TRANSPORT NOTES TRANSPORT ECONOMICS, POLICY AND POVERTY THEMATIC GROUP THE WORLD BANK, WASHINGTON, DC Traspor Noe No. TRN-6 Jauary 2005 Noes o he Ecoomic Evaluaio of Traspor Projecs I respose o may requess for help i he applicaio of boh coveioal cos beefi aalysis i raspor ad addressig of he ewer opics of ieres, we have prepared a series of Ecoomic Evaluaio Noes ha provide guidace o some of issues ha have prove more difficul o deal wih. The Ecoomic Evaluaio Noes are arraged i hree groups. The firs group (TRN-6 o TRN 10) provides crieria for selecio a paricular evaluaio echique or approach; he secod (TRN-11 o TRN-17) addresses he selecio of values of various ipus o he evaluaio, ad he hird (TRN-18 o TRN-26) deals wih specific problemaic issues i ecoomic evaluaio. The Noes are preceded by a Framework (TRN-5), ha provides he coex wihi which we use ecoomic evaluaio i he raspor secor. The mai ex of mos of he Noes was prepared for he Traspor ad Urba Developme Deparme (TUDTR) of he World Bak by Peer Mackie, Joh Nellhorp ad James Laird, a he Isiue for Traspor Sudies (ITS), Uiversiy of Leeds, UK (The draf ex of Noe 21 was prepared for ITS by I.T. Traspor Ld). TUDTR saff have made a few chages o he draf Noes as prepared by ITS. Fudig was provided from he Traspor ad Rural Ifrasrucure Services Parership (TRISP) bewee he Deparme of Ieraioal Developme (DFID) of he Goverme of he Uied Kigdom ad he World Bak. The Noes will be revised periodically ad we welcome commes o wha chages become ecessary. Suggesios for addiioal Noes or for chages or addiios o exisig Noes should be se o rcarruhers@worldbak.org 1 WHEN AND HOW TO USE NPV, IRR 2 AND MODIFIED IRR BACKGROUND TO NPV, IRR AND MODIFIED IRR All hree are summary measures of projec performace. Each oe provides a sigle figure summarizig he impac of he projec o ecoomic welfare. Each of he hree measures does, however, give subly differe iformaio: NPV focuses o he oal welfare gai over he whole life of he projec; IRR ad Modified IRR focus o he rae a which beefis are realized followig a iiial raspor ivesme3. Table 1 gives a illusraive example of some resuls. Table 1. Example Resuls - Highway Rehabiliaio Projec. Ecoomic aalysis over 30 years: NPV@12% per aum = $530m IRR = 20% per aum As we will see below, hese resuls would idicae ha he Modified IRR = 15% per aum projec me he World Bak s basic accepabiliy crierio. They also provide a basis for compariso wih oher uses of he resources. Firs, hough, we cosider he meaig ad calculaio of he NPV, IRR ad Modified IRR. 1 The abbreviaios sad for: Ne Prese Value (NPV), Ieral Rae of Reur (IRR) ad Modified Ieral Rae of Reur (MIRR) 2 Ecoomic Rae of Reur (ERR) is a ear-ideical cocep. The formula is he same - he oly differece is i he applicaio. IRR ca be used o decribe fiacial or ecoomic flows. The label ERR idicaes ha he flow beig described is a flow of ecoomic coss ad beefis. 3 Noe ha he IRR oly works i siuaios srucured like his. I does o work i siuaios such as a ax reform, where here is o iiial ivesme. See he Hadbook Techical Appedix Paragraphs 10-12 for furher guidace.
Page 2 Traspor Noe No. TRN-6 Jauary 2005 Ne Prese Value NPV is a measure of he absolue welfare gai over he whole life of he projec 4. Fuure beefis ad coss are discoued a a compoud rae, r, ypically 12% per aum 5. Beefis, e of coss, are he summed across all years. Box 1 shows how he calculaios are made. Box 1. Calculaig he NPV Ne Prese Value = B 0 0 B1 1 + (1 + r) B2 + (1 + r) 2 2 B +... + (1 + r) B +... + (1 + r) = B = 0 ( 1+ r) 1 (1 where B are he beefis i year, C are he coss i year, r is he discou rae, ad is he horizo year. + r) is called he discou facor i Year. Noe ha if Prese Value of Beefis (PVB) is he sum of he discoued beefi sream, B = 0 1+ r) (, ad Prese Value of Coss (PVC) is he sum of he discoued cos sream, he NPV = PVB PVC. A example is give i Table 2. C = 0 1+ r) (, The NPV ca be calculaed usig spreadshee sofware such as Microsof Excel, mos of which coveiely have a NPV fucio buil-i. Cauio Excel users: Users should exercise cauio, sice Excel sars discouig from he firs year of he series. I a appraisal for he World Bak, he firs year will ofe be he Base Year (he year i which = 0 ad he discou facor is 1.0). Uder hese circumsaces, ake care o calculae he NPV from year = 1 owards ad add he udiscoued e beefi i year = 0 o he resul. Noe also ha if coss are beig calculaed for each caledar year, beefis mus be calculaed for he same period. Care should be ake whe ipuig beefis from HDM-4 o esure ha he ime periods are cosise. 4 See he Framework (Secio o CBA Parameers ad Noe 13: Projecs wih a Very Log Life). 5 There are wo pricipal raioales for discouig: (i) o reflec he Opporuiy Cos of Capial; or (ii) o reflec Social Time Preferece. Accordig o curre evidece, hese raioales lead o discou raes i he regio of 10-12% or 5% respecively. The laer migh be appropriae for a projec which made o draw o capial, however such projecs are presumably o likely o be fuded by he World Bak. See Paragraphs 49-57 of he Techical Appedix o he Hadbook o Ecoomic Aalysis of Ivesme Operaios (World Bak, 1998) [1] for more deailed guidace o deermiig he appropriae Opporuiy Cos of Capial, if required.
Page 3 Traspor Noe No. TRN-6 Jauary 2005 Ieral Rae of Reur IRR is he rae a which beefis are realized followig a iiial raspor ivesme. I ca be hough of as he cosa compoud rae of reur which is equivale o he acual flucuaig rae of reur over he projec lifeime. IRR is also closely relaed o he NPV: he IRR is he rae of discou a which he NPV of he projec is reduced o zero. Box 2. Calculaig he IRR ad he MIRR B 0 0 B1 1 B2 2 + + 1 + IRR) (1 + IRR) ( 2 B +... + (1 + IRR) B +... + (1 + IRR) = 0 This ca be solved by a search procedure, which is available i mos spreadshee packages - such as Microsof Excel. A example is give i Table 2,. Table 2. Example Calculaios - Highway Rehabiliaio Projec Beefis, Coss, Discou Discoued Discoued Discoued Ne B C facor @12% beefis, coss e beefis beefi, DF = 1 / 1.12 B *DF C *DF (B -C )*DF (B -C ) 325.0 1.00 325.0-325.0-325.0 285.0 0.89 254.5-254.5-285.0 110.0 0.80 87.7 87.7 110.0 113.6 0.71 80.9 80.9 113.6 117.3 0.64 74.6 74.6 117.3 124.6 0.57 70.7 70.7 124.6 128.3 0.51 65.0 65.0 128.3 135.6 0.45 61.4 61.4 135.6 143.0 0.40 57.7 57.7 143.0 150.3 0.36 54.2 54.2 150.3 157.6 0.32 50.8 50.8 157.6 165.0 0.29 47.4 47.4 165.0 176.0 0.26 45.2 45.2 176.0 187.0 0.23 42.8 42.8 187.0 198.0 0.20 40.5 40.5 198.0 205.3 0.18 37.5 37.5 205.3 212.6 0.16 34.7 34.7 212.6 223.6 0.15 32.6 32.6 223.6 230.9 0.13 30.0 30.0 230.9 238.3 0.12 27.7 27.7 238.3 241.9 0.10 25.1 25.1 241.9 245.6 0.09 22.7 22.7 245.6 249.3 0.08 20.6 20.6 249.3 252.9 0.07 18.7 18.7 252.9 256.6 0.07 16.9 16.9 256.6 260.3 0.06 15.3 15.3 260.3 267.6 0.05 14.1 14.1 267.6 274.9 0.05 12.9 12.9 274.9 278.6 0.04 11.7 11.7 278.6 274.1 0.04 10.2 10.2 274.1 Prese Value of Beefis (PVB) = 1109.4 Prese Value of Coss (PVC) = 579.5 Ne Prese Value (NPV) = 530.0 Ieral Rae of Reur (IRR) = 20%
Page 4 Traspor Noe No. TRN-6 Jauary 2005 Modified Ieral Rae of Reur (MIRR) The Modified IRR is similar o he IRR, bu overcomes wo weakesses of he IRR. The MIRR provides a es of he robusess of he IRR o oe of he uderlyig assumpios: The IRR assumes ha all he beefis from he projec uder review are re-ivesed a he ierally geeraed rae of reur, yieldig furher beefis i he ex period. However, beefis from raspor projecs for example, i he form of ravel ime savigs may o be re-ivesible. If he beefis cao be reivesed or if hey are re-ivesible bu oly a a lower rae, he he IRR will oversae he rue rae of reur. The MIRR correcs for his by assumig beefis are re-ivesed a he opporuiy cos of capial. I he calculaes he IRR which gives a esimae of he rue value of he reurs. The MIRR also avoids he problem of muliple IRRs, discussed earlier. Box 3. Calculaig he Modified IRR The MIRR ca be calculaed usig he followig seps: Esimae all cash flows as for he IRR Calculae he fuure value (FV), a ime, of all cash iflows, usig he cos of capial as he ieres rae Fid he PV of all cash ouflows, usig cos of capial as he discou rae Fid he modified IRR as he rae which equaes he FV of iflows o he PV of ouflows PV coss = FV / (1 + MIRR) The Modified IRR ca be calculaed usig he MIRR fucio i Microsof Excel. MIRR = (values, fiace rae, reives rae) The Reives Rae has o be eered i he form R%; Excel will he calculae he modified IRR. I he example give i Table 2, if he beefis cao be re-ivesed a all, he Modified IRR will be 8%. If he beefis ca oly be ivesed a a marke ieres rae of 12% raher ha a he IRR, he Modified IRR will be 15%. Agai, he calculaios ca be made usig spreadshee sofware. I pracice, i migh be reasoable o assume simply ha: he reveue sream is fully reivesible; he user beefis are o reivesible, or reivesible oly a a lower rae.
Page 5 Traspor Noe No. TRN-6 Jauary 2005 Box 4. Chia: Liaoig Urba Traspor Projec. Icorporaig he MIRR The Liaoig Urba Traspor projec (USD 150 millio) offers a example i he use of he modified ERR, i addiio o he ERR ad he NPV. The projec icluded ivesmes i, ad improvemes o, he operaio of he urba raspor sysem i he ciies of Sheyag, Fushu, ad Asha i he Liaoig provice of Chia. I each ciy, he projec provided fuds for public raspor, raffic maageme, road ifrasrucure ad road maieace aciviies. Ivesmes covered jucio improvemes, road maieace ad recosrucio, cosrucio of cycle roues, desigaig ad adapig ifrasrucure for bus-oly laes, ad equipme for raffic maageme. The evaluaio of ecoomic beefis followed a coservaive approach ad was resriced o reducios i vehicle operaig coss (VOC) ad savigs i ravel ime for raspor sysem users, icludig cycliss. Beefis / coss o pedesrias were excluded from he aalysis due o daa cosrais, as were beefis resulig from safey improvemes. A subsaial share of overall beefis, 25%, was hose due o ime savigs uder he sraigh ERR calculaios, i is assumed ha all beefis are re-ivesed a he ierally geeraed ROR. I cases where i is believed ha some or all of he beefis cao be re-ivesed (for example, ime savigs), he use of he modified rae of reur offers a more realisic esimae of ecoomic reurs. Whe comparig projecs, he rakig of projecs usig he IRR ad MIRR remais uaffeced so log as he same se of beefis are evaluaed uder boh crieria. For he projec, he ecoomic evaluaio icluded calculaio of he MIRR assumig ha projec beefis were reivesed a he average rae of reur o public ivesmes, ha is, 12 %. For all compoes, he chage i reivesme rae led o a declie i he MIRR by approximaely half bu was sill well above he Bak cu-off rae of 12% for projec accepabiliy. If ime savigs are assiged a zero value i his example, he projec would sill be accepable (per Bak orms) wih a MIRR of approximaely 13 perce (assumig a12% reur o oher savigs). Sheyag Asha Fushu P rojec ERR (%) 32.2 42.8 44.9 34.9 MERR (%) 16.7 20.8 19.8 17.4 WHEN AND HOW SHOULD EACH MEASURE BE USED? A Ne Prese Value or a Ieral Rae of Reur is a esseial resul from ay ecoomic appraisal, icludig appraisals of raspor projecs. The Hadbook o Ecoomic Aalysis of Ivesme Operaios (World Bak, 1998) [1] is a source of geeral advice o he usage of NPV ad IRR. The appropriae use of NPV ad IRR (or Modified IRR) depeds o he decisio coex. Four impora ypes of decisio are worh highlighig. (i) The accep/rejec decisio. The World Bak cosiders a projec o be accepable if i reaches he followig miimum sadard of performace 6 : Crieria for accepabiliy: NPV > 0 or IRR > he discou rae, r 6 For furher guidace see he Hadbook o Ecoomic Aalysis of Ivesme Operaios, Chaper 12 Paragraph 14 (World Bak, 1998) [1].
Page 6 Traspor Noe No. TRN-6 Jauary 2005 This es will be applied o all projecs, however, i is oly he firs of several hurdles o be jumped. (ii) Choosig bewee muually exclusive aleraives. Ecoomic appraisal is also used o iform he choice bewee aleraive courses of acio. I raspor, hese choices iclude: choice bewee differe roues for road ad rail liks, ad differe locaios for pors ad ierchages of all ypes; choice bewee differe egieerig soluios, eg. uels versus bridges, or mero versus ligh rail soluios; choice bewee differe approaches o improvig raspor, eg. ifrasrucure ivesme versus improved maieace (see TRN 13: Treame of Maieace versus orgaisaioal reform (see Noe 24: Ecoomic Appraisal of Regulaory Reform versus pricig opios (see Noe 23: Evaluaio Implicaios of Sub-Opimum Pricig); choice bewee public provisio, privae provisio ad parership arragemes; ad choice of projecs o iclude wihi a Programme or Pla for raspor. Here he quesio is o simply wheher he projec would coribue o ecoomic welfare, bu wheher is i has bee show o be he bes of he available aleraives i hese erms. This ca be esed by comparig projecs i erms of heir NPV ad IRR, as follows. Whe all he aleraives beig compared are ivesme projecs, feaurig a iiial ivesme followed by a flow of beefis i he fuure, oe (or preferably boh) of he followig summary measures should be provided: NPV for boh projecs A ad B Icremeal IRR of Projec A over Projec B, IRR A-B (for calculaios see Box 4) Whe he aleraives beig compared do o fi he sadard ivesme profile, he appropriae compariso is: NPV for boh projecs A ad B To sar wih, here is a presumpio i favor of he soluio wih he lowes capial cos. This ca be desigaed Projec A. Aleraives o Projec A ca be compared wih Projec A eiher based o heir NPV a higher NPV is preferred or by uderakig a icremeal aalysis, as follows. Box 5. Icremeal Aalysis Projec Beefis i each Year, $000 0 1 2 3 4 5 6 Icremeal NPV Icremeal IRR A -12,000 3,500 3,500 3,500 3,500 3,500 3,500 1,268 14.1 B-A -8,000 2,500 2,500 2,500 2,500 2,500 2,500 1,477 17.0 C-B -8,000 2,000 2,000 2,000 2,000 2,000 2,000-418 7.9 D-C -4,000 800 800 800 800 800 800-967 0.0 The projecs are iroduced i ascedig order of capial cos. This example shows ha swichig o Projec B from Projec A has a high reur a posiive Icremeal NPV ad a Icremeal IRR greaer ha he discou rae. Projec C is poor value, however i has a egaive icremeal NPV ad Icremeal IRR less ha he discou rae. Projec D has ohig o coribue i welfare erms.
Page 7 Traspor Noe No. TRN-6 Jauary 2005 Icremeal aalysis applies where he choice is bewee oe soluio or aoher. There may of course be siuaios where boh projecs could usefully be uderake. If so, he releva crierio is he oal NPV of he se of ivesmes proposed. I pracice, projecs are ofe composed of packages of compoes. I his case, icremeal aalysis should be used o es wheher paricular compoes are worhwhile, i erms of heir icremeal NPV or IRR. (iii) Timig of ivesme. The imig of a projec is a impora decisio ha eeds o be aalyzed i every case. Jus because a projec s beefis exceeds is coss i does o mea ha he projec should be sared immediaely. Pospoig a projec may chage he ime profile of beefis ad coss ad hece he projec s NPV. If he profile of beefis ad coss is o chaged, bu oly pospoed, he imig is o a issue, as he prese value of he beefis ad coss will chage proporioally by he discou facor used. Thus, if (a) he prese value of a projec s beefis discoued a 20 perce is $12M, (b) he prese value of coss is $6M, ad (c) pospoig he projec oe year merely shifs all coss ad beefis by oe year, he prese value of boh beefis ad coss will be reduced by he same perceage, as will he NPV of he projec iself. I hese cases, he sooer he projec sars, he higher he NPV. If, o he oher had, he beefi or cos profile chages wih pospoeme, he imig becomes a issue. Cosider a projec ha begis o geerae beefis durig is hird year of life, wo years afer is iiiaio (Table 3 op pael). The projec has a four year operaig life. Table 3. Pospoeme of Projec Year 0 1 2 3 4 5 6 Beefis, $M 0.0 0.0 2.0 7.0 7.0 8.0 0.0 Coss, $M -3.0-2.0-1.0-1.0-1.0-1.0 0.0 Ne Beefis, $M -3.0-2.0 1.0 6.0 6.0 7.0 0.0...afer pospoeme: Beefis, $M 0.0 0.0 0.0 7.0 7.0 8.0 8.0 Coss, $M 0.0-3.0-2.0-1.0-1.0-1.0-1.0 Ne Beefis, $M 0.0-3.0-2.0 6.0 6.0 7.0 7.0 The e prese value of his flow, discoued a 12%, is $8.1M. If we were o pospoe he projec by oe year ad hereby shif all beefis ad coss oe year io he fuure, he e beefis as well would be shifed by oe year ad hece heir prese value would be reduced i proporio o he discou rae ad he projec s e prese value would fall o 7.2 = 8.9 1.12. I his case waiig would o pay. Suppose, however, ha a oe year pospoeme were o shif all coss by oe year, leavig he gross beefis uchaged. The ew e beefis profile would be as show i he boom pael of Table 3. By pospoig he projec we would be forgoig $2M of gross beefis i year wo i exchage for $8M of gross beefis i year six. The e prese value of his ew flow, discoued a 12 perce, would be $11.3M, idicaig ha pospoeme would be advisable. The differece bewee hese wo examples is ha i he firs case pospoeme merely shifed he cos ad beefi sreams by oe year, while i he secod case pospoeme alered he sreams. The opimal imig for a projec occurs i he year i which is NPV peaks. The bes way o ideify ha year is o examie he effecs of pospoeme year by year uil he opimal year is foud. I should be oed ha i boh cases we evaluaed he NPV of he projec wih respec o he same base year, amely year zero, whe = 0. I all cases we eed o evaluae he prese value of he flows wih respec o he same base year.
Page 8 Traspor Noe No. TRN-6 Jauary 2005 THE ROLE OF THE DISCOUNT RATE I is clear ha a key variable whe calculaig he NPV, IRR ad Modified IRR is he discou rae. Box 6. Discou Rae The World Bak coveio is o use a discou rae of 12 perce whe evaluaig Bak fiaced raspor projecs. This figure is o ecessarily a precise reflecio of he opporuiy cos of capial i borrower couries, isead i ca be viewed as a raioig device for World Bak fuds. If appraisal requiremes a he coury level call for a differe discou rae, he he 12% rae ad he coury-specific rae may boh be esed. The resuls usig he 12% rae should be repored i he Projec Appraisal Repor ad will be impora i he World Bak s decisio-makig. Bear i mid ha he discou rae is oe of he easies appraisal parameers o vary paricularly oce a spreadshee has bee se up o make he calculaios. A srog jusificaio is required if a discou rae oher ha 12% is o be used as he mai rae. A discou rae lower ha 10% is ulikely o be jusified, sice mos research has show ha he cos of capial for developig couries is higher ha 10%. Task maagers will eed o demosrae ha ay aleraive rae has bee jusified i he Coury Assisace Sraegy. Furher advice ad furher readig refereces o discouig are give i he earlier secio o Ne Prese Value. Some cosideraio is ow beig give o he possibiliy of usig he sadard 12% for all fiacial coss ad beefis ad a differe, ad probably lower, rae for o-fiacial coss ad beefis ha more closely reflecs he social ime preferece rae. Should his resul i ay chage i he recommedaio of wha discou rae o use, his will be repored i a updae o his Framework. SUMMARY Summary measures of projec performace, such as he NPV, IRR or AIRR, are used o idicae he overall performace of a projec uder ecoomic evaluaio: eiher a NPV or a IRR (or AIRR) is a esseial resul, o be icluded i he Projec Appraisal Repor; as a miimum, o be accepable a projec should have a NPV greaer ha zero or a IRR (or AIRR) greaer ha he discou rae, which is coveioally 12% for Bak-fuded raspor projecs; he NPV or IRR (or AIRR) measure should also be used o compare aleraive soluios, for example aleraive roues for road ad rail liks, ad differe locaios for pors ad ierchages of all ypes; The World Bak has a presumpio i favour of he soluio wih he lowes capial cos icremeal aalysis ca he be used o assess he value for moey offered by more expesive aleraives; someimes i ca pay, i ecoomic erms, o pospoe he implemeaio of a projec o a laer dae he NPV ca be used o es wheher he imig of ivesme is opimal.
Page 9 Traspor Noe No. TRN-6 Jauary 2005 FURTHER READING [1] The World Bak (1998), Hadbook o Ecoomic Aalysis of Ivesme Operaios. Washigo, DC: The World Bak. Techical Appedix. Available olie a: hp://www.worldbak.org/educaio/ecoomicsed/projec/projwork/hadbook.pdf Traspor Ifrasrucure Noes are available o-lie a: hp://www.worldbak.org/hml/fpd/raspor/publica/pub_mai.hm Traspor Noes are available o-lie a: hp://www.worldbak.org/hml/fpd/raspor/publica/pub_mai.hm Urba Ifrasrucure Noes are available o-lie a: hp://www.worldbak.org/hml/fpd/urba/publica/pub_oe.hm Urba Noes are available o-lie a: hp://www.worldbak.org/urba/upgradig/urba-oes.hm 2004 The Ieraioal Bak for Recosrucio ad Developme/The World Bak 1818 H Sree NW Washigo, DC 20433 Telephoe 202-473-1000 Iere www/worldbak.org The fidigs, ierpreaios, ad coclusios expressed here are hose of he auhor ad do o ecessarily reflec he views of he Board of Execuive Direcors of he World Bak or he govermes hey represe. To order addiioal copies of his publicaio, please sed a e-mail o he Traspor Help Desk raspor@worldbak.org