BIOREFINERIES: INTEGRATION OF DIFFERENT TECHNOLOGIES - Biomass as a Sustainable Energy Source for the Future - page 487

Example 15.3 NPV and sensitivity analysis to major investment parameters

Taking the same data as presented in Example 15.2, assuming in addition an inter-
est rate of 6%, calculate both the NPV and the sensitivities of changes of the initial
investment ( I 0 ), CF , expected lifetime of the installation ( n ), and interest rate ( i ).

Solution
As the CF pattern is constant, Equation (15.11) holds

n 10

I 0 + CF 1+ i

ð Þ − 1 ð 1+0 6 Þ − 1

:

NPV i % = −

n =

− 20 M € +2 : 5M €

10 =

− 1 : 6M €

i 1+ i ð Þ

0 06 1 + 0 ð 06 Þ

: :

The sensitivity of NPV i % with respect to I 0 can be found by simple

differentiation:

∂ NPV i %

∂ I 0

= − 1

Regarding the sensitivity to CF ,

n 10

∂ NPV i %

∂

ð 1+ i Þ − 1 ð 1+0 06 Þ − 1

:

=

n =

10 =+7

4

:

CF i 1+ i ð Þ

0 : 06 1 + 0 ð : 06 Þ

With respect to the expected lifetime, and therefore depreciation time considered
( n ), the sensitivity is

∂ NPV i %

∂

= CF ln 1 + i

ð Þ ln 1 + 0 ð 06 Þ

:

n =2

5M

10 =1

4M

: € : €

n i 1+ i ð Þ

0 : 06 1 + 0 ð : 06 Þ

Finally, with respect to the interest rate, the sensitivity is

n +1 +1 10 + 1 +1

∂ NPV i %

∂ i

= CF in +1

ð Þ− ð 1+ i Þ 0 : 06 10 + 1 ð Þ− ð 1+0 : 06 Þ

=2 5M

: €

n +1

06 2 1+0

10 + 1

i 2 1+ i ð Þ 0 ð : 06 Þ

:

= − 87 1M

: €

This example shows that the time value of money matters; whereas a POT anal-
ysis shows payback time of 8 years, the NPV is — given the interest rate of 6% —

still negative!

A way to estimate the investment costs of process equipment is illustrated in the cal-
culation sheet presented in Table 15.3 with an explanation of terms in Table 15.4.
Once the investment cost is known for a certain process equipment ( I equipment ) with
a capacity A (e.g., expressed in terms of mass flow, volumetric flow, or power unit),