Environmental Engineering Reference
In-Depth Information
Table 6.5
Annuity Factors
a
for Various Interest Rates
ir
and
Interest Periods
n
Interest rate (discount rate)
ir
=
q
- 1
n
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
10
0.1056 0.1113 0.1172 0.1233 0.1295 0.1359 0.1424 0.1490 0.1558 0.1627
15
0.0721 0.0778 0.0838 0.0899 0.0963 0.1030 0.1098 0.1168 0.1241 0.1315
20
0.0554 0.0612 0.0672 0.0736 0.0802 0.0872 0.0944 0.1019 0.1095 0.1175
25
0.0454 0.0512 0.0574 0.0640 0.0710 0.0782 0.0858 0.0937 0.1018 0.1102
30
0.0387 0.0446 0.0510 0.0578 0.0651 0.0726 0.0806 0.0888 0.0973 0.1061
the result is
(6.13)
The annuity factor
a
is:
(6.14)
Table 6.5 shows the annuity factors
a
for different interest periods
n
and
interest rates
ir
. The annuity factor is sometimes simply called
annuity
and the
interest rate is also known as the
discount rate
.
With the annuity factor
a
and the annual generated amount of energy
E
a
the levelled cost for one unit of energy
c
E
is easy to calculate:
(6.15)
The level of the interest rate depends on the risk of the investment.
Risks
associated with renewable energy systems can include the overestimation of the
available renewable energy resource such as solar irradiation or wind energy at
one location, unforeseen technical troubles or changing legal conditions. Since
these risks are usually higher than those of a typical bank account, the discount
rates are also higher. However, it is nearly impossible to make reliable
calculations for the level of the discount rate. In the end, the market with all its
moods and the subjective feelings of investors define the discount rate.
The calculations above can be extended by applying price increases on
operating and maintenance costs or fuel costs for conventional energy systems.
However, statements on price increases over long investment periods are very
difficult to make. Unforeseen events such as crises in oil-producing regions or
shortages of fossil energy resources can change future fuel or raw material
prices significantly. Therefore, statements on future fuel prices or operating
and maintenance costs are not given here; instead the final sections give a
critical overview of conventional interest calculations.
