ReprtU 17o . J0 A ! -1 7 This report may not be published nor may it be quoted as representing the view of the Bank and Its afiliated organizations. They do not accept responsibility for its accuracy or completeness. INTRNATIONAL BANK FOR RECONSTRUCTION AND DEVELOPMENT INTERNATTCNAL D;VELOPM;NT ASSOCIATION THE ECONOMIC COMPARISON OF HYDR TCWr10TC P EC WITH ALTERNATIVE DEVELOPMENTS OF THERMAL ELECTRIC POWER July 15, 1963 Economic Staff Prepared by Herman G.Van der Tak TABLE OF CONTENTS Page No. Intrducion............ .......... ................ 1 A.* Comparison of hydro and thermal power alternatives: General shape of the proble .......... 0........... .. 2 B. Impact of variations in costs and prices on return nJ Cj Laa hroIULUW iLve stLeUJ.. ....*I.... . .* . . ........... L U-r_ U! - U -.L.UW ±UL LU.! --- 2 -- - Ipact of different cost estimates0a.................. 6 C. Impact of different growth of load on return on additional hydro investment...8.......................... 8 Higher load - actual case.......................... 8 Stylized examples of different patterns of load growth. 10 Effect of different cost data........................ 12 Curvilinear growth of load........................ .. 13 D. Summary and Conclusions..... ................ ....... ...... lb - ii - TABLE OF CONTENTS (continued) TABLES 1. Cash Flow of Costs - Hydro Development - Lower Load 2. Cash Flow of Costs - Thermal Development - Lower Load 3, Cash Flow of Costs - Hydro Developme*nt - Higher load 4. Cash Flow of Costs - Thermal Development - Higher Load 5. Summary of Present Worth of Costs (Lower Load Development) 6. Present Worth of Costs: Comparison of Higher and Lower Load Development, 1962-2028) 7a. Different Patterns of Growth of Load: Simplified Cash Flows of Alternative Hvdro and Thermal Tnvestments 7b. Different Patterns of Growth of Load: Simplified Cash Flows of Alternative Hydro ;qnd Thermnl Tnvestments 8. Present Worth of Costs of Hydro/Thermal Alternatives for Different Loading Times 9. Influence of Different Proportions of Basic Costs on Relation Between Rate of Return and Loading Time 10a. Some Stylized Curvilinear Patterns of Load Growth: Simplified Cash Flows o*f Alterna4-4-Tive - Hy-r anThema -Invetmnt V 011 J.L% Jj~V0 j -jV.LJ L1dMQ.LVt; U .u ciu 1IIermdd± J-1Vt::dU[1U11iL1 10b. Some Stylized Curvilinear Patterns of Load Growth: Simplified Cshol Flows Uf A-lUeVnative Hyuro and Thermal Investments CHARTS 1. Comparison of Cash Flows of Hydro and Thermal Development - Lower Load 2. Illustrative Patterns of Load Growth 3, Relationship Between Rate of Return on Investment in Hydro and Length of Loading Time of Dam 4. Return on Hydro Investment for Different Load Growth The Economic Comparison of Hydroelectric Projects with AlternpAve Devnrments of The-rmil lpnetri Pnwnr _1. The esse=ce of the ecooicealaio_ roesisdtemnigwhte ..J. W 44 wat; '.1 iL' evczJ4UVL L JJL 4ut, - L. D± ~ a project involves a better use of resources than its possible alternatives. I n imany cases lChe al1 terna1 -tie thmele ma no be cla and the compari--_ ---- 1 -_1- ___34 i..L cl± Ul tVU E.J S~1 v U11tj111SCJvU MadY' 110 u 1A- kI_Ld_L cU ulU LULJ1;, I.- sons have to be approximated. This is the purpose of using a minimnum rate of return as representing what capital might earn in alternative uses, or what is known as the "opportunity cost of capital". If a project is excected to yield less than this minimum, it should not be undertaken for there are presumably more productive uses for capital elsewhere. The case where specific alternatives are under consideration representing different ways of producing the same good. or service whose need is given is a special ty-pe of this general problem, In this case the immediate comparison is clear. The choice is limited to the given alternatives, one of which must be selected, The "opportunity cost of canital" comes into the problem in helping to determine which of the alternatives involves the most economical use of resources in the light of general investment opportunities in the economy. 2. An excellent example of this special type is the comparison of alterna- tive methods of producing electric power. A KWH is a KWH, whatever way it is produced. The question is which method of generation is the cheapest. This is an important problem in practice since it is at the basis of the economic appraisal of all hydroelectric projects, In some cases the answer is obvious. The cost of fuel may be very high and the cost of constructing hydro plants very low. In important cases, however. more detailed analysis of the alternatives may be essential to the appraisal and although the problem of determining the least expensive solution may be simple in concept, the analysis itself may not be so. 3. It is the purpose of this paper to set down in a systematic way a logically correct method for handling +he economic comparison of alterna- tive power developments. The discounted cash flow method of computing returns which is used here has come to be generally accepted ir recent yearsq There is no need to give a detailed justification of this approach at this date. that has alrady been done most .i cpetel b othes.1./ Howver, there is merit in working out an example of a specific and imprtant applica- tion. By focussing on the techniue itself ad pn which the analysis may be simplified this paper may be of particular use to others farer r?i+.h a4milov- a il problems. t s--hu gowithou si that the less an appraisal mission has to concern itself with problems of method, the more it can concentrate on the essential aspects of its analysis. =/ See, for example, "Project Evaluation I, The Return on Capital", i.B. King, EDI Seminar Paper, 1960; Principles of Engineering Economy, E.L. Grant and W.G. Ireson, N.Y., 190; Water Supply, Economics, Technology and Policy, J. Hirshleifer, J.C. DeHaven and J.W. Milliman, Chicago 1960. kbee especialy Chapter VII.) - 2 - . Firthermore if the method is well understood and if some preliminary appraisal has already been made by consultants, the sensitivity of the results to changes in key data can be worked out in advance so that effort in the field may be concentrated on the most critical items. if lack of provisional data prevents this, the same procedure can be applied to the mission's own preliminary results, so that critical variables may be pinpointed at this later stage and subjected to further scrutiny. In any case such analysis is required to determine under what conditions, if any, the project is justified. This is particularly important if estimates of future developments have to deDend on decisions which have still to be made and which could materially affect the attractiveness of a project. 5. This Tper deals with the specific problem of comparing alternative developments of a power svstem to supply a demand for power (W) and energy (KWH) that must be met.,/ It is essentially a comparison of a hvdro with a thermal system of development However, the method employed need not necessarily be confined to comparisons of power proiects- Any nossieh1 st of PlternativPs coul b'e compared and in fact the method coul.d equally well be applied to any number of alterna- ivesv 6. To mae the demnstration realistic the data used in this paper are in large part based on the preliminary work sheets of an -ctual project. The following section briefly discusses the application of discounted cash flow methods to a comparison of hydro and thermal system developments, nihsecia reeec 4to 4te approriat len- t o1f 4-h,e cash- lOw. It3i followed by an analysis of the effect of variations in cost estimates on the r l fulUions, Tle 1inal part deals with UIte effU t of different patterns of growth of demand for power on the economic appraisal of the project. A. Comparison of hydro and thermal power alternatives: General shape of the problem 7. In comparing alternative ways to produce the same output, the economic selection problem is simply to determine which way is the cheapest. In the particular problem under consideration, it is assumed that the demand for power should be met.2/ The question is not whether to invest in power or in some other sector but rather which type of power investment represents the best use of resources, given the decision to invest in power. In other words, benefits from the investment however measured are the same regardless of which system of development is chosen, only the costs are different. 1L/ In t case considered here it is assumed that there are no irrigation, navigation or flood control benefits associated with the hydro project. Where this is not the case the problem of analysis is more complicated since the investment cost of the hydro power cannot be determined simply. 2/ Techniques of estimating future demands for power, and of designing corresponding system developments, are not discussed here. This paper is concerned only with the analysis of the data thus obtained. -3- 8. The comparison of costs between the two alternatives is not atraign- forward, as alternatives have decidedly different patterns of expenditures over time. Typically the hydro alternative will involve higher expenditures in the early years and the thermal alternative higher expenditures in the later years. In a simplified way, the choice can be stated in term of whether higher investment costs of hydro in the early years are or are not justified by its lower operating costs in the later years.1/ The only way a proper comparison can be made between series of expenditures with differ- ent time patterns (cash flows) is by making specific allowance for the time factor and summing them up as of a particular point in time. This is accomplished by discounting the two cash flows to a comon year. The sLn of the discounted values, that is the "present values", can then be compared directly. This procedure involves three types of decisions - what is to be included in the costs or expenditures, over what length of time should the computations be extended, and what interest rate should be used for discounting. 9. In the calculation of costs only actual expenditures on goods and services should be included and these should be entered in the year in which they occur. Financial charges and accounting items, such as interest, depreciation and amortization, should be excluded. Depreciation and interest on rAittl invshmPnit ar taken inton acnount by the discounting procedure itself. Amortization and interest on loans are financial items dependent on specific ftrms of finaning and not inherent in thA nature of the project. They are not relevant for the economic appraisal. 10. The length of time over which the cash flow should be extended depends onn circumltance, a d fli in +o, par q Then firs+ "M peir r sV0Q the M. .3 -J -~ -OL* - LJ3 -SA t -S .~ I _ _ - I_ - - _. _- years of expansion of the system. This should be continued until the year where after th e relative cos ts o f al ternative W6yas of furthe epn t h system is no longer significantly prejudiced by the investment decision now tUke. Thi U.LLieLae Vh aI_ dLL-V ICLU± Ve sysm VC developmen-ts to Ue com11Ipared at this time. Often this will be the year of full utilization of the power capacity of a hydro dam.2/ For the purpose of calculating the return on additional hydro investment, expansion of the system stops in this year. The cash flow, however, should be further extended, for a second period which should extend until differences in costs of operating the alternative systems at the costntleelrechdbeam isiniicn in terms of their discounted present worth. These costs involNe not only expenses for full maintenance and current operation, but also for replace- ment investments, the latter being entered in the year in which they fall due. This applies to necessary replacement both of existing plant and of new plant installed during the expansion period. Replacement does not necessarily consist of exactly the same units as previously installed. It may be more reasonable to replace them by units of a larger size, more appropriate to the level of output reached in the meanwhile. For thermal plant, lifetime 1/ This is illustrated in Chart 1 for a complicated and realistic case; see paragraph 14 below. 2/ This is not necessarily so. Buildinf the dam may make possible a later second stage of the project - or construction of a dam elsewhere in the same river system, providing cheaper additional power than from alternative thermal plants. As long as the present investment decision significantly influences such later investment choices, the expansion of the system should be extended for purpose of appraisal. -4 - is usually taken to be 30 years and for hydro plante 60 years. Life of dam and reservoir may be longer still. 11. Finally, thesa flows of costs should be compared. The same answer may be obtained by different methods. One method is to find, by trial and error, the rate of discount which equalizes the present worth of the two cost streams to be compared. Alternativel. the same result may be obtained by deducting the thermal cost stream from the hydro cost stream, thus obtaining one stream of positive and negative items, as shown by the dotted line in Chart 1. The positive items are the additional costs of the hvdr alternative. and ocnur mainly in the earlier years; the negative items are the savings in cost of the hydro alternative ("its benefits"). The Hiqnumint ratp uhi-r-h Aanlivuqn the nrmeent unrth of the nonitive and of the negative items will be the same as the one which equalizes the present value of the two separate cost streams and may be thought of as the rate of return on the additional (initial) investment in the hydro alterna- tive. 12. The- rate of e tetir" huswo should e cpred wh th+ etatedn opportunity cost of capital (the so-called shadow rate of interest) in order to assess Whlethmer the return Js paeu+ Al+en+4irly, +Mhi se. rate (opportunity cost of capital) may be used to obtain the present worth uIlt U1 D~A U QLVCL 1 Vaieo .L Ul=-I VJWV G6.LV11LLL1.LVUQ* L~ JIsJ 1U '.L&uuc V v L.,ULA AV1,C lowest cost, in terms of present worth, should be considered the better project. B. impact of Variations in cos's and prices On returin o additional hydro investment 13. The foregoing exposition has been concerned only with the form of the calculations. It assumes that all the necessary data on costs and markets are given. In actual appraisals, however, the available data are often incomplete and always of varying quality. For some items, reliable cost estimates may be relatively easy to obtain; for others, data may simply not exist. In some cases, it may be possible to relate the projections of demand to firmly-based future trends in its main determinants; in other cases this may not be so, especially if the future demand is expected to be heavily dependent on particular investments in power intensive industries, which may or may not take place at a given time. Furthermore, the cost of foreign exchange may be undervalued and the cost of labor overvalued in terms of their real cost to the econor. Thus the appraisal must be made on the basis of data with widely differing degrees of reliability. It is necessary to appraise the data, improve them iihere possible, organize them so as to give an answer within the limits of their accuracy, and so come up with a judgment on the overall economic merits of the project. It is thus obviously important to be able to determine the effect of variations in the main cost and demand parameters of the problem on the overall outcome; only then can efforts of estimation, and necessary judgments, be focused on the most critical elements of the appraisal. This part of the study (B) will consider ways of estimating the impact of variations in costs. The influence of different demand patterns will be taken up in the final part (C). Use of sub-cashflows for cost coMonents LL. Tables 1 and 2 show detailed cash flows for the hydro development and thermal development,1/ respectively, both to meet the "lower" ioad.W/ The column "total", represented in Chart 1, is the only one required for calcu.- lating the return on the higher initial investment necessary in the hydro development., As will be noted,, the present worth of the cash cost streams of both hydro and thermal development are about 1260 thousand, when dis- counted at 1 1. This indicates that the return on the additional hydro investment is 7 -, For a convenient check on the extent to which this outcome is altered if some of the cost items were different, the cash flows can be broken down by components as shown in Tables 1 and 2. The degree of disaggregation, and the categories of cost selected, depend upon the particular case to be investigated but, as a minimum, such items as dam, hydro units, thermal plant and fuel costs should be specified. The various sub-cashflows, for each of the cost components, are then discounted at 7!L. The results are shown at the bottom of Tables 1 and 2, and summarized in Table 5. The present worth has been calculated separate1- for costs occurring in the period 1962-1980 (the exvansion period) a.d 1981-2028 (the constant period). Thus it is possible to distin-uish the influence of costs occurring in either period on the return obtained. 15. Tables 1 and 2. and sumarv Table P, also show the present worth of the cost flows if discounted at 82%. Normally at least two calculations at different discount rates have to he maie in order to Arrive, hv trial and error, at the rate which equalizes the present worth of the costs of the alternqtive. These calculations also ive a rough indication of what is a "significant" change in the underlying cost estimates. Table 5 shows, for eximple, that a difference in discount rate of one per cent (between 7- and 8 ) results in a difference of "70" in the total present worth. By crude linear interpolation tis ndca es that a dj ifferenC o "3" in present worth is equivalent to a change of one-half of one per cent in the rate -Of return for variationS around A8%. 1 "vFomTle x,L iu isO apparent that the- omeO deeddhaiy itte present worth of the cost estimates of the dam, hydro units, thermal plants, fuel., And possibDly operating cost of production pl1ant 4- or ; inst-ce a 20-%v reduction in the cost of the dam would change the return on the hydro unvstmn byu about one percentage point. A- rse of close too 30 in theL L LX.VO 1UV fuel price would have the same effect. It should be noticed that the "weights" - i.e. the present worth of the various cost items - decline at higher discount rates, so that somewhat greater percentage changes in costs are necessary to produce a change in the return of, say, one percentage point, than those indicated by the present worth figures obtained at 7%,. The effect is symall, however, for small changes in the discount rate, except for items such as fuel costs where a large part of the difference in present 1/ Hydro development and thermal development refer to alternative system developments; the hydro alternative does, in fact, include some use of therma plants, as may be seen from Table 1. A more rapid growth of demand for power - the "higher" load - is discussed in part C below; cf. Tables 3 and 4. - 6 - worth between hydro and thermal alternatives occurs in the later years (1981-2028). Some of the other items - for example, the operating cost of the transmission lines - are small so that even a 50% change in the estimate affects the total present worth (and the return) only marginally. Others, such as investment in transmission (230 kv) and frequency conversion, are substantial, but any change in the cost estimates affects the thermal and hydro alternatives almost equally. Similarly the possible impact of under- or overestimation of the large item "operating costs of production plant" may be much reduced by offsetting changes for bcth alternatives.l/ 17. Offsetting items, in terms of present worth, may obviously result simply from the same item occurring in the same year in the basic cash flows of both alternatives. In practical application, such items would have been eliminated beforehand, (that is, before making the present worth calcula- tions) in order to economize on comnuting time. Comparison of Tables 1 and 2 will show that this would eliminate columns "transmission 115 kv" and "frequency conversion", and a good many items in the columns "transmission 230 kv" and "thermal plant".2/ Items of the same order of magnitude in thP same var will -imilarlv (Trptly,) canel ont. Offsetting itAms in terms of present worth may also result, however, from the discounting process itself. Thus the+ di ffe ronrce in fel csnts is much reduced P the fact that costs are roughly the same for both alternatives in the early yea_rs n r rin ir yif-fv, -rant1r lao+.er n Ypect o,+ %f di ffeen c+ s +simte 18. Costs different from those shown in the basic cash flows of Tables 1 and 2 may be due to under- or overestimation of physical inputs required, and/or of prices of inputs. Amongst the physical inputs, it is especially difficult to estimate accurately the input requirements of the dam. Difference of opinion is also possible on the fuel efficiency of thermal plants and other itenE. It will be clear by now, however, that the quanti- tati ve sivnificace of such di fferences rn Pslv h analsvqPd by reference to Table 5. If, for example, the operating costs of thermal plant (exclud- inr NP-l) hnd hen systeatically underestitnated by 2 their present worth at 7 would have to be adjusted upward by 25%, and this would be equivalent to an increase of about 1% in the true return on hro investment. It also becomes easy to see, for example, that under-estimating labor efficiency in therrl plants hy 20A in thie pe-rioi 1Q9An and oer_ estimating it by 10% in the later period 1981-2028, would result in raising the return by close to one-half of one per cent. 19-s. Simiar.A.ly m , c easily i tigat the effect of using prices o)thellOr than those used in the basic cash flows. There is bound to be some unccrtAint"Yr in the estimates of fuur marke pries The- anyt -a LL~.~ ~iC1J.y~Li1 &1~ Q LiLLIL L J. . LUULA.LX7 11L %.UZU P.L.L%.VQ L.LL CLAdlU YOU Liluayi. also wish to determine the effect of using so-called shadow prices - far example, for foreign eange, ag res ful, e tc.P - if I has reason to think that market prices do not give a reasonable approximation of i7-Thisq isi t.rueo if +.he uiner_oestimote= is dhume% oJth wnage -na+e, aff -nectiAngr both alternatives. The error may be due, however, to different efficiency in use of labor in thermal pnfo ts, afecng vI mil +1 er altentive (see below, paragraph 18). The same composite item "operating cost of p ir .dutio pla nt" 4n h cash .LJw of both alenvesLL i omwIa I - 11" Q leading as it refers largely to different costs - for thermal plants and ydo lans espctvel. T+ would have been +-fral 4o4distinguis those in the cash flows. 2/ Cf. footnote 1/ above. economic value to the country as a whole. To illustrate, what is the effect 0 a revisi5on of ta eUXL11n ratdo UUWLWdbyL LJ %J oash eu on hydro investment? The outcome depends, of course, on the foreign exchange component of the various cost items. Let us assume t1at in our example the foreign exchange components and thus the increases in costs resulting from lowering (devaluing) the exchange rate by 20% through- out the period 1962-2028, are as follows: Increase in cost resulting from Foreign exchange 20% lower foreign Item component exchange rate per cent per.cent Dam 50 10 Hydro units 80 16 Thermal units 75 15 Transmission 80 16 Other 0 0 20. The cost of the hydro alternative in terms of present worth at 7A%, therefore, will rise by 10% of 331 (dam) plus 16% of 265 (hydro units) plus 16% of 105 (additional transmission)-7-91; and the cost of the thermal alternative (in terms of present worth), will rise by 15% of 361 (additional thermal plant) = 54. Thus the relative cost of the hydro alternative goes up by 37. and the return on investment in hvdro goes down by about one-half per cent. 21. In similar fashion one can investigate whether a shadow wage rate for unskillnei labor makes murh differenf- to the return on the hvdro investment. If, for example, unskilled labor amounts only to 2% of the total cost of the darnm - which is an actual though probably exvtrpne case - an adjustment in the wage rate can at most lower the cost of the dam by 2% - with a negligible effect on the return. In such a case it is, Therefore, n necessary to devote time and energy to trying to find a proper value for the shadow wage rate of unskilled labor. 22. The question may also arise whether the market price for cement is appropriate for the economic evaluation of the alternatives. Large over- capacity in a local cement industry may argue for using a lower price. Is this significant? Once again, it depends upon the "cement content" oL W11 Udm. I. this is, say 1, a 1 UUU2ULUL Jrci in te U1Ln priCe lowers the dam costs by one per cent, i.e., an insignificant amount. Relatively small adjustments in The cement price are therefore irrelevant. Even a 50% reduction in the cement price results only in 4% lower dam costs, and an increase of less than one-quarter of one per cent in the return on the investment in the hydro alternative. 23. Thus the order of magnitude of the impact of various adjustments in input prices on the return can be established. This kind of analysis brings out whether further refinement of the estimates made is worthwhile or not. Adjustments so small as not to affect the return calculation are irrelevant, and the analyst is tetter employed trying to estimate the crucial variables. 0 -u- 24. As already pointed out above, one of the crucial variables in hydro/ thermal comparisons is the price of fuel. In this particular case a 15% change upward or downward in the fuel price changes the return of the hydro investment by approximately one-half of one per cent. The form of the analysis also permits experimentation with more complicated changes in fuel prices, varying over timea1/ If there is reason for thinking that fuel prices will later, say, from 1981 onward, be higher or lower than at present, the quantitative significance of this can easily be established.2/ Present fuel costs to the economy may be low because of overcapacity in fuel production itself or in transport facilities. In due course, over- capacity may disappear, or alternative uses may develop for a fuel such as natural gas, and a higher price may become appropriate. The present analysis can show how sensitive the return on the hydro investment is to such changes in fuel prices. C. Impact of different growth of load on return on additional hydro investment Higher load - actual case 25. The return on the hydro investment will tend to be n2gher, of course, if the capacity of the dam can. be fully utilized at an earlier date. The initial capital costs of the dam will then weigh less heavily on the hydro alternative. This is illustrated in Tables 3 and 1, which are similnr to Tables 1 and 2 except that the system development is geared to a more rnpri -ratr of growth of he power load. As a re ,- h _apc- of the J'a - --- - , -j ..I w1c; V VIIZ dam is fully utilized by 1979, and not by 1981 as in the previous example. Cocqetl h etr nthe addLU%ItIa-l ydroU JInVestm-en-tu is somewhIILat higher, about 8 %, as will be seen by comparing the figures for present worth of total cost, at 7-% and 8% respectively, shown at the bottom of the tables. 26. Comparison of the present worth of cost components for the "higher" and "lower' load system development (summarized in Table 6), indicates more precisely the reason for the greater return with the "higher" load. -Uith more rapid growth of the load, the present worth of costs of hydro units rises somewhat for the hydro alternative, and the present worth of - -, - --- -N ---- I - - - . costs of thIUrmal plant rises rather more for the thermal alternative. Operating expenses of production plant increase slightly for both alternatives, but largely cancel out. The most important difference, however, is the increase in fuel costs in the thermal alternative, offset only to a minor extent by an increase in fuel costs for thb hydro alterna- tive. The relative increase in fuel costs with "higher" load growth accounts for more than two-thirds of the total relative increase in cost (in terms of present worth) of the thermal alternative. 1/ In fact, the basic data used in this note, incorporate such changes in fuel prices over time. 2/ In our example, this is only convenient in two periods, 1962-1980 and 1981-2028, but a further breakdown by periods could, of course, easily have been provided. 27. From the general set-up of the problem - see paragraph 10 above - it might be thought that the period from 1981 onwards does not play any role in these differences. It will be remembered that in the "higher" load growth variant, the system is kept at a constant level (for purpose of return calculations) from 1979 onwards, the year in which full capacity of the dam is reached. And similarly, from 1981 onward for the "lower" variant. There may be further complications, however. Reference to Tables 1-4 shows that, in our example, about half the difference in fuel costs between the higher and the lower load developments occurs in the period 1981-2028. This results mainly from the higher load factor which, in this case, is associated with more rapid growth of the load. In terms of MT the systems are the same, after 1981, but with the "higher" load growth it happens to require more KWH and, therefore, more fuel for the thermal alternative.l/ This effect is significant enough, in this case, to account for a difference of about one-quarter of one per cent in the return on additional hydro investment, between the higher and lower load curve (out of a total difference of about three-quarters of one per cent). A higher load factor is not an essential feature, however, of a faster rate of growth of the load. It depends on the reasons for the more rapid growth, i.e., on the growth of the components of the load. Conversely, different load factors may be associated vith the same expansion of the load. A higher load factor tends, of course, to make the investment in the hydro alternative more attractive. as it raises the fuel nostq of the thermal alternative while costs of the hydro alternative remain the same. The quantitative significance of this can he analyed along the linas previoisly indicated. In the original example (Table 5), an increase in the load factor by_ say, 1) per cent over the whole periodA962-2028, raises the fuel costs of the thermal alternative by 1I4 per cent - i.e., the return on theaddtinalhyrov- 4nvestment4 b one-hl of4%- one per cent. 28. The "pure" effect of a faster growth of the load on the re turn on additional hydro investment is small in our example - about one-half of one per cent.. GiVen the many uncertaintie of the- esime inove .i 17' 1 'J ."'-S* ' A~ILC6LA~y LL"&%,VL . L41OJqs J. LALMU I VO4J.41ULUVO LA1VU.LVVU, .L U would appear therefore that a delay of two years in fully utilizing the dam 12 years rather than 10 years after the dai is finshed - results in an insignificant difference in the return. In view of the fact that the underlying load projections used in this case show the "higher" load in 1980 to be more than 25% higher than the "lower" load, this may be somewhat surprising. The explanation is to be found in te shape of The curves representing the growth of the load. The follo.ing paragraphs use various heavily stuylized examples to illustrate the effect of differences in load growth on the return on additional hydro investment. 1/ To a minor extent, the differences between higher and lower development are also due to the imnossibility in the nAlulMtions of mittin off the expansion of the system at exactly the same point. 2/ A neglirible difference results also from a slight shift forward V n the replacement investments in thermal plant, - 10 - Stlized examples of different patterns of load growth 29. Chart 2 depicts the basic patterns of load growth used in these examples. In the case represented by Curve I, for example, the load rises from 500 MW in year zero ("the year of decision") to one thousand NW in year 5, in which the dan would be finished, and to 2,500 MW in year 25. Tables 7 (a-b) show simplified discounted cash flow calculations for hydro and thermal system developments fitting the various cases represented in graph 2. The dam is assumed to take 5 years to build, and to cost 1000 (all incurred for convenience sake in year 3); a hydro unit to cost 100, and a thermal unit 150. Additional cost (including fuel) of operating thermal plants rather than hydro units is assumed to be 1/15 per TW. Both thermal unit and hydro units are 150 MW. Total capacity of the dam is 10 units or 1,500 MW. Lifetime of a thermal unit is 30 years, of a hydro unit 60 years, and of the dam more than 60 years. The same basic cost and size assumptions will be used throughout the remainder of this paper, unless otherwise noted. 30. The present worth calculation shows that the return on investment in hydro is about 8% if the load grows as represented by Curve I (see bottom of Case I, Table 7). It should be noted that the return would also be 8% - as the cash flows would be exactly the same - if the load were to grow as in Curves Ia or Ib, their very different rates of growth notwithstanding. In Case Ia the load quadruplesbEween years 5 and 25, and in Case Ib it only increases by two-thirds& Calculated from year zero, on the other hand, the rate of growth of Ib is much greater than that of la.l/ These differenc-es in rates of growth are irrelevant. however; what counts is the absolute increase in the load from the year that the dam is finished, not from the time the estimate is mAe or the construction of the dam is started. In our example, the absolute growth of the load after yar determines the speed withh %hih the dam can be "loaded" .2/ The much greater absolute increase in Case Ib between year 0 1/ Case I is intermediate in between these two extremes. 7/ The loading time of the dam does not depend solely on the growth on the load. Possible replacements of existing thermal plants may provide additional scope for using hydro power, and thus shortening the time needed for the dam to get fully loaded. The importance of this factor depends, of course, on the age structure of existing plant in year zero. Thermal plant installed during construction period of the dam (of. 1/ p.11) only plays a role in this if the loading time of the dam is very long (more than 25 years); otherwise their replacement affects both the thermal and hydro development equally. The effect of "replacement load bonuses" on the return can be analyzed by simply adding them to the growth in the load derived from estimates of future demand for power. - 11 - and 5, i.e. during the construction period, does not help.2/ The absolute annual increases after year $ are the same in all three Cases. I. a and 1b: hence, the same return on the additional hydro investment.2/ 31. Obviously, it is not simply a question of the total "loading time", hut alqo of +he QInn of n-h lo ^MA rothcurve. Cuiiy"re T TT ndr TT (cf. Chart 2) all show an increase by 1,500 MW between year 5 and 25.3/ However, inemnt in hyror isn, obviouly -monre- amvantageu in Cas II:T discounted at 8% the present worth of costs of thermal power far exceeds that Y o L hydro pwe. Eprmetto shows th-1at the internal rate of return is about 10%. Case Ha is obviously the worst - if it were decidU Uo put in the dam immediateLy, althoughe niaeed only10 years 1latr - with a return of only 6%. Case IIa is indeed a text book example of the need for postponing the investment: if construction is postponed by 10 years so that the dam is ready in year 15, the pattern of loading is the sarie as in Case II, and so is the internal return of 10% (i.e., higher than for Case I).h/ 1/ Different rates of growth of load during the construction period affect. of course, the need for additional poxer capacitn the inte'rim period. Our heavily stylized examples assume that this does not significantly affect the system development from year 5 onward. The faster rate of growth in the interim period is not necessarily an advantage; i t may absorh e%is tng excess capacity; it may also necessitate new invst- ment in excess of load requirements in year 5. 2/ These considerations also caution against overestimating the influence on the return of an increase in the service area by interconnection. In comari,n JnEg -ro,W,th o f th' ,e interconecte and the non-iLn'Lterconnrected"-u locad, it should be noticed that the starting point of the former is higher. The -P .- - - 'i gap beteen -the two loadS af.ter saiC Jy, overestimates, therefore, the difference in their absolute increases by this difference in starting level. The higher starting level broadens the base, of course, so that any given rate of growth of the load results in a larger, absolute increase. SL..LcL L,Ly speakning, thU eU urves Uave a UL.LeretIU loaU.Uig Uime; years in Case I, 10 years in Case II and 5 years in Case III. Cases II and III may be thought of, however, as "exaggerated" examples of load curves rapidly rising in the early years and flattening out later, so that they also get fully loaded after 20 years. h/ This does not mean that both are equally good hydro investments. If the rate of interest is, say, 8% the cost advantage of hydro over thermal is much larger in Case II than in Case IIa, as may be verified by comparing the figures shown at the bottom of Table 7. This simply reflects that, in that case, a return of 10% as of now is better than the same return as of 10 years later. - 12 - 32. As seen iust above, shortening of the "loading time" of the dam from 20 years (Case I) to 10 years (Case II) raises the return in this case from 8c to 10. Further shortening of the loading time to 5 years (Case III) raises the return further to about 13-$. Clearly, the mvimiim rp+.nrn i rached in t.he CaRM of instantaneous loading, in year 5. of the dai. In that case additional investment in the hydro alternative of 1n00 + 1o0 - 1ff00l - c400 given avingn in operating costs of 100 per annum "forever after"1ii.e., a return of (nearly) 20%. These results are presented graphically in Ch a 3 (See Curve A: origLnal data) uhich is suggestive of the relationship existing between the loading time (with r straight-line~ lo~ad growth) ad the~ rehu'rn o-nn the inve.tment in hydro power. The impact on the return of a year's delay in reaching the fulcapacit of th da becme less th loge it take. A he level 4. LV,~j.P&4.I, LJ W.4I UCU11 ULJ1V1LQ .LUQO kAX JW&r - - - - - of a loading time of 5 years one year sooner or later is equivalent, in tisL example, to U iference in tereturn of the order o ne rct But around a 10 year loading time it takes a delay of roughly 2 years, and at a level of 10 years a delay of some 4 yearsj to have a imLar effect. This would seem to suggest that small differences in rates of growth, both of which result in the dam reaching f\ull capacity beyond, say, 10 years, are not very important. The return appears not to be very sensitive to such differences in the load growth. Much more importance, of cUurSep attaches to 7,bat happens in the early years. Ef"cot of different cost data 33. The particnlar result obtained here depends, of comse., on the cost data used in this example. With different cost data for the dam, hydro units, thermal plants, and/or additional operating cost of thermal plant, the return on hydro investment - and the sensitivity of the return to changes in loading time - will be different. For example, if the dam costs are raised by nearly hO%, the maximum return, at instantaneous loading, drops sharply from 20% to 12%. But a 10 year loading period gives then a return of nearly 8% (as compared with 10% before) and a 20 year loading period gives a return of about 6% (as compared with 8% before). This is illustrated by Curve C in Chart 3, which also shows the returns obtaining at different loading tines if dam costs are raised by nearly 20% (Curve B) and by nearly 60% (Curve D).2/ These results suggest that investments in hydro alternatives with lower maximum ("instantaneous loading") returns are much less sensitive to delays in fully loading the dam capacity, but that the difference is small for loading times beyond 10 years. 34. A further check was made of the influence of different proportions of the four major categories of' costs distinguished here on the return on hydro investment for different loading times. Obviously, an "instantaneous loading" return of. for example, 20% as yielded by our basic data. could also be obtained if an increase in the cost of the dam by, say, nearly 0% were offset by an increase in cost of thermal plant (by about 9 per unit) or in additional operating cost of the thermal development (by about 75% per NW). Perhans more surprisingly, the shape of the curves showg, for Negecting the replacement cost of thermal plants in year 35. P The present worth of costs at various discount rates are given for Cases I, II and III in Table 8. - 13 - these changed cost data, the relationship between the rate of qturn on additional hydro investment and the length of the loading timeV is not very different from those daown in Chart 3. If the increase in dam costs is offset by higher costs of thermal plant, so as to yield the same instantaneous loading return, returns for longer loading times tend to be somewhat lowr than before: if offset by higher additional operating cost of thermal development, returns for longer loading time tend to be some- wtl-nt higher than before_/ Roth differences are small, however, - amount- ing to very roughly some one-half of one per cent from the original rate of rrtinrn -nd -hm thrA cirvP. run roughly narallel from year 5 onward. at least over the relevant range of years.2/ This suggests that the instant- aneous loading rate of retu-ir.n - which can always seedily be calculated - gives a useful indicating of the return for longer loading times. Thus it becomes possible to see how .rica the demaind nrniectinn is for the outcome of the return calculation. Curvilinear growth of load 35. The load curves considered so far have one feature in common: they all Show growth Jin c*ns4.ant stPgtln ashion_ from the, time of d.±± ~Ii UW ~UWI.,IL liiAI~L U~1 OU ,XL A .L L L L A, L~J~ 4.1 --A' completion of the dam - over the relevant range unti1 the dam is fully loaded.4/ Some imprini1 U te riturn U on addi hj41oyL 4 iv Uj. with load curves having "curvilinear" expansion paths may be obtained by inspection. It is obvious, for example, that growth of the load intermediate between the cases represented in Chart 2 will result in an "intermediate" return on the additional investment in hydro. The results of some experi- ments alon;, these lines are shown in Chart 4. Thin lines represent the previous Cases, I, II, Ha and III, with their respective rates of return (based on the original cost data of Table 7) written in along side. Cases lib a q i11a, intermediate between Ii and III, nave a return of about 111 and 11 respectively, as compared with 1015 far Case II and 134' for Case III. It should be noted that the return in Case 1lia is higher than in Case l10, although its "loading time" is longer - 10 years rather than 5 years; this is outweighed by the higher load in the early years. 1/ It should be remembered that the whole argument here is based on "straight- line" growth of the load. C1 ±l., UA .LUd U.L~LU11 Ott LAJ U' UILU 14.L_VWLU1rv LU14ux l ±Lc%LL1X, u'"Ile vei'-L. lower costs, in terms of present worth, because costs are delayed, but to raise them because the discount rate (internal return) becomes lower. On balance, this lowers cost of thermal plant, in terms of present worth, and raises the additional operating cost of thermal development; cf. Table 9. For "fuel", the "discount rate" effect outweighs the "delay effect", as the bulk of the cost occurs in later years. Thus an increase in cost of thermal plant, sufficient to compensate "instantaneously" an increase in dam costs, falls short if the loading time is longer - so that the return on hydro is relatively lower than on the original data. And vice versa for additional operating cost of thermal development. 3j The relevant data on present worth of costs, varied as indicated, are sunarized in Table 9. # / This applies also to Case IIa with the proviso that the starting point of its growth is delayed by 10 years, after completion of the dam. 5/ The basic data for Cases II b and IIa and other curvilinear cases referred to below, are given in Table 10. - 14 - 36. A somewhat more difficult exercise perhaps, is the attempt to guess the return on adational hyrho investment in cases which "cross over" the straight-line growth cases. Cases IVa and IVb have rapid initial ro.4h of e load, anm innreAe thereafter, so as to reach full capacity only after 20 years. Once again, the importance of the early years stands out. Case IVa has about the same return a Case II. and Case IVb roughly the same return as Case III, although the respective loading times of Cases Iva and IVb are much longer. Inversely, the in- fluence of slow initial growth of the load and rapid increases later, can be seen by comparing the with benchmarks of the return on additional hydro investment in extreme cases of "delayed instantaneous loading" - shown along the horizontal axis of Chart h. It is apparent that rapid increases in the load after, say, 10 years, have only a marginal effect on the return. D. Summary and Conclusions 37* This paper has demonstrated a systematic and logically correct method for comparing the economic merits of alternative power developMents. It has shown how the different cost streams involved can be compared by dis- counting them to obtain their present values, and it has indicated the critical nature of the discount rate used. It has noted that the discount (interest) rate which makes the present values of two alternative cost streams equal is a measure of the return on the additional investment in one (hydro) resulting from the savings in operating costs (over those of the alternative thermal system) for the life of the project. It has shown how to appraise the sensitivity of this return to changes in key data of costs and demand. In particular, it has illustrated a convenient way of assessing the impact of changes in individual cost items on the return by breaking down the usual discounted cash flow calculations by cost components and periods. In this way the sensitivity of return calculations to different estimates of input requirements or input prices can readily be seen and the crucial cost variables can be identified. 38. While variations in the estimated value of inputs - dam, generating, equiPment, fuel, labor. etc. - can be made in the cost streams of alterna- tive power developments without changing the timing and capacity of the projected investments., this is not the case with variations in the estimated growth of the market. A more rapid expansion of the market will tend to favor a hvdro over a thermal devel1onmeint but the actual effect of a given increase in the growth of demand can only be determined by working out the consequeninces in terms of a chnnn pttarn nf investmPnt. Biecause the market is a very important and often uncertain element in the appraisal and because the effect of changes in marke+. eAtimnte are not readily evident, it would be most desirable to be able to approximate the effect of such changes on the return ca lcultios in aane,f -54g 4a , m-Ai i +t 4rvn+4fw their importance before devoting effort to the often laborious task of re- 3. Aato work ou r some rou` rules- of humbU or- tipros has -)70 AnL atl U UU W'L VJ L UI U.~LAVA LJ%PC WJ.L IALUISLJ .L%0 ' L J.L J60 J'J D 11 been made in this paper. This has been done through the use of simplified d@acf1-)U are L to.capacitUyL overk.L .UJ1 tWU.116 ILU 1diYLfrU p dtUL.LU.L mAS dam) are! loaded to capacity over different periods of time. The maximum - 15 - rate of return is obtained, of course, on the extreme and convenient assump- tion that the load grows fast enough to mak psil %e full ut i of the dam's capacity immediately on its completion. Tentatively it emerges from the analysis that this maduma rate is a good benchmark from which to estimate the lower returns obtained with slower rates of growth. For simple straight-line growth curves the return drops fairly rapidly and regularly from this maximum rate as the period required for full loading is extended. After 10 years the effect on the return of delays of a year rapidly becomes negligible. Different cost structures appear to have only a small in- fluence on these relationships between the rate of return and the loading time. In the case of less simple load-growth curves it is much more dif- ficult to generalize, but the examples presented give some idea of iat may be expected. Hydro development Ier löad Table 1. Cash Floui of Coets - dt- ler Load Inveatente 2rating xpenneI trnfrani ion tranpisso trnsmeiion theal production frequency e- D bro unito 230 KV 40 115 plant plant a) fiff trae-~ion coiversion Total 1961 1962 11,750 16,4o 9,959 1963 23,600 14,000 2,000 16,44o 1.1,086 30,000 1964 106,200 25,0o 2,000 16,4c, 11,763 30,000 1965 147,500 38,000 2,000 16,640 13,695 30,000 19,66 74900 51,100 14,620 9,296 830 1967 43,300 57,200 12,900 14,620 1o,7C4 830 1968 38,700 1,62o 13,62 959 1969 51,100 51,500 16,220 3,532 959 1970 57,200 52,300 16,220 7,540 959 1971 16,520 2,052 2,384 1972 51,100 16,520 2,052 2,384 1973 57,200 16,520 2,052 2,386 1974 -17,520 2,052 2,386 1975 51,100 17,520 2,052 2,384 1976 57,200 17,520 2,052 2,386 1977 18,620 2,052 2,384 1978 51,3Do 18,620 2,052 2,384 1979 57,200 18,620 2,052 2,384 1980 ( 19,320 2,052 2,386 19,320 2,052 2,38 1983 90,000 1985 180, 000 1995 77,000 6,o 1997 12,900 2000 142,500 2013 90,000 2015 180,2 o00 205 77,000 6,000 2027 12,900 95 2028 19,320 2,I 52 2,j8h Present wort in 1962 (NW) of couta in period: 1962-1980) 330,58k 265,123 85,L43 74,231 5,201 0 176,168 78,973 12,112 78,016 1,105,847 1981.2028)at 7% 0 0 9,126 9,032 615 59,966 63,165 6,709 7,794 0 156,407 Total 1962.2028) 330.580 265,123 94.569 83,263 5.816 59.966 239.333 85.682 1,0 78.016 1,262,256 1962-1980) 322,035 2.3,575 80,046 72,169 5,108 0 165,105 75,999 10,926 76,621 1,051,882 19Bl..2028)at 84% 0 0 6,bl9 6,å73 442 47,582 17,279 5,022 5,B34 0 119,051 Total 1962..2028) 322,035 2U,575 86.965 7142 5.550 47582 212.38: 81 021 16.758 76.621 1,170.933 s) operating and maintenance exoenaes if both hydro and thermal plan t. N.B. The cash flo, of costs does not include any transactionn that are merely finanrcial or accountLg such as deprociation, azortisation and intere,t. It includes only expenditures on goods and servicen in the year in which they are made. The hydro development results in a systeT using not only hyd-o but alzo some thermal plarts. Thermal devel opor,nt lоиэг lоад ТаЫе ? саа� P1w nt Coete - 2Ъвгяаl Ibвa_�mt - La,er Ioad (1n Thoaвacidn ) L�ваеТлепТв 1 Operatiл¢ еивлаеs � trana�aelon Lnиsmlasion transalsaioa thегпкl I �аодисцоn I fгеqивп9 Теэт _ Ibe `.?с�-о ;гг,:`.п ;,00 *F .ЭО 'f,: г,lагп. j рlапс киеl tranвoslвalon 1 елпvеrеlоп Tote1 19Ы 1962 16,440 9,959 196Э :Ш,ооо 2,w0 16,L1,o ц,о86 Т�,ооо 19Ь�4 г5,ооо 2,Ооо 16,41,о ц,'ГЬЭ уо,ооо 1965 _'р,:ЮС , „ i6,i,цй i3,69y' 3�D,o0o 1966 29r�) 14.620 9,296 8:10 1967 59,ООо 1L,620 10,704 В;10 196В 59,оа) 16,18о 12,z73 еЭо 1969 59,�г> 17,т4о 1э,за2 е3о 1970 30,OIX) 19,300 16,255 830 19i1 г9,оа) 2о,86о 17,895 8'10 1972 3о,о0о 2о,86о 19,ЭЬЭ 8:lо 197з z9,ooo zz,4zo 19,8ЭЬ еЭо 1974 59,�) 22,42о 21,ЭоВ В:lо 1975 59,Оа) 2Э,98о z5,434 еЭо 1976 Эо,оа) 25,54о 29,718 е+о 1977 29,�) г7,� 31,54z ВЭо 1978 В8,ООо 27,100 3Ls062 8:l0 1979 89,оа) 28,ЬЬо Э9',904 83о 1�01�) Эо,аа) 31,78о 42,791 8:l0 ЭЭ,ЭЬо 54„6Э1 B:fo 198Э 9о, оа) � А '�ь 1985 18о,оа� ' 1 � 1 � � 1995 'n,o� Ь,�� 1 1 1 1999 90,Ор) � I � 2000 90,ООо � � 1 1 2002 90,000 � j 1 20W, 90,Ор) ) I 20об 9о,оа) I � 2008 9о,ооо � ь + 1 ( 2ФD 180,Од� ', 1 1 �3 �' ��1 4 1 2015 180,OPJ � � � г � 1 2025 77,ооо Ь,о0о � г � �� 2028 Э3,Э4о 51ь 31 В�О Ргаяепt �yorth 1п 1962 (F'�) пf cosLS iп регlод: 1А57-1980) 3L 7ц 0 0 п Ь5,245 5,2vi. 326,567 2tki,20Г 16},рб2 5,89д i'В,016 &70,196 19�91-гОгВ) о о о 7,888 ЬL 94,255 1о9,оо2 17f1,бц 2,7i4 о 39Э,о85 Tota1 1952-2028) 0 0_ `0 7Э� 5,81lг 420j222 Э1 209 ЭЬц,Ь7Э 8•Ы2 j1016 1 26 281 1А52-1980) 0 0 о ЬЭ,В90 5,1оЕ1 296,346 191,7Э9 I6fS,133 5,39Ь 1'Ь,Ь21 807,235 198I-zo28) аг 6}�д о о о 5,667 4l,2 7о,961 81,589 133,691 2,оЭ1 о 294,Э61 тосаl 1952-zoze) о о_ _о �s91557 5.55г? зь7,зоо 27з,з28 �'.,824 7,4zi тб1бzl 111о1•6i6 И_д. 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Ч Ё S w � й �' п у � � F _� М �+ �G г� �' N N I W W� �P�Wе.� I �oрΡ. а и Ч N `о О О О О О О О и�' � �00`О I`д�00j(� 1 1 1 1 ✓ у � й о ь V1 д 8 � �Й vt �=� у ииииии f� `��' �^ ° r' � "' й�"`vь ~�' ь ь �ь р '� б F�oo� FVOON ������ �8 �8 I� � � $ Ia � � � �+ �� а О� Р О ю�О и N N`F' Ф �"1 �F � �йй°rn �orn°� S RRX �' �о t/ _ _ _ ат ��� I�� � � � ,ч �g � � уΡ �.+ �.+ I ry�уΡг I7 I� N� LФО� N `1��0 С � J � �1 N ФЙС N7 � IF+ � � ГNW°� f�N°� � � � � � ���� I�� I� у `�' Q П � � � � I � С ���{' (�"�1 и � �л � Р О� Ч� ю � j''Qд-� � �� �О�OФ �TVtлf°-� О О 000 �q� � 1Ч �✓+ 9� q 1` РрΡ, 1 �е � О 6 бIF, ry да р I'`Н■pq 'л I м �� Гийо° Г•л`°оо g' � �� 1С� Ь��Б!! �в. �йй ��.О� О О ° О ''�� � вq � � �� II,_ ~ I�-'т�~ r rr мr+ rи+r й 'а �� LF''у`л� Lи,�но� � Уой�i��-��йiт��'л�о�а�о~.о�о�о. �� 14N�i. ;:�.��� ��- '_ - - - -- - - - -- - э�3��цhТйййrиуйn�i�2���Ё�� �Е� � Б ^� � � v ovvvvv°дооvооадооо iв �в о � I�B � � уΡ Ф �+ �.+ �vрΡ ��рΡ LГФ= = NT� С NрΡ� NONO�o N`o NрΡ� ЮрΡNрΡФ� ` WG�уΡG�O 7 't `v�a'Р 1bйЙN ��VФР й "' ` _ _"_ __ _ - __'�йNN�NйNNNГO�ФOYJb��I I� � О � б�+ G � и гв F+a Р: F+YI �.О` = О N NNNNNNNNN ~ )� 10 д� ����о �а�а� ��- - - - - - - - - - - ��L������������o �� s ® д� � ы� �� � � 5�. 1о, о. 1о о ооо �� �� С6' IC,'°°'L' Irn.°°о�. 888 Ia� �� ё �ГФ` � `.и� I�,q Р�t О I� � ��wN�P II14abй Ph.er.^ь.1 деvеlортепъ H�gher 1с�ад ТаЫе !г. Cash [�1гн аР ooate - 7Фвгтаl Dевеlв�®nt - Нt�цзнд (1д 'Пгоъ�sалдв) 11]УС9Тд1РЛL tinn �_Хре^.°е::_ «ме..^а"_'h trans�aission tranmm.гGSion trar:�sniзs-or�, tУ.епааl �oг.�,:cLio.n �'reyuency iец Oaami hydro units 4а7 xv 23о KG' 17�ки рlапt ���� 1р anL .Рие1 trал;smission c:onverslan ToLa1 1961 1962 16,440 10,,00'% 1>ЬЭ 1�г 11.�,�о 2,ооо 16,44о ц,,178 3о,ооо 1г� z5,o� z,COC 16,44о ц„85ч 3о оао 1��5 38,оио г,оСо 16,440 1,3,719 зо,ооо 29,о00 14,620 ц„об8 Вэо 15�67 59,000 14 620 12; В32 tiз0 196е 59,ооо 16;18о � >,З,б44 83о 1s�ьs 59,ооо 17 74о 14,59о Взо 197о � ' 15>Т1 ЭС,о00 19,3оо 17,01Э Iззо 1972 25',о00 20,860 19,239 Взо 197э 59,ооо 2о,ебо ц,г79 1Эзо 1974 59,�о 22,42о 22я592 83о 59,ооо z3,9ao ?э.ыз5 езо 15'75 59',аоо z5,54o zь,93т Взо 15�76 В8,00о 27,1о0 3h.rц9o В3о 1977 В9',�о 28,660 40,11+3 lЭЭо 157е1474 зо,ооо з1,7во 45,,66Т езо 1s�eo зэ,з4о 52„ег5 Взо (1981D n 52,875 л. 15�в3 Ы,53z , 9С', ооо л 1985 1Во,ооо , 1 15�55 77,оао б,ооо � 15'99 � 1 27С,ооо � i 20�+ 18а,аоо 1 ! гао7 1 1 27о,ооо � ! 2о1э 9о,ооо � i 2о15 I � 18о,00о 1 i I ге25 77,ооо б,ооо , � 2°28 зз�з4о ы`;5зz B3b Pres�ent xorth 1п 1962 (R7) of aoete 1п регlод: 1962-197В) 1979-.198о) at 7}¢ о о о 65 о�5 5,02о1 Э43�1о4 193,�9 175,,357 5,1',29 78,о16 ВЬ5,3Ы 19В1..2о28) о о U 16,820 29,BL8 1i69 о й,9,1э7 7,88В 615 97,61о 1о9,оо2 2о1,,173 2,'Тц о 41.9,оо'г то1.а1 196г-го28) о о о тз,1э3 ;,ei6 �t,a,714 зго,езl 4об,Э7е y5iz 78,о1ь 1,ээз•5оо 1962-1978) 0 о 0 Ьэ 89q 5,108 э;1;,3 � i80,6i2 164,,jft8 ц,у98 76,621 8iri1,y49 1979-198о) at 8�� о о о 'о о с�^ ьб,сое 25,э86 198 о 41,794 1981-2о28) о о о 5,�7 LL2 7Э,5о1 81,589 15о,579 г,оЭ1 о Э7.Э,Во9 тоzаl 196z-zoze) о _ о о 69,55т s sso звг,езз z�e� э�о,355 1,z7 7ь.ьи 1,1Е� ss2 Ч_5. The cash flоы оГ costs does not цiсlиде ;и�у trarasaction�s that аге тетеlу financial or дccoцnLing ецсh as depreciation, вmorti::atlon :цгд �nt.г:rest, It irю]ludes огг),у ехрепдаитец оп goods алд ;:ervices in the уеаг in vhich they аге таде. Lower Load Table 5;. SwmIa17 Of ~nt Worth of Costa (Iýnmer Load Dervel ent) (in thousanäs of Thous~ Period 1962-2028 Period 11962-1980 Per-Lod 19,31-2028 hydro theroul hydro themil hydro thermal Cost Coimonent dov. dev. Difference dc-,,. -V. DUference dev. dev. Difference (Present worth a-t 73å per cent) Dam 331 331 331 3,31 Hydro units 265 265 265 - 265 1ý,an~Lseion 400 KV, 95 - 95 85 85 Ttansmiiision 230 KV 83 -73 10 74 6ý 9 9 8 1 Tranmtmion 115 KV' 6 6 - 5 5 1 1 TUrval plant 60 421 .361 - 327 -327 60 94 _ä Operating cost prodtuction plant 239 3:15 - 76 176 206 - 30 63 109 .416 Fukel 86 3452 -276 79 183 -1.04 7 179 -L12 kerating cost transmission 20 9 u 12 6 6 8 3 5 Frequercy corrwersien 78 78 - 78 78 - - - - Total 1262 1263 -1 U06 870 236 156 393 -2.37 (Present worth a-t 81 per cent) Dam 322 - 322 322 1,22 - - - Hydro uni ta 244 - 244 244 244 Transmission 400 KV 86 B6 80 - 80 Tr,arw"3aim ý230 19 79 7; 9 72 64 8 7 6 Tr-anod..331M . 1.15 191 6 6 - 5 5 - i i Thermal plant 48 Y97 -319 - 296 -296 48 71 Operating cost production plant 212 273 - 61 165 192 - 27 47 Bi Puma 1 Bi 302 -221 76 168 - 92 5 134 -129 Opmeratbig cost transmission 17 7 10 11 5 6 6 2 4 Ftequmj corrversion 77 77 - 77 77 - - - - Total L171 1102 69 1052 807 245 119 295 -v% N.B. For basic data see Tables 1 and 2. Lower Load Higher Load Table 6. Present Worth of Costs: Comoarison of Higher and Lower Load Development. 1962 - 2028 (in thousands of Thousands) .ydrlevel anent Thermal development Difference hZo - thermal) Loer load Higher loa.d Difference Lower load Higher load Difference Lower load Higher load Difference (1) (2) (2).- (1) (1) (2) (2)- (1) (1) (2) (2)- (1) (present worth at 7 per cent) Cost Comp ent Dam 331 331 - - - - 331 331 - Hydro units 265 273 - - - 265 273 8 Transmission 00 KV 95 95 - - - 95 95 - Tranantission 230 KV 83 83 - 73 73 - 10 10 - Transmission 15 KV 6 6 6 6 - - - - Therral plant 60 60 - 421 441 20 -361 -381 .40 Operating cost production plant 239 243 4 315 321 6 - 76 - 76 - 2 Fuel 86 92 6 362 406 44 -276 -311j. -38 Operating cost transmission 20 20 - 9 9 - 11 11 - Frequency conversion 78 78 * 78 78 -- Total 1262 1280 18 1263 1334 71 -1 54 13 (present worth at 82 per cent) Dam 322 322 - - - - 322 322 - Hydro unita 244 252 8 - - - 244 252 8 Transmission 400 KV 86 86 - - - - 86 86 - Transmission 230 KV 79 79 . 70 70 - 9 9 - Transmission 15 KV 6 6 - 6 6 - Thermal plant 48 48 - 367 388 21 -319 -360 -21 Operating cost production plant 212 215 3 273 278 5 - 61 - 63 - 2 Fuel 81 87 6 302 340 38 -221 -253 -32 Operating cost transmission 17 17 - 7 7 - 10 10 - Frequency conversion 77 77 * 77 77 - - Total. 1170 1188 18 1102 1166 64 69 22 46 N.B. For basic data see Tables 1, 2, 3 and 4. Tablå 7& Dlifferent patteres of of load: ~iplifled caah fla alternative and2thrnal ioø~ute Ca5e I (la and I) a- I oaa cos load c05t additional operating addi tional opera ting hydro thernnal cost of thermal hydro thernal cost of ther-al S1da unita units development MW dao ts u nits development 01 500 500 i 600 600 2 700 700 3 800 800 b 900 900 Slo00 1000 loo 150 3om0 lo0o 1o0 1en 6 1075 5 1150 100 150 10 7 1150 100 150 10 1300 100 150 20 8 1225 15 350 100 10 30 13000 150 2L v01 I50 uu 10 1375 25 1750 loo 1;o 50 11 3150 100 150 30 1500 100 150 60 12 1525 35 2050 100 150 70 13 1600 100 150 L0 2200 100 150 8o 1L 1675 45 2350 100 150 90 15 1750 100 150 50 2500 100 16 1825 55 17 1800 100 50 60 18 1875 65 19 2050 100 150 70 20 2125 75 21 2200 100 150 80 22 2275 85 23 2350 100 150 90 24 2425 95 25 2500 100 26 a) a) 15U 150 b5 2500 lo 2500 Pres.t oorth in yer 5 (PW) of costs in years: 5-15) low 423 63. 163 1000 725 1087 327 16-25) at 8% 0 128 192 231 0 0 3 u 26-65) 0 0 82 256 0 0 108 256 Tot.l 5-A5) ir c, 4e1 le1 I-n,., 10 10 9 -nternal rate of return on additional hydro investment: 8 per cent 10 per cent a) replacemnt investenta Asau,ptiona. 1 thermal unit - 1 hydro unit - 150 M o..ste. dam: 1000 Total capacity dam, 10 unite ' 1500 W ¯ 1 hydro unit: 100 Life: thermal unit - 30 years 1 thermal unit: 150 .ydrc unit 60 -oy-r dd. oper. c dan - more thm 60 yearf (ncl. fuel) of theral dev.: 1/15 per w ТаЫе DцfeпnL paLLerne ot grv�th of 1оад: а1лд:11riед cash flora ot alterлaLlve hydro впд theгmal lrrvee4nnLa лве аве lоад со оа сов � addltlosfal opeгating �3i{ оп га ng I hydro 1Ьегтаl cost of thermal I I hудп therмl сое о� t�,�rau Ув�, 1l`NЬ! дат units unlta developmenC I МЧ7 дат unlte unlte беvеlорпкпt о 5оо 50о 1 ЬОО 600 2 700 700 Э 800 ВОО 4 9оо 9оо 5 lаоо [ToooJ х) 1о0о lооо 2оо Эоо Ь Ь8.Э 1300 200 300 20 7 7п•n 7гцn 2т 3т ьп 9 71.7 1900 200 3W 60 э г3.Э 22оо гоо 300 Во 1о г5.о 25оо - _ 1оо ц гб г в. _ 12 78.3 I , 1 13 80.G 7L 81.7 ,5 ,мп ?мп7_] ,п., ,гп я3 � I � �-.,..-г , , 16 ц5о 1оо г5о 85.о 17 lзоо 1оо 15о 86.7 18 1L5o 1оо 15о 88.3 19 1600 100 15о э0.0 I 20 175о 100 150 91.7 21 1900 100 150 9Э.Э z2 zo5o 1оо 15о 95.0 2Э [CVO 1W 15о 90,7 zL г35о 1оо 150 98.3 г5 z5oo - _ 1оо 26 Т t 1 I I �а310 I а-а) I j9 300 45 1,0 � �. �_ I I � � �ц ��� � � I l � � wv[ 2[м 1м 2Cnn 1пп �� n�esent - п уеаг 5 (гwi л£ гosts 1л ;�ears: 5-lc? ) L э 1 8Ь 129 16-2г,) а_r е�_ �бо 299 4Э4 Is� � � � i�� z6-6>) о о 5о 256 о о 129 z5б PoUa1 5-б>) 46Э 335 55Э 130� 1000 862 ]L22 1056 Internel гасе of гвtш•л оп addlt]опаl 1�удто lтгеsЪпепtг 6 рвг свпt (х) ог 10 рег cenL (у) 13} рег oent а) гер7асатеп[ lnveв+.mante As9umpLjone: 1 thermвl и_n1t � t _�г{ю un1t. � 1_КО М_W nwtл: Лят: 7_ппо Tota1 сар.мl[у деп: 10 unlte � 1500 Мд 1 tqdro un1t: 1D0 I1fa: tппгтаl un1.t - 30 уаакro 1 thвrmal vn1L: 1$0 hyг3ro unlt - ЬО уеш•в вдд, орат. ooat д�: --_.а ьь_.; бп_ .. ••,.. (��с1_ nу,л_) от � thetпal два.: 1/15 рет !N Table 8 Present worth of costs of hydro/thermal alternatives for different loading times PFe-sent Cost ---, VVVI, LIII 14Z 12 UZ lot 9Z 899 71 M: Case i Dam ? 1000 a) 1000 a) 1000 a) 1000 a) hydro units) 551 586 625 672 Inermal unl Y73 Th 900 1100 1241 Add. opere cost) 650 730 907 1141 wl wIvA.AM-L UK;; V TT Dam 1000 a) 1000 a) 1000 a) Hydro 'Laiits) 676 700 725 Thermal units 1072 1129 U95 Add. oper. cost) 612 7o8 894 of thermal dev.) Case iii N a) ____a) Dairi ILUU 1.UUU LUUU -LUUU LUUU Hydro units) 782 807 820 848 862 Thermal units LL96 1250 1283 1367 31s22 Add* A71 I n*; of thermal de v. a) Or the higher dam costs used in deriving Curves B-D in Chart 3* Note: Cases Is Us and M refer to "straight line" loading timaB-of 20, 10 and 5 years respectively. Of* Chart 2 and Table 7. Basic cost da+A_as in para. 299 and Table 7. Dam costs may be varieds as discussed in para. 26; the resultir4, effect on the rate of return emerges from the table* For examples with dam costs at -64- --4-- -0 --4--- 4- M --- T I- a --& flr%M A. C!el M Qf%A A ACff) .LVVU VALV A-CLV0 V.L LOWL&L41j, LAL kjcLat: Ls L0 V per cen t %100 - ;.51 - 9W 1 -.5- -a With dam costs nearly 40 per cent higher., at 1383. the return falls to 6 per cent (1,;Aq + Aqc = II + 907 %--- --- -00 Table 9 Influence of different proportiansof basio oosts on relation betweetn rata of return and loadinc time Cost a Original Modified cost data Comnonentq cost data a) b) Instantaneous loading (PW at 20 per cent) Dan )1000 1383 1383 Hydro units) 1000 1000 1000 Thermal units ) 1507 1883 1507 Add. oper. cost) 50) 500 875 of thermal dev.) rate of return 20% 20% 20% Case I (PW at 8 per cent) Dam ) 1000 1383 1383 Hydro units) 551 551 551 Thermal units ) 908 1135 908 Add. Oper. cost) ~ 65 650 1135 of thermal devo) rate of return 8% c. 7j% o. 8a 1 Case II (PW at 10 per cent) Dam )_V 1000 18313) Hydro units) 676 676 676 Thermal units ) 1072 1340 1072 Add. oper* cost) 612 612 1071 of thermal dev.) rate of return 10% go 0c10 Sase TTT (PU a+- 13. pe cnt Dam ) 1000 1383 1383 Hydro units) 782 782 782 Thermal units ) 1196 1495 1196 Add. oper. cost) 559 559 980 rate of retun 1 0.12 n. aThg a) dam cost, plus 38 per cent; thermal unit cost, plus 25 per cent b) dam cost plus 38 per cent; additional operating cost of thermal development, 1.us 75 p.c. No-e See + te -, para. -P- --or expanai.4 Cae I T II TdII refe-r to sragtLine" ..., .* 9O IJLAG ;', .L±-~ .c L VCJU L VW L, ± J.L ..ILU .LJ.V. AV4t%. gIIV L"ILW loading times of 20, 10 and 5 years respectively. Cf. Chart 2 and Table 7. Present worth data at discount rate annroYimate1v ffrirht" for Case connsidered; the t1wnight" of cost increases varies with this discount rate. гаьlв 1оа 5оте е цеед оцтvlцлеаг tterдeot lоад � оlдqгцriед oaeh flовео2 аlЕвпи л о ид t2ureal lтееЪвпttа ав�- аве а _�� lоад coet lоад ooet а о operat а t опв орегл hydro Иегтsl cost о[ thетлиl 1и1то lhеттвl совЕ of therмl veY;• ми ла,п ��iи ,:п1и л.,,ei„�ent нц ,ит ,-�r� �..з�� ...i„�;;. -- 1 1 - - -- - � � - - ....._ _ � о 5оо 5оо 1 ЬОО ЬОО 7w з еоо ёоо L 9оо 9оо 5 lооо lооо 1оо д5о lаоо lооо 2оо 3оо Ь i1.5G iйo i,SG 1й i3w 2w jйй 2о г lзоо 1оо 15о 2о 1боо 2оо зоо 4о В 1L5o 1оо 15о эо lвоо 53.э 9 1боо ЬОО 900 р0 19о0 100 15о бо 1� zSгw 1оо 2йкю 1од 15о бб,б 11 2100 73.Э 1г 22оо 1оо 15о ео 13 2300 100 150 ВЬ,Ь Li 24о0 9Э.э 15 I I 2500 100 15 Il � 1 1г 1гз I I � � 19 20 2.7 2li I I I I 1' I '�гга'. �.. I 1 � ла,"" � » уии эб 15о 76 эоо Э7 15о 37 Зоо зВ цо •• � � эУ 9VO I I �i2 j50 I I I I ' у I II II II II � 65 25оо 1Оо г5оо � тп�е,•п�1 т._+. �г т.r,_� . ,ллlrlоп?_� Fydro lnлetamnti -.. _ цj; рвт oent 11� psr oent а) тср]аснтвпL lmeetmenta Assurt Е1� опв: _-' _ е Уй __ _ _ � м ___ _ '_ _ Total�capaclty dami 10�vп1Еду • 1500 !б! -- 1 1р�дто иц tг ,100 I1is: theяral ип1Е - 30 уевте 1 thermal un1t� 15о 1ц•дто ипlt - 60 уевтв адд. орет. coet аат••тою iьвп 5о уеагв 11ло1. гив11 о2 Lhereul 1ev.� 1/15 рат tы Н 1-� _ _ Ф�� о' м �`�' -�PЙF�I.+гJf+p�pФ�I�TЙ�WNGO`ОФ�lPИCWNF+'о IФ .. вq� У .� т ^Р1 �� S'д F+ У Cr �� � о �gP � О g1 ° � � � �.. �' .�. О� �4 < И r ; - аг � �. а�t а ё_ �iS'ооб дI �о �иrчw и+ы+г�г+и+r ����� ° g . уΡ� ц ■� м � �' � -�BEi°о�Ь`Hii°оо�оооц�о�'оо�о�оц��НоЬ '7� Й�ё о о �� � 8 Е $ � : � � 8 8$ о в�8 � о 5����� к s�� v 1 6 o F+ й•lрР.�в.О.��.W� � � уΡ I � �� • � � w / p а! � е � ,а. и ь+ 3 й fл й G. й Й к й й У й й й R б' � V @� о�� о о � о о о о 25 у о о i� о о о � r��1 "�1 �� i.. м �й�� � л ,о, rk N О и 000 � � I� � ~ -� � к) (а Ф �1 н О. И С С ��� ~ � 'у[ 8` BcпWQo�woйvi�йwFi�tл`(wEio.�Eo`1л' ь°.R'� S i � oe�WOO�woo�woo.2+olo.Loo.WOO. t`Э � - � уΡ"�' � с �гг ����, р � 'I� � � _ NNiNNNN NN � iй `^�р -��+ Е'�F�'wWU�:.ivйииiи+r �ciq уΡQ�+ и FFF'eгбJi 8 �3v�ой8•.�ол�i�Сй$��Sй�й7iй�82S�оо° �д � ,� а � Б � в в - "к "в � �� � S�i о� g е�:� �: � У = О F г+ O�v г+ а�+ t� � 0 С U О О О •�. а аа � в�� -i �рΡ иию�рΡ Фттгnа+�ч-�Nч�рΡ. ���о 8СоРИlМ��ОФР\лV� ОФРИ�w~ОФ oL,�oW-�г�L-(��L-�o�:.-(о�.,�о�. �5'й а n�.� � COMPARISOCY OF GASH FLOVIS OF HYDRO AND THEIRMIAL DEVELOPIMENT - LOMIER LOAD %INI 300 7-r7-TT--7 7ý7TT-F-r- V-T- -F-r-TTT-F-FT i l -T-T-T-7~T-T- THERMAL HYDRO 200 till 100 vx.11 0 1. .11 ............. ........ ......... .1 låt -100 g ADDITIONIAL HYDRO cos-rs '00 zon i j 1962 1970 1980 1990 2000 2010 2020 2028 NOTE- For bosic doto see Tobles I and 2 x 19RD - Econornic Stoff 2157 -4 CHART 2 ILLUSTRATIVE PATTERNS OF LOAD GROWTH (MW) Ib 2,000 0 3,000 2,000 I 1,000 0 0 5 C) 15 20 25 IBRD - Economic Stoff _ _ _ _ _ 21581 CHART 3 RELATIONSHIP BETWEEN RATE OF RETURN ON INVESTMENT IN HYDRO AND LENGTH OF LOADING TIME OF DAM (RATE OF RETURN -PERCENT) ___________ 2 2 I.....I I NB Free-hand curves based on data from Table 7, 1 ___with modified dam costs as specified. "Straight 20O o _ _ _ J line" growth of load; Cases I,1[,and 1 refer to different icading periods -see Chart 2I n Table 7. See further text, paro. 32-34 15 66 A / SIJ_____ I LEGEND. A BASED ON ORIGINAL DATA 2 -B 13ASED ON DAM COSTS PLUS (NEARLY) 20% C BASED ON DAM COSTS PLUSI(ERY 0 D BASED ON DAM COSTS PLUS (NEARLY) 60% 0 L 0 _4 6 8 10 12 14 I6 I8 20ll 22 24 2 1 5CASED ODM COSSE LU (NERLY 20 LOADING TIME (YEARS) IBRD - Economc Staff (R) 2 159 CHART 4 RETUN N HYDRO INVESTMENT FOR CHqRT 1 IJOFFFREINT LOALJ GRvVO WTi 3,000 IIIab... / I mIVb ./ 2,000( 1 ~ % 6% Ir/- IV- 1,000 4"V: 20% 9 4% 7% L II _____- - 0 5 10 15 20 25 YEAR YEAR 1BRID -Economnic stas'f (R)2160J NOTE: Thin f:nes represent the original Cases I,!,!c,and ! Thick lnes represent the new "Curvilinear" Cases Eb,1a,Za, and Mb. Respective rates of return (based on Original Cost data of Table 7) are written in alongside. Rates of return written in along horizontal axis refer to instantaneous loading of dam capacity in year indicated. See futher text, para. 35-36.