How To Calculate A Capial Budgeig

Transcription

1 CAPITAL BUDGETING Capial Budgeig Techiques Capial budgeig refers o he process we use o make decisios cocerig ivesmes i he logerm asses of he firm. The geeral idea is ha he capial, or log-erm fuds, raised by he firms are used o ives i asses ha will eable he firm o geerae reveues several years io he fuure. Ofe he fuds raised o ives i such asses are o uresriced, or ifiiely available; hus he firm mus budge how hese fuds are ivesed. Imporace of Capial Budgeig because capial budgeig decisios impac he firm for several years, hey mus be carefully plaed. A bad decisio ca have a sigifica effec o he firm s fuure operaios. I addiio, he imig of he decisios is impora. May capial budgeig projecs ake years o impleme. If firms do o pla accordigly, hey migh fid ha he imig of he capial budgeig decisio is oo lae, hus cosly wih respec o compeiio. Decisios ha are made oo early ca also be problemaic because capial budgeig projecs geerally are very large ivesmes, hus early decisios migh geerae uecessary coss for he firm. Geeraig Ideas for Capial Budgeig ideas for capial budgeig projecs usually are geeraed by employees, cusomers, suppliers, ad so forh, ad are based o he eeds ad experieces of he firm ad of hese groups. For example, a sales represeaive migh coiue o hear from some of his or her cusomers ha here is a eed for producs wih paricular characerisics ha he firm s exisig producs do o possess. The sales represeaive preses he idea o maageme, who i ur evaluaes he viabiliy of he idea by cosulig wih egieers, producio persoel, ad perhaps by coducig a feasibiliy sudy. Afer he idea is cofirmed o be viable i he sese i is saleable o cusomers, he fiacial maager mus coduc a capial budgeig aalysis o esure he projec will be beeficial o he firm wih respec o is value. Projec Classificaios capial budgeig projecs usually are classified usig he followig erms: o Replaceme decisio a decisio cocerig wheher a exisig asse should replaced by a ewer versio of he same machie or eve a differe ype of machie ha does he same hig as he exisig machie. Such replacemes are geerally made o maiai exisig levels of operaios, alhough profiabiliy migh chage due o chages i expeses (ha is, he ew machie migh be eiher more expesive or cheaper o operae ha he exisig machie). o Expasio decisio a decisio cocerig wheher he firm should icrease operaios by addig ew producs, addiioal machies, ad so forh. Such decisios would expad operaios. o Idepede projec he accepace of a idepede projec does o affec he accepace of ay oher projec ha is, he projec does o affec oher projecs. For example, if you have a large sum of moey i he bak ha you would like o sped o yourself, say, $50,000. You decide you are goig o buy a car ha coss abou $30,000 ad a ew sereo sysem for your house ha coss less ha $5,000. The decisio o buy he car does o affec he decisio o buy he sereo hey are idepede decisios. Capial Budgeig

2 o Muually exclusive projecs i his case, he decisio o ives i oe projec affecs oher projecs because oly oe projec ca be purchased. For example, if i he above example you decided you were goig o buy oly oe auomobile, bu you were lookig a wo differe ypes of cars, oe is a Chevrole ad he oher is a Ford. Oce you make he decisio o buy he Chevrole, you have also decided you are o goig o buy he Ford. Similariies Bewee Capial Budgeig ad Asse Valuaio o make a capial budgeig decisio, we eed o compare he cos of he projec o he value he projec will provide he firm. To deermie he value of a asse, we eed o compue he prese value of he cash flows he asses is expeced o geerae over is life. This compuaio of value is he same as was discussed i he secio abou valuaio of fiacial asses ha is, bods ad socks. Oce he value of he asse is deermied, he firm ca deermie wheher o ives i he asse by comparig is compued value o how much he asse coss o purchase. Followig his decisio-makig procedure helps esure he firm will maximize is value ha is, if a asse has a value o he firm ha is greaer ha is cos, he firm s value would be icreased if he firm purchases he asse. Capial Budgeig Evaluaio Techiques i his secio, he basic echiques ha are used o make capial budgeig decisios are described. To illusrae he echiques, le s assume a firm is cosiderig ivesig i a projec ha has he followig cash flows: Year Expeced Afer-Tax () Ne Cash Flows, 0 $(5,000) ,500 4,00 5 3,00 0 = $(5,000) represes he e cos, or iiial ivesme, ha is required o purchase he asse he pareheses idicae ha he cash flow is egaive. If he firm s required rae of reur is perce, he cash flow ime lie for he asse is: Capial Budgeig

3 0 % (5,000.00) ,500,00 3, , , Payback period he umber of years, icludig he fracio of he year, i akes o recapure he iiial ivesme. The followig able shows he payback for his projec: Year Cash Flow Cumulaive 0 $(5,000) $(5,000) 800 (4,00) 900 (3,300) 3,500,800) 4,00 ( 600) 5 3,00,600 This able shows ha he payback period is bewee four years ad five years. The acual payback is: Payback period Number of years before recovery of origial ivesme Amou of ivesme remaiig o be recapured Toal cash flow durig year of payback years $600 $3,00 As he compuaio shows, i akes a lile more ha four years for he firm o recapure is origial ivesme for his projec. The accepace rule for payback ca be saed as follows: Accep he projec if Payback, PB < some umber of years se by he firm This projec would be accepable if he firm was o recapure is ivesmes coss wihi five years, bu i would o be accepable if he firm was o recapure he coss wihi hree years. Eve hough he cocep of payback is very simple, here are problems wih usig payback o make capial budgeig decisios. The primary problem is ha his echique does o use ime value of moey coceps ha is, we do o compue he prese values of he fuure cash flows. Aoher Capial Budgeig 3

4 problem is ha he cash flows beyod he payback period are igored. For example, if he projec described above had a $,000,000 cash flow i Year 5 raher ha he $3,00 give, he projec would sill have a payback equal o jus over four years ad i would o be a accepable projec if he payback period imposed by he firm is hree years. o Ne prese value (NPV) o deermie he NPV of a projec, you eed o compue he prese value of all he fuure cash flows associaed wih he projec, sum hem up, ad he subrac (or add a egaive amou o) he iiial ivesme of he projec. The resulig value represes he amou by which he firm s value will icrease, o a prese value basis, if he firm ivess i he projec. For example, if he NPV of a projec is $,000, he he value of he firm should icrease by $,000 oday. Thus, a projec is accepable if is NPV is posiive. If a projec has a posiive NPV, he i geeraes a reur ha is greaer ha he cos of he fuds ha are used o purchase he projec. The NPV compuaio is: NPV The NPV for he projec i our example is: NPV $800 $900 $,500 $,00 $3,00 $5, ).).).).) 5 $5,000 $800(0.8986) $900(0.7979) $,500(0.778) $,00(0.6355) $3,00( ) $77.8 The resul of his compuaio is he same as ha give i he cash flow ime lie diagram. Accordig o he accepace crierio, he projec i our example should be purchased. Remember ha if he firm acceps a projec wih a posiive NPV is value should icrease, ad vice versa. Therefore, if he projec had a egaive NPV i would o be accepable because such a projec would decrease he value of he firm. The easies way o compue he NPV for a projec is o use he cash flow regiser o your Capial Budgeig 4

5 calculaor. Refer o he isrucios ha came wih your calculaor o deermie how o use he regiser. If you have a Texas Isrumes BAII PLUS, you ca use he seps give i he Time Value of Moey secio of he oes. The ipus should be 0 = 5,000, = 800, = 900, 3 =,500, 4 =,00, 5 = 3,00, ad I =. Press he NPV key (or CPT, he he NPV key) o fid NPV = You ca also use a spreadshee o compue NPV. Usig Excel, you could se up he spreadshee as follows: To solve for he prese value of he fuure cash flows, pu he cursor i cell D3 ad click o he Fiacial fucio amed NPV. I he box ha appears ipu he followig cell locaios: Capial Budgeig 5

6 The rage B3:B7 coais he values of he cash flows for Year hrough Year 5 because he NPV fucio programmed io he spreadshee compues he prese value of he fuure cash flows oly. Whe you click OK you will see he resul of he compuaio, which is $5,077.8, appear i cell D3. Bu, because his resul represes he prese value of he fuure cash flows, you eed o add 0 o he resul o iclude he amou of he iiial ivesme. I his case, he compuaio is compleed i cell D4, where 0 is added o he resul of he NPV compuaio ha appears i cell D3. Cell D4 should ow show he correc aswer for he NPV, which is $77.8. We ca use he prese values of he fuure cash flows o compue he discoued payback. To do so, we simply apply he cocep of he radiioal payback o he prese values of he fuure cash flows as follows: Year Cash Flow PV of Cumulaive PV 0 $(5,000) $(5,000.00) $(5,000.00) (4,85.7) (3,568.4) 3,500, (,500.57) 4, ,737.95) 5 3,00, Thus, he discoued payback is Capial Budgeig 6

7 Payback period Number of years before full recovery of origial ivesme PVof ivesme remaiig PVof oal cash flow durig year of o be recapured payback 4.96 years 4 $, $,85.77 Whe usig he discoued payback, a projec is accepable if is payback is less ha is life. I his case, 4.96 years is less ha five years, so he projec is accepable. Noice, however, we could have made he decisio by lookig a he las lie of he colum labeled Cumulaive PV because ha value is he NPV. So, if you se up he problem as we did i he above able ad he edig value for he Cumulaive PV is greaer ha zero, he NPV > 0 ad he projec is accepable. o Ieral rae of reur (IRR) i was meioed above ha a projec ha has a posiive NPV geeraes a reur ha is greaer ha he cos of he fuds used o purchase he projec. The IRR is defied as he rae of reur he firm would ear, o average, if i purchases he projec. To deermie he IRR, we wa o compue he rae of reur ha causes he NPV of he projec o equal zero, or where he prese value of he fuure cash flows equals he iiial ivesme. I oher words: NPV 0 IRR) IRR) IRR) 0 0 IRR) IRR) IRR) If his compuaio seems familiar, i should be, because he compuaio for IRR is he same as he compuaio for he yield o mauriy (YTM) o a bod, which was discussed i he oes abou valuaio. The IRR for our projec is NPV $5,000 $800 IRR) $900 IRR) $,500 IRR) 3 $,00 IRR) 4 $3,00 IRR) 5 0 $5,000 $800 IRR) $900 IRR) $,500 IRR) 3 $,00 IRR) 4 $3,00 IRR) 5 I is o easy o solve for he IRR wihou a calculaor because you have o use a rial-ad-error mehod ha is, plug i various values for IRR uil he righ side of he equaio equals he lef side of he equaio. Wih a fiacial calculaor, however, i is very easy o solve for IRR. Capial Budgeig 7

8 Follow he same seps you would o compue he NPV, bu press he IRR key (or CPT ad he he IRR key) isead of he NPV key. You should fid ha IRR=.5%. Usig a spreadshee o compue he IRR for he projec, se up he problem as before: To solve for he ieral rae of reur for his projec, pu he cursor i cell D5 ad click o he Fiacial fucio amed IRR. I he box ha appears ipu he followig cell locaios: Capial Budgeig 8

9 The rage B:B7 coais he values of all he cash flows for he projec. Whe you click OK, he aswer,.50%, will appear i cell D5. A projec is accepable usig IRR if is IRR is greaer ha he firm s required rae of reur ha is, IRR > r. Remember ha he IRR represes he rae of reur he firm will ear if he projec is purchased. So, simply saed, he projec mus ear a reur ha is greaer ha he cos of he fuds used o purchase i. I our example, IRR =.5%, which is greaer ha r = %, so he projec is accepable. Compariso of he NPV ad IRR Mehods summarizig wha we have discussed o his poi, we kow ha a projec is accepable if is NPV is greaer ha zero. If a projec has a NPV greaer ha zero, he i geeraes a reur ha is greaer ha he cos of he fuds used o purchase he projec. We also kow ha a projec is accepable if is IRR is greaer ha he firm s required rae of reur. Whe a projec has a IRR greaer ha he required rae of reur, he i geeraes a reur ha is greaer ha he cos of he fuds used o purchase he projec. As you ca see by he ialicized phrases, accepig a projec usig he NPV echique provides he same beefi as accepig a projec usig he IRR echique. As a resul, boh he NPV echique ad he IRR echique should always give he same accep/rejec decisio ha is, if a projec is accepable usig he NPV mehod, i also is accepable usig he IRR mehod, ad vice versa. As we will discover shorly, however, whe comparig wo or more projecs, he wo echiques do o always agree as o which projec is bes. o NPV profiles a NPV profile is a graph ha shows he NPVs of a projec a various required raes of reur. To cosruc a NPV profile, compue he NPV of a projec a differe discou raes ad he plo he resuls. For our example, he followig able shows he resuls of compuig he NPV of he projec a differe discous raes, or required raes if reur: Discou rae NPV 0.0%, , (360.47) 8.0 (745.03) 0.0 (975.57) If hese values are ploed, he NPV profile for his projec is: Capial Budgeig 9

10 $3,000 NPV NPV Profile $,000 $,000 IRR =.5% $0 $,000) Discou Rae (%) As you ca see, he poi where he curve iersecs he horizoal axis represes he projec s IRR. Le s assume he firm i our example is cosiderig aoher projec wih he followig characerisics: Year Cash Flow PV of 0 $(5,000) $(5,000.00),400,4.86,800, $ = NPV The NPVs for his projec, which we will call Projec B, a various discou raes would be: Discou rae NPV 0.0% $, ( 97.6) 8.0 ( 355.4) 0.0 ( 53.8) Ploig hese NPVs wih he NPVs of he firs projec, which we call Projec A, produces he followig NPV profile graph: Capial Budgeig 0

11 $3,000 NPV NPV Profiles for Projec A ad Projec B $,000 $,000 NPV A Crossover Rae = 0.% IRR B = 3.9% $0 $,000) NPV B IRR A =.5% Discou Rae (%) I examiig he graph you should oice a few pois: ) A lower discou raes Projec A has a higher NPV, while Projec B has he higher NPV a higher raes. The reaso for his is ha, alhough Projec B geeraes less oal cash flow over is life (ha is, $,700 compared o $,600 for Projec A), he cash flows are received sooer ha for Projec A. As a resul, he cash flows ca be reivesed o produce a higher rae of reur, which is evideced by he fac ha IRR B > IRR A. () The slope of he curve for Projec A is seeper ha for Projec B, which idicaes ha he NPV of Projec A is more sesiive o chages i he discou rae ha Projec B ha is, he NPV chage is greaer for Projec A ha for Projec B whe he discou rae chages. (3) There is a poi, which we refer o as he crossover poi, where NPV A = NPV B. I his case he crossover poi is where he discou rae equals 0. perce. This rae was compued by akig he differece bewee he cash flows for boh projecs ad he deermiig he IRR of he resuls. I oher words, Cash Flows Year Projec A Projec B Differece 0 $(5,000) $(5,000) $0 800,400,600) 900,800 ( 900) 3, , ,00 700,500 Trea he values i he las colum as a separae cash flow sream ad he compue he IRR jus like you would for eiher Projec A or Projec B ha is, 0 = $0, = $,600, = $900, 3 = $600, 4 = $300, ad 5 = $,500. You should fid IRR = 0.%, which is he crossover poi. As he graph shows, if he discou rae is below 0. perce, he NPV of Projec A is greaer ha he NPV of Projec B ad, if he discou rae is above 0. perce he NPV of Projec A is less ha he NPV of Projec B. If he discou rae equals 0. perce, he NPV A = NPV B. Capial Budgeig

12 o Idepede projecs if projecs are idepede, he simple rule is o ives i all projecs ha have posiive NPVs (IRRs greaer ha he firm s required rae of reu. Remember, ha if a projec has a posiive NPV, he is IRR is greaer ha he firm s required rae of reur. o Muually exclusive projecs he firm cao ives i all projecs ha have posiive NPVs if hey are muually exclusive, because, by defiiio, oly oe projec ca be purchased. Eve hough we kow ha whe NPV > 0, IRR > r i every case, here are isaces whe we evaluae wo projecs ad fid he followig: NPV > NPV > 0 ad r < IRR < IRR Accordig o our decisio rules, boh projecs are accepable. Bu, if he projecs are muually exclusive, which should be chose? The NPV of Projec is greaer ha he NPV of Projec, bu he IRR of Projec is greaer ha he IRR of Projec. This poses a problem, because oe projec is more accepable usig NPV while he oher projec is more accepable usig IRR. The reaso his coflic occurs is because he wo echiques have differe reivesme assumpios. NPV assumes he cash flows received i he fuure ca be reivesed a he firm s required rae of reur, while IRR assumes ha he cash flows ca be reivesed a he projec s IRR. Which is a more appropriae assumpio? Mos people geerally agree ha he firm ca reives a is required rae of reur, bu o always a he projec s IRR. Thus, we coclude ha he NPV mehod should be used o deermie which projec should be purchased whe such a coflic occurs whe evaluaig muually exclusive projecs. I his case, he, Projec is more accepable ha Projec because NPV > NPV. o Muliple IRRs if a projec has a ucoveioal cash flow paer such ha e cash ouflows alerae wih e cash iflows more ha oce, he i could have more ha oe IRR. Each ime he sig of he e cash flow chages (ha is, from posiive o egaive, or vice versa) he projec will have aoher IRR. I our examples o his poi, he projecs have had oly oe sig chage from egaive i Year 0 o posiive i Year so hey oly have oe IRR. If we iroduced a projec wih a similar cash flow paer as he previously meioed projecs excep here was a e cash ouflow a some poi durig he life of he projec (i addiio o he iiial ivesme a Year 0), say, i Year 3, he he ew projec would have wo IRRs. If you would like o see how we correc for muliple IRRs, see he appedix o he capial budgeig chaper i he ex. Modified Ieral Rae of Reur (MIRR) represes he rae of reur ha equaes he prese value of a projec s cash ouflows wih he prese value of is cash iflows, which are saed i erms of dollars a he ed of he projec s life. MIRR is compued as flows: 0 COF 0 CIF MIRR) Capial Budgeig

13 Here COF represes cash ouflows, CIF represe cash iflows, r is he firm s required rae of reur, ad is he life of he projec. The MIRR ca be used o solve rakig problems ad muliple IRRs. Example: Cash Flows Year Projec A Projec B 0 (7,000) (8,000),000 6,000,000 3, ,000, , Followig are he resuls of solvig for NPV, IRR, ad discoued payback: Asse A Asse B Tradiioal PB.80 yrs.67 yrs Discoued PB 3.7 yrs.78 yrs NPV $498. $49. IRR 8.0% 9.03% Uderlies represe he asse wih he beer resuls. A rakig coflic exiss. Compuig he MIRRs, we have 7,000,000.5) 3,000.5) 5,000.5) MIRR ) A 3,000.5) 0 3,4.5 MIRR A ) Calculaor soluio: N = 4, PV = -7,000, PMT = 0, FV = 3,4.5; I/Y = 6.99 = MIRR A 8,000 6,000.5) 3 3,000.5),000.5) MIRR ) B 500.5) 0 4,74.75 MIRR ) B Calculaor soluio: N = 4, PV = -8,000, PMT = 0, FV = 4,74.75; I/Y = 6.5 = MIRR B MIRR A > MIRR B, which idicaes ha Projec A is preferable. Projec Cash Flows ad Risk Cash Flow Esimaio whe evaluaig a capial budgeig projec, we mus esimae he afer-ax cash flows he asse is expeced o geerae i he fuure. (Remember ha he value of a asse is he prese value of he fuure cash flows he asse is expeced o geerae.) Esimaig fuure cash flows is o easy because he fuure cao be prediced wih perfec ceraiy. Some cash flows ca Capial Budgeig 3

14 be prediced more accuraely ha ohers. For example, he cash flows associaed wih a projec ha has exised for a log ime a uiliy power pla migh be fairly easy o predic, while he cash flows associaed wih a projec ha was iroduced recely a do.com compay migh be exremely difficul o predic. Accurae cash flow forecass are impora because icorrec forecass could cause he firm o eiher accep projecs ha acually are uaccepable or rejec projecs ha acually are accepable. Releva Cash Flows cash flows ha mus be evaluaed i capial budgeig decisios. o Cash flow versus accouig icome we are cocered wih cash flows raher ha icome because cash flows pay he bills ad cash flows ca be ivesed o ear posiive reurs; icome cao. Always use cash flows afer axes ha is, afer-ax cash flows because cash mus be used o pay axes. The compuaio of accouig icome ofe icludes ocash iems, such as depreciaio. Thus, i simple erms, we ca use he followig relaioship o esimae operaig cash flows: Ne cash flow = Ne icome + Depreciaio = Reur o capial + Reur of capial o Icremeal cash flows whe coducig a capial budgeig aalysis, we are cocered wih he margial, or icremeal, cash flows associaed wih he asse. I oher words, we should examie oly hose cash flows ha are affeced, or chage, if he asse is purchased. Whe examiig icremeal cash flows keep he followig i mid: Suk coss if a cash ouflow associaed wih he projec has already occurred ad will o be affeced by he decisio o purchase he asse, i is cosidered a suk cos. For example, a firm migh pay $50,000 for a feasibiliy sudy o deermie wheher a ew produc should be iroduced. The $50,000 will be paid wheher he firm decides o pursue he idea furher ha is, coduc a capial budgeig aalysis or drops he idea afer examiig he compleed feasibiliy sudy. Thus, he cos of he feasibiliy sudy is a suk cos. This cos should o be icluded i he capial budgeig aalysis because i is o a icremeal fuure cash flow associaed wih he decisio o maufacure he produc ha is, we should oly evaluae he cash flows ha chage i he fuure as a resul of he capial budgeig decisio. Opporuiy coss he reur ha ca be eared by ivesig fuds i asses similar o hose he firm already ows ha is, he ex bes reur he firm ca ear if he fuds are o ivesed i he proposed capial budgeig projec. For example, if a compay ows a empy warehouse wih a marke value of $3.5 millio ha i is cosiderig coverig io office space for he firm, he $3.5 millio is cosidered a opporuiy cos associaed wih he decisio o ur he warehouse io a office buildig. Exeraliies: effecs o oher pars of he firm ay effec a projec is expeced o have o aoher par of he firm s operaios mus be icluded i a capial budgeig aalysis. For example, may firms ha have radiioally sold heir producs i sores are ow sellig merchadise o he Iere. If a compay decides o examie viabiliy of sellig o he Iere, he capial budgeig aalysis mus ake io cosideraio he fac ha some of he cash flows geeraed by Iere sales will be derived from cusomers who previously purchased a he sores. These rasfer cash flows should o be icluded as par of he Capial Budgeig 4

15 icremeal cash flows for he purposes of evaluaig his projec because his porio of sales is o ew, or icremeal. Shippig ad isallaio coss hese coss geerally are o icluded i he quoed purchase price of a asse, bu hey are effecively par of he purchase price because he firm cao use he asse uil i is received ad pu i operaig codiio. Also, he depreciable basis of a asse ha is, he amou ha ca be depreciaed over he life of he asse icludes he purchase price plus whaever i coss o make he asse operaioal, which icludes shippig ad isallaio. Iflaio iflaio expecaios should be buil io he forecass of he fuure cash flows associaed wih a projec; oherwise, he aalysis could produce icorrec resuls. Ideifyig Icremeal Cash Flows we geerally ideify hree ypes of icremeal cash flows: o Iiial ivesme oulay icludes cash flows ha occur oly a he begiig of he projec s life. Cash flows icluded i his caegory are he purchase price of he asse, shippig ad isallaio coss, he cash flows associaed wih disposal of he old asse if ha asse is beig replaced (his could be he cash received from sellig he asse), axes, chages i e workig capial, ad ay oher up-fro cash flows associaed wih a capial budgeig projec. The iem chages i e workig capial refers o he fac ha i may cases iveory or oher workig capial accous are affeced whe a ew machie is purchased ad added o he firm or whe a old machie is replaced by a ew, more echologically advaced machie. I some cases iveory will icrease, which meas here will be a addiioal cash ouflow associaed wih purchasig he addiioal iveory, ad i oher cases iveory will decrease, which meas here will be a cash iflow associaed wih purchasig he asse because iveory ca be sold uil he ew, lower level of iveory is aaied. o Icremeal operaig cash flows chages i cash flows ha are susaied hroughou he life of he asse ha is, he cash flow effecs are ogoig. Cash flows icluded i his caegory are permae chages i cash sales, salaries, coss of raw maerials, ad oher cash operaig reveues ad expeses ha chage because he asse is purchased. Oe iem ha mus be icluded i icremeal cash flows is he effec of axes if reveues ad expeses chage, he here is a good chace he ax liabiliy of he firm chages also. I mos cases, icremeal operaig cash flows ca be compued usig he followig equaio: Icremea l operaig cash flow ( ( Cash reveues NI EBT S S Depr T) OC OC ) Depr Depr ) Cash expeses T) T( T) Depr ) Depr Taxes where Δ represes a chage, hus ΔNI is he chage i e icome associaed wih he projec. The oher variables are defied as follows: S represes sales, OC is operaig coss, T is axes, ad Depr is depreciaio. Capial Budgeig 5

16 o Termial cash flow he cash flows ha occur oly a he ed of he life of he asse. Cash flows icluded i his caegory are he salvage value of he asse, which could be posiive if he asse is sold for cash or egaive if he firm has o pay o have he asse ake away, ay axes associaed wih salvage, chages i e workig capial, ad ay oher cash flows ha occur a he ed of he life of he asse oly. The iem chages i e workig capial icluded here is he opposie of he chage i e workig capial ha is icluded i he iiial ivesme oulay. The raioale for his adjusme is ha he firm will reur o he same operaig posiio i was i before he asse was purchased so ha iveories ad oher workig capial accous reur o heir ormal levels. As a resul, if a icrease i iveory is required whe he asse is purchased, he iveory should decrease o is ormal level whe he firm disposes of he asse, which would represe a cash iflow a he ed of he asse s life. Capial Budgeig Projec Evaluaio o Expasio projecs evaluaio of expasio projecs is relaively simple because ideifyig he icremeal cash flows associaed wih such projecs geerally is sraighforward. The iiial ivesme oulay icludes he asse s purchase price, shippig ad isallaio coss, ad ay chages i e workig capial; he icremeal operaig cash flows iclude icreases i cash sales ad he cash expeses associaed wih icremeal sales ad he impac of such chages o axes; ad he ermial cash flow icludes he salvage value of he asse afer axes ad he reversal of he chages i e workig capial ha occurred whe he asse was purchased. Oce he cash flows are ideified, we ca apply eiher NPV or IRR o deermie wheher he asse should be purchased. o Replaceme aalysis evaluaio of replaceme projecs is slighly more ivolved compared o expasio projecs because a exisig asse is beig replaced. Whe ideifyig he cash flows for replaceme projecs, keep i mid ha he cash flows associaed wih he exisig (replaced) asse will o loger exis if he ew asse is purchased. Therefore, we mus o oly deermie he cash flows ha he ew asse will geerae, bu we mus also deermie he effec of elimiaig he cash flows geeraed by he replaced asse. For example, if a ew asse ha will produce cash sales equal o $00,000 per year is purchased o replace a exisig asse ha is geeraig cash sales equal o $75,000, he he icremeal, or margial, cash flow relaed o sales is $5,000. Likewise, if he asse ha is replaced ca be sold for $350,000, he he purchase price of he ew asse effecively is $350,000 less ha is ivoice price. I oher words, for replaceme decisios, we mus deermie he overall e effec of purchasig a ew asse o replace a exisig asse he cash flows associaed wih he old asse will be replaced wih he cash flows associaed wih he ew asse. Two iems ha you mus remember o iclude whe deermiig he icremeal cash flows are depreciaio o because i is a cash flow, bu because i affecs cash flows hrough axes ad axes, boh of which geerally chage whe a older asse is replaced wih a ewer asse. Icorporaig Risk i Capial Budgeig Aalysis whe evaluaig a capial budgeig projec, we eed o examie he risk associaed wih he projec ad how he exisig asses of he firm will be affeced if he projec is purchased. The reaso we eed o evaluae he risk of a projec is o deermie if he appropriae required rae of reur is used o compue he projec s NPV (or o compare o is IRR). If a firm is cosiderig a projec ha is much riskier ha he exisig asses, Capial Budgeig 6

17 he i makes sese ha he firm should expec o ear a higher reur o he projec ha o is exisig asses. There are hree risks ha we geerally ideify whe evaluaig a projec: ) sad-aloe risk, which is he risk of he asse whe i is held i isolaio ha is, whe i sads aloe; () corporae, or wihi-firm, risk, which is measured by he impac a asse is expeced o have o he operaios of he firm ha is, how a asse will affec he firm s oal risk if i is purchased ad added o exisig asses; ad (3) bea, or marke, risk, which is he porio of a asse s risk ha cao be elimiaed hrough diversificaio ha is, how a asse will affec he firm s marke risk, or bea, if i is purchased ad added o exisig asses. For a more deailed discussio of how each of hese ypes of risks is measured, see he oes for he Risk ad Reur secio. Sad-Aloe Risk geerally his is he risk ha we compue whe evaluaig capial budgeig projecs because i is easier o deermie ha he oher wo ypes of risk ad i is usually very highly correlaed o he oher ypes of risk. To examie sad-aloe risk, we eed o deermie how ucerai a projec s cash flows are. To do his, we ofe apply he followig echiques: o Sesiiviy aalysis deermie by how much he fial resul of a compuaio, such as NPV, chages whe he values (ipus) eeded for he compuaio are chaged. For example, if we examie he NPV of a projec a various levels of sales ad fid ha he resul chages very lile, he sales would be cosidered a fairly isesiive variable i he compuaio. Geerally, if he fial resuls are very sesiive o he value of a variable (he variable is said o be sesiive), greaer care is ake o esure a accurae forecas of he variable is aaied so ha he fial resuls are more accurae. Sesiiviy aalysis is easy o perform usig a spreadshee because you ca ipu umerous values for he variable beig evaluaed. o Sceario aalysis compue oucomes usig various circumsaces, or scearios. Ofe firms will compue he NPVs of a projec usig he ormal, or mos likely, siuaio, a coservaive, or wors-case, siuaio, ad a opimisic, or bes-case, siuaio. Afer deermiig he NPVs, a probabiliy is assiged o each sceario, ad he expeced NPV ad sadard deviaio of he NPV are compued. For example, cosider he followig: Sceario Probabiliy, Pr i NPV NPV Pr i Bes case 0.30 $75,00,530 Mos likely case ,500 7,50 Wors case 0.0 ( 5,00) (,040) E(NPV) = $38, (75,00 38,740) 0.5(34,500 38,740) 0.( 5,00 38,740) $8,38 Coefficie of variaio CV $8,38 $38, I his case, if he compay s asses have a average CV =.0, his projec probably would be desirable. Remember ha a lower CV is beer ha a higher CV whe we are measurig risk relaive o reur. Capial Budgeig 7

18 o Moe Carlo simulaio we ry o simulae he real world by ideifyig all he possible oucomes for all he siuaios, or variables, ha are associaed wih a capial budgeig projec. For example, oe variable ha geerally eeds o be forecas is he chage i sales ha will occur if a projec is implemeed. Whe usig simulaio, you mus predic every sales level ha is feasible uder various circumsaces for example, sales if projecios are me durig good ecoomic imes, sales if projecios are o me durig good ecoomic imes, sales if projecios are me durig ormal ecoomic imes, ad so forh. Afer ideifyig all he possible sales oucomes, you mus deermie he possibiliy (probabiliy) ha such oucomes will occur. This process is compleed for each variable icluded i he fial oucome (e.g., NPV) ad he all he iformaio is ipu io a compuer program ha deermies a fial oucome value based o he various values ad he probabiliies ha were provided. The compuaio is compleed umerous imes such ha he fial produc is a disribuio of values for he fial oucome. If he NPV of a projec is he fial resul, he he compuer program produces values for he NPV uder various circumsaces. This helps us deermie he mos likely oucome for NPV, he rage wihi which NPV is likely o fall, ad he riskiess of he projec. Corporae (wihi-firm) Risk deermie how a capial budgeig projec is relaed o he exisig asses of he firm. If he firm was o diversify is risk, i will ry o ives i projecs ha are egaively relaed (or have lile relaioship) o he exisig asses. If a firm ca reduce is overall risk, he i geerally becomes more sable ad is required rae of reur decreases. Bea (Marke) Risk a leas heoreically, ay asse has a bea,, or some way o measure is sysemaic risk (see he oes for Risk ad Raes of Reur for a deailed discussio). o If we ca deermie he bea of a asse, he we ca use he capial asse pricig model, CAPM, o compue is required rae of reur as follows: r proj = r RF + (r M - r RF ) proj Accordig o he CAPM, he greaer a projec s sysemaic risk as measured by, he greaer he reur he firm should require o ives i he projec. For example, if a firm uses he CAPM ad deermies r proj = 6%, he he IRR for he projec mus be greaer ha 6 perce for i o be accepable. The cocep of bea ca also be used o deermie he impac of addig a projec o exisig asses. Remember ha he bea of a porfolio is he weighed average of he beas of he idividual ivesmes. The bea for a firm ca be hough of as he weighed average of he beas of he idividual asses i possesses. For example, if he firm s bea equals.5, he he weighed average of he beas of all he asses i he firm is.5. Suppose he firm adds a ew projec. If he ew projec has a bea equal o 3.0 ad i will cosiue 0 perce of he firm s operaios oce i is added, he he bea of he firm afer he projec is added, ew, will be: ew = (0.0 x projec) + (0.80 x old) = (0.0 x 3.0) + (0.80 x.5) =.8 Capial Budgeig 8

19 o Measurig bea risk for a projec i is difficul o deermie he bea for a projec. Oe mehod we use o deermie a projec s bea is o examie a firm ha sells oly oe produc, he produc ha is ideical o he projec, ad he use he bea of ha firm as he bea of he projec. Whe a sigle-produc compay is used o ideify characerisics of a like capial budgeig projec, i is called he pure play mehod. How Projec Risk Is Cosidered i Capial Budgeig Decisios i realiy, risk geerally is icorporaed io capial budgeig decisios somewha arbirarily. The firm geerally uses is ormal, or average, required rae of reur o evaluae projecs ha have average risk, a few perceage pois are added o he average required rae of reur o evaluae projecs ha have above-average risk, ad a few perceage pois are subraced from he average required rae of reur o evaluae projecs ha have below-average risk. I is impora ha a projec s risk be cosidered i capial budgeig aalysis, because icorrec decisios migh be made if risk is o cosidered. For example, if he firm s average rae of reur is used o evaluae all capial budgeig projecs, regardless of heir risk, he projecs wih lile (grea) risk migh be rejeced (acceped) whe hey should be acceped (rejeced). Capial Raioig i mos cases firms do o have access o ulimied amous of fuds or fiacial maagers do o wa o access addiioal fuds, which migh mea ha some accepable capial budgeig projecs are o purchased. If he amou of fuds ha is ivesed i capial budgeig projecs is cosraied, he capial raioig exiss. I such siuaios, he firm should ives i he combiaio of projecs ha provides he highes combied NPV ha is, ha icreases he firm s value by he mos. Muliaioal Capial Budgeig for he mos par, he capial budgeig projecs of muliaioal firms should be evaluaed he same as for domesic firms. However, he muliaioal firm mus be aware ha may couries have resricios o how much cash ca be se back o he pare compay from is foreig subsidiaries (repariaio of cash). Resricios o he repariaio of cash (earigs) ca ofe be very severe, hus he cash flows ha are releva o he pare compay are hose ha ca be repariaed, o hose ha mus say i he foreig coury. Also, capial budgeig projecs associaed wih foreig operaios geerally are cosidered riskier ha hose associaed wih domesic operaios because ) movemes i exchage raes ha is, exchage rae risk affec he raslaio of foreig currecy io domesic currecy, ad () here is a risk ha foreig govermes will akeover or severely resric operaios of foreig subsidiaries ha is, poliical risk exiss. Such risks mus be cosidered whe evaluaig capial budgeig projecs of foreig subsidiaries. Capial Budgeig 9