ProfessorJohnGeanakoplos:
Sowe'respendingacoupleclassesthesedayslearningbasicfactsandvocabularyaboutfinance,andalongthewaywe'retryingtoapplythesimplelessonsthatIrvingFishertaughtaboutturningafinancialproblemintoageneralequilibriumproblemandmakinguseinparticularofthebudgetset.
Thatverysimplebudgetsetwewrotedownattheverybeginningturnsouttobequiteusefulandpeopleoftencangetquiteconfused.Sothelastissueweendedwith,I'mgoingtotakeupagain.Supposethatyou'vegotaverylong-livedinstitutionlikeYale.HowshouldYalethinkofhowmuchtospendeveryyear?
WhatisYale'sbudgetset?
AlmosteverybiginstitutionlikeYalecreatesafictionofanannualbudgetandtheytalkaboutthedeficitandhavingtobringthedeficitundercontrolandmakingcutstoclosethedeficitgap,butreallythereisnosuchthingasaone-yearbudgetset.Imean,whyoneyear?
Whynotonemonth?
Whynotoneday?
NobodyexpectsYaletobalanceitsbudgeteveryday.Someexpenditurecomesinoneday.Theyhavetohireanelectriciantofixsomethingunexpected.They'regoingtospendmoremoneythantheytakeinstudenttuitionthatday.Sothefactthatthey'resupposedtobudgetthebalanceeveryyearisjustafiction.
IrvingFishertaughtusthatYalereallyhas--ifyoucanborrowandlendandyoudon'thavetoworryaboutriskthere'soneinfinite-livedbudgetset.It'saninfinitehorizonbudgetsetwhereyoujusttakethepresentvalueofalltheexpenditures,that'sthelefthandside,andthepresentvalueofalltherevenue,that'stherighthandside,andmakesurethatthelefthandsideissmallerthantherighthandsideoverthewholecourseofYale'slife.
Sothatsimpleprinciplehasatremendousimplicationwhichwasoverlooked,tothechagrinofthelastYalepresident.SoasIsaid,theissuewasin1997,Ibelieve,itcouldhavebeen'96somethinglikethat,1997,BennoSchmidt,whowasthentheYalepresident,releasedawhitepaper,hecalledit,documentingthefactthatYalehaddeferredmaintenanceinthebuildings,hecalledit,andastudythathecommissioned,averygoodstudythathecommissioned,arguedthatthedeferredmaintenance--Yalecouldbebroughtuptosnuffandthengoonafterwardsasanormalrunninginstitutionprovideditspent100milliondollarsayearfortenyears,andthatincludedfixingeverycollege--they'regoingtodomorethanoneayearovera10yearperiod.
SoYale'stotalbudget,asItoldyou,wasabout1billiondollarsatthetime,andthenhereallofasuddenwasthis100milliondollarayearexpensefor10years.That's10percentoftheYalebudget.Andalotofthecostsyoucan'tchange.Youhavetohavethelightson.Youhavetoheatthebuildings.
Youcan'treallyreducethosecosts.SoBennoSchmidtcametotheconclusionthathe'dhavetoreducethecostshecouldchangeby15percentinordertobalancethebudget,tocutabout100milliondollarsayearoutofthebudget.Soheannouncedonedaythathewasgoingtofire15percentofthefacultybyattrition.Iftheywerejuniorfacultyhewouldn'tpromotethem,andiftheywereseniorfaculty,waituntiltheyretiredandnotreplacethem.Sothis,needlesstosay,causedatremendouscommotionamongthefaculty,andasItoldyouacommitteewasformedandIhadtopresentthereport.
Soactuallythereportwentprettycarefullythroughallthecalculationsmadeinthewhitepaper,buttheheartofthereportwassimplytoapplythelessonofIrvingFisher.SowhatisthelessonofIrvingFisher?
Let'ssupposethatthere'snoinflationsothatwhentheysay100milliondollarsayeartheymean100millionrealdollarsayear.SoIrvingFisherwouldsayYale'sgoingtoliveforever.Let'ssupposethatYalewantsthesamequalityofeducationeveryyearforever,soitshouldhavethesamerealspendingeveryyearforeverafteritcompensatesforinflation.Soatthemomentwe'reassumingthere'snoinflation.Sowhatdoesthatmean?
Thatmeansthatyoujustlookattherighthandsideandyousay,what'sYale'srevenue?
Well,whateveritwasbeforeweweretoldbythisreportofthepresidentthataslongasyoudidthedeferredmaintenanceYalewouldbebackinbalance.Sowhat'sthelossofrevenueontherighthandside?
It's10yearsof100milliondollarsayearasyoucansee.
Now,youneedaninterestrate.Whatshouldtheinterestratebe?
Well,shoulditbethenominalinterestrateortherealinterestrate?
Well,we'resupposingnowthere'snoinflationsoitshouldbetherealinterestratebecauseallthehundredshavenoinflationinthem.Sowhatrealinterestrateshallweuse?
Well,thewhitepaperused5percentbecausetheythoughtthatwasthenumberthatYalecouldearnafterinflationprettyreliablyeveryyear.Theythinkthat'stherealrateofreturnYalegets,andsotheydiscountedit5percent.Nowtherealrateofinteresttypicallyintheeconomyis3percent,butlet'ssupposethatwecalculatedthisat5percent.Thepresentvalueof100for10yearsis772.
Now,howcouldyoudothatinyourhead?
Well,weknowthat5percentisgoingtodoubleevery14years,5into72isabout14.Ifitdoublesevery14years10yearsisgoingtobelessthanhalfthevalueofthebond.Soifyougot100foreverat5percentinterestthatwouldbe2billion,andweknowforonly10yearsit'slessthanhalfthevalue,soconsiderablylessthanhalfthevalue,soit'snotonebillionit'ssomethinglessthanthat.It's772.
SoIjustdidthatinExcelandIcalculated772,butinyourheadyouknowthatifithadgoneonfor14yearsthenthepresentvalue,ourformula,ourfamousformulaisthatyouwouldtakethecoupon100dividedbytheinterestrate.05times（1-1over（1+R）tothe10th）.Andsoweknowthatifthiswere14insteadof10you'dgetahalfhere.Sothisis20times100whichis2billiontimes1halfwouldbe1billion,butsinceit'sonly10yearsandnot14yearsit'slessthanabillion,so772.
Soinyourheadyoucouldhaveprobablyfiguredthatoutapproximately.SoyoucouldbesittingthereintheaudiencehearingBennoSchmidttalkandbecomputinginyourheadthatwe'retalkingaboutsomethingunder1billion,like3quartersof1billion.Sonow,howmuchdoesthatmeanreductionineveryyear?
Well,ifYale'sgoingtospendthesameamounteveryyearthatmeansitshouldbespending5percentof772lesseveryyear.That's38.6milliondollarslesseveryyear.Sothat'sadrasticallysmallernumberthan100milliondollarsayear.It'scrazyjusttothinkthatbecauseyou'vegottheseexpendituresfor10yearsandthennoexpendituresafterthat,thatyoushouldcutthebudgetbya100millionandthenletitgoupafter10years.Soyou'donlyneedtocutitby38million.
Now,bytheway,5percentisaprettyarbitrarynumber.Supposeyouput3percenthere?
Well,3percentwouldgiveyouamuchhigherpresentvalue,butthenwhenyoumultiplyitby3percentattheendfortheannualreductionitwillgiveyouamuchsmallernumber.Anyway,thisnumber,whichIcomputedinExcel,butagainyoucandoitsortofinyourhead,is853million,butyoumultiplythatby3percentandyouget26millionayear.Sonowthereductionisstartingtosoundlikeit'snotsuchafrighteningthing.
Solet'sstickwiththe5percentwhichiswhatthewhitepaper,takealltheassumptionsofthewhitepaperandtakeitliterally,andthennoticethattheyneversaidanythingaboutinflation.Soactually,thiscalculationofpresentvalueloss--there'sinflation,andsaytheinflationatthattimeisaround4percent.InfactalltheYalecontractsthatarestillinplaceassumea4percentinflationeventhoughinflation'slessthanthatnow.
Butanyway,sothat100millionayearofdollarsisactuallylessinpresentvaluetermsbecausewhatshouldyoudiscountby?
Ifyoulookatthepresentvalueof100milliondollarsover10yearsandyoutakeintoaccountitsdollarsyoushouldbediscountingbytherealinterestratetimestheinflation,soby9percent,atinybitover9percent.Soifyoudiscountthatby9percentyouget641millionasthepresentvaluelosstoYale.
Now,giventhatthere'sinflationhowmuchshouldyoubespendingeveryyear?
Youshouldbespendinginrealdollars,reducingyourexpenditurehowmuchinrealdollars?
Well,by5percentofthe641million.Soifyouhave641,that'stoday'spresentvalue.Therehasn'tbeenanyinflationyet.Sothat'sthereallossindollars.Soifyouask,what'stherealexpenditurereductioneveryyear,it's5percentof641andthat's32million.
So32millionisafarsmallernumberthan100millionandrequiresafarsmallerdropinexpenses,soourcommitteerecommendedthatwecutthefacultyby6percentinsteadofby15percent,and6percent--therearealotofpeopleleavingeveryyear.Youcando6percentprettyquickly.Sotheupshotofthisisthatitisasimpleapplicationofpresentvalue,averyelementarycalculation.Itcameassomewhatofarevelationtoouradministrators,I'mafraid,andthedayafterthereporttheprovostoftheuniversityresigned.
Twoweekslaterthedeanoftheuniversityresignedandtwomonthslaterthepresidentoftheuniversityresigned.AndRickLevin,thecurrentpresident,tookoverandhecutthefacultyby6percent,butbynomorethanthat.Andthen,ofcourse,thefinancesofYalegotmuchbetterandhe'ssinceaddedbackthat6percentplusalittlebitmorethanthat.
Sojusttotellyou,though,somethinggoodabouttheYaleadministration,theprovostwhoresignedthatnextdayhappenstobeafriendofmine.I'vehaddinnerwith
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