Appendix A 219uniform series of the same length. Equivalence in this context means that
the present value (P) calculated from the gradient series is numerically
equal to the present value (P) calculated from the uniform series. One way
to accomplish this task with the time value of money factors we have al-
ready considered is to convert the gradient series to a present value using
a (P|G,i,n) factor and then convert this present value to a uniform series
using an (A|P,i,n) factor. In other words:
A = [G (P|G,i,n)] (A|P,i,n)
An alternative approach is to use a factor known as the gradient-
to-uniform series conversion factor, symbolized by (A|G,i,n). Tables of
(A|G,i,n) are provided in Appendix 4A. An algebraic expression can
also be derived for the (A|G,i,n) factor, which expresses A in terms of G,
i, and n. The derivation of this formula is omitted here, but the resulting
expression is shown in the summary table (Table A-6) at the end of this
section.
A.6.9 Summary of Time Value of Money Factors
Table A-6 summarizes the time value of money factors introduced
in this section. Time value of money factors are useful in economic analy-
sis, because they provide a mechanism to accomplish two primary func-
tions: (1) they allow us to replace a cash flow at one point in time with an
equivalent cash flow (in a time value of money sense) at a different point
in time and (2) they allow us to convert one cash flow pattern to another
(e.g., convert a single sum of money to an equivalent cash flow series or
convert a cash flow series to an equivalent single sum). The usefulness of
these two functions when performing economic analysis of alternatives
will become apparent in Sections A.7 and A.8, which follow.
A.6.10 The Concepts of Equivalence and Indifference
Up to this point the term “equivalence” has been used several times
but never fully defined. It is appropriate at this point to formally define
equivalence, as well as a related term, “indifference.”
In economic analysis, “equivalence” means “the state of being equal
in value.” The concept is primarily applied to the comparison of two or
more cash flow profiles. Specifically, two (or more) cash flow profiles are
equivalent if their time value of money worths at a common point in time
are equal.