chap020 Working Capital Management.docx

chap020 Working Capital Management.docx

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chap020WorkingCapitalManagement

SolutionstoChapter20

WorkingCapitalManagement

1.a.Thediscountis:

1%of$1,000=$10

b.Thecustomergainsanextra40daysofcredit.

c.Withthediscount,thecustomerpays$990.Withoutthediscount,thecustomerpays$1,000.Thedifferenceis:

$10/$990=1.01%

Arateof1.01%per40daysofextracreditisequivalenttoanannualrateof:

（1.0101）365/40–1=0.0960=9.60%

2.openaccount

commercialdraft

tradeacceptance

thecustomer’s

banker’sacceptance

3.a.Perishablegoods（bread）callforashortercreditperiod.

b.Rapidinventoryturnover（higherturnoverratio）callsforashortercreditperiod.

c.Thefirmsellingtocustomerswiththemoretangibleandsaleableassetswillgrantalongercreditperiod.Thisisthefirmsellingtoelectricutilities.

4.a.Theservicechargediscourageslatepayment.Theduelagdecreasesand,therefore,paylagdecreases.

b.Companiesmightbeforcedtostretchpayables.Duelagand,therefore,paylagincrease.

c.Termslagincreasesand,therefore,paylagincreases.

5.Thecurrenttermsallowa3%discountifthecustomergivesupanextra40–20=20daysofcredit.Theeffectiveannualrateis:

[1+（3/97）]（365/20）–1=0.7435=74.35%

a.Theimplicitrateincreasesbecausethediscountishigher:

[1+（4/96）]（365/20）–1=1.1064=110.64%

b.Theimplicitrateincreasesbecausetheextradaysofcredit‘bought’byforfeitingthediscountdecreaseto:

40–30=10days

[1+（3/97）]（365/10）–1=2.0397=203.97%

c.Theimplicitrateincreasesbecausetheextradaysofcredit"bought"byforfeitingthediscountdecreasesto:

30–20=10days

[1+（3/97）]（365/10）–1=2.0397=203.97%

6.Ledgerbalance=startingbalance–payments+deposits

Ledgerbalance=$250,000–$20,000–$60,000+$45,000=$215,000

Thepaymentfloatistheoutstandingtotalofnot-yet-clearedcheckswrittenbythefirm,whichequals$60,000inthiscase.

Thenetfloatis:

$60,000–$45,000=$15,000

7.Ifyoupayyourbillbywritingacheckinthetraditionalmanner,therewillbeadelayofseveraldaysbeforethecheckispresentedtoyourbank,andthebankdebitsyouraccount.Duringthisperiod,themoneystaysinyouraccountandyoumayearninterestonthefunds.Incontrast,ifyouusetheInternettoorderyourbanktosendoutacheckonyourbehalf,thebankcandebityouraccountimmediately,atwhichpointyouwillstopearninginterestonthefunds.Thebank,however,stillhasaccesstothefundsuntilthecheckitsendsoutactuallyclears.Therefore,thebankiswillingtoprovideyouthisservice“forfree.”Inaddition,itischeaperforthebanktoprocesselectronicorderpaymentsthanpaperpayments,whichisanothersourceofsavingsthatinducethemtooffertheservicefornoextracharge.

8.a.Paymentfloat=$20,0006=$120,000

Availabilityfloat=$22,0003=$66,000

Netfloat=$54,000

b.Ifavailabilityfloatwerereducedbyoneday,theninterestcouldbeearnedon$22,000.Annualinterestearningswouldbe:

0.06$22,000=$1,320

9.a.Thelock-boxreducescollectionfloatby:

400paymentsperday$2,000perpayment2days=$1,600,000

Dailyinterestsaved=0.00015$1,600,000=$240

Thebankchargeeachdayis:

400paymentsperday$0.40perpayment=$160

Thelock-boxisworthwhile;interestearningsexceedthebankcharges.

b.Break-evenoccurswheninterestearnedequalsthebankfees:

0.00015[400$2,000Dayssaved]=$160Dayssaved=1.33

10.concentrationbanking

wiretransfer

alock-boxsystem

11.a.Two-thirdsofcustomerspaywithin15days.Theotherone-thirdofcustomerspaybyday30.Therefore,theaccountsreceivableperiodis:

（2/315）+（1/330）=20days

b.InvestmentinA/R=accountsreceivableperioddailysales

c.Withgreaterincentivetopayearly,morecustomerswillpaywithin15daysinsteadof30days.Therefore,theaccountsreceivableperiodislikelytodecrease.

12.a.PVofacash-on-deliverysale=$50–$40=$10percarton

Underthepresentcash-on-deliverypolicy,unitsalesequal1,000cartonspermonth:

$10percarton1,000cartons=$10,000

Ifcreditisextended,salesincrease,butpresentvaluepercartondecreasesto:

PVofrevenue–Cost

percarton

$9.505percarton1,060cartons=$10,075

Thehighersalesmorethanmakeupforthetimevaluecostofthecreditextended.

b.Iftheinterestrateis1.5%,PVpercartondecreasesto:

PVofrevenue–Cost

percarton

$9.261percarton1,060cartons=$9,817

Atthehigherinterestrate,thehighersalesnolongerareenoughtomakeupforthecostofthecreditextended.

c.ThePVoftheoldcustomersremainsunaffected.ThePVofthenewcustomersispositive:

Theadditionalsalesgainedbyextendingcreditis60cartons.Theprofitmargin（inpresentvalueterms）is:

percarton

13.PV（COST）=96

PV（REV）=101/1.01=100

a.Theexpectedprofitfromasaleis:

[0.93（$100–$96）]–（0.07$96）=–$3

Thefirmshouldnotextendcredit.

b.Atthebreak-evenprobability,expectedprofitequalszero:

[p（$100–$96）]–[（1–p）$96]=0p=0.96

Soifthefirmistobreakeven,96%ofitscustomersmustpaytheirbills.

c.Apayingcustomernowrepresentsaperpetuityofprofitsequalto:

$100–$96=$4permonth

Thepresentvalueis:

$4/0.01=$400

Sothepresentvalueofasale,givena7%defaultrate,is:

（0.93$400）–（0.07$96）=$365.28

Itclearlypaystoextendcredit.

d.（p$400）–[（1–p）$96]=0p=0.194=19.4%

Sotheprobabilityofpaymentmustbegreaterthan19.4%tojustifyextendingcredit.

14.a.Theexpectedprofitforasaleis:

[0.95（$1,200–$1,050）]–（0.05$1,050）=$90

b.Thebreak-evenprobabilityofcollectionisfoundbysolvingforpasfollows:

[p（$1,200–$1,050）]–[（1–p）$1,050]=0p=1,050/1,200=0.875

15.Fromthediscussioninthetextregardingfinancialratios（seeChapter4）,importantratiostoconsiderare:

∙Cashflow/Totaldebt

∙Netincome/Totalassets

∙Totaldebt/Totalassets

∙Workingcapital/Totalassets

∙Currentassets/Currentliabilities

16.Thecostis$50.

PV（revenues）

Theexpectedprofitfortheorderistherefore:

[0.75（57.74–50）]–（0.2550）=–$6.70periron

Youshouldrejecttheorder.

17.Themorestringentpolicyshouldbeadoptedbecauseprofitwillincrease,asshowninthefollowingtable.Forevery$100ofcurrentsales:

CurrentPolicyMoreStringentPolicy

Sales100.095.0

Lessbaddebts*6.03.8

Lesscostofgoods**80.076.0

Profits14.015.2

*6%ofsalesundercurrentpolicy;4%underproposedpolicy.

**80%ofsales

18.a.Allowingforthepossibilityofdefault,thepresentvalueofasaleundercurrentcredittermsis:

Underacash-on-deliverypolicy,saleswouldbe40%lower,butdefaultsandthetimevaluecostofextendedcreditwouldbeeliminated.Presentvalue（assumingsalesvolumeequalto60%ofcurrentlevels）wouldbe:

0.6（15–10）=3

TheswitchtoaCODpolicyseemstomakesense.

b.Ifcustomerswhopaybillsontimegeneratesixadditionalrepeatsales,theneachsuccessfulsaleisrepeatedanadditionalsixtimes;incontrast,adefaultingsaleoccursonlyonce.ThePVofacreditsalebecomes（notethatthe6-monthannuityfactorfor1%permonthis5.7955）:

annuityfactor（1%,6months）（0.2510）=$22.23

Thepresentvalueofacash-on-deliverypolicygiventhelowersalesvolumeis:

0.60[（15–10）+（15–10）Annuityfactor（1%,6months）]=$20.39

Inthiscase,repeatsalesmaketheextensionofcreditapreferablestrategy.

19.Profitsfromcashsalesarecurrently:

100（$101–$80）=$2,100

a.Ifonemonth（30days）freecreditisgranted,thepresentvalueofrevenueperunitdecreasesto:

$101/1.01=$100

Assumingthatbotholdandnewcustomerstakeadvantageofthefreecredit,thepresentvalueofprofitswillincreaseto:

110（$100–$80）=$2,200

Allowingtradecreditthereforeisbeneficial.

b.Nowassumethat5%ofallcustomerswilldefaultontheirbills.Theexpectedvalueof（discounted）profitsbecomes:

Unitssold[pPV（REV–COST）–（1–p）PV（COST）]=

$110[0.95（$100–$80）–（0.05$80）]=$1,650

Thisislessthancurrentprofitof$2,100,whichmeansthattradecreditshouldnotbeallowed.

c.Ifonlynewcustomersposedefaultrisk,youneedtolookattheincrementalprofitfromthenewcustomersthefirmwillattractbyrelaxingcreditpolicyminusthevalueofthefreecreditthatthefirmextendstoitscurrentcustomers.Thefreecreditcoststhefirm$1percurrentcustomer,sincethepresentvalueofasalefallsfrom$101to$100.

Valueofnewcustomers=10[0.95（$100$80）–（0.05$80）]=$150

Costoffreecredittocurrentcustomers=100$1=$100

Netbenefitfromadvancingcredit=$150–$100=$50

Nowitappearsworthwhiletoallowtradecredit.

20.a.Collectionfloatdecreasesby:

$15,000perday2dayssaved=$30,000

b.Dailyinterestsaving=0.0002$30,000=$6

c.Monthlysavings=30$6=$180

ThisisthemaximumfeeSherman’sshouldpay.

21.a.Thelockboxwillcollectanaverageof:

$300,000/30=$10,000perday

Themoneywillbeavailablethreedaysearlier;thiswillincreasethecashavailabletoJACby$30,000.Thus,JACwillbebetteroffacceptingthecompensatingbalanceoffer:

$25,000istiedupinthecompensatingbalance,butthelock-boxfreesup$30,000.

b.Letxequaltheaveragechecksizeforbreak-even.Thenthenumberofcheckswrittenpermonthis（300,000/x）andthemonthlycostofthelockboxis:

（300,000/x）0.10

Thealternativeisthecompensatingbalanceof$25,000;itsmonthlycostisth