The EthanolGas Flex Fuel car: What is the option value of choosing your own Fuel

1
The Ethanol-Gas Flex Fuel car What is the
option value of choosing your own Fuel?
Carlos Bastian-Pinto Luiz Eduardo T.
Brandão Mariana de Lemos Alves
12th International Conference on Real Options
Rio de Janeiro, 2008
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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
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 leads ethanol producers to exercise
their option to switch to sugar production. This
creates fuel shortages for ethanol cars owners.
In Brazil during the 1980s, Bosch decided to
develop a way for combustion engine to use both
fuels in any proportion.
...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
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
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Introduction
Flex Fuel
BiFuel

• 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

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Vehicle Production in Brazil by Fuel Type
5

• Is there enough Ethanol to substitute Gasoline?

6
Agricultural Potential of Brazil
Land for Agriculture per Country (millions of ha.)
400
Available
Used
300
328
81
200
0
88
60
42
188
100
169
132
31
116
44
96
66
45
27
0
Brazil
USA
Russian
European
India
China
Canada
Argentina
Fed.
Union
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100 million hectares is...
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100 million hectares is...
9
100 million hectares is...
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Environmental Sustainability
Amazon Rain Forest
Pantanal Area
Current Sugar Cane Production Areas
Sources IBGE (Vegetation) CTC (Cane)
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Productivity Gains
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Relative Efficiency of Sugar Cane Ethanol
Energy Generated / Energy Consumed
9
6
8.3
3
1.9
1.6
1.2
0
Beet (EU)
Wheat (EU)
Corn (USA)
Sugar Cane (BR)
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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.

What is the Option Value of Choosing your own
Fuel?
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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.
Theory
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.
Flex Fuel
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Model
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).

• 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.

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Price Evolution of Ethanol and Gasoline
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Which Stochastic Process to use?
First consider the price series St lnSt a
b lnSt-1 et, which can also be written as
lnSt - lnSt-1 a (b 1) lnSt-1 et
et i.i.d Normal (0, s2/N). Running the above
regression for both price series (gasoline and
ethanol), yields the following t statistics
Gasoline Ethanol a 0.0913 0.0782 b-1 -0.
1015 -0.1020 t statistic for (b-1) -2.055 -1.8
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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.
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Stochastic Process of the Variables
Modeled as a Geometric Brownian Movement

• Ethanol
• µE 0.06 (year)
• sE 19.92 (year)
• Discrete Model

• Gasoline
• µG -1.43 (year)
• sG 10.33 (year)
• Discrete Model

Correlation of return of price series ?GE
0.5168
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Stochastic Process of the Variables
Modeled as a Geometric Mean Reverting Movement

• Gasoline
• Ethanol
• Where for both variables ? reversion speed, s
  volatility parameter, Long term mean of
  variables
• Discrete Models for simulation

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Stochastic Process of the Variables
Parameter estimation for Geometric MRM

• 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 s? (standard error of regression)

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Stochastic Process of the Variables
Parameter estimation for Geometric MRM
Ethanol ?E 1.2915 (year) sE 20.59
(year) Long term mean E 2.1878 (R/liter)

• Gasoline
• ?G 1.2848 (year)
• sG 10.61 (year)
• Long term mean
• G 2.4585 (R/liter)

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Model

• 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

Assumptions
Hypothetical Example

• 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 R2.50
• Initial ethanol price R1.75

• 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 R250 (2.5
  x 40 x R2.50 R250)
• Cost of Ethanol N of fuel tanks, x tank capacity
  x ethanol price per liter. Cost with ethanol is
  R250 (2.5/0.7 x 40 x R1.75 R250)

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Simulation results
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Simulation results

• 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.

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Sensitivity to correlation
Sensibility of the option value to the
correlation factor ?GE
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Sensitivity to correlation

• It is also worth nothing that the option value is
  not zero even if both uncertainties are totally
  correlated (?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.

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Sensitivity to volatility
Sensibility to the volatility of gas and ethanol
modeling with GBM
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Sensitivity to volatility
Sensibility to the volatility of gas and ethanol
modeling with MRM
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Sensitivity to volatility

• 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 GBMs variance which grow
  indefinitely with t, contrary to the MRM where
  the variance is bounded.

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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 option value of the flex fuel car may help
  explain the success achieved by this type of
  vehicle in Brazil, even though its price is
  higher than the non flex model.