FV*

Excel -FVExcelFVExcelFV (Future Value)Excel FV*

Future Value (FV)100100100

*

ExcelFV(pv)(pmt)1003%31002%20

*

(pv)(rate)(nper)(FV)FV = pv*(1+ rate)nper

*

*

10,00010%6 pv = 10000nper = 6rate = 10% fv = 10000*(1+10%)6 Excel=10000*(1+10%)^6 = 17,716*

(nper)(pmt)(rate)pmt-*

*

1000610% pmt = 1000nper = 6rate = 10% fv = 1000*((1+10%)6-1)/10% Excel=1000*((1+10%)^6-1)/10% = 7,716*

(1+rate)

*

*

1000610% pmt = 1000nper = 6rate = 10% fv = 1000*(1+10%)*((1+10%)6-1)/10% Excel=1000*(1+10%)*((1+10%)^6-1)/10% = 8,487*

ExcelFVExcel FVExcelFV

*

FVFV =FV(rate, nper, pmt, pv, type)ratenperpvpmttype() rate nperpmtpvtypeFVpv = 0; type = 0()*

*

ratenperpmtpvtype 0() 1

pvpmtFV(pv)(pmt)pvpmt()()

*

()()()()()()*

FVFV~~~FV(pv)(pmt)(pv) + (pmt) + FV = 0

*

(pmt)(pv) + FV = 0FV = - (pv)

*

pvFV100(pv=-100)10%3 = -100*(1+10%)^3 = -133.1FV = -(-133.1) = 133.11003133.1(pv)100(FV)133.1

*

(pv)(pmt) + FV = 0FV = - (pmt)(pv) + (pmt) + FV = 0FV = - ((pv) + (pmt))*

pvpmtpvpmt()FV()pvpmtFVpvpmt(pv)(pmt)FV 0(pv)(pmt)*

ExcelFVExcel

*

James1010%2James=FV(10%, 2, 0, 100000) = -121,000James10Jamespv = 100,000-121,000James()121,000

*

*

Lisa2%=FV(2%/12, 12, -10000, 0 , 1) = 121,308Lisa10,000( pmt = -10,000)(type = 1)(FV)121,308()

*

*

Michael3520030200305%60=FV(5%, 25, -300000, -2000000) = 21,090,840(pv)(pmt)200(pv=-2,000,000)(type = 0)30(pmt = -300,000)21,090,840*

*

Peter1001010%13,215.0745=FV(10%/12, 12*5, -13215.074,1000000) = -621,972(pv)(pmt)pvpmtPeter100(pv = 1,000,000)13,215.074(pmt = -13,215.074)5pvpmt-62,1972621,972nper5(12*5)10(12*10)FV0 =FV(10%/12, 12*10, -13215.074,1000000) = 0

*

*

ExcelExcelFV(pv)(pmt)(1+rate*type)FV*

*

FV(FVIFFVIFA)Excel FVFV*

Excel FVFVIF(r, n)=FV(rate, nper, 0, -1) FVIFA(r, n)=FV(rate, nper, -1) FVIFA(r, n)

ExcelFV(5%)ExcelFV*

PV*

Excel -PVExcelPVExcelPV (Present Value)Excel PV*

Present Value (PV)(Discount)5%510078.478.45%5100510078.4*

ExcelPV51003%4%3*

(fv)(rate)(nper)(PV)PV = fv / (1+ rate)nper

*

*

10%617,716 fv = 17716nper = 6rate = 10% pv = 17716/(1+10%)6 Excel=17716/(1+10%)^6 = 10,000*

(nper)(pmt)(rate)pmt

(nper)(pmt)(rate)pmt *

*

PeterJason100061%JasonPeter pmt = 1000nper = 6rate = 1%type =1 pv = 1000*(1+1%)*(1-1/(1+1%)6)/1% Excel=1000*(1+1%)*(1-1/(1+1%)^6)/1% = 5,853*

ExcelPVExcelPV*

PVPV =PV(rate, nper, pmt, fv, type)ratenperfvpmttype() rate nperpmtfvtypePVfv = 0; type = 0()

*

PV =PV(rate, nper, pmt, fv, type)ratenperfvpmttype() rate nperpmtfvtypePVfv = 0; type = 0()*

*

ratenperpmtfvtype 0() 1

fvpmtPV(fv)(pmt)fvpmt

*

()()()()()()()()*

PVPV~~~PV(fv)+ (pmt) + PV = 0

*

(pmt=0)(fv) + PV = 0PV = - (fv)fvPV*

100(fv=-100)310%PV = -(-100/(1+10%)^3) = 75.175.13100(PV)75.1(fv)100 fv=0 (pmt)(pmt) + PV = 0PV = - (pmt)(fv) + (pmt) + PV = 0PV = - ((fv) + (pmt))

*

fvpmtfvpmt()PV()fvpmtPVfvpmtPVfvpmtPV 0*

ExcelPVExcel*

*

Lisa2%Lisa=PV(2%/12, 12, -10000) = 118,710Lisa10,000( pmt = -10,000)(PV)118,710()

*

*

Michael3560305%2000Michael=PV(5%, 25, -300000, 20000000) = -1,677,872(fv)(pmt)2000(fv=20,000,000)(type = 0)30(pmt = -300,000)-1,677,8721,677,872

*

3050 =PV(5%, 25, -500000, 20000000) = 1,140,917 30(pmt = -300,000)16850(pmt = -500,000)114PV=0pmt30~50-419,049*

*

Peter1010%13,215.075621,972Perter=PV(10%/12, 12*5, -13215.07, -621972) = 1,000,000(fv)(pmt)fvpmtPeter13,125.07(pmt = -13215.07)562(fv = -621972)1,000,000

*

ExcelPVratenperpmtfvtypePV*

PV(PVIFPVIFA)Excel PVPV*

Excel PVPVIF(r, n)=PV(rate, nper, 0, -1) PVIFA(r, n)=PV(rate, nper, -1) PVIFA(r, n)=PV(rate, nper, -1, 0, 1)

ExcelPV(5%)ExcelPV-

*

PMT*

Excel-PMTPMTExcelPMT--*

PMTExcelPV()PMT()FV()RATE()NPER(()*

*

NPERRATEPV()PMT()FV()RATEPVRATENPERPVPMTFV*

PVPMTFVRATENPER*

PVPMTFV

()*

*

PVPMTPVPMTPVPMTPVPMT*

*

PVPMTPVPMTFVPVPMTFVPVPMT*

*

Excel PMTRATENPERPVFVPMT*

PMTPMT =PMT(rate, nper, pv, fv, type) rate nperpvfvtypetype()PMTfv = 0; type = 0()

*

ratenperpvfvtype 0() 1

Jeff5603%PV=0NPER =12*5rate = 3%/12FV =600,000 =PMT(3%/12, 12*5, 0, 600000) =-9,281

*

9,281*

Susan1005%20240(NPER=240)=5%/12Susan100(PV=1,000,000)(FV=0)=PMT(5%/12,240,1000000) =-6,600

*

6,600*

2Susan1005%3(36)905,717Susan36(NPER=36)=5%/12Susan100(PV=1,000,000)905,717(FV=-905,717)=PMT(5%/12,36,1000000,-905717) =-6,600

*

Suan6,600*

Peter200151500Peter8%200(PV=-2,000,000)15(NPER=15)8%(RATE=8%)151500(FV=15,000,000)=PMT(8%,15,-2000000,15000000) =-318,784

*

31.8152001,500*

RATE*

Excel-RATE100206,600320%Excel*

RATERATERATEExcelPV()PMT()FV()RATE()NPER(()*

*

NPERRATEPV()PMT()FV()RATEPVRATENPERPVPMTFV*

PVPMTFVRATENPER*

PVPMTFV

*

()*

*

PVPMTPVPMTPVPMTPVPMT*

*

PVPMTPVPMTFVPVPMTFVPVPMT*

*

Excel RATERATE(NPER)PVPMTFV*

*

RATERATE =RATE(nper, pmt, pv, fv, type, guess) nperpmtpv3fvtypeguess

*

*

nperpmtpvfvtype 0() 1 guess

type()RATE type = 0()fv( = 0)guess

*

guessRATEExcelRATEPVPMTFVNPERRATEExcelrate(10%)rate 0.00001 20RATE #NUM! guess

*

guessRATERATEguess4.14% =RATE(10, 0, -100000, 150000, 0, 10%) =RATE(10, 0, -100000, 150000, 0, 8%) =RATE(10, 0, -100000, 150000, 0, 4%)*

()Peter101015PV=-100,000NPER =10PMT=0FV =150,000 =RATE(10, 0, -100000, 150000, 0, 10%) = 4.14%

*

*

()Peter10102,00065PV=-100,000PMT=-2,000NPER =120FV =650,000 =RATE(120, -2000, -100000, 650000, 0, 1%)*12 = 9.4%RATE12

*

*

Susan100206,600240(NPER =240)100(PV=1,000,000)6,600(PMT=-6,600)(FV = 0) =RATE(240, -6600, 1000000, 0, 0, 1%)*12 = 5.0%

*

*

NPER*

Excel-NPERExcelNPER (Number of Period)*

NPERNPERNPERExcelPV()PMT()FV()RATE()NPER(()*

*

NPERRATEPV()PMT()FV()RATEPVRATENPERPVPMTFV*

PVPMTFVRATENPER*

PVPMTFV

*

()*

*

PVPMTPVPMTPVPMTPVPMT*

*

PVPMTPVPMTFVPVPMTFVPVPMT*

*

Excel NPERNPER(RATE)PVPMTFV*

*

NPERNPER =NPER(rate, pmt, pv, fv, type) ratepmtpv2fvtype*

type()NPER type = 0()fv( = 0)*

ratepmtpvfvtype 0() 1

Queena3002.2%30,000PV=3,000,000RATE =2.2%/12PMT=-30000FV = 0 =NPER(2.2%/12, -30000, 3000000, 0) = 110.6110*

*

Pete30200308%1,500PV=-2,000,000PMT=-300,000RATE =8%FV =15,000,000 =NPER(8%, -300000, -2000000, 15000000) =15.4~~~Peter1545

*

*

Susan1003%205,5465803,088Susan30Susan503,088(PV=803,088-300,000)3%(RATE=3%/12)5,546(PMT=-5,546)(FV = 0) =NPER(3%/12, -5546, 803088-300000) =103103

*

*

IRRXIRRMIRR*

Excel -IRRXIRRMIRRIRR(Internal Rate of Return)ExcelIRR IRRXIRRMIRR*

(Cash Flow)IRR*

IRRIRR*

rate(NPV)C0C1C2C3...Cnn0 = C0 + C1/(1+rate)1 + C2/(1+rate)2 + C3/(1+rate)3....+ Cn/(1+rate)nraterate

*

IRR=IRR(Values, guess)

*

ValuesguessIRR

IRRValuesIRRValue=IRR({-100, 7, 107})=IRR(B2:B4)

*

=IRR({-100, 7, 107}) =IRR(B2:B4) 7%*

IRR{-100, 7, 107}30()1001721070IRRIRR12*

100172107{-100, 7, 107}=IRR({-100, 7, 107}) = 7%*

100172107{-100, 7, 107}IRR 7%1284%IRR*

guess-guessIRRExcelIRRIRR{-100, -102, -104, -106, 450}rate0 = -100 -102/(1+rate)1 -104/(1+rate)2 -106/(1+rate)3 + 450/(1+rate)4*

4Excelrate(10%)rate 0.00001 20IRR #NUM! guess *

guessIRRIRRguess3.60% =IRR({-100, -102, -104, -106, 450}) =IRR({-100, -102, -104, -106, 450}, 1%) =IRR({-100, -102, -104, -106, 450}, 2%)*

guessguessExcel10%1%*

XIRRIRR

XIRRIRRXIRR*

2007/8/15-100,0002007/11/623,6502008/3/425,0002009/6/882,500

XIRRXIRR(values, dates, guess)

*

ValuesdatesguessXIRR

IRR(dates)(dates)(Value)B7 =XIRR(A2:A5,B2:B5)24.56%

*

XIRR#NAME? 1) / 2) 3)

*

MIRRMIRRMIRR(values, finance_rate, reinvest_rate)

*

valuesfinance_ratereinvest_rate

MIRRModified Internal Rate of ReturnIRRIRRIRRIRRMIRRFVPVMIRR=(FV/PV)1/n - 1

*

*

{-10000, 500, 500, 10500}10,00015002500310500IRR=IRR({-10000, 500, 500, 10500}) = 5%

*

10,0005%5003100005%5002%2%3= 500*(1+2%) + 500*(1+2%)2 +10500 ( Excel =500*(1+2%)+500*(1+2%)^2 + 10500 ) = 11,530

*

10,000311,530 = (11530/10000)1/3-1 (Excel =(11530/10000)^(1/3)-1 ) = 4.86% 10,0004.86%311,530MIRR2% = MIRR(({-10000, 500, 500, 10500}), 0, 2%) = 4.86%

*

*

()4% = MIRR(({-10000, 500, 500, 10500}), 0, 4%) = 4.95%5% = MIRR(({-10000, 500, 500, 10500}), 0, 5%) = 5.00%5%MIRR = IRR = 5%IRR

*

0()(PV)PV530,0003%5%MIRR= MIRR({-50000, -50000, 30000, 30000, 30000, 30000}, 5%, 3%) = 5.15%MIRRMIRR

*

*

()25%(PV) =50000 + 50000/(1+5%) =97,619 5%97,61954()3%(FV) = 30000 + 30000*(1+3%) + 30000*(1+3%)^2 + 30000*(1+3%)^3 =125,508 *

97,619125,5085 = (125508/97619)^(1/5)-1 = 5.15%MIRR5.15%(finance_rate)

*

*

Excel2096%ExcelExcelFVPVRATEPMTNPER *

*

*

Excel*

(TYPE) *

Excel(PV)()()(PV)(FV)

*

(PV)PMT(FV)(PV)PV() *

(RATE)(NPER) (RATE) (RATE)(/ 12)

*

2.26%12NPER =12RATE = 2.26% / 12 1,000,0002.26%$1,022,600$1,022,836()122.26% / 12 = 0.1883% =FV(2.26%/12, 12, 0, -1000000) = $1,022,836

*

*

FV()=FV(rate, nper, pmt, [pv], [type])PV=PV(rate, nper, pmt, [fv], [type])RATE=RATE(nper, pmt, pv, [fv], [type], [guess])PMT=PMT(rate, nper, pv, [fv], [type])NPER=NPER(rate, pmt, pv, [fv], [type])

RATEPVPMTNPERFV Excel Excel5(FV)(PV)(RATE)(PMT)(NPER)

*

Future Value(FV)RATENPERPVPMTFV =FV(rate, nper, pmt, [pv], [type]) Excel-FV*

5% RATE = 5% / 12 ( = / 12) NPER = 6(6) PMT = 0 (0) PV = -1,000,000() =FV(5%/12, 6, 0, -1000000) = $1,025,262 $1,025,262

*

4.5%(12) RATE = 4.5% / 12 ( = / 12) NPER = 12(12) PMT = -10,000() PV = 0 () =FV(4.5%/12, 12, -10000, 0, 1) = $122,966 $122,966

*

37606%RATE = 6%/12( = / 12) NPER = 12*(60-37)( 276) PMT = -30,000(3) PV = -2,000,000(200) =FV(6%/12, 12*(60-37), -30000, -2000000, 1) = $25,778,895

*

8%6%8% =FV(8%/12, 12*(60-37), -30000, -2000000, 1) = $36,336,094

*

Present Value (PV) RATENPERFVPMTPV =PV(rate, nper, pmt, [fv], [type]) Excel-PV

*

2% RATE = 2%(2%) NPER = 5(5) PAYMENT = 0(0) FV = 2,000,000()=PV(2%, 5, 0, 2000000) = -1,811,461 1,811,461 181200

*

5% RATE:= 5% / 2(2) NPER = 7 () PAYMENT = 30,000() FV = 1,000,000() =PV(5%/2, 7, 30000, 1000000) = -1,031,747 -1,031,747

*

(RATE) NPERPMTPVFVRATE =RATE(nper, pmt, pv, [fv], [type], [guess])

*

802060336$19,360NPER = 36 (36) PMT= -$19,360(19,360) PV = 600,000(60) =RATE(36, -19360, 600000) = 0.83324094142316% 1210.00%

*

I 10522 NPER = 5(5) PMT = 0(0) PV = -$100,000(10) FV = $220,000(22) =RATE(5, 0, -100000, 220000) = 17.08% 17.08%

*

II 1580NPER = 5*12(60) PMT = -10,000(10,000) PV = 0() FV = $800,000(80) =RATE(5*12, -10000, 0, 800000,1)*12 = 10.89%10.89% (RATE12)

*

PAYMENT (PMT) PVRATENPERFVPMT =PMT(rate, nper, pv, [fv], [type])

*

3503.5%20 RATE = 3.5%/12( = / 12) NPER = 20*12(20*12 = 240) PV = $3,500,000(350) =PMT(3.5%/12, 20*12, 3500000) = -$20,299 $20,299 ()

*

2001510006%RATE = 6%/12( = / 12) NPER = 15*12(15*12 = 180) PV = -$2,000,000(200) FV = $10,000,000(1000)=PMT(6%/12, 15*12, -2000000, 10000000) = -17,509

*

17,509 20 =PMT(6%/12, 20*12, -2000000, 10000000) = -7,314

*

(NPER) RATEPMTPVFV =NPER(rate, pmt, pv, [fv], [type])

*

20010006%RATE = 6%/12( = / 12) PMT = -50,000(5) PV = $-2,000,000(200) FV = $10,000,000(1000) =NPER(6%/12, -50000, -2000000, 10000000) = 103 128.5

*

*

Excel-(PMT/IPMT/PPMT/CUMIPMT/CUMPRINC)ExcelPMTIPMTPPMTCUMIPMTCUMPRINC

*

PMT(+)IPMTnPPMTnCUMIPMT(m~n)CUMPRINC(m~n)

306.5%24(2)24(13,364)

*

*

PMTPMT PMTPMT(rate,nper,pv, fv, type)

*

rate6.5% / 12nper24pv300000fv(0)type(?)

PMTfvtype=pmt(6.5%/12, 24, 300000) = -13,364 ()12rate6.5%/12

*

PMT(B4)

*

*

=300000*(6.5%/12) = 1,625=13364-1625=11,739=300000-11739=288,261 =288261*(6.5%/12) = 1,561=13364-1561=11,802=288261-11802=276,459 ... ()

*

(B31)*

IPMTPPMTExcelIPMTPPMTIPMTPPMTIPMT(rate, per, nper, pv, fv, type) PPMT(rate, per, nper, pv, fv, type)PMTper4IPMT =IPMT(6.5%/12, 4, 24, 300000) = -1,433 D11

*

*PPMT4 =PPMT(6.5%/12, 4, 24, 300000) = -11,931 C11

*IPMTPPMTExcelIPMTPPMT

CUMIPMTCUMPRINCExcelCUMIPMTCUMPRINCCUMIPMT(rate,nper,pv,start_period,end_period,type) CUMPRINC(rate,nper,pv,start_period,end_period,type)rate, nper, pv, typestart_peridoend_perido

*

*

ratenperpvpvstart_periodend_periodtype0 10

#NAME? 1) / 2) 3)

*

266.5%/12243000002~6 =CUMIPMT(6.5%/12, 24, 300000, 2, 6, 0) = -7,164 () 2~67,164()*

*266.5%/12243000002~6 =CUMPRINC(6.5%/12, 24, 300000, 2, 6, 0) = -59,655 () 2~659,655()

nExcelCUMPRINC101~1010 =300000 + CUMPRINC(6.5%/12, 24, 300000, 1, 10, 0) --------CUMPRINC =179,708*

= * - 13363.875430053424 =24*13363.8754300534 = 320,733 3020,733CUMIPMT124 =CUMIPMT(6.5%/12, 24, 300000, 1, 24, 0) = -20,733 *

*