Appendix A 221Question: 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
Analysis Approach 1: Compare worths at t = 0 (present worth).
PW(1) = 1,322.50(P|F,15,2) = 1322.500.756147 = 1,000 PW(2) = 1,000
Answer: Cash Flow 1 and Cash Flow 2 are equivalent.
Analysis Approach 2: Compare worths at t = 2 (future worth).
FW(1) = 1,322.50
FW(2) = 1,000(F|P,15,2) = 1,0001.3225 = 1,322.50
Answer: Cash Flow 1 and Cash Flow 2 are equivalent.
Generally the comparison (hence the determination of equivalence)
for the two cash flow series in this example would be made as present
worths (t = 0) or future worths (t = 2), but the equivalence definition holds
regardless of the point in time chosen. For example:
Analysis Approach 3: Compare worths at t = 1.
W1(1) = 1,322.50(P|F,15,1)
= 1,322.500.869565 = 1,150.00
W1(2) = 1,000(F|P,15,1) = 1,0001.15 = 1,150.00
Answer: Cash Flow 1 and Cash Flow 2 are equivalent.
Thus, the selection of the point in time, t, at which to make the
comparison is completely arbitrary. Clearly, however, some choices are
more intuitively appealing than others (t = 0 and t = 2 in the above
example).
In economic analysis, “indifference” means “to have no prefer-
ence.” The concept is primarily applied in the comparison of two or
more cash flow profiles. Specifically, a potential investor is indifferent
between two (or more) cash flow profiles if they are equivalent.
Question: Given the following two cash flows at 15%/yr, which do you
prefer?
Cash Flow 1: Receive $1,322.50 two years from today
Cash Flow 2: Receive $1,000.00 today
Answer: Based on the equivalence calculations above, given these two
choices, an investor is indifferent.