The importance of the dynamic methods lies in the fact that the results obtained using the simpler
static methods of calculation described in chapter 8.3 can become problematic, if the point in time at
which payments become due is of increasing importance. Any investor naturally will set a lower
valuation to revenues that are due a decade from now than to those which are coming in at present.
Consequently, he would want to compound past payments and discount future payments to obtain
their respective present values.
Net-present-value method
The most commonly employed method of dynamic micro-economic analysis is the net-present-
value method used by many extension officers. It enables evaluation of both the absolute and
relative advantages of a biogas-plant investment (as compared to other investment alternatives) on
the basis of the anticipated minimum interest rate above and beyond the net present value of the
investment. Simultaneously, the netpresent-value method also serves as a basis for calculating the
dynamic payback period and for calculations based on the annuities method. (For details on the
net-present-value and other dynamic methods of calculation, please refer to the aforementioned
publication by Finck/Oelert.)
The inflation problem: Either the entire calculation is based on nominal incomes and expenditures,
and market interest rates (= calculatory interest) are assumed, or the income and expenditures are
presumed to remain constant, and the calculation is based on the real interest rate. The latter is
calculated according to the following formulae (p = market rate of interest and a = rate of inflation):
i
=
100
100
+
+
p
a
⋅100
−
100
Example: market rate of interest = 48%; rate of inflation = 34%
i = [(100 + 48)/(100 +34)]* 100-100=10.4%
Discounting factors: The compounding and discounting factors for the net-present-value method are
shown in table 10.11 (Appendix) for interest rates of 1-30% and service lives of 1-15 years.
Calculatory procedure: The following information is drawn from the appendicized data survey:
calculatory rate of interest, i (item 1.3); investment costs, I (item 2) and the returns (item 8). Much
like the static mathematical models discussed in chapter 8.3, the calculatory procedures are again
made more readily understandable by inserting the appropriate data from the formsheet (table
10.10, Appendix). In a real case, those data naturally would have to be replaced by the actual on-
site data.
Results: The biogas plant can be regarded as profitable, if its net present value is found to be equal
to or greater than zero for the minimum acceptable interest rate, e.g. i= 10%. The net present value
is arrived at by cumulating the cash-flow value. Among several alternative investments, the one with
the highest net present value should be chosen.
Sample calculation: For a plant service life of 10 years (conservative estimate), the cash flow values
reflecting the annual returns times the discounting factor need to be determined and cumulated (cf.
table 8.4). In this example, the net present value, at 129, would be positive, i.e. the potential
investment would be worthwhile. The effects of discounting future income to its present value are
substantial. For example, the return listed as 200 in item 10 would have a cash-flow value of 77 for
a calculatory interest rate of 10°,to.
101