G. Silakova
O. Sopizhenko
OPTIMIZATION OF CAPITAL OF ENTERPRISE STRUCTURE IS ON
BASIS OF THE USE OF GAME-THEORETICAL APPROACH
Summary. The article examines approaches to the definition of «optimal capital structure of
the enterprise». The main criteria and impact factors of enterprise optimal capital structure
formation were specified. The usage of game-theoretic approach in the capital structure
optimization process of the enterprise was suggested.
Key words: equity, loan capital, capital structure, capital structure optimization, gametheoretic approach.
Problem statement. In competitive business environment, the process of
capital formation, optimization of its structure, balanced correlation fixing of
different sources of funds and the management of capital quality nowadays assume a
great significance. Relying on the investigations of foreign and native scientists it is
appropriate to highlight the significance of optimal capital structure for the
effectiveness of enterprise performance and inefficiency of scientific processing of
issues; search of financial sources in a resource-constrained environment, defining
the influence of internal and external environment on the process of their
mobilization.
Sufficient capital level facilitates the upgrading of enterprise competitive
ability during the whole period of its operation supporting its liquidity, capacity to
pay and financial firmness.
Consummation of optimal capital structure is realized with the help of
sufficient administration in the system of enterprise management. Each enterprise
should develop by itself the policy of capital forming taking into account the strategy
of development. Moreover, maximal management efficiency can be attained
assuming that system approach, efficient combination of strategic and tactful
measures are adhered.
As a result, detailing of theoretical basics and explanation of particular
practical recommendations for improvement of methodological approaches for
solving the mentioned problem in actual conditions is important task of research
activities. The effectiveness of enterprise operation depends on the right strategy of
capital management strategy. Its important part is to optimize the capital structure.
Therefore, the goal should guide the formation of the most appropriate capital
structure of the enterprise to its continued effective operation.
Analysis of the last research and publication. Theoretically-methodical
aspects of the problem of capital structure optimization are embodied in the works of
foreign and native scientists. The main methodological approaches of research in
capital formation sources were devised in classical works of J. M. Keynes, K. Marks,
A. Marshall, A. Smith, J. Tobin, M. Friedman, F. Hayek, J. Schumpeter and others.
The problems of forming and management of capital structure, its influence on
the final results of enterprise operating were researched in fundamental works of I.
Blank, R. Brayley, E. Brigham, J. Van Horne, L. J. Gitman, T. Golovko, I.
Ivashkovska, V. Koval’ova, N. Lahmetkina, S. Meyers, R. Merton, M. Miller, F.
Modiliani, W. Sharp and others.
At the same time in site of the existence of a big amount of scientific research
results, the problems of capital structure optimization of enterprises in current
situation of native economic development are still not adequately investigated.
The aim of this article is to devise the approach of capital structure
optimization in order to choose the efficient correlation of core and debt capital of the
enterprise.
Description of the basic material. The problem of the enterprise capital
structure optimization is one of the main ones in the sphere of financial management.
There are a lot of theories and models oriented to correlation identification of the core
and debt capital of the enterprise, but there is still no consensus of the optimal capital
structure.
In economic literature there are a lot of different approaches of identification of
the optimal capital structure. Some authors [1, p. 70; 2, p. 156] believe that the
optimal capital structure is some correlation of core capital and debt capital that leads
to maximization of enterprise stock value. This approach has the well-defined aim of
optimal capital structure searching but this approach has the general nature for the
practical activity of financial managers. Besides, it is difficult enough to be used by
the enterprises which are not public joint-stock companies.
Other scientists have another point of view. These scientists are I. O. Blank, T.
V. Golovko, S. V. Saganova, H. I. Lahmetkina, V. O. Podol’ska, O. V. Yarish and
others [3, p. 213; 4, p. 8; 5, p. 64; 6, p. 355]. Mentioned above scientists believe that
optimal capital structure is a correlation of core and debt resources usage with the
most effective differential ratio between profit ratio of core capital and financial
stability index so the market price of the enterprise maximizes.
The main criteria of optimal capital structure of the enterprise are [7, p. 180]:
 asset financing policy . The capital structure of the enterprise , taking into account
the criteria based on the study of the relationship between asset and liability balance
and to determine the necessary size and proportion of various sources of financing;
 enterprise value . There are various theories that examine the relationship of
capital structure and cost of the enterprise as a business. This is an optimal capital
structure that maximizes the market value of the company;
 cost of capital. Since both own and borrowed capital for companies with a cost the cost of maintenance , the optimal structure from this perspective - the structure
that minimizes the cost of capital;
 risks. When the capital structure the company has various types of risks . Yes, this
includes the risk of partial or complete failure to return borrowed money , the risk of
debt servicing (default interest) , the risk of bankruptcy. This company can supply
problem of optimal capital structure under the existing constraints in terms of
reducing certain risks;
 profitability. It is generally accepted that borrowing resources can lead to an
increase in return on equity of the enterprise due to the effect of financial leverage .
The optimal capital structure in this case maximizes profitability , that allows you to
get the most profit from the current level of own resources.
So it is right to believe that optimal capital structure is the correlation of core
and debt sources of the enterprise which has the best values of optimization criterion
with the given level of financial stability in order to attain its maximum market value.
During the forming the optimal financial structure of the enterprise it is
necessary to consider the influence of the subjective and objective factors. We
classified the combination of these factors according to the place of their origin
(factors of the internal and external environment) and according to the manner of
influence (institutionally-legal, financially-economic and socially-administrative), the
Table 1 is given [8, 9, 10, 11].
Table 1
Factors of influence on the optimal capital structure of the enterprise
Factors of the external environment
Factors of the internal environment
Institutionally-legal
 legislatively guaranteed requirements  guaranteed in statutory documents
for the value and the creation procedure
requirements for the value and the
of particular core and debt capital of
creation procedure of core capital of the
enterprise (the minimal statutory capital
enterprise (value of the statutory, reserve
dimension, reserve capital value, limits of capital, requirements for the additional
preferred stocks emission and others);
stock emission, etc.) and the debt capital
 legislatively guaranteed requirements (implication of credits, emission of
bonds, etc.);
for the value of the core capital of the
 guaranteed in statutory documents
enterprise during performing particular
types of activity;
issues of control over enterprise
 influence of the external stakeholders; administration;
efficiency of legal system, property rights conflicts between the agents and the
protection level of administration,
protection, etc.
attraction of funding sources.
Financially-economic
 investment climate of the country;
 characteristics of the enterprise
connected with its field, areal and
 rates of economic dynamics;
structural specification;
 economical and political policy;
 life-cycle phase;
 efficient taxation system;
 concept of economic development,
 refinancing rate of NBU;
 level of development and condition of type of financial policy (conservative,
moderate, aggressive);
financial and credit markets;
 planned progress rate of economic
 resource availability of financial
dynamics;
market for the enterprises;
 tendencies of field and regional market  value of the enterprise capital;
 actual capital structure;
condition;
investment attractiveness of the field and  risks of economic operations and
financial standing of the enterprise;
the region.
 pattern of product demand and the
steadiness of acquisition of income;
asset profile according to the degree of
liquidity.
Socially-administrative
 corporate administration in the
 level and quality of corporate
country, region, field;
administration and control;
 social stability;
 level and quality of financial
management, etc.
 level of criminalization and
corruption.
It is also should be noted that factors of the external environment do not fall
under the influence of the enterprise and these factors should be taken for granted.
The factors of internal environment can be corrected by making and implementation
the different administrative decisions.
The main classical methods of capital structure optimization have the
disadvantage that disallows fully consider the influence of the external market
condition and connected uncertainty which will show the risk of upcoming both
advantageous and disadvantageous market condition. So it can be said that forming of
optimal capital structure will take place with regard to influence of the uncertainty
factor.
The science that searches the optimal solutions in conditions of uncertainty is
the game theory [12, p. 71]. The peculiarity of game theory with a nature is that one
of the participants is player consciously making decisions and other participant is
nature (in this case market condition) that is not conscious player, it does not resist
and does not mind the game result.
In any market condition, the top-priority goal for financial manager is
maximizing the enterprise value. We think that this goal should be used with the
money flows discounting (MFD) which allows determining the value of the
enterprise on the basis of its money flows and the capital value (WACC).
According to the MFD model, the value of the enterprise is inversely
proportional to the value of its capital: the lower the value of the capital – the higher
the value of the enterprise and vice versa. So in an effort to increase the value of the
enterprise the financial manager should decrease the value of the capital.
The main components of the game with nature are player, nature, player’s
strategies, nature conditions, and player’s prizes. Let’s say that the player (MDP –
making decisions person) is financial manager making decisions of the enterprise
capital structure. Player’s strategies are different variants of enterprise capital
structures. Let the player has m possible Astrategies which are corresponded to the
next variants of the capital structures:
А1: d1=(dвк/dпк)1, А2: d2=(dвк/dпк)2 … Аm: dm=(dвк/dпк)m,
wheredвкis a part of core capital;
dпкis a part of debt capital.
Earning power of the index UICE (Rm) is in the capacity of the nature (П). In
the capacity of possible state of nature let us take the belonging of earning power of
the index UICE to one of the n intervals. In such a way, the state of nature Пj
corresponds that the index UICE will be placed in the interval (aj; aj+1).
For example, let the nature has 5 states (n=5): П1, П2, П3, П4 andП5, which
correspond to the following income interval of the index UICE:
П1: Rm  (;  25% , П2: Rm  (25%; 10% , П3: Rm  (10%;10% ,
П4: Rm  (10%; 25% , П5: Rm  (25%; ) .
The state of the nature can be also defined in another way. Let’s determine in
the capacity of the price the value inversely proportional to the average capital value:
1/(1+WACC). Then player’s prize, in case of the A strategy of the state of nature Пj ,
will be aij:
aij 
1
1  WACCij
(1)
whereWACCijis the average capital value in condition of the correspondence of
the capital structure of the Ai strategy and the income power of the index UICE that
corresponds the state of nature Пj.
Price dependence on the chosen strategy and its particular state of nature is
determined with the help of the following formula:
CAPM  R f   ( Rm  R f ) ,
whereRfis risk-free rate of return;
βisration beta;
Rmis stock market profitability.
Gains matrix (game matrix) A will be the next:
(2)
Пj
Ai
A1
A2
…
Аi
…
Аm
П1
П2
…
Пj
…
Пn
а11
a21
…
ai1
…
am1
а12
а22
…
аi2
…
аm2
…
…
…
…
…
…
а1j
а2j
…
аij
…
аmj
…
…
…
…
…
…
а1n
а2n
…
аin
…
аmn
After the forming of game matrix we can move to the determination of the
optimal player’s strategy. In the model playing with nature, the search of optimal
strategies implies in the following. Depending on the risk proneness, the player
chooses the optimality criterion according to which he will act. According to the
chosen criterion, the strategy having the maximum efficiency factor is chosen. Such
strategy is called the optimal according the given optimality criterion. Strategy being
optimal according to one optimality criterion can be not optimal according to another
optimality criterion.
Let us assume that the probabilities of the nature states П are known (in this
case it is accepted to say that the game takes place under the risk). In this case the
optimal strategy will be defined with the help of Bayes’ criterion [12, p.75]. The
index of Ai strategy effectiveness is:
n
Bip (q)   q jaij ,
j 1
(3)
whereqjis the probability of the fact that the nature will have the state Пj .
The optimal strategy according to the Bayers’ criterion is the Аопт strategy with
the maximum effectiveness index according to the same criterion:
Aопт  max Bip (q ) .
(4)
In practice, it is not always possible to determine the possibility of nature
states. If the possibilities of the nature states are unknown, it is accepted to say that
the game takes place in conditions uncertainty. One of the optimality criterions which
is used in the conditions of uncertainty is the Laplace’ criterion [12, p. 114].
According to this criterion all states of nature are equally possible. Then the
effectiveness index Lip of the Ai strategy will be the arithmetic mean of the strategy
prizes:
1 n
p
Li   aij , і=1, 2, …, m.
(5)
n j 1
According to the Laplace’s strategy, the optimal strategy is:
Aопт  max Lip .
(6)
In condition of uncertainty, the choice of the optimal strategy often depends on
the player’s subjective risk perception. Making decisions the player can be too
pessimistic so, be not risk-prone; he can also be optimistic, i.e. be ready to take the
risk or to take the middle ground.
If the player is too pessimistic and he thinks of no risk, it means that the nature
will have its worst state for him which leads to his prize to be minimal at each
strategy. Optimal strategy of pessimistic player can be determined according to the
Wald’s criterion [12, p. 274]. According to this criterion, the index of effectiveness is
the smallest prize Wi with the pure strategy Ai.
Wi  min aij , і=1, 2, …,m.
1 jn
(7)
The optimal strategy is the strategy with the maximum index of effectiveness:
Aопт  max Wі .
1 j  n
(8)
Optimal solution chosen according to the Wald criterion eliminates the risk.
This means that the decision-maker can face the worse results than he expects to face.
As the decision made according to the Wald criterion is aimed not to maximize the
prize but to minimize the loss, so in the end, such pessimism can lead to the most
beneficial result.
If the player is too optimistic, he expects the nature to have its best state for
him so he can get the maximum prize in any strategy. Maximax criterion [12, p. 350]
can be used for determining the optimal strategy of the optimistic player. The
effectiveness index of the Ai strategy is the biggest prize of player A at this strategy:
M i  max aij , і=1, 2, …,m.
1 j  n
(9)
According to the maximax criterion, the optimal strategy is one with the
biggest index of effectiveness:
Aопт  max M i .
1 j  m
(10)
In the practice, the extra optimism of maximax criterion is not always
appropriate as it can lead to unreasonably high risks of getting insufficient result.
Most commonly, the player chooses some average position between the pessimism
and optimism.
It is possible to come to the compromise between the Wald extreme criterion
and maximax criterion with the help of the Hurwitz criterion [12, p. 350] that
represents the linear combination of those two criterions with the index 
determining the level of player’s optimism. The index is established by the player on
the basis of analysis of statistic data or his own experience in making decisions in
such situations. The choice of the value is dependent on the liability: the worse
consequences of made decisions, the bigger desire of decision-maker to get insured
and the bigger index of optimism leads to zero, and vice versa.
According to the Hurwitz criterion, the index of Ai strategy effectiveness is the
combination of indexes of total pessimism Wi and the total optimism Mito the
optimism index  :
( Hur )ip  (1   )Wі  М і ,
(11)
So the player A using the Hurwitz criterion has more tram position than if he
used the Wald criterion or maximax criterion.
According to the Hurwitz criterion, the optimal strategy with the index  , the
optimal strategy is one with the biggest value of effectiveness:
Aопт  max ( Hur )ip ( ).
1 j  m
(12)
Along with the game taking place in the conditions of risk and uncertainty,
sometimes it the conditions of half-uncertainty are mentioned. The game takes place
in conditions of half-uncertainty if the probabilities of nature states П upcomingare
already known but the player A is suspicious about it.
To find the optimal strategy in the conditions of half-uncertainty, we can use
such criterions [12, p.181, 394, 634] as Hermeyer criterion, Hodge-Lehmann
criterion, Hermeyer-Hurwitz criterion, etc.
Conclusion. This investigation enabled us to draw a conclusion that in modern
financial practice, financial managers of the enterprise while determining the optimal
capital structure should use the combination of few theoretical approaches which take
into account the instability of different factors. At the same time, the usage of the
given game-theoretic approach in the capital structure optimization process,
considering the influence of the market condition, allows persistently forming the
capital structure which will provide its most effective usage at the enterprise.
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