&DW1#1R1#98043;4

2ZQHUV#0DQXDO'XDO03RZHUHG

6FLHQWLILF#&DOFXODWRU

&RPPRQ#7ULJRQRPHWULF#)RUPXODV

65-1081.fm Page 1 Monday, November 22, 1999 9:38 AM

5 #4

6 FRPPRQ#DQG#QDWXUDO#ORJDULWKPV

DGYDQFHG#VWDWLVWLFV#IXQFWLRQV

WULJRQRPHWULF#IXQFWLRQV

ORJLF#FDOFXODWLRQV

,QGHSHQGHQW#0HPRU\## OHWV#\RX#VWRUH#VXE0WRWDOV# LQWR#PHPRU\#DQG# WKHQ#DGG# WR#RU# UHFDOOWKH#PHPRU\#IRU#DGGLWLRQDO#FDOFXODWLRQV1

)OLS02XW#6WDQG##OHWV#\RX#WLOW#WKH#GLVSOD\#IRUEHWWHU#YLHZLQJ1

$XWR#3RZHU02II##VDYHV#EDWWHU\#OLIH#E\#VKXW0WLQJ#RII#DIWHU#DERXW#;#PLQXWHV#DIWHU#\RX#ILQLVKXVLQJ#LW1

$OJHEUDLF#2SHUDWLRQ##OHWV#\RX#HQWHU#FDOFX0ODWLRQV#H[DFWO\#DV#WKH\#DUH#ZULWWHQ1

0DQ\# RI# \RXU# FDOFXODWRUV# NH\V# KDYH# PRUHWKDQ# RQH# IXQFWLRQ1# 7R# SHUIRUP# WKH# IXQFWLRQSULQWHG#RQ#WKH#NH\/#SUHVV#WKH#NH\1#7R#XVH#WKHIXQFWLRQ#SULQWHG#LQ#\HOORZ#DERYH#WKH#NH\/#ILUVWSUHVV# #WKHQ#SUHVV#WKH#NH\1

1RWH=# 7KLV#PDQXDO# JLYHV# FRPSOHWH# LQVWUXF0WLRQV# RQ# KRZ# WR# XVH# \RXU# FDOFXODWRUV# IXQF0WLRQV1#+RZHYHU/#LW#GRHV#QRW#WHDFK#PDWK1#5HIHUWR# \RXU# ORFDO# OLEUDU\# IRU# ERRNV# DERXW# EDVLFPDWK#DQG#WULJRQRPHWULF#IXQFWLRQV1

,19

65-1081.fm Page 3 Monday, November 22, 1999 9:38 AM

7&217(176

%DVLF#,QIRUPDWLRQ# 111111111111111111111111111111111111 #8'LVSOD\#)RUPDWV#1111111111111111111111111111111111 #8$OJHEUDLF#(QWU\#0HWKRG# 1111111111111111111111 #9&DOFXODWRU#0RGHV#11111111111111111111111111111111 #:

2SHUDWLRQ# 111111111111111111111111111111111111111111111111 #437XUQLQJ#WKH#&DOFXODWRU#2Q#DQG#2II# 1111 #43&RUUHFWLQJ#(QWU\#(UURUV# 111111111111111111111 #43&DOFXODWLRQ#(UURUV# 11111111111111111111111111111 #438VLQJ#3DUHQWKHVHV# 111111111111111111111111111 #448VLQJ#0HPRU\# 1111111111111111111111111111111111 #45

)XQFWLRQ#5HIHUHQFH# 1111111111111111111111111111111 #46([DPSOHV# 111111111111111111111111111111111111111111111111 #53

0L[HG#$GGLWLRQ/#6XEWUDFWLRQ/#0XOWLSOLFDWLRQ/#'LYLVLRQ# 1111111111111111111111 #53&RQVWDQW#&DOFXODWLRQV#11111111111111111111111 #53/RJLFDO#&DOFXODWLRQV#11111111111111111111111111 #543RZHUV#DQG#5RRWV# 1111111111111111111111111111 #573HUFHQWDJH#&DOFXODWLRQV#1111111111111111111 #57'HJUHH25DGLDQV2*UDGV#&RQYHUVLRQV# #58'HJUHHV20LQXWHV2#6HFRQGV#&RQYHUVLRQV#11111111111111111111111111111111111111 #593RODU25HFWDQJXODU#&RQYHUVLRQV# 11111111 #5;&RPSOH[#1XPEHUV# 1111111111111111111111111111 #63/RJ#1111111111111111111111111111111111111111111111111111 #65'HFLPDO2+H[DGHFLPDO22FWDO2%LQDU\#&DOFXODWLRQV#DQG#&RQYHUVLRQV# 1111111111 #656WDWLVWLFV#&DOFXODWLRQV#11111111111111111111111 #67

&DOFXODWLRQ#5DQJH# 111111111111111111111111111111111 #69&DUH# 111111111111111111111111111111111111111111111111111111111 #73

5HSODFLQJ#WKH#%DWWHULHV# 11111111111111111111 #746SHFLILFDWLRQV# 1111111111111111111111111111111111111111 #75

65-1081.fm Page 4 Monday, November 22, 1999 9:38 AM

8%$6,,1)250$7,21#

',63/$

9$/*(%5$,(175

:,Q#VRPH#FDVHV/# WKHVH# UXOHV#PLJKW#FDXVH# WKHFDOFXODWRU#WR#JLYH#\RX#D#UHVXOW#RWKHU#WKDQ#ZKDW\RX#H[SHFW1#)RU#H[DPSOH/#\RX#NQRZ# WKDW# WKHVTXDUH#RI#D#QHJDWLYH#QXPEHU# LV#DOZD\V#SRVL0WLYH1# +RZHYHU/# LI# \RX# HQWHU# # #

/#'(*#

;6'7KH#FDOFXODWRU#LV#LQ#WKH#VWDWLVWLFV#PRGH1#+ # ,

,19

43

23(5$7,21#

7851,1*#7+(#&$/&8/$725#21#$1'#2))#3UHVV#21#+&2&(,#WR#WXUQ#RQ#WKH#FDOFXODWRU1#

,I#\RX#GR#QRW#SUHVV#D#EXWWRQ#IRU#DERXW#9;#PLQ0XWHV/#WKH#FDOFXODWRU#DXWRPDWLFDOO\#WXUQV#RII1#7RWXUQ#LW#RII#VRRQHU/#SUHVV#2))1

1RWH=#7KH#FDOFXODWRU#ORVHV#DQ\#SHQGLQJ#FDOFX0ODWLRQV#ZKHQ#LW#WXUQV#RII1#+RZHYHU/#DQ\#PHPR0U\#FRQWHQWV#DUH#VDYHG1

&255(&7,1*#(175

44

SHUIRUP# D# FDOFXODWLRQ# WKDW# UHVXOWV# LQ# DYDOXH#RI#4# #43433#RU#ODUJHU1

WU\#WR#GLYLGH#D#QXPEHU#E\#]HUR1

WU\#WR#FDOFXODWH#WKH#VTXDUH#URRW#RI#D#QHJD0WLYH#QXPEHU1

+LQ#VWDWLVWLFV#FDOFXODWLRQ#PRGH,#DWWHPSW#WRREWDLQ#D#VLQJOH0YDULDEOH#FDOFXODWLRQ#ZLWK0RXW#ILUVW#HQWHULQJ#GDWD1

H[FHHG#6#OHYHOV#RI#QHVWHG#SDUHQWKHVHV#LQVWDWLVWLFV# PRGH/# RU# XVH# PRUH# WKDQ# 48RSHQ#SDUHQWKHVHV1

LQ#VWDWLVWLFV#FDOFXODWLRQ#PRGH/# WU\# WR# ILQG/# /# /#ZKHQ#Q# #31

H[FHHG#D#IXQFWLRQV#FDOFXODWLRQ#UDQJH1

7R#FOHDU#DQ#HUURU/#SUHVV# 1

86,1*#3$5(17+(6(67KH#FDOFXODWRU#SHUIRUPV#FDOFXODWLRQV#DFFRUG0LQJ# WR# WKH#SULRULW\#RI# WKH# IXQFWLRQV#\RX#HQWHU+VHH# $OJHEUDLF# (QWU\# 0HWKRG# RQ# 3DJH 9,1

45

86,1*#0(025

46

)81&7,21#5()(5(1&(#

7KLV#VHFWLRQ#SURYLGHV#D#EULHI#GHVFULSWLRQ#RI#DOOWKH#FDOFXODWRUV#IXQFWLRQV1

47

&KDQJHV#WKH#VLJQ#RI#WKH#GLVSOD\HG#QXPEHU1

7RWDOV#DOO#SHQGLQJ#RSHUDWLRQV#DQG#DGGV#WKH#UHVXOW#WR#PHPRU\1

5HFDOOV#WKH#YDOXH#VWRUHG#LQ#PHPRU\1

# 5HSODFHV#WKH#PHPRU\#FRQWHQWV#ZLWK#WKH#GLVSOD\HG#QXPEHU1

#([FKDQJHV#WKH#GLVSOD\HG#QXPEHU#ZLWK#WKH#QXPEHU#LQ#PHPRU\1

6ZLWFKHV#EHWZHHQ#GHJUHHV/#UDGLDQV/#DQG#JUDGV#IRU#WULJRQRPHWULF#IXQFWLRQV1

#

6ZLWFKHV#EHWZHHQ#GHJUHHV/#UDGLDQV/#DQG#JUDGV#IRU#WULJRQRPHWULF#IXQFWLRQV>#FRQYHUWV#WKH#GLVSOD\HG#QXPEHU#EHWZHHQ#WKHVH#GLIIHUHQW#XQLWV1

3UHVV#EHIRUH#D#WULJRQRPHWULF#IXQFWLRQ#WR#SHUIRUP#WKH#K\SHUEROLF#IRUP#RI#WKH#IXQFWLRQ1

#3UHVV#EHIRUH#D#WULJRQRPHWULF#IXQFWLRQ#WR#SHUIRUP#WKH#DUF#K\SHUEROLF#IRUP#RI#WKH#IXQFWLRQ1

&DOFXODWHV#WKH#VLQH#RI#WKH#GLVSOD\HG#QXPEHU1

#&DOFXODWHV#WKH#LQYHUVH#+DUF,#VLQH#RI#WKH#GLVSOD\HG#QXPEHU1

48

&DOFXODWHV#WKH#FRVLQH#RI#WKH#GLVSOD\HG#QXPEHU1

#&DOFXODWHV#WKH#LQYHUVH#+DUF,#FRVLQH#RI#WKH#GLVSOD\HG#QXPEHU1

&DOFXODWHV#WKH#WDQJHQW#RI#WKH#GLV0SOD\HG#QXPEHU1

#&DOFXODWHV#WKH#LQYHUVH#+DUF,#WDQJHQW#RI#WKH#GLVSOD\HG#QXPEHU1

&DOFXODWHV#WKH#QDWXUDO#ORJ#EDVH#H#RI#WKH#GLVSOD\HG#QXPEHU1

#&DOFXODWHV#WKH#DQWLORJDULWKP#EDVH#H#RI#WKH#GLVSOD\HG#QXPEHU1

#&DOFXODWHV#WKH#DQWLORJDULWKP#EDVH#43#RI#WKH#GLVSOD\HG#QXPEHU1

&DOFXODWHV#WKH#ORJ#EDVH#43#RI#WKH#GLV0SOD\HG#QXPEHU1

&DOFXODWHV#WKH#VTXDUH#RI#WKH#GLVSOD\HG#QXPEHU1

# # &DOFXODWHV#WKH#\#SRZHU#RI#[1

#&DOFXODWHV#WKH#VTXDUH#URRW#RI#WKH#GLV0SOD\HG#QXPEHU1

#&DOFXODWHV#WKH#FXEH#URRW#RI#WKH#GLV0SOD\HG#QXPEHU1

49

# &DOFXODWHV#WKH#UHFLSURFDO#RI#WKH#GLV0SOD\HG#QXPEHU1

2SHQV#D#SDUHQWKHWLFDO#H[SUHVVLRQ1

&ORVHV#D#SDUHQWKHWLFDO#H[SUHVVLRQ1

#&KDQJHV#WKH#GLVSOD\HG#QXPEHU#IURP#IORDWLQJ#GHFLPDO#WR#HQJLQHHULQJ#+VFLHQ0WLILF,#QRWDWLRQ1

&RQYHUWV#D#QXPEHU#HQWHUHG#DV#''1006666#+GHJUHHV/#PLQXWHV/#DQG#VHFRQGV,#WR#VWDQGDUG#GHFLPDO#QRWD0WLRQ1

#&RQYHUWV#D#GHFLPDO#QXPEHU#WR#GHJUHH0PLQXWH0VHFRQG#QRWDWLRQ#+''1006666,1

(QWHUV#D#SURSHU#RU#LPSURSHU#IUDFWLRQ1

# # 7RJJOHV#EHWZHHQ#D#PL[HG#QXPEHU#DQG#DQ#LPSURSHU#IUDFWLRQ1

&RQYHUWV#WKH#[#DQG#\#YDOXHV#HQWHUHG#ZLWK#WKH# /# /#DQG# #NH\V#LQWR#SRODU#FRRUGLQDWHV#+U#DQG#q ,#DQG#GLVSOD\V#WKH#UDGLXV1#3UHVV# #

#WR#VHH#WKH#DQJOH1

# 6ZDSV#WKH#LPPHGLDWH#SHQGLQJ#WRWDO#ZLWK#WKH#QXPEHU#RQ#WKH#GLVSOD\1

4:

# #

,Q#WKH#VWDQGDUG#FDOFXODWLRQ#PRGH/#UHFDOOV#RU#HQWHUV#HLWKHU#WKH#DQJOH#+IRU#D#SRODU#FRRUGLQDWH,#RU#WKH#\#YDOXH#+IRU#UHFWDQJXODU#FRRUGLQDWHV,1

# # 3HUIRUPV#SHUFHQWDJH#FDOFXODWLRQV1

# (QWHUV#WKH#YDOXH#IRU#SL1

# 6HOHFWV#WKH#IORDWLQJ#GHFLPDO#PRGH1

# &RQYHUWV#WKH#GLVSOD\HG#QXPEHU#WR#ELQDU\#DQG#VHOHFWV#WKH#ELQDU\#PRGH1

# &RQYHUWV#WKH#GLVSOD\HG#QXPEHU#WR#RFWDO#DQG#VHOHFWV#WKH#RFWDO#PRGH1

#&RQYHUWV#WKH#GLVSOD\HG#QXPEHU#WR#GHFLPDO#DQG#VHOHFWV#WKH#GHFLPDO#PRGH1

#6SHFLILHV#WKH#QXPEHU#RI#GHFLPDO#GLJLWV#LQ#WKH#PDQWLVVD#RI#WKH#GHFLPDO#FDOFXOD0WLRQ#UHVXOWV1

#&RQYHUWV#WKH#GLVSOD\HG#QXPEHU#WR#KH[DGHFLPDO#DQG#VHOHFWV#WKH#KH[DGHF0LPDO#PRGH1

,Q#WKH#KH[DGHFLPDO#PRGH/#HQWHUV#WKH#KH[#GLJLW#$1

,Q#WKH#KH[DGHFLPDO#PRGH/#HQWHUV#WKH#KH[#GLJLW#%1

4;

,Q#WKH#KH[DGHFLPDO#PRGH/#HQWHUV#WKH#KH[#GLJLW#&1

,Q#WKH#KH[DGHFLPDO#PRGH/#HQWHUV#WKH#KH[#GLJLW#'1

,Q#WKH#KH[DGHFLPDO#PRGH/#HQWHUV#WKH#KH[#GLJLW#(1

,Q#WKH#KH[DGHFLPDO#PRGH/#HQWHUV#WKH#KH[#GLJLW#)1

# # 6HOHFWV#WKH#VWDWLVWLFV#FDOFXODWLRQ#PRGH1

,Q#WKH#VWDWLVWLFV#PRGH/#HQWHUV#WKH#GLV0SOD\HG#YDOXH#DV#D#GDWD#LWHP1

# 5HFDOOV#WKH#QXPEHU#RI#GDWD#YDOXHV1

#&DOFXODWHV#WKH#IDFWRULDO#RI#WKH#GLV0SOD\HG#QXPEHU1

#,Q#WKH#VWDWLVWLFV#PRGH/#UHFDOOV#WKH#SRS0XODWLRQ#VWDQGDUG#GHYLDWLRQ1

#,Q#WKH#VWDWLVWLFV#PRGH/#UHFDOOV#WKH#VDP0SOH#VWDQGDUG#GHYLDWLRQ1

# #,Q#WKH#VWDWLVWLFV#PRGH/#UHFDOOV#WKH#PHDQ#RI#WKH#HQWHUHG#GDWD1

#,Q#WKH#VWDWLVWLFV#PRGH/#UHFDOOV#WKH#VXP#RI#WKH#HQWHUHG#GDWD#YDOXHV1

4#FRPELQDWLRQ#RI#;25#DQG#1271

# 1HJDWLRQ=#SURGXFHV#WKH#RSSRVLWH#YDO0XHV#RI#WKH#LQSXW1

53

(;$03/(6#

0,;('#$'',7,21/#68%75$&7,21/#08/7,3/,&$7,21/#',9,6,21

1RWH=#,I#D#FORVHG#SDUHQWKHVLV#IDOOV#DW#WKH#HQGRI#DQ#HTXDWLRQ/#\RX#GR#QRW#KDYH#WR#HQWHU#LW1

&2167$17#&$/&8/$7,216#7KH#FRQVWDQW#IHDWXUH#OHWV#\RX#SHUIRUP#UHSHWL0WLYH# FDOFXODWLRQV# ZLWKRXW# UH0HQWHULQJ# D# FRQ0VWDQW# YDOXH# DQG# IXQFWLRQ# HDFK# WLPH1# 7KHFRQVWDQW# LV#DXWRPDWLFDOO\#VHW#ZKHQ#\RX#SHU0IRUP#D#FDOFXODWLRQ#ZLWK#DGGLWLRQ/#VXEWUDFWLRQ/PXOWLSOLFDWLRQ/#GLYLVLRQ/#RU#WZR0YDOXH#SRZHUV#RUURRWV1

54

/2*,&$/#&$/&8/$7,216#

55

$1'#&DOFXODWLRQ

25#&DOFXODWLRQ

,QSXW 2XWSXW

$ % ;

4 4 4

4 3 3

3 4 3

3 3 3

7UXWK#7DEOH

'$% #;,QSXW 2XWSXW

,QSXW 2XWSXW

$ % ;

4 4 4

4 3 4

3 4 4

3 3 3

7UXWK#7DEOH

$#%# #;

,QSXW 2XWSXW

65-1081.fm Page 22 Monday, November 22, 1999 9:38 AM

56

:KHQ#HQWHULQJ#DQ#;125#RU#127#FDOFXODWLRQ/WKH#ODVW#GLJLW#RI#WKH#GLVSOD\HG#QXPEHU#LV#WKH#UH0VXOW/#UDWKHU#WKDQ#WKH#HQWLUH#QXPEHU1

;25/#;125#&DOFXODWLRQ

127#&DOFXODWLRQ

,QSXW 2XWSXW

$ % ;#25 ;#125

4 4 3 4

4 3 4 3

3 4 4 3

3 3 3 4

7UXWK#7DEOH

$% #;

,QSXW 2XWSXW

$%

2#;

,QSXW 2XWSXW

,QSXW#$

2XWSXW#;

4 3

3 4

7UXWK#7DEOH

$ 2#;,QSXW 2XWSXW

65-1081.fm Page 23 Monday, November 22, 1999 9:38 AM

57

32:(56#$1'#52276#

3(5&(17$*(#&$/&8/$7,216#7KH# FDOFXODWRU# HDVLO\# SHUIRUPV# DGG0RQ# DQGGLVFRXQW#SHUFHQWDJHV1

58

'(*5((25$',$162*5$'6#&219(56,2167KH# FDOFXODWRU# SHUIRUPV# WULJRQRPHWULF# IXQF0WLRQV#+VLQH/#FRVLQH/#DQG#VR#RQ,#XVLQJ#HLWKHU#GH0JUHHV/# UDGLDQV/# RU# JUDGV# DV# WKH# EDVLF# XQLW1%HFDXVH# GLIIHUHQW# DSSOLFDWLRQV# XVH# GLIIHUHQWEDVLF# XQLWV/# WKH# FDOFXODWRU# FDQ# FRQYHUW# EH0WZHHQ#WKH#GLIIHUHQW#XQLWV1

48(#GLVFRXQWHG#IURP#

59

7R#VHOHFW#D#XQLW/# UHSHDWHGO\#SUHVV# #XQWLOWKDW#XQLWV#LQGLFDWRU#+'(*/#5$'/#RU#*5$',#DS0SHDUV#DW#WKH#WRS#RI#WKH#GLVSOD\1

7R#FRQYHUW#EHWZHHQ#XQLWV/#VHW#WKH#FDOFXODWRU#WRWKH#ILUVW#XQLW#DQG#HQWHU#WKH#YDOXH1#7KHQ#UHSHDW0HGO\#SUHVV# # #XQWLO#WKH#FDOFXODWRU#GLV0SOD\V# WKH# WDUJHW# XQLW1# 7KH# GLVSOD\HG# YDOXHFKDQJHV#WR#WKH#HTXLYDOHQW#YDOXH#RI#WKH#WDUJHWXQLW1

-5HSHDWHGO\#SUHVV#'5*#XQWLO#'(*#DSSHDUV1

'(*5((620,187(62#6(&21'6#&219(56,216#6RPH#FDOFXODWLRQV#DUH#HDVLHU#WR#HQWHU#DV#GH0JUHHV/#PLQXWHV/#DQG# VHFRQGV1#+RZHYHU/# WKHWULJRQRPHWULF#IXQFWLRQV#H[SHFW#YDOXHV#WR#EH#LQGHFLPDO#HTXLYDOHQWV1#2QH#PLQXWH# LV# 4293#RI#DGHJUHH/#DQG#4#VHFRQG#LV#4293#RI#D#PLQXWH1

5:

5DWKHU# WKDQ# FRQYHUW# GHJUHHV/#PLQXWHV/# DQGVHFRQGV# WR#D#GHFLPDO#QXPEHU#E\#KDQG/#\RXFDQ#HQWHU#WKH#YDOXH# LQ#WKH#IRUP#''10066VV+'' GHJUHHV/# 00 PLQXWHV/# 66 VHFRQGV/VV KXQGUHGWKV#RI#D#VHFRQG,#DQG#WKHQ#TXLFNO\FRQYHUW#WKH#YDOXH#WR#LWV#GHFLPDO#HTXLYDOHQW1

$IWHU# \RX# SHUIRUP# D# FDOFXODWLRQ/# LW# LV# RIWHQPXFK#HDVLHU# WR#XQGHUVWDQG# WKH# UHVXOW# LI# LW# LVSUHVHQWHG#DV#GHJUHHV/#PLQXWHV/#DQG#VHFRQGV/UDWKHU#WKDQ#DV#D#GHFLPDO#QXPEHU1#7KH#FDOFXOD0WRU#OHWV#\RX#HDVLO\#FRQYHUW#GHFLPDO#QXPEHUV#WRGHJUHH/#PLQXWH/#DQG#VHFRQG#UHSUHVHQWDWLRQ1

5;

32/$525(&7$1*8/$5#&219(56,216#7KH#FDOFXODWRU#HDVLO\#FRQYHUWV#EHWZHHQ#SRODUDQG#UHFWDQJXODU#FRRUGLQDWHV1#%H#VXUH#WR#VHOHFWWKH#FRUUHFW#DQJXODU#XQLWV#+GHJUHHV/#UDGLDQV/#RUJUDGV,#EHIRUH#\RX#EHJLQ#FDOFXODWLRQV1

7R# VWRUH# DQG# UHFDOO# SRODU# UHFWDQJXODU# XQLWV/SUHVV# #DQG# # 1

[#D[LV

\#D[LV

+[/#\,

5HFWDQJXODU

U

q

q q

q

+U/# qq q

q ,

3RODU

5 3 ,19 ;