Valoração da flexibilidade dos

insumos na produção do Biodiesel

THE OPTION VALUE OF SWITCHING INPUTS IN A BIODIESEL PLANTLuiz BrandãoGilberto Master PenedoCarlos Bastian-Pinto

Advantages of Biodiesel in Brazil Reduction of foreign dependency Agricultural development Family agriculture: Social inclusion of poorer families Renewable source of energy Reduction of Greenhouse Gases Emission Higher lubricating capacity Allowed by Law since 2005 Mandatory since 2008 (B2) and 2013 (B5)

Biodiesel Production Process

•Soy

•Coton

•Castor

•Sun-flower

•Palm

• Jatropha

•Babassu

•Colza Husks/Pie Oil (market)

Oil

BiodieselGlycerol

Transesterification

Ethanol

Methanol

Oil (market)

Tallow/ Oil (recicled)

•Macaúba

• .....

Crushing

•Soy

Seeds:

Biodiesel Production Feedstock

Real Option in this Study

•Soy

•Coton

•Castor

•Sun-flower

•Palm

• Jatropha

•Babassu

•Colza Husks/Pie Oil (market)

Oil

BiodieselGlycerol

Transesterification

Ethanol

Methanol

Oil (market)

Tallow/ Oil (recicled)

•Macaúba

• .....

Crushing

•Soy

Seeds:

Real Option in this Study

•Soy

•Coton

•Castor

•Sun-flower

•Palm

• Jatropha

•Babassu

•Colza Soy Husks Oil (market)

Oil

BiodieselGlycerol

Transesterification

Ethanol

Methanol

Oil (market)

Tallow/ Oil (recicled)

•Macaúba

• .....

Crushing

•Soy

Seeds:

Castor Husks Stochastic

Fixed

Biodiesel Production Process Prices of biomass oil feedstock, and of oil itself, are

stochastic;

Biodiesel plants are multi-oil, meaning that producer is able to choose between a variety of input feedstocks;

Alcohol reagents of the process can be either ethanol or methanol, prices of which are also stochastic.

Production Assumptions

Joint crushing and transesterification processes; Feedstocks are available No transportation costs (or similar to both

feedstocks); Biodiesel an Glycerol prices do not depend on

type of feedstock used Castor pie price constant Input flexibility at a monthly level All vegetable oil derived from crushing goes to

Transesterification process.

Choice of inputs (feedstock)

Castor x Soy Methanol as reagent, (more pollutant but more efficient).

Soybean

128,06 BAGS of 60 kg 6.770 kg of soybean husks + 910 kg of soybean oil

910 kg of soil oil + 128,44 kg of methanol 1.000 l biodiesel + 86,24 kg glycerol

Castor Bean

52,86 BAGS of 60 kg 2.220 kg of castor bean husks + 950 kg of castor oil

950 kg of castor oil + 133,87 kg of methanol 1.000 l biodiesel + 89,89 kg glycerol

Modeling Steps

Sequence of European Options of the use of feedstock (soy or castor beans). Option analysed is:

Stochastic processes of prices of inputs (beans) and output (husks) modeled with Monte Carlo Simulation using @Risk.

Stochastic processes simulated as GBM and MRM, with comparison of the results obtained.

( ) ( )Biodiesel BiodieselBiodieselCF Incomes Costs

.

.

(1000 6,77 0,086 )

(0,128 128,06 )

BioSoy Biod Soy husks Glic

Methanol Soy bag

CF P P P

P P

.

.

(1000 2, 22 0,090 )

(0,134 52,86 )

BiodCastor Biod Castor husks Glic

Methanol Castor bag

CF P P P

P P

Data Collection

0

10

20

30

40

50

60

70

80

jan-02 jan-03 jan-04 jan-05 jan-06 jan-07

Cas

tor

(R$/

60kg

) &

So

y (R

$/60

kg)

0

100

200

300

400

500

600

700

800

So

y h

usk

s (R

$/to

n)

S oy C a stor S oy husks

Deflated Price Series for Soy, soybean husks and castor bean price - Bahia

Parameter determination for GBM Volatility parameter (σ) can be estimated as the standard deviation

of the difference in log return of the price series used

Drift value: average of this same log return plus half the variance already estimated.

Soy Castor Soy Husks

R$/BAG R$/60 BAG kg R$/ton

Month Annual Month Month Annual Month

Volatility - σ 8,55% 29,63% 8,49% 29,41% 10,25% 35,52%

ν = (r-σ2/2) 0,0963% 1,6106% 0,1017% 1,6744% -0,0637% -0,3098%

Initial Price - P037,70 74,81 570,43

Parameter determination for MRMThe regressions mentioned above can be used for MRM

parameter estimation:

Soy - Regression MGB x MRM

y = -0,0639x + 0,2236R ² = 0,0333

-0.30

0.202.80 3.00 3.20 3.40 3.60 3.80 4.00

L n(P t-1)

Ln(p

t)-L

n(pt

-1)

Castor - Regression MGB x MRM

y = -0,0251x + 0,1075R ² = 0,0077

-0.300

0.2003.00 3.50 4.00 4.50

L n(P t-1)

Ln(p

t)-L

n(pt

-1)

tttt xbaxx 11 1

Parameter determination for MRM With coeficients a, b and σε (regression standard error)

Mean reversion coefficient:

Volatility coefficient:

Long term mean price:

log b

22log 1b b

2 2exp 1 1P a b b Soy Castor Soy husks

R$/BAG R$/60 BAG kg R$/ton

Month Annual Month Annual Month Annual

Volatility - σ 8,55% 29,63% 8,49% 29,41% 10,25% 35,52%

Mean Rev, Coef - η 0,0660 0,7924 0,0254 0,3050 0,0877 1,0529

Long term Mean

Price - 30,19 43,13 458,33

Initial Price - P037,70 74,81 570,43

P

Simulation models used

Option calculated as bundle of european options through Monte Carlo Simulation;

Model used for GBM modeling (risk neutral):

Model used for MRM modeling (risk neutral):

λ: market price of risk for the series, obtained by regressing return of these to return of market

P

2

( )2

1

t t

t tP P e

2 2

1

1exp ln ln( ) (1 )

2 2

tt t

t t

eP P e P e

Results: Comparing MRM x MGB Results from Monte Carlo simulation (10,000 interactions

with @Risk) – Net revenue present value:

Stochastic Process: MRM GBM

InputNPV w/

DCF

NPV w/

options

NPV w/

DCF

NPV

w/options

Basic

Project

Soy 47.139,8750.216,44

40.938,2787.744,82

Castor 19.185,46 (28.122,24)

Option

Value

Soy 3.076,57 46.806,55

Castor 31.031,04 115.867,06

Limitations

Did not take into account correlation between the three variables

Did not consider investment costs, depreciation expenses of taxes

Several other options are available which were not included

Castor seed supply is not guaranteed Business feasibility of the project was not

appraised Possible future drop in husks prices due to

increase in larger was disregarded