1 FLEXIBILITY AND UNCERTAINTY IN AGRIBUSINESS PROJECTS : INVESTING IN A COGENERATION PLANT

La generacion de energia de la biomasa se ha convertido en una fuente creciente de interes en vista de la creciente preocupacion sobre el posible agotamiento de los combustibles fosiles en todo el mundo. En este articulo nos fijamos en una planta productora de azucar y etanol en Brasil, que tiene tan bien una posibilidad de expansion como una opcion de agregar una unidad de cogeneracion que le permita la venta de energia excedente generada por la quema del bagazo de cana de azucar, mientras que la segunda opcion es dependiente de la primera. Fueron modelados los precios del azucar, etanol y electricidad, como procesos de reversion a la media geometrica y fue aplicado el enfoque de opciones reales para cuantificar esta flexibilidad en la gestion, ya que estas dos opciones tienen diferentes activos subyacentes. La opcion de expandir la produccion es una funcion del valor esperado de los precios de futuros de azucar y etanol, mientras que la opcion de invertir en una planta de cogeneracion dependera del precio futuro de la electricidad. Ambas decisiones se modelan como opciones americanas compuestas sobre sus activos subyacentes. El modelo se resuelve utilizando un arbol binomial recombinante para reversion sin censura a la media propuesta por Bastian-Pinto, Brandao y Hahn (2010) utilizando el software DPLTM. Los resultados indican que la flexibilidad de escoger el momento optimo para invertir en las dos opciones de expansion genera un valor significativo: la inversion en la unidad de cogeneracion anade un valor igual a la expansion de la produccion de azucar y etanol, y representan a 44% del VAN proyectado tradicional de $ 195,900,000. Se concluye que, dado que solo la mitad de las plantas de cana de azucar en Brasil tienen unidades de cogeneracion instaladas, y tambien dada la demanda cada vez mayor de fuentes limpias y renovables de energia, esto puede indicar que existe un potencial importante para inversiones y desarrollo de unidades de cogeneracion de bioelectricidad, asi como de adaptacion de las plantas mas viejas, y que los incentivos que el gobierno ha dado son una contribucion efectiva en este desarrollo.


Introduction
Concerns about global warming and high oil prices have spearheaded the search for alternate and more environmentally friendly sources of energy.One of the developments that has shown exceptional value is the increasing use of ethanol derived from biomass such as sugarcane, corn, beet and wheat.As the world's largest producer of sugar cane, Brazil has benefited from this trend to become also the largest producer of ethanol after the United States.
An important by-product of sugar cane processing is the bagass, which is the cellulose fibers that remain after the removal of water, sucrose and other sugars and minerals.The bagasse represents 25% to 30% in weight of the sugar cane, and has traditionally been applied to generate the heat used in the production of sugar and ethanol.On the other hand, only one third of the total energy contained in a sugarcane plant corresponds to ethanol, while the remaining is due to the byproducts of the distillation process, such as bagasse.This implies that there is the potential to significantly increase the energy yield of the ethanol production process through a more effective use of the bagasse.
More recently, sugar cane mills have begun to adopt the use of high pressure boilers where, rather than burning bagasse to generate heat directly, the bagasse is used as fuel to generate steam which can then be easily transformed into other forms of energy such as heat, traction and even electricity.This simultaneous production of electricity and thermal or mechanical energy from the same primary source is called cogeneration, and represents a highly efficient process since the use of the generated heat minimizes energy losses.Since almost no additional costs are involved, the revenue from cogeneration of bioelectricity from sugarcane processing plants has great potential to increase profitability and can reach levels of up to 60 to 80 kWh per ton of sugar cane.
Aside from being a clean and renewable source of energy, bioelectricity requires minimal investment in transmission lines, since the power plants are largely located close to consumption centers.Strategically, it is an energy source that supplements Brazil's hydro generation which accounts for over 85% of the country's electrical energy matrix, since it is generated during the harvest, which is the dry season, when reservoir levels are at their lowest.
In order to encourage the generation of electricity form sugar cane bagasse, the Brazilian government has taken steps that allow cogeneration units to sell their surplus energy into the grid.As of 2008, the aggregate capacity of bagasse cogeneration units in Brazil was 1,800 MW, approximately 3% of the total electrical energy consumption, and was expected to increase 8,000 MW by the year 2015.(UNICA, 2010) The sugar cane industry, as is typical of agribusiness projects, presents many uncertainties and significant flexibilities that require the use of option pricing methods when valuing these types of projects.Silva (1999) used real options to analyze the effects of industrial policies in the agro-industrial chains.Figueiredo Neto (2003) analyzes land lease contracts as an option for growing crops, while Brobouski (2004) assesses a forestry partnership agreement with a floor price.Bastian-Pinto, Brandao, & Hahn (2009) also use the real options approach to analyze the flexibility to switch outputs between sugar and ethanol in a sugar cane processing plant.Schatzki (2003) considers the option to switch between agriculture production and reforestation that is available to landowners, while Musshoff & Odening (2005) examine the option to change from traditional to organic farming in Germany.Ge, Mourits, & Huirne (2005) calculate the flexibility in controlling diseases of livestock, and Scatasta & Wesseler (2008) assess the adoption of transgenic crops.Cardoso, Martin, Marçal, Kayo, & Kimura (2009) also use the real options approach to study the case of the optimal timing to invest and disinvest in a coffee plantation in Brazil.However, none of these papers analyze the impact of flexible investment in bioelectricity cogeneration units to the value of agricultural projects, and to the best of our knowledge this topic has not been addressed in the literature.
In this study we use an innovative discrete binomial mean reverting tree model based on Bastian-Pinto, et al. (2010) to model the uncertainties and embedded flexibilities in a greenfield sugar cane mill that produces sugar and ethanol.The project has the option to expand production after the third year of operation and also to add a cogeneration unit.The decision to expand is a function of the expected future prices of sugar an ethanol, while the decision to invest in the cogeneration plant will depend on future prices of energy.Both decisions are modeled as American type compound options over their respective underlying uncertainties, which are assumed to follow a mean reverting diffusion process.
This paper is organized as follows.In the next section we present and overview the Brazilian sugar cane industry and the generation of bioelectricity.In section three we introduce the case study of the project and in section four we perform the real option analysis and present the results.Finally in section five we conclude.

The Sugar Cane Industry
The sugar cane industry in Brazil is closely linked to the economic development of the country.Sugar cane was first brought to Brazil in 1530 from the Portuguese islands of São Tomé e Madeira, and by the end of the sixteenth century, Brazil had already become the world's largest producer and supplier of sugar.Due to its potential for generating wealth, sugar was one of the main reasons for the Dutch invasion of the Northeast of the country in 1624 where they remained for thirty years until they were eventually expelled by the Portuguese in 1654.With full knowledge of the sugar cane technology acquired during the period of the invasion, the Dutch developed this culture in the Dutch Guyana, now Suriname, which eventually spread to other countries, contributing to the decline of this economic cycle in Brazil in the eighteenth century.
Currently, the Brazilian production of sugar cane is primarily concentrated in the South-Central region, which accounts for 88% of the production, and the Northeast, with the remaining 12%.The vast Brazilian territory and its favorable climate provide a large supply of arable land, of which only 60 million hectares are currently used for agriculture and only 6 million hectares for sugar cane production.The development of new genetically engineered varieties and advances in production technology have increased the competitiveness of Brazilian sugar cane industry to a point where sugar cane based ethanol is the first renewable fuel that is able to compete with gasoline in terms of international costs.The sugar cane harvest of 2009/2010 was 590 million metric tons, which produced 33 million tons of sugar and 25 million cubic meters of ethanol (UNICA, 2010).Brazil ranks first in production of sugar cane worldwide, first in sugar and second in ethanol, with this industry alone being responsible for 1.2% of the total GDP and for 26.5% of the agricultural GDP of the country and employing over one million people.
Due to strong international demand for sugar and the consolidation of ethanol as a cost efficient source of energy, the sugar cane industry has experienced significant growth in recent years, which has sparked the interest of major energy firms.In the beginning on 2010, Cosan, the world´s largest ethanol producer with 23 sugar cane mills, 15 cogeneration power plants with 1,200 MW capacity and a sugar cane crushing capacity of 60 million tons per year, announced a joint venture with Shell Oil.The new firm will have revenues of US$ 20 billion and over 4,000 gas stations, half of which as the result of the purchase of Brazilian assets of Exxon by Cosan in 2008.Odebrecht, a large petrochemical and construction group, also announced the purchase of Brenco, creating a US$ 7 billion dollar business with 40 million tons of sugar cane crushing and 500 MW of cogeneration capacity.This industry trend towards consolidation is expected to reduce the number of producerr from the current 300 to less than 20 in the next ten years.
Approximately 40% of the sugar and 80% of the ethanol produced is consumed domestically.Ethanol has been used as automotive fuel since 1975, when the ProAlcool program was created.This program came as an attempt to reduce the vulnerability of the country to the high prices of imported oil, and provided incentives for the production of ethanol and ethanol powered automobiles.A mixture of 20% to 25% of anhydrous ethanol to all gasoline was also mandated, which still remains in place to date.After a vigorous growth in the 1980's, the production of ethanol vehicles came to a halt as oil prices dropped and the government subsidies to ethanol producers were eliminate.
The introduction of flex fuel vehicles in 2003 renewed the demand for ethanol as an automotive, and the consumption has increased significantly.Flex fuel vehicles are designed to operate on gasoline, ethanol or any mixture of the two, and according to the National Association of Automobile Manufacturers -ANFAVEA ( 2010), sales of flex fuel vehicles reached more than 2.5 million units in 2009, representing 80% of all vehicles sales.Approximately 85% of the current Brazilian automotive fleet consists of vehicles powered exclusively by gasoline, suggesting that there is significant room to increase the proportion of flex fuel vehicles as the fleet is renewed, which will lead to an even greater demand for ethanol.
The sugar cane bagasse is the cellulose fiber that remain after the extraction of the nutrients.In the past, burning bagasse was seen as a way to eliminate the vast quantities generated in the process, with little regard for any form of efficiency either in the generation or the use of energy.Additionally, when manually harvesting of the crop, producers typically set fire to the sugar cane fields in order to burn the sharp edges of the leafs in order to protect workers from cuts.This practice not only produces large amount of atmospheric emissions, but also puts to waste the energy stored in the leafs.
More recently, sugar cane mills have been designed with efficient cogeneration units with high pressure boilers that are fully integrated into the production process.A greater concern with energy efficiency both in the use and generation process, and the use of modern automated harvesting technology which eliminates the need for burning of the leafs, can significantly increase the energy yield of the mill allowing the generation of surplus energy.The fact that sugar cane bioelectricity is produced during the harvest, which coincides with the dry season when levels in the reservoirs of hydroelectric power plants are at their lowest, makes this source of energy particularly attractive.Older mills can also be retrofitted in order to take advantage of this increase in energy generating capacity.The sale of bioelectricity provides an important source of revenue to the sugar mill since once the capital investment is made, there are practically no incremental operational costs involved.
The production of bioelectricity has been made possible due to significant structural changes in the past two decades in the Brazilian Electricity Industry (BEI), which included the creation of a free market for energy and a series of initiatives which allowed surplus energy to be sold both in the free market for electricity and in a regulated environment.In 1995, the concept Independent Power Producers was created by law, and large energy consumers (more than 3 MW) were allowed to purchase electricity directly from a supplier of their own choice.In 1996, law 9427 created ANEEL, the National Electric Energy Agency, to regulate the electricity industry.In 1998, law 9648 provided for the establishment of an independent system operator (ISO) responsible for the technical coordination and management of the transmission services.The Brazilian electrical energy wholesale market (Câmara de Comercialização de Energia Elétrica -CCEE) was also created at that time.
In 2004, a new proposal for reforming the BEI was approved by the Congress.The main points of the new rules were the creation of two contracting environments (regulated and free) and the creation of a pool for electricity procurement by the distribution companies.In the regulated environment, distribution companies buy generation capacity for several years ahead (15 years for thermal plants and 30 years for hydro plants), and these firms must contract electricity for 100% of their market need, as projected five and three years in advance.In the non-regulated market of electricity, generation and trading companies and also eligible consumers are allowed to freely buy and sell electricity under bilateral contracts.
The first support measures for alternative energy sources, including bioelectricity, was created in 2004 under the PROINFA program of incentives, which offered 20-year fixed tariffs, subsidized capital and other benefits.In 2007, ANEEL established trading rules for alternative generation sources including biomass, allowing non-captive consumers with more than 0.5 MW to purchase electricity with 50% of discount in the distribution tariff.In 2008, decree 6353 created reserve electricity auctions to enhance the security of the grid system.In the reserve contracts, all the consumption agents pay for the electricity, and the first reserve electricity auction in 2008 was directed to contract biomass electricity only.
Currently there are approximately 400 sugar cane mills in operation in Brazil, of which almost all are energy self sufficient.There are about 200 cogeneration projects being implemented or under analysis, which have the potential to add 10,000 MW of capacity by the year 2013 from burning bagasse.

The Project
We analyze a typical greenfield sugar cane mill with a nominal processing capacity of 1,000,000 tons/year to produce sugar and ethanol with a production mix of 50%, using typical industry data and parameters.There is a ramp up period of three years as the neighboring sugar cane fields mature as production grows from 350,000 to 1 million tons of sugar cane processed per year.All energy produced from bagasse is used to power the mill, with no surplus capacity.After the first three years, the firm has an option to expand capacity to 1.8 million tons per year, and once this expansion takes place, a more efficient cogeneration unit that will provide surplus energy can also be built.
Total capital investment for the base case is R$ 100 million, which is depreciated linearly in a ten year period.The forecasting period is 10 years, with an expected growth rate of zero beyond the forecasting horizon and the corporate income tax rate is 34%.Sugar and ethanol prices are forecasted based on historical price series.The project free cash flows (F) are a function of the prices (P E and P S ) of each commodity, the volume of sugar cane processed (V), production yield of ethanol (Y E ) and sugar (Y S ), direct taxes and production costs of ethanol (C E ) and sugar (C S ), fixed costs (FC), income taxes (T), and depreciation of investment (D), as shown in Equation ( 1): As the mix of output products is assumed fixed (50% of each product), in order to model a single uncertainty, an equivalent price (P EQ ) for the 50/50 production mix which considers the yield and different sales tax of each commodity, is determined for use as input in the analysis.

(
) Substituting this variable (P EQ ) in Equation ( 1) we obtain: ( ) (1 ) where The corporate cost of capital (WACC) is assumed to be 18.5% and the risk free rate 7.0%.The value of the project under these conditions is R$ 112.7 million, which is equivalent to a net present value of R$ 12.7 million.If we assume that the expansion will occur for certain at the end of the third year, the project value is R$ 195.9 million, or a NPV of R$ 95.9 million.

Real Option Analysis of Project Flexibilities
The previous analysis does not take into account the value of the option to expand production after year two, or the possibility of investing in a cogeneration unit that will allow the project to sell surplus electricity into the power grid.The expansion of sugar cane processing capacity to 1.8 million tons per year requires an additional investment of R$ 26 million, a lead time of one year and a ramp up phase of three years.Due to the change in scale of the project, the Free Cash Flow function used in the model will also change from year to year.The decision on whether to expand the project will depend both on the prices of sugar and ethanol and the cost of the expansion.
The cogeneration plant involves an investment of R$ 38 million in plant and equipment, and due to its high cost and economies of scale, it is conditional on the prior expansion of capacity to 1.8 million tons.It is assumed that both investments will only be executed if expected prices of sugar, ethanol and electricity allow adequate return to the shareholders.
The free cash flows (FCF) from the sale of surplus electricity is distinct from the FCF of the sugar and ethanol sales, as bagasse is a by-product of the of the sugarcane crushing process, so no variable cost are involved.Specific fixed costs are also minimal and therefore surplus electricity FCF is given by Equation (3): where:

Project Expansion
The main drivers of the option to expand are the future expected prices for sugar and ethanol.The daily prices of sugar and ethanol paid to producers, published by the Center of Advanced Studies in Applied Economics from the University of São Paulo (CEPEA-USP) are shown in Figures 1 and 2. The equivalent price (P EQ ) considering price of sugar and ethanol, their yields and direct taxes was modeled as a Mean Reverting Diffusion process as follows: [ ] ( ) where : η: Is the mean reversion coefficient parameter of the process; σ: Is the volatility of the process; P : Is the equilibrium level to which the process reverts in the long run; dz: Is the standard Weiner increment.
Using the price series of sugar and ethanol described above, a series of equivalent prices (P EQ ) was calculated and the required parameters were derived by running the following regression: The mean reversion coefficient η is obtained from the regression output as ( ) , the volatility is given by ( ) ( ) where 2 ε σ is the variance of the regression's errors, and the long term mean is given by For option pricing purposes, the risk neutral measure must be used.In mean reverting models, this also involves a downward adjustment to the long term mean.For a more detailed discussion of the parameter definition and the user of mean reverting models for option pricing, we refer the reader to Bastian-Pinto, et al. (2009).The plotted regression line and its corresponding equation for the data can be seen in Figure 3.

Figure 3. Equivalent Prices (P EQ ) regression
The results of parameter definition for P EQ are listed in Table 1.To solve for the option value of the expansion, we model the Sugar/Ethanol equivalent price uncertainty as a discrete mean reverting binomial lattice Bastian-Pinto, et al. (2010),where the values at each branch are the free cash flows of the project that correspond to the prices in each state.The discounted expected value of these free cash flows provides the value of the project.The model developed by these authors is a non-censored mean reverting binomial lattice, similar to the GBM lattice of Cox, Ross, & Rubinstein (1979) but with varying values of the probability p for the up move.
Consider: x t + x* t = log (P t ), where: is the deterministic part of the process, and x* t is the stochastic part, modeled as an Ornstein Uhlenbeck arithmetic mean reversion, with long term mean = 0, and starting value also = 0.
x* t is modeled into a mean reverting lattice, with: Adding the zero mean lattice values x* t to the deterministic values of x t , we obtain a lattice describing the mean reversion process, with values at each nod after i up movements, and j down movements will be: x e x e i j t To model the geometric mean reversion process describing the behavior of prices such as P EQ , we use: P (i,j) = exp [x (i,j) ] , and: , already in the risk neutral form, where λ is the risk premium of the process.The value of x was estimated through numerical procedures, by equating the present value of the base project discounting cash flows at the risk adjusted rate (WACC) and that of risk neutral cash flows (adjusted through this risk premium λ) discounted at the risk free rate.The probability p of an up move at each node is calculated by Equation ( 5).This Mean Reverting lattice was then modeled with the aid of the DPL TM program and the option to expand modeled as a recurring decision opportunity betweens years two and nine.Figure 1 illustrates the first six years of the binomial tree model used.

Figure 1. Sugar and Ethanol Production Expansion Model
The value of the project considering the option to expand sugar and ethanol production is R$ 237.3 million, as shown in Figure 2, which compares to the value of R$ 195.9 million of the static analysis that assumes a mandatory expansion in year three.This represents a value of R$ 41.4 million for the option to defer the expansion, which is significant, and implies that early exercise may not be optimal in this case.The analysis of the probability of the expansion occurring shows that flexibility to defer to the latter years is what creates option value: probability of exercise in year 8 is 38% and 46% in year 10.

Investment in Cogeneration
Once the decision to expand production has been made, the firm has the option to invest in a cogeneration plant that will allow the production of surplus energy to be sold.We assume that once the cogeneration unit becomes available, the firm will enter into a long term sales contract at the prevailing spot price of energy at the time, and therefore, no further electricity price uncertainties will exist for the project.The daily spot energy prices (Preço de Liquidação de Diferenças -PLD) informed by the Brazilian Electrical Energy Clearing Chamber (CCEE) are shown in Figure 3.

Figure 3. PLD Energy Brazil daily spot prices
As of January 2010, the spot price of energy was at its lowest level (about R$ 12.80/MW, or US$ 7.00/MW) since higher than normal rainfalls had left the hydro power plant's reservoirs filled to capacity.At these exceptionally low price levels, most energy investments will yield negative returns, but since energy prices are stochastic, highly volatile, and with a long term mean of R$ 120/MW, nonetheless, the option to invest in such projects may yield positive results.We model future electricity (P EEt ) prices as a MRM diffusion process using the same framework as with the equivalent sugar-ethanol price.Parameters for this process are listed in Table 2. Once the stochastic electricity prices are modeled, we use Equation (3) to determine the corresponding project free cash flows in each year and for each possible state of the prices.Given that hydro power is the main source (90%) of electrical energy in Brazil, the main factor driving prices is the amount of local rainfall in any particular year.On the other hand, ethanol and sugar prices are determined by international prices, which take into account crop output in the main producing countries worldwide.As such, these prices are uncorrelated, and options written on these underlying uncertainties can be valued independently.A stand alone analysis of the cogeneration unit, assuming an investment of R$ 38.0 million, that the investment occurs between years 4 and 10, and with no expected growth beyond the forecasting horizon, has a net present value (year 0) of R$ 44.3 million.
Due to economies of scale, on the other hand, the investment in the cogeneration plant can only occur after the sugar-ethanol plant has undergone expansion.Therefore, the option to invest in the cogeneration project is conditional to the expansion option of the original sugarethanol project being exercised, creating a compound option problem, which requires that both options be valued simultaneously.Both options were then modeled using the same DPL TM software used in the valuation of the sugar and ethanol expansion option.Figure 4 shows the first five years of the complete lattice model.

Figure 4. Sugar and Ethanol Expansion and Cogeneration Options Model
With this framework, the option to invest in a cogeneration unit between the fourth and tenth year of the project life unit increases the project value to R$ 275.9 million, an increase of R$ 38.6 million, over the value of the project considering the sugar-ethanol expansion option only.It is interesting to note that when analyzed as a compound option, there is a decrease in value of R$ 5.8 million over the stand alone cogeneration project.This is due to the conditional aspect of the cogeneration unit option on sugar/ethanol option.As the first option -delaying the base case expansion -gains value, the second option -investing in cogeneration -diminishes in value.But considering the value of both options together, these have a value of R$ 79.92 million (R$ 275.9 minus R$ 195.9 million of the year 3 expanded base case project), or an increase in 40.8% in value.The optimal investment time for the cogeneration unit is also concentrated in the final years of the projection horizon: 10% in year 5, 6% in year 7 and 73% in year 9.These probabilities are determined by running the simulation model with the corporate WACC rate, rather than the risk free rate, so that the correct probabilities can be computed, rather than risk neutral probabilities.
The sensitivity analysis for the long term mean of the ethanol and sugar equivalent price shows that the value of the project is very sensitive to changes in this variable.For a negative variation of 20%, which brings this value below R$ 50.00, the project has negative NPV, considering that the initial capital investment is R$100 million (Figure 5).

Figure 5. Sensitivity Long Term Mean of Sugar and Ethanol Equivalent Price
On the other hand, the sensitivity analysis of the long term mean of spot electricity prices (Figure 6) indicates that the impact on the project is not as severe as is the case of sugar and ethanol, which is reasonable, since the volumes and revenues from surplus electricity are much smaller than those of sugar and ethanol.

Conclusions
We analyzed a sugar cane mill that has significant embedded flexibilities to expand production and to add a cogeneration unit that will allow it to sell surplus electricity.We apply the real options approach to determine the value of this managerial flexibility, considering that these options have three distinct underlying assets.While the key uncertainties for the expansion of the mill are the futures prices of sugar and ethanol, the investment in the cogeneration plant will depend on the evolution of the future prices of energy.We model these simultaneous uncertainties as mean reverting processes, and the project flexibilities as two distinct compound American type options.The model is then solved using the non censored binomial mean reverting lattice proposed by Bastian-Pinto, et al. (2010) using the DPL TM software.
The results show that the flexibility to choose the optimal time to invest in plant expansion adds R$ 41.4 million in value, or 44% of the project NPV of R$ 95.9 million.The cogeneration unit adds an almost equivalent amount, which is significant, considering that cogeneration is not the core business of the sugar cane mill.Given that only half of the sugar cane crushing mills currently has cogeneration units installed and the increasing demand for cleaner and renewable sources of energy, this may indicate that there is a significant potential for investment and further development of bioelectricity cogeneration power plants, and even in the retrofit of older cogeneration units.Government incentives have been effective in contributing for this development which is growing at a very fast pace.
However, a few restrictions apply.Parameter determination is a problem that affects any valuation model, and real option analysis is not immune to this.The sensitivity analysis indicates that the results are very sensitive to the input parameters of the model, in particular to the level of the long term mean prices of the outputs, and small variations in this parameter may lead to different results.On the other hand, additional flexibilities that are inherent to this type of project were not considered in our analysis.Rather than a fixed 50/50 proportion of sugar and ethanol, the producer may have the option to change this proportion and switch outputs in response to relative variations in prices.

Figure 2 .
Figure 2. Value of the Project with Sugar and Ethanol Expansion

Figure 6 .
Figure 6.Sensitivity to Long Term Mean of Electricity Prices