PRESENT and FUTURE EQUIVALENT VALUES of SINGLE CASH FLOWS
Based on equations F = P(1 + i) N and P = F (1 + i)- N , the following three simple rules
apply when performing arithmetic calculations with cash flows:
Rule 1: Cash flows cannot be added or subtracted unless they occur at the same point in
time.
Rule 2: to move a cash flow forward in time by one time unit, multiply the magnitude of
the cash flow by (1 + i), where i is the interest rate that reflects the time value of
money.
Rule 3: To move a cash flow backward in time by one time unit, divide the magnitude of
the cash flow by (1 + i).
A UNIFORM SERIES to ITS PRESENT and FUTURE EQUIVALENT VALUES
Figure 4-7 on p. 142 of the 13th. Ed. or 3-6 on p. 86 of the 12th. Ed. shows a general cash
flow diagram involving a series of uniform (equal) receipts, each amount A, occurring at
the end of each period for N periods with interest at i% per period. Such a uniform series
is often called an annuity. It should be noted that the formulas and tables used in the text
and this course are derived such that A occurs at the end of each period, and thus,
1. P (present equivalent value) occurs one interest period before the first A (uniform
amount),
2. F (future equivalent value) occurs at the same time as the last A, and N periods
after P, and
3. A (annual equivalent value) occurs at the end of periods 1 through N, inclusive.
The timing relationships for P, A, and F can be observed in Figure 4-7 [3-6] and the
Table of Discrete Cash Flows.
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