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Company valuation as result of risk analysis:

replication approach as an alternative to the

CAPM

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

1

company va-

luation has to be questioned due to many imperfec-

tions

2

of the capital market

3

. 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

4

. 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

5

, return on equity

or company-specific risks) are taken into account in

the valuation models

6

. This leads to a replacement of

capital market-oriented valuation approaches with

procedures that - in the tradition of investment theo-

retical valuation approaches

7

- 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

8

. 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-

ket).

In contrast to pure investment theoretical methods

9

,

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

¨t

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”.

1

I.e. financial theoretical.

2

See the overview of empirical studies at Gleißner, 2014.

3

Hering 2014.

4

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.

5

Esp. of assets (see Chen/Novy-Marx/Zhang, 2011 and Fama/French,

2015.

6

See Ang et al 2006 and 2009; the empirical studies (and alternative

models) at Fama/French, 2015; Kaserer/Hanauer, 2017; Walksha

¨usl,

2013; Zhang, 2009.

7

See Matschke/Bro

¨sel, 2013 and Hering, 2014.

8

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.

9

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

n

Volume 1 - Issue 1

cially by means of a simplex algorithm)

10

. In the tradi-

tion of risk-value models

11

, 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)

12

. 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

13

. 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

statements.

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

14

. 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’’

15

(in the case of the risk premium

method) or ‘‘in the numerator’’ (in the case of the risk

discount method)

16

.

It should be noted that risks potentially affect (1) the

expected value of the cash flow Eð

f

CF ) and (2) the

cost of capital

17

at the same time. The effect of a risk R

is simplistically shown in graph 1.

10

The evaluation is understood as a comparison procedure and not

as an optimization procedure.

11

See Sarin/Weber, 1993.

12

This is why the term ‘‘semi-investment theory approach’’ is also

used here, see Gleißner, 2011.

13

See Bamberg/Dorfleitner/Krapp, 2006 and the overview at Schosser/

Grottke, 2013.

14

See Moxter, 1983 and Dehmel/Hommel, 2017.

15

Which is not recommended (see Spremann, 2004).

16

See especially how to deal with insolvency risks that lead to a

termination of the cash flow to the owner, Gleißner, 2017c.

17

By means of a risk discount in the numerator or a risk premium r

z

in the interest rate in the denominator.

4Business Valuation OIV Journal Spring 2019

Volume 1 - Issue 1

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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

18

. The

unrealistic assumptions of a perfect (or complete) ca-

pital market, as in financial theory valuation methods,

are not required

19

.

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

20

. 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 (

f

CF ), i.e. the extent of

possible deviations from the expected value ðEð

f

CF Þ)

can be considered in the following two ways

using the risk premium method, i.e. the calcula-

tion of the cost of capital

21

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

CF

)

is added to the risk-free interest rate (r

f

). This results in

a discount rate (c) (approximately the cost of capital)

for discounting the expected future cash flows

22

. The

formula for the discount rate is as follows:

(1)

r

CF

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

f

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

CF

.

The value of a risky cash flow (

f

CF1) at time t = 0 is

obtained by discounting the expected value Eð

f

CF1)

with the cost of capital c:

(2)

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

23

. This can be ex-

plained as follows. The basic idea behind discounting

18

And generally not consistent with the valuation-relevant risk

scope of the cash flow.

19

See Ballwieser, 2008; see also the criticism at Dempsey, 2013;

Gleißner, 2014; Hering, 2014 and Ferna

´ndez, 2013 und 2017.

20

I.e. free cash flows or flows to equity.

21

This approach is usually applied in business valuation practice.

22

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).

23

See Spremann, 2004, p. 253.

Business Valuation OIV Journal Spring 2019 5

Company valuation as result of risk analysis

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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

24

. It is therefore

advisable to use the certainty equivalence method,

which provides correct valuations

25

.

3.2 Certainty equivalence method

The certainty equivalence method is based on the

following equation:

(3)

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

f

CF )

26

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

f

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

if

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:

(4)

with as correlation coefficient of the uncertain

cash flow and the uncertain return of the market

e

rm;ð

f

CF ) as standard deviation of the expected cash

flows (scope of risk expressed in monetary units) and

re

m¼Eðe

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

f

CF1and the uncertain return of the market e

rM

(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

replication

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)

27

. 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

24

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.

25

For derivation see Gleißner/Wolfrum, 2009.

26

It is worth to mention that a risk measure Rð

f

CF Þe.g. ð

f

CF Þis

not necessary if it is intended to get implied cost of capital (Bini, 2018).

27

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

28

risk-free invest-

ment with an interest rate r

f

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

flow

f

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

29

with an uncer-

tain return e

rMand

- a risk-free investment with the interest rate r

f

.

It is important to note that in contrast to CAPM or

valuation methods based on the assumption of an ar-

bitrage-free capital market

30

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

31

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-

rage-free

32

. 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

33

.

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

f

CFA. The risk is measured by a suitable risk measure

Rð

f

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

28

At least, so to speak.

29

This is an ‘‘empirical’’ market portfolio (like a stock market in-

dex). Not necessarily the theoretical market portfolio based on the

CAPM-Assumptions.

30

No-arbitrage conditions.

31

At least, so to speak.

32

See for an explanation of the terms and their relationship,

Friedrich, 2015, pp. 13.

33

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

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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

34

.

(5)

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

Eð

f

CFAÞ.

(6)

The value of the risky cash flow

f

CFAcorresponds to

the sum of the two investments xand y. The same risk

and the same expected value imply the same value.

(7)

The replication equation can be derived from equa-

tions (6) and (7)

35

.

(8)

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

f

CFAÞ¼Eð

f

CFAÞþVaR

ð

f

CFAÞ

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-

tance.

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)

36

. This applies to

these (see Rockafellar/Uryasev/Zabarankin, 2002):

(9)

With equation (9) equation (8) simplifies to

(10)

For the value one obtains by transformations (and by

neglecting a time index)

37

(11)

with

A special variant of equation (3) has thus been de-

rived

38

. 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

value-at-risk).

Now assume the risk measure Rð

f

CF Þis the standard

deviation and so Rðaþb

f

CFA¼bð

f

CFAÞ. Now

the following equation shows how is the value of the

cash flow

f

CFA.

(12)

The cost of capital (c) is thus implicitly the ratio of

the cost of Eð

f

CFAÞto V alue0ð

f

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

f

CF ; e

rMÞ, so that the following equation re-

sults:

(13)

Equation (14) corresponds to the certain equiva-

lence equation of the CAPM (3)

39

. The following

conditions apply:

34

Position-independent. See Dorfleitner/Gleißner, 2018.

35

See Dorfleitner/Gleißner, 2018.

36

See Dorfleitner/Gleißner, 2018 for translation- invariant risk mea-

sures.

37

f

CF ¼

f

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.

38

See Gleißner/Wolfrum, 2009.

39

See Robichek/Myers, 1966; Rubinstein, 1973.

8Business Valuation OIV Journal Spring 2019

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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

f

CFAÞ¼AÞ.

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

40

.

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

ð

f

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:

(14)

If one resolves this equation with equation (14) for

the value Vafter c, one obtains the risk-adequate cost

of capital. If

f

CF is the operating free cash flow

(oFCF), cis the weighted cost of capital (WACC));

if

f

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

41

:

(15)

The ratio of cash flow risk ð

f

CFAÞto expected cash

flow Eð

f

CFAÞis the coefficient of variation V. The

variable shows the excess return per unit of risk

(Sharpe Ratio).

(16)

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)

42

.

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

43

. 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

f

CFA.Ifflowtoequityisusedascash

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

40

See Dorfleitner/Gleißner, 2018.

41

For

42

It is the proportion of Rð

f

CF Þto additional (‘‘incremental’’) risk

in the portfolio of the owner caused by the company (see Gleißner,

2011 and Tasche/Tibiletti, 2003).

43

‘‘Risk factor model’’; see Gleißner, 2017a, pp. 261-263.

Business Valuation OIV Journal Spring 2019 9

Company valuation as result of risk analysis

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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

1

for the detailed planning period

and a cost of capital c

2

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

Rð

f

CF Þ

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

risks

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

risks

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

44

.

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

45

. 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

uncertainty.

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

e

X, but to a centered random variable

e

XEð

e

XÞ, the result is a position-independent risk

measure

46

. 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-

cordingly:

positive homogeneity (PH) is defined by

Rða

e

XÞ¼aRð

e

XÞ,

translation invariance (TI) is defined by

Rð

e

XþaÞ¼Rð

e

XÞa,

position invariance (PI) is defined by

Rð

e

XþaÞ¼Rð

e

XÞ

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

47

.

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.

44

See Grisar/Meyer, 2015 and 2016 on significance.

45

See cf. Gleißner, 2017a and Artzner et al., 1999, Pedersen/Satchell,

1998, Albrecht/Maurer, 2005 and Brandtner, 2012.

46

See Pedersen/Satchell, 1998.

47

See Gleißner, 2010 and Friedrich, 2015 and 2016 and Lahmann/

Schreiter/Schwetzler, 2018.

Business Valuation OIV Journal Spring 2019 11

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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

48

(see graph 2),

which must be taken into account when calculating

the terminal value (TV)

49

. This applies here:

(17)

This also applies if cost of capital or discount rates

(c) are calculated according to the CAPM.

With a growth rate

50

(g), the (conditional) expected

values of the cash flows Eð

f

CF Þ

51

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)

52

:

(18)

The value of a company (or its terminal value) with

g= 0 is then:

(19)

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)

53

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.

48

See Shaffer, 2006, Gleißner, 2010; Knabe, 2012; Saha/Malkiel,

2012; Ihlau/Duscha, 2019.

49

See Gleißner, 2017c, Knabe,2012andSaha/Malkiel, 2012 and

Lahmann/Schreiter/Schwetzler, 2018.

50

On the relationship between wand cin inflation-, accumulation-

and tax-indexed (endogenous) growth see Tscho

¨pel/Wiese/Willershau-

sen, 2010.

51

Without insolvency (conditional expected value) and period-in-

variant probability of insolvency (here for T, i.e. after detailed planning

phase).

52

Eð

f

CF Þis the expected value of growth and probability of insol-

vency. If Eð

f

CF Þis interpreted as cash flow before probability of in-

solvency, (1 + g) is omitted.

53

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-

ment

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

overhang.

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

54

.

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:

r

f

= 3% (for all periods)

re

m¼5% (market risk premium)

ß= 0.75 (calculated with a market price of the risk

¼0:25)

55

From the information provided, the following time-

invariant cost of capital results.

(23)

The following applies to the value

(24)

Table 1: Company valuation based on planned values and

CAPM

T 1 2 TV NPV of

the cash

flows

and TV

Cash flow

(planned)

10 15 (15 ...)

c (CAPM, Beta) 6.75% 6.75% 6.75%

Value 9.37 13.16 195.01

56

217.54

On the basis of the cash flows and terminal value

shown in table 1, the company value is calculated as

(25)

6.3 First step: Transfer from plan values to expected

values

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).

54

For t = 3, 4, ..., 8.

55

It shall apply to company i: c¼rfþiwith ias the

standard deviation of the stock return of i.

56

The present value in t = 0 of the TV in t = 2 is 195.01 = 15 /

((0.0675)(1 + 0,0675)

2

).

Business Valuation OIV Journal Spring 2019 13

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Table 2: Company valuation based on expected values and

CAPM

T 1 2 TV NPV of

the cash

flows

and TV

Cash flow

(planned)

10 15 15

Cash flow

(expected)

91313

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

2

= 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

57

.

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

flows

and TV

Cash flow

(planned)

10 15 15

Cash flow

(expected)

91313

probability

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

3

= 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

(26)

In this third step, the company value is now deter-

mined with a cost of capital ccorresponding to the

earnings risks.

57

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

flows

and TV

Cash flow

(planned)

10 15 15

Cash flow

(expected)

91313

probability

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

V)

7.71% 7.71% 7.71%

Value 8.23 10.86 115.47 134.56

The resulting value is now Value

4

= 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

0Þ.

Empirical studies

58

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-

agement): orientation towards the interests of the

owners, but use of the best available information -

and these are not always those of the capital market.

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