MÉTODOS QUANTITATIVOS APLICADOS À...

21
!"#$%&’#()(% (% ’+, -)!., / !’- "#$%&%’()*+, -./0#% 123%$ 4)5,$ 6,$%0$) % 7)8%/ 6)’,%9 :,8$0;/%& 8% "$)<=, > ?0(% @%92A 8, B)$C D !"#$%$& ()*+#,#*#,-$& *./,0*%$& 1 0$+#*2,/,%*%3 .4$56 %46 /),7 8$9$ 0$44*4 !:;<=>?@A;B CDE:= />FA= !A=:G=> : #>@:H !>?A:I 46 @: *=>JKA &G<: 2:IDL @A .>=M N .I>?A @: *HI> !"#$% ’"(’"))*+ #,-!./-$ 0 1234 #567896237 ):$ ,+#4$%)O9$ "; ;58743 <2343 5;2 =2>8?=@6 94A@ @372> >@62<84B2A2 <4; 457>23 A523 45 ;283 =2>8?=@83C $338; 3@BA4D 94A@;43 2E5372> 5; ;4A@64D F5@ 9@>;872 A@3<>@=@> 5;2 >@62GH4 68B@2> @I837@B7@ @B7>@ 5;2 =2>8?=@6 A@9@BA@B7@ J @ A523 45 ;283 =2>8?=@83 8BA@9@BA@B7@3D 45 3@E2D A8=@>323 =2>8?=@83 @I968<278=23D 94A@; 3@> 57868K2A23 92>2 9>@=@> 4 =264> A@ 5;2 =2>8?=@6 A@9@BA@B7@C L4334 8B7@>@33@ 2M4>2 N 4 @375A4 A4 ;4A@64 A@ >@M>@33H4 <4; ;283 =2>8?=@83 8BA@9@BA@B7@3D =832BA4 2 ;@6O4> <4;9>@@B3H4 A4 <4;94>72;@B74 A2 =2>8?=@6 A@9@BA@B7@C P52BA4 7>2B3Q4>;2;43 5; ;4A@64 @<4BR;8<4 <4; ;283 A@ 5;2 =2>8?=@6 @I968<278=2 @; 3@5 ;4A@64 @3727S378<4 <4>>@394BA@B7@D 92332;43 2 A@38MB?T64 <4;4 LA@:IA @: =:P=:;;QA LJI<GRI>6 !A@:IA S:=>IB /2>2 ;283 A@ A523 =2>8?=@83 G?@:R:?@:?<:;D @; Q5BGH4 A@ 5;2 =2>8?=@6 @:R:?@:?<:6 !#$ ! %$ & & %$ ( ( % ))))))) % $ * * % " #$%& ( BU;@>4 A@ =2>8?=@83 V8BA@9@BA@B7@3WC X$3 =2>8?=@83 8BA@9@BA@B7@3 3H4 <O2;2A23 72;YN; =2>8?=@83 9>@A874>23 45 =2>8?=@83 Z[C ! E 5)9,$ #$%80(,$ 8) 5)$0C5%9 8%#%’8%’(% F GH)9H/9)8, ) #)$(0$ 8) %./)*+, 8% $%;$%&&+, A<9(0#9)IJ K D LK M L JJJJJJJL K N L &+, )& 5)$0C5%0& 0’8%#%’8%’(%&J $ O E 0’(%$H%#(, FL ,/ 5)9,$ 8% F ./)’8, (,8)& )& 5)$0C5%0& #$%80(,$)& &+, P%$,J + D E %&(0A)(05) 8% $ O L 3)&%)8) ’,& 8)8,& )A,&($)0&J $ D E 0’H90’)*+, 8% F %A $%9)*+, Q 5)$0C5%9 K D L A)’(%’8, H,’&()’(%& )& 5)$0C5%0& K M LK R L JJJJL K N J + D E %&(0A)(05) 8% $ O L 3)&%)8) ’,& 8)8,& )A,&($)0&J $ M E 0’H90’)*+, 8% F %A $%9)*+, Q 5)$0C5%9 K M L A)’(%’8, H,’&()’(%& )& 5)$0C5%0& K D LK R L JJJL K N J J J J

Transcript of MÉTODOS QUANTITATIVOS APLICADOS À...

Page 1: MÉTODOS QUANTITATIVOS APLICADOS À CONTABILIDADE..."#$%&%’()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)’,%9!:,8$0;/%&!8%!"$)!?0(%!@%92A!8,!B)$C!!!!Z! +&=264>&A@&EW’U’YkfWj&Xb#&0&a2>8?=@6&Z][D&8BA8

!"#$%&'#()(%*(%*'+,*-)!.,*/*!'-*!

"#$%&%'()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)',%9!:,8$0;/%&!8%!"$)<=,!!>!?0(%!@%92A!8,!B)$C!!!!D!

!!""##$$%%$$&&''(())**++##,,##**##,,--$$&&''**..//,,00**%%$$&&''11''00$$++##**22,,//,,%%**%%33''.4$56'%46'/),7'8$9$'0$44*4'!:;<=>?@A;B'CDE:='/>FA='!A=:G=>':'#>@:H'!>?A:I'46'@:'*=>JKA'&G<:'2:IDL'@A'.>=M'N'.I>?A'@:'*HI>''''!!""##$$%%&&''""((''""))))**++&&##,,--!!..//--$$&&00&&11223344&&##556677889966223377&&))::$$&&&&,+#4$%)O9$'&

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

P52BA4& 7>2B3Q4>;2;43& 5;& ;4A@64& @<4BR;8<4& <4;& ;283& A@& 5;2& =2>8?=@6&@I968<278=2&@;&3@5&;4A@64&@3727S378<4&<4>>@394BA@B7@D&92332;43&2&A@38MB?T64&<4;4&LA@:IA'@:'=:P=:;;QA'LJI<GRI>6'&&!A@:IA'S:=>IB''

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

Page 2: MÉTODOS QUANTITATIVOS APLICADOS À CONTABILIDADE..."#$%&%’()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)’,%9!:,8$0;/%&!8%!"$)!?0(%!@%92A!8,!B)$C!!!!Z! +&=264>&A@&EW’U’YkfWj&Xb#&0&a2>8?=@6&Z][D&8BA8

!"#$%&'#()(%*(%*'+,*-)!.,*/*!'-*!

"#$%&%'()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)',%9!:,8$0;/%&!8%!"$)<=,!!>!?0(%!@%92A!8,!B)$C!!!!M!

$*!E!0'H90')*+,!8%!F!%A!$%9)*+,!Q!5)$0C5%9!KNL!A)'(%'8,!H,'&()'(%&!)&!5)$0C5%0&!KDL!KML!KRL!JJJJL!KNJ!ε0!E!%$$,!)9%)(S$0,!%A!TL!#)$)!)!,3&%$5)*+,!,J!!!!"#$%"& #$& '()*& +,(-./$-*0& !26& ;4A@64& @B=46=@& 29@B23& 7>\3& =2>8?=@83%& 5;2&A@9@BA@B7@&XJ[&@&A523&8BA@9@BA@B7@3&XZ]&@&Z^[D&8374&N%&J_&)XZ]D&Z^[C&'

T'U'EA'V'EWXWG'V'EYXYG'V'εεεεG&'*RIGZ>[QA'@A'!A@:IA'& && $& 2968<2GH4& 3@>?& >@268K2A2& 92>2& 2& 2B?683@& A4& <4;94>72;@B74& A43& 153743&.BA8>@743&A@&`2Y>8<2GH4&X1.`[&@;&Q5BGH4&A@&<2A2&5;2&A23&a2>8?=@83&Xb#+c&@&b#[&83462A2;@B7@&@&@;&Q5BGH4&A@3723&A523&=2>8?=@83&38;5672B@2;@B7@C&&''''''''''#>E6W\'0ALR>?]G>'!HI<GRI>;<'&^*N';D=G:'@:'@>@A;'=:I><GFA;'>A;'W_'JI<GLA;'L:;:;'''

!:;:;' 0,5' C!' /.']& deCeed& ]Cdd^& f]&^& dfCedg& ]Cg^h& ^^&f& ghC]i]& ]Cefi& fj&i& e]Cjgk& ]Chhe& ih&k& d^Cegk& ]Cfgf& fj&e& gdCedk& ]Cjkd& i]&d& dgCikh& ]Cke]& ig&g& dhCefi& ]Ciei& fi&j& efCi]d& ]Ckik& ^k&]h& keChkd& ]C]]j& ^j&]]& edCiie& ]Cfg^& fk&]^& d^C]h^& ]Cf^h& id&]f& egCkff& ]C^ei& ij&]i& ejChdj& ]Cfii& ^j&]k& gkCkkh& ]Cghf& ig&]e& kgC]jd& ]Ch^^& fg&]d& e]Ce^e& ]Ck]h& ^]&]g& ghCegj& ]Cdjf& ^j&]j& kgC^ke& ]C]ij& ^d&^h& kkCffd& ]C]kk& ^^&^]& gkC]hg& ]Cgid& fg&^^& deCigk& ]Cgf^& ^f&^f& edCdgf& ]C]fe& i^&^i& keCfjg& ]C]fe& ^^&^k& eeCe^^& ]Cffh& ff&^e& efCiji& ]Cfkg& ^e&^d& gjCi]e& ]Cgg^& ik&^g& edCk]g& ]C]di& ik&^j& dfCegh& ]Ceif& f]&fh& eeC]f^& ]Cfg]& ^e&

&

Page 3: MÉTODOS QUANTITATIVOS APLICADOS À CONTABILIDADE..."#$%&%’()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)’,%9!:,8$0;/%&!8%!"$)!?0(%!@%92A!8,!B)$C!!!!Z! +&=264>&A@&EW’U’YkfWj&Xb#&0&a2>8?=@6&Z][D&8BA8

!"#$%&'#()(%*(%*'+,*-)!.,*/*!'-*!

"#$%&%'()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)',%9!:,8$0;/%&!8%!"$)<=,!!>!?0(%!@%92A!8,!B)$C!!!!R!

&14;&Y23@&B43&<?6<5643&29>@3@B72A43&B4&"I<@6D&Q2>@;43&2&8B7@>9>@72GH4&A23&

@378;278=23D&4Y@A@<@BA4&4&3@M58B7@&<4;2BA4%&'-*4,`-3,&B'aC!b''

!" 153743&.BA8>@743&A@&`2Y>8<2GH4&X1.`[&@;&Q5BGH4&A23&b4>23&#?F58B2&Xb#[&&'*+`/,&3'%$&'43&)/#*%$&''&!" `5BGH4%&&1.`&&_&&^dCjh]D^f&l&&^jD]fb#&

m&&&&&&_&&&&&&Y4&&&&&&l&&&&&&Y]I]8&&&/4A@;43&2Q8>;2>&F5@%&&+&<4@Q8<8@B7@&2BM562>&XN&2&8B<68B2GH4&A2&>@72&F52BA4&T&N&8BQ65@B<82A4&9@64&=264>&A@&cb'A2&=2>8?=@6&8BA@9@BA@B7@&b#D&27@BA@&243&>@F5838743&@39@<SQ8<43&B4&7@37@&A@&O89n7@3@&A2&>@M>@33H4C&o&A8Q@>@B7@&A@&K@>4&@&2338;&<2>2<7@>8K2&2&@I837\B<82&A@&>@M>@33H4D&;437>2BA4T3@&2&5;&BS=@6&A@&*+,$+)+-.$-+/&A@&hDhkC&&

&+& 1"$2-3-$4'$& #$& #$'$(5-4,67"& "8& $9:%-3,67"& ;<=>D& N& A@& defWYg6& P5@>&

A8K@>&F5@&2&a2>8?=@6&.BA@9@BA@B7@&0&b#D&N&>@394B3?=@6&94>&diD]^&p&A23&=2>82Gq@3&4<4>>8A23&<4;&4&15374&.BA8>@74&A@&`2Y>8<2GH4&X1.`[D&45&3@E2&diD]^&p&A23&=2>82Gq@3&4<4>>8A23&<4;&4&1.`D&3H4&@I968<2A23&9@62&=2>82GH4&4<4>>8A2&<4;&2&b#D&@BF52B74&F5@&^kDgg&p&A23&=2>82Gq@3&4<4>>8A23&<4;&4&1.`D&BH4&3H4&@I968<2A23&94>&b#C&.374&ND&3H4&A@<4>>@B7@3&A@&-/0*/*'/1&/234+/*'BH4&@39@<8Q8<2A23&B4&;4A@64C&&

4'N'hH>@=>@A'>KH;<>@A&%&N&<26<562A4&92>2&>@Q6@78>&72B74&4&BU;@>4&A@&=2>8?=@83&@I968<278=23& B4& ;4A@64D& F52B74& 4& 72;2BO4& A2& 2;437>2C& L4& 9>@3@B7@& <234D& @6@&A@;4B37>2&F5@&b#&N&>@394B3?=@6&94>&dfD^hp&A23&=2>82Gq@3&4<4>>8A23&B4&1.`C&

&&

&'")r#+&c+)&'")r-!$c+)&1.`&_&Q&Xb#[& &

5*2/26*2+-/'%&'4&,4&**78''&;U678964& hDgehjfkd]d&'TP52A>2A4& hDdi]^]hf]&4\hH>@=>@A'>KH;<>@A'ifdjWkldmYW'">>4&92A>H4& khhfD]^k]ig&+Y3@>=2Gq@3& fh&&&

Page 4: MÉTODOS QUANTITATIVOS APLICADOS À CONTABILIDADE..."#$%&%’()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)’,%9!:,8$0;/%&!8%!"$)!?0(%!@%92A!8,!B)$C!!!!Z! +&=264>&A@&EW’U’YkfWj&Xb#&0&a2>8?=@6&Z][D&8BA8

!"#$%&'#()(%*(%*'+,*-)!.,*/*!'-*!

"#$%&%'()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)',%9!:,8$0;/%&!8%!"$)<=,!!>!?0(%!@%92A!8,!B)$C!!!!U!

&*+*/,&*+%$'*'&,S+,5,0n+0,*'&

$L+a$& & & & & &'' ,1' 9:' ;:' <' <'%&'*+,$+)+-/=78'

'@M>@33H4& ] ^hhdihe]^^& ^hhdihe]^^&ghD]jkjefge& ]Dhfd]e"Thj&'@3SA54& ^gdhhgdkf]iDg& ^khf]^e]D^i&& &!4726& ^j ^dhg^g]ifd&&& && &&&&"'*+`/,&3'%$'5'04o#,0$'&M6&_&B&0&/&0&]&&M6&_&fh&0&]&0&]&&M6&_&^g&&V!!hDhk&b4&%&`&s&`&X]D^g[&t&>@E@872&ghD]jkjefge&s&iD^h&""""

0011223311**44**!!@372&2&@F52GH4&A@&>@M>@33H4&<4;4&5;&74A4C&&r32A2&@;&>@M>@33H4&;U678962&&`&A@&38MB8Q8<2GH4&_&hDhhhhhhhh]hfd]e&LS=@6&A@&<4BQ82BG2&_&hDjk&LS=@6&A@&38MB8Q8<uB<82&_&hDhk&!!4:P=>'S:=>I'&)@&`&v&hDhk&p&XLS=@6&A@&38MB8Q8<uB<82[&%&'@M>@33H4&)8MB8Q8<278=2&&)@&hDhhhhhhhh]hfd]e&v&hDhk%&O?&'@M>@33H4&)8MB8Q8<278=2&)@&`&w&hDhk&p&XLS=@6&A@&38MB8Q8<uB<82[%&'@M>@33H4&LH4&)8MB8Q8<278=2&!L4&@I@;964D&4&=264>&iD^h&N&4&V`W&<>S78<4&X`&A@&`83<O@>[&!x>@2&=28&532>&ghD^h&27N&Q8B26&N&kpC&""

5678*79*

:

3D!

W08%!4%50'%L!#C;J!XUD!

Page 5: MÉTODOS QUANTITATIVOS APLICADOS À CONTABILIDADE..."#$%&%’()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)’,%9!:,8$0;/%&!8%!"$)!?0(%!@%92A!8,!B)$C!!!!Z! +&=264>&A@&EW’U’YkfWj&Xb#&0&a2>8?=@6&Z][D&8BA8

!"#$%&'#()(%*(%*'+,*-)!.,*/*!'-*!

"#$%&%'()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)',%9!:,8$0;/%&!8%!"$)<=,!!>!?0(%!@%92A!8,!B)$C!!!!Y!

""""""""""""""""&&

2[& 7@;43&F5@&9@64&;N74A4&A4&<:;<:''R&&F5@%&• )@&4&=264>&&R&&Q4>&;284>&45&8M526&2&pD&&2&O89n7@3@&B562&N&2<@872&''''&Xb+B&R&q&p[C&+QA&O?&>@M>@33H4&• &)@&4&=264>&&9&&Q4>&;@B4>&A4&F5@&yD&2&O89n7@3@&B562&N&>@E@872A2&• Xb]%&R&r&p[C&CM&>@M>@33H4z&&&

Y[& 7@;43&&9@62&:;<><s;<GZ>'5&F5@%&• X`s`3&X&9D&B&0&9&0&]&[&>@E@872&b4&• X`v`3&X&9D&B&0&9&0&]&[&2<@872&b]&

&& L@372&>@M>@33H4D&7@;43&F5@&4&&F>IA='R&N&A@&ifiiiiiiiiWijdWl&94>72B74&r'pD&=:K:G<>'C$D&&@&>Z:G<>'C]D&&@&<4BQ8M5>2BA4&2&@I837\B<82&A@&>@M>@33H4C&&

/@62&@3727S378<2&5B&5&U'mifWk_kljml't'5;' aWfYmb'U'efYiD&94>&<4B3@M58B7@&>@E@872&b+D& & @& 2<@872& b]C& "B7H4& 8BQ@>8;43& <4;& 5;& BS=@6& A@& 38MB8Q8<uB<82& A@& hDhk& F5@D& N&9>4=?=@6& F5@& O2E2& >@M>@33H4& 68B@2>D& <4;& 5;2& Q4>7@& <4>>@62GH4& @B7>@& 23& =2>8?=@83D&4BA@&2&=2>8?=@6&@I968<278=2&>@62<84B2T3@&243&M23743&A@&1.`C&&&&*+*/,&*+%$'*',+0/,+*O9$'"

'' >8&)+-+&$2&*' 5448'?/%478' 92/2'2' @/184AB' CDE'+$)&4+84&*'CDE'*0?&4+84&*' F$)&4+84'CDG!E'90?&4+84'CDG!E'.B7@>3@GH4&^djh]D^^dki&ig^gDkedehd&kDddgfekfhd&fDf^gh]"The& ]gh]hDfiihd& fddj^D]]]h^& ]gh]hDfiihd& fddj^D]]]h^&b#& ^jD]fi]iejd&fD^kff]ik]e&gDjkk^]jj^^&]Dhfd]e"Thj& ^^Didhh^edj& fkDdjg^ed]i& ^^Didhh^edj& fkDdjg^ed]i&

&&&

14;&Y23@&B43&A2A43&2<8;2D&=:K:G<AH\;:'>']GRu<:;:'@>'G?ZIG?>[QA';:='GPH>I'>'v:=AD&4&F5@&38MB8Q8<2&2A;878>;43&2&@I837\B<82&A@&<5374&Q8I4C&"

Page 6: MÉTODOS QUANTITATIVOS APLICADOS À CONTABILIDADE..."#$%&%’()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)’,%9!:,8$0;/%&!8%!"$)!?0(%!@%92A!8,!B)$C!!!!Z! +&=264>&A@&EW’U’YkfWj&Xb#&0&a2>8?=@6&Z][D&8BA8

!"#$%&'#()(%*(%*'+,*-)!.,*/*!'-*!

"#$%&%'()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)',%9!:,8$0;/%&!8%!"$)<=,!!>!?0(%!@%92A!8,!B)$C!!!!Z!

+&=264>&A@&EW'U'YkfWj&Xb#&0&a2>8?=@6&Z][D&8BA8<2&F5@D&92>2&<2A2&<>@3<8;@B74&<4>>@394BA@B7@&2&5;2&5B8A2A@&@;&ZD&@378;2T3@&F5@&4&=264>&J&<>@3G2&2&5;2&;NA82&A@&^jD]f&5B8A2A@3C&&

.374&ND&92>2&<2A2&<>@3<8;@B74&<4>>@394BA@B7@&24&BU;@>4&A@&b4>23&#?F58B2D&4&;4A@64&2E5372A4&9>@=\&2&@378;278=2&A@&F5@&43&<53743&8BA8>@743&A@&Q2Y>8<2GH4&X1.`[&<>@3G2;&@;&^jD]f&5B8A2A@3&;4B@7?>823C&

&c@9>@@BA@T3@&2338;&F5@D&3@&2&b4>2&#?F58B2&25;@B72&@;&]h&5B8A2A@3& XA@&

7@;94& T& O4>23[D& @39@>2T3@& F5@& 43& <53743& 8BA8>@743& A@& Q2Y>8<2GH4& <>@3G2;& ^j]Dfi&5B8A2A@3C&&&

+& G?<:=Z:R<AD& =264>& A@& EA' ' U' Yd6kiWfYj' & >@9>@3@B72& 4& =264>& ;NA84& A@& TD&F52BA4&c&N&8M526&2&Xh[&K@>4C&+5&3@E2D&8BA8<2&F5@&4&<5374&8BA8>@74&A@&Q2Y>8<2GH4&N&A@&^dCjh]D^f&92>2&5;2&>@Q@>\B<82&Xh[&K@>4&A4&BU;@>4&A@&b4>23&#?F58B2&XZ[C&""m&_&Yh&l&Y]I]8&m&_&^dCjh]D^f&l&^jD]f&{&h& & & & & &w'U'Yd6kiWfYj'""""""'")r#+&c+)&'")r-!$c+)&1.`&_&Q&Xb#[& &

5*2/26*2+-/'%&'4&,4&**78'4'LJI<GRIA' ifmlikj_dWd''TP52A>2A4& hDdi]^]hf]&'TF52A>2A4&2E5372A4&hDdf]jedg^]&">>4&92A>H4& khhfD]^k]ig&+Y3@>=2Gq@3& fh&""

+&1"$2-3-$4'$&#$&1"(($%,67"& ;<>?&N&A@&mlfik'gf'4&F5@& 8BA8<2&F5@&O?&5;2&Q4>7@&<4>>@62GH4&X2334<82GH4[&68B@2>D&A8>@72D&@B7>@&4&15374&.BA8>@74&A@&`2Y>8<2GH4&@&23&b4>23&#?F58B2C&""

"""""

14;4&0,5'D' 28467"& '@:'C!D&<4;&5;&=264>&A@&;H4&A@&4Y>2&A8>@72&@6@=2A4D&7@>@;43&5;&@6@=2A4&<5374&8BA8>@74&A@&Q2Y>8<2GH4C&&

MXJ[ODLMR

T!

]!

;&<4#=,*

DD!>D! O!

OL\ZO

Page 7: MÉTODOS QUANTITATIVOS APLICADOS À CONTABILIDADE..."#$%&%’()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)’,%9!:,8$0;/%&!8%!"$)!?0(%!@%92A!8,!B)$C!!!!Z! +&=264>&A@&EW’U’YkfWj&Xb#&0&a2>8?=@6&Z][D&8BA8

!"#$%&'#()(%*(%*'+,*-)!.,*/*!'-*!

"#$%&%'()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)',%9!:,8$0;/%&!8%!"$)<=,!!>!?0(%!@%92A!8,!B)$C!!!!X!

b?&jk&p&A@&9>4Y2Y868A2A@&A@&F5@&Y]&Xb#[&@37@E2&B4&8B7@>=264&A@&X^^Didz&fkDgh[&@&A@&F5@&Y4&&@37@E2&B4&8B7@>=264&A@&X]gCh]hDfiz&fdCdj^D]][C&""

"""*+`/,&3'%$&'43&o%)$&'&

";Y4>2& @I8372& 5;2& 2;962& A839@>3H4& B4& M>?Q8<4& A@& >@3SA543D& BH4& O?& 5;&92A>H4& 292>@B7@C& +3& >@3SA543& 92>@<@;& @372>& 5B8Q4>;@;@B7@& @3926O2A43& 2<8;2& @&2Y28I4&A@&iD&92>2&43&A8Q@>@B7@3&=264>@3&A@&c& Xb#[C&/4>72B74&94A@;43&<4B<658>&F5@&@;&>@62GH4&243&A2A43&34Y>@&4&1.`&@&b#D&F5@&4&;4A@64&2E5372A4D&92>@<@&29>49>82A4C&&&

'")r-!$c+)&c"&'")|cr+)& & && & & &#H*&4@/=78' B4&@+*28I/J'>F<' K&*6%08*' K&*6%08*'?/%478'

] djk^eDjfkjd& T^gkjDjfkjej& ThDkg]dighfd&^ ghj^kDfdkh^& Td^idDfdkh^f& T]Didi^hjjjd&f dkkheDi^fej& iefiDkdef]^& hDji^df^gg&i kd^]hD]djfj& iddiDg^hehd& hDjd]^ehfgd&k eg]jfDdk^g& iij]D^id^h]& hDj]fkddgg^&e gij]eDdkf]e& ^dkgD^iegi^& hDke]hef]k]&d dffdjDefhje& khdhDfejhi]& ]Dhf]fdgdej&g dhkkfDe]gd& ghDfg]^jeej& hDh]efkhkjd&j d^j]fDigie]& TjijeDigiehg& T]Djf]dhghf^&]h ehkh^Dffg& TiiikDffg& ThDjhi^fjfkk&]] eg]eiDe]gek& Td]gDe]gek^]& ThD]ie]defie&]^ eefkgDfh]ki& kdifDejgie& ]D]egfi^ejg&]f eid^eDdgjf]& fgheD^]hej& hDddi^f^kdg&]i edhkdDk^]hd& ^h^]Didgjff& hDi]]]jkh]]&]k ghifhDhjik^& k]]jDjhkidk& ]Dhi]ikk]^]&]e kdedeDf^kdi& k^hDedi^kkj& hD]hkj]]gj]&]d d]gjfDdgjie& T]h^edDdgjie& T^Dhggeh]ifk&]g gh]fgDdkfhe& kkhD^iejiid& hD]]]j^dfkj&]j e]fdeDfe^i]& Tf]^hDfe^ihj& ThDefid^^]k&^h e]kk]D]ed^j& Te^]iD]ed^j]& T]D^eihi^]kk&^] g]d]]Djjejj& ffjeDhhfhhj& hDejhdj]h^&^^ g]^diDjgidj& TidgjDjgidgd& ThDjdifiijdg&^f ehjjdDe]gk& edgkDfg]kh^& ]Dfgh^fik^d&^i ehjjdDe]gk& TikjjDe]gijg& ThDjfke^^hhg&^k eeeijDeifh]& T^dDeifhhjg]& ThDhhke^^jie&

RYL\MMLU M[LD

RXJX[MLDDD\JODOLRU! MXJ[ODLMR

.>?@**#AB1C>DC* .>?@*'EF1C>DC*

Page 8: MÉTODOS QUANTITATIVOS APLICADOS À CONTABILIDADE..."#$%&%’()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)’,%9!:,8$0;/%&!8%!"$)!?0(%!@%92A!8,!B)$C!!!!Z! +&=264>&A@&EW’U’YkfWj&Xb#&0&a2>8?=@6&Z][D&8BA8

!"#$%&'#()(%*(%*'+,*-)!.,*/*!'-*!

"#$%&%'()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)',%9!:,8$0;/%&!8%!"$)<=,!!>!?0(%!@%92A!8,!B)$C!!!!\!

^e ediekDfjj]^& Tfjd]Dfjj]^k& ThDghdgfihie&^d g^df]Dej^]i& eegiDfhdgek& ]Dfkjedigi&^g e^]hiDd]ehg& ki]fD^gfj]d& ]D]h]]f^hjg&^j dkdegDef]h]& T^hggDef]h]& ThDi^igkie]i&fh eg]fkDigik]& T^hhfDigikhk& ThDihdkfid]]&

&!!!!!!!!!!!!!!!!*********G)FH2*I*IAJK>216*D*LDA3CDKIMDC*AND*B>LDE*2I3>2B1>3D*LD?*D*FDM1C*%OFK>LI3>PD*MI*&1QC122ND6*1*FCDLECDE*IAIK>2IC*?1KRDC*D*FCDL122D*M1*FCDMESND6*LDALKE>AMD*TE1*D*AU?1CD*M1*.D312*M1*-CDMESND*V.-W*IB13I?*D2*LE23D2*>AM>C13D2*M1*BIXC>LISND*MECIA31*D*?Y2@*)22>?*C12DKP1E*1B13EIC*E?I*ADPI*IAJK>21*3D?IAMD*FDC*XI21*I2*MEI2*PIC>JP1>2*>AM1F1AM1A312*VZ[*1*.-W\@*!!!

C!'.IA<>P:L'@:'=:;s@HA;

T]^hhh

T]hhhh

Tghhh

Tehhh

Tihhh

T^hhh

h

^hhh

ihhhehhh

ghhh

T khh ]Chhh ]Ckhh ^Chhh ^Ckhh

C!

4:;s@HA;

Page 9: MÉTODOS QUANTITATIVOS APLICADOS À CONTABILIDADE..."#$%&%’()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)’,%9!:,8$0;/%&!8%!"$)!?0(%!@%92A!8,!B)$C!!!!Z! +&=264>&A@&EW’U’YkfWj&Xb#&0&a2>8?=@6&Z][D&8BA8

!"#$%&'#()(%*(%*'+,*-)!.,*/*!'-*!

"#$%&%'()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)',%9!:,8$0;/%&!8%!"$)<=,!!>!?0(%!@%92A!8,!B)$C!!!![!

!14;&Y23@&B43&<?6<5643&29>@3@B72A43&B4&"I<@6D&@&92>2&&@Q@874&@I964>27n>84D&

Q2>@;43&2&8B7@>9>@72GH4&A23&@378;278=23D&4Y@A@<@BA4&4&3@M58B7@&<4;2BA4%&'-*4,`-3,&B'a/.b''

!" 153743&.BA8>@743&A@&`2Y>8<2GH4&X1.`[&@;&Q5BGH4&A43&-47@3&A@&/>4A5GH4&X-/[&

&'*+`/,&3'%$&'43&)/#*%$&''&!" `5BGH4%&&1.`&&_&&k^CedkDf]&l&&k]gD]k-/&

m&&&&&&_&&&&&&Y4&&&&&&l&&&&&&Y]I]8&&&/4A@;43&2Q8>;2>&F5@%&&+&<4@Q8<8@B7@&2BM562>&XN&2&8B<68B2GH4&A2&>@72&F52BA4&T&N&8BQ65@B<82A4&9@64&=264>&A@&cb'A2&=2>8?=@6&8BA@9@BA@B7@&-/D&27@BA@&243&>@F5838743&@39@<SQ8<43&B4&7@37@&A@&O89n7@3@&A2&>@M>@33H4C&o&A8Q@>@B7@&A@&K@>4&@&2338;&<2>2<7@>8K2&2&@I837\B<82&A@&>@M>@33H4D&;437>2BA4T3@&2&5;&BS=@6&A@&*+,$+)+-.$-+/&A@&hDhkC&&

&+& 1"$2-3-$4'$& #$& #$'$(5-4,67"& "8& $9:%-3,67"& ;<=>D& N& A@& YjfWjg6& P5@>&

A8K@>& F5@& 2& a2>8?=@6& .BA@9@BA@B7@& 0& -/D& N& >@394B3?=@6& 94>& 29@B23& ^fD]f&p& A23&=2>82Gq@3&4<4>>8A23&<4;&4&15374&.BA8>@74&A@&`2Y>8<2GH4&X1.`[D&45&3@E2&^fD]f&p&A23&=2>82Gq@3&4<4>>8A23&<4;&4&1.`D&3H4&@I968<2A23&9@62&=2>82GH4&4<4>>8A2&<4;&2&-/C&

&4'N'hH>@=>@A'>KH;<>@A%&N&<26<562A4&92>2&>@Q6@78>&72B74&4&BU;@>4&A@&=2>8?=@83&

@I968<278=23& B4& ;4A@64D& F52B74& 4& 72;2BO4& A2& 2;437>2C& L4& 9>@3@B7@& <234D& @6@&A@;4B37>2&F5@&-/&N&>@394B3?=@6&94>&^hDfg&p&A23&=2>82Gq@3&4<4>>8A23&B4&1.`C&

&&

'")r#+&c+)&'")r-!$c+)&1.`&_&Q&X-/[& &

5*2/26*2+-/'%&'4&,4&**78''&;U678964& hDighjkehge&'TP52A>2A4& hD^f]f]gdke&4\hH>@=>@A'>KH;<>@A' ifYijml_m__'">>4&92A>H4& ge^^Dekk^ke&+Y3@>=2Gq@3& fh&&&&&!

Page 10: MÉTODOS QUANTITATIVOS APLICADOS À CONTABILIDADE..."#$%&%’()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)’,%9!:,8$0;/%&!8%!"$)!?0(%!@%92A!8,!B)$C!!!!Z! +&=264>&A@&EW’U’YkfWj&Xb#&0&a2>8?=@6&Z][D&8BA8

!"#$%&'#()(%*(%*'+,*-)!.,*/*!'-*!

"#$%&%'()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)',%9!:,8$0;/%&!8%!"$)<=,!!>!?0(%!@%92A!8,!B)$C!!!!DO!

!!*+*/,&*+%$'*'&,S+,5,0n+0,*'!!

$L+a$& & & & & &'' ,1' 9:' ;:' <' <'%&'*+,$+)+-/=78'

'@M>@33H4& ]& e^eide^ji& e^eide^ji& gDi^eh^^]ik hDhhd]fiegj&'@3SA54& ^g& ^hg]ghk]if& difkh]gfDed&& &!4726& ^j& ^dhg^g]ifd&&& && &&

!!!!*+`/,&3'%$'5'04o#,0$'&M6&_&B&0&/&0&]&&M6&_&fh&0&]&0&]&&M6&_&^g&&]!!hDhk&b4&%&`&s&`&X]D^g[&t&>@E@872&gDi^eh^^]ik&s&iD^h&""!!

0011223311**44**!!@372&2&@F52GH4&A@&>@M>@33H4&<4;4&5;&74A4C&&r32A2&@;&>@M>@33H4&;U678962&&`&A@&38MB8Q8<2GH4&_&hDhhd]fiegj&LS=@6&A@&<4BQ82BG2&_&hDjk&LS=@6&A@&38MB8Q8<uB<82&_&hDhk&!!4:P=>'S:=>I'&)@&`&v&hDhk&p&XLS=@6&A@&38MB8Q8<uB<82[%&'@M>@33H4&)8MB8Q8<278=2&&)@&hDhhd]fiegj&v&hDhk%&O?&'@M>@33H4&)8MB8Q8<278=2&)@&`&w&hDhk&p&XLS=@6&A@&38MB8Q8<uB<82[%&'@M>@33H4&LH4&)8MB8Q8<278=2&!L4&@I@;964D&4&=264>&iD^h&N&4&V`W&<>S78<4&X`&A@&`83<O@>[&!x>@2&=28&532>&ghD^h&27N&Q8B26&N&kpC&

5678*79*

:

3D!

W08%!4%50'%L!#C;J!XUD!

Page 11: MÉTODOS QUANTITATIVOS APLICADOS À CONTABILIDADE..."#$%&%’()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)’,%9!:,8$0;/%&!8%!"$)!?0(%!@%92A!8,!B)$C!!!!Z! +&=264>&A@&EW’U’YkfWj&Xb#&0&a2>8?=@6&Z][D&8BA8

!"#$%&'#()(%*(%*'+,*-)!.,*/*!'-*!

"#$%&%'()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)',%9!:,8$0;/%&!8%!"$)<=,!!>!?0(%!@%92A!8,!B)$C!!!!DD!

&&&&&&&&&&&&&&&&&&

<[& 7@;43&F5@&9@64&;N74A4&A4&<:;<:''R&&F5@%&• )@&4&=264>&&R&&Q4>&;284>&45&8M526&2&pD&&2&O89n7@3@&B562&N&2<@872&''''&Xb+B&R&q&p[C&+QA&O?&>@M>@33H4&• &)@&4&=264>&&9&&Q4>&;@B4>&A4&F5@&yD&2&O89n7@3@&B562&N&>@E@872A2&• Xb]%&R&r&p[C&CM&>@M>@33H4z&&&

A[& 7@;43&&9@62&:;<><s;<GZ>'5&F5@%&• X`s`3&X&9D&B&0&9&0&]&[&>@E@872&b4&• X`v`3&X&9D&B&0&9&0&]&[&2<@872&b]&

&& L@372&>@M>@33H4D&7@;43&F5@&4&&F>IA='R&N&A@&ifiidWjelmk&94>72B74&r'pD&=:K:G<>'C$D&&@&>Z:G<>'C]D&&@&<4BQ8M5>2BA4&2&@I837\B<82&A@&>@M>@33H4C&&

/@62&@3727S378<2&5B&5&U'mfeYliYYWe_'t'5;' aWfYmb'U'efYiD&94>&<4B3@M58B7@&>@E@872&b+D& & @& 2<@872& b]C& "B7H4& 8BQ@>8;43& <4;& 5;& BS=@6& A@& 38MB8Q8<uB<82& A@& hDhk& F5@D& & 2&>@M>@33H4& 68B@2>& @I837@D& <4;& E>GX>' ZA==:I>[QAD& @;Y4>2& @I8372D' 4BA@& 2& =2>8?=@6&@I968<278=2&>@62<84B2T3@&243&M23743&A@&1.`C&&&*+*/,&*+%$'*',+0/,+*O9$'"&

'' >8&)+-+&$2&*' 5448'?/%478' 92/2'2' @/184AB'CDE'

+$)&4+84&*'CDE'

*0?&4+84&*'F$)&4+84'CDG!E'

90?&4+84'CDG!E'

.B7@>3@GH4&k^edkDfhggi& e^j^Dj^ihg]&gDfdhke]e^d&iD]deie"Thj&fjdgiDg^fdf& ekkekDdjfjk&fjdgiDg^fdf& ekkekDdjfjk&-/& k]gD]ik^igg& ]dgDkhhg^^d&̂ Djh^de]]^i&hDhhd]fiegj&]k^Dkh^idg^& ggfDdggh]jk&]k^Dkh^idg^& ggfDdggh]jk&

&&

14;&Y23@&B43&A2A43&2<8;2D&=:K:G<AH\;:'>']GRu<:;:'@>'G?ZIG?>[QA';:='GPH>I'>'v:=AD&4&F5@&38MB8Q8<2&2A;878>;43&2&@I837\B<82&A@&<5374&Q8I4C&"

Page 12: MÉTODOS QUANTITATIVOS APLICADOS À CONTABILIDADE..."#$%&%’()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)’,%9!:,8$0;/%&!8%!"$)!?0(%!@%92A!8,!B)$C!!!!Z! +&=264>&A@&EW’U’YkfWj&Xb#&0&a2>8?=@6&Z][D&8BA8

!"#$%&'#()(%*(%*'+,*-)!.,*/*!'-*!

"#$%&%'()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)',%9!:,8$0;/%&!8%!"$)<=,!!>!?0(%!@%92A!8,!B)$C!!!!DM!

+&=264>&A@&EW'U'_WmfW_&X-/&0&a2>8?=@6&Z][D&8BA8<2&F5@D&92>2&<2A2&<>@3<8;@B74&<4>>@394BA@B7@&2&5;2&5B8A2A@&@;&ZD&@378;2T3@&F5@&4&=264>&J&<>@3G2&2&5;2&;NA82&A@&k]gD]k&5B8A2A@3C&&

.374& ND& 92>2& <2A2& <>@3<8;@B74& <4>>@394BA@B7@& 24& BU;@>4& A@& -47@3& A@&/>4A5GH4D& 4& ;4A@64& 2E5372A4& 9>@=\& 2& @378;278=2& A@& F5@& 43& <53743& 8BA8>@743& A@&Q2Y>8<2GH4&X1.`[&<>@3G2;&@;&k]gD]k&5B8A2A@3&;4B@7?>823C&

&c@9>@@BA@T3@& 2338;& F5@D& 3@& 43& -47@3& A@& />4A5GH4& 25;@B72;& @;& ]h&

5B8A2A@3& XA@& 7@;94& T& O4>23[D& @39@>2T3@& F5@& 43& <53743& 8BA8>@743& A@& Q2Y>8<2GH4&<>@3G2;&kC]g]Dik&5B8A2A@3&;4B@7?>823C&&&

+& G?<:=Z:R<AD& =264>& A@& EA' ' U' _Y6ld_fji' & >@9>@3@B72& 4& =264>& ;NA84& A@& TD&F52BA4&c&N&8M526&2&Xh[&K@>4C&+5&3@E2D&8BA8<2&F5@&4&<5374&8BA8>@74&A@&Q2Y>8<2GH4&N&A@&k^CedkDfh&92>2&5;2&>@Q@>\B<82&Xh[&K@>4&A4&BU;@>4&A@&-47@3&A@&/>4A5GH4&XZ[C&&""m&_&Yh&l&Y]I]8&m&_&k^CedkDf]&l&k]gD]i&{&h& & & & &w'U'_Y6ld_fjW'""""""'")r#+&c+)&'")r-!$c+)&1.`&_&Q&X-/[& &

5*2/26*2+-/'%&'4&,4&**78''&;U678964& hDighjkehge&'TP52A>2A4& hD^f]f]gdke&'TF52A>2A4&2E5372A4& hD^hfgekgkk&">>4&92A>H4& ge^^Dekk^ke&+Y3@>=2Gq@3& fh&""

+&1"$2-3-$4'$&#$&1"(($%,67"&;<>?&N&A@&emfWi'gf'4&F5@&8BA8<2&F5@&O?&Y28I2&<4>>@62GH4& X2334<82GH4[& 68B@2>D& A8>@72D& @B7>@& 4& 15374& .BA8>@74& A@& `2Y>8<2GH4& @& 43&-47@3&A@&/>4A5GH4&X-/[C&""""""

14;4&0,5'D'28467"&'@:'/.D&4&<5374&8BA8>@74&A@&Q2Y>8<2GH4&3@>?&8BQ65@B<82A4&9@64&25;@B74&B4&=465;@&A@&-47@3&A@&/>4A5GH4&X-/[C&&

YMJZXYLRD

!T!

]!

;&<4#=,*

D>D O

OLU\DO!

Page 13: MÉTODOS QUANTITATIVOS APLICADOS À CONTABILIDADE..."#$%&%’()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)’,%9!:,8$0;/%&!8%!"$)!?0(%!@%92A!8,!B)$C!!!!Z! +&=264>&A@&EW’U’YkfWj&Xb#&0&a2>8?=@6&Z][D&8BA8

!"#$%&'#()(%*(%*'+,*-)!.,*/*!'-*!

"#$%&%'()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)',%9!:,8$0;/%&!8%!"$)<=,!!>!?0(%!@%92A!8,!B)$C!!!!DR!

b?& jk& p& A@& 9>4Y2Y868A2A@& A@& F5@& Y]& X-/[& @37@E2& B4& 8B7@>=264& A@& X]k^Dkhz&ggfDdj[&@&A@&F5@&Y4&&@37@E2&B4&8B7@>=264&A@&XfjCdgiDg^z&ekCkekDdj[C&""

"""*+`/,&3'%$&'43&o%)$&'&&

";Y4>2& @I8372& 5;2& 2;962& A839@>3H4& B4& M>?Q8<4& A@& >@3SA543D& BH4& O?& 5;&92A>H4& 292>@B7@C& +3& >@3SA543& 92>@<@;& @372>& 5B8Q4>;@;@B7@& @3926O2A43& 2<8;2& @&2Y28I4&A@&iD&92>2&43&A8Q@>@B7@3&=264>@3&A@&c& Xb#[C&/4>72B74&94A@;43&<4B<658>&F5@&@;&>@62GH4&243&A2A43&34Y>@&4&1.`&@&b#D&F5@&4&;4A@64&2E5372A4D&92>@<@&29>49>82A4C&&&

'")r-!$c+)&c"&'")|cr+)& & && & & &#H*&4@/=78' B4&@+*28I/J'>F<' K&*6%08*' K&*6%08*'?/%478'

]& egdfdDg]]kk& dj^jD]ggiie& hDjfkgkf]fe&^& eihdiDkhif]& jehfDijkege& ]D]ffiekkh]&f& d^gg^Djdfki& d^kgDh^eike& hDgkeefgffj&i& dfih]D]]gdj& T]]i]eD]]gdj& T]Dfidih^dg^&k& d^gg^Djdfki& T]jdDjdfkiii& ThDh^ffeehji&e& dfj]jD^eihi& ]fdkkDdfkje& ]De^fkfj^ie&d& ddkieD^ghdg& jhfDd]j^]e& hD]heee^edd&g& dh^j^D^idf& fi]Ddk^ejjg& hDhihffkg^^&j& eke^gDjihhe& T^^]]Djihhe]& ThD^e]hed^h^&]h& eddh]Dk^]he& T]]eiiDk^]he& T]Dfdifeh^ee&]]& dhg]hDfj^kk& TffeiDfj^kij& ThDfjdhgejkg&]^& ddh^gD]fkki& Tij^eD]fkkfk& ThDkg]i]fddk&]f& dgheiDi^ehf& Tjkf]Di^ehff& T]D]^ijkjfgf&]i& eddh]Dk^]he& ]fddDidgjii& hD]e^kdgghe&]k& ddkieD^ghdg& ghhfDd]j^]e& hDjiieijdf&]e& d^feiDg^gf& T]i]edDg^gf& T]Ded^]dejjj&]d& efkkeDfkjhd& T]jfhDfkjhek& ThD^^dgff^^e&]g& eddh]Dk^]he& ]^jgdDidgji& ]Dkf^geiedg&]j& eeeekD^fhke& TgihjD^fhkkg& ThDjj^k]hdk^&^h& eihdiDkhif]& TgdfdDkhif]i& T]Dhf]^kkdhi&^]& d^feiDg^gf& ]^difD]d]d& ]Dkhih^jjgg&^^& eikj^Deijke& ]]gj^Dfkhii& ]Dihfe]heef&^f& diifdDihj^j& TeekiDihj^j]& ThDdgkfjke]]&^i& eihdiDkhif]& TdedeDkhif]i& ThDjheh^jdk]&

\\RLX[!DYMLYO! YD\LDY

ZYJYZYLX[R[JX\UL\M! YMJZXYLRD

.>?@**#AB1C>DC* .>?@*'EF1C>DC*

Page 14: MÉTODOS QUANTITATIVOS APLICADOS À CONTABILIDADE..."#$%&%’()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)’,%9!:,8$0;/%&!8%!"$)!?0(%!@%92A!8,!B)$C!!!!Z! +&=264>&A@&EW’U’YkfWj&Xb#&0&a2>8?=@6&Z][D&8BA8

!"#$%&'#()(%*(%*'+,*-)!.,*/*!'-*!

"#$%&%'()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)',%9!:,8$0;/%&!8%!"$)<=,!!>!?0(%!@%92A!8,!B)$C!!!!DU!

^k& ejddiD]h^hk& Tf]k^D]h^hk]& ThDfd^hf]hge&^e& ee]idDhgkf]& T^ekfDhgkfhj& ThDf]f]ffjei&^d& dkjj]Dgikhi& ]fi^iD]kije& ]Dkgiihfjkf&^g& dkjj]Dgikhi& TgidfDgikhfd& T]Dhhh]fejef&^j& egdfdDg]]kk& iji^D]ggiie& hDkgffhgii^&fh& ee]idDhgkf]& T]kDhgkfhji]& ThDhh]dghiei&

&&&&&&&&&&&&&&&&&&&&&

/.'.IA<>P:L'@:'>KH;<:'@:'IG?]>

T]hChhh^hChhhfhChhhihChhhkhChhhehChhhdhChhhghChhhjhChhh]hhChhh

T ]h ^h fh ih kh eh

/.

0,5 1.`

/>@=8374X2[&1.`

/.'.IA<>P:L'@:'=:;s@HA;

T^hhhh

T]khhh

T]hhhh

Tkhhh

h

khhh

]hhhh

]khhh

^hhhh

T ]h ^h fh ih kh eh

/.

4:;s@HA;

Page 15: MÉTODOS QUANTITATIVOS APLICADOS À CONTABILIDADE..."#$%&%’()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)’,%9!:,8$0;/%&!8%!"$)!?0(%!@%92A!8,!B)$C!!!!Z! +&=264>&A@&EW’U’YkfWj&Xb#&0&a2>8?=@6&Z][D&8BA8

!"#$%&'#()(%*(%*'+,*-)!.,*/*!'-*!

"#$%&%'()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)',%9!:,8$0;/%&!8%!"$)<=,!!>!?0(%!@%92A!8,!B)$C!!!!DY!

&14;&Y23@&B43&<?6<5643&29>@3@B72A43&B4&"I<@6D&Q2>@;43&2&8B7@>9>@72GH4&A23&

@378;278=23D&4Y@A@<@BA4&4&3@M58B7@&<4;2BA4%&'-*4,`-3,&B'aC!f'/.b''

!" 0H;<A;',?@G=:<A;'@:'5>E=GZ>[QA'a0,5b&@;&Q5BGH4&A23&CA=>;'!MhHG?>&aC!b&@&/A<:;'@:'.=A@H[QA&a/.b&

&'*+`/,&3'%$&'43&)/#*%$&''&!" `5BGH4%&&1.`&&_&&}&Xb#D&-/[&!" `5BGH4%&&1.`&&_&&]]Ce^hDjf&&l&&^gDdfb#&&l&&ijiD^d-/&

m&&&&&&_&&&&&&Y4&&&l&&&&Y]I]8&&&l&&&&Y^Z^&&&/4A@;43&2Q8>;2>&F5@%&&+&<4@Q8<8@B7@&2BM562>&XN&2&8B<68B2GH4&A2&>@72&F52BA4&T&N&8BQ65@B<82A4&9@64&=264>&A@&cb'A23&=2>8?=@83&8BA@9@BA@B7@3&b#&@&-/D&27@BA@&243&>@F5838743&@39@<SQ8<43&B4&7@37@&A@&O89n7@3@&A2&>@M>@33H4C&o&A8Q@>@B7@&A@&K@>4&@&2338;&<2>2<7@>8K2&2&@I837\B<82&A@&>@M>@33H4D&;437>2BA4T3@&2&5;&BS=@6&A@&*+,$+)+-.$-+/&A@&hDhkC&&

&+&1"$2-3-$4'$& #$& #$'$(5-4,67"& "8& $9:%-3,67"& ;<=>D& N& A@& k_fWl'g6& P5@>&

A8K@>&F5@&23&a2>8?=@83&.BA@9@BA@B7@3&0&b#&@&-/D&3H4&>@394B3?=@83&94>&jkD]e&p&A23&=2>82Gq@3&4<4>>8A23&<4;&4&15374&.BA8>@74&A@&`2Y>8<2GH4&X1.`[D&45&3@E2&jkD]ep&A23&=2>82Gq@3&4<4>>8A23&<4;&4&1.`D&3H4&@I968<2A23&9@623&=2>82Gq@3&4<4>>8A23&<4;&2&b#&@&-/D&3@&7>272A23&<4BE5B72;@B7@D&@BF52B74&F5@&iDgi&p&A23&=2>82Gq@3&4<4>>8A23&<4;&4&1.`D&BH4&3H4&@I968<2A23&94>&b#&@&-/C&.374&ND&3H4&A@<4>>@B7@3&A@&-/0*/*'/1&/234+/*'BH4&@39@<8Q8<2A23&B4&;4A@64C&&

4'N'hH>@=>@A'>KH;<>@A%&N&<26<562A4&92>2&>@Q6@78>&72B74&4&BU;@>4&A@&=2>8?=@83&@I968<278=23& B4& ;4A@64D& F52B74& 4& 72;2BO4& A2& 2;437>2C& L4& 9>@3@B7@& <234D& @6@&A@;4B37>2& F5@& b#& @& -/D& <4BE5B72;@B7@D& 3H4& >@394B3?=@83& 94>& jiDghD]ep& A23&=2>82Gq@3&4<4>>8A23&B4&1.`C&

&&&

'")r#+&c+)&'")r-!$c+)&1.`&_&Q&Xb#D-/[& &

5*2/26*2+-/'%&'4&,4&**78''&;U678964& hDjdkidghjj&'TP52A>2A4& hDjk]kkdk^]&'TF52A>2A4&2E5372A4&hDjidjej]gj&">>4&92A>H4& ^^hiDffghfk&+Y3@>=2Gq@3& fh&&&&

Page 16: MÉTODOS QUANTITATIVOS APLICADOS À CONTABILIDADE..."#$%&%’()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)’,%9!:,8$0;/%&!8%!"$)!?0(%!@%92A!8,!B)$C!!!!Z! +&=264>&A@&EW’U’YkfWj&Xb#&0&a2>8?=@6&Z][D&8BA8

!"#$%&'#()(%*(%*'+,*-)!.,*/*!'-*!

"#$%&%'()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)',%9!:,8$0;/%&!8%!"$)<=,!!>!?0(%!@%92A!8,!B)$C!!!!DZ!

&*+*/,&*+%$'*'&,S+,5,0n+0,*''&

$L+a$& & & & & &'' ,1' 9:' ;:' <' <'%&'*+,$+)+-/=78'

'@M>@33H4& ^& ^kddhgkkdh& ]^ggki^dgk& ^ekD]g]hf]^& ]Ddghke"T]g&'@3SA54& ^d& ]f]]jkgeeDe& igkj]heD]d]&& &!4726& ^j& ^dhg^g]ifd&&& && &&

&&"'*+`/,&3'%$'5'04o#,0$'&M6&_&B&0&/&0&]&&M6&_&fh&0&^&0&]&&M6&_&^d&&V!!hDhk&b4&%&`&s&`&X^D^d[&t&>@E@872&^ekD]g]hf]^&s&fDfk&""""

0011223311**44**!!@372&2&@F52GH4&A@&>@M>@33H4&<4;4&5;&74A4C&&r32A2&@;&>@M>@33H4&;U678962&&`&A@&38MB8Q8<2GH4&_&hDhhhhhhhhhhhhhhhhh]dghke&LS=@6&A@&<4BQ82BG2&_&hDjk&LS=@6&A@&38MB8Q8<uB<82&_&hDhk&!!4:P=>'S:=>I'&)@&`&v&hDhk&p&XLS=@6&A@&38MB8Q8<uB<82[%&'@M>@33H4&)8MB8Q8<278=2&&)@&hDhhhhhhhhhhhhhhhhh]dghke&v&hDhk%&O?&'@M>@33H4&)8MB8Q8<278=2&)@&`&w&hDhk&p&XLS=@6&A@&38MB8Q8<uB<82[%&'@M>@33H4&LH4&)8MB8Q8<278=2&!L4&@I@;964D&4&=264>&fDfk&N&4&V`W&<>S78<4&X`&A@&`83<O@>[&!x>@2&=28&532>&^ekD]g&27N&Q8B26&N&kpC&"

^6^_*7`*

7

3D!

W08%!4%50'%L!#C;J!XUD!

3M!

Page 17: MÉTODOS QUANTITATIVOS APLICADOS À CONTABILIDADE..."#$%&%’()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)’,%9!:,8$0;/%&!8%!"$)!?0(%!@%92A!8,!B)$C!!!!Z! +&=264>&A@&EW’U’YkfWj&Xb#&0&a2>8?=@6&Z][D&8BA8

!"#$%&'#()(%*(%*'+,*-)!.,*/*!'-*!

"#$%&%'()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)',%9!:,8$0;/%&!8%!"$)<=,!!>!?0(%!@%92A!8,!B)$C!!!!DX!

""""""""""""""""""&

@[& 7@;43&F5@&9@64&;N74A4&A4&<:;<:''R&&F5@%&• )@&4&F>IA=''R&&Q4>&;284>&45&8M526&2&pD&&2&O89n7@3@&B562&N&2<@872&''''&Xb+B&R&q&p[C&+QA&O?&>@M>@33H4&• &)@&4&F>IA=''R&&Q4>&;@B4>&A4&F5@&pD&2&O89n7@3@&B562&N&>@E@872A2&• Xb]%&R&r&p[C&CM&>@M>@33H4z&&&

Q[& 7@;43&&9@62&:;<><s;<GZ>'5&F5@%&• X`s`3&X&9D&B&0&9&0&]&[&>@E@872&b4&• X`v`3&X&9D&B&0&9&0&]&[&2<@872&b]&

&& L@372&>@M>@33H4D&7@;43&F5@&4&&F>IA='R&N&r'pD&94>72B74&=:K:G<>'C$D&&@&>Z:G<>'C]D&&@&<4BQ8M5>2BA4&2&@I837\B<82&A@&>@M>@33H4C&&

/@62&@3727S378<2&5B&5&U'Yl_fWmWijWY't'5;' aYfYdb'U'jfj_D&94>&<4B3@M58B7@&>@E@872&b+D& & @& 2<@872& b]C& "B7H4& 8BQ@>8;43& <4;& 5;& BS=@6& A@& 38MB8Q8<uB<82& A@& hDhk& F5@D& N&9>4=?=@6& F5@& O2E2& >@M>@33H4& 68B@2>D& <4;& 5;2& Q4>7@& <4>>@62GH4& @B7>@& 23& =2>8?=@83D&4BA@&23&=2>8?=@83&@I968<278=23&>@62<84B2;T3@&243&M23743&A@&1.`C&&&*+*/,&*+%$'*',+0/,+*O9$'""

'' >8&)+-+&$2&*' 5448'?/%478' 92/2'2' @/184AB'CDE'

+$)&4+84&*'CDE'

*0?&4+84&*'F$)&4+84'CDG!E'

90?&4+84'CDG!E'

.B7@>3@GH4& ]]e^hDj^dhk& ^ehkD]^gde]& iDiehdgdjdk& hDhhh]^je^^& e^dkDeidjfj& ]ejeeD^he]e&e^dkDeidjfj& ]ejeeD^he]e&b#& ^gDd^gg^kg& ]Diffgdfdji& ^hDhfkg]^h^& jDdfkfe"T]g& ^kDdgede]de& f]Dedhggjgi&̂ kDdgede]de& f]Dedhggjgi&-/& ijiD^eghfi]& ikDeigfgdei& ]hDg^dd^]ef& ^Dkhjdf"T]]& ihhDehkfi^& kgdDjfhd^e]& ihhDehkfi^& kgdDjfhd^e]&

&&

14;&Y23@&B43&A2A43&2<8;2D&=:K:G<AH\;:'>']GRu<:;:'@>'G?ZIG?>[QA';:='GPH>I'>'v:=AD&4&F5@&38MB8Q8<2&2A;878>;43&2&@I837\B<82&A@&<5374&Q8I4C&

Page 18: MÉTODOS QUANTITATIVOS APLICADOS À CONTABILIDADE..."#$%&%’()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)’,%9!:,8$0;/%&!8%!"$)!?0(%!@%92A!8,!B)$C!!!!Z! +&=264>&A@&EW’U’YkfWj&Xb#&0&a2>8?=@6&Z][D&8BA8

!"#$%&'#()(%*(%*'+,*-)!.,*/*!'-*!

"#$%&%'()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)',%9!:,8$0;/%&!8%!"$)<=,!!>!?0(%!@%92A!8,!B)$C!!!!D\!

"+&=264>&A@&EY'U'ekefYd&X-/&0&a2>8?=@6&Z^[D&8BA8<2&F5@D&92>2&<2A2&<>@3<8;@B74&

<4>>@394BA@B7@&2&5;2&5B8A2A@&A@&Z^D&;2B7@BA4T3@&8B267@>2A2&b#D&@378;2T3@&F5@&4&=264>&A4&1.`&<>@3G2&2&5;2&;NA82&A@&ijiD^d&5B8A2A@&;4B@7?>823C&

&+&=264>&A@&EW'U'Ymfdj&Xb#&0&a2>8?=@6&Z][D&8BA8<2&F5@D&92>2&<2A2&<>@3<8;@B74&

<4>>@394BA@B7@&2&5;2&5B8A2A@&@;&Z]D&;2B7@BA4T3@&8B267@>2A2&-/D&@378;2T3@&F5@&4&=264>&A@&T&<>@3G2&2&5;2&;NA82&A@&^gDdf&5B8A2A@3&;4B@7?>823C&&

.374&ND&92>2&<2A2&<>@3<8;@B74&<4>>@394BA@B7@&24&BU;@>4&A@&b4>23&#?F58B2D&4&;4A@64&2E5372A4&9>@=\&2&@378;278=2&A@&F5@&43&<53743&8BA8>@743&A@&Q2Y>8<2GH4&X1.`[&<>@3G2;&@;&^gDdf&5B8A2A@3&;4B@7?>823C&

&c@9>@@BA@T3@&2338;&F5@D&3@&2&b4>2&#?F58B2&25;@B72&@;&]h&5B8A2A@3& XA@&

7@;94& T& O4>23[D& @39@>2T3@& F5@& 43& <53743& 8BA8>@743& A@& Q2Y>8<2GH4& <>@3G2;& ^gdD^j&5B8A2A@3&;4B@7?>823C&&

&.M526&>2<84<SB84&3@&2968<2&2&-/C&c@3A@&F5@&;2B78A4&8B267@>2A4&b#C&

&+& G?<:=Z:R<AD& =264>& A@& EA' ' U' WW6lYifkj' & >@9>@3@B72& 4& =264>& ;NA84& A@& TD&

F52BA4& cW' :' cY& 3H4& 8M5283& 2& Xh[& K@>4C& +5& 3@E2D& 8BA8<2& F5@& 4& <5374& 8BA8>@74& A@&Q2Y>8<2GH4& N& A@& ]]Ce^hDjf& 92>2& 5;2& >@Q@>\B<82& Xh[& K@>4& A4& BU;@>4& A@& b4>23&#?F58B2&XZ][&@&-47@3&A@&/>4A5GH4&XZ^[C&"""m&_&Yh&l&Y]I]8&l&Y^Z^8&m&_&]]Ce^hDjf&l&^gDd^b#&l&ijiD^d-/& & & & & &w'U'WW6lYifkj'"""""""'")r#+&c+)&'")r-!$c+)&1.`&_&Q&Xb#D-/[& &

5*2/26*2+-/'%&'4&,4&**78''&;U678964& hDjdkidghjj'TP52A>2A4& hDjk]kkdk^]4\hH>@=>@A'>KH;<>@A'ifkedklkWmk">>4&92A>H4& ^^hiDffghfk+Y3@>=2Gq@3& fh"

&&+& &<& @&A8,#(,#"&BC8*',#"?&N&A@&kefmi'gf'4&F5@& 8BA8<2& F5@&O?&5;2& Q4>7@&

<4>>@62GH4& X2334<82GH4[& 68B@2>D& A8>@72D& @B7>@& 4& 15374& .BA8>@74& A@& `2Y>8<2GH4& @& 23&a2>8?=@83&b4>23&#?F58B2&Xb#[&@&-47@3&A@&/>4A5GH4&X-/[C&

DDJZMOL[R!

T!

]!

;&<4#=,*

Page 19: MÉTODOS QUANTITATIVOS APLICADOS À CONTABILIDADE..."#$%&%’()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)’,%9!:,8$0;/%&!8%!"$)!?0(%!@%92A!8,!B)$C!!!!Z! +&=264>&A@&EW’U’YkfWj&Xb#&0&a2>8?=@6&Z][D&8BA8

!"#$%&'#()(%*(%*'+,*-)!.,*/*!'-*!

"#$%&%'()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)',%9!:,8$0;/%&!8%!"$)<=,!!>!?0(%!@%92A!8,!B)$C!!!!D[!

""""""

&&14;4&0,5'D'28467"&'@:'C!':'/.D&<4;&5;&=264>&A@&b4>23&#?F58B2&@:45&-47@3&

A@&/>4A5GH4D&@6@=2A43D&7@>@;43&5;&@Q@874&38;862>D&>@9@><578BA4&@;&<5374&8BA8>@74&A@&Q2Y>8<2GH4C&

&b?& jk&p& A@& 9>4Y2Y868A2A@& A@& F5@& Y^& X-/[& @37@E2& B4& 8B7@>=264& A@& & XihhDe]z&

kgdDjf[&A@&F5@&Y]&Xb#[&@37@E2&B4&8B7@>=264&A@&X^kDdjz&f]Ded[&@&A@&F5@&Y4&&@37@E2&B4&8B7@>=264&A@&XeC^dkDekz&]eCjeeD^][C&"""""''''''''''''''*+`/,&3'%$&'43&o%)$&'&

";Y4>2&@I8372&5;2&2;962&A839@>3H4&B4&M>?Q8<4&A@&>@3SA543&A@&b#&@&-/D&BH4&O?& 5;& 92A>H4& 292>@B7@C& +3& >@3SA543& 92>@<@;& @372>& 5B8Q4>;@;@B7@& @3926O2A43&2<8;2& @& 2Y28I4& A@& iD& 92>2& 43& A8Q@>@B7@3& =264>@3& A@&cW' aC!b' :' cY& a/.bC& /4>72B74&94A@;43&<4B<658>&F5@&@;&>@62GH4&243&A2A43&34Y>@&4&1.`D&b#&@&-/D&F5@&4&;4A@64&2E5372A4D&92>@<@&29>49>82A4C&&& &&&

D!D!>D! O!

86a598*

Y\XL[R!UOOLZD! U[ULMX!

RDLZX!MYLX[! M\LXM!

.>?@**#AB1C>DC* .>?@*'EF1C>DC*

DZJ[ZZLMD!ZJMXYLZY! DDJZMOL[R!

X7*

X:*

X8*

Page 20: MÉTODOS QUANTITATIVOS APLICADOS À CONTABILIDADE..."#$%&%’()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)’,%9!:,8$0;/%&!8%!"$)!?0(%!@%92A!8,!B)$C!!!!Z! +&=264>&A@&EW’U’YkfWj&Xb#&0&a2>8?=@6&Z][D&8BA8

!"#$%&'#()(%*(%*'+,*-)!.,*/*!'-*!

"#$%&%'()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)',%9!:,8$0;/%&!8%!"$)<=,!!>!?0(%!@%92A!8,!B)$C!!!!MO!

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

C!'.IA<>P:L'@:'=:;s@HA;

TehhhTihhhT^hhh

h^hhhihhhehhh

T khh ]Chhh ]Ckhh ^Chhh ^Ckhh

C!

4:;s@HA;

/.'.IA<>P:L'@:'=:;s@HA;

TehhhTihhhT^hhh

h^hhhihhhehhh

T ]h ^h fh ih kh eh

/.

4:;s@HA;

Page 21: MÉTODOS QUANTITATIVOS APLICADOS À CONTABILIDADE..."#$%&%’()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)’,%9!:,8$0;/%&!8%!"$)!?0(%!@%92A!8,!B)$C!!!!Z! +&=264>&A@&EW’U’YkfWj&Xb#&0&a2>8?=@6&Z][D&8BA8

!"#$%&'#()(%*(%*'+,*-)!.,*/*!'-*!

"#$%&%'()*+,!-./0#%!123%$!4)5,$!6,$%0$)!%!7)8%/!6)',%9!:,8$0;/%&!8%!"$)<=,!!>!?0(%!@%92A!8,!B)$C!!!!MD!

&-34,5,0*+%$'*'!)/#,0$/,+3*4,%*%3'''14;4&E?&=8;43D&2&!HI<GZAIG?:>=G@>@:&3@&A?&F52BA4&23&=2>8?=@83&@I968<278=23&3H4&Q4>7@;@B7@&>@62<84B2A23&@B7>@&38C&&VL@3323&38752Gq@3D&=2>8?=@83&<468B@2>@3&BH4&Q4>B@<@;&B4=23&8BQ4>;2Gq@3D&@&74>B2T3@&A8QS<86&3@92>2>&4&@Q@874&A@3323&=2>8?=@83&B2&=2>8?=@6&A@9@BA@B7@&45&=2>8?=@6&>@394372WC'& & & & & & & -@=8B@&0&V"3727S378<2%&!@4>82&@&$968<2Gq@3W&0&-!1&"A874>2C&&Vr;&;N74A4&A@&;@B35>2GH4&A2&<468B@2>8A2A@&57868K2&4&x><A='G?xI>ZGA?M=GA'@>'F>=Gy?ZG>'a5,-b'&92>2&<2A2&=2>8?=@6&@I968<278=2WC&&V$338;&3@BA4D&4&5,-'3@>82&<26<562A4&A@&5;2&Qn>;562&B4&Q4>;274&A@%&&U'W^aW\F>IA='@:'=Ybz6&&&{&:'HL'ZA?KH?<A'@:'F>=GMF:G;':XRIGZ><GF>;'?QA'xA='ZA==:I>ZGA?>@A'5,-K';:=M'GPH>I'>'Wz'aA'P=GxA'D'?A;;Ab6''";&B4334&<234&43&A2A43&>@=@62;&4&3@M58B7@%&&&0$443/*O9$' & & && & & &

'' >F<' L;' MB'1.`& ]&& &b#& hDgehjfkd]d& ]&&-/& hDighjkehge& hDh^e]heekg& ]&& & & && 5,-''''U' ]& &&&+QA']M'&#5678<468B@2>8A2A@&@B7>@&23&=2>8?=@83&@I968<278=23C&14B<65S;43&94>72B74&F5@&43&<4@Q8<8@B7@3&3H4&<4BQ8?=@83C&&&&"!!