Present worth analysis is also applied extensively to compare various alternative projects with the goal of selecting one  project for implementation.  An important distinction that arises between an analysis involving multiple alternatives and one involving a single project is the treatment of unequal project lives.  And even if the project lives of the alternatives are the same, the analysis period and the project life could be different. When this happens we need to account for the need to replace projects when the project life is shorter than the analysis period, or to account for the surplus value of projects at the end of the analysis period, when the analysis period is shorter than the project life.  The problem of different lengths of analysis period and project life, is something that can occur even in the case of a single project.   We had ignored this problem so far; we will deal with it in this Section.

The analysis period is synonymous with study period or planning horizon. This period is usually determined by company policy.   We can also call it the required service period.

Adjustments in the analysis are required when the project lives and the analysis period are not of equal length.  Various scenarios of this problem can emerge for any given problem.  The complete set of possibilities is shown in Figure 7.13.

Equal Analysis Period and Project Lives

The simplest case arises when the analysis period equals the project lives.  When this happens no adjustment is needed.  The NPW is calculated for each of the alternatives under consideration.  The project with the most optimal NPW is selected for implementation.

The optimal NPW depends on the type of projects analyzed.  If only costs are considered, because the revenue generated by each of the projects is the same, then the optimal NPW is the one with the lowest value (i.e., the least negative value).   Projects that fit this description are called service projects.   With different project revenues, however, the optimal NPW is the highest-valued NPW.  Projects that belong to the second category are known as revenue projects.

Different Analysis Period and Project Lives 

Two cases can occur under this category: project life longer than analysis period, and project life shorter than analysis period.  In the first case, we have to estimate the salvage value of projects that are retired before their useful lives.  Example 7.11 illustrates this case.  Note that in this example the salvage values at the end of the operable lives of both models are not considered in the NPW analysis since an estimate of salvage values for both alternatives at the end of the analysis period (which is 2 years) has been provided.

In the second case, when the project life is shorter than the analysis period, we have to deal with the problem of replacing the project when its initial life comes to an end.   This replacement can occur one or more number of times, depending on the length of the analysis period.

The most common way of dealing with the replacement problem is to assume that a replacement with an exactly the same type of project is possible.  This simplifies the analysis; it is not necessary, however.  With a new replacement project we will just have to use a different set of cost and revenue figures.  But no matter how the replacement is handled, if any useful life of the replaced project remains after the analysis period expires, we will have to account for salvage value just as in the case discussed earlier.

Analysis Period Equal to the Longest Project Life

This is a special case.  It occurs in the case of revenue projects in which only a one-time investment is needed.  Projects involving extraction of a fixed quantity of natural resource such as oil or minerals are good examples of this case.  The alternatives considered can have different lives, but since the need for the project is only one time, the analysis can proceed with a period that is equal to the longest life of the alternatives.  The cash flows for shorter projects are assumed to be zero for periods beyond their life times, in this type of analysis.  Example 7.13 illustrates this case.

Analysis Period Unspecified