AD ALTA
JOURNAL OF INTERDISCIPLINARY RESEARCH
Figure 1: The cash flow structure of an average BSP project in
EUR
Source: Authors.
The initial cash flows involving 32 payments within the life
expectancy of the project captured in Tab. 2 can be replaced by
the equivalent flows with seven payments (see Fig. 1). The CF
payments of the years 1-5 are the forecasted cash flows of the
10
th
row of Tab. 2. The present values PV
5
and PV
21
are
“shadow” payments, which are equivalent to the effect of
annuities that replace them. In view of Tab. 2 and Fig. 1, the set
of relations (2) applies-see Tab. 3:
Table 3: The set of relation (2) corresponding to the simplified
CF structure of an average BSP project calculated in Tab. 2
CF
− 2000
0
(2)
CF
− 500
1
CF
0.76 · a · σ − 1050 = 0.76 · 1800 · σ −1050 = 1360 · σ − 1050
2
CF
0.76 · b · σ − 970 = 0.76 · 2100 · σ − 970 = 1600 · σ − 970
3
CF
0.76 · c · σ − 1480 = 0.76 · 2500 · σ − 1480 = 1900 · σ − 1480
4
CF
0,76 · d · σ −1780 = 0.76 · 3800 · σ −1780 = 2900· σ − 1780
5
PV
For the annuity payments of the 16- year annuity it applies:
5
0.76 · d · σ −1780 = 0.76 · 3800 · σ − 1780 = 2900 · σ − 1780.
Considering the internal yield of 7 % and the annuity factor of
9.447 it corresponds to the present value PV
(2900 · σ − 1780) · 9.4 = 27260 · σ − 16732
5
PV
For the annuity payments of the 10-year annuity it applies:
21
0.76 · d · σ − 1820 = 0.76 · 3800 · σ − 1820 = 2900 · σ − 1820
Considering the internal yield of 7 % and the annuity factor of 7
it corresponds to the present value PV
(2900 · σ − 1820) · 7 = 20300 · σ − 12700
21
Note: in kEUR. The net internal yield of 7% is applicable in the
Czech Republic for renewable energy projects
Source: Authors.
3.1
The course of NPV dependence on σ parameter
The above procedure to the project cash flow calculation is
applicable for all possible depreciation schedules and compatible
with the targeted derivation of NPV criterion.
Based on the set of relations (2) in Tab. 3 and relation (1), for the
course of the budgeted NPV at the required internal yield of 7%
depending on the σ parameter it applies:
= – 2000 – 500 + (1360 · σ − 1050) / 1.07 + (1600 · σ
− 970) / 1.072 + (1900 · σ
− 1480) / 1.073 + (2900 · σ
− 1780) / 1.074 + (27260 · σ
− 16732) / 1.075 + (20300 · σ
− 12700) / 1.0721
= − + · .For NPV
= 0 applies σ = 0.71.
(3)
Figure 2: The course of NPV development depending on the
market risk σ, where σ = P / PE, σ
∈
(0,1
〉
Source: Authors.
A drop in the
purchase price P in the σ relation leads to a
decrease in NPV (see Fig. 2); NPV
≤ 0 occurs at σ ≤ 0.71, see
relation (3) and Fig. 2.
The course of NPV recorded in Fig. 2 and relation (3) is
meaningful only in the case that the reduction of the purchase
price P will not affect other renewable resource energy projects
than the biofuel plant projects. Thus, the discount rate i remains
stable reflecting the internal rate of return on investment. In
situation of a proportional reduction of the purchase price P in
comparison to the budgeted price P
E
3.2 Expected net present value with regard to certainty
degree
of all subsidized renewable
energy projects, the discount rate i also decreases due to the
lower internal yield on investment.
When estimating the project expected profitability, we take into
account the degree of certainty ρ associated with a potential
legislative change (see Tab. 1). Let ρ parameter be the weight in
the formula for E[NPV] calculation. For the expected
profitability of a subsidized project then applies:
E[NPV]=NPV
σ=1
∙ρ+NPV
σ<1
∙(1−ρ)
(4)
The first part of the sum in relation (4) stands for the optimistic
scenario within which the legislation is not anticipated (ρ)
resu
lting in σ = 1; the second part of the sum admits pessimistic
scenario with the possibility of undesirable legislation change
(1 –
ρ) resulting in σ < 1. Thus, the ρ parameter directly
influences the level of the change in purchase price (in the case
of ρ, any undesirable change is not expected, thus σ = 1;
analogically, the value 1 –
ρ signals the risk of an undesirable
change, thus σ < 1).
Let us assume that σ parameter does not drop under 0.71 within
the pessimistic scenario (σ < 0.71 would imply a loss-making
project). Then the average biofuel plant expected profitability
E[NPV] is determined by the value of the weight ρ in relation
(4), the result of which is shown in the last column of Tab. 4.
Table 4: The E[NPV] value in kEUR in dependence of the
d
egree of certainty ρ given for selected countries with variable
σ = 0.75 in pessimistic scenario
Country
ρ parameter
=
∙
<1
∙(−) E[NPV]
Croatia
0.517
4538.7
575.5
5114.2
Czech Republic
0.577
5065.5
504.0
5569.5
Estonia
0.7
6145.3
357.5
6502.8
Hungary
0.587
5153.3
492.1
5645.4
Latvia
0.6
5267.4
476.6
5744.0
Lithuania
0.61
5355.2
464.7
5819.9
Poland
0.64
5618.6
428.9
6047.5
Slovak Republic
0.598
5249.8
479.0
5728.8
Slovenia
0.65
5706.4
417.0
6123.4
Source: Authors.
- 115 -