Page 172 - Sustainable On-Site CHP Systems Design, Construction, and Operations

CHP Economic Analysis 145

In order to be able to calculate equivalence, a common time basis is required. The
overall duration of the analysis must be the same, such as a 20-year analysis. However,
different alternatives could have cash flows that are based on time periods. For exam-
ple, Alternative A may consider the interest earned on the money not spent on a monthly
basis, whereas Alternative B may consider the cost savings of the installed project on an
annual basis. In engineering economics, this is typically accomplished by calculating
the present worth of the cash flow, which is discussed further in the following section.
Another aspect of economic equivalence is equating the interest rate over the mul-
tiple time periods analyzed. If the interest rate were to change at a time period of the
analysis, then economic equivalence would change and have to be recalculated.
Utilizing the above described concepts of economic equivalence, any variable of a
project can be analyzed to assess the point of equivalence, or breakeven point. For
example, the fuel price escalation rate at which the two alternatives have the same eco-
nomic effect can be calculated. It can be further determined that at a fuel price escala-
tion rate above that found to provide equivalence, that one alternative is favored
over the other, and vice versa. For example, at annual fuel escalation rates of less than
X percent, the proposed project may be found to result in annual cost savings over its
anticipated service life and is therefore economically viable; however, at annual fuel
escalation rates greater than X percent, that same project may be found to cost more
than the BAU case, and therefore not be economically viable. At a fuel escalation rate of
X percent, the BAU case and the proposed project would have the same economic outcome.
The concept of equivalence can be applied to any of the factors of the analysis, such
as discount factors, escalation rates, capital costs, and maintenance costs. Evaluation of
multiple cases of these factors is called a sensitivity analysis, and is used to determine
how sensitive the economic equivalence of the project is to actual input factors.

Present Worth
Present worth (also called present value) is the current value of a future series of annual
payments. The future payments that make up a cash flow are discounted to reflect the time
value of money. Present worth can be calculated to determine the effect of interest paid, the
discount rate applied, or inflation. The mathematical definition of present worth is
C = C/(1 + i) t
t
where C = present value of C monetary units t time periods in the future (present value
t
or PV)
i = discount or inflation rate
t = number of time periods
Table 9-2 represents the present worth of a simple series of future payments dis-
counted at a rate of 5 percent. As shown the present value of the future payments is less
(discounted) each year.

Net Present Value
The net present value of a series of cash flows is simply the sum of the present worth of
each of the anticipated cash flows:

NPV = (C + C + C + C + ··· + C )
1 2 3 4 n