Some Variations
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Future Worth Analysis

Instead of computing the present worth of a project we can also compute its future worth.  When the future worth is computed with net cash flows for each period during the analysis period, the resulting value is known as the net future worth (NFW).   The NFW of a project is also known as the terminal project balance or project surplus.  Though the NFW could be computed at any point in time other than the present, it is usually computed at the end of the project life (or analysis period).

The procedure for computing NFW is similar to NPW.  The difference is in compounding the net cash flows in each period to some future time as opposed to discounting to the present in the case of NPW.  Equation 7.2 illustrates this method.   The decision rule regarding the selection of the project is similar to the one used in NPW analysis.  The logic of finding the equivalent worth of a project at the present or the future can be extended to apply to any time period, if needed.   Example 7.7 illustrates this special case.

Capitalized Equivalent Worth Analysis

There are cases sometimes in which a uniform series cash flow continues for an indefinite period of time.  This occurs when the life of the project is perpetual or extremely long (40 years or more).  Many civil engineering projects qualify for this definition.

Finding the present or the future worth of an infinite series using Equations 7.1 or 7.2 would be impossible.  But by using the mathematical concept of limits this summing procedure can be simplified as shown in the derivation leading to Equation 7.3.   This process of finding the PW cost of an infinite series of uniform costs is known as the capitalization of project cost and the computed cost is known as the capitalized cost.  The capitalized cost is the amount of money that needs to be invested today to yield some uniform amount at the end of each period for an infinite number of periods.  The present worth computed in this fashion is known as the capitalized equivalent (CE) amount.  Examples 7.8 and 7.9 illustrate the use of this concept.  Note that on Page 303 the notation used for the equivalent sum of money at year 0 does not match with the definition provided on Page 100 of the text.  Specifically, V1 on Page 303 is actually V0 for investment and V2 is V0 for benefits or receipts.  To distinguish the two V's, it might have been better to use V01 and V02.