Economic appraisal of production flexibility in different regions of the Brazilian sugar and ethanol industry

Purpose – The main goal of this study is to demonstrate the value of flexibility within sugar and ethanol production. We use real data for the Southeast and Northeast regions of Brazil, which are subject to different taxes rates. Design/methodology/approach – The framework of this study is based on Real Options valuation. We valued the option to switch between sugar and ethanol production. The dynamics of prices was based on the recombinant trees of Nelson and Ramaswamy (1990) and on the bivariate trees of Hahn e Dyer (2011). Empirical data is from the Center of Advanced and Applied Economic Studies (CEPEA), ESALQ-USP, from May/2003 through July/2014. Prices were deflated using the Brazilian Price Index (IGP-DI), available at the Ipeadata site based on July/2014. Findings – The results show that, in both regions, flexible systems have greater value than those that produce only one product. Southeast plants exhibit greater value added if compared with Northeast plants, not only because of lower taxes, but also due to higher productivity. Originality/value – This paper quantifies value added by the flexible system in the production of sugar and ethanol in two Brazilian regions subject to different taxes. Moreover, it demonstrates that regulators can use policies and incentives to establish flexible plants. In this way, both producers and fiscal authorities will achieve greater gains.


Introduction
The development of the Brazilian ethanol industry is the best example in the world of the production and use of renewable energy on a large scale.In order to achieve this growth, Brazil carried out extensive technological advancement (technology generation, importation, adaptation and transfer) in agricultural and industrial production, in logistics and in end-uses over the last thirty years.It was also crucial to have specific legislation, as well as initial subsidies and permanent negotiation between the main stakeholders involved: ethanol producers, vehicle manufacturers, government regulatory sectors and the oil industry, in an intense and continuous learning process (Macedo, 2007).These facts led to the development of the ethanol industry, which, along with the technology of flexible production plants, give businessmen the option of producing two commodities: sugar and/or ethanol, depending on which is most profitable at a given time.
On the other hand, taxation plays an important role in ethanol and sugar prices across different Brazilian regions.We refer specifically to the Brazilian tax on the circulation of goods on interstate and county transportation and communications services [Imposto sobre Operações relativas à Circulação de Mercadorias e sobre Prestações de Serviços de Transporte Interestadual e Intermunicipal e de Comunicação, ICMS], which is a state tax, that is, only state governments and Brazil's federal district have the power to institute it.For example, according to the Sugarcane Industry Union [União da Indústria de Cana-de-Açúcar, UNICA] -the largest local organization representing the sugar and ethanol industry in Brazil -, in 2013 the ICMS in São Paulo was 12%, while in Pará it was 30%.
Since producers have no control over commodity price fluctuations in the international market -a reference for prices in the local market -, there is a great deal of uncertainty regarding their future values; this uncertainty lends value to the flexibility that a plant can have to modify its production process and thus meet the demands of the commodity that is most profitable over a given period.
In real assets investment analysis under uncertainty, it is appropriate to use the Real Options (RO) theory, which takes into account the different managerial flexibilities that decisionmakers can use to change the course of a project while uncertainties are revealed.Thus, one can measure the value resulting from the flexibility of postponing, contracting, expanding, temporarily halting or abandoning a project, or of changing inputs and/or products.Flexible plants harbor within their facilities a system that allows for the production of one product or another.In this way, according to product prices, producers can choose to produce one product or another.Investing in a flexible system means being able to produce the most lucrative product in the future.The real options methodology quantifies the gains resulting from this flexibility.D i s c r e t e m o d e l i n g t h r o u g h t h e recombinant binomial tree developed by Cox, Ross and Rubinstein (1979) to evaluate financial options was extremely successful by discreetly approaching the model of Black and Scholes (1973); the latter is widely used to assess options whose underlying assets follow a Geometric Brownian Motion (GBM).Boyle (1988), on the other hand, introduced the bivariate binomial tree concept, which was followed by Nelson and Ramaswamy (1990), who presented a binomial sequence method in a comprehensive model that can be used in stochastic processes which follow either a GBM or a Mean Reversion Process (MRP).Hahn and Dyer (2011) modeled within discrete-time two-factor processes using bivariate binomial trees, by means of a two-dimensional tree format for the same problems analyzed by Schwartz and Smith (2000).
In this paper, we will calculate the value of switching between producing sugar (with ethanol as a byproduct) and ethanol, thus assessing to what extent this flexibility adds value to a project.We will evaluate two plants that only produce sugar David Eduardo Lopez Pantoja / Carlos Patricio Mercado Samanez / Javier Gutierrez Castro / Fernando Antonio Lucena Aiube or ethanol; next, we will compare their valuations to that of a flex plant that is capable of switching between producing two different commodities (sugar and ethanol).Analysis includes the Southeast and Northeast regions of Brazil, assuming that the main source of uncertainty in cash flows is the price of commodities.Given this premise, and after carrying out comparative analysis of the best fit to the behavior of historical price series between GBM and MRP, we chose to compute the values of the options using the MRP, following the methodologies of Nelson and Ramaswamy (1990) and Hahn and Dyer (2011).
This study was divided into seven sections.In section 1, we present the introduction and context of the research, defining its goal; in section 2, we address the alcohol and sugarcane industry in Brazil; in section 3, we define the real options of change and introduce the stochastic processes theory; in section 4, we develop the mean reversion process' binomial, recombinant binomial and bivariate modeling processes; in section 5, we calculate the value of the option of switching between ethanol and sugar; and in section 6 we present the conclusions of the research.

Ethanol in brazil
The first uses of ethanol as fuel in Brazil occurred around the end of the 1920s, when the Serra Grande Alagoas factory [Usina Serra Grande Alagoas, USGA], in the municipality of São José da Laje -in the Brazilian state of Alagoas -, produced this fuel for the first time.Meanwhile, Brazil's National Institute of Technology also produced alcohol for automobile propulsion.In 1931, mixing 5% of ethanol into gasoline became compulsory in order to drain the Brazilian sugar industry's surplus production, and this percentage gradually increased.Over the following years, even during World War II, thousands of cars were running on alcohol in the Brazilian states of Pernambuco and Minas Gerais, from sugarcane and cassava, respectively.However, production was weak and failed to compete with gasoline, more commonly used as fuel.Moreover, to the extent that the problems caused by economic recession began to decline, prices of oil and of its derivatives also begun to decrease; this eventually made the production of ethanol impossible at that time (Cavalcante, 2010).
Brazil's National Alcohol Program (Programa Nacional do Álcool, Proálcool), established on November 14, 1975 by federal government decree n. 76.593, aimed to focus efforts on the production of anhydrous fuel ethanol (AFE) from sugarcane, to be used in the mixture with gasoline in Otto cycle engines, at a 20% ratio.According to the program, the production of ethanol derived from sugarcane, cassava or any other input should be encouraged by expanding the supply of raw materials, with special emphasis on increasing agricultural production, on modernizing and expanding existing distilleries and on installing new production units, whether attached to plants or autonomous, and storage units (Nascimento, 2012).Lima et al. (2013) mention that Proálcool is a milestone in the evolution of ethanol within the Brazilian market.The program can be divided into three stages: the first spans 1975-1979, following an increase in oil prices; the second, 1980-1990, the Proálcool apex;, the Proálcool apex;the third, 1991-2003, including program stagnation in the 1990s and an unsuccessful attempt to reactivate Proálcool in 1996, followed by sugar and ethanol industry deregulation.
Flex fuel technology has given new impetus to the domestic consumption of alcohol.Car that can run both on gasoline and on alcohol -or on a mixture of the two fuels = were introduced in Brazil in March 2003 and quickly seduced consumers.Currently, flex-fuel vehicles present higher market shares than those that run only on gasoline.
Economic appraisal of production flexibility in different regions of the Brazilian sugar and ethanol industry

Brazil and sugarcane
Sugarcane is Brazil's third largest agricultural activity in terms of production area and gross produced value; soy and corn are the country's main crops.Sugarcane can be produced across almost all Brazilian regions.The largest producers are the states of São Paulo, Paraná, Triângulo Mineiro -in the state of Minas Gerais -and the Brazilian Northeast's Zona da Mata.
According to the second survey of 2013/2014 crops carried out by the Brazilian Ministr y of Agriculture, Livestock and Supply [Ministério da Agricultura, Pecuária e Abastecimento, MAPA] in cooperation with the National Supply Company [Companhia Nacional de Abastecimento, CONAB] in August 2013, the area of sugarcane crops for sugar and cane production was estimated at 8,799,150 hectares, distributed across all producing states according to their characteristics.The state of São Paulo remains the largest producer, with 51.31% (4,515,360 hectares) of planted area, followed by Minas Gerais, with 8.0% (781,920 hectares); Goiás, with 9.3% (818,390 hectares); Paraná, with 7.04% (620,330 hectares); Mato Grosso do Sul, with 7.09% (624,110 hectares); Alagoas, with 5.02% (442,590 hectares); and Pernambuco, with 3.25% (286,030 hectares).In other Brazilian states these areas are smaller, with representations below 3.0%.

Ethanol prices
The Brazilian sugar and ethanol industry faced major institutional changes with the deregulation process at the end of the 1990s.From the creation of Proálcool in 1975 on, the Brazil State was responsible for the planning and marketing of these products, as well as for regulating and mediating conflicts between agents.For a detailed description of the deregulation process, see Moraes (1999).For a review on the subject, see Barros and Moraes (2002), who report the deregulation process covering the period between March 1996 and February 1999.
According to Brazil's law n.9.478/1997, later amended by law n.9.990/2000, a price freedom regime was established across the chain of fuel production and marketing, distribution and retailing.This removed price tables, maximum and minimum values, government involvement in pricing or prior authorization to increase fuel prices.The regulator of activities within the oil and natural gas and biofuels field in Brazil is the National Petroleum Agency [Agência Nacional do Petróleo, ANP], which monitors prices through price surveys and fuel marketing margins (Nascimento, 2012).
We should highlight that, due to the field's deregulation, producers, anticipating problems that could arise, created in 1999 the São Paulo Council of Sugarcane, Sugar and Ethanol Producers [Conselho dos Produtores de Cana-de-Açúcar, de Açúcar e Etanol do Estado de São Paulo, COSENCANA-SP], responsible for establishing the quality of sugarcane and its valuation.Thus, a mechanism for pricing the raw material used for producing sugar and ethanol was established; its use by agents was optional.Furthermore, the Council established a model contract to reduce supply procurement costs, making the relationship between sugarcane chain agents easier.Other states began to adapt it according to their regional characteristics (COSENCANA-SP http://www.consecana.com.br/).2014) emphasize the importance of the ICMS, which is different for each state and for each type of fuel.These different taxes make ethanol prices vary across states and regions, rendering it more or less attractive to consumers, although its use is more beneficial to the environment than gasoline.

Ethanol taxation in Brazil
With the adoption of Brazil's provisional measure n. 613 on May 7, 2013 and its subsequent conversion into law n.12.859 on 10 September 2013, the PIS/COFINS presumed credit was established for ethanol producers; it effectively zeroed the R$ 0.12 per liter rate for ethanol.Thus, there are no longer any federal taxes on ethanol.However, state taxes still exist; the most relevant one is ICMS.
Table 1 presents ICMS rates for different regions of Brazil.In it, one can distinguish that the Brazilian state with the smallest ICMS is São Paulo, at 12% over ethanol, and the state with the greatest ICMS is Pará, at 30%.In the authorized capacity of ethanol production, the states of São Paulo, Goiás and Minas Gerais represent approximately 70% of both anhydrous and hydrous ethanol.The state of São Paulo has the largest authorized capacity, representing around 50% of the total capacity, both of anhydrous ethanol and hydrous ethanol.
Economic appraisal of production flexibility in different regions of the Brazilian sugar and ethanol industry

Literature review
The literature of real options applied to the sugarcane industry in Brazil includes articles that highlight the use of flex vehicles, such as Samanez et al. ( 2014), and articles that deal with the production of alternative sources of energy, such as Bastian-Pinto et al. (2009).
On the other hand, empirical research referring to this field reveals analyses based on econometric models established in literature.In Melo and Sampaio ( 2016), the authors use VAR in the analysis of how ethanol and sugar offers respond to shocks on ethanol, sugar and gasoline prices.The results of the impulse-response functions indicate that producers respond more strongly to a change in the price of sugar than in ethanol.Boff (2011) studies the relationship between ethanol/sugar and ethanol/gasoline prices in the retail market in the cities of Rio de Janeiro and São Paulo over the 2001-2010 period, through co-integration analysis (VAR-VECM).The author concludes that the model to explain the long-term behavior of the ethanol market in São Paulo is adequate.However, for the Rio de Janeiro market, the model is only partly suitable, as the study reports.
Balcombe and Rapsomanikis ( 2008) analyze the influence of the behavior of ethanol, sugar and oil prices on the Brazilian market.They use a bivariate error correction model that is best suited to the co-integration behavior of price series, which captures potential nonlinearities of errors when compared to long-run equilibrium.Models are estimated according to the Markov chain Monte Carlo (MCMC).They conclude that oil prices define sugar prices, and that nonlinearities were found in the adjustment of sugar and ethanol prices to oil prices.Moreover, the adjustment between ethanol and sugar is predominantly linear.
This study uses the real options methodology, analyzing the gains of plants that produce sugar and ethanol compared to those who do not have this flexibility.The real options methodology gained momentum in the 1990s, although its first article belongs to Tourinho (1979).It is appropriate for evaluating investments under uncertainty, such as uncertainty in future prices, costs or other variables involved in the cash flow.The classic texts on the subject are Dixit andPindyck (1994) andTrigeorgis (1996).
The contribution of this study refers mainly to the analysis of gains arising from operational flexibility in two major Brazilian producing regions that process different loads and are subject to different taxes.Implications for sector policy regulators refer to the fact that flexibility, because of its greater gains, results in greater tax collection, thus making room for the creation of fiscal incentives, especially in places where rates are higher.

Real options theory and stochastic processes followed by the prices of commodities
The real options theory is a robust approach to investment analysis, in which the problem is dealt with as a case of optimization under uncertainty, seeking to maximize asset value through the optimum use of embedded options, subject to uncertainties and physical, legal and other restrictions.There are various types of real options, but in this article we will model and value the switch option, in which the plant owner can choose between producing sugar or ethanol, depending on the market price behavior of the two commodities.Valuing the option to switch means valuing the flexibility to change between various inputs and/or outputs in a production process in order to achieve the highest profit according to price fluctuations.As mentioned above, the details of the Real Options Theory can be found in Pindyck andDixit (1994) andTrigeorgis (1996).
One often used way of modeling asset prices and, thus, of determining the value of a real option are stochastic processes.A stochastic process describes the behavior of a variable David Eduardo Lopez Pantoja / Carlos Patricio Mercado Samanez / Javier Gutierrez Castro / Fernando Antonio Lucena Aiube whose changes are uncertain over time, i.e., is a random process as a function of time.In the real options approach, to model and simulate the prices of assets in order to value the options embedded in the investment alternatives, three types of stochastic processes are generally used: Geometric Brownian Motion (GBM), Mean Reversion Motion (MRP) and MRP with Poisson jumps.MRP can be understood by considering that, in a competitive market, if the commodity price is far below the long-term average, supply decreases, forcing prices up due to a shortage of the product in the market; the same applies in the opposite direction.Given this assumption, the series of prices of a commodity has a natural tendency to revert to its long-term average, i.e., to the average of market balance, however slow this reversal process may be (the application of MRP in commodities can be seen in Schwartz (1997) and in Schwartz and Smith ( 2000)).As demonstrated by Aiube and Samanez (2014) and Samanez et al. ( 2014), MRP is the process that best describes commodity prices, and it will be used in this study to simulate ethanol and sugar prices.

Mean Reversion Motion
Literature on finance generally adopts the mean reversion motion when modeling commodities.The motions of price increases and decreases, due to product shortage and oversupply, are the arguments on the side of economic intuition to justify the dynamics of reversion.Nevertheless, empirical studies can capture the reversion process.Bessembinder et al. (1995) show that, under equilibrium, the mean reversion property is detected for agribusiness, metals and energy commodities.For agricultural commodities and for oil, the reversion rate is significant and of high magnitude.Pindyck (1999) analyzes the behavior of energy commodities considering long historical series, and concludes that the data adheres to the reversion behavior.In this article, we follow the standards of literature and model the dynamics of ethanol and sugar prices using the mean reversion process.As is usual in articles of this nature, the adherence of historical prices to the reversion process was verified, as detailed in section 3.3.
The Mean Reversion Motion (MRP) is defined by the following stochastic differential equation: Eq. 1 Where: X = stochastic variable; = speed of the stochastic variable's mean reversion; σ= volatility of the stochastic variable; dz= increase or Wiener differential; = long-term average of the stochastic variable; dt = instantaneous time variation.
The conditional distribution of X t is normal, with average and variance given by Equations 2 and 3 (Dixit and Pindyck, 1994): Eq. 2 Eq. 3

Discretization and estimation of MRP parameters
The discretized form of MRP is given by Equation 4.

Eq. 4
Where is the interval of time and N(0,1) is standard normal distribution.
So that MRP may be used to simulate prices, it is necessary to estimate the parameters present in its stochastic equation, that is, its volatility, its long-term average and the speed of its mean reversion.Thus, linear regression on the historic prices of commodities is carried out, according to Equation 5.

Eq. 5
Economic appraisal of production flexibility in different regions of the Brazilian sugar and ethanol industry Where x t is the commodity price and .Parameters a and b are obtained through linear regression.
As demonstrated in Dixit and Pindyck (1994), MRP parameters are calculated according to equations summarized in Table 2.

Determining MRP parameters based on historical series of prices
The Southeast and Northeast are the biggest producers in Brazil.So, since they are representative of the industry, they are the regions to be examined in this article.
Price data was obtained from the Center for Advanced Studies in Economics Using Equation 5, the regression parameters of the historical price series were estimated.Table 3 shows the values that were found.Estimation results show that the b parameter, related to the reversion process, is significant at the 1% level to ethanol, and at 5% for sugar.Thus, empirical data shows the adherence of the analyzed price series to MRP.

Assessment through event trees
Because they are easy to use, versatile and accurate, event trees are one of the most used methodologies for pricing options.Used for discrete-time models, event trees contain uncertainty nodes describing the possible behaviors of stochastic factors.In trees, the use of branches is flexible and can be adapted when changing the initial situation.Cox et al. (1979) were pioneers in the assessment of options using recombinant binomial trees, showing that in this type of tree the value of a European-type option converges to the value given by the formula of Black and Scholes (1973).However, Boyle (1988) was the first one to use the approach of Cox et al. (1979) in a trinomial tree to assess options with a single underlying asset.By using stochastic processes with two factors, the author introduces a new concept, that of bivariate trees.Subsequently, using the same approach, Nelson and Ramaswamy (1990) developed a model for assets that follow both GBM and MRP.
To model the price of the commodity and to calculate the abandonment option of an oil well, Hahn (2005), following the basic structure proposed by Nelson and Ramaswamy (1990), used a model with two factors.Following this same approach, Bastian-Pinto et al. ( 2009) worked with the price of two commodities, sugar and ethanol, using as a stochastic process one MRP to assess an input switch option, thus developing a quadrinomial tree.Hahn and Dyer (2011) worked with stochastic processes with two factors and bivariate binomial trees for discretetime modeling, using a two-dimensional tree format.In Brazil, Samanez and Costa (2014) assessed swing type options in natural gas market contracts, using bivariate binomial trees.Nelson and Ramaswamy (1990) propose a general method to develop recombinant binomial trees.The problem is to find a binomial sequence that converges to the following stochastic differential equation:

Recombinant binomial trees
Eq. 6 Where X(t) is the natural logarithm of asset price at instant t, that is, ; and are the process growth rate (drift) and the standard deviation, respectively, and dz is the standard Wiener increase.
To solve this problem, the authors proposed a simple binomial sequence with n periods of ∆t duration.This sequence is given by: is the motion upwards (up); is the motion downwards (down); is the probability of up; is the probability of down.
With this set of equations, it is possible to determine the values of up e down for each branch, as well as probability p t for each node, and, thus, to generate the recombinant tree (lattice).However, the values for certain probabilities in each node may be negative; as a result, the authors proposed certain censorship, forcing the values to fit into interval 0 ≤ p t ≤ 1.
Substituting α(X,t) and σ(X,t) in Equation 6by factors and it is possible to obtain the stochastic differential equation for MRP (Equation 1).In this case, the binomial sequence will be given by: , the motion upwards (up) Eq. 7 , the motion downwards (down) Eq. 8 Probabilities of censored motion upwards up: Eq. 9 The following is a summary for probabilities: Eq. 10 Probability will vary over time depending on X(t), where X(t)=ln(x t ).This censored probability produces a model that converges weakly to a mean reversion process.
As an illustration, Figure 1 presents the tree for variable X which varies ∆X in the interval of time ∆t.The variations of ∆X are as follows: and .Considering that represents the natural price logarithm, then and .Thus: Eq. 11 Eq. 12 As an illustration, Figure 2 presents the final tree.
Economic appraisal of production flexibility in different regions of the Brazilian sugar and ethanol industry In the assessment of prices, the neutral form of risk to the stochastic process is normally used, so as to be able to discount with the riskfree rate (r).Thus, for MRP, the neutral process to risk is given by the following differential equation Eq. 13 Where the risk prize is (μ is the total return), and term π/η is a normalized risk prize which penalizes the price logarithm.
Thus, the probability of risk-adjusted Martingale is given by: Eq. 14

Bivariate modeling of the Mean Reversion process
In bivariate modeling, one seeks to combine, in one single tree, two uncertain correlated variables that accompany autoregressive processes.Schwartz and Smith (2000) break down into two factors the natural price logarithm by applying an GBM for the long term and an MRP for the short term.Hahn and Dyer (2011) developed a method for the construction of a bivariate binomial tree that is applicable to the two-factor model of Schwartz and Smith (2000).
Following Hahn and Dyer (2011), the combination of the two variables lead to a quadrinomial tree, as presented in Figure 3.  Hahn and Dyer (2011) In the case of the commodities this paper deals with, we presume that the sugar price logarithm (X) and the ethanol price logarithm (Y) follow an MRP.Thus, , and . The relationship between the increases in the two processes is given by , where ρ is the correlation coefficient.
Hahn and Dyer (2011) use the same basic method used by Boyle (1988) to determine the joint probabilities of the processes.These probabilities are given by: Eq. 15 Where the increases are and . Naturally, the sum of all the joint probabilities has to be equal to 1, thus and .The drift of the processes is given by and .The approach of Hahn and Dyer (2011) combine two recombinant trees, and is based on Nelson and Ramaswamy (1990), in which the probabilities of the prices in each node of the tree are censored, when the reversion leads to values greater than one and smaller than zero.Unfortunately, since there are two factors and, thus, four nodes, censorship cannot be carried David Eduardo Lopez Pantoja / Carlos Patricio Mercado Samanez / Javier Gutierrez Castro / Fernando Antonio Lucena Aiube out directly, as in the case of one single factor.Given this impossibility, Hahn and Dyer (2011) propose applying Bayesian rules to decompose the joint probabilities in the marginal and conditional product of the probabilities: .Thus, the marginal probabilities for X would be: Eq. 16 As Equações 15 são divididas pelas probabilidades marginais de X (Equações 16) para se obter as probabilidades condicionais (Equações 17).No presente estudo, as probabilidades apresentadas em Hahn & Dyer (2011) foram corrigidas, pois foram encontrados erros de sinais.A formulação correta, e que foi utilizada neste estudo, é a seguinte: Eq. 17 Equations 15 are divided by the marginal probabilities of X (Equations 16) to obtain conditional probabilities (Equations 17).In this study, the probabilities presented in Hahn and Dyer (2011) were corrected, since signs of errors were found.The correct formula, which was used in this study, is the following: The quadrinomial tree with joint probabilities is now divided into two stages of probabilities, conditional and marginal, in the same interval ∆ t , for variables X and Y, respectively, which is illustrated in Figure 4.As mentioned, following Nelson and Ramaswamy (1990), in this approach the probabilities are also censored so as not to reach values that are negative or greater than one.Hahn and Dyer (2011) In this new formula the following should be adhered to: and .For each of the marginal and conditional probabilities, censorship has to be to the necessary extent.
For the Regions studied in this article (Brazil's Northeast and Southeast), there are two differential stochastic equations, one for sugar and one for ethanol: Eq. 18

Eq. 19
David Eduardo Lopez Pantoja / Carlos Patricio Mercado Samanez / Javier Gutierrez Castro / Fernando Antonio Lucena Aiube With the Gross Revenue, one can model the cash flow (CF), which can be represented according to Equation 20.

FC= RB[(1-ICMS)-CVT-CFT]×(1-IR) Eq. 20
To determine the components of cash flow some considerations were carried out, such as: total variable cost (TVC) is 20% of gross revenue (GR), total fixed cost (TFC) is 10% of GR, and income tax (IT) is 19% (Bastian-Pinto et al., 2009).Thus, the cash flows for the two commodities in the two regions can be modeled in two ways: (1) considering that ethanol is produced exclusively, or (2) considering that the sugar/ ethanol mix provided by CONAB (as shown in Table 4) is produced.In the latter case, it is necessary to consider the proportions of sugar and ethanol to multiply by the production, as follows: CF in the Southeast Region (in R$1.000): (1) CF considering total production of ethanol: Eq.21 (2) CF considering sugar/ethanol production mix: Eq. 22 CF in the Northeast Region (in R$1.000): (3) CF considering total production of ethanol: Eq. 23 (4) CF considering sugar/ethanol production mix: Eq. 24 Table 5 presents the ICMS rates for the two commodities in the two regions.

Assessment using recombinant trees
For the construction of recombinant trees, it is necessary to set some parameters.First, it is considered a real (r) risk free interest rate equal to 7.25% p.y..This value was determined from the average yield of Brazilian Treasury Bills [Letras do Tesouro Nacional, LTN] maturing in 2011,2012,2013,2014.The time horizon used is five years, taking samples every six months (T = 5, n =10 e ∆t = 0.5).The risk premium π deflated for the sugar and alcohol sector was calculated using the David Eduardo Lopez Pantoja / Carlos Patricio Mercado Samanez / Javier Gutierrez Castro / Fernando Antonio Lucena Aiube marginal and conditional probabilities, which, when multiplied, result in the joint probabilities.
Table 8 presents, for the two regions studied, the results of the present values (PV) of cash flows for plants that produce ethanol or sugar (sugar/ethanol mix), and the present value (PV) of cash flows for flexible plants.The results shown prove that, in the case of the Northeast, the flex plant has a higher value (higher PV) when compared to a plant that produces sugar (sugar/ethanol mix); the difference is 9.6%.As for the comparative case of a plant whose production is focused exclusively on ethanol, the difference from the flex plant is 58.9%, favorable to the latter.In other words, the use of flex plants in Northeast adds R$ 160 million present value to the business when compared to ethanol production, and approximately R$ 38 when compared to sugar production.
Economic appraisal of production flexibility in different regions of the Brazilian sugar and ethanol industry In the case of the Southeast, the difference in favor of flex is 73.7% and 47.8%, when compared to a plant that produces only ethanol and one that produces sugar (sugar/ethanol mix), respectively.This means that the decision to use the flex plant increases the present value of the business in R$ million when compared to ethanol production, and R$ 522 million, when compared to sugar production.
These gains, both in the Northeast and in the Southeast, occur despite the greater efficiency in sugar production compared to ethanol (note the efficiency parameters in the equations that compute the Gross Revenue).This means that the investment in flexibility for the construction of a flex plant is advantageous to the levels of the mentioned gains.That is, the additional investment in the flex plant compared to a nonflex plant should not be smaller than the gain derived from the operation of changing the production of one product to another throughout the plant's productive life.
After identifying the gains from operating flexible plants, two aspects should be highlighted.The first one refers to the investing agent: investing in inflexible systems means neglecting this gain (i.e."leaving money on the table ").The second one refers to the regulating agent: a flexible plant results in greater gains for the investor and, therefore, more tax collection (ceteris paribus), and this means that there is room for tax policies aimed at encouraging the construction of flexible systems.In short, the possibility of increasing flexibilization depends on the investor's knowledge of potential gains and incentives for the construction of such systems by regulating authorities.
In the case of the value of the flexibility (switching) option, we observed that this value in the Southeast region is more significant when compared to the Northeast.This was to be expected, because the comparative advantages (smaller ICMS and greater production) are better in this region.For both regions, Table 8 shows that flexibility adds a significant value.We observed that, in the case of ethanol, the switching option value is 327.4% greater in the Southeast than in the Northeast.The same applies to the case of sugar, where, for the Southeast, this option's value is 1278% greater than in the Northeast.

Conclusions
Biofuels such as ethanol are emerging from increasing concern about issues such as the developing technologies that are an alternative to fossil fuels -that are cleaner and present According toSamanez et al. (2014), the final price of fuel is made up of four components: the first is the realization price, which is the selling price of goods at the plant or refinery without tax or shipping to fuel distributors; the second refers to taxes, and includes social integration program and civil service asset formation program federal taxes PIS/PASEP [Programa de Integração Social and Programa de Formação do Patrimônio do Servidor Público] and the contribution to social security financing COFINS federal tax [Contribuição para Financiamento da Seguridade Social], the ICMS state tax on the circulation David Eduardo Lopez Pantoja / Carlos Patricio Mercado Samanez / Javier Gutierrez Castro / Fernando Antonio Lucena Aiube of goods and on interstate and intermunicipal transportation and communications services [Imposto sobre Operações relativas à Circulação de Mercadorias e sobre Prestações de Serviços de Transporte Interestadual e Intermunicipal e de Comunicação], which taxes producers and distributors, and the contribution for intervention in the economic domain CIDE tax [Contribuição de Intervenção no Domínio Econômico], belonging exclusively to the Brazilian State, which taxes producers; the third price component is logistics or freight costs in the different offices through which the product has to pass to reach the end point (plant-distributor-resale); and the fourth component is the profit margin divided between distributors and retailers.Furthermore, Samanez et al. ( (http:// www.cepea.esalq.usp.br), which is part of the Department of Economics, Management and Sociology at ESALQ-USP.The historical series (CEPEA, 2014) were analyzed in a monthly format between May 2003 and July 2014, containing 134 observations.Prices were deflated by the general price index of domestic supply IGP-DI [Índice Geral de Preços Disponibilidade Interna], provided by the Getúlio Vargas Foundation (FGV-IBRE, 2014) and available on a monthly basis in the site http://portalibre.fgv.brsite, using July 2014 as reference.

Figure 4 .
Figure 4. Marginal conditional division of the quadrinomial tree Source:Hahn and Dyer (2011)

Figure 5 .
Figure 5. Present value (PV) of the cash flows for the bivariate quadrinomial tree of the Northeast region

Figure 6 .
Figure 6.Present value (PV) of the cash flows for the bivariate quadrinomial tree of the Southeast region

Table 1 -
ICMS rates across Brazilian regions in 2013 The Brazilian Ministry of Mines and Energy's (MME) October 2013 bulletin shows that ANP authorized the operation of 365 ethanol plants, adding up to a total capacity of approximately 194 million liters of hydrous ethanol per day and of 99 million liters of anhydrous ethanol per day.

Table 5 ICMS for the Northeast and Southeast regions
Source:CEPEA (2014)