$ FDOFXODGRUD JUiILFD QR HVWXGR GH IXQo}HV
Ë1',&(
,QWURGXomR
)XQomRRXWDOYH]QmR
$OJXQVFRPHQWiULRV
9DPRVGHVHQKDU,
$OJXQVFRPHQWiULRV
(PWRUQRGRYpUWLFHGDSDUiEROD
$OJXQVFRPHQWiULRV
2PHWHRUR
$OJXQVFRPHQWiULRV
)XQo}HVSROLQRPLDLV
$OJXQVFRPHQWiULRV
)XQomRSDUtPSDU
$OJXQVFRPHQWiULRV
9DPRVGHVHQKDU,,
$OJXQVFRPHQWiULRV
%LEOLRJUDILD
+HOHQD 5RFKD
,QWURGXomR
2 FRQMXQWR GH SURSRVWDV GH WUDEDOKR TXH DTXL VH DSUHVHQWD LQFLGH VREUH R WHPD GH
)XQo}HV DR QtYHO GR HQVLQR VHFXQGiULR H HPERUD QmR H[FOXVLYDPHQWH
IXQGDPHQWDOPHQWHDRQtYHOGRžDQRGHHVFRODULGDGH
&DGDWDUHIDpVHJXLGDGH$OJXQVFRPHQWiULRVDRORQJRGRVTXDLVVHSURFXUDDSUHVHQWDU
DOJXPDV GDV SRVVtYHLV UHVSRVWDV jV TXHVW}HV FRORFDGDV EHP FRPR VXJHULU DOJXPDV
KLSyWHVHV GH H[SORUDomR GDV SRWHQFLDOLGDGHV GLVSRQLELOL]DGDV SHOD FDOFXODGRUD H TXH
SRGHUmR HYHQWXDOPHQWH QmR VHU GR FRQKHFLPHQWR GH DOJXQV GRV OHLWRUHV PHQRV
IDPLOLDUL]DGRVFRPHVWDWHFQRORJLD
(PERUDVHSUHWHQGDGHL[DURVDVSHFWRVPHWRGROyJLFRVDRFXLGDGRGRSURIHVVRUTXHRSWD
SRUXWLOL]DUHVWDVWDUHIDVRIDFWRGHPXLWDVGHODVWHUHPVLGRFRQFHELGDVFRPRLQWXLWRGH
OHYDURVDOXQRVDDERUGDUQRYRVDVSHFWRVSUHVVXS}HDUHDOL]DomRGHDOJXPWUDEDOKRGH
QDWXUH]D LQYHVWLJDWLYD 1HVWH WLSR GH WUDEDOKR R DOXQR p OHYDGR D H[SORUDU VLWXDo}HV ±
DQDOLVDQGR GLVFXWLQGR H[SHULPHQWDQGR ± SHOR TXH R WUDEDOKR GH JUXSR VXUJH FRPR R
PDLVDGHTXDGR
$ FDOFXODGRUD XWLOL]DGD QD HODERUDomR GRV FRPHQWiULRV IRL D 7, 1R HQWDQWR
QHQKXPD GDV SURSRVWDV GH WUDEDOKR p H[FOXVLYD GHVWH PRGHOR HPERUD DOJXPDV QmR
SRVVDP VHU UHDOL]DGDV FRP WRGRV RV PRGHORV 1D WDEHOD GD SiJLQD DR ODGR LQGLFDVH
SDUD FDGD WDUHID DV GLIHUHQoDV H[LVWHQWHV HQWUH DV FDOFXODGRUDV 7, H 7,
UHODWLYDPHQWHj7,
$ FDOFXODGRUD JUiILFD QR HVWXGR GH IXQo}HV
$VSHFWRVDWHUHPDWHQomRQDOHLWXUDGDVSDUWHV$OJXQVFRPHQWiULRV
VHHPYH]GRPRGHOR7,IRUXWLOL]DGRRPRGHOR7,RX7,
7DUHID
)XQomR
RXWDOYH]QmR
7,
7,
1mRUHDOL]iYHOQmRJXDUGD
ILJXUDVHPPHPyULD
$QiORJDj7,PDVDSHQDV
SHUPLWHJXDUGDUHPPHPyULD
VHLVILJXUDVQ~PHURVGHD
1mRUHDOL]iYHOQmRDGPLWHD
XWLOL]DomRGHOLVWDVQDVIXQo}HV
9DPRVGHVHQKDU,
HRQ~PHURPi[LPRGHIXQo}HV
DGPLVVtYHOQmRpVXILFLHQWH
$QiORJDj7,PDVHVWD
(PWRUQRGRYpUWLFH FDOFXODGRUDQmRGHWHUPLQDDV
GDSDUiEROD
FRRUGHQDGDVGRYpUWLFHGD
SDUiEROD
1DUHJUHVVmRTXDGUiWLFDp
QHFHVViULRLQGLFDUDVOLVWDVD
XWLOL]DURXVHMDRFRPDQGR
GHYHUiVHU4XDG5HJ//
$RSomR$VNQmRHVWi
GLVSRQtYHOQDWDEHODSHORTXH
2PHWHRUR
QmRpSRVVtYHOFRORFDUQDFROXQD
GR[DSHQDVRVYDORUHVTXH
GHVHMDPRV
2PHQX&$/&QmRHVWi
GLVSRQtYHOSHORTXHQmRp
SRVVtYHOGHWHUPLQDUYDORUHVGH
XPDIXQomRSRUHVWHSURFHVVR
)XQo}HV
,GrQWLFDj7,
SROLQRPLDLV
)XQomRSDU
,GrQWLFDj7,
tPSDU
1mRUHDOL]iYHOQmRDGPLWHD
XWLOL]DomRGHOLVWDVQDVIXQo}HV
9DPRVGHVHQKDU,,
HRQ~PHURPi[LPRGHIXQo}HV
DGPLVVtYHOQmRpVXILFLHQWH
,GrQWLFDj7,
,GrQWLFDj7,
$QiORJDj7,
,GrQWLFDj7,
,GrQWLFDj7,
,GrQWLFDj7,
$OJXPDV GDV DFWLYLGDGHV SURSRVWDV QmR SRGHP VHU UHDOL]DGDV FRP HVWH PRGHOR GH
FDOFXODGRUDQRHQWDQWRWDOQmRLPSHGHTXHHVWDVQmRVHMDPDGDSWDGDVGHPRGRDTXHWDO
SDVVH D VHU SRVVtYHO 3RU H[HPSOR DV GXDV DFWLYLGDGHV 9DPRV GHVHQKDU SRGHUmR
SHUIHLWDPHQWH VHU H[SORUDGDV FRP HVWD FDOFXODGRUD VH VH FRQVLGHUDUHP ILJXUDV TXH
DSHQDVHQYROYDPTXDWURIXQo}HVRQ~PHURPi[LPRGHIXQo}HVTXHpSRVVtYHOWUDEDOKDU
HPVLPXOWkQHRQHVWDPiTXLQD
+HOHQD 5RFKD
)XQomRRXWDOYH]QmR
1DPHPyULDGDVXDPiTXLQDHQFRQWUDPVHDUPD]HQDGRVRVJUiILFRVGH
FRUUHVSRQGrQFLDV 2EVHUYHRV H LQGLTXH TXDLV RV TXH VmR JUiILFRV GH
IXQo}HVHGHVVHVTXDLVRVTXHUHSUHVHQWDPIXQo}HVLQMHFWLYDV
3DUD YLVXDOL]DU R JUiILFR GH FDGD XPD GDV FRUUHVSRQGrQFLDV SUHVVLRQH
VXFHVVLYDPHQWH
QG'5$:9$56
VHJXLGR GR Q~PHUR GR JUiILFR TXH TXHU YLVXDOL]DU GH D H SRU ILP
(17(5
$QWHV GH FKDPDU XP QRYR JUiILFR WHP TXH OLPSDU R pFUDQ SDUD LVVR
SUHVVLRQHFRPRJUiILFRQRYLVRUQG'5$:(17(5
$ FDOFXODGRUD JUiILFD QR HVWXGR GH IXQo}HV
$OJXQVFRPHQWiULRV
(VWD WDUHID DSUHVHQWD XPD JUDQGH YHUVDWLOLGDGH DR SHUPLWLUQRV FRP WRGD D IDFLOLGDGH
YDULDURVJUiILFRVDQDOLVDGRV$VLPSOLFLGDGHFRPTXHQRVpSRVVtYHODOWHUDURVJUiILFRV
FRP TXH RV DOXQRV LUmR WUDEDOKDU SHUPLWHQRV DGHTXDU D SURSRVWD GH WUDEDOKR jV
FDUDFWHUtVWLFDVGDWXUPDDOWHUDQGRDVHDVVLPRHQWHQGHUPRVGXUDQWHDDXODH PHVPR
VH IRU QHFHVViULR GLYHUVLILFDQGRD HP IXQomR GDV FDUDFWHUtVWLFDV HVSHFtILFDV GH FDGD
DOXQRWRUQDQGRDVVLPSRVVtYHOXPDLQGLYLGXDOL]DomRGRHQVLQR
$RSUHSDUDUHVWDWDUHIDpQHFHVViULRFRPHoDUSRUHVFROKHUTXDLVRVJUiILFRVFRPTXHRV
DOXQRVLUmRWUDEDOKDUHPVHJXLGDJXDUGiORVQDPHPyULDGDFDOFXODGRUDFRPRILJXUDVH
MiQDDXODWUDQVIHULORVSDUDDVFDOFXODGRUDVTXHRVDOXQRVLUmRXWLOL]DU
9HMDPRV HQWmR DOJXQV JUiILFRV FXMD DQiOLVH SRGHUi VHU LQWHUHVVDQWH H D IRUPD GH RV
UHFULDUQDFDOFXODGRUD
7RGRVRVJUiILFRVDSUHVHQWDGRVIRUDPWUDoDGRVXVDQGR
D MDQHOD GH YLVXDOL]DomR GD ILJXUD MXQWD TXH SRGH VHU
REWLGD LQWURGX]LQGR FDGD YDORU HP :,1'2: RX
SUHVVLRQDQGR VLPSOHVPHQWH =220 H VHOHFFLRQDQGR D
TXDUWDRSomR='HFLPDO
SRQWHDGR R TXH SRGH VHU GHILQLGR SDUD WRGDV DV IXQo}HV QD WHFOD 02'(
VHOHFFLRQDQGR 'RW RX GLUHFWDPHQWH QR pFUDQ RQGH LQWURGX]LPRV D H[SUHVVmR GD
IXQomRGHVORFDQGRRFXUVRUSDUDDHVTXHUGDGH<HSUHVVLRQDQGRVXFHVVLYDPHQWH
(17(5DWpDRVtPERORTXHDtDSDUHFHVHFRQYHUWHUQXPSRQWHDGR
&RPRMiVDEHPRVDMDQHODGHYLVXDOL]DomRHVFROKLGDWHPXPDLQIOXrQFLDGHWHUPLQDQWH
QR DVSHFWR GRV JUiILFRV TXH LUHPRV REWHU PDV QR FDVR FRQFUHWR GHVWD WDUHID HVVD
LQIOXrQFLDSRGHUiDLQGDVHUDFHQWXDGDXPDYH]TXHQHPWRGDVDVMDQHODVQRVSHUPLWHP
DYLVXDOL]DomRGDVGHVFRQWLQXLGDGHVGRVJUiILFRV
(VWHJUiILFRFRUUHVSRQGHjIXQomR< L3DUW[2FRPDQGR
L3DUWSRGHVHUREWLGRQRPHQX0$7+GHVORFDQGRRFXUVRU
SDUDDGLUHLWDSDUDVHOHFFLRQDU180H
HVFROKHQGRGHSRLVDWHUFHLUDRSomR
8P VHJXQGR JUiILFR SRGH VHU IDFLOPHQWH REWLGR SHGLQGR j
FDOFXODGRUD SDUD WUDoDU D FRUUHVSRQGrQFLD LQYHUVD GD IXQomR
DQWHULRU 3DUD LVVR PDQWHQGR D H[SUHVVmR GD IXQomR HP < PDV VHP TXH HVWD HVWHMD
+HOHQD 5RFKD
VHOHFFLRQDGD SDUD VHU UHSUHVHQWDGD JUDILFDPHQWH FRORTXH R
FXUVRU HP FLPD GR VLQDO GH LJXDO H SUHVVLRQH(17(5 DWp
GHL[DU GH YLVXDOL]DU R VLQDO HQYROWR QXP TXDGUDGR HVFXUR
YDPRV SUHVVLRQDU QG '5$: VHOHFFLRQDU D RLWDYD RSomR
'UDZ,QYSUHVVLRQDU9$56VHOHFFLRQDUVXFHVVLYDPHQWH<9$56)XQFWLRQ<HSRUILP
SUHVVLRQDU(17(5
8PRXWURJUiILFRSRGHPXLWRVLPSOHVPHQWHVHURGDIXQomR
VHQ [ ( Mi DJRUD SRGHPRV WDPEpP
LQFOXLURGDVXDFRUUHVSRQGrQFLDLQYHUVD
&RQVLGHUHPRV LJXDOPHQWH XPD SDUiEROD SRU H[HPSOR <
[±
$V UHFWDV WDPEpP VmR LQWHUHVVDQWHV 3RGHPRV SHQVDU QD
IXQomR FRQVWDQWH < ± RX QD IXQomR
LGHQWLGDGH < [ RX DWp QXPD UHFWD
YHUWLFDO 3DUD WUDoDU XPD UHFWD YHUWLFDO
YDPRVFRPRFXUVRUQXPDOLQKDHPEUDQFR
GR pFUDQ SULQFLSDO SUHVVLRQDU QG '5$: VHOHFFLRQDU
9HUWLFDO HP VHJXLGD HVFUHYHU R YDORU RQGH TXHUHPRV TXH D
UHFWDLQWHUVHFWHRHL[RGRV[[HSUHVVLRQDU(17(5
8PDFLUFXQIHUrQFLDWDPEpPSRGHSHUIHLWDPHQWHFRQVWLWXLU
XPD ILJXUD D FRQVLGHUDU 3DUD D REWHU SUHVVLRQH FRP R
FXUVRU QXPD OLQKD HP EUDQFR GR pFUDQ SULQFLSDO QG
'5$: VHOHFFLRQH D QRQD RSomR &LUFOH LQWURGX]D DV
FRRUGHQDGDV GR FHQWUR H R UDLR GD FLUFXQIHUrQFLD
VHSDUDGRVSRUYtUJXODVHSUHVVLRQH(17(5
8P RXWUR JUiILFR SRGH VHU R GD IXQomR < I3DUW[ (VWH
FRPDQGRHVWiGLVSRQtYHOQRPHVPRPHQXTXHL3DUWRXVHMD
$ FDOFXODGRUD JUiILFD QR HVWXGR GH IXQo}HV
QRPHQX0$7+HQRVXEPHQX180
$OpP GH GHFLGLUPRV TXDLV DV
ILJXUDV
TXH
YDPRV
XWLOL]DU
QHFHVVLWDPRV WDPEpP FRPR Mi IRL
UHIHULGR GH PHPRUL]DU FDGD XPD
GHODV QD FDOFXODGRUD 3DUD LVVR H
DSyV WHUPRV HODERUDGR FDGD ILJXUD
WHPRV TXH SUHVVLRQDU QG '5$: VHOHFFLRQDU 672 H D SULPHLUD RSomR 6WRUH3LF
SUHVVLRQDUDWHFOD9$56VHOHFFLRQDUDTXDUWDRSomR3LFWXUHGHSRLVHVFROKHURQ~PHUR
GHDTXHTXHUHPRVDWULEXLUjILJXUDHSUHVVLRQDU(17(5
-iQDVDODGHDXODSUHFLVDPRVGHWUDQVIHULUWRGDVDVILJXUDVSDUDDVFDOFXODGRUDVTXHRV
DOXQRVYmRXWLOL]DU3DUDLVVRYDPRVFRPHoDUSRULQWURGX]LUILUPHPHQWHRFDERQDSDUWH
LQIHULRUGDVFDOFXODGRUDV6HJXLGDPHQWHYDPRVOLJDUDV
FDOFXODGRUDVHFRPHoDUSHODTXHYDLUHFHEHURVGDGRV
3URVVHJXLPRV SUHVVLRQDQGR QG /,1. VHOHFFLRQDQGR
5(&(,9( H SRU ILP FDUUHJDQGR QD WHFOD (17(5
$SDUHFHUiDPHQVDJHP:DLWLQJ
1D FDOFXODGRUD TXH YDL WUDQVPLWLU RV GDGRV
SUHVVLRQDPRVQG/,1.HVHOHFFLRQDPRV
D VpWLPD RSomR3LF $SDUHFHUi DVVLP
XPD OLVWD GH WRGDV DV ILJXUDV TXH VH
HQFRQWUDP QD PHPyULD GD PiTXLQD
8WLOL]DQGR DV WHFODV GH PRYLPHQWR GR
FXUVRU YDPRV GHVORFDU D VHWD TXH DSDUHFH j HVTXHUGD HP FLPD SUHVVLRQDQGR
VXFHVVLYDPHQWH (17(5 GH PRGR D TXH DSDUHoD XP SHTXHQR TXDGUDGR MXQWR GD
GHVLJQDomR GH FDGD ILJXUD LQGLFDQGR TXH HVWD HVWi VHOHFFLRQDGD SDUD VHU WUDQVPLWLGD
7HUPLQDGD HVWD IDVH YDPRV GHVORFDU R FXUVRU SDUD D GLUHLWD SDUD VHOHFFLRQDU
75$160,7HSUHVVLRQDU(17(5
8PDPHQVDJHPLQGLFDUiQDVGXDVFDOFXODGRUDVTXHDWUDQVPLVVmRIRLFRQFOXtGD
+HOHQD 5RFKD
8PDGDVJUDQGHVYDQWDJHQVGHVWDWDUHIDpFRPRMiIRLUHIHULGRDIDFLOLGDGHFRPTXHp
SRVVtYHODOWHUDURVJUiILFRVDDQDOLVDU1RHQWDQWRDRSHQVDUPRVHPFULDUQRYDVILJXUDV
FRQYpPWRPDUPRVDOJXPDVSUHFDXo}HV(IHFWLYDPHQWHDVUHGX]LGDVGLPHQV}HVGRpFUDQ
GD FDOFXODGRUD REULJDP D TXH D GHILQLomR FRP TXH RV
JUiILFRV VmR WUDoDGRV QHP VHPSUH VHMD D PHOKRU 7DO IDFWR
OHYDDTXHIDFLOPHQWHVXUMDPJUiILFRVFRPRRGDILJXUDMXQWD
HPTXHGHFLGLUVHHVWDPRVRXQmRSHUDQWHR JUiILFR GH XPD
IXQomR SRGH QmR VHU IiFLO UHSDUHVH TXH R JUiILFR p
FRQVWLWXtGR SRU GLYHUVRV VHJPHQWRV YHUWLFDLV HVSHFLDOPHQWH TXDQGR DSHQDV VH GLVS}H
GDUHSUHVHQWDomR JUiILFD H DLQGD VH HVWi D FRQVROLGDU D QRomR GH IXQomR $LQGD DVVLP
HVWHVHUi XP DVSHFWR TXH XP DOXQR TXH OLGD UHJXODUPHQWH FRP HVWH WLSR GH WHFQRORJLD
QmRSRGHUiGHL[DUGHFRQKHFHUHFRPSUHHQGHU
$ FDOFXODGRUD JUiILFD QR HVWXGR GH IXQo}HV
9DPRVGHVHQKDU,
3URFXUHUHFULDUDVILJXUDVDSUHVHQWDGDV
+HOHQD 5RFKD
$OJXQVFRPHQWiULRV
(VWDWDUHIDSHUPLWHHIHFWXDURHVWXGRGDLQIOXrQFLDGDYDULDomRGRVSDUkPHWURVGDIXQomR
DILP &RP HIHLWR DR WHQWDU UHFULDU FDGD XPD GDV ILJXUDV RV DOXQRV VmR OHYDGRV D
DQDOLVDU R TXH p TXH QD H[SUHVVmR GD IXQomR SURYRFD DOWHUDo}HV QD VXD LQFOLQDomR H R
TXHSHORFRQWUiULRPDQWpPDLQFOLQDomRGDVUHFWDVSHUPLWLQGRWUDoDUUHFWDVSDUDOHODVH
DLQGDRTXHGHWHUPLQDDLQWHUVHFomRGHFDGDUHFWDFRPRHL[RGRV[[HFRPRHL[RGRV
\\
$V WHQWDWLYDV GH WUDoDU XP FRQMXQWR GH UHFWDV YHUWLFDLV VmR WDPEpP XPD IRQWH GH
GLVFXVVmR HQULTXHFHGRUD 6HQGR HVWD j SDUWLGD XPD WDUHID LPSRVVtYHO D VXD
FRQFUHWL]DomRQmRpDILQDOGLItFLOXPDYH]TXHDWHQGHQGRjVOLPLWDo}HVGHGHILQLomRGR
pFUDQ GD FDOFXODGRUD XPD UHFWD FRP ³DOJXPD´ LQFOLQDomR VHUi YLVXDOL]DGD FRPR XPD
UHFWDYHUWLFDO
0DVYHMDPRVFRQFUHWDPHQWHFDGDXPDGDVILJXUDV
8PDILJXUDVHPHOKDQWHjSULPHLUDSRGHVHUREWLGDFRPDV
VHJXLQWHVIXQo}HV
(VWD QmR p QR HQWDQWR D ~QLFD IRUPD D TXH SRGHPRV
UHFRUUHU SDUD LQWURGX]LU DV IXQo}HV 4XDQGR
SUHWHQGHPRV WUDoDU R JUiILFR GH YiULDV IXQo}HV GH XPD PHVPD IDPtOLD SRGHPRV
LQWURGX]LU QXPD Vy IXQomR WRGDV DV H[SUHVV}HV UHFRUUHQGR SDUD LVVR D XPD OLVWD GH
SDUkPHWURV1HVWHFDVRSRGHUtDPRVWrORIHLWRGDVHJXLQWH
IRUPD
$R HQFRQWUDU XPD OLVWD QD H[SUHVVmR GH XPD IXQomR D
FDOFXODGRUD FRQVLGHUD VXFHVVLYDPHQWH FDGD XP GHVVHV
YDORUHVRTXHOKHSHUPLWHWUDoDURJUiILFRGHWRGDVDVIXQo}HVSUHWHQGLGDV
1RFDVRGDVHJXQGDILJXUDWHUtDPRVPHVPRTXHRSWDUSRU
HVWD ~OWLPD HVWUDWpJLD SRLV GH RXWUD IRUPD QmR
FRQVHJXLUtDPRV UHSURGX]LU R GHVHQKR XPD YH] TXH
QHFHVVLWDUtDPRV GH LQWURGX]LU RQ]H IXQo}HV H D
FDOFXODGRUDDSHQDVSHUPLWHDLQWURGXomRGHGH]
$ FDOFXODGRUD JUiILFD QR HVWXGR GH IXQo}HV
3DUD D WHUFHLUD ILJXUD H[LVWHP YiULDV SRVVLELOLGDGHV GH LQWURGX]LU DV IXQo}HV 3RGHPRV
ID]rORUHFRUUHQGRDSHQDVDXPDIXQomRRXDGXDVIXQo}HV
3RGHPRVDLQGDUHSDUDUTXHTXDQGRUHFRUUHPRVDGXDVIXQo}HVDOLVWDGHSDUkPHWURVp
VHPSUH D PHVPD 1HVVH FDVR SRGHPRV RSWDU SRU
GHILQLU HVVD OLVWD QR pFUDQ SULQFLSDO GDQGROKH SRU
H[HPSOR R QRPH / H GHSRLV XWLOL]iOD VHPSUH TXH
TXLVHUPRV VHP WHU TXH D UHHVFUHYHU GH QRYR 3DUD
XWLOL]DU HVWD HVWUDWpJLD UHSURGX]D QD FDOFXODGRUD RV
pFUDQVGDILJXUDDRODGR7HQKDSUHVHQWHTXHD VHWD TXH Dt
DSDUHFHpREWLGDSUHVVLRQDQGRGLUHFWDPHQWHDWHFOD672
6H WLYHUPRV RSWDGR SRU HVWD ~OWLPD SRVVLELOLGDGH DV
H[SUHVV}HV GD TXDUWD ILJXUD VmR IDFLOPHQWH LQWURGX]LGDV
EDVWDQGR LQVHULU XP VLQDO HP FDGD XPD GDV IXQo}HV GD
ILJXUDDQWHULRU
$TXLQWDILJXUDpFRQVWLWXtGDSRUUHFWDVKRUL]RQWDLVVHQGRIiFLOHQFRQWUDUDVH[SUHVV}HV
TXHOKHGmRRULJHP
$VH[WDILJXUDQmRSRGHVHUYHUGDGHLUDPHQWHWUDGX]LGDSRU
IXQo}HV PDVH[LVWHPYiULDVIXQo}HVTXHLQWURGX]LGDVQD
FDOFXODGRUDGmRRULJHPjTXHOHJUiILFR$SUHVHQWDVHXPD
GDVSRVVLELOLGDGHV
$VUHVWDQWHVILJXUDVSRGHPVHUREWLGDVGHPRGRVDQiORJRV
$VVLP WHPRV SDUD DV
VpWLPDHRLWDYDILJXUDV
DV SRVVLELOLGDGHV LOXV
WUDGDV QDV ILJXUDV HP
TXH VH UHFRUUHX WDPEpP j
FULDomR GH XPD OLVWD GH
SDUkPHWURV D TXH VH GHX D
GHVLJQDomRGH/
+HOHQD 5RFKD
5HODWLYDPHQWH jV QRQD H GpFLPD ILJXUDV D VXD UHSURGXomR
SRGH VHU IHLWD FRPR p DSUHVHQWDGR QDV ILJXUDV H
UHFRUUHQGR LJXDOPHQWH j FULDomR GH XPD OLVWD GH
SDUkPHWURV D TXH QHVWH FDVR VH GHX R QRPH GH / 'H
UHIHULU FRQWXGR TXH QmR p IRUoRVR LU FULDQGR OLVWDV FRP
QRPHV GLIHUHQWHV 1R HQWDQWR HVWH SURFHGLPHQWR WHP D
YDQWDJHPGHSHUPLWLUXWLOL]DUQRYDPHQWHDPHVPDOLVWD
VHHYHQWXDOPHQWHYROWDUPRVDSUHFLVDUGHODVHPWHUTXHDUHLQWURGX]LUXPDYH]TXHHVWD
FRQWLQXDQDPHPyULDGDFDOFXODGRUD6H
Mi VRXEHUPRV j SDUWLGD TXH QmR
YROWDUHPRV D QHFHVVLWDU GH XWLOL]DU
QRYDPHQWH HVVD OLVWD GH YDORUHV HQWmR
SRGHPRV XWLOL]DU VHPSUH D PHVPD
GHVLJQDomRSDUDDOLVWDHRVYDORUHVGDOLVWDDQWHULRUVHUmRVXEVWLWXtGRVSHORVQRYRV
3RU ILP SDUD D ~OWLPD ILJXUD H SRUTXH DSHQDV HVWmR HQYROYLGDV VHLV IXQo}HV R PDLV
VLPSOHV p LQGLVFXWLYHOPHQWH LQWURGX]LU
GLUHFWDPHQWH DV UHVSHFWLYDV H[SUHVV}HV
0DV VH SRU DFDVR ILFRX HQWXVLDVPDGR
FRPDXWLOL]DomRGHOLVWDVGHSDUkPHWURV
QDV H[SUHVV}HV GDV IXQo}HV SRGHUi FRQWLQXDU D ID]rOR
1HVWHFDVRSRGHUiRSWDUSRUWUDEDOKDUFRPGXDVOLVWDVGHYDORUHVHPVLPXOWkQHR$VVLP
SRGHUiFRPHoDUSRUFULDUDOLVWD^`HJXDUGiODHP/DVHJXLUFRSLHHVVD
OLVWDSDUD/HYiDRPHQX/,67HVFROKD236HDtDSULPHLUDRSomRRXVHMD6RUW$R
TXHOKHSHUPLWLUiUHRUGHQDURVYDORUHVSRURUGHPDVFHQGHQWH
HDVVLPREWHUDOLVWD^`$
SDUWLU GDTXL VH LQWURGX]LU D H[SUHVVmR
DSUHVHQWDGD QD ILJXUD SRGHUi REWHU XP
JUiILFRLGrQWLFRDRSUHWHQGLGR
$ FDOFXODGRUD JUiILFD QR HVWXGR GH IXQo}HV
(PWRUQRGRYpUWLFHGDSDUiEROD
&RQVLGHUHDIXQomR D[ E[ F FRP D  ƒ ? ^` H E F  ƒ
x 4XHYDORUHVGHYHPWHUDEHFSDUDTXHRYpUWLFHGDSDUiERODFRLQFLGD
FRPDRULJHP"
x (SDUDTXHRYpUWLFHVHHQFRQWUHVREUHRHL[RGRV\\"
x 1HVWH~OWLPRFDVRTXHUHODomRH[LVWHHQWUHDVFRRUGHQDGDVGRYpUWLFHH
RVYDORUHVGHDEHF"
x 3URFXUH GHVFREULU XP SURFHVVR GH GHWHUPLQDU D DEFLVVD GR YpUWLFH GH
XPDSDUiERODTXDOTXHU
6XJHVWmRFRPHFHSRUFRQVLGHUDURFDVRSDUWLFXODUHPTXHD +HOHQD 5RFKD
$OJXQVFRPHQWiULRV
&RPHVWDWDUHIDSUHWHQGHVHOHYDURVDOXQRVDGHVFREULUXPSURFHVVRSDUDGHWHUPLQDUD
DEFLVVDGRYpUWLFHGHXPDSDUiERODTXDOTXHUDSDUWLUGDH[SUHVVmRGDIXQomR$LGHLDp
TXHRVDOXQRVUHFRUUHQGRjFDOFXODGRUDSDUDH[SHULPHQWDUIRUPXODUHWHVWDUFRQMHFWXUDV
HFRPHoDQGRSRUFDVRVVLPSOHVVHYmRVXFHVVLYDPHQWHDSUR[LPDQGRGRFDVRJHUDO
1D SULPHLUD TXHVWmR pQRV SHGLGR TXH QRV FHQWUHPRV QDV SDUiERODV FRP YpUWLFH QD
RULJHP H [ VXUJH GH LPHGLDWR FRPR XPD
SULPHLUDKLSyWHVH$SDUWLUGDTXLHDSyVDOJXPD
H[SORUDomR QmR VHUi GLItFLO FRQFOXLU TXH R
JUiILFR GH TXDOTXHU IXQomR GR WLSR D[ VHUi
SUHFLVDPHQWH XPD SDUiEROD QDV FRQGLo}HV
SHGLGDV$VVLPWRGDVDVIXQo}HVGRWLSRD[
E[FFRPDzHPTXHEHFWHQKDPRYDORU
]HURFRUUHVSRQGHUmRDSDUiERODVGHYpUWLFHQDRULJHP
4XDQWR D SDUiERODV TXH WHQKDP R YpUWLFH VREUH R HL[R GRV\\ EDVWDUi SHQVDUPRV HP
GHVORFDo}HV YHUWLFDLV GDV SDUiERODV GD TXHVWmR DQWHULRU
(VWDUHPRVHQWmRDFRQVLGHUDUIXQo}HVGRWLSRD[FRX
VHMDIXQo}HVTXDGUiWLFDVHPTXHEWRPDRYDORU]HURHD
H F SRGHP DVVXPLU TXDOTXHU YDORU VHQGR VHPSUHDz
FODUR 5HODWLYDPHQWH jV FRRUGHQDGDV GR YpUWLFH GHVWDV
SDUiERODVDDEFLVVDVHUiREYLDPHQWHQXODXPDYH]TXH
R YpUWLFH VH HQFRQWUD VHPSUH VREUH R HL[R GRV\\ H D
RUGHQDGDDVVXPLUiRYDORUGRSDUkPHWURF2XVHMDDVSDUiERODVGHVWHWLSRWHUmRRVHX
YpUWLFHQRSRQWRGHFRRUGHQDGDVF
$~OWLPDTXHVWmRpFODUDPHQWHDPDLVGLItFLOSHORTXHSRGHUi
VHUFRQYHQLHQWHFRPHoDUSRUFRQVLGHUDURFDVRSDUWLFXODUHP
TXH D 1HVWH FDVR QmR p PXLWR GLItFLO FRQFOXLU DSyV D
DQiOLVHGHDOJXPDVIXQo}HVTXHDDEFLVVDGRYpUWLFHVH
VLWXDUiHP±E
8PD YH] DOFDQoDGD HVWD FRQFOXVmR HVWDUHPRV HP
FRQGLo}HV GH DERUGDU R FDVR JHUDO H GHVFREULU TXH R
$ FDOFXODGRUD JUiILFD QR HVWXGR GH IXQo}HV
YDORUGHDWDPEpPDIHFWDRYDORUGDDEFLVVDGRYpUWLFHHFKHJDUILQDOPHQWHjFRQFOXVmR
GHTXH±EDGHVLJQDUiDDEFLVVDGRYpUWLFHGHTXDOTXHUSDUiERODGRWLSRD[E[F
$LGHLDpTXHDRORQJRGDDFWLYLGDGHRYpUWLFHVHMDGHWHUPLQDGRYLVXDOPHQWHDSDUWLUGR
JUiILFRXPDYH]HQFRQWUDGDXPMDQHODGHYLVXDOL]DomRDGHTXDGD1RHQWDQWRHPDOJXQV
FDVRV SRGHPRV VHQWLU QHFHVVLGDGH GH R GHWHUPLQDU R TXH
SRGH VHU IHLWR UHFRUUHQGR DR PHQX&$/& H HVFROKHQGR Dt D
RSomR PLQLPXP RX PD[LPXP FRQVRDQWH R YpUWLFH
FRUUHVSRQGD DR SRQWR RQGH D IXQomR DOFDQoD R VHX YDORU
Pi[LPR RX PtQLPR (P VHJXLGD WHUHPRV GH FRORFDU R FXUVRU QR OLPLWH LQIHULRU GR
LQWHUYDOR RQGH TXHUHPRV TXH D FDOFXODGRUD FDOFXOH R H[WUHPR SUHVVLRQDU(17(5
LQGLFDU GH LJXDO PRGR R OLPLWH VXSHULRU GR LQWHUYDOR H DSUR[LPDU R FXUVRU GR H[WUHPR
SUHWHQGLGRRXVLPSOHVPHQWHFDUUHJDU(17(5PDLVXPDYH]HILQDOPHQWH REWHUHPRV
DVFRRUGHQDGDVGRSRQWRGHVHMDGR
+HOHQD 5RFKD
2PHWHRUR
(PFDGDDQRKiPLOKDUHVGHPHWHRURVTXHSHQHWUDPQDDWPRVIHUDWHUUHVWUH
4XDQGR R PHWHRUR HQWUD QD DWPRVIHUD VRIUH XP DTXHFLPHQWR UiSLGR H
DGTXLUH R DVSHFWR GH XPD HVWUHOD FDGHQWH 2 JUDX D TXH R PHWHRUR p
DTXHFLGR GHSHQGH GD VXD YHORFLGDGH RX VHMD D WHPSHUDWXUD Pi[LPD
DOFDQoDGD SHOR PHWHRUR p IXQomR GD YHORFLGDGH D TXH HVWH SHQHWUD QD
DWPRVIHUD 1D WDEHOD TXH VH VHJXH HQFRQWUDPVH DOJXQV YDORUHV
DSUR[LPDGRVGHVWDIXQomR
9HORFLGDGH
NPV
7HPSHUDWXUD
0i[LPDž&
3URFXUHGHVFREULUDH[SUHVVmRGDIXQomR
&RQVLGHUDQGR D IXQomR TXH HQFRQWURX FRPR PRGHOR GD VLWXDomR TXDO
VHUi D Pi[LPD WHPSHUDWXUD DOFDQoDGD SRU XP PHWHRUR TXH SHQHWUH QD
DWPRVIHUDDXPDYHORFLGDGHGHNPV"(VHIRUDNPV"
( VH GD WDEHOD DSHQDV FRQKHFHVVH RV GRLV SULPHLURV YDORUHV KDYHULD
RXWUDVIXQo}HVSRVVtYHLV"
$ FDOFXODGRUD JUiILFD QR HVWXGR GH IXQo}HV
$OJXQVFRPHQWiULRV
(VWDSRGHVHUXPDWDUHIDLQWHUHVVDQWHSDUDSURSRUDDOXQRVGXUDQWHRHVWXGRGDVIXQo}HV
SROLQRPLDLVRXPHVPRGXUDQWHRHVWXGRGDIXQomRTXDGUiWLFD
1DSULPHLUDTXHVWmRSHGHPQRVTXHHQFRQWUHPRVDH[SUHVVmRGHXPDIXQomRTXHSDVVD
SRU FLQFR SRQWRV GDGRV $VVLP R PHOKRU p FRPHoDUPRV SRU FULDU XPD UHSUHVHQWDomR
JUiILFDGHVVHVSRQWRVTXHSRVWHULRUPHQWHQRVIDFLOLWHDSURFXUDGDUHIHULGDIXQomR3DUD
LVVR SRGHPRV RSWDU SRU GRLV FDPLQKRV OLJHLUDPHQWH GLIHUHQWHV 3RGHPRV FRPHoDU SRU
FULDUGXDVOLVWDVTXHSRGHPRVGHVLJQDUSRU/H/WDPEpP
SRGHPRVHVFROKHUQRPHVPDLVVXJHVWLYRVXPDYH]TXHD7,
QRV SHUPLWH HVFROKHU QRPHV SDUD DV OLVWDV FRQWHQGR D
SULPHLUD RV YDORUHV GD YHORFLGDGH H D VHJXQGD RV GD
WHPSHUDWXUDPi[LPDDOFDQoDGDSHORPHWHRURSURFHGD FRPR
LQGLFDGR QD ILJXUD XWLOL]H D WHFOD672 SDUD REWHU D VHWD H QmR VH HVTXHoD GH FDUUHJDU
(17(5QRILQDO
(P DOWHUQDWLYD SRGHPRV DFHGHU j HVWDWtVWLFD 67$7
VHOHFFLRQDU (GLW H LQWURGX]LU RV GDGRV QD WDEHOD FRPR VH
SRGHYHUDRODGR
8PD YH] FULDGDV DV OLVWDV YDPRV SHGLU j FDOFXODGRUD TXH DV
XVHQDFRQVWUXomRGHXPJUiILFR3DUDLVVRYDPRVSUHVVLRQDU
QG < SDUD DFHGHU D6WDW 3ORW H FDUUHJDU(17(5 SDUD GHILQLU R SULPHLUR JUiILFR D
PiTXLQD SHUPLWH TXH VHMDP GHILQLGRV DWp WUrV JUiILFRV 3ORW 3ORW H 3ORW
9LVXDOL]DPRV HQWmR XP pFUDQ FRPR R DSUHVHQWDGR
GHYHQGR RV VRPEUHDGRV VHU FRORFDGRV WDO FRPR QD ILJXUD
SDUD TXH D FDOFXODGRUD WUDFH XP JUiILFR GH SRQWRV
XWLOL]DQGR RV YDORUHV GH / QR HL[R GRV [[ H RV GH / QR
HL[R GRV \\ %DVWD DJRUD WUDoDU R JUiILFR SUHVVLRQDQGR
*5$3+HSURYDYHOPHQWHUHDMXVWDURVYDORUHVGHZLQGRZ
8PDYH]REWLGDXPDUHSUHVHQWDomRJUiILFDGRVGDGRV
SRGHPRV SURVVHJXLU SRU WHQWDWLYDV H XWLOL]DQGR RV
FRQKHFLPHQWRVDWpHQWmRDGTXLULGRVVREUHRVJUiILFRV
GHIXQo}HVSROLQRPLDLVDWp HQFRQWUDUXPDH[SUHVVmR
SDUDHVWDIXQomR
+HOHQD 5RFKD
1RHQWDQWRWDPEpPpSRVVtYHOXWLOL]DUDFDOFXODGRUDSDUDUHFRUUHQGRDXPDUHJUHVVmR
TXDGUiWLFDHQFRQWUDUDH[SUHVVmRGHXPDIXQomRTXHFRQVWLWXDXPDERDDSUR[LPDomRGD
TXH SUHWHQGHPRV SUHVVLRQDQGR H VHOHFFLRQDQGR VXFHVVLYDPHQWH 67$7 &DOF H
4XDG5HJ R TXH QHVWH FDVR FRQFUHWR DWp QRV SHUPLWH HQFRQWUDU PHVPR D H[SUHVVmR
SUHWHQGLGD
$UHVSRVWDjVHJXQGDTXHVWmRSRGHVHUREWLGDSRUYiULRVSURFHVVRV
3RGHPRV UHFRUUHU j WDEHOD SUHVVLRQDQGR QG *5$3+
1HVWH FDVR FRQYpP WHU R FXLGDGR GH
GHILQLU
R
LQFUHPHQWR
GD
WDEHOD
SUHVVLRQDQGR QG 7%/6(7 SRU H[HP
SOR SDUDGHIRUPDDTXHQRVVHMDSRV
VtYHOYLVXDOL]DURVYDORUHVGDIXQomRSDUD[ H[ 7DPEpPpSRVVtYHOGHILQLUD
WDEHOD GH PRGR D TXH QRV VHMD SHUPLWLGR FRORFDU QD FROXQD
GRVYDORUHVGH[DSHQDVRVQ~PHURVTXHGHVHMDPRV3DUDLVVR
WHPRV GH FRORFDU HP 7%/6(7 D YDULiYHO LQGHSHQGHQWH
HP$VN(VWDRSomRSHUPLWHQRVYLVXDOL]DUXPDWDEHODHP
EUDQFR RQGH SRGHPRV SUHHQFKHU RV YDORUHV GH [ H
YLVXDOL]DURFRUUHVSRQGHQWHYDORUGH \FDUUHJDQGRDSHQDV
HP(17(5
8PD RXWUD SRVVLELOLGDGH p FHQWUDUPRQRV QR
JUiILFRHUHFRUUHUSRUH[HPSORjRSomRYDOXHGR
PHQX&$/&1HVWHFDVRpQRHQWDQWRQHFHVViULR
TXH R YDORU GH [ TXH YDPRV LQWURGX]LU VH
HQFRQWUH HQWUH RV YDORUHV GH ;PLQ H ;PD[ GR
ZLQGRZ $FDOFXODGRUDDSUHVHQWDHQWmRRYDORUFRUUHVSRQGHQWHDR\HFRORFDXPDFUX]
QRUHVSHFWLYRSRQWRGRJUiILFR
$~OWLPDTXHVWmRSURFXUDOHYDURVDOXQRVDDSHUFHEHUHPVHGDPXOWLSOLFLGDGHGHIXQo}HV
TXH p SRVVtYHO HQFRQWUDU D SDVVDU SRU XP FRQMXQWR UHGX]LGR GH SRQWRV 8PD SRVVtYHO
DERUGDJHPVHULDSHUPLWLUDOLYUHSURFXUDGHRXWUDVIXQo}HVQDVFRQGLo}HVLQGLFDGDV
$ FDOFXODGRUD JUiILFD QR HVWXGR GH IXQo}HV
)XQo}HVSROLQRPLDLV
3URSRQKD XPD H[SUHVVmR SDUD FDGD XPD GDV IXQo}HV UHSUHVHQWDGDV
JUDILFDPHQWH WHQGR HP FRQWD TXH FDGD ILJXUD H[LEH WRGRV RV DVSHFWRV
IXQGDPHQWDLVGRFRPSRUWDPHQWRGHVVDIXQomR
1RWDDHVFDODXWLOL]DGDpVHPSUHXPDXQLGDGH
+HOHQD 5RFKD
$OJXQVFRPHQWiULRV
(VWD WDUHID IRL SHQVDGD SDUD VHU UHDOL]DGD TXDQGR RV DOXQRV Mi SRVVXHP DOJXQV
FRQKHFLPHQWRVUHODWLYRVjUHSUHVHQWDomRJUiILFDGHIXQo}HVSROLQRPLDLVHDSyVRHVWXGR
GDIDFWRUL]DomRGHSROLQyPLRV&RPHIHLWRRVFRQKHFLPHQWRVDVVRFLDGRVjIDFWRUL]DomR
GH SROLQyPLRV SHUPLWHP TXH D H[SUHVVmR GR SROLQyPLR FRPHFH SRU VHU FRQVWUXtGD j
FXVWDGRV]HURVGHFDGDIXQomRHTXHYiVHQGRDSHUIHLoRDGDDWUDYpVGRUHFRQKHFLPHQWR
GHDVSHFWRVFRPRRJUDXGRSROLQyPLRRVLQDOGRFRHILFLHQWHGLUHFWRUHWF
$RORQJRGDDFWLYLGDGHRVDOXQRVWHUmRRFDVLmRGHVHLUDSHUFHEHQGRGDH[LVWrQFLDHQWUH
RVJUiILFRVDSUHVHQWDGRVGHSROLQyPLRVFRPUDt]HVP~OWLSODVHGHUHFRQKHFHUQRJUiILFR
DVFDUDFWHUtVWLFDVTXHLQGLFLDPDSUHVHQoDGHVVDVUDt]HV
&DGDJUiILFRIRLUHSUHVHQWDGRUHFRUUHQGRDGLIHUHQWHVMDQHODVGHYLVXDOL]DomRSHORTXHR
SULPHLUR SDVVR WHUi VHPSUH GH FRQVLVWLU QD HVFROKD GRV YDORUHV DGHTXDGRV DWUDYpV GD
VLPSOHVOHLWXUDGDHVFDODGHFDGDJUiILFRHDVXDDOWHUDomRHP:,1'2:
$SULPHLUDIXQomRpPXLWRVLPSOHV'HSRLV
GH DOWHUDUPRV RV YDORUHV GD MDQHOD GH
YLVXDOL]DomR EDVWD DWHQGHU DRV VHXV ]HURV
SDUD FRQVHJXLUPRV REWHU XPD H[SUHVVmR
TXH Gi RULJHP SUHFLVDPHQWH DR JUiILFR
SUHWHQGLGR
1D VHJXQGD IXQomR VH DSHQDV DWHQGHUPRV jV
LQWHUVHFo}HV GR JUiILFR FRP R HL[R GRV [[
YDPRV
REWHU
XP
JUiILFR
³LQYHUWLGR´
UHODWLYDPHQWH DR SUHWHQGLGR 6RPRV DVVLP
OHYDGRV D SHQVDU QR FRHILFLHQWH GLUHFWRU GR
SROLQyPLR TXH QHVWH FDVR WHUi GH VHU XP
Q~PHURQHJDWLYR±
$ IXQomR VHJXLQWH Mi p XP SRXFR PDLV
FRPSOLFDGD SRLV R VHX JUiILFR DSRQWD SDUD
WUrV]HURVPDVVDEHPRVQmRVHUHVWHRDVSHFWR
GRJUiILFR GH XP SROLQyPLR GR WHUFHLUR JUDX
$ LQIRUPDomR GLVSRQtYHO SHUPLWHQRV QR
$ FDOFXODGRUD JUiILFD QR HVWXGR GH IXQo}HV
HQWDQWRFRQFOXLUTXHVHWUDWDGHXPSROLQyPLRGHJUDXtPSDUSRLVRJUiILFR³FRPHoD´H
³WHUPLQD´HPODGRVRSRVWRVGRHL[RGRV[[RTXHQRVOHYDDSHQVDUTXHWDOYH]VHMDGH
JUDXHFRPRWDOTXHGXDVGDVUDt]HVVHMDPGXSODV(ROKDQGRSDUDRJUiILFRDWpQHP
pGLItFLOGHVFREULUTXDLVDVTXHVHUmRGXSODV0DVRJUiILFRDLQGDQmRHVWiFRUUHFWRSRLV
DLQWHUVHFomRFRPRHL[RGRV\\ILFDDEDL[RGRTXHGHYHULDVHQGRQHFHVViULRHQFRQWUDU
RYDORUDGHTXDGRSDUDRFRHILFLHQWHGLUHFWRU
2 TXDUWR JUiILFR WHP DOJXPDV VHPHOKDQoDV FRP R DQWHULRU 'HVWD YH] WHPRV GXDV
LQWHUVHFo}HVFRPRHL[RGRV[[PDVVDEHPRVTXHHVWHQmRpRJUiILFRGHXPDSDUiEROD
SHORTXHVHGHYHWUDWDUGHPDLVXPFDVRGHXPSROLQyPLRFRPUDt]HVP~OWLSODV$OpP
GLVVR R IDFWR GDV GXDV ³H[WUHPLGDGHV´ GR
JUiILFR VH HQFRQWUDUHP GR PHVPR ODGR GR
HL[R GRV [[ LQGLFDQRV TXH VH WUDWD GH XP
SROLQyPLRGHJUDXSDU6RPRVDVVLPOHYDGRV
DS{UDKLSyWHVHGHVHWUDWDUGHXPSROLQyPLR
GR TXDUWR JUDX FRP GXDV UDt]HV GXSODV
([SHULPHQWHPRV $LQWHUVHFomRFRPRHL[RGRV\\RFRUUHQRYDORUSUHWHQGLGRSHORTXH
WDPEpPHVWiHQFRQWUDGRRYDORUDGHTXDGRSDUDRFRHILFLHQWHGLUHFWRU
$TXLQWDIXQomR pPDLVXPFDVRGH XP SROLQyPLR FRP UDt]HV P~OWLSODV SRLV HPERUD
H[LVWDP DSHQDV GXDV LQWHUVHFo}HV FRP R HL[R GRV[[ VDEHPRV TXH QmR VH WUDWD GR
JUiILFRGHXPSROLQyPLRGHJUDX&RPRHVWDPRVSHUDQWH XP SROLQyPLR GH JUDX SDU
SRLVPDLVXPDYH]DVGXDV³H[WUHPLGDGHV´GRJUiILFRVHVLWXDPGRPHVPRODGRGRHL[R
GRV[[SRGHPRVS{UDKLSyWHVHGHVHWUDWDUGHXPSROLQyPLRGRTXDUWRJUDXFRPGXDV
UDt]HV GXSODV 1R HQWDQWR R DVSHFWR GR JUiILFR HP WRUQR GDV GXDV UDt]HV p EDVWDQWH
GLIHUHQWH FRQWUDULDPHQWH DR TXH DFRQWHFLD QR
JUiILFR DQWHULRU RQGH H[LVWLDP GXDV UDt]HV
GXSODV R TXH SRGHUi LQGLFLDU PXOWLSOLFLGDGHV
GLVWLQWDV
3RGHUHPRV
HQWmR
SHQVDU
HP
FRQVLGHUDU XPD UDL] VLPSOHV H RXWUD WULSOD 2
DVSHFWRGRJUiILFRDVVLPREWLGRpVHPHOKDQWHDR
SUHWHQGLGRPDVDLQGDQmRpLJXDO5HDMXVWHPRVHQWmRRYDORUGRFRHILFLHQWHGLUHFWRUGH
PRGRDTXHDLQWHUVHFomRFRPRHL[RGRV\\ VHMDDSUHWHQGLGD
$~OWLPDIXQomRpXPSRXFRPDLVFRPSOLFDGD7UDWDQGRVHGHXPJUiILFRFRPDSHQDV
GXDV LQWHUVHFo}HV FRP R HL[R GRV[[ TXH QmR SRGH FRUUHVSRQGHU D XP SROLQyPLR GH
JUDXHHPTXHDPEDVDVUDt]HVSDUHFHPVHUVLPSOHVTXHWLSRGHH[SUHVVmRGHYHPRV
+HOHQD 5RFKD
WHQWDU FRQVWUXLU" 2UD VH R QRVVR SROLQyPLR p
SHORPHQRVGR TXDUWRJUDXHDSHQDVWHPGXDV
UDt]HV VLPSOHV p SRUTXH HVWH LQFOXL XPD
SDUFHODTXHQmRWHPUDt]HVSRUH[HPSOR[
6H H[SHULPHQWDUPRV YHPRV TXH FRQVHJXLPRV
REWHU XP JUiILFR VHPHOKDQWH DR SUHWHQGLGR
VHQGRDSHQDVQHFHVViULRDMXVWDURYDORUGRFRHILFLHQWHGLUHFWRU
$ FDOFXODGRUD JUiILFD QR HVWXGR GH IXQo}HV
)XQomRSDUtPSDU
x &RPSOHWH R JUiILFR GH FDGD IXQomR GH PRGR D TXH HVWD VH FRQYHUWD
QXPD IXQomR SDU RX tPSDU FRQIRUPH LQGLFDGR H SURFXUH HQFRQWUDU D
H[SUHVVmRDQDOtWLFDTXHOKHFRUUHVSRQGH
IXQomRSDU
IXQomRtPSDU
IXQomRtPSDU
IXQomRSDU
x $QDOLVHDOJXPDVIXQo}HVjVXDHVFROKDTXDQWRjSDULGDGH
'HVFXEUDXPDIXQomRTXHVHMDVLPXOWDQHDPHQWHSDUHtPSDUHRXWUDTXH
QmRVHMDQHPSDUQHPtPSDU
x $VIXQo}HVSROLQRPLDLVSDUHVHQFRQWUDPVHHQWUHRVSROLQyPLRVGHTXH
JUDXV"
(DVIXQo}HVSROLQRPLDLVtPSDUHV"
+HOHQD 5RFKD
$OJXQVFRPHQWiULRV
&RP HVWD WDUHID SUHWHQGHVH OHYDU RV DOXQRV D H[SORUDU GR SRQWR GH YLVWD JUiILFR D
QRomR GH IXQomR SDU H GH IXQomR tPSDU LQFLGLQGR SDUWLFXODUPHQWH QDV IXQo}HV
SROLQRPLDLV H DSHODQGR D DOJXQV GRV FRQKHFLPHQWRV TXH RV DOXQRV WrP VREUH HVWDV
IXQo}HV
8PD YH] FRPSOHWDGR FDGD XP GRV JUiILFRV QDV FRQGLo}HV SHGLGDV p QHFHVViULR
HQFRQWUDUDH[SUHVVmRGDIXQomRTXHOKHFRUUHVSRQGH3DUDLVVRGHYHUHPRVUHFRUUHUDRV
QRVVRVFRQKHFLPHQWRVVREUHJUiILFRVGHIXQo}HVSROLQRPLDLVHLUIRUPXODQGRHWHVWDQGR
KLSyWHVHVGHH[SUHVV}HVTXHSRVVDPFRUUHVSRQGHUDRSUHWHQGLGR
1RFDVRGRSULPHLURJUiILFRSDUDTXHD IXQomRVHMD
SDU p QHFHVViULR DQWHV GH PDLV TXH SDUD FDGD UDL]
H[LVWD D UDL] VLPpWULFD 6RPRV HQWmR OHYDGRV D
FRQVLGHUDURSROLQyPLRGHILQLGRSRU[[[±
1R HQWDQWR R JUiILFR GHVWH SROLQyPLR QmR YDL WHU R
DVSHFWR SUHWHQGLGR SRLV p GR WHUFHLUR JUDX H FRPR
WDO QmR VHUi VLPpWULFR UHODWLYDPHQWH DR HL[R GRV\\
3UHFLVDPRVHQWmRGHXPSROLQyPLRGHJUDXSDUTXHPDQWHQKDDVLPHWULDHQWUHDVUDt]HV
2SROLQyPLRGRTXDUWRJUDX[[[±SDUHFHFRUUHVSRQGHUDRSUHWHQGLGR
3DUD R VHJXQGR JUiILFR SUHFLVDPRV GH FRQVLGHUDU
XPDIXQomRFRPDVUDt]HV±H0DVRSROLQyPLR
[ [ [ ± WHP XP JUiILFR ³LQYHUWLGR´
UHODWLYDPHQWHDRDSUHVHQWDGRSHORTXHSUHFLVDPRVGH
DOWHUDURFRHILFLHQWHGLUHFWRU
5HODWLYDPHQWH DR WHUFHLUR JUiILFR H XPD YH] TXH VH
WUDWD GH XP IXQomR OLQHDU QmR p GLItFLO HQFRQWUDU D
H[SUHVVmR H HVWD VXUJLUi PXLWR SURYDYHOPHQWH j
SULPHLUDWHQWDWLYD
$ FDOFXODGRUD JUiILFD QR HVWXGR GH IXQo}HV
2 ~OWLPR JUiILFR LQGLFLD D H[LVWrQFLD GH GXDV UDt]HV
VLPSOHV H H GH GXDV UDt]HV GXSODV H &RQWXGRRJUiILFRGDIXQomR[[[±[
± QmR FRUUHVSRQGH DR JUiILFR DSUHVHQWDGR H
HPERUDVHMDyEYLRTXHRFRHILFLHQWHGLUHFWRUWHUiTXH
VHU QHJDWLYR D SURFXUD GR YDORU DGHTXDGR SRGHUi
OHYDUQRVDLQGDDOJXPWHPSR
$ VHJXQGD TXHVWmR SURFXUD DERUGDU XPD LGHLD HUUDGD PDV EDVWDQWH FRPXP HQWUH RV
DOXQRV D LGHLD GH TXH XPD IXQomR RX p SDU RX p tPSDU QmR H[LVWLQGR QXQFD D
SRVVLELOLGDGHGHQmRVHUQHPXPDFRLVDQHPRXWUDRXGHVHUDVGXDVFRLVDVDRPHVPR
WHPSR
$ IXQomR QXOD p XP H[HPSOR GH XPD IXQomR TXH p VLPXOWDQHDPHQWH SDU H tPSDU (
PDQWHQGRQRVQDVIXQo}HVSROLQRPLDLVQmRFRUUHVSRQGHUiDXPDIXQomRSDUQHPDXPD
IXQomR tPSDU TXDOTXHU SROLQyPLR TXH LQGHSHQGHQWHPHQWH GR VHX JUDX SDUD FDGD UDL]
QmR WHQKD WDPEpP D UDL] VLPpWULFD $VVLP QmR VmR SDUHV QHP tPSDUHV DV VHJXLQWHV
IXQo}HV
$ ~OWLPD TXHVWmR WDO FRPR D DQWHULRU SURFXUD DIDVWDUVH XP SRXFR GRV FDVRV
SDUWLFXODUHV DSHODQGR D XPD YLVmR PDLV DEUDQJHQWH GD QRomR GH SDULGDGH 2 WLSR GH
VLPHWULDH[LJLGRHPFDGDXPGRVFDVRVHRVFRQKHFLPHQWRVDUHVSHLWRGRVJUiILFRVGDV
IXQo}HVSROLQRPLDLVSHUPLWHPQRVFRQFOXLUTXHVyRVSROLQyPLRVGHJUDXSDUSRGHUmR
VHUIXQo}HVSDUHVHVyRVSROLQyPLRVGHJUDXtPSDUSRGHUmRVHUIXQo}HVtPSDUHV
+HOHQD 5RFKD
9DPRVGHVHQKDU,,
5HSURGX]DHVWHVGHVHQKRV
6HUiSRVVtYHOUHSURGX]LUFDGDGHVHQKRSRUGLIHUHQWHVSURFHVVRV"2X
VHMDVHUiSRVVtYHOUHSURGX]LUFDGDILJXUDUHFRUUHQGRDGLIHUHQWHVFRQMXQWRV
GHIXQo}HV"
$ FDOFXODGRUD JUiILFD QR HVWXGR GH IXQo}HV
$OJXQVFRPHQWiULRV
&RPHVWDWDUHIDSUHWHQGHVHOHYDURV DOXQRVDH[SORUDUDLQIOXrQFLDGDYDULDomR GH XP
SDUkPHWUR GH XPD IXQomR WULJRQRPpWULFD QD VXD UHSUHVHQWDomR JUiILFD (PERUD RV
DOXQRV SRVVDP Mi WHU HVWXGDGR RV HIHLWRV SURGX]LGRV SHOD YDULDomR GH SDUkPHWURV QRV
JUiILFRVGHRXWURVWLSRVGHIXQo}HVWDOYH]DLQGDQmRVHWHQKDPDSHUFHELGRTXHDOJXQV
GHVVHVHIHLWRVQmRGHSHQGHPGRWLSRGHIXQo}HVHQYROYLGDVRXVHMDTXHSRUH[HPSORD
DGLomRGHXPQ~PHURDXPD IXQomRSURGX]VHPSUH R PHVPR WLSR GH DOWHUDomR QR VHX
JUiILFR LQGHSHQGHQWHPHQWH GH VH WUDWDU GH XPD IXQomR WULJRQRPpWULFD SROLQRPLDO RX
UDFLRQDO $LQGD DVVLP DV IXQo}HV WULJRQRPpWULFDV WrP XPD FDUDFWHUtVWLFD TXH DV
GHVWLQJXHGDVRXWUDVTXHRVDOXQRVSRGHUmRMiWHUHVWXGDGRVmRIXQo}HVSHULyGLFDV(VWD
SHULRGLFLGDGH ID] FRP TXH VHMD SRVVtYHO UHSURGX]LU FDGD ILJXUD GH GLYHUVDV IRUPDV
VHQGR HVWH XP DVSHFWR TXH VH HVSHUD TXH RV DOXQRV WHQKDP HP FRQWD DR ORQJR GD
DFWLYLGDGH0DVYHMDPRVDSURSRVWDGHWUDEDOKRHPFRQFUHWR
6HQGR SHGLGR TXH VH UHSURGX]D QD FDOFXODGRUD XP FRQMXQWR GH ILJXUDV FRQYpP
FRPHoDUSRUDOWHUDURVYDORUHVGDMDQHOD:LQGRZGHPRGRDTXHHVWHVFRLQFLGDPFRP
RVLQGLFDGRVSRLVVyDVVLPVHUiSRVVtYHOFRQVHJXLUXPDYLVXDOL]DomRTXHHIHFWLYDPHQWH
FRUUHVSRQGDjSUHWHQGLGD3DUDLVVRSRGHPRVRSWDUSRU DOWHUDUFDGDXPGRVYDORUHVGH
:LQGRZ RX SRU DOWHUiORV WRGRV GH XPD YH] 1HVWH ~OWLPR FDVR EDVWD LU D=RRP
VHOHFFLRQDU=WULJ H RV YDORUHV GD MDQHOD GH YLVXDOL]DomR ILFDUmR GH LPHGLDWR LJXDLV DRV
SUHWHQGLGRV (P TXDOTXHU GRV FDVRV FRQVHJXLUHPRV R SUHWHQGLGR PDV QXQFD
YLVXDOL]DUHPRV XP pFUDQ DQiORJR DR DSUHVHQWDGR QR HQXQFLDGR XPD YH] TXH D
FDOFXODGRUD FRQYHUWH VHPSUH RS HP Q~PHUR
GHFLPDO $VVLP QD FDOFXODGRUD R pFUDQ GR
:LQGRZ DSUHVHQWDGR QR HQXQFLDGR VHUi VXEV
WLWXtGR SRU RXWUR FRQIRUPH LOXVWUD D ILJXUD
MXQWD
8PDYH]DOWHUDGRVRVYDORUHVGR:LQGRZHVWDPRVHPFRQGLo}HVGHWHQWDUHQFRQWUDUDV
H[SUHVV}HVTXHQRVSHUPLWHPUHSURGX]LUD
SULPHLUDILJXUD7DOSRGHVHUIHLWRDWUDYpV
GDVIXQo}HVDSUHVHQWDGDVQDILJXUD
+HOHQD 5RFKD
0DV H WDO FRPR Mi IRL UHIHULGR QRV FRPHQWiULRV j WDUHID
9DPRV GHVHQKDU , WDPEpP R SRGHPRV ID]HU UHFRUUHQGR D
OLVWDVGHSDUkPHWURVHXWLOL]DQGRDSHQDVDIXQomR<
( XPD YH] TXH D IXQomR VHQR p SHULyGLFD GH SHUtRGR S
H[LVWHXPDLQILQLGDGHGHFRQMXQWRVGHIXQo}HVTXHQRVSHUPLWHPREWHUDPHVPDILJXUD
WRGDVDVIXQo}HVGDIRUPDVHQ[NS^`FRPN=
0DV HVWDV QmR VmR DV ~QLFDV IXQo}HV HP TXH SRGHPRV SHQVDU &RP HIHLWR WDPEpP p
SRVVtYHO WUDGX]LU HVWD ILJXUD UHFRUUHQGR j IXQomR FRVHQR 3RGHPRV DVVLP FRQVLGHUDU
IXQo}HVFRPRFRV[±S^`RXFRV[S^
`HQWUHPXLWDVRXWUDV
&RPR HP WRGDV DV IXQo}HV HVWDPRV D XWLOL]DU D PHVPD OLVWD GH SDUkPHWURV SRGHPRV
RSWDU SRU GHVLJQDU HVVD OLVWD SRU SRU H[HPSOR / GHL[DQGR DVVLP GH QHFHVVLWDU GH D
GLJLWDU FDGD YH] TXH D TXHUHPRV XWLOL]DU $V ILJXUDV TXH VH VHJXHP LOXVWUDP FRPR
SURFHGHUQHVWHFDVR
&RQYpP WHUPRV SUHVHQWH TXH D VHWD TXH DSDUHFH QR SULPHLUR pFUDQ p REWLGD
SUHVVLRQDQGRGLUHFWDPHQWH D WHFOD672 H TXH SDUD SDVVDU GR SULPHLUR SDUD R VHJXQGR
pFUDQ GHYHUHPRV DSHQDV SUHVVLRQDU (17(5 4XDQWR DRV WUrV ~OWLPRV pFUDQV GL]HP
REYLDPHQWHUHVSHLWRDWUrVGDVSRVVtYHLVIXQo}HVMiUHIHULGDV
5HODWLYDPHQWH j VHJXQGD ILJXUD GD WDUHID D VXD JUDQGH VHPHOKDQoD FRP D SULPHLUD
SHUPLWHQRV VHJXLU XP SURFHVVR DQiORJR 7DPEpP QHVWH FDVR DV SRVVLELOLGDGHV VmR
LQILQLWDVSHORTXHVHDSUHVHQWDPDSHQDVDOJXQVH[HPSORVGHIXQo}HVTXHQRVSHUPLWHP
REWHUDGHVHMDGDUHSURGXomR
$ FDOFXODGRUD JUiILFD QR HVWXGR GH IXQo}HV
$WHUFHLUDILJXUDMipGHXPDQDWXUH]DXPSRXFRGLIHUHQWHFRH[LVWLQGRIXQo}HVGHGRLV
WLSRV GLVWLQWRV RX GRLV SDUkPHWURV HP FDGD IXQomR e FODUR TXH WDPEpP DTXL D
SHULRGLFLGDGHGDVIXQo}HVHQYROYLGDVQRVSHUPLWHHQFRQWUDUXPDLQILQLGDGHGHVROXo}HV
&RQVLGHUHPRVDOJXPDVKLSyWHVHV
(VWDILJXUDSRGHVHUREWLGDjFXVWDGH
DOJXPDV IXQo}HV HQYROYHQGR R
FRVHQR RX DWHQGHQGR j UHODomR
H[LVWHQWH HQWUH R VHQR H R FRVHQR j
FXVWDGHDOJXPDVIXQo}HVHQYROYHQGR
R VHQR ( LVWR SRGH VHU IHLWR
UHFRUUHQGR RX QmR D OLVWDV GH
SDUkPHWURV
0DVWDPEpPpSRVVtYHORSWDUSRUUHFRUUHUDGRLVFRQMXQWRVGH
IXQo}HV
(FODURSRGHUtDPRVDLQGDFRQVLGHUDUXPDPLVWXUDGHVWHVGRLV
WLSRV
$TXDUWDILJXUDpXPSRXFRPDLVVLPSOHVHHPERUDWDPEpP
H[LVWDPLQ~PHUDVVROXo}HVRPDLVSURYiYHOpTXHVXUMDPDV
H[SUHVV}HVDSUHVHQWDGDV
$TXLQWDILJXUDHQYROYHWDOFRPRDDQWHULRUDPXOWLSOLFDomR
SRUXPSDUkPHWURPDVpSUHFLVRFRQVLGHUDUYDORUHVQHJDWLYRV
RX UHFRUUHU D PDLV TXDOTXHU FRLVD SDUD FRQVHJXLU D
VLPHWULDHPWRUQRGRHL[RGRV[['DVTXDWURIXQo}HV
UHSUHVHQWDGDV JUDILFDPHQWH GXDV GHODV VmR GH IiFLO
GHILQLomR XPD YH] TXH Mi LQWHJUDYDP D ILJXUD
DQWHULRU H DV UHVWDQWHV SRGHP VHU WUDGX]LGDV SHOR
+HOHQD 5RFKD
VLPpWULFR GHVWDV RX SRU XPD WUDQVODomR KRUL]RQWDO GHVVDV GXDV IXQo}HV ( FODUR R
UHFXUVRDIXQo}HVHQYROYHQGRRFRVHQRpLJXDOPHQWHSRVVtYHOHPERUDXPSRXFRPDLV
FRPSOH[R
$ ILJXUD VHJXLQWH p D ~QLFD HP TXH REULJDWRULDPHQWH WHPRV GH ID]HU WUDQVODo}HV
KRUL]RQWDLV GDV IXQo}HVVHQ [ HRX FRV [ $SUHVHQWDPVH DOJXPDV SRVVLELOLGDGHV e
FXULRVRREVHUYDUHFOD
UR SURFXUDU SHUFHEHU
SRUTXr TXH HP GXDV
GDV KLSyWHVHV DSUHVHQ
WDGDVD~QLFDGLIHUHQoD
UHVLGH QD IXQomR WUL
JRQRPpWULFD XWLOL]DGD VHQR RX FRVHQR XPD YH] TXH RV SDUkPHWURV XWLOL]DGRV VmR
SUHFLVDPHQWHRVPHVPRV
$VpWLPDILJXUDSRGHVXVFLWDUDOJXPDVGLILFXOGDGHVXPDYH]TXHFRQWUDULDPHQWHDWRGDV
DVRXWUDVHQYROYHXPDRXWUDFRQKHFLGDIXQomRD
IXQomR PyGXOR (VWD IXQomR p UHSUHVHQWDGD QD
FDOFXODGRUD SHOD H[SUHVVmR DEV TXH SRGH VHU
REWLGD DWUDYpV GD WHFOD 0$7+ VHOHFFLRQDQGR
180VHJXLGRGDSULPHLUDRSomRLVWRpGHDEV
8PDRXWUDKLSyWHVHSDUDDFHGHUjH[SUHVVmRDEVpSUHVVLRQDU
QG &$7$/2* VHJXLGR GH (17(5 XPD YH] TXH HVWH p R
SULPHLURFRPDQGRGLVSRQtYHOQRFDWiORJRGDFDOFXODGRUD
$ IRUPD PDLV VLPSOHV GH UHFULDU HVWD ILJXUD VHUi HQWmR D
VHJXLQWH
$ ILJXUD VHJXLQWH p EDVWDQWH VLPSOHV SRGHQGR REYLDPHQWH
VHUREWLGDUHFRUUHQGRjIXQomRFRV[1RHQWDQWRDUHSUHVHQWDomRJUiILFDGHIXQo}HV
FRPR FRV [ FRV[ FRV [ RX FRV[ SRGH UHYHODUVH XPD H[SHULrQFLD
VXUSUHHQGHQWH(IHFWLYDPHQWHDVOLPLWDo}HVGHGHILQLomRGDPiTXLQDSRGHPGDURULJHP
DDOJXQVJUiILFRVLQHVSHUDGRVTXHQRVSRGHUmROHYDUDFRPHWHUHUURVVHQmRHVWLYHUPRV
GHYLGDPHQWHDOHUWDGRVSDUDVLWXDo}HVFRPRHVWD
$ FDOFXODGRUD JUiILFD QR HVWXGR GH IXQo}HV
$ QRQD ILJXUD GLIHUH SRXFR GD DQWHULRU H HPERUD HVWHMDP
HQYROYLGDV PDLV IXQo}HV QmR VHUi FHUWDPHQWH GLItFLO
HQFRQWUDUXPDH[SUHVVmRFRPRDDSUHVHQWDGD
$ ~OWLPD ILJXUD p VHP G~YLGD XP FDVR LQWHUHVVDQWH 1mR
DSUHVHQWDQGRRDVSHFWRVLQXVRLGDOFDUDFWHUtVWLFRGDV IXQo}HV
VHQR H FRVHQR QHP SDUHFH FRUUHVSRQGHU j UHSUHVHQWDomR JUiILFD GH IXQo}HV
&RQWUDULDPHQWHDRTXHDFRQWHFLDFRPDVUHVWDQWHVILJXUDVRREMHFWLYRDJRUDQmRpOHYDU
RVDOXQRVDH[SORUDUDLQIOXrQFLDGDYDULDomRGHTXDLVTXHUSDUkPHWURVQDUHSUHVHQWDomR
JUiILFD GD IXQomR PDV VLP FRQVFLHQFLDOL]iORV GD LPSRUWkQFLD GH XPD XWLOL]DomR
LQWHOLJHQWHGDFDOFXODGRUD(PERUDQmRVHMDHVWDFHUWDPHQWHDSULPHLUDYH]HPTXHRV
DOXQRV VH GHIURQWDP FRP VLWXDo}HV VHPHOKDQWHV QXQFD p GH PDLV UHFRUGDU TXH DV
UHGX]LGDV GLPHQV}HV GD PiTXLQD TXH OKH FRQIHUHP D JUDQGH YDQWDJHP GH VHU
IDFLOPHQWH WUDQVSRUWiYHO WrP SRU YH]HV R LQFRQYHQLHQWH GH QmR SHUPLWLU XPD JUDQGH
GHILQLomRGRYLVRU
5HODWLYDPHQWH jV H[SUHVV}HV TXH QRV SHUPLWHP REWHU
HVWD UHSUHVHQWDomR JUiILFD HODV VmR REYLDPHQWH
LQILQLWDVHLQFOXHPIXQo}HV FXMRVJUiILFRVQmRVmRGH
PRGR DOJXP LGrQWLFRV PDV TXH DVVLP VmR
UHSUHVHQWDGRVSHODFDOFXODGRUD
+HOHQD 5RFKD
%LEOLRJUDILD
-DFREV+(OHPHQWDU\$OJHEUD:+)UHHPDQDQG&RPSDQ\
3LFFLDWWR + 0DNH WKHVH GHVLJQV 0DWKHPDWLFV 7HDFKHU SS
5RFKD+,QYHVWLJDQGRFRPDFDOFXODGRUDJUiILFD,Q3$EUDQWHV
//HDO-3RQWH(GV,QYHVWLJDUSDUDDSUHQGHU0DWHPiWLFD±WH[WRV
VHOHFFLRQDGRVSS/LVERD$30
5RFKD + $OXQRV H SURIHVVRUHV HP DFWLYLGDGHV GH LQYHVWLJDomR
(GXFDomRH0DWHPiWLFDQžSS
Download

A calculadora gráfica