interfaces aço.concreto - Sky Light Estruturas Metálicas

interfaces aço.concreto - Sky Light Estruturas Metálicas

,17(5)$&(6
$d2&21&5(72
6pULH ³ 0DQXDO GH &RQVWUXomR HP $oR´
•
•
•
•
•
•
•
•
•
•
*DOS}HVSDUD8VRV*HUDLV
/LJDo}HVHP(VWUXWXUDV0HWiOLFDV
(GLItFLRVGH3HTXHQR3RUWH(VWUXWXUDGRVHP$oR
$OYHQDULDV
3DLQpLVGH9HGDomR
5HVLVWrQFLDDR)RJRGDV(VWUXWXUDVGH$oR
7UDWDPHQWRGH6XSHUItFLHH3LQWXUD
7UDQVSRUWHH0RQWDJHP
6WHHO)UDPLQJ$UTXLWHWXUD
,QWHUIDFHV$oR&RQFUHWR
,/'21<+e/,2%(//(,
,17(5)$&(6
$d2&21&5(72
,167,7872%5$6,/(,52'(6,'(585*,$
&(1752%5$6,/(,52'$&216758d­2(0$d2
5,2'(-$1(,52
© ,167,7872%5$6,/(,52'(6,'(585*,$&(1752%5$6,/(,52'$
&216758d­2(0$d2
1HQKXPDSDUWHGHVWDSXEOLFDomRSRGHVHUUHSURGX]LGDSRUTXDLVTXHUPHLRVHPDSUpYLDDXWRUL]DomR
GHVWD(QWLGDGH
%L
%HOOHL,OGRQ\+pOLR
,QWHUIDFHVDoRFRQFUHWR,OGRQ\+pOLR%HOOHL5LRGH-DQHLUR,%6&%&$
SFP²6pULH0DQXDOGH&RQVWUXomRHP$oR
%LEOLRJUDILD
,6%1
$oR&RQFUHWR$oR&RQFUHWR3ODFDVGH%DVH%DUUDVGHFLVDOKDPHQWR
3LODUHVHPEXWLGRV/LJDo}HVYLJDVGHDoR,7tWXORVVpULH
&'8
,QVWLWXWR%UDVLOHLURGH6LGHUXUJLD&HQWUR%UDVLOHLURGD&RQVWUXomRHP$oR
$Y5LR%UDQFRR $QGDU
5LRGH-DQHLUR5-
HPDLO FEFD#LEVRUJEU
VLWHZZZFEFDLEVRUJEU
680È5,2
&DStWXOR
&KXPEDGRUHV
,QWURGXomR
'LPHQVLRQDPHQWRGRVFKXPEDGRUHVDoR6$(
¬&LVDOKDPHQWR
¬7UDomR
¬7UDomRFRPFLVDOKDPHQWR
&iOFXORGRVFRPSULPHQWRVGHDQFRUDJHPGRVFKXPEDGRUHVjWUDomR
&iOFXORGRFRPSULPHQWRGHDQFRUDJHPSDUDFKXPEDGRUHVFRP
H[WUHPLGDGHLQIHULRUUHWDž
&iOFXORGRFRPSULPHQWRGHDQFRUDJHPSDUDFKXPEDGRUHVFRP
H[WUHPLGDGHLQIHULRUWHQGRXPDFKDSDRXSRUFD
5HFRPHQGDo}HV
&DStWXOR
3ODFDVGHEDVH
,QWURGXomR
7LSRVGHEDVH
%DVHVURWXODGDV
%DVHVHQJDVWDGDV
&iOFXORGDVSODFDVGHEDVH
3ODFDVGHEDVHjFRPSUHVVmRD[LDOSDUDSHUILV,H+
3DUkPHWURVSDUDFiOFXORGDHVSHVVXUDGDVSODFDVGHEDVH
'LPHQVLRQDPHQWR
3ODFDVGHEDVHSDUDSHUILVWXEXODUHV
3ODFDVGHEDVHjWUDomR
'LPHQVLRQDPHQWR
3ODFDVGHEDVHjFRPSUHVVmRD[LDOFRPPRPHQWR
3ODFDVGHEDVHFRPUHIRUoR
&iOFXORGDVFKDSDVGHUHIRUoR
5HFRPHQGDo}HV
&DStWXOR
%DUUDVGHFLVDOKDPHQWR
,QWURGXomR
&iOFXORGDEDUUDGHFLVDOKDPHQWR
'LPHQVLRQDPHQWRGDVROGDGHOLJDomRGDEDUUDGHFLVDOKDPHQWRFRP
SODFDGHEDVH
&DStWXOR
3LODUHVHPEXWLGRVQDVIXQGDo}HV
,QWURGXomR
&iOFXORGRFRPSULPHQWRQHFHVViULR/DVHUHPEXWLGR
(PIXQomRGDUHVLVWrQFLDGRSHUILOHGDUHVLVWrQFLDGRFRQFUHWR
(PIXQomRGDVFDUJDVMiGHILQLGDV
'HWDOKHVFRQVWUXWLYRV
&DStWXOR
/LJDo}HVYLJDVGHDoRFRPHOHPHQWRVGHFRQFUHWR
,QWURGXomR
6ROXo}HVGXUDQWHDFRQVWUXomR
9LJDVGHDoRDSRLDGDVHPFKDSDVGHDoRVREUHFRQFUHWRRXDOYHQDULD
/LJDomRHQWUHYLJDVGHDoRHSLODUHVRXSDUHGHVGHFRQFUHWRDWUDYpV
GHFKDSDVHSLQRV
&RQVROHVIHLWRSUHYLDPHQWHQRFRQFUHWR
1LFKRVIHLWRVSUHYLDPHQWHQRFRQFUHWR
6ROXo}HVDSyVDFRQVWUXomRSURQWD
7LSRVGHIL[DGRUHV
(VSHVVXUDVGRVSLODUHV
3LODUGHJUDQGHVHVSHVVXUDV
3LODUGHSHTXHQDVHVSHVVXUDV
'HWDOKHFRQVWUXWLYR
5HIHUrQFLDV%LEOLRJUiILFDV
$QH[RV
$SUHVHQWDomR
2PDQXDODERUGDGHIRUPDSUiWLFDDVSULQFLSDLVLQWHUIDFHVHQWUHSLODUHVIXQGDo}HVHGHYLJDVGHDoRFRP
HOHPHQWRVGHFRQFUHWR(PYLUWXGHGDQRUPD$%17 1%5HVWDUHPSURFHVVRGHUHYLVmRWRGRVRV
FiOFXORVIRUDPIHLWRVGHDFRUGRFRPDVHVSHFLILFDo}HVDPHULFDQDVGR $,6&$6' QRPpWRGRGDVWHQV}HV
DGPLVVtYHLVH $,6&/5)'QRPpWRGRGRVHVWDGRVOLPLWHV$VHVSHFLILFDo}HVGR$,6&XWLOL]DGDVVmR
UHIHUHQWHVjD HGLomRGH
2VHWRUVLGHU~UJLFRDWUDYpVGR&HQWUR%UDVLOHLURGD&RQVWUXomRHP$oR&%&$WHPDVDWLVIDomRGHWRUQDU
GLVSRQtYHOSDUDRXQLYHUVRGHSURILVVLRQDLVHQYROYLGRVFRPRHPSUHJRGRDoRQDFRQVWUXomRFLYLOHVWH
PDQXDORGpFLPRGHXPDVpULHUHODFLRQDGDjFRQVWUXomRHPDoR
&HQWURGLQkPLFRGHVHUYLoRVFRPIRFRH[FOXVLYDPHQWHWpFQLFRHFDSDFLWDGRSDUDFRQGX]LUXPDSROtWLFDGH
SURPRomRGRXVRGRDoRQDFRQVWUXomRR&%&$HVWiVHJXURGHTXHHVWHPDQXDOHQTXDGUDVHQRREMHWLYR
GHFRQWULEXLUSDUDDGLIXVmRGHFRPSHWrQFLDWpFQLFDHHPSUHVDULDOQR3DtV
&DStWXOR
&KXPEDGRUHV
&KXPEDGRUHV ,QWURGXomR 2VFKXPEDGRUHVVmREDUUDVTXHWrPSRU
ILQDOLGDGHIL[DUDVSODFDVGHEDVHGRVSLODUHV
jVIXQGDo}HV(PJHUDOVmRIRUPDGRVSRUEDU
UDV UHGRQGDV WRGDV URVTXHDGDV RX Vy
URVTXHDGDHPXPDRXGXDVH[WUHPLGDGHVQRU
PDOPHQWHIRUPDGDV GHDoR 6$( H $ 670
$FXMRVOLPLWHVGHHVFRDPHQWRHUXSWXUDVmR
)\N1FP
)XN1FP
6$(
$670$
(P YLVWD GDV SHTXHQDV GLIHUHQoDV QDV
SURSULHGDGHV GRV DoRV HPSUHJDGRV QRV
FKXPEDGRUHVQHVWHPDQXDODGRWDUHPRVDVSUR
SULHGDGHVGR6$(FRPRUHIHUrQFLDSDUD
DVH[SUHVV}HVGHFiOFXOR
2VFKXPEDGRUHVSRGHPVHUGLPHQVLRQD
GRVGDVVHJXLQWHVIRUPDV
D$FLVDOKDPHQWR)LJD
E$WUDomR)LJG
F$WUDomRFRPFLVDOKDPHQWR
)LJEHF
2VFKXPEDGRUHVVXMHLWRVVRPHQWHDHV
IRUoRVGHFLVDOKDPHQWRFRPRpRFDVRGHSLOD
UHVGHWDSDPHQWR)LJDSRGHPWHUFRP
SULPHQWRVGHDQFRUDJHPSHTXHQRVDRFRQWUi
ULRGRVVXMHLWRVjWUDomRTXHSUHFLVDPWHUXP
FRPSULPHQWRGHDQFRUDJHPSURSRUFLRQDODRV
HVIRUoRV
(VWDPRVLQFOXLQGRQHVWH0DQXDOGXDVWD
EHODVSDUDFKXPEDGRUHVSDGURQL]DGRV7DE
HFRPYiULRVWLSRVSRURUGHPGHIDFLOLGDGH
GHIDEULFDomRVHQGRRPDLVVLPSOHVRWLSR&&
HPJDQFKRUHWRHRVPDLVVRILVWLFDGRVWLSR&$*
2 FRPSULPHQWR GH DQFRUDJHP GRV
FKXPEDGRUHVjWUDomRIRLGHWHUPLQDGRSHODUH
VLVWrQFLDjWUDomRGDEDUUDHSHODUHVLVWrQFLD
GRFRQHGHUHVLVWrQFLDGRFRQFUHWR
3DUDFRPSRUDVWDEHODVGHILQLPRVWLSRV
GHFKXPEDGRUHVFRPRRVPDLVXVXDLVGHILQL
GRVDVHJXLU
&&±FKXPEDGRUXVDGRVRPHQWHSDUD
FLVDOKDPHQWR
&$/±FKXPEDGRUGHDQFRUDJHPFRPD
SDUWHLQIHULRUIRUPDQGRXP/
&$&±LGHPWHQGRXPDFKDSDSDUWH
LQIHULRU
&$3LGHPWHQGRXPDSRUFDFRP
FKDSDQD SDUWHLQIHULRU
&$5LGHPWHQGRXPDFKDSDFRP
UHIRUoRQD SDUWHLQIHULRU
&$*±FKXPEDGRUHPJDQFKRFRPQLFKR
SDUD DQFRUDJHPHPXPDRXWUD
EDUUD
2VWLSRV&&&$/&$&&$3H&$5VmR
IL[DGRVGXUDQWHDFRQFUHWDJHPSRUPHLRGHJD
EDULWRVHFRQIHULGRVSRUPHLRGHXPDERDWRSR
JUDILDPLOLPpWULFD2WLSR&$*pXVDGRTXDQGR
QmRH[LVWHERDSUHFLVmRGRVEORFRVRXTXDQGR
VH GHVHMD PDLRU IOH[LELOLGDGH QD PRQWDJHP
HPERUDVHMDPPDLVFDURVTXHRVRXWURVHPWR
GRVRVDVSHFWRV
)LJXUD±)RUoDVQRVFKXPEDGRUHV
±'LPHQVLRQDPHQWRGRV
FKXPEDGRUHVDoR6$(
$QHF iUHDQHFHVViULDGRVFKXPEDGRUHV
±¬WUDomR
D0pWRGR$,6&$6'
)W )X
7
GF
[)X
$FKW iUHDWRWDOGRVFKXPEDGRUHVjWUDomR
$QHF
$FKF iUHDWRWDOGRVFKXPEDGRUHVjFLVDOKD
PHQWR
7
[
QW Q~PHURGHFKXPEDGRUHVjWUDomR
QF Q~PHURGHFKXPEDGRUHVjFLVDOKDPHQWR
GF GLkPHWURGRFKXPEDGRUFP
7 FDUJDD[LDOQRUPDOGHWUDomRN1
7X FDUJDD[LDOIDWRUDGDGHWUDomRN1
GF ⇔
7
GF
QW
7
QW
E0pWRGR$,6&/5)'
)WX )X
$QHF
7X
GF
[)X
+ FDUJDKRUL]RQWDOQRUPDON1
7X
7X
7X
GF ⇔
[ QW
QW
+X FDUJDKRUL]RQWDOIDWRUDGDN1
±¬WUDomRFRPFLVDOKDPHQWR
¬FLVDOKDPHQWR
D0pWRGR$,6&$6'
D0pWRGR$,6&$6'
)Y )X
$QHF +
G F
[)X
+
+
GF
× ⇔ ×QF
E0pWRGR$,6&/5)'
)YX )X
+X
GF
=
[)X
+X
[
GF ⇔
+X
QF
7
$FKW
+X
GF
QF
IY =
+
$FKF
IW + IY < )W = N1FP
I =
E±0pWRGR$,6&/5)'
I WX =
+
GF QF
$QHF
IW =
IX =
7X
$FKXW
IWX + IYX < )WX = N1FP
±&iOFXORGRVFRPSULPHQWRVGH
DQFRUDJHPGRVFKXPEDGRUHVj
WUDomR
2FRPSULPHQWRGHDQFRUDJHPGHYHVHU
GHILQLGRHPIXQomRGRWLSRGRFKXPEDGRUHGR
FRQHGHDQFRUDJHPGRFRQFUHWR2$,6&±6WHHO
&KXPEDGRUHV 'HVLJQ*XLGH6HULHVQRHVWDEHOHFHGRLVFULWp
ULRV
&KXPEDGRUHV IRUPDGRV SRU EDUUDV
FRPH[WUHPLGDGHLQIHULRUD2 )LJD
&KXPEDGRUHVIRUPDGRVSRUEDUUDVWHQ
GR XPD FKDSD RX SRUFD QD VXD H[WUHPLGDGH
LQIHULRU)LJE
6HQGRGFRGLkPHWURGD
EDUUDH/K RFRPSULPHQWRGD
SDUWHUHWDKRUL]RQWDO
)LJXUD ± &KXPEDGRU HP /
D0pWRGR$,6&$6'
5HFRPHQGDXPIDWRUGHVHJXUDQoDGH
DVHUDSOLFDGRQDHTXDomRDEDL[RHFRQVLGHUD
VHTXHVRPHQWHPHWDGHGDFDSDFLGDGHGHWHQ
VmRGDEDUUDpGHVHQYROYLGD
)LJXUD 7LSRV GH FKXPEDGRUHV
(VWDEHOHFHWDPEpPFRPSULPHQWRVHGLV
WkQFLDVPtQLPDV
7 $FKX )W)W )X
/K =
7DEHOD±&RPSULPHQWRVHGLVWkQFLDVPt
QLPDV
7LSRVGHDoR
&RPSULPHQWR
/F
'LVWkQFLD
HQWUHFKXPE
*
;
GF
$670$
$
GF
GF
IFN
=
7
IFNGF
7
IFNGF
GF !PP
E±0pWRGR$,6&/5)'
GF !PP
±&iOFXORGRFRPSULPHQWRGHDQFRUD
JHPSDUDFKXPEDGRUHVFRPH[WUHPLGDGHLQ
IHULRUUHWD2
³)LVKHU´UHFRPHQGDTXHRJDQFKRGDEDU
UDGHYHVHUFDOFXODGRDRHVPDJDPHQWRSDUD
XPDFDSDFLGDGH7K GDGDSHODHTXDomR
2FRPSULPHQWRWRWDOVHUi/F /K
6$(
$
$670$
7K IFNGF/K
/K =
7
1RFDVRQmRWHPRVRIDWRUGHVHJXUDQoD
LJXDOD
7X )X$FKX
/K =
7X
7X
⇔ /K =
IFNGF
IFNGF
([HPSOR ±'HWHUPLQDURFRPSULPHQ
WR GR FKXPEDGRU IRUPDGR SRU XPD EDUUD GH
PPHP DoR6$( jWUDomR2 IFNGR
FRQFUHWRVHUiGHN1FP
$&KX FP
D0pWRGR$,6&$6'
7 [[ N1
/K [
[
FP
/F [ FP7DE
/K /F ⇒ FP
'LVWkQFLDHQWUHFKXPEDGRUHV
; [ PPXVDUPtQLPRPP
)LJXUD± &RQHGHFRQFUHWR
2FRQHpUDGLDODVVXPLGRSRUXPkQJXOR
GH HDWHQVmRGHILVVXUDRFRUUHDRORQJRGD
VXSHUItFLHGRFRQHSDUDXPDWHQVmRGH
D0pWRGR$,6&$6'± IFN HP³SVL´
DSUR[LPDGDPHQWHGHIFN
E±0pWRGR$,6&/5)'
E0pWRGR$,6&±/5)' ĭW
7X [[ N1
³SVL´DSUR[LPDGDPHQWHGHIFNVHQGR
ĭW /K FP
[[
/F/K aFP
; PP
±&iOFXORGRFRPSULPHQWRGH
DQFRUDJHPSDUDFKXPEDGRUHVFRP
H[WUHPLGDGHLQIHULRUWHQGRXPDFKDSDRX
SRUFD
(VWH WLSR GH FKXPEDGRU WHP XP PHQRU
FRPSULPHQWRGHDQFRUDJHPHDVXDUHVLVWrQFLD
GHFDOFXORpEDVHDGDWDPEpPQRFRQHGHDQ
FRUDJHPGRFRQFUHWR$ILVVXUDRFRUUHTXDQGR
DEDUUDVHURPSHRXRFRQHGHFRQFUHWRVHVH
SDUDGDIXQGDomR)LJ
IFN HP
$VHVSHFLILFDo}HVGHFiOFXORPDLVFRQVHU
YDGRUDVVLPSOLILFDPHLQGLFDPTXHDWHQVmR
VHUiSHUSHQGLFXODUjVXSHUItFLHGRFRQH$FD
SDFLGDGHGHUHVLVWrQFLDVHUiLJXDODRYDORUGD
WHQVmRSHODiUHDGDVXSHUItFLHFLUFXODUGRFRQH
3DUD P~OWLSODV DQFRUDJHQV SRGH KDYHU
VXSHUSRVLomRGRVFRQHVGHDQFRUDJHPRTXH
GHYHVHUOHYDGRHPFRQWD$IyUPXODDVHJXLU
SHUPLWHFDOFXODUHVWDiUHD
$ = π/F
−
+
;
/F −
FRV−; /Fπ/F
+
;
&KXPEDGRUHV
⎡
; ⎞⎤
−⎛
⎟⎟⎥
⎢× /F × FRV ⎜⎜
×
/
⎢
⎝
⎠⎥⎦
F
+
$FRQH = × /F − ⎣
;
/F −
;
E±0pWRGR$,6&/5)'
&iOFXORGDiUHDQHFHVViULDGRFKXPEDGRU
$FKX =
FP
7X
)X
±&iOFXORGDiUHDGRFRQH
3DUDHIHLWRGDVWDEHODVHIRLFRQVL
GHUDGRXPDVREUHSRVLomRGHQRVFRQHV
GHDUUDQFDPHQWRGRFRQFUHWRHRVFKXPEDGRUHV
IL[RVWrPXPFRPSULPHQWRGHDQFRUDJHPVXSH
ULRUDRPtQLPRQHFHVViULRGHYH]HVRGLk
PHWUR EHP FRPR DV GLVWkQFLDV HQWUH
FKXPEDGRUHVVXSHULRUHVDYH]HVRGLkPHWUR
2VYDORUHVFRQWLGRVQHVWDVDWHQGHPSHUIHLWD
PHQWHDPDLRULDGRVSURMHWRV
1DWDEHODLQGLFDPRVDVGLVWkQFLDVPt
QLPDVHQWUHFKXPEDGRUHVHFKXPEDGRUHVH[
WUHPLGDGHVTXHDWHQGHPEHPGDQGRXPDUH
VLVWrQFLDGRFRQHVXSHULRUjGRVFKXPEDGRUHV
$FRQH =
7X
IFN
(FP)= [ IFN
/F =
$FRQH
([HPS OR 'HWHUPLQDU R GLkPHWUR GR
FKXPEDGRUHVHXFRPSULPHQWRGHDQFRUDJHP
SDUDUHVLVWLUDXPDIRUoDGHWUDomRDWXDQWH
7 N1HIDWRUDGD7X N1
$oR6$()X N1FP
IFN N1FP
&iOFXORGDiUHDQHFHVViULDGRFKXPEDGRU
7
)X
±&iOFXORGDiUHDGRFRQH
=
$FRQH
7
IFN FRQVLGHUDQGR XP IDWRU GH
VHJXUDQoDLJXDODWHPRV
$FRQH =
7
IFN
(FP)
³
7
IFN SVL³
&iOFXORGRFRPSULPHQWRGHDQFRUDJHP
/F $&RQH
;
SVL
±&iOFXORGRFRPSULPHQWRGHDQFRUDJHP
D0pWRGR$,6&$6'
$FKX =
7X
D±0pWRGR$,6&$6'
$FKX =
= FP XVDUG PP
F
× $ FP
$FRQH =
/F =
= FP
× = FP ≅ FP
'HDFRUGRFRPDWDEHODRFRPSULPHQ
WRPtQLPRGRFKXPEDGRUVHUi/F [GF [
FP H D GLVWkQFLD PtQLPD HQWUH
FKXPEDGRUHVVHUi[ [GF [ FP
!FP(PERUD/F FPVHMDRQHFHVViULR
SDUD DWHQGHU D iUHD GR FRQH VHP
VREUHSRVLomRGHYHPRVXVDUR/FPtQLPRGH
FPHGLVWkQFLDHQWUHHOHV; FP
E±0pWRGR$,6&/5)'
$FKX =
= FP XVDU
× GFPtQ PP$ FP
$FRQH =
/F =
= FP
× = FP ≅ FP
'HDFRUGRFRPDWDEHODRFRPSULPHQWR
PtQLPRGRFKXPEDGRUVHUi/F [GF FP
HDGLVWkQFLDPtQLPD; [GF !FP
([HPSOR ± 'HWHUPLQDU VH R FRQH WHP
UHVLVWrQFLDSDUDVXSRUWDUDVFDUJDVLQGLFDGDV
QR H[HPSOR DQWHULRU SDUD FKXPEDGRUHV GH
PPWHQGRXPDGLVWkQFLDHQWUHHOHV
; FPFRP/F FP
(
)
× × &26− × +
$FRQH = × −
+ −
−
× + × = FP
D0pWRGR$,6&$6'
5FRQH [[ N1!
5FKX GF N1!2.7DE
E0pWRGR$,6&/5)'
5FRQH [[ N1!
5FKX GF N1!2.7DE
0HVPRFRPXPDVREUHSRVLomRDUHVLVWrQFLD
GRFRQHGHFRQFUHWRDWHQGH
&KXPEDGRUHV 5HFRPHQGDo}HV
D6REUHGLkPHWUR
'HYLGRjVGLILFXOGDGHVGHUHSDURQRVFKXPEDGRUHVpUHFRPHQGiYHOTXHRFDOFXOLVWDDGLFLRQHPP
DRGLkPHWURFDOFXODGRSDUDSHUPLWLUXPDPDLRUVREUHYLGD
E&KXPEDGRUHVVLWXDGRVHP]RQDGHFRUURVmR
2VFKXPEDGRUHVVLWXDGRVSUy[LPRD]RQDVFRPDOWRJUDXGHFRUURVmRGHYHUmRWHUVXDSDUWHH[WHUQD
]LQFDGDDIRJR
F&KXPEDGRUHVjWUDomR
3DUDFKXPEDGRUHVjWUDomRpSUXGHQWHFRORFDUGXDVSRUFDVSDUDDXPHQWDUDUHVLVWrQFLDGRVILOHWHV
GHURVFD)LJ
)LJXUD G±1LFKRV
$IROJDGRVQLFKRVSDUDDFRORFDomRGRVFKXPEDGRUHVGHYHVHUWDOTXHSHUPLWDXPDFRORFDomRIiFLO
VHPIROJDVH[DJHUDGDV$WDEHODLQGLFDHVWDVIROJDVSDUDFKXPEDGRUHVWLSR&$*
V
V
&KXPEDGRUHV ;
;
;
&DStWXOR
3ODFDVGHEDVH
3ODFDVGHEDVH
±,QWURGXomR
$OLJDomRGRSLODUFRPDIXQGDomRPHUHFH
HVSHFLDODWHQomRGRSURMHWLVWDFDOFXOLVWDSRLVR
FRPSRUWDPHQWRGDVHVWUXWXUDVHVWiLQWLPDPHQ
WHOLJDGRQHVWHVLVWHPDGHIL[DomR
(PJHUDORVSLODUHVVmRIL[DGRVjVIXQGD
o}HVDWUDYpVGHSODFDVGHEDVHHFKXPEDGRUHV
H[FHWRHPDOJXQVFDVRVHPTXHRVSLODUHVVmR
HPEXWLGRVGLUHWDPHQWHGHQWURGREORFRGHIXQ
GDomR9HU&DStWXOR
4XDQGRRVSLODUHVVmRODUJRVHVHTXHU
URWXODUXPGRVDUWLItFLRVpUHGX]LUDVXDODUJXUD
SUy[LPDjEDVH)LJF
(VWHVWLSRVGHEDVHVVmRDVPDLVHFRQ{
PLFDVSDUDDVIXQGDo}HVHSRGHPVHUXVDGDV
HPTXDOTXHUWLSRGHVROR
5HFRPHQGDPRVXPDHVSHVVXUDPtQLPD
GHPPSDUDDVSODFDVGHEDVHHGHPP
SDUDRVFKXPEDGRUHV
$VSODFDVGHEDVHWrPSRUILQDOLGDGHGLV
WULEXLUDVFDUJDVGRVSLODUHVHPXPDGHWHUPLQD
GDiUHDGREORFRGHIXQGDomRHRVFKXPED
GRUHVWrPSRUIXQomRIL[DUHVWDEDVHDREORFR
GHWDOPDQHLUDTXHRHVTXHPDHVWUXWXUDODGRWD
GRVHMDUHVSHLWDGR
1RGLPHQVLRQDPHQWRFRQVLGHUDPRVTXH
XPDGLIHUHQoDGHDWpQDHVSHVVXUDSRGHUi
VHUXWLOL]DGD
±7LSRVGHEDVH
([LVWHPSUDWLFDPHQWHGRLVWLSRVGLVWLQWRV
GHEDVHVSDUDXQLURSLODUjIXQGDomRTXHVmR
%DVHV URWXODGDV TXH UHFHEHP FDUJDV
D[LDLV
%DVHVHQJDVWDGDVTXHUHFHEHPFDUJDV
D[LDLVHPRPHQWRV
±%DVHVURWXODGDV
$V EDVHV URWXODGDV VmR GLPHQVLRQDGDV
VRPHQWH SDUD UHVLVWLU jV FDUJDV YHUWLFDLV GH
FRPSUHVVmRHKRUL]RQWDLVVHPWUDQVPLWLUPR
PHQWRjVIXQGDo}HV
$EDVHURWXODGDLGHDOVHDVVHPHOKDDXPD
UyWXODSHUIHLWD(VWHWLSRGHEDVHpSRXFRXWLOL
]DGRSRGHQGRWRUQDUVHFRPSOLFDGRDVXDID
EULFDomR)LJ D$EDVHURWXODGDPDLVVLP
SOHVpDIRUPDGDSRUXPDFKDSDVROGDGDQDEDVH
GRSLODUHSHODFRORFDomRGHGRLVFKXPEDGRUHV
QRFHQWURRPDLVSUy[LPRSRVVtYHOGRVHXHL[R
GHURWDomR)LJE
)LJXUD %DVHV URWXODGDV
±%DVHVHQJDVWDGDV
$VEDVHVHQJDVWDGDVVmRXVDGDVTXDQ
GRVHWHPDOpPGDVFDUJDVYHUWLFDLVHKRUL]RQ
WDLVHVIRUoRVGHPRPHQWRHWDPEpPTXDQGR
VHQHFHVVLWDGDUjHVWUXWXUDXPDPDLRUULJLGH]
jVGHIRUPDo}HVODWHUDLV
3DUDSODFDVGHEDVHHQJDVWDGDVUHFRPHQGD
VH XPD HVSHVVXUD PtQLPD GH PP H
FKXPEDGRUHVFRPGLkPHWURGHPP
3RUHVVHPRWLYRDVHVWUXWXUDVSRGHPVH
WRUQDUXPSRXFRPDLVHFRQ{PLFDVHPGHWULPHQ
WRGHIXQGDo}HVPDLVRQHURVDV
eRWLSRGHEDVHDGRWDGRQRFDVRGHSLOD
UHVLVRODGRVTXHVXSRUWDPSRQWHVURODQWHVTXH
SHUPLWHPHQRUGHIRUPDomRODWHUDO
6XDILQDOLGDGHpHQJDVWDURVSLODUHVjVIXQ
GDo}HVSRUPHLRGHXPDVpULHGHDUWLItFLRVWRU
QDQGRDVPDLVFRPSDWtYHLVHPUHODomRDRHV
TXHPDHVWUXWXUDODGRWDGR
6mRGLPHQVLRQDGDVSDUDUHVLVWLUjVFDU
JDVYHUWLFDLVKRUL]RQWDLVHDRVPRPHQWRVGH
HQJDVWDPHQWRV
$EDVHHQJDVWDGDPDLVVLPSOHVHDPDLV
XVDGDpDTXHODHPTXHRSLODUpVROGDGRjSOD
FDGHEDVHFRPRVFKXPEDGRUHVDIDVWDGRVGD
OLQKDGHFHQWURIRUPDQGRXPEUDoRGHDODYDQFD
)LJD4XDQGRDVFDUJDVVmRHOHYDGDVH
RFiOFXORLQGLFDFKDSDVFRPJUDQGHVHVSHVVX
UDVXVDVHRDUWLItFLRGHHQULMHFrODVFRPSH
TXHQDVQHUYXUDVSDUDVHREWHUHVSHVVXUDVPH
QRUHV)LJE2XWUDDOWHUQDWLYD pIL[DURV
FKXPEDGRUHVDXPDDOWXUDGHDPPGD
EDVHSURSRUFLRQDQGRXPyWLPRHQJDVWDPHQWR
(VWDVROXomRpPXLWRXVDGDHPJDOS}HVSHVD
GRV)LJF4XDQGRDFDUJDYHUWLFDOpSH
TXHQDHPUHODomRDRPRPHQWRDVROXomRpXVDU
WUDYHVVDVTXHSURSRUFLRQHPXPERPHQJDVWHH
XPJUDQGHDIDVWDPHQWRGRVFKXPEDGRUHVRTXH
SHUPLWHPHQRUHVGLkPHWURV)LJG
1RVSLODUHVWUHOLoDGRVQRUPDOPHQWHHQJDVWDGRV
SHODSUySULDFRQILJXUDomRDGRWDVHXPDEDVH
SDUDFDGDSpGHSLODU)LJ
)LJXUD ± %DVHV HQJDVWDGDV
)LJXUD ± %DVHV GH SLODUHV WUHOLoDGRV
3ODFDVGHEDVH
±&iOFXORGDVSODFDVGHEDVH
3ODFDVGHEDVHjFRPSUHVVmRD[LDO
SDUDSHUILV,H+
$VSODFDVGHEDVHGHSLODUHVVXEPHWLGRV
D FDUJDV YHUWLFDLV GH FRPSUHVVmR D[LDO
FHQWUDGDVVmRGHWHUPLQDGDVHPIXQomRGHXP
SHUFHQWXDOGDUHVLVWrQFLDFDUDFWHUtVWLFDIFNGR
FRQFUHWRGDEDVH
'HSRVVHGDFDUJD1$6'RX1X/5)'
HGDWHQVmROLPLWHGRFRQFUHWR)FGHWHUPLQDVH
DiUHDPtQLPDGDFKDSDVHQGRDVGLPHQV}HV
%H&XPSRXFRPDLRUHVGRTXHDVGLPHQV}HV
GRSLODUHDVHJXLUGHWHUPLQDVHDWHQVmRHIHWL
YDQRFRQFUHWRIFTXHpXQLIRUPHPHQWHGLVWULEX
tGDRXVHMD
IF 1
1X
HIFX %&
%&
2VYiULRVVHWRUHVGDSODFDVRIUHPGLYHU
VDVIRUPDVGHIOH[mR4XDQGRRSLODUpVROGDGR
jSODFDVHPQHQKXPUHIRUoRDGLFLRQDO)LJ
DH[LVWHPWUrVVHWRUHVSDUDFiOFXORGH PQQ¶
2VYDORUHVGH P HQ VmRGHWHUPLQDGRVSHODH[
WUHPLGDGHGDVFKDSDVTXHWUDEDOKDPFRPRFRQ
VROHVHGHYHPVHUGLPHQVLRQDGRVFRPRWDO
2VHWRU Q¶ pGHWHUPLQDGR HPIXQomRGD
UHODomR G [EIVHQGR
Q
=
GEI
(VWHpR~QLFRSURFHVVRSUiWLFRSDUDVHGHWHU
PLQDUDHVSHVVXUDGDSODFDTXDQGRDVGLPHQ
V}HVGDPHVPDVmROLJHLUDPHQWHPDLRUHVGR
TXHDVGRSHUILO)LJE
'HSRVVHGRVYDORUHVFDOFXODGRVXVDQGR
RPDLRUGRVWUrVGHWHUPLQDVHDHVSHVVXUDGD
FKDSDGHVWDFDQGRVHXPDIDL[DFRPODUJXUDGH
FP
)LJXUD ± (VTXHPD SDUD FiOFXOR GH SODFD GH EDVH FRP
FDUJD D[LDO SDUD SHUILV , RX +
3DUkPHWURVSDUDFiOFXORGDHVSHV
VXUDGDVSODFDVGHEDVH
P & −G
Q % −EI
GEI
$ %[& iUHDGDSODFDHPFPGHWHUPLQDGD
HPIXQomRGH)F
$ iUHDGDFDEHoDGREORFRGHFRQFUHWR
HPFP ≤ $
)F WHQVmRDVHUXVDGDQRFRQFUHWRHPIXQomR
GHIFNHPN1FP
1
1X
RXIFX WHQVmRDWXDQWHQR
$
$
$
$
FRQFUHWRHPN1FP IF IFN UHVLVWrQFLDSUHYLVWDSDUDRFRQFUHWRDRV
GLDVHPN1FP
Δ GEI
Q¶ 'LPHQVLRQDPHQWR
D0pWRGR$,6&$6'
1 FDUJDYHUWLFDO
)E )\
)F = IFN
$
≤ IFN
$
IF 1
)F IFNSDUD$ $
$
$
$ ≤
IF 1
)F IFNSDUD$ $
$
$ ≤
0 : IFO
RQGH O PDLRUGHPQQ¶
W
1S FDUJDOLPLWHQRFRQFUHWR
1X ϕF1S
W HVSHVVXUDGDSODFDHPFP
IFO
W
IF
WHPRV W = O )\
3DUD
)\ N1FP
$
ϕFIFN$
$
$
ϕF ±IDWRUGHUHVLVWrQFLDDRHVPDJDPHQWR
QRFRQFUHWR
1S ϕFIFN$
,JXDODQGRRVGRLV)EWHPRV
)\ )EX )\
1X FDUJDYHUWLFDOIDWRUDGD
0 IFO
)E =
:
W
E0pWRGR$,6&/5)'
1X IFN$
W = O IF
)\ N1FP
W = O IF
)\ N1FP
W = O IF
$UHVLVWrQFLDDGPLVVtYHOGRFRQFUHWRp
FDOFXODGDHPIXQomRGDUHODomR
$
$
$
3DUDIDFLOLWDULQGLFDPRVQD7DEHODRVYDORUHV
GH)FQRLQWHUYDORHQWUH$ $D$ $
SDUDXPIFN N1FP 03D
)FX IFN
$
IFN$
$
$ ≤
$
IFN
$
$ ≤
IFX 1X
IFNSDUD$ $
$
$
$ ≤
IFX 1X
IFNSDUD$ $
$
$ ≤
0X IFXO
φE0Q!0X
)EX 0X
:
RQGH O pRPDLRUGHPQQ¶
φE 0Q φE0S φE :)\
H
φE 0S )\1XW
)\W
φE :)\ : W 3ODFDVGHEDVH
LJXDODQGR0X 0SWHPRV
IFXO
W =
=
)\W
IFX
IFXO
W = O
⇔
)\
)\
3DUD
)\ N1FP
W = O IFX
)\ N1FP
W = O IFX
)\ N1FP
W = O IFX
$UHVLVWrQFLDPi[LPDGRFRQFUHWRpFDOFXODGD
$
$
$
3DUDIDFLOLWDULQGLFDPRVQD7DEHODRV
YDORUHVGH)FXQRLQWHUYDORHQWUH$ $D$
$SDUDXPIFN N1FP 03D
HPIXQomRGDUHODomR
±3ODFDVGHEDVHSDUDSHUILVWXEXODUHV
3DUDRVSHUILVFRPIRUPDGHWXERVWLSRV
FLUFXODUHVTXDGUDGRVHUHWDQJXODUHV FDOFX
ODVHDSHQDVRVSDUkPHWURVPHQFRQIRUPH
LQGLFDGRQD)LJHRGLPHQVLRQDPHQWRGDV
SODFDV p IHLWR FRQIRUPH LQGLFDGR SDUD R GRV
SHUILV,RX+
)LJXUD ± (VTXHPD SDUD FiOFXOR GD SODFD GH EDVH SDUD
SHUILV WXEXODUHV
([HPSOR 'HWHUPLQDUDHVSHVVXUDGDSODFD
GHEDVHSDUDXPSHUILO:[NJPEI FPG FPWI FPVXMHLWRDXPD
FDUJDGHFRPSUHVVmRGH
1&3 N11&$ N1
$oRGDSODFD
)\ N1FP
&RQFUHWRGDEDVHIFN N1FP
D0pWRGR$,6&$6'
1 N1
&RQVLGHUDQGR$ $
)F [ N1FP 7DE
FP
$ Δ GEI
Δ [[ VHQGR&
FP
$+Δ ⇔
N1FP 2.
[
&iOFXORGRVSDUkPHWURV
− × FP
− × FP
Q P Q
=
× = FP
− [
FPHQ¶ FP
&RPLVWRIF N1FP
× W × FP
3ODFDGHEDVH &K[[PP
ÈUHDGREORFR$ [[ FP
%ORFRGH[ FP
&RQVLGHUDQGR FRPR DOWHUQDWLYD XP EORFR
GHFRQFUHWR $ [ FP HDSODFD
GHEDVH$ [ FP
⇔ FP
% 7HQVmRQRFRQFUHWR
IF Q JRYHUQD
±&iOFXORGDHVSHVVXUDGDSODFD
W = × = FP
W FPXVDUPP
$
$
$
3DUDHVWDUHODomR)F N1FP 7DE
WHPRV
9DQWDJHP HP UHODomR j DQWHULRU PHQRU
EORFRGHIXQGDomR
E±0pWRGR$,6&/5)'
$VFDUJDVIDWRUDGDVVmR
1X [[ N1
&RQVLGHUDQGR$ $
)FX [ N1FP 7DE
&RPR$pSUDWLFDPHQWHRPHVPRGRPpWRGR
DQWHULRUYDPRVXVDU% FPH
& FP
3ODFDGHEDVH&K[[PP
7HQVmRQRFRQFUHWR
&RPRRYDORUTXHHVWiJRYHUQDQGRpFP
SRGHPRVDPSOLDURWDPDQKRGDSODFDHSDVVDU
DVGLPHQV}HVSDUD[FPGDQGR
− [
FP
P IFX )FX
× P FPQ FPHQ¶ FP
W = × = FP
3ODFDVGHEDVH
3ODFDGHEDVH&K[[PP
([HPSOR± 'LPHQVLRQDUDSODFDGHEDVHH
FKXPEDGRUHVSDUDXPSHUILOWXEXODUUHGRQGR [PP VXMHLWRjVVHJXLQWHVFDUJDV
1&3 N1
1&$ N1
+&$ N1
+&3 N1
)\SODFD N1FP IFN N1FP
&KXPEDGRUHV6$(
)D]HQGR$ &SRUTXHVW}HVFRQVWUXWLYDV
$ & ⇔ FP
7HQVmRQRFRQFUHWR
IF 2N
× &iOFXORGRSDUkPHWUR P P − × FP
W × ≅ PP
3ODFDGHEDVH&K[[PP
&iOFXORGRVFKXPEDGRUHVDFLVDOKDPHQWR
+ N1
FP
GF FRUURVmR FP PP
GF E±0pWRGR$,6&/5)'
)F 7DE[ N1FP
1X [[ N1
7HQVmRQRFRQFUHWR
IFX × 2.
WS × ≅ PP
3ODFDGHEDVH&K[[PP
D±0pWRGR$,6&$6'
&iOFXORGRVFKXPEDGRUHV
1 N1
+X [[ N1
&RQVLGHUDQGR$ $
)F 7DE[ N1FP
GF $QHF FP
FP
GF FP XVDUGF PP
([HPSOR± 'LPHQVLRQDUDSODFDGHEDVHH
RVFKXPEDGRUHVSDUDXPSHUILOWXEXODUUHWDQJXODU
[[PPVXMHLWDjVVHJXLQWHVFDUJDV
1&3 N1
+&3 N1
)\SODFD N1FPT
&KXPEDGRU6$(
1&$ N1
+&$ N1
IFN N1FP
7HQVmRQRFRQFUHWR
IF 2.
× &iOFXORGRVSDUkPHWURV P H Q P Q − × FP
− × FP
W × FP
3ODFDGHEDVH&K[[PP
&iOFXORGHFKXPEDGRUHV
+ N1
FP
GF FPXVDUGF PP
GF E±0pWRGR$,6&/5)'
1X [[ N1
)FX 7DE[ N1FP
7HQVmRQRFRQFUHWR
IFX 2.
× W × FP
3ODFDGHEDVH&K[[PP
D±0pWRGR$,6&$6'
&iOFXORGHFKXPEDGRUHV
1 N1
&RQVLGHUDQGR$ $
+X [[ N1
)F [ N1FP WDE
GF 'LPHQV}HVGDSODFDSRUPRWLYRVFRQVWUXWLYRV
& FPH$ FP
FP
GF FPXVDUGF PP
3ODFDVGHEDVH
±3ODFDVGHEDVHjWUDomR
(PFHUWDVFRQGLo}HVDVSODFDVGHEDVH
SRGHPHVWDUVXMHLWDVDXPDFDUJDD[LDOGHWUD
omRQHVWHFDVRKDYHUiQHFHVVLGDGHGHXPD
YHULILFDomRGDUHVLVWrQFLDGDPHVPDjIOH[mR
(PJHUDOHVWDVSODFDVWrPDSUR[LPDGDPHQWHR
PHVPRWDPDQKRGRSLODUFRPRDSUHVHQWDGRQD
)LJ2VFKXPEDGRUHVHPEXWLGRVQRFRQFUH
WRGHYHPUHVLVWLUDRHVIRUoRGHWUDomRMXQWD
PHQWHFRPDSODFD
W=
1WJ
1WJ
W = ⇔
EI)\
EI)\
3DUD
)\ N1FP W = 1WJ
EI
)\ N1FP W = 1WJ
EI
)\ N1FP W =
1WJ
EI
6HEI!G
W=
1WJG
1WJG
⇔ )\(G + EI)
)\(G + EI )
SDUD
1WJG
)\ N1FP ⇔ W= G + EI
(
)
1WJG
)\ N1FP ⇔ W= (G + EI )
1WJG
)\ N1FP ⇔ W= G + EI (
E0pWRGR$,6&/5)'
6HEI ≤ GVHQGR φE = )LJXUD±3ODFDVGHEDVHjWUDomR
±'LPHQVLRQDPHQWR
D0pWRGR$,6&$6'
2$,6&$6'XVDXPFRHILFLHQWHGHVHJXUDQoD
LJXDODHLPS}HDFRQGLomR
6HEI ≤ G
W=
1XWJ
φE EI)\
1XWJ
⇔ W EI)\
3DUD
)\ N1FP
⇔
)\ N1FP
⇔
W = 1XWJ
EI
W = 1XWJ
EI
)
)\ N1FP
⇔
W = 1WXJ
EI
EI [ FP
6HEI!G
W D0pWRGR$,6&$6'
1XW JG
1XWJG
)\G + EI
)\G + EI 3DUD
1XWJG
)\ N1FP ⇔ W = G + EI
)\ N1FP ⇔ W = 1XWJG
G + EI
)\ N1FP ⇔ W = 1XWJG
G + EI
([HPSOR 'HWHUPLQDUDHVSHVVXUDGDSODFD
GHEDVHSDUDVXSRUWDUXPDFDUJDGHWUDomR1W
N1 GHYLGR DR YHQWR 2 SLODU XP :
[FRPG FPHEI FP
$GLVWkQFLDHQWUHFKXPEDGRUHVJ FP
&KDSDGHDoR)\ N1FP
&RPRDFDUJDpGHYHQWRSHUPLWHXPDUHGXomR
GHHQWmRWHPRV
1W [ N1
W = × FPPP
3ODFDGHEDVH&K[[PP
7FKXPE N1!GF PP7DE
N12.
E0pWRGR$,6&/5)'
EI [ FP
2IDWRUGHFDUJDSDUDRYHQWRpGDQGR1XW
[ N1
W = 1XWJ
× ⇔ W = = FP
EI
3ODFDGHEDVH &K[[P
7XFKXPE N1GF PP7DE
N12.
±3ODFDVGHEDVHjFRPSUHVVmR
D[LDOFRPPRPHQWR
$SODFDGHEDVHGHXPSLODUVXEPHWLGRj
FRPSUHVVmRH[FrQWULFDRXVHMDFRPPRPHQ
WRVH[HUFHXPDSUHVVmRLUUHJXODUVREUHDVX
SHUItFLHGREORFRGHIXQGDomR$SODFDFRPSUL
PHDFDEHoDGREORFRGHIXQGDomRQRVHQWLGR
GHDomRGRPRPHQWRHQTXDQWRGRRXWURODGR
VHYHULILFDDVXDWHQGrQFLDGHVHGHVSUHQGHU
GDVXSHUItFLHGDPHVPD)LJRTXHpLP
SHGLGRSHODDomRGRVFKXPEDGRUHVGHDQFR
UDJHPeRFDVRWtSLFRGHEDVHVHQJDVWDGDV
1RSURFHVVRGHFiOFXORDGRWDVHHPSUL
3ODFDVGHEDVH
PHLUROXJDUDODUJXUDGDSODFD2FRPSULPHQWR
/GDSODFDGHEDVHpGHWHUPLQDGRGHWDOIRUPD
TXHDWHQVmRPi[LPDGRFRQFUHWRMXQWRjH[WUH
PLGDGHIFVHMDLQIHULRUjWHQVmROLPLWHjFRP
SUHVVmR)F
IFPi[ 1 0
1 0
+
=
+
)F
%/
: %/ %/ ≤
1HVWHFDVRDWHQVmRGHWUDomRPtQLPDTXH
VHYHULILFDQDH[WUHPLGDGHRSRVWDGDSODFDp
IFPLQ 1 0
1 0
−
=
−
%/
: %/ %/
FDVHVHDVWHQV}HVPi[LPDVHVWmRGHQWURGR
SUHYLVWR&DVRFRQWUiULRGHWHUPLQDVHRYDORU
PtQLPRGH/LJXDODQGRVHjSULPHLUDHTXDomR
FRPIF
1
+
/ %IF
⎛ 1 ⎞
0
⎜⎜
⎟⎟ +
%IF
⎝ %IF⎠
'HSRVVHGDVGLPHQV}HVILQDLVGDSODFD
ID]VH D GHWHUPLQDomR GH VXD HVSHVVXUD GH
DFRUGRFRPRGLDJUDPDGHWHQV}HVRXGHXPD
PDQHLUDPDLVVLPSOLILFDGDFRQVLGHUDQGRDFDU
JDXQLIRUPHPHQWHGLVWULEXtGDSDUDRVHWRUTXH
HVWiVHQGRDQDOLVDGR9HUH[HPSOR
1RFiOFXORGRVFKXPEDGRUHVSDUWHVHGD
VXSRVLomRGHTXHDIRUoDGHWUDomR7GHWHUPL
QDGDSHOD]RQDWUDFLRQDGDGRGLDJUDPDGHWHQ
V}HV)LJpVXSRUWDGDWRWDOPHQWHSHORV
FKXPEDGRUHV3DUDLVVRFRPS}HVHDHTXDomR
GHHTXLOtEULRHPUHODomRDRFHQWURGHJUDYLGDGH
GD]RQDFRPSULPLGDWULDQJXODUGRGLDJUDPDGH
WHQV}HVREWHQGRVH
01D±7\ 2 HVIRUoR WRWDO 7 DWXDQWH HP WRGRV RV
FKXPEDGRUHVGRODGRGD]RQDWUDFLRQDGDVHUi
7 0 − 1D
\
'DFRUUHODomRJHRPpWULFDGHWHUPLQDVH
IFPD[/
/ &
−
VHQGR& IF + IF PD[
PLQ
IFHPYDORUDEVROXWR
D \ / −
)LJXUD ± %DVH HQJDVWDGD
&DVRMiVHWHQKDGHWHUPLQDGRRFRPSUL
PHQWRGDSODFDSRUUD]}HVFRQVWUXWLYDVYHULIL
&
− H
2EVHUYDo}HV
3DUD1D!0QmRKiWUDomRQRFKXPEDGRUH
QHVWHFDVR& /
3DUD1 & /
3DUDRFiOFXORGDHVSHVVXUDGDSODFDGH
EDVHHGRFKXPEDGRUpSUHFLVRDGRWDUDVFRP
ELQDo}HV GH FDUJD PDLV GHVYDQWDMRVDV SDUD
FDGDXPSRLVDSLRUSDUDDSODFDSRGHQmR
VHUDSLRUSDUDRVFKXPEDGRUHV
&RQFUHWRGDEDVHIFN N1FP
&RQVLGHUDU$a$
D0pWRGR$,6&$6'
$IRUPXODomRGDGDSHUPLWHFDOFXODUDHV
SHVVXUDGDSODFDGHEDVHHGRFKXPEDGRUSHOR
0pWRGRGDVWHQV}HV DGPLVVtYHLV $,6&$6'
RX SHOR 0pWRGR GRV HVWDGRV OLPLWHV$,6&
/5)'
IF
1
0
+
IFN [ N1FP
N1
N1FP
N1
D0pWRGR$,6&±$6'
1 &DUJDYHUWLFDODWXDQWHHPN1
0 PRPHQWRDWXDQWHHPN1FP
)F IFN
W $
≤ IFN
$
$
0S
0S
W ⇔
)\
)\
E±0pWRGR$,6&/5)'
1X &DUJDYHUWLFDODWXDQWHIDWRUDGDHPN1
0X 0RPHQWRDWXDQWHIDWRUDGRHPN1FP
)FX × IFN
)FX IFN
W $
$
[[IFN
$ ≤
$
IFN
$
$ ≤
0SX
0SX
⇔ W = )\
)\
([HPSOR ±3URMHWDUHGLPHQVLRQDUDSODFD
GHEDVHGRSLODU&96[NJP
EI WI WZ FP VXMHLWR jV
VHJXLQWHVFDUJDV
1&3 N1
0&3 N1FP
+&3 N1
1&$ N1
0&$ N1FP
+&$ N1
3ODFDGHEDVH)\ N1FP
&KXPEDGRU6$(
&iOFXORGH/
1
+
/ %IF
⎛ 1 ⎞
0
⎜⎜
⎟⎟ +
%IF
⎝ %IF⎠
3ODFDVGHEDVH
⎞ × ⎛
+ ⎜
⎟ +
/ × × ⎝ × × ⎠
× / FPDGRWDGR
± &iOFXORGRVFKXPEDGRUHVFRPFKDSDRX
SRUFDLQIHULRU
)X N1FP
)W )X N1FP
)Y )X N1FP
&iOFXORGHIF
IFPD[
3ODFDGHEDVH&K[[PP
& FP
1
0
× +
+
/%
%/ × × < /−
IFPLQ N1FP
&iOFXORGH&
IFPD[/
× = FP
& IF + IF
PD[
PLQ
&iOFXORGDHVSHVVXUDGDSODFD
− H = − − = FP
D / &
− = − = FP
7 0 − 1D − [
=
= N1
\
IFPD[IFPLQ N1FP
&
6HMDGF PP$ FP
8VDQGRFKXPEDGRUHV
IW × IY × I IW + IY + × &iOFXORGDVROGDGHOLJDomR3LODU±SODFD
GHEDVH
K FP
)LJXUD 0S
W )\
× × +
N1FP
0S W = FP ≅ PP
:V EK+
EK
SRUFP
FP
3V [[ FP
:V [ +
IE N1FP
IY N1FP
IV + × N1FP
DV 7DE$ VROGDGHPP
IFXPD[IFXPLQ &iOFXORGH&
E±0pWRGRGR$,6&/5)'
& IFX [ N1FP
1X [[ N1
× FP
&iOFXORGDHVSHVVXUDGDSODFD
0X [[ N1FP
+X [[ N1
)LJXUD W 0SX
)\
× × +
N1FP
0SX W )LJXUD &iOFXORGH/
FP
3ODFDGHEDVH&K[[PP
⎛
⎞ × + ⎜
⎟ +
/ × × ⎝ × × ⎠
× &iOFXORGRVFKXPEDGRUHVFRPFKDSDRX
SRUFDLQIHULRU
/ DGRWDGR2.
)WX [ N1FP
&iOFXORGHIFX
)YX [ N1FP
× +
IFXPD[ × × IFXPD[ 2.
IFXPLQ ± N1FP
& FP
< / =
&
− H ± FP
3ODFDVGHEDVH
D / &
−
7X ± FP
0X−1XD − × =
<
±3ODFDVGHEDVHFRPUHIRUoR
3DUDSLODUHVVXMHLWRVDFDUJDVGHJUDQGH
LQWHQVLGDGHDVSODFDVSRGHPUHVXOWDUHPHV
SHVVXUDVH[FHVVLYDV8PDDOWHUQDWLYDpDFROR
FDomRGHFKDSDVGHUHIRUoRFRPRDSUHVHQWD
GRQDILJXUD
N1
6HMDGLkPHWURGHPP
IWX N1N1FP
× IYX N1N1FP
× (VWHVUHIRUoRVDWXDPMXQWDPHQWHFRPD
SODFDSDUDUHVLVWLUDRVHVIRUoRVGHIOH[mR
$ SODFD GH EDVH SDVVD HQWmR D VHU
GLPHQVLRQDGDFRPRYLJDFRQWtQXDSHUSHQGLFX
ODUjVFKDSDVGHUHIRUoR
'HDFRUGRFRPDVILJXUDVFRQWLGDVQD)LJ
LQFOXtPRVQHVVHLWHPIRUPXOiULRVHVSHFtIL
FRVGHDFRUGRFRP5RDUN5-H<RXQJ&:DUUHQ
±)RUPXODVIRU6WUHHVDQG6WUDLQ±D
$HVSHVVXUDGDSODFDSDUDWRGRVRVFD
VRVVHUiGLPHQVLRQDGDSRU
IX + × ≅ 2.
$,6&$6'W E
β IF
)\
$,6&/5)'W E
β IFX
)\
6ROGDGDOLJDomR3LODUSODFD
: FP FP
3HULPHWURVROGD FP
IEX N1FP
IYX N1FP
±3ODFDHQJDVWDGDQRVODGRV
IVX + × N1FP
6ROGDGHPP N1FP
DV PP7DE$
D
E
ȕ
±3ODFDHQJDVWDGDHPWUrVODGRVHXPOLYUH
D
E
ȕ
±3ODFDDSRLDGDHPWUrVODGRVHOLYUHHPXP
D
E
ȕ
±3ODFDDSRLDGDQRVTXDWURODGRV
±3ODFDHQJDVWDGDHPXPODGRDSRLDGDHP
GRLVHOLYUHHPXP
D
E
ȕ
D
E
ȕ
±3ODFDHQJDVWDGDHPGRLVODGRVHOLYUHHP
RXWURVGRLV
±&iOFXORGDVFKDSDVGHUHIRUoR
$VROXomRPDLVIiFLOHVLPSOHVGHVHIDEUL
FDUXPDSODFDGHEDVHpXPDSODFDVLPSOHVVHP
UHIRUoRVPDVjVYH]HVSRUTXHVW}HVGHHVWR
TXHHRXGLILFXOGDGHGHDTXLVLomRWHPRVQH
FHVVLGDGHGHXVDUXPDFKDSDPDLVILQDTXH
VypSRVVtYHOVHFRORFDUPRVUHIRUoRVSRUPHLR
GHRXWUDVFKDSDVTXHpRQRVVRREMHWLYRQHVWH
LWHP
2FiOFXORGDFKDSDGHUHIRUoRpIHLWRGH
XPDPDQHLUDVLPSOHVDFKDQGRVHDSDUFHODGD
SUHVVmR TXH D PHVPD HVWD VXMHLWD H
GLPHQVLRQiOD
D
E
ȕ
(PJHUDODVELEOLRJUDILDVFRQVXOWDGDVUH
FRPHQGDPTXHDDOWXUDGDFKDSDGHYHVHUDSUR
3ODFDVGHEDVH
[LPDGDPHQWHRGREURGDVXDODUJXUDHWHUXPD
UHODomRODUJXUDHVSHVVXUDGHQWURGRHVSHFLIL
FDGRSHODVQRUPDV
3DUDXPPHOKRUHQWHQGLPHQWRYDPRVID]HUGRLV
H[HPSORVSDUWLQGRGHH[HPSORVMiH[HFXWDGRV
W3 × × FP
6HWRU
([HPSOR±6HMDRH[HPSORSDUDXPD
SODFDGHEDVH[XVDQGRFKDSDGHUHIRUoR
FRQIRUPHLQGLFDGR
1 N1
P FP
Q¶ FP
D E D E 1X N1
Q FP
ȕ W3 × FP
3ODFDGHEDVH&K[[PPDQWHULRU
&KPPQHVWHFDVRQmRKRXYHJDQKR
&iOFXORGDFKDSDGHUHIRUoR
D0pWRGR$,6&$6'IF N1FP
±&iOFXORGDSODFDGHEDVH
6HWRU
D E FP
D E
ȕ
)LJXUD $FKDSDGHUHIRUoRHVWDUiVXMHLWDDRHVIRUoR
GHPRPHQWR
× × N1FP
0&+ 6HMDXPDFKDSDGH[[FP
:&+
IE × FP
)\ N1FP 2.
EW )\
&KDQWHULRUQHVWHFDVRQmRKRXYH
YDQWDJHP
±9HULILFDomRGDFKDSDGHUHIRUoR
0FK
[[
9HULILFDomRDRFLVDOKDPHQWR
:FK × × )\ N1FP
IY × IEX × N1FP
FP
)\ N1FP 2.
±9HULILFDomRGDVROGD
[[
)\ N1FP
IYX [
&DUJDQDVROGD1V [[ N1
±9HULILFDomRGDVROGD
/ILOHWH FP
)RUoDQDVROGD1VX [[ N1
)V N1FP
/ILOHWH FP
)VX 6ROGDGHFP N17DE$
DV FPVROGDGHPP
6ROGDPtQLPDGHYLGRDHVSHVVXUDGHPP
6HUiGHPP7DE$
N1FP
6ROGDGHFP N17DE$
DV FPVROGDGHPP
6ROGDPtQLPDPP7DEHOD$
E0pWRGR$,6&/5)'
IFX N1FP
±&iOFXORGDSODFDGHEDVH
6HWRUSLRUFDVR
W3 × FP
× 3ODFDGHEDVH&K[[PP
3ODFDVGHEDVH
([HPSOR ±6HMDRH[HPSORFRPFKDSD
GHUHIRUoR
W3 × FP
3ODFDGHEDVH&K[[PP
DQWHULRU&KGHPP
±&iOFXORGDFKDSDGHUHIRUoR
× × 0FK
:FK N1FP
WFK ×
WFK
)E[ )\ [ N1FP
0
)E[
: FPXVDUFKPP
× &K[[PP
WFK × × )\ N1FP
IY × ±9HULILFDomRGDVROGD
D±0pWRGR$,6&$6'
1 N10 N1FP
IF N1FP
IE [ N1FP
16 [[ N1
/ILOHWH FP
)6 &iOFXORGDSODFDGHEDVH
D6 6HWRU
D FPE FP
N1FP
FP
XVDUVROGDPtQLPDGHPP7DEHOD$
E±0pWRGR$,6&/5)'
D
E ȕ 1X N10X N1FP
IFX N1FP
)EX [ N1FP
&iOFXORGDSODFDGHEDVH
6HWRU
W3 × FP
3ODFDGHEDVH &KGH[[PP
&KDQWHULRUQHVWHFDVRQmRKRXYH
YDQWDJHP
9HULILFDomRGD&KPPGHUHIRUoR
0FK
× × N1FP
)EX )\ [ N1FP
:FK IE × FP
D±0pWRGR$,6&$6'
&iOFXORGDSODFDGHEDVH
6HWRU
D FPE FP
2.
D
E [[
IY N1FP
[
ȕ 9HULILFDomRGDVROGD
1VX [[ N1
/ FP
)VX FP
DV VROGDPtQLPDPP7DE$
([HPSOR 2PHVPRH[HPSORDQWHULRUFRP
DFRORFDomRGHPDLVXPDFKDSDGHUHIRUoRHQWUH
RVFKXPEDGRUHV
W3 [ FP
8VDU&K[[PPDQWHULRUPP
&iOFXORGDFKDSDGHUHIRUoR
0FK × × N1FP
WFK × &K[[PPPLQLPD
:FK WFK
IY × × × N1FP
3ODFDVGHEDVH
±9HULILFDomRGDVROGD
1V [[ /6 FP
)V D6 N1FP
FP
8VDUVROGDPtQLPDGHPP7DEHOD$
E±0pWRGR$,6&/5)'
±&iOFXORGDSODFDGHEDVH
WS × FP
3ODFDGHEDVH&K[[PP
DQWHULRUPP
±9HULILFDomRGDFKDSDGHUHIRUoR
0FK :FK
× × N1FP
× FP
IEX N1FP
IYX × × 2.
× 8VDUFKDSDGHUHIRUoRPtQLPDGH
&K[[
±9HULILFDomRGRILOHWHGHVROGD
1VX [[ N1
/ILOHWH FP)VX N1FP
FPXVDUVROGDPtQLPDGH
PPGHYLGRDHVSHVVXUDGDSODFDGHEDVH
DV ([HPSOR ±'LPHQVLRQDUDSODFDGHEDVH
HDVFKDSDVGHUHIRUoRSDUDRSLODULQGLFDGR
QDILJXUDVXMHLWRjVVHJXLQWHVFDUJDV
1&3 N11&$
0&3 N1FP0&$
+&3 N1+&$
IFN
)\ N1FP
N1
N1FP
N1
N1FP
&iOFXORGRVFKXPEDGRUHV
D0pWRGR$,6&$6'
1 N1
0 N1FP
+ N1
)D]HQGR$ $ IF WDE
±&iOFXORGRVSDUkPHWURV
1
+
/ ×%× IF
⎛
0
1 ⎞
⎜⎜
⎟⎟ +
%× IF
⎝ × %× IF⎠
FP2.
&
±H FP
D / & − =
− FP
7 0 −1× D − × =
N1
<
6HMDGF PP$ FP
IW ⎛ ⎞ × + ⎜
⎟ +
/ [× ⎝ [× ⎠
× N1FP
× IY × I + × &iOFXORGHIF
IFPD[ < /±
× 1
0
+
+
× × %× / %× /
2.
&iOFXORGDSODFDFRQVLGHUDQGRUHIRUoR
6HWRU
N1FP 2.
IFPLQ ± DE IFPD[IFPLQ N1FP
ȕ &iOFXORGH&
& IFPD[ × /
× FP
IFPD[ + IFPLQ
& 6HWRU
FP
DE &iOFXORGDHVSHVVXUDGDSODFDVHP
UHIRUoR
× 0S W ȕ N1FP
FP ⇒ PP
W3 E β× IF
×
FP
× )\
3ODFDVGHEDVH
8VDU&K[[PP
±&iOFXORGDVFKDSDVGHUHIRUoR
&DOFXODQGRRPRPHQWRTXHDFKDSDYDLDEVRU
YHUSRUVHWRUGHDFRUGRFRPDiUHDGHLQIOXrQ
FLD
× ,\ U\ FP
FP
)D )\[3
3 )\ λ 3 [ Ȝ )D [[ N1FP
)LJXUD 9HULILFDomRjIOH[mR
ID IE +
=
+
2.
)D )E ±&iOFXORGDFKDSDVXSHULRU
× × N1FP
6HMD&K[[
0 :FK
× FP
IE )\ N1FP
EW 2.
)LJXUD ȕ 9HULILFDomRDRFLVDOKDPHQWR
DE 1FK [[ N1
I&+6 × [FKDSDV IY N1FP
× × 9HULILFDomRjFRPSUHVVmRFRPIOH[mR
W&+6 $FK [ FP
8VDU&K[[PP
ID N1FP
FP
±&iOFXORGDVROGD
&iOFXORGH&
&RQVLGHUDQGRFRUG}HVGHVROGD
× FP
& FP
& /V FP
)V = ±&iOFXORGDHVSHVVXUDGDSODFDVHP
UHIRUoR
5VGHFP N1FP
× 0SX FPXVDUILOHWHGHPP
W E±0pWRGR$,6&/5)'
±&iOFXORGRVFKXPEDGRUHV
1X [[ N1
< FP
0X [[ N1FP
D − FP
+X [[ N1
7 − × N1
IFX [ N1FP 7DE
N1FP
FP
× 6HMDGF PP$ FP
±&iOFXORGRVSDUkPHWURV
IWX &iOFXORGH/
⎛ ⎞ × + ⎜
⎟ +
/ [× ⎝ × [⎠
× FP2.
&iOFXORGHIFX
IFXPD[
× +
× × N1FP 2.
IFXPLQ N1FP
× IYX × IX + + × 2.
±&iOFXORGDSODFDFRQVLGHUDQGRUHIRUoR
DE WS β [
FP
[
IFXPD[IFXPLQ N1FP
3ODFDVGHEDVH
&K[[PP
±&iOFXORGDVFKDSDVGHUHIRUoR
9HULILFDomRDIOH[mR
× × W&+ × FP
× &K[[PP
0FK N1FP
6HMDXPDFKDSDGH[[FP
:FK × = FP
XVDUILOHWHPtQLPRGHPP
([HPSOR ±'HWHUPLQDUDHVSHVVXUDGDSOD
FDGHEDVHHRGLkPHWURGRVFKXPEDGRUHVSDUD
DFROXQDWUHOLoDGDVXMHLWDDRVHVIRUoRVLQGLFD
GRVQDILJXUD
EW 9HULILFDomRDRFLVDOKDPHQWR
1FX [[ N1
IYX )VX D FP
IE &iOFXORGDVROGD
N1FP
× )\ N1FP
$ $
IFN N1FP
$/7(51$7,9$,
9HULILFDomRjFRPSUHVVmRFRPIOH[mR
Ȝ )FU )\R3
3 )\ λ )FU N1FP
ID N1FP
× +
2.
&iOFXORGDFKDSDVXSHULRU
DE I&+ × ȕ &DUJDV
%DVH$&RO95
1&3 N1
135PD[ N1SRQWHURODQWH
135PLQ N1SRQWHURODQWH
+35 N1+9 N1YHQWR
%DVH%&RO&RE
1&$ N1FREHUWXUD
1&3 N1
+9 N1YHQWR
0RPHQWRV
035 ± N1P0Y N1P
D±0pWRGR$,6&$6'
$ $7DE!!)F N1FP
)DWRUGHUHGXomRGRYHQWR
D%DVH$
1 N1
1 × N1
1 N1
2EV1RVRPDWyULRGDVFDUJDVTXDQGRVRPD
PRVFDUJDGDVSRQWHVURODQWHVFRPYHQWRXVDU
DSHQDVGHXPDGHODVHPXOWLSOLFDURUHVXO
WDGRSRUVLJQLILFDDXPHQWDUDVWHQV}HVHP
+ N1
+ [ N1
+ N1
±&iOFXORGDSODFDGHEDVH
W3 O IF [ &K[[PP
±&iOFXORGRV&KXPEDGRUHV
1 N1+ N1
6HMDGF PtQLPRGHPP $ FP
IW IY × × I + × 1 N1
⎛
× ⎞
⎟
N1
1 ⎜⎜ +
⎟⎠
⎝
±&iOFXORGDSODFDGHEDVH
IF 2.
× W3 [ FP
&K[[PP
±&iOFXORGRVFKXPEDGRUHV
[ IF × 1 ±
− × FP!JRYHUQD
P − × FP
N1FP
D±%DVH%
'LPHQVmRPtQLPDGDSODFDGHEDVH[FP
Q FP
N1
+ [
N1
1 1 Q¶ N1
⎛
× ⎞
⎟
N1
1 ⎜ − −
⎠
⎝
+ N1
3ODFDVGHEDVH
6HMDGF IW $ FP
× N1FP
× IYX N1FP
× IX + × 2.
IY IFX + [ N1FP2.
E±0pWRGR$,6&/5)'
$ $7DE!!)XF N1FP
E±%DVH$
1X 1&31&$135 [[ N1
[
N1
1X 1X 1&31&9
[
N1
1X 1&3[135035
[[ N1
[
E±%DVH%
[
N1
1X [[
[+ [
1X [[
N1
[+ [
1X [[
N1
1X [
[+ [
N1
±&iOFXORGDSODFDGHEDVH
IFX × WS [ +X [[[ N1
&K[[PP
&iOFXORGDSODFDGHEDVH
±&iOFXORGRVFKXPEDGRUHV
7DE
)FX × +X [ N1
W3 O IFX [ FP
1X N1
3ODFDGHEDVH&K[[PP
6HMDGF $ FP
±&iOFXORGRVFKXPEDGRUHV
6HMDGF IWX $ FP
N1FP
× IWX × IYX × IX + × 2.
$/7(51$7,9$,,
3ODFDGHEDVH[[PP
E±0pWRGR$,6&/5)'
E±%DVH$
2.
IFX [
WS [[ FP
3ODFDGHEDVHGH[[PP
E±%DVH%
IFX 2.
[
WS [ FP
D0pWRGR$,6&$6'
D0pWRGR$,6&$6'
D±%DVH$
9HULILFDomRDSHQDVGDSODFDGHEDVH
2.
IF [
P Q − [
FP
− [
JRYHUQD
Q¶ [
FP
3ODFDGHEDVHGH[[PP
±5HFRPHQGDo}HV
D±8VLQDJHP
$VSODFDVGHEDVHGHHVSHVVXUDLQIHULRU
RXLJXDODPPQmRQHFHVVLWDPVHUXVLQDGDV
SRGHQGRVHUSHUIHLWDPHQWHGHVHPSHQDGDVSDUD
JDUDQWLURFRQWDWRSHUIHLWRFRPDFROXQD3ODFDV
FRPHVSHVVXUDHQWUHDPPGHYHPVHU
XVLQDGDVGHXPODGRODGRGRFRQWDWRFRPD
FROXQD3DUDLVVRGHYHPVHUSUHYLVWRVDFUpV
FLPRVGHPP3DUDSODFDVPDLRUHVTXH
PPGHYHVHUSUHYLVWDXVLQDJHPGRVGRLVODGRV
HDFUpVFLPRGHHVSHVVXUDGHPP)LJ
WS [ FP
3ODFDGHEDVH[[PP
D%DVH%
IF N1FP
[
WS [ FP
)LJXUD 3ODFDVGHEDVH
E± 1LYHODPHQWR
F±,QWHUOLJDomRSODFDFKXPEDGRUHV
3DUDHIHLWRGHQLYHODPHQWRGHYHVHSUH
YHUDUJDPDVVDGHHQFKLPHQWRGHQRPtQLPR
PP$QWHVGHVHFRORFDUDDUJDPDVVDGHHQ
FKLPHQWRpQHFHVViULRID]HURQLYHODPHQWRGD
SODFD FRP FDOoRV )LJD SDUDIXVRV
FDODQWHV )LJE RX SRUFDV )LJF
3DUDHYLWDUXPDFRQFHQWUDomRPXLWRJUDQGHGH
FDUJDHPSRQWRVGREORFRGHIXQGDomRDSODFD
GHEDVHTXHYDLVHUQLYHODGDGHYHVHUFDOoDGD
FRPXPQ~PHURQHFHVViULRGHFDOoRVHPJHUDO
GHD
+iGXDVPDQHLUDVGHVHID]HUDLQWHUOLJD
omRGDSODFDFRPRVFKXPEDGRUHVSRUPHLR
GHVROGDRXGHSRUFDVHDUUXHODV6HDSODFDIRU
VROWD DV GXDV KLSyWHVHV VmR SRVVtYHLV )LJ
DE0DVVHDSODFDIRUVROGDGDjFROXQD
GXUDQWHDIDEULFDomRFRPRpRQRUPDOVRPHQWH
DLQGLFDGDQD)LJEpSRVVtYHO3DUDHVWD
UHFRPHQGDPRVGHL[DUXPDIROJDQRVIXURVGD
SODFD SURSRUFLRQDO DR GLkPHWUR GRV
FKXPEDGRUHVSDUDSHUPLWLUXPPHOKRUDOLQKD
PHQWRGDVFROXQDVFRQIRUPHLQGLFDGRQD7DE
D
D
E
E
)LJXUD $WDEHODLQGLFDXPDVpULHGHSHUILVFRP
SODFDGHEDVHHFKXPEDGRUHVSDUDVHUHPXVD
GRVHPSLODUHVGHWDSDPHQWR
F
)LJXUD %
3ODFDVGHEDVH
&
&
PP
FP
FP
&DStWXOR
%DUUDVGHFLVDOKDPHQWR
%DUUDVGHFLVDOKDPHQWR ±,QWURGXomR
4XDQGRDVFDUJDVKRUL]RQWDLVVmRGHJUDQ
GHPDJQLWXGHHQmRVHTXHUWUDQVIHULUHVWDVFDU
JDVSHORVFKXPEDGRUHVXPGRVDUWLItFLRVpD
FRORFDomRGHFKDSDVRXSHUILVVROGDGRVQDIDFH
LQIHULRUGDSODFDGHEDVHSDUDWUDQVPLWLODVjV
IXQGDo}HV
2$,6&LQGLFDTXHVyKDYHUiDIRUoDKRUL
]RQWDO QD EDUUD GH FLVDOKDPHQWR DSyV VHU
YHQFLGDDIRUoDGHDWULWRHQWUHDSODFDGHEDVHH
RFRQFUHWRRXHQFKLPHQWR2YDORUHVSHFLILFDGR
SDUDRFRHILFLHQWHGHDWULWR— 1RFDVRGR
$6'RYDORUGH—VHUiGLYLGLGRSRUXPFRHILFL
HQWHGHVHJXUDQoDLJXDOD1RFDVRGHVH
XVDUR/5)'RFRHILFLHQWHVHUi
VHUiWUDQVIHULGDSRUDWULWRLJXDOjFDUJDSHUPD
QHQWH1&3 YH]HVRFRHILFLHQWHGHDWULWR$SRU
omRDVHUUHVLVWLGDSHODEDUUDVHUiDGLIHUHQoD
GDFDUJDKRUL]RQWDODSOLFDGDPHQRVDDEVRUYL
GDSHORDWULWR
+E +± ȝ
1&3
$iUHDGHHVPDJDPHQWRGDEDUUDRXSHUILO
VHUi
+E
$E IFNFP
'HWHUPLQDU DV GLPHQV}HV GDV EDUUDV GH
FLVDOKDPHQWRGDSRUomRTXHRFRUUHDEDL[RGR
HQFKLPHQWR
&DOFXODURPRPHQWRDWXDQWHSRUFRPSULPHQWR
XQLWiULRQDEDUUD
IE +E
IFN
E× / ≤
⎛+E⎞ ⎛ /
⎞
⎟ × ⎜ + *⎟
0E ⎜
⎠
⎝ E ⎠ ⎝ &iOFXORGDHVSHVVXUDGDEDUUD
)E )\
)LJXUD ± )RUoDVQD EDUUD
$E iUHDGDEDUUDFP
* HQFKLPHQWR³*URXW´FP
/ DOWXUDGDEDUUDFP
E ODUJXUDGDEDUUDFP
0E PRPHQWRPi[LPRQDEDUUDN1FP
WE HVSHVVXUDGDEDUUDFP
3V SHUtPHWURGDVROGD
±&iOFXORGDEDUUDGH
FLVDOKDPHQWR
D0pWRGR$,6&$6'
'HWHUPLQDUDSRUomRGHFLVDOKDPHQWRTXH
WE 0E
0E
⇔ WE = )\
)\
3DUD
)\ N1FP
WS 0E
)\ N1FP
WS 0E
)\ N1FP
WS 0E
E0pWRGR$,6&/5)'
'HWHUPLQDUDSRUomRGHFLVDOKDPHQWRTXH
VHUiWUDQVIHULGDSRUDWULWRXVDQGRXPIDWRU
ĭ&3 Hĭ&9 +EX +X± ȝĭ1X&3 +X±[[1X&3
+EX +X1X&3
IEX +EX
IFN
E× / ≤
$iUHDGHHVPDJDPHQWRGDEDUUDVHUi
+EX
+EX
$EX × φ × IFN = IFN
VHQGR φ
'HWHUPLQDUDVGLPHQV}HVGDEDUUDGHFLVDOKD
PHQWRGDSRUomRTXHRFRUUHDEDL[RGRHQFKL
PHQWR
&DOFXODURPRPHQWRDWXDQWHSRUFRPSULPHQWR
XQLWiULRGDEDUUD
IEX +FX
IFN
E× / ≤
D±0pWRGR$,6&$6'
&RQVLGHUDQGRXPFRHILFLHQWHGHDWULWRGH
HRGHVHJXUDQoDWHPRV
)DWRUGHUHGXomRGHYLGRDRYHQWR ⎛+EX⎞ ⎛ /
⎞
⎟ × ⎜ + *⎟
0EX ⎜
⎝ E ⎠ ⎝ ⎠
+E
±&iOFXORGDHVSHVVXUDGDEDUUD
$E )E )\FRPLVWR
0X × )\ ×
WE E× W
E FP
0EX
0EX
WE= ⇔
)\
)\
3DUD
)\ N1FP
WE 0EX
)\ ³WE 0EX
( [)− × = N1
= FP
× &RQVLGHUDQGRE FPWHPRV
/ = FP ⇔ FP
* FPDGRWDGR/* FP
&iOFXORGDHVSHVVXUDGDEDUUD
⎛ ⎞ ⎛ ⎞
⎟ × ⎜ + ⎟ = N1FP
0E ⎜
⎝ ⎠ ⎝ ⎠
)\ ³WE 0EX
([HPSOR± 'HWHUPLQDUDEDUUDGH
FLVDOKDPHQWRSDUDXPDSODFDGHEDVHGH
[PPVXMHLWDDVVHJXLQWHVFDUJDV
1&3 N11&$ N1H
+Y N1YHQWR
&RQVLGHUDUSDUDDEDUUD)\ N1FP
IFNGRFRQFUHWR N1FP
WE FPXVDUFKDSDGHPP
&K[[PP
E0pWRGR$,6&/5)'
ĭFYYHQWR Hĭ&3 +EX (× ) − (× × ) N1
%DUUDVGHFLVDOKDPHQWR D±0pWRGR$,6&$6'
FP
$E × +E N10E N1FP
E FPWE FP
5HVLVWrQFLDGRILOHWHGHVROGD N1FP
7DE$
&RQVLGHUDQGRE FP
/ FP FP
)+ ILOHWHV N1
* FPDGRWDGR/* FP
)9 &iOFXORGDHVSHVVXUDGDEDUUD
I+ ⎛⎞ ⎛ ⎞
⎟ × ⎜ + ⎟ N1FP
0EX ⎜
⎝ ⎠ ⎝ ⎠
N1
I9 IV + N1FP
WE FPXVDUPP
8PDVROGDGHFPFPUHVLVWHDN1
&K[[PP
6ROGDD ±'LPHQVLRQDPHQWRGDVROGDGH
OLJDomRGDEDUUDGHFLVDOKDPHQWR
FRPSODFDGHEDVH
PP
8VDUVROGDPtQLPDD PPGHDFRUGRFRP
DVHVSHVVXUDGDVFKDSDVDVROGDU
E±0pWRGR$,6&/5)'
)+ +
0
)Y WE
)LJXUD D GLPHQVmRGDVROGD
$V iUHDGDVROGD ED
E FRPSULPHQWRGDEDUUD
I+ )+
$V
I9 )Y
$V
IV I + + IY
([HPSOR±'LPHQVLRQDUDVROGDGR
([HPSOR
+EX N10EX N1FP
E FPWE FP
5HVLVWrQFLDGRILOHWHGHVROGDN1FP
7DE$
)+ N1
)9 N1
I+ N1FP
I9 N1FP
IV + N1FP
8PDVROGDGHFPFPUHVLVWHDN1
7DE$
FP PP
8VDUVROGDPtQLPDD PP
6ROGDD ([HPSOR± 'HWHUPLQDURSHUILOTXHGHYHUi
IXQFLRQDUFRPREDUUDGHFLVDOKDPHQWRSDUDXPD
SODFD GH EDVH GH [ PP VXMHLWD jV
VHJXLQWHVFDUJDV
1&3 N11&$ N1
+&S N1+&$ N1+&9 N1
&RQVLGHUDU)\ N1FP
IFNGRFRQFUHWR N1FP
+ N1FP
0S )E [)\ [ N1FP
:QHF FP
8PSHUILO&96[: FP!2.
G FPEI FPWI FP
2EVDDOWXUDHODUJXUDGRSHUILOHVWiVHQGRFR
PDQGDGDSHODWHQVmROLPLWHGRFRQFUHWR
&iOFXORGDVROGD
3V FP
K FP
I+ N1FP
I9 N1FP
× IV + D±0pWRGR$,6&$6'
N1FP
FP
8VDUVROGDGHPP
6ROGDD ĭ UHGXWRUGHYLGRDRYHQWR
+ N1
+ N1
+F −
$E × N1
FP
× &RQVLGHUDQGRXPSHUILOVROGDGRWLSR&96
FRPG FPHEI FP
FP* FP
/ /* FP
E0pWRGR$,6&/5)'
ĭFYYHQWR H
ĭ&3 HHĭ&$ + [[[ N1
+ [[ N1
+FX [[ N1
$E FP
× &RQVLGHUDQGRXPSHUILOVROGDGRWLSR&96
FRPG FPHEI FP
%DUUDVGHFLVDOKDPHQWR FP* FP
/* FP
/ ⎛⎞ ⎛ ⎞
⎟ × ⎜ + ⎟ N1FP
0S ⎜
⎝ ⎠ ⎝ ⎠
)E )\ N1FP
:QHF FP
8PSHUILO&96[NJP
: !2.
2EV$DOWXUDGRSHUILOHVWiVHQGRFRPDQGDGD
SHODWHQVmRGRFRQFUHWR
&iOFXORGDVROGD
3V FP
I+X N1FP
I9X N1FP
× I6X + 6ROGDD FP
8VDUVROGDGHPP
N1FP
&DStWXOR
3LODUHVHPEXWLGRVQDV
IXQGDo}HV
3LODUHVHPEXWLGRVQDVIXQGDo}HV ±,QWURGXomR
2VSLODUHVHPEXWLGRVQDVIXQGDo}HVSR
GHPHP PXLWRVFDVRV VHUXPD VROXomRPDLV
UiSLGDHPDLVEDUDWDHYLWDQGRVHDFRORFDomR
GHSODFDVGHEDVHHFKXPEDGRUHV
(VWDVROXomRQmRpPXLWRXVXDOHWHPVLGR
XVDGDQDIL[DomRGHSRVWHVHHVWUXWXUDVFRP
SHTXHQDVFDUJDVHHVWUXWXUDVSURYLVyULDV
$FDUJDYHUWLFDOpUHVLVWLGDSHODIRUoDGH
DWULWRODWHUDOHQWUHRSLODUGHDoRHRFRQFUHWRHR
PRPHQWRpUHVLVWLGRSHODVIRUoDVGHFRPSUHV
VmRQRFRQFUHWRDWXDQGRPDVPHVDVGRVSHU
ILV
(PIXQomRGDVFDUJDVHRXGDFDSDFLGD
GHGRSHUILOHGRFRQFUHWRGHWHUPLQDVHDSUR
IXQGLGDGH/GHHPEXWLPHQWRGRPHVPR
(PQRVVDVSHVTXLVDVHQFRQWUDPRVDXWR
UHVTXHOHYDPHPFRQVLGHUDomRDSHQDVXPDGDV
PHVDVGRSHUILOWLSR,RX+RXWURVDVGXDVPH
VDVHRTXHQRVSDUHFHPDLVUD]RiYHODVDSUH
VHQWDGDV SHORV DXWRUHV <YRQ /HVFRXDUF¶K H
$QGUp&ROVRQTXHFRQVLGHUDPTXHDPHVDLQ
WHUQDFRODERUDFRPDSHQDVGDDOWXUDGR
SHUILOYDORUHVWHREWLGRFRQVLGHUDQGRDUHVLVWrQ
FLDGRFRQFUHWRDFLVDOKDPHQWR(VWDEHOHFHP
SRUTXHVW}HVSUiWLFDVTXHRFRPSULPHQWRDVHU
HPEXWLGRQRFRQFUHWRQmRGHYHVHUPHQRUGR
TXHYH]HVDDOWXUDGRSHUILOHTXHRVSULPHL
URVFPSRUUD]}HVFRQVWUXWLYDVQmRGHYHPVHU
OHYDGRVHPFRQWDQRFRPSULPHQWRFDOFXODGRRX
VHMDGHYHPRVDGLFLRQDUPDLVFPDHVWHYDORU
$ILJXUDDSUHVHQWDSDUDSHUILVDEHUWRV
HWXEXODUHVRGLDJUDPDGHWHQV}HVTXHSHUPLWH
FDOFXODUDSURIXQGLGDGHHPIXQomRGDFDSDFL
GDGHGRFRQFUHWR
)LJXUD &iOFXORGRFRPSULPHQWR
QHFHVViULR/DVHUHPEXWLGR
(PIXQomRGDUHVLVWrQFLDGRSHUILOH
GDUHVLVWrQFLDGRFRQFUHWR
D±0pWRGR$,6&$6'
IF IFN
)E[ WHQVmRDGPLVVtYHODIOH[mRQRDoR
:[ PyGXORHOiVWLFRGDVHomRGRSHUILO
G DOWXUDGRSHUILO
EI ODUJXUDGDPHVDGRSHUILO
WI HVSHVVXUDGDPHVD
/ FRPSULPHQWRQHFHVViULRDVHUHPEXWLGR
/F FRPSULPHQWRWRWDODVHUHPEXWLGR
)DWRUGHDGHUrQFLDDoRFRQFUHWR
ID N1FP
) IRUoDWRWDOGHDGHUrQFLD
EI
WI )DWRUGHDGHUrQFLDDoRFRQFUHWR
ID N1FP
⎛ IF ⎞ ⎛ /EI ⎞ IF× EI × /
⎟=
) ⎜ ⎟ × ⎜
⎝ ⎠ ⎝ ⎠
/
⎛ IFX ⎞ ⎛ /⎞
⎟ × ⎜ ⎟ × EI ⇔ )X = IFX× EI ×
)X ⎜
⎝ ⎠ ⎝ ⎠
3DUDXPSHUILO W LSR,RX+ XVDGRFRPRSLODU
RPRPHQWRUHVLVWHQWH~OWLPRGRFRQFUHWRVHUi
3DUDSHUILV,RX+XVDU
E EIGQROXJDUGHEI
3DUDXPSHUILOWLSR ,RX+XVDGRFRPRSLODU
RPRPHQWRUHVLVWHQWHGRFRQFUHWRVHUi
0 × ) ×
0 IF × / ×
/⎞ /
/ ⎛
= ⎜× IF× ER× ⎟
⎝
⎠ ER
0[ PRPHQWRUHVLVWHQWHGDVHomRGRSHUILO )E[:[
0X × ) ×
0X IFX × / ×
)D]HQGR0 0[WHPRV
/ = )\× :[
)\ ×:[
/ IF× ER
±3DUDXP SHUILOWXEXODUUHGRQGR IF ×/ ×
ER
/ = )\× :[
)\ × :[
IF× EI
,JXDODQGR0X 0[XWHPRV
IFX ×/ ×
ER
E
0[X PRPHQWR~OWLPRGDVHomRGRSHUILO )\:[
)E[ )\SHUILORXWXERTXDGUDGR
)E[ )\WXERUHGRQGR
IF ×/ ×
/ ⎛
/⎞
/
= ⎜× IFX× ER× ⎟ × ×
⎝
⎠
ER
= × )\× :[
)\ × :[
IFX× E
±3DUDXP SHUILOWXEXODU IFX ×/ ×
/ ER
= [× )\× :[
×× )\ × :[
IFX× EI
/ )\[:[
IFX[EI
([HPSOR±'HWHUPLQDURFRPSULPHQWRGR
SHUILOXP&96[TXHGHYHUiVHUHPEXWLGR
QRFRQFUHWR
E±0pWRGR$,6&/5)'
IFX IFN
)EX[ WHQVmRDIOH[mRQRHVWDGROLPLWHGR
SHUILOGHDoR
3LODUHVHPEXWLGRVQDVIXQGDo}HV / × × /& FP
/PLQ [ FP
3DUDDFDUJDGHFRPSUHVVmRWHPRV
6 [ FP
$ FP
:[ FP
)\ N1FP
3HUtPHWUR FP
IFN N1FP
D0pWRGR$,6&$6'
IF [ N1FP
)\ N1FP
)E[ )\ N1FP
E [ FP
$GHUrQFLDDoRFRQFUHWR
)D [ N1FP
/ × × /& FP
/PLQ [ FP
$FDUJDGHFRPSUHVVmRpFDOFXODGDDVVXPLQGR
TXHPHWDGHGRSHUtPHWURWUDQVPLWHHVWDFDUJD
3DUD R HVPDJDPHQWR GR FRQFUHWR D WHQVmR
DGPLVVtYHOVHUiWDPEpPN1FP
3HULP [ FP
6 3HULP[/& [ FP
1 6[$[ 1 [[ N1
E±0pWRGR$,6&/5)'
IFX [ N1FP
)E[X [ N1FP
$GHUrQFLDDoRFRQFUHWR
)DX [ N1FP
1X [[ N1
([HPSOR ±,GHPSDUDXPSHUILO W XEXODU
TXDGUDGR[PP
:[ FP
$ FP
EI FP
D±0pWRGR$,6&$6'
/ × × /& FP
/PLQ [ FP
3HULP [[ FP
6 [/F [ FP
1 [[ N1
E±0pWRGR$,6&/5)'
/ × × /& FP
6 [ FP
1 [[ N1
(PIXQomRGDVFDUJDVMi
GHILQLGDV
&DOFXODVH D SURIXQGLGDGH HP IXQomR GD
UHVLVWrQFLDGRFRQFUHWRVXSRQGRVHTXHRSHUILO
GHDoRMiIRLYHULILFDGR
1 FDUJDYHUWLFDODWXDQWH
1X FDUJDYHUWLFDOIDWRUDGD
+ FDUJDKRUL]RQWDODWXDQWH
+X FDUJDKRUL]RQWDOIDWRUDGD
0 PRPHQWRDWXDQWH
0X PRPHQWRDWXDQWHIDWRUDGR
D±0pWRGR$,6&$6'
IF IFN
$QDOLVDQGRDILJXUDWHPRVDVVHJXLQ
WHVHTXDo}HVSDUDRFiOFXORGDSURIXQGLGDGHD
VHUDQFRUDGDQRFRQFUHWRFRQVLGHUDQGRDVWHQ
V}HVDEVRUYLGDV HPXPDIDFH EIQR FDVRGH
SHUILVWXEXODUHE EIGSDUDSHUILV,RX
+
([HPSOR± 'HWHUPLQDUD SURIXQGLGDGH/
QHFHVViULDSDUDIL[DURSHUILOXP&96[
GRSRVWHVXMHLWRDVFDUJDVLQGLFDGDVQDILJXUD
WHQGRRFRQFUHWRGDEDVHXPIFN N1FP
1 N11X N1$ FP
+ N1+X N1
E±0pWRGR$,6&/5)'
IFX IFNHDVFDUJDVHQWUDPQDH[SUHVVmR
IDWRUDGDV
)LJXUD I&0 0 + +× /
EI × / +
I&+ EI × /
(0 + +× /)
EI × /
E EIG
IPD[ I&+I&0
⎛ + ⎞ ⎛
/⎞
⎟⎟ + ⎜ 0 + +× ⎟ ×
< IF
IPD[ ⎜⎜
⎠ EI × /
⎝ EI ×/⎠ ⎝
±3DUDSHUILVWXEXODUHV
⎛ + ⎞ ⎛
⎟⎟ × ⎜+ + × EI × IF× 0 ⎞⎟
/ ⎜⎜
+ ⎠
⎝ EI × IF⎠ ⎝
3DUDSHUILO,RX+
⎛ + ⎞ ⎛
⎟⎟ × ⎜+ + × ER× IF× 0 ⎞⎟
/ ⎜⎜
+ ⎠
E
IF
×
⎝ ⎠ ⎝
D±0pWRGR$,6&$6'
0 [ N1P 1FP
)F [ N1FP
ER EIG [ FP
× ⎛
+
× × × ⎞
⎟ / × × ⎜⎜+
⎟
⎝
⎠
/& FP
/PLQ [ FP
9HULILFDomRGDFDUJDYHUWLFDO1
3HULPHWUR FP
6 [ FP
1 [[ N1!2.
3LODUHVHPEXWLGRVQDVIXQGDo}HV E±0pWRGR$,6&/5)'
IFX IFN
/& FP
/PLQ [ FP
0X [ N1P N1FP
)FX [ N1FP
FP
6 [ FP
× ⎛
+ × × × ⎞
⎜
⎟
+
/ × ⎜
⎟
⎝
⎠
FP
3HU 1D [[ N1!2.
E0pWRGR$,6&/5)'
/& FP
/PLQ [ FP
× ⎛
+ × × × ⎞
⎟ / × ⎜⎜+
⎟
⎝
⎠
9HULILFDomRGDFDUJD1X
6 [ FP
1DX [[ N1!2.
≅ FP
2EV3HODFDSDFLGDGHGRSHUILO([WHPRV
/ FP!!$,6&$6'
/ FP!!$,6&/5)'
6 [ FP
([HPSOR ± 'HWHUPLQDU D SURIXQGLGDGH
QHFHVViULD SDUD IL[DU R SHUILO GR SLODU XP :
[ GR JDOSmR LQGLFDGR QD ILJXUD
&RQVLGHUDUIFN N1FP
([HPSOR ±2H[HPSORDQWHULRUFRQVLGHUDQ
GRXPSLODUWXEXODUUHWDQJXODUGH[[PP
3HUtPHWUR FP
$ FP
EI FP)E[ N1FP
:[ FP
/& FP
1DX [[ N1!2.
EI FPG FP
E [ FP
$ FP
3HUtPHWUR FP
D±0pWRGR$,6&$6'
3HORVHVIRUoRV
× ⎛
+ × × × ⎞
⎟ / × ⎜⎜+
⎟
⎝
⎠
D±0pWRGR$,6&$6'
/& FP
/PLQ [ FP
/ =
× ⎛
+ × × × ⎞
⎜+
⎟ = 3HODFDSDFLGDGHGRSHUILO
⎟
× ⎜⎝
⎠
FP
/ × FP
× 8VDU/ FP
E±0pWRGR$,6&/5)'
3HORVHVIRUoRV
× ⎛
+ × × × ⎞
⎟
/ × ⎜⎜+
⎟
⎝
⎠
/ ≅ /& FP
/PLQ [ FP
3HODFDSDFLGDGHGRSHUILO
/ )LJXUD 'HWDOKHV &RQVWUXWLYRV
× × /& FP
±'HWDOKHVFRQVWUXWLYRV
$VHJXLUDSUHVHQWDUHPRVDOJXQVGHWDOKHV
FRQVWUXWLYRVQD)LJ
3DUDFDUJDVYHUWLFDLVVHPDUUDQFDPHQWRV
DVVROXo}HVLQGLFDGDVQD)LJDEHFUHVRO
YHP3DUDSHTXHQRVDUUDFDPHQWRVSRGHPRV
XVDUDVVROXo}HVGD)LJG
&DStWXOR
/LJDo}HVYLJDVGHDoRFRP
HOHPHQWRVGHFRQFUHWR
/LJDo}HVYLJDVGHDoRFRPHOHPHQWRVGHFRQFUHWR ±,QWURGXomR
([LVWHPYiULDVPDQHLUDVGHVHUHVROYHUDV
OLJDo}HVGRVHOHPHQWRVGHDoRFRPRVGHFRQ
FUHWRFRPRXVRGHQLFKRVFRQVROHVGHFRQ
FUHWRRXDoRFKDSDVFRPSLQRVHFKXPEDGRUHV
GHH[SDQVmRRXSURWHQGLGRV
3DUDHIHLWRGLGiWLFRSRGHPRVGLYLGLUHV
WDV LQWHUIDFHV HP GXUDQWH D FRQVWUXomR H
DSyVDFRQVWUXomR
G
)LJXUD 7LSRV GH DSRLR
±6ROXo}HVGXUDQWHDFRQVWUXomR
1DIDVHGHSURMHWRSRGHPRVGHILQLUTXDOD
PHOKRUVROXomRDVHUH[HFXWDGDGXUDQWHDIDVH
GHFRQVWUXomR3RGHUPRVGHVWDFDUDVVHJXLQ
WHVVROXo}HV
$WUDYpVGHFKDSDVGHDSRLR)LJD
3RUPHLRGHFKDSDVHSLQRVSUHYLDPHQ
WHGHL[DGRVQRFRQFUHWR)LJE
3RUPHLRGHFRQVROHVIHLWRVQRFRQFUH
WR)LJF
3RUPHLRGHQLFKRVSUHYLDPHQWHIHLWRV
QRFRQFUHWR)LJG
±9LJDVGHDoRDSRLDGDVHPFKDSDV
GHDoRVREUHFRQFUHWRRXDOYHQDULD
)LJXUD 'HWDOKH DSRLR GH YLJD
P %
−.
G − G
SDUDSHUILOODPLQDGR
. HVSHVVXUDGDVROGDSDUDSHUILOVROGDGR
. D±0pWRGR$,6&$6'
9HULILFDomRQRFRQFUHWR
D
IF 1
)F IFN
%& ≤
'LPHQVLRQDPHQWRGDSODFD9HULWHP
WS P
IF
)\
9HULILFDomRGDDOPDGRSHUILOVHPHQULMHFHGRU
E
F
1
IZ & + .W ≤ )\
Z
E±0pWRGR$,6&/5)'
IF 2.
× 1X
)FX IFN
IFX %& ≤
P ± FP
'LPHQVLRQDPHQWRGDSODFD
WS × 9HULILFDomRGRFRQFUHWR
WS P
IFX
)\
&K[[PP
9HULILFDomRGDDOPD
9HULILFDomRGDDOPDGRSHUILOVHP
HQULMHFHGRU
)\ N1FP
IZ × 1X
IZX & + .W ≤ )\
Z
E±0pWRGR$,6&/5)'
([HPSOR±'LPHQVLRQDUDSODFDGHEDVH
TXHVHUYLUiGHDSRLRSDUDXPDYLJDXP:[
NJPSDUDWUDQVPLWLUXPDFDUJDYHUWLFDO1&3
N1H1&$ N1VREUHXPPXURGHFRQ
FUHWRWHQGRXPDODUJXUDPi[LPDSDUDDSRLRGD
SODFD& FP
)FX [ N1FP
1X [[ N1
% XVDUFP
× N1FP2.
IFX × P − FP
WS × )FN N1FP
G PP
WZ PP
)\ N1FP
G¶ PP
EI PP
− PP FP
&. [ FP
. FP
FP
&K[[PP
9HULILFDomRGDDOPD
)\ N1FP
IZX × ([HPSOR ±2H[HPSORDQWHULRUFRPRXVR
GHXP9([
D0pWRGR$,6&$6'
)F [ N1FP
1 N1
% FP
× XVDUFP
/LJDo}HVYLJDVGHDoRFRPHOHPHQWRVGHFRQFUHWR WZ PP. D PPVROGD
D±0pWRGR$,6&$6'
&. [ FP
% FP
P − FP
WS × XVDU&KPP
DYLJDVHQJDVWDGDVQRFRQFUHWR
&K[[PP
9HULILFDomRGDDOPD
IZ N1FP 12.
× +i QHFHVVLGDGH GH FRORFDomR GH
HQULMHFHGRUHVQRVDSRLRV
E±0pWRGR$,6&/5)'
% FPP ± FP
EYLJDVURWXODGDVQRFRQFUHWR
XVDU&KPP
&K[[
WZ × 9HULILFDomRGDDOPD
WZ ≅ 2.
× &RPR D LJXDOGDGH HVWi PXLWR SUy[LPR
DFRQVHOKDPRV D FRORFDomR GH HQULMHFHGRUHV
QRVDSRLRV
±/LJDomRHQWUHYLJDVGHDoRHSL
ODUHV RX SDUHGHV GH FRQFUHWR DWUDYpV GH
FKDSDVHSLQRV
3RGHPRVID]HUHVWDOLJDomRSDUDWUDQVPL
WLU VRPHQWHIRUoDV YHUWLFDLV RXYHUWLFDLV PDLV
KRUL]RQWDLVHPRPHQWRV$)LJHVFODUHFH
EHPDVGXDVVLWXDo}HV
'(7
'(7
)LJXUD ± 6ROXo}HV GH IL[DomR GDV FKDSDV
1R FDVR HVSHFLILFR GLPHQVLRQDUHPRV D
SODFDGHOLJDomRHRVSLQRVFRPRVHIRVVHP
XPDSODFDGHEDVHHQJDVWDGD9HULWHP
DOHPGLVVRKiQHFHVVLGDGHGHVHYHULILFDURV
VHJXLQWHVLWHQV
'LPHQV}HVGDSODFD
'LPHQV}HVGRVSLQRV
(VPDJDPHQWRGRFRQFUHWR
6ROGDHQWUHSODFDHSLQRV
$VGLPHQV}HVGDSODFDGHYHPDWHQGHUDV
GLPHQV}HVGDFKDSDRXFDQWRQHLUDVGHOLJDomR
GDYLJDTXHVmRGLPHQVLRQDGDVGHDFRUGRFRP
DVVXDVUHDo}HV9HU7DE$H$EHPFRPR
DVGLVWkQFLDVPtQLPDVHQWUHSLQRVHSLQRVH[
WUHPLGDGHV
17 )RUoDDWXDQWHGHWUDomR
9 )RUoDDWXDQWHGHFLVDOKDPHQWR
1D $S[)W
9D $S[)Y
$S ÈUHDGRVSLQRVFP
3LQRV6$()X N1FP
2VSLQRVSDUDVHUHPHILFLHQWHVGHYHPWHU
GLkPHWURPtQLPR PP
FRPSULPHQWRPtQLPR GS
GLVWkQFLDPtQLPDHQWUHHOHV GS
GLVWkQFLDPtQLPDDERUGDGDFKDSD GS
GLVWkQFLDPtQLPDDERUGDGRFRQFUHWR GS
GS GLkPHWURGRSLQR
D0pWRGR$,6&$6'
1D $S[ 7UDomR)X
9D $S[ &RUWH)X
6ROGDHPWRUQRGRVSLQRV7DE$
SDUDILOHWHGHPP N1FP
E0pWRGR$,6&/5)'
1DX $S[7UDomR)X
9DX $S[&RUWH)X
6ROGDHPWRUQRGRVSLQRV7DE$
SDUDILOHWHGHPP N1FP
2VH[HPSORVDVHJXLUHVFODUHFHP
([HPSOR ±'HWHUPLQDUDHVSHVVXUDGDSOD
FDHRVSLQRVQHFHVViULRVSDUDUHVLVWLUDRVHV
IRUoRVLQGLFDGRVQDILJXUDSDUDXP96[
FRPEI PP
)LJXUD ± 'LVWkQFLDV PtQLPDV
3LQR6$()X N1FP
&KDSD)\ N1FP
&RQFUHWRIFN N1FP
2FRPSULPHQWRGHDQFRUDJHPQHFHVVi
ULRGRSLQR/FVHUiDYDOLDGRGHDFRUGRFRPR
LWHPVHQGR
/F $FRQH
2HVPDJDPHQWRGRFRQFUHWRQDUHJLmR
GRVSLQRVGHYHVHUYHULILFDGRSDUDXPDWHQVmR
QRFRQFUHWRGH
$,6&$6'IHVP IFN
$,6&/5)'IXHVP IFN
$YHULILFDomRTXDQGR H[LVWHWUDomRFRP
FRUWDQWHGHYHVHUIHLWDSHODIyUPXODDEDL[R
⎛17 ⎞ ⎛ 9 ⎞
⎜⎜
⎟⎟ + ⎜⎜ ⎟⎟ VHQGR
1
⎝ D ⎠ ⎝ 9D ⎠
D±0pWRGR$,6&$6'
7DE$/ W GS 3 N1
)F [ N1FP
5&3 N10&3 [ N1FP
/LJDo}HVYLJDVGHDoRFRPHOHPHQWRVGHFRQFUHWR 'HDFRUGRFRPLWHPWHPRV
&iOFXORGRFRPSULPHQWRQHFHVViULR
±'LPHQV}HVGDSODFD
9HULILFDomRGH/ FP
ID]HQGR% FP
$FRQ 7
FP
[IFN [
/F FP
/ 0
× =
FP2.
%IF
× &iOFXORGHIFUHDOFRPR+ IFPD[ IFPLQ 0
× 2.
%/ × 6HQGRIFPD[ IFPLQ & FP
FP
& /PLQ [GS [ FP
8VDUSLQRVGH[PP
'LVWkQFLDHQWUHHOHVQRVHQWLGRKRUL]RQWDO
E [ FP
(VPDJDPHQWRGRFRQFUHWRQRVSLQRV
&RQVLGHUDQGRDSHQDVDPHWDGHGRSHUtPHWUR
/SLQR [G [ FP
GR3HUtPHWUR [[ [
SLQRV FP
&iOFXORGDHVSHVVXUDGDSODFDLWHP
× IHVP 0S N1FPFRQVHUYDGRU
FP
WS &DOFXORGDVROGDQRVSLQRV
IWV IYV &iOFXORGRVSLQRVLWHP
< / −
− H FP
0 =
N1
1W 7 <
PtQLPRPP
2EV&RPRRSLQRYDLWUDEDOKDUDWUDomRFRP
FLVDOKDPHQWRYDPRVXVDUGLkPHWURGHPP
GS !!$ FP
SLQRVDWUDomRHDFLVDOKDPHQWR
1WD [[ N1
9D [[ N1
GS +
2.
7
QGS
&K[[PPPtQLPD
&
N1FP 2.
× =
N1FP
× × N1FP
× × I + [
N1FP
6ROGDGHFPUHVLVWHDN1FP
7DE$
)LOHWHGHVROGDHPWRGDYROWDQRVSLQRV
FP PP
XVDUVROGDPtQLPDGHPPHPWRGDYROWD
GHYLGRDHVSHVVXUDGRSLQR7DE$
E±0pWRGR$,6&/5)'
7DE$/ W GS 3 N1
1X [ N1
0X [ N1FP
& & FP
× × &iOFXORGDHVSHVVXUDGDSODFD
IFXPD[ IFXPLQ × N1FP
0SX FP,WHP
PtQLPRPP
WS IWXV N1FP
× × IYXV N1FP
× × IX + [
N1FP
6ROGDGHFPUHVLVWHDN1FP
7DE$
&K[[PP
)LOHWHVROGDHPWRGDYROWDQRVSLQRV
&iOFXORGRVSLQRV
N1
< FP1WX 7X 6HMDĭ!!$ FP
1WX N1 9X N1
1DX [[ N1
9DX [[ N1
+
2.
$FRQH
7X
FP
[ [
/F FP
FP!PP
8VDUVROGDPtQLPDGHPPGHYLGRD
HVSHVVXUDGRSLQR
([HPSOR ±'HWHUPLQDUDHVSHVVXUDGDSOD
FDHRGLkPHWURGRVSLQRVSDUDUHVLVWLUDRVHV
IRUoRVLQGLFDGRVQDILJXUDSDUDXP:[
NJP
3LQR6$()\ N1FP
&KDSD)\ N1FP
&RQFUHWRIFN N1FP
9&3 N19&$ N1
0&3 N1FP0&$ N1FP
+&3 N1+&$ N1
/PLQ [ FP
8VDUSLQRV[PP
'LVWkQFLDHQWUHHOHVQRVHQWLGRKRUL]RQWDOGHE
[ PP
2XWUDDOWHUQDWLYDPDLVIROJDGDpXVDUSLQRVGH
PP
(VPDJDPHQWRGRFRQFUHWRQRVSLQRV
/SLQR [ FP3 FP
IXHVP 2.
× &iOFXORGDVROGDQRVSLQRV
D±0pWRGR$,6&$6'
7DE$/ W GS 3 N1
)F [ N1FP
9 N1
+ N1
/LJDo}HVYLJDVGHDoRFRPHOHPHQWRVGHFRQFUHWR 0 N1FP
07 [ N1FP
'HDFRUGRFRPLWHPWHPRV
±&iOFXORGDHVSHVVXUDGDFKDSD
9HULILFDomRGH/ FP
ID]HQGR% FP
/ +
+
%IF
⎛ + ⎞
0
⎜⎜
⎟⎟ +
%IF
⎝ %IF⎠
&K[[PP
&iOFXORGRVSLQRV
6HMM D ĭPP $ FP
17 7 N19 N1
17D [[ N1
9D [[ N1
+
2.
$FRQH 7
FP
[IFN [
/F FP
⎛
⎞ × + ⎜
⎟ +
/ × × ⎝ × × ⎠
× FP2.
&iOFXORGHIFUHDO
+
0
+
IF /% %/
× +
× × N1FP N1FP 2.
IF IFPLQ N1FP
IFPD[IFPLQ N1FP
IFPD[ /
× & IF + IF = = PD[
PLQ
FP
< FP
/PLQ [ FP
8VDUSLQRV ‘ [PP
'LVWkQFLDHQWUHHOHVQRVHQWLGRKRUL]RQWDO
E [ FP
(VPDJDPHQWRQRFRQFUHWRQRVSLQRV
/SLQR [ FP
3HU [[[ FP
2.
× &iOFXORGDVROGDQRVSLQRV
IHVP IWV N1FP
× × & IYV N1FP
× × D / & − =
− FP
IV 7 0 −+D − × =
N1
<
6ROGDGHFP5V N1FPFP
&iOFXORGDHVSHVVXUDGDFKDSD
× 0S N1FP
FP ≅ PP
LWHP
WS + × N1FPFP
)LOHWHGHVROGDHPWRGDYROWDQRVSLQRV
FP
8VDUILOHWHPtQLPRGHPPGHYLGRD
HVSHVVXUDGRSLQR
E±0pWRGR$,6&/5)'
7DE$/ W GS 3 N1
9X [[ N1
+X [[ N1
0X [[[
N1FP
)F IFN [ N1FP
±&iOFXORGDHVSHVVXUDGDFKDSD
9HULILFDomRGH/ FP
/ ⎛
⎞ × + ⎜
⎟ +
[[ ⎝ × × ⎠ × FP2.
&iOFXORGHIFXUHDO
× +
× × N1FP
IFXPLQ N1FP
IFXPD[IFXPLQ N1FP
IFXPD[ × & FP
< FP
& D − × N1
1WX 7X × N1FP
0SX FP ≅ PP
LWHP
WS &K[[PP
+
2.
8VDUSLQRVGH[PP
'LVWkQFLDHQWUHHOHVQRVHQWLGRKRUL]RQWDO E
[ FP
(VPDJDPHQWRGRFRQFUHWRQRVSLQRV
/SLQR [ FP
3HU [[[ FP
2.
× &iOFXORGDVROGDQRVSLQRV
IHVP IWXV × × IYXV × × IXV + × N1FP
6ROGDGHFP5V N1FPFP
)LOHWHGHVROGDHPWRGDYROWDQRVSLQRV
FP
8VDUILOHWHGHPP
±&RQVROHVIHLWRSUHYLDPHQWHQR
FRQFUHWR
(VWDpXPDERDDOWHUQDWLYDGHFRORFDomR
GDVYLJDVGHDoRMXQWRDRSLODUGHFRQFUHWRYLV
WRIDFLOLWDUDPRQWDJHPGDVPHVPDVVHPQH
FHVVLGDGHSUpYLDGHFRORFDomRGHFKDSDVFRP
SLQRV TXH VmR SRVLFLRQDGDV GXUDQWH D
FRQFUHWDJHP(VWDVROXomRH[LJHFRPRPHGL
GDGHVHJXUDQoDDFRORFDomRGHFKXPEDGRUHV
SDUDFLVDOKDPHQWR
$FKDSDGHDSRLRGHYHVHUFDOFXODGDFRQ
IRUPHLWHP
&iOFXORGRVSLQRV
6HMD ĭPP$ FP
1WX N19X N1
1DX [[ N1
9DX [[ N1
)LJXUD ± &RQVROHV
/LJDo}HVYLJDVGHDoRFRPHOHPHQWRVGHFRQFUHWR ± 1LFKRV IHLWR SUHYLDPHQWH QR
FRQFUHWR
(VWDWDPEpPpXPDVROXomRPXLWRXWLOL]D
GDSDUDDSRLRVGDVYLJDVGHDoRQRVSLODUHVGH
FRQFUHWRHPERUDH[LMDPXPSRXFRPDLVGHFDX
WHODQDPRQWDJHPGDVYLJDVGHYLGRDVGLPHQ
V}HVGRVQLFKRV$FKDSDGHDoRGRDSRLRGHYH
VHUFDOFXODGDGHDFRUGRFRPRLWHP
)LJXUD ± &KXPEDGRU GH H[SDQVmR
±)L[DGRUHVFRPDGHVLYRVTXtPLFRV
)LJXUD ± 1LFKRV
±6ROXo}HVDSyVDFRQVWUXomR
SURQWD
3DUDHVWHFDVRDVROXomRPDLVYLiYHOpD
FRORFDomRGHFKDSDVYHUWLFDLVIL[DGDVDWUDYpV
GHFKXPEDGRUHVGHH[SDQVmRRXGHIL[DGRUHV
FRPDGHVLYRVTXtPLFRV
$JDPDHQFRQWUDGDQRPHUFDGRpPXLWR
JUDQGHHHQWUHHVWHVSRGHPRVFLWDU
(VWHWLSRGHIL[DGRUpFRPSRVWRSRUXPD
EDUUDURVFDGDGHDoRMXQWRFRPXPDDPSRODRX
FDUWXFKRGHDGHVLYRTXtPLFRTXHSHUPLWHXPD
IL[DomRUiSLGDHVHJXUD(PJHUDOSRVVXLERD
UHVLVWrQFLDjWUDomRHDRFRUWHVHQGRXPGRV
PDLVXVDGRV(PJHUDOVXDUHVLVWrQFLDjWUDomR
YDULDGHDN1GHSHQGHQGRGRGLkPH
WURGDUHVLVWrQFLDGRFRQFUHWRGDSURIXQGLGD
GHGDGLVWkQFLDHQWUHHOHV HGDGLVWkQFLDjV
ERUGDV,WHP2VSDUDIXVRVWrPHPPp
GLDXPDUHVLVWrQFLDjUXWXUDHOHYDGDGDRUGHP
GHDN1FPHVmRHQFRQWUDGRVQRVGLk
PHWURVGHDPPHPYiULDVFRPSULPHQ
WRV
7LSRVGHIL[DGRUHV
&KXPEDGRUHVGHH[SDQVmR
(VWHWLSRGHFKXPEDGRUpFRQVWLWXtGRSRU
XPDKDVWHGHDoRFRPXPDFDSDQDSRQWDTXH
SHUPLWHDDEHUWXUDTXDQGRDSHUWDGRIL[DQGRVH
SRUPHLRGHDGHUrQFLDQRFRQFUHWR(PJHUDOD
VXDUHVLVWrQFLDGHWUDomRpSHTXHQDYDULDQGR
GHDN1GHSHQGHQGRGDGLVWkQFLDHQWUH
HOHVSRLVH[LJHXPDGLVWkQFLDPtQLPD
6mRXVDGRVSDUDIL[Do}HVGHSHTXHQDLQ
WHQVLGDGHGHFDUJD
)LJXUD ± )L[DGRU TXtPLFR
$SUHVHQWDPRVQDVWDEHODV$D$YD
ORUHVPpGLRVSDUDFiOFXORGDUHVLVWrQFLDFRP
HVWHVWLSRVGHIL[DGRUHV
2SURMHWLVWDGHYHFRQVXOWDURVFDWiORJRV
GRVIDEULFDQWHVSDUDHVFROKHUDTXHOHTXHPH
OKRUOKHDWHQGD
± &iOFXOR GD 5HV LVW rQF LD GRV I L[DGRUHV
TXtPLFRVHPIXQomRGDVGLVWkQFLDV
(PJHUDODUHVLVWrQFLDGRVFKXPEDGRUHV
TXLPLFRVpFDOFXODGRSHODVHJXLQWHHTXDomR
)5 )7 IU ID
)5 YDORUGHFDUJDUHFRPHQGDGDMiDSOLFDGR
RFRHILFLHQWHGHVHJXUDQoD
)7 YDORUGDFDUJDGHWUDomRRXFRUWDQWH
WDEHODGRIHLWRSRUHQVDLRV
IU YDORUGHUHGXomRTXDQWRDERUGD
ID YDORUGHUHGXomRTXDQWRDGLVWkQFLDHQWUH
HOHV
6H H[LVWH PDLV GH XPD GLVWkQFLD D ERUGD RX
HQWUHDQFRUDJHQVGHYHVHUDSOLFDGRRIDWRUGH
UHGXomRSDUDFDGDFRQGLomRGHLQIOXrQFLD3DUD
ERUGD IU IU IU IU
3DUDGLVWkQFLDHQWUHHOHV ID ID ID ID
6 GLVWkQFLDHQWUHDQFRUDJHQV!GD
& GLVWkQFLDGDDQFRUDJHPDWpDERUGD!
GD
KQRP SURIXQGLGDGHGDDQFRUDJHP!GD
KHI SURIXQGLGDGHHIHWLYDGHDQFRUDJHP
KHI !KQRP
GD GLkPHQWURGDDQFRUDJHP
$VGLVWkQFLDVPtQLPDVWDPEpPGHYHPVHU
UHVSHLWDGDVHVmR
6PLQ !KHI H 6FU KHI
&PLQ !KHI H &FU KHI
)yUPXODVSDUDFiOFXORGRIDWRUGHUHGXomR
SDUDDQFRUDJHPSRUDWULWR
$QFRUDJHPSDUDFDUJDVSHVDGDV7DE$
)DWRUGHGLVWkQFLDHQWUHDQFRUDJHQV 7UDomRH
&RUWH
ID [6
KHI
)DWRUGHDMXVWHGHERUGDSDUD 7UDomR
IUW [&
KHI
)DWRUGHDMXVWHGHERUGDSDUD &RUWH
SHUSHQGLFXODUDERUGD
IUY [&
KHI
)DWRUGHDMXVWHGHERUGDSDUD &RUWH SDUDOHOR
DERUGD
IUY [&
KHI
1RFDVRGHKDYHUFDUJDFRPELQDGDGHWUDomRH
FRUWHpQHFHVViULRXPDYHULILFDomRDGLFLRQDO
DWUDYpVGDVVHJXLQWHVIyUPXODV
)LJXUD ± 'LVWkQFLDV HQWUH DQFRUDJHQV H DQFRUDJHQV H
ERUGDV
3DUDTXHQmRRFRUUDPUHGXo}HVDVVHJXLQWHV
GLVWkQFLDVGHYHPVHUUHVSHLWDGDV
1
9
+
1UHF 9UHF ≤ FRQVHUYDGRUD
/LJDo}HVYLJDVGHDoRFRPHOHPHQWRVGHFRQFUHWR ⎛ 1 ⎞
⎟⎟
⎜⎜
1
⎝ UHF ⎠
⎛ 9 ⎞
⎟⎟
+ ⎜⎜
9
⎝ UHF ⎠
3LODUHVGHSHTXHQDVHVSHVVXUDV
2EV1R$QH[R$VmRIRUQHFLGRVDV7DEHODV$
D$SDUDHIHLWRGHSURMHWR
3DUD H[HFXomR FRQVXOWDU R FDWiORJR GR
IDEULFDQWH
(VSHVVXUDVGRVSLODUHV
3LODUHVGHJUDQGHVHVSHVVXUDV
6HRSLODUIRUGHGLPHQVmRODUJXUDRXFRP
SULPHQWRDFLPDGHPPSRGHVHFRORFDU
SDUDIXVRVGHH[SDQVmRRXTXtPLFRVFRPRGLk
PHWURHSURIXQGLGDGHVQHFHVViULRVSDUDDWHQ
GHUDVFDUJDVGHDFRUGRFRPRWLSRHIDEULFDQWH
)LJDE
6HRSLODUIRUGHGLPHQVmRFRPSULPHQWR
RXODUJXUDLQIHULRURXLJXDODPPDPHOKRU
VROXomRpDFRORFDomRGHFKXPEDGRUHVRXSD
UDIXVRVSDVVDQWHVTXHDWUDYHVVDPWRGDDHV
SHVVXUDIL[DQGRVHHPXPDRXWUDFKDSDQRRX
WURODGRGDQGRXPDSURWHQVmRQRFKXPEDGRU
)LJF
8PDERDVROXomRWDPEpPpRXVRGHEDU
UDVSURWHQGLGDVWLSR'<:'$*TXHVmRDSUH
VHQWDGDVQRPHUFDGRFRPGLkPHWURGHPP
FRPUHVLVWrQFLDjUXWXUDGHN1HGHHVFRD
PHQWRGHN18VDVHXPFRHILFLHQWHGHVH
JXUDQoDFRPXPDFDUJDGHWUDEDOKRGDRU
GHPGHN1
([LJHVH XPD GLVWkQFLD YHUWLFDO PtQLPD
HQWUHFHQWURVGHDQFRUDJHQVGHFPHDGLV
WkQFLDKRUL]RQWDOPtQLPDHQWUHEDUUDVGHFP
([HPSOR± 9HULILFDUVH XPDDQFRUDJHPGH
IL[DGRUTXtPLFRGHGHDFRUGRFRPDV7DE
$D$DWHQGHP$VFDUJDVLQGLFDGDVQD
ILJXUDVmRGHYLGRDRYHQWR2SLODUpXPWXER
UHWDQJXODUGH[FP
D
E
F
)LJXUD )L[DomR DWUDYpV GH FKXPEDGRUHV GH H[SDQ
VmR TXtPLFRV RX SURWHQGLGRV
D±0pWRGR$,6&$6'
9HULILFDomRGDDQFRUDJHP
'HDFRUGRFRPDWDEHOD$SDUDFDUJDV
DGPLVVtYHLVQRFRQFUHWRH$QDEDUUDGHDoR
WHPRV
IFN 03D N1FP
7F N19F N17DE$FRQF
7D N19D N17DE$±6XSHU
KHI FP& & FPDGRWDGR
+
2.
±9HULILFDomRGDSODFDGHEDVHDWUDomR
,WHP
)\ N1FP G EI FPJ FP
'HDFRUGRFRPWHPRVSDUDEI!G
1W JG
G + EI
6 FP!KHI [ 2.
6FU [KHI [ FP!2.
& FP![ 2.
&FU [ 2.
&DUJDDWXDQWH1W N19 N1
WS )DWRUGHDMXVWHSDUDGLVWkQFLDHQWUHDQFRUDJHQV
7UDomRH&RUWH
8VDU&K[[PP
× ID +
)DWRUGHDMXVWHSDUDGLVWkQFLDGHERUGD
7UDomR
IUQ +
× XVDU
)DWRUGHDMXVWHGHGLVWkQFLDSHUSHQGLFXODUD
ERUGD&RUWH
IUY [
± XVDU
)DWRUGHDMXVWHGHGLVWkQFLDSDUDOHODDERUGD
&RUWH
× XVDU
IUY &DUJDGHWUDEDOKRUHFRPHQGDGD
7UDomR
1UHF 17 ID IUW [[ N1
&RUWH
9UHF 9IDIUYIUY [[ N1
WS ,WHP
× × FP
+ × E0pWRGR$,6&/5)'
±9HULILFDomRGDDQFRUDJHP
'HDFRUGRFRPDWDEHOD$IDWRUDGDSRUH
$
IFN N1FP
7XF [ N1QRFRQFUHWR
9XF [ N1³
7XD N16XSHU
9XD N1
&DUJDVDWXDQWHVIDWRUDGDV
1WX [ N1
1YX [ N1
&RQFUHWRSLRUFDVR
1XUHF [[ N1
9XUHF [[ N1
+
2.
±9HULILFDomRGDSODFDGHEDVHDWUDomR
'HDFRUGRFRPWHPRV
WS FP
1WXJG
× × G + EI
+ × /LJDo}HVYLJDVGHDoRFRPHOHPHQWRVGHFRQFUHWR 8VDU&K[[PP
([HPSOR± 'LPHQVLRQDURFRQVROHHDOLJD
omRMXQWRDRSLODUGHFRQFUHWRMiFRQVWUXtGRFRP
IFN 03D N1FP GHDFRUGRFRPDV
FDUJDVLQGLFDGDVQDILJXUDFRQVLGHUDQGR
D)L[DGRUTXtPLFRFRPDoR6XSHU
7DE$
E %DUUDSURWHQGLGDWLSR'<:,'$*67
$oRSDUDRFRQVROH)\ N1FP
F
D
G
3DUDHIHLWRGHFiOFXORSDUDDVWHQV}HVQR
FRQFUHWRYDPRVFRQVLGHUDU$ $
D±0pWRGR$,6&$6'
E
9&3 N19&$ N1
9 N1
0 [ N1FP
)F IFN [ N1FP
/ FP%LQIHULRU FP
/QHF 0
× =
2.
%IF
× &iOFXORGHIFUHDOHSDUkPHWURV
IFPD[ IFPLQ & / =
FP& < / −
7 0 × =
2.
%/ × &
− H FP
0 =
N1
< &iOFXORGDHVSHVVXUDGDFKDSDVHPUHIRUoR
× N1FP
0S WS × × N1FP
6HMD&K[
0 × : IE FP
)\ 2.
&iOFXORGDFKDSDGDPHVDVXSHULRUGR
FRQVROH
FP ⇒ PP
&iOFXORGDHVSHVVXUDGDFKDSDFRPRVUHIRUoR
FRQIRUPHILJXUD
DE ȕ )LJXUD ȕ IS [ N1FP
DE WS β IF
× FP
WS E
)\
× 8VDU&K[[PP
&iOFXORGDFKDSDGHUHIRUoR
× × 8VDU&K[[PP
9HULILFDomRGDDOPD
1D N1
)Y [ N1FP
)Y2.
× &iOFXORGRILOHWHGHVROGD
IY IV N1FP
× )LJXUD /LJDo}HVYLJDVGHDoRFRPHOHPHQWRVGHFRQFUHWR
FP PP
8VDUVROGDPtQLPDPP
&iOFXORGRVIL[DGRUHVGHDQFRUDJHP
7DEHODV$H$6XSHU
DV IW SDUDI N1
IY SDUDI N1
3DUDIXVRĭ ó´ PP SURI PP
1RFRQFUHWR7DE$
)WF N1)YF N1
1RSLQRGHDoR6XSHU7DE$
)WD N1)YD N1
& FP6 FPKHI FP
&!KHI 2.6!KHI 12.
6&5 ![KHI [ 12.
&&5 ![KHI [ 2.
&iOFXORGRVIDWRUHVGHDMXVWH
'LVWkQFLDGHERUGD D7UDomRHDR&RUWH
ID +
× 'LVWkQFLDHQWUHDQFRUDJHQV 7UDomR
ID +
× XVDU
'LVWkQFLDGDERUGD S HUSHQGLFXODU&RUWH
IUY × ± XVDU
'LVWkQFLDGDERUGD S DUDOHOD&RUWH
× XVDU
1RFRQFUHWR
1QHF [[ N1
9QHF [[ N1
IUY +
1
9
+
1QHF 9QHF
2.
1RSLQRGHDoR
1QHF [[ N1
9QHF [[ N1
2.
3URIXQGLGDGHPP7DE$
(VPDJDPHQWRQRFRQFUHWR
/SLQR FP
3 [[ IHVP 2.
× %DUUDSURWHQGLGDWLSR'<:,'$*
1 N1$FK [[[
FP
ĭ !1SURM N1!N12.
7HQVmRQRFRQFUHWR 2.
E±0pWRGR$,6&/5)'
9X [[ N1
0X [ N1FP
/ FP% FP
)FX [ N1FP 7DE
&iOFXORGHIFUHDOHSDUkPHWURV
× N1FP
IFXPD[ IFXPLQ × & & < N1
&iOFXORGDHVSHVVXUDGDFKDSDVHPUHIRUoR
7 × 0SX &iOFXORGRILOHWHGHVROGD
N1FP
N1FPDV FP
× 6ROGDPLQLPDGHPP
IVX FP!!PP
&iOFXORGDFKDSDFRPUHIRUoR
WS DE ȕ × FP!PP
WS [
&iOFXORGDFKDSDGHUHIRUoR
× × N1FP
6HMDFKDSDPtQLPDGHPP
0SX × FP
:[ [ 2.
&iOFXORGDPHVDVXSHULRUGRFRQVROH
&iOFXORGRVIL[DGRUHVGHDQJRUDJHP
7DE$H$±6XSHU
1X SDUDI N1
9X SDUDI N1
3DUDIXVRĭ ó´ PP
ID IUY 1RFRQFUHWR7DE$
1XQHF [[ N1
9XQHF [[ N1
2.
1RSLQRGHDoR$
1XD N19XD N1
1XQHF [[ N1
9XQHF [[ N1
IEX 2.
N1FP
× DE ȕ %DUUDSURWHQGLGDWLSR'<:,'$*
'HVIDWRUDUHFRQVLGHUDUFRPRQDVWHQV}HV
DGPLVVtYHLV
ISX WS × FP
[
'HWDOKH&RQVWUXWLYR
8VDU&K[[PP
9HULILFDomRGDDOPDWZ PP
N1
)YX )\ [ N1FP
1DX IYX 2.
× )LJXUD
%LEOLRJUDILD
%LEOLRJUDILD
$PHULFDQ,QVWLWXWHRI6WHHO&RQVWUXFWLRQ
$,6&$6'/5)'D $PHULFDQ,QVWLWXWHRI6WHHO&RQVWUXFWLRQ
&ROXQDV%DVH3ODWHV±6WHHO'HVLJQ*XLGH
6HULHV1R ±-RKQ7'HZROIH'DYLG7
%LFNHU±$ $PHULFDQ,QVWLWXWHRI6WHHO&RQVWUXFWLRQ
,QGXVWULDO%XLOGLQJ±*XLGH6HULHV1R ±
0)LVKHU±
$PHULFDQ,QVWLWXWHRI6WHHO&RQVWUXGWLRQ
$,6&(QJLQHHULQJ -RXUQDO ± VHFRQG
TXDUWHU±+HDG6WHHO$QFKRUXQGHU
&RPELQHG/RDGLQJ3DWULFN-0FPDFNLQ
5RJHU*6OXWWHUDQG-RKQ:)LVKHU
$PHULFDQ,QVWLWXWHRI6WHHO&RQVWUXFWLRQ
±$,6&±(QJLQHHULQJ-RXUQDO±ILUVWTXDUWHU
±0RPHQWH5HVLVWLQJ&RQQHFWLRQVIRU
0L[HG &RQVWUXFWLRQ ± 1HLO 0 +DZNLQV
'HQLV0LWFKHOODQG&KDUOHV:5RHGHU
$PHULFDQ,QVWLWXWHRI6WHHO&RQVWUXFWLRQ
±$,6&±(QJLQHHULQJ-RXUQDO±ILUVWTXDUWHU
±&RQQHFWLRV%HWZHHQ6WHHO)UDPHV
DQG&RQFUHWH:DOOV±&:5RHGHUDQG
1HLO0+DZNLQV
(GLWRUD1HZQHV
$QGUDGH3pULFOHV%DUUHWR&XUVREiVL
FRGH(VWUXWXUDVGH$oR,($(GLWRUDD
5*2JGHQ%D5+HQOH\&RQVWUXF
WLRQV%HWZHHQ6WHHODQG2WKHU0DWHULDOV
,QWHUIDFHV
6DOPRQ*&KDUOHV-RKQVRQ-RKQ(
6WHHO6WUXFWXUHV'HVLJQDQG%HKDUYRUD
%HOOHL,OGRQ\+(GLItFLRVLQGXVWULDLVHP
DoR(GLWRUD3LQLD HGLomR
%HOOHL,OGRQ\+3LQKR)HUQDQGR2
3LQKR0DXUR2(GLItFLRVGHP~OWLSORVDQ
GDUHVHPDoR(GLWRUD3LQL
0DQXDO7pFQLFRGH3URGXWRV±+,/7,±
6LVWHPD GH SURWHQVmR '<:,'$*
7HFQDUW±6LVWHPDGHIL[DomR±
860GR%UDVLO3DUDEROW
1%5±3URMHWRHH[HFXomRGHHV
WUXWXUDVGHDoRGHHGLItFLRVHPUHYLVmR
0XNQRY.(VWUXWXUDV0HWiOLFDV(GLWRUD
0LU±0RVFRX
%ORGJHWW 2 : 'HVLJQ RI :HOGHG
6WUXFWXUHV-DPHV)±/LQFROQ$UF:HOGLQJ
)RXQGDWLRQ
/HVFRXDUF¶K ,YRQ &ROVRQ $QGUH
&RQVWUXFWLRQ 6WHHO 'HVLJQ ± $P
,QWHUQDWLRQDO *XLGH ± (OVHYHU $SSOLHG
6FLHQFH±
0DF *LQOH\7 - 6WUXFWXUDO 6WHHZRUN
:DOV\PD6LVWHPDGHIL[DomR
$QH[RV
$QH[RV
$QH[RV
$QH[RV