An Indirect Utility Model of Multiple Car Ownership and

TI 2004-085/3
Tinbergen Institute Discussion Paper
An Indirect Utility Model of Multiple
Car Ownership and Use
Jan Rouwendal1
John Pommer2
1 Faculty
of Economics and Business Administration, Vrije Universiteit Amsterdam, and Tinbergen
Institute;
Connekt, Delft.
2
Tinbergen Institute
The Tinbergen Institute is the institute for
economic research of the Erasmus Universiteit
Rotterdam, Universiteit van Amsterdam, and Vrije
Universiteit Amsterdam.
Tinbergen Institute Amsterdam
Roetersstraat 31
1018 WB Amsterdam
The Netherlands
Tel.:
Fax:
+31(0)20 551 3500
+31(0)20 551 3555
Tinbergen Institute Rotterdam
Burg. Oudlaan 50
3062 PA Rotterdam
The Netherlands
Tel.:
Fax:
+31(0)10 408 8900
+31(0)10 408 9031
Please send questions and/or remarks of nonscientific nature to [email protected].
Most TI discussion papers can be downloaded at
http://www.tinbergen.nl.
$QLQGLUHFWXWLOLW\PRGHORIPXOWLSOHFDURZQHUVKLSDQGXVH
-DQ5RXZHQGDO DQG-RKQ3RPPHU 'HSDUWPHQWRI6SDWLDO(FRQRPLFV
)UHH8QLYHUVLW\
'H%RHOHODDQ
+9$PVWHUGDP
7KH1HWKHUODQGV
7HO
)D[
(PDLOMURXZHQGDO#IHZHEYXQO
7KLVYHUVLRQ-DQXDU\
.H\ZRUGVDXWRPRELOHGHPDQGPXOWLSOHFDURZQHUVKLSGHPDQGIRUFDUNLORPHWHUV
-(/&ODVVLILFDWLRQ&RGHV5'
$EVWUDFW
7KHQXPEHURIKRXVHKROGVZLWKWZRRUPRUHFDUVLVVWHDGLO\LQFUHDVLQJRYHUWLPH7KLVKDV
SRWHQWLDOO\VLJQLILFDQWLPSOLFDWLRQVIRUWKHUHDFWLRQRIFDUXVHDQGRZQHUVKLSWRFKDQJHVLQIXHO
SULFHVDQGIL[HGFDUFRVWV,QWKLVSDSHUZHGHYHORSDPRGHOWKDWLVEDVHGRQWKHLGHDWKDWOLPLWHG
VXEVWLWXWDELOLW\EHWZHHQGHVLUHGFDUXVHRIGLIIHUHQWKRXVHKROGPHPEHUVLVWKHGULYLQJIRUFH
EHKLQGPXOWLSOHFDURZQHUVKLS:HGHYHORSDPRGHOVWUXFWXUHWKDWLVFRQVLVWHQWZLWKHFRQRPLF
WKHRU\DQGVKRZWKDWLWFDQEHXVHGWRH[WHQGDQH[LVWLQJPRGHOIRURZQHUVKLSDQGXVHRIDVLQJOH
FDUWRPXOWLSOHFDURZQHUVKLSDQGXVH7KHH[WHQGHGPRGHOLVHVWLPDWHGRQ'XWFKGDWD
FRQFHUQLQJKRXVHKROGVZLWKRQHRUWZRFDUV$QDSSOLFDWLRQWRWKHHIIHFWVRIVKLIWLQJWKHEXUGHQ
RIFDUWD[HVIURPIL[HGWRYDULDEOHFRVWVLVSURYLGHG
-DQ5RXZHQGDOLVDOVRDWWKHGHSDUWPHQWRI6RFLDO6FLHQFHVRI:DJHQLQJHQ8QLYHUVLW\+HLVDIILOLDWHGWRWKH
7LQEHUJHQ,QVWLWXWH$PVWHUGDP
-RKQ3RPPHULVDOVRDW&RQQHNW'HOIW
,QWURGXFWLRQ
7KHDXWRPRELOHLVRQHRIWKHPRVWLPSRUWDQWFRQVXPSWLRQJRRGVLQPRGHUQVRFLHWLHV,WPD\HYHQ
EHVDLGWKDWZLGHVSUHDGDXWRPRELOHRZQHUVKLSLVRQHRIWKHGHILQLQJFKDUDFWHULVWLFVRIWKHVH
VRFLHWLHV3DUWLFLSDWLRQLQVRFLDOOLIHLVGLIILFXOWIRUWKRVHZKRGRQRWRZQDFDUDQGLWLVWKHUHIRUH
QRWVXUSULVLQJWKDWFDURZQHUVKLSKDVEHHQVWHDGLO\LQFUHDVLQJRYHUWLPH)RULQVWDQFHLQWKH
1HWKHUODQGVWKHVKDUHRIKRXVHKROGVQRWRZQLQJDFDUKDVEHHQGHFUHDVLQJIRUGHFDGHVDQGPRUH
UHFHQWO\WKDWRIKRXVHKROGVRZQLQJMXVWRQHFDUKDVDOVRVWDUWHGWRGHFUHDVH 7KHLQFUHDVLQJVKDUH
RIPXOWLSOHFDUKRXVHKROGVKDVSRWHQWLDOO\LPSRUWDQWFRQVHTXHQFHVIRUWKHUHDFWLRQWRFKDQJHVLQ
IL[HGDQGYDULDEOHFRVWVRIFDUV:KHQIXHOSULFHVLQFUHDVHPXOWLSOHFDUKRXVHKROGVFDQFKDQJH
WKHGLVWULEXWLRQRIKRXVHKROGFDUNLORPHWHUVWRZDUGVWKHYHKLFOHZLWKWKHORZHVWIXHOFRVWVSHU
NLORPHWHUZKHUHDVVLQJOHFDUKRXVHKROGVFDQRQO\UHDOL]HVXFKDQHIIHFWE\UHSODFLQJWKHFDU
:KHQFDUSULFHVRUIL[HGFRVWVDVVRFLDWHGZLWKFDURZQHUVKLSLQFUHDVHLWLVHDVLHUIRUPXOWLSOH
FDUKRXVHKROGVWRGHFUHDVHWKHVL]HRIWKHLUFDUSDUNWKDQLWLVIRUVLQJOHFDUKRXVHKROGV,WPD\
WKHUHIRUHEHFRQMHFWXUHGWKDWWKHLQFUHDVLQJVKDUHRIPXOWLSOHFDUKRXVHKROGVKDVFRQVHTXHQFHV
IRUWKHUHDFWLRQVWRERWKW\SHVRIFRVWFKDQJHV,QWKLVSDSHUZHGHYHORSDQHFRQRPLFPRGHOWKDW
DOORZVXVWRVWXG\WKLVSKHQRPHQRQ
(FRQRPLFWKHRU\VXJJHVWVWKDWGHFLVLRQVZLWKUHVSHFWWRFDURZQHUVKLSDQGXVHDUHEDVHGRQD
VLQJOHVHWRISUHIHUHQFHV'HFLVLRQVPDGHZLWKUHVSHFWWRWKHQXPEHURIFDUVWREHRZQHGDQGWKH
QXPEHUVRINLORPHWHUVWREHGULYHQZLWKWKHPVKRXOGWKHUHIRUHEHGHULYHGIURPWKHPD[LPL]DWLRQ
RIWKHVDPHXWLOLW\IXQFWLRQXQGHUWKHDSSURSULDWHEXGJHWFRQVWUDLQW$SSOLFDWLRQRIWKLV
VWUDLJKWIRUZDUGUHDVRQLQJLQHPSLULFDOZRUNLVFRPSOLFDWHGE\WKHIDFWWKDWFDUVKDYHGLVFUHWH
RZQHUVKLSDVZHOODVFRQWLQXRXVXVHDVSHFWVWRFRQVXPHUV7KHIL[HGFRVWGHSUHFLDWLRQHWF
FDQEHLQWHUSUHWHGDVDNLQGRIHQWUDQFHIHHWKDWDOORZVDKRXVHKROGWRFRQVXPHDVPDQ\FDU
NLORPHWHUVDVLWOLNHVDWWKHYDULDEOHFRVWVDVVRFLDWHGZLWKWKHFDU+RXVHKROGVGHFLGHWRRZQDFDU
RQO\ZKHQWKHEHQHILWVDVVRFLDWHGZLWKFDUXVHH[FHHGWKHIL[HGFRVW7KLVUHDVRQLQJZDV
HODERUDWHGLQWRDQHPSLULFDOPRGHOIRURZQHUVKLSDQGXVHRIDVLQJOHFDUE\'H-RQJDQG
WKHPRGHOVWUXFWXUHZHGHYHORSLQWKLVSDSHUHQDEOHVXVWRJHQHUDOL]HLWWRPXOWLSOHFDURZQHUVKLS
DQGXVH
7KHDQDO\VLVRIRZQHUVKLSDQGXVHGHFLVLRQVRIPXOWLSOHFDUKRXVHKROGVZLWKLQDWKHRUHWLFDOO\
FRQVLVWHQWIUDPHZRUNLVGHPDQGLQJ7KHXVHRIHOHPHQWDU\GLVFUHWHFKRLFHPRGHOVZKLFKKDYH
EHHQSRSXODULQWKHVWXG\RIFDUW\SHFKRLFHVVLQFHWKHLUGHYHORSPHQWLQWKHVLVUXOHGRXWE\
5R\¶VLGHQWLW\ZKLFKUHODWHVWKHXWLOLW\RIRZQLQJDFDUWRWKHQXPEHURINLORPHWHUVGULYHQE\LW
7KHOLQHDULW\RIWKHXWLOLW\IXQFWLRQVFRQYHQWLRQDOO\XVHGLQWKHVHPRGHOVZRXOGLPSO\DGHPDQG
IRUNLORPHWHUVWKDWLVLQVHQVLWLYHWRSULFHDQGLQFRPH(YHQWKRXJK7UDLQSURSRVHGD
SDUWLDOVROXWLRQWRWKLVSUREOHPE\LQFOXGLQJFRPPXWLQJWULSVLQDQHVWHGPRGHOVWUXFWXUHLQ
JHQHUDODGLVFUHWHFKRLFHPRGHOZLWKDQRQOLQHDUXWLOLW\IXQFWLRQLVUHTXLUHGIRUDWKHRUHWLFDOO\
FRQVLVWHQWPRGHORIRZQHUVKLSDQGXVH0DQQHULQJDQG:LQVWRQSURYLGHGRQHRIWKHILUVW
DQDO\VHVRIDXWRPRELOHGHPDQGWKDWXVHGVXFKDPRGHO
$QRWKHUUHTXLUHPHQWLPSOLHGE\WKHWKHRU\LVWKDWWKHXWLOLW\RIQRWRZQLQJDFDUVKRXOGEHUHODWHG
WRWKDWRZQLQJRQH7KHXWLOLW\RIQRWRZQLQJDFDUIROORZVIURPUHVWULFWLQJWKHQXPEHURI
NLORPHWHUVGULYHQZLWKWKDWFDUWR]HURDQGUHPRYLQJWKHIL[HGFRVWVIURPWKHEXGJHWUHVWULFWLRQ
$OWHUQDWLYHO\RQHFRXOGVHWWKHYLUWXDOSULFHRIFDUXVHHTXDOWRWKHUHVHUYDWLRQYDOXHLQWKH
LQGLUHFWXWLOLW\YDOXH'H-RQJVHHPVWRKDYHEHHQWKHILUVWWRJLYHDULJRURXVWUHDWPHQWRI
)RULQVWDQFHLQWKH1HWKHUODQGVWKHVKDUHRIKRXVHKROGVRZQLQJRQHFDUZDVVWDEOHDWEHWZHHQDQG
EXWKDVVWHDGLO\GHFUHDVHGWRVLQFHWKHQ7KHVKDUHRIKRXVHKROGVRZQLQJWZRRUPRUHFDUVKDVLQFUHDVHGIURP
LQWRRYHU6RXUFH&%66WDWOLQH
WKLVLVVXHLQDQHPSLULFDOPRGHO+LVLQYHVWLJDWLRQLVUHVWULFWHGWRVLQJOHFDUKRXVHKROGVDQG
WKHUHIRUHWRWKHFKRLFHEHWZHHQRZQLQJRUFDU$VIDUDVZHDUHDZDUHWKHUHKDYHEHHQQR
JHQHUDOL]DWLRQVRIWKLVDSSURDFKWRKRXVHKROGVZLWKPXOWLSOHFDUVZLWKWKHH[FHSWLRQRI'H-RQJ
WREHGLVFXVVHGODWHULQWKLVSDSHU
6XFKDJHQHUDOL]DWLRQUHTXLUHVDIUDPHZRUNIRUDQDO\VLVLQZKLFKDKRXVHKROGFDQKDYHDWOHDVW
WZRFDUVZKLOHWKHNLORPHWHUVGULYHQE\WKHVHFDUVDUHLPSHUIHFWVXEVWLWXWHV7KLVLPSOLHVWKDWLQ
JHQHUDOZHFDQQRWGHDOZLWKWKHWRWDOQXPEHURINLORPHWHUVGULYHQE\KRXVHKROGPHPEHUVDVD
VLQJOHFRPPRGLW\7KHEHKDYLRURIKRXVHKROGVZLWKDVLQJOHFDUFDQEHDQDO\]HGE\LPSRVLQJWKH
UHVWULFWLRQWKDWWKHQXPEHURINLORPHWHUVGULYHQE\RQHFDULVHTXDOWRDQGWKDWRIKRXVHKROGV
ZLWKRXWDFDUE\VHWWLQJERWKQXPEHUVRINLORPHWHUVHTXDOWR6XFKDIUDPHZRUNLVQHFHVVDU\IRU
DWKHRU\FRQVLVWHQWDQDO\VLVRIWKHEHKDYLRURIPXOWLSOHFDUKRXVHKROGVEXWLWLVQRWHDV\WR
LPSOHPHQW)RULQVWDQFH0DQQHULQJDQG:LQVWRQGHDOVZLWKKRXVHKROGVRZQLQJRQHRU
WZRFDUV7KHLQGLUHFWXWLOLW\IXQFWLRQDQGWKHFDUXVHHTXDWLRQWKH\HVWLPDWHIRUKRXVHKROGVZLWK
WZRFDUVDUHDQDORJRXVWRWKDWRIVLQJOHFDUKRXVHKROGV7KLVPHDQVWKDWWKH\VSHFLI\WKHLQGLUHFW
XWLOLW\RIRZQLQJWZRFDUVWREHWKHVDPHIXQFWLRQDVWKDWRIRZQLQJWZRFDUVZKLOHDOORZLQJWKH
SDUDPHWHUVWREHGLIIHUHQW(FRQRPLFWKHRU\VXJJHVWVWKDWWKHVSHFLILFDWLRQVRIWKHLQGLUHFWXWLOLW\
IXQFWLRQVUHIHUULQJWRRZQHUVKLSRIRQHDQGWZRFDUVVKRXOGEHGLIIHUHQWZKLOHWKHVDPH
SDUDPHWHUVVKRXOGRFFXULQERWK7KHWKHRU\UHTXLUHVWKDWWKHXWLOLW\RIRZQLQJRQHFDUFDQEH
GHULYHGIURPWKDWUHIHUULQJWRRZQHUVKLSRIWZRFDUVE\UHVWULFWLQJWKHQXPEHURINLORPHWHUV
GULYHQE\RQHRIWKHFDUVWRDQGWDNLQJLQWRDFFRXQWWKDWWKHUHDUHIL[HGFRVWRIRQHFDURQO\
7KHPRGHOWREHGHULYHGLQWKHSUHVHQWSDSHUIROORZVWKLVDSSURDFK
(YHQWKRXJKWKHSUREOHPVWKDWDUHHQFRXQWHUHGZKHQGHYHORSLQJDVWUXFWXUDOPRGHOIRU
RZQHUVKLSRIPXOWLSOHFDUVDUHVXEVWDQWLDOWKLVGLGRIFRXUVHQRWPHDQWKDWPXOWLSOHFDU
RZQHUVKLSDQGUHODWHGLVVXHVKDYHQRWEHHQVWXGLHG5DWKHULWLPSOLHGWKDWVRPHRIWKHULJRURI
HFRQRPLFWKHRU\KDGWREHJLYHQXSLQRUGHUWRDUULYHDWDWUDFWDEOHPRGHOIRUPXODWLRQ0DQ\
LQWHUHVWLQJILQGLQJVZHUHUHSRUWHGLQWKHOLWHUDWXUHRQWKHEDVLVRIVXFKVWXGLHV)RULQVWDQFH
0DQQHULQJDQG:LQVWRQUHSRUWWKDWWKHGHPDQGIRUDXWRPRELOHNLORPHWHUVRIKRXVHKROGV
ZLWKWZRFDUVLVOHVVVHQVLWLYHWRFKDQJHVLQRSHUDWLQJFRVWVWKDQWKDWRIVLQJOHFDUKRXVHKROGV
7KH\DWWULEXWHWKLVTXLWHSODXVLEO\WRWKHSRVVLELOLW\WRVXEVWLWXWHEHWZHHQWKHWZRFDUVHYHQ
WKRXJKWKHLUPRGHOGRHVQRWH[SOLFLWO\LQFRUSRUDWHVXFKEHKDYLRU0DQQHULQJDQG7UDLQ
SURYLGHDILQHYHUEDOGLVFXVVLRQRIDQXPEHURIDVSHFWVWKDWDUHUHOHYDQWLQVWXG\LQJKRXVHKROGV
ZLWKWZRRUPRUHYHKLFOHV)RULQVWDQFHWKH\GHDOZLWKWKHUHODWLRQEHWZHHQWKHQXPEHUDQGW\SH
RIDXWRVRZQHGDQGWKHUHODWLRQEHWZHHQWKHQXPEHUVRIPLOHVWUDYHOHGRQHDFKYHKLFOHLQPXOWL
YHKLFOHKRXVHKROGV7KHUHLVDQHQRUPRXVDPRXQWRIOLWHUDWXUHRQPXOWLSOHFDURZQHUVKLSWKDW
XVHVDUHGXFHGIRUPDSSURDFKRUPRGHOVWKDWDUHFRQGLWLRQHGRQVRPHDVSHFWVVXFKDVWKH
QXPEHURIFDUV:HZLOOQRWDWWHPSWDUHYLHZKHUHEXWLQVWHDGGLVFXVVDIHZRIWRSLFVWKDWDUH
UHOHYDQWIRUWKHSXUSRVHVRIWKHSUHVHQWSDSHU
2XULQWHQWLRQWRFRQFHQWUDWHRQVRPHVSHFLILFDVSHFWVRIPXOWLSOHFDURZQHUVKLSLPSOLHVWKDWZH
SD\OHVVDWWHQWLRQWRVRPHRWKHUDVSHFWVRIWKHGHPDQGIRUFDUV,QSDUWLFXODURQHDVSHFWWKDWKDV
EHHQGHDOWZLWKH[WHQVLYHO\LQWKHOLWHUDWXUHEXWZLOOUHFHLYHOHVVHPSKDVLVLQWKHSUHVHQWSDSHULV
WKHFKRLFHRIWKHFDUW\SH6HHIRULQVWDQFH7UDLQDQG/RKUHUWKDWODWHUDSSHDUHGDVD
FKDSWHULQ7UDLQ IRUDGLVFUHWHFKRLFHPRGHOGHDOLQJZLWKFDUW\SHFKRLFHRIKRXVHKROGV
ZLWKRQHDQGWZRFDUV7KLVPRGHOGRHVQRWGHDOZLWKFDUXVHDQGLVWKHUHIRUHOHVVVXLWDEOHWR
6HHIRRWQRWH
2WKHUUHIHUHQFHVDUHSURYLGHGLQ0DQQHULQJDQG7UDLQ
VWXG\WKHLQWHUDFWLRQEHWZHHQFDUXVHDQGRZQHUVKLS 7KHPRGHORIWKHSUHVHQWSDSHUZLOOIRFXV
RQWKLVLQWHUDFWLRQEXWSD\VRQO\OLPLWHGDWWHQWLRQWRW\SHFKRLFH
7KHUHDUHDQXPEHURIVWXGLHVWKDWFRQVLGHUFDUXVHLQPXOWLSOHFDUKRXVHKROGVZKLOHWDNLQJWKH
QXPEHURIFDUVDVJLYHQ(DUO\H[DPSOHVDUH0DQQHULQJZKRFRQVLGHUHGWZROLQHDU
VLPXOWDQHRXVHTXDWLRQVUHIHUULQJWRWKHXVHRIWKHWZRFDUVLQDKRXVHKROGDQG+HQVKHU
ZKRXVHVDPRUHH[WHQVLYHV\VWHPRIHTXDWLRQVUHIHUULQJDOVRWRIXHOFRVWSHUNLORPHWHUDQGIXHO
HIILFLHQF\0DQQHULQJVWUHVVHVWKHSRWHQWLDOLPSRUWDQFHRIVXEVWLWXWLRQWRZDUGVWKHPRUHHIILFLHQW
YHKLFOHLQUHVSRQVHWRIXHOSULFHFKDQJHVZKLOH+HQVKHU¶VSRVLWLRQLVQXDQFHGE\WKHODUJHU
DPRXQWRIGHWDLOVSUHVHQWLQKLVPRGHO0RUHUHFHQWO\*ROREDQGFRDXWKRUVVHH*RORE.LPDQG
5HQ*ROREDQG0F1DOO\XVHGV\VWHPVRIOLQHDUHTXDWLRQVLQRUGHUWRVWXG\DFWLYLW\
SDUWLFLSDWLRQDQGFDUXVHE\KRXVHKROGPHPEHUV2QHRIWKHVHVWXGLHVREVHUYHVWKDWWKHKLJKHU
RSHUDWLQJFRVWRIRQHYHKLFOHUHVXOWVLQDVKLIWLQXVDJHWRWKHRWKHU*RORE.LPDQG5HQ
S$QLPSRUWDQWVXJJHVWLRQHPHUJLQJIURPWKLVOLWHUDWXUHLVWKDWFDUXVHZLWKLQWKH
KRXVHKROGLVHPEHGGHGZLWKLQWKHSDWWHUQRIKRXVHKROGDFWLYLWLHV2ZQHUVKLSDQGXVHRIWKHILUVW
DQGVHFRQGFDUVKRXOGWKHUHIRUHQRWEHUHJDUGHGDVVHSDUDWHLVVXHVEXWDVLQWHUUHODWHG
,WLVWKHSXUSRVHRIWKHSUHVHQWSDSHUWRGHYHORSDQGHVWLPDWHDPRGHORIFDURZQHUVKLSDQGXVHLQ
PXOWLSOHFDUKRXVHKROGVWKDWLVFRQVLVWHQWZLWKHFRQRPLFWKHRU\$QREYLRXVDGYDQWDJHRIVXFKD
VWUXFWXUDOPRGHOLVWKHFORVHUUHODWLRQZLWKHFRQRPLFWKHRU\DQGWKHRSHUDWLRQDOPRGHO$UHODWHG
DVSHFWLVWKHSRVVLELOLW\WRLQWHUSUHWWKHSDUDPHWHUVDVHOHPHQWVRIWKHKRXVHKROG¶VXWLOLW\IXQFWLRQ
ZKLFKHQKDQFHVWUDQVSDUHQF\DQGHDVHVLQWHUSUHWDWLRQ$VLQJOHVHWRISDUDPHWHUVUHIHUULQJWRWKH
XWLOLW\IXQFWLRQH[SODLQVDOOREVHUYHGEHKDYLRUZLWKUHVSHFWWRRZQHUVKLSDQGXVH7KLVPDNHVWKH
PRGHOSDUVLPRQLRXV)LQDOO\WKHVHIHDWXUHVRIWKHPRGHOPD\LQFUHDVHLWVVXLWDELOLW\IRUSROLF\
VLPXODWLRQV
,QWKHQH[WVHFWLRQZHGHYHORSWKHJHQHUDOPRGHOVWUXFWXUHIRURZQHUVKLSDQGXVHRIFDUVWKDWLV
VXJJHVWHGE\VWDQGDUGPLFURHFRQRPLFWKHRU\:HSURFHHGWKHUHDVIROORZV7KHNLORPHWHUV
GULYHQE\GLIIHUHQWFDUVDSSHDUDVVHSDUDWHFRPPRGLWLHVLQWKHKRXVHKROGXWLOLW\IXQFWLRQ,QRUGHU
WRFRQVXPHWKHVHFRPPRGLWLHVWKHKRXVHKROGPXVWRZQFDUVZKLFKLVFRVWO\7KHVHFRVWVFDQEH
RYHUFRPHE\WKHEHQHILWVGHULYHGIURPFDUXVH$FDUZLOOWKHUHIRUHRQO\EHRZQHGLIWKHEHQHILWV
RIXVLQJLWH[FHHGLWVIL[HGFRVW:HLPSRVHDGGLWLRQDOVWUXFWXUHRQWKHPRGHOE\UHTXLULQJWKDW
WKHYDULDEOHFRVWVRIWKHFDUVRZQHGE\WKHKRXVHKROGHQWHULQGLUHFWXWLOLW\WKURXJKDYDULDEOHWKDW
FDQEHLQWHUSUHWHGDVDFRPSRVLWHSULFHRIFDUPRELOLW\,QWKHVSHFLDOFDVHLQZKLFKWKH
NLORPHWHUVGULYHQE\WKHVHFDUVDUHSHUIHFWVXEVWLWXWHVWKHFRPSRVLWHSULFHLVHTXDOWRWKHORZHVW
RIWKHYDULDEOHFRVWVRIWKHVHSDUDWHFDUVDQGRQO\WKHFKHDSHVWFDUZLOOEHXVHG7KLVPHDQVWKDW
WKHKRXVHKROGZLOOQHYHUXVHPRUHWKDQRQHFDUDQGWKHUHIRUHZLOOQHYHURZQPRUHWKDQRQHFDU
,QWKHPRUHOLNHO\FDVHZKHUHFDUNLORPHWHUVDUHLPSHUIHFWVXEVWLWXWHVWKHUHLVVRPHWKLQJWREH
JDLQHGE\RZQLQJWZRFDUVLQVWHDGRIRQH,PSHUIHFWVXEVWLWXWDELOLW\RFFXUVDVVRRQDVWZR
KRXVHKROGPHPEHUVZRXOGOLNHWRXVHDFDUDWWKHVDPHWLPHIRUGLIIHUHQWWULSV$QREYLRXV
H[DPSOHLVDGXDOHDUQHUKRXVHKROGZLWKWKHWZRZRUNHUVHPSOR\HGDWGLIIHUHQWORFDWLRQVDQG
ERWKZRXOGOLNHWRXVHWKHFDUIRUFRPPXWLQJSXUSRVHV(YHQWKRXJKLQWKLVVLWXDWLRQDVLQJOHFDU
FDQEHXVHGZKHQRQHZRUNHUEULQJVWKHRWKHUWRZRUNLQWKHPRUQLQJDQGSLFNVKLPRUKHUXSLQ
5RXZHQGDODQGGH9ULHVZKRVWXG\WKHFKRLFHRIIXHOW\SHZLWKDGLVFUHWHFRQWLQXRXVPRGHOILQGD
VLJQLILFDQWHIIHFWRIWKHYDULDEOHFRVWRQWKHGHPDQGIRUNLORPHWHUV
:KHQWKHFRVWVRIWKHWZRFDUVDUHHTXDOWKHGLVWULEXWLRQRIWKHFDUNLORPHWHUVRYHUWKHFDUVLVDPDWWHURI
LQGLIIHUHQFH7KHKRXVHKROGPD\WKHUHIRUHDVZHOODOORFDWHDOOWKHVHNLORPHWHUVWRRQHFDUDQGVDYHWKHIL[HGFRVWRI
WKHRWKHU
WKHHYHQLQJLWLVXVXDOO\PXFKPRUHFRQYHQLHQWWRKDYHWZRFDUVDYDLODEOH7KHJDLQLQXWLOLW\
DVVRFLDWHGZLWKRZQHUVKLSRIWZRFDUVDSSHDUVLQWKHPRGHODVDORZHUSULFHIRUWKHFRPSRVLWH
JRRG7KLVJDLQLVWUDGHGRIIDJDLQVWWKHKLJKHUIL[HGFRVWVDVVRFLDWHGZLWKRZQLQJWZRFDUV
7KHUHPDLQGHURIWKHSDSHULVRUJDQL]HGDVIROORZV,Q6HFWLRQZHGLVFXVVWKHGDWDVHWZHXVHLQ
WKHHPSLULFDOZRUNDQGSHUIRUPVRPHH[SORUDWRU\DQDO\VHV6HFWLRQGLVFXVVHVVRPHHVWLPDWLRQ
LVVXHVDQGUHSRUWVHVWLPDWLRQUHVXOWV6HFWLRQSURYLGHVIXUWKHUGLVFXVVLRQRIWKHVHUHVXOWVDQGD
VLPXODWLRQRIWKHHIIHFWVRIVKLIWLQJWKHEXUGHQRIFDUWD[HVIURPIL[HGWRYDULDEOHFDUFRVWV
6HFWLRQFRQFOXGHV
$QHFRQRPLFPRGHOIRUPXOWLSOHFDURZQHUVKLS
,QWURGXFWLRQ
,QWKLVVHFWLRQZHGHYHORSRXUPRGHORIDKRXVHKROGWKDWKDVWRGHFLGHRQWKHQXPEHURIFDUVWR
EHRZQHGDQGWKHLUXVH:HVWDUWLQVXEVHFWLRQZLWKDJHQHUDOPRGHOLQZKLFKWKHQXPEHURI
FDUVLVIL[HG7KLVLVEDVLFDOO\WKHVWDQGDUGPRGHORIDXWLOLW\PD[LPL]LQJFRQVXPHUDVGHVFULEHG
IRULQVWDQFHLQ'HDWRQDQG0XHOOEDXHU7KHRQO\VSHFLILFIHDWXUHWKDWKDVEHHQDGGHGLV
WKDWWKHFRQVXPHUKDVWRSD\DIL[HGFRVWLQRUGHUWREHDEOHWRFRQVXPHFDUNLORPHWHUV
7KHIL[HGQXPEHURIFDUVVKRXOGEHLQWHUSUHWHGDVWKHPD[LPXPQXPEHUWKDWFDQEHRZQHGE\WKH
KRXVHKROG7KHFKRLFHRIWKLVQXPEHULVQRWFUXFLDOIRURXUUHVXOWVDVORQJDVLWLVVHWDWD
VXIILFLHQWO\KLJKYDOXHDVZLOOEHH[SODLQHG
7KLVFKRLFHRIWKHDFWXDOQXPEHURIFDUVLVLQWURGXFHGLQVXEVHFWLRQE\DGGLQJDFRQVWUDLQWRQ
WKHQXPEHURIFDUVWRWKHEDVLFPRGHO7KLVFRQVWUDLQWGHWHUPLQHVWKHDFWXDOQXPEHURIFDUV
RZQHGE\WKHKRXVHKROGDQGVKRXOGEHLQWHUSUHWHGDVVHOILPSRVHG7KHIDFWWKDWRQHRUPRUH
SRWHQWLDOO\DYDLODEOHFDUVFDQQRWEHXVHGZLOOGHFUHDVHRUDWOHDVWQRWLQFUHDVHXWLOLW\EXWVLQFH
QRIL[HGFRVWVKDYHWREHSDLGIRUWKHVHFDUVWKHQHWHIIHFWRIWKHUHVWULFWLRQRQXWLOLW\PD\ZHOOEH
SRVLWLYH7KHRSWLPDOQXPEHURIFDUVLVWKDWIRUZKLFKXWLOLW\LVPD[LPDO
,QVXEVHFWLRQZHLQWURGXFHWKHQRWLRQRILQGLUHFWVHSDUDELOLW\,WPHDQVWKDWWKHYDULDEOHFRVWV
RIWKHYDULRXVFDUVHQWHUWKHLQGLUHFWXWLOLW\IXQFWLRQRQO\YLDDIXQFWLRQWKDWZLOOEHLQWHUSUHWHGDV
DFRPSRVLWHSULFHRIFDUXVH5DWLRQLQJWKHQXPEHURIFDUVRZQHGE\WKHKRXVHKROGLQFUHDVHVWKH
FRPSRVLWHSULFHRIFDUPRELOLW\DQGWKLVLQFUHDVHLQGLFDWHVWKHFRVWRIOLPLWLQJWKHQXPEHURI
FDUV7KHFRPSRVLWHSULFHIXQFWLRQGHWHUPLQHVWKHGLVWULEXWLRQRIWKHWRWDOQXPEHURINLORPHWHUV
GULYHQE\WKHKRXVHKROGRYHUWKHFDUVLWRZQV7KHSRVVLELOLWLHVWRVXEVWLWXWHEHWZHHQXVHRIWKH
YDULRXVFDUVFDXVHGE\GLIIHUHQFHVLQYDULDEOHFRVWVDUHWKHUHIRUHDOVRGHWHUPLQHGE\WKLVIXQFWLRQ
6XEVHFWLRQGLVFXVVHVWKHLQWURGXFWLRQRIGLIIHUHQFHVLQFDUTXDOLW\LQWRWKHPRGHO$OWKRXJK
TXDOLW\FKRLFHLVQRWDFHQWUDOWRSLFRIWKHSUHVHQWSDSHUZHKDYHWRWDNHLWLQWRDFFRXQWLQRUGHU
GHDOZLWKWKHVXEVWLWXWLRQEHWZHHQWKHXVHRIFDUVZLWKLQWKHKRXVHKROGWKDWRFFXUVLQUHDFWLRQWR
GLIIHUHQFHVLQYDULDEOHFRVWV6XFKGLIIHUHQFHVUHIOHFWGLIIHUHQFHVLQRWKHUFDUFKDUDFWHULVWLFV
ZKLFKZHVXPPDUL]HDVµTXDOLW\¶:HRXWOLQHDPRGHOLQZKLFKKLJKHUTXDOLW\FDQEHREWDLQHGDW
WKHH[SHQVHRIKLJKHUIL[HGDQGYDULDEOHFRVWV
)LQDOO\ZHSURSRVHDVSHFLILFDWLRQRIWKHIXQFWLRQGHVFULELQJWKHFRPSRVLWHSULFHRIFDUXVHLQ
VXEVHFWLRQDQGGLVFXVVLWVLPSOLFDWLRQVLQVXEVHFWLRQ,WLVXVHGWKHUHWRJHQHUDOL]HGH
-RQJ¶VLQGLUHFWXWLOLW\PRGHOGHVFULELQJWKHFKRLFHEHWZHHQQRFDUDQGDVLQJOHFDUWRFDVHV
LQZKLFKDQDUELWUDU\QXPEHURIFDUVFDQEHRZQHG7KLVVSHFLILFDWLRQLVXVHGLQWKHHPSLULFDO
VHFWLRQ
$EDVLFPRGHO
,QRXUEDVLFPRGHODOOFDUVDUHLGHQWLFDOWKH\KDYHWKHVDPHIL[HGDQGYDULDEOHFRVWVDQGRWKHU
FKDUDFWHULVWLFV7KHPRGHOFRQFHUQVDKRXVHKROGWKDWGHULYHVXWLOLW\IURPWKHNLORPHWHUVGULYHQE\
1 VXFKLGHQWLFDOFDUVDQGDFRPSRVLWHFRQVXPSWLRQJRRG1 LVWKHSUHGHWHUPLQHGPD[LPXP
QXPEHURIFDUVWKDWFDQEHRZQHGE\WKHKRXVHKROG1 FDQEHDUELWUDULO\ODUJHEXWLQSUDFWLFH
WKHUHDUHIHZKRXVHKROGVWKDWRZQPRUHWKDQIRXUFDUV7KHDPRXQWFRQVXPHGRIWKHFRPSRVLWH
JRRGLVGHQRWHGDVTDQGWKHQXPEHUVRIFDUNLORPHWHUVGULYHQDV[ZLWK[ DQ1GLPHQVLRQDO
YHFWRU7KHXWLOLW\IXQFWLRQLV
X X T [ 8WLOLW\LVPD[LPL]HGVXEMHFWWRDEXGJHWFRQVWUDLQW
S[ T \ N1
\
ZKHUHS GHQRWHVWKH1GLPHQVLRQDOYHFWRURIYDULDEOHFRVWVRIWKHFDUV7KHSULFHRIWKH
FRPSRVLWHJRRGLVXVHGDVWKHQXPpUDLUH7KHULJKWKDQGVLGHRIWKLVHTXDWLRQJLYHVWKH
KRXVHKROG¶VGLVSRVDEOHLQFRPH \ ZKLFKLVGHILQHGDVWKH³GLIIHUHQFHEHWZHHQKRXVHKROG
LQFRPH\DQGWKHIL[HGFRVWVRIWKHFDUVRZQHGE\WKHKRXVHKROG´7KHVHFRVWVDUHLQGLFDWHGDV
N1ZLWKN WKHIL[HGFRVWVSHUFDU
0D[LPL]DWLRQRIXWLOLW\VXEMHFWWRWKLVEXGJHWFRQVWUDLQWOHDGVWRGHPDQGHTXDWLRQVIRUWKHFDU
NLORPHWHUVDQGWKHFRPSRVLWHJRRG7KHXWLOLW\H[SHULHQFHGE\WKHKRXVHKROGLVJLYHQE\WKH
LQGLUHFWXWLOLW\IXQFWLRQY
Y Y \ S 7KHPRGHOGHYHORSHGWKXVIDUWDNHVWKHQXPEHURIFDUVDVJLYHQDQGWKHUHIRUHFDQQRWEHXVHGWR
VWXG\WKHFKRLFHRIWKHQXPEHURIFDUV:HFRQVLGHUWKDWH[WHQVLRQLQWKHQH[WVXEVHFWLRQEXW
QRWHKHUHWKDWWKHPRGHODVGHYHORSHGWKXVIDUFDQEHXVHGWRVWXG\WKHXVHRIGLIIHUHQWFDUVLQWKH
KRXVHKROGDWDYHU\JHQHUDOOHYHO(YHQWKRXJKZHKDYHDVVXPHGWKDWDOOFDUVDUHLGHQWLFDOWKH
XVHRIWKHYDULRXVFDUVRZQHGE\DKRXVHKROGPD\ZHOOEHGLIIHUHQWVLQFHZHKDYHQRWDVVXPHG
WKDWWKHXWLOLW\IXQFWLRQX LVV\PPHWULFLQWKHQXPEHUVRINLORPHWHUVGULYHQE\WKHYDULRXVFDUV
7KHPDUJLQDOXWLOLW\IXQFWLRQVRIWKHNLORPHWHUVGULYHQE\GLIIHUHQWFDUVPD\WKHUHIRUHGLIIHUDQG
VRPD\WKHRSWLPXPQXPEHUVRINLORPHWHUV)RULQVWDQFHRQHFDUPD\EHXVHGIRUFRPPXWLQJ
DQGDQRWKHURQHIRUVRFLDOSXUSRVHVVKRSSLQJDQGKROLGD\V7KLVJHQHUDOLW\LVDFRQVHTXHQFHRI
RXUWUHDWPHQWRIWKHNLORPHWHUVGULYHQE\GLIIHUHQWFDUVDVVHSDUDWHFRPPRGLWLHV7KXVWKH
NLORPHWHUVGULYHQE\YDULRXVFDUVPD\EHVXEVWLWXWHVDVZHOODVFRPSOHPHQWVWKHNLORPHWHUV
GULYHQE\RQHFDUPD\EHDQLQIHULRUJRRGZKHUHDVWKRVHGULYHQE\DQRWKHUFDUDUHQRUPDOHW
FHWHUD
,WVHHPVUHDVRQDEOHWRH[SHFWWKDWDKRXVHKROGZLOOQRWXVHDOOLWVFDUVLQWHQVLYHO\LIWKHLUQXPEHU
LVODUJH,WPD\HYHQEHWKHFDVHWKDWVRPHFDUVDUHQRWXVHGDWDOO7KHSRVVLELOLW\RI]HUR
FRQVXPSWLRQLVDOVRSUHVHQWLQFRQYHQWLRQDOPRGHOVRIFRQVXPHUEHKDYLRUDQGLVLPSRUWDQWIRU
GHDOLQJZLWKIRULQVWDQFHQRQVPRNHUV+RZHYHULQWKHSUHVHQWFRQWH[WWKHUHLVDQDGGLWLRQDO
HOHPHQWLQYROYHGVLQFHDEVWDLQLQJIURPWKHXVHRIDFDURSHQVWKHSRVVLELOLW\WRGHFUHDVHWKHIL[HG
FRVWVDVVRFLDWHGZLWKFDURZQHUVKLSE\PDNLQJWKHDFWXDOQXPEHURIFDUVVPDOOHUWKDQ17KH
ORZHUIL[HGFRVWLQFUHDVHVWKHDPRXQWRIPRQH\WKDWFDQEHVSHQWRQRWKHUJRRGVDQGWKLVHQDEOHV
WKHKRXVHKROGWRUHDFKDKLJKHUOHYHORIXWLOLW\,WPD\WKHUHIRUHEHLQWKHLQWHUHVWRIWKHKRXVHKROG
WRUHVWULFWWKHDFWXDOQXPEHURIFDUVWRDYDOXHORZHUWKDQ1
%HFDXVHRIWKHORZHUIL[HGFRVWDVVRFLDWHGZLWKOLPLWHGFDURZQHUVKLSWKHKRXVHKROGZLOOILQGLW
EHQHILFLDOQRWWRRZQWKHPD[LPXPQXPEHURIFDUVLIWKHSUHGHWHUPLQHGYDOXHRI1 LVVHWODUJH
HQRXJK7KHRSWLPDOQXPEHURIFDUVZLOOWKHQDOZD\VEHVPDOOHUWKDQ1 ,IWKHPD[LPXPQXPEHU
RIFDUVZRXOGEHVHWDWDKLJKHUOHYHOHJ1WKHRSWLPDOQXPEHURIFDUVZLOOQRWFKDQJHDQG
IRUWKLVUHDVRQWKHFKRLFHRI1 LVDUELWUDU\DVORQJDVLWLVDVXIILFLHQWO\ODUJHQXPEHU
2SWLPDOFKRLFHRIWKHQXPEHURIFDUV
7KHFKRLFHRIWKHRSWLPDOQXPEHURIFDUVZLOOQRZEHLQWURGXFHGLQWRWKHPRGHOE\DGGLQJD
UHVWULFWLRQRQFDUXVH7KLVUHVWULFWLRQVD\VWKDWWKHQXPEHURINLORPHWHUVRIVRPHFDUVYL]WKRVH
QRWRZQHGE\WKHKRXVHKROGKDVWREHHTXDOWR7KLVPHDQVWKDWIRUWKHVHFDUVWKHGHPDQGIRU
FDUNLORPHWHUVLVUDWLRQHG,IDKRXVHKROGRZQVQFDUVZLWK d Q 1 WKHQ1Q HOHPHQWVRI[
ZLOOEHHTXDOWR
1RZFRQVLGHUDKRXVHKROGZKRVHFDURZQHUVKLSLVGHVFULEHGE\DQ1GLPHQVLRQDOYHFWRUG ZLWK
RQO\¶VDQG¶VDVHOHPHQWVZLWKWKH¶VUHIHUULQJWRWKHRZQHGFDUVDQGWKH¶VWRWKHRWKHUV
7KHHIIHFWRIUDWLRQLQJRQWKHLQGLUHFWXWLOLW\RIWKHKRXVHKROGFDQEHGHVFULEHGE\YLUWXDOSULFHV
IRUWKHNLORPHWHUVRIWKHFDUVQRWRZQHGE\WKHKRXVHKROG7KHVHYLUWXDOSULFHVDUHWKHYDOXHVRI
WKHYDULDEOHFRVWVWKDWZRXOGLQGXFHWKHKRXVHKROGWRGULYHQRNLORPHWHUVZLWKWKHVHFDUVZHUH
WKH\DYDLODEOH 7KHYLUWXDOSULFHVDUHDIXQFWLRQRIWKHRWKHUSULFHVDQGRIWKHKRXVHKROG¶V
GLVSRVDEOHLQFRPHFRPSXWHGZLWKRXWWKHIL[HGFRVWVRIWKHFDUVWKDWDUHQRWRZQHG7KH\DUH
DOZD\VDWOHDVWDVKLJKDVWKHDFWXDOSULFHVRIWKHFRPPRGLW\FRQFHUQHG
7KHUHOHYDQWSULFHVIRUFDUXVHRIWKLVKRXVHKROGDUHWKHQJLYHQE\DYHFWRUS¶GZLWKYDULDEOH
FRVWVS RQWKHSRVLWLRQVRIWKHRZQHGFDUVDQGYLUWXDOSULFHVLQWKHRWKHUSRVLWLRQV7KHYLUWXDO
SULFHVZLOOLQJHQHUDOEHGLIIHUHQWDQGGHSHQGRQWKHQHHGIRUXVLQJWKHVHFDUV'LVSRVDEOH
LQFRPHLVQRZGHILQHGDV \ \ NQ DQGLQGLUHFWXWLOLW\FDQEHZULWWHQDV
Y Y \ NQ S G ,IWKHKRXVHKROGZRXOGXVHDOO1 FDUVLIWKH\DUHRZQHGLHWKHGHPDQGIRUNLORPHWHUVZRXOGEH
VWULFWO\SRVLWLYHIRUDOOFDUVWKHQWKHYLUWXDOSULFHVRIWKHFDUVQRWRZQHGDUHKLJKHUWKDQWKHLU
YDULDEOHFRVWV7KHVHKLJKHUYDOXHVUHIOHFWWKHFRVWRIWKHUDWLRQLQJ7KHEHQHILWDVVRFLDWHGZLWK
WKHUDWLRQLQJLVWKDWGLVSRVDEOHLQFRPHLVKLJKHUEHFDXVHRIWKHORZHUIL[HGFDUFRVWV7KHQHW
HIIHFWRQXWLOLW\RIUHVWULFWLQJWKHQXPEHURIFDUVWKXVGHSHQGVRQWKHUHODWLYHPDJQLWXGHRIERWK
HIIHFWV
,IWKHKRXVHKROGZRXOGQRWXVHDOO1 FDUVUHVWULFWLQJWKHQXPEHURINLORPHWHUVRIWKHVHFDUVWR
LPSRVHVQRUHDOUHVWULFWLRQRQKRXVHKROGEHKDYLRU7KHYLUWXDOSULFHLVLQWKLVFDVHHTXDOWRWKH
DFWXDOSULFH7KLVPHDQVWKDWWKHUHLVQRFRVWLQWHUPVRIXWLOLW\LQYROYHGLQQRWRZQLQJVXFKD
FDU,WLVWKHUHIRUHDOZD\VEHQHILFLDOQRWWRRZQVXFKDFDUEHFDXVHRIWKHIL[HGFRVWVLQYROYHG
$ILQDOLVVXHWREHGLVFXVVHGLQWKHSUHVHQWVXEVHFWLRQFRQFHUQVWKHFKRLFHRIWKHFDUVWREH
DEDQGRQHG,QWKHPRGHOGHYHORSHGDERYHZHFDQGLVWLQJXLVKEHWZHHQKRXVHKROGVWKDWRZQWKH
VDPHQXPEHURIFDUVEXWDUHORFDWHGDWGLIIHUHQWSRVLWLRQVRIWKHYHFWRUG+RZHYHULQSUDFWLFH
ZHFDQQRWGLVWLQJXLVKEHWZHHQKRXVHKROGVZLWKGLIIHUHQWYHFWRUVG EXWWKHVDPHQXPEHURIFDUV
)RULQVWDQFHLIDKRXVHKROGRZQVRQHFDULWLVLPSRVVLEOHWRNQRZZKHWKHUWKLVFDULVLQWKHILUVW
VHFRQGRU1WKSRVLWLRQRIG DQGWKHLUXWLOLWLHVPD\GLIIHU,WLVWKHUHIRUHXVHIXOWRUHIRUPXODWH
WKHPRGHOLQVXFKDZD\WKDWZHFDQUHIHUWRKRXVHKROGVRZQLQJQ FDUVZLWKRXWKDYLQJWRVSHFLI\
WKHSRVLWLRQVRIWKHVHFDUVLQWKHYHFWRUG
,QRUGHUWRGRWKLVZHLQWURGXFHVRPHDGGLWLRQDOQRWDWLRQ/HW' EHWKHVHWRIDOO1GLPHQVLRQDO
YHFWRUVZLWKRQO\¶VDQG¶VDVHOHPHQWVDQG'QWKHVXEVHWRIDOOYHFWRUV G  ' ZLWKWKH
QXPEHURIRQHVHTXDOWRQ WKDWLV G G Q 7KHXWLOLW\YQ RIRZQLQJQ FDUVLVGHILQHGDVµWKH
6HH1HDU\DQG5REHUWV
PD[LPXPXWLOLW\WKDWFDQEHUHDFKHGE\DKRXVHKROGZKRVHFDURZQHUVKLSLVGHVFULEHGE\DQ
HOHPHQWRI'Q¶7KDWLV
Y Q PD[ ^Y \ NQ S G `
Q 1 G ' Q 7KHXWLOLWLHVYQ WDNHLQWRDFFRXQWWKHIOH[LELOLW\WKDWDKRXVHKROGKDVLQDVVLJQLQJWKHDYDLODEOH
FDUVWRWKHWDVNVRUSHUVRQVPRVWLQQHHGRIWKHP
7KHPRGHOFDQQRZEHXVHGWRVWXG\WKHFKRLFHRIWKHQXPEHURIFDUV7KHRSWLPDOQXPEHUQ LV
WKDWIRUZKLFKXWLOLW\LVKLJKHVW
Q DUJ PD[^YL L 1 `
7KHPRGHOWKDWKDVEHHQGHYHORSHGKHUHLVFRPSOHWHO\JHQHUDOLQWKDWLWGRHVQRWXVHRWKHU
DVVXPSWLRQVWKDQWKRVHFRQYHQWLRQDOO\PDGHLQHFRQRPLFDQDO\VLVLQRUGHUWRGHULYHGHPDQG
IXQFWLRQVIRUFRPPRGLWLHVXQGHUFRQGLWLRQVRIUDWLRQLQJ7KHKRXVHKROGLVDVVXPHGWRUHDFWLQDQ
RSWLPDOZD\WRUHVWULFWLRQVRQWKHQXPEHURIFDUV6XFKDUHDFWLRQPD\LQYROYHEDUJDLQLQJ
EHWZHHQKRXVHKROGPHPEHUVDQGLWLVDVVXPHGWKDWWKHRXWFRPHRIWKLVSURFHVVFDQEHGHVFULEHG
E\DKRXVHKROGXWLOLW\IXQFWLRQSRVVHVVLQJDOOFRQYHQWLRQDOSURSHUWLHV
,QGLUHFWVHSDUDELOLW\
(YHQWKRXJKWKHJHQHUDOLW\RIWKHPRGHOGHYHORSHGDERYHLVDFOHDUDGYDQWDJHHPSLULFDOZRUN
UHTXLUHVIXUWKHUVSHFLILFDWLRQ:HZLOOQRZLQWURGXFHVRPHDGGLWLRQDOVWUXFWXUHRQWKHLQGLUHFW
XWLOLW\IXQFWLRQWKDWJLYHVVRPHJXLGDQFHIRUVSHFLI\LQJVXFKDQHPSLULFDOPRGHO:HDVVXPHWKDW
WKHLQGLUHFWXWLOLW\IXQFWLRQLVVHSDUDEOHLQWKHFRVWVRIFDUNLORPHWHUV7KLVPHDQVWKDWYDULDEOH
FDUFRVWVHQWHUWKHLQGLUHFWXWLOLW\IXQFWLRQY YLDDIXQFWLRQ3,QRWKHUZRUGVLWVD\VWKDWZHFDQ
UHSODFHWKHYHFWRURIYDULDEOHFRVWVS LQE\DVFDODU3ZKRVHYDOXHLVGHWHUPLQHGE\WKHVH
YDULDEOHFRVWV
Y Y
\ 3
DQG
3 3 S G \ ZLWK \ \ QN 7KHIXQFWLRQ 3ZKLFKPD\GHSHQGRQGLVSRVDEOHLQFRPHZLOOEHLQWHUSUHWHGDV
FRPSRVLWHSULFHIRUFDUNLORPHWHUVDQGLWPXVWEHLQFUHDVLQJZLWKWKHYDULDEOHFRVWVRIDOOFDUV
$QDGYDQWDJHRIWKLVIXUWKHUVSHFLILFDWLRQRIWKHLQGLUHFWXWLOLW\IXQFWLRQLVWKDWLWDOORZVXVWRJLYH
DQLQWXLWLYHDFFRXQWRIWKHFRVWVDVVRFLDWHGZLWKUHVWULFWHGFDURZQHUVKLS:HKDYHMXVWVHHQWKDW
VRPHRUDOORIWKHYDULDEOHFRVWVDUHYLUWXDOSULFHVZKHQWKHDFWXDOQXPEHURIFDUVLVORZHUWKDQ
WKHPD[LPXPQXPEHU7KLVPHDQVWKDWWKHDFWXDOSULFHRIFDUPRELOLW\LVKLJKHUWKDQLWZRXOGEH
LIWKHPD[LPXPQXPEHURIFDUVZHUHRZQHG7KLVLVEHFDXVHKDYLQJOHVVWKDQWKHPD[LPXP
SRVVLEOHQXPEHURIFDUVDWWKHLUGLVSRVDOUHVWULFWVWKHKRXVHKROGPHPEHUVLQWKHLUDFWLYLWLHVIRU
LQVWDQFHE\HOLPLQDWLQJWKHSRVVLELOLW\WRFDUU\RXWVHTXHQFHVRIDFWLYLWLHVWKDWZRXOGEHSRVVLEOH
LIDQDGGLWLRQDOFDUZHUHDYDLODEOH7KHGLIIHUHQFHEHWZHHQWKHFRQVWUDLQHGDQGXQFRQVWUDLQHG
YDOXHVRI3 WKXVJLYHVDXVHIXOVXPPDU\PHDVXUHRIWKHEHQHILWVRIRZQLQJDODUJHUQXPEHURI
FDUV$QRWKHUFRQVHTXHQFHRIWKLVVSHFLILFDWLRQLVWKDWLWDOORZVXVWRJHQHUDOL]HGH-RQJ¶V
PRGHOWRVLWXDWLRQVZLWKWZRRUPRUHFDUVDVZLOOEHVKRZQODWHULQWKLVVHFWLRQ
7KHQXPEHURINLORPHWHUVGULYHQE\FDUL RZQHGE\WKHKRXVHKROGFDQEHGHULYHGIURPE\
PHDQVRI5R\¶VLGHQWLW\DV
wY
w3
w3 wSL
[L wY
wY
w3
w\ w3 w\ ZKHUH3 VKRXOGEHHYDOXDWHGDWSU DQG]U,WLVXVHIXOWRFRQVLGHUFDUXVHE\DKRXVHKROGDV
GHVFULEHGE\WKHWRWDOQXPEHURINLORPHWHUVGULYHQDQGWKHVKDUHRIHDFKRZQHGFDULQWKLVWRWDO
7KHWRWDOQXPEHURIFDUNLORPHWHUV; LVHTXDOWR
wY
w3
¦
1
w3 L2 wS L
; ¦ [L wY
wY
w3
L w\ w3 w\ ZKHUH2 GHQRWHVWKHVHWRIFDUVRZQHGE\WKHKRXVHKROG7KHVKDUHVL [L;RIWKHLWKFDULQWKH
WRWDOQXPEHURINLORPHWHUVGULYHQE\WKHKRXVHKROGFDQQRZEHGHWHUPLQHGDV
w3
wS L
L2 VL
w3
¦
L2 wS M
7KLVHTXDWLRQVKRZVWKDWWKHGLVWULEXWLRQRIWRWDOFDUNLORPHWHUVRYHUWKHLQGLYLGXDOFDUVLV
FRPSOHWHO\GHWHUPLQHGE\WKHIXQFWLRQ3$FFRUGLQJWRWKHHPSLULFDOVWXGLHVGLVFXVVHGLQWKH
LQWURGXFWLRQWKHVHVKDUHVDUHVHQVLWLYHWRWKHYDOXHVRIWKHYDULDEOHFRVWVRIWKHFDUVRZQHGE\WKH
KRXVHKROG+LJKHUIXHOSULFHVVKRXOGLQGXFHVXEVWLWXWLRQWRZDUGVWKHOHDVWH[SHQVLYHFDUDQGD
ODUJHUJDSEHWZHHQWKHYDULDEOHFRVWVVKRXOGKDYHDVLPLODUHIIHFWRQWKHXVHRIDOOFDUV7KH
UHDVRQIRUWKLVSKHQRPHQRQPXVWWKHUHIRUHEHIRXQGLQWKHVSHFLILFDWLRQRI3,WPD\EHREVHUYHG
KRZHYHUWKDWWKHPRGHODVGHYHORSHGWKXVIDUH[FOXGHVWKLVSKHQRPHQRQVLQFHLWDVVXPHVWKDWDOO
FDUVDUHLGHQWLFDO:HZLOOWKHUHIRUHQH[WFRQVLGHUWKHH[WHQVLRQRIWKHPRGHOWRFDVHVLQZKLFK
FDUVFDQGLIIHULQIL[HGDQGYDULDEOHFRVWV
&DUTXDOLW\FKRLFH
,QUHDOLW\WKHUHDUHPDQ\EUDQGVDQGPDNHVRIDXWRPRELOHVDQGHYHQWKRXJKWKLVSDSHUZLOOQRW
FRQFHQWUDWHRQTXDOLW\FKRLFHWKHREVHUYDWLRQPDGHDWWKHHQGRIWKHVXEVHFWLRQDERYHFOHDUO\
LQGLFDWHVWKHGHVLUDELOLW\RIWDNLQJWKLVKHWHURJHQHLW\LQWRDFFRXQWLQRXUPRGHO,QRUGHUWRGRVR
ZHDVVXPHWKDWFDUVDUHGLVWLQJXLVKHGE\TXDOLW\]4XDOLW\VKRXOGEHLQWHUSUHWHGDVDFRPSRVLWH
VFDODUPHDVXUHRIWKRVHFDUFKDUDFWHULVWLFVWRZKLFKFRQVXPHUVDWWDFKDSRVLWLYHYDOXHHJ
DFFHOHUDWLRQSRZHUVSDFHSUHVHQFHRIDLUEDJVDLUFRQGLWLRQLQJ9DULDEOHDQGIL[HGFRVWVDUH
DVVXPHGWREHLQFUHDVLQJIXQFWLRQVRITXDOLW\$OWKRXJKWKHQXPEHURIDYDLODEOHFDUEUDQGVDQG
PDNHVLVILQLWHLQUHDOLW\WKHLUQXPEHUVVHHPODUJHHQRXJKWRMXVWLI\ZRUNLQJZLWKDFRQWLQXRXV
DSSUR[LPDWLRQ
7KHWUHDWPHQWRITXDOLW\DVDVFDODUYDULDEOHLVOHVVUHVWULFWLYHWKDQLWPD\DSSHDUWREHDWILUVW
VLJKW,QPDQ\PRGHOVRIFDUW\SHFKRLFHWKHXWLOLW\DVVRFLDWHGZLWKDSDUWLFXODUEUDQGRUPDNHLV
VSHFLILHGDVDOLQHDUIXQFWLRQRIFDUTXDOLW\FKDUDFWHULVWLFVDQGFRVWV7KHSDUWRIWKLVIXQFWLRQ
UHIHUULQJWRWKHTXDOLW\FKDUDFWHULVWLFVFDQWKHQEHLQWHUSUHWHGDVDVFDODULQGLFDWRURITXDOLW\DQG
LIWKHQXPEHURIFDUW\SHVLVODUJHWUHDWLQJLWDVDFRQWLQXRXVYDULDEOHZLOOQRWGRPXFKKDUP
&RQVLGHUILUVWDKRXVHKROGZLWK1 FDUV,WVXWLOLW\IXQFWLRQLVJLYHQE\ZKHQDOOFDUVKDYHWKH
VDPHTXDOLW\:HQRZLQWURGXFHWKHTXDOLW\RIWKH1 FDUVDVVHSDUDWHYDULDEOHVDQGWDNHDFFRXQW
RIWKHGHSHQGHQFHRIFRVWVRQTXDOLW\)RUJLYHQTXDOLWLHVRIWKHFDUVWKHLQGLUHFWXWLOLW\IXQFWLRQ
WKHQEHFRPHV
Y
Y \ ¦ N ] S ] S ] 1 ] ] 1 1
L 0D[LPL]DWLRQZLWKUHVSHFWWRWKHTXDOLW\RIWKHFDUVJLYHVILUVWRUGHUFRQGLWLRQV
GN ] L wY
wY wS ] L wY
L 1 w \ ¦L N ] L G] L
wS ] L w] L
w] L
:HDVVXPHWKDWWKHVHILUVWRUGHUFRQGLWLRQVKDYHDXQLTXHVROXWLRQDQGWKDWWKHVHFRQGRUGHU
FRQGLWLRQVDUHIXOILOOHG7KHRSWLPDOYDOXHVIRUYDULDEOHFRVWVIL[HGFRVWVDQGTXDOLW\ZLOOEH
GHQRWHGDV SLR N LR DQG ] LR UHVSHFWLYHO\IRUL Q,QJHQHUDOWKH\DUHIXQFWLRQVRIDOO
SDUDPHWHUVRIWKHPRGHOLPSO\LQJIRULQVWDQFHWKDWWKHLUYDOXHVZLOOFKDQJHLIWKHYDULDEOHDQG
IL[HGFRVWVRIFDUEUDQGVDQGPDNHVFKDQJH,QGLUHFWXWLOLW\FDQEHZULWWHQLQWHUPVRIWKHRSWLPDO
YDOXHVRITXDOLW\DQGIL[HGDQGYDULDEOHFRVWVDV
Y
Y \ ¦ N LR SR S 1R ]R ] 1R Y
Y \ ¦ G L N LU SU S 1U ]U ] 1U 1
L 1RZFRQVLGHUWKHFDVHLQZKLFKWKHKRXVHKROGRZQVOHVVWKDQ1 FDUV:HDVVXPHWKDW
wX w] L ZKHQHYHU [L 9LUWXDOSULFHVFDQVWLOOEHGHULYHGIRUWKHQRQRZQHGFDUVDQG
VLQFHYDULDEOHFRVWVDUHDQLQFUHDVLQJIXQFWLRQRITXDOLW\TXDOLW\LVGHWHUPLQHGE\WKHYDOXHRIWKH
LQYHUVHRIWKLVIXQFWLRQDWWKHYLUWXDOSULFH7KLVYLUWXDOTXDOLW\DOVRGHWHUPLQHVWKHYLUWXDOIL[HG
FRVWVRIWKHQRQRZQHGFDUV
)RUWKHRZQHGFDUVZHFDQGHULYHWKHRSWLPDOYDOXHVRIIL[HGDQGYDULDEOHFRVWVDQGTXDOLW\LQ
WKHVDPHZD\DVGLVFXVVHGDERYHIRUWKHFDVHLQZKLFK1 FDUVDUHRZQHGDVVXPLQJWKHFRQGLWLRQV
IRUDXQLTXHRSWLPXPDUHVDWLVILHG1RZOHWNU EHWKHYHFWRUZKLFKKDVWKHRSWLPDOIL[HGFRVW
N LR DVLWVLWKHOHPHQWZKHQFDUL LVRZQHGGL DQGWKHYLUWXDOIL[HGFRVWV N LY ZKHQFDULLVQRW
RZQHGGL 7KHYHFWRUVSU DQG]U DUHGHILQHGDQDORJRXVO\DQGLQGLUHFWXWLOLW\LV
1
L :KHQDOO1 FDUVDUHRZQHGG FRQWDLQVRQO\¶VDQGEHFRPHVLGHQWLFDOWR
7KHXWLOLW\YQ RIRZQLQJQFDUVLVGHILQHGDV
1
­
½
Y Q PD[ ®Y \ ¦ G L N LU SU S 1U ]U ] 1U ¾
Q 1
G ' Q L ¯
¿
DQGWKHRSWLPXPQXPEHURIFDUVQ LV
Q DUJ PD[^YL L 1 ` )XUWKHUVSHFLILFDWLRQRIWKHFRPSRVLWHSULFHIXQFWLRQ
:HQRZGLVFXVVWKHVSHFLILFDWLRQRI3WKDWZLOOEHXVHGLQWKHHPSLULFDOZRUNWREHUHSRUWHGLQ
6HFWLRQ$OWKRXJKZHQRZDOORZWKHYDULDEOHDQGIL[HGFRVWVRIWKHFDUVRZQHGE\WKH
KRXVHKROGWREHGLIIHUHQWZHZLOOQRWGHDOH[SOLFLWO\ZLWKTXDOLW\GLIIHUHQFHVXQWLOWKHHQGRIWKLV
VXEVHFWLRQ
,QRXUHPSLULFDOZRUNZHXVHWKHIROORZLQJVSHFLILFDWLRQRI3
§ 1
·
¨ ¦ ZL H JSL ¸
¨L
¸
OQ
3
1
¨
¸
J
¨ ¦ ZL ¸
© L
¹
ZKHUHJDQGWKHZL!IRUDOOL7KHH[SUHVVLRQLQEUDFNHWVLVDZHLJKWHGDYHUDJHRIWKH
H[SRQHQWLDWHGYDULDEOHFRVWVWKDWKDYHEHHQPXOWLSOLHGE\ J 7KHZHLJKWVZL PD\EHIXQFWLRQVRI
GLVSRVDEOHLQFRPHDQGRWKHUYDULDEOHV7KH\UHIOHFWWKHLPSRUWDQFHRIDSDUWLFXODUFDUIRUWKH
KRXVHKROG,IWKHYDULDEOHFRVWVRIDOOFDUVLQWKHKRXVHKROGDUHHTXDOWKHQXPEHURINLORPHWHUV
GULYHQE\FDULLVDSSUR[LPDWHO\SURSRUWLRQDOWRZL
1RWHWKDWIRUSRVLWLYHYDULDEOHFRVWVWKHH[SUHVVLRQLQEUDFNHWVZLOOEHSRVLWLYHEXWVPDOOHUWKDQ
,WVORJDULWKPLVWKHUHIRUHQHJDWLYHEXWVLQFHLWLVGLYLGHGE\JWKHSULFHLQGLFDWRU3 LVDOZD\V
SRVLWLYH
$IWHUWDNLQJWKHORJDULWKPRIWKHZHLJKWHGVXPDQGGLYLGLQJWKURXJK J ZHDUULYHDWVRPHWKLQJ
WKDWFDQEHLQWHUSUHWHGDVVRPHNLQGRIDYHUDJHYDULDEOHFRVWV,QGHHGLWLVQRWGLIILFXOWWRYHULI\
WKDW3 WDNHVRQDYDOXHEHWZHHQWKHPLQLPXPDQGWKHPD[LPXPRIWKHYDULDEOHFRVWVRIWKH
YDULRXVDXWRPRELOHVWKDWFRXOGEHXVHG
(YHQWKRXJK3 FDQEHLQWHUSUHWHGDVDNLQGRIDYHUDJHSULFHLVQRWKRPRJHQHRXVRIGHJUHH
LQWKHYDULDEOHFRVWVSL1RWHKRZHYHUWKDWWKLVSURSHUW\LVXQGHVLUDEOHLQWKHSUHVHQWFRQWH[W
7KHUHDVRQLVWKDWLWZRXOGLPSO\WKDWWKHVKDUHVVLEHLQJWKHILUVWGHULYDWLYHVRI3DUH
KRPRJHQHRXVRIGHJUHHLQWKHVHYDULDEOHFRVWV$SURSRUWLRQDOFKDQJHLQDOOYDULDEOHFRVWV
RFFXUULQJIRULQVWDQFHDVDUHVXOWRIDQLQFUHDVHLQWKHIXHOSULFHZRXOGWKHUHIRUHOHDYHWKHVH
VKDUHVXQFKDQJHG$VQRWLFHGLQWKHLQWURGXFWRU\VHFWLRQWKHUHLVVRPHHPSLULFDOHYLGHQFHWKDW
VXFKDFKDQJHZRXOGLQGXFHVXEVWLWXWLRQWRZDUGVWKHFDUZLWKWKHORZHVWYDULDEOHFRVWV,QWKH
FRQWH[WRIWKHSUHVHQWPRGHOLWLVWKHUHIRUHGHVLUDEOHWKDWDQLGHQWLFDOSHUFHQWDJHFKDQJHLQDOO
YDULDEOHFRVWVGRHVQRW OHDGWRDFKDQJHLQ3 E\WKHVDPHSHUFHQWDJH
7KHVKDUHVRIDXWRPRELOHNLORPHWHUVLPSOLHGE\DUH
ZL H JSL
VL
1
JS M
¦ ZMH
M ,WLVLQVWUXFWLYHWRVHHZKDWKDSSHQVWRWKHVKDUHVLIWKHIXHOSULFHFKDQJHV,WVHHPVUHDVRQDEOHWR
DVVXPHWKDWDOOYDULDEOHFRVWVDUHSURSRUWLRQDOWRWKHIXHOSULFHDWOHDVWDSSUR[LPDWHO\7KLV
PHDQVWKDWDOOYDULDEOHFRVWVFKDQJHE\WKHVDPHSHUFHQWDJHLIWKHIXHOSULFHFKDQJHV$VD
FRQVHTXHQFHWKHUHODWLYHGHFUHDVHLQH[SSZLOOEHODUJHVWIRUWKHFDUZLWKWKHKLJKHVWYDULDEOH
FRVWVDQGVPDOOHVWIRUWKHFDUZLWKWKHORZHVWYDULDEOHFRVWV7KHVKDUHRIWKHPRVWH[SHQVLYHFDU
LQWKHKRXVHKROG¶VFDUNLORPHWHUVZLOOWKHUHIRUHGHFUHDVHZKLOHWKDWRIWKHOHDVWH[SHQVLYHFDU
ZLOOLQFUHDVH
,QDWZRFDUKRXVHKROGDODUJHUJDSEHWZHHQWKHYDULDEOHFRVWVRIWKHFDUVZLOOLPSO\DGHFUHDVH
LQWKHXVHRIWKHH[SHQVLYHFDULQWHUPVRIYDULDEOHFRVWVDQGDQLQFUHDVHLQWKDWRIWKHFKHDSFDU
:KHQWKHUHDUHWKUHHRUPRUHFDUVSUHVHQWKLJKHUYDULDEOHFRVWVIRUWKHPRVWH[SHQVLYHFDU
PHDQVDODUJHUJDSZLWKWKHFRVWVRIDOORWKHUFDUVDQGDORZHUVKDUHRIWKDWFDU6LPLODUO\ORZHU
YDULDEOHFRVWVIRUWKHOHDVWH[SHQVLYHFDUVPHDQVDODUJHUJDSZLWKWKHFRVWVRIDOORWKHUFDUVDQGD
ODUJHUVKDUHRIFDUNLORPHWHUVIRUWKLVOHDVWH[SHQVLYHFDU
&RPSDUHHTXDWLRQEHORZ
:HPD\FRQFOXGHWKDWVSHFLILFDWLRQLVDEOHWRUHSURGXFHDKRXVHKROG¶VW\SLFDOUHVSRQVHVWR
GLIIHUHQFHVLQYDULDEOHFDUFRVWVDQGFKDQJHVLQIXHOSULFHVDVUHSRUWHGLQWKHOLWHUDWXUHGLVFXVVHG
LQWKH,QWURGXFWLRQ
7KHHIIHFWVRIUHVWULFWLRQVRQWKHKRXVHKROG¶VFDURZQHUVKLSDUHUHDGLO\DQDO\]HG7KHYLUWXDO
SULFHVIRUWKHFDURUFDUVWKDWDUHQRWRZQHGDUHWKHSULFHVWKDWPDNHWKHVKDUHVRIWKHVHFDUVHTXDO
WR$OOYLUWXDOSULFHVDUHWKHUHIRUHLQILQLWHO\SRVLWLYHLPSO\LQJWKDWH[SSYHTXDOV7KLV
PHDQVWKDWWKHVKDUHVRIWKHFDUVRZQHGE\WKHKRXVHKROGDUHGHWHUPLQHGDVLIRQO\WKHFDUVLQD
VHW2 DUHDYDLODEOHWRWKHKRXVHKROG1RWHKRZHYHUWKDWWKHUHLVDQHIIHFWRIUDWLRQLQJRQ3
EHFDXVHWKHSRVLWLYHZHLJKWVZL RIWKHFDUVQRWRZQHGE\WKHKRXVHKROGUHPDLQSUHVHQWLQWKH
GHQRPLQDWRURIWKHUDWLRLQ
1H[WZHQRWHWKDWKDVDVDQDGGLWLRQDODWWUDFWLYHSURSHUW\YL]WKDWWKHVXPRILWVSDUWLDO
GHULYDWLYHVZLWKUHVSHFWWRWKHYDULDEOHFRVWVHTXDOV
1
w3
¦
L wS L
$VDUHVXOWRIWKLVSURSHUW\HTXDWLRQZKLFKJLYHVWKHWRWDOQXPEHURINLORPHWHUVGULYHQE\WKH
KRXVHKROGFDQEHVLPSOLILHGWR
wY
w3
; wY
wY
w3
w\ w3 w\ 7KHULJKWKDQGVLGHLV5R\¶VLGHQWLW\IRUWKHWRWDOQXPEHURINLORPHWHUVLQWHUSUHWHGDVDVLQJOH
JRRGZLWKSULFH3(TXDWLRQWKXVVKRZVWKDWWKHWRWDOGHPDQGIRUFDUNLORPHWHUVFDQEH
GHWHUPLQHGDVLI3ZHUHWKHSULFHIRUFDUNLORPHWHUVLQJHQHUDO,IWKHSDUWLDOGHULYDWLYHRI3 ZLWK
UHVSHFWWRGLVSRVDEOHLQFRPHHTXDOVWKLVWRWDOQXPEHURINLORPHWHUVLVFRPSOHWHO\GHWHUPLQHG
E\WKHIXQFWLRQ Y DQGWKHUHLVDFOHDUGLVWLQFWLRQEHWZHHQWULSJHQHUDWLRQWKURXJKWKHIXQFWLRQ
Y DQGWULSGLVWULEXWLRQWKURXJKWKHIXQFWLRQ3
7KHSUHYLRXVGLVFXVVLRQKDVLJQRUHGGLIIHUHQFHVLQFDUTXDOLW\EXWEHIRUHFRQFOXGLQJWKLV
VXEVHFWLRQZHKDYHWRFRQVLGHULWVUROHLQWKHIXUWKHUVSHFLILFDWLRQRIWKHPRGHO:HKDYH
LQWHUSUHWHG3 DVDFRVWRIFDUPRELOLW\DQGKLJKHUFDUTXDOLW\VKRXOGEHH[SHFWHGWRORZHUWKLV
SULFH$WILUVWVLJKWLWPD\VHHPDWWUDFWLYHWRLQWURGXFHTXDOLW\DVRQHRIWKHGHWHUPLQLQJ
YDULDEOHVRIWKHZHLJKWV+RZHYHUWKLVZRXOGEULQJXVLQWRFRQIOLFWZLWKWKHUHTXLUHPHQWWKDW
wY w] L ZKLFKLVHTXDOWR wY w3 w3 w] L PXVWEHHTXDOWRZKHQWKHGHPDQGIRUNLORPHWHUV
IRUFDUL LVHTXDOWR7KHDOWHUQDWLYHSRVVLELOLW\LVWKDWZHUHIRUPXODWH3 LQWHUPVRITXDOLW\
DGMXVWHGSULFHVUL IRUDXWRPRELOHVHUYLFHV
§ 1
·
¨ ¦ ZL H JUL ¸
¨L
¸
OQ
3
1
¨
¸
J
¨ ¦ ZL ¸
© L
¹
ZLWK
UL U S L ] L DQGZHUHTXLUHWKDW OLP U
SL o f
f 7KLVIRUPXODWLRQVHHPVWREHDUHDVRQDEOHRQHDQGLWFRYHUVIRU
LQVWDQFHWKHUHSDFNDJLQJPRGHORI)LVKHUDQG6KHOOZKLFKKDV UL
XQLWRITXDOLW\
SL ] L DVWKHSULFHSHU
$JHQHUDOL]DWLRQRIGH-RQJ¶VPRGHO
7KHSUHYLRXVVXEVHFWLRQVKDYHH[DPLQHGWKHZD\DKRXVHKROGXVHVWKHFDUVLWKDVDYDLODEOHDQG
WKHQXPEHURIFDUVWREHRZQHG7KHGLVFXVVLRQWKXVIDUKDVEHHQFDVWLQJHQHUDOWHUPV,WZLOO
QRZEHPDGHPRUHFRQFUHWHE\FKRRVLQJDSDUWLFXODUVSHFLILFDWLRQRIWKHLQGLUHFWXWLOLW\
IXQFWLRQ)RUWKLVSXUSRVHZHDGRSWGH-RQJ¶VVSHFLILFDWLRQRIWKHLQGLUHFWXWLOLW\IXQFWLRQ
Y
\ 3 \ D H[SG E3 E
D
'H-RQJXVHGWKHSULFHRIDVLQJOHFDULQWKLVIXQFWLRQEXWZHKDYHLPSXWHGWKHFRPSRVLWHSULFH3
VSHFLILHGDFFRUGLQJWRLQRUGHUWREHDEOHWRGHDOZLWKFDVHVLQZKLFKWKHQXPEHURIFDUV
H[FHHGV
,I3 GRHVQRWGHSHQGRQGLVSRVDEOHLQFRPHWKHWRWDOQXPEHURINLORPHWHUVGULYHQE\WKH
KRXVHKROGLVJLYHQE\WKHIROORZLQJGHPDQGHTXDWLRQ
OQ ; G E3 D OQ \ $PRUHFRPSOLFDWHGH[SUHVVLRQWKDWIROORZVIURPDQGLVQRWGLVFXVVHGKHUHUHVXOWVLI3
GHSHQGVRQGLVSRVDEOHLQFRPH
,IDKRXVHKROGGRHVQRWRZQDOO1 FDUVGHPDQGIRUNLORPHWHUVRIWKHQRQRZQHGFDUVVKRXOGEH
HTXDOWR7KHVDPHPXVWEHWUXHIRUWKHVKDUHVRIWKHNLORPHWHUVGULYHQE\WKHVHFDUVLQWRWDO
GHPDQGIRUNLORPHWHUVDQGLWLVHDVLO\VHHQIURPWKDWWKHYLUWXDOSULFHVDWZKLFKWKLVKDSSHQV
DUHSRVLWLYHLQILQLWH 6LQFHJ LVQHJDWLYHWKLVPHDQVWKDWWKHVHYDULDEOHFRVWVGLVDSSHDUIURPWKH
QXPHUDWRULQ+RZHYHUWKHLUZHLJKWVUHPDLQSUHVHQWLQWKHGHQRPLQDWRUDQGWKLVLPSOLHV
WKDW3 ZLOOEHKLJKHUZKHQDFDULVUHPRYHG,QRWKHUZRUGVWKHHIIHFWRIUDWLRQLQJDVVRFLDWHG
ZLWKRZQLQJDOLPLWHGQXPEHURIFDUVLVDKLJKHUFRPSRVLWHSULFH3 RIFDUNLORPHWHUV
,IDKRXVHKROGRZQVRQHFDUWKHYDOXHRI3 LV
3 S L OQ ZL ¦ Z M J /LPLWHGSRVVLELOLWLHVIRUVXEVWLWXWLRQEHWZHHQWKHXVHRIGLIIHUHQWFDUVLPSO\DYDOXHRI WKDWLV
FORVHWROHDGLQJWRDYDOXHRI3 XQGHUUDWLRQLQJWKDWLVPXFKKLJKHUWKDQSL,QRWKHUZRUGV
OLPLWHGSRVVLELOLWLHVIRUVXEVWLWXWLRQLPSO\ODUJHFRVWVRIUDWLRQLQJ
,IWKHIRUPXODIRU3 LQWKHFDVHZKHUHMXVWRQHFDULVRZQHGLVVXEVWLWXWHGLQWRWKHVHFRQG
WHUPRQWKHULJKWKDQGVLGHFDQEHDEVRUEHGLQWRG7KHUHVXOWLQJLQGLUHFWXWLOLW\IXQFWLRQLVWKH
RQHXVHGE\GH-RQJIRUVLQJOHFDURZQLQJKRXVHKROGV
,WPXVWEHQRWHGKRZHYHUWKDWLQWKHPRGHORI)LVKHUDQG6KHOOWKHYDULHWLHVZKLFKFRUUHVSRQGLQWKHSUHVHQW
FRQWH[WWRWKHYDULRXVFDUVRZQHGE\WKHKRXVHKROGDUHSHUIHFWVXEVWLWXWHVZKLFKLVQRWXVHIXOIRUWKHSXUSRVHVRI
WKHSUHVHQWSDSHU
7KHFKRVHQVSHFLILFDWLRQRI3 LPSOLHVWKDWFDUVZLOOEHXVHGZKHQHYHUWKH\DUHRZQHG
'H-RQJKDVSURSRVHGDGLIIHUHQWH[WHQVLRQRIWKHPRGHOWRVLWXDWLRQVLQZKLFKKRXVHKROGVFDQRZQ
WZRFDUV,WLVEDVHGRQDXWLOLW\IXQFWLRQY¶ \¶.H[S/ SH[S/ S7KLVOHDGVWRGHPDQG
HTXDWLRQVIRUWKHNLORPHWHUVGULYHQE\ERWKFDUVLQZKLFKWKHYDULDEOHFRVWVRIWKHRWKHUFDUGRHVQRWDSSHDU7KHUH
DUHWKHUHIRUHQRVXEVWLWXWLRQHIIHFWVSUHVHQWLQWKLVPRGHO
7KHGDWD
,QWKLVVHFWLRQZHLQWURGXFHWKHGDWDVHWXVHGLQWKLVSDSHUGLVFXVVVRPHDVSHFWVRIWKHVHGDWDWKDW
DUHRIVSHFLDOLQWHUHVWDQGSUHVHQWUHGXFHGIRUPHTXDWLRQVIRUYDULDEOHDQGIL[HGFRVWVRIWKHFDUV
'HVFULSWLRQRIWKHGDWD
7KHGDWDVHWXVHGLQWKLVSDSHURULJLQDWHVIURPWKUHHGLIIHUHQWGDWDVRXUFHV
WKHµFDUSDQHO¶FRQGXFWHGE\WKH'XWFK&RQVXPHU¶V$VVRFLDWLRQ&RQVXPHQWHQERQG
DKRXVHKROGVXUYH\WKDWVXSSOHPHQWHGWKHFDUSDQHOTXHVWLRQQDLUHLQWKHSHULRG
WHFKQLFDOFDUDWWULEXWHVSURYLGHGE\WKH'XWFK0RWRULVWV¶$VVRFLDWLRQ$1:%
7KHµFDUSDQHO¶FRQVWLWXWHVWKHEDVLVRIWKHGDWDVHW,WFRQWDLQVLQIRUPDWLRQDERXWSDVVHQJHU
FDUV3DUWLFLSDQWVDUHUHFUXLWHGDPRQJWKHPHPEHUVRIWKHDVVRFLDWLRQZLWKWKHSULPDU\SXUSRVHRI
JHQHUDWLQJLQIRUPDWLRQDERXWWKHFRVWVRIWKHPRVWSRSXODUFDUW\SHV 7ZLFHD\HDUWKHSDQHO
FDURZQHUVKDYHWRILOOLQDIRUPZLWKTXHVWLRQVDERXWUHSDLUDQGPDLQWHQDQFHFRVWVQXPEHURI
NLORPHWHUVUHFRUGHGDQGDWWULEXWHVRIWKHSDQHOFDU0LOHDJHLVDOVRUHFRUGHGWKHQ
7KHLQIRUPDWLRQJDWKHUHGIRUWKHFDUSDQHOZDVVXSSOHPHQWHGLQWKHSHULRGE\D
KRXVHKROGVXUYH\FRQGXFWHGDVSDUWRIDSXEOLFLW\FDPSDLJQWKDWVWDUWHGWRZDUGVWKHHQGRI
DQGZKLFKZDVLQLWLDWHGE\WKH'XWFK$JHQF\IRU(QHUJ\DQG(QYLURQPHQW1RYHP7KH
FDPSDLJQZDVDLPHGDWDFKLHYLQJDPRUHIXHOHIILFLHQWFDUXVHDQGDFTXLVLWLRQEHKDYLRUDPRQJ
SDVVHQJHUFDURZQHUV,QRUGHUWRPRQLWRUWKHHIIHFWVRIWKHFDPSDLJQGDWDZHUHFROOHFWHGIURP
WKHSDUWLFLSDQWVRIWKHFDUFRVWSDQHORIWKH'XWFK&RQVXPHU¶V$VVRFLDWLRQLQ2FWREHU1RYHPEHU
RIWKHFRQVHFXWLYH\HDUVDQG,QDGGLWLRQWRWKHLQIRUPDWLRQJDWKHUHGIRUWKH
SDQHOFDUFRVWUHVSRQGHQWVZHUHDOVRTXHVWLRQHGDERXWWKHSUHVHQFHRIDVHFRQGDQGWKLUGFDUDQG
WKHQXPEHURINLORPHWHUVGULYHQZLWKWKHVHFDUV7KLVDGGLWLRQDOLQIRUPDWLRQZDVFUXFLDOIRUWKH
SXUSRVHVRIWKHSUHVHQWSDSHU
7DEOH'HVFULSWLYHVWDWLVWLFV
9DULDEOH
+RXVHKROGV
,QFRPH[
1XPEHURIZRUNHUV
1XPEHURISHUVRQV
1XPEHURIOLFHQVHGGULYHUV
1XPEHURIFRPSDQ\FDUV
6HFRQGFDUSUHVHQW
&DUV
0RQWKO\NP
9DULDEOHFRVWV
)L[HGFRVWV
0DLQGULYHULVPDOH
0HDQ
6WG'HY
0LQ
0D[
1XPEHURIREVHUYDWLRQVKRXVHKROGV+RXVHKROGVZLWKVHFRQGFDU1XPEHURIREVHUYHGFDUV
7KHUHDUHFDUW\SHVIRUZKLFKLQIRUPDWLRQLVFROOHFWHG&DUVFDQEHLQFOXGHGLQWKHSDQHOZKHQD WKH
RGRPHWHUPXVWQRWH[FHHGNLORPHWUHVEWKHFDULVDWPRVW\HDUVROGDQGFWKHFDUFRYHUVDWOHDVW
EXWDWPRVWNLORPHWHUVD\HDU
7KHWHFKQLFDOLQIRUPDWLRQWKDWFRQVWLWXWHVWKHWKLUGSDUWRIRXUGDWDFRQFHUQVLFDUDWWULEXWHVLL
IXHOFRQVXPSWLRQLLLIL[HGDQGYDULDEOHGHSUHFLDWLRQUDWHVLYPDUNHWSULFHVRIQHZDQG
VHFRQGKDQGYHUVLRQVRIHDFKRIWKHPDNHPRGHOFRPELQDWLRQVDQGYWKHWLPHSHULRGLQ
ZKLFKWKHYHUVLRQZDVDYDLODEOHIRUSXUFKDVHRQWKHPDUNHW7KHILJXUHVUHIHUULQJWRDYHUDJHDQG
YDULDEOHFRVWVWKDWDUHXVHGLQWKLVSDSHURULJLQDWHIURPWKLVGDWDVRXUFH
7KHGDWDIURPWKHVHWKUHHVRXUFHVZHUHDPDOJDPDWHGLQWRVL[ZDYHVRISDQHOGDWD,QWKHSUHVHQW
SDSHUZHXVHWKHWKZDYHZKLFKUHIHUVWRWKHVHFRQGKDOIRI6RPHGHVFULSWLYHVWDWLVWLFV
DUHSUHVHQWHGLQ7DEOH
7KHDYHUDJHDQQXDOPLOHDJHRIWKHFDUVLQRXUVDPSOHLVYHU\FORVHWRWKDWRIWKH'XWFKFDUIOHHW
7KHKRXVHKROGVLQRXUVDPSOHKDYHVOLJKWO\PRUHPHPEHUVWKDQWKH'XWFKKRXVHKROGVFRPSDQ\
FDUVDSSHDUWREHXQGHUUHSUHVHQWHGDQGWKHDYHUDJHDJHRIWKHFDURZQHUVLQRXUVDPSOHLVVOLJKWO\
KLJKHUWKDQWKDWLQWKHWRWDO'XWFKSRSXODWLRQ
'LVFXVVLRQRIVRPHDVSHFWVRIWKHGDWD
$VHFRQGFDULVRIFRXUVHHVSHFLDOO\XVHIXOLIWKHUHLVPRUHWKDQRQHSHUVRQZLWKDGULYHU¶V
OLFHQVHLQWKHKRXVHKROG 7KLVVXJJHVWVWKDWRQHVKRXOGHVWLPDWHDPRGHOIRUPXOWLSOHFDU
RZQHUVKLSRQO\RQGDWDUHIHUULQJWRKRXVHKROGVZLWKDWOHDVWWZROLFHQVHGGULYHU+RZHYHU
HVWLPDWLRQRIVHSDUDWHSURELWPRGHOVIRUWKHFKRLFHRIHLWKHURQHRUWZRFDUVIRUKRXVHKROGVZLWK
RQHDQGWZRRUPRUHOLFHQVHGGULYHUVUHVXOWHGLQFRHIILFLHQWVWKDWDUHQRWVLJQLILFDQWO\GLIIHUHQW
$SRVVLEOHH[SODQDWLRQRIWKLVUHVXOWLVWKDWWKHQXPEHURIGULYHU¶VOLFHQVHVLVDGMXVWHGWRWKHQHHG
IRUDVHFRQGFDU:HKDYHWKHUHIRUHHVWLPDWHGWKHPRGHORQGDWDUHIHUULQJWRDOOKRXVHKROGV
$VHFRQGLVVXHWKDWQHHGVGLVFXVVLRQLVWKHXVHRIDFRPSDQ\FDU6XFKFDUVKDYHEHFRPHPXFK
PRUHSRSXODULQWKH1HWKHUODQGVVLQFHILVFDOOHJLVODWLRQZDVFKDQJHGLQWKHHDUO\V
&RPSDQ\FDUVDUHXVXDOO\EXWFHUWDLQO\QRWH[FOXVLYHO\RIIHUHGWRZRUNHUVZKRKDYHWRGULYHD
ORWIRUEXVLQHVVSXUSRVHV%HFDXVHRILWVUHODWLRQZLWKWUDYHOIRUEXVLQHVVSXUSRVHVRQHFRXOG
UHJDUGWKHFRPSDQ\FDUDVDPRUHRUOHVVH[RJHQRXVDGGLWLRQWRWKHKRXVHKROG¶VYHKLFOHVWRFN
+RZHYHUWKHUHDUHVHYHUDOUHDVRQVIRUTXHVWLRQLQJWKHDSSURSULDWHQHVVRIVXFKDQDSSURDFK,Q
PDQ\ILUPVDODUJHQXPEHURIHPSOR\HHVPD\RSWIRUDFRPSDQ\FDUUHJDUGOHVVRIWKHQHHGWR
GULYHIRUEXVLQHVVSXUSRVHV&KRRVLQJWKLVRSWLRQPHDQVWKDWWKHLUVDODU\LVORZHU0RUHRYHU
ZRUNHUVZLWKDFRPSDQ\FDUKDYHWRDGGSDUWRILWVYDOXHWRWKHLUWD[DEOHLQFRPHZKLFKPHDQV
WKDWWKH\KDYHWRSD\VRPHIL[HGFRVWV7KHNLORPHWHUVWKH\GULYHIRUEXVLQHVVSXUSRVHVDQGDOVR
KRPHZRUNWULSVDUHXVXDOO\SDLGE\WKHLUHPSOR\HUVEXWPDQ\ZRUNHUVKDYHWRSD\YDULDEOH
IXHOFRVWVWKHPVHOYHVLIWKHQXPEHURISULYDWHNLORPHWHUVH[FHHGVDSUHGHWHUPLQHGWKUHVKROG
7KLVPHDQVWKDWLQPDQ\FDVHVWKHUHOHYDQWPDUJLQDOFRVWVDUHHTXDOWRWKHIXHOFRVW(YHQ
WKRXJKWKHFKRLFHRIFDUEUDQGDQGPDNHIRUFRPSDQ\FDUVLVQRWFRPSOHWHO\IUHHPRVWZRUNHUV
FDQFKRRVHIURPDEURDGUDQJHZKLFKLVVRPHWLPHVUHODWHGWRWKHW\SHRIMRE
7KHSUHYLRXVGLVFXVVLRQVXJJHVWVWKDWZRUNHUVZLWKDFRPSDQ\FDUDUHQRWWRRGLIIHUHQWIURP
ZRUNHUVZKRKDYHERXJKWWKHLUFDUWKHPVHOYHVDQGWKDWWKHUHLVQRQHHGWRXVHDFRPSOHWHO\
GLIIHUHQWPRGHOVSHFLILFDWLRQIRUKRXVHKROGVZLWKDQGKRXVHKROGVZLWKRXWVXFKDFDU,QWKH
PRGHOHVWLPDWHGLQWKHQH[WVHFWLRQZHZLOOXVHDGXPP\IRUFRPSDQ\FDUVDVDQLQGLFDWRURIWKH
GHPDQGIRUNLORPHWHUV
,QWKHVDPSOHWKHUHDUHKRXVHKROGVZLWKRQHGULYHU¶VOLFHQVHRIWKHPKDYHWZRFDUV
(VWLPDWLRQUHVXOWVDUHDYDLODEOHXSRQUHTXHVW
'HWHUPLQDQWVRIFDUFRVWV
:HLQGLFDWHGLQWKHSUHYLRXVVHFWLRQWKDWWKHSUHVHQWSDSHUZLOOQRWIRFXVRQTXDOLW\FKRLFHHYHQ
WKRXJKZHFDQQRWLJQRUHWKDWLVVXHVLQFHVXEVWLWXWLRQEHWZHHQWKHXVHRIWKHWZRFDUVLVUHODWHGWR
GLIIHUHQFHVLQFRVWVWKDWDUHUHODWHGWRTXDOLW\GLIIHUHQFHV,Q6HFWLRQZHRXWOLQHGDPRGHOWKDW
LQFRUSRUDWHVTXDOLW\FKRLFH+LJKHUTXDOLW\FRXOGEHUHDOL]HGDWWKHH[SHQVHRIKLJKHUIL[HGDQG
YDULDEOHFRVWV3UHVXPDEO\WKHWUDGHRIIEHWZHHQEHQHILWVDQGFRVWVGHSHQGVSUHVXPDEO\RQ
KRXVHKROGFKDUDFWHULVWLFVDQGWKHUHGXFHGIRUPHTXDWLRQVRIVXFKDVXEPRGHOZRXOGWKHUHIRUH
UHODWHIL[HGDQGYDULDEOHFRVWVWRKRXVHKROGFKDUDFWHULVWLFV,QWKLVVXEVHFWLRQZHGLVFXVV
HVWLPDWLRQUHVXOWVRIVXFKUHGXFHGIRUPHTXDWLRQV:HVWDUWZLWKYDULDEOHFDUFRVWV
7DEOHDERYHVKRZVWKDWWKHYDULDWLRQLQYDULDEOHFRVWVLVOLPLWHGWKHILJXUHVDUHDOOLQWKH
LQWHUYDO>@&DVXDOHYLGHQFHVXJJHVWVKRZHYHUWKDWLWPD\QHYHUWKHOHVVEHLQWHUHVWLQJWR
LQYHVWLJDWHWKHGHWHUPLQDQWVRIWKHGLIIHUHQFHV(VWLPDWLRQUHVXOWVRIDOLQHDUUHJUHVVLRQDUHVKRZQ
LQ7DEOH7KH\FRQILUPWKHFRPPRQVHQVHRSLQLRQWKDWPDOHVGULYHFDUVZLWKKLJKHUYDULDEOH
FRVWVHYHQWKRXJKWKHGLIIHUHQFHLVQRWODUJH:KHQKRXVHKROGLQFRPHLVKLJKHUYDULDEOHFRVWV
WHQGWRJRXS+RZHYHUJLYHQLQFRPHDQGWKHYDOXHVRIWKHRWKHUH[SODQDWRU\YDULDEOHVYDULDEOH
FRVWVWHQGWREHVOLJKWO\ORZHULIWKHQXPEHURIZRUNHUVLVODUJHU7KHSUHVHQFHRIPRUHOLFHQVHG
GULYHUVLVDVVRFLDWHGZLWKKLJKHUYDULDEOHFRVWVEXWWKHSUHVHQFHRIPRUHFDUVLVDVVRFLDWHGZLWK
ORZHUYDULDEOHFRVWV7KHUHLVQRGLIIHUHQFHLQWKLVUHVSHFWEHWZHHQFDUVZLWKDPDOHRUDIHPDOH
PDLQGULYHU+LJKHUIL[HGFRVWVDUHRIWHQDVVRFLDWHGZLWKKHDYLHUFDUVLPSO\LQJPRUHIXHOXVHSHU
NLORPHWHUDQGWKXVKLJKHUYDULDEOHFRVWVDUHODWLRQVKLSWKDWLVFRQILUPHGE\WKHVLJQLILFDQW
SRVLWLYHFRHIILFLHQWIRUIL[HGFRVWV
7DEOH9DULDEOHFRVWVSHUNLORPHWHUDQGKRXVHKROGFKDUDFWHULVWLFV
9DULDEOH
(VWLPDWHVWHUURU
&RQVWDQW
0DOH
,QFRPH[
1XPEHURIZRUNHUV
&RPSDQ\FDU
+RXVHKROGVL]H
1XPEHURIOLFHQVHGGULYHUV
6HFRQGFDUSUHVHQW
0DOHVHFRQGFDUSUHVHQW
)L[HGFRVW[
5
Q
6WDQGDUGHUURUVDUHUHSRUWHGLQSDUHQWKHVHV&RHIILFLHQWVLQEROGSULQWDUHVLJQLILFDQWDWS 7DEOHUHSRUWVHVWLPDWLRQUHVXOWVWKDWUHIHUWRWKHORJDULWKPRIIL[HGFDUFRVWV+HUHZHILQGD
VXEVWDQWLDOHIIHFWRIWKHJHQGHURIWKHPDLQGULYHU0DOHVXVHFDUVWKDWKDYHRQDYHUDJHPRUH
WKDQKLJKHUIL[HGFRVWVWKDQIHPDOHV$KLJKHULQFRPHLVDVVRFLDWHGZLWKKLJKHUIL[HGFDU
FRVWVDQGLIWKHQXPEHURIZRUNHUVLQFUHDVHVWKHVHFRVWVWHQGWREHHYHQKLJKHU&RPSDQ\FDUV
WHQGWRKDYHKLJKHUIL[HGFRVWV7KHSUHVHQFHRIDVHFRQGFDULVDVVRFLDWHGZLWKORZHUIL[HGFRVWV
DQGDJDLQZHILQGQRGLIIHUHQFHLQWKLVUHVSHFWEHWZHHQFDUVZKRVHPDLQGULYHULVPDOHDQGWKRVH
ZKRVHPDLQGULYHULVIHPDOH
$VPHQWLRQHGDERYHZHZLOOXVHWKHVHHVWLPDWLRQUHVXOWVWRSUHGLFWWKHIL[HGDQGYDULDEOHFRVWVRI
WKHVLQJOHFDURUWKHWZRFDUVXVHGE\WKHKRXVHKROGVLQRXUVDPSOHLQRUGHUWRHVWLPDWHWKH
VWUXFWXUDOPRGHO7KLVPHDQVWKDWZHZLOOLQWHUSUHWWKHSUHGLFWLRQVRIWKHIL[HGDQGYDULDEOHFRVWV
IURPWKHVHHTXDWLRQVDVWKHRSWLPDOYDOXHVLPSOLHGE\DPRGHORITXDOLW\FKRLFH7KHHVWLPDWHG
HTXDWLRQVJLYHUHDVRQDEOHYDOXHVIRUWKHIL[HGDQGYDULDEOHFRVWV)RULQVWDQFHWKHDYHUDJH
SUHGLFWHGIL[HGFRVWVIRUDKRXVHKROGZLWKRQHFDULV'XWFKJXLOGHUVZKHUHDVWKHDYHUDJH
IL[HGFRVWVRIWZRFDUKRXVHKROGVDUH'XWFKJXLOGHUVIRUWKHPDOHGULYHUDQG'XWFK
JXLOGHUVIRUWKHIHPDOHGULYHU$YHUDJHSUHGLFWHGYDULDEOHFRVWVDUHLQDOOWKUHHFDVHVEHWZHHQ
DQG'XWFKJXLOGHUVSHUNLORPHWHU
7DEOH)L[HGFRVW
9DULDEOH
&RQVWDQW
0DOH
/QLQFRPH
1XPEHURIZRUNHUV
&RPSDQ\FDU
+RXVHKROGVL]H
1XPEHURIOLFHQVHGGULYHUV
6HFRQGFDUSUHVHQW
0DOHVHFRQGFDUSUHVHQW
5
Q
(VWLPDWHVWHUURU
'HSHQGHQWYDULDEOH/RJ)L[HG&RVW6WDQGDUGHUURUVDUHUHSRUWHGLQSDUHQWKHVHV&RHIILFLHQWVLQEROGSULQWDUH
VLJQLILFDQWDWS (VWLPDWLRQRIWKHVWUXFWXUDOPRGHO
,QWURGXFWLRQ
,QWKLVVHFWLRQZHGLVFXVVWKHHVWLPDWLRQRIWKHVWUXFWXUDOPRGHOGHULYHGLQ6HFWLRQ*LYHQWKH
GDWDGLVFXVVHGLQWKHSUHYLRXVVHFWLRQWKHPRGHOLVIRFXVHGRQWKHFKRLFHWRRZQRQHRUWZRFDUV
$FFRUGLQJO\LWWDNHVWKHPD[LPXPQXPEHURIFDUVSHUKRXVHKROGWREHHTXDOWRWZRDQGWKH
PLQLPXPWREHRQH
:HZLOOQRWPDNHDGLVWLQFWLRQEHWZHHQILUVWDQGVHFRQGFDUVVLQFHLWZRXOGIRUFHXVWRLQWURGXFH
DQHOHPHQWRIDUELWUDULQHVVLQWRWKHPRGHO7KHUHLVQRLQWULQVLFUHDVRQZK\RQHFDUVKRXOGEH
ODEHOHG³SULPDU\´DQGWKHRWKHU³VHFRQGDU\´:HKDYHWKHUHIRUHWUHDWHGWKHFDUVV\PPHWULFDOO\
7KHUHLVRIFRXUVHJRRGUHDVRQWRVXSSRVHWKDWFDUXVHZLOOEHGHSHQGHQWRQWKHFKDUDFWHULVWLFV
RIWKHPDLQGULYHU)RUWKLVUHDVRQZHKDYHUHODWHGGLIIHUHQFHVLQFDUXVHWRGLIIHUHQFHVLQGULYHU
FKDUDFWHULVWLFV0RUHVSHFLILFDOO\ZHKDYHGLVWLQJXLVKHGEHWZHHQFDUVZLWKPDOHDQGWKRVHZLWK
IHPDOHPDLQGULYHUV
7KHOLNHOLKRRGIXQFWLRQ
:HGHOHWHGKRXVHKROGVZLWKPRUHWKDQWZRFDUV
:HXVHWKHHVWLPDWHGHTXDWLRQVIRUIL[HGDQGYDULDEOHFRVWVWRSUHGLFWWKHYDOXHVRIWKHVH
YDULDEOHVIRUDOOKRXVHKROGVLQRXUVDPSOHZKHQWKH\RZQDVLQJOHFDUDQGWZRFDUV7KHYDOXHV
IRUWKHIL[HGFRVWVZLOOEHGHQRWHGDVN ZKHQDVLQJOHFDULVRZQHGDQGDVN DQGN ZKHQWZR
FDUVDUHRZQHG7KHFRPSRVLWHSULFHVIRURQHDQGWZRFDUVDUHFRPSXWHGRQWKHEDVLVRIWKH
SUHGLFWHGYDULDEOHFRVWVDQGZLOOEHUHIHUUHGWRDV3 DQG3UHVSHFWLYHO\,QRUGHUWRJHWVRPH
LGHDRIWKHGHWHUPLQDQWVRIWKHVHYDULDEOHVZHKDYHVHSDUDWHO\HVWLPDWHGVKDUHHTXDWLRQVWKDW
IROORZIURP $QLPSRUWDQWUHVXOWZDVWKDWWKHFRHIILFLHQWIRUKRXVHKROGLQFRPHZDVQHYHU
VLJQLILFDQWZKLFKLPSOLHVWKDWFDQEHXVHGDVWKHGHPDQGHTXDWLRQIRUWKHWRWDOQXPEHURI
NLORPHWHUVGULYHQE\WKHKRXVHKROG$QRWKHUIHDWXUHWKDWVKRXOGEHPHQWLRQHGLVWKHWUHDWPHQWRI
TXDOLW\6LQFHTXDOLW\LWVHOILVXQREVHUYHGZHLQFOXGHGIL[HGFDUFRVWVDVDQLQGLFDWRUEXWZH
ZHUHXQDEOHWRILQGDVLJQLILFDQWFRHIILFLHQWLQWKHYDULRXVVSHFLILFDWLRQZHWULHG$SDUWIURPWKH
YDULDEOHFRVWRQO\WKHJHQGHURIWKHPDLQGULYHUDSSHDUWRKDYHDVLJQLILFDQWHIIHFWRQWKH
GLVWULEXWLRQRIWKHWRWDOQXPEHURINLORPHWHUVRYHUWKHWZRFDUV2QWKHEDVLVRIWKHVHHVWLPDWLRQ
UHVXOWVZHKDYHFKRVHQSDUVLPRQLRXVVSHFLILFDWLRQRIWKHFRPSRVLWHSULFHWKDWLQFOXGHVRQO\
WKHVHWZRYDULDEOHV
§ HT, PDOH JS ·
§ HT, PDOH ·
¸
¸
OQ¨¨
OQ¨
3
S
J © HT ¸¹
J ¨© HT ¸¹
DQG
·
¸
¸
¹
ZKHUH,LVDQLQGLFDWRUYDULDEOHWKDWLVHTXDOWRLIWKHPDOHGULYHULVPDOHDQGHTXDOWR
RWKHUZLVH)RUWZRFDUKRXVHKROGVZHKDYHDGRSWHGWKHFRQYHQWLRQWKDWFDULVWKHRQHXVHGE\
WKHPDOHGULYHU
7KHVSHFLILFDWLRQRIWKHLQGLUHFWXWLOLW\IXQFWLRQRIGH-RQJZDVJLYHQLQ7KHXWLOLW\
RIRZQLQJDVLQJOHFDULV
X
\ N D H[SG E 3 E
D
DQGWKDWRIRZQLQJWZRFDUV
\ N N D H[SG E 3 X
E
D
2ZQLQJDVLQJOHFDULPSOLHVORZHUIL[HGFDUFRVWVEXWDKLJKHUFRPSRVLWHSULFHIRUFDUPRELOLW\
7KHFRVWVRIRZQLQJWZRFDUVWKXVDSSHDULQWKHILUVWWHUPRQWKHULJKWKDQGVLGHRIWKHDERYH
HTXDWLRQVZKLOHWKHEHQHILWVHPHUJHLQWKHVHFRQGWHUP7KHPDJQLWXGHRIWKHEHQHILWVLV
GHSHQGHQWRQWKHYDOXHRIWKHUDQGRPYDULDEOH/ZKLFKLVDVVXPHGWREHDGUDZLQJIURPD
QRUPDOGLVWULEXWLRQZLWKPHDQ/ DQGVWDQGDUGGHYLDWLRQ1/,WFDQWKHUHIRUHEHZULWWHQDV
G PG V G H ZLWK0 DGUDZLQJIURPWKHVWDQGDUGQRUPDOGLVWULEXWLRQ,I0 LVVXIILFLHQWO\ODUJHWKHXWLOLW\RI
RZQLQJWZRFDUVZLOOH[FHHGWKDWRIRZQLQJDVLQJOHFDU7KHFULWLFDOYDOXHHFDQEHGHWHUPLQHG
DV
·
\ N D \ N D
§ E
¸
H
OQ¨¨
V G © D H[S PG H[S E 3 H[S E 3 ¸¹
3
T JS
JS
§ H H ¨
OQ
J ¨©
H T
(VWLPDWLRQUHVXOWVDUHDYDLODEOHXSRQUHTXHVW
7KHSUREDELOLW\RIRZQLQJWZRFDUVLVHTXDOWRWKHSUREDELOLW\WKDW0 H[FHHGVLWVFULWLFDOYDOXHDQG
WKHSUREDELOLW\RIRZQLQJRQHFDULVLWVFRPSOHPHQW7KHSDUDPHWHU0 LVIXUWKHUVSHFLILHGDVD
OLQHDUIXQFWLRQRIKRXVHKROGFKDUDFWHULVWLFVK
PG G ¦ G N KN N
7KHRXWFRPHRIWKHFKRLFHEHWZHHQRZQLQJWZRFDUVRURQHLVQRZIRUPXODWHGDVDQRQOLQHDU
SURELWPRGHO
7KHQXPEHURINLORPHWHUVGULYHQE\WKHKRXVHKROGLVGHWHUPLQHGFRQGLWLRQDORQWKHFKRVHQ
QXPEHURIFDUV7KHUDQGRPYDULDEOH/ DSSHDUVLQWKHGHPDQGHTXDWLRQDQGZHPXVW
DFFRXQWIRUWKHWUXQFDWLRQFDXVHGE\WKHFDURZQHUVKLSGHFLVLRQ)ROORZLQJGH-RQJZH
DGGDQRUPDOGLVWULEXWHGUDQGRPWHUP ZLWKH[SHFWDWLRQDQGYDULDQFH1WRWKLVHTXDWLRQLQ
RUGHUWRWDNHLQWRDFFRXQWPHDVXUHPHQWDQGRSWLPL]DWLRQHUURUVDQGHVWLPDWH
OQ ; G ¦ G N KN ( H _ P FDUV E 3P D OQ \ K
N
$P K
IRUP WKHQXPEHURIFDUVRZQHGE\WKHKRXVHKROG:KHQRQHFDULVRZQHG H d H DQG
ZKHQWZRFDUVDUHRZQHG H ! H 7KHFRQGLWLRQDOH[SHFWDWLRQIRU0 LQFDQEHGHWHUPLQHG
ZLWKVWDQGDUGIRUPXODVJLYHQIRULQVWDQFHLQ9HUEHHN
:HDUHQRZDEOHWRIRUPXODWHWKHOLNHOLKRRGIXQFWLRQ7KHOLNHOLKRRGOL RIDQREVHUYDWLRQL LVWKH
SURGXFWRIWKHSUREDELOLW\WKDW0 LVLQWKHUHOHYDQWUDQJHPXOWLSOLHGE\WKHYDOXHRIWKHQRUPDO
GHQVLW\IRUWKH WKDWIROORZVIURPVHWWLQJHTXDOWRWKHREVHUYHGWRWDOQXPEHURINLORPHWHUV
8VLQJDVXIIL[L WRGLVWLQJXLVKREVHUYDWLRQVWKLVJLYHV
§ $ OQ ; L ·
§
·
¸ , PL 3U H ! H L I ¨ $L OQ ; L ¸ O L , PL 3U H d H L I ¨ L
¨
¸
¨
¸
VK
VK
©
¹
©
¹
ZKHUH,LVWKHLQGLFDWRUYDULDEOHDQG V K LVWKHVWDQGDUGGHYLDWLRQRI
,QRUGHUWRHVWLPDWHWKHSDUDPHWHUVRI3 VLPXOWDQHRXVO\ZLWKWKHRWKHUSDUDPHWHUVZHVXEVWLWXWH
WKHH[SUHVVLRQJLYHQLQLQWRDQGDQGWKHUHVXOWLQJH[SUHVVLRQVLQ
,WPD\EHREVHUYHGWKDWWKHOLNHOLKRRGIRUPXODWHGLQGRHVQRWXVHWKHLQIRUPDWLRQZHKDYHRQ
WKHGLVWULEXWLRQRIWKHWRWDOQXPEHURINLORPHWHUVRIKRXVHKROGVRZQLQJWZRFDUVRYHUERWKFDUV
,QRUGHUWRXVHWKLVLQIRUPDWLRQDVZHOOQRWHWKDWWKHGHPDQGNLORPHWHUVRIFDUN WREH
UHIHUUHGWRDV;N LVGHWHUPLQHGDV;N VNZLWKVN WKHVKDUHRIWKLVFDULQKRXVHKROGNLORPHWHUV
(TXDWLRQVKRZVKRZWKLVVKDUHLVUHODWHGWRWKHFRPSRVLWHSULFH37KHVKDUHVLPSOLHGE\WKH
SDUVLPRQLRXVIRUPXODWLRQRI3 DUH
T JS
H V T JS
JS
H H DQG
H
JS T JS
JS
H H 7KHGHPDQGIRUNLORPHWHUVWKDWLVSUHGLFWHGE\WKHPRGHOHTXDOVWRWDOGHPDQGIRUNLORPHWHUVE\
WKHKRXVHKROGWLPHVWKHVKDUHRIWKHSDUWLFXODUFDU:HDVVXPHGWKDWWKHHUURULQWKHGHPDQG
HTXDWLRQIRUHDFKFDURQRQHDQGWZRFDURZQLQJKRXVHKROGVLVDQRUPDOGLVWULEXWHGUDQGRP
YDULDEOHZKRVHVWDQGDUGGHYLDWLRQVKRXOGEHHVWLPDWHG:HDOORZWKHHUURUVLQWKHGHPDQGIRU
NLORPHWHUVRIWZRFDUVLQWKHVDPHKRXVHKROGWREHFRUUHODWHG
V )RUPDOO\WKHGHPDQGHTXDWLRQVWREHHVWLPDWHGIRUWKHKRXVHKROGVRZQLQJWZRFDUVDUH
OQ ; N G ¦ G N [ N ( H _ FDUV E 3P D OQ \ OQV N K N
N
%N K N ZKHUHVN GHQRWHVWKHNLORPHWHUVKDUHRIWKHNWKFDUDVJLYHQLQIRU1 7KHOLNHOLKRRG
IXQFWLRQIRUREVHUYDWLRQLQRZEHFRPHV
§ $ OQ ; L ·
¸
O L , PL 3UH d H L I ¨ L
¨
¸
V
K
©
¹
§ %L OQ ; L %L OQ ; L ·
U ¸
, PL 3UH ! H L I ¨
¨
¸
V
V
K
K
©
¹
ZKHUHI GHQRWHVWKHGHQVLW\RIWKHELYDULDWHQRUPDODQG! WKHFRUUHODWLRQEHWZHHQWKHWZR
YDULDWHV
7DEOH(VWLPDWLRQUHVXOWVIRUWKHRZQHUVKLSXVHPRGHO
7RWDOGHPDQG
6\PERO
D
E
G
G
G
G
G
V
V/
T
J
U
9DULDEOH
,QFRPH
3ULFH
&RQVWDQW
1XPEHURIZRUNHUV
&RPSDQ\FDU
+RXVHKROGVL]H
1XPEHURIOLFHQVHGGULYHUV
6HGHPDQGHTXDWLRQ
6HLGLRV\QFUDWLFGHPDQG
0DOH
'LIIHUHQFHLQYDULDEOHFRVW
&RUUHODWLRQEHWZHHQHUURUV
LQGHPDQGHTXDWLRQV
(VWLPDWHVWHUU
'HPDQGIRULQG
&DUV
(VWLPDWHVWHUU
/RJOLNHOLKRRG
Q
1RWH+RXVHKROGVZLWKDQLQFRPHOHVVWKDQWZRWLPHVWKHDYHUDJHIL[HGFRVWVRIFDURZQHUVKLSZHUHUHPRYHGIURP
WKHVDPSOH
(VWLPDWLRQUHVXOWV
7KHPRGHOWKDWKDVEHHQIRUPXODWHGLQWKH6HFWLRQDERYHLVKLJKO\QRQOLQHDULQWKH
SDUDPHWHUVDQGZHVWDUWHGHVWLPDWLRQZLWKDWZRVWHSSURFHGXUHLQZKLFKWKHUHVXOWVRIVHSDUDWH
HVWLPDWLRQRIWKHSDUDPHWHUVRIWKHVKDUHHTXDWLRQZHUHXVHGWRFRPSXWHWKHFRPSRVLWHSULFH
IXQFWLRQDQGWKHVHYDOXHVZHUHLPSXWHGLQWKHOLNHOLKRRGIXQFWLRQ7KHRWKHUSDUDPHWHUV
ZHUHWKHQHVWLPDWHG,QWKLVZD\ZHREWDLQHGVWDUWLQJYDOXHVIRUDOOSDUDPHWHUVRIWKHPRGHO:H
WKHQXVHGWRREWDLQVLPXOWDQHRXVHVWLPDWHVRIDOOWKHSDUDPHWHUV/LNHOLKRRGIXQFWLRQ
ZDVWKHQHVWLPDWHGZLWKWKHUHVXOWVRIHVWLPDWLQJDVVWDUWLQJYDOXHV(VWLPDWLRQUHVXOWVDUH
JLYHQLQ7DEOHZKHUHWKHFROXPQODEHOHGµWRWDOGHPDQG¶UHIHUVWROLNHOLKRRGIXQFWLRQDQG
WKHRQHODEHOHGµGHPDQGIRULQGLYLGXDOFDUV¶WR
7KHSDUDPHWHUVD DQGE KDYHWKHH[SHFWHGVLJQVDQGDUHVLJQLILFDQW7KHIRUPHUFDQEH
LQWHUSUHWHGDVWKHLQFRPHHODVWLFLW\RIWKHWRWDOGHPDQGIRUNLORPHWHUVDQGWKHSULFHHODVWLFLW\LV
HTXDOWR37KHLQFRPHHODVWLFLWLHVLPSOLHGE\WKHWZRPRGHOVDUHDOPRVWHTXDOEXWWKHPRGHO
EDVHGRQLQGLYLGXDOFDUNLORPHWHUVLPSOLHVDVPDOOHUDEVROXWHYDOXHIRUWKHSULFHHODVWLFLW\7KH
QXPEHURIZRUNHUVKDVDSRVLWLYHHIIHFWRQWKHGHPDQGIRUFDUNLORPHWHUVDQGRQWKHSUREDELOLW\
RIRZQLQJWZRFDUV7KHUHLVDVLPLODUHIIHFWRIKDYLQJDFRPSDQ\FDU7KHFRHIILFLHQWIRU
KRXVHKROGVL]HLVLQVLJQLILFDQW7KHUHLVODUJHDQGKLJKO\VLJQLILFDQWHIIHFWRIWKHQXPEHURI
OLFHQVHGGULYHUVLQWKHPRGHOEDVHGRQWRWDONLORPHWHUVGULYHQE\WKHKRXVHKROG7KHFRHIILFLHQW
WKDWPHDVXUHVWKLVHIIHFWEHFRPHVPXFKVPDOOHULIZHHVWLPDWHWKHPRGHORQLQGLYLGXDOFDU
NLORPHWHUVEXWLWUHPDLQVKLJKO\VLJQLILFDQW7KHDEVROXWHYDOXHRIWKHFRHIILFLHQWJ LVVPDOO
EXWKLJKO\VLJQLILFDQW
:HKDYHDOVRH[SHULPHQWHGZLWKPRUHH[SODQDWRU\YDULDEOHVIRUWKHFRPSRVLWHSULFHIXQFWLRQDQG
WKHVKDUHHTXDWLRQVEXWZHZHUHXQDEOHWRILQGPRUHVLJQLILFDQWFRHIILFLHQWV
:HKDYHDOVRWULHGDVSHFLILFDWLRQLQZKLFKZHDOORZHGWKHSULFHFRHIILFLHQWWREHGLIIHUHQWIRU
FRPSDQ\FDUVEXWZHGLGQRWILQGDVWDWLVWLFDOO\VLJQLILFDQWGLIIHUHQFH
'LVFXVVLRQRIWKHUHVXOWVDQGDQDSSOLFDWLRQ
,QWKLVVHFWLRQZHGLVFXVVWKHLQWHUSUHWDWLRQRIWKHHVWLPDWLRQUHVXOWVDQGSURYLGHDQDSSOLFDWLRQ
WRDFKDQJHLQWUDQVSRUWSROLF\ZKLFKKDVUHSHDWHGO\EHHQFRQVLGHUHGLQWKH1HWKHUODQGVYL]D
SDUWLDOVKLIWRIWKHEXUGHQRIWD[DWLRQIURPIL[HGWRYDULDEOHFDUFRVWV7KURXJKRXWWKHVHFWLRQZH
IRFXVRQDPRGHOHVWLPDWHGRQLQGLYLGXDOFDUNLORPHWHUVZKLFKLVUHJDUGHGDVWKHSUHIHUUHG
PRGHOVSHFLILFDWLRQ
(VWLPDWLRQUHVXOWVHODVWLFLWLHVDQGVXEVWLWXWLRQSRVVLELOLWLHV
7KHSDUDPHWHU. LVHTXDOWRWKHLQFRPHHODVWLFLW\RIWKHGHPDQGIRUNLORPHWHUVFRQGLWLRQDORQWKH
QXPEHURIFDUV,WVYDOXHVHHPVUHDVRQDEOH7KHHTXLYDOHQWSULFHHODVWLFLW\LVHTXDOWR3
DSSUR[LPDWHO\7KHDEVROXWHYDOXHVRIERWKHODVWLFLWLHVDUHDWWKHORZHUHQGRIWKHUDQJH
IRXQGLQRWKHUVWXGLHV VHHDPRQJRWKHUV*UDKDPDQG*ODLVWHUDQG(VSH\
$FHQWUDOIHDWXUHRIRXUPRGHOLVWKHVXEVWLWXWDELOLW\EHWZHHQWKHNLORPHWHUVGULYHQE\WKHWZR
FDUV7KLVVXEVWLWXWDELOLW\LVVXPPDUL]HGE\WKHFRHIILFLHQWZKLFKLVIRXQGWREHKLJKO\
VLJQLILFDQWLQDOOYDULDQWVRIWKHPRGHO7KHHDUOLHUOLWHUDWXUHUHIHUUHGWRLQWKHLQWURGXFWLRQ
VXJJHVWVWKHVLJQLILFDQFHRIWKLVVXEVWLWXWLRQHIIHFWDQGWKHVWUXFWXUDOPRGHOWKXVFRQILUPVWKLV
+RXVHKROGVWHQGWRXVHWKHFDUZLWKWKHORZHUYDULDEOHFRVWVPRUHRIWHQZKHQWKHGLIIHUHQFH
EHWZHHQWKHYDULDEOHFRVWVRIWKHWZRFDUVLVODUJHU
,QRUGHUWRVHHZKDWWKLVLPSOLHVIRUWKHHIIHFWRIFKDQJHVLQWKHIXHOSULFHWKHIROORZLQJHTXDWLRQ
LVKHOSIXO
G OQ V V J
G S S 7KLVFRQILUPHGWKHUHVXOWVRIWKHSUHOLPLQDU\DQDO\VLVLQZKLFKWKHVKDUHHTXDWLRQVZHUHHVWLPDWHGVHSDUDWHO\
7KH\DUHORZHUWKDQWKRVHLPSOLHGE\WKHHVWLPDWLRQUHVXOWVRIWKHILUVWYDULDQWZKLFKZHUHDOUHDG\RQWKHORZVLGH
'H-RQJIRXQGDKLJKDEVROXWHYDOXHIRUWKHSULFHHODVWLFLW\1RWHKRZHYHUWKDWRXUUHVXOWVGRQRWLQFOXGH
WKHSRVVLEOHHIIHFWRIFKDQJHVLQGULYLQJVW\OHRULQWKHFKRLFHRIDXWRPRELOHTXDOLW\WKDWRFFXULQUHDFWLRQWRFKDQJHV
LQIXHOSULFHV
7KHFRHIILFLHQW HTXDOVWKHFKDQJHLQWKHORJDULWKPRIWKHUDWLRRIWKHNLORPHWHUVKDUHVLQGXFHG
E\DFKDQJHLQWKHGLIIHUHQFHEHWZHHQWKHYDULDEOHFRVWVRIWKHWZRFDUV)XUWKHUHODERUDWLRQRI
WKLVHTXDWLRQJLYHV
GV J V V G S S 1RWHWKDW V V LVDWPRVWHTXDOWR*LYHQWKHHVWLPDWHGYDOXHRIWKLVLPSOLHVWKDWWKH
FKDQJHLQWKHVKDUHRIFDULVDWPRVWRIWKHFKDQJHLQWKHJDSEHWZHHQWKHWZRYDULDEOH
FRVWV7KLVJDSLWVHOIHTXDOVRQDYHUDJH 6LQFHFKDQJHVLQWKLVJDSZLOOXVXDOO\EHDVPDOO
IUDFWLRQRILWVYDOXHLWLVFOHDUWKDWVXEVWLWXWLRQEHWZHHQWKHWZRFDUVDVDFRQVHTXHQFHRIFKDQJHV
LQYDULDEOHFRVWVZLOOLQJHQHUDOEHVPDOO)RULQVWDQFHLIIXHOSULFHVDUHPXOWLSOLHGE\NWKH
LPSOLHGFKDQJHLQWKHYDULDEOHFRVWJDSHTXDOV N S S DQGDSULFHLQFUHDVHRIIRU
LQVWDQFHLPSOLHVWKDWN HTXDOV,WPXVWWKHUHIRUHEHFRQFOXGHGWKDWDFFRUGLQJWRRXU
HVWLPDWLRQUHVXOWVWKHVXEVWLWXWLRQEHWZHHQWKHNLORPHWHUVGULYHQE\FDUVLQGXFHGE\FKDQJHVLQ
IXHOSULFHVLVOLPLWHG
7KHSRVVLELOLW\WRVXEVWLWXWHWKHXVHRIRQHFDUIRUWKDWRIWKHRWKHUDOVRSOD\VDQLPSRUWDQWUROHLQ
WKHFRVWVDVVRFLDWHGZLWKKDYLQJMXVWRQHFDU7KHSULFH3 RIFDURIDVLQJOHFDUKRXVHKROGLV
3 S OQZ Z Z J ,IWKHYDULDEOHFRVWVRIDOOFDUVDUHHTXDOWKHVHFRQGWHUPRQWKHULJKWKDQGVLGHHTXDOVWKH
DGGLWLRQDOFRVWRIFDUPRELOLW\FDXVHGE\WKHDEVHQFHRIDVHFRQGFDU6LQFHWKHYDULDWLRQLQ
YDULDEOHFRVWVDPRQJFDUVLVOLPLWHGWKHYDOXHRIWKLVWHUPSURYLGHVDJRRGDSSUR[LPDWLRQ7KH
W\SLFDOVLQJOHFDUKRXVHKROGKDVDPDOHPDLQGULYHUDQGWKHYDOXHRI OQ Z Z Z J LVWKHQ
HTXDOWR7KLVDGGLWLRQDOFRVWLVWKHUHIRUHDPXOWLSOHRIWKHYDULDEOHFRVWVZKLFKDUHRQ
DYHUDJHHTXDOWR2XUPRGHOHVWLPDWHVWKHUHIRUHVXJJHVWWKDWWKHFRVWVLPSOLHGE\WKH
UHVWULFWLRQRIKDYLQJDVLQJOHFDUDUHVXEVWDQWLDO7KHVHKLJKFRVWVDUHWKHPLUURULPDJHRIWKH
OLPLWHGSRVVLELOLWLHVIRUVXEVWLWXWLRQEHWZHHQWKHNLORPHWHUVGULYHQE\WKHWZRFDUVWKDWZHUH
GLVFXVVHGDERYH
(IIHFWVRISULFHDQGLQFRPHFKDQJHVRQFDURZQHUVKLSFDQEHFRPSXWHGE\VLPXODWLQJD
LQFUHDVHLQYDULDEOHFDUFRVWVDQGLQFRPHRQWKHVKDUHRIKRXVHKROGVLQRXUVDPSOHZKLFKKDYH
WZRFDUV7KHTXDVLHODVWLFLWLHVDUHDQGUHVSHFWLYHO\PHDQLQJWKDWDLQFUHDVHLQWKH
YDULDEOHFDUFRVWVLPSOLHVDGHFUHDVHLQWKHVKDUHRIKRXVHKROGVRZQLQJWZRFDUVRIZKHUHDV
WKHHIIHFWRIDLQFUHDVHLQLQFRPHLVJUHDWHULQPDJQLWXGHDQGRIRSSRVLWHVLJQ7KHSULFH
HODVWLFLWLHVRIWKHGHPDQGIRUNLORPHWHUVRIRQHDQGWZRFDUKRXVHKROGVDUHDQG
UHVSHFWLYHO\DQGWKHWRWDOHIIHFWRIDFKDQJHLQYDULDEOHFRVWVRQFDUNLORPHWHUVHTXDOV
7KHGLIIHUHQFHLVFDXVHGE\WKHIDFWWKDWVRPHVHFRQGFDUVDUHDEDQGRQHGLQUHDFWLRQWRWKHSULFH
LQFUHDVH6LPLODUO\WKHWRWDOHIIHFWRIDFKDQJHLQLQFRPHRQWKHWRWDOQXPEHURIFDU
NLORPHWHUVRIRQHDQGWZRFDUKRXVHKROGVLVDQGUHVSHFWLYHO\+RZHYHUWKHWRWDO
HIIHFWRIDQLQFUHDVHLQLQFRPHLVPXFKODUJHUGXHWRWKHKLJKLQFRPHHODVWLFLW\RIGHPDQGIRU
VHFRQGFDURZQHUVKLSLWHTXDOV
$SSOLFDWLRQVKLIWLQJWKHEXUGHQRIWD[HVIURPIL[HGWRYDULDEOHFRVWV
7KHJDSLVFRPSXWHGDVWKHDYHUDJHDEVROXWHYDOXHRIWKHGLIIHUHQFHEHWZHHQWKHYDULDEOHFRVWVRIWKHWZRFDUVIRU
WZRFDUKRXVHKROGV
+RZHYHULWPD\EHQRWHGWKDWRXUGLVFXVVLRQDVVXPHVWKDWERWKFDUVXVHWKHVDPHIXHOW\SH/DUJHUHIIHFWVPD\EH
UHDOL]HGLIRQHFDUXVHVJDVROLQHDQGWKHRWKHUGLHVHODQGWKHSULFHRIRQHIXHOW\SHFKDQJHVZKLOHWKDWRIWKHRWKHU
UHPDLQVFRQVWDQW
:HZLOOQRZXVHWKHHVWLPDWHGPRGHOWRVWXG\WKHHIIHFWRIVKLIWLQJWKHEXUGHQRIWD[DWLRQIURP
IL[HGFDUFRVWVWRYDULDEOHFDUFRVWV,QJHQHUDORQHH[SHFWVDGHFUHDVLQJHIIHFWRIVXFKD
µYDULDELOL]DWLRQ¶RIFDUWD[HVRQWKHQXPEHURIFDUNLORPHWHUVVLQFHWKHPDUJLQDOFRVWVRIGULYLQJ
LQFUHDVHV+RZHYHUWKHORZHUIL[HGFRVWVZLOOLQFUHDVHFDURZQHUVKLSDQGWDNLQJWKLVLQWR
DFFRXQWQRWRQO\IRURZQLQJDVLQJOHFDUEXWDOVRIRUWZRFDUVPD\FKDQJHWKHSLFWXUH,QRUGHU
WRLQYHVWLJDWHWKLVTXHVWLRQZHFRQVLGHUHGDGHFUHDVHLQIL[HGFDUFRVWVRI'XWFKJXLOGHUVSHU
\HDUILQDQFHGE\DQLQFUHDVHLQYDULDEOHFDUFRVWVRI'XWFKJXLOGHUSHUNLORPHWHU,IFDU
RZQHUVKLSDQGWKHQXPEHURINLORPHWHUVGULYHQZLWKWKHFDUVUHPDLQXQFKDQJHGWKHVHFKDQJHV
ZRXOGKDYHQRHIIHFWRQWKHJRYHUQPHQWEXGJHW7KHGHFUHDVHLQIL[HGFDUFRVWVFDQEHUHDOL]HG
E\IRULQVWDQFHDGHFUHDVHLQWKHFDUWD[:HFRQVLGHUWZRYDULDQWVWKHGHFUHDVHLQWKHWD[PD\
EHWKHVDPHIRUDOOFDUVRULWPD\EHSURSRUWLRQDOWRWKHIL[HGFRVWVWKHPVHOYHVDOWKRXJKRQ
DYHUDJHVWLOOHTXDOWRJXLOGHUVSHU\HDU7KHDFWXDOFDUWD[LQWKH1HWKHUODQGVGHSHQGVRQWKH
ZHLJKWRIWKHFDU)RUWKHFKDQJHLQYDULDEOHFRVWVZHDOVRFRQVLGHUWZRSRVVLELOLWLHVLWLVHLWKHU
HTXDOIRUDOOFDUVRUSURSRUWLRQDOWRWKHYDULDEOHFRVWVWKHPVHOYHV7KHILUVWPD\EHLQWHUSUHWHGDV
DNLORPHWHUFKDUJHWKHVHFRQGDVDQLQFUHDVHLQWKHFDUIXHOWD[7DEOHJLYHVWKHHIIHFWVRIWKH
YDULRXVFRPELQDWLRQV7KHILUVWSDQHORIWKHWDEOHJLYHVWKHHIIHFWVRIWKHFKDQJHLQIL[HGFRVWV
RQO\WKHVHFRQGSDQHOWKDWRIWKHFKDQJHLQWKHYDULDEOHFRVWVRQO\DQGWKHWKLUGWKHFRPELQHG
HIIHFWRIWKHWZRPHDVXUHV
7DEOH(IIHFWVRIVKLIWLQJWD[HVIURPIL[HGWRYDULDEOHFRVWV
(TXDOGHFUHDVHLQ (TXDOGHFUHDVHLQ 3URS'HFUHDVHLQ
IL[HGFRVWV
IL[HGFRVWV
IL[HGFRVWV
(TXDOLQFUHDVHLQ SURSLQFUHDVHLQ (TXDOLQFUHDVHLQ
YDULDEOHFRVWV
YDULDEOHFRVWV
YDULDEOHFRVWV
(IIHFWRIFKDQJHLQIL[HGFRVWV
&KDQJHLQVKDUH
RIWZRFDU
KRXVHKROG
FKDQJHLQ
NLORPHWHUVGULYHQ
(IIHFWRIFKDQJHLQYDULDEOHFRVWV
&KDQJHLQVKDUH
RIWZRFDU
KRXVHKROG
FKDQJHLQ
NLORPHWHUVGULYHQ
(IIHFWRIWKHFRPELQHGFKDQJHV
&KDQJHLQVKDUH
RIWZRFDU
KRXVHKROG
FKDQJHLQ
NLORPHWHUVGULYHQ
3URSGHFUHDVHLQ
IL[HGFRVWV
SURSLQFUHDVHLQ
YDULDEOHFRVWV
7KHPRVWVDOLHQWIHDWXUHRIWKHILJXUHVLQWKHWDEOHLVWKDWRXUPRGHOLPSOLHVUHODWLYHO\ODUJH
HIIHFWVRIWKHFKDQJHLQIL[HGFRVWV,QRUGHUWRLQWHUSUHWWKLVILQGLQJLWPD\EHQRWHGWKDWWKH
VPDOOHVWLPDWHGYDOXHRID LPSOLHVWKDWLQGLUHFWXWLOLW\LVDOPRVWOLQHDULQLQFRPHPLQXVIL[HG
DXWRPRELOHFRVWVVHHHTVDQG$FKDQJHLQWKHGLIIHUHQFHEHWZHHQWKHIL[HGFRVWVRI
KDYLQJRQHRUWZRFDUVWKXVLPSOLHVDFKDQJHLQWKHGLIIHUHQFHEHWZHHQWKHDVVRFLDWHGLQGLUHFW
XWLOLWLHVRIDSSUR[LPDWHO\WKHVDPHVL]H(YHQWKRXJKWKHHIIHFWRIWKLVFKDQJHRQWKHSUREDELOLW\
RIKDYLQJWZRFDUVUXQVYLDDORJDULWKPLFWUDQVIRUPDWLRQVHHHTLWLVODUJHLQFRPSDULVRQ
ZLWKWKHHIIHFWRIWKHFKDQJHLQWKHYDULDEOHFRVWVFRQVLGHUHGKHUH ,IWKHFKDQJHLQIL[HGFRVWVLV
HTXDOIRUDOOFDUVWKHHIIHFWRQWKHGLIIHUHQFHLQGLVSRVDEOHLQFRPHLVDOZD\VHTXDOWR'XWFK
JXLOGHUVSHU\HDU,IWKHFKDQJHLVPDGHSURSRUWLRQDOWRIL[HGFRVWVWKHHIIHFWLVPXFKVPDOOHU
7KHUHDVRQLVWKDWLIDKRXVHKROGRZQVDVLQJOHFDULWLVXVXDOO\DUHODWLYHO\H[SHQVLYHRQHLQ
WHUPVRIIL[HGFRVWVLQFRPSDULVRQZLWKWKHWZRFDUVWKDWZRXOGRWKHUZLVHKDYHEHHQRZQHG
,QGHHGWKHFKDQJHLQWKHGLIIHUHQFHEHWZHHQWKHGLVSRVDEOHLQFRPHVZKHQRZQLQJRQHRUWZR
FDUVLVRQDYHUDJHHTXDOWR'XWFKJXLOGHUVXQGHUDSURSRUWLRQDOFKDQJHLQIL[HGFRVWVLH
DOPRVWKDOIRILWVYDOXHXQGHUDIL[HGFKDQJH,WIROORZVWKDWDSURSRUWLRQDOFKDQJHLQIL[HGFRVWV
DOVRKDVDPXFKVPDOOHULPSDFWRQRZQHUVKLSRIWZRFDUVDVLVVKRZQLQWKHODVWWZRFROXPQVRI
7DEOH
7KHLQFUHDVHLQYDULDEOHFRVWVKDVDPXFKVPDOOHULPSDFW7KHUHDVRQLVRIFRXUVHWKDWWKHSULFH
HODVWLFLW\LVVPDOO7KHLPSDFWRQWKHSULFHV3 DQG3 LVWKHUHIRUHDOVROLPLWHG$VDFRQVHTXHQFH
WKHHIIHFWVRQFDURZQHUVKLSDQGRQWKHQXPEHURINLORPHWHUVGULYHQDUHPRGHVW+HQFHWKH
HIIHFWRIWKHFKDQJHLQIL[HGFRVWVGRPLQDWHVWKDWRIWKHVLPXOWDQHRXVLQWURGXFWLRQRIWKHFKDQJHV
LQIL[HGDQGYDULDEOHFRVWV,QDOOIRXUYDULDQWVFRQVLGHUHGWKHQHWUHVXOWRIWKHVKLIWLQWD[HVIURP
IL[HGWRYDULDEOHFRVWVLVDQLQFUHDVH LQWKHQXPEHURINLORPHWHUVGULYHQ,WVKRXOGWKHUHIRUHEH
FRQFOXGHGWKDWWKHHIIHFWVRIVKLIWLQJWKHEXUGHQRIFDUWD[HVIURPIL[HGWRYDULDEOHFRVWVGHSHQG
FUXFLDOO\RQWKHLULQIOXHQFHRQPXOWLSOHFDURZQHUVKLS
1RWHDOVRWKDWWKHPRGHOHVWLPDWHGLQWKLVSDSHUFRQFHUQVRQO\WKHFKRLFHEHWZHHQRQHRUWZR
FDUV$GGLWLRQDOHIIHFWVRQFDURZQHUVKLSPD\EHFDXVHGE\KRXVHKROGVZKRKDYHQRWRZQHGD
FDUWKXVIDUEXWGHFLGHWREX\RQHEHFDXVHRIWKHWD[SROLF\PHDVXUHDQGE\PXOWLSOHFDURZQLQJ
KRXVHKROGVGHFLGLQJWRLQFUHDVHWKHLUQXPEHURIFDUVHYHQIXUWKHU1RWHDOVRWKDWEHFDXVHZHXVHG
LPSXWHGYDOXHVRIIL[HGDQGYDULDEOHFRVWVZHZHUHXQDEOHWRFRPSXWHWKHSRVVLEOHHIIHFWVRIWKH
SROLF\PHDVXUHRQWKHVHYDULDEOHVWKURXJKWKHFKRLFHRIFDUEUDQGVDQGPDNHVTXDOLW\
&RQFOXVLRQ
,QWKLVSDSHUZHKDYHFRQVLGHUHGWKHGHPDQGIRUVHFRQGFDUVRQWKHEDVLVRIDJHQHUDOPRGHOIRU
PXOWLSOHFDURZQHUVKLSDQGXVH,QWKHPRGHOZHKDYHHVWLPDWHGWKHUHLVLPSHUIHFW
VXEVWLWXWDELOLW\EHWZHHQWKHXVHRIWKHWZRFDUVSRWHQWLDOO\RZQHGE\DKRXVHKROG$VD
FRQVHTXHQFHRZQLQJRQHFDULPSOLHVDORVVLQXWLOLW\WKDWPD\RXWZHLJKWKHORZHUIL[HGFRVWV
7RWDOGHPDQGIRUFDUNLORPHWHUVLVGHWHUPLQHGE\DFRPSRVLWHSULFHIRUFDUNLORPHWHUVWKDWOLHV
EHWZHHQWKHYDULDEOHFRVWVRIWKHWZRFDUV,IRQHFDULVRZQHGWKLVFRPSRVLWHSULFHLVDOZD\V
KLJKHUWKDQZKHQWZRFDUVDUHRZQHG7KHORZHUFRPSRVLWHSULFHWKDWLVWKHUHVXOWRIRZQLQJWZR
FDUVUHIOHFWVWKHEHQHILWVRIWKHVHFRQGFDUWRWKHKRXVHKROG7KHVHEHQHILWVDUHODUJHUZKHQ
VXEVWLWXWLRQEHWZHHQWKHNLORPHWHUVRIWKHWZRFDUVLVPRUHGLIILFXOW7KHFRVWVRIRZQLQJWZR
FDUVDUHKLJKHUIL[HGFRVWVZKLFKLPSOLHVWKDWOHVVPRQH\LVDYDLODEOHIRUFRQVXPSWLRQJRRGV
7KHSUHIHUUHGYHUVLRQRIRXUPRGHOLQGLFDWHVWKDWVXEVWLWXWLRQEHWZHHQWKHNLORPHWHUVGULYHQE\
WKHWZRFDUVLVUHODWLYHO\GLIILFXOWDQGWKHSULFHVHQVLWLYLW\RIWRWDOGHPDQGIRUFDUNLORPHWHUVLV
UHODWLYHO\ORZ7KHODWWHUUHVXOWLVLQOLQHZLWKRWKHUVWXGLHVRIWKHGHPDQGIRUFDUNLORPHWHUVHYHQ
WKRXJKWKHDEVROXWHYDOXHRIWKHSULFHHODVWLFLW\HVWLPDWHGKHUHLVRQWKHORZVLGHRIWKHUDQJH
UHSRUWHGLQWKHOLWHUDWXUH7KHPRGHOZDVHVWLPDWHGRQWKHEDVLVRILPSXWHGFRVWILJXUHVWKDWDUH
,WPD\DOVREHQRWHGWKDWZHKDYHQ¶WVFDOHGGLVSRVDEOHLQFRPHZKHQHVWLPDWLQJWKHPRGHO
EDVHGRQUHGXFHGIRUPUHJUHVVLRQVIRUIL[HGDQGYDULDEOHFDUFRVWV,GHDOO\RQHZRXOGGHULYH
VXFKHTXDWLRQVIURPDQH[SOLFLWPRGHORIFDUTXDOLW\FKRLFH,QVXFKDPRGHODKLJKHUTXDOLW\
LPSOLHVKLJKHUIL[HGDQGRUYDULDEOHFRVWV2XUFDUFRVWUHJUHVVLRQVZHUHLQWHUSUHWHGDVWKHUHVXOWV
RIVXFKDPRGHOEXWLWVGHYHORSPHQWLVRXWVLGHWKHVFRSHRIWKHSUHVHQWSDSHU$FRQVHTXHQFHRI
WKHSURFHGXUHIROORZHGKHUHLVWKDWLWLVQRWSRVVLEOHWRLQYHVWLJDWHWKHHIIHFWRIFKDQJHVLQIXHO
SULFHVRURWKHUWD[HVRQWKHFKRLFHRIFDUTXDOLW\DQGRQIL[HGDQGYDULDEOHFDUFRVWV
7KHPRGHOZHKDYHHVWLPDWHGHPSKDVL]HVWKHUHODWLRQVKLSEHWZHHQWKHGHPDQGIRUNLORPHWHUVRI
WKHWZRFDUV,QGHHGWKHPRGHOFDQEHLQWHUSUHWHGDVILUVWGHWHUPLQLQJWKHWRWDOGHPDQGIRUFDU
NLORPHWHUVDQGVXEVHTXHQWO\GLVWULEXWLQJWKLVWRWDORYHUWKHWZRFDUVRQWKHEDVLVRIWKHPDLQ
GULYHU¶VJHQGHUDQGWKHGLIIHUHQFHLQYDULDEOHFRVWVEHWZHHQWKHWZRFDUV7KHSDUDPHWHUWKDW
LQGLFDWHVWKHVHQVLWLYLW\RIWKLVGLVWULEXWLRQIRUWKHFRVWGLIIHUHQFHDOVRLQGLFDWHVWKHVXEVWLWXWLRQ
SRVVLELOLWLHV2WKHUKRXVHKROGYDULDEOHVVXFKDVLQFRPHDQGWKHQXPEHURIZRUNHUVGLGQRWDSSHDU
WRKDYHDVLJQLILFDQWLQIOXHQFHRQWKLVGLVWULEXWLRQ
:HXVHGWKHHVWLPDWHGPRGHOWRVLPXODWHWKHHIIHFWVRIDVKLIWRIWKHEXUGHQRIFDUWD[HVIURP
IL[HGWRYDULDEOHFRVWVDQGIRXQGVRPHZKDWVXUSULVLQJO\WKDWVXFKDVKLIWZLOOLQFUHDVHWKH
GHPDQGIRUFDUNLORPHWHUV7KHKLJKHUYDULDEOHFRVWVKDYHRQO\DOLPLWHGHIIHFWRQWKHGHPDQGIRU
NLORPHWHUVVLQFHWKHSULFHHODVWLFLW\LVORZLQDEVROXWHYDOXH+RZHYHUGHPDQGIRUVHFRQGFDUV
LVKLJKO\VHQVLWLYHWRFKDQJHVLQGLVSRVDEOHLQFRPHDQGWKLVPHDQVWKDWWKHGHFUHDVHLQIL[HGFDU
FRVWVKDVDUHODWLYHO\ODUJHHIIHFWRQWKHRZQHUVKLSRIVHFRQGFDUV7KHLQFUHDVHLQWKHGHPDQGIRU
NLORPHWHUVWKDWUHVXOWVIURPWKHODUJHUQXPEHURIVHFRQGFDUVRXWZHLJKVWKHHIIHFWRIWKHLQFUHDVH
LQYDULDEOHFRVWV
5HIHUHQFHV
%ODFNRUE\&'3ULPRQWDQG555XVVHOO'XDOLW\6HSDUDELOLW\DQG)XQFWLRQDO
6WUXFWXUH$PHULFDQ(OVHYLHU1HZ<RUN
'HDWRQDQG0XHOOEDXHU(FRQRPLFVDQG&RQVXPHU%HKDYLRU&DPEULGJH8QLYHUVLW\3UHVV
&DPEULGJH
(VSH\0*DVROLQH'HPDQG5HYLVLWHG$Q,QWHUQDWLRQDO0HWD$QDO\VLVRI(ODVWLFLWLHV
(QHUJ\(FRQRPLFV )LVKHU)0DQG.6KHOO7DVWHDQG4XDOLW\&KDQJHLQWKH3XUH7KHRU\RIWKH&RVWRI
/LYLQJ,QGH[LQ=*ULOOLFKHVHG3ULFH,QGH[HVDQG4XDOLW\&KDQJH+DUYDUG
8QLYHUVLW\3UHVV&DPEULGJH0DSS
*RORE7)6.LPDQG:5HQ+RZ+RXVHKROGV8VH'LIIHUHQW7\SHVRI9HKLFOHV$
6WUXFWXUDO'ULYHU$OORFDWLRQDQG8VDJH0RGHO7UDQVSRUWDWLRQ5HVHDUFK$ *RORE7)DQG0*0F1DOO\$0RGHORI$FWLYLW\3DUWLFLSDWLRQDQG7UDYHO
,QWHUDFWLRQ%HWZHHQ+RXVHKROG+HDGV7UDQVSRUWDWLRQ5HVHDUFK% *UDKDP'-DQG6*ODLVWHU7KH'HPDQGIRU$XWRPRELOH)XHO$6XUYH\RI(ODVWLFLWLHV
-RXUQDORI7UDQVSRUW(FRQRPLFVDQG3ROLF\ +HQVKHU'$$Q(FRQRPHWULF0RGHORI9HKLFOH8VHLQWKH+RXVHKROG6HFWRU
7UDQVSRUWDWLRQ5HVHDUFK%
-RQJ*&GH$Q,QGLUHFW8WLOLW\0RGHORI&DU2ZQHUVKLSDQG3ULYDWH&DU8VH(XURSHDQ
(FRQRPLF5HYLHZ -RQJ*&GH$0LFUR(FRQRPLF0RGHORIWKH-RLQW'HFLVLRQRQ&DU2ZQHUVKLSDQG&DU
8VHLQ0HWKRGVIRU8QGHUVWDQGLQJ7UDYHO%HKDYLRULQWKHV 3URFHHGLQJV
&RQIHUHQFH,QWHUQDWLRQDOVXU OHV&RPSRUWHPHQWV GH'HSODFHPHQWV4XHEHFSS
0DQQHULQJ)/ $Q(FRQRPHWULF$QDO\VLVRI9HKLFOH8VHLQ0XOWLYHKLFOH+RXVHKROGV
7UDQVSRUWDWLRQ5HVHDUFK $ 0DQQHULQJ)/DQG.7UDLQ5HFHQW'LUHFWLRQVLQ$XWRPRELOH'HPDQG0RGHOOLQJ
7UDQVSRUWDWLRQ5HVHDUFK%
0DQQHULQJ)/DQG&:LQVWRQ$'\QDPLF(PSLULFDO$QDO\VLVRI+RXVHKROG9HKLFOH
2ZQHUVKLSDQG8WLOL]DWLRQ5$1'-RXUQDORI(FRQRPLFV
1HDU\-3DQG.:65REHUWV7KH7KHRU\RI+RXVHKROG%HKDYLRXUXQGHU5DWLRQLQJ
(XURSHDQ(FRQRPLF5HYLHZ
5RXZHQGDO-DQG)GH9ULHV7KH7D[DWLRQRI'ULYHUVDQGWKH&KRLFHRI&DU)XHO7\SH
(QHUJ\(FRQRPLFV 7UDLQ.4XDOLWDWLYH&KRLFH$QDO\VLV0,73UHVV&DPEULGJH0D
7UDLQ.DQG0/RKUHU9HKLFOH2ZQHUVKLSDQG8VDJH$Q,QWHJUDWHG6\VWHPRI
'LVDJJUHJDWH'HPDQG0RGHOV3DSHUSUHVHQWHGDW75%$QQXDO0HHWLQJ
9HUEHHN0$*XLGHWR0RGHUQ(FRQRPHWULFV :LOH\&KLFKHVWHU