英文版羅斯公司理財(cái)習(xí)題答案Chap009

1、暗CHAPTER皚 芭9昂RISK AN擺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擺1.唉阿Forecas癌ting ri捌sk is t班he risk巴 that a昂 poor d壩ecision皚 is mad拜e becau扒se of e愛(ài)rrors i扳n proje瓣cted ca佰sh flow稗s. The 疤danger 傲is grea奧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愛(ài)riable 板is exam罷ined ov皚er a br扮oad ran辦ge of v壩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I(lǐng)t is t阿rue tha捌t if av凹erage r扒

3、evenue 頒is less頒 than a斑verage 斑cost, t骯he firm佰 is los愛(ài)ing mon瓣ey. Thi頒s much 按of the 搬stateme柏nt is t爸herefor熬e corre啊ct. At 拜the mar絆gin, ho胺wever, 半accepti啊ng a pr皚oject w般ith mar壩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敗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辦eed the俺 accoun伴ting an絆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辦er (you巴r) weal暗th.耙5.埃阿The pro稗ject

5、wi靶l(wèi)l reac懊h the c百ash bre澳ak-even氨 first,巴 the ac矮countin藹g break拔-even n搬ext and稗 finall百y the f邦inancia愛(ài)l break瓣-even. 唉For a p班roject 搬with an俺 initia奧l inves哎tment a鞍nd sale靶s after靶, this 埃orderin懊g will 瓣always 骯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愛(ài)oo cons襖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 愛(ài)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礙ses the俺 NPV of巴 the pr俺oject.拜7.襖昂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壩tion to頒 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 藹for gro凹wth. 敗First e壩ntry in敖to a ma敖rket, w矮hether 挨an enti骯rely ne盎w marke哎t, or w骯ith a n阿ew prod罷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. 皚8.般罷扒Sensiti百vity an邦alysis 藹can det佰ermine 按how the爸 financ班ial bre叭ak-even愛(ài) point 般changes斑 when s瓣ome fac骯tors (s捌uch as 俺fixed c瓣osts, v藹ariable皚 costs,叭 or rev藹enue) c疤hange.胺9.皚哎There a拌re two 傲sources辦 of val半ue with頒 t

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

11、i半n the i巴ndustry把 have m澳odels t啊o estim藹ate the白 future佰 growth唉 of a f暗orest d哎ependin捌g on it藹s age. 般10.罷罷When th暗e addit拜ional a愛(ài)nalysis懊 has a 翱negativ骯e NPV. 佰Since t白he addi敗tional 礙analysi奧s is li皚kely to澳 occur 霸almost 安immedia背tely, t壩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藹uction 鞍in the 笆possibi哎lity of柏 making擺 a bad 柏decisio跋n. Of c盎ourse, 拌the add捌itional昂 benefi吧ts are 案often d壩ifficul拌t, if n吧ot impo班ssible,半 to mea拌sure, s礙o much 翱of this辦 柏decisio扒n is ba皚sed on 埃experie

13、懊nce.哀Solutio頒ns to Q啊uestion矮s and P板roblems哀NOTE: A礙ll end 叭of chap耙ter pro斑blems w稗ere sol壩ved usi阿ng a sp扳readshe瓣et. Man暗y probl藹ems req唉uire mu懊ltiple 絆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襖s are i懊ncluded頒 in thi愛(ài)s solut百ions ma拌nual, r挨oundin

14、g氨 may ap耙pear to稗 have o爸ccurred礙. Howev挨er, the捌 final 邦answer 八for eac奧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襖lem.Basic皚1巴.盎柏a斑.背拌To calc把ulate t疤he acco伴unting 胺breakev頒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 = $礙896扮,000/邦8稗 愛(ài)熬搬Depreci敖ation =翱 疤$隘112邦,000 pe鞍r year皚皚八And the唉 accoun昂ting br伴eakeven稗 is:芭白耙Q襖A翱 = ($斑9氨00,000 埃+ 1百12辦,000)/(佰$3澳8百 耙2版5愛(ài)) 耙吧唉Q熬A半 皚= 叭77,846版 units癌百b.扒癌We will唉 use th敖e tax s拌hield a澳pproach愛(ài) to cal稗culate 愛(ài)the OCF盎. The O絆CF is:哀八絆OCF懊base拔 = (P 隘 v)Q 吧 FC(

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

17、版15%,瓣8瓣) 搬捌瓣NPV佰base安 辦= $埃446,606疤.60哎凹礙To 昂calcula般te拔 the se罷nsitivi癌ty of t盎he NPV 藹to chan耙ges in 拔the qua俺ntity s白o(hù)ld, we奧 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敗 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愛(ài) 唉2氨5拌)(1頒0叭5,000)

18、 霸 斑$白9把00,000拌(0.65) 敖+ 0.35(癌$1熬12絆,000) 骯佰傲OCF霸new澳 鞍= $拌3白41,450稗擺耙And the皚 NP案V拌 is:扒埃藹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藹 佰= $伴636,195佰.93岸敗鞍So, the佰 change扒 in NPV半 for ev鞍ery uni按t chang伴e in sa拌les is:翱笆俺NPV/奧S = ($搬636,195癌.93礙 哎446,606佰.60阿)/(1爸0絆5,000 扒 1案0扒0,

19、000) 唉邦巴NPV/背S 巴= +$3暗7.918啊扮頒If sale傲s were 斑to drop皚 by 1骯00 unit盎s, then辦 NPV wo安uld dro叭p by百:頒吧熬NPV dro擺p =按 $3稗7.918啊(1佰00) = $耙3,791.8半0斑按壩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壩ulate t佰he chan伴ge in N白PV

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

21、 敗dollar 辦change 頒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(cuò) OCF a巴t a var靶iable c扳ost of 敗$24 is:哎叭半OCF癌new哎 = ($澳38藹 熬24霸)(1哀0敗0,000) 按 奧9般00,000傲(0.65) 拜+ 0.35(骯$1版12班,000) 稗頒皚OCF凹new拌 俺= $俺364,200昂案背So, the艾 change皚 in OCF辦 for a 叭$1

22、 chan斑ge in v頒ariable版 costs 哎is:矮安啊OCF/板v = ($叭299,200案 敖364,200奧)/($癌25頒 挨24艾) 把稗懊OCF/隘v 皚= $懊65,000敗芭邦I(lǐng)f vari岸able co柏sts 拔decreas絆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敗 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辦or the 隘best-ca暗se scen岸ario, t絆he pric班e and q瓣uantity頒 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敗ent inc埃rease. 靶The var班iable a百nd fixe襖d costs挨 both d巴ecrease唉 by 10 奧percent按, so we癌 will m拜ultiply哀 th

24、e ba八se case骯 number吧s by .9昂, a 10 柏percent奧 decrea佰se. Doi般ng so, 拜we get:絆翱OCF翱best跋 = ($壩38把)(1.1) 澳 ($藹25唉)(0.9)敗(矮100K巴)(1.1) 昂 捌$岸900K百(0.9)(百0.65) +罷 0.35(胺$拔112襖K) 俺哎OCF哀best皚 百= $佰892,650藹八The bes般t-case 礙NPV is:俺氨NPV百best罷 = $擺896案,000 + 拌$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,襖 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壩e will 藹multipl捌y the b罷ase cas跋e numbe鞍rs by 1頒.1,

26、a 1罷0 perce班nt incr絆ease. D柏oing so艾, we ge敗t:胺盎OCF皚worst靶 = ($礙38埃)(0.9) 胺 ($背25胺)(1.1)襖(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壩啊The wor辦st-case哎 NPV is扒:翱隘NPV愛(ài)worst澳 = $巴896擺,000 襖按 $挨212,350鞍(PVIFA唉15%,笆8斑) 把安NPV挨worst敖 鞍= $礙1,848,8白82.72百3昂.百疤We can 疤use

27、the捌 accoun跋ting br敗ea伴k稗even eq熬uation:安芭Q扒A拜 = (FC 芭+ D)/(P礙 v) 拜靶to solv班e for t爸he unkn搬own var擺iable i靶n each 白case. D凹o(jì)ing so藹, we fi扳nd:啊佰(1): 按阿Q般A柏 = 1巴30,200把 = (骯85靶0,阿000 + D岸)/(翱擺41阿 藹30靶) 背邦白氨D = 耙58百2,200頒芭(2): 叭哀Q奧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、): 絆叭Q澳A頒 = 皚5,478跋 = (耙案160巴,000 + 絆105哀,000)/(罷哀10扒5跋 v) 挨拌案v = 伴白5扳6.62芭4搬.頒澳When ca皚lculati挨ng the 懊financi白al brea疤keven p擺oint, w板e(cuò) expre襖ss the 罷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襖t by th阿e seven巴-year a愛(ài)nnuity 哀factor,安 discou

29、熬nted at骯 12 per哀cent, t般he EAC 佰of the 藹initial壩 invest拔ment is挨:傲盎EAC = I敖nitial 耙Investm擺ent / P胺VIFA疤12%,5挨柏EAC = 稗藹200,000般 / 3.60扒478啊啊EAC = 懊懊55,481.奧95暗半Note, t板his cal昂culatio瓣n solve稗s for t襖he annu哎ity pay按ment wi骯th the 絆initial藹 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罷)扳艾安200,000熬 = 矮C背1 (拔1/1.12)百5澳 / .1哀2擺版C笆 = 吧胺55,481.般95 芭奧The ann壩ual dep跋reciati靶on is t礙he cost芭 of the佰 equipm哎ent div拔ided by癌 the ec扒onomic 暗life, o骯r:搬盎Annual 班depreci俺ation =熬 癌安200,000埃 / 5搬懊Annual 班depreci壩ation =辦 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襖oint fo骯r this 敖project斑 is: 按瓣Q礙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)骯 阿安Q把F隘 = 耙20,532.藹13 or a般bout 20氨,532 un按its鞍5.埃半If w

32、e p擺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 皚of the 斑incr安eased c絆ash flo昂ws, so:爸藹NPV哀0半 = 澳挨1,500,0哀00 + 案絆280,000皚(PVIFA班12%,10絆) 吧皚NPV伴0暗 = 阿敗82,062.芭45盎阿We shou敗ld not 鞍purchas爸e the m白achine 俺today. 熬W(wǎng)e woul奧d want 拔to purc凹hase th跋e machi皚ne when芭 the NP

33、哀V is th半e highe絆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頒l be th挨e cost 懊plus th壩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敗 order 艾to make爸 the co凹rrect d伴ecision奧, the N霸PV for 背each ye靶ar must隘 be tak藹en to a百 com

34、mon絆 date. 岸We will熬 discou捌nt all 百of the 傲NPVs to安 today.捌 Doing 凹so, we 邦get:愛(ài)絆Year 1:奧 般皚NPV按1般 = 礙矮1,375,0巴00 + 佰扒280,000艾(PVIFA辦12%,9矮) / 1.哀12 罷八隘NPV爸1耙 = 百唉104,383拔.88盎吧Year 2:鞍 扒哀NPV吧2壩 = 壩叭1,250,0俺00 + 伴熬280,000扳(PVIFA礙12%,8搬) / 1.唉12氨2啊 吧暗半NPV拔2捌 = 癌敗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 = 罷盎108,796斑.91笆氨Year 4:半 安埃NPV佰4般 = 般版1按,000,00擺0 + 壩巴280,000矮(PVIFA壩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 盎愛(ài)NPV疤5壩 = 把擺1,000,0搬00 + 霸案280,000胺(PVIFA八12%,5疤) / 1.把12頒5伴 背熬八NPV澳5案 = 挨吧5,298.2阿6叭安Year 6:皚 八巴NPV凹6白 = 癌斑1,000,0壩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 = 絆巴75,762.昂72柏半The com骯pany sh阿ould pu案rch辦ase the八 machin愛(ài)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骯 to cal懊culate 澳the NPV把 of the背 two op百tions, 阿go dire班ctly to氨 market辦 now, o唉r utili半ze test絆 market芭ing fir皚st. The八 NPV

37、 of叭 going 疤directl八y to ma拔rket no俺w is:唉襖NPV = C盎Success耙 疤(Prob. 伴of Succ唉ess) + 按 C靶Failure班 吧(Prob. 埃of Fail熬ure)頒芭NPV = $疤20,000,礙000(0.佰4艾5) + $5按,000,00笆0(0.5吧5芭)叭板NPV = 傲$1骯1按,笆75熬0,000辦吧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罷keting 瓣require敖s a $2 岸million艾

38、cash o隘utlay. 伴 Choosi芭ng the 百test ma辦rketing愛(ài) option鞍 will a伴lso del癌ay the 八launch 壩of the 把product芭 by one跋 year. 襖 Thus, 礙the exp版ected p擺ayoff i頒s delay案ed by o阿ne year芭 and mu愛(ài)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 骯(Prob. 半of Succ案ess) +稗 C靶Failure拌 拌(Prob. 岸of Fail哎ur

39、e) 襖/ (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敗埃The com叭pany sh百ould 俺not 阿go dire佰ctly to癌 market熬 with t礙he prod拜uct sin敖ce that俺 option伴 has 頒lower唉 expect懊ed payo瓣ff. 佰7.霸壩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 奧= C盎Success靶 背(Prob. 般of Succ耙ess) 艾拜NPV 敖= 柏Rs.癌1,200,0骯00 (0.稗55骯)壩按NPV 翱= 背Rs.660啊,000壩吧The N愛(ài)PV 拔of the 柏focus g爸roup is跋:艾 斑搬NPV拔 藹= C骯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敗 + 敗Rs.拌1,200,0骯00 (0.7半0) 白背NPV 扒= 岸Rs.霸720,000半拔And the唉 NPV of阿 using 頒the con壩sulting伴 firm i襖s:骯跋NPV愛(ài) 奧= C阿0芭 + C矮Success癌 哎(Prob. 挨of Succ稗ess) 凹啊NPV 翱= 案背Rs.壩400,000捌 + 瓣Rs.扳1,200,0俺00 (0.9盎0)拌八NPV 靶= 巴Rs.背680,000敗挨The fir扳m shoul礙d condu百ct a fo絆cus gro絆up sinc擺e that 版option 拜has

42、 the絆 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礙atest N邦PV. So,拔 if the澳 compan罷y goes 隘to mark爸et imme捌diately辦, the N俺PV is:版哎NPV = 礙C八Success辦 班(Prob. 骯of Succ安ess) + 板C岸Failure靶 懊(Prob. 扳of Fail鞍ure)佰敗NPV = 稗安30,000,盎000(.55皚) + 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擺arch 凹require扒s a 捌霸1 milli疤on cash盎 outlay俺. Choos唉ing the昂 resear皚ch opti懊on will百 also d跋elay th俺e launc叭h of th拔e produ藹ct by o擺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敗k to ye

44、頒ar 0. S岸o, the 芭NPV of奧 the cu鞍stomer 芭segment昂 resear罷ch is:敗扳NPV= C絆0絆 + C佰Success疤 半(Prob. 邦of Succ礙ess) +叭 C版Failure罷 凹(Prob. 瓣of Fail澳ure) 耙/ (1 + 拌R板)耙t暗辦NPV = 胺案1,000,0版00 + 跋瓣30,000,鞍000 (0.安70) + 熬辦背3,000,0奧00 (0.3敗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皚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辦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擺gest NP皚V.凹9.爸挨a.拌凹The acc壩ounting扳 breake案ven is 八the aft隘ertax s澳um of t襖he fixe叭d costs哎 and de鞍preciat皚ion cha耙rge div啊ided by版 the af奧tertax 邦contrib昂ution m佰argin (絆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: 奧 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敗 = ($3艾40,000 般+ $20,0奧00) (1 班 0.35)扒 / ($阿2.00 安0.72) (壩1 0.3靶5)按唉爸罷哎Q笆A絆 = 唉281,250瓣.00頒爸b.背柏When ca般lculati把ng the 啊financi皚al 擺breakev拔en poin版t, 拔we 襖express傲 the in白itial i傲nvestme絆nt半 奧as an e背quivale襖nt annu捌al cost胺 (EAC).敗

48、Dividi扒ng the 斑in巴 initia絆l inves盎tment b澳y the s傲even-ye骯ar annu皚ity fac巴tor, di敖scounte哀d at 15礙 percen艾t拔, the E隘AC of t扒he init伴ial 叭investm哎ent百 is:扒巴壩EAC = I把nitial 笆Investm捌ent / 瓣P(guān)VIFA隘15%,7扒吧阿EAC 拜= $140,辦000 / 隘4.1604版 翱佰愛(ài)EAC 耙= $33,6拜50.45伴矮稗Note, t凹his cal奧culatio辦n solve唉s for t安he annu

49、耙ity pay靶ment wi拜th the 稗initial半 invest辦ment as絆 the pr俺esent v擺alue of扳 the an奧nuity, 吧in othe礙r words辦:案按八PVA = 氨C頒(1 吧1/(1 + 跋R柏)班t伴 / 襖R笆)瓣八靶$140,00襖0 = 扮C白1 (挨1/1.15)傲7阿 / .1扮5案翱愛(ài)C鞍 = $33,襖650.45 骯吧按Now we 佰can cal皚culate 澳the fin霸ancial 阿breakev阿en poin叭t. 藹The fin耙ancial 挨breakev暗en poin辦t f

50、or t搬his pro氨ject is班:奧 爸疤案Q翱F頒 = 埃EAC案 百+啊 FC挨(1 皚 t胺C骯) 壩Depreci擺ation背(跋t翱C笆) / (翱P 澳 V擺C拌)(1 罷t鞍C佰) 霸擺拔Q敖F捌 = 拌$33,65拜0.45 + 皚$340,00霸0(.65) 頒爸 $20,00艾0(.35)鞍 / ($2懊 艾佰 0.72) 板(.65) 胺安八Q擺F哎 敖= 敖297,656百.79熬 or abo稗ut 藹297,657挨 units傲10.疤 襖胺When ca敗lculati拔ng the 芭financi把a(bǔ)l brea捌keven p翱oint, w稗

51、e expre翱ss the 礙initial案 invest拜ment as愛(ài) an equ凹ivalent鞍 annual案 cost (百EAC). D凹ividing笆 the in艾 initia昂l inves鞍tment b罷y the f斑ive-yea挨r annui般ty fact襖or, dis半counted翱 at 8 p壩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 = 埃愛(ài)300,000哎 / 3.60拔478芭

52、白EAC = 邦叭75,136.隘94柏扒Note, t辦his cal稗culatio巴n solve藹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奧nuity, 拜in othe跋r words鞍:靶絆PVA = 懊C岸(1 捌1/(1 + 敗R氨)癌t百 / 埃R版)擺艾敗300,000爸 = 凹C霸1 (絆1/1.08)鞍5扳 / .0唉8癌暗C艾 = 敖礙75,136.哎94 皚般The ann挨ual dep昂reciati挨on is

53、t疤he cost骯 of the敗 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A(yù)nnual 凹depreci鞍ation =皚 安芭60,000埃把Now we 奧can cal版culate 唉the fin頒ancial 拔breakev暗en poin搬t(yī). The 隘financi艾al brea壩keven p辦oint fo辦r this 敖project版 is: 板扳Q把F襖 = EAC耙 + FC(1柏 t敖C愛(ài)) Dep骯recia

54、ti佰on(t疤C暗) / (唉P VC)挨(1 t拌C壩) 鞍頒Q鞍F頒 = 阿75,136.邦94 + 哎凹100,000邦(.66) 捌 辦鞍60,000(哀0.34) 敖/ (爸罷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骯1鞍.跋拌a笆.伴懊At the 捌account擺ing bre背akeven,骯 the IR柏R is ze巴ro perc拌ent sin吧ce the 伴project骯 recove百rs the 哎initial盎 invest伴ment. T板he

55、 payb拔ack per八iod is 礙N years氨, the l拜ength o吧f the p叭roject 礙since t昂he init爸ial inv氨estment胺 is exa靶ctly re皚covered柏 over t疤he proj罷ect lif瓣e.敗 The NP翱V at th案e accou背nting b佰reakeve壩n is:奧 巴斑瓣稗NPV = I耙 (1/N)盎(PVIFA半R%,N藹) 1翱辦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辦, and t版he NPV 傲is nega捌tive an奧d equal傲 to the氨 initia扒l cash 氨outlay.皚啊c胺.扳艾The def奧inition疤 of the般 financ絆ial bre搬akeven 礙is wher擺e the N襖PV of t扒he proj熬ect is 疤zero. I靶f this 哎is true瓣, then 稗the IRR礙 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壩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辦 projec頒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罷, the u拔ndiscou挨nted ca阿sh flow背s are g案reater 拔than th皚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皚2罷.奧礙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礙l be:奧岸OCF = 俺(P v)唉Q FC氨(1 t安C靶) + t斑C瓣(D) 癌暗OCF按 = ($頒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奧20,000/骯4疤) 案敗OCF 骯= $襖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皚 quanti辦ty sold凹 is arb瓣itrary 挨and 哎irrelev皚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(cuò) 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:罷矮OCF = 哀($2敖8凹 1扮9皚)(111,0埃00) 1襖5氨0氨,000(0胺.6

60、6) + 板0.34($4哀20,000/澳4骯) 翱襖OCF 柏= $癌5版96懊,澳0俺40氨拔The sen岸sitivit藹y of th隘e OCF t隘o chang挨es in t叭he quan鞍tity so絆ld is:拜霸Sensiti阿vity =頒 唉OCF/哎Q = ($5啊96壩,笆0唉40巴 5矮90百,敗1鞍00)/(11阿1,000 擺 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.頒94氨 for ev愛(ài)ery add百itional哀 unit s拌old.白 翱1唉3把.熬澳a阿.拌