world bank document · robert w. bacon is a professor of economics at lincoln college, oxford...
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WORLD BANK TECHNICAL PAPER NO. 325
Energy Series
Estimating ConstructionCosts and SchedulesExperience with Power GenerationProjects in Developing Countries
Robert W Bacon, John E. Besant-Jones,andJamshidHeidarian
The World BankWashington, D. C.
Copyright © 1996The Intemational Bank for Reconstructionand Development/THE WORLD BANK1818 H Street, N.W.Washington, D.C. 20433, U.S.A.
All rights reservedManufactured in the United States of AmericaFirst printing August 1996
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ISSN: 0253-7494
Cover: Detail from William Gropper, "Construction of the Dam" (mural study, Department of the Interior, Wash-ington, DC., 1937).
Used by permission of the National Museum of American Art, Smithsonian Institution, transfer from the U.S. De-partment of the Interior, National Park Service.
Robert W. Bacon is a professor of economics at Lincoln College, Oxford University, England, and a consultant tothe Industry and Energy Department at the World Bank. John Besant-Jones is a principal economist in the Power De-velopment, Efficiency and Household Fuels Division of the Industry and Energy Department at the World Bank.Jamshid Heidarian is a professor of economics at the University of the District of Columbia, Washington, D.C., andconsultant to the Industry and Energy Department at the World Bank.
Library of Congress Cataloging-in-Publication Data
Bacon, Robert, 1942-Estimating construction costs and schedules: experience with
power generation projects in developing countries / Robert W. Bacon,John E. Besant-Jones, and Jamshid Heidarian.
p. cm. - (World Bank technical paper, ISSN 0253-7494 ; no.325) (Energy series)
Includes bibliographical references.ISBN 0-8213-3670-31. Electric power plants-Design and construction-Estimates-
Developing countries. 2. Electric power plants-Developingcountries-Costs-Statistics. 1. Besant-Jones, John, 1941-11. Heidarian, Jamshid. III. Title. IV. Series: WorldBank technical paper. Energy series.TK1193.D44B33 1996 96-22845621.31'21-dc2O CIP
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Contents
Foreword ............................................................... xi
Abstract ............................................................... xiii
Acknowledgments ............................................................... xiv
Abbreviations and Acronyms ............................................................... xv
Units of Measure ............................................................... xv
Executive Summary ................................................................ 1
1. Importance of Cost and Schedule Estimation for Power GenerationProjects ............................................................... 5
2. Framework for Evaluating the Performance of Cost and ScheduleEstimates ...........................................................................................................7
3. Data Base of Power Generation Projects ............................................................ 11
4. Statistical Approach to Analyzing the Performance of Cost and ScheduleEstimates ............................................................. 15
5. The Overall Performance of Power Project Cost and Schedule Estimates .... 23
Group Performance of All Power Generation Projects ............................................. 23
Distinction between Thermal Power Projects and Hydropower Projects ................. 27
Prevalence of Bias and Uncertainty in Cost and Schedule Estimates ....................... 29
Ex Post Analysis of Responsibility for Schedule Slip .......................... .................... 31
Reliability of the World Bank's Methodology for Computing PriceContingencies ............................................................. 33
6. Significant Project Characteristics and External Variables for Cost andSchedule Estimates ............................................................. 37
Thermal Power Project Costs ............................................................. 40
Hydropower Project Costs .............................................................. 43
Thermal Power Project Schedules ................................ .............................. 45
Hydropower Project Schedules .............................................................. 46
Grouping of Significant Variables ............................. ................................ 47
v
7. Implications of the Analysis for Power System Planning .............. ................... 51
Principal Findings .............................................................. 52
Using Regressions to Improve Predictions for Project Costs and Schedules ........ ... 53
Risk and Planning Issues ............................................................. 57Measurement of Project Risk ............................................................. 58
Distribution of Possible Project Outcomes ......................................................... 59
Planning Issues Involving Choice between Sequences of Projects .......... .......... 60
Basic Recommendations ............................................................. 61
Annex 1: World Bank-Supported Power Generation Projects 1965-86 Usedfor the Analysis of Cost and Schedule Estimating Performance ....... 63
Annex 2: Regression Results with All Variables Included ................................... 69
Annex 3: Comparisons of Actual Ratios and Predicted Ratios fromRegressions for Costs and Schedules ................................................... 75
Annex 4: Statistics for Single-Variate Analysis of All Variables ........... .............. 79
Annex 5: Ex Post Attribution of Factors Responsible for Schedule Slip inWorld Bank-Supported Power Generation Projects ............ ................ 83
Annex 6: Methodology for Deriving Actual Project Costs in Constant PriceTerms ............................................................... 85
Annex 7: Analysis of Relationships for the Performance of PriceContingencies ............................................................. 89
1 Relation between Actual and Estimated Current Costs ................. ....................... 89
2 Link between Actual Current Costs and Actual Constant Costs ........... ............... 90
3 Relation between Actual and Estimated Cost Escalation ................. .................... 91
4 Relation between Cost Overrun in Current Price Terms, in Constant PriceTerms, and Errors in Predicting Inflation Rates and Project Schedules ......... .... 91
Appendix A7.1 Composition of the World Bank's Price ContingencyFormula for Predicting Project Cost Escalation .................................................. 93
Annex 8: Computations of Probabilities of Exceeding Specific ProjectCosts ............................................................... 95
Appendix A8.1 The Variance of a Predicted Value from a Regression ......... ......... 98
Appendix A8.2 Probability that the Outcome of One Project Is Greater ThanThat of the Other ............................................................. 98
vi
Annex 9: Assigning Probabilities to Scenarios for Risk Analysis ........... ........... 101
Annex 10: The Calculation of the Mean and Variance of the Cost of TwoProjects ............................................................ 105
Annex 11: Applying the Option Approach to Construction Costs andSchedules .......................................................... 107
A. Investment Valuation Under Uncertainty Using the Options Approach ............. 107
B. General Solution Methods .............................................................. 109
C. A Simple Model for the Investment Option and Optimal Timing ........... 11........... I
D. Application of the Simple Options Model to Construction Costs andSchedules .............................................................. 112Dl. General Assumptions .............................................................. 113
D2. General Formulation to Estimate Option Model Uncertainty ..................... 113
D3. The Cases of Thermal and Hydropower Plants ........................................... 115
Annex 12: Performance of Power Demand Forecasts and of World Bank OilPrice Projections ........................................................... 117
References .......................................................... 119
Tables
3.1 Geographical Distribution of Power Generation Projects in the Data Base .......... ...... 12
3.2 Distribution of Power Generation Projects by Year of Approval in the Data Base .... 12
3.3 Distribution of Power Generation Projects by Installed Capacity in the Data Base .... 13
3.4 Distribution of Thermal Projects by Production Technology, Primary Fuel, andUnit Size in the Data Base .......................................................... 13
4.1 Variables and Characteristics Used in Regressions on Construction Cost Overrunand Schedule Slip .......................................................... 18
5.1 Cases Omitted from Analysis .......................................................... 26
5.2 Overall Statistics for Cost and Schedule Performance ..................................... ........... 26
5.3 Comparison of Squared Correlations between Actual and Estimated Costs, andbetween Actual and Estimated Schedules for World Bank-Supported PowerGeneration Projects .......................................................... 28
5.4 Comparison of Cost Overrun and Schedule Slip between World Bank-SupportedPower Generation Projects and All Bank-Supported Projects ..................................... 30
5.5 Chances of Overruns Exceeding 20 Percent Sensitivity Level .................................... 30
5.6 Squared Correlations between Cost Overruns and Schedule Slips for ThermalPower and Hydropower Projects .......................................................... 31
vil
5.7 Ex Post Attribution of Responsibility for Project Schedule Slip ................................. 32
6.1 Significant Variables for Thermal Power Project Costs (current values) .................... 40
6.2 Significant Variables for Thermal Power Project Costs (constant values) .................. 42
6.3 Significant Variables for Hydropower Project Costs (current values) ............ ............ 43
6.4 Significant Variables for Hydropower Project Costs (constant values) ........... ........... 44
6.5 Significant Variables for Thermal Power Project Schedules ....................................... 45
6.6 Significant Variables for Hydropower Project Schedules ........................................... 46
6.7 Grouping of Significant Variables for Project Cost and Schedule Estimates .............. 48
7.1 Sensitivity of the Levels of Predicted Values to Indicator Variables ............ .............. 56
A1.1 World Bank-Supported Power Generation Projects 1965-86 Used for theAnalysis of Cost and Schedule Estimating Performance .63
A2.1 Variables for Log of Thermal Power Project Costs (Current Values) .69
A2.2 Variables for Log of Thermal Power Project Costs (Constant Values) .70
A2.3 Variables for Log of Hydropower Project Costs (Current Values) .71
A2.4 Variables for Log of Hydropower Project Costs (Constant Values) .72
A2.5 Variables for Log of Thermal Power Project Schedules .73
A2.6 Variables for Log of Hydropower Project Schedules .74
A4.1 Single-Variate Regression Correlations .80
A4.2 Comparison of Significant Variables at 90 Percent Confidence Level betweenMultivariate Analysis and Single-Variate Analysis .81
A5.1 Ex Post Attribution of Factors Responsible for Schedule Slip inWorld Bank-Supported Power Generation Projects .83
A6.1 Standard Disbursement Profiles for Project Cost in Current Price Terms .86
A6.2 Example of Project Cost Derivation in Constant Price Terms:Algeria, Base Year 1973 .87
A8.1 Probability that Project 1 Has Higher Cost (Schedule) than Project 2 .97
A9.1 Pairs of Parametric Values that Fit the Required Regression Variance of 0.035 forScenarios where the External Variance Is a Function of the Size of theMiddle Value .102
A9.2 Pairs of Parametric Values that Fit the Required Regression Variance of 0.01 forScenarios where the External Variance Is Not a Function of the Size of theMiddle Value .102
A9.3 Probabilities for Scenarios With Predetermined Variances for Costs and Demand.... 103
viii
Figures
5.1 Relationship between Actual Costs and Estimated Costs for World Bank-Supported Thermal Power Projects and Hydropower Projects, 1965-1986 ................ 24
5.2 Relationship between Actual Schedules and Estimated Schedules for WorldBank-Supported Thermal Power Projects and Hydropower Projects, 1965-1986 ...... 25
5.3 Distribution of Cost Performance for World Bank-Supported Thernal PowerProjects and Hydropower Projects, 1965-1986 (current prices) ............... .................. 27
5.4 Distribution of Schedule Performance for World Bank-Supported Thermal PowerProjects and Hydropower Projects, 1965-1986 ........................................................... 28
5.5 Errors in Cost Escalation Estimates for World Bank-Supported Power GenerationProjects Approved between 1970 and 1986 ................................................................. 34
A3.1 Plot of Actual and Predicted Ratios for Thermal Costs (current) .............. .................. 76
A3.2 Plot of Actual and Predicted Ratios for Thermal Costs (constant) .............................. 76
A3.3 Plot of Actual and Predicted Ratios for Thermal Schedules ........................................ 77
A3.4 Plot of Actual and Predicted Ratios for Hydro Costs (current) ............... .................... 77
A3.5 Plot of Actual and Predicted Ratios for Hydro Costs (constant) .............. ................... 78
A3.6 Plot of Actual and Predicted Ratios for Hydro Schedules ........................................... 78
A7.1 Comparison of MUV Index Actual Values with Values from Forecasts Madebetween 1974 and 1988 (Based on actual value in 1980 = 100) .................................. 92
A12.1 Performance of Power Demand Forecasts for Developing Countries ........... .............. 117
A12.2 World Bank Oil Price Projections in Constant 1987 US$ per Barrel ............ .............. 117
ix
ForewordOne of the main reasons for the ongoing reforms to power sectors around the world is
the desire for better management of the economic and financial risks of investing in largepower supply projects. These risks arise from uncertainty about future power demand,fuel prices, and-as shown in this paper-construction costs and schedules.Conventional planning approaches based on deterministic scenarios of the future undercentralized decisionmaking have seldom given sufficient attention to, or reliable guidanceon, these risks. Now, however, under the more decentralized planning process cominginto use in reformed power sectors, both public and private decisionmakers will have torespond to the concerns of shareholders, consumers, financiers, and the general publicabout the risks of investing in large power projects.
Although the risks from construction cost overruns and schedule delays are oftenserious for developing countries, they have been poorly understood to date. In response,the paper puts forward a number of straightforward techniques to improve the analysis ofthese construction cost and schedule risks. The paper also complements several otherIndustry and Energy Department and Energy Sector Management Assistance Programme(ESMAP) publications and seminars on structuring and financing power generationprojects.
Richard StemDirectorIndustry and Energy Department
xi
AbstractThis paper helps national planning and finance ministries, power utilities, and
financing agencies to improve the reliability of their estimates for construction costs andschedules of power generation projects in developing countries and thereby to improvethe selection and implementation of these projects.
The paper examines estimates of construction costs and schedules that were made fora group of power generation projects approved for financing by the World Bank between1965 and 1986. This group of some 64 thermal power plants and 71 hydroelectric plantsis then subjected to a statistical analysis. From this analysis, the paper assesses thereliability of the estimates and identifies factors that were significantly associated withbias and uncertainty in them.
The paper draws the following conclusions. First, the average estimating error amongprojects as a whole was too large to be ignored. Second, estimated values weresignificantly biased below actual values, and the accuracy of estimated values had a largevariance. Third, the performance of cost estimates was much better for thermal powerprojects than for hydropower projects, but schedule estimates performed similarly forthese two groups of projects. Fourth, the performance of estimated values can be relatedto a number of indicator variables through regression analysis, and these regressions canbe used to derive expected values that carry less uncertainty than the correspondingestimated values.
The paper then demonstrates how to improve the prediction of the actual constructioncost or schedule for a power generation project by deriving an unbiased expected valuefrom the estimated value and the appropriate regression equation for the project. There isa proviso, however, that the project has similar technology and implementationarrangements (i.e., public sector) to those that characterize the projects analyzed in thepaper. The paper recommends that analyses of power generation projects include a casein which expected values are used for construction costs and schedules. This case wouldsupplement the standard analysis that is based on appraised estimates of these values.
Nevertheless, substantial uncertainty remains about the reliability of even theexpected values. The regressions given in the paper can be used to provide a measure ofproject risk arising from this source. Consequently, the paper also recommends that theeconomic and financial risks associated with the selection of a particular power project orpower development strategy should be explicitly considered during project appraisal.This analysis would elicit valuable insights about the riskiness of power generationprojects under consideration, such as projects considered to be the least-cost option fromthe customary deterministic approach to power system planning. The paper presentsstraightforward techniques for evaluating frequently encountered questions of risk aboutpower projects and development programs.
xiii
AcknowledgmentsThe authors gratefully acknowledge the valuable comments on drafts of the paper
given by Dennis Anderson, William Buehring, Joseph Gilling, Vladimir Koritarov, SpirosMartzoukos, Lucio Monari, Lant Pritchett, Mark Segal, Charles Siebenthal, and OddYstgaard.
Thanks also go to Vonica Burroughs and Carole-Sue Castronuovo for wordprocessing assistance and to Paul Wolman for his editorial and production work.
The authors take responsibility for any errors and omissions in the paper.
xlv
Abbreviations and AcronymsCPI consumer price index
forex foreign exchange
G-5 France, Germany, Japan, United Kingdom, and UnitedStates
G&T generation and transmission
GDP gross domestic product
ICB international competitive bidding
IDA International Development Association
MUV UN Unit Value Index of manufactured goods exportedfrom G-5 countries to developing countries
NPV Net Present Value
O&M operation and maintenance
RPI Retail Price Index
SAR Staff Appraisal Report
SD standard deviation
SEE standard error of estimate
SER standard error of regression
UN United Nations
Units of Measuredollars US$
GW gigawatt
GWh gigawatt hour
MW megawatt
xv
Executive SummaryThis paper helps national planning and finance ministries, power utilities, and
financing agencies to improve the reliability of their estimates for construction costs andschedules of power generation projects in developing countries and thereby to improvethe selection and implementation of these projects.
Project cost and schedule estimates can deviate from actual costs and schedules intwo ways. First, estimates may be generally biased, in that the mean of the estimates for agroup of projects differs significantly from the mean of the actual costs or schedules forthe group. Second, even when such typical project bias is allowed for, estimates are stillsubject to uncertainty, in which the relationship between estimated and actual valuesshows a large variance around their mean values. By identifying and allowing for factsthat lead to variations in the degree of bias in the estimates for particular types of projects,it is possible to reduce the overall uncertainty for the financing of power projects and thedevelopment of power systems.
The paper proceeds in three main stages. First, it examines estimates of constructioncosts and schedules that were made for a group of power generation projects approved forfinancing by the World Bank between 1965 and 1986. This group of some 64 thermalpower plants and 71 hydroelectric plants is then subjected to a statistical analysis. Fromthis analysis, the paper assesses the reliability of past estimates and identifies factors thatwere significantly associated with bias and uncertainty in them. The paper concludes byreviewing the implications of these findings for the treatment of bias and uncertainty inestimates of construction costs and schedules for power system planning.
The paper has four important findings:
* Estimates of construction costs and schedules were fairly strongly correlated with theactual outcomes, but the average estimating error among projects as a whole was toolarge to be ignored.
* These estimated values were significantly biased below actual values, and theaccuracy of estimated values had a large variance.
* The performance of estimated costs was much better for thermal power projects thanfor hydropower projects, but schedule estimates performed similarly for these twogroups of projects.
* The performance of estimated values can be related to a number of indicator variablesthrough regression analysis, and these regressions can be used to derive expectedvalues that carry less uncertainty than the corresponding estimated values.
In covering only World Bank-supported projects, this analysis does not give a reliableimpression of estimating performance for projects financed and implemented by privatesector enterprises.
1
2 Estimating Construction Costs and Schedules
For all power generation projects, appraisal estimates showed substantial optimisticbias and major uncertainty. For this group, the actual project cost (in current prices andexcluding interest during construction) exceeded the estimated project costs on averageby 21 percent of the estimated project cost, with a standard deviation of 36 percent.Likewise, the actual project implementation periods exceeded the estimated periods onaverage by 36 percent of the estimated periods, with a standard deviation of 42 percent.Cost overruns and schedule slips were weakly correlated, especially for hydropowerprojects. A simple sensitivity test reflected inadequately the inherent uncertainty in theestimates of project costs and schedules. Bias and uncertainty on such extensive scaleshave major impacts on investment selection and financing.
In addition, the reliability of the World Bank's methodology for computing pricecontingencies for project cost estimates was examined. The results show that the Bank'smethodology improved the prediction of cost escalation, but that substantial room forimprovement remains.
A multivariate regression analysis was undertaken to identify correlation between fourperformance ratios and 29 possible explanatory variables. Ten projects (five thermal andfive hydro) were omitted from this analysis because of truly exceptional differencesbetween their estimated and actual values that would give rise to misleading regressions.Thermal power projects were explicitly distinguished from hydropower projects becausecost estimates for these groups behaved differently (average cost underestimation forthermal projects was 6 percent, for hydro projects, 27 percent). The six regressions thatwere analyzed thus covered thermal power costs (in current terms and constant terms),thermal power schedules, hydropower costs (current and constant), and hydropowerschedules. The dependent variables were the ratios of actual to estimated values. Theexplanatory variables reflected project technology, project size, procurement method,host-country features, and World Bank appraisal guidelines. Of these variables, 18 werefound to be correlated significantly with one or more of the performance ratios, asfollows: 7 variables were significant in one of the regressions, 4 variables in two of theregressions, 5 variables in three of the regressions, 1 variable-estimated cost-in four ofthe regressions, and I variable-station extension dummy-was significant for fiveregressions. These variables were able to explain about half of the observed variations inthe ratios of actual to estimated costs and schedules. The significance of many individualvariables indicates that the use of an "average adjustment factor" (determined over allprojects) would itself be biased.
The analysis accepted fairly weak evidence of systematic correlation (10 percentsignificance test) to be sure of picking up significant factors. The findings show thatfurther analysis should lead to better models of reducing risk in estimating project con-struction cost and schedules, in which risk assessment is able to rely on lower measuresof risk.
The paper then demonstrates how to improve the prediction of the actual constructioncost or schedule for a power generation project by deriving an unbiased expected value
Executive Summary 3
from the estimated value and the appropriate regression equation for the project. There isa proviso, however, that the project has similar technology and implementationarrangements (i.e., public sector) to those that characterize the projects analyzed in thepaper. The paper recommends that the analysis of power generation projects shouldinclude a case in which expected values are used for construction costs and schedules.This case would supplement the standard analysis that is based on appraised estimates ofthese values.
Nevertheless, substantial uncertainty remains about the reliability of even theexpected values. The regressions given in the paper can be used to provide a measure ofproject risk arising from this source. Consequently, the paper also recommends that theeconomic and financial risks associated with the selection of a particular power project orpower development strategy are explicitly considered during project appraisal. Thisanalysis would elicit valuable insights about the riskiness of power generation projectsunder consideration, such as projects considered to be the least-cost option from thecustomary deterministic approach to power system planning.
The final section thus presents straightforward techniques for evaluating the followingfrequently encountered questions of risk about power projects and developmentprograms. These techniques avoid undue analytical complexity yet overcome thedeficiencies of simplistic sensitivity analysis, and hence they are intended to supplementstandard least-cost analysis. Briefly stated, the techniques aim at
* Ascertaining the cost level for a given project that will be exceeded with a specificprobability and the probability that the project cost will exceed a specified value(similarly with project schedule).
- Choosing between projects based on the probability of exceeding a cost limit andevaluating which project has the lower probability of exceeding a given cost limit.
* Assigning probabilities to costs or schedule scenarios for risk analysis that areconsistent with the variance of cost or schedule outcomes derived from theregressions.
* Making the choice between a large project and a set of two or more smaller projects,where the reliability of estimates depends on the scale variables identified in theregression and risks also depend on project size.
* Deciding whether to delay a project or not, where the crucial issue is the need formore time to improve estimates of key planning parameters-such as site geology,hydrology, or environmental impacts-for the project or its alternatives. Anapplication of the financial options approach to the optimal timing of projects underuncertainty about construction costs and schedules is developed in the paper.
Finally, the paper recommends that these techniques be tested operationally anddeveloped in case studies, so that guideline/s can be formulated for using them in theappraisal of power generation projects.
1
Importance of Cost and Schedule Estimation forPower Generation Projects
Developing countries are planning massive investments to meet their power needs(Moore and Smith 1990).1 The construction costs and schedules of power generationprojects thus affect national economic development and the financial viability of projectinvestors. Power projects are capital-intensive and require lengthy construction periods.In total, they account for a substantial proportion-averaging about 10 percent-of adeveloping country's total physical investment. Some hydroelectric and thermal powercomplexes in the largest developing countries rank among global megaprojects costingbillions of dollars. Even modest-sized schemes-by global standards-in smalldeveloping countries can be huge in relation to the size of their economies.
Reliable estimates of construction costs and schedules presented by power utilitiesand their consultants at the time of project approval are important for justifying a projecton economic grounds and for planning the means of financing it. Faced with the hugeeconomic and financial costs of expanding power supply, governments of developingcountries are under pressure to ensure that power projects are selected with dueconsideration for the economic and commercial risks that arise from the uncertainty inthese estimates.
The economic impact of a construction cost overrun is the possible loss of theeconomic justification for the project. A cost overrun can also be critical to policies forpricing electricity on the basis of economic costs, because such overruns lead tounderpricing. The financial impact of a cost overrun is the strain on the power utility andon national financing capacity in terms of foreign borrowings and domestic credit. Therecourse in this situation is to reduce the scale of a project to a level commensurate with
1. It is estimated that developing countries are planning to install 384 GW of new generating capacityduring the 1990s at a cost of about US$450 billion in 1989 price terms, which would increase their totalinstalled generating capacity by about 80 percent over the amount installed in 1989. The principalproduction technologies for this new capacity are coal-fired steam plants (172 GW) and hydroelectric plants(137 GW). Gas turbines, fueled with natural gas, comprise 34 GW. Oil-fired steam plants comprise only14 GW.
5
6 Estimating Construction Costs and Schedules
the planned financial outlay, but this alternative is seldom rational for a power generationproject because power generation units can produce benefits (i.e., power) only if they arefully installed.2
The delay of output caused by slippage in a construction project schedule imposeseconomic costs when the power system is short of capacity or is supplying power fromplants with high variable costs. The financial impacts on the power utility of scheduleslippage are an increase in its financing charges and the possibility of incurring projectloan repayments before the project generates revenues.
This paper helps national planning and finance ministries, power utilities, andfinancing agencies to improve the reliability of their estimates for construction costs andschedules of power generation projects in developing countries and thereby to improvethe selection and implementation of these projects. From an analysis of World Bankexperience with estimating the costs and schedules for constructing power generationprojects, the paper identifies factors that were significantly associated with the reliabilityof cost and schedule estimates.3 In particular, it investigates whether projectcharacteristics-size, technology and procurement conditions, and external variables(notably, country conditions and changes in World Bank guidelines for projectappraisals)-were associated with differences in estimating reliability. From this casestudy, the paper draws implications for improving power system planning.4
The paper is structured as follows. Chapter 2 lays out the framework for evaluatingthe performance of estimates of construction costs and schedules for power generationprojects in developing countries. Chapter 3 summarizes the data base of powergeneration projects assembled for this evaluation. Chapter 4 describes the statisticalapproach used to analyze the performance of the cost and schedule estimates. Chapter 5assesses the overall performance of estimates for the group of power generation projectsas a whole, particularly the prevalence of bias and uncertainty in this performance. It alsoexamines the reliability of the World Bank's methodology for computing pricecontingencies for project cost estimates. Chapter 6 identifies project characteristics thatshow a significant correlation with cost overrun and schedule slip. Chapter 7 concludesthe paper by examining the implications of the analysis for the treatment of bias anduncertainty in power system planning.
2. The exception to this situation is to defer installation of one or more generation units in a multi-unitgeneration station, but this decision is usually made at the time of project approval rather than duringimplementation.
3. The paper does not compare estimates with actual values for fuel costs of thermal power plants oroperation and maintenance (O&M) costs.
4. The results of this analysis could provide information for innovative planning methodologies. See,for example, Crousillat (1989).
2Framework for Evaluating the Performance of
Cost and Schedule EstimatesProject cost and schedule estimates can deviate from actual costs and schedules in
two ways. First, estimates might be biased generally, in that the mean of the estimates fora group of projects differs significantly from the mean of the actual costs or schedules forthe group. If the estimates of all options for increasing power generation capacity weresimilarly biased, the net distortion to project selection would then be confined toerroneous timing rather than to incorrect choice of project, since the bias could beexplicitly allowed for. Where the bias is not identical for all projects (as is actually thecase), then a consistent direction in the bias for particular types of project can indicate thepresence of a strong influence on estimates that, once identified, is often correctable infuture estimates. Second, even when typical project biases are allowed for, estimates arestill subject to uncertainty, in which the relationship between estimates and actual valuesshows a large variance around their mean values. By identifying and allowing for factorsthat lead to variations in the degree of bias in the estimates for particular types of projects,it is possible to reduce the overall uncertainty for the financing of power projects anddevelopment of power systems.5
Most causes of deviation between estimates and actual values of costs and schedulesfall into three categories: (a) poor development of estimates and supervision of projectsby the project sponsor (normally a power utility) and its engineers; (b) poor projectimplementation by suppliers and contractors; and (c) changes to the external conditions(economic and regulatory) for a project. The long time span covered by the projects inthis analysis encompasses a variety of economic and market conditions, as indicated byperiods of high and low inflation and by several boom-and-bust cycles in the internationalmarket for power plant construction. Poor assessment of the prevailing pressures on the
5. Significant bias and uncertainty appear to exist in forecasts and estimates of most of the majorplanning parameters for power system development. For example, power demand forecasts in developingcountries are shown to have this feature in Sanghvi and Vernstrom (1989). Oil price forecasts also havebeen highly inaccurate. The historic forecasting performance for these two parameters is shown inAnnex 12.
7
8 Estimating Construction Costs and Schedules
suppliers and contractors at the time of bidding for projects can lead to inaccurateestimates. Furthermore, projects that are marginally economic and politically motivatedmay be more liable to have optimistic cost estimates relative to actual construction coststhan projects that show good economic returns because the sponsors of politicallymotivated and marginal projects are seeking to obtain approval for financing and to avoidcriticism about high costs. Changes in project scope during implementation can have asignificant impact on the project costs and schedules. Such changes can arise, forexample, from the inability of design-stage investigation to eliminate risks from unknowngeological conditions for construction of underground works, particularly for manyhydropower projects. In addition, for first-of-a-kind projects in developing countries-and many of the power projects in the data base fall into this category-project estimatorsdo not have a track record of similar projects as a basis for carefully analyzing majorconstruction risks and deriving reliable contingencies for them. Instead, they often relyon unreliable rules of thumb for such contingencies. Some account must also be taken ofsuch unpredictable events as natural disasters and civil disturbances that severely disruptproject implementation. In practice, however, it is virtually impossible to obtain a directand reliable quantification of the allocation of responsibilities for cost and scheduledeviations between these categories from the available information on project appraisal
6and implementation. The closest approximation to this analysis that could be attemptedwas a broad allocation of responsibilities for slippage in project implementationschedules (see, in chapter 5, the section on ex post analysis of responsibility for scheduleslip).
Because a direct analysis of project factors that lead to cost and schedule overrunscould not be undertaken, the paper evaluates the estimating performance of cost andschedules for a group of completed World Bank-supported power generation projects bymeans of a statistical analysis of the following relationships:
* The prevalence of bias and uncertainty within Bank-supported power generationprojects and in relation to all Bank-supported projects.
* On the basis that significant bias and uncertainty is found in the first step, the relationbetween the estimated performance and various project characteristics, such asproduction technology and project size.
* The relation between external factors associated with project implementation andestimating performance, particularly procurement method, country economicconditions, and pressure to complete the project because of demand for its output.
The analysis is based on a comparison of the estimated cost at the time of projectapproval with the actual cost of implementing the project (as determined after project
6. This problem may explain the lack of published studies of cost and schedule estimating performancefor capital projects (as opposed to the published studies that derive econometric models for predictingconstruction costs and schedules that are based on the actual costs and schedules for completed projects).
Framework for Evaluating the Performance of Cost and Schedule Estimates 9
completion) and a similar comparison for the project implementation schedule. Thetechnique of analysis used is multiple regression (using the statistical packageMicroTSP), which allows for the simultaneous correlation of the overruns with severalindicators that may themselves be correlated.7
The analysis of cost performance is done in both current price terms and constantprice terms, since there is no prior basis for assuming that cost performance in the twocases is affected identically by factors that cause deviations between actual and estimatedvalues. In other words, price effects on costs would have to be purely random to justifysuch an assumption, and the analysis reported in this paper does not support thisassumption, even though the factors influencing cost performance were found to besimilar for the two cases. The actual current costs are directly observable, whereas theactual constant costs have to be derived from the former. Estimates of project costs inboth current and constant price terms are routinely given in World Bank staff appraisalreports. Both forms of costs exclude interest during construction for this analysis.
The analysis of costs in current price terms allows for the impact of failure to allowcorrectly for price inflation. In the World Bank's appraisal of a project, the cost estimatein current prices is derived by adding to the constant price estimate a contingency forprice inflation during the project construction period.8 This price contingency allowsparticularly for the expected effect on the project cost of contractual price adjustmentclauses relating to materials, labor, and equipment.9 In view of the importance of thisprice contingency in estimates of project costs, this paper also includes in chapter 5 ananalysis of the reliability of the Bank's methodology for computing price contingencies.
The constant price cost estimate is the estimated cost of the project at the time ofnegotiating the project loan provided that there is no major alteration in project scope,
7. Where none of the indicators are correlated among themselves, a series of single-variablecorrelations between the overruns and the indicators would give identical results to a multiple correlation.Where such variables are intercorrelated, as in this study, multiple correlation is able to reveal whichvariables are significantly related to the overruns, allowing for the fact that other variables are also includedin the explanation. Thus, some variables that appear significant in a single-variable context are notsignificant when other more important variables are included. Other variables that may not appearsignificant in a single-variable context can be revealed as significant in the multiple-variable context. Thisfeature is illustrated in Annex 4 for the projects studied in this paper.
8. The World Bank's practice on contingencies for the projects under review is given in now-superseded World Bank internal documents (Central Projects Note [CPN] 3.11 of February 25. 1982;"Project Cost Estimates and Contingency Allowances." and its Operational Manual Statement (OMS] 2.21of May 1980, "Economic Analysis of Projects"). The World Bank has used explicit price contingencies forproject cost estimates from 1970 onward. The present methodology for computing price contingencies wasintroduced around 1976.
9. Another vintage effect on estimating performance is the request by the World Bank's Board ofExecutive Directors in the mid-1970s that all projects presented for its consideration have completeddesigns. Before then. most projects presented to the Board had cost estimates based on feasibility levelwork.
10 Estimating Construction Costs and Schedules
quantities, or contract prices during project implementation. The World Bank includes acontingency in this estimate for cost (not price) increases attributable to minor changes inproject scope and quantities that are expected to occur between the time of projectappraisal and project completion. This physical contingency forms part of the estimatedvalue of the project cost and is not intended to compensate for the possibility of biastoward underestimation.
The paper also assesses the reliability of the World Bank's standard sensitivity test foruncertainty in estimating project costs and schedules. It is not the World Bank's practiceto use contingency allowances as safety margins for bias and uncertainty. However, theWorld Bank does test the sensitivity of its economic analysis for power developmentprograms to deviations from its estimates for project costs and schedules, typically for a20 percent overrun from the expected value.'I
In covering only World Bank-supported projects, the analysis applies to projects thatwere generally implemented by state-owned power enterprises with government financialsupport. This analysis therefore does not give a reliable impression of estimatingperformance for projects that were financed and implemented by private sectorenterprises.
10. The World Bank also performs sensitivity analysis on the robustness of the economic justificationby comparing the maximum discount rate at which the project forms part of the least-cost means of meetingpower demand, with an estimate of the opportunity cost of capital to the host country.
3Data Base of Power Generation Projects
The data base assembled for this paper consists of 135 power generation projects indeveloping countries financed with World Bank loans and International DevelopmentAssociation (IDA) credits, of which 64 were thermal power plants and 71 werehydroelectric plants. Information on these projects is taken from World Bank documents(principally staff appraisal reports and project completion reports). These projectsconstitute virtually all the power generation projects approved for financing by the WorldBank between 1965 and 1986. The analysis thus captures the World Bank's experiencewith estimation of project costs and schedules over the long term. Issues related tosampling were avoided in this case by including all, but only, World Bank-supportedprojects of this type. The projects are listed in Annex 1.
World Bank-supported power generation projects are a suitable class for this type ofanalysis because they are
* Based on classifiable technologies for providing the same product
* Planned, designed, and procured according to well-established and identifiablepractices
e Not prone to significant changes in scope during implementation, so that estimatedand actual outcomes are comparable
* Fully implemented because they have to be completed to provide any output and,thus, project benefits
* Well represented throughout all types of developing countries and over the threedecades under study
* Well documented in Bank staff project appraisal reports and project completionreports, in which the data on appraisal estimates and actual implementation costs andschedules have been objectively checked by World Bank staff.
The actual project total costs cover a wide range-between $3.2 million and $1,782million in current-price terms. The actual project implementation schedules also cover awide range-between 1.2 and 14.4 years. The projects were implemented in 52developing countries and were distributed between regions in the manner shown in Table
11
12 Estimating Construction Costs and Schedules
3.1. The majority of the thermal power projects were located in Asia and in Europe, theMiddle East and North Africa, whereas the majority of the hydroelectric projects werelocated in Latin America and the Caribbean and in Sub-Saharan Africa.
Table 3.1 Geographical Distribution ofPower Generation Projects in the Data Base
AllThermal projects Hydroelectric projects projects
Regiona Number % Number % %
Africa (Sub-Saharan) 6 9 19 27 19
Asia 28 44 12 17 30
Europe, Middle Eastand North Africa 18 28 11 15 21
Latin American andCaribbean 12 19 29 41 30
TOTAL 64 100 71 100 100
aRegions in this table correspond to the prevailing World Bank organizational categories.
In terms of project vintage the data base is fairly well distributed over the 20-yearrange as shown in Table 3.2.
Table 3.2 Distribution of Power Generation Projects byYear of Approval in the Data Base
AllThermal projects Hydroelectric projects projects
Period Number % Number % %
1965-69 8 12 19 27 20
1970-74 19 30 16 23 26
1975-79 23 36 18 25 30
1980-86 14 22 18 25 24
TOTAL 64 100 71 100 100
In terms of project size, the data base is well represented in all the capacity ranges forthese projects, and the two groups have similar features, as shown in Table 3.3.
Data Base of Power Generation Projects 1 3
Table 3.3 Distribution of Power Generation Projects byInstalled Capacity in the Data Base
AllCapacity range Thermal projects Hydroelectric projects projects
(MW) Number % Number % %
0-49 18 28 11 15 22
50-199 13 20 24 33 27
200-499 15 23 22 31 27
500-999 10 16 9 13 14
1,000-2,499 8 13 5 7 10
TOTAL 64 100 71 100 100
The distribution of the thermal projects by type of production technology, primaryfuel, and unit size is summarized in Table 3.4. The size of generating plant in the groupof projects varies from about 2 MW diesel units to 400 MW and 500 MW units in recentcoal-fired steam plants (India, Indonesia, and Korea) and a 550 MW dual-fired (fuel oiland natural gas) steam plant in Thailand.
Table 3.4 Distribution of Thermal Projects by Production Technology,Primary Fuel, and Unit Size in the Data Base
Number of Range of unit sizeTechnology projects % (MW)
Steam turbine
Coal-fired 12 19 30-500
Fuel-oil-fired 24 37 25-500
Lignite-fired 3 5 300-330
Gas-fired 1 2 150
Multi-fueleda 6 9 125-550
Subtotal steam turbine 46 72
Gas turbine 3 5 12-40
Combined-cycle 1 2 300
Diesel 14 22 2.2-20
TOTAL 64 100
aComprising two projects with coal and fuel oil; two projects with natural gas and fuel oil; andtwo projects with coal, fuel oil, and natural gas as alternative fuels.
14 Estimating Construction Costs and Schedules
The hydropower projects encompass a wide range of hydraulic heads from 12 to1,035 meters, dams from 11 to 230 meters in height, tunnels from zero to 34 kilometers inlength, and reservoirs from virtually zero to about 840,000 hectares in surface area.
Extensions to existing thermal power stations accounted for 34 (53 percent) of all thethermal power projects, whereas for hydropower projects 19 (27 percent) wereextensions.
4Statistical Approach to Analyzing the Performance
of Cost and Schedule EstimatesThe performance of estimates is measured by the following ratios:
Cost performance. This is the ratio of the actual project cost to the estimated projectcost. It therefore measures construction cost overrun. The analysis is done for twospecifications of cost, one in current prices and the other in constant prices. Interestduring construction is excluded in both cases. The estimate is usually based onsubstantial preparation work before the time of approval to lend by the main projectfinanciers. These costs cover the capital works for the power generators andassociated transmission facilities, engineering services, and local duties on imports. I'
* Schedule performance. This is the ratio of the actual project implementation periodto the estimated project implementation period. It therefore measures slippage of theconstruction program. The start of the implementation period is taken to be the dateof project approval by the main financiers, and the end is the date of entry into serviceof the completed generation plant (formal acceptance by the power utility).
These ratios standardize the measurement of performance for differences in projectcost and schedule. This feature enables the performance of estimates to be analyzed interms of statistical distributions.
A value of unity for a performance ratio implies that the impact of associated factorson actual implementation has been correctly anticipated in the estimate. It does notnecessarily imply that actual implementation was the best feasible and that the estimatewas made correctly on this basis. Any deviation from unity represents the net effect oftwo deviations: that of actual implementation from the best feasible implementationperformance and that of the estimate from the best estimate (equal to best feasibleimplementation, by definition).
I1. Local import duties cannot be excluded because the actual payments for these duties are not givenin the World Bank's project completion reports.
15
16 Estimating Construction Costs and Schedules
The crucial point is that estimates should allow for all foreseeable events andexperience with similar projects, so that deviations between estimates and actualoutcomes should be unforeseen and random. This is the "null" hypothesis. The analysisreported in this paper tests this hypothesis by finding patterns through correlations. Theanalysis does not specifically examine the effects of unforeseen and unforeseeableconditions during project construction. These effects can only be assessed from an expost analysis such as the assessment (reported in chapter 5 of this paper) of force majeureevents on project schedules.
The analysis proceeds in two main stages. In the first stage (reported in chapter 5),the analysis assesses the prevalence among the group of generation power projects as awhole of bias and uncertainty in estimating performance for costs and schedules in thefollowing steps:
* Among power generation projects themselves as a group.
* Against all audited World Bank projects since 1974 (and thus approved from 1968),in all economic sectors for which reliable data are available on actual and estimatedperformance, numbering 2,032 projects. 2
* Against a reference distribution for the performance ratios based on the World Bank'sstandard sensitivity test for whether a project is still justified under a 20 percentoverrun from the estimate (see, in chapter 5, the section on prevalence of bias anduncertainty).
i An ex post assessment of the relative impact on schedule slip of the actions ofclients/engineers, suppliers/contractors, and uncontrollable events.
• The reliability of the World Bank's methodology for computing price contingencies.
Once the overall performance of estimating costs and schedules for power generationprojects has been described, the second stage of the analysis focuses on identifyingexternal variables and project characteristics that show a significant correlation with costoverrun and with schedule slip (as reported in chapter 6). The approach is to look forvariables and characteristics that are known at the inception of the project, and that areplausibly correlated with actual costs or schedules, so that if these links are misestimated,these variables would also turn out to be correlated with the degree of cost overrun orschedule slip. If sufficiently strong correlations can be established, then experience ofthis effect can lead to better estimates of the likely costs and schedules for future projects.In such cases there would be less measured overrun or slip.
The statistical analysis is thus searching for factors that have not been fully taken intoaccount in constructing cost and schedule estimates and whose presence affect costs andschedules and will thus be correlated with the degree of cost overrun and schedule slip.
12. The analysis of cost and schedule performance for audited World Bank projects is reported in aWorld Bank Operations Evaluation Department Report (World Bank 1992).
Statistical Approach to Analyzing the Performance of Estimates 17
Because it is not possible to identify these factors reliably in advance of the analysis forthis paper, it was decided to include a wide-ranging group of variables and characteristicsin the analysis to maximize the possibility of identifying factors that are significantlyassociated with inaccurate cost and schedule estimates.
Information was extracted from World Bank project reports on 29 project variablesand external characteristics that might be expected to have some correlation with thedegree of costs and schedules for projects as a whole. These characteristics and variablesare listed in Table 4.1. They are organized to bring out some of the underlying factorsthat influence the performance of project cost and schedule estimates. Project-specificvariables are categorized under technology, size, and procurement. Externalcharacteristics are assigned either to country variables or to World Bank guidelines forproject appraisal.
Technology variables reflect complexity of project construction, and it might beexpected that the uncertainty of cost and schedule estimates increases with thiscomplexity. The basic distinction in technology is between thermal power andhydropower, particularly in terms of the amount of plant and equipment that isconstructed under the suppliers' control on their own premises, which is greater forthermal power projects. On the other hand, civil works at the project sites are moreprominent in hydropower projects and face the uncertainties of local conditions. On thesegrounds alone, hydropower project estimates are expected to be subject to greater biasand uncertainty. An extension to an existing station is expected to produce betterestimates than for a new station because estimators should be familiar with the specificstation design and do not have to face the uncertainties associated with opening up a newsite.
Greater project size also is expected to increase project complexity and, thus, bias anduncertainty for estimates. Size is not only reflected in the obvious variables-generatorunit capacity, station capacity, total cost, and construction schedule. Rather, certainproject parameters carry their own estimating risks, such as the well-known uncertaintyassociated with underground works. Length of tunnel is thus tested, although theuncertainty often arises from difficult ground conditions (e.g., karstic limestone; seeWorld Bank 1984) or from inadequate site investigation. Dam height and hydraulic headare features that reflect overall project size, not necessarily simultaneously (e.g., a projectwith a high dam can have a relatively low hydraulic head, and vice-versa). Reservoir areareflects another aspect of size-project impact on the immediate vicinity, especiallydisplacement of resident population. It is expected that hydropower project schedules areaffected by the time required to relocate people from the reservoir area and other project-related areas, since this component has carried a high degree of uncertainty for many pastprojects.
18 Estimating Construction Costs and Schedules
Table 4.1 Variables and Characteristics Used in Regressions onConstruction Cost Overrun and Schedule Slip
Project-specific variablesTechnology
Hydropower project or thermal power project (dummy variable)
New power station or station extension (dummy variable)
Civil works-estimated cost as a proportion of estimated total project cost(percentage)
Thermal power fuel and technology:
Diesel-fueled combustion turbine (dummy variable)
Coal- or lignite-fueled steam turbine (dummy variable)
Fuel-oil-fired steam turbine (dummy variable).
SizeGenerator unit capacity (MW)
Total project generation capacity (MW)
Estimated project cost in current price terms (US$ million)
Estimated construction schedule (years)
Hydropower project features:
Dam height for new hydropower station (meters)
Hydraulic head for new hydropower station (meters)
Reservoir area created by project (hectares)
Length of tunnels (kilometers).
ProcurementYear of World Bank loan agreement
Anticipated sources of suppliers and contractors, by estimated project foreignexchange costs as a proportion of estimated total project costs (percentage)
Competitiveness of procurement process, by anticipated amount contractedunder international competitive bidding as a proportion of estimated total projectcosts (percentage)
Number of financing agencies in the project
Main contractor is from the host country (dummy variable).
Country variablesPer capita income of host country in year of loan approval (constant US$)
Statistical Approach to Analyzing the Performance of Estimates 19
Average actual cost growth rate for project components procured from hostcountry between year of loan approval and year of project completion-the GDPdeflator (percentage)
Actual growth in national (or state) power sales (GWh) between year of loanapproval and year of project completion (percentage)
Indian thermal power projects (dummy variable)
Brazilian hydropower projects (dummy variable)
Colombian hydropower projects (dummy variable)
Index of actual average cost growth rate for imported project componentsbetween year of loan approval and year of project completion (UN Unit ValueIndex of manufactured goods exported from G-5 countries to developingcountries-in constant US$ terms).
World Bank appraisal guidelinesBasis of project cost estimate-recent similar projects or tenders for majorcomponents of the project itself (dummy variable)
Pre-1970 loan agreement (dummy variable)
Post-1976 loan agreement (dummy variable).
Procurement methods are particularly important for estimating project costs andschedules because they reflect the degree of competition in the tendering and contractaward process. Since international suppliers and contractors dominate the market forconstructing power stations in nearly all developing countries, the prevailing state of theorder book for these firms is an important indicator of competition for a project. In theabsence of a detailed analysis of this feature from the mid-1960s to the mid-1980s, thebest available proxy indicator is project vintage, taken to be the year of the World Bankloan agreement, which usually corresponds closely to the time of award of majorcontracts for a project. This variable also captures any long-term secular change inestimating performance over the period of the project loan approvals. The specific degreeof competition for a project can be indicated by the amount of procurement that tookplace under international competitive bidding (ICB), as opposed to other procurementapproaches for the project, and by the proportion of foreign procurement measured by theproportion of total project costs that are incurred in foreign exchange. The origin of themain project contractor (from the host country rather than another country) is included asa dummy variable to provide an additional test for procurement. Finally, since officialfinancing agencies tend to follow their own procurement guidelines (ranging from ICB bymultilaterals to own-country preferences by bilaterals), procurement complexity, and
20 Estimating Construction Costs and Schedules
hence estimating uncertainty, tends to increase with the involvement of more financingagencies in a project.
Three country-specific characteristics and one international characteristic are testedfor their impact on estimating performance. The first is the general level of economicsupport that a country can provide for the construction of complex facilities such as apower station, which relieves and mitigates the uncertainty from reliance on imports. Thebest available proxy for most countries is country-per-capita income (although this is nota perfect indicator because, for example, India and China have low per capita incomes butsubstantial industrial capacity, whereas a small middle-income country may have to relyvirtually entirely on imported goods and services). The inflation rate in the host countryduring project construction is an indicator of economic (and, in some cases, political)stability and hence of an important element of uncertainty for constructing complexprojects. The inflation rate for imported goods and services used in a project alsoinfluences the reliability of cost project estimates. The growth rate in power sales in thecountry is an indicator of how quickly the new power capacity is required and therefore ofthe keenness of the host power company to complete the project within the estimated timeand cost. The international characteristic is a measure of international inflation thatreflects cost growth for imported components of these construction projects. 13
In three countries, however-namely India, Brazil, and Colombia-the World Bankhas supported a sufficiently large number of power generation projects to enable acountry variable to be tested specifically for each of these countries. Country dummy is aco-variate-it picks up an average effect of variables whose coefficients are not allowedto be country specific. Where a country dummy is found to be significant, a formalregression of projects in that country would be the ideal approach to identifying thecountry-specific significant variables. In such a situation, the covariance of risk amongprojects in a country could then be explicitly considered. Tests for country-specificgroupings for economic variables were not generally carried out because of lack ofdegrees of freedom with the number of countries (52) covered by the group of projects.Nevertheless, remarkably strong results are obtained given the huge variation in economicconditions encountered among the large number countries covered in the study.
Finally, the World Bank's guidelines for project appraisal specify some key practicesfor estimating project costs and schedules. From the mid-1970s onward, such estimateswere based, wherever possible, on bids for major project components. Otherwise, theseestimates were based on completed designs and actual costs for recent similar projects.Likewise, a formal price contingency in the Bank's cost estimates has been required since1970, and the current methodology was introduced in 1976. The analysis tests theimpacts of these requirements. (A detailed assessment of the reliability of this
13. In cases where the change in price index (foreign or local) or power sales was negative (3 cases),the data on the variables are omitted from the data base because they cannot be used in log form for theregression equations.
Statistical Approach to Analvzing the Performance of Estimates 21
methodology is described in chapter 5, in the section entitled Reliability of the Bank'sMethodology for Computing Price Contingencies.)
Using multiple regression analysis, a sequential analysis is undertaken in which thecost and schedule overruns are each correlated with all the above variables andcharacteristics; then, variables and characteristics that are insignificant (using a t test) aredropped one at a time; and, finally, the regression equation is re-estimated. Theprocedure is iterated until all the remaining variables are significant. The final regressionequations are taken as the "best" available predictors of cost and schedule overruns, basedon knowledge of the set of variables and characteristics used for the analysis.
5The Overall Performance of
Power Project Cost and Schedule EstimatesThis chapter is organized in the following stages. First, the performance of cost and
schedule estimates is given for World Bank-supported power generation projects as awhole. Second, estimating performance is analyzed separately for the group of thermalpower projects and the group of hydropower projects. Third, the prevalence of bias anduncertainty in cost and schedule estimates is examined. The fourth section examines anex post attribution of responsibility for schedule slip. The final section assesses thereliability of the World Bank's methodology for computing price contingencies in itsconstruction cost estimates.
Group Performance of All Power Generation Projects
The group of power generation projects as a whole has a correlation (squared) of 0.76between actual costs and estimated costs (in current prices and excluding interest duringconstruction) and a correlation of 0.55 between actual schedules and estimated schedules(see Figures 5.1 and 5.2). It is clear that the estimates are fairly strongly related to theactual outcomes but that there is considerable inaccuracy among projects as a whole inthe estimation of costs and schedules. Preliminary screening of the data on the ratios ofactual to estimated values for both costs and schedules reveals a few cases with trulyexceptional differences between estimated and actual values that should be treated assuch and omitted from any statistical analysis that is looking for regularities. The nineomnitted cases are shown in Table 5.1.
In addition, a hydropower project in Portugal (Seventh Power Project) consists of anumber of dams, so that it is impossible to relate overall cost and schedule slip to thecharacteristics of a single construction, as is the case for all the other projects. Omittingthese exceptional cases leaves 59 thermal power projects and 66 hydropower projects fordetailed analysis.
23
24 Estimating Construction Costs and Schedules
Figure 5.1 Relationship between Actual Costs and Estimated Costs for WorldBank-Supported Thermal Power Projects and Hydropower Projects, 1965-1986
(in current prices, US$ million)
Estimated current cost
10000log scale
3 Thermal
3150 A Hydro N
x/
1000 - 33u/
E Sh A
100 N NA
,E~~~~N NE A
ig ~ ~ A NEA A
Xh x
3132
Xx AYA~~~~~~
/tx~~~tA
/ ~~~~~~~~~~~~~~~~~~~~log scale
100N
0 3 10 32 100 313 1000 3150 10000
Actual current cost
The data on the variables for these projects are almost complete, with the exception ofinformation on reservoir area. Experiments with this variable on the subset of availableobservations suggest that it does not have a significant correlation with the accuracy ofcost or schedule estimates for hydropower projects.
The Overall Performance of Estimates 25
Figure 5.2 Relationship between Actual Schedules and Estimated Schedules forWorld Bank-Supported Thermal Power Projects and Hydropower Projects,
1965-1986
Estimated schedule (months)
log scale *K Thermal250
Hydro200
160
125
100
80 _
63
40
31 _ A
25 A
20 - *
16
13 log scale
1010 13 16 20 25 31 40 50 63 80 100 125 160 200 250
Actual schedule (months)
26 Estimating Construction Costs and Schedules
Table 5.1 Cases Omitted from Analysis
Country Project
Brazil Hydro: Volta Grande
Colombia Hydro: Las Mesitas
Panama Thermal: San Francisco
Romania Thermal: Second Turceni
Sierra Leone Thernal: Third Power Project (King Tom station)
Turkey Thermal: Elbistan
Uruguay Thermal: Battle Unit 6
Yugoslavia Hydro: Middle Neretva project: Grabovica and Salakovac dams
Zambia Hydro: Kariba North
Note: These projects were more prone to force majeure events than other projects and thus faced genuinelyunpredictable major risks. (The impact of force majeure events and schedules are discussed in the sectionbelow on ex post analysis of responsibility for schedule slip.) The criterion for omitting observations (ratiosof actuals to estimates) is that they were more than 4 standard deviations from the mean of the remainingpoints. Including such observations can give rise to seriously misleading regressions, since they force theregression into explaining such large outliers rather than the bulk of the more central observations. All theremaining observations lie within 2.5 standard deviations from the mean.
The overall statistics-mean and standard deviation-for the group of projects beforeand after removing the exceptional cases are given in Table 5.2.
Table 5.2 Overall Statistics for Cost and Schedule Performance (%)
Project group Mean SD
With exceptional casesCost overrun
Current costs 21.4 39.9
Constant costs 21.9 37.8
Schedule slip 36.5 41.5
Without exceptional casesCost overrun
Current costs 17.4 33.9
Constant costs 18.1 31.9
Schedule slip 29.0 28.5
Note: SD = standard deviation.
The Overall Performance of Estimates 27
Distinction between Thermal Power Projects and Hydropower ProjectsThe first regression carried out examined cost overrun for the whole group of projects
in the data base. Twenty-one of the independent variables are relevant to all classes ofprojects. The correlation coefficient for this regression was 0.56 without attempting tostrip out the insignificant variables. With so many variables, this is a moderate result. Itwas therefore decided to examine the scope for obtaining a stronger correlation bycarrying out separate regressions for thermal power projects and hydropower projects.Discriminating between these two project types allows variables that are significant toonly one or the other type to be identified and, thus, improves the regressions. This initialseparation can also be understood in physical terms because these groups of projectsinvolve qualitatively different construction techniques, and also because preliminaryindications showed that as groups they behave differently, especially as regards thetypical cost overrun (see Figures 5.3 and 5.4). 14
Figure 5.3 Distribution of Cost Performance for World Bank-Supported ThermalPower Projects and Hydropower Projects, 1965-1986 (current prices)
Percent of projects
40 Thermal Hydro -
30
20
10
< 0.80 0.80 - < 1.00 1.00 - < 1.25 1.25 - < 1.50 1.50 - < 2.00 > 2.00
Ratio of actual cost to estimated cost
14. One indication of this difference is the much higher proportion of costs that are accounted by civilworks in hydropower projects (53 percent average) than in thermal power projects (18 percent average).
28 Estimating Construction Costs and Schedules
Figure 5.4 Distribution of Schedule Performance for World Bank-SupportedThermal Power Projects and Hydropower Projects, 1965-1986
Percent of projects
60- Thermal Hydro
50
40-
30 -
20 -
10 -
0< 0.80 0.80 - < 1.00 1.00-< 1.25 1.25-< 1 50 1.50-< 2.00 > 2.00
Ratio of actual cost to estimated cost
One concern about splitting the group of projects into two subgroups is whether thereare sufficient degrees of freedom (number of observations less number of independentvariables). Significance tests take account of both the number of observations and thenumber of variables used in any of the regressions. In this case, it was possible to identifyseveral strongly significant variables in each regression.
The first step in this analysis was to find the correlations between actual andestimated costs and schedules for all World Bank-supported power generation projects,thermal power projects, and hydropower projects-excluding the 10 outliers. Thesecorrelations are compared in Table 5.3.
Table 5.3 Comparison of Squared Correlations between Actual and EstimatedCosts, and between Actual and Estimated Schedules for World Bank-Supported
Power Generation Projects
CostProject group Current Constant Schedule
All power projects 0.82 - 0.63
Thermal power projects 0.90 0.78 0.72
Hydropower projects 0.81 0.93 0.52
Note: Sample excludes the 10 outlier projects.
The Overall Performance of Estimates 29
These results indicate (particularly for schedules) only a moderate correlation betweenactual and estimated values. Thermal power projects had a high correlation for both costsand schedules.
Prevalence of Bias and Uncertainty in Cost and Schedule EstimatesAnalysis of the basic data on cost overrun and schedule slip for the 59 thermal power
projects and 66 hydropower projects-excluding the 10 outliers-gives the followingresults.
For thermal power projects as a whole there was a relatively small bias for costs,with an average underestimation of 6 percent, but for schedule there was a large averageunderestimation of 30 percent. Both the cost estimates and the schedule estimatesshowed substantial variation around these mean values, with a standard deviation of 23percent (around a mean of 106 percent for actual to estimated values), for costs and astandard deviation of 30 percent (around a mean of 130 percent) for schedules.
For hydropower projects both the average cost overrun of 27 percent and the averageschedule slip of 28 percent were very substantial. The cost ratios showed an extremelyhigh standard deviation of 38 percent (around a mean of 127 percent), whereas that forthe schedule ratios was 28 percent (around a mean of 128 percent).
Thus, even after removing the quite exceptional cases, it is clear that forecasts ofschedules generally seriously underestimate the actual schedule for both thermal powerand hydropower projects and that cost estimates were seriously underestimated forhydropower projects. Costs for thermal power projects were generally only slightlyunderestimated. There was also a very large variation in the reliability of estimates forcosts and schedules for both thermal power and hydropower projects. Even with attemptsto correct estimates by adding on a "typical" slip factor of (say) 27 percent forhydropower project cost estimates, deviations would still have been large.
Costs and schedules for power generation projects have been estimated moreaccurately than for World Bank-supported projects in general, both with respect to themean error and the standard deviation of these errors. The single exception is that costoverruns for hydropower projects have shown a substantially larger average error than theaverage cost overrun for the totality of World Bank-supported projects. The comparisonwith World Bank-supported projects as a whole is shown in Table 5.4.
30 Estimating Construction Costs and Schedules
Table 5.4 Comparison of Cost Overrun and Schedule Slip between World Bank-Supported Power Generation Projects and All Bank-Supported Projects (%)
Cost overrun Schedule slipProject group Mean SD Mean SD
All Bank projects 11 45 117 80
Thermal power projects 6 23 30 30
Hydropower projects 27 38 28 28
Note: SD = standard deviation. The effective cost overrun for all World Bank-supported projects mayhave been much higher than indicated here because the scope of many of these projects was substantiallyreduced during implementation to keep total project expenditure within the available funding (this did nothappen with power generation projects).
Source. World Bank (1992).
A 20 percent sensitivity test for economic analysis is inadequate to allow for theinherent bias and variation in the estimates of power project costs and schedules. Thissensitivity test can be expressed as a null hypothesis that the average forecast error is zeroand the standard deviation of the forecast error is 20 percent. Assuming errors to benormally distributed, it follows from this hypothesis that 16 percent of all projects wouldbe expected to have an actual-to-estimated ratio exceeding 120 percent (one standarddeviation), and only 2 percent of projects would have this ratio exceeding 140 percent(two standard deviations).15 That is, one in six of projects might be expected to have alarger cost or schedule overrun than the one used for sensitivity analysis. In the light ofthe larger actual means and standard deviations found above for overruns, the chances ofexceeding the sensitivity criterion are as given in Table 5.516
Table 5.5 Chances of Overruns Exceeding 20 Percent Sensitivity Level (%)
CostProject grouip Current Constant Schedule
Thermal power projects 27 32 63
Hydropower projects 57 59 61
15. Sensitivity tests are usually conducted only for overruns, so that a right-skewed distribution wouldbe more accurate than a normal distribution. Finding an appropriate distribution would require an analysisof residuals, and hence a normal distribution was chosen just to illustrate the limitation of this type ofsensitivity test.
16. For example, for the thermal power project cost overrun that has a normal distribution with mean1.06 and standard deviation of 0.23, this is equivalent to asking what the chance is that a random drawingexceeds 1.2. The answer is equal to the probability of drawing from a standard normal distribution a valueexceeding (1.2 - 1.06)/0.23 = 0.61. which is 27 percent.
The Overall Performance of Estimates 31
Even allowing for 20 percent underestimation, the majority of hydropower projectscould be expected to have a larger cost overrun and schedule slip, and the majority ofthermal power projects could be expected to have a larger schedule slip, than thesensitivity analysis value. In order to construct a sensitivity test at a level where only afew projects could be expected to show larger cost overruns or schedule slip, a 40 percentlevel would be more appropriate. With such a large test deviation, however, standarddeterministic approaches to project justification become virtually unworkable. Thisfinding thus underscores the need for proper risk analysis rather than simplistic sensitivitytesting.
Finally, the standard procedure of testing sensitivity to cost overruns and scheduleslips separately fails to capture the compounding effect on the benefit/cost ratio of aproject when both errors occur. In this case, the increase in cost arising from scheduleslip through the effect of time on the value of money would lead to higher chances ofoverruns exceeding the 20 percent level than those given in Table 5.5.
The correlations between costs overruns and schedule slips for thermal power andhydropower projects were found to be weak, as shown in Table 5.6.
Table 5.6 Squared Correlations between Cost Overruns andSchedule Slips for Thermal Power and Hydropower Projects
Thermal power cost overrun 0.24Thermal power schedule slip I
Hydropower cost overrun 0.01Hydropower schedule slip 0
The difference in magnitude of these correlations suggests that the unanticipatedfactors may have some common factors for costs and schedules of the thermal powerplants but that for hydropower plants the unanticipated factors are completely different asregards cost overruns and schedule slip.
Ex Post Analysis of Responsibility for Schedule SlipAn ex post analysis of the causes of slippage in project implementation schedules was
undertaken to attribute responsibility between the two main parties for project andimplementation-namely client/engineer and contractor/supplier-as well as touncontrollable events. This analysis covered 103 of the power generation projectsapproved for financing by the World Bank between 1965 and 1986. The relativeimportance of the causes was identified by counting the number of times each cause wascited in project completion reports.
A wide range of causes were cited (they are listed in Annex 5; 25 for thermal powerprojects, 41 for hydropower projects). Many of the causes (transportation difficulties,
32 Estimating Construction Costs and Schedules
delays in contract award, equipment failure during testing, replacement of substandardwork, and shortages of materials) were cited in both classes of projects. Other frequentlycited causes for hydroelectric projects were geological problems, design changes, badweather, and poor project management. Thermal power projects were also subject todelays caused by labor disputes and shortages of skilled labor.
A noticeable feature of the list of causes is the emphasis on implementationdifficulties, with the implication that they would not have been anticipated in scheduleestimates based on the assumption of good project implementation performance.However, it can be argued that project clients and their engineers should have been ableto anticipate problems under their control (and have had the incentives to do so) inpreparing their estimates of project schedules, even if they had to assume that contractorsand suppliers would perform soundly and that uncontrollable events (such as naturaldisasters and civil disturbance) were too unpredictable to factor into their estimates.
The citations were then attributed to categories-client/engineer, contractor/supplier,and uncontrollable events (relative frequencies of the citations are shown in Table 5.7).
Table 5.7 Ex Post Attribution of Responsibility for Project Schedule Slip (%)
Party orfactor Type of projectresponsible for slip Hydropower Thermal power
Client/engineer 43 34
Contractor/supplier 48 50
Uncontrollable events 9 16
In order to test whether these factors are captured by the variables used in theregression analysis (see chapter 6), a simple test is used. Three "dummy" variables arecreated for the three causes of slip, and for any project the dummy is given a value ofunity if that factor was identified as having been a problem during implementation (andzero if not). The best regressions for schedule slip, as given below, are then rerun withthe inclusion of the three dummy variables. For neither thermal project schedule norhydro project schedule are any of the dummy variables significant, suggesting that theincluded variables, which are known in advance of project implementation, are assuccessful as a crude ex post analysis in identifying sources of schedule slip. If thefactors used to construct the dummy variables could be given weightings, rather thansimply dichotomized as present or absent, then ex post analysis might be able to identifysome of the variation that is unexplained by the regression.
The Overall Performance of Estimates 33
Reliability of the World Bank's Methodology forComputing Price Contingencies
To allow for escalation in its project cost estimates during project implementation, themethodology introduced in 1976 by the World Bank computes a price contingency fromthe following three basic parameters:
* Estimated project cost in constant price terms of year project approved ("base year")
* Forecast escalation factor for the costs of imported project components
* Forecast escalation factor for the costs of locally procured project components.
This apparently simple formulation in fact involves a complex set of relationshipsbetween numerous variables, as shown by the fully expanded formula given in theappendix to Annex 7. The World Bank's formula thus has the disadvantage ofcompounding the uncertainties involved in forecasting many variables. The extent of thisuncertainty is shown by the wide range of errors in cost escalation estimates for WorldBank-supported power generation projects that is shown in Figure 5.5. It is noticeablethat the greatest errors occurred during the periods of highest international inflationbetween 1970 and 1986.
The factors that determine the reliability of this cost escalation formula are thus theaccuracy of the projections for these variables together with the forecast pattern ofcommitments to project expenditures over the estimated schedule of projectimplementation.
If full ex post information on assumptions and actual values for all these variableswere available for the projects, the reliability of the formula could be gauged by a simpledisaggregation of the formula to derive the contributions to cost escalation. Some of thisinformation is not available, however, particularly on the proportions of actual costs thatare incurred in each year of implementation. For purposes of assessing the reliability ofthis formula from the available project data, the analysis therefore proceeds in thefollowing manner.
The estimate of project cost in constant price terms is noted as CO(E). To this value,a price contingency factor is added to give an estimate in current price terms, CU(E).
At the termination of project construction, the actual cost in current price terms,CU(A), is revealed. From this cost, an implicit actual value in constant prices, CO(A), iscalculated using the disbursement formula described in Annex 6. The analysis proceedsby examining the cost overrun in current price terms, O(CU) = CU(A)/CU(E), andfinding factors that are correlated with the extent to which actual costs exceed estimatedcosts (both measured in current prices). The analysis is carried out on the record of thegroup of power generation projects covered by this paper.
34 Estimating Construction Costs and Schedules
Figure 5.5 Errors in Cost Escalation Estimates for World Bank-Supported PowerGeneration Projects Approved between 1970 and 1986
Year of approval1986 $1985
1984
1983
1982
1981
1980
1979 _
1978
1977
1976
1975
1974
1973
1972
1971
1970 l_l_l
-4 -2 0 2 4 6 8 10
Ratio
Note: Ratio of (Actual Cost Growth less Estimated Cost Growth) to Estimated Cost Growth, where costgrowth is the difference between project cost in current prices and project cost in constant (base year) prices.
The Overall Perfonnance of Estimates 35
Since the estimate of current costs is based on an estimate of constant costs togetherwith estimates of the price factors, errors in either or both of the latter terms will lead toerrors in cost estimates expressed in current prices.
The basis of this analysis is to examine a series of price relationships to findinterrelationships between these different measurements. Four separate links areexplored:
a. The link between actual costs in current prices and estimated costs in current prices
b. The link between current actual costs and constant actual costs
c. The link between actual cost escalation (current actual costs relative to constant actualcosts) to estimated cost escalation (current estimated costs relative to constantestimated costs)
d. The link between the cost overrun (actual versus estimated) in current terms to costoverrun in constant price terms and the errors in predicting inflation rates and projectschedule.
These four links are interconnected and follow a natural sequence. The first revealsthe degree of accuracy of the central value-the cost in current prices-whereas thesecond indicates the importance of inflation in the actual cost that emerges. Given thatthere is inflation (cost escalation), the third reveals the extent to which the estimated costescalation is an adequate predictor of actual cost escalation. The fourth examines therelationship between the failure to produce unbiased estimates of actual costs (in currentterms) and the failures to predict costs in constant price terms (the physical dimension)and to predict inflation (a function of inflation rates and construction schedule) correctly.Once it is established that any failure to forecast costs well is due to failures to predictcosts in constant terms as well as to failure to predict inflation, then it is important tosearch for factors that are known at the time of project preparation that tend to becorrelated with errors in cost estimation, so that an appropriate adjustment can be made tothe estimates or a warning given on possible bias.
Annex 7 presents the statistical analysis of these four links. The principal findings areas follows:
a. The actual and estimated values, both measured in current costs, are strongly but farfrom perfectly correlated. Moreover, estimated values are significantly below actualvalues. Such a difference can be due to differences in predicting the physical costs(constant prices) or the inflation rate.
b. In order to check the accuracy of the working of the price contingency formula, theactual current cost was correlated against the actual constant cost value, as well as theactual domestic inflation, the actual inflation of imported manufactures, and the actualschedule length. The strong relation between these variables (especially for thermalpower projects) confirms that the "physical" aspect of the project can be separatedfrom the inflation component.
36 Estimating Construction Costs and Schedules
c. The actual cost escalation is correlated with the estimated cost escalation, and thisrevealed a strong but not perfect relationship, leaving room for further improvementsin constructing this aspect of a project cost forecast. As expected, no difference inforecasting performance was found between thermal and hydropower projects.
d. A regression was made of the cost overrun in current price terms on the cost overrunin constant price terms, errors in forecasting domestic inflation and importedinflation, and errors in estimating the schedule period. This showed that both thephysical and inflation aspects of forecasting errors could be identified, because errorsin estimating three of these variables-constant project costs, domestic inflation, andschedule length-were all significantly related to the overall error in estimatingproject cost in current terms. The relationship was weaker for hydropower than forthermal power projects, confirming an earlier finding that forecasting for the physicalcomponent for hydropower projects has been less successful than for thermal powerprojects.
6Significant Project Characteristics and External
Variables for Cost and Schedule EstimatesIn view of the size and distribution of the errors in estimating project costs and
schedules, it is desirable to look for a method that identifies classes of projects that tendto have high or low cost overruns or schedule slips. The approach is to recognize that anumber of project-specific factors will affect the actual cost and actual constructionschedule of any project. Many of these factors are quantifiable (such as project size,measured either in costs or some physical unit), although some are only classifiable bytheir presence or absence (whether a project is new or merely an extension of an earliercompleted project).
Chapter 4 described in detail some 29 variables that can plausibly be considered to becorrelated with actual costs and schedule. For these links, the sign of the correlationmight be predictable (e.g., that in higher income countries the actual costs of a givenproject would be less than they would be if the same project were constructed in a lower-income country). If such features are known and fully recognized, they would be takeninto account in constructing the estimates of costs and schedules. Any errors inestimation are then associated with unforeseeable events or with incorrect assessments ofthe importance of the project-specific factors. In other words, the results of the regressionanalysis do not specifically identify the main risk factors but rather how well they aretreated. Thus, some risk factors may appear significant because estimators did notconsider them with due care, even though these factors would not generally be consideredas among the most significant factors. Conversely, factors known to be risky may be sowell treated that they do not appear among the significant factors in this analysis.
Regarding the group of projects as a whole, purely random factors would makeestimates diverge from actual, with some above and some below. Moreover, there wouldbe no pattern in the errors taken in their entirety: Not only would the average error for alarge enough group of projects be zero (or very near to zero) but the error and anyobservable variable known at the time of constructing the estimate would not becorrelated. Where a factor has been allowed for but its impact is systematically under- oroveremphasized, the regression residual would then be correlated with that factor. Even
37
38 Estimating Construction Costs and Schedules
when a factor is positively (say) correlated with actual costs, the error can be negativelyor positively correlated with that factor depending on whether the implicit link is over- orunderestimated. ' 7
When all the relevant systematic factors have been allowed for in constructingestimated values, and when the strength of these links has been correctly identified, thenthe ratio of the actual to estimated values should fluctuate randomly around a mean ofunity. This is then the null hypothesis-that no variables should have a significantcorrelation with the ratio of actual to estimated values. If a significant correlation can beidentified, then the analysis has picked up tendencies to over- or undercompensate forrisk factors by the project analyst. In this situation, the estimates were capable ofsystematic improvement taken for the group of projects as a whole.
The use of regression techniques allows both the identification of any such significantfactors and the quantification of their relative importance in terms of the amount ofvariance explained by them. The factors with the largest t values are significant at thehighest confidence levels. For example. a t value of 1.67 gives a 90 percent confidencelimit, and a t value of 3 gives a 99 percent confidence limit, for the number ofobservations that correspond to the number of power projects in the thermal group or thehydro group. The unexplained variance after allowing for the effect of significant factorshas to be treated as the unpredictable risk for these estimates. As given by the formula inAnnex 4, the t ratio on each variable in a regression can be used to calculate its partialcorrelation with the dependent variable. The squared partial correlation is the percentageof total variation in a model not explained by the set of all other variables included in theequation that is explained by the variable in question. The higher the t ratio, the higherthe partial correlation attached to that variable.
Although even preliminary inspection can reveal that certain variables are stronglycorrelated with differences in the accuracy of estimating actual values, with so manypossible variables to check it is necessary to adopt a systematic search procedure,particularly since there are no prior indications of which factors have been taken intoaccount imperfectly in arriving at the estimated values. Accordingly, multiple regressionsof cost overrun and schedule slip were carried out on the factors described in Table 4.1.Trials with such regressions for quantitative variables, including the performance ratio
17. These ideas can be formalized: Let actual values (A) of costs or schedules be related to anindicator X and a random term u by the loglinear form: A = aXb * eU; while the estimated value (E) iscalculated on the basis of the level of factor X by the form: E = cXd. Hence the log of the ratio of actual toexpected values is given by log (A/E) = log (a/c) + (b - d) log X + u. which is a simple form of the modelused in the multiple regressions. The sign of (b - d) depends both on the sign of the actual relation and thedegree to which the schedule is misestimated.
Significant Project Characteristics and External Variables 39
itself. indicated that it was most satisfactory to run a "double log" form of regression sothat individual parameters can be interpreted as elasticities.'8
Once the most "general" equation that included all variables had been estimated,variables that were "insignificant" (based on a 90 percent confidence level) were removedone at a time, and the equation re-estimated omitting that variable.'9 The systematicelimination of insignificant variables not only reduces the degree of bias in the remainingregression but also reduces the overall level of uncertainty (variance) in it because itremoves the variances associated with these variables.
Given that it is not possible to predict which variables will be correlated with failuresto estimate costs and schedules accurately before the analysis, it was consideredreasonable both to use a large size of significance test in order to pick up even weakregularities in the data, and to use a two-sided test since the impact of a variable onarriving at estimated values could be either under- or overvalued. The final selectedequation thus has only "significant" variables.
The multiple correlation (R-squared) coefficient measures the percentage of the totalvariation of the performance ratio that is explained by the inclusion of the variables. Acorrelation of zero would indicate that the explanation was no better than that achieved byjust using the sample mean of the dependent variable, whereas a correlation of 100percent would indicate that a complete explanation for the variation had been achieved.A linearized correlation is obtained by correlating the anti-logs of the fitted values of theequation with the actual ratios. From this latter equation, the average residual (linearizedstandard error of regression) is calculated that indicates the unexplained residual variationin the ratio by the regression and that can be compared to the standard deviation of thebasic data.
The same approach is used for the analysis of both the cost overrun ratio and theschedule slip ratio. The log of each ratio is correlated with all variables, and theninsignificant variables are sequentially removed. No attempt was made to impose thesame factors in the analysis of schedule slip that were found to be important for costoverrun or vice-versa.
The analysis for significant variables was carried out separately for the following sixcases: thermal power project costs, hydropower project costs (costs in both current and
18. It should also be noted that in absolute terms the ratio of actual to estimate must fall between zeroand infinity (a skewed distribution), whereas the log form of the ratio will be more symmetric and fallbetween plus and minus infinity. Taking logs thus supports the presumption that regression residuals willbe normally distributed.
19. A confidence level of 90 percent (test size, 10 percent) indicates that were the null hypothesis of nocorrelation to be true, such a regression value would be expected to occur in random sampling in less than10 percent of the time. It is possible to see from the test that some of the variables would have passed ahigher significance test of 5 percent or even I percent (two-tailed significance results).
40 Estimating Construction Costs and Schedules
constant values), thermal power project schedules, and hydropower project schedules.Annex 2 shows the regression results with all the tested variables included in theequation. Annex 3 shows plots of the actual ratio (actual value to estimated value) andpredicted ratio (predicted value from one of the regression equations to estimated value)for the cost and schedule of each power generation project. These plots show how wellthe regressions are generally able to predict the value for each project over the wideranges of the actual ratios among these projects.
Thermal Power Project CostsThe performance of project cost estimates is analyzed for two cases: first for costs
expressed in current values (including the effect of price inflation on costs) and secondfor costs expressed in constant values. The results of the analysis for thermal powerproject costs (current values) are given in Table 6. 1.
Table 6.1 Significant Variables for Thermal Power Project Costs (current values)
Regression 2-tailedVariable coefficient Standard error t-stat. significance
Intercept 0.525 0.124 4.226 0.000
Log estimated cost -0.146 0.028 -5.193 0.000
Log estimated 0.287 0.106 2.708 0.010schedule
Extension dummy -0.156 0.054 -2.862 0.007
India dummy 0.201 0.074 2.728 0.010
Log civils costs ratio 0.083 0.034 2.466 0.018
R-squared 0.523 Mean of dependent 0.018
SER 0.177 SD of dependent 0.242
Linearized R-squared 0.573 Linearized SER 0.169
Note: Dependent variable is log of the thermal cost ratio, based on 45 observations and using 10percent retention rule.
civils = civil works; SD = standard deviation; SER = standard error of regression.
In the case of thermal power project cost overruns, the multiple correlation based onall explanatory variables was 80 percent (Annex 2). Once all the insignificant variableshad been removed, a strong (linearized) correlation of 57 percent was obtained with five
Significant Project Characteristics and External Variables 41
significant variables. Since any regression that includes an intercept has the property thatits mean prediction is equal to the mean of the actual data, this regression has an averageprediction error (residual) of zero (compared to the bias of 6 percent in the raw data). Byallowing for the variations in the measured indicator variables between projects, thisregression is also able to reduce the variation around this unbiased value by about one-quarter, from the standard deviation of 0.23 for the cost ratios of thermal power projectsas a whole (reported in chapter 5 at the beginning of the section on prevalence of bias anduncertainty) to the 0.17 of the linearized standard error of regression.
Both estimated costs and station extension dummy had a negative association withcost overruns. Thermal power projects in India, projects with long estimated schedules,and projects with a large estimated civil works component all had a positive associationwith cost overruns. The two variables related to project size (cost and schedule) thusinfluenced estimating performance in opposite directions. Where the variables areentered into the regressions in log form, the coefficients are elasticities. Thus, Table 6.1shows that a 1 percent increase in the level of estimated costs is associated with a 0. 14percent decrease in cost overruns, whereas a 1 percent increase in the share of civil workscosts is associated with a 0.08 percent increase in cost overrun.
The use of the regression equation to predict the actual fitted values is illustrated forone of the observations on thermal costs where the estimate was substantially too low.The India 911 project (loan date, 1978) had an estimated cost of $405.9 million, but theactual cost turned out to be $491.1 million. The ratio of actual to estimated values istherefore 1.21, rather than the unit value it should have had if the estimate had correctlypredicted the actual outcome. Given that the group of thermal projects as a whole had a 6percent cost overrun, it can be seen that even applying this average correction to theestimated costs would have still produced a substantial error. The regression equation inTable 6.1 is a project-specific way of making a prediction of the ratio of actual toestimated costs. For the India 911 thermal power project the estimated cost was 405.9(natural log value 6.006); the estimated schedule was 5.33 years (log value 1.673); theproject was not an extension (dummy value 0.0); the project was in India (dummy value1.0) and the civil cost ratio was 0.192 (log value -1.655). Multiplying these values by theregression coefficients shown in Table 6.1 and then summing these values gives a fittedvalue for the log of the cost ratio of 0.192, and the antilog of this ratio gives a predictedvalue of the cost ratio of 1.211. In this case, the regression model is extremely accurateand clearly outperforms the basic estimate (ratio unity) or the average bias correction(ratio 1.06) as a predictor of the ratio of actual to estimated costs. Not all projects arepredicted as well as this, but the linearized correlation of 57 percent shows that more thanhalf the variation that would be left unexplained by the average bias correction approach(equivalent to using a regression model with just an intercept as independent variable) isexplainable in terms of a few simple variables whose values were known at the time ofloan approval.
42 Estimating Construction Costs and Schedules
The results of the analysis for thermal power project costs in constant values are givenin Table 6.2.
Table 6.2 Significant Variables for Thermal Power Project Costs (constant values)
Regression Standard 2-tailedVariable coefficient error t-stat significance
Intercept -10.574 2.957 -3.575 0.000
Log of loan approval date 2.626 0.705 3.721 0.000
Log of estimated cost -0.274 0.054 -5.083 0.000
Log of estimated schedule 0.174 0.090 1.932 0.059
Log of MUV index -0.081 0.043 -1.899 0.063
Log of unit size 0.115 0.041 2.745 0.008
Extension dummy -0.126 0.055 -2.299 0.025
Dummy for 1976 -0.264 0.110 -2.388 0.020
Indiadummy 0.171 0.070 2.448 0.018
R-squared 0.463 Mean of dependent 0.065
SER 0.173 SD of dependent 0.219
Linearized R-squared 0.447 Linearized SER 0.179
Note: Dependent variable is log of the thermal constant cost ratio, based on 57 observations and using 10percent retention rule.SD = standard deviation; SER = standard error of regression.
Lower correlations are obtained in the case of constant costs than in that of currentcosts, although the standard errors of regression are virtually equal. The multiplecorrelation based on all explanatory variables for constant cost overruns is 58 percent(Annex 2), and on only the significant variables, 46.3 percent. Nevertheless, there aremore significant variables for the constant costs case (8) than for the current costs case(5). Four variables-estimated cost, estimated schedule, extension dummy, and Indiadummy-are significant in both cases. Project size seems to be highly significant for theconstant cost case, since estimated cost and estimated schedule, as well as unit size, aresignificant variables for this case. The significance of the MUV index and the 1976dummy could indicate that the World Bank's methodology for computing pricecontingencies (see chapter 5) has a significant bearing on the performance of project costestimates in constant values.
Significant Project Characteristics and External Variables 43
Hydropower Project CostsThe results of the analysis for hydropower project costs (current values) are given in
Table 6.3.
Table 6.3 Significant Variables for Hydropower Project Costs (current values)
Regression 2-tailedVariable coefficient Standard error t-stat significance
Intercept 0.397 0.394 1.009 0.317
Log estimated cost -0.193 0.043 -4.468 0.000
Log forex -0.224 0.073 -3.062 0.003
Log station size 0.117 0.042 2.828 0.006
Log GDP deflator 0.076 0.032 2.383 0.021
Extension dummy 0.360 0.198 1.819 0.074
Log hydraulic head 0.110 0.035 3.131 0.003
Colombia dummy -0.423 0.102 -4.167 0.000
Log financing 0.234 0.083 2.832 0.006agencies
R-squared 0.511 Mean of dependent 0.192
SER 0.224 SD of dependent 0.301
Linearized R-squared 0.511 Linearized SER 0.267
Note: Dependent variable is log of the hydropower cost ratio, based on 66 observations and usingio percent retention rule.SD = standard deviation; SER = standard error of regression.
For hydropower projects, where the mean and standard deviations of the cost overrunare much larger than for thermal power projects, and where the regression on all variableshas a correlation of 62 percent (Annex 2), the final regression is fairly successful, sincethe squared correlation is 51 percent. The linearized standard error of regression of 0.27shows that the regression reduces the uncertainty around the mean overrun by one-thirdfrom the standard deviation of 0.38 for the cost ratios of hydropower projects as a whole.Again, the log of the estimated cost variable has a negative sign, indicating that a givenpercentage cost overrun was less likely with a larger financing plan. The log of thepercentage of foreign exchange also had a strong negative relation. The station size had apositive relation, as did the local inflation rate. The hydraulic head (for projects that arenot extensions) had an important positive relation with cost overrun, since this is avariable that can vary greatly in magnitude among projects. A particularly interesting
44 Estimating Construction Costs and Schedules
finding is that the group of Colombian hydropower projects as a whole tended to have alower percentage cost overrun than would be expected for their size, hydraulic head, andnumber of financing agencies (about six). A project-by-project analysis of this groupconfirms that their mean cost overrun (measured in current prices) was only 1.5 percent,compared with 27 percent for hydropower projects as a whole.2 0 No such country-specific effect was found for the group of Brazilian hydropower projects.
The results of the analysis for hydropower project cost in constant values are given inTable 6.4.
Table 6.4 Significant Variables for Hydropower Project Costs (constant values)
Regression Standard 2-tailedVariable coefficient error t-stat significance
Intercept 0.117 0.383 0.305 0.761
Log estimated cost -0.253 0.063 -3.971 0.000
Log forex -0.144 0.080 -1.792 0.080
Log station size 0.174 0.057 3.063 0.003
Extension dummy 0.370 0.193 1.913 0.062
Log hydraulic head 0.110 0.033 3.265 0.002
Log financing agencies 0.336 0.092 3.654 0.000
Colombiadummy -0.364 0.143 -2.538 0.014
R-squared 0.472 Mean of dependent 0.216
SER 0.216 SD of dependent 0.276
Linearized R-squared 0.499 Linearized SER 0.259
Note: Dependent variable is the log of the hydropower constant cost ratio, based on 51 observations andusing 10 percent retention rule.
SD = standard deviation; SER = standard error of regression.
Slightly lower correlations are obtained in the constant costs case than in the currentcosts case. The multiple correlation for constant cost overruns based on all explanatoryvariables is 56 percent (Annex 2), and on only the significant variables, 47.2 percent. Thetwo cases share seven significant variables, and the exception is that GDP deflator issignificant for only the current costs case.
20. The Las Mesitas Hydropower project is omitted from the data set because of its schedule slip of160 percent. Its cost overrun was high at 60 percent, but even including this one raises the average for theColombian projects to only 8 percent.
Significant Project Characteristics and External Variables 45
Thermal Power Project SchedulesThe results of the analysis for thermal power project schedules are given in Table 6.5.
Table 6.5 Significant Variables for Thermal Power Project Schedules
Regression 2-tailedVariable coefficient Standard error t-stat significance
Intercept -7.989 3.844 -2.078 0.043
Log loan approval date 2.335 0.930 2.511 0.015
Log forex -0.277 0.078 -3.573 0.001
Log station size -0.081 0.021 -3.802 0.000
Post-1976 dummy -0.283 0.101 -2.815 0.007
Post-1970dummy -0.105 0.101 -1.834 0.073
India dummy -0.231 0.100 -2.309 0.025
R-squared 0.405 Mean of dependent 0.242
SER 0.180 SD of dependent 0.221
Linearized R-squared 0.479 Linearized SER 0.220
Note: Dependent variable is log of the thermal power schedule ratio, based on 57 observations and using10 percent retention rule.forex = foreign exchange; SD = standard deviation; SER = standard error of regression.
For the schedule slip of thermal power projects, which have a substantial mean andstandard deviation, the regression on all variables has a correlation of 58 percent (Annex2). After dropping insignificant variables, the regression is again fairly successful,accounting for 40 percent of the total variance. The linearized standard error ofregression of 0.22 is again about two-thirds of the standard deviation of 0.30 for theschedule ratios of thermal power projects as a whole.
The positive sign for the log of the loan approval date indicates that for a given set ofvalues of the other variables, thermal power projects approved later tended to have largerschedule slips. The interactions between the date of the loan approval and the post-1970and post-1976 dummies indicate a general deterioration in the trend for estimatingperformance for thermal power construction schedules, both before 1970 and after 1976but also show, that around those dates, steep improvements in performance, so that thetrend decline was from a smaller level of underestimation from 1977 onward than it hadbeen before 1970. The amount of project costs incurred in foreign exchange, the station
46 Estimating Construction Costs and Schedules
size, and thermal power projects in India were all negatively correlated with schedule slipfor thermal power projects.
Hydropower Project SchedulesThe results of the analysis for hydropower projects schedules are given in Table 6.6.
Table 6.6 Significant Variables for Hydropower Project Schedules
Regression Standard 2-tailedVariable coefficient error t-stat significance
Intercept 0.457 0.314 1.457 0.151
Log estimated schedule -0.286 0.071 -4.031 0.000
Log per capita income 0.057 0.024 2.406 0.019
Log % ICB -0.132 0.054 -2.456 0.017
Extension dummy 0.502 0.114 4.396 0.000
Log hydraulic head 0.070 0.021 3.324 0.002
R-squared 0.438 Mean of dependent 0.222
SER 0.153 SD of dependent 0.197
Linearized R-squared 0.434 Linearized SER 0.200
Note: Dependent variable is the log of the hydropower schedule ratio, based on 63 observations,and using 10 percent retention rule.
SE = standard error; SD = standard deviation; SER = standard error of regression.
The regression for hydropower project schedule slip is moderately successful,accounting for 44 percent of the total variance (compared to the regression on allvariables that had a correlation of 70 percent, Annex 2). Again, the linearized standarderror of regression of 0.20 indicates that the uncertainty is reduced by about one-thirdfrom the standard deviation of 0.28 for the schedule ratios of hydropower projects as awhole. The mean prediction of the ratio is equal to the mean of the ratio of actual toestimated schedules. The regression indicates that the schedule estimates were relativelymore reliable at high levels of estimated schedule but less reliable for extension projectsand for larger hydraulic heads on new projects. Schedule slip for hydropower projectswas also positively correlated with per capita income and negatively correlated with theproportion of the project that was subject to international competitive bidding.
Significant Project Characteristics and External Variables 47
Grouping of Significant VariablesThe multivariate analysis of the performance of estimates for project construction
costs (current values) and schedules reported in the previous sections identified a total of18 significant variables at the 90 percent confidence level for the six regression equationsthat cover thermal power and hydropower projects separately. Of these variables, 7variables are significant in one of the four regressions, 4 variables in two of theregressions, 5 variables in three of the regressions, I variable-estimated cost-in four ofthe regressions, and 1-extension dummy-was significant for five regressions. Thus,many factors are significant, but each has a relatively small impact on overall estimatingperformance.
The 18 significant variables are distributed widely among the 29 tested variableslisted in Table 4. 1. In terms of the five categories used for these variables, 2 of thesignificant variables (station extension and civil works costs) are technological; 5(estimated cost, estimated schedule, station size, unit size, and hydraulic head) relate toproject size; 4 (loan approval date, foreign costs, number of financing agencies, andproportion of ICB) reflect procurement; 5 (local inflation, per capita national income,MUV index, Colombia dummy, and India dummy) are country-specific; and 2 (post-1976dummy and post-1970 dummy) fall under the category of World Bank appraisalguidelines. Variables from the same category, however, seldom reinforce each others'impacts because they tend to be scattered among the regression equations and in somecases are correlated in opposing directions. These results are summarized in Table 6.7.
The presence of many variables in the regressions confirms the anticipatedrelationships postulated in the selection of variables for this analysis (chapter 4). Tobegin with, the basic technological distinction between thermal and hydropower projectsis strongly confirmed. But the significance of civil works only for thermal costs issurprising, which indicates that the impact of this factor in estimates of schedules hasbeen generally well handled. On the other hand, the finding of a greater underestimationof costs and schedules for extensions to hydropower projects, but a lesser underestimationof costs for extensions to thermal power projects. indicates that extension projects oftenare not as straightforward as expected.2
In the case of thermal power projects, fuel type and production technology were notfound to be significant variables in multivariate regression, although the diesel dummywas significant in the single variate analysis for both costs and schedules, and the coaldummy was significant for costs.
21. Since plant extensions constitute about 40 percent of the projects in the data base, it could beargued that this subcategory of projects should be analyzed separately to test whether its regressions havesignificantly different coefficients than those for the whole database. However, in this case (and also in thecases of the other dummy variables), the intercept is likely to capture the mean impact of any change ofslope in the regression line, so it should give a good approximation of the impact of this variable.
48 Estimating Construction Costs and Schedules
Table 6.7 Grouping of Significant Variables forProject Cost and Schedule Estimates
Thermal power projects Hydropower projects
Cost overrun Schedule Cost overrun Schedule
Significant variable Current Constant slip Current Constant slip
Extension dummy - - + + ++
Log civil costs ratio +
Log estimated cost - - - -
Log estimated schedule + + *
Logstation size * 0 - + ++ +
Log unit size *+ *
Log hydraulic head n.r. n.r. n.r. + + + + + +
Log loan approval date * ++ + *
Log forex - - -
Log financing agencies + + +
Log % ICB . . .
Log MUV index -
Log GDPdeflator +
Log per capita income . . +
Colombia dummy n.r. n.r. n.r. - -
India dummy + + - n.r. n.r. n.r.
Post-1976 dummy - - * *
Post-1970 dummy * * -
Key: + positive correlation at 90 percent confidence level- negative correlation at 90 percent confidence level+ + positive correlation at 99 percent confidence level- negative correlation at 99 percent confidence level* correlation is not significant at 90 percent confidence leveln.r. not relevant
The relationship between estimating performance and variables related to project sizewas mixed. For power generation projects as a whole, there appears to be a tendency forthe percentage overrun to decline with the size of the estimated cost in current values.The fact that this variable appears for both hydropower and thermal power projectsindicates that whatever leads to a failure to take into account fully the level of estimated
Significant Project Characteristics and External Variables 49
costs is common to both types of projects. On the other hand, estimated schedule waspositively correlated with thermal cost estimation performance and negatively correlatedwith hydro schedule estimating performance. Similarly, station size was positivelycorrelated with the estimating performance for hydro costs but negatively correlated withthe estimating performance of thermal schedules. Hydraulic head had a strong positivecorrelation with the performance of both hydro costs and hydro schedules.2 2
One particularly striking feature of the analysis is that many of the variables listed inTable 4.1 are not correlated significantly with the cost or schedule ratios, either singly orin combination with other variables in the multiple regression context. In the case ofhydropower projects, for example, the dam height and tunnel length for new projects havesingle squared correlations of under 2 percent with the cost ratio and schedule ratio (avalue of 5 percent would be needed to indicate significance for a single variable), andthey are never significant in the multiple regression context. This suggests that thefactors associated with those variables that affect costs and schedules have been correctlyallowed for in constructing the estimates, but that there is some aspect caught by the sizeof the hydraulic head that was not fully allowed for in either the cost or the scheduleestimates.23
Procurement and country variables had mixed significance. Estimates forhydropower projects seem to be more sensitive than those for thermal power projects tolocal income levels (for schedules) and to foreign inflation rates (for costs). TheColombian hydropower projects tended to have lower costs overruns than generally afterallowing for the impacts of other significant variables on estimating performance;likewise, Indian thermal power projects tended to have higher cost overruns but lowerschedule slips.
World Bank appraisal guidelines for computing price contingencies do not appear tohave been a significant factor for cost-estimating performance in current terms. The 1976guideline was found to be significant in the case of thermal costs in constant terms, butthis could reflect a technicality because it was used to derive the actual costs in constantterms for the analysis (Annex 6). The significance of both guidelines (1970 and 1976) onthermal project schedule estimating performance is discussed in the section on thermalproject schedules above.
22. The use of explanatory variables that reflect project cost (schedule) with a dependent variable thatis the ratio of actual to estimated costs (schedules) can introduce a problem of spurious correlation, such asthat residuals are heteroskedastic. In fact the use of actual costs (schedules) as a dependent variable withestimated costs (schedules) as an explanatory variable exhibits very strong heteroskedasticity (see Annex 7,section 1). Using the ratio, however, produces homoskedastic residuals.
23. This observation might be related to the finding that the Colombia dummy is significant forhydropower cost estimations performance, but the Brazil dummy is not significant. since the hydraulicheads of the Colombian projects are among the highest, and those of Brazilian projects are among thelowest, in the group of hydropower projects.
50 Estimating Construction Costs and Schedules
Finally, the difference in conclusions about significant variables between themultivariate analysis and a single variate analysis are considerable, as shown in Annex 4.In the four regressions, single-variate analysis predicted only 11 of the 24 variables thatwere significant in the multivariate analysis at the 90 percent confidence level. None ofthe 6 significant variables that occur in two or three regressions in multivariate analysiswere found significant in two or more regressions in single-variate analysis. The latteralso falsely indicated 19 variables as significant.
7Implications of the Analysis for
Power System PlanningThe paper has focused so far on analyzing the performance of past estimates of
construction costs and schedules for World Bank-financed power generation projects indeveloping countries. This concluding section examines the implications of the analysisfor dealing with future projects. Estimates of construction costs and schedules are, ofcourse, two of many parametric estimates and forecasts that characterize risk anduncertainty in choosing power generation projects (see Sanghvi and Vernstrom 1989 andthe discussion in chapter 2 above, footnote 5). Most published analyses on this subjecttend to focus on uncertainty in predicting future power demand, fuel prices, and cost ofcapital. This chapter thus fills a significant gap in the treatment of risk and uncertainty inthis class of projects.
The analysis identified two problems with historical estimates that need to berecognized in future project evaluation. First, for the group of projects as a whole (whichcovered virtually all Bank lending for completed generation projects since the mid-1960s), there has been a very large downward bias in the estimation of costs and in theestimation of schedules. Clearly it is necessary to recognize that standard methods ofestimating costs and schedules tend to be overoptimistic. If all projects had experiencedequal or nearly equal bias in the estimation of costs and schedules, then the remedy wouldbe simple: multiply the standard estimates by an "adjustment factor." Provided projectsin the future were similar to those financed during the period of analysis, and providedthat the methods of estimating costs and schedules were not changed substantially, thenthis simple adjustment would, on average, produce accurate predictions for the actualoutcomes.
In fact, such a simple adjustment rule is unlikely to be optimal because of the secondfeature of estimated costs and schedules identified in this paper in that, even allowing forthe average underestimation, there is very large variation around this value. The averageshortfall in cost estimates for all projects was 21 percent, but some projects came in onbudget, whereas others had cost overruns of 40 percent or more. This variation in theaccuracy of estimation presents a more substantial problem for project evaluation.
51
52 Estimating Construction Costs and Schedules
This paper has shown how the apparent variability of cost and schedule estimationcan be reduced by categorizing the projects by type, through regression analysis. It hasalso revealed that despite an intensive search for indicator factors that are known ex anteand that correlate strongly with actual cost and schedule overruns, there appears to be asubstantial unpredictable element in these estimates.
Once all predictable aspects of estimating performance for costs and schedules havebeen taken into account, there will be no overall bias in the predictions for anyidentifiable type of project. The residual inaccuracy can then be seen as the riskassociated with costs and schedules rather than a systematic element in expected costs orschedules for a particular group of projects.
The first section below recapitulates the principal findings of the paper. The nextsection then indicates how the regressions developed in the paper can be utilized to obtainmore accurate predictions of project construction costs and schedules. The last sectionaddresses the question of risk in predicting these costs and schedules. Variousapproaches to incorporating risks, as estimated from the regressions, into projectdecisionmaking are outlined. The chapter concludes by dealing with special issues thatarise in choosing between power development programs that involve more than oneproject.
Principal FindingsA number of important implications for the planning of power generation projects in
developing countries emerge from the analysis of the actual performance of constructioncost and schedule estimates for such projects:
a. Estimates were fairly strong correlated with the actual outcomes, but the averageerror among projects as a whole was too large to be ignored. The group of powerprojects as a whole has a (squared) correlation of 0.76 between actual and estimatedcosts (in current prices) and 0.55 between actual and estimated schedules. Themodest values of these correlations indicates that the estimation process is ratherinexact and that large errors have often been made. This is the first justification forseeking a method of improving the predictions of actual costs and schedules.
b. The estimated values were significantly biased below actual values. The secondcrucial finding is that the estimated costs and schedules were, on average, severelybiased downward. Estimated construction costs for projects as a whole were onaverage 21 percent below actual costs, whereas estimated schedules were on average36 percent below actual values. Even when cases with exceptionally large overrunsare omitted from the group of projects, estimated costs still averaged 17 percentbelow actual costs, whereas estimated schedules were an average 29 percent belowactual values. Both of these findings indicate that, on average, an overoptimistic viewof project costs and schedule performance was taken.
Implications of the Analysis for Power System Planning 53
C. The performance of estimated values differed sharply between different types ofgenerating plants. The most striking difference found was between thermal andhydropower projects. The average cost underestimation for thermal projects was only6 percent, whereas for hydro projects the average was 27 percent. Schedule estimateswere rather similar, with thermal projects showing a 30 percent averageunderestimation and hydro projects on a 28 percent average underestimation. Theseresults indicate that in attempting to make any adjustment to the estimates of costsand schedules, it would certainly be necessary to treat the costs of thermal projectsdifferently from those of hydro projects.
d. The performance of estimated values can be related to a number of indicatorvariables through regression analysis. Regression analysis, based on a large set ofpossible variables, indicated that 18 project variables had a significant relationship (atthe 90 percent confidence level) in one or more of the six regression equationsanalyzed (for thermal and hydro project costs-current and constant-and schedules).Of the variables, 2 (station extension, and civil works cost) are technological; 5(estimated cost, estimated schedule, station size, unit size, and hydraulic head) relateto project size; 5 (local inflation, per capita national income, MUV index, Colombiadummy, and India dummy) are country specific; and 2 (post-1976 dummy, post1970-dummy) relate to World Bank guidelines. The residual variances from theregressions can be used to provide a measure of risk.
These variables were used in the analysis of the ratio of actual to estimated costs andthe ratio of actual to estimated schedules and were able to explain between 48 percent and57 percent of the variation in these ratios. In other words, about half the variation in thesepercentage errors that would be left unexplained by using an average correction factor forall projects is explicable in terms of a few simple variables whose values were known atthe time the project loan was approved. In addition, the significance of individualvariables indicates that for a class of projects that took a particular value of the variable,the use of an "average adjustment factor" (determined over all projects) would itself bebiased.
Using Regressions to Improve Predictions for Project Costs and SchedulesThe size of the bias in estimating project costs and schedules indicates that the
simplest way to make some improvement in predicting actual values would be to attachaverage correction factors to such estimates. If, for the set of 135 projects analyzed, costestimates had been adjusted upward by a factor of 1.21 and schedule estimates by a factorof 1.36, then overall the adjusted estimated value would have been unbiased (i.e., theaverage ratio of predicted to actual values would have been unity). However, forindividual subgroups of projects there would still have been a bias in the predicted values.Regression analysis also reveals that about half the variation in the differences among theratios of actual to adjusted values is capable of being predicted and hence should not betreated as if it were a residual "risk."
54 Estimating Construction Costs and Schedules
Using the regressions and the known values of the relevant associated variables,predictions can be made of the ratio of actual to estimated costs, and hence an improvedprediction of actual costs can be obtained. The approach is illustrated for the India 911thermal project. For this project, the actual costs turned out to be $491. 1 million, whereasthe estimate of costs used for appraisal was $405.9 million. The project cost was thusunderestimated by 21 percent. If it had been agreed to use the overall adjustment factorfor thermal power project costs, then the estimated value would have been increased by 6percent, still leaving a 15 percent underestimate. On the other hand, using the regression,as described in the first section of chapter 6, to produce a predicted cost would have givena predicted ratio of actual costs to estimated costs, for this class of project, of 1.207.Applying that factor to the estimated cost of $405.9 million yields a prediction of justunder $490 million, very close to the true value.
It is therefore recommended that the analysis of power generation projects includes acase in which expected values are used for construction costs and schedules. Theseexpected values can be derived from estimated values by applying ratios obtained fromthe regression equations given in chapter 6 in the manner illustrated above for the India911 project. This case supplements the standard analysis that is based on appraisedestimates of costs and schedules.
The regression approach is designed to give the most accurate statistical prediction ofactual costs and schedules based on historic experience. Two very important limitationsmust be noted. The very best regressions explain less than 60 percent of the variance ofthe ratio of actual to estimated values, with the remaining variation attributable tounidentified factors. If no substantial improvement in this goodness of fit can be found,then indeed a substantial element of genuine risk is present in appraising the constructioncosts and schedules of power generation projects. This implies that it is important that acoherent view is taken of the treatment of risk in project appraisal. Although 60 percentcorrelation is a low value relative to those obtained in many time series econometricstudies, it is important to remember that the present study is of a cross-section type(where correlations are typically lower than in time series) and that the dependent variableis the ratio of the actual value to the estimated value rather than simply the actual value.Since the estimated value itself already encapsulates much specialist knowledge of theparticular project, the regression is in effect seeking for influences on costs or schedulesthat have been systematically over- or undervalued by project appraisers. Rememberingthis interpretation, it is not likely that substantially higher correlations can be found (i.e.,what is unexplained is indeed largely risk). Regression analysis cannot be expected toprovide a perfect solution to the problem of forecasting actual values.
The second aspect of the use of regressions for prediction is that a relation estimatedon one set of data to predict outcomes for new data will give unbiased predictions only ifthe same relationship continues to hold between the indicator variables and the ratio ofactual to estimated values as in the historic sample. If the relationship changes-becausea new type of plant (e.g., combined cycle) is being considered, where the indicator factors
Implications of the Analysis for Power System Planning 55
affect cost and schedule overruns to a different degree than in the sample (e.g., diesels);or because of new ownership and contractual arrangements introduced, such as projectsbeing undertaken by the private sector rather than by the past practice of the public sector;or because the accuracy of estimation itself changes-then bias can result from using theregressions. However, in such cases it is still likely to be more accurate to use theregression than to make no adjustments to estimated values, unless huge differencesbetween the past and present relationships are expected. The analysis of the impact of thedummy variables for changes in World Bank estimating procedures on the accuracy of theestimates tends to confirm this view. For four of the six equations the dummy variableswere insignificant, suggesting that changes in World Bank procedures in 1970 and 1976were not associated with a significant improvement in estimation. Only for thermalschedules was there a measurable improvement in the accuracy of estimation. It thusseems reasonable to assume that it is unlikely that dramatic improvements in the accuracyof estimating costs and schedules will occur. However, where new technologies areinvolved there can be less confidence that the estimation errors will be similar in nature tothose identified in the sample.
The regressions also throw some light on the nature of the systematic underestimationof costs and schedules. Each significant variable in a regression points to a factor whoseimpact on the estimate was undervalued (positive sign) or overvalued (negative sign), andthe size of the coefficients indicates the magnitude of such effects. For example, in thecase of thermal project cost estimates (Table 6.1), the larger the estimated cost of theproject itself, and for projects that were extensions of existing projects, the lower was thetendency to underestimate costs. Alternatively, the longer the estimated constructionschedule, or the higher the ratio of civil to total costs, and if the project was in India, thegreater was the tendency to underestimate costs. Although the construction of the costestimates took into account the scale of the project, they tended to underplay economiesof scale to costs themselves but not to make enough allowance for the fact that projectswith a lengthy construction period would tend to have higher costs than projects ofsimilar physical size with shorter estimated construction periods. Not enough allowancewas made for the tendency for costs on thermal power projects in India to be higher thanfor similar projects elsewhere.
The factors summarized in Table 6.7 highlight the significant variables. For anyproject where a variable is known to have a large value (e.g., a large hydraulic head for ahydropower project), it is sensible to be alert to the tendency to misestimate such projects.Where the project is only marginally viable, this can indicate the need for extensivesensitivity analysis to alternative cost scenarios or even for design modifications thatreduce the influence of the problematic variable.
The magnitude of the coefficients allows a quantification of the likely sensitivity ofthe estimates to the presence of the significant factor. Since the equations are estimatedin double log form, the coefficients on the logs of the indicator variables measureelasticities-for a I percentage point increase in the size of the variable, the coefficient
56 Estimating Construction Costs and Schedules
measures the percentage increase in the predicted actual cost levels for given values of theother indicator variables. Where the indicators are dummy (zero/one) variables, forwhich logs cannot be used, the exponent of the coefficient measures the percentageimpact on the level of predicted costs of the presence of the variable. Table 7.1 shows themagnitudes of the elasticities for the factors found significant in the six regressions.
Table 7.1 Sensitivity of the Levels of Predicted Values to Indicator Variables
Thermnal costs Thermal Hydro costs Hydro
Variable Current Constant Schedules Current Constant schedules
Extension dummy* 0.856 0.882 1.433 1.448 1.652Civil cost ratio 0.083Estimated costa 0.854 0.726 0.807 0.747
Estimated schedule 0.287 0.174 0.714Station size -0.081 0.117 0.174Unit size 0.115Hydraulic head 0.110 0.110 0.070Loan approval date 2.626 2.335Forex -0.277 -0.224 -0.144
Financing agencies 0.234 0.336MUV index -0.081% ICB -0.132GDP deflator 0.076National income 0.057Colombia dummy* 0.655 0.695India dummy* 1.223 1.186 0.794Post-1976 dummy* 0.768 0.753Post- 1970 dummy 0.900
Note: Percentage changes of predicted values given a I percent change in a continuous variable andthe presence* versus absence of a dummy variable. Consider the stylized fitted regression
log (A*/E) = + M D + ylogX (X)
where A* is the predicted level of costs (or schedules) from regressions, E is the estimate of costs,D is a dummy variable (value I when the certain factor is present and zero when absent), and X is the levelof some indicator variable. Greek letters denote estimated regression coefficients. Taking antilogs andexpressing the equation in terms of the desired variable (A*) yields:
A* = E exp(a) exp(OD) X. (2)
The elasticity of A* with respect to X is given by XoA/A6X and is equal to y. The impact on A*,for a given value of X and E, of the presence (versus absence) of the dummy variable factor is measured bythe ratio exp(p)/ exp(0) = exp(1). A value of less than unity indicates that the presence of the factor lowersthe predicted outcome. The elasticity of the predicted value (A*) with respect to the estimated value (E) isunity, except in the case where the variable X is itself the estimated value. In the latter case the elasticity is(I + y), which measures the "scale" effect between E and A*.
'Where the estimated value is the explanatory variable, the sensitivity coefficient (elasticity) is 1+regression coefficient (see the note above).
Implications of the Analysis for Power System Planning 57
For the dummy variables, the impact of their presence is proportional solely to thecoefficients given above. It can be seen that the most important factor leading to anupward adjustment in the prediction is the impact on hydro schedules of the project beingan extension. Here the estimated value, adjusted by the other factors, needs to bemultiplied by a factor of exp(0.502), that is, by 1.652. The largest downward adjustmentis to estimated costs for hvdro projects in Colombia, after allowing for effects of othervariables, which need to be multiplied by exp(-0.423), that is, by 0.655.
For variables where elasticities are available, the importance of a factor depends notonly on the coefficient but on the scale. The equation expressed in form (2) in the note toTable 7.1 shows clearly the nonlinear nature of the relationship. To determine whichfactor is the most important, it is necessary to consider how much such a variable mightchange between projects. Where a factor exhibits high percentage changes betweenprojects, such a factor will be more important (for a given value of the elasticity) inexplaining variations in the predicted values between projects. Hence, both thecoefficient and the ratio of the indicator values are important.
Risk and Planning IssuesBesides showing the presence of systematic errors in estimating performance, the
regression analysis has revealed that it is not possible to make perfect predictions of theoutcomes of project costs and construction schedule from the factors used in the analysisand that the degree of uncertainty is large. The standard deviation of the ratio of actual toestimated costs was 36 percent, and for the ratio of actual to estimated schedules it was42 percent. In predicting the ratio of actual to estimated values for projects categorizedthrough the regression analysis, the estimated standard deviations of the errors variedbetween 16.9 percent for thermal costs (current) and 26.7 percent for thermal schedules.Insofar as the regression models have captured all systematic variation, these magnitudescan be regarded as measures of the risk associated with costs and schedules. They alsoallow expressions to be constructed for the probability distribution of outcomes for aparticular project.
Such expressions can be adapted for use in proprietary power system planning modelsthat specifically analyze financial and economic risk for a sequence of investments inlong-term expansion programs for power systems.25 Where risk is to be explicitly
24. Comparing two projects, alike in all respects (including the estimated values) apart from indicatorvalue X, the ratio of predicted values will be from equation 2 in the note to Table 7. 1: Al/A2 = (X1/X2 )'-
25. Some planning models treat key operating variables-such as power demand, fuel prices, andhydrology-stochastically to derive a distribution of possible outcomes for the net present value of aselected power development program. employing such techniques as Monte Carlo simulations. Stochasticrepresentation of construction costs and schedules could conceivably be added to such models. Thestochastic outcomes of alternative programs could then be compared by a straightforward statisticaltechnique (see the subsection below on planning issues involving choices between sequences of projects).
58 Estimating Construction Costs and Schedules
factored into project analysis, it is possible either to use a discount factor appropriate tothe degree of risk involved or to use a riskless discount factor and add in adjustments forthe risks involved to the benefit/cost stream such as those derived in this paper.
The assumption that similar factors will affect the outcomes of costs and schedulesfor future projects as they affected the projects in the sample allows the variance of errorsfrom the regression equation to provide a measure of risk for future projects (i.e., aquantifiable probability distribution of outcomes). There will of course be genuineuncertainty-eventualities for which no probability can be constructed from historicexperience-but for planning purposes it is valuable to have measures of risk available.
Traditional investment analysis, where the outcomes are risky and investors are riskaverse, tends to focus on the explicit tradeoff between mean return (or cost) and thevariance. Investors choose the highest available "equal value" contour between meansand variances that reflects their underlying attitude toward risk. (In effect, this techniquerequires the introduction of an extra explicit evaluation criterion that allows the investor'sattitude toward risk to be encapsulated in the analysis.) This technique is feasible wherethe composition of numerous investments in a portfolio can be continuously varied toachieve the desired risk profile. It is less directly applicable to the selection of powergeneration projects, where only a few alternatives are to be considered and where thedecision is faced only periodically and concerns a relatively large investment.Nevertheless, the measures of mean cost and variance of costs (or schedules) derived inthis paper can be used to examine important planning issues for power generationprojects, as illustrated in the following subsections.
Measurement of Project Risk
If the project is such that risk is to be taken into account in the decision makingprocess, then the regressions provide a measure of project risk arising from variability inconstruction cost and schedule estimates. This measure is the standard error of theregression. Standard analysis of publicly financed projects under uncertainty (Arrow andLind 1994) shows that if returns from the investment are independent of othercomponents of national income, the government should choose the project thatmaximizes the expected return when using a discount rate appropriate for investmentswith certain returns. That is, because project risk can be spread thinly over a largetaxpaying population, the government should ignore uncertainty in evaluating publicprojects.
Where the share of the risk borne by individual taxpayers is substantial relative totheir income, this conclusion has to be modified. Similarly, if some of the risk accruesdirectly to individuals, this should be discounted for, just as if it were a private
Implications of the Analysis for Power System Planning 59
26investment:. Where the return of the project is likely to be correlated with nationalincome, Little and Mirrlees (1974) provide an adjusted criterion for determining whetheror not to undertake the project. This criterion also requires the evaluation of the risk ofthe project and the correlation between the project return and the level of national income.
Distribution of Possible Project Outcomes
The regressions provide estimates of the distribution of the possible outcomes due touncertainA, in construction costs and schedules, which can be used in risk analysis. Indeciding whether to go ahead with a given project (or not), or which of two mutuallyexclusive projects to select, the basic criterion focuses on the expected value of returns,and hence on the expected values of costs and schedules. Nevertheless, in cases wherethe financing of a major cost overrun or an overrun beyond a specific limit to availablefunds would impose an unacceptable budgetary strain, it is important to have a high levelof confidence that the predicted value has been truly identified by the regression with thebest performance (i.e., the one least likely to have omitted any systematic factor).However, it is recognized that the actual cost is a random variable as seen from the exante standpoint, whose mean is the predicted value from the regression. Moreover, thevariance of this random variable can be estimated from the regression. If it is assumedthat the variable used in the regression (the log of the ratio of actual to estimated values)is normally distributed, then the distribution of outcomes can be computed. With the aidof this distribution it is possible to calculate information that can be used as a supplementto the decision making process.
Examples of such calculations are described in Annexes 8 and 9 for the followingquestions:
a. Finding the cost level for a given project that will be exceeded with a specificprobability and the probability of the project cost exceeding a specified value(similarly with project schedule).
b. Choosing between projects on the basis of the probability of exceeding a cost limit,evaluating the probability of exceedance that has the same cutoff value for theprojects. and evaluating which project has the lower probability of exceeding a givencost limit.
c. Assigning probabilities for risk analysis to a low scenario, an expected scenario, and ahigh scenario, where values are assigned to these scenarios so that these values andprobabilities are consistent with a prior view of the variance of cost or scheduleoutcome, such as obtained from one of the regression equations derived in this paper.
26. This distributional issue may also apply to the low-income groups that do not benefit directly fromthe project (i.e., lack access to the public electricity supply system) but that would be adversely affected byreduced government expenditures on social services caused by a cost overrun for a power project.
60 Estimating Construction Costs and Schedules
Planning Issues Involving Choice between Sequences of Projects
Analysis of a program for power system expansion can involve choices that requiremore selections than an alternative between single projects. Three cases that are ofconsiderable practical importance are frequently encountered:
a. The choice between one large project and a set of two or more smaller projects, wherethe reliability of estimates of costs and schedules depends on the scale variablesidentified in the regressions, and risks also depend on project size.
b. The choice between two power expansion programs, each made up of a sequence ofseveral projects, where the crucial issue is fuel diversity (e.g., between a hydropower-dominated program and a mixed hydro/thermal power program).
c. The choice of whether or not to delay a project, where the crucial issue is often thatof improving the estimates for construction costs and schedules for a project or itsalternatives by providing more time for further investigations into such aspects asproject site conditions (e.g., geology, topography, and environmental impacts).27
The first two cases raise the technical issue of how to construct the prediction of thetotal program cost and its variance from values for the individual projects derived fromthe regression analysis. Annex 10 shows how the mean and variance of a sum of the costof two projects are derived, as well as how to obtain the mean and variance for thepredicted cost (or schedule) when the regression model provides a predicted value for thelog of the ratio of actual to estimated values.
The formulas in Annex 10 can be manipulated to explore the possibility that a seriesof smaller projects with approximately the same total cost and output as a single largeproject may have a rather lower variance of costs and hence be less risky. Where the riskof the project is an important factor, a strategy of risk reduction through the use of a seriesof smaller component projects may be an important planning option.
The decision to delay a project to obtain better information on costs and schedules canbe taken in the context of the types of risk analysis outlined in Annexes 8 and 9.28 If the
27. Delaying a project is sometimes proposed under concerns about uncertainty of future fuel costs andpower market demand. An interesting case is the use of financial options analytical methods for a powergeneration project whose output is sold under competitive bidding, where the main concern is uncertaintyabout the power sales price. See EPRI (1995). Another interesting application of this approach is to thecase of extending a transmission system, for which see Martzoukos and Teplitz-Sembitzky (1992).
28. In addition to the uncertainty about the performance of estimates at project appraisal that are basedon feasibility studies, engineering design work, and contract bidding, as reported in this paper, this issue canalso arise in the context of preappraisal decisions because it is generally presumed that the reliability ofestimates of construction costs and schedules improves as a project progresses through successivepreparation stages-identification, prefeasibility, feasibility, engineering design, and contract bidding.Intuitively this presumption appears realistic when just considering bias in the estimates. However, thesubstantial variance found for the performance of appraisal estimates should caution against overconfidencein obtaining better estimates by delaying projects to obtain more information about them.
Implications of the Analysis for Power System Planning 61
project appears to have too high a risk or an excessive cost or construction schedule, thenit can be sensible to consider delaying the project while more evidence on estimated costsand schedule is collected about the project or alternatives. The delay option can then beevaluated in terms of the change in expected costs and schedules from present estimatesby means of decision-tree analysis or by adapting the financial options approach. Anapplication of the options approach to the optimal timing of projects under uncertaintyabout construction costs and schedules is developed in Annex 11. Unless there is specificevidence to the contrary, it is probably sensible to assume that there will be no change inthe variance of estimates by delaying a project.
Basic Recommendations
Two basic recommendations for operational analysis emerge from the analysis ofestimates for construction costs and schedules of power generation projects in developingcountries. First, because methods of estimating costs and schedules have beenoveroptimistic, the robustness of the analysis should be tested by applying a correction tothe estimates of costs and schedules. An "expected" value should be used for this test,and it can be calculated using the appropriate regression once the features of the projecthave been identified.
Second, because the regression analysis shows that the uncertainty in predicting costsand schedules is also too large to ignore, even when expected values are used, it is alsorecommended that the economic and financial risks associated with the selection of aparticular power project or power development strategy are explicitly considered duringproject appraisal. A measure of risk is provided by the product of the estimated value andthe standard error of the regression equation, as shown in Annex 10.
Risk should be considered in the context of specific questions rather than in anabstract context. There are some basic questions that should be examined to elicitvaluable insights about the riskiness of power generation projects that are considered tobe the least-cost option from the customary deterministic approach to power systemplanning. The paper proposes straightforward techniques for analyzing some of thesequestions (see the section above on risk and planning issues, as well as Annexes 8, 9, and10). These techniques should be tested operationally and developed in case studies, sothat guidelines can be formulated for using them in the appraisal of power generationprojects.
Annex 1: World Bank-Supported PowerGeneration Projects 1965-86 Used for theAnalysis of Cost and Schedule Estimating
Performance
Table A1.1 World Bank-Supported Power Generation Projects 1965-86 Used forthe Analysis of Cost and Schedule Estimating Performance
Installed Loancapacity approval
Country Project name (MW) year
Thermal power projectsAfghanistan (Power I) Kabul 40 1976Algeria Algiers 98 1974Bangladesh Ashunganj Thermal 450 1982Botswana Morupule 90 1983Costa Rica (Power IV) San Antonia 38 1972Costa Rica (Fifth Power Project) Moin 30 1974Cyprus (Power III) Moni Station Unit No. 4 30 1969Cyprus (Power IV) Moni Station Unit No. 6 60 1972Ecuador (Third Power Project) Cumbaya 18 1971Egypt (Power II & III) Shourbrah El Kheiam 900 1979Guatemala Guacalate 99 1968Guyana (G&T Project) Garden of Eden/Rotterdam 36 1972Haiti (Power I) Varreux 21 1976Haiti (Second Power Project) Varreux 25 1979Haiti (Third Power Project) Carrefur 16 1982Honduras Nispero Power 30 1965Honduras (Fifth Power Project) La Ceiba 24 1972India Second Kothagudem 120 1978India Singrauli 600 1977India Third Trombay 500 1978India Korba 600 1978India Ramagundam 600 1979India Second Singrauli 1400 1980India Farakka 600 1980India Second Ramagundam 1500 1982
(continued on next page)
63
64 Estimating Construction Costs and Schedules
(Table Al. I continued)
Installed Loancapacity approval
Country Project name (MW) year
Thermal power projects (continued)India Second Korba 1500 1982India Fourth Trombay 500 1984India Comb. Cycle: Kawas, Anta, & Auraiya 1500 1986Indonesia Power IV: Muara Karang No. 3 100 1975Indonesia Power VI: Muara Karang 400 1977Indonesia Power VII: Semarang Harbor 200 1978Indonesia Power VIII & IX: Suralaya Units I & 2 800 1979Indonesia Power XII & XIV: Suralaya Units 3 & 4 800 1984Ireland Power II: Tarbert 250 1971Ireland Power III: Tarbert 250 1972Jordan Power I: Zarqa 78 1973Jordan Second Hussein Thermal 33 1975Jordan Power V: Aqaba Power Station 260 1982Korea Gojeong Power 1000 1979Malaysia Port Dickinson & Johore Bahru Thermal 180 1966Malaysia Power IV: Prai & Port Dickinson Thermal 150 1969Malaysia Power V: Port Dickinson Thermal 360 1970Malaysia Power VII: Prai Thermal Extension 360 1975Malaysia Power VIII: Pasi Gudang 240 1977Pakistan Karachi 'C' Thermal Power Station 125 1967Panama Power III: San Francisco Thermal 25 1973Philippines Power IV: Bataan Thermal Plant 75 1967Philippines Power V: Bataan Thermal Electric No. 2 150 1972Romania First Turceni Thermal 1320 1974Romania Second Turceni Thermal 330 1979Sierra Leone Power II: King Tom Thermal 7 1968Sierra Leone Third Power Project: King Tom Thermal 9 1977Sri Lanka Power VIII: Sapugaskanda 80 1982Sudan Sudan Power II: Burri & Juba Thermal 15 1975Syria First Mehardeh Power 150 1974Syria Second Mehardeh Power 150 1975Thailand South Bangkok Thermal No. 3 310 1970Thailand Bang Pakong Thermal Power 550 1970
Annex 1: World Bank-Supported Power Generation Projects 65
Installed Loancapacity approval
Country Project name (MW) year
Thermal power projects (continued)Thailand South Bangkok Thermal No. 4 310 1971Turkey Elbistan 1200 1974Uruguay Power IV: Battle Unit No. 6 125 1971Yemen Wadi Hadramout Power Project 16 1978Yemen Power II: Wadi Hadramawt Thermal 7 1982Zimbabwe Power I: Hwange II 400 1983
Hydropower projectsArgentina El Chocon 600 1968Bolivia Second Empresa Nacional de Electricidad 34 1969Brazil Estreito 1050 1964Brazil Xavantes 400 1965Brazil Volta Grande 400 1967Brazil Porto Colombia 320 1968Brazil Marimbondo 1400 1969Brazil Salto Osorio 700 1970Brazil Sao Simao 1608 1971Brazil Paulo Afonso IV 2460 1974China Lubuge 600 1984Colombia Third Medellin 280 1964Colombia El Colegio & Conoas 200 1966Colombia Chivor 500 1969Colombia Guatape Second 280 1972Colombia First San Carlos 620 1978Colombia Las Mesitas 600 1978Colombia Second San Carlos 620 1979Colombia Guadalupe IV 213 1980Colombia Playas 204 1981Costa Rica Fifth Power: Rio Macho & Cachi 62 1974Ecuador (Third Power Project) Nayon 30 1971Ethiopia Finchaa 99 1968Fiji Manasow-Wailou 40 1977Ghana Second Volta River Authority 324 1968Ghana Kpong Hydroelectric 160 1976
(continued on next page)
66 Estimating Construction Costs and Schedules
(Table Al. I continued)
Installed Loancapaciry approval
Country Project name (MW) year
Hydropower projects (continued)Guatemala Aguacapa 90 1977Guatemala Chixoy 300 1977Honduras Fifth & Sixth Power: Rio Lindo 40 1973Honduras Nispero Power 22 1977Honduras El Cajon 292 1980Iceland Sigalda 100 1972Indonesia Power X: Saguling 700 1981Ireland Pumped Storage 292 1968Kenya Kamburu 60 1970Kenya Gitaru 134 1974Kenya Kiambere 140 1984Lao-PDR Nam Ngum 40 1981Madagascar Andekaleka 56 1978Malawi Tedzani Sate I 16 1969Malawi Nkula Falls II 54 1976Malaysia Power IX: Bersia & Kenering 192 1980Morocco Sidi Cheho-AI Massira 120 1976Myanmar Kinda (Nyaunggyat Multipurpose) 56 1980Nepal Kulekhani 60 1974Panama (Second Power) Bayano 150 1970Panama Fortuna 300 1977Papua New Guinea Upper Ramu 45 1970Peru Matucana Power 120 1966Portugal (Power Project VII) 8 Hydro Plants 1495 1983Romania Riui Mare-Retezat 349 1975Sudan Roseires 90 1966Sudan (Second Power) Roseires Extension 42 1974Sudan Roseires Extension 80 1980Swaziland Third Power: Lupohlo-Ezulwini 20 1981Tanzania Kidatu Hydroelectric Stage I 100 1969Tanzania Kidatu Hydroelectric Stage II 200 1975Tanzania Power IV: Mtera 80 1983Thailand Ban Choa Nen Srinagarind 450 1973
Annex 1: World Bank-Supported Power Generation Projects 67
Installed Loancapacitv approval
Countrv Project name (MW) year
Hydropower projects (continued)Thailand Pattan I 72 1977Thailand Khao Laem 300 1979Thailand (Power Subsector Project) Lan Suan and Chiewlarn 240 1981Turkey Third & Fourth Cukurova Power 56 1964Turkey Karakoya 1800 1980Turkey Sir 284 1986Yugoslavia Middle Neretva Hydro: Grabovica and Salakovac Dams 322 1978Yugoslavia Middle Neretva Hydro: Mostar Dam 65 1978Yugoslavia Visegrad 315 1985Zaire Ruzizi II 26 1984Zambia Kariba North 600 1970Zambia Kafue Hydroelectric Stage II 300 1972
Annex 2: Regression Results withAll Variables Included
Table A2.1 Variables for Log of Thermal Power Project Costs (Current Values)Based on 42 Observations
Regression Standard 2-tailedVariable coefficient error t-stat. significance
Intercept -18.756 6.647 -2.821 0.011Log loan date 4.676 1.617 2.890 0.0091970 dummy -0.186 0.157 -1.185 0.250Log estimated cost -0.302 0.122 -2.463 0.023Log estimated schedule 0.214 0.138 1.544 0.139Log forex -0.097 0.120 -0.806 0.430Log per capita income -0.015 0.050 -0.297 0.769Log station size 0.072 0.147 0.487 0.632Log % ICB 0.054 0.080 0.673 0.508Log MUV growth -0.050 0.060 -0.826 0.419Log GDP deflator -0.040 0.056 -0.713 0.484Log unit size 0.064 0.105 0.617 0.544Basis for costs dummy 0.015 0.091 0.167 0.869Diesel dummy 0.241 0.246 0.977 0.340Coaldummy -0.019 0.118 -0.165 0.871Steam dummy 0.079 0.097 0.815 0.425Extension dummy -0.177 0.089 -1.987 0.061Log sales growth -0.046 0.039 -1.183 0.251Log agencies -0.022 0.103 -0.216 0.831Contractor dummy 0.030 0.137 0.223 0.8251976 dummy -0.300 0.151 -1.982 0.062India dummy 0.186 0.137 1.353 0.192Log estimated civil 0.100 0.037 2.638 0.016
R-squared 0.803 Mean of dependent 0.024SER 0.159 SD of dependent 0.244
Linearized R-squared 0.798
69
70 Estimating Construction Costs and Schedules
Table A2.2 Variables for Log of Thermal Power Project Costs (Constant Values)Based on 55 Observations
Regression Standard 2-tailedVariable coefficient error t-stat. significance
Intercept -16.286 5.201 -3.130 0.003
Log of loan date 4.052 1.270 3.189 0.003
Dummy for 1970 -0.202 0.158 -1.278 0.209
Log of estimated cost -0.310 0.100 -3.083 0.004
Log of estimated schedule 0.128 0.117 1.091 0.282
Log of forex -0.054 0.112 -0.480 0.633
Log per capita income 0.038 0.048 0.780 0.440
Log station size 0.052 0.110 0.470 0.640
Log % ICB -0.017 0.080 -0.220 0.826
Log of MUV growth -0.097 0.049 -1.954 0.059
Log GDP deflator -0.020 0.058 -0.346 0.731
Log of unit size 0.100 0.070 1.430 0.161
Basis for cost dummy -0.061 0.072 -0.844 0.404
Diesel dummy 0.010 0.150 0.071 0.943
Coal dummy -0.141 0.099 -1.421 0.164
Steam dummy 0.048 0.081 0.591 0.558
Extension dummy -0.158 0.076 -2.064 0.046
Log sales growth -0.026 0.035 -0.727 0.471
Log agencies 0.001 0.105 0.015 0.988
Dummy for 1976 -0.322 0.132 -2.432 0.020
India dummy 0.240 0.140 1.711 0.096
R-squared 0.579 Mean of dependent 0.066
SER 0.182 SD of dependent 0.223
Linearized R-squared 0.601
Annex 2: Regression Results with All Variables Included 71
Table A2.3 Variables for Log of Hydropower Project Costs (Current Values)Based on 50 Observations
Regression Standard 2-tailedVariable coefficient error t-stat. significance
Intercept 3.768 7.814 0.482 0.634
Log loan date -1.038 1.858 -0.558 0.581
1970 dummy 0.154 0.229 0.676 0.505
Log estimated cost -0.184 0.215 -0.858 0.398
Log estimated schedule -0.027 0.200 -0.136 0.893
Log forex -0.086 0.193 -0.444 0.660
Log per capita income 0.037 0.067 0.558 0.581
Log station size 0.267 0.189 1.407 0.171
Log % ICB 0.098 0.127 0.776 0.444
Log MUV growth 0.034 0.117 0.292 0.772
Log GDP deflator 0.056 0.066 0.842 0.407
Log unit size -0.228 0.172 -1.325 0.196
Basis for costs dummy 0.021 0.110 0.193 0.848
Extension dummy 0.447 0.500 0.894 0.379
Log sales growth -0.073 0.076 -0.966 0.343
Log height ( new) 0.059 0.078 0.763 0.452
Log head (new) 0.094 0.074 1.256 0.220
Log agencies 0.195 0.156 1.250 0.222
Colombia dummy -0.381 0.197 -1.929 0.065
Brazil dummy 0.231 0.289 0.799 0.431
Tunnel length 0.007 0.010 0.665 0.511
Contractor dummy 0.329 0.326 1.010 0.321
Log civil ratio 0.056 0.162 0.350 0.729
1976 dummy -0.014 0.234 -0.061 0.952
R-squared 0.616 Mean of dependent 0.185SER 0.255 SD of dependent 0.301
Linearized R-squared 0.631
72 Estimating Construction Costs and Schedules
Table A2.4 Variables for Log of Hydropower Project Costs (Constant Values)Based on 45 Observations
Regression Standard 2-tailedVariable coefficient error t-stat. significance
Intercept -3.778 10.881 -0.347 0.731
Log of loan date 0.933 2.573 0.362 0.719
Dummy for 1970 -0.057 0.254 -0.227 0.822
Log of estimated cost -0.201 0.107 -1.875 0.072
Log of estimated schedule -0.047 0.169 -0.278 0.783
Log of forex -0.211 0.199 -1.064 0.297
Log per capita income -0.071 0.074 -0.954 0.348
Log station size 0.142 0.167 0.852 0.402
Log % ICB 0.032 0.131 0.243 0.809
Log of MUV growth -0.017 0.108 -0.163 0.871
Log GDP deflator 0.022 0.088 0.249 0.805
Log of unit size 0.012 0.150 0.082 0.934
Extension dummy 0.789 0.372 2.118 0.044
Log sales -0.066 0.078 -0.844 0.406
Log dam height 0.008 0.074 0.116 0.908
Log head 0.177 0.060 2.934 0.007
Log agencies 0.445 0.178 2.489 0.019
Dummy for 1976 -0.084 0.235 -0.359 0.722
Brazil dummy 0.172 0.334 0.517 0.609
Colombia dummy -0.410 0.245 -1.674 0.106
R-squared 0.562 Mean of dependent 0.212SER 0.255 SD of dependent 0.291
Linearized R-squared 0.577
Annex 2: Regression Results with All Variables Included 73
Table A2.5 Variables for Log of Thermal Power Project SchedulesBased on 42 Observations
Regression Standard 2-tailedVariable coefficient error t-stat. significance
Intercept 1.311 7.711 0.170 0.867
Log loan date -0.310 1.877 -0.165 0.870
1970 dummy -0.051 0.177 -0.293 0.772
Log estimated cost 0.117 0.136 0.856 0.402
Log estimated schedule 0.055 0.160 0.347 0.732
Log forex -0.044 0.134 -0.332 0.743
Log per capita income -0.013 0.055 -0.238 0.814
Log station size -0.303 0.160 -1.889 0.074
Log % ICB 0.160 0.088 1.816 0.085
Log MUV growth 0.115 0.066 1.744 0.097
Log GDP deflator -0.076 0.062 -1.222 0.237
Logunitsize 0.187 0.113 1.654 0.114
Basis for costs dummy -0.057 0.097 -0.589 0.562
Diesel dummy 0.146 0.268 0.544 0.592
Coal dummy -0.004 0.130 -0.034 0.973
Steamdummy -0.162 0.105 -1.544 0.139
Extension dummy -0.152 0.098 -1.550 0.137
Log sales growth 0.001 0.043 0.034 0.973
Log agencies 0.193 0.113 1.696 0.106
Contractor dummy 0.293 0.150 1.946 0.067
1976 dummy -0.099 0.166 -0.601 0.555
India dummy -0.035 0.152 -0.233 0.818
Log estimated civil -0.021 0.042 -0.498 0.624
R-squared 0.575 Mean of dependent 0.200SER 0.174 SD of dependent 0.182
Linearized R-squared 0.659
74 Estimating Construction Costs and Schedules
Table A2.6 Variables for Log of Hydropower Project SchedulesBased on 50 Observations
Regression Standard 2-tailedVariable coefficient error t-stat. significance
Intercept 2.706 4.767 0.567 0.575
Log loan date -0.464 1.134 -0.409 0.685
1970 dummy 0.057 0.139 0.408 0.686
Log estimated cost 0.004 0.131 0.036 0.971
Log estimated schedule -0.431 0.122 -3.538 0.002Log forex 0.010 0.118 0.090 0.929
Log per capita income 0.113 0.041 2.740 0.011
Log station size 0.082 0.115 0.710 0.484
Log % ICB -0.175 0.077 -2.261 0.032
Log MUV growth 0.002 0.071 0.040 0.968
Log GDP deflator 0.007 0.040 0.186 0.853
Log unit size -0.105 0.105 -0.998 0.327
Basis for costs dummy 0.059 0.067 0.873 0.390
Extension dummy 0.256 0.305 0.840 0.408
Log sales growth 0.019 0.046 0.423 0.676
Log height ( new) 0.000 0.047 -0.016 0.987
Log head ( new) 0.020 0.045 0.453 0.654
Log agencies -0.032 0.095 -0.337 0.739
Colombia dummy 0.144 0.120 1.194 0.243
Brazil dummy -0.123 0.176 -0.701 0.489
Tunnel length 0.004 0.006 0.623 0.538
Contractor dummy 0.040 0.198 0.204 0.840
Log civil ratio 0.099 0.099 1.002 0.325
1976 dummy -0.080 0.143 -0.563 0.578
R-squared 0.698 Mean of dependent 0.211SER 0.156 SD of dependent 0.206
Linearized R-squared 0.719
Annex 3: Comparisons of Actual Ratios andPredicted Ratios from Regressions for
Costs and SchedulesFigures A3.1 to A3.6 are plots of actual ratio (actual value to estimated value) and
predicted ratio (predicted value from one of the regression equations given in chapter 6 toestimated value) for each power generation project, for each of the following variables:
* Thermal power project costs (current values)
* Thermal power project cost (constant values)
* Hydropower project costs (current values)
* Hydropower project costs (constant values)
* Thermal power project schedules
* Hydropower project schedules
The numbers along the horizontal axis are references to individual projects. Thenumbers along the vertical axis are values of the ratios.
75
76 Estimating Construction Costs and Schedules
Figure A3.1 Plot of Actual and Predicted Ratios for Thermal Costs (current)
Ratlo of actual to predicted value
2.0
1.80'
1.60"
1.40'A Actual ratio
1.20A Predicted ratio
1.00
0.80
0.60)
0.40
1 10 20 30 40
Project number (ordered by date of loan agreement)
Figure A3.2 Plot of Actual and Predicted Ratios for Thermal Costs (constant)
Ratio of actual to predicted value
1.80__ __ _
1.60
1.40
1.20 -a- - Actual ratio
- -A-- Predicted ratio1.00
0.80
0.60
0.40 __ _ _
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55
Project number (ordered by date of loan agreement)
Annex 3: Comparisons of Actual and Predicted Ratios 77
Figure A3.3 Plot of Actual and Predicted Ratios for Thermal Schedules
Ratio of actual to predicted value2.40 __ _ _ ---
2.00
1.6 NE Actual ratioD Predicted ratio
1.2
0.80
1 3 5 7 9 11 13 15 16 18 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57
Project number (ordered by date of loan agreement)
Figure A3.4 Plot of Actual and Predicted Ratios for Hydro Costs (current)
Ratio of actual to predicted value
2.50
2.00
1.50 Actual ratio-- Predicted ratio
1.00
0.50
65 75 85 95 105 115 125 130
Project number (ordered by date of loan agreement)
78 Estimating Construction Costs and Schedules
Figure A3.5 Plot of Actual and Predicted Ratios for Hydro Costs (constant)
Ratio of actual to predicted value
2.50-
2.00
HT-Actual ratio1.50 - Predicted ratio
1.00;0
0.50 _ _ _ _ _ _ _ _ _ _ _
65 75 85 95 105 115Project number (ordered by date of Ioan agreement)
Figure A3.6 Plot of Actual and Predicted Ratios for Hydro Schedules
Ratio of actual to predicted value
2.20 -.
2.00-
1.80
1.60 O Actlal ratio
A Predicted ratio1.40
1.20
1.00
0.80
65 75 85 95 105 115 125
Project number (ordered by date of loan agreement)
Annex 4: Statistics for Single-Variate Analysis ofAll Variables
This annex contains schedules of single-variate correlations for all the variablesincluded in the regression equations. These correlations are presented to show how thevariables that are found to be significant from single variate analysis differ from thosefound to be significant from multivariate analysis.
There is an equation that links the (unsquared) correlation coefficient to a t statisticthat would be obtained in the single-variable regression:
20.5r = t (t2 +N-2)
t = r{(N -2) (I - r2
(N is the number of observations)
Hence a critical value of the correlation can be obtained from a t table. For example,with 54 observations, the critical value of t (two-sided test) at 90 percent is 1.67, and at95 percent it is 2.01. The corresponding critical values for r are thus (plus or minus)0.223 and 0.266. Larger values than 0.05 for r2 thus indicate a significant correlationbetween the variables at the 90 percent confidence level. In other words, finding a smallr2 is equivalent to finding a nonsignificant t-stat.
79
80 Estimating Construction Costs and Schedules
Table A4.1 Single-Variate Regression Correlations
Thermal power projects Hydropower projects
Cost overrun Cost overrunVariable (current) Schedule slip (current) Schedule slip
Log loan date -0.320* -0.216 -0.233* -0.049
Post 1970 dummy 0.167 -0.127 -0.136 0.061
Log estimated cost 0.508* -0.384* -0.191 -0.303*
Log estimated schedule -0.271* -0.270* 0.118 -0.415*
Log forex 0.117 0.055 -0.302* 0.043
Log per capita income -0.091 0.029 0.028 0.227*
Log station size -0.464* -0.045 0.082 -0.202
Log % ICB 0.050 0.080 -0.090 -0.062
Log MUV growth 0.247* 0.230* 0.372* -0.001
Log GDP deflator -0.181 -0.179 0.235* -0.057
Log unit size -0.404* -0.390* 0.122 -0.196
Basis for cost dummy 0.005 -0.032 0.285* 0.028
Diesel dummy 0.285* 0.300* - -
Coal dummy -0.306* -0.140
Steam dummy -0.018 -0.207 - -
Extension dummy -0.178 -0.042 -0.205 0.334*
Log sales growth -0.123 0.045 0.015 0.155
Log agencies -0.233* -0.034 -0.087 -0.081
Post 1976 dummy -0.402* -0.352* -0.203 -0.030
India dummy -0.064 -0.253* - -
Local contractor dummy -0.037 0.094 -0.050 -0.031
Log civil costs ratio" 0.366* -0.009 0.246* 0.014Log dam height (new) - - 0.171 -0.327*
Log head (new) - - 0.234* -0.164
Colombia dummy - - -0.169 0.209
Brazil dummy - - 0.402* -0.210
Tunnel length - - 0.154 0.119Note: Number of observations for all the regressions: 54. Significant value of correlation r at 90 percentconfidence level: ±0.233.
* Variable is significantly correlated at 90 percent confidence level.
45 observations.
Annex 4: Statistics for Single-Variate Analysis of All Variables 81
Table A4.2 Comparison of Significant Variables at 90 Percent Confidence Levelbetween Multivariate Analysis and Single-Variate Analysis
Relationship Thermal power projects Hydropower projectsbetween Cost overrun Cost overrunvariables (current values) Schedule slip (current values) Schedule slip
Common Log civil costs ratio (+) Post 1976 dummy (-) Log hydraulic head (+) Extension dummy (+)
vagriable Log estimated cost (-) India dummy (-) Log forex (-) Log estimated schedule (-)with same Post 1976 dummy ( Log GDP deflator (+) Log national income (+)signs (I I)
Common Log estimated schedulevariables (+ for multi. - for single)but oppositesigns (I)
Significant Extension dummy (-) Log station size (-) Extension dummy (+) Log hydraulic head (+)
for multi- India dummy (+) Log loan approval date (+) Log estimated cost (-) Log % ICB (-)variate, notsignificant Log forex (-) Log station size (+)for single Post 1970 dummy (-) Log financing agencies (+)variate (13)
Colombia dummy (-)
Significant Log loan approval date (-) Log estimated cost (-) Log loan approval date (-) Log estimated cost (-)
for single Log station size LLogestimatedschedule(-) Log MUV growth(+) Log dam height(-)variate, notsignificant Log MUV growth (+) Log MUV growth (+) Basis for cost dummy (+)
for multi- Log unit size Log unit size (-) Brazil dummy (+)variate (19)
Diesel dummy (-) Diesel dummy (-) Log civil costs ratio (+)
Coal dummy (-)
Log financing agencies (-)
Annex 5: Ex Post Attribution of FactorsResponsible for Schedule Slip in World Bank-
Supported Power Generation Projects
Table A5.1 Ex Post Attribution of Factors Responsible for Schedule Slip inWorld Bank-Supported Power Generation Projects
Responsible party orfactor Specificfactor or event
Thermal power projectsClient/engineer Legal requirements/bureaucratic procedure for awarding contracts
Initial schedule was too optimisticBid evaluation difficultiesDelays in procurement/placement of ordersChange in project scopeModifications to major equipment requiredDisagreement between Bank and borrower over contract awardSite change
Contractor/supplier Labor disputes/strikes in manufacturer's countryLabor disputes/strikes in project countryShipping delays due to oil crisisSubstandard work had to be redoneEquipment failure during testingSkilled labor shortageManufacturing difficultiesShortage of materialsContractor inefficiency/lack of coordinationTechnical problems with equipmentContractor bankruptcyTransportation difficulties
Uncontrollable events Damage/need to redesign civil works due to earthquake or other naturalDisasterUnusually bad weatherAccident-damage to equipmentPolitical turmoil/coup/invasionCivil disturbance
(continued on next page)
83
84 Estimating Construction Costs and Schedules
Responsible party orfactor Specific factor or event
Hydroelectric power projectsClient/engineer Initial schedule too optimistic
Geological problemsFinancial difficulties/tariff implementation problemsInefficient project management/institutional weaknessDesign changesChange in project scopeRelocation problemsDelay in award of contracts/bid evaluation difficultiesDesign faultsProcurement delays/difficultiesSite changeLand acquisition/site access problemsCommunication problemsNo bids received due to working conditionsMajor currencv devaluation threatened project viabilityProject sponsors backed outLegal problems/delay in settling claimsWorld-wide inflation
Supplier/contractor Contractor bankruptcyContractor inefficiency/inexperience/incompetenceDelays in shipping/deliver of equipment, transportation difficultiesSubstandard work had to be redoneShortage of materialsManufacturing difficultiesDam or tunnel collapseDamage to equipment (other than dam/tunnel)Water infiltration/pressure damageFireEquipment failure during testingLabor disputes/strikes in manufacturer's countryFuel shortageLabor disputes/strikes in project countryCommunication problemsSkilled labor shortageChange in contractorsLegal problems/delay in settling claims
Uncontrollable events Landslides/mudsl ides/rockfallsUnusually bad weatherPolitical turmoil/coup/invasion/warFlood damageEarthquake
Note: Factors attributed in World Bank Project Completion Reports.
Annex 6: Methodology for Deriving Actual ProjectCosts in Constant PriceTerms
Since World Bank project completion reports do not provide data on project costs inconstant-price terms and the actual disbursement patterns over the project implementationperiod, the methodology described below is used to derive equivalent actual constant-price costs from the actual current-price costs given in these reports. This methodology isthe reverse of the World Bank's methodology for computing the price contingency forproject cost estimates.
a. Total actual project costs are allocated among the project implementation yearsaccording to standard disbursement profiles related to the total project implementationperiods. These profiles are shown on the next page.
b. The actual annual disbursements are divided between foreign exchange and localcurrency costs by the proportion of each in the total actual project cost.
c. The stream of annual foreign exchange costs in U.S. dollar (US$) terms is convertedto constant-price terms in the project start year with the actual MUV indices for theimplementation period.
d. The stream of annual local currency costs in local currency terms is converted toconstant price terms in the project start year with the actual country CPI or GDPdeflator for the implementation period. The local currency cost in constant priceterms is converted into equivalent US$ terms at the average exchange rate in theproject start year.
e. The total project cost in constant US$ terms for the project start year is the sum ofsteps (c) and (d).
A worked example is given in this annex.
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86 Estimating Construction Costs and Schedules
Table A6.1 Standard Disbursement Profiles for Project Cost in Current PriceTerms
Annualdisbursement
(of total)in years Implementation periods (years)
11 10 9 8 7 6 5 4 3 2
1 0.02 0.03 0.03 0.04 0.05 0.10 0.15 0.20 0.25 0.35
2 0.03 0.04 0.07 0.10 0.15 0.20 0.25 0.30 0.50 0.65
3 0.06 0.08 0.12 0.15 0.20 0.25 0.35 0.40 0.25
4 0.10 0.12 0.15 0.25 0.25 0.25 0.20 0.10
5 0.20 0.20 0.20 0.20 0.20 0.15 0.05
6 0.20 0.20 0.20 0.15 0.10 0.05
7 0.15 0.15 0.12 0.07 0.05
8 0.10 0.10 0.08 0.04
9 0.08 0.05 0.03
10 0.04 0.03
11 0.02
SUM 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Source: These profiles are based on the generic formula for expenditure flow patterns for large capitalprojects given below. The formula was used by Independent Project Analysis, Inc. of Reston, Va., in areport published by the Industry and Energy Department of the World Bank (Merrow and others 1990).
Proportion of total expenditure that occurs in year i of a total project construction period of I years:
i [L (Cos )4.08 ]
Annex 6: Methodology for Deriving Actual Project Costs 87
Table A6.2 Example of Project Cost Derivation in Constant Price Terms:Algeria, Base Year 1973
LocalForex cost
percent percent0.58 0.42
Foreign AnnualAnnual MUVfor cost in Annual local Local cost
Annual forex foreign Year I local Average cost Local In Year Icost cost costs price terms cost annual (million CPI price terms
Schedule (USS (US$ (Year] (US$ (USS exchange rate of (Year I = (million ofyear million) million)a 1.00) million) million)t (Dinnar/US$) Dinnar) 1.00) Dinnar)
1 2.9 1.68 1.00 1.68 1.22 3.96 4.83 1.00 4.832 10.0 5.80 1.22 4.75 4.20 4.18 17.56 1.06 16.573 11.0 6.38 1.35 4.73 4.62 3.95 18.25 1.11 16.444 16.7 9.69 1.37 7.07 7.01 4.16 29.16 1.21 24.105 15.0 8.70 1.51 5.76 6.30 4.15 26.15 1.32 19.816 8.3 4.81 1.74 2.76 3.49 3.97 13.86 1.48 9.367 3.6 2.09 1.97 1.06 1.51 3.85 5.81 1.73 3.36
TOTAL 67.5 39.15 10.16 27.81 28.35 115.62 94.47Local cost @ Year I Price andExchange Rate: US$ million 23.86
Forex percent 0.58. b Local cost percent 0.42.
In Year I Price Terns:USS million
Total foreign cost 27.81Total local cost 23.86
Total cost 51.67
Forex = foreign exchange.
Annex 7: Analysis of Relationships for thePerformance of Price Contingencies
1 Relation between Actual and Estimated Current CostsThe first relationship serves to highlight the nature and extent of the difference
between actual and estimated current costs. Were they always approximately equal,project appraisal could rely confidently on the estimated costs. Where these series aredifferent, it is important first to be aware of the possible magnitude of the difference andnext to analyze it for predictable features to be incorporated into project appraisal.
For the group of projects as a whole, the regression of the actual cost in current priceterms (CU(A)) on the estimated cost in current price terms (CU(E)) gave the result shownin equation A7. 1:
CU(A) = 25.8 + 0.985 CU(E)
(1.7) (20.8) (A7. 1)
R2= 0.76, Standard error of estimate (SEE) = 296; t statistics are in parentheses.
If the estimated cost is on average an unbiased estimate of the actual value, thenequation A7.1 should satisfy the hypothesis that the intercept is zero and the slope isunity. An F test comparing equation A7. 1 with the equation:
CU(A) = CU(E)
gives an F value of 0.55, compared with the critical value of 3.07. However, the standarderror of estimate, which is the average difference between the actual current cost and thevalue predicted by this relationship (and is the same as the standard error of theregression), is extremely large at 296 when compared with the sample mean actualcurrent cost of 216 (in million US$). Moreover, the residuals are strongly heteroskedastic(being larger in absolute values at larger values of estimated cost), so that valid inferencescannot be based on the standard F test. The mean value of the ratio of actual to estimatedcurrent costs for the whole sample is 1.21, and this is significantly greater than unity, asshown by equation A7.2:
CU(A)/CU(E) = 1.21 (A7.2)
(35.5)
SEE = 0.40
Once the data is put into ratio terms, the absolute values of the residuals do notexhibit heteroskedasticity, and so standard significance tests on equation A7.2 are valid.From this analysis it can be concluded that the actual and estimated current values arestrongly, but far from perfectly, correlated. It appears that the ratio of actual to estimatedvalues is significantly greater than unity and that there is a significant percentage bias in
89
90 Estimating Construction Costs and Schedules
the estimation of current prices. There is a very large difference in the ratio for thermalpower projects (1.06) and hydro projects (1.27), which indicates that the bias inestimating thermal power project costs in current price terms has been relatively small.Both groups have substantial standard deviations, but again that for hydropower projects(38 percent) is higher than that for thermal projects (23 percent). This difference can bedue to differences in predicting either the physical costs (constant prices) or the inflationrates, but is likely to be primarily due to the former, since it would be expected that errorsin forecasting the latter would not depend on the type of project involved.
2 Link between Actual Current Costs and Actual Constant CostsIn order to analyze the sources of error in current price forecasting, it is necessary to
look at the error in forecasting the constant price cost, as well as the errors in forecastinginflation. In order to check this physical error, it is important to check that the valuederived for the actual constant cost from the disbursement formula described in Annex 6is strongly related to the actual current value. If these two series are only weakly linked,then doubt would be cast on the construction of the actual constant price series and, as aresult, analysis of the success in predicting the "physical" aspect of the project, bycomparing actual and estimated constant costs, would be of less value.
The regression includes as explanatory variables not only the actual constant price(CO(A)) but also the actual (annual) rate of inflation (ID), the actual (annual) rate ofinflation of imported manufactures (IF), and the actual schedule length (SA). All thesevariables are involved in the relation between actual costs in constant prices and actualcosts in current prices. The regression on the set of observations for which there are datais given in equation A7.3:
CU(A) = 91.8 + 0.78 CO(A) + 0.25 ID(14.8) (0.63) (A7.3)
-14.0 IF+ 14.7 SA(4.1) (2.0)
R2 = 0.74, SEE = 153
This equation shows that there is certainly a strong relation between the constructedactual constant cost value and the actual current cost value, allowing for actual inflationrates and schedule length. Separate regressions for thermal and for hydropower plantsshow that the relation is extremely close for thermal power projects (R2 = 0.98) and isweaker for hydropower projects (R2 = 0.75). Since none of these "explanatory" variablescan be known in advance, the equation cannot be used in a direct, predictive fashion.However, it does justify the attempt to separate out the inaccuracy in estimating the"physical" or constant cost dimension of the project from errors in estimating inflationrates and schedule lengths.
Annex 7: Analysis of Relationships for the Performance of Price Contingencies 91
3 Relation between Actual and Estimated Cost EscalationIn order to check the extent to which errors are made in predicting actual current
prices because of failures to anticipate cost inflation correctly (as opposed to the physicalaspects of the project), the actual cost escalation, RA = CU(A)/CO(A), is regressed on theestimated cost escalation, RE = CU(E)/CO(E), in equation A7.4.
RA= 0.30+0.70RE (A7.4)(7.3) (22.1)
R2 = 0.79, SEE = 0.20
This relation appeared stable over time, in that the introduction of extra variables suchas the date of the loan agreement or a post-1976 dummy3 0 make only very slight changesto the fitted equation.
Separation of the thermal power and hydropower project subsamples showed littledifference in the relationship for types of plant, which is to be expected, since the failuresto predict the inflation component should not depend on the type of plant but rather onassumptions that are common to all plant types. Failure to predict cost escalationcorrectly suggests that there is an aspect of the current cost forecast that is always likelyto be in error, unless general rules for predicting domestic and international inflation canbe improved.
The results show that the World Bank's procedures were fairly accurate in predictingcost escalation, but that with an average error of 0.20, compared with the sample meanactual cost escalation of 1.14, there was still room for improvement in the construction ofthis aspect of the project price forecast.
4 Relation between Cost Overrun in Current Price Terms, in Constant PriceTerms, and Errors in Predicting Inflation Rates and Project Schedules
The themes of the three previous sections are pulled together by regressing the costoverrun in current price terms O(CU) on the cost overrun in constant price terms (O(CO))and the errors in predicting foreign inflation (O(F)), domestic inflation (0(D)), andschedule (O(S)) in equation A7.5 to give:
O(CU)= -0.10 + 0.82 0(CO) + 0.02 O(D) + 0.090(F)(1.10) (12.4) (2.0) (1.6) (A7.5)
+0.12 O(S)(2.2)
R2= 0.73, SEE = 0.20
29. The estimated cost in constant price terms (CO(E)) includes the physical contingency for costincreases that is mentioned in section 2.
30. See main text footnotes 8 and 9 about changes in the World Bank's guidelines.
92 Estimating Construction Costs and Schedules
Equation A7.5 shows that errors in estimating the project cost in constant price terms,errors in estimating the domestic inflation rate, and errors in estimating the projectschedule were all significantly related to the overall error in estimating project costs incurrent terms.
There was no significant relation with the error in estimating the imported rate ofinflation; this finding does not mean that if an error were made in estimating the importedinflation rate (Figure A7. 1), such an error would not be reflected in total project costerrors, but rather that such errors were on average sufficiently small to be dominated bythe other sources of error. The overall goodness of fit is quite high and indicates that thisdecomposition is fairly successful in identifying the sources of the cost overruns by type.Disaggregation into thermal power and hydropower project subsamples again shows astronger fit for thermal power projects (R2 = 0.85) and a weaker fit for hydropowerprojects (R2 = 0.67), which suggests that the attempt to split the cost overrun into itscomponents is rather less satisfactory for hydropower projects. This may well relate tothe basic problem identified earlier in predicting the physical aspects of costs forhydropower projects correctly.
Figure A7.1 Comparison of MUV Index Actual Values with Values from ForecastsMade between 1974 and 1988 (Based on actual value in 1980 = 100)
220
200 1979
180 . 19811988
160 -
140
120
100
60
40 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93
YearNote: Forecasts used for World Bank Project Appraisals of the Unit Value Index (in US$terms) of manufactured goods exported from G-5 countries (France, Germany, Japan,UK., and U.S.) to developing countries.
Annex 7: Analysis of Relationships for the Performance of Price Contingencies 93
Appendix A7.1 Composition of the World Bank's Price ContingencyFormula for Predicting Project Cost Escalation
The World Bank's formula for computing price contingencies is:
EE= B *C*pf +Cd *pd *ed
where:
EE is the estimated price contingency for escalation in project costs.
i is a year in the project implementation schedule of n years.
B is the estimated total project cost expressed in base year prices (i=l).
Bi is the proportion of B that is committed in year i.
cf is the estimated proportion of Bi that consists of imported components.d
Cd is the estimated proportion of B, that consists of domestically procured
components, and thus equals ( I - C-).
f is the projected price index in year i relative to the price index in the project base
year for imported project components, which is taken to be the forecast change inUN Unit Value Index (in US$ terms) of manufactured goods exported from theG-5 countries to developing countries (the "MUV Index").
p is the projected price index in year i relative to the project base year for the
domestic economy, which is usually taken to be the domestic Retail Price Index("RPI").
ed is the forecast change in the exchange rate in year i relative to project base year
for the domestic currency in US$ terms (for estimating a price contingency inUS$ terms).
Annex 8: Computations of Probabilities ofExceeding Specific Project Costs
Case 1: The cost level for a given project that will be exceeded with a specifiedprobability. If a variable (X) follows a normal distribution N(m,s), where m is the meanand s the standard deviation, there is a 50 percent chance that the actual value will exceedthe mean. As a control of unlikely outcomes it is possible to calculate the "cut-off' atwhich there is only a specified (usually small) probability of exceeding this value. Forexample, the "cut-off' (K) value at which there is only a 10 percent chance of a higheroutcome is given by the solution to the equation
0.1 = fX(m,s)dxK
which is equivalent to the equation expressed in standard normal terms:
0.1 = |X(O,l)dx(K- m)/s
The ordinates that solve such an equation are given in standard tables of the normaldistribution. For example, the value of the standardized score that cuts off the top 25percent of the distribution is 0.675. Hence, for known values of m and s, the cut-offvalue for X itself is
K = m + 0.675*s
This approach can be applied to the Indian power project discussed in chapter 6. Thepredicted log of the ratio of actual to estimated costs was 0.192, while the standard errorof the regression was 0.189 (Appendix A8.1 to this annex shows how to compute thevariance of a forecast). Hence, the cut-off value of the log of the ratio, which has only a25 percent chance of being exceeded, is:
K=0.192+0.675 * 0.189=0.320
The cut-off value of the ratio itself is thus 1.377 and, given that the estimated value ofcosts was $406 million, the cut-off predicted actual value is $559 million, as compared withthe central predicted value of $492 million. The regression thus takes the estimated value($406.29) and produces a predicted value of $492 million, which is the appropriate figurefor standard econornic evaluation. It also indicates that the value at which there is only a 25percent chance of a higher cost is $559 million, and this finding can be used in risk analysis.
This approach can be inverted to ask for a given cost limit, what is the probability ofthe project cost exceeding such a value. The fornal equation is:
95
96 Estimating Construction Costs and Schedules
f3= |X(m,s)dXL
where L is the specified limit, and 1 is the probability of exceedance. Again this is putinto standard normal form:
f= |X(O,l)dX(L-m)/s
and, for a given standardized limit, the value of 1 can be derived from standard normaltables. In the above example, if the cash limit were set to $575 million, this implies theratio of actual to estimated values would be 1.416, with a log of 0.348. The standardizedvalue would then be (0.348 - 0.192)/0.189 = 0.825, which has a 20 percent chance ofbeing exceeded. Hence with a cash limit of $575 million, on a project estimated to cost$406 million, there is still a 20 percent chance of some overrun beyond the cash limit.
Case 2: Chzoosing between projects on the basis of the probability of exceeding a costlimit. The approach indicated above for augmenting the analysis of a single project can beextended to the choice between two (alternative) projects. The standard question is: whichproject has the lower cut-off value of the distribution of costs that will be exceeded with a50 percent chance in each case; and the answer is simply the lower of the predictedoutcomes. Alternatively, the question can be focused on the smaller probability level ofexceeding a higher cost level (K) than the predicted outcomes. Consider projects withmeans ml and m2, and standard deviations s, and s2. With a cut-off probability of 25percent the standardized score for each is, as before, 0.675. Hence the cut-off cost levelsare:
K, = ml + 0.675 * si
K2 = m2 + 0.675 * s,
It is then desired to choose that project with the lower value of K. If the values of thestandard deviations are different then it is possible that a project with the higher mean costratio might nevertheless have a lower K value, because of its smaller standard deviation.
It also is possible to calculate the probability (P) of exceedance that has the same cut-off value (H) for each project (H = Ki). At this value:
ml + H * sI = m2 + H * S2
H=(ml -m2)/(S2-sI)
The standard table for a normal distribution then indicates the probability of exceedingthe common cut-off value of H.
Annex 8: Computations of Probabilities of Exceeding Specific Project Costs 97
This approach also can be inverted to ask which project has the lower probability ofexceeding a given cost limit R. Since the expected values will in general be different forthe two projects (El and E2), the logs of the ratios of the cash limit to expected values (r1and r2) will also be different. Putting both ratios into standardized form then allows theprobability of exceedance of the absolute cash limit for project I to be compared with thatfor project 2. If project I has the lower probability, then
fX(0, I)dX < f X(O, I)dX(ri-mo)Isi (r2 -m2)5S2
When there is indifference between projects (i.e., the same probability of exceeding Rapplies to both projects), the limits of integration are equal, so that
(r, - ml) / s = (r2 - Mi2) / S2
This expression can then be used to determine the specific value of R for indifferencebetween projects, since it yields
[ln(R/E1 ) - ml]/s, = [ln(R/E2) - m2 1/S2
or
R = exp [( s2(0nEI + ml) - s1(lnE2 + M2 ) 1/ts2 - si }]
A final criterion of interest is to ask what is the probability that project I will be moreexpensive than project 2, even when the mean value for project 1 is lower. The answerdepends on the evaluation of a double integral (details are shown in Appendix A8.2 tothis annex). Table A8. 1 gives some selected values for different parameter combinations.
Table A8.1 Probability that Project 1 Has Higher Cost (Schedule) than Project 2
VW 0 0.4 0.8 1.1 1.6 2.0
0.20 0.500 0.347 0.216 0.120 0.058 0.025
0.60 0.500 0.377 0.266 0.174 0.106 0.059
1.00 0.500 0.398 0.299 0.207 0.141 0.089
1.67 0.500 0.421 0.343 0.271 0.208 0.154
5.00 0.500 0.488 0.472 0.456 0.441 0.425
Where: V = (m2 - m)s, W = s2/sl.
An important result is that whenever m) is larger than ml, the probability that projectI is more expensive has as an upper limit 0.5 as the ratio of s2 to si increases. For lowvalues of this ratio, the chance that project 1 is more expensive can be very small.
98 Estimating Construction Costs and Schedules
Consider projects where the value of m2 is 0.2 and ml is 0.16, while S2 is 0.05 and s, is0.125. The parameter V is 0.8, and W is 2.5. The chance that project 2 is moreexpensive is 39 percent, despite the very much greater standard deviation. The table alsoassumes that there is no correlation between the outcomes of the alternative projects.Calculations showed that allowing for substantial positive or negative correlations hadlittle effect on the probabilities, so that this issue could be ignored.
Appendix A8.1 The Variance of a Predicted Value from a Regression
The predicted value YF is based on regression of a sample size T between J knownvariables (XI... XJ) including the constant (XI = I all t) and the dependent variable. Thepredicted outcome is given by
YF = EJ I1 jX;F~F
where the f3j denote estimated parameter values, and XjF are the assumed known values ofthe indicator variables. The variance of the forecast around the actual value is given bythe standard formula:
VarYF = a2 + a2 {E i; (XjFXiF) COV (Pi3j))
where Cov (fipj) is the estimated covariance or variance (i=j) of the regression parameters.
For large samples, such as are used in the regressions in this paper, the terms in bracestend to be much smaller than unity, so that the variance of the forecast will beapproximately equal to the residual variance (square of the standard error of regression). Incomparing projects with similar mean outcomes, small differences in the variance canbecome important, and in such a case it would be more important to estimate the variancecorrectly. This facility is provided on modem regression programs. For example, the caseof the India project referred to in the text has a variance of the residuals of 0. 1772 = 0.031(for the log of the ratio) from the regression, while the true variance of the predicted value is0.035.
Appendix A8.2 Probability that the Outcome of One Project Is Greater ThanThat of the Other
Let X and Y be the random outcomes of the two projects, which follow a bivariatenormal (correlated) distribution f(X,Y). The probability that a drawing X (project 1) islarger than the Y value (project 2) depends on the integral:
f f f(X, Y) dX DY0 Y
Annex 8: Computations of Probabilities of Exceeding Specific Project Costs 99
This can be transformed to standard bivariate form:
J f g(X, Y) dX dY- wY+V
where g denotes the standard bivariate normal distribution, and
V = (M 2 - m1 )/sI, W = S2/SI.
For particular values of V and W, the bivariate normal distribution is used to evaluatethe above double integral (by a numerical method), and the results are shown in TableA8.1 for an uncorrelated distribution. Allowing the correlation coefficient to take valuesof -0.5, 0.0, or +0.5 made very little difference to the results.
Annex 9: Assigning Probabilities toScenarios for Risk Analysis
In the analysis of risky projects, it is necessary to choose alternative scenarios and toattach probabilities to these scenarios. For example, a project will have an expected costoutcome, and it is desired to investigate high and low outcomes and assign probabilitiesto all three cases. This method can then be extended to other planning variables such asdemand growth, to give a multivariate probability of joint outcomes (e.g., high cost, lowdemand).
The issue is how to combine the values chosen for the three scenarios withprobabilities to be attached to them. The combination of the range of values chosen andthe probabilities imply a variance to the set of outcomes. Since there is a prior view onthe variance of cost or schedule outcome from the regression equations in this paper (andthere may also be a view for the variance of the demand growth rate), it would be sensibleto ensure that the sets of values chosen are consistent with these variances. This annexshows how this assignment can be done.
Consider an expected cost outcome of M (middle). This is the expected value derivedfrom the project analysis, adjusted if necessary from an estimated value by the regressionequation. The analysis suggests that the variance of cost levels is a 2 M2, where a 2 is thevariance from the regression errors. Alternative scenario values L (low) and H (high) areto be chosen, together with probabilities for all three cases.
To simplify the analysis it is assumed that the low and high outcomes are equidistantfrom the mean (expected) outcome. This in turn implies that, for the mean of thedistribution to equal M, the probabilities of high and low cases must be equal. Let theprobability of the middle case be ir, so that the probabilities for the other two cases areeach (1 - ir )/2.
The key insight is that if the variance across these three outcomes is equal to theknown value or 2 M2, there is a relation between the relative distance of L from M and theprobability that must be assigned to the middle value itself. Let the value of L beexpressed as A M ( where A will be less than unity), then the relationship is given by theformula (see the technical note at the end of this annex for derivation):
Ir= I-{r/(l-A)} 2 (A9.1)
An illustration is given using the India 911 example. The central cost estimate usingthe regression approach is 491.5 (M) with the variance of the regression (C52) equal to0.035. Table A9. 1 shows combinations of A and ir that would produce a set of L, M,and H values with variance (a2 M2) equal to 8460 (the variance of the cost level).
101
102 Estimating Construction Costs and Schedules
Table A9.1 Pairs of Parametric Values that Fit the Required Regression Varianceof 0.035 for Scenarios where the External Variance Is a Function of the Size of the
Middle Value
0.813 0.000
0.800 0.126
0.750 0.440
0.700 0.612
The above table shows, for example, that with a value of A of 0.75, whichcorresponds to a low cost of 368 (491.5 x 0.75) and a high cost of 614 (491.5 x 1.25), theprobability that must be assigned to the middle value outcome is 44 percent, while bothlow and high outcomes must each have a probability of 28 percent. It can also be seenthat if the high and low values are taken too near the medium value, there exists no set ofprobabilities that would yield a variance over the three outcomes equal to 8460, aspredicted by external analysis.
In the case where the variance of outcomes is not proportional to the value of themean outcome, then a different formula is required. In this case the relation between theprobability of the central case and the range of cases (as expressed by A ) is:
7r=l-{C/[(-_A)Mj) 2 (A9.2)
where M is the value of the middle estimate.
Consider a central growth rate of 0.04 (4 percent per annum), where the variance ofgrowth rates of demand has been established from other studies to be 0.01. Table A9.2gives the corresponding tradeoffs.
Table A9.2 Pairs of Parametric Values that Fit the Required Regression Varianceof 0.01 for Scenarios where the External Variance Is Not a Function of the
Size of the Middle Value
A 7
0.750 0.000
0.700 0.306
0.600 0.609
Hence when A = 0.600, a low-growth-rate scenario of 0.024 and a high-growth-ratescenario of 0.056, combined with a probability for the middle-scenario-growth rate of60.9 percent, will provide a set of growth rates and probabilities with variance 0.01.
Annex 9: Assigning Probabilities to Scenarios for Risk Analysis 103
Probabilities can be simply multiplied to obtain joint events provided that the costdistribution is independent of the demand distribution. Combining the two examplesgives the probability matrix in Table A9.3 that has a variance for costs of 8460 and avariance for demand of 0.01.
Table A9.3 Probabilities for Scenarios withPredetermined Variances for Costs and Demand
Costs
368 491 614
0.024 0.0546 0.0858 0.0546
Demand 0.040 0.1708 0.2684a 0.1708
0.056 0.0546 0.0858 0.0546
aDerived from the corresponding values for it in Tables A9.1 and A9.2,namely, 0.440 x 0.609.
The method could be extended to correlated distributions, but this is much morecomplicated and it would also require an estimate of the correlation between demanderrors and cost errors. A different extension to nonsymmetric probabilities of high andlow cases is also possible, but again the formulas will be much more complex.
Technical Note: The Derivation of Equation [email protected]
For a symmetrical distribution of outcomes, the values are A M, M, and (2 - A )M,which yields an expected value of M whatever the probabilities. Denoting the probabilityof M by ir, it follows that the variance across these three outcomes is:
(I -i (AmM-M)2 + -27 )[(2-A)M-M]2 = (I-7r)[(l-A)M] 2
Equating this to the externally identified variance of a 2M2 yields equation A9. 1.
Annex 10: The Calculation of the Mean andVariance of the Cost of Two Projects
Let mi be the expected (mean) cost predicted for project i (i=1,2), and v; (=si2) be thepredicted variance of project i.
From standard statistical theory, the mean and the variance of the sum of the costs ofthe two projects is given by
m=ml +m 2
v = vl + v,- + 2cov12
where m is the mean of the total, v is the variance of the total, and coV12 is the covarianceof the distribution of costs for the two projects. Assuming that the distribution of costsare independent, the variance of the sum is equal to the sum of the variances. Hence, thestandard deviation of the sum is given by
s = 4(vI + V2 )
These formulas3 ' can be applied to the expressions developed in the paper forpredicting mean costs and the variances of costs. The regression model predicts the logof the ratio of actual costs to expected cost, where the latter are the values in the WorldBank Staff Appraisal Reports (SARs). Denote the predicted values from the regressionby P
P = log (A/E)
Now P is determined from the regression equation in terms of the characteristics ofprojects, while E is available from the SAR. Hence, to obtain the prediction of the actualvalue we have:
A = E exp (P)
This can be justified as the mean (or unbiased) value of A, where P is the meanprediction of the log of the ratio, by the general statistical results that
if E(x) = 0
then E [g (x)] = g (e)
31. The formulas can be generalized for more than two projects. Where the projects are implementedsequentially over time under a long-term development program, the costs of the projects should beexpressed in terms of their present values in a common base year (usually year 0 of the developmentprogram) according to when they would be constructed under the program.
105
106 Estimating Construction Costs and Schedules
hence 0 = g-' {E [g (x)])
The variance of A also is required and here an approximation is used. Following theabove general notation:
Var [g (x)] = (dg/dx)2 Var[x]
where the derivative is evaluated at the mean of x (i.e., at 0).
Since the variance of P is known from the regression equation, as shown in Annex 8,Appendix A8. 1, and is denoted W:
W = Var [log (A/E)] = (1/A)2 Var A
Var A = A2W
So the standard error of the predicted cost is approximately equal to the predicted costmultiplied by the standard error of regression. For example, the India 911 project had avariance for the log of the ratio of actual to estimated (W) of 0.035, while the predictedactual value (A) was 491.5. Hence, the variance of the actual value is 8460, with astandard deviation of 92.
For two projects with their predicted costs and variances of costs, the overallpredicted total cost and variance of the total cost can then be calculated.
It can be seen that if (a) project costs are independent; (b) the predicted value of theratio of actual to expected costs is independent of project size; and (c) the variance of theratio is independent of project size, then the variance of a sum of two smaller projects isless than that of a single larger project with the same predicted cost as the sum of thepredicted costs of the two projects. For example, where the predicted costs of the smallprojects are each 50 percent of the predicted cost of the one larger project, their meantotal cost is the same, while the variance of the large project would be twice that of thesum of the variances of the two smaller projects.
Annex 11: Applying the Option Approach toConstruction Costs and Schedules
This annex illustrates the application of the option approach to investment timing forcapital projects that are subject to uncertainty about their construction costs andschedules.32 It uses the results of the regression analysis in this paper for powergeneration projects in developing countries to provide the estimates of unbiased valuesand variances that are needed to apply the option approach to this class of projects.
The first two sections of the annex give a general introduction to investment valuationunder uncertainty using the option approach and to general solution methods for thisapproach. The third section develops a simple model for finding the optimal timing forinvestments, which is then applied in the final section to the general cases of thermal andhydropower projects. These cases provide generic measures of the critical benefit/cost(B/C) ratios and their variances for the optimal timing of investments in these twosubclasses of projects. The results confirm the findinas of the main analysis in thepaper-that investment risks from construction are greater for hydropower projects thanfor thermal power projects. Under some plausible assumptions about uncertainty, it isshown that the critical value of the B/C ratio has a premium over the value based onexpected (nonbiased values) equal to about 17 percent in the case of thermal powerprojects, and likewise to 21 percent for hydropower projects. The variance forhydropower projects is also greater than that for thermal power projects.
A. Investment Valuation Under Uncertainty Using the Options ApproachThe so-called real option approach deals with the theory of investments under
uncertainty, where uncertainty is treated in a continuous time framework. It examines theimpact of irreversibility induced by the existence of fixed capital costs under conditionsof uncertainty. Capital costs are viewed as sunk; that is, little, if any, of these costs can berecovered after the investment. The main assumption is that investment can always bedeferred. Future investment is viewed as a mutually exclusive alternative to investingtoday. Even without uncertainty the problem is one of optimal timing, because althoughthe Net Present Value (NPV) of investing today may already be positive, deferring theinvestment would be preferable if it increased the NPV. Keeping the investment optionalive is thus valuable. When the result from the option analysis is not to invest, theinvestment prospect is not abandoned completely but is deferred to the future.
Option models are an improvement on simple NPV models because they capture theeconomic risk that new information might be revealed by waiting, possibly by investing
32. This annex is based on text and analysis provided by Spiros Martzoukos, to whom the authors aregrateful for this contribution.
107
108 Estimating Construction Costs and Schedules
in further studies. Option models do not consider all kinds of uncertainty, and in thatsense they are a partial treatment of risk. They certainly cannot capture directly the riskof changes to the external economic and regulatory conditions, if such conditions affectthe economics of the project only after initiation. Option models can capture such risk ifrelevant information is revealed during the study period. They indirectly capture the expost uncertainty by requiring a premium before investing. Ideally, such uncertaintyshould be captured by appropriately discounting the expected project payoffs, regardlessof the adoption of the option models.
Two premiums are considered by the option model. One is due to deterministicgrowth trends that capture optimal timing in the deterministic sense. The other is apremium for learning something by waiting under uncertainty. This does not necessarilyimply that uncertainty is reduced by waiting, although this could be also the case, forexample, in the case of technological uncertainty. It implies mainly that the estimate forthe mean changes. The timing (waiting) premium only has zero value when optimaltiming has been reached. Investing earlier kills this premium. The optimal time to investoccurs when the value of the underlying asset (the benefits of the investment) exceeds itscost by some predetermined margin. This margin is a function of the discount rates andparameters of the stochastic processes of the underlying variables, such as growth trends(if any) for the underlying investment benefits and costs, and uncertainty. For thediscount rates, a continuous time capital asset pricing model is assumed to hold.
Option models capture the value of the flexibility to invest in the future if it isprofitable to do so but not to invest if conditions worsen. This flexibility is captured inthe asymmetry of the distribution of the expected payoff function under the flexibility toinvest only if it is profitable to do so. This distribution is unaffected for positive futureNPVs but is truncated for negative NPVs, which are replaced by the value of zero. Theresulting asymmetry often values the option more highly than investing today, whichimplies that optimal timing has not been reached yet. An even higher NPV is required tojustify a commitment to invest. Uncertainty enhances the effect of irreversibility, andhence the value of flexibility, by increasing the required margin before investment shouldtake place. Thus the option theory revises the conclusion of the classical approach toinvestment valuation that investment should take place immediately when NPV becomespositive. Such an NPV valuation rule is applicable only when investment is notdeferrable.
Instead of looking at the NPV, the ratio of benefits over costs is often compared witha critical ratio derived from the model. Only when the actual ratio reaches the criticalratio has optimal timing been achieved. Using a B/C ratio allows option models to beused for two uncertain parameters, namely uncertain benefits and uncertain costs, eventhough they were originally designed to incorporate only one uncertain parameter. Ifmore than one large investment alternative exist, then the one-alternative analysisunderestimates the critical B/C ratio. Assuming two investments of similar scale, the
Annex 11: Applying the Option Approach to Construction Costs and Schedules 109
critical ratio for the best option depends on the ratio for the second-best one (Martzoukos1995).
The theory of financial option valuation has been adapted to the economic analysis ofcapital investments.3 3 For power projects a least-cost approach is used to select capitalinvestments. The preferred investment is the one that achieves the system goals at theleast economic cost. To incorporate this criterion into the option formulation, a do-nothing or a minimal-investment scenario can be used as the alternative to the proposedlarge investment, where expansion of supply is achieved (for a while at least) throughpurchase or import of power or through investments in small and versatile thermal units.The large investment alternative, such as a large hydropower or thermal plant, or atransmission line to connect a load center to a central grid, which involves much highercapital costs but lower operating costs than the alternative, would incur fixed (sunk)costs. The do-nothing alternative has its own operating costs, which are avoided if thelarge investment is implemented. Hence, in the option model the sunk capital costs areconsidered to be the costs of exercising the investment option, and the avoided costs ofthe do-nothing scenario to be the benefits of investing. Both the capital costs on one sideand price of power imports or fuel on the other side are effectively cost components butrepresent different types of uncertainty. Capital costs represent technological orinstitutional uncertainty, whereas the other costs represent import price or fuel priceuncertainty. In a least-cost approach (that is now obviously equivalent to the option B/Canalysis), the "benefits" should at least exceed the "costs." The question is, by how much?
B. General Solution MethodsThere are two alternative methodologies to find a solution to a specific investment
problem. The first is the contingent claims (option) approach, and the second is thestochastic dynamic optimization approach. Both methods are effectively equivalent to astochastic optimization of the expected benefits minus the expected costs and differ onlyin the method of approximation to the same problem specification.
The investment option valuation problem is expressed as a fundamental partialdifferential equation for the option value, which can be solved by numerical methods (seeBrennan and Schwartz 1978), or, more rarely (except for simple problem formulations),analytically. The numerical methods can be adjusted to treat options with discretechanges in the benefits and costs if investment is deferred. They can also be adjusted totreat options when the relevant parameters are not constant but are continuous and
33. In the real options literature, important reviews are Pindyck (1991), Dixit (1992), and Dixit andPindyck (1994). The last is the most updated comprehensive review and is a highly recommended technicalreference. A comparison of alternative treatments for uncertainty is given in Crousillat (1989).Applications in the power sector have appeared in Paddock and others (1988), Crousillat and Martzoukos(1991), and Martzoukos and Teplitz-Sembitzky (1992). A recent World Bank application was in an energyoptions study of Pakistan in July 1995. The importance of the deterministic optimal timing is highlighted inSchramm (1989).
110 Estimating Construction Costs and Schedules
deterministic functions of time (see Martzoukos 1995a). The prolific financial economicsliterature on option pricing can be used when it offers a model that has the same orsimilar assumptions to the problem at hand.34
Another way to solve the same option problem, and of course derive the same result,is the so-called lattice approach. The underlying continuous stochastic process can beapproximated by a discrete-time random walk in a decision-tree-like (lattice) fashion.Dynamic programming can then be used to value the initial investment option. Thesolution methodology starts at the terminal boundary conditions (option maturity, usuallya very large number of possible outcomes after many intermediate steps at which optionsare faced over a long time horizon) by valuing each terminal option at the maximum of itsexercise price or zero. Then the analysis proceeds backward in time to derive the initialoption value. At every step, the option value is a probability weighted average of thesubsequent option values. The process at each step allows for the possibility ofexercising an option (at a node in the lattice) by calculating the maximum of the liveinvestment option value or its exercise value (the NPV).35 This method thus derives thevaluation of the investment option and the estimation of the critical B/C ratio throughproperly discounting the asymmetric expected payoffs of the option. Although thismethod uses the concept of dynamic programming in a solution methodology that evolvesbackward, it is not explicitly formulated as a dynamic programming problem. It is rathera hybrid of the option approach to the problem formulation and a backward decision-treesolution methodology.
The standard deviation used in the option model (and captured indirectly in thenumerical solution for the partial differential equation or directly in the tree-type lattice)effectively replicates a scenario approach. This scenario predicts increasing forecast errorin terms of the time frame and is given as a continuous (lognormal) distribution instead ofonly a few discrete points with some probabilities attached to them. For example, astandard deviation of 10 percent per year, which is equal to a variance of I percent peryear, would imply that the variance of the percent change in the underlying variablewould be 9 percent around the forecast in 9 years; this equals a standard deviation of 30percent for that year. The method is an improvement over scenario methods since (a) acontinuous distribution captures more information than just a few selected points, (b) itcaptures the asymmetry of the flexibility to invest in the future only if and when it isoptimal to do so, and (c) it inherently discounts properly under uncertainty. Scenario ordecision-tree methods cannot estimate the critical B/C ratio nor can they indicate howclose the scenario is to the optimal decision.
Option theory gives the correct discounting methodology for cash flows underuncertainty. A feature of option models is that they allow different discount rates for
34. The first seminal papers of the financial options literature include Samuelson (1967), Black andScholes (1973), and Merton (1973).
35. The methodology was demonstrated by Cox and Ross (1976).
Annex I1l: Applying the Option Approach to Construction Costs and Schedules 111
benefits and the costs. Furthermore, this discount rate could be a function of time (inmodels that are solved with numerical techniques). Stochastic dynamic programming is amathematical methodology that does not deal with the problem of correct discounting butcan benefit in this respect from insights gained from the option methodology.Consequently, the two methods can be made strictly equivalent, and they should give thesame results.36
C. A Simple Model for the Investment Option and Optimal TimingIn the deterministic sense, optimal timing implies an optimization of the function
defined as benefits (B) minus costs (C). When investment is deferred, these componentsgrow continuously at gB and gc. The discount rate (risk-free rate for a risk neutral option)is denoted as R. The terms 8B and °c are defined as the difference between the discountrate and the actual expected growth rates for the investment benefits and costs. Both ofthem are effective discount rates. The first is the opportunity cost of not investing, andthe second is the opportunity cost of investing.
The deterministic optimization problem solves
max[B*exponent(-5Bt) - C*exponent(-6ct)]
where maximization is in respect to time t. Equating the derivative with respect to timeto zero gives the optimal timing:
t = log[8cC/(8BB)]/(8B-6c)
In the absence of uncertainty, 8C/8B equals the critical B/C ratio.37
A case for the investment option under uncertainty with a known analytic solution isthe McDonald and Siegel (1986) model, which extends Samuelson's (1967) work to thecase of investment timing.
It can be easily solved with a calculator or a spreadsheet. The critical B/C ratio isgiven by
T/(, - 1) (A 11. 1)
where the parameter X equals
= (0.5 - (5B - C)/2) + [((6B - 5C)/G 2 - 0.5)2 + 28C/a 2 ].
The variance used in the option model equals
ay2 = (y2B + Cy2 c - 2cBYcrBC (Al 1.2)
36. The relationship between the option approach and dynamic programming is discussed in Dixit andPindyck (1994, chapter 4).
37. At optimal time, t* equals zero, so the critical benefit-cost ratio equals 8c/°sa
112 Estimating Construction Costs and Schedules
and is in fact the variance of the actual B/C ratio given as a function of the individualvariances and the correlation between them. The negative sign implies that if benefitsand costs are very strongly and positively correlated, the effective variance that affects theoption price decreases.
The following simple example shows how this model works in the two parametercase with growth rates of the deferred investment benefits and costs both equal to zero,the continuous discount rate equal to 10 percent, and the cost uncertainty and the benefitsuncertainty both equal to 10 percent. It is also assumed that the correlation between costsand benefits is 10 percent. If these assumptions about zero growth rates are not proper,then the model that assumes constant model parameters would not hold. In that case itwould be necessary to test first whether the deterministic optimal timing has beenreached, which can be done by assuming that the investment is deferred for one or twoyears. Then the economic analysis is repeated in which the benefits and costs arediscounted to the present. If the NPV of the deferred investment exceeds the NPV ofinvesting today, then clearly the investment should wait and it would not be necessary toproceed with the option analysis. Otherwise, the analysis follows with the use of theoption model.
The effective uncertainty cs equals
\(.10*.10+.l10* 10 -2 .*.10*.10)=0.134
and the critical B/C ratio equals 1.348.
As expected the results are sensitive to the values chosen for uncertainty. If oneuncertainty equals 10 percent and the other equals 5 percent, then the effectiveuncertainty equals 10.7 percent and the critical ratio equals 1.270. If one uncertaintyequals 10 percent and the other equals 15 percent, then the effective uncertainty equals17.2 percent and the critical ratio equals 1.465. In an example similar to the base caseabove for when two large investment alternatives of similar scale exist, Martzoukos(1 995b) shows that if the actual ratio of the second-best equals 1.0 (or 1.20 or 1.40), thenthe critical ratio for the best investment equals 1.30 (or 1.41 or 1.57).
D. Application of the Simple Options Model to Construction Costs andSchedules
In this section, the options valuation approach to investment timing is applied to theproblem of uncertainty in construction costs and schedules, using the generic regressionequations for thermal and hydropower generation projects in developing countries that arederived in this paper. The simple model given in section C of this annex is used for thisexample.
Annex 1 1: Applying the Option Approach to Construction Costs and Schedules 113
Dl. General Assumptions
The following four assumptions apply to this example:
a. Uncertainty is measured around the expected value, so that a correction has beenapplied for bias to the estimated value.
b. The linearized errors of the regressions are used as proxy for the ex ante uncertaintyused in the option model, although in fact they represent ex post tuncertainty. Theyare specific to the time horizon (corrected for bias) for project completion, so in theoption models "option variance" = variance*t; this implies that the derived optionmodel uncertainty for the relevant parameter (schedule or cost) is a forecast error thatis specific to the time adjusted for bias, and is a forecast error increasing in respect totime. The detailed derivation of option model standard deviations is morecomplicated and follows in the next section for both the benefits (related to scheduleslip) and costs.
c. The relationship betwveen normal and lognormal distributions. When a variable isnormally distributed as N(g,c), the notation implies a normal distribution with mean,u and standard deviation (.
If the logarithm of a variable is distributed N(I.,o), then the variable is said to belognormally distributed with mean equal to exp(ji+.5C2 ) and variance equal toexp(2u+cy2 ){exp(a2)-l 1. To derive a yearly option model a, a2 is replaced in theequation above with a 2 t, where t is the best estimate for the time to projectcompletion and is adjusted for bias.
d. Definition of linearized error. The logarithm of the ratio of actual cost over predicted(estimated) cost is the dependent regression variable:
Ln(C/Cpred) = Cregr + error
Thus, by taking the exponent of both the left and right sides of the regressionequation:
C = exp(lnCpred + Cregr) + (linearized error)J(Cpred)
The first expression on the right side equals the mean of a lognormal distribution andhas a standard deviation equal to the linearized error adjusted with 4(Cpred). A similarresult holds for schedule slippage.
D2. General Formulation to Estimate Option Model Uncertainty
This section derives the estimate of the uncertainty for the benefits and costs that canbe used in the option model. This estimate is case specific. It depends on the percentcorrection for bias that is given by the regression model for both schedule and costs, andthe actual time predicted.
114 Estimating Construction Costs and Schedules
a. Approximating schedule uncertainty. Demand uncertainty and fuel priceuncertainty are usually considered to be the factors associated with benefit uncertainty.38
Construction slip uncertainty can augment these two factors, and can even replace themon the assumption that:
1. Project timing given by the deterministic methodology is in generaloptimal in terms of excess capacity, so that demand uncertainty for aproject of given capacity is small; and
2. Fuel price uncertainty is not reduced by waiting due to the long projectconstruction period.
By considering schedule slippage uncertainty as the relevant uncertainty for thebenefits (or, in any case, as one of the relevant uncertainties for the benefits) in the optionmodel, it is implicitly accepted that waiting will improve the estimate for the expectedtime to complete the project. Since time to completion can only be a positive number,this complies with the lognormal distribution assumption of the option model.
The benefits from the investment option are denoted as B, and they equalexp(-tR)Num, where t equals the project completion time, R the continuous discount rate,and Num a number that represents the expected benefits discounted to the end of theproject completion period.
First, the variance a2 of B is needed for the option model if the variance of t is known.It is assumed that Num is not sensitive to the estimate of t. In the option model, the entityB is lognormally distributed, thus InB equals -tR + ln(Num) and is normally distributedwith variance a 2t. So the variance of t equals a2t/R. Because t is the predicted timecorrected for bias, the variance equals a2 tpredexp(tregr)/R.
Second, the variance of t is estimated from the regression model. It is known thatln(t/tpred) = tregr, thus "t/tpred" equals exp(tregr), with the standard deviation equal to thelinearized error e multiplied by tp,d. So the standard deviation of t equals e'I(tpred).
From the above:
el(tpmd) = a'l[(tpredexp(tregr)/R]
from which:
a = e4[R/exp(tregr)] (Al 1.3)
(b) Approximating cost uncertainty. Cost uncertainty relates directly to the cost C ofexercising the investment option.
From the regression model ln(C/Cpred) = Cregr,
38. The considerable uncertainty that exists in forecasts for oil prices and power demand is confirmedby the Bank's experience, as shown in Annex 12.
Annex I 1: Applying the Option Approach to Construction Costs and Schedules 115
CCpred := exp(Cregr)
with standard deviation equal to the linearized error e. Equivalently it is assumed that thestandard deviation of C equals eaCpred-
The option model gives the assumption that C is lognormally distributed, so InChas a standard deviation of C2t, where t equals the expected time and is adjusted for biasto tpredexp(tregr).
The relation between the means of normal and lognormal distribution is used toderive p:
C = Cpredexp(Cregr) = exp(Q+.5e2 Cpred)
SO .L = InCpred + Cregr - .5e2 Cpred.
Finally, an approximate value of a is derived by solving iteratively the equation forthe relationship between the variances of the log-normal and the normal distributions:
e2Cpred = exp(2g+a 2 t){exp(a 2t)-l } (Al 1.4)
D3. The Cases of Thermal and Hydropower PlantsThe following linearized errors for the two main groups of power generation projects
were derived in chapter 6 of the paper:
Thermal HydroSchedule 0.220 0.200
Cost (constant) 0.179 0.259
The predicted and adjusted schedules are given by ln(t/tpred) = tregr, where t/tpred is theaverage schedule slip derived from the regression equations (30 percent for thermal, 28percent for hydro):
Thermal Hydrotregr ln(1.30) = .262364 ln(1.28) = .24686
The predicted and adjusted costs are given by ln(C/Cpred) = Cgr, where C/Cp,d is theaverage cost overrun derived from the regression equations (6 percent for thermal, 27percent for hydro):
Thermal HydroCregr ln(l.06) = .058269 In(1.27) = .239017
Assuming a continuous discount rate R of 10 percent, equation Al 1.3 is solved forthe investment option benefits CB:
Thermal HydroaB .061017 .055902
116 Estimating Construction Costs and Schedules
Equation A 11.4 is solved by numerical methods for the investment option cost ac:
Thermal Hydroac .0735 .0685
Assuming a squared correlation between cost overrun and schedule slip for thermalpower projects of .24 and for hydro power projects of .01 (Table 5.6 of the paper), whichimply correlations of .4899 and .1, the relevant standard deviations are computed fromequation A 11.2 and the critical B/C ratios are computed from equation AI 1.1 (section C),as follows:
Thermal HydroCSB/C .069 .084
(B/C) 1.166 1.206
Thus the critical benefit-cost ratios that account just for uncertainty in constructioncosts and schedules about expected (unbiased) values (assuming that the deterministicoptimal timing is already exceeded) are case specific. In general they are shown to behigher for hydro power plants, mainly because of the lower correlation between costs andschedules for hydropower projects.
To recapitulate the main insight from this application of the option approach, ifuncertainty changes in the way that is modeled, then the invest now option should beexercised only when the estimated benefit/cost ratio exceeds 1.166 based on expected(unbiased) values in the general case of thermal power generation projects, and exceeds1.206 in a similar fashion for hydropower generation projects.
Annex 12: Performance of Power Demand Forecastsand of World Bank Oil Price Projections
Figure A12.1 Performance of Power Demand Forecasts for Developing Countries
Deviation (percent)60I
50 -
40
30 -- Mean-1 STD- ' +Mean deviation
20 -- Mean +1 STD
10
0
-10.Year 1 Year 3 Year 7 Year 10
Note: Deviation percent is deviation of forecast demand from actual demand as a proportion of actualdemand based on a sample of about 200 power demand forecasts. Source: Sanghvi and Vernstrom (1989).
Figure A12.2 World Bank Oil Price Projections in Constant 1987 US$ per Barrel
Dollars per barrel70-
1980 forecast 1982 forecast
60-- 60 - 8 ' ' - ~~~~~~~ ' / ~~1984 forecast
50- -
40--
30 Actual /
20-1978 forecast 1988 forecast
10
1974 1979 1984 1989 1994 1999
Source: Crousillat (1989).
117
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