International Journal of Fuzzy [613139]

123
International Journal of Fuzzy
Systems

ISSN 1562-2479

Int. J. Fuzzy Syst.
DOI 10.1007/s40815-016-0159-zDeveloping an Adaptive Fuzzy Controller
for Risk Management of Company Cash
Flow
Marcel Ioan Boloș & Diana Claudia
Sabău-Popa

123
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Developing an Adaptive Fuzzy Controller for Risk Management
of Company Cash Flow
Marcel Ioan Bolo ș1·Diana Claudia Sab ău-Popa1
Received: 11 August 2015 / Revised: 22 November 2015 / Accepted: 1 February 2016
©Taiwan Fuzzy Systems Association and Springer-Verlag Berlin Heidelberg 2016
Abstract This study is part of research from corporate
governance domain, knowing that one of the major con-
cerns of stakeholders is to identify decisions that ensure
adequate control over costs and hence over the risk of cash
flow, in order to ensure a high level of performance. The
immediate consequence is that the decision to control the
risk of cash flow has impact on the market value of the
listed companies. In this context, the paper addresses the
issue of cash flow risk in terms of leverage, except that the
debt service of a company is often a “fixed cost” and the
company has a certain level of affordability of this cost.
This level of cost affordability for capital is determined by
the existence of the free cash flow available for being used
in subsequent reimbursement of the borrowed capital.
Moreover, since the free cash flow has a certain evolution
during the period the capital has to be repaid, the question
of maintaining security in the debt service of free cash flow
is raised. The objective of this study is achieved using a
fuzzy adaptive controller.
Keywords Corporate governance cost of capital · Free
cash flow · Cash flow risk · Fuzzy adaptive controller1 Introduction
Corporations, given a tough fight to maintain on the market
the products and services obtained, are interested to control
costs regardless of their nature, in order to make the selling
price attractive for the consumer, ensuring adequate qual-
ity. Investments in equipments and technology underlying
the development strategies, but these companies need a
mix of financing sources: the financial market and their
own sources. [ 1].
The decision to purchase the needed capital for invest-
ment projects is not simple. It depends essentially both on
the cost of capital ( kc) and the carrying capacity ( CSD)o f
the debt service by the company. One of the most popular
ways to get a reasonable capital cost for the corporation is
the mix of funds used to finance investment, which leads to
the formation of the weighted average cost of capital.
The simplest rule that is used by corporate decision
makers has two categories of funding sources: own sources
(Spr) with the cost funding sources ( kpr) and borrowed
sources S^i/C0/C1
with the cost funding sources k^i/C0/C1
, leads to the
formation of weighted average cost of capital (CMPC)
computed with the formula CMPC ¼Spr/C2kprțS^i/C2k^i/C0/C1
.
The literature considers that it is relevant to compute
the weighted average cost of capital, only considering the
influence that the financial structure of the company in
question exerts on the cost of each source of funding. In
addition to the monetary costs which are explicitly
attributed to a source of funding (e.g., interest, dividend),
it may entail implicit costs, a change to other funding
sources, which are passed on the weighted average cost of
capital.
Furthermore, estimating the cost of capital is essential
for the efficient allocation of capital and generally depends
on the investor’s portfolio structure and the level of&Marcel Ioan Bolo ș
marcel_bolos@yahoo.com
Diana Claudia Saba ˘u-Popa
dianasabaupopa@yahoo.ro
1Department of Finance and Accounting, University of
Oradea, Oradea, Romania
123Int. J. Fuzzy Syst.
DOI 10.1007/s40815-016-0159-z
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earnings brought by new investment compared with the
rest of the portfolio. In the context of alternative invest-
ments, such allocations of capital represent a big part of the
investor’s portfolio and have nonlinear rewards comparedwith the rest of the portfolio at timelines that allow
rebalancing [ 2].
Regardless of the existing theories regarding invest-
ments, the debt service regularly engages important values
of cash flow in the company, wherever it occurs payment at
maturity that can embarrass its current activity. If there is a
large gap between the amount of time purchased for
impairment of capital for investment projects and the timerequired for repayment of borrowed capital, cash flow
deficits that affect the long-term carrying capacity of the
debt service company can be generated.
Regardless the strategy identified by the company to
minimize the cost of capital, it is necessary to consider the
factors on which the debt service affordability depends toavoid cash flow deficits and default risk, that on long-term
lead to the degradation of economic performance
indicators.
2 State of Research in the Literature
The risk of cash flow, as well as the capital cost, in terms offree cash flow are presented in numerous papers in inter-national literature.
The cost of capital modern approach is based on the
classical work of the American economists, Nobel laure-ates, Modigliani and Miller [ 3] “The cost of capital,
corporation finance and the theory of investment.” This
work provides the foundation for defining and calculatingthe cost of all forms of capital, used by companies,
including debt and equity, in terms of uncertain returns.
Modigliani and Miller concluded that the type of securitiesissued by a company is irrelevant. Since then, many
researchers have tried to explain what factors can influence
the cost of capital.
Building on the work of Miller and Modigliani, Ber-
tomeu and Cheynel [ 4] analyze the risk premium using the
Cara-Normal model and conclude that the informationaffects the cost of capital, but this effect is ambiguous and
does not mean that the information may be a factor influ-
encing the share price, having explanatory power beyondthe other factors related to real decisions.
Jurek and Stafford [ 2] developed a method for calcu-
lating the cost of capital for alternative investments, theauthors focusing on large-scale investments. The conclu-
sion of the study is that despite seemingly attractive history
of the alternative investments yields, many investors havenot covered the cost of capital.Some recent research shows that implicit cost of capital
(CIC), predicted by the financial analysts, and the prices of
shares listed on a regulated market may underlie the fore-
casting yield market [ 5]. However, it is a necessary caution
in the use of CIC as a basis for estimating the cost of equity
or the required return on the company level. They show
that CIC is a more consistent and reliable predictor thanother traditional variables such as dividend/share price and
gain/share price, to estimate the performance of the port-
folio and higher CIC shares are associated with a greater
likelihood of listing [ 6].
Meanwhile, Jensen [ 7] defines free cash flow as the
excess of the cash flow toward the required for financing
projects of companies that have positive net present value.
This free cash flow has to be paid to shareholders if thecompany managers want to streamline and maximize its
value. Moreover, the paper shows that the share prices of
listed companies will increase with the unexpectedincreasing of payments to shareholders and will decrease
with the reducing payments or new applications for funds
from shareholders. The managers and shareholders inter-ests and incentives generate major issues such as the
optimal size of the company and payments to shareholders,
particularly to large companies with free cash flow andfewer profitable investment opportunities.
Parsian and Koloukhi [ 8] analyze the factors that influ-
ence the amount of dividends paid to shareholders, becausedividend payments made by companies over time have a
bearing stable on: the price per share, the future growth of
revenue, and on the equity value. The authors used multi-variate regression with seven variables. They have
analyzed 102 companies and the empirical results have
shown a significant negative relationship between thepercentage of free cash flow to total assets (independent
variable) and the financial rate of return (independent
variable), whereas the relationship between lever rate(dependent variable) and the financial rate of return (in-
dependent variable) is positive and significant. And the
most important result of the study is that the financial rateof return (independent variable) is the factor that most
influences the dividends paid to shareholders (dependent
variable) [ 9].
The international literature studied the relationship
between earnings management and free cash flow, namely
whether these gains increase or decrease in free cash flowconditions. The results show that those companies that
have generous free cash flow tend to increase the earnings.
But audit committees, external quality audit, and companyownership structure reduces the earnings under conditions
of free cash flow. However, the steering committee and the
supervisory board do not have a significant impact onearnings management, suggesting that the corporate gov-
ernance mechanism, through its monitoring role, reducesInternational Journal of Fuzzy Systems
123
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the earnings management under conditions of free cash
flow [ 10].
The calculation of VaR resembles with the calculation
of risk of cash flow for companies operating in the nonfi-nancial sector [ 11]. Since VaR measures the maximum
total amount that a company can expect to lose in fore-
seeable conditions in a given horizon of time, the risk ofcash flow measures the maximum deficit that the company
is willing to tolerate. Calculating the risk of cash flow
implies a forecast of the probability distribution associated
with future cash flow levels [ 12].
3 Cash Flow Risk Measurement Under Debt
In the literature, the available cash flow depends on the
surplus of the corporation earnings before interest and
taxes (EBIT), the working capital variation DCpr/C0/C1
, and
the necessary capital investment (CI) after a relationship of
the form:
CFd¼EBIT țDepreciation țAmortization /C0DCpr
/C0C^I: ð1Ț
From this available cash flow, known in the interna-
tional literature as “free cash flow,” will be supported by
the corporation debt service (SD) consisting of cash out-flows arising from the payment of the capital rates ( R
cf) and
payment of the cost of capital ( Cc) known as interest
expense. The ratio of debt service and available gross cashflow before debt service (CI), indicates for each year of
analysis of the investment projects, if there is a risk of cash
flow generated by purchased capital from the financialmarket, after the following relationship:
R
cf¼SD
CFD b: ð2Ț
In reality, any company may incur a debt service
throughout its repayment duration at least equal to theavailable cash flows updated after a relationship of the
form
SD¼X
DR
i¼1CFD i/C21
ð1țraȚi: ð3Ț
The cash flow risk is defined in the literature as the risk
that transmits information about the negative cash flow
associated with a certain probability with which a company
could face a certain period of time. But especially becauseof the insufficient investments, as a result of the funding
constraints, the cash flow risk should refer explicitly to
external sources of financing [ 13], including borrowed
financing sources. Regardless of how the cash flow risk is
treated in literature, it is important to note that the biggestinfluences have the borrowed capital that takes the form of
a “fixed cost” during repayment [ 14].
The cash flow risk ( R
cf) due to any corporation borrowed
capital will be determined as the difference between debtservice and available gross cash flow before the capital
required for investment, for each year of the term of
repayment after a relationship of the form
R
cf¼XDR
i¼1C^I
DR/C21
ð1țraȚițXDR
i¼1C^I/C0i/C2C^I
DR/C18/C19
/C2rd
1țra/C18/C19i
/C0XDR
i¼1CFD bi/C21
ð1țraȚi: ð4Ț
The size of the cash flow risk is expressed in absolute
value. According to this relationship, the corporate cash
flow risk depends on the available gross cash flow and on
the borrowed capital (interest rate as the debt servicecomponent). The biggest is the difference between bor-
rowed capital plus interest and available cash flow, the
lower is the cash flow risk, while the reverse situation if thedifference between borrowed capital including interest and
available cash flow is lower, the higher is the cash flow risk
and the corporation may run into difficulty with therepayment of capital rates.
The cash flow risk can be expressed in a percentage
form. When is measured the intensity manifested by the
cash flow risk in a corporation are identified those situa-
tions that may arise from cash flow deficits, after arelationship of the form:
R
cf¼CFD b/C0SD
CFD b%½/C138: ð5Ț
In essence, the relationship between cost of capital and
carrying capacity of the company is determined by the“available gross cash flow.” Thus, if the difference between
“available gross cash flow” and debt service is high then
the company is in financial safety margin, otherwise if thedifference is small, the cash flow risk is imminent. The
financial contagion emerge in conditions of high cash flow
risk, because the other stakeholders will be affected by thecash flow risk.
4 Development and Application of an Adaptive
Fuzzy Controller for Cash flow Risk
Computational intelligence is used by at least two decades
for data modeling in finance. Odom and Sharda [ 15] used
for the first time class neural network (based on ArtificialNeural Networks) to estimate the credit risk tolerance in
order to highlight fault tolerance. However, the neural
network cannot explain the causal relationship betweenM. Bolo ș, D. Sab ău-Popa: Developing an Adaptive Fuzzy Controller for Risk Management of Company Cash Flow
123
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variables, so there are still restrictions in the estimation
process with its aid [ 16].
Fuzzy theory, which was developed by Lotfi A. Zadef in
1971, better approximates the human judgment and can beused to describe the problem. Fuzzy theory allows the
existence of inaccuracies and uncertainties in datasets [ 17].
Based on this theory, more adaptive fuzzy control schemeshave been developed for a class of uncertain nonlinear
systems. In these schemes, the system loop is closed, being
established in accordance with the Lyapunov theory. To
cope the rounding errors (errors of modeling or construc-
tion errors) and external disorders, these adaptive fuzzycontrollers are amplified by a robust compensator, which
may take the form of a supervisory control, a sliding mode
control, and/or H ∞control [ 18].
In general, for modern control strategies, commonly
used to decrease the complexity, are required the fuzzy
controllers, that are highly competitive in performanceapplications. Several researchers believe that the ratio
performance/complexity is greater when adaptive fuzzy
controllers are used [ 19].
The developed adaptive fuzzy controller is based on the
relationship between free cash flow and debt service (in-
vested capital) to keep the company in the financial safetyzone, on the assumption that cash flow will always be
variable during repayment, while the necessary capital
investments will play a “fixed cost.” The adaptive fuzzycontroller aims to identify situations of difficulty when the
company deviates from the rules of financial security and
also aims to identify the corrective measures that thecompany must apply for the reintegration in the financial
security zone.
The adaptive fuzzy controller relies on a number of
assumptions that are based on the fact that the company’s
debt service consists of necessary cash flow to pay the
interest rates on borrowed capital (CI) may not be higherthen the available gross cash flow (CFDb) relationship of
the form:
CF
db/C0CI/C210: ð6Ț
Moreover, the cash flow required for debt service must
be provided constantly, according to the schedule for
repayment of debt service, while available gross cash flow
largely depends on the company’s activity. In this context,for the adaptive fuzzy controller, the following basic
notions are defined:
The company’s financial safety margin defined as the
company reserves for financial security with which is
ensured the repayment of debt service, which is equal to
the difference between available gross cash flow andrequired cash flow for the debt service, which has to be
situated within the limit of țp%CF
d;considered sufficientto ensure the financial safety margin necessary to pay the
debt service according to the relationship:
MS f¼CFdb/C0CI/C21ț p%CFdb: ð7Ț
The percentage of available cash flow for interpretation
of results can be set according to user requirements. Forexample, a percentage of 10 % of CFDb can be considered
sufficient for analyzing financial safety margin. In any
case, negative variations of CFDb may be high-risk alarm
for the company’s cash flow risk.
The company’s financial safety margin variation
between two time periods ( t+1 ; t) established by the
difference between the margin value in two consecutive
time periods, depends on the change in the available grosscash flow and on the variation of the necessary cash flow
for the interest rate and has to be located around țk%CF
db
according to
DMS f¼MS ftț1/C0MS ft/C21ț k%CFdb ð8Ț
or
DMS f¼DCFdb/C0DCI/C21ț k%CFdb: ð9Ț
If the pace of variation in the available gross cash flow is
higher than the pace of variation in the necessary cash flow
for the dept service, it can be appreciated that the variation
of the safety margin will certainly reduce a part of the cashflow risk, because there will be resources to ensuring cash
flow for debt service. Otherwise, if the pace of variation in
the necessary cash flow for the dept service is higher thanthe pace of CFDb variation, then the cash flow risk may
affect the company’s performance.
The available gross cash flow adjustor before invested
capital is computed using the following formula:
VAjCF
bb¼1țAjCFbb ðȚ CFdb/C0CI: ð10Ț
The financial safety margin adjustor represents the
adjustment value for available CFDb (with a percentage + k
% CFD) by the means at company disposal when variation
is below the safety margin ðțk%DCFdȚ. It may be in this
context the famous “capital injection” from shareholders.
The financial safety margin adjustor has values defined as
follows:
AjMS f¼0%CFdb if
k%CFdb if
kțnðȚ %CFdbifDMS f[țk%DCFdb
DMS f2ð0%/C4țk%/C138DCFdb
DMS f/C20ð /C0 k%/C00%/C138DCFdb8
><
>:
ð11Ț
The final form of financial safety margin is given by
MS f¼ð1țAjMS fȚ/C2CFdb/C0CI: ð12Ț
The financial safety margin adjustor is determined by
the values recorded by the available cash flow variation andInternational Journal of Fuzzy Systems
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required cash flow for debt service variation. For the sim-
ulation of the adaptive fuzzy controller were considered the
following basic assumptions:
1. The financial safety margin can range between 0 and
50 % of CFDb;
2. The financial safety margin variation can range
between 0 and 100 % of CFDb;
3. The value of the financial safety margin adjustor is
determined using an adaptive fuzzy controller.
The working assumptions of the adaptive fuzzy con-
troller can be changed according to the company needs, byimposing conditions of entry into the controller according
to the specific of the company. The for the algorithm that
underly the functioning of the adaptive fuzzy controllerare:
Step 1 There are built the membership functions for input
variables as fuzzy sets: the financial safety margin ðMS
fȚ;
which can range on the interval 0 %CFdb ½/C4 50%CFdb/C138,
according to linguistic values: low (Re), medium (M), and
high (R). The financial safety margin variation ðDMS fȚcan
range on the interval 0 %DCFdb ½/C4 100%DCFdb/C138;accord-
ing to linguistic values: low (Re), medium (M), and high
(R).
The triangular membership function for input variables
MS fandDMS fis determined on ranges of values for the
input variables. For example if MS f20%CFD b ½
/C450%CFD b/C138then the triangular membership function for
the financial safety margin will be
lMS fðȚ¼0% if MS f\0%DiMS f[50%;
MS f/C025%CFd
25%CFd/C00%CFdif 0%CFD/C20MS f/C2025%CFD;
50%CFd/C0MS f
50%CFd/C025%CFdif 25 %CFD/C20MS f/C2050%CFD;8
>>>>><
>>>>>:
ð13Ț
Step 2 For the control variable (which checks whether the
safety margin variation will not affect the company’s
ability to support the debt service) are established values on
the 0 %CFdb/C450%CFdb ½/C138 ;for some linguistic values:
very small (Fm), small (m), average /C22M, high (M), and very
high (FM).
The membership function for the control variable is built
on ranges. For example, if the safety margin adjustor
AjMS f215%CFdb;100%CFdb ½/C138 then the function of
belonging will be of the form
lAjMS f/C0/C1
¼0%CFddaca^15%CFdb\0%DiCFdb[50%;
AjMS f/C015%CFd
45%CFd/C015%CFddaca^15%CFdb/C20DMS f/C2045%CFdb
100%CFd/C0AjMS f
100%CFd/C045%CFddaca^45%CFdb/C20DMS f/C20100%CFdb8
>>>>><
>>>>>:
ð14ȚStep 3 Are built the adaptive fuzzy control rules to deter-
mine what measures should be taken to preserve the
company’s financial safety margin so as not to impair its
ability to meet debt service.
In the table above are set the fuzzy control rules.
Specific to these rules is that they are based on two con-
ditions, namely “if” and “then,” that are established by the
experts regarding the factors that influence the risk of cash
flow.
The number of fuzzy rules will be equal to 32 = 9 and
the financial safety margin adjustor will be divided into five
risk categories, namely: very high, high, medium, low, andvery low. The controller input variables for the fuzzy rules
remain variables that influence the cash flow risk and are
represented by the linguistic values from the table, forfinancial safety margin and for the variation of the financial
safety margin.
The established fuzzy rules shall be the following: if the
safety margin is low and the variation of the safety margin
is also reduced, then the adjustor will be high (R1,1 of the
table); or if financial safety margin is average and thevariation of the safety margin is reduced, then the adjustor
will be higher (R1,2 of the table). The linguistic values of
the influence factors will be established by the expert bycategories and the combinations of influencing factors will
determine the size of the output variable, the adjustor for
the financial safety margin.Step 4 Using the control rules presented in Table 1will be
realized the fuzzy inferences to the following conditions
for the input variables (conditions for input variables canbe set according to the needs of the company):
MS
f20%CFdb;10%CFdb;20%CFdb;30%CFdb; ½
40%CFdb;50%CFdb/C138ð15Ț
DMS f¼0%CFdb;20%CFdb;40%CFdb;60%CFdb; ½
80%CFdb;100%CFdb/C138:
ð16Ț
For the output variable (financial safety margin adjus-
tor), the values will be obtained by defuzzification, using
the center of gravity method. The adaptive fuzzy controller
behavior was studied for all the above-mentioned six sit-uations known as simulation cycle.
Table 1 Establishment of fuzzy control rules
MS f
DMS fLow (Re) Medium (M) High (R)
Low (Re) Very high (FM) High (M) Medium ð/C22MȚ
Medium (M) Medium ð/C22MȚ Low (m) Very low (Fm)
High (R) Low (m) Very low (Fm) Very low (Fm)M. Bolo ș, D. Sab ău-Popa: Developing an Adaptive Fuzzy Controller for Risk Management of Company Cash Flow
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With the help of fuzzy control rules, for output variable
“financial safety margin adjustor” are established the fol-
lowing rules for the adaptive fuzzy controller:If
(MS f¼MȚandðDMS f¼ReȚthen (Fig. 1).
ðAjMS f¼MȚ,Reg fuzzymin 0 :60;0:55 ðȚ ¼ 0:55 MðȚ ð 17Ț
IfðMS f¼ReȚandðDMS f¼ReȚthen
ðAjMS f¼FMȚ,Reg fuzzymin 0 :35;0:55 ðȚ ¼ 0:35 ReðȚ:
ð18Ț
For the output variable of the adaptive fuzzy controller
(safety margin adjustor), the membership function will take
the values of 0.55 (M) 0.35 (Re), and its value will bedetermined using the centroid method. The other simula-
tion cycles for input variables of fuzzy controller, menus
properly according to the rules described above. Results forthe financial safety margin adjustor for each of the five
simulation cycles were generated using MATLAB [ 20].
As regards, the evolution of the financial safety margin
adjustor according to the value of financial safety margin
and its variation, the results are shown in the following
chart: (Fig. 2)
In the simulation cycles, the growth rate of financial
safety margin R
MSF¼MSbț1
MSb/C2100 is lower then the growth
rate of financial safety margin variation RMSF¼MS ftț1
MS ft/C2
100 which means that the safety margin adjustor gradually
decreases to a certain value, then regardless of the growth
rates of financial safety margin or financial safety marginvariation, the value of the financial safety margin adjustor
becomes inelastic.
The inflection point for the financial safety margin
adjustor represents the time from which there are not
necessary adjustments for the available cash flow. In allother working hypotheses for the adaptive fuzzy controller
(maintaining constant growth rate, or a rate of increasing of
the safety margin higher then the safety margin variation)is observed that there is an inflection point from which the
safety margin adjustor becomes inelastic.5 Generating Loops Within Adaptive Fuzzy
Controller
The basic rule for the adaptive fuzzy controller is that
through simulation are obtained the values that should have
safety margin adjustor at certain moments of time, so thatthe limits of the company’s financial safety margin to be
maintained in the monitored parameters by investors [ 21].
Adaptive fuzzy controller can measure the dynamic valuesthat should have the financial safety margin adjustor.
According to this rule, in the adaptive fuzzy controller are
available the following equations: [ 22]
MS
f¼1țAjMS f/C0/C1
/C2CFdb/C0CFRCțD ð19Ț
MS f¼CFdb/C0CFRCțD/C21ț p%CFdb ð20Ț
DMS f¼MS ftț1/C0MS ft/C21ț k%CFdb: ð21Ț
To generate the value margin adjustor between two
consecutive time points ( t+1 , t), the following equations
define the financial safety margin.
MS ft¼1țAjMS ft/C0/C1
/C2CFdtb/C0CFRCțDtand
MS ftț1¼1țAjMS ftț1/C0/C1
/C2CFdtț1b/C0CFRCțDtț1:ð22Ț
In these circumstances, the financial safety margin
variation at time t+ 1, with the constraint k%CF d, can be
rewritten as follows:
DMS ftț1¼1țDAjMS f/C0/C1
/C2CFdtb/C21țRCF d ðȚ
/C0CFRCțDt/C21țRRCțD ðȚ /C21 k%CFdb:ð23Ț
At time t+nthe state equation of adaptive fuzzy con-
troller becomes
DMS ftțn¼Xn
i¼11țAjMS fi/C0/C1
/C2CFdtb/C21țRCFdi ðȚ
/C0Xn
i¼11țRRCțDi ðȚ CFRCțDt: ð24Ț
Fig. 1 The fuzzy adaptive controller. Source Own sources
Fig. 2 The evolution of MSF, DMS f,AjMS fto the different values of
the simulation cycle. Source Own calculations using MatlabInternational Journal of Fuzzy Systems
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Suppose that at time tfor a simulation cycle the values
for CF dband CF RCțDare for start base 1000 and 800 u.m.,
implying that the financial safety margin is 200 um, 20 %
of CF db. At the time t+ 1 the values for CF dband CF RCțD
becomes 1.100 and 850 u.m., which requires a financial
safety margin of 350 um, 35 % of CF d. For this simulation
cycle, the input values in the adaptive fuzzy controller are
MSftț1¼350u :m and DMSftț1¼ț150 u :m;
According to the fuzzy control rules we haveIf (MS
f¼MȚandðDMS f¼ReȚ, then
ðAjMS f¼MȚ,Regfuzzymin 0 :35;0:25 ðȚ ¼ 0;25 ReðȚ ð 25Ț
IfðMS f¼MȚandðDMS f¼MȚ, then
ðAjMS f¼mȚ,Regfuzzymin 0 :35;0:55 ðȚ ¼ 0:35 MðȚ ð 26Ț
If (MS f¼RȚandðDMS f¼MȚ, then
ðAjMS f¼/C22MȚ,Regfuzzymin 0 :35;0:55 ðȚ ¼ 0:35 RðȚ ð 27Ț
If (MS f¼RȚandðDMS f¼ReȚ, then
ðAjMS f¼/C22MȚ,Regfuzzymin 0 :60;0:25 ðȚ ¼ 0:25 ReðȚ:ð28Ț
For the output variable, the values are determined using
MATLAB and the centroid method. For the first simulationcycle, the financial safety margin adjustor is around 10 %. In
these circumstances, the financial safety margin after
applying the adjustor will take the value MS
f¼1ț10% ðȚ
1100/C0850¼360 u :m:
The new simulation cycle will have the coordinates
MS f¼360u :m:DiDMS f¼160u :m:which represents a
36 % increase in financial safety margin and 43.85 %
increase in CF dbeing met the adaptive fuzzy controller
initial conditions. A simulation loop is considered closed ifthe original requirements of fuzzy input variables are
respected [ 23].
The cash flow risk in loop is computed as the difference
between financial safety margin achieved by the company
and the financial safety margin determined using fuzzy
controller, by the following formula:
R
CF¼MSfr/C0MSfAjabsolute valueðȚ ð 29Ț
RCF¼MSfr/C0MSfAj
MSfAj/C2100 procentual valueðȚ ð 30Ț
MS fadjusted ¼CFdbð1țCFdadjusted =100Ț/C0CI ð31Ț
CF dadjusted is computed using MATLAB. The fig-
ure above illustrates the company’s status in terms of cash
flow risk (Fig. 3).
The green area indicates a favorable situation, when the
company is not in the danger zone, while the red zone
reflects the manifestation of the cash flow risk. It can be
seen that the risk situation emerge when the MS fcurve isbelow the adjusted financial safety margin curve. In this
case, the company must come up with an infusion of
capital to remedy the situation.
6 The Applicability Sphere of the Fuzzy
Controller and the Comparison to Other Models
The developed fuzzy controller can be successfully applied
to characterize the extent of the financial margin adjustor,
respectively, of that value with which is adjusted theavailable cash flow of the company, not to register major
deviations of the margin from the amount deemed necessary
to ensure the financial stability of the company [ 24,25].
The input variables set for the fuzzy controller are the
financial safety margin and the variation margin of the
financial safety. As output variable, the adjustor value isdetermined by values of the input variables. The major
advantage is that the fuzzy controller adjustor size is
determined by the dynamics of the financial safety marginand by its change that directly influences the adjuster value.
The applicability of the fuzzy controller can be extended
using other input variables that have direct impact on thecash flow risk of the company in terms of debt [ 26].
For simulation were used theoretical data, taking cal-
culation hypotheses for different values of the availablecash flow of the company and for the debt service. Being
an innovative tool in the field of simulation data is con-
sidered to be sufficient, according to the authors, totheoretically substantiate the fuzzy controller operation. As
research progress, both authors intend to develop the con-
troller using real case studies and using fuzzy regulators asa mean to improve the research results.
In the literature were devoted to cash flow risk analysis
models that compute cash flow indicators (rate) as
R
cf¼F1=F2/C2100: ð32Ț
Fig. 3 The simulation cycle in the adaptive fuzzy controller. Source
Own calculations using MatlabM. Bolo ș, D. Sab ău-Popa: Developing an Adaptive Fuzzy Controller for Risk Management of Company Cash Flow
123
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Some studies regarding the cash flow risk belong to Oral
and Akkaya [ 27], who observed that the operation pro-
cesses of an enterprise are influenced by the cash levels.
They built a model that predicted the cash levels. Dong andLi [28] and Han et al. [ 29] performed quantitative analysis
in order to study the risk factors that influence the cash
flow. Also, a prediction of the enterprises cash flow was
conducted.
The major disadvantage of these models is capturing the
size of the cash flow risk in certain moments of time,
depending on different values of the influence factors.
These results are then interpreted by experts.
Using the fuzzy controller for the cash flow risk analy-
sis, these calculations using discrete variables are no longer
taken into consideration, being used the influence variableson the cash flow risk, characterized by linguistic values. In
this way, the result of cash flow risk will be expressed also
using the structured language class values, based on theassessment of experts. The transformation of linguistic
values into discrete values takes place in the framework of
defuzzification, which is specific to fuzzy sets.
Using fuzzy controller for the study of the cashflow risk
allows the proximity of human reasoning with the real
impact of the variables of influence on the output variable(cash flow risk) and also allows the causality of the influ-
ence variables and output variables.
7 Concluding Remarks
The developed adaptive fuzzy controller offers the possi-bility of a new philosophy for the affordability of the debt
service capacity of the company by taking into account therisk of cash flow. In this respect, the rules of fuzzy con-
troller are based on three new concepts namely: the
corporate financial safety margin, the variation of thefinancial safety margin, and the safety margin adjustor of
the companies. The simulation cycles showed that if the
pace of growth of financial safety margin is lower than thegrowth rate of variation of the financial safety margin, then
the safety margin adjustor also increases to a point where it
becomes inelastic. From that point it is considered that anycompany is protected from the risk of cash flow, the
explanation being that the safety margin adjustor value is
almost zero.
The adaptive fuzzy controller loops were generated
through simulation cycles and are linked through the safety
margin adjustor. A loop of the controller is consideredcompleted if the initial conditions to entry into the loop are
respected. Otherwise, the simulation cycle resumes with
the new values for financial safety margin, the variation ofthe financial safety margin. Simulations have led to thesame assumption: the adjustor value remains constant,
inelastic, if the pace of growth of the input variables
increases above a certain value. The controller loops have
the advantage that they take into account the initial valuesof the input variables of the controller and in these con-
ditions the adjustor value is adapted to the actual conditions
of the company.
The adaptive fuzzy controller can be a good decision
tool for managers in companies since using the rules
underpinning their operation can be identified as the risk of
cash flow, which leads to diminishing the risk that credit
rates and interest rates are not reimbursed to maturity.
References
1. Bradea, I.A., Delcea, C., Scarlat, E., Bolo ș, M.: KRIs in hospitals
—network, correlations and influences, Econ. Comput. Econ.Cybern. Stud. Res. 48(1), pp. 81–94 (2014) ISSN: 0424-267X
2. Jurek, J.W., Stafford, E.: The cost of capital for alternative
investments. Harvard Business School Working Paper, no.
1910719 (2013)
3. Modigliani, F., Miller, M.H.: The cost of capital, corporation
finance and the theory of investment. Am. Econ. Rev. 48(3), 261–
297 (1958)
4. Bertomeu, J., Cheynel, E.: Disclosure and the cost of capital: a
survey of the theoretical literature. Columbia Business School
Research Paper, no. 15–16 (2014)
5. Andre ´n, N., Jankensga ˚rd, H., Oxelheim, L.: Exposure-based cash-
flow-at-risk for value- creating risk management under macroe-conomic uncertainty. IFN Working Paper, No. 843, Research
Institute of Industrial Economics (2010)
6. Jankensga ˚rd, H.: Cash flow-at-risk and debt capacity. Lund
Institute of Economic Research Working Paper Series, no. 2(2008)
7. Jensen, M.C.: The free cash flow theory of takeovers: a financial
perspective on mergers and acquisitions and the economy. Pro-ceedings of the Conference “The Merger Boom”, pp. 102–143
(1987)
8. Parsian, H., Koloukhi, A.S.: A study on the effect of free cash
flow and profitability current ratio on dividend payout ratio:evidence from Tehran Stock Exchange. Manag. Sci. Lett. 4, 63–
70 (2014)
9. Bradea, I.A., Delcea, C., Scarlat, E., Bolos ¸, M., Chirit ¸a˘, N.: Grey
incidence between bank’s risks and their performance. In:Computational Collective Intelligence Technologies and Appli-
cations, Lecture Notes in Computer Science, Springer, Berlin,
vol. 8083, pp. 80–89, ISBN: 978-3-642- 40495-5 (2013)
10. Bradea, I.A.: Risks in hospitals. Assessment and management.
The Romanian Economic Journal REJ, issue 54, year XVII,
pp. 25–37, ISSN: 2286-2056 (2014)
11. Bradea, I.A., Ma ˘ra˘cine,V.: Grey incidence between KPIs and
hospital performance. Grey Systems: Theory and Application.
Special Issue: Perspectives on grey economic systems, vol. 5,
issue 2, Emerald, ISSN: 2043-9377, pp. 234–243 (2015)
12. Delcea, C., Cotfas, L., Bradea, I. et al.: KRI and firms’ perfor-
mance—a grey theory approach. Proceedings of 2013 IEEE
International Conference on Grey Systems and Intelligent Ser-
vices (GSIS), pp. 260–264 (2013c)
13. Sabbadini, A., Lim, M.: Cash Flow Risk Management—in Good
Times and Bad. ERM Symposium, Chicago (2011)International Journal of Fuzzy Systems
123
Author's personal copy

14. Maracine, V., Delcea, C., Bradea, I. et al.: Banking sector risks
identification via GRA. Proceedings of 2013 IEEE International
Conference on Grey Systems and Intelligent Services (GSIS),pp. 11–15 (2013)
15. Odom, M.D., Sharda, R.: A neural network model for bankruptcy
prediction. Proc. Int. Joint Conf. Neural Netw. II, 163–167
(1990)
16. Delcea, C., Bradea, I.A., Scarlat, E.: A computational grey based
model for companies risk forecasting. The Journal of Grey System,
vol. 25, issue 3, pp. 70–83. Londra, ISSN: 0957-3720 (2013a)
17. Fang, H.: Adaptive neurofuzzy inference system in the applica-
tion of the financial crisis forecast. Int. J. Innov. Manag. Technol.
3(3), 250–254 (2012)
18. Boulkroune, A., Tadjine, M., M’Saad, M., Farza, M.: How to
design a fuzzy adaptive controller based on observers foruncertain affine nonlinear systems. Fuzzy Sets Syst. 159, 926–
948 (2008)
19. Jung, J.W., Choi, Y.S., Leu, V.Q., Choi, H.H.: Fuzzy PI-type
current controllers for permanent magnet synchronous motors.
IET Electr. Power Appl. 5(1), 143–152 (2011)
20. Delcea, C., Bradea, I.A., Ma ˘ra˘cine, V., Scarlat, E., Cotfas, L.:
GM(1, 1) in bankruptcy forecasting. Grey Systems: Theory andApplication, Editura Emerald, vol. 3, issue 3, pp. 250–265, ISSN:
2043-9377 (2013b)
21. Delcea, C., Bradea, I.A., Paun, R., Friptu, A.: A healthcare
companies’ performance view through OSN, New trends inintelligent information and database systems. Series Title: Studies
in Computational Intelligence, vol. 598, pp. 333–342, Springer,
Berlin, ISBN: 978-3-319-16211-9 (2015)
22. Ordonez, R., Zumberge, J., Spooner, J.T., Passino, K.M.: Adap-
tive fuzzy control: experiments and comparative analyses. IEEE
Trans. Fuzzy Syst. 5(2), 167–187 (1997)
23. Lee, C.C.: Fuzzy logic in control systems: fuzzy logic controller
—Part I. IEEE Trans. Syst. Man Cybern. 20(2), 404–418 (1990)
24. Delcea, C.: Not black not even white definitively grey economic
systems. J. Grey Syst. 26(1), 11–25 (2014)
25. Jensen, M.C.: Agency costs of free cash flow, corporate finance,
and takeovers. Am. Econ. Rev. 76(2), 323–329 (1986)
26. Scarlat, E., Chirita ˘, N., Bradea, I.A.: Indicators and metrics used
in the enterprise risk management (ERM). Econ. Comput. Econ.Cybern. Stud. Res. J., issue 4, vol. 46, pp. 5–18, ISSN: 0424–
267X (2012)
27. Oral, C., Akkaya, G.C.: Cash Flow at risk: A Tool for financial
planning, Procedia Economics and Finance, vol. 23, pp. 262–266,
ISSN: 2212-5671 (2015)
28. Dong, M.X., Li, Y.X.: Cash flow risk management in central
enterprises an analysis based on audit announcements. Proceed-ings of the 6th International Conference on Financial Risk and
Corporate Finance Management, vol. S. I and II, pp. 1330138,
ISBN: 978-7-89437-112-6 (2014)
29. Han, S.H., Park,H.K., Yeom, S.M., Chae, M.J., Kim, D.Y.: Risk-
integrated cash-flow forecasting for overseas construction pro-
jects, KSCE Jornal of Civil Engineering, vol. 18, issue 4,
pp. 875–886, ISSN: 1226-7988 (2014)
Marcel Ioan Bolo șis a Professor at the Faculty of Economics in the
University of Oradea and holds two PhDs in Finance-Accounting andManagement. His areas of interest are financial economics, fuzzy
systems, applied mathematics, and corporate governance. His
research activity was materialized in works published in books, bookchapters, articles in journals, and articles presented at internationalconferences. He also led numerous research projects that were won
through international competition. He teaches Budget and Public
Treasury; Finances of Public Institutions; Public Institutions Account-ing; Corporate Governance; International Standards of Public Sector
Accounting; and International Financial Markets at University of
Oradea.
Diana Claudia Sab ău-Popa is an Associate Professor at the
University of Oradea, Faculty of Economics, Department of Finance
and Accounting, where she is a titular professor since 2003. Her
research focuses on the thematic of the subjects that she teach,specifically on Public Finance, Capital Markets, and the EuropeanUnion’s Finances. In recent years, she has focused on the study of
various links and influences between the economic and financial
indicators and the macroeconomic variables using models taken fromCybernetics.M. Bolo ș, D. Sab ău-Popa: Developing an Adaptive Fuzzy Controller for Risk Management of Company Cash Flow
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