Abstract

Thiscasedealswithcapitalbudgeting.ItdealswithevaluationofaprojectusingNetPresentValue(NPV)andtheInternalRateofReturn(IRR)methods.StudentswilllearnaboutNPVandIRRmethodsandtheiradvantagesanddisadvantages.TheywilllearnhowtocomputetheNPVandtheIRRoftheproject.TheywillalsolearnabouttheproblemswiththeIRRmethod.Finally,studentswillpreparetheNPVProfileoftheproject anduseittomorecriticallyevaluatetheproject.Thisisahands-onexperienceforstudentswhowanttolearnmoreaboutcapitalbudgeting.

Introduction

RashidhasjuststartedworkingundertheAssistantTreasurerofafirm.Hisfirmisconsideringashort-termcapitalinvestment.HisbossCaroline(whoisthecurrentAssistantTreasurer)assignedhimthetaskofevaluatingthisproject.Thedeadlineisintwodays.

In ordertogetsomehelp,hevisitsSarah,oneofhiscolleagues."Sarah,Ineedyourhelp"Sarahresponds,"O.K.HowcanIassistyou?"

"Iamtaskedwithevaluatingaprojectandthenpossiblycomparingthatprojecttoanotherpotentialinvestment.I know,itshouldbeaneasytask,butunfortunatelyIhavealreadyforgottenaboutthesetopics.Couldyoupleasehelpmealittlebit?"Rashidasks.

Sarahsays"Noproblem.Givemelikefifteenminutes.FirstIwillwrapupmycurrentworkandthenIcanvisityouinyouroffice."

"ThanksSarah!Seeyouovertherethen."

Fifteenminuteslater,theywereinRashid'soffice.Rashidstartstheconversation"Sarah,Idon'trememberwheretousetheNetPresentValue(i.e.NPV)methodversustheInternalRateofReturn(i.e.IRR)method.Canweuseanyofthesemethodstoevaluateaproject?"

"First,youneedtorememberthatNPVgivesyouadollarvalue.Itis thepresentvalueofallexpectedcashflowsfromaproject.IfNPVis+$10millionforexample,makingthisinvestmentisexpectedtoadda$10millionvaluetoourfirm.So,itis agoodproject.Ontheotherhand,ifNPVisnegative,thenourfirmwilllosevalueifwemakethisinvestment.Ontheotherhand,IRRgivesusthepercentagereturn.IfIRRisgreaterthanourrequiredreturn,thenitisagoodprojectthatwouldaddvaluetoourfirm.Inotherwords,NPVwouldbepositiveforthatproject.Ontheotherhand,ifIRRislessthanourrequiredreturn,thanweshouldn'tinvestinthatproject,becauseNPVwouldbenegative"Sarahresponds.

Rashidconfirms"Yes,Irememberthesealittlebit,butIguessIstillneedtoreadmore."

Sarahadds"Sotheanswertoyourquestionisyes.Aslongasyouaretalkingaboutasingleproject,bothNPVandIRRwouldwork.Forasingleproject,bothNPVandIRRwillreachthesamedecision.Forexample,ifNPVispositive,meaningthatitisagoodproject,soweshouldacceptit,thenIRRshouldbegreaterthantherequiredreturn,whichalsomeansthatweshouldaccepttheproject."

Rashidcontinues"Also,thereistheissueofcomparison.IfIneedtocomparetwoprojectsandchoosethebestone,whatshouldIdo?AgaincanIusebothNPVandIRRforcomparisons?"

Sarahanswers"Forcomparisons,youneedtobecareful.Youcancomparethetwoprojects'NPVsandchoosethehigherNPVproject.SonoproblemwithcomparingtheNPVs.But,itisriskytocomparetheIRRs.YoucannotdirectlycomparetheIRRsandthenchoosethehigherIRRproject.Sometimes,thehigherIRRprojectis notthehigherNPVproject.Inotherwords,sometimes,NPVchoosesoneprojectandIRRchoosestheotherproject.Ithinkyouneedtoreadmoreaboutthe"mutuallyexclusiveprojects."Searchthewebfor"mutuallyexclusiveprojects"andyouwillunderstandwhyusingIRRcanbeproblematicwhencomparingprojects."

Rashidthanks"O.K.ThankyouSarahforallyouradvice.Now,Ithinkthistaskisnotthatsimple.Ineedtodolotsofreading.Idon'twanttomesseverythingup!"

"Iamsureyoucandothis.Justbecareful.Andbeforeyousubmityourwork,Icanlookatit,ifyou'dlike."

"ThanksSarah.Youhelpedmesomuch!"

NPVandIRR

Torefreshhismemoryoncapitalbudgetingtechniques,Rashidhaslookedatsomefinancial

websites.Hehasfoundexplanationsfor NPVandIRRonthesewebsites.Ononeofthesewebsites(businessdictionary.com),hefindsthefollowingexplanationforNetPresentValue:"Thedifferencebetweenthepresentvalueofthefuturecashflowsfromaninvestmentandtheamountofinvestment.Presentvalueoftheexpectedcashflowsiscomputedbydiscountingthemattherequiredrateofreturn."

Ontheotherhand,Investopedia.comexplainsNPVanditscalculationasfollows:

"NetPresentValue(NPV)is thedifferencebetweenthepresentvalueofcashinflowsandthepresentvalueofcashoutflows.NPVisusedincapitalbudgetingtoanalyzetheprofitabilityofaprojectedinvestmentorproject.TheformulaforcalculatingNPVisasshownbelow:

where

Ct=netcashinflowduringtheperiodt

Co=totalinitialinvestmentcosts

r=discountrate,and

t=numberoftimeperiods

Rashidknows thatapositivenetpresentvalueindicatesthatthepresentvalueofexpectedpositivecashflowsfromtheprojectexceedsthepresentvalueofexpectednegativecashflows(includingtheinitialinvestment)fromtheproject.HeknowsthatifaprojecthasapositiveNPV,itisexpectedtoaddvaluetothecompany.Ontheotherhand,anegativecashflowmeansthattheprojectmakesthecompanytolosevalue.

Rashidhaslearnedfromthesesources(whichincludesthesewebsitesplusthewebsitewww.boundless.comandthe"EssentialsofCorporateFinance"textbook)that"Internalrateofreturn(IRR)"isanothermetriccommonlyusedasan NPValternative.Hehaslearnedthat"thediscountrateofan investmentwhenNPViszeroistheinvestment'sIRR,essentiallyrepresentingtheprojectedpercentagereturnforthatinvestment."

Althoughhenowhasgatheredlotsof informationonthesecapitalbudgetingtechniques,Rashidthinksthathestillneedstoreadmoreonthesetopics.Heisespeciallyinterestedinlearningabouthowtocomparetwoprojects."Welearnedaboutthesemutuallyexclusiveprojects"atschoolbutIforgotwhatwerewedoingwhenchoosingthebestproject.Anyways,IguessIneedmorehelp"hesighs.

TheDecision

Rashidhasrequestedsomehelpinestimatingtheproject'scashflowsfromhisboss.Theexpectedcashflowsfortheprojectisfinalizedasfollows:

ExpectedCFsAssociatedwiththeProject:

tCF

0-$10million

1+$13million

2-$2million

Rashidthinksthatitisasimpletask,soheshouldbedoneverysoonwithhisanalysisandhisfinalreport.Heknowsthattheyhavepreviouslyusedarequiredreturnof10%forinvestmentswithsimilarrisktothisone,sohewantstousethatreturninhiscalculations.

1.First,hewantstousetheIRRmethodtofindtheexpected%returnfromthisinvestment.Whenheentersthecashflowsintohiscalculator,hefindstheIRR.Bylookingatthisnumber,heknowswhetherhiscompanyshouldinvestinthisproject.Justashewaswritinghisreport,herememberedsomethingfromhisundergraduateclass.Maybethedecisionisnotassimpleashethinks.Whatdoyouthink?Shouldhegoaheadandsubmithisfinalreporttohisbossorshouldhecontinueanalyzingthenumbers?

Hint:ThinkabouttheproblemswithIRR.TheIRRmethodisweakinsomecases.

2.WhattypeofproblemsdoestheIRRmethodhaveingeneral?HasRashidencounteredanyoneoftheseproblems?

3.Whenevaluatingaproject,doesNPVandIRRalwaysleadtothesameconclusion(accept,orreject)?Whyorwhynot?

4.Rashiddecidesto draw the NPVProfileforthisproject.AfterdrawingtheNPVProfile,"Ahha"hesaid.HenowseesthatthedecisionherecanbemademoreeasilywiththeNPVProfile.Hefindsthatoveracertainrangeofdiscountrates,theprojectisacceptable.Whatdoyouthinktheacceptablerangeofdiscountratesisforthisproject?

AfterRashidcompletesthetasksuccessfully,hisbossassignedhimasecondtask.Heissayingthatthereisanotherinvestmentopportunity:theymaybuyanindependentlyownedminethatisonsaleinthetargetarearatherthanstartingonethemselves.Hewonderswhatthebestprojectwouldbe:openinganewminethemselvesorpurchasingtheindependentlyownedmine.Theexpectedcashflowsfromtheindependentlyownedmineisasfollows:

tCF

0-$20million

1+$30million

2-$7million

5.Whichmethodcanbeusedtocomparethetwoprojects?ArebothNPVandIRR

applicable?

6.Rashidfiguresoutthebestprojectforhiscompany.Whichprojectdidhechoose?

7.AccordingtoIRR,willRashidalwayschoosethesameproject(eventhoughthediscountrateishigherorlower)?

8.AccordingtoNPV,willRashidalwayschoosethesameproject(eventhoughthediscountrateishigherorlower)?

9.AfterdrawingtheNPVProfiles,Rashidrealizesthatovercertainrangeofdiscountratesthefirstprojectisbetter,otherwisethesecondprojectisbetter.OverwhatrangeofdiscountratesisProject1(i.e.startinganewminingoperation)better?