Review of whole course

1
Review of whole course

• A thumbnail outline of major elements
• Intended as a study guide
• Emphasis on key points to be mastered
• REFER TO LAST YEARS EXAM POSTED

2
Major Elements Covered (1st half)

• Modeling of production possibilities
• Valuation Issues
• over time DR as opportunity cost, CAPM
• evaluation criteria
• Optimization of production and cost
• marginal analysis
• constrained optimization
• Decision Analysis
• Trees and Analysis
• Value of Information

3
Modeling of Production Possibilities

• Basic Concept Production Function
• locus of technical efficiency
• defined in terms of technology only
• Characteristics
• marginal products, marginal rates of substitution
• isoquants -- loci of equal production
• returns to scale ( ? economies of scale!)
• convexity of feasible region? Know when!
• Generally defined by systems models that
  calculate performance of possibilities

4
Trade Space
5
Valuation Issues -- over time

• Resources have value over time
• Discount rate (DR) , r /period
• Formulas ert for continuous compounding
• Choice of discount rate defined by best
  alternatives, at the margin
• DR 10 or more ? long term benefits beyond 20
  years have little consequence
• Money may change value via inflation
• Make sure you compare like with like

6
Valuation Issues CAPM

• Capital Asset Pricing Model Adjusts Discount Rate
  to reflect risk aversion
• Accounts for Unavoidable (market) risks
• Assumes Project risks can be avoided
• for investors, not so simple for owners
• Discount rate adjusted for relative volatility
  (by beta)
• r r (risk free) (beta) risk (market)
  - risk (free)

7
Valuation Issues WACC

• Weighted Average Cost of Capital reflects past
  experience based on historical data
• It is an average for organization
• as such, it may be appropriate for average
  projects
• Only reflects future opportunity costs to the
  extent that past trends extrapolate to future
• Is a reasonable first approximation

8
Valuation issues-- criteria

• Many types -- none best for all cases
• Net Present value -- no measure of scale
• Benefit / Cost -- sensitive to recurring
  costs
• Cost / Effectiveness -- no notion of value
• Internal Rate of Return -- ambiguous, does not
  reflect actual time value of
  money
• Pay-Back Period -- omits later returns
• Choose according to situation (if allowed)
• In practice, people may use several criteria
• Including VARG, Capex, Robustness

9
Optimization -- Marginal Analysis

• Economic efficiency merges technical
  opportunities (Prod. Fcn) and Values (Costs)
• For continuous functions, convex feasible region
  in domain of isoquants
• Optimization subject to Constraints
• Optimum when MP/MC ratios all equal
• Expansion path is locus of resources that define
  optimal designs
• Cost function Cost f(Optimum Production)
• Economies of Scale (? increasing returns to
  scale)
• Good Concepts, often not applicable in detail

10
Recognition of Uncertainty

• Psychology Resistance to this basic fact
• Descriptively Forecast always wrong
• Reasons surprises, trend-breakers
• Examples technical, market, political
• Theoretically Forecasts gt house of cards of
  difficult to defend assumptions about
• Data range
• Drivers of phenomenon (independent variables)
• Form of these variables
• Equation for model

11
Analysis under Uncertainty

• Primitive Models
• sensitivity to irrelevant alternatives, states
• sensitivity to basis of normalization
• Decision Analysis
• Organization of Tree
• Analysis
• Results
• ? those on Average forecasts (flaw of averages)
• Middle road, that provides flexibility to respond
• Second best choices, flexibility costs

12
Value of Information

• Extra information has value
• Value taken as improvement over base case
• Is compared to cost of getting information
• Value of Perfect Information
• Purely hypothetical / Easy to calculate
• Provides easy upper bound
• Value of Sample information
• Bayes Theorem
• Repeated calculations
• Worthwhile in important choices

13
Major Elements Covered (2nd half)

• Concept Option right, but not obligation
• Financial, on and in systems
• Lattice for future evolution
• Dynamic Programming for Optimization
• Path independence
• Cumulative return function
• Arbitrage pricing of options
• Concept, development of Black-Scholes Approach
• Meaning of q risk-neutral probabilities
• Issues in the choice of methods

14
Options

• Concept
• A right but not an obligation
• to do something (buy, sell, change design)
• Acquired with some effort (design change or cost)
• Financial -- those referring to traded assets
• Calls, Puts ( insurance) // American, European
• Real -- Applied to physical projects
• on and in projects
• The Mantra of the 3 types of options above

15
Spreadsheet Analysis

• Simplistic but transparent
• The Case of the Parking Garage
• Requires some decision rule for exercise
• Appears to provide good motivation
• Value at Risk and Gain (VARG) curves
• Cumulative distribution functions
• Show chance for any result or less or more
• Illustrate how options -- Reduce Downside Risk
  Increase Upside Opportunity
• Complement Expected NPV metric

16
Lattice Analysis

• Like a Decision Tree
• Binomial approach ? recombination cell merges
  ? analysis linear in N, stages
• Easily reproduces Normal and LogNormal
  distributions assumed associated with random
  events
• Formulas for u, d, and p depend on
• Sigma, the standard deviation
• nu, the average rate of growth
• p 0.5 0.5 (?/s)v?T u esv?T 1/d

17
Expected Value with Lattice

• Since Lattice provides easy way to represent
  distribution
• Can be used to show effect of uncertainty on
  value of project
• A (relatively) easy way to demonstrate
• Importance of considering Uncertainty
• Possibility of Major gains and losses
• Motivates Analysis of Options

18
Dynamic Programming

• Based on concept of independent stages that can
  assume variety of states
• Easiest to visualize as time, space sequences
• Can apply to separate projects
• Implicitly enumerates all possibilities
• Thus, works over non-convex feasible regions
• Crucial for situations with exponential growth
• Basic formula cumulative return function
• fS (K) Max or Min of giXi , fS-1 (K)

19
DP Valuation of Option

• DP is the way to value options in lattice
• Proceeds from end states
• Knowing these possibilities, can calculate best
  choice for previous stage
• Repeats to beginning
• Obtains best choice for each state in each stage
• Calculation of best choice
• do nothing versus exercise option values
• value discounted expected value of outcomes

20
DP in practice

• REFER TO BINOMIAL TREE MODEL.xls
• Know how to do this manually!
• (for sure!!!)

21
Arbitrage Valuation of Options

• This is the theoretically correct view
• Assumes
• Market for asset
• replicating portfolio (RP) can be constructed
• RP defines a value for Option which is NOT
  expected value it is Arbitrage Enforced
• Valuation
• At Risk-free discount rate (because of Arbitrage)
• Of properly weighted proportion of asset, loan
• ? Black-Scholes formula

22
Black-Scholes

• Black-Scholes formula
• C S N(d1) - K e- rt N(d2)
• Understand intuition behind it
• Weighting of
• owning Asset (S) and
• having a loan (K) that you will have to repay

23
Arbitrage Enforced Valuation

• In Lattice, same procedure as previously
  presented
• However, special features
• q risk-neutral probability (1 rf) d
  /(u d)
• discount at each stage using risk-free rate rf
• This approach is
• Standard basis for all valuations of financial
  options
• Limited application to options in systems, for
  which no markets may exist
• Unclear when suitable for options on systems

24
Valuation of Options Practice

• For Real options, finance theory may not work
• No traded assets, so arbitrage-enforced not
  right
• no statistical history, to determine sigma, nu
• Understand range of Alternative approaches
• Decision Tree (Kodak)
• Simulation (Antamina)
• Hybrid (Ford -- Neely)
• Calculation issues
• What design element should be flexible
  (Bartolomei)
• Path Dependent Analysis (Wang)

25
Valuation of Real Options Issues

• What is the asset involved modeling?
• NPV of project?
• What drives or affects that value?
• What is variability of project?
• Historical Data may not exist
• Data may not be random
• How do we develop results?
• What can engineering team handle?
• How to we explain results?
• What can client or audience handle?

26
Research issues in Options

• What method best in practice?
• Formal real options analysis
• decision analysis
• net present value in some form?
• How to apply in specific areas, depending on
• Economies of Scale
• Path dependency over time
• Interactions between design features
• How to present results to owners/managers of
  major projects?

27
Some Closing Thoughts

• System designers need to
• Think beyond technical mechanics to performance
  of system in context
• Communications Satellites
• technically brilliant but abysmal failure as
  system
• Value Flexibility systematically
• Monitor System, to know when to use option
• Maintain flexibility to act dont let yourself
  get locked into a fixed plan

28
Take-Away 1Standard Design Practice Wrong

• Standard Design Practice optimizes to fixed
  parameters (oil price, etc) on basis of
  deterministic criteria (e.g., NPV)
• This is wrong for 2 reasons
• We can do better because we live in uncertain
  world, we must deal with expectations, and
  recognize that deterministic optimum is usually
  not highest expected value (Jensens Law)
• Deterministic optimization gives misleading idea
  that flexibility costs -- when flexibility can
  in fact reduce costs as examples have
  demonstrated

29
Take-Away 2New Paradigm Better

• New design paradigm recognizes parameters are
  uncertain (oil price, etc) and need to focus on
  expectations (e.g., E NPV)
• We can thus improve in several ways
• Increase value (over optimized design)
• Decrease cost, thus improving rate of return
• Recognize and exploit ability to manage system
  evolution intelligently, avoiding downside and
  taking advantage of upside opportunities
• Real Options in systems
• enable win-win designs

30
Best Wishes on Examand for rest of your studies!

• The teachers really hope you will do excellently!
• (and make us look good!)
• Weve enjoyed being with you and
• hope our relationship
• can grow over time
• Richard
• Mike, Richard-Duane, Reza