Transcript Slide 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
IAG – PUC-Rio
2008
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
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…
1989: Low oil prices lead
to low ethanol prices,
while sugar prices
become very high in the
international market…
In Brazil during the
1980s, Bosch decided to
develop a way for
combustion engine to
use both fuels in any
proportion.
2003: the first flex
fuel automobile, a
Volkswagen Gol
Total Flex, is
launched in the
market
...which allows the mass
production of these
vehicles to become
economically feasible in
Brazil
...which leads ethanol
producers to exercise
their option to switch to
sugar production. This
creates fuel shortages for
ethanol cars owners.
In the US, a 1988 law,
allows the mixture of
85% ethanol and 15%
gasoline known as E85
...but sales suffer from
lack of distribution
infrastructure for ethanol
and methanol.
1980: Bifuel car
technology is developed
in the US, Europe and
Japan...
Lack of fuel creates a
credibility gap for ethanol
powered cars, and sales
of ethanol cars come to a
halt.
Introduction
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.
Flex Fuel
 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
Vehicle Production in Brazil by Fuel Type
2,0
Million vehicles
1,8
1,6
1,4
1,2
1,0
0,8
0,6
0,4
0,2
Ethanol
Flex
Gasoline
20
07
20
05
20
03
20
01
19
99
19
97
19
95
19
93
19
91
19
89
19
87
19
85
19
83
19
81
19
79
0,0
Is there enough Ethanol to
substitute Gasoline?
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
116
96
66
31
45
44
27
0
Brazil
USA
Russian European
Fed.
Union
India
China
Canada Argentina
100 million hectares is...
100 million hectares is...
100 million hectares is...
Environmental Sustainability
Amazon Rain Forest
Pantanal Area
Current Sugar Cane
Production Areas
Sources: IBGE (Vegetation) & CTC (Cane)
Productivity Gains
131.1
123.2
119.9
119.1
Production
113.9
(millions of tons)
100.3
81.1
76.0
68.4
78.4
73.6
82.4
96.7
83.0
76.6
68.3
Area
57.9
(1.000 ha)
37.9
38.5
90
91
35.6
92
39.1
38.5
37.0
36.6
93
94
95
96
35.0
36.9
37.8
37.9
97
98
99
00
40.2
01
43.9
02
47.4
49.0
47.3
46.1
03
04
05
06
Relative Efficiency of Sugar Cane Ethanol
Energy Generated / Energy Consumed
9
6
8,3
3
1,9
1,2
1,6
0
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 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?
Real Options and Flex Fuel
Uncertainty
Flexibility
Theory
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.
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
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.
Model
Simulation Models
 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.
 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
$3,00
$2,50
$2,00
$1,50
$1,00
Gasoline
Ethanol (real)
Ethanol adjusted (1/70%)
$0,50
jul-01
jul-02
jul-03
jul-04
jul-05
jul-06
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
Modeled as a Geometric Brownian Movement:
Ethanol
Gasoline
dG  GGdt   GGdz
µG = -1,43% (year)
σG = 10,33% (year)
Gt 1  Gt e
µE = 0,06% (year)
σE = 19,92% (year)
 Discrete Model:
 Discrete Model:
( G 
dE  E Edt   E Edz
 G2
2
) t  G  t
Correlation of return of price series:
( E 
Et 1  Et e
ρGE = 0.5168
 E2
2
) t  E  t
Stochastic Process of the Variables
Modeled as a Geometric Mean Reverting Movement:
Gasoline:
Ethanol:
dG    ln G  ln G  Gdt   Gdz
dE    ln E  ln E  Edt   Edz
Where for both variables:
parameter,
η – reversion speed, σ
– volatility
Long
E and
G term mean of variables
 Discrete Models for simulation:


 G2 
1  e2G t 
G t
G t
Gt  exp  ln  Gt 1   e
 ln  G 
)  G
G 
  (1  e


2G 
2G





 E2 
1  e2E t 
 E t
 E t
Et  exp  ln  Et 1   e
 ln  E 
) E
E 
  (1  e


2 E 
2 E



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:
ln  St / St 1   a  b  1 ln  St 1   t
 Compare with discretization equation:




ln  St St 1   ln( S )   2 2  1  e t  ln  St 1  e t  1
 Then we can estimate parameters from regression results:
a, b
and
σ (standard error of regression)
Stochastic Process of the Variables
Parameter estimation for Geometric MRM
ln  b 

t
  
Gasoline
ηG = 1.2848 (year)
σG = 10.61 % (year)
Long term mean:
G = 2.4585 (R$/liter)
2ln  b 
b
2

 1 t
 a
 2 
S  exp 

2
1

b
1

b


Ethanol
ηE = 1.2915 (year)
σE = 20.59 % (year)
Long term mean:
E = 2.1878 (R$/liter)
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
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: R$2,50
 Initial ethanol price: R$1,75
Assumptions
 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$250)
Simulation results
GBM model
Results
(R$)
MRM model
Results
(R$)
PV of total expense
with gas only
20.595
PV of total expense
with gas only
21,883
PV of total expense
with cheapest fuel
18.434
PV of total expense
with cheapest fuel
18,481
Value of the Flex Fuel
Option
2.161
Value of the Flex Fuel 3,402
Option
Flex Fuel Option as
% of total
expenditures
10,49%
Flex Fuel Option as
% of total
expenditures
15.55%
Results from simulation
► Both the GBM and the MRM models show that the flex fuel
option adds significant value to the owner of the vehicle by
reducing fueling expenditures during the lifetime of the
asset.
► As the present value of this expenditure during the lifetime
of the vehicle (assuming 10 years) is proportional to the
projected fuel prices, this projection will be strongly
affected by the stochastic model adopted.
► This is due to the fact that when using a GBM with a
slightly negative drift the expected value of fuel decreases
during the full period of projection. When using a mean
reverting model, which seems more adequate for
commodity prices such as Ethanol and Gas, the expected
value of the projected price will revert to that mean and not
fall indefinitely.
Results – sensitivity do correlation
Sensibility of the option value to the correlation factor ρGE
Option Value (R$) x ρ
R$
8.000
7.000
6.000
5.000
4.000
3.000
GBM
2.000
MRM
1.000
Base Cases
-1,00
-0,75
-0,50
-0,25
0,00
0,25
Correlation ρ GE
0,50
0,75
1,00
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.
Results – sensitivity do volatility
Sensibility to the volatility of gas and ethanol modeling with GBM
R$
6.000
5.000
Base Cases
Varying volatility of ethanol
4.000
Varying volatility of gasoline
3.000
2.000
1.000
7,0%
12,0%
17,0%
22,0%
27,0%
σ
Results – sensitivity do volatility
Sensibility to the volatility of gas and ethanol modeling with MRM
R$
8,000
7,000
6,000
5,000
4,000
3,000
2,000
Base Case
Varying Volatility of Ethanol
1,000
Varying Volatility of Gasoline
7%
12%
17%
22%
27%
σ
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.