2.6. PROBLEMATIC METHODOLOGICAL QUESTIONS OF INVESTMENT PROJECT EVALUATION

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1 2.6. Problematic methodological questios of ivestmet project evaluatio Mária ILLÉS DOI: /dBEM.M ch PROBLEMATIC METHODOLOGICAL QUESTIONS OF INVESTMENT PROJECT EVALUATION Summary There are some scietific questios related to the NPV ad IRR which have ot bee worked up. From these issues, this paper discusses the ecoomic cotet of the two categories ad the questios of usability for project evaluatio ad rakig. The mai research methods are methodological aalysis, model editig ad examiatio of the mathematical formulas. The paper proves that the NPV is the discouted amout of the surplus profit geerated above the profit requiremet, ad poits out, that cotet bad of the real reivestmet rate assumptio is fudametally differet from everythig that ca be foud about this i the literature. Because of the NPVs are ot comparable, the paper systematically elimiates the distortio effects. Thus, the NPV trasforms ito a special kid of rate, amely, the differece betwee the factual rate ad the required rate of retur. This NPV rate (with equal required rates of retur) gives the same rakig list as the IRR. The aggregate capital eeds is a ew coceptio ad gives a ew viewpoit to aalysis of ivestmet projects evaluatio. The paper defies the special cotet of aggregate capital eeds ad compiles a idex umber for it. Keywords: NPV, IRR, rakig, aggregate capital eeds, reivestmet rate assumptio Literature review The paper examies the two mai tools of ivestmet project evaluatio, i.e. the et preset value (NPV) method ad iteral rate of retur (IRR) method. Applicatio appropriateess of the two methods is sharply debated from the first half of the last cetury. May writigs already were bor i the 1950s (see Alchia, 1955; Solomo, 1956; Bierma ad Smidt, 1957). Sice the the discussio is ruig. The literature of fiace expresses a very determied preferece for NPV. I spite of this, busiess professioals of developed coutries apply the IRR i a large proportio for decisio-makig. For example Arold ad Hope (1990) cite two surveys doe i the 1970s ad 1980s, demostratig that the largest British compaies (that are otherwise able to pay the best experts) defiitely rak the IRR higher tha the NPV i practice. They metio that a lot of America surveys prove that the practice prefers the IRR i the USA as well. The practical method prefereces are widely researched. Szűcsé Markovics (2012) gives a literature review about the researches o methods which are used by compaies throughout the world. Illés ad Keszthelyi (1998), Illés (2000) ad Daróczi (2004) examied the practical use of differet methods based o empirical researches o the complex evaluatio of decisio-makig process. Accordig to my experieces, i busiess ecoomics literature geerally there is ot a strog method preferece, but the IRR method ofte seems to be better. Differet discipliary roots Accordig to Volkma s (1997) research, the emergece of method qualificatio cotradictio could be attributed to the fact that fiace propagates the more 145

2 Illés, M. advatageous ature of NPV method based o oe of Fisher s works (Fisher, 1930) published i the first half of the past cetury while busiess ecoomists (ad busiess professioals) prefer the IRR method based primarily o the works of Boehm-Bawerk (1889) ad Keyes (1936). However, this is oly the surface. Serious methodological cotradictios are caused by the differet discipliary foudatios. Fiace, amely, is based o stadard microecoomics, or as Volkma says based o orthodox ecoomic theory (Volkma, 1997, p.75). Problems caused by microecoomic roots are metioed by Woods ad Radall (1989) as well. There is a sigificat differece betwee the theorems of fiace ad busiess ecoomics as far as the proximity to real-life problems is cocered. Basically, there is o direct passage withi microecoomics ad busiess ecoomics because of the very differet abstractio level, differet category system ad differet approach. Microecoomics is ot a busiess practice orieted sciece. The fiace does ot take this ito accout, ad uses microecoomic categories ad methods. I cocerig methodological questios the fiace-based fidigs ad coclusios are based o two geeral assumptios: the ivestmet opportuities are ulimited ad the reivestmet rate is equal to the required rate of retur. (Although these assumptios are regularly behid the fiace models, it is ot always stated clearly.) These coditios are ever met i reality. That is why these doctries should be lead through coditios that are close to reality before they are offered for corporate professioals. The abstractio level of busiess ecoomics is relatively low ad a cosiderable part of its research results adjusted to the characteristics of the give compay may be directly used i the corporate practice. The busiess ecoomics literature ofte metios the importace of the professioal clarity ad practical implicatios of the suggested methodology (e.g. Garriso, 1988, p. 712; Arold ad Hope, 1990 p. 260; Schmale, 2002, pp ). That is, the majority of the busiess experts ca oly apply the methodology correctly if they ca fit methods to their way of thikig, ad if they ca somehow coect them to the logic of the ecoomic process. The argumets for superiority of NPV There are o strog ad methodically supported argumets to demostrate the primacy of the NPV over the IRR. The literature puts forward three particularistic argumets to chage thigs aroud. Oe of them is that the NPV meas also that amout, which will be added to the shareholder value by the project. The secod argumet is based o the reivestmet rate assumptios. The third oe is that there oly oe NPV ca occur as opposed to the opportuity of several IRR. NPV as a shareholder value surplus Amog the advatages of NPV, fiace literature regularly metios the theorem accordig to which the NPV idicates the project s cotributio to the shareholder value (e.g. Va Hore ad Vachowicz, 2008; Crudwell, 2008). The publicatios ofte refer to Fisher s related theorem. There are also a cosiderable umber of authors who iterpret the NPV primarily or simultaeously as the surplus of compay (or firm) value (Keae, 1975; Baker ad 146

3 2.6. Problematic methodological questios of ivestmet project evaluatio Powell, 2005; Laux, 2011). However, i the reality (as it is well kow) the shareholder value is ot equal with the firm value, ad the maximizatio of the firm value is ot the same as the maximizatio of shareholder value. The paper of Woods ad Radall (1989, p. 85) says that the direct relatioship of NPV ad shareholder wealth has ever bee prove: ( the liks betwee NPV ad shareholder wealth are ot made explicit i the literature. Textbooks merely state the equivalece as a geeral premise without rigorous proof ). The theorem are still alive today, eve though it caot be prove moreover it cotais may logical cotradictios (Illés, 2012b). The reivestmet rate assumptios Accordig to the mai directio of reivestmet rate assumptio the NPV method assumes the required rate of retur, while the IRR method assumes the IRR as the reivestmet rate of aual yields (as log as the project lasts). The debate about this bega i the 1950s (Solomo, 1956; Reshaw, 1957), ad is still uderway. The cotested coceptio emerged as a kid of treatmet of the rakig coflict which ofte occurs betwee the NPV ad the IRR. The supporters of the described above reivestmet rate assumptio cocept esure automatic priority to the NPV method by emphasizig that reivestmet accordig to the high IRR is hard eough (a typical example is Laux, 2011). The debate is slightly oe-sided. Oe of the domiat groups does ot argue ad does ot react to the opposig views, just repeats the validity of the reivestmet rate assumptio as a well-kow relatioship. These views ca be cosidered roughly uiform. The represetatives of the sigificatly smaller group of those who partially or fully reject the reivestmet rate assumptio try to prove that this assumptio is wrog. They use differet logical argumets as well as mathematical or exemplary evidece. Their methodical solutios are also varied (e.g. Dudley, 1972; Carlso et al., 1974; Keae, 1979; Lohma, 1988; Johsto et al., 2002; Crea, 2005; Rich ad Rose, 2014). I a great umber of studies i this topic, may uclear coditios, categories ad phrases ca be foud. For istace, the reivestmet rate assumptio itself is iterpreted as either a explicit, implicit, or some kid of geeral assumptio. The type of reivestmet amout is ot always obvious, either. These amouts ca mostly be iterpretable as yields comig from a project i differet years of its duratio, more rarely as differeces computed from yields of two examied projects. Sometimes the examied problem is ot actually the reivestmet rate assumptio, but the critical reivestmet rate (e.g. Alchia, 1955; Dudley, 1972; Meyer, 1979). I the latter cases, refereces date back to Fisher (1930). Meyer s paper (1979) examies this questio accordig to the system tools ad categories of microecoomics. Several authors poit out their disapproval with the oe-sided teachig of faulty doctries. Amog them, Johsto et al. (2002) call attetio to the fact that a umber of fiace textbooks completely igore scietific fidigs that disprove the reivestmet rate assumptio of the two methods. Due to this, they urge reforms. I the itroductio of their paper, Walker et al. (2011) give a detailed descriptio of teachig completely cotroversial materials. Their research jois to the study of Keef ad Roush (2001), which draws the attetio to the fact that fiace textbooks use the 147

4 Illés, M. reivestmet rate assumptio higher proportio tha textbooks i maagemet accoutig. The fidigs of their ow research doe a decade later show a similar directio. They make a importat statemet emphasizig the lack of cosistecy amogst disciplies: Fiace books fall at oe ed of the cotiuum with 64 percet usig the assumptio while the egieerig ecoomics books fall at the other ed with just 20 percet usig the assumptio (Walker et al., 2011, pp ). I my research results, this sort of reivestmet rate assumptios as a automatism of these methods has ever proved. Oly oe NPV ca occur The argumet that there oly oe NPV ca occur as opposed to the opportuity of several IRR sometimes appears as comprehesive problem (Brealey ad Myers, 1988). However it is geerally kow that, the multiple iteral rates of retur occur oly i cases of uorthodox cash flow patters. Accordig to the geeral academic opiio, the NPV method is suitable for evaluatio i the case of uorthodox (o-ormal) cash flow patters as well, as there ca be oly oe NPV as opposed to the opportuity of several iteral rates of retur (e.g. Arold ad Hope, 1990; Bierma ad Smidt, 2012). However, there is absolutely o evidece that the NPV of a uorthodox cash flow patter shows a real ecoomic cotet. Literary treds i preferrig of NPV method I the literature a sort of harmoy appears o the issue of project classificatio, that both the NPV ad IRR method will always give the same result, either rejectig or acceptig a project (e.g. essetially the same is discussed by Bierma ad Smidt, 1986; Brigham ad Ehrhardt, 2008; Kha ad Jai, 2008; Kiey ad Raibor, 2012). This cosistecy, however, does ot limit the declaratios cocerig the NPV s superiority. Behid the NPV preferece, three mai treds with a slight boudaryblurrig ca be revealed as follows: 1. The NPV method is the best i all aspects. Most of the represetatives of the tred accordig to which the NPV is the best as a selectio tool ad as a rakig creatig tool as well apply the above shareholder value cocept as a kid of guidig priciple. There is a very iterestig forecast. Laux (2011) says that academics cosider the NPV approach is superior ad some of them so fid that over time practitioers have come to agree. I fact, the Fisher s itersectio was bore o the basis of comparability of NPVs as well (Fisher 1930). The Fisher s itersectio is amed the poit where NPV curves of two ivestmet projects are equal. This itersectio is ofte referred as a decisio preparig problem owadays as well (Baker ad Powell, 2005; Hill, 2008; Va Hore ad Vachowicz, 2008). Several decades ow kow that the NPVs are ot directly comparable. Geerally, the comparability is distorted by the differeces of iitial ivestmet, duratios ad the rapidity of payback (Keae, 1975). Despite of this, the oe-sided recommedatio of NPV has ot disappeared. 2. The NPV is the best as a selectio tool, but the NPV divided by the iitial ivestmet (or the profitability idex) is suitable to be a rakig creatig tool. The NPV divided by the iitial ivestmet ad the profitability idex gives the same rakig. Namely, 148

5 2.6. Problematic methodological questios of ivestmet project evaluatio the profitability idex ca be writte i the followig form as well: [1+ NPV divided by the iitial ivestmet]. For example Brealey ad Myers (1988), Albrecht et al. (2007), Watso ad Head (2009) suggest the profitability idex for rakig creatig. The paper of Damodara (2010) suggests for this purpose the NPV divided by the iitial ivestmet, however, this rate there is amed profitability idex. By these suggestios oly the distortio effect of differeces i iitial ivestmets is avoided (two of distortio affects are remaied). 3. The NPV is the best as a selectio tool, however, the equivalet aual average sum of the NPV is suitable to be a rakig creatig tool. This rakig tool suggestio ofte appears maily i the fiacial literature i the last three decade (e.g. Helfert, 1991; Baker ad Powell, 2005; Lee at al., 2009). The way of quatifyig the average is NPV divided by the auity factor, which i busiess ecoomics meas multiplyig by the loa repaymet factor. (Busiess ecoomics always uses the loa repaymet factor. The fiacial literature uses the auity factor, which is the reciprocal of the previous formula.) This solutio oly elimiates the distortio effect of the differeces i duratio (two of them are remaied). I the literature, it does ot seem ambitio to simultaeous elimiate the three distortig factors. Purpose ad method The mai objectives of this paper are as follows: To defie the ecoomic cotet of the NPV ad IRR ad to diagose the usability for project evaluatio ad rakig. To preset the profit requiremet calculatio accordig to required rate of retur. To defie the special cotet of aggregate capital eeds, to compile a idex umber for it, ad to highlight the importace of takig the aggregate capital eeds ito cosideratio. To show the essetials of the real reivestmet rate assumptio i case of orthodox cash flow patter. The mai research methods are methodological aalysis, model editig ad examiatio of formulas. The provig ways of fidigs are logical ad mathematical processes as well. The iterests of clarity, the paper uses the followig coditios ad categories: 1. The traditioal cocept of the NPV ad the IRR methods: The paper iterprets ad aalyses the cotet backgroud of NPV ad IRR methods i the classic sese. Amog others, the paper uses the term capital as a homogeeous sum i terms of owership (ad as ivestable or ivested moey). Profit is iterpreted as a pre-tax profit. The iterpretatio ad aalysis of methods are related exclusively to ivestmet projects. 2. Busiess ecoomics approach ad system of aspects: The busiess ecoomics iterprets ad maages the database as well as the results of calculatios accordig to the coditios i reality. (As featured i the first sectio fiace is iheretly built o stadard microecoomic foudatios.). This study examies the NPV ad IRR from the aspect of busiess ecoomics by usig its category system. 3. The calculatio logic follows the real process of maagemet ad after the close of this, returs to the discoutig method: The paper assumes that the maagemet 149

6 Illés, M. relatios ca be clarified movig forward i time accordig to the maagemet process. The plaig ad thikig of corporate executives works the same way. The mai ad well-kow questio of strategy makig is: where are we ow ad where we wat to arrive? It would be difficult to work out backwards this. The movig forward is the oly way i which the emergece ad realizatio of retur requiremets as well as the process of the surplus profit formatio ca be see through. Therefore, this study uses a detour to substitute for the classical methods. I order to show the cotet tally with the classical methodology of project evaluatio, after the systematic exploratio of cotet relatios, the aalysis returs to the classical method. Discoutig back to the start time makes the cotet examiatio of the retur process impossible. 4. The NPV ad IRR methods ca provide acceptable ad ecoomically meaigful outcomes oly i case of orthodox cash flow patters: (This is proved by Illés 2016.) Therefore the aalyses ad coclusios are oly cocerig to the cases of ivestmet projects with orthodox cash flow patters. (The well-kow criteria of orthodox cash flow patters are: a series of the differece of aual reveues ad expeditures starts with egative amout or amouts ad the sig of these differeces chages oly oce. That is, from a poit i time where this differece first turs ito positive, this positive sig does ot chage.) 5. Yield aalysis accordig to the retur structure: Examiatios ad aalyses of the retur process ca be solved by followig the formatio of iteral structure of the yield. The yield is the differece betwee the aual reveues ad aual expeditures. So the yield belogs to the types of aual idicators. A positive amout of yield is surplus sales reveue i terms of fiacial eeds i a give year. Therefore the yield exits from the project at the ed of the examied year. The coditios of further utilizatio of this usually do ot affect the evaluatio of the aalysed project. I the case of orthodox cash flow patters, the cotet of the yield with a positive sig ca cosist of capital retur ad/or profit. I the NPV method, the profit part of the yield may cosist of further two parts: profit accordig to the required rate of retur ad surplus profit. Util meetig the retur requiremets, the yield cosists of profit accordig to the required rate of retur ad capital retur. After the fulfilmet of retur requiremets, the cotet of the emergig yield is surplus profit. I the IRR method, the yield all alog cosists of capital retur ad profit accordig to the iterest rate, there is o surplus profit. I this case, collatio with the retur requiremets takes place after calculatios. 3. The ecoomic cotets The ecoomic cotet of IRR Earlier i busiess ecoomics the IRR was amed time-adjusted rate of retur (Garriso, 1988). IRR calculatio meas searchig for the rate of retur which makes the sales reveue lie ad the expediture lie equal to each other. (IRR is usually determied by a process of trial ad error. Usig computer the calculatio is very quick.) I case of ivestmet projects with orthodox cash flow patters, the IRR shows the factual time-adjusted profitability rate of the ivestmet. This cotet is regarded geerally kow i busiess ecoomics literature. For istace Garriso (1988) ad 150

7 2.6. Problematic methodological questios of ivestmet project evaluatio Arold ad Hope (1990) iterpret this rate as a true yield percetage. (This sort of cotet approach is ot typical i fiace literature.) The acceptability criteria of the project are decided by how large factual profitability rate is geerated compared to the required rate of retur. The differece shows how large surplus rates (or lack of rates) are geerated compared to the required rate of retur. Geerally, this differece eeds ot be defied umerically; this becomes visible whe writig the two rates ext to each other. Where the two rates are equal, that still meas that required profitability is exactly achieved. Havig more tha oe IRR is the characteristic of uorthodox cash flow patter projects oly. It is occurs that fiacial literature does ot hadle the distictio of orthodox ad uorthodox cash flow patters ad deies the expediece of the IRR (e.g. Brealey ad Myers, 1988). It ofte says that the IRR is without meaig (Hill, 2008). These statemets are valid oly the case of uorthodox cash flow patters. I this case the multiple IRRs i reality are oly techical factors, ad they really are without ecoomic meaig. The ecoomic cotet of NPV The NPV literature does ot deal with ecoomic cotet clarificatio. Accordig to my research results, the ecoomic cotet of the NPV is clear oly i case of orthodox cash flow patters. I this case, the NPV is the sum of the surplus profit geerated above the required oe, discouted for the preset time. This is explicable i logical way ad demostrable mathematically as well (Illés, 1990, 2007, 2012a). Two basic formulas I well-kow theory, the NPV is calculated so that the discouted sum of all expeditures is subtracted from the discouted sum of sales reveue that is associated with the examied ivestmet project. The calculatio ca also be made with the time series of the differece of reveues ad expeditures. The the aual differeces are discouted ad summarized. Hereiafter, i order to simplify modellig, that sort of model will be examied where the paymet of iitial ivestmet occurs at the same time as operatio is started. This is date zero. The first reveues will occur oe year later, by this time the aual reveues exceed the aual expeditures. The two basic formulas of NPV method are used i this paper are as follows: 1 NPV Bt Kt - E0 Bt - Kt 0 t t 1 (1) Where B t = sales reveues i year t, K t = expeditures i year t, E 0 = iitial ivestmet (the ivestmet sum is occurrig i the zero poit of time), i = required rate of retur, t = serial umber of years, = duratio of the project. 1 NPV - E0 Ht Ht 0 (2) t t 1 151

8 Illés, M. H t = differece betwee sales reveues ad expeditures i year t (where Ht > 0 for orthodox cash flow patter projects). Accordig to NPV method the ivestmet project is acceptable if the NPV is ot less tha zero. I the followig the aalysis deals with positive or zero NPV. Geeral demostratio The ecoomic efficiecy of ivestmet projects ca be examied correctly by several methods, ot oly by the published oes. Such a o familiar method ca be the retur calculatio based o followig up the retur process. At the ed of this process the output is the sum of surplus profit (accordig to all of aual surplus profits is charged with the required rate of retur by the ed of the duratio). The essece of the proof is that the discoutig of this surplus profit leads to the NPV. The first stage of the demostratio describes the retur process of the cost of capital. The cost of capital is the sum of the retur requiremet of the capital face value ad its required profit accordig to the required rate of retur. The amout of the cost of capital ot yet retured ad the retur status is at the ed of Year 1: E0 H1 at the ed of Year 2: E0 H1 H2 at the ed of Year 3: { E0 (1 i) H1 (1 i) H 2} (1 i) H 3 ad so o. After the retur requiremet is met, the formula becomes positive. Assumig that the retur status at the ed of Year 3 already shows the patter of the developmet of the process through time, the simplificatio is itroduced. Elimiatig the curly ad square brackets: 3 2 E0 H1 H2 H3 The umerical defiitio of the retur status iscribed for the ed of Year 3 ca be applied further for the full duratio of the ivestmet: -1-2 E0 H1 H2... H-1 H (3) I the secod stage of the demostratio the surplus profits calculated above to the ed of duratio is trasformed ito preset value. The three steps of it are: prescribig the discoutig formula, fulfillig the discoutig process, simplifyig the resulted formula [ E0 H1 H2... H-1 H ] (4) E0 H1 H2...H-1 H 2-1 (5) 1 - E0 Ht (6) t t 1 (1 i) The Formula (6) has arrived at oe of the basic NPV formula that is the Formula (2). The proof is complete. The deductio proved that i the case of orthodox cash flow 152

9 2.6. Problematic methodological questios of ivestmet project evaluatio patter projects the NPV is the discouted amout of the surplus profit geerated above the profit requiremet accordig to the discout rate (Illés, 2012a). The ecoomic backgroud of the NPV curve The NPV curve is well kow (Figure 1). The plottig of this is a regularly appearig topic withi the literature of ivestmet projects evaluatio. The authors also cosider that this figure is well-kow ad widely used; therefore do ot use ay professioal referece. The figures ad related explaatios are itroduced from differet perspectives: oce a geeral theoretical relatioship (Arold ad Hope, 1990), aother time as a solutio of a exercise or a itroductio of a problem through a example (Brealey ad Myers, 1988; Va Hore ad Wachowicz, 2008). Figure 1: The sum of the NPV i the fuctio of iterest rate Source: Widely used illustratios of the relatioship (e.g. Arold ad Hope, 1990, p.254, Brealey ad Myers, 1988, p. 79; Va Hore ad Wachowicz, 2008, p. 329) Figure 1 shows the NPV curve. By this the higher the iterest rate is, the smaller the NPV. As a result of icreasig iterest rate, this decrease first reaches the zero NPV, the further icreasig results i higher ad higher egative NPVs. The iterest rate that is at the itersectio of axis x ad that results i zero NPV is the IRR. (This is well kow.) As I kow, there are o literature sources o the pre-coditios ad detailed cotet backgroud of the illustrated relatioship. I order to specify the problem it must be laid dow that the curve i Figure 1 is valid for most but ot all projects i questio. The relatioship is oly valid for profitable projects with orthodox cash flow patter. Namely, the NPV is mootoously decreasig, there is oly oe itersectio, ad the curve starts i the positive rage (Illés, 2014). The illustrated NPV curve starts from zero percet iterest rate. Whe the required rate of retur is zero, the the NPV is calculated by the Formula (1) as follows: NPV Bt - Kt - E0 M i 0 t 1 t 1 (7) M= Total accoutig profit that is the differece of the omial value of total reveues ad total expeditures icludig iitial ivestmet arisig durig the whole duratio of the project. As Formula (7) shows, at zero percet iterest rate the NPV is the differece betwee the omial value of total reveues ad total expeditures icludig iitial ivestmet. 153

10 Illés, M. This differece ca also be cosidered as a accoutig profit summed up i omial value for the total duratio of the project. This gives the coclusio that if o profit is gaied at omial value, the startig poit of NPV curve caot be i a positive rage. (Because of this, the figure is ot valid for projects that do ot geerate accoutig profit.) The profit calculated at omial value for the whole duratio meas the coverage possibilities of the profit requiremets. If the profit requiremets are ot larger tha the omial value of all accoutig profits, the the project is acceptable. Calculatio of profit requiremet The profit requiremet is iterpretable o the yearly sums of ot retured part of iitial ivestmet. The ot retured capital ca be oly withi the pay off period (whe the NPV is ot egative). I the remaiig years of the duratio there is ot profit requiremet, therefore the yields of these years are surplus profits. Calculatio mechaism of the profit requiremets accordig to the ot retured part of iitial ivestmet (after the payback period the sum of the ot retured capital is zero): I the first year: Ms1 E0 i (8) I the secod year: Ms2 Eli ; where E1 H1 E0 i - E0 (9) I the third year: Ms3 E2i ; where E2 H2 - E1i - E1 (10) For the t >1 year geerally: Mst Et-1i ; where Et-1 Ht-1 - Et-2i - Et- 2 (11) E t = the ot retured part of iitial ivestmet at the ed of year t, M st = the profit requiremet i year t accordig to the ot retured part of capital ad required rate of retur, If the yearly profit requiremet is larger tha the yield i curret year, the the differece is automatically added to the capital still to be retured. Accordig to Formula (11) the total profit requiremets that arise durig the duratio of the project ca be calculated as follows: t 1 st t 1 M E i where Et-1 Ht-1 - Et-2 i - Et- 2 (12) t 1 The calculatio of surplus profits ad its preset value I the last ear of pay-off period the ecoomic cotet of yield cosists of three elemets: profit retur accordig to required rate of retur, capital retur ad surplus profit. O this basis Formula (13) describes the calculatio of surplus profit cocerig the fial year of the pay-off period. H z (Ez-1 i Ez-1 ) ΔHz Hz Ez-1 1 i 0 (13) z = umber of years of the pay-off period (icludig the last commeced year). ΔH z = sum of the surplus profit i the last commeced year of pay-off period. The yield occurrig i the years after the retur totally cosists of surplus profit. The 154

11 2.6. Problematic methodological questios of ivestmet project evaluatio descriptio of its quatificatio begis by makig formula for the calculatio of the aual amouts. The sum of the surplus profit at the ed of the first, the secod ad the third year after the pay-off period: Hz 1 ΔH z (1 i) ; H z 2 [H z 1 ΔH z 1 i ] 1 i H H [H ΔH 1 i ] 1 i }1 i z 3 {z 2 z 1 z 155 ; Cosiderig the third year s formula, the sum of all of aual surplus profits charged with the iterest rate ca be calculated by the ed of the duratio as follows: s j 1 z j s j 1 i ΔH 1 i s FVΔM H (14) Z FVΔM = the sum of the surplus profit charged with iterest rate at the ed of the duratio, j = the ordial umber of the years of operatig period after the pay-off, s = the umber of years of the operatig period after the pay-off (s = z). Because of the iterest rates are charged, Formula (14) cotais some false iterest icome. Accordig to Formula (15) the false iterest icome falls out durig discoutig. Surplus profits will be discouted from the year of their occurrece. The preset value of the discouted ad summed surplus profits is the NPV itself: s s j s 1 NPV [ Hz j 1 i ΔHz 1 i ] (15) 1 i j 1 = duratio of the project (z + s). After simplificatio [usig ( = s+z)] there will be a clear formula, accordig to which the NPV ca be reached by discoutig ad assumig the surplus profits accordig to the date of occurrece: s H z j H z NPV 1 i z (16) j 1 i z j 1 Startig from the classical versio of the NPV iscriptio it caot be see that oly surplus profits remai amog the really discouted items. The real reivestmet rate assumptio i the case of orthodox cash flow patter Accordig to the logic of time goig forward, firstly the capital ad profit requiremets should be recovered. These items gradually quit the project ad calculatios, accordig to their retur. (The method does ot charge farther retur requiremets for these items.) The yields geerated after the fulfilmet of retur requiremets are the surplus profit. These sums also leave the project so they caot be regarded as the orgaic part of the project. However, these sums remai i the calculatios. The NPV method focuses o the quatificatio of sums iterpreted i this paper as surplus profit. The discoutig mechaism related to the surplus profit automatically assumes that the profitability of this surplus will be equal to the required rate of retur accordig to the project. This way the real reivestmet rate assumptio will prevail, but oly regardig

12 Illés, M. the surplus profit appearig above the profit as to the required rate of retur. It is importat to emphasize that the this real assumptio cocers oly the surplus profit ad it cocers either the total yield, or the yield part for capital retur, or the yield part for retur o profit requiremet. The cotet bad of the real reivestmet rate assumptio is fudametally differet from everythig that ca be foud about this i the literature. The real reivestmet rate assumptio exclusively is prevailed for the surplus profit. This does ot cause ay icoveiece. For orthodox cash flow patters the IRR method does ot eforced ay reivestmet rate assumptio. The IRR covers the whole profit sum, so techically there is o surplus profit (o lack, either). Accordigly, the automatic reivestmet rate assumptio caot be realized. It should be oted that i the case of uorthodox cash flow patters the real reivestmet rate assumptio are eforced i both method. Here the sigificace of this may be very large. I this area there are loss-makig projects with positive NPV. However, i the case of orthodox cash flow patters the loss-makig projects are automatically rejected by both methods. The most importat poit of the problem is as follows: the calculatio mechaism of the NPV method hadles the false iterest icomes of temporary surplus profit as real moey. Discoutig the uused part of the false iterest icome leads to a positive NPV. The NPV emergig this way is false as well. Detailed proof ad aalysis of these are i Illés, 2016) Compariso of expressive power of the two idicators The ecoomic cotet of the IRR of orthodox cash flow patter is clear. This is the profitability rate of ivested capital. This iformatio is i accordace with a almost commoplace basic truth of ecoomics, that i the competitive market the capital goes where the highest retur rate ca be achieved at a give risk. I cotrast with this, a NPV with positive sig has the followig message for the decisio-maker: the profit requiremets accordig to the required rate of retur will be fulfilled ad surplus profit calculated i preset value will also be gaied. If the questio is whether the profit requiremets are fulfilled, this aswer is satisfactory. But it is ot easy to tell what advatage this amout exactly meas. A quite ordiary example: for a idividual who is fixig 300,000 euro i a bak for oe year, it is more meaigful to do so at a iterest rate of 4.5% tha to be told that he will get 3% iterest o his deposit plus 4,500 euro more. This special sort of deposit is more difficult to see through with a log-term commitmet (Illés, 2012b). The rakig problem As it was metioed i the first sectio, the comparability of NPVs may distort the differeces i iitial ivestmets, the duratios ad the rapidity of capital returs. There are literary sources for suggestio of certai correctios to elimiate of the distortio effects. These suggestios, however, oly cocer for the first or the secod out of the three distortio effects listed above. (There is o visible pursuit of a complex correctio.) 156

13 2.6. Problematic methodological questios of ivestmet project evaluatio The suggestio for dividig the NPV by the iitial ivestmet [ NPV ] or usig the E 0 profitability idex [ NPV 1 ] as a rakig tool, elimiates oly the distortio effect E 0 of differeces i iitial ivestmets. The suggested equivalet aual average sum of the NPV as a rakig creatig tool oly elimiates the distortio effect of the differeces i duratio. The formula of this time-adjusted average is: q NPV (where q is the loa repaymet factor, withi the required rate of retur ad duratio of the project). Aother step could be although I did ot fid ay suggestios for this i the literature mergig of the above two methods, that is, the umerical defiitio of the equivalet aual average sum of the NPV divided by iitial ivestmet, that is NPV q. I the last formula there are elimiated distortio effects of iitial ivestmets ad duratios, however, there is o elimiated the distortio effect of retur rapidity. The methodological elaboratio of calculatig a coefficiet which could measure retur rapidity seems to be very complicated i this structure. I believe that the calculatio of this coefficiet is ot ecessary, but very importat to kow its essece. Fudametal cases: a) Retur by years is uiform. Tha the coefficiet is 1. b) Retur is quickly. The larger yields arise at the begiig of the duratio. I this case the coefficiet is bigger, tha 1 (advatageous). c) Retur is slow. The larger yields arise at the ed of the duratio. I this case the coefficiet is lesser, tha 1 (disadvatageous). The cleased formula is as follows: NPV q λ r - i ε (17) E 0 = coefficiet of payback rapidity, r = iteral rate of retur, = miscalculatio factor. The cleased NPV is a special rate-differece betwee the factual retur rate ad the required oe. This cotet is followed from exhibited calculatig procedure. The ratecharacter has appeared whe the NPV was divided by iitial ivestmet. The matter of rate-differece is followig from that, the NPV is a surplus yield. Multiplyig this surplus yield rate with the loa repaymet factor it trasforms the time-adjusted average of NPV rate. The last step is the correctio with the coefficiet of retur rapidity. This way has formed the modified differece betwee the IRR ad the required rate of retur. This method caot lead to the accurate differece of two rates. This is comig from the special cleaig solutio i which are mixig the elemets of static ad dyamic procedures for ivestmet project evaluatio. This is idicated by a calculatio error factor (Illés, 2012a). The surplus profitability over the required rate of retur (if the required rate is equal for all examied project) will be the highest for the project where the IRR is the highest. Thus the same projects will gai the first, secod, etc. place i both rakigs. I this correct way, there is ot methodological superiority. E 0 157

14 Illés, M. Aggregate capital eeds The project s aggregate capital eeds meas the amout of capital eeded for operatio of the project durig its full duratio. This is a ew busiess ecoomics category. Quatificatio ad cosideratio of it could sigificatly improve the ecoomic evaluatio ad compariso of ivestmet projects. The sum of the aggregate capital eeds depeds o the iitial ivestmet, duratio of project ad the rapidity of capital retur. For the calculatio it shall be aggregated the yearly tied-up capital that is the ot-retured parts of the iitial ivestmet for each year (Illés, 2014). The calculatio method of tied-up capital for the first three years ad for the t>1 year geerally are preseted i Equitatio (8) - (11). Based o all these, the idex umber of aggregate capital eeds (E ACN ) is as follows: E E (18) ACN t 1 Tied-up capital is a state idicator, ad therefore the tied-up capitals of differet years caot be summed up from this aspect. However, i cosideratio the icomeproducig potetial eeds to take ito accout simultaeously the tied-up capital ad tied-up time. The cotet of the idex-umber meas a capital amout which is tied up for oe year. So the measuremet uit of this is oe uit tied-up capital for oe year. Accordig to the calculatio method used above a three-year tie-up of oe capital uit is equal to three capital uits tied up for oe year. This solutio is cosidered to be correct because the tied-up capital is computed with a database where i the first step the profit requiremets are subtracted from the yields of certai years. The remaider is iterpreted as a retur part of iitial ivestmet i a give year. It is useful to examie how much total capital is used i a ivestmet project, to geerate a give NPV ad a give IRR. It is favourable if smaller aggregate capital eeds result i a higher NPV or greater aggregate capital eeds result i a higher IRR. The category of the aggregate capital eeds has a sigificat opiio-formig role. It is advisable to take ito accout the aggregate capital eeds as well. t-1 Refereces 1. Albrecht, W., Stice, J., Stice, E., Mote Swai, M. (2007): Accoutig: Cocepts ad Applicatios. Cegage Learig Thomso South-Wester 2. Alchia, A.A. (1955). The Rate of Iterest, Fisher's Rate of Retur over Costs ad Keyes' Iteral Rate of Retur. America Ecoomic Review, 45(5), Arold, J., Hope, T. (1990): Accoutig for Maagemet Decisios. Pretice Hall Iteratioal (UK) Ltd. 4. Baker, H. K., Powell, G. E. (2005): Uderstadig Fiacial Maagemet: A Practical Guide. Joh Wiley & Sos. USA, UK, Australia 5. Bierma, H., Smidt, S. (1957): Capital Budgetig ad the Problem of Reivestig Cash Proceeds, The Joural of Busiess, 30, No. 4: Bierma, Jr. H., Smidt, S. (1986): Fiacial Maagemet for Decisio Makig. Macmilla, New York 158

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