Page 269 - Plant design and economics for chemical engineers

INTEREST AND INVESTMENT COSTS 237

TABLE 4
Summary of significance and meaning of discount and compounding factors
presented in Tables 3,5,6,7, and St (Continued)

For part (f) in Table 3
Cl = Compounding factor to give future worth for cash flows which occur uniformly
over a period of years T before the reference point. (P is the total cash flow for
the T-year period.)
erT - 1
s = cg c , = ~
rT
For n = T, C, = F,/F. = F,C,.
NOTE: On basis of above relationship, C, can be generated from F, and F, values given in
Tables 5 and Y.
t r = nominal interest compounded continuously, percent/loo; n = number of years;
T and nT = number of years in a time period.

time period is 5 years, the appropriate factor, as shown in Table 3, is
1 1
Factor = - = ~ = 0.368
&QX5)
2.7183
(b) Dkcount factors to give present worths for cash flows which occur uniformly
over one-year periods after the reference point. For this situation, the factor
would convert one dollar of money, as the total yearly amount flowing
continuously and uniformly during the year (such as cash receipts for one
year), to the present worth of this one dollar at zero time with continuous
interest compounding. Thus, i? (or 3) for the year in question is 1.0, and the
appropriate equation for calculating the factor, based on Eqs. (23) and
(12), is
e’ - 1
Factor = 1 .O -e -m _ (32)
- Fb
r
As an example, if r represents 20 percent and n is the fifth year, the
appropriate factor, as shown in Table 3, is

ew - 1 1 1.2214- 1 1
Factor = - = ~ = 0.407
0.2 ewx5) 0.2 2.7183
(c) Discount factors to give present worths for cash flows which occur uniformly
over a period of years. For this situation, a total amount of one dollar over a
given time period is used as the basis. The cash flows continuously and
uniformly during the entire period, and the factor converts the total of one
dollar put in over the given time period to the present worth at zero time.
This condition would be applicable to a case where cash receipts are steady
over a given period of time, such as for five years. Designating T as the time