Apostila Egenharia Econômica

8/16/2019 Apostila Egenharia Econômica

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Engenharia Econômica – Profa. Regina Maura Martins Dias Chiquetano

APOSTILA DE

ENGENHARIA ECONÔMICA

2016


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1 INTRODUÇÃO A ENGENHARIA ECONÔMICA

A administa!"# d$ %ma $m&$sa $'%$ '%$ $m t#d# m#m$nt# s$(am t#madas

d$)is*$s d$ di+$s#s tis, '%$ d$+$m t$ )#m# m$ta # #-($ti+# da $m&$sa. S$

)#nsid$am#s %ma $m&$sa ins$ida $m %ma $)#n#mia d$ /i+$ ini)iati+a $ $m

$im$ d$ )#n)#n)ia, d$m#s di$ '%$ # #-($ti+# da administa!"# 3 a

ma4imia!"# da i'%$a d#s &#&i$t5i#s. Os $)%s#s s"# /imitad#s, iss# d$+$s$

administa/#s &aa '%$ ssam s$ %ti/iad#s da m$/7# man$ia ss8+$/, +isand#

atini #s #-($ti+#s da $m&$sa.

O #-($ti+# d$ %ma an5/is$ $)#n9mi)a 3: #-t$ a m$/7# #t%nidad$ ss8+$/ &aa

# $m&$# d#s $)%s#s /imitad#s.

M%itas d$)is*$s s"# t#madas a &ati da $4&$in)ia d#s administad#$s, # '%$

m%itas +$$s d$ /$+a a $s)#/7a d$ a/t$nati+as '%$ d$m n"# s$ as m$/7#$s

$)#n#mi)am$nt$. A $4&$in)ia &#)i#na a# administad# %ma s$nsi-i/idad$ '%$ 3

m%it# imtant$, na t#mada d$ d$)is"#, mas '%$ si s; n"# 3 s%

D$ssa


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O %# 3 )#-ad# $m


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1. UROS SIMPLES FS

N# $im$ d$ )a&ita/ia!"# sim&/$s, #s (%#s in)id$m a&$nas s#-$ # )a&ita/ ini)ia/

#% &in)i&a/, is n"# $4ist$ )a&ita/ia!"# d$ (%#s n$ss$ $im$. P#tant#, #

$ndim$nt# s$5 s$m&$ # m$sm# $m )ada &$8#d#.O )a&ita/ )$s)$5 a %ma ta4a /in$a $ a ta4a d$ (%#s t$5 %m )#mtam$nt# /in$a

$m $/a!"# a# t$m. P# iss#, a ta4a d$ (%#s d$ s$ )#n+$tida &aa #%t# &a#

'%a/'%$ )#m -as$ $m m%/ti&/i)a!*$s $ di+is*$s, mant$nd# a &#)i#na/idad$

$4ist$nt$ $nt$ +a/#$s $a/i5+$is $m di


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#nd$: (%#s #% $ndim$nt#

S M#ntant$B

P Pin)i&a/

C#m# n# $im$ d$ )a&ita/ia!"# sim&/$s, #s (%#s d$ )ada &$8#d# s"# s$m&$

)a/)%/ad#s s#-$ # m$sm# &in)i&a/, a&/i)and#s$ %m )a&ita/ d%ant$ n &$8#d#s d$

t$m, # (%# s$5:

J = P. i . n F2

#nd$: (%#s #% $ndim$nt#B

P &in)i&a/B

i ta4a d$ (%#sB

n &$8#d# d$ t$m.

I%a/and#s$ a $'%a!"# F1 )#m a F2, #-t3ms$ # M#ntant$ $m


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N# $im$ d$ (%#s )#mst#s, a $m%n$a!"# $ada &$/a a&/i)a!"# s$5 s#mada

a# )a&ita/ ini)ia/ $


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O +a/# &$s$nt$ d$ %m +a/#

1.K. E=UIALNCIA DE CAPITAIS A .C.O &in)8&i# da $'%i+a/n)ia d$ )a&itais 3


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Ca&ita/ Ms d$ +$n)im$nt#

J2.000 1

J2.200 2

J2.K20

J2.662 K

1. PERVODO DE CAPITALIWAÇÃO TAA NOMINAL E TAA E@ETIA DEUROS


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P$8#d# d$ )a&ita/ia!"# 3 # &$8#d# $m '%$ %ma '%antia $nd$ a %ma ta4a d$

(%#s i, a&;s # '%a/, #s +a/#$s d#s (%#s s"# s#mad#s '%antia ini)ia/ #% a)%m%/ada.

1..1 TAA DE UROS NOMINAL

=%and# #s (%#s s"# )a&ita/iad#s mais d$ %ma +$ n# &$8#d# a '%$ s$ $


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• K a.t. )a&ita/iad#s tim$sta/m$nt$.

=%and# # &$8#d# da ta4a d$ (%#s )#in)id$ )#m a &$i#di)idad$ )#m '%$ #s

(%#s s"# )a&ita/iad#s, a ta4a d$)/aada 3 a &;&ia ta4a $


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C#nsid$and# # an# )#m$)ia/ F60 dias, a s$%int$ id$ntidad$ &$mit$

$/a)i#na a/%mas ta4as $


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E4.:


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O +a/# &$s$nt$ da s3i$ %ni


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P#-/$ma : Um -$m )%(# &$!# +ista 3 d$ JK.000, s$5 &a# $m &$sta!*$s

m$nsais i%ais &aas a#


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O +a/# &$s$nt$ P da &$&$t%idad$, d$sitad# $m %m


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P#-/$ma 12: S$nd# d$ 2K a.a. a ta4a n#mina/ d$ (%#s )#-ada %ma instit%i!"#, )a/)%/a

# )%st# $

P#-/$ma 1K: Uma m5'%ina 3 +$ndida $m 12 &$sta!*$s m$nsais d$ J0. A (%#s $

P#-/$ma 16: Uma m$)ad#ia '%$ )%sta a +ista J1.6,61


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• %#s d# &$8#d#: s$+i!# da d8+ida )#$snd$nt$ a# sa/d# d# $m&3stim# ainda

n"# $$m-#/sad#.

PRESTAÇÃO = AMORTIAÇÃO + JUROS

O t$m# )an)ia d$sina # &$8#d# '%$ +ai d$sd$ a data d$ )#n)$ss"# d#

$m&3stim# at3 a data $m '%$ s$5 &aa a &im$ia &$sta!"#. Em $a/, $ss$ &$8#d#

3 n$#)iad# $nt$ # )$d# $ # m%t%5i#. =%a/'%$ sist$ma d$ am#tia!"# d$ t$ #%

n"# # &a# d$ )an)ia.

Os &in)i&ais $ mais %sad#s sist$mas d$ am#tia!"# d$ $m&3stim#s s"#:

a) Sist$ma @an)s d$ Am#tia!"# Ta-$/a Price;

3) Sist$ma d$ Am#tia!"# C#nstant$ SACB

1..1 SISTEMA @RANCS DE AMORTIWAÇÃO TA`ELA PRICE

Essa d$n#mina!"# +$m d#


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Ms

Ft

Sa/d# D$+$d#

FSDt Q SDt1 At

Am#tia!"#

FAt Q Rt t

%#s

Ft Q i 4 SDt1

P$sta!"#

FRt

0

1

2

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1..2 SISTEMA DE AMORTIWAÇÃO CONSTANTE SACN# SAC, a am#tia!"# 3 dada &$/# +a/# d# &in)i&a/ di+idid# &$/# nm$# d$

&$8#d#s d$ &aam$nt#. N$st$ )as#, a am#tia!"# 3 )#nstant$, as &$sta!*$s s"#

d$)$s)$nt$s $ #s (%#s s"# d$)$s)$nt$s tam-3m. Ess$ ti d$ sist$ma 3 %sad# s

+$$s &$/# Sist$ma @inan)$i# d$ Ha-ita!"# FS@H, &$/#s -an)#s )#m$)iais $m s$%s


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K

2. ALTERNATIAS ECONÔMICAS: MTODO DO ALOR PRESENTE LV=UIDO

=%and# t$m#s +5ias a/t$nati+as $)#n9mi)as, 75 a n$)$ssidad$ d$ )#m&a5/as a


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P#-/$ma 2: C#nsid$$ %ma a/t$nati+a d$ in+$stim$nt# '%$ $'%$ %m d$s$m-#/s#

ini)ia/ d$ J200.000, $ $$

P#-/$ma 2K: A $n)ia d$ %ma


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P#-/$ma 2: C#nsid$and# d%as a/t$nati+as m%t%am$nt$ $4)/%d$nt$s, $ h,

a&$s$ntadas n# '%ad# a-ai4#, $ %m )%st# d# )a&ita/ d$ 10 a.a., '%a/ 3 a

&$

E'%i&am$nt# In+$stim$nt# FJ @/%4# d$ )ai4aan# FJ ida ti/ Fan#s 12 ,0 h 1 2,

P#-/$ma 26: N%ma an5/is$ $a/iada $m d$t$minada $m&$sa,


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2.1. ALTERNATIAS DE DURAÇgES DESIGUAIS

A En$n7aia E)#n9mi)a )#m&aa s$m&$ a/t$nati+as '%$ d$+$m a&$s$nta

d%a!*$s i%ais.

Cas# as a/t$nati+as ti+$$m #iinaiam$nt$ d%a!*$s d$si%ais, &$)isam#s

$st%d5/as a


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E'%i&am$nt# An# 0 FJ An# 1 FJ An# 2 FJ An# FJ 10 6 6 h K K K

2.2 MTODO DO ALOR @UTURO LV=UIDO @L

O m3t#d# d# @L t$m


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( ) nn

t i FC VFL += ∑ 1

"

Ond$:

@L +a/#

2.2.1 S$/$!"# da m$/7# a/t$nati+a

S$ ti+$m#s +5ias a/t$nati+as, d$+$m#s s$/$)i#na a'%$/a '%$ a&$s$nta # +a/#

mais )#n+$ni$nt$ &aa # &#-/$ma $m '%$st"#. D$+$m#s $s)#/7$ a a/t$nati+a '%$

a&$s$nta # MAIOR @L, ad#tand#s$ $)$ita )#m# siti+# $ )%st#s, n$ati+#.=%and# ti+$m#s s#m$nt$ )%st#s, $s)#/7$s$ a a/t$nati+a d$ MENOR )%st#.


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2.2.2. A/t$nati+as d$ d%a!*$s i%ais

P#-/$ma 2: D#is $'%i&am$nt#s s"# $4aminad#s. C#nsid$and# s$ a TMA

iQ20a.a., '%a/ # $'%i&am$nt# '%$ d$+$ s$ ad'%iid# ana/isand#s$ &$/# m3t#d# d#

@L>

E'%i&am$nt# j E'%i&am$nt# LC%st# J0.000 J0.000C%st# an%a/ d$ )#ns$+a!"# J20.000 J1.000a/# $sid%a/ & +$nda JK.000 J.000D%a!"# $m an#s 10 10

2.2. A/t$nati+as d$ d%a!*$s d$si%ais

a/$m a'%i as m$smas #-s$+a!*$s (5 a&$s$ntadas #)asi"# da $4&/ana!"#

d# m3t#d# d# PL.


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P#-/$ma 0: T$n7# a #t%nidad$ d$ ad'%ii %m $'%i&am$nt#, $)$-$nd# d%as

#


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P#-/$ma 1: Dad#s #s di+id$nd#s 20, 0, 10 $ K0 $)$-id#s n#s &$8#d#s 1, 2. $ K,

tans


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S$ UL e 0, 75 &$d#min[n)ia d#s -$n$


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Paa )ada a/t$nati+a )#nsid$am#s %ma d%a!"# i%a/ a# m.m.). das d%a!*$s.

Cada d%a!"# #iina/ 3 )#nsid$ada )#m# s$nd# %m )i)/# '%$ s$ $&$t$ at3 $s#ta a

d%a!"# d# m.m.).

O UL d$ )ada a/t$nati+a s$5 # m$sm# UL na $&$ti!"# d# )i)/#. P#tant#, n"#

75 n$)$ssidad$, n$ss$ m3t#d# d$ a)7a # m.m.). d$ )ada a/t$nati+a, is #s +a/#$s

d# UL da a/t$nati+a #iina/ s$"# i%ais a# UL na $&$ti!"# d# )i)/#.

P#-/$ma : =%a/ das a/t$nati+as m%t%am$nt$ $4)/%si+as $ h, d$+$ s$ $s)#/7ida

s$ # )%st# d# )a&ita/ 3 d$ 10 a.a.> Uti/ia # m3t#d# d# UL.

A/t$nati+a An# 0 An# 1 An# 2 An# j J10 J6 J6L J JK JK JK

.+ MTODO DA TAA INTERNA DE RETORNO


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A ta4a int$na d$ $t#n# FTIR 3 a ta4a d$ (%#s '%$ t#na # +a/# &$s$nt$ /8'%id#

i%a/ a $#. O% s$(a, 3 n$sta ta4a '%$ a s#mat;ia das $)$itas s$ t#na i%a/

s#mat;ia d#s dis&ndi#s.

PL Q ` C

S$ PL Q 0, $nt"# l ` Q C

( ) "

11

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+−= ∑=

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t

t

t

i

FC I VPL

=%and# # PL Q 0, #-t$$m#s, $m )#ns$'n)ia, a ta4a d$ $t#n# a '%a/ s$ia

m%it# a&$)iada s$


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P#-/$ma K: Uma

P$8#d#In+$stim$nt#

n$)$ss5i# FJR$)$itas FJ C%st#s FJ

a/# $sid%a/

FJ

@/%4# d$

)ai4a d#

&#($t# FJ0 12.000 12.0001 .000 1K.00 1K.60 K.02 K.000 2.0 2.0 2.000 2.22 2.1 .00K 6.600 2.20 .60

6.600 2.20 .606 6.600 2.20 .60 6.600 2.20 .60 6.600 2.20 .60 6.600 2.20 .6010 6.600 2.20 .6011 6.600 2.20 .6012 6.600 2.20 .601 6.600 2.20 .601K 6.600 2.20 .601 6.600 2.20 .6016 6.600 2.20 .60

1 6.600 2.20 .601 6.600 2.20 .601 6.600 2.20 .6020 6.600 2.20 6.6 10.6K

R$s#/%!"#:


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2. MTODO DO PAYBACK DESCONTADO

O ]&ac-a)Y^ d$s)#ntad# )#nsist$ na d$t$mina!"# d# nm$#s d$ &$8#d#s

n$)$ss5i#s &aa $)%&$a # )a&ita/ in+$stid#. Ent"# a $m&$sa, -as$ada n#s

&ad*$s d$ t$m &aa $)%&$a!"# d# in+$stim$nt#, d$)id$ s#-$ a a)$ita!"# #% n"#

d# &#($t#.


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( )∑= +

+−=n

t

t

t

i

FC I VPL

1 1

P#-/$ma : Uma a/t$nati+a d$ in+$stim$nt# $'%$ %m d$s$m-#/s# ini)ia/ d$

J200.000, $ $a


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D$&$)ia!"# C#nt5-i/: 3 a dimin%i!"# d# +a/# )#nt5-i/ d$ %m -$m, $s%/tant$ d#

d$)%s# d# &a# d$)#id# d$sd$ a s%a a'%isi!"# at3 # instant$ ati-%8d# a# d$sast$


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an%ais. C#nsid$and# '%$ a $m&$sa &aa d$ Imst# d$ R$nda $ '%$ 3 d$

10 a.a. a ta4a m8nima d$ atati+idad$, di$ '%a/ a m$/7# a/t$nati+a.

• A/t$nati+a: C#m&a

Ms @4 C4 ant$s

d# IR Fa

D$&$)ia!"#

an%a/ F-

L%)# Ti-.

) Q a -

IR

d Q 0,K 4 )

@4 C4 a&;s # IR

$ Q a d012K6

10

• A/t$nati+a: A/%%$/

Ms @4 C4 ant$s

d# IR Fa

D$&$)ia!"#

an%a/ F-

L%)# Ti-.

) Q a -

IR

d Q 0,K 4 )

@4 C4 a&;s # IR

$ Q a d012K6


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10

SU`STITUIÇÃO DE E=UIPAMENTOS

=%and# %m $'%i&am$nt# $st5 $m %s#, 75 #)asi*$s $m '%$ )#n+3m ana/isa a)#n+$nin)ia #% n"# d$ %ma $+$nt%a/ s%-stit%i!"#. As &in)i&ais a*$s &aa %ma

s%-stit%i!"# s"#:

1. )%st# $4a$ad# da #&$a!"# $ da man%t$n!"# d$+id# a d$sast$


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012K

610

D$&$)ia!"# an%a/:

D$s&$sa )#nt5-i/ Q D Q

• E!"i#$%en&o Ms @4 C4 ant$s d#

IR Fa

D$&$)ia!"# an%a/

F-

L%)# Ti-.

) Q a -

IR

d Q 0,K 4 )

@4 C4 a&;s #

IR $ Q a d012K6

10

D$&$)ia!"# an%a/:

D$s&$sa )#nt5-i/ Q D Q


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6. E4$)8)i#s

P#-/$ma : Uma m5'%ina $st5 $stimada $m J16.000,00 )#m +ida $)#n9mi)a i%a/ a

6 an#s. A&;s $ss$ t$m, a m5'%ina s$5 $tiada d$ #&$a!"# )#m +a/# $sid%a/

/8'%id# n%/#. D%ant$ a %ti/ia!"#, a)$ditas$ '%$ +$n7am a s$ $d%idas d$s&$sas

)#m m"#d$#-a $m J.000,00 $m )ada an#. S$nd# a a/8'%#ta d# IR d$ a.a.,

+$i


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• A/8'%#ta d# IR:

=%a/ 3 a $)#m$nda!"# d# d$&atam$nt# d# $$nt$>

P#-/$ma K0: Uma m5'%ina $st5 $stimada $m J16.000,00 )#m +ida $)#n9mi)a i%a/ a

6 an#s. A&;s $ss$ t$m, a m5'%ina s$5 $tiada d$ #&$a!"# )#m +a/# $sid%a/

/8'%id# d$ J.000. D%ant$ a %ti/ia!"#, a)$ditas$ '%$ +$n7am a s$ $d%idas

d$s&$sas )#m m"#d$#-a $m J.000,00 $m )ada an#. $i

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