Chap010newWord下载.docx

Chap010newWord下载.docx

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b.Averagecost=$3.50million/2million=$1.75/burger

c.Thefixedcostsarespreadacrossmoreburgers—thustheaveragecostfalls.

4.a.（Revenue–expenses）changesby$1million–$0.5million=$0.5million.

After-taxprofitsincreaseby$0.5million（1–0.35）=$0.325million.

Becausedepreciationisunaffected,cashflowchangesbythesameamount.

b.Expensesincreasefrom$5millionto$6.5million.

After-taxincomeandcashflowdecreaseby:

$1.5million（1–0.35）=$0.975million

5.The12%,10-yearannuityfactoris:

TheeffectonNPVequalsthechangeinCF5.65022.

a.$0.325million5.65022=$1.836million

$0.975million5.65022=$5.509million

b.Fixedcostscanincreaseuptothepointatwhichthehighercosts（aftertaxes）reduceNPVby$2million:

Increaseinfixedcosts（1–T）annuityfactor（12%,10years）=$2million

Increaseinfixedcosts（1–0.35）5.65022=$2million

Increaseinfixedcosts=$544,567

c.Accountingprofitsarecurrently$（10–5–2）million（1–0.35）=$1.95million.

Fixedcostscanincreasebythisamountbeforepretaxprofitsarereducedtozero.

06–10

6.Revenue=pricequantity=$26million=$12million

Expense=variablecost+fixedcost=（$16million）+$2million=$8million

Depreciationexpense=$5million/5years=$1millionperyear

Cashflow=（1T）（revenue–expenses）+（Tdepreciation）

=[0.60（$12million–$8million）]+（0.4$1million）=$2.8million

a.NPV=–$5million+[$2.8millionannuityfactor（10%,5years）]

=–$5million+$2.8million

million

b.Ifvariablecost=$1.20,thenexpensesincreaseto:

（$1.206million）+$2million=$9.2million

CF=[0.60（$12million–$9.2million）]+（0.4$1million）=$2.08million

NPV=–$5million+[$2.08millionannuityfactor（10%,5years）]

=–$5million+$2.08million

c.Iffixedcosts=$1.5million,expensesfallto:

（$16million）+$1.5million=$7.5million

Cashflow=[0.60（$12million–$7.5million）]+（0.4$1million）=$3.1million

NPV=–$5million+[$3.1millionannuityfactor（10%,5years）]

=–$5million+$3.1million

d.CallPthepriceperjar.Then:

Revenue=P6million

Expense=（$16million）+$2million=$8million

Cashflow=[（1–0.40）（6P–8）]+（0.401）=3.6P–4.4

NPV=–5+[（3.6P–4.4）annuityfactor（10%,5years）]

=–5+[（3.6P–4.4）

=–5+[（3.6P–4.4）3.7908]=–21.6795+13.6469P=0P=$1.59perjar

11–15

7.

MostLikely

BestCase

WorstCase

Price

$50

$55

$45

Variablecost

$30

$27

$33

Fixedcost

$300,000

$270,000

$330,000

Sales

30,000units

33,000units

27,000units

Cashflow=[（1–T）（revenue–cashexpenses）]+（Tdepreciation）

Depreciationexpense=$1million/10years=$100,000peryear

Best-caseCF=0.65[33,000（$55–$27）–$270,000]+（0.35$100,000）=$460,100

Worst-caseCF=0.65[27,000（$45–$33）–$330,000]+（0.35$100,000）=$31,100

12%,10-yearannuityfactor=

Best-caseNPV=（5.65022$460,100）–$1,000,000=$1,599,666

Worst-caseNPV=（5.65022$31,100）–$1,000,000=–$824,278

8.Ifpriceishigher—forexample,becauseofinflation—variablecostsmayalsobehigher.Similarly,ifpriceishighbecauseofstrongdemandfortheproduct,thensalesmaybehigher.Itdoesn’tmakesensetoformulateascenarioanalysisinwhichuncertaintyineachvariableistreatedindependentlyofallothervariables.

9.Atthebreak-evenlevelofsales（60,000units）profitwouldbezero:

Profit=[60,000（2–variablecostperunit）]–20,000–10,000=0

Solvetofindthatvariablecostperunit=$1.50.

10.a.Eachdollarofsalesgenerates$0.60ofpretaxprofit.Depreciationexpenseis$100,000peryear,andfixedcostsare$200,000.Therefore:

Accountingbreak-evenrevenue=（$200,000+$100,000）/0.60=$500,000

Thefirmmustsell5,000diamondsannually.

b.LetQ=thenumberofdiamondssold.

Cashflow=[（1–0.35）（revenue–expenses）]+（0.35depreciation）

=[0.65（100Q–40Q–200,000）]+（0.35100,000）

=39Q–95,000

Therefore,forNPVtoequalzero:

（39Q–95,000）5.65022=$1,000,000Q=6,974diamondsperyear

11.a.Theaccountingbreak-evenpointwouldincreasebecausethedepreciationchargewillbehigher,therebyreducingnetprofit.

b.Thebreak-evenpointwoulddecreasebecausethepresentvalueofthedepreciationtaxshieldwillbehigherwhenalldepreciationchargescanbetakeninthefirst5years.

12.Theaccountingbreak-evenpointwouldbeunaffectedsincetaxespaidarezerowhenpretaxprofitiszero,regardlessofthetaxrate.

Thebreak-evenpointwouldincreasesincetheafter-taxcashflowcorrespondingtoanylevelofsalesfallswhenthetaxrateincreases.

13.Cashflow=netincome+depreciation

Ifdepreciationispositive,thencashflowwillbepositiveevenwhennetincome=0.Therefore,thelevelofsalesnecessaryforcashflowbreak-evenislessthanthelevelofsalesnecessaryforzero-profitbreak-even.

14.Ifcashflow=0fortheentirelifeoftheproject,thenthepresentvalueofcashflows=0,andprojectNPVwillbenegativeintheamountoftherequiredinvestment.

15.a.Variablecost=75%ofsalesrevenue

Therefore,additionalprofitper$1ofadditionalsales=$0.25.

Depreciationexpense=$3,000/5=$600peryear

Break-evenlevelofsales=

Thissaleslevelcorrespondstoaproductionlevelof$6,400/$80perunit=80units.

TofindtheNPVbreak-evenlevelofsales,firstcalculatecashflow.

Withnotaxes:

Cashflow=（0.25sales）–1,000

The10%,5-yearannuityfactoris:

Therefore,ifprojectNPVequalszero:

PV（cashflows）–investment=0

[3.79079（0.25sales）–1,000）]–3,000=0

（0.94770sales）–3,790.79–3,000=0sales=$7,166

Thissaleslevelcorrespondstoaproductionlevelof$7,166/$80=almost90units.

b.Nowtaxesare35%ofprofits.Accountingbreak-evenisunchangedsincetaxesarezerowhenprofits=0.

TofindNPVbreak-even,recalculatecashflow:

Cashflow=[（1–T）（revenue–cashexpenses）]+（Tdepreciation）

=0.65[（0.25sales）–1,000]+（0.35600）=（0.1625sales）–440

Theannuityfactoris3.79079,sowefindNPVasfollows:

3.79079[（0.1625sales）–440]–3,000=0sales=$7,578

Thiscorrespondstoproductionof$7,578/$80=almost95units.

16.a.Accountingbreak-evenlevelofsalesincreases.MACRSresultsinhigherdepreciationchargesintheearlyyearsoftheproject,requiringahighersaleslevelforthefirmtobreakevenintermsofaccountingprofits.

b.NPVbreak-evenlevelofsalesdecreases.TheaccelerateddepreciationincreasesthepresentvalueofthetaxshieldandthusreducesthelevelofsalesnecessarytoachievezeroNPV.

c.MACRSmakestheprojectmoreattractive.ThePVofthetaxshieldishigher,sotheNPVoftheprojectatanygivenlevelofsalesishigher.

17.

Sales$16,000,000

Variablecosts12,800,000（80%ofsales）

Fixedcosts2,000,000

Depreciation500,000（includesdepreciationon

newcheckoutequipment）

=Pretaxprofit$700,000

Taxes（at40%）280,000

=Profitaftertax$420,000

+Depreciation500,000

=Cashflowfromoperations$920,000

a.Cashflowincreasesby$140,000[from$780,000（seeTable9-1）to$920,000].

Thecostoftheinvestmentis$600,000.Therefore:

NPV=–$600,000+[$140,000annuityfactor（8%,12years）]

=–$600,000+$140,000

=–$600,000+$140,0007.53608=$455,051

b.Theequipmentreducesvariablecostsfrom81.25%ofsalesto80%ofsales.Pretaxsavingsarethereforeequalto（0.0125sales）.Ontheotherhand,annualdepreciationexpenseincreasesby$600,000/12=$50,000.Therefore,accountingprofitsareunaffectedifsalesequal$50,000/0.0125=$4,000,000.

c.Theprojectreducesvariablecostsfrom81.25%ofsalesto80%ofsales.Pretaxsavingsarethereforeequalto（0.0125sales）.Annualdepreciationexpenseincreasesby$50,000.Therefore,after-taxcashflowincreasesby:

[（1–T）（revenue–expenses）]+（Tdepreciation）

=[（1–0.4）（0.0125sales）]+（0.450,000）=（0.0075sales）+20,000

ForNPVtoequalzero,theincrementtocashflowtimesthe12-yearannuityfactormustequaltheinitialinvestment:

Cashflow7.5