1. The Ethanol-Gas Flex Fuel car: What is the option value of choosing your own Fuel? IAG – PUC-Rio 2008 Carlos Bastian-Pinto Luiz Eduardo T. Brandão Mariana de Lemos Alves

2. Introduction Transportation in Brazil is concentrated in roadways, which leaves it vulnerable to changes in fuel prices 1973: First oil crisis, with negative effects on the balance of payments of Brazil, which imports 90% of its oil needs at the time. 1975: Government sponsors an Ethanol production program (Proálcool) to develop this alternative renewable fuel 1979: Second oil crisis. Ethanol powered vehicles begin to be produced and sold in Brazil and by 1987 represent 70% of new car sales 1989: Low oil prices lead to low ethanol prices, while sugar prices become very high in the international market…...which leads ethanol producers to exercise their option to switch to sugar production. This creates fuel shortages for ethanol cars owners. Lack of fuel creates a credibility gap for ethanol powered cars, and sales of ethanol cars come to a halt. 1980: Bifuel car technology is developed in the US, Europe and Japan......but sales suffer from lack of distribution infrastructure for ethanol and methanol. In the US, a 1988 law, allows the mixture of 85% ethanol and 15% gasoline known as E85 In Brazil during the 1980s, Bosch decided to develop a way for combustion engine to use both fuels in any proportion. 1994: The first prototype of a flex fuel car is presented in Brazil 1999: another automobile technology firm, Magneti Marelli, develops a different flex fuel technology. Brazilian government lowers tax on flex fuel cars to the same level as ethanol only cars…...which allows the mass production of these vehicles to become economically feasible in Brazil 2003: the first flex fuel automobile, a Volkswagen Gol Total Flex, is launched in the market

3. Introduction Technology initially developed in the US. The bifuel engine is derived from the conventional gasoline engine The proportion between the two fuels is fixed. In the US, this technology has mainly being adopted in California, with corn based ethanol. Technology developed in Brazil The flex fuel is derived from the ethanol engine, which has a higher compression rate. There is no requirement for a fixed proportion between ethanol and gasoline Flex fuel engine can run with any mixture of these two fuels. Ethanol has an energy yield of 70% of that of gasoline Flex Fuel BiFuel

4. Vehicle Production in Brazil by Fuel Type

5. Is there enough Ethanol to substitute Gasoline?

6. Agricultural Potential of Brazil BrazilUSARussian Fed. European Union IndiaChinaCanadaArgentina 66 328 188 81 132 88 116 60 169 0 96 42 45 31 27 44 0 100 200 300 400 Land for Agriculture per Country (millions of ha.) Available Used

7. 100 million hectares is...

10. Environmental Sustainability Sources: IBGE (Vegetation) & CTC (Cane) Amazon Rain Forest Pantanal Area Current Sugar Cane Production Areas

11. Productivity Gains 37.9 38.5 35.6 39.1 38.5 37.0 36.6 35.0 36.9 37.837.9 40.2 43.9 47.4 49.0 47.3 46.1 57.9 68.468.3 76.0 81.1 73.6 78.4 76.6 82.4 83.0 100.3 96.7 123.2 119.1 113.9 119.9 131.1 9091929394959697989900010203040506 Area (1.000 ha) Production (millions of tons)

12. Relative Efficiency of Sugar Cane Ethanol Energy Generated / Energy Consumed 1,9 1,2 1,6 8,3 0 3 6 9 Beet (EU)Wheat (EU)Corn (USA)Sugar Cane (BR)

13. The Problem The flexibility to choose the cheapest fuel each time the car is fueled…...the uncertainty in the future prices of ethanol and gasoline Generate an option value for the flex fuel automobile When the first flex fuel cars where launched the manufacturers did not charge a premium of this type of vehicle. Currently, flex fuel vehicles are sold at a higher price than the same gasoline powered model. When the first flex fuel cars where launched the manufacturers did not charge a premium of this type of vehicle. Currently, flex fuel vehicles are sold at a higher price than the same gasoline powered model. What is the Option Value of Choosing your own Fuel?

14. Real Options and Flex Fuel When analyzing an investment opportunity, the investor is faced with three factors that will determine the nature and the value of the investment: Irreversibility Uncertainty Flexibility In most investments, the initial cost is at least partially irreversible and cannot be recouped if the project turns out to be a loss. There may be uncertainty over the future benefits of the project. A project may have managerial flexibility to alter and in some way affect the future cash flows in response to new market developments. This is applicable to the purchase of an automobile. There is an initial cost which is partially forgone if the customer decides not to keep the car. In the case of the flex fuel vehicle, the uncertainty lies in the future prices of the ethanol and gasoline fuels, since the evolution of their price in the future is unknown. There is the flexibility to choose the fuel with the best cost/benefit relation, each time the vehicle is fueled. Theory Flex Fuel

15. Model Attempt to generate a series of scenarios based on the parameters of the stochastic processes defined for the variable of interest. Requires the use of computational applications to generate a large number of iterations. Allows the analysis of many different probability distributions that are representative of the project Also known as Monte Carlo Simulation No limit on number of periods to be modeled. Simulation Models The simulation method used in this research is the Monte Carlo method. This will allow us to model a larger number of periods, which would be impractical with the Quadrinomial model. One limitation of simple Simulation models is that they can only be used for the valuation of European Options. The use of Simulation methods for American Options is more elaborate, and was first proposed by Longstaff and Schwartz (2001).

16. Price Evolution of Ethanol and Gasoline

17. Which Stochastic Process to use? First consider the price series S t : ln[S t ] = a + b ln[S t-1 ] + ε t, which can also be written as ln[S t ] - ln[S t-1 ] = a + (b – 1) ln[S t-1 ] + ε t εt i.i.d ~ Normal (0, σ2/N). Running the above regression for both price series (gasoline and ethanol), yields the following t statistics: GasolineEthanol a0.09130.0782 b-1-0.1015-0.1020 t statistic for (b-1)-2.055-1.863 t statistics for both series of prices are above the critical value of 10% significance for unit root test (-2.57), indicating failure to statistically reject the presence of a unit root. Therefore the series can be modeled by a geometric brownian motion (GBM). But we also note that both coefficients b are 10 % bellow the value of 1, indicating also the presence of mean reversion.

18. Stochastic Process of the Variables Gasoline µ G = -1,43% (year) σ G = 10,33% (year) Discrete Model: Ethanol µ E = 0,06% (year) σ E = 19,92% (year) Discrete Model: Modeled as a Geometric Brownian Movement: Correlation of return of price series: ρ GE = 0.5168

19. Stochastic Process of the Variables Gasoline: Ethanol: Where for both variables: η – reversion speed, σ – volatility parameter, Long term mean of variables Discrete Models for simulation: Modeled as a Geometric Mean Reverting Movement:

20. Stochastic Process of the Variables Parameter estimation for MRM is more complicated than GBM. Without future prices, historical prices series must be used. Run the following regression on both price series: Compare with discretization equation: Then we can estimate parameters from regression results: a, b and σ  (standard error of regression) Parameter estimation for Geometric MRM

21. Stochastic Process of the Variables Gasoline η G = 1.2848 (year) σ G = 10.61 % (year) Long term mean: G = 2.4585 (R$/liter) Ethanol η E = 1.2915 (year) σ E = 20.59 % (year) Long term mean: E = 2.1878 (R$/liter) Parameter estimation for Geometric MRM

22. Model Tank Capacity of flex fuel: 40 liters Ethanol Efficiency: 70% Monthly gas consumption: 2,5 fuel tanks Risk free rate: 0,55% a.m. Periods: 10 years Initial gas price: R$2,50 Initial ethanol price: R$1,75 At time zero, the consumer is indifferent between consuming ethanol or gasoline. Cost of Gasoline: Number of fuel tanks, x tank capacity x gas price per liter. The monthly cost with gasoline at the initial price is R$250 (2,5 x 40 x R$2,50 = R$250) Cost of Ethanol: N of fuel tanks, x tank capacity x ethanol price per liter. Cost with ethanol is R$250 ([2,5/0,7] x 40 x R$1,75 = R$250) Assumptions Hypothetical Example We consider two distinct stochastic models for the simulation of the variables: Geometric Brownian Motion and Geometric Mean Reversing Motion Both models are simulated for a ten year period of the use of a flex fuel vehicle We consider two distinct stochastic models for the simulation of the variables: Geometric Brownian Motion and Geometric Mean Reversing Motion Both models are simulated for a ten year period of the use of a flex fuel vehicle

23. Simulation results GBM modelResults (R$) PV of total expense with gas only 20.595 PV of total expense with cheapest fuel 18.434 Value of the Flex Fuel Option 2.161 Flex Fuel Option as % of total expenditures 10,49% MRM modelResults (R$) PV of total expense with gas only 21,883 PV of total expense with cheapest fuel 18,481 Value of the Flex Fuel Option 3,402 Flex Fuel Option as % of total expenditures 15.55%

24. Results from simulation ► Both the GBM and the MRM models show that the flex fuel option adds significant value to the owner of the vehicle by reducing fueling expenditures during the lifetime of the asset. ► As the present value of this expenditure during the lifetime of the vehicle (assuming 10 years) is proportional to the projected fuel prices, this projection will be strongly affected by the stochastic model adopted. ► This is due to the fact that when using a GBM with a slightly negative drift the expected value of fuel decreases during the full period of projection. When using a mean reverting model, which seems more adequate for commodity prices such as Ethanol and Gas, the expected value of the projected price will revert to that mean and not fall indefinitely.

25. Sensibility of the option value to the correlation factor ρ GE Results – sensitivity do correlation

26. ► It is also worth nothing that the option value is not zero even if both uncertainties are totally correlated (ρ GE = 1) as can be seen in the figure. ► This is explained by the fact that the volatility factors of these variables are different, so even with fully correlated diffusion processes, the switch option can still be exercised and has a value of R$ 2,348 with the MRM modeling, and R$ 989 obtained with the GBM modeling.

27. Sensibility to the volatility of gas and ethanol modeling with GBM Results – sensitivity do volatility

28. Sensibility to the volatility of gas and ethanol modeling with MRM Results – sensitivity do volatility

29. ► The volatility of gasoline prices in Brazil has been relatively low, especially when compared to that of ethanol prices, which is subject to seasonality factor due to harvesting periods. ► This effect has been partially mitigated by changing the mix of anhydrous ethanol which is added to gasoline in Brazil. ► It is interesting to note that when modeling the fuel prices with GBM the option value is much more sensible to the volatility of ethanol price than when modeling with MRM. This is due to the characteristic of GBM’s variance which grow indefinitely with t, contrary to the MRM where the variance is bounded.

30. Conclusions ► The flex fuel car is a new technology developed in Brazil which allows consumers to choose any mixture of ethanol or gas each time the car must be refueled. Since its introduction to the market in 2003, the growth of this technology has been significant and currently represents 70% of the production of new vehicles in the country. ► Our results indicate that the flex option adds significant value to the car owner, and can generate savings in fuel costs of approximately 10% to 15% during the life of the vehicle, depending of the stochastic process used to model the option. ► The options value of the flex fuel car may help explain the success achieved by this type of vehicle in Brazil, even if its price is higher than the non flex model.