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Fig're? :ot in #rinted =ook
Inp'ts and 9ey Res'lts for Active ,cenario + ollars in %ho'sands,cenario :a&e =ase#robability of ,cenario 2>EInp'ts?"@'ip&ent cost 772>,alvage val'e* e@'ip&ent* <ear 4/Bpport'nity cost >"xternalities +cannibali ation >Dnits sold* <ear 1 1>*>>>Ann'al change in 'nits sold* after <ear 1 12E,ales price per 'nit* <ear 1 1.2>Ann'al change in sales price* after <ear 1 E;ariable cost per 'nit +;C * <ear 1 1.>7Ann'al change in ;C* after <ear 1 /E:onvariable cost +:on-;C * <ear 1 !1!>Ann'al change in :on-;C* after <ear 1 /E#ro$ect WACC 1>E%ax rate >EWorking capital as E of next year(s sales 12E
9ey Res'lts?:#; 1*> G
IRR 1/.7 E
0IRR 1!.7GE
#ro5tability index 1.1>
#ayback :ot fo'nd
isco'nted payback :ot fo'nd
%o create a s'&&ary sheet sho ing all scenarios* go to ata* What-If Analysis* ,cenario 0anager* and clselect the cells ith the key res'lts. %he ,'&&ary ill be sho n in a ne orksheet. For convenience*
orksheet and sho it belo . If yo' &ake changes to any scenarios* yo' &'st r'n the ,'&&ary again--ia'to&atcially 'pdate.
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We copied the ,cenario ,'&&ary fro& the orksheet here it as created and &oved it here. It ill no
,cenario ,'&&ary
Current 2aluesH
Changing Cells?" 4! $ase $ase orst
#robability ,' ,' .," 4
"@'ip&ent ++,' ++,' 4.,',alvage 7&3 7&3 7&3
BppCost ' ' '"xternalities ' ' '
Dnits ,old /' ''' /' ''' 4 ,''ro th in Dnits ,old /, /, ,
,ales #rice */!,' */!,' */!.,ro th in ,ales #rice per Dnit - - -
;ariable cost per 'nit */!'+ */!'+ */!/+
ro th in ;C per Dnit & & &
:onvariable Costs ./.' ./.' .&&'
ro th in :onvariable costs & & &
WACC /' /' /'
%ax Rate -' -' ,'
:BWC as percent of next year sa /, /, /,Res'lt Cells?:#; */ '-4 */ '-4 I*+ ,-&IRR /&!+3 /&!+3 I.3!-'
0IRR /.!+4 /.!+4 I..!.&#ro5tability Index /!/' /!/' '!.&
#ayback &!&3 &!&3 1ot foundisco'nted #ayback &!4' &!4' 1ot found
1otesH Current 2alues column represents values of changing cells attime 9cenario 9ummar> Report was created! Changing cells for eachscenario are highlighted in gra>!
$ase%Case9cenario
orst%Case9cenario
Created b> Mi;ehrhardt on
76,6.'/.
Created b> Mi;ehrhardt on
76,6.'/.Modi=ed b>Mi;e hrhardton 76,6.'/.
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1J!2J!>1/
changing cells. In this orksheet* eio 0anager(s ,'&&ary feat're.
there is only 1 col'&n for inp'ts andbelo . In other ords* all three scenarioss o n separate changing cells. %he
eat're in the ,cenario 0anager illa na&e. For exa&ple* e na&es the cell
scenario* and click L,ho .L %he &odel tos section belo .
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Analysis for ,cenario ,ho n =elo ?
=aseInter&ediate Calc'lations >
Dnit sales
,ales price per 'nit
;ariable cost per 'nit +excl. depr.:onvariable costs +excl. depr.
,ales reven'es H Dnits #riceJ'nit
!!2>
=asis for depreciation 772>
Ann'al depreciation rate +0ACR,
Ann'al depreciation expense
Re&aining 'ndepreciated val'e
Cash Flo Forecast>
,ales reven'es H Dnits #riceJ'nit
;ariable costs H Dnits CostJ'nit:onvariable costs +excl'ding depreciation
epreciation
"arnings before interest and taxes +"=I%
%axes on operating pro5t + >E rate
:et operating pro5t after taxes
Add back depreciation
"@'ip&ent p'rchases N 7*72>
,alvage val'e
Cash )o d'e to tax on salvage val'e + >E rate
Cash )o d'e to change in WC N !*!2>
Bpport'nity cost* after taxes >
After-tax cannibali ation or co&ple&entary e3ect
#ro$ect net cash )o s? %i&e ine KKK#ro ect "va 'at on 0eas'res:#; 1*> G
IRR 1/.7 E
0IRR 1!.7GE
#ro5tability index 1.1>
#ayback "rr?2>
isco'nted payback "rr?2>
Calc'lations for #ayback <ear? >
C'&'lative cash )o s for payback -1>>>> isco'nted cash )o s for disc. payback -1>>>> C'&'lative disco'nted cash )o s -1>>>>
:BWC t H 12E+Reven'es tM1
ick on ,'&&ary* ande have copied that
does :B%
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'pdate a'to&atically.
$est.,
+.,'7&3
''
// ,''.,
*/!+,-
*'!3+
&
/3/'
&
/'
&'
/,
*/3 -747.!-/-&!-3
.!3'/!4&.!'+
$est%Case9cenario
Created b>Mi;e hrhardton 76,6.'/.
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1 ! /
1>*>>> 11*2>> 1/*!!2 12*!>
1.2> 1.24 1.4! 1.4
1.>7 1.1> 1.1 1.17!1!> !1G/.4 !! .1>G !*/17
12>>> 17 > !1 24.! !2*44!
!4 1 /!1G. /4 KKK >
//.//E . 2E 1 .G1E 7. 1E
!2G/.>72 / .G72 11 7.772 27 .!72
2144. !2 17!!.>2 27 .!72 >Cash Flo s at "nd of <ear
1 ! /
12*>>> 17* > !1* 24 !2*44!
1>*7>> 1!*47 12*>1/ 17*7G!!*1!> !*1G !*! !*/17
!*2G/ /* 2 1*1 G 27
N >/ N /4/ /*> 7 * GG
N 141 N 1 2 1*!1 1* 2
N ! ! N !1G 1*G!G !* /
!*2G/ /* 2 1*1 G 27
4/
N !24
N 1 N 2!7 N 4/1 /*G
> > > >
> > > >
1* >> !*7>> !*/ 2 7*G>>
1 ! /
-G> .77 -2/ . >4 KKK *7 2KKK KKK KKK 2*/!GKKK KKK KKK 1*> G
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Worksheet -,i&'lation ith 1>> %rials
:ote? this section is relatively technical and so&e instr'ctors &ay choose to skip it ith no loss in con
Fig're 11-7Inp'ts and 9ey Res'lts for the C'rrent ,i&'lation %rial + ollars in %ho'sands
"@'ip&ent cost 7*72> /2 1.11/ G*1,alvage val'e of e@'ip. in <ear X X 4/Bpport'nity cost X X >"xternalities +cannibali ation X X >Dnits sold* <ear 1 KKK 1*>41 1.//> 11* 11E Y in 'nits sold* after <ear 1 12.>>E 7.>7E >.7! !>.12E,ales price per 'nit* <ear 1 1.2> >.1G >.2G2 1.4>E Y in sales price* after <ear 1 X X .>>E;ar. cost per 'nit +;C * <ear 1 1.>7 >.>7 1.7!! 1.1E Y in ;C* after <ear 1 X X /.>>E:onvar. cost +:on-;C * <ear 1 !*1!> 1 G N1.G!! 1*GE Y in :on-;C* after <ear 1 X X /.>>E#ro$ect WACC X X 1>.>>E%ax rate >.>>E 7.>7E N>.!2 /G.17E
:BWC as E of next year(s sales X X 12.>>E
0onte Carlo si&'lation is si&ilar to scenario analysis in that di3erent val'es of key inp'ts are 'sed.0onte Carlo si&'lation dra s a trial set of inp't val'es fro& speci5ed probability distrib'tions and ththis trial. %his process is repeated for h'ndreds* or even tho'sands* of trials* ith key res'lts +like :After r'nning the n'&ber of desired trials* the :#;s fro& the trials can be averaged to esti&ate the ptrial res'lts can also be 'sed to provide a histogra& sho ing the pro$ect(s possible o'tco&es.
#anel A* sho n in the bl'e-bordered box belo and slightly to the right* sho s the inp'ts fro& the pralso sho s the expected val'e and standard deviation for those inp'ts based on the probability of eaapples and apples* e ill ass'&e that the inp'ts for the si&'lation analysis are dra n fro& a nor&aexpected val'e and standard deviation as the inp'ts fro& the scenario analysis +these are sho n in tsection in Col'&ns C and . Po ever* any of the inp't val'es in Col'&ns C and &ay be changed byaddition to the inp'ts for all the variables 'sed previo'sly* the inp'ts section also has an inp't val'ebet een 'nits sold in <ear 1 and changes in 'nits sold in later years.
%he 5g're belo sho s the trial inp'ts and key res'lts. %he inp'ts 'sed f'rther belo in the &odel arare dra n fro& a nor&al distrib'tion ith the &ean and standard deviation speci5ed in Col'&ns C anprocess. Col'&n " sho s a standard nor&al rando& variable created ith "xcel(s rando& n'&ber gentransfor&s the standard nor&al rando& variable into a nor&al rando& variable ith the desired &ea%o see 'pdated val'es* hit the F key.
%o change an inp't* change one of the bl'e val'es in Col'&ns C or . %o see an 'pdatedset of trial val'es* hit the F key. Inp'ts and key res'lts ill 'pdate for the c'rrent trial.
Inp'ts for ,i&'lation#robabilityistrib'tions
Rando& ;ariables Dsed inC'rrent ,i&'lation %rial
"xpected;al'e of
Inp't
,tandardeviationof Inp't
,tandard:or&al Rando&
;ariable;al'e Dsed inC'rrent %rial
Ass'&ed correlation bet een'nits sold in <ear 1 and ann'al
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42.>>E
9ey Res'lts =ased on C'rrent %rial:#; /*!!4IRR 1 .G7E
0IRR 17./7E#I 1./>
#ayback :ot fo'ndisco'nted payback :ot fo'nd
#anel =? #ro$ect Analysis for C'rrent %rial in ,i&'lation Dsing Inp'ts fro& Fig're 11-7 Col'&n FInter&ediate Calc'lations > 1 !Dnit sales 11* 11 1/*71>,ales price per 'nit 1.4> 1.47;ariable cost per 'nit +excl. depr. 1.1 1.!/:onvariable costs +excl. depr. KKK KKK,ales reven'es H Dnits #riceJ'nit KKK KKK
KKK KKK KKK
=asis for depreciation KKKAnn'al depreciation rate +0ACR, //.//E . 2EAnn'al depreciation expense KKK KKKRe&aining 'ndepreciated val'e KKK KKKCash Flo Forecast Cash Flo s
> 1 !,ales reven'es H Dnits #riceJ'nit 1G*! 7 !!*G4/;ariable costs H Dnits CostJ'nit 1/*2 14*G!:onvariable costs +excl'ding depreciation 1*G 1* >2
epreciation !*71 /*4!>"arnings before interest and taxes +"=I% 1/ 2>%axes on operating pro5t + >E rate 21 1:et operating pro5t after taxes G/ /12Add back depreciation !*71 /*4!>
"@'ip&ent p'rchases N G*1,alvage val'eCash )o d'e to tax on salvage val'e + >E rateCash )o d'e to change in WC N !*7 2 N 4G2 N G24Bpport'nity cost* after taxes > > >After-tax cannibali ation or co&ple&entary e3ect > >#ro$ect net cash )o s? %i&e ine N 1>*GGG !*11! /*>7#ro$ect "val'ation 0eas'res:#; /*!!4IRR 1 .G7E0IRR 17./7E#ro5tability index 1./>#ayback "rr?2>
isco'nted payback "rr?2>Calc'lations for #ayback <ear? > 1 ! C'&'lative cash )o s for payback KKK KKK KKK isco'nted cash )o s for disc. payback KKK KKK KKK C'&'lative disco'nted cash )o s KKK KKK KKK
change in 'nits sold in lateryears? ρ =
:BWC t H 12E+Reven'es tM1
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Po the ,i&'lation Works
Col'&n inp't cell to LtrickL "xcel into 'pdating rando& variables in ata %able? /
/
:ote? If res'lts are all eros* go back to ro 1 and LcheckL the box by clicking it ith
Fig're 11-G
,'&&ary of ,i&'lation Res'lts +%ho'sands of ollars:'&ber of %rials 1>> Inp't ;ariables
Average G*1 11* 11 12E 1.21 1.>7,tandard deviation > > 7E >.17 >.>7
0axi&'& G*1 11* 11 ! E 1.G2 1.!0ini&'& G*1 11* 11 NGE 1.>4 >. !
Correlation ith 'nit sales >E
:#;
We 'se a ata %able to perfor& the si&'lation +the ata %able is belo shaded in lavender . When thill insert ne rando& variables for each of the inp'ts e allo to change in Fig're 11-7 above* r'n t
above* and then save the :#; for each trial. +We also save the inp't variables for each trial so that behaving as e expect. We set the 5rst col'&n of the ata %able +the variable to be changed in eac
1>>. We don(t really 'se these n'&bers any here in the analysis* b't if e tell the ata %able to treatinp'ts* "xcel ill recalc'late all ite&s in the ata %able* incl'ding the rando& inp'ts and the res'ltingLtrickL "xcel into doing a si&'lation. We tell "xcel to insert each of the Col'&n inp'ts in the ata %ablbelo this box. %his cell isn(t linked to anything else* b't each ti&e "xcel 'pdates a ro of the ata %
ill be 'pdated.
"xcel nor&ally 'pdates all val'es in a ata %able each ti&e any cell that is related to the ata %able chave rando& variables in the ata %able* so each ti&e any cell in the orksheet &akes a calc'lation* tthe ata %able has &any ro s* 'pdating it can take 'p to !> or /> seconds. %his is ok hen e ant tannoying to ait /> seconds any ti&e e &ake any changes in the orksheet. %he Lcheck boxL explaiannoyance.
%o p't rando& variables in the ata %able for the si&'lation* the box sho n belo &'st be checked8contains only ero(s and doesn(t 'pdate hen the sheet &akes a calc'lation +other than the 5rst ti&einsert or delete ro s or col'&ns . If the box is 'nchecked and yo' check it* the check &ark on(t sho'pdated* so don(t get i&patient and click it t ice. After yo' have checked the box* the ata %able illchange a cell in the orksheet. ,o to &ake the ata %able 'pdate* &ake s're the box is checked and t
#'t a check in the box belo to p't trialsinto the data table8 other ise* the data table
ill have only eros.
Re&e&ber to 'ncheck the box above hen yo' are thro'gh ith the si&'lation* or the ata %able ill&ake a change in the orksheet* hich ill slo do n all other calc'lations in the orksheet.
<o' don(t need to change anything in this section. It ill be 'pdated a'to&atically if yo' do a si&'latsi&'lation res'lts and the histogra& are based on the si&'lation trials in the ata %able belo and a
hen yo' do a si&'lation.
,'&&ary ,tatistics for,i&'lated Inp't ;ariables
"@'ip&entcost
Dnits sold* <ear 1
Ann'al changein 'nits sold*after <ear 1
,ales priceper 'nit* <ear 1
;ariablecost per
'nit +;C * <ear 1
,'&&ary ,tatistics for ,i&'latedRes'lts
Must be chec;ed to put random variable in data table for simulation
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Average 1*1G7,tandard deviation 2*1 >
0axi&'& 14*1470ini&'& N 1 *7>1
0edian //2#robability of :#; Z > 2G.>E
CoeScient of variation ./7
Output of Simulation in Data Table
Equipment cost4/-&!7./7+'33 //-/'!4,7- '!.'/,/4/+ /!7'&---,'3& /!/3/+-+&,&+ /4-3!&37'-,
/ 4/-&!7./7+'33 //-/'!4,7- 0.1302220415 /!7.4+,44&. /!'&4-7443&. .'+&!3.-+&.. 4/-&!7./7+'33 //-/'!4,7- 0.2270622875 /!.3/.344,-/ /!/'7.4/,4'. .&,4!,.+-'.& 4/-&!7./7+'33 //-/'!4,7- 0.1696882815 /!7+/47--3+. /!'&'+&-&37, ./,'!4.3-,+- 4/-&!7./7+'33 //-/'!4,7- 0.2887668165 /!+',++./-.3 /!.'44//'+3+ .'3'!..&,/,, 4/-&!7./7+'33 //-/'!4,7- 0.1351632468 /!,7,74.+7&+ /!',,+.-3.4/ .'.3!&./'74
7 4/-&!7./7+'33 //-/'!4,7- 0.1792002023 /!+4./73/,3+ /!//&.-77-.- .'7.!&3/-+4+ 4/-&!7./7+'33 //-/'!4,7- 0.0666970205 /!4-,-/3,&4. /!'//.+4'3 /3,&!4'/,3+4 4/-&!7./7+'33 //-/'!4,7- 0.0720210744 /!4.-&/3-+77 /!''/+7&,3'4 ....!.++,/&3 4/-&!7./7+'33 //-/'!4,7- 0.1793119835 /!,&,/.343,. /!/&/7/,&777 .'33!-+3',7
/' 4/-&!7./7+'33 //-/'!4,7- 0.1363881237 /!,.7/..3&', /!',&&,&3,7. ./-4!.3++--// 4/-&!7./7+'33 //-/'!4,7- 0.130987976 /!77,-,.+,-7 /!./,-4/4,', ./'4!7/4-,+/. 4/-&!7./7+'33 //-/'!4,7- 0.1566386637 /!+&74,&.&7/ '!33',&'3, /4.,!&,37-/& 4/-&!7./7+'33 //-/'!4,7- 0.0656094458 /!.&3'-.-773 /!'43//./'.& ..77!3437-+/- 4/-&!7./7+'33 //-/'!4,7- -0.077842513 /!,++,'''.+4 /!//-3,33,-+ ..73!7&&/34/, 4/-&!7./7+'33 //-/'!4,7- 0.0128160781 /!-..&'7+'+. /!''4,.//3/. ./+&!.+/-/+/7 4/-&!7./7+'33 //-/'!4,7- 0.1700240307 /!73-,/,-+74 /!'3.,7+,44- ../'!7&/7&-
Trial NumberUnits sold,
Year 1
% Δ in unitssold, after Year
1Sales price per unit,
Year 1Var cost per unit
!V"#, Year 1
Non$ar cost!Non V"#, Year
1
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1&'(&')1*
tin'ity.
:ote? %heseFig're 11-7Inp'ts and 9ey
=ase Worst =est
#robability of ,cenario2>E !2E !2E
7*72> G*!2> 7*!2> 7*72> /2 "@'ip&ent cos4/ 4/ 4/ ,alvage val'e
> > > Bpport'nity co> > > "xternalities +c
1>*>>> G*2>> 11*2>> 1>*>>> 1*>41 Dnits sold* <ea12.>>E 2.>>E !2.>>E 12.>>E 7.>7E E Y in 'nits so
1.2> 1.!2 1.72 1.2> >.1G ,ales price per.>>E .>>E .>>E E Y in sales pri
1.>7 1.17 >. 7 1.>7 >.>7 ;ar. cost per '/.>>E /.>>E /.>>E E Y in ;C* afte
!*1!> !*//> 1* 1> !*1!> 1 G :onvar. cost +:/.>>E /.>>E /.>>E E Y in :on-;C*
1>.>>E 1>.>>E 1>.>>E #ro$ect WACC>.>>E 2>.>>E />.>>E >.>>E 7.>7E %ax rate
12.>>E 12.>>E 12.>>E :BWC as E of
nlike scenario analysis*en co&p'tes the :#; for; saved fro& each trial.ro$ect(s expected :#;8 the
vio's scenario analysis. Ith scenario. %o co&pare
l distrib'tion ith the sa&ee 5g're belo in the bl'ethe 'ser if desired. Inor the ass'&ed correlation
e sho n in dark red andd . We do this in a !-steperator. Col'&n F
and standard deviation.
#anel A? ;al'es fro& ,cenario Analysis and %heir "xpected ;al'es and,tandard eviations
%o change an iset of trial val
Inp'ts fro& ,cenario Analysis forCo&parison to ,i&'lation
"xpected ;al'eof Inp't
,tandardeviationof Inp't
Ass'&ed corre'nits sold in <
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9ey Res'lts
=ase Worst =est 9ey Res'lts =a1*> G - 7*2 / 1 * 4G :#;1/.7 E -171. 4E 4!. 1E IRR1!.7GE -!!.!/E /. E 0IRR
1.1> >.!/ !. > #I/./ :ot fo'nd :ot fo'nd #ayback /.G> :ot fo'nd :ot fo'nd isco'nted payback isc
/14* 7/ 1 *7 /
1.7/ 1.G>1.!4 1./>KKK !*>!1KKK /2*7>>
KKK >
1 .G1E 7. 1EKKK KKKKKK >
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4/N !
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c ange n 'n tyears?
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,i&'lation control*
/on(t change the red cell.
yo'r c'rsor.
%ax rate!*1!7 / . E
142 7.>E!* G7 41./E1*77G !2.!E
,cratch ork for chart? see co&&ents.Co'nt
Range botto ' #ercent
ata %able is 'pdated* ite analysis in #anel =
e can verify that they arero to n'&bers fro& 1-
these as the Col'&n:#;. In other ords* ee into the cell i&&ediatelyble* all the rando& val'es
@ou might wonder "what:s the deal about this chec; bo# and wis useful for the simulation and how do >ou use a chec; bo# fothen tal; about chec; bo#es! This chec; bo# is lin;ed to cell $/bo# is unchec;ed then it returns a " AB9 " value! The reason >same as the bac;ground color so it wouldn:t be distracting! $el
9ee it reads either True or alse depending on whether the bocells $.'7 to <.'7 use this value to determine whether or not tis K< (*$*/-- &4 ')! <f $/-- is TR5 then the cell returns theAB9 then it returns '! The other formulas in that row are sim
no formulas to evaluate (ever>thing is Fero) and if it is TR5 t @ou didn:t reall> need a chec; bo#G >ou could Lust as well havestatements in row .'7 chec; instead for whether $/-- is equ
anges. In o'r case* ehe ata %able is 'pdated. If
o 'pdate the %able* b't it ised belo helps ith this
ther ise* the ata %ableyo' check this box or if yo'
'p 'ntil the %able is'pdate any ti&e yo'hen hit the F key.
1ow for how to use orms in #cel! To insert a chec; bo# in #c These are instructions for #cel .'/' or later versions of #ce
#cel help! Clic; the ile tab then clic; ?ptions then clic; Custselect the Developer chec; bo#!
?n the Developer tab in the Controls group clic; on <nsert anli;e a tool bo#)! Boo; at the orms Control section and clic; on>ou:d li;e the chec; bo# to go and clic; there! A name li;e Chand clic; on ormat Control! Then under the Control tab ma;e
in the Cell lin; bo#! e had *$*/-- in that bo#! 9uppose >ou pon the chec; bo# cell 0/7+ will displa> TR5 and when it is novalues in >our #cel programming! All that is left is to put in aconfused about what the bo# is for! Nust clic; on the chec; bo#want something special to happen to the spreadsheet" (li;e en
recalc'late any ti&e yo'
ion. %he s'&&ary of thee 'pdated a'to&atically
:onvariablecost
+:on-;C * <ear 1
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0.4285022455 .77+!73+&.&&0.3821498163 ,43&!47.,&-70.4024688069 %/.&&!-/'..,70.5346997032 &3,4!7-..-3/0.3377087481 .74!4.+7/7,-0.4627800377 %.&4-!74&.&770.3624066567 %,'37!-.&--/0.3644346846 /-'.!.&-.+7+0.3980397746 %.4&-!//,,&/70.3854186573 %/+.,!'/-/-'70.6134314275 %/./!&&4.,''70.3331981392 7+/!4.44,,.+0.4007439366 /'/,/!3,./470.5215183231 %+.&!+3+,7.+-0.4537843945 +,&&!7',7-370.4156201497 /'4+-!4'&+&70.3912746345 3.4,!77.3-730.4209241857 +,7.!.+.-'+0.3978903962 %.3++!4.+++7&0.4021603121 %&./,!..3&.'40.4550774072 --7/!&3-'+,.0.3683780763 ,4&&!3,-'.'40.2842265861 %./&3!'&-&33-0.3248449017 %,3!73./73--.0.4663354691 %.'47!,3'/.+,0.4687944139 ./&'!.&+7.-0.3677087989 ..4!74,-/,4+
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are the 5xed val'es fro& the si&'lation that is sho n in the textbook.
Res'lts for the C'rrent ,i&'lation %rial + ollars in %ho'sands
7*72> /2 N>.142 7*4 !f e@'ip. in <ear X X X 4/
st X X X > annibali ation X X X >
1 KKK 1*>41 N>.>4 * !7d* after <ear 1 KKK 7.>7E >.7/ !>.1 E'nit* <ear 1 1.2> >.1G 1. /1 1.Gce* after <ear 1 X X X .>>E
it +;C * <ear 1 1.>7 >.>7 N1.>G7 >.r <ear 1 X X X /.>>Eon-;C * <ear 1 !*1!> 1 G >.21 !*1 4after <ear 1 X X X /.>>E
X X X 1>.>>EKKK 7.>7E N1.211 ! ./!E
ext year(s sales X X X 12.>>E
p't* change one of the bl'e val'es in Col'&ns C or . %o see an 'pdatedes* hit the F key. Inp'ts and key res'lts ill 'pdate for the c'rrent trial.
Inp'ts for ,i&'lation#robability istrib'tions
Rando& ;ariables Dsed inC'rrent ,i&'lation %rial
"xpected;al'e of
Inp't
,tandardeviation of
Inp't,tandard :or&alRando& ;ariable
;al'e Dsedin C'rrent
%rial
lation bet eenar 1 and ann'al
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ρ 42.>>E
sed on C'rrent %rial:#; KKKIRR KKK
0IRR KKK#I !. 2
#ayback 1. Go'nted payback !.!2
so n ater
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check boxes* and for&s
:ote? %hese are the 5xed val'es fro& the si&'lation that is sho n in the textbook.Fig're 11-G
,'&&ary of ,i&'lation Res'lts +%ho'sands of ollars:'&ber of %rials 1>*>>> Inp't ;ariables
"@'ip. costAverage 7*72> * G! 12.>E 1.2> 1.>7 !*1!!
,tandard deviation /2 1*>27 7.1E >.1G >.>7 12>0axi&'& *>7! 1 *>>2 2.>E !.12 1./! !*4G!0ini&'& 4*/ 7 4*17! N1/. 7E >.G1 >.7G 1*2
Correlation ith 'nit sales 42. E
:#;
h> does it wor; this wa>J" There are . parts to this questionH h> ititJ Bet:s answer the "wh> it is useful for a simulation" question =rst
--! <f >ou clic; on the bo# $/-- returns a "TR5 " value and if theou can:t see an>thing in $/-- is because we made the font color theow here:s what is in cell $/--H
# is chec;ed or not! The formulas in the simulation data table inhe data table should be evaluated! or e#ample the formula in $.'7value in &4 which is the simulated equipment cost! <f $/-- is
ilar! The end result is that if $/-- is AB9 then the data table hasen it has formulas to evaluate and it records the simulation results!
left $/-- visible and either put a / or a ' in it and had the <al to /! $ut the chec; bo# is neat!
el .'/' >ou must =rst enable the Developer tab on >our Ribbon!l >ou can =nd instructions for this b> searching on "chec; bo#" inomiFe Ribbon! 5nder CustomiFe the Ribbon and under Main Tabs
then in the orm Controls section clic; on <nsert (the picture thathe icon that loo;s li;e a chec; mar;! Move >our cursor to where
ec; $o# ., will show up ne#t to the bo#! Right clic; on the chec; bo#sure the "unchec;ed" button is pressed then put in a cell reference
ut in *0*/7+ for >our bo#! @ou are mostl> done 1ow when >ou clic;chec;ed 0/7+ will displa> AB9 ! @ou can use these two logicalseful description for the chec; bo#! @ou don:t want >our users to be
area and edit the name to be something li;e "Clic; this bo# if >ouable the data table to do its calculations )!
,'&&ary ,tatistics for,i&'lated Inp't ;ariables
Dnits sold* <ear1
E Y in 'nitssold* after
<ear 1
,alesprice per
'nit* <ear 1
;ariablecost per
'nit +;C * <ear 1
:onvar. cost+:on-;C *
<ear 1
,'&&ary ,tatistics for,i&'lated Res'lts /!. #robability
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Average 1*1!>,tandard deviation 2*1/!
0axi&'& !4* >40ini&'& N 14*7G2
0edian 7/7#robability of :#; Z > 24. E
CoeScient of variation .2G
1'
'!.
'!-
'!7
'!4
/
:#; +
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%ax rate/ . E
7.1E4G.7E1/.2E
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Worksheet b-,i&'lation ith 1>*>>> %rials
Fig're 11-7Inp'ts and 9ey Res'lts for the C'rrent ,i&'lation %rial + ollars in %ho'sands
"@'ip&ent cost 7*72> /2 1.1G G*144,alvage val'e* e@'ip&ent* <ear X X 4/Bpport'nity cost X X >"xternalities +cannibali ation X X >Dnits sold* <ear 1 1>*>>> 1*>41 >./7 1>*/ 1Ann'al change in 'nits sold* after <ear 1 12.>>E 7.>7E >.7 !>.27E,ales price per 'nit* <ear 1 1.2> >.1G N>.7 1./7Ann'al change in sales price* after <ear X X .>>E;ariable cost per 'nit +;C * <ear 1 1.>7 >.>7 1. / 1.17Ann'al change in ;C* after <ear 1 X X /.>>E
:onvariable cost +:on-;C * <ear 1 !*1!> 1 G >.7 !*!/7Ann'al change in :on-;C* after <ear 1 X X /.>>E#ro$ect WACC X X 1>.>>E%ax rate >.>>E 7.>7E N>./1 /7.G!EWorking capital as E of next year(s sales X X 12.>>E
42.>>E9ey Res'lts =ased on C'rrent %rial
:#; KKKIRR KKK
0IRR KKK#I >.22
#ayback t fo'nd
%his orksheet is exactly like the orksheet a-,i&1>> except that this orksheet does 1>*>>> trials instead osi&'lation* go to Ro 1 and check the box. Re&e&ber to 'ncheck the box hen yo' 5nish* other ise any chbe very sl'ggish.
0onte Carlo si&'lation is si&ilar to scenario analysis in that di3erent val'es of key inp'ts are 'sed. Dnlike scesi&'lation dra s a trial set of inp't val'es fro& speci5ed probability distrib'tions and then co&p'tes the :#;is repeated for h'ndreds* or even tho'sands* of trials* ith key res'lts +like :#; saved fro& each trial. After rdesired trials* the :#;s fro& the trials can be averaged to esti&ate the pro$ect(s expected :#;8 the trial res'ltprovide a histogra& sho ing the pro$ect(s possible o'tco&es.
#anel A* sho n in the bl'e-bordered box belo and slightly to the right* sho s the inp'ts fro& the previo's scsho s the expected val'e and standard deviation for those inp'ts based on the probability of each scenario. %apples* e ill ass'&e that the inp'ts for the si&'lation analysis are dra n fro& a nor&al distrib'tion ith thstandard deviation as the inp'ts fro& the scenario analysis +these are sho n in the 5g're belo in the bl'e sePo ever* any of the inp't val'es in Col'&ns C and &ay be changed by the 'ser if desired. In addition to the'sed previo'sly* the inp'ts section also has an inp't val'e for the ass'&ed correlation bet een 'nits sold in <sold in later years.
%he 5g're belo sho s the trial inp'ts and key res'lts. %he inp'ts 'sed f'rther belo in the &odel are sho n ifro& a nor&al distrib'tion ith the &ean and standard deviation speci5ed in Col'&ns C and . We do this in asho s a standard nor&al rando& variable created ith "xcel(s rando& n'&ber generator. Col'&n F transfor&srando& variable into a nor&al rando& variable ith the desired &ean and standard deviation. %o see 'pdated
%o change an inp't* change one of the bl'e val'es in Col'&ns C or . %o see an 'pdated set oftrial val'es* hit the F key. Inp'ts and key res'lts ill 'pdate for the c'rrent trial.
Inp'ts for ,i&'lation
#robability istrib'tions
Rando& ;ariables Dsed in
C'rrent ,i&'lation %rial"xpected;al'e of
Inp't
,tandardeviation of
Inp't
,tandard:or&al Rando&
;ariable;al'e Dsed inC'rrent %rial
Ass'&ed correlation bet een 'nits soldin <ear 1 and ann'al change in 'nitssold in later years? ρ =
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isco'nted payback fo'nd
#anel =? #ro$ect Analysis for C'rrent %rial in ,i&'lation Dsing Inp'ts fro& Fig're 11-7 Col'&n FInter&ediate Calc'lations > 1 !Dnit sales 1>*/ 1 1!*2!,ales price per 'nit 1./7 1. !
;ariable cost per 'nit +excl. depr. 1.17 1.!1:onvariable costs +excl. depr. KKK KKK,ales reven'es H Dnits #riceJ'nit KKK KKK
KKK KKK KKK=asis for depreciation KKKAnn'al depreciation rate +0ACR, //.//E . 2EAnn'al depreciation expense KKK KKKRe&aining 'ndepreciated val'e KKK KKKCash Flo Forecast Cash Flo s
> 1 !,ales reven'es H Dnits #riceJ'nit 1 *!!7 17*G >;ariable costs H Dnits CostJ'nit 1!*17> 12*11:onvariable costs +excl'ding depreciation !*!/7 !*/>
epreciation !*7!! /*4/>"arnings before interest and taxes +"=I% N !* >! N /*!>G%axes on operating pro5t + >E rate N 1*> G N 1*!1/:et operating pro5t after taxes N 1*G> N 1* 2Add back depreciation !*7!! /*4/>"@'ip&ent p'rchases N G*144,alvage val'eCash )o d'e to tax on salvage val'e + >E rateCash )o d'e to change in WC N !*1/ N 2 ! N 4G>Bpport'nity cost* after taxes > > >After-tax cannibali ation or co&ple&entary e3ect > >#ro$ect net cash )o s? %i&e ine N 1>*/>> /72 24#ro$ect "val'ation 0eas'res:#; - *414 H:#;+"4 *F111?I111 M"111IRR -4. 1E HIRR+"111?I1110IRR -2.1 E H0IRR+"111?I111*"4 *"4#ro5tability index >.22 H:#;+"4 *F111?I111 J+-"111#ayback "rr?2> H#"RC":%RA:9+"1!>?I1!>*>*4 OI11
isco'nted payback "rr?2> H#"RC":%RA:9+"1!!?I1!!*>*4 OI11Calc'lations for #ayback <ear? > 1 ! C'&'lative cash )o s for payback KKK KKK KKK isco'nted cash )o s for disc. payback KKK KKK KKK C'&'lative disco'nted cash )o s KKK KKK KKK
Po the ,i&'lation Works
:BWC t H 12E+Reven'es tM1
We 'se a ata %able to perfor& the si&'lation +the ata %able is belo shaded in lavender . When the ata %abne rando& variables for each of the inp'ts e allo to change in Fig're 11-7 above* r'n the analysis in #anel:#; for each trial. +We also save the inp't variables for each trial so that e can verify that they are behaving5rst col'&n of the ata %able +the variable to be changed in each ro to n'&bers fro& 1-1>>. We don(t reallyany here in the analysis* b't if e tell the ata %able to treat these as the Col'&n inp'ts* "xcel ill recalc'lat%able* incl'ding the rando& inp'ts and the res'lting :#;. In other ords* e LtrickL "xcel into doing a si&'latieach of the Col'&n inp'ts in the ata %able into the cell i&&ediately belo this box. %his cell isn(t linked to an"xcel 'pdates a ro of the ata %able* all the rando& val'es ill be 'pdated.
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Col'&n inp't cell to LtrickL "xcel into 'pdating rando& variables in ata %able? /
'
:ote? If res'lts are all eros* go back to ro 1 and LcheckL the box by clicking it ith yo'Fig're 11-G,'&&ary of ,i&'lation Res'lts +%ho'sands of ollars:'&ber of %rials 1>*>>> Inp't ;ariables
Average > > >E >.>> >.>>,tandard deviation > > >E >.>> >.>>
0axi&'& > > >E >.>> >.>>0ini&'& > > >E >.>> >.>>
Correlation ith 'nit sales K I;J>Q
:#;Average >
,tandard deviation >0axi&'& >0ini&'& >
0edian >#robability of :#; Z > >.>E
CoeScient of variation K I;J>Q
"xcel nor&ally 'pdates all val'es in a ata %able each ti&e any cell that is related to the ata %able changes. Ivariables in the ata %able* so each ti&e any cell in the orksheet &akes a calc'lation* the ata %able is 'pdat&any ro s* 'pdating it can take 'p to !> or /> seconds. %his is ok hen e ant to 'pdate the %able* b't it isseconds any ti&e e &ake any changes in the orksheet. %he Lcheck boxL explained belo helps ith this ann
%o p't rando& variables in the ata %able for the si&'lation* the box sho n belo &'st be checked8 other ise*only ero(s and doesn(t 'pdate hen the sheet &akes a calc'lation +other than the 5rst ti&e yo' check this boxro s or col'&ns . If the box is 'nchecked and yo' check it* the check &ark on(t sho 'p 'ntil the %able is 'pdi&patient and click it t ice. After yo' have checked the box* the ata %able ill 'pdate any ti&e yo' change a&ake the ata %able 'pdate* &ake s're the box is checked and then hit the F key.
#'t a check in the box belo to p'ttrials into the data table8 other ise* the
data table ill have only eros.
Re&e&ber to 'ncheck the box above hen yo' are thro'gh ith the si&'lation* or the ata %able ill recalc'lachange in the orksheet* hich ill slo do n all other calc'lations in the orksheet.
<o' don(t need to change anything in this section. It ill be 'pdated a'to&atically if yo' do a si&'lation. %heres'lts and the histogra& are based on the si&'lation trials in the ata %able belo and are 'pdated a'to&atisi&'lation.
,'&&ary ,tatistics for,i&'lated Inp't ;ariables
"@'ip&entcost
Dnits sold* <ear 1
Ann'al changein 'nits sold*after <ear 1
,ales priceper 'nit* <ear 1
;ariablecost per
'nit +;C * <ear 1
,'&&ary ,tatistics for , i&'latedRes'lts
Must be chec;ed to put randomvariable in data table for simulation
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Output of Simulation in Data Table
Equipment cost' ' ' ' ' '
/ ' ' 0 ' ' '. ' ' 0 ' ' '& ' ' 0 ' ' '- ' ' 0 ' ' ', ' ' 0 ' ' '7 ' ' 0 ' ' '+ ' ' 0 ' ' '4 ' ' 0 ' ' '3 ' ' 0 ' ' '
/' ' ' 0 ' ' '// ' ' 0 ' ' '/. ' ' 0 ' ' '/& ' ' 0 ' ' '/- ' ' 0 ' ' '/, ' ' 0 ' ' '/7 ' ' 0 ' ' '/+ ' ' 0 ' ' '/4 ' ' 0 ' ' '/3 ' ' 0 ' ' '.' ' ' 0 ' ' './ ' ' 0 ' ' '.. ' ' 0 ' ' '.& ' ' 0 ' ' '.- ' ' 0 ' ' '., ' ' 0 ' ' '
.7 ' ' 0 ' ' '
.+ ' ' 0 ' ' '
.4 ' ' 0 ' ' '
.3 ' ' 0 ' ' '&' ' ' 0 ' ' '&/ ' ' 0 ' ' '&. ' ' 0 ' ' '&& ' ' 0 ' ' '&- ' ' 0 ' ' '&, ' ' 0 ' ' '&7 ' ' 0 ' ' '&+ ' ' 0 ' ' '
Trial Number
Units sold, Year
1
-nnual c.an/ein units sold,
after Year 1
Sales price per unit,
Year 1
Variable cost per
unit !V"#, Year 1
Non$ariablecost !Non V"#,
Year 1
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&4 ' ' 0 ' ' '&3 ' ' 0 ' ' '-' ' ' 0 ' ' '-/ ' ' 0 ' ' '-. ' ' 0 ' ' '-& ' ' 0 ' ' '-- ' ' 0 ' ' '-, ' ' 0 ' ' '
-7 ' ' 0 ' ' '-+ ' ' 0 ' ' '-4 ' ' 0 ' ' '-3 ' ' 0 ' ' ',' ' ' 0 ' ' ',/ ' ' 0 ' ' ',. ' ' 0 ' ' ',& ' ' 0 ' ' ',- ' ' 0 ' ' ',, ' ' 0 ' ' ',7 ' ' 0 ' ' ',+ ' ' 0 ' ' ',4 ' ' 0 ' ' ',3 ' ' 0 ' ' '7' ' ' 0 ' ' '7/ ' ' 0 ' ' '7. ' ' 0 ' ' '7& ' ' 0 ' ' '7- ' ' 0 ' ' '7, ' ' 0 ' ' '77 ' ' 0 ' ' '7+ ' ' 0 ' ' '74 ' ' 0 ' ' '73 ' ' 0 ' ' '+' ' ' 0 ' ' '+/ ' ' 0 ' ' '+. ' ' 0 ' ' '+& ' ' 0 ' ' '+- ' ' 0 ' ' '+, ' ' 0 ' ' '+7 ' ' 0 ' ' '++ ' ' 0 ' ' '+4 ' ' 0 ' ' '+3 ' ' 0 ' ' '4' ' ' 0 ' ' '4/ ' ' 0 ' ' '4. ' ' 0 ' ' '4& ' ' 0 ' ' '4- ' ' 0 ' ' '4, ' ' 0 ' ' '
47 ' ' 0 ' ' '4+ ' ' 0 ' ' '44 ' ' 0 ' ' '43 ' ' 0 ' ' '3' ' ' 0 ' ' '3/ ' ' 0 ' ' '3. ' ' 0 ' ' '3& ' ' 0 ' ' '3- ' ' 0 ' ' '3, ' ' 0 ' ' '37 ' ' 0 ' ' '3+ ' ' 0 ' ' '
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/7. ' ' ' ' ' '/7& ' ' ' ' ' '/7- ' ' ' ' ' '/7, ' ' ' ' ' '/77 ' ' ' ' ' '/7+ ' ' ' ' ' '/74 ' ' ' ' ' '/73 ' ' ' ' ' '/+' ' ' ' ' ' '/+/ ' ' ' ' ' '/+. ' ' ' ' ' '/+& ' ' ' ' ' '/+- ' ' ' ' ' '/+, ' ' ' ' ' '/+7 ' ' ' ' ' '/++ ' ' ' ' ' '/+4 ' ' ' ' ' '/+3 ' ' ' ' ' '/4' ' ' ' ' ' '/4/ ' ' ' ' ' '/4. ' ' ' ' ' '/4& ' ' ' ' ' '/4- ' ' ' ' ' '
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7,&. ' ' ' ' ' '7,&& ' ' ' ' ' '7,&- ' ' ' ' ' '7,&, ' ' ' ' ' '7,&7 ' ' ' ' ' '7,&+ ' ' ' ' ' '7,&4 ' ' ' ' ' '7,&3 ' ' ' ' ' '7,-' ' ' ' ' ' '7,-/ ' ' ' ' ' '7,-. ' ' ' ' ' '7,-& ' ' ' ' ' '7,-- ' ' ' ' ' '7,-, ' ' ' ' ' '7,-7 ' ' ' ' ' '7,-+ ' ' ' ' ' '7,-4 ' ' ' ' ' '7,-3 ' ' ' ' ' '7,,' ' ' ' ' ' '7,,/ ' ' ' ' ' '7,,. ' ' ' ' ' '7,,& ' ' ' ' ' '7,,- ' ' ' ' ' '
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77.' ' ' ' ' ' '77./ ' ' ' ' ' '77.. ' ' ' ' ' '77.& ' ' ' ' ' '77.- ' ' ' ' ' '77., ' ' ' ' ' '77.7 ' ' ' ' ' '77.+ ' ' ' ' ' '77.4 ' ' ' ' ' '77.3 ' ' ' ' ' '77&' ' ' ' ' ' '77&/ ' ' ' ' ' '77&. ' ' ' ' ' '77&& ' ' ' ' ' '
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7733 ' ' ' ' ' '7+'' ' ' ' ' ' '7+'/ ' ' ' ' ' '7+'. ' ' ' ' ' '7+'& ' ' ' ' ' '7+'- ' ' ' ' ' '7+', ' ' ' ' ' '7+'7 ' ' ' ' ' '7+'+ ' ' ' ' ' '7+'4 ' ' ' ' ' '7+'3 ' ' ' ' ' '7+/' ' ' ' ' ' '7+// ' ' ' ' ' '7+/. ' ' ' ' ' '7+/& ' ' ' ' ' '7+/- ' ' ' ' ' '7+/, ' ' ' ' ' '7+/7 ' ' ' ' ' '7+/+ ' ' ' ' ' '7+/4 ' ' ' ' ' '7+/3 ' ' ' ' ' '7+.' ' ' ' ' ' '7+./ ' ' ' ' ' '7+.. ' ' ' ' ' '7+.& ' ' ' ' ' '7+.- ' ' ' ' ' '7+., ' ' ' ' ' '7+.7 ' ' ' ' ' '
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7+.+ ' ' ' ' ' '7+.4 ' ' ' ' ' '7+.3 ' ' ' ' ' '7+&' ' ' ' ' ' '7+&/ ' ' ' ' ' '7+&. ' ' ' ' ' '7+&& ' ' ' ' ' '7+&- ' ' ' ' ' '7+&, ' ' ' ' ' '7+&7 ' ' ' ' ' '7+&+ ' ' ' ' ' '7+&4 ' ' ' ' ' '7+&3 ' ' ' ' ' '7+-' ' ' ' ' ' '7+-/ ' ' ' ' ' '7+-. ' ' ' ' ' '7+-& ' ' ' ' ' '7+-- ' ' ' ' ' '7+-, ' ' ' ' ' '7+-7 ' ' ' ' ' '7+-+ ' ' ' ' ' '7+-4 ' ' ' ' ' '7+-3 ' ' ' ' ' '
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7+7- ' ' ' ' ' '7+7, ' ' ' ' ' '7+77 ' ' ' ' ' '7+7+ ' ' ' ' ' '7+74 ' ' ' ' ' '7+73 ' ' ' ' ' '7++' ' ' ' ' ' '7++/ ' ' ' ' ' '7++. ' ' ' ' ' '7++& ' ' ' ' ' '7++- ' ' ' ' ' '7++, ' ' ' ' ' '7++7 ' ' ' ' ' '7+++ ' ' ' ' ' '7++4 ' ' ' ' ' '7++3 ' ' ' ' ' '7+4' ' ' ' ' ' '7+4/ ' ' ' ' ' '7+4. ' ' ' ' ' '7+4& ' ' ' ' ' '7+4- ' ' ' ' ' '7+4, ' ' ' ' ' '7+47 ' ' ' ' ' '7+4+ ' ' ' ' ' '7+44 ' ' ' ' ' '7+43 ' ' ' ' ' '7+3' ' ' ' ' ' '7+3/ ' ' ' ' ' '
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7+3. ' ' ' ' ' '7+3& ' ' ' ' ' '7+3- ' ' ' ' ' '7+3, ' ' ' ' ' '7+37 ' ' ' ' ' '7+3+ ' ' ' ' ' '7+34 ' ' ' ' ' '7+33 ' ' ' ' ' '74'' ' ' ' ' ' '74'/ ' ' ' ' ' '74'. ' ' ' ' ' '74'& ' ' ' ' ' '74'- ' ' ' ' ' '74', ' ' ' ' ' '74'7 ' ' ' ' ' '74'+ ' ' ' ' ' '74'4 ' ' ' ' ' '74'3 ' ' ' ' ' '74/' ' ' ' ' ' '74// ' ' ' ' ' '74/. ' ' ' ' ' '74/& ' ' ' ' ' '74/- ' ' ' ' ' '
74/, ' ' ' ' ' '74/7 ' ' ' ' ' '74/+ ' ' ' ' ' '74/4 ' ' ' ' ' '74/3 ' ' ' ' ' '74.' ' ' ' ' ' '74./ ' ' ' ' ' '74.. ' ' ' ' ' '74.& ' ' ' ' ' '74.- ' ' ' ' ' '74., ' ' ' ' ' '74.7 ' ' ' ' ' '74.+ ' ' ' ' ' '74.4 ' ' ' ' ' '
74.3 ' ' ' ' ' '74&' ' ' ' ' ' '74&/ ' ' ' ' ' '74&. ' ' ' ' ' '74&& ' ' ' ' ' '74&- ' ' ' ' ' '74&, ' ' ' ' ' '74&7 ' ' ' ' ' '74&+ ' ' ' ' ' '74&4 ' ' ' ' ' '74&3 ' ' ' ' ' '74-' ' ' ' ' ' '74-/ ' ' ' ' ' '74-. ' ' ' ' ' '74-& ' ' ' ' ' '74-- ' ' ' ' ' '74-, ' ' ' ' ' '74-7 ' ' ' ' ' '74-+ ' ' ' ' ' '74-4 ' ' ' ' ' '74-3 ' ' ' ' ' '74,' ' ' ' ' ' '74,/ ' ' ' ' ' '74,. ' ' ' ' ' '74,& ' ' ' ' ' '74,- ' ' ' ' ' '74,, ' ' ' ' ' '74,7 ' ' ' ' ' '
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74,+ ' ' ' ' ' '74,4 ' ' ' ' ' '74,3 ' ' ' ' ' '747' ' ' ' ' ' '747/ ' ' ' ' ' '747. ' ' ' ' ' '747& ' ' ' ' ' '747- ' ' ' ' ' '747, ' ' ' ' ' '7477 ' ' ' ' ' '747+ ' ' ' ' ' '7474 ' ' ' ' ' '7473 ' ' ' ' ' '74+' ' ' ' ' ' '74+/ ' ' ' ' ' '74+. ' ' ' ' ' '74+& ' ' ' ' ' '74+- ' ' ' ' ' '74+, ' ' ' ' ' '74+7 ' ' ' ' ' '74++ ' ' ' ' ' '74+4 ' ' ' ' ' '74+3 ' ' ' ' ' '
744' ' ' ' ' ' '744/ ' ' ' ' ' '744. ' ' ' ' ' '744& ' ' ' ' ' '744- ' ' ' ' ' '744, ' ' ' ' ' '7447 ' ' ' ' ' '744+ ' ' ' ' ' '7444 ' ' ' ' ' '7443 ' ' ' ' ' '743' ' ' ' ' ' '743/ ' ' ' ' ' '743. ' ' ' ' ' '743& ' ' ' ' ' '
743- ' ' ' ' ' '743, ' ' ' ' ' '7437 ' ' ' ' ' '743+ ' ' ' ' ' '7434 ' ' ' ' ' '7433 ' ' ' ' ' '73'' ' ' ' ' ' '73'/ ' ' ' ' ' '73'. ' ' ' ' ' '73'& ' ' ' ' ' '73'- ' ' ' ' ' '73', ' ' ' ' ' '73'7 ' ' ' ' ' '73'+ ' ' ' ' ' '73'4 ' ' ' ' ' '73'3 ' ' ' ' ' '73/' ' ' ' ' ' '73// ' ' ' ' ' '73/. ' ' ' ' ' '73/& ' ' ' ' ' '73/- ' ' ' ' ' '73/, ' ' ' ' ' '73/7 ' ' ' ' ' '73/+ ' ' ' ' ' '73/4 ' ' ' ' ' '73/3 ' ' ' ' ' '73.' ' ' ' ' ' '73./ ' ' ' ' ' '
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73.. ' ' ' ' ' '73.& ' ' ' ' ' '73.- ' ' ' ' ' '73., ' ' ' ' ' '73.7 ' ' ' ' ' '73.+ ' ' ' ' ' '73.4 ' ' ' ' ' '73.3 ' ' ' ' ' '73&' ' ' ' ' ' '73&/ ' ' ' ' ' '73&. ' ' ' ' ' '73&& ' ' ' ' ' '73&- ' ' ' ' ' '73&, ' ' ' ' ' '73&7 ' ' ' ' ' '73&+ ' ' ' ' ' '73&4 ' ' ' ' ' '73&3 ' ' ' ' ' '73-' ' ' ' ' ' '73-/ ' ' ' ' ' '73-. ' ' ' ' ' '73-& ' ' ' ' ' '73-- ' ' ' ' ' '
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73,3 ' ' ' ' ' '737' ' ' ' ' ' '737/ ' ' ' ' ' '737. ' ' ' ' ' '737& ' ' ' ' ' '737- ' ' ' ' ' '737, ' ' ' ' ' '7377 ' ' ' ' ' '737+ ' ' ' ' ' '7374 ' ' ' ' ' '7373 ' ' ' ' ' '73+' ' ' ' ' ' '73+/ ' ' ' ' ' '73+. ' ' ' ' ' '73+& ' ' ' ' ' '73+- ' ' ' ' ' '73+, ' ' ' ' ' '73+7 ' ' ' ' ' '73++ ' ' ' ' ' '73+4 ' ' ' ' ' '73+3 ' ' ' ' ' '734' ' ' ' ' ' '734/ ' ' ' ' ' '734. ' ' ' ' ' '734& ' ' ' ' ' '734- ' ' ' ' ' '734, ' ' ' ' ' '7347 ' ' ' ' ' '
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+'/' ' ' ' ' ' '+'// ' ' ' ' ' '+'/. ' ' ' ' ' '+'/& ' ' ' ' ' '+'/- ' ' ' ' ' '+'/, ' ' ' ' ' '+'/7 ' ' ' ' ' '+'/+ ' ' ' ' ' '+'/4 ' ' ' ' ' '+'/3 ' ' ' ' ' '+'.' ' ' ' ' ' '+'./ ' ' ' ' ' '+'.. ' ' ' ' ' '+'.& ' ' ' ' ' '
+'.- ' ' ' ' ' '+'., ' ' ' ' ' '+'.7 ' ' ' ' ' '+'.+ ' ' ' ' ' '+'.4 ' ' ' ' ' '+'.3 ' ' ' ' ' '+'&' ' ' ' ' ' '+'&/ ' ' ' ' ' '+'&. ' ' ' ' ' '+'&& ' ' ' ' ' '+'&- ' ' ' ' ' '+'&, ' ' ' ' ' '+'&7 ' ' ' ' ' '+'&+ ' ' ' ' ' '+'&4 ' ' ' ' ' '+'&3 ' ' ' ' ' '+'-' ' ' ' ' ' '+'-/ ' ' ' ' ' '+'-. ' ' ' ' ' '+'-& ' ' ' ' ' '+'-- ' ' ' ' ' '+'-, ' ' ' ' ' '+'-7 ' ' ' ' ' '+'-+ ' ' ' ' ' '+'-4 ' ' ' ' ' '+'-3 ' ' ' ' ' '+',' ' ' ' ' ' '+',/ ' ' ' ' ' '
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+'+, ' ' ' ' ' '+'+7 ' ' ' ' ' '+'++ ' ' ' ' ' '+'+4 ' ' ' ' ' '+'+3 ' ' ' ' ' '+'4' ' ' ' ' ' '+'4/ ' ' ' ' ' '+'4. ' ' ' ' ' '+'4& ' ' ' ' ' '+'4- ' ' ' ' ' '+'4, ' ' ' ' ' '+'47 ' ' ' ' ' '+'4+ ' ' ' ' ' '+'44 ' ' ' ' ' '
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+/-' ' ' ' ' ' '+/-/ ' ' ' ' ' '+/-. ' ' ' ' ' '+/-& ' ' ' ' ' '+/-- ' ' ' ' ' '+/-, ' ' ' ' ' '+/-7 ' ' ' ' ' '+/-+ ' ' ' ' ' '+/-4 ' ' ' ' ' '+/-3 ' ' ' ' ' '+/,' ' ' ' ' ' '+/,/ ' ' ' ' ' '+/,. ' ' ' ' ' '+/,& ' ' ' ' ' '
+/,- ' ' ' ' ' '+/,, ' ' ' ' ' '+/,7 ' ' ' ' ' '+/,+ ' ' ' ' ' '+/,4 ' ' ' ' ' '+/,3 ' ' ' ' ' '+/7' ' ' ' ' ' '+/7/ ' ' ' ' ' '+/7. ' ' ' ' ' '+/7& ' ' ' ' ' '+/7- ' ' ' ' ' '+/7, ' ' ' ' ' '+/77 ' ' ' ' ' '+/7+ ' ' ' ' ' '+/74 ' ' ' ' ' '+/73 ' ' ' ' ' '+/+' ' ' ' ' ' '+/+/ ' ' ' ' ' '+/+. ' ' ' ' ' '+/+& ' ' ' ' ' '+/+- ' ' ' ' ' '+/+, ' ' ' ' ' '+/+7 ' ' ' ' ' '+/++ ' ' ' ' ' '+/+4 ' ' ' ' ' '+/+3 ' ' ' ' ' '+/4' ' ' ' ' ' '+/4/ ' ' ' ' ' '
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+.+' ' ' ' ' ' '+.+/ ' ' ' ' ' '+.+. ' ' ' ' ' '+.+& ' ' ' ' ' '+.+- ' ' ' ' ' '+.+, ' ' ' ' ' '+.+7 ' ' ' ' ' '+.++ ' ' ' ' ' '+.+4 ' ' ' ' ' '+.+3 ' ' ' ' ' '+.4' ' ' ' ' ' '+.4/ ' ' ' ' ' '+.4. ' ' ' ' ' '+.4& ' ' ' ' ' '
+.4- ' ' ' ' ' '+.4, ' ' ' ' ' '+.47 ' ' ' ' ' '+.4+ ' ' ' ' ' '+.44 ' ' ' ' ' '+.43 ' ' ' ' ' '+.3' ' ' ' ' ' '+.3/ ' ' ' ' ' '+.3. ' ' ' ' ' '+.3& ' ' ' ' ' '+.3- ' ' ' ' ' '+.3, ' ' ' ' ' '+.37 ' ' ' ' ' '+.3+ ' ' ' ' ' '+.34 ' ' ' ' ' '+.33 ' ' ' ' ' '+&'' ' ' ' ' ' '+&'/ ' ' ' ' ' '+&'. ' ' ' ' ' '+&'& ' ' ' ' ' '+&'- ' ' ' ' ' '+&', ' ' ' ' ' '+&'7 ' ' ' ' ' '+&'+ ' ' ' ' ' '+&'4 ' ' ' ' ' '+&'3 ' ' ' ' ' '+&/' ' ' ' ' ' '+&// ' ' ' ' ' '
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+&/. ' ' ' ' ' '+&/& ' ' ' ' ' '+&/- ' ' ' ' ' '+&/, ' ' ' ' ' '+&/7 ' ' ' ' ' '+&/+ ' ' ' ' ' '+&/4 ' ' ' ' ' '+&/3 ' ' ' ' ' '+&.' ' ' ' ' ' '+&./ ' ' ' ' ' '+&.. ' ' ' ' ' '+&.& ' ' ' ' ' '+&.- ' ' ' ' ' '+&., ' ' ' ' ' '+&.7 ' ' ' ' ' '+&.+ ' ' ' ' ' '+&.4 ' ' ' ' ' '+&.3 ' ' ' ' ' '+&&' ' ' ' ' ' '+&&/ ' ' ' ' ' '+&&. ' ' ' ' ' '+&&& ' ' ' ' ' '+&&- ' ' ' ' ' '
+&&, ' ' ' ' ' '+&&7 ' ' ' ' ' '+&&+ ' ' ' ' ' '+&&4 ' ' ' ' ' '+&&3 ' ' ' ' ' '+&-' ' ' ' ' ' '+&-/ ' ' ' ' ' '+&-. ' ' ' ' ' '+&-& ' ' ' ' ' '+&-- ' ' ' ' ' '+&-, ' ' ' ' ' '+&-7 ' ' ' ' ' '+&-+ ' ' ' ' ' '+&-4 ' ' ' ' ' '
+&-3 ' ' ' ' ' '+&,' ' ' ' ' ' '+&,/ ' ' ' ' ' '+&,. ' ' ' ' ' '+&,& ' ' ' ' ' '+&,- ' ' ' ' ' '+&,, ' ' ' ' ' '+&,7 ' ' ' ' ' '+&,+ ' ' ' ' ' '+&,4 ' ' ' ' ' '+&,3 ' ' ' ' ' '+&7' ' ' ' ' ' '+&7/ ' ' ' ' ' '+&7. ' ' ' ' ' '+&7& ' ' ' ' ' '+&7- ' ' ' ' ' '+&7, ' ' ' ' ' '+&77 ' ' ' ' ' '+&7+ ' ' ' ' ' '+&74 ' ' ' ' ' '+&73 ' ' ' ' ' '+&+' ' ' ' ' ' '+&+/ ' ' ' ' ' '+&+. ' ' ' ' ' '+&+& ' ' ' ' ' '+&+- ' ' ' ' ' '+&+, ' ' ' ' ' '+&+7 ' ' ' ' ' '
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+&++ ' ' ' ' ' '+&+4 ' ' ' ' ' '+&+3 ' ' ' ' ' '+&4' ' ' ' ' ' '+&4/ ' ' ' ' ' '+&4. ' ' ' ' ' '+&4& ' ' ' ' ' '+&4- ' ' ' ' ' '+&4, ' ' ' ' ' '+&47 ' ' ' ' ' '+&4+ ' ' ' ' ' '+&44 ' ' ' ' ' '+&43 ' ' ' ' ' '+&3' ' ' ' ' ' '+&3/ ' ' ' ' ' '+&3. ' ' ' ' ' '+&3& ' ' ' ' ' '+&3- ' ' ' ' ' '+&3, ' ' ' ' ' '+&37 ' ' ' ' ' '+&3+ ' ' ' ' ' '+&34 ' ' ' ' ' '+&33 ' ' ' ' ' '
+-'' ' ' ' ' ' '+-'/ ' ' ' ' ' '+-'. ' ' ' ' ' '+-'& ' ' ' ' ' '+-'- ' ' ' ' ' '+-', ' ' ' ' ' '+-'7 ' ' ' ' ' '+-'+ ' ' ' ' ' '+-'4 ' ' ' ' ' '+-'3 ' ' ' ' ' '+-/' ' ' ' ' ' '+-// ' ' ' ' ' '+-/. ' ' ' ' ' '+-/& ' ' ' ' ' '
+-/- ' ' ' ' ' '+-/, ' ' ' ' ' '+-/7 ' ' ' ' ' '+-/+ ' ' ' ' ' '+-/4 ' ' ' ' ' '+-/3 ' ' ' ' ' '+-.' ' ' ' ' ' '+-./ ' ' ' ' ' '+-.. ' ' ' ' ' '+-.& ' ' ' ' ' '+-.- ' ' ' ' ' '+-., ' ' ' ' ' '+-.7 ' ' ' ' ' '+-.+ ' ' ' ' ' '+-.4 ' ' ' ' ' '+-.3 ' ' ' ' ' '+-&' ' ' ' ' ' '+-&/ ' ' ' ' ' '+-&. ' ' ' ' ' '+-&& ' ' ' ' ' '+-&- ' ' ' ' ' '+-&, ' ' ' ' ' '+-&7 ' ' ' ' ' '+-&+ ' ' ' ' ' '+-&4 ' ' ' ' ' '+-&3 ' ' ' ' ' '+--' ' ' ' ' ' '+--/ ' ' ' ' ' '
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+--. ' ' ' ' ' '+--& ' ' ' ' ' '+--- ' ' ' ' ' '+--, ' ' ' ' ' '+--7 ' ' ' ' ' '+--+ ' ' ' ' ' '+--4 ' ' ' ' ' '+--3 ' ' ' ' ' '+-,' ' ' ' ' ' '+-,/ ' ' ' ' ' '+-,. ' ' ' ' ' '+-,& ' ' ' ' ' '+-,- ' ' ' ' ' '+-,, ' ' ' ' ' '+-,7 ' ' ' ' ' '+-,+ ' ' ' ' ' '+-,4 ' ' ' ' ' '+-,3 ' ' ' ' ' '+-7' ' ' ' ' ' '+-7/ ' ' ' ' ' '+-7. ' ' ' ' ' '+-7& ' ' ' ' ' '+-7- ' ' ' ' ' '
+-7, ' ' ' ' ' '+-77 ' ' ' ' ' '+-7+ ' ' ' ' ' '+-74 ' ' ' ' ' '+-73 ' ' ' ' ' '+-+' ' ' ' ' ' '+-+/ ' ' ' ' ' '+-+. ' ' ' ' ' '+-+& ' ' ' ' ' '+-+- ' ' ' ' ' '+-+, ' ' ' ' ' '+-+7 ' ' ' ' ' '+-++ ' ' ' ' ' '+-+4 ' ' ' ' ' '
+-+3 ' ' ' ' ' '+-4' ' ' ' ' ' '+-4/ ' ' ' ' ' '+-4. ' ' ' ' ' '+-4& ' ' ' ' ' '+-4- ' ' ' ' ' '+-4, ' ' ' ' ' '+-47 ' ' ' ' ' '+-4+ ' ' ' ' ' '+-44 ' ' ' ' ' '+-43 ' ' ' ' ' '+-3' ' ' ' ' ' '+-3/ ' ' ' ' ' '+-3. ' ' ' ' ' '+-3& ' ' ' ' ' '+-3- ' ' ' ' ' '+-3, ' ' ' ' ' '+-37 ' ' ' ' ' '+-3+ ' ' ' ' ' '+-34 ' ' ' ' ' '+-33 ' ' ' ' ' '+,'' ' ' ' ' ' '+,'/ ' ' ' ' ' '+,'. ' ' ' ' ' '+,'& ' ' ' ' ' '+,'- ' ' ' ' ' '+,', ' ' ' ' ' '+,'7 ' ' ' ' ' '
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+,'+ ' ' ' ' ' '+,'4 ' ' ' ' ' '+,'3 ' ' ' ' ' '+,/' ' ' ' ' ' '+,// ' ' ' ' ' '+,/. ' ' ' ' ' '+,/& ' ' ' ' ' '+,/- ' ' ' ' ' '+,/, ' ' ' ' ' '+,/7 ' ' ' ' ' '+,/+ ' ' ' ' ' '+,/4 ' ' ' ' ' '+,/3 ' ' ' ' ' '+,.' ' ' ' ' ' '+,./ ' ' ' ' ' '+,.. ' ' ' ' ' '+,.& ' ' ' ' ' '+,.- ' ' ' ' ' '+,., ' ' ' ' ' '+,.7 ' ' ' ' ' '+,.+ ' ' ' ' ' '+,.4 ' ' ' ' ' '+,.3 ' ' ' ' ' '
+,&' ' ' ' ' ' '+,&/ ' ' ' ' ' '+,&. ' ' ' ' ' '+,&& ' ' ' ' ' '+,&- ' ' ' ' ' '+,&, ' ' ' ' ' '+,&7 ' ' ' ' ' '+,&+ ' ' ' ' ' '+,&4 ' ' ' ' ' '+,&3 ' ' ' ' ' '+,-' ' ' ' ' ' '+,-/ ' ' ' ' ' '+,-. ' ' ' ' ' '+,-& ' ' ' ' ' '
+,-- ' ' ' ' ' '+,-, ' ' ' ' ' '+,-7 ' ' ' ' ' '+,-+ ' ' ' ' ' '+,-4 ' ' ' ' ' '+,-3 ' ' ' ' ' '+,,' ' ' ' ' ' '+,,/ ' ' ' ' ' '+,,. ' ' ' ' ' '+,,& ' ' ' ' ' '+,,- ' ' ' ' ' '+,,, ' ' ' ' ' '+,,7 ' ' ' ' ' '+,,+ ' ' ' ' ' '+,,4 ' ' ' ' ' '+,,3 ' ' ' ' ' '+,7' ' ' ' ' ' '+,7/ ' ' ' ' ' '+,7. ' ' ' ' ' '+,7& ' ' ' ' ' '+,7- ' ' ' ' ' '+,7, ' ' ' ' ' '+,77 ' ' ' ' ' '+,7+ ' ' ' ' ' '+,74 ' ' ' ' ' '+,73 ' ' ' ' ' '+,+' ' ' ' ' ' '+,+/ ' ' ' ' ' '
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+,+. ' ' ' ' ' '+,+& ' ' ' ' ' '+,+- ' ' ' ' ' '+,+, ' ' ' ' ' '+,+7 ' ' ' ' ' '+,++ ' ' ' ' ' '+,+4 ' ' ' ' ' '+,+3 ' ' ' ' ' '+,4' ' ' ' ' ' '+,4/ ' ' ' ' ' '+,4. ' ' ' ' ' '+,4& ' ' ' ' ' '+,4- ' ' ' ' ' '+,4, ' ' ' ' ' '+,47 ' ' ' ' ' '+,4+ ' ' ' ' ' '+,44 ' ' ' ' ' '+,43 ' ' ' ' ' '+,3' ' ' ' ' ' '+,3/ ' ' ' ' ' '+,3. ' ' ' ' ' '+,3& ' ' ' ' ' '+,3- ' ' ' ' ' '
+,3, ' ' ' ' ' '+,37 ' ' ' ' ' '+,3+ ' ' ' ' ' '+,34 ' ' ' ' ' '+,33 ' ' ' ' ' '+7'' ' ' ' ' ' '+7'/ ' ' ' ' ' '+7'. ' ' ' ' ' '+7'& ' ' ' ' ' '+7'- ' ' ' ' ' '+7', ' ' ' ' ' '+7'7 ' ' ' ' ' '+7'+ ' ' ' ' ' '+7'4 ' ' ' ' ' '
+7'3 ' ' ' ' ' '+7/' ' ' ' ' ' '+7// ' ' ' ' ' '+7/. ' ' ' ' ' '+7/& ' ' ' ' ' '+7/- ' ' ' ' ' '+7/, ' ' ' ' ' '+7/7 ' ' ' ' ' '+7/+ ' ' ' ' ' '+7/4 ' ' ' ' ' '+7/3 ' ' ' ' ' '+7.' ' ' ' ' ' '+7./ ' ' ' ' ' '+7.. ' ' ' ' ' '+7.& ' ' ' ' ' '+7.- ' ' ' ' ' '+7., ' ' ' ' ' '+7.7 ' ' ' ' ' '+7.+ ' ' ' ' ' '+7.4 ' ' ' ' ' '+7.3 ' ' ' ' ' '+7&' ' ' ' ' ' '+7&/ ' ' ' ' ' '+7&. ' ' ' ' ' '+7&& ' ' ' ' ' '+7&- ' ' ' ' ' '+7&, ' ' ' ' ' '+7&7 ' ' ' ' ' '
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+7&+ ' ' ' ' ' '+7&4 ' ' ' ' ' '+7&3 ' ' ' ' ' '+7-' ' ' ' ' ' '+7-/ ' ' ' ' ' '+7-. ' ' ' ' ' '+7-& ' ' ' ' ' '+7-- ' ' ' ' ' '+7-, ' ' ' ' ' '+7-7 ' ' ' ' ' '+7-+ ' ' ' ' ' '+7-4 ' ' ' ' ' '+7-3 ' ' ' ' ' '+7,' ' ' ' ' ' '+7,/ ' ' ' ' ' '+7,. ' ' ' ' ' '+7,& ' ' ' ' ' '+7,- ' ' ' ' ' '+7,, ' ' ' ' ' '+7,7 ' ' ' ' ' '+7,+ ' ' ' ' ' '+7,4 ' ' ' ' ' '+7,3 ' ' ' ' ' '
+77' ' ' ' ' ' '+77/ ' ' ' ' ' '+77. ' ' ' ' ' '+77& ' ' ' ' ' '+77- ' ' ' ' ' '+77, ' ' ' ' ' '+777 ' ' ' ' ' '+77+ ' ' ' ' ' '+774 ' ' ' ' ' '+773 ' ' ' ' ' '+7+' ' ' ' ' ' '+7+/ ' ' ' ' ' '+7+. ' ' ' ' ' '+7+& ' ' ' ' ' '
+7+- ' ' ' ' ' '+7+, ' ' ' ' ' '+7+7 ' ' ' ' ' '+7++ ' ' ' ' ' '+7+4 ' ' ' ' ' '+7+3 ' ' ' ' ' '+74' ' ' ' ' ' '+74/ ' ' ' ' ' '+74. ' ' ' ' ' '+74& ' ' ' ' ' '+74- ' ' ' ' ' '+74, ' ' ' ' ' '+747 ' ' ' ' ' '+74+ ' ' ' ' ' '+744 ' ' ' ' ' '+743 ' ' ' ' ' '+73' ' ' ' ' ' '+73/ ' ' ' ' ' '+73. ' ' ' ' ' '+73& ' ' ' ' ' '+73- ' ' ' ' ' '+73, ' ' ' ' ' '+737 ' ' ' ' ' '+73+ ' ' ' ' ' '+734 ' ' ' ' ' '+733 ' ' ' ' ' '++'' ' ' ' ' ' '++'/ ' ' ' ' ' '
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++'. ' ' ' ' ' '++'& ' ' ' ' ' '++'- ' ' ' ' ' '++', ' ' ' ' ' '++'7 ' ' ' ' ' '++'+ ' ' ' ' ' '++'4 ' ' ' ' ' '++'3 ' ' ' ' ' '++/' ' ' ' ' ' '++// ' ' ' ' ' '++/. ' ' ' ' ' '++/& ' ' ' ' ' '++/- ' ' ' ' ' '++/, ' ' ' ' ' '++/7 ' ' ' ' ' '++/+ ' ' ' ' ' '++/4 ' ' ' ' ' '++/3 ' ' ' ' ' '++.' ' ' ' ' ' '++./ ' ' ' ' ' '++.. ' ' ' ' ' '++.& ' ' ' ' ' '++.- ' ' ' ' ' '
++., ' ' ' ' ' '++.7 ' ' ' ' ' '++.+ ' ' ' ' ' '++.4 ' ' ' ' ' '++.3 ' ' ' ' ' '++&' ' ' ' ' ' '++&/ ' ' ' ' ' '++&. ' ' ' ' ' '++&& ' ' ' ' ' '++&- ' ' ' ' ' '++&, ' ' ' ' ' '++&7 ' ' ' ' ' '++&+ ' ' ' ' ' '++&4 ' ' ' ' ' '
++&3 ' ' ' ' ' '++-' ' ' ' ' ' '++-/ ' ' ' ' ' '++-. ' ' ' ' ' '++-& ' ' ' ' ' '++-- ' ' ' ' ' '++-, ' ' ' ' ' '++-7 ' ' ' ' ' '++-+ ' ' ' ' ' '++-4 ' ' ' ' ' '++-3 ' ' ' ' ' '++,' ' ' ' ' ' '++,/ ' ' ' ' ' '++,. ' ' ' ' ' '++,& ' ' ' ' ' '++,- ' ' ' ' ' '++,, ' ' ' ' ' '++,7 ' ' ' ' ' '++,+ ' ' ' ' ' '++,4 ' ' ' ' ' '++,3 ' ' ' ' ' '++7' ' ' ' ' ' '++7/ ' ' ' ' ' '++7. ' ' ' ' ' '++7& ' ' ' ' ' '++7- ' ' ' ' ' '++7, ' ' ' ' ' '++77 ' ' ' ' ' '
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++7+ ' ' ' ' ' '++74 ' ' ' ' ' '++73 ' ' ' ' ' '+++' ' ' ' ' ' '+++/ ' ' ' ' ' '+++. ' ' ' ' ' '+++& ' ' ' ' ' '+++- ' ' ' ' ' '+++, ' ' ' ' ' '+++7 ' ' ' ' ' '++++ ' ' ' ' ' '+++4 ' ' ' ' ' '+++3 ' ' ' ' ' '++4' ' ' ' ' ' '++4/ ' ' ' ' ' '++4. ' ' ' ' ' '++4& ' ' ' ' ' '++4- ' ' ' ' ' '++4, ' ' ' ' ' '++47 ' ' ' ' ' '++4+ ' ' ' ' ' '++44 ' ' ' ' ' '++43 ' ' ' ' ' '
++3' ' ' ' ' ' '++3/ ' ' ' ' ' '++3. ' ' ' ' ' '++3& ' ' ' ' ' '++3- ' ' ' ' ' '++3, ' ' ' ' ' '++37 ' ' ' ' ' '++3+ ' ' ' ' ' '++34 ' ' ' ' ' '++33 ' ' ' ' ' '+4'' ' ' ' ' ' '+4'/ ' ' ' ' ' '+4'. ' ' ' ' ' '+4'& ' ' ' ' ' '
+4'- ' ' ' ' ' '+4', ' ' ' ' ' '+4'7 ' ' ' ' ' '+4'+ ' ' ' ' ' '+4'4 ' ' ' ' ' '+4'3 ' ' ' ' ' '+4/' ' ' ' ' ' '+4// ' ' ' ' ' '+4/. ' ' ' ' ' '+4/& ' ' ' ' ' '+4/- ' ' ' ' ' '+4/, ' ' ' ' ' '+4/7 ' ' ' ' ' '+4/+ ' ' ' ' ' '+4/4 ' ' ' ' ' '+4/3 ' ' ' ' ' '+4.' ' ' ' ' ' '+4./ ' ' ' ' ' '+4.. ' ' ' ' ' '+4.& ' ' ' ' ' '+4.- ' ' ' ' ' '+4., ' ' ' ' ' '+4.7 ' ' ' ' ' '+4.+ ' ' ' ' ' '+4.4 ' ' ' ' ' '+4.3 ' ' ' ' ' '+4&' ' ' ' ' ' '+4&/ ' ' ' ' ' '
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+43+ ' ' ' ' ' '+434 ' ' ' ' ' '+433 ' ' ' ' ' '+3'' ' ' ' ' ' '+3'/ ' ' ' ' ' '+3'. ' ' ' ' ' '+3'& ' ' ' ' ' '+3'- ' ' ' ' ' '+3', ' ' ' ' ' '+3'7 ' ' ' ' ' '+3'+ ' ' ' ' ' '+3'4 ' ' ' ' ' '+3'3 ' ' ' ' ' '+3/' ' ' ' ' ' '+3// ' ' ' ' ' '+3/. ' ' ' ' ' '+3/& ' ' ' ' ' '+3/- ' ' ' ' ' '+3/, ' ' ' ' ' '+3/7 ' ' ' ' ' '+3/+ ' ' ' ' ' '+3/4 ' ' ' ' ' '+3/3 ' ' ' ' ' '
+3.' ' ' ' ' ' '+3./ ' ' ' ' ' '+3.. ' ' ' ' ' '+3.& ' ' ' ' ' '+3.- ' ' ' ' ' '+3., ' ' ' ' ' '+3.7 ' ' ' ' ' '+3.+ ' ' ' ' ' '+3.4 ' ' ' ' ' '+3.3 ' ' ' ' ' '+3&' ' ' ' ' ' '+3&/ ' ' ' ' ' '+3&. ' ' ' ' ' '+3&& ' ' ' ' ' '
+3&- ' ' ' ' ' '+3&, ' ' ' ' ' '+3&7 ' ' ' ' ' '+3&+ ' ' ' ' ' '+3&4 ' ' ' ' ' '+3&3 ' ' ' ' ' '+3-' ' ' ' ' ' '+3-/ ' ' ' ' ' '+3-. ' ' ' ' ' '+3-& ' ' ' ' ' '+3-- ' ' ' ' ' '+3-, ' ' ' ' ' '+3-7 ' ' ' ' ' '+3-+ ' ' ' ' ' '+3-4 ' ' ' ' ' '+3-3 ' ' ' ' ' '+3,' ' ' ' ' ' '+3,/ ' ' ' ' ' '+3,. ' ' ' ' ' '+3,& ' ' ' ' ' '+3,- ' ' ' ' ' '+3,, ' ' ' ' ' '+3,7 ' ' ' ' ' '+3,+ ' ' ' ' ' '+3,4 ' ' ' ' ' '+3,3 ' ' ' ' ' '+37' ' ' ' ' ' '+37/ ' ' ' ' ' '
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+37. ' ' ' ' ' '+37& ' ' ' ' ' '+37- ' ' ' ' ' '+37, ' ' ' ' ' '+377 ' ' ' ' ' '+37+ ' ' ' ' ' '+374 ' ' ' ' ' '+373 ' ' ' ' ' '+3+' ' ' ' ' ' '+3+/ ' ' ' ' ' '+3+. ' ' ' ' ' '+3+& ' ' ' ' ' '+3+- ' ' ' ' ' '+3+, ' ' ' ' ' '+3+7 ' ' ' ' ' '+3++ ' ' ' ' ' '+3+4 ' ' ' ' ' '+3+3 ' ' ' ' ' '+34' ' ' ' ' ' '+34/ ' ' ' ' ' '+34. ' ' ' ' ' '+34& ' ' ' ' ' '+34- ' ' ' ' ' '
+34, ' ' ' ' ' '+347 ' ' ' ' ' '+34+ ' ' ' ' ' '+344 ' ' ' ' ' '+343 ' ' ' ' ' '+33' ' ' ' ' ' '+33/ ' ' ' ' ' '+33. ' ' ' ' ' '+33& ' ' ' ' ' '+33- ' ' ' ' ' '+33, ' ' ' ' ' '+337 ' ' ' ' ' '+33+ ' ' ' ' ' '+334 ' ' ' ' ' '
+333 ' ' ' ' ' '4''' ' ' ' ' ' '4''/ ' ' ' ' ' '4''. ' ' ' ' ' '4''& ' ' ' ' ' '4''- ' ' ' ' ' '4'', ' ' ' ' ' '4''7 ' ' ' ' ' '4''+ ' ' ' ' ' '4''4 ' ' ' ' ' '4''3 ' ' ' ' ' '4'/' ' ' ' ' ' '4'// ' ' ' ' ' '4'/. ' ' ' ' ' '4'/& ' ' ' ' ' '4'/- ' ' ' ' ' '4'/, ' ' ' ' ' '4'/7 ' ' ' ' ' '4'/+ ' ' ' ' ' '4'/4 ' ' ' ' ' '4'/3 ' ' ' ' ' '4'.' ' ' ' ' ' '4'./ ' ' ' ' ' '4'.. ' ' ' ' ' '4'.& ' ' ' ' ' '4'.- ' ' ' ' ' '4'., ' ' ' ' ' '4'.7 ' ' ' ' ' '
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4'.+ ' ' ' ' ' '4'.4 ' ' ' ' ' '4'.3 ' ' ' ' ' '4'&' ' ' ' ' ' '4'&/ ' ' ' ' ' '4'&. ' ' ' ' ' '4'&& ' ' ' ' ' '4'&- ' ' ' ' ' '4'&, ' ' ' ' ' '4'&7 ' ' ' ' ' '4'&+ ' ' ' ' ' '4'&4 ' ' ' ' ' '4'&3 ' ' ' ' ' '4'-' ' ' ' ' ' '4'-/ ' ' ' ' ' '4'-. ' ' ' ' ' '4'-& ' ' ' ' ' '4'-- ' ' ' ' ' '4'-, ' ' ' ' ' '4'-7 ' ' ' ' ' '4'-+ ' ' ' ' ' '4'-4 ' ' ' ' ' '4'-3 ' ' ' ' ' '
4',' ' ' ' ' ' '4',/ ' ' ' ' ' '4',. ' ' ' ' ' '4',& ' ' ' ' ' '4',- ' ' ' ' ' '4',, ' ' ' ' ' '4',7 ' ' ' ' ' '4',+ ' ' ' ' ' '4',4 ' ' ' ' ' '4',3 ' ' ' ' ' '4'7' ' ' ' ' ' '4'7/ ' ' ' ' ' '4'7. ' ' ' ' ' '4'7& ' ' ' ' ' '
4'7- ' ' ' ' ' '4'7, ' ' ' ' ' '4'77 ' ' ' ' ' '4'7+ ' ' ' ' ' '4'74 ' ' ' ' ' '4'73 ' ' ' ' ' '4'+' ' ' ' ' ' '4'+/ ' ' ' ' ' '4'+. ' ' ' ' ' '4'+& ' ' ' ' ' '4'+- ' ' ' ' ' '4'+, ' ' ' ' ' '4'+7 ' ' ' ' ' '4'++ ' ' ' ' ' '4'+4 ' ' ' ' ' '4'+3 ' ' ' ' ' '4'4' ' ' ' ' ' '4'4/ ' ' ' ' ' '4'4. ' ' ' ' ' '4'4& ' ' ' ' ' '4'4- ' ' ' ' ' '4'4, ' ' ' ' ' '4'47 ' ' ' ' ' '4'4+ ' ' ' ' ' '4'44 ' ' ' ' ' '4'43 ' ' ' ' ' '4'3' ' ' ' ' ' '4'3/ ' ' ' ' ' '
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4'3. ' ' ' ' ' '4'3& ' ' ' ' ' '4'3- ' ' ' ' ' '4'3, ' ' ' ' ' '4'37 ' ' ' ' ' '4'3+ ' ' ' ' ' '4'34 ' ' ' ' ' '4'33 ' ' ' ' ' '4/'' ' ' ' ' ' '4/'/ ' ' ' ' ' '4/'. ' ' ' ' ' '4/'& ' ' ' ' ' '4/'- ' ' ' ' ' '4/', ' ' ' ' ' '4/'7 ' ' ' ' ' '4/'+ ' ' ' ' ' '4/'4 ' ' ' ' ' '4/'3 ' ' ' ' ' '4//' ' ' ' ' ' '4/// ' ' ' ' ' '4//. ' ' ' ' ' '4//& ' ' ' ' ' '4//- ' ' ' ' ' '
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4/.3 ' ' ' ' ' '4/&' ' ' ' ' ' '4/&/ ' ' ' ' ' '4/&. ' ' ' ' ' '4/&& ' ' ' ' ' '4/&- ' ' ' ' ' '4/&, ' ' ' ' ' '4/&7 ' ' ' ' ' '4/&+ ' ' ' ' ' '4/&4 ' ' ' ' ' '4/&3 ' ' ' ' ' '4/-' ' ' ' ' ' '4/-/ ' ' ' ' ' '4/-. ' ' ' ' ' '4/-& ' ' ' ' ' '4/-- ' ' ' ' ' '4/-, ' ' ' ' ' '4/-7 ' ' ' ' ' '4/-+ ' ' ' ' ' '4/-4 ' ' ' ' ' '4/-3 ' ' ' ' ' '4/,' ' ' ' ' ' '4/,/ ' ' ' ' ' '4/,. ' ' ' ' ' '4/,& ' ' ' ' ' '4/,- ' ' ' ' ' '4/,, ' ' ' ' ' '4/,7 ' ' ' ' ' '
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4.4+ ' ' ' ' ' '4.44 ' ' ' ' ' '4.43 ' ' ' ' ' '4.3' ' ' ' ' ' '4.3/ ' ' ' ' ' '4.3. ' ' ' ' ' '4.3& ' ' ' ' ' '4.3- ' ' ' ' ' '4.3, ' ' ' ' ' '4.37 ' ' ' ' ' '4.3+ ' ' ' ' ' '4.34 ' ' ' ' ' '4.33 ' ' ' ' ' '4&'' ' ' ' ' ' '4&'/ ' ' ' ' ' '4&'. ' ' ' ' ' '4&'& ' ' ' ' ' '4&'- ' ' ' ' ' '4&', ' ' ' ' ' '4&'7 ' ' ' ' ' '4&'+ ' ' ' ' ' '4&'4 ' ' ' ' ' '4&'3 ' ' ' ' ' '
4&/' ' ' ' ' ' '4&// ' ' ' ' ' '4&/. ' ' ' ' ' '4&/& ' ' ' ' ' '4&/- ' ' ' ' ' '4&/, ' ' ' ' ' '4&/7 ' ' ' ' ' '4&/+ ' ' ' ' ' '4&/4 ' ' ' ' ' '4&/3 ' ' ' ' ' '4&.' ' ' ' ' ' '4&./ ' ' ' ' ' '4&.. ' ' ' ' ' '4&.& ' ' ' ' ' '
4&.- ' ' ' ' ' '4&., ' ' ' ' ' '4&.7 ' ' ' ' ' '4&.+ ' ' ' ' ' '4&.4 ' ' ' ' ' '4&.3 ' ' ' ' ' '4&&' ' ' ' ' ' '4&&/ ' ' ' ' ' '4&&. ' ' ' ' ' '4&&& ' ' ' ' ' '4&&- ' ' ' ' ' '4&&, ' ' ' ' ' '4&&7 ' ' ' ' ' '4&&+ ' ' ' ' ' '4&&4 ' ' ' ' ' '4&&3 ' ' ' ' ' '4&-' ' ' ' ' ' '4&-/ ' ' ' ' ' '4&-. ' ' ' ' ' '4&-& ' ' ' ' ' '4&-- ' ' ' ' ' '4&-, ' ' ' ' ' '4&-7 ' ' ' ' ' '4&-+ ' ' ' ' ' '4&-4 ' ' ' ' ' '4&-3 ' ' ' ' ' '4&,' ' ' ' ' ' '4&,/ ' ' ' ' ' '
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4&,. ' ' ' ' ' '4&,& ' ' ' ' ' '4&,- ' ' ' ' ' '4&,, ' ' ' ' ' '4&,7 ' ' ' ' ' '4&,+ ' ' ' ' ' '4&,4 ' ' ' ' ' '4&,3 ' ' ' ' ' '4&7' ' ' ' ' ' '4&7/ ' ' ' ' ' '4&7. ' ' ' ' ' '4&7& ' ' ' ' ' '4&7- ' ' ' ' ' '4&7, ' ' ' ' ' '4&77 ' ' ' ' ' '4&7+ ' ' ' ' ' '4&74 ' ' ' ' ' '4&73 ' ' ' ' ' '4&+' ' ' ' ' ' '4&+/ ' ' ' ' ' '4&+. ' ' ' ' ' '4&+& ' ' ' ' ' '4&+- ' ' ' ' ' '
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4&43 ' ' ' ' ' '4&3' ' ' ' ' ' '4&3/ ' ' ' ' ' '4&3. ' ' ' ' ' '4&3& ' ' ' ' ' '4&3- ' ' ' ' ' '4&3, ' ' ' ' ' '4&37 ' ' ' ' ' '4&3+ ' ' ' ' ' '4&34 ' ' ' ' ' '4&33 ' ' ' ' ' '4-'' ' ' ' ' ' '4-'/ ' ' ' ' ' '4-'. ' ' ' ' ' '4-'& ' ' ' ' ' '4-'- ' ' ' ' ' '4-', ' ' ' ' ' '4-'7 ' ' ' ' ' '4-'+ ' ' ' ' ' '4-'4 ' ' ' ' ' '4-'3 ' ' ' ' ' '4-/' ' ' ' ' ' '4-// ' ' ' ' ' '4-/. ' ' ' ' ' '4-/& ' ' ' ' ' '4-/- ' ' ' ' ' '4-/, ' ' ' ' ' '4-/7 ' ' ' ' ' '
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4-/+ ' ' ' ' ' '4-/4 ' ' ' ' ' '4-/3 ' ' ' ' ' '4-.' ' ' ' ' ' '4-./ ' ' ' ' ' '4-.. ' ' ' ' ' '4-.& ' ' ' ' ' '4-.- ' ' ' ' ' '4-., ' ' ' ' ' '4-.7 ' ' ' ' ' '4-.+ ' ' ' ' ' '4-.4 ' ' ' ' ' '4-.3 ' ' ' ' ' '4-&' ' ' ' ' ' '4-&/ ' ' ' ' ' '4-&. ' ' ' ' ' '4-&& ' ' ' ' ' '4-&- ' ' ' ' ' '4-&, ' ' ' ' ' '4-&7 ' ' ' ' ' '4-&+ ' ' ' ' ' '4-&4 ' ' ' ' ' '4-&3 ' ' ' ' ' '
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4-,- ' ' ' ' ' '4-,, ' ' ' ' ' '4-,7 ' ' ' ' ' '4-,+ ' ' ' ' ' '4-,4 ' ' ' ' ' '4-,3 ' ' ' ' ' '4-7' ' ' ' ' ' '4-7/ ' ' ' ' ' '4-7. ' ' ' ' ' '4-7& ' ' ' ' ' '4-7- ' ' ' ' ' '4-7, ' ' ' ' ' '4-77 ' ' ' ' ' '4-7+ ' ' ' ' ' '4-74 ' ' ' ' ' '4-73 ' ' ' ' ' '4-+' ' ' ' ' ' '4-+/ ' ' ' ' ' '4-+. ' ' ' ' ' '4-+& ' ' ' ' ' '4-+- ' ' ' ' ' '4-+, ' ' ' ' ' '4-+7 ' ' ' ' ' '4-++ ' ' ' ' ' '4-+4 ' ' ' ' ' '4-+3 ' ' ' ' ' '4-4' ' ' ' ' ' '4-4/ ' ' ' ' ' '
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4-4. ' ' ' ' ' '4-4& ' ' ' ' ' '4-4- ' ' ' ' ' '4-4, ' ' ' ' ' '4-47 ' ' ' ' ' '4-4+ ' ' ' ' ' '4-44 ' ' ' ' ' '4-43 ' ' ' ' ' '4-3' ' ' ' ' ' '4-3/ ' ' ' ' ' '4-3. ' ' ' ' ' '4-3& ' ' ' ' ' '4-3- ' ' ' ' ' '4-3, ' ' ' ' ' '4-37 ' ' ' ' ' '4-3+ ' ' ' ' ' '4-34 ' ' ' ' ' '4-33 ' ' ' ' ' '4,'' ' ' ' ' ' '4,'/ ' ' ' ' ' '4,'. ' ' ' ' ' '4,'& ' ' ' ' ' '4,'- ' ' ' ' ' '
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4,/3 ' ' ' ' ' '4,.' ' ' ' ' ' '4,./ ' ' ' ' ' '4,.. ' ' ' ' ' '4,.& ' ' ' ' ' '4,.- ' ' ' ' ' '4,., ' ' ' ' ' '4,.7 ' ' ' ' ' '4,.+ ' ' ' ' ' '4,.4 ' ' ' ' ' '4,.3 ' ' ' ' ' '4,&' ' ' ' ' ' '4,&/ ' ' ' ' ' '4,&. ' ' ' ' ' '4,&& ' ' ' ' ' '4,&- ' ' ' ' ' '4,&, ' ' ' ' ' '4,&7 ' ' ' ' ' '4,&+ ' ' ' ' ' '4,&4 ' ' ' ' ' '4,&3 ' ' ' ' ' '4,-' ' ' ' ' ' '4,-/ ' ' ' ' ' '4,-. ' ' ' ' ' '4,-& ' ' ' ' ' '4,-- ' ' ' ' ' '4,-, ' ' ' ' ' '4,-7 ' ' ' ' ' '
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4,4- ' ' ' ' ' '4,4, ' ' ' ' ' '4,47 ' ' ' ' ' '4,4+ ' ' ' ' ' '4,44 ' ' ' ' ' '4,43 ' ' ' ' ' '4,3' ' ' ' ' ' '4,3/ ' ' ' ' ' '4,3. ' ' ' ' ' '4,3& ' ' ' ' ' '4,3- ' ' ' ' ' '4,3, ' ' ' ' ' '4,37 ' ' ' ' ' '4,3+ ' ' ' ' ' '4,34 ' ' ' ' ' '4,33 ' ' ' ' ' '47'' ' ' ' ' ' '47'/ ' ' ' ' ' '47'. ' ' ' ' ' '47'& ' ' ' ' ' '47'- ' ' ' ' ' '47', ' ' ' ' ' '47'7 ' ' ' ' ' '47'+ ' ' ' ' ' '47'4 ' ' ' ' ' '47'3 ' ' ' ' ' '47/' ' ' ' ' ' '47// ' ' ' ' ' '
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47/. ' ' ' ' ' '47/& ' ' ' ' ' '47/- ' ' ' ' ' '47/, ' ' ' ' ' '47/7 ' ' ' ' ' '47/+ ' ' ' ' ' '47/4 ' ' ' ' ' '47/3 ' ' ' ' ' '47.' ' ' ' ' ' '47./ ' ' ' ' ' '47.. ' ' ' ' ' '47.& ' ' ' ' ' '47.- ' ' ' ' ' '47., ' ' ' ' ' '47.7 ' ' ' ' ' '47.+ ' ' ' ' ' '47.4 ' ' ' ' ' '47.3 ' ' ' ' ' '47&' ' ' ' ' ' '47&/ ' ' ' ' ' '47&. ' ' ' ' ' '47&& ' ' ' ' ' '47&- ' ' ' ' ' '
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4+-. ' ' ' ' ' '4+-& ' ' ' ' ' '4+-- ' ' ' ' ' '4+-, ' ' ' ' ' '4+-7 ' ' ' ' ' '4+-+ ' ' ' ' ' '4+-4 ' ' ' ' ' '4+-3 ' ' ' ' ' '4+,' ' ' ' ' ' '4+,/ ' ' ' ' ' '4+,. ' ' ' ' ' '4+,& ' ' ' ' ' '4+,- ' ' ' ' ' '4+,, ' ' ' ' ' '4+,7 ' ' ' ' ' '4+,+ ' ' ' ' ' '4+,4 ' ' ' ' ' '4+,3 ' ' ' ' ' '4+7' ' ' ' ' ' '4+7/ ' ' ' ' ' '4+7. ' ' ' ' ' '4+7& ' ' ' ' ' '4+7- ' ' ' ' ' '
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44'+ ' ' ' ' ' '44'4 ' ' ' ' ' '44'3 ' ' ' ' ' '44/' ' ' ' ' ' '44// ' ' ' ' ' '44/. ' ' ' ' ' '44/& ' ' ' ' ' '44/- ' ' ' ' ' '44/, ' ' ' ' ' '44/7 ' ' ' ' ' '44/+ ' ' ' ' ' '44/4 ' ' ' ' ' '44/3 ' ' ' ' ' '44.' ' ' ' ' ' '44./ ' ' ' ' ' '44.. ' ' ' ' ' '44.& ' ' ' ' ' '44.- ' ' ' ' ' '44., ' ' ' ' ' '44.7 ' ' ' ' ' '44.+ ' ' ' ' ' '44.4 ' ' ' ' ' '44.3 ' ' ' ' ' '
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44-- ' ' ' ' ' '44-, ' ' ' ' ' '44-7 ' ' ' ' ' '44-+ ' ' ' ' ' '44-4 ' ' ' ' ' '44-3 ' ' ' ' ' '44,' ' ' ' ' ' '44,/ ' ' ' ' ' '44,. ' ' ' ' ' '44,& ' ' ' ' ' '44,- ' ' ' ' ' '44,, ' ' ' ' ' '44,7 ' ' ' ' ' '44,+ ' ' ' ' ' '44,4 ' ' ' ' ' '44,3 ' ' ' ' ' '447' ' ' ' ' ' '447/ ' ' ' ' ' '447. ' ' ' ' ' '447& ' ' ' ' ' '447- ' ' ' ' ' '447, ' ' ' ' ' '4477 ' ' ' ' ' '447+ ' ' ' ' ' '4474 ' ' ' ' ' '4473 ' ' ' ' ' '44+' ' ' ' ' ' '44+/ ' ' ' ' ' '
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44+. ' ' ' ' ' '44+& ' ' ' ' ' '44+- ' ' ' ' ' '44+, ' ' ' ' ' '44+7 ' ' ' ' ' '44++ ' ' ' ' ' '44+4 ' ' ' ' ' '44+3 ' ' ' ' ' '444' ' ' ' ' ' '444/ ' ' ' ' ' '444. ' ' ' ' ' '444& ' ' ' ' ' '444- ' ' ' ' ' '444, ' ' ' ' ' '4447 ' ' ' ' ' '444+ ' ' ' ' ' '4444 ' ' ' ' ' '4443 ' ' ' ' ' '443' ' ' ' ' ' '443/ ' ' ' ' ' '443. ' ' ' ' ' '443& ' ' ' ' ' '443- ' ' ' ' ' '
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43+- ' ' ' ' ' '43+, ' ' ' ' ' '43+7 ' ' ' ' ' '43++ ' ' ' ' ' '43+4 ' ' ' ' ' '43+3 ' ' ' ' ' '434' ' ' ' ' ' '434/ ' ' ' ' ' '434. ' ' ' ' ' '434& ' ' ' ' ' '434- ' ' ' ' ' '434, ' ' ' ' ' '4347 ' ' ' ' ' '434+ ' ' ' ' ' '4344 ' ' ' ' ' '4343 ' ' ' ' ' '433' ' ' ' ' ' '433/ ' ' ' ' ' '433. ' ' ' ' ' '433& ' ' ' ' ' '433- ' ' ' ' ' '433, ' ' ' ' ' '4337 ' ' ' ' ' '433+ ' ' ' ' ' '4334 ' ' ' ' ' '4333 ' ' ' ' ' '3''' ' ' ' ' ' '3''/ ' ' ' ' ' '
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3''. ' ' ' ' ' '3''& ' ' ' ' ' '3''- ' ' ' ' ' '3'', ' ' ' ' ' '3''7 ' ' ' ' ' '3''+ ' ' ' ' ' '3''4 ' ' ' ' ' '3''3 ' ' ' ' ' '3'/' ' ' ' ' ' '3'// ' ' ' ' ' '3'/. ' ' ' ' ' '3'/& ' ' ' ' ' '3'/- ' ' ' ' ' '3'/, ' ' ' ' ' '3'/7 ' ' ' ' ' '3'/+ ' ' ' ' ' '3'/4 ' ' ' ' ' '3'/3 ' ' ' ' ' '3'.' ' ' ' ' ' '3'./ ' ' ' ' ' '3'.. ' ' ' ' ' '3'.& ' ' ' ' ' '3'.- ' ' ' ' ' '
3'., ' ' ' ' ' '3'.7 ' ' ' ' ' '3'.+ ' ' ' ' ' '3'.4 ' ' ' ' ' '3'.3 ' ' ' ' ' '3'&' ' ' ' ' ' '3'&/ ' ' ' ' ' '3'&. ' ' ' ' ' '3'&& ' ' ' ' ' '3'&- ' ' ' ' ' '3'&, ' ' ' ' ' '3'&7 ' ' ' ' ' '3'&+ ' ' ' ' ' '3'&4 ' ' ' ' ' '
3'&3 ' ' ' ' ' '3'-' ' ' ' ' ' '3'-/ ' ' ' ' ' '3'-. ' ' ' ' ' '3'-& ' ' ' ' ' '3'-- ' ' ' ' ' '3'-, ' ' ' ' ' '3'-7 ' ' ' ' ' '3'-+ ' ' ' ' ' '3'-4 ' ' ' ' ' '3'-3 ' ' ' ' ' '3',' ' ' ' ' ' '3',/ ' ' ' ' ' '3',. ' ' ' ' ' '3',& ' ' ' ' ' '3',- ' ' ' ' ' '3',, ' ' ' ' ' '3',7 ' ' ' ' ' '3',+ ' ' ' ' ' '3',4 ' ' ' ' ' '3',3 ' ' ' ' ' '3'7' ' ' ' ' ' '3'7/ ' ' ' ' ' '3'7. ' ' ' ' ' '3'7& ' ' ' ' ' '3'7- ' ' ' ' ' '3'7, ' ' ' ' ' '3'77 ' ' ' ' ' '
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3'7+ ' ' ' ' ' '3'74 ' ' ' ' ' '3'73 ' ' ' ' ' '3'+' ' ' ' ' ' '3'+/ ' ' ' ' ' '3'+. ' ' ' ' ' '3'+& ' ' ' ' ' '3'+- ' ' ' ' ' '3'+, ' ' ' ' ' '3'+7 ' ' ' ' ' '3'++ ' ' ' ' ' '3'+4 ' ' ' ' ' '3'+3 ' ' ' ' ' '3'4' ' ' ' ' ' '3'4/ ' ' ' ' ' '3'4. ' ' ' ' ' '3'4& ' ' ' ' ' '3'4- ' ' ' ' ' '3'4, ' ' ' ' ' '3'47 ' ' ' ' ' '3'4+ ' ' ' ' ' '3'44 ' ' ' ' ' '3'43 ' ' ' ' ' '
3'3' ' ' ' ' ' '3'3/ ' ' ' ' ' '3'3. ' ' ' ' ' '3'3& ' ' ' ' ' '3'3- ' ' ' ' ' '3'3, ' ' ' ' ' '3'37 ' ' ' ' ' '3'3+ ' ' ' ' ' '3'34 ' ' ' ' ' '3'33 ' ' ' ' ' '3/'' ' ' ' ' ' '3/'/ ' ' ' ' ' '3/'. ' ' ' ' ' '3/'& ' ' ' ' ' '
3/'- ' ' ' ' ' '3/', ' ' ' ' ' '3/'7 ' ' ' ' ' '3/'+ ' ' ' ' ' '3/'4 ' ' ' ' ' '3/'3 ' ' ' ' ' '3//' ' ' ' ' ' '3/// ' ' ' ' ' '3//. ' ' ' ' ' '3//& ' ' ' ' ' '3//- ' ' ' ' ' '3//, ' ' ' ' ' '3//7 ' ' ' ' ' '3//+ ' ' ' ' ' '3//4 ' ' ' ' ' '3//3 ' ' ' ' ' '3/.' ' ' ' ' ' '3/./ ' ' ' ' ' '3/.. ' ' ' ' ' '3/.& ' ' ' ' ' '3/.- ' ' ' ' ' '3/., ' ' ' ' ' '3/.7 ' ' ' ' ' '3/.+ ' ' ' ' ' '3/.4 ' ' ' ' ' '3/.3 ' ' ' ' ' '3/&' ' ' ' ' ' '3/&/ ' ' ' ' ' '
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3/&. ' ' ' ' ' '3/&& ' ' ' ' ' '3/&- ' ' ' ' ' '3/&, ' ' ' ' ' '3/&7 ' ' ' ' ' '3/&+ ' ' ' ' ' '3/&4 ' ' ' ' ' '3/&3 ' ' ' ' ' '3/-' ' ' ' ' ' '3/-/ ' ' ' ' ' '3/-. ' ' ' ' ' '3/-& ' ' ' ' ' '3/-- ' ' ' ' ' '3/-, ' ' ' ' ' '3/-7 ' ' ' ' ' '3/-+ ' ' ' ' ' '3/-4 ' ' ' ' ' '3/-3 ' ' ' ' ' '3/,' ' ' ' ' ' '3/,/ ' ' ' ' ' '3/,. ' ' ' ' ' '3/,& ' ' ' ' ' '3/,- ' ' ' ' ' '
3/,, ' ' ' ' ' '3/,7 ' ' ' ' ' '3/,+ ' ' ' ' ' '3/,4 ' ' ' ' ' '3/,3 ' ' ' ' ' '3/7' ' ' ' ' ' '3/7/ ' ' ' ' ' '3/7. ' ' ' ' ' '3/7& ' ' ' ' ' '3/7- ' ' ' ' ' '3/7, ' ' ' ' ' '3/77 ' ' ' ' ' '3/7+ ' ' ' ' ' '3/74 ' ' ' ' ' '
3/73 ' ' ' ' ' '3/+' ' ' ' ' ' '3/+/ ' ' ' ' ' '3/+. ' ' ' ' ' '3/+& ' ' ' ' ' '3/+- ' ' ' ' ' '3/+, ' ' ' ' ' '3/+7 ' ' ' ' ' '3/++ ' ' ' ' ' '3/+4 ' ' ' ' ' '3/+3 ' ' ' ' ' '3/4' ' ' ' ' ' '3/4/ ' ' ' ' ' '3/4. ' ' ' ' ' '3/4& ' ' ' ' ' '3/4- ' ' ' ' ' '3/4, ' ' ' ' ' '3/47 ' ' ' ' ' '3/4+ ' ' ' ' ' '3/44 ' ' ' ' ' '3/43 ' ' ' ' ' '3/3' ' ' ' ' ' '3/3/ ' ' ' ' ' '3/3. ' ' ' ' ' '3/3& ' ' ' ' ' '3/3- ' ' ' ' ' '3/3, ' ' ' ' ' '3/37 ' ' ' ' ' '
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3/3+ ' ' ' ' ' '3/34 ' ' ' ' ' '3/33 ' ' ' ' ' '3.'' ' ' ' ' ' '3.'/ ' ' ' ' ' '3.'. ' ' ' ' ' '3.'& ' ' ' ' ' '3.'- ' ' ' ' ' '3.', ' ' ' ' ' '3.'7 ' ' ' ' ' '3.'+ ' ' ' ' ' '3.'4 ' ' ' ' ' '3.'3 ' ' ' ' ' '3./' ' ' ' ' ' '3.// ' ' ' ' ' '3./. ' ' ' ' ' '3./& ' ' ' ' ' '3./- ' ' ' ' ' '3./, ' ' ' ' ' '3./7 ' ' ' ' ' '3./+ ' ' ' ' ' '3./4 ' ' ' ' ' '3./3 ' ' ' ' ' '
3..' ' ' ' ' ' '3../ ' ' ' ' ' '3... ' ' ' ' ' '3..& ' ' ' ' ' '3..- ' ' ' ' ' '3.., ' ' ' ' ' '3..7 ' ' ' ' ' '3..+ ' ' ' ' ' '3..4 ' ' ' ' ' '3..3 ' ' ' ' ' '3.&' ' ' ' ' ' '3.&/ ' ' ' ' ' '3.&. ' ' ' ' ' '3.&& ' ' ' ' ' '
3.&- ' ' ' ' ' '3.&, ' ' ' ' ' '3.&7 ' ' ' ' ' '3.&+ ' ' ' ' ' '3.&4 ' ' ' ' ' '3.&3 ' ' ' ' ' '3.-' ' ' ' ' ' '3.-/ ' ' ' ' ' '3.-. ' ' ' ' ' '3.-& ' ' ' ' ' '3.-- ' ' ' ' ' '3.-, ' ' ' ' ' '3.-7 ' ' ' ' ' '3.-+ ' ' ' ' ' '3.-4 ' ' ' ' ' '3.-3 ' ' ' ' ' '3.,' ' ' ' ' ' '3.,/ ' ' ' ' ' '3.,. ' ' ' ' ' '3.,& ' ' ' ' ' '3.,- ' ' ' ' ' '3.,, ' ' ' ' ' '3.,7 ' ' ' ' ' '3.,+ ' ' ' ' ' '3.,4 ' ' ' ' ' '3.,3 ' ' ' ' ' '3.7' ' ' ' ' ' '3.7/ ' ' ' ' ' '
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3.7. ' ' ' ' ' '3.7& ' ' ' ' ' '3.7- ' ' ' ' ' '3.7, ' ' ' ' ' '3.77 ' ' ' ' ' '3.7+ ' ' ' ' ' '3.74 ' ' ' ' ' '3.73 ' ' ' ' ' '3.+' ' ' ' ' ' '3.+/ ' ' ' ' ' '3.+. ' ' ' ' ' '3.+& ' ' ' ' ' '3.+- ' ' ' ' ' '3.+, ' ' ' ' ' '3.+7 ' ' ' ' ' '3.++ ' ' ' ' ' '3.+4 ' ' ' ' ' '3.+3 ' ' ' ' ' '3.4' ' ' ' ' ' '3.4/ ' ' ' ' ' '3.4. ' ' ' ' ' '3.4& ' ' ' ' ' '3.4- ' ' ' ' ' '
3.4, ' ' ' ' ' '3.47 ' ' ' ' ' '3.4+ ' ' ' ' ' '3.44 ' ' ' ' ' '3.43 ' ' ' ' ' '3.3' ' ' ' ' ' '3.3/ ' ' ' ' ' '3.3. ' ' ' ' ' '3.3& ' ' ' ' ' '3.3- ' ' ' ' ' '3.3, ' ' ' ' ' '3.37 ' ' ' ' ' '3.3+ ' ' ' ' ' '3.34 ' ' ' ' ' '
3.33 ' ' ' ' ' '3&'' ' ' ' ' ' '3&'/ ' ' ' ' ' '3&'. ' ' ' ' ' '3&'& ' ' ' ' ' '3&'- ' ' ' ' ' '3&', ' ' ' ' ' '3&'7 ' ' ' ' ' '3&'+ ' ' ' ' ' '3&'4 ' ' ' ' ' '3&'3 ' ' ' ' ' '3&/' ' ' ' ' ' '3&// ' ' ' ' ' '3&/. ' ' ' ' ' '3&/& ' ' ' ' ' '3&/- ' ' ' ' ' '3&/, ' ' ' ' ' '3&/7 ' ' ' ' ' '3&/+ ' ' ' ' ' '3&/4 ' ' ' ' ' '3&/3 ' ' ' ' ' '3&.' ' ' ' ' ' '3&./ ' ' ' ' ' '3&.. ' ' ' ' ' '3&.& ' ' ' ' ' '3&.- ' ' ' ' ' '3&., ' ' ' ' ' '3&.7 ' ' ' ' ' '
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3&.+ ' ' ' ' ' '3&.4 ' ' ' ' ' '3&.3 ' ' ' ' ' '3&&' ' ' ' ' ' '3&&/ ' ' ' ' ' '3&&. ' ' ' ' ' '3&&& ' ' ' ' ' '3&&- ' ' ' ' ' '3&&, ' ' ' ' ' '3&&7 ' ' ' ' ' '3&&+ ' ' ' ' ' '3&&4 ' ' ' ' ' '3&&3 ' ' ' ' ' '3&-' ' ' ' ' ' '3&-/ ' ' ' ' ' '3&-. ' ' ' ' ' '3&-& ' ' ' ' ' '3&-- ' ' ' ' ' '3&-, ' ' ' ' ' '3&-7 ' ' ' ' ' '3&-+ ' ' ' ' ' '3&-4 ' ' ' ' ' '3&-3 ' ' ' ' ' '
3&,' ' ' ' ' ' '3&,/ ' ' ' ' ' '3&,. ' ' ' ' ' '3&,& ' ' ' ' ' '3&,- ' ' ' ' ' '3&,, ' ' ' ' ' '3&,7 ' ' ' ' ' '3&,+ ' ' ' ' ' '3&,4 ' ' ' ' ' '3&,3 ' ' ' ' ' '3&7' ' ' ' ' ' '3&7/ ' ' ' ' ' '3&7. ' ' ' ' ' '3&7& ' ' ' ' ' '
3&7- ' ' ' ' ' '3&7, ' ' ' ' ' '3&77 ' ' ' ' ' '3&7+ ' ' ' ' ' '3&74 ' ' ' ' ' '3&73 ' ' ' ' ' '3&+' ' ' ' ' ' '3&+/ ' ' ' ' ' '3&+. ' ' ' ' ' '3&+& ' ' ' ' ' '3&+- ' ' ' ' ' '3&+, ' ' ' ' ' '3&+7 ' ' ' ' ' '3&++ ' ' ' ' ' '3&+4 ' ' ' ' ' '3&+3 ' ' ' ' ' '3&4' ' ' ' ' ' '3&4/ ' ' ' ' ' '3&4. ' ' ' ' ' '3&4& ' ' ' ' ' '3&4- ' ' ' ' ' '3&4, ' ' ' ' ' '3&47 ' ' ' ' ' '3&4+ ' ' ' ' ' '3&44 ' ' ' ' ' '3&43 ' ' ' ' ' '3&3' ' ' ' ' ' '3&3/ ' ' ' ' ' '
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3&3. ' ' ' ' ' '3&3& ' ' ' ' ' '3&3- ' ' ' ' ' '3&3, ' ' ' ' ' '3&37 ' ' ' ' ' '3&3+ ' ' ' ' ' '3&34 ' ' ' ' ' '3&33 ' ' ' ' ' '3-'' ' ' ' ' ' '3-'/ ' ' ' ' ' '3-'. ' ' ' ' ' '3-'& ' ' ' ' ' '3-'- ' ' ' ' ' '3-', ' ' ' ' ' '3-'7 ' ' ' ' ' '3-'+ ' ' ' ' ' '3-'4 ' ' ' ' ' '3-'3 ' ' ' ' ' '3-/' ' ' ' ' ' '3-// ' ' ' ' ' '3-/. ' ' ' ' ' '3-/& ' ' ' ' ' '3-/- ' ' ' ' ' '
3-/, ' ' ' ' ' '3-/7 ' ' ' ' ' '3-/+ ' ' ' ' ' '3-/4 ' ' ' ' ' '3-/3 ' ' ' ' ' '3-.' ' ' ' ' ' '3-./ ' ' ' ' ' '3-.. ' ' ' ' ' '3-.& ' ' ' ' ' '3-.- ' ' ' ' ' '3-., ' ' ' ' ' '3-.7 ' ' ' ' ' '3-.+ ' ' ' ' ' '3-.4 ' ' ' ' ' '
3-.3 ' ' ' ' ' '3-&' ' ' ' ' ' '3-&/ ' ' ' ' ' '3-&. ' ' ' ' ' '3-&& ' ' ' ' ' '3-&- ' ' ' ' ' '3-&, ' ' ' ' ' '3-&7 ' ' ' ' ' '3-&+ ' ' ' ' ' '3-&4 ' ' ' ' ' '3-&3 ' ' ' ' ' '3--' ' ' ' ' ' '3--/ ' ' ' ' ' '3--. ' ' ' ' ' '3--& ' ' ' ' ' '3--- ' ' ' ' ' '3--, ' ' ' ' ' '3--7 ' ' ' ' ' '3--+ ' ' ' ' ' '3--4 ' ' ' ' ' '3--3 ' ' ' ' ' '3-,' ' ' ' ' ' '3-,/ ' ' ' ' ' '3-,. ' ' ' ' ' '3-,& ' ' ' ' ' '3-,- ' ' ' ' ' '3-,, ' ' ' ' ' '3-,7 ' ' ' ' ' '
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3-,+ ' ' ' ' ' '3-,4 ' ' ' ' ' '3-,3 ' ' ' ' ' '3-7' ' ' ' ' ' '3-7/ ' ' ' ' ' '3-7. ' ' ' ' ' '3-7& ' ' ' ' ' '3-7- ' ' ' ' ' '3-7, ' ' ' ' ' '3-77 ' ' ' ' ' '3-7+ ' ' ' ' ' '3-74 ' ' ' ' ' '3-73 ' ' ' ' ' '3-+' ' ' ' ' ' '3-+/ ' ' ' ' ' '3-+. ' ' ' ' ' '3-+& ' ' ' ' ' '3-+- ' ' ' ' ' '3-+, ' ' ' ' ' '3-+7 ' ' ' ' ' '3-++ ' ' ' ' ' '3-+4 ' ' ' ' ' '3-+3 ' ' ' ' ' '
3-4' ' ' ' ' ' '3-4/ ' ' ' ' ' '3-4. ' ' ' ' ' '3-4& ' ' ' ' ' '3-4- ' ' ' ' ' '3-4, ' ' ' ' ' '3-47 ' ' ' ' ' '3-4+ ' ' ' ' ' '3-44 ' ' ' ' ' '3-43 ' ' ' ' ' '3-3' ' ' ' ' ' '3-3/ ' ' ' ' ' '3-3. ' ' ' ' ' '3-3& ' ' ' ' ' '
3-3- ' ' ' ' ' '3-3, ' ' ' ' ' '3-37 ' ' ' ' ' '3-3+ ' ' ' ' ' '3-34 ' ' ' ' ' '3-33 ' ' ' ' ' '3,'' ' ' ' ' ' '3,'/ ' ' ' ' ' '3,'. ' ' ' ' ' '3,'& ' ' ' ' ' '3,'- ' ' ' ' ' '3,', ' ' ' ' ' '3,'7 ' ' ' ' ' '3,'+ ' ' ' ' ' '3,'4 ' ' ' ' ' '3,'3 ' ' ' ' ' '3,/' ' ' ' ' ' '3,// ' ' ' ' ' '3,/. ' ' ' ' ' '3,/& ' ' ' ' ' '3,/- ' ' ' ' ' '3,/, ' ' ' ' ' '3,/7 ' ' ' ' ' '3,/+ ' ' ' ' ' '3,/4 ' ' ' ' ' '3,/3 ' ' ' ' ' '3,.' ' ' ' ' ' '3,./ ' ' ' ' ' '
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3,.. ' ' ' ' ' '3,.& ' ' ' ' ' '3,.- ' ' ' ' ' '3,., ' ' ' ' ' '3,.7 ' ' ' ' ' '3,.+ ' ' ' ' ' '3,.4 ' ' ' ' ' '3,.3 ' ' ' ' ' '3,&' ' ' ' ' ' '3,&/ ' ' ' ' ' '3,&. ' ' ' ' ' '3,&& ' ' ' ' ' '3,&- ' ' ' ' ' '3,&, ' ' ' ' ' '3,&7 ' ' ' ' ' '3,&+ ' ' ' ' ' '3,&4 ' ' ' ' ' '3,&3 ' ' ' ' ' '3,-' ' ' ' ' ' '3,-/ ' ' ' ' ' '3,-. ' ' ' ' ' '3,-& ' ' ' ' ' '3,-- ' ' ' ' ' '
3,-, ' ' ' ' ' '3,-7 ' ' ' ' ' '3,-+ ' ' ' ' ' '3,-4 ' ' ' ' ' '3,-3 ' ' ' ' ' '3,,' ' ' ' ' ' '3,,/ ' ' ' ' ' '3,,. ' ' ' ' ' '3,,& ' ' ' ' ' '3,,- ' ' ' ' ' '3,,, ' ' ' ' ' '3,,7 ' ' ' ' ' '3,,+ ' ' ' ' ' '3,,4 ' ' ' ' ' '
3,,3 ' ' ' ' ' '3,7' ' ' ' ' ' '3,7/ ' ' ' ' ' '3,7. ' ' ' ' ' '3,7& ' ' ' ' ' '3,7- ' ' ' ' ' '3,7, ' ' ' ' ' '3,77 ' ' ' ' ' '3,7+ ' ' ' ' ' '3,74 ' ' ' ' ' '3,73 ' ' ' ' ' '3,+' ' ' ' ' ' '3,+/ ' ' ' ' ' '3,+. ' ' ' ' ' '3,+& ' ' ' ' ' '3,+- ' ' ' ' ' '3,+, ' ' ' ' ' '3,+7 ' ' ' ' ' '3,++ ' ' ' ' ' '3,+4 ' ' ' ' ' '3,+3 ' ' ' ' ' '3,4' ' ' ' ' ' '3,4/ ' ' ' ' ' '3,4. ' ' ' ' ' '3,4& ' ' ' ' ' '3,4- ' ' ' ' ' '3,4, ' ' ' ' ' '3,47 ' ' ' ' ' '
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3,4+ ' ' ' ' ' '3,44 ' ' ' ' ' '3,43 ' ' ' ' ' '3,3' ' ' ' ' ' '3,3/ ' ' ' ' ' '3,3. ' ' ' ' ' '3,3& ' ' ' ' ' '3,3- ' ' ' ' ' '3,3, ' ' ' ' ' '3,37 ' ' ' ' ' '3,3+ ' ' ' ' ' '3,34 ' ' ' ' ' '3,33 ' ' ' ' ' '37'' ' ' ' ' ' '37'/ ' ' ' ' ' '37'. ' ' ' ' ' '37'& ' ' ' ' ' '37'- ' ' ' ' ' '37', ' ' ' ' ' '37'7 ' ' ' ' ' '37'+ ' ' ' ' ' '37'4 ' ' ' ' ' '37'3 ' ' ' ' ' '
37/' ' ' ' ' ' '37// ' ' ' ' ' '37/. ' ' ' ' ' '37/& ' ' ' ' ' '37/- ' ' ' ' ' '37/, ' ' ' ' ' '37/7 ' ' ' ' ' '37/+ ' ' ' ' ' '37/4 ' ' ' ' ' '37/3 ' ' ' ' ' '37.' ' ' ' ' ' '37./ ' ' ' ' ' '37.. ' ' ' ' ' '37.& ' ' ' ' ' '
37.- ' ' ' ' ' '37., ' ' ' ' ' '37.7 ' ' ' ' ' '37.+ ' ' ' ' ' '37.4 ' ' ' ' ' '37.3 ' ' ' ' ' '37&' ' ' ' ' ' '37&/ ' ' ' ' ' '37&. ' ' ' ' ' '37&& ' ' ' ' ' '37&- ' ' ' ' ' '37&, ' ' ' ' ' '37&7 ' ' ' ' ' '37&+ ' ' ' ' ' '37&4 ' ' ' ' ' '37&3 ' ' ' ' ' '37-' ' ' ' ' ' '37-/ ' ' ' ' ' '37-. ' ' ' ' ' '37-& ' ' ' ' ' '37-- ' ' ' ' ' '37-, ' ' ' ' ' '37-7 ' ' ' ' ' '37-+ ' ' ' ' ' '37-4 ' ' ' ' ' '37-3 ' ' ' ' ' '37,' ' ' ' ' ' '37,/ ' ' ' ' ' '
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37,. ' ' ' ' ' '37,& ' ' ' ' ' '37,- ' ' ' ' ' '37,, ' ' ' ' ' '37,7 ' ' ' ' ' '37,+ ' ' ' ' ' '37,4 ' ' ' ' ' '37,3 ' ' ' ' ' '377' ' ' ' ' ' '377/ ' ' ' ' ' '377. ' ' ' ' ' '377& ' ' ' ' ' '377- ' ' ' ' ' '377, ' ' ' ' ' '3777 ' ' ' ' ' '377+ ' ' ' ' ' '3774 ' ' ' ' ' '3773 ' ' ' ' ' '37+' ' ' ' ' ' '37+/ ' ' ' ' ' '37+. ' ' ' ' ' '37+& ' ' ' ' ' '37+- ' ' ' ' ' '
37+, ' ' ' ' ' '37+7 ' ' ' ' ' '37++ ' ' ' ' ' '37+4 ' ' ' ' ' '37+3 ' ' ' ' ' '374' ' ' ' ' ' '374/ ' ' ' ' ' '374. ' ' ' ' ' '374& ' ' ' ' ' '374- ' ' ' ' ' '374, ' ' ' ' ' '3747 ' ' ' ' ' '374+ ' ' ' ' ' '3744 ' ' ' ' ' '
3743 ' ' ' ' ' '373' ' ' ' ' ' '373/ ' ' ' ' ' '373. ' ' ' ' ' '373& ' ' ' ' ' '373- ' ' ' ' ' '373, ' ' ' ' ' '3737 ' ' ' ' ' '373+ ' ' ' ' ' '3734 ' ' ' ' ' '3733 ' ' ' ' ' '3+'' ' ' ' ' ' '3+'/ ' ' ' ' ' '3+'. ' ' ' ' ' '3+'& ' ' ' ' ' '3+'- ' ' ' ' ' '3+', ' ' ' ' ' '3+'7 ' ' ' ' ' '3+'+ ' ' ' ' ' '3+'4 ' ' ' ' ' '3+'3 ' ' ' ' ' '3+/' ' ' ' ' ' '3+// ' ' ' ' ' '3+/. ' ' ' ' ' '3+/& ' ' ' ' ' '3+/- ' ' ' ' ' '3+/, ' ' ' ' ' '3+/7 ' ' ' ' ' '
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3+/+ ' ' ' ' ' '3+/4 ' ' ' ' ' '3+/3 ' ' ' ' ' '3+.' ' ' ' ' ' '3+./ ' ' ' ' ' '3+.. ' ' ' ' ' '3+.& ' ' ' ' ' '3+.- ' ' ' ' ' '3+., ' ' ' ' ' '3+.7 ' ' ' ' ' '3+.+ ' ' ' ' ' '3+.4 ' ' ' ' ' '3+.3 ' ' ' ' ' '3+&' ' ' ' ' ' '3+&/ ' ' ' ' ' '3+&. ' ' ' ' ' '3+&& ' ' ' ' ' '3+&- ' ' ' ' ' '3+&, ' ' ' ' ' '3+&7 ' ' ' ' ' '3+&+ ' ' ' ' ' '3+&4 ' ' ' ' ' '3+&3 ' ' ' ' ' '
3+-' ' ' ' ' ' '3+-/ ' ' ' ' ' '3+-. ' ' ' ' ' '3+-& ' ' ' ' ' '3+-- ' ' ' ' ' '3+-, ' ' ' ' ' '3+-7 ' ' ' ' ' '3+-+ ' ' ' ' ' '3+-4 ' ' ' ' ' '3+-3 ' ' ' ' ' '3+,' ' ' ' ' ' '3+,/ ' ' ' ' ' '3+,. ' ' ' ' ' '3+,& ' ' ' ' ' '
3+,- ' ' ' ' ' '3+,, ' ' ' ' ' '3+,7 ' ' ' ' ' '3+,+ ' ' ' ' ' '3+,4 ' ' ' ' ' '3+,3 ' ' ' ' ' '3+7' ' ' ' ' ' '3+7/ ' ' ' ' ' '3+7. ' ' ' ' ' '3+7& ' ' ' ' ' '3+7- ' ' ' ' ' '3+7, ' ' ' ' ' '3+77 ' ' ' ' ' '3+7+ ' ' ' ' ' '3+74 ' ' ' ' ' '3+73 ' ' ' ' ' '3++' ' ' ' ' ' '3++/ ' ' ' ' ' '3++. ' ' ' ' ' '3++& ' ' ' ' ' '3++- ' ' ' ' ' '3++, ' ' ' ' ' '3++7 ' ' ' ' ' '3+++ ' ' ' ' ' '3++4 ' ' ' ' ' '3++3 ' ' ' ' ' '3+4' ' ' ' ' ' '3+4/ ' ' ' ' ' '
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3+4. ' ' ' ' ' '3+4& ' ' ' ' ' '3+4- ' ' ' ' ' '3+4, ' ' ' ' ' '3+47 ' ' ' ' ' '3+4+ ' ' ' ' ' '3+44 ' ' ' ' ' '3+43 ' ' ' ' ' '3+3' ' ' ' ' ' '3+3/ ' ' ' ' ' '3+3. ' ' ' ' ' '3+3& ' ' ' ' ' '3+3- ' ' ' ' ' '3+3, ' ' ' ' ' '3+37 ' ' ' ' ' '3+3+ ' ' ' ' ' '3+34 ' ' ' ' ' '3+33 ' ' ' ' ' '34'' ' ' ' ' ' '34'/ ' ' ' ' ' '34'. ' ' ' ' ' '34'& ' ' ' ' ' '34'- ' ' ' ' ' '
34', ' ' ' ' ' '34'7 ' ' ' ' ' '34'+ ' ' ' ' ' '34'4 ' ' ' ' ' '34'3 ' ' ' ' ' '34/' ' ' ' ' ' '34// ' ' ' ' ' '34/. ' ' ' ' ' '34/& ' ' ' ' ' '34/- ' ' ' ' ' '34/, ' ' ' ' ' '34/7 ' ' ' ' ' '34/+ ' ' ' ' ' '34/4 ' ' ' ' ' '
34/3 ' ' ' ' ' '34.' ' ' ' ' ' '34./ ' ' ' ' ' '34.. ' ' ' ' ' '34.& ' ' ' ' ' '34.- ' ' ' ' ' '34., ' ' ' ' ' '34.7 ' ' ' ' ' '34.+ ' ' ' ' ' '34.4 ' ' ' ' ' '34.3 ' ' ' ' ' '34&' ' ' ' ' ' '34&/ ' ' ' ' ' '34&. ' ' ' ' ' '34&& ' ' ' ' ' '34&- ' ' ' ' ' '34&, ' ' ' ' ' '34&7 ' ' ' ' ' '34&+ ' ' ' ' ' '34&4 ' ' ' ' ' '34&3 ' ' ' ' ' '34-' ' ' ' ' ' '34-/ ' ' ' ' ' '34-. ' ' ' ' ' '34-& ' ' ' ' ' '34-- ' ' ' ' ' '34-, ' ' ' ' ' '34-7 ' ' ' ' ' '
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34-+ ' ' ' ' ' '34-4 ' ' ' ' ' '34-3 ' ' ' ' ' '34,' ' ' ' ' ' '34,/ ' ' ' ' ' '34,. ' ' ' ' ' '34,& ' ' ' ' ' '34,- ' ' ' ' ' '34,, ' ' ' ' ' '34,7 ' ' ' ' ' '34,+ ' ' ' ' ' '34,4 ' ' ' ' ' '34,3 ' ' ' ' ' '347' ' ' ' ' ' '347/ ' ' ' ' ' '347. ' ' ' ' ' '347& ' ' ' ' ' '347- ' ' ' ' ' '347, ' ' ' ' ' '3477 ' ' ' ' ' '347+ ' ' ' ' ' '3474 ' ' ' ' ' '3473 ' ' ' ' ' '
34+' ' ' ' ' ' '34+/ ' ' ' ' ' '34+. ' ' ' ' ' '34+& ' ' ' ' ' '34+- ' ' ' ' ' '34+, ' ' ' ' ' '34+7 ' ' ' ' ' '34++ ' ' ' ' ' '34+4 ' ' ' ' ' '34+3 ' ' ' ' ' '344' ' ' ' ' ' '344/ ' ' ' ' ' '344. ' ' ' ' ' '344& ' ' ' ' ' '
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33/. ' ' ' ' ' '33/& ' ' ' ' ' '33/- ' ' ' ' ' '33/, ' ' ' ' ' '33/7 ' ' ' ' ' '33/+ ' ' ' ' ' '33/4 ' ' ' ' ' '33/3 ' ' ' ' ' '33.' ' ' ' ' ' '33./ ' ' ' ' ' '33.. ' ' ' ' ' '33.& ' ' ' ' ' '33.- ' ' ' ' ' '33., ' ' ' ' ' '33.7 ' ' ' ' ' '33.+ ' ' ' ' ' '33.4 ' ' ' ' ' '33.3 ' ' ' ' ' '33&' ' ' ' ' ' '33&/ ' ' ' ' ' '33&. ' ' ' ' ' '33&& ' ' ' ' ' '33&- ' ' ' ' ' '
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33-3 ' ' ' ' ' '33,' ' ' ' ' ' '33,/ ' ' ' ' ' '33,. ' ' ' ' ' '33,& ' ' ' ' ' '33,- ' ' ' ' ' '33,, ' ' ' ' ' '33,7 ' ' ' ' ' '33,+ ' ' ' ' ' '33,4 ' ' ' ' ' '33,3 ' ' ' ' ' '337' ' ' ' ' ' '337/ ' ' ' ' ' '337. ' ' ' ' ' '337& ' ' ' ' ' '337- ' ' ' ' ' '337, ' ' ' ' ' '3377 ' ' ' ' ' '337+ ' ' ' ' ' '3374 ' ' ' ' ' '3373 ' ' ' ' ' '33+' ' ' ' ' ' '33+/ ' ' ' ' ' '33+. ' ' ' ' ' '33+& ' ' ' ' ' '33+- ' ' ' ' ' '33+, ' ' ' ' ' '33+7 ' ' ' ' ' '
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33++ ' ' ' ' ' '33+4 ' ' ' ' ' '33+3 ' ' ' ' ' '334' ' ' ' ' ' '334/ ' ' ' ' ' '334. ' ' ' ' ' '334& ' ' ' ' ' '334- ' ' ' ' ' '334, ' ' ' ' ' '3347 ' ' ' ' ' '334+ ' ' ' ' ' '3344 ' ' ' ' ' '3343 ' ' ' ' ' '333' ' ' ' ' ' '333/ ' ' ' ' ' '333. ' ' ' ' ' '333& ' ' ' ' ' '333- ' ' ' ' ' '333, ' ' ' ' ' '3337 ' ' ' ' ' '333+ ' ' ' ' ' '3334 ' ' ' ' ' '3333 ' ' ' ' ' '
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1&'(&')1*
=ase Worst =est#robability of ,cenario
2>E !2E !2E
7*72> G*!2> 7*!2> 7*72> /24/ 4/ 4/
> > >> > >
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9ey Res'lts=ase Worst =est
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1.1> >.!/ !. > #I/./ :ot fo'nd :ot fo'nd #ayback
f 1>>. %o activate thisnges in the orkbook ill
nario analysis* 0onte Carlofor this trial. %his process'nning the n'&ber of
can also be 'sed to
nario analysis. It alsoco&pare apples andsa&e expected val'e and
tion in Col'&ns C and .inp'ts for all the variablesar 1 and changes in 'nits
n dark red and are dra n!-step process. Col'&n "the standard nor&alal'es* hit the F key.
#anel A? ;al'es fro& ,cenario Analysis and %heir "xpected ;al'es and,tandard eviations
Inp'ts fro& ,cenario Analysis forCo&parison to ,i&'lation
"xpected;al'e of Inp't
,tandardeviation of
Inp't
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/.G> :ot fo'nd :ot fo'nd isco'nted payback
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t "nd of <ear/!!*/71 !G*>2!1G*77> !/*/11
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,i&'lationle is 'pdated* it ill insert= above* and then save theas e expect. We set these these n'&bersall ite&s in the ata
n. We tell "xcel to insertthing else* b't each ti&e
@ou might wonder "what:s the deal about this chec; bo# and wh> doeand how do >ou use a chec; bo# for itJ Bet:s answer the "wh> it is uscell $/--! <f >ou clic; on the bo# $/-- returns a "TR5 " value and if$/-- is because we made the font color the same as the bac;ground
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'on(t change the red cell.
c'rsor.
%ax rate> >.>E
> >.>E> >.>E> >.>E
,cratch ork for chart? see co&&ents.Co'nt
Range bott ' #ercent' 0 '' 0 '' 0 '' 0 '' 0 '' 0 '
' 0 '' 0 '' 0 '' 0 '' 0 '' 0 '' 0 '' 0 '' 0 '' 0 '' 0 '' 10000 /''
9ee it reads either True or alse depending on whether the bo# is chto determine whether or not the data table should be evaluated! orthe value in &4 which is the simulated equipment cost! <f $/-- is A$/-- is AB9 then the data table has no formulas to evaluate (eversimulation results! @ou didn:t reall> need a chec; bo#G >ou could Lustrow .'7 chec; instead for whether $/-- is equal to /! $ut the chec
o'r case* e have rando&d. If the ata %able hasnnoying to ait />yance.
the ata %able containsor if yo' insert or delete
ated* so don(t getell in the orksheet. ,o to
1ow for how to use orms in #cel! To insert a chec; bo# in #cel .'/.'/' or later versions of #cel >ou can =nd instructions for this b> sCustomiFe Ribbon! 5nder CustomiFe the Ribbon and under Main Tabs
?n the Developer tab in the Controls group clic; on <nsert and thenorms Control section and clic; on the icon that loo;s li;e a chec; m
Chec; $o# ., will show up ne#t to the bo#! Right clic; on the chec;button is pressed then put in a cell reference in the Cell lin; bo#! e1ow when >ou clic; on the chec; bo# cell 0/7+ will displa> TR5 an>our #cel programming! All that is left is to put in a useful descriptioclic; on the chec; bo# area and edit the name to be something li;e "data table to do its calculations )!
te any ti&e yo' &ake a
s'&&ary of the si&'lationally hen yo' do a
:onvariablecost
+:on-;C * <ear 1
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ec;ed or not! The formulas in the simulation data table in cells $.'7 to <.'7 use this value#ample the formula in $.'7 is K< (*$*/-- &4 ')! <f $/-- is TR5 then the cell returns
B9 then it returns '! The other formulas in that row are similar! The end result is that ifthing is Fero) and if it is TR5 then it has formulas to evaluate and it records thes well have left $/-- visible and either put a / or a ' in it and had the < statements inbo# is neat!
' >ou must =rst enable the Developer tab on >our Ribbon! These are instructions for #celearching on "chec; bo#" in #cel help! Clic; the ile tab then clic; ?ptions then clic;
select the Developer chec; bo#!
in the orm Controls section clic; on <nsert (the picture that li;e a tool bo#)! Boo; at ther;! Move >our cursor to where >ou:d li;e the chec; bo# to go and clic; there! A name li;eo# and clic; on ormat Control! Then under the Control tab ma;e sure the "unchec;ed"had *$*/-- in that bo#! 9uppose >ou put in *0*/7+ for >our bo#! @ou are mostl> donewhen it is not chec;ed 0/7+ will displa> AB9 ! @ou can use these two logical values in
n for the chec; bo#! @ou don:t want >our users to be confused about what the bo# is for! Nustlic; this bo# if >ou want something special to happen to the spreadsheet" (li;e enable the
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Fig're 11-Replace&ent Analysis +%ho'sands of ollars
Applies to?
#art I. Inp'ts?
Cost of ne &achine !>>>
After-tax salvage val'e old &achine >>,ales reven'es +5xed !2>>Ann'al operating costs except depr. 1!>> !G>%ax rate >EWACC 1>E
epreciation 1 ! / %otals?epr. rates +ne &achine //.//E . 2E 1 .G1E 7. 1E 1>>E
epreciation on ne &achine 447 GG ! 4 1 G !>>>epreciation on old &achine // /// > > 447
[? Change in depreciation /// 224 ! 4 1 G 1///#art II. :et Cash Flo s before Replace&ent? Bld 0achine
> 1 ! /,ales reven'es !2>> !2>> !2>>Bperating costs except depreciation 1*!>> 1*!>> 1*!>>
epreciation // /// > %otal operating costs 12/ 12// 1!>>Bperating inco&e 44 47 1/>>%axes >E /G4 /G7 2!>After-tax operating inco&e 27 .4 2G>.! 7G>Add back depreciation // /// >
> 1/.4 1/.! 7G>#art III. :et Cash Flo s after Replace&ent? :e 0achine
> 1 ! /:e &achine cost? KKKAfter-tax salvage val'e* old &achine >>
,ales reven'es !*2>> !*2>> !*2>>Bperating costs except depreciation !G> !G> !G>
epreciation 447 GG ! 4 %otal operating costs 7 1*14 274
Bperating inco&e 1*22/ 1*//1 1* !%axes >E 4!1 2/! 77>After-tax operating inco&e /! 7 1*12Add back depreciation 447 GG ! 4
N 1*4>> 1*2 1*4GG 1* 2>#art I;. Incre&ental CF? Ro 21 N Ro /G N 1*4>> 4G2 77 47>#art ;. "val'ation :#; H 2G .>! IRR H !4.//E 0IRR H
#art ;I. Alternative Calc'lation for :et Cash Flo s:e &achine cost -!>>>,alvage val'e* old &achine >>:et cost of ne &achine -14>>
Bther operating cost savings H Bld X :e !> !> !>
A-% savings H Bther cost savings +1 X %ax rate 22! 22! 22![ epreciation H +:e X Bld /// 224 ! 4epr(n tax savings H [ epreciation %ax rate 1// !!! 11G
=oth0achines
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:et cash )o s after replace&ent
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:CF H A-% cost savings M epr(n tax savings -14>> 4G2.> 77 . 47>. G
%he :et Cash Flo ti&e line is the s'& of the larger* boldfaced* boxed* red n'&bers. %
A B C D E F G H
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!2>>1*!>>
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411.!G
e cash
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Wor
11-4 ,cenario Analysis--Repeate Pere fo
Fig're 11-2 Repeated Pere for convenience.Inp'ts and 9ey Res'lts for "ach ,cenario + ollars in %ho'san
,cenario :a&e
#robability of ,cenarioInp'ts?"@'ip&ent cost
%his orksheet extends the scenario analysis +sho n in %abandoning the pro$ect if de&and is lo . We also provideconvenience* e repeat the scenario analysis before addr
We add orst-case and best-case scenarios* incl'ding the sho n belo in Fig're 11 -2. 0anage&ent deter&ined that sfro& the base-case levels* and the :#; as not terribly senchange only 4 inp'ts? e@'ip&ent cost* 'nits sold in <ear 1price per 'nit* variable cost per 'nit* nonvariable cost* anexperts in their &arketing* operations* logistics* PR* acprobability of each scenario and the val'es to 'se for the o
We sho these base-case* orst-case* and best-case val'e2 belo * identi5ed by the cells ith larger* non-black fonkey res'lts sho n i&&ediately belo the inp't col'&n ill binp'ts are linked to a &odel for that partic'lar set of inp'ts8Fig're 11-2. If yo' ant to ret'rn to the o'r original inp'ts fo+ ata* What-If Analysis* ,cenario 0anager and pick the
We chose to create a separate scenario ith its o n set of beca'se this allo s a 'ser to &odify each scenario separatet o scenarios. Po ever* in orksheet L/b. ,cen.L e shogro'p +i.e.* all three scenarios have the sa&e changing cefeat're.
A B C 12
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Appendix 11A
"#R"CIA%IB: %A= ",
Depreciation percenta/es personal propert0 !i e , assets ot.er
t.an real estate#, as stated in 2S i3(4' "lass of n$estment
* Year ( Year 5 Year 1) Year
1 ** **% ') ))% 13 '6% 1) ))% 1' 33 3(% *' ))% '3 36% 17 ))% '* 13 71% 16 ')% 15 36% 13 3)% *3 5 31% 11 ('% 1' 36% 11 ('% 32 11 ('% 7 6*% 6 ''% 24 ( 54% 7 6'% 5 *5% 47 7 6*% 4 ((% 7G 3 34% 4 ((% G
4 (4%1> 4 ((% 1>11 * '7% 11
1>>.>>E 1>>.>>E 1>>.>>E 1>>.>>E 1!1/11214171G1!>
0ACR, for Residential Real #roperty
0onth #ropert <ear 1 ! / 2 4
1 /. G2E /.1G!E !.G7 E !.274E !.!7/E 1. 7>E!-!7 /.4/4E /.4/4E /.4/4E /.4/4E /.4/4E /.4/4E
!G 1. 7>E !.!7/E !.274E !.G7 E /.1G!E /. 2GE! >.>>>E >.>>>E >.>>>E >.>>>E >.>>>E >.>>>E
. E . E . E . E . E . 4E
O8ners.ip Year
O8ners.ipYear
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0ACR, for :onresidential Real #roperty0onth #ropert
<ear 1 ! / 2 41 !. 41E !.! 7E !.>//E 1.G1 E 1.4>2E 1./ 1E
!-/ !.24 E !.24 E !.24 E !.24 E !.24 E !.24 E> >.1>7E >./!1E >.2/2E >.7 E >. 4/E 1.177E
1>>.>>E 1>>.>>E 1>>.>>E 1>>.>>E 1>>.>>E 1>>.>>E
Ro'nded #ercentages Dsed in Analysis#roperty ife +in years ? /
epreciation in <ear 1 +ass'&ing half-year convention ? 1./>ERo'nded epreciation in <ears !-/ ? !.4>E
epreciation in <ear >? 1./>E
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1J!2J!>1/