Build-operate-transfer of airport in fuzzy cost of capital and fuzzy capital budgeting.ABSTRACT Most previous studies concerning financial performance evaluation Performance evaluation The assessment of a manager's results, which involves, first, determining whether the money manager added value by outperforming the established benchmark (performance measurement) and, second, determining how the money manager achieved the calculated return focus merely on the cost control, which might directly influence the survival of a company. This paper attempts to construct a new optimal capital planning decision method. The topic is based on fuzzy fuzz·y adj. fuzz·i·er, fuzz·i·est 1. Covered with fuzz. 2. Of or resembling fuzz. 3. Not clear; indistinct: a fuzzy recollection of past events. 4. capital cost and fuzzy capital budgeting under fuzzy economic scenario. And it is developed focus on BOT (Build-Operate-Transfer) of airport. To efficiently handle the fuzziness fuzz·y adj. fuzz·i·er, fuzz·i·est 1. Covered with fuzz. 2. Of or resembling fuzz. 3. Not clear; indistinct: a fuzzy recollection of past events. 4. of decision variable with respect to planning and decision of optimal capital on airport, the linguistic values, subjectively represented by triangular fuzzy numbers, are used to act as the evaluation tool. To introduce the computational Having to do with calculations. Something that is "highly computational" requires a large number of calculations. methods of fuzzy weighted average cost of capital Weighted average cost of capital (WACC) Expected return on a portfolio of all a firm's securities. Used as a hurdle rate for capital investment. Often the weighted average of the cost of equity and the cost of debt The weights are determined by the relative proportions of equity (FWACC) and fuzzy modified internal rate of return Modified Internal Rate of Return (MIRR) is a financial measure used to determine the attractiveness of an investment. It is generally used as part of a capital budgeting process to rank various alternative choices. (FMIRR) are the base of fuzzy capital budgeting proposed in this study. By utilizing the new finance decision method, not only the decision-maker can handle more true information and make the best planning. But also the government decision-maker can make a well decision for airport in BOT under fuzzy economic scenario. Keywords: Earning management, Risk management, Fuzzy capital budgeting, Fuzzy capital cost, Triangular fuzzy number 1. INTRODUCTION Since the Asian financial crisis in 1997, the government's expenditures are curtailed. Therefore, the government would like to cooperate with some corporations to reduce its expense. The purpose of this paper is to present some attempts under financial plan on build-operate-transfer (BOT) of airport in fuzzy cost and fuzzy capital budgeting. However, successful packaging of a BOT proposal means getting all of the political, technical, commercial and financial elements of a project put together in a proposal so that adequate funds can be committed and advanced to the project company and construction can begin (Tiong and Alum, 1997). Therefore, we construct a new optimal financial planning Financial planning Evaluating the investing and financing options available to a firm. Planning includes attempting to make optimal decisions, projecting the consequences of these decisions for the firm in the form of a financial plan, and then comparing future performance against decision method based on fuzzy capital cost and fuzzy capital budgeting focused on the BOT (Build-Operate-Transfer) of an airport. BOT is a deal between the government and corporations. The government hands over the right of build and operation of an airport to corporations. After 30 or 50 years, the Years, The the seven decades of Eleanor Pargiter’s life. [Br. Lit.: Benét, 1109] See : Time airport has to be transferred to the government for free. The entrepreneurs must take a long view in such financial contract, because of the long duration and high capital costs of infrastructure projects and changing priority of the host governments. Upon successful construction of the projects, the actual concession period can last for 3050 years depending on the type of project. During these operational phases, the maintenance of throughput in line with original forecast remains an area of great uncertainty and challenge to the entrepreneurs (Yeo and Tiong, 2000). How the corporation establishes a good financial evaluation planning under uncertain environment on the cost and budget control before investment on an airport is an important issue and deserves a through investigation in its own right. Thus, this paper studies the cost capital and capital budgeting of an airport that corporation can establish a good financial plan in order to reduce investment risk. Variables of cost control and budgeting management are uncertain. And for maintenance of throughput in line with original forecast remains, we should not only view a forecast point. There are many fields of science Fields of science are widely-recognized categories of specialized expertise within science, and typically embody their own terminology and nomenclature. Natural sciences
Branch of mathematics that deals with analysis of random events. Probability is the numerical assessment of likelihood on a scale from 0 (impossibility) to 1 (absolute certainty). . There are many situations in which the source of uncertainly is not a random variable but can be represented the form of linguistic variables. The main reason is that result is a very precision value. It could not represent to fluctuate according to according to prep. 1. As stated or indicated by; on the authority of: according to historians. 2. In keeping with: according to instructions. 3. the economic situation. In 1965 L. A. Zadeh introduced the fuzzy theory is to grasp the uncertainty in information. Fuzzy numbers are used to quantify Quantify - A performance analysis tool from Pure Software. the inexact in·ex·act adj. 1. Not strictly accurate or precise; not exact: an inexact quotation; an inexact description of what had taken place. 2. information such as "around," "very," "little," and so on. These fuzzy numbers allow us to manipulate inexact knowledge using mathematical operators and programming techniques (Zadeh, 1975). Thus, this paper will use fuzzy method to resolve in the build-operate-transfer of an airport. 2. LITERATURE REVIEW 2.1 Related Research Issues in Fuzzy Finance Turtle, Bector and Gill (1994) studied on the using of fuzzy logic fuzzy logic, a multivalued (as opposed to binary) logic developed to deal with imprecise or vague data. Classical logic holds that everything can be expressed in binary terms: 0 or 1, black or white, yes or no; in terms of Boolean algebra, everything is in one set or in corporate finance. An example of a multinational cash flow netting problem was studied. Uncertain cash flows from subsidiaries make this problem difficult to be specified in a traditional crisp environment. They provided feasibile ranges and the shadow price for changes within the feasible range. Beside, they were successful linking sensitivity analysis and fuzzy logic. Korvin, Strawer and Siegel (1995) engaged a study in the area of cost variance analysis. Cost accountants cost accountant n. An accountant who keeps records of the costs of production and distribution. cost accounting n. Noun 1. must continually be in a good sense and provide professional judgment in the accounting process to deal with the ambiguity Ambiguity Delphic oracle ultimate authority in ancient Greece; often speaks in ambiguous terms. [Gk. Hist.: Leach, 305] Iseult’s vow pledge to husband has double meaning. [Arth. of the cost. The use of fuzzy sets Fuzzy sets are sets whose elements have degrees of membership. Fuzzy sets have been introduced by Lotfi A. Zadeh (1965) as an extension of the classical notion of set. In classical set theory, the membership of elements in a set is assessed in binary terms according to a bivalent to build fuzzy control systems A fuzzy control system is a control system based on fuzzy logic - a mathematical system that analyzes analog input values in terms of logical variables that take on continuous values between 0 and 1, in contrast to classical or digital logic, which operates on discrete values of provides a method to incorporate the ambiguity into expert systems. Chiu and Park (1998) studied on the capital budgeting decisions with fuzzy projects. The authors proposed a capital budgeting model under uncertainty in which the cash flow information was specified as a special type of fuzzy numbers-triangular fuzzy numbers. Sanchez, Liao, Ray and Triantaphyllou (1999) gave an example for dealing with the impreciseness Noun 1. impreciseness - the quality of lacking precision imprecision inexactitude, inexactness - the quality of being inaccurate and having errors of future cash flows during the selection of economic alternatives. That paper presented an approach of how to deal with the imprecision im·pre·cise adj. Not precise. im  pre·cise ly adv. of future cash flows. They represented the
cash flows as triangular fuzzy numbers. The following figure is showed
the relationship among previous related researches.2.2 Related Research Issues in BOT Tiong, Robert and Alum (1997) primarily concerned with the evaluation of tender proposals for BOT projects particularly in Asia-Pacific regions. It describes the selection process and examines the current evaluation practices and techniques that based on the net present value (NPV NPV See: Net present value ) method, the scoring system Noun 1. scoring system - a system of classifying according to quality or merit or amount rating system classification system - a system for classifying things and the Kepnoe-Tregon decision-making technique. (The major elements in Kepnoe-Tregon decision-making technique consist of the evaluation statement, the MUST criteria; they responses were solicited from BOT practitioners to establish the major criteria that are commonly used by governments in evaluating BOT proposals. It concludes that government's evaluation goal should be to select a balanced proposal that is financially attractive and technically cost-effective. Tiong, Robed and Alum (1997) presents an analysis of the issues related to financial commitments of funds required from the lenders and promoters in a BOT tender. It wants to investigate the extent of importance of a high level of financial commitments in a BOT tender, and whether the level of financial commitments provides the competitive advantage and increases the chances of success in a competitive BOT tender. Finally, it recommends the strategies required for developing a successful and competitive financial proposal for a BOT project. It concludes concentrate on three key areas in the process. (A) Developing the financial framework and the financing plan. (B) Developing the financial framework structure and financial risks. (C) And Develop formulation formulation /for·mu·la·tion/ (for?mu-la´shun) the act or product of formulating. American Law Institute Formulation of financial strategies. Yeo and Tiong (2000) proposed a risk reduction strategy in winning and managing BOT concession. Examples of successful and unsuccessful BOT projects are selectively used to illustrate the elements of the framework. The proposed soft systems methodology process encourages proactive management of BOT negotiation and concession, especially in the positive management of differences and control of variations, and the problem solving problem solving Process involved in finding a solution to a problem. Many animals routinely solve problems of locomotion, food finding, and shelter through trial and error. capability of an entrepreneurial promoter. 2.3 Related Research Issues in WACC WACC See: Weighted average cost of capital Babusiaux and Pierru (2001) point out a firm using a discount rate defined at the corporate scale as a WACC may have to value projects subject to a different tax rate from the one used to calculate its discount rate. To determine the economic value of a project, the WACC and Arditti-Levy methods need to be adjusted if the firm allocated to this project a loan representing proportionally more (or less) than the fraction corresponding to the target debt ratio defined by the firm for the projects, in the same class or risk. First, it proposes a method that corresponds to the adjustment of standard WACC calculations. The formulation adopted ("generalized gen·er·al·ized adj. 1. Involving an entire organ, as when an epileptic seizure involves all parts of the brain. 2. Not specifically adapted to a particular environment or function; not specialized. 3. ATWACC method") has the advantage of being independent of any consideration related to debt ratios. Cigola and Peccati (2003) point out the valuation of levered investment in the practice is made with the WACC approach, even if the superior technique of APV APV See: Adjusted Present Value is available. It shows that the APV can be interpreted as the arbitrage arbitrage: see foreign exchange. arbitrage Business operation involving the purchase of foreign currency, gold, financial securities, or commodities in one market and their almost simultaneous sale in another market, in order to profit from price free value of the portfolio made by an investment and a supporting loan. Therefore the WACC evaluation allows for arbitrage. The economic environment is uncertain they would like to get good answer, me too. We use fuzzy method to solve what the project could not display clearly on cost, income and risk. 3. METHODS We will define fuzzy set theory, triangular fuzzy numbers, calculation fuzzy [alpha]-cut, fuzzy membership range, Fuzzy Weighted Average Cost of Capital (FWACC) and Fuzzy Modified Internal Rate of Return (FMIRR). And incorporate fuzzy numbers into the financial analysis of BOT of an airport. 3.1 Fuzzy Set Theory Let X be the set of universe, a fuzzy set A in X is characterized char·ac·ter·ize tr.v. character·ized, character·iz·ing, character·iz·es 1. To describe the qualities or peculiarities of: characterized the warden as ruthless. 2. by a membership function [f.sub.A](x) which is associated with each element in X a real number in the interval [0, 1], with the value of [f.sub.A](x) representing the "degree of membership" of [x.bar] in A. Thus, the closer the value of [f.sub.A](x) to the unity the higher is the degree of membership of [x.bar] in A. When A is a crisp set, its membership function can take on only two values 0 and 1 representing that an element does not or does belong to A correspondingly (Zadeh, 1965). 3.2 Triangular Fuzzy Number A fuzzy number A (Dubois and Prade, 1978) in R (real line) is a triangular fuzzy number whose membership function [f.sub.A] [??] R [right arrow] [0, 1] is defined as: f [sub.A.(x) = {(x - c)/(a - c), c [less than or equal to] x [less than or equal to] a, (x - b)/(a - b), a [less than or equal to] x [less than or equal to] b, 0, otherwises Where -[[infinity infinity, in mathematics, that which is not finite. A sequence of numbers, a1, a2, a3, … , is said to "approach infinity" if the numbers eventually become arbitrarily large, i.e. ].bar]<[c.bar][a.bar][less than or equal to][b.bar]<[[infinity].bar] A triangular fuzzy number [A.bar] can be represented by (c.bar], [a.bar], [b.bar], the triplet triplet /trip·let/ (trip´let) 1. one of three offspring produced at one birth. 2. a combination of three objects or entities acting together, as three lenses or three nucleotides. 3. as show in Figure 1. Triangular fuzzy number [A.bar] has a maximum degree of membership on [a.bar]. i.e. [[f.bar].sub.[A.bar]](a)=1. In addition, [c.bar] and [b.bar] are the lower and upper bounds of the support of A which is used to reflect the fuzziness of the spread of the uncertainty. The narrow the interval [[c.bar], [b.bar]] is, the less uncertain the A is. [FIGURE 1 OMITTED] 3.3 The Algebraic 1. (language) ALGEBRAIC - An early system on MIT's Whirlwind. [CACM 2(5):16 (May 1959)]. 2. (theory) algebraic - In domain theory, a complete partial order is algebraic if every element is the least upper bound of some chain of compact elements. Operations of Fuzzy Numbers based on the a-Cut Concept The [alpha]-cut of the fuzzy number A is defined as [A.sup.[alpha]] = { x [member of] X [greater than or equal to] [f.sub.A] (x) [greater than or equal to] [alpha], 0[less than or equal to][alpha][less than or equal to]1} = [[A.sub.l.sup.[alpha]], [A.sub.u.sup.[alpha]]]. The A and B are positive fuzzy numbers, i.e., [A.sub.l.sup.[alpha]]>0, [B.sub.l.sup.[alpha]]>0, for all [alpha][member of][0, 1]. Let [A.sup.[alpha]] = [[A.sub.l.sup.[alpha]], [A.sub.u.sup.[alpha]]] and [B.sup.[alpha]] = [[B.sub.l.sup.[alpha]], [B.sub.u.sup.[alpha]]. According to extension principle (Zadeh, 1965) and vertex A corner point of a triangle or other geometric image. Vertices is the plural form of this term. See vertex shader. method (Dong and Shah Shah is a Persian term for a monarch (ruler) that has been adopted in many other languages. This term is a Post Islamic Revolution term for monarchs in Iran which is replaced by valie faghih or Supreme Leader. , 1987), the algebraic operations of any two positive fuzzy numbers [A.bar] and [B.bar] can be expressed as: Fuzzy addition: [(A[??]B).sup.[alpha]] =[[A.sub.l.sup.[alpha]] +[B.sub.l.sup.[alpha]], [A.sub.u.sup.[alpha]] + [B.sub.u.sup.[alpha]]] Fuzzy subtraction subtraction, fundamental operation of arithmetic; the inverse of addition. If a and b are real numbers (see number), then the number a−b is that number (called the difference) which when added to b (the subtractor) equals : [(A[??]B).sup.[alpha]]=[[A.sub.l.sup.[alpha]]-[B.sub.u.sup.[alpha]], [A.sub.u.sup.[alpha]]-[B.sub.l.sup.[alpha]]] Fuzzy multiplication multiplication, fundamental operation in arithmetic and algebra. Multiplication by a whole number can be interpreted as successive addition. For example, a number N multiplied by 3 is N + N + N. : [(A [??] B).sup.[alpha]] =[[A.sub.l.sup.[alpha]] [B.sub.l.sup.[alpha]], [A.sub.u.sup.[alpha]] [B.sub.u.sup.[alpha]]]) Fuzzy division: [(A[??]B).sup.[alpha]] =[[A.sub.l.sup.[alpha]]/[B.sub.u.sup.[alpha]], [A.sub.u.sup.[alpha]]/[B.sub.l.sup.[alpha]]] 3.4 Ranking of Fuzzy Numbers A fuzzy set can be expressed in terms of the concept of a-cut without resorting to the membership function (Terano, Asai and Sugeno, 1991). Thus, we use the [alpha]-cut method to sort fuzzy numbers. Let [A.sub.1],[A.sub.2], ..., [A.sub.i] ..., [A.sub.n], be n fuzzy numbers, and the left and right membership function of fuzzy number [A.sub.i] are [MATHEMATICAL EXPRESSION A group of characters or symbols representing a quantity or an operation. See arithmetic expression. NOT REPRODUCIBLE re·pro·duce v. re·pro·duced, re·pro·duc·ing, re·pro·duc·es v.tr. 1. To produce a counterpart, image, or copy of. 2. Biology To generate (offspring) by sexual or asexual means. IN ASCII ASCII or American Standard Code for Information Interchange, a set of codes used to represent letters, numbers, a few symbols, and control characters. Originally designed for teletype operations, it has found wide application in computers. ] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Suppose that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are the inverse functions inverse function Mathematical function that undoes the effect of another function. For example, the inverse function of the formula that converts Celsius temperature to Fahrenheit temperature is the formula that converts Fahrenheit to Celsius. of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] , respectively. Define the left integral value [I.sup.L]([A.sub.i]) and right integral value [I.sup.R]([A.sub.i]) of [A.sub.i] as (Liou and Wang, 1992; Yager, 1981): Let [alpha] [member of] [0,1], j=0, 1, 2, ..., k, and 0 = [[alpha].sub.0] < [[alpha].sub.1] < ... <[[alpha].sub.j]< ... <[[alpha].sub.k] = l, then [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2) where [??][alpha].sub.j]=[[alpha.sub.j]-[[alpha].sub.j-1, in this paper the ranking value R(A) of fuzzy number A is defined as R(A)=[[I.sup.R](A) + [I.sup.L](A)]/2. Define the ranking of the fuzzy number [A.sub.i] and [A.sub.j] based on the following rules: [A.sub.i] > [A.sub.j] [??] R([A.sub.i]) > R ([A.sub.j]) [A.sub.i] < [A.sub.j] [??] R([A.sub.i]) < R ([A.sub.j]) [A.sub.i] = [A.sub.j] [??] R([A.sub.i]) = R ([A.sub.j]) 3.5 Fuzzy Weighted Average Cost of Capital (FWACC) The cost of capital used to analyze capital budgeting decisions should be the company's required return on equity. However, most firms raise a substantial portion of their capital as long-term debt Long-Term Debt Loans and financial obligations lasting over one year. Notes: For example debts obligations such as bonds and notes which have maturities greater than one year would be considered long-term debt. , and many also use preferred stock Stock shares that have preferential rights to dividends or to amounts distributable on liquidation, or to both, ahead of common shareholders. Preferred stock is given preference over common stock. Holders of preferred stock receive dividends at a fixed annual rate. . For these firms, the cost of capital must reflect the average cost of the various sources of long-term funds used, not just the firms' costs of equity. Assume that corporation a 10% cost of debt, a 10.3% cost of special equity and a 13.4% cost of equity. Further, assume that corporation has made the decision to finance next year's projects by selling debt. The argument is sometimes made that the cost of capital for these projects is 10 percent, because only debt will be used to finance them. However, this position is incorrect. If corporation finances a particular set of projects with debt, the firm will be using up some of its potential for obtaining new debt in the future. As expansion occurs in subsequent years, corporation will at some point find it necessary to raise additional equity to prevent the debt ratio from becoming too large. Thus, when we want to fix debt ratio we will change the ratio about equity that is the concept of weight average cost of capital. The following is a compute To perform mathematical operations or general computer processing. For an explanation of "The 3 C's," or how the computer processes data, see computer. of example (Brigham, 1996). WACC-[W.sub.d][K.sub.d] (1-T] + [W.sub.ps] [K.sub.ps] + [W.sub.s] [K.sub.s] =0.45(10%)(0.6)+0.02(10.3%)+0.53(13.4%) =10% The following equation (3) is the fuzziness character of weighted average cost of capital to calculate fuzzy weighted average cost of capital. And the figure 2 that we change it into to fuzziness character model of fuzzy weighted average cost of capital. The [FWACC.sub.1] and [FWACC.sub.2] are not isosceles triangles, because they have the lowest and highest boundary, for example, [FWACC.sub.1] = (2, 2, 9) or [FWACC.sub.2]=(7, 10, 10). Thus, we will be known that left or right number and middle number are the same. [FIGURE 2 OMITTED] FWACC = [W.sub.d] [??] F[K.sub.d] [??] (1 [??] FT) [??] [W.sub.s] [F[K.sub.s] (3) FWACC: Fuzzy Weighted Average Cost of Capital [W.sub.d]: Debt Ratio [W.sub.s]: Common Equity Ratio F[K.sub.d]: Fuzzy Cost of Debt F[K.sub.s]: Fuzzy Cost of Common Equity FT: Fuzzy Margin Tax 3.6 Fuzzy Modified Internal Rate of Return (FMIRR) We can modify the IRR IRR In currencies, this is the abbreviation for the Iranian Rial. Notes: The currency market, also known as the Foreign Exchange market, is the largest financial market in the world, with a daily average volume of over US $1 trillion. and make it a better indicator of relative profitability, hence better for use in capital budgeting. The new measure is called the modified IRR or MIRR MIRR Modified Internal Rate of Return MIRR Material Inspection & Receiving Report MIRR Materials Issued Review Report . Conclusion is that the modified IRR is superior to the regular IRR as an indicator of a project's "true" rate of return, or "expected long-term rate of return". Here COF refers to cash out flows (negative numbers), or the cost of the project, and CIF (1) (Common Intermediate Format) A standard video format used in videoconferencing. CIF formats are defined by their resolution, and standards both above and below the original resolution have been established. The original CIF is also known as Full CIF (FCIF). refers to cash in flows (all positive numbers). The left term is simply the present value (PV) of the investment outlays Outlays Payments on obligations in the form of cash, checks, the issuance of bonds or notes, or the maturing of interest coupons. when discounted at the cost of capital, and the numerator numerator the upper part of a fraction. numerator relationship see additive genetic relationship. numerator Epidemiology The upper part of a fraction of the right term is the future value of the in flows, assuming that the cash in flows are reinvested at the cost of capital. The future value of the cash inflows is also called the terminal value, or terminal value (TV). The discount rate that forces the PV of the TV to equal the PV of the costs is defined as MIRR (Brigham, 1996). [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] C(PV): Investment Cost (Present Value) COF: Cash out Flow at period t K: Cost of Capital The following equation (4) is the fuzziness character of Modified Internal Rate of Return to calculate fuzzy present value. FC = [FTV/[(1 [direct sum]FMIRR).sup.n]] = [[n.summation summation n. the final argument of an attorney at the close of a trial in which he/she attempts to convince the judge and/or jury of the virtues of the client's case. (See: closing argument) over (t=0)][FCIF See CIF. .sub.t][cross product][(1[direct sum]FWACC).sup.n-t]/[(1[direct sum]FMIRR).sup.n]] FC: Fuzzy Present Value FTV FTV Fashion TV FTV First Time Video FTV Free to View (satellite television) FTV Flight Test Vehicle FTV Finish the Verse FTV Functional Test Vehicle FTV Franchise Tax voucher (California ) : Fuzzy Terminal Value FCIF: Fuzzy Cash in Flow at period t FWACC: Fuzzy Weighted Average Cost of Capital FMIRR: Fuzzy Modified Internal Rate of Return 4. CASE STUDY OF BOT 4.1 Date of Case Study This case is an airport BOT. According to Taiwan's law of incentive in investment on BOT. The corporation has minimum of 30% equity capital, other 70% capital can borrow from banks. It depends on what kind of capital to be constituted is good for corporation. In this case that corporation spend 4 years to build and 20 years to operate and income cash flow. The interest has to depend on the Taiwan's law of incentive in investment on Taiwan High Speed Rail The Taiwan High Speed Rail (Traditional Chinese: 台灣高速鐵路, also known as the THSR) is Taiwan's high-speed rail network, running approximately 335. BOT plan that borrow from many banks is between 3% and 5% (1999). The following table 1 is information about build fuzzy investment. On the other hand, debt ratio ([W.sub.d]) is from 0%, 10%, 20%, 30%, 40%, 50%, 60% and 70%. The equity ratio is [W.sub.s] = 1 - [W.sub.d]. Fuzzy cost of common equity is [FK.sub.s]. The [FK.sub.s] is the cost including issue cost, agency cost and so on. The fuzzy tax (T) is (40%, 40%, 40%). The information is following as table 1 and 2. 4.2 Fuzzy Weighted Average Cost of Capital Computation Computation is a general term for any type of information processing that can be represented mathematically. This includes phenomena ranging from simple calculations to human thinking. We use above BOT plan information to compute that before tax the fuzzy weighted cost of debt and fuzzy weighted cost of common equity result as following table 3. And fuzzy weighted average cost of capital to be used by equation (3), under difference [alpha]-cut is 0, 0.2, 0.4, 0.6, 0.8 and 1, as following table 4. We have got [alpha]-cut of fuzzy weighted average cost of capital under difference debt ratio. Thus, according table 5 and equations (1) and (2), we can calculate left and right integration, [I.sup.L](FWACC) and [I.sup.R](FWACC), besides, addition [I.sup.L](FWACC) and [I.sup.R](FWACC) will get R(FWACC) numbers. 4.3 Capital Budgeting of Fuzzy Modified Internal Rate of Return After fuzzy weighted average cost of capital calculation to be accomplished than under fuzzy weighted average cost of capital of range minimum number to compute fuzzy modified internal rate of return. We got the range minimum number R(FWACC)=5.394) that is when the debt ratio is 40%. Its fuzzy cost is (2.34%, 2.664%, 3.12%), thus, we use equation (4) and BOT plan of table 1, 2 to be calculated the FMIRR = (6.19%, 6.5%, 10.62%). It has explained very clearly. When fuzzy weighted average cost of capital_subtract A relational DBMS operation that generates a third file from all the records in one file that are not in a second file. from FMIRR and they have (3.07%, 3.836%, 8.28%), the benefit interval between 3.07% and 8.28%. 5. CONCLUSION Under the difficult handle situation of cost of capital and capital budgeting. We need more information gained for finance planning management. But decision-makers usually are often uncertain and fuzziness on their knowledge. Under this situation, it is difficult to make good decision. Especially, the BOT investment not only to be developed by corporation but also has opposite benefit to government. About cost, income and risk of BOT that this paper construct of solution investment of BOT in finance. Besides, we create the WACC and MIRR methods on fuzzy concept A fuzzy concept is a concept of which the content or boundaries of application vary according to context or conditions. Usually this means the concept is vague, lacking a fixed, precise meaning, without being meaningless altogether. . Based on this, we get an advantage of the fuzzy finance. The results of research explained under uncertain environment that decision marker more understand what is the interval of profit. In this case, we got the lowest at 2.34% interest, the higher at 3.12% interest. The investor will get what kind of cost they have to pay. On the other hand, the net benefit interval between 3.07% and 8.28%. The normal return level is at 3.836%. The investor also can get income and risk information from this methods. Thus, this model is offer a new thinking way and information supply for corporations. 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Notes: Because of the additional interest income, bondholders can make larger investment returns if they reinvest received coupon payments. : Tutorial An instructional book or program that takes the user through a prescribed sequence of steps in order to learn a product. Contrast with documentation, which, although instructional, tends to group features and functions by category. See tutorials in this publication. Extension" The Financial Review, August 1986, 369-385. Sanchez, SN, Liao, T. W., Ray, T. G. and Triantaphyllou, E., "An example for dealing with the impreciseness of future cash flows during the selection of economic alternatives", INT J IND ENG-THEORY Vol. 6, 1, 1999, 38-47. Terano, Toshiro, Asai, Kiyoji and Sugeno, Michio, Fuzzy System Theory, USA, 1991 Tiong, Robert L. K. and Alum, Jahidul, "Evaluation of proposals for BOT projects", International Journal of Project Management, Vol. 15, 2, 1997, 67-72 Tiong, Robert L. K. and Alum, Jahidul, "Financial Commitment for BOT projects", International Journal of Project Management, Vol. 15, 2, 1997, 73-78 Turtle Harry, Bector, C. R., and Gill, A. "Using fuzzy logic in corporate finance: An example of a multinational cash flow netting problem", Managerial Finance Vol. 20, 8, 1994, 36-54. Yager R. R., "A procedure for ordering fuzzy subsets of the unit interval For the data transmission signaling interval, see . In mathematics, the unit interval is the interval [0,1], that is the set of all real numbers x such that zero is less than or equal to x and x is less than or equal to one. ", Information Science Vol. 24, 1981, 143-101 Yeo K. T. and Tiong, Robert L. K., "Positive management of differences for risk reduction in BOT projects", International Journal of Project Management, Vol. 18, 2000, 257-265 Zadeh, L. A. "The concept of a linguistic variable and its application to approximate reasoning", Part 1, 2 and 3, Information Science Vol. 8, 1975-1976, 199-249, 301-357, 43-58. Zadeh, L. A., "Fuzz sets", Information Control, Vol. 8, 1965, 338-353. Kang-Lin Chiang, National Taiwan Ocean University National Taiwan Ocean University (NTOU 國立臺灣海洋大學) is a national university in Keelung, Taiwan. History The predecessor of NTOU was a junior college for the study of maritime science and technology, founded in 1953. , TAIWAN Kuang Lin, National Taiwan Ocean University, TAIWAN Hsuan-Shih Lee, National Taiwan Ocean University, TAIWAN Gin-Shuh Liang, National Taiwan Ocean University, TAIWAN Dr. Kang-Lin Chiang earned his Ph.D. at National Taiwan Ocean University in department of shipping and transportation management, Taiwan. Dr. Kuang Lin currently he is a professor of department of shipping and transportation management at National Taiwan Ocean University, Taiwan. Dr. Hsuan-Shih Lee currently he is a professor of department of shipping and transportation management at National Taiwan Ocean University, Taiwan. Dr. Gin-Shuh Liang currently he is a professor of department of shipping and transportation management at National Taiwan Ocean University, Taiwan.
TABLE 1. UNDER DIFFERENCE DEBT RATIO THAT FUZZY COST OF
CAPITAL, FUZZY COST OF COMMON EQUITY AND FUZZY TAX
[W.sub.d] [FK.sub.d] (%) [FK.sub.s] (%) FT (%)
0% -- (2.7, 2.7, 3.2) (40, 40, 40)
10% (3, 3, 5) (2.7, 2.72, 3.2) (40, 40, 40)
20% (3, 3.25, 5) (2.7, 2.75, 3.2) (40, 40, 40)
30% (3, 3.5, 5) (2.7, 2.84, 3.2) (40, 40, 40)
40% (3, 3.75, 5) (2.7, 2.94, 3.2) (40, 40, 40)
50% (3, 4, 5) (2.7, 3.05, 3.2) (40, 40, 40)
60% (3, 4.5, 5) (2.7, 3.15, 3.2) (40, 40, 40)
70% (3, 5, 5) (2.7, 3.2, 3.2) (40, 40, 40)
TABLE 2. CASH IN FLOW OF OPERATE
Years Cash in flows
1 (65, 72, 77)
2 (72, 77, 82)
3 (69, 74, 79)
4 (118, 123, 128)
5 (113, 118, 123)
6 (108, 113, 118)
7 (88, 93, 98)
8 (168, 173, 178)
9 (161, 166, 171)
10 (154, 159, 164)
11 (146, 151, 156)
12 (9160, 165, 170)
13 (152, 157, 162)
14 (144, 149, 154)
15 (135, 140, 145)
16 (127, 132, 137)
17 (140, 145, 150)
18 (131, 136, 141)
19 (9121, 126, 131)
20 (119, 124, 129)
Unit: million
TABLE 3. THE FUZZY WEIGHTED COST OF DEBT
AND FUZZY WEIGHTED COST OF COMMON EQUITY
[W.sub.d] [W.sub.d] [W.sub.s]
[cross product] [cross product]
[FK.sub.d](%)(1-T) [FK.sub.s](%)
0% -- (2.7, 2.7, 3.2)
10% (0.18, 0.18, 0.3) (2.43, 2.448, 2.88)
20% (0.36, 0.39, 0.6) (2.16, 2.2, 2.56)
30% (0.54, 0.63, 0.9) (1.89, 1.988, 2.24)
40% (0.72, 0.9, 1.2) (1.62, 1.764, 1.92)
50% (0.9, 1.2, 1.5) (1.35, 1.525, 1.6)
60% (1.08, 1.62, 1.8) (1.08, 1.26, 1.28)
70% (1.26, 2.1, 2.1) (0.825, 0.96, 0.96)
TABLE 4. FUZZY WEIGHTED AVERAGE COST OF
CAPITAL UNDER A=O, 0.2, 0.4, 0.6, 0.8 AND 1
Debt ratio [alpha] Fuzzy Weighted Average
Cost of Capital (FWACC) (%)
0% 0 [2.7, 3.2]
0.2 [2.7, 3.1]
0.4 [2.7, 3.0]
0.6 [2.7, 2.9]
0.8 [2.7, 2.8]
1 [2.7, 2.7]
10% 0 [2.61, 3.18]
0.2 [2.6136, 3.0696]
0.4 [2.6172, 2.9592]
0.6 [2.6208, 2.8488]
0.8 [2.6244, 2.7384]
1 [2.628, 2.628]
20% 0 [2.52, 3.16]
0.2 [2.534, 3.046]
0.4 [2.548, 2.932]
0.6 [2.562, 2.818]
0.8 [2.576, 2.704]
1 [2.59, 2.59]
30% 0 [2.43, 3.14]
0.2 [2.4676, 3.3056]
0.4 [2.5052, 2.9312]
0.6 [2.5428, 2.8268]
0.8 [2.5804, 2.7224]
1 [2.618, 2.618]
40% 0 [2.34, 3.12]
0.2 [2.4048, 3.0288]
0.4 [2.4696, 2.9376]
0.6 [2.5344, 2.8464]
0.8 [2.5992, 2.7552]
1 [2.664, 2.664]
50% 0 [2.5, 3.1]
0.2 [2.345, 3.025]
0.4 [2.44, 2.95]
0.6 [2.535, 2.875]
0.8 [2.63, 2.8]
1 [2.725, 2.725]
60% 0 [2.16, 3.08]
0.2 [2.304, 3.04]
0.4 [2.448, 3.0]
0.6 [2.592, 2.96]
0.8 [2.736, 2.92]
1 [2.88, 2.88]
70% 0 [2.085, 3.06]
0.2 [2.28, 3.06]
0.4 [2.475, 3.06]
0.6 [2.67, 3.06]
0.8 [2.865, 3.06]
1 [3.06, 3.06]
TABLE 5. RANGE OF FUZZY WEIGHTED AVERAGE COST OF CAPITAL
Debt ratio FWACC
[I.sup.L](FWACC) [I.sup.R](FWACC) R(FWACC)
0% 2.7 2.95 5.65
10% 2.619 2.904 5.523
20% 2.555 2.875 5.43
30% 2.524 2.879 5.403
40% 2.502 2.892 5.394
50% 2.4875 2.9125 5.4
60% 2.52 2.98 5.5
70% 2.5725 3.06 5.6325
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