1 NORTHWESTERN UNIVERSITY J.L. KELLOGG GRADUATE SCHOOL OF MANAGEMENT Tim Thompson Finance D30 Teaching Noe: Projec Cash Flow Analysis Inroducion We have discussed applying he discouned cash flow framework o he valuaion of invesmens in real asses (capial budgeing projecs) and have discussed using he differen decision rules (NPV, IRR, PI, ec.) o selec capial invesmens. In his noe, we will confine our discussion o decisions made using he ne presen value rule. Our model for deermining he presen value, NPV, of he an invesmen generaing 0 cash flows of CF, = 0,1,...,N is: ' j W' &) W %U W (1) where CF is he oal cash flow generaed by he projec a dae, r is he opporuniy cos of capial for he invesmen projec (assumed o be he same for all ) and 1/(1+r) is he presen value facor used o discoun he cash flow a ime back o he presen. Equaion (1) summarizes he basic principles of he discouned cash flow (DCF) mehod of esimaing value: 1. I is cash flow ha maers, i.e., he iming and magniude of he cash flows of he invesmen are wha is relevan. 2. All he fuure cash flows of an invesmen are relevan, no jus he near erm. Long erm. 3. The presen value of he fuure cash flows discouns each cash flow by is opporuniy cos of capial, i.e., he expeced rae of reurn he shareholders could earn if hey invesed in securiies in he capial marke wih similar characerisics, especially risk. The purpose of his eaching noe is o discuss how o esimae he cash flows of he invesmen. To
2 Projec cash flows, page 2 focus on his aspec of he problem, we will assume away some complicaions: firs, we will no discuss esimaing he opporuniy cos of capial or he riskiness of he invesmen. These asks are deferred o Chapers 7-9 of Brealey and Myers. In fac, we will implicily assume here is no risk in he fuure cash 1 flows --- ha hey are known wih cerainy. Second, we will assume here are no imporan erm srucure effecs; i.e., r will be he same for all fuure daes,. We have covered how he erm srucure of ineres raes affecs presen values in he eaching noe, "Bond Valuaion under Cerainy." Valuaion of corporae cash flows is an applicaion of our "nea and clean" valuaion mehodology which runs head on ino wo disciplines which are very "messy": accouning principles and ax requiremens. In finance, we ofen rea hese areas like "necessary evils," bu masering some aspecs of boh areas is a prerequisie for making good invesmen decisions in pracice. Undersanding accouning principles is imporan because ofen he source of informaion used o generae he cash flow forecass is derived from he projec s effec on he accouning saemens of he company (e.g., he income saemen). Undersanding relevan aspecs of he ax code is crucial, because, as we shall see below, all cash flows should be esimaed on an afer-ax basis. The ax reamen of many iems in cash flow analysis will affec he iming and magniude of he ax liabiliies associaed wih an invesmen, hence affecing is ne presen value. While he "necessary evils" of generally acceped accouning principles and he ax reamen of cash flow componens are imporan, i is beyond he scope of his noe and, hankfully, his course o cover hese 1 The assumpion of perfec cerainy has several impacs on our analysis of capial budgeing: firs, many of he issues we will deal wih below, e.g., he reamen of cannibalizaion, will be overly simplified because we will assume he exisence of and he amoun of cannibalizaion of oher produc lines is known wih cerainy. Addressing such issues in he conex of uncerainy is deal wih no only in Chaper 9, bu also in Chaper 10 which discusses sensiiviy analysis and decision ree analysis. These issues are beyond he scope of his noe. Assuming perfec cerainy also eliminaes from consideraion he value of managerial opions, e.g., he opion o expand capaciy if he projec does well, or o abandon early if he projec does poorly. Managerial opions may be imporan, if no crucial, o he value of capial budgeing projec. The value of hese opions derives from heir coningen naure: hey are only exercised if i is in he shareholders ineres, and his depends on somehing which is, from oday s perspecive, random. In a cerainy model, we know when and wheher he "opions" will be exercised and wha hey are worh. Chaper 20 inroduces mehods for valuing coningen claims and Chaper 21 applies hese mehods o capial budgeing problems.
3 Projec cash flows, page 3 areas in deail. Hopefully, we will show some imporan differences beween some accouning variables and cash flow and how hese and axes affec he value of capial budgeing projecs. Our reamen of accouning and axes will be shamelessly simplisic, however, so ha we can focus on he finance insead. 2 Wha we inend o do is flesh ou wha we mean by he "oal cash flow generaed by he projec" a each dae, =0,1,...,N. There are hree imporan conceps in esimaing he cash flows for an invesmen. 1. Only cash flow is relevan. 2. Only incremenal cash flow is relevan. 3. Be consisen in reamen of inflaion. Once we have deermined which cash flows are incremenal o he invesmen, we mus esimae he cash flows on he correc basis. The relevan cash flow generaed by he projec a dae is he Operaing Free Cash Flow a dae. We will ake hese conceps up in urn, and hen we will presen general formulas for calculaing he projec s Operaing Free Cash Flow for each period,, of he projec s life. Only cash flow is relevan. The fundamenal componen of he discouned cash flow framework is cash flow. I is he cash flow impac of a decision ha maers, no is effec on earnings per se. This used o be he disinguishing mark of he finance field versus he accouning profession: accounans placed he corporae focus on earnings variables such as EPS and ROE, while finance argued he focus for decision-making should be on cash flow. Cos accouning was he firs field which jumped ship, and mos cos accouning exs handle he capial budgeing problem in a fashion indisinguishable from ours. In he lae 70 s and early 80 s came wha some call he "shareholder value revoluion," which saw he birh of several firms (e.g., Sern-Sewar, Alcar, HOLT) using discouned cash flow valuaion mehods for esimaing corporae value, for evaluaing he shareholder value impac of changes in financial and operaing sraegies, in evaluaing mergers and 2 Tax rules and accouning regulaions change relaively frequenly as well, whereas financial principles do no. The ineresed suden is direced o he Kieso and Weygand ex and he U.S. Maser Tax Guide, for he mos recen year.
4 Projec cash flows, page 4 acquisiions, and evaluaing corporae resrucuring alernaives. Mos large accouning/consuling firms and sraegy consuling firms have deparmens which specialize in some aspec of using discouned cash flow mehods o analyze corporae decisions. In 1987, he FASB required companies complee a new financial saemen called he saemen of cash flows. 3 Depreciaion is no a cash flow. To illusrae he difference beween cash flow vs. accouning income reamens of cash flow iems, consider he immediae purchase of capial equipmen for $10,000. The cash flow impac of he invesmen is -$10,000 a ime zero. The income saemen does no recognize his invesmen as a curren expense, bu insead depreciaes he asse over ime. The annual depreciaion amouns are subjec o GAAP rules. If we assume he asse is depreciaed sraigh line over five years o zero esimaed salvage value, he annual depreciaion is ($10,000-0)/5 = $2,000 per year in years one hrough five. The cash flow recogniion of he iniial cash oulay is he relevan measure o use o assess he economic cos of he equipmen. The annual depreciaion amouns are no, in and of hemselves, cash flows a all. As we will see below, he $10,000 will no be ax deducible immediaely; insead, he expendiure will allow for ax reducions (or ax shields) in laer periods when i is depreciaed. I is imporan o noe, however, ha he relevan depreciaion for capial budgeing purposes is he depreciaion ha is allowed for ax purposes, no ha allowed for reporing purposes. Timing of recogniion of revenue and expense: working capial For mos corporaions, accouning for reporing purposes is done on an accrual basis: revenue from 3 The major place where cash flow seems o ake a back sea o earnings is in he financial analys communiy and how corporaions communicae wih his communiy. There remains a ludicrous focus on quarerly and annual EPS and ROE by boh analyss and CFO s which doubless leads o many value-reducing decisions, bu ha is beyond he scope of his noe also. The ineresed reader is direced o he Copeland, Koller and Murrin book and he Rappapor book.
5 Projec cash flows, page 5 sales of goods is recognized when he sale akes place, no when he cash is received for he sale. Expenses are mached agains revenues: if you purchase maerials (suppose you pay cash) which go ino he producion of a finished produc and he produc has no been sold a he end of he year, here is no recogniion of he expense for reporing purposes. In he following year, when he finished produc is sold, you recognize he cos of he earlier purchases in Coss of Goods Sold. From a cash flow perspecive, we would like o record he sales revenue when we receive he cash and would like o record he expense of he purchases when we pay cash for hem. Because, however, we will ofen use he income saemen as he saring poin in our analysis of cash flows, we will ime he above revenue "oo early" and he expense "oo lae." As an example, suppose we sell $100,000 of widges in 19X2 which are sill in accouns receivable (a curren asse) a he end of he year (assume he receivables are good); 19X2 revenue will include he $100,000, and accouns receivable will include he $100,000. In 19X3, he $100,000 will no be revenue and accouns receivable will drop by $100,000 as we receive he cash. If here were no oher changes in he accouns receivable accoun during 19X2 and 19X3, we could calculae he cash revenue (associaed wih he $100,000) in 19X2 and 19X3 by he following: Cash revenue (19X2) = Sales (19X2) - Chg. in Accouns Receivable (19X2) = $100,000 - $100,000 = 0 Cash revenue (19X3) = Sales (19X3) - Chg. in Accouns Receivable (19X3) = 0 + $100,000 = $100,000 Noice he increase in he curren asse, accouns receivable, is considered a cash ouflow, or an invesmen. Similarly, if we purchased $50,000 in raw maerials in cash a he end of 19X2 and did no sell any producs agains which o mach hese expenses in 19X2, we would have an increase in invenory (a curren asse) in 19X2 and no expense in 19X2. If here were no oher changes in invenory in 19X3, and he subsequen sales are made, we will have $50,000 in expenses in 19X3 and a reducion in invenory of $50,000 in 19X3. Using he above analysis:
6 Projec cash flows, page 6 Cash expense (19X2) = Expense (19X2) - Chg. in Invenory (19X2) = $0 - $50,000 = -$50,000 Cash expense (19X3) = Expense (19X3) - Chg. in Invenory (19X3) = -$50,000 + $50,000 = $0 Noice, again, he increase in invenory is considered an invesmen or cash ouflow. Timing differences beween he recogniion of income and receip of cash flow is incorporaed ino he required ne working capial for he projec. Ne working capial is defined as curren asses minus curren liabilies. Curren asse accouns include cash, markeable securiies, invenories, accouns receivable, and ohers. Curren liabiliies are liabiliies of he firm which will come due wihin one year and include accouns payable, shor-erm deb, curren porions of long-erm deb, income axes payable, and ohers. To simplify he discussion, we will consider ne working capial o be Cash and Markeable Securiies + Invenories + Accouns Receivable - Accouns Payable. Increases in ne working capial are cash ouflows (invesmens) and decreases in ne working capial 4 are cash inflows. Cash which mus be lef available for unexpeced expendiures, invenories which mus be buil up for expeced growh and o avoid sockous, receivables which are used o faciliae rade represen uses of cash ha could be used elsewhere in he firm (or spen by he shareholders, perish he hough) and are correcly considered invesmens made by he firm. These increases in curren asses will usually by parially offse by corresponding increases in accouns payable, which reduces he size of he invesmen. A complee capial budgeing analysis would forecas he cash required, he fuure accouns receivable and accouns payable, and invenory requiremens over he life of he invesmen projec. The 5 purpose of any forecasing analysis is o generae forecass which are as accurae as possible. The 4 Noice ha, in boh examples, he increase (decrease) in curren asses seems o have been offse by a decrease (increase) in cash: when he receivables are paid, cash goes up, when he invenory is paid for, cash goes down. The assumpion we make is he he operaing level of he cash accoun is mainained as proecion agains unexpeced cash requiremens. When he cash is drawn down, i mus be replenished o is earlier level and when we ge "excess cash," i is invesed elsewhere and is no in he "operaing cash accoun." For pracical purposes, he operaing cash accoun increases and decreases only due o he need for a larger or smaller proecive cash accoun. 5 Acually, his depends on he loss funcion associaed wih forecasing errors. Discussion of loss funcions is beyond he scope of his noe.
7 Projec cash flows, page 7 appropriae model for forecasing accouns receivable may be o calculae he pas percenage of accouns receivables o sales and assume ha raio will remain consan in he fuure. Of course, if he produc is sufficienly differen ha your oher producs, his may no be he case. Similarly, if you begin making differen credi erms available o your cusomers, he relaionship beween accouns receivable and sales may change. Similarly, you could model payables and invenories separaely. The one general poin which can be made is ha mos of he ne working capial caegories increase wih he scale of he firm, i.e., as sales increase, operaing ne working capial increases. For capial budgeing projecs which are revenue expanding projecs, here will be an increase in ne working capial a he beginning of he projec; as he projec s sales grow during is lifeime, addiional ne working capial will be needed; as he projec maures and is sales level off, addiional ne working capial invesmens will be less necessary or unnecessary; and as he projec declines, working capial requiremens aper off. If he projec has a naural ending dae, i can be assumed ha you could sell he remaining invenory, he remaining accouns receivable and payable are seled and he need for operaing cash goes o zero. Therefore, if we forecas an ending dae or erminaion dae for he invesmen, we normally assume ha earlier invesmens in working capial can be recovered a ha ime. See he discussion abou erminaion of projecs below. Incremenal Cash Flows The mos imporan concep in cash flow analysis is ha he relevan cash flows for decision making are he incremenal cash flows he projec generaes. The criical comparison o make is he "wih versus wihou" disincion: is he cash flow incurred wih he new projec, and would he cash flow have been incurred wihou he new projec? If he cash flow will be incurred wih he new projec and oherwise would no have been incurred, i is an incremenal cash flow and should be included in he analysis. Omi sunk coss.
8 Projec cash flows, page 8 Expendiures which were made in he pas such as research and developmen expendiures, es markeing expenses, even capial expendiures which have been made prior o he analysis, are no incremenal o he curren decision. They can no be "unincurred": if he projec has a posive NPV ignoring hese coss, aking he projec would sill make you wealhier han you are now; if he projec has a negaive NPV ignoring hese coss, aking he projec will make you less wealhy han you are now --- he prior 6 invesmen is already gone. The fac ha managers make misakes such as he sunk cos fallacy is no surprising. While we assume ha he goal of he firm is always o maximize he ne presen value of all he firm s aciviies, assuming his does no make i so. Decision makers (e.g., he CEO or divisional managers) may have significan human capial riding on a paricular projec and i is naural for hem o view he projec from is effec on hem raher han on he shareholders. The abandonmen of an invesmen ha has already cos a lo of money may be equivalen o admiing failure. Brealey and Myers have a good example of he sunk cos fallacy a work in he Lockheed Tri-Sar case. An equally sarling example was he "smokeless cigaree," which was a pe projec of RJR-Nabisco s CEO Ross Johnson: RJR had spen millions for years in research and developmen despie markeing research ha srongly suggesed ha no one would ever use i. When RJR was aken privae, one of he firs iems of wase ha was eliminaed was invesmen funds direced owards his projec. 7 Include opporuniy coss. 6 Mos principles in finance are jus warmed over epihes from grandmohers everywhere. We have seen "a penny saved is a penny earned" and "a sich in ime becomes nine." The sunk cos principle is simply says "There s no use crying over spilled milk" or "Le byegones be byegones." Similarly, we could say "Don hrow good money afer bad," bu I don hink my grandmoher ever sounded ha mercenary. Laer, we will revisi grandmohers for advice concerning he opimal ransporaion of eggs. 7 Ineresed readers are direced o Barbarians a he Gae, by Bryan Burrough and John Helyan. Or if you are lazy, you can ren he movie.
9 Projec cash flows, page 9 One of he mos difficul aspecs of capial budgeing is he fac ha so many resources wihin a company are shared across differen projecs. A new projec will make use of exising plan space or will require consrucion on land ha he firm already owns. A new produc can be packaged on exising packaging equipmen which has slack capaciy. Each of hese siuaions involves he firm incurring some opporuniy cos: he opporuniy cos in any of hese siuaions is he loss of being able o use he resource in quesion in is nex bes alernaive. The reason ha hese opporuniy coss are "difficul" is ha he cos is difficul o measure. Someimes he cos is reasonably easy o esimae: suppose you have office space in an office building for your consuling firm and have some excess space currenly. You are considering using some of he excess space o pu in a sae-of-he-ar educaion faciliy. The space is currenly being rened by you and would be rened by you wih he projec, bu he wih vs. wihou disincion requires an esimae of he opporuniy cos of he space. If he space could be separaed such ha he office building could ren i o anoher enan, hen he opporuniy cos would be he renal reducion you could ge (ne of coss) if you did no build he classroom. You have o be careful: if you do no build he classroom, supposedly you will have o use an off-sie classroom and you will have o ren hese faciliies as needed. The poin of his example was no o ouline he enire cash flow analysis bu o idenify he opporuniy cos of he space. More generally, he opporuniy cos of using excess capaciy or space can be viewed as an applicaion of he cos of excess capaciy mehod, discussed in Brealey and Myers, Secion 6-3. I should be poined ou ha here may be opporuniy benefis as well as coss: if a new invesmen requires he purchase of plan and equipmen which, because of he minimum economic scale of he plan and equipmen, involves subsanial slack capaciy, his capaciy is hen available for laer invesmens o use. If his allows he firm o speed up growh opporuniies or follow-up invesmens, a measure of he opporuniy benefis should be included also.. The relevan amoun of overhead coss for he new invesmen are he incremenal amoun, no he allocaed
10 Projec cash flows, page 10 amoun. The opporuniy coss discussed above, while difficul o esimae, are a leas siuaions where here are idenifiable asses used by he new projec. More generally, overhead expenses associaed wih all projecs, such as general and adminisraive coss, CEO and secreary salaries, insurance and ohers are simply overhead. Overhead coss may no be relaed o any paricular projec bu mus be paid for in aggregae for he firm o be profiable. Overhead expenses are oalled and allocaed across he differen projecs in he cos accouning process for assessmen of he subsequen performance of he differen projecs. The allocaion mehod used may be based on square fooage used, or direc labor, direc maerials, or whaever. For capial budgeing purposes, a projec should no be "charged" for allocaed overhead, bu should be charged for is incremenal effec on overhead expenses. Because overhead expenses are no relaed o a specific projec, i may be impossible o esimae he precise incremenal effec of a new projec on overhead expenses. A rule of humb is ha overhead expenses end o be posiively associaed wih he scale of he firm. If a projec is revenue expanding here will be, on average, an increase in overhead expenses. The relaionship beween sales and overhead coss may be esimaed using pas daa by regression mehods. 8 In conras, if he projec is purely cos reducing, e.g., he replacemen of old machinery wih new ha has no effec on he scale of he firm, i may have no effec on he oal overhead coss of he firm. This issue could be looked a as anoher applicaion of he cos of excess capaciy mehod, bu because here is lile direc relaion beween he projec and he usage of shared resources, i may be impossible o esimae via his mehod. Include incidenal effecs: synergies, cannibalizaion, ec. 8 See any cos accouning exbook for informaion on using regression analysis o esimae hese relaionships.
11 Projec cash flows, page 11 Ofen making a new invesmen has significan effecs on oher ongoing projecs of he firm (and projecs he firm has no begun ye). These ineracions beween projecs should be aken ino accoun in esimaing he incremenal cash flow for he new invesmen. Brealey and Myers discuss an example of a railway company considering building a new saion connecing a new branch line o is exising rail sysem. They argue ha hey should no only include he direc revenue of rail raffic on he new branch line, bu also he revenue associaed wih he incremenal raffic on he res of heir railway sysem due o he branch line. The laer incremenal revenue can be considered a synergy beween he old rail asses and he new rail asses. Two ses of asses, A and B, are said o have synergies if he value of A and B ogeher is differen han he value of A by iself (as a sand alone business) plus he value of B by iself (as a sand alone business). The value of synergies can be posiive (as in he railway example) or can be negaive. Produc cannibalizaion is an example of a negaive incidenal effec. I is ofen argued ha if an auomobile company inroduces a new model of car, ha i will erode (cannibalize) he sales of heir oher models. Similarly, if Kraf inroduces a new cheeze produc i will ake away some of he demand for Kraf Singles or oher cheeze producs ha Kraf makes. If here is cannibalizaion of sales of oher producs due o he inroducion of he new projec, hese should be aken ino consideraion in deermining he incremenal cash flows for he new invesmen. The following example illusraes some of he issues involved in esimaing produc cannibalizaion. Example: You are he divisional manager of high-fiber cereals a a large cereal producer. Upper managemen wans o ake advanage of perceived increase in demand for high-fiber cereals. You have pu ogeher a produc proposal for Hemp Squares, a very high fiber cereal. For simpliciy s sake we consider only revenues in he following discussion, bu he same concep would apply o coss, ec. You have forecas annual revenues of $500,000 for Hemp Squares. The divisional manager of he high-sugar cereals argues ha his figure oversaes incremenal revenues for Hemp Squares because his division s oher producs (especially heir big seller, Sugar Shells) will lose approximaely $70,000 per year in revenues o people swiching o Hemp Squares. Wha is he correc esimae of incremenal revenue for he Hemp Squares projec, $500,000 or $430,000? The answer o his quesion is based on he wih versus wihou disincion. If hey produce Hemp Squares,
12 Projec cash flows, page 12 hey believe ha heir oher producs (especially Sugar Shells) will lose $70,000 in sales. Bu, if hey do no produce Hemp Squares, wha will heir los sales of heir oher producs be? In oher words, wha is he real cause of he decline in sales of he oher producs, your company s inroducion of Hemp Squares, or a shif in demand of consumers waning o buy high-fiber cereals (or some oher reason)? The quesion of how much cannibalizaion is relevan for capial budgeing purposes is inegrally relaed o he marke srucure of he indusry in which he firm operaes. If he firm is compleely compeiive in his marke and consumers have no loyaly o brand names or company names, hen anoher compeior could be expeced o produce he new produc if you don, and you would lose he sales anyway. Even if consumers do exhibi brand loyaly (which gives he firm some laiude relaive o he compeiion), i is no clear ha new produc inroducions will cannibalize oher produc lines. In he Hemp Squares example, he demand for high fiber cereals is probably wha is driving he revenue forecass for Hemp Squares; hese cusomers will sop buying Sugar Shells anyway. If you don produce Hemp Squares, hey will buy he compeiion s Bran Bombs. If your division makes oher high fiber cereals and consumers do exhibi some brand loyaly o your company (which is quesionable oo), hen here probably will be cannibalizaion of sales of oher similar high-fiber cereals. If he produc you produce is a commodiy produc like whea, wha is he likelihood ha you will cannibalize sales? Suppose you are a whea farmer wih 1,000 acres on which you grow whea and are considering purchasing 500 more acres o increase your crop size. Should you consider ha cusomers buying your new crop s whea will be aking away sales of your old crop s whea? If we were alking abou an island economy where you conrolled he bulk of he whea oupu of he naion, maybe. Chances are his is a iny amoun of he world supply of whea and you won affec he price you will receive for whea. Cannibalizaion is zero in his example. Suppose you are a business supply company and you carry a wide array of paper faseners, paper clips, and he like, bu you don sell any saples or saplers. If you inves in invenory of saples and saplers
13 Projec cash flows, page 13 o sell also, should you consider he possible los sales of oher paper faseners, papers clips, ec.? Wha is he likelihood ha your cliens were going wihou sapling documens ha needed sapling? They were probably jus buying saples and saplers elsewhere. Offering saples and saplers in your produc line will jus give your cusomers he chance o buy saples and saplers from you insead of somewhere else. Probably no cannibalizaion. Auomobiles and oher consumer durables, ec., however, may be quie differen. People exhibi considerable company-brand loyaly in car purchases. If Toyoa decides o inroduce a new sedan beween he size of he Corolla and he Camry, i will probably ake some sales away from Corollas and Camry s. The boom line is ha cannibalizaion and oher synergies are ofen difficul o esimae exacly, bu he rule o use is he wih versus wihou rule. Do no include financing cash flows in your cash flows Suppose you make a $5 million invesmen in building a new sore o add o your chain of sores. The invesmen funds are raised via a bank loan of $5 million a 8% ineres per year. Should your fuure cash flow forecass include a deducion for.08($5 million) = $40,000 per year in ineres expenses? Is he ineres expense incremenal? In a sense, yes. You ake ou he loan o build he new sore and had you no buil he new sore, le s suppose you would no have borrowed any addiional money. The ineres expense seems o be incremenal o he projec. Why do we say no o include he financing cash flows in your cash flow forecass? Because including financing cash flows would be double couning. In equaion (1), we discoun he fuure cash flows o he projec by he opporuniy cos of capial on he invesmen. The opporuniy cos of capial includes all coss associaed wih raising he enire invesmen amoun: all ineres and principal repaymens on borrowings, all dividends and reurns of capial o equiy conribuors. Therefore, he value
14 Projec cash flows, page 14 of he invesmen should be deermined by discouning he incremenal operaing cash flows on he 910 invesmen a he opporuniy cos of capial for he invesmen., Be consisen in your reamen of inflaion If your forecased cash flows have no incorporaed anicipaed fuure inflaion or have already had i removed (i.e., hey are inflaion adjused), hen hey are real cash flows and should be discouned a a real discoun rae. If your forecased cash flows incorporae anicipaed fuure inflaion, hen hey are nominal dollars and should be discouned a a nominal discoun rae. Formulas for calculaing a projec s Operaing Free Cash Flows We begin wih a ypical income saemen approach and modify i o esimae he cash flows of an invesmen. In every year of he projec s life ( = 0, 1,..., N), we could esimae he incremenal effec of he projec on he company s income saemen --- we have o be careful, we are alking abou he income saemen for ax purposes, no for reporing purposes. The income saemen in year, (=0,...,N), would look like his: minus Revenues Coss of Goods Sold Gross Profi 9 I will never be said ha he language of finance is very clear. When I use he erm operaing cash flows, i is o disinguish hem from financing cash flows, such as ineres, principal, dividends, ec. "Operaing" cash flows is ofen used o disinguish beween he cash flows resuling from he operaions of asses in place and "Invesmen" cash flows resuling from buying new asses. Boh "Operaing" and "Invesmen" cash flows are operaing cash flows for our purposes because hey are no financing cash flows. An alernaive erm could be o call operaing cash flows asse cash flows, in ha hey are generaed by asse decisions and no by financing decisions. 10 We are assuming ha he opporuniy cos of capial incorporaes all coss of financing he asses in quesion and, in essence, ha he opporuniy cos of capial is no a funcion of how he asses are financed. In Chaper 17, we will see ha his assumpion is equivalen o assuming he Modigliani-Miller Proposiions are rue, which is no so palaable in pracice. Modifying our analysis o ake ino accoun he effec of financing decisions on he NPV analysis is he subjec of Chaper 19.
15 Projec cash flows, page 15 minus Depreciaion (depreciaion may be included in Coss of Goods Sold) minus Oher Operaing Expenses minus Ineres Expense (or oher financing expenses) Profi before Tax minus Tax (acual ax going o Bill and Hilary) Ne Income The income saemen for year does no capure our definiion of cash flow: i subracs ou financing charges such as Ineres Expense (effecively on an afer ax basis) when we should leave ha in. I subracs ou Depreciaion as if i were a cash flow, which i is no. I correcly akes ino accoun he ax shield associaed wih he Depreciaion expense. Noice ha I have separaed he Depreciaion line ou so he reader can see ha i is here; depreciaion is ofen jus included in Coss of Goods Sold. Lasly, i does no subrac off capial expendiures, CAPEX, when hey occur, nor does i incorporae he changes in ne working capial, )NWC, ha are required o ake on he new invesmen. How do we modify he above income saemen o calculae he projec s cash flow correcly? We mus add back Ineres Expense o Profi Before Tax o ge Operaing Profi before Tax. Then we would muliply Operaing Profi Before Tax by he effecive ax rae of he company (which would be calculaed as Tax /Profi before Tax ) o ge Adjused Taxes (ofen called Cash Taxes). Then we subrac Adjused Taxes from Operaing Profi before Tax o ge Ne Operaing Profi Less Adjused Taxes, which goes by he appeizing acronym NOPLAT (alhough I don hink i s pronounced like he yogur). Lasly, we add back Depreciaion because i is no a cash ouflow (bu leave is ax shield effec in he ax accoun) and subrac off any incremenal CAPEX required in year and any incremenal change in ne working capial in year. Our operaing cash flow saemen in year becomes: minus minus minus Revenues Coss of Goods Sold Gross Profi Depreciaion Oher Operaing Expense Operaing Profi before Tax (We lef ou financing charges.)
16 Projec cash flows, page 16 minus Adjused Taxes (Effecive ax rae imes Op Prof bef Tax) Ne Operaing Profi Less Adjused Taxes (NOPLAT ) plus Depreciaion Expense (Add back non-cash charges.) minus Capial Expendiures (CAPEX ) minus Change in Ne Working Capial ()NWC ) equals Free Cash Flow from Operaions (Op. FCF ) 11 Example of calculaing Free Cash Flow from Operaions Suppose a seel company is considering adding a new blas furnace o is operaions. You have jus compleed a $1 M feasibiliy sudy and have found he following: adding he blas furnace will resul in $50 M in new sales per year and will save $90 M per year in expenses. Suppose ha he furnace coss $1,000 M (o be paid in advance) and uses some pars from a (fully depreciaed) reired furnace. Removing he pars will render he old furnace worhless; oherwise, he old furnace could be sold for $30 M. The furnace will las en years, bu you will have o inves $200 M in replacemen pars in year 5. Assume he replacemen pars can be depreciaed five years sraigh line o a zero esimaed salvage value. The blas furnace (including he replacemen pars) will have a salvage value of $200 M a he end of en years. Finally, you esimae ha he company requires $.40 in addiional ne working capial for every dollar of incremenal sales. 12 Suppose he firm uses sraigh-line depreciaion for ax purposes and depreciaes he blas furnace invesmen over a 10 year life o a zero esimaed salvage (noice he esimaed salvage for ax purposes is differen ha he rue expeced salvage value of he furnace) and pays 50% in corporae axes. Lasly suppose 11 I hank Bob Korajczyk for he numerical example. 12 in his conex, means Ahe change from year o i.e., Incremenal sales in year = Sales - Sales -1. In our example, if he firs year of sales using he new blas furnace is year 1, hen incremenal sales in year 1 would be $50 M. In every subsequen year, since sales are no changing, incremenal sales is zero. If he projec erminaes a year 10, hen incremenal sales in year 11 would be -$50 M. Be careful, in capial budgeing analyses, generally means Awih vs.
17 Projec cash flows, page 17 ha he firm will borrow half he invesmen funds $500 M via a en-year public bond issue on which hey mus pay annual ineres paymens of $80 M and mus pay he las annual ineres paymen and repay he full principal a he end of en years. Le s consruc our free cash flows. Do you hink he cash flows, as saed, are nominal or real? I s no clear by he above ex. We will assume all cash flows discussed above are nominal cash flows, hen afer we calculae he Free Cash Flow from Operaions in each year of he projec, we will revisi his issue. A ime zero, we have o pay for he blas furnace, -$1,000 M, a capial expendiure; we lose he afer-ax opporuniy cos of selling he old blas furnace, -$30 M(1-.50) = -$15 M, and if we assume he company mus have is incremenal ne working capial on hand a he beginning of he firs year, -.4($50 M) = -$20 M. If we assume he annual cash flows from he operaions of he blas furnace occur a he end of years 1 o 10, we have esimaed he Free Cash Flow from Operaions for =0 o be -$1035 M. Noice we omi he sunk cos of he feasibiliy sudy. See he Table 1 on he nex page. Oher poins o noice on Table 1:
18 Projec cash flows, page 18 Table 1. Blas furnace capial budgeing analysis, par I. (All amouns are in millions.) Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 10 Revenues Coss of Goods Sold Gross Profi Depreciaion Oher Op Exp Operaing Profi before Tax Tax Ne Operaing Profi afer Tax Add back Depreciaion Less CAPEX Less Chg. Ne Working Capial Salvage value afer ax Free Cash Flow from Operaions -1,
19 Projec cash flows, page The annual incremenal revenue is $50 M, he annual cos savings is $90 M, giving an incremenal gross profi of $140 M per year. 2. The annual depreciaion in years 1-5 is 100M, which is he annual depreciaion on he original $1,000M purhcase of he blas furnace: (1,000M - 0)/10 = 100 M. In years 6-10, he annual depreciaion is he depreciaion on he original blas furnace plus he addiional depreciaion on he replacemen pars purchased in year 5. The laer annual depreciaion is (200M - 0)/5 = 40 M per year. So he oal depreciaion in years 6-10 is 140 M per year. 3. Operaing Profi before Tax is Gross Profi minus Depreciaion minus Oher Operaing Expenses. Tax is.5 imes Operaing Profi before Tax. 4. Depreciaion is a ax deducible expense, so i is aken ou in he calculaion of Operaing Profi before Tax; in ha way he ax line incorporaes he depreciaion ax shield. Bu depreciaion is no a cash expense, so i mus be added back. 5. Noice ha he financing cash flows are omied. Where he $1,035 M comes from is no he issue. The fuure ineres and principal paymens on he deb, as well as he fuure paymens o equiyholders are no considered in he cash flows. The enire cos of financing he invesmen is incorporaed via he discoun rae, which is he opporuniy cos of capial. If his invesmen could earn a risk-adjused expeced rae of reurn (via he CAPM or APT, or oher model) of 10%, hen invesors will no wan o inves in his projec if he presen value of is fuure expeced cash flows (a 10%) is less han $1035. We assume ha he opporuniy cos of capial, r, is independen of financial srucure of he firm. 6. In year 5, we have o make $200 M in addiional capial expendiures, which are reaed he same way as he iniial capial expendiure of $1,000M. I is imporan o noe ha he $200 M is no an expense. If we could expense he replacemen pars we would, because we would reduce axable income by $200 M immediaely a ime 5 raher han recognize he expense as $40 M per year for
20 Projec cash flows, page 20 five years. From a cash flow perspecive, he $200 M is a cash ouflow a ime 5, bu is ax deducible via is depreciaion in years A he end of en years, we are assuming we will erminae he invesmen. A ha ime (you could assume he erminaion cash flows ake place in Year 11 if ha is more realisic) we can sell he blas furnace for $200 M, which will be fully axable (because he basis of he furnace and replacemen 13 pars will be zero), so he afer ax salvage proceeds is $200 M - (200M - 0)(.5) = $100 M. If he projec is erminaing, hen he incremenal revenue in year 11 will be -$50 M, which will allow us o reduce our ne working capial invesmen by.4(50 M) = 20M (cash in for he recovery of working capial). See Terminaion cash flows below. 8. Free Cash Flow from Operaions = FCF(Ops) = NOPLAT + Depreciaion - CAPEX - )NWC + Afer-ax Salvage Wha if he cash flow forecass are real raher han nominal? The fuure revenue and coss savings are forecas as annuiies in he las example whereas, if produc price and cos per uni are affeced by inflaion, we would expec hese amouns o increase over ime raher han be consan. Le s suppose ha our forecass of revenues and cos savings were, in fac, real dollars (in oday s purchasing power) and assume ha he annual inflaion rae will be 5% per year in every fuure year. Le s assume ha capial expendiure we have o make in five years was forecas in nominal dollars. Reforecasing cash flows from he blas furnace invesmen making use of his informaion, we wan o be consisen in our reamen of inflaion: ha is, we wan o discoun nominal cash flows a a nominal rae and/or discoun real cash flows a a real rae. We could conver all nominal fuure cash flows o real cash flows, we could conver all real fuure cash flows o nominal cash flows or we could separae ou he nominal 13 The salvage proceeds afer ax (as well as any asse sales) can be considered a negaive capial expendiure. I separaed his iem ou o show is effec on afer ax cash flow more clearly.
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Economics Honors Exam 2008 Soluions Quesion 5 (a) (2 poins) Oupu can be decomposed as Y = C + I + G. And we can solve for i by subsiuing in equaions given in he quesion, Y = C + I + G = c 0 + c Y D + I
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Complee he form in BLOCK LETTERS Provide deails on separae shees if required To Responden Address THE LAW SOCIETY OF THE AUSTRALIAN CAPITAL TERRITORY Personal Injury Claim ificaion pursuan o he Civil Law
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Enropy: From he Bolzmann equaion o he Maxwell Bolzmann disribuion A formula o relae enropy o probabiliy Ofen i is a lo more useful o hink abou enropy in erms of he probabiliy wih which differen saes are
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