Manual do usuário HP 10BII

[. . . ] hp 10BII calculadora financeira guia do usuário Edição 1 Número de peça HP F1902-90004 Aviso REGISTRO SEU PRODUTO EM : www. register. hp. com ESTE MANUAL E TODOS OS EXEMPLOS CONTIDOS AQUI SÃO FORNECIDOS "DO JEITO QUE ESTÃO" E ESTÃO SUJEITOS À MUDANÇAS SEM AVISO PRÉVIO. A COMPAINHA HEWLETTPACKARD NÃO FAZ GARANTIA DE NENHUM TIPO COM RESPEITO A ESTE MANUAL OU OS EXEMPLOS CONTIDOS AQUI, INCLUINDO, MAS NÃO SE LIMITANDO ÀS GARANTIAS IMPLÍCITAS DE COMERCIABILIDADE, NÃO-VIOLAÇÃO E APTIDÃO PARA UM PROPÓSITO PARTICULAR. NÃO SERÁ RESPONSÁVEL POR QUAISQUER ERROS OU POR DANOS ACIDENTAIS OU CONSEQUENCIAIS RELACIONADOS COM O FORNECIMENTO, DESEMPENHO, OU USO DESTE MANUAL OU OS EXEMPLOS CONTIDOS AQUI. © Copyright 1988, 1989, 2001, 2004 Hewlett-Packard Development Company, L. P. Reprodução, adaptação, ou tradução deste manual é proibido sem permissão prévia por escrito de Hewlett-Packard Company, exceto quando permitido pelas leis de direitos autorais. Hewlett-Packard Company 4995 Murphy Canyon Rd, Suite 301 San Diego, CA 92123 Histórico da Tiragem Edição 1 Maio 2003 Bem-vindo à HP 10BII $ VXD +3 %, , UHIOHFWH D TXDOLGDGH VXSHULRU H D DWHQomR DRV GHWDOKHV GH HQJHQKDULD H GH IDEULFDomR TXH Ki DQRV GLVWLQJXHP RV SURGXWRV +HZOHWW3DFNDUG $ +HZOHWW3DFNDUG p UHVSRQViYHO SRU HVWD FDOFXODGRUD ³ H RIHUHFHPRV D QRVVD H[SHULrQFLD QR VXSRUWH j VXD XWLOL]DomR FRQVXOWH D SDUWH LQWHUQD GD ~OWLPD FDSD H DVVLVWrQFLD WpFQLFD HP WRGR R PXQGR Qualidade Hewlett-Packard $V QRVVDV FDOFXODGRUDV VmR IHLWDV REMHFWLYDQGR D H[FHOrQFLD H D IDFLOLGDGH GH XWLOL]DomR n (VWD FDOFXODGRUD IRL SURMHFWDGD SDUD VXSRUWDU SLQJRV YLEUDo}HV SROXHQWHV QHYRHLUR R]RQR H[WUHPRV GH WHPSHUDWXUD H YDULDo}HV GH KXPLGDGH TXH SRGHP VHU HQFRQWUDGRV QR GLDDGLD n $ FDOFXODGRUD H R VHX PDQXDO IRUDP SURMHFWDGRV H WHVWDGRV SDUD XPD IiFLO XWLOL]DomR $FUHVFHQWDPRV GLYHUVRV H[HPSORV SDUD GHVWDFDU RV YiULRV XVRV GD FDOFXODGRUD 0DWHULDLV DYDQoDGRV H WHFODV FRP OHWUDV SHUPDQHQWHV SURSRUFLRQDP XPD YLGD ORQJD SDUD R WHFODGR H XPD SRVLWLYD VHQVDomR WiFWLO n 2 VLVWHPD HOHFWUyQLFR GH EDL[D SRWrQFLD H R VLVWHPD GH JHVWmR GH HQHUJLD DYDQoDGR SURSRUFLRQDP XPD PDLRU YLGD ~WLO j EDWHULD n 2 PLFURSURFHVVDGRU IRL RSWLPL]DGR SDUD XP SURFHVVDPHQWR FRPSXWDFLRQDO UiSLGR H FRQILiYHO XWLOL]DQGR LQWHUQDPHQWH GtJLWRV SDUD D REWHQomR GH UHVXOWDGRV SUHFLVRV n 0HGLDQWH XPD H[WHQVD SHVTXLVD IRL FULDGR XP GHVLJQ TXH PLQLPL]RX RV HIHLWRV DGYHUVRV GD HOHFWULFLGDGH HVWiWLFD TXH p XPD FDXVD SRWHQFLDO GR PDX IXQFLRQDPHQWR H GD SHUGD GH GDGRV QDV FDOFXODGRUDV Bem-vindo à HP 10BII 3 Recursos 2V UHFXUVRV H R PDQXDO GD +3 %, , UHIOHFWHP DV QHFHVVLGDGHV H RV DQVHLRV GH PXLWRV FRQVXPLGRUHV n 9LVRU JUDQGH GH FDUDFWHUHV n 6HFomR GH , QVWUXo}HV , QLFLDLV QR PDQXDO SDUD UHIHUrQFLD UiSLGD n $SOLFDo}HV SDUD VROXomR GH RSHUDo}HV FRPHUFLDLV H ILQDQFHLUDV 9DORU 7HPSRUDO GR , QYHVWLPHQWR )ROKDV GH FiOFXOR GH HPSUpVWLPR SRXSDQoD DOXJXHU H DPRUWL]DomR &RQYHUVmR GH -XURV 7D[DV QRPLQDLV H HIHFWLYDV )OX[RV GH &DL[D 9DORU OtTXLGR DFWXDO H WD[D LQWHUQD GH UHQWDELOLGDGH 3HUFHQWDJHQV &RPHUFLDLV &iOFXOR GH DOWHUDomR SHUFHQWXDO PDUJHP H PDUJHP GH OXFUR (VWDWtVWLFD 0pGLD GHVYLR SDGUmR FRHILFLHQWH GH FRUUHODomR H HVWLPDWLYD GH UHJUHVVmR OLQHDU DOpP GH RXWURV FiOFXORV HVWDWtVWLFRV n 0HPyULD VXILFLHQWH SDUD DUPD]HQDU XP IOX[R GH FDL[D LQLFLDO GH JUXSRV GH IOX[R GH FDL[D FRP DWp IOX[RV GH FDL[DV SRU JUXSR n 'H] UHJLVWRV GH DUPD]HQDPHQWR QXPHUDGRV n 2 DFHVVR IiFLO jV IXQo}HV HFRQRPL]D HWDSDV GH GLJLWDomR H SHUPLWH PDLRU FRQYHQLrQFLD &DSDFLGDGH GH LQFUHPHQWDomR DXWRPiWLFD SDUD IROKDV GH FiOFXOR GH DPRUWL]DomR (WLTXHWDJHP SDUD DPRUWL]DomR H IOX[RV GH FDL[D &RQVWDQWH DXWRPiWLFD WHFODV GH PHPyULD n +i PXLWRV H[HPSORV QR PDQXDO TXH SRGHP VHU FRPELQDGRV FRQIRUPH DV VXDV QHFHVVLGDGHV HVSHFtILFDV 4 Bem-vindo à HP 10BII Índice 11 11 12 13 14 15 16 17 18 19 21 Visão Rápida , QVWUXo}HV %iVLFDV ³ 9LVmR 5iSLGD 3HUFHQWXDLV ³ 9LVmR 5iSLGD 7HFODV GH 0HPyULD ³ 9LVmR 5iSLGD 9DORU 7HPSRUDO GR 'LQKHLUR 790 ³ 9LVmR 5iSLGD +LSyWHVHV 790 ³ 9LVmR 5iSLGD $PRUWL]DomR ³ 9LVmR 5iSLGD &RQYHUVmR GH 7D[D GH -XURV ³ 9LVmR 5iSLGD , 55<5 H 139 ³ 9LVmR 5iSLGD (VWDWtVWLFDV ³ 9LVmR 5iSLGD 7HFODV Instruções Iniciais /LJDQGR H 'HVOLJDQGR D &DOFXODGRUD $MXVWH GR &RQWUDVWH GR 9LVRU &iOFXORV $ULWPpWLFRV 6LPSOHV &DUDFWHUtVWLFDV GR 9LVRU H GR 7HFODGR &XUVRU ([FOXVmR GH 'DGRV GR &RQWH~GR GD &DOFXODGRUD ([FOXVmR GR &RQWH~GR GH 'DGRV GD 0HPyULD , QGLFDGRUHV 7HFOD GH 3UHIL[R 7HFOD GH (VWDWtVWLFD 7HFOD , 1387 7HFOD 6:$3 )XQo}HV 0DWHPiWLFDV )RUPDWR GRV 1~PHURV QR 9LVRU (VSHFLILFDomR GDV &DVDV 'HFLPDLV ([LELGDV 1RWDomR &LHQWtILFD ([LELomR GH 1~PHURV FRP 3UHFLVmR 7RWDO , QWHUFkPELR HQWUH 3RQWR H 9tUJXOD $UUHGRQGDPHQWR GH 1~PHURV 0HQVDJHQV Índice 5 1 23 23 23 23 25 25 25 25 26 27 27 28 28 28 29 30 30 31 31 31 32 2 33 33 33 34 34 35 35 36 36 37 37 37 39 40 41 42 43 43 Percentagens para Negócios 7HFOD GH 3HUFHQWDJHP &iOFXOR GH XPD 3HUFHQWDJHP $GLomR RX 6XEWUDFomR GH XPD 3HUFHQWDJHP 9DULDomR 3HUFHQWXDO &iOFXORV GH 0DUJHP H 0DUJHP GH /XFUR &iOFXORV GH 0DUJHP 0DUJHP GH /XFUR HP &iOFXORV GH &XVWR 8VR GH 0DUJHP H 0DUJHP GH /XFUR -XQWRV Armazenamento de Números e Aritmética 8WLOL]DomR GH 1~PHURV $UPD]HQDGRV SDUD VH (IHWXDU &iOFXORV 8WLOL]DomR GH &RQVWDQWHV 8WLOL]DomR GR 5HJLVWUDGRU 0 8WLOL]DomR GH 5HJLVWUDGRUHV 1XPHUDGRV ([HFXomR GH &iOFXORV $ULWPpWLFRV HP 5HJLVWUDGRUHV ([HFXomR GH &iOFXORV $ULWPpWLFRV 2SHUDGRU GH 3RWHQFLDomR 8WLOL]DomR GH 3DUrQWHVHV HP &iOFXORV Identificação de Problemas Financeiros &RPR DERUGDU XP 3UREOHPD )LQDQFHLUR 6LQDLV GH )OX[RV GH &DL[D 3HUtRGRV H )OX[RV GH &DL[D -XUR 6LPSOHV H -XUR &RPSRVWR -XUR 6LPSOHV -XUR &RPSRVWR 7D[DV GH -XURV 'RLV 7LSRV GH 3UREOHPDV )LQDQFHLURV 5HFRQKHFLPHQWR GH XP 3UREOHPD 790 5HFRQKHFHQGR XP 3UREOHPD GH )OX[R GH &DL[D 3 4 45 45 46 47 47 47 48 49 49 49 51 6 Índice 5 53 53 55 55 55 61 64 68 73 74 75 77 77 79 79 80 82 83 86 87 89 89 90 90 90 91 91 91 92 93 95 98 Cálculo do Valor Temporal do Dinheiro 8WLOL]DomR GD $SOLFDomR 790 ([FOXVmR GR &RQWH~GR GH 790 0RGRV %HJLQ , QtFLR H (QG )LP &iOFXORV GH (PSUpVWLPRV &iOFXORV GH 3RXSDQoD &iOFXORV GH $OXJXHUHV $PRUWL]DomR &RQYHUV}HV GH 7D[DV GH -XURV , QYHVWLPHQWRV FRP 3HUtRGRV GH &RPSRVLomR 'LVWLQWRV 3HUtRGRV GH &RPSRVLomR H 3DJDPHQWR 'LIHUHQWHV Cálculos de Fluxo de Caixa 8WLOL]DomR GR $SOLFDWLYR GH )OX[R GH &DL[D 139 H , 55<5 )OX[RV GH &DL[D 'HVFRQWtQXRV 2UJDQL]DomR GH )OX[RV GH &DL[D , QFOXVmR GH )OX[RV GH &DL[D 9LVXDOL]DomR H 6XEVWLWXLomR GH )OX[RV GH &DL[D &iOFXOR GR 9DORU 3UHVHQWH /tTXLGR &iOFXOR GD 7D[D , QWHUQD GH 5HWRUQR $UPD]HQDPHQWR $XWRPiWLFR GH , 55<5 H 139 Cálculos Estatísticos ([FOXVmR GH 'DGRV (VWDWtVWLFRV , QFOXVmR GH 'DGRV (VWDWtVWLFRV (VWDWtVWLFDV FRP 8PD 9DULiYHO (VWDWtVWLFDV FRP 'XDV 9DULiYHLV H 0pGLD 3RQGHUDGD &RUUHomR GH 'DGRV (VWDWtVWLFRV &RUUHomR GH 'DGRV FRP 8PD 9DULiYHO &RUUHomR GH 'DGRV FRP 'XDV 9DULiYHLV 5HVXPR GH &iOFXORV (VWDWtVWLFRV 0pGLD 'HVYLR 3DGUmR H (VWDWtVWLFDV GH 6RPDWyULRV 5HJUHVVmR /LQHDU H (VWLPDWLYD 0pGLD 3RQGHUDGD 6 7 Índice 7 8 99 99 99 100 101 102 102 102 104 105 107 109 110 111 113 113 115 117 118 118 120 Outros Exemplos $SOLFDo}HV HP 1HJyFLRV 'HILQLomR GH XP 3UHoR GH 9HQGD 3URMHomR %DVHDGD QR +LVWyULFR &XVWR GD 'HVFRQVLGHUDomR GH 'HVFRQWR SDUD 3DJD PHQWR j 9LVWD (PSUpVWLPRV H +LSRWHFDV 7D[D $QXDO 6LPSOHV &RPSRVLomR &RQWtQXD 5HQGLPHQWR GH XPD +LSRWHFD FRP 'HVFRQWR RX ÉJLR 3HUFHQWXDO $QXDO SDUD XP (PSUpVWLPR 7D[DGR (PSUpVWLPR FRP XP 3ULPHLUR 3HUtRGR 3DUFLDO )UD FLRQiULR (PSUpVWLPR SDUD &RPSUD GH $XWRPyYHO +LSRWHFDV &DQDGHQVHV +LSyWHVHV HP &iOFXORV 790 3RXSDQoDV 3RXSDQoD SDUD 3DJDPHQWR GH 8QLYHUVLGDGH *DQKRV 1mR 7ULEXWDGRV DWp D 5HWLUDGD 9DORU GH XPD &RQWD GH $SRVHQWDGRULD 7ULEXWiYHO ([HPSORV GH )OX[RV GH &DL[D +LSRWHFDV 5HILQDQFLDGDV 9DORU )XWXUR /tTXLGR Atendimento ao Cliente, Baterias e Assistência Técnica 5HVSRVWDV D 3HUJXQWDV &RPXQV /LPLWDo}HV $PELHQWDLV (QHUJLD H %DWHULDV , QGLFDGRU GH 3RXFD (QHUJLD (VSHFLILFDo}HV GD %DWHULD , QVWDODomR GDV %DWHULDV , GHQWLILFDomR GD 1HFHVVLGDGH GH $VVLVWrQFLD 7pFQLFD *DUDQWLD /LPLWDGD GH 8P $QR 2 4XH e &REHUWR 2 4XH 1mR e &REHUWR A 123 123 125 125 125 125 126 127 128 128 129 8 Índice 129 130 130 130 131 131 131 132 133 133 7UDQVDo}HV GH &RQVXPR QR 5HLQR 8QLGR 6H D &DOFXODGRUD 3UHFLVDU GH $VVLVWrQFLD 7pFQLFD 2EWHQomR GH $VVLVWrQFLD 7pFQLFD 7D[D GH 6HUYLoR , QVWUXo}HV SDUD (QYLR *DUDQWLD VREUH D $VVLVWrQFLD 7pFQLFD $FRUGRV GH $VVLVWrQFLD 7pFQLFD , QIRUPDo}HV 5HJXODWyULDV 3DUD -DSmR VRPHQWH 7HUPRV H &RQGLo}HV GR 8VXiULR )LQDO Informações Adicionais sobre Cálculos &iOFXORV GH , 55<5 3RVVtYHLV 5HVXOWDGRV GR &iOFXOR GH , 55<5 6XVSHQVmR H 5HLQtFLR GH , 55<5 , QFOXVmR GH XPD 6XSRVLomR SDUD , 55<5 (IHLWR GR 8VR GH ² SDUD &RUUHomR GH 'DGRV , QWHUYDOR GH 1~PHURV (TXDo}HV &iOFXORV GH 0DUJHP H 0DUJHP GH /XFUR 9DORU 7HPSRUDO GR 'LQKHLUR 790 $PRUWL]DomR &RQYHUV}HV GH 7D[DV GH -XURV &iOFXORV GH )OX[R GH &DL[D (VWDWtVWLFDV Mensagens Índice remissivo B 135 135 135 136 136 137 137 138 138 138 139 139 140 141 143 145 C Índice 9 Visão Rápida (VWD VHomR GHVWLQDVH jTXHOHV TXH Mi HVWmR IDPLOLDUL]DGRV FRP D RSHUDomR GD FDOFXODGRUD RX FRP FRQFHLWRV ILQDQFHLURV (OD SRGH VHU XVDGD FRPR XPD UHIHUrQFLD UiSLGD 2 UHVWDQWH GR PDQXDO RIHUHFH H[SOLFDo}HV H H[HPSORV GRV FRQFHLWRV DSUHVHQWDGRV QHVWD VHomR Instruções Básicas -- Visão Rápida I B B ! [. . . ] P/YR = 1 1 2 3 . . . N=? PMT = 0 PV = -2. 000, 00 &RPR D FRQWD QmR WHP SDJDPHQWRV UHJXODUHV 307 SDJDPHQWR p LUUHOHYDQWH (QG RX %HJLQ  R PRGR GH B8 B Teclas: 1 Visor: 0, 00 1, 00 Descrição: @Æ ­2. 000, 00 $SDJD WRGRV RV UHJLVWRV &RQILJXUD 3<5 SDUD Mi TXH R MXUR p FRPSRVWR DQXDOPHQWH $UPD]HQD D LPSRUWkQFLD SDJD QR SULPHLUR GHSyVLWR 5: Cálculo do Valor Temporal do Dinheiro 61 !G % F $ G 3. 000, 00 7, 20 5, 83 $UPD]HQD D LPSRUWkQFLD TXH VH GHVHMD DFXPXODU $UPD]HQD D WD[D GH MXUR DQXDO &DOFXOD R Q~PHUR GH DQRV QHFHVViULRV SDUD TXH D FRQWD DWLQMD &RPR R YDORU FDOFXODGR GH 1 HVWi HQWUH H R LQGLYtGXR OHYDUi VHLV DQRV GH FRPSRVLomR DQXDO SDUD DWLQJLU R VDOGR GH SHOR PHQRV &DOFXODU R VDOGR DFWXDO DR ILP GH VHLV DQRV 6, 00 3. 035, 28 &RQILJXUD DQRV &DOFXOD R YDORU TXH SRGHUi UHVJDWDU DSyV DQRV SDUD Exemplo: Uma Conta de Reforma Individual. 8P LQGLYtGXR DEULX XPD FRQWD GH UHIRUPD LQGLYLGXDO HP GH $EULO GH FRP XP GHSyVLWR GH 6mR GHVFRQWDGRV GLUHFWDPHQWH GR FRQWUDFKHTXH H R LQGLYtGXR UHFHEH R VHX VDOiULR TXLQ]HQDOPHQWH $ FRQWD SDJD GH MXURV DQXDLV FRPSRVWRV TXLQ]HQDOPHQWH 4XDQWR KDYHUi QD FRQWD HP GH $EULO GH " FV= ? (Períodos quinzenais) 1234 I/YR = 6, 3% N = 360 (15 anos × 24 quinzenas) P/YR = 24 . . . 360 PMT = -80, 00 PV = -2. 000, 00 62 5: Cálculo do Valor Temporal do Dinheiro &RQILJXUH R PRGR (QG 3UHVVLRQH VHQGR H[LELGD ByVHDL QGLFDomR BEGIN HVWLYHU Descrição: "B @Æ &@P $!F #B G Teclas: Visor: 24, 00 ­2. 000, 00 ­80, 00 6, 30 360, 00 52. 975, 60 'HILQH R Q~PHUR GH SHUtRGRV SRU DQR $UPD]HQD R GHSyVLWR LQLFLDO $UPD]HQD GHSyVLWRV TXLQ]HQDLV UHJXODUHV $UPD]HQD D WD[D GH MXUR $UPD]HQD R Q~PHUR GH GHSyVLWRV &DOFXOD R VDOGR Exemplo: Uma Conta de Anuidade. 8P LQGLYtGXR RSWRX SRU XPD UHIRUPD DQWHFLSDGD DSyV XPD FDUUHLUD GH VXFHVVR (OH DFXPXORX XPD SRXSDQoD GH TXH UHQGH QD PpGLD MXURV GH DQXDLV FRPSRVWRV PHQVDOPHQWH 4XDO VHUi R YDORU GD DQXLGDGH UHWLUDGD GH IXQGRV UHSHWLWLYD H XQLIRUPH UHFHELGD QR LQtFLR GH FDGD PrV VH HOH TXLVHU TXH HVVD FRQWD GH SRXSDQoD R VXVWHQWH SHORV SUy[LPRV DQRV" PMT = ?1 2 . . . I/YR = 7% N = 600 (50 × 12) P/YR = 12 599 600 FV = 0 PV = -400. 000, 00 Modo Begin 5: Cálculo do Valor Temporal do Dinheiro 63 &RQILJXUH R PRGR %HJLQ 3UHVVLRQH VHQGR H[LELGD ByVHDL QGLFDomR QmR HVWLYHU Descrição: B "@ÃÆ %F #B G P Teclas: Visor: 12, 00 ­400. 000, 00 7, 00 600, 00 0, 00 2. 392, 80 'HILQH RV SDJDPHQWRV SRU DQR $UPD]HQD R SpGH PHLD FRPR XPD VDtGD GH FDL[D $UPD]HQD D WD[D GH MXUR DQXDO HVSHUDGD $UPD]HQD R Q~PHUR GH UHWLUDGDV $UPD]HQD R VDOGR GD FRQWD DSyV DQRV &DOFXOD R YDORU TXH SRGH VHU UHWLUDGR DR LQtFLR GH FDGD PrV Cálculos de Alugueres 8P DOXJXHU p XP HPSUpVWLPR GH SURSULHGDGH GH YDORU FRPR LPyYHLV DXWRPyYHLV RX HTXLSDPHQWRV SRU XP SHUtRGR GH WHPSR HVSHFtILFR HP WURFD GH SDJDPHQWRV UHJXODUHV $OJXQV DOXJXHUHV VmR HVFULWRV FRPR DFRUGRV GH FRPSUD FRP RSomR GH FRPSUD DR ILP GR DOXJXHU DOJXPDV YH]HV SRU PHUR  2 YDORU IXWXUR GHILQLGR )9 GD SURSULHGDGH DR ILP GR DOXJXHU p jV YH]HV FKDPDGR GH ´YDORU UHVLGXDOµ 7RGDV DV FLQFR WHFODV GH DSOLFDo}HV 790 SRGHP VHU XVDGDV HP FiOFXORV GH DOXJXHUHV +i GRLV FiOFXORV FRPXQV n , GHQWLILFDomR GR SDJDPHQWR GH DOXJXHU QHFHVViULR SDUD DWLQJLU XP UHQGLPHQWR HVSHFLILFDGR n , GHQWLILFDomR GR YDORU SUHVHQWH YDORU FDSLWDOL]DGR GH XP DOXJXHU 2 SULPHLUR SDJDPHQWR GH XP DOXJXHU JHUDOPHQWH RFRUUH QR LQtFLR GR SULPHLUR SHUtRGR $VVLP D PDLRU SDUWH GRV FiOFXORV XVDP R PRGR %HJLQ 64 5: Cálculo do Valor Temporal do Dinheiro Exemplo: Cálculo de um Pagamento de Aluguer. 8P FOLHQWH HVSHUD DUUHQGDU XP DXWRPyYHO TXH FXVWD HP WUrV DQRV 2 DOXJXHU LQVHUH XPD RSomR GH FRPSUD GR DXWRPyYHO SRU DR ILP GR SHUtRGR 2 SULPHLUR SDJDPHQWR PHQVDO GHYH VHU IHLWR QR GLD HP TXH R FOLHQWH UHWLUD R DXWRPyYHO 6H R YHQGHGRU TXLVHU UHWLUDU DQXDOPHQWH FRPSRVWRV PHQVDOPHQWH TXDO VHUi R YDORU GRV SDJDPHQWRV" &DOFXOH RV SDJDPHQWRV GR SRQWR GH YLVWD GR YHQGHGRU FV = 7. 500, 00 PMT = ?1 2 O dinheiro recebido pelo arrendador é positivo. I/YR = 10% N = 36 P/YR = 12 PV = -13. 500, 00 Modo Begin . . . 35 36 O dinheiro pago pelo arrendador é negativo. &RQILJXUH R PRGR %HJLQ 3UHVVLRQH VHQGR H[LELGD ByVHDL QGLFDomR QmR HVWLYHU Descrição: B F !#@Æ %#G !$ P Teclas: Visor: 12, 00 10, 00 ­13. 500, 00 7. 500, 00 36, 00 253, 99 'HILQH RV SDJDPHQWRV SRU DQR $UPD]HQD D UHWLUDGD DQXDO GHVHMDGD $UPD]HQD R SUHoR GR DOXJXHU $UPD]HQD R UHVLGXDO $UPD]HQD D GXUDomR GR DOXJXHU HP PHVHV &DOFXOD R SDJDPHQWR PHQVDO GR DOXJXHU 5: Cálculo do Valor Temporal do Dinheiro 65 2EVHUYH TXH PHVPR TXH R FOLHQWH HVFROKD QmR FRPSUDU R DXWRPyYHO R DUUHQGDGRU DLQGD LQVHUH XP IOX[R GH FDL[D GH HQWUDGD DR ILP GR DOXJXHU LJXDO DR YDORU UHVLGXDO GR DXWRPyYHO 6H R FOLHQWH FRPSUDU R DXWRPyYHO RX VH HVWH IRU YHQGLGR QR PHUFDGR DEHUWR R DUUHQGDGRU HVSHUD UHFXSHUDU Exemplo: Leasing com Pagamentos Adiantados. $ HPSUHVD 4XLFN . LW 3ROH %DUQV SODQHLD DOXJDU XPD HPSLOKDGRUD SDUD VHX DUPD]pP 2 DOXJXHU p HVFULWR SDUD XP WHUPR GH DQRV FRP SDJDPHQWRV PHQVDLV GH 2V SDJDPHQWRV GHYHP VHU IHLWRV QR LQtFLR GR PrV FRP R SULPHLUR H ~OWLPR SDJDPHQWRV IHLWRV QR LQtFLR GR DOXJXHU $ HPSUHVD WHP D RSomR GH FRPSUDU D HPSLOKDGRUD SRU DR ILP GR SHUtRGR GH DOXJXHU 6H D WD[D GH MXUR DQXDO p GH TXDO p R YDORU FDSLWDOL]DGR GR DOXJXHU" Modo Begin PV = ?I/YR = 9% N = 48 P/YR = 12 1 2 3 4 . . . 44 45 46 47 48 PMT = -2. 400, 00 (48º pagamento devido inicial) FV = -15. 000, 00 (VVD UHVROXomR UHTXHU TXDWUR HWDSDV &DOFXODU R YDORU SUHVHQWH GRV SDJDPHQWRV PHQVDLV ï  ² $FUHVFHQWDU R YDORU GR SDJDPHQWR DGLDQWDGR DGLFLRQDO , GHQWLILFDU R YDORU SUHVHQWH GD RSomR GH FRPSUD 6RPDU RV YDORUHV FDOFXODGRV QDV HWDSDV H 66 5: Cálculo do Valor Temporal do Dinheiro Etapa 1 , GHQWLILFDU R YDORU SUHVHQWH GRV SDJDPHQWRV PHQVDLV &RQILJXUH R PRGR %HJLQ 3UHVVLRQH VHQGR H[LELGD ByVHDL QGLFDomR QmR HVWLYHU B "% "@P G 'F Æ Teclas: Visor: 12, 00 47, 00 ­2. 400, 00 0, 00 9, 00 95. 477, 55 Descrição: 'HILQH RV SDJDPHQWRV SRU DQR $UPD]HQD R Q~PHUR GH SDJDPHQWRV $UPD]HQD R SDJDPHQWR PHQVDO $UPD]HQD )9 SDUD D HWDSD $UPD]HQD D WD[D GH MXUR &DOFXOD R YDORU SUHVHQWH GH SDJDPHQWRV PHQVDLV Etapa 2. $FUHVFHQWDU R SDJDPHQWR DGLDQWDGR DGLFLRQDO DR 39 $UPD]HQDU R UHVXOWDGR (P@1 Å 97. 877, 55 97. 877, 55 $FUHVFHQWD R SDJDPHQWR DYDQoDGR DGLFLRQDO $UPD]HQD R UHVXOWDGR QR UHJLVWR 0 Etapa 3. , GHQWLILFDU R YDORU SUHVHQWH GD RSomR GH FRPSUD 48, 00 "& P #@G Æ 0, 00 ­15. 000, 00 10. 479, 21 $UPD]HQD R PrV QR TXDO D RSomR GH FRPSUD RFRUUHUi $UPD]HQD R SDJDPHQWR ]HUR SDUD HVWD HWDSD GD UHVROXomR $UPD]HQD R YDORU GH GHVFRQWR &DOFXOD R YDORU SUHVHQWH GR ~OWLPR IOX[R GH FDL[D 5: Cálculo do Valor Temporal do Dinheiro 67 Etapa 4. 6RPD RV UHVXOWDGRV GDV HWDSDV H 1 Teclas: Visor: 108. 356, 77 Descrição: &DOFXOD R YDORU SUHVHQWH FDSLWDOL]DGR GR DOXJXHU $V GLVFUHSkQFLDV UHVXOWDQWHV GH DUUHGRQGDPHQWRV VmR H[SOLFDGDV QD SiJLQD  Amortização $ DPRUWL]DomR p R SURFHVVR GH GLYLVmR GH XP SDJDPHQWR HQWUH R YDORU TXH VH DSOLFD DR MXUR H R YDORU TXH VH DSOLFD DR SULQFLSDO 2V SDJDPHQWRV SUy[LPRV DR LQtFLR GH XP HPSUpVWLPR FRQWULEXHP PDLV MXURV H PHQRV SULQFLSDO GR TXH RV SDJDPHQWRV IHLWRV DR ILP GH XP HPSUpVWLPR PAGAMENTO $ PRINCIPAL $ JURO $ TEMPO 68 5: Cálculo do Valor Temporal do Dinheiro $ WHFOD WH TXH VH FDOFXOH n 2 YDORU DSOLFDGR DR MXUR QXP LQWHUYDOR GH SDJDPHQWRV n 2 YDORU DSOLFDGR DR SULQFLSDO QXP LQWHUYDOR GH SDJDPHQWRV n 2 VDOGR GR HPSUpVWLPR DSyV XP Q~PHUR HVSHFLILFDGR GH SDJDPHQWRV HQKD FDOFXODGR XP SDJDPHQWR RX $ IXQomR DUPD]HQDGR RV YDORUHV GH DPRUWL]DomR DGHTXDGRV HP , <5 39 )9 307H 3<5 BÄGD+3%, , SHUPL BÄVXS}HTXHVHW F Æ G P B 7D[D GH MXUR QRPLQDO DQXDO 6DOGR LQLFLDO 6DOGR ILQDO 9DORU GR SDJDPHQWR DUUHGRQGDGR SDUD R IRUPDWR GR YLVRU 1~PHUR GH SDJDPHQWRV SRU DQR 2V Q~PHURV H[LELGRV GH MXURV SULQFLSDO H VDOGR VmR DUUHGRQGDGRV GH DFRUGR FRP D FRQILJXUDomR DFWXDO GR YLVRU 3DUD DPRUWL]DU XP LQWHUYDOR GH SDJDPHQWRV GLJLWH Q~PHUR GR SHUtRGR LQLFLDO UR GR SHUtRGR ILQDO H HP VHJXLGD SUHVVLRQH $ +3 %, , H[LEH D LQGLFDomR PER VHJXLGD SHORV SDJDPHQWRV LQLFLDO H ILQDO TXH VHUmR DPRUWL]DGRV (P VHJXLGD SUHVVLRQH LGDPHQWH SDUD SHUFRUUHU RV YDORUHV GH MXURV SULQFLSDO H VDOGR H SDUD SDVVDU SDUD R SUy[LPR JUXSR GH 3UHVVLRQH SHUtRGRV (VVH UHFXUVR GH DXWRLQFUHPHQWR HYLWD TXH WHQKD TXH GLJLWDU RV QRYRV SHUtRGRV LQLFLDO H ILQDO 6H IRUHP DUPD]HQDGRV UHFXSHUDGRV RX H[HFXWDGRV RXWURV FiOFXORV Ui PDLV SDUD SHUFRUUHU R MXUR R GXUDQWH D DPRUWL]DomR D WHFOD SULQFLSDO H R VDOGR 3DUD UHWRPDU D DPRUWL]DomR FRP R PHVPR JUXSR GH SHUtRGRV SUHVVLRQH(BÄ BÄ 1SDUDYHURM 1QRYDPHQW 1SDUDSHUFRUUHURVPHVPRVYDO HQ~PH BÄ 1UHSHW BÄQRYDPHQW 1QmRVHUYL Para Amortizar. 3DUD DPRUWL]DU XP ~QLFR SDJDPHQWR GLJLWH R Q~PHUR GR SHUtRGR H SUHVVLRQH $ +3 %, , H[LEH D LQGLFDomR PER VHJXLGD GRV SDJDPHQWRV LQLFLDO H ILQDO TXH VHUmR DPRUWL]DGRV XUR INT 3UHVVLRQH H SDUD YHU R 3UHVVLRQH SULQFLSDO PRIN H PDLV XPD YH] SDUD YHU R VDOGR BAL &RQWLQXH D SUHVVLRQDU RUHV QRYDPHQWH 5: Cálculo do Valor Temporal do Dinheiro 69 Exemplo: Amortização de um Intervalo de Pagamentos. &DOFXOH RV SULPHLURV GRLV DQRV GD DPRUWL]DomR DQXDO SURJUDPDGD SDUD XPD KLSRWHFD GH SRU DQRV FRP MXURV DQXDLV GH H SDJDPHQWRV PHQVDLV &RQILJXUH R PRGR (QG 3UHVVLRQH VHQGR H[LELGD ByVHDL QGLFDomR BEGIN HVWLYHU Descrição: B !B %%#F &Æ G P Teclas: Visor: 12, 00 360, 00 7, 75 180. 000, 00 0, 00 ­1. 289, 54 'HILQH RV SDJDPHQWRV SRU DQR $UPD]HQD R Q~PHUR WRWDO GH SDJDPHQWRV $UPD]HQD R MXUR DQXDO $UPD]HQD R YDORU SUHVHQWH $UPD]HQD R YDORU IXWXUR &DOFXOD R SDJDPHQWR PHQVDO 6H R XWLOL]DGRU Mi FRQKHFHU R YDORU GR SDJDPHQWR GD KLSRWHFD SRGH GLJLWiOR H DUPD]HQiOR FRPR DUPD]HQRX RV RXWURV TXDWUR YDORUHV (P VHJXLGD DPRUWL]DU R SULPHLUR DQR H BÄ 1 1 1 12_ 1­ 12 ­1. 579, 82 ­13. 894, 66 178. 420, 18 , QVHUH RV SHUtRGRV LQLFLDO H ILQDO ([LEH D LQGLFDomR 3(5 H R LQWHUYDOR ([LEH D LQGLFDomR 35, 1 H R SULQFLSDO SDJR QR SULPHLUR DQR ([LEH D LQGLFDomR , 17 H R MXUR SDJR QR SULPHLUR DQR ([LEH D LQGLFDomR %$/ H R VDOGR GR HPSUpVWLPR DSyV XP DQR 70 5: Cálculo do Valor Temporal do Dinheiro 2 YDORU SDJR FRUUHVSRQGHQWH DR MXUR H DR SULQFLSDO  p LJXDO DR WRWDO GRV SDJDPHQWRV PHQVDLV ï  2 VDOGR UHVWDQWH p LJXDO j KLSRWHFD LQLFLDO VXEWUDLQGRVH R YDORU DSOLFDGR QR SULQFLSDO ²  $PRUWL]DU R VHJXQGR DQR 13­ 24 BÄ 1 1 1 ­1. 706, 69 ­13. 767, 79 176. 713, 49 ([LEH 3(5 H R SUy[LPR LQWHUYDOR GH SHUtRGRV ([LEH 35, 1 H R SULQFLSDO SDJR QR VHJXQGR DQR ([LEH , 17 H R MXUR SDJR QR VHJXQGR DQR ([LEH %$/ H R VDOGR GR HPSUpVWLPR DSyV SDJDPHQWRV 2 YDORU FRUUHVSRQGHQWH GH MXUR H SULQFLSDO  p LJXDO DR WRWDO GH SDJDPHQWRV PHQVDLV ï  2 VDOGR UHVWDQWH p LJXDO j KLSRWHFD LQLFLDO VXEWUDLQGRVH R YDORU DSOLFDGR QR SULQFLSDO ² ²  0DLV GLQKHLUR p DSOLFDGR DR SULQFLSDO GXUDQWH R VHJXQGR DQR H QmR QR SULPHLUR 2V DQRV VHJXLQWHV FRQWLQXDUmR GD PHVPD IRUPD Exemplo: Amortização de um Único Pagamento. $PRUWL]DU R SULPHLUR R H R SDJDPHQWR GR DOXJXHU GH FLQFR DQRV GH XP DXWRPyYHO 2 YDORU GR DOXJXHU p H D WD[D GH MXUR p GH 2V SDJDPHQWRV VmR PHQVDLV H FRPHoDP LPHGLDWDPHQWH &RQILJXUH R PRGR %HJLQ 3UHVVLRQH VHQGR H[LELGD ByVHDL QGLFDomR QmR HVWLYHU 5: Cálculo do Valor Temporal do Dinheiro 71 B #B #F " #Æ G P Teclas: Visor: 12, 00 60, 00 11, 50 14. 250, 00 0, 00 ­310, 42 Descrição: 'HILQH RV SDJDPHQWRV SRU DQR $UPD]HQD R Q~PHUR GH SDJDPHQWRV $UPD]HQD R MXUR DQXDO $UPD]HQD R YDORU SUHVHQWH $UPD]HQD R YDORU IXWXUR &DOFXOD R SDJDPHQWR PHQVDO $PRUWL]DU R H R SDJDPHQWR 1. 00 1­ 1 H BÄ 1 1 1 ­310, 42 0. 00 13. 939, 58 #H BÄ 1 1 72 25, 00 25­ 25 ­220, 21 ­90, 21 , QVHUH R SULPHLUR SDJDPHQWR ([LEH 3(5 H R SHUtRGR GH SDJDPHQWR DPRUWL]DGR ([LEH 35, 1 H R SULPHLUR SDJDPHQWR GR SULQFLSDO ([LEH , 17 H R MXUR ([LEH %$/ H R VDOGR GR HPSUpVWLPR DSyV XP SDJDPHQWR , QVHUH R SDJDPHQWR D VHU DPRUWL]DGR ([LEH 3(5 H R SHUtRGR GH SDJDPHQWR DPRUWL]DGR ([LEH 35, 1 H R SULQFLSDO SDJR QR SDJDPHQWR ([LEH , 17 H R MXUR SDJR QR SDJDPHQWR 5: Cálculo do Valor Temporal do Dinheiro 1 #"H BÄ 1 1 1 9. 193, 28 54, 00 54­ 54 ­290, 37 ­20, 05 1. 801, 57 ([LEH %$/ H R VDOGR DSyV R SDJDPHQWR , QVHUH R SDJDPHQWR D VHU DPRUWL]DGR ([LEH 3(5 H R SHUtRGR GH SDJDPHQWR DPRUWL]DGR ([LEH 35, 1 H R SULQFLSDO SDJR QR SDJDPHQWR ([LEH , 17 H R MXUR SDJR QR SDJDPHQWR ([LEH %$/ H R VDOGR DSyV R SDJDPHQWR Conversões de Taxas de Juros BÈ BHB $ DSOLFDomR GH &RQYHUVmR GH 7D[D GH -XURV XVD WUrV WHFODV (ODV ID]HP D FRQYHUVmR HQWUH DV WD[DV GH MXURV QRPLQDLV H DQXDLV HIHFWLYDV (VVDV WD[DV VmR GHVFULWDV QD SiJLQD 6H R XWLOL]DGRU FRQKHFHU XPD WD[D GH MXUR QRPLQDO DQXDO H TXLVHU UHVROYHU D WD[D HIHFWLYD DQXDO FRUUHVSRQGHQWH 'LJLWH D WD[D QRPLQDO H SUHVVLRQH 'LJLWH R Q~PHUR GH SHUtRGRV GH FRPSRVLomR H SUHVVLRQH &DOFXOH D WD[D HIHFWLYD SUHVVLRQDQGR 3DUD FDOFXODU XPD WD[D QRPLQDO GH XPD WD[D HIHFWLYD FRQKHFLGD 'LJLWH D WD[D HIHFWLYD H SUHVVLRQH 'LJLWH R Q~PHUR GH SHUtRGRV GH FRPSRVLomR H SUHVVLRQH &DOFXOH D WD[D QRPLQDO SUHVVLRQDQGR 1D DSOLFDomR 790 BÈ B B BÈ BÈHFFRPSDUW B B LOKDP R PHVPR UHJLVWR 5: Cálculo do Valor Temporal do Dinheiro 73 $V FRQYHUV}HV GH MXURV VmR XVDGDV SULQFLSDOPHQWH HP GRLV WLSRV GH SUREOHPDV n &RPSDUDomR GH LQYHVWLPHQWRV FRP SHUtRGRV GH FRPSRVLomR GLVWLQWRV n 5HVROXomR GH SUREOHPDV 790 FRP SHUtRGRV GH SDJDPHQWR H GH MXURV GLIHUHQWHV Investimentos com Períodos de Composição Distintos Exemplo: Comparação de Investimentos. 8P FOLHQWH HVWi D SHQVDU HP DEULU XPD FRQWD GH SRXSDQoD QXP GH WUrV EDQFRV 4XH EDQFR SRVVXL D WD[D GH MXURV PDLV IDYRUiYHO" %DQFR %DQFR %DQFR 1º Banco GH MXURV DQXDLV FRPSRVWRV WULPHVWUDOPHQWH GH MXURV DQXDLV FRPSRVWRV PHQVDOPHQWH GH MXURV DQXDLV FRPSRVWRV YH]HV DR DQR $%BÈ "B B Teclas: 2º Banco Visor: 6, 70 4, 00 Descrição: 6, 87 $UPD]HQD D WD[D QRPLQDO $UPD]HQD RV SHUtRGRV GH FRPSRVLomR WULPHVWUDLV &DOFXOD D WD[D HIHFWLYD DQXDO $$#BÈ B B 6, 65 12, 00 6, 86 $UPD]HQD D WD[D QRPLQDO $UPD]HQD RV SHUtRGRV GH FRPSRVLomR PHQVDLV &DOFXOD D WD[D HIHFWLYD DQXDO 74 5: Cálculo do Valor Temporal do Dinheiro 3º Banco $$!BÈ !$B B 6, 63 360, 00 6, 85 $UPD]HQD D WD[D QRPLQDO $UPD]HQD RV SHUtRGRV GH FRPSRVLomR &DOFXOD D WD[D HIHFWLYD DQXDO 2 %DQFR RIHUHFH XPD YDQWDJHP OLJHLUDPHQWH PDLRU Mi TXH p PDLRU TXH H Períodos de Composição e Pagamento Diferentes $ DSOLFDomR 790 VXS}H TXH RV SHUtRGRV GH FRPSRVLomR H RV SHUtRGRV GH SDJDPHQWR VmR LJXDLV $OJXQV HPSUpVWLPRV D SUHVWDomR RX GHSyVLWRV H UHWLUDGDV GH SRXSDQoD QmR FRLQFLGHP FRP RV SHUtRGRV GH FRPSRVLomR GR EDQFR 6H R SHUtRGR GH SDJDPHQWR IRU GLIHUHQWH GR SHUtRGR GH FRPSRVLomR DMXVWH D WD[D GH MXURV SDUD TXH FRUUHVSRQGD DR SHUtRGR GH SDJDPHQWR DQWHV GH UHVROYHU R SUREOHPD 3DUD DMXVWDU XPD WD[D GH MXUR TXDQGR R SHUtRGR GH FRPSRVLomR IRU GLIHUHQWH GR SHUtRGR GH SDJDPHQWR VLJD DV HWDSDV DEDL[R 'LJLWH D WD[D QRPLQDO H SUHVVLRQH 'LJLWH R Q~PHUR GH SHUtRGRV GH FRPSRVLomR QXP DQR H SUHVVLRQH 5HVROYD D WD[D HIHFWLYD SUHVVLRQDQGR 'LJLWH R Q~PHUR GH SHUtRGRV GH SDJDPHQWR QXP DQR H SUHVVLRQH 5HVROYD D WD[D QRPLQDO DMXVWDGD SUHVVLRQDQGR Exemplo: Pagamentos Mensais, Composição Diária. $ SDUWLU GH KRMH XP FOLHQWH GHSRVLWD QXPD FRQWD TXH SDJD GH MXURV FRPSRVWRV GLDULDPHQWH XVDQGR XP DQR GH GLDV 4XDO VHUi R VDOGR HP VHWH DQRV" B BÈ B B BÈ 5: Cálculo do Valor Temporal do Dinheiro 75 Etapa 1. &DOFXODU D WD[D HTXLYDOHQWH FRP FRPSRVLomR PHQVDO #BÈ !$#B Teclas: Visor: 5, 00 365, 00 Descrição: B B BÈ 5, 13 12, 00 5, 01 $UPD]HQD D WD[D SHUFHQWXDO QRPLQDO $UPD]HQD RV SHUtRGRV GH FRPSRVLomR GR EDQFR SRU DQR &DOFXOD D WD[D HIHFWLYD DQXDO $UPD]HQD SHUtRGRV PHQVDLV &DOFXOD D WD[D SHUFHQWXDO QRPLQDO HTXLYDOHQWH SDUD FRPSRVLomR PHQVDO &RPR 120 H , <5 FRPSDUWLOKDP R PHVPR UHJLVWR HVVH YDORU HVWi SURQWR SDUD VHU XVDGR QR UHVWR GR SUREOHPD Etapa 2. &DOFXODU R YDORU IXWXUR &RQILJXUH R PRGR %HJLQ 3UHVVLRQH VHQGR H[LELGD Æ #@P %B G ByVHDL QGLFDomR QmR HVWLYHU $UPD]HQD R YDORU SUHVHQWH $UPD]HQD R SDJDPHQWR $UPD]HQD R Q~PHUR WRWDO GH SDJDPHQWRV &DOFXOD R VDOGR DSyV DQRV 0, 00 ­25, 00 84, 00 2. 519, 61 76 5: Cálculo do Valor Temporal do Dinheiro 6 Cálculos de Fluxo de Caixa Utilização do Aplicativo de Fluxo de Caixa 2 DSOLFDWLYR GH IOX[R GH FDL[D p XVDGR SDUD UHVROYHU SUREOHPDV QRV TXDLV RV IOX[RV GH FDL[DV RFRUUHP HP LQWHUYDORV UHJXODUHV PDV FRP YDORUHV YDULiYHLV 2 DSOLFDWLYR WDPEpP SRGH VHU XVDGR HP FiOFXORV GH IOX[RV GH FDL[D SDUD UHVROYHU SUREOHPDV FRP IOX[RV GH FDL[D UHJXODUHV LJXDLV H SHULyGLFRV PDV HVVDV VLWXDo}HV VmR IHLWDV PDLV IDFLOPHQWH FRP R UHFXUVR 790 (P JHUDO HVWDV VmR DV HWDSDV SDUD FiOFXORV GH IOX[R GH FDL[D QD +3 %, , 2UJDQL]H VHXV IOX[RV GH FDL[D HP SDSHO 8P GLDJUDPD GH IOX[R GH FDL[D p ~WLO $SDJXH R FRQWH~GR GRV UHJLVWUDGRUHV 'LJLWH R Q~PHUR GH SHUtRGRV SRU DQR 'LJLWH R YDORU GR LQYHVWLPHQWR LQLFLDO 'LJLWH R YDORU GR SUy[LPR IOX[R GH FDL[D 6H R YDORU LQIRUPDGR QD HWDSD RFRUUHU PDLV GH XPD YH] FRQVHFXWLYDPHQWH GLJLWH R Q~PHUR GH YH]HV HP TXH HOH RFRUUHUi 5HSLWD DV HWDSDV H SDUD FDGD IOX[R GH FDL[D H JUXSR 3DUD FDOFXODU R YDORU SUHVHQWH OtTXLGR GLJLWH D WD[D GH MXUR DQXDO SUHVVLRQH H HP VHJXLGD SUHVVLRQH 2X SDUD FDOFXODU D WD[D LQWHUQD DQXDO GH UHWRUQR SUHVVLRQH F Bx BW Exemplo: Um Investimento de Curto Prazo. 2 GLDJUDPD GH IOX[R GH FDL[D DEDL[R UHSUHVHQWD XP LQYHVWLPHQWR HP Do}HV SRU WUrV PHVHV $V FRPSUDV IRUDP IHLWDV QR LQtFLR GH FDGD PrV H DV Do}HV IRUDP YHQGLGDV DR ILP GR WHUFHLUR PrV &DOFXOH DV WD[DV LQWHUQDV DQXDO H PHQVDLV GH UHWRUQR 6: Cálculos de Fluxo de Caixa 77 XXX 11. 765, 29 Os são fluxos recebidos positivos. 1 2 3 -2. 000, 00 Os são fluxos pagos negativos. -4. 000, 00 -5. 000, 00 B8 B #@D Teclas: Visor: 0, 00 12, 00 ­5. 000, 00 Descrição: @D "@D %$# 'D BW d 1 78 ­2. 000, 00 ­4. 000, 00 11. 765, 29 38, 98 3, 25 $SDJD WRGRV RV UHJLVWUDGRUHV $UPD]HQD SHUtRGRV SRU DQR , QFOXL R IOX[R GH FDL[D LQLFLDO ([LEH R Q~PHUR GR JUXSR GH IOX[R GH FDL[D HQTXDQWR D WHFOD SHUPDQHFH SUHVVLRQDGD , QFOXL R SUy[LPR IOX[R GH FDL[D , QFOXL R SUy[LPR IOX[R GH FDL[D , QFOXL R ~OWLPR IOX[R GH FDL[D &DOFXOD R UHQGLPHQWR QRPLQDO DQXDO 5HQGLPHQWR PHQVDO D 6: Cálculos de Fluxo de Caixa NPV e IRR/YR: Fluxos de Caixa Descontínuos 2 FDStWXOR GHPRQVWURX R XVR GH GLDJUDPDV GH IOX[R GH FDL[D SDUD UHVROYHU SUREOHPDV ILQDQFHLURV (VWD VHomR GHVFUHYH RV IOX[RV GH FDL[D GHVFRQWDGRV $V IXQo}HV 139 H , 55<5 VmR IUHTHQWHPHQWH FKDPDGDV GH IXQo}HV GH IOX[RV GH FDL[D GHVFRQWDGRV 4XDQGR XP IOX[R GH FDL[D p GHVFRQWDGR R XVXiULR FDOFXOD VHX YDORU SUHVHQWH 4XDQGR YiULRV IOX[RV GH FDL[D VmR GHVFRQWDGRV R XVXiULR FDOFXOD RV YDORUHV SUHVHQWHV H RV VRPD $ IXQomR GH YDORU SUHVHQWH OtTXLGR 139 HQFRQWUD R YDORU SUHVHQWH GH XPD VpULH GH IOX[RV GH FDL[D $ WD[D GH MXUR QRPLQDO DQXDO GHYH VHU FRQKHFLGD SDUD R FiOFXOR GR 139 $ IXQomR GH WD[D LQWHUQD GH UHWRUQR , 55<5 FDOFXOD D WD[D GH MXUR QRPLQDO DQXDO QHFHVViULD SDUD IRUQHFHU XP YDORU SUHVHQWH OtTXLGR LJXDO D ]HUR $ XWLOLGDGH GHVVDV GXDV IHUUDPHQWDV ILQDQFHLUDV WRUQDVH FODUD DSyV DOJXQV H[HPSORV $V GXDV SUy[LPDV VHo}HV GHVFUHYHP FRPR R XVXiULR GHYH RUJDQL]DU H LQFOXLU IOX[RV GH FDL[D 9HMD DEDL[R H[HPSORV GH FiOFXORV 139 H , 55<5 Organização de Fluxos de Caixa $ VpULH GH IOX[RV GH FDL[D p RUJDQL]DGD HP XP IOX[R GH FDL[D LQLFLDO &)  H JUXSRV GH IOX[R GH FDL[D VXFHVVLYRV DWp IOX[RV GH FDL[D &) RFRUUH QR LQtFLR GR SULPHLUR SHUtRGR 8P JUXSR GH IOX[R GH FDL[D FRQVLVWH HP XP YDORU GH IOX[R GH FDL[D H QR Q~PHUR GH UHSHWLo}HV 3RU H[HPSOR QR GLDJUDPD GH IOX[R GH FDL[D DEDL[R R IOX[R GH FDL[D LQLFLDO p ² 2 SUy[LPR JUXSR GH IOX[RV GH FDL[D FRQVLVWH HP VHLV IOX[RV GH ]HUR FDGD VHJXLGR SRU XP JUXSR GH WUrV IOX[RV GH FDL[D GH 2 JUXSR ILQDO FRQVLVWH HP XP IOX[R GH FDL[D GH 6: Cálculos de Fluxo de Caixa 79 C F 3 = 1 0 . 0 0 0, N 2 = 3 CF 1 = 0, N 1 = 6 1 2 3 4 5 6 7 8 9 10 CFO = -11. 000 6HPSUH TXH YRFr LQFOXLU XPD VpULH GH IOX[RV GH FDL[D p LPSRUWDQWH FRQWDELOL]DU FDGD SHUtRGR GR GLDJUDPD GH IOX[R GH FDL[D PHVPR DTXHOHV FRP UHVXOWDGR ]HUR Inclusão de Fluxos de Caixa $ +3 %, , SRGH DUPD]HQDU XP IOX[R GH FDL[D LQLFLDO DOpP GH RXWURV JUXSRV GH IOX[RV GH FDL[D &DGD JUXSR GH IOX[R GH FDL[D SRGH WHU DWp IOX[RV GH FDL[D , QFOXD IOX[RV GH FDL[D VHJXLQGR DV HWDSDV DEDL[R 3UHVVLRQH SDUD DSDJDU R FRQWH~GR GRV UHJLVWUDGRUHV 'LJLWH R Q~PHUR GH SHUtRGRV SRU DQR H SUHVVLRQH 'LJLWH R YDORU GR LQYHVWLPHQWR LQLFLDO H SUHVVLRQH 2 ´Mµ VLJQLILFD R ´Q~PHURµ GR IOX[R GH FDL[D GH D  'LJLWH R YDORU GR SUy[LPR IOX[R GH FDL[D H SUHVVLRQH 6H R YDORU GLJLWDGR QD HWDSD RFRUUHU PDLV GH XPD YH] FRQVHFXWLYDPHQWH GLJLWH R Q~PHUR GH UHSHWLo}HV H SUHVVLRQH 5HSLWD DV HWDSDV H SDUD FDGD H X[RV GH FDL[D WHQKDP VLGR LQFOXtGRV B8 Bg D BgDWpTXHWRGRVRVIO B D D 80 6: Cálculos de Fluxo de Caixa Exemplo. , QFOXD IOX[RV GH FDL[D GR GLDJUDPD DQWHULRU H FDOFXOH , 55<5 (P VHJXLGD FDOFXOH D WD[D GH MXUR HIHWLYD 6XSRQKD TXH KDMD SHUtRGRV SRU DQR B8 B @D Teclas: Visor: 0, 00 12, 00 ­11. 000, 00 Descrição: D $Bg D !Bg D BW 0, 00 6, 00 1. 000, 00 3, 00 10. 000, 00 21, 22 $SDJD WRGRV RV UHJLVWUDGRUHV &RQILJXUD SDUD , QFOXL R IOX[R GH FDL[D LQLFLDO ([LEH R Q~PHUR GR JUXSR GH IOX[R GH FDL[D HQTXDQWR D WHFOD HVWLYHU VHQGR SUHVVLRQDGD , QFOXL R SULPHLUR YDORU GR JUXSR GH IOX[RV GH FDL[D , QFOXL R Q~PHUR GH UHSHWLo}HV , QFOXL R VHJXQGR YDORU GR JUXSR GH IOX[RV GH FDL[D , QFOXL R Q~PHUR GH UHSHWLo}HV , QFOXL R ~OWLPR IOX[R GH FDL[D &DOFXOD R UHQGLPHQWR QRPLQDO DQXDO D 6: Cálculos de Fluxo de Caixa 81 Visualização e Substituição de Fluxos de Caixa 3DUD YHU XP IOX[R GH FDL[D SUHVVLRQH n D SDUD H[LELU RV IOX[RV GH FDL[D GH D n D SDUD H[LELU RV IOX[RV GH FDL[D GH D n SDUD YHU R SUy[LPR IOX[R GH FDL[D n SDUD YHU R IOX[R GH FDL[D DQWHULRU RX n SDUD YHU R IOX[R GH FDL[D DWXDO n n n n n (Dà Ã'à (Dà Ã"à (D (Dà (DD 3DUD VXEVWLWXLU XP XP YDORU GH IOX[R GH FDL[D SUHVVLRQH 3DD' SDUD DUPH]DQDU R QRYR YDORU HP IOX[RV GH FDL[D GH D 3DD" SDUD DUPD]HQDU R QRYR YDORU HP IOX[RV GH FDL[D GH D 3D SDUD DUPD]HQDU R YDORU QR SUy[LPR IOX[R GH FDL[D 3D SDUD DUPD]HQDU R YDORU QR IOX[R GH FDL[D DQWHULRU RX 3DD SDUD DUPD]HQDU R YDORU QR IOX[R GH FDL[D DWXDO 3DUD VXEVWLWXLU R Q~PHUR GH RFRUUrQFLDV GH XP IOX[R GH FDL[D HVSHFtILFR SUHVVLRQH ( VREUH R IOX[R TXH GHVHMD DOWHUDU (P VHJXLGD GLJLWH R Q~PHUR GH RFRUUrQFLDV H SUHVVLRQH Bg &RPR IOX[RV GH FDL[D QmR SRGHP VHU DSDJDGRV RX LQVHULGRV XVH B8 SDUD LQLFLDU QRYDPHQWH 82 6: Cálculos de Fluxo de Caixa Cálculo do Valor Presente Líquido $ IXQomR GH YDORU SUHVHQWH OtTXLGR 139 p XVDGD SDUD GHVFRQWDU WRGRV RV IOX[RV GH FDL[D SDUD R LQtFLR GD OLQKD GH WHPSR XVDQGR XPD WD[D GH MXUR QRPLQDO DQXDO IRUQHFLGD SHOR XVXiULR (VWDV HWDSDV GHVFUHYHP FRPR FDOFXODU 139 3UHVVLRQH SDUD DUPD]HQDU R Q~PHUR GH SHUtRGRV SRU DQR HP 3<5 , QFOXD R IOX[R GH FDL[D XVDQGR H $UPD]HQH D WD[D GH MXUR QRPLQDO DQXDO HP , <5 H SUHVVLRQH B8 D g Bx Exemplo: Um Contrato Descontado, Fluxos de Caixa Irregulares. 8P LQGLYtGXR WHP D RSRUWXQLGDGH GH DGTXLULU XP FRQWUDWR FRP RV VHJXLQWHV IOX[RV GH FDL[D Fim do mês Valor 4XDQWR R LQGLYtGXR GHYH SDJDU SHOR FRQWUDWR VH GHVHMD XP UHQGLPHQWR FRP WD[D DQXDO GH QR LQYHVWLPHQWR" I/YR = 15% 5. 000 4 5. 000 9 10 7. 500 10. 000 15 25 6: Cálculos de Fluxo de Caixa 83 B8 B D Teclas: Visor: 0, 00 12, 00 0, 00 Descrição: D !Bg #D D "Bg #D Bg D "Bg %#D D 'Bg D 84 0, 00 3, 00 5. 000, 00 0, 00 4, 00 5. 000, 00 2, 00 0, 00 4, 00 7. 500, 00 0, 00 9, 00 10. 000, 00 $SDJD R FRQWH~GR GRV UHJLVWUDGRUHV 'HILQH RV SDJDPHQWRV SRU DQR , QFOXL R IOX[R GH FDL[D LQLFLDO ]HUR 2 Q~PHUR GR IOX[R GH FDL[D p H[LELGR HQTXDQWR D SHUPDQHFH WHFOD SUHVVLRQDGD , QFOXL R SULPHLUR IOX[R GH FDL[D , QFOXL R Q~PHUR GH RFRUUrQFLDV , QFOXL R VHJXQGR IOX[R GH FDL[D , QFOXL R WHUFHLUR IOX[R GH FDL[D , QFOXL R Q~PHUR GH RFRUUrQFLDV , QFOXL R TXDUWR IOX[R GH FDL[D , QFOXL R Q~PHUR GH RFRUUrQFLDV , QFOXL R TXLQWR IOX[R GH FDL[D , QFOXL R Q~PHUR GH RFRUUrQFLDV , QFOXL R VH[WR IOX[R GH FDL[D , QFOXL R VpWLPR IOX[R GH FDL[D , QFOXL R Q~PHUR GH RFRUUrQFLDV , QFOXL R SUy[LPR IOX[R GH FDL[D D 6: Cálculos de Fluxo de Caixa 2V IOX[RV GH FDL[D TXH GHVFUHYHP R LQYHVWLPHQWR SURVSHFWLYR HVWmR DJRUD QD FDOFXODGRUD 2 XVXiULR SRGH SUHVVLRQDU VHJXLGR GH H UHSHWLGDPHQWH SDUD YHU RV IOX[RV GH FDL[D H R Q~PHUR GH RFRUUrQFLDV (D (Bg #F Bx Teclas: (D 'HSRLV GH LQFOXLU RV IOX[RV GH FDL[D DUPD]HQH D WD[D GH MXUR H FDOFXOH R YDORU SUHVHQWH OtTXLGR Visor: 15, 00 27. 199, 92 Descrição: $UPD]HQD D WD[D GH MXUR DQXDO &DOFXOD R YDORU SUHVHQWH OtTXLGR GH IOX[RV GH FDL[D DUPD]HQDGRV &RQVXOWH R H[HPSOR GH DUUHGRQGDPHQWR GD SiJLQD  2 UHVXOWDGR PRVWUDUi TXH VH R UHQGLPHQWR HVSHUDGR IRU GH DR DQR GHYHP VH SDJRV SHOR FRQWUDWR 2EVHUYH TXH HVVH YDORU p SRVLWLYR 2 YDORU SUHVHQWH OtTXLGR p VLPSOHVPHQWH R YDORU VRPDGR GH XPD VpULH GH IOX[RV GH FDL[D TXDQGR VmR GHVFRQWDGRV QR LQtFLR GD OLQKD GH WHPSR NPV = 27. 199, 92 7. 330, 34 6. 224, 95 4. 415, 91 4. 471, 10 4. 757, 62 1 3 7. 500, 00 5. 000, 00 5 7 9 11 13 15 17 19 21 23 25 6: Cálculos de Fluxo de Caixa 85 1% = 15% Anual 10. 000, 00 Cálculo da Taxa Interna de Retorno 3UHVVLRQH SDUD DUPD]HQDU R Q~PHUR GH SHUtRGRV SRU DQR HP 3<5 , QFOXD R IOX[R GH FDL[D XVDQGR H 3UHVVLRQH B8 BW D g 4XDQGR , 55<5 p FDOFXODGR p REWLGD D WD[D QRPLQDO DQXDO TXH IRUQHFH XP 139 ]HUR 2 H[HPSOR DEDL[R XVD RV IOX[RV GH FDL[D LQFOXtGRV QR H[HPSOR DQWHULRU 3RGH H[LVWLU PDLV GH XP , 55<5 6H D PHQVDJHP No Solution DSDUHFHU FRQVXOWH R $SrQGLFH % SiJLQD  H YRFr DFHLWDU HVVH SUHoR TXDO VHUi R UHQGLPHQWR" (VWH FiOFXOR , 55<5 UHTXHU XPD OLJHLUD PRGLILFDomR QRV IOX[RV GH FDL[D DUPD]HQDGRV DWXDOPHQWH 10. 000 7. 500 Exemplo. 6H R YHQGHGRU GR FRQWUDWR GR H[HPSOR DQWHULRU GHVHMD 5. 000 5. 000 1 3 5 7 9 11 13 15 17 19 21 23 25 IRR/YR = ? -28. 000 &@B3 D BW Teclas: 86 Visor: ­28. 000, 00 12, 49 Descrição: $OWHUD R IOX[R GH FDL[D LQLFLDO &DOFXOD R UHQGLPHQWR QRPLQDO DQXDO 9HMD PDLV H[HPSORV TXH XVDP FiOFXORV 139 H , 55<5 QR FDStWXOR ´2XWURV ([HPSORVµ 6: Cálculos de Fluxo de Caixa Armazenamento Automático de IRR/YR e NPV (Æ 1R FiOFXOR GH , 55<5 R UHVXOWDGR WDPEpP p DUPD]HQDGR HP , <5 3DUD R H[HPSOR DQWHULRU SUHVVLRQH (F SDUD H[LELU R UHQGLPHQWR DQXDOL]DGR GH 4XDQGR 139 p FDOFXODGR R UHVXOWDGR p DUPD]HQDGR HP 39 SRU FRQYHQLrQFLD 3DUD UHFXSHUDU HVVH UHVXOWDGR SUHVVLRQH 6H RV YDORUHV GH 790 QmR WLYHUHP VLGR DOWHUDGRV GHVGH R ~OWLPR H[HPSOR GH XVR GH 139 SiJLQD  DR SUHVVLRQDU R UHVXOWDGR VHUi (Æ 6: Cálculos de Fluxo de Caixa 87 7 Cálculos Estatísticos $V WHFODV H VmR XVDGDV SDUD LQFOXLU H DSDJDU GDGRV HP HVWDWtVWLFDV GH XPD H GXDV YDULiYHLV 2 VRPDWyULR GH GDGRV p DUPD]HQDGR QD PHPyULD $V HWLTXHWDV DFLPD GDV WHFODV D LQGLFDP TXDO VRPDWyULR GH GDGRV HVWi VHQGR DUPD]HQDGR $SyV D LQFOXVmR GRV GDGRV SRGHVH XVDU DV IXQo}HV HVWDWtVWLFDV SDUD FDOFXODU 0pGLD H GHVYLR SDGUmR (VWDWtVWLFDV GH UHJUHVVmR OLQHDU (VWLPDWLYD OLQHDU H SURMHo}HV 0pGLD SRQGHUDGD 6RPDWyULRV HVWDWtVWLFRV Q [ [ \ \ H [\ A *@ n n n n n Exclusão de Dados Estatísticos $SDJD RV UHJLVWUDGRUHV HVWDWtVWLFRV DQWHV GD LQFOXVmR GH QRYRV GDGRV 6H RV UHJLVWUDGRUHV QmR IRUHP DSDJDGRV RV GDGRV DUPD]HQDGRV DWXDOPHQWH VmR DXWRPDWLFDPHQWH LQFOXtGRV QRV FiOFXORV GH VRPDWyULRV 3DUD DSDJDU RV UHJLVWUDGRUHV HVWDWtVWLFRV SUHVVLRQH 2 YLVRU WDPEpP p DSDJDGR *j 7: Cálculos Estatísticos 89 Inclusão de Dados Estatísticos 1mR Ki OLPLWH SDUD R Q~PHUR GH YDORUHV TXH SRGHP VHU DFXPXODGRV QRV UHJLVWUDGRUHV HVWDWtVWLFRV Estatísticas com Uma Variável 3DUD LQFOXLU [ GDGRV SDUD HVWDWtVWLFDV FRP XPD YDULiYHO VLJD DV HWDSDV DEDL[R $SDJXH RV UHJLVWUDGRUHV HVWDWtVWLFRV SUHVVLRQDQGR 'LJLWH R SULPHLUR YDORU H SUHVVLRQH $ +3 %, , H[LELUi Q R Q~PHUR GH LWHQV DFXPXODGRV &RQWLQXH DFXPXODQGR YDORUHV GLJLWDQGR RV Q~PHURV H SUHVVLRQDQGR 2 YDORU Q p LQFUHPHQWDGR FRP FDGD HQWUDGD A *j A Estatísticas com Duas Variáveis e Média Ponderada 3DUD GLJLWDU SDUHV [ \ GH GDGRV HVWDWtVWLFRV VLJD DV HWDSDV DEDL[R $SDJXH RV UHJLVWUDGRUHV HVWDWtVWLFRV SUHVVLRQDQGR 'LJLWH R SULPHLUR YDORU [ H SUHVVLRQH $ +3 %, , H[LEH R YDORU [ 'LJLWH R YDORU \ FRUUHVSRQGHQWH H SUHVVLRQH $ +3 %, , H[LEH Q R Q~PHUR GH SDUHV GH LWHQV DFXPXODGRV &RQWLQXH D LQFOXLU SDUHV [\ 2 YDORU Q p LQFUHPHQWDGR FRP FDGD HQWUDGD 0 *j A 3DUD GLJLWDU GDGRV SDUD FDOFXODU D PpGLD SRQGHUDGD GLJLWH FDGD YDORU GH GDGRV FRPR [ H VHX SHVR FRUUHVSRQGHQWH FRPR \ Se os dados estatísticos fizerem com que o valor de um registro ultrapasse ±9, 99999999999 × 10499, a HP 10BII exibirá um aviso de estouro temporário (OFLO). 90 7: Cálculos Estatísticos Correção de Dados Estatísticos (QWUDGDV LQFRUUHWDV SRGHP VHU DSDJDGDV SUHVVLRQDQGRVH 6H R YDORU GH XP SDU [\ HVWLYHU LQFRUUHWR DSDJXH H GLJLWH QRYDPHQWH *@ Correção de Dados com Uma Variável 3DUD DSDJDU H GLJLWDU QRYDPHQWH GDGRV HVWDWtVWLFRV 'LJLWH R YDORU [ D VHU DSDJDGR 3UHVVLRQH SDUD DSDJDU R YDORU 2 YDORU Q p UHGX]LGR HP XPD XQLGDGH 'LJLWH R YDORU FRUUHWR XVDQGR *@ A Correção de Dados com Duas Variáveis 3DUD DSDJDU H GLJLWDU QRYDPHQWH SDUHV [\ GH GDGRV HVWDWtVWLFRV 'LJLWH R YDORU [ SUHVVLRQH H GLJLWH R YDORU \ 3UHVVLRQH SDUD DSDJDU RV YDORUHV 2 YDORU Q p UHGX]LGR HP XPD XQLGDGH 'LJLWH R SDU [\ FRUUHWR XVDQGR H *@ 0 0 A 7: Cálculos Estatísticos 91 Resumo de Cálculos Estatísticos $OJXPDV IXQo}HV UHWRUQDP GRLV YDORUHV $ LQGLFDomR STAT PRVWUD TXH GRLV YDORUHV IRUDP UHWRUQDGRV 3UHVVLRQH SDUD YHU R YDORU RFXOWR *i *$ *E Teclas Descrição *i para exibir 0pGLD GRV YDORUHV \ VH KRXYH D LQFOXVmR GH GDGRV \ 0pGLD DULWPpWLFD GRV YDORUHV [ 0pGLD GRV YDORUHV [ SRQGHUDGRV SHORV YDORUHV \ 'HVYLR SDGUmR GD DPRVWUD GRV YDORUHV [ 'HVYLR SDGUmR GH SRSXODomR GRV YDORUHV [ *: *M \YDORU [YDORU à 'HVYLR SDGUmR GD DPRVWUD GRV YDORUHV \ VH KRXYH D LQFOXVmR GH GDGRV \ 'HVYLR SDGUmR GH SRSXODomR GRV YDORUHV \ VH KRXYH D LQFOXVmR GH GDGRV \ *3 *4 (VWLPDWLYD GH [ SDUD XP &RHILFLHQWH GH YDORU HVSHFtILFR GH \ FRUUHODomR (VWLPDWLYD GH \ SDUD XP YDORU HVSHFtILFR GH [ , QWHUVHomR GH \ E QD OLQKD FDOFXODGD , QFOLQDomR P GD OLQKD FDOFXODGD , QFOLQDomR P GD OLQKD FDOFXODGD *4 PÃqrvÃhqmÃqhÃhhÃ}rÃrÃÃqhqÃmÃhÃhhÃqrÃÃpwÃhvÃrÃpyrÃqrà qhqÃPÃqrvÃhqmÃqrÃyhomÃ}rÃrÃÃqhqÃpvrÃhÃyhomÃhy à PÃprsvpvrrÃqrÃpryhomÃpÃÃ~rÃÃvr hyò Ãhà ÃrÃrqrÃpÃÃqhqÃrÃhwhÃhÃyvuhà phypyhqhÃVÃhyà ÃvqvphÃhÃpryhomÃrsrvhrrÃvvhÃrò ÃvqvphÃhÃpryhomÃrsrvhrrà rthvhÃVÃhyÃyvÃhÃrÃvqvphÃrÃhÃyvuhÃrÃhwrÃvhqrhq 92 7: Cálculos Estatísticos )+ ); )= )\ )g )f Teclas Descrição 1~PHUR GH SRQWRV GH GDGRV GLJLWDGRV 6RPD GRV YDORUHV [ 6RPD GRV YDORUHV \ 6RPD RV TXDGUDGRV GRV YDORUHV [ 6RPD RV TXDGUDGRV GRV YDORUHV \ 6RPD GRV SURGXWRV GRV YDORUHV [ H \ Média, Desvio Padrão e Estatísticas de Somatórios e SRVVtYHO FDOFXODU D PpGLD [  R GHVYLR SDGUmR GD DPRVWUD 6[ H GHVYLR SDGUmR GH SRSXODomR [ VRPDWyULR HVWDWtVWLFR Q [ H [ GH GDGRV [ 3DUD GDGRV [\ WDPEpP SRGHVH FDOFXODU PpGLD GHVYLR SDGUmR GD DPRVWUD H GHVYLR SDGUmR GH SRSXODomR GRV GDGRV \ H R VRPDWyULR HVWDWtVWLFR \ \ H [\ Exemplo 1. $ FRPDQGDQWD GH XP LDWH TXHU GHWHUPLQDU R WHPSR XVDGR HP XPD WURFD GH YHOD (OD HVFROKH DOHDWRULDPHQWH VHLV LQWHJUDQWHV GD WULSXODomR RV REVHUYD HQTXDQWR ID]HP D WURFD GH YHOD H UHJLVWUD RV Q~PHURV GH PLQXWRV QHFHVViULRV &DOFXOH D PpGLD H R GHVYLR SDGUmR GD DPRVWUD GDV WURFDV GH YHODV $OpP GLVVR FDOFXOH D UDL] TXDGUDGD PpGLD XVDQGR D IyUPXOD x 2 / n Teclas: *j A A A A A A *$ Visor: 0, 00 1, 00 2, 00 3, 00 4, 00 5, 00 6, 00 3, 50 Descrição: $SDJD R FRQWH~GR GRV UHJLVWUDGRUHV HVWDWtVWLFRV , QFOXL D SULPHLUD WURFD , QFOXL D VHJXQGD WURFD , QFOXL D WHUFHLUD WURFD , QFOXL D TXDUWD WURFD , QFOXL D TXLQWD WURFD , QFOXL D VH[WD WURFD &DOFXOD D PpGLD 7: Cálculos Estatísticos 93 *: )\ d)+ *T 0, 85 77, 13 6, 00 3, 59 &DOFXOD R GHVYLR SDGUmR GD DPRVWUD ([LEH [ ([LEH Q &DOFXOD D UDL] TXDGUDGD PpGLD 2V GHVYLRV SDGUmR FDOFXODGRV SRU H VmR RV GHVYLRV SDGUmR GD DPRVWUD (OHV VXS}HP TXH RV GDGRV VmR XPD DPRVWUD GH XP FRQMXQWR PDLRU H FRPSOHWR GH GDGRV 6H RV GDGRV FRQVWLWXHP D SRSXODomR FRPSOHWD RV GHVYLRV SDGUmR GH SRSXODomR YHUGDGHLURV SRGHP VHU FDOFXODGRV H SUHVVLRQDQGRVH *: *:*i *M *M*i Exemplo 2. 2 WUHLQDGRU GH XP WLPH FRQWUDWRX TXDWUR QRYRV MRJDGRUHV PHGLQGR H FHQWtPHWURV GH DOWXUD H SHVDQGR H TXLORV 'HVFXEUD D PpGLD H R GHVYLR SDGUmR GH SRSXODomR GDV DOWXUDV H SHVRV H VRPH RV GDGRV \ Teclas: *j 0A 0A 0A 0A *$ *i *M *i )= 94 Visor: 0, 00 1, 00 2, 00 3, 00 4, 00 184, 25 82, 75 5, 80 4, 71 331, 00 Descrição: $SDJD R FRQWH~GR GRV UHJLVWUDGRUHV HVWDWtVWLFRV , QFOXL D DOWXUD H R SHVR GR MRJDGRU , QFOXL D DOWXUD H R SHVR GR MRJDGRU , QFOXL D DOWXUD H R SHVR GR MRJDGRU , QFOXL D DOWXUD H R SHVR GR MRJDGRU &DOFXOD D PpGLD GDV DOWXUDV [ ([LEH D PpGLD GRV SHVRV \ &DOFXOD R GHVYLR SDGUmR GH SRSXODomR SDUD DV DOWXUDV [ &DOFXOD R GHVYLR SDGUmR GH SRSXODomR SDUD RV SHVRV \ ([LEH R WRWDO GRV YDORUHV \ 7: Cálculos Estatísticos Regressão Linear e Estimativa $ UHJUHVVmR OLQHDU p XP PpWRGR HVWDWtVWLFR GH HVWLPDWLYD H SURMHomR e XVDGR SDUD HQFRQWUDU XPD OLQKD UHWD TXH PHOKRU VH DMXVWD D XP FRQMXQWR GH GDGRV [\ 'HYHP H[LVWLU SHOR PHQRV GRLV SDUHV [\ GLIHUHQWHV $ UHWD IRUQHFH XPD UHODomR HQWUH DV YDULiYHLV [ H \ \ P[ E RQGH P p D LQFOLQDomR H E p D LQWHUVHomR \ Regressão Linear. [. . . ] A HP garante ao cliente usuário final que o hardware da HP, seus acessórios e suprimentos estarão livres de defeitos materiais e de mão-de-obra após a data de compra, durante o prazo especificado acima. Se a HP receber a notificação de tais defeits durante o prazo de garantia, a HP, a seu critério, reparará ou substituirá os produtos comprovadamente defeituosos. Os produtos substituídos podem ser novos ou seminovos. A HP garante que o software da calculadora não falhará na execução de suas instruções de programação após a data de compra, durante o prazo especificado acima, devido a defeitos materiais e de mão-deobra quando corretamente instalada e utilizada. [. . . ]