BIOREFINERIES: INTEGRATION OF DIFFERENT TECHNOLOGIES - Biomass as a Sustainable Energy Source for the Future - page 486

c. This is a straight line starting at year 0 at a value of − 20 M and crossing the

€

time axis at year 8 (= POT ).

Question : What changes when a tax rate, t , of 0.4 is employed?

The aforementioned indicators do not appreciate the fact that the value of money is
time dependent. The most important factor is that one can profit from interest obtained
yearly.
Now, two basic approaches exist to evaluate profitability accounting for the time
value of money. These are the discounted cash flow rate of return ( DCFRR ) and the
net present value ( NPV ).
The discounted CF in year j is

CF j
1+ i

DCF j = ð Eq : 15 : 11 Þ

j

ð Þ

Thus, a certain CF generated in the early years of a project is worth more than the
CF generated in later years as expressed in the division by the factor (1 + i ) j . The NPV
given a relative interest rate i ( NPV i % ) is directly related to the DCF j values via the sum
from year 0 to year n :

NPV i % = X

n

CF j
1+ i

n with CF 0 =

− I 0 ð Eq 15 12 Þ

: :

ð Þ

j =0

The advantage of calculating the NPV is that it is independent of the way of paying
off the financed I 0 and the way of depreciation when one evaluates a project or invest-
ment; on the company level, the way of depreciation, though, plays a role as

tax paid over profit plays a significant role.
Now, if the situation is such that each year the same CF j is generated and if I d =0,
then Equation (15.12) simplifies to

“ higher ”

NPV i % = X

n n

CF j
1+ i

I 0 + CF 1+ i

ð Þ − 1

n =

− ð Eq 15 13 Þ

: :

n

ð Þ i 1+ i ð Þ

j =0

The DCFRR method is based on the principle that the value NPV becomes zero at a
certain value of the internal interest rate. This method s background is that when a

project has a DCFRR of x% than the invested capital in it, the project

'

s lifetime yearly
generates a profit equal to x% of the part left of the original investment in that year
next to a complete payoff of the original investment:

'

NPV DCFRR =0= X

n

CF j
1+ DCFRR

n with CF 0 =

− I 0 ð Eq : 15 : 14 Þ

ð Þ

j =0