Youdiscoverthefollowingfurtherdetails:

SMALL’spolicywastofinancebothworkingcapitalandinvestmentbyabankoverdraft.A12%interestrateappliedatthetimeofevaluation.

A25%writingdownallowanceonareducingbalancebasisisofferedfornewinvestment.SMALL’sprofitsaresufficienttoutilizefullythisallowancethroughouttheproject.

Corporatetaxispaidayearinarrears.

Oftheoverheadcharge,abouthalfreflectabsorptionofexistingoverheadcost.

Themarketresearchwasactuallyundertakentoinvestigatetwoproposals,theotherprojectalsohavingbeenrejected.Thetotalbillforallthisresearchhasalreadybeenpaid.

BIGitselfrequiresanominalaftertaxcostofcapitalat20percent,andasnoplanstouseanydebtfinanceinthefuture.

Required:decidewhethertheprojectshouldbeundertaken.

Year0

Year1

Year2

Year3

Year4

Year5

Sales

1,400

1,600

1,800

1,000

Material

(400)

(450)

(500)

(250)

Labour

(400)

(450)

(500)

(250)

O.H.(50%)

(50)

(50)

(50)

(50)

TaxableCashFlow

550

650

750

450

Taxat33%

(182)

(215)

(248)

(149)

+Taxsavingfromallowance

74

56

42

125

Initialinvestment

(900)

Residualvalue

0

Workingcapital

(100)

100

Netcashflow

(1,000)

540

542

591

344

(24)

Discountfactor20%

1

0.833

0.694

0.579

0.483

0.402

PV

(1,000)

458

376

342

166

19)

NPV

332

Working1:TaxSavingonCapitalAllowance

Year

￡000

Taxsaving33%

1

InitialInvestment

900

WDA25%

(225)

74

2

Bookvalue

675

WDA25%

(169)

56

3

Bookvalue

506

WDA25%

(127)

42

4

Bookvalue

379

Balanceallowance

(379)

125

Residualvalue

0

2013JuneQ1

復雜NPV計算

HDWCoisalistedcompanywhichplanstomeetincreaseddemandforitsproductsbybuyingnewmachinerycosting$5million.Themachinerywouldlastforfouryears,attheendofwhichitwouldbereplaced.Thescrapvalueofthemachineryisexpectedtobe5%oftheinitialcost.Capitalallowanceswouldbeavailableonthecostofthemachineryona25%reducingbalancebasis,withabalancingallowanceorchargeclaimedinthefinalyearofoperation.

Thisinvestmentwillincreaseproductioncapacityby9,000unitsperyearandalloftheseunitsareexpectedtobesoldastheyareproduced.Relevantfinancialinformationincurrentpricetermsisasfollows:

Forecastinflation

Sellingprice

$650perunit

4·0%peryear

Variablecost

$250perunit

5·5%peryear

Incrementalfixedcosts

$250,000peryear

5·0%peryear

Inadditiontotheinitialcostofthenewmachinery,initialinvestmentinworkingcapitalof

$500,000willberequired.

Investmentinworkingcapitalwillbesubjecttothegeneralrateofinflation,whichisexpectedtobe4·7%peryear.HDWCopaystaxonprofitsattherateof20%peryear,oneyearinarrears.Thecompanyhasanominal(moneyterms)after-taxcostofcapitalof12%peryear.

Required:

Calculatethenetpresentvalueoftheplannedpurchaseofthenewmachineryusinganominal(moneyterms)approachandcommentonitsfinancialacceptability.

(14marks)

Discussthedifferencebetweenanominal(moneyterms)approachandarealtermsapproachtocalculatingnetpresentvalue. (5marks)

IdentifyTWOfinancialobjectivesofalistedcompanysuchasHDWCoanddiscusshoweachofthesefinancialobjectivesissupportedbytheplannedinvestmentinnewmachinery. (6marks)

(25marks)

Year

1

2

3

4

5

$000

$000

$000

$000

$000

Salesincome

6,084

6,327

6,580

6,844

Variablecost

(2,374)

(2,504)

(2,642)

(2,787)

Contribution

3,710

3,823

3,938

4,057

Fixedcosts

(263)

(276)

(289)

(304)

Cashflow

3,447

3,547

3,649

3,753

Taxation

(689)

(709)

(730)

(751)

CAtaxbenefits

250

188

141

372

After-taxcashflow

3,447

3,108

3,128

3,164

(379)

Workingcapital

(24)

(25)

(26)

(27)

Scrapvalue

250

Netcashflow

3,423

3,083

3,102

3,387

(379)

Discountat12%

0·893

0·797

0·712

0·636

0·567

Presentvalues

3,057

2,457

2,209

2,154

(215)

$000

PVoffuturecashflows

9,662

Initialinvestment

(5,000)

Workingcapital

(500)

NPV

4,162

Asthenetpresentvalueof$4·161millionispositive,theexpansioncanberecommendedasfinanciallyacceptable.

Workings:

Year

1

2

3

4

Sellingprice($/unit)

676·00

703·04

731·16

760·41

Sales(units/year)

9,000

9,000

9,000

9,000

Salesincome($000)

6,084

6,327

6,580

6,844

Year

1

2

3

4

Variablecost($/unit)

263·75

278·26

293·56

309·71

Sales(units/year)

9,000

9,000

9,000

9,000

Variablecost($000)

2,374

2,504

2,642

2,787

Year

1

2

3

4

$000

$000

$000

$000

Capitalallowance

1,250·0

937·5

703·1

1,859·4

Taxbenefit

250

188

141

372

Workings:

Year

1

2

3

4

Sellingprice($/unit)

676·00

703·04

731·16

760·41

Sales(units/year)

9,000

9,000

9,000

9,000

Salesincome($000)

6,084

6,327

6,580

6,844

Year

1

2

3

4

$000

$000

$000

$000

Workingcapital

523·50

548·11

573·87

600·84

Incremental

24

25

26

27

ComplementaryAnswer1：Capitalallowance

Beginof

yr

$000

Tax

saving*20%

Timin

g

1

BV

5,000

WDA25%

(1,250)

250

2

2

BV

3,750

WDA25%

(938)

188

3

3

BV

2,812

WDA25%

(703)

141

4

4

BV

2,109

Balanceallowance

(1,859) 372 5

Residual 250

ComplementaryAnswer2：:WCmovement

Year0

1

2

3

4

500

524

548

574

601

(500)

(24)

(24)

(26)

(27)

WCrequired(4.7%inflation)

WCmovement

Note:題目中提到attheendofwhichitwouldbereplaced,暗示項目并沒有結束，所以忽略營運資本回收。如不明確，可以自己寫假設。

AlternativeNPVcalculationwherecapitalallowancesaresubtractedandaddedback

Year

1

2

3

4

5

$000

$000

$000

$000

$000

Cashflow

3,447

3,547

3,649

3,753

Capitalallowances

(1,250)

(938)

(703)

(1,859)

Taxableprofit

2,197

2,609

2,946

1,894

Taxation

(439)

(522)

(589)

(379)

After-taxprofit

2,197

2,170

2,424

1,305

(379)

Capitalallowances

1,250

938

703

1,859

After-taxcashflow

3,447

3,108

3,127

3,164

(379)

Workingcapital

(24)

(25)

(26)

(27)

Scrapvalue

250

Netcashflow

3,423

3,083

3,101

3,387

(379)

Discountat12%

0·893

0·797

0·712

0·636

0·567

Presentvalues

3,057

2,457

2,208

2,154

(215)

NPV=9,661–5,000–500=$4·161million

Anominal(moneyterms)approachtoinvestmentappraisaldiscountsnominalcashflowswithanominalcostofcapital.

Nominalcashflowsarefoundbyinflatingforecastvaluesfromcurrentpriceestimates,forexample,usingspecificinflation.

Applyingspecificinflationmeansthatdifferentprojectcashflowsareinflatedbydifferentinflationratesinordertogeneratenominalprojectcashflows.

Arealtermsapproachtoinvestmentappraisaldiscountsrealcashflowswitharealcostofcapital.Realcashflowsarefoundbydeflatingnominalcashflowsbythegeneralrateofinflation.Therealcostofcapitalisfoundbydeflatingthenominalcostofcapitalbythegeneralrateofinflation,usingtheFisherequation:

(1+realdiscountrate)x(1+inflationrate)=(1+nominaldiscountrate)

Thenetpresentvalueforaninvestmentprojectdoesnotdependonwhetheranominaltermsapproachorarealtermsapproachisadopted,sincenominalcashflowsandthenominaldiscountratearebothdiscountedbythegeneralrateofinflationtogiverealcashflowsandtherealdiscountrate,respectively.Bothapproachesgivethesamenetpresentvalue.

Tutorialnoteforillustrativepurposes:

Therealafter-taxcostofcapitalofHDWCocanbefoundasfollows:1·12/1·047=1·07,i.e.therealafter-taxcostofcapitalis7%.

Thefollowingillustrationdeflatesnominalnetcashflows(NCF)bythegeneralrateofinflation(4·7%)togiverealNCF,whicharethendiscountedbytherealcostofcapital(7%).

Year

1

2

3

4

5

$000

$000

$000

$000

$000

NominalNCF

3,423

3,083

3,102

3,387

(379)

RealNCFs

3,269

2,812

2,703

2,819

(301)

Discountat7%

0·935

0·873

0·816

0·763

0·713

Presentvalues

3,057

2,455

2,206

2,151

(215)

Allowingforrounding,theillustrationshowsthatthepresentvaluesoftherealcashflowsarethesameasthepresentvaluesofthenominalcashflows,andthattherealtermsapproachNPVof$4·154millionisthesameasthenominaltermsapproachNPVof$4·161million.ThetwoapproachesproduceidenticalNPVsandofferthesameinvestmentadvice.

思路總結：

Shareholderwealthmaximisation=PVoffutureCFPositiveNPVprojectsupportsthisobjective.

Profitmaximistion(EPS)dependsonthesourceoffinanceFinancingbyshareissue,diluteEPS

Financingbydebt,interestpaymentwilldcreaseprofit.

AlistedcompanysuchasHDWCoislikelytohavearangeoffinancialobjectives.Maximisationofshareholderwealthisoftensuggestedtobetheprimaryfinancialobjective,andthiscanbesubstitutedbytheobjectiveofmaximisingthecompany’sshareprice.OtherfinancialobjectivesthatmightbeusedbyHDWCocouldrelatetoearningspershare(forexample,atargetEPSvalueforagivenperiod),operatingprofit(forexample,atargetlevelofprofitbeforetaxorPBIT),revenue(forexample,adesiredincreaseinrevenueorsales)andsoon.Theseexamplesoffinancialobjectivescanallbequantified,sothatprogresstowardsmeetingthemcanbemeasuredovertime.

TheinvestmentinthenewmachinewillenableHDWCotomeetincreaseddemandforitsproductsandthecompanyexpectstobeabletosellalloftheincreasedproductionataprofit.Thiswillleadtoincreasedrevenueandoperatingprofit(profitbeforeinterestandtax),sofinancialobjectivesrelatingtotheseaccountingfigureswillbesupported.

Whetherafinancialobjectiverelatingtoincreasingearningspershare(EPS)willbesupportedwilldependonhowtheinvestmentisfinanced.Forexample,raisingequityfinancebyissuingnewshareswilldilute(decrease)EPS,whileraisingdebtfinancewillincreaseinterestpayments,whichwillalsodiluteEPS.

Theinvestmentinthenewmachinehasapositivenetpresentvalue(NPV),sothemarketvalueofthecompanyisexpectedtoincreasebytheamountoftheNPV.Thisincreasesthewealthofshareholdersirrespectiveofhowtheinvestmentisfinanced,sincefinancingcostswereaccountedforbythediscountrate(whethernominalorreal).Theinvestmentinthenewmachinewillthereforesupporttheobjectiveofshareholderwealthmaximisation.

2010JuneQ1NPV改錯

Thefollowingdraftappraisalofaproposedinvestmentprojecthasbeenpreparedforthe?nancedirectorofOKMCobyatraineeaccountant.TheprojectisconsistentwiththecurrentbusinessoperationsofOKMCo.

Netpresentvalue=1,645,000–2,000,000=($355,000)sorejecttheproject.

Thefollowinginformationwasincludedwiththedraftinvestmentappraisal:

Theinitialinvestmentis$2million

Sellingprice:$12/unit(currentpriceterms),sellingpricein?ationis5%peryear

Variablecost:$7/unit(currentpriceterms),variablecostin?ationis4%peryear

Fixedoverheadcosts:$500,000/year(currentpriceterms),?xedcostin?ationis6%peryear

$200,000/yearofthe?xedcostsaredevelopmentcoststhathavealreadybeenincurredandarebeingrecoveredbyanannualchargetotheproject

Investment?nancingisbya$2millionloanata?xedinterestrateof10%peryear

OKMCocanclaim25%reducingbalancecapitalallowancesonthisinvestmentandpaystaxationoneyearinarrearsatarateof30%peryear

Thescrapvalueofmachineryattheendofthefour-yearprojectis$250,000

TherealweightedaveragecostofcapitalofOKMCois7%peryear

Thegeneralrateofin?ationisexpectedtobe4·7%peryear

Required:

Identifyandcommentonanyerrorsintheinvestmentappraisalpreparedbythetraineeaccountant. (5marks)

Preparearevisedcalculationofthenetpresentvalueoftheproposedinvestmentprojectandcommentontheproject’sacceptability (12marks)

Solution(a)Errors

Errors