 3 years. The superior performance of the strategy is attributable to a rather systematic exploitation of cross-sectional mispricing among momentum stocks. (Look inside via Springer Nature SharedIt:
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We propose a method to estimate the cost of debt in a continuous-time framework with an infinite time horizon. The approach builds on the class of well-known earnings before interest and taxes (EBIT)-based models. It extends other approaches based on option-pricing theory with a finite one-period horizon. The model is capable of splitting the observed yield spread of a corporate bond into the risk premium, which adds to the expected return of bondholders, and the default premium, which accounts for expected losses. The model can easily be calibrated for non-public firms, since most of its input parameters are readily observable, while the output, the model-implied cost of debt, proves to be very insensitive with respect to the remaining non-observable parameters, the EBIT growth rate, and the bankruptcy costs of the firm. We demonstrate the applicability of the cost of debt to calculate an approximate weighted average cost of capital for the purpose of firm and project valuation, and its usage and limitations.
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We provide further evidence that markets trend on the medium term (months) and mean-revert on the long term (several years). Our results bolster Black's intuition that prices tend to be off roughly by a factor of 2, and take years to equilibrate. The story behind these results fits well with the existence of two types of behaviour in financial markets: "chartists", who act as trend followers, and "fundamentalists", who set in when the price is clearly out of line. Mean-reversion is a self-correcting mechanism, tempering (albeit only weakly) the exuberance of financial markets.
Die vorliegende Studie überträgt die Erkenntnis eines inversen Rendite/Risiko-Zusammenhangs von der Volatilitätsanomalie auf die Fundamentalebene der Unternehmung. Erstens, Unternehmen mit niedrigem Leverage und niedriger Gewinnfluktuation weisen über die Zeit eine persistent höhere bilanzielle Profitabilität auf. Zweitens, Unternehmen mit niedrigen Fundamentalrisiken (niedrigem Leverage und niedriger Gewinnfluktuation) schneiden risikoadjustiert signifikant besser ab als der Markt und Unternehmen mit hohen Fundamentalrisiken. Drittens, die festgestellte Outperformance kann nicht durch gängige Kapitalmarktmodelle wie dem CAPM oder Fama-French-Modell erklärt werden, so dass von einer Fundamentalrisikoanomalie auf dem deutschen Aktienmarkt auszugehen ist. (in: Corporate Finance biz, 03/2013, 119-123.)
The success of a company basically depends on the quality of entrepreneurial decisions taken by the executives, which means that the systems and tools for preparing such decisions are critical success factors for the quality of decisions itself. A company’s management systems and especially its procedures for preparing decisions therefore must be in a position to enable the decision makers to weigh possible returns against the associated risks as only focusing on the returns could lead to misjudgements. By doing so, it is necessary to not only predict the possible implications of a decision on the company’s future earnings, but also on the rating grade and on the company’s value as a measure of success. When a decision is being prepared, their effects on enterprise value and rating grade must be made transparent as part of the decision-making. We argue that this is done best by means of integrated management systems which, in particular, link management control and risk management. The methodology behind are simulations based on the risks analysed and modelled in the context of the planning.
Based on risk-value models, we introduce a multiperiod approach to the valuation of streams of risky cashflows. The valuation is based on the (expected) value of the output’s or input’s magnitude and the risk of the output cashflow, as captured by a risk measure. We derive three formulas for valuing single cashflows and utilize the principles of separate valuation and of cumulating the cashflows to derive a multiperiod valuation method. In an axiomatic way, the paper sets out the foundations for a new approach and suggests several directions for its further development.