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.

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

Introduction

Transportation in Brazil is concentrated in

roadways, which leaves it vulnerable to changes in

fuel prices

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.

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

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

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…

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.

...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.

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...

1980: Bifuel car technology is developed

in the US, Europe and Japan...

...but sales suffer from lack of distribution

infrastructure for ethanol and methanol.

...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 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.

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

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.

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…

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

...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

2003: the first flex fuel automobile, a Volkswagen Gol

Total Flex, is launched in the

market

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 FuelFlex FuelBiFuelBiFuel

Vehicle Production in Brazil by Fuel Type

Million vehicles

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

2,0

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

Ethanol Flex Gasoline

Is there enough Ethanol to substitute Gasoline?

Agricultural Potential of Brazil

Brazil USA RussianFed.

EuropeanUnion

India China Canada Argentina

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

100 million hectares is...

100 million hectares is...

100 million hectares is...

Environmental Sustainability

Sources: IBGE (Vegetation) & CTC (Cane)

Amazon Rain Forest

Pantanal Area

Current Sugar Cane Production Areas

Productivity Gains

37.9 38.535.6

39.1 38.5 37.0 36.6 35.0 36.9 37.8 37.9 40.243.9

47.4 49.0 47.3 46.1

57.9

68.4 68.3

76.081.1

73.678.4 76.6

82.4 83.0

100.396.7

123.2119.1

113.9119.9

131.1

90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06

Area(1.000 ha)

Production(millions of tons)

Relative Efficiency of Sugar Cane Ethanol

Energy Generated / Energy Consumed

1,91,2 1,6

8,3

0

3

6

9

Beet (EU) Wheat (EU) Corn (USA) Sugar Cane (BR)

The Problem

The flexibility to choose the

cheapest fuel each time the car

is fueled…

The flexibility to choose the

cheapest fuel each time the car

is fueled…

...the uncertainty in the future

prices of ethanol and gasoline

...the uncertainty in the future

prices of ethanol and gasoline

Generate an option value for

the flex fuel automobile

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?What is the Option Value of Choosing your own Fuel?

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:

When analyzing an investment opportunity, the investor is faced with three factors that will determine the nature and the value of the investment:

IrreversibilityIrreversibility UncertaintyUncertainty FlexibilityFlexibility

In most investments, the initial cost is at least partially

irreversible and cannot be recouped if the project turns

out to be a loss.

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.

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.

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.

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.

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.

There is the flexibility to choose the fuel with the best

cost/benefit relation, each time the vehicle is fueled.

Th

eory

Th

eory

Flex F

uel

Flex F

uel

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 ModelsSimulation 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).

Price Evolution of Ethanol and Gasoline

Gasoline and Ethanol prices (R$) - deflated IGP-M

$0,50

$1,00

$1,50

$2,00

$2,50

$3,00

jul-01 jul-02 jul-03 jul-04 jul-05 jul-06

GasolineEthanol (real)Ethanol adjusted (1/70%)

Which Stochastic Process to use?

First consider the price series St:

ln[St] = a + b ln[St-1] + εt, which can also be written as

ln[St] - ln[St-1] = a + (b – 1) ln[St-1] + εt εt i.i.d ~ Normal (0, σ2/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 -1.863

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.

Stochastic Process of the Variables

Gasoline

µG = -1,43% (year)

σG = 10,33% (year)

Discrete Model:

G GdG Gdt Gdz

Ethanol

µE = 0,06% (year)

σE = 19,92% (year)

Discrete Model:

E EdE Edt Edz

2

( )2

1

GG Gt t

t tG G e

2

( )2

1

EE Et t

t tE E e

Modeled as a Geometric Brownian Movement:

Correlation of return of price series: ρGE = 0.5168

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:

22

1

1exp ln ln (1 )

2 2

G

G G

tt tG

t t G GG G

eG G e G e

Modeled as a Geometric Mean Reverting Movement:

ln lndG G G Gdt Gdz

ln lndE E E Edt Edz

2 2

1

1exp ln ln (1 )

2 2

E

E E

tt tE

t t E EE E

eE E e E e

and E G

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

1 1ln / 1 lnt t t tS S a b S

21 1ln ln( ) 2 1 ln 1t t

t t tS S S e S e

Stochastic Process of the Variables

Gasoline

ηG = 1.2848 (year)

σG = 10.61 % (year)

Long term mean:

G = 2.4585 (R$/liter)

Ethanol

ηE = 1.2915 (year)

σE = 20.59 % (year)

Long term mean:

E = 2.1878 (R$/liter)

Parameter estimation for Geometric MRM

2

2ln

1

b

b t

ln b

t

2

2exp

1 1

aS

b b

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)

AssumptionsAssumptionsHypothetical ExampleHypothetical 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

Simulation results

GBM model Results (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 model Results (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%

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.

Sensibility of the option value to the correlation factor ρGESensibility of the option value to the correlation factor ρGE

Results – sensitivity do correlation

Option Value (R$) x ρ

-

1.000

2.000

3.000

4.000

5.000

6.000

7.000

8.000

-1,00 -0,75 -0,50 -0,25 0,00 0,25 0,50 0,75 1,00Correlation ρ GE

R$

GBM

MRM

Base Cases

Results – sensitivity do correlation

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

Sensibility to the volatility of gas and ethanol modeling with GBMSensibility to the volatility of gas and ethanol modeling with GBM

Results – sensitivity do volatility

-

1.000

2.000

3.000

4.000

5.000

6.000

7,0% 12,0% 17,0% 22,0% 27,0% σ

R$

Base Cases

Varying volatility of ethanol

Varying volatility of gasoline

Sensibility to the volatility of gas and ethanol modeling with MRMSensibility to the volatility of gas and ethanol modeling with MRM

Results – sensitivity do volatility

-

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

7% 12% 17% 22% 27% σ

R$

Base Case

Varying Volatility of Ethanol

Varying Volatility of Gasoline

Results – sensitivity do 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 GBM’s variance which grow indefinitely with t, contrary to the MRM where the variance is bounded.

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.