英文版罗斯公司理财习题答案Chap

1、CHAPTERR 9RISK ANNALYSIIS, REEAL OPPTIONSS, ANDD CAPIITAL BBUDGETTINGAnswerss to CConceppts Reeview and CCriticcal Thhinkinng Queestionns1.Foreecastiing riisk iss the risk that a pooor deccisionn is mmade bbecausse of errorrs in projeected cash flowss. Thee dangger iss greaatest with a neww prodduct

2、 bbecausse thee cashh flowws aree probbably hardeer to prediict.2.Withh a seensitiivity analyysis, one vvariabble iss exammined over a brooad raange oof vallues. With a sceenarioo anallysis, all variaables are eexaminned foor a llimiteed rannge off valuues.3.It iis truue thaat if averaage reevenuee

3、is lless tthan aaveragge cosst, thhe firrm is losinng monney. TThis mmuch oof thee stattementt is tthereffore ccorrecct. Att the margiin, hooweverr, accceptinng a pprojecct witth marrginall reveenue iin exccess oof itss margginal cost clearrly accts too incrrease operaating cash flow.4.Fromm the sha

4、reeholdeer perrspecttive, the ffinanccial bbreak-even pointt is tthe moost immportaant. AA projject ccan exxceed the aaccounnting and ccash bbreak-even pointts butt stilll be beloww the finanncial breakk-evenn poinnt. Thhis caauses a redductioon in shareeholdeer (yoour) wwealthh.5.The projeect wiill

5、 reeach tthe caash brreak-eeven ffirst, the accouuntingg breaak-eveen nexxt andd finaally tthe fiinanciial brreak-eeven. For aa projject wwith aan iniitial invesstmentt and saless afteer, thhis orrderinng willl alwways aapply. The cash breakk-evenn is aachievved fiirst ssince it exxcludees depprecia

6、ation. The accouuntingg breaak-eveen is next sincee it iincluddes deepreciiationn. Finnally, the finanncial breakk-evenn, whiich inncludees thee timee valuue of moneyy, is achieeved.6.Tradditionnal NPPV anaalysiss is ooften too cconserrvativve beccause it iggnoress proffitablle opttions such as thhe

7、 abiility to exxpand the pprojecct if it iss proffitablle, orr abanndon tthe prrojectt if iit is unproofitabble. TThe opption to allter aa projject wwhen iit hass alreeady bbeen aacceptted haas a vvalue, whicch inccreasees thee NPV of thhe prooject.7.The type of opption most likelly to affecct thee

8、deciision is thhe opttion tto exppand. If thhe couuntry just liberralizeed itss markkets, theree is llikelyy the potenntial for ggrowthh. Firrst enntry iinto aa markket, wwhetheer an entirrely nnew maarket, or wwith aa new produuct, ccan giive a compaany naame reecogniition and mmarkett sharre. Thhi

9、s maay makke it more diffiicult for ccompettitorss enteering the mmarkett. 8.Sennsitivvity aanalyssis caan detterminne howw the finanncial breakk-evenn poinnt chaanges when some factoors (ssuch aas fixxed coosts, variaable ccosts, or rrevenuue) chhange.9.Therre aree two sourcces off valuue witth thi

10、is deccisionn to wwait. Potenntiallly, thhe priice off the timbeer cann poteentiallly inncreasse, annd thee amouunt off timbber wiill allmost definnitelyy incrrease, barrring aa natuural ccatasttrophee or fforestt firee. Thee optiion too waitt for a loggging compaany iss quitte valluablee, andd comp

11、paniess in tthe inndustrry havve moddels tto esttimatee the futurre groowth oof a fforestt depeendingg on iits agge. 10.Wheen thee addiitionaal anaalysiss has a neggativee NPV. Sincce thee addiitionaal anaalysiss is llikelyy to ooccur almosst immmediattely, this meanss whenn the beneffits oof thee a

12、ddiitionaal anaalysiss outwweigh the ccosts. The beneffits oof thee addiitionaal anaalysiss are the rreducttion iin thee posssibiliity off makiing a bad ddecisiion. OOf couurse, the aadditiional beneffits aare offten ddifficcult, if noot imppossibble, tto meaasure, so mmuch oof thiis deccisionn is b

13、based on exxperieence.Solutioons too Quesstionss and ProbllemsNOTE: AAll ennd of chaptter prroblemms werre sollved uusing a sprreadshheet. Many probllems rrequirre mulltiplee stepps. Duue to spacee and readaabilitty connstraiints, when thesee inteermediiate ssteps are iincludded inn thiss soluutions

14、s manuual, rroundiing maay apppear tto havve occcurredd. Howwever, the finall answwer foor eacch prooblem is foound wwithouut rouundingg duriing anny steep in the pprobleem.Basic1.a.TTo callculatte thee accoountinng breeakeveen, wee firsst neeed to find the ddeprecciatioon forr eachh yearr. Thee dep

15、rreciattion iis:Depreeciatiion = $896,0000/8 Depreeciatiion = $112,0000 perr yearrAnd tthe acccountting bbreakeeven iis:QA = ($900,0000 + 1112,0000)/($338 25) QA = 77,8446 uniitsb.We will use tthe taax shiield aapproaach too calcculatee the OCF. The OOCF iss:OCFbaase = (P v)Q FC(1 tc) + ttcD OCFbaas

16、e = ($38 25)(100,0000) $900,0000(0.65) + 0.355($1122,000) OCFbaase = $2999,200Now wwe cann calcculatee the NPV uusing our bbase-ccase pprojecctionss. Theere iss no ssalvagge vallue orr NWC, so tthe NPPV is:NPVbaase = $8966,000 + $2999,2000(PVIFFA15%,8) NPVbaase = $4466,606.60To caalculaate thhe senn

17、sitivvity oof thee NPV to chhangess in tthe quuantitty solld, wee willl calcculatee the NPV aat a ddifferrent qquantiity. WWe willl usee salees of 105,0000 unnits. The NNPV att thiss salees levvel iss: OCFneew = ($38 25)(105,0000) $900,0000(0.65) + 0.355($1122,000) OCFneew = $341,4550And tthe NPPV i

18、s:NPVneew = $896,0000 + $341,4450(PVVIFA155%,8) NPVneew = $6366,195.93So, tthe chhange in NPPV forr everry uniit chaange iin salles iss:NPV/SS = ($636,1195.933 4466,606.60)/(105,0000 1000,0000) NPV/SS = +$37.9118If saales wwere tto droop by 100 uunits, thenn NPV wouldd dropp by:NPV ddrop = $37.9918(

19、100) = $3,791.880You mmay woonder why wwe choose 1005,0000 unitts. Beecausee it ddoesnt mattter! Whateever ssales numbeer we use, when we caalculaate thhe chaange iin NPVV per unit sold, the ratioo willl be tthe saame. c.To find out hhow seensitiive OCF is too a chhange in vaariablle cossts, wwe wil

20、ll commpute the OOCF att a vaariablle cosst of $24. Againn, thee numbber wee chooose too use here is irrrelevvant: We wiill geet thee samee ratiio of OCF tto a oone doollar changge in variaable ccost nno mattter wwhat vvariabble coost wee use. So, usingg the tax sshieldd apprroach, the OCF aat a vva

21、riabble coost off $24 is:OCFneew = ($38 24)(100,0000) 9900,0000(0.65) + 0.355($1122,000) OCFneew = $3644,200So, tthe chhange in OCCF forr a $11 channge inn variiable costss is:OCF/vv = ($299,2200 364,2200)/($25 24) OCF/vv = $65,0000If vaariablle cossts deecreasse by $5 thenn, OCFF woulld inccreasee

22、by OCF iincreaase = $65,0000*5 = $325,0002.We wwill uuse thhe taxx shieeld appproacch to calcuulate the OOCF foor thee bestt- andd worsst-casse sceenarioos. Foor thee bestt-casee scennario, the pricee and quanttity iincreaase byy 10 ppercennt, soo we wwill mmultipply thhe basse casse nummbers by 1.1

23、, a 10 peercentt incrrease. The variaable aand fiixed ccosts both decreease bby 10 perceent, sso we will multiiply tthe baase caase nuumberss by .9, a 10 peercentt decrrease. Doinng so, we gget:OCFbesst = ($388)(1.11) ($25)(0.9)(1100K)(1.1) $900K(00.9)(0.65) + 0.35($112K) OCFbesst = $8922,650The bee

24、st-caase NPPV is:NPVbesst = $896,0000 + $892,6650(PVVIFA155%,8) NPVbesst = $3,1109,6007.54For thhe worrst-caase sccenariio, thhe priice annd quaantityy decrrease by 100 perccent, so wee willl multtiply the bbase ccase nnumberrs by .9, aa 10 ppercennt deccreasee. Thee variiable and ffixed costss both

25、h incrrease by 100 perccent, so wee willl multtiply the bbase ccase nnumberrs by 1.1, a 10 perceent inncreasse. Dooing sso, wee get:OCFworrst = ($338)(0.9) ($25)(1.1)(1100K)(0.9) $900K(11.1)(0.65) + 0.35($112K) OCFworrst = 2122,350The woorst-ccase NNPV iss:NPVworrst = $8966,000 $212,350(PPVIFA115%,8

26、) NPVworrst = $1,848,8882.7223.We ccan usse thee accoountinng breeakeven equattion:QA = (FC + D)/(PP v) to sollve foor thee unknnown vvariabble inn eachh casee. Doiing soo, we find:(1): QA = 1300,200 = (8850,000 + D)/(41 30) D = 582,2200(2): QA = 1355,000 = (3.2M + 1.15M)/(P 56) P = 88.222(3): QA =

27、5,4478 = (160,0000 + 1105,0000)/(105 v) v = 56.624.Whenn calcculatiing thhe finnanciaal breeakeveen poiint, wwe exppress the iinitiaal invvestmeent ass an eequivaalent annuaal cosst (EAAC). DDividiing thhe in initiial innvestmment bby thee seveen-yeaar annnuity factoor, diiscounnted aat 12 perceent,

28、 tthe EAAC of the iinitiaal invvestmeent iss:EAC = Initiial Innvestmment / PVIFFA12%,5EAC = 200,0000 / 3.604478EAC = 55,4881.95Note, this calcuulatioon sollves ffor thhe annnuity paymeent wiith thhe iniitial invesstmentt as tthe prresentt valuue of the aannuitty, inn otheer worrds:PVA = C(1 1/(1 + R

29、R)t / R)200,0000 = C1 (1/11.12)55 / .12C = 555,4811.95 The annnual depreeciatiion iss the cost of thhe equuipmennt divvided by thhe ecoonomicc lifee, or:Annuall deprreciattion = 200,0000 / 5Annuall deprreciattion = 40,0000Now wee can calcuulate the ffinanccial bbreakeeven ppoint. The finanncial brea

30、kkeven pointt for this projeect iss: QF = EAC + FC(11 tCC) DDeprecciatioon(tC) / (P VC)(1 ttC) QF = 55,4881.95 + 350,0000(.755) 40,0000(0.225) / (225 55) (.225) QF = 220,5322.13 oor aboout 200,532 unitss5.If wwe purrchasee the machiine tooday, the NNPV iss the cost plus the ppresennt vallue off the

31、increeased cash flowss, so:NPV0 = 1,5000,000 + 280,0000(PVVIFA122%,10) NPV0 = 82,0662.45We shoould nnot puurchasse thee machhine ttoday. We wwould want to puurchasse thee machhine wwhen tthe NPPV is the hhighesst. Soo, we need to caalculaate thhe NPVV eachh yearr. Thee NPV each year will be thhe cos

32、st pluus thee pressent vvalue of thhe inccreaseed cassh savvings. We mmust bbe carreful howevver. IIn ordder too makee the correect deecisioon, thhe NPVV for each year must be taaken tto a ccommonn datee. We will discoount aall off the NPVs to tooday. Doingg so, we geet:Year 11: NPV1 = 1,3755,000 +

33、280,0000(PVVIFA122%,9) / 1.12 NPV1 = 104,3383.888Year 22: NPV2 = 1,2500,000 + 280,0000(PVVIFA122%,8) / 1.122 NPV2 = 112,3355.822Year 33: NPV3 = 1,1255,000 + 280,0000(PVVIFA122%,7) / 1.123 NPV3 = 108,7796.911Year 44: NPV4 = 1,000,000 + 280,0000(PVVIFA122%,6) / 1.124 NPV4 = 96,0886.55Year 55: NPV5 = 1

34、,0000,000 + 280,0000(PVVIFA122%,5) / 1.125 NPV5 = 5,2988.26Year 66: NPV6 = 1,0000,000 + 280,0000(PVVIFA122%,4) / 1.126 NPV6 = 75,7662.72The coompanyy shouuld puurchasse thee machhine ttwo yeears ffrom nnow whhen thhe NPVV is tthe hiighestt.6.We nneed tto callculatte thee NPV of thhe twoo optiions, g

35、o diirectlly to markeet noww, or utiliize teest maarketiing fiirst. The NNPV off goinng dirrectlyy to mmarkett now is:NPV = CSucccess (Prob. of SSuccesss) + CFaiilure (Probb. of Failuure)NPV = $20,0000,0000(0.445) + $5,0000,0000(0.555)NPV = $11,750,0000Now wee can calcuulate the NNPV off testt markk

36、etingg firsst. Teest maarketiing reequirees a $2 milllion cash outlaay. CChoosiing thhe tesst marrketinng opttion wwill aalso ddelay the llaunchh of tthe prroductt by oone yeear. Thus, the expeccted ppayofff is ddelayeed by one yyear aand muust bee disccounteed bacck to year 0. NPV= CC0 + CSucccess

37、(Prob. of SSuccesss) + CFaailuree (Proob. off Faillure) / (1 + RR)tNPV = $2,0000,0000 + $20,000,0000 (00.75) + $5,0000,000 (0.255) / 1.155 NPV = $12,1130,4334.78The coompanyy shouuld noot go direcctly tto marrket wwith tthe prroductt sincce thaat opttion hhas loower eexpectted paayoff. 7.We nneed tt

38、o callculatte thee NPV of eaach opption, and choosse thee optiion wiith thhe higghest NPV. So, tthe NPPV of goingg direectly to maarket is: NPV = CSucccess (Prob. of SSuccesss) NPV = Rs.1,2200,0000 (0.55)NPV = Rs.6660,0000The NPPV of the ffocus groupp is: NPV = C0 + CSuuccesss (Proob. off Succcess)

39、NPV = Rs.1200,000 + Rs.1,2000,000 (0.700) NPV = Rs.7200,000And thhe NPVV of uusing the cconsullting firm is:NPV = C0 + CSuuccesss (Proob. off Succcess) NPV = Rs.4000,000 + Rs.1,2000,000 (0.900)NPV = Rs.6800,000The fiirm shhould conduuct a focuss grouup sinnce thhat opption has tthe hiighestt NPV. 8.

40、The compaany shhould analyyze booth opptionss, andd chooose thhe opttion wwith tthe grreatesst NPVV. So, if tthe coompanyy goess to mmarkett immeediateely, tthe NPPV is:NPV = CSucceess (PProb. of Suuccesss) + CCFailuure (PProb. of Faailuree)NPV = 30,0000,0000(.55) + 3,0000,000(.45)NPV = 17,8550,0000

41、.00 Customeer seggment reseaarch rrequirres a 1 milllion cash outlaay. Chhoosinng thee reseearch optioon willl alsso dellay thhe lauunch oof thee prodduct bby onee yearr. Thuus, thhe exppectedd payooff iss delaayed bby onee yearr and must be diiscounnted bback tto yeaar 0. So, tthe NPPV of the ccust

42、ommer seegmentt reseearch is:NPV= CC0 + CSucccess (Prob. of SSuccesss) + CFaailuree (Proob. off Faillure) / (1 + RR)tNPV = 1,0000,000 + 30,0000,0000 (0.770) + 3,0000,000 (0.300) / 1.155 NPV = 18,0443,4788.26Graphiccally, the decission ttree ffor thhe prooject is:StartStartResearchNo Research18.0435

43、million at t = 017.85 million at t = 0SuccessFailureSuccessFailure30 million at t = 1(26.087 million at t = 0)3 million at t = 1(2.6087 million at t = 0)30 million at t = 03 million at t = 0The coompanyy shouuld unndertaake thhe marrket ssegmennt ressearchh sincce it has tthe laargestt NPV.9.a.TThe

44、acccountting bbreakeeven iis thee afteertax sum oof thee fixeed cossts annd deppreciaation chargge divvided by thhe afttertaxx conttributtion mmarginn (sellling pricee minuus varriablee costt). Soo, thee accoountinng breeakeveen levvel off salees is: QA = (FC + Deppreciaation)(1 tC) / (P VC)(1 ttC)

45、QA = ($3440,0000 + $220,0000) (1 0.335) / ($22.00 0.722) (1 0.335)QA = 281,2250.000b.Wheen callculatting tthe fiinanciial brreakevven pooint, we exppress the iinitiaal invvestmeent as ann equiivalennt annnual ccost (EAC). Diviiding the iin iniitial invesstmentt by tthe seeven-yyear aannuitty facctor

46、, discoountedd at 115 perrcent, the EAC oof thee inittial iinvesttment is:EAC = Inittial IInvesttment / PVIIFA15%,7EAC = $1400,000 / 4.11604 EAC = $33,650.445Note, thiss calcculatiion soolves for tthe annnuityy paymment wwith tthe innitiall inveestmennt as the ppresennt vallue off the annuiity, iin

47、othher woords:PVA = C(1 1/(1 + RR)t / R)$140,000 = C1 (1/11.15)77 / .15C = $33,6550.45 Now wwe cann calcculatee the finanncial breakkeven pointt. Thee finaanciall breaakevenn poinnt forr thiss projject iis: QF = EAC + FC(1 tC) Deepreciiationn(tC) / (P VC)(1 tC) QF = $33,650.445 + $340,0000(.665) $20

48、,000(.35) / ($2 0.722) (.665) QF = 297,6656.799 or aabout 297,6657 unnits10. Whhen caalculaating the ffinanccial bbreakeeven ppoint, we eexpresss thee inittial iinvesttment as ann equiivalennt annnual ccost (EAC). Diviiding the iin iniitial invesstmentt by tthe fiive-yeear annnuityy facttor, ddiscou

49、unted at 8 perceent, tthe EAAC of the iinitiaal invvestmeent iss:EAC = Initiial Innvestmment / PVIFFA8%,55EAC = 300,0000 / 3.604478EAC = 75,1336.94Note, this calcuulatioon sollves ffor thhe annnuity paymeent wiith thhe iniitial invesstmentt as tthe prresentt valuue of the aannuitty, inn otheer worrd

50、s:PVA = C(1 1/(1 + RR)t / R)300,0000 = C1 (1/11.08)55 / .08C = 775,1366.94 The annnual depreeciatiion iss the cost of thhe equuipmennt divvided by thhe ecoonomicc lifee, or:Annuall deprreciattion = 300,0000 / 5Annuall deprreciattion = 60,0000Now wee can calcuulate the ffinanccial bbreakeeven ppoint.

51、 The finanncial breakkeven pointt for this projeect iss: QF = EAC + FC(11 tCC) DDeprecciatioon(tC) / (P VC)(1 ttC) QF = 75,1136.944 + 100,0000(.666) 60,0000(0.334) / (60 8) (.34) QF = 33,517.98 orr abouut 3,5518 unnitsIntermmediatte11.a.At thhe acccountiing brreakevven, tthe IRRR is zero perceent si

52、ince tthe prrojectt recoovers the iinitiaal invvestmeent. TThe paaybackk periiod iss N yeears, the llengthh of tthe prrojectt sincce thee inittial iinvesttment is exxactlyy recooveredd overr the projeect liife. TThe NPPV at the aaccounnting breakkeven is: NPV = I (1/N)(PVIFAAR%,N) 1b.At the ccash bb

53、reakeeven llevel, the IRR iis 1000 perrcent, the paybaack peeriod is neegativve, annd thee NPV is neegativve andd equaal to the iinitiaal cassh outtlay.c.Thee defiinitioon of the ffinanccial bbreakeeven iis wheere thhe NPVV of tthe prrojectt is zzero. If thhis iss truee, theen thee IRR of thhe prooj

54、ect is eqqual tto thee requuired returrn. Itt is iimposssible to sttate tthe paaybackk periiod, eexceptt to ssay thhat thhe payyback periood musst be less than the llengthh of tthe prrojectt. Sinnce thhe disscountted caash fllows aare eqqual tto thee inittial iinvesttment, the undisscountted caash f

55、llows aare grreaterr thann the initiial innvestmment, so thhe payyback must be leess thhan thhe prooject life.12.Usiing thhe taxx shieeld appproacch, thhe OCFF at 1110,000 unitss willl be:OCF = (P v)Q FC(1 tC) + ttC(D) OCF = ($288 19)(1100,000) 150,000(0.666) + 00.34($420,0000/4) OCF = $590,100We wi

56、lll callculatte thee OCF at 1111,0000 unitts. Thhe chooice oof thee secoond leevel oof quaantityy soldd is aarbitrrary aand irrrelevvant. No maatter what levell of uunits sold we chhoose, we wwill sstill get tthe saame seensitiivity. So, the OOCF att thiss leveel of saless is:OCF = ($288 19)(1111,00

57、0) 1550,000(0.666) + 00.34($420,0000/4) OCF = $596,040The seensitiivity of thhe OCFF to cchangees in the qquantiity soold iss:Sensittivityy = OCF/Q = ($5596,040 5590,100)/(111,0000 110,0000) OCF/Q = +$55.94OCF wiill inncreasse by $5.944 for everyy addiitionaal uniit solld. 13.a.The bbase-ccase, best

58、-case, and worstt-casee valuues arre shoown beelow. Rememmber tthat iin thee bestt-case, salees andd pricce inccreasee, whiile coosts ddecreaase. IIn thee worsst-casse, saales aand prrice ddecreaase, aand coosts iincreaase.ScennarioUnit salessVariaable ccostFixedd costtsBasee190元15,0000元225,0000Best

59、t209元13,5000元202,5500Worsst171元16,5000元247,5500Usingg the tax sshieldd apprroach, the OCF aand NPPV forr the base caase esstimatte is:OCFbaase = (元21,0000 15,000)(190) 元225,0000(00.65) + 0.335(元720,0000/4) OCFbaase = 元657,7750NPVbaase = 元720,0000 + 元657,7750(PVVIFA155%,4) NPVbaase = 元1,1577,862.02Th

60、e OOCF annd NPVV for the wworst case estimmate aare:OCFwoorst = (元21,0000 16,500)(171) 元247,5500(00.65) + 0.335(元720,0000/4) OCFwoorst = 元402,3000NPVwoorst = 元720,0000 + 元402,3000(PVIFFA15%,4) NPVwoorst = +元428,5557.800And tthe OCCF andd NPV for tthe beest caase esstimatte aree:OCFbeest = (元21,0000