Fuzzy Logic in Financial Analysis

450 Pages·2005·4.895 MB·English

by  Professor Dr. Anna Maria Gil-Lafuente (auth.)

AnnaMariaGil-Lafuente
FuzzyLogicinFinancialAnalysis
StudiesinFuzzinessandSoftComputing,Volume175
Editor-in-chief
Prof.JanuszKacprzyk
SystemsResearchInstitute
PolishAcademyofSciences
ul.Newelska6
01-447Warsaw
Poland
E-mail:[email protected]
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FuzzyLogicinFinancialAnalysis,2005
ISBN3-540-23213-3
Anna Maria Gil-Lafuente
Fuzzy Logic
in Financial Analysis
123
ProfessorDr.AnnaMariaGil-Lafuente
UniversidaddeBarcelona
FacultaddeCiencias
Econo´micasyEmpresariales
Dept.deEconom´ıayOrganizacio´ndeEmpresas
Av.Diagonal,690
08034Barcelona
Spain
E-mail:[email protected]
ISSNprintedition:1434-9922
ISSNelectronicedition:1860-0808
ISBN-10 3-540-23213-3SpringerBerlinHeidelbergNewYork
ISBN-13 978-3-540-23213-1SpringerBerlinHeidelbergNewYork
LibraryofCongressControlNumber:2004117077
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Preface
With ever increasing frequency, financial studies in business are acquiring
greater importance in the field of management as a consequence of the com-
plexity of the problems arising in present day society. The old treaties that
included certain aspects on the raising and placing of payment means have
been relegated to history, leaving the way open to monographic studies that
include and treat in depth specific aspects of financial activities in business.
The work we are presenting intends to set out an ordered set of basic
elements on which to base financial analysis in business in the XXI century.
Initareincludedaseriesofpreviousworkswhichserveasthebasisandfoun-
dation to the new contributions that are being made in the field of financial
economy and provide business with certain instruments and models that are
suitable for the treatment of the new economic context.
But a work such as this would not have any sense if it were not to be
oriented towards the solution of the problems arising in current reality. It is
well known that we are immersed in times that are characterised by certain
socialandeconomicchangesthatareextremelyfastandprofoundandwhich
have no precedent whatsoever throughout the whole history of mankind. We
are immersed in a world in which every event occurs and develops with such
speedthatitbecomespracticallyimpossibletoknowwithanydegreeofexac-
titudewhatthefutureholdsinstoreforus.Alltheeventsandcircumstances
we can expect are charged with a high degree of uncertainty.
Inordertobeabletotackletheproblemsofageneraleconomicorbusiness
nature arising from this uncertainty, which is implicit in all future events,
knowledgebasedonformallogicisnolongersufficient.Theso-calledmodern
mathematics based on mechanistic schemes, as well as Boolean algebra, are
no use for explaining and foreseeing those actions which we should carry out
in the future and they become impotent when faced with the new manner of
acting of our society.
In order to be able to adequately attend to the requirements, which very
often are brought up relative to a certain type of forecast or opinion on the
natureoffutureevents,ithasbecomeessentialtouseanewsetoftechniques
based on uncertainty. This manner of operation has as its objective the ex-
pressionintheresultsarrivedatwithallthesubtlenessandsubjectivitythat
characterises human thought. Unlike these new techniques, up to just a few
VI Preface
years ago what were used were certain models based some times on certain
data, at others on probabilistic elements the data of which was measurable
or verifiable. The first of these is not applicable today, because the uncer-
tainty that characterises the future events of our society does not permit us
to work with certain data. Neither are the second usable for the same rea-
sons, since to be able to apply a probability it is necessary to have, in the
first place, a succession of phenomena that are repeated under determined
circumstances and, in the second, be able to apply the results arrived at on
another phenomenon submitted to the same conditions as the former.
If we place ourselves in the sphere of business of our day and age, there
isnodoubtwhatsoeveroftheimportanceoffinancialdecisions.Anincorrect
decision can easily cause the disappearance of the business from the market.
Inthiscontextofuncertainty,thedecisionstobetakenareincreasinglymore
complex due to the changing circumstances relative to legal provisions, the
influence of other sectors and countries, prospects of changes in monetary
systems,etc.Thiscausestheexistingproblemstobemultipleandvaried:ex-
pansion,modernisation,financialbalance,qualityoftheworkplace,etcetera,
isonlyaverysmallsample.Ifweonlyconcentrateononeaspect,technology,
it can be seen that on a daily basis more models appear aimed at savings
in energy, effort and space, causing ever increasing requirements for invest-
ment in order to attain greater expansion and profits, precisely due to the
uncertainty relative to what will happen the next day.
But, in spite of all the technological advances, in spite of the fact that
increasingly mankind will have a greater need to be supported by the so-
called“artificialintelligence”inordertobeabletohandlealargeramountof
information at one and the same time, in spite of all this, there is something
availabletousallandwhichmakesussuperiortoanymechanicalapparatus:
that is imagination, a quality which allows us to be creative, to think and
decide.
The financier, in the exercise of the activity, is obliged to take decisions
for an uncertain tomorrow, all of which are subject to very rapid and sub-
stantialchanges.Inorderforthebusinesstoreachthedesiredobjectivesitis
necessary,increasinglymorefrequently,toresorttotheaidofexperts.These,
based on their knowledge and experience, should be able to orient the busi-
ness activity and attempt to decrease the range of possibilities for erroneous
decisions. To base the studies of financial analysis on the opinions of experts
instead of doing this on past data or on probabilistic forecasts, constitutes a
radical change, which we hope will bring fruitful results.
But the individualised opinion of an expert is not exempt from a certain
degree, more or less high, of subjectivity. It is for this reason that a good
partofthisworkisdedicatedtotheproblemofaggregationoftheopinionof
experts in the financial field, with the object of limiting, wherever possible,
thesubjectivecomponentoftheopinionsandmakingsurethatthedecisions
have the best guarantee of reaching the desired objectives.
Preface VII
The future faced by the businessman, financier, is uncertain and full of
risks, although also very full of great prospects. Fortunately current science
allows for the drawing up of techniques, previously unthinkable, which are
very suitable for the treatment of the problems of our society, of our busi-
nesses, of our finances. All that is required is that advantage be taken of
all the tools available to the executive to be able to advance through the
competitive jungle arising from the new economic conglomerates.
February 2005 Anna Maria Gil-Lafuente
Contents
1 The Financial Activity of Businesses...................... 1
1.1 The Changeability of Financial Phenomena ................ 1
1.2 Business within the Framework of Monetary Circulation..... 2
1.3 Classical and Modern Aspects of Financial Studies.......... 6
1.4 The Economic-Financial and Dividend Policy .............. 9
2 Basic Elements for the Treatment
of Uncertainty ............................................ 13
2.1 From Binary Logic to Multivalent Logic ................... 13
2.2 Fuzzy Logic and Fuzzy Sub-Sets.......................... 19
2.3 Imprecise Numbers ..................................... 22
2.4 With Regard to the Problem of Subjectivity ............... 29
3 Accountancy and Decision Techniques .................... 37
3.1 Financial Statements, Representative Hub
of the Financial Situation................................ 37
3.2 Accounting Instruments Faced with the Future............. 40
3.3 Management in Uncertainty ............................. 42
4 The Estimate of Economic-Financial Values
by Means of the Budget .................................. 45
4.1 Budgeting Activity in Business........................... 45
4.2 Budgeting Development ................................. 48
4.2.1 Flexible Budgets ................................. 49
4.2.2 Budget Planned by Programmes ................... 50
4.2.3 The French System RCB ......................... 52
4.2.4 The Zero-Base Budget ........................... 54
4.3 The Drawing Up of Provisional Statements ................ 56
5 Long Term Financial Solvency ............................ 61
5.1 Working Capital ....................................... 61
5.2 Medium and Long-Term Solvency ........................ 65
5.3 Variations in Working Capital............................ 67
5.4 Statement of Source and Application
of Working Capital in Uncertainty ........................ 72
X Contents
5.5 The Intervention of Counter-Experts ..................... 72
6 Short Term Financial Solvency ........................... 77
6.1 The Cash-Flow......................................... 77
6.2 Statement of Source and Cash-Flow Application............ 79
6.3 Estimating the Cash-Flow Faced with an Uncertain Future .. 81
6.4 Estimating the Cash-Flow by Means of the Opinion of Experts 82
6.5 The Difference of Opinion Between Experts................ 88
7 Financial Analysis by Means of Ratios.................... 95
7.1 Preliminary Considerations .............................. 95
7.2 Forecasting Profitability and Solvency by Means of Ratios ... 98
7.3 Representation of Ratios by Confidence Intervals ........... 102
7.3.1 Arriving at the Quotient Between Confidence Intervals 102
7.3.2 Comparing Confidence Intervals.................... 104
7.4 Use of Intervals in the Event of Several Strategies .......... 107
7.5 The Du Pont Scheme in Uncertainty ...................... 113
8 Risk Analysis............................................. 117
8.1 Risk in Management Studies ............................. 117
8.2 The Relationship Between Indebtedness
and Financial Profitability in Uncertainty ................. 118
8.3 The Approach with Confidence Triplets
as a Triangular Approximation........................... 120
8.3.1 First Alternative ................................. 120
8.3.2 Second Alternative ............................... 121
8.3.3 Third Alternative ................................ 122
8.4 Considerations on Estimating the Uncertainty of Profitability 125
8.5 From Financial Risk to Insolvency ........................ 130
9 Inference Chains in Financial Analysis.................... 135
9.1 Valuation of Financial Phenomena........................ 135
9.2 Considerations on Multivalent Logic ...................... 136
9.3 Multivalent Inferences................................... 137
9.4 Objectives in Inference Chains ........................... 141
9.5 The Result by Means of the Lukaciewicz Inference.......... 144
9.6 Inference Chains as an Element for Decision ............... 151
10 The Effect of Fixed Costs on Profit....................... 159
10.1 The Breakeven Point
as a Threshold for Profitability........................... 159
10.2 The Threshold of Profitability. Point or Interval? ........... 162
10.3 The Reduction of the Interval Representing
the Threshold of Profitability ............................ 165
10.4 The “Lever Effect” or Leverage........................... 172
Contents XI
11 Capital Cost.............................................. 179
11.1 Concept and Characteristics of Capital Cost ............... 179
11.2 The Cost of Outside Means of Financing .................. 181
11.3 Outside Capital Cost in Uncertainty ...................... 185
11.4 The Cost of Own (in House) Financial Means .............. 191
11.5 The Determination of the Cost of the Capital .............. 193
12 Relation between Financial Structure and Capital Cost... 203
12.1 An Overview of the Different Doctrinal Positions ........... 203
12.2 Uncertain Capital Cost and Financial Structure ............ 205
12.3 The Constancy of the Cost of Equity and Outside Capital ... 208
12.4 Mechanisms that Justify the Constancy of Capital Cost ..... 211
13 Incidence of the Financial Structure
on the Value of the Business.............................. 217
13.1 Classical Treatment of the Problem ....................... 217
13.2 New Approaches for Arriving at the Long-Term Value....... 223
13.3 Determination of the Value in the Hypothesis of Convergence 224
13.4 Development of the Scheme in the Event of Periodicity...... 234
13.5 Attempts for Solution of Other Cases ..................... 239
14 Sequential Study of the Modifications
in the Ratio of Indebtedness.............................. 241
14.1 Prior Considerations .................................... 241
14.2 General Approach to the Problem ........................ 242
14.3 Sequential Development of the Model ..................... 246
14.4 The Solution by Means of Dynamic Programming .......... 250
14.5 Incorporation of Uncertain Ratios ........................ 253
15 Determination of the Possible Strategies
for Reducing Indebtedness in Business.................... 257
15.1 Approach to the Problem................................ 257
15.2 Sequential Movements of the Index of Indebtedness ......... 259
15.3 Possibilities of Arriving at the Objective
in Two Periods......................................... 262
15.4 Establishment of Valuations
by means of Inferences ................................. 264
15.5 Arriving at the Objective
in the Medium and Long Term........................... 265
15.6 Direct Financial Policies................................. 273
15.7 Final Considerations .................................... 276