5.1 Mutually Exclusive and Independent Alternatives

In conducting an economic evaluation of two or more alternatives, the first step is to determine if the alternatives are mutually exclusive or independent.  When alternatives are mutually exclusive only one can be selected because only one is needed.  Therefore, the alternatives are compared against each other and the one having the most favorable PW is identified as “the best”.  For example, in evaluating locations for construction of a new manufacturing facility, only one site would be selected because only one is needed.  As soon as the best one is identified, all of the others are automatically excluded.  Mutually exclusive projects can be of two general types:  those having only costs (because they are part of a larger project which has already been economically justified) and those having both costs and revenues.  The former are identified as cost alternatives and the latter are known as revenue alternatives.  For cost alternatives, one must be selected, and it would be the one with the lowest cost (i.e. least negative).  For revenue alternatives, one may be selected, but only if one or more had a PW0, in which case the one with the largest PW would be chosen.  On the other hand, when alternatives are said to be independent, they must be revenue alternatives, and none, one, more than one, or all of them can be selected.  This is because the alternatives are only compared against the MARR,  not against each other.  Therefore, all alternatives which yield a return of at least the MARR are accepted.  In terms of a present worth analysis, all alternatives which have a PW equal to or greater than 0 when i is equal to the MARR would be considered as acceptable alternatives.  For example, in evaluating which new products a company should manufacture, all those whose present worth of costs is lower than their present worth of receipts would be manufactured.

Hereafter, alternatives are assumed to be mutually exclusive unless otherwise specified.


Example 5.1 – Mutually Exclusive Cost Alternatives

An economic analysis of three mutually exclusive cost projects yielded the results shown below.   Which one(s) should be selected?

Project ID AX BX CX
PW @ i = MARR -$10,000 -$7000 -$15,000

(A) Only AX
(B) Only AX and CX
(C) Only BX
(D) Only CX

 Solution:       Since the projects are mutually exclusive cost projects, only one can be selected.  The one with the lowest cost is alternative BX.  Therefore, the answer is (C).


Example 5.2 – Mutually Exclusive Revenue Alternatives

From the economic analysis results of the mutually exclusive revenue alternatives shown below, determine which ones should be selected:

Project ID A5 B5 C5
PW @ i = MARR -$10,000 -$2000 -$6,000

(A) Only A5
(B) Only B5
(C) Only C5
(D) None

 Solution:

Since the projects are mutually exclusive revenue alternatives, only one can be selected, but only if the PW @ i = MARR is greater than 0.  In this case, none exceed the MARR (because all PW’s are <0 and they are revenue alternatives).  Therefore, the answer is (D).


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