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Modulul 4 -�6WUDWHJLD�ILQDQFLDU
SSTTRRAATTEEGGIIAA FFIINN AANN CCIIAARR
x GHILQLUHD� QR LXQLL� GH� LQYHVWL LL�� FODVLILF UL� X]XDOH� DOH� DFHVWRUD� úL� HYLGHQ LHUHD�
elementelor financiare ale acestora;
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profitabilitate);
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x SUH]HQWDUHD� JHQHUDO � D� vPSUXPXWXOXL� REOLJDWDU� úL� DFFHQWXDUHD� DVSHFWHORU�
caracteristice ale REOLJD LXQLL�
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RSHUD LXQH�SUHFXP�úL�D�HWDSHORU�GHUXO ULL�XQXL�DVWIHO�GH�contract;
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metode dinamice bazate pe actualizare, metode patrimoniale, metode hibride;
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venituri superioare, dar probabile; ¾ în sens contabil: alocarea unei trezorerii disponibile pentru procurarea unui activ fix care va
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&/$6,),&$5($�,19(67, ,,/25 'XS �XQ�SULP�FULWHriu se pot clasifica în: ¾ LQYHVWL LL� WHKQLFH��DFKL]L LD��FRQVWUXF LD� úL�PRQWDMXO�XQRU�PDúLQL�� XWLODMH�� LQVWDOD LL��PLMORDFH�
de transport; ¾ LQYHVWL LL�XPDQH��IRUPDUHD��FDOLILFDUHD��VSHFLDOL]DUHD�HWF���D�SHUVRQDOXOXL� ¾ LQYHVWL LL�VRFLDOH��FRQVWUXF LD�vQ�vQWUHSUinderi a unei cantine restaurant etc.; ¾ LQYHVWL LL�ILQDQFLDUH��FXPS UDUHD�GH�WLWOXUL�GH�SDUWLFLSD LH�OD�DOWH�VRFLHW L�FRPHUFLDOH�HWF�� ¾ LQYHVWL LL�FRPHUFLDOH��SHQWUX�SXEOLFLWDWH�úL�UHFODP �HWF�
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e) %HQHILFLLOH� VXSOLPHQWDUH� VDX� HFRQRPLLOH� VDX� HFRQRPLLOH� GH� PDWHULDOH� úL� PDQRSHU �SUHYL]LELOH�F �VH�YRU�RE LQH��VXQW�IOX[XUL�GH�WUH]RUHULH�PDUJLQDOH�GHWHUPLQDte de punerea în IXQF LXQH�D�RELHFWLYXOXL�GH�LQYHVWL LL�
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DecizLD�GH�LQYHVWL LL�HVWH�LPSRUWDQW �GHRDUHFH� x HD�DQJDMHD] �YLLWRUXO�ILUPHL� x HD� LPSOLF � QXPHURDVH�GLUHF LL� SHQWUX� HYDOXDUHD� SURLHFWHORU�GH� OD�GLUHF LD� FRPHUFLDO � OD�
GLUHF LD�ILQDQFLDU ��OD�GLUHF LD�WHKQLF ��OD�GLUHF LD�GH�SHUVRQDO�
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1. EXPUNEREA CRITERIULUI $��(QXQ DUHD�FULWHULXOXL 2� LQYHVWL LH� HVWH� DFFHSWDELO � GDF � YDORDUHD� VD� DFWXDO � QHW � HVWH� SR]LWLY �� DGLF � GDF � HD�FRQWULEXLH�OD�FUHúWHUHD�YDORULL�DFWXDOH�WRWDOH�D�vQWUHSULQGHULL� Pentru a calcula criteriuO� 9$1� HVWH� VXILFLHQW � FDOFXODUHD� YDORULL� DFWXDOH� D� IOX[XULORU� GH�OLFKLGLW L�YLLWRDUH�JHQHUDWH�GH�LQYHVWL LH��DSRL�GHGXFHUHD�VXPHL�LQL LDOH�D�LQYHVWL LHL� 'HVHPQ P�SULQ�&t�IOX[XO�GH�OLFKLGLW L�SUHY ]XW��DúWHSWDW��GH�OD�LQYHVWL LH�SHQWUX�SHULRDGD�W��Suma LQYHVWL LHL� LQL LDOH� HVWH� ,0�� 5DWD� GH� DFWXDOL]DUH� FRQVLGHUDW � HVWH� 5t pentru un flux care se produce la finele perioadei t. 9$1�HVWH�DWXQFL�HJDO �FX�
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¾ GXUDWD� GH� YLD � D� LQYHVWL LHL� ILLQG� GH� Q� SHULRDGH�� ,QYHVWL LD� HVWH� DFFHSWDW � GDF � VH� SHUPLWH�FUHúWHUHD� YDORULL� vQWUHSULQGHULL�� DGLF � GDF � YDORDUHD� DFWXDO � D� IOX[XULORU� GH� OLFKLGLW L� HVWH�VXSHULRDU �FRVWXOXL�LQYHVWL LHL�,0.
Exemplu�� FRQVLGHU P� R� LQYHVWL LH� vQ� VXP � LQL LDO � ,0� � ������ 'XUDWD� VD� GH� YLD � HVWH� GH� �� DQL��Fluxurile de lLFKLGLW L��DúWHSWDWH��SUHYL]LRQDWH��VXQW�&1� �����úL�&2 = 700. Aceste fluxuri se produc UHVSHFWLY�OD�ILQHOH�SHULRDGHL���úL�SHULRDGHL����5DWD�GH�DFWXDOL]DUH�HVWH�GH�����SHQWUX�SHULRDGHOH���úL����6 �GHWHUPLQ P�9$1�SHQWUX�DFHDVW �LQYHVWL LH�
Perioada Factor de actualizare )OX[�GH�OLFKLGLW L 9DORDUHD�DFWXDO 0 = 1 -1.000 -1.000 1 1/(1,1) = 0.909 600 545,5 2 1/(1,1)2 = 0,826 700 578,5 VAN = 124
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B. Alegerea ratei de actualizare 5DWD�GH�DFWXDOL]DUH� UHSUH]LQW �FRVWXO�GH�RSRUWXQLWDWH�DO�FDSLWDOXOXL� LQYHVWLW�� LQkQG�FRQW�GH�ipoteza de ceUWLWXGLQH�FDUH�D�IRW�SXV ��UDWD�GH�DFWXDOL]DUH�HVWH�FRQVWLWXLW �GLQ�UDWD�GREkQ]LL�SH�SLD D�ILQDQFLDU ��FDUH�UH]XOW �GLQ�FRQIUXQWDUHD�RIHUWHL�úL�D�FHUHULL�GH�FDSLWDOXUL��$FHDVW �UDW �HVWH�XQLF �FD�urmare a ipotezelor avute în vedere. 'DF �� GLPSRWULY �� VH� LQWURGXFH� LQFHUWLWXGLQHD� vQ� UD LRQDPHQW�� GHWHUPLQDUHD� DFHVWHL� UDWH�depinde de costul riscului. &��9DULD LD�UDWHL�GREkQ]LL�úL�VWUXFWXUD�OD�WHUPHQ�D�UDWHORU�GREkQ]LL 1q�$OHJHUHD�UDWHL�GH�DFWXDOL]DUH�úL�SHULRDGD�vQ�FDUH�VXUYLQH�IOX[XO��UDW �D�GREkQ]LL�OD�YHGere,
UDW �GH����UHQWDELOLWDWH�OD�VFDGHQ � 5DWD� GH� DFWXDOL]DUH� ED]DW � SH� UDWD� GREkQ]LL� GH� SH� SLD D� ILQDQFLDU �� SRDWH� YDULD� vQ� ILHFDUH�SHULRDG ��GXS �HYROX LD�FRQGL LLORU�RIHUWHL�úL�FHUHULL�SH�SLD D�GH�FDSLWDO��'UHSW�FRQVHFLQ ��DU�WUHEXL�vQ�PRG�QRUPDO�V �VH�XWLOL]H]H�R�UDW �GH�DFWXDOL]DUH�GLIHULW �vQ�IXQF LH�GH�VFDGHQ D�IOX[XULORU�GH�OLFKLGLW L. 'HVHPQ P� SULQ� 0Rd –� UDWD� GREkQ]LL� H[LVWHQW � DVW ]L� SHQWUX� R� RSHUD LH� GH� vPSUXPXW� SH� R�GXUDW � GH� ³G´� DQL�� DFHDVW � UDW � GHQXPLW � UDW � OD� YHGHUH� UHSUH]LQW �� LQkQG� cont de ipoteza de FHUWLWXGLQH�� UDWD� GH� DFWXDOL]DUH� GH� XWLOL]DW� SHQWUX� XQ� IOX[� GH� OLFKLGLW L� FDUH� VH� SURGXFH� OD� ILQHOH�DQXOXL�³G´��$VWIHO��UHOD LD�GH�GHWHUPLQDUH�D�9$1-XOXL�DU�WUHEXL�V �VH�VFULH�
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2q Structura la termen a ratelor dobânzii Structura la termen a ratelor�GREkQ]LL�VH�SRDWH�FRQVWUXL�SXQkQG�vQ�UHOD LH�VFDGHQ D�úL�UDWH�GH�UHQWDELOLWDWH� D� GLIHULWHORU� SODVDPHQWH� FDUH� QX� GLIHU � GHFkW� SULQ� VFDGHQ D� ORU�� HD� SHUPLWH� DVWIHO�DQDOL]DUHD� UHOD LHL� GLQWUH� UDWHOH� SODVDPHQWHORU� SH� WHUPHQ� VFXUW� úL� UDWHOH� SODVDPHQWHORU� SH� WHrmen VFXUW��6WUXFWXUD�UDWHORU�OD�XQ�PRPHQW���VH�GHWHUPLQ �SRUQLQG�GH�OD�DQVDPEOXO�UDWHORU�OD�YHGHUH�0Rd FRQVWDWDWH�SHQWUX�GLIHULWH�VFDGHQ H�³G´� 6WUXFWXUD�OD�WHUPHQ�D�UDWHORU�SRDWH�vPEU FD�QXPHURDVH�IRUPH��(D�SRDWH�IL�FUHVF WRDUH��SODW �VDX�GHVFUHVF WRDUH��GXS �DQWLFLS ULOH�LQYHVWLWRULORU��2�VWUXFWXU �FUHVF WRDUH�UH]XOW �DQWLFLS UL�ED]DWH�SH� R� FUHúWHUH� D� UDWHORU� GH� GREkQG �� 2� VWUXFWXU � SODW � SUHVXSXQH� F � LQYHVWLWRULL� QX� DQWLFLSHD] �PRGLILF UL� DOH� UDWHORU� GREkQ]LL��2� VWUXFWXU � GHVFUHVF WRDUH� SUHVXSXQH�F � LQYHVWLWRULL� DQWLFLSHD] �R�VF GHUH�D�UDWHORU�
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VAN la 10%
A -1.000 1.000 1 -90,9
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$FFHSWDUHD� VDX� UHVSLQJHUHD� SURLHFWXOXL� SUHVXSXQH� F � VH� SRDWH� FDOFXOD� UDWD� GH� UHQWDELOLWDWH�FRQWDELO �� ILH� FDOFXODW � DVXSUD� DQVDPEOXOXL� DFWLYHORU� vQWUHSULQGHULL�� fie pornind de la o medie VHFWRULDO ��'DU�XQ�DVHPHQHD�SUDJ�HVWH�vQ�WRWDOLWDWH�DUELWUDU��UHQWDELOLWDWHD�PHGLH�D�vQWUHSULQGHULL�VDX�FHD�D�VHFWRUXOXL�SRDWH�IL�LQVXILFLHQW � 'DF �VH�GHWHUPLQ �9$1-XULOH�DIHUHQWH�FHORU�GRX �LQYHVWL LL�&�úL�'��HOH�VXQW�UHVSHFWLY GH������PLL�SHQWUX�&�úL�������PLL�SHQWUX�'��,QYHVWL LD�FDUH�HVWH�PDL�UHQWDELO �HVWH�GHFL�'��vQ�WLPS� FH� GLQ� SXQFW� GH� YHGHUH� DO� UDWHL� GH� UHQWDELOLWDWH� FRQWDELO � FHOH� GRX � SURLHFWH� VXQW�HFKLYDOHQWH�� $FHVW� FULWHULX� SRDWH� GHFL� V � FRQGXF � OD� GHFL]LL� FRQWUDUH� REiectivului de maximizare a valorii. 5DWD�GH�UHQWDELOLWDWH�FRQWDELO �VH�GLIHUHQ LD] �GH�9$1�SULQ�XUP WRDUHOH�
• VXPD�LQYHVWL LHL�HVWH�GHWHUPLQDW �SULQ�YDORDUHD�QHW �FRQWDELO �PHGLH��ÌQ�SULPXO�UkQG��QX� H[LVW � HFKLYDOHQ � vQWUH� GHILQL LD� FRQWDELO � úL� GHILQL LD� ILQDQFLDU � D� LQYHVWL LHL��DQXPLWH� FKHOWXLHOL� VXQW� FRQVLGHUDWH� SULQ� FRQWDELOLWDWH� FD� ILLQG� FKHOWXLHOL� úL� QX� FD�LQYHVWL LL.
• în al doilea rând, calculul astfel efectuat nu corespunde cu calculul financiar care se RE LQH� SRUQLQG� GH� OD� VXPHOH� HIHFWLY� GHEXUVDWH�� 6H� SRDWH� UHPDUFD� vQ� SOXV� IDSWXO� F ��calculul contabil depinde de modul de amortizare practicat;
• QX�H[LVW �LGHQWLWDWH�vQWUH�EHQHILFLL�DúD�FXP�VXQW�HOH�HYDOXDWH�vQ�FRQWDELOLWDWH�úL�IOX[XULOH�GH�OLFKLGLW L� )OX[XULOH� GH� OLFKLGLW L� FRUHVSXQG� GLIHUHQ HL� GLQWUH� vQFDV UL� úL� FKHOWXLHOL� VXSOLPHQWDUH�DQWUHQDWH�GH�LQYHVWL LH 'HWHUPLQDUHD�EHQHILFLXOXL�VH�IDFH�SRUQLQG�GH�OD�YHQLWXUL�úL�FKHOWXLHOL�úL�GHSLQGH�vQ�VSHFLDO�GH�PRGXO�GH�DPRUWL]DUH�UH LQXW�
• costul de oportunitate al fondurilor investite nu este luat în calcul; beneficiile nu sunt actualizate.
&ULWHULXO�UDWHL�GH�UHQWDELOLWDWH�FRQWDELO �DSDUH�vQ�FRQVHFLQ �FD�ILLQG�XQ�FULWHULX�PDL�FULWLFDELO�decât perioada de recuperare.
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
C. 5DWD�LQWHUQ �GH�UHQWDELOLWDWH 1q�*HQHUDOLW L 5DWD� LQWHUQ � GH� UHQWDELOLWDWH� �5,5�� VDX� UDWD� LQWHUQ � GH� UDQGDPHQW� HVWH� UDWD� GH� DFWXDOL]DUH�SHQWUX�FDUH�VH�RE LQH�R�9$1�QXO ��6H�GHWHUPLQ �UH]ROYkQG�HFXD LD�
0I)RIR1(
CVAN
n
1t0t
t =−+
= ∑=
&RQVLGHU P�R�LQYHVWL LH�vQ�VXP �GH�������������DOH�F UHL�IOX[XUL�GH�OLFKLGLW L�DúWHSWDWH�VXQW�respectiv 5.000.00�� úL� ����������� SHQWUX� DQLL� �� úL� ��� 5DWD� LQWHUQ � GH� UHQWDELOLWDWH� VH� GHWHUPLQ �rezolvând:
0000.900.11)RIR1(
000.000.10
)RIR1(
000.000.5VAN
2=−
++
+=
RIR-XO�DFHVWHL�LQYHVWL LL�HVWH�GH������6H�SRDWH�UHSUH]HQWD�JUDILF��HD�VH�VLWXHD] �OD�LQWHUVHF LD�IXQF LHL�UHSUH]HQWkQG�9$1-XO�vQ�IXQF LH�GH�UDWD�GH�DFWXDOL]DUH�úL�D[D�DEFLVHORU�
7DEHOXO����9$1�úL�UDWD�LQWHUQ �GH�UHQWDELOLWDWH VAN-XO�ILLQG�SR]LWLY�SHQWUX�WRDWH�UDWHOH�GH�DFWXDOL]DUH�LQIHULRDUH�UDWHL�GH�UHQWDELOLWDWH�LQWHUQ �VDX�VH�DMXQJH�OD�FRQFOX]LD�F ��LQYHVWL LD�HVWH�DFFHSWDELO �GDF �UDWD�GH�UHQWDELOLWDWH�D�LQYHVWL LHL�HVWH�VXSHULRDU �UDWHL�GH�DFWXDOL]DUH��DGLF �FRVWXOXL�GH�RSRUWXQLWDWH�IRQGXULORU�LQYHVWLWH� 6H�SRDWH�GHPRQVWUD�F �GDF �IXQF LD�FH�UHSUH]LQW �9$1�HVWH�PRQRWRQ �GHVFUHVF WRDUH�H[LVW �HFKLYDOHQ �vQWUH�FULWHULLOH�9$1�úL�5,5�GLQ�SXQFW�GH�YHGHUH�DO�DFFHSW ULL�SURLHFWXOXL� 7RWXúL�� 5,5� SUH]LQW � LQFRQYHQLHQWH� úL� FRQGXFH� vQ� DQXPLWH� FD]XUL� OD� GHFL]LL� QHFRQIRUPH�criteriului VAN. 2q�5DWD�LQWHUQ �GH�UHQWDELOLWDWH�úL�LSRWH]D�UHLQYHVWLULL� Atunci când se recurge la rata intHUQ �GH�UHQWDELOLWDWH�VH�FRQVLGHU �LSRWH]D�LPSOLFLW ��F �UDWD�GH�UHQWDELOLWDWH�D�IOX[XULORU�UHLQYHVWLWH�HVWH�FKLDU�UDWD�LQWHUQ �GH�UHQWDELOLWDWH� (YDOX P�YDORDUHD�YLLWRDUH�vQ�DQXO�Q�D�IOX[XULORU�UHLQYHVWLWH�OD�5,5�
∑=
−+=n
1t
tnt )RIR1(C)n(VF
3H�GH�DOW �SDUWH��GXS �GHILQL LD�5,5�VH�DMXQJH�OD�
∑= +
=n
1tt
t0
)RIR1(
CI
de unde se poate deduce multiplicând cei doi membri prin (1 + RIR)n astfel încât se ajunge la:
3.100
15% = RIR
VA
Rata de actualizare
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
∑=
− =+=+n
1t
tnt
n0 )n(VF)RIR1(C)RIR1(I
FHHD�FH�GHPRQVWUHD] �F �DWXQFL�FkQG�VH�XWLOL]HD] �5,5��VH�IDFH� LSRWH]D�F � UDWD�GH� UHLQYHVWLUH�HVWH�chiar RIR-XO��$FHDVW �LSRWH] �HVWH�GLIHULW �GH�FHD�FDUH�SUHVXSXQH�F �UHFXUJHUHD�OD�9$1�XQGH�UDWD�GH�UHLQYHVWLUH�HVWH�UDWD�GH�DFWXDOL]DUH��UDWD�GREkQ]LL�SH�SLD D�ILQDQFLDU �vQ�FD]�GH�FHUWLWXGLQH���,SRWH]D�GH� UHLQYHVWLUH� OHJDW � GH� 5,5� HVWH� LQDFFHSWDELO �� &ULWHULXO� 9$1� SUHVXSXQH� F � YD� IL� vQWRWGHDXQD�SRVLELO �SODVDUHD�IOX[XULORU�YLLWRDUH�OD�UDWD�GH�DFWXDOL]DUH�UH LQXW �FDUH�SRDWH�YDULD�FX�SHULRDGD�
'LYL]kQG�SULQ�����úL�SXQkQG�)RIR1(
1x
+= �VH�SRDWH�VFULH�DFHDVW �HFXD LH�sub forma:
100x2 – 100x + 16 = 0 &HOH� GRX � UDWH� LQWHUQH� GH� UHQWDELOLWDWH�� VROX LLOH� DFHVWHL� HFXD LL�� VXQW� UHVSHFWLY� GH� ���� úL�������3UHVXSXQHP�F � UDWD� GH�DFWXDOL]DUH� HVWH� GH� ����� ÌQ� DFHVW� FD]�9$1-ul este de –1.934.000. 'XS � FULWHULXO� 9$1-ului, proiectXO� HVWH� GHFL� GH� UHIX]DW� �GH� UHVSLQV��� &HOH� GRX � UDWH� LQWHUQH� GH�UHQWDELOLWDWH� ILLQG� VXSHULRDUH� UDWHL� GH�DFWXDOL]DUH�� DU� WUHEXL� GLPSRWULY � V � VH� DGRSWH� LQDGHFYDW�� QX�QXPDL�F �H[LVW �PDL�PXOWH�5,5-XUL�VH�GRYHGHúWH�úL�QLFL�XQXO�QX�HVWH�IRQGDW�GHFkW�DOWXO��GDU�SH�GH�DOW �SDUWH�FRQIUXQWDUHD�DFHVWRU�UDWH�FHOHL�RE LQXWH�XWLOL]kQG�9$1-ul. 3q Clasamente contradictorii ale proiectelor ÌQ� DQXPLWH� FD]XUL�� vQWUHSULQGHUHD� WUHEXLH� V � DOHDJ � vQWUH� PDL� PXOWH� SURLHFWH� úL�� GHFL�� V �VWDELOHDVF � XQ� FODVDPHQW�� &ODVDPHQWHOH� RE LQXWH� SRW� GLIHUL� GXS � FULWHULXO� UH LQXW�� 9$1� úL� 5,5��$FHVWH�GLYHUJHQ H�SRW�DYHD�PDL�PXOWH�RULJLQL��GLIHUHQ �vQWUH�VXPHOH�LQYHVWLWH�VDX�vQ�SURILOXO�IOX[XUL� a) 'LIHUHQ �vQWUH�VXPHOH�LQYHVWLWH�
&RQVLGHU P�GRX �SURLHFWH�$�úL�%�PXWXDO�H[FOXVLYH�DOH�F URU�VXPH�GLIHU �DVWIHO�vQFkW�XQ�DO�treilea proiect fictiv H = B –�$��D�F UHL�VXP �FRUHVSXQGH�GLIHUHQ HL�VXPHORU�OXL�$�úL�%�úL�DOH�F URU�IOX[XUL�VXQW�FRQVWLWXLWH�SULQ�IOX[XULOH�GLIHUHQ LDOH� 4q�&D]XUL�SDUWLFXODUH��LQH[LVWHQ D�5,5-XOXL�úL�SUH]HQ D�XQRU�UDWH�PXOWLSOH� a) ,QH[LVWHQ D�UDWHL�LQWHUQH�GH�UHQWDELOLWDWH�
3HQWUX�DQXPLWH�VHFYHQ H�DOH�IOX[XOXL��5,5-XOXL�QX�H[LVW ��&RQVLGHU P�LQYHVWL LD�XUP WRDUH��I0� �����úL�IOX[XULOH�&1 = 200, C2 = -�����5DWD�GH�DFWXDOL]DUH�HVWH�GH������(FXD LD�GH�GHWHUPLQDUH�D�RIR-ului este atunci:
0100)RIR1(
150
)RIR1(
2002
=−+
++
'LYL]kQG� SULQ� ���� úL� SXQkQG�)RIR1(
1x
+= � VH� SRDWH� VFULH� DFHDVW � HFXD LH� VXE� IRUPD�
WUDGL LRQDO �D�XQHL�HFXD LL�GH�JUDGXO�GRL� 1,5x2 – 2x + 1 = 0 $FHDVW �HFXD LH�QX�DUH�U G FLQL�UHDOH��HVWH��GHFL��LPSRVLELO �GHWHUminarea RIR-ului. 'DF �VH�HYDOXHD] �9$1-XO�DFHVWHL�LQYHVWL LL�OD�UDWD�GH�����VH�RE LQH�9$1� �-���úL�SURLHFWXO�este respins. b) 3UH]HQ D�XQRU�QXPHURDVH�UDWH�LQWHUQH�GH�UHQWDELOLWDWH�
ÌQ�FD]XO�vQ�FDUH�H[LVW �VFKLPE UL�GH�VHPQH�vQ�VHFYHQ D�IOX[XULORU�GH�OLFKLGLW L��HVWH�SRVLELO �RE LQHUHD� XQRU� QXPHURDVH� UDWH� LQWHUQH� GH� UHQWDELOLWDWH�� $VWIHO�� GDF � VH� FRQVLGHU � LQYHVWL LD�XUP WRDUH��VH�RE LQ�GRX �UDWH�
,QYHVWL LD�HVWH�vQWU-R�VXP �LQL LDO �GH������������IOX[XO�DQXOXL���HVWH�GH��������úL�IOX[XO�GLQ�anul 2 este de –��������(FXD LD�GH�GHWHUPLQDUH�D�5,5-ului se scrie atunci:
0000.600.1)RIR1(
000.10
)RIR1(
000.10VAN
2=−
+−
+=
$FHDVW �LQYHVWL LH�HVWH�GHQXPLW �LQYHVWL LH�GLIHUHQ LDO �
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
Proiect 6XP )OX[XUL�GH�OLFKLGLW L RIR în % VAN la 10% A 1.000 2.000 100 818 B 5.000 7.000 40 1.364
H = B - A 4.000 5.000 25 546 3URLHFWHOH� $� úL� %� VXQW� DFFHSWDELOH� GLQ� SXQFWXO� GH� YHGHUH� D� FHORU� �� FULWHULL�� ÌQ� DQVDPEOX��FODVDPHQWXO�HVWH�FRQWUDGLFWRULX�GXS �FULWHULXO�XWLOL]DW��&ULWHULXO�9$1�FRQGXFH�OD�DOHJHUHD�SURLHFWXOXL�%� FDUH� SHUPLWH� RE LQHUHD� XQXL� 9$1� GH� ������ ID � GH� ���� vQ� FD]XO� SURLHFWXOXL� $�� &ULWHULXO� 5,5�FRQGXFH�OD�R�FRQFOX]LH�FRQWUDU ��SURLHFWXO�$�OD�R�5,5�GH������ID �GH�����vQ�FD]XO�SURLHFWXOXL�%� &HOH� GRX � SURLHFWH� ILLQG� GH� GLPHQVLXQL� IRDUWH� GLIHULWH�� VH� SRDWH� vQWUHED� DVXSUD� XWLOL] ULL�GLIHUHQ HL� GH� IRQGXUL� vQWUH� FHOH� GRX � SURLHFWH�� &RQVLGHU P� GLIHUHQ D� GH� FDSLWDO� LQYHVWLW� GH� �������H[LVWHQW �vQWUH�SURLHFWHOH�$�úL�%��DFHDVW �GLIHUHQ �GH�FDSLWDOXUL�LQYHVWLWH�SHUPLWH�RE LQHUHD�XQXL�IOX[�GLIHUHQ LDO�GH������OD�ILQHOH�SHULRDGHL����5,5-XO�LQYHVWL LHL�GLIHUHQ LDOH�+�DVWIHO�FRQVWLWXLWH�HVWH�GH�����úL�9$1-XO�V X�GH����������9$1-XO�ILLQG�SR]LWLY�úL�5,5-ul fiind superior ratei de actualizare de ����HVWH�UHQWDELO��GXS �FHOH�GRX �FULWHULL�FDUH�VXQW�FRQFRUGDQWH��GH�D�UHDOL]D�LQYHVWL LD�GLIHUHQ LDO �H. Investitorul� WUHEXLH� GHFL� V � UHDOL]H]H�DQVDPEOXO� �SURLHFWXO�$�SOXV� LQYHVWL LD� GLIHUHQ LDO ��� DOWIHO�spus trebuie ales proiectul B.
ÌQ� FRQVHFLQ �� FRQVLGHUkQG� LQYHVWL LD� GLIHUHQ LDO �� XWLOL]DUHD� FHORU� �� FULWHULL�� 5,5� úL� 9$1�FRQGXFH�OD�DFHHDúL�FRQFOX]LH��WUHEXLH�DOHV�Sroiectul B, care singurul conduce la maximizarea VAN-ului. c) (JDOLWDWHD�VXPHORU�LQYHVWLWH��GLIHUHQ �vQ�SURILOXO�IOX[XULORU��6LWXD LD�GH�FRQWUDGLF LH�D�FULWHULLORU�
VH�SRDWH�vQWkOQL�vQ�DOWH�FD]XUL�GHFkW�GLIHUHQ D�vQWUH�GLPHQVLXQLOH�LQYHVWL LLORU��(D�VH�SRDWH�produce FD� XUPDUH� D� SURILOXOXL� IOX[XULORU� � GLIHULWH�� &RQVLGHU P� GRX � LQYHVWL LL� &� úL� '� FDUH� DX�FDUDFWHULVWLFLOH�XUP WRDUH�
Proiect Suma )OX[�GH�OLFKLGLW L RIR în % VAN la 9% C 155,22 100 100 14 13,74 D 155,22 0 221 12,5 15,44
K = D - C 0 -100 121 10 1,70 3HQWUX�R�UDW �GH�DFWXDOL]DUH�GH�����SURLHFWHOH�&�úL�'�GH�VXPH�LGHQWLFH�VXQW�FODVDWH�GLIHULW�GH�FULWHULLOH� 9$1� úL� 5,5�� 3HQWUX� R� UDW � GH� DFWXDOL]DUH� GH� ����� 9$1-urile lor sunt egale. Tabelul XUP WRU�LQGLF �]RQHOH�GH�FRQFRUGDQ �úL�GH�GLVFRUGDQ �D�FULWHriilor.
7DEHOXO����5HOD LD�vQWUH�9$1�úL�5,5 0
ZONA DE ',6&25'$1 VAN C > VAN D RIR C > RIR D
Proiect C
9% 12,5% 14% Rata de RIR D RIR C actualizare
=21$�'(�&21&25'$1 VAN C > VAN D RIR C > RIR D
,QWHUVHF LD�)LVFKHU �UDWD�GH�LQGLIHUHQ �GH�����
Proiect D
65,78 VAN
60
14,78
15,44 13,74
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
5q�5DWD�GH�DFWXDOL]DUH�QX�HVWH�FRQVWDQW �vQ�WLPS 'DF �VWUXFWXUD�OD�WHUPHQ�D�UDWHL�GREkQ]LL�QX�HVWH�SODW ��UDWD�GH�DFWXDOL]DUH�GH�XWLOL]DW�QX�PDL�HVWH�FRQVWDQW �vQ�WLPS��ÌQ�DFHVW�FD]�UDWD�OD�FDUH�WUHEXLH�FRPSDUDW �UDWD�LQWHUQ �GH�UHQWDELOLWDWH�HVWH�UDWD�GH�UHQWDELOLWDWH�OD�VFDGHQ ��FDUH�HVWH�UDWD�XQLF �FH�SHUPLWH�RE LQHUHD�DFHOHDúL�9$1� 2�LQYHVWL LH�GH�����������SHUPLWH�JHQHUDUHD�XQRU�IOX[XUL�GH���������vQ�DQXO���úL���������vQ�anul 2. 5DWHOH�GH�DFWXDOL]DUHD�VXQW�GH�����SHQWUX�DQXO���úL�GH�����SHQWUX�DQXO��� VAN-XO�DFHVWHL�LQYHVWL LL�HVWH��������úL�UDWD�GH�UHQWDELOLWDWH�OD�VFDGHQ �HVWH�GH���������5DWD�LQWHUQ �GH�UHQWDELOLWDWH�VH�SRDWH�GHWHUPLQD�DVWIHO�
0000.000.1)RIR1(
000.700
)RIR1(
000.6002
=−+
++
de undH� UH]XOW � R� 5,5� GH� ������� &XP� DFHDVWD� HVWH� VXSHULRDU � UDWHL� GH� UHQWDELOLWDWH� OD� VFDGHQ ��LQYHVWL LD�HVWH�DFFHSWDELO � ÌQ� FRQFOX]LH�� FKLDU� GDF � UDWD� LQWHUQ � GH� UHQWDELOLWDWH� DUH� IXQGDPHQWH� WHRUHWLFH� PDL� VROLGH�GHFkW� SHULRDGD� GH� UHFXSHUDUH� úL� UDWD� GH� UHQWDELOLWDWH� FRQWDELO �� DFHVW� OXFUX� QH� SRDWH� FRQGXFH� vQ�DQXPLWH� FD]XUL� OD� DOHJHUL� GLIHULWH� GHFkW� FHOH� LQGLFDWH� GH� 9$1�� &D� XUPDUH�� HD� WUHEXLH� XWLOL]DW �prudent.
D. Indicele de profitabilitate
,QGLFHOH�GH�SURILWDELOLWDWH�VH�FDOFXOHD] �UDSRUWkQG�YDORDUHD�DFWXDO �D�IOX[XULORU�GH�OLFKLGLW L�JHQHUDWH�GH�SURLHFWH�OD�VXPD�LQYHVWL LHL��$VWIHO��GDF �VH�FRQVLGHU �FHOH���SURLHFWH��SUHFHGHQWH�$�úL�%�vQ�VXPHOH�UHVSHFWLYH�GH�������úL��������YDORDUHD�DFWXDO �D�IOX[XULORU�HVWH�GH�������SHQWUX�$�úL�������pentru B. Indicele de profitabilitate este atunci:
Proiect A: 818,1000.1
8181
I
VAN1
I
VAIP
00=+=
+==
Proiect B: 273,1000.5
364,11IP =
+=
3URLHFWHOH� VXQW� DFFHSWDELOH� GDF � LQGLFHOH� HVWH� PDL� PDUH� GH� ��� vQ� DFHVW� FD]�� 9$1-ul este SR]LWLY��([LVW �GHFL�HFKLYDOHQ �vQ�FHHD�FH�SULYHúWH�DFFHSWDUHD�SURLHFtelor. În schimb, clasamentele RE LQXWH�SRW�IL�GLYHUJHQWH��$VWIHO��vQ�H[HPSOXO�FRQVLGHUDW�LQGLFHOH�GH�SURILWDELOLWDWH�DFRUG �SUHIHULQ �proiectului A, în timp ce VAN-XO�GHVHPQHD] �SURLHFWXO�%� �9$1�$�� ����� úL�9$1�%�� ���������&KLDU�GDF �SHQWUX�5,5��FRQWUDGLF LD�SRDWH� IL� UH]ROYDW �FRQVLGHUkQG� LQYHVWL LD�GLIHUHQ LDO �HJDO � FX�GLIHUHQ D�LQWUH�VXPHOH�SURLHFWHORU�$�úL�%� ,QGLFHOH�GH�SURILWDELOLWDWH�D�LQYHVWL LHL�GLIHUHQ LDOH�+�HVWH� • 6XP �GLIHUHQ LDO � ������� • 9DORDUHD�DFWXDO �D�IOX[XULORU�GLIHUHQ LDOH��������– 1.818 = 4.546; • Indice de profitabilitate: IP – 4.546/4.000 = 1,1365. ÌQ� FRQVHFLQ �� HVWH� UHQWDELO � UHDOL]DUHD� SURLHFWXOXL� %��9$1-XO� LQYHVWL LHL� GLIHUHQ LDOH� ILLQG�SR]LWLY�úL�LQGLFHOH�V X�GH�SURILWDELOLWDWH�ILLQG�PDL�PDUH�GH����,QGLFHOH�GH�SURILWDELOLWDWH�este criteriul cel mai apropiat de VAN.
4.1.4.EVALUAREA VALORII ACTUALE NETE
Utilizarea criteriului VAN presupune în prealabil estimarea ansamblului fluxului de OLFKLGLW L�OHJDWH�GH�LQYHVWL LH��$FHDVW �HVWLPDUH�WUHEXLH�V �VH�RSHUH]H�vQWU-un mod diferit�GLIHUHQ LDO��FX�úL�I U �UHDOL]DUHD�SURLHFWXOXL�GH�LQYHVWL LH�VWXGLDW���DGLF �FRQVLGHUkQG�DQVDPEOXO�LQFLGHQ HORU�SH�FDUH�OH�SRDWH�DYHD�LQYHVWL LD�DVXSUD�IOX[XOXL�GH�OLFKLGLW L�DO�vQWUHSULQGHULL�
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
���(VWLPDUHD�IOX[XULORU�GH�OLFKLGLW L Estimarea fluxurilRU�VH�SRDWH�IDFH�GLVWLQJkQG�vQ�PRG�DUELWUDU�WUHL�ID]H�vQ�YLD D�SURLHFWXOXL�GH�LQYHVWL LL��SHULRDGD�LQL LDO ��SHULRDGHOH�LQWHUPHGLDUH�úL�SHULRDGD�ILQDO �
A. 3HULRDGD�LQL LDO ��GHWHUPLQDUHD�FDSLWDOXOXL�LQYHVWLW� 1q Cheltuielile luate în calcul &RQVLGHU P�R�VLWXD LH�VLPSOLILFDW �vQ�FDUH�LQYHVWL LD�VH�IDFH��UHDOL]HD] ��OD�R�GDW ����GHEXWXO�SHULRDGHL�����'DF � LQYHVWL LD� V-DU� UHDOL]D� vQ�PDL�PXOWH�SHULRDGH��DU� WUHEXL� DWXQFL� V � VH�DFWXDOL]H]H�LHúLULOH�GH�IRQGXUL�FDUH�VH�SURGXF�vQ�SHULRDGHOH�XOWHULRDUH� Suma investi LHL� VH� FDOFXOHD] � HYDOXkQG� GLIHUHQ LDO� DQVDPEOXO� LQFLGHQ HORU� GLUHFWH� VDX�LQGLUHFWH�SH�FDUH�OH�SRDWH�DYHD�SURLHFWXO�DVXSUD�OLFKLGLW LORU�vQWUHSULQGHULL�OD�GDWD��� Trebuie astfel luate în calcul pentru un proiect dat: • IRQGXULOH� LQYHVWLWH� vQ� DFKL]L LRQDUHD� GH� LPRELOL] UL� FRUSRUDOH�� LPRELOL] UL� LQFRUSRUDOH� �EUHYHWH��
P UFL��OLFHQ H�HWF����LPRELOL] UL�ILQDQFLDUH� • FKHOWXLHOL� FRQWUDFWDWH� FX� RFD]LD� SXQHULL� vQ� IXQF LXQH� D� LQYHVWL LHL� �IRUPDUHD� SHUVRQDOXOXL��
cheltuieli de cercetare); • YDULD LD�GH�QHYRLH�GH�IRQG�GH�UXOPHQW�DQWUHQDW �GH�SURLHFW� • FRVWXULOH�GH�RSRUWXQLWDWH��GDF ��GH�H[HPSOX��vQWUHSULQGHUHD�XWLOL]HD] �XQ�WHUHQ�GH�FDUH�HD�GLVSXQH�
vQ�SUH]HQW�SHQWUX�UHDOL]DUHD�XQHL�QRL�LQYHVWL LL��HD�WUHEXLH�V �LD�vQ�FDOFXO�VXPD�DFHVWHL�LQYHVWL LL��OLFKLGLW LOH�SH�FDUH�OH-DU�IL�SXWXW�RE LQH�SULQ�YkQ]DUHD�DFHVWXL�WHUHQ�
• HIHFWHOH� LQGXVH� DVXSUD� DOWRU� SURLHFWH�� DVWIHO�� GDF � SURLHFWXO� DQWUHQHD] � FHVLXQHD� GH�PDWHULDOH��YHQLWXULOH�RE LQXWH�GLQ�DFHDVW �FHVLXQH�GLPLQXHD] �VXPD�LQYHVWLW �vQ�SHULRDGD�LQL LDO �
• LQFLGHQ HOH�ILVFDOH��WRDWH�LHúLULOH�GH�IRQGXUL�GH�RULJLQH�ILVFDO ��RULFDUH�DU�IL�IRUPD�GH�LPSR]LWDUH��DQWUHQDWH� GH� SURLHFW�� GLUHFW� VDX� LQGLUHFW� úL� FDUH� VH� SURGXF� vQ� SHULRDGD� LQL LDO �� WUHEXLH�� GH�DVHPHQHD��OXDWH�vQ�FRQVLGHUD LH�
2q Cheltuielile care nu se iau în calcul Anumite FKHOWXLHOL�QX�VXQW�GH�UH LQXW��$VWIHO��GDF �vQ�SUHDODELO���vQDLQWHD�SHULRDGHL�vQ�FDUH�VH�GHFLGH� LQYHVWL LD��DX�IRVW�DQJDMDWH�FKHOWXLHOL�GH�VWXGLX��DFHVWHD�QX� WUHEXLHVF�V �ILH� LQFOXVH�vQ�VXPD�LQYHVWLW �� GHRDUHFH� HOH� QX� PDL� LQWHUYLQ� vQ� GHFL]LH�� HVWH� YRUED� GH cheltuieli trecute care sunt considerate drept fonduri pierdute (sunk costs). Exemplu���)LH�R�LQYHVWL LH�vQ�VXP �GH������������)OX[XULOH�DúWHSWDWH��SUHYL]LRQDWH��SHQWUX�XUP WRULL�FLQFL�DQL�VXQW�GH���������úL�UDWD�GH�DFWXDOL]DUH�HVWH�GH������ÌQ�SUHDODELO��înainte de data de decizie), vQWUHSULQGHUHD�D�DQJDMDW�FKHOWXLHOL�GH�VWXGLL�vQ�VXP �GH������������OD�vQFHSXWXO�DQXOXL�SUHFHGHQW��/D�momentul (perioada) 0, VAN-XO�LQYHVWL LHL�HVWH�GH�
∑=
=−=5
1tt
000.137000.000.1)1,1(
000.300VAN
úL�LQYHVWL LD�HVWH�DFFHSWDW ��QX�VXQW�OXDWH�vQ�FRQVHFLQ �FKHOWXLHOLOH�GH�VWXGLL� 'DF ��GLPSRWULY ��HYDOXDUHD��GHWHUPLQDUHD��UHQWDELOLW LL�DU�IL�DYXW�ORF�OD�vQFHSXWXO�SHULRDGHL�SUHFHGHQWH�� FX� DFHOHDúL� GDWH�� UH]XOWDWXO� DU� IL� IRVW� GLIHULW�� 9$1-ul evaluat la momentul (perioada) z = -1, ar fi fost:
∑=
−=−−=6
2tt
200.875000.000.11,1
000.000.1
)1,1(
000.300VAN
úL�LQYHVWL LD�Q-DU�IL�IRVW�DFFHSWDELO �
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
B. Perioade intermediare: determinarea fluxurilor
1q� 'RX � SULQFLSLL� IXQGDPHQWDOH�� HYDOXDUHD� GLIHUHQ LDO � úL� LQGHSHQGHQ D� vQ� UDSRUW� FX�PRGDOLW LOH�GH�ILQDQ DUH�
a) (YDOXDUHD�GLIHUHQ LDO �D�IOX[Xrilor. &D� úL� SHQWUX� GHWHUPLQDUHD� LQYHVWL LHL� LQL LDOH�� WUHEXLH� UD LRQDW� GLIHUHQ LDO� SHQWUX� HYDOXDUHD�IOX[XULORU� JHQHUDWH� GH� LQYHVWL LD� FRQVLGHUDW �� $FHVW� SULQFLSLX� LPSOLF � FX� SUHF GHUH� F � QX� WUHEXLH�QLFLRGDW �LPSXWDWH�FKHOWXLHOL�IL[H�OHJDWH�GH�DOWH�DFWLYLW L�DOH�vQWUHSULQGHULL�SHQWUX�D�HYDOXD�IOX[XULOH�OHJDWH�GH�XQ�SURLHFW�GH�LQYHVWL LL� Exemplu��)LH�R� vQWUHSULQGHUH�FDUH�H[HUFLW �R�XQLF �DFWLYLWDWH�FDUH� vL�DGXFH�XQ�IOX[�GH������������vQDLQWH� GH� LPSXWDUHD� D� ���������� FKHOWXLHOL� IL[H� SO WLELOH�� $FHDVW � vQWUHSULQGHUH� SURLHFWHD] � V �vQWUHSULQG �R�QRX � LQYHVWL LH�FX�XQ�DOW�SURILO� GH�DFWLYLWDWH��'XS �GHGXFHUHD�FKHOWXLHOLORU�YDULDELOH��IOX[XO�DúWHSWDW�FD�XUPDUH�D�DFHVWHL�QRL� LQYHVWL LL�HVWH�GH�������������$FHVW�QRX�SURLHFW�DQWUHQHD] �����������FKHOWXLHOL�IL[H�SO WLELOH�VXSOLPHQWDUH�� LQkQG�FRQW�GH�IDSWXO�F �VHUYLFLLOH�JHQHUDOH�YRU�SXWHD�IL�XWLOL]DWH�SHQWUX�UHDOL]DUHD�DFHVWHL�QRL�DFWLYLW L�
7DEHOXO����)OX[XUL�GLIHUHQ LDOH�úL�UHSDUWL LD�FKHOWXLHOLORU�IL[H
Întreprinderea vQDLQWH�GH�LQYHVWL LH�(activitate veche)
ÎQWUHSULQGHUHD�GXS �LQYHVWL LH��YHFKHD���
noua activitate)
9DULD LD�LQYHVWL LHL��QRXD�
activitate) 2SWLF �ILQDQFLDU ��I U �UHSDUWL LD cheltuielilor fixe) )OX[��GXS �FKHOWXLHOL�YDULDELOH� 10.000.000 20.000.000 10.000.000 SO WLELOH� Cheltuieli fixH��SO WLELOH� 5.000.000 7.000.000 2.000.000 Flux final 5.000.000 13.000.000 8.000.000 2SWLFD�FRQWDELOLW LL�DQDOLWLFH )OX[��GXS �FKHOWXLHOL�YDULDELOH 10.000.000 20.000.000 10.000.000 SO WLELOH� &KHOWXLHOL�IL[H��SO WLELOH� 4.000.000 7.000.000 3.000.000 Flux final 6.000.000 13.000.000 7.000.000
'DF � VH� UD LRQHD] � vQ� WHUPHQL� GLIHUHQ LDOL�� IOX[XO� GH� UH LQXW� SHQWUX� HYDOXDUHD� UHQWDELOLW LL�noului produs este de 10.000.000 –����������� ������������ÌQ�QLFL�XQ�FD]�QX� WUHEXLH�V �VH�LPSXWH�asupra acestXL�IOX[�R�FRW �SDUWH�D�FKHOWXLHOLORU�IL[H�FH�SURYLQ�GLQ�YHFKHD�DFWLYLWDWH��5D LRQDPHQWXO�ILQDQFLDU� VH�VHSDU � WRWDO�GLQ�DFHVW�SXQFW�GH� UD LRQDPHQWXO�SUDFWLFDW�GH�FRQWDELOLWDWHD�DQDOLWLF �FDUH�FRQVW ��FHO�PDL�DGHVHD��GLQ�UHSDUWL]DUHD�FKHOWXLHOLORU�IL[H�vQWUH�GLIHULWH�DFWLYLW L� b) ,QGHSHQGHQ D�GH�HYDOXDUH�D�IOX[XULORU�vQ�UDSRUW�GH�PRGDOLW LOH�GH�ILQDQ DUH (YDOXDUHD� WUHEXLH� V � VH� IDF � vQWU-XQ� PRG� LQGHSHQGHQW� GH� PRGDOLW LOH� GH� ILQDQ DUH� DOH�LQYHVWL LHL��(VWH�YRUED�GH�D�P VXUD��FXDQWLILFD��IOX[XULOH�FH�SURYLQ�FD�XUPDUH�D�XWLOL] ULL�DFWLYXOXL�vQ�VFRSXO� GH� D� HYDOXD� UHQWDELOLWDWHD� VD� HFRQRPLF �� &RPSDUD LD� DFHVWHL� UHQWDELOLW L� FX� H[LJHQ HOH�aporturilor de fonduri se va face ulterior, actualizând fluxurile la costul de oportunitate al FDSLWDOXOXL��FDUH�UHSUH]LQW �FRVWXO�GH�ILQDQ DUH��5HQWDELOLWDWHD�GHJDMDW �WUHEXLH�V �ILH�GHVWXO�GH�PDUH�SHQWUX�FD�vQWUHSULQGHUHD�V �SRDW �UHPXQHUD�DSRUWRULL�GH�IRQGXUL��ÌQ�FRQVHFLQ ��QX�WUHEXLH�vQ�QLFL�XQ�FD]�OXDWH�vQ�FDOFXO�FKHOWXLHOLOH�ILQDQFLDUH�úL�HFRQRPLLOH�GH�LPSR]LWH�OHJDWH�GH�aceste cheltuieli pentru GHWHUPLQDUHD�IOX[XULORU��R�DVHPHQHD�SURFHGXU �DU�FRQGXFH� OD�LQFOXGHUHD�GH�GRX �RUL�D�FRVWXOXL�GH�ILQDQ DUH��R�SULP �GDW �vQ�HYDOXDUHD�IOX[XOXL��R�D�GRXD�RDU �vQ�DFWXDOL]DUH�
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
2q Metodele uzuale de determinare a fluxurilor de lichidLW L 6H�UHFXUJH�OD�GRX �PHWRGH�SHQWUX�P VXUDUHD��FXDQWLILFDUHD��IOX[XULORU� a) Metoda 1��HVWLPDUHD�GLUHFW �D�IOX[XULORU�GH�OLFKLGLW L� $FHDVW �SULP �PHWRG �FRQVW � vQ�HYDOXDUHD�GLUHFW �D�IOX[XULORU�GH� OLFKLGLW L��FRQVWUXLQG�XQ�buget de trezorerie.
TrebuiH�� GHFL��PDL� vQWkL� V � VH� HVWLPH]H� IOX[XULOH�GH� WUH]RUHULH�GH� LQWUDUH�� DFHVWH� IOX[XUL� GH�intrare pot rezulta fie dintr-XQ�VXSOLPHQW�GH� vQFDV UL�� ILH�GLQ�HFRQRPLL��'H�DVHPHQHD��IOX[XULOH�GH�LHúLUH�SRW�ILQ�FRQVWUXLWH�ILH�SULQ�FKHOWXLHOL�VXSOLPHQWDUH��ILH�SULQtr-R�SLHUGHUH�GH�vQFDV UL��2�LQYHVWL LH�SRDWH�� vQ�DQXPLWH�FD]XUL��V �DQWUHQH]H�R� OLSV �GH�FkúWLJ�DVXSUD�DOWRU� LQYHVWL LL�GH�FDUH�WUHEXLH� LQXW�FRQW��ÌQ�RULFH�FD]��WUHEXLH�LJQRUDWH�LQFLGHQ HOH�PRGXOXL�GH�ILQDQ DUH�D�LQYHVWL LHL� ,QFLGHQ D�ILVFDO ��LPSR]LW�SH�SURILW��WUHEXLH�DWXQFL�V �ILH�HYDOXDW �vQ�PRG�VHSDUDW��PRGXO�V X�de evaluare fiind bazat pe contabilitate). b) Metoda 2��GHWHUPLQDUHD�FRQWDELO �D�IOX[XULORU $FHDVW �D��-D�PHWRG �HVWH�PDL�IUHFYHQW�XWLOL]DW ��HD�VH�ED]HD] �SH�FRQWXO�GH�UH]XOWDWH�SHQWUX�detHUPLQDUHD�IOX[XULORU�GH�OLFKLGLW L�
%D]D�PHWRGHL�FRQVW �vQ�FRQVWUXLUHD�XQXL�FRQW�GH�UH]XOWDWH�VFKHPDWLF�úL�GLIHUHQ LDO��FX�úL�I U �LQYHVWL LL�úL�LJQRUkQG�FKHOWXLHOLOH�ILQDQFLDUH�
7DEHOXO����&RQW�GH�UH]XOWDWH�GLIHUHQ LDO ) U �LQYHVWL LH &X�LQYHVWL LH DLIHUHQ Cifra de afaceri 50.000 60.000 10.000 Costuri variabile 30.000 33.000 3.000 Marja asupra costurilor variabile 20.000 27.000 7.000 &KHOWXLHOL�IL[H��I U �DPRUWL]DUH� 10.000 11.000 1.000 Excedent btur de exploatare 10.000 16.000 6.000 Amortismente 4.000 6.000 2.000 Rezultat economic 6.000 10.000 4.000 Impozit pe profit (cota de 37%) 2.220 3.700 1.480 5H]XOWDW�HFRQRPLF�GXS �LPSR]LW 3.780 6.300 2.520 Flux de fonduri = EBE - Impozit 7.780 12.300 4.520
Fluxul final este un flux de fonduri, adLF � HO� D� IRVW� HYDOXDW� SRUQLQG� GH� OD� GDWHOH� GH�vQUHJLVWUDUH�FRQWDELOH�úL�GH�OD�QR LXQLOH�FRQWDELOH��YHQLWXUL�úL�FKHOWXLHOL��(O�VH�GLIHUHQ LD] �DVWIHO�GH�IOX[XO�GH�OLFKLGLW L�FDUH�HVWH�GHWHUPLQDW�SH�ED]D�GDWHORU�HIHFWLYH�DOH�UHQWDELOLW LL�úL�DOH�LHúLULORU�de fonduri. 3HQWUX� GHWHUPLQDUHD� IOX[XULORU� GH� OLFKLGLW L� SRUQLQG� GH� OD� IOX[XULOH� GH� IRQGXUL� WUHEXLH� LQXW�FRQW�GH�GHFDODMHOH�FDUH�VXUYLQ�vQWUH�GDWHOH�GH�vQUHJLVWUDUH�FRQWDELO �úL�GDWHOH�HIHFWLYH�GH�vQFDV UL�úL�SO L��GH�H[HPSOX��GHFDODMXO�GLQWUH� vQFDV UL�úL�FLIUD�GH�DIDFHUL���3HQWUX�HYDOXDUHD�DFHVWRU�GHFDODMH�� WUHEXLH�P VXUDW �SHQWUX�ILHFDUH�SHULRDG �YDULD LD�QHYRLL�GH�IRQG�GH�UXOPHQW�DQWUHQDW �GH�SURLHFWXO�GH�LQYHVWL LL� ÌQ� H[HPSOXO� SUHFHGHQW�� GDF � VH� HYDOXHD] � DFHDVW � YDULD LH� OD� ������� IOX[XO� GH� OLFKLGLW L�înainte de plata impozitului pe profit este de: 6.000 –������� ��������'DF �VH�SUHVXSXQH�F �IOX[XO�GH�OLFKLGLW L�DQWUHQDW�GH�LPSR]LW�VH�SURGXFH�OD�GDWD�GH�vQUHJLVWUDUH�FRQWDELO ��IOX[XO�GH�OLFKLGLW L�ILQDO�HVWH��������IOX[�GH�OLFKLGLW L�vQDLQWH�Ge impozit) – 1480 (impozit) = 3.520. 'DF �VH�UH LQ�IOX[XULOH�GH�IRQGXUL�vQ�HFXD LD�9$1-XOXL��WUHEXLH�DWXQFL�FRQVLGHUDWH�YDULD LLOH�QHYRLL�GH�IRQG�GH�UXOPHQW�FRQVLGHUDW �FD�LQYHVWL LH�VXSOLPHQWDU �vQ�ILHFDUH�DQ� Exemplu��3UHVXSXQHP�F � LQYHVWL LD�VWXGLDW � vQ� WDEHOXO�SUHFHGHQW�HVWH� vQ�VXP �GH���������$FHDVW �VXP � LD� vQ� FDOFXO� YDULD LD� QHYRLL� GH� IRQG� GH� UXOPHQW� VXE� IRUPD� XQXL� VWRF� VXSOLPHQWDU� GH� �������SURYRFDW �GH�LQYHVWL LH�
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
)OX[XO�GH� OLFKLGLW L�DQXDOH�GXS �GHGXFHUHD� LPSR]LWXOXL�SH�SURILW�HVWH�GH��������'Xrata de YLD � D� LQYHVWL LHL� HVWH� GH� �� DQL��1HYRLD� GH� IRQG� GH� UXOPHQW� WRWDO � DQWUHQDW � GH� LQYHVWL LH� HVWH� GH������� vQ� DO� FLQFLOHD� DQ��9DULD LD� DQXDO � D� DFHVWHL� LQYHVWL LL� D� IRVW� GH� ������� (D� HVWH� UHFXSHUDW � OD�finele celui de-al cincilea an. Evaluarea VAN-XOXL�SRUQLQG�GH�OD�IOX[XUL�GH�OLFKLGLW L��3HQWUX�R�UDW �GH�DFWXDOL]DUH�GH������HFXD LD�9$1-ului se scrie:
∑=
=−+=5
1t5t
069.6000.11 )1,1(
000.6
)1,1(
520.3 VAN
Evaluarea VAN-ului pornind de la fluxuri de fonduri. Considerând demersul bazat pe fluxuri de fonduri se ajunge la�HFXD LD�XUP WRDUH�
∑ ∑= =
=−+−=5
1t
5
1t5tt
069.6 000.11 )1,1(
000.6
)1,1(
000.1
)1,1(
520.4 VAN
3q�,QFLGHQ D�LQIOD LHL�DVXSUD�FDOFXOXOXL�9$1-ului ,QIOD LD�DUH�HIHFWH� LPSRUWDQWH�DVXSUD�UHQWDELOLW LL�UHDOH�D� LQYHVWL LHL��(D� LPSOLF �QHFHVLWDWHD�GH�D�IL�FRHUHQW�vQ�SURFHGXUD�GH�DOHJHUH�D�LQYHVWL LHL��'DF �VH�XWLOL]HD] �FULWHULXO�9$1-ului, trebuie OXDW�vQ�FDOFXO��VLPXOWDQ��HIHFWHOH�LQIOD LHL�DVXSUD�IOX[XULORU�GH�OLFKLGLW L�úL�DVXSUD�UDWHL�GH�DFWXDOL]DUH�
A. 5DWD�GH�DFWXDOL]DUH�úL�OXDUHD�vQ�FDOFXO�D�LQIOD LHL
5DWD� GH� DFWXDOL]DUH� UHSUH]LQW � FRVWXO� GH� RSortunitate a fondurilor investite. Aportorii de FDSLWDO� �GH LQ WRULL� GH� FDSLWDO�� VROLFLW � GH� OD� LQYHVWL LLOH� ORU� R� UDW � GH� UHQWDELOLWDWH� UHDO � 5�� FDUH� vL�UHPXQHUHD] � SHQWUX� VDFULILFLXO� FRQVXPXOXL� LPHGLDW�� DFHDVW � UDW � HVWH� LQGHSHQGHQW � GH� LQIOD LH��,QVLVW P�DVXSUD�IDSWXOXL�F �WUHEXLH�DFWXDOL]DW��FKLDU�GDF �UDWD�LQIOD LHL�HVWH�QXO �
'DF � LQYHVWL LD� HVWH� GH� ������ úL� GDF � UDWD� GH� UHQWDELOLWDWH� UHDO � FXUHQW � HVWH� GH� ���� XQ�LQYHVWLWRU�YD�SULPL�R�VXP �GH�������OD�FDS WXO�XQXL�DQ�
3UHVXSXQHP�vQ�SUH]HQW�R�LQIOD LH�D�F UHL�UDW �DQXDO �HVWH�GH������'DF �YHQLWXULOH�LQYHVWL LHL�QX�VXQW�DMXVWDWH�OD�LQIOD LH��LQYHVWLWRUXO�YD�vQFDVD�vQWRWGHDXQD��������GDU�DFHDVW �VXP �YD�IL�SLHUGXW ��GLQ�FDX]D�LQIOD LHL������GLQ�SXWHUHD�VD�GH�FXPS UDUH��3RVLELOLW LOH�GH�FRQVXP�DOH�LQYHVWLtorului vor IL�PDL�PDUL�GHFkW�OD�vQFHSXWXO�DQXOXL��,QL LDO��HO�SXWHD�FRQVXPD��������XQ�DQ�PDL�WkU]LX�HO�QX�YD�PDL�putea consuma decât 1.050/1,1 –� ������� OD� vQFHSXWXO� DQXOXL�� 5DWD� GH� UHQWDELOLWDWH� UHDO � 5� D�LQYHVWL LHL�HVWH�DWXQFL�GH�
(954,5 – 1.000)/1.000 = -4,55% úL��GHVHPQkQG�SULQ�U�UDWD�QRPLQDO �D�SODVDPHQWXOXL��GH����úL�SULQ�M�UDWD�LQIOD LHL��GH������VH�SRDWH�VFULH�SHQWUX�R�LQYHVWL LH�GH���
1)j1(
)r1(R −
++= �úL� [ ] RjjR1)j1)(R1(r ++=−++=
([SUHVLD�UDWHL�QRPLQDOH�U�HVWH�XQHRUL�VLPSOLILFDW ��SUHVXSunând termenul Rj neglijabil, sub IRUPD�DSUR[LPDWLY �� jRr +≅ �UDWD�QRPLQDO �HVWH�HJDO �FX�VXPD�GLQWUH�UDWD�UHDO �úL�UDWD�LQIOD LHL�
Flux de OLFKLGLW L
Recuperarea nevoii de fond
de rulment
,QYHVWL LH�LQL LDO
Flux de fonduri
9DULD LD�DQXDO �D�
NFR
Recuperarea NFR
,QYHVWL LD�LQL LDO
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
$WXQFL�FkQG�VH�FRQVLGHU �UDWH�DQWLFLSDWH��DFHDVW �UHOD LH�HVWH�UHOD LD�OXL�)LVFKHU��HD�H[SULP �F ��UDWD�QRPLQDO �REVHUYDW �HVWH�HJDO �FX�UDWD�UHDO �DQWLFLSDW �5�FUHVFXW �FX�UDWD�LQIOD LHL�DQWLFLSDWH�M� ÌQ�FRQVHFLQ ��SHQWUX�D�RE LQH�R�UDW �GH�UHQWDELOLWDWH�UHDO �GH����LQYHVWLWRUXO�� LQkQG�FRQW�GH�LQIOD LH��WUHEXLH�V �RE LQ �R�UDW �GH�UHQWDELOLWDWH�QRPLQDO �GH��������VDX�GH�����XWLOL]kQG�UHOD LD�GH�DSUR[LPDUH���DGLF �XQ�YHQLW�GH�����OD�LQYHVWL LD�VD�GH�������
B. Indexarea fluxurilor &RQVLGHU P� UHOD LD� YDORULL� DFWXDOH� �9$�� úL� SUHVXSXQHP� F � DQVDPEOXO� IOX[XULORU� V � ILH�
LQGH[DWH�OD�UDWD�LQIOD LHL�M��vQWU-un mod simetriF�UDWH�GH�DFWXDOL]DUH�QRPLQDO �U�LQWHJUHD] �LQIOD LD��6H�poate atunci scrie:
[ ]∑ ∑ ∑
= = = +=
+++=
++=
n
1t
n
1t
n
1tt
tt
tt
t
tt
)R1(
C
)j1)(R1(
)j1(C
)r1(
)j1(CVA
6H� DMXQJH� OD� FRQFOX]LD� F �� GDF � DQVDPEOXO� IOX[XULORU� VXQW� LQGH[DWH� SHQWUX� D� LQH� FRQW� GH�LQIOD LH�úL�GDF �UDWD�GH�DFWXDOL]DUH�LQWHJUHD] �LQIOD LD��9$�RE LQXW ��úL�GHFL�9$1��HVWH�LGHQWLF �
ÌQ� FRQVHFLQ �� SHQWUX� FD� LQIOD LD� V � ILH� QHXWU �� WUHEXLH� FD� WRDWH� IOX[XULOH� V � ILH� LQGH[DWH� OD�DFHHDúL�UDW ��2UL��QX�HVWH�FD]XO��VDODULLOH�DX�HYROXDW�PXOW�WLPS�PDL�UDSLG�GHFkW�DQXPLWH�SRVWXUL�FDUH�intervin în determinarea fluxurilor de exploatare. Anumite rubrici, precum cea a amortismentelor VXQW�FDOFXODWH�SH�ED]D�YDORULORU�FRQWDELOH�LVWRULFH�úL�HFRQRPLLORU�GH�LPSR]LW�SH�FDUH�HOH�OH�SHUPLW��QX�XUPHD] �ULWPXO�LQIOD LHL��,PHGLDW��FHO�PDL�DGHVHD��XUPHD] �R�VF GHUH�D�UHQWDELOLW LL�UHDOH� Exemplu�� FRQVLGHU P� R� LQYHVWL LH� GH� ������ FDUH� JHQHUHD] � XQ� IOX[� GH� IRQGXUL� GH� H[SORDWDUH��YDULD LD�(%(�DQWUHQDW �GH�LQYHVWL LH��GH������WLPS�GH���DQL��,QYHVWL LD�LQL LDO �FXSULQGH�����LQYHVWL LL�vQ�1)5�GH�H[SORDWDUH��FDUH�U PkQH�VWDELO �vQ�WHUPHQL�UHDOL�WLPS�GH���DQL��6H�SUHVXSXQH�F �SUH XO�GH�FHVLXQH�DO�LQYHVWL LHL�vQ�DO�FLQFLOHD�DQ�HVWH�GH������5DWD�GH�DFWXDOL]DUH�UHDO �³5´�HVWH�GH�����UDWD�GH�LQIOD LH� DQWLFLSDW � ³M´� GH� ��� úL� UDWD� GH� DFWXDOL]DUH� QRPLQDO � ³U´� GH� ����� 'HWHUPLQ P� 9$1-ul acestei�LQYHVWL LL�FRQVLGHUkQG�VXFFHVLY���LSRWH]H��LQIOD LH�QXO ��LQIOD LH�GH�����)OX[XULOH�GH�IRQGXUL�GH� H[SORDWDUH� 1)5� úL� SUH XO� GH� FHVLXQH� VXQW� SUHVXSXVH� LQGH[DWH� OD� LQIOD LH�� 5DWD� GH� FDOFXO� D�LPSR]LWXOXL�SH�SURILW�VH�SUHVXSXQH�D�IL�GH�����SHQWUX�XúXULQ �vQ�Falcule. Ipoteza 1��LQIOD LH�QXO
Tabelul 6: Evaluarea VAN-XOXL�I U �OXDUHD�vQ�FDOFXO�D�LQIOD LHL
Anii 1 2 3 4 5 Flux de fonduri de exploatare 700 700 700 700 700 Amortismente 200 200 200 200 200 Rezultat înainte de impozit 500 500 500 500 500 Impozit pe profit (cota de 50%) 250 250 250 250 250 1. Flux de fonduri înainte de impozit 450 450 450 450 450 ���9DULD LD�1)5�GH�H[SORDWDUH 0 0 0 0 0 Cesiune 300 Impozit pe plus valoare pe termen scurt 150 3. Flux net cesiune 150 4. Recuperarea NFR 200 ���)OX[XUL�WRWDOH��IOX[XUL�GH�OLFKLGLW L� 450 450 450 450 800 (5 = 1 – 2 + 3 – 4)
VAN-XO�LQYHVWL LHL�VH�FDOFXOHD] �vQ�DFHVW�FD]�OD�UDWD�GH�DFWXDOL]DUH�UHDO ��GH�5� ����
∑=
=−+=4
1t5t
5,022.1200.1)05,1(
800
)05,1(
450VAN
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
Ipoteza 2: luarea în cDOFXO�D�XQHL�LQIOD LL�GH��� )OX[XULOH�GH�IRQGXUL�GH�H[SORDWDUH��1)5�GH�H[SORDWDUH�úL�SUH XO�GH�FHVLXQH�VXQW�SUHVXSXVH�D�IL�LQGH[DWH�OD�LQIOD LH��5DWD�GH�DFWXDOL]DUH�FRQVLGHUDW �HVWH�UDWD�QRPLQDO �GH�����
Tabelul 7: Evaluarea VAN-ului cu luarea în calcul D�LQIOD LHL
Anii 1 2 3 4 5 Flux de fonduri de exploatare 735 772 810 851 893 Amortismente 200 200 200 200 200 Rezultat înainte de impozit 535 572 610 651 693 Impozit pe profit (cota de 50%) 267 286 305 325 346 ��)OX[�GH�IRQGXUL�GXS �LPSR]LW 468 486 505 526 547 ��9DULD LD�1)5�GH�H[SORDWDUH 10 11 11 12 12 Cesiune 383 Impozit pe plus-valoare pe termen scurt 192 3.Flux net de cesiune 192 4.Recuperarea NFR 256 ��)OX[XUL�WRWDOH��IOX[XUL�GH�OLFKLGLW L� 458 475 494 514 983 (5 = 1 – 2 + 3 + 4)
VAN-XO�SHQWUX�R�UDW �GH�DFWXDOL]DUH�QRPLQDO �³U´�GH�����HVWH�DWXQFL�GH�
942200.1)1,1(
983
)1,1(
514
)1,1(
494
)1,1(
475
)1,1(
458VAN
5432=−++++=
VAN-XO�LQYHVWL LHL�HVWH��vQ��DFHVW�FD]��QHW�LQIHULRU�9$1-XOXL�HYDOXDW�I U �OXDUHD�vQ�FDOFXO�D�LQIOD LHL��UHQWDELOLWDWHD�UHDO �D�LQYHVWL LHL�D�IRVW�GHFL�GLPLQXDW � ([HPSOXO�SUH]HQWDW�GHPRQVWUHD] �QHFHVLWDWHD�GH�D�SUDFWLFD�HYDOXDUHD�LQYHVWL LLORU�SRUQLQG�GH�OD�IOX[XUL�QRPLQDOH�úL�GH�D�UH LQH�R�UDW �GH�DFWXDOL]DUH�DMXVWDW �SHQWUX�D�OXD�vQ�FDOFXO�LQIOD LD�
4.1.5.PROBLEME PARTICULARE 1.'HFL]LD�GH�LQYHVWL LL�úL�SURLHFWH�FX�GXUDWH�GH�YLD �GLIHULWH. Compararea VAN-ului aferent XQRU�SURLHFWH�GH�LQYHVWL LL�QX�SRDWH�IL�I FXW �GLUHFW�DWXQFL�FkQG��GXUDWHOH�GH�YLD �DOH�DFHVWRU�SURLHFWH�GLIHU ��1XPHURDVH�PHWRGH�VXQW�DWXQFL�XWLOL]DELOH�
A. Metoda cHOXL�PDL�PLF�PXOWLSOX�FRPXQ�DOH�GXUDWHORU�GH�YLD &RQVLGHU P� � R� vQWUHSULQGHUH� FDUH� DUH� GH� DOHV� vQWUH� GRX � WLSXUL� GH� PDúLQL� $� úL� %� SHQWUX�
UHDOL]DUHD�XQHL�DFHOHLDúL�SURGXF LL� 0DúLQD� $� DUH� R� GXUDW � GH� YLD � GH� �� DQL� úL� UHSUH]LQW � R� LQYHVWL LH� GH� ������� )OX[ul de
OLFKLGLW L�GH�H[SORDWDUH�DúWHSWDW�DQXDOH�HVWH�GH������0DúLQD�%�DUH�R�GXUDW �GH�YLD �PDL�PLF �GH���DQL��VXPD�GH�LQYHVWLW�HVWH�GH�����úL�IOX[XO�GH�OLFKLGLW L�GH�H[SORDWDUH�DQXDOH�HVWH�GH�����
(YDOX P�9$1-XO�SHQWUX�R�UDW �GH�������D�ILHF UHLD�GLQ�DFHVWH�PDúLQL�
0DúLQD��$�: ∑=
=−=3
1tt
1,492000.1)1,1(
600)A(VAN
0DúLQD��%�: ∑=
=−=2
1tt
8,367500)1,1(
500)B(VAN
0DúLQD�$�DSDUHQW�HVWH�SUHIHUDELO �GHRDUHFH�9$1-XO�V X�HVWH�PDL�ULGLFDW��'DU�DFHDVW �PDúLQ �WUHEXLH�V �ILH�vQORFXLW �OD�FDS WXO�D���DQL��ID �GH�QXPDL���DQL�vQ�FD]XO�PDúLQLi B. Decizia de înlocuire GHSLQGH� GH� DOHJHUHD� LQL LDO �� QX� VH� SRDWH� FRQVLGHUD� vQWU-XQ� PRG� LQGHSHQGHQW� DFHDVW � GLQ� XUP �GHFL]LH��3HQWUX�DOHJHUHD�LQYHVWL LHL�LQL LDOH�WUHEXLH�V �VH�UD LRQH]H�SH�XQ�RUL]RQW�HFRQRPLF�LGHQWLF�
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
Cel mai mic multiplu comun al duraWHORU�GH�YLD �ILLQG���DQL��YRP�FRQVLGHUD�XQ�RUL]RQW�GH���DQL�úL�SUHVXSXQHP�F �FHOH�GRX �PDúLQL�VXQW�vQORFXLWH�vQ�PRG�LGHQWLF�� OD�FDS WXO�GXUDWHORU�GH�YLD �respective. VAN-XULOH�SHQWUX�FHOH�GRX �PDúLQL�VXQW�DWXQFL� 0DúLQD�$��PDúLQD�FDUH�HVWH�vQORFXLW �GXS ���DQL�QHFHVLW �XQ�IOX[�VXSOLPHQWDU�GH�–1.000 în anul 3. VAN-ul total pe cei 6 ani este de:
−+
−= ∑∑
==
6
4t3t
3
1tt )1,1(
000.1
)1,1(
600000.1
)1,1(
600)A(VAN
VAN(A) = 492,1 + 369,7 = 861,8 0DúLQD�%��PDúLQD�HVWH�vQORFXLW �vQ�DQLL���úL����úL�GHFL�QHFHVLW �FkWH�XQ�IOX[�VXSOLPHQWDU�GH�–500 la
ILQHOH�DQLORU���úL����9$1-ul total este de:
−+
−+
−= ∑∑∑
===
6
5t4t
4
3t2t
2
1tt )1,1(
500
)1,1(
500
)1,1(
500
)1,1(
500500
)1,1(
500)B(VAN
VAN(B) = 367,8 + 303,9 + 251,2 = 922,9 ÌQ�DFHVW�FD]��PDúLQD�%�DSDUH�SUHIHUDELO ��9$1�%��ILLQG�VXSHULRU�OXL�9$1�$�� $FHDVW � PHWRG � VH� SRDWH� GRYHGL� JUHRDLH� úL� HVWH� SUHIHUDELO� UHFXUJHUHD� OD� PHWRGD� DQXLW LL�echivalente.
B. 0HWRGD�DQXLW LL�HFKLYDOHQWH
$QXLWDWHD�HFKLYDOHQW �$(4�UHSUH]LQW �DQXLWDWHD�FDUH�SHUPLWH�RE LQHUHD�DFHOHLDúL�9$1�GH-a OXQJXO� GXUDWHL�GH� YLD � D�SURLHFWXOXL�� ILH� SHQWUX�XQ�SURLHFW� FX�GXUDW � GH�YLD �GH�³Q´� úL� R� UDW � GH�actualizare “R”:
[ ]∑
=
−+−⋅=+
=n
1t
n
t R
)R1(1AEQ
)R1(
AEQVAN
3HQWUX�SURLHFWXO�$�FX�R�GXUDW �GH�YLD �GH���DQL�úL�SHQWUX�R�UDW �GH�DFWXDOL]DUH�GH����� $(4�$�� �������FHHD�FH�SHUPLWH�vQ�FHL���DQL�RE LQHUHD�XQXL�9$1�GH�������
[ ]
1,0
)1,1(19,1971,492
2−−=
3HQWUX�PDúLQD�%�VH�RE LQH�SHQWUX�R�GXUDW �GH�YLD �GH���DQL� $(4�%�� �������FHHD�FH�SHUPLWH�vQ�FHL���DQL�RE LQHUHD�XQXL�9$1�GH�������
[ ]
1,0
)1,1(19,2118,367
2−−=
6H�DOHJH�GHFL�LQYHVWL LD�D�F UHL�DQXLWDWH�HFKLYDOHQW �HVWH�PDL�ULGLFDW ��DGLF �SURLHFWXO�%� 2.Determinarea unei politic optimale de înlocuire &RQVLGHU P�R�PDúLQ �vQ�VXP �GH��������FX�R�GXUDW �GH�YLD �GH���DQL��IOX[XO�GH�OLFKLGLW L�GH�
H[SORDWDUH� DQXDO� HVWH� GH� ������� ÌQWUHSULQGHUHD� SRDWH� vQORFXL� DFHDVW �PDúLQ � SULQWU-R� QRX �PDúLQ �înainte de finele celor 5 ani. MaúLQD�DFWXDO �DUH�R�YDORDUH�UH]LGXDO �GH�������vQ�DQXO����GH�������vQ�DQXO����GH�������vQ�DQXO����GH�������vQ�DQXO���úL�GH��� vQ�DQXO����3UREOHPD�UH]LG � vQ�GHWHUPLQDUHD�perioadei optimale de înlocuire.
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
3UHVXSXQkQG� R� UDW � GH� DFWXDOL]DUH� GH� ���� úL� GDF � VH� FDOFXOHD] � 9$1-ul fluxurilor de OLFKLGLW L��I FkQG�LSRWH]D�VXFFHVLY �F �PDúLQD�HVWH�FHGDW �OD�ILQHOH�ILHF UXL�DQ��VH�RE LQH� • Cesiune în anul 1:
817.1000.10)1,1(
000.8
)1,1
000.5)1(VAN =−+=
• Cesiune în anul2:
∑=
=−+=2
1t2t
462.4000.10)1,1(
000.7
)1,1(
000.5)2(VAN
• Cesiune în anul 3:
∑=
=−+=3
1t3t
941.6000.10)1,1(
000.6
)1,1(
000.5)3(VAN
• Cesiune în anul 4:
∑=
=−+=4
1t4t
216.7000.10)1,1(
000.2
)1,1(
000.5)4(VAN
• Cesiune în anul 5:
∑=
=−+=5
1t5t
955.8000.10)1,1(
0
)1,1(
000.5)5(VAN
VAN-XO�PD[LPDO�VH�RE LQH�SHQWUX�R�FHVLXQH�UHDOL]DW �vQ�DQXO����'DU�DFHVW�UH]XOWDW�QX�LPSOLF �F �GHFL]LD�RSWLPDO �GH�vQORFXLUH�V �DLE �ORF�vQ�DQXO����ÌQWU-DGHY U, în fiecare caz orizontul economic FRQVLGHUDW� QX� HVWH� LGHQWLF�� FHHD�FH� GHIDYRUL]HD] �HYLGHQW� GHFL]LLOH� GH� vQORFXLUH�FDUH� VH�SURGXF�SH�WHUPHQ�VFXUW��&D�úL� vQ�FD]XO�FRPSDU ULL�SURLHFWHORU�FX�GXUDWH�GH�YLD �GLIHULWH�� WUHEXLH�V � VH�SRDW �UD LRQD�SH�XQ�RUL]RQt economic identic. 3UHVXSXQHP�F �RUL]RQWXO�FRQVLGHUDW�HVWH�LQILQLW�úL�VWXGLHP��GH�H[HPSOX��FD]XO�XQHL�FHVLXQL�vQ�DQXO����([LVW �vQ�DFHVW�FD]�XQ�ODQ �LQILQLW�GH�vQORFXLUL�FDUH�YRU�DYHD�ORF�vQ�ILHFDUH�DQ��9$1-ul unui DVHPHQHD�ODQ �HVWH�DWXQFL�
∞+++
++
++=
)R1(
)1(VAN...
)R1(
)1(VAN
R1
)1(VAN)1(VANVAN
2
987.191,0/7,998.1R
)R1()1(VAN1
0R1(
1)1(VANVAN
1tt
==+=
+
+= ∑
∞
=
6H�SRDWH�GHPRQVWUD�F ��SHQWUX�R�vQORFXLUH�FDUH�DUH�ORF�vQ�WR L�³P´�DQL��VH�RE LQH�SHQWUX�XQ�orizont infinit:
])R1/(11[(
)m(VANVAN
m+−=
Astfel, pentru m = 2, VAN-ul este de 25.710, pentru m = 3 de 27.911, pentru m = 4 de �������úL�SHQWUX�P� ���GH�������� ÌQ� FRQVHFLQ �� SROLWLFD� RSWLPDO � GH� vQORFXLUH� HVWH� FHD� GH� vQORFXLUH� GXS � FkWH� �� DQL� �9$1�PD[LPDO �GH���������
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
4.1.6. Documentar A. &5,7(5,,/(�),1$1&,$5(�5(&20$1'$7(�'(�%$1&$�021',$/ ÎN VEDEREA ALEGERII UNUI PRO,(&7�'(�,19(67, ,,
Criteriul 5HOD LD�GH�FDOFXO Interpretare 1.Valoarea DFWXDOL]DW �QHW (VAN)
VAN = V0 – I0 = ∑=
−+
++
n
1tI
n)K1(
nVRt)K1(
tCF
-� VH� GHWHUPLQ � FD� GLIHUHQ � vQWUH� IOX[XULOH� GH�WUH]RUHULH�YLLWRDUH�úL�DFWXDOL]DWH�OD�UDWD�GREkQ-]LL�GH�SLD �UHVSHFWLY�YDORDUHD�ORU�DFWXDO �SH�GH
în care: R�SDUWH�úL�FDSLWDOXO�LQYHVWLW�SH�GH�DOW �SDUWH� V0� �YDORDUHD�DFWXDO �D�FDVK-flow-urile viitoare (CFt) inclusiv a valorii reziduale (VRn) -�UHJXOD�9$1�SRUQHúWH�GH�OD�LSRWH]D�FRQIRUP� I0 –�FKHOWXLHOLOH�LQL LDOH�GH�LQYHVWL LL� F UHLD�FDSLWDOXULOH��,��SRW�IL�RULFkQG�UHLQYHVWLWH�
→=+
+= 0I
K1
)1VR1F(VAN SH�SLD D�PRQHWDU �OD�UDWD�GREkQ]LL�GH�SLD ��.��SHQWUX� D� RE LQH� IOX[XUL� GH� WUH]RUHULH� YLLWRDUH�(CF);
-�SHQWUX�R�SHULRDG - toate proiectele care vor avea VAN po]LWLY
∑=
−+
++
=n
1tI
n)K1(
nVRt)K1(
tCFVAN
sunt preferabile plasamentelor monetare la o GREkQG �GH�SLD �³.´�
- pentru “n” perioade ��5DWD� LQWHUQ �de rentabilitate (RIR)
-�SHQWUX�R�SHULRDG �
10I
1VR1CFRIR −
+=
- considerând rata medie a dobânzii ca un UDQGDPHQW�GH�UHIHULQ �vQ�PDWHULH�GH�LQYHVWL LL��regula VAN de evaluare a proiectelor de in- YHVWL LL�SRDWH�IL�WUDQVSXV �vQ�WHUPHQL�GH�UHQWD-
- pentru “n” perioade: bilitate a acestora (este vorba de ratele de ren-
∑= +
++
=n
1t n)RIR1(
nVRt)RIR1(
tCF0I
tabilitatH� VSHFLILFH� ILHF UXL� SURLHFW� GH� LQYHV-WL LL��PRWLY� SHQWUX� FDUH� HOH� VH� PDL� QXPHVF� úL�rate interne de rentabilitate);
-�UHJXOD�5,5�HVWH�HFKLYDOHQW �FX�UHJXOD�9$1� vQ�VHOHF LD�SURLHFWHORU�GH�LQYHVWL LL ��5DWD� LQWHUQ �de rentabilitate PRGLILFDW �(RIRM)
-�SHQWUX�R�SHULRDG �
( )
0I
1VR)ir1(0FRIRM
++=
-� LQFRQYHQLHQWXO� 5,5� HVWH� LSRWH]D� PL� SX LQ�UHDOLVW � D� UHLQYHVWLULL� FRQVWDQWH� vQ� DFHHDúL� vQ- WUHSULQGHUH�úL� OD�DFHHDúL�5,5�D�YHQLWXULORU�YLL- toare , motiv pentru care s-a propus utilizarea
- pentru “n” perioade: unei RIR modificate, în ipoteza reinvestirii
1n
0I
n
1tVRtn)ir1(tCF
RIRM −∑=
+−+=
YHQLWXULORU� YLLWRDUH� OD� R� UDW � GH� UHQWDELOLWDWH�VSHFLILF � vQWUHSULQGHULL� úL� QX� SURLHFWXOXL� GH�LQYHVWL LL�DQDOL]DW
unde: rI� �UDWD�GH�UHQWDELOLWDWH�VSHFLILF �vQWUH- prinderii la care pot fi reinvestite veni- turile viitoare 4.Termenul de recuperare (TR)
an/actCF
0ITR = -� H[SULP �QXP UXO�GH�DQL� GH� UHFXSHUDUH�� SULQ�cash-flow-urile medii anuale actualizate (Cfact/an) a capitalului investit (I0);
n
n
1t n)K1(
nVRt)K1(
tCF
an/actCF
∑= +
++
=
-� UHSUH]LQW � QXP UXO� GH� DQL� GXS � FDUH� VXPD�fluxurilor marginale de trezorerie (actualizate) GHYLQH�HJDO � �úL� DFRSHULWRDUH�� FX� VXPD� LQYHV-WL LHL�
-�DFHVW�LQGLFDWRU�DVLJXU �R�DOHJHUH�D�YDULDQWHORU�de inveVWL LL�vQ�IXQF LH�GH�UDSLGLWDWHD�UHFXSHU -
rii capitalului investit.
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
5.Indicele de profitabilitate (IP)
0I
n)K1(
nVRt)K1(
tCF
0I
0VIP
∑+
++
==
-�H[SULP �UHQWDELOLWDWHD�UHODWLY �D�LQYHVWL LHL�SH�vQWUHDJD� GXUDW � GH� YLD � D� DFHVWHLH�� UHVSHFWLY�YDORDUHD�DFWXDO ��V0��VFRQWDW �SHQWUX�R�FKHOWX- LDO �LQL LDO �HJDO �FX��� -�VXQW�UH LQXWH�DFHOH�SURLHFWH�GH�LQYHVWL LH�FDUH
VAN0I0V += au IP > 1;
1
0I
VAN
0I
0IVANIP +=
+=
-� GXS � DFHVW� FULWHULX� YRU� IL� VHOHFWDWH� DFHO�SURLHFWH� GH� LQYHVWL LL� FDUH� FX� FHO mai mare indice de profitabilitate.
B. (/(0(17(/(�),1$1&,$5(�$/(�81(,�,19(67, ,,�Ì1�0(',8/�&(57 ���&+(/78,(/,/(�,1, ,$/(�'(�,19(67, ,,��,0) ¾ UHSUH]LQW � P ULPHD� QHW � D� FDSLWDOXOXL� QHFHVDU� SHQWUX� SXQHUHD� vQ� H[SORDWDUH� D� LQYHVWL LHL��
Elementele componente alH�VXPHL�LQL LDOH�D�LQYHVWL LHL�VXQW�IRUPDWH�GLQ� • FRVWXO�DFKL]L LHL�DFWLYHORU�IL[H��IL]LFH�VDX�ILQDQFLDUH� • FKHOWXLHOLOH�GH�LQVWDODUH�úL�PRQWDM�DO�HFKLSDPHQWHORU�úL�LQVWDOD LLORU�QRL�úL�FKHOWXLHOLOH�
de specializare a personalului în exploatarea noi tehnologi; • FUHúWHUHD� QHYRLL� GH� IRQG� GH� UXOPHQW� UHVSHFWLY� FUHúWHUHD� VWRFXULORU� úL� D� FUHDQ HORU�
FOLHQ L�PLQXV� FUHúWHUHD� GDWRULLORU� GH� H[SORDWDUH� GHWHUPLQDWH� GH� QRXD� FDSDFLWDWH� GH�SURGXF LH�
• SUH XO� GH� UHYkQ]DUH�� HYHQWXDO�� DO� DFWLYHORU� IL[H� GH]YLQYHVWLWH� �vQORFXLWH�� Srin noua LQYHVWL LH��LQFOXVLY�SOXV�VDX�PLQXV�YDORDUHD�UH]XOWDW �GLQ�DFHDVW �FHVLXQH�
���'85$7$�'(�9,$ �$�,19(67, ,(, ¾ HVWH� R� QR LXQH� FX� VHPQLILFD LL� GLYHUVH� UH]XOWDWH� GLQ� GLIHULWH� XQJKLXUL� GH� LQWHUHV� SHQWUX� DFHVW�
element financiar: • GXUDWD�ILVFDO ��FRQWDELO � • GXUDWD�WHKQLF � • GXUDWD�FRPHUFLDO � • GXUDWD�MXULGLF �HWF�
3. FLUXURILE NETE DE TREZORERIE (CASH-FLOW-URI DISPONIBILE, CFD) )OX[XULOH�YLLWRDUH�GH�WUH]RUHULH��&)'��H[SULP ��GH�IDSW��H[FHGHQWHOH�GH�WUH]RUHULH�GLVSRQLELOH�pentru plata dividendelor. CFD = CFexpl. –� �,02�–� �1)5 CFexpl. = Pr.net + Amo = EBIT (1 - τ) + Amo Pr.net = EBT (1 - τ) = EBIT (1 - τ) EBT = EBIT – Dob EBIT = EBE – Amo în care: EBIT -� SURILWXO� vQDLQWH�GH�GREkQ]L� úL�GH� LPSR]LW� �HDUQLQJ�EHIRUH� LQWHUHVWV�DQG� WD[HV�� în
HQJOH] �� EBT -�SURILO�vQDLQWH�GH�LPSR]LW��HDUQLQJ�EHIRUH�WD[HV��vQ�HQJOH] �� Dob - Dobânzi;
τ - cota impozitului pe profit.
���9$/2$5($�5(=,'8$/ ��95� ¾ H[SULP � YDORDUHD� SRVLELO � GH� UHFXSHUDW� GXS � vQFKHLHUHD� GXUDWHL� GH� YLD � D� LQYHVWL LHL� �SULQ
vânzare, prin valorificarea pieselor, subansamblelor etc.); � YDORDUHD�UH]LGXDO �DU�WUHEXL�V �FXSULQG �FHO�SX LQ�XUP WRDUHOH�HOHPHQWH�
• YDORDUHD� LPRELOL] ULORU� FRUSRUDOH� OD� SUH XO� GH� UHYkQ]DUH� HVWLPDW�� FRUHFWDW� FX�impozitele sau cu economia de impozit, aferente plus sau minus-calorii ce ar rezulta;
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
• YDORDUHD� LPRELOL] ULORU� QHFRUSRUDOH� úL� D� FHORU� ILQDQFLDUH� OD� SUH XO� GH� SLD � VDX� FHO�HVWLPDW�GH�H[SHU L�ILQDQFLDUL�
• VXPD�FXPXODW �D�FUHúWHULL�DQWHULRDUH�D�QHYRLL�GH�IRQG�GH�UXOPHQW� Impactul valorii reziduale asupUD�9$1�HVWH�FX�DWkW�PDL�PDUH�FX�FkW�P ULPHD�HVWLPDW �D�95�HVWH�PDL�PDUH�úL�FX�FkW�PRPHQWXO�GH]LQYHVWLULL�HVWH�PDL�DSURDSH�GH�PRPHQWXO�LQYHVWLULL��IDFWRUXO�GH�DFWXDOL]DUH�D������N��HVWH�GHVFUHVF WRU�SH�GXUDWD�GH�YLD �HFRQRPLF �D�LQYHVWL LHL�� 5. RATA DE ACTUALIZARE � HVWH�XQ�FRVW�GH�RSRUWXQLWDWH�DO�FDSLWDOXOXL�LQYHVWLW�ILLQG�GHFL�FRVWXO�GH�ILQDQ DUH�DO�LQYHVWL LHL�GLQ�
FDSLWDOXUL�SURSULL�úL�DSUHFLDW�FD�R�UDW �GH�UHQWDELOLWDWH�FHUXW ��QRUPDO ��GH�LQYHVWLWRUL�DVXSUD�XQXL�proiect;
� în mediul economic cert, invesWL LD�HVWH�I U �ULVF��LDU�UDWD�GH�UHQWDELOLWDWH�FHUXW �GH�LQYHVWLWRULL�GH�FDSLWDO�HVWH�UDWD�GH�GREkQG �I U �ULVF��GHRDUHFH�SLD D�ILQDQFLDU �HVWH�vQ�HFKLOLEUX�
� UDWD� GH� DFWXDOL]DUH� �.�� FH� WUHEXLH� XWLOL]DW � VH� FDOFXOHD] �� GHFL�� SRUQLQG� GH� OD� UDWD� UHDO � GH�dobkQG ��UU��úL�GH�OD�UDWD�GH�LQIOD LH��UI);
(1 + K) = (1 + rr)(1 + ri��SHQWUX���DQ�úL�GHFL�.� �Ur + rr � ri
(1 + K)n = (1 + rr)n (1 + ri)
n�SHQWUX�Q�DQL�úL�GHFL� 1)r1()r1(K n ni
nr −++=
� LSRWH]D�PHGLXOXL�HFRQRPLF�FHUW�IDFH�LPSOLFLW �úL�LSRWH]D�XQHL�FXUEH�SODWH�D�UDWHORU�GH�GREkQG �vQ�care ratele anuale sunt egale cu ratele pe termen mediu sau lung.
&��(/(0(17(/(�),1$1&,$5(�$/(�81(,�,19(67, ,, 9$/2$5($� 5(&83(5$%,/ � �95�� GLQ� GH]LQYHVWLUH� UHSUH]LQW � VXPD� IOX[XULORU� QHWH�DFWXDOL]DWH� GH� WUH]RUHULH�� FH� UH]XOW � GXS � vQFHWDUHD� DFWLYLW LL� úL� YDORULILFDUHD� �SULQ� YkQ]DUH�� D�DFWLYHORU�FH�DSDU LQ�DFWLYLW LL�GH]LQYHVWLWH�
9DORDUHD�UHFXSHUDELO �VH�VWDELOHúWH�GXS �GHGXFHUHD�FKHOWXLHOLORU�RFD]LRQDWH�GH�RSHUD LLOH�GH�GH]LQYHVWLUH��&'� �GHPRQWDUHD�úL�GHPRODUHD�� LQGHPQL]D iile pentru personalul concediat, avizarea IXUQL]RULORU�úL�FOLHQ LORU�HWF���D�FKHOWXLHOLORU�FH�GHFXUJ�GLQ�DVXPDUHD�REOLJD LLORU��SHQWUX�DFWLYLWDWHD�FDUH� D� vQFHWDW� �&2� � IDEULFD LD� XQXL� VWRF� GH� SLHVH� GH� VFKLPE�� PHQ LQHUHD� VHUYLFH-XOXL�� úL� D�cheltuielilor de� UHRUJDQL]DUH� D� DFWLYLW LL� vQWUHSULQGHULL� �&5� � UHFDOLILFDUHD� SHUVRQDOXOXL� DIHFWDW��reorganizarea atelierelor etc.). )OX[XULOH�PRQHWDUH�SR]LWLYH�DOH�GHFL]LHL�GH�LQYHVWLUH�VH�UHIHU �OD�
• vQFDVDUHD� QHW � GLQ� FHVLXQHD� DFWLYHORU� IL[H� GH]LQYHVWLWH� �9).��� UH]XOWDW � GXS �GHGXFHUHD� LPSR]LWXOXL� SH� YHQLWXULOH� GH� FDSLWDO� VDX� GXS � DGL LRQDUHD� HFRQRPLHL� GH�LPSR]LW��GLQ�SLHUGHUHD�GH�FDSLWDO�OD�RSHUD LD�GH�FHVLXQH�
• UHFXSHUDUHD� FDSLWDOXOXL� LQYHVWLW� vQ� PLMORDFH� FLUFXODQWH� �&.&�� DIHUHQWH� DFWLYLW LL�dezinvestite;
• economiile marginale actualizate (EMA) care vor rezulta la cheltuielile cu noua LQYHVWL LH�
ÌQ�FRQVHFLQ ��YDORDUHD�UHFXSHUDELO �VH�GHWHUPLQ �GXS �UHOD LD� VR = (VKF + VKC + EMA) – (CD + CO + CR) '85$7$� '(� 9,$ � (&2120,& � 5 0$6 � �'95� a obiectivului supus
dezinvestLULL� UHSUH]LQW � � QXP UXO� GH�DQL� � LQkQG�FRQW� GH� FRQGL LLOH� GLQ�PRPHQWXO� GH]LQYHVWLULL�� vQ�care s-DU�PDL�IL�SXWXW�H[SORDWD�UHVSHFWLYD�DFWLYLWDWH��GDF �QX�V-ar pune problema dezinvestirii.
VENITURILE VIITOARE (MARGINALE) PIERDUTE (VVP) UHSUH]LQW � SURILWXULOH QHWH�GH�H[SORDWDUH�SUHYL]LRQDWH�FDUH�DU�UH]XOWD�GLQ�DFWLYLWDWHD�VXSXV �RSHUD LHL�GH�GH]LQYHVWLUH�GDF �DFHDVW �GLQ�XUP �QX�DU�DYHD�ORF�
9HQLWXULOH� YLLWRDUH� SLHUGXWH� �993�� VH� GHWHUPLQ �� vQ� ILHFDUH� DQ� DO� GXUDWHL� GH� YLD � U PDVH��GXS �UHOD LD�XUP WRDUH�
VVP = (CA – V – F) (1 - τ) + A ⋅ τ în care:
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
CA – cifra de afaceri; V - cheltuielile variabile evitate; F - cheltuielile fixe evitate (eventual); T -�FRWD�XQLF �GH�LPSR]LW� A -�DPRUWL] UL�SLHUGXWH� 9$/2$5($� 5(=,'8$/ � 9,,72$5(� 3,(5'87 � �95P)� UHSUH]LQW � IOX[XULOH�PRQHWDUH�SR]LWLYH�SUHYL]LRQDWH�FDUH�DU�UH]XOWD�OD�VIkUúLWXO�GXUDWHL�GH�YLD �U PDVH�GDF �GH]LQYHVWLUHD�nu ar avea loc. RATA DE ACTUALIZARE (a)�D�YHQLWXULORU�YLLWRDUH�PDUJLQDOH�SLHUGXWH�VH�GHWHUPLQ ��vQ�general, la nivelul costului PHGLX� SRQGHUDW� DO� FDSLWDOXOXL� vQWUHSULQGHUL� �vQ� IXQF LH� GH� VWUXFWXUD�ILQDQ ULL��PDMRUDW�FX�SULPD�GH�ULVF�VSHFLILF �DFWLYLW LL�FH�VH�VXSXQH�GH]LQYHVWLULL��ÌQ�FD]XO�SDUWLFXODU�DO�GH]LQYHVWLULL�vQ�PHGLX�FHUW��UDWD�GH�DFWXDOL]DUH�YD�IL�UDWD�GREkQ]LL�I U �ULVc (Rf).
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4.2.1.1. CONSTITUIREA CAPITALULUI SOCIAL &RQVWLWXLUHD�FDSLWDOXOXL�VRFLDO�UHSUH]LQW �SULPD�ID] �GH�ILQDQ DUH�D�XQHL�VRFLHW L�FRPHUFLDOH� Cea mai mare parte a întreprinderilor sH�RUJDQL]HD] �FD�VRFLHW L�GH�FDSLWDO��DGLF �VRFLHW L�vQ�care aportul de capital se face prin titluri liber-QHJRFLDELOH�� FDUH� QX� DQJDMHD] � UHVSRQVDELOLWDWHD�DGXF WRUXOXL�GHFkW�SHQWUX�VXPD�VXEVFULV � 7LSXUL�GH�VRFLHW L�GH�FDSLWDO� (1) FHD� PDL� U VSkQGLW � HVWH� VRFLHWDWHD� DQRQLP � SH� DF LXQL� FDUH� VH� FDUDFWHUL]HD] � SULQ� IDSWXO� F �
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Modulul 4 -�6WUDWHJLD�ILQDQFLDU
&H�GHPRQVWUHD] " � YLDELOLWDWHD� vQWUHSULQGHULL� �OXFUHD] � UHQWDELO�� úL�DUH�XQ�HIHFW�SR]LWLY� WHU LORU� �E QFL��SDUWHQHUL�GH�
contracte) sporind încrederea acestora în întreprindere. &XP�VH�UHDOL]HD] " � SULQ�DXWRILQDQ DUH��ILQDQ DUH�LQWHUQ �� � SULQ�DSRUWXUL�vQ�QXPHUDU�DOH�DF LRQDULORU��ILQDQ UL�H[WHUQH�FX�IRQGXUL�SURSULL�� � prin încorporarea rezervelor.
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create actiuni de Numarul
actionari de adus CapitalulVn =
unde: Vn –�YDORDUHD�QRPLQDO �D�DF LXQLORU� 8OWHULRU�QXP UXO�DF LXQLORU�FUHúWH�SULQ� � aporturi noi în numerar; � incorporarea rezervelor; � conversiunea datoriilor.
&UHúWHUHD�FDSLWDOXOXL�VH�UHDOL]HD] �SULQ� a) PXOWLSOLFDUHD�QXP UXOXL�DF LXQLORU� b) P ULQG�YDORDUHD�QRPLQDO �D�DF LXQLORU�
&DUDFWHULVWLFL�DOH�FUHúWHULL�GH�FDSLWDO��SULQ�DSRUWXUL�QRL�vQ�QXPHUDU�� a) PLMORF�GH�ILQDQ DUH�SULQ�IRQGXUL�SURSULL�FD�úL�DXWRILQDQ DUHD� b) GHRVHELUH� ID � GH� DXWRILQDQ DUH�� DXWRILQDQ DUHD� HVWH� R� ILQDQ DUH� LQWHUQ � SULQ� HIRUWXO� SURSULX� DO�
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000.20
2,1
000.20VA
22=++=
ValoDUHD� DFWXDO � D� FDSLWDOXOXL� QX� YD� IL� DIHFWDW � GDF � UDWD� QRPLQDO � FRUHVSXQGH� FX� UDWD�GREkQ]LL�GH�SLD �³.´�
142,9
14 16 18
20% 22% 24% 26%
125
111,1
90,9
83,3
76,9
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
(2) K = 25%, n = 2 ani, (PR)P1� ����������SULP � ��
800.92)25,1(
000.100
)25,1(
000.20
25,1
000.20VA
22=++=
3LHUGHUHD�GH�FDSLWDO�HVWH�HYLGHQW �vQ�H[HPSOXO�QRVWUX�
%45
1
000.100
000.20P −=
−=
OD�ILHFDUH�SURFHQW�GH�YDULD LH�D�UDWHL�GH�SLD ��SUH XO�LQL LDO�DO�REOLJD LXQLL�YDULD] ��vQ�VHQV�LQYHUV��FX�4% 100.000 ⋅ 4% = 4.000 lei.
(3) K = 25%, n = 2 ani, (PR)P1 = 111.250, prima “en dehors” = 11.250
000.100)25,1(
250.11
)25,1(
000.20
25,1
000.20VA
22−++=
Prima de rambursare de 11.����YLQH�V �FRPSHQVH]H�SLHUGHUHD�GH�FDSLWDO�GLQ�FDX]D�LQIOD LHL��9DORDUHD� DFWXDO � D� FDSLWDOXOXL� HVWH� HJDO �FX� YDORDUHD� QRPLQDO � D� REOLJD LXQLL� úL�� GH�DVHPHQHD�� FX�SUH XO�GH�HPLVLXQH����������� 3ULPD�SRDWH�IL�³HQ�GHKRUV´�HJDO �FX���������31 = 111.250), “en�GHGDQV´�HJDO �FX��������35���31 = ��������GDU�3(� ���������VDX�R�GXEO �SULP ��HJDO �FX���������GDF �3(� ��������úL��35��31 = 108.125). &X�R�SULP �³HQ�GHGDQV´�GH�������VH�UHFRQVWLWXLH�SULQ�DFWXDOL]DUH�SUH XO�GH�HPLVLXQH�
PE800.92)25,1(
000.100
)25,1(
000.20
25,1
000.20VA
22==++=
$FHODúL�OXFUX�VH�SHWUHFH�FX�R�GXEO �SULP �GH��������úL�XQ�SUH �GH�UDPEXUVDUH�HJDO�FX���������
PE000.98)25,1(
125.108
)25,1(
000.20
25,1
000.20VA
22==++=
5D LRQDPHQWXO� SUH]HQWDW� PDL� GHYUHPH� U PkQH� vQWRWGHDXQD� YDODELO� GDF � UDPEXUVDUHD�vPSUXPXWXOXL� VH� IDFH�³LQ� ILQH´�FHHD�FH��GH� IDSW�� VH� vQWkPSO �PDL� UDU�� ÌQ�SULYLQ D� UDPEXUV ULL� SULQ�WUDJHUH�OD�VRU L��FD]XO�FHO�PDL�IUHFYHQW��LQFLGHQ D�LQIOD LHL�YD�GHSLQGH�GH�GDWD�UDPEXUV ULL� 3ULPLL�LQYHVWLWRUL�UDPEXUVD L�YRU�IL�IDYRUL]D L�vQ�UDSRUW�FX�LQIOD LD�GDU�HL�YRU�UHOXD�ULVFXO�XQHL�reinvestiri a capitalului. ÌQ�DFHVW�FD]� UD LRQDPHQWXO�SRDWH�FRQWLQXD�GDF �VH�VXEVWLWXLH�SUH XO�GH�FXPS UDUH� vQ�%XUV ��GH� H[HPSOX�� VDX� SUH XO� GH� HPLVLXQH� úL� VH� LD� vQ� FDOFXO� IUDF LD� GH� FXSRQ� VFXUV�� &DOFXOXO� DFWXDULDO�WUHEXLH�V �LD�vQ�FRQVLGHUDUH�FXUVXO�EXUVLHU�DO�REOLJD LXQLL�³OD�SLFLRUXO�FXSRQXOXL´��GHGXFHUHD�I FXW �DFHVWHL�IUDF LXQL�D�FXSRQXOXL�VFXUV��GH�OD�XOWLPD�VFDGHQ � Anticiparea ratei nominale $QWLFLSDUHD�UDWHL�QRPLQDOH�³L´�FDUH�WUHEXLH�V �vQJOREH]H�LQIOD LD�³[´�OD�R�UDW �GH�UDQGDPHQW�UHDO�³U´�DúWHSWDW �VH�IDFH�GXS �UHOD LD�ELQHFXQRVFXW �D�OXL�)LVFKHU� 1 + i = (1 + r) (1 + x) pentru primul an (1 + i)2 = (1 + r)2 (1 + x)2 pentru al doilea an
(1 + I)n = (1 + r)n (1 + x)n pentru ultimul an ÌQ�H[HPSOXO�QRVWUX�� GDF � HPLWHQWXO� GRUHúWH� V -úL� DVLJXUH� R� UDW � UHDO � GH����� vQ� FRQGL LLOH�XQHL�LQIOD LL�GH�����SH�DQ��HO�WUHEXLH�V �IL[H]H�UDWD�QRPLQDO �OD�������
%5,261)15,1()10,1(i 22 =−⋅= &X� R� DVHPHQHD� UHPXQHUD LH� LQYHVWLWRUXO� FDUH� D� FXPS UDW� REOLJD LXQHD� UHFXSHUHD] � vQWUHJ�FDSLWDOXO�V X�LQYHVWLW�LQL LDO�OD�FDS WXO�D���DQL�
000.100)265,1(
500.126
265,1
500.26VA
2=+=
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
$FHDVWD�VHPQLILF � IDSWXO�F �SLD D�SULQ� UDWD�VD�GH�GREkQG �DVLJXU �R� UDW � UHDO �GH�FHO�SX LQ�����vQ�DFHOHDúL�FRQGL LL�GH�LQIOD LH��[� ������ &XUVXO�REOLJD LXQLL &RWD LD�REOLJD LXQLL “au pair” (PE = VN) se face la piciorul cuponului (cuponul scurs dedus) úL�vQ�SURFHQWDM��91�HVWH�FRQVLGHUDW �������'DU�FXUVXO�FRWDW�QX�LQFOXGH�IUDF LD�GH�FXSRQ�VFXUV�GH�OD�XOWLPD�GHWDúDUH� 6XPD� FXSRQXOXL� VFXUV� ³&´� HVWH� FDOFXODW � vQ� WRDWH� ]LOHOH� vQ� IXQF LH� GH� YDORDUHD� QRPLQDO ��91���GH�UDWD�QRPLQDO �D�GREkQ]LL��³L´��úL�GH�QXP UXO�GH�]LOH�GH�OD�XOWLPD�SODW �D�FXSRQXOXL�³W´� C = VN.i.t/365 sau în procentaj C% = i.t/365. ÌQ�H[HPSOXO�QRVWUX��SHQWUX����GH�]LOH�GXS �GHWDúDUH�FXSRQXO�VFXUV�UH]XOW �LPHGLDW� C = 100.000 ⋅ 26,5% ⋅ 73/365 – 5.300 lei sau C% = 26,5 ⋅ 73/365 = 5,3% /D�R�UDW �D�GREkQ]LL�GH�SLD �GH�����FXUVXO�REOLJD LXQLL�HVWH�GH�����
%106%25
500.26 = úL�YDORDUHD�GH�DFKL]L LH��vQ�%XUV ��D�REOLJD LXQLL�HVWH�GH������������������
106 + 5,3 = 111,3% sau 100.000 + 111,3% = 111.300 lei
4��������,QWHUGHSHQGHQ D�GLQWUH�UDWD�GREkQ]LL�úL�FXUVXO�REOLJD LXQLORU $FHDVW � LQWHUGHSHQGHQ � SRDWH� IL� H[SULPDW � DVWIHO�� FUHúWHUHD� UDWHL� GREkQ]LL� SH� SLD �JHQHUHD] �R�VF GHUH�D�FXUVXOXL�EXUVLHU� 'LQWUH�H[SOLFD LLOH�GDWH�XQHL�DVWIHO�GH�FRUHOD LL�VH�UH LQ�XUP WRDUHOH� a) DWXQFL�FkQG�UDWD�GREkQ]LL�FUHúWH��REOLJD LXQLOH�GH LQ�LQYHVWL LL�PDL�DWU J WRDUH�SHQWUX�LQYHVWLWRUL�
'DF ��GH�H[HPSOX��GREkQGD�WUHFH�GH�OD�����OD�����DWXQFL�DFHVWH�WLWOXUL�YRU�J VL�PDL�UHSHGH�plasament.
2UL��SHQWUX�D�FXPS UD�DFHVWH�REOLJD LXQL�WUHEXLH�V �VH�J VHDVF �UDSLG�GLVSRQLELOLW LOH�E QHúWL��6H� SURGXF� YkQ] UL�PDVLYH� GH� DF LXQL�� FHHD� FH� IDFH� V � VFDG � FXUVXO� ORU��$úDGDU�� FUHúWHUHD� UDWHL�GREkQ]LL� REOLJD LXQLORU� IDFH� V � VFDG � FXUVXO� DF LXQLORU� SULQ� DUELWUDMXO� SH� FDUH� RSHUDWRULL� vO�realizeaz �vQWUH�DF LXQL�úL�REOLJD LXQL�
b) DWXQFL�FkQG�UDWD�GREkQ]LL�OD�REOLJD LXQL�FUHúWH��GLYLGHQGHOH�YLLWRDUH�VXQW�DFWXDOL]DWH�OD�R�UDW �PDL�PDUH��FHHD�FH�IDFH�V �VFDG �FXUVXO�DF LXQLORU�
3HQWUX�VXUSULQGHUHD�PDL�H[DFW �D�UDSRUWXOXL�LQYHUV�SURSRU LRQDO�GLQWUH�UDWD�GREkQ]LL�úL�FXUVXO�REOLJD LXQLORU��VH�FDOFXOHD] �VHQVLELOLWDWHD�REOLJD LXQLL�FD�SURFHQW�GH�VF GHUH�D�FXUVXOXL�DQWUHQDW �GH�FUHúWHUHD�UDWHL�GREkQ]LL�FX�R�XQLWDWH�
Sensibilitatea S se poate scrie astfel:
e
T
1tt
t
P
)r1(
tA
r1
1S
∑= +
⋅
⋅+
−=
în care: Pe -�SUH XO�GH�HPLVLXQH�VDX�YDORDUHD�UHDO �D�REOLJD LXQLORU� At - anuitatea la momentul t; t - anul respectiv; r -�UDWD�GH�DFWXDOL]DUH�EUXW � Cel de-DO�GRLOHD�IDFWRU�DO�UHOD LHL�H[SULP �GH�VLQH�VW W WRU�R�DOW �FDUDFWHULVWLF �D�REOLJD LXQLL�úL�anume durata de LPXQL]DUH� ³'´�� FDUH� DUDW � vQ� FkW� WLPS� FkúWLJXULOH� GLQ� GREkQ]LOH� vQFDVDWH� SRW�FRPSHQVD�HIHFWHOH�LQIOD LHL�
e
T
1tt
t
P
)r1(
tA
D∑= +
⋅
=
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
ÌQ�IXQF LH�GH�UHOD LD�GH�PDL�VXV�³6´�GHYLQH�
Dr1
1S ⋅
+−=
Sensibilitatea “S” este cu atât mai mare cu cât�³'´�HVWH�PDL�PDUH��9DORDUHD�OXL�³6´�úL�D�OXL�³'´�VH�VFKLPE �R�GDW �FX�UDWD�GREkQ]LL�ILLQG�QHFHVDU �UHFDOFXODUHD�DFHVWRUD�OD�ILHFDUH�YDULD LH�D�UDWHL�dobânzii. &XQRDúWHUHD�VHQVLELOLW LL� XQHL�REOLJD LXQL�SHUPLWH� HIHFWXDUHD�GH�DQDOL]H� úL�SH�DFHDVW �ED] �cuQRDúWHUHD�YDULDQWHL�RSWLPH�SHQWUX�VXEVFULHUHD�OD�HPLVLXQHD�GH�REOLJD LXQL� &X� FkW� ³'´� HVWH� PDL� PDUH�� FX� DWkW� VHQVLELOLWDWHD� ³6´� HVWH� PDL� SXWHUQLF � úL� VH� YD� SXWHD�EHQHILFLD�GH�VF GHUHD�UDWHL�GREkQ]LL��ÌQWU-R�DVWIHO�GH�FRQMXQFWXU �YRU�IL�FXPS UDWH�DFHOH�WLWluri cu cea PDL�PDUH�GXUDW �³'´�SRVLELO � ,QYHUV�� GDF � VH� DúWHDSW � R� FUHúWHUH� D� UDWHL� GREkQ]LL� FDUH� DUH� HIHFW� QHJDWLY� DVXSUD� FXUVXOXL�REOLJD LXQLORU�� VH� YRU� DOHJH� DFHOH� WLWOXUL� FX�FHD�PDL�PLF � GXUDW � ³'´� úL� LPSOLFLW� FX� FHD�PDL�PLF �sensibilitate “S”. RatD�QRPLQDO �úL�PRGXO�GH�FDOFXO�DO�GREkQ]LORU 5DWD�QRPLQDO �D�GREkQ]LL��UDWD�IDFLDO ��HVWH�UDWD�FDUH�SHUPLWH�GHWHUPLQDUHD�VXPHL�GREkQ]LORU�SRUQLQG�GH�OD�YDORDUHD�QRPLQDO �D�WLWOXOXL��$FHDVW �UDW �QX�WUHEXLH�V �ILH�FRQIXQGDW �FX�UDWD�DFWXDO �care se evalueaz �FDOFXOkQG�UDWD�GH�UHQWDELOLWDWH�LQWHUQ �D�LQYHVWL LHL�vQ�REOLJD LXQL� )LH� R� REOLJD LXQH� FX� R� YDORDUH� QRPLQDO � GH� ������ úL� R� GXUDW � GH� YkUVW � GH� ��� DQL�� UDWD�QRPLQDO �HVWH�GH�����úL�FRQGXFH� OD�SODWD�XQHL�GREkQ]L�DQXDOH�GH������$FHDVW �REOLJD LXQH�D�IRVW�HPLV �GH����� 3ULPD�GH�HPLVLXQH�HVWH�GHFL�GH�����(D�YD�IL�UDPEXUVDW �OD�������SULPD�GH�UDPEXUVDUH�HVWH�GH���� 5DWD�DFWXDULDO �5�HVWH�DWXQFL�GH�
∑= +
++
=10
1t10t )R1(
050.1
)R1(
100980 úL R = 10,64%
$FHDVW � UDW � UHSUH]LQW � UHQWDELOLWDWHD� RSHUD LHL� SHQWUX� LQYHVWLWRUL� LQJQRUkQG� LQFLGHQ D�ILVFDOLW LL�SHUVRQDOH�úL�FRVWXULOH�GH�WUDQ]L LH�
���������0RGDOLW L�GH�UDPEXUVDUH�D�vPSUXPXWXOXL�REOLJDWDU ([LVW �PDL�PXOWH�PRGDOLW L�GH�UDPEXUVDUH�D�vPSUXPXWXOXL�REOLJDWDU� 1) Rambursarea la finalul perioadei ¾ Rambursarea capitalului se�IDFH�R�VLQJXU �GDW �OD�ILQHOH�GXUDWHL�GH�YLD �D�vPSUXPXWXOXL��6LQJXUD�
FKHOWXLDO � VXSRUWDW � vQDLQWHD� VFDGHQ HL� HVWH� SODWD� GREkQ]LORU�� $FHDVW � PHWRG � HVWH� vQVR LW �adeseori de constituirea unui fond de rambursare.
2) 5DPEXUVDUHD�SULQ�DQXLW L�FRQVWDQWH ¾ &RQVW � vQ� UDPEXUVDUHD� vQ� ILHFDUH� DQ� D� XQHL� VXPH� FRQVWDQWH� HJDO � FX� VXPD� GREkQ]LORU� úL� D�
UDPEXUV ULL�FDSLWDOXOXL� 5DWD�GH�UDPEXUVDW�GLQ�ILHFDUH�DQ�VH�GHWHUPLQ �UDSRUWkQG�YDORDUHD�QRPLQDO �D�vPSUXPXWXOXL�
OD� GXUDWD� GH� YLD �� LDU� GREkQGD� VH� GHWHUPLQ � vQ� ILHFDUH� DQ� Srin aplicarea ratei dobânzii la YDORDUHD�U PDV �GH�UDPEXUVDW�
3) Rambursarea prin serii egale ¾ &RQIRUP�DFHVWHL�PHWRGH��vQWUHSULQGHUHD�DPRUWL]HD] �XQ�DFHODúL�QXP U�GH�REOLJD LXQL�vQ�ILHFDUH�
an. Serviciul împrumutului cuprinde atunci o rambursare a capitalului cRQVWDQW� úL� R� VXP � D�GREkQ]LORU�GHVFUHVF WRDUH�FX� WLPSXO��&KHOWXLHOLOH�ILQDQFLDUH�VXQW�PDL�PDUL� OD� vQFHSXWXO�GXUDWHL�GH�YLD �D�vPSUXPXWXOXL�
4) Rambursarea sub forma cuponului unic ¾ 3UHVXSXQH� FD� GREkQ]LOH� V � QX� ILH� Y UVDWH� DQXDO� FL� GRDU� FDSLWDOL]DWH� úL� UHJODWH� R� GDW � FX�
rambursarea la finele perioadei a sumei împrumutate. 9DORDUHD�UHDO �D�REOLJD LXQLORU��UHVSHFWLY�SUH XUL�GH�HPLVLXQH�DO�DFHVWRUD��HVWH�LQIOXHQ DW �GH�
PRGDOLW LOH�GH�UDPEXUVDUH�D� vPSUXPXWXOXL�GHRDUHFH�IOX[XULOH�JHQHUDWH�GH�UDPEXUVDUH� LQWU � vQ�relD LD�GH�FDOFXO�D�YDORULL�UHDOH��SUH XO�GH�HPLVLXQH��
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
Cazul amortizare în serii egale (rambursare).
∑= +
==T
1tt
tre
)i1(
AVP ,
în care: At - anuitatea de anul “t” (dobânda anului “t” + rata de rambursat în anul “t”); i - rata dobânzii la termen; t -�GXUDWD�GH�YLD �D�vPSUXPXWXOXL� Cazul rambursare sub forma cuponului unic.
t
dt
t
re)r1(
)i1(VNVP
++= ,
în care: I -�UDWD�QRPLQDO �D�GREkQ]LL� Rdt - rata dobânzii la termen. 9DORDUHD�UHDO �D�REOLJD LXQLL Exemplu: 1) Fie împrumut obligatar cu o dXUDW � GH� YLD � GH� �� DQL�� vQ� FDGUXO� F UXLD� V-au emis ��������REOLJD LXQL�D�FkWH������� �91��5DWD�QRPLQDO �D�GREkQ]LL�HVWH�GH�������6H�FRQVLGHU �LSRWH]D�DPRUWL] ULL�SULQ�VHULL�HJDOH��6 �VH�GHWHUPLQH�FDUH�HVWH�YDORDUHD� UHDO �D�DFHVWXL� vPSUXPXW�REOLJDWDU�cunosFkQG�F �UDWHOH�GREkQ]LL�OD�WHUPHQ�vQFHSkQG�GLQ�SULPXO�DQ�SkQ �vQ�DO�FLQFLOHD�DQ�VXQW�GH���� Rezolvare��3HQWUX�R�REOLJD LXQH�
• ratele de rambursat 1.000/5 an = 200/an • GREkQ]LOH�DIHUHQWH�ILHF UXL�DQ���������������������
Anul Valoarea
QRPLQDO Rata de rambursat
Dobânda Valoarea U PDV
Anuitatea
1 1.000 200 (1.000 * 8,5%)85 800 285 2 800 200 (800 * 8,5%)68 600 268 3 600 200 (600 * 8,5%)51 400 251 4 400 200 (400 * 8,5%)34 200 234 5 200 200 (200 * 8,5%)17 -- 217
9DORDUHD�UHDO �D�XQHL�REOLJD LXQL�VH�SRDte determina astfel:
∑=
=+
++
++
++
++
=+
=5
1t54321t
tr 6,963
)10,01(
217
)10,01(
234
)10,01(
251
)10,01(
268
)10,01(
285
)r1(
AV
5H]XOWDWXO�RE LQXW�DUDW �F �SHQWUX�XQ� LQYHVWLWRU�FDUH�FXPS U �REOLJD LXQL��SUH XO�GH��������
HVWH�DFRSHULW�GH�IOX[XULOH�ILQDQFLDUH�YLLWRDUH�DFWXDOL]DWH�vQ�IXQF LH�GH�UDWD�GREkQ]LL�SH�SLD �
Pentru întreg împruPXWXO�VXPD�FH�SRDWH�IL�SO WLW �OD�VXEVFULHUH�HVWH�
100.000 oblig. ⋅ 963,65 = 96.365.000
���&DUH�HVWH�SUH XO�GH�FXPS UDUH�DO�XQHL�REOLJD LXQL�HPLV �SHQWUX�R�GXUDW �GH����DQL�� OD�R�
YDORDUH�QRPLQDO �GH�������úL�FX�R�UDW �QRPLQDO �D�GREkQ]LL�GH������FXQRVFkQG�F �UDPEXUVDUHD�VH�
face sub forma cuponului unic în care rata dobânzii la termen este de 15%?
Rezolvare��'HRDUHFH�UDWD�GH�DFWXDOL]DUH�EUXW �HVWH�FHD�FDUH�HJDOL]HD] �YDORDUHD�DFWXDO �D�DQXLW LORU�
YLLWRDUH�FX�SUH XO�SO WLW�SHQWUX�REOLJD LXQH�vQ�PRPHQWXO�FXPS U ULL�HL��HVWH�QHFHVDU�V �VH�GHWHUPLQH�
DFHVW�SUH �
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
Anul Valoarea QRPLQDO
Rata de rambursat
Dobânda Valoarea U PDV
Anuitate
1 1.800 450 216 1.350 666 2 1.350 450 162 900 612 3 900 450 108 450 558 4 450 450 54 0 504
91,684.1)13,01(
504
)13,01(
558
)13,01(
612
)13,01(
666P
432e =+
++
++
++
=
SH� VFULH� vQ�FRQWLQXDUH� SUH XO� GLQ�PRPHQWXO� HPLVLXQLL� REOLJD LXQLORU� FD� ILLQG� HJDO� FX� VXPD�DQXLW LORU�YLLWRDUH�DFWXDOL]DWH�vQ�IXQF LH�GH�UDWD�GH�DFWXDOL]DUH�EUXW ��³U´��
432 )r1(
504
)r1(
558
)r1(
612
)r1(
66691,684.1
++
++
++
+=
Utilizând tabelele matematice se poate determina rata r = 13%. 6HQVLELOLWDWHD�REOLJD LXQLORU )LH�XQ�vPSUXPXW�FX�R�GXUDW �GH�YLD �GH���DQL��vQ�FDGUXO�F UXLD�V-DX�HPLV���������REOLJD LXQL�OD�R�YDORDUH�QRPLQDO �GH������3UH XO�SO WLW�GH�VXEVFULLWRU�vQ�PRPHQWXO�FXPS U ULL�REOLJD LXQLORU�HVWH�395 pentru fiecare, iar raWD�QRPLQDO �HVWH�GH�����$PRUWL]DUHD�VH�IDFH�vQ�VHULL�FRQVWDQWH��LDU�UDWD�GH�DFWXDOL]DUH� EUXW � HVWH� GH� ������ 6 � VH� VWDELOHDVF � SODQXO� GH� DPRUWL]DUH� DO� vPSUXPXWXOXL� úL� V � VH�GHWHUPLQH�VHQVLELOLWDWHD�REOLJD LXQLORU�
Rezolvare: Planul de amortizare al unei oblLJD LXQL�VH�SUH]LQW �DVWIHO�
Anul Rata de rambursat Dobânda Anuitatea r)tt/(1At +⋅
1 62,5 80 142,5 129
2 62,5 73,75 136,25 112,6
3 62,5 67,5 130 97,74
4 62,5 61,25 123,75 84,52
5 62,5 55 117,5 72,98
6 62,5 48,75 111,25 62,85
7 62,5 42,50 105 54,12
8 62,5 36,25 98,75 46,14
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6HQVLELOLWDWHD�úL�GXUDWD�GH�LPXQL]DUH 5DQGDPHQWXO�DFWXDULDO�DO�XQHL�REOLJD LXQL�HPLV � OD�R�YDORDUH�QRPLQDO �GH��������SHQWUX�R�dXUDW �GH����DQL�úL�UDPEXUVDELO �OD�ILQDOXO�SHULRDGHL��HVWH�GH������� 6 �VH�GHWHUPLQH�VHQVLELOLWDWHD��³6´�úL�GXUDWD�GH�WLPS�³'´�vQ�FDUH�IOX[XULOH�ILQDQFLDUH�RE LQXWH�GLQ� GREkQ]L� FRPSHQVHD] � SLHUGHUHD� SURYRFDW � GH� UDWD� LQIOD LHL�� FXQRVFkQG� F � YDORDUHD� UHDO a REOLJD LXQLL�HVWH��������LDU�UDWD�QRPLQDO �D�GREkQ]LL�GH����� Rezolvare��6LWXD LD�DPRUWL] ULL�vPSUXPXWXOXL�HVWH�SUH]HQWDW �vQ�WDEHOXO�XUP WRU�
Anul Rate de rambursat Dobânda Anuitatea (At) U�WW���$ W �� 1 1.500 1.500 1367,98 2 1.500 1.500 2495,217 3 1.500 1.500 3413,48 4 1.500 1.500 4150,81 5 1.500 1.500 4731,6 6 1.500 1.500 5178,36 7 1.500 1.500 5509,78 8 1.500 1.500 5744,37 9 1.500 1.500 5892,62
10 15.000 1.500 16.500 65684,71
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• ����REOLJD LXQL�FX�91� ��������WRWDO� ��������� • PE = 990, PR = 1.025, D = 10,50%, T = 8 ani; • cheltuieli de seUYLFLX�DOH�vPSUXPXWXOXL� ���REOLJD LXQH� • UHGXFHUHD� VDUFLQLORU� ILVFDOH� DVXSUD� FKHOWXLHOLORU� ILQDQFLDUH� úL� D� FKHOWXLHOLORU� GH� VHUYLFLX�
ale împrumutului = 50%. 6 �VH�GHWHUPLQH�FRVWXO�vPSUXPXWXOXL�REOLJDWDU�
Rezolvare��6H�REVHUY �F �vQWUHSULQGHUHD�DQJDMHD] �úL alte cheltuieli decât cele financiare (principal �� GREkQG ��� GDU� UHDOL]HD] � úL� R� HFRQRPLH� GH� FKHOWXLHOL� HJDO � FX� ���� GLQ� WRWDOXO� FKHOWXLHOLORU�(cheltuieli financiare + cheltuieli de serviciu). LQkQG� FRQW� GH� FDUDFWHULVWLFLOH� vPSUXPXWXOXL�� SHQWUX� R� REOLJD LXQH� FKHOWXLHOLOH� DQXDOH� DOH�emitentului sunt de 55.
552
5%)50,10000.1( =+⋅
/D� R� LQWUDUH� QHW � GH� WUH]RUHULH� GH� ���� �3(�� FRUHVSXQG� LHúLUL� QHWH� GH� WUH]RUHULH� GXS � FXP�XUPHD] �
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
• 55 în fiecare din primii 7 ani; • 1.080 în al 8-lea an (PR = 1.025, dobânzi = 55). &RVWXO� QHW� DO� vPSUXPXWXOXL� REOLJDWDU� VH� RE LQH� SULQ� FDOFXOXO� DFWXDULDO�� UH]ROYkQG� HFXD LD�
XUP WRDUH�
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025.1300
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55300...
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55300
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55300990300
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GH�XQGH�VH�RE LQH�L� �������
�������),1$1 $5(�35,1�&5(',7-BAIL (LEASING)
���������'HVFULHUHD�RSHUD LXQLL În ultimii ani, în� DUD� QRDVWU �� WHUPHQXO� GH� ³OHDVLQJ´� D� GHYHQLW� GLQ� FH� vQ� FH�PDL� IUHFYHQW�XWLOL]DW��FX�SUHSRQGHUHQ �vQ�VIHUD�HFRQRPLFXOXL� /D�SULPD�YHGHUH��DFHDVWD�GHILQHúWH�R�RSHUD LXQH�FRPHUFLDO � VSHFLILF �VH�SDUH�QX� úL-D�J VLW�corespondent în terminologia de specialitDWH� URPkQHDVF �� 3ULQFLSDOXO� DYDQWDM� DO� SURFHVXOXL� HVWH�XUP WRUXO��vQFKLULH]L�XQ�EXQ��SHQWUX�FDUH�OD�RUD�UHVSHFWLY �QX�DL�EDQL�V -O�DFKL]L LRQH]L�GHILQLWLY��vO�XWLOL]H]L��FUHkQG�QRL�YDORUL�úL��vQ�ILQDO��GHYLL�SURSULHWDUXO�V X��1X�HVWH�YRUED�GH�R�YkQ]DUH�SH�credit GHFkW�vQ�FHHD�FH�SULYHúWH�REOLJD LD�GH�SODW �D�XQHL�S U L�GLQ�SUH XO�GH�YkQ]DUH�DO�EXQXOXL��LQFOXV �vQ�chirie. Leasing-XO� SRDWH� IL� FRQVLGHUDW� úL� FD� R� IRUP �DSDUWH� D� FUHGLWXOXL� EDQFDU�� vQ� ORF� GH� EDQL� VXQW�vPSUXPXWDWH�P UIXUL�FRQFUHWH��PDúLQL��XWLODMH��LQVWDOD LL��DSDUDWXU ��GLYHUVH�EXQXUL�PRELOH�VDX�LPRELOH� ÌQ�JHQHUDO��OD�H[SLUDUHD�FRQWUDFWXOXL�GH�OHDVLQJ��EHQHILFLDUXO�WUHEXLH�V �RSWH]H�SHQWUX�SUHOXQJLUHD�FRQWUDFWXOXL�FX�R�FKLULH�PDL�PLF �VDX�FXPS UDUHD�EXQXOXL�UHVSHFWLY�VDX�UHVWLWXLUHD�DFHVWXLD� Prin prisma VRFLHW LL�GH� OHDVLQJ�RSHUD LXQHD�UHSUH]LQW �R�FXPS UDUH�D�XQXL�EXQ�vQ�VFRSXO�vQFKLULHULL��XUPDW �GH�R�vQFKLULHUH�vQ�VFRSXO�YkQ] ULL��'DF �OD�VIkUúLWXO�SHULRDGHL�GH�vQFKLULHUH�EXQXO�WUHFH�vQ�SURSULHWDWHD�EHQHILFLDUXOXL��SXWHP�VSXQH�F �OHDVLQJ-uO�UHSUH]LQW �R�RSHUD LXQH�GH�YkQ]DUH�FX�SODWD�vQ�UDWH��DVHP QDUHD�ILLQG�HYLGHQW �QXPDL�SULQ�SULVPD�ILQDOLW LL��'HRVHELUHD�FRQVW �vQ�IDSWXO�F ��GDF �SULQ�RSHUD LXQHD�GH�YkQ]DUH��XQ�DQXPLW�EXQ�HVWH�VFKLPEDW�vQ�PDUI ��RE LQkQGX-se echivalentul HL�E QHVF��SULQ�OHDVLQJ�VH�FHGHD] �GUHSWXO�GH�IRORVLQ �D�XQXL�EXQ� Din punct de vedere al beneficiarului, leasing-XO�FRQVWLWXLH�R�IRUP �vQ�FDGUXO�F UHLD�VXPHOH�QHFHVDUH�DFKL]L LRQ ULL�EXQXOXL�VH�RE LQ�GLQ�H[SORDWDUHD�DFHVWXLD��LDU�UDPEXUVDUHD�OXL�VH�IDFH�HúDORQDW�sub IRUPD� UDWHORU� GH� OHDVLQJ� úL�� vQ� ILQDO�� D� SUH XOXL� UH]LGXDO�� &UHGLWXO� RE LQXW� QX� HVWH� VXE� IRUP �E QHDVF ��FL�VXE�IRUP �GH�HFKLSDPHQWH� Leasing-XO�VH�GHRVHEHúWH�GH�XQ�FRQWUDFW�GH��vQFKLULHUH�GLQ�XUP WRDUHOH�SXQFWH�GH�YHGHUH�
• la calculul ratelor de leasing: UDWHOH� GH� OHDVLQJ� VH� VWDELOHVF� vQ� IXQF LH� GH� SUH XO� GH�DFKL]L LH� DO�EXQXOXL� úL� GH�XQHOH� HOHPHQWH� SUHGHILQLWH� �GREkQG ��SURILW�� ULVF��79$�HWF����FKLULD� OD� vQWUH LQHUH�VH�VWDELOHúWH� vQ�IXQF LH�GH�FRQGL LLOH�H[LVWHQWH�SH�SLD �úL� UHSUH]LQW �contravaloarea dreSWXOXL�GH�IRORVLQ �
• DO�GUHSWXOXL�GH�SURSULHWDWH��OD�OHDVLQJ��OD�ILQHOH�SHULRDGHL�GH�ORFD LH�EXQXO�SRDWH�WUHFH�vQ�SRVHVLD�EHQHILFLDUXOXL� vQ� ED]D� FKLULHL� SO WLWH� úL� D� XQXL� SUH � UH]LGXDO�� EXQXO� vQFKLULDW�QX�SRDWH� WUHFH� vQ� SURSULHWDWHD� FKLULDúXOXL� OD� VIkUúLWXO� ORFD LHL�� SHQWUX� RSHUD LXQHD� GH�închiriere, decât în baza unui contract distinct de vânzare-FXPS UDUH�
���������3DUWLFLSDQ LL�OD�RSHUD LXQHD�GH�OHDVLQJ &XYkQWXO� ³OHDVLQJ´�FDUH�SURYLQH�GLQ�HQJOH]HVFXO�³WR� OHDVH´�VHPQLILFkQG�³D� O VD� vQ�JULM �� D�închiria” QH�DUDW �SRVLELOLWDWHD�GH�RE LQHUH�D�GUHSWXOXL�GH�IRORVLQ �HFRQRPLF �D�XQXL�DFWLY�SHQWUX�R�SHULRDG �GHWHUPLQDW ��)DSWXO�F �YDORDUHD�XQXL�DFWLY�Q�UH]LG �vQ�SURSULHWDWHD��FL�vQ�XWLOLWDWHD�DFHVWXLD��este pe deplin confirmat de amploarea pe care a înregistrat-o leasing-XO� GXS � DO� GRLOHD� U ]ERL�PRQGLDO� vQ� ULOH� RFFLGHQWDOH�� 2ULFH� VRFLHWDWH� FRPHUFLDO � DWLQJH� OD� XQ� PRPHQW� GDW�� vQ� FDGUXO�SURFHVXOXL� GH� GH]YROWDUH� QRUPDO �� VWDGLXO� OD� FDUH� GHYLQH� LQWHUHVDW � GH� HFKLSDPHQWH� úL� XWLODMH� GH�SURGXF LH�VXSOLPHQWDUH��3HQWUX procurarea acestora, firma poate folosi resurse financiare interne sau H[WHUQH��DWUDVH���'LQ�DFHDVW �FDWHJRULH�GH�VXUVH�GH�ILQDQ DUH�IDFH�SDUWH�úL�OHDVLQJ-ul.
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
ÌQ� HVHQ �� OHDVLQJ-XO� HVWH� R� RSHUD LXQH� FDUH� SUHVXSXQH�� vQ� SULQFLSLX�� GRX � FRQWUDFWH�� XQXO� GH�vânzare-FXPS UDUH�� vQFKHLDW� vQWUH� RUJDQL]D LD� SURGXF WRDUH�� FD� YkQ] WRU� úL� RUJDQL]D LD� ILQDQFLDU ��VRFLHWDWHD�GH�OHDVLQJ��FDUH�FUHGLWHD] �RSHUD LXQHD�GH�OHDVLQJ�vQWUH�VRFLHWDWHD�GH�OHDVLQJ�úL�R�WHU �SHUVRDQ � 2�WUDQ]DF LH�VWDQGDUG�GH�OHDVLQJ�LPSOLF �XUP Wori factori:
• locatarul –�FXPS U WRUXO�úL�SURSULHWDUXO�HFKLSDPHQWXOXL� • locatarul – debitorul sau lesantul; • furnizorul –�YkQ] WRUXO�EXQXOXL� • VXUVD�GH�ILQDQ DUH�–�R�EDQF ��XQ�IRQG�GH�LQYHVWL LL�VDX�R�FRPSDQLH�GH�FUHGLW�ILQDQFLDU� • R�FRPSDQLH�GH�DVLJXU UL�FDUH�DVLJXU �HFKLSDPHQWXO Locatarul VHOHF LRQHD] �HFKLSDPHQWXO�QHFHVDU�SH�SLD �úL�QHJRFLD] �XQ�FRQWUDFW�FX�ORFDWDUXO�
(o companie de leasing). El este beneficiarul leasing-XOXL�úL�DUH�GUHSWXO�GH�IRORVLQ �DVXSUD�EXQXOXL�vQFKLULDW��GHFLGH�DVXSUD�DFKL]L LRQ ULL�DFHVWXLD��U VSXQGH�GH�PRGXO�GH�XWLOL]DUH�D�DFHVWXLD�úL�VXSRUW �SHQDOLW L�vQ�FD]XO�QHUHVSHFW ULL�FODX]HORU�FRQWUDFWXDOH�
Obiectul leasing-XOXL�QX�YD�IL�VXSXV�LPSR]LWXOXL�SH�DFWLYLW L�OXFUDWLYH�úL�QLFL�LPSR]LWXOXL�SH�profit, iar ratele de leasing sunt înregistrate ca fiind cheltuieli ale întreprinderii.
/D�VIkUúLWXO�ORFD LHL��EHQHILFLDUXO�SRDWH�GREkQGL�vQ�SURSULHWDWH�EXQXO�vQ�ED]D�FKLULHL�SO WLWH�úL�D�XQXL�SUH �UH]LGXDO�FDUH�FRQVWLWXLH�XOWLPD�WUDQú �GH�SODW �
Locatarul, utilizând fondurile furnizate de surseOH�SURSULL�GH�ILQDQ DUH��FXPS U �HFKLSDPHQWXO�GH� OD� IDEULFDQW� úL� vO� vQFKLULD] � ORFDWDUXOXL�� (O� HVWH� SURSULHWDUXO� MXULGLF� úL� HFRQRPLF� DO� RELHFWXOXL� GH�OHDVLQJ��OD�DFHDVWD�DUH�ORF�LPSXQHUHD�úL� vQUHJLVWUDUHD�vQ�ELODQ �D�RELHFWXOXL�GH�OHDVLQJ��/RFDWDUXO�VDX�fiQDQ DWRUXO�YHULILF �DO WXUL�GH�EHQHILFLDU�VWDUHD�EXQXULORU�OLYUDWH��SUHFXP�úL�PRGXO�GH�H[SORDWDUH�D�ORU��VWDELOHúWH�úL�vQFDVHD] �UDWHOH�GH�OHDVLQJ��vQFKHLH�úL�HYHQWXDO�UH]LOLD] �FRQWUDFWXO�GH�OHDVLQJ�WUDQVIHUkQG�în final dreptul de proprietate asupra benefLFLDUXOXL�GXS �DFKLWDUHD�YDORULL�UH]LGXDOH.
Furnizorul� vQFDVHD] � FRQWUDYDORDUHD� EXQXOXL� OLYUDW� F WUH� EHQHILFLDU� úL� HYHQWXDO� DVLJXU �service-XO�SH�SHULRDGD�GH�ORFD LH��3UH XULOH�GH�FXPS UDUH�D�EXQXULORU�FXPS UDWH�GH�F WUH�IXUQL]RUXO�de leasing sunt scadente�OD�SODW �GXS �SUHOXDUHD�ORU�GH�F WUH�EHQHILFLDUXO�GH�OHDVLQJ�
În vederea ILQDQ ULL�LQYHVWL LLORU�GH�OHDVLQJ��VRFLHW LOH�GH�OHDVLQJ�IRORVHVF�IRQGXUL�SURSULL��FRQWUDFWHD] �FUHGLWH�EDQFDUH�úL�VDX�vúL�SURFXU �PLMORDFHOH�QHFHVDUH�SULQ�YkQ]DUHD�FUHDQ HORU�DVXpra beneficiarilor leasing-ului.
Pentru a-úL� SURWHMD� LQWHUHVHOH� úL� SHQWUX� D� VH� DVLJXUD� F � YD� SXWHD� SO WL� FHD� FH� GDWRUHD] �ILQDQ DWRUXOXL� V X�� ORFDWDUXO� YD� vQFKHLD� XQ� FRQWUDFW� FX� R� VRFLHWDWH� GH� DVLJXU UL� úL� YD� DVLJXUD�HFKLSDPHQWXO��DFHDVW �FKHOWXLDO �UHFXSHrându-VH�GH�OD�ORFDWDU�úL�UHSUH]HQWkQG�SUH XO�FH�WUHEXLH�SO WLW�SHQWUX�D�RE LQH�FUHGLWXO�� ÌQ� FD]XO� vQ�FDUH�HVWH�PDL�DYDQWDMRV� �SHQWUX� ORFDWDU� V � vQFKHLH�HO� vQVXúL�R�SROL � GH� DVLJXUDUH�� GDF � DFHDVWD� vL� HVWH� SHUPLV� SULQ� FRQWUDFW�� DFHVWD� YD� VXSRUWD� ULVFXO� SLerderii obiectului (riscul pierderii nu va mai fi inclus în rata de leasing), societatea de leasing primind o SROL �GH�DVLJXUDUH�GLQ�SDUWHD�VRFLHW LL�GH�DVLJXU UL�
���������(WDSHOH�GHUXO ULL�RSHUD LXQLL�GH�OHDVLQJ Leasing-XO� HVWH� R� DFWLYLWDWH� FRPSOH[ � FDUH� SUHVXSXQH� H[LVWHQ D� D� QXPHURDVH� RSHUD LXQL� úL�GRFXPHQWH�SULQ�FDUH�VH�UHJOHPHQWHD] �FRQGL LLOH�HFRQRPLFR-MXULGLFH�vQ�FDUH�VH�GHVI úRDU ��'HUXODUHD�XQHL�RSHUD LXQL�GH�OHDVLQJ�QHFHVLW �SDUFXUJHUHD�PDL�PXOWRU�HWDSH�SH�FDUH�OH�YRP�HQXPHUD�PDL�MRV: 1) CercetareD�SLH HORU�LQWHUQH�úL�H[WHUQH�vQ�YHGHUHD�LGHQWLILF ULL�SURGXVHORU�FDUH�YRU�IL�SURPRYDWH�
SULQ�GLIHULWH�IRUPH�GH�FRPHU �úL�VWXGLHUHD�ERQLW LL�RSHUD LXQLORU� %HQHILFLDUXO�YD�DQDOL]D�WRDWH�H[LVWHQWH�SH�SLD �úL�GLQWUH�DFHVWHD�YD�DOHJH�RIHUWD��VDX�RIHUWHOH��
caUH�HVWH�PDL�DYDQWDMRDV �SHQWUX�RELHFWLYHOH�VDOH� Trece apoi la negocieri cu furnizorul echipamentelor cu privire la toate detaliile legate de
HFKLSDPHQWHOH�GH�FDUH�DUH�QHYRLH��GH�OD�FDUDFWHULVWLFLOH�WHKQLFH�SkQ �OD�SUH XO�ILQDO�DO�DFHVWRUD��)LUPD�de leasinJ�QX�LQWHUYLQH�vQ�DOHJHUHD�I FXW �GH�FOLHQW�GHFkW�vQ�HYHQWXDOLWDWHD�vQ�FDUH�SRDWH�SURSXQH�R�YDULDQW �PDL�FRQYHQDELO �GLQ�SXQFW�GH�YHGHUH�DO�SHUIRUPDQ HORU��DO�UDSRUWXOXL�FDOLWDWH-SUH �
ÌQ� PRPHQWXO� vQ� FDUH� EHQHILFLDUXO� DUH� RIHUWD� ILQDO � �FXSULQ]kQG� WRDWH� GHtaliile din partea IXUQL]RUXOXL��SRDWH�WUHFH�OD�SDVXO�XUP WRU�
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
2) Negocierea contractului de leasing��&OLHQWXO�FRQWUDFWHD] �R�ILUP �GH�OHDVLQJ�úL�LQWU �vQ�WUDWDWLYH�FX� DFHDVWD� SUH]HQWkQG�R� FHUHUH� GH� RE LQHUH� D� XQRU� EXQXUL� vQ� OHDVLQJ�� 7UDWDWLYHOH� FX� VFRSXO� V FRQYLQJ � ILUPD�GH� OHDVLQJ�V �FXPSHUH�XWLODMXO� � UHVSHFWLY��SH�FDUH�XUPHD] �V -l închirieze apoi FOLHQWXOXL��ÌQ�YHGHUHD�FRQVWLWXLULL�XQXL�GRVDU�FkW�PDL�IXQGDPHQWDW�úL�FX�úDQVH�UHDOH�GH�DSUREDUH��FOLHQWXO� WUHEXLH� V � SUH]LQWH� R� VHULH� GH� GRFXPHQWH� SHQWUX� D-úL� VXV LQH� FkW�PDL� ELQH� SXQFWXO� GH�YHGHUH��VFXUW�LVWRULF�DO�ILUPHL��ELODQ XO�FX�WRDWH�DQH[HOH��LQFOXVLY�UDSRUWXO�GH�JHVWLXQH�SH�XOWLPHOH�2-��H[HUFL LL�ILQDQFLDUH��EDODQ D�GH�YHULILFDUH�OD�]L��IOX[XO�GH�QXPHUDU�SUHYL]LRQDW�SH�R�SHULRDG �de minim 2 ani).
3) Semnarea contractului de leasing�� ÌQ�FD]XO� vQ�FDUH�SURLHFWXO�úL� ILUPD�VROLFLWDQW �GH�XWLODMH�GH�
SURGXF LH� vQGHSOLQHVF� WRDWH� FRQGL LLOH� VROLFLWDWH�� VRFLHWDWHD�GH� OHDVLQJ� YD� DSURED� WUDQ]DF LD��$U�XUPD� VHPQDUHD� FRQWUDFWXOXL� vQWUH� S U L� �OHVDQW� úL� OHVRU��� FX� WRDWH� GUHSWXULOH� úL� REOLJD LLOH� FH�GHFXUJ�GLQ�DFHDVWD��%HQHILFLDUXO�GH�OHDVLQJ�YD�RE LQH�R�FRQILUPDUH�D�VROLFLW ULL�OHDVLQJ-ului, un H[HPSODU�VHPQDW�DO�FRQWUDFWXOXL�GH�OHDVLQJ��SUHFXP�úL�R�FRQILUPDUH�GH�SUHOXDUH��$OWH�GRFXPHQWH�ale contractului sunt elaborate în�IXQF LH�GH�VWUXFWXUD�RSHUD LXQLL�úL�GH�vQ HOHJHUL��ÌQ�DFHODúL�WLPS�firma de leasing încheie contractul de vânzare-FXPS UDUH�D�XWLODMXOXL�FX�IXUQL]RUXO�DFHVWXLD�
4) Livrarea bunurilor�� $FHDVW � VDUFLQ � FDGH� vQ� VHDPD� SURGXF WRUXOXL� HFKLSDPHQWXOXL� FDUH� YD�
trebuLH� V � OLYUH]H� HFKLSDPHQWXO� GLUHFW� EHQHILFLDUXOXL� GH� OHDVLQJ�� 'XS � RE LQHUHD� RELHFWXOXL�leasing-XOXL��EHQHILFLDUXO�GH�OHDVLQJ�WULPLWH�R�FRQILUPDUH�OHJDO �GH�SULPLUH�OD�vQWUHSULQGHUHD�GH�OHDVLQJ�� )DFWXUD� HPLV � GH� ILUPD� SURGXF WRDUH� YD� IL� RQRUDW � SH� ORF� GH� ILrma de leasing. %HQHILFLDUXO�GH�OHDVLQJ�SULPHúWH�R�GHFRQWDUH�VRPD LH�GH�SODW �FRQ LQkQG�GDWH�GHILQLWLYH�GH�SODW �(termenul de intrare în vigoare a contractului, valoarea facturii, ratele de leasing etc.). Ratele de OHDVLQJ�VH�SO WHVF�GH�RELFHL�SULQ�EDQF �
5) 2S LXQHD� EHQHILFLDUXOXL��/D� VIkUúLWXO� FRQWUDFWXOXL� DUH� ORF� UHWXUQDUHD�HFKLSDPHQWXOXL� VRFLHW LL�GH� OHDVLQJ�� 'DF � EHQHILFLDUXO� GRUHúWH� V � SUHOXQJHDVF � FRQWUDFWXO� VDX� V � LQWUH� vQ� SRVHVLD�HFKLSDPHQWXOXL� UHVSHFWLY�� QRXD� FKLULH� �PDL� PLF �� VDX� DFKL]L LRQDUHD� EXQului (la o valoare UH]LGXDO �VWDELOLW �DQWHULRU��VH�YRU�UHJOHPHQWD�SULQ�DFRUGXUL�vQFKHLDWH�VHSDUDW�
4.2.3.4. Rata de leasing 5DWD�GH�OHDVLQJ�HVWH�XQ�HOHPHQW�GHRVHELW�GH�LPSRUWDQW�DO�RSHUD LXQLL�GH�OHDVLQJ��0HWRGHOH�GH�FDOFXO� GLIHU � GH� OD� R� VRFLHWDWH� OD� DOWD�� vQ� HVHQ � HOH� FXSULQG� R� VHULH� GH� HOHPHQWH�FX� R� YDODELOLWDWH�JHQHUDO �
¾ SUH XO�GH�DFKL]L LH�DO�EXQXOXL�OD�FDUH�VH�DGDXJ �FKHOWXLHOLOH�HIHFWXDWH�FX�WUDQVSRUWXO��SODWD�WD[HORU�GH�FXPS UDUH�úL�DOWH�FKHOWXLHOL�OHJDWH�GH�DFKL]L LRQDUHD�HFKLSDPHQWXOXL�
¾ valoarHD� UH]LGXDO �HVWH� UHJOHPHQWDW �SULQ� OHJH� vQ�XQHOH� UL�� LDU�DFROR�XQGH�QX�H[LVW �R�astfel de lege se va negocia prin contract;
¾ GXUDWD� ORFD LHL� úL� FXDQWXPXO� DPRUWL] ULL� LQIOXHQ HD] � FXDQWXPXO� úL� QXP UXO� UDWHORU� GH�OHDVLQJ�� 'XUDWD� DPRUWL] ULL� ILVFDOH� HVWH�� GH� UHJXO �� LGHQWLF � FX� GXUDWD� QRUPDO � GH�IXQF LRQDUH�� $PRUWL]DUHD� ILVFDO � HVWH� FDOFXODW � SURFHQWXDO�� VH� DSOLF � FKHOWXLHOLORU� GH�capital;
¾ DVLJXUDUHD��JDUDQ LD��SLHUGHUH��IXUW��IRF��GDF �HVWH�UHDOL]DW �GH�IXUQL]RUXO�OHDVLQJ-ului este VXSRUWDW �GH�EHQHILFLDU�
¾ FKHOWXLHOLOH�QHSUHY ]XWH�VH�FDOFXOHD] �FD�SURFHQW�GH�PD[LP����GLQ�P ULPHD�ILQDQ ULL��VXQW�GLILFLO�GH�FXDQWLILFDW�úL�VH�IRORVHVF�SHQWUX�D�DFRSHUL�XQHOH�HOHPHQWH�GH�FKHOWXLHOL�FH�SRW�DS UHD�QHSUHY ]XW�
¾ GREkQGD�VH�DSOLF �DVXSUD�YDORULL� ILQDQ ULL�úL�FXDQWLILF �VHUYLFLLOH� VDX�DMXWRUXO� ILQDQFLDU�SH� FDUH� vO� DFRUG � VRFLHWDWHD� GH� OHDVLQJ� FOLHQWXOXL�� $FHDVW � VXP � UHSUH]LQW � FRWH�SURFHQWXDOH�FDUH�DVLJXU �UHFXSHUDUHD�GREkQ]LORU�SH�FDUH�WUHEXLH�V �OH�SO WHDVF �VRFLHWDWHD�GH�OHDVLQJ�SHQWUX�FUHGLWHOH�RE LQXWH��SUHFXP�úL�SURILWXO�SH�FDUH�DFHDVWD�vO�RE LQH�vQ�XUPD�LQYHVWL LHL�I FXWH�
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
¾ SURILWXO�HVWH�YDULDELO�GH�OD�EXQ�OD�EXQ�úL��vQ�JHQHUDO��QX�GHS úHúWH����� ¾ WD[D� SH� YDORDUHD� DG XJDW � HVWH� SO WLW � GH� ILQDQ DWRU� OD� SODWD� IDFWXULL� F WUH� IXUQL]RUXO�
HFKLSDPHQWXOXL� úL� UHFXSHUDW �Dpoi de la beneficiarul leasing-ului prin ratele de leasing. Beneficiarul leasing-XOXL�SO WHúWH�79$�SH�FDUH�vO�HYLGHQ LD] �OD�UkQGXO�V X�WRW�D�LPSR]LW�vQ� DYDQV��'DF � EXQXO� UHVSHFWLY� HVWH� GLQ� LPSRUW� SRDWH� IL� VFXWLW� GH� LPSR]LW� VDX� GH� WD[H�vamale;
¾ comisionul dH�JHVWLXQH�GHSLQGH�GH�SUH XO�HFKLSDPHQWXOXL�úL�GH�FKHOWXLHOLOH�JHQHUDOH�DOH�VRFLHW LL�� 8QHOH� VRFLHW L� GH� OHDVLQJ� VWDELOHVF� R� WD[ � IL[ �� DOWHOH� SHUFHS� FRPLVLRQXO� FD�SURFHQW�GLQ�YDORDUHD�ILQDQ ULL�
¾ UDWD�GHYDORUL] ULL�PRQHGHL�HVWH�OXDW �vQ�FRQVLGHUDUH�GH�Pajoritatea firmelor specializate de leasing prin cuantificarea ratelor într-R� YDOXW � IRUWH� FX� úDQVH�PDUL� GH� VWDELOLWDWH� SH�SLD D�YDOXWDU ��ÌQ�DFHVW�PRG�UDWHOH�YRU�IL�SO WLWH�OD�FXUVXO�YDOXWDU�GLQ�]LXD�VFDGHQ HL��ULVFXO�cursului valutar fiind astfel suportat de beneficiarul de leasing;
4.2.3.5. Derularea unui contract de leasing 6RFLHWDWHD�*(1(5$/�$872�6�5�/�HVWH�R�FRPSDQLH�URPkQ �FX�FDSLWDO�SULYDW��DO�F UHL�RELHFW�GH�activitate îl constituie transportul de diferite bunuri. Societatea are sediu în Rm. VâlceD� úL� HVWH�UHSUH]HQWDW �vQ�WUDQ]DF LLOH�SH�FDUH�OH�vQFKHLH�GH�0DQDJHUXO�úL�$GPLQLVWUDWRUXO�*HQHUDO�DO�ILUPHL� 'LQ� GRULQ D� GH� D� VH� GH]YROWD� D� UH]XOWDW� QHFHVLWDWHD� FD� ILUPD� PDL� VXV� PHQ LRQDW � V -úL�P UHDVF � QXP UXO� YHKLFXOHORU� GH� WUDQVSRUW�� $VWIHO� vQ� OXQD� IHbruarie a anului 1997 încheie un FRQWUDFW�GH�OHDVLQJ�FX�VRFLHWDWHD�$),1�,17(51$7,21$/�,1&���FRPSDQLH�DPHULFDQ �FX�VHGLX�OD�'HODZDUH�� 8�6�$�� SHQWUX� vQFKHLHUHD� XQXL� DXWRWUDFWRU� ,9(&2� (8527(&+� úL� D� XQHL� UHPRUFL� FX�SUHODW � 6&+0,7=�� )XUQL]RULL� YHKLFXOHORU� VXQW�� ,9(&2� 6S$� 7RULQR�� ,WDOLD� úL� ,17(5&$0,21�GmbH, Altenberge, Germania. 'XUDWD� FRQWUDFWXOXL� GH� OHDVLQJ� HVWH� GH� WUHL� DQL�� PRQHGD� vQ� FDUH� VH� HIHFWXHD] � UDWHOH�WULPHVWULDOH�GH� OHDVLQJ�HVWH�'0��YDORDUHD�XQHL� UDWH�GH� OHDVLQJ�HVWH��������'0��9DORDUHD� WRWDO � D�reteORU�GH�OHDVLQJ�HVWH�GH���������'0��9DORDUHD�GH�ED] �HVWH���������'0� 3UH]HQW P� PDL� GHSDUWH� GHUXODUHD� RSHUD LXQLL� GH� OHDVLQJ�� DVWIHO�� VRFLHWDWHD� FRPHUFLDO �*(1(5$/� $872� 6�5�/�� YD� IL� PHQ LRQDW � FD� ³%HQHILFLDU´� VDX� ³8WLOL]DWRU´�� &RPSDQLD� $),1�INTERNATIONAL I1&��YD�IL�PHQ LRQDW �úL�FD�³OHVRU´� ÌQ�GDWD�GH�������������6�&��*(1(5$/�$872�6�5�/�� WULPLWH�R�FHUHUH�GH�RIHUW � VRFLHW LL�PROTRUCK INTERNATIONAL S.R.L., concesionar autorizat IVECO SpA, cu sediul situat în %XFXUHúWL��SULYLQG�DFKL]L LRQDUHD�GH�DXWRWUDFWRDUe IVECO EOROTECH. PH������������352758&.�,17(51$7,21$/�6�5�/��WULPLWH�RIHUWD�SURIRUP �OD�6�&�*(1(5$/�$872�6�5�/���SHQWUX�SURGXVXO�,9(&2�(8527(&+�03����(���7�3��RIHUW �FDUH�FXSULQGH:
• GHVFULHUHD�WHKQLF �D�YHKLFXOXOXL� • SUH XO�XQLWDU�DO�YHKLFXOXOXL� • FRQGL LD�de livrare; • termenul de livrare.
3H� GDWD� GH� ������������ vQ� XUPD� FHUHULL� SHQWUX� DFKL]L LRQDUHD� XQXL� DXWRWUDFWRU� ,9(&2�(8527(&+�úL�D�XQHL�UHPRUFL�FX�SUHODW �6&+0,7=��WULPLV �GH�6�&��*(1(5$/�$8725�6�5�/��VRFLHW LL�352758&.��DFHDVWD�GLQ�XUP �WULPLWH�F WUH�6�&��*(1(5$/�$872�6�5�/��RIHUWD�IHUP �SULYLQG�DFKL]L LRQDUHD�FHORU�GRX �YHKLFXOH��RIHUW �FDUH�FXSULQGH� 1) &RQGL LL�SHQWUX�DFKL]L LRQDUHD�YHKLFXOHORU�úL�VH�UHIHU �OD�
• lesor: AFIN INTERNATIONAL INC.; • valoarea contractului de leasing: 200.000 DM; • avansul (30% sau 35% din valoarea contractului); • WD[HOH�GH�RSHUDUH�����GLQ�YDORDUHD�FRQWUDFWXOXL��FH�VH�SO WHVF�vQ�WHUPHQ�GH����]LOH�GH�OD�
semnarea contractului; • termenul de contract: 3 ani;
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
• YDORDUHD�UDWHORU�úL�PRGXO�GH�SODW �����UDWH�WULPHVWULDOH�SO WLELOH�vQ�GHYDQV��SULPD�UDW �vQ���luni de la livrare), valoarea unei rate fiind e 13.552 DM;
• YDORDUHD�UH]LGXDO �����GLQ�YDORDUHD�FRQWUDFWXOXL� 2) *DUDQ LLOH�RIHULWH�FDUH�VH�UHIHU �OD�
• SHULRDGD�GH�JDUDQ LH� • service-ul acordat.
3) 2EOLJD LLOH�6�&�*(1(5$/�$872�6�5�/��FDUH�VH�UHIHU �OD� • SUH]HQWDUHD�DFWHORU�SHQWUX�VWXGLHUHD�SRVLELOLW LL�DFRUG ULL�OHDVLQJ-ului. Aceste acte sunt:
� FRSLH�GXS �&HUWLILFDWXO�GH�ÌQPDWULFXODUH� � XOWLPD�%DODQ �OXQDU � � XOWLPXO�ELODQ �DQXDO��LQFOXVLY�UH]XOWDWHOH�ILQDQFLDUH�OD����OXQL�� � lista parcului de vehicule actual; � VFULVRUL�GH�UHIHULQ �GH�OD�MRL�SDUWHQHUL� � VFULVRDUH�GH�ERQLWDWH�GH� OD�EDQFD�SULQFLSDO � úL� OLVWD� VHPQ WXULORU� FDUH�SRW�RSHUD�
FRQWXO�FXUHQW�GH�OD�EDQF � � OHJDOL]DUHD�QRWDULDO �D�FHOXL�FH�YD�VHPQD�FRQWUDFWXO�GH�OHDVLQJ� � VFXUW �SUH]HQWDUH�D�ILUPHL��RELHFW principal de activitate, scurt istoric).
• RE LQHUHD�XQHL�VFULVRUL�GH�JDUDQ LH�vQ�OHL��HPLV �GH�RULFH�EDQF �URPkQ �SHQWUX�JDUDQWDUHD�F WUH�'LUHF LD�9 PLORU�D�WD[HORU�YDPDOH�
4) Valabilitatea ofertei: 30 zile ÌQ� XUPD� ³DFFHSW ULL´� RIHUWHL� IHUPH�� 6�&�� *(1(5$/� $8725� 6�5�/�� LQWU � vQ� FRQWDFW� FX�FRPSDQLD�DPHULFDQ �$),1�,17(51$7,21$/�,1&� 3H������������VH�vQFKHLH�FRQWUDFWXO�GH�OHDVLQJ�vQWUH�$),1�,17(51$7,21$/�,1&�úL�6�&��GENERAL AUTO S.R.L., contract care cuprinde:
$��3 U LOH�FRQWUDFWDQWH�� • AFIN INTERNATIONAL INC. ca lesor; • S.C. GENERAL AUTO S.R.L. ca beneficiar.
B. Obiectul contractului:
• un vehicul comercial IVECO; • R�UHPRUF �
Furnizorii: • IVECO SpA; • INTERCAMION GmbH.
Caracteristicile contractului prezentat pe scurt: • durata contractului de leasing: 3 ani; • moneda în FDUH�VH�HIHFWXHD] �SO LOH�UDWHORU�GH�OHDVLQJ��'0� • YDORDUHD�GH�ED] �D�FRQWUDFWXOXL����������'0� • YDORDUHD�WRWDO �D�UDWHORU�GH�OHDVLQJ����������'0� • EDQFD�OHVRUXOXL�F WUH�FDUH�VH�WUDQVIHU �UDWHOH� • planificarea ratelor; • DFKLWDUHD�WD[HL�GH�RSHUDUH�F WUH�OHVRU�
9HKLFXOXO�YD�IL�OLYUDW�EHQHILFLDUXOXL�vQ�WHUPHQ�GH���OXQL�GH�OD�GDWD�FRQILUP ULL�SO LL�WD[HL�GH�RSHUDUH�úL�D�SULPHL�UDWH�GH�OHDVLQJ�
&��&RQGL LLOH�JHQHUDOH�DOH�FRQWUDFWXOXL�VH�UHIHU �OD�
1) &RQGL LLOH� GH� OLYUDUH� úL� LPSOLFD LLOH� vQ� FD]XO� GH� DQXODUH� D� FRQWUDFtului de leasing din vina beneficiarului.
Leasing-XO� GHYLQH� HIHFW� OD� GDWD� OLYU ULL� YHKLFXOHORU� F WUH� EHQHILFLDUL�� GDW � FH� UH]XOW � GLQ�SURWRFROXO�FH�HYLGHQ LD] �DFFHSWDUHD�YHKLFXOHORU�GH�F WUH�EHQHILFLDU�
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
Lesor-XO� YD� vQúWLLQ D� EHQHILFLDUXO� FX� �� ]LOH� vQDLQWHD� GLVSRQLELOL] ULL� OLYU ULL� YHKLFXOHORU��%HQHILFLDUXO� IDFH� IRUPDOLW LOH� GH� SULPLUH� úL� VHPQHD] � IRUPHOH� GH� SULPLUH� ([:RUNV8OP��Germania.
'DF �FRPDQGD�VDX�IXUQL]DUHD�VH�DQXOHD] �GLQ�YLQD�EHQHILFLDUXOXL��DFHVWD�YD�SO WL�OHVRU-ului 200.000 DM pentru anularea comenzii.
2) Ratele de leasing 5DWHOH�GH�OHDVLQJ�VH�YRU�SO WL�FRQIRUP�WDEHOXOXL�GH�SODQLILFDUH�D�SO LORU��vQ�FRQWXO�EDQFDU�DO�
lesor-ului. %HQHILFLDUXO� YD� VXSRUWD� WRDWH� WD[HOH� DGPLQLVWUDWLYH� FHUXWH� GH� OHJLVOD LD� URPkQ � SHQWUX� D�
DVLJXUD�HIHFWXDUHD�SO LORU�OD�termenele stabilite. 3) *DUDQ LD�EDQFDU �F WUH�YDP
La cererea beneficiarului, lesor-XO�YD�GHVFKLGH�R�JDUDQ LH�EDQFDU �FX�R�YDODELOLWDWH�SkQ �OD����DXJXVW� ����� úL� OD� YDORDUHD� LQGLFDW � GH� EHQHILFLDU�� vQ� IDYRDUHD� 9 PLL� 5RPkQH�� vQ� QXPHOH�beneficiarului.
4) Livrarea vehiculelor 9HKLFXOHOH�YRU�IL�OLYUDWH�vQ�WHUPHQ�GH�WUHL�OXQL�GH�OD�GDWD�FRQILUP ULL�SO LL�WD[HL�GH�RSHUDUH�úL�
a primei rate de leasing. 5) *DUDQ LD
9HKLFXOHOH� VXQW� JDUDQWDWH� ��� OXQL� GH� OD� GDWD� OLYU ULL� FRQIRUP�&RQGL LLORU� ,QWHUQD LRQDOH� GH�*DUDQ LH� ,9(&2�SOXV�DOWH���� OXQL� VDX���������NP�SHQWUX�JUXSXO�PRWRSURSXOVRU��*DUDQ LD�HVWH�VXSRUWDW �GH�IXUQL]RU�vQ�ED]D�FRQWUDFWXOXL�vQFKHLDW�vQWUH�DFHVWD�úL�OHVRU�
6) Folosirea vehiculelor %HQHILFLDUXO�VH�REOLJ �vQ�PRG�FDWHJRULF�ID �GH�OHVRU�
• V �IRORVHDVF �YHKLFXOHOH�FRQIRUP�VSHFLILFD LLORU�IXUQL]RUXOXL� • V �QX�GHD�vQ�IRORVLQ �YHKLFXOXO�XQHL�DOWH�S U L� • V �vQWUH LQ �YHKLFXOXO�FRQIRUP�LQVWUXF LXQLORU�IXUQL]RUXOXL�
7) 3 VWUDUHD�úL�FRQVHUYDUHD�YHKLFXOXOXL %HQHILFLDUXO�HVWH�U VSXQ] WRU�GH�RULFH�ULVFXUL�GH�DYDULH�VDX�úL�GH�SLHUGHUHD� WRWDO �SDU LDO �D�
YHKLFXOXOXL��GLQ�RULFH�PRWLYH��GLQ�YLQD�EHQHILFLDUXOXL�VDX�ILLQG�UH]XOWDWXO�SXUHL�vQWkPSO UL�VDX�DO�XQRU�vQWkPSO UL�LPSUHYL]LELOH�
8) Asigurarea /HVRUXO�YD�HIHFWXD�DVLJXUDUHD�WXWXURU�YHKLFXOHORU�SH�QXPHOH�úL�VRFRWHDOD�EHQHILFLDUXOXL��3ROL a de
DVLJXUDUH�YD�DFRSHUL��5�&�$���&DUWHD�9HUGH��&$6&2�úL�&�0�5��%HQHILFLDUXO�DVLJXU ULL�YD�IL�OHVRUXO� 9) 'HVS JXELUL
3HQWUX� SLHUGHUHD� WRWDO � EHQHILFLDUXO� SO WHúWH� OHVRUXOXL� GHVS JXELUHD� HJDO � FX� vQWUHJXO� VROG�GDWRUDW�SO WLELO�OD�PRPHQWXO�UHVSHFWLY�SOXV�GREknda LIBOR (în raport cu DM).
3HQWUX� GHWHULRUDUHD� SDU LDO � VDX�úL� DYDULHUHD� YHKLFXOXOXL� EHQHILFLDUXO� H[HFXW � UHSDUD LLOH� FX�propriile cheltuieli.
10) Expirarea contractului &RQWUDFWXO� H[SLU � DXWRPDW� OD� SODWD� XOWLPHL� UDWH� GH� OHDVLQJ��3UHGDUHD�YHKLFXOHORU� VH� IDFH la
DWHOLHUXO�DXWRUL]DW�,9(&2�GLQ�%XFXUHúWL�VDX�H[LVW �SRVLELOLWDWHD�vQ�FD]XO�vQGHSOLQLULL�OD�WHUPHQ�D�WXWXURU�REOLJD LLORU�GH�D�FXPS UD�YHKLFXOH�OD�YDORDUHD�UH]LGXDO �
11) Returnarea vehiculelor La înapoierea vehiculelor se face un protocol de predare-primire� VHQDW� vQWUH� EHQHILFLDU� úL�
DWHOLHUXO�DXWRUL]DW�GLQ�%XFXUHúWL� 'DF �H[LVW �R�vQWkU]LHUH�PDL�PDUH�GH����]LOH�GH�OD�H[SLUDUHD�FRQWUDFWXOXL�GH�OHDVLQJ��OHVRUXO�
DUH� GUHSWXO� V � FHDU � EHQHILFLDUXOXL� R� SHQDOL]DUH� HJDO � FX� UDWD� GH� OHDVLQJ� SH� XQ� WULPHVWUX��VehiculelH�YRU�IL�UHWXUQDWH�QXPDL�GDF �EHQHILFLDUXO�QX�úL-D�PDQLIHVWDW�RS LXQHD�GH�DOH�FXPS UD�
12) Anularea contractului�GDWRULW �neîndeplinirii�REOLJD LLORU�IXUQL]RUXOXL 'DF �OLYUDUHD�YHKLFXOHORU�F WUH�EHQHILFLDU�QX�V-a realizat în totalitate, din motive care nu depind GH�OHVRU��DWXQFL�OHVRUXO�DUH�GUHSWXO�V �DQXOH]H�DFHVW�FRQWUDFW�GH�vQFKLULHUH��FX�DQXODUHD�RULF URU�UHYHQGLF UL�vQWUH�S U LOH�FRQWUDFWDQWH�
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
13) Anularea contractului�GDWRULW �neîndeplinirii�REOLJD LLORU�EHQHILFLDUXOXL 'DF �EHQHILFLDUXO�HVWH�YLQRYDW�GH�vQGHSOLQLUH�WRWDO �VDX�SDU LDO �D�FODX]HORU�SUHY ]XWH�OD�SXQFWHOH�
2. Ratele de leasing 4. Livrarea 6. Folosirea vehiculului ���3 VWUDUHD�úL�FRQVHUYDUHD�YHKLFXOHORU 8. Leasing
'DF �YHKLFXOXO�QX�VH�vQDSRLD] �FRQIRUP�VFULVRULL�GH�DQXODUH�D�FRQWUDFWXOXL��lesorul are dreptul SULQ�DJHQ LL�V L�DXWRUL]D L�VDX�WHU H�SHUVRDQH�FH�UHSUH]LQW �OHVRUXO��V �LQWUH�vQ�ORFXO�XQGH�VH�DIO �DXWRYHKLFXOHOH�úL�V �OH�SUHLD�SH�ULVFXO�úL�FKHOWXLDOD�EHQHILFLDUXOXL�
14) 7D[H�úL�LPSR]LWH 7RDWH� WD[HOH�SUH]HQWH�úL�YLLWRDUH�FDUH� UH]XOW �Gin acest contract de leasing vor fi suportate de S U LOH�FRQWUDFWDQWH�vQ�IXQF LH�GH�ORFXO�XQGH�VH�SHUFHS�DFHVWH�WD[H�úL�LPSR]LWH��$VWIHO��GDF �ORFXO�GH� SHUFHSHUH� D� DFHVWRU� WD[H� úL� LPSR]LWH� HVWH� 5RPkQLD�� DFHVWHD� YRU� IL� VXSRUWDWH� GH� F WUH�beneficiar, iar în DIDUD�5RPkQLHL��GH�F WUH�OHVRU�
15) &RQGL LLOH�ILQDOH ������&RQWUDFWXO�GHYLQH�HIHFWLY�GH�OD�GDWD�LQWU ULL� vQ�YLJRDUH�úL� vQFHWHD] �GXS �SODWD�WXWXURU�
ratelor de leasing. 15.2. Lesorul poate înceta acest contract în orice moment 15.3. Lesorul are dreptul de înceWDUH� D� FRQWUDFWXOXL� GH� OHDVLQJ� GDF � EHQHILFLDUXO�� GXS �
vQF OFDUHD�REOLJD LLORU�VDOH�QX�VH�VXSXQH�DYHUWLVPHQWXOXL�VFULV�DO�OHVRUXOXL��vQ�WHUPHQ�GH�30 de zile de la primirea acestuia.
16) Clauze de arbitraj 'DF �vQ�WHUPHQ�GH����GH�]LOH�GXS �FH�R�SDUWH�D�H[SXV�GH]DFRUGXO�FHOHLODOWH�S U L��QX�VH�DMXQJH�
OD�XQ�DFRUG�VFULV��VH�YD�SURFHGD�OD�&RPLVLD�GH�$UELWUDM�FDUH�HVWH�IRUPDW �GLQ�WUHL�MXGHF WRUL� 17) Valabilitatea contractului
9DODELOLWDWHD� DFHVWXL� FRQWUDFW� YD� IDFH� RELHFWXO� UHFXQRVFXW� GH� F WUH� DXWRULW LOH� URPkQH� úL�italiene de drept.
18) 1RWLILF ULOH 7RDWH�QRWLILF ULOH�úL�FRPXQLF ULOH�YRU�IL�VFULVH�vQ�OLPED�HQJOH] �úL�vQPkQDW�SHUVRQDO�VDX�SULQ�
SRúWD�UHFRPDQGDW �VDX�SULQ�WHOHID[�RUL�ID[�
1. 3/$1,),&$5($�5$7(/25�'(�/($6,1*�3(�3(5,2$'$�'(58/ 5,,�&2175$&78/8,
1RWD LL� Qkl - aPRUWLVPHQWXO�FRUHVSXQ] WRU�WULPHVWUXOXL���DO�DQXOXL�N� dkl -�GREkQGD�VLPSO �FRUHVSXQ] WRDUH�GDWRULHL�H[LVWHQWH�OD�vQFHSXWXO�WULPHVWUXOXL���DO�
anului k; Skl -�YDORDUD�UDWHL�FRUHVSXQ] WRDUH�SHULRDGHL�����N� Sk = Qkl + dkl Vkl -�YDORDUHD�GDWRULHL�U PDVH�GXS �SODWD�OXL�4kl; Rkl -�YDORDUHD�GDWRULHL�SO WLWH�GXS �SODWD�OXL�4kl; p = 100 i = procentul real anual; q = 100 j4� �SURFHQWXO�QRPLQDO�DQXDO�FRUHVSXQ] WRU�IUDF LRQ ULL�DQXOXL�vQ�WULPHVWUH� 'DWH�LQL LDOH� 9DORDUHD�GH�ED] = 200.000 DEM 30% avans = 60.000 DEM V0 = 140.000 DEM 5% taxe de operare = 10.000 DEM ���YDORDUH�UH]LGXDO = 2.000 DEM d = 14,5% ⇒�,� ��������DQXDO �
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
D��3O L�SRVWLFLSDWH��GREkQG �SRVWLFLSDW � PERIOADA Vk, l - 1 Qk, l dk, l S vk, l Rk, l
1,1 140.000 9.520 5.075 14.595 130.480 9.520 1,2 130.480 9.165 4.730 14.595 120.615 19.385 1,3 120.615 10.223 4.372 14.595 110.392 29.608 1,4 110.392 10.594 4.001 14.595 99.798 40.202 2,1 99.798 10.978 3.617 14.595 88.820 51.180 2,2 88.820 11.376 3.219 14.595 77.444 62.556 2,3 77.444 11.788 2.807 14.595 65.656 74.344 2,4 65.656 12.245 2.380 14.595 53.441 86.559 3,1 53.441 12.658 1.937 14.595 4.783 99.217 3,2 40.783 13.117 1.478 14.595 27.666 112.334 3,3 27.666 13.593 1.002 14.595 14.073 125.927 3,4 14.073 14.073 522 14.595 0 140.000
TOTAL 140.000 35.140 175.140 - -
1 –�6XPD�GH�SODW ��������– Dobânda 3 –�6XPD�WRWDO �GH�SO WLW E��3O L�DQWLFLSDWH��GREkQG �DQWLFLSDW �
PERIOADA Vk, l - 1 Qk, l dk, l S vk, l Rk, l
1,1 140.000 9.446 4.732 14.178 130.554 9.446 1,2 130.480 9.801 4.377 14.178 120.753 19.247 1,3 120.753 10.169 4.009 14.178 110.584 29.416 1,4 110.584 10.552 3.626 14.178 100.032 39.968 2,1 100.032 10.949 3.229 14.178 89.083 50.917 2,2 89.083 11.361 2.818 14.178 77.722 62.278 2,3 77.722 11.788 2.390 14.178 65.934 74.066 2,4 65.934 12.231 1.947 14.178 53.703 86.297 3,1 53.703 12.691 1.487 14.178 41.012 98.988 3,2 41.012 13.169 1.009 14.178 27.843 112.157 3,3 27.843 13.665 513 14.178 14.178 125.822 3,4 14.178 14.178 0 14.178 0 140.000
TOTAL 140.000 30.136 170.136 - -
Graficul: Plati posticipate / Dobanda posticipata
175140
140000
35140
020000400006000080000
100000120000140000160000180000
1 2 3
DM
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
1 –�6XPD�GH�SODW ��������– Dobânda 3 –�6XPD�WRWDO �GH�SO WLW c) 3O L�DQWLFLSDWH��GREkQG �SRVWLFLSDW
PERIOADA Vk, l - 1 Qk, l dk, l S vk, l Rk, l
1,1 140.000 14.084 0 14.084 125.916. 14.084 1,2 125.196 9.520 4.564 14.084 116.396 23.064 1,3 116.396 9.865 4.219 14.084 106.531 33.469 1,4 106.531 10.223 3.861 14.084 96.308 43.692 2,1 96.308 10.593 3.491 14.084 85.715 54.285 2,2 85.715 10.976 3.108 14.084 74.739 65.261 2,3 74.739 11.374 2.710 14.084 63.365 76.635 2,4 63.365 11.787 2.297 14.084 51.578. 88.422 3,1 51.578 12.214 1.870 14.084 39.364 100.636 3,2 39.364 12.657 1.427 14.084 26.707 113.293 3,3 26.707 13.116 968 14.084 13.591 126.409 3,4 13.591 13.591 493 14.084 0 140.000
TOTAL 140.000 29.008 169.008 - -
Graficul: Plati anticipate / Dobanda anticipata
175140
140000
35140
02000040000
6000080000
100000120000
140000160000180000
1 2 3
DM
Graficul: plati posticipate / Dobanda posticipata
175140
140000
35140
0
2000040000
6000080000
100000120000
140000160000
180000
1 2 3
DM
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
1 –�6XPD�GH�SODW ��������– Dobânda 3 –�6XPD�WRWDO �GH�SO WLW
4.2.3.6. Costul leasing-ului Credit-EDLOXO� �OHDVLQJXO�� UHSUH]LQW � R� WHKQLF � GH� ILQDQ DUH� D� LQYHVWL LLORU� FDUH� V-a dezvoltat SXWHUQLF� vQ� ULOH� FX�HFRQRPLH�GH]YROWDW � úL� FDUH� SRDWH� IL�GH]YROWDW � úL� vQ� FDGUXO� ULL� QRDVWUH��'H�H[HPSOX��DFHDVW �IRUP �GH�ILQDQ DUH�UHSUH]HQWD�DSURDSH����GLQ�ILQDQ DUHD� LQYHVWL LLORU�SURGXFWLYH�DOH�vQWUHSULQGHULORU�IUDQFH]H�úL�PDL�PXOW�GH�����SHQWUX�vQWUHSULQGHULOH�PLFL�úL�PLMORFii. Pe plan juridic, credit-bail-XO� VH� DQDOL]HD] � FD� XQ�PRG� GH� ORFD LH� �vQFKLULHUH�� vQVR LW� GH� R�RS LXQH� GH� FXPS UDUH� �SURPLVLXQH� GH� YkQ]DUH� GLQ� SDUWHD� FUHGLWRUXOXL���$QDOL]D� HFRQRPLF � DSDUH�vQV �FD�ILLQG�GLIHULW ��8WLOL]DWRUXO��HVWH�GLQ�SXQFW�GH�YHGHUH�Hconomic proprietarul bunului; locatarul LPSXQH� U VFXPS UDUHD� EXQXOXL� SHQWUX� XQ� SUH � GHWHUPLQDW� FDUH� FRQVWLWXLH� SUH XO� GH� H[HUFL LX� DO�RS LXQLL�GH�YkQ]DUH�DO�EXQXOXL� Credit-bail-XO�QX�FRQVWLWXLH�GHFkW�XQ�PRG�GH�ILQDQ DUH�SDUWLFXODU�úL��SULQ�XUPDUH��WUHEXLH�V �ILH�DQDOL]DW�SH�SODQXO�GHFL]LHL�ILQDQFLDUH�QX�FD�R�DOWHUQDWLY �ORFD LH�FXPS UDUH��FL��PDL�GHJUDE ��FD�R�DOWHUQDWLY �D�DOWRU�VXUVH�GH�ILQDQ DUH�úL�FHO�PDL�DGHVHD�FD�XQ�VXEVWLWXW�DO�vQGDWRU ULL�SH�WHUPHQ�PHGLX�sau lung. $VSHFWH�MXULGLFH�úL�ILVFDOH Vom prezenta succesiv, mai întâi credit-bail-ul mobiliar, apoi credit-bail-XO�LPRELOLDU��ÌQV ��LQGLIHUHQW�GH�IRUPD�FRQVLGHUDW ��XWLOL]DWRUXO�QX�HVWH�SURSULHWDUXO�EXQXOXL�vQFKLULDW�úL��vQ�SOXV��WUHEXLH�UH LQXW�IDSWXO�F �FRQWUDFWXO�SUHYHGH�R�GXUDW �LUHYRFDELO de utilizare a bunului. Credit-bail mobiliar 6XQW� FRQVLGHUDWH�� vQ� DFFHS LXQHD� ULORU� FX� HFRQRPLH�GH� SLD � GH]YROWDW �� FD� RSHUD LXQL� GH�credit-EDLO�PRELOLDU��RSHUD LXQLOH�GH�ORFD LH�DOH�EXQXULORU�GH�HFKLSDPHQW�VDX�DOH�XWLODMHORU�FXPS UDWH�în vederea loFD LHL�GH�F WUH�vQWUHSULQGHULOH�FDUH�U PkQ�SURSULHWDUH��DWXQFL�FkQG�RSHUD LXQL��RULFDUH�DU�IL� FDOLILFDUHD� ORU�� GDX� ORFDWDUXOXL� SRVLELOLWDWHD� GH� D� DFKL]L LRQD� vQ� WRWDOLWDWH� VDX� SDU LDO� EXQXULOH�vQFKLULDWH��SULQ�LQWHUPHGLXO�XQXL�SUH �FRQYHQLW�úL�FDUH� LQH�FRQW�FHO�SX LQ�GH�Y UV PLQWHOH�HIHFWXDWH�FX�titlul de chirii. 3H� SODQ� MXULGLF� HVWH� YRUED� GH� R� ORFD LH� vQVR LW � GH� R� SURPLVLXQH� XQLODWHUDOH� GH� YkQ]DUH� v�IDYRDUHD� ORFDWDUXOXL�� /RFDWDUXO� DUH�� vQ� ILQDO�� GH� DOHV� vQWUH� WUHL� SRVLELOLW L�� V � FXPSHUH� EXQXO� OD�valoaUHD�UH]LGXDO �IL[DW �vQ�FRQWUDFW��V �UHvQQRLDVF �FRQWUDFWXO�GH�ORFD LH�VDX�V �UHVWLWXLH�EXQXO� Pe plan fiscal, chiriile constituie cheltuieli de exploatare care în mod normal sunt deductibile FX�FRQGL LD�FD�SHULRDGD�V �FRQFRUGH�FX�GXUDWD�GH�YLD �HFRQRPLF �QRUPDO �D�EXQXOXL�
Graficul: Plati anticipate / Dobanda posticipata
169008
140000
29008
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
1 2 3
DM
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
Credit-bail imobiliar Credit-bail-XO� LPRELOLDU� GHVHPQHD] � RSHUD LXQLOH� SULQ� FDUH� R� vQWUHSULQGHUH� G � vQ� ORFD LH�EXQXUL� LPRELOLDUH� GH� X]� SURIHVLRQDO� FXPS UDWH� GH� HD� VDX� FRQVWUXLWH� vQ� LQWHUHVXO� ORU�� DWXQFL� FkQG�DFHVWH�RSHUD LXQL��RULFDUH�DU�IL�FDOLILFDUHD� ORF��SHUPLW� ORFDWDULORU� V �GHYLQ �SURSULHWDUL�� vQ� WRWDOLWDWH�VDX� SDU LDO� DVXSUD� EXQXULORU� vQFKLULDWH�� FHO�PDL� WkU]LX� OD� H[SLUDUHD� WHUPHQXOXL� GH� ORFD LH�� ILH� SULQ�cesiune în executarea unei promisiuni unilaterale de vânzare, fie prin achL]L LRQDUHD� GLUHFW � VDX�LQGLUHFW � D� GUHSWXULORU� GH� SURSULHWDWH� DVXSUD� WHUHQXULORU� SH� FDUH� DX� IRVW� FRQVWUXLWH� LPRELOHOH�vQFKLULDWH�� ILH� SULQ� WUDQVIHUXO� GHSOLQ� DO� SURSULHW LL� FRQVWUXF LLORU� UHDOL]DWH� SH� WHUHQXO� FH� DSDU LQH��locatarului. Pe plan fiscal, întUHSULQGHUHD� ORFDWDU � SRDWH� GHGXFH� GH-D� OXQJXO� GXUDWHL� ORFD LHL� FKLULLOH�SO WLWH�� $FKL]L LRQDUHD� LPRELOXOXL� OD� H[SLUDUHD� FRQWUDFWXOXL� GH� ORFD LH� DQWUHQHD] �� HYHQWXDO�� R�UHLQWHJUDUH� ILVFDO � vQ� EHQHILFLLOH� LPSR]LWDWH�� 6XP � FDUH� VH� UHLQWHJUHD] � GHSLQGH� GH� GXUDta FRQWUDFWXOXL�GH�ORFD LH��GH�YDORDUHD�QHW �FRQWDELO �úL�GH�SUH XO�GH�FHVLXQH�DO�EXQXOXL� 6XPD�DPRUWLVPHQWHORU�SUDFWLFDWH�DVXSUD�FRQVWUXF LLORU�DFKL]L LRQDWH�HVWH�vQ�IXQF LH�GH�GXUDWD�FRQWUDFWXOXL� úL� GH� GDWD� RS LXQLL� GH� FXPS UDUH�� 3H� GH� DOW � SDUWH�� vQ� FD]� GH� FHGDUH� XOWHULRDU � D�imobilului, plus-YDORDUHD��FkúWLJXO�GH�YDORDUH��HYHQWXDO�UHDOL]DW� ��YD�IL�FDOFXODW �FD�GLIHUHQ �vQWUH�YDORDUHD� ILVFDO �D�EXQXOXL� �SUH XO�GH�FXPS UDUH�PDMRUDW�FX� UHLQWHJUDUHD�ILVFDO �� úL�DPRUWLVPHQWHOH�contabilizate. Regimul fiscal al credit-bail-ului imobiliar ne apare astfel avantajos deoarece el permite, LQkQG� FRQW� GH� GHGXFWLELOLWDWHD� FKLULLORU�� SH� GH� R� SDUWH� GH� DPRUWL]DUHD� ILVFDO � PDL� UDSLG � D�FRQVWUXF LLORU� úL� SH� GH� DOW � SDUWH� GH� ³DPRUWL]DUHD´� WHUHQXULORU�� 5HLQWHJUDUHD� ILVFDO � QX� GHWHUPLQ �GHFkW�SLHUGHUHD�XQHL�S U L�GLQ�DFHVW�DYDQWDM�� LQkQG�FRQW�GH�DFWXDOL]DUH�
$QDOL]D�HFRQRPLF �D�RSHUD LHL�GH�FUHGLW-bail Punctul de vedere al creditorului
3UHVXSXQHP�F �FUHGLWRUXO�HVWH�XQ�VWDELOLPHQW�ILQDQFLDU�FDUH�vúL�DFRUG �FRQFXUVXO�V X� î mod HJDO�DWkW�VXE�IRUPD�XQXL�vPSUXPXW�FODVLF�FkW�úL�VXE�IRUPD�FUHGLW-bail-ului. Credit-bail-XO�FRQVWLWXLH�XQ�VXEVWLWXW�SHUIHFW�DO�vPSUXPXWXOXL�FODVLF��FHHD�FH�VHPQLILF �IDSWXO�F �ULVFXO�HFRQRPLF�DQWUHQDW�GH�R�RSHUD LH�GH�OHDVLQJ�HVWH�LGHQWLF�FX�ULVFXO�DQWUHQDW�GH�R�RSHUD LH�GH�vPSUXPXW�FODVLF�SHQWUX�VWDELOLPHQWXO�ILQDQFLDU��$FHVWD�GLQ�XUP �VROLFLW �LQYHVWL LLORU�VDOH�R�UDW �GH�UHQWDELOLWDWH� HFRQRPLF � GXS � GHGXFHUHD� LPSR]LWXOXL� QRWDW � FX� 5a
b� HJDO � FHO� SX LQ� FX� FRVWXO�FDSLWDOXOXL�V X� 'DF �GHVHPQ P�SULQ�&MPb –�FRVWXO�FDSLWDOXOXL�VWDELOLPHQWXOXL�ILQDQFLDU�úL�SULQ�5d
e costul GDWRULHL� SHQWUX� ORFDWDU� úL� LQkQG� FRQW� GH� FRWD� GH� LPSR]LWDUH� D� FUHGLWRUXOXL� �7b) , atunci costul minimal al datoriei pentru locatar devine:
)T1/(CMPR bbed −=
Ca urmare a identLW LL�SUHVXSXQH�D�ULVFXOXL�HFRQRPLF�vQWUH�RSHUD LXQHD�GH�vPSUXPXW�FODVLF�úL� RSHUD LXQHD� GH� FUHGLW-EDLO�� DFHVW� FRVW� UHSUH]LQW �� GH� DVHPHQHD�� FRVWXO� FUHGLW-bail-ului pentru locatar. Costul capitalului creditorului &RVWXO�FDSLWDOXOXL�FUHGLWRUXOXL�VH�SRDWH�H[SULPD�FX�DMXWRUXO�UHOD LHL�XUP WRDUH�
DCP
D)T1(R
DCP
CPR
DCP
DT1RCMP bb
dbcb
ba
b
+⋅−+
+=
+⋅−=
unde: '�úL�&3�VXQW�VXPHOH�FDUH�H[SULP �GDWRULD�ILQDQFLDU �úL�FDSLWDOXULOH�SURSULL�DOH�FUHGLWRUXOXL��Rc
b� úL� 5db� VHPQLILF � FRVWXO� IRQGXULORU� SURSULL� úi costul datoriei pentru creditor; Tb� H[SULP � FRWD�
(rata) de impozitare a creditorului.
(YDOXDUHD�UHQWDELOLW LL�RSHUD LXQLL�GH�FUHGLW-bail pentru creditor 9RP� HYDOXD� FDUH� HVWH� vQ� SUH]HQW� UHQWDELOLWDWHD� RSHUD LXQLL� GH� FUHGLW-bail pentru creditor recurgânG� OD� 9$1�� 5DWD� GH� DFWXDOL]DUH� HVWH� FRVWXO� FDSLWDOXOXL� SH� FDUH� WRFPDL� QRL� GRULP� V -l GHWHUPLQ P�
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
)OX[XULOH�GH�OLFKLGLW L�vQFDVDWH�GH�F WUH�FUHGLWRU�VXQW�FRQVWLWXLWH�GH�
• SH�GH�R�SDUWH��GH�FKLULLOH�GXS �GHGXFHUHD�LPSR]LWXOXL��DGLF � )T1(L bt − ;
• SH� GH� DOW � SDUWH�� GH� HFRQRPLLOH� GH� LPSR]LW� SURFXUDWH� �JHQHUDWH�� FD� XUPDUH� D�GHGXFWLELOLW LL�DPRUWLVPHQWHORU�SUDFWLFDWH�DVXSUD�EXQXOXL�vQFKLULDW��DGLF �7b DAt pentru perioada t.
3UHVXSXQkQG�F �YDORDUHD� UH]LGXDO �D�EXQXOXL�HVWH�QXO � úL�F � VXPD� LQYHVWL LHL�Hste I, atunci 9$1�HVWH�XUP WRDUHD�
[ ] I)CMP1/(DAT)T1(LnVAN tb
1tt
bbt −++−= ∑
=
Punctul de vedere a locatarului 3HQWUX� ORFDWDU�� RSHUD LD� GH� FUHGLW-EDLO� FRUHVSXQGH� VLPXOWDQ� FX� R� GHFL]LH� GH� LQYHVWL LL� úL� R�
GHFL]LH� GH� ILQDQ DUH�� 'DF � FRQGL LLOH� GH� UHSDUDELOLWDWH� VXQW� VDWLVI FXWH�� FHOH� GRX � GHFL]LL� SRW� IL�VWXGLDWH� VHSDUDW�� 'HFL]LD� GH� LQYHVWL LL� VH� DQDOL]HD] � vQWU-XQ� PRG� WUDGL LRQDO�� LQYHVWL LD� HVWH�DFFHSWDELO �GDF �9$1�HVWH�SR]LWLY��(YDOXDUHD�UHQWDELOLW LL�VH�IDFH�vQ�PRG�LQGHSHQGHQW�GH�PRGXO�GH�ILQDQ DUH�DGRSWDW�
5 PkQH�DWXQFL�V �VWXGLHP�GHFL]LD�GH�ILQDQ DUH��UHVSHFWLY�V �FRPSDU P�UHFXUJHUHD�OD�FUHGLW-EDLO� FX� UHFXUJHUHD� OD� vPSUXPXW�� 6HSDUDELOLWDWHD� SUHVXSXQH� IDSWXO� F � FUHGLW-bail-XO� DUH� DFHHDúL�LQFLGHQ � FD� úL� vPSUXPXWXO� DVXSUD� FDSDFLW LL� GH� vQGDWRUDUH�� vQWUHSULQGHUHD� FDUH� FRQWUDFWHD] � XQ�credit-EDLO� UHQXQ � OD� XQ� vPSUXPXW� GH� YDORDUH� HFKLYDOHQW �� /D� R� VWUXFWXU � ILQDQFLDU � HJDO ��procentajul de îndatorare la care se va recurge pentru a-úL�ILQDQ D�SURLHFWHOH�VDOH�GH�LQYHVWL LL�YD�IL�PDL�UHGXV��'HFL]LD�QX�DUH�LQFLGHQ �DVXSUD�FRVWXOXL�FDSLWDOXOXL�VRFLHW LL�
9RP� H[DPLQD� GHFL� SULQ� FRPSDUD LH� FX� vPSUXPXWXO�� FDUH� YD� IL� LQFLGHQ D� FUHGLW-bail-ului DVXSUD�IOX[XULORU�GH�OLFKLGLW L�
Credit-bail-XO�DQWUHQHD] ��JHQHUHD] ��FRQVHFLQ HOH�XUP WRDUH� • vQWUHSULQGHUHD�QX�SRDWH�GHEXUVD�VXPD�LQYHVWL LHL��,���VLWXD LD�HVWH�HFKLYDOHQW �FX�FHD�vQ�FDUH�HD�DU�
fi avut-R�GDF �SH�GH�R�SDUWH�DU�IL�SULPLW�XQ�vPSUXPXW�vQ�VXP �GH�0� �,�úL�SH�GH�DOW �SDUWH�úLD-r fi SO WLW�LQYHVWL LD�
• HD�SO WHúWH�R�FKLULH�/t�vQ�ILHFDUH�SHULRDG ��GXS �GHGXFHUHD�LPSR]LWXOXL�DVXSUD�UH]ultatului, chiria devine Lt (1 – Te), Te fiind cota sa de impozitare;
• HD�UHQXQ �OD�HFRQRPLLOH�GH�LPSR]LW�DIHUHQWH�DPRUWLVPHQWHORU�SH�FDUH�OH-DU�IL�SXWXW�SUDFWLFD�GDF �HD�DU�IL�IRVW�SURSULHWDU ��GHFL�OD�7e DAt;
• HD�UHQXQ ��GH�DVHPHQHD��OD�HFRQRPLLOH�GH�LPSozit aferente cheltuielilor financiare FFt pe care le-DU�IL�UHDOL]DW�GDF �V-DU�IL�ILQDQ DW�SH�VHDPD�XQXL�vPSUXPXW�FODVLF��GHFL�OD�7e FFt.
6H�GHWHUPLQ �9$1�D�ILQDQ ULL��GLPLQXkQG�VXPD�0�SULPLW �FX�VXPD�DFWXDOL]DW �D�IOX[XULORU�GH�OLFKLGLW L�SH�FDUH�OH�DQWUHQHD] ��5DWD�GH�DFWXDOL]DUH�FDUH�VH�DSOLF �HVWH�vQ�IXQF LH�GH�QLYHOXO�GH�ULVF�FDUH�FDUDFWHUL]HD] �IOX[XULOH��ÌQ�FD]XO�OHDVLQJ-ului nivelul de risc fiind presupus identic cu cel al vPSUXPXWXOXL�FODVLF� WUHEXLH��SULQ�XUPDUH�� V � VH�XWLOL]H]H�FRVWXO�GDWRULHL�Hchivalente Rd
e înainte de deducerea impozitului. VAN a credit-bail-XOXL�VH�FDOFXOHD] �DWXQFL�vQ�PDQLHUD�XUP WRDUH�
[ ]∑
= +++−=
n
1tte
d
te
tee
t
)R1(
FFTDAT)T1(L-Mbail-credit VAN
úL�VH�SRDWH�GHPRQVWUD�vQWU-XQ�PRG�HFKLYDOHQW��F �
[ ]
[ ]∑= −+
+−=n
1tte
de
tee
t
R)T1(1
DAT)T1(L-Mbail-credit VAN
În cazul în care Te = Tb, VAN a credit-bail-XOXL�SHQWUX�ORFDWDU�HVWH�DVWIHO�HJDO �FX�9$1�D�RSHUD LHL�GH�FUHGLW-EDLO��LQYHVWL LH��SHQWUX�FUHGLWRU�
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
METODE UZUALE DE DETERMINARE A COSTULUI CREDIT-BAIL-ULUI &HOH� GRX �PHWRGH� FDUH� VXQW� úL� FHOH� PDL� X]XDOH� GH� GHWHUPLQDUH� D� FRVWXOXL� FUHGLW-bail-ului cRUHVSXQG�FHORU�GRX �PHWRGH�GH�GHWHUPLQDUH�D�UHQWDELOLW LL�XQHL�LQYHVWL LL��9$1�úL�UDWD�LQWHUQ �GH�rentabilitate. (1) 0HWRGD�9$1�D�ILQDQ ULL�VDX�PHWRGD�UDWHL�vPSUXPXWXOXL�GH�ED]
• UHJXOD�GH�ED] � Evaluarea VAN a credit-bail-XOXL�VH�IDFH�SRUQLQG�GH�OD�UHOD LD�pe care tocmai am expus-o în
prealabil:
[ ]
[ ]∑= −+
+−=n
1tte
de
tee
t
R)T1(1
DAT)T1(L-Mbail-credit VAN
$FHDVW � PHWRG � HVWH�� GH� DVHPHQHD�� GHQXPLW � ³PHWRGD� UDWHL� vPSUXPXWXOXL� GH� UHIHULQ ´��GHRDUHFH�VH�XWLOL]HD] �FD�R�UDW �GH�DFWXDOL]DUH��UDWD�DFWXDULDO �UHSUH]HQWkQG��FRVWXO�vPSUXPXWXOXL�alternativ pe care întreprinderea l-DU� IL� SXWXW� XWLOL]D�SHQWUX� D� VH� ILQDQ D��(D�SRDWH� IL� DGRSWDW �SHQWUX� D� LQH� FRQW� GH� GHFDODMHOH� FDUH� LQWHUYLQ� vQWUH� DQXPLWH� IOX[XUL�� GH� H[HPSOX�� FKLULLOH� úL�economiile de impozit care le corespund.
Utilizarea acestui criteriu esWH�LPHGLDW ��GDF �9$1�HVWH�SR]LWLY ��DWXQFL�FUHGLW-bail-ul este de preferat împrumutului clasic.
(2) Metoda ratei actuariale
0HWRGD� UDWHL� DFWXDULDOH� HVWH� HFKLYDOHQW � FX�PHWRGD� FULWHULXOXL� UDWHL� LQWHUQH� GH� UHQWDELOLWDWH�DSOLFDWH�FRVWXOXL�ILQDQ ULL��5HODWLY�OD credit-EDLO��UDWD�DFWXDULDO �VH�GHWHUPLQ �SULQ�F XWDUHD�UDWHL�5�DVWIHO�vQFkW�V �VH�UHVSHFWH�HJDOLWDWHD�XUP WRDUH�
[ ]
0)R1(
DAT)T1(L-Mbail-credit VAN
n
1tt
tee
t =+
+−= ∑=
5DWD�5�DVWIHO�RE LQXW � LQH�FRQW�GH�LQFLGHQ HOH�ILVFDOH�
4.2.4. Costul capitalului Conceptul de cost al capitalului� MRDF � XQ� URO� LPSRUWDQW� vQ� JHVWLXQHD� ILQDQFLDU �� DWkW� OD�DOHJHUHD�GHFL]LHL�GH�LQYHVWL LL�FkW�úL�OD�OXDUHD�GHFL]LHL�GH�ILQDQ DUH� $FHVW�FRVW�DO�FDSLWDOXOXL�XWLOL]DW�FD�R�UDW �GH�DFWXDULDOH�GHSLQGH�GH�XQ�QXP U�PDUH�GH�SDUDPHWUL��rata dobânzii datoriilor, poOLWLFD�GH�GLYLGHQGH��VWUXFWXUD�ILQDQFLDU �D�VRFLHW LL��ULVF��SLD D�ILQDQFLDU � &DOFXOXO�FRVWXOXL�FDSLWDOXOXL�WUHEXLH�V �VH�IDF �DGRSWkQG�R�RSWLF �SH�WHUPHQ�OXQJ�úL�FDOFXOkQG�FRVWXO�PHGLX�SRQGHUDW�SHQWUX�WRDWH�VXUVHOH�GH�ILQDQ DUH� Se va avea în vedere:
• FRVWXO�vQGDWRU ULL� • costul capitalurilor proprii; • costul mediu ponderat al capitalurilor; • costul marginal al capitalului; • FRVWXO�PDUJLQDO�DO�FDSLWDOXOXL�úL�DOHJHUHD�GHFL]LHL�GH�LQYHVWL LH�
���������&RVWXO�vQGDWRU ULL Datoriile sunt reprezentate de:
• împrumuWXUL�OD�E QFL�úL�RUJDQLVPH�ILQDQFLDUH�VSHFLDOL]DWH� • REOLJD LXQL�HPLVH�SH�SLD D�ILQDQFLDU �
Costul datoriei poate fi determinat atât înainte de plata impozitului pe profit (având în YHGHUH�IDSWXO�F �vQ�5RPkQLD�SHQWUX�vQFXUDMDUHD�XQRU�DFWLYLW L�HFRQRPLFH��VRFLHW L�FRPHUFLDOH�úL�D�LQYHVWL LLORU�VWU LQH�V-a operat cu scutiri de la plata acestui impozit pe perioada de la 6 luni la 5 ani în IXQF LH�GH� VSHFLILFXO� DFWLYLW LL�� FkW� úL�GXS �SODWD� LPSR]LWXOXL�SH�SURILW� �FD]XO� DJHQ LORU� HFRQRPLFL�care nu pot beneficiD�GH�VFXWLUL�VDX�GHS úHVF�SHULRDGD�GH�VFXWLUH�DFRUGDW ��
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
1) Costul datoriei înainte de impozitare &RVWXO� H[SOLFLW� DO� vPSUXPXWXOXL� HVWH� FDOFXODW� SRUQLQG� GH� OD� YDORDUHD� DFWXDO �� 'DF �
vQWUHSULQGHUHD�D�FRQWUDFWDW�R�GDWRULH�SH�FDUH�R�QRW P�FX�(��FDUH�DQWUHQHD] �UDPEXUV UL�DQXDOH�(dobânzi + anuitate de rambursat) egale cu E1, E2 … En, costul explicit al datoriei CD va fi GHWHUPLQDW�FX�DMXWRUXO�UHOD LH�
N
D
n2
D
2
D
1
)C1(
E...
)C1(
E
C1
E
+++
++
+
Calculul lui CD�VH�HIHFWXHD] �FD�XQ�FDOFXO�DO�XQHL�UDWH�LQWHUQH�GH�UDQGDPHQW��SRUQLQG�GH�la tabele de actualizare.
2) &RVWXO�GDWRULHL�GXS �LPSR]LWDUH
5DWD�GREkQ]LL�GXS �LPSR]LWDUH�HVWH�HJDO �FX��&'� ⋅ (1 - τ) unde τ este cota impozitului pe profit.
,PSR]LWXO�SH�SURILW�GLPLQXHD] �vQWU-un mod sensibil costul datoriei pentru întreprinderi, de vreme ce cheltuielile financiare sunt în general deductibile (sistemul actual de impozitare a SURILWXOXL�vQ� DUD�QRDVWU �PHQ LRQHD] �IDSWXO�F �VXPD�PD[LP �D�FKHOWXLHOLORU�FX�GREkQ]LOH�FDUH�SRDWH�IL�GHGXV �GH�F WUH�FRQWULEXDELOL�HVWH�R�VXP �HJDO �FX�VXPD�YHQLWXUilor din dobânzi plus 20% din alte venituri ale acestora).
ÌQ�VLWXD LD�vQ�FDUH�vQWUHSULQGHUHD�HVWH�GHILFLWDU �FRVWXO�GDWRULHL�U PkQH�OD�QLYHOXO�V X�GLQDLQWH�GH�LPSR]LWDUH�GH�YUHPH�FH�HD�QX�SRDWH�GHGXFH�FKHOWXLHOLOH�VDOH�ILQDQFLDUH��VDX�P FDU�R�SDUWH�GLQ�elH��GLQ�EHQHILFLXO�V X�EUXW�
4.2.4.2. Costul capitalurilor proprii &RVWXO�FDSLWDOXULORU�HVWH�HJDO�FX�UDWD�GH�UDQGDPHQW�DúWHSWDW �GH�DF LRQDUL� 5DWD�GH�UDQGDPHQW�DúWHSWDW �GH�F WUH�DF LRQDUL�FRUHVSXQGH�UDWHL�UDQGDPHQWXOXL�PLQLPDO�FDUH�LQFLW �DF LRQDUXO�SRWHQ LDO�V �FXPSHUH�R�DF LXQH�úL�GHWHUPLQ �DF LRQDUXO�DFWXDO�V �FRQVHUYH�WLWOXO�GH�valoare. 1) Costul capitalurilor proprii într-R�VWUXFWXU �GH�FDSLWDOXUL�GDWH
&RPHQVXUDUHD�FRVWXOXL�FDSLWDOXULORU�SURSULL�HVWH�SRVLELO �FX�DMXWRUXO�PHWRGHL�FH�DSHOHD] �OD�dividende.
2�DF LXQH��QHDYkQG�R�GDW �VFDGHQW ��VSUH�GHRVHELUH�GH�R�REOLJD LXQH�VH�SRDWH�FRQVLGHUD�F �YDORDUHD�DFWXDO �D�XQHL�DF LXQL�VDX�SUH XO�XQHL�DF LXQL��3$��HVWH�HJDO� ��FX�VXPD�DFWXDOL]DW �D�dividendelor viitoare:
)C1(
D...
)C1(
D
)C1(
DP
A2
A
2
A
1A +
+++
++
= ,
unde: PA -�SUH XO�DF LXQLL�³$´� Dt - dividende la momentul t = 1, 2…; CA -�FRVWXO�DF LXQLORU�VDX�UDWD�GH�UDQGDPHQW�DúWHSWDW �GH�DF LRQDUL� 'DF �VH�SUHVXSXQH�F �GLYLGHQGH�LQL LDO�'1�FUHúWH�vQ�PRG�UHJXODW�FX�R�UDW �GH�FUHúWHUH�QRWDW �FX�J��VH�SRDWH�DMXQJH�OD�XUP WRDUHD�UHOD LH�
)C1(
)g1(D...
)C1(
D
)C1(
DP
A
12
A
)g1(1
A
1
++++
++
+= +
$FHDVW � H[SUHVLH� HVWH� VXPD� XQHL� SURJUHVLL� JHRPHWULFH� GH� SULP� WHUPHQ��A
1
C1
D
+� úL�
UD LDAC1
g1
++
, care se mai poate scrie:
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
A
A
A
1A
C1
g11
)C1(
)g1(1
C1
DP
++−
++−
⋅+
=
6H�SUHVXSXQH�F �&A= g. Atunci când 1�WLQGH�VSUH�LQILQLW��HFXD LD�GHYLQH�
gC
D
)C1/()g1(1
1
C1
DP
A
1
AA
1A −
=++−
⋅+
=
LDU�FRVWXO�DF LXQLORU��&A) va fi: gP
DC
A
1A += .
2) &RVWXO�QRLORU�DF LXQL
(PLVLXQHD�GH�QRL�DF LXQL�DQWUHQHD] �SHQWUX�vQWUHSULQGHUH�FKHOWXLHOL�GH�HPLVLXQH�GH�WLWOXUL�QRL� • cheltuieli legate de titluri noi; • cheltuieli de publicitate; • FRPLVLRDQH�DOH�E QFLL�
$FHVWH�FKHOWXLHOL�VXQW�DGHVHD� vQ�IXQF LH�GH� LPSRUWDQ D�HPLVLXQLL�úL� UHSUH]LQW �DSURDSH�����suma emisiunii. 3HQWUX� FD� YHFKLL� DF LRQDUL� V � QX� ILH� SHQDOL]D L� SULQ� HPLVLXQHD� GH� QRL� DF LXni (diluare a EHQHILFLLORU�� YD� WUHEXL� FD� QRLOH� LQYHVWL LL� DOH� vQWUHSULQGHULL� V � JHQHUH]H� R� UDW � GH� UDQGDPHQW�� GH�DVHPHQHD� ULGLFDW � SHQWUX� D� SHUPLWH� Y UVDUHD� GH� GLYLGHQGH� D� F URU� YDORDUH� DFWXDO � V � ILH� HJDO � FX�SUH XO�QHW�SH�FDUH�vQWUHSULQGHUHD�vO�SULPHúWH�SHQWUX�QRLOH�VDOH�DF LXQL� Desemnând prin: PN –�SUH �QHW�vQFDVDW�GH�ILUP �SHQWUX�R�DF LXQH�QRX � CN –�FRVW�DO�DF LXQLORU�QRL� Dt -�GLYLGHQGH�OD�PRPHQWXO�W��W������«��VH�YD�RE LQH� 3UH XO�QHW�SH�R�DF LXQH�QRX ��vQFDVDW�GH�vQWUHSULQGHUH�HVWH� PN – P(1 – e), unde: e – cheltuielile de emisiune, exprimate în procentaj din totalul sumei emisiunii. $YkQG�vQ�YHGHUH��vQ�SUHDODELO��LSRWH]D�GH�FUHúWHUH�D�GLYLGHQGHORU�FX�R�UDW �GH�FUHúWHUH�QRWDW �cu g, se poate scrie:
gC
D)e1(P
N
1
−=−
de undH�VH�RE LQH�FRVWXO�QRLORU�DF LXQL�� g)e1(P
DC 1
N +−
= .
3) Costul rezervelor Rezervele sau beneficiile nerepartizate, au un cost (CR) un cost de oportunitate sau un cost
implicit. $FHVW�FRVW�SRDWH�IL�FRQVLGHUDW�FD�ILLQG�HJDO�FX�UDWD�GH�UDQGDPHQW�DúWHSWDW�GH�DF LRQDUL�SHQWUX�
DF LXQLOH�ORU�
gP
DCR +==
$QXPL L� DXWRUL� FRQVLGHU � FRVWXO� UH]HUYHORU� FD� ILLQG� XQ� FRVW� GH� RSRUWXQLWDWH� HJDO� FX� UDWD�UDQGDPHQWXOXL�SH�FDUH�vQWUHSULQGHUHD�vO�YD�SXWHD�RE LQH�SODVkQG�IRQGXULOH�VDOH�vQ�H[WHULRU� 4) &RVWXO�DF Lunilor privilegiate
$WXQFL�FkQG�R�vQWUHSULQGHUH�HPLWH�DF LXQL�SULYLOHJLDWH�úL�FkQG�HD�SULPHúWH�3N pentru fiecare QRX �DF LXQH��FRVWXO�DFHVWRU�DF LXQL�SULYLOHJLDWH��&P) este egal cu:
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
N
PP P
DC =
unde: PN –�SUH XO�QHW�vQFDVDW�GH�vQWUHSULQGHUH�SHQWUX�R�DF LXQH�SULYLOHJLDW � DP –�GLYLGHQGH�Y UVDWH�DF LXQLORU�SULYLOHJLDWH�
4.2.4.3. Costul mediu ponderat al capitalului &DOFXOXO�FRVWXOXL�PHGLX�SRQGHUDW�DO�FDSLWDOXOXL�VDX�FRVWXO�FDSLWDOXOXL�vQWUHSULQGHULL�QHFHVLW �anumite etape preliminare:
• calculXO�FRVWXOXL�FDSLWDOXOXL�ILHF UXLD�GLQWUH�VXUVHOH�GH�ILQDQ DUH�XWLOL]DWH� • FDOFXOXO�SRQGHULL�ILHF UHLD�GLQWUH�VXUVHOH�GH�ILQDQ DUH�SHQWUX�LQYHVWL LLOH�YLLWRDUH� • calculul costului mediu ponderat. Costul global al capitalului sau costul mediu ponderat al capitDOXOXL�VH�RE LQH�I FkQG�VXPD�
SURGXVHORU� FRVWXOXL� ILHF UXLD� GLQ� VXUVHOH� GH� ILQDQ DUH� úL� SRQGHUHD� SH� FDUH� HO� vO� SUH]LQW � vQ� WRWDO�resurse.
4.2.4.4. Teoria costului capitalului dependent de îndatorare $FHDVW �WHRULH�VWLSXOHD] �F �FRVWXO�XQLWDU�DO�FDSLWDOXOXL�FD�úL�SUH XO�DF LXQLORU�VXQW�DIHFWDWH�GH�FUHúWHUHD�vQGDWRU ULL�vQWUHSULQGHULL� &XP�FRVWXO�GDWRULHL�HVWH�vQ�JHQHUDO�LQIHULRU�FRVWXOXL�FDSLWDOXULORU�SURSULL��R�FUHúWHUH�D�GDWRULHL�DUH�XQ�LPSDFW�IDYRUDELO�DVXSUD�UHQWDELOLW LL�vQWUHSULQGHULL� Ipotezele de ED] �VXQW�XUP WRDUHOH� a) 6WUXFWXUD�FDSLWDOXOXL�vQWUHSULQGHULL�FXSULQGH�QXPDL�DF LXQL�úL�REOLJD LXQL� b) 3LH HOH�GH�FDSLWDOXUL�VXQW�SUHVXSXVH�SHUIHFWH��DGLF �
• QX�H[LVW �FRVWXOXL�DOH�WUDQ]DF LLORU� • LQIRUPD LD�HVWH�GLVSRQLELO �SHQWUX�WR L� • comportamentul investitoULORU�HVWH�UD LRQDO�
c) $QWLFLSD LLOH�EHQHILFLLORU�I FXWH�GH�LQYHVWLWRUL�VXQW�LGHQWLFH� d) %HQHILFLLOH�vQWUHSULQGHULORU�QX�VXQW�VXSXVH�LPSR]LW ULL� e) &RVWXO�DF LXQLORU�U PkQH�FRQVWDQW�FkQG�vQGDWRUDUHD�FUHúWH� f) &RVWXO�GDWRULHL�U PkQH�FRQVWDQW�FkQG�vQGDWRUDUHD�FUHúWH.
3RUQLQG�GH�OD�DFHVWH�LSRWH]H��SDUWL]DQLL�DFHVWHL�WHRULL�FRQVLGHU �F �XWLOL]DUHD�XQHL�vQGDWRU UL�PDL�LPSRUWDQWH�QX�VFKLPE �FRVWXO�FDSLWDOXULORU�SURSULL�
$FHDVW � vQGDWRUDUH� DU� SHUPLWH� GLPLQXDUHD� FRVWXOXL� FDSLWDOXOXL� vQWUHSULQGHULL�� *UDILFXO�XUP WRU�LOXVWUHD] �DFHDVW �WHRULH�
Costul capitalului
CA CM CD
0,10 0,30 0,70 0,90 1,00 Rata de îndatorare Datorii/Pasiv
9
6
3
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
&RVWXO�DF LXQLORU�U PkQH��GH�DVHPHQHD��FRQVWDQW� &RVWXO� PHGLX� SRQGHUDW� DO� FDSLWDOXOXL� �&0�� VH� GLPLQXHD] � FRQVWDQW� SH�P VXU � FH� UDWD� GH�vQGDWRUDUH�FUHúWH�GH�YUHPH�FH�GDWRULLOH�DX�XQ�FRVW�PDL�VF ]XW�GHFkW�DF LXQLOH� &RQIRUP�DFHVWHL�WHRULL��YDORDUHD�DF LXQLORU�DU�FUHúWH�vQ�DFHODúL�WLPS�FX�vQGDWRUDUHD��GH�YUHPH�FH�FRVWXO�PHGLX�SRQGHUDW�DO�FDSLWDOXOXL�VH�GLPLQXHD] �vQ�PRG�UHJXODW�
���������7HRULD�LQGHSHQGHQ HL�FRVWXOXL�FDSLWDOXOXL�GH�vQGDWRUDUH
$FHDVW �WHRULH�HVWH�RSXV �WHRULHL�SUHFHGHQWH�úL�HVWH�vQ�DFHODúL�WLPS�ED]DW �SH�DFHOHDúL�LSRWH]H�SULYLWRDUH�OD�SLD D�FDSLWDOXULORU��FRVWXO�GDWRULHL�úL�OD�ILVFDOLWDWH� &RQIRUP� DFHVWHL� WHRULL� H[SXV � GH� 0�+�� 0LOOHU� úL� )�� 0RGLJOLDQL� vQ� ������ FRVWXO� PHGLX�ponderat al capitalului nu estH�LQIOXHQ DW�GH�vQGDWRUDUHD�vQWUHSULQGHULL� $SDU�DLFL���FRQGL LL�FHUXWH�GH�H[SXQHUHD�WHRULHL� a) ÌQWUHSULQGHULOH�FRWDWH�SH�SLD �VXQW�vPS U LWH�SH�FODVH�GH�ULVF��ILHF UHL�FODVH�GH�ULVF�vL�HVWH�DVRFLDW �
R�UDW �GH�FDSLWDOL]DUH�SDUWLFXODU ��&r); b) Valoarea bursieU �
0�+��0LOOHU�úL�)��0RGLJOLDQL�FRQVLGHU �F ���vQWUHSULQGHUL�FDUH�vQUHJLVWUHD] �DFHODúL�EHQHILFLX�EUXW�úL�FDUH�DX�DFHODúL�JUDG�GH�ULVF�WUHEXLH�V �DLE �DFHHDúL�YDORDUH�GH�SLD ��YDORDUH�EXUVLHU ���RULFDUH�DU�IL�VWUXFWXUD�GH�ILQDQ DUH�
9DORDUHD�EXUVLHU �D�XQHL�vQWUHSULQGHUL�VH�RE LQH�FDSLWDOL]kQG�EHQHILFLXO�EUXW�DúWHSWDW�OD�R�UDW �
de capitalizare (Cr��FRUHVSXQ] WRDUH�JUDGXOXL�GH�ULVF��(D�HVWH�LQGHSHQGHQW �GH�VWUXFWXUD��ILQDQFLDU �D�
întreprinderii.
ÌQ�DFHDVW �WHRULH��SUH XO�DF LXQLORU�U PkQH�FRQVWDQW�DWXQFL�FkQG�QLYHOXO�vQGDWRU ULL�FUHúWH� Aprecierea teoriei 3HQWUX� vQWUHSULQGHUL�� DFHDVW � WHRULH� DU� DYHD� GUHSW� FRQVHFLQ � IDSWXO� F � QX� H[LVW � VWUXFWXUD�ILQDQFLDU �RSWLPDO ��GHRDUHFH�FRVWXO�PHGLX�SRQGHUDW�DO�FDSLWDOXOXL�U PkQH�FRQVWDQW� Aceast �WHRULH�D�I FXW�RELHFWXO�D�QXPHURDVH�FULWLFL�PDL�DOHV�SHQWUX�DQXPLWH�LSRWH]H�DOH�VDOH�QHUHDOLVWH��QHOXDUHD�vQ�FRQVLGHUD LH�D�LPSR]LWXOXL�SH�SURILW�HWF��� 'H� DVHPHQHD�� DFHDVW � WHRULH� HVWH� GLILFLO� GH� WHVWDW� GH� YUHPH� FH� HD� FRQVLGHU � YHQLWXULOH�anticipate.
Cost (%)
5DW �GH�vQGDWRUDUH
CA
CM
CD
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
4.2.4.6. Costul de oportunitate al resurselor 1. '(),1, ,(�ù,�,1752'8&(5(�Ì1�&21&(37
1) 'HILQL LH
Pasivul întreprinderii este la un moment dat constituit din ansamblul resurselor contractate de întreprindere. Aceste resurse financiare sunt caracterizate prin cosWXO�ORU�H[SOLFLW��DGLF �FRVWXO�OD�care societatea le-D�RE LQXW��úL�SULQ�FRVWXO�ORU�GH�RSRUWXQLWDWH�
&RVWXO�GH�RSRUWXQLWDWH�D�XQHL�VXUVH�GH�IRQGXUL�GHMD�RE LQXWH�HVWH��OD�XQ�PRPHQW�GDW��FRVWXO�OD�FDUH� vQWUHSULQGHUHD� DU� IL� SXWXW� RE LQH� R� UHVXUV � LGHQWLF � FX� DFHDVWD�� (O� UHSUH]LQW � GHFL�UHVSRQVDELOLWDWHD�SH�FDUH�R�FHU�GH LQ WRULL�GH�IRQGXUL�GDF �vQWUHSULQGHUHD�DU�UHFXUJH�OD�HOH�SHQWUX�D-úL�reînnoi sursele sale.
2) Introducere în concept
&RVWXO�GH�RSRUWXQLWDWH�SUH]LQW �SHQWUX�vQWUHSULQGHUH�R�LPSRUWDQ �FRQVLGHUDELO ��vQ�P VXUD�vQ�FDUH�HO�UHSUH]LQW �FRVWXO�OD�FDUH�vQWUHSULQGHUHD�úL-DU�IL�SXWXW�FUHúWH�PDUJLQDO�YROXPXO�PLMORDFHORU�VDOH�GH�ILQDQ DUH�
6H�PHUJH� SkQ � DFROR� vQFkW� VH� VXV LQH� F � FRVWXO� GH� RSRUWXQLWDWH� HVWH� HVHQ LDO� vQ� FD]XO� XQHL�vQWUHSULQGHUL� DOH� F UHL� WLWOXUL� VXQW� FRWDWH� OD� EXUV �� GHRDUHFH� DFHVW� FRVW� HVWH� GHWHUPLQDW� GH�FRPSRUWDPHQWXO�DFHVWRU�WLWOXUL��DF LXQL�úL�REOLJD LXQL��SH�SLH HOH�VHFXQGDUH�
7RWXúL��FRQFHSWXO�GH�FRVW�GH�RSRUWXQLWDWH�QX� VH� OLPLWHD] �QXPDL� OD� vQWUHSULQGHULOH�FDUH� IDF�DSHO�OD�SLD D�ILQDQFLDU ��HO�VH�DSOLF �PDL�PXOW�VDX�PDL�SX LQ�GLUHFW�OD�RULFH�vQWUHSULQGHUH��SHQWUX�FDUH�HO�UHSUH]LQW �FRVWXO�PDUJLQDO�DO�XQHL�XQLW L�PRQHWDUH�GH�UHVXUVH�VXSOLPHQWDUH�LGHQWLFH�FX�UHVXUVHOH�actuale.
2. MECANISMUL COSTULUI DE OPORTUNITATE
1) 5HYL]XLUHD�VLVWHPDWLF a modului de evaluare a pasivului exigibil 3LD D� ILQDQFLDU � PRGLILF � vQ� PRG� FRQVWDQW� YDORDUHD� SH� FDUH� R� DWULEXLH� REOLJD LXQLORU�
întreprinderii. &RQVLGHU P��FX�WLWOX�GH�H[HPSOX��R�vQWUHSULQGHUH�FDUH�HPLWH�REOLJD LXQL�GH������UDPEXUVDELOH�
în 10 ani prin uniW L�FRQWDQWH�� OD�R�HSRF � vQ�FDUH�SLD D�VROLFLW � �FHUH��R�GREkQG �GH�����DIHUHQW �SODVDPHQWHORU� VDOH� REOLJDWDUH�� 6FDGHQ DUXO� IOX[XOXL� OHJDW� GH� R� REOLJD LXQH� VH� VWDELOHúWH� GXS � FXP�XUPHD] �
Anii 0 1 2 3 4 5 6 7 8 9 10 + + 100 -16,27 -16,27 -16,27 -16,27 -16,27 -16,27 -16,27 -16,27 -16,27 -16,27
/D�VIkUúLWXO�SULPXOXL�DQ��SLD D� ILQDQFLDU �QX�PDL�VROLFLW �SHQWUX�DFHODúL� ULVF��GHFkW�R� UDW �D�dobânzii de 8% pe an. 'LQ�FDX]D�DFHVWHL�VF GHUL�D�UDWHL�GREkQ]LL��VH�UHHYDOXHD] �PRG�DXWRPDW�DFWLYXO�ILQDQFLDU�OD�10������YDORDUH�DFWXDOL]DW �OD����D�������SULPL L�DQXDO�WLPS�GH���DQL�� 8UPHD] �IDSWXO�F ��-�SH�GH�R�SDUWH��GH LQ WRUXO�UHYLQGH�WLWOXO�V X�vQ�SULPXO�DQ��YD�vQFDVD�vQ�DFHVW�PRPHQW�XQ�SUH �GH�UHYkQ]DUH�FUHVFXW�–�P ULW�–�FX�GREkQG �DQXDO �
16,27 + 101,64 = 117,91 úL�YD�DYHD�GHFL�R�UHQWDELOLWDWH�DQXDO �GHJDMDW �GH�SODVDPHQWXO�V X�GH���������LDU��SH�GH�DOW �SDUWH��LQYHVWLWRUXO�FRPSHQVkQG�REOLJD LXQHD�OD��������vQ�SULPXO�DQ�YD�vQFDVD�������SH�DQ�WLPS�GH���DQL��SODVDPHQWXO�V X�GHJDMkQG�GHFkW�R�UHQWDELOLWDWH�DQXDO �GH���� 3HU� WRWDO�� UHQWDELOLWDWHD� DFWXDULDO � RE LQXW � GH� GH LQ WRUXO� FDUH� D� FXPS UDW� WLWOXO� FKLDU� vQ�PRPHQWXO� HPLVLXQLL� OXL� úL� S VWUkQGX-O� SkQ � OD� VFDGHQ �� HVWH� GH� �����(D� VH� GHVFRPSXQH� vQ� GRX �UHQWDELOLW L�GH�RSRUWXQLW L�FDUH�DMXQJ�SkQ �OD�
• 17,91% în primul an; • ���vQ�XUP WRULL�DQL�
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
,QYHUV��FRVWXO�H[SOLFLW�DO�vPSUXPXWXOXL�U PkQH�SHQWUX�vQWUHSULQGHUH�HJDO�FX�����GH-a lungul GXUDWHL�VDOH��GDU�VH�GHVFRPSXQH�vQ�GRX �FRVWXUL�GH�RSRUWXQLWDWH�GLVWLQFWH�
• ������� vQ� SULPXO� DQ�� vQ� DO L� WHUPHQL�� GDF � ILUPD� DU� WUHEXL� V -úL� U VFXPSHUH�WLWOXULOH�VDOH�OD�EXUV ��HD�DU�WUHEXL�V �SO WHDVF ����������úL�QX������SHQWUX�ILHFDUH�titlu;
• ���WLPS�GH���DQL��XUP WRULL��� vQ�DO L� WHUPHQL�� vQWUHSULQGHUHD�DU�IL�SXWXW� OD�ILQHOH�SULPXOXL�DQ�V �VH�UHvQGDWRUH]H�OD����WLPS�GH���DQL�
În defLQLWLY��ILQDO��vQWUHSULQGHUHD�QX�YD�Y UVD�HIHFWLY��GH-D�OXQJXO�GXUDWHL�vPSUXPXWXOXL�V X��GHFkW�UDWD�GREkQ]LL�GH�����SUHY ]XW �LQL LDO��7RWXúL��DFHVW�FRVW�H[SOLFLW�VH�YD�GHVFRPSXQH�vQ�GLIHULWH�FRVWXUL� GH� RSRUWXQLWDWH� GXS � HYROX LD� UDWHL� GREkQ]LL� SH� SLD D� ILQDQFLDU �� DFHDVWD� GLQ� XUP �modificându-úL�v�PRG�FRQVWDQW�SURSULD�VD�HVWLPDUH�FX�SULYLUH�OD�YDORDUHD�REOLJD LXQLL�
2) Principiul de anticipare a rezultatelor: costul de oportunitate al capitalurilor proprii
'DF � PRGLILF ULOH� GH� HYDOXDUH� D� SLH HL� ILQDQFLDUH� VH supun, pentru capitaluri proprii, la PHFDQLVPH�VWULFW�LGHQWLFH�FHORU�FDUH�DIHFWHD] �SDVLYXO�H[LJLELO��HOH�FDS W �R�VHPQLILFD LH�PDL�ODUJ �vQ�P VXUD�vQ�FDUH�SLD D�UHFRQVLGHU �úL�DQWLFLSHD] �vQ�SHUPDQHQ �UH]XOWDWHOH�vQWUHSULQGHULL��&XP�DFHVWH�IOXFWXD LL�VXnt foarte importante, determinarea costului de oportunitate aferent capitalurilor proprii, pune întreprinderii probleme considerabile din punct de vedere financiar.
$FHVW�FRVW�HVWH�IXQF LH�GH�FXUVXO�DF LXQLL�SH�SLD D�VHFXQGDU ��HO� UHSUH]LQW �FRVWXO�XQXL�QRu DSHO�DO�DF LRQDULORU��'H�DLFL�UH]XOW �LPSRUWDQ D�IXQGDPHQWDO �D�FXUVXOXL�EXUVLHU�vQ�SROLWLFD�ILQDQFLDU �D�vQWUHSULQGHULL��GHWHUPLQkQG�FRVWXO�GH�RSRUWXQLWDWH�DO�XQXL�DSHO�DO�DF LRQDULORU��HO�GHILQHúWH�UHVXUVHOH�SRWHQ LDOH�DOH�vQWUHSULQGHULL�vQ�PDWHULH�GH�capitaluri proprii.
De asemenea, determinarea costului de oportunitate al capitalurilor proprii presupune DQDOL]D�SDUDPHWULORU�FDUH�H[SOLF �HYROX LD�XQHL�DF LXQL�SH�SLD D�ILQDQFLDU ��DGLF �IRUPDUHD�FXUVXOXL�bursier.
3. DETERMINAREA COSTULUI DE OPORTUNITATE A CAPITALURILOR
PROPRII
1. Parametrii analizei cursului bursier �����3R]L LD�SUREOHPHL $QDOL]D�FXUVXOXL�EXUVLHU�DO�RULF UHL�vQWUHSULQGHUL�VH�ORYHúWH�GH�XQ�GXEOX�SDUDGR[� � SH�GH�R�SDUWH��HYDOXDUHD�FXUVXOXL�EXUVLHU�VH�ED]HD] �vQ�PRG�HVHQ LDO�SH�SURLHFWDUHD parametrilor
HFRQRPLFL� SURSULL� DL� XQHL� vQWUHSULQGHUL�� DFWXDOL]D L� OD� UDWD� GH� UHQWDELOLWDWH� FHUXW � SH� SLD D�ILQDQFLDU �� FXUVXO� EXUVLHU� UH]XOW � GHFL� FD� XUPDUH� D� JHVWLXQLL� VRFLHW LL� úL� D� DWLWXGLQLL� SLH HL�ILQDQFLDUH�FDUH�VDQF LRQHD] �DFHDVW �JHVWLXQH�
� pe de� DOW �SDUWH��FKLDU�SLD D� ILQDQFLDU � VROLFLW �R�UDW �GH� UHQWDELOLWDWH�GLVWLQFW �GH� UHQWDELOLWDWHD�HFRQRPLF � D� vQWUHSULQGHULL�� HD� DSOLF � DFHDVW � UDW � OD� SDUDPHWULL� LQWHUQL� DL� vQWUHSULQGHULL�� FDUH�LPSXQH�GLQ�DFHVW�PRWLY�DF LRQDUXOXL�SURSULD�VD�UHQWDELOLWDWH��RULFDUH�DU�IL�UHQWDELOLWDWHD�FHUXW �SH�SLD ��UHQWDELOLWDWHD�DF LXQLL��QX�YD�IL�vQ�PRG�JOREDO�GHFkW�UHQWDELOLWDWHD�GHJDMDW �GH�DFHDVWD�
'LQ�FDX]D�DFHVWXL�GXEOX�SDUDGR[�GHFXUJ�SDUDPHWULL�FDUH�WUHEXLH�V �ILH�OXD L�vQ�FRQVLGHUDUH�vQ�evaluarea cursului bursier�DO�XQHL�VRFLHW L� 1.2. Aspect teoretic &XUVXO�EXUVLHU�GHSLQGH�GH�FRQMXQFWXUD�D�GRL�IDFWRUL�HVHQ LDOL��UHQWDELOLWDWHD�vQWUHSULQGHULL�SH�GH� R� SDUWH� úL� VWDUHD� SLH HL� ILQDQFLDUH� SH� GH� DOW � SDUWH�� GHRDUHFH� DF LXQHD� YD� SXWHD� RULFkQG� V � ILH�VFKLPEDW �VDX�QHJRFLDW �SH�SLD ��(O�HVWH�IXQGDPHQWDO�OHJDW�GH�SDUDPHWULL�vQWUHSULQGHULL�úL�GH�GDWHOH�SLH HL� ILQDQFLDUH�� &XUVXO� EXUVLHU� UHSUH]LQW � SH� GH� DOW � SDUWH�� HVWLPDUHD� SDUDPHWULORU� vQWUHSULQGHULL�HYDOXD L�SH�SLD �OD�UDWD�GH�RSRUWXQLWDWH�SH�FDUH�úL-R�DOHJH�DF LRQDUXO� LQkQG�FRQW�GH�ULVFXO�OD�FDUH�VH�expune. 9DORDUHD�ILQDQFLDU �D�vQWUHSULQGHULL�HVWH��GHFL��vQDLQWH�GH�WRDWH��R�YDORDUH�DQWLFLSDW �
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
�����6SHUDQ D�DF LRQDUXOXL 5HQWDELOLWDWHD�SH�FDUH�DF LRQDUXO�R�SULPHúWH�FD�XUPDUH�D�DMXQJHULL�OD�VFDGHQ �D�WLWOXOXL�V X�GH SURSULHWDWH�QX�SRDWH�� vQ�SULQFLSLX�� V �GLIHUH� vQ�PRG�JOREDO�GH� UHQWDELOLWDWHD�GHJDMDW �GH�DFWLYLWDWHD�întreprinderii. 7RWXúL��DF LRQDUXO�DQWLFLSHD] �HYROX LD�SDUDPHWULORU�ILQDQFLDUL�DL�vQWUHSULQGHULL�úL�vL�HVWLPHD] �vQ� IXQF LH� GH� XQ� DQXPLW� FRVW� GH� RSRUWXQLWDWH�� FXUVXO� EXUVLHU� UHIOHFW � GLQ� DFHVW�PRWLY� R� VDQF LXQH�DWULEXLW �vQ�DYDQV�vQWUHSULQGHULL�SH�SLD D�ILQDQFLDU � 9DORDUHD�HVWLPDW ��VSHUDW ��GH�DF LRQDU�SUH]LQW �R�PDUH�LPSRUWDQ �SHQWUX�VRFLHWDWH�GHRDUHFH�VH�J VHúWH�OD�RULJLQHD�DMXVW ULL�FXUVXULORU��&RQVLGHU P�R�vQWUHSULQGHUH�D�F UHL�YDORDUH�ILQDQFLDU �HVWH�����vQ�DQXO���úL�FDUH�FDSLWDOL]HD] �WRWDOLWDWHD�EHQHILFLLORU�VDOH�UHLQYHVWLQGX-le la rata de 10% (rata sa GH�UHQWDELOLWDWH�PHGLH���(D�VH�GH]YROW �GXS �FXP�XUPHD] � Anii 0 1 2 3 4 Beneficiu - 10 11 12,1 13,31 Capitaluri proprii 100 110 121 133,1 146,41
'DF � DF LRQDUXO� VRFLHW LL� VSHU � HIHFWLY� OD� R� UDW � GH� UHQWDELOLWDWH� GH� ����� YDORDUHD� GH�HFKLOLEUX��DGLF �YDORDUHD�ILQDQFLDU �D�vQWUHSULQGHULL�� vQ�DQXO���YD�IL�HJDO �FX������'DF � vQ�VFKLPE��
DF LRQDUXO�QX�DúWHDSW �GHFkW�R�UHQWDELOLWDWH�GH����úL�VH�DSUHFLD] �F �R�vQWUHSULQGHUH�RE LQH�EHQHILFLL�
VXSHULRDUH� FHORU� VFRQWDWH�� HO� YD� UHDMXVWD� FXUVXO� DF LXQLL�� DFWXDOL]kQGX-O� OD� ��� �úL� QX� OD� ������EHQHILFLLOH�YLLWRDUH�úL�VH�YD�IL[D�GHFL�YDORDUHD�EXUVLHU �D�VRFLHW LL�OD�������vQ�DQXO���úL�OD�������vQ�
DQXO����(O�YD�RE LQH�HIHFWLY�R�UHQWDELOLWDWH�GH����FD�úL�R�SOXV�YDORDUH�GH�������������–�����DIHUHQW �YDORULL�DF LXQLL�VDOH��GDF �VH�GHFLGH�V �UHYkQG �DF LXQHD�OD�ILQHOH�DQXOXL���� ,QYHUV��GDF �SLD D�DúWHDSW �R�UHQWDELOLWDWH�GH�����HO�YD�UHDMXVWD�FXUVXO�DF LXQLL�VXE�IRUP �GH�
SLHUGHUH�GH�YDORDUH��IL[kQG�FXUVXO�OD�������vQ�DQXO���úL������vQ�DQXO����6H�REVHUY �LPSRUWDQ D�SH�FDUH�
R� SUH]LQW � SHQWUX� vQWUHSULQGHUH� UHQWDELOLWDWHD� VSHUDW � �DúWHSWDW �� GH� DF LRQDU�� GDF � DFHVWD nu este PXO XPLW��YDORDUHD�ILQDQFLDU �D�vQWUHSULQGHULL�VH�YD�GHSUHFLD��LQYHUV��GDF �HO�VROLFLW �R�UHQWDELOLWDWH�LQIHULRDU �UHQWDELOLW LL�RIHULWH�GH�vQWUHSULQGHUH�DFHDVW �YDORDUH�YD�IL�UHDMXVWDW �vQ�VHQVXO�FUHúWHULL� 6WXGLXO�VSHUDQ HORU�DF LRQDUXOXL�SHUPite, deci, degajarea parametrilor fundamentali care vor VHUYL�FD�ED] �vQ�GHWHUPLQDUHD�FXUVXOXL�EXUVLHU�DO�VRFLHW LL��$FHúWL�SDUDPHWUL�SRW�IL�DVWIHO�GHILQL L�
3URLHFWDUHD�UHQWDELOLW LL � beneficii � dividende
Parametrii interni ai întreprinderii
Parametrii externi ai întreprinderii
5DWD�GREkQ]LL�úL�ULVFXO��SHUFHSXW�SH�SLD
Tipologie a fluxurilor GH�IRQGXUL�OHJDW �GH�GH LQHUHD�XQHL�DF LXQL
5DWD�GH�UHQWDELOLWDWH�FHUXW � SH�SLD D�ILQDQFLDU
DFWXDOL]DW �OD CURS BURSIER
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
���6WXGLHUHD�UDWHL�GH�UHQWDELOLWDWH�FHUXW �GH�SLD D�ILQDQFLDU 2.1. Principii ale modelelor de evaluare (YDOXDUHD� UDWHL�GH� UHQWDELOLWDWH� FHUXWH�GH�SLD �� DGLF � FRVWXO�GH�RSRUWXQLWDWH�D� FDSLWDOXULORU�SURSULL�VH�ORYHúWH�GH�R�VHULH�GH�LQFHUWLWXGLQL��(D�QHFHVLW �vQWUH-DGHY U�GHWHUPLQDUHD�UDWHL�FHUXWH�úL�R�vQ HOHJHUH� D� SUHYL]LXQLORU� VWDELOLWH� GH� SLD � FX� SULYLUH� OD� SDUDPHWULL� LQWHUQL� DL� � vQWUHSULQGHULORU��EHQHILFLL�úL�GLYLGHQGH�� 'H�DVHPHQHD��PRGHOHOH�GH�DQDOL] �D�FXUVXOXL�EXUVLHU�DX�IRVW�HODERUDWH�vQ�VFRSXO�GH�D�vQ HOHJH�LSRWH]HOH� LPSOLFLWH� FH�GHWHUPLQ � IRUPDUHD�FXUVXOXL��(OH�SUH]LQW � interesul de a oferi întreprinderii SRVLELOLWDWHD�GH�D�FRPSDUD�SURSULLOH�VDOH�SUHYL]LXQL�FX�DQWLFLSD LLOH�SLH HL�ILQDQFLDUH�UHVSHFWLY�vQ�DO L�WHUPHQL�GH�D�DQDOL]D�SHUFHSHUHD�vQWUHSULQGHULL�GH�SLD � 0RGHOHOH� GH� HYDOXDUH� D� FXUVXOXL� EXUVLHU� UHOLHIHD] � SH� DFHDVW � ED] �� YDORULOH� SDUDPHWULORU�LQWHUQL�DL�vQWUHSULQGHULL�vQ�HYROX LD�FXUVXOXL��'RX �VXQW�PRGHOHOH�DYXWH�vQ�YHGHUH�
� evaluarea prin dividende; � evaluarea prin beneficii.
2.1. A. Evaluarea prin dividende Prezentarea modelului Demersul teoretic 6H� FRQVLGHU �� într-XQ� SULP� PRPHQW� F � LQWU ULOH� GH� IRQGXUL� DúWHSWDWH� GH� DF LRQDUL� VXQW�FRQVWLWXLWH�GLQ�GLYLGHQGH�úL�GLQ�YDORDUHD�GH�UHYkQ]DUH�D�DF LXQLL�OD�ILQHOH�SHULRDGHL�GH�GH LQHUH��(VWH�DWXQFL�SRVLELO �FDOFXODUHD�UHQWDELOLW LL�DúWHSWDWH�GH�LQYHVWLWRU��$VWIHO��DF LRQDUXO�VRFLHW LL�³$´�FDUH�D�FXPS UDW�FX�����R�DF LXQH�GH�OD�FDUH�DúWHDSW �OD�ILQHOH�DQXOXL�XQXL�GLYLGHQG�GH���úL�FDUH�VSHU �V-o UHYkQG �FX������DúWHDSW �GH�OD�LQYHVWL LD�VD�R�UHQWDELOLWDWH�.�HJDO �FX� K = (4 + 106)/100 – 1 = 10% úL�VH�SRDWH��GH�DVHPHQHD��H[SULPD�SULQ�HFXD LD�XUP WRDUH� 100 = 4/(1 + K) + 106/(1 = K) vQ�FDUH�.�UHSUH]LQW � UDWD�GH�DFWXDOL]DUH�FDUH�HJDOHD] �YDORDUHD� LQL LDO �GH�FXPS UDUH�GH�DF LXQL�FX�VXPD� DFWXDOL]DW � D� IOX[XULORU� GH� IRQGXUL� DúWHSWDWH�� (VWH� XúRU� JHQHUDOL]DUHD� UD LRQDPHQWXOXL SUHVXSXQkQG�F �DF LRQDUXO�DUH�LQWHQ LD�GH�D�FRQVHUYD�WLWOXO�V X�XQ�DQ� 'DF �HO�S VWUHD] �WLWOXO�GRL�DQL�úL�GDF �DúWHDSW �vQ�DO�GRLOHD�DQ�XQ�GLYLGHQG�GH������úL�vQ�SOXV�VSHU �V �UHYkQG �WLWOXO�OD�SUH XO�GH���������UHQWDELOLWDWHD�VSHUDW �.�VH�GHGXFH�GLQ�HFXD LD� 100 = 4/(1 + K) = 4,40/(1 + K)2 XQGH�.�U PkQH�HJDO�FX����� 3UHVXSXQHP� vQ� SUH]HQW� F � LQYHVWLWRUXO� DUH� LQWHQ LD� V � FRQVHUYH� WLWOXO� V X� WLPS� GH� ��� DQL��(FXD LD�GHYLQH�
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unde: P0 -�SUH XO�GH�FXPS UDUH�vQ�DQXO��� n - num UXO�GH�DQL�FH�FRQVWLWXLH�GXUDWD�LQYHVWL LHL� Dn -�GLYLGHQGXO�DúWHSWDW�vQ�DQXO�Q� P10 -�SUH XO��GH�FHVLXQH�VSHUDW�vQ�DQXO���� Principii 0RGHOXO� WHRUHWLF� GH� HYDOXDUH� SULQ� GLYLGHQGH� SUHVXSXQH�� vQ� SULPXO� UkQG� F � YDORDUHD� ILQDO ��VDX�SUH XO�GH�FHVLXQH��DO�DF LXQLL�HVWH�UHVSLQV �OD�LQILQLW� 9DORDUHD�GH�SLD �D� WLWOXOXL�HVWH�DWXQFL�HJDO �FX�VXPD� LQILQLW �D�GLYLGHQGHORU�DFWXDOL]DWH� OD�UDWD�LQYHVWLWRUXOXL�ILQDQFLDU ��DWXQFL�
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Modulul 4 -�6WUDWHJLD�ILQDQFLDU
IRUPXO � vQ� FDUH�.� HVWH� UDWD� GH� DFWXDOL]DUH� DGDSWDWH� SH� SLD D� VDX� UDWD� GH� RSRUWXQLWDWH� D� LQYHVWL LHL�marginale. 6H�SUHVXSXQH�vQ�DO�GRLOHD�UkQG��F �DF LRQDUXO�VSHU �R�FUHúWHUH�DQXDO ��J���D�GLYLGHQGHORU�SH�FDUH� XUPHD] � V � OH� SULPHDVF �� UDWD� �J�� HVWH� IXQF LH� GH� DSUHFLHUHD� vQ� SHUVSHFWLY � � �YLLWRU�� D�întreprinderii úL�GH�SROLWLFD�DGRSWDW �GH�DFHDVWD�vQ�WUHFXW� Formula de evaluare devine atunci: P0 = D0(1 + g) / (1 + K) + D0(1 + g)2 / (1 + K)2 + … + D0(1 + g)n / (1 + k)n ceea ce revine la a scrie, atunci când “n” tinde spre infinit: P0 = D0 / K – g sau K = D0 / P0 + g Critica modelului] 6H� SRDWH� UHSURúD� DFHVWXL� PRGHO� IDSWXO� F � VH� SUHVXSXQH� R� FUHúWHUH� DQXDO � FRQVWDQW � D�GLYLGHQGHORU�Y UVDWH��DFHDVW �LSRWH] �QHSXWkQG�V �VH�DSOLFH�GHFkW�OD�XQ�QXP U�UHGXV�GH�vQWUHSULQGHUL��(O� SUH]LQW � vQ� DFHODúL� WLPS� DYDQWDMXO� GH� D� SURSXQH� R� PHWRG � GH� HYDOXDUH� FDUH� YD� IL� vQWRWGHDXQD�SRVLELO �GH�DGDSWDW�XQHL�PRGLILF UL�D�UDWHL�GH�FUHúWHUH�D�GLYLGHQGHORU�DúWHSWDWH��'DF ��GH�H[HPSOX��DF LRQDUXO�DúWHDSW �vQ�FXUVXO�SULPLORU�³P´�DQL�R�FUHúWHUH�³J´�úL��SULQ�XUPDUH��R�FUHúWHUH�³J´�D�VXPHL�dLYLGHQGHORU�Y UVDWH��IRUPXOD�SUHFHGHQW �GHYLQH�
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)K1(
)g1(D
2.1. B. Evaluarea prin beneficii 3RDWH�S UHD�SDUDGR[DO�FRQFHSHUHD�XQXL�PRGHO�GH�HYDOXDUH�SULQ�EHQHILFLL� vQ�P VXUD� vQ�FDUH�acestea nu constituie pentru întreprindere fluxuri de trezorerie. %HQHILFLXO�SH�DF LXQH��%3$��HVWH�vQ�JHQHUDO�FRQVLGHUDW�FD�XQXO�GLQ�FULWHULLOH�IXQGDPHQWDOH�FH�VHUYHVF� FD� UHIHULQ � DF LRQDUXOXL� FH� GRUHúWH� HYDOXDUHD� UHQWDELOLW LL� LQYHVWL LHL� VDOH� SULQ� UDWD� GH�FDSLWDOL]DUH�EXUVLHU � S-D�Y ]XW�F �UHQWDELOLWDWHD�DúWHSWDW �GH�DF LRQDU�úL�YDORDUHD�SH�FDUH�DFHVWD�R�DFRUG �DF LXQLL�FH�R�GH LQH��VHUYHúWH�FD�ED] �OD�GHWHUPLQDUHD��FRVWXOXL�GH�RSRUWXQLWDWH�DO�vQWUHSULQGHULL��2UL��GDF �GH�H[HPSOX��R�DF LXQH�HVWH�FRWDW �OD�����vQ�WLPS�FH�HD�DGXFH�XQ�%3$�GH����SH�DQ�3(5-ul sau rata de FDSLWDOL]DUH� HVWH� HJDO � FX� ������� � ���� LQYHUVXO� 3(5-XOXL� UHSUH]LQW � UHQWDELOLWDWHD� DúWHSWDW � GH�DF LRQDUL" Inversul PER-XOXL�P VRDU �UHQWDELOLWDWHD�DúWHSWDW �GH�DF LRQDUL�vQ�FD]XUL�ELQH�SUHFL]DWH� D��GDF �WRDWH�EHQHILFLLOH�GHJDMDWH�GH�R�vQWUHSULQGHUH�VXQW�GLVWULEXLWH�DF LRQDULORU��YHQLWXO�DúWHSWDW�GH�
DFHúWLD� GDF � .� HVWH� UDWD� GH� UHQWDELOLWDWH� VROLFLWDW � �FHUXW �� úL� FDUH� DLFL� HVWH� IRORVLW � FD� UDW � GH�actualizare.
n32 )K1(
B...
)K1(
B
)K1(
B
K1
BC
+++
++
++
+=
YDORDUHD� DFWXDO � GH� UHYkQ]DUH� SXWkQG� IL� FRQVLGHUDW � FD� QXO �� DF LRQDUXO� DFWXDOL]kQGX-úL� YHQLWXULOH�VDOH� OD� LQILQLW�� XWLOL]DUHD� IRUPXOHL� SHUPL kQG� FDOFXODUHD� OLPLWHL� VXPHL� WHUPHQLORU� XQHL� SURJUHVLL�
geometrice de prim termen: )K1(
B
+�úL�GH�UD LH�
)K1(
1
+, deci:
K
BC = fie
curs
beneficiu
C
BK ==
Inversul PER-XOXL�HVWH�GHFL��vQ�DFHVW�FD]��HJDO�FX�UDWD�GH�UHQWDELOLWDWH�DúWHSWDW �GH�DF LRQDU� b) GDF � UHQWDELOLWDWHD� DúWHSWDW � GH� DF LRQDUL� HVWH� HJDO � FX� UHQWDELOLWDWHD� vQWUHSULQGHULL�� DGLF � GDF �
UHQWDELOLWDWHD�ILQDQFLDU �D�LQYHVWL LHL�DF LRQDULORU�HVWH�HJDO �FX�UHQWDELOLWDWHD�IRQGXULORU�LQYHVWLWH�de întreprindere, inversul PER-XOXL��UHSUH]LQW �vQF �VSHUDQ D�GH�UHQWDELOLWDWH�D�DF LRQDULORU�
3HQWUX�D�LOXVWUD�DFHDVW �UHJXO ��FRQVLGHU P�H[HPSOXO�XQHL�VRFLHW L�FDUH�D�HPLV�DF LXQi la un FXUV�GH������úL�GHJDMHD] �R�UHQWDELOLWDWH�HFRQRPLF �GH�����FD�XUPDUH�D�LQYHVWL LLORU�VDOH��GLVWULEXLQG�����GLQ�EHQHILFLLOH�VDOH�DF LRQDULORU�
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
În anul 1: � beneficiul degajat este 10; � beneficiile distribuite sunt 5; � raportul curs-beneficiu este egal cu 10; � LQYHUVXO�DFHVWXL�UDSRUW��FXUV�EHQHILFLX��HVWH������ ������DGLF �UHQWDELOLWDWHD�HFRQRPLF � În anul 2: � FXUVXO�DF LXQLL�DMXQJH�OD����� � beneficiul degajat este egal cu 105; � inversul PER-XOXL�HVWH�vQF �HJDO�FX���������� �����úL������VXQW�GLVWULEXL L�DF Lonarilor. $FHVW� UD LRQDPHQW� SRDWH� IL� SUHOXQJLW� OD� LQILQLW� úL� GHPRQVWUHD] � F �� vQ� DFHVW� FD]� SUHFLV��
inversul PER-XOXL�UHSUH]LQW �vQF �UHQWDELOLWDWHD�DúWHSWDW �GH�DF LRQDUL� Limitele de evaluare prin inversul PER-ului Cazurile de echilibru precedente, fiind�UHODWLY�H[FHS LRQDOH��VH�FRQYLQH�O UJLUHD�PRGHOXOXL�GH�
HYDOXDUH�úL�SHQWUX�DFHDVWD�VH�IDFH�DSHO�OD�R�IRUPXODUH�PDWHPDWLF �PDL�HODERUDW �GH�DSURSLHUH�SULQ�beneficii.
'HVHPQ P� SULQ� %t beneficiul anului t, 1t partea beneficiilor reinvestite în activitatea întUHSULQGHULL� úL�FRQVDFUDWH� LQYHVWL LLORU�QRL�� LDU�'t dividendele distribuite în anul t. Deoarece prin GHILQL LH�� 't = Bt – 1t�� YDORDUHD� DF LXQLL� vQ� PRPHQWXO� LQL LDO� &0� HVWH� GHWHUPLQDW � SULQ� VXPD�GLYLGHQGHORU�DFWXDOL]DWH�OD�UDWD�.��UHQWDELOLWDWHD�FHUXW �GH�DF LRQDU��
...)K1(
D...
)K1(
D
K1
DC
nn
221
0 ++
+++
++
=
∑∞
= +==
1tt
tt0
)K1(
1BC
3HQWUX�D�SUHFL]D�GRPHQLLOH�GH�DSOLFDUH�DOH�DFHVWXL�PRGHO�FRQVLGHU P�FD]XO�XQHL�vQWUHSULQGHUL�FH�UHLQYHVWHúWH�R�VXP �GH�EHQHILFLL�FRQVWDQWH�vQ�LQYHVWL LL�QRL�FDUDFWHUL]DWH�SULQWU-o rentabilitate r. În DO L�WHUPHQL��%t = Bt + 1 + 1⋅ rt��W�UHSUH]HQWkQG�QXP UXO�GH�DQL�DL�SHULRDGHL�FRQVLGHUDWH�
(FXD LD�SUHFHGHQW �GHYLQH�DWXQFL��vQORFXLQG�%t�SULQ�YDORDUHD�VD�FDOFXODW �vQ�IXQF LH�GH�%0:
∑ ∑∑∞
=
∞
=
∞
=
+−+
+=
+−+
1t 1tt
t
1tt
0t
t0
)K1(
)1r(1
)K1(
B
)K1(
)1r(1B
care devine, când “t” tinde spre infinit:
2
00
K
)Kr(1
K
BC
−+=
$FHDVW �IRUPXO �GHPRQVWUHD] �FDUDFWHUXO�JHQHUDO�DO�PRGHOXOXL�SHUPL kQG� � UHJ VLUHD�FD]XOXL�vQ�FDUH�LQYHUVXO�3(5-XOXL�HVWH�HJDO�FX�UHQWDELOLWDWHD�DúWHSWDW �GH�DF LRQDUL��ÌQWU-
DGHY U�� GDF � DFHDVW � UHQWDELOLWDWH� ILQDQFLDU � .� HVWH� HJDO � FX� UHQWDELOLWDWHD� .� VH� REVHUY � F ��
K
BC 0
0 = de unde curs
beneficiu
C
BK
0
0 == = inversul PER;
� FRQVWDWDUHD�F �LQYHVWL LD�QRX �QX�FUHúWH��GLQ�SXQFWXO�GH�YHGHUH�DO�DF LRQDULORU�DFWXDOL��YDORDUHD�vQWUHSULQGHULL� GHFkW� GDF � UHQWDELOLWDWHD� VD� HFRQRPLF � HVWH� VXSHULRDU � UHQWDELOLW LL� ILQDQFLDUH�DúWHSWDWH�
3UHVXSXQHP�F �³U´�HVWH�VXSHULRU�OXL�.�úL�F �HVWH�SRVLELO �GH�D�IL�H[SULPDW ��U� �D�⋅ K. ÌQ�DFHVW�FD]��HFXD LD�SUHFHGHQWD�GHYLQH�
K
)1a(1
K
B
K
)KaK(1
K
BC 0
20
0++=−+=
de unde se deduce valoarea lui K: 0
0 C
)1a(1BK
−+= .
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
5H]XOW �F � � GDF � D� !� ��� UHQWDELOLWDWHD� HFRQRPLF � D� vQWUHSULQGHULL� U� HVWH� VXSHULRDU � UHQWDELOLW LL� FHUXWH� GH�
DF LRQDUL�� .� HVWH� DWXQFL��0
0
C
BK > . Criteriul inversul PER-ului conduce deci la subestimarea
UHQWDELOLW LL�VROLFLWDWH�GH�DF LRQDUL��DGLF �FRVWXO�FDSLWDOXULORU�SURSULL�DOH�vQWUHSULQGHULL�
� GDF �D������U�HVWH�LQIHULRU�OXL�.�úL�0
0
C
BK < de vreme ce 1(a – 1) < 0.
Criteriul inversului PER-XOXL� VXEHVWLPHD] � GHFL�� vQ� DFHVW� FD]�� UHQWDELOLWDWHD� FHUXW � GH�DF LRnari, În definitiv, apropierea prin dividende apare mai exact decât apropierea prin beneficii.
$FHVWH�PRGHOH�J VHVF�OLPLWD�ORU�vQ�DFHHD�F �HOH�WUDGXF�vQ�JHQHUDO�IHQRPHQXO�FUHúWHULL�SULQWU-o FUHúWHUH� FRQVWDQW � D� DFWLYHORU�� D� EHQHILFLLORU� úL� D� GLYLGHQGHORU� vntreprinderii. Ori, aceasta nu FRQVWLWXLH� GHFkW� R� � DSUR[LPDUH� YDJ � D� UHDOLW LL�� LPSOLFD LLOH� FUHúWHULL� DVXSUD� YDORULL� ILQDQFLDUH� D�firmei fiind mult mai complexe.
ÌQ�ILQDO��FRVWXO�GH�RSRUWXQLWDWH�DO�VLWXD LHL�QHWH�D�XQHL�vQWUHSULQGHUL�SRDWH�IL�GHILQLW� � fiH�FD�FRVWXO�IOX[XULORU�GLYLGHQGHORU�Y UVDWH�OD�LQILQLW�DF LRQDULORU� � ILH�FD�FRVWXO�FDSLWDOXOXL�FUHVFXW�FX�R�SULP �GH�ULVF�
4.2.4.7. Documentar A. COSTUL CAPITALURILOR PROPRII
9DORDUHD�GH�SLD 9DORDUHD�GH�SLD 9DORDUHD�GH�SLD = + a întreprinderii a capitalurilor proprii a datoriilor
∑ ∑ ∑= = = +
++
=+
n
1t
n
1t
n
1tt
d
obtt
fin
tt
ec
t
)K1(
D
)K1(
PN
)K1(
CF,
unde: Kec -�UDWD�GH�DFWXDOL]DUH�D�IOX[XULORU�GH�WUH]RUHULH��FH� LQH�FRQW�GH�WRDWH�ULVFXULOH�vQWUHSULQGHULL�(de exploatare);
Kfin - rata de actualizare a profiturilor nHWH��FH�FRQ LQH�FRQW�úL�GH�ULVFXO�ILQDQFLDU� Kd -�UDWD�GH�GREkQG ��FH� LQH�FRQW�GH�ULVFXO�GH�IDOLPHQW� ÌQ� LSRWH]D� XQRU� IOX[XUL� GH� WUH]RUHULH� DQXDOH� FRQVWDQWH� SH� R� SHULRDG � GH� WLPS� vQGHOXQJDW ��QHGHILQLW ��
d
ob
cc
1
fin
1
K
D
K
CF
L
PN 1−= ,
unde; PN1, CF1, Dob1 – rezultatele financiare estimate pentru anul viitor; - vQ� ULOH�GH]YROWDWH�FX�EXUVH�GH�YDORUL�DFWXDOH
PER
1Kfin = unde:
1
0
PNA
PPER = ,
în care: PER -�FRHILFLHQW�GH�FDSLWDOL]DUH�EXUVLHU ��SULFH�HDUQLQJ�UDWLR�� P0 -�YDORDUHD�GH�SLD ��FXUVXO�EXUVLHU��DO�DF LXQLORU� PNA1 -�SURILWXO�QHW�SHU�DF LXQH�vQ�DQXO�FXUHQW� &RVWXO�FDSLWDOXULORU�SURSULL�vQ�FRQGL LL�GH�FUHúWHUH�HFRQRPLF
∑ ∑∑= ==
+
+⋅=+
+⋅⋅=+
=n
1t
n
1t
t
fin0t
fin
t0
n
1t fin
t0 K1
g1DIV
)K1(
)g1(tDIV
)K1(
DIVP
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
n → ∞ ⇒ Modelul Gordon – Shapiro: gP
DIVK
0
1fin +=
Kfin - rata de actualizare a dividendelor;
0
1
P
DIV -�UDWD�DQXDO �GH�UHPXQHUDUH�SULQ�GLYLGHQGH�SO WLWH�
g -�UDWD�DQXDO �GH�FUHúWHUH�D�GLYLGHQGHORU� B. COSTUL CAPITALULUI ÎMPRUMUTAT
Fonduri împrumutate = ∑=
n
1t
Ramburs t
d
obt
)K1(
Dt
++
Kd –�FRVWXO�H[SOLFLW�DO�vPSUXPXWXOXL�VROLFLWDW�SHQWUX�ILQDQ DUHD�LQYHVWL LLORU�QRL�
Cazul împrumutului ordinar
∑= +
=n
1tt
d
t0
)K1(
AV ,
unde: V0 – suma împrumutului ordinar; At -�DQXLW L� Kd – costul explicit al unui împrumut ordinar. 6XE�LQFLGHQ D�LPSR]LWXOXL�
∑=
−′+
τ−⋅⋅+=n
1tt
d
1tt0
)K1(
)1(dVRV ,
în care: →=n
VR 0
t într-R�DPRUWL]DUH�SURSRU LRQDO �D�vPSUXPXWXOXL�
d –�UDWD�QRPLQDO �D�GREkQ]LL� τ - rata impozitului pe profit. Cazul împrumutului obligatar cu prLP �GH�UDPEXUVDUH
∑= +
τ⋅−⋅−=⋅N
1tt
d
0tt
)K1(
)EV(XAEX , în care: )1(VdRA 1ttt τ−⋅+= −
unde: X -�QXP U�REOLJD LXQL� V0 -�YDORDUH�QRPLQDO � E -�SUH �GH�HPLVLXQH� Kd - costul împrumutului obligatar; Xt (V0 – E) ⋅ τ - economie de impozit. C. COSTUL LEASINGULUI
∑= +
++
⋅τ+τ−=n
1tn
tt
c
tt
)K1(
PR
)K1(
ACH)1(E ,
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
în care: τ - rata impozitului pe profit;
E -�FRVWXO�GH�DFKL]L LH�úL�PRQWDM�DO�HFKLSDPHQWHORU�vQFKLULDW� CH -�FKLULD�DQXDO � PR -�SUH XO�UH]LGXDO� Kt - costul actuarial al leasing-ului. D. COSTUL CAPITALURIL25�35235,,� Ì1�&21', ,,�'(�&5(ù7(5(�(&2120,& �
',)(5(1 ,$7 ��3(�)$=(�
∑= +
++
=n
1tn
fin
n
fin
t0
)K1(
P
)K1(
DIVP
unde: P0 –�YDORDUHD�DFWXDOL]DW �D�GLYLGHQGHORU�FH�YRU�IL�Y UVDWH�vQ�SULPD�ID] �GH�DQ�DQL��GH�FUHúWHUH�IRUWH��úL�D�YDORULL�UH]LGXDOH�DEWHQDELOH�OD�VIkUúLWXO�DFHVWHL�prime faze.
Modelul de evaluare BATES
∑=
+
++
+
+⋅=n
1t
n
fin
t
fin0 K1
g1PER
K1
)g1(dPER
PN
DIVd = o rata de distribuire a dividendelor
PERan →�FRHILFLHQWXO�GH�FDSLWDOL]DUH�EXUVLHU �GLQ�SUH]HQW��3(50��úL�GH�SHVWH�³Q´�DQL��3(5n)
A
)PERBd(PER n
0+⋅= ,
unde: n
fin
g1
K1A
+
+= úL finKg
A1)g1(B
−−+=
Modelul lui HOLT
+
+
+
−−
fin
fin
fin0
K1
g1ln
K1
gKPER1ln
DR cu curent PNA
anual CursPER0 =
DR –�GXUDWD�GH�UHFXSHUDUH�vQ�QXP U�GH�DQL��D�FXUVXOXL�DFWXDO�SULQ�SURILWXO�QHW�SHU�DF LXQH� E. COSTUL MEDIU PONDERAT AL CAPITALULUI
DATCPR
DATK
DATCPR
CPRKK dfincc +
⋅++
= ,
unde: Kcc - costul mediu ponderat al capitalului; Kfin -�FRVWXO�FDSLWDOXULORU�SURSULL�HFKLYDOHQW�FX�UHQWDELOLWDWHD�VFRQWDW �GH�DF LRQDUL� Kd -�FRVWXO�FDSLWDOXULORU�vPSUXPXWDWH�HFKLYDOHQW�FX�GREkQGD�VFRQWDW �GH�vPSUXPXWXri.
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
§ 4.3. EVALUAREA ÎNTREPRINDERII
(YDOXDUHD�vQWUHSULQGHULL�FRQVWLWXLH�I U �vQGRLDO �SUREOHPD�ILQDQFLDU �FHD�PDL�FRPSOH[ ��(D�UHSUH]LQW �XQ�GRPHQLX�GH�VLQWH] �vQ�FDUH�WUHEXLH�V �VH�UHFXUJ �vQ�PRG�VLPXOWDQ�OD�GLIHULWH�PHWRGH�
�������3UREOHPDWLFD�HYDOX Uii 6H� YD� vQ HOHJH� SULQ� YDORDUHD� vQWUHSULQGHULL� YDORDUHD� SRUWRIROLXOXL� V X� GH� DFWLYH�� $FHDVW �YDORDUH�HVWH�FkWHRGDW � �XQHRUL��GHQXPLW �YDORDUH�EUXW ��3UH XO�SURSXV�GH�FXPS U WRU�FRUHVSXQGH�DFHVWHL� YDORUL��$WXQFL� FkQG� VH� GHGXFH� YDORDUHD� GDWRULLORU�� VH� RE LQe valoarea capitalurilor proprii, DGLF �YDORDUHD�SDWULPRQLXOXL�DF LRQDULORU��$FHDVWD�GLQ�XUP �HVWH�XQHRUL�FDOLILFDW �FD�YDORDUH�QHW ��&HOH�GRX �YDORUL�WUHEXLH�V �ILH�vQ�PRG�FODU��GLVWLQFWH�
���������3XQFWXO�GH�YHGHUH�DO�YkQ] WRUXOXL &RQVLGHU P�PDL�vQWkL�SXQFWXO�GH�YHGHUH�DO�YkQ] WRUXOXL� Decizia de vânzare constituie pentru el o dezinvestire. Conform criteriului VAN, el nu va YLQGH� vQWUHSULQGHUHD�GHFkW�GDF �YDORDUHD�DFWXDO �9$��&03V��D� IOX[XULORU�GH� OLFKLGLW L�YLLWRDUH� OD�costul capitalului CMPV (costul FDSLWDOXOXL�YkQ] WRUXOXL���SH�FDUH�SRDWH�RE LQH�XUP ULQG�H[SORDWDUHD�HVWH�LQIHULRDU �SUH XOXL�30�RIHULW�GH�FXPS U WRU�
0DL�SUHFLV��L�VH�RIHU �WUHL�SRVLELOLW L� � SULPD� VH� RSUHúWH� OD� H[SORDWDUH� úL�� GXS � GH]PHPEUDUH�� YLQGH� DFWLYHOH� FH� FRPSXQ�
întreprinderea peQWUX�YDORDUHD�ORU�GH�FHVLXQH�SH�SLD D�VHFXQGDU ��DFHDVW �YDORDUH�UHSUH]LQW �valoare de lichiditate��9/���1RW P��FX�DFHDVW �RFD]LH��F �YDORDUHD�GH�OLFKLGDUH�D�EXQXULORU�FHGDWH� SH� SLD D� VHFXQGDU � FRUHVSXQGH� FX� YDORDUHD� SH� FDUH� R� DúWHDSW � FXPS U WRULL� PHGLL��FHHD�FH�VHPQLILF �F �DO L�DJHQ L�SRW� WUDJH�XQ�PDL�EXQ�X]��IRORV��DO�EXQXULORU�YkQGXWH�GHFkW�YkQ] WRUXO�
În acest caz: VL > VA (CMPv��úL�9/�!�30. � vQ�DO�GRLOHD�UkQG��HO�XUP UHúWH�H[SORDWDUHD��FHHD�FH�VHPQLILF �F �YDORDUHD�DFWXDO �HVWLPDW �OD�FRVWXO�
capitalulXL�YkQ] WRUXOXL�&03v�HVWH�PDL�ULGLFDW �GHFkW�YDORDUHD�GH�OLFKLGDUH�9L�úL�GHFkW�SUH XO�RIHULW�
Fie VA (CMPv) = ∑=
>+
n
1tt
v
t V)CMP1(
F�úL��9$�&03v���úL�30 > VL ,
unde: Ft –�IOX[XO�GH�OLFKLGLW L�vQ�SHULRDGD�W�DúWHSWDW�GH�YkQ] WRU��2UL]RQWXO�HVWH�GH�Q�SHULRDde. � vQ�DO�WUHLOHD�UkQG��HO�YLQGH�vQWUHSULQGHUHD�OD�SUH XO�30�RIHULW�GH�FXPS U WRU��ÌQ�DFHVW�FD]��30
> VA (CMPv� �� úL� 30 > VL�� &XPS U WRUXO� YDUV � XQ� SUH � PDL� ULGLFDW� SHQWUX� vQWUHSULQGHUH�GHFkW� SUH XO� SH� FDUH� O-DU� IL� SO WLW� SHQWUX� U VFXPS UDUHD� DFWLYHORU� SH� SLD D� VHFXQGDU �� 8Q�DVHPHQHD�IHQRPHQ�VH�SRDWH�H[SOLFD�GHRDUHFH�DQXPLWH�DFWLYH��³DFWLYHOH�XPDQH´�úL�DQXPLWH�active necorporale nu sunt negociabile direct.
ÌQ� DFHVW� FD]�� SUH XO� FHUXW�3d� GH� YkQ] WRU� YD� IL� FHO� SX LQ� HJDO� FX� YDORDUHD� FHD�PDL� ULGLFDW �dintre valoDUHD�DFWXDO �úL�YDORDUHD�GH�OLFKLGDUH�
[ ]Lvd V),CMP(VAMaxP ≥
���������3XQFWXO�GH�YHGHUH�DO�FXPS U WRUXOXL $FKL]L LRQDUHD�vQWUHSULQGHULL�UHSUH]LQW �SHQWUX�FXPS U WRU�R�GHFL]LH�GH�LQYHVWL LL��'HFL]LD�YD�GHSLQGH� GH� YDORDUHD� DFWXDO �9$�&03a ) la costul FDSLWDOXOXL� FXPS U WRUXOXL� �&03a� ��� GH� SUH XO�cerut Pd�GH�YkQ] WRU�úL�GH�YDORDUHD�GH�UHFRQVWLWXLUH�D�vQWUHSULQGHULL�9r, în cazul în care aceasta este SRVLELO ��6H�SRW�GLVWLQJH�GH�DVHPHQHD�WUHL�VLWXD LL� � Prima, în care VR > VA(CMPc���úL�3d > VA(CMPa ). Cump U WRUXO�QX�UHDOL]HD] �DFKL]L LRQDUHD�
úL�DEDQGRQHD] �VROX LD�UHSUH]HQWDW �GH�UHFRQVWLWXLUH��GHRDUHFH�YDORDUHD�GH�UHFRQVWLWXLUH��HVWH�PDL�PDUH�GHFkW�YDORDUHD�DFWXDO ��,QYHVWL LD�QX�HVWH�UHQWDELO �
� A doua, în care VA(CMPc���!�95�úL�3d > VR��FXPS U WRUXO�UHQXQ �OD�DFKL]L LRQDUH�úL�SUHIHU �V �UHFUHH]H�vQWUHSULQGHUHD�SULQ�U VFXPS UDUHD�GLIHULWHORU�DFWLYH�
� A treia, în care VA(CMPa ) > Pd�úL�3d > VR��FXPS UDUHD�HVWH�UHDOL]DW ��3UH XO�FHUXW�ILLQG�LQIHULRU�YDORULL�GH�UHFRQVWLWXLUH��FXPS U WRUXO�DUH�LQWHUHV�V �SURFHGH]H�OD�U VFXPS UDUH�
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
ÌQ� FD]XO� DFKL]L LRQ ULL�� SUH XO� RIHULW�PD[LPDO� 30� YD� IL� FHO�PXOW� HJDO� FX� YDORDUHD�PLQLPDO �vQWUH�YDORDUHD�DFWXDO �úL�YDORDUHD�GH�FRQVWLWXLUH�
[ ]Ra0 V),CMP(VAMinP ≤
���������'HWHUPLQDUHD�ILQDO �D�SUH XOXL 3UHVXSXQHP�F �DYHP�LHUDUKLD�XUP WRDUH�D�YDORULORU� [ ] LvRa V)CMP(VA.......................................V)CMP(VA >>>> ����]RQ �GH�QHJRFLHUH ]RQD�GH�QHJRFLHUH�D�SUH XOXL�ILQDO�V-ar situa între VR –�YDORDUHD�GH�UHFRQVWLWXLUH�SHQWUX�FXPS U WRU�úL�9$�&03v ) -�YDORDUHD�DFWXDO �D�IOX[XULORU�GH�OLFKLGLW L�YLLWRDUH�SHQWUX�YkQ] WRU�
���������&D]XO�SDUWLFXODU�DO�VRFLHW LORU�FRWDWH 3H� R� SLD � ILQDQFLDU �� FDUH� IXQF LRQHD] � ELQH�� SUH XO� HVWH� HJDO� FX� YDORDUHD�� ÌQ� FRQVHFLQ ��FDSLWDOL]DUHD�EXUVLHU �D�VRFLHW LL�FDUH�VH�YLQGH��FUHVFXW �FX�YDORDUHD�GH�SLD �D�GDWRULLORU�VDOH�Hste HJDO �FX�YDORDUHD�GH�SLD � &XPS U WRUXO� FXQRDúWH� DWXQFL� SUH XO� QHFHVDU� SHQWUX� DFKL]L LRQDUHD� VRFLHW LL�� $FHVW� SUH �UHIOHFW �YDORDUHD�vQWUHSULQGHULL�SHQWUX�DQVDPEOXO�FHORU�FDUH�LQWHUYLQ�SH�SLD � 'DF �FXPS U WRUXO�HVWH�SUHJ WLW�V �SO WHDVF �PDL�PXOW�GHFkW�YDORDUHD�SH�SLD ��HVWH�SHQWUX�F �HO� HVWLPHD] � F � vQWUHSULQGHUHD� DFKL]L LRQDW � YD� YDORUD� PDL� PXOW� vQ� SRVHVLD� VD� GHFkW� vQ� SRVHVLD�FRQFXUHQ LORU� V L�� GHFL� F � HO� GLVSXQH� ILH� GH� LQIRUPD LL� SULYLOHJLDWH�� ILH� GH� FRPSHWHQ H� FDUH� vL� YRU�permite degajarea unHL� UHQWH� HFRQRPLFH� úL� GH� D� RE LQH� DVWIHO� R� 9$1� SR]LWLY � D� LQYHVWL LHL� VDOH��&XPS U WRUXO�WUHEXLH��vQ�DFHODúL�WLPS��V �VH�JkQGHDVF �OD�IXQGDPHQWXO�UHDO�DO�DFHVWXL�DYDQWDM� 8Q� SXQFW� GH� YHGHUH� SDUWLFXODU� PHULW � V � ILH� VHPQDODW�� $WXQFL� FkQG� U VFXPS UDUHD� XQHL vQWUHSULQGHUL�VH�IDFH�FX�GH LQHUHD�FRQWUROXOXL�PDMRULW LL�FDSLWDOXOXL��SUH XULOH�RIHULWH�FXSULQG�FHO�PDL�DGHVHD�R�SULP �GH�FRQWURO�vQ�UDSRUW�FX�SUH XO�HYDOXDW�SRUQLQG�GH�OD�FXUVXO�QRUPDO�DO�DF LXQLL�
4.3.2. Metode dinamice de evaluare bazate pe actualizare 3ULQWUH�GLIHULWHOH�YDORUL�FDUH� WRFPDL�DX�IRVW� LQYRFDWH�úL�FDUH�SRW�VHUYL�FD�ED] � OD�GHVFULHUHD�SURFHVXOXL�GH�GHWHUPLQDUH�D�SUH XOXL��XQHOH�VXQW�PHWRGH�DFWXDULDOH�FDUH�DX�IRVW�SUH]HQWDWH�OD�VWXGLXO�LQYHVWL LLORU� Metodele bazate pe cursurile bursiere constituite, de asemenea, metode actuariale deoarece FXUVXULOH� UHSUH]LQW � YDORUL� DFWXDOH� DOH� IOX[XOXL� FH� UHYLQ� DF LRQDULORU�� 9DORULOH� GH� OLFKLGDUH� úL� GH�reconstituire se opun valorilor actuale. 9DORDUHD� DFWXDO � ED]DW � SH� DFWXDOL]DUHD� IOX[XULORU� GH� OLFKLGLW L� YLLWRDUH� HVWH� YDORDUHD�ansamblului activelor. 3URFHVXO�GH�HYDOXDUH�HVWH�JOREDO��QX�H[LVW �HYDOXDUH�D�GLIHULWHORU�HOHPHQWH�FRPSRQHQWH�DOH�DFWLYXOXL�� 0HWRGHOH� ED]DWH� SH� YDORDUHD� EXUVLHU � úL� PHWRGD� YDORULL� GH� UDQGDPHQW� VXQW� PHWRGH�actuariale ce permit eYDOXDUHD�YDORULL�FDSLWDOXULORU�SURSULL��2E LQHUHD�YDORULL�JOREDOH�D�DFWLYHORU�VH�UHDOL]HD] �DG XJkQG�OD�YDORDUHD�IRQGXULORU�SURSULL��YDORDUHD�GH�SLD �D�GDWRULLORU�ILQDQFLDUH�
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Modulul 4 -�6WUDWHJLD�ILQDQFLDU
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'HWHUPLQDUHD�IOX[XULORU�GH�OLFKLGLW L
a) Principii (YDOXDUHD�IOX[XULORU�GH�OLFKLGLW L�WUHEXLH�V �VH�IDF �vQWU-XQ�PRG�GLIHUHQ LDO��DGLF �HYDOXkQG�
DQVDPEOXO� LQFLGHQ HORU� DFKL]L LHL� DVXSUD� IOX[XULORU� GH� H[SORDWDUH� DOH� vQWUHSULQGHULL� FXPS U WRDUH��&RQVHFLQ HOH� SRW� IL� GLUHFWH� GDU� HOH� SRW� IL�� GH� DVHPHQHD�� LQGLUHFWH�� )HQRPHQH� GH� VLQHUJLH� VH� SRW�produce��DQWUHQkQG�R�SXWHUQLF �FUHúWHUH�D�YkQ] ULORU�VDX�R�VF GHUH�D�FRVWXULORU�
'LPSRWULY �� U VFXPS UDUHD� XQHL� QRL� vQWUHSULQGHUL� SRDWH� DYHD�� GH� DVHPHQHD�� FRQVHFLQ HOH�negative în materie de costuri de reorganizare.
(YDOXDUHD� WUHEXLH� V � VH� IDF � HOLPLQkQG� RULFH� LQFLGHQ � D� PRGXULORU� GH� ILQDQ DUH�� ÌQ�FRQVHFLQ �� QX� WUHEXLH� vQ� QLFL� XQ� FD]� FRQVLGHUDW � YDULD LD� FDSDFLW LL� GH� DXWRILQDQ DUH� OHJDW � GH�DFKL]L LD�FD�IOX[�GHRDUHFH�GHWHUPLQDUHD�VD�SHUPLWH�LQWHUYHQ LD�FKHOWXLHOLORU�ILQDQFLDUH�
b) )OX[XULOH�GH�OLFKLGLW L�LQWHUPediare
)OX[XULOH�DQWUHQDWH�GH�FXPS UDUH�úL�OXDWH�vQ�FDOFXO�VXQW�XUP WRDUHOH� 9DULD LD�(7( ±�9DULD LD�LPSR]LWXOXL�SH�SURILW��FX�H[FHS LD�LQFLGHQ HL�FKHOWXLHOLORU�ILQDQFLDUH� + Cesiuni de active
-�,QYHVWL LL��vQ�LPRELOL] UL� = Ft –�IOX[�JOREDO�GH�OLFKLGLW L 5HPDUF P� F � IOX[XO� JOREDO� GH� OLFKLGLW L� UHSUH]LQW � YDULD LD� IOX[XOXL� GHWHUPLQDW� GH�
SRUWRIROLXO�GH�DFWLYH�DO�vQWUHSULQGHULL�FXPS U WRDUH��DQWUHQDW�GH�U VFXPS UDUH�
c) )OX[�FRQVWLWXLW�GH�YDORDUH�WHUPLQDO /D�ILQHOH�RUL]RQWXOXL�FRQVLGHUDW��WUHEXLH�HYDOXDW �YDORDUHD�WHUPLQDW ��VDX�YDORDUHD�UH]LGXDO ��
97�D� vQWUHSULQGHULL� U VFXPS UDWH�� LQkQG�FRQW�GH� LQYHVWL LLOH� FDUH�DX� IRVW� I FXWH��$FHDVW �HYDOXDUH�HVWH��vQ�SDUWLFXODU��GHOLFDW �GHRDUHFH�DFHDVW �YDORDUH�HVWH�HD�vQV úL�IXQF LH�GH�IOX[XULOH�YLLWRDUH��&HO�mai adeVHD��úL�SHQWUX�VLPSOLILFDUH��V-a recurs pentru evaluarea acestei valori terminale, la valoarea FRQWDELO �SUHYL]LRQDO �D�DFWLYHORU�OD�DFHDVW �HSRF �
2UL]RQWXO�GH�UH LQXW &D� úL� vQ� RULFH� SUREOHP � GH� DOHJHUH� D� LQYHVWL LHL�� VH� SXQH� SUREOHPD� RUL]RQWXOXL� GH� UH LQut.
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3UHFL] P�vQ�DFHODúL�WLPS�F �PHFDQLVPXO�GH�DFWXDOL]DUH�IDFH�FD�HURULOH�FRPLVH�vQ�SUHYL]LXQLOH�IOX[XULORU�FHOH�PDL�vQGHS UWDWH�vQ�WLPS�DSDV �PDL�SX LQ�JUHX�GHFkW�HURULOH�GH�HVWLPDUH�FRPLVH�DVXSUD�fluxurilor mai apropiate.
Rata de actualizare (D�VH�GHWHUPLQ �vQ�DFHODúL�PRG�FD�úL�SHQWUX�DOHJHUHD�LQYHVWL LHL��'DF �DFKL]L LD�QX�DQWUHQHD] �
PRGLILFDUHD� FRVWXOXL� FDSLWDOXOXL� FXPS U WRUXOXL�� WUHEXLH� FRQVLGHUDW � DFHDVWD� GLQ� XUP � FD� UDW � GH�actualizare.
'DF ��GLPSRWULY �� ULVFXO�HFRQRPLF�HYROXHD] �úL�GDF �VWUXFWXUD�GH�ILQDQ DUH�HVWH�PRGLILFDW �VXEVWDQ LDO��YD�WUHEXL�HYDOXDW �R�UDW �GH�DFWXDOL]DUH�VSHFLILF �SHQWUX�DFHDVW �RSHUD LH� Exemplu: fluxurLOH�DúWHSWDWH�DOH�SRUWRIROLXOXL�GH�DFWLYH�DOH�VRFLHW LL�2PHJD�DX�IRVW�HYDOXDWH�SHQWUX�XUP WRULL�FLQFL�DQL��9DORDUHD�FRQWDELO �D�VRFLHW LL� OD�ILQHOH�FHOXL�GH-al cincilea an este de 14.048. (YDOX P� YDORDUHD� SH� FDUH� R� UHSUH]LQW � 2PHJD�� SHQWUX� R� DOW � VRFLHWDWH� �3KL�� DO� F UXL� FRVW� DO�FDSLWDOXOXL� HVWH� GH� ���� 6H� SUHVXSXQH� F � U VFXPS UDUHD� VRFLHW LL� 2PHJD� QX� DQWUHQHD] � QLFL� R�LQFLGHQ �DVXSUD�IOX[XULORU�JHQHUDWH�GH�DFWLYLW LOH�DFWXDOH�DOH�VRFLHW LL�3KL� 9DORDUHD�VRFLHW LL�2PHJD�HVWH�HJDO �FX�9$��IOX[XULORU�DúWHSWDWH�SH���DQL�XUP WRUL��9DORDUHD�WHUPLQDO �HVWH�HJDO �FX�YDORDUHD�FRQWDELO �
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
142.10)08,1(
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LQWHUPHGLDUH�VXQW�FRQVWLWXLWH�SULQ�(7(�GXS �GHGXFHUHD�LPSR]LWXOXL�SH�SURILW��FRUHFWDW�FX�LQFLGHQ HOH�LQYHVWL LLORU� úL� GH]LQYHVWL LLORU�� 6H� UHPDUF � IDSWXO� F � DFHVWH� IOX[XUL� VH� RE LQ� GLrect pornind de la SODQXO� GH� ILQDQ DUH�� 9DORDUHD� WHUPLQDO � VH� SRDWH� GHWHUPLQD� GXS � DFHODúL� SULQFLSLX� FD� úL� SHQWUX�FXPS U WRU��5DWD�GH�DFWXDOL]DUH�GH�XWLOL]DW�HVWH�FRVWXO�FDSLWDOXOXL�YkQ] WRUXOXL�
9DORDUHD�RE LQXW �HVWH�DGHVHD�IRDUWH�GLIHULW �GH�YDORDUHD�DFWXDO �GHWHUPLQDW �GH�FXPS U WRU��$QWLFLSD LLOH�vQ�FHHD�FH�SULYHúWH�IOX[XULOH�YLLWRDUH�FD�úL�UDWHOH�GH�DFWXDOL]DUH�GLYHUJ�vQ�JHQHUDO�vQWUH�FXPS U WRU�úL�YkQ] WRU�
4.3.2.2. Metode bursiere 0HWRGHOH�GH�HYDOXDUH�EXUVLHUH� VH� LQVSLU �GXS �PRGHOHOH�GH�DFWXDOL]DUH�D�GLYLGHQGHORU� úL�D�beneficiilor utilizate pentru evaluarea costului capitalurilor proprii. Aceste metode permit, de asemenea, cunoscând ratele cerute de investitori asupra fondurilor lor proprii, determinarea (evaluarea) valorii capitalurilor proprii. 3HQWUX� D� RE LQH� YDORDUHD� JOREDO � D� vQWUHSULQGHULL� HVWH� VXILFLHQW �� DWXQFL�� DG XJDUHD� YDORULL�datoriilor. 8Q�PRGHO� IUHFYHQW� XWLOL]DW�� PRGHOXO� OXL� %DWHV�� FDUH� UHSUH]LQW � R� DUDQMDUH� D�PRGHOXOXL� GH�DFWXDOL]DUH�D�GLYLGHQGHORU��PHULW �R�DWHQ LH�SDUWLFXODU � Prezentarea modelului lui Bates )XQGDPHQWXO�PRGHOXOXL�OXL�%RWHV�HVWH�UHOD LD�GH�HYDOXDUH�XUP WRDUH�
∑= +
++
=n
1tt
c
nt
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DIVP ,
unde: P0 -�FXUVXO�LQL LDO� Pn - cursul la finele perioadei “n”; DIVt – dividendul perioadei t; Rc - rata de rentabilitatH�VROLFLWDW �GH�LQYHVWLWRUL�DVXSUD�IRQGXULORU�ORU�SURSULL� 6H�SUHVXSXQH� F � GLYLGHQGXO� UHSUH]LQW � R� SURSRU LH� FRQVWDQW � ³G´�D� EHQHILFLXOXL� SH�DF LXQH�LQL LDO�%3$0�úL�F �UDWD�VD�GH�FUHúWHUH�³J´�HVWH�FRQVWDQW � 3H�GH�DOW � SDUWH�� 30 = BPA0 x m, cu “m” multipOLFDWRUXO� �3�(� UDW �� OD� vQFHSXWXO� DQXOXL� ���Cursul la finele perioadei Pn = BPAn�[�0�úL�%3$n = BPA0(1 + g)n��0�ILLQG�PXOWLSOLFDWRUXO�SUHY ]XW�SHQWUX�ILQHOH�DQXOXL�³Q´�úL�SHQWUX�WLSXO�GH�DF LXQH�FRQVLGHUDW��6H�GHGXFH�GLQ�UHOD LLOH�SUHFHGHQWH�F �
[ ] [ ]
M)R1(
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)R1(
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nc
n0
n
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Simplificând prin BPA0�VH�RE LQH�
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c
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modelul se scrie: m = d ⋅ B + M ⋅ A
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
%DWHV�D�VWDELOLW�WDEHOH�FDUH�GDX�YDORUL�SDUDPHWULORU�$�úL�%��vQ�IXQF LH�GH�³J´�UDWD�GH�FUHúWHUH�DQWLFLSDW �D�GLYLGHQGHORU��5c –�UDWD�VROLFLWDW �GH�DF LRQDUL�úL�Q�–�QXP UXO�GH�DQL� Exemplu��SUHVXSXQHP�F ��SHQWUX�XQ�RUL]RQW�GH�Q� ���DQL��UDWD�GH�FUHúWHUH�DQWLFLSDW �D�GLYLGHQGHORU�HVWH� J� � ����� UDWD� VROLFLWDW � 5c� � ���� úL� ³G´� UDWD� GH� distribuire a dividendelor de 50%. M PXOWLSOLFDWRUXO�SUHY ]XW�OD�FDS WXO�D���DQL�HVWH�GH�����'XS �WDEHOH��$� �����úL�%� ����� 3ULQ�XUPDUH��PXOWLSOLFDWRUXO�LQL LDO��P� �����⋅ 4,4 + 10 ⋅ 0,8 = 10,2. 'DF �%3$�LQL LDO�HVWH�GH�����FXUVXO�SUHY ]XW�SULQ�PRGHO�Ya fi de 50 ⋅ 10,2 = 510. Critica�� &D� úL� DOWH� PHWRGH� GH� FUHúWHUH� D� GLYLGHQGHORU�� PRGHOXO� OXL� %DWHV�� VH� ED]HD] � SH�LSRWH]H� H[WUHP� GH� VLPSOLVWH�� FRQVWDQW � D� UDWHL� GH� FUHúWHUH� D� GLYLGHQGXOXL�� FRQVWDQW � D� UDWHL� GH�solicitare asupra fondurilor proprii, constant �D�UDWHL�GH�GLVWULEXLUH�D�GLYLGHQGHORU� $SOLFDUHD�VD�QHFHVLW �HVWLPDUHD�GLIHUL LORU�SDUDPHWUL�SH�ED]D�F URUD�HVWH�IRQGDW�� ÌQ�VSHFLDO��HVWLPDUHD�PXOWLSOLFDWRUXOXL�0�DSOLFDELO�OD�ILQHOH�RUL]RQWXOXL�FRQVLGHUDW��WUHEXLH�V �IL�UHDOL]DW �vQWU-un mod arbitrar.
���������9DORDUHD�GH�UDQGDPHQW�úL�YDORDUHD�GH�UHQWDELOLWDWH 9DORDUHD� GH� UDQGDPHQW� HVWH� vQ� PRG� GLUHFW� LQVSLUDW � GLQ� PRGHOXO� GH� DFWXDOL]DUH� D�dividendelor. Ea permite evaluarea valorii fondurilor proprii:
Valoarea de randament = ∑= +
++
n
1tn
c
nt
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DIV,
unde: VTn –�YDORDUHD�WHUPLQDO �D�IRQGXULORU�SURSULL�OD�ILQHOH�SHULRDGHL�³Q´� 3UHVXSXQkQG�XQ�RUL]RQW�LQILQLW�úL�XQ�GLYLGHQG�FRQVWDQW�',9�VH�RE LQH�
Valoarea de randament = cR
DIV.
$QXPL L�DQDOLúWL�XWLOL]HD] �GH�DVHPHQHD�YDORDUHD�GH�UHQWDELOLWDWH�FDUH�VH�HYDOXHD] �SRUQLQG�de la beneficiul net curent B.
Valoarea de rentabilitate = cR
B.
(VWH�YRUED�GH�R�DSOLFDUH�GLUHFW �D�PRGXOXL�GH�DFWXDOL]DUH�D�EHQHILFLLORU��%HQHILFLXO�GH�UH LQXW�HVWH� EHQHILFLXO� QRUPDO�� GXS � HYHQWXDOH� FRUHFWRUL� DOH� SUHOHY ULORU� DQRUPDOH� úL� FRQVLGHUkQG�amortismentele justificate economic. Cel mai adesea se substituie Rc – rata de rentabilitate a FDSLWDOXULORU�SURSULL��ILH�UDWD�GREkQ]LL�SH�SLD ��REOLJD LXQL���ILH�R�UDW �GH�UHQWDELOLWDWH�PHGLH�SHQWUX�EUDQú ��DFHVWH�GRX �VROX LL�VXQW�H[WUHP�GH�FULWLFDELOH�
4.3.3. Metodele patrimoniale 0HWRGHOH� DFWXDULDOH� VH� ED]HD] � SH� LSRWH]D� GH� FRQWLQXDUH� D� H[SORDW ULL�� HOH� SUHVXSXQ� R�VHFYHQ �D�IOX[XULORU�GH�OLFKLGLW L�YLLWRDUH� Metodele patrimoniale se opun metodelor aFWXDULDOH�vQ�P VXUD�vQ�FDUH�HYDOXDWRUXO�FRQVLGHU �LPSOLFLW�F �vQWUHSULQGHUHD�HVWH�GH]PHPEUDW �úL�F �HYDOXDUHD�VH�IDFH�UH LQkQG��ILH�SUH XULOH�GH�FHVLXQH�SRVLELOH� DOH� GLIHULWHORU� DFWLYH� FDUH� FRPSXQ� vQWUHSULQGHUHD� �RSWLF � GH� OLFKLGDUH��� ILH� SUH XO� GH�U VFXPS UDUH� DOH� DFHORUDúL� DFWLYH� �RSWLF � GH� UHFRQVWLWXLUH��� 3UH XULOH� GH� U VFXPS UDUH� QX� VXQW�LGHQWLFH�FX�SUH XULOH�GH�FHVLXQH�DOH�DFWLYHORU�SH�SLH HOH�GH�RFD]LH� ÌQ� SULPXO� UkQG�� LQWHUPHGLDULL� SUHOHY �PDUMD� ORU�� ÌQ� DO� GRLOHD� UkQG�� FRVWXULOH� GH� WUDQ]DF LH� SRW� IL P ULWH��ÌQ�DO�WUHLOHD�UkQG��WUDQ]DF LLOH�SRW�IL�IRDUWH�UDUH�DVXSUD�DQXPLWRU�DFWLYH�úL�SUH XULOH�SRW�YDULD�VHQVLELO�GH�OD�XQ�YkQ] WRU�OD�DOWXO��FX�DWkW�PDL�PXOW�FX�FkW�FDOLWDWHD�EXQXULORU�GH�RFD]LH�SRDWH�IL�IRDUWH�YDULDELO � 1RW P� F � HVWH� IRDUWH� DGHVHD� LPSRVLELO� GH� D� UHFRQVWLWXL� R� vQWUHSULQGHUH� FXPS UkQG� XQ�ansamblu de active. Anumite active, precum activele necorporale sau activele umane, sunt adesea XQLFH��ÌQ�FRQVHFLQ ��YDORULOH�DFWXDULDOH�VXQW�vQ�PRG�QRUPDO�GLIHULWH�GH�YDORULOH�SDWULPRQLDOH� DiferitelH�PHWRGH�SDWULPRQLDOH�SRW�IL�FODVDWH�GLVWLQJkQG�SH�GH�R�SDUWH��PHWRGH�FDUH�UH LQ�RSWLFD�YkQ] WRUXOXL� úL� FDUH� SUHVXSXQ� vQFHWDUHD� DFWLYLW LL� úL�� SH� GH� DOW � SDUWH�� PHWRGH� ED]DWH� SH� RSWLFD�FXPS U WRUXOXL��ÌQ�DFHVW�GLQ�XUP �FD]��LSRWH]D�GH�FRQWLQXDUH�D�DFWLYLW LL�HVWH�UH LQXW ��vQ�PRG�LPSOLFLW�
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
��������� 0HWRGH� GH� HYDOXDUH� SDWULPRQLDO � vQWU-R� RSWLF � GH� vQFHWDUH� D� DFWLYLW LL��RSWLFD�YkQ] WRUXOXL
$FHVWH�PHWRGH�LQWHUHVHD] �vQ�SULQFLSDO�YkQ] WRUXO� 9DORULOH� GLIHULWHORU� DFWLYH� YRU� GHSLQGH� GH� FRQGL LLOH� UHDOL] ULL� ORU�� $VWIHO�� SUH XO�RE LQXW� SULQ� FHGDUHD� XQXL� DFWLY� vQ� FRQGL LL� FXUHQWH� HVWH� FHO� PDL� DGHVHD� PXOW� PDL� PDUH�GHFkW� SUH XO� GH� FHVLXQH� RE LQXW� vQ� FRQGL LL� GH� OLFKLGDUH� MXGLFLDU � IRU DW �� 3ULQFLSLXO�FRQWDELO� GH� FRQWLQXLWDWH� D� H[SORDW ULL� SUHVXSXQH� F � vQWUHSULQGerea nu este într-R� VLWXD LH�GH� OLFKLGDUH� IRU DW �� ÌQ� FRQVHFLQ �� YDORULOH�YRU� YDULD� GXS � FXP� vQFHWDUHD�DFWLYLW LL� HVWH�GHFLV � vQ� PRG� YROXQWDU� GH� YkQ] WRU� VDX� UH]XOW � vQ� XUPD� XQHL� GHFL]LL� H[WHUQH� FDUH� HVWH�LPSXV .
A. 9$/2$5($�&217$%,/ �ù,�$&7,98/�1(7�&217$%,L
9DORDUHD�FRQWDELO �D�vQWUHSULQGHULL�HVWH�HJDO �FX�VXPD�YDORULORU�QHWH�FRQWDELOH�DOH�GLIHULWHORU�DFWLYH��$FHVWH�YDORUL�VH�ED]HD] �SH�YDORULOH�GH�RULJLQH�FRUHFWDWH�vQ�IXQF LH�GH�SULQFLSLL�GH�HYDOXDUH�FRQWDELO �
Activul net contabil este egal cu valoarea coQWDELO � D� DFWLYXOXL� GLPLQXDW � FX� YDORDUHD�GDWRULLORU�� LQkQG�FRQW�GH�SULQFLSLLOH�SUXGHQ HL�úL�GH�FRQWLQXLWDWH�D�DFWLYLW LL�UH LQXWH�GH�FRQWDELOLWDWH�DFHDVW �PHWRG �G �R�YDORDUH�GH�ED] �
B. ACTIVUL NET REEVALUAT
Activul net reevaluat (activul net corectat) se� HYDOXHD] �FRUHFWkQG�DFWLYXO�QHW�FRQWDELO��6H�VXSULP �FKHOWXLHOLOH�DFWLYDWH�SUHFXP�FKHOWXLHOLOH�GH�FRQVWLWXLUH�VDX�FKHOWXLHOLOH�GH�UHSDUWL]DW�SH�PDL�PXOWH� H[HUFL LL�� ,PRELOL] ULOH� QHFRUSRUDOH� VXQW� HYDOXDWH� vQ� IXQF LH� GH� YDORDUHD� ORU� SUREDELO � GH�negociere.� $FHDVWD� VH� SRDWH� DSUHFLD� ILH� GLUHFW�� vQ� IXQF LH� GH� WUDQ]DF LLOH� FDUH� VH� UHIHU � OD� EXQXUL�comparabile, fie indirect recurgând la indici.
9DORDUHD�GH�DVLJXUDUH�UH LQXW �GH�FRPSDQLLOH�GH�DVLJXU UL�SRW�IL�XWLOL]DWH�vQ�DQXPLWH�FD]XUL��Activul net reevaluat estH� vQ� ILQDO� FDOFXODW � VXVWU JkQG� GDWRULLOH� úL� DQJDMDPHQWHOH� GLQ� YDORDUHD�UHHYDOXDW �D�DFWLYXOXL�
C. 9$/25($�/,&+,'$7,9 �ù,�9$/2$5($�'(�/,&+,'$5(
9DORDUHD�OLFKLGDWLY �VH�ED]HD] �SH�LSRWH]D�XQHL�UHDOL] UL�SURJUHVLYH�D�DFWLYHORU�GHFLVH�GH�întreprindere. Costurile� GH� WUDQ]DF LH� VXQW� QRUPDOH�� 9DORDUHD� DVWIHO� GHWHUPLQDW � HVWH�� vQ�PDMRULWDWHD� WLPSXOXL�� LQIHULRDU � YDORULL� FRQWDELOH�� 3DVLYXO� U PkQH� HYDOXDW� OD� YDORDUHD� VD�FRQWDELO �
9DORDUHD� GH� OLFKLGDUH� UH]XOW �� GLPSRWULY �� FD� XUPDUH� D� XQHL� OLFKLG UL� IRU DWH�� 9DORULOH� Ge UHDOL]DUH�DOH�DFWLYHORU�VXQW��FHO�PDL�DGHVHD��IRDUWH�PLFL�vQ�UDSRUW�FX�SUH XULOH�RU�GH�FHVLXQH�vQ�FRQGL LL�QRUPDOH��3H�GH�DOW �SDUWH�� YDORDUHD�QHW �HYHQWXDO � FDUH� UHYLQH�DF LRQDULORU�HVWH�� vQ�JHQHUDO�� IRDUWH�VF ]XW ��FHO�PDL�DGHVHD�QXO �
4.3.3.2. Metode GH� HYDOXDUH� SDWULPRQLDO � vQWU-R� RSWLF � GH� UHFRQVWLWXLUH�� RSWLFD�FXPS U WRUXOXL
Metodele de evaluare patrimoniale dintr-R�RSWLF �GH�UHFRQVWLWXLUH�VXQW�IRDUWH�GLYHUVH��0HWRGD� DFWLYXOXL� QHW� FRUHFWDW� SUHVXSXQH� F �� FXPS U WRUXO� HVWH� LQWHUHVDW� GH� DQVDPEOXO�actiYHORU�� vQ� WLPS� FH� DOWH� PHWRGH� QX� LDX� vQ� FDOFXO� GHFkW� DFWLYHOH� QHFHVDUH� FRQWLQX ULL�DFWLYLW LL.
$��$&7,98/�1(7�&25(&7$7�6$8�9$/2$5($�,175,16(& �6$8�9$/2$5($�DE UZ (FOLOSIRE)
$FWLYXO� QHW� FRUHFWDW� VDX� YDORDUHD� LQWULQVHF � GH� X]� UHSUH]LQW � VXPD� IRQGXULORU� FDUe ar fi QHFHVDUH�XQHL� LQYHVWLUL� SHQWUX�D� UHFRQVWLWXL�SDWULPRQLXO� vQWUHSULQGHULL� vQ�VWDUHD� VD� DFWXDO ��$FHDVW �PHWRG �HVWH��vQ�SULQFLSLX��ED]DW �SH�F XWDUHD��FHUFHWDUHD��YDORULL�GH�vQORFXLUH�
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
B. 9$/2$5($�68%67$1 ,$/
9DORDUHD�VXEVWDQ LDO �IDFH�RELHFWXO�XQRU�GHILQL LL�GLYHUVH��$FHVWHD�FRQFRUG�vQ�JHQHUDO�DVXSUD�HOHPHQWHORU�XUP WRDUH�
• HVWH� YRUED� GH� R� YDORDUH� EUXW �� HYDOXDW � vQ� IXQF LH� GH� FRVWXULOH� GH� vQORFXLUH� úL� GXS � R�RSWLF �GH�FRQWLQXDUH�D�H[SORDW ULL�
• bunurile durabile încheiate sunt incluse; • bunurile care nu VXQW�QHFHVDUH�H[SORDW ULL�VXQW�H[FOXVH� 9DORDUHD�VXEVWDQ LDO �FRUHVSXQGH�GHFL�YDORULL� LQVWUXPHQWXOXL�HFRQRPLF�SHQWUX�FXPS U WRU��
6H�SRDWH�GHILQL�R�YDORDUH�VXEVWDQ LDO �QHW �GHGXFkQG�SDVLYXO�H[LJLELO�
C. &$3,7$/85,�1(&(6$5(�(;3/2$7 5,,
Capitalurile necesare exSORDW ULL�FXSULQG�LPRELOL] ULOH�QHFHVDUH�H[SORDW ULL�úL�QHYRLD�GH�IRQG�GH�UXOPHQW�GH�H[SORDWDUH��,PRELOL] ULOH�QHFHVDUH�VXQW�HYDOXDWH�SRUQLQG�GH�OD�VXPD�QHW �GH�IRQG�GH�rulment de exploatare pornind de la nivelul de activitate previzional.
$FHDVW �QR LXQH�HVWH�IRDUWH�DSURSLDW �GH�FHD�D�DFWLYXOXL�HFRQRPLF�
�������0HWRGH�KLEULGH�úL�QR LXQHD�GH�³JRRGZLOO´ 0HWRGHOH� KLEULGH� vQFHDUF � V � UHFRQVWLWXLH� YDORULOH� RE LQXWH� SULQ� PHWRGHOH� DFWXDULDOH�� GDU�pornind de la diferite elemente ale portofoliului de active. Intr-DGHY U�� XQXO� GLQ� SULQFLSDOHOH�LQFRQYHQLHQWH�DOH�PHWRGHORU�SDWULPRQLDOH�HVWH�F �HOH�FRQGXF�OD�UH LQHUHD�vQ�HYDOXDUH�GHFkW�D�EXQXULORU�FDUH� IDF�RELHFWXO� WUDQ]DF LLORU�SH�SLD D� VSHFLILF ��$FHVWH�PHWRGH�QX� LDX� vQ� FDOFXO�QLFLRGDW �YDORDUHD�pasivelor necorporalH�úL�XUPDUH�FDUH�FRQVWLWXLH�DGHVHD�R�SDUWH�VXEVWDQ LDO �D�YDORULL�XQHL�vQWUHSULQGHUL� *RRGZLOO� VDX� VXSUDYDORDUHD� UHSUH]LQW � YDORDUHD� DFHVWRU� DFWLYH� QHJRFLDELOH� úL� FRUHVSXQGH�GHFL�GLIHUHQ HL�vQWUH�R�YDORDUH�GH�WLS�DFWXDULDO�úL�R�YDORDUH�GH�WLS�SDWULPRQLDO� Valoarea întreprinderii DSDUH�DVWIHO�FRPSXV �GLQ�GRX �HOHPHQWH��YDORDUHD�SDWULPRQLDO �úL�JRRGZLOO� 6XPD� JRRGZLOO� YDULD] � GXS � FXP� HVWLPDUHD� HVWH� I FXW � GH� FXPS U WRU� VDX� YkQ] WRU�� 6 �H[DPLQ P�SULQFLSDOHOH�PHWRGH�GH�HYDOXDUH�JRRGZLOO�
4.3.4.1. Metoda indiUHFW $FHDVW �PHWRG �HVWH��GH�DVHPHQHD��GHQXPLW �PHWRGD�JHUPDQ �VDX�PHWRGD�SUDFWLFLHQLORU��(D�SUHVXSXQH� F � YDORDUHD� IRQGXULORU� SURSULL� 9cp� HVWH� HJDO � FX� PHGLD� YDORULL� GH� UHQWDELOLWDWH� �GH�UDQGDPHQW�� 95� úL� D� DFWLYXOXL� QHW� FRUHFWDW� $1&� �DFWLYXOXL� QHW� UHHYDOuat). Valoarea fondurilor
proprii: 2
)ANCVR(Vcp
+= ��*RRGZLOO�*:�VH�HYDOXHD] � vQWU-XQ�PRG�LQGLUHFW�SULQ�GLIHUHQ � vQWUH�
YDORDUHD�IRQGXULORU�SURSULL�úL�DFWLYXO�QHW�FRUHFWDW�
2
)ANCVR(ANCVGW cp
−=−=
$FHDVW � PHWRG � DSDUH� IRDUWH� DUELWUDU �� 1X� H[LVW � QLFL� R� MXVWLILFDUH� SHQWUX� SRQGHUDUHD�XWLOL]DW ��5HFXUJHUHD�OD�YDORDUHD�GH�UHQWDELOLWDWH�HVWH�IRDUWH�FULWLFDELO �GHRDUHFH�DFHDVWD�SUHVXSXQH�R�stabilitate a beneficiului curent pe un orizont infinit.
4.3.4.2. Metode directe. Metodele directe sunt bazate pe� R� HYDOXDUH� GLUHFW � D�goodwill
9DORDUHD�WRWDO �D�IRQGXULORU�SURSULL�HVWH�FDOFXODW �DG XJkQG�OD�JRRGZLOO��DFWLYXO�QHW�FRUHFWDW�
A. 0(72'$�(;3(5 ,/25�&217$%,/,�(8523(1, Conform acestei metode, valoarea fondurilor proprii Vcp�HVWH�FDOFXODW �DVWIHO� )ANCiBNC(aANCGWANCV ncp ⋅−+=+=
Goodwill este determinat prin actualizarea unui supraprofit pe care-O� SRDWH� RE LQH�FXPS U WRUXO�GDWRULW �GH LQHULL�GH�DFWLYH�QHFRUSRUDOH��VXSHUSURILWXO� �%1&�– i ⋅ ANC) este egal cu GLIHUHQ D� vQWUH� %1&�� EHQHILFLXO� FXUHQW� �GXS � GHGXFHUHD� FKHOWXLHOLORU� ILQDQFLDUH� úL� D� LPSR]LWXOXL��
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
SUHYL]LRQDO� úL� UHPXQHUD LD� OD� UDWD� GREkQ]LL� QRUPDOH� L� D� DFWLYXOXL� QHW� FRUHFWDW�� 5DWD� L�� vQ� JHQHUDO��UH LQXW �HVWH�FHD�D�REOLJD LXQLORU�GH�VWDW��VXSHUSURILWXO�HVWH�DFWXDOL]DW�OD�UDWD�L�FDUH�LQWHJUHD] �R�SULP �de risc egaO �FX�����GLQ�UDWD�L��)DFWRUXO�PXOWLSOLFDWLY�DQ�HVWH�XQ�IDFWRU�GH�DFWXDOL]DUH�FXPXODW�SH�Q�ani:
[ ]
1
n1
ni
)i1(1a
−+−=
(OHPHQWHOH� GHWHUPLQDWH� DUELWUDU� FDUH� DSDU� vQ� DFHDVW � PHWRG � VXQW� QXPHURDVH�� EHQHILFLXO�FXUHQW�FRQVWDQW��GXUDWD�GH�YLD ��SULPD�GH�ULVc.
B. METODA ANGLO-6$;21
Metoda anglo-VD[RQ �HVWH�IRDUWH�DSURSLDW �GH�PHWRGD�SUHFHGHQW ��(D�GLIHU �GHRDUHFH�UH LQH�un orizont infinit pentru a evalua goodwill.
⋅−+=+=
i
ANCiBNCANCGWANCVcp
C. 81�(;(03/8�'(�&203$5$ ,(�$�',)(5,7(/25�0(72'(
)LH�R�vQWUHSULQGHUH�DO�F rui activ net corectat (ANC) este de 500. Beneficiul curent este de ������5DWD�GREkQ]LL�GH�SLD �HVWH�GH������6H�SUHVXSXQH�F �L¶� �����FRUHVSXQ] WRDUH�UDWHL�VROLFLWDWH�(cerute) aferente fondurilor proprii.
0HWRGD�GLUHFW
Valoarea de rentabilitate 7,66615,0
100
’i
BNCVR === .
Valoarea fondurilor proprii este atunci de: 3,5832
)5007,666(
2
)ANCVR(Vcp =+=+=
ÌQ�FRQVHFLQ ��JRRGZLOO�HVWH�HJDO�FX��*:� �9cp – ANC = 583,3 – 500 = 83,3 0HWRGD�H[SHU LORU�FRQWDELOL�HXURSHQL��LSRWH]D�SH�XQ�RUL]RQW�GH����DQL� (YDOX P�
[ ]
018,515,0
)15,1(1a
10
10 =− −
De unde: 751)50010,0100(018,5500)ANCiBNC(aANCV ncp =⋅−+=⋅−+=
Goodwill este egal cu: 251500751ANCVGW cp =−=−=
Metoda anglo-VD[RQ
( ){ } ( ){ } 83315,0/50010,0100500’i/ACN.iBNCANCVcp =×−+=−+=
Goodwill este egal cu:
333500833ANCVGW cp =−=−=
4.3.5. Documentar
A. (9$/8$5($�3$75,021,$/ �ù,�),1$1&,$5 �$�Ì175(35,1'(5,,
Tipuri de cash-flow-XUL�FDUH�GHWHUPLQ �YDORDUHD�vQWUHSULQGHULL 1° Într-R�RSWLF �D�YkQ] WRUXOXL�vQWUHSULQGHULL��IOX[XULOH�GH�WUH]RUHULH�VXQW�FHOH�UH]XOWDWH�GLQ�YkQ]DUHD�LPHGLDW �D�SDWULPRQLXOXL��vQ�vQWUHJLPH�VDX�EXFDW �FX�EXFDW � Se poate vorbi de: � valoarea� OLFKLGDWLY �� UH]XOWDW � GLQ� YkQ]DUHD� DFWLYHORU� SH� SLH HOH� ORU� FDUDFWHULVWLFH� vQ� FRQGL LL�
QRUPDOH�GH�WUDQ]DF LRQDUH�
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
� valoarea de asigurare�� FH� SRDWH� IL� RE LQXW � GLQ� HYDOX ULOH� I FXWH� GH� VRFLHW LOH� GH� DVLJXUDUH��atunci când iau în asigurare active similare cu cele ale întreprinderii;
� valoarea de lichidare�� UH]XOW � GLQWU-R� OLFKLGDUH� IRU DW � D� vQWUHSULQGHULL�� vQ� FD]� GH� IDOLPHQW��9DORDUHD� GH� OLFKLGDUH� HVWH� LQIHULRDU � YDORULL� OLFKLGDWLYH�� GHWHUPLQDW � vQ� FRQGL LL� GH� WUDQ]DF LL�normale.
2° Într-R� RSWLF � D� FXPS U WRUXOXL� vQWUHSULQGHULL�� IOX[XULOH� GH� WUH]RUHULH� SHQWUX� FXPS UDUHD�vQWUHSULQGHULL�VXQW�FHOH�RFD]LRQDWH�GH�FXPS UDUHD�LPHGLDW ��SH�GH-D�vQWUHJXO�VDX�EXFDW �FX�EXFDW �D�activelor întreprinderii. Se poate vorbi de: � valoarea de înlocuire a întreprinderii, rezultDW �GLQ�VXPD�SUH XULORU�GH�FXPS UDUH�GH�SH�SLD D�GH�
RFD]LH� D� DFWLYHORU� vQWUHSULQGHULL�� DúD� FXP� VH� SUH]LQW � HOH� vQ� SULYLQ D� X]XULL� úL� D� FRQGL LLORU� GH�utilizare;
� YDORDUHD�LQWULQVHF �VDX�YDORDUHD�X]XDO HVWH�FHD�GHWHUPLQDW �GH�P ULPHD�IRQGXULORU�QHFHVDUH�pentru reconstituirea patrimoniului, pe de-D�vQWUHJXO��vQ�VWDUHD�VD�DFWXDO �
� YDORDUHD�VXEVWDQ LDO ��96� GHWHUPLQDW �GH�YDORDUHD�LQWULQVHF �D�DFWLYHORU�GH�H[SORDWDUH�QHW �GH�GDWRULL�úL�GH�IRQG�FRPHUFLDO��SULYLW �vQWU-R�SHUVSHFWLY �GH�FRQWLQXDUH�D�DFWLYLW LL�
Activele de Fondul
VS = - - Datorii exploatare comercial Activele de Active Active în = - + Leasing exploatare totale DIDUD�H[SORDW ULL � FDSLWDOXULOH�SHUPDQHQWH�QHFHVDUH�H[SORDW ULL��&31(� conduc spre o valoDUH�VXEVWDQ LDO ��GDU�
FDUH� LQH�FRQW�GH�PRGXO�GH�ILQDQ DUH�D�DORF ULORU�GH�FDSLWDO��vQ�DFWLYH�FRUSRUDOH�GH�H[SORDWDUH� ,PRELOL] UL Nevoia de fond 5DPEXUV UL�GH
CPNE = + - nete de rulment previzionate datorii financiare
3° Într-R�RSWLF �D�LQYHVWLWRUXOXL�GH�FDSLWDO��IOX[XULOH�GH�WUH]RUHULH�VXQW�FHOH�DúWHSWDWH�D�VH�RE LQH�GLQ�FRQWLQXDUHD�DFWLYLW LL�vQWUHSULQGHULL��6H�SRDWH�YRUEL�GH� � YDORDUHD�GH�UDQGDPHQW��ILQDQFLDU ��FD�VXP �DFWXDOL]DW �D�IOX[XULORU�GH�WUH]RUHULH��HVWLPDWH�Se
WRDW �GXUDWD�GH�YLD �HFRQRPLF �D�vQWUHSULQGHULL� � YDORDUHD� EXUVLHU � FD� UH]XOWDW� DO� SURGXVXOXL� GLQWUH� EHQHILFLXO� �SURILWXO�� SHU� DF LXQH� �%3$�� úL�
FRHILFLHQWXO�GH�FDSLWDOL]DUH�EXUVLHU ��3(5���PXOWLSOLFDW�FX�QXP UXO�GH�DF LXQL�HPLVH� � YDORDUHD� PL[W � ED]DW � SH� JRRGZLOO� úL� DPRUWL]DUHD� DFHVWXLD�� UHVSHFWLY� YDORDUHD� GH� SLD � D�
DFWLYHORU�FRUSRUDOH�SOXV�YDORDUHD�QHFRQWDELOL]DW �D�DFWLYHORU�QHFRUSRUDOH�
9DORDUHD�SDWULPRQLDO �D�vQWUHSULQGHULL
Patrimoniul net ����9DORDUHD�FRQWDELO ������������9DORDUHD�FRQWDELO ����9DORDUHD�FRQWDELO = - = sau activul net ���D�DFWLYHORU�RE LQXWH a datoriilor a capitalurilor proprii 9DORDUHD�ILQDQFLDU ��GH�UDQGDPHQW��D�vQWUHSULQGHULL Determinarea cash-flow-urilor disponibile: CFgest = EBIT – Impozit + Amo = PN + Dob + Amo în care: EBIT –�SURILW�GLQ�H[SORDWDUH� vQDLQWH�GH�GREkQ]L� úL� LPSR]LW� �HDUQLQJV�EHIRUH� LQWHUHVWV�DQG�
WD[HV��vQ�HQJOH] ��
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
Impozit = (EBIT – Dob) ⋅ τ τ -�FRWD�XQLF �GH�LPSR]LW�SH�SURILW� PN = profit net = (EBIT – Dob) (1 - τ) $PR� �P ULPHD�DPRUWL] ULL�DQXDOH� CFD = CFgest –� �,PR�–� �1)5 în care: �,PR� �,PR1 – Imo0 + Amo + VCR Imo1���� �YDORDUHD�QHW �D�LPRELOL] ULORU�GLQ�ELODQ XO�OD�VIkUúLWXO������UHVSHFWLY�OD�vQFHSXWXO�����DQXOXL� 9&5� �YDORDUHD�FRQWDELO �U PDV �D�DFWLYHlor vândute (dezinvestite). �1)5� �1)51 – NFR0, unde: NFR = ACR – DEXP = nevoia de fond de rulment; ACR –�DFWLYH�FLUFXODQWH��LQFOXVLY�WUH]RUHULD�QHW � DEXP – datorii de exploatare. CFD – CFDact + CFDcr CFDact = PN –� �&35� �FDVK-flow-ul disponibil�SHQWUX�DF LRQDUL unde: PN – profit net; �&35�– CPR1 – CPR0 cu: CPR1(0) –�FDSLWDOXULOH�SURSULL�OD�VIkUúLWXO�����UHVSHFWLY�OD�vQFHSXWXO�����DO�DQXOXL� CFDcr = Dob –� �'$7� �FDVK-flow-ul disponibil pentru creditori unde: �'$7� �'$71 – DAT0 cu: DAT1(0) –�GDWRULLOH�F WUH�vPSUXPXW WRUL�OD�VIkUúLWXO�����UHVSHFWLY�OD�vQFHSXWXO�����DQXOXL� (YDOXDUHD�ILQDQFLDU �D�vQWUHSULQGHULL�úL�D�FDSLWDOXULORU�DFHVWHLD
∑= +
++
=n
1tn
ec
nt
ec
t0
)K1(
VR
)K1(
CFD)AE(V
în care: V0(AE) –�YDORDUHD�DFWXDO ��GH�UDQGDPHQW��D�vQWUHSULQGHULL��D�DFWLYXOui ei economic = AE); t - 1, 2,…, n ani perioada de previziune a valorii; CFDt - cash-flow-uri disponibile ale întreprinderii estimate în anul t; VRn -�YDORDUHD�UH]LGXDO �D�vQWUHSULQGHULL�HVWLPDW �vQ�DQXO�Q� Kec - costul mediu ponderat al capitalului la întreprinderea medie din clasa de risc a
întreprinderii analizate.
unde: AE
DAT)1(K
AE
CPRKK dobfinec τ−+=
cu: Kfin -�FRVWXO�FDSLWDOXOXL�SURSULX�OD�DFHHDúL�vQWUHSULQGHUH�PHGLH� Kdob - costul nominal al împrumuturilor (al dobânzilor) lD�DFHHDúL�vQWUHSULQGHUH�PHGLH
∑=
⋅+
++
=n
1tn
fin
n)CPR(t
fin
nact0
)K1(
VR
)K1(
CFD)CPR(V
∑=
⋅+
++
=n
1tn
d
n)DAT(t
d
tcr0
)K1(
VR
)K1(
CFD)DAT(V
în care: V0(CPR) -�YDORDUHD�DFWXDO �D�FDSLWDOXULORU�SURSULL� V0(DAT) -�YDORDUHD�DFWXDO �D�GDWRULLORU�
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
CFDact ⋅ t - cash-flow-XUL�GLVSRQLELOH�SHQWUX�DF LRQDUL�HVWLPDWH�în anul t; Kfin - costul capitalurilor proprii; CFDcr ⋅ t - cash-flow-uri disponibile pentru creditori estimate în anul t; Kd - costul nominal al datoriilor; VR(CPR)n -�YDORDUHD�UH]LGXDO �D�FDSLWDOXULORU�SURSULL�HVWLPDW �vQ�DQXO�n; VR(DAT)n -�YDORDUHD�UH]LGXDO ��GH�UDPEXUVDW��D�GDWRULLORU�HVWLPDW �vQ�DQXO�Q� V0(CPR) + V0(DAT) = V0(AE)
B. 12 ,81($�'(�*22':,//��9$/2$5($�'(�)/8;�$�*22':,//-ULUI 'LIHUHQ D� SR]LWLY � vQWUH� YDORDUHD� ILQDQFLDU � �9)�� úL� YDORDUHD� SDWULPRQLDO � �93�� H[SULP �QR LXQHD� GH�*RRGZLOO� VDX� GH� )RQG� FRPHUFLDO�� UHVSHFWLY� GH� FDSDFLWDWHD� vQWUHSULQGHULL� GH� D� DGXFH�profituri mai mari decât cele normale. Goodwill = VF – VP VF = VP + GW *RRGZLOO�UHSUH]LQW �H[FHGHQWXO�GH�YDORDUH�D�vQWUHSULQGHULL�SHVWH�YDORDUHD��GH�SLD ��DWULEXLW �elementelor identificabile ale activelor sale la un moment dat.
∑= +
⋅⋅−=n
1tt
fin )K1(
t)iANCP(GW ,
unde: P - profitul previzional; ANC - activul net corectat; i -�UDWD�GH�UHPXQHUDUH�GH�F WUH�SLD �D�FDSLWDOXULORU�LQYHVWLWH�vQ�vQWreprinderi; W� �������«��Q�DQL�GLQ�SODQXO�GH�LQYHVWL LL�SHQWUX�H[SORDWDUHD�vQWUHSULQGHULL�FXPS UDWH� Kfin - costul capitalurilor proprii ale întreprinderii. 'XS �PHWRGD�DQJOR-VD[RQ ��vQ�LSRWH]D�XQHL�GXUDWH�GH�H[SORDWDUH�QHOLPLWDWH�
finK
iANCPGW
⋅−=
'XS �PHWRGD�8QLXQLL�([SHU LORU�&RQWDELOL�(XURSHQL
a
iANCPGW
⋅−=
n)i1(
11
ia
+−
= ,
unde: a -�DQXLWDWHD�GH�DPRUWL]DUH�D�XQXL�OHX�vQ�³Q´�DQL�OD�R�UDW �GH�GREkQG �HJDO �FX�UHQWDELOLWDWHD�medie a sectorului industrial al întreprinderii.
ÌQ�DúD-QXPLWD�³PHWRG �D�SUDFWLFLHQLORU´�YDORDUHD�JOREDO �D�vQWUHSULQGHULL�HVWH�HJDO �FX�PHGLD�DULWPHWLF �GLQWUH�YDORDUHD�DFWLYXOXL�QHW�FRUHFWDW��$1&��úL�YDORDUHD�IOX[XOXL��3�L��
+=
i
PANC
2
1V ,
unde: ANC – activ net corectat; P/i -� YDORDUHD� GH� UDQGDPHQW� �ILQDQFLDU ��� SURILWXO� UDSRUWDW� OD� UDWD� UHQWDELOLW LL� FHUXW � SH�
SLD �SHQWUX�vQWUHSULQGHUHD�UHVSHFWLY ��L��
ANCi
PGW −= GWANC
i
P +=
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
2
GWANC)GWANC2(
2
1
i
PANC
2
1Vi +=+=
+=
i
ANCiP
2
1ANC
i
PANC
2
1Vi
⋅−⋅+=
+=
Goodwill-ul� FD� UHPXQHUDUH� D� DF LRQDULORU� úL� D� FUHGLWRULORU� vQWUHSULQGHULL�� 0HWRGD�
ED]DW �SH�YDORDUHD�VXEVWDQ LDO �EUXW ��96%�
∑= +
⋅−=n
1tt
ec)K1(
)VSBiP(GW ,
în care: P - profit; t -�SHULRDGD�GH�LQYHVWL LL�D�FDSLWDOXOXL��vQ�³Q´�DQL�� Kec - rata de aFWXDOL]DUH�VSHFLILF �vQWUHSULQGHULL� VSB -�YDORDUHD�VXEVWDQ LDO �EUXW � i -�UDWD�UHQWDELOLW LL�FHUXWH�GH�SLD �SHQWUX�vQWUHSULQGHUH�D�F UHL�YDORDUH�HVWH�PDL�PLF �
decât Kec. 0HWRGD�ED]DW �SH�FDSLWDOXULOH�SHUPDQHQWH�QHFHVDUH�H[SORDW ULL��&31()
∑= +
⋅−=n
1tt
ec)K1(
CPNEiPEGW ,
în care: PE - profitul din exploatare în perioada t; CPNE -�FDSLWDOXULOH�QHFHVDUH�H[SORDW ULL�vQ�SHULRDGD�W� n - perioada de capitalizare; i -�UDWD�GH�UHPXQHUDUH�FHUXW �GH�SLD �SHQWUX�&31(� Kec -�UDWD�GH�DFWXDOL]DUH�VSHFLILF �vQWUHSULQGHULL�
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
RREEZZUUMMAATT
x 1R LXQHD�GH�LQYHVWL LL�SRDWH�IL�GHILQLW �DWkW�GLQ�SXQFW�GH�YHGHUH�ILQDQFLDU��VFKLPEDUHD�XQHL�VXPH�GH�EDQL�SUH]HQW �úL�FHUW �vQ�VSHUDQ D�RE LQHULL�XQRU�YHQLWXUL�YLLWRDUH�VXSHULRDUH��GDU�SUREDELOH�� SUHFXP� úL� GLQ� SXQFW� GH� YHGHUH� FRQWDELO�� DORFDUHD� XQHL� WUH]RUHULL� GLVSRQLELOH�SHQWUX� SURFXUDUHD� XQXL� DFWLY� IL[� D� F UXL� XWLOL]DUH� YD� GHWHUPLQD� IOX[XUL� ILQDQFLDUH� GH�vQFDV UL�úL�SO L�
x Pentru a calcula criteriul VAN� HVWH� VXILFLHQW � FDOFXODUHD� YDORULL� DFWXDOH� D� IOX[XULORU�GH�OLFKLGLW L�YLLWRDUH�JHQHUDWH�GH�LQYHVWL LH��DSRL�GHGXFHUHD�VXPHL�LQL LDOH�D�LQYHVWL LHL�
x Perioada (termenul) de recuperare� VH� GHILQHúWH� FD� ILLQG� QXP UXO� GH� SHULRDGH� QHFHVDre pentru a recupera fondurile investite.
x 5DWD�GH�UHQWDELOLWDWH�FRQWDELO �VH�GHWHUPLQ �UDSRUWkQG�EHQHILFLXO�PHGLX�JHQHUDW�GH�LQYHVWL LH�OD�VXPD�LQYHVWL LHL�PHGLL�GHWHUPLQDW �FRQWDELO��DGLF �SRUQLQG�GH�OD�YDORDUHD�QHW �FRQWDELO �PHGLH�.
x 5DWD�LQWHUQ �GH�UHQWabilitate��5,5��HVWH�DFHD�UDW �GH�DFWXDOL]DUH�SHQWUX�FDUH�VH�RE LQH�R�9$1�QXO � x Indicele de profitabilitate� VH� FDOFXOHD] � UDSRUWkQG� YDORDUHD� DFWXDO � D� IOX[XULORU� GH�
OLFKLGLW L�JHQHUDWH�GH�SURLHFWH�OD�VXPD�LQYHVWLW � x &UHúWHUHD� FDSLWDWXOXL� VH� UHDOL]HD] � SULQ� PXOWLSOLFDUHD� QXP UXOXL� DF LXQLORU� VDX� P ULQG�
YDORDUHD�QRPLQDO �D�DF LXQLORU� x &UHúWHULOH�GH�FDSLWDO�SULQ�FRQYHUVLXQHD�GDWRULLORU�VXQW�SURSULL�PDULORU�VRFLHW L�FRPHUFLDOH�
SH� DF LXQL� FDUH� DQWHULRU� DX� HIHFWXDW� vPSUXPXWXUL� REOLJDWDUH�� HPL kQG� REOLJD LXQL�coQYHUWLELOH�vQ�DF LXQL�
x &DSLWDOXO� FRQVWLWXLW� SULQ� YkQ]DUHD� DF LXQLORU� SRDWH� IL�� FDSLWDO� DXWRUL]DW�� FDSLWDO� VXEVFULV��FDSLWDO�Y UVDW��FDSLWDO�HPLV�úL�Y UVDW�
x Sub aspectul valorii scriptice DF LXQLOH�SRW�IL��FX�YDORDUH�QRPLQDO �úL�I U �YDORDUH�QRPLQDO . x $F LXnile emise pot oferi diferite privilegii GH LQ WRULORU��SULYLOHJLXO�GH�YRW��SULYLOHJLXO�GH�
GLYLGHQG�� SULYLOHJLXO� GH� GLYLGHQG� FXPXODWLY�� SULYLOHJLXO� GH� SDUWLFLSD LH�� SULYLOHJLXO� GH�FRQYHUVLXQH��SULYLOHJLXO�GH�U VFXPS UDUH�
x Împrumutul obligatar�UHSUH]LQW �XQ contract de credit, o modalitate de procurare a resurselor ILQDQFLDUH�QHFHVDUH�FUHúWHULL�HFRQRPLFH�úL�UHVSHFW ULL�XQRU�REOLJD LL�GH�SO L�DVXPDWH.
x 2EOLJD LXQHD�HVWH�XQ�WLWOX�GH�FUHGLW�SH�WHUPHQ�OXQJ�HPLV�GH�F WUH�R�VRFLHWDWH�SH�DF LXQL�VDX�R� LQVWLWX LH� JXYHUQDPHQWDO � VDX� PXQLFLSDO � D� F UHL� UDPEXUVDUH� HVWH� vQ� PRG� RELúQXLW�JDUDQWDW �SULQ�EXQXUL�SDWULPRQLDOH�VDX�LSRWHFL�
x &DUDFWHULVWLFLOH�REOLJD LXQLL�VXQW��YDORDUHD�QRPLQDO ��SUH XO�GH�HPLVLXQH��SULPD�GH�HPLVLXQH��UDWD� QRPLQDO � D� GREkQ]LL�� FXSRQXO�� UDWD� DFWXDULDO � EUXW �� UDWD� GREkQ]LL� OD� WHUPHQ�� FXUVXO�REOLJD LXQLL��SUH XO�GH�SLD �DO�REOLJD LXQLL��SUH XO�GH�UDPEXUVDUH��SULPD�GH�UDPEXUVDUH�HWF.
x ÌQ�HVHQ �� leasing-ul� HVWH�R�RSHUD LXQH�FDUH�SUHVXSXQH� vQ�SULQFLSLX�GRX �FRQWUDFWH��XQXO�GH�vânzare –� FXPS UDUH� vQFKHLDW� vQWUH� RUJDQL]D LD� SURGXF WRDUH� FD� YkQ] WRU� úL� RUJDQL]D LD�ILQDQFLDU � �VRFLHWDWHD� GH� OHDVLQJ�� FDUH� FUHGLWHD] � RSHUD LXQHD� GH� OHDVLQJ� vQ� FDOLWDWH� GH�FXPS U WRU�úL�XQ�FRQWUDFW�GH�ORFD LXQH��vQFKHLDW�vQWUH�VRFLHWDWHD�GH�OHDVLQJ�úL�R�WHU �SHUVRDQ �
x Costul capitalului�XWLOL]DW�FD�RUDW �GH�DFWXDOL]DUH�GHSLQGH�GH�XQ�QXP U�PDUH�GH�SDUDPHWUL��UDWD�GREkQ]L�GDWRULLORU��SROLWLFD�GH�GLYLGHQGH�� VWUXFWXUD� ILQDQFLDU � D�VRFLHW LL�� ULVF��SLD D�ILQDQFLDU �
x Evaluarea întreprinderii�FRQVWLWXLH�I U �vQGRLDO �SUREOHPD�ILQDQFLDU �FHD�PDL�FRPSOH[ �úL�UHSUH]LQW �XQ�GRPHQLX�GH�VLQWH] �vQ�FDUH�WUHEXLH�V �VH�UHFXUJ �vQ�PRG�VLPXOWDQ�OD�GLIHULWH�metode.
Modulul 4 -�6WUDWHJLD�ILQDQFLDU
BBIIBBLLIIOOGGRRAAFFIIEE
Petre Brezeanu –�³*HVWLXQHD�ILQDQFLDU �D�vQWUHSULQGHULL�vQ�HFRQRPLD�GH�SLD ´ (GLWXUD�)XQGD LHL�³5RPkQLD�GH�0kLQH´��%XFXUHúWL������� Petre Brezeanu –�³*HVWLXQHD�ILQDQFLDU �úL�SROLWLFLOH�ILQDQFLDUH�DOH�vQWUHSULQGHULL´��
(GLWXUD�)XQGD LHL�³5RPkQLD�GH�0kLQH´��%XFXUHúWL������� Petre Brezeanu –� ³*HVWLXQHD� ILQDQFLDU � D� vQWUHSULQGHULL´�� (GLWXUD� )XQGD LHL� 5RPkQLD�
GH�0kLQH´��%XFXUHúWL�������
Petre Brezeanu –� ³*HVWLXQHD�ILQDQFLDU �D�DJHQ LORU�HFRQRPLFL� vQ�HFRQRPLD�GH�SLD ´��/LWR�$6(��%XFXUHúWL�������
Petre Brezeanu –�³)LQDQ H�úL�JHVWLXQH�ILQDQFLDU ´��(GLWXUD�(FRQRPLF �� Mihai Toma %XFXUHúWL��������
Ion Stancu –�³)LQDQ H��7HRULD�SLH HORU�ILQDQFLDUH��)LQDQ HOH�vQWUHSULQGHULL�
$QDOL] �úL�JHVWLXQH�ILQDQFLDU ´��(GLWXUD�(FRQRPLF ��%XFXUHúWL�������
*HRUJHWD�9LQWLO –� ³*HVWLXQHD� ILQDQFLDU � D� vQWUHSULQGHULL´�� (GLWXUD� 'LGDFWLF � úL�3HGDJRJLF ��%XFXUHúWL�������
Paul Halpern – ³)LQDQ H�PDQDJHULDOH´��(GLWXUD�(FRQRPLF ��%XFXUHúWL������� J.Fred Weston Eugene F.Brigham