P h v= <19/ <1:/ <1;/ <144/ <145/ <149/ 4<14/ 4<15/ 4<16/ 4<1:/ 4<143/ 4<144/ 4<145/ 4<147 fkdqjh lq wkh f dslwdo vwxfwxh gr hv qrw dhfw wkh lvn ri wkh dvvhwv/ dqg vr @rre wkh Vhfxlw P dnh w O lq h / dqg dvvxplqj s 6 k h wr w do pdnh w ydoxh ri rxwvwdqglqj ghew lv '633> vwr fn/ wkh rxwvwdqglqj pdnhw ydoxh lv '83 43> kxv Orhohl*v zh ljkwhg dyhdjh frvw ri fdslwdo lv= '833> d frvw ri gh ew f dslwdo ri ;(= hpdlq wkh vdph1 w kh f rpp rq d frvw ri htxlw fdslwdo ri 48( exvlqhvv lvn lv xqfkdqjh g/ wkh frpsdq *v zhljkwhg dyhdjh frvw ri fdslwdo zloo qrw f kdqjh1 kh qdqf ldo vwxfwxh / krzhyh/ kdv fkdqjhg= frpprq vwr fn lv qrz zrwk '583> ydoxh ri ghew dqg wkh f rvw ri ghew fdslwdo dh xqfkdqjhg/ zh fdq xvh wkh vdph htxdwlrq dv lq sdw +d, wr fdofxodwh wkh qhz frvw ri htxlw fdslwdo/ e^ä + dqg vr e^ä + lvn0ih h ghew/ @rre Sdfwlfh Sreohpv Zlwk Vroxwlrqv Ir rslf 4: Sreohpv= Ehdoh Vroxwlrqv= EP <19 d1 @rre @ +3,+433, +=5,+73, +4=5,+533, 43373533 @ =:6 e1 D f1 Xvlqj @ 8( dqg @rre @ s @rre +6 Ã s, @ 46(> @rre @ =38 =:6 +=46 Ã =38, @ =43; r 43=;( zloo EP <1: d1 wlphv > zlwk r > zlwk Ir = @rre r @ 633 > 633 > 833> +=3;, 833> 633> 833> +=48, @rre r @ =457 r 45=7( e1 Ehfdxvh = D vvx pl qj wk d w wk h pdnh w = =457 @ 633> 633> 583> +=3;, 583> e^ä + 633> 583> EP <1; d1 Zlwk @ =4::> r 4:=:(= @+H@ = khhirh/,e^ä + sjj_ @ =:+=;, @ =89 e,es @ =;+4 =9,@4=5; SÅe6 @ =9+4=5, @ =:5 e1 @rre @ =8+=89, =6+4=5;, =5+=:5, @ =;4 4
Vwloo dvvxplqj lvn0ihh ghew/ zklfk lpsolhv e^ä + zh wkh Vhfxlw P dnh w O lq h / kdyh lvn ghew/ wkhdw ri d frxs g*ì wdw phdqv wkdw wkh h{shfwhg dovr lqf hdvh wkh glvfrxqw dwh/ exw rqo li lw lqf hdvhv pdnhw lvn1 h{s hfwh g f dvk rz lv =58+3, lvn dv wkh h vw ri wkh frpsdq *v exvlqhvv/ S @ '4;:> rz lv ohvv wkdq '583> wkhdw frxog d1 Vlqfh wkh lvn ri d g kroh lv xqolnho wr eh pdnhw h odwhg/ zh f dq xvh wkh vdph glvfrxqw dwh dv ir sr gxflqj zhoov1 kxv/ xvlqj wkh Vhfxlw P dnhw Olqh / dqg nqrzlqj wkdw zh kdyh Ã'758> Ã'6> @rre @+H@,e^Ä + =;4 @ =9e^Ä + @4=68= f1 Xvlqj @rre @ s @rre +6 Ã s, sjj_ @ =3: =89+ =48 Ã =3:, @ =448> r e,es @ =3: 4=5;+ =48 Ã =3:, @ =4:5> r SÅe6 @ =3: =:5+ =48 Ã =3:, @ =45;> r 44=8( 4:=5( 45=;( g1 Zlwk s JJ_ @ =6+=5, =:+=;, @ =95 dqg e,es @ =5+=5, =;+4 =9,@4=65 dqg SÅe6 @ =7+=5, =9+4=5, @ =;3 dqg sjj_ @45=3( e,es @4:=9( SÅe6 @46=7( EP <144 d1 kh fdvk = kh e1 kh =:8+583>,> r 833 = Dvv xpl q j wk dw wk h f dv k rz lv d e rx w d v EP <145 4;:> 833 4=45 @ '49:> 744?J6?@, @ =39 =<+=3;, @ =465 > r 46=5( +4?J6?@,, @+4 oe@,,+4?s,@ J?, e1 oe@, @ 4=465 4=37 Ã 4@ =3;;8/ r;=;8( Q S @ Ã43 Q S r @ Ã=758;/ Q S 2 @ Ã43 f[ ' D[ ' Q S r 2 @ Ã6=5557/ 6 4=5;;8 @ Ã436+6=4<47, 5 4=5;;8 @ Ã435+6=6;;;, 555> 733 5
hfwhg lqf rph lv =5+3, lvfrxqwlqj dw ;=;8( ri '6 irp Zhoo 4> dqg =5+3, '8> '6> irp Zhoo 5= Zhoo 4> rqh fdq fhwdlqo qg d glvfrxqw dwh +dqg kh qfh d ixgjh idf wr, w kd w / d s solhg wr f dvk rzv s h hd ir 43 zloo lhog wkh f rhf w QS ri '8> pl od o / i r Zh o o 5> rqh fdq fh wdlqo qg wkh dssrsldwh ixgjh idfwr1 Krzhyh/ wkhvh ixgjh idfwrv zloo eh glh hqw1 Vs hflfdoo / Zhoo 5 kdyh d vpdooh ixgjh idfwr e hf dxvh lwv fdvk rzv dh prh g lv wd q w + z lw k prh g l vwd q w f d vk rz v/ d vpdooh dgglwlrq wr wkh glvfrxqw dwh kdv d odjh lpsdfw rq shvh qw ydoxh,1 Dw w @5> dh wzr s rvvleoh ydoxh v ri wkh srmhfw*v QS +doo qxpe hv dh lq ploolrqv,= ghew lv dgmxvwhg wr pdlqwdlq wkh 73( Q S @ zh xvh wkh edvlf ghqlwlrq ri DS= kh irhfdvwhg wd{ vklhog lv +=68,+=3:,+733> klv jlyhv whvw lv qrw vxffhvvixo @ Edvh fdvh Q S @ whvw lv vxffhvvixo @ Ã wkh q wkh Plohv0H}}h o irpxod lv dssrsldwh= fdvh Q S '<> hd1 kxv/ k lv lv h vv h qw l do o wk h vd ph d qv zh d v zh jr w i r sdw +e,/ f rq v lghlqj wkh pdjqlwxgh v ri wkh fdvk rz qxpe hv1 f1 H{s jlyhv =;+6, @ '5=7 ploolrq =;+5, @ '4=9 ploolrq Q S r @ Ã435=7+9=7935, @ 8=8378> Q S r 2 @ Ã43 4=9+;=4659, @ 6=3455> 837> 833 345> 533 g1 Ir ploolrq hdv/ 837> 833= Vl zloo EP <149 wkhh Q S li 2 Q S li 2 3 Ã8 =: =45 @ =;66 khhirh / dw w @3> =73+3, =93+ =;66, Q S f @Ã=8 @ Ã=578 4=73 2 / r Ã'578> EP 4<14 d1 Li dwlr/ @ O ( 4 4 ( 4 =43 @ =43 Ã =7+=3:,+=68, @ =3;<< 4 =3: Ã4>> ;8> =3;<< @ 838 Ã'87> e1 Khh Edvh S + wd{ vklhog, Ã4>> ;8> @ Ã'483> =43,> r <> S wd{ vklhog @ ;33 sh ;33 4 =43 @'433>:7; =43 4 =3: Ã483> 433> :7; @ Ã'7<> 585 6
klv wkh PP irpxod lv dssrsldwh= Q S @ wkh ghew lv {hg/ dqg vr wkh wd{ vklhog rq ghew lv dvvxphg frqvwdqw dqg s hs hwxdo1 lpsolhv Edvh fdvh Q S @ vh f d vh Q S klv lv h vvh qwldoo wkh vdph dqvzh dv zh jrw ir sdw +f,1 +wd{ vklhog, kh lpphgldwh vrxfh ri ixqgv +l1h1/ erwk wkh srs rwlrq e rrzh g dqg wkh h{s hf whg hwxq rq wkh vwr fnv vrog, lv lh oh ydqw1 kh srmhfw zrxog qrw eh dq prh ydoxdeoh li wkh xqlyhvlw vrog vwr fn v rh lqj d orzh hwxq1 Li errzlqj lv d }hr0qs df wlylw ir d wd{0 h{hpsw xqlyhvlw / wkhq edvh fdvh QS htxdov DS/ dqg wkh dgm xvwhg f rvw ri fdslwdo QS lv qhjdwlyh> wkh xqlyhvlw vkrxog qrw lqyhvw1 Zh pdnh wkhh dgmxvwphqwv wr wkh edodqfh vkh hw= h txdov wkh rss rwxqlw frvw ri fdslwdo zlwk doo h txlw qdqflqj1 Khh/ edvh fdvh 0 L j qrh ghihhg wd{h v> wkhvh dh dq dff rxqwlqj hqw dqg hshvhqw qh lwkh d oldelolw qr d vrxfh ri ixqgv 0Qhw rxw dff rxqwv sd deoh djdlqvw f xhqw dvvhwv 0Xvh wkh pdnhw ydoxh ri htxlw + :=79 Å Qrz wkh ljkw0kdqg vlgh ri wkh edodqf h vkhhw +lq wkrxvdqgv, or rnv olnh = Vk r w0 wh p gh ew ':8> Orqj0whp ghew 53;> Vkdhkrogh htxlw 676> r w d o '95:> kh diwh0wd{ zhljkwhg dyh djh frvw ri fdslwdo i rpxod/ zlwk rqh hohphqw ir hdfk vrxfh ri ixqglqj/ lv V O H I f1 Khh @ +4 Ã O, @ =43 ^4 Ã =68+ =7,` @ =3;93 Ã4>> ;8> =3;93 @ Ã'44 > 95; g1 Khh Ed S S wd{ vklhog @ Ã4>> ;8> @ Ã'483> =43 =68+ =3:,+733>, @'473> =3: Ã483> 473> @ Ã'43> EP 4<15 EP 4<16 ploolrq '79, 933 933 493 693 @ (37A +4 Ã S, Ã (3A +4 Ã S, Ã :8> 933 53;> 933 676> 493 @ =39+4 Ã =68, =3; +4 Ã =68, =48 95:> 693 95:> 693 95:> 693 @ =337:33 =34:5<3 =3;537< @ =4373> r 43=73( 7
Edvh fdvh @ hew dw Lqwh hvw S \h d Vwdw r i \h d Lqwhhvw d{ Vklhog +d{ Vklhog, Qr wh wk h i r o orz l qj = 0kh frvwv ri ghew dqg htxlw dh qrw ;=8 dh sdlg h yh hd/ qrw mxvw dw lvvxh1 4< '436> '<6> hvs hf wlyho 1 kh vh jxh v dvvxph wkh lvvxh frvwv 0kh idfw wkdw Exqvhq fdq qdqfh wkh hqwlh frvw ri wkh srmhf w zlwk gh ew lv lhohydqw1 kh frvw ri fdslwdo gr hv qrw gh sh qg rq wkh lpphgldwh vrxf h ri ixqgv> zkdw pdwwhv lv wkh srmhfw*v frqwlexwlrq wr wkh p*v ryhdoo e rrzlqj s rzh1 0kh srmhfw lv h {sh fwhg wr vxss rw ghew lq s hs hwxlw 1 kh idfw wkdw wkh vw gh ew lvvxh lv ir 53 lv lh ohydqw1 rqo Dvvxph wkh srmh fw kdv wkh vdph exvlqhvv lvn dv wkh p*v rwkh dvvhwv1 Ehfdxvh lw lv d s hshwxlw / zh fdq xvh wkh p*v zhljkwhg0dyhdjh frvw ri fdslwdo +li zh ljqrh lvvxh f rvwv,1 Dw klv h{fh hgv wkh wdqvdfwlrq f rvw ri hlwkh qdqflqj dowh qdwlyh/ vr zh nqrz wkh srmhf w lv d jr r g rqh1 Zkdw de rxw qdqf lqjb kh lvvxhv dh= Vw r f n l v vxh = Erqg lvvxh = hew lv fohdo fkh ds h0srm hfw QS qhw ri lvvxh frvwv lv hgxfhg wr '586> y h / li ghew lv xvh g/ wkh p*v ghew dwlr zloo e h deryh wdjhw/ dqg prh h t xl w zloo kdyh wr e h dlvhg odwh1 Li wklv fdq eh grqh e hwdlqlqj hdqlqjv/ wkhq wkh h dh qr rwkh lvvxh frvwv wr frqvlgh 1 Li vwrf n zloo kdyh wr e h lvvxh g wr hjdlq wkh wdjhw ghew dwlr/ dq dgglwlrqdo lvvxh frvw lv lqfxhg1 D f dhixo hvwlpdwh ri wkh lvvxh frvwv dwwlexwdeoh wr wklv srmh fw zrxog htxlh d fr psdl v rq r i E xq vh q *v q dqfldo s od q z l wk d v f r psdh g w r zlwkrxw wklv srmh fw1 EP 4<1: d1 Ã4 933 4=45 :33 4=45 2 @<6=:8> r :83 4 633 57 :=53 9=9: 5 483 45 6=93 6=3< <6=:8 9=9: 6=3< @ 436=8> r 833 EP 4<143 dqg shfhqw hdv @ +4Ã S, ( @ +4Ã =67, +=3:, +=7, +=47, +=9, @ =4358 H > 463> QS @Ã4>> =4358 @ '59;> =38 +4> >, @ '83> =348 +4> >, @ '48> + '59;> Ã'48>,= Krzh EP 4<144 8
wkh wh{w zh nqrz wkdw S ri d1 Irp È @ +4Ã, ( Ã S H Ã S @ H@ È @ +4Ã, ( 4 Ã S 4 Ã @ S @ È @ +4Ã =67, +=48, =88 =78 +4=3<, 4 Ã =67+=88, 4 Ã =67+ =88, @ =9:36 e1 Xvlqj wkh Vhfxlw Pdnhw Olqh/ zh fdofxodwh wkh rssrwxqlw frvw ri fdslwdo ir Vskdjqxp*v dvvhwv= È @ s È +6 Ã s, È @ =3< =9:36+=3;8, @ =47:> r 47=:( f1 Iroorzlqj PP*v rljlqdo dqdo vlv dqg frqvlghlqj rqo frsrdwh wd{hv/ zh kdyh wkdw= @ +4 Ã S O, @ =47: ^4 Ã =67 +=88,` @ =44<8> r derxw 45( klv pdwfkhv wkh frqvxowdqw*v hvwlpdwh ir wkh zhljkwhg dyhdjh frvw ri fdslwdo1 EP 4<145 lvdjhh1 kh fdofxodwlrqv ri Edqnhv vw +zkhh gr wkh jhw wkhvh qdphv irp/ dq zd B, dvvxph wkdw wkh frvw ri ghew zloo hpdlq frqvwdqw/ zklfk lv d jrrg dvvxpswlrq/ exw wkh dovr dvvxph wkdw wkh frvw ri htxlw fdslwdo zloo qrw fkdqjh hyhq wkrxjk wkh p*v qdqfldo vwxfwxh kdv fkdqjhg> wklv lv d yh srr dvvxpswlrq1 EP 4<147 d1 Slqflsdo dw Slqflsdo Lqwhhvw Qhw Fdvk \hd Vwdw ri \hd Uhsd phqw Lqwhhvw ohvv d{ Iorz rq Ordq 4 8=3 6<:=8 583=3 495=8 893=3 5 7935=8 74:=7 563=4 47<=9 89:=3 6 74;8=4 76;=5 53<=6 469=3 8:7=5 7 6:79=< 793=5 4;:=6 454=: 8;4=< 8 65;9=: 7;6=5 497=6 439=; 8<3=3 9 5;36=8 83:=6 473=5 <4=4 8<;=7 : 55<9=5 865=: 447=; :7=9 93:=6 ; 4:96=8 88<=6 ;;=5 8:=6 949=9 < 4537=5 8;:=6 93=5 6<=4 959=7 43 949=< 949=< 63=; 53=3 969=< khhirh/ ordq @ 893 4+4Ã =68, + =3;, ÄÄÄ 969=< 4+4Ã =68, +=3;, f @'7>863> dqg doxh ri vxevlg @'8>> Ã '7> 863> @ '7:3> 9
e1 \hv1 kh ydoxh ri wkh vxevlg phdvxhv wkh dgglwlrqdo ydoxh wr wkh p irp d jryhqphqw ordq dw 8(> dwkh wkdq xvlqj dq xqvxevlgl}hg ordq dw 43(= Lw vkrxog wkhhirh fdofxodwh DS/ lqfoxglqj S +wd{ vklhogv, rq wkh xqvxevlgl}hg ordq/ dqg wkhq dgg lq wkh ydoxh ri wkh vxevlg 1 f1 Djdlq/ fdofxodwh DS dvvxplqj qrpdo qdqflqj +63( ri pdnhw ydoxh, dqg wkhq dgg lq wkh ydoxh ri wkh vxevlg 1 Ri frxvh/ li wkh vxevlgl}hg ordq wdnhv wkh p deryh lwv wdjhw ghew dwlr/ lw zrxog qhhg wr hgxfh lwv xqvxevlgl}hg errzlqj1 :