Page 262 - Plant design and economics for chemical engineers

232 PLANT DESIGN AND ECONOMICS FOR CHEMICAL ENGINEERS
zero for either type of reactor, and both could be replaced at a cost equal to the
original price. On the basis of equal capitalized costs for both types of reactors,
what should be the useful-life period for the stainless-steel reactor if money is
worth 6 percent compounded annually?

Sdution. By Eq. (28), the capitalized cost for the mild-steel reactor is
CR $5000
K=C,+
(1 + i)” - 1 = SsOOO + (1 + 0.06Q - 1
K = $5000 + $26,180 = $31,180
Therefore, the capitalized cost for the stainless-steel reactor must also be
$31,180.
For the stainless-steel reactor,
CR $15,000
$31,180 = c, + (1 + i)” _ 1 = $15,~ +
(1 + 0.06)” - 1

Solving algebraically for n,
II = 11.3 years

Thus, the useful-life period of the stainless-steel reactor should be 11.3
years for the two types of reactors to have equal capitalized costs. If the
stainless-steel reactor would have a useful life of more than 11.3 years, it would
be the recommended choice, while the mild-steel reactor would be recom-
mended if the useful life using stainless steel were less than 11.3 years.

RELATIONSHIPS FOR CONTINUOUS CASH
FLOW AND CONTINUOUS INTEREST
OF IMPORTANCE FOR
PROFITABILITY ANALYSES
The fundamental relationships dealing with continuous interest compounding
can be divided into two general categories: (1) those that involve instantaneous
or lump-sum payments, such as a required initial investment or a future
payment that must be made at a given time, and (2) those that involve
continuous payments or continuous cash flow, such as construction costs dis-
tributed evenly over a construction period or regular income that flows con-
stantly into an overall operation. Equation (12) is a typical example of a
lump-sum formula, while Eqs. (23) and (25) are typical of continuous-cash-flow
formulas.
The symbols S, P, and R represent discrete lump-sum payments as future
worth, present principal (or present worth), and end-of-period (or end-of-year)
payments, respectively. A bar above the symbol, such as 5, P, or E, means that
the payments are made continuou.$y throughout the time period under consid-