INVESTMENT PROJECT EFFICIENCY EVALUATION

Transcription

1 368 Miljeko Crjac Domiika Crjac INVESTMENT PROJECT EFFICIENCY EVALUATION Miljeko Crjac Professor Faculy of Ecoomics Drsc Domiika Crjac Faculy of Elecrical Egieerig Osijek Summary Fiacial efficiecy of ivesme projec is beig evaluaed i his paper I is showed ha he e prese value fucio is cosa ad ha quoa value is equal o c whe i coverges o he ifiie Opimal raes i are aalyzed i cerai cases ad everyhig is illusraed hrough examples Keywords: ivesme efficiecy projec ivesor moey flow ieres rae Iroducio Give ha projec jusificaio appraisal is carried ou by measurig ivesmes ad he effecs of hese ivesmes ad give ha hese effecs ca geerally be differe we ca observe hem i differe codiios ad from differe pois of view I his paper we will cocerae o fiacial efficiecy of ivesme projec which should aswer he quesio how jusified i is o ives fiacial asses io a cerai projec from he viewpoi of he compay makig he ivesme The projec duraio period is T() I ime T() ivesmes ad expeced ivesme effecs are observed For may busiess projecs i is o possible o deermie exac moey flow herefore saisical heory is used Assumig ha c is moey differece bewee moey icome ad moey oulay i ay ime ierval durig he projec c = moey icome i mome moey oulay i mome If moey flow is cosa he moey flow e rae ca be expressed as follows: c( ) = c ( ) c ( ) where c () is icome rae ad c () is oulay rae of moey asses i he projec mome

2 INVESTMENT PROJECT EFFICIENCY EVALUATION 369 If he differece bewee icome ad oulay is larger he zero he we alk abou posiive moey flow ad if he differece is less he zero he we alk abou egaive moey flow For a paricular ivesme projec le us assume ha we kow T() (ecoomic duraio of a projec) ad e effecs c I is o hard o coclude ha he ivesme projec value a is begiig is i a discree case: () c c c c NVSV ( i) = c+ + + K i ( + i) ( + i) ( + i) ie: Where: ( ) ( ) () k NVSV i = ck + i Equaio NVSV () (i) e prese value a he begiig of a projec i ieres rae T() projec duraio (usually years) c k projec e effec a he ed of year k I is i ivesor s bes ieres o measure ivesme profiabiliy wih regard o oher ivesmes as his will idicae wheher i is advisable o eer he fiacial busiess The issue here is wheher we ca erich he give capial beer ha crediors Similarly o he previous siuaio a he ime T whe he projec fiishes we have he followig siuaio: c T T T ( + i) + c( )( + i) d hus he e prese value depede o ieres rae i equals o: T T NVSV ( i) c ( i) = + + c( )( + i) d Equaio T

3 37 Miljeko Crjac Domiika Crjac If we presume ha c() = he we ge Equaio () By subsiuig q = ( + i) - we ge NVSV ( i) Noe = c q i e () If he projec duraio ime is ifiie accumulaio is o defied whereas e prese value is defied by Equaio () I is o hard o see ha he fucio NVSV(i) is a coiuous fucio of ieres rae ad ha lim NVSV ( i) = c Assumig ha he ivesme is wih fixed ieres rae i equaio () leads o he coclusio ha he projec is profiable if ad oly if NVSV(i) > If NVSV(i) is movig from posiive o egaive values for i ad aroud i he he projec is profiable uder hese codiios if ad oly if i < i Noe Fiacial efficiecy evaluaio of a projec ca be deermied by mahemaical aalysis of a fucio graph NVSV(i) Whe usig e prese value crieria he problem is how o choose opimal ieres rae i i which moey flows are discoued i Examples Example If here is oe ivesme c a he begiig of he projec duraio ad if all effecs are cosa ad greaer ha zero hroughou he projec he e prese value is: p where r = + i i = The ivesme projec is: r ( ) () NVSV ( i ) = c+ c r r M Crjac Maemaika za ekoomise Ekoomski fakule Osijek () M Crjac Maemaika za ekoomise Ekoomski fakule Osijek ()

4 INVESTMENT PROJECT EFFICIENCY EVALUATION 37 Example ) efficie if NVSV () (i )> ) eural if NVSV () (i )= 3) iefficie if NVSV () (i )< Ieral profiabiliy rae i r is he rae a which e prese value of ivesme projec is equal o zero So NVSV () (i r )= ie c k ( + i r ) = Give ha i is he profiabiliy rae a which commo eerprise projecs are approved i is o hard o coclude ha he ivesme projec is: efficie for i r > i eural for i r = i 3 iefficie for i r < i Usig ieraive mehods i is o hard o calculae ieral profiabiliy rae from he equaio c k ( + i r ) = Example 3 Asse reur ime T(i p ) is he ime ecessary o reur ivesmes I ca be calculaed by he equaio T ( i p ) () NVSV ck ip ( ) = ( + ) = where NVSV () () is he fucio of ime If is he reur ime for similar projecs he ivesme projec is: accepable if T(i p ) < eural if T(i p ) = 3 uaccepable if T(i p ) > Usig he permaecy priciple we ca calculae:

5 37 Miljeko Crjac Domiika Crjac NVSV () () = c () NVSV = ck () ( ) k () NVSV = ck () ( ) k 3 () NVSV = ck (3) ( ) k () : NVSV ( ) = c ( + i ) k p uil we ge NVSV () ()< ad NVSV () (+) hus havig reur ime T(i p ) from he ope ierval ( +) By usig liear ierpolaio 3 we have: T ( i ) = + p () NVSV ( ) ( ) ( + ) () () NVSV NVSV Refereces: ) J Bedeković i koauori; Plairaje ivesicijskih projekaa Ekoomski isiu Zagreb (993) ) R Sciovski R Galić i M Šilac-Bešić; Numerička maemaika vjerojaos i saisika Elekroehički fakule Osijek (993) 3) B Novak Odlučivaje u fiacijskom upravljaju Ekoomski fakule Osijek () 4) M Crjac Maemaika za ekoomise Ekoomski fakule Osijek () 3 R Sciovski R Galić i M Šilac-Bešić; Numerička maemaika vjerojaos i saisika Elekroehički fakule Osijek (993)