Use of Simulation in Valuation Outline for today - MIT
Use of Simulation in Valuation Outline for today - MIT
Use of Simulation in Valuation Outline for today - MIT
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<strong>Use</strong> <strong>of</strong> <strong>Simulation</strong> <strong>in</strong> <strong>Valuation</strong><br />
Richard de Neufville<br />
Pr<strong>of</strong>essor <strong>of</strong> Eng<strong>in</strong>eer<strong>in</strong>g Systems<br />
and <strong>of</strong><br />
Civil and Environmental Eng<strong>in</strong>eer<strong>in</strong>g<br />
<strong>MIT</strong><br />
Eng<strong>in</strong>eer<strong>in</strong>g Systems Analysis <strong>for</strong> Design Richard de Neufville ©<br />
Massachusetts Institute <strong>of</strong> Technology <strong>Use</strong> <strong>of</strong> <strong>Simulation</strong> Slide 1 <strong>of</strong> 17<br />
Outl<strong>in</strong>e <strong>for</strong> <strong>today</strong><br />
• Context: Approaches to <strong>Valuation</strong><br />
• <strong>Simulation</strong> Procedures<br />
• Example <strong>of</strong> <strong>Use</strong>: Antam<strong>in</strong>a M<strong>in</strong>e<br />
— Separate Slide show<br />
Eng<strong>in</strong>eer<strong>in</strong>g Systems Analysis <strong>for</strong> Design Richard de Neufville ©<br />
Massachusetts Institute <strong>of</strong> Technology <strong>Use</strong> <strong>of</strong> <strong>Simulation</strong> Slide 2 <strong>of</strong> 17<br />
Page 1
Context <strong>for</strong> Option <strong>Valuation</strong>s<br />
• Many Approaches to <strong>Valuation</strong>, differ<strong>in</strong>g by<br />
way they Model and Value Uncerta<strong>in</strong>ty<br />
• Presentation so far <strong>of</strong> Standard Choices<br />
— DCF, Decision Analysis, Black-Scholes etc<br />
• Beg<strong>in</strong>n<strong>in</strong>g Now: New, pragmatic approaches<br />
— <strong>Use</strong> <strong>of</strong> <strong>Simulation</strong> (Antam<strong>in</strong>a M<strong>in</strong>e)<br />
— F<strong>in</strong>d<strong>in</strong>g Options (Bartolomei, Kalligeros)<br />
— Hybrid Analysis (Neely, auto case)<br />
— Non-Recomb<strong>in</strong>ant Lattices (Wang)<br />
Eng<strong>in</strong>eer<strong>in</strong>g Systems Analysis <strong>for</strong> Design Richard de Neufville ©<br />
Massachusetts Institute <strong>of</strong> Technology <strong>Use</strong> <strong>of</strong> <strong>Simulation</strong> Slide 3 <strong>of</strong> 17<br />
Context <strong>for</strong> <strong>Valuation</strong>s -- Table<br />
Model<strong>in</strong>g <strong>of</strong> Uncerta<strong>in</strong>ty<br />
<strong>Simulation</strong><br />
Non-Recombi<br />
-nant Lattice<br />
GBM<br />
Lattice<br />
Subjective<br />
Probabilities<br />
None<br />
Garage<br />
Case<br />
DCF<br />
None<br />
Homework<br />
Assignment<br />
Homework<br />
Assignment<br />
Decision<br />
Analysis<br />
CAPM<br />
Neely<br />
Hybrid<br />
<strong>Valuation</strong> <strong>of</strong> Uncerta<strong>in</strong>ty<br />
Eng<strong>in</strong>eer<strong>in</strong>g Systems Analysis <strong>for</strong> Design Richard de Neufville ©<br />
Massachusetts Institute <strong>of</strong> Technology <strong>Use</strong> <strong>of</strong> <strong>Simulation</strong> Slide 4 <strong>of</strong> 17<br />
Antam<strong>in</strong>a<br />
Example<br />
Wang<br />
Thesis<br />
Black-S.<br />
B<strong>in</strong>omial<br />
Replicat<strong>in</strong>g<br />
Portfolio<br />
Page 2
Context <strong>for</strong> <strong>Valuation</strong>s -- Issue<br />
• Given Many <strong>Valuation</strong> Possibilities…<br />
• The question is, which do we choose?<br />
• At present, no def<strong>in</strong>itive answer …<br />
• A subject <strong>of</strong> much research<br />
• Rest <strong>of</strong> Semester presents some recent<br />
developments – start<strong>in</strong>g with <strong>Simulation</strong><br />
Eng<strong>in</strong>eer<strong>in</strong>g Systems Analysis <strong>for</strong> Design Richard de Neufville ©<br />
Massachusetts Institute <strong>of</strong> Technology <strong>Use</strong> <strong>of</strong> <strong>Simulation</strong> Slide 5 <strong>of</strong> 17<br />
Outl<strong>in</strong>e <strong>of</strong> <strong>Simulation</strong> Portion<br />
• What is <strong>Simulation</strong>?<br />
• How is it done?<br />
• General Procedure <strong>for</strong> us<strong>in</strong>g<br />
<strong>Simulation</strong> to Value Options<br />
• Example: Antam<strong>in</strong>a M<strong>in</strong>e<br />
Eng<strong>in</strong>eer<strong>in</strong>g Systems Analysis <strong>for</strong> Design Richard de Neufville ©<br />
Massachusetts Institute <strong>of</strong> Technology <strong>Use</strong> <strong>of</strong> <strong>Simulation</strong> Slide 6 <strong>of</strong> 17<br />
Page 3
What is <strong>Simulation</strong>?<br />
• Replicates outcomes <strong>of</strong> a probabilistic process<br />
(<strong>of</strong>ten called “Monte Carlo” simulation)<br />
— As <strong>in</strong> “Garage case”<br />
• It provides a way to describe what may occur,<br />
<strong>in</strong> the l<strong>in</strong>e <strong>of</strong><br />
— Decision tree, which enables discrete, trendbreak<strong>in</strong>g<br />
outcomes<br />
— Lattice, based on expand<strong>in</strong>g distribution over time<br />
• Can use any variety <strong>of</strong> irregular distributions<br />
Eng<strong>in</strong>eer<strong>in</strong>g Systems Analysis <strong>for</strong> Design Richard de Neufville ©<br />
Massachusetts Institute <strong>of</strong> Technology <strong>Use</strong> <strong>of</strong> <strong>Simulation</strong> Slide 7 <strong>of</strong> 17<br />
<strong>Use</strong> <strong>of</strong> <strong>Simulation</strong> is New<br />
• Recent s<strong>of</strong>tware makes simulation feasible<br />
— Simple example: Excel Add-<strong>in</strong> (see ESD 70)<br />
— Expensive, slick example: Crystal Ball<br />
• 1000’s <strong>of</strong> repetitions <strong>in</strong> seconds<br />
• Often, model <strong>of</strong> consequences simple, <strong>for</strong><br />
example, spreadsheet model<strong>in</strong>g pr<strong>of</strong>its<br />
— Example: Garage Case<br />
• More Complicated: See Antam<strong>in</strong>a case<br />
Eng<strong>in</strong>eer<strong>in</strong>g Systems Analysis <strong>for</strong> Design Richard de Neufville ©<br />
Massachusetts Institute <strong>of</strong> Technology <strong>Use</strong> <strong>of</strong> <strong>Simulation</strong> Slide 8 <strong>of</strong> 17<br />
Page 4
Requirements <strong>for</strong> <strong>Simulation</strong><br />
• Distributions <strong>for</strong> Key parameters<br />
— May be observed, assumed, estimated, or guessed<br />
• Examples:<br />
— Observed: Ra<strong>in</strong>fall, river flows over years<br />
— Assumed: Market data as GBM (price <strong>of</strong> metal)<br />
— Estimated: Technical Cost Models (<strong>of</strong> m<strong>in</strong>e ops)<br />
— Guessed: Judgment (ore quantity, quality)<br />
Eng<strong>in</strong>eer<strong>in</strong>g Systems Analysis <strong>for</strong> Design Richard de Neufville ©<br />
Massachusetts Institute <strong>of</strong> Technology <strong>Use</strong> <strong>of</strong> <strong>Simulation</strong> Slide 9 <strong>of</strong> 17<br />
<strong>Simulation</strong> Process Consists <strong>of</strong>:<br />
1. Hav<strong>in</strong>g a model <strong>of</strong> system (Ex: NPV <strong>of</strong> m<strong>in</strong><strong>in</strong>g)<br />
2. Def<strong>in</strong><strong>in</strong>g the distributions <strong>of</strong> key parameters<br />
(Ex: ore quantities, price <strong>of</strong> metal)<br />
3. Sampl<strong>in</strong>g a process (Ex: the distribution <strong>of</strong> the<br />
quality <strong>of</strong> ore <strong>in</strong> a m<strong>in</strong>e), to...<br />
4. Obta<strong>in</strong> a value <strong>of</strong> a parameter (Ex: ore quality)<br />
5. Calculat<strong>in</strong>g the consequences <strong>of</strong> that factor (Ex:<br />
the pr<strong>of</strong>it from that m<strong>in</strong>e)<br />
6. Repeat<strong>in</strong>g 1000’s <strong>of</strong> times, to get probability<br />
distribution <strong>of</strong> consequence (Ex: the pr<strong>of</strong>it)<br />
7. Calculat<strong>in</strong>g EV(NPV) and plott<strong>in</strong>g Value at Risk<br />
and Ga<strong>in</strong> (VARG) curve<br />
Eng<strong>in</strong>eer<strong>in</strong>g Systems Analysis <strong>for</strong> Design Richard de Neufville ©<br />
Massachusetts Institute <strong>of</strong> Technology <strong>Use</strong> <strong>of</strong> <strong>Simulation</strong> Slide 10 <strong>of</strong> 17<br />
Page 5
Option Value by <strong>Simulation</strong><br />
• Step 1: Get distribution <strong>of</strong> consequences<br />
(Ex: pr<strong>of</strong>itability <strong>of</strong> M<strong>in</strong>e) and expected NPV<br />
• Step 2: Assume option exercised only <strong>in</strong><br />
favorable circumstances, thus drop<br />
unpr<strong>of</strong>itable outcomes from distribution<br />
=> revised NPV distribution, EV(NPV)<br />
• Step 3: Value <strong>of</strong> Option is difference<br />
Eng<strong>in</strong>eer<strong>in</strong>g Systems Analysis <strong>for</strong> Design Richard de Neufville ©<br />
Massachusetts Institute <strong>of</strong> Technology <strong>Use</strong> <strong>of</strong> <strong>Simulation</strong> Slide 11 <strong>of</strong> 17<br />
Range <strong>for</strong> Option Value by <strong>Simulation</strong><br />
• Both Market and Technical Uncerta<strong>in</strong>ties<br />
— This is a most important feature <strong>for</strong> real options<br />
— Standard f<strong>in</strong>ancial approach ignores technical<br />
uncerta<strong>in</strong>ties <strong>of</strong> any project – why is this?<br />
Reason<strong>in</strong>g is that <strong>in</strong>vestors can diversify among<br />
projects and so should ignore project risks<br />
— Project owners however cannot ignore!<br />
• Both types <strong>of</strong> real options<br />
— “on” projects, where technology is a “black box”<br />
— “<strong>in</strong>” projects, with options designed <strong>in</strong>to project<br />
Eng<strong>in</strong>eer<strong>in</strong>g Systems Analysis <strong>for</strong> Design Richard de Neufville ©<br />
Massachusetts Institute <strong>of</strong> Technology <strong>Use</strong> <strong>of</strong> <strong>Simulation</strong> Slide 12 <strong>of</strong> 17<br />
Page 6
Antam<strong>in</strong>a M<strong>in</strong>e Example<br />
• General Context<br />
— Peru government wanted to develop a m<strong>in</strong>e<br />
— M<strong>in</strong>e had uncerta<strong>in</strong> quality and quantity <strong>of</strong> ore<br />
— Step 1: explore geology, topography <strong>for</strong> access<br />
— Step 2: decide to develop and spend 3 years on<br />
build<strong>in</strong>g facilities be<strong>for</strong>e gett<strong>in</strong>g pr<strong>of</strong>its <strong>in</strong> Year 6<br />
• Government plan<br />
— Required bidd<strong>in</strong>g on 2-stage process<br />
— Companies must bid <strong>for</strong> right to explore and<br />
must decide on development <strong>in</strong> 2 years<br />
— Big penalty <strong>for</strong> not develop<strong>in</strong>g (why?)<br />
Eng<strong>in</strong>eer<strong>in</strong>g Systems Analysis <strong>for</strong> Design Richard de Neufville ©<br />
Massachusetts Institute <strong>of</strong> Technology <strong>Use</strong> <strong>of</strong> <strong>Simulation</strong> Slide 13 <strong>of</strong> 17<br />
Antam<strong>in</strong>a M<strong>in</strong>e -- Options<br />
• Option “on” project<br />
— W<strong>in</strong>n<strong>in</strong>g Company has “right, not obligation” to<br />
abandon m<strong>in</strong>e <strong>in</strong> 2 years “European” put<br />
— Option Cost = Price to Peru + Exploration Costs<br />
— Strike Price = Costs <strong>for</strong>feited to Peru<br />
• Options “<strong>in</strong>” project<br />
— Technical staff can create Options “<strong>in</strong>” system<br />
— Ex: build up port dur<strong>in</strong>g 2 years <strong>of</strong> exploration,<br />
to provide “right, not obligation” to expedite<br />
development <strong>in</strong> only 2 years – and thus advance<br />
revenue stream by 1 year and <strong>in</strong>crease NPV<br />
Eng<strong>in</strong>eer<strong>in</strong>g Systems Analysis <strong>for</strong> Design Richard de Neufville ©<br />
Massachusetts Institute <strong>of</strong> Technology <strong>Use</strong> <strong>of</strong> <strong>Simulation</strong> Slide 14 <strong>of</strong> 17<br />
Page 7
Antam<strong>in</strong>a M<strong>in</strong>e <strong>Simulation</strong><br />
• System Model: NPV <strong>of</strong> Pr<strong>of</strong>it as function <strong>of</strong>:<br />
— ore quality, quantity<br />
— cost <strong>of</strong> m<strong>in</strong><strong>in</strong>g<br />
— value <strong>of</strong> metals (mostly copper, z<strong>in</strong>c and “moly”)<br />
• Distributions <strong>for</strong> Key parameters<br />
— Assumed: Market data as GBM (lattice evolution<br />
from current price <strong>of</strong> metal)<br />
— Estimated: Technical Cost Models (<strong>of</strong> m<strong>in</strong>e ops)<br />
— Guessed: Expert Judgment to be revised by<br />
results <strong>of</strong> exploration (ore quantity, quality)<br />
Eng<strong>in</strong>eer<strong>in</strong>g Systems Analysis <strong>for</strong> Design Richard de Neufville ©<br />
Massachusetts Institute <strong>of</strong> Technology <strong>Use</strong> <strong>of</strong> <strong>Simulation</strong> Slide 15 <strong>of</strong> 17<br />
Antam<strong>in</strong>a M<strong>in</strong>e <strong>Valuation</strong><br />
• Assumed operators could “lock <strong>in</strong>” price <strong>for</strong><br />
metal by long-term contracts over life <strong>of</strong> m<strong>in</strong>e<br />
— Probably not possible <strong>in</strong> fact. However, it is<br />
necessary assumption to know value <strong>of</strong> ore to use<br />
as basis <strong>for</strong> valu<strong>in</strong>g NPV <strong>of</strong> m<strong>in</strong>e over its life<br />
• Value <strong>of</strong> “on” Option = EV(all positive NPV) –<br />
EV(project without option to abandon)<br />
• Value <strong>of</strong> “<strong>in</strong>” Option = further improvements<br />
<strong>in</strong> NPV due to flexibility provided<br />
• See special Antam<strong>in</strong>a slide show<br />
Eng<strong>in</strong>eer<strong>in</strong>g Systems Analysis <strong>for</strong> Design Richard de Neufville ©<br />
Massachusetts Institute <strong>of</strong> Technology <strong>Use</strong> <strong>of</strong> <strong>Simulation</strong> Slide 16 <strong>of</strong> 17<br />
Page 8
Take-Aways<br />
• <strong>Simulation</strong> is a useful way to represent pdfs<br />
<strong>of</strong> outcomes that will def<strong>in</strong>e value <strong>of</strong> option<br />
— Computationally efficient<br />
• Can deal with all k<strong>in</strong>ds <strong>of</strong> uncerta<strong>in</strong>ties<br />
— Contrast to B-S, lattice techniques<br />
• Relatively easy to expla<strong>in</strong> to decision-makers<br />
— No complicated math, no “replicat<strong>in</strong>g portfolio”,<br />
no confus<strong>in</strong>g trees or “messy bushes”<br />
CAN BE A VERY GOOD APPROACH<br />
Eng<strong>in</strong>eer<strong>in</strong>g Systems Analysis <strong>for</strong> Design Richard de Neufville ©<br />
Massachusetts Institute <strong>of</strong> Technology <strong>Use</strong> <strong>of</strong> <strong>Simulation</strong> Slide 17 <strong>of</strong> 17<br />
Page 9
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