Natura czasu a kwoty amortyzacji środków trwałych

Pełen tekst

(1)Zeszyty Naukowe nr. 829. 2010. Uniwersytetu Ekonomicznego w Krakowie. 0LHF]\VãDZ'RELMD .DWHGUD5DFKXQNRZRĂFL. Natura czasu a kwoty amortyzacji ŋURGNyZWUZDã\FK :SURZDG]HQLH 3RPLDUGHSUHFMDFMLŋURGNyZWUZDã\FKMHVW]DJDGQLHQLHPZFLćŧRWZDUW\P DREHFQLHMHV]F]HQDELHUDMćF\P]QDF]HQLD]HZ]JOĕGXQDZ\UDťQLH]DU\VRZDQH LGHDOLVW\F]QHGćŧHQLHZ\UDŧRQHZ0LĕG]\QDURGRZ\FKVWDQGDUGDFKVSUDZR] GDZF]RŋFLILQDQVRZHM>%RQKDPLLQV@DE\VSUDZR]GDZF]RŋþGRVWR VRZ\ZDãDVLĕGRZDUWRŋFLJRG]LZ\FK:RGQLHVLHQLXGRU]HF]RZ\FKDNW\ZyZ WUZDã\FKNWyU\FKNRV]W\SR]\VNDQLDSRQRV]RQHVćZRNUHVDFKZF]HŋQLHMV]\FK QLŧX]\VNLZDQHNRU]\ŋFLRF]HNXMHVLĕDE\Z\ND]\ZDQDZELODQVLHZDUWRŋþQHWWR ŋURGNDWUZDãHJRZ\UDŧDãDWHUDťQLHMV]ćZDUWRŋþSU]\FKRGyZ]SR]RVWDãHJRRNUHVX Xŧ\WNRZDQLD7RSRGHMŋFLHRGGDZQDUHSUH]HQWRZDOLXF]HQLNWyU]\DQDOL]RZDOL SRPLDUDPRUW\]DFMLZDVSHNFLHZDUWRŋFLILUP\MDNQDSU]\NãDG*)HOWKDP L-2KOVRQ>@,FKFHOHPE\ãRDE\ZDUWRŋþNVLĕJRZDILUP\]UyZQ\ZDãDVLĕ ]ZDUWRŋFLćU\QNRZć -HŋOLSRQDGWRGćŧ\VLĕGRSUHF\]\MQHJRRV]DFRZDQLDNRV]WXMHGQRVWNRZHJR SU]H] VWRVRZDQLH QD SU]\NãDG V\VWHPX $%& WR ZDUXQNLHP NRQLHF]Q\P GR RVLćJQLĕFLDWHJRFHOXMHVWDGHNZDWQRŋþNZRWDPRUW\]DFMLF]\OLNZRWRGSLVXRG ZDUWRŋFLQDSRF]ćWHNURNXUyZQRZDŧćF\FKU]HF]\ZLVWćXWUDWĕZDUWRŋFL0LPRŧH DEVROXWQDSUHF\]MDMHVWQLHRVLćJDOQDLPRŧHQDZHWQLHSRWU]HEQD]HZ]JOĕGXQD URVQćFHNRV]W\LQIRUPDFMLWRGćŧHQLHGRVIRUPXãRZDQLDWHRULLRNUHŋODMćFHMNZRW\ RNUHVRZ\FKRGSLVyZMHVWFHORZHDDXWRPDW\]DFMDSURFHVyZZ\WZyUF]\FKMHV]F]H WĕNZHVWLĕZ\RVWU]D=ZLĕNV]HQLHSUHF\]MLSRPLDUXRNUHVRZHJR]\VNXLGćŧHQLD GRZLHUQHJRLU]HWHOQHJRREUD]XWDNŧHZ\PDJDMćGRNãDGQRŋFLZRNUHŋODQLXNZRW DPRUW\]DFML 2%XUW>@ZVZRMHMSRGVWDZRZHMSUDF\GRW\F]ćFHMDPRUW\]DFMLSRG]LHOLã DNW\ZDQDGZLHJUXS\'RSLHUZV]HMQDOHŧćWH]NWyU\FKVXPDX]\VNLZDQ\FK.

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(17) 10. 0LHF]\VãDZ'RELMD. ]PLDQ$E\PyJãVLĕGRNRQDþWDNV]\ENLUR]ZyMMDNLREVHUZXMHVLĕZSLHUZV]\FK ODWDFKŧ\FLDF]ãRZLHNDPXVLPLHþPLHMVFHGXŧHUR]SURV]HQLHSLHUZRWQHMHQHUJLL ŧ\FLDGXŧ\Z]URVWHQWURSLLF]\OLMHMSU]HPLDQDQDLQQHURG]DMHHQHUJLLSRGOHJD MćFHGDOV]\PSU]HPLDQRPLRVWDWHF]QLHUR]SURV]HQLX:V]\ENLPUR]ZRMXG]LHFND XMDZQLDVLĕSUDZLGãRZRŋþZ\UDŧRQDSU]H]3$WNLQVDÅŊZLDWQDSĕG]DXQLZHUVDOQD WHQGHQFMDGRSRJUćŧDQLDVLĕZFKDRVLHµ 7DEHOD=PQLHMV]DQLHVLĕSRF]ćWNRZHMZDUWRŋFLVLãŧ\FLRZ\FKF]ãRZLHND 6WDQHQHUJLL SRF]ćWNRZHM. 3URFHQW]PQLHM V]HQLD. =PQLHMV]HQLH. 6WDQQDNRQLHF. 3LHUZV]\. . . . . 'UXJL. . . . . 7U]HFL. . . . . &]ZDUW\. . . . . 3LćW\. . . . . …. …. …. …. . . 5RNŧ\FLD. … 2VLHPG]LHVLćW\ 6WRGZXG]LHVW\. Ã. …. ². . Ã. ². Ã ². …. …. …. …. ']LHZLĕþVHWSLĕþ G]LHVLćW\ 1RH

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(20) GODOXG]NLHJRŧ\FLD3RQDGWRQDWHMSURFHQWRZHMZLHONRŋFLRSLHUDVLĕGREU]HMXŧ ]ZHU\ILNRZDQ\UDFKXQHNNDSLWDãXOXG]NLHJR ''HXWVFKWZLHUG]LŧH]GURZRUR]VćGNRZHSRMPRZDQLHF]DVXMHVWVSU]HF]QH ]QDXNć1LHMHVWWRVWDQU]HF]\MHGQR]QDF]QLH]JRGQ\]U]HF]\ZLVWRŋFLć=ZUyþP\ XZDJĕŧHUR]ZDŧDQLDGRW\F]ćF]DVXF]ãRZLHNDLZW\PVHQVLH]GURZ\UR]VćGHN.

(21) 11. Natura czasu a kwoty amortyzacji…. F]ãRZLHND]JDG]DVLĕ]WHUPRG\QDPLF]QćVWU]DãNćF]DVXZSRGDQHMLQWHUSUH WDFML0LMDF]DVNDOHQGDU]RZ\LF]ãRZLHNVLĕVWDU]HMH7DGHVWUXNFMDMHVWťUyGãHP SRVWĕSXVWDU]HQLHVLĕMHVWNRQLHF]Q\PZDUXQNLHPRVLćJQLĕþ1LHMHVWWRMHGQDN F]DVDEVROXWQ\,QQ\XSã\ZF]DVXFKDUDNWHU\]XMHMDNLŋURG]DM]ZLHU]ćWDOERE\W\ SODQHWDUQHNWyUHWUZDMćPLOLDUG\ODW5R]XPLHQLHWHUPRG\QDPLF]QHMVWU]DãNL F]DVXSR]ZDODZV]F]HJyOQRŋFLEDUG]LHMSUHF\]\MQLHRNUHŋODþSU]HSã\Z\ZDUWRŋFL ZSURFHVDFKHNRQRPLF]Q\FKLGRNãDGQLHMXVWDODþNZRW\Z\QDJURG]HĸEćGťDPRU W\]DFMLŋURGNyZWUZDã\FK 3RPLDUXSï\ZXZHZQÚWU]QHJRF]DVXĂURGNöZWUZDï\FK =UR]ZDŧDĸRWHUPRG\QDPLF]QHMVWU]DãFHF]DVXZ\QLNDŧHZRGQLHVLHQLXGR ŋURGNyZWUZDã\FKDGHNZDWQHVSRVRE\XVWDODQLDNZRWDPRUW\]DFMLWRPHWRG\SU]\ VSLHV]RQHZNWyU\FKSRGVWDZćREOLF]HĸMHVWELHŧćFHVDOGR7HJRURG]DMXPHWRG\ Vć]QDQHSRGQD]ZćÅ]PQLHMV]DMćFHJRVDOGDµ GHFOLQLQJEDODQFH

(22) LVWRVRZDQH]H ZVSyãF]\QQLNDPL:VSyãF]\QQLNR]QDF]DŧHSURFHQWRGSLVXRGVDOGD ELHŧćFHJRMHVW7 7²OLF]EDODWXŧ\WNRZDQLD

(23) SU]\ZVSyãF]\QQLNXSURFHQW MHVW7LWS6WRVRZDQHVćFKĕWQLHRGGDZQDERZLHPMDNWZLHUG]LZLHOXDXWRUyZ QS>'DYLGVRQ'UDNH@>&RPPHQWV@

(24) SR]ZDODMćRQHRVLćJDþNRU]\ŋFL SRGDWNRZH =DXZDŧP\ŧHRNUHŋOHQLHZDUWRŋFLSRF]ćWNRZHMZDUWRŋFLSRRNUHVLHXŧ\W NRZDQLDLOLF]E\ODWXŧ\WNRZDQLD]DZLHUDZVRELHZV]\VWNLHGDQHSRWU]HEQHGR Z\]QDF]HQLDWHPSDXSã\ZXF]DVX:]ZLć]NX]W\PPRŧQDGRMŋþGRZ]RUX RJyOQHJRRNUHŋODMćFHJRSURFHQWRGSLVX]DSRŋUHGQLFWZHPWHPSDXSã\ZXF]DVXGOD GDQHJRŋURGNDWUZDãHJR8]\VNXMHP\WRUR]ZLć]XMćFUyZQDQLH W p e –pT = Wk ,. JG]LH Wp ²VWDQRZLZDUWRŋþSRF]ćWNRZć WN²RNUHŋODZDUWRŋþSR]RVWDãćSRRNUHVLHXŧ\WNRZDQLDŋURGNDWUZDãHJR 7 ²OLF]EDODWXŧ\WNRZDQLDŋURGNDWUZDãHJR :LHONRŋþpMHVWRNUHŋORQDIRUPXãć W p = – T1 ln Wk . p. =NROHLREOLF]\P\SURFHQWZHGãXJNWyUHJR]PQLHMV]DVLĕVDOGRSRF]ćWNRZH3R SLHUZV]\PRNUHVLHXŧ\WNRZDQLDVDOGRSRF]ćWNRZHRVLćJQLHVWDQ Wp + 1 = Wp e. 1 ln Wk T Wp. 1. W T = W p d Wk n = W pT p. Wk Wp ..

(25) 12. 0LHF]\VãDZ'RELMD. =DWHPNZRWDDPRUW\]DFMLMHVWUyZQD W p – W p + 1 = W p e1 –T. Wk Wp o,. F]\OLSURFHQWUZ\]QDF]DMćF\RGSLV]DGDQ\RNUHVMHVWRNUHŋORQ\Z]RUHP r = 1 –T. Wk Wp .. 3URFHQWUMHVWVWDã\WR]QDF]\WDVDPDZLHONRŋþU]PQLHMV]DVDOGRSRF]ćWNRZH DŧGRRVLćJQLĕFLDZLHONRŋFLW NSRXSã\ZLH7RNUHVyZDPRUW\]RZDQLD-HVWWR ]QDQ\RGGDZQDZ]yU>&RPPHQWV@MHGQDNMHJRREHFQHZ\SURZDG]HQLH]D SRŋUHGQLFWZHPWHPSDXSã\ZXF]DVXXND]XMHMHJRJãĕEV]ćQDWXUĕ:SUDNW\FH VWRVXMHVLĕXSURV]F]RQHSRGHMŋFLD IDNW\F]QLHRQHNRPSOLNXMć]DJDGQLHQLH

(26) SU]\M PXMćF]DSXQNWZ\MŋFLDSURFHQWDPRUW\]DFMLOLQLRZHMSRPQRŧRQ\RGSRZLHGQLP ZVSyãF]\QQLNLHP 3U]\NãDG6SRU]ćG]LþSODQDPRUW\]DFMLGODŋURGNDWUZDãHJRRZDUWRŋFLSRF]ćW NRZHM]ãRNUHVLHXŧ\WNRZDQLD7 ODWZDUWRŋFLSRXSã\ZLHODW]ã 2EOLF]DP\SURFHQWRGSLVX r = 1 –T. Wk 5 Wp = 1 –. 5000 100000 = 0,450719728 _ 45%i .. 7DEHOD3ODQDPRUW\]DFMLŋURGNDWUZDãHJR2GSLV\URF]QH Rok. 6DOGRQDSRF]ćWHN roku. 3URFHQWRGSLVX. .ZRWDDPRUW\]DFML. 6XPDXPRU]HQLD. . . . . . . . . . . 3. . . . . . . . . . . . . . . WN. ]ã. ². ². ². ŤUyGãRREOLF]HQLDZãDVQH. =DXZDŧP\ŧHZZ\SDGNXQLHOLQLRZHMDPRUW\]DFMLNZRW\PLHVLĕF]QHQLH VćãDWZRGRVWĕSQHMDNZZ\SDGNXDPRUW\]DFMLOLQLRZHM$E\]DWHPREOLF]\þWH NZRW\QDOHŧ\XVWDOLþPLHVLĕF]Q\SURFHQWRGSLVXSU]\MPXMćF7 Ã :WHG\RWU]\PXMHVLĕZDUWRŋþ r = 1 –T. Wk 60 Wp = 1 –. 5000 100000 = 0,0487 _ 4,87%i ..

(27) 13. Natura czasu a kwoty amortyzacji… 7DEHOD3ODQDPRUW\]DFMLŋURGNDWUZDãHJR2GSLV\PLHVLĕF]QH 0LHVLćF 3 … :DUWRŋþQD NRQLHFRNUHVX. 6DOGRQDSRF]ćWHN PLHVLćFD. 3URFHQWRGSLVX. .ZRWD DPRUW\]DFML. 6XPDXPRU]HQLD. … . … . … . … . . ŤUyGãRREOLF]HQLDZãDVQH. 5HODW\ZL]PF]DVXLSODQDPRUW\]DFMLVWDWNXNRVPLF]QHJR 3ODQDPRUW\]DFMLVWDWNXNRVPLF]QHJRSRZLQLHQXZ]JOĕGQLDþ]PLHQQHWHPSR XSã\ZXF]DVX]DOHŧQHRGSUĕGNRŋFLSRMD]GXF]\OLUHODW\ZL]PF]DVX7UDNWXMćF VWDWHNNRVPLF]Q\MDNRQDOHŧćF\GRGUXJLHMJUXS\F]\OLSRGOHJDMćF\GHSUHFMDFML.

(28) 14. 0LHF]\VãDZ'RELMD. ZUHODFMLGRF]DVXXZ]JOĕGQLDP\]MDZLVNRG\ODWDFMLF]DVXF]\OLMHJR]DXZDŧDOQLH ZROQLHMV]HJRXSã\ZXSU]\EDUG]RGXŧ\FKSUĕGNRŋFLDFK .RQFHSFMDWHUPRG\QDPLF]QHMVWU]DãNLF]DVXMHVWWDNŧH]JRGQD]H]MDZLVNLHP UHODW\ZL]PXXSã\ZXF]DVX-DNZLDGRPRUHODW\ZL]PF]DVXRNUHŋODSU]HNV]WDã FHQLH)LW]JHUDOGD/RUHQW]D]QDMGXMćFHGDOV]H]DVWRVRZDQLHZWHRULLZ]JOĕGQRŋFL JG]LHSRMDZLDVLĕSDUDGRNVEOLťQLćW$E\IRUPDOQLHSU]HGVWDZLþUHODW\ZL]P XSã\ZX F]DVX Z DVSHNFLH RPDZLDQHM VWU]DãNL F]DVX SU]\MPXMĕ Z\MŋFLRZć UyZQRŋþ (QHUJLDFDãNRZLWD (c

(29) (QHUJLDVSRF]\QNRZD (V = P c

(30) (QHUJLDNLQHW\F]QD (N

(31) . =DWHPSU]\VWDQGDUGRZ\FKR]QDF]HQLDFK 2 m0 v 2 Ec = m0 c + 2 = m0 c 2 d1 + v 2 n = mc 2, 2c 2. JG]LHPR]QDF]DPDVĕUHODW\ZLVW\F]QćDcSUĕGNRŋþŋZLDWãD -HŋOLRELHNW RVREDOXESU]HGPLRW

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(33) @ ²

(34) ODW3URFHQWRGSLVXZDUWRŋFLSRF]ćWNRZHMMHVWUyZQ\ Z]DRNUćJOHQLX r = 1 –T. Wk 8, 462 Wp = 1 –. 5000 100000 = 0,30.. :Z\SDGNXJG\VWDWHNNRVPLF]Q\QLHE\ãZF]HŋQLHMXŧ\ZDQ\GRSRGUyŧ\ ]ZLHONLPLSUĕGNRŋFLDPLOXEE\ãZ\NRU]\VW\ZDQ\SU]\SUĕGNRŋFLDFKQLHZ\ZRãX MćF\FKG\ODWDFMLF]DVXSU]H]N²ODWWRMHŋOLZ\UXV]DQDGDOHNćZ\SUDZĕNRVPLF]Qć QDOHŧ\Z\]QDF]\þQRZ\SODQDPRUW\]DFML:W\PFHOXQDOHŧ\XVWDOLþ ² ZDUWRŋþNVLĕJRZćŋURGNDWUZDãHJRQDSRF]ćWHNNWHJRURNX ² WHPSRXSã\ZXF]DVXSU]\SU]HZLG\ZDQHMSUĕGNRŋFL ² SR]RVWDã\RNUHVXŧ\WNRZDQLD ² DGHNZDWQ\SURFHQWDPRUW\]DFML 3. 2VWDWNXNRVPLF]Q\P]DNãDGDP\WHVDPHZLHONRŋFLMDNRŋURGNXWUZDã\P]ZF]HŋQLHMUR] SDWU\ZDQHJRSU]\NãDGX.

(35) 15. Natura czasu a kwoty amortyzacji… 7DEHOD3ODQDPRUW\]DFMLVWDWNXNRVPLF]QHJR Rok. 6DOGRQDSRF]ćWHN PLHVLćFD. 3URFHQWRGSLVX. .ZRWDDPRUW\]DFML. 6XPDXPRU]HQLD. . . . . . . . . . . 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ŤUyGãRREOLF]HQLDZãDVQH. 3U]\MPLMP\]DWHPŧHSRGZyFKODWDFKXŧ\WNRZDQLDZ8NãDG]LH6ãRQHF]Q\P VWDWHN Z\UXV]D ] PLVMć GR SODQHW\ (UUD Z JZLD]GR]ELRU]H 3OHMDG ] SUĕG NRŋFLćSRGUyŧQćNPV&]\QQLNUHODW\ZLVW\F]Q\MHVW Y 兾c ) = 兾Ã

(36) 5R]ZLć]XMćFUyZQDQLHHx RWU]\PXMHP\ Z\NãDGQLNUyZQ\2EOLF]DP\]PQLHMV]RQHWHPSRXSã\ZXF]DVX p⬘ ² ². 1DWHMSRGVWDZLHREOLF]DP\RGSRZLHGQLRNUHVXŧ\WNRZDQLD7⬘ >兾 ²

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(38) ODW=DWHPSURFHQWRGSLVXZDUWRŋFLSRF]ćWNRZHMMHVWUyZQ\ r = 1 –T. Wk 8, 33 Wp = 1 –. 5000 = 0,1943399. 30250. 7DEHOD3ODQDPRUW\]DFMLVWDWNXNRVPLF]QHJRNWyU\SRGUXJLPURNXLVWQLHQLDZ\UXV]D ZSRGUyŧ]SUĕGNRŋFLćNPV Rok. 6DOGRQDSRF]ćWHN roku. 3URFHQWRGSLVX. .ZRWDDPRUW\]DFML. 6XPDXPRU]HQLD. . . . . . . . . . . 3. . . . . . . . . . . . . . . . . . . . . . . . . . 3ODQHWD(UUDSREUDQLHKWWSZZZNDULQ\DFRP3ODQHW(UUDKWPO.

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