中財課后習(xí)題答案ch06

CHAPTER6

PresentValueConcepts

andMeasurement

ASSIGNMENTCLASSIFICATIONTABLE(BYTOPIC)

Brief

TopicsQuestionsExercisesExercisesProblems

1.Presentvalueconcepts.

2.Useoftables.81

3.Presentandfuturevalue

problems:

a.Unknownfutureamount.1,5,132,4,6,7,11

b.Unknownpayments.6,12,177,16,172,6

c.Unknownnumberof4,98,152

periods.

d.Unknowninterestrate.3,11,167,9,142,7

e.Unknownpresentvalue.2,7,8,10,142,3,4,5,6,8,1,4,7,13,14

12,17,18,19

4.Valueofaseriesof3,5,8

irregulardeposits;

changinginterestrates.

5.Valuationofleases,1510,12,13,3,5,6,8,9,

pensions,bonds;choice14,1510,13,14

betweenprojects.

6.Deferredannuity.7

7.ExpectedCashFlows.20,2113,14

*8.Usesofacalculator.22,23,2415,16,17

ASSIGNMENTCLASSIFICATIONTABLE(BYLEARNINGOBJECTIVE)

Brief

LearningObjectivesExercisesExercisesProblems

1.Identifyaccountingtopicswherethetime

valueofmoneyisrelevant.

2.Distinguishbetweensimpleandcompound2

interest.

3.Useappropriatecompoundinteresttables.1

4.Identifyvariablesfundamentaltosolving

interestproblems.

25

J

5.Solvefutureandpresentvalueofproblems.1,2,3,2,3,6,9,o31,

4,7,810,12,15,f

18,19

45

5

6.Solvefuturevalueofordinaryandannuity5,6,9,133,4,5,6,&3,1o

dueproblems.12,15,169,

45

5

7.Solvepresentvalueofordinaryandannuity10,11,12,3,4,5,6,2,3,1o

dueproblems.14,16,1711,12,16,8,9,‘

17,18,19,14

12

8.Solvepresentvalueproblemsrelated157,8,13,14w,

6,

todeferredannuitiesandbonds.

4

*9.Applyexpectedcashflowstopresent20,21

valuemeasurement.

3,

17

*10.Useafinancialcalculatortosolvetime22,23,245,6,.

valueofmoneyproblems.

ASSIGNMENTCHARACTERISTICSTABLE

LevelofTime

ItemDescriptionDifficulty(minutes)

E6-1Usinginteresttables.Simple5-10

E6-2Simpleandcompoundinterestcomputations.Simple5-10

E6-3Computationoffuturevaluesandpresentvalues.Simple10-15

E6-4Computationoffuturevaluesandpresentvalues.Moderate15-20

E6-5Computationofpresentvalue.Simple10-15

E6-6Futurevalueandpresentvalueproblems.Moderate15-20

E6-7Computationofbondprices.Moderate12-17

E6-8Computationsforaretirementfund.Simple10-15

E6-9Unknownrate.Moderate5-10

E6-10Unknownperiodsandunknowninterestrate.Simple10-15

E6-11Evaluationofpurchaseoptions.Moderate10-15

E6-12Analysisofalternatives.Simple10-15

E6-13Computationbondliability.Moderate15-20

E6-14Computationofpensionliability.Moderate15-20

E6-15Investmentdecision.Moderate15-20

E6-16Retirementofdebt.Simple10-15

E6-17Computationofamountofrentals.Simple10-15

E6-18Leastcostlypayoff—ordinaryannuity.Simple10-15

E6-19Leastcostlypayoff—annuitydue.Simple10-15

E6-20Expectedcashflows.Simple5-10

E6-21Expectedcashflowsandpresentvalue.Moderate15-20

*E6-22Determinetheinterestrate(withacalculator).Simple3-5

*E6-23Determinetheinterestrate(withacalculator).Simple3-5

*E6-24Determinetheinterestrate(withacalculator).Simple3-5

P6-1Varioustimevaluesituations.Moderate15-20

P6-2Varioustimevaluesituations.Moderate15-20

P6-3Analysisofalternatives.Moderate20-30

P6-4Evaluatingpaymentalternatives.Moderate20-30

P6-5Analysisofalternatives.Moderate20-25

P6-6Purchasepriceofabusiness(deferredannuities).Moderate25-30

P6-7Timevalueconceptsappliedtosolvebusinessproblems.Complex30-35

P6-8Analysisofalternatives.Moderate20-30

P6-9Analysisofbusinessproblems.Complex30-35

P6-10Analysisofleaseversuspurchase.Complex30-35

P6-11Pensionfunding,deferredannuity.Complex25-30

P6-12Pensionfunding-ethicsModerate20-25

P6-13Expectedcashflowsandpresentvalue.Moderate20-25

P6-14Expectedcashflowsandpresentvalue.Moderate20-25

*P6-15Varioustimevalueofmoneysituations.Moderate10-15

*P6-16Varioustimevalueofmoneysituations.Moderate10-15

*P6-17Varioustimevalueofmoneysituations.Moderate10-15

ANSWERSTOQUESTIONS

1.Moneyhasvaluebecausewithitonecanacquireassetsandservicesanddischargeobligations.

Theholding,borrowingorlendingofmoneycanresultincostsorearnings.Andthelongerthe

timeperiodinvolved,thegreaterthecostsortheearnings.Thecostorearningofmoneyasa

functionoftimeisthetimevalueofmoney.

Accountantsmusthaveaworkingknowledgeofcompoundinterest,annuities,andpresentvalue

conceptsbecauseoftheirapplicationtonumeroustypesofbusinesseventsandtransactions

whichrequirepropervaluationandpresentation.Theseconceptsareappliedinthefollowingareas:

(1)sinkingfunds,(2)installmentcontracts,(3)pensions,(4)long-termassets,(5)leases,(6)notes

receivableandpayable,(7)businesscombinations,and(8)amortizationofpremiumsand

discounts.

2.Somesituationsinwhichpresentvaluemeasuresareusedinaccountinginclude:

(a)Notesreceivableandpayable-theseinvolvesinglesums(thefaceamounts)andmayinvolve

annuities,ifthereareperiodicinterestpayments.

(b)Leases-involvemeasurementofassetsandobligations,whicharebasedonthepresent

valueofannuities(leasepayments)andsinglesums(ifthereareresidualvaluestobepaidat

theconclusionofthelease).

(c)Pensionsandotherdeferredcompensationarrangements—involvediscountedfutureannuity

paymentsthatareestimatedtobepaidtoemployeesuponretirement.

(d)Bondpricing—thepriceofbondspayableiscomprisedofthepresentvalueoftheprincipalor

facevalueofthebondplusthepresentvalueoftheannuityofinterestpayments.

(e)Long-termassets-evaluatingvariouslong-terminvestmentsorassessingwhetheranassetis

impairedrequiresdeterminingthepresentvalueoftheestimatedcashflows(maybesingle

sumsand/oranannuity).

3.Interestisthepaymentfortheuseofmoney.Itmayrepresentacostorearningsdependingupon

whetherthemoneyisbeingborrowedorloaned.Theearningorincurringofinterestisafunction

ofthetime,theamountofmoney,andtheriskinvolved(reflectedintheinterestrate).

Simpleinterestiscomputedontheamountoftheprincipalonly,whilecompoundinterestis

computedontheamountoftheprincipalplusanyaccumulatedinterest.Compoundinterest

involvesinterestoninterestwhilesimpleinterestdoesnot.

4.Theinterestrategenerallyhasthreecomponents:

(1)Purerateofinterest—Thiswouldbetheamountalenderwouldchargeiftherewereno

possibilitiesofdefaultandnoexpectationofinflation.

(2)Expectedinflationrateofinterest—Lendersrecognizethatinaninflationaryeconomy,theyare

beingpaidbackwithlessvaluabledollars.Asaresult,theyincreasetheirinterestrateto

compensateforthislossinpurchasingpower.Wheninflationaryexpectationsarehigh,interest

ratesarehigh.

(3)Creditriskrateofinterest-Thegovernmenthaslittleornocreditrisk(i.e.,riskofnonpayment)

whenitissuesbonds.Abusinessenterprise,however,dependinguponitsfinancialstability,

profitability,etc.canhavealoworahighcreditrisk.

Accountantsmusthaveknowledgeaboutthesecomponentsbecausethesecomponentsare

essentialinidentifyinganappropriateinterestrateforagivencompanyorinvestoratanygiven

moment.

5.(a)Presentvalueofanordinaryannuityat8%for10periods(Table6-4).

(b)Futurevalueof1at8%for10periods(Table6-1).

(c)Presentvalueof1at8%for10periods(Table6-2).

(d)Futurevalueofanordinaryannuityat8%for10periods(Table6-3).

QuestionsChapter6(Continued)

6.Heshouldchoosequarterlycompounding,becausethebalanceintheaccountonwhichinterest

willbeearnedwillbeincreasedmorefrequently,therebyresultinginmoreinterestearnedonthe

investment.Asshowninthefollowingcalculation:

Semiannualcompounding,assumingtheamountisinvestedfor2years:

n=4

$1,000X1.16986=$1,169.86

i=4

Quarterlycompounding,assumingtheamountisinvestedfor2years:

n=8

$1,000X1.17166=$1,171.66

i=2

Thus,withquarterlycompounding,Billcouldearn$1.80more.

7.$24,208.02=$18,000X1.34489(futurevalueof1at2%for12periods).

8.$27,919.50=$50,000X.55839(presentvalueof1at6%for10periods).

9.Anannuityinvolves(1)periodicpaymentsorreceipts,calledrents,(2)ofthesameamount,

(3)spreadoverequalintervals,(4)withinterestcompoundedonceeachinterval.

Rentsoccurattheendoftheintervalsforordinaryannuitieswhiletherentsoccuratthebeginning

oftheintervalsforannuitiesdue.

$30000

10.Amountpaideachyear=；八二(presentvalueofanordinaryannuityat12%for4years).

J.UJ!OD

Amountpaideachyear=$9.877.03.

卡［AO

11.Amountdepositedeachyear=1~364；O0(futurevalueofanordinaryannuityat10%for4years).

Amountdepositedeachyear=$34,475.33.

12.Amountdepositedeachyear=霽翳燃器°徵;晶anannuitydueat10%for4years

Amountdepositedeachyear=$31.341.21.

13.Theprocessforcomputingthefuturevalueofanannuitydueusingthefuturevalueofanordinary

annuityinteresttableistomultiplythecorrespondingfuturevalueoftheordinaryannuitybyone

plustheinterestrate.Forexample,thefactorforthefuturevalueofanannuityduefor4yearsat

12%isequaltothefactorforthefuturevalueofanordinaryannuitytimes1.12.

14.Thebasisforconvertingthepresentvalueofanordinaryannuitytabletothepresentvalueofan

annuityduetableinvolvesmultiplyingthepresentvalueofanordinaryannuityfactorbyoneplus

theinterestrate.

QuestionsChapter6(Continued)

15.Presentvalue=presentvalueofanordinaryannuityof$25,000for20periodsat?percent.

$210,000=presentvalueofanordinaryannuityof$25,000for20periodsat?percent.

$210,000

Presentvalueofanordinaryannuityfor20periodsat?percent=$25,000-0

Thefactor8.4isclosestto8.51356inthe10%column(Table6-4).

16.4.96764Presentvalueofordinaryannuityat12%foreightperiods.

2.40183Presentvalueofordinaryannuityat12%forthreeperiods.

2.56581Presentvalueofordinaryannuityat12%foreightperiods,deferredthreeperiods.

Thepresentvalueofthefiverentsiscomputedasfollows:

2.56581X$10,000=$25.658.10.

17.(a)Presentvalueofanannuitydue.

(b)Presentvalueof1.

(c)Futurevalueofanannuitydue.

(d)Futurevalueof1.

18.$27,000=PVofanordinaryannuityof$6,900forfiveperiodsat?percent.

$27000

為6600-=PVofanordinaryannuityforfiveperiodsat?percent.

3.91304=PVofanordinaryannuityforfiveperiodsat?.

3.91304=approximately9%.

19.TheIRSarguesthatthefuturereservesshouldbediscountedtopresentvalue.Theresultwould

besmallerreservesandthereforelessofachargetoincome.Asaresult,incomewouldbehigher

andincometaxesmaythereforebehigheraswell.

SOLUTIONSTOBRIEFEXERCISES

BRIEFEXERCISE6-1

8%annualinterest

i=8%

PV=$10,000FV=?

0123

n=3

FV=$10,000(FVF3,8%)

FV=$10,000(1.25971)

FV=$12,597.10

8%annualinterest,compoundedsemiannuallv

i=4%

PV=$10,000FV=?

0123456

n=6

FV=$10,000(FVF6,4%)

FV=$10,000(1.26532)

FV=$12,653.20

BRIEFEXERCISE6-2

12%annualinterest

i=12%

PV=?FV=$20,000

01234

n=4

PV=$20,000(PVF4,12%)

PV=$20,000(.63552)

PV=$12,710.40

12%annualinterest,compoundedquarterlv

i=3%

PV=?FV=$20,000

012678

n=16

PV=$20,000(PVF16)3%)

PV=$20,000(.62317)

PV=$12,463.40

BRIEFEXERCISE6-3

i=?

PV=$30,000FV=$222,000

02192021

n=21

FV=PV(FVF211i)PV=FV(PVF21ii)

OR

$222,000=$30,000(FVF21)i)$30,000=$222,000(PVF21ij)

FVF2i,i=7.40000PVF2i,i=.13514

i=10%i=10%

BRIEFEXERCISE6-4

i=5%

PV=$10,000FV=$13,400

n=?

FV=PV(FVFn,5%)PV=FV(PVFn,5%)

OR

$13,400=$10,000(FVFn)5%)$10,000=$13,400(PVFn)5%)

FVFn)5%=1.34000PVFn,5%=.74627

n=6yearsn=6years

BRIEFEXERCISE6-5

Firstpavmenttodav

i=12%

R=FV-AD=

$5,000$5,000$5,000$5,000$5,000?

012181920

n=20

FV-AD=$5,000(FVF-OA20,I2%)1.12

FV-AD=$5,000(72.05244)1.12

FV-AD=$403,494

Firstpaymentatvear-end

i=12%

FV-OA=

?

$5,000$5,000$5,000$5,000$5,000

012181920

n=20

FV-OA=$5,000(FVF-OA20,I2%)

FV-OA=$5,000(72.05244)

FV-OA=$360,262

BRIEFEXERCISE6-6

i=11%

FV-OA=

?$200,000

10

n=10

$200,000=R(FVF-OA10)11%)

$200,000=R(16.72201)

$200,000

=R

16.72201

R=$11,960

BRIEFEXERCISE6-7

12%annualinterest

i=12%

PV=?FV=$350,000

PV=$350,000(PVF5,12%)

PV=$350,000(.56743)

PV=$198,600.50

BRIEFEXERCISE6-8

Withquarterlycompounding,therewillbe20quarterlycompounding

periods,at1/4theinterestrate:

PV=$350,000(PVF20,3%)

PV=$350,000(.55368)

PV=$193,788

BRIEFEXERCISE6-9

i=10%

FV-OA=

R=$100,000

$12,961$12,961$12,961

n=?

$100,000=$12,961(FVF-OAn,i0%)

$100,000

FVF-OAn)10%==7.71545

12,961

Therefore,n=6years

BRIEFEXERCISE6-10

Firstwithdrawalatvear-end

i=8%

PV-OA=R=

?$20,000$20,000$20,000$20,000$20,000

0128910

n=10

PV-OA=$20,000(PVF-OA1018%)

PV-OA=$20,000(6.71008)

PV-OA=$134,202

Firstwithdrawalimmediatelv

i=8%

PV-AD=

?

R=

$20,000$20,000$20,000$20,000$20,000

0128910

n=10

PV-AD=$20,000(PVF-AD1O,8%)

PV-AD=$20,000(7.24689)

PV-AD=$144,938

BRIEFEXERCISE6-11

i=?

PV=R=

$1,124.40$75$75$75$75$75

012161718

n=18

$1,124.40=$75(PVF-OA18,i)

$1,124.40

PVF18)i=14.992

75

Therefore,i=2%permonth

BRIEFEXERCISE6-12

i=8%

PV=

$200,000R=?

181920

n=20

$200,000=R(PVF-OA20>8%)

$200,000=R(9.81815)

R=$20,370

BRIEFEXERCISE6-13

i=12%

R=

$20,000$20,000$20,000$20,000$20,000

12/31/0612/31/0712/31/0812/31/1212/31/1312/31/14

n=8

FV-OA=$20,000(FVF-OA8J12%)

FV-OA=$20,000(12.29969)

FV-OA=$245,994

BRIEFEXERCISE6-14

i=8%

PV-OA=R=

n=4n=8

PV-OA=$20,000(PVF-OA12.4,8%)PV-OA=$20,000(PVF-OA&8%)(PVF4)8%)

OR

PV-OA=$20,000(7.53608-3.31213)PV-OA=$20,000(5.74664)(.73503)

PV-OA=$84,479PV-OA=$84,479

BRIEFEXERCISE6-15

i=8%

PV=?

PV-OA=R=$1,000,000

?$70,000$70,000$70,000$70,000$70,000

n=10

$1,000,000(PVF10,8%)=$1,000,000(.46319)=$463,190

70,000(PVF-OA10,8%)=$70,000(6.71008)469,706

$932.896

BRIEFEXERCISE6-16

PV-OA=$20,000

$4,864.51$4,864.51$4,864.51$4,864.51

0126

$20,000=$4,864.51(PV-OA6,i%)

(PV-OA6.i%)=$20,000+$4,864.51

(PV-OA61i%)=4.11141

Therefore,i%=12

BRIEFEXERCISE6-17

PV-AD=$20,000

$?$?$?$?

01256

$20,000=Payment(PV-AD6>12%)

$20,000.(PV-AD6I12%)=Payment

$20,000-4.60478=$4,343.31

SOLUTIONSTOEXERCISES

EXERCISE6-1(5-10minutes)

(a)(b)

Rateof9I9n6terestNumbero9fPeriods

a.396

59620

b.30

c.

a.E996

52625

30

c.32628

EXERCISE6-2(5-10minutes)

(a)Simpleinterestof$1,600peryearX8$12,800

Principal20,000

Totalwithdrawn$32.800

(b)Interestcompoundedannually—Futurevalueof

1@8%for8periods1.85093

X$20,000

Totalwithdrawn$37.018.60

(c)Interestcompoundedsemiannually—Future

valueof1@4%for16periods1.87298

X$20,000

Totalwithdrawn$37.459.60

EXERCISE6-3(10-15minutes)

(a)$7,000X1.46933=$10,2