CF2-Ch-02-Time-Value-of-Money-公司财务与金融-课件.ppt
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- CF2 Ch 02 Time Value of Money 公司财务 金融 课件
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1、1Chapter 2Time Value of Money2Time Value TopicsnFuture valuenPresent valuenRates of returnnAmortization3Time lines show timing of cash flows.CF0CF1CF3CF20123i%Tick marks at ends of periods,so Time 0 is today;Time 1 is the end of Period 1;or the beginning of Period 2.4Time line for a$100 lump sum due
2、 at the end of Year 2.100012 Yeari%5Time line for an ordinary annuity of$100 for 3 years1001001000123i%6Time line for uneven CFs100 50 750123i%-507FV of an initial$100 after3 years(i=10%)FV=?012310%Finding FVs(moving to the righton a time line)is called compounding.1008After 1 yearFV1=PV+INT1=PV+PV(
3、i)=PV(1+i)=$100(1.10)=$110.00.9After 2 yearsFV2=FV1(1+i)=PV(1+i)(1+i)=PV(1+i)2=$100(1.10)2=$121.00.10After 3 yearsFV3=FV2(1+i)=PV(1+i)2(1+i)=PV(1+i)3=$100(1.10)3=$133.10In general,FVn=PV(1+i)n.11Three Ways to Find FVsnSolve the equation with a regular calculator.nUse a financial calculator.nUse a sp
4、readsheet.12Financial calculator:HP10BIInAdjust display brightness:hold down ON and push+or-.nSet number of decimal places to display:Orange Shift key,then DISP key(in orange),then desired decimal places(e.g.,3).nTo temporarily show all digits,hit Orange Shift key,then DISP,then=13HP10BII(Continued)
5、nTo permanently show all digits,hit ORANGE shift,then DISP,then.(period key)nSet decimal mode:Hit ORANGE shift,then./,key.Note:many non-US countries reverse the US use of decimals and commas when writing a number.14HP10BII:Set Time Value ParametersnTo set END(for cash flows occurring at the end of t
6、he year),hit ORANGE shift key,then BEG/END.nTo set 1 payment per period,hit 1,then ORANGE shift key,then P/YR15Financial calculators solve this equation:FVn+PV(1+i)n=0.There are 4 variables.If 3 are known,the calculator will solve for the 4th.Financial Calculator Solution16310-100 0NI/YR PV PMTFV 13
7、3.10Clearing automatically sets everything to 0,but for safety enter PMT=0.Set:P/YR=1,END.INPUTSOUTPUTHeres the setup to find FV17Spreadsheet SolutionnUse the FV function:see spreadsheet in“CF2 Ch 02 Mini Case.xls”n=FV(Rate,Nper,Pmt,PV)n=FV(0.10,3,0,-100)=133.101810%Whats the PV of$100 due in 3 year
8、s if i=10%?Finding PVs is discounting,and its the reverse of compounding.1000123PV=?19Solve FVn=PV(1+i)n for PVPV=FVn(1+i)n=FVn()11+in PV=$10011.10 =$100 0.7513 =$75.13.3203 10 0100N I/YR PV PMTFV -75.13Either PV or FV must be negative.HerePV=-75.13.Put in$75.13 today,take out$100 after 3 years.INPU
9、TSOUTPUTFinancial Calculator Solution21Spreadsheet SolutionnUse the PV function:see spreadsheet in“CF2 Ch 02 Mini Case.xls”n=PV(Rate,Nper,Pmt,FVn=PV(0.10,3,0,100)=-75.132220%2012?-1 FV=PV(1+i)n Continued on next slideFinding the Time to Double23Time to Double(Continued)$2=$1(1+0.20)n (1.2)n=$2/$1=2n
10、LN(1.2)=LN(2)n=LN(2)/LN(1.2)n=0.693/0.182=3.8.24 20 -1 0 2NI/YR PV PMTFV 3.8INPUTSOUTPUTFinancial Calculator Solution25Spreadsheet SolutionnUse the NPER function:see spreadsheet in“CF2 Ch 02 Mini Case.xls”n=NPER(Rate,Pmt,PV,FV)n=NPER(0.10,0,-1,2)=3.826?%20123-1 FV=PV(1+i)n$2=$1(1+i)3 (2)(1/3)=(1+i)1
11、.2599=(1+i)i=0.2599=25.99%.Finding the Interest Rate273 -1 0 2NI/YR PV PMTFV25.99INPUTSOUTPUTFinancial Calculator28Spreadsheet SolutionnUse the RATE function:n=RATE(Nper,Pmt,PV,FV)n=RATE(3,0,-1,2)=0.259929Ordinary AnnuityPMTPMTPMT0123i%PMTPMT0123i%PMTAnnuity DueOrdinary Annuity vs.Annuity Due30Whats
12、 the FV of a 3-year ordinary annuity of$100 at 10%?100100100012310%110 121FV=33131FV Annuity FormulanThe future value of an annuity with n periods and an interest rate of i can be found with the following formula:=PMT(1+i)n-1i=100(1+0.10)3-10.10=33132Financial Calculator Formula for AnnuitiesnFinanc
13、ial calculators solve this equation:FVn+PV(1+i)n+PMT(1+i)n-1i=0.There are 5 variables.If 4 are known,the calculator will solve for the 5th.333 10 0 -100 331.00NI/YRPVPMTFVHave payments but no lump sum PV,so enter 0 for present value.INPUTSOUTPUTFinancial Calculator Solution34Spreadsheet SolutionnUse
14、 the FV function:see spreadsheet.n=FV(Rate,Nper,Pmt,Pv)n=FV(0.10,3,-100,0)=331.0035Whats the PV of this ordinary annuity?100100100012310%90.9182.64 75.13248.69 =PV36PV Annuity FormulanThe present value of an annuity with n periods and an interest rate of i can be found with the following formula:=PM
15、T1-1(1+i)ni=1001-1(1+0.10)30.10=248.6937Have payments but no lump sum FV,so enter 0 for future value.3 10 100 0NI/YRPVPMTFV-248.69INPUTSOUTPUTFinancial Calculator Solution38Spreadsheet SolutionnUse the PV function:see spreadsheet.n=PV(Rate,Nper,Pmt,Fv)n=PV(0.10,3,100,0)=-248.6939Find the FV and PV i
16、f theannuity were an annuity due.100100012310%10040PV and FV of Annuity Due vs.Ordinary AnnuitynPV of annuity due:n=(PV of ordinary annuity)(1+i)n=(248.69)(1+0.10)=273.56nFV of annuity due:n=(FV of ordinary annuity)(1+i)n=(331.00)(1+0.10)=364.141310 100 0 -273.55 NI/YRPVPMTFVINPUTSOUTPUTPV of Annuit
17、y Due:Switch from“End”to“Begin42310 0 100 -364.1 NI/YRPVPMTFVINPUTSOUTPUTFV of Annuity Due:Switch from“End”to“Begin43Excel Function for Annuities DuenChange the formula to:n=PV(10%,3,-100,0,1)nThe fourth term,0,tells the function there are no other cash flows.The fifth term tells the function that i
18、t is an annuity due.A similar function gives the future value of an annuity due:n=FV(10%,3,-100,0,1)44What is the PV of this uneven cash flow stream?010013002300310%-504 90.91247.93225.39-34.15530.08 =PV45Financial calculator:HP10BIInClear all:Orange Shift key,then C All key(in orange).nEnter number
19、,then hit the CFj key.nRepeat for all cash flows,in order.nTo find NPV:Enter interest rate(I/YR).Then Orange Shift key,then NPV key(in orange).46Financial calculator:HP10BII(more)nTo see current cash flow in list,hit RCL CFj CFjnTo see previous CF,hit RCL CFj nTo see subsequent CF,hit RCL CFj+nTo se
20、e CF 0-9,hit RCL CFj 1(to see CF 1).To see CF 10-14,hit RCL CFj.(period)1(to see CF 11).47nInput in“CFLO”register:nCF0 =0nCF1 =100nCF2 =300nCF3 =300nCF4 =-50nEnter I=10%,then press NPV button to get NPV=530.09.(Here NPV=PV.)48Excel Formula in cell A3:=NPV(10%,B2:E2)ABCDE1012342100300300-503530.0949N
21、ominal rate(iNom)nStated in contracts,and quoted by banks and brokers.nNot used in calculations or shown on time linesnPeriods per year(m)must be given.nExamples:n8%;Quarterlyn8%,Daily interest(365 days)50Periodic rate(iPer)niPer=iNom/m,where m is number of compounding periods per year.m=4 for quart
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