Murray Fulton教授 项目分析与贴现率加拿大萨斯卡彻温大学农经系合作研究中心.docx

1、Murray Fulton教授 项目分析与贴现率加拿大萨斯卡彻温大学农经系合作研究中心项目分析与贴现率MurrayFulton教授加拿大萨斯卡彻温大学农经系、合作研究中心引言Introduction前两讲关于肥料经济学的讨论论述了为获得最大利润，用于不同作物的各种肥料施用量的决策原则，其共同的主题是，肥料的最佳分配发生在肥料单位用量的增加所带来的边际收益等于由此而产生的边际成本的时候。这一原则的得出是基于一个假设条件，即成本和收益发生在同一个时期。Inthetwolecturesontheeconomicsoffertilization,Ipresentedaframeworkformakin

2、gdecisionsabouttheamountsofvariousfertilizerstouseondifferentcropsinordertomaximizeprofits.Acommonthemeinbothlectureswasthatanoptimalallocationoffertilizerwouldtakeplacewhenthemarginalbenefitofapplyinganotherunitoffertilizerequaledthemarginalcostofthisadditionalunit.Implicitinthedevelopmentofthisrul

3、ewastheassumptionthatthecostsandbenefitsoccurredatthesametime.然而，众所周知，项目的成本和收益很少同时发生。在许多情况下，费用得现在支付，而收益则要一段时间后才能获得。此外，一旦开始有了收益，往往会持续一段时间。Itiswellknown,however,thatthecostsandbenefitsassociatedwithprojectsrarelyoccuratthesamepointintime.Forexample,inmanycases,thecostisincurrednow,whilethebenefitsmayt

4、akesometimetooccur.Inaddition,whenthebenefitsdooccur,theymaylastforaperiodoftime.例如，新建一个化肥厂需要现在投资，而收益却要等到正式投产后才能获得，且投产后头几年的收益会比以后少，因为新增的产量需要一定的时间才能充分进入分销系统。同样地，一个对农民进行平衡施肥培训的推广项目，涉及到大量的创办费，而一旦进行了投资，相当长的一段时间内都能从中获益。而且与建肥料厂一样，项目实施头几年的收益可能会比较小。这是因为，新技术和措施刚出现时通常不容易被采用，虽说少部分农民也许会先采用，大多数却愿意等等，看这种新方法是否真有好处

5、。最后一个例子与肥料施用有关，施用磷肥和钾肥的经济效益在施肥当季并不能全部发挥出来，而是在以后的各季中能继续发挥作用。Forexample,theconstructionofanewfertilizerplantmeansincurringacostnow.Thebenefits,however,donotoccuruntiltheplantisoperating.Eventhen,thebenefitsintheearlyyearsarelikelytobelessthaninlateryears,whentheadditionalproductioncanbefullyintegrated

6、intothedistributionsystem.Inasimilarfashion,thedevelopmentofanextensionprogramtoeducatefarmersaboutthebenefitsofbalancedfertilizerinvolvesamajorinitialcost.Oncethiscostisincurred,thebenefitsarelikelytolastforasubstantialperiodoftime.Inaddition,aswiththefertilizerplant,thebenefitsarelikelytobesmaller

7、intheearlyyears.Thisisbecausenewtechniquesandpracticesarenotusuallyadoptedwhentheyfirstemerge.Whilesomeofthefarmersmightbeearlyadopters,themajorityliketowaitandseeifthenewideasprovetobeadvantageous.Afinalexampleinvolvesfertilizerapplication.Thebenefitsofpotashandphosphatearenotcompletelyrealizedinth

8、eyearthefertilizersareapplied,butinsteadcontinueonforanumberofyears.解决收益和成本不同时发生的一个方法是使用贴现率率。贴现率率提供了一个比较目前的成本与第二年或十年后的收益的方法。Onewaytotakeaccountofsituationswherethebenefitsandcostsdonotoccuratthesametimeistousediscounting.Discountingprovidesawayofcomparingacosttodaywithabenefitnextyearortenyearsfromn

9、ow.本讲座的主题是贴现率率。这一概念被用来分析当成本和收益发生在不同时期时，某个项目的经济可行性。首先分析贴现率率和通货膨胀在测定项目的经济可行性中所起的作用；然后分析预算限制对项目选择的影响；最后将讨论项目实施后的受益者和损失者。Thefocusofthislectureisdiscounting.Thisconceptisusedtoexaminetheeconomicfeasibilityofaprojectwherethecostsandbenefitsoccuratdifferentpointsintime.Therolethediscountrateplaysindetermin

10、ingtheeconomicfeasibilityofaprojectisexamined,asistheroleofinflation.Theeffectofbudgetconstraintsonprojectselectionwillalsobeexamined.Thelectureconcludeswithsomeobservationsonwhobenefitsandwholosesasaresultofprojectsbeingundertaken.贴现率Discounting介绍贴现率概念最好是举例说明。表1是一个假设项目的成本和收益。假定该项目是个推广项目或是新品种开发项目。如表

11、所示，成本和收益不发生在同一个时期。Thebestwaytointroducethenotionofdiscountingisthroughtheuseofanexample.Table1presentsthecostsandbenefitsassociatedwithahypotheticalproject.Thisprojectmightbeanextensionprogramorthedevelopmentofanewseedvariety.Ascanbeseen,thecostsandbenefitsdonotoccuratthesametime.(表：表1项目在一定时期内的收益和成本

12、)Year年Benefits收益Costs成本NetBenefits纯收益10100-1002730-23388410105151562020725258303093030103030Total总计17513045比较发生在不同时期的成本和收益最容易的方法是简单地把它们加起来，表1的最后一排为成本和收益相加的结果。从表上看来，该项目似乎在经济上是合理的，因为收益比成本大45。Theeasiestwaytocomparethecostsandbenefitsthatoccuratdifferentpointsintimeistosimplyaddthemtogether.Thelastrowin

13、Table1showstheresultsofaddingthecostsandthebenefitstogether.Ascanbeseen,thisprojectappearstobeonethatiseconomicaltoundertake,sincethebenefitsexceedthecostsby45.这里我很谨慎地用“似乎是经济的”，因为有人会辩驳说，直接比较发生在现在的成本与发生在将来的收益是不合适的。原因之一可能是通货膨胀。如果经济中存在着通货膨胀，那么；将来的一元钱就不会有和今天的一元钱同样的购买力。本讲随后将对通货膨胀进行更详细的讨论。Ideliberatelyuse

14、thephraseappearstobeeconomicalbecauseitcanbearguedthatitisnotpropertodirectlycomparethebenefitsthatoccurinthefuturewiththecoststhatoccurnow.Onereasonmightbeinflation.Ifinflationispresentintheeconomy,thenoneyuaninthefuturedoesnothavethesamepurchasingpowerasoneyuantoday.Theroleofinflationwillbeexamine

15、dinmoredetaillaterinthislecture.即使我们假设没有通货膨胀，也并不解决问题，因为还存在着另一个问题，即将来的一元钱常常不如今天的一元钱值钱。原因是，如果今天有一元钱，它可以用于很多方面，如投资一个项目以获得资本回收率，或者用来购买少了这一元钱便无力支付的东西。因此，今天没有这一元钱意味着放弃了一个机会，这可能是将来多挣一元钱的机会，或者是现在购买某种东西而从中受益的机会，而不是等到将来。用经济术语来说，这里存在着一个机会成本。Assumingthatthereisnoinflation,however,doesnotsolvetheproblem.Anotherp

16、roblemexists,namelythatoneyuaninthefutureisoftennotworthasmuchasoneyuantoday.Thereasonisthatiftheyuanwasavailabletoday,itcouldbeusedinsomeotherfashion.Itcouldbeinvestedinanotherprojectthatearnsarateofreturn,oritcouldbeusedtopurchasesomethingwhichotherwisecouldnotbeafforded.Nothavingtheyuantoday,ther

17、efore,meansanopportunityhasbeengivenup.Thismaybetheopportunitytoearnadditionalyuaninthefuture,oritmaybetheopportunitytoreceivethebenefitsofapurchasenowratherthanlater.Ineconomicterms,anopportunitycostexists.这个机会成本的存在说明，人们不会用今天的一元钱换取一年以后的一元钱，如果有人这样做了，他会失去某些东西。因此，人们只愿意用少于今天的一元来换得一年后的一元钱，换句话说，将来的一元与今天的

18、一元并不等值。Thepresenceofthisopportunitycostmeansthatpeoplewillnottradeoneyuantodayforoneyuanayearfromnow.Ifsomebodywastogiveuponeyuantodayinexchangeforoneyuanayearfromnow,theywouldbelosingsomething.Asaresult,peopleareonlywillingtogiveupanamountthatislessthanoneyuantodayinexchangeforoneyuanayearfromnow.A

19、notherwayofsayingthisisthatoneyuaninthefutureisnotworthasmuchasoneyuantoday.某一东西从现在到将来一定时间价值减低的过程叫贴现，贬值的比率称为贴现率，如上面所说的，贴现率的概念与资本回收率有关。为了更好地理解贴现率，先讨论一下资本回收率和复利。Thedevaluingofthingsobtainedinthefutureisknownasdiscounting,whiletherateatwhichthingsaredevaluedisknownasthediscountrate.Aswasshownabove,then

20、otionofdiscountingcanberelatedtoratesofreturn.Toobtainabetterunderstandingofdiscounting,itisusefultofirstconsiderratesofreturnandcompounding.假如，资本回收率为10%，也就是说，今天投资1元，一年以后可得到1.10元，这1.10元是用最初的1元投资乘以系数1.10而得出的。如用这1.10元再投资，再过一年（即投资第二年）可得到1.21元（1.21=1.10（1.10）=1.102），如再投资，第三年可得1.331元（1.331=1.21(1.10)=1.1

21、03）。Forexample,supposearateofreturnoftenpercentcanbeearned.Thismeanstheinvestmentofoneyuantodayresultsin1.10yuanayearfromnow.Thevalueof1.10isobtainedbymultiplyingtheinitialinvestmentofoneyuanbyafactorof1.10.Ifthis1.10yuanisreinvested,thenoneyearlater(i.e.,inthesecondyearfromtheoriginalinvestment),it

22、willbeworth1.21(1.21=1.10(1.10)=1.102).Thereinvestmentofthisamountwillresultin1.331yuan(1.331=1.21(1.10)=1.103)inthethirdyear.以此类推，T年后，1元的投资可得到的价值为VT=1.0(1.10)T其中，VT是T年后的投资价值，(1.10)表示资本回收率为10%。一元钱随着时间的推移而增长为VT的过程称为复利过程。Byextendingthisprocess,thevalueofaoneyuaninvestmentTyearsinthefuture(VT)canbewrit

23、tenasVT=1.0(1.10)TIntheaboveexpression,VTisthevalueoftheinvestmentinyearT,whiletheterm(1.10)indicatestherateofreturnistenpercent.TheprocessbywhichoneyuangrowsovertimetoreachVTisknownascompounding.一般地说，如果资本回收率为i（i为百分数），那么，T年后1元投资的价值为VT=1.0(1+i)T其中，(1+i)T称为增长因素。表2表示利率为2.5%、5.0%、7.5%和10%时，1元投资10年后的增值或复

24、利（注意，如果i=5.0%，那(1+i)=1.05）。图1是表2的图形化。注意复利的结果使最初的投资成指数增长。Moregenerally,iftherateofreturnisgivenbyi(iisexpressedinpercentageterms),thenthevalueofaoneyuaninvestmentTyearsinthefutureisgivenbyVT=1.0(1+i)TTheexpression(1+i)Tiscalledthegrowthfactor.Table2showshowaoneyuaninvestmentgrowsorcompoundsoveratenye

25、arperiodatinterestratesof2.5,5.0,7.5,and10.0percent(notethatifi=5.0percent,then(1+i)=1.05).Figure1graphsthevaluesinTable2.Itisimportanttoobservethatcompoundingresultsinexponentialgrowthoftheoriginalinvestment.(表：表2对不同的回收率，一元钱投资在一定时期内的增值)Year(T)年RateofReturn(i)回收率2.55.07.510.001.0001.0001.0001.00011.

26、0251.0501.0751.10021.0511.1031.1561.21031.0771.1581.2421.33141.1041.2161.3351.46451.1311.2761.4361.61161.1601.3401.5431.77271.1891.4071.6591.94981.2181.4771.7832.14491.2491.5511.9172.358101.2801.6292.0612.594注释：GrowthFactor=(1+i)T(图：图1不同回收率下一元钱随时间的增值) 贴现率与上面所说的复利过程正好相反。假如某人一年后得到1元钱，这1元钱现在值多少呢？如果贴现率为

27、5%，那一年后的1元钱为今天的0.952元(0.952=1/1.05)。如果某人两年后得到1元钱，以贴现率率为5%计算，那1元钱相当于今天的0.907元(0.907=0.952/1.05=1/(1.05)2)。Discountingturnsthecompoundingprocessdescribedabovecompletelyaround.Supposeapersonisofferedoneyuanayearfromnow.Howmuchisthisoneyuanworthtoday?Ifthediscountfateisfivepercent,thenthevaluetodayofoneyuanayearfromnowis0.952yuan,where0.952=1/1.05.Ifapersonisof