Proceedings of World Business and Economics Research Conference
24 - 25 February, 2014, Rendezvous Hotel, Auckland, New Zealand, ISBN: 978-1-922069-45-0
Assessing the Minimum Demandable Selling Price for a Company
Assuming the Seller Pursues Wealth Accumulation
Thomas Hering*, Christian Toll** and Dipl.-Kffr. Polina K. Kirilova***
In this paper a company owner (valuation subject) is interested in selling a
certain company (valuation object), pursuing wealth maximisation. We
apply an investment theory approach to determine his minimum
demandable selling price. The seller may accept this price without the
transaction proving disadvantageous from his point of view. The state
marginal price-model allows us to determine this price under realistic
imperfect market conditions. For the sake of simplicity, all modelling is
done under the premise of monovalent cash streams.
JEL Codes: D46, G31 and G34
1. Introduction
Before engaging in a negotiation, a presumptive seller needs to know the worth of his company
from his point of view. So he can decide whether the transaction is advantageous or not at a certain
price. The sale promotes the interest of the potential seller (valuation subject) as long as the price
he receives in exchange for the sold company (valuation object) does not come below the
subjective value he associates with it. The price simply constitutes the negotiation outcome,
whereas the value – according to the subjective value theory founded by Gossen (1854) and
Menger (1871) – results from the marginal utility regarding a predefined subjective aim (Baum,
Crosby & MacGregor, 1996; Peto, French & Bowman, 1996; French, 2011). The valuation process
depends on the decision field, which is constituted of all opportunities for action available to the
valuation subject, as well as on the target function (usually prosperity maximisation, i.e. wealth or
income maximisation). The seller‟s calculations are based on the future uncertain cash stream
expected to be realised.
Thus the seller will only engage in a transaction, if the sale results in a target achievement level at
least not lower than the one attainable when refraining from the transaction. A business valuation
shall help to judge on the economic adequacy of a given price for the transfer of the valuation
object. It is important to bear in mind that each appraisal is subject to the intended purpose. The
functional business valuation theory facilitates such purpose-orientated valuation by providing
guidelines for the different valuation tasks. The three main functions – decision, mediation and
argumentation – imply intended change in ownership (Matschke & Brösel, 2013). The most
important among them is the decision function (Hering, 1999: 3). It provides the decision value for
the valuation subject, which constitutes its limit of concession willingness in the specific conflict
situation.
*Prof. Dr. Thomas Hering, Chair of Business Administration, esp. Investment Theory and Business Valuation,
Fern-Universität in Hagen, Germany, Email: thomas.hering@fernuni-hagen.de
**Dr. Christian Toll, Chair of Business Administration, esp. Investment Theory and Business Valuation,
Fern-Universität in Hagen, Germany, Email: christian.toll@fernuni-hagen.de
***Dipl.-Kffr. Polina K. Kirilova, Chair of Business Administration, esp. Investment Theory and Business Valuation, FernUniversität in Hagen, Germany, Email: polina.kirilova@fernuni-hagen.de
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Proceedings of World Business and Economics Research Conference
24 - 25 February, 2014, Rendezvous Hotel, Auckland, New Zealand, ISBN: 978-1-922069-45-0
In the case of a company sale, the seller seeks to surrender the ownership of the company in
return for a – typically monetary – compensation. Focal point of the emerging negotiation is the
agreement upon the conditions of the ownership transfer. To avoid any economic disadvantage,
the presumptive seller should be aware of his individual limit of concession willingness in the given
negotiation. Provided that the only controversial issue is the amount of the monetary compensation,
this limit is equal to the minimum price (marginal or critical price) he may accept without suffering
an economic disadvantage (Matschke, 1975; Ballwieser & Hachmeister, 2013: 3; Baum, Crosby &
MacGregor, 1996: 37; French, 2011: 313; Hutchison & Nanthakumaran, 2000: 35 f.).
Applying the investment theory, models were developed to compute the subjective decision value.
Those models can either be general, as showed in this paper, or partial. In fictitious perfect capital
market the Fisher-Separation (Fisher, 1930) holds and the marginal price can be relatively easy
obtained applying a partial model (Hering, 2006: 36 ff.; Ballwieser & Hachmeister, 2013: 13 ff.;
Drukarczyk & Schüler, 2009: 203 ff.). The future earnings value can then be calculated without
minding the entire complex decision field of the valuation subject, as the interest rate is exogenous.
In a real imperfect market it is inevitable to consider the interdependent investment, financing and
consumption decisions simultaneously. The consumption preference of the valuation subject is
expressed in the predefined structure of withdrawals and is no longer separable from the time
preference of the money. It affects the temporal distribution and the level of the individual
withdrawals as well as the investment and financing decisions. Thus, the shadow prices for each
period (the endogenous marginal interest rates), which are required for the partial model, can only
be determined for the specific conflict situation as a by-product of the general model solution
(Hirshleifer, 1958; Dean, 1969).
In our paper we will exemplary assess the subjective limit of concession willingness for a potential
seller. As this is to be done under realistic conditions, the business valuation method of choice is
the general model “state marginal price model”. For the sake of simplicity, all modelling is done
under the premise of certainty. The subjective target of the presumptive seller is wealth
maximisation, i.e. he strives for the greatest possible asset value as opposed to maximising the
income stream size.
2. Literature Review
In order to calculate the decision value in the context of a company sale, the state marginal price
model will be introduced below (Hering, 2006: 43 ff.). This model combines the advantages of the
mixed integer model of Laux/Franke (1969) with the two-step procedure of Jaensch (1966: 138)
and Matschke (1975: 253 ff. and 387 ff.).
Laux/Franke (1969: 207-210) calculate the marginal price of a certain cash stream within an
imperfect capital market by applying the multi-period simultaneous planning approaches of Hax
(1964) and Weingartner (1963). Thereby, they set an obviously advantageous price into their linear
optimisation model. Afterwards Laux/Franke (1969) vary this price continuously in a parametric
manner until the change in ownership of the valuation object becomes disadvantageous. This
means that the variable representing the valuation object is no longer part of the optimal investment
and financing programme (Laux & Franke, 1969: 208 f.). So the model of Laux/Franke (1969)
requires a numerically extensive mixed-integer parametric optimisation.
The models of Jaensch (1966) and Matschke (1975) handle this problem by determining the
decision value in a two-step procedure. The first step is to calculate – as a so-called base
programme – the investment and financing programme, which maximises the target function value
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Proceedings of World Business and Economics Research Conference
24 - 25 February, 2014, Rendezvous Hotel, Auckland, New Zealand, ISBN: 978-1-922069-45-0
(income EN or asset value GW) under unchanged property conditions regarding the valuation
object. Subsequently, in a second step the valuation object has to be removed from the investment
programme of the presumptive seller in the case of a company sale. Then, the minimum
demandable price as an immediate payment is searched. Hence, the decision field is altered by
removing the valuation object at a price of p and additionally supplemented by the condition that at
least the target function contribution of the base programme must be achieved again. The result of
this second step is the so-called valuation programme with its optimal value p* that indicates the
requested lower price limit as an immediate payment (i.e. decision value or marginal price).
As opposed to Laux/Franke (1969), the models of Jaensch (1966) and Matschke (1975) suffer from
the blemish that the imperfect capital market is not considered in the lapse of time. Instead, a
single accumulated number of success is assigned to each multi-period investment and financing
object (Matschke, 1975: 253 ff.). The state marginal price model combines the advantages of these
models in a way that allows to determine the marginal price at the time t = 0 under imperfect capital
market conditions by setting up a base and a valuation approach without being dependent on the
mixed-integer parametrical optimisation as the Laux/Franke model (Laux & Franke, 1969).
3. The Methodology and Model
In the following sections it is assumed that the valuation subject pursues the target wealth
maximisation, wherefore he strives for the greatest possible GW (Hering, 2006: 57 ff.; Hering,
2008: 142 ff.; Toll, 2011: 76 ff.). GW is the sum of the weighted withdrawals w t  G t for each point
in time t. The weightings w t reflect the consumption preference of the valuation subject. A fixed
income stream may be considered in order to ensure an adequate spending opportunity. To ensure
the existence of the company beyond the planning horizon n, the autonomous cash flow bn has to
additionally consider a sufficient terminal asset as a fictive withdrawal. This terminal asset
represents the present value of a perpetual annuity and thus allows the continuation of the desired
dividend level. The autonomous cash flow bt results beyond that from the predetermined payments
(e.g., from current business operations and existing loan obligations), is independent of the
assessed available objects j and can be positive, negative or zero.
Furthermore, the following assumptions are made for the valuation subject as the presumptive
seller (Hering, Toll & Kirilova, 2013: 40 f.). The planning period extends n periods, whereas t = 0
defines the valuation and decision point in time. In the baseline situation m investment and
financing objects j are at the valuation subject‟s disposal (j = 1, ..., m). This also includes at any
point in time the opportunity of borrowing money, the opportunity to invest money in financial assets
as well as unlimited cash holdings. The cash stream of the object j is determined as follows: gj :=
(gj0, gj1, …, gjt, …, gjn) with gjt being the cash flow of object j at time t. The variable xj shows how
often an investment or financing object j can be realised. For the variables xj there are upper
bounds xjmax (which may also be ). The n + 1 liquidity constraints ensure that at any point in time t
the sum of all cash flows remains non-negative. In other words, the liquidity constraints have to
ensure that at any time t the sum of all cash flows from the realised investment and financing
objects as well as from autonomous payments suffice to enable the desired withdrawals. Moreover,
the variables Gt and xj are limited to non-negative values.
All in all, the base programme (the combination of financing and investment options that maximises
the valuation subject‟s success without the company sale in question) results from the in figure 1
presented linear optimisation approach “max GW“ (Hax, 1964: 435 ff.; Franke & Laux, 1968: 755;
Hering, 2008: 144; Brösel, Matschke & Olbrich, 2012: 250; Hering, Olbrich & Steinrücke, 2006:
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Proceedings of World Business and Economics Research Conference
24 - 25 February, 2014, Rendezvous Hotel, Auckland, New Zealand, ISBN: 978-1-922069-45-0
410; Matschke, Brösel & Matschke, 2010: 13 f.; Lerm, Rollberg & Kurz, 2012: 265; Hering, Toll &
Kirilova, 2013: 42). The simplex algorithm (Dantzig, 1966) calculates the optimal solution of this
linear approach resulting in a maximum target function value GW*. Selling the company at a price p
is then only economically viable if the valuation programme yields at least the optimal target
function value GW* of the base programme (Hering, 2006: 58 and 82; Toll, 2011: 100). If the
valuation subject no longer possesses the company V, it gives up the cash stream gV := (0, gV1,
gV2, ... , gVt, ... , gVn). For this reason, these cash flows gVt have to be subtracted from the
autonomous payments bt. In exchange he receives the price p at time t = 0.
The decision value is then to be determined (Hering, Olbrich & Steinrücke, 2006: 410 f.; Brösel,
Matschke & Olbrich, 2012: 250). The presumptive seller has to know which price he must at least
demand, without the sale putting him into a worse position than if he had kept the company and
implemented the available base programme. In this manner, p must consequently be minimised,
taking into account the restrictions of the original decision field as well as the loss of the payment
stream from the sold company and subject to the additional condition of not violating GW*. The
answer can be found with the help of the valuation approach “min U“ in figure 1 (Hering, 2006: 82;
Toll, 2011: 101). Again, the simplex algorithm generates the optimal solution (valuation programme)
and thus provides not only the marginal price p* (min. p, i.e. the decision value) but also the seller‟s
optimal investment and financing programme, restructured by the removal of the sold company‟s
payments in exchange for the price p = p*.
Figure 1: base and valuation approach
max. GW; GW :=
min. U; U := p
– p  b0
 b0
 bt – gVt
 bt
–
xj 
xj, Gt  0
 t  {1, 2, ... , n}
 –GW*
xj 
xj, Gt, p  0
 j  {1, 2, ... , m}
 j  {1, 2, ... , m},
 t  {0, 1, 2, ... , n}
4. Exemplary Presentation and Findings
Now, a fictive example will be conceived in order to illustrate the procedure presented above. Matter
of interest is the firm A aspiring to sell the daughter company V. The management forecasts that if the
ownership of the company V is not surrendered, it will be accompanied in the planning period (n = 5)
by the cash stream gV = (0, 20, 25, 30, 20, 10) and from the sixth year on by a perpetual annuity in the
amount of 5 monetary units (MU). At the valuation date t = 0 company A expects that the previous
business activity leads to a perpetually arising deposit excess amounting to 100 MU. The perpetual
annuities are taken into account in the example, using the generally estimated interest rate of 5% p.a.
for t > n = 5, resulting in an autonomous cash stream b of the structure (0, 120, 125, 130, 120, 2 210).
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Proceedings of World Business and Economics Research Conference
24 - 25 February, 2014, Rendezvous Hotel, Auckland, New Zealand, ISBN: 978-1-922069-45-0
In order to reduce the complexity of the example, we assume that firm A has only a few investment
and finance options. Firstly, at t = 0 company A can invest in a tangible asset (e.g., a modernisation of
the existing production lines) which is associated with the payment stream (–200, 15, 15, 15, 15, 315)
and can be realised partially. Secondly, firm A is able to invest an unlimited amount of money in
financial assets that promise a return of 5% per annum (p.a.). For financing a five-year zero coupon
loan is available at t = 0 provided by the local bank at an annual interest rate of 7% restricted to 70
MU. Furthermore, company A can debit a revolving line of credit at a short-term interest rate of 12%
p.a. limited to 100 MU. Company A pursues wealth maximisation, striving only for a maximum terminal
asset value EW at the end of the planning horizon n. Thus, the weightings are w t = 0 for 0  t < n and
w n = 1. Furthermore, for t = 1 to 5 A requires a fixed withdrawal in the amount of 90 MU for dividend
payout purposes.
Taking the given decision field (without the sale of company V = baseline situation), the terminal asset
value GW* = EW* = 2 355.8064 MU results from the base approach. Due to the credit bottleneck only
85% of the tangible asset investment can be realised. Not only the zero coupon loan is fully utilized,
but also in the first three years additional short-term financing is required. At t = 0 the complete credit
line of 100 MU is exhausted. Investments in financial assets take place in fourth and the fifth year.
Table 1 shows the base programme as a complete finance schedule.
Table 1: Complete finance schedule of the base programme in the case of a credit limit
Time
bt
Tangible asset
(85%)
Zero coupon loan
Revolving line
Financial asset
Repayment
Fixed withdrawal
Credit balance
t=0
t=1
t=2
t=3
t=4
t=5
0
120
125
130
120
2 210
–170
12.75
12.75
12.75
12.75
267.75
70
100
0
69.25
0
29.81
0
0
–98.1786
–100
–112
–90
–69.25
–77.56
–90
–29.81
–19.3628
–33.3872
–90
19.3628
–63.0809
20.3309
–90
63.0809
66.235
–90
2 355.8064
In a second step company V accompanied by the cash stream gV has to be removed from the
investment programme of firm A. In exchange the presumptive seller A has to answer the question
which immediate payment he can just accept without violating the terminal asset value EW*.
According to the valuation approach, this marginal price p* is 140.6413 MU. The complete valuation
programme can be described as follows: Company V is no longer part of the optimal investment and
financing programme. That‟s why the tangible asset investment can now be realised completely. Due
to the improved financing situation, only 52.91% of the zero coupon loan is necessary to fund the
valuation programme. Short-term financing is only required at time t = 0 (22.3214 MU). In the second
year neither short-term financing nor investment in financial assets are possible. From the third year
on investments in financial assets are executed. Company A is still able to provide the terminal asset
value EW* = 2 355.8064 MU. Table 2 shows the valuation programme as a complete finance
schedule.
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Proceedings of World Business and Economics Research Conference
24 - 25 February, 2014, Rendezvous Hotel, Auckland, New Zealand, ISBN: 978-1-922069-45-0
Table 2: Complete finance schedule of the valuation programme in the case of a credit limit
Time
bt – gVt
Marginal price p*
Tangible asset
Zero coupon loan
(52.91%)
Revolving line
Financial asset
Repayment
Fixed withdrawal
Credit balance
t=0
0
140.6413
–200
t=1
100
t=2
100
t=3
100
t=4
100
15
15
15
15
315
37.0373
0
0
0
0
–51.9468
22.3214
0
0
–25
–90
0
–25
0
–90
25
–51.25
26.25
–90
51.25
–78.8125
53.8125
–90
78.8125
82.7531
–90
2 355.8064
–22.3214
t=5
2 100
In order to illustrate in what way changes in the decision field of the valuation subject may affect the
decision value, the example will now be modified as follows: In addition to the zero coupon loan, the
local bank grants an unlimited overdraft facility at a short-term interest rate of 12% p.a.
This affects in first place the optimal decisions in the baseline situation. Due to the improved financing
situation the tangible asset investment can now be completely realised in the base programme (Table
3). This results in a higher terminal asset value EW* = 2 366.2048 MU. Additionally to the zero coupon
loan, in the years one, two, three and four no investments in financial assets are possible as
borrowings have to be engaged. Both at the decision point t = 0 as well as in the second year A
borrows more than 100 MU. In year five, investments in financial assets are executed.
Table 3: Complete finance schedule of the base programme in the case of an unlimited overdraft
facility
Time
bt
Tangible asset
Zero coupon loan
Revolving line
Financial asset
Repayment
Fixed withdrawal
Credit balance
t=0
t=1
t=2
t=3
t=4
t=5
0
–200
70
130
120
15
0
100.6
125
15
0
62.672
130
15
0
15.1926
120
15
0
2 210
315
–98.1786
–130
–145.6
–90
–100.6
–112.672
–90
–62.672
–70.1926
–90
–15.1926
–27.9842
17.0158
–90
27.9842
29.3835
–90
2 366.2048
The changes in the decision field of company A further influence the valuation programme (Table 4).
The minimum demandable price for V at time t = 0 is now 148.0552 MU. The desired terminal asset
value of the base programme can also be realised in the valuation programme. As the price for V
flows at t = 0 only 42.32% of the zero coupon loan and short-term financing only in the first year
suffice to finance the valuation programme. In the second year neither short-term financing nor
investment in financial assets takes place, but from the third year on A invests in financial assets.
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Proceedings of World Business and Economics Research Conference
24 - 25 February, 2014, Rendezvous Hotel, Auckland, New Zealand, ISBN: 978-1-922069-45-0
Table 4: Complete finance schedule of the valuation programme in the case of an unlimited overdraft
facility
Time
t=0
t=1
t=2
t=3
t=4
t=5
bt – gVt
0
–200
100
15
100
15
100
15
100
15
2 100
315
29.6234
0
0
0
0
–41.5483
22.3214
0
0
–25
–90
0
–25
0
–90
25
–51.25
26.25
–90
51.25
–78.8125
53.8125
–90
78.8125
82.7531
–90
2 366.2048
Tangible asset
Zero coupon loan
(42.32%)
Revolving line
Financial asset
Repayment
Fixed withdrawal
Credit balance
–22.3214
5. Summary and Conclusions
The discussion above demonstrates that a company valuation cannot be executed completely
detached from the individual expectations and plannings of the specific valuation subject (Matschke &
Brösel, 2013: 18). Appraisal always depends on the subjective aim and the decision field of the
valuation subject. Even when the same company is being assessed from the perspective of different
valuation subjects the decision value may vary, especially if they pursue different types of prosperity
maximisation. In this paper we assumed that the valuation subject as a presumptive seller is
interested in selling a certain company, pursuing the target wealth accumulation. He desires only a
small fixed income stream and the greatest possible terminal asset value at the end of the planning
horizon. The example shows that even the same valuation subject may come to diverging limits of
concession willingness regarding the same valuation object when the underlying decision field
changes (Hering, Toll & Kirilova, 2013: 44.; Matschke & Brösel, 2013: 368). The minimum
demandable price for the very same cash stream depends on the available opportunities for action.
We have shown that simply removing the short-term credit upper limit alters the minimum
demandable price of the same company noticeably.
Valuation methods based on financing theory assume a fictitious perfect market. These methods do
not take into consideration the individual expectations and plannings of the specific valuation subject.
Instead, they seek the one “true” value that has to be valid in general for everybody (Hering, Toll &
Kirilova, 2013: 44). For this reason, such methods are not appropriate to determine the critical price
under realistic market conditions. Accordingly, its calculation can only be achieved by a business
valuation based on investment theory, which can consider – as shown in this article – the existing
market imperfections as well as the individual expectations and plannings of the presumptive seller.
Of course, the determination of the decision value using the state marginal price model has also
engendered criticism (Koch, 1982: 25 ff.; Rollberg, 2002: 4 ff.; Ballwieser, 1990: 28 f.; Hering, Toll &
Kirilova, 2013: 44). In a general model all investment and financing objects are directly included in a
simultaneous optimisation approach. As this requires elaborate information gathering and processing,
a centralised simultaneous planning with general models is often marked by complexity and
clumsiness. Even if it were possible to develop a general model considering all data and
interdependences, this model would suffer from a solution defect, since the optimal solution could not
be found at economically viable expense.
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Proceedings of World Business and Economics Research Conference
24 - 25 February, 2014, Rendezvous Hotel, Auckland, New Zealand, ISBN: 978-1-922069-45-0
References
Ballwieser W 1990, Unternehmensbewertung und Komplexitätsreduktion, Wiesbaden: Gabler.
Ballwieser W and Hachmeister D 2013, Unternehmensbewertung, Stuttgart: Schäffer Poeschel.
Baum A, Crosby N and MacGregor B 1996, „Price formation, mispricing and investment analysis in the
property market‟, Journal of Property Valuation and Investment, Vol. 14, No. 1, pp. 36-49.
Brösel G, Matschke MJ and Olbrich M 2012, „Valuation of entrepreneurial businesses‟ International
Journal of Entrepreneurial Venturing, Vol. 4, No. 3, pp. 239-256.
Dantzig GB 1969, Lineare Programmierung und Erweiterungen, Berlin, Heidelberg, New York:
Springer.
Dean J 1969, Capital Budgeting, New York/London: Columbia University Press.
Drukarczyk J and Schüler A 2009, Unternehmensbewertung, München: Vahlen.
Fisher I 1930, The Theory of Interest, New York: Macmillan.
Franke G and Laux H 1968, „Die Ermittlung der Kalkulationszinsfüße für investitionstheoretische
Partialmodelle‟, Schmalenbachs Zeitschrift für betriebswirtschaftliche Forschung, Vol. 20, pp.
740-759.
French N 2011, „Valuing in the downturn: understanding uncertainty‟, Journal of Property Investment
& Finance, Vol. 29, Vol. 3, pp. 312-322.
Gossen HH 1854, Entwickelung der Gesetze des menschlichen Verkehrs, und der daraus fließenden
Regeln für menschliches Handeln, Braunschweig: Friedrich Vieweg und Sohn.
Hax H 1964, „Investitions- und Finanzplanung mit Hilfe der linearen Programmierung‟, Schmalenbachs
Zeitschrift für betriebswirtschaftliche Forschung, Vol. 16, No. 6, pp. 430-446.
Hering T 1999, Finanzwirtschaftliche Unternehmensbewertung, Wiesbaden: Deutscher UniversitätsVerlag.
Hering T 2006, Unternehmensbewertung, München/Wien: Oldenbourg.
Hering T 2008, Investitionstheorie, München: Oldenbourg.
Hering T, Olbrich M and Steinrücke M 2006: „Valuation of start-up internet companies‟, International
Journal of Technology Management, Vol. 33, No. 4, pp. 406-419.
Hering, T, Toll, C, Kirilova PK 2013 „Decision-oriented Business Valuation in Preparation for a
Company Purchase‟, in: Zarzecki, D (ed.), Proceedings of the 14th International Financial
Management Conference 2013, Bd. I: Business Valuation, Value-Based Management, Risk
Management, Stettin: Publishing House of University of Stettin, pp. 37-47.
8
Proceedings of World Business and Economics Research Conference
24 - 25 February, 2014, Rendezvous Hotel, Auckland, New Zealand, ISBN: 978-1-922069-45-0
Hirshleifer J 1958, „On the Theory of Optimal Investment Decision‟, Journal of Political Economy, Vol.
66, No. 4, pp. 329-352.
Hutchison N and Nanthakumaran N 2000, „The calculation of investment worth - Issues of market
efficiency, variable estimation and risk analysis‟, Journal of Property Investment & Finance, Vol.
18, pp. 33-52.
Koch H 1982, Integrierte Unternehmensplanung, Wiesbaden: Gabler.
Laux H and Franke G 1969, „Zum Problem der Bewertung von Unternehmungen und anderen
Investitionsgütern‟, Unternehmensforschung, Vol. 13, pp. 205-223.
Lerm, M, Rollberg, R and Kurz, P 2012, „Financial valuation of start-up businesses with and without
venture capital‟, International Journal of Entrepreneurial Venturing, Vol. 4, No. 3, pp. 257-275.
Matschke MJ 1975, Der Entscheidungswert der Unternehmung, Wiesbaden: Gabler.
Matschke MJ, Brösel G and Matschke X 2010, „Fundamentals of Functional Business Valuation‟,
Journal of Business Valuation and Economic Loss Analysis, Vol. 5, No. 1, Article 7, pp. 1-39.
Matschke MJ and Brösel G 2013, Unternehmensbewertung, Wiesbaden: Springer Gabler.
Menger C 1871, Grundsätze der Volkswirthschaftslehre, Wien: Wilhelm Braumüller.
Peto R, French N and Bowman G 1996, „Price and worth Developments in valuation methodology‟,
Journal of Property Valuation and Investment, Vol. 14, No. 4, pp. 79-100.
Rollberg R 2002,
„Integrierte Unternehmensplanung auf
Betriebswirtschaftliche Forschung und Praxis, Vol. 54, pp. 1-20.
unvollkommenen
Märkten‟,
Toll C 2011, Investitionstheoretische Unternehmensbewertung bei Vorliegen verhandelbarer
Zahlungsmodalitäten, Wiesbaden: Gabler.
Weingartner HM 1963, Mathematical Programming and the Analysis of Capital Budgeting Problems,
Englewood Cliffs: Prentice Hall.
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