Estimating Cost Contingency

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Estimating Cost Contingency

• A Real Options Approach
• Dr. Said Boukendour
• Professor at University of Quebec

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Contingency

• One of the most common project failure is to
  start with an inadequate budget
• How to assess uncertainties affecting cost in
  order to be able to set competitive targets and
  achievable commitments ?

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Contingency

• Contingency is probably the most misunderstood
  and misapplied word.
• It can mean different things to different people
  
• tolerance in specification
• float in schedule
• money in budget

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Contingency

• Contingency is an amount added to an estimate to
  allow for additional costs that experience shows
  will likely be required (AACE 1998)
• Total Budget Base EstimateContingency

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Contingency

• What things it is meant to cover for ?
• Costs that may result from incomplete design,
  unforeseen and unpredictable conditions, or
  uncertainties within the defined project scope
• What things is it not meant to cover for?
• Changes in scope or or unforeseeable major events
  such as strikes or earthquakes

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Contingency
Acts of God
Scope Changes
Cost Uncertainties
Scope Definition
Contingency
Price Escalation
Base Estimate
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How might contingencies be calculated?

• For most contractors, price setting and
  commitments raise a dilemma between being
  competitive enough to get the work and the
  avoidance of possible losses
• Pressure to secure orders might undermine
  rational assessment of project cost and schedule
  risks

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How might contingencies be calculated?

• As a part of a projects cost estimate,
  contingency under estimation or over estimation
  can lead an owner to
• Undertake a project that should be rejected
• Reject a project that should be accepted
• Misallocate resources during project
  implementation

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Deterministic Method

• Also known as Traditional Add-on
• Projects characteristics related directly to a
  percentage figure on the base estimated costs
• The percentages may be developed from checklists
  or by matching project characteristics to the
  characteristics of previously completed projects
  stored in the database
• The cost engineer makes a judgement should more
  or less contingency be added to this situation

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Recommended Percents
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Problems

• Single-figure implies degree of certainty that
  is simply not justified
• Arbitrary - Difficult to justify
• Double-counting - Hidden Contingency in each cost
  element (padding) to total cost
• Padded estimate self-fulfilling prophecy means
  money allocated is money spent
• Spent padded budget misleading historical
  database

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Probabilistic Method

• Assign a probability distribution for each cost
  component
• Three points estimate is the most used
  distribution

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Probabilistic Method

• Calculate cost mean and variance for each
  component as follows

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Probabilistic Method

• Sum all means and variance to get the cost mean
  and variance for the whole project
• Central Limit Theorem total cost has normal
  distribution

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Probabilistic Method

• Probability tables (z scores) Change Z for X
• Choose C for desirable level

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Monte Carlo Simulation

• Monte Carlo is a city of Monaco, where the
  primary attractions are casinos containing games
  of chance.
• The random behavior in games of chance is similar
  to how a Monte Carlo simulation selects variable
  values at random to simulate a model.
• When a die is rolled, the outcome is unknown
  within the range of one to six.
• A similar situation exists for project coststhat
  have a range of values (assigned by the cost
  uncertainty analysis)

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Monte Carlo Simulation

• Inputs and Outputs

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Monte Carlo Simulation
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Project As Short Selling

• A project is a promise of delivering something
  which does not exist yet
• At completion, the project will be completed for
  the actual cost, which remains uncertain

• A short seller sells some quantity of goods
  without owning it
• At expiration, the short seller will buy the
  goods for the market price, which remains
  uncertain

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Hedging Strategy

• To hedge against the price rise, the short seller
  can buy a call option that gives him the right to
  buy the quantity of goods for a determined price
  at the expiration date of the contract
• The short sellers expense will be limited to a
  ceiling amount made up of the contract amount
  plus the option premium.

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Contingency As Risk Market Price

• Let us assume there is a stock that exactly
  mirrors the project cost volatility,
• Thus, it would be possible to buy a call option
  on this stock for an amount equivalent to the
  project estimated cost
• The option, which expires at the completion date,
  will be exercised only if the spot price will
  exceed the strike price

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Contingency As Risk Market Price

• In this case, the stock acquired for the strike
  price will be immediately sold for the spot price
• According to the perfect correlation assumed
  above, the profit that will result will
  completely offset the cost overrun
• By the same token, the projects cost will be
  limited to a total amount made up of the budgeted
  cost plus the option premium

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Contingency As Risk Market Price

• For that hedge to be effective, it is necessary
  that the mirrored stock actually exists
• The purpose is not to transfer this risk to any
  third-party but to price it fairly.
• Fair contingency can be defined as the risk
  premium that would be required by the market is
  the project was traded in.

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Software Cost Estimation Using COCOMO II

• COCOMO is a parametric estimation model based on
  a study of hundreds of software projects
• The COCOMO calculations are based on the estimate
  of projects size in Source Lines of Code (SLOC)
• Effort (PM) 2.94EAF(KSLOC)E
• http//sunset.usc.edu/research/COCOMOII/

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Option Pricing

• Black-Scholes formula
• CSN(d1)-Xe-rtN(d2)
• With

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Option Pricing

• Taking
• S median (16.9(26.4-16.9)/221.65)
• X strike price or most probable cost 21.1
• r 0
• Sigma sqr(t) ((26.4-16.9)0.25)/21.65 11 with
  95 confidence
• We get
• C21.65N(0.28)-21.1N(0.18)1.24

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Option Pricing
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Option Pricing
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Conclusions

• The main contribution of this research is to
  bring the market into the cost estimation process
  in order to eliminate the arbitrary and to
  improve rationality and efficiency in investment
  decision making and resource allocation