1. Engineering Systems Analysis for Design Richard de Neufville  Massachusetts Institute of Technology Use of Simulation Slide 1 of 19 Use of Simulation in Valuation Richard de Neufville Professor of Engineering Systems and of Civil and Environmental Engineering MIT

2. Engineering Systems Analysis for Design Richard de Neufville  Massachusetts Institute of Technology Use of Simulation Slide 2 of 19 Outline l Concept of Simulation — What is it? How is it done? l Using Simulation to Value Options l Key Concept: Operating Rules l Example: Antamina Mine (other Slide show) l Creation of VARG for Simulation — And for Lattice… And Decision Analysis l Recall Garage Case

3. Engineering Systems Analysis for Design Richard de Neufville  Massachusetts Institute of Technology Use of Simulation Slide 3 of 19 What is Simulation? l Replicates outcomes of uncertain process (often called “Monte Carlo” simulation) — As in “Garage case” l It provides a way to describe what may occur, in the line of — Decision tree, which enables discrete, trend- breaking outcomes — Lattice, based on expanding distribution over time l Can use variety of irregular distributions

4. Engineering Systems Analysis for Design Richard de Neufville  Massachusetts Institute of Technology Use of Simulation Slide 4 of 19 Use of Simulation is New l Recent software makes simulation feasible — Simple example: Excel Add-in (see ESD 70) — Expensive, slick example: Crystal Ball l 1000’s of repetitions in seconds l Often, model of consequences simple, for example, spreadsheet modeling profits — Example: Garage Case l More Complicated: See Antamina case

5. Engineering Systems Analysis for Design Richard de Neufville  Massachusetts Institute of Technology Use of Simulation Slide 5 of 19 Requirements for Simulation l Distributions for Key parameters — May be observed, assumed, estimated, or guessed l 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)

6. Engineering Systems Analysis for Design Richard de Neufville  Massachusetts Institute of Technology Use of Simulation Slide 6 of 19 Simulation Process Consists of: Step 1.Having a model of system 2.Defining the distributions of key parameters 3.Sampling a process or distribution to... 4.Obtain value of a parameter 5.Calculating the consequences of that factor 6.Repeating 1000’s of times, to get pdf of consequence 7.Calculating EV(NPV) and plotting VARG curve Examples 1. NPV of Mining 2. Ore quantities, price of metal 3. Distribution of quality of Ore in Mine 4. Ore Quantity 5. Profit for that scenario 6. Overall Profit

7. Engineering Systems Analysis for Design Richard de Neufville  Massachusetts Institute of Technology Use of Simulation Slide 7 of 19 Range for Option Value by Simulation l 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! l Both types of real options — “on” projects, where technology is a “black box” — “in” projects, with options designed into project

8. Engineering Systems Analysis for Design Richard de Neufville  Massachusetts Institute of Technology Use of Simulation Slide 8 of 19 Option Value by Simulation l Step 1: Get distribution of consequences for plan or design without flexibility => NPV, EV(NPV); also VARG l Step 2: Repeat above, but considering availability of option, and its exercise at desired times => new NPV pdf, EV(NPV); VARG l Step 3: Value of Option is difference ; VARG Comparison shows source of value

9. Engineering Systems Analysis for Design Richard de Neufville  Massachusetts Institute of Technology Use of Simulation Slide 9 of 19 Key Concept: Operating Rule l How do we know when to exercise option? l In simulation, this time cannot be calculated l Why? l Because number of possible future paths, states are too large to be searched l Procedure: set up a priori conditions for when to exercise option l These known as “operating rule”

10. Engineering Systems Analysis for Design Richard de Neufville  Massachusetts Institute of Technology Use of Simulation Slide 10 of 19 Example of Operating Rule Consider Parking Garage l “Expand if demand > capacity for 2 years” l Why would this make sense? => Because, want some assurance that growth is ‘permanent’ l How could this be improved? => Change rule toward end of life? No addition in last 5 years?

11. Engineering Systems Analysis for Design Richard de Neufville  Massachusetts Institute of Technology Use of Simulation Slide 11 of 19 Antamina Mine Example l 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 l 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?)

12. Engineering Systems Analysis for Design Richard de Neufville  Massachusetts Institute of Technology Use of Simulation Slide 12 of 19 Antamina Mine -- Options l 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 l 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

13. Engineering Systems Analysis for Design Richard de Neufville  Massachusetts Institute of Technology Use of Simulation Slide 13 of 19 Antamina Mine Simulation l System Model: NPV of Profit as function of: — ore quality, quantity — cost of mining — value of metals (mostly copper, zinc and “moly”) l 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)

14. Engineering Systems Analysis for Design Richard de Neufville  Massachusetts Institute of Technology Use of Simulation Slide 14 of 19 Antamina Mine Valuation l Assumed operators could “lock in” price for metal by long-term contracts over life of mine — 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 l Value of “on” Option = EV(all positive NPV) – EV(project without option to abandon) l Value of “in” Option = further improvements in NPV due to flexibility provided l See special Antamina slide show

15. Engineering Systems Analysis for Design Richard de Neufville  Massachusetts Institute of Technology Use of Simulation Slide 15 of 19 A break for Antamina Mine Slide Show

16. Engineering Systems Analysis for Design Richard de Neufville  Massachusetts Institute of Technology Use of Simulation Slide 16 of 19 Creation of VARG for Simulation l At end of Simulation, we have many trials l What is probability of each? l They are equal l How do we get pdf? l “Binning” the outcomes by ranges (= bins) — Percent of samples in a bin = P(outcome in bin) l Note: We look at all simulations! — But binning process easily automated (see ESD 70)

17. Engineering Systems Analysis for Design Richard de Neufville  Massachusetts Institute of Technology Use of Simulation Slide 17 of 19 Creation of VARG for Lattice l Remember what lattice analysis provides: — Value at any state in a stage — the best choice, by comparing expected values — Information on distributions not cumulated l So, how do we proceed? l 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 l We will distribute spreadsheet for this

18. Engineering Systems Analysis for Design Richard de Neufville  Massachusetts Institute of Technology Use of Simulation Slide 18 of 19 Creation of VARG for Decision Analysis l As with Lattice, must look at all paths and probability of each l Task simpler in general – why? l Because fewer stages, and thus fewer possible paths

19. Engineering Systems Analysis for Design Richard de Neufville  Massachusetts Institute of Technology Use of Simulation Slide 19 of 19 Take-Aways l Simulation is a useful way to represent pdfs of outcomes that will define value of option — Computationally efficient l Can deal with all kinds of uncertainties l 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