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HP12cCalculatorSkillsforRealEstateSelfStudyGuide/CertificationTestPreparation
GetREFM.com
Copyright2013byRealEstateFinancialModeling,LLC.Allrightsreserved.
HewlettPackard,HPandHP12caretrademarksofHewlettPackardDevelopmentCompanyL.P.
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Overview.TheHewlettPackard HP12c is themostwidelyused financial
calculator
inrealestate.Youwillseeitinmeetings,boardroomsandonfinancialanalystbullpendesks.Topcommercialrealestatefinanceprofessionalshaveswornbyitsinceitsintroductionin1981(beforeExcelevenexisted!).Unfortunately,whiletheHP12cispowerful,usingitisnot
thatstraightforward in that thekeystrokesall seemtobe
totallybackwardsvs.whatyourintuitionwouldtellyoutodo.This guide
will teach you in plain English the skills and steps critical to
successfullyleveragetheHP12cforyourrealestateanalyses.Enjoy!TheREFMTeamQuestionsorcomments?Emailfaq@GetREFM.com
Provewhatyouvelearned!TaketheHP12cSkillsCertificationTest!
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TableOfContents
OverviewofHP12cCalculatorKeys 41.FinancialRegisters
52.SimpleInterestOnA360Or365DayBasis 63.CompoundInterest
74.PeriodicandAnnualInterestRates
105.NominalInterestRateConversiontoEffectiveInterestRate
116.EffectiveInterestRateConversiontoNominalInterestRate
127.WeightedAverageFunctions
138.DiscountingCashFlows:NetPresentValueandIRR 14
9.ModifiedInternalRateofReturn(MIRR)
1810.AnnualPercentageInterestRateCalculationswithFees
2211.PriceofaMortgageTradedataDiscountorPremium
2412.YieldofaMortgageTradedataDiscountorPremium 26
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OverviewofHP12cCalculatorKeys
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1. FinancialRegisters
What It Is: A register in 12cspeak is a place in the calculators
memory where
aspecificdatavalueisstoredforuseinanongoingcalculation.FinancialRegistersareasubsetofthemanydifferentStorageRegistersthatthe12cpossesses.Itisimportanttoremembertocleartheseregisterswhenthevaluesarenolongerneeded.Application:Tostoreanumericvalueyouwanttoassociatewithavariable,suchastomake
$1,000.00, as a constant Payment Amount, the value associated with
the PMTvariable.HowTo:
a. Storeanumberintoafinancialregister:
i.
Keythenumberintothedisplay,thenpressthekeyforthecorrespondingvariablee.g.,[n],[i],[PV],[PMT],[FV]
Example:Store90as[n],thenumberofdays
1. 90[n]
b. Recallastoredregistervalue:
i. [RCL]followedbythecorrespondingvariableyouwishtorecall
Example:Recallthenumberofdays1. [n]
c. Clearallthefinancialregistersatonce:
i. [f][REG]
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2. SimpleInterestOnA360or365DayBasis
What It Is: Simple interest is interest that is calculated in
each period off of thebeginningofperiodaccountbalance,where
theaccountbalancedoesnot
includeanyinterestearnedfrompreviousperiods.Theannualinterestratecanbeappliedagainsta360daycalendarora365daycalendar.The12ccalculatesonbothbasesatonce,butdisplaysona360daybasisasadefault.Youcantoggletoseetheamountona365daybasisasdescribedbelow.Application:Tocalculatehowmuchinterestisbeingearnedbyalenderoveraspecifiedtimeperiod.HowTo:
a. Calculatesimpleinteresti.
Enterthenumberofdaystobeusedandpress[n]ii.
Entertheannualinterestrate,thenpress[i]iii.
Entertheprincipalamountborrowed,thenpress[CHS][PV]iv.
Press[f][INT]tocalculateanddisplaytheinterestaccruedona360
daybasis.v.
Ifyouwishtoseetheinterestvalueona365daybasis,press
[R][x>
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3. CompoundInterest
WhatItIs: Compound interest is interestthat
iscalculatedineachperiodoffofthebeginning of period account
balance,where the account balance includes the sum ofunreturned
principal loaned and unpaid interest amounts that have been earned
todate. The key element in calculating compound interest is the
specification of
thecompoundingperiod,i.e.,theintervalandfrequencyatwhichthecompoundingoccurs.Application:
To calculate how much interest is being earned by a lender over
aspecifiedtimeperiod,whereinterestcompoundsmonthly,orquarterly,orannually.HowTo:
a.
Setupthecompoundingperiodsandinterestrate(usingmonthlyasanexample)
i. Enterthenumberofyearsandpress[g][12x]thisautomatically
entersthetotalnumberofcompoundingperiodsintothe[n]registerii.
Calculateandstorethemonthlyinterestrate,entertheannual
interestrateandpress[g][12]thisautomaticallyentersthemonthlyinterestrateintothe[i]register
b.
Calculatethenumberofpaymentsorcompoundingperiodsrequiredtopay
offaloan:
i. Press[f][FIN]toclearthefinancialregistersii.
Entertheperiodicinterestratewith[i]or[12]iii.
Enteratminimum2ofthefollowingmetrics
a. PresentValue,[PV]b. PaymentAmount,[PMT]
a.
Ifapaymentvaluehasbeenentered,press[g][BEG]or[g][END]tosetthepaymentmodeasoccurringeitheratthebeginningofeachperiodorattheendofeachperiod
c. FutureValue,[FV]iv.
Press[n]tocalculatethenumberofpaymentsorperiods
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Example: Investor X takes a loan of $150,000 at 10% annual
interest,compounded monthly, to buy a rental property. If Investor
X makespayments at the end of each month of $1,500, how many
payments arenecessarytopayofftheloan?Howmanyyearswillittake?
1. [f][FIN]2.
10[g][12]calculatesandstoresthemonthlyinterestrate3. 150,000[PV]4.
1,500[CHS][PMT]5. [g][END]6. [n]
Answer:216Numberofpaymentsrequiredtopaydowntheloan7. 12[]
Answer:18.00Numberofyearsrequiredtopayofftheloan
c.
Calculateafinalfractionalpayment(anamountlessthantheconstantperiodicpaymentamount),orafinalballoonpayment(anamountmorethantheconstantperiodicpaymentamount)requiredtopayoffaloan:AFinalFractionalPayment:Letssaythatinsteadof216paymentsbeingneededtopayofftheloan,therewereonly215needed.Thiswouldmeanthatitwouldtake17.91667yearstopayofftheloaninsteadofexactly18.00years.Howdowecalculatethefinalfractionalpaymentamount?
1. 216[n]2. [FV]thisgivesustheoverpaymentamountif216full
paymentsweremade($140.80)3. [RCL][PMT]4. [+]
Answer:$1,359.20
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AFinalBalloonPayment:Letssaythatinsteadof216fullpaymentsbeingneededtopayofftheloan,therewereactually215fullpaymentsneeded,plusapartial216thpaymentthatwasafractionofthefullpaymentamount.Whatisthefinalballoonpaymentamount(payment#215)?
1. 215[n]2. [FV]thisgivesustheremainingbalanceafter215full
paymentsweremade($1,347.96)3. [RCL][PMT]4. [+]
Answer:$2,847.96(thisistheregular$1,500PMTplus$1,347.96)
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4. PeriodicandAnnualInterestRates
What It Is: The rate of interest on a loan expressed either
annually or in
anotherintervalthatismorefrequentthanannually(e.g.,monthly,quarterly).Application:
To back solve for what interest rate is needed, given a frequency
ofcompounding,toproduceafuturevalueofagiveninvestmentamount.HowTo:
a. Calculateaperiodicinterestrate:
i. Press[f][FIN]toclearthefinancialregistersii.
Enternumberofpaymentsorperiodswith[n]or[g][12x]iii.
Enteratminimumtwoofthefollowingmetrics
a. PresentValue,[PV]b. PaymentAmount,[PMT]
a.
If[PMT]wasentered,thenenter[g][BEG]or[g][END]tospecifythetimingofthepayments
c. FutureValue,[FV]iv.
Press[i]tocalculatetheperiodicinterestratev.
Togeneratetheannualinterestrate,enterthenumberofperiodsper
yearandpress[X]
Example:Toaccumulate$10,000in6yearsonaninvestmentof$7,000,whatistheannualinterestraterequiredifitiscompoundingquarterly?
1. [f][FIN]2. 6[ENTER]4[X][n]3. 7,000[CHS][PV]4. 10,000[FV]5.
[i] 1.497%isthequarterlyinterestrate6. 4[X]Answer:5.988%
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5. NominalInterestRateConversionToEffectiveInterestRate
WhatItIs:Thenominalinterestrateistheannualinterestrateinnamee.g.,an8%annualrate.However,whenloaninterestiscompoundinginnature,thisnominalrateisin
fact lower than the actual, or effective interest rate that results
from thecompounding.Application: To find out what rate of annual
interest one is truly paying on a
loanwheretheinterestcompounds.HowTo:
a.
Convertthenominalannualinterestratetotheeffectiveannualinterestrate:
i. [g][END]thissetsthemodeoftheinterestpaymentii.
[f][FIN]thisclearstheregistersiii.
Entertheannualnominalrateasapercentageandpress[ENTER]iv.
Enterthenumberofcompoundingperiodsperyearandpress
[n][][i]v. Enterin100andpress[CHS][ENTER][PV]vi.
Press[FV][+]
Example:Calculatetheeffectiveannualinterestrateassumingtheannualnominalrateis6.25%andcompoundedquarterly
1. [g][END]2. [f][FIN]3. 6.25[ENTER]4. 4[n][][i]5.
100[CHS][ENTER]6. [PV]7.
[FV][+]Answer:6.398%thisisthevalueoftheeffectiveannualinterestrate
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6. EffectiveInterestRateConversionToNominalInterestRate
WhatItIs:Thenominalinterestrate,istheannualinterestrateinnamee.g.,an8%annualrate.However,whenloaninterestiscompoundinginnature,thisnominalrateisin
fact lower than the actual, or effective interest rate that results
from
thecompounding.Application:Tofindoutwhatrateofnominalannualinterestoneispayingonaloanwheretheinterestcompounds.HowTo:
a.
Converttheeffectiveannualinterestratetothenominalannualinterestrate:
i. [f][FIN]thisclearstheregistersii.
Enterthenumberofperiodsperyearthenpress[n]iii.
Enterthevalue100andpress[ENTER][PV]iv.
Entertheeffectiveannualrateasapercentageandthenpress
[+][CHS][FV][i]v. Press[RCL][n][X]
Example:Giventheeffectiveannualrateof5.25%compoundingquarterly,whatisthenominalrate?
1. [f][FIN]2. 4[n]100[ENTER][PV]3. 5.25[+][CHS]4. [FV][i]5.
[RCL][n][X]Answer:5.149%thisisthevalueofthenominalannualinterestrate
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7. WeightedAverageFunction
What It Is: Theweighted average is the average of a series of
values inwhich
eachquantitytobeaveragedisassignedaweight.Application:Tofindouttheaveragepricepaidperlotforlandtobedevelopedintoahousingsubdivision.HowTo:
a. AccumulateStatistics:
i.
Dataisenteredusingthesummation[+]key,whichcalculatesandstoresstatisticaldataintothestorageregistersR1R6(theseareknownasthestatisticsregisters).Beforeenteringstatisticaldata,itisimportanttoclearthestatisticregisterswiththefollowingkeystrokes:[f][]
a.
Instatisticalcalculationswithonevariable,toenteradatapointreferredtoasthexvaluekeythexvalueintothemaindisplay,thenpress[]
b. Calculatetheweightedaverageofaseriesofvalues:
i. Press[f][]thisclearsthestatisticalregistersii.
Keyinthevalueandpress[ENTER]iii.
Keyintheweight(numberoftimesthevalueoccurs)andpress[+]iv.
Repeatstepsiiandiiiforalladditionalvaluesv.
Press[g][xw]theresultantvaluewillbetheweightedaverage
Example:Arealestatebrokerissellingaparceloflandthathasbeensubdividedinto
lots. The prices and quantities are as follows: 2 Lots are $200,000
each,
4Lotsare$230,000each,14Lotsare$190,000each,and9Lotsare$290,000each.Whatistheweightedaveragepriceperlot?
1. [f][]2. 200,000[ENTER]2[+]3. 230,000[ENTER]4[+] 4.
190,000[ENTER]14[+]5. 290,000[ENTER]9[+]6.
[g][xw]Answer:$227,241
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8.
DiscountingCashFlows:NetPresentValue(NPV)andInternalRateofReturn(IRR)
WhatItIs:Theconceptofthetimevalueofmoneyandtheactofdiscountingofcashflowsaretheunderlyingpremisesofrealestatefinance.Theshortversionis:adollartoday
isworthmore than a dollar tomorrow, and predictable (safe) cash
flows
aremorevaluablethanunpredictable(risky)cashflows.TheNetPresentValueisthesumof
theTime0 investmentamountand thediscountedvaluesof the futurecash
flows,givenanassumedDiscountRate.TheIRRisthatdiscountratethatwillgenerateanNPVof0,orthoughtofanotherway,theaverageannualreturnonthecapitalinvestment.Application:Toperformavaluationofanexistingincomeproducingrealestateassetsuchasanofficebuildingorretailplazabyprojectingandthendiscountingthosefuturecashflows.HowTo:
a. Keyincashflowstreams:
i. [f][REG]thisclearstheregistersii.
Entertheinitialinvestment,andpress[CHS]tomakethevalue
negative,thenpress[g][CF0]a.
ifthevalueis0,thenenter0[g][CF0]
iii.
Enterthevalueofthenextcashflow,andpress[CHS]ifthecashflowisnegative
iv. Press[g][CFj]a. Ifthecashflowamountis0press0[g][CFj]
v. Repeatstepsiiiandivasneededuntildone
b. CalculatetheNetPresentValue(NPV):
i. Oncethecashflowshavebeenstored:a.
Entertheinterestrate,using[i]or[12]b. Press[f][NPV]
Exampleonnextpage
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Example:Anincomeproducingpropertyispurchasedfor$100,000incash.Theassetwillbeheldfor5yearsandsoldfor$170,000attheendoftheholdperiod.Theinvestorhasprojectedtheprojectcashflowsasfollows:Year0,100,000;Year1,1,000;Year2,9,000;Year3,11,000;Year4,8,000;Year5,170,000.IftheInvestorsdiscountrateis13%,whatistheNPV?
1. [f][REG]2. 100,000[CHS][g][CF0]3. 1,000[CHS][g][CFj]4.
9,000[g][CFj]5. 11,000[g][CFj]6. 8,000[g][CFj]7. 170,000[g][CFj]8.
[RCL][n]9. 13[i]10. [f][NPV]Answer:$10,962.66
c. CalculatetheInternalRateofReturn(IRR):
i. Entercashflowsusingmethoddescribedaboveinsection8(a)ii.
Press[f][IRR]
Example:UsingthesamevaluesfromtheExampleabove,calculatetheIRR.
1. [f][REG]2. 100,000[CHS][g][CFj]3. 1,000[CHS][g][CFj]4.
9,000[g][CFj]5. 11,000[g][CFj]6. 8,000[g][CFj]7. 170,000[g][CFj]8.
[f][IRR]Answer:15.56%
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d. ChangeCashFlowEntries:
i. Entertheamountintothedisplayii. Press[STO]iii.
Enterthenumberoftheregistercontainingthecashflowamountto
bechanged.
e.
Tochangethenumberoftimesthatthecashflowamountoccursconsecutively:
i. Storethenumberofthecashflowamountinthenregisterii.
Keythenumberoftimesthecashflowamountoccursconsecutively
intothedisplayiii. Press[g][Nj]
Example:Assumingthecashflowisstoredintheregister,changethesecondCFvaluefrom11,000to8,000.ThencalculateanewNPVfora15%return.
1. 8000[STO]22. 15[i]3. [f][NPV]
f.
Enteraseriesofinvestmentcashflowsifthenumberofcashflowsexceed20,
andifamongthecashflowsthereareanyequalconsecutivecashflows:
i. [f][REG]thisclearstheregistersii.
Entertheinitialinvestment,andpress[CHS]tomakethevalue
negative,thenpress[g][CF0]1.
ifthevalueis0,thenenter0[g][CF0]
iii.
Givenaninitialinvestmentofmorethanonecashflowoftheamountenteredabove,thenenterthenumberofthosecashflows,thenpress[g][Nj]
1.
If[g][Nj]isnotpressed,itisassumedthatthefirstcashflowamount=1.
iv.
Entertheamountofthenextcashflow,andpress[CHS]ifthatcashflowisnegative,thenpress[g][CFj].
1. Ifthecashflowamountis0inthenextperiod,press0[g][CFj]
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v.
Iftheamountenteredinstep4occursmorethanonceconsecutively,keyinthenumberoftimesthatthatcashflowamountoccursconsecutivelythenpress[g][Nj].
1.
If[g][Nj]isnotpressed,thecalculatorassumesthatNjis1fortheCFjjustentered.
vi.
Repeatthestepsaboveuntilallofthecashflowshavebeenentered.
Example:Investorlookstopurchasepropertyfor$100,000andhasa15%DiscountRate.Heintendstoholdfor10yearsandsellfor$200,000.YearlyCashflowsareasfollowsduringyears110:$14,000,$11,000,$10,000,$10,000,$10,000,$9,100,$9,000,$9,000,$4,500,$200,000
1. [f][REG]2.
100,000[CHS][g][CF0]Entersthefirstcashflowlineitem3.
14,000[g][CFj]4. 11,000[g][CFj]5. 10,000[g][CFj]6.
3[g][Nj]Entersthenumberofinstancesthattheprevious
linesCFappears7. 9,100[g][CFj]8. 9,000[g][CFj]9. 2[g][Nj]10.
4,500[g][CFj]11. 200,000[g][CFj]12. 15[i]13.
[f][NPV]Answer:$1,268.19
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9. ModifiedInternalRateofReturn(MIRR)
WhatItIs:ThetraditionalInternalRateofReturnfallsshortofproducingmeaningfulresults
incertainsituations,suchasthoseinwhichtherearemultiplechangesinsign(positivetonegativeamounts)inaseriesofcashflowsinsteadofjustasinglechangeinsign(anegativeinitialinvestmentamount,andeither$0amountsorpositivecashflowsthereafter).ThefundamentalissuewithtraditionalIRRisthatinitscalculation,itisassumedthatall
cash flows are either reinvested or discounted at the computed IRR
rate. MIRRsolves for this by using userprovided reinvestment and
borrowing rates.
Theborrowingrateisalsoknownasthesaferate,whichisaratethatreflectsthereturnonaninvestmentinahighlyliquidaccounte.g.,ashorttermU.S.TreasuryBill.Application:Calculate
the IRR for an investment that contains a series of cash
flowsthatcontainmorethanonechangeofsign.HowTo:
a. CalculatetheMIRR:
i.
First,calculatetheFutureValue(FV)ofthepositivecashflowsatthe
reinvestmentrateii.
Second,calculatethePresentValue(PV)ofthenegativecashflowsat
thesaferateiii.
Withaknownnumberofperiods(n),FVandPV,wecansolveforthe
MIRR(i)Exampleonnextpage
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Example for Annual Cash Flows: An investment group is
raisingcapital foravalueaddedrealestateprivateequity
fund.Theprojectedcashflows(in$Millions)atthefundlevelareasfollows:Time0:100Year1:7Year2:6Year3:1Year4:0Year5:3Year6:9.5Year7:155What
is the MIRR if the assumed safe rate is 3% and the
assumedreinvestmentrateis20%?
Step1of2:FindFutureValue(FV)ofthepositive(or$0ifanegativeamount)cashflowsatthereinvestmentrate:
1. [f][REG]2. 0[g][CF0]Investmentcashflowrepresentedas$03.
7[g][CFj]4. 6[g][CFj]5. 0[g][CFj]Negativecashflowrepresentedas$06.
0[g][CFj]7. 3[g][CFj]8. 9.5[g][CFj]9. 155[g][CFj]10.
20[i][f][NPV]$57.6411. [CHS][PV]12.
7[n][FV]7cashflowperiods(Time0doesnotcount
asacashflowperiod)InterimStep1Answer(FVofpositivecashflows):$206.55
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Step2of2:FindNetPresentValue(NPV)ofthenegative(or$0ifa$0amountorapositiveamount)cashflowsatthesaferate:
1. 100[CHS][g][CF0]Investmentcashflow2. 0[g][CFj]Year1cashflow3.
0[g][CFj]Year2cashflow4. 1[CHS][g][CFj]5. 3[i][f][NPV]$100.926.
7[n][i]7cashflowperiods(Time0doesnotcountas
acashflowperiod)Answer(AnnualMIRR):10.77%
Example forMonthly Cash Flows: An investment group is
raisingcapital foravalueaddedrealestateprivateequity
fund.Theprojectedcashflows(in$Millions)atthefundlevelareasfollows:Time0:100Month1:7Month2:6Month3:1Month4:0Month5:3Months6through11:9.5Month12:155What
is the MIRR if the assumed safe rate is 3% and the
assumedreinvestmentrateis20%?
Continuedonnextpage
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Step1of2:FindFutureValue(FV)ofthepositive(or$0ifanegativeamount)cashflowsatthereinvestmentrate:
1. [f][REG]2. 0[g][CF0]Investmentcashflowrepresentedas$03.
7[g][CFj]4. 6[g][CFj]5. 0[g][CFj]Negativecashflowrepresentedas$06.
0[g][CFj]7. 3[g][CFj]8. 9.5[g][CFj]9. 155[g][CFj]10.
20[g][12][f][NPV]$162.1211. [CHS][PV]12.
7[n][FV]7cashflowperiods(Time0doesnotcount
asacashflowperiod)InterimStep1Answer(FVofpositivecashflows):$182.00
Step2of2:FindNetPresentValue(NPV)ofthenegative(or$0ifa$0amountorapositiveamount)cashflowsatthesaferate:
1. 100[CHS][g][CF0]Investmentcashflow2.
0[g][CFj]Month1cashflow3. 0[g][CFj]Month2cashflow4.
1[CHS][g][CFj]5. 3[g][12][f][NPV]$100.996.
7[n][i]7cashflowperiods(Time0doesnotcountas
acashflowperiod);thisgivesustheMonthlyMIRRof8.78%
7.
12[X]Answer(AnnualMIRR):105.34%(Note:thisissohighbecausewemadesomuchmoneyinonly7months)
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10.AnnualPercentageRateCalculationswithFees
What It Is: The Annual Percentage Rate is the calculated rate
for a mortgage
thataccountsforthecashfeesthatborrowersarechargedinconnectionwiththeloan.Application:Calculate
exactlywhat a loan is costing a borrower on an annual
basisgivenafeeamountpaidupfrontatloanfunding.HowTo:
b. CalculatetheAnnualPercentageRatewithFees:
i. First,calculateandentertheperiodicpaymentamountontheloan:
a. [g][END]b. [f][FIN]thisclearsthefinancialregistersc.
Entertotalnumberofpaymentperiods;press[n]d.
Enterperiodicinterestrateasapercentage;press[i]e.
Entermortgageamount;press[PV]f.
Press[PMT]forperiodicpaymentamount
ii. Second,calculateandentertheactualnetamountdisbursed:
a.
Ifthefeesarestatedasapercentageofthemortgageamount,recallthemortgageamount([RCL][PV]),thenkeyinthefeerateandpress[%][][PV]
a.
Ifthefeesarestatedasaflatcharge,recallthemortgageamount([RCL][PV]);enterthefeeamount;press[][PV]
b.
Iffeesarestatedasapercentageofthemortgageamountplusaflatcharge,recallthemortgageamount([RCL][PV]);keyinthefeerate,press[%][];keyinthefeeamount;press[][PV].
iii. Press[i]toreturntheinterestratepercompoundingperiodiv.
Toreturntheannualnominalpercentagerate,enterthenumberof
periodsperyearandpress[X].
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Example:Alendercharges2pointstotheborrowerfortheissuanceofhis
mortgage. Given a mortgage of $100,000 amortized over 30
yearswithanannual interest rateof6%,what is the
trueannualpercentageratethattheborrowerispaying?
1. Enter[g][END]2. [f][FIN]3.
30[g][12x]EntersthenumberofMonths(30Yearsx
12Months)4. 6[g][12]Calculatespercentmonthlyinterestrate5.
100,000[PV]ConvertsLoanAmounttoPresentValue
(PV)6. [PMT]Calculatesmonthlypayment7.
[RCL][PV]2[%][][PV]Actualamountreceivedby
borrower(PV)8. [i]9. 12[X]Answer:6.189%
Assumingthesameinformationfromtheexampleabove,whatistheAPRifthemortgagefeeisstatedat2pointsplus$500?
1. [g][END]2. [f][FIN]3. 30[g][12x]4. 6.00[g][12]5.
100,000[PV]6. [PMT]7. [RCL][PV]2[%][]8. 500[][PV]9. [i]10.
12[X]Answer:6.237%
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11.PriceofaMortgageTradedataDiscountorPremium
WhatItIs:Mortgagesareoftentradedinsteadofbeingheldonthebalancesheetoftheissuing
bank. They can be sold and bought either at a discount to the
remainingprincipalbalance,oratapremium.Application: Calculating a
mortgage purchase price given a targeted (desired)
yieldamount.HowTo:
a. Calculatethevalueofaloanthatisboughtorsoldatapremium.Given
the amount of the mortgage, the periodic payment, the timing
andamountoftheballoonpaymentandthedesiredyieldrate,wecanbacksolveforthepriceofthemortgage:
i. [g][END]ii. [f][FIN]thisclearsthefinancialregistersiii.
Enterthenumberofperiodsuntiltheballoonpaymentorprepayment
occurs.Press[n].(Followthisevenifthereisnoballoonpaymentorprepayment)
iv. Entertheperiodicinterestrate,press[i]v.
Entertheperiodicpaymentamount;press[PMT]vi.
Entertheballoonpaymentamountandpress[FV]vii.
Press[PV]toobtainthepurchasepriceofthemortgage
Example:Aborrowerelectstoprepayhisloan.Thecurrentannualinterestrateis5%with60monthlypaymentsof$150remainingandaballoonpaymentattheendofthefifthyearof$2,000.Thelenderhaschosentodiscountthefuturepaymentsat5%.Whatistheamounttheborrowermustprepayonthenote?
1. [g][END]2. [f][FIN]3. 60[n]4. 5[g][12]5. 150[PMT]6.
2,000[FV][PV]Answer:$9,507.02
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Example2:
A5.5%annualinterestratemortgagewith25yearsremainingandabalanceof$35,000isavailableforpurchase.Whatpricewillgeneratea15%yield?
1. [g][END]2. [f][FIN]3. 25[g][12x]4. 5.5[g][12]5.
35,000[CHS][PV][PMT]6. 15[g][12]7. [PV]Answer:$16,780.57
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12.YieldofaMortgageTradedataDiscountorPremium
WhatItIs:Mortgagesareoftentradedinsteadofbeingheldonthebalancesheetoftheissuing
bank. They can be sold and bought either at a discount to the
remainingprincipalbalance,oratapremium.Application:Calculating an
expected yield amount for a
targetedmortgagepurchaseprice.HowTo:
a. Calculatetheyieldofamortgagepurchasedatadesiredprice:
Ifweknowtheoriginalmortgageamount,theinterestrate,periodicpaymentamount,thenumberofperiodicpaymentsperyearandtheamountoftheballoonpayment,wecanbacksolvetowhattheyieldwouldbeforatargetedmortgagepurchasepriceamount.
a. [g][END]b. [f][FIN]c.
Enterthetotalnumberofperiodspriortotheballoon
payment.Press[n]d. Entertheperiodicpaymentamountandpress[PMT]e.
Enterthepurchasepriceofthemortgageandpress[PV]f.
Entertheballoonpaymentamountandpress[FV]g.
Hitthe[i]keyfortheperiodicyieldh.
Multiplybythenumberofperiodsperyear(e.g.,12[X])
Example:InvestorApurchasesanamortizingloanissuedfor$160,000takenoutat8%for30years.36monthsofpaymentshavebeenmade.Ifthe
purchase price of the mortgage is $120,000, what is the
annualyield?
1. [g][END]2. [f][FIN]3. 30[g][12x]4. 8[g][12]5.
160,000[CHS][PV]6. [PMT]7. [RCL][n]8. 36[][n]9.
120,000[CHS][PV]
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10. [i]11. 12[X]
Answer:11.15%
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