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UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE Prof. Alexandre Leme Sanches, MSc. Prof. Edson de Oliveira Pamplona,

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Apresentação em tema: "UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE Prof. Alexandre Leme Sanches, MSc. Prof. Edson de Oliveira Pamplona,"— Transcrição da apresentação:

1 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE Prof. Alexandre Leme Sanches, MSc. Prof. Edson de Oliveira Pamplona, Dr. Prof. José Arnaldo Barra Montevechi, Dr.

2 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE Itajubá

3 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE Itajubá

4 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE

5 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE Universidade Federal de Itajubá

6 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE 1. Introduction 2. Objectives 3. Methodological aspects 4. Literature revision 5. Operations with Triangular Fuzzy Numbers (TFN) 6. Fuzzyfication and Defuzzyfication 7. The Net Present Value 8. Application of Fuzzy Numbers in Investiments Analysis 9. Analyzing the Fuzzy NPV 10. Real Case Aplication 11. Conclusions

7 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE Uncertainties associated with Investment Analyses Alternatives methods Decision making process Optimization of financial resources 1.Introduction:

8 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE Main Objective : Demonstrate the use of fuzzy logic in the evaluation of investment projects under uncertaint conditions; 2.Objectives: Secondary Objective : Presentation of a software prototype to calculate the fuzzy NPV and relative analyses.

9 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE 3.Methodological aspects: The research method to be used is known as quasi- experiment: Pre and Post Test, TROCHIN (2001). Doesnt have total control over the input variables of the system, BRYMAN (1989). Theres a non-random treatment of the experiment, TROCHIN (2001). Where the human behavior is present, TROCHIN ( apud GONÇALVES (2003)).

10 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE Investment Data (selected group) Deterministic NPV Calculation – viability (pre-test) Sensibility Analyses (uncontrolled) Definition of the variables to be Fuzzyfied Fuzzyfication of the selected variables (specialist) Fuzzy NPV Calculation Viability and possibilities analyses associated with the Fuzzyfied NPVs (post-test). Defuzzyfication of the NPV (if necessary) Comparison with the Deterministic NPV - The Proxy Pretest Design LOGICLOGIC FUZZYFUZZY METHODMETHOD

11 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE 4.Literature revision The Fuzzy Logic: Fuzzy logic is a bridge which connects the human thinking to the machines logic; In a fuzzy set, the transitions between a member or a non-member occur continuously; The degree of membership is not probability, but a measure of compatibility between object and the concept represented by the fuzzy set.

12 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE 4.1. Membership Fuction - Example: A c d a b A a b cd x 1 A d a b c 1 A a b cd x 0.5 Boolean Logic (binary) Fuzzy Logic (continuous) A(x): Membership

13 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE 4.2. Fuzzy Number – General Definition, KUCHTA (1996) Where: are real numbers and : is a continuous real function non decreasing defined in the interval [0,1], such that: : is a continuous real function non increasing defined in the interval [0,1], such that: and

14 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE 4.3. Fuzzy Number: a1a1 a4a4 x a2a2 a3a3 1 0 A (x)

15 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE 4.4. Triangular Fuzzy Number (TFN): If and are linear functions and a 2 = a 3 : a1a1 a3a3 A (x) x 1 a2a2 A = (a 1, a 2, a 3 )

16 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE 4.5. Fuzzy Number – Example I: A Fuzzy Set representing the NPV: Rates: Low/Medium/High Low Medium High 0 1 ROR 26%18% 10%

17 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE 4.6. Fuzzy Number – Example II: A Fuzzy Set representing: (The value of one Dolar on 16/10/03): Subjectivity 0 1 Reais 2,6 2,7 3,0 0.5

18 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE 5.Operations with Triangular Fuzzy Numbers (TFN): : Addition : If A = (a 1, a 2, a 3 ) and B = (b 1, b 2, b 3 ), so: A (+) B = (a 1, a 2, a 3 ) + (b 1, b 2, b 3 ) = (a 1 + b 1, a 2 + b 2, a 3 + b 3 ), is a TFN. Example: 0 0, A B A + B x µ(x)

19 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE Subtraction: If A = (a 1, a 2, a 3 ) and B = (b 1, b 2, b 3 ), so: A (-) B = (a 1, a 2, a 3 ) - (b 1, b 2, b 3 ) = (a 1 - b 3, a 2 - b 2, a 3 - b 1 ), is a TFN. Example: B 0, A - B A B x µ(x)

20 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE Aproach by Chiu e Park (1994) Multiplication: Using the line equations: A * B = [[Al(y)* Bl(y), Ar(y)*Br(y)] is not a TFN. Example: 0 0, A B A x B x µ(x)

21 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE Division: (two diferents cases) 1) If A and B are both positives: A / B = [A l(y) / B r(y), A r(y) /B l(y) ] 2) If A is positive and B is negative: A / B = [A l(y) / B l(y), A r(y) /B r(y) ] The result in the first case is a positive fuzzy number and in the second case is a negative fuzzy number.

22 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE An: (where n is a real number) A B : (where B is a TFN (b1, b2, b3)) undefined

23 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE A n : (where n is a real number) A B : (where B is a TFN (b1, b2, b3)) x undefined

24 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE 6.Fuzzyfication and Defuzzyfication: Fuzzyfication: Is the maping of real numbers domain (generally discrete) to the fuzzy domain. Defuzzyfication: Is the proceeding in which the value of the output linguistic, inferred by the fuzzy rules, will be transletad to a discrete value. SHAW I. S. (1999)

25 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE Fuzzyfications example: 1 Very LowLowMediumHighVery High ROR (%)

26 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE Defuzzyfications example: NPV Bad Medium Good Very good Very bad

27 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE 7.The Net Present Value: Where: NPV: net present value CF 0 : first cash flow CF i : cash flow on period i (i=1...n) n: number of periods r: discount rate

28 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE 8.Application of Fuzzy Numbers in Investiments Analysis: The Fuzzy Net Present Value: According to BUCKLEY (1987) the Membership Function to NPV is givem: To i = 1, 2,... where k = i if F is negative and k = 3 - i if F is positive. Comparing:

29 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE 9.Analyzing the Fuzzy NPV Investiment Sure and Viable

30 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE Investiment Sure and Unviable

31 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE Investiment Unsure and Viable

32 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE Investiment Unsure and Unviable

33 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE Negative area Positive area

34 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE 10.Real Case Aplication: The Problem: Observing the great expansion of its clients business, and having abundant available raw material, the Mining company has shown interest in the feldspar processing, and in entering in the market as a competitor of its clients.

35 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE

36 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE The value of NPV found is R$ ,38. Therefore, in a simple Deterministic evaluation, the investiment could be acepted NPV Calculations Using Software Excel

37 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE

38 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE Fuzzyinvest 1.0 Main Screen Fuzzynvest 1.0 presentation:

39 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE Gráfico Sheet

40 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE Cálculos Sheet

41 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE Fuzzyinvest 1.0 Main Screen Analysing the results.

42 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE 1 Very Low Low Medium High Very High (27,51) % The failure possibility of the project.

43 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE Fuzzy classification array of the failure possibility of the investment Decision of the company Very LowUnconditionally Accept LowAccept with caution AverageAccept under restrictions High (27.51%)Reject and review project Very HighUnconditionally Reject Investment Projects Acceptance Criteria

44 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE 11.Conclusions: 1) The most relevant conclusion, concerns the comparison of the deterministic NPV with the Fuzzy NPV, being the uncertainty dimension made a go investment, in the deterministic method, turn into a rejected one.

45 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE Conclusions: 2) The way to evaluate an investment doesnt change much, when applied to another object of analyses. 3) One of the most relevant information, obtained from the fuzzy NPV, is the failure possibility of the project, it is obtained from a proportion of the area seen under the membership curve, which takes us to an analogy with the PDF (Probability Density Function) using statistical methods.

46 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE Conclusions: 4)The uncertainty associated with the fuzzy NPV, is characterized by the amplitude of the fuzzy number that represents the fuzzy NPV, that is, a3 – a1, therefore, the uncertainty associated to the investment and the investment viability are totally independent. 5)It is also important to point out the great visual analyses power of the fuzzy number, the visualization of the membership graph takes us to another analyses dimension, improving even more the decision making resources.

47 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE Conclusions: 6)The computerized resources allow us to deal with possible difficulties found in the calculation, with speed and accuracy, what happens with Fuzzyinvest 1.0. The software values the visual aspect and the relevant information, emphasizing the membership graph and the failure possibility.

48 UNIVERSIDADE FEDERAL DE ITAJUBÁ – BRASIL V Encontro Internacional de Finanças - CHILE Questions?


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