8QLYHUVLGDGGH1DYDUUD 1DIDUURDNR8QLEHUWVLWDWHD (VFXHOD6XSHULRUGH,QJHQLHURV ,QJHQLDULHQ*RL0DLODNR(VNROD $6,*1$785$*$,$7(&12/2*Ì$6'()$%5,&$&,Ð1 7LHPSRKRUD SXQWRV 120%5(,=(1$ &8562.85762$ 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\GHGHVSUHQGLPLHQWRWHyULFRVVRQGH\UHVSHFWLYDPHQWH +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 W DY = 7LHPSRGHDYDQFH / PP = S ¼ 1 PP ¼ 1 (VQHFHVDULRFRQRFHUODYHORFLGDGGHJLUR1 9& = P = p ¼ ¼ - PP ¼ 1 PLQ W DY = 6XVWLWX\HQGRHQ 7LHPSRGHUHWLUDGD W UHW = 1~PHURGHSDVDGDV 1 = USP PP = PLQ PP ¼ USP / PP = = PLQ 9IPi[ ¼ PP PLQ 1 SDV = 6DEHPRVTXH $ & PP $UHD 7RWDO $ 7 = $& $& 'LEXMDQGRHOSHUILOGHODURVFDSDUDFDOFXODU $ 7 ILJXUD 3,(=$ + + + $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 $ & 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 = K % = ¼ K ¼ WDQ 6XVWLWX\HQGRHQ ¼ $& = ¼ $& ¼ PP ¼ ( ¼ K ¼ WDQ ) ¼ K = K ¼ WDQ GHGRQGH K = = = PP WDQ WDQ /DFRRUGHQDGD;GHODSXQWDGHODKHUUDPLHQWDUHVSHFWRDOHMHGHODURVFDVHUiLJXDOD ; = - K = - = PP 3RUTXHKDFHUORDVtVHUtDGREOHPHQWHFRPSOHMRSDUDHORSHUDULR 35(*817$ 9 SXQWRV SXQWRV 9 I 6HFFLyQ$$ h a 9 F g I I I 9 a F I h g h 3,(=$ $ U $ $ & I h +(55$0,(17$ h = DUFWDQ a U )LJXUD 9I S¼1 S = DUFWDQ = DUFWDQ = DUFWDQ = 9& p¼'¼1 p¼' p ¼ a = a - h = - = U a I g = g + h = + = 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 D Z D & = D 3 = D Z ¼ FRV = PP DI = $ & PP = = PP D Z PP $& = PP D S SXQWRV SXQWRV