/133 0INDUSTRY AND ENERGY DEPARTMENT WORKING PAPERENERGY SERIES PAPER No. 39

Decision Making Under Uncertainty-An Option Valuation Approach to PowerPlanning FILE COPY

Report No.:11330 Type: (MIS)Title: DECISION MAKING UNDER UNCERTAIIAuthor:Ext.: 0 Room: Dept.:

August 1991 AUGUST 1991

The.World Bank Industry and EnergyDepartment.PR. .

x, . . : . , ., > , . . .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~U

Th Wol BankX *nur and Enrg D*atmn PRE

Pub

lic D

iscl

osur

e A

utho

rized

Pub

lic D

iscl

osur

e A

utho

rized

Pub

lic D

iscl

osur

e A

utho

rized

Pub

lic D

iscl

osur

e A

utho

rized

DECISCON MAKING NDER UNCERTAINTY

AN OPTION VALVATION APPROACH TO POWER PLANNING

by

Enrique Crousillat and Spiros Nartzoukos

August 1991

Copyright (c) 1991The World Bank1818 H Street, N.W.Washington, D.C. 20433U.S.A.

This report is one of a series issued by the Industry and EnergyDepartment for the information and guidance of Bank staff. Thereport may not be published or quoted as representing the views ofthe Bank Group, nor does the Bank Group accept responsibility forits accuracy or completeness.

This paper addresses the problem of irreversibility of investments,a topic related to the recently evolving "real options" literature.In the presence of alternatives, the opportunity to invest in alarge "irreversible" project with uncertain benefits and costs issimilar to a financial "call" option. In exercising this option oneforgoes the potential gains from postponing the investmentdecision. Conventional economic appraisal techniques ignore thisopportunity cost, thus usually tending to accept larger inflexibleprojects. This problem is particularly important in powerinvestment decisions, where the presence of uncertain demand, fuelprices, construction cost, etc. makes the opportunity cost too highto ignore. The present paper includes an exposition of the optionsapproach, a discussion on the main model and its parameters, andIENED's experience in applying this innovative approach in fourpower planning case studies.

ACKNOWLZDGKBMNT8

The authors are grateful for the contribution of Witold Teplitz-Sembitzky and James Paddock (Tufts University) who provided advicefrom the init4.al stages of our work and supervised several partsof this analytical effort. We also thank John Besant-Jones for hiscareful review of an earlier draft. The valuable contribution ofHernan Garcia and Rama Skelton, who reviewed the paper, is alsoacknowledged.

Table of Comtents

EXECUTIVE SUMMARY. . . . . . . . . . . . . . . . . . . . . .i

1. INTRODUCTION . . . . .a . . . . . . . . . . . . . . . . . 1

2. REAL OPTIONS ........... . . ...... ... . 5The Perpetual option . . . . . . . . . . . . . . . . . . 6

3. CASE STUDIES . . . . . . . . . . . . . . . . . a . . . . 123.1 Costa Rica Case Study . . . . . . . . . . . . . . 13

Costs and Benefits . a .. . .. . ..*. . . .. a 14Estimation of Option Model Parameters . . . . . . 16Results .............. .*.*. . 18

3.2 Hungary Case Study . . . . . . . . . . . . . . . 19Costs and Benefits ............... 20Estimation of Model Parameters . . . . . . . . 22R*esults .. .. .. .. .. .. .. .. .. . .. 22

3.3 Manantali Hydropower Plant . . . . . . . . . . . 23Costs and Benefits .. .. ..... ..... 24Estimation of Model Parameters . . . . . . . . . 25Results . .. .. .. .. .. .. .. .. . . .. 26

3.4 Optimal Timing of Transmission Line Investments . 27Costs and Benefits . . . . . . . . . . . . . . . 28Model Parameters ............................... 294 Oesults . . . . .. . . . . . . . . . . . . . . . 29

4. CONCWaSIONS ................. 31

ANNEX 1 - The Perpetual Option . .* ....... . . . .. 33

ANNEX 2 - Costa Rica Case Study . a . . . . .. .* . . .. 48

ANNEX 3 - Hungary Case Study . . . . . . . . . . . . . . . 56

ANNEX 4 - Optimal Timing of Transmission Investment . . . 68

ANNEX 5 - Glossary . . . . . . . . . . . . . . * . . . . . 69

REFERENCES . . * . . . a . . . . . . a . . . . * * . . . . 71

List of Figures

1 Sensitivity of Critical Ratio on 6V. . . . . . . . . . 8

2 Sensitivity of Critical Ratio on . . . . . . . . . . 9

3 Critical Ratio.as a Function of Standard Deviation . . 10

4 Unit Lognormal Stochastic Variable . . . . . . . . . 11

1.1 U - Shape of Investments Present Value . . . . . . . 35

1.2 Unit Lognormal Stochastic Variable (a = 5%) . . . . . 40

1.3 Unit Lognormal Stochastic Variable (a = 10%) . . . . 41

1.4 Unit Lognormal Stochastic Variable (a = 15%) . . . . 42

1.5 Unit Lognormal Stochastic Variable (a = 20%) . . . . 43

1.6 Unit Lognormal Stochastic Variable (a = 25%) . . . . 44

1.7 Unit Lognormal Stochastic Variable (a = 30%) . . . . 45

2.1 Costa Rica: Monte Carlo Simulation . . . . . . . . . 55

3.1 Hungary: Nonte Carlo Simulation (Nuclear) . . . . . . 66

3.2 Hungary: Monte Carlo Simulation (Coal) . . . . . . . 67

List of Tals

1 Costa Rica: Economic and Technical Data . . . . . . . . 15

2 Costa Rica: Costs and Savings for the two Expansion Plans 16

3 Costa Rica: Critical Ratios . . . . . . . . . . . . . . 18

4 Hungary: Economic and Technical Data . . . . . . . . . 21

5 Hungary: Costs and Savings ... ........... 21

6 Hungary: Critical Ratios ............... 23

7 Manantali: Costs and Benefits . . . . . . . . . . . . . 25

8 Manantali: Critical Ratios . . . . . . . . . . . . . . 27

9 Optimal Timing of Transmission Line: Economic andTechnical Data . . . . . . . . . . . . . . . . . . . . 28

10 Transmission: Net Savings and Actual Ratio . . . . . . 29

1.1 Difference between Continuous and Regular Discounting . 46

2.1 Costa Rica: Power Expansion Scenarios . . . . . . . . . 48

2.2 Reject - Acceptance Matrix: Hydro . . . . . . . . . . . 50

2.3 Reject - Acceptance Matrix: Geothermal . . . . . . . . 51

2.4 Sensitivity Analysis: Hydro . . . . . . . . . . . . . . 52

2.5 Sensitivity Analysis: Geothermal . . . . . . . . . . . 53

3.1 Hungary: Power Expansion Scenarios . . . . . . . . . . 56

3.2 Costs and Savings under different Scenarios . . . . . . 58

3.3 Sensitivity Analysis: Nuclear . . . . . . . . . . . . . 60

3.4 Sensitivity Analysis: Coal . . . . . . . . . . . . . . 61

3.5 Sensitivity Analysis: Nuclear (dual fired) * . . . . . 62

3.6 Sensitivity Analysis: Coal (dual fired) . . . . . . . . 63

Deislomnauking Under Uncertainty:An Option Valuation Approach to Power Planning

Executive Summary

Development agencies play a major role in financing the ension of powersystems among their member countries. Since the 1960s and 1970s,decsionmakers in these agencies have relied on models such as WASP to findleast-cost solutions to problems of meeting expected demand. The problem thathas arsen is not in the accuracy of these models in finding least-cost solutions butin the accuracy of the ftrecasts on which the solutions are based. Once aen asa given, forecasts have become increasingly inaccurate-a tendency reinforcedduring the 1980s, when energy prices and growth varied abruptly andunpredictably. In fact, recent evaluations of demand and investment costforecasting by the World Bank have demonstrated a trend among forecasts tooverstmate the growth of demand for power and underesimate the costs, andyet also a significant dispersion of errors that indicates a high degree ofuncerainty in making any particular investment c cision.

An *optimal expansion plan" designed for a scenario that fails tomateralie is no longer optimal. Overestimating demand and underestmatingcost of a capital-intensive power project can lead to overdimensioned orunderfimded projects-either one potentially disastrous to a developing country.Hence, the need for an improved method of appraising power investments hasbecome apparent, and the World Bank has sought to find a methodology fortaking into acoount elements of risk and uncertainty in power planning. Thispaper focuses on one approach to decisionmaking under uncerinty, the optanvaluation appxvach.

The options approach is particularly useful in dealing with the problem ofirreversible' investments, in which the political and economic reecussions ofabandoning a project once it is well under way-such as a typical power project,with its high proportion of sunk costs-are so high as to make abandonmentimpracticable. Generally, when an environment is uncertain, investors can forgoor deay investment untl more favorable conditions are at hand. In either case,the investor has kept the options open. But in exersing the opportunity toinvest, the decisionmar loses this flexibility. Conventional analysis techniques,including standard least-cost power planning, ignore the cost of the lost option.Yet the value of the option to -wait to invest' could be large enough to invalidatethe usua decsin rule, to invest when benefits exceed costs. In effect, thecorrect decision rule under such circumstances should be to invest when benefitsexceed costs by an amount at least equal to the value of the lost (forgone) option.

i

How can the analyst or decisionmaker calculate the value of the option toinvest? The financial literature provides a methodology for calculating the valueof an option and the "critical ratio of benefits to costs at which it becomesoptimal to invest. The model used here is the perpetual option model or theoption to %Wzt to invest. Derived from the work of McDonald and Siegel (1986),the perpeual option model provides a relatively simple methodology (requiringonly two formulas for application) for deriving the critical ratio. The criticalratio so derived includes a penalty equal to the opportunity cost of the lost optionas the irreversible decisionr to invest is exercised. Thus, the decision sile forinvestment is that investment is viable when the benefit-cost ratio exceeds thecritical ratio.

How does the perpetual option model work in practice? To test this, theauthors sought to compare relatively large and irreversible projects, such as hydroplants or nuclear plants, with a nodular-type expansion of smaller thermal plants,such as gas turbines or smaller diesel plants. Tle loss of investment flexibilityrelated to undeatkng the large, "irreversible" investment decision would bemodeled as a perpetual option and addressed in quantitative terms. Costs (e.g.,of construcion) and benefits (e.g., fuel ani. operation and mainteace savings,capital costs avoided on alterative expnsion plans) would be considereduncertain, but generally to relate to fuel pricis, demand growth, and capital costs.These would be estimated through a simple z7mulation of alternative investmentprograms or obtained from power system planning models. The flexibilityvariable concerns the ability to wait instead of malkng the i-vesible investmentin the hydro or nuclear plant, and the product of this analysis is the critical ratioderived from the perpetual option model. The actual ratio of savings to coststhen would be compared with the critical ratio, and the comparison would indicatewhether the actWal ratio of benefits to costs was equal to or greter than thecritic raio. If the actual ratio was less than the critical ratio, the investor wouldbe better off wating, since the value of the flexibility lost would exceed theproject's net benefits.

The authors applied the model to cases of lage power projects in fourcountries-Costa Rica, Hungary, Mali, and Senegal-drawing on previous datacollection and analyses by Martzoukos and Paddock (1991), Martwoukos andTeplitz-Sembitzky (1991), and Schramm (1989). In all of the case studies, theoption valuation approach was easy to handle and provided a simple andmeaningful decision rule that should appeal to analysts and decisionmakers. Theaccuracy and reliability of the model still depends on the extent to which themodel's assumptions hold in pracdte and on whether the simplificationsundertak during the modeling are faithful to the actual circumstances. The casestudies show, generally, that the penalty of forgoing flexibility can beconsiderable. In the Costa Rica and Hungary studies, the penalty, reflected in the

ii

critical ratio, varied betwee 21 percent and 26 percent of total costs. In theManantali Dam case, a regional project on the Senegal River Basin in Mali,alterative long-term expansion programs were compared, and uncertainty washigher. The penalty thus was higher, increasing to a value of 35 percent of totalcosts. In the fourth study, which concerned the capital-intensive task ofconnecting rural areas currently serviced by decentralized plants to main powergrids, uncertainty created an incer-five to delay investment in the costlyconnection to te main grid by almost three years beyond the "optimal" date toavoid losses from exercising the investment option. Fuller explanations of themethods and details of analyses are provided in text and Annexes.

The study thus suggests that the option valuation approach addresses asignificant problem with risks of a large order of magnitude; that it would posea significant change in, and improvement on, classical benefit-st approaches;and that the critical ratio provides a relatively practical and easy-to-apply tool foranalysts and decisiomakers to better anticipate the risks of forgoing flexibilityin large investent decisiom The approach is applicable to investment problemsoutside the power subsector as w'ell.

iii

DECIXSON MARING UNDER NCERTaXWfN - AN OPTION VALIUaON APPROACETO POwER PLANNING

1. INYRODuCTxON

Most development agencies have an important role in financing powersystem expansion plans among their member countries. Themethodologies for appraising these expansion plans were developedand refined largely in the sixties and seventies, and generallyconsist of finding the least-cost solution to the problem ofmeeting a forecast demand, which is usually thought of as a given.Power systems planning models - such as WASP - are widely used inalmost all developing countries to formulate least-cost ex_-ansionplans. While these methodologies have become very sophisticated,there has been a growing realization that they may be inadequateor insufficient, not because they fail to achieve their limitedobjective, but because it is impossible to make accurately theforecasts they require. This perception has been reinforced duringthe last decade, after a period of abrupt changes in energy pricesand disruptions to economic growth, a decade through whichforecasts have become more unreliable.

Studies carried out by the Bank show that the track record offorectisting in the power sector is poor. Bank ex-post evaluationsof forecasts on demand growth (Sanghvi et.al., 1989),implementation time and capital costs of new plants (Merrow et.al.,1990), fuel costs and technological innovation reveal thefollowing:

- Forecasting errors have been in general high and clearlybiased in one direction. There is clear evidence of anoptimistic bias reflected in the overestimation of demandgrowth and the underestimation of costs and implementationtime.

- The great aispersion found in forecasting errors indicates ahigh degree of uncertainty in making particular powerinvestment decisions.

- The wide spread of errors found is very seldom captured by thenarrow margins usually adopted in sensitivity analysis.

A so-called optimal expansion plan designed for a scenario thatfails to materialize is no longer optimal. Therefore it isdifficult to escape the conclusion that if the methods of appraisaldo not take into account elements of risk and uncertainty, theycannot be relied upon to yield truly optimal expansion plans.Furthermore, the forecasting trends - i.e. the overestimation ofdemand growth and underestimation of costs - suggest that thesemethods would tend to prescribe overdimensi^Ded and/or underfunded

plans while choosing larger and less flexible plants. This problemis the more worrisome because of the capital intensiveness of powerprojects and the fact that governments and utilities of developingcountries are planning huge power investment programs for the1990Q, which will require around US$1 trillion of financialresources (Moore and Smith, 1990). Therefore, errors in the timingand scale of power investment decisions or in the choice oftechnologies have a potential of impacting negatively the overalleconomy of developing countries.

Generally speaking, the World Bank's approach to the economicappraisal of individual projects is theoretically sound. Hovever,the Bank's practice departs considerably from its guidelines,apparently due to institutional reasons and the difficulties thatsome analytical tools place for their application (Little andMirrlees, 1990). This situation appears to be particularly true ir.the treatment of risk and uncertainty. The theory urierlying theBank's approach to project appraisal under uncertainty is quiteconse-vative. It proposes an allowance for uncertainty only forprojects where profits were expected to be correlated with thegeneral state of the economy (Little and Mirrlees, 1974). It issometimes argued that this allowance should be made also forspecially large projects, relative to the country economy. Clearly,the approach is more concerned about the effects of risk at a macrolevel and thus understates the problem of relative flexibility andrisks associated to competing projects. However, Bank's guidelinesgo a step further (World Bank, 1980, 1980a and 1984). Theyrecognize that some elements in the cost and benefit streams ofprojects are uncertain, and therefore recommend the use ofsensitivity analy?is and, if necessary, formal risk analysis forproject appraisal . Unfortunately, sensitivity and risk analysesface two main practical problems that have hampered their effectiveuse: (i) sensitivity analysis is usually undertaken at a late stageof the project cycle only to confirm the robustness of theevaluation conclusion to arbitrary, and unduly narrow, variationsin a few planning parameters, and (ii) the guidelines for riskanalysis are insufficient since they just recommend the use of aprobabilistic risk method, a costly simulation approach with strongelements of black box, without providing much guidance on how todo it.

I It should be noted also that current Bank Guidelines forpower, water supply and telecommunications -(World Bank, 1978)consider a least cost planning approach as an alternative toproject benefit/cost analysis when economic benefits are difficultto quantify. The case studies presented in this paper areundertaken along those lines, since in all cases avoided costs areestimated as a proxy for benefits. This approach, thoughconceptually correct, does not include all benefits thus excludingthe consumers surplus.

2

To address this problem, the World Bank is undertaking a programdesigned to incorporate risk and uncertainty into power planning.A first stage of this effort consisted in a survey of theliterature and current day practices, and the identification ofsuitable approaches (Crousillat, 1989). It was found then thatpower planners in industrialized countries have largely abandonedformal least cost planning as an explicit goal and are givingincreasing attention to flexible or robust plans able to adapt toa changing world. The literature review found three promisingapproaches to deal with the problem, namely: (1) stochasticoptimization, (2) strategic models, particularly risk-tradeoffanalysis, and (3) the option valuation approach.

A second stage of the Bank's program on risk in power planningconsisted in testing the three identified approaches in severalcase studies. This stage concerns the undertaking of country levelcase studies on dissimilar power systems with the objective ofultimately answering the following questions: (1) is it advisableto abandon the methods currently in use in favor of an approachthat addresses the question of risk and uncertainty?, (2) wbat arethe policy implications of incorporating risk and uncertainty inpower planning?, and (3) are any of the identified methods suitableto produce a practical tool which Bank staff and/or country powerplanners might use in appraising power expansion plans? The resultsof the case studies, plus a final comparative evaluation, areexpected to answer the above questions.

This paper reports on World Bank's experience in the study andapplication of one of the approaches, namely the option valuationapproach to power planning2. Chapter 2 addresses the basic theoryof options, describes the standard model developed for realoptions, and discusses its parameters and assumptions. Finally, itexamines the critical assumptions underlying the estimation of themain decision indicator: the critical ratio that should be comparedto the conventional investment benefit-cost ratio. To facilitateits reading, some sections are presented in separate annexes whichinclude the mathematical formulation of the optiors model, itsunderlying assumptions and a glossary.

Chapter 3 describes four case studies. The first two undertakecomparisons of generation projects on a project-to-project basis,without the use of a systems approach. The first case is a typicalhydro vs. thermal project comparison in the Costa Rica powersystem, and the second a comparison of thermal generatingtechnologies in Hungary. The third case study is a speciallyinteresting exercise of combining the use of a power system

2 Initial investigative work was done by Teplitz-Sembitzky(1989). Case studies are drawn from Martzoukos and Paddock (1991),Nartzoukos and Teplitz-Sembitzky (1991) and on further in-houseanalytical work.

3

planning model with the options model. Here, the comparison is doneon two alternative expansion plans for the Mali and Senegal powersystems. The last case refers to the problem of determining theoptimal timing of transmission line investments for their extensionto isolated systems. Finally, Chapter 4 draws conclusions from thisexperience and provides some practical recommendations.

4

2. 2 AML OPTIONS

The term "real option" refers to a concept analogous to that offinancial investment options. Real options are faced in manyactivities. They can be related to a choice of technology, aproduction decision, decisions on investment timing, the option totemporarily or permanently shut down a plant, as well as to manyother decisions dealing with real (physical) assets.

The options approach addresses the problem of "irreversibility" ofinvestments. Very often investment decisions are irreversible,since they imply embarking on rigid programs with a subsequentlarge proportion of sunk costs. This is particularly true in thecapital intensive power sector where once we are committed to aparticular investment, the political and economic costs ofabandonment can be extremely high thus making almost impossible toreverse a decision. Generally speaking, prior to making aparticular investment decision, we can always "wait to invest" andlearn more about the parameters that affect the economic viabilityof this investment. Once an irreversible decision is made, theflexibility gained with time from the potential reduction ofuncertainty is lost. As a rule, the higher the uncertainty relatedto critical variables like energy demand, fuel prices andconstruction costs, the higher will be the value of the flexibilityloss.

In an uncertain environment, an investment could be delayed untilmore favorable conditions occur. In the case of worseningconditions though, there would be no obligation to invest and wecould keep our options open - an opportunity - for undertakingalternative decisions that, in that case, would result in a morefavorable outcome. This opportunity is similar to a "stock option".In exercising the decision to invest we forego the potential gainsof postponing the decision, i.e. we incur in an opportunity cost -a lost option - as the irreversible investment reduces ourchoices, thus reducing our flexibility. Conventional economicanalysis techniques, including standard least cost power planning,ignore the cost of the lost option and tend to accept less flexibleprojects too easily.

The value of this foregone option 3 could be large enough toinvalidate the usual decision rule: to invest when benefits exceedcosts. In contrast, the correct decision rule should be: to investwhen benefits exceed costs by an amount at least equal to the valueof the foregone option.

The financial literature provides option models to calculate the

3 The value of the option "to wait to invest".

5

value of an option and the critical ratio of benefits to costs atwhich it becomes optimal to invest. The model used in this paperis known as the perpetual option' or the option to wait to invest.This model was developed by McDonald and Siegel (1986) as anextension of a previous work done by Samuelson (1965). A completemathematical formulation of the perpetual option model, includinga discussion of its parameters and assumptions, is presented inAnnex 1. Here, we include the main expressions of the model, whichare in fact the only two formulas needed for the application of theperpetual option model.

The Perpetual Option

The critical ratio provided by the perpetual option is given by:

C = t/(1t-3)

where the parameter r is given by:

I = (0.5 - (6f-6 )/c2) + [((6f_ 6 v)/a2 _ 0.5)2 + 2Sf/02]

and "a'", the total effective variance, is an overall measure ofuncertainty and equals a v + af - 2r f0vaf. The critical ratioincludes a penalty equal to the opportunity cost of the lost optionas we exercise an irreversible investment decision.

The value of the investment opportunity is given by:

w = (C-1-)F(V/WCY

where:

V 5 present value of benefits ("stock price equivalent" in thefinance terminology).

F = present value of costs ("exercise price").°v = standard deviation of benefits, on the expected rate of

change.af = standard deviation of costs (on expected rate of change).r = correlation between benefits and costs.Sv , 8fZ effective discount rates representing the opportunity cost

on the benefits and costs of deferring investment,respectively, equal to the difference between thecorresponding discount rate and the growth rate ofbenefits and costs.

Values C and W constitute the main contribution of the model. C

4 It was originally called "perpetual option" because it hasno finite expiration (maturity) date. When the option can beexercised at any time, it is called an American option. A Europeanoption can be exercised only at the expiration date.

6

is the critical ratio that should be exceeded by the actualBenefit-cost ratio in order to make the investment viable underuncertainty. Therefore, the decision rule will be:

Benefit/Cost Ratio > Critical Ratio

W is a quantitative measure that indicates in monetary terms thevalue of the investment5 plus an option penalty due to the lostflexibility.

The relationships between the critical ratio and the mainparameters as well as the model's assumptions are discussed inAnnex 1. In summary, these relationships are as follows:

a) The critical ratio is a decreasing function of 6v and anincreasing function of Sf. If the effective discount rate onthe benefits (6,,) is higher, the opportunity cost of theforegone savings would be lower, therefore the requiredflexibility premium would be also lower. Figure 1 displaysthis relationship. On the other hand, if the effectivediscount rate on the costs (68) is higher, the requiredflexibility premium is also higher because the opportunitycosts of deferring construction are lower. This relationshipis presented in Figure 2.

b) The critical ratio is an increasing function of the overalluncertainty (standard deviation a). If uncertainty is higher,the value of waiting to receive more information is higher andthe required flexibility ,remium should be higher too. Figure3 presents this relationship, keeping other model parametersconstant (i.e. discount rate: 10%, and savings appreciationand cost appreciation: 1.3%). It can be seen that the criticalratio and thus the investment decision are very sensitive tothe estimate or perception of the underlying uncertainty.

It is important to understand the implications of the randomwalk hypothesis used in the model. For illustrative purposeswe provide in Figure 4 a distribution of future values for avariable that has no growth (drift) but fluctuates with astandard deviation of 15% per year. Assuming an initial valueof 1 and that the variable follows a random walk, i.e. thatafter fluctuating in one period, the variable has no tendencyto revert to a previous "normal" value, the extreme values ofthis variable after 5 years would vary between 0.52 and 1.96for a confidence level of 95% (and between 0.72 and 1.4 fora confidence level of 65%). For a standard deviation of 10%the corresponding range for the 95% confidence interval wouldbe between 0. 67 and 1. 54. A set of graphs for these and other

s In fact, the net present value of the investment withoptimal deterministic timing.

7

Figure 1

SENSITIVITY OF CRITICAL RATIO ON 6v6v - effective discount fote on soving:

110

100 _

90 _

80-

0 70 -600

750

._*0 40 -

30 0

20 -

60

*~~ _040

0.1 0.087 0.07 0.05 0.04 0.03 0.02 0.01 0.005 0.0025 0.001

dv = Discount rate - growth rate

uncertainty levels is included in Annex 1. These figuresreveal the wide range of values that can be expected in thefuture even for relatively low standard deviations, and arethus an indication of the need to be specially cautious whenquantifying uncertainty in any practical appiication of themodel.

c) The critical ratio is also a decreasing function of thecorrelation between benefits and costs (rv). Regardless of theunderlying uncertainty, if benefits and costs fluctuatetogether and in the extreme, if they are perfectly correlated,the critical ratio will be considerably reduced. If benefitsand costs are poorly correlated, the effects of uncertaintywould increase since there will be always the possibility ofhaving simultaneously higher than expected costs and lowerthan expected benefits.

8

Figure 2

SEN'.JTIVITY Or CRITICAL RATiO ON 6 f6f - effective discount rate on costs

2.6

2.5-

2.4-

2.3 -

2.2 -

Cc 2.1

2

co 1.7 _-).

16 1.

1.3

1.6

(-I~~~~~~~~~~~~~~~~~

0.2 0.15 0.12 0.1 0.087 0.07 0.05 0.04 0.03 0.02 0.01

4.f - Discount rote - growth rote

The main assumptions of the perpetual option model are:

a) Variables are log-normally distributed. The practicalimplication of this first assumption is that negative valuesshould be excluded, therefore all benefits and costs shouldhave a positive sign. If for example an investment in a hydroscheme results in avoiding construction costs in analternative development, these costs should not be subtractedfrom the construction costs but should be added to thebenefits. This has, of course, a direct implication for theestimation of the relevant uncertainty of costs and benefits.

9

Figure 3

CRITICAL DATIO AS A FUNCTION OF "a"AMERICAN TYPE, iNFINITE MATURITY OPTION

2.9

2.8

2.7

2.6

2.5-

2.4-

2.3 -

2.2-O 21 -2

2

1.9c1.8

1.7

1.6

1.5-1.4-

1.3

1.2

1.1

0.030 0.060 0.090 0.120 0.150 0.195 0.255 0.345 0.450

TOTAL EFFECTIVE N"o

b) The model is defined in continuous time and assumes constantrates of change, which implies a perpetual exponential growthof benefits and costs. For practical purposes we apply a"rotations" approach, i.e. the repetition of a finite timeprofile of benefits and costs. It should be noted, however,that under the normal practice of heavy discounting, thelength of the rotations is not crucial if the life of theirreversible alternative if sufficiently long.

10

C) The model assumes that the dynamics of the uncertain variablescan be described in terms of a Brownian motion in continuoustime. This implies continuous discounting for the estimationof present values. Compared to regular discrete timediscounting, continuous discountinc -.nderestimates" presentvalues. The difference between -.. th approaches is anincreasing function of the discount rate and the period ofanalysis. However, the impact of these differences in powerplanning problems tends to be minor since it will affectsimilarly the present value of benefits and costs.

Figure 4

UNIT LOGNORMAL STOCHASTIC VARIABLE95X ANO 65% CONFICENCE NtERVALS

3.4

3.2

:3

2 8

2.6

W 2.4

>41. 2.2i:,J 2

.D- i.8 - _ f16OD1.4

(A9 1.2

0.8

0.6. .. ......

0.4

0.2 i I '

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Time- stondard deviclion * 15X

0 Inner (outer) 2 curves - 65X (952) confidence intervol.

6 See Annex I page 33, for the model formulation or Karlinand Taylor (1975) for mathematics relevant to stochastic processes.

11

3. ORs S¶IUb

This chapter presents four case studies on the application of theperpetual option model. The first two cases undertake comparisonsof generation projects pertaining different technologies (on aproject-to-project basis, i.e. they do not follow a systemsapproach). The first case is a classic hydro vs. thermalcomparison, in the Costa Rica power system. The second casecompares different thermal technologies: i.e. combined cycle, coaland nuclear, in the Hungarian power system. The third case studyis an effort to combine the use of a traditional power system modelwith the options model. The analysis is done on several alternativeexpansion plans for the Mali and Senegal power systems, includingas a main generating alternative the Manantali hydropower plant.The last case addresses the problem of optimal timing for theextension of a transmission line to an isolated area, a frequentdecision problem in power systems.

The Costa Rica and Hungary cases are drawn from Martzoukos andPaddock (1991), an IENED internal report that discusses extensivelytheoretical and practical issues of the options approach. TheNanantali hydropower case study is an extension to the economicanalysis undertaken by a consultant, Association Nomentanee, anduses the results of their power systems analysis (draft report ofMar. 1991). The transmission line case study is drawn from work byMartzoukos and Teplitz-Sembitzky (1991), which is an extension totheoretical work by Schramm (1989).

All these applications compare a relatively large and irreversibleproject, usually fuel-efficient but capital intensive (such as ahydro plant, nuclear plant or the interconnection with a majorsystem), versus a modular type expansion based on smaller thermalplants (a set of gas turbines, combined cycle modules or smallerdiesel plants). The loss of flexibility related to the largeinvestment decision is modelled as a perpetual option, and isassessed in quantitative terms. In the general case, both costs(construction costs of the irreversible project or program) andbenefits (mostly fuel and O&M savings, plus some capital costsavoided on alternative expansion) are considered uncertain. Thesources of uncertainty are case specific, however they usuallyrefer to fuel prices, demand growth and capital costs.

The type of flexibility addressed is related to the ability to waitinstead of investing immediately in the hydro or other irreversibleproject, and thus have the option of investing later when it maybe more valuable to do so. The method analyzes the convenience ofdelaying the investment decision on a large and/or irreversibleproject taking into account that an alternative expansion plancould become more advantageous. In the analogy between the realoption and the financial option, the benefits or savings correspondto the equivalent "stock" and the project costs correspond to the"exercise price".

12

In order to proceed with the application we need two types of data:

a) The actual costs and savings associated to the largeinvestment. This data was either estimated through a simplesimulation of alternative investment programs or obtained frompower system planning models.

b) Variables relevant to the options model, such as quantitativemeasures for the relevant uncertainty (on costs and benefits),specifically the standard deviation of uncertain variables andthe correlation between these variables, as well as relevantdiscount rates and the appreciation rates of benefits andcosts.

The actual ratio of savings to costsT from part (a) is compared tothe critical =atio given by the options model from part (b). Thiscomparison deteraines whether the investment should be exercised,i.e. if the actual ratio is equal or greater than the criticalratio. Otherwise, we would be better off waiting since the valueof the flexibility lost would exceed the projectes net benefits.

The first application presented below refers to the Costa Ricacase. In the effort to present a complete illustrative example,this case includes an extensive description of the computationalprocess and its assumptions. To avoid repetition, the remainingcase studies are presented briefly, supported by separate annexeswhen necessary.

3.1 Costa Riaa Case Study

The Costarrican power system had in 1989 an instalLed capacity of772 NW, about 90% of this capacity consisted of hydropower plantsand the rest by small thermal plants of different types (InstitutoCostarricense de Electricidad - ICE, 1989). During the 1980s demandfor electricity grew at an average rate of 7%. However, this rateof growth is expected to decline to annual rates between 3% to 5%during the 1990s.

The investment lecision to be analyzed is that of a large 177MWhydropower plant and a 104MW geothermal program, both irreversibleand fuel-efficient investments, compared to a sequence of diesel-fired gas turbines (36MW units). In both cases the question to beanswered is: should we invest now in the large project, or shouldwe wait, keep our options open and meanwhile, if necessary, installa small gas turbine? Applying the options model we will assess thevalue of the flexibility loss, i.e. the benefits foregone as wecommit to a specific project and can no longer pursue a more

t That is, the standard benefit-cost ratio obtained throughregular deterministic present value techniques.

13

flexible plan which, under certain future conditions, could turnout to be more advantageous. The main variables considereduncertain are fuel prices, demand growth and construction costs.

The analysis consists of comparing the benefit-cost ratios obtainedfor the two major investments using a standard deterministicapproach, to the critical ratios -.alculated by the options model.

Costs and Benefits

To determine the costs and benefits (savings) for each alternative,we need to simulate the investment expansion. This was done byconsidering the following three alternative plans:

a) The hydro plant complemented by gas turbines.

b) The geothermal program (2x52MW) complemented by gas turbines.

c) A program of 36MW gas turbines, to be compared with the hydroand geothermal programs.

The comparison of programs (a) and (b) with (c) permits theestimation of the required costs and benefits. These are definedas follows:

- costs: construction costs for the hydro and geothermalprograms.

- Benefits: fuel and O&M savings plus avoided construction costsof gas turbines. Fuel and O&M savings are computed as thedifference in these two variables when comparing (a) and (b)to (c). Avolded construction costs are obtained directly fromprogram (c) .

The estimation of costs and benefits was done following standardpractices. This includes:

- A reserve available capacity margin of 10% was consideredabove the maximum load. This value was obtained from ICE's useof the WASP model taking into account the effective capacityof hydro plants during the dry period.

8 It should be noted that as it is assumed that variables arelog-normally distributed, benefits and costs should have a positivesign (see Chapter 2, p.8, 1st assumptio i). In this particular casewe are calculating the differences (savings) in fuel and O&M costs,instead of adding them separately on each side, because thesedifferences are positive. However, this is not always the case. Asit should be expected, these choices on the costs and benefitscomponente will affect directly our analysis on the relevantuncertain-ties.

14

Since alternative generating technologies usually havedifferent economic lives, the replacement of short-life plantswas taken into account. A salvage value was included at theend of the period of analysis using straight-linedepreciation.

Energy dispatch rules followed an economic criterion. In casesof excess capacity, least fuel efficient plants were affected.Accordingly, it was assumed that the hyydro plant would be ableto dispatch all its energy after four years of operation,while the smaller geothermal plants would achieve the samestate after three years.

A diesel oil price of $ 25 per barrel was considered for thebase year. A real cost increase of 1.3% was assumed for fuel,construction and maintenance costs. The uncertainty wasmodelled around these values.

A discount rate of 10% was used.

The basic data used for the comparison of expansion programs ispresented in the following table.

Table .Costa Rica: Economic and Technical Data.

Gas Turbine Hydro Geothermal

Installed capacity 36 NW 177 MW 104 KW (2x52)

Economic life 15 yrs 40 yrs 25 yrs

Max. capacity factor .72 .64 .81

Fixed investment cost 17.08 M$ 289.26 M$ 226.98 M$

Variable fuel cost 0.049$/kwh ----- ----

0 + M 2.87$/kw-mo 0.7$/kw-mo 1.21$/kw-mo

Construction period 1 yr. 5 yrs 3 yrs

The three expansion plans are presented in Annex 2. It was foundthat the hydro plant would reduce future investment by 5 gas

9 This case study, as well as the Hungary case, wasundertaken without the recourse of an operation simulation model.It was considered that, due to the project-to-project nature of thecomparative approach, simple dispatch rules were sufficient.

15

5 gas turbines, while the geothermal program would reduce it by 3gas turbines.

Present values of costs and savings for the hydro and geothermalplans are presented in the following table.

Table 2Costa Rica: Costs and Savings for the two Expansion Plans.

(present value in million US S)

Hydro Geothermal

Costs 289.3 227.0

Benefits- Fuel savings 303.7 251.9- 0+M savings 28.8 14.5- Avoided cost 64.8 4o.5

Total Benefits 397.3 312.9

Actual Ratio 1.374 1.379

Rate of Return 12.2% 13.05%

Batimation of the Option Model Parameters

The model parameters to be estimated are the standard deviation andcorrelation of the underlying uncertain variables (a., af and rvf),and the two effective discount rates 8v and 6f (see formulation ofthe model in Chapter 2, p.6).

The estimation of the uncertainty related to benefits is ratherdelicate since these benefits include fuel and O&M savings, andavoided construction costs. In addition, fuel savings are afunction of fuel prices and demand uncertainty. The standarddeviations used for each of these variables are:

a) Fuel price uncertainty; afue- fce= 10%. A conservative valueconsidering that direct measu6es give a log-relative value ofarour.d 20% for crude oil prices. The rationale for using alower value is based on the fact that the options modelassumes that fuel prices follow a random walk behavior, whichtends to extend excessively the range of possible futurevalues (see Figure 4).

b) Demand uncertainty was estimated to be around 20%. However,it should be noted that the effects of this uncertainty on the

16

fuel savings attributed to an individual plant areconsiderably reduced. In fact, this uncertainty would affectfuel savings only during the relatively short period whenplant capacity is not fully utilized. Accordingly, in orderto represent the periods when demand uncertainty does countwe weighted this value (of demand uncertainty) by the ratiobetween this initial period to the plants total life.Resulting ratios were: for hydro 4 out of 40 years = 0.10; forgeothermal, 3 out of 25 years - 0.12. Although this may be anarbitrary way of estimating uncertainty, it offers theadvantage of being intuitively rational and consistent in itsapplication.

c) The aggregate fuel savings uncertainty is computed as follows:

For the hydro project; a,,,,- [(.1)2+(.10*.20)2] = 0.102

For geothermal; fu = -/(.l)2+(.12*.20)2] = 0.103

This calculation assumes that the two uncertainties (fuelprices and demand) have a multiplicative effect on the totalfuel savings uncertainty; they are also assumed to be non-correlated.

d) Total savings uncertainty would be equal to the weightedaverage of fuel savings and avoided costs uncertainties.Considering a cost uncertainty of 5.6% (see next paragraph),final benefits uncertainties will be:

Hydro project; v = t((1-.1631).*.102)2+(.1631*.056) 2]rvy 0.086

Geothermal; - ¶/((1-.1486)*.103) 2+ (.1486*.056) 2]UV 0.088

The estimation of costs uncertainty is straight forward since theyonly include construction costs. A standard deviation of u= 5.C6%was chosen for hydro projects, based on the annual (at overrunsinferred from Merrow's paper (1990). This value was also used forgeothermal costs, assuming that the uncertainty surroundinggeothermal costs is similar to that of hydro developments.

The correlation between construction costs and savings is assumedto be 15% for the base case. This value was chosen on the basisthat fuel costs account for approximately 10% - 15% of constructioncosts and about 90% of total savings.

The effective discount rates, that represent the opportunity costson the benefits and costs of deferring the investment, are equalto the difference between the discount rate and the rate of growthof benefits and costs (escalation). As explained before, thediscount rate selected is 10% while a real cost increase of 1.3%

17

was assumed for all costs10. Therefore effective rates for both thehydro and geothermal analyses will be equal to 8.7%.

Results

The critical ratios obtained for the hydro and geothermal expansionplans (always lower than the actual ratios) reveal that in the faceof uncertainty, the decisions to proceed remain optimal whencompared to the option to wait to invest. However, results indicatethat in both cases the value of the flexibility loss is quiteconsiderable since it reaches 26% of total costs. Hence, these twoprojects, which have actual (benefit/cost) ratios of 1.37 and 1.38under a deterministic approach, are no longer so attractive.

Table 3Costa Rica: Critical Ratios

Actual Ratio Critical Ratio Optimal Decision------------------------------------------------------------ __--

Hydro 1.374 1.256 Build

Geothermal 1.379 1.261 Build

It is interesting to examine the sensitivity of results,particularly the optimal decision, to changes in our perceptions.or estimates of the underlying uncertainty. This sensitivity issummarized as follows:

a) For the hydro project;

- the decision is reversed, i.e. it is no longer optimal toinvest now, if the uncertainty about savings (standarddeviation, oav) exceeds 13%, and

- the decision is quite robust to the uncertainty aboutcosts and the correlation between costs and savings. Itis not affected for values within the analyzed range, i.e.an uncertainty on costs up to 8.6% and a correlationcoefficient (which is inversely related to the criticalratio) down to 5%.

b) For the geothermal program, the results are quite sj.milar;

- the decision would be reversed if the uncertainty aboutsavings is slightly higher than 13%, and

10 It should be note4 that this cost escalation could becountry specific and that benefits and costs are likely to havedifferent escalations. In that case 6. and 6f would not be equal.

18

- the decision is not affected by the uncertainty aboutcosts nor the correlation between costs and savings, forthe same range of values applied to the hydro projectanalysis.

More complete results on the sensitivity of the decision to themain uncertain variable, savings, is presented in Annex 2, whichincludes accept-reject matrices for savings uncertainty anddiscount rate, together with tables that display the sensitivityanalysis undertaken for all relevant variables.

In addition, Annex 2 includes the results of a Monte Carlosensitivity analysis aimed at studying the overall impact ofvariations in the model parameters to the critical ratio. Thisanalysis reveals that there is considerable uncertainty regardingthe estimates of the critical ratio. However, they also indicatethat the decision recommended by the model is quite robust sinceit concludes that the probabilities of having a critical ratiogreater than the actual ratio (i.e. of reversing the decision) arevery low, being 1.4% and 1% for the hydro and geothermal projects,respectively.

3.2 Hungary Case Study

The Hungarian power system has an installed capacity of about700OMW. This capacity is composed of a great variety of thermalgenerating technologies, from oil and gas fired plants, to coal,lignite and nuclear. In addition, Hungary has been importing1,850MW through a long term agreement with the Soviet Union, inorder to satisfy their power needs. Peak demand reaches 6,500MW andis expected to continue growing at a modest rate of about 1.3%during the current decade. However, there is uncertainty about thisgrowth. Other and apparently more important uncertain variables areconstruction costs and fuel prices.

The investment decision to be analyzed in this exercise is that ofa large 480MW nuclear plant and a 270MW coal-fired plant, bothconsidered irreversible and relatively efficient in terms of fuel,compared to a program of combined-cycle 135MW units. As in theCostarrican example, the question to be answered is whether weshould invest now in the nuclear or coal plant, or would we bebetter off waiting. The application of the options model willassess the value of the flexibility loss on exeruising either ofthe two investment decision so as to appLy a simple decision ruleunder the face of uncertainty.

19

Costs ind Benefits

The analysis consists in comparing two expansion plans that includealternatively a nuclear and a coal-fired plant, to a third pi,"based on a sequence of distillate-fuelled combined cycle plants'.These comparisons produce the required costs and benefits which iredefined as follows:

- Costs: Construction costs for the nuclear and coal expansionprograms.

- Benefits: fuel and O&M savings plus avoided constructioncosts. Fuel and O&M savings are computed as the differencebetween the nuclear and coal program compared to the combined-cycle program, i.e. the scenario without the project beinganalyzed. Avoided construction costs are those correspondingto the combined-cycle program.

The estimation of costs and benef its was undertaken taking intoaccount the following considerations:

- A reserve capacity margin of 25% was considered above themaximum load. This coincides with the reliability standardsused by the Hungarian Electricity Board (Magyar Villamos MuvekTroszt - MNVMT) in its power planning practices.

- End-of-period adjustment similar to those used in the CostaRica study were applied (see p.15).

- Fuel :rice: Coal $ 40/tonDistillate S 25/barrel

- Discount rate: 10%

- Exchange rate: 63 Forints per US.$

Technical and economic data on the alternative generatingtechnologies were drawn from MVMT's data base and a recent WorldBank report (Moore and Crousillat, 1991). These data are presentedin Table 4.

The three expansion plans are presented in Annex 3. This annexincludes, in addition, the results of a comparison based on dual-fired combined cycle units, considering both distillate and naturalgas in equal shares.

11 A second set of analyses considered a combined-cycle programusing two fuels, distillate and imported natural gas, in equalshares. This particular case is presented in Annex 3.

20

Table 4Eungary: zaonomic and Teohnical Data

Combined-Cycle Nuclear Coal

Capacity 135 MW 480 MW 270 NW

Economic life 20 yrs 25 yrs 25 yrs

Max. capacity factor 65 % 65 % 65 %

Fixed investment cost 35 106.2 83.2(in 1000 Forints/KW)

Variable fuel cost .032 0.008 0.014(in $/KWH)

Operations & maintenance 4 % 2 % 2.5 %(% of inv. cost per year)

Construction time 3 yrs 7 yrs 5 yrs

Present values of costs and savings for the nuclear and coal plansare presented in Table 5.

Table 5Nungary: Costs and Savings

(Present value in million Forint)

NUCLEAR COAL

Gross fixed cost 50976.0 22464.0decommissioning 242.9 -------

Total Fixed Cost 51218.9 22464.0

Fuel savings 22541.6 10446.6O+M savings -1952.9 -1191.8Avoided Costs 9402.6 6978.5

Total savings 29991.3 16233.2

Actual Ratio .586 .723

Rate of Return 6.10% 6.95*

21

Estimation Of Model Parameters

The model parameters to be estimated are the standard deviation ofbenefits and costs (7v and of, both measures of uncertainty), thecorrelation between these two variables (rv) and the two effectivediscount rates Sv and 6f.

The estimation of costs uncertainty is straight forward since theyonly include construction costs. We have chosen 5.6%, the samevalue used for the Costa Rica case. However, it should be notedthat this uncertainty should be a function of the technologyanalyzed.

Benefits are considered to be a function of fuel savings andavoided costs. In this case fuel savings will not be affected bydemand variations because both the nuclear and coal plants areexpected to have lower variable costs compared to existing andother future thermal plants. Therefore, their energy dispatch, andthus the fuel savings attributed to these plants, will not beaffected by a lower demand. Accordingly, fuel savings uncertaintywill be equal to fuel price uncertainty: 10%.

Total savings uncertainty is computed as a weighted average of fuelsavings and avoided costs.

Nuclear Project; a, = ,[((l-.6865)*.10)2+'.6865*0.056)2 ] = 0.071

Coal project; ClV = 4[((l-.570)*.10)2+( .570*0.056)2] = 0.062

The correlation between costs and benefits is assumed to be 7%(lower than in Costa Rica) considering that nuclear and coalgenerating plants are less dependent on fuel during theirconstruction.

The effective discount rates used are the same of those chosen forthe Costa Rica case (see pp.17-18), i.e. S.7% for both benefits andcosts.

Results

The actual ratios for the two expansion plans are lower than one,which indicates that these projects are not viable even under adeterministic scenario. Furthermore, when analyzing these projectsin the face of uncertainty, they become even less attractive sincethe critical ratios reveal a penalty of around 22%. These resultsare shown in Table 6.

Knowing the deterministic result, the option analysis may appearredundant. However, the application of the options approachprovides additional insight. It reveals option prices (denoted byX in Tables 3.3 to 3.6, Annex 3) that, for the base case, are equalto 229.7 and 249.7 million Forint for the nuclear and coal plant,

22

respectively. These figures are useful to value the rights fordeveloping the large plants, nuclear and coal-fired, if they areto be sold to a third party. Therefore, the investment opportunitystill has some value, and it may be reasonable to "keep alive"although it is currently not profitable.

Table 6Hungary: critical Ratios

------------------------------------------------------------- __-

Actual Ratio Critical Ratio Optimal Decision------------------------------------------------------------ __--

Nuclear 0.586 1.232 Don't build

Coal 0.723 1.213 Don't build

----------------------------------------------------------------

Sensitivity analyses on all variables are presented in Tables 3.3to 3.6, including those for a dual fuel combined cycle program. AMonte Carlo simulation analysis on the critical ratio was alsoperformed. All these analyses confirmed the study's initialfindings, i.e. that the two large projects are not viable and thatunder the face of uncertainty they would become more unattractive.

3.3 Nanantali Hydropower Plant

The construction of the Manantali dam, completed in 1988, wasundertaken with the purpose of developing a capacity to regulateriver flows for irrigation, power supply and navigation in theSenegal River. It has been proposed to build a hydropower plant atthe dam site, taking advantage of the head (fall) and waterregulation provided by the existing reservoir. The plant isdesigned for an installed capacity of 200MW in five units of 40MW;however, its implementation program is a function of the scope ofthe development to be chosen.

Two development programs have been proposed. A relatively smalldevelopment constrained to Mali's power market, and a largedevelopment that considers the construction of a 900 Km long, 225-kV transmission line to the west coast, reaching Dakar, Senegal,in order to supply power also to Senegal and Mauritania. While tpefirst alternative, named "Hydro-Mali", implies a phased program ,the second alternative ("Large-Hydro") considers the installationof all five units by 1996.

12 The installation of two generating units (2x40MW) in 1996,one in 2005 and a fourth in 2008. This case does not consider theinstallation of the fifth unit during the 25-year period ofanalysis.

23

The present application of the options model is based entirely onthe data set and simulation results obtained from the consultant'sdraft report (Association Momentanee, 1991). The analysis is donefor two investment decisions, (i) the decision to invest in thesmaller Hydro--Li alternative, and (ii) the decision to extend thesmaller development to a larger one undertaking a major trans-mission investment oriented towards the power markets ot the threecountries, i.e. Senegal, Mali and Mauritania. The small Hydro-Maliproject is compared to a hydro-thermal development for the corres-ponding electrical system (Bamako-Segou, in Mali), while the Large-Hydro is compared to the Hydro-Mali development complemented bythermal plants. These two comparisons are aimed at assessing theeconomic viability of each alternative. In the first case, thecosts and benefits of the hydropower development in Manantali areconfined to the regional market. In the second case, we measurethe economic merits of building a major transmission line to Dakar,thus allowing a full utilization of Manantali's hydro energy duringthe initial years and a better dispatch of thermal generation.

costs and Benefits

In both cases, costs and benefits are computed as follows:

- Costs: Investment costs plus fixed operating costs.

- Benefits: Avoided investment costs (in altepativedevelopments) plus fuel and non-served energy savings .

All values were obtained from the consultant's simulations of thesystem(s), which rest on the following assumptions:

- Energy demand growth rates of 6.5%, 6.6% and 3.5% for Mali,Mauritania and Senegal, respectively.

- Discount rate: 10%

- Expansion period: 25 years.

- Economic analysis period: 50 years.

- Fuel prices computed for each location, based on aninternational crude oil price of US$ 20/barrel.

- Energy dispatch followed strict economic efficiency rules,i.e. plants with lowest variable costs had priority indispatching their energy.

13 Non-served energy savings are measured as the difference inthis variable when comparing the situation with and without theproject.

24

Present values of costs and benefits for the Hydro-Mali and Large-Hydro programs are presented in Table 7.

Table 7ianantali Projeots Costs and Benefits

(Present value in million US $)

…---------------------------------------------------------------Hydro-Mali Large-Hydro

Costs 68.1 194.1

Benefits- Savings1' 31.9 44.2- Avoided investment 83.5 148.8

Total benefits 115.3 193.0

Actual Ratio 1.695 0.994

Rate of Return15 30.0% 9.9%

----------------------------------------------------------------

Estimation of model parameters

The model parameters to be estimated are the standard deviation andcorrelation of benefits and costs (ov,, of and rv), and the twoeffective discount rate Sv and &.

Costs are a function of construction costs and demand growth.Demand is specially relevant since this case refers to the costsof 25 year expansion plans, and not to a single project. Assumingthat the uncertainty related to construction costs and demand isreflected by standard deviations of 5.6% and 20% (see Costa Ricacase), costs uncertainty for both cases should be computed asfollows:

af = 9(0.0562 + 0.202) = 0.2077

Benefits are assumed to be a function of fuel savings (includingsavings in non-served energy) and avoided costs. In addition, fuelsavings are a function of fuel prices and demand uncertainty. Thestandard deviations for case 1, i.e. Hydro-Mali alternative, were

14 Fuel and non served energy savings.

15 The consultant's estimate for rates of return were 35% (theyactually reported "above 30%") and 10.6%. The difference residesin the fact that the option model discounts in a continuous manner,thus increasing slightly the effects of discounting.

25

estimated as follows:

a) Using the same approach as in previous cases, fuel savingsuncertainty is computed as follows:

OfueI-savfng = 4E((9/50)*.20)2 + (.10)23 0.1063

considering demand and fuel price uncertainties of 20% and 10%respectively, and a period of 9 years during which thehydroplant's energy dispatch will be affected by demandvariations.

b) Total savings uncertainty are computed as a weighted averageof fuel savings and avoided costs.

aV = vL((l-.7237)*.1063)2 + (.7237*.2077)23 0.1525

The correlation between costs and benefits in case 1 is assumed tobe equal to the ratio of avoided costs to total savings, i.e. 73%.

Benefits uncertainty in case 2 (Large-Hydro) were estimated asfollows:

a) 0 fu.-.lavings 4E(.10*.20)2 + .102 ] = 0.1020

considering the same uncertainties as before and that demandvariations will affect fuel savings during the initial 5 yearsof the hydroplant's operation.

b) Total savings uncertainty:

ov = 4[((l-.7710)*.1020) 2 + (.7710*.2077)2] 3 0.1618

The correlation between costs and benefits in case 2 is assumed tobe equal to the ratio of avoided costs to total savings, i.e. 77%.

Dividend terms are equal to the difference between the discountrate and the rate of growth (escalation). As no escalation on anycosts is considered, dividend terms will be equal to the discountrate, i.e. 10%.

Results

The critical ratios estimated for the two cases indicate that, inthe face of uncertainty, the Hydro-Mali program is a robustinvestment decision, while the Large-Hydro alternative - an

26

economically marginal project under a deterministic point of view1 6- is highly risky. These results are shown in Table 8. The criticalratios obtained indicate that penalties of 38% and 34% should beadded to the program's costs to incorporate the additional costsof the lost flexibility.

Table 8Manantali Project: Critical Ratios

…-----…------------------------------------------------------___Actual Ratio Critical Ratio optimal Decision

…-----------------------------------------------------------__--Hydro-Mali 1.695 1.376 Build

Large-Hydro 0.994 1.343 Don't build

----------------------------------------------------------------

The estimated critical ratios correspond to overall uncertainties(a) of 14.3% and 13.2%. As stated before, these deviations capturethe effects of uncertain demand growth, construction costs and fuelprices. The sensitivity of the critical ratio upon variations inthe overall standard deviation was analyzed for both cases. In theHydro-Mali case a range between 11% to 17% was studied, concludingthat in all cases the investment was appropriate under the face ofuncertainty (the critical ratio ranged from 1.28 to 1.46, alwaysbelow the actual ratio: 1.69). For the Large-Hydro case, thecritical ratio varied from 1.25 to 1.42 for standard deviations of10% and 16%, concluding that in all cases the investment should berejected.

3.4 Optimal Timing of Transmission Line Investment

A common problem with rural electrification programs is that remoteareas characterized by dispersed demand and low loads are costlyto connect and supply from a main electricity grid. Decentralizedsolutions on the basis of diesel generating units may prove moreattractive in an early stage. However, as demand grows, theconditions tend to change in favor of an interconnection with themain grid. The present case study addresses the problem of optimaltiming for this interconnection in an uncertain environment.

16 At this stage of the project, it was argued correctly thatthe Large-Hydro project design could be improved in itstransmission component, thus increasing its economic merits.However, it is not likely that this improvement would affect theresults of the present study.

27

This case study uces the perpetual option model as applied to theproblem of optimal timing of investment (Martzoukos and Teplitz-Sembitzky, 1991). The model developed to estimate the expectedperiod of time after which it will be worth investing in thetransmission line is presented in Annex 4. The technical andeconomic assumptions of this hypothetical case are explained below.

Costo and Benefits

It is assumed that there is an initial peak load of 4MW, with aload factor of 0.35, which is typical for isolated rural areas. Theinstalled capacity amounts to 6MW provided by 'existing' dieselplants. Demand is expected to grow annually at 7%. Incrementaldemand can be met with new diesel units of 2MW, assuming thateconomies of scale are negligible. In this case, after a period of11 years the required capacity would be O1MW; after 17 years itwould be 14MW. It is also assumed that diesel plants need to bereplaced every 15 years.

Alternatively, there is the option to invest in a 230kVtransmission line that would be sufficient to supply up to 200MWfrom the main grid. The length of this line is assumed to be 120Km.Table 9 presents additional economic and technical data.

The benefits provided by the transmission option are defined interms of the parameters that are sensitive to changes in demand.These include fuel savings, the avoided investment costs in diesel

Table 9optimal !iing of Transmission Line

Uconomic and Teoonical Data

Transmission Line Diesel Program

Capacity 230 kV 2 MW/unit

Reserve Capacity -- 35% of peak

Economic Life 35 years 15 years

Construction Time 3 years 1 year

Capital Costs 12 million $ 1,000 $/kW

Fuel/Energy Costs $ 0.026/kWh $ 0.065/kWh

Fixed O&M 2% cap. costs 2% cap. costs

Variable O&M -- $ 0.26/kWh

28

plants and the savings in variable OCa costs.

On the other hand, costs include the initial investment costs forthe transmission line, the corresponding O&N costs minus the fixed(demand independent) costs of operating and maintaining the dieselplants.

Model Parameters

Assumptions have to be made on the overall uncertainty (a), and theeffective discount rates on savings (6.) and costs (6 f). Thediscount rate is assumed to be 10%. Since demand is expected togrow at a 7% rate, the effective rate on savings is 68 3%.Accordingly, assuming that the expected increase in transmissionline costs is 1.3% per year, the corresponding effective rate oncosts will be &f = 8.7%. The composite standard deviation isassumed to be a = 15%.

Results

Tab] a 10 presents the resulting values for the discounted netsavings (V-F, discounted to year t), the ratio of discountedsavings to costs (actual ratio V/F), and the present value of netsavings for the initial year t=O, which is denoted as PVO(V-F). Allthese values correspond to a deterministic situation and refer tovarious commissioning years t.

Table 10Net Savings and Actual Ratio(savings in million US $)

year (t) V - F V/F PV0(V-F)

0 15.084 2.257 15.0841 16.891 2.389 15.2832 18.838 2.530 15.4233 20.936 2.678 15.5104 23.195 2.835 15.5485 25.628 3.001 15.5446 28.247 3.177 15.5027 31.066 3.364 15.4278 34.100 3.561 15.3229 37.364 3.770 15.191

10 40.875 3.991 15.03711 44.650 4.225 14.86312 48.711 4.473 14.671

------------ …------------…--------------------------------------

From the table we can observe that in the face of certain savings,the optimal timing to invest would be after 4.4 years, i.e. whenthe present value of net benefits is maximized.

29

The critical ratio obtained from the options model (on the basisof the assumed parameters) is 3.429. Thus with uncertain savingsit can be expected that after 7.34 years it will becomeeconomically viable to exercise the transmission option. Althougheven in the case of no uncertainty it would pay to wait to invest,the deterministic decision rule would lead to a prematureinvestment. The analysis therefore shows that the incorporation ofuncertainty creates an incentive to delay the transmission lineinvestment.

30

4. oONCLUSXONS

We have seen in four case studies that the option valuationapproach is quite easy to handle, it does not require muchinformation, and it provides a simple and very meaningful decisionrule that should appeal to analysts. However, its accuracy andreliability depend on the extent to which the model's assumptionshold in practice and whether the simplification undertaken duringthe modeling process does not distort the problem in question. Inapplying the options model to the Manantali hydropower project,the simplifying element was reduced since all costs and benefitsstreams were obtained directly from the results of a power systemplanning model. In the other case studies simplification could bean issue since the project-to-project comparison does not addressthe complexities of a multi-decision problem that is usuallythought to require a systems approach.

The options approach emphasizes that an uncertain environmentimposes a penalty to reflect the flexibility foregone asirreversible investment decisions are taken. The case studiespresented in this paper show that this penalty can be considerableand should not be ignored. This penalty, which is reflected in thecritical ratio, is a case-specific function of the generaluncertainty conditions found in the country and, most important,of the particular conditions of the problem in question. in theCosta Rica and Hungary studies, this value varies between 21% to26% of total costs. In the Manantali case study, where we comparelong term expansion programs instead of an specific generatingproject, uncertainty is higher and, therefore, the penaltyincreases to a value accounting for 35% of total costs. In the caseof the transmission line, uncertainty creates an incentive to delaythe investment by almost 3 years beyorid the date that would beoptimal if we do not consider any loss of flexibility.

Although the application of the options approach may appear to beeasy due to its reduced computational effort, it is in reality arather delicate analytical process. Some important aspects thatshould be addressed with special care in any application of theoptiono model are:

- The extent to which the model results are sensitive tovariations of key parameters and the problem formulation, suchas: (i) the estimation of uncertainty; a very delicate issuethat should require inputs from experienced planners, and (ii)the choice of what should be included in costs and inbenefits/savings, and the potential impact of these choiceson the decision rule. On the basis of the experience gainedin the above case studies it is recommended to analyze thesensitivity of results, and specifically of the recommendeddecision, with respect to variations in the key parameters.

31

- To what extent do basic assumptions of the model hold. Herewe are referring essentially to the assumptions related to thebehavior of key variables, i.e. the random walk hypothesis.Since in many cases it will be almost impossible to provestatistically whether the model variables follow a randomwalk, it is recommended to make final assumptions onuncertainty (i.e. on standard deviations) taking into account,in an iterative fashion, the impact of our assumptions on thefuture dispersion of values (see for example Figure 4) andcompare them with our perceptions of the underlyinguncertainty.

- The correlation between benefits and costs. Although the casestudies undertaken do not reveal a significant impact of thisparameter on results, it should be recognized that theestimation of this correlation is rarely a straight forwardstatistical exercise. The estimation of the correlationcoefficient is a case-specific problem requiring carefuljudgement.

In general, the application of the options model should becomplementary to conventional least-cost planning tools. Itshould be seen as an additional decision tool aimed atchecking and, when necessary modifying, the results ofdeterministic planning models.

A complete evaluation of the options approach and other riskmethodologies, including a comparative analysis, will be presentedin a final report on IENED's risk and uncertainty program.

32

AmX I

The lernetual Option t4h valu of vaiting to invest).

model Wo@aulation

The solution to the perpetual option is in fact a result ofstochastic optimization. The benefit-cost rotio is the stochasticvariable *that follows geometric Brownian' motion; a criticalbarrier C is defined, at which the (positive) investment decisionis optimal. If the actual ratio exceeds C we invest, otherwiseinvestment is deferred. The result is a generalization of thedeterministic optimization (say optimal timing) of the investmentproblem. The deterministic problem will be exposed first, since itleads to a better understanding of the model parameters.

In the deterministic case, it can be shownta that even an investmentwith a positive Net Present Value could optimally be deferred.Consider the investment with NPV today equal to "V - F", where "V"represents the benefits and "PO" the costs; also consider that ifthe investment is deferred, benefits will exhibit a growth of Gand costs a growth of Gf. Assuming exponential growth (anZcontinuous discounting) the value after time T will equal Ve -WT and the benefit-cost ratio will equal (V/F)e,(v-G)T The sign ofQ - Gf determines whether this function is increasing in T.PZositive sign gives an increasing function, negative gives adecreasing function, and 0 gives a constant function. If we use adiscount rate of R, optimal timing is when the NPV is maximized1 :

maxT 1Ve (R 6V)T_Fe-(R-]f )T .

17 Brownian motion is a continuous time Markov stochasticprocess; as such, its future evolution does not depend on thecomplete history (past realizations) of the process, but only onthe last one. The implication of this (so-called Narkovian)property is that the process has no tendency to revert to a normalmean. It was first used by the physicist Brown to model particlemovements. For the relevant mathematics, see Karlin and Taylor(1975). When the natural logarithm of a variable follows Brownianmotion, the variable is said to follow a geometric Brownian motion.

18For an example of a Transmission line case, see Schramm(1989).

"Positive NPV is equivalent to a Benefit-Cost ratio greaterthan one, and for monotonically changing present value functions(with respect to time) it can be shown that maximizing NPV isequivalent to maximizing the benefit-cost ratio. ','he rate of changeof the benefit-cost ratio equals Gv-Gf.

33

Let's name the differences R-GV and R-Gf as 6 and fs, Greekntheltas" denoting the effective discount rate on Ienef its 'V" andcosts "F"; they represent the opportunity cost on the benefits andcosts, if investment is deferred. It is easy to see the optimumwhen F/V becomes equal to 6f/6v; thus We invest if V6f x F6 . Theabove ratio of 6S/6v defines a deterministic critical ratio that iscompared with the actual. The S. should be above 0; if it equalszero the investment is never implemented since the critfcal ratiois plus infinity. Both 6 and 6f should be above zero for theproblem to be well define&.

The NPV function in general will plot as an inverted U-shape; itis increasing for 6f>6ve The optimum is at the maximum of the U-shape, as it appears in Figure 1.1 that plots the U-shape for aninvestment that at time zero exhibits (in arbitrary monetary units)benefits = .95, costs - 1, G - .03, Gf - .013, and the discountrate equals 10%. Thus the benefit-cost ratio today is .95, Iequals .07, 6 .087, the NPV equals -.05, and optimaldeterministic timing is after 15.81 years (given later by formula1), when the actual ratio is projected to reach a critical ratioof 1.243 (given later by formula 4a).

If the actual benefit-cost ratio is below this critical ratio, itcan be shown that optimal timing occurs for:

(1) T = Ln((6IF)/(6VV)]/(GV-Gf) if GV-Gf > 0,

T = +co if Gv-Gf - 0, and

T is undefined if GV-Gf < 0.

Under uncertainty, McDonald and Siegel have shown that the abovecritical ratio is given by:

(2) Cw = ij(r-1),

where the parameter r is given by:

(2a) r - (0.5 - (6f-6V2) + .25)2 + 26f/e]

and "a2" equals e,, + ef - 2rvovaf where the rv, denotes correlation;thus the variance of the percentage change of the benefit-costratio is a function of the individual variances and the correlationamong the benefits and costs' percentage change.

2This is because we assume perpetual constant growth. An assetcan not grow at a rate equal to or above the discount rate forever. For a discussion of such issues in a continuous timestochastic framework, see Brock, Rothschild, and Stiglitz (1988).

34

Figure 1.1

U-SHAPE UF- INvESTMENT'S PRESENT VALUEA FUNCTION OF INVESTMENT TIMiNG

0.07

0.06

0.05 _

0.04-

2 0.03 _

° 0.01 _ f

0 O /

- -0.02 -

-0.03 _

-0.04 1

-0.06 -

-0.02 O 1216 1' '

-0.0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 |1 3 5 7 9 11 13 15 17 19

Investment Timing

the parameter Or" must not be below 1; McDonald and Siegel havedefined it as the weighing factor that determines the requiredreturn 'll on the investment opportunity2, given the requiredreturn on assets with systematic risk similar to that of benefitsand costs.

The perpetual option model gives the value "WN of this investmentopportunity (for actual ratio less than the critical) as:

(3) W = (Cd-l)F(V/Fc)?

and when the actual ratio becomes equal to the critical, W equalsthe difference between benefits and costs; under the deterministic

2180 gA - v*Rv + (l-v)*Rf, where RP and Rf are the requiredreturn on assets with (approximately) the same systematic risk withbenefits and costs respectively; it is equivalent to going long onthe benefits and short on the costs.

35

approach (02 0) this reducesU to:

(4) W - (C -1)F(V/FC')t/(ftV) and

(4a) C /

In this case 6 f should be greater than or equal to 6v, otherwise wedo not wait but we invest now (if actual ratio is at least unity)or never.

It has been shown2 that the optimal timing of the investment under

22It can be shown that Ve eqKation that gives r can berewritten as r = 2f/ ( /[ ( 6 f_ 6 V_o) +26fa ] + (6f-6V-/2) ) and for zerovariance r -> 6fl(4-6Under no uncertainty the investment opportunity W of formula (3)also equals the Net Prpfsent Value under optimal deterministictiming -> W = Ve " - Fe''f where T is given by formula (1).

3See Martzoukos and Teplitz (1991). The result seemsintuitive, but the proof requires use of the martingale stoppingtheorem; for such applications in a Brownian motion context, seeKarlin and Taylor (1975) pp. 357-365. In addition, the introductionof an arbitrary lower "absorbing barrier" where the investmentoption becomes insignificant (i.e., actual ratio of 0.001) givesthe following modified formulae for the optimal timing:

E(T) - (Ln]eiP - Ln[V/F] + *(l-P])/(G4-Gf) if Gv-Gf > O,

E(T) = 2 ( cj]p + In2[V/F] - 2LOEC"]Ln1V/F]P+ *(l-P)(#-2Ln[V/F]))/ if Gy-Gf = 0, and

B(T) is undefined for G,-Gf < O

where P is the probability that the actual ratio becomes equal tothe critical before it drops to the lower value *, and is given by:

p _ {1 _ [(F/V) 0l-n]-2 Gv-Qf)/b/}il - [lO0^/C ]'2(VGf)/b)

if Gv - Gf > 0,

P = (Ln[V/F]/n + Lnl10])/{Ln(C']/n + Ln[10]) if G. - GO = °

b equals the variance "a 2 " and * equals Ln[l0"]; for example for alower benefit-cost ratio of 0.001 the parameter n equals 3 and 0equals -6.9078. Such a lower barrier has the significance that lowvalue options can be abandoned due, for example, to the highadministrative costs of keeping them alive although theoreticallyoptions always will have a positive value. Another significance ofthese formulae is that, even if Gv - Gf = 0, uncertainty is expectedto be resolved in finite time; here optimal timing is redefined tomean the time that the actual ratio either reaches the critical,

36

uncertainty is given by the following, where "E" denotes theexpectation operator:

(5) E(T) = Ln(CeF/V)/(Gv-Gf) if Gv-Gf > O,

E(T) = +0 if Gv-Gf = 0, a;.d

E(T) is undefined if GV-Gf < 0

where C* denotes the critical benefit-cost ratio under uncertainty.

The decision rule whether to invest in both cases is given by thecomparison of the critical ratio and the actual ratio; we investif actual ratio is greater than or equal to the critical ratio. Theimpact of uncertainty is that the critical ratio is higher than inthe no uncertainty case; uncertainty thus defers investmentassigning a premium to waiting so as to receive more informationabout the future evolution of critical uncertain variables.

The Model Parameters and Assumptions (perpetual option to vait toinvest).

The decision whether to invest or not is a result of the comparisonbetween the critical and the actual rati-.

The main model parameters for the critical ratio are the dividendyields "6 " and "6,", and the variance "a'" of the rate of change ofthe benefit-cost ratio. The dividend terms (effective discountrates or opportunity costs) equal the difference between thecorresponding discount rate and the rate of growth as:

6v - R - Gv and 6f = R - G,.

The a2 equals a2v + a2f - 2 rfavaf; it is a function of the varianceof the benefits and costs' rate of change and their correlation.

The critical ratio is an increasing function of 6 (positive firstderivative) and decreasing function of Sv (negative first deri-vative). If the effective discount rate on the costs is higher therequired flexibility premium is also higher since the opportunitycosts (of deferring construction) are lower; if the effectivediscount rate on the benefits is higher the required flexibilitypremium is lower, since the opportunity cost on the foregonesavings is higher.

or falls to the lower barrier and in any case uncertainty about theinvestment is resolved.

37

The two dividend terms should always be positive24. By constructionthe perpetual option model considers the underlying savings andcosts as the present value of perpetual cash flows. If theeffective discount rate were zero, the value of the perpetualstream of cash flows (ratio of an annual cash flow over theeffective discount rate) would be infinite. Also if the effectivediscount rate were negative, the value of the perpetuity would benegative too; thus both cases are not feasible.

In the deterministic case if condition 6, > 6 is satisfied, thXinvestment should be deferred; 6S / 6v equals the critical ratio"Cd" If this critical ratio is not above unity, the investment iseither profitable to exercise now (NPV > 0) or is never.exercised.In the presence of uncertainty the critical ratio "C " is evenhigher ("C* " is greater than or equal to "Cn) If the twodividends are equal, then the parameters "T" and C are simplified:

(6) t .5 + 4(.25 + 26f/02)

(6a) Ce -. 5 + 4(.25 + 26,/a2)] / [/(.25 + 26,1a2) - .5]

Figure 1 (in the main text) F;hows the critical ratio as a functionof 6v, keeping the other mod l parameters constant (i.e., discountrate 10%, cost apprecia ion 1.3%, total effective standarddeviation 15%).

Figure 2 (also in the main text) shows the critical ratio as afunction of Sf,, keeping the other model parameters constant (i.e.,discount rate 10%, savings' appreciation 1.3%, total effectivestandard deviation 15%).

The critical ratio is also an increasing function of the totaleffective variance *la2"; if uncertainty is higher, the value ofwaiting to receive more information is higher and the requiredflexibility premium is higher too. Note that this is not alwaystrue for the individual standard deviations, since the totaleffective standard deviation is a (quadratic) function of the twostandard deviations and the correlation.

Figure 3, in the main text, shows the critical ratio as a functionof total effective standard deviation, keeping the other model

24In the case of stock options and in the absence of dividendswe would have 6 - 0 and it can be shown that the perpetual optionvalue equals the stock value; the critical ratio becomes infinite,and the option is never exercised. The same result stands forfinite maturity stock options, thus the European and the Americanoptions are equivalent; the option is exercised at maturity only.

2'Lets denote the critical rat.io in the deterministic approachand under uncertainty as ed and Cu respectively.

38

parameters constant (i.e., discount rate 10%, savings' appreciation1.3*, cost appreciation 1.3%).

As was discussed before, in the absence of uncertainty (a2 = 0) theformulas for the critical ratio reduce to the ones under thedeterministic approach; (2) as a function of (2a) reduces to (4a)as regards the critical ratio; (3) to (4) as regards the investmentopportunity; and (5) to (1) as regards the optimal timing of theinvestment.

As we see from Figure 3, the critical ratio and thus the investmentdecision is very sensitive to our estimate of the underlying uncer-tainty. Our unwillingness to invest unless a flexibility premiumis received is equivalent to hedging against this uncertainty. Itis important to understand what this uncertainty implies. Forexposition we provide a set of graphs (Figures 1.2 to 1.7) for alognormally distributed variable (with value of 1 at time zero andstandard deviation varying from 5% to 30%) and the 65% and 95%confidence intervals for the possible values this variable couldtake in the future. The graphs assume zero drift for the underlyingBrownian motion process which is equivalent with accepting thatbenefits and costs exhibit the same growth rate, since the growthrate of the benefit-cost ratio equals the difference of the twogroath rates. The extension to the case with arbitrary drift isstraightforward.

Critical Assumptions Affecting the actual Ratio

a) The lognormalitv for the distributional characteristics of theunderlying assets.

b) The existence of perpetually constant rates of change (thatimply constant effective discount rates).

c) Continuous time assumption as a result of modeling theunderlying assets with Brownian motion.

The first assumption is relevant to the way the benefit-cost ratiois estimated. Both benefits and costs individually are (approxi-mately) lognormally distributed; thus negative values should beexcluded. To avoid violating the above assumption, all sub-partsof the benefits and costs should have a positive sign (i.e.,, theyshould be additive). If for example an investment in a Hydro schemeresults in avoiding construction of thermal generation facilities,the avoided construction costs should not be subtracted from thecosts but should be added to the savings. Note the implication onestimating the relevant uncertainty of the costs and savings.

The second assumption is relevant to the way savings and costs areestimated. It can be shown that a constant rate of change impliesa perpetual stream of cash flows; the benefits and costs due to theinvestment should either be expressed in the equivalent perpetuity

39

UNIT LOGNORMAL STOCHASTIC VARIABLE95% AND 65% CONFIDENCE INTERVALS

1.6

1.5

1.4

1.314 ;

1.2

1.1 t i

0.7 _ _ __;,

0.60 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Time; standord deviation = 5%Inner (outer) 2 curves = 65% (95%) confidence intervol.

UNIT LOGNORMAL STOCHASTIC VARIABLE95% AND 65% CONFIDENCE INTERVALS

2.3

2.22.1

2

1.8

1.71.6

g: 1.5 ---1.4

tL 1.3 -,_ W 1.2 X I--

to 1.0 1 C;

0.9 _

0.8 -^

0.7 _ i- --------

0.6__:v ; _.

0.5 .l _ _ _l : I - L_

0.40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Times; stondord deviation = 10%Inner (outer) 2 curves = 65% (95%) confidence intervol.

UNIT LOGNORMAL STOCHASTIC VARIABLE95% AND 65% CONFIDENCE INTERVALS

3.4.

3.2

3

2.8

2.6

2.4

2.2

2 I'

1.8

1.4 1.4

o 1.2

0.8

0.6

0.44

0.2 I I I I - I I . I L I .0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Time; stondord deviation 1 157Inner (outer) 2 curves = 65% (95%) confidence interval.

UNIT LOGNORMAL STOCHASTIC VARIABLE95% AND 65% CONFIDENCE INTERVALS

5

4.5

4.

3.5

.1 2iL

0.5 ------a

Li '-a

to~~~

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Time: standard deviation = 20%Inner (outer) 2 curves = 65% (957e) confidence intervol.

UNIT LOGNORMAL STOCHASTIC VARIABLE95% AND 65% CONFIDENCE INTERVALS

8

7

6

v 4S 4 _

2

0t /

a 1 2 3 4 5 6 7 8 9 10 11 ;2 13 14 15

rime; stondord devatto-P 25XInner (outer) 2 curves = 657* (95%) confidence interval.

UNIT LOGNORMAL STOCHASTIC VARIABLE95% AND 65% CONFIDENCE INTERVALS

10 A

9

a

7

6

4 _ _ _ _ ____ 0(_ w

--J

4

O I

o

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Time; standord deviation = 30%Inner (outer) 2 curves = 65% (957.) confidence inteval.

form or we should consider several "rotations"26 of similarinvestments and increase the benefits and costs accordingly. Weadapt the second method because it is intuitively easier toquantify the underlying uncertainty. For practical purposes, thisadaptation is not crucial if the life of the irreversiblealternative is sufficiently large.

The third assumption is important27 for the way present values ofthe cash flows are estimated; the need for continuous discountingis obvious where the effective discount rate is the difference "S"between the discount rate and the growth rate. The following tableshows the difference between continuous and regular discounting atthree levels of discount rate, notably 8%, 10%, and 12%. Theregular discounting would overestimate cash flows relative to thecontinuous discounting. For the relevant formulae for lump-sums,annuities and growth annuities under continuous discounting seeCopeland and Weston (1983).

Table 1.1

% DIFFEP ENCE BETWEEN CONTINUOUS AND REGULAR DISCOUNTING.

annuitiesDiscount rate: 8% 10% 12%

5yrs 0.0087 0.0132 0.0186lOyrs 0.0149 0.0223 0.03092Oyrs 0.0246 0.0355 0.04733Oyrs 0.0312 0.0434 0.05594Oyrs 0.0354 0.0477 0.05985Oyrs 0.0379 0.0498 0.0614

lumpsumsDiscount rate: 8% 10% 12%

5yrs 0.0153 0.0237 0.0339lOyrs 0.0309 0.0480 0.069020yrs 0.0627 0.0983 0.142730yrs 0.0955 0.1511 0.221640yrs 0.1293 0.2063 0.305850yrs 0.1641 0.2643 0.3959

26This Is referred to ae the rotations problem, and results ina different Net Present Value and Benefit-Cost ratio; if theeffective discount rates "w6" and "Ef are the same, the benefit-cost ratio remains unchanged. This adaptation is used very oftenwhen comparing projects with unequal lives.

"Note that the same assumption also implies continuoustrading. We can reasonably assume this to hold without practicalimplications.

46

Note that the above table exhibits the percent of overestimationof the present value of cash flows when the regular discountingmethod is used.

47

A11B3 2

costa Rica Case StudY

After considering the investment expansion of the local utility,the following alternative scenarios were considered:

a) all Gas Turbines (denoted by GT),

b) the Hydro plant plus Gas Turbines (denoted by HYD),

c) the Geothermal plant plus Gas Turbines (denoted by GEO).

The following table shows the forecasted energy demand and totalcapacity expansion under each scenario for the years 1988 to 1998,with #T, #H, and #G denoting the number of Gas Turbines, Hydro, andGeothermal plants constructed under each scenario. We assume thatconstruction is to begin in 1991, with decision taken by the endOf 1990.

Table 2.1Power Uxpansion scenarios.

Max load forecasts (+ margin 10%) and investment plans (T, H, G)

Demand GT #T HYD #T #H GEO #T #G

1988 729.3 751.0 751.0 751.01989 751.9 751.0 751.0 751.01990 774.5 787.0 1 787.0 1 -- 787.0 1 --

1991 798.5 823.0 1 823.0 1 -- 891.0 1 --

1992 824.0 823.0 -- 823.0 -- -- 891.0 -- --

1993 859.5 859.0 1 1000.0 1 -- 891.0 -- 11994 901.6 895.0 1 1000.0 1 -- 927.0 -- --

1995 951.2 967.0 2 1000.0 -- 1 963.0 1 --

1996 992.1 1003.0 1 1000.0 -- -- 999.0 1 --

1997 1040.7 1039.0 1 1036.0 -- -0

1998 1092.7 1111.0 2 1108.0 1 -- ..... .

Notes:

The increase in maximum forecasted load was .031, .03, .031, .032,.043, .049, .055, .043, .049, and .05 from year 1989 to year 1998.

2The installed capacity was 751NW at the end of 1988, andmaximum load demand vas 663MW for the same year. These figures werethe starting point for our demand and capacity projections. Weassume that during 1990 a diesel plant will be added to the networkto increase capacity.

48

The capacity expansion considers the addition of 177 NW for theHydro plant, 104 KW for the Geothermal plant, and 36 MW for eachGas Turbine.

We can see that the Hydro plant will reduce the future investmentby 5 Gas Ttrbines and the Geothermal plant will reduce futureinvestment by 3 Gas Turbines.

Sensitivity analysis

The Acceptance - Rejection matrix that follows in Tables 2.2 and2.3 for the Hydro and the Geothermal, respectively, shows theactual and critical values for different combinations of discountrates and uncertainty, defining two regions in the plane: one wherethe investment is accepted and one where it is rejected.

Tables 2.4 and 2.5 present complete results of the sensitivityanalysis.

49

Table 2. 2REWJCTION - ACCEP!ANCZ MATRIX

IT SHOWS THE PAIRS OF CRITICAL BENEFIT CST RATIO (UPPER) ANDACTUAL BENEFIT COST RATIO (LOWER)

COSTA RICA, HYDRO - PROJECT (I.R.R.=12.2%)

MAIN UNCERTAINTY: FUEL SAVINGS (WHILE COSTS HAVE CONSTANT STD 5.6%AND 15% CORRELATION WITH FUEL SAVINGS)

STANDARD DEVIATION OF PERCENTAGE CHANGE OF SAVINGS

DISCOUNT II .05 .10 .15 .20 .25RATES %

.075 1.9942.074

1.944.08 1.901

1.682.085 1.747

1.654.09 ACCEPT 1.609

1.452.095 1.485

1.292 1.437.10 1.374 1.374

1.283.105 1.273

1.170.11 1.182

1.166.115 1.100

.12 REJECT

.13

50

Table 2.3R8EJCTION - ACCEPTANCE UlTRIX

IT SHOWS THE PAIRS OF CRITICAL BENEFIT COST RATIO (UPPER) ANDACTUAL BENEFIT COST RATIO (LOWER)

COSTA RICA, GEOTHERMAL - PROJECT (I.R.R.=13.05%)

MAIN UNCERTAINTY: FUEL SAVINGS (WHILE COSTS HAVE CONSTANT STD 5.6%AND 15% CORRELATION WITH FUEL SAVINGS)

STANDARD DEVIATION OF PERCENTAGE CHANGE OF SAVINGS

DISCOUNT | .05 .10 .15 .20 .25RATES% ii

2.199.06 2.252

2.119.065 2.108

1.713.08 1.744

1.682.085 1.642

.09 ACCEPT

1.452.095 1.459

1.437.10 1.379

1.283.105 1.304

1.274.11 1.234

1.160.115 1.208

1.156.12 1.134 REJECT

.13

51

Table 2.4SENSITIVITY ANALYSIS, COSTA RICA BYDRO VIS THERMAL UNITS.

FLEXIBILITY OPTION TO WAIT TO INVEST

V F DV DF SV SF RVF C X

397.31 289.26 0.042 0.087 0.086 0.056 0.15 2.26512 149.433397.31 289.26 0.057 0.087 0.086 0.056 0.15 1.71718 121.541397.31 289.26 0.072 0.087 0.086 0.056 0.15 1.42125 108.591397.31 289.26 0.087 0.087 0.086 0.056 0.15 1.25613 114.833397.31 289.26 0.102 0.087 0.086 0.056 0.15 1.16594 151.802397.31 289.26 0.117 0.087 0.086 0.056 0.15 1.11631 246.174397.31 289.26 0.132 0.087 0.086 0.056 0.15 1.08739 462.545

397.31 289.26 0.087 0.042 0.086 0.056 0.15 1.09351 389.148397.31 289.26 0.087 0.057 0.086 0.056 0.15 1.1250r 217.841397.31 289.26 0.087 0.072 0.086 0.056 0.15 1.17620 143.529397.31 289.26 0.087 0.087 0.086 0.056 0.15 1.25613 114.833397.31 289.26 0.087 0.086 0.086 0.056 0.15 1.24980 115.882397.31 289.26 0.087 0.117 0.086 0.056 0.15 1.50124 111.096397.31 289.26 0.087 0.132 0.086 0.056 0.15 1.64983 118.032

397.31 289.26 0.087 0.087 0.056 0.056 0.15 1.19103 134.412397.31 289.26 0.087 0.087 0.066 0.056 0.15 1.21075 125.835397.31 289.26 0.087 0.087 0.076 0.056 0.15 1.23256 119.425397.31 289.26 0.087 0.087 0.086 0.056 0.15 1.25613 114.833397.31 289.26 0.087 0.087 0.096 0.056 0.15 1.28120 111.689397.31 289.26 0.087 0.087 0.106 0.056 0.15 1.30761 109.673397.31 289.26 0.087 0.087 0.116 0.056 0.15 1.33521 108.534397.31 289.26 0.087 0.087 0.130 0.056 0.15 1.37569 108.051397.31 289.26 0.087 0.087 0.150 0.056 0.15 1.43692 108.958

397.31 289.26 0.087 0.087 0.086 0.026 0.15 1.22860 120.406397.31 289.26 0.087 0.087 0.086 0.036 0.15 1.23471 118.922397.31 289.26 0.087 0.087 0.086 0.046 0.15 1.24396 116.960397.31 289.26 0.087 0.087 0.086 0.056 0.15 1.25613 114.833397.31 289.26 0.087 0.087 0.086 0.066 0.15 1.27093 112.804397.31 289.26 0.087 0.087 0.086 0.076 0.15 1.28809 111.055397.31 289.26 0.087 0.087 0.086 0.086 0.15 1.30736 109.687

397.31 289.26 0.087 0.087 0.086 0.056 0.05 1.27094 112.802397.31 289.26 0.087 0.087 0.086 0.056 0.08 1.26656 113.347397.31 289.26 0.087 0.087 0.086 0.056 0.12 1.26063 114.156397.31 289.26 0.087 0.087 0.086 0.056 0.15 1.25613 114.833397.31 289.26 0.087 0.087 0.086 0.056 0.17 1.25309 115.321397.31 289.26 0.087 0.087 0.086 0.056 0.20 1.24849 116.114397.31 289.26 0.087 0.087 0.086 0.056 0.25 1.24068 117.619

Actual ratio: 1.374

Note: if the actual ratio is greater than the critical ratio, theoption price "X" is not valid, and should be equal to thedifference between savings 'V" and costs "F"

52

Table 2.5SZNSI!XTVZY ANaXIYSZ, COomTAa RICA UOH aL VIa !REoKAL UNIT8.

FLUXIBZLITY OPTZON TO WAVT TO INVUBS

V F DV DF SV SF RVF C X

312.91 226.98 0.042 0.087 0.088 0.056 0.15 2.27139 118.260312.91 226.98 0.057 0.087 0.088 0.056 0.15 1.72287 96.447312.91 226.98 0.072 0.087 0.088 0.056 0.15 1.42665 86.354312.91 226.98 0.087 0.087 0.088 0.056 0.15 1.26103 91.131312.91 226.98 0.102 0.087 0.088 0.056 0.15 1.17005 119.305312.91 226.98 0.117 0.087 0.088 0.056 0.15 1.11963 190.332312.91 226.98 0.132 0.087 0.088 0.056 0.15 1.09007 350.518

312.91 226.98 0.087 0.042 0.088 0.056 0.15 1.09653 295.054312.91 226.98 0.087 0.057 0.088 0.056 0.15 1.12878 168.600312.91 226.98 0.087 0.072 0.088 0.056 0.15 1.18068 112.898312.91 226.98 0.087 0.087 0.088 0.056 0.15 1.26103 91.131312.91 226.98 0.087 0.086 0.088 0.056 0.15 1.25469 91.932312.91 226.98 0.087 0.117 0.088 0.056 0.15 1.50571 88.272312.91 226.98 0.087 0.132 0.088 0.056 0.15 1.65390 93.646

312.91 226.98 0.087 0.087 0.058 0.056 0.15 1.19479 106.343312.91 226.98 0.087 0.087 0.068 0.056 0.15 1.21496 99.649312.91 226.98 0.087 0.087 0.078 0.056 0.15 1.23714 94.679312.91 226.98 0.087 0.087 0.088 0.056 0.15 1.26103 91.131312.91 226.98 0.087 0.087 0.098 0.056 0.15 1.28638 88.709312.91 226.98 0.087 0.087 0.108 0.056 0.15 1.31304 87.160312.91 226.98 0.087 0.087 0.118 0.056 0.15 1.34087 86.290312.91 226.98 0.087 0.087 0.130 0.056 0.15 1.37569 85.932312.91 226.98 0.087 0.087 0.150 0.056 0.15 1.43692 86.535

312.91 226.98 0.087 0.087 0.088 0.026 0.150 1.23421 95.2270312.91 226.98 0.087 0.087 0.088 0.036 0.150 1.24012 94.1512312.91 226.98 0.087 0.087 0.088 0.046 0.150 1.24913 92.7113312.91 226.98 0.087 0.087 0.088 0.056 0.150 1.26103 91.1315312.91 226.98 0.087 0.087 0.088 0.066 0.150 1.27555 89.6080312.91 226.98 0.087 0.087 0.088 0.076 0.150 1.29244 88.2806312.91 226.98 0.087 0.087 0.088 0.086 0.150 1.31145 87.2303

312.91 226.98 0.087 0.087 0.088 0.056 0.050 1.27599 89.5677312.91 226.98 0.087 0.087 0.088 0.056 0.080 1.27156 89.9873312.91 226.98 0.087 0.087 0.088 0.056 0.120 1.26558 90.6105312.91 226.98 0.087 0.087 0.088 0.056 0.150 1.26103 91.1315312.91 226.98 0.087 0.087 0.088 0.056 0.170 1.25796 91.5070312.91 226.98 0.087 0.087 0.088 0.056 0.200 1.25332 92.1169312.91 226.98 0.087 0.087 0.088 0.056 0.250 1.24544 93.2736

Actual ratio: 1.379

Note: if actual ratio is greater than the critical ratio, theoption price "X" is not valid, and should be equal to thedifference between savings "V" and costs "F"

53

Monte Carlo simulation.

The following figure shows the results of the Monte Carlosimulation. The computer work was done with SAS (on the WorldBank's mainframe, CMS operating system). The parameters were asfollows (for the perpetual warrant "option to wait to invest"):

V = the "stock price equivalent" (total savings),F = the "exercise price" (construction costs),DV = the "dividend equivalent" of total savings,DF = the "dividend equivalent" of construction costs,SV = the uncertainty of the total savings,SF = the uncertainty of the construction costs,RVF = the correlation between total savings and costs,C the critical ratio, andx = the option price (to wait to invest)

The Monte Carlo simulation was based on the following assumptionsfor the underlying distributions the characterize our uncertaintyon the model parameters:

Option to wait to invest, Hydro and Geothermal vis thermalalternatives.

DV -> triangular distribution between .0787 and .0987DF -> triangular distribution between .0787 and .0987SV -> triangular distribution between .067 and .107SF -> triangular distribution between .046 and .066RVF -> triangular distribution between .13 and .17

The Monte Carlo simulation results show that there is considerableuncertainty regarding the estimates of the critical benefit-costratio, but in both cases the conclusions stay the same. Thesimulation results are synopsized as follows:

option to wait to invest for hydro or geothermal vis thermal

#replications mean std minimum maximum

critical ratio: 30000 1.26048 .04626 1.12803 1.47356

Percentage of replications where the critical ratio exceeded theactual benefit-cost ratio:

- hydro: 1.4%- geothermal: 1.0%

54

Figure 2.1MONTE CARM ON CRITICAL C,N30000, COSTA RICA, NYDRO - GEOTNERMAL

N Mean Std Dev Minimum Maximum_____________-____-_--------------- _____________-- - ---------

30000 1.2604795 0.0462615 1.1280266 1.4735634--------------------------------------------------------- __--

Percentage

] ~~~**

6 +

5 +

4 +

3

3 +

12 + *********

1 + ************] ************************* actual benefit-cost3 **************************s ratio

] ******************************** *---------------------------------------------

11111111111111111111111111111111111111111111

111111111222222222222233333333333344444444442345667890012344567889012234566789001234456786420864208642086420864208642086420864208642

C Midpoint

55

A1533 3

Iunaar! Case Study

The 3 scenarios under consideration are: CC (only combined cycleunits), NUCL (combined cycle units with the addition of a nuclearplant), and COAL (combined cycle units with the addition of a coalplant).

Table 3.1Power Nzpansion scenarios.

YR Demand Capac. CC #CC NUCL #N #CC COAL #C #CC

1991 8000 7643 8048 3 8048 - 3 8048 - 31992 8104 7643 8048 - 8048 - - 8048 - -1993 8209 7643 8183 1 8183 - 1 8183 - 11994 8316 7643 8318 1 8318 - 1 8318 - 11995 8424 7643 8453 1 8453 - 1 8588 1 -1996 8534 7445 8525 2 8525 - 2 8525 - 11997 8645 7369 8584 1 8929 1 - 8584 - 11998 8757 7343 8693 1 8903 - - 8693 - 11999 8871 7316 8801 1 8876 - - 8801 - 12000 8986 7289 8909 1 8984 - 1 8909 - 12001 9103 7120 9145 3 9085 - 2 9145 - 32002 9221 7093 9253 1 9133 - 1 9253 - 1

_e_r_.r,- -- - --- -- -- -

Notes:

The capacity at year 1991 equals 7643 NW after reducing theexisting 8393 NW by 750 NW. Hungary was importing 1850 MW powerfrom the Soviet Union, but from 1991 only the 1100 NW are ensuredby contracts.

Demand refers to (projected) maximum load demand pluS 25% marginduring any year. Capac. refers to capacity available during theyear, taking into account the retirement of existing plants, beforeany additional capacity.

CC stands for capacity after expansion only with combined cycleunits.

NUCL stands for capacity after expansion with a nuclear plant andcombined cycle units.

COAL stands for capacity after expansion with a coal plant andcombined cycle units.

#CC, #N, and #C stand for number of combined cycle units, nuclearplants, and coal plants respectively.

56

The #CC (new investment in combined cycle) in the nuclear and thecoal scenario respectively subtracted from the first #CC (newcombined cycle units in all combined cycle scenario) denote theconstruction savings in number of combined cycle units.

As the final capacity under the nuclear scenario is 9193 NW(instead of 9253 under the other coal scenario) we consider theadditional savings of one unit of combined cycle with half thecapacity assumed for combined cycle units that could be availableat the start of year 2001, so as to give the same reliability tothe power system. This way we assume away economies of scale forthis part of the capacity expansion, which is acceptable due to theheavy discounting. Practically at the end of year 2001 we considerthe installation of 2.5 CC units.

In either icenario the investments are fully utilized (to the limitof their capacity factor) from the first year of their operation;this implies the existence of older plants with higher variablecosts that would be displaced in the energy dispatch priorities sodemand uncertainty is not important for these "irreversible"investments.

57

Table 3.2Costs and Bavings under Different 8cenarios.

CC ALTERNATIVE DISTILLATE ONLY 50% DISTILIATE-50% GASVIS NUCLEAR COAL NUCLEAR COAL

in mill Forints -

Gross fixed cost 50976.0 22464.0 50976.0 22464.0decommissioning 242.9 ----- 242.9 -----

Total Fixed Cost 51218.9 22464.0 51218.9 22464.0

Fuel savings 22541.6 10446.6 16436.6 6674.2O+K savings -1952.9 -1191.8 -1952.9 -1191.8Total fuel SavingsD 20588.7 9254.7 14483.7 5482.4

Cost savings 9402.6 6978.5 9402.6 6978.5

Total Savings 29991.3 16233.2 23886.3 12460.9

Actual Ratio .586 .723 .466 .555

IRR 6.10% 6.95% 4.3% 4.3%

Notes:

The actual ratio is that between the sum of the fuel and O+Msavings plus the avoided diesel CC-construction costs over thetotal fixed cost of the investment.

The above appraisal is based on discount rates of 10%.

The cost of the combined cycle units is assumed to appreciate by1.3% (real) per year.

The fuel prices (and O+M costs) are assumed to appreciate by 1.3%(real) per year.

2The total fuel savings are calculated after taking intoaccount:a) the fuel (and O0+) savings will materialize after the fuel-efficient plant will be in operation, for the life time of thisplant, discounted to the present.b) a constant appreciation rate for the savings of 1.3% per year.c) the use of negative O+M savings violates the rule stemming fromthe assumption that savings are log-normal; however, the effect ofthis violation is negligible (the effect on the actual ratio forthe distillate fuel case is very small: nuclear .601 instead of.586, coal .738 instead of .723).

58

The decommissioning cost for the nuclear plant is assumed30 to be130 $/KW (or 8190 For/KVs), appreciating by 1.3% (real) per year.

The nuclear and coal plants are fully utilized from the first yearof their operation, being used for both base and peak load; theyreplace other thermal type units.

The current fixed cost for the different units is 50976 mill-Forfor the nuclear plant, 22464 mill-For for the coal plant, and 4725mill-For for each combined-cycle unit.

The remaining model parameters are the variance terms and the driftterms (dividend equivalent) used to calculate option values whichare discussed in the main text.

3See Traiforos et.al., "The Status of Nuclear Plant Techlology- An Update", IEN Energy Series Paper No.27

59

Table 3.3SENSITIVITY ANRLYSIS8 NW3RY NUCLA VIS CC UOSING DISX!LL&TB FUL.

FLEXIBILITY OPTION TO WAIT TO INVEST

v F DV DF SV SF RVF C X

29.99 51.22 0.042 0.087 0.071 0.056 0.070 2.23557 5.604529.99 51.22 0.057 0.087 0.071 0.056 0.070 1.69003 2.635129.99 51.22 0.072 0.087 0.071 0.056 0.070 1.39517 0.943829.99 51.22 0.087 0.087 0.071 0.056 0.070 1.23231 0.229729.99 51.22 0.102 0.087 0.071 0.056 0.070 1.14605 0.038529.99 51.22 0.117 0.087 0.071 0.056 0.070 1.10043 0.005129.99 51.22 0.132 0.087 0.071 0.056 0.070 1.07465 0.0006

29.99 51.22 0.087 0.042 0.071 0.056 0.070 1.07924 0.001029.99 51.22 0.087 0.057 0.071 0.056 0.070 1.10726 0.007629.99 51.22 0.087 0.072 0.071 0.056 0.070 1.15462 0.049729.99 51.22 0.087 0.087 0.071 0.056 0.070 1.23231 0.229729.99 51.22 0.087 0.086 0.071 0.056 0.070 1.22605 0.210229.99 51.22 0.087 0.117 0.071 0.056 0.070 1.47988 1.408529.99 51.22 0.087 0.132 0.071 0.056 0.070 1.63050 2.2850

29.99 51.22 0.087 0.087 0.031 0.056 0.070 1.16031 0.058129.99 51s22 0.087 0.087 0.041 0.056 0.070 1.17417 0.081929.99 51.22 0.087 0.087 0.061 0.056 0.070 1.21067 0.166029.99 51.22 0.087 0.087 0.071 0.056 0.070 1.23231 0.229729.99 51.22 0.087 0.087 0.081 0.056 0.070 1.25573 0.309129.99 51.22 0.087 0.087 0.091 0.056 0.070 1.28068 0.404329.99 51.22 0.087 0.087 0.101 0.056 0.070 1.30697 0.5150

29.99 51.22 0.087 0.087 0.071 0.026 0.070 1.19350 0.122629.99 51.22 0.087 0.087 0.071 0.036 0.070 1.20335 0.146729.99 51.22 0.087 0.087 0.071 0.046 0.070 1.21642 0.181929.99 51.22 0.087 0.087 0.071 0.056 0.070 1.23231 0.229729.99 51.22 0.087 0.087 0.071 0.066 0.070 1.25065 0.291029.99 51.22 0.087 0.087 0.071 0.076 0.070 1.27111 0.366629.99 51.22 0.087 0.087 0.071 0.086 0.070 1.29342 0.4567

29.99 51.22 0.087 0.087 0.071 0.056 0.020 1.23894 0.251129.99 51.22 0.087 0.087 0.071 0.056 0.035 1.23696 0.244629.99 51.22 0.087 0.087 0.071 0.056 0.055 1.23431 0.236129.99 51.22 0.087 0.087 0.071 0.056 0.070 1.23231 0.229729.99 51.22 0.087 0.087 0.071 0.056 0.085 1.23030 0.223429.99 51.22 0.087 0.087 0.071 0.056 0.115 1.22623 0.210829.99 51.22 0.087 0.087 0.071 0.056 0.150 1.22142 0.1964

Actual ratio: .586

Note: if actual ratio is greater than the critical ratio, theoption price *X" is not valid, and should be equal to thedifference between savings *V" and costs "F"

60

Table 3.4UNSITIVITY AMLYSIS, NUNGARY COAL VIS CC USING DISTILLaTE FVL.

FLEXIBILITY OPTION TO WAIT TO INVUST

V F DV DF SV SF RVF C X

16.L3 22.46 0.042 0.087 0.062 0.056 0.070 2.21250 3.534416.23 22.46 0.057 0.087 0.062 0.056 0.070 1.66849 1.859816.23 22.46 0.072 0.087 0.062 0.056 0.070 1.37401 0.792516.23 22.46 0.087 0.087 0.062 0.056 0.070 1.21275 0.249716.23 22.46 0.102 0.087 0.062 0.056 0.070 1.12988 0.059716.23 22.46 0.117 0.087 0.062 0.056 0.070 1.08772 0.012416.23 22.46 0.132 0.087 0.062 0.056 0.070 1.06458 0.0024

16.23 22.46 0.087 0.042 0.062 0.056 0.070 1.06810 0.0033316.23 22.46 0.087 0.057 0.062 0.056 0.070 1.09315 0.0162516.23 22.46 0.087 0.072 0.062 0.056 0.070 1.13711 0.0717116.23 22.46 0.087 0.087 0.062 0.056 0.070 1.21275 0.2497316.23 22.46 0.087 0.086 0.062 0.056 0.070 1.20653 0.2321816.23 22.46 0.087 0.117 0.062 0.056 0.070 1.46279 1.1187316.23 22.46 0.087 0.132 0.062 0.056 0.070 1.61523 1.67233

16.23 22.46 0.087 0.087 0.032 0.056 0.070 1.16154 0.1195616.23 22.46 0.087 0.087 0.042 0.056 0.070 1.17574 0.1520416.23 22.46 0.087 0.087 0.052 0.056 0.070 1.19299 0.1954516.23 22.46 0.087 0.087 0.062 0.056 0.070 1.21275 0.2497316.23 22.46 0.087 0.087 0.072 0.056 0.070 1.23458 0.3144016.23 22.46 0.087 0.087 0.082 0.056 0.070 1.25816 0.3887016.23 22.46 0.087 0.087 0.092 0.056 0.070 1.28325 0.47171

16.23 22.46 0.087 0.087 0.062 0.026 0.070 1.16992 0.1383516.23 22.46 0.087 0.087 0.062 0.036 0.070 1.18102 0.1648816.23 22.46 0.087 0.087 0.062 0.046 0.070 1.19546 0.2019916.23 22.46 0.087 0.087 0.062 0.056 0.070 1.21275 0.2497316.23 22.46 0.087 0.087 0.062 0.066 0.070 1.23243 0.3078316.23 22.46 0.087 0.087 0.062 0.076 0.070 1.25413 0.3757216.23 22.46 0.087 0.087 0.062 0.086 0.070 1.27757 0.45263

16.23 22.46 0.087 0.087 0.062 0.056 0.020 1.21892 0.2675416.23 22.46 0.087 0.087 0.062 0.056 0.035 1.21708 0.2622016.23 22.46 0.087 0.087 0.062 0.056 0.055 1.21461 0.2550716.23 22.46 0.087 0.087 0.062 0.056 0.070 1.21275 0.2497316.23 22.46 0.087 0.087 0.062 0.056 0.085 1.21087 0.2443916.23 22.46 0.087 0.087 0.062 0.056 0.115 1.20708 0.2337116.23 22.46 0.087 0.087 0.062 0.056 0.150 1.20259 0.22127

Actual ratio. .723

Note: if actual ratio is greater than the critical ratio, theoption price OX" is not valid, and should be equal to thedifference between savings 'V" and costs "F"

61

Table 3.5SUNBITIVTTY AMhLYSIS, RIGARY NUCLXAR VIS CC USING FUEL NIX.

FLEXIBIXITY OPTION TO WAIT TO INVEST

V F DV DF SV SF RVF C X

23.89 51.22 0.042 0.087 0.051 0.056 0.070 2.18843 3.5330323.89 51.22 0.057 0.087 0.051 0.056 0.070 1.64565 1.3298223.89 51.22 0.072 0.087 0.051 0.056 0.070 1.35099 0.2998823.89 51.22 0.087 0.087 0.051 0.056 0.070 1.19114 0.0284023.89 51.22 0.102 0.087 0.051 0.056 0.070 1.11223 0.0010523.89 51.22 0.117 0.087 0.051 0.056 0.070 1.07412 0.0000223.89 51.22 0.132 0.087 0.051 0.056 0.070 1.05396 0.00000

23.89 51.22 0.087 0.042 0.051 0.056 0.070 1.05648 0.0000023.89 51.22 0.087 0.057 0.051 0.056 0.070 1.07818 0.0000423.89 51.22 0.087 0.072 0.051 0.056 0.070 1.11806 0.0015323.89 51.22 0.087 0.087 0.051 0.056 0.070 1.19114 0.0284023.89 51.22 0.087 0.086 0.051 0.056 0.070 1.18499 0.0241423.89 51.22 0.087 0.117 0.051 0.056 0.070 1.44451 0.5779723.89 51.22 0.087 0.132 0.051 0.056 0.070 1.59911 1.14469

23.89 51.22 0.087 0.087 0.021 0.056 0.070 1.15019 0.0076623.89 51.22 0.087 0.087 0.031 0.056 0.070 1.16031 0.0112123.89 51.22 0.087 0.087 0.041 0.056 0.070 1.17417 0.0176823.89 51.22 0.087 0.087 0.051 0.056 0.070 1.19114 0.0284023.89 51.22 0.087 0.087 0.061 0.056 0.070 1.21067 0.0449223.89 51.22 0.087 0.087 0.071 0.056 0.070 1.23231 0.0687523.89 51.22 0.087 0.087 0.081 0.056 0.070 1.25573 0.10120

23.89 51.22 0.087 0.087 0.051 0.026 0.070 1.14247 0.0055423.89 51.22 0.087 0.087 0.051 0.036 0.070 1.15547 0.0094023.89 51.22 0.087 0.087 0.051 0.046 0.070 1.17192 0.0164923.89 51.22 0.087 0.087 0.051 0.056 0.070 1.19114 0.0284023.89 51.22 0.087 0.087 0.051 0.066 0.070 1.21260 0.0468123.89 51.22 0.087 0.087 0.051 0.076 0.070 1.23589 0.0732723.89 51.22 0.087 0.087 0.051 0.086 0.070 1.26074 0.10903

23.89 51.22 0.087 0.087 0.051 0.056 0.020 1.19664 0.0325923.89 51.22 0.087 0.087 0.051 0.056 0.035 1.19501 0.0313123.89 51.22 0.087 0.087 0.051 0.056 0.055 1.19281 0.0296323.89 51.22 0.087 0.087 0.051 0.056 0.070 1.19114 0.0284023.89 51.22 0.087 0.087 0.051 0.056 0.085 1.18947 0.0272023.89 51.22 0.087 0.087 0.051 0.056 0.115 1.18609 0.0248723.89 51.22 0.087 0.087 0.051 0.056 0.150 1.18208 0.02227

Actual ratio: .466

Note: if actual ratio is greater than the critical ratio, theoption price "X" is not valid, and should be equal to thedifference between savings "V" and costs "r

62

Table 3.6SBNSITIVITY ANILYIZS, HUNGARY COAL VX8 CC USING FMlL MIX.

FLXMIBILITY OPTION TO WAIT TO INVEST

V F DV DF SV SF RVF C X

12.46 22.46 0.042 0.087 0.046 0.056 0.070 2.17905 2.1127712.46 22.46 0.057 0.087 0.046 0.056 0.070 1.63662 0.8859912.46 22.46 0.L72 0.087 0.046 0.056 0.070 1.34171 0.2393712.46 22.46 0.087 0.087 0.046 0.056 0.070 1.18231 0.0302712.46 22.46 0.102 0.087 0.046 0.056 0.070 1.10509 0.0016912.46 22.46 0.117 0.087 0.046 0.056 0.070 1.06871 0.0000612.46 22.46 0.132 0.087 0.046 0.056 0.070 1.04978 0.00000

12.46 22.46 0.087 0.042 0.046 0.056 0.070 1.05195 0.0000012.46 22.46 0.087 0.057 0.046 0.056 0.070 1.07227 0.0000912.46 22.46 0.087 0.072 0.046 0.056 0.070 1.11038 0.0023012.46 22.46 0.087 0.087 0.046 0.056 0.070 1.18231 0.0302712.46 22.46 0.087 0.086 0.046 0.056 0.070 1.17618 0.0262112.46 22.46 0.087 0.117 0.046 0.056 0.070 1.43723 0.4297012.46 22.46 0.087 0.132 0.046 0.056 0.070 1.59278 0.78260

12.46 22.46 0.087 0.087 0.016 0.056 0.070 1.14672 0.0113112.46 22.46 0.087 0.087 0.026 0.056 0.070 1.15474 0.0146312.46 22.46 0.087 0.087 0.036 0.056 0.070 1.16682 0.0206612.46 22.46 0.087 0.087 0.046 0.056 0.070 1.18231 0.0302712.46 22.46 0.087 0.087 0.056 0.356 0.070 1.20062 0.0443812.46 22.46 0.087 0.087 0.066 0.056 0.070 1.22125 0.0637812.46 22.46 0.087 0.087 0.076 0.056 0.070 1.24382 0.08906

12.46 22.46 0.087 0.087 0.046 0.026 0.070 1.13059 0.0061712.46 22.46 0.087 0.087 0.046 0.036 0.070 1.14464 0.0105312.46 22.46 0.087 0.087 0.046 0.046 0.070 1.16213 0.0181712.46 22.46 0.087 0.087 0.046 0.056 0.070 1.18231 0.0302712.46 22.46 0.087 0.087 0.046 0.066 0.070 1.20461 0.0478412.46 22.46 0.087 0.087 0.046 0.076 0.070 1.22863 0.0715912.46 22.46 0.087 0.087 0.046 0.086 0.070 1.25410 0.10189

12.46 22.46 0.087 0.087 0.046 0.056 0.020 1.18745 0.0339312.46 22.46 0.087 0.087 0.046 0.056 0.035 1.18592 0.0328212.46 22.46 0.087 0.087 0.046 0.056 0.055 1.18386 0.0313512.46 22.46 0.087 0.087 0.046 0.056 0.070 1.18231 0.0302712.46 22.46 0.087 0.087 0.046 0.056 0.085 1.18074 0.0292012.46 22.46 0.087 0.087 0.046 0.056 0.115 1.17758 0.0271112.46 22.46 0.087 0.087 0.046 0.056 0.150 1.17383 0.02475

Actual ratio: .555

Note: if actual ratio is greater than the critical ratio, theoption price "X" is not valid, and should be equal to thedifference between savings "V" and costs "F"

63

Monte Carlo situlatioa.

The following tables show the sensitivity analysis and the MonteCarlo simulation. The computer work was done with SAS (on the WorldDank's mainframe, CMS operating system). The parameters were asfollows (for the perpetual warrant "option to wait to invest"):

V = the "stock price equivalent" (total savlngs),F - the "exercise price" (construction costs),DV = the "dividend equivalent" of total savings,DF - the "dividend equivalent" of construction costs,SV - the uncertainty of the total savings,SF = the uncertainty of the construction costs,RVF - the correlation between total savings and costs,C the critical ratio, andx - the option price (to wait to invest)

The Monte Carlo simulation was based on the following assumptionsfor the underlying distributions the characterize our uncertaintyon the model parameters:

option to wait to invest, Nuclear (or Coal) vis CC with distillatefuel.

DV -> triangular distribution between .0787 and .0987DF -> triangular distribution between .0787 and .0987SV -> triangular distribution between .051 and .091

(or .042 to .082 for Coal)SF -> triangular distribution between .046 and .066RVF -> triangular distribution between .05 and .09

Option to wait to invest, Nuclear (or Coal) vis CC with distillateand gas fuel mix.

DV -> triangular distribution between .0787 and .0987DF -> triangular distribution between .0787 and .0987SV -> triangular distribution between .031 and .071

(or .026 to .046 for Coal)SF -> triangular distribution between .046 and .066RVA -> triangular distribution between .05 and .09

The Monte Carlo simulation results show that there is considerableuncertainty regarding the estimates of option values, but in bothcases the conclusions stay the same. The simulation results aresynopsized as follows:

64

Option to wait to invest for nuclear or coal via CC alternativeMONTE CARLO SIMULATION ==---

#replications mean std minimum maximum

Nuclear via CC with distillate fuel:critical ratio: 30000 1.2345 0.0451 1.1119 1.4328Nuclear via CC with distillate and gas fuel mix:critical ratio: 30000 1.1940 0.0428 1.0783 1.3806Coal via CC with distillate fuel:critical ratio: 30000 1.2154 0.0441 1.0947 1.4072Coal vis CC with distillate and gas fuel mix:critical ratio: 30000 1.1858 0.0424 1.0692 1.3712

65

Figure 3.1NWONT ChMeO ON CRITICAL C,N=30000,N 4A2Y* NUCLDAR VXS CC JIZNGDWSThL&TN 1UBL.

N Mean Std Dev Minimum Maximum---------------------------------------- __------------------

30000 1.2344809 0.0450760 1.1119530 1.4328322a--------------------------------------- -…-----------------

Percentage

7 +**]+ ***

6 +

3

5 +

4 + *****

3 ****J **********111112222333341257**********

2 +********

1 **********

I ****************~********

3 ******************************

*........ .... *...@..*.....e.....*...................*......... . *0* **

111111111112222222222222333333333333444441223456678900123445678890122345667890012320864208642086420864208642086420864208642

C Midpoint

66

Figure 3.2NOMTZ CARL ON CROTXICL C,N30000,NUNGARY, COAL VIS CC UOINGDZSTXLLaZ PQULs

N Mean Std Dev Minimum Maximum-------------------------------------------------------------

30000 1.2153529 0.0441309 1.0946875 1.4071990--------------------------------------------------------- __--

Percentage

] **5 +

4 +

3 +

2+

1 +

] ***************************

-- 11--1111111-111-111111-1-11-1-1--1111-11-1-1--11111-

011111111111111111222222222222222223333333333333333449001123344566778990012233455667889!: 31122344556778890051739517395173951739517395173951739517395173951739517

C Midpoint

67

am2 X 4

ODtial Timinag o Transmission Investment

The expected period of time after which it will be worthwhileexercising the option to invest is expressed as:

ln(C6)P - ln(V/7) + i11-P]B(T) = _ ; for G.>Gf

3(T) = [lnfC4) ln(V/r)] Cln{V/F) - 0 / o2 for G(=Gf

Also, as 0 -^ -0

Z(T) - lnC 4F/V)/(Gv-Gf) for GV>Gf1 and 3(T) 4- O for Gv-Gf

where,

6= critical ratio provided by the option modelV = present value of benefits ("stock equivalent price")F = present value of costs ("exercise price")Gy = growth rate of benefits,. = growth rate of costsP - probability of reaching the critical ratio

= lower barrier for critical ratioa - total effective standard deviation, equal to:

a = , aV2 + af2 _ .rvflavaf1 (see page 6 in main text)

68

UNEsX 5

GLOSSARY

American Option: an option that can be exercised any time up to theexpiration (maturity) date.

At-The-No9ey: an option is said to be at the money when the priceof the underlying instrument is almost equal to the exercise price.

Actuaj Rio: standard benefit-cost ratio obtained through regulardeterministic present value techniques.

Black-Scholes Model: a model developed by Black and Scholes; it isEuropean type with finite maturity and fixed (non-stochastic)exercise price.

Brownian Motion: a continuous time Markov process, as such itsfuture evolution does not depend on the complete history of theprocess, but only on the last period.

call ption: an option to "purchase" the underlying asset at aprice that is predetermined or uncertain; see also option.

Conti_ngcn Claim: a claim the value of which is dependent upon someother asset(s) or security(ies); see also option.

Critical Ratio: ratio provided by the perpetual option approachthat should be exceeded by the standard benefit-cost ratio in orderto make the investment viable under uncertainty.

Buropean Option: an option that can be exercised only at theexpiration (maturity) date.

Exercise Price: the price at which the option holder can purchasethe underlying asset; this price can be fixed (like in Black-Scholes model) or uncertain, i.e., changing with time.

EDiration: the maturity (date) of the option; if not exercised bythat date, it becomes worthless.

Flexibility O=tion: a real option is called flexibility option whenthe asset and the exercise price represent the savings and costsrespectively that are incurred due to an irreversible investment.See also real option.

Geometric Brownian Motion: when a variable .ollows a Brownianmotion, its natural logarithm is said to follow a geometricBrownian motion.

IZnhThena=: an option is said to be in the money if exercisingit is profitable; the price of the underlying asset is higher than

69

the exercise price in the case of a call option, and lower in thecase of a put option.

Maturity: see expiration.

Cption: the right (but not the obligation) to buy (call option) orto sell (put option) an asset by paying the exercise price; thisprice can be predetermined or uncertain.

Out-Of-The-Money: an option is said to be out of the money if itis not profitable exercising it; the price of the underlying assetis lower than the exercise price in the case of a call option, andhigher in the case of a put option.

Put Otion: an option to "sell" the underlying asset at apredetermined or uncertain exercise price; see also option.

z2epeanl Warrant: an option with no finite expiration (maturity)date; it can be exercised any time and thus is of the Americantype.

Real OQtion: an option is called real when the underlying asset isnot observable, i.e.,, is not a financial instrument tradeable inthe market.

Stochastic Variable: a random variable is considered stochasticwhen its probability distribution changes as a function of time (orin a more general sense as a function of any index; usually theindex is time).

Writer: the party that originally creates the option by selling itto another party; he carries the full obligation implied by theoption to the present owner.

Nnrrant: see option.

70

RnRC's

Association Nomentanee: Tractebel, Hydro-Quebec/Dessau, Electricitede France International (Mar. 1991) "OMVS Project Energie - EtudeEconomique Complementaire du Reseau 225 kV de la Centrale deManantali, Rapport de Phase III. Draft report prepared for theWorld Bank.

Brock, W. A., M. Rothschild, and J. E. Stiglitz (1988) "StochasticCapital Theory", Ch. 20 in Essays in Honour of Joan Robinson,Feiwal ed., Cambridge Univ. Press.

Copeland, Thomas and Fred Weston (1983) Financial Theory andCorporate Policy, 2nd edition, Addison Wesley, pp. 701-706.

Crousillat, Enrique (Jun. 1989) "Incorporating Risk and Uncertaintyin Power System Planning", IEN Energy Series Paper No. 17. The WorldBank.

Instituto Costarricense de Electricidad (1989) "Programa DQsarrolloBlectrico II, Periodo 1990-1994 - Programa de Expansion de laGeneracion", San Jose, Costa Rica.

Karlin, Samuel and Howard M. Taylor (1975) A First Course inStochastic Processes, 2nd ed., Academic Press.

Little, I.M. D., and James A. Mirrless (1974) Project Appraisal andPlanning, London: Heinemann.

Little, I.M.D., and James A. Mirrless (1990) "Project Appraisal andTwenty Years On", in Proceedings of the World Bank AnnualConference on Development Economics, The World Bank.

Martzoukos, Spiros H. and James Paddock (Summer 1990, revisedWinter 1991) "Option Models, Flexibility, and the Power Sector"unpublished document, prepared for the IENED (PPR), the World Bank.

Martzoukos, S. H. and W. Teplitz-Sembitzky (April 1991) "OptimalTiming of Transmission Line Investments in the Face of UncertainDemand - An Option Valuation Approach", Working Paper.

McDonald, Robert and Daniel Siegel (November 1986) "The Value ofWaiting to Invest", Ouarterly Journal of Economics, V.101, N.4.

Merrow, Edward W. and Ralph F. Shangraw Jr. (Jul. 1990)"Understanding the Costs and Schedules of World Bank SupportedHydroelectric Projects", IEN Energy Series Paper No.31. The WorldBank.

Moore, Edwin A. and Enrique Crousillat (May 1991) "Prospects forGas-Fueled Combined-Cycle Power Generation in the DevelopingCountries", ZEN Energy Series Paper No.35. The World Bank.

71

Moore, Edwin A. and George Smith (Feb. 1990) "Capital Expendituresfor Electric Power in the Developing Countries in the 1990s", IENEnergy Series Paper No.21. The World Bank.

Samuelson, Paul A. (1965) "Rational Theory of Warrant Pricing",Iustrial ManaaeXent Review, Vol. 6, No. 2, Spring, pp. 13-31,reprinted in Samuelson 1972 (Merton editor).

Sanghvi, Arun, Robert Vernstrom and John Besant-Jones (Jun. 1989)"Review and Evaluation of historic Electricity ForecastingExperience (1960-1985)", IEN Energy Series Paper No.18. The WorldBank.

Schram,, G. (July 1989) "Optimal Timing of Transmission LineInvestment", Energy Economics, V. 11, N.3.

Teplitz-Sembitzky, W. (1989) "Option Pricing in Power Planning",working paper (mimeo), IENED. The World Bank.

Traiforos, Spiros, Achilles Adamantiades and Edwin Moore (Apr.1990) "The Status of Nuclear Power Technology - An Update", IENEnergy Series Paper No.27. The World Bank.

World Bank (1878) "Operational Maznual Statement 3.72 - Energy,Water Supply and Sanitation and Telecommunications (EWT)".

World Bank (1980) "Operational Manual Statement 2.21 - EconomicAnalysis of Projects".

World Bank (1980a) "Central Projects Note 2.02 - Risk andSensitivity Analysis in The Economic Analysis of Projects".

World Bank (1984) "Energy Department Note No. 59 - Preparation andAppraisal of Electric Power Projects", Power Advisory Unit, EnergyDepartment.

72

.FMiWX,Y ERIS PA,PERS

No. 1 Enrg Issues in the Developing Wo¢id, February 1988.

No. 2 Review of World Bank Lending for Electric Power, March 1988.

No. 3 Some Considerations in Collecting Data on Household Energy Consumption,March 1988.

No. 4 hmproving Power System Efficiency in the Developing Countdes throughPerfmance Contracting, May 1988.

No. 5 Inpact of Lower Oil Prices on Renewable Energy Technologies, May 1988.

No. 6 A Comparison of Lamps for Domestic Lighting in Develcping Countries, June1988.

No. 7 Recent World Bank Activities in Energy (Revised October 1989).

No. 8 A Visual Overview of the World Oil Markets, July 1988.

No. 9 Current Interational Gas Trades and Prices, November 1988.

No. 10 Promotng Investment for Natual Gas Exploration and Production inDeveloping Countries, January 1988.

No. 11 Technology Suvey Report on Electric Power Systems, February 1989.

No. 12 Recent Developments in the U.S. Power Sector and Their Relevance for theDeveloping Countries, February 1989.

No. 13 Domestic Energy Pricing PoLicies, April 1989.

No. 14 Fmancing of the Energy Sector in Developing Countries, April 1989.

No. 15 The Future Role of Hydropower in Developing Countries, April 1989.

No. 16 Fuelwood Stumpage: Considetidons for Developing Country Energy Planning,June 1989.

No. 17 bI poating Risk and Unctainty in Power System Planning, June 1989.

No. 18 Review and Evaluation of Historic Electricity Forecasting Experience, (1960-1985), June 1989.

No. 19 Woodfwel Supply and Envimental Management, July 1989.

No. 20 The Malawi Charcoal Project - Experience and Lessons, January 1990.

No. 21 Capil Expenditres for Electri Power in the Developing Counties in the199s, February 1990.

No. 22 A Review of Region of the Power Sectors in Developing Countries,February 1990.

No. 23 Summary Data Sheets of 1987 Power and Commercial Energy Statistics for 100Developing Countries, Match 1990.

No. 24 A Review of the Treatment of Envirounental Aspects of Bank Energy Projects,Mach 1990.

No. 25 The Status of Liquified NatWal Gas Worldwide, March 1990.

No. 26 Popultion Growth, Wood Fuels, and Resource Problems in Sub-SaharanAfrica, March 1990.

No. 27 Ihe Stats of Nuclear Power Technology - An Update, April 1990.

No. 28 Decommissioning of Nuclear Power Facilities, April 1990.

No. 29 Infte Substitution ad Changes in the Way Households Use Ener: TheCase of Coolkng and Lightng Behavior in Urban Java, October 1990.

No. 30 Regulation, Deregulaion, or Reregulation-What is Needed in LDCs PowerSector? July 1990.

No. 31 Understanding the Costs and Schedules of World Ban.-k Supported HydroelectricProjects, July 1990.

No. 32 Review of Elecicity Tariffs in Developing Countries During the 1980s,November 1990.

No. 33 Private Sector Paricipation in Power through BOOT Schemes, December 1990.

No. 34 Identffying the Basic Conditions for Eonomic Genemon of Public Electicityfrom Sumplus Bagasse in Sugar Mills, April 1991.

No. 35 Prospects for Gas-Fueled Combined-Cycle Power Generation in the DevelopingCountries, May 1991.

No. 36 Radioactive Waste Maagement -A Background Study, June 1991.

No. 37 A Study of the Trnsfer of Ptrleum Fuels Pollution, July 1991.

No. 38 Inprving Chaoaling Efficency in the Tradidonal Rural Sector, July 1991.

No. 39 Decision Maing Under Uncertainty - An Option Valuation Approach to PowerPlanning, August 1991.

For copies, please call extension 33616 (rom S-3W7).

INDUSIRY SERIES PAPERS

No. 1 Japanese Direct Foreign Investment. Patterns and Implications forDeveloping Countries, February 1989.

No. 2 Emerging Patterns of International Compedtion in Selected IndustrialProduct Groups, February 1989.

No. 3 Changing Firm Boundaries: Analysis of Technology-Sharing Alliances,February 1989.

No. 4 Technological Advance and Organ izatonal Innovation in theEngineering Industry, March 1989

No. 5 Export Catalyst in Low-Income Countries, November 1989.

No. 6 Overview of Japanese Industrial Technology Development, March 1989.

No. 7 Reform of OwCiership and Control Mechanisms in Hungary and China,April 1989.

No. 8 The Computer Industry in Industrialized Economies: Lessons for theNewly Industrializing, February 1989.

No. 9 Institutions and Dynaimc Comparative Advantage Electronics Industryin South Korea and Taiwan, June 1989.

No. 10 New Environments for Intellectual Property, June 1989.

No. 11 Managing Entry Into International larkets: Lessons From the EastAsian Experience, June 1989.

No. 12 Impact of Technological Change on Industrial Prospects for the LDCs.June 1989.

No. 13 The Protection of Intellectual Property Rights and IndustrialTechnology Development in BraziL September 1989.

No. 14 Regional Integration and Economic Development, November 1989.

No. 15 Specialization, Technical Change and Competitiveness in the BrazilianElectronics Industry, November 1989.

INDUSTRY SERIES PAPERS cont'd

No. 16 Small Trading Companies and a Successful Export Response: LessonsFrom Hong Kong, December 1989.

No. 17 Flowers: Global Subsector Study, December 1989.

No. 18 The Shrimp Industry: Global Subsector Study, December 1989.

No. 19 Garments: Global Subsector Study, December 1989.

No. 20 World Bank Lending for Small and Medium Enterprises: Fifteen Yearsof Experience, December 1989.

No. 21 Reputation in Manufactured Goods Trade, December 1989.

No. 22 Foreign Direct Investment From the Newly Industrialized Economies,December 1989.

No. 23 Buyer-Sellez Unks for Export Development, March 1990.

No. 24 Technology Strategy & Policy for Industrial Competitiveness: ACase Study of Thailand, February 1990.

No. 25 Investment, Productivity and Comparative Advantage, April 1990.

No. 26 Cost Reduction, Product Development and the Real Exchange Rate,April 1990.

No. 27 Overcoming Policy Endogeneity: Strategic Role for DomesticCompetition in Industrial Policy Reform, April 1990.

No. 28 Conditionality in Adjustment Lending FY80-89: The ALCID Database,May 1990.

No. 29 International Competitiveness: Determinants and indicators,March 1990.

No. 30 FY89 Sector Review Industry, Trade and Finance, November 1989.

No. 31 The Design of Adjustment Lending for Industry: Review of Current Practice,June 1990.

INDUSTRY SERIES PAPERS cont'd

No. 32 National Systems Supporting Technical Advance in Industry: The BrazilianExperience, June 26, 1990.

No. 33 Ghana's Small Enterprise Sector: Survey of Adjustment Response andConstraints, June 1990.

No. 34 Footwear: Global Subsector Study, June 1990.

No. 35 Tightening the Soft Budget Constraint in Reforming Socialist Economies,May 1990.

No. 36 Free Trade Zones in Export Strategies, December 1990.

No. 37 Electronics Development Strategy: The Role of Government, June 1990

No. 38 Export Finance in the Philippines; Opportunities and Constraints forDeveloping Country Suppliers, June 1990.

No. 39 The U.S. Automotive Aftermarket: Opportunities and Constraints forDeveloping Country Suppliers, June 1990

No. 40 Investment As A Determinant of Industrial Competitiveness and ComparativeAdvantage: Evidence from Six Countries, August 1990 (not yet published)

No. 41 Adjustment and Constrained Response: Malawi at the Threshold ofSustained Growth, October 1990.

No. 42 Export Finance - Issues and Directions Case Study of the Philippines,December 1990

No. 43 The Basics of Antitrust Policy: A Review of Ten Nations and the EEC,February 1991.

No. 44 Technology Strategy in the Economy of Taiwan: Exploiting Foregin Linkagesand Investing in Local Capability, January 1991

No. 45 The Impact of Adjustment Lending on Industry in African Countries,June 1991.

Note: For extra copies of these papers please contact Miss Wendy Young onextension 33618, Room S-4101