## Jl

1,000

Figure 4.8 Two investments evaluated using payback period certainty. Frequently, although this assumption does not hold exactly, it is not considered restrictive in terms of potential investment decisions. If however the lack of certainty is a significant issue then the analysis is stochastic and the assumptions of certainty are relaxed using probability distributions and statistical techniques to conduct the analysis. The remainder of this section deals with deterministic economic analysis so the assumption of certainty will be assumed to hold. Stochastic techniques are introduced in Section 4.9.5.

### 4.8.2 Deterministic Unconstrained Analysis

Deterministic economic analysis can be further classified into unconstrained deterministic analysis and constrained deterministic analysis. Under unconstrained analysis, all projects within the set available are assumed to be independent. The practical implication of this independence assumption is that an accept/reject decision can be made on each project without regard to the decisions made on other projects. In general this requires that (1) there are sufficient funds available to undertake all proposed projects, (2) there are no mutually exclusive projects, and (3) there are no contingent projects.

A funds restriction creates dependency since, before deciding on a project being evaluated, the evaluator would have to know what decisions had been made on other projects to determine whether sufficient funds were available to undertake the current project. Mutual exclusion creates dependency since acceptance of one of the mutually exclusive projects precludes acceptance of the others. Contingency creates dependence since prior to accepting a project, all projects on which it is contingent must be accepted.

If none of the above dependency situations are present and the projects are otherwise independent, then the evaluation of the set of projects is done by evaluating each individual project in turn and accepting the set of projects which were individually judged acceptable. This accept or reject judgment can be made using either the PW, AW, IRR, or SIR measure of worth. The unconstrained decision rules for each or these measures of worth are restated below for convenience.

Unconstrained PW Decision Rule: If PW >0, then the project is attractive.

Unconstrained AW Decision Rule: If AW >0, then the project is attractive.

Unconstrained IRR Decision Rule: If IRR is unique and IRR >MARR, then the project is attractive.

Unconstrained SIR Decision Rule: If SIR >1, then the project is attractive.

### Example 17

Consider the set of four investment projects whose cash flow diagrams are illustrated in Figure 4.9. If MARR is 12%/yr and the analysis is unconstrained, which projects should be accepted?

Using present worth as the measure of worth:

PWA = -1000+600*(P | A,12%,4) = -1000+600(3.0373) = $822.38 ^ Accept A

PWB = -1300+800*(P | A,12%,4) = -1300+800(3.0373) = $1129.88 ^ Accept B

PWC = -400+120*(P|A,12%,4) = -400+120(3.0373) = -$35.52 ^ Reject C

PWD = -500+290*(P | A,12%,4) = -500+290(3.0373) = $380.83 ^ Accept D

Therefore,

Accept Projects A, B, and D and Reject Project C

4.8.3 Deterministic Constrained Analysis

Constrained analysis is required any time a dependency relationship exists between any of the projects

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