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Decision making among alternativesUnit VII A decision criterion is a rule or procedure that prescribes how to select investment alternatives so that certain objectives can be achieved.Types of investment proposals : An investment proposal is a single undertaking or project being considered as an investment possibility.Whether proposals are independent of each other or whether they are dependent in some way determines the selection process by which one proposal will be judged superior to another proposal.Independent proposals : A proposal is said to be independent when the acceptance of a proposal from a set has no effect on the acceptance of any of the other proposals in the set.For example, proposals concerning the purchase of a NC milling machine, a security system, office furniture and fork lift trucks would, under most circumstances, be considered independent.Dependent proposals:For many decision situations, a group of proposals will be related to one another in such a way that the acceptance of one of them will influence the acceptance of the others.Proposals are said to be mutually exclusive if the proposals contained in the set of proposals being considered are related so that the acceptance of one proposal from the set precludes (prevents) the acceptance of any of the others.Mutually exclusive proposals usually occur when a decision maker is attempting to fulfill a need and there are a variety of proposals, each of which will satisfy that need.A contingent (conditional) proposal is one whose acceptance is dependent on the acceptance of some prerequisite proposal , whose acceptance in turn is independent of acceptance of the contingent proposal.Thus the purchase of computer software is contingent on the purchase of computer hardware.The construction of the third floor of a building is contingent on the construction of the first and second floors.A contingent relationship is a one way dependency between proposals.Investment alternative: it is important to distinguish an investment proposal from an investment alternative.An investment alternative is a decision option that represents a course of action. Forming mutually exclusive alternatives: Engineering proposals can be independent, mutually exclusive, or contingent and additional interdependencies among them can exist if there is a limited amount of money to invest.To devise special rules to include each of these different relationships in a decision criterion would make the procedure complicated and difficult to apply.A general procedure for forming mutually exclusive alternatives from a given set of proposals is based on an enumeration of all possible combinations of the proposals . For example, if two proposals (P1 and P 2) are being considered, four mutually exclusive investment alternatives exist, as shown in Table 7.1. Note that a binary variable, Xj =0 or 1 is used to indicate proposal rejection or acceptance. Table 7.1AlternativesProposal P1Proposal P2ActionA000Do nothingA110Accept P1A201Accept P2A311Accept P1 and P2Generalization of the procedure used in Table 7.1 for k proposals, k=1,2,3 leads to a number of alternatives A , given by A=2k .A0-1 matrix exhibiting all possible alternatives (row) is shown in Table 7.2Let 1,2,3k-1,k designate proposals ( columns) from left to right.Moving down P1, the first column (k=1), place a single zero followed by a single one alternating until all alternatives have been assigned a zero or one. Next, go to P2, the second column (k=2). Move down the column and place 2(k-1) zeros followed by 2(k-1) ones , alternating until each alternative has an entry.

For the third column, P3, k=3 so that 2(k-1) =4 Thus moving down that column, place 4 zeros followed by 4 ones, repeating until all alternatives have an assigned value.This process is repeated for each proposal ( column) and the results are presented in Table 7.2Since all the entries in row 1 will be zero, A0 represents the Do Nothing alternative.The approach just presented makes possible the consideration of a variety of proposal relationships in a single form; the mutually exclusive alternative.Investment alternativesProposal ,P1Proposal P2Proposal P3Proposal P(k-1)Proposal P(k)A0000.00A1100.00A201000A311000A400100A510100A(2k -2)01111A(2k -1)11111TABLE 7.2GENERAL 0-1 MATRIX OF INVESTMENT ALTERNATIVES7.3 ELEMENTS OF DECISION CRITERIA;7.3.1 Differences between alternatives: When comparing mutually exclusive alternatives, it is the difference between them that is relevant for determining the economic desirability of one compared to the other.7.3.2 Minimum attractive rate of return(MARR):The maximization of equivalent profit, given that all investment alternatives must yield a return that exceeds some minimum attractive rate of return.The minimum attractive rate of return (MARR) is a cut off rate representing a yield on investments that is considered minimally acceptable.7.3.3 The Do Nothing Alternative: It means that the investor will do noting about the projects being considered and the funds made available by not investing will be placed in investments that yield an IRR equal to the MARR.For the Do Nothing alternative their result of these assumptions is summarized as i* A0 =MARRBecause the IRR is defined as the interest rate that causes the present worth, annual equivalent, or future worth amounts to equal zero, for the Do Nothing alternative it follows that PW(MARR)A0=0AE(MARR)A0 =0FW(MARR)A0=0These expressions indicate that when the Do Nothing alternative is evaluated at the MARR, its equivalent profit is always zero.7.6 COMPARISONS BASED ON TOTAL INVESTMENT:7.6.1 Present worth on Total investment: The present worth on total investment criterion is one of the most frequently used methods for selecting an investment alternative from a set of mutually exclusive alternativesSince the stated objective is to choose the alternative with the maximum present worth, the rules for this criterion are rather simple.If PW(i)A2>PW(i)A1;accept A2

PW(i)A2AE(i) A1 : accept A2AE(i)A2FW(i)A1:accept A2FW(i)A20 ( the study period may be selected to be any time span)Assumption : Actual costs and revenue will equal the values estimated.Method 2( calculate the AE(i) of the Capital costs and the AE(i) of all other costs and revenues over each alternatives life.- appropriate for service alternatives and revenue alternatives.-n>0 ( the study period may be selected to be any time span.Method 3 : ( calculate the PW(i) or FW(i) of each alternative over its particular life.)Appropriate for revenue alternatives onlyn*>life of longest lived alternative. (alternatives must have lives shorter than or equal to the study period.)Assumption : all cash flows will be reinvested at an interest rate, i, until the end of the study period.KEY POINTS:All investment options can be rearranged into mutually exclusive alternatives.The fundamental rule, on which the comparison of mutually exclusive alternatives is based, requires that the difference between alternatives be evaluated.

The minimum attractive rate of return (MARR) is a cut-off rate that represents the yield on investments the firm considers minimally acceptable.The rate should reflect the opportunity to invest if the investments under consideration are not undertaken.The Do Nothing alternative, A0, represents the option to invest at an interest equal to the MARR .Thus the PW(MARR) A0=0PW(i), AE(i), and FW(i) can be correctly applied on total investment or incremental investment. The internal rate of return , i*, will provide the same results as the investment criteria just mentioned only if it is applied on incremental investment.When comparing alternatives with unequal lives the comparison must be made over equal periods of timeThree different methods are presented for placing such alternatives over equal periodsEach method is based on a different set of assumptions and there is no assurance that the three methods will provide the same conclusions.

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