The Journal of Financial and Quantitative Analysis, Vol. 13, No. 5. (Dec., 1978), pp

Transcription

1 Some New Capial Budgeing Theorems William Beranek The Journal of Financial and Quaniaive Analysis, Vol. 13, No. 5. (Dec., 1978), pp Sable URL: hp://links.jsor.org/sici?sici=22-19% %2913%3a5%3c89%3asncbt%3e2..co%3b2-e The Journal of Financial and Quaniaive Analysis is currenly published by Universiy of Washingon School of Business Adminisraion. Your use of he JSTOR archive indicaes your accepance of JSTOR's Terms and Condiions of Use, available a hp:// JSTOR's Terms and Condiions of Use provides, in par, ha unless you have obained prior permission, you may no download an enire issue of a journal or muliple copies of aricles, and you may use conen in he JSTOR archive only for your personal, non-commercial use. Please conac he publisher regarding any furher use of his work. Publisher conac informaion may be obained a hp:// Each copy of any par of a JSTOR ransmission mus conain he same copyrigh noice ha appears on he screen or prined page of such ransmission. The JSTOR Archive is a rused digial reposiory providing for long-erm preservaion and access o leading academic journals and scholarly lieraure from around he world. The Archive is suppored by libraries, scholarly socieies, publishers, and foundaions. I is an iniiaive of JSTOR, a no-for-profi organizaion wih a mission o help he scholarly communiy ake advanage of advances in echnology. For more informaion regarding JSTOR, please conac suppor@jsor.org. hp:// Sun Oc 21 9:33:3 27

2 JOURNAL OF FINANCIAL AND QUANTITATIVE ANALYSIS December 1978 SOME NEW CAPITAL BUDGETING THEOREMS W i l liam Beranek* I has been shown by Haley and Schall [4], Modigliani and Miller [7], Myers [81, Solomon [lo], and Vickers [I21 ha if (1) a firm's invesmens always yield cash flows ha are consan forever, and if (2) he firm main- ains, likewise ino perpeuiy, a consan deb/equiy raio in erms of mar- ke values, a consan per period cos of capial can be derived which involves as weighs he marke values of deb and equiy.' Since hese sufficien con- diions, which were se forh for posiive purposes, pose severe limiaions on he usefulness of hese resuls for normaive purposes, derivaions which are less resricive would be helpful for decision making. This paper invesigaes an alernaive procedure o he cos-of-capial, accep-rejec problem. Se forh are condiions sufficien o yield an accep- rejec procedure which may be applied o projecs of any duraion (single period, muli period, or infinie period), o expeced cash flow sreams ha are eiher level or uneven, o invesmens eiher lumpy or coninuous, o firms operaing eiher a heir invesmen margin or inramarginally, and o coss of equiy and deb ha may vary over ime. An imporan resul emerges: ha a ne-presen value decision rule in- volving a weighed average cos of capial (WACC) as a discoun rae is derived under condiions of shareholder wealh maximizaion. This procedure may be used o es for accep-rejec purposes any economically independen invesmen opporuniy. The derived WACC, which is no resriced o be consan over ime, conains in a sense book weighs, which will be referred o hereafer as C-values o disinguish hem from accouning book values. A C-value WACC in boh per- peuiy and single-period cases is derived in Beranek [2]. While Haley and Schall [41 have suggesed ha i is possible o derive, in a sense, a book value WACC for he general n-period case, his is he firs derivaion of i for finie, muli-period projecs. The paper is divided ino several secions. The firs ses forh he * The Universiy of Georgia. The auhor has benefied from he commexs of David Penico, Bruce Gouldey, and Richard Bernhard. o ow ever, Linke and Kim [6 I have derived similar resuls for finie, raher han infinie, lived invesmens wihou requiring consan expeced cash flows. Their approach has poenial operaional advanages. 89

3 assumpions, while he second derives he basic heorem for a firm ha is assumed o liquidae when is one, and only, invesmen opporuniy expires. To derive our cos of capial in he capial-budgeing sense, we mus firs assume ha he firm's invesmen generaes expeced cash flows exacly suf- ficien o saisfy he expeced claims of all securiy claimans, no more and no less. Afer he projec is acceped, he nex secion considers he period- by-period adjusmens ha mus be made, leading o he so-called abandonmen decision, an inegral par of he procedure. Following his, our cos of capi- al is shown o apply even when an invesmen's expeced cash flows are in excess of capial claims. In he following secion he resuls are exended o he firm ha is examining addiional projecs over ime, while he las par discusses addiional feaures of he procedure. Of course, our purpose is nor- maive raher han posiive. I. The Assumpions Assume ha a firm is o be formed solely o develop an n-period invesmen opporuniy and he firm is o be liquidaed a he end of period n. I will acquire resources a he end of period in he amoun of Bop financing B wih he fracion a of deb (which may be risky) bearinq he borrowinq rae r ( = 1,2,...,n), and he fracion (1 - a) of equiy. The firm is subjec o he corporae ax rae X and, regardless of he mehod of ax depreciaion em- ployed, is periodic ax shield, including any invesmen ax credi, is denoed 2 A negaive income ax liabiliy in any period is assumed o be recoverable from he ax auhoriies in he year he claim arise^.^ Nonaxable cash flows in year, such as salvage value and he release of ne working capi- al, are denoed by s ' Sockholders are assumed o be indifferen beween receiving dividends and capial gains while heir required rae of reurn per period, k, we sress, fully reflecs boh he operaing and financial risks of his proposed firm. A clear undersanding of his assumpion is crucial. I means ha wheher k L~hismeans is he ax shield plus he invesmen ax credi in period. For example, assuming sraigh line depreciaion, he ax shield is XB /n and, in he absence of an invesmen ax = XB /n for = 1, 2,...,n. ax carryforwards and carrybacks complicae he analysis considerably wihou changing he conclusions. 81

4 is prediced by he Securiy Marke Line [41, by Modigliani and Miller's Propo- siion I1 [71, or by some oher hypohesis, he full effec of he firm's in- vesmen and capial srucure is refleced in k ' This implies, for example, ha if he projec is wealh-enhancing and he firm's raio of he marke value of is deb o he marke value of is equiy should consequenly decline, pos-invesmen, hen k for = 2,3,...,n will no decline because k is pre sumed o reflec hese consequences. Again his assumpion, while sufficien, is no necessary. Even if we assume ha k is heoreically overesimaed, i.e., does no reflec he decreased financial risk caused by a wealh increasing pro- jec, neverheless as will be shown he derived accep-rejec rule will no accep a wealh-decreasing projec. Expeced operaing cash flow in period (i.e., he flow before axes and ineres bu afer all expendiures expeced o be required o generae some or all cash flows in period and hereafer, and assumed, solely for he sake of simpliciy, o be ax deducible in period ) is denoed by A (= 1, 2,...,n). If L and E denoe expeced ye-o-be defined C-values of deb and equiy a he end of period, respecively, hen Q, he expeced amoun available for repaymen o bondholders and shareholders afer hey receive heir required 4 reurns is Our definiion of he C-value of deb and equiy can now be derived. I can be shown ha if he firm repays (or acquires) deb in he amoun of aq and equiy in he amoun (1- a)q hen L and E can be expressed as r and 4 The required reurn o sk.areho1der.s in period, k E is inroduced -1' ino equaion (1) solely for he sake of deriving our heorem. In exending he heorem o he reained earnings case, his condiion is relaxed.

5 where Q =.5 Observe ha (2) and (3) provide explici accouning procedures for obaining boh L and E. We will always use (2) and (3) wih he equiva- len expressions ab subsiued for L and (1 - a)b for Eo. The index runs only o n-1 since a =n he firm dissolves implying L = E = as well as n n aqn - Ln-l and (1 - a) Qn = En-l. I can be shown, following a proof similar o one developed by Linke and Kim [61, ha if he firm repays capial o bondholders a he end of in he amoun aq while he sum (1 - a)q is repaid o equiy ineress, he firm's ' 6 deb o capial raio will be mainained a a hroughou he life of his firm. Bu because we will be defining he required rae of reurn for inernal pur- poses in he capial budgeing sense, i.e., he rae which makes he share- holders indifferen beween accepance or rejecion of he projec, hen we mus have Q = aq + (1 - a)qr where a negaive Q is inerpreed as requiring T = expeced amoun of deb repaid a end of period, R = expeced residual cash flow paid o equiy ineress a end of period in addiion o he sum k E -1' Firs, no? ha boh L and E can be expressed in erms of lagged values and repaymens. Thus, by definiion, and and hence Coninuing in his vein we have L-l -= L-2 - T-l' L = L - -2 T-l - T. L= Lo - C T where T =, while similarly for E we have T' T=o E - Eo - C RT, where R =. T=o Since aq and (1 - a)q are equal, by definiion, o T and R, respecively, equaions (2) and (3) follow. 6~ubsiuing L = ab and E = (1 - a) B ino (2) and (3), respecively, we have, by definiion, he raio of deb o capial a period, p '

6 new financing in he proporion aq of deb and (1) - a)q of equiy. This condiion saes, in effec, ha he firm's expeced cash flows mus equal he expeced claims of he firm's capial claimans--heir capial plus hei'r required or conracual reurn. Consequenly, while his condiion is, by definiion, necessary for deriving our accep-rejec condiion, i need no and, frequenly will no, hold when applying he decision rule o he esing of projecs. Obviously, projecs ha are jus exacly accepable, no more and no less, are less frequenly encounered han ohers. I 11. Proof of he Theorem The heorem we seek o esablish is saed as follows: =l,2,...,n-1, which implies p = a. I The relaionship beween C-value and accouning book value should be ex- plained. Leing d denoe accouning depreciaion during period, for he simples siuaion expeced accouning profi in, P is defined as ' Q - d + k E Hence he expeced book value of equiy a, BV is -1' r BV,-~ + P - Q - k E -1' example may be helpful. Suppose we ake To see hese quaniies in a sharper focus, a numerical dl = $2 Expeced accouning profi in period 1 is $1 - $2 + (.1)($1,) = $18 while BV1 is, because BV mus equal Eo for a new firm $1, + $18 - $1 = $98. However, he corresponding C-value a period 1 is Eo - (1-.2)$1 or $92, which is less han he expeced accouning book value by $6 ($98 - $92). L 1 is equal o $25-(.2)$1 or $23 and a is sill equal o.2 ($23/(23 + $92)). Of course, he realized, ex-pos, value of he random variable A in period 1 1 will very likely differ from is expeced value, A1, implying ha he real- ized afer-required-capial-coss cash flow will deviae from is expeced value, As will be shown laer, hese ypes of deviaions do no invalidae he Q,. decision procedure

7 If he firm is expeced o mainain a consan deb-equiy raio in erms of C-values and seeks o maximize he wealh of exising shareholders, he period cos of capial, B+, i can employ for accep-rejec purposes wih he ne presen value procedure is qiven by To prove he ne-presen value dechion rule coupled wih B as he discoun rae will require several seps. Firs, we mus assume ha he flucuaing sream of expeced cash flows A is exacly sufficien o discharge all of he firm's obligaions and o provide only he exac required rae of reurn o boh bondholders and shareholders, no more and no less. implies ha he expeced cash flow Q is jus sufficien o saisfy L Second, his n n-1 En-l. If so, hen Q mus be jus sufficien o saisfy (L - L ) + n-1 n-2 n-1 (En-* - En-1), and so on back o Q = (Lo - L1) + (Eo - El). Third, saring 1 wih he condiion Q = L + E we will express, by backward inducion, n n-1 n-1' he expeced flows An, An-l,...,A in erms of B and Bo. Finally, by leing 1 B~ = A (1- ) + s for = 1,2,...,n, his leads o he condiion and he sandard, break-even ne-presen value condiion, elling us ha all of he previous condiions imply he venure is jus barely worhwhile, he implicaion we sough o derive. We seek he firm's cos of capial in he capial budgeing sense, i.e., he rae of reurn on he firm's invesmen B such ha shareholders would be indifferen beween accepance and rejecion of he venure. If so, hen as assered above, a he end of period n he firm should have a cash flow Q n jus sufficien o saisfy L n-l + En-l, he remaining ineress of bondholders and shareholders. (Noe ha we are imposing his consrain because we are seeking o derive a condiional proposiion--he rae of reurn ha leaves shareholders indifferen beween acceping and rejecing he opporuniy.) Consequenly, Q can neiher exceed nor fall shor of he sum L + E n n-1 n-1' Therefore, recalling ha B = A(l - A) s, a he end of period n we mus have I, I

8 which can be rewrien as B n = Ln-l [l + rn(l - A)] + E n-1 (1 + kn), and, afer subsiuing (2) and (3) for L and E respecively, n-1 n-1' which implies, afer seing Bn = k (1 - a) + ar (1 - A), n n If we divide (7) by he quaniy (1 + B ) we have, on he lef side of (8), n :? presen value of he ne cash flow B discouned by Bn a he beginning of n period n (or a he end of n - 1): which cin be pu in he form We noe ha Q which is he n-1s erm in he sum C Q,, is given by n-1',=o Therefore he second erm on he lef side of (9) can be wrien as Again subsiuing (2) and (3) for L and E respecively, (9) can be re- n-2 n-2' wrien as

9 and hence, afer simplifying and muliplying hrough by 1/(1 + f3n-1), which is seen o have he same form as (9). The firs wo erms on he lef represen he presen value of he cash flows a n-1 discouned by Bn-l, and hose a n discouned by boh fin-l and En, respecively. The balance of he proof is achieved hrough inducion. Coninuing as above we hypohesize we can express, a he beginning of period, he presen value of he cash flows appearing a period, +l,...,n as Assume ha he form (11) holds for. To prove ha i holds for -1, we proceed as before and rewrie (11) as follows: which may-also be expressed as Afer furher simplificaion and division by (1 + B -1) and allowing boh y and E o equal, we have which has he same form as (9). Since he form (11) holds for -1, i holds in general, even for =2 in

10 which case (12), because Q =Or reduces o If we make he change of variable = y+l in equaion (13), we hus have a form of he sandard, exbook NPV minimum accepance crierion. To show ha a venure saisfying (14) will neiher increase nor decrease shareholder wealh, we se forh he presen value of all cash flows o shareholders, evaluaed a he risk-adjused discoun rae k as he lef side of r which when equaed o (1 - a)b implies ha shareholders are indifferen be- ween accepance and rejecion of he venure. Recall ha (14) emerges as he condiion if he expeced cash flows are jus sufficien o saisfy all capial claimans, no more and no less. If, however, he venure's flows are such ha when subsiued ino he lef side of (14), he magniude of he lef side exceeds B hen since bondholders receive only heir required reurn, shareor holders mus receive an expeced cash flow in excess of heir required flow, i.e., hey receive "exra" dividends, so o speak. If so, hen he lef side of (15) mus exceed (1- ")Bop he shareholder's oulay or he righ side of (15). In urn, his means ha shareholder wealh will be enhanced, raher han mainained, by he venure. The converse of he proposiion is likewise rue--a venure elevaing he value of shareholder equiy above (1 - a)b will likewise raise he lef side of (14) above B ' We conclude ha he venure will be accepable o shareholders if a form of he heavily advocaed exbook crierion.

11 Now ha he decision rule embodied in equaion (16) has been derived, we abandon he analyic expression used o capure he marke value of he firm's equiy, i.e., he lef side of equaion (15), since i is no necessary o compue he incremen in expeced equiy marke value of a venure in order o es is accepabiliy. Since f3 is he rae of discoun o employ in he NPV form given by (14), i follows ha an equivalen special-case decision rule involving he inernal rae of reurn i as given by where i is assumed o be unique, is i 2 B, provided ha B is consan over = 1, 2,...,n, he proof of which is available in any sandard finance ex- 8 book. We assered earlier ha even if he assumed value for k did no fully reflec he ex-pos invesmen decline in he firm's financial risk (as measured, say, by he raio of deb o he marke value of equiy), (16) was sill valid. This mus be rue since an ex-pos wealh-enhancing invesmen will reduce he raio of deb o he marke value of equiy, which we can ake as a measure of financial risk. This, in urn, we can hypohesize, will reduce k for = 2, 3, n. Bu a reducion in k will only make 6 smaller, no larger. There fore, a projec saisfying (16) wih an ex-ane, overesimaed, value of k will also saisfy (16) evaluaed wih he ex-pos value of k. Of course, some opions ha are marginally accepable on an ex-pos basis will, on an ex-ane basis, be rejeced. Neverheless, all inferior projecs will be rejeced Some Observaions Noe ha solely for he purpose of deriving he minimum accepance rule given by (14), we explicily assumed ha he series A was exacly sufficien o saisfy capial claimans, and ha Q wheher posiive or negaive, was ' enirely exhaused in proporional disribuions, again eiher posive or negaive, among bondholders and shareholders. We have jus shown ha for purposes of implemening he minimum accepance rule (14), he above resricion on he 8N'oe ha while negaive cash flows can provide difficulies in obaining real, posiive roos of equaion (17), he presence of such flows does no aler he validiy of (16), our major resul.

12 series A can be relaxed, hus yielding he general accep-rejec rule (16), i.e., (:6) is valid even if he series A exceeds he minimum capial require mens. Afer an opion is adoped, however, i is wih virual cerainy, ha a leas one of wo consequences will follow: will deviae from is expeced value; (2) fi value which was held a =O. (1) he realized cash flow in period will be revised from is expeced A he realized ime =l,he adoped opion mus be reevaluaed in erms of expecaions and opporuniies prevailing a ha ime. Regarding opporuniies, if he firm has a bes offer of B' dollars for 1 all of is asses, hen BV1 is he opporuniy cos of holding and coninuing o operae is exising asses. The opion of coninuing o operae he exis- ing asses may hen be evaluaed by equaion (16), wih revised expeced cash flows, revised a's, a new possible level of deb, and wih BI1 serving as he. quaniy B in (16). This procedure describes, of course, wha oher wriers have called he "abandonmen decision," a decision which can be made periodically. Financial managemen does no cease wih he mere adopion of a projec. In sum, wha we have derived is an accep-rejec procedure for period, a procedure which depends upon relevan forecass bu which is no rendered in- valid by whaever may befall he firm in periods 1, 2,...,n. Given he ou- comes and he alered sae of he world in a subsequen period, he invesmen may be reevaluaed wih equaion (16), using appropriaely revised values for A and a. Bu we have no derived a procedure which guaranees he success of a given decision. The above implies ha, afer adoping an opion, we do he bes we can o live wih is consequences, wheher specacular success or ragic failure. Should disaser srike, however, his would no imply ha condiion (16) is an invalid crierion or ha, if faced wih he same risky opporuniy again, he firm would rejec he opion. I is equally clear ha i is no necessary for he firm o hold, or rnainain, a a is forecased period- value hroughou he life of he invesmen in order o validae eiher he decision procedure (16) or he decision. obviously difficul for he firm o conrol r and k ' I is Moreover, he firm may even wan o change, for raional ex-pos reasons, he value of a from he ex- 9 peced value held a period. 'The reader is cauioned agains inferring ha, since i is possible for L and E o go o zero, his invalidaes he procedure because oal asses would be zero. In he firs place, even if his even should occur, i does no 819

13 IV. Exension o he Ongoing Firm Condiion (16) may be employed wheher he new invesmen belongs in he same risk class as he firm's exising invesmens or no. In eiher case, we assume ha each invesmen opion is economically independen of all oher 1 opions and of exising resources and is financed in he proporions a of deb wih appropriae ineres rae r and (1-a) of equiy wih a required rae of reurn k which fully reflecs boh he operaing and financial risk condiions ' of he opion. Each opion can be viewed as a "firm" uno iself, and if he v6lue addiiviy principle is sufficienly robus, he value of shareholder wealh under hese condiions becomes addiive; hence, oal value of share- holder equiy becomes he sum of he equiy values of each individual "firm. "'' 1.2 Consequenly, condiion (16) will lead o maximizing expeced shareholder wealh. imply ha book asses are zero since here is no correspondence beween C- values and accouning book values. Secondly, and wha is mos imporan, he periodic abandonmen decision will preclude his even from occurring unless of course, we have he special case of firm erminaion--eiher liquidaion or in- solvency. loof course, i is no necessary in a pracical sense ha he projec iself be lierally financed in hese exac proporions. The firm will raise he proporion a of deb over some budgeing period, say, hree years, and he sum represening deb will be allocaed o each projec in he proporion a of is iniial cos B. ''perfec markes along wih he moive of invesor wealh maximizaion are sufficien o yield his principle. See Schall [91. 12T'he above analysis also applies o financing wih reained earnings. Le us assume, in he simples case, ha dividends o shareholders are nonaxable. Suppose shareholders finance he equiy in he above new "firms," i.e., he new projecs, by reinvesing heir cash dividends immediaely upon receip. Bu his, of course, is equivalen o he firm's reaining earnings. Consequenly, he shareholder required reurn ha is explicily allowed for in equaion (I), is no resricive and R applies even if equiy is financed hrough ke-l reained earnings. The assumpion of nonaxable dividends is of course no necessary o obain + B. AS in oher derived WACC procedures, wha is necessary is ha he cos of reained earnings is equal o k Theoreically and empirically, his is an ' unseled quesion. I is well known, for example, ha he exisence of a preferenial capial gains ax can imply a reained earnings cos which is less han k. Bu he magniude of his difference depends on he disribuion of axpayer-shareholders by marginal ax brackes and oher facors. In addiion, he increasingly "heads-i-win-ails-you-lose" characer of he curren U.S. personal capial gains ax reduces he apparen capial gains ax advanage over ordinary income. Finally, wha is more imporan is ha Black and Scholes [31, in one of he mos peneraing empirical sudies ye performed on his subjec, have drawn he conclusion "...ha a dollar of dividends has he same value as a dollar of capial gains in he marke. There are virually no differenial reurns earned by invesors who buy high dividend yielding securiies or low dividend yielding securiies once we conrol for he crucial risk variable."

14 V. Observaions on he P rocee 1. Any economically independen opporuniy may be esed for accep-rejec purposes by employing eiher equaion (16) or (17). An economically de- penden projec can be sudied by comparing he ne presen values "wih" and "wihou" he projec, respecively. 2. The procedure applies o projecs of any duraion and wih flucuaing ex- peced cash flows. Of he references cied, only Linke and Kim [61 have derived a WACC which does no require ha he invesmen be a perpeuiy wih consan expeced flows. 3. The procedure permis 6 o vary over ime. All oher mehods for obaining a WACC require ha i be consan over ime. This implies ha if a firm expecs r or k, or boh, o change over ime, his informaion canno be used in hese alernaive procedures. 4. The procedure applies wheher invesmens are coninuous or lumpy, marginal, or inra-marginal. Noe ha a projec is jus worh underaking, i.e. ha is a he margin, would have an equiy marke value exacly equal o he equiy oulay required, by definiion. In his special case, derivaion of he WACC by our procedure would lead o ex-pos equiy marke-value weighs because, under hese condiions, marke and C-value weighs are idenical. This fac, which has some heoreical significance, probably has lile operaional conen. 5. The responsibiliy of financial managemen coninues beyond he accep deci- sion. Circumsances change, leading he firm o revise is forecass of r k, a and of he projec's cash flows. These, in urn, lead o revalu- ' aions of he venure in subsequen periods. For his purpose all on-going, previously acceped projecs can be pooled ino one, and a single accep- rejec analysis performed for he aggregae of he firm's exising resources. To be more explici, here is a a given ex-pos period T an aggregae level of deb LT, an aggregae value B' obainable for he firm's oal resources, and hence an implied level of sockholder invesmen, i.e., B' - L = E. T T T 6. The procedure draws aenion o he fac ha an operaional WACC mus be a forecas, since i depends upon elemens ha are forecass--r r k, and a. However, even if he forecased r k and a are no realized ex-pos, ' he procedure is sill valid as a condiional saemen for leading o he + Oher derived WACC procedures do no aemp o deal wih reained earnings in a world of personal income axes. Hence, if hey admi of reained earnings, hey mus assume ha he cos of such earnings is equal o he cos of equiy capial.

15 choice of projecs ha will enhance expeced shareholder wealh. To he exen hey are o have normaive significance, marke value WACC procedures require forecass of relevan parameers as well (See [41, [71, [81, [lo], [Ill and also Linke and Kim [61.) Thus he use of forecased cos-of- capial parameers is no really new, bu direcing aenion o his fea- ure of hem is imporan o inerpre properly heir normaive use. 7. Equaion (4) has no necessary relevance for deermining an opimal capial srucure. ime. This holds even for he special case where 6 is consan over 8. The procedure is less resricive han ohers in ha i applies wheher he opion's expeced cash flows are level or uneven, wheher he opion's life is finie or infinie, and wheher or no he WACC is expeced o be consan over ime. 9. The individual capial coss, r (1- A) and k are risk-adjused raes ' reflecing operaing risks of he proposed venure as well as he financial risks inheren in he proposed capial srucure, however he risks may be perceived by invesors. However, even if k is overesimaed, he rule sill will no accep opions ha reduce shareholder wealh. 1. The expeced cash flow appropriae o R is he sum B = A (1-1) + $ + s, where A is he expeced operaing cash flow (including expendiures required o produce some or all fuure cash flows), 4 he income ax shield provided by he opporuniy, and s a nonaxable cash flow which, a period n, is normally he expeced salvage value plus he release of ne working capial. This, we noe, corresponds o leading exbook definiions, hus faciliaing 13 he adopion of he procedure for pedagogical purposes. 11. One objecive of his paper has been o derive a procedure ha is boh pracical and ye consisen wih he empirically confirmed proposiions of descripive financial economics. In his connecion a sufficien, ye ap- ~arenly quie simple, accep-rejec decision procedure is given by replac- ing he equaliy in equaion (15) wih he weak inequaliy 2, a decision rule which is equivalen o equaion (16). While here is no difference be- ween his modified version of (15) and equaion (16) on logical grounds, here is a marked difference in he ease of undersanding by business execuives. Eiher because of prior exbook raining or oher facors, execuives end o undersand more readily, and o be more comforable wih and 13See, e.g., [51, [Ill and [131.

16 far more recepive o, equaion (16) han he modified (15). If so, hen anexpression like (16) can be useful o a large segmen of American in- dusry. REFERENCES [l] Beranek, W. "The Cos of Capial, Capial Budgeing, and Shareholder Wealh Maximizaion." Journal of Financial and Quaniaive Analysis (March 1975). [21. "The Weighed Average Cos of Capial and Shareholder Wealh Maximizaion." Journal of Financial and Quaniaive Analysis (March 1977). [3] Black, F., and M. Scholes. "Dividend Yields and Common Sock Reurns: A New Mehodology." Working Paper No , Sloan School of Managemen, Massachuses Insiue of Technology (Sepember 197). [4] Haley, C., and L. Schall. The Theory of Financial Decisions, Chaper 13, New York, NY: McGraw-Hill Book Co. (1973). [5] Johnson, R. W. Financial Managemen, 4h ed. Boscm, Mass. : ~llyn& Bacon, Inc. (1971), pp [61 Linke, C. M., and M. K. Kim. "More on he Weighed Average Cos of Capi- al: A Commen and Analysis." Journal of Financial an? Quaniaive Ana- lysis (December 1974). [7] Modigliani, F., and M. H. Miller. "Corporae Income Taxes and he Cos of Capial: A Correcion. " The American Economic Review, Vol. 53 (June 1963), pp [81 Myers, S. C. "Ineracions of Corporae Financing and Invesmen Budge- ing." Journal of Finance, Vol. 29, No. 1 (March 19741, pp [9] Schall, L. D. "Asse Valuaion, Firm Invesmen and Firm Diversificaion." Journal of Business, Vol. 46, No. 1 (January 1972), pp [lo] Solomon, E. The Theory of Financial Managemen. Universiy Press (1963). New York, N.Y.: Colurnbi a [Ill Van Horne, J. C. Financial Managemen and Policy, 3rd ed. Englewood Cliffs, N.J.: Prenice-Hall, Inc. (19741, pp Vickers, D. "The Cos of Capial and he Srucure of he Firm." The Journal of Finance, Vol. 25, No. 1 (March 197). [13] Weson, J. F., and E. Brigham. Managerial Finance, 4h ed. b ins dale, Illinois: The Dryden Press (1972), pp