Mutually Exclusive Alternatives

Go to questions covering topics below

One or more of several analysis methods can be used to select among mutually exclusive alternatives.  They include present worth (PW), equivalent annual worth (EAW), equivalent annual cost (EAC), incremental rate of return (IRR), and incremental benefit-cost (B/C).  EAW (or EAC) is recommended for choosing among alternatives with unequal lives because of its relatively light computational burden.

The appropriate decision criterion for each of these analysis techniques is given in the table below.  Following the table is a set of short cuts that can be used in incremental IRR analysis and incremental B/C ratio analysis.

 

An implicit assumption in these methods is that all alternatives that exceed the budget available have been eliminated before the analysis begins.

 

 

Method Criterion
PW* If at least one alternative has a PW at the MARR that is positive, choose the alternative with the highest PW.  Otherwise choose the do-nothing alternative.
FW* If at least one alternative has a FW at the MARR that is positive, choose the alternative with the highest FW.  Otherwise choose the do-nothing alternative.
EAW If at least one alternative has a EAW at the MARR that is positive, choose the alternative with the highest EAW.  Otherwise choose the do-nothing alternative.
EAC If the do-nothing alternative is not an option, choose the alternative with the lowest EAC at the MARR.  Choose the do-nothing alternative if feasible and if all EAC values at the MARR are positive.
Incremental IRR* Perform incremental IRR analysis by pairwise comparison in a defender/challenge approach.  At each comparison, choose the higher cost alternative (challenger) if the incremental IRR exceeds the MARR.  Otherwise choose the lower cost alternative (defender).  Continue until all alternatives have been considered.
Incremental B/C ratio Perform incremental B/C ratio analysis by a pairwise comparison in a defender/challenger approach.  At each comparison, choose the higher cost alternative (challenger) if the incremental B/C ratio exceeds 1.0.  Otherwise choose the lower cost alternative (defender).  Continue until all alternatives have been considered.  Use EAW for comparison if alternative lives differ.

 

*If alternative lives differ, a common analysis period should be selected.

 

Three short cuts may reduce the computational burden of incremental IRR analysis.  They are:

1. Eliminate the do-nothing alternative if at least one other alternative has a IRR greater than or equal to the MARR.

2. Eliminate any alternative that has a IRR < MARR.

3. Eliminate any alternative that is dominated by another.  X dominates Y if the initial cost of X is greater than or equal to the initial cost of Y, and if the IRR of X is greater than or equal to the IRR of Y.

 

Two short cuts may reduce the computational burden of incremental B/C analysis:

1.  Eliminate any alternative with a B/C ratio less than 1.0.

2.  Eliminate any alternative dominated by another.  A dominates B if A has a higher initial cost than B and if A has a higher B/C ratio than B.