Page 272 - Analysis, Synthesis and Design of Chemical Processes, Third Edition

Table 9.1 lists the most frequently used discount factors in this text with their common names and
corresponding formulae.

Table 9.1 Commonly Used Factors for Cash Flow Diagram Calculations

The key to performing any economic analysis is the ability to evaluate and compare equivalent
investments. In order to understand that the equations presented in Table 9.1 provide a comparison of
alternatives, it is suggested to replace the equal sign with the words “is equivalent to.” As an example,
consider the equation given for the value of an annuity, A, needed to provide a specific future worth, F.
From Table 9.1, Equation (9.11) can be expressed as

F (Future value) is equivalent to {f (i,n) A(Annuity value)}

where

f(i,n) = (F/A, i, n)

Example 9.14 illustrates a future value calculation.

Example 9.14

You have just won $2,000,000 in the Texas Lottery as one of seven winners splitting up a jackpot of
$14,000,000. It has been announced that each winner will receive $100,000/year for the next 20 years.
What is the equivalent present value of your winnings if you have a secure investment opportunity
providing 9.5% p.a.?

From Table 9.1, Equation (9.14), for n = 20 and i = 0.075,
20
20
P = ($100,000)[(1 + 0.075) – 1]/[(0.075)(1 + 0.075) ]