武汉大学公司金融课件(二)

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1、GROWINGPERPETUITY-Anannuityinwhichthecashflowcontinuesforever,butgrowsataconstantrateof“g”peryean-Thestreamofincomelookslike:q(i+£)+Ci(i+d+…d+r)2(1+r)3-Fortunately,thereisaneasierwaytopresentandcalculatethisvalue.PVgrowingperpetuity-Thisisaveryimportantequationintheev

2、aluationofcommonstock.>FVt=PV*(1+r)1>PV=FVt*1d+r)1>pva(m)=C*1-(1/(1+r)v)>FVA(r,t)=C5k(1+r)(・1>PVperpetuity-Cr>PVgrowingperpetuity=°丄_r-gWHATISTHEINTERESTRATE?Yourbankeroffersthefollowing5choices:>7.75%compoundeddaily>7.75%compoundedweekly>7.75%compoundedmonthly>7.75%c

3、ompoundedquarterly8%compoundedannuallyWHICHOPTIONDOYOUPREFER?STATEDorQUOTEDINTERESTRATE-theinterestrateexpressedintermsoftheinterestpaymentmadeeachperiod>■Example:aquotedrateof7.75%peryear,compoundedweekly.■Example:astatedrateof7.75%peryear,compoundedmonthly.EFFECTIVE

4、ANNUALRATE:EAR:theinterestrateexpressedasifitwerecompoundedonceperyeanEAR=(1+QR/m)n,-1Where:QR=quotedrateperyearm=numberoftimescompoundedperyean■Example:aquotedrateof7.75%peryear,compoundedweekly.EAR=(1+.0775/52严一1EAR=(1+.00149)52-1EAR=8.052%EXAMPLEAtthelocalloanshark

5、,youpay$1perweekcompoundedweeklyforevery$100thatyouborrow.Actuallysoundsverylenientdoesiftit?WhatistheEAR?EXAMPLE:Mortgagesarequotedinannualratesbutareusuallycompoundedsemi-annually>WhatistheEARfora9%mortgage?DEFINITIONANNUALPERCENTAGERATE(APR)♦Theinterestratechargedp

6、erperiodmultipliedbythenumberofperiodsperyeanEXAMPLEAcreditcardrequiringmonthlypaymentscarriesanAPRof14.4%andinterestiscalculatedandcompoundedmonthly.WhatistheEAR?EXAMPLE:>Youaretoreceive$1,000permonthfor25years.>Interestiscompoundedmonthly.>Thepresentvalueofthisannui

7、tyis$155,206.86・(I)WHATISTHESTATEDORQUOTEDMONTHLYRATE?(II)WHATISTHEEAR?LOANS&BONDSLOANTYPES❖PureDiscountLoans-e・g.Treasurybills❖Interest-onlyLoans■e.g.securedloansfrombanks❖AmortizedLoansAMORTIZEDLOANS❖Wherethelenderrequirestheborrowertorepaypartsoftheloanamountoverti

8、me.❖TvvoBasicApproaches:•Simplemethod:paytheaccruedinterestplussomeportionoftheprincipaL•Fixedpaymentperperiod,whichisablend