Joseph Berechman and Qing Fu

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Cost Overrun Risk Analysis in P3 Transportation
Investments

• Joseph Berechman and Qing Fu

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Outline

• Objective of Study
• Cost Overrun Risk Models
• The VIHP Case Study
• Risk Projections A Numerical Example
• Conclusions

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I. Objective

• The main objective of this study is to propose
  and test quantitative methods for projecting cost
  overruns in P3 transportation infrastructure
  investments.

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Main sources of risk in transportation
infrastructure projects (1)

• Technological risks
• Construction risks
• Demand and revenue risk
• General economic and financial risks
• Regulatory risks
• Organizational and project management risks
• Political risks
• Contractual or legal risks

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Main sources of risks and their impacts (2)
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II Models of Cost Overrun Risk Analysis

• Probability Distribution Fitting Models
• - Beta distribution model
• Regression Model
• Simulation Models
• - Simulation Model I
• - Simulation Model II (Noise/Residual-adjusted
  simulation model)

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III Probability Distribution Models

• The conditions for using these models
• Similar construction and management technologies
• Similar project size
• Similar economic and political environments
• Similar Private-Public investment policies

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The Beta Distribution

• Features of the Beta Distribution (P, Q, A, B)
• Finite limits, represented by value parameters A
  and B (A lower bound B upper bound)
• Flexible shape, represented by shape parameters P
  Q
• The Beta Distribution Probability Density
  Function
• Where

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II.II The Regression Model

• Independent Risk Factors
• Interest Rate Level and Variation
• Average interest rate over the construction
  period
• Standard deviation of interest rates
• Construction Duration
• Public-Private Investment Makeup
• Percentage investment of the private sector
• Percentage investment of the federal government
• Risk Allocation between the public and private
  parties

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The Model

• Average annual interest rate change over
  construction period
• Annual interest rate variability
• Project construction duration
• Investment ratio of private sector in total
  project funding
• Investment ratio of federal government in
  total project funding
• Degree of private cost overrun risk bearing
• Public Private cost overrun risk allocation
  (dummy variable)
• Constant term
• Regression coefficients of each independent
  variable

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Simulation Model

• A simulation model follows these steps
• 1. Make assumptions on the probability
  distributions of the studied variables
• 2. Generate a large number of random numbers
  from the assumed probability distribution of each
  variable
• 3. Use these randomly drawn values to estimate
  the parameters of the studied variable
• 4. Use these parameters to calculate moments
  (e.g., the mean and standard deviation)

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Distribution Fitting vs. Simulation (1)

• Simulation Models
• Advantages
• Capable of handling complicated variables when
  sufficient germane data is unavailable
• Provide flexible scenario analysis
• Disadvantages
• Needs assumptions on underlying probability
  distribution
• Truly random draws are not available
• Model validation may be impossible

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Distribution Fitting vs. Monte Carlo Simulation
(2)

• Distribution Fitting
• Advantages
• A method based on actual data and, therefore,
  relatively more accurate and objective
• Disadvantages
• limited when sufficient data are unavailable

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II.III The Simulation Models (1)

• Simulation Model I

VIHP Budget Data
VIHP Budget Data
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II.III The Simulation Models (2)

• Simulation Model II

VIHP Budget Data
Budget Distribution
Budget Sample Data
Regression
Cost Overrun Sample Data
Expected Cost
Expected Cost for VIHP Data
Residual Adjusted Cost Estimates
VIHP Costs Expected Costs
Residuals for VIHP Data
Residual Distribution
Residuals Sample Data
Cost Overrun Distribution
Expected Costs Residuals
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III. Vancouver Island Highway P3 (VIHP) Case
Study
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VIHP Data Range

• Cost Overrun Ratio (COR) Project Costs/Project
  budget

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Cost Overrun Ratio Histograms

• a. Road/Highway Projects b. Bridge/Tunnel
  Projects
• Both of the histograms are right skewed.

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Cost Overrun Ratio Descriptive Statistical Report
Distribution parameter estimates are close for
these two project groups.
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Cost Overrun Ratio Beta Distribution Fitting (1)
P and Q are shape parameters for Beta
distribution A and B are value parameters for
minimum and maximum values respectively.
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Cost Overrun Ratio Beta Distribution Fitting (2)
For projects with cost overrun ratio over 1.25,
this Model may give conservative estimates
Most VIHP data fit this Beta distribution well
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Probability Estimations for Project Cost Overrun
Ratio over Certain Values
A similar transportation construction project
would have a probability of 58 to have costs
over project budgets.
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Cost Estimates Comparison (1) The Regression
Model vs. Beta Distribution Fitting vs. Simulation
For a road and highway project with budget of
1.2 million, the models have the cost estimates
as the followings
Beta distribution has the highest cost estimates
among these four models though they should be
regarded as conservative estimates, as was seen
from the above Beta probability plot.
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Cost Overruns Estimates (2) Comparison of
Results from the Three Models
General comparison for the cost estimates of
these four models
R/H Road and Highways B/T Bridges and Tunnels
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Comparisons (3) Cost Prediction Interval
(Regression) and Confidence Interval (Beta
Distribution)
The estimated ranges are close to each other.
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Key Conclusions

• 1. P3 investments can and should be analyzed
  relative to the risk of cost overruns using
  quantitative risk models
• 2. P3 tends not to increase, probably lower, the
  risk of cost overruns

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Further Research Questions

• 1. In what aspects of transportation
  infrastructure investments the private sector is
  more efficient relative to the risk of cost
  overruns?
• 2. How to analyze the risk of demand and revenues
  shortage?
• How to treat regulatory risks?

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Thank You!