HP 10BII Manual
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5: Time Value of Money Calculations 71 $PRUWL]HWKHVWWKDQGWKSD\PHQWV 01.00(QWHUVILUVWSD\PHQW *1– 1LVSOD\V3(5DQGWKH DPRUWL]HGSD\PHQWSHULRG –310.42LVSOD\V35,1DQGWKHILUVW SULQFLSDOSD\PHQW 0.00LVSOD\V,17DQGWKHLQWHU HVW 13,939.58LVSOD\V%$/DQGWKHORDQ EDODQFHDIWHURQHSD\PHQW 025.00(QWHUVSD\PHQWWRDPRU WL]H * 25– 25LVSOD\V3(5DQGWKH DPRUWL]HGSD\PHQWSHULRG –220.21LVSOD\V35,1DQGWKH SULQFLSDOSDLGRQWKHWK SD\PHQW –90.21LVSOD\V,17DQGWKHLQWHU HVWSDLGRQWKHWKSD\ PHQW 9,193.28LVSOD\V%$/DQGWKHEDO DQFHDIWHUWKHWKSD\ PHQW 054.00(QWHUVSD\PHQWWRDPRU WL]H *54– 54LVSOD\V3(5DQGWKH DPRUWL]HGSD\PHQWSHULRG –290.37LVSOD\V35,1DQGWKH SULQFLSDOSDLGRQWKHWK SD\PHQW –20.05LVSOD\V,17DQGWKHLQWHU HVWSDLGRQWKHWKSD\ PHQW 1,801.57LVSOD\V%$/DQGWKHEDO DQFHDIWHUWKHWKSD\ PHQW .book Page 71 Wednesday, June 21, 2000 5:19 PM
72 5: Time Value of Money Calculations Interest Rate Conversions 7KH,QWHUHVW&RQYHUVLRQDSSOLFDWLRQXVHVWKUHHNH\V *\b*ZDQG*b7KH\FRQYHUWEHWZHHQQRPLQDO DQGDQQXDOHIIHFWLYHLQWHUHVWUDWHV1RPLQDODQGHIIHFWLYH LQWHUHVWUDWHVDUHGHVFULEHGRQSDJH ,I\RXNQRZDQDQQXDOQRPLQDOLQWHUHVWUDWHDQG\RXZLVK WRVROYHIRUWKHFRUUHVSRQGLQJDQQXDOHIIHFWLYHUDWH (QWHUWKHQRPLQDOUDWHDQGSUHVV *\b (QWHUWKHQXPEHURIFRPSRXQGLQJSHULRGVDQGSUHVV *b &DOFXODWHWKHHIIHFWLYHUDWHE\SUHVVLQJ *Z 7RFDOFXODWHDQRPLQDOUDWHIURPDNQRZQHIIHFWLYHUDWH (QWHUWKHHIIHFWLYHUDWHDQGSUHVV *Z (QWHUWKHQXPEHURIFRPSRXQGLQJSHULRGVDQGSUHVV *b &DOFXODWHWKHQRPLQDOUDWHE\SUHVVLQJ *\b ,QWKH790DSSOLFDWLRQ *\bDQG.VKDUHWKHVDPHUHJLVWHU ,QWHUHVWFRQYHUVLRQVDUHXVHGSULPDULO\IRUWZRW\SHVRISUREOHPV n&RPSDULQJLQYHVWPHQWVZLWKGLIIHUHQWFRPSRXQGLQJSHULRGV n6ROYLQJ790SUREOHPVZKHUHWKHSD\PHQWSHULRGDQGWKHLQWHUHVW SHULRGGLIIHU Investments With Different Compounding Periods Example: Comparing Investments.
5: Time Value of Money Calculations 73 First Bank Second Bank Third Bank )LUVW%DQNRIIHUVDVOLJKWO\EHWWHUGHDOVLQFHLVJUHDWHUWKDQDQG Compounding and Payment Periods Differ 7KH790DSSOLFDWLRQDVVXPHVWKDWWKHFRPSRXQGLQJ SHULRGVDQGWKHSD\PHQWSHULRGVDUHWKHVDPH6RPHORDQ LQVWDOOPHQWVRUVDYLQJVGHSRVLWVDQGZLWKGUDZDOVGRQRW FRLQFLGHZLWKWKHEDQN·VFRPSRXQGLQJSHULRGV,IWKH SD\PHQWSHULRGGLIIHUVIURPWKHFRPSRXQGLQJSHULRG DGMXVWWKHLQWHUHVWUDWHWRPDWFKWKHSD\PHQWSHULRG EHIRUHVROYLQJWKHSUREOHP Keys: Display: Description: *\b6.706WRUHVQRPLQDOUDWH *b4.006WRUHVTXDUWHUO\ FRPSRXQGLQJSHULRGV *Z6.87&DOFXODWHVDQQXDO HIIHFWLYHUDWH *\b6.656WRUHVQRPLQDOUDWH *b12.006WRUHVPRQWKO\FRP SRXQGLQJSHULRGV *Z6.86&DOFXODWHVDQQXDO HIIHFWLYHUDWH *\b6.636WRUHVQRPLQDOUDWH *b360.006WRUHVFRPSRXQGLQJ SHULRGV *Z6.85&DOFXODWHVDQQXDO HIIHFWLYHUDWH .book Page 73 Wednesday, June 21, 2000 5:19 PM
74 5: Time Value of Money Calculations 7RDGMXVWDQLQWHUHVWUDWHZKHQWKHFRPSRXQGLQJSHULRGGLIIHUVIURPWKH SD\PHQWSHULRGFRPSOHWHWKHIROORZLQJVWHSV (QWHUWKHQRPLQDOUDWHDQGSUHVV *\b(QWHUWKHQXPEHURI FRPSRXQGLQJ SHULRGVLQD\HDUDQGSUHVV *b6ROYHIRUWKHHIIHFWLYH UDWHE\SUHVVLQJ *Z (QWHUWKHQXPEHURI SD\PHQWSHULRGVLQD\HDUDQGSUHVV *b 6ROYHIRUWKHDGMXVWHGQRPLQDOUDWHE\SUHVVLQJ *\b Example: Monthly Payments, Daily Compounding. 6WDUWLQJWRGD\ \RXPDNHPRQWKO\GHSRVLWVRIWRDQDFFRXQWSD\LQJ\bLQWHUHVW FRPSRXQGHGGDLO\XVLQJDGD\\HDU\f:KDWZLOOWKHEDODQFHEHLQ VHYHQ\HDUV Step 1. &DOFXODWHWKHHTXLYDOHQWUDWHZLWKPRQWKO\FRPSRXQGLQJ 6LQFH 120\b DQ G,
6: Cash Flow Calculations 75 6 Cash Flow Calculations How to Use the Cash Flow Application 7KHFDVKIORZDSSOLFDWLRQLVXVHGWRVROYHSUREOHPVZKHUH FDVKIORZVRFFXURYHUUHJXODULQWHUYDOVEXWDUHRIYDU\LQJ DPRXQWV
76 6: Cash Flow Calculations XXX Keys: Display: Description: *&0.00&OHDUVDOOUHJLVWHUV *b12.006WRUHVSHULRGVSHU\HDU (,–5,000.00(QWHUVLQLWLDOFDVKIORZ LVSOD\VFDVKIORZ JURXSQXPEHUZKLOH \RXKROGGRZQ , (,–2,000.00(QWHUVQH[WFDVKIORZ (,–4,000.00(QWHUVQH[WFDVKIORZ ,11,765.29(QWHUVILQDOFDVKIORZ *938.98&DOFXODWHVDQQXDO QRPLQDO\LHOG d3.250RQWKO\\LHOG 12 3 -5,000.00 -2,000.00 -4,000.0011,765.29 Flows received are positive. Flows paid out are negative. chapt_6.fm Page 76 Thursday, June 22, 2000 12:32 PM
6: Cash Flow Calculations 77 NPV and IRR/YR: Discontinuing Cash Flows &KDSWHUGHPRQVWUDWHVWKHXVHRIFDVKIORZGLDJUDPVWRFODULI\ILQDQFLDO SUREOHPV7KLVVHFWLRQGHVFULEHVGLVFRXQWHGFDVKIORZV7KH139DQG ,55
78 6: Cash Flow Calculations :KHQHYHU\RXHQWHUDVHULHVRIFDVKIORZVLWLVLPSRUWDQWWRDFFRXQWIRU HYHU\SHULRGRQWKHFDVKIORZGLDJUDPHYHQSHULRGVZLWKFDVKIORZVRI ]HUR Entering Cash Flows 7KH+3%,,FDQVWRUHDQLQLWLDOFDVKIORZSOXVDGGLWLRQDOFDVKIORZ JURXSV(DFKFDVKIORZJURXSFDQKDYHXSWRFDVKIORZV(QWHUFDVK IORZVXVLQJWKHIROORZLQJVWHSV 3UHVV *&WRFOHDUWKHUHVLVWHUV (QWHUWKHQXPEHURISHULRGVSHU\HDUDQGSUHVV *b (QWHUWKHDPRXQWRIWKHLQLWLDOLQYHVWPHQWWKHQSUHVV ,7KH´Mµ VWDQGVIRUWKHFDVKIORZ´ QXPEHUµWKURXJK\f (QWHUWKHDPRXQWRIWKHQH[WFDVKIORZDQGSUHVV , ,IWKHDPRXQWHQWHUHGLQVWHSRFFXUVPRUHWKDQRQFH FRQVHFXWLYHO\ HQWHUWKHQXPEHURIWLPHVLWRFFXUVDQGSUHVV *C 5HSHDWVWHSVDQGIRUHDFK ,DQG*CXQWLODOOFDVKIORZVKDYH EHHQHQWHUHG CF1=0,N1=6 CFO = -11,000 CF 2 = 1,000 ,N2=3 CF 3 = 10,000 ,N3=1 12 345678910 chapt_6.fm Page 78 Thursday, June 22, 2000 12:32 PM
6: Cash Flow Calculations 79 Example. (QWHUWKHFDVKIORZVIURPWKHSUHFHGLQJGLDJUDPDQG FDOFXODWHWKH ,55
80 6: Cash Flow Calculations 7RUHSODFHDFDVKIORZDPRXQWSUHVV n!,WRWRVWRUHWKHQHZDPRXQWLQFDVKIORZVWR n!,WRWRVWRUHWKHQHZDPRXQWLQFDVKIORZVWR n!, WRVWRUHWKHDPRXQWLQWKHQH[WFDVKIORZ n!,WRVWRUHWKHDPRXQWLQWKHSUHYLRXVFDVKIORZ n!, ,WRVWRUHWKHDPRXQWLQWKHFXUUHQWFDVKIORZ 7RUHSODFHWKHQXPEHURIWLPHVDSDUWLFXODUFDVKIORZRFFXUV WKH FDVKIORZZKRVHQXPEHURIRFFXUUHQFHVZLOOFKDQJH7KHQHQWHUWKH QXPEHURIWLPHVLWRFFXUVDQGSUHVV *C 6LQFHFDVKIORZVFDQQRWEHGHOHWHGRULQVHUWHGXVH *&WRVWDUWRYHU Calculating Net Present Value 7KHQHWSUHVHQWYDOXH139\fIXQFWLRQLVXVHGWRGLVFRXQWDOOFDVKIORZV WRWKHIURQWRIWKHWLPHOLQHXVLQJDQDQQXDOQRPLQDOLQWHUHVWUDWHWKDW\RX VXSSO\ 7KHVHVWHSVGHVFULEHKRZWRFDOFXODWH139 3UHVV *&DQGVWRUHWKHQXPEHURISHULRGVSHU\HDULQ 3