P1_JUN_03

8QLYHUVLGDGGH1DYDUUD
1DIDUURDNR8QLEHUWVLWDWHD
(VFXHOD6XSHULRUGH,QJHQLHURV
,QJHQLDULHQ*RL0DLODNR(VNROD
$6,*1$785$*$,$7(&12/2*Ì$6'()$%5,&$&,Ð1
7LHPSRKRUD
SXQWRV
120%5(,=(1$
&8562.85762$ž
3B-81B
)(&+$'$7$
6HWUDWDGHUHDOL]DUXQDURVFDPpWULFDGHSDVRPPVREUHHOGLiPHWURGHPPGHODILJXUD
/DPiTXLQDHVXQWRUQRGH&RQWURO1XPpULFRFRQODVVLJXLHQWHVFDUDFWHUtVWLFDV
9HORFLGDGDQJXODUGHOKXVLOORSULQFLSDOFDEH]DOJDPDFRQWLQXDHQWUH\USP
9HORFLGDGHVGHDYDQFHGHFDUURV;=JDPDFRQWLQXDHQWUH\PPLQ
&DUDFWHUtVWLFDVGHOSURFHVR
(ODYDQFHSRUSDVDGDVHUHDOL]DUiHQODGLUHFFLyQGHOSHUILOGHODURVFDQRHQHOVHQWLGRUDGLDOFRPRHQ
PiTXLQD FRQYHQFLRQDO \ WLHQH XQ YDORU WDO TXH HQ WRGDV ODV SDVDGDV VH HOLPLQD OD PLVPD VHFFLyQ GH
YLUXWDODFXDOQRGHEHVHUVXSHULRUDPP (Q OD ILJXUD VH PXHVWUD HO SHUILO GH OD URVFD D PHFDQL]DU 3DUD HO FiOFXOR GH OD VHFFLyQ GH YLUXWD
FRQVLGHUDUTXHODSXQWDGHODURVFDWLHQHUDGLRQXORHVGHFLUGHVSUHFLDUHOUHGRQGHRGHDOWXUD+
/D YHORFLGDG GH FRUWH VHOHFFLRQDGD SDUD OD RSHUDFLyQ HV PPLQ 1R VH GD OD FDUDFWHUtVWLFD GH
SRWHQFLDGHOWRUQRSRUTXHVHVDEHTXHHQHVWDRSHUDFLyQODSRWHQFLDQRVXSRQHQLQJXQDOLPLWDFLyQ
6HSLGH
7LHPSR GH RSHUDFLyQ WRS VDELHQGR TXH HO GH SRVLFLRQDPLHQWR GH OD SXQWD GH OD KHUUDPLHQWD HQWUH
SDVDGDVHVGHVSUHFLDEOH\TXHHOUHWURFHVRVHUHDOL]DDODPi[LPDYHORFLGDG7RPDU PP
S
9DORU GH OD FRRUGHQDGD ; GH OD SXQWD GH OD KHUUDPLHQWD UDGLR QXOR GXUDQWH OD SDVDGD Q~PHUR ¢3RU TXp UD]yQ HQ OD PiTXLQD FRQYHQFLRQDO HO DYDQFH SRU SDVDGD QR VH UHDOL]D WDPELpQ HQ OD
GLUHFFLyQGHOSHUILOGHODURVFD"S
9DORUGHORV iQJXORVUHDOHVGHLQFLGHQFLD \ GH GHVSUHQGLPLHQWRGHOILORSULQFLSDOGHODKHUUDPLHQWD
6HVDEHTXHVHFFLRQDQGRGLFKRILORSRUXQSODQRTXHFRQWLHQHDODYHORFLGDGGHFRUWH\ODYHORFLGDG
GHOFDUUR=ORViQJXORVGHLQFLGHQFLD\GHGHVSUHQGLPLHQWRWHyULFRVVRQGHž\žUHVSHFWLYDPHQWH
+DFHUXQGLEXMRFODURGH ODYLVWDHQSODQWDGHOD KHUUDPLHQWD \GDUOHODVHFFLyQDGHFXDGDSDUDYHU
GLFKRV iQJXORV HQ YHUGDGHUDPDJQLWXG ¢&XiO VHUtD HO YDORU GH HVRV iQJXORV HQ HO FDVR GH TXH OD
RSHUDFLyQVHUHDOL]DUDHQXQWRUQRFRQYHQFLRQDO"5D]RQDUODUHVSXHVWDS
6REUHODILJXUDVHxDODUORVSDUiPHWURVDIDSDZDFFRUUHVSRQGLHQWHVDOD~OWLPDSDVDGD&DOFXODU
VXVYDORUHV\SDUDHOORGHVSUHFLDUFRPRDQWHVHOUHGRQGHRGHODKHUUDPLHQWDS
3B-81B
[
)LJXUD
0[
+
3,(=$
+
+
)LJXUD
35(*817$
/DH[SUHVLyQGHOWLHPSRGHRSHUDFLyQHV
W RS = (W DY + W UHW ) ¼ 1 3$6 œ
W DY =
7LHPSRGHDYDQFH /
PP
=
S ¼ 1 PP ¼ 1
(VQHFHVDULRFRQRFHUODYHORFLGDGGHJLUR1
9& = P
= p ¼ ¼ - PP ¼ 1 PLQ
W DY =
6XVWLWX\HQGRHQ
œ
7LHPSRGHUHWLUDGD
W UHW =
œ
1~PHURGHSDVDGDV
1 = USP PP
= PLQ PP ¼ USP
/
PP
=
= PLQ 9IPi[ ¼ PP PLQ
1 SDV =
6DEHPRVTXH $ & ˆ PP $UHD 7RWDO $ 7
=
$&
$&
'LEXMDQGRHOSHUILOGHODURVFDSDUDFDOFXODU $ 7 ILJXUD
3,(=$
ž
+
+
ž
ž
+
$7 = ¼ %¼
%
S )LJXUD
+VHSXHGHFDOFXODUSRUWULJRQRPHWUtDVDELHQGRTXH
S
PP
WDQ =
= =
Ë Û
¼+
¼+
Ì + ܼ+
Í Ý
+ = PP %VHSXHGHSRQHUHQIXQFLyQGH+
%
WDQ = +
% = ¼ + ¼ WDQ 6XVWLWX\HQGRHQ
$7 =
'H 1 SDV =
+
¼ ¼ + ¼ WDQ ¼
= PP PP = PP 6HHOLJHQ 1 SDV = \DTXHFRQQRVHFXPSOLUtD $ & ˆ PP (OiUHDGHFRUWHVHUiLJXDOD
$& =
$ 7 PP =
= PP < PP 1 SDV
6XVWLWX\HQGRORVYDORUHVFDOFXODGRVHQ
W RS = ( + ) ¼ = PLQ SXQWRV
35(*817$
(QODILJXUDVHUHSUHVHQWDODVLWXDFLyQH[LVWHQWHGXUDQWHODWHUFHUDSDVDGD
(MHGHODURVFD
3,(=$
;
«
$
$
K
$
%
S )LJXUD
6HVDEHTXH $ + $ + $ = ¼ $ & = ¼ % ¼ K %
WDQ ž = K
“
% = ¼ K ¼ WDQ ž 6XVWLWX\HQGRHQ
¼ $& =
¼ $&
¼ PP ¼ ( ¼ K ¼ WDQ ž ) ¼ K = K ¼ WDQ ž GHGRQGH K =
=
= PP WDQ ž
WDQ ž
/DFRRUGHQDGD;GHODSXQWDGHODKHUUDPLHQWDUHVSHFWRDOHMHGHODURVFDVHUiLJXDOD
; =
- K =
- = PP 3RUTXHKDFHUORDVtVHUtDGREOHPHQWHFRPSOHMRSDUDHORSHUDULR
35(*817$
9
SXQWRV
SXQWRV
9
I
6HFFLyQ$$
h
a ž
9
F
g ž
I
I
I
9
a ž
F
I
h
g h
3,(=$
$
U
$
$
&
I
h
+(55$0,(17$
h = DUFWDQ
a
U
)LJXUD
9I
S¼1
S
= DUFWDQ
= DUFWDQ
= DUFWDQ
= ž 9&
p¼'¼1
p¼'
p ¼ a = a - h = ž -ž = ž U
a
I
g = g + h = + ž = ž U
I
SXQWRV
(QWRUQRFRQYHQFLRQDOVHUtDORPLVPR\DTXHhHVLGpQWLFR\GHSHQGHVyORGH'\GHS\pVWRVQR
FDPELDQ
SXQWRV
35(*817$
D
I
D
Z
$
3,(=$
D
&
D
3
)LJXUD
+
+
= - = = = PP FRV ¼ ¼ œ
D Z
œ
D & =
œ
D 3 = D Z ¼ FRV ž = PP œ
DI =
$ & PP =
= PP D Z
PP
$&
= PP D S
SXQWRV
SXQWRV