Transcript Production Functions - Massachusetts Institute of Technology

Use of Simulation in Valuation
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
Use of Simulation

Slide 1 of 19
Outline

Concept of Simulation
—
What is it? How is it done?
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Using Simulation to Value Options
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Key Concept: Operating Rules

Example: Antamina Mine (other Slide show)
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Creation of VARG for Simulation
—
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And for Lattice… And Decision Analysis
Recall Garage Case
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Use of Simulation

Slide 2 of 19
What is Simulation?

Replicates outcomes of uncertain process
(often called “Monte Carlo” simulation)
—
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As in “Garage case”
It provides a way to describe what may
occur, in the line of
Decision tree, which enables discrete, trendbreaking outcomes
— Lattice, based on expanding distribution over
time
—

Can use variety of irregular distributions
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Use of Simulation

Slide 3 of 19
Use of Simulation is New

Recent software makes simulation feasible
Simple example: Excel Add-in (see ESD 70)
— Expensive, slick example: Crystal Ball
—


1000’s of repetitions in seconds
Often, model of consequences simple, for
example, spreadsheet modeling profits
—

Example: Garage Case
More Complicated: See Antamina case
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Use of Simulation

Slide 4 of 19
Requirements for Simulation

Distributions for Key parameters
—

May be observed, assumed, estimated, or guessed
Examples:
Observed: Rainfall, river flows over years
— Assumed: Market data as GBM (price of metal)
— Estimated: Technical Cost Models (of mine ops)
— Guessed:
Judgment (ore quantity, quality)
—
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Use of Simulation

Slide 5 of 19
Simulation Process Consists of:
Step
Examples
1. Having a model of system
1. NPV of Mining
2. Defining the distributions of
key parameters
2. Ore quantities, price of
metal
3. Sampling a process or
distribution to...
3. Distribution of quality
of Ore in Mine
4. Obtain value of a parameter
4. Ore Quantity
5. Calculating the
consequences of that factor
5. Profit for that scenario
6. Repeating 1000’s of times, to
get pdf of consequence
6. Overall Profit
7. Calculating EV(NPV) and
plotting VARG curve
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Use of Simulation

Slide 6 of 19
Range for Option Value by Simulation

Both Market and Technical Uncertainties
This is a most important feature for real options
— Standard financial approach ignores technical
uncertainties of any project – why is this?
Reasoning is that investors can diversify among
projects and so should ignore project risks
— Project owners however cannot ignore!
—

Both types of real options
“on” projects, where technology is a “black box”
— “in” projects, with options designed into project
—
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Use of Simulation

Slide 7 of 19
Option Value by Simulation



Step 1: Get distribution of consequences
for plan or design without flexibility
=> NPV, EV(NPV); also VARG
Step 2: Repeat above, but considering
availability of option, and its exercise at
desired times
=> new NPV pdf, EV(NPV); VARG
Step 3: Value of Option is difference ;
VARG Comparison shows source of value
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Use of Simulation

Slide 8 of 19
Key Concept: Operating Rule

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How do we know when to exercise option?
In simulation, this time cannot be calculated
Why?
Because number of possible future paths,
states are too large to be searched
Procedure: set up a priori conditions for
when to exercise option
These known as “operating rule”
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Use of Simulation

Slide 9 of 19
Example of Operating Rule
Consider Parking Garage
 “Expand if demand > capacity for 2 years”


Why would this make sense?
=> Because, want some assurance that
growth is ‘permanent’
How could this be improved?
=> Change rule toward end of life? No
addition in last 5 years?
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Use of Simulation

Slide 10 of 19
Antamina Mine Example

General Context
Peru government wanted to develop a mine
— Mine had uncertain quality and quantity of ore
— Step 1: explore geology, topography for access
— Step 2: decide to develop and spend 3 years on
building facilities before getting profits in Year 6
—

Government plan
Required bidding on 2-stage process
— Companies must bid for right to explore and
must decide on development in 2 years
— Big penalty for not developing (why?)
—
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Use of Simulation

Slide 11 of 19
Antamina Mine -- Options

Option “on” project
Winning Company has “right, not obligation” to
abandon mine in 2 years  “European” put
— Option Cost = Price to Peru + Exploration Costs
— Strike Price = Costs forfeited to Peru
—

Options “in” project
Technical staff can create Options “in” system
— Ex: build up port during 2 years of exploration,
to provide “right, not obligation” to expedite
development in only 2 years – and thus advance
revenue stream by 1 year and increase NPV
—
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Use of Simulation

Slide 12 of 19
Antamina Mine Simulation

System Model: NPV of Profit as function of:
ore quality, quantity
— cost of mining
— value of metals (mostly copper, zinc and “moly”)
—

Distributions for Key parameters
Assumed: Market data as GBM (lattice evolution
from current price of metal)
— Estimated: Technical Cost Models (of mine ops)
— Guessed:
Expert Judgment, revised of exploration
of ore quantity, quality (as in a decision tree)
—
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Use of Simulation

Slide 13 of 19
Antamina Mine Valuation

Assumed operators could “lock in” price for
metal by long-term contracts over life of mine
—
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Probably not possible in fact. However, it is
necessary assumption to know value of ore to use
as basis for valuing NPV of mine over its life
Value of “on” Option = EV(all positive NPV) –
EV(project without option to abandon)
Value of “in” Option = further improvements
in NPV due to flexibility provided
See special Antamina slide show
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Use of Simulation

Slide 14 of 19
A break for Antamina Mine Slide Show
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Use of Simulation

Slide 15 of 19
Creation of VARG for Simulation
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At end of Simulation, we have many trials
What is probability of each?
They are equal
How do we get pdf?
“Binning” the outcomes by ranges (= bins)
—

Percent of samples in a bin = P(outcome in bin)
Note: We look at all simulations!
—
But binning process easily automated (see ESD 70)
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Use of Simulation

Slide 16 of 19
Creation of VARG for Lattice

Remember what lattice analysis provides:
Value at any state in a stage
— the best choice, by comparing expected values
— Information on distributions not cumulated
—
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So, how do we proceed?
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We have to create distribution of outcomes
Must look at each path – and thus all!
— Must look at probability of each path
— This determines pdf and then VARG
—
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We will distribute spreadsheet for this
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Use of Simulation

Slide 17 of 19
Creation of VARG for Decision Analysis
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As with Lattice, must look at all paths and
probability of each
Task simpler in general – why?
Because fewer stages, and thus fewer
possible paths
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Use of Simulation

Slide 18 of 19
Take-Aways

Simulation is a useful way to represent pdfs
of outcomes that will define value of option
—
Computationally efficient

Can deal with all kinds of uncertainties
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Relatively easy to explain to decision-makers
No complicated math
— No confusing trees or “messy bushes”
— No high-powered theory (see later in course)
—
CAN BE A VERY GOOD APPROACH
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
Use of Simulation

Slide 19 of 19