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ISSN 2029-9230
673
2017, Vol. 23, No. 3 (46)
Introduction
Poplar plantations play one of the key roles in the
industrial wood supply in countries such as China, France,
India, Italy and Turkey, and each of them produces more
than 1 million m3 of poplar wood from specialised planta-
tions (Spinelli and Magagnotti 2011). Managed on 10 to
30 years rotations, some of the clones can produce ve-
neer logs (Hongyuan 1992).
Poplars are one of the most productive tree species
in Serbia, which production complexity requires rational
and well-planed management, whereby the site and spe-
cies potentials would be maximally used (Keèa and Pajiã
2010). Conventional poplar growing in Serbia is charac-
terized by the high costs of plantation establishment, as
it is common to use the technology of full ground and
soil preparation, with a lot of working operations (Keèa
and Pajiã 2015). Alluvial plains along the rivers Danube,
Sava, Tisa, Ibar and Morava Rivers are suitable for the
growth of several broadleaved tree species (Quercus
robur L., Fraxinus angustifolia Vahl., Populus spp.)
(Keèa et al. 2015). Serbias forest reserves, which cover
approximately 27% of the countrys land area, or about
two million hectares, are estimated to be containing 235
million m3 of the standing inventory (Keèa and Keèa
2015). About 36.000 ha of poplar plantations are located
in Vojvodina (Bankoviã 2009).
The controversy of optimal forest management has
a long history in forestry economics (Chladna 2007).
Determination of the Optimal Financial Rota-
tion Period in Poplar Plantations
LJILJANA KEÈA
Faculty of Forestry, University of Belgrade, Chair of Forestry Economics and Organisation, 1, Kneza Viðeslava
street, 11030 Belgrade, Serbia, Tel. +381641794648 and +381113053959, E-mail: ljiljana.keca@sfb.bg.ac.rs
Keèa, L. 2017. Determination of the Optimal Financial Rotation Period in Poplar Plantations. Baltic Forestry 23(1):
673682.
Abstract
Due to trends in the consumption of wood and particularly soft broadleaves, poplar cultivation has gained importance in
Serbia and worldwide in the field of production, economics and environmental protection issues. The present study was
performed to determine the optimal financial rotation lengths for hybrid poplar plantations (Populus Euramericana Gunier
cv. I-214) in a selected area of Serbia. The aim of this study is to apply the method of assessment and calculation of the optimal
production cycle length in order to determine the optimal production cycle length of poplar plantations in the localities of
Serbia from a financial standpoint. The selected discount rate for the calculation is 6% (close to the maximum recorded
internal rate of yield in the observed compartments). It was concluded that the production cycle length of poplar in the study
area ranges from 12-19 years, depending on the soil type. The longest rotation is obtained for humofluvisol (alluvial
semigley). The estimation based on the NPVs criterion determined a desired optimal production cycle length of about 16 years
Keywords: financial rotation, poplar, plantation, optimum
Many studies applying different methodologies have
been conducted in this area, and most of them are related
to stochastic optimal rotation models (Willassen 1998,
Alvarez and Koskela 2004). Nowadays, a lot of forest
economists believe that the net present value approach
is a true innovation in forest management and economics
science. The fact that a total of 313 papers with this topic
have been published since Faustmann speaks in favour
of its importance. However, over two-thirds of these pa-
pers (211) have come since 1985 (Newman 2002).
In short rotation plantation forestry, high biomass
productivity and economic profitability are given prior-
ity and harvest time usually coincides with the age when
mean annual increment is the highest (Tullus et al. 2012).
Therefore, the economic success of poplar plantations
usually depends on obtaining the largest possible
amount of top grade veneer logs, whose value can com-
pensate the high establishment and management costs
(Spinelli and Magagnotti 2011).
The aim of this research is to apply the method of
assessment and the method of calculating the optimal
production cycle length in order to determine the optimal
production cycle length (Keèa 2014) of poplar planta-
tions in the studied localities from an economic stand-
point.
The purpose of this research is to provide guide-
lines for forestry practices aimed at the improvement of
the situation in the field of assessment of the optimal
production cycle length in poplar plantations.
L. KEÈA
BALTIC FORESTRY
DETERMINATION OF THE OPTIMAL FINANCIAL ROTATION PERIOD IN POPLAR PLANTATIONS
The research objects are: the number of trees, vol-
ume of trees and other elements that will be quantified
and numerically analyzed.
Material and methods
The method of assessment was used in the article to
prove the hypothesis that poplar achieved the best finan-
cial effects of production at the ages between 10 and 20
years. This problem comes down to the choice of the ap-
propriate criterion in financial analysis and the monitoring
of its trend for different lengths of the production cycle,
as well as finding the age when the value of the selected
criteria culminates. This is achieved by using regression
and correlation analysis. If statistical significance of the
regression model of the selected indicators trend is pro-
vided, we find the maximum of curves and determine the
time when the financial success is the highest.
The total net present value (NPV) and the average
net present value (NPVs) of wood production in the
analyzed poplar plantations were selected as the criteria
for the assessment of the financial effects, calculated
according to the method of the present value and the
resultant value and then expressed per unit area. The
basic principle on which the method of the present value
is based is that stand value is equated with the value of
timber of the selected trees (in this case poplar), in the
exact proportion that represented the assortment volume
of categories that at the time of assessment are present
in the market, reduced by the costs of forest utilization:
Vs = (V1·P1+ V2·P2++Vn·Pn) - Cs
where: Vs-value of the stand, V1,2,n - volume of the timber
assortment categories, P1,2,n prices of timber assort-
ment categories, Cs costs of forest utilization.
The investigated sample plots were established from
Populus × euramericana cl. I-214, with a 6 × 3 m (555 trees
per ha) planting spacing for technical wood production,
and they were located in the Northern province of
Vojvodina. Nineteen (19) compartments (52 stands) aged
24-42 years with a total area of 362.35 ha were investi-
gated. Soil types in these plots are: a / b-b gley; alluvial
semigley; fossil hydromorphic black soil on loess-alluvium
and fossil hydromorphic black soil (humosemigley) on
loess-alluvium. The research was carried out in poplar plan-
tations located in the area of the Sava River during the
2002 2014 period. Data pertaining to costs during years
0-5 (soil preparation, planting, care and protection, etc.)
were obtained from the archives of the forest enterprise
which managed the studied plantations, and also the data
from material books (Keèa 2010a). The costs of ground
preparation for afforestation are 2040.50 /ha in the start-
ing year. In the first year, the costs of maintenance and
protection of plants are 209.44 /ha. In the second year,
afforestation with rooted cuttings and maintenance and
protection of the plantation costs are 207.48 /ha. In the
third, fourth and fifth years, the costs of tending (inter-
row treatment and weed control) amount to 305.45 /ha.
The costs in the sixth year are 825.91 /ha, because of the
costs of schematic thinning and cutting, processing and
extraction of timber, and in the final year, the costs amount
to 3397.0 /ha. On the other hand, the revenues range be-
tween 11 088.3 23 676.36 /ha. Since all the studied stands
are state-owned and managed by the Public Forest Enter-
prise Vojvodinaðume, the value (cost) of the land (land
rent) did not enter into the calculations (Keèa et al. 2011).
Estimates were made separately for each soil type,
bearing in mind the possibility that different surfaces can
behave differently and the effects of financial trends ob-
served. The criteria for the assessment of the financial
effects were the selected total net present value (NPV)
and the average net present value (NVPs) of production of
poplar wood in the analyzed plantations, calculated ac-
cording to the method of the present value of felling ripe-
ness, and the resultant value then expressed per unit area.
The chosen discount rate to be used in the calcula-
tion was 6%. This discount rate is very close to the maxi-
mum recorded internal rate of return in the observed
stands, which amounts to 5.56% (Keèa 2010, Tullus et al.
2012). The return on investment from the stands at a cer-
tain age should be equal to the available alternative rate
of return on the capital invested (rather than percentage
changes in costs). Stands or trunks are only in this case
the financial mature (Duerr et al. 1956, Keèa and Keèa
2014). In forestry, the valuation of forests is performed
with the interest rate of capitalization (it is the basis for
the capitalization of rents, discounting and prolonging
of financing rents). Therefore, the basis for determining
interest rates in forestry is the rate of value growth. The
higher increment of a stand, the higher the interest rate
(Figuriã 1996).
The assessment was made separately for each soil
type in three variants. The first variant (M0) is based on
real data on costs and revenues created in the compart-
ments on the same ground, totally focused on them when
calculating total and average net present value of pro-
duction. Bearing in mind that in all cases it has reliable
information at the beginning of the production cycle (es-
tablishment and care of plantations costs) and its end
(harvest and production assortments revenues and
associated costs).
The following two variants are created as an attempt
to compile an expert assessment of data about possible
values from the central segment of production cycle
length. In that way, the obtained data were incorporated
into the calculation. The assessment starts from the two
typical cases which form two clearly visible contradic-
tions. The second variant (M1) is based on an estimation
that in the period of culmination of the financial effects
ISSN 2029-9230
674
2017, Vol. 23, No. 3 (46)
L. KEÈA
BALTIC FORESTRY
DETERMINATION OF THE OPTIMAL FINANCIAL ROTATION PERIOD IN POPLAR PLANTATIONS
there is no complex assortment structure, but at this age
stacked wood usually dominates in the assortment struc-
ture of the produced volume of poplar wood. It was taken
as an assumption that the entire realized production is of
simple assortment structure and belongs to the category
of cordwood.
The third variant (M2) is based on the assumption
that the assortment structure may still affect movement
of the culminating point of the observed criterion. How-
ever, at this moment there are no data related to complete
final felling at these ages in sample plots, remaining as
an opportunity to assess the income and expenses at
these ages. The estimation of revenues from timber, in
this case, is the most complex part of the assessment,
and is made through the assortment structure obtained,
based on the method of model tailoring of the trunks
(Nikoliã 1988). This method assumes that assortment
structure depends only on the dimensions of trunks and
does not take into account possible errors of the spin-
dles of tree trunks that affect the result of cutting in prac-
tice. Such a developed assortment structure can be con-
sidered ideal, and (theoretically) as a result brings the
highest revenues from the sales of wood.
In this way, there is the opportunity to compare the
results of three assessments (real lack of data from
the central segment of the length of the production cy-
cle, minimalistic the actual data associated data, where
income is assessed only on the basis of the least valu-
able assortments and maximalistic the actual data
associated the data were obtained on the basis of a
calculation of income based on the ideal assortment struc-
ture). Such access is provided to summarize the possible
similarities or differences in results and provide a more
precise definition of the age range at which the greatest
financial effects can be expected.
To conduct the calculation of missing data on in-
come in the variant M2, for stands at ages that are miss-
ing, in the field we required compartments to meet the
requirement that they include trees of such ages (rang-
ing between 9-23 years). Such departments are found in
each category of soil, but their number is not the same in
each of them. In the next step, data on the dimensions
(diameter and height) of all trees from each of the se-
lected compartments were collected and processed. The
dimensions of trees in the selected classes were obtained
from the Special plan of forest management of this area.
During data processing, it was noticed that trees in the
researched artificial poplar plantations at the same age
(same compartment) have approximately the same dimen-
sions (height variation coefficient is Ch = 5.23%, and the
thickness of Cd = 4.31%) (Table 1). That means it can be
operated with a single tree of average size (mean tree
as a representative of all trees in the department in which
the trees are of the same age (Bankoviã and Pantiã 2006).
Model tailoring based on the principle of maxi-
mum utilization (Nikoliã 1988) was applied for the selected
trees (Table 2), and a total of 33 trees of different ages
(from 12-28 years) were chosen.
Ta b l e 1 . Coefficients of variations of
dimensions of trees in plantations of
poplar with a 6×6 m planting space;
T age of plantation, N number of
stands, Cd coefficient of variations
in diameter, Ch coefficient of vari-
ations in height
T N Cd Ch
age % %
15
1 7,5 4,8
2 6,8 5,1
3 6,9 5,2
Average 7,1 5,0
20
1 7,1 4,6
2 7,5 5,3
3 5,2 4,2
Average 6. 6 4,7
25
1 5,8 4,1
2 7,0 4,4
3 6,4 4,7
Average 6, 4 4,4
Tab le 2. Age and number of stands whose derived trees
were used for the purposes of model tailoring
So il T ype Age of the stands Numb er of
stands year
* á / â-â gley 12, 14, 16, 18, 19, 23, 26, 28 8
*RC 13, 14, 1 5, 16, 1 7, 19, 23, 25, 26, 2 7 10
14, 15, 16, 18, 19, 22, 23 7
ASG 9, 1 2, 14 , 15, 16, 18, 23, 24 8
Ó / 33
As a result of the model tailoring, mean trees by
volume assortments were obtained in each selected de-
partment. These mean trees are the next step multi-
plied by the appropriate prices and the number of trees in
each of these departments, in order to obtain the value of
revenues by departments. These are dependent on the
assortment structure, soil type and the age of stands. In
the following calculation, the resulting value of income
is divided by the surface area of each department to ob-
tain the amount of revenue per hectare. So, as input data
for the assessment of income, we used data on the
number and size of trees in the selected departments on
the ground (to obtain the average dimensions of trees
and assess assortment structure), market prices assort-
ments for 2014 (the valid price list PE Vojvodinaðume)
and the area of the observed compartments. The whole-
sale prices of PE Vojvodinaðume (VAT is excluded) for
tree assortments are as follows: for class F, the price is
66.06 /m3, class L 51.75 /m3, class I 38.53 /m3 and class
II 30.28 /m3.
The present value of the income and expenses (with
a discount rate of 6%), total and average net present
value were calculated on the basis of the database, and
finally the time of their culmination was estimated. The
assessment of culmination was done in a way that data
were flat out (even) by a regression curve (cubic parable,
i.e. polynomial of third-degree). After that, we found the
maximum of the given function as the time of culmination
*RC-fossil hydromorphic black soil (humosemigley) on loess-al-
luvium, AS ASGalluvial semigley, LC-fossil hydromorphic black
soil on loess-alluvium, a / b-b gley
a / b-b
S
ISSN 2029-9230
675
2017, Vol. 23, No. 3 (46)
L. KEÈA
BALTIC FORESTRY
DETERMINATION OF THE OPTIMAL FINANCIAL ROTATION PERIOD IN POPLAR PLANTATIONS
of the total and average net present income for the 4
researched types of poplar forests.
Finally, the criteria for the greatest financial impacts
were chosen. In order to compare the financial effects of
the total and average net present values, it is necessary
to reduce them to the same level. Therefore, procedures
are multiplying the average net present value with the
age at which the total net present value (tNPVmax) culmi-
nates. After that, we compared the result obtained in that
way between the results (NPVt) and the total net present
value (NPV), and the selected value that has a higher
validity (Rankoviã 1996). The formula for such a calcula-
tion would have the following form:
a choice when compared would be as follows:
if the requirement that the NPVt ³ NPV is met, then
further analysis related to the average net present value
(NPVs would be a criterion for observation and analysis);
if the opposite condition (NPVt £ NPV) is fulfilled,
then total net present value (NPV) is the criterion in rela-
tion to which further observation and analysis are to be
performed.
Results
According to the available data from the field on a /
b-b gley soil type, 8 stands aged 12, 14, 16, 18, 19, 23, 26
and 28 years (Table 3) were researched. They were evalu-
ated in terms of the size of NPV and NVPs presented by the
regression curve trend (cubic parabola) (Figures 1, 2).
tNPV
max
s
NPV NPV t
Tabl e 4. Optimal lenght of production cycle and the highest
value of NPV and NPVs
On the basis of these elements, it can be stated that
the estimation based on criteria NPVs represents the re-
quired optimum length of the production cycle and it is
17 years (Table 4).
y = -0,0066x3 - 1 ,4092x2 + 109,0 6x - 2688 ,7
R2 = 0,798 5
y = 0,1464x3 - 11,248x
2 + 252,7 7x - 1690,9
R2 = 0,860 7
-3000
-2500
-2000
-1500
-1000
-5 00
0
500
010203040
Figure 1. NPV and NPVs in estimation variant M1 (in all
figures NPV is in red, and NPVs is in blue)
y
= -0, 1458x3 + 6,415 8x2 + 26, 626x - 2521
R2 = 0,8733
y
= 0,1415x3 - 1 0,989x2 + 250,5 2x - 1687,4
R2 = 0,8637
-30 00
-25 00
-20 00
-15 00
-10 00
-5 00
0
500
1000
010203040
Figure 2. NPV and NPVs in estimation variant M2
Variant of
estim ation
Time of
culmination Maximum value Verification of
criteri a
NPV NPVs NPVmax
NPVsmax NPVsmax· tNPVmax
(tNPVmax=32)
year ·ha 1
M / / / / /
M 32 7 855, 72,82 2.33,2
M2 32 7 23,26 9,8 2.95,8 7
According to the data available from the field on RC
soil type was researched 10 stands aged 13, 14, 15, 16, 17,
19, 23, 25, 26 and 27 years (Table 5) (Figures 3, 4, 5).
On the basis of these elements, it can be said that
the estimation based on the NPVs criterion represents the
required optimum length of the production cycle, which
is 15 years (Table 6).
According to available data from the field, on LC
soil type was researched 7 stands of the following ages:
14, 15, 16, 18, 19, 22 and 23 years (Table 7) (Figures 6, 7).
Tab le 3 . Values of NPV and NPVs in three variants of esti-
mation
Age
year
Variants of estimation
M0 M1 M
2
NPV NP Vs NP V NPVs NPV NPV s
·ha1
1 2.040,48 2.04 0,4 8 2.040,48 2.040,48 2.040,4 8 2 .040, 48
2 2.238,06 1.11 9,0 3 2.238,06 1.119,03 2.238,0 6 1 .119, 03
3 2.422,72 807 ,57 2.422,72 807 ,57 2.42 2,7 2 807,57
4 2.516,46 629 ,12 2.516,46 629 ,12 2.51 6,4 6 629,12
5 2.593,22 518 ,64 2.593,22 518 ,64 2.59 3,2 2 518,64
6 2.665,63 444 ,27 2.665,63 444 ,27 2.66 5,6 3 444,27
7 2.227,16 318 ,17 2.227,16 318 ,17 2.22 7,1 6 318,17
12 / / 1.270,07 105,84 1. 392,1 5 116,01
14 / / 1.131,06 80,79 1 .133,4 2 8 0,9 6
16 / / 1.129,19 70,57 843,70 52,73
18 / / 1.077,86 59,88 273,23 15,18
19 / / 1.005,04 52,90 427,12 22,48
23 / / 1.117,19 48,57 784,25 34,10
26 / / 1.039,30 39,97 597,52 22,98
28 / / 1.144,09 40,86 326,94 11,68
43 1060,86 24,67 1.060,86 24,67 1.060,8 6 2 4,67
ISSN 2029-9230
676
2017, Vol. 23, No. 3 (46)
L. KEÈA
BALTIC FORESTRY
DETERMINATION OF THE OPTIMAL FINANCIAL ROTATION PERIOD IN POPLAR PLANTATIONS
Age
year
Variants of es timat ion
M0 M1 M2
NPV NP Vs NPV NPV s NPV NPVs
·ha1
1 2040, 48 2040, 48 2040, 48 2040, 48 2040, 48 20 40,48
2 2238, 06 1119, 03 22 38,06 1119, 03 2238, 06 11 19,03
3 2422, 72 80 7,57 24 22,72 80 7,5 7 2422, 72 807,57
4 2516, 46 62 9,12 25 16,46 62 9,1 2 2516, 46 629,12
5 2593, 22 51 8,64 25 93,22 51 8,6 4 2593, 22 518,64
6 2665, 63 44 4,27 26 65,63 44 4,2 7 2665, 63 444,27
7 2227, 16 31 8,17 22 27,16 31 8,1 7 2227, 16 318,17
13 / / 1141,62 87,82 13 19,09 10 1,4 7
14 / / 1141,99 81,57 608,6 0 43 ,47
15 / / 1119,72 74,65 10 83,78 72 ,25
16 / / 90 3,1 9 56,45 10 29,56 64 ,35
17 / / 80 5,4 1 52,65 144, 58 8,50
19 / / 89 5,0 3 61,04 43 ,41 2,28
23 / / 1159,81 50,43 396,3 8 17 ,23
25 / / 1237,94 49,52 107,3 5 4, 29
26 / / 1205,75 46,38 443,7 9 17 ,07
27 / / 1158,08 42,89 569,7 0 21 ,10
29 27 5,6 0 9, 50 275,60 9,50 27 5,60 9,50
30 38,2 4 1, 27 38,24 1,27 38 ,24 1,27
32 31 5,8 9 9, 87 315,8 9 9,87 31 5,89 9,87
Tab le 5 . Values of NPV and NPVs in three variants of esti-
mation
y = -0, 4145x3 + 21,504x
2 - 212,72x - 1920,7
R2 = 0,9833
y = 0,3185 x3 - 20,686x2 + 401,73x - 2066,1
R2 = 0,9175
-3000
-2500
-2000
-1500
-1000
-500
0
500
0 5 10 15 20 25 30 35
Figure 3. NPV and NPVs in estimation variant M0
y = 0,058 5x3 - 3,9599x2 + 141,85 x - 2759,7
R2 = 0,7815
y = 0,2875 x
3 - 17,176x2 + 317,5 x - 1836
R2 = 0,9013
-3000
-2500
-2000
-1500
-1000
-500
0
500
1000
0 10203040
Figure 4. NPV and NPVsin estimation variant M1
y = -0,3082x3 + 12,069x2 - 12 ,088x - 2462,1
R2 = 0,8711
y = 0,2716x 3 - 1 6,519x2 + 312x - 1826,7
R2 = 0,9021
-3000
-2500
-2000
-1500
-1000
-500
0
500
0 5 10 15 20 25 30 35
Figure 5. NPV and NPVs in estimation variant M2
Tab le 6. Optimal lenght of production cycle
and the highest value of NPV and NPVs
Varian t of
estimation
Time of
culm inat ion Max imum value Verifi cation
of criter ia
NPV NPVs NPVma x NPV
year ·ha1
M0 28 15 116,83 380,44 10.652,32
M1 / 15 / 32,21 /
M2 26 15 34,67 53,18 1.382,55
Ages
year
Variants of estimation
M0 M1 M2
NPV NPVs NPV NPVs NP V NP Vs
·ha1
1 2.040,48 2.040,48 2.040,48 2.040,48 2.040,48 2.040,48
2 2.2 38,06 1.119,03 2.238,06 1.1 19 ,03 2.2 38, 06 1.119,03
3 2.422 ,72 807,57 2.422 ,72 8 07,57 2 .422,72 807,57
4 2.516 ,46 629,12 2 .5 16,46 6 29 ,12 2 .516 ,46 629,12
5 2.593 ,22 518,64 2.593,22 518,6 4 2.5 93,22 518,64
6 2.665 ,63 444,27 2.665,63 444,2 7 2 .665 ,63 444,27
7 2.227 ,16 318,17 2.227,16 318,1 7 2 .227 ,16 318,17
14 / / 1.358 ,64 97,05 1.168 ,11 8 3, 44
15 / / 1.259 ,21 83,95 8 11,7 1 5 4,11
16 / / 1.217 ,31 76,08 823 ,81 5 1, 49
18 / / 1.186 ,83 65,94 6 21,6 5 3 4,54
19 / / 1.114 ,57 58,66 804,19 42,33
22 / / 1.175 ,63 53,44 341,51 15,52
23 / / 1.199 ,77 52,16 339,48 14,76
25 237,3 5 9,49 237,35 9 ,49 2 37 ,35 9,49
Ta b l e 7 . Values of NPV and NPVs in three variants of esti-
mation
y = -0, 4224x3 + 1 8,2 99x2 - 138,56x - 2115
R2 = 0,8734
y = 0,62 95x3 - 30,339x2 + 4 53,32x - 2121,3
R2 = 0,9357
-3 00 0
-2 50 0
-2 00 0
-1 50 0
-1 00 0
-500
0
500
1000
0 10203040
Figure 6. NPV and NPVs in estimation variant M1
ISSN 2029-9230
677
2017, Vol. 23, No. 3 (46)
L. KEÈA
BALTIC FORESTRY
DETERMINATION OF THE OPTIMAL FINANCIAL ROTATION PERIOD IN POPLAR PLANTATIONS
On the basis of these elements, it can be said that
the estimation based on the NPVs criterion represents the
required optimum length of the production cycle, which
is 12 years (Table 8).
According to the data available from the field 8 stand
at the AS ASG soil type of the ages: 9, 12, 14, 15, 16, 18, 23
and 24 years (Table 9), which were evaluated in NPV and
NVPs (Figures 8, 9, 10).
Table 8. Optimal lenght of production cycle and
the highest value of NPV and NPVs
y = -1, 2307x3 + 50,073x2 - 421,3x - 1587,4
R2 = 0,9482
y = 0,5867x3 - 28,713x2 + 439,51x - 2096,3
R2 = 0,9322
-3000
-2500
-2000
-1500
-1000
-500
0
500
1000
0 10203040
Figure 7. NPV and NPVs in estimation variant M2
Vari ant of
estimation
Time of
culm ination Maximum value Verific ation
of criteria
NPV NPVs NPVmax NPV
year ·ha1
M
0 / / / / /
M
1 25 12 742,13 3 7 , 5 0 937,50
M
2 22 12 274,8 4 56,97 1.253,34
Age
year
Variants of estimation
M0 M1 M2
NPV NP Vs NPV NPV s NPV NP Vs
·ha1
1 2.040,48 2.040,48 2.040,48 2.040,48 2.040,48 2.040,48
2 2.227,48 1.113,74 2 .23 8,06 1.11 9,03 2 .238, 06 1.119, 03
3 2.392,88 797,63 2.42 2, 72 807,57 2.42 2, 72 8 07,57
4 2.472,35 618,09 2.516,46 629,12 2.516,46 6 29 ,12
5 2.533,93 506,79 2.59 3, 22 518,64 2.593,22 518,64
6 2.588,92 431,49 2.665,63 444,27 2.66 5, 63 4 44 ,27
7 2.273,80 324,83 2.22 7, 16 318,17 2.22 7,16 3 18,17
9 / / 856,69 95,19 1.881,25 209,03
12 / / 859,78 71,65 1.64 6,98 137,25
14 / / 943,98 67,43 1.444, 57 103,18
15 / / 854,08 56,9 4 800 ,30 53,35
16 / / 833,39 52,09 411,19 25,70
18 / / 899,12 49,9 5 447,41 24,86
23 / / 1.011,41 43,97 527,92 22,95
24 / / 1.021,35 42,56 514,06 21,42
25 1.743,02 69,7 2 237,35 9,49 237,35 9,49
27 1.609,37 5 9,6 1 553,64 20,51 553,64 20,51
29 1.725,41 59, 50 335,17 11,56 335,17 11,56
30 1.896,30 6 3,2 1 363,49 12,12 363,49 12,12
38 1.999,57 5 2,6 2 124 ,02 3,26 124,02 3,26
43 2.161,99 50,28 1.097,84 25,53 1.097,84 25,53
Tab le 9 . Values of NPV and NPVs in three variants of esti-
mation
y = -0, 1078x3 + 6,5503x2 - 85,523x - 2130
R2 = 0,816
y = 0,1938x3 - 15,119x2 + 338,15x - 1913,6
R2 = 0,8898
-3000
-2500
-2000
-1500
-1000
-500
0
500
1000
-5 5 15253545
y = -0,0875x3 + 2,7829x2 + 79,488x - 2579,7
R2 = 0,7928
y = 0,1242x3 - 9,8204x2 + 233,07x - 1631,7
R2 = 0,8565
-3000
-2500
-2000
-1500
-1000
-500
0
500
1000
-5 5 15253545
y = -0,1758x3 + 7,3024x2 + 42,339x - 2621,7
R2 = 0, 8763
y = 0,117x3 - 9 ,399 1x 2 + 227,71x - 1627,8
R2 = 0,8666
-3000
-2500
-2000
-1500
-1000
-500
0
500
1000
0 1020304050
Figure 8. NPV and NPVs in estimation variant M0
Figure 9. NPV and NPVs in estimation variant M1
Figure 10. NPV and NPVs in estimation variant M2
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2017, Vol. 23, No. 3 (46)
L. KEÈA
BALTIC FORESTRY
DETERMINATION OF THE OPTIMAL FINANCIAL ROTATION PERIOD IN POPLAR PLANTATIONS
On the basis of these elements, it can be said that
the estimation based on the NPVs criterion represents the
required optimum length of the production cycle ranging
from 16 to 19 years (Table 10).
According to the available data from the field, 19
compartments of different ages (1-7, 25, 27, 29, 30, 32, 38
and 43) were available on all soil types together, and they
were evaluated in the size of NPV and NVPs. If we analyze
the results of NVPs for the researched soil types (Table
11) and evaluation methods, it can be concluded that the
average value for all types of soil is 16 years. This sug-
gests that the estimated optimal length of the production
cycle is not dependent on the method of estimation. The
culminating point of NPVs is regularly the same, and does
not depend on whether the whole harvested volume is
treated as stacked wood (minimalistic variant) or used as
assortment structure obtained by model tailoring
(maximalistic variant). In other words, according to these
findings, and used methods of evaluation of the revenues
from timber, the time of NPVs (optimal length of the pro-
duction cycle) culmination is not sensitive to the assort-
ment structure between the ages of 10 and 20, although it
was found exactly at this segment of age (Figure 11).
Table 10. Optimal lenght of production cycle and
the highest value of NPV and NPVs
Variant of
estimation
Tim e of
culmination Max imum val u e Ve rifi cation
of criteria
NPV NPVs NPVmax NPV
year ·ha1
M0 32 16 1.692,62 420,14 13.444,48
M1 31 18 47,92 106,10 3.289,10
M2 30 19 474,03 108,18 3.245,40
Soil type
Variant of estim ation
M2 M0 M1
NPVs R
2 NPVs R
2 NPVs R
2
* á / â-â gley 17 0,87 / / 17 0,80
*RC 15 0, 90 15 0,92 15 0,90
12 0, 93 / / 12 0,94
ASG 19 0, 87 16 0,89 18 0,86
Average 16 / 16 / 16 /
sis can be used for project design, the selection of ap-
propriate size of the project, optimization of the timing of
activities and determination of the strategy of forest man-
agement. However, in addition to financial parameters,
decision-making on plantation establishment must take
other parameters into account, such as the interests of
local communities, government policy and environmen-
tal protection (Neumayer 2011, Perez 2004). Forests are
among the most valuable natural resources that human-
ity possesses, but it is difficult to make economic quan-
tification of their values. There are benefits of forests,
especially plantations, which cannot be quantified finan-
cially, such as their aesthetic, habitat, protective and anti-
erosion functions.
And finally, if a forest ecosystem has to fulfil all the
requirements it is facing (especially environmental pro-
tection, reduction of CO2 in the atmosphere (Holopainen
2008) and mitigation of the greenhouse effect), it is nec-
essary to establish the sustainability of their manage-
ment. According to some authors, for sustainable man-
agement it is necessary to size the plantations be at least
several hundred hectares (Rose et al. 1981, Medareviã
2006, Allen et al. 2008).
The optimal length of the production cycle in poplar
plantations may be treated as short, compared to the pro-
duction cycle of other economically important species
such as beech, spruce, oak and others. The duration of a
short rotation can be divided into three categories (Pope
Table 12. Optimal lenght of production cycle and the high-
est value of NPV and NPVs
Tab le 11 . The estimated optimal length of
the production cycle to NPVs and coeffi-
cients of the regression of model
a / b-b
On the basis of these elements, it can be stated that
the estimation based on the NPVs criterion represents the
required optimum length of the production cycle, which
is 16 years (Table 12).
Discussion
Financial analysis is an objective means by which
cost-intensive plantations can be compared to cultivat-
ing crops (e.g. agriculture) (Mitchell et al. 1999, Current
et al. 1995, Sharma 1996, Sabadi 1986, 1997). This analy-
y = -0, 2328x3 + 13,154x2 - 111,05x - 2161,4
R2 = 0,9408
y = 0,1745x3 - 14,025x2 + 325,41x - 1890, 8
R2 = 0,908
-3000
-2500
-2000
-1500
-1000
-500
0
500
010203040
Figure 11. NPV and NPVs in estimation variant Mo
Variant of
estimation
Tim e of
culmination
Maximu m
value
Verification
of c rite ria
Variant of
estimation
Tim e of
culmination
NPV NPVs
M0
32 16 132,52 445,26 14.693,58
M1 / / / / /
M2 / / / / /
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2017, Vol. 23, No. 3 (46)
L. KEÈA
BALTIC FORESTRY
DETERMINATION OF THE OPTIMAL FINANCIAL ROTATION PERIOD IN POPLAR PLANTATIONS
and Dawson, 2005): (I) 5-10 years - of intense culture for
obtaining biomass; (II) 10-20 years - for receiving pulp-
wood (for paper, wood chips for the production of pan-
els, firewood, pallets, certain chemicals such as ethylene
glycol, and alcohols); (III) 20-40 years for obtaining
technical wood (for construction, peeled veneer, produc-
tion of furniture). The largest poplar plantation areas are
intended for the production of veneer, peeling and cutting
logs, all of which (about 350,000 m3 round wood year-1) is
processed in Serbia and used in the production of pack-
aging, veneer, pallets, various types of board, furniture,
and other articles (Keèa et al. 2012). Short rotations (5-10
years) and the long ones (15 years) are different, both in
terms of cost-efficiency, and energy efficiency. Short ro-
tation plantations generate income earlier and more of-
ten. Due to shorter rotations, the risk of loss has not yet
been so great, and the occurrence of damages was not so
often. They allow the use of all technological advances
and frequent introduction of newly selected hybrids in
plantations (Rose et al. 1981). There are several factors
that significantly affect the length of production cycle,
but the most important are: the choice of the planting
site, planting density, the costs of establishing planta-
tions and the wood market conditions (Birler 1984).
The values obtained for the optimal length of the
production cycle ranged in the interval from 16 to 19 years.
The longest rotations in poplar plantations were obtained
for alluvial semigley. This is the most suitable soil of all
studied soils for the cultivation of poplar (Keèa and Keèa
2012), in addition to fluvisol and therefore the return that
is achieved can bear financial burden with an interest
rate of 6% (Keèa et al. 2011). A shorter length of rotation
was obtained on the black soil type. Similar results were
obtained by Kohn J.P. (1994), except that in hybrid pop-
lars with a 6 × 6 m planting space and different soil types
this interval ranges from 11 to 17 years (Chapman and
Meyer, 1947, Tahvonen and Seppo 1999). Researches
conducted in Turkey estimated the length of financial
rotation to 11 years (Engindeniz 2003). In the United
States, there is legislation (Forest Practice Act of 2008)
which exactly prescribes the production cycle length in
12-20 years old poplar plantations, depending on their
purpose. In Canada, van Kooten (1999) stated that the
optimal production cycle length for poplar ranged from 9
to 12 years.
It should be emphasized that the length of the eco-
nomic and financial rotation, generally do not overlap
(Anderson and Luckert 2006). The reason for this situa-
tion can be explained by the fact that the financial rota-
tion usually varies depending on the price of poplar wood
and interest rates (rate of interest), while the economic
changes if there is a change in the productivity of land
and habitat productivity (Kohn 1997).
Conclusions
The length of the production cycle for poplar in the
project area ranges from 10-20 years. The values obtained
for the length of financial rotation are in the range be-
tween 12 and19 years. The longest rotations were ob-
tained for alluvial semigley and they ranged between 16
and 19 years, depending on the applied methods. The
estimation based on the NPVs criterion represents the
required optimum length of the production cycle, which
is about 16 years for poplar plantations in Serbia. How-
ever, it has been noted that the better soil for growing
poplar (e.g. alluvial semigley) suffers a longer produc-
tion cycle (19 years) in the case of NPVs. According to
the optimal length of the production cycle for Euro-
American poplars, it is recommended to use the culmina-
tion of the average net present value. The statistical
analysis shows that the obtained results for the two re-
gression curves are characterized by high values of the
coefficient of determination and the parameters are the
most significant at the 0.05 level of significance, while
the parameters in NPVs in all variants are statistically sig-
nificant, so that the observations and reasoning based
on these regression models can be accepted as reliable.
The level of statistical significance is high (R2³0,91),
and the correlation coefficient is precisely calculated
(F=42.75).
In the future, private forest owners can be advised
to invest in such a production of poplar wood. On the
other hand, there is a state interest in poplar plantations.
Plantations are very efficient in CO2 consumption, as
shelterbelts, as well as in flood control, etc. Therefore, in
the future the state can stimulate forest owners to invest
in poplar production on river banks and on more quality
soil types, which tends to be more profitable.
Acknowledgement
Gratitude for the implementation of this research
authors suggest the Ministry of Education and Science
of the Republic of Serbia, which financially supported
this research within the project Sustainable manage-
ment of total resources of forests in the Republic of Ser-
bia EVNo. 37008, and Forest plantations in order
to increase afforestation in Serbia EVNo. 31041 COST
Action FP1403 NON-NATIVE TREE SPECIES FOR EU-
ROPEAN FORESTS: EXPERIENCES, RISKS AND OP-
PORTUNITIES (NNEXT)".
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2017, Vol. 23, No. 3 (46)
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DETERMINATION OF THE OPTIMAL FINANCIAL ROTATION PERIOD IN POPLAR PLANTATIONS
