SWP-610 Economic Appraisal of Rural Reads Simplified Operational Procedures for Screening and Appraisal H. L. Beenhakker A. M. Lago WORLD BANK STAFF WORKING PAPERS Number 610 HF336 .3 B34 1983 c.2 Economic appraisal of rural roads: simplified operational p SLCO33 126 'ARLD BANK STAFF WORKING PAPERS Number 610 Economic Appraisal of Rural Roads Simplified Operational Procedures f(or Screening and Appraisal H. L. Beenhakker A. M. Lago SECTORAL LIBRARY INTERNATIONAL BANK RECONSTRUCTION AND DEVELOPMENT 1 '984 INTERNATIONAL MONETARY FUND WASHINGTON. D.C The World Bank Washington, D.C., U.S.A. Copyright © 1983 The International Bank for Reconstruction and Development / THE WORLD BANK 1818 H Street, N.W. Washington, D.C. 20433, U.S.A. First printing October 1983 All rights reserved Manufactured in the United States of America This is a working document published informally by the World Bank. To present the results of research with the least possible delay, the typescript has not been prepared in accordance with the procedures appropriate to formal printed texts, and the World Bank accepts no responsibility for errors. The publication is supplied at a token charge to defray part of the cost of manufacture and distribution. The views and interpretations in this document are those of the author(s) and should not be attributed to the World Bank, to its affiliated organizations, or to any individual acting on their behalf. Any maps used have been prepared solely for the convenience of the readers; the denominations used and the boundaries shown do not imply, on the part of the World Bank and its affiliates, any judgment on the legal status of any territory or any endorsement or acceptance of such boundaries. The full range of World Bank publications is described in the Catalog of World Bank Publications; the continuing research program of the Bank is outlined in World Bank Research Program: Abstracts of Current Studies. Both booklets are updated annually; the most recent edition of each is,available without charge from the Publications Distribution Unit of the Bank in Washington or from the European Office of the Bank, 66, avenue d'Iena, 75116 Paris, France. H. L. Beenhakker is regional and rural transport adviser in the Transportation Department of the World Bank; A. M. Lago, president of Ecosometrics, Inc., of Bethesda, Maryland (U.S.A.), is a consultant to the Transportation Department. Library of Congress Cataloging in Publication Data Beenhakker, Henri L. Economic appraisal of rural roads. (World Bank staff working papers ; no. 610) Bibliography: p. 1. Roads-Economic aspects. 2. Rural development. 3. Economic development projects--Evaluation. I. Lago, Armando M. II. Title. III. Series. HE336.E3B34 1983 388.l'l 83-16720 ISBN 0-8213-0250-7 Abstract This paper suggests simple operational approaches to the screening and economic appraisal of road components of rural roads and rural development projects. It is based on a review of appraisal and preparation documents of 15 "traditional" Bank rural roads projects and 5 rural development projects with rural road components, as well as relevant literature. The objective is to simplify screening and appraisal methods without reducing their reliability to unacceptable levels. The proposed screening methods are based on the principles of discriminant analysis and a process of finding a quick and rough estimation of an economic return. Discriminant analysis is a simple statistical technique to classify rural roads or groups of interdependent rural roads into two sets: likely feasible and unfeasible ones. Simplified economic appraisal procedures are presented in increasing order of complexity. If a proposed investment passes the test of a simple method, no further analysis is needed. If it does not pass this appraisal, the use of a more time-consuming method is recommended. In other words, the simplest method becomes the final appraisal if as a result of its application a proposed investment is accepted. Acknowledgments We have benefited from discussing the subject matter of this paper with a large number of professionals engaged in the preparation of rural roads and rural development projects, both within and outside the Bank, and it is impossible to mentLon them all. Special recognition should, however, be given to Christopher Willoughby, Vincent Hogg, Esra Bennathan, Clell Harral, Arabinda Kundu and Victor Wouters, who reviewed and provided useful comments on earlier drafts. Cynthia Cook prepared Annex B. As the drafts and final version of the paper were developed, heather Mattheisz displayed a cheerful patience as she produced efficient transcripts of illegible copy and incomprehensible symbols. None of the people credited is, however, responsible for any errors or omissions. Table of Contents Page No. Summary ................................................................................... i I. INTRODUCTION, .................................................. 1 II. SCREENING RURAL ROADS. .......... .. * ....... 7 III. SIMPLE ECONOMIC APPRAISAL METHODS ........17 IV. SIMILARITIES AND DIFFERENCES. .......................... 37 ANNEXES A. Data Sources Reviewed .......... . ...................... ... 41 B. Local Participation ...... ............ ..46 C. Example of a Prescreening Method.. .............................50 D. Consumer Surplus versus Producer Surplus Methods .................52 E. Brazil: Screening on Cost per Kilometer., .......................56 F. India: Screening on a Proxy Benefit/Cost Ratio ................. 59 G. Screening via Discriminant Analysis ....... ............. . ............ .61 H. Screening via Regression Analysis ........* ...... .. ............... 83 I. Sample Design and Characteristics...... ... ..... ... ... . .89 J. Indonesia: Screening on Cost per Population and Cost per Cultivated.Area. .....o**....oooo ..... 92 K. Rural Road Construction Costs and Vehicle Operating Costs......... 94 L. Critical Values of Average Daily Traffic .............. .... 100 M. Details on Simple Appraisal Methods . ............. 190 N. Economic Returns (ERs) for Net Benefits Growing at a Compound Rate ............. o . ....... ............ ....... . 202 0. Economic Analysis of Road and Agricultural Investments.......... 211 Table of Contents (contd ......) Page No. TABLES 1. ER of Uniform Cost and Net Benefit Streams. .. 13 2. ER of Standardized Uneven Cost and Net Benefit Streams . .......5 3. Critical Values of Average Daily Traffic, N = 10, g 5, i = 12 ....19 4. ER for Net Benefits Growing at 5% Compound Rate .... . 20 5. Crop's Present Unit Values as a Function of Years to Achieve Full Potential Benefits (CPV) for N = 5, 10, 15, 20 and 25. 24 6. Crop Area Breakdown, Yields and Production Values .26 7. Annual Agricultural Production, Transport and Road Road Maintenance Costs ...29 8. Annual On-Farm (Home) Consumption, Hlkl and H 2k2.........31 9. F1(q2 - ql)-.................................................. 34 10. Simplified Methods and Underlying Assumptions . .36 11. Overview of RRs in Selected Municipalities of the Cacao Region in the State of Bahia........... . 57 12. Variable Definitions..... 69 13. Discriminant Functions for Investments (i = 12%) . .71 14. Reliability and Prediction Errors of Discriminant Functions for Investments (i = 12%) .73 15. Discriminant Functions for Investments (i = 10%) . .74 16. Reliability and Prediction Errors of Discriminant Functions for Investments (i = 10%) .76 17. Discriminant Functions for Investments (i = 14%) .77 18. Reliability and Prediction Errors of Discriminant Functions for Investments (i = 14%) .79 19. Discriminant Functions for Investments (i = 16%) . ...80 20. Reliability and Prediction Errors of Discriminant Functions for Investments (i = 16%) ..82 21. Summary Statistics of the Regression Analysis Methods for Screening Rural Roads ..... . 85 22. Reliability of Regression Equation No. 1 . .86 23. Reliability of Regression Equation No. 3 ....... 87 24. Reliability of Regression Equation No. 4 . . ...88 25. Sample Sizes Required for Different Relative Error Levels .90 26. Identification of Roads in the Sample ... ......... 27. Typical Construction Costs for Selected Rural Road Projects .95 28. Vehicle Operating Cost (VOC) by Means and Surface Types in Flat Terrain (US dollars, 1981 prices) . .97 Note: Tables 11 through 28 pertain to annexes. Table of Contents (contd ......) Page No. FIGURES 1. Uniform Cost and Net: Benefit Streams ................ ....... 13 2. Standardized Uneven Cost and Net Benefit Streams ......................15 3. Graphical Presentation of the Relations between C/B1, N, g and ER ..... 22 4. Production Equilibrium ............. . . ...... . .................. 53 5. Output Transportation Demand ............. . . ................. 54 6. Graphical Representation of Use of Discriminant Analysis for Rural Roads Screening ................ ................ . ....... 64 7. Exportable Surplus ...............o....... ... 211 8. Demand and Supply Curves...................... . .................... 213 9. Surplus versus Faragate Price ................ ................... 215 10. Surplus versus Fare ................... ...... *. . * .... ........... . 215 11. Home Consumption versus Farmgate Price ......... 12. Exports versus Prices ........... . ...... ............... ... 218 Note: Figures 4 throug'h 12 pertain to annexes. Summary i. This paper suggests some simple operational approaches to the screening and economic appraisal of road components of rural roads (RRs) and rural development (RD) projects. It is based on a review of appraisal and preparation documents of 15 "traditional" Bank RRs projects and 5 RD projects with RR components, as well as relevant literature. The objective is to simplify screening and appraisal methods without reducing their reliability to unacceptable levels. ii. Most screening methods heretofore used are not very reliable and efficient. The reliability of any particular screening method is defined as the probability that it will accept when it should accept, and it will reject when it should reject, a proposed investment for further analysis. "Should accept" and "should reject" are defined as acceptance and rejection decisions based on economic analysis. iii. The use of screening methods which are based on a combination of political, social and economic factors is not recommended since they may accept a large number of RR candidates, which are subsequently rejected in the economic appraisal. Prescreening based on social and political factors followed by screening based on economic criteria is preferred. Such pre- screening procedures depend on the specific preferences and priorities a government organization or financial institution attaches to certain invest- ments. There is no Bank policy on the use of prescreening methods based on non-economic factors. iv. The use of two alternate screening methods based on economic cri- teria is suggested. The first one, which is based on the principles of dis- criminant analysis, is recommended when it is proposed to improve a large number of low-standard RRs to the level of all-weather, unpaved RRs which would have their principal impact in the agricultural sector. Discriminant analysis is a simple eitatistical technique for classifying RRs or groups of interdependent RRs in two sets: likely feasible and unfeasible ones. For other situations, a second screening method is suggested. This method con- sists of a quick and rough estimation of cost and net benefit streams of a proposed investment and obtaining a rough estimate of its economic return (ER) from an available table. The reliability of both methods has been assessed by subjecting the results of their use in a sample of 110 RRs from the aforementioned 20 Bank projects to various tests. As a result, their reliability is estimated to be close to 90%. - ii - v. An attempt was made to use regression analysis to develop equa- tions, based on the sample data, that would permit the estimation of an ER for RRs, interdependent RRs, or investment packages of interdependent RRs and agricultural components, by using a limited number of variables. The method assumes that a relationship exists between the ER and appropriately defined measures of key variables. Although some of the equations developed provided reasonably reliable estimates in terms of the reliability as defined in para. (ii), the standard error of the estimates was too high for the equa- tions to be used as acceptable proxy measures of the ER for project compo- nents. It is therefore concluded that regression analysis can only produce satisfactory results in the context of a particular country, where a more homogeneous group of RR candidates and more homogeneous agricultural produc- tion patterns should result in a significantly lower standard error. Of course, regression analysis would only make sense in situations where a very large number of road links need to be evaluated, so that correct decisions could be confidently predicted on the basis of an adequate sample. vi. The simplified economic appraisal procedures are based on the prin- ciples of the consumer surplus (CS) method, producer surplus (PS) method or combinations thereof. The CS approach stresses the quantification of road user savings and is best suited for cases where the existing or normal traffic, or its projected growth, is substantial and the estimated transport cost savings are a reliable measure of project benefits. The PS approach stresses the assessment of economic activity, particularly agricultural pro- duction, in the RR's zone of influence. It is best suited for situations where there are reasonably accurate data regarding boundaries of the zone of influence, prices and yields of agricultural products produced in this area, and the agricultural potential. Both in the literature and in practice con- siderable confusion exists as to whether the CS or PS method results in more accurate estimates of ERs. This paper demonstrates that both methods will result in the same ER when correctly used. vii. The first proposed simplification is to determine the ER for groups of RRs rather than for individual RRs. This is legitimate if the proposal satisfies the following conditions: 1. The per km cost of construction or improvement of each of the RRs belonging to the group is equal to or less than US$10,000 equivalent; 2. The variation of the per km cost of construction among the RRs belonging to the group is less than US$2,000. If the appraisal is to be made by the PS method (or a combination of PS and CS) the project must in addition satisfy the following conditions: 3. The RRs which constitute a group are located in areas where proposed agricultural investments are interdependent with each other; and 4. The RRs which constitute a group are located in areas where farms with typical farm budgets are evenly distributed so that present and future values of agricultural production in these areas can be assumed to be the same. viii. Eight simplified economic appraisal procedures are presented in in- creasing order of complexity. There is not much difference in time required to carry out the sixth, seventh, or eighth simplified method; the difference between these methods pertains to different requirements for input data rather than degree of complexity. If a proposed investment passes the test of a simple method, no further analysis is needed. If it does not pass this appraisal, the use of a more time-consuming method is recommended. In other words, the simplest method becomes the final appraisal if as a result of its application a proposed investment is accepted. In still other words, to save time one accepts a project component or group of interdependent components if its "simple" ER exceeds the opportunity cost of capital. "Simple" ER is de- fined as an ER based on a significant portion of quantifiable benefits rather than all. Simple ERs are, therefore, understatements of actual ERs. ix. The definition of the reliability of a simplified method is similar to the definition of the reliability of a screening method; it is the prob- ability that it will accept when it should accept, and it will reject when it should reject a proposed investment. "Should accept" and "should reject" refer to decisions based on an actual ER or an ER obtained with a complete economic analysis. The reliability of individual simplified procedures is of little interest if the aforementioned approach is followed. The reliability of the approach is as good as the reliability of the most complex methods proposed. These methods, which are the last three presented, are also based on a number of simplifications and were found to have a reliability of about 95%. These more complex methods also provide a practical tool for examining alternative road and agricultural investment strategies to determine an opti- mal investment package for the zone of influence of a RR or group of inter- dependent RRs. x. The majority of RRa reviewed for this study had actual ERs which significantly exceeded prevailing opportunity costs of capital. Conse- quently, a significant portion of time devoted to economic analyses would have been saved had this paper's approach been followed, since the simple ERs computed with one of the simplified methods would, in many cases, have been larger than the appliceble opportunity costs of capital. xi. The text presents the eight simplified economic appraisal proce- dures in the form of simple step-by-step procedures. The theoretical back- ground of the procedures as well as that of discriminant analysis is given in annex form. iv - xii. The Bank's practice in the appraisal of RRs projects is to deter- mine the ER for each RR or groups of interdependent RRs. In the appraisal of RRs in RD projects, however, one often establishes only one ER for the entire investment including all roads and agricultural components such as irrigation works, supply of inputs, extension services and credit in all project areas. There is no prima facie evidence that roads in proposed RD projects should be subjected to screening and appraisal methods different from those used in typical RR projects. In both types of projects proper attention should be given to interdependence among transport and agricultural components. With the exception of RRs for which the conditions of para. vii are satisfied, ERs are to be established for individual RRs, groups of interdependent RRs, or investment packages consisting of interdependent RR and agricultural compo- nents. Assuming interdependence among project components of a RD project without testing it may result in the financing of RRs in RD projects which would have been rejected had they been part of a RRsproject. xiii. This paper does not claim to present an exhaustive set of methods useful for any conditions prevailing in RRs and RD projects; no guideline can be a substitute for imagination and resourcefulness on the part of profes- sionals involved in project preparation. However, these professionals may find the experience with RRs screening and appraisal analyzed helpful in their work. xiv. The paper also briefly mentions suggestions for improvements in preparation activities other than screening and appraisal. These suggestions are based on similarities and differences observed during the review and per- tain to (a) accuracy of vehicle operating and construction costs, (b) consi- deration of the nature of crops during the selection of road standards, (c) state of project preparation before Board presentation, (d) policy questions to be raised during appraisal and/or sector work, and (e) testing of inter- dependency among project elements. xv. Except for Annexes L and N, which consist of tables to be used in connection with two proposed simplified appraisal methods, all annexes present material for those interested in the "nuts and bolts. Their reading is not a prerequisite to the understanding of screening and simplified appraisal methods discussed in the text. I. INTRODUCTION 1. Preamble. Many governments, particularly those of countries in Sub-Saharan Africa, are faced with the problems of how to reduce time and costs of the appraisal of RRs. This problem is especially acute since most developing nations have limited qualified staff and a large number of kilometers of RRs to be improved or built. In addition, the experience of various staff members from transport and agricultural divisions of the Bank indicates that a mDre efficient approach to the appraisal of RRs is highly desirable. The appraisal. of RR investments can simply not demand the same amount of time as that oi large irrigation works or highways. 2. Projects Reviewed. The screening and simple appraisal methods presented in this paper aire primarily a combination and further development of methods discussed in appraisal reports and other preparation documents related to 15 RR projects and five RD projects. Of the 15 RR projects reviewed (Annex A) for this study, one included agricultural investments as part of the project, six were designed at least partly in support of Bank-financed agricultural projects, seven relied exclusively on government assurances that agricultuiral investments would be made in the project areas, and one did not require complementary investments. The five RD projects reviewed included both agricultural and RRs investments. The methods presented may be used in the appraisal of both RRs and RD projects 1/ with RR components. 3. Selection, Screening, Evaluation, Ranking. The preparation of RR components in a Bank project may include the following steps: (a) selection of the RR "candidates"j (b) prescreening oE the candidates based on criteria other than economic ones, such as social and/or political considerations; (c) screening of the candidates based on economic criteria; (d) ranking of the candidates; and (e) economic appraisal of the candidates. 4. Selection of Candidate Roads. RR "candidates" are simply a collection of RRs which local, provincial or central government organizations propose for improvement or construction. Annex B describes ways these organizations can play a role in the selection. Depending on local conditions and government policies, steps (b) and (d) may be eliminated. Carrying out steps (c) and (e) is recommended to (i) save time of analyses 1/ RD projects refer to projects with one or mDre agricultural components and RR components; in the Bank they may be classified as RD projects, agriculture, irrigation or forestry projects. and (ii) arrive at economically viable investments, respectively. Each of the aforementioned five phases may apply to individual RRs, groups of interdependent RRs, or a package of interdependent agricultural and RRs investments. 5. Prescreening the Candidates. Prescreening procedures usually combine some political and social criteria and, sometimes, include general guidelines to reduce the risk that RRs which are not likely to be economically viable are selected for further consideration. Examples of prescreening criteria are: - distribution of farm sizes (for instance, RRs in areas with a predominance of large farms are excluded); - density of RR network (for example, distances between parallel RRs should not be less than 3 km); - connection to all-weather roads; - connection to towns, municipal centers, etc.; and - access to health, education, and/or public administration centers. Such prescreening methods do not provide any guarantee that the RRs selected will be economically viable. Thus, further analysis is required when governments and/or financing institutions are concerned with the economic viability of investments. 6. Annex C describes an interesting example of prescreening methods. 2/ This paper does not give any further attention to prescreening procedures, since they depend on the specific preferences and priorities of specific governments. There is no Bank policy on the use of prescreening methods based on non-economic factors. 7. Screening Candidates. Application of screening methods based on economic criteria to RR candidates is necessary if one wishes to save time and costs of analyses by rejecting project components which are not likely to be economically viable. Screening methods based on economic criteria miay be applied after the use of prescreening procedures, or after the selection of RR candidates (first step) if a prescreening method is not used. Based on a testing of the reliability of various screening methods, Section II recommends the use of a screening method based on the principles of discriminant analysis and another one which involves the quick and rough estimation of an ER. The reliability of any particular screening method is defined as the probability that a project component will be accepted or rejected for further analysis when the component should correctly be so accepted or rejected. "Should accept" and "should reject" are defined as acceptance and rejection decisions based on an economic analysis. 2/ See C. Carnemark, J. Biderman and D. Bovet, The Economic Analysis of Rural Road Projects, Annex 3, World Bank Staff Working Paper No. 241, 1976, for another example of a prescreening method. - 3 - 8. Ranking Candidates. Ranking of project component candidates is sometimes done after having carried out the screening process based on economic criteria or the appropriate economic appraisal step when the total costs of implementing a set of RRs and agricultural improvements exceed the available budget. The ranking may be based on weighted or unweighted socio-political criteria or technical factors similar to those used in prescreening procedures. Alternatively, the candidates may be ranked in descending order of ERs as computed by one of the methods in Section III, and go down this list until the point where the available budget is exhausted. It can be shown, however, that the process of ranking investment packages simply in their descending order of ERs, NPVs, or B/C ratios does not guarantee the implementation of an optimal combination of such packages where a given capital constraint does not permit the undertaking of all proposed projects. By optimal combination is meant that combination of investment proposals which has a maximum value of total discounted net benefits. Only the use of heuristic, linear, integer, or dynamic programming procedures 3/ can provide such an optimal combination. The application of these methods to the analysis of RRs, while intellectually satisfying, would be time-consuming and costly and is not recommended in the conditions found in most Bank borrowing countries. There is no specific Bank policy with regard to the use or otherwise of ranking procedures. 9. Economic Appraisal of the Candidates. A set of simplified economic appraisal methods in increasing order of complexity, is presented in Section III below. The operational principle inherent is that where a proposed investment passes the test of a simple method then no further analysis is required provided the decision body using the method is willing to accept the reliability of the approach. The use of a more time-consuming method is recommended only when an investment does not pass a simple appraisal method. The use of these methods is recommended to save time and cost in the appraisal of RRs and RD projects. The definition of the reliability of a simple method is similar to the definition of the reliability of a screening method (para. 7); it is the probability that it will accept when it should accept, and it will reject when it should reject a proposed investment. "Should accept" and "should reject" refer to decisions based on an actual ER or an ER obtained with a complete economic analysis. 3/ See H. L. Beenhakker, Handbook for the Analysis of Capital Investments, Chapter 4 (Greenwood Press, Westport, Connecticut, London, 1976) for a description of these procedures and problems related to ranking based on ERs, NPVs or B/C ratios. 10. Consumer Surplus vs. Producer Surplus. The consumer surplus (CS) approach to the economic evaluation of RRs stresses the quantification of road user savings. 4/ This method, which is sometimes referred to as the vehicle operating cost (VOC) savings method, is best suited for cases where the existing or normal traffic, or its projected growth, is substantial and the estimated transport cost savings are a reliable measure of project benefits. The producer surplus (PS) or value added approach 5/ to the economic analysis of RRs stresses the assessment of economic activity, particularly agricultural production, in the RR's zone of influence. The PS method is best suited for situations where there are reasonably accurate data regarding boundaries of the zone of influence, prices and yields of agricultural products produced in this area, and the agricultural potential. It has the advantage that it is intuitively more satisfying to non-economists; however, it cannot be applied to non-agricultural traffic. Both in literature and in practice considerable confusion exists as to whether the CS or PS method results in more accurate estimates of ERs. It can be shown that both methods will result in the same ER if available data regarding existing and future traffic, its mix, VOCs, boundaries of the zone of influence, prices and yields of agricultural products, etc., are of the same accuracy (Annex D). The simplified economic appraisal procedures of Section III are based on the principles of the CS method, PS method or combinations thereof. Section IV describes variations in VOCs observed in the analysis of the 20 projects reviewed, together with other observed similarities and differences. The large variations in VOCs indicate that the PS method has a wider potential use than the CS method. 11. RR's Zone of Influence. The PS approach establishes an investment package of agricultural and RR investments in the zone of influence of a RR or group of interdependent RRs. These zones of influence are determined by (i) the RR network around the road(s) being analyzed, (ii) the distance between farms and local markets, (iii) the terrain, and (iv) the means of transport used such as headloading, pack animals, animal-drawn carts, agricultural pickups, trucks, passenger cars, and buses. Mathematical expressions have been developed for computing the area of a zone of influence. 6/ These expressions require input data which may not be easily available and become rather complex without making a number of simplifying assumptions such as a situation where only one crop is produced in the zone of influence, no variations in topography, and zero impact of other exi7sting or planned transport links in the vicinity of the RR(s) being analyzed. The method followed in the preparation of the RR appraisals reviewed under the present study is, therefore, preferred. This method establishes the 4/ See H. G. van der Tak and Anandarup Ray, The Economic Benefits of Road Transport Projects, World Bank Staff Occasional Paper No. 13, 1971, for a review of this methodology. 5/ See C. Carnemark et al., 2p. cit., and H. L. Beenhakker and A. Chammari, Identification and Appraisal of Rural Roads Projects, World Bank Staff Working Paper No. 362, 1979, for reviews of various aspects of the PS approach. 6/ See, for instance, C. Carnemark et al., ibid. Annex 4. boundaries of zones of influence by examining the terrain (for instance, presence of rivers, mountains, valleys), RRs network, and present patterns of travel and transport. This methodology could be improved by conducting sample interviews of people moving over a RR to be improved or expected to nove over a new RR, or by the use of aerial photography or ERTS imagery when available. 12. As stated earlier, the main objective of this paper is to arrive at a more simple and less time-consuming approach to the appraisal of RRs. The approach used was to develop procedures that use only part of the data normally available for appraisal. If using only part of the data can produce the same conclusions regarding economic viability of a project as would have been obtained using more complex procedures and all the ex-ante data, time and cost savings will result. 13. First Simplification. The first proposed simplification is to determine the ER for groups of RRs rather than for individual RRs. This is legitimate if the proposal satisfies the following conditions: 1. The per km cost of construction or improvement of each of the RRs belonging to the group is equal to or less than US$10,000 equivalent; 2. The variation of the per km cost of construction among the RR8 belonging to the group is less than US$2,000. If the appraisal is to be made by the PS method (or a combination of PS and CS) the project must in aLddition satisfy the following conditions: 3. The RRs which ctonstitute a group are located in areas where proposed agricultural investments are interdependent with each other; and 4. The RRs which constitute a group are located in areas where farms with typical farm budgets are evenly distributed so that present and future values of agricultural production in these areas can be assumed to be the same. The threshold of US$10,000 per km is based on the principle that the cost of investment for these RRs is so low compared with per km costs of other RRs or highways that their evaluation does not warrant the costs and time required for the computation of Ells of individual RRs; the threshold of US$2,000 per km reduces the risk of "mixing in" of productive and unproductive elements. - 6 - For instance, if two RRs with costs of construction of $10,000 per km and $5,000 per km were grouped for purposes of the ER calculation, it is possible that both roads would be accepted for implementation, while the one costing $10,000 per km would not be accepted on its own "merits" or separate ER. Although RRs satisfying the aforementioned conditions are not necessarily interdependent, they may be treated in the same way as interdependent groups of RRs when applying the techniques proposed in Sections II and III. - 7 - II. SCREENING RURAL ROADS 14. Purpose. Screening methods include a variety of techniques of gireat simplicity and spee(d of application. The object is to arrive at an :Lnitial sifting of RRs, groups of interdependent RRs, or investment packages :onsisting of interdependent RRs and agricultural investments prior to an economic appraisal. Screening of potential project components is therefore Dased on fairly limited information about them. L5. It is not advisable to combine political, social and economic factors in one screening method if agricultural and/or RR components selected wiith this method are subsequently to be subjected to an economic appraisal since such an approach may be time-consuming. This is so since such screening may accept a large number of RR candidates, which are subsequently rejected in the economic appraisal. Prescreening based on social and political factors (paras. 5 and 6) followed by screening based on economic criteria is therefore preferred. The screening methods discussed here are based on economic criteria only, since the overall objective of this paper is to save time and costs of preparation of RRs and RD projects. Only two of the projects reviewed had screening methods based solely on economic criteria. These methods (Annexes E and F) are not presented here since they rely on country specific data and relationships, which restricts their use on a worldwide basis. 16. Quantitative Approach. Quantitative methods, such as regression or discriminant analysis, provide relatively simple and inexpensive techniques for developing screening procedures for RRs and RD projects. By definition these procedures predict the outcome of a full economic appraisal for each RR, group of interdependent RRs, or investment packages consisting of interdependent RR and agricultural components, by using a limited number of variables for which data can be readily collected. The variables normally considered and tested in this study were basically of three types: (1) measures of producer sur)lus (PS) effects (such as agricultural value added, increased agricultural production, increased land brought under cultivation, area of cultivated land served); (2) measures of consumer surplus (CS) effects (such as vehicle operating cost savings for normal traffic, possibl.y divided into passenger and goods traffic); and (3) costs of RRs and agricultural investments. The relationships to be tested can be expressed in the general form: EF is a function of PS/C and CS/C or EF = f(PS/C, C';/C) ........... (1) where EF = economic feasibility of a RR, group of interdependent RRs, or investment package of interdependent RR and agricultural investments, PS = producer surplus (value added of future, agriculture production), - 8 - CS - consumer surplus (vehicle operating cost savings due to improved or new RR(s)), and C - cost of RR(s) and agricultural investments. Expression (1) should not be interpreted as double counting benefits because it refers to both PS and CS. The following paragraphs show that one of the proposed screening methods considers benefits related to PS and CS at different points in time of the investment's expected life. 17. In RRs projects without agricultural components, the above term C represents the cost of constructing and maintaining a RR or group of interdependent RRs. If such projects complement ongoing agricultural projects, the costs of existing agricultural investments are sunk costs and therefore should not be taken into account in expression (1). The only PS value to be considered in this case is the value which could not be realized without the improved or new RR or group of interdependent RRs. Costs and benefits of components of planned (future) agricultural projects which are dependent on RR components of a proposed RR project should be considered together, regardless of potential source of financing. This situation calls for the formulation of investment packages consisting of interdependent RR(s) and agricultural components. 18. In this study, a number of possible screening procedures based on variations of expression (1) were developed and tested on a worldwide sample of 110 RRs with or without agricultural components dependent on RRs, drawn from Bank project files. About half of these 110 RRs represented RRs without dependent agricultural investments. Some of these procedures, especially the simpler ones, proved to have an unacceptably low reliability in terms of their ability to predict the outcome of a full economic appraisal. Discriminant analysis was the most successful method and provides the tool which is recommended here for use in screening components of RRs and RD projects by staff of government organizations and the Bank involved in the preparation of these projects. The method is described below while details are provided in Annex G. The use of another screening method (para. 24) which involves a quick and rough approximation of an ER, is recommended for situations where large amounts of passenger and non-agricultural traffic are expected to generate most of the benefits. Screening based on the principles of regression analysis is described in Annex H. Its intended use on a worldwide basis is very limited. Annex I describes the data base used for testing these approaches. 19. Discriminant Analysis Approach. Discriminant functions can be used to classify RRs, interdependent groups of RRs, or investment packages of RR and agricultural investments into one of two groups, defined as feasible and unfeasible. For the purpose of this analysis, the criterion of feasibility was first defined for a country with a prevailing opportunity cost of capital of 12%. To find out whether a project component is feasible or not, one first computes Sl and S2 values with the help of the following equations: Sl - -98.54 + 113.60 x +256.82 y + 0.32 z .......... (2) S2 - -359.66 + 451.75 x +745.35 y + 0.81 z ......... (3) - 9 - where x = incremental agricultural value added in the year of full production divided by the present value of costs of intvestments and maintenance of RR and agricultural components, y = opening year benefits stemming from savings in vehicle Operating costs accruing to normal traffic, divided by th,e present value of costs of investments and maintenance of RR and agricultural components, and z = initial or preproject net value in US dollars' equivalent of agricultural production per hectare of cultivated area in the road's zone of influence. Another way of stating expressions (2) and (3) is: Incremental agricultural Present value of Sl =- 98.54 + 113.60 value added in year of full - investment and production maintenance costs of RR and agricultural components Opening year benefits from Present value of + 256.82 VOC savings accruing to investment and normal traffic I maintenance costs of RR and agricultural components Initial net value of agricultural + 0.32 production per ha Agricultural value added in Present value of S2 -359.66 + 451.75 year of full production investment and maintenance costs of RR and agricultural components Opening year benefits from Present value of + 754.35 VOC savings accruing to investment and normal traffic ~ maintenance costs of RR and agri- cultural components Initial net value of agricultura + 0.81 production per ha - 10 - The figures of equations (2) and (3) are to be interpreted as relative weights given to the main criteria used to determine whether an investment is economically feasible. They are derived from statistical comparisons and analysis. 20. The comments on C and expression (1) of para. 17 apply equally to the costs of investments and maintenance in expressions (2) and (3). Maintenance costs are defined as the incremental maintenance costs during the expected life of the project component(s) when comparing the situations with and without the project. To simplify one may ignore maintenance costs if their present value is small (about 15%) relative to the present value of investment costs. Such simplification is not likely to influence the decision as to whether a project component is feasible or not. If maintenance costs are not small compared to costs of investment and if project components of an investment package have different expected lives, it is suggested for simplicity to consider maintenance costs only during the period corresponding to the shortest expected life of the project components. 21. For a country with an opportunity cost of capital of 12%, a project component or group of interdependent components is feasible if the Sl value is smaller than the S2 value; otherwise it is unfeasible. In other words, if the S1 value is equal to or greater than the S2 value, the project component(s) are unfeasible. Expressions (4) and (5), (6) and (7), and (8) and (9) represent Sl and S2 values for countries with prevailing opportunity costs of capital of 10%, 14%, and 16%, respectively. Opportunity cost of capital 10%: S1 = - 95.78 + 94.68 x + 182.08 y + 0.30 z ......... (4) S2 = -287.81 + 353.17 x + 661.46 y + 0.65 z ......... (5) Opportunity cost of capital 14%: S= = -105.83 + 129.61 x + 276.92 y + 0.35 z ......... (6) S2 = -375.13 + 476.70 x + 791.37 y + 0.80 z ......... (7) Opportunity cost of capital 16%: S1 = -189.41 + 236.14 y + 0.40 q - 0.30 z ......... .(8) S2 ' -221.61 + 427.67 y - 0.02 q + 1.00 z ......... .(9) Where q = present value of costs of investments and maintenance of RR and agricultural components divided by the equivalent increase in area cultivated in hectares; this increase is defined as the increase in cultivated land in the year of full production of the with-project situation (as compared to the without-project situation) plus the ratio of the difference in with- and without-project yields to without-project yields - 11 - mtultiplied by the cultivated area (hectares) in the without-project situation, in the year of full production, and all other variables are as defined in para. 19. Another way of stating expressions (8) and (9) is: Opening year benefits from Present value of S1 -189.41 + 236.14 VOC savings accruing to investment and normal traffic - maintenance costs of RR and agricultural components _~~~~~~~ Present value of investment Equivalent + 0.40 and maintenance costs of RR increase in area and agricultural components - cultivated in ha initial net value of agricul- - 0.30 tural production per ha j Opening year benefits from VOC Present value of S2 = -221.61 + 427.67 savings accruing to normal investment and traffic t maintenance costs of RR and agri- cultural compo- nents Present value of investment Equivalent in- - 0.02 and maintenance costs of RR crease in area and agricultural components - cultivated in ha Jnitial net value of agricul- + 1.00 tural production per ha J 22. Reliability. The reliability (para. 7) of the discriminant analysis approach was found to be high; it resulted in 87% correct decisions. In addition, the method is conservative in that it has an extremely low probability (less than 1%) of accepting a project component that should be rejected. Practically all of the incorrect decisions resulting from the test on a sample of 110 RRs (para. 18) were of the type where an actually feasible project component would have been classified in the unfeasible group, as shown in the following. - 12 - Decision Based on Scre ning Complete EconomLic Analysis Accept Reject Accept Reject 66 44 78 32 The sensitivity of S1 and S2 to variations in one or more of the dependent variables of expressions (2) through (9) should be assessed Lf the accuracy of data required for these variables is being questioned. 23. The use of S, and S2 values is recommended as a preliminary screening measure in cases where a large number of low-standard rural roads are proposed for improvement to all-weather, unpaved standards. The sample from which these values were determined was heavily weighted toward roads whose principal impact would be felt in the agricultural sector. Thus these values should be used with caution in situations where large amounts of passenger or non-agricultural commodity traffic are expected to account for most of the benefits. The screening based on discriminant analysis is also not recommended when full production occurs either before year 4 or after year 10 following the opening of the road. Finally, this screening has not been tested for penetration roads (roads proposed to "open" areas which in the without-project situation are isolated or do not have any road connection), since required information on such roads is not available. In such situations the use of the screening method described below, which requires a few more input data and is based on simplification of a project's net benefit streams, may be preferable. 24. Rough ER Approximation. This method was originally developed for finding the starting point for an ER calculation of a given cash flow if the ER is to be found by trial and error. 7/ It has, however, good potential for screening of RRs, groups of interdependent RRs, or investment packages consisting of interdependent RR and agricultural components. The screening involves the approximation of the ER of a project component or group of interdependent components. The component "passes" the screening or is selected for further analysis if the approximated ER equals or exceeds the opportunity cost of capital. 25. The approximate ER is read from one of two tables each of which represents variations of standardized cost and net benefit streams. In other words, standardized cost and net benefit streams are selected as an approximation to the cost and benefit streams of project component(s) to be screened. The first standardized cost and net benefit streams consist of 7/ Walter Schaefer-Kehnert, How to Start an Internal Rate of Return Calculation, EDI Training Materials, Course Note Series, CN30, October 1981. - 13 - uniform or rectangular functions of costs and benefits as presented in Figure 1. This figure portrays a situation where costs of investment ("negative cash flow") of project component(s) are $80 million in each of the first two years of implementation and annual net benefits ("positive cash flow") amount to $35 million during years 3 through 15. Figure 1; Uniform Cost and Net Benefit Streams 60 Benefits 40 - (S milion) 20 -- 4 -20 Costu -40 - lS million) -60 - -80 _ I I I I I ! l X l 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ----~ Yeas 26. Table 1 presents ERs for variations of the cost and net benefit streams of Figure 1, where the variations consist of combinations of uniform costs incurred over a period from one to five years, and uniform benefits incurred over periods of 5, 10 and 20 years. Table 1: ER of Uniform Cost and Net Benefit Streams No. of Years No. of Average Annual Net Benefits as % of Investment with Invest- Benefit Costs ment Costs Years 10 20 30 40 50 60 80 100 1 5 - 0 15 29 41 53 75 97 10 0 15 27 38 49 59 80 100 20 8 19 30 40 50 60 80 100 2 5 - 0 13 23 33 47 56 69 10 0 13 24 32 40 48 61 73 20 7 18 26 34 41 48 61 73 3 5 - 0 11 20 27 33 45 54 10 0 12 21 28 34 40 50 58 20 7 16 24 30 36 41 50 59 4 5 - 0 9 17 23 28 37 45 10 0 11 19 25 30 35 42 49 20 7 15 22 27 32 36 43 50 5 5 - 0 8 15 20 25 32 38 10 0 10 17 22 27 31 37 42 20 6 14 20 24 29 32 38 43 - 14 - 27. To explain the use of Table 1, consider the following simple example: Year 1 2 3 4 5-14 Investments Costs ($ million) 25 25 25 25 Net Benefits ($ million) 50 Thus, investment costs are incurred over a period of four years ($25 million per year) and annual net benefits amount to $50 million during years 5 through 14. One determines the sum of investment costs or $100 million; average annual net benefits or $50 million, and average annual net benefits as a percentage of investment costs or 50%. Table 1 indicates that these cost and benefit streams have an ER of 30%. If cost and benefit streams are indeed uniform functions, this ER is exact rather than an approximation. 28. If cost and net benefit streams are not uniform, an approximate ER to be used for screening (para. 24) can still be obtained from Table 1. Take the following example: Year 1 2 3 4-7 8-10 11-14 15 16 Investment Costs ($ thousand) 954 530 131 Net Benefits (S thousand) 456 340 456 307 153 The sum of investment costs equals $1,615 thousand. Average annual net benefits amount to $394 thousand and represent 24% of $1,615 thousand. The approximate ER is obtained by computing the arithmetic average of the following four ER values read from Table 1: Number of Average Annual % Net Benefits Benefit Years 20 30 Number of Years 10 12 21 with Investment Costs = 3 20 16 24 The average of 12, 16, 21 and 24% amounts to 18%, which is the value of the approximated ER. 29. If the cost and benefit streams to be analyzed are very uneven in the sense that investment costs are high at the beginning and then decline, and that annual net benefits gradually build up over a number of years before they stabilize, the ER can be considerably lower than shown in Table 1. The use of Table 2 is recommended to approximate these conditions. Table 2 is based on standardized cost and net benefit streams which assume a linear decline of the costs during a period ranging from one to five years followed by a linear buildup of annual net benefits over the first five years that follow. Figure 2 portrays an example of such standardized cost and net benefit streams. - 15 - Table 2: ER of Standardized Uneven Cast and Net Benefit Streams No. of No. of Average Annual Net Benefits as x Years with Benefit of Investment Costs Invest. Costs Year s 10 20 30 40 50 60 80 100 1 5 - 0 12 22 30 38 52 64 10 0 12 21 28 34 40 50 59 20 7 16 23 28 34 38 47 55 2 5 - 0 10 19 25 30 40 49 10 0 11 18 24 29 34 42 48 20 6 14 20 25 29 33 40 46 3 5 - 0 9 15 21 25 33 40 10 0 10 16 21 26 29 36 41 20 6 13 18 23 26 29 35 40 4 5 - 0 7 13 18 22 28 34 10 0 9 15 19 23 26 31 36 20 6 12 17 21 24 26 31 35 5 5 - 0 7 12 16 19 25 29 10 0 8 13 17 21 23 28 32 20 5 12 16 19 22 24 28 31 Figure 2: Standardized Uneven Cost and Net Benefit Streams 60- 40- Benefnts ($ thousand) 20 - 6 7 8 9 10 11 12 13 14 - -Years -20- Com.s (S thousand) -40 30. To illustrate the use of Table 2 as a tool to establish an approximate ER for screening purposes, consider the following example: - 16 - Year 1 2 3 4 5 6 7 8-10 11-15 Investment Costs ($ thou.) 11,200 2,806 402 Net Benefits ($ thou.) 3,189 6,795 7,997 4,497 7,997 12,000 Thus, the sum of investment costs equals $14,408 thousand, average annual net benefits amount to $8,872 thousand and represent 62% of $14,408 thousand. According to Table 2, the ER should be about 29%. 31. When deciding whether Table 1 or 2 should be used, a simple inspection will indicate whether the cost and net benefit streams to be analyzed are closer to a uniform or uneven distribution. A figure laying between Table 1 and Table 2 values for ER may be chosen if the cost and net benefit streams are in between the two standardized cost and net benefit streams. 32. Reliability. The reliability of the screening method which uses Table 1 or Table 2 depends on how close the underlying standardized cost and net benefit streams are to the cost and benefit streams to be analyzed. It is amazing how close the results often are, even with cost and benefit streams which do not appear to be very close to the standardized ones. For example, the actual ERs pertaining to the examples of paras. 28 and 30 amount to 18% and 29%, respectively. The use of Tables 1 and 2 is not recommended when annual net benefits decrease over time, since the approximated ER would in most cases be too much undervalued and therefore too many project components which deserve further analysis would be rejected. Fortunately, RRs and RD projects do not often have project components with decreasing annual net benefits. 33. Regression Analysis Approach. An attempt was made to use regression analysis to develop equations, based on the sample data, that would permit the estimation of an ER for RRs, interdependent RRs, or investment packages of interdependent RR and agricultural components, by using a limited number of variables. The method assumes that a relationship exists between the ER and appropriately defined measures of key variables. Although some of the equations developed provided reasonably reliable estimates in terms of the reliability as defined in para. 7, the standard error of the estimates was too high for the equations to be used as acceptable proxy measures of the ER for project components (Annex H). It is therefore concluded that regression analysis can only produce satisfactory results in the context of a particular country, where a more homogeneous group of RR candidates and more homogeneous agricultural production patterns should result in a significantly lower standard error. Annex J presents an example of how screening methods can be developed using regression analysis. Of course, regression analysis would only make sense in situations where a very large number of road links need to be evaluated, so that correct decisions could be confidently predicted on the basis of an adequate sample. - 17 - III. SIMPLE ECONOMIC APPRAISAL METHODS 34. Purpose. This section presents simple appraisal methods in increasing order of complexity. There is not much difference in degree of complexity of the last three methods presentedj the difference between these methods pertains to different input requirements. If a proposed RR, group of interdependent RRs or investment packages of interdependent RR and agricultural components lpasses the test of a simple appraisal method, no further analysis is required unless the analyst wishes to know the percentage points by which an ER exceeds the opportunity cost of capital. In other words, to save time one accepts a project component or group of interdependent components if its "simple" ER exceeds the opportunity cost of capital. "Simple' ER is defined as an ER based on a significant portion of quantifiable benefits rather than on all. Simple ERs are all understatements of actual ERs. If project component(s) do not pass a simple appraisal, the use of a more time-consuming method is recommended. 35. The reliability (para. 9) of individual simple methods is of little interest if the aforementioned approach is followed. The reliability of the approach is as good as the reliability of the most complex methods (parasD 61, 62 and 66) proposed. These methods, which are also based otl a number of simplifications, were found to have a reliability of about 95%. 36. It is of interest to note that the majority of RRs reviewed for this study had actual ERs which significantly exceeded prevailing opportunity costs of capital. Consequently, a significant portion of time devoted to economic analyses would have been saved had the approach described below been followed. It is suggested that in addition to the simple ERs for project components, the actual ER for an entire RRs or RD project (i.e., not individual components) be computed when this approach is followed. In addition, the carrying out of sensitivity testing as normally done in appraisals may be done to test the sensitivity of simple ERs of project components. One should use a more time-consuming method if as a result of such testing a component is rejected. The reader may decide that some of the methods described below are so simple (e.g., simplified methods I, II, and III) that it is not worthwhile to first screen project components with one of the proposed methods of Section II. 37. Simplified Method I. This method is a simplified version of the consumer surplus (CS) approach. Its use is recommended in deciding whether an existing RR should be improved, wherever (i) existing traffic is significant, (ii) potential producer surplus benefits are insignificant, (iii) traffic is expected to grow at a constant rate, and (iv) traffic composition is not going; to change significantly. Traffic composition is the composition of types of vehicles such as private cars, motorcycles, horse- or ox-drawn vehicles, buses and cycles. 38. Table 3 is a tool for determining whether a particular RR improvement satisfies the condition that the ER equals the opportunity cost of capital (i) of 12% or more. It is assumed in this table that the average daily traffic (ADT) grouts at a rate (g) of 5% per annum in the with-project situation and that the expected life of the RR (N) is 10 years. The condition about the ER is then satisfied for any RR having vehicle operating - 18 - costs (VOC) and VOC savings (VOCS) as shown in the extreme left-hand columns; per kilometer costs of investment (CI) as shown in the top row of the table, and actual ADT no less than what is shown at the intersection of the appropriate VOCS row and the appropriate CI column. The improvement costs are defined as the present value of construction and incremental maintenance costs. Para. 20 mentions that maintenance costs may be ignored if their present value is less than 15% of the present value of the construction costs. The following example illustrates the use of Table 3. Suppose a decision is to be made about the economic viability of a proposed RR with the following characteristics: CI = $25,000 VOC = $ 0.50 VOCS = 25% g = 5% i 12% N = 10 years ADT = 95 (actual) The above ADT of 95 is compared with the ADT of Table 3 which pertains to g = 5%, VOC - $0.50, and VOCS = 25%. The proposed RR is economically viable if the actual ADT (95 in the example) is equal to or greater than the ADT obtained from Table 3 (77 in the example); otherwise it is not. Thus the RR of the example is feasible. Interpolation between CI, VOC and VOCS values of Table 3 may be required if the actual figures are not found in the table. 39. The ADT figures represent passenger cars, vans, medium and large trucks, buses, motorcycles, and animal-drawn vehicles. The VOC figures to be used are weighted averages of VOC of vehicles observed on the existing RR. Annex K shows ranges of CI and VOC values observed during the study. Annex L presents tables similar to Table 3 for combinations of variations in i ranging from 10% to 18%, variations in g ranging from 5% to 15%, and values of N equal to 10 and 15, while Annex M describes the manner in which these tables have been developed. 40. The tables of Annex L cannot be directly applied if costs of RR improvements occur over more than one year. In this case, the cost in each year must be adjusted to determine its worth in a base year. This is achieved by calculating its worth in the year just before benefits start accruing (year of opening). 41. Simplified Method II. Wouters' 8/ tables provide a simple way by which, with an acceptable degree of approximation, the ER of a proposed RR improvement can be established. The tables show ERs for benefit streams growing at compound rates varying between 5% and 20% and for periods of 10, 15, 20, 25, 30 and 40 years (Annex N). Use of the tables is recommended if (i) existing traffic is significant, (ii) potential producer surplus benefits are insignificant, and (iii) net benefits stemming from the improved RR are expected to grow at a given compound rate. 8/ V. Wouters, Internal Rates of Return Tables, World Bank, December 1967. Tab le 3 Critical Values of Average Daily Traffic!'/ • VOC VC- Cl ($/KR) a • (S/KN) 3 8000 11)000 18000 I0000 as00o 3s000 50000 75000 125000 a00000 isogoc . * 0.10 0.05 a .15 768 3383 1536 1920 2689 3841 5781 9602 15363 19204 a a 0,10 0.10 a 307 384 691 768 980 1344 1920 2661 480) 7882 9602 a a 0.10 0.15 a a'i% 256 461 S1? 840 696 1260 1920 3201 5121i 6401 a a 0.10 0.25 a 123 154 271 307 384 S38 788 1152 1920 3073 3841 a * 1 0ao o.i Oa 110 198 239 274 364 549 823 1372 M19 2743 a 0.10 o.so 4 6 77 130 154 192 289 3684 578 980 1538 1920 0.010 .0.75 Is 41 St 92 102 12 179 256 384 640 1024 1260o * 0.25 0.05 a 246 307 553 6)5 768 1075 1538 2305 384t 6145 7842 a 0.25 0.10 a 123 154 277 307 384 535 788 3152 1920 3073 3841 * 0.25 0.15 a aa 102 564 205 256 316 51278 1 260lag 2048 2581 * 0.25 0.25 a 49 65 III 123 154 2)5 307 48) 788 12I29 111836 U 0.25 0.35 a 35 44 79 88 IS0 154 219 329 S49 $87 1097U a 0.25 0.50 6 as 31 55 fit 77 )Og k 154 030 *aq p .g5 v6 & a 0.25 0.75 a 16 20 .31 41 51 72 10a 154 258 410 512 * 0.50 0.05 * 32Si 154 27 307 384 538 788 1152 1920 3073 3841a * 0.50 0.50 a 61 77 Ila 154 192 289 384 78960 1538 1920 a 0.50 o.js a dil St 92 102 128 III 256 384 640 1024 1260 * o.so 0.25 a as 31 Ss 81 77 108 154 230 384 815 766 * 0.50 0.35 a 18 22 40 44 55 71 I10 185 274 439 549. * 0.50 0.50 a l2 is 28 31 38 54 77 115 192 307 )64 * 0.50 0.75a Al 30 to 20 26 36 St 77 1a8 205 258. A 1.00 0.05 a b1 77 138 154 192 289 J84 .576 980 1536 190ao a 3.00 0.10 6 31 38 69 77 96 134 192 288 480 768 980 a 1.00 0.15 a 20 28 46 St 64 90 128 192 320 512 640 a a 3.00 0.25 a 12 is 28 31 38 54 77 115 192 307 384 a. 1.00 0.35, a 9 )) 20 22 27 38 55 82 137 219 274U * 1.00 0.,SOa 8 8 14 Is 19 27 S8 so 96 154 192. * 1.00 0.75 a 4 5 9 10 13 18 26 38 84 102 126 .--a …-------------------- .W----- --------0.. ................…... ...W.. a 2.00 0.05 a 31 38 89 77 96 134 192 266 480 788 960 S * 2.00 0.10 a Is 19 35 30 48 8? 98 144 240 384 460Q a 2.00 0ti5 a 10. 13 23 26 32 45 64 96 180 256 320 o 2.00 0.5as 6 8 14 I5 59 27 38 s8 98 154 192. a 2.00 0.3S a 4 10 II 14 19 27 41 69 I10 137 a 2.00 0.50 a 3 4 7 a 10 13 19 29 48 ?7 96. * 2.00 0.7,.a a I5 5 6 9 13 19 32 Si 64* …a------------------------------- ..p... ......W... ... .............…………… * 4.00 0,05 a Is 19 35 38 48 67 98 144 240 384 460 * 4,00 0.io e a 10 17 19 24 34 48 71 120 192 140. * 4.00 0.55 a 5 6 le 13 16 22 32 48 g0 128 180 * 4.00 0.25 a 3 4 7 a to 13 19 29 48 77 96a * fl.00 0.35 a a 3 55 7 10 14 21 34 5s 69 * 4.00 0.50 a 3 4 7 1 14 24 38 48 * 4.00 0.75 a I 2 3 3 4 6 10 36 26 32 1/ it is clear that th sijtuations 1 withsoe ofthe hihADTs and hihcosts o construction reporCe1nh the exception for *RRs and RD projects; thege situations have been included since they were observed in a few cases of the 20 projects reviewed. 2/ 0.05, 0.10, etc., mean a 5 percent, 10 percent, etc., saving in VOC of first column. - 20 - 42. The procedure for determining the ER with the help oiE Wouters' tables, consists of the following steps: Step 1: calculate the ratio C/B1, where C - the cost of RR improvement 9/ and Bl = the first year benefits or benefits in the base year; Step 2: refer to the appropriate compound growth rate -- that is, the rate at which net annual benefits are assumed to be growing; Step 3: locate the value closest to C/Bl in the a&ppropriate expected life column; Step 4: read off the corresponding ER. 43. Table 4 shows one of the tables of Annex N. To illustrate its use, consider a road authority that is examining the gravelling of a RR at a cost of $110,000. It estimates that this will save about $10,000 initially in VOC and these savings will increase each year at 5% per annum over an assumed 15-year life of the road. Thus, C/Bl = 11; Table 4 shows for C/Bl - 11.2679 an ER of 9%. Table 4: ER for Net Benefits Growing at 52 Compound Rate ""-N - l0 yrs 15 yrs 20 yrs 25 yre 30 yrs 40 yre 1 12.4587 20.7554 30.8305 43.0650 57.9219 97.8713 2 11.7691 19.0636 27.4958 37.2431 48.5107 76.5920 3 11.1327 17.5552 24.6260 32.4105 40.9806 60.8032 4 10.5444 16.2073 22.1477 28.3793 34.9162 48.9670 5 10.0000 I.0000 20.0000 25.0000 30.0000 40.0000 6 9.4955 13.9163 18.1324 22.1533 25.9881 33.1335 7 9.0275 12.9413 16.5027 19.7435 22.6925 27.8180 8 8.5927 12.0622 15.0759 17.6936 19.9674 23.6580 9 8.1884 11.2679 13.8225 15.9414 17.6991 20.3664 10 7.8118 10.5487 12.7177 14.4365 15.7986 17.7335 11 7.4608 9.8962 11.7408 13.1379 14.1961 15.6046 12 7.1331 9.3028 10.8741 12.0121 12.8361 13.8651 13 6.8269 8.7622 10.1028 11.0315 11.6748 12.4291 14 6.5405 8.2687 9.4143 10.1737 10.6770 11.2318 15 6.2723 7.8174 8.7978 9.4199 9.8146 10.2240 16 6.0209 7.4037 8.2440 8.7546 9.0649 9.3680 17 5.7849 7.0239 7.7452 8.1651 8.4095 8.6346 18 5.5632 6.6746 7.2946 7.6405 7.8334 8.0011 19 5.3547 6.3526 6.8864 7.1718 7.3245 7.4498 20 5.1585 6.0555 6.5155 6.7515 6.8726 6.9665 21 4.9736 5.7806 6.1778 6.3732 6.4693 6.5399 22 4.7991 5.5261 5.8693 6.0314 6.1080 6.1612 23 4.6345 5.2899 5.5870 5.7216 5.7827 5.8229 24 4.4789 5.0703 5.3278 5.4399 5.4887 5.5192 25 4.3318 4.8660 5.0d94 5.1828 5.2229 5.2451 26 4.1925 4.6755 4.8696 4.9476 4.9789 4.9966 27 4.0605 4.4976 4.6664 4.7317 4.7569 4.7704 28 3.9353 4.3313 4.4783 4.5329 4.5532 4.5636 29 3.8166 4.1755 4.3037 4.3495 4.3659 4.3738 30 3.7037 4.0294 4.1414 4.1798 4.1931 4.1992 9/ See para. 38 for the treatment of maintenance costs; alternatively, annual incremental maintenance costs may be deducted from annual benefits. - 21 - 44. Martinez IO/ haii developed a variation of the Wouters' tables. Ilis tables show EResfor net benefit streams growing at compound rates varying 'between 1% and 35X, for expected lives of 20, 25 and 30 years and -onstruction periods of 1, 2, 3, 4 and 5 years, so that the adjustment -entioned in para. 40 can be avoided. However the tables are not available Eor expected lives shorterc than 20 years. Instead of Annex N one may use 'Ialone's graphical method 11/ to determine the ER if the aforementioned C/Bj ratio, the expected life N, and the growth rate of g are given. Figure 3 presents Malone's method; the instructions given on this figure are self-explanatory. $.5. Simplified Method III. This method, which is a simplified version of the producer surplus (PS) approach, as well as Methods IV, V, VI, VII, and VIII is based on the following simplifying assumptions: (a) negligible salvage values of investments of the investment package; (b) no distinction between production patterns on farms of different size in road's zone of influence; (c) no distinction between farmgate prices of on-farm consumption and prices of exports from the road's zone of influence; and (d) no consideration of on-farm consumption by animals. With the possible exception of items (c) and (d), the effect of the above assumptions on the ER of project component(s) is to understate it. The effect of assumptions (c) and (d) could be either an understatement or overstatement of the simple ER. In the projects reviewed the effect of all four assumptions on the actual ERs was negligible. 46. Method III assumes that in addition to assumptions (a) through (d): (i) local market prices in the with- and without-project situations remain the same; (ii) the VOC savingsi related to non-agricultural traffic are negligible; (iii) on-farm (home) consumption in the with- and without-project situations is negligible; (iv) the value of production of the crops in the zone of influence in the with-project situation increases at a linear rate until it levels off ("full production"), while the corresponding value in the without-project situation either remains constant during the project's expected life or also increases at a linear rate until it levels off; and I0/ M. Martinez, Benefit-Cost Calculations: Tables for Internal Rates of Return and Sensitivity Tests, World Bank, January 1979. 11/ P. 0. Malone, Graphical Presentation of the Relations between C/B , N, and ER, EDI, World Bank, December 1967. - 22 - Figure 3: Graphical Presentation of the Relations between C/B, N, g and ER N = 4() year, t.,// ~~~~~~~~45%.. $ / - ~~~209% 7-15%40 10% Rate of Growthi (g) 5% 35%- 0 c The chart expresses, diagrammatically, the relationship 30_' between the variables in the exprcssion: C |U=(+) (I +g)+ (1+g)2 (1 +g)N 0U (I +R) (I +R)2 (I +R )3 If U= the ratio investment (C) base-year benefits (B) 25% If g = the annual rate of growth of benefits (assumed constant) If R discount rate UIfN = number of years then the diagram may be used to determine the discount rate (i.e. the internal rate of return) which satisfies the 20%- above equation for specific values of U, g, and N. Use of diagraen: Find point A in the family of curves corresponding to specific values of U and N. From A , K draw a line, parallel to the base of diagram to meet the heavy vertical line in B. From B draw a straight line 15% - tirough the point on the rate of growth line correspond- ing to the specific value of g. to meet the right-liand vertical line in point C. C then represents thc internal rate of return. 10%- 5 10 15 I [Ratio I e tment (C) Base-year benefits (B1)1 Source: EDI (World Bank) Training Materials. - 23 - (v) full production in the without-project situation is reached before or at the same time full production in the with-project situation is reached (thiti is normally the case). 'rhus, Method Ill should not be used in situations where existing traffic on i:he RR(s) is significant and agricultural production is marginal. A slightly different variation of this method was used in the appraisal of the Bihar Itural Roads Project. 47. Table 5 shows a crop's present unit value (CPV) as a function of :rears to achieve full potential benefits, project components' expected '.ives (N), and simple ERs.. The table is used by first determining the value of agricultural production when full production is reached in the with- project situation, the corresponding value in the without-project situation, aind the difference between these values. Calling this difference the approximate value added (AVA) one next establishes the ratio C/(AVA) where C i.s the present value of investment and maintenance costs of project c:omponents. The ER may now be obtained from Table 5 by locating the value :losest to this ratio in the appropriate "years to achieve full potential agricultural benefits" column; the ER which corresponds to this value is read (off in the first column of Table 5. Annex M discusses the manner in which C:PV factors have been derived and the justification for their use. t8. The procedure for determining the ER with the help of Table 5, consists of the following steps: Step 1: establish for each crop in the zone of influence in the without:- and with-project situations the year during which full production is reached and call these years P1 and P2, respectively; Step 2: determine for each crop in the zone of influence in the without-project situation the production in year P1 by computing the product of "area cultivated with the crop" times "its yield"; Step 3: determi.ne for each crop in the zone of influence in the with-project situation the production in year P2 by computing the sum of "unimproved area cultivated with the crop" t.imes "its yield" and "improved area cultivated with the crop" times "its yield"; Step 4: with the prevailing local market price, annual production of Step 2 and annual cost of production, calculate for each crop its net value in year Pl, and obtain the sum Z of these values; Step 5: with the prevailing local market price, annual production of Step 3, and annual cost of production, calculate for each crop its net value in year P2, and obtain the sum Z2 of these values; Step 6: select the largest P2 value from the P2 values established in Step 1 and call it P; - 24 - Table 5: Crop's Present Unit Values as a Function of Years to Achieve Full Potential 3enefits (CPV) for N - 5. 10. 15. 20 and 25 YEARS TO ACHIEVE FULL POTENTIAL AGRICULTURAL BENEFITS (P) 1 2 3 4 5 N-56 7 8 9 10 15 2f 101 3.8 3.3 2.9 2.5 111 3.7 3.2 2.8 2.4 12X 3.6 3.2 2.7 2.4 13S 3.5 3.1 2.7 2.3 141 3.4 3.0 2.6 2.2 15S 3.4 2.9 2.5 2.2 162 3.3 2.8 2.5 2.1 171 3.2 2.8 2.4 2.0 181 3.1 2.7 2.3 2.0 N10 10 6.1 5.7 5.3 4.9 4.5 4.1 3.8 3.5 3.2 111 5.9 5.4 5.0 4.6 4.3 3.9 3.6 3.3 3.0 121 5.7 5.2 4.8 4.4 4.0 3.7 3.4 3.1 2.8 132 5.4 5.8 4.6 4.2 3.8 3.5 3.2 3.0 2.7 141 5.2 4.8 4.4 4.0 3.7 3.4 3.1 2.8 2.5 151 5.0 4.6 4.2 3.8 3.5 3.2 2.9 2.7 2.4 161 4.8 4.4 4.0 3.7 3.3 3.0 2.8 2.5 2.3 171 4.7 4.2 3.8 3.5 3.2 2.9 2.6 2.4 2.2 181 4.5 4.1 3.7 3.3 3.0 2.8 2.5 2.3 2.1 N-15 101 7.6 6.7 6.7 6.3 5.9 5.6 5.3 5.0 4.6 4.4 3.2 112 7.2 6.3 6.3 5.9 5.6 5.2 4.9 4.6 4.3 4.0 2.9 121 6.8 6.0 5.9 5.6 5.2 4.9 4.6 4.3 4.0 3.8 2.7 13X 6.5 5.6 5.6 5.2 4.9 4.6 4.3 4.0 3.7 3.5 2.5 141 6.1 5.3 5.3 4.9 4.6 4.3 4.0 3.7 3.5 3.2 2.3 151 5.8 5.0 5.0 4.7 4.3 4.0 3.7 3.5 3.2 3.0 2.2 16% 5.6 4.8 4.8 4.4 4.1 3.8 3.5 3.3 3.0 2.8 2.0 171 5.3 4.5 4.5 3.2 3.8 3.6 3.3 3.1 2.8 2.6 1.9 181 5.1 4.3 4.3 3.9 3.6 3.4 3.1 2.9 2.7 2.5 1.8 N-2C 101 8.5 8.1 7.6 7.2 6.9 6.5 6.2 5.9 5.6 5.3 4.1 11 8.0 7.5 7.1 6.7 6.3 6.0 5.7 5.4 5.1 4.8 3.7 121 7.5 7.0 6.6 6.2 5.9 5.5 5.2 4.9 4.7 4.4 3.4 131 7.0 6.6 6.2 5.8 5.4 5.1 4.8 4.6 4.3 4.0 3.1 14X 6.6 6.2 5.8 5.4 5.1 4.8 4.5 4.2 4.0 3.7 2.8 152 6.3 5.8 5.4 5.1 4.7 4.4 4.1 3.9 3.7 3.4 2.6 161 5.9 5.5 5.1 4.8 4.4 4.1 3.9 3.6 3.4 3.2 2.4 172 5.6 5.2 4.8 4.5 4.1 3.9 3.6 3.4 3.1 3.0 2.2 181 5.4 4.9 4.5 4.2 3.9 3.6 3.4 3.1 2.9 2.7 2.0 N-25 101 9.1 8.6 8.2 7.8 7.4 7.1 6.7 6.4 6.1 5.8 4.7 3.8 11% 8.4 8.0 7.6 7.2 6.8 6.4 6.1 5.8 5.5 5.3 4.2 3.3 121 7.8 7.4 7.0 6.6 6.2 5.9 5.6 5.3 5.0 4.8 3.7 3.0 13X 7.3 6.9 6.5 6.1 5.8 5.4 5.1 4.9 4.6 4.4 3.4 2.7 14Z 6.9 6.4 6.0 5.7 5.3 5.0 4.7 4.5 4.2 4.0 3.1 2.4 151 6.5 6.0 5.6 5.3 4.9 4.6 4.4 4.1 3.9 3.6 2.8 2.2 161 6.1 5.7 5.3 4.9 4.6 4.3 4.0 3.8 3.6 3.4 2.5 2.0 171 5.8 5.3 5.0 4.6 4.3 4.0 3.7 3.5 3.3 3.1 2.3 1.8 181 5.5 5.0 4.7 4.3 4.0 3.7 3.5 3.3 3.0 2.9 2.1 1.7 - 25 - Step 7: establish the ratio "maintenance and investment costs of project components" over the "difference between Z2 and Z1 valu(es" and call it C/AVA; Step 8: read off the ER in the first column of Table 5 by locating the value closest to the C/AVA value in the column corresponding to the P value of Step 6. 49. The following example is presented to elucidate the use of the above step-by-step procedure. The construction of a 30 km gravel road and small irrigation works is proposed in a zone of influence of 6,500 ha. The opportunity cost of capltal is 12%. Present values of costs of construction and maintenance of the road and irrigation works amount to $1.20 and $0.20 million, respectively; each of these components has an expected life of 10 years. Table 6 gives the crop area breakdown and the crops' yields for the without- and with-project situations. Local market prices of the products considered, wheat and tomatoes, are $150 and $60 per ton respectively. Costs of wheat production per hectare are $80 for unimproved production and $90 for improved agricultural production technology. Similarly, the costs of production of tomatoes per hectare are $520 with unimproved and $550 with improved production technology. 50. The computatiOn of the ER proceeds as follows: Columns (20) and (21) of Table 6 present the sum of net agricultural production values for the two crops. The sixth year corresponds to the year where both with-project production values are at maximum or full production. Therefore year P - 6 (Step 6) and the net value added for that year is $0.52 million. The ratio of the present value of costs to value added benefits in year P is given by 1.40 - 2.69 (Step 7). rSearching in Table 5 under the column P = 6, the 0.52 nearest value to the ratio is 2.8 which corresponds to an ER - 18%. This simple ER is an understatement. 51. The step-by-step procedure does not call for the computation of all values of columns (7) through (10), and (16) through (21) of Table 6. These values are only needed for the years mentioned in Step 1. The other values are only presented because they pertain to examples of other simplified methods described below. 52. The comments about costs of investments and maintenance and project components with different expected lives made in paras. 17 and 20 apply equally to Simplified Method III. A further simplification may be introduced in carrying out the step-by-step procedure of this method by applying it first to the major crops in the zone of influence. If an acceptable simple ER is obtained, computations related to other minor crops can be omitted; otherwise they have to be carried out to check the resulting ER. While following this further simplification, one should, however, take into account costs of agricultural investments for both major and minor crops. 53. Simplified Method IV. Except for assumptions (iv) and (v) of para. 46, this method is based on the assumptions of paras. 45 and 46. The resulting simple ER is therefore less at risk of understating the actual ER than the simple ER obtained with Method III. Use of Method IV is not Table 6: Crop Area Breakdown, Yields and Production Values WHEAT TOMATOES w/o w/Project Production w/o w/Project Production Prod-Value Value .dded Proj. Areas Yields Production Value Project Areas Yields Production Value (all crops) (all crops) Year Areas (000 ha) (ton/ha) (000tons) (000$) Areas (000 ha) (ton/ha) (O00tons) (000$) (000$) (000$) (OOOha) Unimp Imp Unimp Imp w/o With w/o With (OOOha) Unimp Imp Unimp Imp w/o With w/o With w/o With (i) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (2t1 (22) 1 4.00 4.00 1.00 0.56 0.90 2.240 3.140 16 61 0.30 0.30 0.16 9.11 15.0 2.733 5.133 8 64 24 125 101 2 4.50 3.50 2.00 0.59 0.90 2.655 3.865 38 120 0.30 0.20 0.18 9.55 20.0 2.865 5.980 16 130 54 248 194 3 4.50 3.10 2.40 0.61 1.00 2.750 4.291 53 180 0.30 0.20 0.28 10.00 20.0 3.000 7.600 24 198 77 378 301 4 4.85 2.00 3.50 0.63 1.00 3.055 4.760 70 239 0.40 0.10 0.39 10.00 20.0 4.000 8.800 32 261 102 500 398 5 4.90 1.00 4.70 0.65 1.00 3.190 5.350 87 300 0.50 0.00 0.50 10.00 20.0 5.000 10.000 40 325 127 625 498 6 5.00 0.00 6.00 0.70 1.00 3.500 6.000 125 360 0.50 0.00 0.50 10.00 20.0 5.000 10.000 40 325 165 685 520 7 5.00 0.00 6.00 0.70 1.00 3.500 6.000 125 360 0.50 0.00 0.50 10.00 20.0 5.000 10.000 40 325 165 685 520 8 5.00 0.00 6.00 0.70 1.00 3.500 6.000 125 360 0.50 0.00 0.50 10.00 20.0 5.000 10.000 40 325 165 685 520 9 5.00 0.00 6.00 0.70 1.00 3.500 6.000 125 360 1 0.50 0.00 0.50 10.00 20.0 5.000 10.000 40 325 165 685 520 10 5.00 0.00 6.00 0.70 1.00 3.500 6.000 125 360 I 0.50 0.00 0.50 10.00 20.0 5.000 10.000 40 325 165 685 520 Note: Column 7 = Column (2) x Column (5) " 8 = Column (3) x Column (5) + Column (4) x Column (6) " 9 = Column (7) x $150 - Column (2) x $80 10 = Column (8) x $150 - Column (3) x $80 - Column (4) x $90 16 -Column (11) x Column (14) j " 17 = Column (12) x Column (14) + Column (13) x Column (15) 18 = Column (16) x 60 - Column (11) x $520 " 19 = Column (17) x 60 - Column (12) x $520 - Column (13) x $550 " 20 - Column (9) + Column (18) 21 -Column (10) + Column (19) 22 = Column (21) - Column (20) - 27 - recommended if existing traffic on RR(s) is significant and agricultural production is marginal. 54. The annual benefits B stemming from investments in RR and agricultural components in a zone of influence with one agricultural crop are given by: 12/ B = Pm(Q2 - Q1 - C2 - Q2k2 + Cl + Q1k1 ................. (10) where Pm = crop's local market price ($ per ton), Q2t Ql = annual production of crop in with- and without-project situation, respectively (tons), C2, C1 = economic cost of producing Q2 and Ql, respectively ($), k2, ki = economic costs of transport over the RR in the with- and without-project situation, respectively ($ per ton). Another way of stating expression (10) is: Crop's annual Local Crop's annual Crop's annual Crop's annual value added =markel: x incremental - incremental - incremental price production production transport iF iL _ _ __ costs costs 55. To determine the simple ER one has to (i) compute the crop's net annual value for each year of the expected life and (ii) carry out similar computations for all other crops in the zone of influence. Once all benefit streams and costs of investment and maintenance of RR(s) and agricultural components have been established, the simple ER is computed in a manner similar to the conventional ER computations. Since techniques for calculating ERs are well known they are not illustrated here. The simplification referred to in para. 52 may also be introduced in Method IV. 56. The step-by-step procedure for determining the benefit streams required for the computation of the simple ER is as follows: Step 1: determine for each crop in the zone of influence in the without-project situation the annual production during the 12/ See Annex M for derivations of expressions (10) and (11); Annex 1 of Staff Working Paper 362 (H. L. Beenhakker and A. Chammari, October 1979) is reproduced as Annex 0 of this paper, since Annex M uses some of the results of this Annex 1. - 28 - expected life by computing the product of "area cultivated with this crop" times "its yield"; Step 2: determine for each crop in the zone of influence in the with-project situation the annual production during the expected life by computing the sum of "unimproved area cultivated with the crop" times "its yield" and "improved area cultivated with the crop" times "its yield"; Step 3: with the prevailing local market price and annual production of Steps 1 and 2, calculate annual production values in the without- and with-project situations and consequent annual incremental production values; Step 4: for each crop in the zone of influence, determine annual incremental agricultural production costs during the expected life; Step 5: for each crop in the zone of influence, determine the annual incremental transport costs during the expected life; and Step 6: estimate annual incremental road maintenance costs (routine and periodic). Results of Steps 3 through 6 together with costs of investments of RR(s) and agricultural components are all the data necessary to establish the simple ER. Further simplifications in carrying out the steps may be introduced by doing the calculations only for every 2 or 3 years of the expected life and obtaining values for intervening years by interpolation. 57. The following example illustrates the use of the step-by-step procedure. The construction of a 30 km gravel road and wells together with a strengthening of extension services is proposed in a zone of influence of 6,500 ha. Costs of constructing the road and wells amount to $1.00 and $0.20 million, respectively. The expected life of these components is 10 years. Table 6 gives the crop area breakdown and the crops' yields, while Table 7 shows the crops' annual production costs, including costs of extension services, costs per ton of transport, and road maintenance costs in the with- and without-project situations. The costs of per ton of transport in columns (8) and (9) have been arrived at by multiplying the length of the road (30 km) by the per ton-km transport costs in the without- and with-project situations ($0.29 and $0.11, respectively). Results of: Step 1 are shown in columns (7) and (14) of Table 6, Step 2 are shown in columns (8) and (15) of Table 6, Step 3 are shown in columns (20), (21) and (22) of Table 6, Step 4 are shown in columns (6) and (7) of Table 7, Step 5 are shown in columns (14) and (15) of Table 7, Step 6 are shown in column (18) of Table 7. The investment costs of $1.00 and $0.20 million and cost and benefit streams obtained from carrying out Steps 3 through 6 result in an ER of 30.99X. Table 7: Anal wiculturel Productiou. Tran_rt and load antenaoe Cwats TYer A4ridturl prondction &ar= smr ro6yo 2 ucra1 -r "'-. ' zzv. :^:-e-rt-rt 1=rt tl *-tS rl !A t4ont"eoaC r-t- t new,arnt.A Road Etbout-Situ tion Co t t OOOS) Prdution Costs ('0000) S per ton km Coaut9t to tb-St tlon0 Tranprt. CwCt ( OOOS) ( OOOS) (an costs Wigre ii)I With-Situation Without-SItuai Witb-Sltuation o10o Wheat StoO0 WhaI t T toa Whet T to Without Wth "beat Tonaions Wheat Ttoem Wheat at., Without With (1) (2) (3) (4) (5) (6) (e (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) 1 328.00 1M6.601 423.00 245.40 95.00 88.80 8.70 3.30 19.49 23.77 10.36 16.94 -9.13 -6.83 0 0 0 2 369.00 156.60 477.00 230.40 108.00 73.80 8.70 3.30 23.10 24.93 12.75 19.73 -10.35 -5.20 0 0 0 3 369.00 156.60 482.20 259.80 113.20 103.20 8.70 3.30 23.93 26.10 14.16 25.08 -9.77 -1.02 0 10 10 4 397.70 208.80 896.50 268.65 98.80 59.85 8.70 3.30 26.58 34.80 15.71 29.04 -10.87 -5.76 0 10 10 5 401.80 261.00 528.50 277.50 126.70 16.50 8.70 3.30 27.75 43.50 17.66 33.00 -10.09 -10.fO 0 10 10 6 410.00 261.00 570.00 277.50 160.00 16.50 8.70 3.30 30.45 43.50 19.80 33.00 -9.78 -10.50 0 25 25 7 410.00 261.00 570.00 277.50 160.00 16.50 8.70 3.30 30.45 43.50 19.80 33.00 -10.65 -10.50 0 10 10 8 410.00 261.00 570.00 277.50 160.00 16.50 8.70 3.30 30.45 43.50 19.80 33.00 -10.65 -10.50 0 10 10 1 9 410.00 261.00 570.00 277.50 160.00 16.50 8.70 3.30 30.45 43.50 19.80 33.00 -10.65 -10.50 0 10 10 10 410.00 261.00 570.00 277.50 160.00 16.50 8.70 3.30 30.45 43.50 19.80 33.00 -10.65 -10.50 0 25 25 note: Colum (6) - Colmn (4) - Column (2) Colu n(7) - Coluasn (5) - Colim (3) Colum (10) - Colimm (7) of table 6 tm Colun (8) a/ The agricultural productio costs Include both the agricultural production costs of Table 6 and the Colum (11) - Colun (16) of Table 6 tim. Colaln (8) anal coat of the extenion services. The annual costs of extension servicee per hectare are Colum (12) - Column (8) of Table 6 tims Colun (9) $2 for un12roved production and $5 for inproved prodution tehbnology. Colo (13) - Colm (17) of Table 6 times Column (9) Colun (14) - colum (12) - Column (10) Colunn (15) - Columm (13) - Colum (11) Colum (18) - Colm (17) - Colm (16) - 30 - 58. Simplified Method V. Except for assumptions (iii), (iv) and (v) of para. 46, this method is based on the assumptions of paras. 45 and 46. Method V, unlike Method IV, thus allows for a home consumption in the with- and without-project situations. Home consumption was included in the economic analysis in one of the 20 projects reviewed. Consideration of home consumption may be important if subsistence farming prevails in the without-project situation while exports from the RRs' zones of influence are expected in the with-project situation. 59. If home consumption is taken into account, the value of B of expression (10) has to be reduced by: (Hlkl - H2k2) ............... (11) where H1H2 = on-farm (home) consumption of an agricultural crop produced in the area of influence, in the without- and with-project situation, respectively (tons), and k1k2 = economic costs of transport over the RR in the without- and with-project situation, respectively ($ per ton). Method V requires the following step in addition to steps 1 through 6 of Method IV: Step 7: for each crop in the zone of influence, determine the difference between the products of "annual home consumption" times "economic costs of transport" in the without- and with-project situations. Results of Steps 3 through 6 of para. 56, the above Step 7 together with costs of investments of RR(s) and agricultural components are all the data needed to establish the simple ER. 60. To determine home consumption, the population in the zone of influence is first determined. Referring to the example of para. 57, suppose the area of influence has a base population of 60,000 which is growing at a rate of 2.5% per annum and has a per capita home consumption of 15 kg and 12 kg of wheat and 0.5 kg and 0.3 kg of tomatoes in the without- and with-project situation, respectively. Table 8 shows the results of Step 7 applied to this example. Table 8: Annual On-Farm (Home)- Consumption, H1k1, and H2 k2 1/ 1 Year Population Wheat On Farm Tomatoes On Farm Wheat Tomatoes-/ ('000) Consumption Consumption H k) H2 k2 H1kl H2k2; Hlk1 H2 k2 (H1 k1 - H2 k2) ('000 tons) ('000 tons) (00 ('000$) (000$) J ('000 $) ('000 $) ('000$) Without With Without With (H1) (H2) (H1) (H2) 1? {(2) (3T (4) (5s (6) (7) (8) (9) (10) (11) (12) 1 60.00 0.90 0.90 0.03 0.03 7.83 2.97 4.86 0.26 0.10 0.16 2 61.50 0.92 0.92 0.03 0.03 8.00 3.04 4.96 0.26 0.10 0.16 3 63.00 0.95 0.76 0.03 0.02 8.26 2.51 5.75 0.26 0.07 0.19 4 66.20 0.99 0.79 0.03 0.02 8.61 2.61 6.00 0.26 0.07 0.19 5 67.80 1.02 0.81 0.03 0.02 8.87 2.67 6.20 0.26 0.07 0.19 6 69.50 1.04 0.83 0.03 0.02 9.05 2.74 6.31 0.26 0.07 0.19 7 71.30 1.07 0.86 0.04 0.02 9.31 2.84 6.47 0.35 0.07 0.28 8 73.10 1.10 0.88 0.04 0.02 9.57 2.90 6.67 0.35 0.07 0.28 9 74.90 1.12 0.90 0.04 0.02 9.74 2.97 6.77 0.35 0.07 0.28 10 76.80 1.15 0.92 0.04 0.02 10.01 3.04 6.97 0.35 0.07 0.28 1/ k, and k2 values are given in Columns (8) and (9) of Table 7, respectively. Note: Column 7 = Column (3) times Column (8) of Table 7 Column 8 - Column (4) times Column (9) of Table 7 Column 10= Columm (5) times Column (8) of Table 7 Column 11= Column (6) times Column (9) of Table 7 Column (9) = Column (7) - Column (8) Column (12) = Column (10) - Column (11) - 32 - Columns (9) and (12) indicate that, unless the population in the zone of influence is large, the effect of on-farm consumption on the simple ER is small. The ER of 30.17% is slightly lover than computed in para. 57. 61. Simplified Method VI. Except for assumptions (ii) through (v) of para. 46, this method is based on the assumptions of para. 45. In other words, the VOC savings related to non-agricultural traffic are not negligible. Consequently, annual savings from this source have to be added to the cost and benefit streams established by Steps 1 through 6 of Method IV and Step 7 of Method V. Naturally Step 7 may be omitted If the effects of home consumption on the ER are insignificant. The manner in which VOC savings are computed is not discussed here, since this is done elsewhere in the literature. 13/ 62. Simplified Method VII. This method is based on the same assumptions as those underlying Method VI. The difference between Methods VI and VII is that number VI uses local market prices while number VII uses farmgate prices in the without-project situation. We define: Pm = local market price of an agricultural product ($/ton), P1 = farmgate price of an agricultural product in the without- project situation ($/ton), P2 - farmgate price of an agricultural product in the with-project situation ($/ton), F1 - freight rate for transporting one ton of agricultural products over the RR in the without-project situation ($/ton), and F2 = freight rate for transporting one ton of agricultural products over the RR in the with-project situation ($/ton). Note that Pm = P2 + F2 - P1 + F1. To use the farmgate price in the without-project situation rather than the local market price, one replaces Pm by P1 in expression (10) and adds F1(q2 - ql) where q2 and q1 are the quantities of an agricultural product "exported" from the zone of influence (Annex M). Thus q2 - Q2 - H2 and q 1 - - Hl. 63. The step-by-step procedure consists of Steps 1 through 6 of Method IV (para. 56) with Pm replaced by Pl, folloved by Step 7 of Method V (para. 59) if home consumption is significant, followed by the determination of the VOC savings related to non-agricultural traffic of Method VI,, followed by Step 8. The determination of VOC savings may be skipped if non-agricultural traffic is insignificant. Step 8: for each crop in the zone of influence determine the product of "freight rate for transporting one ton of agricultural products on the RR in the without-project situation" times "annual Incremental exports from the zone of influence." 13/ See, for instance, H. G. van der Tak and Anandarup Ray, ibid. - 33 - Referring to the example of paras. 57 and 60, suppose the freight rate per ton km in the without-project situation amounts to $0.36, or $10.8 per ton over the 30 km RR. Table 9 shows the results of Step 8 applied to this example. 64. Note that Pm - P2 + F2 - Pi + F1 may be expanded by defining: r2,rl - truckeir's profit related to his transporting one ton over the RR in the with- and without-project situation, respectively ($ per ton), so that PM m P2 + F2 - PI + F1 - Pa + k2 + r2 - PI + kl + rl, where k, and k2 are as defined in para. 59. It is evident that P1 in Method VII may be replaced by (Pm - F1), (P2 + F2 - 71) (Pm - kl - rl), or (Pm + k2 + r2 - kl - r ). The method has baeu described in terms of P1 since information about P1 is generally more readily available than information about F2, r1 and r2. 65. Compared with the first five simplifying methods, Methods VI and VII, including Step 7 and VOC savings of non-agricultural traffic, are based on the smallest number of simplifying assumptions. They also offer the additional advantage of providing a practical tool for examining alternative road and agricultural investment strategies to determine an optimal investment package. In most cases the difference between their resulting ERs and actual ERs is expected to be insignificant. The actual ERB of the 20 projects reviewed were the same as the ERs computed by Methods VI and VII. 66. Simplified Method VIII. This method, which is based on the assumptions of para. 45, allows for a difference in local market prices in the without- and with-project situations. This difference may occur when the quality of agricultural products in the with-project situation is better than that in the without-project situation. The difference may also occur when increases in production due to significant agricultural investments in RRs' zones of influence are so substantial that they may affect the prices of agricultural products in a country. Price effects caused by a project, which are often included in the definition of externalities, are the exception. Such effects were not observed in the 20 projects reviewed. To allow for the aforementioned difference in local market prices, one defines: Pml - local market price of an agricultural product in the without-project situation ($/ton); Pm2 - local inrket price of an agricultural product in the with-project situation ($/ton). Note that Pm3 - P1 + k1 + rl, and Pm2 - P2 + k2 + r2 where Pi, P2, k1, k2, r, and r2 are as defined above. - 34. - Table 9: F (Q- q) 12 2 .- 1(q2-.ql ) Year Wheat Exports Tomato Exports Incremental Exports Wheat Tomatoes ('000 tons) ('000 tons) ('000 tons)- .ithout With Without With Wheat Tomatoes (1) (2) (3) (4) (5) (6) (7) (8) (9) 1 1.34 2.24 2.70 5.10 0.90 2.40 9.72 25.92 2 1.74 2.95 2.84 5.95 1.21 3.11 13.07 33.59 3 1.80 3.53 2.97 7.58 1.73 4.61 18.68 49.79 4 2.07 3.97 3.97 8.78 1.90 4.81 20.52 51.95 5 2.17 4.54 4.97 9.98 2.37 5.01 25.60 54.11 6 2.36 5.17 4.96 9.98 2.81 5.02 30.35 54.22 7 2.43 5.14 4.96 9.98 2.71 5.02 29.27 54.22 8 2.40 5.12 4.96 9.98 2.72 5.02 29.38 54.22 9 2.38 5.10 4.96 9.98 2.72 5.02 29.38 54.22 10 2.35 5.08 4.96 9.98 2.73 5.02 29.48 54.22 Note: Column (2) - Column (2) of Table 7 - Column (3) of Table 8 Column (3) = Column (4) of Table 7 - Column (4) of Table 8 Column (4) = Column (3) of Table 7 - Column (5) of Table 8 Column (5) - Column (4) of Table 7 - Column (6) of Table 8 Column (6) Column (3) - Column (2) Column (7) = Column (5) - Column (4) Column (8) = Column 6 times $10.8 Column 9 = Column 7 times $10.8 - 35 - 67. Ignoring for the time being home consumption and VOC savings related to non-agricultural traffic, the annual benefits B stemming from :Fnvestments in RR and agricultural components in a zone of influence with one n3gricultural crop are given by: B = Pm2Q2 - Pm1Q1 - C2 - Q2k2 + C1 + Qlkl ...... (12) w,here all terms are as defined earlier. Note that the difference between expressions (10) and (12) relate to local market prices. The step-by-step procedure for determining the benefit streams required for the computation of The simple ER is, with the following exception, like the one described in para. 56 under Method IV. The exception is that Step 3 of this procedure -eads as follows: Step 3: With the prevailing local market prices Pm1 and Pm2 and annual production of Steps 1 and 2, determine annual production values in the without- and with-project situat:Lons and consequent annual incremental production values. Trhe procedures described inder Method V to allow for home consumption and Aethod VI to allow for VOC savings related to non-agricultural traffic remain inchanged (paras. 59 and 61). j8. If the analyst is reluctant to make the assumptions underlying {ethod VIII or the assumptions of para. 45, the use of the Rural Roads Computer Program 14, is recommended. This program also provides a RR aetwork analysis, an examination of the links between savings in transport costs and improved farmgate prices, an aggregation of benefits by beneficiary groups, and the determination of optimal investment years. It is, however, nore time-consuming to use than the eight methods described here, since computer data files have to be prepared. 69. Sequence of Simplified Methods. To save time, it is important to know which simplified method to start with and in what sequence to try other methods. For instance, it would not make sense to start with Methods I or II if existing traffic is insignificant and significant producer surplus benefits are anticipated. Alternatively, it would not be wise to start with Method III if significant VOC savings related to non-agricultural traffic are expected. If one foresees significant consumer and producer surplus benefits, the first simplified method to be used should be Method VI. In situations where only significant producer surplus benefits are expected, and on-farm consumption is insignificant, the sequence of Methods III, IV, and VII without VOC savings related to non-agricultural traffic may 'be right. Table 10 summarizes the assumptions made in each of the methods. 14/ H. L. Beenhakker and A. Chammari, ibid. - 36 - Table .0: Simplified Methods and Underlying Asswwptions (1) (2) (3) (4) (5) (6) (7) (8) (9) Simplifled Method W f Assumption I II III IV V Vl VI_ VIII Significant existing traffic X X Constant growth rate of traffic X No change in traffic composition X Potential producer surplus benefits insignificant X X Constant growth rate of net benefits steaming from rural road improvement X Full production in the without-project situation is reached before or at the same time full production in the with_ project situation is reached X Negligible salvage values of invest- ments of the investment package X X X X X X No distinction between production patterns on farms of different size in road's zone of influence X X X x X X No distinction between farmgate prices of on-farm consumption and prices of exports from the road's zone of influende x x x X I X No consideration of on-farm consumption by animals X X X X X X Local market prices in the with- and without-project situations remain the same X X X X X VOC savings related to non-agricultural traffic insignificant X X X On-farm consumption in the with-.and withoub-project situations negligible X X Value of production of the crops in the zone of influence in the with-project situation increases at linear rate until it levels off ("full production") while the corresponding value in the X without-project situation either remain constant during the project's expected life or -also- increases at a ltnear rate until it levels off. 1/ A check in one of the columns 2-9 means that the asmsuption. of column (1) in made. - 37 - IV.. SIMILARITIES AND DIFFERENCES 70. Purpose. This siection discusses similarities and differences observed in the review of the 20 projects listed in Annex A and suggests areas for improvement or frurther analysis. The reader is reminded that the principal objective of the study was the development of simple operational aLpproaches to screening and appraisal which save time for the project analyst. Consequently, the areas for improvement discussed below are not necessarily exhaustive bul: only those suggested by the study. 11. VOC Savings. Ahnex K shows a wide variation in VOC savings :reported in the feasibility reports analyzed. These variations reflect to some extent differences between the Kenya VOC tables developed by the rransport and Road Research Laboratory ±5/ and earlier tables developed by ,le Weille, 16/ Bonney and Stevens, 17/ iand others. For earth and gravel roads these tables show large differences in VOCs. 72. There is, therefore, a need for analyzing VOC savings to be had Erom improved earth and gravel RRs. Such an analysis should also cover the sffects of possible shifts from animal-drawn carts to motorized vehicles after road improvements have been implemented. 73. Construction Coists. The feasibility reports also showed significant discrepancy in per kilometer costs of regravelling and paving (bituminous surface treatment) of RRs (Annex K). Costs of regravelling per kilometer range from $8,000 to $25,000 and the per kilometer costs of treating a gravel road with a bituminous surface range from $100,000 to $200,000. Most of the discrepancy is probably explained by factors such as topography, soil conditions, wage levels, fuels, and location of the source of building materials. However, the variations may also imply differences in design standards for RRs 'with about the same ADT among countries. 74. Another conclusion from the review is that more attention might be given in the selection of road improvements to the nature of the crops in a zone of influence. Some projects propose the same road standards for zones growing crops susceptible to damage such as tomatoes, peaches and pears as, for other regions where the crops are damage-resistant. 15/ S. W. Abayanayaka et al., Tables for Estimating Vehicle Operating Costs in Developing Countries, TRRL Report 723, Transport and Road Research Laboratory, 1976. 16/ Jan de Weille, Quantification of Road User Savings, World Bank Occasional Paper No. 2, The John Hopkins Press, 1966. 17/ R. S. P. Bonney & N. F. Stevens, Vehicle Operating Costs on Bituminous, Gravel and Earth Roads in East and Central Africa, Road Research Technical Paper No. 76, Road Research Laboratory, Ministry of Transport, London. Her Majestyts Stationery Office, 1967, p. 22. - 38 - 75. State of Project Preparation. The state of preparation of engineering work at the point of appraisal varies between RRs and RD projects. In RRs projects, the engineering work for the first year's program has normally been completed at the time of appraisal. In RD projects, it is often done after a Bank loan or credit is granted. Moreover, in some RD projects the exact location and alignment of RRs is not established during appraisal. The implementation of RR improvements in RD projects is therefore often behind schedule with the result that disbursements are delayed. The minimum requirement is that the engineering necessary for the first year's program, which may be limited in scope (para. 76), is completed before Board presentation (OMS 2.28). This should be sufficient for starting construction and should also provide an adequate basis for the cost estimate of the project. 76. For many simple RR improvements it may be enough to complete limited engineering work provided that design standards, construction procedures, and reliable historical data (updated) for representative items are available at the time of appraisal. "Final" engineering as appropriate to such cases would normally be performed only shortly before construction starts (OMS 2.28). 77. Maintenance Costs. Tests performed on the sample of 110 RRs (para. 18) revealed that in most situations it may be possible to ignore RR maintenance costs without significantly affecting the economic feasibility of a proposed RR. The improvement of only one out of the 110 RRs examined ceased to be economically viable when maintenance costs were included. 78. Prescreening. Some of the projects reviewed used a prescreening technique based on a combination of social, political, technical'and economic factors. This practice is not to be recommended if project components subjected to such prescreening are subsequently subjected to an economic evaluation (para. 15) since it may be time-consuming. This is so since the prescreening may accept a large number of RR candidates, which are subsequently rejected in the economic appraisal. A more efficient approach starts with prescreening based on social, technical and political criteria followed by screening on the basis of economic criteria. 79. Agricultural Response Rates. Only two projects among those reviewed (Benin and Tunisia RRs projects) analyzed the response of the farmers in the zone of influence to improved RRs or lower freight cost. The reason is that little is known about the quantitative relation between changes in transport cost and in production. Policy questions about the distribution of transport benefits among farmers, truckers and final consumers were often inadequately considered in the projects. The distributional aspect of projects does require consideration if one wants to bring about a more equal distribution of income and a better response rate on the part of farmers. Related questions to be raised at the policy level include: - are transport services fully competitive or hampered by regulation? - are crop prices adequate? - 39 - - what is the land tenure situation? and - how is accessi to credit and what are its terms and conditions? f80. Employment Benefits. The treatment of these effects varies among t:he projects. In the majority of cases these effects were ignored. Some projects count them direct:ly as benefits stemming from participation in RR ctonstruction by locals; others apply shadow pricing to the labor employed in road construction. Il1. Interdependencies. The Bank's practice in the appraisal of RRs projects is to determine l:he ER for each RR, as was done in the 15 RRs projects reviewed. In the appraisal of RRs in RD projects the practice is to itstablish an ER for the entire investment including all roads and aigricultural components such as irrigation works, supply of inputs, extension ,ervices and credit in all project areas. The latter practice may have i7esulted in Bank financing of RRs in RD projects which would have been rejected had they been part of a RR project. The reason for the difference :Ln these practices is based on the argument that the establishment of 3eparate ERs for the roads components of a RD project requires arbitrary dlecisions on how to attribute essentially joint results to different Lnvestment components. 32. The basis for this argument is often weak or non-existing. Project ,alements, including RRs, should constitute an economically viable package of Investment and production techniques through their appropriate design, 3tandards and synergism. A project may consist of one or more of such packages. In addition, a project may, together with other ongoing or planned projects, constitute a set of economically viable packages. RRs of a RD project should not, however, a priori, be thought of as being interdependent among each other and agricultural components as well. Neither is it necessarily true that a RR component of an investment package which constitutes part of a RD project is dependent on agricultural components of this package. Clear cases of interdependence among RR and agricultural components are (i) the coastruction of irrigation canals and dams together with that of RRs to maintain the irrigation works, (ii) the construction of all-weather RRs in areas where agricultural investments are proposed and where the present condition of such RRa would impede farm operations during the rainy season, and (iii) the improvement of RRs in areas with proposed investments for the production of perishable products such as tomatoes, peaches, pears, etc. Assuming interdependency without testing it may lead to the "mixing in" of production elements with elements which by themselves would not offer an acceptable ER. 83. CPN 2.01 describes the manner in which interdependency among project elements should be tested. First, one has to carefully specify the interrelationships between the various components. Next, an identification of all feasible and meaningful combinations of project components is called - 40 - for. If, for instance, there are three components, A, B, and C, the maximum number of options to choose from are A, B, C, A+B, B+C, A+C, and A+B+C. Next, the net present value (NPV) or ER of each feasible combination is computed to determine whether it is economically viable. 18/ There is no apparent reason why the identification of feasible combinitEions of project elements of a RD project should differ from such identification in RRs projects. The identification of feasible project combinations of RD projects or RRs projects complementing ongoing or planned agricultural projects calls for the consideration of possible interdependency among RRs, among agricultural components, and among RR and agricultural components. For RRs and RD projects covering large areas, such consideration should start with a breakdown of subareas. 18/ CPN 2.01 points out that the use of the ER does not necessarily lead to the choice of the optimal combination if this choice is based on the highest ER value. - 41 - ANNEX A Page 1 DATA SOURCES REVIEWED This annex reports the main data sources used in the analysis. The documents reviewed are classified into three major groups: 1. Data Sources for Selecting the Sample of 110 Rural Roads Analyzed in the Study. 2. World Bank Documents. 3. Other Pertinent Documents. 1. Data Sources for Selecting Sample of 110 Rural Roads Country Documents Honduras . Gitec Consult GMBH. Report on the Preparation of Rural Roads Components of the Proposed Eighth Highway Project. Prepared for the Honduras Ministry of Communications, Public Works and Transport. Tegucigalpa, D.C., Honduras. January 1980 (2 vols.) Brazil . BNDE-BIRD-DNER-Estado da Bahia. Secretaria Dos Transportes e Comunicacoes. Coordenacao Dos Transportes, Consorcio Rodoviario. Rodovias Vicinais. Estudo de Viabilidade Tecnico-Economica: Avaliacao Economica: Region Cacaueira. Vol. II. Tomo 3.1.2 1979. India . Government of Bihar. Rural Engineering Organization, Advance Planning Wing. World Bank data. Bihar, India. May 1978. Computer Printouts of Selected Roads in the Bihar files. Colombia . Republica de Colombia, Ministerio de Obras Publicas y Transportes. Fondo Nacional de Caminos Vecinales, Oficina de Planeacion. Caminos para la Integracion Nacional: Estudios de Seleccion. Bogota, Colombia, 1981. - 42 - ANNEX A Page 2 Country Documents Indonesia . World Bank data. Indonesia Rural Roads Development. December 10, 1981. Tunisia . BCEOM-SCET International. Projet de Pistes Agricoles (Identifications et Factibilites). Rapport Regional II. Volume 15, Rapport de Synthese. Republique Tunisienne, Ministere de l'Equipement, Direction des Ponts et Chaussees, Tunis, Octobre 1980. Computer Printouts of the Economic Analysis of Rural Roads. Benin . Scott Wilson Kirkpatrick & Partners. Benin Rural Feeder Roads. Evaluation Report of the Proposed Road Projects for Construction Program of 1980. December 1979. Philippines . World Bank data. Working Papers on Economic Evaluation of Project (undated). 2. World Bank Documents (1) Rural Roads Projects Benin . World Bank data. Feeder Roads Project, People's Republic of Benin. May 10, 1977. Brazil . World Bank data. Second Feeder Roads Project, Brazil. June 6, 1979. Cameroon . World Bank data. Feeder Roads Project, United Republic of Cameroon. November 15, 1977. Colombia . World Bank data. Rural Roads Project, Colombia. March 9, 1981. - 43 - ANNEX A Page 3 Country Documents Ecuador . World Bank data. Sixth Highway Project, Ecuador. May 30, 1980. Ethiopia . World Bank data. Sixth Highway Project, Ethiopia. March 31, 1975. Honduras . World Bank data. Eighth Highway Project, Honduras. August 16, 1980. India World Bank data. Bihar Rural Roads Project, India. October 10, 1980. Indonesia World Bank data. Rural Roads Development Project, Indonesia. December 10, 1981. Kenya . World Bank data. Rural Access Roads Project, Republic of Kenya. June 3, 1976. Malawi . World Bank data. Fourth Highway Project, Malawi. December 22, 1980. Philippines . World Bank data. Rural Roads Improvement Project, Philippines. April 30, 1980. Senegal . World Bank data. Feeder Roads Project, Senegal. March 4, 1976. Tunisia . World Bank data. Rural Roads Project, Tunisia. June 2, 1978. Upper Volta . World Bank data. Rural Roads Project, Upper Volta. June 6, 1975. (2) Rural Development Projects with Major Road Components Brazil . World Bank data. Second Rural Development Project, State of Minas Gerais, Brazil. May 30, 1980. - 44 - ANNEX A Page 4 Country Documents India . World Bank data. Maharashtra Irrigation II Project, India. September 13, 1979. Korea . World Bank data. Rural Infrastructure Project, Korea. February 15, 1976. Morocco . World Bank data. Fes-Karia Tissa Agricultural Project, Kingdom of Morocco. June 12, 1978. Philippines . World Bank data. Rural Infrastructure Project I, Philippines. March 23, 1978. 3. Other Pertinent Documents Kenya . Republic of Kenya. Ministry of Works. Roads Department. Selection and Evaluation Criteria for Rural Access Roads. Report No. P-05-78. A discussion paper presented at the Annual Review and Evaluation Meeting of the Rural Access Roads Programme in Nairobi, Kenya. March 13-22, 1978. Republic of Kenya. Ministry of Works. Roads Department. Rural Access Roads Programme. Evaluation of Roads in Nakuru. Nairobi, Kenya. August 1977. - 45 - ANNEX A Page 5 Country Documents Colombia . Republica de Colombia. Ministerilo de Obras Publicas y Transportes. Fondo Nacional de Caminos Vecinales. Oficina de Planeacion. Metodologia y Criterios para la Seleccion de Caminos. Doc. O.P. No. 031. Bogota. September 1980. Indonesia . Republic of Indonesia. Ministry of Public Works. Directorate General CIPTA KARYA. Direktorat Tata Kota dan Tata Daerah. Working Papers prepared by ENEX and BIEC International Inc. Working Paper No. 12. Level of Access (November 1980). Working Paper No. 13. Level of Service (November 1980). Working Paper No. 15. A Simplified Procedure for Screening and Ranking Rural Road Programmes (June 1981). Republic of Indonesia. Ministry of Public Works. Directorate General BINA MARGA. Directorate BINA Program JALAN. Attachment 3a. Manual: Procedures for Preparing Rural Road Programme Proposals at Kabupaten Level. January 1982. Papua New Guinea . T.P. O'Sullivan and Partners, and GITEC Consult GMBH. Provincial Rural Transport Study. Interim Report (2 vols.) Independent State of Papua New Guinea, Department of Transport and Civil Aviation, June 1981. - 46 - ANNEX B Page 1 LOCAL PARTICIPATION 1. The selection of specific rural road (RR) links to be included in a RRs or rural development (RD) project generally comes from one of two sources: (a) a technical study conducted by a project team, with or without the help of consultants; or (b) proposals put forward by local officials, agency representatives, or community groups. The 20 projects reviewed for this study were about equally divided between these two categories, based on data provided in Bank documents. 2. In some cases the selection of RRs to be improved was carried out by consultants, but the project provided technical assistance aimed at developing a capacity for project selection, screening and evaluation within the road-building agency. This approach was particularly prevalent in West Africa. In cases where communities or local officials were permitted to propose links for improvement, there were efforts to develop the capacity for technical and economic analysis of these proposals and their assimilation into a coherent work program at an appropriate level within the road-building agency. In rural infrastructure projects, funds were sometimes provided directly to communities for the construction or improvement of RRs which they would both plan and carry out. In this case, the technical analysis capability was to be developed within the planning institutions responsible for the disbursement of funds (usually the Ministry of Interior, Home Affairs or Local Government), rather than within the country's road-building agency. 3. The projects reviewed include projects in which roads were initially identified by locally elected authorities, committees of local agency representatives, regional cooperatives, and district planners. These projects are described in greater detail in the following paragraphs. 4. One of the best documented examples is the Kenya Rural Access Roads program. This program makes use of the District Development Committees (DDCs) established on an experimental basis under Kenya's Special Rural Development Program (SRDP) in the early 19709. The DDCs include district political and planning officers and line agency representatives of the central government, as well as locally elected officials and tribal leaders. Within certain broad guidelines established by the Ministry of Works for prescreening of RRs, the DDCs annually propose a set of RR improvements to the District Engineer. The roads are screened for compliance with the Ministry of Public Works' guidelines, and those which pass are subjected to a summary technical and economic analysis. Roads are prioritized and programmed for improvement according to the constraints imposed by the - 47 - ANNEX B Page 2 District Engineer's technical and financial resources. The resulting work program is then presented to the DDCs for approval, which can serve a valuable feedback function. 5. In India, RREs in the state of Bihar are initially selected for improvement by Block Development Committees. These proposals are forwarded to the State Planning Department, where they presumably receive an informal political/social prescreening. Approved projects go to the Rural Engineering Organization (REO), a branch of the Rural Department, for technical and economic analysis. High priority projects then go into the REO's work program to the extent resources will allow. 6. The Rural Roads project in Tunisia is designed to meet needs identified by permanenl: interagency planning committees at the provincial level. Regional Agricultural Development Commissions (CRDA) recommend RR improvements to the provincial heads of the Ministry of Public Works (MPW). Those proposals are forwarded to the central headquarters of MPW and analyzed there by its Directorate of Road Studies which develops a work program for the entire country for approval by an interministerial coordinating committee at the national level. 7. In Indonesia, decisions on RR improvements are made by planners at the provincial and district levels. Selection of potential RR components is the responsibility of district planners in consultation with local political authorities. Provincial planners will then evaluate the proposals and allocate the available funds. This system contrasts with the INPRES road program in Indonesia, under which funds are given directly to communities for minor RR improvements, which are sometimes carried out on a self-help basis. 8. The Cameroon Feeder Roads project envisaged selection of road links for the second, third and fourth year programs by the staff of the implementing agencies for the Bank and other donor-financed agricultural development projects to be served by the road. In one case this would be a government regional authority (ZAPI East); in the other two cases the implementing agency would be a federation of cooperatives. The feasibility of this design for local participation in planning was never tested, since the government was unaLble to construct the first-year program which had been drawn up by central government planners. 9. In Honduras, the Eighth Highway project includes a RR component to be constructed using labor-based methods. A methodology for RR selection was developed by consultants, using information obtained through structured interviews with community officials. The first year's program was selected by the government in conjunction with consultants. Future work programs are - 48 - ANNEX B Page 3 now based on community initiative developed by the road-building agency, using the same methodology. In other words, community input at the planning stage was limited to providing socio-economic data on road links already identified by government planners. 10. The Rural Roads project in Colombia operates on a somewhat similar set of principles. However, the initial source of RR proposals in this case is a list of petitions submitted by communities. This list is subjected to a prescreening by district officers of the road agency. Proposed improvements which pass this test are then investigated in detail, including interviews with local officials to obtain data for the economic evaluation. These interviews include data on the availability of local labor for construction. 11. Through two RRs projects in Brazil, the Bank has promoted the development of local capacity to select and prepare road components to a level where they would be eligible for Bank financing. Funds are provided to the National Development Bank for on-lending to communities which prepare acceptable proposals. The National Highway Department, through its state agencies, provides technical support to the National Development Bank in the evaluation of proposals and to communities in proposal preparation. The proposals are based upon a preliminary design of the RRs. Upon approval of a proposal, funds are made available to communities or groups of communities (consortia) to hire consultants for detailed design and construction supervision, and contractors to carry out the road works. Although, in this model the Development Bank and the road-building agencies retain substantial responsibility for the technical and economic aspects of project evaluation, responsibility for project implementation (and loan repayment) ultimately rests with the local communities. 12. Two projects have been going on simultaneously in the Philippines: (1) a rural roads project being implemented through the Ministry of Local Government; and (2) a rural infrastructure project, the roads component of which is being implemented by the traditional road-building agency. This apparently anomalous situation actually involves both institutions in collaboration, in a situation where neither one commands the necessary resources to do the job alone. In principle, the planning and financing of RR improvements should be the responsibility of the municipalities, with technical assistance from the Ministry of Local Government. In practice, the Ministry of Public Highways is the only agency with the required technical expertise. The Philippines appear to be still searching for a system that can assure centralized control over funds and yet be responsive to community needs and priorities. - 49 - ANNEX B Page 4 13. In the first Korea Rural Infrastructure project, RR improvements and other investments such as minor irrigation, water supply, fuel-wood plantations and rural electrification are selected and carried out by communities with direct fiscal support from the government. The program is part of the Samaeul Undong or village self-help movement and is similar in some respects to Indonesia's INPRES road program. The Bank's efforts in this case were focussed on developing a capacity for subproject screening and evaluation within the Samaeul Guidance Division of the Ministry of Home Alffairs. Although the program is viewed as successful, political priorities in the country changed and the RR component was dropped from the Second Rural Infrastructure Project for Korea. 14. Staff appraisal reports do not give sufficient information to assess in detail the extent to which community initiatives are relied upon to identify and screen RRs. There is a tendency in developing countries for planners to take over and. "technify' the project selection process. Yet, in a situation of expanding needs and increasingly limited resources, community commitment will become am ever more essential factor in project implementation and in subsequent maintenance. Involvement at the planning stage can do much to prepare communities for realistic decision-making and mobilization of resourcesa when improvements are implemented. It can also improve the project selection process, by providing quantitative and qualitative data on local conditions which are essential to the realization of expected benefits. - 50 - ANNEX C Page 1 EXAMPLE OF A PRESCREENING METHOD 1. The prescreening method described below is one of the more ambitious attempts to develop proxy measures for rural roads screening. The method was originally developed for the low-standard, labor-intensive Pico y Pala (pick and shovel) RR improvements financed by USAID in Colombia. The Bank has accepted this methodology as a prescreening procedure for a RRs project in this country but requires that it be followed up with a simplified economic appraisal for roads to be financed under the project. Although prescreening based on a combination of social, technical and economic factors is not necessarily an efficient procedure (Section IV of text), the method is presented because of the interesting approach to criteria other than the economic one. 2. The prescreening methodology is based on the computation of three types of scores for each RR candidate: (1) a physical score (maximum score 100 points) related to the factors that affect cost; (2) a social score (maximum score - 30 points) related to population density in the zone of influence and the distribution of land by size of holdings; and (3) an economic score (maximum = 84 points) related to agricultural production potential. A project is deemed feasible if: social score + economic score > 1.0 physical score RRs that achieve ratios above 1.0 are accepted for the simplified economic appraisal. 3. The economic score consists of points awarded for each of the following factors: (1) percentage of land to be brought under cultivatidn (10 points); (2) soil type (20 points); (3) use of agricultural credit (10 points); (4) use of technical assistance (3 points); (5) use of agricultural inputs (5 points); (6) providing service to towns and municipal capitals (5 points); (7) development plans for the area (14 points); (8) distance to market (7 points); and (9) percentage savings in vehicle operating costs (VOC) per kilometer (10 points). The social score includes density of population (15 points) and distribution of land by farm size (15 points). 4. A fairly complex set of factors goes into the computation of the physical score which is primarily based on technical and cost considerations. The physical score is calculated from the following factors: (1) earthmovement quantities (with the points varying from a miLnimum of 14 for movements less than 10,000 m3 per kilometer in flat terrain to 47 points for movements of 25,000 m3 per kilometer in mountain terrain); (2) culvert requirements (with a score of 2 points in flat terrain and 4 points in mountain terrain); (3) distance for the transport of gravel and other - 51 - ANNEX C Page 2 iiaterials (with a maximum score of 16 points for distances of more than 15 km aind a minimum score of 6 points for distances less than 5 km); and (4) bridges, with 2 points be.Lng assessed per lineal meter of bridge or pontoon. tn addition, there are limaitations on the maximum length of the road (25 km), earthwork (25,000 m3 per kim), and bridge size (less than 25 meters) among others. ;5. Social variableis have a fairly important effect on the screening 3core since the economic score also includes social variables such as providing services to towns and municipalities (maximum score - 5 points) and plans for doing so in the future (maximum score = 5 points) as part of area ievelopment plans. Thus the overall score gives a maximum of 40 points out of 214 points to social factors. 5. It is noted that the allocation of points to factors such as percentage VOC savings can lead to incorrect decisions based on economic criteria since total VOC savings may depend more on volume of traffic, which is not considered in the prescreening, than on the percentage reduction in VOC. In addition, the economic score does not consider crop yields and values, which are often important factors for the economic evaluation. Experience with this prescreening shows that the method is not very successful in weeding out unfeasible RR components while it can reject feasible components. - 52 - ANNEX D Page 1 CONSUMER SURPLUS VERSUS PRODUCER SURPLUS METHODS 1. This annex demonstrates that the use of the consumer surplus (CS) method and that of the producer surplus (PS) method will result in the same economic return (ER) provided available data regarding traffic, vehicle operating costs (VOC), prices, yields of agricultural products, etc., are of the same accuracy. To simplify the demonstration, we consider the situation where: (i) one road exists between the marketplace and area of production; (ii) one agricultural product is produced in this road's zone of influence; (iii) all farms are located at one center, such that they face the same distance from the marketplace; and (iv) the trucking industry is perfectly competitive. 2. The following notation is introduced: PMm' local market price of agricultural product; Pg - farmgate price of agricultural product; k - economic transport cost (per ton-km); F - freight rate (per ton-kkm); r - profit of trucker per ton-km or (F-k); L - distance between farms and marketplace (km); C - total production cost; N - marginal production cost; and q - export of the agricultural product from the road's zone of influence (ton). - 53 - ANNEX D Page 2 ro show that the PS and CS methods result in the same ER, it is sufficient to demonstrate that producer surplus equals consumer surplus in farmers' transportation demand. What follows applies to both the without- and with-project situation. 3. Under the assumption of profit maximization, the farmers will export q* tons of output such that marginal production cost will equal faragate price of output: M Pg .......... (1) Note that pg Pm - FL .... ...... (2) and F k + r . ...... ...(3) and, therefore, M Pm - (k + r)L .......... (4) 4. Figure 4 shows the determination of equilibrium output q*. Figure 4: Production Equilibrium Marginal cost M Farmgate price, marginal cost PM_ -m (k +rIL. qo 0 output q (tons) Production surplus of fa,rmers is represented by the shaded area above the marginal cost curve in FLgure 4, but below the farmgate price P Pm - (k+r)L. This area, whicb is referred to as PS, can be expresseg by the following formula: - 54 - ANNEX D Page 3 PS =LPm*-(k+r*)LJq*- M(q)dq=Pm*q*-(k+r*)Lq*-C(q*) ............ (S ) where Pm* and r* are Pm and r associated with output q*. In addition to expression (5), total benefits of a rural road include the truckers' benefits ("normal profit"), or: r*(q*+x*)L ............ (6) where x* is the volume of inputs transported into the zone of influence to produce output q*. Combining equations (5) and (6) gives the total benefits B: B = P,*q*-(k+r*)Lq*-C(q*)+r*(q*+x*)L ............ (7) 5. The equilibrium output, under the present assumptions, is equal to the equilibrium level of output transported and can be derived by using the farmers' transportation demand approach. From equations (1) and (2) follows: F.L = Pm7M . ........... (8) Equation (8) implies a downward sloping demand curve since dF - - M' where M' dq L is the slope of the marginal cost curve of Figure 4. This downward sloping curve is portrayed in Figure 5. Figure 5: Output Transportation Demand Freight nrate for the whole trip on the rural road (FULA F- .L supply of transportation (F r.) L q- q S volume of output trnsported (toral - 55 - ANNEX D Page 4 6. The supply of transport services is infinitely elastic at freight rate F* and the equilibrium volume of farmers' transportation is determined at the intersection of supply and demand or point A of Figure 5. Note that q* of Figure 4 is identical to q* of Figure 5 since they are obtained as a solution to the same equat:ion. The benefits to farmers are in Figure 5 represented by the shaded area below the demand curve and above the supply curve for transport. This area, which is referred to as CS, can be expressed by the following formula: CS (Pm-M)dq-]*Lq*=P *q*-C(q*)-F*Lq*=Pm*q*-C(q*)-(k+r*)Lq*.... (9) Ahdditional benefits accrue to truckers in terms of normal profits. Profits on transportation of output are in Figure 5 represented by the vertically shaded area r*q*L. Profits on transportation of inputs into the zone of Influence amount to r*x*L. Total benefits are: B - CS+r*q*L+r*x*L or B - Pm*q*-C(q*).-(k+r*)Lq*+r(q*+x*)L )....... ......... (10) 7. Equations (5) and (9) confirm that the PS and CS are equivalent while equations (7) and (10) show that benefits accruing to farmers and truckers are the same with the PS and CS approaches. Assumptions (i) through (iv) of para. 1 were introduced to simplify the presentation. Following an argument similar to the one described above, one can, however, show that the CS and PS methods result in the same ER if these assumptions are relaxed. 8. Confusion about equality of CS and PS may arise if the supply curve for transportation of Figure 5 is estimated without using information on, farmers' home consumption in both the without- and with-project situations. To allow for home consumption, identically the same correction has to be introduced into the expressions for PS (equation 5) and CS (equation 9) and, therefore, the equality between the two surpluses is maintained. Note that if home consumption is non-negligible and if it moves inversely with changes in farmgate prices and fatrmers' incomes (as determined by the project), the benefits of the project vrill be overestimated in both approaches (PS and CS) if the prediction of benefits is based exclusively on changes in farm outputs. - 56 - ANNEX E Page 1 BRAZIL: SCREENING ON COST PER KILOMETER 1. An innovative screening method for RR components has been proposed in connection with the improvement to all-weather standards of RRs in Brazil. The proposed methodology for screening may be summarized as follows: (1) select RRs' zones of influences which are homogeneous with respect to crop patterns, farm sizes, yields and cultivated areas; (2) calculate the benefits, costs and economic rate of return (ER) for the package of improvements (RR and agricultural improvements), proposed for a group of homogeneous zones of influence; (3) normalize the flow of net benefits by imputing to each road the average value of net benefits per km of road; (4) estimate the "target" cost per kilometer corresponding to the benefits calculated in (3) evaluated at the prevailing opportunity cost of capital; and (5) accept those RRs of this group whose costs per kilometer are smaller than the target cost per kilometer estimated in (4), and reject those RRs whose costs exceed the target cost level. 2. This screening method is valid if truly homogeneous areas can be identified. The problem is that the requirement of homogeneity in the zone of influence is difficult to meet. In order to make a test of the proposed methodology it was decided to select road links in the same country, in areas with a single cash crop, and to subject them to the screening criteria. Seven Class F road links were selected from the files of the Second Feeder Roads Project in Brazil. Table 11 presents an overview of the roads selected, their costs and ERs as calculated in the feasibility study. 3. Application of the methodology to roads in the municipality of Una would result in a target cost per kilometer of US$53,563, corresponding to a 20% opportunity cost of capital, as shown below:l/ 1/ A rather high opportunity cost of capital is assumed to show that the screening may lead to incorrect decisions with the available data. Incorrect decisions are, however, also possible with lower opportunity costs of capital. Table 11: Overview of RRa in Selected Municipalities of the Cacao Region of the State of Bahia Area of Influence Per km of Road Yields Total Agricultural Population Cost Per Road Ecoxi (Arrobas Farm Area. Area Served RR km Hiik lit- No. RArn (FUn per be) Sizel/ (li ) (haj: per RR km US Itabuna 20 23.3% 37 Large 4.0 36.6 81.3 35,858 21 70.5% 33 Small 1.7 85.7 33.9 24,035 Una 01 16.7% 45 Sm/Lg 5.2 32.4 76.1 40,692 17 33.4% 40 Sm/Med 2.9 39.0 42.4 23,906 18 70.3% 60 Medium 3.4 69.0 49.2 32,260 19 19.7% 43 Unspecified 2.8 41.7 41.6 43,548 22 23.4% 35 Small 4.1 48.5 59.3 36,157 1/ These farm size categories are undefined in the source document. Source: BNDE-BIRD-DNER-ESTADO DA BAHIA. Secretaria Dos Ttansportes. Consorcio Rodoviario. Rodovias Vicinais Regiones Cacaveira e Leitera. Estudio de Viabilidad Tecnico Economica. 1980 0Yl - 58 - ANNEX E Page 3 UNA - RRs Total net benefits to all roads (from project file data) $11,417,600 Total road length = 99 km Net benefits per km - $115,329 Present value of costs per km at 20% = $53,563 With a 20% opportunity cost of capital, two roads (Nos. 01 and 19) would have been accepted using this methodology when in fact they should have been rejected. In the case of Itabuna a 20% opportunity cost of capital corresponds to a cost per km of US$55,202, which leads to a "correct" acceptance of both roads. 4. This method of screening will work in cases where the areas analyzed are truly homogeneous with respect to agricultural activity (crop patterns, yields, cultivated area per km of road, etc.). However, in practice finding these homogeneous areas is difficult. Caution should therefore be exercised when using this method. - 59 - ANNEX F Page 1 INDIA: SCREENING ON A PROXY BENEFIT/COST RATIO 1. This annex describes a methodology developed in connection with the Rural Roads Project for the State of Bihar in India. Prescreening and a simplified economic appraisal method are used in this project; this appraisal is similar to Method III of the text. 2. The prescreening of the Bihar roads consists of a set of exclusionary criteria. That is all roads must (1) connect to a paved road, (2) connect to a nearby market, and (3) not fall within the zone of influence of another road (this requirement means that it should be 3-5 kilometers away from any other road), and (4) complementary investments in irrigation must be present or planned for the impact zone. The appraisal methodology then distinguishes two types of roads: (a) roads carrying motorized vehicle traffic; and (b) roads with no motorized vehicle traffic. The first group of roads is subjected to analysis on the basis of vehicle operating cost savings, while the latter group is assessed on the basis of producer surplus benefits. 3. For roads carrying motorized vehicle traffic, the following expression approximating the benefit/cost ratio at a 12% cost discount rate is computed: R D (9.8) (365) (T) (S) 5.66 (Cm+ 0.18 Cc) where R = the ratio of approximate benefits to approximate costs, T = annual aveirage daily traffic (ADT), S = average vehicle operating cost saving per vehicle-kilometer, Cm = annual incremental maintenance cost per kilometer, and Cc = construction cost per kilometer. The present value factors used are as follows: 9.8 = the present value of a one-dollar benefit series growing at 5% annually during a ten-year period and discounted at 12% interest rate, - 60 - ANNEX F Page 2 0.18 = the capital recovery factor to annualize the construction costs, at a 12% discount rate over ten years, 5.66 = the present value factor for a one-dollar annuity at a 12% discount rate. If the proxy benefit/cost ratio R is greater than or equal to 1.0, the road is accepted into the project. 4. In the case of roads with no traffic, only producer surplus benefits are considered in the following fashion: R 3 A(PI) (PA) (V) (0.70) (Pv) 5.66 (Cm + 0.18 Cc) where R = the ratio of approximate benefits to approximate costs, A = area of the road's zone of influence (in hectares) per kilometer of road, PI - proportion of arable land that is irrigated, PA = proportion of land in the influence area that is arable, V - incremental agriculture value added per hectare in year of full maturity (net of annual irrigation and maintenance costs), Pv = present value factor corresponding to the number of years required for the project to achieve its full maturity, and Cm and Cc as defined above. The factor of 0.70 corresponds to the assumption that only 70% of the total production potential of the road's zone of influence will be achieved within the project's time frame. If the proxy benefit/cost ratio R is greater than or equal to 1.0, the road is accepted into the project. 5. The simplified appraisal method has been developed over time through a trial and error approach. Difficulties were encountered in the early phases due to an underestimation of the costs of complementary investments. This problem, while crucial to the project's overall viability, does not affect the validity of the appraisal method as long as it is consistently applied in all cases. The method is the one case in current Bank practice which appears to be closely linked to the concept of economic feasibility, and which therefore should prove successful in predicting the outcome of the economic appraisal across a wide variety of project types. - 61 - ANNEX G Page 1 SCREENING VIA DISCRIMINANT ANALYSIS 1. Introduction. This annex describes the results of economic and statistical analysis of the factors that affect the economic performance of rural roads. The purpoise of the analysis is to identify those factors that accurately predict the economic return (ER) of a given rural road (RR). Following the methodology presented in Bank Staff Working Papers Nos. 241 and 362, the ER of a given rural road is primarily a function of three factors: (i) the producer surplus or net agricultural value added of the RR's zone of influence; (ii) the consumer surplus represented by the vehicle operating cost savings accruing to normal traffic on the RR; and (iii) the cost of the RR's improvements and any associated agricultural investments in the RR's zone of influence. These three factors may be combined in the following manner: EF = f ( PS , CS ).......... (1) C C where EF - economic feasibility of a RR, group of interdependent RRs, or investment package of interdependent RR and agricultural investments, PS - producer surplus benefits, CS - consumer surplus benefits, and C - cost of the RR(s) and any associated agricultural investments. The screening methods described in this annex use functions derived from the above expression by applying proxy variables for the producer surplus, consumer surplus, and cost elements. 2. Producer Suriplus Variables. The most important proxy variable for the producer surplus effect is the net agricultural value added in the last year of the analysis period (defined in this case as 10 years). However, other simpler expressions were tested as proxies for the producer surplus. These proxy variables include: (1) the increase in tons of agricultural products generated by year 10; (2) the increase in equivalent hectares brought into cultivation by the year 10 (defined as the increase in new cultivated land plus the ratio of the with-project value added per hectare to - 62 - ANNEX G Page 2 without-project value added per hectare times the number of hectares under cultivation at the start of the project);2/ (3) the initial agricultural area cultivated in the zone of influence; and (4) the population of the zone of influence. 3. Consumer Surplus Variables. The most important proxy variable for the consumer surplus effect is the opening year level of vehicle operating cost savings accruing to normal traffic. Other possible proxies for the consumer surplus include: (1) passenger-kilometers and ton-kilometers of normal traffic; (2) the initial level of average annual daily traffic on the road; and (3) the population (as a proxy for passenger-kilometers) and the agricultural production tonnage (as a proxy for ton-kilometers) of the zone of influence. 4. Intervening Variables. Other variables may affect the role and function of rural roads in developing countries. These variables are called intervening variables. The sample of 110 RRs tested was separately stratified along each of these dimensions in order to test the sensitivity of each screening method to these variables. They include: (1) Technology of agricultural production: traditional, semi-technified or technified. Operational measures used as proxies for this variable include with-project yields and net agricultural value added per hectare of cultivated land; (2) Associated agricultural investments: (i) none; (ii) a minimum package of agricultural investments for the RR's zone of influence; or (iii) an integrated agricultural development program for the region in which the RRs are located; (3) Type of agricultural crops produced: (i) tree crops; (ii) annual cash crops; or (iii) annual subsistence crops; 2/ Or alternatively this factor may be calculated as the increase in new hectares brought into cultivation plus the ratio of the increase in tons of production divided by the without-project yields in the zone of influence. - 63 - ANNEX G Page 3 (4) Connection to the highway network: (i) a paved road; (ii) an all-weather road; or (iii) an earth road; and (5) Road type: (i) a collector or arterial road; (ii) a feeder road; (iii) a farm-to-market road. 5. Data problems. Some of the sensitivity testing suggested above could not be carried out due to limited numbers of cases in the sample or lack of data needed to correctly classify specific roads. For example, feeder roads account for 96% of the sample, so that the effect of road type was not researched. Similarly the sample of roads with tree crop production is small; a separate analysis for this type of crop could, therefore, not be conducted. 6. Background orL Discriminant Analysis. Discriminant analysis is a powerful statistical technique used to distinguish between two or more groups of cases with respect t:o two or more variables simultaneously. In this study discriminant analysis is used to predict whether a given RR and associated agricultural investments in its zone of influence should be classified into the group of investments whose ER is less than the opportunity cost of capital (defined as unfeasible), or the group of roads whose ER is equal to or greater than the coiot of capital (defined as feasible). The discriminant analysis performed in this study used four alternative values of the cost of capital (10%, 12%, 14% and 16%) in the development of predictive relationships for class3ifying rural roads into feasible or unfeasible groups. 7. At the outset, a set of explanatory variables that can aid in the classification of investments into the two groups (feasible vs. unfeasible) is defined. These explanatory variables, called discriminating variables, measure characteristics on which the two groups of investments are expected to differ. For instance, the groups of feasible vs. unfeasible investments may differ in their agricultural potential, or in their vehicle operating cost savings. The objective of discriminant analysis is to derive linear combinations of the discriminating variables, appropriately weighted, so that the maximum statistical differentiation between the two groups of investments is obtained. The discriminant functions, estimated from axioms derived from the principal axis theorem, are linear combinations of the type: Di = dio+ dil Xl + di2 X2 + ...+dij Xj+ ...+ din Xn ....... (2) where Di is the discriminant analysis score, dij are the weight coefficients and Xj are the standardized values of the n discriminating variables. Figure 6 provides a graphic representation of a discriminant analysis problem. - 64 - ANNEX G Page 4 Figure 6: Graphical Representation of Use of Discriminant Analysis for Rural Roads Screening ECONOMIC RETURN pefmnt 72 40 48 J ~~~;X) GROtJP No. 2 ,: . .. . t : 5 (Economlcaily Feadble Invssvmnn or £ ' ;, ' '~ I > , ° , ' ' A nw.tmatws ER@t2%) 36 24 12 4' tscDc,mrtmnnt Functloni ,*.,I XiG ROUP No.6 X2i2 + d. Xi +. I+dil1Xn Dbedminsalng VYiebi Agfulturdl Velue Added per km, PapaWln Served, atcI D3sc,1mlgiatIi ~ ~ WorgdVunk-2I2D - 65 - ANNEX G Page 5 8. In this study, discriminant analysis is used for classification purposes. By classification is meant the process of identifying the likely group membership of a rural road and associated agricultural investments in its zone of influence, if any, whose characteristics are reflected in the discriminating variables. This classification process is achieved through a series of classification functions, one for each group of investments (feasible or unfeasible). The classification functions are derived from the discriminant function (2). The resulting classification coefficients are multiplied by the values of the original variables and a classification score thus results. The investments are classified into the group (feasible or unfeasible) with the highest score. The classification functions for each group of investments are given by: Ci - Cio + c1i X1 + ci2 X2 + .-.+cij Xj+-**+cin Xn ........... (3) where Ci is the classification score for investment group i, ciZ. represent the classification coefficients, and Xj are the discriminating variables. 9. Discriminant Analysis: Interpretation of Results and Tests of Significance. A series of tests of significance have been developed to test for the degree of discrimination achieved by the discriminant functions, specifically whether the unexplained differences between the groups after the estimation of the discriminant functions are the result of sampling or measurement errors rather than a truly different dimension. 10. The Canonical Correlation Coefficient. The canonical correlation coefficient is a measure of association which describes the degree of relatedness between the groups and the discriminant function. The canonical correlation coefficient varies between 0 and 1, its formula is given by: ri* ' / 1 (I + i) ........ (4) where denotes the eigenvalue corresponding to the ith relevant discriminant function. 11. Wilks' Lambda Measure of Residual Discrimination. Given that the data on the groups of rural roads are from a sample rather than constituting the entire population, the sampling process may produce cases which show discrimination estimated when in fact there are no group differences in the underlying population. - 66 - ANNEX G Page 6 12. The most common test for the statistical significance of the discriminant functions is the Wilks' lambda test of residual discrimination. By residual discrimination is meant the ability of the variables in the discriminant function to discriminate among groups beyond the information already extracted from the previous discriminant functions. If the residual discrimination is too small, then it is meaningless to derive any more functions even if they exist mathematically. 13. Wilks' lambda is a multivariate measure of group differences between the discriminating variables. It is computed as the product of several transformations of eigenvalues as follows: q A 1+T = 1 . 1 . ..... 1 ( 5 (5) ilk- 1 1+4k+1 l+kk+2 1+&q where k represents the number of discriminant functions previously derived and the symbol [ denotes that the individual terms are to be multiplied to estimate the final product. 14. Wilks' lambda is an inverse measure. Values of lambda near the zero value denote high discrimination (i.e., the group centroids are greatly separated and very distinct relative to the amount of dispersion within the groups). When lambda equals 1.0, the group centroids are identical, denoting no group differences. 15. Test of Significance of Wilks' Lambda. The significance of Wilks' lambda can be tested by converting lambda into an approximation of either the chi-square or F distribution. The F-tables can then be used to determine the significance level. The formula for the testing is: X2 '- [m - (pL gi) - 1] loge kk ). ( ) 2 with (p - k) (g - k - 1) degrees of freedom, and where m - total number of cases over all groups, 8 ' number of groups, p = number of discriminating variables, k = number of functions already derived, lk - Wilks' lambda after k discriminant functions, 1lge - natural log. - 67 - ANNEX G Page 7 16. The chi-square test provides information on whether the results came from a population which did have differences between the groups. However, the analysis described in this Annex, whose purpose is to derive simplified screening methods for rural roads, assumes that a single dimension can represent all the observed differences between the groups. It was decided at the outset not to develop a second discriminant function (i.e., add another dimension and thereby create a discriminant plane) on the assumption that it would not add any differences which we could confidently say exist in the population of rural roads. Given that only two groups of investments (feasible and. unfeasible) are considered in this study, the above assumption is reasonable. 17. Results of the Discriminant Analysis. Five discriminant analysis equations were estimated -- corresponding to an opportunity cost of capital of 12% -- using the varia,bles defined in Table 12. The results are presented in Table 13. These functions vary in the complexity of the information required. The discrimina,nt function requiring the least data and complexity is No. 3, while the most complex function (requiring the estimation of full value added) is function No. 1. The canonical correlation coefficients of the five discriminant functions are very close in value, ranging from .54 (Equation 3) to .67 (Equation 5). This measure indicates a moderately strong association between the actual groups and the groups defined by the discriminant function in each case. The value of Wilks' lambda measures the statistical significance of a result based on sample data. In each case, these values indicate that the functions are statistically significant (i.e., there is a very low probEibility that these functions would be determined from the sample data in the catse where there was actually no difference between the groups). 18. As may be seen from the reliability analysis presented in Table 14, the first discriminant function is the one that predicts most accurately the correct classification of unfeasible roads. It is in both the Bank's and the Borrower's interest that unfeasible roads be properly screened and excluded from further consideration. Therefore the use of the first discriminant function is recommended. As may be seen from Table 14, the various functional forms are almost indistinguishable in their overall accuracy, predicting correct decisions in 86%-87% of the cases. 19. The discriminant functions for prevailing opportunity costs of capital of 10%, 14% and 1.6% are in Tables 15, 17 and 19 respectively. The reliability of these functions is analyzed in Table 16 (for 10%), Table 18 (for 14%) and Table 20 (lor 16%). - 68 - ANNEX G Page 8 20. Regarding the evaluation of discriminant functions with opportunity costs of capital of lOX and 14%, whose parameters are presented in Tables 15 and 17, it is recommended that discriminant functions No. 1 (in both tables) be used for screening purposes. These functions No. 1 provide the best combination of forecasting accuracy of unfeasible roads with overall significance of the discriminant functions, significance attested by the canonical correlation coefficient and by the chi-square test. 21. With respect to the prediction of roads whose economic return is equal to or greater than 16%, equation No. 1 of Table 19 is recommended. This function's overall predictive performance is good and provides a good discrimination of unfeasible roads. Equation No. 3 of Table 19 outperforms all others in predicting unfeasible roads but at the cost of rejecting too many good roads. Equation 3 is also inferior to Equation No. 1 in terms of its canonical correlation coefficient. 22. Summary. The discriminant analysis results show that it is possible to predict the performance of rural roads with some minimum data requirements. Discriminant equations No. 1 of Tables 13, 15, 17 and 19 provide good results in the predictions of the feasibility of roads at different levels of opportunity costs of capital. - 69 - ANNEX G Page 9 Table 12: Variable Definitions Value Added = net agricultural value added (VA) in year of full production (with-project VA minus without-project VA) Cost = present value of costs of the RRs (including construction and incremental maintenance costs) and agricultural components in the RRs' zone of influence VOCS = opening year benefits stemming from savings in vehicle operating costs accruing to normal traffic Net Value per Ha = without-project initial value of agricultural production per hectare of cultivated land in the zone of influence Has. Served = number of cultivated hectares in the zone of influence in the without-project situation Traditional Agriculture = a dummy variable taking the value of 1 if without-project initial yields are less than 1.5 tons per hectare of cultivated land, or if the without-projec.t initial value added is less than US$150 equivalent per hectare; otherwise the value of this variable is 0 Tons - increase in agricultural production (with- minus without-project) in the year of full production, expressed in tons Pass-km = opening year passenger traffic: in terms of passenger-kilometers Ton-km - opening year goods traffic in terms of ton-kilometers - 70 - ANNEX G Page 10 contd..... Table 12: Variable Definitions Tons per Ha. = initial productivity of agr:Lculture in the zone of influence, defined as tons per hectare produced on cultivated land in the zone of influence of the road Market = a dummy variable taking the value of 1 if the road provides direct access to a market less than 20 km away; otherwise taking a value of 0 A Ha. = equivalent increase in hectares of area cultivated. This increase is defined as the increase in newly cultivated land (with- minus without-project) in the year of full production plus the ratio of the "difference in with- and without-project yields to without-project yields" multiplied by the "cultivated area (hectares) in the without-project situation," in the year of full production Net Value per Ton = without-project initial net value of the production in the zone of influence of the road divided by the agricultural production (in tons) in the zone of influence ER = economic rate of return of a RR or group of interdependent RRs, plus associated agricultural investments (if any) in the zone of influence - 71 - ANNLX G Page 11 T,able 13: Discriminant Functions for Investments (i - 12X) 1/ Unstandardized Classification Function DiEicriminating Discriminant Coefficients Evaluation Statistics Variables (Xj) Coefficients FOR FOR ' Canonical WILKS 2 foE ach Function (Di ) _ ER <12% ER . 12Z Correlation LAMBDA X Diucriminating Coefficient Furtction No. 1 Value added+ Cost 2.0225 1.1360 4.5175 VOi'S + Cost 2.9219 2.5682 7.4534 0.5596 0.6869 49.21 Net Value per ha 0.002968 0.003158 0.008122 Intercept -1.9113 -0.9854 -3.5966 jconstant) '_' Discriminating Furction No. 2 V015 I' Cost -1.2259 1.9426 3.8958 Cost.. (A tons 0.001139 0.002294 0.0004797 0.5898 0.6522 45.52 Net Value per ha -0.003446 0.002726 0.008216 Intercept (Constant) 0.1908 -2.1886 -1.9619 Discriminating Function No. 3 VOIc . Cost -1.347812 3.9908 5.8566 Cost .. (A tons 0.001193 0.002068 0.0004163 0.5358 0.7129 36.04 Traditional Agriculture 0.8244 3.1974 2.0561 Intercept (constant) -1.0048 -3.2013 -1.4095 1/ i - opportunit cost of capital. contd...... - 72 - ANNEX G Page 12 contd..... Table 13: Discriminant Functions for Investments- (i = 12%) I/ Unstandardized Classification Function Discriminating Discriminant Coefficients Evaluation St2tistics Variables (X' Functions FOR_FOR____T__KS_I for i be (X) Coefficients FOR FOR Canonical 2.TIKS' 2 Each Function (Di_) ER _ 12R , 12% Correlation '.....B 23DA x Coefficient Discriminating Function No. 4 Cost -;- 6Stons) -0.001137 0.002294 0.0004817 .Pass-km 4 Cost 0.021791 0.063991 0.09872 0.5899 0.6519 45.34 Ton-.km + Cost 0.023147 -0.005186 0.031711 Net Value per ha 0.0033583 0.002979 0.008692 Intercept (constant) -0.1980 -2.2074 -1.9919 Discriminating Function No. 5 VOCS - Cost 0.8067 2.2713 3.8581 Cost 4, (A ha'..) -0.002609 0.005320 0.0001885 0.6696 0.5516 63.36 Net Value per ha 0.006812 -0.005387 0.008013 Intercept (constant) -0.1225 -2.4747 -1.9066 1/ i - oppo tunity cost of capi :al. - 73 ANNEX G Page 13 Table [4: Reliability and Prediction Errors of Discriminant Functions for Investments (i = 12%) 1/ Percent D lscriminant Predicted Group Membership Classified Function No. Actual Groups No. of Cases ER C 12% E 12% Correctly No. 1 ER 12% 32 31 1 97% ER 12% 78 13 65 83% 110 44 66 87% No. 2 ER 4 12% 32 24 8 75% ER 2% 78 6 72 92% 110 30 80 87% ND. 3 ER 4. 12% 32 23 9 72% ER 12% 78 5 73 94% 110 28 82 87% No. 4 ER . 12% 32 24 8 75% ER p 12% 78 6 72 92% 110 30 80 87% ND. 5 ER 44 12% 32 23 9 72% ER 7 12% 78 6 72 92% 110 29 81 86% 1/1 = opportunity cost of capital. 74 - ANNEX G Page 14 _able 15: Discriminant Functions for Investments (i = 10% 1/ Unstandardized Classification Function Discriminant Discriminant Coefficients Evaluation Statistics Variables (X ) for Functions Each Functiot Coefficients FOR FOR Canonical Wilk's 2 (Di) ER <10% ER 7 10% Correlatio Lambda X Coefficient Discriminant Function No. 1 Value Added S Cost 1.8552 0.9468 3.5316 VOCS _ Cost 3.4406 1.8208 6.6145 0.5076 0.7422 31.74 Net Value per ha 0.002533 0.002998 0.006529 Intercept/Constant -1.7581 -0.9578 -2.8781 .- Discriminant Function No. 2 Value Added _. Cost 2.0826 1.6596 4.2974 vocs - Cost 3.8733 4.7785 9.6843 0.4721 0.7770 26.87 Traditional Agriculture -0.3974 3.3255 2.8221 Intercept/Constant -1.1574 -2.0939 -3.1223 Discriminant Function No. 3 VOCS - Cost 1.3585 1.6081 3.9044 Cost+ S ha -0.002424 0.004936 0.000839 0.5815 0.661& 43.96 Net Value Per ha 0.005934 -0.003878 0.006152 Intercept/Constant -0.0660 -2.4368 -1.7693 1/ i - opportunity cost of capital. contd. - 75 - ANNEX G Page 15 contd..... Table I5:. Discriminant Functions for Investments (i - 10%)!: Unstandardized Classification Function Discriminant Discriminant Coefficients Evaluation tatistics Variables (Xi) for Functions FOR FOR Canonical Wilk's 2 Each Function Coefficients ER 1 10% ER %>10% Correlation Lambda X Coefficient Discriminant Function No. 4 Cost - & Tons -0.001282 0.001848 0.000081 Pass ka -.-Cost 0.0518 0.0782 0.1497 0.5036 0.7436 30.86 ron km --Cost 0.02123 0.006964 0.0362 Net Value per ha 0.00130 0.002249 0.004042 Net Value per ton 0.00495 0.003975 0.0108 Intercept/Constant -0.3968 -2.1400 -2.1688 Discriminant Function No. 5 Cost±- Has.Served -0.00202 0.003391 0.000833 Pass km -*Cost 0.0294 0.0598 0.0971 0.4719 0.7772 26.71. Ton km :-Cost 0.0241 -0.0114 0.0191 Net Value per ha 0.0048 0.00109 0.00722 Intercept/Constant -0.3976 -1.7233 -1.7896 1/ i - opportunity cost of capital. - 76 - ANREX G Page 16 Table 16: Reliability and Prediction Errors of Discrimlnant Functions for Investments -(i - 101) _J Discriminant Actual No. of Predicted Grc ap Membership Percent Function No. Groups Cases Classified = ER ( 10? ER 7, 10% Correctly No. 1 ER4 102 25 24 1 96.0O ER 10% 85 19 66 77.6% 110 67 81.82 No. 2 ER< 102 25 24 1 96.02 ER - 102 85 18 67 78.82 110 42 68 82.7% No. 3 ER 4 10% 25 17 8 68.0% ER a 102 85 11 74 87.12 110 28 82 82.7% No. 4 ER 4. 102 25 17 8 68.02 ER > 10% 85 10 75 88.2% . 110 27 83 83.62 No. 5 ER, 10% 25 21 4 84.0% ER ? 10% 85 15 70 82.4Z _ 110 36 74 82.7% 1/ i - opportunity cost of capital. - 77 - ANNEX G Page 17 Table 17. Discriminant Functions for Inveutaento (i - 14Z) 1/ Unstamlardized Classification Function Variablen Discrininant Coefficients Evaluatio Statisti cs '~aribles(X )for punction FgeO Each Function Coefficients FOR FOR Canonical Wilk's 2 ER 4 2 ER 2 14% Correlation Lambda X Coefficient - Discrimineut Function No. 1 Value Added 4. Cost 2.1000 1.2961 4.7669 lOCs * Cost 3.1127 2.7691 7.9137 0.6163 0.6201 50.88 Net Value Per ha 0.00.2732 0.003528 0.008043 lntercept/Constant -1.9149 -1.0583 -3.7513 Discriminant FLnction No. 2 Value Added * Cost 2.3657 1.2299 4.7009 VOCS J Cost 3.7785 2.9603 8.5040 0.5706 0.6744 41.95 1hne per ha 0.0551 C.2052 0.2920 litercept/Constant -1.6313 -0.9937 -3.0159 DLscrlsinant Function No. 3 Vuilue Added Cost 2.2750 1.7533 5.1666 V,O5 I Cost 3.3817 5.4789 10.5508 0.5790 0.6647 43.49 T-aditional A4;riculture -0.5257 3.3641 2.5757 ITtercept/Constant -1.1651 -2.1594 -3.5183 1/ i - opportunity cost of capitnti. contd. - 78 - ANNEX G Page i8 contd.... Ta'be 17: Discriminant Functions for. Investments (i = 14%) 11 Unstandardized Classification Function Evaluation Statistics Discriminant Discriminant Coffici nt_ Variables (X) for Functions FOR FOR Ctmonical Wilk's 2 Each Function Coefficients ER L 14% ER ; 141 Correlation Lambda X (DI) Coefficient Discriminant Function No. 4 VOCS Cost 0.9731 2.1921 3.9833 Cost ,' A ha -0.002584 0.004906 0.000148 0.6570 0.5682 60.19 Net Value per ha 0.006632 -0.004166 0.008042 Intercept/Constant -0.1069 -2.3061 -1.9177 Discriminant Function No. 5 Cost + A ha -0.002502 0.005082 0.000412 N et Value per ha 0.006700 -0.003696 0.008809 Market 0.4472 1.5378 2.3725 0.6622 0.5614 61.47 Intercept/Constant -0.2492 -2.5131 -2.3767 1/ i - opportunity co It of capital. - 79 - ANNEX G Page 19 Table 18: Reliabilitr and Prediction Errors of Discriminant Functlons for Investuents (i - 14%) 1/ Discriminant Actual. No. of Predicted Group Mmbership Percent Function No. GroupEs Cases Classified ER C 14% ER '7>14% Correctly No. 1 ER 4 141: 36 33 3 91.7% ER p.14%': 74 15 59 79.7% 110 48 62 83.6% No. 2 ER 4 14X 36 36 0 100.0% ER ? 14% 74 18 56 75.7% 110 54 56 83.6% No. 3 ER 4 14' 36 32 4 88.9% ER p142. 74 14 60 81.1% 110 46 64 83.6% No. 4 ER 4 14%; 36 25 11 69.4% ER . 14% 74 6 68 91.92 110 31 79 84.6% No. 5 ER < 14X 36 27 9 75.0% ER >14% 74 6 68 91.9% 110 33 77 86.4% 1/ I - opportunity cost oE capital. ANNEX G - 80 - Page 20 Table 19: Discrioinant Functions for Investments (i = 16%) 1/ Unstandardized Classification Function _ Discriminating Discriminant Coefficients Evaluation SL' t ics Variables (X ) for Coefficients FOR FOR Canonical Wilks' 2 Each Functi n (Di ) ER <16) 16' Correlation Lambda X _ ~~~~Coefficient Discriminant _ - Function No.1 VOCS 4... Cost 1.0587 2.3614 4.2767 Cost +- (A ha) -0.002307 0.00398 -0.000190 O.6652 0.5575 62.23 Net Value per ha 0.007186 -0.002985 0.01001 Intercept (constant) -0.3753 -1.8941 -2.2161 Discriminant Function No. 2 Cost 4- (dA h4.) -0.002333 0.004133 -0.000101 Pass-km -.- Cost -0.007303 0.1139 0.1006 Ton-km +4- Cost 0.05470 -0.0588 0.0405 0.6665 0.5558 62.25 Net Value per ha 0.00730 -0.00290 0.0104 Intercept (Constant) -0.3413 -1.9760 -2.2360 Discriminant Function No.3 Value Added-g-Cost 2.4724 1.5463 5.6395 VOCS + Cost 3.8419 3.4985 9.8590 0.6318 0.6008 54.28 Tons per ha 0.09075 0.2042 0.3545 Intercept (Constant) -1.7537 -1.0377 -3.6421 1I - opportunity co t of capital. - 81 - ANNEX G Page 21 contd..... Table 19-- Discriminant Functions for Investments ( 16 - / Unstandardized Classification lunction Discriminating Discriminact Coefficients Evaluation Statistirs 'Variables (Xi) for Coefficients FOR 16% 67 3 64 96% 110 41 69 93% No.2 ER 16% 43 35 8 81% ER > 16% 67 3 64 96% 110 38 72 90% No.3 ER 4 16% 43 42 1 98% ER > 16% 67 15 52 78% 110 57 53 85% NO.4 ER 4.16% 43 39 4 91% ER 0 16% 67 14 53 79% 110 53 57 84% No.5 ER 4.16% 43 35 8 81% ER 16% 67 11 5;6 84% 110 46 64 83% 1/i = opportunity cost of capital. - 83 - ANNEX H Page 1 SCIEENING VIA REGRESSION ANALYSIS 1. The regression method provides an estimate of the economic rate of return (ER) of a rural road or group of interdependent RRs with associated agricultural investments, if any, in the RR's zone of influence, while the discriminant analysis method (Annex G) simply determines whether or not a road or group of roads will pass a feasibility test (fixed ER criterion). The regression analysis predicts the ER of the investment as a function of the characteristics which affect its economic performances. These independent variables include producer surplus measures (agricultural value added, increase in tonnage, increase in cultivated area, etc.), consumer surplus measures (vehicle operating cost savings of normal traffic, passenger-kilometers, ton-kilometers, etc.) and investment and maintenance cost variables. The regression equations presented in Table 21 are derived from data on the worldwide sample of 110 RRs. Two important problems with this method of estimating the ER of an investment should be noted: (1) non-linearity; and (2) heteroskedasticity. Regression analysis assumes that the relationships among the appropriately lefined variables are linear, in the sense that the regression coefficients ire linear. However, it can be observed from the data set that the relationships between ER and the independent variables are not linear. It was not possible to use logarithmic transformations to better fit the data because of the large number of zeros in the data base. Use of polynomial terms was rejected as suc'h expressions would unduly complicate a supposedly i3imple screening procedure. As a consequence, the regression equations overestimate the ERs of unfeasible investments and underestimate those ERs aibove the 35-40% level. .n intercept adjustment was later used to correct `or the overestimation of ERs for unfeasible investments. A second problem concerns heteroskedasticity or unequal variance of regression residuals. The heteroskedasticity problem common to cross-sectional analysis :Ls present in these regressions. No corrections l:hrough proper weighting procedures were attempted in this limited study, because the unbiased property of the regression coefficients remains unaffected. However, the regression estimates are inefficient in the sense that they are not minimum--variance estimates. 4. Results of the Analysis. The regression analyses results are Eiresented in Table 21. (Variable definitions are the same as those given in Table 12 of Annex G). Regression equation No. 1 exhibits the best degree of statistical fit (R2 - .64), followed by equations Nos. 3 and 4. Regression equations Nos. 2 and 5 are certainly inferior to the others in terms of both degree of closeness of fit: (i.e., R s) and significance of the regression - 84 - ANNEX H Page 2 coefficients (F-statistic). Measures of producer surplus benefits prove to be the most important predictors, as shown by their generally higher statistical significance. 5. In view of the non-linearity problem it was decided to reduce the intercept (constant) of the regression equations in order to adjust for the overprediction of the ERs of unfeasible investments. The aipproach taken was to find the average error E using the following formula: E 1 (Ra - Rp) n where n total number of unfeasible investments, Ra = actual ER as estimated in the feasibility studies of projects, and Rp = predicted ER as established by regression equations Nos. 1, 3 and 4. The adjusted intercept constant C' is then estimated as follows: C' = C - E where C = the intercept value estimated through regression equations Nos. 1, 3 or 4. The resulting equations after intercept adjustments are presented in Tables 22, 23 and 24 along with measures of their reliability. As shown in these tables, the reliability of the regression equations improves after the intercept (constant) adjustment. 6. The reliability of regression equations Nos. 1, 3 and 4 ranges from 81% to 85% without the intercept adjustment and from 84% to 93% with the intercept adjustment, as shown in Tables 22 through 24. However, the large standard errors associated with these equations make them of limited usefulness in estimating the actual ER of a particular RR or group of RR8 with associated agricultural investments, if any, in the RR's zone of influence. Although the results of the reliability testing (about 84% to 93% correct decisions) are satisfying, the use of regression analysis is, therefore, not recommended due to the high standard errors of the estimate which result from the regressions estimated. Consequently, there is no guarantee that the satisfactory reliability will be maintained in the population represented by the sample. - 85 - ANNEX H Page 3 Table 21; Sumary Statistics of the Regression Analysis Methods for Screening Rural Roads Evaluation Statistics Standard Standard ]legression Error of 2 Error of kjtression No. 1 Coefficient Coefficient F-Test R the Estimate Intercept (constant) 5.023 0.637 11.297 Value Added g Cost 24.1951 2.31 109.6 VocS *, Cost 77.964 8.85 77.7 Net: Value per ha 0.00949 0.005 2.5 Regression No. 2 Intercept (constant) 21.373 0.313 15.545 Cost ', (4 tons) --0.00736 0.0018 15.54 Pais-km '. Cost 1.2878 0.302 18.17 Net Value per ha 0.025 0.008 9.69 Re"jression No. 3 Intercept (constant) 22.762 0.412 14.392 Coat . (A ha) -0.0201 0.0033 35.76 Pass-im . Cost 1.1182 0.287 15.70 Net Value per ha 0.0509 0.008 39.03 Rep.ression No. 4 Intercept (constant) 22.667 0.468 13.6,86 VocS TCst i56.9466 10.6446 28.62 Cost . (8 ha ) -0.0203 0.0031 40.94 Net Value per ha 0.0450 0.0078 32.95 Repression No. 5 Intercept (constant) 21.288 0.358 15.029 VOCS Cost 60.424 11.660 26.85 Cost . ( Tons) -0.0072 0.002 15.86 Net Value per ha 0.0184 0.0077 5.59 - 86 - ANNEX H Page 4 Table 22: Reliability of Regression Equation No. 1 With Intercept Adjustment Predicted Group Membership Percent Classified Actual Groups No. of Cases ER < 12% ER ; 12% Correctly ER 4 12% 32 29 3 91% ER 12% 78 5 73 94% 110 34 76 93% Note: The intercept adjustment results in a negligible intercept value. The resulting regression equation after the intercept adjustment is: ER = 24.1951 [value added cost] + x 77.964 fVOCS . cost] + 0.0095 [net value per ha] Without Intercept Adjustment Predicted Group Membershi Percent Classified Actual Groups No. of Cases ER C E 12% Correctly ER t 12% 32 17 15 53% ER > 12% 78 2 76 97% 110 19 91 85% Note: The resulting equation is identical to the one presented in Table 21. - 87 - ANNEX H Page 5 Table 23; Reliability of Regression Equation No. 3 With Intercept Adjustment Predicted Group Membership Percent Predicted Acl:ual Groups No. of Cai;es ER < 12% ER > 12% Correctly ER 4 12% 32 26 6 81% ER Z 12% 78 11 67 86% 110 37 73 84% Niote: The resulting reg7ression equation after the intercept adjustment is: ER = 12.262 - 0.0201 [cost ', (A tons)] + +1.1182 (Vai3s-km - cost) + 0.0509 [net value per ha] W:thout Intercept Adjustment Predicted Group Membership Percent Predicted Actual Groups No. of Catses ER i4 127 ER j 12 _ Correctly ]ER < 12% 32 11 21 34% !R > 12% 78 0 78 100% 110 11 99 81% Note: The resulting equation is identical to the one presented in Table 21. - 88 - ANNEX E Page 6 Table 24: Reliability of Regression Equation No. 4 With Intercept Adjustment Peited Group Membership Percent Classified Actual Groups No. of Cases ER.< 12% ER 'B.12% Correctly ER <12% 32 31 1 97% ER 312% 78 11 67 85 110 42 68 89% Note: The resulting equatlon after the intercept adjustment is: ER = 13.327 + 56.9466 [VOCS. cost] + - 0.0203 [cost .(A bIfte + 0.0450 [net value per ha] Without Intercept Adiustment Predicted Group Membership Percent Classified Actual Groups No. of Cases ER6.12% ER > 12% Correctly ER 12% 32 12 20 38% ER 12% 78 0 78 100% 110 12 98 82% Note: The resulting equation 1s identical to the one presented in Table 21. - 89 - ANNEX I Page 1 SAMPLE DESIGN AND CHARACTERISTICS 1. Introduction. The sample of rural roads (RRs) used for this analysis was selected from Bank project files. In the initial review of rural roads and rural development projects, eight projects were identified which had project file data on specific links. These projects provided reasonable geographical coverage of the developing world with, however, a rather strong emphasis on Latin America (three of eight projects). The other projects were in North nind West Africa, South and East Asia. Only East Africa fails to be represented in the sample. A key assumption for the analysis is that this sample frame adequately represents the universe of potential road projects in the developing world. 2. Sample Size. The number of RRs to be selected from those for which project files are available was determined according to standard statistical procedures. The characteristic of the RR population which we wish to estimate on the basis of the sample is the proportion of roads passing (or failing) screening tests which will also pass (or fail) the economic feasibility test. This is defined to be the measure of reliability for a specific screening method. Equation (1) presents the formula for determining the coefficient of variation (CV) of a proportion estimated via random sampling without replacement. C V a T .... ..(CL1) where p - the proportion sought, (p - standard deviation of the proportion, n - sample size, and CV - a measure of the level of relative error associated with estimates based on sample data (i.e., the coefficient of variation). Acceptable ranges of relative errors are given by coefficients of variation which range from 0.01 to 0.10. In other words, the size of the relative error ranges from 1/100 to 1/10 the value of the estimate (in this case, the proportion of correct decisions). - 90 - ANNEX I Page 2 3. Table 25 shows the sample sizes required to achieve coefficients of variation ranging from 0.5 to 0.10. A sample size of 110 RRs was selected on the basis of available data and distribution considerations (para. 4). This sample size assures that the relative error of the estimate will not exceed 5% for values of the estimate in the vicinity of 80%. In other words, if the application of a given screening method to the sample roads results in 80% correct predictions, we can be confident that the true value for the roads represented by the sample lies between (.80) (1 - .05) - 76% and (.80) (1 + .05) - 84%. For success rates of greater than 80%, we can be even more confident that the sample accurately represents what would happen if the same test were applied to all roads in the project files. Table 25: Sample Sizes Required for Different Relative Error Levels Required Sample Size (n) for Different Levels of Coefficients of Variation (CV) Proportion of Correct Decisions CV - 0.10 CV = 0.05 0.8 26 101 0.7 44 172 0.6 68 267 4. Sample Distribution. Some of the projects had data for hundreds of road links recorded in the project files, while others had data for only three or four roads. In order not to allow one or two countries to overwhelm the sample, the number of roads to be selected from each project was predetermined in order to provide approximately equal geographic distribution among the regions. The projects and specific roads selected are shown in Table 26. 5. Sample Characteristics. With the exception of the four Indonesia roads, which will be paved, all of the sample roads were all-weather gravel roads. Very few earth roads were found in the project files. Thus the reliability of the screening methods tested in this study can only be assumed to apply to all-weather, unpaved roads. - 91 - ANNEX I Page 3 Table 26: Identification of Roads in the Sample No. of Country Roads Location Road Identification Brazil 12 Class E roads in state Routes #1, 10, 11, 17, 23,28, 37, 38, 39, of Blahia (serving 40, 43, 47 CacLo) llonduras 10 Roads in Yoro, Masica Guayape Valley: Roads #6, 8, 13, 33 and Guayape Valleys Masica Valley: Roads #1, 4, 7 Yoro Valley: Roads #1, 2, 3 Colombia 12 Roatls in 7 regions Reg. Huila: Routes #02, 03, 23 Reg. Narino: Route #04, 05 Reg. Tolima: Route #10 Reg. Quindio: Route #55 Reg. Risaralda: Route #53 Reg. Sucre: Route #61 Reg. Choco: Routes #63, 64, 65 India 19 Roa,ds in state of Bihar Routes: Minapur-Belsaud, Bihar Silao-Gorma, Sisai-Basia, N/Beg/6k, S/SAS/8k, S/GAY/13k, S/GAY/20k S/GAY/28k, S/AUR/12k, S/GAY/12k, S/AUR/13k, C/KHU/3k, t:/DA/2k, C/RAN/2P N/MOT/3k, N/BEG/lk, S/DIN/lk, N/SAH/3k S/GAY/7k Indonesia 4 Java Collector roads Java roads #1, 2, 3, 4 Philippines 6 Roads in 2 provinces Iloilo Province Roads #41.05, 41.03/ alone and with Agricultural Investments Cebu Province Roads #13.05, 43.03 Benin 22 Roads in 3 provinces Atacora Province Roads: a, b, c, d, e, f, g, h, i, J, k, 1, m, n, o, p, q, Zou Province Roads: #r, s, t Mono Province Roads: u, v Tunisia 25 Roads in 6 provinces Province of Gabes: Routes #807, 808 809, 851, 852 Province of Gafsa: Routes #708, 711 Province of Kasserine: Routes #508, 551, 552 Province of Medenine: Routes #1801, 1802, 1803, 1804, 1805, 1854, 1855 Province of Sidi Bouzid: Routes #609 662, 663, 665 Province of Monastir: Routes #1502, 1503, 1505, 1506 Total 110 - 92 - ANNEX J Page 1 INDONESIA: SCREENING ON COST PER POPULATION AND COST PER CULTIVATED AREA 1. The simplicity of this screening method makes it an attractive alternative to more complicated methods. It is believed to work well in Indonesia because of the relatively high volumes of both freight and passenger traffic on the roads to be improved. Both types of traffic are closely linked to the key parameters selected for screening purposes. 2. A prescreening procedure eliminates from analysis those roads that (1) lie within a 3 km distance of an alternative road, (2) are less than 2 km in length, or (3) do not fit the definition of rural roads. Three types of rural roads are distinguished: (a) collector and through roads; (b) development access roads; and (c) service roads, which comprise all the remaining rural road improvements not otherwise classified. 3. Collector and through roads are evaluated on a 20% sample basis on the basis of vehicle operating cost savings, and while there has been an attempt to relate their ERs to parameter values of cost per person served, the results are still tenuous. 4. Development access roads and service roads are screened on the basis of two key ratios, namely: (i) the cost of road construction per person residing in the zone of influence 5 years after construction; and (ii) the cost of road construction per hectare of cultivated land in the zone of influence 5 years after construction. 5. Economic analysis conducted by a consultant team has determined that for access/service roads an economic rate of return (ER) of 12% corresponds to ratios of US$200 equivalent road construction costs per hectare of cultivated land or alternatively US$50 of road construction costs per person. In highly dense areas of Java, project justification requires road construction costs of US$10 per person or US$400 of road construction costs per hectare of cultivated area served. In less densely populated areas outside of Java, the cultivated area becomes more important than population. In addition, these roads are the subject of an economic evaluation on a 10% sample basis. 6. The population variable plays an important role in the screening of rural roads in Indonesia. The Indonesian project is one of the few cases - 93 - ANNEX J Page 2 where project planners have attempted to measure passenger and non-agricultural freight traffic on a development access; road. The consultants estimate that 48 trips per person will be made every year with the development access; road (16% in motor vehicles, and another 5% on motor-cycles, and the rest by foot and non-motorized vehicles), compared to 38.4 annual trips per person without the access roads (none of which are by motor vehicles). As a consequence the consumer surplus benefits (savings in vehicle operating costs) account for 70% of the total benefits from the rural roads. 7. This methodology was tested by developing a regression function relating the ER to the two key variables, cost per person served and cost per cultivated area served, for the worldwide sample of 110 rural roads. The resulting regression yields an R2 of 0.062. In other words, these two parameters explain only 6% of the observed variance of the ER., Furthermore, on this sample the regression coefficient of the population variable is not statistically significantly different from zero at the 95% significance level. 8. The US$50 cost per person criterion was also used to screen the worldwide sample of rural roads into two groups, i.e., economlcally feasible ones and unfeasible ones. This criterion led to 44% incorrect decisions, compared to the results of full feasibility studies, with particularly high error rates in the relatively densely populated zones of infLuence of roads in India and the Philippines. This appears to be due to the! fact that the calculation of consuner benefits in the sample of roads in these two countries (and indeed in most of the countries in the sample) considered that the passenger and non-eagricultural freight traffic would be insignificant. 9. The reliability of the screening criteria in predicting ERs in Indonesia is currently being tested by regional staff, using data from the subprojects included in the first year program for the five sample kabupatens, for which individual ERs have been calculated. Preliminary results indicate that these criteria in fact are not very reliable even in the Indonesian situation, due to the wide variation in improvement types as well as to the variability of ERs within improvement types covered by the sample. Further work is planned by regional staff to define and test new measures which may prore to be more accurate predictors of ERs in Indonesia. - 94- ANNEX K Page 1 RURAL ROAD CONSTRUCTION COSTS AND VEHICLE OPERATING COSTS 1. Introduction. For the purpose of developing the tables presented in Annex L on the level of ADT traffic required to justify rural road (RR) investments, an attempt was made to collect data on typical costs of construction of RRs and vehicle operating costs on these roads. This annex describes the results of this investigation. Construction Costs of RRs 2. RR Construction Costs. The analysis that follows is conducted in reference to five major types of rural road investments: (1) construction of earth roads without drainage; (2) construction of earth roads with drainage facilities; (3) construction of all-weather gravel roads; (4) re-gravelling of previously gravelled roads; and (5) construction of roads with bituminous surface treatment. Typical construction costs for these improvements are given in Table 27. These costs have been obtained by actualizing to December 1981 prices the costs of a list of IBRD-financed rural road projects compiled by C.R. Willoughby.3/ The procedure used in projecting costs to 1981 levels was as follows: first, the costs in domestic currency were projected to 1981 using consumer price indexes in the respective countries; second, the projected costs in domestic currencies were converted into dollars at the market exchange rates. The source of the price indexes and the exchange rates is the data compiled by the International Monetary Fund.4/ 3/ C.R. Willoughby, Labor-Intensive Construction Techniques: Report of a Bank Seminar, March 9-11, 1977. IBRD Transportation Department, September 15, 1977. 4/ The consumer price index is the only price series reported on a regular basis for most of the countries in the original list compiled by Willoughby. See International Monetary Fund, International Financial Statistics, Volume XXXV, No. 6, June 1982. - 95 - ANNEX K Page 2 Table 27: Typical Construction Costs for Selected Rural Road Projects (1) (2) (3) With-Project Without-Project Construction Costs per km-/ Situation Situation (USDollars, 1981 prices) Earth Road without Impassable Tracks 6,000-10,000 Drainage Earth Road with Impassable Tracks 14,000-20,000 Drainage Iravel Road Earth Road without 15,000-35,000 D rainage Regravelled Road Gravel Road in Poor 8,000-25,000 Condition Road with Gravel Road _OO,000-200,000 Bituminous Surface LCosts to improve the coniditions of tracks/roads of Column (2) t.o the conditions of roads of Column (1). - 96 - ANNEX K Page 3 3. The cost estimates presented in Table 27 are nothing more than benchmark factors to aid in this study. They should not be used for costing specific projects. In fact the research showed instances where the costs of construction of rural roads were multiples of the figures presented in Table 27. For example, all-weather gravel roads are being constructed in Paraguay at costs of $125,000 per kilometer. The large variations observed may be indicative of a need to improve RR design standards and specifications. 4. Vehicle Operating Cost Savings. A wide discrepancy in vehicle operating cost savings was found in the feasibility reports analyzed. Most of the discrepancies concerned the savings related to improving tracks to earth roads and earth roads to gravel roads. In addition, some projects exhibited very high savings per ton-kilometer. Table 28 presents the range of vehicle operating costs and cost savings observed. These costs were actualized to December 1981 utilizing the procedure described earlier for the rural road construction costs.5/ Unfortunately, since the VOCs from the feasibility studies do not disaggregate costs into component elements, it was not possible to apply different price indexes to the fuel costs vs. the other cost components. The differences in cost savings observed in Table 28 to some extent reflect discrepancies between the Kenya tables developed by the Transport and Road Research Laboratory6/ and the previous research of de Weille,7/ Bonney and Stevens8/ and othIers. Differences between the Kenya tables and the research studtes which preceded them are acute for earth and gravel roads. To skirt around this problem of lack of consensus on estimates of vehicle operating cost savings, it was decided to develop the tables of Annex L in a manner which enables the analyst to consider a large range of alternative vehicle operating cost savings estimates. 5/ With the data available this is the best possible procedure; however, it is weak since insufficient attention is given to increases in fuel prices. 6/ S.W. Abaynayaka et al., Tables for Estimating Vehicle Operating Costs in Developing Countries. TRRL Laboratory Report 723, Transport and Road Research Laboratory, 1976. 7/ Jan de Weille, Quantification of Road User Savings, World Bank Occasional Paper No. 2, The John Hopkins Press, 1966. 8/ R.S.P. Bonney and N.F. Stevens, Vehicle Operating Costs on Bituminous, Gravel and Earth Roads in East and Central Africa, Road Research Technical Paper No. 76, Road Research Laboratory, Ministry of Transport, London. Her Majesty's Stationery Office, 1967, p. 22. - 97 - ANNEX K Page 4 Table. 28: Vehicle Operating Cost (VOC) by-Means and Surface T es in Flat Terrain (US dollars, 1981 prices) Lkrth Roads - Flat Terrain VOC on Earth Roads Earth Roads in Good Condition in good condition Mirbans CountrY Cost per Costs per Costs per as Proportion of VOC - ((year ofstudy vehicle-km ton-km pass-km on Earth ionAd in Bad Condition Passenger Honduras (80) 0.168 77.2% Car Upper Volta (75) 0.213 53.3% Benin (76) 0.313 77.8% Tunisia (78) 0.179 88.3% Tunisia (81) 0.193 n.a. Indonesia (80) 0.267 52-62% lus-unspec. Honduras (80) 0.302 76.92 Tunisia (78) 0.591 84.1% bus-light Indonesia (80) 0.256 45-552 Bus-Heavy Indonesia (80) 0.399 40-50% light Vehicle/ Honduras (80) 0.110 0.013 76.0% Hinibus Tunisia.' Minibus (81) 0.633 n.a. 7rucks-2 ton Upper Volta (75) 0.234 48.6% Benin (76) 0.214 49.42 Trucks-7 ton Upper Volta (75) 0.433 49.9% Benin (76) 1.058 84.3% Truck-Light Indonesia (80) 0.272 44-54% Truck-Med. Indonesia (80) 0.320 40-50% Trucks- Jnspec. Honduras (80) 0.462 76.8% Honduras (80) 0.474 0.04-0.07 91.1% Tunisia (78) 45782.9 Tunisia (81) 0.511 n.a. Oxcarts/ Honduras (80) 0.220 0,46-0.73 95% H3rsecarts Bibar (80) 0.12-0.36 0.12-0.36 100% Tunisia (78) 0.207 100% Sri Lanka (78) 0,68-0.80 n.a. Indonesia (80) 0.268 100% BLcycle Indonesia (80) 0.085 98-99% MHLles Honduras (80) 0.086 0.87-1.44 0.09-0.17 94% Tunisia (78) 0.058 100% Padestrian Honduras (80) 0.058 0.06-0.17 100% P.adestrian/ ,ackpack Philippines (79) 0.036 3.21 (Head-carry) 0.036 100% Indonesia (80) 0.177 100% - 98 - ANNEX K Page S contd... Table 28: , Vehicle Operating Cost (VOC) by Means and Surface Types in Flat Terrain (US dolars, 1981 prices) Gravel Roads - Flat Terrain VOC on Gravel Roads in good condition as piroportiop of VOC on Gravel Roads in Good Condition Gravel Road Earth Road Country Cost per Cost per in ''od--66ndition in Good Means (year of study) vehicle-km ton-km Costs-k condtilon Passenger Honduras (80) 0.158 71.3% 94.5% Car Benin (76) 0.212 n.a. 67.6% Tunisia (78) 0.145 89.5% 80.6% Tunisia (81) 0.133 n.a. 68.9% Indonesia (80) 0.267 60-69% 99.8% Bus-unspec. Honduras (80) 0.276 71.3% 91.6% Tunisia (78) 0.389 80.0% 65.8% Bus-light - Indonesia (80) 0.224 52-62% 87.2% Bus-heavy Indonesia (80) 0.375 49-59% 93.9% Light Tunisia (81) 0.36 n.a 56.8% Vehicle/ Philippines (79) 0.088 0.013 61-66% n.a. Minibus Jeepney Philippines (79) Minibus 0.008 63.6% n.a. Trucks-2 ton Benin (76) 0.292 n.a. 67.2% Trucks-6 ton Senegal (74) 0.591 0.197 n.a. n.a. Trucks-7 ton Benin (76) 0.737 n.a. 69.7% Trucks-10 ton Senegal (74) 0.757 0.151 n.a. n.a. Trucks-25 ton Senegal (74) 1.12 0.088 n.a n. Trucks-light Indonesia (80) 0.241 50-60% 88.oa% Trucks-med. Indonesia (80) 0.299 49-59% 93.9% Trucks-Unsp. Honduras (80) 0.403 71.3% 87.9% Tunisia (78) 0.281 77.1% 61.6% Tunisia (81) 0.258 n.a. 50.2% Colombia (81) 0.97-1.09 n.a. n.a. Philippines (79) 0.037 62.0% n.a Tricyles Philippines 79 0.185 0.023 na Bicycle Indonesia (80), 0.085 01502399% 100.0% - 99 - ANNEX K Page 6 contd..... Table 28: Vehicle Operating CstM and Surface Tyes in Flat Terrain (US dollars, 1981 prices) Paved Roads - Flat Terrain Paved Roads in Good Condition VOC on Paved Roads Country Cost per Cost per Costs per as Proportion of Means (year of study) vehicle-km ton-km pass-km VOC on_ Pavea koan in LGravel Road in Bad Condition Good Condition PEssenger Honduras (80) 0.112 66.9% 70.8% CUr Indonesia (80) 0.264 61.-72% 99.2% Tunisia (78) 0.125 95.1% 86.3% Bts-unspec. Honduras (80) a,Z05 66.7% 74.5% Tunisia (78) 0,319 91,72 81.9% Bus-Light Indonesia (80) 0.220 53-63% 98.6% Bus-Heavy Indonesia (80) 0.354 49-59% 94.3% Trucks-6 ton Senegal (74) 0.503 0.168 n.a. 85.1% Trucks-10 ton Senegal (74) 0.647 0.129 n.a. 85.4% Trucks-25 ton Senegal (74) 0.962 0.076 n.a. 85.9% Truck-Light Indonesia (80) 0.238 51-61% 98.7% Truck-Med. Indonesia (80) 0.283 49-59% 94.3% Trucks-Unsp. Honduras (80) 0.346 66.7% 85.7% Tunisia (78) 0.222 91.6% 79.1% Critical Values of Average Daily Traffic NatO 6- 5 IS101/ * voC VOCS *' CZ (8/Km) a WSM I) I 6000 10000 14000 10000 25000 35000 50000 7S000 1Z5000 200000 250000 3 * 0.10 0.05 * 561 701 1263 1403 4754 245S 3507 5261 8768 14029 17S36 e * 0.10 0.10 * 261 351 b31 701 877 1228 1754 2630 4384 1014 8766 a * 0.10 0.15 * 187 234 421 468 ses 818 1169 1754 2923 4676 5645 S * 0.10 0.25 1 112 t40 25S 281 3SI 491 701 1052 1754 2606 3507 e * o.1o O.35 s o0 tO0 160 200 251 351 S01 752 1253 2004 asos . * 0.10 0.50 * 56 70 126 14u 175 246 351 526 677 1403 1754 a * 0.10 0.75 * 37 47 84 94 117 164 234 351 585 935 1169 a …_._-------------------__------------- ___--- _-- _---- _---- -__- _--- _-- _____ _- _.---- __- _- _- _--- _- __---- _--- _a------ -----.- ----------- * 0.25 0.05 a 224 281 sob 561 701 982 1403 2104 3507 5611 7014 a * 0.25 0.10 a 112 140 253 281 351 491 701 1052 1754 2806 3507 a * 0.25 0.15 * 75 94 160 187 234 327 468 701 1169 1870 2336 a * 0.25 0.25 a 45 56 101 112 140 196 261 421 701 1122 1403 a * 0.25 0.35 a 32 40 7. 80 100 140 200 301 501 802 1002 a * 0.25 0.50 a 22 s28 St S 70 98 140 210 351 561 701 a * 0.25 0.75 * 15 19 34 37 47 65 94 140 234 374 468 a m--…---------------------------_-_-------- _- ----_----------_-----_---- __--- _..---__--__ -*___-__*__................................ * 0.50 0.0S * 112 140 253 261 351 491 701 1052 1754 2606 3507 * * 0.50 0.10 * 56 70 12b 140 175 246 351 526 877 1403 1756 a * 0.50 o.1S * 37 47 84 94 117 164 234 351 585 935 1169 a * 0.50 0.25 C 22 28 51 56 70 96 140 210 351 561 70t * * 0.50 0.35 a 16 20 30 40 S0 70 100 150 251 401 501 * * OS0. 0.50 C 11 14 25 28 35 49 70 105 175 281 351 3 * 0.50 0.75 * 7 9 17 19 23 33 47 70 117 167 234 * * 1.00 0.05 a 56 70 126 140 175 246 351 526 877 1403 1754 U * 1.00 0.10 * as 35 63 70 88 123 175 263 438 701 677 l * 1.00 0.15 a 19 23 42 47 58 82 117 175 292 466 565 * 1.0O 0.25 a 11 14 25 28 35 49 70 105 175 21 I 351 * 1.00 0.35 a 6 1o 1o 20 25 35 S0 75 12S 200 251e * 1.00 o.so' qj 7 Is 14 18 25 35 53 68 140 175. * 1.00 0.75 % 4 5 a 9 12 16 23 35 S5 94 117 * 2.00 o.os C 28 35 63 70 so 123 175 263 438 701 677 U * 2.00 0.10 * 14 18 32 35 44 61 68 132 219 351 436 * 2.00 0.15 ' 9 12 21 23 29 41 Ss 66 146 234 292. * 2.00 0.25w 6 7 13 14 16 25 35 53 88 140 175 * 2.00 o.3S a 4 5 9 10 13 16 25 38 63 100 12S5 * 2.00 0.50 C 3 4 6 7 9 12 16 26 44 70 asu * 2.00 0.75 * 2 2 4 5 6 a 12 1i 29 47 So6 * 4.00 0.05 * 14 18 32 3S 44 61 86 132 219 351 436 * 4.00 0.10 *7 9 10 16 22 31 44 66 110 175 19 a 4.00 0.15 * 5 6 11 12 IS 20 29 44 73 117 146 * * 4.00 0.25 3 3 4 0 7 9 12 18 26 44 70 8as * 4.00 0.35 * 2 3S 5 5 6 9 13 19 31 50 63 U * 4.00 0.50 a 1 2 ' 4 4 6 9 13 22 35 44 4 * 4.00 0.75 A I 1 2 2 3 4 6 9 15 23 296 …--------------------___---_--------------------_---.---_-------_____--___-_-___-_-_-_--__----.__--_--__-__--__-..-.--....--.--.... 1/ Note that the text and Annex N use i and 8 for the opportunity cost of capital and grovth rate of. traffic, respectively, while this annex, which is a computer printout, uses I and G. - t NB: Additional tables for values of N equal to 20 as well as other variations in G are available in TWD (N-932). Nalo Go S I411 * VUC VOC6 '. 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This annex presents the mathematical derivations of the simplified appraisal methods presented in Section III of the report. 2. Simplified Method I. The first method presented in Section III is concerned with the economic justification of rural roads (RRs) solely based on vehicle operating cost (VUC) savings. Consequently, for a road to be economically feasible, the present value of the VOC savings must be equal to or exceed the present value of the costs of construction and maintenance of the road. Thus: N B CR . t .............. (1) t=l (l+i)t where, CR = present value of the costs of construction and maintenance of the road, Bt = benefits during year t, in this case defined in terms of VOC savings, i = opportunity cost of capital, and N = years of expected life of the road. Note that: Bt = (KM) (365)t(ADTlt)(VOClt)- (ADT2t) (VOC2t)d ............. (2) where, KM = length of the road in kilometers, ADT i' ADT2 = the average daily vehicle traffic on the road in year t ADTlt, 2t in the without- and with-project situation, respectively, and VOC1t, VOC2t the weighted average (based on composition of typical vehicles) vehicle operating cost per vehicle-kilometer during year t in the without- and with-project situation, respectively. Expression (2) ignores benefits related to generated traffic in view of assumptions (iii) and (iv) of para. 37 of the text. The relation between the - 191 - ANNEX M Page 2 present value of benefits growing at an annual compound rate g and the first year benefit is: 9/ N B ~~~~~N tN BtD(l+g) -1 t (1+g) -1+i (l+i) where, B1 = first year benefits (or Bt for t=l), g = annual compound growth rate of benefits, and i and N are as defined above. The terms by which B1 is multiplied in expression (3) may be referred to as the Present Value Factor for a given i, N, and g. Thus, expression (3) may be written as: N B ____ ___ B (PVF .. . .. . .. . .(4) t=l (l+i)t I i,g,Nl*...... where, PVFi N = present value factor of a pecuniary benefit unit growing ,g, at an annual compound rate of g over N years and discounted at rate i. Combining expressions (2) and (4) gives: £ Bt = (KK) (365) FAT (VOC11 - vOC21) (PVF i,g,N . () t=l (l+i)t L 1 1 1 ,, 9/ M. Martinez, Benef.it-Cost Calculations: Tables for Internal Rates of Return and Sensitivity Tests, World Bank, January 1979. - 192 - ANNEX M Page 3 The initial condition to justify the road solely on VOC savings, expression (1), may now be written as: CR C (KM) (365) {ADT1i (VOC1 - VOC2) (PVFigN) .............. (6) or, CR < 365 ADT (VOc11 - V0C21)j (PVFi gN) .............. (7) From equation (7) the initial level of traffic required to justify the road on VOC savings may be calculated as: ADT R2 11- 365 (VOC11 - V0C21) (PVFigN) .............. ig(83 or, ADT _ CR/ KM .............. (9) 11 (365) (VOC 11)( C11 - VoC21 (PVi)g,N The ADT figures of Aninex L, which are minimum ADTs required to economically Justify the construction or improvement of a RR, have been calculated with expression (9). 10/ 3. Simplified Method III. This simplification justifies the RR and agricultural investments, if any, in the RR's zone of influence on the basis of the producer surplus concept. For economically feasible investments the following inequality has to be satisfied: C__ N VA2t - VAt t=l (l+i)t ............. (10) 10/ See V. Wouters, Internal Rates of Return Tables, World Bank, Washington, D.C., 1967, for the derivation of Simplified Method II. - 193 - ANNEX M Page 4 where, C = present value of the costs of construction and maintenance of rural road and agricultural components, if any, in the zone of influence, VA , VA = agriculitural value added in the zone of influence during t 2t year t of the without- and with-project situation, respectively, and i and N are as defined earlier. Define year p as the year when the agricultural value added in both with- and without-project situations is at maximum. In addition,year p1 is defined as tlte year in which the full agricultural production or maximum value added is first achieved in the without-project situation, while P2 corresponds to the year when full agricultural. production or maximum value added in the with- project situation is first achieved. Case p >P2. Assuming proportional linear growth of agricultural production between year 1 and year p1 in the without-project situation and similarly between year 1 and year P2 in the with-project situation, the present value oE benefits may be calculat:ed for situations where P i P2. Thus, defining x as x p p1 - p2. the present value of benefits is given by: N ~ VA 2t-VAlt V( A V p- A f'l\ VV(A (k' VA N 2t lt) 2P2- I( T) P1P ( 2 ) VA2 ~ 1 2 V 1 t=l (i+i)t (1+i) (l+i)2 ( Y3 VA (3N VA. ( P12 VA _)_ ) (P1 X 2p 1p_ p2 L2P 2 (-) VA1p +~~~~~~~~~~~~~~~~ 3p -X x-*+ l_ (+i) (l+)i) PIX- VA - - VA VA1 VA1 (+% + +,......... .. ( U.......... (11 P2 1'2- p p1 2p p1 (l+i)p (1+i) VA 2 -VA lpVA -p2 VA 1 (l+i) 1 (l+i)N A similar expression is later derived for the case pl 1 -+<) ..+ l -~__ ( )..................... < 13) (l+i) p1 X (1+i) P1-1 since p expression (13) results in: N VA2t -VA I N VA - VA E 2 1t 2t it>o ..... ......(14) t=l (I+i)t t=l (1+i)t and: N VA2t - IVA t N V 2t lt (15) t=l (1+i)t t-I (1+i)t so that the true benefits are underestimated. Conversely it may also be shown that evaluating expressLon (11) at P2 would result in an overestimate of the true benefits. - 196 - ANNEX M Page 7 Case p1Overestimation 1 > P2 If p1 used >Underestimation pl P2 Correct estimation If p used - Underestimation Pl< P2 If p1 used- >Overestimation In view of these results, assumption (v) of para. 46 of the text has been introduced. By defining p as the larger of p1 and P2, expressions (11) and (16) can be further simplified as: NVA2t_ VAlt I - P- ( )= P + _P 2+0'+ P + 1 + 1 +.....+ ti(1+i)Pl ~1 +i)P (1+i)p+l .(1) .,. . . . . . (21) - 199 - ANNEX M Page 10 The terms in brackets may be expressed as the crop unit value factors (:Pv,i N p) corresponding to the present value of one pecuniary unit benefit La year p, discounted at the opportunity cost of capital i during N years. These crop unit value factors have been calculated and are presented in Table 5 of the text. Introduction of these crop unit value factors into ejuation (21) results in: t=l 2t - VApltC=VVAN P) ......................V. (22) E= (1+1) iN S-zbstituting equation (22) into expression (10) results in the following decision rule: for the investment in RR and agricultural components, if any, in its zone of influence to be economically justified: C -<(VA) (P Vi,N,) ..................... ,(23) The ERs of Table 5 of the text have been established with expression (23). 4. Simplified Method IV. Expression (10) of the text may be derived from expression (9) of Annex 1 of Staff Working Paper No. 362 (H.L. Beenhakker and A. Chammari, October 1979) as follows: B = Pmq2 R2 P mql + R 1+ [-P1 (H1-H2) - 1/2 (H1-H2) (P2-pl)] ........(.......... {24) Nlte that q2 = Q2 and q1 Q1, since 11 =2 Ecpression (24) therefore becomes: B= P (Q2 - Q1) - C2- Q2k2 + C1 + Q1k3 .. .. . (25) since R2 = C2 + k2Q2 and R1 = C1 + klQl ihere all terms are defined as in the aforementioned Annex 1, which is reproduced In Annex 0 of this paper. Expression (25) is the same as expression (10) of the text. - 200 - ANNEX M Page 11 5. Simplified Method V. Expression (11) of the text may be derived by substituting (Q2-H2) for q2 and (Q1-Hl) for q,, in expression (24): B PM (Q2-R2) - - Pm (QRl ) + - P1 (H1-H2) - 1/2(H1-H2) (P2 P1) Note that R1 C1 + (Q1-Hl) k, - C1+ q1 kl, and R2 C2 + (Q2-H2)k2 = C2 + q2 k2 Therefore: B- PQ- Q - c (-H )k + C + mQ2 mQl 2 2 2 2 1 + (Q -H )k- PmR2 +P HE- P1( 1 2 - 1/2(1 -H2)( P2 -P1) PmQ2 - mxQl C2 - (Q2-H2)k2 + C1 + (Q1-1 I)k1 + + (P m-P (H1-H2) - 1/2(H1-H2) (P2-Pl) PmA2 - PmQl - C2 - (Q2-H2)k2 + C1 + + (Q1-R )k1 + (HU-H2) (Pm-1/2PI- 1/ 2P2) Ignoring (ffl-H2)(Pm-1/2Pl-/12P2) since the value of this expression is normally close to zero, one obtains: m 2 m1 2 Q2k2 + C1+ Qlkl + 2k2 2 H1k1 where the first six terms and the last two terms represent expressions (10) and (11) of the text, respectively. - 201 - ANNEX M Page 12 11/ 6. Simplified Method VII. Expression (12) of the text may be derived by substituting (P:iF1) for Pm' (QI-H1) for q, and (Q2-H2) for q2 in expression (24): B = (pl+ F1)[(Q2-H 2) - (Ql-Hl)] - R2 + R + - P1(Hl-H2) - 1/2(H1-H2) (P2-p1) = = 1 2 H2)+ F1(Q2-H2) - P1(Q1-Hl) - - F1(Q1-Hl) R2 + R1- pH-H2) - 1/2(H1-H2) (2-P 1) = F1(q2-ql) -R2 + R + P1Q2 - PlQ1 - - 1/2 (H -H2) (P2 1) 1 q2-q1) C2 C1 q2k2 q 1k1 + P1 (Q2-Q1) 1/2(H1-H2) (P2-pl) P1(Q -Q1) - c - Q2k2 + C1 + QIk1 + k2H2 - k1H1 + F(q2-q1) + - 1/2(H1-H2) (P2-P1) Ignoring 1/2(H1-H2) (P2--P1) since the value of this expression is normally close to zero, one obtains: B =P (Q2-Q) - C2- Q2k2 + c1 + Q1k1 + k 2-kH + 1 B = (expression (10) of the text with PM= P1) - - (expressi,Dn (11) of the text) + + (the expression mentioned in para. 62 of the text). 1l/ Simplified Methods VI and VIII are explained in the text.. - 202 - ANNEX N Page 1 ECONOMIC RETURNS (ERs) FOR NET BENEFITS GROWING AT A COMPOUND RATE Present Value of One Dollar Growing at 5% L 1- Y.c S lb YRS 20 YRS 25 YItS 30 YRS 40 VRS 1 12.4587 20.7554 30.8305 43.0650 57.9219 97.8713 2 11.7691 19.0636 27.4958 37.z431 48.5107 76.5920 3 11.1321 17.5552 24.6260 32.4105 40.9806 60.8032 4 10.5444 16.2073 22.1477 28.3793 34.9162 48.9670 5 LO.0000 15.0000 20.0000 25.0000 30.0000 40.0000 6 9.4955 13.9163 18.1324 22.1533 25.9881 33.1335 1 9.0275 12.9413 16.5027 19.7435 22.6925 27.8180 8 8.5927 12.0622 15.0759 17.6936 19.9674 Z3.6580 9 8.1884 11.2679 13.8225 15.9414 17.6991 20.3664 t0 7.8118 10.5487 12.7177 14.4365 15.7986 17.7335 It 7.4608 9.8962 11.7408 13.1379 14.1961 15.6046 12 7.1331 9.3028 10.8741 12.0121 12.8361 13.8651 13 6.8269 8.7622 10.1028 11.0315 11.6748 12.4291 14 6.5405 8.2687 9.4143 10.1737 10.6770 11.2318 6.2723 7.8174 8.7978 9.4199 9.8146 io.2240 Lt 6.0201 7.4037 8.2440 8.7546 9.0649 9.36dO it 5.7849 1.0239 1.1452 8.1651 8.4095 8.6346 to 5.5632 6.6746 7.2946 1.6405 7.8334 8.0011 1s 5.3547 6.3526 6.8864 7.1118 7.3245 7.4498 20 5.1585 6.0555 6.5155 6.7515 6.8726 6.9665 21 4.9736 5.7806 6.1778 6.3732 6.4693 6.5399 22 4.7991 5.5261 5.8693 6.0314 6.1080 6.1b12 23 4.6345 5.2899 5.5870 5.7216 5.7H27 s.8229 24 4.4789 5.0703 5.3278 5.4399 5.4887 S.5192 2., 4.3318 4.8660 5.0894 5.1828 5.2219 5.2451 2, *4.19?s 4.675S 4.8696 4.9476 4.9189 4.9966 71 4.0605 4.4976 4.6664 4.7317 4.7569 4.7704 2e 3.9353 4.3313 4.4783 4.5329 4.5532 4.5636 29 3.ul)6 4.1755 4.3037 4.3495 4.3659 4.3738 It, 3.7037 4.0294 4.1414 4.1798 4.1931 4.1992 -203 ANNEX N Pa-ge 2 Present Valuc of One Dollar Growing at 6% L N = 1) YAS 1L YRS 20 YRS 25 YRS 30 YRS I I3.17Cl 22.5626 34.5219 49.7493 69.1380 125.2588 2 1.2.4316 20.8880 30.6952 42.8247 57.5266 96.9450 3 11.7504 19.0105 27.4085 37.0937 48.2739 76.0782 . 11.1211 17.z284 24.5758 32.3275 40.8537 60.5473 5 10.5391 16.1953 22.1260 28.344s 34.8649 48.8704 6 10.0000 ls.o000 20.0000 25.0000 30.0000 40.0000 7 9.5001 13.9260 18.1488 22.1780 26.0224 33.1903 a 9.0360 12.9588 16.5315 19.7854 22.7490 21.9065 - 8.6046 12.0859 15.1138 17.7473 20.0378 23.7626 10 8.2031 11.2965 13.8669 16.0028 17.7775 20.4775 ll 7.8290 10.5811 12.7668 14.5026 15.8811 17.8453 12 7.4800 9.9315 11.7930 13.2065 14.2799 15.7138 13 7.1540 9.3403 10.9283 12.0816 12.9194 13.9698 14 6.8493 8.8013 10.1580 11.1010 11.7564 12.5285 15 6.564L 8.3089 9.4698 10.24z2 10.7561 11.3255 16 6.2969 7.8583 8.8531 9.487o 9.8908 10.3121 it 6.0462 7.4450 8.2988 8.8199 9.1380 91.4501 la 5.8109 7.0653 7.1991 8.2284 8.4795 8.7122 19 5.5896 6.7159 7.3475 7.7016 7.9003 83.0741 20 5.3815 6.3937 6.9380 1.Z308 7.3882 7.5184 21 5.1855 6.0961 6.5659 6.0083 6.9334 7.0312 2.1 5.0o0d .8208 6.2268 6.4Ž78 6.52714 6.bol 23 4.8264 5.5656 5.9170 6.0840 6.1634 6.2190 24 4.6618 5.3287 5.6332 5.7722 5.8356 5.8778 25 4.5062 5.1085 5.31727 5.4885 5.5393 5.5711 26 4.3589 ..9034 5.1329 5.2296 5.2703 5.2947 21 4.2195 4.7122 4.9117 4.9926 5.0253 5.0440 28 4.0873 4-5335 4.1073 4.7750 4.8014 4.8156 29 3.9619 4.3664 4.5179 4.5747 4.5960 4.6069 30 3.8429 4.2099 4.3421 4.3898 4.4070 4.4154 Present Value of One Dollar Growing at 7% 1 13.9249 24.54714 38.7229 57.6398 82.8841 161.5280 2 13.1342 22.4100 34.3296 49.3952 68.5336 123.7303 3 12.4052 20.6220 30.5632 42.5906 57.1420 '16.0465 4 11.7321 18.9744 27.3233 36.9419 48.0430 75.5782 s 11.1098 17.5021 24.5287 32.2464 40.7298 ,,0.2975 6 10.S336 16.1835 22.1047 28.310s 34.8147 48.7759 1 10.0000 Is.0000 20.0000 25.0000 30.0000 o0.0000 a 9.5046 13.9355 18.1650 22.2022 26.0560 33.2462 9 9.0444 12.9759 16.5598 19.8267 22.8047 27.9938 ID 8.6163 12.1092 15.1511 17.8002 20.1072 23.8660 11 8.2176 11.3246 13.9307 16.0633 17.8550 20.5875 12 7.8459 10.6130 12.8152 14.5678 15.9627 17.9562 13 7.4989 9.9663 11.8445 13.2744 14.3628 15.8222 14 7.1747 9.3773 10.981v 12.1506 13.0019 14.0739 iS 6.8714 8.8399 10.2126 11.1698 11.8373 12.6273 I6 6.5b74 8.3487 9.>248 10.3102 10.8347 11.4188 1I 6.3211 7.8987 8.9080 9.5536 9.9666 10.3999 18 6.0713 7.4859 8.3531 8.8848 9.2108 9.5332 19 5.8365 7.1063 7.8527 8.2913 8.5491 8.7897 20 5.6158 6.7568 7.4000 7.7625 7.9668 8.1469 21 5.4081 6.4344 6.9894 1.2895 7.4518 7.5870 21 5.2123 6.1364 6.6160 6.8649 6.9940 7.0958 23 5.0271 5.8606 6.2756 6.4023 6.5853 6.6621 24 4.8530 5.6049 5.9644 6.1364 b.2186 6.27bs 25 4.6089 5.3674 5.6792 5.8226 5.8884 5.9326 26 4.5332 5.1465 5.4173 5.5370 5.5898 5.6234 27 4.J858 4.9407 5.1762 5.2762 5.3187 5.3444 2a 4.2462 4.7487 4.953d 5.0315 5.0717 5.0913 29 4.1139 4.5693 4.7481 4.8183 4.8458 4.8609 30 3.9883 4.4014 4.5574 4.6164 4.6387 4.6502 - 204 - ANNEX N Page 3 Present Value of One Dollar Growing at 8% j< ' 10 YKS 15 Yi4s 20 YRS 25 YRS 30 YRS 40 YRS 1 14.7257 26.7276 43.5064 66.9635 99.7568 209.695t 2 13.8793 24.4254 38.4604 57.1384 81.9954 159.0989 3 13.0992 22.3796 34.1422 49.0508 67.9467 122.251? 4 12.3793 20.5576 30.4344 42.3624 56.7676 95.1745 5 11.7141 18.9312 27.2400 36.8055 47.8178 75.0915 6 11.Oq88 17.4763 24.4787 32.1670 40.6086 60.0537 7 10.5287 16.1719 22.0838 ?8.2772 34.7654 48.6834 a 10.0000 15.0000 20.0000 25.0000 30.0000 40.0000 9 9.5090 13.9448 18.1809 22.2261 26.0891 33.3011 to 9.052E1 12.9928 L6.5876 19.8673 22.8595 28.0199 II 8.6278 12.1321 15.1878 17.8523 20.1757 23.9681 12 8.2319 11.3523 13.9540 16.1231 17.9315 20.6963 1i 7.862, 10.6445 12.8630 14.6323 t6.0433 18.0660 14 7.5176 10.0006 11.8955 13.3415 14.4450 15.9297 15 7.1951 9.4t39 1I.0347 12.2188 13.0838 14.1773 16 6.8932 8.8781 10.2667 11.2381 11.9176 12.7256 1L 6.6104 8.3880 9.5793 10.3777 10.9128 11.5117 is 6.3451 7.9388 8.9624 9.6198 10.0420 10.4873 19 6.0960 7.5263 8.4071 8.9493 9.2832 9.6154 20 5.8619 7.1470 7.9058 8.3539 8.6L85 8.8670 21 5.6417 6.7974 7.4521 7.8230 8.0331 8.2196 22 5.4343 6.4148 7.0404 1.3479 7.5151 7.6554 23 5.2388 6.1764 6.6658 6.9212 7.0545 7.1604 24 5.0544 5.9002 6.3241 6.5365 6.6430 6.7231 25 4.8802 5.6439 6.0116 6.1886 6.2738 6.3346 26 4.7151 5.4058 5.7251 5.8728 5.9411 5.9874 2t 4.5599 5.1842 5.4618 5.5853. 5.b402 5.6155 2e 4.4125 4.9777 5.2194 5.3228 5.3670 S.3940 2( 4-.728 4.7850 4.9957 5.0823 5.1180 5.1386 30 4.1403 4.6049 4.1887 4.8614 4.8002 4.9081 Present Value of One Dollar Growing at 9% - 15.5753 29.1228 48.9555 77.9896 120.4940 273.8112 2 14.6693 26.5714 43. 1579 66.2725 98.4846 205.9325 3 13.8347 24.3065 38.2050 56.6515 81.1343. 156.7561 4 13.0649 22.2914 33.9596 48.7156 67.3767 120.8208 5 12.3539 20.4946 30.3086 42.1399 56.4032 94.3278 6 11.6966 18.8890 27. L585 36.6664 47.5980 74.6175 7 11.0879 17.4511 24.4316 32.0894 40.4900 59.8155 8 10.5237 16.t606 22.0634 28.2445 34.7172 48.5927 9 10.000U 15.0000 20.0000 25.0000 30.0000 40.000o 10 9.5134 13.9540 18.1965 22.2495 26.1217 33.3552 11 9.0601 13.0094 16.6150 19.9073 22.9135 28.1648 12 8.6391 12.1547 15.2240 17.9037 20.2432 24.0690 13 8.2469 11.3796 13.9966 16.1820 18.0071 20.8040 14 7.8789 10.6755 12.9103 14.6961 16.1232 18.1749 15 7.536C 10.0345 11.9458 13.4079 14.5264 16.0365 16 7.2151 9.4500 11.0o71 12.2864 1).X149 14.2800 lt 6.9147 8.9158 10.3202 11.3057 11.9974 12.8234 la 6.6330 8.4268 9.6333 10.4446 10.9903 11.6042 19 6.3687 7.9184 9.0163 9.6s55 10.1169 10.5745 Z( 6.1204 7.5664 8.4605 9.0134 9.3552 9.6973 21 5.8870 1.1872 7.9586 8.4161 8.6875 8.9441 22 5.6672 6.8376 7.5039 7.8813 8.0992 8.2921 23 5.46u2 6.5148 7.0911 7.40f1 7.57143 7.7237 2'. 5.2650 6.2161 6.7153 6.9773 7.1148 7.2248 25 5.0808 5.9394 6.3723 6.5906 6.7006 6.7841 26 4.9068 5.6826 6.0585 6.2406 6.3288 6.3923 21 4.7422 5.4439 5.7707 5.9229 5.9938 6.0422 2a 4.5865 5.2217 5.5062 5.6335 5.6906 5.7276 29 4.4390 5.0145 5.2624 5.3692 5.4152 5.4435 30 4.2991 4.8211 5.0374 S.1210 5.1642 5.1860 - 205 - ANNEX N Page 4 Present Value of One Dollar Growing at 10% N - 10 YAS IS YRS 20 YRS 25 YRS 30 YRS 40 YRS 1 16.,.765 31.7542 55.16648 91.0380 146.0080 359.3153 2 15.5069 28.9267 48.5019 77.0562 118.7080 268.0904 3 14.6141 26.4191 42.8191 65.6027 97.2545 202.31142 4 13.7911 24.1904 37.9563 56.1785 80.2996 154.4951 5 13.0313 22.2052 33.7815 48.3894 66.8228 119.4354 6 12.3291 20.4330 30.1858 41.9230 56.0482 93.5056 7 11.6793 18.8477 27.0788 36.5305 47.3835 74.1558 8 11.0773 17.4264 24.3855 32.0134 40.3741 59.5829 9 10.5187 16.1495 22.0433 28.2125 34.6699 48.5040 10 10.0000 15.0000 20.0000 25.0000 30.0000 40.0000 11 -9.5177 13.9631 18.2118 22.2726 26.1537 33.'.084 12 9.0686 13.0258 16.6420 19.9467 22.9666 28.2484 13 8.6502 12.1769 15.2596 17.9544 20.3099 24.1686 1'. 8.2597 11.4065 14.0386 16.2403 18.0818 20.9106 IS 7.89S1 10.7061 12.9569 14.7591 16.2021 18.2828 16 7.5541 10.0680 11.9956 13.4736 14.5070 16.1424 17 7.2349 9.4856 11.1389 12.3533 13.2454 14.3821 18 6.9359 8.9531 10.3731 11.3728 12.0765 12.'9207 19 6.6554 8.4653 9.6C67 10.5111 11.0674 11.6962 20 6.3921 8.0176 9.0697 9.1507 10.1914 10.6613 21 6.1446 7.6061 8.5136 9.0770 9.4269 9.7791 22 5.9111 7.2271 8.0109 8.4780 8.7563 9.0209 23 5.6925 6.8775 7.5554 7.9432 8.1650 8.3645 24 5.4859 6.5545 7.1415 7.4640 7.6412 7.7920 2 5.2910 6.2555 6.7645 7.0332 7.1749 7.2892 26 5.100 5.9784 6.4203 6.6444 6.7581 6.8449 2'7 4.9330 S.7211 6.1052 6.2925 6.3838 6.4500 28 4.76H5 5.4818 5.8161 5.9729 6.0463 6.0969 29 4.6128 5.2590 5.5503 5.6816 5.7409 5.7796 3D 4.4652 5.0511 5.3053 5.4156 5.4634 5.4931 Present Value of One Dollar Growing at 11% 1 17.4324 34.6454 62.2424 106.4880 177.4260 473.5044 ? 16.3949 31.5119 54.5837 89.7960 143.5374 350.7387 3 15.4400 28.7358 48.0611 76.1529 116.9846 262.6048 4 14.5602 26.2707 42.4898 64.9530 96.0645 198.8322 S 13.. 1464 24.0772 37.7141 55.7188 79.4901 152.3122 6 12.9985 22.1210 33.6078 48.0718 66.2844 118.0935 7 12.3048 20.3728 30.0659 41.7113 55.7024 92.7067 8 11.6624 18.8072 27.0009 36.3977 47.1741 73.7059 9 11.066H 17.4021 24.3404 31.9390 40.2607 59.3556 It0 10.5139 16.1386 22.0236 28.1811 34.6236 48.4170 11 10.0000 15.0000 20.0000 25.0000 30.0000 40.0000 12 9.5219 13.9719 18.2769 22.2953 26.1852 33.4608 1I 9.0765 13.0419 16.6685 19.9854 23.0190 28.3310 1'. 8.6611 12.1987 15.2948 18.0043 20.3756 24.2671 15 8.2733 11.4330 14.0801 16.2977 18.1556 21.0161 Ib 7.911u 10.7362 13.0029 14.8213 16.2803 18.3898 11 1.5719 10.1010 12.0447 13.53t7 14.6868 16.2475 18 7.2544 9.5208 11.1901 12.4196 13.3252 14.4835 19 6.9568 8.9899 10.4255 11.4392 12.1551 13.0174 20 6.6715 8.5033 9.7397 10.5769 11.1439 11.7879 21 6.4151 8.0564 9.1227 9.8154 10.2655 10.7478 22 6.1684 7.6454 8.s662 9.1403 9.4982 9.8605 23 5.9362 7.2666 8.0629 8.5395 8.8247 9.0976 24 5.7175 6.9110 7.6065 8.0028 8.2306 8.4367 27 5.5113 6.5939 7.1916 7.5216 7.7039 7.8601 26 5.3167 6.2946 6.8135 7.0888 7.2349 7.3535 21 5.132a 6.0171 6.4681 6.6981 6.8154 6.9051 2#n 4.9590 5.7593 6.1517 6.3442 6.4386 6.5076 294 4.7946 5.5195 5.8614 6.0227 6.0987 6.1516 30? 4,.6388 5.7960 5.5943 5.7296 5.7911 5.8316 -206- ANNEX N Page 5 Present Value of One Dollar Growing at 12% E N 10 YRS 15 YRS 20 YRS 25 YRS 30 YRS 40 YRS 1 18.4462 37.8219 70.3112 124.7895 216.1392 626.1613 2 17.3362 34.3497 61.5068 104.8551 174.0480 460.7891 3 16.3152 11.2763 54.0203 88.5961 141.1585 342.5385 4 15.3748 2f.5499 47.6342 75.2781 115.3208 257.3409 5 14.5075 26.1261 42.1694 64.3226 94.9128 195.4798 6 13.7067 23.9667 37.4782 55.2719 78.7048 150.2036 7 12.9664 22.0387 33.4384 47.7624 65.7608 116.7931 $ 12.2810 20.3139 29.9487 41.5048 55.3654 91.9302 ) 11.6459 18.7675 26.9247 36.2679 46.9696 73.2673 10 11.0566 17.3184 24.2962 31.8661 40.1497 59.1334 11 1U.5091 16.1279 22.0043 28.1503 34.5782 48.3318 12 10.COCO 15.0000 20.0000 25.0000 30.0000 40.0000 13 9.5260 13.9807 18.2417 22.3175 26.2162 33.5124 14 9.0841 13.057T 16.6947 20.0236 23.0706 28.4123 IS 8.6719 12.2203 15. 3294 18.0536 20.4405 24.3644 16 8.2867 11.4591 14.1210 16.3545 18.2285 21.1205 17 7.9266 10.7660 13.0483 14.8829 16.3576 18.4958 18 7.5895 10.1336 12.0933 13.6030 14.7659 16.3519 19 7.2737 9.5555 11.2407 12.4852 13.4043 14.5843 20 6.9774 9.0263 10.4774 11.5051 12.2330 13.1137 21 6.6993 8.5408 9.7921 10.6423 11.2200 L1.8791 22 6.4379 8.0948 9.1752 9.8797 10.3391 10.8339 23 6.1920 7.6842 8.6184 9.2031 9.5692 9.9417 24 5.9605 7.3057 8.1144 8.6006 8.8929 9.1742 25 5.7423 6.9562 7.6572 8.06?1 8.2959 8.5088 26 5.5364 o.6329 7.2414 7.5790 7.7664 7.9281 27 5.3421 6.3334 6.8621 7.1442 7.2947 7.4177 2a 5.1585 6.0555 6.5155 6.7515 6.8725 6.4665 29 4.9848 5.7972 6.1980 6.3957 6.4933 6.5651 30 4.8204 5.5568 5.9064 6.0723 6.1511 6.2062 Present Value of One Dollar Growing at 13% 1. 19.5213 41.3120 79.5114 146.4754 263.8643 830.3915 2 18.3340 37.4648 69.3893 122.6633 211.5642 607.4828 3. 17.2424 34.0625 60.7946 103.2800 170.8022 448.6671 4 16.2374 31.0471 53.4739 87.4360 138.8665 334.6927 S 15.3111 28.3688 47.2189 74.4308 113.7138 252.2872 6 14.4561 25.9850 41.8577 63.7108 93.7977 192.2504 7 13.6660 23.8587 37.2483 54.8372 77.9426 148.16h1 8 12.9349 21.9583 33.2730 47.4609 65.2515 115.5325 9 12.257T 20.2562 29.8341 41.3032 55.0369 91.1753 13 11.6297 16.7287 26.8501 36.1409 46.7698 72.8398 11 11.0465 17.3551 24.2528 31.7948 40.0411 58.9163 12 10.5045 16.1174 21.9854 28.1201 34.5336 48.2484 13 10.0000 15.0000 20.0000 25.0000 30.0000 40.0000 14 9.5300 13.9e93 18.2563 22.3395 26.2467 33.5631 15 9.0917 13.0732 16.7204 20.0612 23.1215 28.4926 IC 8.6824 12.2415 15.3635 18.1022 20.5046 24.4605 1t 8.2994 11.4849 14.1613 16.4105 18;3006 21.2238 lb 7.9421 10.7953 13.0931 14.9437 16.4340 18.6009 19 7.6069 10.1657 12.1413 13.6666 14.8443 16.4555 20 7.2927 9.5899 11.2908 12.5502 13.4828 14.6845 21 6.9978 9.0623 10.5287 11.5704 12.3104 13.2094 22 6.7208 8.5780 9.8441 10.7071 11.2955 11.9700 23 6.4604 8.1328 9.2271 9.9435 10.4123 10.9198 24 6.2153 7.7227 8.6701 9.2656 9.6397 10.0227 25 5.9844 7.3445 8.1656 8.6614 8.9607 9.2505 26 5.7667 6.9950 7.7076 8.1210 8.3609 8.5808 27 5.5613 6.6716 7.2908 7.6361 7.8287 7.9959 28 5.3673 6.3718 6.9105 7.1994 7.3543 7.4818 29 5.1839 6.0936 6.5628 6.8048 6.9296 7.0271 30 5.0103 5.8349 6.2440 6.4471 6.5478 6.6226 - 207 - ANNEX N Page 6 Present Value of One Dollar Growing at 14% E R 10 YRS 1S YRS 20 YRS 25 VHS 30 YRS 40 YRS I 2U.6612 45.1463 90.0021 172.1766 322.7173 1lu3.7327 2 19.391s 40.8841 78.4653 143.7289 257.7170 803.1636 3 18.2241 37.1181 68.4978 120.6157 207.1774 569.7278 4 17.15C9 33.7833 60.1048 101.7599 167.6813 437.1030 5 16.1616 30.8240 52.9438 86.3142 136.6571 327.1811 6 15.248B 28.1924 46.0153 73.6097 112.1609 247.4324 7 14.4057 25.8473 41.5543 63.1167 92.7174 189.1376 8 13.6261 23.7533 37.0242 54.4144 77.2025 146.1952 9 12.9041 21.8797 33.1116 47.1671 64.7559 114.3100 10 12.2349 20.1998 29.7221 41.1064 54.7166 90.4410 11 1.61i8 18.6907 26.7770 36.0168 46.5746 12.4227 1Z 11.0367 17.3323 24.2104 31.7249 39.9348 58.7039 13 10.4999 16.10i1 21.9668 28.0905 34.4900 48.1665 14 10.0000 15.0000 20.0000 25.0000 30.0000 .0.0000 15 9.5340 13.9917 18.2707 22.3610 26.2767 53.6131 16 9.0991 13.0885 16.7457 20.0983 23.1717 28.5718 17 8.6929 12.2624 15.3971 18.1501 20.5678 24.5555 is 8.3129 11.5102 14.7011 16.4658 1t.3718 21.3260 19 7.9573 10.8242 13.1374 15.0038 16.5097 18.7050 20 7.6240 10.1975 12.1888 13.7296 14.9219 16.5583 21 7.3114 9.6238 11.3404 12.6146 13.5606 14.7840 22 7.0179 9.0978 10.>796 11.6352 12.3877 13.3046 23 6.7421 8.6148 9.d955 10.7t15 11.3705 12.0604 24 6.4826 8.1704 9.2789 10.0069 10.4850 11.0053 25 6.2303 7.7609 8.7215 9.3276 9.7100 10.1034 26 6.0081 7.3829 8.216; 8.7218 9.0282 9.3266 27 5.7909 7.u335 7.7577 8.1797 8.4257 8.6525 '28 5.5859 6.7100 7.3399 7.6929 7.8907 B.0637 29 5.3922 8.4100 6.9586 7.2543 7.4137 7.54s9 30 5.2090 6.1314 6.6098 6.8518 6.9864 7.0877 Present Value of One Dollar Growing at 1 5% 1 21.8696 49.3584 -101.9648 202.6396 395.3046 1469.6296 2 20.5122 44.6373 88.5872 168.6530 314.5125 1064.3058 3 19.2651 40.4692 77.2585 141.0885 251.8345 d77.3562 4 18.1181 36.7814 67.6354 118.6429 202.9679 572.8363 5 17.0616 33.5118 59.4363 100.2922 164.6790 426.0618 6 16.0875 30.6068 52.4293 85.2267 134.5263 319.9848 7 15.1880 28.0204 46.4230 72.8135 110.6595 242.7654 8 14.3565 25.7130 41.2589 62.5396 91.6706 186.1358 9 13.5870 23.6504 36.8057 54.0028 76.4838 144.2891 10 12.8740 21.8028 32.9540 46.8806 64.2735 113.1238 11 12.2125 20.1446 29.6127 40.9142 54.4041 89.17265 12 11.5982 18.6534 26.705S 35.8954 46.3838 72.0159 13 11.0270 17.3099 24.1687 31.6564 39.8307 58.4962 14 10.4954 16.0970 21.9486 28.0614 34.4471 48.0863 LS 10.000%) 15.0000 20.0000 25.0000 30.0000 40.0000 lo 9.5379 14.0060 18.2848 22.3823 26.3062 33.6623 11 9.1064 13.1036 16.7707 20.1348 23.2211 28.6499 la 8.7031 12.2830 15.430) 18.1974 20.6301 24.0494 19 8.3257 11.5352 14.2404 16.5205 18.4422 21.4273 20 7.9723 10.8528 13.1812 L5.0633 16.5846 18.JC83 21 7.6409 10.2288 12.2357 13.7919 14.9987 16.6603 21 7.3299 9.6t13 11.3894 12.6784 13.6377 14.8829 23 7.0317 9.1330 10.6299 11.6994 12.4634 13.3)93 24 6.7630 8.6511 9.9465 10.0353 L1.4451 12.1504 25 6.5045 b.2016 9.3300 10.06b8 10.5574 11.0905 26 6.2810 7.7986 8.7724 9.3892 9.7798 10.1839 27 6.C315 7.4210 8.2669 8.7819 9.0954 9.40Z5 26 S.P148 7.0717 7.8074 8.23.1 8.4902 e.724? 29 S. 61pi2 6.74b8 7.3888 7.7495 1.952o 8.1313 30 5.4168 6.4479 7.0064 7.3090 7.4729 7.o098 ANNEX N -208- Page 7 Present Value of One Dollar Growing at 16% ER -10 YRS 1s YRS 20 YRS 25 YRS 30 YRS 40 YRS I 23.1506 53.9e53 115.6053 238.7469 484.8336 1959.3894 2 21.699b 48.7566 100.?284 198.1455 384.4175 1412.8732 3 20.3671 44.1441 87.2227 165.2712 306.6774 1027.0426 4 19.1420 40.0665 76.1892 138.5486 246.2015 ?52.8735 5 18.0142 36.4543 66.8008 116.7411 198.9265 556.7546 6 16.9745 33.2477 58.7883 98.8743 161.7891 415.5133 7 16.0151 30.3952 51.9297 84.1779 132.4701 313.0859 8 15.1285 27.8527 46.0414 72.0414 109.2072 238.2769 9 14.3084 25.5819 40.9712 61.9788 90.6557 183.2397 10 13.5488 23.5498 36.5925 53.6022 75.7854 142.4445 11 12.8444 21.7276 32.8000 46.6013 63.8038 111.9725 12 12.1906 20.0905 29.5056 40.7264 54.0992 d9.0312 13 11.5829 18.6169 26.6355 35.7766 46.1973 11.6189 14 11.0175 17.2879 24.1279 31.5894 39.7287 58.2930 15 10.4910 16.0870 21.9307 28.0329 34.4051 48.0076 16 10.0000 15.0000 20.0000 25.0000 30.0000 40.0000 17 9.5418 14.0142 18.2987 22.,4032 26.3352 33.108 18 9.1136 13.1185 16.7952 20.1708 23.;693 2S.7270 19 8.7132 12.3032 15.4630 18.2440 20.6917 24.7422 20 8.3383 11.5599 14.2792 16.5744 18.5118 21.5275 21 7.9870 10.8809 13.2244 15.1220 16.6587 18.9106 22 7.6575 10.2597 12.2820 13.8536 15.0749 16.7616 23 7.3481 9.6904 11.4379 12.7416 13.7142 14.9811 24 7.0573 9.1677 10.6797 11.1630 12.5391 13.4935 25 6.7838 .8.6871 9.9970 10.89H6 11.5191 12.2401 26 6.52b2 8.2444 9.1807 10.1323 10.6293 11.1754 27 6.2835 7.8360 8.4230 9.4504 9.8493 10.2641 26 6.0546 7.4587 8.3170 d.8416 9.1623 9.4182 29 5.8385 1.1095 7.8568 8.2961 8.5545 8.7951 30 5.6343 6.7d59 7.4373 7.8058 8.0142 8.1988 Present Value of One Dollar Growing at. 11 1 24.5083 59.0669 131.1575 281.5413 595.2478 2614.7642 2 22.9575 53.2773 113.4854 233.0445 470.4613 1818.1148 3 21.5341 48.1740 98.5559 193.8394 374.0421 1359.3822 4 20.2259 43.6660 85.9058 162.0234 299.1897 991.7908 5 19.0220 39.6757 75.1555 136.1041 240.8040 729.6287 6 17.9128 36.1364 65.9926 114.9068 195.0441 541.4323 7 16.8895 32.9907 58. 1598 97.5038 159.0058 405.4278 8 15.9444 30.1892 51.4444 83.1603 130.4850 306.4681 9 15.0704 27.6892 45.6703 71.2922 107.8019 233.9574 1o 14.2613 25.4540 40.6909 61.4336 89.6714 180.4439 11 13.5114 23.4514 36.3846 53.2121 75.1065 140.6584 12 12.8155 21.6540 32.6496 46.3287 63.3463 110.8547 13 12.1690 20.0375 29.4008 40.5429 53.8017 88.3541 14 11.5679 18.5811 26.5669 35.6603 46.0149 11.2313 1i 11.0082 17.2663 24.0879 31.5236 39.6288 58.0941 16 10.4866 16.0773 21.9131 28.0049 34;3638 47.9304 It 10.00oo 15.0000 20.0000 25.0000 30.0000 40.0000 l8 9.5455 14.0222 18.3123 22.4737 ?6.3638 33.7585 19 9.1201 13.1331 16.8194 20.2062 23.3178 28.8030 20 8.7231 12.3232 15.4952 18.2900 20.7525 24.8339 21 8.3501 11.5842 14.3174 16.6217 18.5806 21.6267 22 8.0016 10.9087 13.2670 15.1801 16.7320 19.0121 2 ?7.6739 10.2903 12.3278 13.9146 15.1503 16.8621 21, 7.3661 9.1231 11.4859 12.8041 13.7900 15.0788 2>, 1.0766 9.2021 10.7291 11.8261 12.6142 13.5872 2:, 6.8042 a.7227 10.0471 10.9614 11.5926 12.3293 21 6.5416 8.2809 9.4310 10.1943 10.7008 11.2600 28 6.3057 7.8730 8.8731 9.5113 9.9185 10.3441 29 6.0771S 7.4960 8.3661 8.9010 9.2289 9.5537 10 5.u619 7.1470 7.9058 8.3539 8.6185 8.8670 -209- ANNE N Page 8 Present Value of One Dollar Growing at 18% o10 YtS IS YRS 20 YRS 25 YMS 30 YRS 40 VRS 1 25.9*70 64.6472 148.8869 332.2535 731.3917 3491.311o 2 24.2901 58.2319 128.5811 274.3387 516.3618 2498 .9389 3 22.7698 52.5926 111.4460 22z.5897 456.7923 1801.7319 4 21.3131 41.6096 96.9439 t89.7108 364.1467 1308.9200 5 20.0883 43.2023 84.6346 158.9026 292.029* 958.4141 ' 18.9050 39.2962 74.1559 133.7501 235.6292 707.5423 7 17;8139 35.82r3 65.2098 113.1367 191.3122 526.8223 a 16.8065 32.7406 57.5501 96.1787 156.3239 395.7792 s 15.8153 29.988* 50.9729 82.1745 128.5677 300.1164 tO 15.0136 27.5297 45.3091 70.5649 106.4414 229.75185 11 14.2152 25.3290 40.4178 60.9035 88.7163 177.7h39 12 13.4747 23.3553 36.1811 52.8321 74.4465 138.9286 13 12.7811 21.5820 32.5026 46.0628 62.9006 109.7689 14 12.1479 19.98s5 29.2983 40.3636 53.5112 d7.6948 15 11.5531 10.5460 26.4997 35.5465 45.8365 10.8529 16 10.9991 17.2452 24.0486 31.4591 39.5309 57.8995 1 10.4823 16.0677 21.8959 27.9774 34.3233 47.8547 18 10.0000 15.0000 20.0000 25.0000 30.0000 40.0(00 19 9.S493 14.0301 18.3258 22.4440 26.3920 j33t855 20 .9.1277 13.1475 16.8432 20.2411 23.3652 28.8181 21 8.1329 12.3*29 1S.5269 18.3354 20.8125 24.9;!46 24 8.1630 11.6082 14.3551 16.6803 18.6486 21.72*8 23 8.0159 10.9362 13.3092 15.2375 16.8045 19.1127 24 7.6901 10.3205 12.3131 13.9750 15.2251 16.9bh8 25 7.3,838 9.7554 11.5333 12.8661 13.8653 15.1758 2S 1.0957 9.2360 10.1779 11.8886 12.6887 13.6803 21 6.8244 8.7579 10.0961 11.0238 11.6657 12.4Th0 28 6.56s8 8.3169 9.4809 10.2559 LO.7719 11.3442 29 6.!1277 7.9097 8.9229 9.5717 9.9812 10.4Z38 36 6.3001 7.5331 8.4160 8.9600 9.29s2 9.6290 Present Value of One DollaT Growing at 19% 1 27.4713 70.7742 169.0948 392.3350 899.2094 4663.1868 2 25.7014 63.6805 145.7685 323.1929 706.6771 3327.0310 i 24.0780 57.4369 126.1051 267.4598 558.4358 2390.3828 4 22.5872 51.9299 109.4829 222.3679 443.7815 1729.8699 s 21.2164 47.0628 95.3896 185.7497 354.7024 1261.2709 6 19.9543 42.752S 83.4066 155.9021 ZS5.1776 926.7653 7 18.1910 38.9276 73.1888 131.4820 230.6643 686.53184 8 17.7174 35.5268 64.4512 111.4277 187.7229 512.8617 9 16.7254 32.4970 56.9583 94.8969 153.7384 386.5424 1o 15.8078 ?9.7926 50.5145 81.2189 126.7148 294.0162 31 14.95bO 27.3140 *4.9574 69.8588 105.1237 225.7918 12 14.1701 25.2069 40.1515 60.3878 87.7893 175.1350 13 13.4388 23.2613 35.9836 52.4617 73.8045 137.2523 14 12.7593 21.5115 32.3590 45.8033 62.4661 I08.7139 15 12.3273 19.9340 29.1980 40.1883 53.2275 87.0524 I. 11.5387 38.511s 26.4339 35.4351 45.6620 70.48i34 I? Io.q90o 17.224* 24.0101 31.3959 39.4350 57.1(190 1I 10.4182 16.0583 21.8789 27.9504 34.2836 47.71104 1s 10.0000 35.0000 20.0000 25.0000 30.0000 40.0000 20 9.5-529 14.0379 18.3390 22.4639 26.4197 33.8518 21 9.1345 13.1616 16.8667 20.2756 23.4118 28.9 22 22 S.T426 12.3623 15.5583 18.3802 20.87L8 25.0142 23 8.3-750 11.6318 14.3924 16.7323 18.7158 21.8220 24 8.C301 10.9632 13.3508 15.2943 16.8763 19.2124 25 7.1060 10.3502 12.4179 14.0348 1s.2991 17.ot08 26 7.4013 9.7873 11.5803 12.9275 13.9399 15.2722 27 7.1145 9.2696 10.0262 11.9506 12.7.27 13.7730 2a 6.0444 8.7927 10.1458 11.0856 11.7383 12.5064 29 6.5891 8.3526 9.5303 10.1170 10.*425 11.4281 38 6.11494 7.9460 8.J022 9.63L7 30.0556 10.5032 ANNEX N - 210 - Page9 Present Value of One Dollar Growing at 20% h = 10 YIS 15 YRS 20 YRS 25 YRS 30 YRS 40 YKS 1 29.0861 71.5000 192.1223 463.4966 1105.9892 6228.4854 2 27.1959 69.6510 165.3340 380.9796 866.9903 4430.9692 3 25.4628 62.7472 142.7760 314.5537 683.2653 3173.4259 4 23.8719 56.6623 123.7258 260.8854 541.4066 2288.5296 S 22.4095 51.2883 107.5923 217.3661 431.3881 1662.1972 6 21.0637 46.5327 93.8901 181.9473 345.6825 1216.2381 1 19.8237 42.3158 82.2200 153.0155 278.6164 896.7868 8 18.6797 38.5694 72.2526 129.2955 225.8982 666.5495 9 17.6232 35.2343 63.7158 109.7770 184.2690 499.5707 10 16.6462 32.2598 56.3837 93.6563 151.2443 377.6939 11 15.7418 29.6018 50.0688 80.2924 124.9235 288.1542 12 14.9036 27.2221 44.6150 69.1728 103.8469 221.9301 13 14.1259 25.0875 39.8919 59.8860 86.8892 172.6130 14 13.4037 23.1694 35.7902 52.1008 73.1798 135.6273 15 12.7321 21.4425 32.2185 45.5499 62.0426 107.6884 16 12.1070 19.8850 29.0998 40.0169 52.9505 86.4264 17 11.5245 18.4778 26.3694 35.3259 45.4912 70.1223 18 10.9812 17.2040 23.9723 31.3339 39.3410 57.5224 19 10.4740 16.0490 21.8623 27.9239 34.2445 47.7076 20 10.0000 15.0000 20.0000 25.0000 30.0000 40.0000 21 9.5505 14.0455 18.352u 22.4835 26.4470 33.8974 2z 9.1413 13.1756 16.8898 20.3095 23.4579 29.0252 23 8.7521 12.3814 15.5892 18.4244 20.9303 25.1028 24 8.3869 11.6551 14.4291 16.7837 18.7822 21.9183 25 8.0440 10.9899 13.3919 15.3505 16.9474 19.3112 26 7.7217 10.3797 12.4622 14.0939 15.3725 17.1S91 27 7.4186 9.8189 11.6261 12.9883 14.0138 15.3679 28 7.1331 9.3028 10.8741 12.0120 12.8361 13.8651 29 6.8641 8.8271 10.1945 11.1469 11.8104 12.59.4 30 6.6104 8.3880 9.5793 10.3777 10.9128 1ii5117 - 211 - ANNEX 0 Page 1 12/ ECONOMIC ANALYSIS OF ROAD AND AGRICULTURAL INVESTMENTS 1. The following presentation pertains to the economic evaluation of an investment package consisting of a rural road (RR) improvement (construetion) and complementary agricultural investments in its zone of influence. The prices on the local market of agricultural products produced in the RR's zone of influence and transported to the local market, which are called the "local market prices", are assumled constant. In other words, the local market is the importing area and the road's zone of influence is the producing area. In addition, to simplify the presentation, non-agricultural traffic is ignored. Thus, all benefits to be had from the investment package accrue to farmers in the zone of influence and/or transporters of agricultural products over the rural road under consideration. 2. No Home Consumption. The benefits (B) accruing to farmers and transporters during a specific year of the situation where only one agricultural crop in the zone of inflnence is cultivated are graphically portrayed in Figure 7. This presentation as well. as expression (1) for these benefits ignore home con- sumption in the with- and without-project situations. F:Lgure 7: Exportable Surplus ~~~ p Rl q2 02 A~~~~~~~~~~~~~ exportable surplus (tons) 12/ This form of presentation was suggested by Anandarup Ray. For extensive analysis along similar lines, see H. G. van der Tak and A. Ray, The Economic Benefits of Road Transport Projects, World Bank Occasional Paper No. 13. - 212 - ANNEX 0 Page 2 B - (Pm q2 R2) - (Pm ql R1) ......... , (1) where Pm = local market price of a specific agricultural product ($/ton) = exports of this product from the road's zone of influence in the without- and with-project situation, respectively (tons) R1, R2 economic cost of producing and transporting to the local market (over the rural road under consideration) q, and q2 tons, respectively ($) Note that P is assumed to be constant in the without- and with-project situ- ations (para. 1). 3. The costs RI and R can be divided into costs of production and cost of transportation: C1, C2 economic cost of producing ql and q2, respectively ($) K1, K2 = economic cost of transporting over the rural road the exports q1 and q2, respectively (S) Thus, expression (1) becomes .B - (m q2 C2 K2).- (P K1 C.l.). (2) 4. The following terms are introduced in order to divide B into B, or benefits accruing to farmers and B2, or benefits accruing to transporEers. kl, k2 - economic costs of transporting over the rural road one ton of q and one ton of q2, respectively ($/ton) Fl F2 = fare of transporting over the rural road one ton of q 2 and one ton q2, respectively ($/ton) Thus, K1 k1 qi K2= k2q2, and K1- K2 = k1 q1 - k2 q2 ' [F, q1 - F2 q2] + [(F2 q2 - F1 q1) - - (k2 q2 - k} q1)] The term fF q -F2q2] represents the difference between the farmer's transport bill in the without-project situation and his bill in the with-project situation, while [(F2q2- Flql) - (k2q2- k q )] represents the portion of transport savings accruing to transporters in the orm of a higher profit. Calling (F2q2- q1q1) - 213 - ANNEX 0 Page 3 the 4 transport revenues and (k2q2- kIq1) the A transport costs, we may alsio write: K2 - -[A transport revenues] + [A transport revenues - - a transport costs] Defining P1, P2 farr-gate price of a specific agricultural product in the without- and with-project situation, respectively ($/ton) results in Pm , P2 4- F2 = P1 + F1 Thus, the farmgate price increases in the with-project situation by (F1 - F2) 5. Expression (2) can now be rewritten as B -fBj)+(B21-([(P2 + F2)q2 - C2] - [(PI + F)q1 - C1) + + [F1 q1 - F2 q2D +.{[F2 q2 - F1 q1] - [k2 q2 - kl qlj -{[P2 q2 - C2] - [Plql - C1l +U[F2 q2 - F1 ql] - - [k2 q2 - kl qlD .......... (3) 6. Home Consumption. Expressions (1, (2) and (3) ignore the home consumption in the without- and with-project situations (para. 2). Reference iii made to Figure 8 in order to examine the effect of home consumption on B1. Figure 8: Demand and Supply Curves 01 :1~H _ _ _1_Q o P2F PI E H2 Hi Q Q Quantities of an agricultural product (tons) - 214 - ANNEX 0 Page 4 The symbols HI, H2, Ql, Q2, Pl and P2 in Figure 2 denote: H1, H2 = on-farm (home) consumptLon of the agricultural product with farm-gate price P1 and P2, respectively (tons) Ql' Q2 = production of tlhe agricultural product with farm-gate price P1 and P2, respectively (ton,) P1, P2 = as defined in para. 4 Note that q Q H and q2 1 1 1 q 2 H2. The benefits accruing to farmers (B1) during a specific year of the situatiOn where one agricultural crop in the zone of influence is cultivated are represented by area ABCD of Figure 8. Assuming that AD and BC of the demand and supply curves of Figure 8 can be approximated by straight lines, gives: area ABCD (P2 -Fl)Ql + (P2 - P1) (Q2 Q1) - [Hl(P2 - P1) 1~~~~ 2 (H1 - H2) (P2 - P1)] (P2- P1) (Ql HI) + 2 (P2 P1) [(Q2 Ql) + (H1 H2)] or, since q= (Q1 - H1) and q2 (Q2 - H2)' area ABCD= (P2 - P)ql + 2 (P2 - P1)[(q2 - qi) + (H1 H2)] = (P2 - PI) (q2 - ql) + (P2 - Pl)ql 2(P2 - PI)(q2 + ql) Defining AP (F2 PI) and Lq = (q2 - ql) results in 1 B1 APql +`6 PAq ...............(4) Another way of expressing B1 is B1 2 (F 1 F2)(q2 + q1) .... ......... (5) since P2 = (Pm - F2) and P1 = (Pm - F1). Expressions (4) and (5) are graphically represented by areas ABCD of Figure 9 and Figure 10, respectively. Note that areas ABED and BEC of Figure 9 correspond to , Pql and & P,4q respectively; areas AECD and ECB of Figure 10 also correspond to% tPql and AP 4q respectively. 7T - 215 - ANNEX 0 Page 5 Figure 9: Surplus versus Figure 10: Surplus versus Famgate Price Fare ' D c 2 / Ul A2 Il A Exportable surplus (tons) Exportable surplus (tons) 7. Another way of taking into consideration the effect of home consumption on B1 is as follows: Bj (P2 Q2 - C2) (1 Q1 - ci) + (S3 - Sl) (6) t?here PI, F2, Ql, Q2, C,