irr explanations and explorations

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Amortization Table Loan ID: 87023 Original Investment 7500 Term 36 month Paments ma!e monthl "tate! Interest #ate $3%75& 'al()late! *)mbers +onthl Interest #ate $3%75,$2& -inan(ial 'al()lator *)mbers n 36 i 0%0$.5833 P/ 7500%00 -/ 0%00 "olve1or P+T 26 %27 +onth 3 a s e ! o 4 A ( t ) a l P a m e n t s $ 2 3 . 5 6 7 8 $0 $$ $2 $3 $. $5 $6 $7 $8 $ 20 2$ 22 23 2. 25

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Investigations of various cash flow streams and IRRs. Help with understanding what IRR means to an investor, and how to decide between several investments that have the same IRR but different CAGRs

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Sheet1Amortization TableLoan ID: 87023Original Investment7500Term36 monthPayments made monthlyStated Interest Rate13.75%

Calculated NumbersMonthly Interest Rate13.75/12%='0.014583333

Financial Calculator Numbersn36i0.0145833PV-7500.00FV0.00

Solve for PMT269.27vsActual PMT255.43MonthBeginningInterestPaymentPrincipalEndingMonthBeginningInterestPaymentPrincipalEndingBased off Actual Payments17500109.3749975255.43146.05500257353.9449975The Payment Amount That it should have been17500109.3749975269.27159.89049519517340.109504804927353.9449975107.2450287622255.43148.18497123787205.760026262227340.1095048049107.043261165269.27162.22223153017177.887273274837205.7600262622105.0839979811255.43150.34600201897055.414024243337177.8872732748104.6775203426269.27164.58797235257013.299300922347055.4140242433102.8914521684255.43152.53854783166902.875476411747013.2993009223102.277279134269.27166.98821356116846.311087361256902.8754764117100.66693173255.43154.763068276748.112408141856846.311087361299.8420344086269.27169.42345828656676.887629074766748.112408141898.4099703694255.43157.02002963066591.092378511166676.887629074797.3712756984269.27171.89421699676504.99341207876591.092378511196.1200949896255.43159.30990501046431.782473500776504.99341207894.8644850911269.27174.4010076046330.59240447486431.782473500793.7968255946255.43161.63317440546270.149299095386330.59240447492.3211371217269.27176.94435557346153.648048900696270.149299095391.4396751884255.43163.99032481166106.158974283896153.648048900689.7406986619269.27179.52479403325974.1232548674106106.158974283889.0481496729255.43166.38185032715939.7771239567105974.123254867487.1226288088269.27182.14286388635791.980390981115939.777123956786.6217477444255.43168.80825225565770.9688717011115791.98039098184.4663787711269.27184.7991139245607.1812770571125770.968871701184.1599607887255.43171.27003921135599.6988324898125607.181277057181.7713917547269.27187.49410094045419.6871761167135599.698832489881.6622727739255.43173.76772722615425.9311052637135419.687176116779.0371028451269.27190.228389855229.4587862667145425.931105263779.1281601431255.43176.30183985695249.6292654068145229.458786266776.2629388899269.27193.00255380525036.4562324615155249.629265406876.557091704255.43178.8729082965070.7563571108155036.456232461573.4483183779269.27195.81717431724840.6390581443165070.756357110873.9485285176255.43181.48147148244889.2748856284164840.639058144370.5926513177269.27198.67284137744641.9662167669174889.274885628471.3019237857255.43184.12807621434705.146809414174641.966216766967.6953391139269.27201.57015358134440.3960631856184705.14680941468.6167227356255.43186.81327726444518.3335321496184440.396063185664.7557744413269.27204.50971825384235.8863449318194518.333532149665.8923625044255.43189.53763749564328.795894654194235.886344931861.7733411183269.27207.49215157684028.394193355204328.79589465463.1282720208255.43192.30172797924136.4941666748204028.39419335558.747413977269.27210.51807871823817.8761146369214136.494166674860.3238718852255.43195.10612811483941.38803856213817.876114636955.6773587325269.27213.58813396263604.2879806742223941.3880385657.4785742485255.43197.95142575153743.4366128085223604.287980674252.5625318501269.27216.7029608453387.5850198292233743.436612808554.591782689255.43200.8382173113542.5983954975233387.585019829249.40228041269.27219.86321228513167.7218075441243542.598395497551.6628920868255.43203.76710791323338.8312875843243167.721807544146.1959419708269.27223.06955072432944.6522568197253338.831287584348.6912884977255.43206.73871150233132.0925760819252944.652256819742.9428444304269.27226.32264826472718.329608555263132.092576081945.6763490238255.43209.75365097622922.3389251058262718.32960855539.6423058853269.27229.62318680982488.7064217452272922.338925105842.6174416837255.43212.81255831632709.5263667894272488.706421745236.2936344875269.27232.97185820762255.7345635377282709.526366789439.5139252792255.43215.91607472082493.6102920686282255.734563537732.8961282997269.27236.36936439542019.3651991422292493.610292068636.3651492615255.43219.06485073852274.5454413301292019.365199142229.4490751477269.27239.81641754741779.5487815948302274.545441330133.1704535945255.43222.25954640552052.2858949246301779.548781594825.9517524717269.27243.31374022341536.2350413714312052.285894924629.9291686169255.43225.50083138311826.7850635415311536.235041371422.4034271746269.27246.86206552051289.3729758509321826.785063541526.6406149011255.43228.78938509891597.9956784426321289.372975850918.803355468269.27250.46213722711038.9108386238331597.995678442623.3041031113255.43232.12589688871365.8697815539331038.910838623815.150782717269.27254.1147099782784.7961286457341365.869781553919.918933859255.43235.5110661411130.358715412934784.796128645711.4449432812269.27257.820549414526.9755792317351130.358715412916.4843975563255.43238.9456024437891.413112969235526.97557923177.6850603548269.27261.5804323403265.395146891436891.413112969212.999774267255.43242.430225733648.982887236236265.39514689143.8703458037269.27265.39514689140Going with Actual Total Payments made on left, uniform payments on rightnetting LC fees9194.98/36255.4161111111IRR Calculation1.14575174%-7500-7500-75001255.43252.5365579993252.87571255.4161111111252.522826442255.43249.6758921275252.87572255.4161111111249.66231611553255.43246.8476311055252.87573255.4161111111246.83420887894255.43244.0514078599252.87574255.4161111111244.03813767675255.43241.2868594754252.87575255.4161111111241.27373961336255.43238.5536271478252.87576255.4161111111238.5406559047255.43235.8513561373252.87577255.4161111111235.83853182828255.43233.1796957224252.87578255.4161111111233.16701668369255.43230.5382991546252.87579255.4161111111230.525763740510255.43227.9268236132252.875710255.4161111111227.914430196811255.43225.3449301608252.875711255.4161111111225.332677133812255.43222.7922836996252.875712255.4161111111222.780169471613255.43220.2685529276252.875713255.4161111111220.256575926214255.43217.7734102956252.875714255.4161111111217.761568966515255.43215.306531965252.875715255.4161111111215.294824771316255.43212.8675977654252.875716255.4161111111212.856023187517255.43210.4562911531252.875717255.4161111111210.44484768918255.43208.0722991704252.875718255.4161111111208.060985334719255.43205.7153124045252.875719255.4161111111205.704126728920255.43203.3850249477252.875720255.4161111111203.373965980421255.43201.0811343573252.875721255.4161111111201.07020066322255.43198.8033416168252.875722255.4161111111198.792531776423255.43196.5513510968252.875723255.4161111111196.540663707424255.43194.3248705167252.875724255.4161111111194.314304191225255.43192.1236109069252.875725255.4161111111192.113164273826255.43189.947286571252.875726255.4161111111189.936958274527255.43187.7956150489252.875727255.4161111111187.785403748628255.43185.6683170802252.875728255.4161111111185.658221450829255.43183.5651165679252.875729255.4161111111183.555135299130255.43181.4857405426252.875730255.4161111111181.475872338931255.43179.4299191269252.875731255.4161111111179.420162707532255.43177.3973855005252.875732255.4161111111177.387739599233255.43175.3878758657252.875733255.4161111111175.3783392305pmt 35 changed to 256.34 to make paid and p_last match loan history34255.43173.4011294128252.875734255.4161111111173.391700806135256.34172.0476527559253.776635255.4161111111171.427566484836254.02168.5592682007251.479836255.4161111111169.4856813462Sum PMTS9194.9875009194.987499.9170381652irrnetfees1.08702%Annualized IRR0.146493925914.64%0.1385310572

Sheet2-100.002.9229%41.2998984%Data10.001-$70,00010.002$12,00010.003$15,00010.004$18,00010.005$21,00010.006$26,00010.0079%10.00810.00910.001010.001110.001213.728719406613.338844447912.960041350912.591995691412.234401974511.886963380711.549391519811.221406191510.902735152610.593113891310.292285407710141.299898415

Sheet3total_funded3321000.27331%-332100total_paid349158.89698.8555555556term369698.8555555556pmt9698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.85555555569698.8555555556

Sheet4http://www.propertymetrics.com/blog/2014/06/09/what-is-irr/Loan ALoan BLoan CYearcashflowIRR per period (yr)(1+perIRR)^(per)cashflow / (1+perIRR)^(per)Simple ROI (Payments Received/Funded)-1YearcashflowIRR per period (yr)(1+perIRR)^(per)cashflow / (1+perIRR)^(per)Simple ROI (Payments Received/Funded)-1PaymentYearcashflowIRR per period (yr)(1+perIRR)^(per)cashflow / (1+perIRR)^(per)Simple ROI (Payments Received/Funded)-10-10000010%1.00000-100000Payments Received1610510-10000010%1.00000-100000Payments Received14447526379.74807947450-10000010%1.00000-100000Payments Received131898.740397373101.100000Funded1000001150001.1000013636.3523613425Funded100000126379.751.1000023981.5693343442Funded100000201.210000Simple ROI61.0510%2150001.2100012396.6737148461Simple ROI44.4750%226379.751.2100021801.4086414056Simple ROI31.8987%301.3310003150001.3310011269.694058949326379.751.3310019819.4460138549401.4641004150001.4641010245.1679461571426379.751.4641018017.663296768851610511.610511000005844751.6105252452.1119187053526379.751.6105216379.680362851161051044475-0.000000000131898.7403973727-0.2323507754Compound Annual Growth Rate [(Ending Balance/Beginning Balance)^(1/n) -1]10.00%Compound Annual Growth Rate [(Ending Balance/Beginning Balance)^(1/n) -1]7.64%Compound Annual Growth Rate [(Ending Balance/Beginning Balance)^(1/n) -1]5.69%

YearRemaining Outstanding InvestmentIRR (Rate of return earned on each dollar invested per period)IRR*Remaining Outstanding InvestmentPaymentInterest Accrued During YearPortion of Payment Towards PrincipleEnding BalanceYearRemaining Outstanding InvestmentIRR (Rate of return earned on each dollar invested per period)IRR*Remaining Outstanding InvestmentPaymentInterest Accrued During YearPortion of Payment Towards PrincipleEnding BalanceYearRemaining Outstanding InvestmentIRR (Rate of return earned on each dollar invested per period)IRR*Remaining Outstanding InvestmentPaymentInterest Accrued During YearPortion of Payment Towards PrincipleEnding Balance010000010%10000010000-10000110000010000010%10000010000-10000110000010000010%10000010000-10000110000111000010%11000011000-11000121000111000010%110001500095005500104500111000010%1100026379.758362.025192052618017.72288742291982.277112578212100010%12100012100-12100133100210450010%10450150008950605098450291982.27711257810%9198.227711257826379.756560.252903310419819.495176164272162.7819364138313310010%13310013310-1331014641039845010%9845150008345665591795.0000000001372162.781936413810%7216.278193641426379.754578.303385693921801.444693780650361.3372426332414641010%14641014641-14641161051491795.000000000110%9179.5150007679.57320.584474.5000000001450361.337242633210%5036.133724263326379.752398.158916315923981.589163158726379.7480794746516105110%16105.116105101610510584474.500000000110%8447.4584475-0.0584475.05-0.5499999999526379.748079474610%2637.974807947526379.75026379.7480794745077156.100000000158921.950000000145088.61443711If IRR is the same and initial funded amount is the same, shouldn't we be indifferent between Loan A, B, and C? How do we reconcile the loans?

We are indifferent between loans A, B, and C if we reinvest the payments of loans at IRR

YearcashflowIRR per period (yr)Years of reinvestment for payment receivedGrowth Factor (1 + perIRR)^(years of reinvestment)Future Value (yr5) of each paymentYearcashflowIRR per period (yr)Years of reinvestment for payment receivedGrowth Factor (1 + perIRR)^(years of reinvestment)Future Value (yr5) of each paymentYearcashflowIRR per period (yr)Years of reinvestment for payment receivedGrowth Factor (1 + perIRR)^(years of reinvestment)Future Value (yr5) of each payment0-10000010%51.610510-10000010%51.610510-10000010%51.610511041.4641011500041.464121961.5126379.7541.464138622.58916315872031.331021500031.33119965226379.7531.33135111.44469378063021.21031500021.2118150326379.7521.2131919.49517616424011.1041500011.116500426379.7511.129017.7228874225161051011610515844750184475526379.750126379.74807947456105116105144475161051.531898.7403973727161051

Compound Annual Growth Rate [(Ending Balance/Beginning Balance)^(1/n) -1]10.00%Compound Annual Growth Rate [(Ending Balance/Beginning Balance)^(1/n) -1]10.00%Compound Annual Growth Rate [(Ending Balance/Beginning Balance)^(1/n) -1]10.00%