Engineering Economic Analysis Canadian Edition

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Engineering Economic AnalysisCanadian Edition

• Chapter 10 Uncertainty in Future Events

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Chapter 10

• uses estimated variables to evaluate a project.
• describes possible outcomes with probability
  distributions.
• combines probability distributions for individual
  variables for joint probability distributions.

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• uses expected values for economic decision
  making.
• measures and uses risk in decision making.
• uses simulations for decision making.

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Precise Estimates Are Still Only Estimates

• All estimates are inherently variable and future
  estimates are often more variable than present
  estimates.
• Minor changes in any estimate(s) may alter the
  results of the economic analysis.

14-1 Clicking on the Excel icon will open a
spreadsheet.
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• Using breakeven and sensitivity analysis allows
  an understanding of how changes in variables will
  affect the economic analysis.

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Decision-Making and theVariability of Future
Consequences

• In the left box, PW(A) gt PW(B)
• In right box, Bs cash flow estimates are not
  fully realized
• Now, PW(B) gt PW(A)

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Sensitivity of Decision-Makingto Cash Flow
Changes

• In upper box, PW(A) gt PW(B)
• In lower box, by how much should Bs 4th year
  cash flow grow
• PW(A) PW(B) Breakeven
• Let PW(A) PW(B) 243.43 and Bs 4th year cash
  flow x
• PW (B) 700(P/A,10,3) x(P/F,10,4)
• x 736

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Sensitivity of Decision-Makingto Cash Flow
ChangesBreakeven Analysis

• Helps to examine the variability of estimates on
  outcomes
• By how and in what direction will a summary
  measure (e.g., PW, EAW, IRR) be affected by the
  variability in estimates?
• Does not take the inherent variability of
  parameters into account in an economic analysis
• Need to consider a range of estimates

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A Range of Estimates

• Usually three scenarios
• Pessimistic
• Optimistic
• Most likely
• Compute the rate of return for each scenario
• Compare MARR and each rate of return
• Each scenario has a ROR gt MARR in previous slide

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• What if MARR gt ROR for one or more scenarios?
• Are scenarios equally important?
• Need weighting scheme.
• Assigning weights
• Assign weight to each of the three scenarios
• Largest weight for the most likely scenario
• Pessimistic and optimistic may have or unequal
  equal weights

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• Calculate the mean value from the weighted
  average of the summary measure (e.g., ROR) for
  each scenario.
• Calculate a summary measure (e.g., ROR) from the
  mean for each parameter (annual benefit and cost
  first cost salvage value).

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• There is often a range of possible values for a
  parameter instead of a single value
• Optimistic
• Most likely (multiply by 4)
• Pessimistic

The expected value E(x) (O 4ML P)/6
Example 14-3 4
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• PW and other calculations for all sets of
  scenarios are useful in understanding the impact
  of future consequences.
• If several variables are uncertain
• Unlikely that ALL variables will be optimistic or
  pessimistic or most likely
• Calculate average or mean values for each
  parameter (e.g., mean first cost) based on
  scenario weights

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• Upper box
• Minimal variability in the parameters among the
  three scenarios
• Lower box
• Considerable variability in the parameters of the
  three scenarios
• Conclusion
• Increased parameter variability ? large
  differences between mean values

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Probability and Risk

• Probabilities of future events can be based on
  data, judgment, or a combination of both.
• Weather and climate data expert judgment on
  events
• Most data has some level of uncertainty.
• Small uncertainties are often ignored
• Variables can be known with certainty
  (deterministic) or with much uncertainty (random
  or stochastic).

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• 0 Probability 1
• The sum of probabilities for all possible
  outcomes 1 or 100.
• Common in engineering economy to use 2 to 5
  outcomes with discrete probabilities.
• Expert judgment limits the number of outcomes.
• Each outcome requires more analysis.

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• Probability can be considered as the long-run
  relative frequency of an outcomes occurrence.

Odds on drawing a card.
Odds on rolling dice.
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Joint Probability Distributions

• Random variables are assumed statistically
  independent.
• project life and annual benefit
• Project criteria depend on all input probability
  distributions.
• (e.g., PW, ROR)
• We need joint probability distributions of
  different combinations of parameters.

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• If A and B are independent
• ? P(A) and P(B) P(A) x P(B)
• Three values and probabilities for the annual
  benefit and two values and probabilities for the
  life.
• Six possible combinations that represent the
  broader set of probabilities than the three
  scenarios, most likely, pessimistic and
  optimistic.

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• Joint probability distributions are burdensome to
  construct when there a large number of variables
  or outcomes

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• Project first cost 25,000 MARR 10.
• Calculate PWs if benefits and life are unrelated

Example 10-6
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Expected Value

• Weighted average of the random variable based on
  the probabilities of occurrence of different
  values of the variable
• EX µ Spjxj for all j
• p probabilities x discrete value of the
  variable
• The expected value is the centre of the
  probability mass.

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• An expected value (mean) may be determined in a
  situation where two or more possible outcomes are
  known and the probability associated with each
  outcome is also known

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• If we know that the expected value (payout) on a
  horse race is less than the money bet (the track
  needs to have an income), then why do so many
  individuals bet?

Example 14-8 The horse race.
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Expected Value PW(EV) ? EV(PW)
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• EV(Benefits)
• 5000(0.3) 8000(0.6) 10,000(0.1)
• 7300
• EV(Life)
• 6(0.67) 9(0.33)
• 7 years

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• EV(PW)
• -3224(20) 9842(40)
• 18553(6.7) 3795(10)
• 21072(20) 32590(3.3)
• 10,209

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• EV(PW)
• Use joint probabilities distribution for benefit
  and life and the resulting probability
  distribution for PW
• See previous graph
• Add individual PW and joint probability products

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Expected Value
Example 10-9
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Decision Tree Analysis

• A decision tree is a logical structure of a
  problem in terms of the sequence of decisions and
  outcomes of chance events.
• Demand for a new household product will depend on
  the availability and quality of substitutes,
  household incomes, etc.

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• Decisions depending on the outcomes of random
  events force decision makers to anticipate what
  those outcomes might be as part of the process of
  analysis.
• This analysis is particularly suited to decisions
  and events that have a natural sequence in time
  or space.

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• A decision tree grows from left to right and
  usually begins with a decision node
• Represents a decision required by the decision
  maker ?
• Branches extending from the decision node
  represent decision options available to the
  decision maker.
• A chance node (circles ) represents events
  whose outcomes are uncertain.

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Decision Tree Analysis Procedure

• Develop decision tree.
• Execute the rollback procedure on the decision
  tree from right to left
• Compute Expected Value (EV) of possible outcomes
  at each chance node.
• Select option with best EV.
• Continue rollback process until the leftmost node
  is reached.
• Select expected value associated with the final
  node.

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Decision Tree Analysis
New Product
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New Product
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Distribution of Outcomes

• Various standard distributions of outcomes have
  been classified. The text describes two of these
  distributions
• Uniform
• Normal
• To understand the simulation of economic
  problems, one must understand how a random sample
  is drawn from a distribution.

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Generating a ProbabilityDistribution Using Excel

• RAND() returns anevenly distributedrandom
  numbergreater than orequal to 0 andless than
  1(changes on recalculation).

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Sample and Population Statistics

• Four common types of normal distribution
• Mean
• Average value of a set of values.
• Standard deviation
• A measure of the deviation of the values in a set
  from the mean.
• Maximum
• Largest value in a set of values.
• Minimum
• Smallest value in a set of values.

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Example 14-11
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Creating a Sample Using Random Normal Numbers

• In Excel, use Tool gt Data analysis gt Random
  number generator gt Select your distribution.

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Simulation

• Simulation is the repetitive analysis of a
  mathematical model.

Example 14-12
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Monte Carlo Simulation

• Attempts to construct the probability
  distribution of an outcome performance measure of
  a project (e.g. NPW, IRR) by repeating sampling
  from the input random variable probability
  distributions.
• The sample frequency distribution generated can
  be a good estimate for the probability
  distribution of the event outcomes.

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• The probability distributions of the individual
  random variables are known in advance.
• By randomly sampling values from the random
  variables from the probability distributions, a
  sample of the overall performance measure of a
  project is produced.
• The process is seen as imitating the randomness
  in the performance measure because of the
  randomness of the project variables or inputs.

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• Sample 200

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