Concepts of Value and Return CHAPTER2LEARNING OBJECTIVESUnderstand what gives money its time value.Explainthemethodsofcalculatingpresentand future values.Highlighttheuseofpresentvaluetechnique (discounting) in financial decisions.Introduce the concept of internal rate of return.2T!e Preference for "one#Timepreferenceformoneyisanindividuals preferenceforpossessionofagivenamountof moneynowratherthanthesameamountatsome future time.!hree reasons may "e attri"uted to the individuals time preference for money# ris$ preference for consumption investment opportunities3Re$ured Rate of Return!hetimepreferenceformoneyisgenerally expressed"yaninterestrate.!hisratewill"e positive even inthe a"sence of any ris$.Itmay "e therefore called the risk-free rate.%ninvestorrequirescompensationforassuming ris$ which is called risk premium. !he investors required rate of return is#Risk-free rate + Risk premium.4Re$ured Rate of Return&ould an investor want 's. ()) today or after one year*+ash flows occurring in different time periods are not compara"le. It is necessary to ad,ust cash flowsfor their differences in timing and ris$. Example # If preference rate -() percent %n investor can invest if 's. ()) if he is offered 's (() after one year. 's (() is the future value of 's ()) today at (). interest rate. %lso 's ()) today is the present value of 's (() after a year at (). interest rate.If the investor gets less than's. (() then he will notinvest. %nythinga"ove 's. (() is favoura"le. 5T!e Value Ad%ust!ent!womostcommonmethodsofad,ustingcash flows for time value of money# Compounding/theprocessofcalculatingfuturevalues of cash flows and Discounting/the process of calculating present values of cash flows. 6&uture ValueCompoundingistheprocessoffindingthefuturevaluesof cash flows "y applying the concept of compound interest.Compoundinterestistheinterestthatisreceivedonthe originalamount(principal)aswellasonanyinterestearned "ut not withdrawn during earlier periods.Simpleinterestistheinterestthatiscalculatedonlyonthe originalamount(principal)andthusnocompoundingof interest ta$es place. 7&uture Value8&uture ValueIn 0icrosoft Excel# Use 12 function. 12(ratenperpmtpvtype)&here#rate-interestrate.nper-nperiods pmt-annuityvaluepv-presentvaluetype- ( for "eginning of the period and ) for end for end of period.9&uture Value' E(a!ple10&uture Value of an Annut#11&uture Value of an Annut#' E(a!ple12Sn)n* &und13E(a!plePresent ValuePresentvalueofafuturecashflow(inflowor outflow)istheamountofcurrentcashthatisof equivalent value to the decision3ma$er. Discountingistheprocessofdeterminingpresent value of a series of future cash flows. !he interest rate used for discounting cash flows is also called the discount rate.15Present Value of a Sn*le Cas+ &lo,16E(a!ple17Present Value of an Annut#18E(a!ple19Captal Reco-er# and Loan A!ortsaton20Loan A!ortsaton Sc+edule21Present Value of an .ne-en Perodc Su!Inmostinstancesthefirmreceivesastreamof unevencashflows.!husthepresentvaluefactors for an annuity cannot "e used.!heprocedureistocalculatethepresentvalueof each cash flow and aggregate all present values. 22PV of .ne-en Cas+ &lo,s' E(a!ple23Present Value of Perpetut#24Present Value of a Perpetut#' E(a!ple25Present Value of Gro,n* Annutes26E(a!ple27E(a!ple28Value of an Annut# /ue29&uture Value of An Annut#' E(a!ple30E(a!ple!he present value of 'e ( paid at the "eginning of each year for 4 years is ( 5 6.(7) 5 (.() - 's 6.48731"ult0Perod Co!poundn*32E1ect-e Interest Rate' E(a!ple33Contnuous Co!poundn*34Net Present Value35Present Value and Rate of Return %"ondthatpayssomespecifiedamountinfuture(without periodicinterest)inexchangeforthecurrentpricetodayis called a zero-interest ond or zero-coupon ond. In such situations one would "e interested to $now what rate ofinteresttheadvertiserisoffering.9necanuse theconcept ofpresentvaluetofindouttherateofreturnoryieldof these offers.!herateofreturnofaninvestmentiscalledinternalrateof returnsinceitdependsexclusivelyonthecashflowsofthe investment. 36Internal Rate of Return 37IRR Calculaton' E(a!ple of Tral0Error "et+od38