公司金融课件3tvalueii

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1、Homework:(1)Read:P88-91(2)Exercise:>Youaretoreceive$l，000permonthfor25years.>Interestiscompoundedmonthly.>Thepresentvalueofthisannuityis$155,206・86・(I)WHATISTHESTATEDORQUOTEDMONTHLYRATE?(II)WHATISTHEEAR?EXAMPLE1Apreferredstockhasa$7.50dividendinperpetuityandtheinterestrate

2、is6・9%・Whatisthevalueofthepreferredstock?PVperpetuity=C/r=7.50/.069Priceofthepreferredstock=$108.70GROWINGPERPETUITY-Anannuityinwhichthecashflowcontinuesforever^butgrowsataconstantrateof“g”peryean-Thestreamofincomelookslike:+C

3、(l+g)2+・••(1+r)3-Fortunately^thereisaneasierwa

4、ytopresentandcalculatethisvalue.PVgrowingperpetuityr-g>FVt=PV*PV=FVt*(l+r)1>PVA©)二C*1一(1/(1+r)t)>FVA(r,t)=C*(l+r)t・1PVperpetuityPVgrowingperpetuityr-gWHATISTHEINTERESTRATE?Youwillsoonbeborrowingalargesumtostartyourownbusiness.Youneedtogetthelowestpossiblerate.Yourbankeroff

5、ersthefollowing5choices:>7.75%compoundeddaily>7.75%compoundedweekly>7.75%compoundedmonthly>7.75%compoundedquarterly>8%compoundedannuallyWHICHOPTIONDOYOUPREFER?STATEDorQUOTEDINTERESTRATE-theinterestrateexpressedintermsoftheinterestpaymentmadeeachperiodsEFFECTIVEANNUALRATE:E

6、AR:theinterestrateexpressedasifitwerecompoundedonceperyear.EAR=(1+QR/m)m一1Where:QR=quotedrateperyearm=numberoftimescompoundedperyeanYourbankeroffers5choices:>7.75%compoundeddaily=8.057>7.75%compoundedweekly=8.052>7.75%compoundedmonthly=8.031>7.75%compoundedquarterly=7.978>

7、8%compoundedannually=8.0Example2Atthelocalloanshark，youpay$1perweekcompoundedweeklyforevery$100thatyouborrow.Actuallysoundsverylenientdoesn^tit?WhatistheEAR?Mortgagesarequotedinannualratesbutareusuallycompoundedsemi-annually>WhatistheEARfora9%mortgage?EAR=(1+.09/2)2_i=(1.0

8、45)2-1EAR=.09203=9.203%Sincemortgagesareusuallypaidmonthly，giventhisEAR,whatisthestatedmonthlyrate?EAR=(1+QR/m)m-11.09203=(1+QR/m)121.092031712=14-QR/mQR/m=.00736=0.736%Aquotedrateof0.736%permonthresultsinanEARof9.203%peryear.ANNUALPERCENTAGERATE(APR)♦Theinterestratecharge

9、dperperiodmultipliedbythenumberofperiodsperyeanEXAMPLE3Acreditcardrequiringmonthlypayment