Transcript Real Options

Allocation of Valuation Effort
With Example application to Copper Mine
Richard de Neufville
Professor of Engineering Systems and of
Civil and Environmental Engineering
MIT
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 1 of 45
Outline

Issue:
– Too many combinations to analyze
– Traditional Approach: very simplified


Analytic Problem: How do we take more
realistic approach, within available analytic
resources (time, modeling complexity)
Proposed Solution:
– Concept: Use of “Catalogs” of Conditions
– Implementation: Depends on Nature of Industry

Example: Analysis for a Garage, Copper Mine
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 2 of 45
The Analytic Issue

A complete analysis of an engineering system
involves modeling and optimizing:
– The basic infrastructure (the plant, the network, etc)
– Considering possible evolutions of several factors
over many periods (price and demand for products;
quality and quantity of mineral in deposit)
– Along with the many modes of operating the
infrastructure (routing of vehicles on network,
allocation of production lines to products, etc)
– To provide a range of measures of merit (Net
Present Value, Amount of Capital expense – Capex,
Return on Investment)
IMPRACTICAL TO DO COMPLETELY!
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 3 of 45
Graphical View: the full problem
S tag e fo r
S ystem
E lem en t
Initial D esign
C onfiguration of
Infrastructure
P rice, D em and,
Q uantity, etc
W ork P lans for
E xisting and
N ew F acilities
N P V , R O I,
C apex , etc
P eriodic D ata on
C ontex t F actors
P eriodic
M anagem ent
A djustm ents
P erform ance
M etrics
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
P o ssib ilities
M any
M any, ov er
m any periods
M any, ov er
m any periods
M any
Richard de Neufville
Allocation of Valuation Effort
©
Slide 4 of 45
Traditional Design Approach
Although Complex, Very Simplified Overall
S tag e fo r
S ystem
E lem en t
P o ssibilities
T rad ition al
D esig n P ractice
Initial D esign
C onfiguration of
Infrastructure
P rice, D em and,
Q uantity, etc
W ork Plans for
E xisting and
N ew F acilities
N P V , RO I,
C apex , etc
M any
M any
M any, ov er
m any periods
M any, ov er
m any periods
O ne V ector
(E ach 1 v alue)
N one
N ot considered
M any
O ne
(the focus)
P eriodic D ata on
C ontex t F actors
P eriodic
M anagem ent
A djustm ents
P erform ance
M etrics
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 5 of 45
Analytic Problem

We know that we can increase value by
– Recognizing Uncertainty
– Dealing Proactively with it, by creating options
– … and Enabling Management to Adjust
How do we take this more realistic approach,
within available analytic resources (time,
modeling complexity)?
 Specifically, how do we

– Focus effort on most productive parts? (Phd by
Bartolomei and other theses – next session)
– Expand Variables considered – and stay within
limits of capability (this session)
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 6 of 45
Size of Problem: Astronomical



A full analysis of variations is impractical
Example 1: possible price variations over 20
periods, if the price could be low, medium or
high. The total number of combinations would
be 3 (exp 20) ~ 2 ½ billion… And this is for
only 3 price levels!
Example 2: possible decisions rules for
expanding a facility (as in parking garage). One
could expand with 1, 2, or 3 units (say); at
different times; under different conditions.
Over 20 periods, the possibilities are orders of
magnitude greater than above.
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 7 of 45
Concept of Solution
We want a

Middle ground between
– the simplest possible assumption typically used
(e.g., price of copper is fixed over project life)
– Complete set of possibilities

Representative range of possibilities
– Small enough to be manageable analytically
– Broad enough to cover all major situations
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 8 of 45
Outline of solution



Use “Catalogs” of possible conditions
The “Catalogs” would provide scenarios
intended to describe relevant patterns
designers might wish to anticipate
Thus, instead of 320 combinations of 3 price
levels over 20 periods, we might consider a
“handful” of scenarios such as:
–
–
–
–
–
Steady rising and falling prices
High prices at beginning, low at end
Low prices at start, surge in prices at end
High volatility of prices around trend
Etc..
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 9 of 45
Graphical view of “Catalog” Approach
S tag e fo r
S ystem
E lem en t
P o ssibilities
“C atalo g”
Ap p ro ach
Initial D esign
M any
M any
P eriodic D ata on
C ontex t F actors
C onfiguration of
Infrastructure
P rice, D em and,
Q uantity, etc
M any, ov er
m any periods
P eriodic
M anagem ent
A djustm ents
P erform ance
M etrics
W ork Plans for
E xisting and
N ew F acilities
N P V , RO I,
C apex , etc
M any, ov er
m any periods
10 to 20
R eprese ntativ e
S cenarios
10 to 20
possible
respon se s
S ev eral
E (N P V ), C apex,
V alue at R isk
and G ain, etc
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
M any
Richard de Neufville
Allocation of Valuation Effort
©
Slide 10 of 45
Benefits of “Catalog” approach


Enables consideration of major scenarios
Encourages deeper investigation of
situations with greatest impact on
performance
– Additional Scenarios easily be added to Catalog


Can be tailored to design problem; Catalog
can be larger or smaller, focused on specific
uncertainties, etc.
Using modern computers, expanding
analysis effort factor of 100 or so is easy.
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 11 of 45
Unknowns about approach


Validity: Only a few applications so far. Seems
promising, but more validation needed
Definition of Catalog: How is this best done?
– All at once at start?
– Incrementally? from a starter set to more scenarios
determined according to their effect on performance

Detailed Characteristics: What level of detail
appropriate to this approximate approach?
A RESEARCH TOPIC !
See Cardin discussion of his thesis next time
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 12 of 45
Conceptual Application to Garage (1)

The traditional definition of the design problem
for “Garage Case” is:
S tag e fo r
S ystem
E lem en t
P o ssibilities
T rad ition al
D esig n P ractice
S tructural
D esign
P eriodic D ata on
C ontex t F actors
P eriodic
M anagem ent
A djustm ents
P erform ance
M etrics
N um ber of
F loors
P rice, D em and,
Q uantity, etc
P rice C hanges;
M ore Floors
M any
M any
M any, ov er
m any periods
M any, ov er
m any periods
O ne P rice,
D em and P rofile
N one
N ot considered
N P V , RO I,
C apex , etc
M any
O ne
(the focus)
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 13 of 45
Conceptual Application to Garage (2)

We expanded analysis, and looked at:
– many different possible demands
– Expansions with a simple decision rule
– Looked at Value at Risk and Gain (VARG)
“G arag e C ase
D esig n ”
S tag e fo r
S ystem
E lem en t
P o ssib ilities
S tructural
D esign
P eriodic D ata on
C ontex t F actors
N um ber of
F loors
P rice, D em and,
Q uantity, etc
M any
M any
M any, ov er
m any periods
P eriodic
M anagem ent
A djustm ents
P erform ance
M etrics
P rice C hanges;
M ore F loors
M any, ov er
m any periods
N P V , R O I,
C apex , etc
M any
O ne P rice,
1000s of
D em and P rofiles
Some
S im ple decision
rule
S everal
NPV, VARG
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 14 of 45
Conceptual Application to Garage (3)

As a next step, Cardin looked at range of
decision rules beyond one assumed:
– Sensitive to amount by which demand>capacity
– Stage in Life of project
– Relative size of addition relative to capacity, etc…
“G arag e C ase
D esig n ”
S tag e fo r
S ystem
E lem en t
P o ssib ilities
S tructural
D esign
P eriodic D ata on
C ontex t F actors
N um ber of
F loors
P rice, D em and,
Q uantity, etc
M any
M any
M any, ov er
m any periods
P eriodic
M anagem ent
A djustm ents
P erform ance
M etrics
P rice C hanges;
M ore F loors
M any, ov er
m any periods
O ne P rice,
1000s of
D em and P rofiles
CAT ALO G S
of decision rule s
N P V , R O I,
C apex , etc
M any
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
S everal
NPV, VARG
Richard de Neufville
Allocation of Valuation Effort
©
Slide 15 of 45
Research Questions


What is a good way to define members of
catalog?
How should search be expanded to more
members of catalog?

When should search be terminated?

Others?
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 16 of 45
Initial Application to Codelco


Codelco is the National Mining Company of
Chile (COmpania nacional DEL CObre)
It owns the biggest copper mines in the world,
near Calama, in North Chile
– Chuquicamata (“Chuqui”) is 4 km long, 2 km wide,
and 800 m deep - a hole as big as Cambridge and
half a mile deep)
– Is known to have enough copper to produce for 90
years at current rate
– More deposits anticipated, but not proven by drills

This project concerns secondary potential
mines – “Cluster Toki”
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 17 of 45
Recognition of Help


This work was done in collaboration with
Gerencia de Recursos Mineros y Desarollo,
Codelco Norte
– Miguel Romero Casanova
– Juan Carlos Peña

Gerencia Corporativa de Recursos Mineros,
Codelco Casa Matriz
– Felipe Azócar H.
– Cristián Barrientos Parant
– Miguel Cabrera Reyes
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 18 of 45
Site Map
Cluster Toki
consists of
the mines in
the lower left
side of the
photograph
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 19 of 45
Outline for Codelco case

Placing “Catalog Methodology” into context

Presenting the Analysis
– Part 1: Staged Analysis, designed to provide a
transparent view of process
– Part 2: Preliminary Results from full analysis
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 20 of 45
Traditional Evaluation of Mine

Design of basic infrastructure is simple:
– Crushing Mill,
– Fleet of BIG trucks

Crux of design lies in “mine plan” the
optimization of sequence of excavations into
body of sterile overburden and mineral
– Huge combinatorial problem ~ 50,000 blocks of
20m to 30m on a side, each with estimate of its
mineral content, etc.
– Takes time, effort, money
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 21 of 45
An Open Pit Mine
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Source: www.codelco.com
Richard de Neufville
Allocation of Valuation Effort
©
Slide 22 of 45
Blasting
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Source: www.codelco.com
Richard de Neufville
Allocation of Valuation Effort
©
Slide 23 of 45
Moving the rock
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Source: www.codelco.com
Richard de Neufville
Allocation of Valuation Effort
©
Slide 24 of 45
Big Trucks !
Source: Briony Hall, BBC News, 10 Dec.
2003 “Monster Trucks Transform
Mining” (in Botswana)
http://news.bbc.co.uk/2/hi/business/329
3889
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 25 of 45
Crushing Mill
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Source: www.codelco.com
Richard de Neufville
Allocation of Valuation Effort
©
Slide 26 of 45
Smelting
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Source: www.codelco.com
Richard de Neufville
Allocation of Valuation Effort
©
Slide 27 of 45
The Product: copper sheets
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Source: www.codelco.com
Richard de Neufville
Allocation of Valuation Effort
©
Slide 28 of 45
Graphical View of Traditional Analysis

The key analytical effort lies in the Mine Plan
S tag e fo r
S ystem
E lem en t
P o ssibilities
T rad ition al
D esig n P ractice
Initial D esign
S ize of C rushing
M ill and Truck
F leet
P rice, D em and,
Q uantity, etc
C hange in the
“M ine Plans”
A F ew
A F ew
M any, ov er
m any periods
M any, ov er
m any periods
O ne V ector
(E ach 1 v alue)
O ne M ine Plan
N P V , RO I,
C apex , etc
M any
O ne
(V A N = NP V )
P eriodic D ata on
C ontex t F actors
P eriodic
M anagem ent
A djustm ents
P erform ance
M etrics
Note: VAN = Valor Anual Neto = NPV
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 29 of 45
Graphical View of “Catalog” Analysis

Innovation: use of representative Mine Plans
and Price Vectors over time, not using
entirely new ones for each detailed variation
S ta g e fo r
S y s te m
E le m e n t
P o s s ib ilitie s
“C a ta lo g
A p p ro a c h ”
In itial D e sig n
S ize of C ru sh in g
M ill a n d T ru ck
F le e t
P rice, D em a n d ,
Q u a n tity, e tc
C h a n g e in th e
“M in e P la n s”
A F ew
A F ew
M a n y, ov e r
m a n y p e rio d s
M a n y, ov e r
m a n y p e rio d s
C A T A L O G of
P rice V e cto rs
C A T A L O G of
M in e P lan s
N P V , R O I,
C a p e x , etc
M any
S ev e ral
(V A N = N P V )
an d V AR G
P e rio d ic D a ta o n
C o n te x t F a cto rs
P e rio d ic
M anagem ent
A d ju stm e n ts
P e rfo rm a n ce
M e trics
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 30 of 45
Metodología
Schematic Methodology
Diseños
Posibles
Possible
Designs
Catalog of Mine Plans
Catalogo de Planes Mineros
Forecast: VAN - Caso Base
Condiciones Aleatorias
60
Frequency
(CH ; Mina)
(36;120)
(45;120)
50
Plan Minero
40
Plan 1
30
Plan 2
20
(36;160)
10
(45;160)
0
-541.305
.
.
-297.338
-53.371
190.596
Plan n
434.563
kUS$
Results
and yAnalysis
Resultados
Análisis
Resultados
y Análisis
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
VAN
Precio Favorable
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Caso 2
Caso 3
Caso 7
Caso Base
Richard de Neufville
Allocation of Valuation Effort
©
Slide 31 of 45
Part 1: Staged Application
Objective of this exercise:
 To demonstrate contribution of proposed
analysis method …


… to the understanding of the sources of
value in the project
… and thus improve the overall value of a
project
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 32 of 45
Concept of Staged Analysis



Starts from simplest situation: base case
with no fluctuation in the price over time, and
with only one long-term price
Step by step increases factors being
considered, for example
1. considering effect of fluctuations in price,
2. then, possible variations in average price,
etc
Until show comprehensive analysis
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 33 of 45
Object of Staged Procedure



To provide a transparent way to see how the
method works
… by indicating clearly the individual effects
of each change in the analysis
… and thus improve the understanding of
the sources of value for a project
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 34 of 45
Application Inspired by Toki



Data can be improved, examples only
Drawn from estimates prepared for other
analyses
Not yet suitable for any investment
planning…
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 35 of 45
Step A: Base Case

Description:
– Single design (Crushing Mill, Capacity) = (36,120)
– Average Price = 130 (historical average in $2005)
– No fluctuations in price over time
– No uncertainty about average price level

NPVA = 396
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 36 of 45
Step B: Includes Fluctuations

Description:
– Single design (Crushing Mill, Capacity) = (36,120)
– Average Price = 130 (historical average in $2005)
– Price varies around the average in a set pattern
– No uncertainty about average price level


NPVB = 541
NPVB - NPVA = + 145
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
(~ + 38%)
Richard de Neufville
Allocation of Valuation Effort
©
Slide 37 of 45
Lessons from Step B



Analysis with a constant price over time
does not reflect reality
Differences large (example: 38%) and
should not be ignored
Note: this particular difference due to cash
flow with early peak. Difference could be
negative.
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 38 of 45
Step C: with Price Level Uncertainty

Description:
– Single design (Crushing Mill, Capacity) = (36,120)
– Average Price = 130 (historical average in $2005)
– Fluctuations in price over life of mine
– Uncertainty about price level: +/- 30 = +/- 23%




NPVc (high price = 160) = 933 (~ + 72%)
NPVc (average price = 130) = 541
NPVc (low price = 100) = 230 (~ - 57%)
Note: Select mine plans according to price!
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 39 of 45
Lessons from Step C
Changes in NPV
 not proportional to Change in price
(a standard result, due to fixed costs)
 not symmetric – management chooses mine
plan depending on price level
 do not balance: + 392 – 3ll = + 81 (~ +15%)
 Must be better – management chooses
operations that improve performance

Differences large and should not be ignored
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 40 of 45
Summary from Staged Analysis



Standard Analysis, with known price without
variations over time, gives unrealistic view
Fluctuations over time must be considered –
offer important sources of improved value
through faster development with high prices
Uncertainty in long-term average prices must
be considered – offers important source of
value through choice of better mine plan
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 41 of 45
Part 2: Full Simulation Analysis



Description of Main Elements:
Variation in Copper Prices over time
Distribution is “log normal”
– negative prices are not permitted

With “regression to the mean”
– Mean is forecast long-term of US $1 /pound CuF
(Cobre Fino = Refined Copper)

Same Mine Plan for all cases
– Analytically difficult to change plans with prices
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 42 of 45
Results: Comparison with Base Case

Recognizing Uncertainty => Greater Value
100%
90%
80%
Frec Porcentual
70%
60%
50%
40%
30%
20%
10%
0%
-500.000 -400.000 -300.000 -200.000 -100.000
0
100.000 200.000 300.000 400.000 500.000 600.000
VAN (%)
Min_120 Ch_36 (BASE)
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Caso Base (Flat prices)
Richard de Neufville
Allocation of Valuation Effort
©
Slide 43 of 45
Explanation of Final Result

Prices can go up more than they go down
– $1 up to over $3 / pound
– $1 down to only about $0.70


Benefits of higher prices proportionately
greater than disbenefits of low prices
These factors combine to explain why the
recognition of variability in prices leads to
greater expected NPV
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 44 of 45
Discussion of Methodology


Methodology is a significant improvement on
current practice which is simplistic as regards
price levels and other outside factors
It is not complete. It does not use a different
mine plan for each simulation. This would
– take far too long
– Be very expensive

Method uses a “catalog” of mine plans
prepared ahead of analysis. These are
designed to be “representative”
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Allocation of Valuation Effort
©
Slide 45 of 45