Transcript Diapositiva 1

MINING ORE VALUATION
BY REAL OPTION
UNDER UNCERTAINTY
AND RISK
Ph.D Manuel Viera
Ceo& Managing Partner Metaproject S.A
www.metaproject.cl
Strategic Mining Investments
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Are exposed to a high level of uncertainty
Big amounts of money on the table
Complex capital structures.
Political risk and all kinds of financial risk.
Flexibility is really important
Open Pit at Codelco´s Andina Division
Zaldivar Open Pit (Placer Dome) and Escondida Open Pit (BHP Billiton)
Blast at Codelco´s Chuquicamata Mine
The companies are getting aware of the risks importance and the impact that they have in the
commercial value and in the resource estimation models.
The real options are now the technique that allows in some way to value and control the risk cover
of the business.
The company valuation could help to respond questions like:
 ¿How much is my business worth?
 ¿How much has been the investment profitability of my business?
 ¿What could be done to improve this profitability and create value?
When ore deposit is economically attractive, arise a
series of questions such as:
How big are the known reserves?
What is the level of confidence?
What is the level of risk associated with?
Which is the expected return?
Value Quality and Risk How increase
NPV?
EVA
Income
Costs
+
-
La Gestión de
Calidad y Riesgo
se justifica si el
beneficio es mayor
a su costo
Quality
Risk
Forecast: Estim ación
10,000 Trials
Frequency Chart
9 Outliers
.025
251
.019
188.2
.013
125.5
.006
62.75
.000
0
180
215
250
285
Certainty is 50.24% from 245 to +Infinity
NPV Expected value
320
DECISION MAKING
HEURÍSTICA DE DECISIÓN - RISKMANAGEMENT
a) Costo Incertidumbre = 0
(p)
0
Fig. D.6
E(NPV)
NPV (+)
b) Hay Costo Incertidumbre (Mayoría de los Proyectos Mineros)
(p)
(-)
0
E(NPV)
VAN (+)
c) Costo Incertidumbre = Flujos de Caja Futuros
(p)
(-)
- E(NPV)
0
NPV (+)
Evolution of Valuation Methods
• DCF analysis was introduced in the 1950’s and first
applied to petrochemical projects.
• Prior to that the Payback method prevailed.
• Sensitivity and Scenario analysis were developed at
the US Air Force and the first corporate use occurred
at Shell later in that decade.
• The advent of computers brought simulation
methods in the 1960’s and decision trees.
• Option theory was developed in 1973, and
applications to real assets occurred a few years
later.
Evolution of Valuation Methods
1930-1950
1950’s
Sensitivity
Analysis
DCF
NPV
IRR
Impact of
Variables
Source:Brandao
1960’s
Simulation
Decision
Trees
1970’s
Option
Pricing
Risk Analysis Risk
CAPM
Management
1980’s
Real Option
Valuation
Value of
Information
Strategic
Considerations
Alternative methods to price real
options
• Analitic (closed formula) models like BlackScholes:Big biases because their
assumptions are unrealistic
• Traditional decision trees.
• Binomial models (lattices).-Good alternative
but we need to know the binomial process
parameters for the underlying project.
• Montecarlo simulation.- Maybe a black box
Mining Projects Integral Evaluation
Methodology through Real Options
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Step 1: Review and Define the Mining Business Strategy
Step 2: Determine Geological Uncertainty Level .
Step 3: Perfect Information Level and Information Quality
Step 4: Mining Resources Cubication and Valuation.
Step 5: Determination of Engineering Level (Information
Quality).
Step 6: Calculation of Optimal Production Rate.
Step 7: Metals and main Supplies Price Projection.
Step 8: Determination of the Project’s Risks and Dangers.
Step 9: The Normal Portfolio of Projects , to determine which
candidates will be evaluated by Real Options
Step 10: Scenarios and variables taken into account to Evaluate
Projects.
Step 11: Definition of the Decision Trees with Flexibilities.
Step12: Selection of the Strategic Flexibilities and Options
ROV VALUE FOR PROJECT
CHARACTERISTICS
FLEXIBILITY
UNCERTAINTY
UNCERTAINTY
HIGH
LOW
Moderate
Value
HIGH
High Value
LOW
Low Value
Moderate Value
Strategic Flexibilities and Options
in a Mining Project
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Option to Postpone the Decision
Option of Expansion
Option of Closure
Option of Knowledge
Option of Technological Package Selection
Option of Optimal Production Rate Selection
Option of Product Quality Improvement
Option to anticipate with the Mining Infrastructure
Preparation and Development
• Option of Selection of the Exploitation Method
02/01/2006
02/01/2005
02/01/2004
02/01/2003
02/01/2002
02/01/2001
02/01/2000
02/01/1999
02/01/1998
02/01/1997
02/01/1996
02/01/1995
02/01/1994
02/01/1993
02/01/1992
02/01/1991
02/01/1990
02/01/1989
METAL PRICE SIMULATION MODEL
450
400
350
300
250
200
150
100
50
0
Brownian Motion with Jumps Model
(Discrete Time Version)
xt 1  xt e
t
Pt 1  e
 x 1  e
1 e
   2
t



 1 e 2
x

0.5
 t 1





Pt  e
2t
xt
t

N  0,1
  2   u  d ·E  2    
  


  
2


x  ln  P 
Being P the mean price to which the series reverts; with a reversion rate  per time
unit, for a time variation t , with a volatility of  . And with frequency parameters of
upwards and downwards u , d subject to a probability distribution of jump size  .
.
Jumps in Copper Price Movements
0.2
Rendimiento diario Precio Cobre
Jumps up
Jumps down
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
03/12/1990
02/11/1992
03/10/1994
02/09/1996
03/08/1998
03/07/2000
03/06/2002
03/05/2004
03/04/2006
Forecast Oil Price ???
120
1982
Tendencia prevista
1981
Dolares por Barril
100
80
1984
60
1985
1986
1987
40 Actual
1991
20
0
1975
1995
1980
1985
1990
Año
1995
2000
2005
Fuente: U.S. Department of Energy,
1998
CASE STUDY
The project consists in applying the Real Options methodology to a real case, that is,
in evaluating the flexibilities to invest in a new in-depth exploitation method. The
options and flexibilities defined for this case are the following:
- Option of Optimal Closure
- Option of Expand from 97 KTPD to 140 KTPD
- Option to Postpone to 1 and 3 years
- Option to Improve Product Quality (diminish the metallurgical recuperation
volatility and Ore grade).
Mining Modeling
Optimum rate production
RITMO DE PRODUCCION METODO ECONOMICO
6.00
Mackenzie
3346 TPD
5.00
4.00
5.00
T
A
Y
L
O
R
Taylor (limite Inferior)
2910TPD
3.00
0.00
-5.00
Williams
4500 TPD
2.00
1.00
-10.00
VAN
3
4
9
1
T
P
D
-15.00
-20.00
7,661
7,842
7,300
7,481
7,119
6,758
1.00
6,939
6,397
6,578
6,036
6,217
5,856
5,494
5,675
5,133
5,314
4,953
4,592
4,772
4,231
4,411
4,050
3,689
3,869
3,328
3,508
3,147
2,786
2,967
2,425
2,606
2,244
1,883
2,064
1,522
1,703
1,161
1,342
0.00
800
DELTA VAN
10.00
Taylor (limite Superior)
4364 TPD
-25.00
-30.00
2.00
-35.00
RITMO DE PRODUCCION
MACKENZIE
TAYLOR
WILLIAMS
Alway there are Risk anyplaces
Please give me the dry device
Table 2: Simulation parameters
Variables
Copper
Molybdenum
Initial price
Time variation t (years)
Temporal Horizont, T (years)
Long-term mean price
Ln (average price), x
Annual reversion speed, 
Reversion Speed per Time Variation
Half Life
Annual Volatility
Upwards leaps Frequency ‫גּ‬u
(5)
Downwards leaps Frequency ‫גּ‬d (5)
Upwards leap size
Downwards leap size
E[Ф²]
342
1
79
120
4.79
0.35
0.35
2
27.38%
0.20
0.20
0.20
-0.10
0.52
28
1
79
22
3
0.35
2
42.64%
0.20
0.20
0.20
-0.10
0.52
Table 3: Montecarlo Simulation Results
NVP (KUS$)
Basic Case
Closure Option
Deterministic
Evaluation
Real Option Result
3186
4756
NVP (KUS$)
Expansion Option
4937
NVP (KUS$)
Postponing 1 year Option
4842
RESULTS Other Case
RESULTADOS DEL ANALISIS DE RIESGO
VAN ( KUS$ ) OPCION SIN AMPLIACION
Summary Information
W orkbook Name
Aplicación Risk.xls
Number of Simulations
1
Number of Iterations
1000
Number of Inputs
14
Number of Outputs
6
Sampling Type
Latin Hypercube
Simulation Start Time
12/06/2007 19:53
Simulation Stop Time
12/06/2007 19:53
Simulation Duration
00:00:06
Random Seed
Statistic
Minimum
30.235
Maximum
243.842
10%
44.237
Mean
112.840
15%
56.775
50.996
20%
66.720
2600550450
25%
77.894
Skewness
0,104700992
30%
84.783
Kurtosis
2,458965983
35%
90.266
Median
110.627
40%
95.907
Mode
127.288
45%
103.076
30.235
50%
110.627
Left X
Left P
5%
55%
117.398
Right X
199.598
60%
125.511
Right P
95%
65%
132.812
Diff X
169.363
70%
140.935
Diff P
90%
75%
149.672
0
80%
159.491
Filter Min
85%
168.217
Filter Max
90%
180.769
95%
199.598
#Errors
#Filtered
Regression Sensitivity for VAN (
KUS$ )/D257
, 956
VALOR ESPERADO / US$/ TMS/ AD60
, 161
VALOR ESPERADO / US$/ TMS/ AD66
, 146
-, 06
K US$ / U S$/T/ D73
F L UJO D E CAJA / -2/F 233
, 024
L EY CUT / 1/ I37
-1
-0,75
Rank
, 254
, 005
-0,5
-0,25
0
0,25
Std b Coefficients
0,5
0,75
1
Value
5%
Variance
L EY CUT / 1/ I37
Summary Statistics
Value
%tile
-19.369
Std Dev
VALOR ESPERADO / US$/ TMS/ AD52
1325422007
0
Sensitivity
Name
Regr
Corr
#1
VALOR ESPERADO
0,956
/ US$/TMS / $AD$52
0,936
#2
LEY CUT / 1 / $I$37
0,254
#3
VALOR ESPERADO
0,161
/ US$/TMS / $AD$60
0,085
#4
VALOR ESPERADO
0,146
/ US$/TMS / $AD$66
0,199
#5
KUS$ / US$/T / $D$73
-0,060
#6
FLUJO DE CAJA / -2
0,024
/ $F$233
0,064
#7
LEY CUT / 1 / $I$37
0,005
0,039
#8
VALOR ESPERADO
0,000
/ US$/TMS / $AD$72
0,012
#9
VALOR ESPERADO
0,000
PRECIO / US$/TMS
0,048 / $AD
#10
VALOR ESPERADO
0,000
/ US$/TMS / $AD$60
0,028
#11
VALOR ESPERADO
0,000
/ US$/TMS / $AD$66
0,057
#12
VALOR ESPERADO
0,000
/ US$/TMS / $AD$72
-0,011
#13
KUS$ / US$/T / $D$73
0,000
0,004
#14
FLUJO DE CAJA / -2
0,000
/ $F$233
0,030
#15
#16
0,182
-0,064
RESULTS
VAN CASO BASE V/S VAN CON AMPLIACIÓN a 60.000 TPM
Mina Cinabrio- C.M. Punitaqui
Metaproject S.A
Mining Plan 2011
Nv-370
Nv-350
Nv-330
C-13
Nv-305
C-18
C-17
C-16 C-15
C-14
Nv-275
C-21
C-20
C-19
Nv-245
C-22
Nv-220
C-24
C-23
Nv-190
C-27
C-26
Nv-160
C-30
C-29 C-28
Nv-135
C-31
Nv-115
C-32
Nv-80
C-34
Nv-50
Nv-25
C-35
C-33
C-25
Cuadro de valoraciòn de Activos por el mètodo del Valor In situ
Recursos
Factor(1)
Mtm
Mt Cu Fino cUS$/Lb
200
300
345,7
400
3086,4
4629,7
5334,9
6172,9
1,3
1,3
1,3
1,3
(1) según metricas de Valor VCD Enero 2007
Valor Activo in situ
MUS$
40,1
60,2
69,4
80,2
Main conclusions
a) The Latin Hypercube or Montecarlo Simulation with
reversion to the mean has resulted to be a good
copper and molybdenum price forecast model,
allowing a better valuation of the mining property
project.
b) The NPV criterion is rigid and doesn’t allow
visualizing the strategic value of mining flexibilities.
The Option to expand has resulted as the best
decision.
c) The DELPHI/HAZOP experts panel is a good method
to determine the uncertainty level of the ore deposit,
in order to apply the Options theory.
MAIN CONCLUSIONS
•
•
The Latin Hypercube or Montecarlo Simulation with
reversion to the mean has resulted to be a good
copper and molybdenum price forecast model,
allowing a better valuation of the mining property
project.
The NPV criterion is rigid and doesn’t allow visualizing
the strategic value of mining flexibilities. The Option to
expand has resulted as the best decision.
•
The DELPHI/HAZOP experts panel is a good method
to determine the uncertainty level of the ore deposit, in
order to apply the Options theory.