## 2000 2000 2000 2000

Figure 4.4. Combined uniform series and gradient series cash flow

An alternative approach is to use a factor known as the gradient-to-uniform series conversion factor, symbolized by (AIG,i,n). Tables of (AIG,i,n) are provided in Appendix 4A. An algebraic expression can also be derived for the (AIG,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 4.6) at the end of this section.

### 4.6.9 Summary of Time Value of Money Factors

Table 4.6 summarizes the time value of money factors introduced in this section. Time value of money factors are useful in economic analysis because they provide a mechanism to accomplish two primary functions: (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 4.7 and 4.8 which follow.

### 4.6.10 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.

Question: Are the following two cash flows equivalent at 15%/yr?

Cash Flow 1: Receive $1,322.50 two years from today Cash Flow 2: Receive $1,000.00 today

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