Comparative Analysis of the Traditional Models for Capital Budgeting

Transcription

1 Internatonal Journal of Marketng Studes; Vol. 8, No. 6; 26 ISSN 98-79X E-ISSN Publshed by Canadan Center of Scence and Educaton Comparatve Analyss of the Tradtonal Models for Captal Budgetng Unversty of Massachusetts Amherst, USA M. J. Alhabeeb Correspondence: M. J. Alhabeeb, Unversty of Massachusetts Amherst, USA. E-mal: Receved: October 2, 26 Accepted: October 24, 26 Onlne Publshed: November, 26 do:.39/jms.v8n6p6 URL: Abstract Fnancal decson makng for nvestng frms requres metrc tools for comparson and analyss. The manageral choce among many nvestment alternatves wth complex possbltes has made t easer to rely on the now more advanced computer programs of smulaton that consders the uncertanty and stochastc changes n the cash flow and rsk levels. The major drawback here, especally n the academc world, s the ncreasng dependency on software and departng from the underlyng mathematcal reasonng that s most practcally fathomed by the manual problem solvng. Ths paper goes back to the tradton on analyzng and comparng the major models of captal budgetng. Keywords: captal budgetng, project evaluaton, net present value, nternal rate of return, proftablty ndex, payback method, crossover rate, rankng reversal. Introducton Captal budgetng focuses on long-term and strategc plans to sustan a stable and more productve future for the frm. In the core of ths long-term thnkng s the ablty and capacty to make decsons to replace, mprove, and expand the frm s major exstng resource base, as compared to only seekng the effcency of the use of that resource base. The emphass would prmarly be placed on assessng the frm s nvestment opportuntes n order to choose the most vable alternatve among them. Gven that alternatve nvestment opportuntes dffer n many aspects such as the level of rsk assocated wth each one and ther capactes to yeld future returns, the crtera for choce would be for the upper management to employ objectve, quanttatve, and credble methods to evaluate the proposed alternatves and select the best, especally n terms of hgher proftablty and less rsk. Over the years, many methods and technques have been developed, tested, and modfed for the best ways to evaluate the worth of nvestment projects. Most of the lterature today, especally n the academc journals, seems to skp over the foundaton of these methods and go drectly to the computerzed applcatons of them. It s analogous to usng the fnancal calculators before knowng the mathematcal reasonng of the operatons performed by the embedded software. It s essental to connect between the theory and applcatons, not only to make practcal sense of the theoretcal deas by renderng them useful n real lfe, but also to explore the ways to modfy, adjust, and adapt the theory to dfferent applcatons and a dversty of condtons and crcumstances. The major objectve of ths paper s to dscuss the approach and techncalty of the decson-makng process n evaluatng nvestment projects. The method would be to dfferentate among the actual and most tradtonal ways of captal budgetng followed n the busness world by exposng ther mathematcal analyses as they are ted to real lfe scenaros. 2. Dscusson 2. The Fundamental Vew to Captal Budgetng Captal expendtures s an outlay of funds whch the frm would rely on to generate a stream of returns enough to cover and exceed the ntal nvestment spendng. Captal budgetng, therefore, would be the process to revew, assess, and select the busness projects that promse to be the most rewardng n the medum and long runs. In other words, t s a long-term plannng and evaluatng captal allocatons whch are expected to generate cash nflows over a future perod of tme. Fgure llustrates the major elements of the process of captal budgetng on a tmelne. It shows 6

2 the typcal dual cash flow scenaro, where the frst of these flows s the cash outflow, whch conssts manly of the ntal captal fund allocated for an nvestment project n the current tme, as well as the captal expendtures made throughout the lfe of assets n ther productve lfe. The second flow s the cash nflow whch ncludes the future annual returns of the project durng ts fve years. Whle the cash outflow s normally measured n ts current value, the cash nflows have to be brought from ther maturty tme back to the current tme. They are dscounted at the frm s cost of captal rate and added up to form the present value of all returns whch has to be ether equal or larger than the cash outflow. Fgure. Tmelne of the cash flow for captal budgetng Typcal examples of captal outlay for the frm s nvestment projects are funds to fnance the purchase of land, buldngs, equpment and busness expanson wth what s requred to enhance the workng captal such as nventores and accounts recevable as well as funds to fnance research and development and pay for promoton and advertsement. Generally, captal budgetng s often assocated wth the followng most common nvestment projects: - Expanson: Includes nvestment projects to move nto the phase of developng and producng ether a new product or addng a new lne of product, or venturng nto a new market. It also ncludes the extenson of servce outlets and the dstrbuton and storage facltes. - Replacement: Includes projects to replace worn-out and damaged machnes and equpment as well as renewng structures and technology for more effcent producton and servces. - Cost Reducton: Includes all the projects amng at reducng the cost of producton through lower labor cost, raw materal, energy, as well as employng hgher technology that ncreases producton and ultmately lowers costs. Also, movng producton to less expensve locatons and spendng on tranng programs could be done to eventually lower the total cost of producton. - Conformng: Includes projects whch comply wth federal or state regulatons and standards on ssues such as health, safety, polluton, reservaton, and alke. 2.2 The Basc Model of Captal Budgetng The underlyng theoretcal framework for captal budgetng s based on the economc equ-margnal prncple. It states that a frm would pursue and contnue to engage n an actvty untl the margnal cost equals ts margnal beneft. As for the frm s decson on nvestment projects, ths prncple s appled n a way that captal would contnue to be allocated for nvestment projects to the pont where the margnal return on nvestment, as represented by the ncremental cash flows, would equal the margnal cost, as represented by the added expendtures of new nvestment captal. Applyng ths prncple would assure the frm s maxmum value. Fgure 2 shows an example of Frm X that s decdng on the worthness of eght proposed nvestment projects, I through VIII, whch are requrng a total of $2 mllon, whch s dstrbuted among dfferent captal funds yeldng dfferent rates of returns: 7

3 Project I: Project II: Project III: Project IV: Project V: Project VI: Project VII: Project VIII: 3 mllon dollars, wth % return. 2 mllon dollars, wth 3% return. 3 mllon dollars, wth % return. 4 mllon dollars, wth 9% return. 2 mllon dollars, wth 8% return. mllon dollars, wth 6% return. 3 mllon dollars, wth % return. 3 mllon dollars, wth 4% return. Total Captal Demanded: 2 mllon dollars. Fgure 2. Competton of several nvestment alternatves by ther rates of return Curve DC s the frm s demand for captal, and curve MCC s the frm s margnal cost of captal. The ntersecton between the two curves at pont A would determne that at maxmum, the frm can only allocate captals for the frst fve projects, I through V, at a total of 4 mllon dollars. The frm s ntal cost of captal rate s 6% whch would contnue to rse after allocatng the frst 3 mllon. So, the frst project yelds a rate of % but t costs 6%; the second project yelds 3% and t costs about 6¼%; the thrd project costs 6½% but t returns %; the fourth project costs 7/3 % and t returns 9%; and the ffth costs 8% and barely returns the same rate back. All the remanng Projects, VI, VII, and VIII, would be rejected snce they cost more than the frm s cost of captal and all of ther returns are below MCC. Project VI returns 6% but t costs ½%, Project VII returns % but t costs 2½%; and Project VIII returns 4% but t costs %. The optmal captal allocaton for the frm s 4 mllon. 2.3 Selecton Process and Project Evaluaton Captal budgetng nvolves a standard, logcal and consstent decson-makng process that may consst of several steps:. Explorng a pool of proposed nvestment projects and generatng a lst of most qualfed proposals to form the alternatve projects under consderaton. By focusng on the ntally strong and promsng projects, ths step would also be a screenng procedure to keep all of the clearly unfeasble or unworthy proposals out so that they won t go further n the process. 2. Estmatng the project cash flow whch s a stream of returns that would occur n a future tme. Ths estmaton should, therefore, be consdered wth the approprate level of uncertanty, rsk, and basedness. A major basedness s the natural subjectve tendency to be over-optmstc whch may end up underestmatng the costs and overestmatng the benefts, especally f there s a certan desre to adopt a specfc project. It s essental to rely on unbased professonals who use objectve measures to mnmze any over or under estmaton. Ths step usually emphaszes three mportant crtera: 8

4 a. Cash flow measurement should be done on an ncremental bass. Ths s to say that a project cash flow s takng a margnal sense as the dfference between the frm s cash flow before and after the constructon of that project. b. Cash flow estmaton should be consdered on after-tax bass usng the frm s margnal tax rate and ncludng the effect of deprecaton and all other non-cash expenses whch would be consdered for ncome tax purposes. c. Cash flow estmaton should nclude all of the ndrect effects of the project throughout ts lfetme such as the possble nterference and overlap wth other products, servces, or functons of the frm. 3. Determnng the frm s cost of captal whch would serve as the dscount rate for convertng the value of cash flow from the future to the present tme. It s equvalent to the requred rate of return by the frm s nvestors. 4. Evaluatng the alternatve nvestment projects n order to choose and accept the best alternatve project that would yeld the most value for the frm. The central crteron that has been establshed to determne a measure of desrablty and preference for a specfc alternatve project s the comparson of the present value of the expected cash nflows wth the ntal cash outflow. The project that wns the allocaton of captal has to have the present value of ts expected returns larger than the ntal captal outlay. There are two groups of methods to evaluate the worthness and desrablty of any nvestment project under consderaton. 2.4 Methods of Evaluaton for Proposed Investment Projects As decson-makng tools for the frm s captal budgetng, there are two groups of methods of evaluaton. The frst group, whch s the most common, s called the value-adjusted method for ts utlzaton of the tme value of money n establshng relable crtera of project worthness. Ths group ncludes three models: the net present value (NPV), the nternal rate of return (IRR), and the proftablty ndex (PI). The second group can be called the value-unadjusted methods for not usng any tme value of money adjustment. Ths group s represented by the payback model Net Present Value (NPV) Model The net present value of an nvestment project s the present value of all the future returns or cash nflows mnus the ntal captal nvested n the project. The basc premse s that the stream of future cash nflows must be dscounted back to the current tme usng the frm s cost of captal as the dscount rate. Ths rate s bascally determned by the frm based on ts assessment of the rsk nvolved n each undertaken nvestment project. Hgh rsk projects are assgned hgher dscount rate whle the low rsk projects are assgned low dscount rate. Net present value (NPV) s probably the most common technque used to assess how worthy a project s and whether t would be accepted for fundng or not. If the present value of all future returns (the cash nflows) s larger than the ntal cost of the project (the cash outflows), the net present value would be postve and the project would be deemed acceptable. Otherwse, f the present value of the cash nflows s smaller than the ntal captal outlay or the cash outflows, the net present value would be negatve and the project cannot be accepted. Let s recall that the current or dscounted value (CV) of any future return (FV) can be obtaned by: CV FV = ( r) n + where r s the nterest rate used for dscountng or brngng the value of return from future back to the present and n s the number of terms such as years. If we refer to an annual return or cash nflow of a project by CF, and to the project cash outflow by I, then the net present value (NPV) would be the dfference between the dscounted stream of both flows throughout the lfe of the project (t): t t CF I n n ( r) + (+ r) NPV = If the project takes only the ntal captal outlay or the startng nvestment fund only, then that ntal amount would be n ts current value already (I ), and does not need to be dscounted. t CF NPV = I n (+ r) 9

5 The crtera for project acceptablty s for the net present value to be non-negatve: NPV Let s suppose that a proposal to expand a fast food restaurant calls for the nvestment of an ntal captal of $42, and promses to delver a return of at least $4, per year durng the next fve years. Would the franchse company approve such an expanson project, gven that ts cost of captal s ½%? t CF NPV = I n (+ r) CF CF CF CF I (+ r) (+ r) (+ r) (+ r) = = 4, 4, 4, 4, 4, , ( +.) ( +.) ( +.) ( +.) ( +.) = 2,6. +,26.3 +, , , , =, , = 9,98.27 Ths expanson project would be accepted snce the net present value turned out to be postve. Fgure 3. Fve-year-return nvestment proposal for fast food franchse Let s consder another example where the development commttee n a constructon company s studyng two nvestment proposals whose cash nflows for the next four years are projected n the table below. Both projects requre a captal allocaton of $2, gven that the cost of captal for the frst project s 8% and for the second s 7½%. Whch of the two proposals would get an approval? Year Cash Inflows r = 8% 3, 4,, 2, Project I Cash Outflows Cash Inflows r = 7.% 2, 4, 4, 9,, Project II Cash Outflow 2, 2

6 Project I: Project II: 4 CF NPV = I n (+ r) = 3, 4,, 2, , ( +.8) ( +.8) ( +.8) ( +.8) = 32, , , ,23.8-2, = 94,96-2, = -,44.26 NPV = 4, 4, 9,, , ( +.7) ( +.7) ( +.7) ( +.7) = 37, , , , , = 223,73.9-2, = 23,73.9 Project I has a negatve NPV and Project II has a postve NPV. The commttee would accept the second and reject the frst project. Fgure 4. Two alternatve nvestment for constructon projects The cash nflow n the net present value formula could be replaced by the frm s proft for any perod can be adjusted for deprecaton and taxes: Snce π = TR - TC ( π ), and t [TR TC ]( T) + D NPV = I n (+ r) where TR and TC are the frm s total revenue and total cost for the th perod; T s the frm s margnal tax rate; and D s the frm s captal deprecaton; and I s the ntal nvestment captal allocated for the project. The followng table shows the estmated projectons for the gross proft based on the total cost, total revenue, and deprecaton allowances of a proposed project durng the frst fve years. How would a fundng decson be made on acceptng or rejectng the request for an ntal captal of $6,, gven that the cost of captal s 8¼% and the margnal ncome tax s 32%? 2

7 Year TR TC (-T) = D π (-t)+d π -.32 (4x+6) (3-2) , 66, 62, 62, 668, 46, 47, 42, 4, 48, 4, 8, 2, 22, 2, ,4 3, 33, 34, 3, 24,6 7,3 72,4 83,7 2, NPV = 24, 6 7, 3 72, 4 83, 7 2, ( +.82) ( +.82) ( +.82) ( +.82) ( +.82) =, , , , ,9.9-6, = 66, , = 6, The proposal would be approved for yeldng a non-negatve NPV. Fgure. Estmated projectons for the gross proft wth deprecaton allowances of a proposed project durng the frst fve years Internal Rate of Return (IRR) Model Another method used to determne the acceptablty of a proposed nvestment s desgned to compare the nternal rate of return wth the frm s cost of captal. The central crteron s that n order for the project to be accepted, t must yeld an nternal rate of return at least equal or larger than the frm s cost of captal. IRR r The nternal rate of return s sometmes called the proft rate or the margnal effcency of nvestment. It s defned as the rate that equates between the present value of cash nflows and the cash outflows. In the net present value formula, such a rate that makes the two cash flows equal must make the net present value (NPV) equal to zero. Ths would mean that the project s not capable of delverng an earnng rate hgher than the cost of captal. Usng the net present value (NPV) formula, we can now replace the frm s cost of captal (r) wth the nternal rate of return (IRR) and set the net present value to zero. CF n NPV = I n = (+ IRR) 22

8 To fnd the rght nternal rate of return that makes the net present value to be zero, we have to solve the equaton above for IRR. Snce a mathematcal soluton s not easy, IRR can be found by many ways such as usng the table values, tral and error, nterpolaton, and other ways. Computers and sophstcated busness calculators can fnd IRR easly. However, a prelmnary ballpark estmaton could be made, and an equaton was developed to get at least a startng pont n such an estmaton of the IRR. Once we get that estmate, we can keep teratng back and forth untl we get the exact rate that makes the value of NPV zero. n CF I IRR = CF where CF s cash nflow, and s the number of any year of the perod n: =, 2, 3,, n, and I s the ntal nvestment. Suppose that a frm s studyng an nvestment proposal that s askng for $, as ntal captal. The projectons for cash nflows durng the fve years are shown n the table below: 2 3 Cash Inflows CF CF ( x 2) ,6 4,2, 6,3 7, 27, CF 3,6 8,4 6, 2,2 37, 9,2 CF IRR IRR CF I CF 27,, 9,2 IRR 3.3% But, ths s only a rough estmate. However, we can reach to the exact rate wth some tral and error attempts, guded by the calculatons of the net present value (NPV) untl t reaches zero. That would be when the present value of all cash nflows are exactly equal the ntal nvestment, n ths case $,. The frst step we take here s to calculate the present value of cash nflows at the dscount rate of 3.3% to see how close t would make the present value to the ntal nvestment of $,. PV = 3,6 4,2, 6,3 7, ( +.33) ( +.33) ( +.33) ( +.33) ( +.33) = 3,77 + 3, , , ,7 = 8,7 So, a rate of 3.3 produces a present value of the cash nflows larger than the ntal nvestment of $,. Snce the rate of dscount has a reverse relatonshp wth the present value, we have to ncrease the rate n the next try to reduce the present value hopng to let t reach $,. 23

9 At a rate of 8%, the present value of cash nflows would be: PV = 3,6 4,2, 6,3 7, ( +.8) ( +.8) ( +.8) ( +.8) ( +.8) = 3, + 3,6 + 3, , ,278 =,942 Now, we are gettng much closer to the $,. We need to try to rase the rate a few more tmes to get the present value to go down to exactly $,. Recall that we can also use the PVIF r,n table value (also comes n another notaton: v n ) to ease up the tedous calculatons wth multple tres. Any table book would show the dscount factor of a dollar for many combnatons of r and n. n PVIF = v = n (+ r) To get the dscounted cash nflow n the thrd year above, we can ether dvde the, by (+.8) 3 or get the dscount factor from the table by lookng up across r = 8% and n = 3, and get the value.686 for the dscount factor and multply t by,. PV = FV[PVIF r,n ] =, [PVIF.8,3 ] =, [.686] = 3,347 Other few tres to get the exact rate revealed that: - at 2%, PV =, - and at exactly 2.4%, PV =,, and that s the nternal rate of return (IRR) that brngs about the equalty between the present value of cash nflows and the ntal nvestment and, therefore, makes the net present value equal to zero. 3,6 4,2, 6,3 7, NPV = , ( +.24) ( +.24) ( +.24) ( +.24) ( +.24) NPV = [2,99 + 2, , + 2, ,964] -, NPV =, -, = Fgure 6. A -year-return project wth a $, captal Comparng NPV to IRR for the Mutually Exclusve Projects The crteron for acceptng or rejectng an nvestment project can ether be based on the hghest net present value (NPV) or the hghest nternal rate of return (IRR). It would make no dfference to the frm as whch of these two measures s followed, smply because they reflect each other consstently. Havng a postve value for the net present value means havng an nternal rate of return that exceeds the frm s cost of captal, and havng a 24

10 negatve value of the net present value refers to havng an nternal rate of return lower than the frm s cost of captal: If IRR > MCC NPV > IRR < MCC NPV < Therefore, ether measure would be fne f followed, but that s especally true f the frm s assessng only a sngle ndependent project. But f the frm wants to assess two or more projects whch are mutually exclusve, then the measures of NPV and IRR may not mean the same thng! Mutually exclusve projects are those projects whch compete to earn the only one decson of approval. In other words, the frm can only choose one project among the alternatves. Year Project I 2, -2, 2, 2, 3, Project II 2, 87, 87, 87, 87, 87, Intal Captal Cash Inflows NPV 3,63 8,973 Dscount Rate IRR 2.2% 22.% 9½% Let s calculate both the net present value (NPV) and the nternal rate of return (IRR) for the two projects whose -year cash nflows are shown n the table, gven that both are competng to get the $2, ntal captal that s to be nvested at least at the frm s 9½% cost of captal. n CF NPCV = I n (+ r) 2, 2, 2, 3, NPVI = , ( +.9) ( +.9) ( +.9) ( +.9) ( +.9) NPV I = [-22, , , ,33] - 2, NPVI = 3,63 IRR I = 2.2% (obtaned usng a calculator). 87, 87, 87, 87, 87, NPVII = , ( +.9) ( +.9) ( +.9) ( +.9) ( +.9) NPV II = [79, , ,64 + 6,862 +,82] = -2, NPVII = 8,973 IRR II = 22.% (obtaned usng a calculator). 2

11 Fgure 7. Mutually exclusve nvestment projects The calculaton shows that the net present value and the nternal rate of return are not consstent across the two projects. Whle Project I have a hgher net present value (NPV I = 3,63 compared to NPV II = 8,973), Project II have a hgher nternal rate of return (IRR II compared to IRR I = 2.2). Therefore, the frm has to choose whch measure would be better to follow and whch one to gnore. Theoretcally, t would be better for the frm to decde acceptablty based on the hgher net present value than the hgher nternal rate of return. One of the theoretcal justfcatons for that s the assumpton that the earned cash nflows are to be renvested at the usually reasonable frm s cost of captal rate, and there would be no guarantees on the renvestment of the cash nflows earned by the other project at ts hgher rate of return. However, practcally most fnancal managers n the busness market tend to favor decsons based on the hgher nternal rate of return. One nterpretaton for such a tendency s the common relance on relatve change than on absolute change whch makes rates more preferable than actual dollar amounts as t s n the case of the net present value amount. The relatve measures can stll reman relable for comparson, especally when the frm faces many nvestment proposals whch cannot afford to fund except the most proftable, due to some budgetary constrants. Let s consder a frm recevng sx nvestment project proposals requrng dfferent captals and promsng dfferent net present values as shown n the followng table. Suppose that the frm can only allocate a maxmum of $8, and one of the proposals s askng for an ntal captal of $8, whch s the total nvestng capacty for the frm. The rest of the proposals are askng for dfferent fundng, rangng from $, to $4,. In ths case, t would be clear that t s better not to look at the absolute amounts of the net present value but to fnd the yeld or the net present value per dollar, obtaned by dvdng the net present value by the amount nvested or the ntal captal allocated (NPV/I ). Projects I NPV NPV/I I. 8, 2,6, 3.2% II. 29, 72, 2.% III. 2, 8, 3.4% IV. 3, 77, 2.2% V. 4,,44, 3.6% VI., 6, 4.% Frm s Total Fundng Capacty: $8, 3.62 The frm can nvest n Project I only gvng all t has and gettng $3.2 per dollar nvested, but a combnaton of more than one project, not only reduces the rsk by dversfcaton but also ncreases the return. So the avalable captal of $8, can be shared by Projects III, V, and VI generatng a total of $2,89, of a net present value (8, +,44, + 6,) whch would be translated nto a 3.62% earnng per dollar nvested 26

12 2,89,. It s hgher than the 3.2% from the frst project that requred the entre nvestment budget. Project I 8, would be dsmssed as wll Projects II and IV NPV Profle, Crossover Rate and the Rankng Reversal A net present value profle s the relatonshp between a project s net present value and several alternatve cost of captal rates. It s expressed n a table and graph such as the ones we see below for Projects I and II. The two expressons, table and graph, show how the net present value changes n response to changes n the frm s cost of captal rate. Cost of Net Present Value Captal I II % 2.% 4% 6% 7.% 8% %.% 3% % 2,,972 2,27,27 9,7 8,76,69 2, ,462 2, 2,66,662 2,498,77 8,76 4, ,48-6,887 IRR 3.3%.7% Fgure 8. The crossover pont Lookng at both the table and graph above, we can make the followng observatons: - Snce the relatonshp between the net present value and the cost of captal s negatve, both curves, NPV I and NPV II are slopng downwards: startng from ther ntal values of $2, and $2, at zero rate, and endng at negatve values at the hghest rate, above.7%. That s to confrm that as the frm s cost of captal ncreases, ts net present value decreases. - The curve for Project II s steeper than the curve for Project I. Ths reflects that Project II s more senstve to the change n cost of captal rate than Project I. NPVII NPVI > r r 27

13 We can observe, for example, that as cost of captal rate goes up by 92% (from 6% to.%), the net present value for Project II goes down by 98%, whle the net present value for Project I declnes by 74%.. 6 = 92% 6 ;,27 2,772 =, 27 74% ; 2, = 98% 2, 498 The dfference n the project senstvty to changes n the cost of captal s due to the dfferences n the magntude as well as the tmng of the cash nflows. Because the dscountng process s just a reverse of the compoundng process, the present value of cash nflows comng n later years would decrease more than those comng n earler years. Ths s the reason for the curves to ntersect at the crossover pont. - When the two net present values of the two projects equal each other, ther curves ntersect at the crossover pont. The cost of captal rate correspondng to that pont s called the crossover rate, 8% n ths case. So the crossover rate s defned as the rate at whch the net present value of two projects get equal to each other and where ther curves ntersect. - The crossover rate serves as the turnng pont where the reversal of project rankng occurs. At any level of cost of captal below the crossover rate, Project II would be preferred for ts hgher net present value. For any cost of captal level hgher than the crossover rate, Project I would be preferred for havng ts net present value hgher ths tme than the net present value of Project II. - The net present value of both projects would declne to zero when they cross the x-axs at ther frm s nternal rate of return. The graph shows that the nternal rate of return for Project I s 3.3%, and for Project II s.7%, and those where the two curves cross the x-axs respectvely Proftablty Index and Captal Ratonng We hnted earler to the relatve measure of net present value and the net present value per dollar nvested. Another relatve measure can serve as one of the crtera for project acceptablty. It s the measure of Proftablty Index (PI) whch s a rato of the present value of cash nflows and the present value of cash outflows: PI = t t CF n ( r) + I n ( + r) It can also be expressed as a rato between the present value of cash nflows and the ntal nvestment. PV(CF ) PI = PI > I The crteron for project acceptablty s for the proftablty ndex to be equal or larger than snce beng equal to would ndcate the equalty between the cost and beneft. In two of the projects mentoned prevously, the net present value for one was $77,, and the other was $6, but because the nvestment captals requred for both respectvely were $3, and $,, ther values to the frm would dffer dramatcally. Calculatng the proftablty ndex for both would reveal that dfference. But, we need to restore the present value for cash flows by combnng the net present value and the ntal nvestment for both: PV = NPV + I PV = 77, + 3, =,2, PV 2 = 6, +, = 7, PI = PV (CF ) I =,2, 3, =

14 PI 2 = 7,, = Payback Method Among the most common methods to evaluate nvestment projects, especally n the past (n the pre-computer age), was the payback method. It may stll be n use n some busness corners for ts smplcty and straghtforwardness. Payback perod refers to the expected number of operatonal years durng whch the ntal nvestment can be recovered. In ths sense, as a crteron for project selecton, the shorter the payback perod the better. The short recovery tme would be a crude measure of lqudty of the project. It can also be an ndcaton for less potental rsk. The fewer the number of years n whch the ntal captal can be fully recovered, the more the project can cut off the potental rsk that may le ahead. The payback perod (PB) can be obtaned by the followng two technques:. For projects yeldng an equal amount of cash nflow durng the project lfe tme, payback perod s obtaned by dvdng the ntal nvestment or the proposed captal (I) by the annual cash flow (CIF): I PB = CIF 2. For projects yeldng varable cash nflows throughout the years of the project operaton. The payback perod (PB) can be obtaned by: I f CIF t = t= + CIFf PB (f ) where: f: s the year n whch the ntal nvestment can be fully recovered. f-: the year before the year of full recovery of the ntal nvestment. I: s the ntal nvestment or the captal proposed for allocaton. CIF t : the cash nflow durng the perod t up to the year before the year of full recovery. CIF f : the cash nflow n the year of full recovery of the ntal nvestment. Let s calculate the payback perod for the followng two proposed projects: The sunshne company s consderng the followng two projects for captal allocaton. Project X s askng for $64, and Project Y s askng for $68,. Calculate the payback perod for both projects: Year Project X ($64,) Project Y ($68,) Expected Profts Expected Profts (after taxes) Cash Inflows (after taxes) Cash Inflows 9, 6, 2, 4,8,2 6, 9, 2,2,2 6,,, 8, 6, 4,, 7, 6, 4, 8, 9, 6, 8,9 6, 29

15 For Project X: For Project Y: I PB = CIF 64, = 6, = 4 years I f CIF f = t= + CIFf PB (f ) = 68, (4,8 + 2, 2 +,) 3 +, = 3. years f: s the fourth year snce the 68, would be wthn the accumulated cash nflows by the end of the fourth year, that s (4,8 + 2,2 +, +, = 73,). f-: s the thrd year (the year before the fourth). CIF f : s the annual cash nflow ($,) n the fourth year as the year n whch the ntal nvestment would be fully recovered. In addton to the major shortcomng of the payback method n gnorng the tme value of money changes, t has also been crtczed for gnorng the dynamcs of the cash nflows obtaned durng the years after the year of full recovery. 3. Concluson Whle we compared the Net Present Value to the Internal Rate of Return, we can conclude that addng the proftablty ndex would make the pcture clearer. Whle the net present value of the frst project ($77,) s 28% larger than the net present value of the second project ($6,), the proftablty ndex of the second project () s 6% larger than the proftablty ndex of the frst project (3.2). Ths would llustrate the benefts of the proftablty ndex as a tool, especally when judgment by the net present value alone would not be conclusve. The relatve measure of the net present value may rse agan when the frm has some constrants on ts capacty of nvestment. Often there s a certan lmt as to how much any frm can fnance ts all avalable feasble projects. Hgh management of the frms may place such a lmt and determne the maxmum capacty of captal nvestment whether project fnancng s done by borrowng from banks and fnancal nsttutons or from the publc n terms of corporate bonds and equty shares. Declarng and recognzng the lmt on nvestment may mean recognzng some sort of captal scarcty, whch should most lkely lead to seekng allocaton effcency, and that s what s called captal ratonng. Captal ratonng s defned as the process of allocatng scarce fnancal captal as effcently as the frm s condtons and crcumstances permt. It s obvous that captal ratonng would be exercsed when the total funds requested to fnance all elgble projects exceeds the frm s affordablty as set by the maxmum level of fundng. Captal ratonng nvolves contemplatng every possble combnaton of projects that can be funded, and choose the best combnaton of projects that satsfy: ) Ther total requred captal would not exceed the frm s maxmum level of fundng. 2) Ther total net present value per dollar s largest among the alternatve combnatons. The followng two tables show how captal s beng ratonalzed. The frst table shows fve competng projects all of whch were consdered worthy, but the frm cannot fund all because the requred total captal s $3, and the frm s maxmum level of fundng s $2,. The second table lsts the possble combnatons of projects wth ther combned captal and combned net present values. It also lsts the remanng funds out of the avalable $2, (column 4) and ther compounded future values (column ). Column 6 adds up the combned net present value to the accumulated future value, and fnally column 7 calculates the adjusted net present value per dollar of funded captal. Ths s the column that shows whch combnaton of project s the best based on the 3

16 hghest adjusted net present value per dollar, and that would be the combnaton contanng projects (, 4, and ) whch shows 79% net present value for each dollar of ntal nvestment. Project Intal Captal NPV 2 3 4, 7,, 4, 3, 6, 4, 3, 3,, 3, 8, Project Combnaton, 2, 3,, 3,, 4, 2, 3, 4, Combned Captal Combned NPV 2 2 Remanng Fund (RM) 2 - (2) Value of Invested Remanng Funds RM(+r) n Fnal NPV (3 + ) NPV Per $ Invested (6 2) References Ahadat, N., & Brueggemann, R. I. (99). Evaluatng an nvestment proposal. Journal of Accountng Educaton, 8(2), Ansar, S. (2). The Captal Budgetng Process. McGraw-Hll/Irwn. Arya, A., Fellngham, J. C., & Glover, J. C. (998). Captal budgetng: Some exceptons to the net present value rule. Issues n Accountng Educaton, (August), Baker, J. C. (984). Captal budgetng n Amercan and European companes. Md Atlantc Journal of Busness, (Summer), -28. Berman, H. Jr., & Smdt, S. (26). The Captal Budgetng Decson: Economc Analyss of Investment Projects (9th ed.). Routledge. Blank, L. L. (988). Project selecton and the varyng level of cost/beneft nformaton. Journal of Cost Management, (Fall), -7. Brck, I. E., & Weaver, D. G. (984). Comparson of captal budgetng technques n dentfyng proftable nvestments. Fnancal Management, (Wnter), Carr, C., Kolehmanen, K., & Mtchell, F. (2). Strategc nvestment decson makng practces: A contextual approach. Management Accountng Research, (September), Carroll, J. J., & Newbould, G. D. (986). NPV vs. IRR: Wth captal budgetng, Whch do you choose? Healthcare Fnancal Management, (November), 62-64, 66, 68. Chen, S. (28). DCF technques and nonfnancal measures n captal budgetng: A contngency approach analyss. Behavoral Research n Accountng, 2(), Chen, Y., & Deng, M. (2). Captal ratonng and manageral retenton: The role of external captal. Journal of Management Accountng Research, (23), Chrstensen, C. M., & van Bever, D. (24). The captalst's delemma. Harvard Busness Revew, (June), Clancy, D. K., & Collns, D. (24). Captal budgetng research and practce: The state of the art. Advances n Management Accountng, (24), Clark, V., Reed, M., & Stephan, J. (2). Usng Monte Carlo smulaton for a captal budgetng project. Management Accountng Quarterly, (Fall),

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