EVALUATION OF THE CONVERSION OPTION OF BIODIESEL VERSUS SOYA OIL IN A SOYA PROCESSING PLANT

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EVALUATION OF THE CONVERSION OPTION OF BIODIESEL
VERSUS SOYA OIL IN A SOYA PROCESSING
PLANT Murilo César de Azevedo Rabelo
Berni muriloberni_at_oi.com.br     Dr. José Antônio
de Sousa Neto jose.antonio.sousa_at_terra.com.br    
Dr Haroldo Guimarães Brasil strategor_at_uai.com.br  

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INTRODUCTION
From the financial perspective of organizations,
the principal objective of business
administration is the maximization of the wealth
of the owners through the increase of the
corporations value, and, in trying to reach this
objective, the evaluation of new investment
projects becomes critical. In summary the
present study evaluates a project for
agro-industrial investment, utilizing the
approach of the Net Present Value and the Real
Options Model. The first approach requires a
projected cash flow and appropriate discount
rate, while the second requires, in addition, the
history of the prices of the products involved in
the undertaking and a simulator of projected cash
flow.
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REAL OPTIONS
.
The area most developed for the application of
the real option is that referring to investment
decisions on the part of companies. However, the
analysis of Real Options has been applied to
different objects, such as investments in
property and development of decisions. The common
element for the use of options pricing is the
following the future is uncertain, and, in a
context of uncertainty, to have the flexibility
to decide what to do after some of these
uncertainties have been better understood is of
real importance.
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REAL OPTIONS

• In terms of real options analysis, we start with
  the calculation of the NPV, aggregating
  managerial flexibility to it. Dixit Pindick
  (1994) define thus the result on the calculations
  of the Expanded Net Present Value (ENPV), where
  the values of the options that there are in the
  project are inserted
•  
• ENPV NPV VO (1)
• where
• NPV is the Net Present Value without
  flexibility and
• VO is the value of the options
• .
• The use of real options started in the analysis
  of projects that would have been rejected by the
  traditional analysis of the NPV, but that
  possessed important embedded options which were
  not captured, or perceived, in the traditional
  model.

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REAL OPTIONS

• Volatility is also one of the parameters
  necessary for the Real Options Model, being, for
  many authors, one of those that most impact on
  the calculation of the price of an option.
• Amram Kulatilaka (1999) , affirming that the
  registration of the oscillations of share prices,
  or of the value of projects, can be used to
  estimate the volatility. Defining
• n1, as the number of observations
• Si, as the price of the share in the nth interval
  (i1, 2, ...n)
• t, as the time interval in years we have
• 
  (2)
• An estimate of the standard deviation of the
  values of ui is given by following formula
• 
  (3)
• in which u is the average of ui.

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REAL OPTIONS

• The quadrinomial approach proposed by Copeland
  Antikarov (2001) determines that the difference
  between the NPV with flexibility and the NPV
  without flexibility corresponds to the value of
  the flexibility in the project. Table 1
  following, illustrates the mathematical operation
  which makes possible the calculation of this
  value, that in this work corresponds to the
  conversion option in the agro-industrial project
  studied.
•  
• TABLE 1
• Value of the flexibility
• Present Value with flexibility
• (-) Present Value without flexibility
• () Value of flexibility
• Source COPELAND ANTIKAROV (2001, p.296).
•  

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PARAMETERS FOR ENTERING AND CALCULATIONS OF THE
REAL OPTIONS MODEL

• Net Present Value without flexibility
• Cash Flows
• For the purposes of analysis, the useful life of
  the projects is 10 years. Soya Oil Project,
  Biodiesel Project and Flexible Project were
  studied based on a time horizon of one decade,
  without considering residual values or
  perpetuities in the cash flows.
• Table 1 shows the real cash flow of the Soya Oil
  Project. The income generated arises from the
  sale of oil and bran, obtained from the
  processing of the soya bean.

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PARAMETERS FOR ENTERING AND CALCULATIONS OF THE
REAL OPTIONS MODEL

• Table 1
• Cash Flow - Soya Oil Project
• DISCRIMINATION/YEAR
  In
  Reais (R)

Source Company ECO (2006)
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PARAMETERS FOR ENTERING AND CALCULATIONS OF THE
REAL OPTIONS MODEL

• Table 2, the real cash flow of the Biodiesel
  Project is shown. The income generated arises
  from the sale of biodiesel, glycerine and soya
  middlings. The same structure of the cash flow
  presented in Table 1 was used, but the
  particularities of the Biodiesel Project, in
  terms of income, costs and investments were
  incorporated.
• The costs of the Biodiesel Project are with
  reference to the costs verified in the Soya Oil
  Project increased, basically, by the additional
  costs for transformation of the oil in biodiesel
  and for its sale. The tax on biodiesel is
  differentiated in relation to soya oil, which is
  also reflected in the projected cash flows,
  presented in Table 2.

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PARAMETERS FOR ENTERING AND CALCULATIONS OF THE
REAL OPTIONS MODEL
TABLE 2

Cash Flow - Biodiesel Project
In Reais
(R)
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PARAMETERS FOR ENTERING AND CALCULATIONS OF THE
REAL OPTIONS MODEL
Discount rate and risk-free rate The cash flows
presented and analyzed in this study are measured
in real terms, as their purchasing power was
given in current terms (year 0, or year 2007).
This being the case the discount rate used in the
decapitalization of the cash flows is real, and
was obtained from the nominal risk-free rate of
12 p.a., discounted at an annual inflation of
4.   Risk-free rate
risk free interest factor
Inflation factor To this rate was added a
risk premium of 5 p.a., resulting in the cash
flows studied being discounted at a real rate of
12.69 p.a. Various works in Brazil consider 6
p.a. a risk-free rate consistent with the
national and global panorama, such as Gonçalves
(2005), Brasil (2002), Marreco (2001) and Dias
(1996). In this sense, the value used here, of
7.69 p.a., is near the values utilized in the
mentioned authors studies.
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PARAMETERS FOR ENTERING AND CALCULATIONS OF THE
REAL OPTIONS MODEL

• Net Present Value without flexibility
• The NPV of the Soya Oil Project is
  R18,169,682.71 and of the Biodiesel Project R
  37,030,267.30. In discounting the net cash on
  hand projected for the base date 2007, at a rate
  of 12.69 p.a., we obtain the values mentioned.
  By the criterion of the NPV, the Soya Oil Project
  should be accepted and the Biodiesel Project
  should not.
• Net Present Value with flexibility Binomial
  approach
• The initial prices considered in this study, for
  the purposes of projection, are R 1,378.25 per
  ton of soya oil and R1.60 per litre of
  biodiesel. The price of oil adopted initially
  corresponds to the monthly average of prices of
  this commodity in the twelve months from February
  2006 to January 2007, in the city of São Paulo.
  The price chosen for biodiesel, corresponds to
  the average value of R1.79 (average price of
  biodiesel in the same period in São Paulo) and
  R1.41 (average price of mineral diesel in the
  same period in São Paulo).
• Starting from the volatility of soya oil prices,
  calculated at 27.39 p.a., the value of the
  rising movements per step, u, were calculated at
  1.32, and the falling movements per step, d, at
  0.76. Starting from an initial price R1,378.25
  and parameters u and d, a binomial projection of
  soya oil prices was constructed.

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PARAMETERS FOR ENTERING AND CALCULATIONS OF THE
REAL OPTIONS MODEL

• Net Present Value with flexibility Binomial
  approach
• YEAR

FIGURE 1 - Binomial projection of soya oil
prices.Source Prepared by the author  
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PARAMETERS FOR ENTERING AND CALCULATIONS OF THE
REAL OPTIONS MODEL

• Net Present Value with flexibility Binomial
  approach
• Starting from the volatility of biodiesel prices,
  calculated at 12.94 p.a., the value of the
  rising movements per step, u, were calculated at
  1.14, and falling movements per step, d, at 0.88.
  Starting from the starting price of R1,600,00
  (thousand litres) and of the parameters u and d,
  the prices of biodiesel from 2007 to 2017 were
  projected.
• YEAR

FIGURE 2 - Binomial projection of biodiesel
prices. Source Prepared by the author
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PARAMETERS FOR ENTERING AND CALCULATIONS OF THE
REAL OPTIONS MODEL

• Net Present Value with flexibility Binomial
  approach
• Considering the binomial projection of soya oil
  prices, the free cash flows (net cash on hand) in
  each year for each price possibility were
  projected. In this way, the impacts of the soya
  oil price oscillations are incorporated into the
  projected results. Figure 3 shows this projection
  of free cash flows.

FIGURE 3 - Binomial projection of net cash on
hand of the Soya Oil Project. Source Prepared by
the author
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PARAMETERS FOR ENTERING AND CALCULATIONS OF THE
REAL OPTIONS MODEL

• Net Present Value with flexibility Binomial
  approach
• Considering the binomial projection of biodiesel
  prices, the net cash on hand in each year for
  each price possibility was projected. Configured
  in this way, as Figure 4 shows, the projections
  incorporate possible oscillations of the biofuel
  price.

FIGURE 4 - Binomial projection of net cash on
hand of the Biodiesel Project. Source Prepared
by the author
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PARAMETERS FOR ENTERING AND CALCULATIONS OF THE
REAL OPTIONS MODEL
Net Present Value with flexibility Binomial
approach Value of the Flexibility In
accordance with the values obtained for the Soya
Oil Project, starting from the analysis of the
static NPV and of the NPV with flexibility, we
arrive at a value of R 145,613,005.63 for the
flexibility in the project. This value is
obtained in accordance with the calculation
exhibited in Table 2. Table 2 Value of the
flexibility Soya Oil Project Present Value
with Flexibility (-) Present Value without
Flexibility () Value of the Flexibility
Source Prepared by the author
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PARAMETERS FOR ENTERING AND CALCULATIONS OF THE
REAL OPTIONS MODEL
Net Present Value with flexibility Binomial
approach Value of the Flexibility For the
Biodiesel Project, the value of the flexibility
obtained was R 158,752,338.67, in accordance
with that shown in Table 3. In a separate
evaluation for the two projects, it was seen that
the Soya Oil Project possesses static Net Present
Value, and with flexibility, higher than the
Biodiesel Project. On the other hand, the value
of the flexibility in the projects is higher in
the Biodiesel Project, seeing that the same is
sufficient to make the value of the project
positive (as it starts from R -37,030,267.30)
and, consequently, feasible.   Table 3 Value of
the flexibility Soya Oil Project Present Value
with Flexibility (-) Present Value without
Flexibility () Value of the Flexibility
Source Prepared by the author
We have, then, flexibilities of the order of R
150 million in the two projects under analysis.
In both cases, the evaluation by the NPV with
flexibility increases the value of the projects,
considering them in isolation.
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PARAMETERS FOR ENTERING AND CALCULATIONS OF THE
REAL OPTIONS MODEL
Net Present Value with flexibility
Quadrinomial approach   Quadrinomial projection
of free cash flows (net cash on
hand) Considering that the combination of the
two binomial cash flow projections results in a
quadrinomial projection, we have in each node the
rising and falling possibilities for the
production of soya oil and biodiesel. In
considering a given node, and its four
descendants, we have the possibilities of (1)
high in the Soya Oil Project combined with high
in the Biodiesel Project (2) high in the Soya
Oil Project combined with low in the Biodiesel
Project (3) low in the Soya Oil Project combined
with high in the Biodiesel Project and (4) low
in the Soya Oil Project combined with low in the
Biodiesel Project. Table 4 Parameters of
the quadrinomial approach Expected growth
Soya Oil Expected growth Biodiesel Correlati
on Soya Oil x Biodiesel  
Source Prepared by the author
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PARAMETERS FOR ENTERING AND CALCULATIONS OF THE
REAL OPTIONS MODEL
Net Present Value with flexibility
Quadrinomial approach   Quadrinomial projection
of free cash flows (net cash on hand) In
possession of the variables of the binomial model
and the parameters exhibited in Table 4, we move
to the calculation of the probabilities of the
quadrinomial approach, exhibited in Table 5.
pu1u2 refers to the probability of rise in the
price of soya oil combined with rise in the price
of biodiesel pu1d2, to the probability of rise
in the price of soya oil combined with fall in
the price of biodiesel pd1u2, to the probability
of fall in the price of soya oil combined with
rise in the price of biodiesel and, finally,
pd1d2 refers to the probability of fall in the
price of soya oil combined with fall in the price
of biodiesel. Table 5 Probabilities of the
quadrinomial approach Flexible Project  
Source Prepared by the author
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PARAMETERS FOR ENTERING AND CALCULATIONS OF THE
REAL OPTIONS MODEL
Net Present Value with flexibility
Quadrinomial approach   Quadrinomial projection
of free cash flows (net cash on hand) Starting
from the cash flow projections of the Flexible
Project, of the probabilities presented above,
and of the risk free rate, stipulated at 7.69
p.a., the value of R 348,068,287.99 was
obtained. This is the expanded NPV of the
flexible project, in which the value of the
conversion option between soya oil and biodiesel
is considered in the evaluation. Figure 5
partially presents the tree used for the
calculation of the NPV with flexibility, spanning
the period from year 0 to year 4 (2007 to 2011).
   
Figure 5 - Net Present Value with flexibility of
the Flexible Project. Source Prepared by the
author
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PARAMETERS FOR ENTERING AND CALCULATIONS OF THE
REAL OPTIONS MODEL
Net Present Value with flexibility
Quadrinomial approach   Value of the Flexibility
Conversion option The calculation of the value
of the flexibility in the Flexible Project
follows the same methodology used in the
identification of this value in the Soya Oil and
Biodiesel Projects. Thus, the difference between
the NPV with flexibility and the static NPV
corresponds to the value of the flexibility
represented, in this point, by the conversion
option between the two ways of operation. In this
calculation, the NPV without the flexibility
considered is the static NPV of the Biodiesel
Project, as it represents the value of the
project for biofuel production when evaluated
without flexibility. In this sense, if the NPV of
the static flows referring to the Biodiesel
Project is R-37,030,267.30, and the NPV of the
quadrinomial flows of the project (considering
managerial flexibility) is R 348,068,287.99, it
can be affirmed that the value of the
flexibility, or of the conversion option, is R
385,098,555.29. Table 6 Value of the
flexibility Flexible Project            
                        Present value with
flexibility                                    
(-) Present value without flexibility            
                        () Value of
flexibility  
source prepared by the author
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PARAMETERS FOR ENTERING AND CALCULATIONS OF THE
REAL OPTIONS MODEL

•  
• FINAL CONSIDERATIONS
• The application of the binomial approach to the
  Soya Oil Project raised its value by R
  18,169,682.71 to R 163,782,688.34, pointing to a
  value of flexibility of the order of R
  145,613,005.63. On the other hand, the
  application of this approach to the Biodiesel
  Project raised its value by R -37.030.267,30 to
  R 121,722,071.37, implying a flexibility valued
  at R 158,752,338.67.
• In a preliminary analysis, based on the
  evaluation of the project in terms of the
  establishment of the soya oil production plant,
  or the biodiesel plant, it seems that to
  establish the oil plant and discard the
  additional investments for the expansion and
  adaptation of the plant (for the production of
  biofuel) is the more interesting option. However,
  the separate analysis of the two alternatives
  shows this to be inappropriate.
•  

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PARAMETERS FOR ENTERING AND CALCULATIONS OF THE
REAL OPTIONS MODEL

•  
• FINAL CONSIDERATIONS
• At each moment of time (or projection node), the
  prices of soya oil and biodiesel can present
  rises or falls in relation to the previous
  period, so that these two movements combined
  provide four possibilities. In this study, these
  four possibilities are (1) rise of the price of
  soya oil combined with rise of the price of
  biodiesel (2) rise of the price of the soya oil
  combined with fall of the price of biodiesel (3)
  fall of the price of soya oil combined with rise
  of the price of biodiesel and, finally, (4) fall
  of the price of soya oil combined with fall of
  the price of biodiesel. In each of these four
  situations, a decision should be taken produce
  soya oil or biodiesel.
• The agro-industrial field is characterized by
  working with commodities that possess high price
  volatility and important managerial and
  operational flexibilities. Accordingly, the
  application of the Real Options Theory in this
  field is indicated, as it possesses
  presuppositions and parameters strongly linked to
  the characteristics of this market. In the
  present study, we tried to show the relevance of
  this theory in the evaluation of investment
  projects.
• In evaluating projects in the light of the Real
  Options Theory, we try to obtain a new vision of
  Investment Analysis, focusing on the principal
  objective of business administration from the
  financial point of view, which is, to maximize
  the shareholders' wealth through the increase of
  the value of the company.
•