英文版罗斯公司理财习题答案Chap009

1、暗CHAPTER皑 芭9昂RISK AN摆ALYSIS,稗 REAL O俺PTIONS,耙 叭AND 芭CAPITAL癌 BUDGET拜ING按Answers暗 to Con扒cepts R翱eview a唉nd Crit拌ical Th霸inking 氨Questio吧ns摆1.唉阿Forecas癌ting ri捌sk is t班he risk巴 that a昂 poor d坝ecision皑 is mad拜e becau扒se of e爱rrors i扳n proje瓣cted ca佰sh flow稗s. The 疤danger 傲is grea奥test wi拜th a ne矮w pro

2、du拌ct beca扳use the案 cash f俺lows ar岸e proba伴bly har熬der to 半predict翱.案2.胺扒With a 稗sensiti昂vity an疤alysis,艾 one va爱riable 板is exam罢ined ov皑er a br扮oad ran办ge of v坝alues. 昂With a 斑scenari氨o analy俺sis, al扳l varia般bles ar扮e exami艾ned for哀 a limi胺ted ran哀ge of v唉alues.俺3.扒邦It is t阿rue tha捌t if av凹erage r扒

3、evenue 颁is less颁 than a斑verage 斑cost, t肮he firm佰 is los爱ing mon瓣ey. Thi颁s much 按of the 搬stateme柏nt is t爸herefor熬e corre啊ct. At 拜the mar绊gin, ho胺wever, 半accepti啊ng a pr皑oject w般ith mar坝ginal r捌evenue 矮in exce盎ss of i柏ts marg傲inal co般st clea搬rly act隘s to in败crease 捌operati敖ng cash挨 flow.阿4.耙佰From th癌e

4、 share癌holder 稗perspec胺tive, t背he fina暗ncial b芭reak-ev霸en poin把t is th背e most 稗importa白nt. A p盎roject 阿can exc办eed the俺 accoun伴ting an绊d cash 半break-e半ven poi拜nts but白 still 爸be belo案w the f笆inancia吧l break扒-even p翱oint. T疤his cau挨ses a r昂eductio俺n in sh隘arehold办er (you巴r) weal暗th.耙5.埃阿The pro稗ject

5、wi靶ll reac懊h the c百ash bre澳ak-even氨 first,巴 the ac矮countin蔼g break拔-even n搬ext and稗 finall百y the f邦inancia爱l break瓣-even. 唉For a p班roject 搬with an俺 initia奥l inves哎tment a鞍nd sale靶s after靶, this 埃orderin懊g will 瓣always 肮apply. 埃The cas拔h break巴-even i笆s achie按ved fir吧st sinc俺e it ex瓣cludes 拌depreci懊a

6、tion. 昂The acc澳ounting叭 break-把even is八 next s案ince it背 includ巴es depr阿eciatio哀n. Fina八lly, th跋e finan班cial br隘eak-eve疤n, whic暗h inclu胺des the扳 time v敖alue of耙 money,版 is ach笆ieved.柏6.凹哎Traditi巴onal NP俺V analy癌sis is 翱often t爱oo cons袄ervativ啊e becau白se it i吧gnores 拔profita鞍ble opt鞍ions su傲ch as t胺he

7、 abil靶ity to 爱expand 扮the pro跋ject if安 it is 敖profita隘ble, or拌 abando背n the p佰roject 佰if it i八s unpro八fitable哎. The o啊ption t般o alter耙 a proj叭ect whe安n it ha唉s alrea巴dy been盎 accept柏ed has 翱a value八, which拔 increa碍ses the俺 NPV of巴 the pr俺oject.拜7.袄昂The typ翱e of op岸tion mo叭st like拔ly to a版ffect t俺he

8、deci挨sion is氨 the op坝tion to颁 expand盎. If th昂e count拌ry just瓣 libera挨lized i哎ts mark佰ets, th啊ere is 稗likely 吧the pot阿ential 蔼for gro凹wth. 败First e坝ntry in敖to a ma敖rket, w矮hether 挨an enti肮rely ne盎w marke哎t, or w肮ith a n阿ew prod罢uct, ca胺n give 佰a compa八ny name叭 recogn半ition a敖nd mark班et shar哎e. This霸

9、may ma俺ke it m版ore dif胺ficult 扒for com俺petitor八s enter懊ing the版 market搬. 皑8.般罢扒Sensiti百vity an邦alysis 蔼can det佰ermine 按how the爸 financ班ial bre叭ak-even爱 point 般changes斑 when s瓣ome fac肮tors (s捌uch as 俺fixed c瓣osts, v蔼ariable皑 costs,叭 or rev蔼enue) c疤hange.胺9.皑哎There a拌re two 傲sources办 of val半ue with颁 t

10、his d扮ecision艾 to wai半t. Pote案ntially蔼, the p隘rice of挨 the ti碍mber ca摆n poten皑tially 鞍increas按e, and 安the amo隘unt of 芭timber 背will al啊most de罢finitel澳y incre唉ase, ba哎rring a奥 natura氨l catas坝trophe 埃or fore搬st fire稗. The o翱ption t唉o wait 鞍for a l奥ogging 柏company八 is qui颁te valu哀able, a绊nd comp班anies

11、i半n the i巴ndustry把 have m澳odels t啊o estim蔼ate the白 future佰 growth唉 of a f暗orest d哎ependin捌g on it蔼s age. 般10.罢罢When th暗e addit拜ional a爱nalysis懊 has a 翱negativ肮e NPV. 佰Since t白he addi败tional 碍analysi奥s is li皑kely to澳 occur 霸almost 安immedia背tely, t坝his mea艾ns when敖 the be氨nefits 埃of the 霸additio鞍nal a

12、na阿lysis o靶utweigh癌 the co氨sts. Th稗e benef扮its of 熬the add半itional癌 analys按is are 扒the red蔼uction 鞍in the 笆possibi哎lity of柏 making摆 a bad 柏decisio跋n. Of c盎ourse, 拌the add捌itional昂 benefi吧ts are 案often d坝ifficul拌t, if n吧ot impo班ssible,半 to mea拌sure, s碍o much 翱of this办 柏decisio扒n is ba皑sed on 埃experie

13、懊nce.哀Solutio颁ns to Q啊uestion矮s and P板roblems哀NOTE: A碍ll end 叭of chap耙ter pro斑blems w稗ere sol坝ved usi阿ng a sp扳readshe瓣et. Man暗y probl蔼ems req唉uire mu懊ltiple 绊steps. 熬Due to 挨space a巴nd read敖ability邦 constr叭aints, 岸when th笆ese int疤ermedia敖te step袄s are i懊ncluded颁 in thi爱s solut百ions ma拌nual, r挨oundin

14、g氨 may ap耙pear to稗 have o爸ccurred碍. Howev挨er, the捌 final 邦answer 八for eac奥h probl巴em is f熬ound wi扒thout r巴ounding白 during百 any st澳ep in t百he prob袄lem.Basic皑1巴.盎柏a斑.背拌To calc把ulate t疤he acco伴unting 胺breakev颁en, we 瓣first n氨eed to 胺find th岸e depre靶ciation疤 for ea白ch year隘. The d搬eprecia班tion is吧:敖挨佰D靶

15、eprecia霸tion氨 = $碍896扮,000/邦8稗 爱熬搬Depreci敖ation =翱 疤$隘112邦,000 pe鞍r year皑皑八And the唉 accoun昂ting br伴eakeven稗 is:芭白耙Q袄A翱 = ($斑9氨00,000 埃+ 1百12办,000)/(佰$3澳8百 耙2版5爱) 耙吧唉Q熬A半 皑= 叭77,846版 units癌百b.扒癌We will唉 use th敖e tax s拌hield a澳pproach爱 to cal稗culate 爱the OCF盎. The O绊CF is:哀八绊OCF懊base拔 = (P 隘 v)Q 吧 FC(

16、1 芭 t阿c芭) + t拌c昂D 凹绊艾OCF胺base昂 懊= ($3案8拔 八2爱5巴)(1癌0败0,000) 啊 熬$皑9百00,000碍(0.65) 澳+ 0.35(拔$1澳12澳,000) 盎疤拌OCF伴base坝 跋= $疤299,200颁扮班Now we 拔can cal癌culate 凹the NPV翱 using 袄our bas拌e-case 伴project昂ions. T啊here is百 no sal白vage va坝lue or 熬NWC, so八 the NP哎V is:搬按班NPV背base扮 = $皑896蔼,000 + 袄$白299,2癌00(PVIF艾A

17、版15%,瓣8瓣) 搬捌瓣NPV佰base安 办= $埃446,606疤.60哎凹碍To 昂calcula般te拔 the se罢nsitivi癌ty of t盎he NPV 蔼to chan耙ges in 拔the qua俺ntity s白old, we奥 will c伴alculat芭e the N把PV at a邦 differ唉ent qua佰ntity. 稗We will邦 use sa按les of 耙105,000败 units.扮 The NP傲V at th笆is sale邦s level拔 is: 哎斑挨OCF拔new瓣 = ($3般8爱 唉2氨5拌)(1颁0叭5,000)

18、 霸 斑$白9把00,000拌(0.65) 敖+ 0.35(癌$1熬12绊,000) 肮佰傲OCF霸new澳 鞍= $拌3白41,450稗摆耙And the皑 NP案V拌 is:扒埃蔼NPV安new拜 = $哀896跋,000 + 扮$佰341,450案(巴PVIFA暗15%,板8白) 捌岸啊NPV巴new蔼 佰= $伴636,195佰.93岸败鞍So, the佰 change扒 in NPV半 for ev鞍ery uni按t chang伴e in sa拌les is:翱笆俺NPV/奥S = ($搬636,195癌.93碍 哎446,606佰.60阿)/(1爸0绊5,000 扒 1案0扒0,

19、000) 唉邦巴NPV/背S 巴= +$3暗7.918啊扮颁If sale傲s were 斑to drop皑 by 1肮00 unit盎s, then办 NPV wo安uld dro叭p by百:颁吧熬NPV dro摆p =按 $3稗7.918啊(1佰00) = $耙3,791.8半0斑按坝You may扮 wonder胺 why we傲 chose 瓣105,000按 units.佰 暗Because霸 it doe柏snt ma盎tter! 啊Whateve暗r sales斑 number稗 we use鞍, when 稗we calc坝ulate t佰he chan伴ge in N白PV

20、 per 搬unit so摆ld, the白 ratio 捌will be霸 the sa爱me. 般阿c.叭爸To find埃 out ho八w sensi隘tiv罢e矮 OCF is按 to a c碍hange i熬n varia蔼ble cos爸ts, we 笆will co白mpute t芭he OCF 拌at a 坝variabl隘e班 cost o背f $24. 蔼Again, 澳the num隘ber we 扳choose 袄to use 哎here is摆 irrele伴vant: W癌e will 按get the摆 same r阿atio of拌 OCF to拜 a one

21、 败dollar 办change 颁in vari佰able co俺st no m暗atter w癌hat var叭iable c癌ost we 岸use. So跋, using霸 the ta扒x shiel巴d appro盎ach, th板e OCF a巴t a var靶iable c扳ost of 败$24 is:哎叭半OCF癌new哎 = ($澳38蔼 熬24霸)(1哀0败0,000) 按 奥9般00,000傲(0.65) 拜+ 0.35(肮$1版12班,000) 稗颁皑OCF凹new拌 俺= $俺364,200昂案背So, the艾 change皑 in OCF办 for a 叭$1

22、 chan斑ge in v颁ariable版 costs 哎is:矮安啊OCF/板v = ($叭299,200案 敖364,200奥)/($癌25颁 挨24艾) 把稗懊OCF/隘v 皑= $懊65,000败芭邦If vari岸able co柏sts 拔decreas绊e翱 by $疤5稗 then, 耙OCF wou拌ld 安increas八e拌 by 邦跋挨OCF inc八rease =班 矮$氨65,0澳00斑*5 = $3稗25,000稗2敖.哀佰We will翱 use th斑e tax s盎hield a艾pproach败 to cal拔culate 矮the OCF阿 for th

23、疤e best-爸 and wo背rst-cas熬e scena澳rios. F办or the 隘best-ca暗se scen岸ario, t绊he pric班e and q瓣uantity颁 increa瓣se by 1耙0 perce扒nt, so 熬we will搬 multip霸ly the 俺base ca佰se numb案ers by 霸1.1, a 翱10 perc败ent inc埃rease. 靶The var班iable a百nd fixe袄d costs挨 both d巴ecrease唉 by 10 奥percent按, so we癌 will m拜ultiply哀 th

24、e ba八se case肮 number吧s by .9昂, a 10 柏percent奥 decrea佰se. Doi般ng so, 拜we get:绊翱OCF翱best跋 = ($坝38把)(1.1) 澳 ($蔼25唉)(0.9)败(矮100K巴)(1.1) 昂 捌$岸900K百(0.9)(百0.65) +罢 0.35(胺$拔112袄K) 俺哎OCF哀best皑 百= $佰892,650蔼八The bes般t-case 碍NPV is:俺氨NPV百best罢 = $摆896案,000 + 拌$爸892,650板(PVIFA鞍15%,澳8般) 隘版NPV阿best白 搬= $背3,109,6

25、芭07.54唉柏For the柏 worst-搬case sc鞍enario,袄 the pr扒ice and艾 quanti邦ty decr斑ease by霸 10 per岸cent, s氨o we wi熬ll mult暗iply th癌e base 暗case nu叭mbers b拜y .9, a爸 10 per百cent de板crease.凹 The va百riable 稗and fix暗ed cost版s both 案increas案e by 10懊 percen稗t, so w坝e will 蔼multipl捌y the b罢ase cas跋e numbe鞍rs by 1颁.1,

26、a 1罢0 perce班nt incr绊ease. D柏oing so艾, we ge败t:胺盎OCF皑worst靶 = ($碍38埃)(0.9) 胺 ($背25胺)(1.1)袄(捌100K癌)(0.9) 拜 班$笆900K柏(1.1)(阿0.65) +芭 0.35(拔$靶112隘K) 班艾OCF芭worst邦 邦= 般212,35暗0坝啊The wor办st-case哎 NPV is扒:翱隘NPV爱worst澳 = $巴896摆,000 袄按 $挨212,350鞍(PVIFA唉15%,笆8斑) 把安NPV挨worst敖 鞍= $碍1,848,8白82.72百3昂.百疤We can 疤use

27、the捌 accoun跋ting br败ea伴k稗even eq熬uation:安芭Q扒A拜 = (FC 芭+ D)/(P碍 v) 拜靶to solv班e for t爸he unkn搬own var摆iable i靶n each 白case. D凹oing so蔼, we fi扳nd:啊佰(1): 按阿Q般A柏 = 1巴30,200把 = (肮85靶0,阿000 + D岸)/(翱摆41阿 蔼30靶) 背邦白氨D = 耙58百2,200颁芭(2): 叭哀Q奥A白 = 1鞍35癌,000 = 疤(稗版3斑.2唉M + 1.癌1挨5M)/(P 拜 瓣版56伴) 笆般霸疤P = 安拌88.22俺叭(3

28、): 绊叭Q澳A颁 = 皑5,478跋 = (耙案160巴,000 + 绊105哀,000)/(罢哀10扒5跋 v) 挨拌案v = 伴白5扳6.62芭4搬.颁澳When ca皑lculati挨ng the 懊financi白al brea疤keven p摆oint, w板e expre袄ss the 罢initial敖 inv扒estment背 as an 耙equival拔ent ann靶ual cos把t (EAC)扒. Divid按ing the氨 in ini拌tial in柏vestmen袄t by th阿e seven巴-year a爱nnuity 哀factor,安 discou

29、熬nted at肮 12 per哀cent, t般he EAC 佰of the 蔼initial坝 invest拔ment is挨:傲盎EAC = I敖nitial 耙Investm摆ent / P胺VIFA疤12%,5挨柏EAC = 稗蔼200,000般 / 3.60扒478啊啊EAC = 懊懊55,481.奥95暗半Note, t板his cal昂culatio瓣n solve稗s for t袄he annu哎ity pay按ment wi肮th the 绊initial蔼 invest扒ment as八 the pr扒esent v叭alue of拌 the an傲nuity, 捌in

30、othe按r words矮:靶啊PVA = 岸C吧(1 埃1/(1 + 哀R岸)扳t版 / 哀R罢)扳艾安200,000熬 = 矮C背1 (拔1/1.12)百5澳 / .1哀2摆版C笆 = 吧胺55,481.般95 芭奥The ann坝ual dep跋reciati靶on is t碍he cost芭 of the佰 equipm哎ent div拔ided by癌 the ec扒onomic 暗life, o肮r:搬盎Annual 班depreci俺ation =熬 癌安200,000埃 / 5搬懊Annual 班depreci坝ation =办 斑斑40,000疤翱Now we 傲can ca

31、l暗culate 柏the fin埃ancial 埃breakev拌en poin稗t. The 暗financi百al brea敖keven p袄oint fo肮r this 敖project斑 is: 按瓣Q碍F白 = EAC芭 + FC(1扒 t翱C唉) Dep案reciati艾on(t隘C耙) / (班P VC)爸(1 t班C佰) 傲傲Q哀F癌 = 鞍盎55,481.氨95 + 懊稗350佰,000(.7唉5) 4按0,000(0岸.25) /俺 (熬25 5)霸 (.25)肮 阿安Q把F隘 = 耙20,532.蔼13 or a般bout 20氨,532 un按its鞍5.埃半If w

32、e p摆urchase叭 the ma岸chine t艾oday, t挨he NPV 靶is the 翱cost pl稗us the 癌present佰 value 皑of the 斑incr安eased c绊ash flo昂ws, so:爸蔼NPV哀0半 = 澳挨1,500,0哀00 + 案绊280,000皑(PVIFA班12%,10绊) 吧皑NPV伴0暗 = 阿败82,062.芭45盎阿We shou败ld not 鞍purchas爸e the m白achine 俺today. 熬We woul奥d want 拔to purc凹hase th跋e machi皑ne when芭 the NP

33、哀V is th半e highe绊st. So,安 we nee捌d to ca稗lculate百 the NP扳V each 按year. T爸he NPV 拔each y叭ear wil颁l be th挨e cost 懊plus th坝e prese拔nt valu啊e of th矮e incre胺ased ca艾sh savi柏ngs. We霸 must b埃e caref斑ul howe霸ver. In败 order 艾to make爸 the co凹rrect d伴ecision奥, the N霸PV for 背each ye靶ar must隘 be tak蔼en to a百 com

34、mon绊 date. 岸We will熬 discou捌nt all 百of the 傲NPVs to安 today.捌 Doing 凹so, we 邦get:爱绊Year 1:奥 般皑NPV按1般 = 碍矮1,375,0巴00 + 佰扒280,000艾(PVIFA办12%,9矮) / 1.哀12 罢八隘NPV爸1耙 = 百唉104,383拔.88盎吧Year 2:鞍 扒哀NPV吧2坝 = 坝叭1,250,0俺00 + 伴熬280,000扳(PVIFA碍12%,8搬) / 1.唉12氨2啊 吧暗半NPV拔2捌 = 癌败112,355半.82凹板Year 3:昂 芭盎NPV邦3佰 = 爸岸1,1

35、25,0艾00 + 案靶280,000扮(PVIFA霸12%,7翱) / 1.挨12矮3癌 凹癌吧NPV跋3扒 = 罢盎108,796斑.91笆氨Year 4:半 安埃NPV佰4般 = 般版1按,000,00摆0 + 坝巴280,000矮(PVIFA坝12%,6笆) / 1.巴12斑4按 艾安把NPV稗4胺 = 把凹96,086.稗55懊安Year 5:把 盎爱NPV疤5坝 = 把摆1,000,0搬00 + 霸案280,000胺(PVIFA八12%,5疤) / 1.把12颁5伴 背熬八NPV澳5案 = 挨吧5,298.2阿6叭安Year 6:皑 八巴NPV凹6白 = 癌斑1,000,0坝00

36、+ 邦傲280,000拌(PVIFA稗12%,4叭) / 1.耙12啊6昂 凹哎啊NPV啊6把 = 绊巴75,762.昂72柏半The com肮pany sh阿ould pu案rch办ase the八 machin爱e two y唉ears fr傲om now 耙when th癌e NPV i百s the h靶ighest.阿6.版柏We need肮 to cal懊culate 澳the NPV把 of the背 two op百tions, 阿go dire班ctly to氨 market办 now, o唉r utili半ze test绊 market芭ing fir皑st. The八 NPV

37、 of叭 going 疤directl八y to ma拔rket no俺w is:唉袄NPV = C盎Success耙 疤(Prob. 伴of Succ唉ess) + 按 C靶Failure班 吧(Prob. 埃of Fail熬ure)颁芭NPV = $疤20,000,碍000(0.佰4艾5) + $5按,000,00笆0(0.5吧5芭)叭板NPV = 傲$1肮1按,笆75熬0,000办吧Now we 挨can cal胺culate 巴the NPV柏 of tes班t marke俺ting fi哎rst. T哎est mar罢keting 瓣require敖s a $2 岸million艾

38、cash o隘utlay. 伴 Choosi芭ng the 百test ma办rketing爱 option鞍 will a伴lso del癌ay the 八launch 坝of the 把product芭 by one跋 year. 袄 Thus, 碍the exp版ected p摆ayoff i颁s delay案ed by o阿ne year芭 and mu爱st be d吧iscount柏ed back八 to yea翱r 0. 胺按NPV= C哎0邦 + C拔Success氨 肮(Prob. 半of Succ案ess) +稗 C靶Failure拌 拌(Prob. 岸of Fail哎ur

39、e) 袄/ (1 + 胺R阿)胺t按哀NPV = 伴$2,000,霸000 + 敖$20,00凹0,000 (癌0.75) 氨+ $5,0斑00,000 叭(0.25)阿 / 1.1版5 扮按NPV = 傲$12,130唉,434.78败埃The com叭pany sh百ould 俺not 阿go dire佰ctly to癌 market熬 with t碍he prod拜uct sin敖ce that俺 option伴 has 颁lower唉 expect懊ed payo瓣ff. 佰7.霸坝We need熬 to cal翱culate 背the 八NPV of 霸each op昂tion唉,

40、and c笆hoose t安he opti笆on with吧 the 邦highest按 NPV.拌 So, th百e NPV o案f going唉 direct俺ly to m斑arket i瓣s:耙 安拔NPV鞍 奥= C盎Success靶 背(Prob. 般of Succ耙ess) 艾拜NPV 敖= 柏Rs.癌1,200,0肮00 (0.稗55肮)坝按NPV 翱= 背Rs.660啊,000坝吧The N爱PV 拔of the 柏focus g爸roup is跋:艾 斑搬NPV拔 蔼= C肮0俺 + C靶Success哎 岸(Prob. 背of Succ熬ess) 熬按NPV 安= 隘半R

41、s.安120,000败 + 败Rs.拌1,200,0肮00 (0.7半0) 白背NPV 扒= 岸Rs.霸720,000半拔And the唉 NPV of阿 using 颁the con坝sulting伴 firm i袄s:肮跋NPV爱 奥= C阿0芭 + C矮Success癌 哎(Prob. 挨of Succ稗ess) 凹啊NPV 翱= 案背Rs.坝400,000捌 + 瓣Rs.扳1,200,0俺00 (0.9盎0)拌八NPV 靶= 巴Rs.背680,000败挨The fir扳m shoul碍d condu百ct a fo绊cus gro绊up sinc摆e that 版option 拜has

42、 the绊 highes半t NPV. 氨 扒8.搬巴The com跋pany 吧should 叭analyze挨 both o懊ptions,瓣 and ch鞍oose th拜e optio埃n with 氨the gre碍atest N邦PV. So,拔 if the澳 compan罢y goes 隘to mark爸et imme捌diately办, the N俺PV is:版哎NPV = 碍C八Success办 班(Prob. 肮of Succ安ess) + 板C岸Failure靶 懊(Prob. 扳of Fail鞍ure)佰败NPV = 稗安30,000,盎000(.55皑) + 瓣熬

43、3,000,0昂00(.45)爸八NPV = 埃八17,850,癌000.00 芭Custome靶r segme跋nt rese摆arch 凹require扒s a 捌霸1 milli疤on cash盎 outlay俺. Choos唉ing the昂 resear皑ch opti懊on will百 also d跋elay th俺e launc叭h of th拔e produ蔼ct by o摆ne year疤. Thus,版 the ex埃pected 俺payoff 唉is dela傲yed by 般one yea拜r and m柏ust be 隘discoun哎ted bac败k to ye

44、颁ar 0. S岸o, the 芭NPV of奥 the cu鞍stomer 芭segment昂 resear罢ch is:败扳NPV= C绊0绊 + C佰Success疤 半(Prob. 邦of Succ碍ess) +叭 C版Failure罢 凹(Prob. 瓣of Fail澳ure) 耙/ (1 + 拌R板)耙t暗办NPV = 胺案1,000,0版00 + 跋瓣30,000,鞍000 (0.安70) + 熬办背3,000,0奥00 (0.3败0) / 扳1.15 矮靶NPV = 跋柏18,043,叭478.26靶Graphic敖ally, t哀he deci巴sion tr澳ee for

45、懊th皑e proje稗ct is:StartResearchNo Research18.0435 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 = 0佰俺The com暗pany sh办ould un版dertake鞍 the ma百rket se稗gment r般es

46、earch拌 since 熬it has 笆the lar摆gest NP皑V.凹9.爸挨a.拌凹The acc坝ounting扳 breake案ven is 八the aft隘ertax s澳um of t袄he fixe叭d costs哎 and de鞍preciat皑ion cha耙rge div啊ided by版 the af奥tertax 邦contrib昂ution m佰argin (绊selling白 price 敖minus v熬ariable挨 cost).哎 So, th白e accou阿nting b板reakeve鞍n level背 of sal哀es is: 奥 芭安

47、翱Q埃A板 = (FC氨 + Depr阿eciatio艾n)(1 白t挨C拌) / (盎P VC)氨(1 t熬C澳) 稗阿佰Q氨A败 = ($3艾40,000 般+ $20,0奥00) (1 班 0.35)扒 / ($阿2.00 安0.72) (坝1 0.3靶5)按唉爸罢哎Q笆A绊 = 唉281,250瓣.00颁爸b.背柏When ca般lculati把ng the 啊financi皑al 摆breakev拔en poin版t, 拔we 袄express傲 the in白itial i傲nvestme绊nt半 奥as an e背quivale袄nt annu捌al cost胺 (EAC).败

48、Dividi扒ng the 斑in巴 initia绊l inves盎tment b澳y the s傲even-ye肮ar annu皑ity fac巴tor, di敖scounte哀d at 15碍 percen艾t拔, the E隘AC of t扒he init伴ial 叭investm哎ent百 is:扒巴坝EAC = I把nitial 笆Investm捌ent / 瓣PVIFA隘15%,7扒吧阿EAC 拜= $140,办000 / 隘4.1604版 翱佰爱EAC 耙= $33,6拜50.45伴矮稗Note, t凹his cal奥culatio办n solve唉s for t安he annu

49、耙ity pay靶ment wi拜th the 稗initial半 invest办ment as绊 the pr俺esent v摆alue of扳 the an奥nuity, 吧in othe碍r words办:案按八PVA = 氨C颁(1 吧1/(1 + 跋R柏)班t伴 / 袄R笆)瓣八靶$140,00袄0 = 扮C白1 (挨1/1.15)傲7阿 / .1扮5案翱爱C鞍 = $33,袄650.45 肮吧按Now we 佰can cal皑culate 澳the fin霸ancial 阿breakev阿en poin叭t. 蔼The fin耙ancial 挨breakev暗en poin办t f

50、or t搬his pro氨ject is班:奥 爸疤案Q翱F颁 = 埃EAC案 百+啊 FC挨(1 皑 t胺C肮) 坝Depreci摆ation背(跋t翱C笆) / (翱P 澳 V摆C拌)(1 罢t鞍C佰) 霸摆拔Q敖F捌 = 拌$33,65拜0.45 + 皑$340,00霸0(.65) 颁爸 $20,00艾0(.35)鞍 / ($2懊 艾佰 0.72) 板(.65) 胺安八Q摆F哎 敖= 敖297,656百.79熬 or abo稗ut 蔼297,657挨 units傲10.疤 袄胺When ca败lculati拔ng the 芭financi把al brea捌keven p翱oint, w稗

51、e expre翱ss the 碍initial案 invest拜ment as爱 an equ凹ivalent鞍 annual案 cost (百EAC). D凹ividing笆 the in艾 initia昂l inves鞍tment b罢y the f斑ive-yea挨r annui般ty fact袄or, dis半counted翱 at 8 p坝ercent,跋 the EA哎C of th凹e initi敖al inve班stment 扮is:佰胺EAC = I霸nitial 柏Investm凹ent / P半VIFA稗8%,5鞍伴EAC = 埃爱300,000哎 / 3.60拔478芭

52、白EAC = 邦叭75,136.隘94柏扒Note, t办his cal稗culatio巴n solve蔼s for t跋he annu瓣ity pay拌ment wi拌th the 安initial拔 invest安ment as伴 the pr巴esent v靶alue of暗 the an奥nuity, 拜in othe跋r words鞍:靶绊PVA = 懊C岸(1 捌1/(1 + 败R氨)癌t百 / 埃R版)摆艾败300,000爸 = 凹C霸1 (绊1/1.08)鞍5扳 / .0唉8癌暗C艾 = 敖碍75,136.哎94 皑般The ann挨ual dep昂reciati挨on is

53、t疤he cost肮 of the败 equipm氨ent div阿ided by百 the ec把onomic 哀life, o昂r:把佰Annual 哀depreci般ation =耙 靶斑300,000霸 / 5扳邦Annual 凹depreci鞍ation =皑 安芭60,000埃把Now we 奥can cal版culate 唉the fin颁ancial 拔breakev暗en poin搬t. The 隘financi艾al brea坝keven p办oint fo办r this 敖project版 is: 板扳Q把F袄 = EAC耙 + FC(1柏 t敖C爱) Dep肮recia

54、ti佰on(t疤C暗) / (唉P VC)挨(1 t拌C坝) 鞍颁Q鞍F颁 = 阿75,136.邦94 + 哎凹100,000邦(.66) 捌 办鞍60,000(哀0.34) 敖/ (爸罢60 8)扒 (.34)稗 霸耙Q昂F拔 = 3,51拌7.98案 or abo胺ut 3,51芭8 units懊胺Interme稗diate胺1肮1鞍.跋拌a笆.伴懊At the 捌account摆ing bre背akeven,肮 the IR柏R is ze巴ro perc拌ent sin吧ce the 伴project肮 recove百rs the 哎initial盎 invest伴ment. T板he

55、 payb拔ack per八iod is 碍N years氨, the l拜ength o吧f the p叭roject 碍since t昂he init爸ial inv氨estment胺 is exa靶ctly re皑covered柏 over t疤he proj罢ect lif瓣e.败 The NP翱V at th案e accou背nting b佰reakeve坝n is:奥 巴斑瓣稗NPV = I耙 (1/N)盎(PVIFA半R%,N蔼) 1翱办b按.爸般At the 唉cash br埃eakeven懊 level,昂 the IR熬R is 1叭00 perc百ent, th白e pa

56、yba跋ck peri稗od is n按egative办, and t版he NPV 傲is nega捌tive an奥d equal傲 to the氨 initia扒l cash 氨outlay.皑啊c胺.扳艾The def奥inition疤 of the般 financ绊ial bre搬akeven 碍is wher摆e the N袄PV of t扒he proj熬ect is 疤zero. I靶f this 哎is true瓣, then 稗the IRR碍 of the跋 projec癌t is eq斑ual to 哎the req挨uired r矮eturn. 佰It is i岸mp

57、ossib胺le to s熬tate th拔e payba啊ck peri坝od, exc巴ept to 拔say tha拜t the p鞍ayback 般period 板must be埃 less t按han the按 length笆 of the办 projec颁t. Sinc佰e the d隘iscount啊ed cash巴 flows 耙are equ巴al to t把he init靶ial inv班estment罢, the u拔ndiscou挨nted ca阿sh flow背s are g案reater 拔than th皑e initi安al inve凹stment,癌 so th

58、e跋 paybac艾k must 爸be less熬 than t癌he proj安ect lif耙e.疤按1皑2罢.奥碍Using t班he tax 柏shield 哎approac暗h, the 胺OCF at 凹11鞍0埃,000 un靶its wil碍l be:奥岸OCF = 俺(P v)唉Q FC氨(1 t安C靶) + t斑C瓣(D) 癌暗OCF按 = ($颁28扮 1隘9背)(110,0扒00) 癌1吧5安0扮,000(0百.66) + 鞍0.34($4奥20,000/肮4疤) 案败OCF 肮= $袄5啊90伴,柏1懊00懊啊We will八 calcul安ate the扮 OCF

59、 at爸 111,00背0 units艾. The c傲hoice o凹f the s八econd l耙evel of皑 quanti办ty sold凹 is arb瓣itrary 挨and 哎irrelev皑ant隘. No ma昂tter wh霸at leve拔l of un班its sol凹d we ch唉oose, w板e will 埃still g霸et the 把same 昂sensiti伴vity埃. So, t班he OCF 唉at this安 level 敖of sale扒s is:罢矮OCF = 哀($2敖8凹 1扮9皑)(111,0埃00) 1袄5氨0氨,000(0胺.6

60、6) + 板0.34($4哀20,000/澳4肮) 翱袄OCF 柏= $癌5版96懊,澳0俺40氨拔The sen岸sitivit蔼y of th隘e OCF t隘o chang挨es in t叭he quan鞍tity so绊ld is:拜霸Sensiti阿vity =颁 唉OCF/哎Q = ($5啊96坝,笆0唉40巴 5矮90百,败1鞍00)/(11阿1,000 摆 110,00阿0) 挨靶OCF/昂Q 矮= +$5.癌94哎艾OCF wil拜l incre耙ase by 邦$5.颁94氨 for ev爱ery add百itional哀 unit s拌old.白 翱1唉3把.熬澳a阿.拌