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within the set to be analyzed. In general dependency exists any time (1) there are insufficient funds available to undertake all proposed projects (this is commonly referred to as capital rationing), (2) there are mutually exclusive projects, or (3) there are contingent projects.

Several approaches have been proposed for selecting the best set of projects from a set of potential projects under constraints. Many of these approaches will select the optimal set of acceptable projects under some conditions or will select a set that is near optimal. However, only a few approaches are guaranteed to select the optimal set of projects under all conditions. One of these approaches is presented below by way of a continuation of Example 17.

The first steps in the selection process are to specify the cash flow amounts and cash flow timings for each project in the potential project set. Additionally, a value of MARR to be used in the analysis must be specified. These issues have been addressed in previous sections so further discussion will be omitted here. The next step is to form the set of all possible decision alternatives from the projects. A single decision alternative is a collection of zero, one, or more projects which could be accepted (all others not specified are to be rejected). As an illustration, the possible decision alternatives for the set of projects illustrated in Figure 4.9 are listed in Table 4.7. As a general rule, there will be 2n possible decision alternatives generated from a set of n projects. Thus, for the projects of Figure 4.9, there are 24 = 16 possible decision alternatives. Since this set represents all possible decisions that could be made, one, and only one, will be selected as the best (optimal) decision. The set of decision alternatives developed in this way has the properties of being collectively exhaustive (all possible choices are listed) and mutually exclusive (only one will be selected).

The next step in the process is to eliminate decisions from the collectively exhaustive, mutually exclusive set that represent choices which would violate one (or more) of the constraints on the projects. For the projects of Figure 4.9, assume the following two constraints exist:

Project B is contingent on Project C, and

A budget limit of \$1500 exists on capital expenditures at t=0.

Based on these constraints the following decision alternatives must be removed from the collectively exhaustive, mutually exclusive set: any combination that includes B but not C (B only; A&B; B&D; A&B&D), any combination not already eliminated whose t=0 costs exceed \$1500 (B&C, A&B&C, A&C&D, B&C&D, A&B&C&D). Thus, from the original set of 16 possible decision alternatives, 9 have been eliminated and need not be evaluated. These results are illustrated in Table 4.8. It is frequently the case in practice that a significant percentage of the original collectively exhaustive, mutually exclusive set will be eliminated before measures of worth are calculated.

The next step is to create the cash flow series for the remaining (feasible) decision alternatives. This is a straight forward process and is accomplished by setting a decision alternative's annual cash flow equal to the sum of the annual cash flows (on a year by year basis) of all projects contained in the decision alternative. Table 4.9 illustrates the results of this process for the feasible decision alternatives from Table 4.8.

The next step is to calculate a measure of worth for each decision alternative. Any of the four consistent measures of worth presented above (PW, AW, IRR,

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