User manual HP 10BII

[. . . ] hp 10BII financial calculator user's guide Edition 1 HP part number F1902-90001 Notice REGISTER YOUR PRODUCT AT: www. register. hp. com THIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE PROVIDED "AS IS" AND ARE SUBJECT TO CHANGE WITHOUT NOTICE. HEWLETT-PACKARD COMPANY MAKES NO WARRANTY OF ANY KIND WITH REGARD TO THIS MANUAL, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY, NON-INFRINGEMENT AND FITNESS FOR A PARTICULAR PURPOSE. SHALL NOT BE LIABLE FOR ANY ERRORS OR FOR INCIDENTAL OR CONSEQUENTIAL DAMAGES IN CONNECTION WITH THE FURNISHING, PERFORMANCE, OR USE OF THIS MANUAL OR THE EXAMPLES CONTAINED HEREIN. Copyright 1988, 1989, 2001, 2004 Hewlett-Packard Development Company, L. P. Reproduction, adaptation, or translation of this manual is prohibited without prior written permission of Hewlett-Packard Company, except as allowed under the copyright laws. Hewlett-Packard Company 4995 Murphy Canyon Rd, Suite 301 San Diego, CA 92123 Printing History Edition 1 May 2003 Welcome to the HP 10BII <RXU +3 %, , UHIOHFWV WKH VXSHULRU TXDOLW\ DQG DWWHQWLRQ WR GHWDLO LQ HQJLQHHULQJ DQG PDQXIDFWXULQJ WKDW KDYH GLVWLQJXLVKHG +HZOHWW3DFNDUG SURGXFWV IRU \HDUV +HZOHWW3DFNDUG VWDQGV EHKLQG WKLV FDOFXODWRUZH RIIHU H[SHUWLVH WR VXSSRUW LWV XVH VHH LQVLGH WKH EDFN FRYHU DQG ZRUOGZLGH VHUYLFH Hewlett-Packard Quality 2XU FDOFXODWRUV DUH PDGH WR H[FHO DQG WR EH HDV\ WR XVH n 7KLV FDOFXODWRU LV GHVLJQHG WR ZLWKVWDQG WKH GURSV YLEUDWLRQV SROOXWDQWV VPRJ R]RQH WHPSHUDWXUH H[WUHPHV DQG KXPLGLW\ YDULDWLRQV WKDW LW PD\ HQFRXQWHU LQ HYHU\GD\ ZRUN OLIH n 7KH FDOFXODWRU DQG LWV PDQXDO KDYH EHHQ GHVLJQHG DQG WHVWHG IRU HDVH RI XVH :H DGGHG PDQ\ H[DPSOHV WR KLJKOLJKW WKH YDULHG XVHV RI WKH FDOFXODWRU n /RZSRZHU HOHFWURQLFV DQG DQ DGYDQFHG SRZHU PDQDJHPHQW V\VWHP JLYHV H[WHQGHG EDWWHU\ OLIH n 7KH PLFURSURFHVVRU KDV EHHQ RSWLPL]HG IRU IDVW DQG UHOLDEOH FRPSXWDWLRQV XVLQJ GLJLWV LQWHUQDOO\ IRU SUHFLVH UHVXOWV n ([WHQVLYH UHVHDUFK KDV FUHDWHG D GHVLJQ WKDW KDV PLQLPL]HG WKH DGYHUVH HIIHFWV RI VWDWLF HOHFWULFLW\ D SRWHQWLDO FDXVH RI PDOIXQFWLRQV DQG GDWD ORVV LQ FDOFXODWRUV Welcome to the HP 10BII 3 Features 7KH IHDWXUHV RI WKH +3 %, , DQG WKH PDQXDO UHIOHFW WKH QHHGV DQG ZLVKHV RI PDQ\ FXVWRPHUV n $ ODUJH FKDUDFWHU GLVSOD\ n $Q $WD*ODQFH VHFWLRQ LQ WKH PDQXDO IRU TXLFN UHIHUHQFH n $SSOLFDWLRQV WR VROYH EXVLQHVV DQG ILQDQFLDO WDVNV 7LPH 9DOXH RI 0RQH\ /RDQV VDYLQJV OHDVHV DQG DPRUWL]DWLRQ VFKHGXOHV , QWHUHVW &RQYHUVLRQ 1RPLQDO DQG HIIHFWLYH UDWHV &DVK )ORZV 1HW SUHVHQW YDOXH DQG LQWHUQDO UDWH RI UHWXUQ %XVLQHVV 3HUFHQWDJHV 3HUFHQW FKDQJH PDUNXS DQG PDUJLQ FDOFXODWLRQV 6WDWLVWLFV 0HDQ VWDQGDUG GHYLDWLRQ FRUUHODWLRQ FRHIILFLHQW DQG OLQHDU UHJUHVVLRQ IRUHFDVWLQJ SOXV RWKHU VWDWLVWLFDO FDOFXODWLRQV n (QRXJK PHPRU\ WR VWRUH DQ LQLWLDO FDVK IORZ DQG FDVK IORZ JURXSV ZLWK XS WR FDVK IORZV SHU JURXS n 7HQ QXPEHUHG VWRUDJH UHJLVWHUV n (DV\ DFFHVV WR IXQFWLRQV VDYHV NH\VWURNHV DQG DGGV FRQYHQLHQFH $XWRLQFUHPHQW FDSDELOLW\ IRU DPRUWL]DWLRQ VFKHGXOHV /DEHOV IRU DPRUWL]DWLRQ DQG FDVK IORZV $XWRPDWLF FRQVWDQW NH\ PHPRU\ n 0DQ\ H[DPSOHV DUH LQFOXGHG LQ WKH PDQXDO VR \RX FDQ FRPELQH WKHP IRU \RXU VSHFLILF QHHGV 4 Welcome to the HP 10BII Contents 11 11 12 13 14 15 16 17 18 19 21 At a Glance. . . [. . . ] $GG WKH UHVXOWV RI VWHSV DQG Display: 108, 356. 77 Description: &DOFXODWHV SUHVHQW FDSLWDOL]HG YDOXH RI OHDVH 5RXQGLQJ GLVFUHSDQFLHV DUH H[SODLQHG RQ SDJH  66 5: Time Value of Money Calculations Amortization $PRUWL]DWLRQ LV WKH SURFHVV RI GLYLGLQJ D SD\PHQW LQWR WKH DPRXQW WKDW DSSOLHV WR LQWHUHVW DQG WKH DPRXQW WKDW DSSOLHV WR SULQFLSDO 3D\PHQWV QHDU WKH EHJLQQLQJ RI D ORDQ FRQWULEXWH PRUH LQWHUHVW DQG OHVV SULQFLSDO WKDQ SD\PHQWV QHDU WKH HQG RI D ORDQ PAYMENT $ PRINCIPAL $ INTEREST $ 7KH KH +3 %, , DOORZV \RX WR FDOFXODWH n 7KH DPRXQW DSSOLHG WR LQWHUHVW LQ D UDQJH RI SD\PHQWV n 7KH DPRXQW DSSOLHG WR SULQFLSDO LQ D UDQJH RI SD\PHQWV n 7KH ORDQ EDODQFH DIWHU D VSHFLILHG QXPEHU RI SD\PHQWV DUH PDGH BNH\RQW BIXQFW TIME LRQ DVVXPHV \RX KDYH MXVW FDOFXODWHG D SD\PHQW RU \RX 7KH KDYH VWRUHG WKH DSSURSULDWH DPRUWL]DWLRQ YDOXHV LQ , <5 39 )9 307 DQG 3<5 5: Time Value of Money Calculations 67 F G P B 1W $QQXDO QRPLQDO LQWHUHVW UDWH 6WDUWLQJ EDODQFH (QGLQJ EDODQFH 3D\PHQW DPRXQW URXQGHG WR WKH GLVSOD\ IRUPDW 1XPEHU RI SD\PHQWV SHU \HDU 7KH QXPEHUV GLVSOD\HG IRU LQWHUHVW SULQFLSDO DQG EDODQFH DUH URXQGHG WR WKH FXUUHQW GLVSOD\ VHWWLQJ To Amortize. 7R DPRUWL]H D VLQJOH SD\PHQW HQWHU WKH SHULRG QXPEHU DQG SUHVV 7KH +3 %, , GLVSOD\V WKH DQQXQFLDWRU PER IROORZHG E\ WKH VWDUWLQJ DQG HQGLQJ SD\PHQWV WKDW ZLOO EH DPRUWL]HG B R VHH LQWHUHVW INT 3UHVV Q WR VHH WKH SULQFLSDO PRIN 3UHVV DQG DJDLQ WR VHH WKH EDODQFH BAL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xample: Amortizing a Range of Payments. &DOFXODWH WKH ILUVW WZR \HDUV RI WKH DQQXDO DPRUWL]DWLRQ VFKHGXOH IRU D \HDU PRUWJDJH DW DQQXDO LQWHUHVW ZLWK PRQWKO\ SD\PHQWV 1DJDL 1W BDJDL B 1UHSHDW HH (B 1ZL 6HW WR (QG PRGH 3UHVV ByL I BEGIN DQQXQFLDWRU LV GLVSOD\HG 68 5: Time Value of Money Calculations B !B %%#F & G P Keys: Display: 12. 00 360. 00 7. 75 180, 000. 00 0. 00 1, 289. 54 Description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 HTXDOV WKH WRWDO RI PRQWKO\ SD\PHQWV  7KH UHPDLQLQJ EDODQFH HTXDOV WKH LQLWLDO PRUWJDJH OHVV WKH DPRXQW DSSOLHG WRZDUG SULQFLSDO  5: Time Value of Money Calculations 69 $PRUWL]H WKH VHFRQG \HDU 13 24 1, 706. 69 B 1 1 1 13, 767. 79 176, 713. 49 'LVSOD\V 3(5 DQG WKH QH[W UDQJH RI SHULRGV 'LVSOD\V 35, 1 DQG WKH SULQFLSDO SDLG LQ WKH VHFRQG \HDU 'LVSOD\V , 17 DQG WKH LQWHUHVW SDLG LQ WKH VHF RQG \HDU 'LVSOD\V %$/ DQG WKH ORDQ EDODQFH DIWHU SD\PHQWV 7KH DPRXQW SDLG WRZDUG LQWHUHVW DQG SULQFLSDO  HTXDOV WKH WRWDO RI PRQWKO\ SD\PHQWV  7KH UHPDLQLQJ EDODQFH HTXDOV WKH LQLWLDO PRUWJDJH OHVV WKH DPRXQW DSSOLHG WRZDUG SULQFLSDO  0RUH PRQH\ LV DSSOLHG WR SULQFLSDO GXULQJ WKH VHFRQG UDWKHU WKDQ WKH ILUVW \HDU 7KH VXFFHHGLQJ \HDUV FRQWLQXH LQ WKH VDPH IDVKLRQ WK SD\PHQWV RI D ILYH \HDU FDU OHDVH 7KH OHDVH DPRXQW LV DQG WKH LQWHUHVW UDWH LV 3D\PHQWV DUH PRQWKO\ DQG EHJLQ LPPHGLDWHO\ 6HW WR %HJLQ PRGH 3UHVV Example: Amortizing a Single Payment. $PRUWL]H WKH VW WK DQG B #B #F " # G P Keys: 70 ByL I DQQXQFLDWRU LV QRW GLVSOD\HG Description: Display: 12. 00 60. 00 11. 50 14, 250. 00 0. 00 310. 42 6HWV SD\PHQWV SHU \HDU 6WRUHV QXPEHU RI SD\PHQWV 6WRUHV LQWHUHVW SHU \HDU 6WRUHV SUHVHQW YDOXH 6WRUHV WKH IXWXUH YDOXH &DOFXODWHV PRQWKO\ SD\PHQW 5: Time Value of Money Calculations $PRUWL]H WKH VW WK DQG WK SD\PHQWV H B 1 1 1 #H B 1 1 1 #"H B 1 1 1 1. 00 1 1 310. 42 0. 00 13, 939. 58 25. 00 25 25 220. 21 90. 21 9, 193. 28 54. 00 54 54 290. 37 20. 05 1, 801. 57 (QWHUV ILUVW SD\PHQW 'LVSOD\V 3(5 DQG WKH DPRUWL]HG SD\PHQW SHULRG 'LVSOD\V 35, 1 DQG WKH ILUVW SULQFLSDO SD\PHQW 'LVSOD\V , 17 DQG WKH LQWHU HVW 'LVSOD\V %$/ DQG WKH ORDQ EDODQFH DIWHU RQH SD\PHQW (QWHUV SD\PHQW WR DPRU WL]H 'LVSOD\V 3(5 DQG WKH DPRUWL]HG SD\PHQW SHULRG 'LVSOD\V 35, 1 DQG WKH SULQFLSDO SDLG RQ WKH WK SD\PHQW 'LVSOD\V , 17 DQG WKH LQWHU HVW SDLG RQ WKH WK SD\ PHQW 'LVSOD\V %$/ DQG WKH EDO DQFH DIWHU WKH WK SD\ PHQW (QWHUV SD\PHQW WR DPRU WL]H 'LVSOD\V 3(5 DQG WKH DPRUWL]HG SD\PHQW SHULRG 'LVSOD\V 35, 1 DQG WKH SULQFLSDO SDLG RQ WKH WK SD\PHQW 'LVSOD\V , 17 DQG WKH LQWHU HVW SDLG RQ WKH WK SD\ PHQW 'LVSOD\V %$/ DQG WKH EDO DQFH DIWHU WKH WK SD\ PHQW 5: Time Value of Money Calculations 71 Interest Rate Conversions B B B 7KH , QWHUHVW &RQYHUVLRQ DSSOLFDWLRQ XVHV WKUHH NH\V DQG 7KH\ FRQYHUW EHWZHHQ QRPLQDO DQG DQQXDO HIIHFWLYH LQWHUHVW UDWHV 1RPLQDO DQG HIIHFWLYH LQWHUHVW UDWHV DUH GHVFULEHG RQ SDJH , I \RX NQRZ DQ DQQXDO QRPLQDO LQWHUHVW UDWH DQG \RX ZLVK WR VROYH IRU WKH FRUUHVSRQGLQJ DQQXDO HIIHFWLYH UDWH (QWHU WKH QRPLQDO UDWH DQG SUHVV (QWHU WKH QXPEHU RI FRPSRXQGLQJ SHULRGV DQG SUHVV &DOFXODWH WKH HIIHFWLYH UDWH E\ SUHVVLQJ 7R FDOFXODWH D QRPLQDO UDWH IURP D NQRZQ HIIHFWLYH UDWH (QWHU WKH HIIHFWLYH UDWH DQG SUHVV (QWHU WKH QXPEHU RI FRPSRXQGLQJ SHULRGV DQG SUHVV &DOFXODWH WKH QRPLQDO UDWH E\ SUHVVLQJ , Q WKH 790 DSSOLFDWLRQ B B B B BDQGFVKDUHW B B KH VDPH UHJLVWHU , QWHUHVW FRQYHUVLRQV DUH XVHG SULPDULO\ IRU WZR W\SHV RI SUREOHPV n &RPSDULQJ LQYHVWPHQWV ZLWK GLIIHUHQW FRPSRXQGLQJ SHULRGV n 6ROYLQJ 790 SUREOHPV ZKHUH WKH SD\PHQW SHULRG DQG WKH LQWHUHVW SHULRG GLIIHU Investments With Different Compounding Periods Example: Comparing Investments. <RX DUH FRQVLGHULQJ RSHQLQJ D VDYLQJV DFFRXQW LQ RQH RI WKUHH EDQNV :KLFK EDQN KDV WKH PRVW IDYRUDEOH LQWHUHVW UDWH" )LUVW %DQN 6HFRQG %DQN 7KLUG %DQN DQQXDO LQWHUHVW FRPSRXQGHG TXDUWHUO\ DQQXDO LQWHUHVW FRPSRXQGHG PRQWKO\ DQQXDO LQWHUHVW FRPSRXQGHG WLPHV SHU \HDU 72 5: Time Value of Money Calculations First Bank $%B "B B Keys: Second Bank Display: 6. 70 4. 00 6. 87 Description: 6WRUHV QRPLQDO UDWH 6WRUHV TXDUWHUO\ FRPSRXQGLQJ SHULRGV &DOFXODWHV DQQXDO HIIHFWLYH UDWH $$#B B B $$!B !$B B 6. 65 12. 00 6. 86 6WRUHV QRPLQDO UDWH 6WRUHV PRQWKO\ FRP SRXQGLQJ SHULRGV &DOFXODWHV DQQXDO HIIHFWLYH UDWH Third Bank 6. 63 360. 00 6. 85 6WRUHV QRPLQDO UDWH 6WRUHV FRPSRXQGLQJ SHULRGV &DOFXODWHV DQQXDO HIIHFWLYH UDWH )LUVW %DQN RIIHUV D VOLJKWO\ EHWWHU GHDO VLQFH LV JUHDWHU WKDQ DQG Compounding and Payment Periods Differ 7KH 790 DSSOLFDWLRQ DVVXPHV WKDW WKH FRPSRXQGLQJ SHULRGV DQG WKH SD\PHQW SHULRGV DUH WKH VDPH 6RPH ORDQ LQVWDOOPHQWV RU VDYLQJV GHSRVLWV DQG ZLWKGUDZDOV GR QRW FRLQFLGH ZLWK WKH EDQNV FRPSRXQGLQJ SHULRGV , I WKH SD\PHQW SHULRG GLIIHUV IURP WKH FRPSRXQGLQJ SHULRG DGMXVW WKH LQWHUHVW UDWH WR PDWFK WKH SD\PHQW SHULRG EHIRUH VROYLQJ WKH SUREOHP 5: Time Value of Money Calculations 73 7R DGMXVW DQ LQWHUHVW UDWH ZKHQ WKH FRPSRXQGLQJ SHULRG GLIIHUV IURP WKH SD\PHQW SHULRG FRPSOHWH WKH IROORZLQJ VWHSV (QWHU WKH QRPLQDO UDWH DQG SUHVV (QWHU WKH QXPEHU RI FRPSRXQGLQJ SHULRGV LQ D \HDU DQG SUHVV 6ROYH IRU WKH HIIHFWLYH UDWH E\ SUHVVLQJ (QWHU WKH QXPEHU RI SD\PHQW SHULRGV LQ D \HDU DQG SUHVV 6ROYH IRU WKH DGMXVWHG QRPLQDO UDWH E\ SUHVVLQJ B B B Example: Monthly Payments, Daily Compounding. 6WDUWLQJ WRGD\ B B \RX PDNH PRQWKO\ GHSRVLWV RI WR DQ DFFRXQW SD\LQJ LQWHUHVW FRPSRXQGHG GDLO\ XVLQJ D GD\ \HDU :KDW ZLOO WKH EDODQFH EH LQ VHYHQ \HDUV" Step 1. &DOFXODWH WKH HTXLYDOHQW UDWH ZLWK PRQWKO\ FRPSRXQGLQJ #B !$#B B B B Keys: Display: 5. 00 365. 00 5. 13 12. 00 5. 01 Description: 6WRUHV QRPLQDO SHUFHQWDJH UDWH 6WRUHV EDQNV FRPSRXQGLQJ SHULRGV SHU \HDU &DOFXODWHV DQQXDO HIIHFWLYH UDWH 6WRUHV PRQWKO\ SHULRGV &DOFXODWHV HTXLYDOHQW QRPLQDO SHUFHQWDJH UDWH IRU PRQWKO\ FRPSRXQGLQJ 6LQFH 120 DQG , <5 VKDUH WKH VDPH UHJLVWHU WKLV YDOXH LV UHDG\ IRU XVH LQ WKH UHVW RI WKH SUREOHP Step 2. &DOFXODWH WKH IXWXUH YDOXH 6HW WR %HJLQ PRGH 3UHVV #@P %B G ByL I DQQXQFLDWRU LV QRW GLVSOD\HG 6WRUHV SUHVHQW YDOXH 6WRUHV SD\PHQW 6WRUHV WRWDO QXPEHU RI SD\PHQWV &DOFXODWHV EDODQFH DIWHU \HDUV 0. 00 25. 00 84. 00 2, 519. 61 74 5: Time Value of Money Calculations 6 Cash Flow Calculations How to Use the Cash Flow Application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x Example: A Short Term Investment. 7KH IROORZLQJ FDVK IORZ GLDJUDP UHSUHVHQWV DQ LQYHVWPHQW LQ VWRFN RYHU WKUHH PRQWKV 3XUFKDVHV ZHUH PDGH DW WKH EHJLQQLQJ RI HDFK PRQWK DQG WKH VWRFN ZDV VROG DW WKH HQG RI WKH WKLUG PRQWK &DOFXODWH WKH DQQXDO LQWHUQDO UDWH RI UHWXUQ DQG WKH PRQWKO\ UDWH RI UHWXUQ 6: Cash Flow Calculations 75 XXX 11, 765. 29 Flows are received positive. 1 2 3 -2, 000. 00 Flows are paid out negative. -4, 000. 00 -5, 000. 00 B8 B #@D Keys: Display: 0. 00 12. 00 5, 000. 00 Description: @D "@D %$# 'D BW d 1 2, 000. 00 4, 000. 00 11, 765. 29 38. 98 3. 25 &OHDUV DOO UHJLVWHUV 6WRUHV SHULRGV SHU \HDU (QWHUV LQLWLDO FDVK IORZ 'LVSOD\V FDVK IORZ JURXS QXPEHU ZKLOH \RX KROG GRZQ (QWHUV QH[W FDVK IORZ (QWHUV QH[W FDVK IORZ (QWHUV ILQDO FDVK IORZ &DOFXODWHV DQQXDO QRPLQDO \LHOG 0RQWKO\ \LHOG D 76 6: Cash Flow Calculations NPV and IRR/YR: Discontinuing Cash Flows &KDSWHU GHPRQVWUDWHV WKH XVH RI FDVK IORZ GLDJUDPV WR FODULI\ ILQDQFLDO SUREOHPV 7KLV VHFWLRQ GHVFULEHV GLVFRXQWHG FDVK IORZV 7KH 139 DQG , 55<5 IXQFWLRQV DUH IUHTXHQWO\ UHIHUUHG WR DV GLVFRXQWHG FDVK IORZ IXQFWLRQV :KHQ D FDVK IORZ LV GLVFRXQWHG \RX FDOFXODWH LWV SUHVHQW YDOXH :KHQ PXOWLSOH FDVK IORZV DUH GLVFRXQWHG \RX FDOFXODWH WKH SUHVHQW YDOXHV DQG DGG WKHP WRJHWKHU 7KH QHW SUHVHQW YDOXH 139 IXQFWLRQ ILQGV WKH SUHVHQW YDOXH RI D VHULHV RI FDVK IORZV 7KH DQQXDO QRPLQDO LQWHUHVW UDWH PXVW EH NQRZQ WR FDOFXODWH 139 7KH LQWHUQDO UDWH RI UHWXUQ , 55<5 IXQFWLRQ FDOFXODWHV WKH DQQXDO QRPLQDO LQWHUHVW UDWH WKDW LV UHTXLUHG WR JLYH D QHW SUHVHQW YDOXH RI ]HUR 7KH XWLOLW\ RI WKHVH WZR ILQDQFLDO WRROV EHFRPHV FOHDU DIWHU ZRUNLQJ D IHZ H[DPSOHV 7KH QH[W WZR VHFWLRQV GHVFULEH RUJDQL]LQJ DQG HQWHULQJ \RXU FDVK IORZV ([DPSOHV RI 139 DQG , 55<5 FDOFXODWLRQV IROORZ Organizing Cash Flows 7KH FDVK IORZ VHULHV LV RUJDQL]HG LQWR DQ LQLWLDO FDVK IORZ &)  DQG VXFFHHGLQJ FDVK IORZ JURXSV XS WR FDVK IORZV &) RFFXUV DW WKH EHJLQQLQJ RI WKH ILUVW SHULRG $ FDVK IORZ JURXS FRQVLVWV RI D FDVK IORZ DPRXQW DQG WKH QXPEHU RI WLPHV LW UHSHDWV )RU H[DPSOH LQ WKH IROORZLQJ FDVK IORZ GLDJUDP WKH LQLWLDO FDVK IORZ LV 7KH QH[W JURXS RI FDVK IORZV FRQVLVWV RI VL[ IORZV RI ]HUR HDFK IROORZHG E\ D JURXS RI WKUHH FDVK IORZV 7KH ILQDO JURXS FRQVLVWV RI RQH FDVK IORZ 6: Cash Flow Calculations 77 CF 3 = 1 0 , 0 0 0, N 3 = 1 CF 2 = 1 , 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 :KHQHYHU \RX HQWHU D VHULHV RI FDVK IORZV LW LV LPSRUWDQW WR DFFRXQW IRU HYHU\ SHULRG RQ WKH FDVK IORZ GLDJUDP HYHQ SHULRGV ZLWK FDVK IORZV RI ]HUR Entering Cash Flows 7KH +3 %, , FDQ VWRUH DQ LQLWLDO FDVK IORZ SOXV DGGLWLRQDO FDVK IORZ JURXSV (DFK FDVK IORZ JURXS FDQ KDYH XS WR FDVK IORZV (QWHU FDVK IORZV XVLQJ WKH IROORZLQJ VWHSV 3UHVV WR FOHDU WKH UHVLVWHUV (QWHU WKH QXPEHU RI SHULRGV SHU \HDU DQG SUHVV (QWHU WKH DPRXQW RI WKH LQLWLDO LQYHVWPHQW WKHQ SUHVV 7KH M VWDQGV IRU WKH FDVK IORZ QXPEHU WKURXJK  (QWHU WKH DPRXQW RI WKH QH[W FDVK IORZ DQG SUHVV , I WKH DPRXQW HQWHUHG LQ VWHS RFFXUV PRUH WKDQ RQFH FRQVHFXWLYHO\ HQWHU WKH QXPEHU RI WLPHV LW RFFXUV DQG SUHVV 5HSHDW VWHSV DQG IRU HDFK DQG XQWLO DOO FDVK IORZV KDYH EHHQ HQWHUHG B8 D Bg B D D Bg 78 6: Cash Flow Calculations FDOFXODWH WKH , 55<5 7KHQ FDOFXODWH WKH HIIHFWLYH LQWHUHVW UDWH $VVXPH WKHUH DUH SHULRGV SHU \HDU Example. (QWHU WKH FDVK IORZV IURP WKH SUHFHGLQJ GLDJUDP DQG B8 B @D Keys: Display: 0. 00 12. 00 11, 000. 00 Description: D $Bg D !Bg D BW (D ' (D " (D (D (DD &OHDUV DOO UHJLVWHUV 6HWV WR (QWHUV LQLWLDO FDVK IORZ 'LVSOD\V FDVK IORZ JURXS QXPEHU IRU DV ORQJ DV \RX KROG GRZQ 0. 00 6. 00 1, 000. 00 3. 00 10, 000. 00 21. 22 D (QWHUV ILUVW FDVK IORZ JURXS DPRXQW (QWHUV QXPEHU RI UHSHWLWLRQV (QWHUV VHFRQG FDVK IORZ JURXS DPRXQW (QWHUV QXPEHU RI UHSHWLWLRQV (QWHUV ILQDO FDVK IORZ &DOFXODWHV DQQXDO QRPLQDO \LHOG Viewing and Replacing Cash Flows 7R YLHZ D FDVK IORZ SUHVV n WR WR GLVSOD\ FDVK IORZV WR RU n WR WR GLVSOD\ FDVK IORZV WR n WR GLVSOD\ WKH QH[W FDVK IORZ n WR GLVSOD\ WKH SUHYLRXV FDVK IORZ n WR GLVSOD\ WKH FXUUHQW FDVK IORZ 6: Cash Flow Calculations 79 7R UHSODFH D FDVK IORZ DPRXQW SUHVV n WR WR VWRUH WKH QHZ DPRXQW LQ FDVK IORZV WR n WR WR VWRUH WKH QHZ DPRXQW LQ FDVK IORZV WR n WR VWRUH WKH DPRXQW LQ WKH QH[W FDVK IORZ n WR VWRUH WKH DPRXQW LQ WKH SUHYLRXV FDVK IORZ n WR VWRUH WKH DPRXQW LQ WKH FXUUHQW FDVK IORZ 3D ' 3D " 3D 3D 3DD WKH 7R UHSODFH WKH QXPEHU RI WLPHV D SDUWLFXODU FDVK IORZ RFFXUV FDVK IORZ ZKRVH QXPEHU RI RFFXUUHQFHV ZLOO FKDQJH 7KHQ HQWHU WKH QXPEHU RI WLPHV LW RFFXUV DQG SUHVV Bg ( 6LQFH FDVK IORZV FDQQRW EH GHOHWHG RU LQVHUWHG XVH B8 WR VWDUW RYHU Calculating Net Present Value 7KH QHW SUHVHQW YDOXH 139 IXQFWLRQ LV XVHG WR GLVFRXQW DOO FDVK IORZV WR WKH IURQW RI WKH WLPH OLQH XVLQJ DQ DQQXDO QRPLQDO LQWHUHVW UDWH WKDW \RX VXSSO\ 7KHVH VWHSV GHVFULEH KRZ WR FDOFXODWH 139 3UHVV DQG VWRUH WKH QXPEHU RI SHULRGV SHU \HDU LQ 3<5 (QWHU WKH FDVK IORZV XVLQJ DQG 6WRUH WKH DQQXDO QRPLQDO LQWHUHVW UDWH LQ , <5 DQG SUHVV B8 D g Bx Example: A Discounted Contract, Uneven Cash flows. <RX KDYH DQ RSSRUWXQLW\ WR SXUFKDVH D FRQWUDFW ZLWK WKH IROORZLQJ FDVK IORZV End of Month Amount 80 6: Cash Flow Calculations +RZ PXFK VKRXOG \RX SD\ IRU WKH FRQWUDFW LI \RX ZLVK WR \LHOG D \HDUO\ UDWH RI RQ \RXU LQYHVWPHQW" I/YR = 15% 5, 000 4 5, 000 9 10 Display: 0. 00 12. 00 0. 00 10, 000 7, 500 15 Description: 25 &OHDUV UHJLVWHUV 6HWV SD\PHQWV SHU \HDU (QWHUV LQLWLDO FDVK IORZ RI ]HUR 7KH FDVK IORZ QXPEHU LV GLVSOD\HG DV ORQJ DV \RX KROG GRZQ NH\ WKH (QWHUV ILUVW FDVK IORZ (QWHUV QXPEHU RI RFFXUUHQFHV (QWHUV VHFRQG FDVK IORZ (QWHUV WKLUG FDVK IORZ (QWHUV QXPEHU RI RFFXUUHQFHV (QWHUV IRXUWK FDVK IORZ (QWHUV QXPEHU RI RFFXUUHQFHV (QWHUV ILIWK FDVK IORZ (QWHUV QXPEHU RI RFFXUUHQFHV (QWHUV VL[WK FDVK IORZ (QWHUV VHYHQWK FDVK IORZ B8 B D Keys: D !Bg #D D "Bg #D Bg D "Bg %#D D 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 D 6: Cash Flow Calculations 81 'Bg D Keys: Display: 9. 00 10, 000. 00 Description: (QWHUV QXPEHU RI RFFXUUHQFHV (QWHUV QH[W FDVK IORZ 7KH FDVK IORZV WKDW GHVFULEH \RXU SURVSHFWLYH LQYHVWPHQW DUH QRZ LQ WKH FDOFXODWRU <RX FDQ SUHVV IROORZHG E\ DQG UHSHDWHGO\ WR YLHZ WKH FDVK IORZV DQG QXPEHU RI WLPHV HDFK RFFXUV 1RZ WKDW \RX KDYH HQWHUHG WKH FDVK IORZV VWRUH WKH LQWHUHVW UDWH DQG FDOFXODWH WKH QHW SUHVHQW YDOXH (D (D (Bg #F Bx Keys: Display: 15. 00 27, 199. 92 Description: 6WRUHV DQQXDO LQWHUHVW UDWH &DOFXODWHV QHW SUHVHQW YDOXH RI VWRUHG FDVK IORZV 6HH URXQGLQJ H[DPSOH RQ SDJH  7KLV UHVXOW VKRZV WKDW LI \RX ZDQW D \LHOG RI SHU \HDU \RX VKRXOG SD\ IRU WKH FRQWUDFW 1RWLFH WKDW WKLV DPRXQW LV SRVLWLYH 7KH QHW SUHVHQW YDOXH LV VLPSO\ WKH VXPPHG RU QHWWHG YDOXH RI D VHULHV RI FDVK IORZV ZKHQ WKH\ DUH GLVFRXQWHG WR WKH IURQW RI WKH WLPH OLQH 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 1% = 15% per year 10, 000. 00 82 6: Cash Flow Calculations Calculating Internal Rate of Return 3UHVV VWRUH QXPEHU RI SHULRGV SHU \HDU LQ 3<5 (QWHU WKH FDVK IORZV XVLQJ DQG 3UHVV B8 BW D g :KHQ \RX FDOFXODWH , 55<5 \RX JHW WKH DQQXDO QRPLQDO UDWH WKDW JLYHV DQ 139 RI ]HUR 7KH IROORZLQJ H[DPSOH XVHV WKH FDVK IORZV WKDW ZHUH HQWHUHG LQ WKH SUHYLRXV H[DPSOH 0RUH WKDQ RQH , 55<5 FDQ H[LVW , I \RX JHW WKH No Solution PHVVDJH VHH $SSHQGL[ % SDJH  Example. , I WKH VHOOHU RI WKH FRQWUDFW LQ WKH SUHYLRXV H[DPSOH ZDQWV DQG \RX DFFHSW WKDW SULFH ZKDW LV \RXU \LHOG" 7KLV LV DQ , 55<5 FDOFXODWLRQ WKDW UHTXLUHV D VOLJKW PRGLILFDWLRQ WR WKH FXUUHQWO\ VWRUHG FDVK IORZV 10, 000 7, 500 5, 000 5, 000 1 3 5 7 9 11 13 15 17 19 21 23 25 IRR/YR = ? -28, 000 D&@B3 BW Keys: Display: 28, 000. 00 12. 49 Description: &KDQJHV LQLWLDO FDVK IORZ &DOFXODWHV DQQXDO QRPLQDO \LHOG 0RUH H[DPSOHV WKDW XVH 139 DQG , 55<5 FDOFXODWLRQV DUH JLYHQ LQ FKDSWHU $GGLWLRQDO ([DPSOHV 6: Cash Flow Calculations 83 Automatic Storage of IRR/YR and NPV :KHQ \RX FDOFXODWH 139 WKH UHVXOW LV VWRUHG LQ 39 IRU \RXU FRQYHQLHQFH 7R UHFDOO WKDW UHVXOW SUHVV , I \RX KDYHQW FKDQJHG WKH 790 YDOXHV IURP WKH ODVW H[DPSOH XVLQJ 139 SDJH  ZKHQ \RX SUHVV WKH UHVXOW LV ( ( :KHQ \RX FDOFXODWH , 55<5 WKH UHVXOW LV DOVR VWRUHG LQ , <5 )RU WKH WR GLVSOD\ WKH DQQXDOL]HG \LHOG SUHYLRXV H[DPSOH SUHVV (F 84 6: Cash Flow Calculations 7 Statistical Calculations 7KH DQG NH\V DUH XVHG WR HQWHU DQG GHOHWH GDWD IRU RQH DQG WZRYDULDEOH VWDWLVWLFV 6XPPDWLRQ GDWD LV VWRUHG LQ PHPRU\ 7KH ODEHOV DERYH WKH WR NH\V LQGLFDWH ZKDW VXPPDWLRQ GDWD LV VWRUHG 2QFH \RX HQWHU WKH GDWD \RX FDQ XVH WKH VWDWLVWLFDO IXQFWLRQV WR FDOFXODWH WKH IROORZLQJ 0HDQ DQG VWDQGDUG GHYLDWLRQ /LQHDU UHJUHVVLRQ VWDWLVWLFV /LQHDU HVWLPDWLRQ DQG IRUHFDVWLQJ :HLJKWHG PHDQ 6XPPDWLRQ VWDWLVWLFV Q [ [ \ \ DQG [\ e Bd "' n n n n n Clearing Statistical Data &OHDU WKH VWDWLVWLFDO UHJLVWHUV EHIRUH HQWHULQJ QHZ GDWD , I \RX GRQW FOHDU WKH UHJLVWHUV GDWD FXUUHQWO\ VWRUHG LV DXWRPDWLFDOO\ LQFOXGHG LQ WKH VXPPDWLRQ FDOFXODWLRQV 7R FOHDU WKH VWDWLVWLFDO UHJLVWHUV SUHVV 7KH GLVSOD\ LV DOVR FOHDUHG B j 7: Statistical Calculations 85 Entering Statistical Data 7KHUH LV QR OLPLW WR WKH QXPEHU RI YDOXHV \RX FDQ DFFXPXODWH LQ WKH VWDWLVWLFDO UHJLVWHUV One-Variable Statistics 7R HQWHU [ GDWD IRU RQHYDULDEOH VWDWLVWLFV FRPSOHWH WKH IROORZLQJ VWHSV &OHDU WKH VWDWLVWLFDO UHJLVWHUV E\ SUHVVLQJ (QWHU WKH ILUVW YDOXH DQG SUHVV 7KH +3 %, , GLVSOD\V Q WKH QXPEHU RI LWHPV DFFXPXODWHG &RQWLQXH DFFXPXODWLQJ YDOXHV E\ HQWHULQJ WKH QXPEHUV DQG SUHVVLQJ 7KH QYDOXH LV LQFUHPHQWHG ZLWK HDFK HQWU\ e Bj e Two-Variable Statistics and Weighted Mean 7R HQWHU [\ SDLUV RI VWDWLVWLFDO GDWD FRPSOHWH WKHVH VWHSV &OHDU WKH VWDWLVWLFDO UHJLVWHUV E\ SUHVVLQJ (QWHU WKH ILUVW [YDOXH DQG SUHVV 7KH +3 %, , GLVSOD\V WKH [ YDOXH (QWHU WKH FRUUHVSRQGLQJ \YDOXH DQG SUHVV 7KH +3 %, , GLVSOD\V Q WKH QXPEHU RI SDLUV RI LWHPV DFFXPXODWHG &RQWLQXH HQWHULQJ [\ SDLUV 7KH QYDOXH LV LQFUHPHQWHG ZLWK HDFK HQWU\ H Bj e 7R HQWHU GDWD IRU FDOFXODWLQJ WKH ZHLJKWHG PHDQ HQWHU HDFK GDWD YDOXH DV [ DQG LWV FRUUHVSRQGLQJ ZHLJKW DV \ If statistical data causes the value of a register to exceed 9. 99999999999 10499, the HP 10BII displays a temporary overflow warning (OFLO). 86 7: Statistical Calculations Correcting Statistical Data , QFRUUHFW HQWULHV FDQ EH GHOHWHG XVLQJ , I HLWKHU YDOXH RI DQ [\ SDLU LV LQFRUUHFW \RX PXVW GHOHWH DQG UHHQWHU ERWK YDOXHV Bd Correcting One-Variable Data 7R GHOHWH DQG UHHQWHU VWDWLVWLFDO GDWD . H\ LQ WKH [YDOXH WR EH GHOHWHG 3UHVV WR GHOHWH WKH YDOXH 7KH QYDOXH LV GHFUHDVHG E\ RQH (QWHU WKH FRUUHFW YDOXH XVLQJ Bd e Correcting Two-Variable Data 7R GHOHWH DQG UHHQWHU [\ SDLUV RI VWDWLVWLFDO GDWD . H\ LQ WKH [YDOXH SUHVV DQG WKHQ NH\ LQ WKH \YDOXH 3UHVV WR GHOHWH WKH YDOXHV 7KH QYDOXH LV GHFUHDVHG E\ RQH (QWHU WKH FRUUHFW [\ SDLU XVLQJ DQG Bd H H e Summary of Statistical Calculations 6RPH IXQFWLRQV UHWXUQ WZR YDOXHV 7KH STAT DQQXQFLDWRU LQGLFDWHV WKDW WZR YDOXHV KDYH EHHQ UHWXUQHG 3UHVV WR VHH WKH KLGGHQ YDOXH Bi B6 Keys Description Bi to Display Bi BX $ULWKPHWLF PHDQ 0HDQ DYHUDJH RI WKH DYHUDJH RI WKH [YDOXHV \YDOXHV LI \RX HQWHUHG \GDWD 0HDQ RI WKH [YDOXHV ZHLJKWHG E\ WKH \YDOXHV 6DPSOH VWDQGDUG GHYLDWLRQ RI WKH [ YDOXHV 6DPSOH VWDQGDUG GHYLDWLRQ RI WKH \YDOXHV LI \RX HQWHUHG \GDWD 7: Statistical Calculations 87 Bw Keys Description Bi to Display 3RSXODWLRQ VWDQGDUG GHYLDWLRQ RI WKH \YDOXHV LI \RX HQWHUHG \GDWD BQ [YDOXH BR BR \YDOXH 3RSXODWLRQ VWDQGDUG GHYLDWLRQ RI WKH [ YDOXHV (VWLPDWH RI [ IRU D JLYHQ &RUUHODWLRQ FRHIILFLHQW YDOXH RI \ (VWLPDWH RI \ IRU D JLYHQ 6ORSH P RI FDOFXODWHG YDOXH RI [ OLQH \LQWHUFHSW E RI WKH FDOFXODWHG OLQH 6ORSH P RI WKH FDOFXODWHG OLQH UurhyrhqhqqrvhvhruhurqhhvhhyvtshyhtrpyrrrsqhhUur yhvhqhqqrvhvhruhurqhhpvrurrvryhv Uurpryhvprssvpvrvhirvurhtrò utu uhrhrupyryurqhhsvur phypyhrqyvr6hyrs vqvphrhrsrpvvrpryhvhqò vqvphrhrsrprthvr pryhv6hyrpyrrvqvphruryvrvhsv AC AY Aa A Ag Af Keys Description 1XPEHU RI GDWD SRLQWV HQWHUHG 6XP RI WKH [YDOXHV 6XP RI WKH \YDOXHV 6XP RI WKH VTXDUHV RI WKH [YDOXHV 6XP RI WKH VTXDUHV RI WKH \YDOXHV 6XP RI WKH SURGXFWV RI WKH [ DQG \YDOXHV Mean, Standard Deviations, and Summation Statistics <RX FDQ FDOFXODWH WKH PHDQ [  VDPSOH VWDQGDUG GHYLDWLRQ 6[ DQG SRSXODWLRQ VWDQGDUG GHYLDWLRQ [ DQG VXPPDWLRQ VWDWLVWLFV Q [ DQG [ RI [GDWD )RU [\ GDWD \RX FDQ DOVR FDOFXODWH WKH PHDQ VDPSOH VWDQGDUG GHYLDWLRQ DQG SRSXODWLRQ VWDQGDUG GHYLDWLRQ RI WKH \GDWD DQG WKH VXPPDWLRQ VWDWLVWLFV \ \ DQG [\ 88 7: Statistical Calculations Example 1. $ \DFKW FDSWDLQ ZDQWV WR GHWHUPLQH KRZ ORQJ LW WDNHV WR FKDQJH D VDLO 6KH UDQGRPO\ FKRRVHV VL[ PHPEHUV RI KHU FUHZ REVHUYHV WKHP DV WKH\ FDUU\ RXW WKH VDLO FKDQJH DQG UHFRUGV WKH QXPEHUV RI PLQXWHV UHTXLUHG &DOFXODWH WKH PHDQ DQG VDPSOH VWDQGDUG GHYLDWLRQ RI WKH WLPHV $OVR FDOFXODWH WKH URRW PHDQ VTXDUH XVLQJ WKH IRUPXOD x 2 / n Keys: Bj "#e "e e !#e !#e !%#e B6 BX A dAC 1B Display: 0. 00 1. 00 2. 00 3. 00 4. 00 5. 00 6. 00 3. 50 0. 85 77. 13 6. 00 3. 59 Description: &OHDUV VWDWLVWLFDO UHJLVWHUV (QWHUV ILUVW WLPH (QWHUV VHFRQG WLPH (QWHUV WKLUG WLPH (QWHUV IRXUWK WLPH (QWHUV ILIWK WLPH (QWHUV VL[WK WLPH &DOFXODWHV WKH PHDQ &DOFXODWHV WKH VDPSOH VWDQGDUG GHYLDWLRQ 'LVSOD\V [ 'LVSOD\V Q &DOFXODWHV WKH URRW PHDQ VTXDUH WKDW WKH GDWD LV D VDPSOLQJ RI D ODUJHU FRPSOHWH VHW RI GDWD , I WKH GDWD FRQVWLWXWHV WKH HQWLUH SRSXODWLRQ WKH WUXH SRSXODWLRQ VWDQGDUG GHYLDWLRQV FDQ EH FDOFXODWHG E\ DQG SUHVVLQJ 7KH VWDQGDUG GHYLDWLRQV FDOFXODWHG E\ BX DQG BX Bi DUH WKH VDPSOH VWDQGDUG GHYLDWLRQV 7KH\ DVVXPH Bw BwBi Example 2. 7KH FRDFK KDV IRXU QHZ SOD\HUV RQ WKH WHDP ZLWK KHLJKWV RI DQG FHQWLPHWHUV DQG ZHLJKWV RI DQG NLORJUDPV )LQG WKH PHDQ DQG SRSXODWLRQ VWDQGDUG GHYLDWLRQ RI ERWK WKHLU KHLJKWV DQG ZHLJKWV WKHQ VXP WKH \GDWD 7: Statistical Calculations 89 Keys: Bj '!H'e & H&e %%H&!e &#H%%e B6 Bi Bw Bi Aa Display: 0. 00 1. 00 2. 00 3. 00 4. 00 184. 25 82. 75 5. 80 4. 71 331. 00 Description: &OHDUV VWDWLVWLFDO UHJLVWHUV (QWHUV KHLJKW DQG ZHLJKW RI SOD\HU (QWHUV KHLJKW DQG ZHLJKW RI SOD\HU (QWHUV KHLJKW DQG ZHLJKW RI SOD\HU (QWHUV KHLJKW DQG ZHLJKW RI SOD\HU &DOFXODWHV PHDQ RI KHLJKWV [ 'LVSOD\V PHDQ RI ZHLJKWV \ &DOFXODWHV SRSXODWLRQ VWDQGDUG GHYLDWLRQ IRU KHLJKWV [ 'LVSOD\V SRSXODWLRQ VWDQGDUG GHYLDWLRQ IRU ZHLJKWV \ 'LVSOD\V WKH WRWDO RI WKH \V Linear Regression and Estimation /LQHDU UHJUHVVLRQ LV D VWDWLVWLFDO PHWKRG IRU HVWLPDWLRQ DQG IRUHFDVWLQJ , W LV XVHG WR ILQG D VWUDLJKW OLQH WKDW EHVW ILWV D VHW RI [\ GDWD 7KHUH PXVW EH DW OHDVW WZR GLIIHUHQW [\ SDLUV 7KH VWUDLJKW OLQH SURYLGHV D UHODWLRQVKLS EHWZHHQ WKH [ DQG \YDULDEOHV \ P[ E ZKHUH P LV WKH VORSH DQG E LV WKH \LQWHUFHSW Linear Regression. &DOFXODWH P E DQG U WKH FRUUHODWLRQ FRHIILFLHQW DV IROORZV &OHDU WKH VWDWLVWLFDO UHJLVWHUV E\ SUHVVLQJ (QWHU WKH ILUVW [YDOXH DQG SUHVV 7KH [YDOXH LV GLVSOD\HG (QWHU WKH FRUUHVSRQGLQJ \YDOXH DQG SUHVV 7KH +3 %, , GLVSOD\V Q WKH QXPEHU RI SDLUV RI LWHPV DFFXPXODWHG &RQWLQXH HQWHULQJ [\ SDLUV 7KH QYDOXH LV LQFUHPHQWHG ZLWK HDFK HQWU\ 7R GLVSOD\ E WKH \LQWHUFHSW SUHVV 7KHQ SUHVV WR GLVSOD\ P WKH VORSH RI WKH OLQH 3UHVV WR GLVSOD\ U WKH FRUUHODWLRQ FRHIILFLHQW H Bj e Bi BQBi BR 90 7: Statistical Calculations Linear Estimation. 7KH VWUDLJKW OLQH FDOFXODWHG E\ OLQHDU UHJUHVVLRQ FDQ EH XVHG WR HVWLPDWH D \YDOXH IRU D JLYHQ [YDOXH RU YLFH YHUVD (QWHU WKH [\ GDWD XVLQJ WKH LQVWUXFWLRQV RQ SDJH (QWHU WKH NQRZQ [YDOXH RU \YDOXH n 7R HVWLPDWH [ IRU WKH JLYHQ \ HQWHU WKH \YDOXH WKHQ SUHVV n 7R HVWLPDWH \ IRU WKH JLYHQ [ HQWHU WKH [YDOXH WKHQ SUHVV BQ BR Example: Forecasting. $OLV $]DOHDV DGYHUWLVHV RQ D ORFDO UDGLR VWDWLRQ )RU WKH SDVW VL[ ZHHNV WKH PDQDJHU KDV NHSW UHFRUGV RI WKH QXPEHU RI PLQXWHV RI DGYHUWLVLQJ WKDW ZHUH SXUFKDVHG DQG WKH VDOHV IRU WKDW ZHHN Week Minutes of Advertising (x-values) Sales (y-values) :KDW LV WKH \LQWHUFHSW WKH VORSH DQG WKH FRUUHODWLRQ FRHIILFLHQW" y 3, 000. 00 (forecasted) 2, 000. 00 Sales in Dollars m = 425. 88 1, 000. 00 b x 1 2 3 4 5 6 7 8 Minutes of Advertising 7: Statistical Calculations 91 Keys: Bj H"e H' e !He #H $#e #H &'e "H e BR Bi BQBi %BR &BR Display: 0. 00 1. 00 2. 00 3. 00 4. 00 5. 00 6. 00 376. 25 425. 88 0. 90 Description: &OHDUV VWDWLVWLFDO UHJLVWHUV (QWHUV PLQXWHV DQG VDOHV IRU FRQVHFXWLYH ZHHNV &DOFXODWHV \LQWHUFHSW E 'LVSOD\V VORSH &DOFXODWHV FRUUHODWLRQ FRHIILFLHQW (VWLPDWH ZKDW WKH OHYHO RI VDOHV ZRXOG EH LI WKH EXVLQHVV SXUFKDVHG RU PLQXWHV RI DGYHUWLVLQJ 3, 357. 38 3, 783. 25 (VWLPDWHV VDOHV LI PLQXWHV RI DGYHUWLVLQJ ZHUH SXUFKDVHG (VWLPDWHV VDOHV LI PLQXWHV ZHUH SXU FKDVHG +RZ PDQ\ PLQXWHV RI DGYHUWLVLQJ VKRXOG $OLV EX\ WR DWWDLQ VDOHV RI " !BQ 6. 16 (VWLPDWHV PLQXWHV RI DGYHUWLVLQJ UHTXLUHG IRU LQ VDOHV 92 7: Statistical Calculations Weighted Mean 7KH IROORZLQJ SURFHGXUH FDOFXODWHV WKH ZHLJKWHG PHDQ RI GDWD SRLQWV [ [ [Q RFFXUULQJ ZLWK ZHLJKWV \ \ \Q 8VH DQG WKH [YDOXHV 3UHVV H e WR HQWHU [\ SDLUV 7KH \YDOXHV DUH WKH ZHLJKWV RI Bi Example. $ VXUYH\ RI RQHEHGURRP UHQWDO DSDUWPHQWV UHYHDOV WKDW RI WKHP UHQW IRU SHU PRQWK IRU IRU DQG IRU :KDW LV WKH DYHUDJH PRQWKO\ UHQW" Keys: Bj #H#"e ##H!e #H&&e #$H' e Bi Display: 0. 00 1. 00 2. 00 3. 00 4. 00 509. 44 Description: &OHDUV VWDWLVWLFV PHPRU\ (QWHUV ILUVW UHQW DQG LWV ZHLJKW (QWHUV VHFRQG UHQW DQG LWV ZHLJKW (QWHUV WKLUG UHQW DQG LWV ZHLJKW (QWHUV IRXUWK UHQW DQG LWV ZHLJKW &DOFXODWHV ZHLJKWHG PHDQ 7: Statistical Calculations 93 8 Additional Examples Business Applications Setting a Sales Price 2QH PHWKRG IRU VHWWLQJ WKH SHU XQLW VDOHV SULFH LV WR GHWHUPLQH WKH FRVW RI SURGXFWLRQ SHU XQLW DQG WKHQ PXOWLSO\ E\ WKH GHVLUHG UDWH RI UHWXUQ )RU WKLV PHWKRG WR EH DFFXUDWH \RX PXVW LGHQWLI\ DOO FRVWV DVVRFLDWHG ZLWK WKH SURGXFW 7KH IROORZLQJ HTXDWLRQ FDOFXODWHV XQLW SULFH EDVHG RQ WRWDO FRVW DQG UDWH RI UHWXUQ 35, &( 727$/ &267 180%(5 2) 81, 76 571  Example. 7R SURGXFH XQLWV \RXU FRVW LV <RX ZDQW D UDWH RI UHWXUQ :KDW SULFH VKRXOG \RX FKDUJH SHU XQLW" "d 4 BB d 1 Keys: Display: 40, 000. 00 20. 00 24. 00 Description: (QWHUV FRVW &DOFXODWHV XQLW FRVW &DOFXODWHV XQLW VDOHV SULFH 8: Additional Examples 95 Forecasting Based on History 2QH PHWKRG RI IRUHFDVWLQJ VDOHV PDQXIDFWXULQJ UDWHV RU H[SHQVHV LV UHYLHZLQJ KLVWRULFDO WUHQGV 2QFH \RX KDYH KLVWRULFDO GDWD WKH GDWD DUH ILW WR D FXUYH WKDW KDV WLPH RQ WKH [D[LV DQG TXDQWLW\ RQ WKH \D[LV Example. *LYHQ WKH IROORZLQJ VDOHV GDWD ZKDW DUH WKH VDOHV HVWLPDWHV IRU \HDUV VL[ DQG VHYHQ" Year 1 2 3 4 5 Sales $ 10, 000 11, 210 13, 060 16, 075 20, 590 Bj He H e !H!$e "H$%#e #H #'e $BR %BR Keys: Display: 0. 00 1. 00 2. 00 3. 00 4. 00 5. 00 22, 000. 50 24, 605. 00 Description: &OHDUV VWDWLVWLFV UHJLVWHUV (QWHUV ILUVW \HDU DQG VDOHV IRU WKDW \HDU (QWHUV VHFRQG \HDUV GDWD &RQWLQXHV GDWD HQWU\ (VWLPDWHV VDOHV IRU \HDU VL[ (VWLPDWHV VDOHV IRU \HDU VHYHQ 96 8: Additional Examples Cost of Not Taking a Cash Discount $ FDVK GLVFRXQW JLYHV D EX\HU D UHGXFWLRQ LQ SULFH LI WKH SD\PHQW LV PDGH ZLWKLQ D VSHFLILHG WLPH SHULRG )RU H[DPSOH 1(7 PHDQV WKDW WKH EX\HU FDQ GHGXFW SHUFHQW LI SD\PHQW LV PDGH ZLWKLQ GD\V , I SD\PHQW LV QRW PDGH ZLWKLQ GD\V WKH IXOO DPRXQW PXVW EH SDLG E\ WKH WK GD\ <RX FDQ XVH WKH HTXDWLRQ VKRZQ EHORZ WR FDOFXODWH WKH FRVW RI IDLOLQJ WR WDNH WKH FDVK GLVFRXQW 7KH FRVW LV FDOFXODWHG DV DQ DQQXDO LQWHUHVW UDWH FKDUJHG IRU GHOD\LQJ SD\PHQW &267 ', 6& = ----------------------------------------------------------------------------------------------------------------------------( ( ', 6& ) (727$/ '$<6 ', 6& '$<6) ) ', 6& LV WKH GLVFRXQW SHUFHQW LI WKH SD\PHQW LV PDGH HDUO\ 727$/ '$<6 LV WKH WRWDO QXPEHU RI GD\V XQWLO WKH ELOO PXVW EH SDLG ', 6& '$<6 LV WKH QXPEHU RI GD\V IRU ZKLFK WKH GLVFRXQW LV DYDLODEOH Example. [. . . ] The separate collection and recycling of your waste equipment at the time of disposal will help to conserve natural resources and ensure that it is recycled in a manner that protects human health and the environment. For more information about where you can drop off your waste equipment for recycling, please contact your local city office, your household waste disposal service or the shop where you purchased the product. End-user terms and conditions HP 10B II Calculator Warranty period: 12 months 1. HP warrants to you, the end-user customer, that HP hardware, accessories and supplies will be free from defects in materials and workmanship after the date of purchase, for the period specified above. If HP receives notice of such defects during the warranty period, HP will, at its option, either repair or replace products which prove to be defective. [. . . ]