Page 263 - Plant design and economics for chemical engineers

INTEREST AND INVESTMENT COSTS 233
erati0n.t For example, consider the case where construction of a plant requires
a continuous flow of cash to the project for one year, with the plant ready for
operation at the end of the year of construction. The symbol P represents the
total amount of cash put into the project on the basis of one year with a
continuous flow of cash. At the end of the year, the compound amount of this
P is
-e’- 1
S =p- = fit startup (29)
a t end of one individual year
r
If the plant is ready for operation after one year of construction time and
the startup of the plant is designated as zero time, the future worth of the plant
construction cost after n years with continuous interest compounding is

S after n years in operation = (Pat startup)e’n = Pqern (30)

For profitability analyses, certain discounting or compounding factors
based on continuous interest compounding are of sufficient importance that
tables have been prepared which give values of the factors for various interest
rates and time periods. Table 3 gives examples of tabulated factors for the
following cases:$$

(a) Discount factors to give present worths for cash flows which occur in an instant
at a point in time after the reference point. These factors are used to convert
one dollar of money, which must be available in an instant after time n
(such as scrap value, working capital, or land value), to the present worth of
this one dollar with continuous interest compounding. The appropriate
equation for calculating the factor, therefore, is based on Eq. (12), and

(31)

For example, if the nominal continuous interest rate is 20 percent and the

tit should be noted that 3, P and i? represent sums accumulated by continuous payment over an
indicated time period without any interest accumulation. R represents a periodic accumulatidn
normally based on one year, while 5 and P represent accumulations during a given period of time.
- -
Thus, 5 and P are interchangeable depending on the basic form of equation being used, and S, P,
and E are interchangeable if the time period under consideration is limited to one year or one basic
interest period.
*See Table 4 for a summary of the significance and meaning of the factors presented in Table 3.
Extended values of the factors for parts (a) to (d) of Table 3 are given in Tables 5 to 8.
OFor illustrations of the applications of continuous interest compounding and continuous cash flow
to cases of profitability evaluation, see Examples 2 and 3 in Chap. 10.