6.marrja e vendimeve sipas npv

Principles of Corporate Finance

Kreu 6Marrja e Vendimeve t Investimeve Sipas Rregullit t Vlers Aktuale Neto

Eighth Edition

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shtjet Kryesorefar t skontojm? Projekti IM&C Ndrveprimi i projekteve Kur t investojm Zgjedhja ndrmjet projekteve me jetgjatsi t ndryshme Prdorimi optimal i aftsis prodhuese t makinave

Beshir Ciceri

Copyright 2006 by The McGraw-Hill Companies, Inc. All rights reserved

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far t skontojm?Tre rregullat themelore q duhen zbatuar: 1. Vetm cash flow sht i rndsishm! 2. Vlerso Cash flow q ndryshon! 3. Vlerso inflacionin!The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again.

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far t skontojm?1. Vetm Cash Flow sht i rndsishmThe image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to d elete the image and then insert it again. The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to d elete the image and then insert it again. The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to d elete the image and then insert it again.

The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again.

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6- 5

far t skontojm?1. Vetm Cash Flow sht i rndsishm! Mos barazo cash flow me fitimin kontabl! Vlerso cash flow pas tatimeve! Vlerso cash flow vetm n astin e realizimit dhe jo kur fillon nj pun ose kur lind nj detyrim!The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again.

Beshir Ciceri


6- 6

far t skontojm?2. Vlerso Cash flow q ndryshon! Mos ngatrro kthimet mesatare me ato marzhinale Prfshi t gjitha efektet ansore (flukset indirekte) Mos harro nevojn pr kapital qarkullues neto Injoro kostot e zhytura (t parifitueshme) Vlerso t gjitha kostot oportune Kujdes me kostot e prgjithshme industriale


Beshir Ciceri


6- 7

Inflacioni3. Rregulli pr inflacionin Trajtoje inflacionin si duhet!! Prdor normn nominale t aktualizimit pr t skontuar flukset nominale. Prdor normn reale t interesit pr t skontuar flukset reale. Rezultati do t jet i njjt, pavarsisht se ciln norm prdorni pr skontimBeshir Ciceri Copyright 2006 by The McGraw-Hill Companies, Inc. All rights reserved


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InflacioniShembull Supozojm se jeni pronar i nj aktivi t dhn me leasing, i cili pas nj viti do t kushtoj $8.000. mimi i aktivit do t rritet me 3% (norma e parashikuar e inflacionit) n vit pr 3 vjet (4 vjet n total). Nse norma e aktualizimit sht 10%, sa sht vlera aktuale e mimit t ktij aktivi?1 norma reale e interesit = 1 + norma nominale e interesit 1 + norma e inflacionit

Beshir Ciceri


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InflacioniShembull shifra nominale

Viti 1 2 3 4

Fluksi monetar PV @ 10% 8000.00 ! 7272.73 8000 1.10 00 8000x1.03 = 8240.00 8240.2 ! 6809.92 1.10 2 20 8000x1.03 = 8487.20 8487.3 ! 6376.56 1.10 3 82 8000x1.03 = 8741.82 8741.4 ! 5970.78 1.10 $26,429.99

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InflacioniShembull shifra reale Viti 1 2 3 48000 1.03 8240 1.032 8487.20 1.033 8741.82 1.034

Fluksi monetar = 7766.99 = 7766.99 = 7766.99 = 7766.997766.99 1.068 7766.99 1.068 2 7766.99 1.0683 7766.99 1.068 4

[email protected]% ! 7272.73 ! 6809.92 ! 6376.56 ! 5970.78 = $ 26 ,429.99

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6- 11

Projekti IM&C Projekti krkon nj investim fillestar $10,000,000 pr ndrtesn dhe makinerit. Vlera e mbetur kontabile $500,000 Vlera e tregut e vlers s mbetur $1,000,000 Jetgjatsia e projektit 6 vjet Amortizimi linear:Amortizimi vjetor = $9,500,000 : 1/6 = $1,583,000

Kostoja oportune e kapitalit sht 20% Inflacioni vjetor parashikohet t jet 10%Beshir Ciceri Copyright 2006 by The McGraw-Hill Companies, Inc. All rights reserved

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Projekti IM&CTabela 6.1 - Parashikimet fillestare (n $1000)Periudha1 2 3 4 5 6 7 8 9 10 11 12 Kapitali i investuar Amortizimi i akumuluar Vlera kontabile e fundvitit Kapitali qarkullues Vlera totale e librit (3+4) Shitjet Kostoja e shitjeve Kostot e tjera Amortizimi Fitimi para tatimit (6-7-8-9) Tatimi me 34% Fitimi pas tatimit (10-11) 0 10,000 10,000 10,000 1 1,583 8,417 500 8,917 475 761 2,000 1,583 (3,869) (1,315) (2,554) 2 3,167 6,833 1,065 7,898 10,650 6,388 1,000 1,583 1,679 571 1,108 3 4,750 5,250 2,450 7,700 24,500 14,690 1,000 1,583 7,227 2,457 4,770 4 6,333 3,667 3,340 7,007 33,400 20,043 1,000 1,583 10,774 3,663 7,111 5 7,917 2,083 2,225 4,308 22,250 13,345 1,000 1,583 6,322 2,149 4,173 6 9,500 500 1,130 1,630 11,130 6,678 1,000 1,583 1,869 635 1,234 7 1,000 -

4,000 (4,000) (1,360) (2,640)

500 170 330

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Projekti IM&CTabela 6.2 - Parashikimet q reflektojn inflacionin (n $1000)0 10,000 10,000 10,000 1 1,583 8,417 550 8,967 523 837 2,200 1,583 (4,097) (1,393) (2,704) 2 3,167 6,833 1,289 8,122 12,887 7,729 1,210 1,583 2,365 804 1,561 Periudha 3 4 4,750 5,250 3,261 8,511 32,610 19,552 1,331 1,583 10,144 3,449 6,695 6,333 3,667 4,890 8,557 48,901 29,345 1,464 1,583 16,509 5,613 10,896 5 7,917 2,083 3,583 5,666 35,834 21,492 1,611 1,583 11,148 3,790 7,358 6 9,500 500 2,002 2,502 19,717 11,830 1,772 1,583 4,532 1,541 2,991 7 (1,949) -

Kapitali i investuar Amortizimi i akumuluar Vlera kontabile e fundvitit Kapitali qarkullues Vlera totale e librit (3+4) Shitjet Kostoja e shitjeve Kostot e tjera Amortizimi Fitimi para tatimit (6-7-8-9) Tatimi me 34% Fitimi pas tatimit (10-11)

4,000

(4,000) (1,360) (2,640)

1,449 493 956

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Projekti IM&CTabela 6.3 - Analiza e cash flow ($1000)Periudha0 1 2 3 4 5 6 7 8 9 Shitjet Kostoja e shitjeve Kostot e tjera Tatimi Cash flow nga veprimtaria (1-2-3-4) Ndryshimi i kapitalit qarkullues Kapitali i investuar dhe dif. vl.mb. Cash flow neto (5+6+7) Vlera aktuale me 20% 1 523 837 2,200 (1,393) (1,121) (550) (1,671) (1,393) 2 12,887 7,729 1,210 804 3,144 (739) 2,405 (1,670) 3 32,610 19,552 1,331 3,449 8,278 (1,972) 6,306 3,649 4 48,901 29,345 1,464 5,613 12,479 (1,629) 10,850 5,232 5 35,834 21,492 1,611 3,790 8,941 1,307 10,248 4,118 6 19,717 11,830 1,772 1,541 4,574 1,581 6,155 2,061 7

4,000 (1,360) (2,640) (10,000) (12,640) (12,640)

2,002 1,456 3,458 965

Vlera aktuale neto = +3,662 (shuma e 9)

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Projekti IM&C NPV duke prdorur cash flow nominale1,671 2,405 6,306 10,850 10,248 NPV ! 12,640 2 3 4 1.20 .20 .20 .20 .20 5 1 1 1 1 6,155 3,458 ! 3,662 ose $3,662,000 6 7 1.20 1.20

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Projekti IM&CTabela 6.4 Parashikimet analitike t cash flow pr vitin 3 ($1000)Cash Flow Parashikimi i t Hyrave Hyrje e parave = Shitjet $31,110 = 32,610 Ndryshimi i Kapitalit Qarkullues - Rritja e gjendjes s Arks - 1,500

Dalje e parave = Kostoja e mallrave t shitura, + Rritja e rezervave neto nga rritja kostot e tjera dhe tatimi e furnitorve $24,804 = (19,552+1,331+3,449) + (972-500)__________________ Cash Flow Neto = Hyrja e Parave - Dalja e Parave $6,306 = 31,110 - 24,804

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ProjektiIM&CTabela 4 - Zhvlersimi i lejuar tatimor sipas MACRS (Sistemi i modifikuar i rifitimit t prshpejtuar t kostos). Shifrat jepen si % ndaj bazs s amortizueshmeSke dula e zhvle r s imit tatimor s ipas klas s s pe riudh s rikupe rue s eVitet 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17-20 21 3-vjecar 33.33 44.45 14.81 7.41 5-vjecar 20 32 19.2 11.52 11.52 5.76 7-vjecar 14.29 24.49 17.49 12.49 8.93 8.92 8.93 4.45 10-vjecar 10 18 14.4 11.52 9.22 7.37 6.55 6.55 6.56 6.55 3.29 15-vjecar 5 9.5 8.55 7.7 6.93 6.23 5.9 5.9 5.9 5.9 5.9 5.9 5.91 5.9 5.91 2.99 20-vjecar 3.75 7.22 6.68 6.18 5.71 5.28 4.89 4.52 4.46 4.46 4.46 4.46 4.46 4.46 4.46 4.46 4.46 2.23

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Projekti IM&CTabela 6.6 - Pagesat tatimore (n $1000)Periudha0 1 2 3 4 5 6 Shitjet* Kostoja e shitjes* Kostot e tjera* Zhvleresimi tatimor Fitimi para tatimit (1-2-3-4) Tatimi me 34%*** 1 2 523 12,887 837 7,729 2,200 1,210 1,583 3,166 (4,097) 782 (1,393) 266 3 32,610 19,552 1,331 3,166 8,561 2,911 4 48,901 29,345 1,464 1,583 16,509 5,613 5 35,834 21,492 1,611 12,371 4,329 6 19,717 11,830 1,772 7

4,000 (4,000) (1,360)

6,115 1449** 2,079 493

* T dhna t marra nga Tabela 6.2, duke zbatuar amortizimin e prshpejtuar. ** Investimi ka vler kontabile neto 500. Prandaj IM&C duhet t paguaj nj tatim pr plusvlern baraz [1949-500=1449]*34% = $493 ***Nj pages tatimi negative prbn nj fluks hyrs, nse supozojm se IM&C mund t prdor kredin tatimore t projektit pr t paksuar t ardhurat nga projektet e tjer.Beshir Ciceri Copyright 2006 by The McGraw-Hill Companies, Inc. All rights reserved

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Projekti IM&CTabela 6.7-Analiza e cash flow t korigjuar (n $1000)Periudha1 2 3 4 5 6 7 8 9 1 Shitjet* 523 Kostoja e mallrave t shitura* 837 Kostot e tjera* 4,000 2,200 Tatimi** (1,360) (1,393) Cash flow nga operacionet (1-2-3-4) (2,640) (1,121) Ndryshimi ne kapitalin qarkullues (550) Kapitali i investuar (10,000) Cash flow neto (5+6+7) (12,640) (1,671) Vlera aktuale = +3,953 (shuma e 9) (12,640) (1,392) 0 2 3 4 5 12,887 32,610 48,901 35,834 7,729 19,552 29,345 21,492 1,210 1,331 1,464 1,611 266 2,911 5,613 4,329 3,682 8,816 12,479 8,402 (739) (1,972) (1,629) 1,307 2,943 2,044 6,844 3,961 10,850 5,232 9,709 3,902 6 19,717 11,830 1,772 2,079 4,036 1,581 5,617 1,881 7

493 (493) 2,002 1,949 3,458 965

NPV = +3,953 (shuma e 9)

* T dhna t marra nga Tabela 6.2 **T dhna t marra nga Tabela 6.6Beshir Ciceri Copyright 2006 by The McGraw-Hill Companies, Inc. All rights reserved

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Projekti IM&C NPV sipas Tabels 3 NPV sipas Tabels 6 $3,662,000 $3,953,000

Shkaku: Prfitimi fiskal nga amortizimi i prshpejtuar Viti 1 Viti 2 Viti 3 Viti 4Amortizimi i prshpejtuar Prfitimi fiskal 1583 538 3166 1076 3166 1076 1583 538

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Ndrveprimi i projekteveKur t investojm? Zgjedhja ndrmjet projekteve me jetgjatsi t ndryshme. Prdorimi optimal i aftsis prodhuese t makinave

Beshir Ciceri


6- 22

Ndrveprimi i projekteveKur t investojm?Projektet me NPV pozitive, mund t bhen m t leverdisshm, nse shtyhen n koh. NPV-ja aktuale rezulton rrjedhimisht Vlera aktuale e vlers s ardhshme t nj projekti t shtyr n koh.

NPV aktuale !

Vlera neto e ardhshme n datn t (1 r )t

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6- 23

Ndrveprimi i projekteveKur t investojm?Mund ta prisni nj pyll me pem n do moment, gjat 5 viteve t ardhshme. Duke ditur FV e shtyrjes n koh t prerjes, cila dat shpyllzimi maksimizon NPV-n aktuale, me norm skontimi 10%?Prerja 2 Viti 3

0

1

4

5

FV neto (n $1000) 50 64.4 77.5 89.4 100 109.4 Ndryshimi relativ i vlers 28.8% 20.3% 15.4% 11.9% 9.4%

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Ndrveprimi i projekteveKur t investojm?Mund ta prisni nj pyll me pem n do moment, gjat 5 viteve t ardhshme. Duke ditur FV e shtyrjes n koh t prerjes, cila dat shpyllzimi maksimizon NPV-n aktuale, me norm skontimi 10%?

64.4 NPV nse pylli pritet n vitin 1 ! ! 58.5 1.10Viti NPV Aktuale 0 50 1 58.5 2 3 64.0 67.2 4 68.3 5 67.9

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6- 25

Ndrveprimi i projekteveProjekte me jetgjatsi t ndryshmeKostoja ekuivalente vjetore Kur llogarisim NPV, shndrrojm cash flows e ardhshm n nj vler t vetme t tashme. Nganjher, mund t bjm t kundrtn: shndrrojm nj investim sot n nj rrjedhje ekuivalente cash flow n t ardhmen. Kjo ndodh kur projektet jan me jetgjatsi t ndryshme. Kostoja ekuivalente vjetore sht cash flow vjetor, i mjaftueshm pr t mbuluar koston e nj investimi, duke prfshir koston e kapitalit t ktij investimi deri n fund t jets ekonomike t tij.

Vlera Aktuale e Kostove Kostoja ekuivalent e vjetore = PVIFABeshir Ciceri Copyright 2006 by The McGraw-Hill Companies, Inc. All rights reserved

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Ndrveprimi i projekteveProjekte me jetgjatsi t ndryshme ShembullDuke iu referuar kostove t funksionimit t dy makinave, q jepen n vijim, dhe pr nj kosto kapitali 6%, przgjidhni makinn me kosto m t ult, duke prdorur metodn e kostos ekuivalente vjetore. Kostot ($1000) Makina C0 C1 C2 C3 PV@6% KEV 10.61 A +15 +5 +5 +5 28.37 B +10 +6 +6 21.00 11.45 Makina A sht m e mir, sepse KEV e saj sht m e ult.

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Ndrveprimi i projekteveProjekte me jetgjatsi t ndryshmeVlera aktuale neto vjetore (ANPV)Projekti A Projekti B Investimi fillestar $77,000 $105,000 Viti Hyrjet operative 1 30,000 40,000 2 35,000 25,000 3 40,000 25,000 4 0 30,000 5 0 20,000 6 0 15,000 Kostoja e kapitalit = 10%

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Ndrveprimi i projekteveProjekte me jetgjatsi t ndryshmeVlera aktuale neto vjetore (ANPV) NPV pr secilin projekt: NPVA = $9,220 NPVB = $12,155 N kt rast do t pranohej Projekti B, sepse ka NPV m madhe. Mirpo, projektet nuk kan jetgjatsi t njjt!?

Beshir Ciceri


6- 29

Ndrveprimi i projekteveProjekte me jetgjatsi t ndryshmeMetoda e vlers aktuale neto vjetore (ANPV) ANPVA = 9,220 / 2.487 = $4,527 ANPVB = 12,155 / 4.355 = $2,253 Konkluzuioni: Do t pranohet Projekti A, sepse ka ANPV m t madhe dhe jo Projekti B, q ka NPV m t madhe.

Beshir Ciceri


6- 30

Ndrveprimi i projektevePrdorimi optimal i aftsis prodhuese t makinave Kompania prdor dy makina, me kapacitet vjetor 1000 njsi secila. Makinat kan jetgjatsi t pafundme dhe asnj vler t mbetur. E vetmja kosto prbhet nga shpenzimet e ushtrimit, $2 pr njsi. Kompania ka aktivitet stinor, si rrjedhoj prodhimi vjetor i secils makin sht 750 njsi, nga 2000 njsi q sht kapaciteti. Norma e skontimit sht 10%. Kompania shqyrton zvendsimin e makinave t vjetra.

Prodhimi vjetor pr makineri

Dy makineri t vjetra 750 njsi

Kostoja operative pr makineri $2 v 750 ! $1,500 PV e kostos operative pr makineri 1,500/.10 ! $15,000 PV e kostos operative pr t dyja makinerit 2 v15,000 ! $30,000

Beshir Ciceri


6- 31

Ndrveprimi i projektevePrdorimi optimal i aftsis prodhuese t makinave Alternativa 1: Zvendsohen t dyja makinat e vjetraDy makineri t reja 750 njsi $6,000 $1v 750 ! $750 6,000 750/.10 ! $13,500 2 v13,500 ! $27,000

Prodhimi vjetor pr makineri Investimi fillestar pr makineri Kostoja operative pr makineri PV e kostos operative pr makineri PV e kostos operative pr dy makinerit

Kursimi: $30,000 - $27,000 = $3,000

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Ndrveprimi i projektevePrdorimi optimal i aftsis prodhuese t makinaveAlternativa 2: Zvendsohet vetm nj makin e vjetrProdhimi vjetor pr makineri Investimi fillestar pr makineri Kostoja operative pr makineri PV e kostos operative pr makineri PV e kostos operative pr dy makinerit nj makineri e vjetr 500 njsi 0 $2 v 500 ! $1,000 1,000/.10 ! $10,000 ................................$26,000 nj makineri e re 1,000 njsi $6,000 1v1,000 ! $1,000 6,000 1,000 / .10 ! $16,000

Duke zvendsuar vetm nj makin, kursejm $4,000 Duke i zvendsuar t dyja makinat, kursejm $3,000

NPV e investimit shtes vetm n nj makin sht $1,000Beshir Ciceri Copyright 2006 by The McGraw-Hill Companies, Inc. All rights reserved

6.marrja e vendimeve sipas npv

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