COMPENDIO EJERCICIOS DE FLUJO DE CAJA 1.
PLANTA MALTEO................................................................................................................................................. ...................................................................................................................................................... ..... 3 1.1.
2.
SOLUCIÓN........................................................................................................................................................... 4
CODEGUA, NUEVO LOCAL PASTELERO................................................................................................... ........................................................................................................... ............ .... 5 2.1.
SOLUCIÓN........................................................................................................................................................... 6
3.
EMPRESA DE SERVICIO DE ALIMENTACIÓ ALIMENTACIÓN N MASIVA...... ............ ........... ........... ............ ............ ............ ............ ............ ............ ............ ............ ............ ........... ......... ........ ....
4.
EMPRESA PLAS!PLAS..................................................................................................................................... ............................................................................................................................................. ........ " 4.1.
5.
REEMPLAZO DE M#$UINAS EN EMPRESA TE%TIL ................................................................................ ........................................................................................ ............. ..... & 5.1.
6.
SOLUCIÓN......................................................................................................................................................... 14
MERCADO DE CORREOS....................................................................................................................................... 1& 8.1.
&.
SOLUCIÓN......................................................................................................................................................... 12
PLANTA AV'COLA............................................................................................................................................. ................................................................................................................................................... ...... 13 7.1.
".
SOLUCIÓN........................................................................................................................................................... 9
ERRORES EN FC................................................................................................................................................... ....................................................................................................................................................... 11 6.1.
.
SOLUCIÓN........................................................................................................................................................... 9
SOLUCIÓN......................................................................................................................................................... 20
PRO(ECTO MINERO 4 A)OS ................................................................................................................ ........................................................................................................................ ................ ........ 22 9.1.
SOLUCIÓN......................................................................................................................................................... 22
10. LICITACIÓN LOCOMOCIÓN COLECTIVA.......................................................................................................... 25 10.1.
SOLUCIÓN......................................................................................................................................................... 26
11. CL'NICA ( NUEVO E$UIPO......................................................................................................................... ............................................................................................................................... ...... 2& 11.1.
SOLUCIÓN......................................................................................................................................................... 30
12. ERRORES EN FC VERSIÓN 2.......................................................................................................................... .............................................................................................................................. 30 12.1.
SOLUCIÓN......................................................................................................................................................... 31
13. GERENTE ( NUEVO E$UIP E$UIPAMIENTO AMIENTO............................................................................................................... 32 14. EMPRESA DE SERVICIO DE ALIMENTACIO ALIMENTACION N...... ............ ............ ............ ........... ........... ............ ............ ............ ............ ............ ............ ............ ............ ............ ........... ......... .... 32 15. FA*RICA DE +ELADOS................................................................................................................................ ..................................................................................................................................... ..... 35 16. ESTUDIANTE ( CRDITO CORFO CO RFO......................................................................................................... ................................................................................................................. ........... ... 35 1. EMPRESA RU*RO VIDRIO ( *OTELL *OTELLAS. AS. ........................................................................................................ ..................................................................................................... ... 36 36 17.1.
SOLUCIÓN......................................................................................................................................................... 36
1". ECONOM'A CON CERTIDUM*RE........................................................................................................ ................................................................................................................ ............. ..... 3& 1&. FACTURAS........................................................................................................................................................ ............................................................................................................................................................ 3& 20. EJERCICIO CON *ALANCE.............................................................................................................................. 40 21. EMPRESA INVERSIÓN AF ........................................................................................................................ ................................................................................................................................ .......... 40 22. CALCULE PUNTEADO ............................................................................................................................. ..................................................................................................................................... ............ 42
MATERIAL DOCENTE IN42A – MARZO 2006
23. PROPUEST PROPUESTA A MA$ MINERA..... MINERA........... ............. ............. ............ ............ ............ ............ ............ ............ ............ ............ ............ ............. ............. ............ ............ ............ ............ ................. ............. 42 23.1.
SOLUCIÓN.................................................................................................................................................. ....... 43
24. GALPÓN...... GALPÓN............ ............ ............ ............ ............ ............ ............ ............. ............. ............ ............ ............ ............ ............ ............ ............ ............ ............ ............. ............. ............ ............ ............ .................. ............45 45 24.1.
SOLUCIÓN.................................................................................................................................................. ....... 46
25. AMIGO E INVERSION.. INVERSION........ ............ ............ ............ ............ ............ ............. ............. ............ ............ ............ ............ ............ ............ ............ ............ ............ ............. ............. ............ ................... ............. 4 25.1.
SOLUCIÓN.................................................................................................................................................. ....... 48
26. EMPR EMPRESARI ESARIO O TRANSPORTE.. TRANSPORTE........ ............ ............ ............ ............ ............ ............ ............ ............ ............ ............. ............. ............ ............ ............ ............ ............ ............ ............ ............. .......4& 4& 26.1.
SOLUCIÓN.................................................................................................................................................. ....... 51
2. CALCULAR CALCULAR FC -CORTO..... -CORTO........... ............. ............. ............ ............ ............ ............ ............ ............ ............ ............ ............ ............ ............. ............. ............ ............ .......................... ........................ 53 2". CAMPERA... CAMPERA......... ............ ............ ............ ............ ............ ............ ............ ............ ............. ............. ............ ............ ............ ............ ............ ............ ............ ............ ............ ............. ............. ................... .................. ..... 53 2&. AMIGO A(UDA........ (UDA.............. ............ ............ ............ ............ ............ ............ ............ ............. ............. ............ ............ ............ ............ ............ ............ ............ ............ ............ ............. ............. ............ ............ ...... 54 29.1.
SOLUCIÓN.................................................................................................................................................. ....... 54
30. PLANTA PLANTA DE CONCENTRADOS. CONCENTRADOS....... ............ ............ ............ ............ ............ ............ ............ ............ ............. ............. ............ ............ ............ ............ ............ .............................55 .......................55 31. PLANTA PLANTA PROCESADOR PROCESADORA A DE MANGO....... MANGO............. ............ ............ ............ ............. ............. ............ ............ ............ ............ ............ ............ ............ ..................... ....................... ........5 5 32. PRO(ECTO PRO(ECTO 50 MIL UNIDADES... UNIDADES......... ............ ............ ............ ............ ............ ............ ............ ............ ............. ............. ............ ............ ............ ............ ................. ........................... ................5& 5& 32.1.
SOLUCIÓN, VER ARCHIVO EXCEL .........................................................................................................................60
33. EMPR EMPRESA ESA CA*LE...... CA*LE............ ............ ............ ............ ............ ............ ............ ............ ............ ............. ............. ............ ............ ............ ............ ............ ............ ............ ............ ..................... ..................... ...... 60 33.1.
SOLUCIÓN, VER ARCHIVO EXCEL .........................................................................................................................60
34. RENOVACIÓN RENOVACIÓN DE E$UIPOS.... E$UIPOS.......... ............ ............ ............ ............ ............ ............ ............ ............ ............. ............. ............ ............ ............ ............ ............ ............ ............ ................... .............61 61 34.1.
SOLUCIÓN.................................................................................................................................................. ....... 61
35. GERENTE GERENTE DE SUPE SUPERMERCA RMERCADO.... DO.......... ............ ............ ............ ............ ............ ............ ............ ............ ............. ............. ............ ............ ............ ............ .............. ....................... ...............62 62 35.1.
SOLUCIÓN.................................................................................................................................................. ....... 63
1. PLA PLANT NTA A MA MALLTEO Un empe!"#$ e!%& '$n!#(e"n($ )" p$!#*#)#("( (e #n+e%# en n" p)"n%" (e m")%e$ (e 'e*"(" en )" VIII e-#n. /)"ne" #n+e%# en n" p)"n%" '$n '"p"'#("( p"" p$('# "!%" 50.000 %$ne)"("! (e m")%" ") "$. L" #n+e!#n en "'%#+$! #$! e e!%#m"(" p$ )$! %'n#'$! en US 7.700.000 !e (e!'$mp$ne en een$ O*"! C#+#)e! S#)$! :";#n"!. E;#p$!
U 80.000
870.000
1.850.000 4.900.000
V#(" 40 20 10
/$ )"! '""'%e"($! p$ )$! "!e!$e! (e) #n+e!#$n#!%", pe(e '$mp"!e )" 'e*"(" ;e e;#e" )" %" p)"n%" p"-"n($ US 100 p$ %$ne)"(" (e 'e*"(" m")%e". L$! e!%(#$! pem#%en '$n')# ;e e) pe'#$ (e +en%" e!pe"($ !e& (e US 240 )" %$ne)"(" (e m")%" , ;e )"! +en%"! !e&n (e 20.000, 35.000, 45.000 %$ne)"("! )$! p#me$! %e! "$!, 50.000 )$! %e! "$! !#-#en%e!. =e*#($ " ;e )" empe!" (e*e '$mp" en !)$ %e! me!e! ?ene$, e*e$ m">$@ %$(" )" 'e*"(" ;e +" " ne'e!#%" ("n%e e) "$ %#ene ;e '"n'e)")" ") '$n%"($, ;e )$! #n-e!$! p$ +en%"! !e e'#*en ") !e-n($ me! (e!p! (e ee'%"(" )" en%e-" (e) p$('%$, !e " e!%#m"($ ;e e) '"p#%") (e %"*"$ e;e#($ p$ e) p$e'%$ e! (e US 10 m#))$ne! ?n$ )$ '")')e, %me)$ '$m$ ("%$@. /"" #n"n'#" )" #n+e!#n, !e pe(e "''e(e " n '(#%$ p$ e) 75 (e )" #n+e!#n m&! e) '"p#%") (e %"*"$ en n *"n'$ )$'") '$n n" %"!" (e #n%e! (e) 8 ($! "$! (e -"'#" ?)$! #n%ee!e! (e) pe<$($ (e -"'#" n$ !e p"-"&n, !e "'m)"&n " )" (e("@, p"-"(e$ en 3 '$%"! "n")e! #-")e!. E) p$e'%$ !e e+")"& " 6 "$!. Sp$n-" ;e )" #n+e!#n !e )#;#("& " n 65 (e ! +")$ #n#'#"). L"! %#)#("(e! '$n%"*)e! (e )" empe!" e!%"&n "e'%"! ") Impe!%$ (e /#me" C"%e-$<" ?15@. $($! )$! +")$e! e!%&n en US (e 2002 ?(e #-") p$(e "(;#!#%#+$, e! (e'#, e! n" n#("( m$ne%"#" e")@ !#n IVA, !p$n-" ;e )" #n+e!#n n$ e!%& "e'%" ") IVA ?n$ !e p"-"@. E) #n+e!#$n#!%" %#ene ! #;e>" "'%") #n+e%#(" en *$n$! (e )"-$ p)">$, ;e )e ("n n" en%"*#)#("( e") "n") (e 10 en ()"e!. E)"*$e n )$ (e '"" p"" e) #n+e!#$n#!%" '$n )$! "n%e'e(en%e! e)e+"n%e! p"" )" (e'#!#n (e "'e e) p$e'%$ (e m")%e<". BRe'$men("<" U(. ;e e) #n+e!#$n#!%" e")#'e e) p$e'%$. Dn("men%e ! e!pe!%".
1.1.
Solución
/e-n%" 1 In+. C"p#%") (e %"*. "'%#+$ een$ OOCC S#)$! :";. e;. $%")
7700000 10000000 US 80000 870000 1850000 4900000 7700000
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21750 92500 490000 604250
VL ?6@ 80000 739500 1295000 1960000 4074500
5005000
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20000 240 4800000 25000 100 2500000
35000 240 8400000 43750 100 4375000
45000 240 10800000 56250 100 5625000
50000 240 12000000 62500 100 6250000
50000 240 12000000 62500 100 6250000
50000 240 12000000 62500 100 6250000
1
2
3
4
5
6
4800000
8400000
10800000
12000000
12000000
1300000
1300000
1300000
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12000000 930500 1300000
520000 2500000
910000 4375000 604250 124250 1086500 162975 923525
1300000 6250000 857151 604250 1346927 341673 51250,9 290422
1300000 6250000 445059 604250
1300000 6250000
604250
1170000 5625000 3447677 604250
0
0
2100691 315103,6 1785587
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0
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0
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5563236 5005000
10000000 4425000
480000
1652025
1817942
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1
2
3
4
5
6008295 3447677 2560619 10714381
6008295 857151 5151145 5563236
6008295 445059 5563236
10000000 17633563
18.683.7 83
Préstamo
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1327500 8 6008295 0
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2. COD CODEGU EGUA, A, NUEV NUEVO O LOCAL LOCAL PAST PASTELE ELERO RO Un '$n$'#($ '$me'#"n%e (e )" )$'")#("( (e C$(e-" ?VI Re-#n@, (e(#'"($ " )" p$(''#n (e p"!%e)e! '#)en$! m"n", e!%& #n%ee!"($ en '$mp" n ne+$ )$'"), m&! "mp)#$ m$(en$ ;e e) ;e "#en(" en )" "'%")#("(, ;e )e pem#%" "men%" )"! +en%"!. S"*#en($ ;e )" D"')%"( (e In-en#e<" e!%& 'e'", !e (##-e " !%e( p"" ;e )e "(e " (e'#(# !# "'e $ n$ )" #n+e!#n. C$m$ e!%(#"n%e, !%e( )e '$*"<" )" m(#'" !m" (e 1.000.000 p$ e+")")e e) p$e'%$. E) '$me'#"n%e )e en%e-" )$! !#-#en%e! ("%$! E) pe'#$ (e +en%" (e) p"!%e) e! 480 - '$n IVA. S p$(''#n +en%" "'%") e! (e 100 -F(<", %"*""n($ ) 2 pe!$n"! m&!. E) !e)($ (e !! "("n%e! e! 170.000 p$ me!. E) ;#n%") (e "#n" ?40 -@ %#ene n +")$ (e 8.500 !#n IVA e) en(#m#en%$ e! (e 1,25 #)$! (e p"!%e) p$ - (e "#n". O%$! #n-e(#en%e! %")e! '$m$ ">'", !"), )e+"(", e+$! m"n" 'e!%"n 30 '$n #+" p$ #)$ (e p"!%e). L$! '$!%$! #$! (e )" "'%") p"!%e)e<", #n')#($ e) "#en($ (e) )$'") en 150.000 Fme!, "!'#en(en " 300.000 men!")e!. E) '"p#%") (e %"*"$ "'%") e! (e 400.000. E) p$e'%$ '$n!#!%e en '$mp" n ne+$ )$'") p$ n +")$ (e 8.000.000, e) '") !e "'$n(#'#$n"<" p$ )" !m" (e 2.000.000 ?!#n IVA@. E) )$'") !e (epe'#" )e-")men%e en 40 "$! )"! #n!%")"'#$ne! en 5 "$!. E) +")$ '$me'#") (e) )$'") !e m"n%#ene '$n!%"n%e en e) %#emp$ )"! #n!%")"'#$ne! %en(&n n +")$ '$me'#") ") ;#n%$ "$ e!%#m"($ en 500.000. A(em&!, !e %en(<" ;e '$mp" n $n$ #%")#"n$ p$ n +")$ (e
US11.000, ""n'e)e! e IVA #n')#($!, '$n n" +#(" %#) )e-") (e 12 "$!. Se e!%#m" ;e e) +")$ '$me'#") (e) $n$ " )$! 5 "$! !e& n 30 (e ! pe'#$ (e '$mp". A(em&!, !e "(;##& e;#p$! (e '$mp%"'#n en US2.500, '$n IVA #n')#($, '" (epe'#"'#n )e-") e! " 5 "$!. A) #n") (e) ;#n%$ "$ )$! e;#p$! '$mp%"'#$n")e! (e*en en$+"!e !e +en(e&n " n pe'#$ e!%#m"($ en e) 20 (e ! +")$ (e "(;#!#'#n. /"" #n"n'#" )" #n+e!#n, e) p"!%e)e$ 'en%" '$n "$$! pe!$n")e! (e 10.150.000 '$)$'"($! en n *"n'$ " n" %"!" (e) 7,0 e") "n"). E) e!%$ p#en!" #n"n'#")$ '$n n '(#%$ *"n'"#$ " n" %"!" (e #n%e! (e) 10,5 "n"). E) !#!%em" (e p"-$ e! en '"%$ '$%"! #"! !#n pe<$($ (e -"'#".
C$n e) ne+$ $n$, ;e !e "-e-" ") "n%e#$, )" p$(''#n p$(''#n "men%"<" en n 100. /"" e))$ ne'e!#%"<" ne'e!#%"<" '$n%"%" n "("n%e m&!. L$! '$!%$! #$! "men%"&n en 100.000 men!")e!. E) '"p#%") (e %"*"$ (e*e& "men%"!e en 150.000. E) %#p$ (e '"m*#$ e! 600 FUS, e) IVA e! 18 )" %"!" (e #mp e!%$ " )" en%" (e p#me" '"%e-$<" e! 15 )" %"!" (e #mpe!%$ " )" en%" e)e+"n%e p"" e) p"!%e)e$ e! 10. I(en%##;e )$! *ene#'#$! '$!%$! e)e+"n%e! p"" )" (e'#!#n (e e")#>" e) p$e'%$ (e!(e )" pe!pe'%#+" (e) p"!%e)e$. C")')e e) m$n%$ (e) p!%"m$ ne'e!"#$ p"" #n"n'#" )" #n+e!#n e) +")$ (e )"! '$%"!, "m$%#>"'#$ne! e #n%ee!e! p"" ! '"n'e)"'#n. C$ne''#$ne e) )$ (e '"" p"" )" (e'#!#n (e e")#>" e) p$e'%$ (e!(e e) pn%$ (e +#!%" (e) p"!%e)e$. BLe e'$men("<" !%e( "'e e) p$e'%$. B/$;
2.1.
Solución
JENEDICIOS
K COSOS E! #mp$%"n%e (e#n# ;e !e (e*en '$n!#(e" (e)%"! (e #n-e!$'$!%$ '"p (e %"*" %"*" $ E#!%e n" m"$ '"p"'#("( p$ )$ %"n%$ m"$ #n e!$ L$! '$!%$! $pe"'#$n")e!?V"@ !e m"n%#enen #-")e! ?"men%" en e) " )" m"$ p$(''#n@ A$$ en A#en($ Amen%" e) C$!%$ D#$ Amen%" e) '$!%$ en :"n$ (e O*" E#!%en +"#"'#$ne! en e) '"p#%") (e %"*"$ E#!%en +"#"'#$ne! en )" #n+e!#n e;e#(" DINANCIA:IENO /e!%"m$ #n%e! C$%" C$%" In%e! Am$%#>"'#n S")($ In!$)%$
6764406 .7 10.50 2157115
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4
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0
1
2
3
4
2157115 710263 1446852 5317555
2157115 558343 1598772 3718783
215711 39047 17666 19521 40
215711 20497 19521
6764406 .7
0
Re' (e (e)%" (e C"p. "* "*"" $ D. C"" IM
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7200000 1800000 1200000 2040000 150000 17264406.78
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1
2
3
4
5
14644 06
14644 06
14644 06
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14644 06
10440 00
10440 00
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10440 00
18000 00 71026 3 17728
18000 00 55834 3 17728
18000 00 39047 2 17728
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33209 49813 28227 20000 17728 81
34728 52092 29519 20000 17728 81
36407 54610 30946 20000 17728 81
38262 57393 32522 20000 17728 81
14468
15987
17666
19521
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17728 10000 00 24322 03 746339 111950 63438 20000 17728 81 70000
V")$ Re!
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7000 00
80000 00 24322
100000 0 886440
0
VANM
20,516,758
17264 40
/e!%"m$! Am$%#>"'#$ne! Amen%$ (e C"p Re' (e (e)%" (e C"p. "*"$ D. C""
67644 0
15000 10650 00
62425 19
65235 70
68341 31
71773 02
15000 0 12034 55 9
Amen%$ (e #;e>" "(#'#$n")
3. EMPRESA EMPRESA DE SERVI SERVICIO CIO DE ALIMENT ALIMENTACIÓN ACIÓN MASI MASIVVA Un #n+e!#$n#!%" e!%& e+")"n($ )" '$n+en#en'#" (e $m" n" empe!" (e !e+#'#$ (e ")#men%"'#n m"!#+" " empe!"! en n eme-en%e !e'%$ #n(!%#") (e )" e-#n me%$p$)#%"n". E) !e'%$ en ;e !e e")#>"<" e) !e+#'#$ !e en'en%" +"#$! #)me%$! (#!%"n%e (e )$! "'%")e! 'en%$! (e $e%", p$ )$ ;e e) !e+#'#$ (e ")#men%"'#n (e )$! emp)e"($! !e " %"n!$m"($ en n p$*)em" e)e+"n%e p"" )"! empe!"! ;e !e "n #n!%")"($ )"! nme$!"! ;e ; e !e e!pe" !e #n!%")en en e) me(#"n$ p)">$ en e) )-". L" empe!" "
'$n%emp)"($ (" )$! !e+#'#$! (e en%e-" (e ")#men%$! en+"!"($!, %"n!p$%e (e ")#men%$! " -"ne) )" '$n'e!#n (e '"!#n$! en e) '"!$ (e empe!"! m"$e!. A p"%# (e e!%" )$! (e '"(" "$ I%em In-e!$! /e!$n") In!m$! G"!%$! *&!#'$! -ene")e! :"n%en#m#en%$ (e e;#p$!,
A$ 1
A$ 2
A$ 3
A$ 4
A$ 5
"n%#'#p"($ 0 10 10 0 5
80.000 35.000 41.000 7.000 2.500
233.000 60.000 120.000 18.000 5.000
418.000 85.000 210.000 21.000 6.500
504.000 95.000 250.000 23.000 7.000
523.000 95.000 260.000 22.000 7.500
85.500
203.000
322.500
375.000
384.500
$%") G"!%$!
E) "#en($ (e) )$'") 'e!%" 1.000 : men!")e!, !e (e*e '"n'e)" "n%#'#p"("men%e, n%$ '$n n me! (e -""n%<". E) %een$ en %"n%$, 'e!%" 100.000 :. E) '$!%$ (e $p$%n#("( (e) (#ne$ p"" e) #n+e!#$n#!%" e! (e) 15 e") "n") )" %"!" ( e #mpe!%$ " )"! %#)#("(e! (e )" emp e!" e! 15. /"" e) ne-$'#$ !e e;#een e")#>" )"! !#-#en%e! #n+e!#$ne! ?" #ne! (e '"(" "$@ P%em C$n!%''#n E;#p"m#en%$ C$'#n" E;#p"m#en%$ '$me($e! O%$! e;#p$! Ve<')$! $%") #n+e!#n
V#(" %#) 30 10 10 3 5
A $0 15.000 5.0 6.0 5.000 31.000
A $1 80.000 20.000 20.000 3.000 5.000 128.000
A $2
5.0 5.0
A $3
V")$ e+en%" e +en%" ?en "$ 5 en 70.000 30.000 5.000 1.000 5.000 110.000
C$n e!%" #n$m"'#n !e p#(e ?4.0 pn%$!@ C")')" e) '"p#%") (e %"*"$ ne'e!"#$ p"" e) n'#$n"m#en%$ (e) p$e'%$ e!%#m" )$! )$! (e '"" (e) p$e'%$ !p$n#en($ n $#>$n%e (e e+")"'#n (e 5 "$!, ;e '"n($ )$! )$! (e '"" !$n p$!#%#+$!, )$! (e$! )$! e%#"n ") #n") (e) "$. BRe'$men("<" )" ee''#n (e) p$e'%$ ") #n+e!#$n#!%". B/$;. ?2.0 pn%$!@ S# ") #n") (e) p#me "$ )e $e'en n p!%"m$ p"" #n"n'#" )" #n+e!#n p$ 200.000 : p"-"(e$ en 3 '$%"! #-")e! '$n 1 "$ (e -"'#" " n" %"!" (e) 12 e") "n") B'$n+en(<" %$m" e) p!%"m$. C"n%##;e e) ee'%$ (e) p!%"m$ en e) V/N (e) p$e'%$.
4. EM EMPR PRES ESA A PLAS! PLAS!PL PLAS AS
L" empe!" /)"!/)"! L%("., (e )" #n(!%#" (e) p)&!%#'$, e!%& e+")"n($ )" p$!#*#)#("( (e eemp)">" !! m&;#n"! (e #ne''#n p$ n m$(e)$ ne+$ (e e'#en%e "p"#'#n en e) me'"($ L$! #n-en#e$! e!%#m"n ;e )"! m&;#n"! ne+"! pem#%#<"n e('# )$! '$!%$! (e )" m"n$ (e $*", )$! m"%e#")e! (em&! '$!%$! (#e'%$! (e )" $pe"'#n, en n$! 15 m#))$ne! ") "$. E!%"! m&;#n"! %#enen n
'$!%$ %$%") (e 130 m#))$ne! ?(e!pe'#e e) ee'%$ (e) IVA (e )" #n+e!#n@, n" +#(" %#) e'$nm#'" (e 15 "$! n +")$ e!#(") e'$nm#'$ (e 5 m#))$ne!. L" '$mp" (e e!%"! m&;#n"! #mp)#'"& "men%" e) '"p#%") (e %"*"$ (e )" empe!" en 16 m#))$ne!. E) Se+#'#$ (e Impe!%$! In%en$! " (e%em#n"($ ;e )" +#(" %#) (e e!%e %#p$ (e m";#n"#"! e! (e 10 "$!, p(#en($ (epe'#"!e "'e)e"("men%e en 3 "$!. /$ $%$ )"($, )" m";#n"#" !"(" %#ene n +")$ )#*$ (e 33 m#))$ne! n +")$ (e me'"($ (e 50 m#))$ne!Q )e e!%" n "$ (e (epe'#"'#n, n$ $*!%"n%e, !e en'en%" en *en"! '$n(#'#$ne! (e n'#$n"m#en%$ ("&,
-2 / E)"*$e e) )$ (e '"" (e) p$e'%$ (e eemp)">" )" m";#n"#" -1.5 / BC$n+#ene eemp)">" )" m";#n"#" !%##;e '"n%#%"%#+"men%e ! e!pe!%". -1 / BC&) e! )" %"!" #n%en" (e e%$n$ (e) p$e'%$ -1.5 / S# e) G$*#en$ e!%+#e" p"%$'#n"n($ n p$e'%$ (e )e ;e (e$-" )" (epe'#"'#n "'e)e"(" p"" #ne! %#*%"#$!. En '$n!e'en'#", %$($! )$! "'%#+$! '$mp"($! " p"%# (e )" e'" (e en+<$ (e) p$e'%$ (e*e&n !e (epe'#"($! n$m")men%e ?en 10 "$! en +e> (e 3@. BC$m$ "e'%" e!%e e'$ " !! e!pe!%"! (e "@ *@ !%##;e '"n%#%"%#+"men%e ! e!pe!%".
4.1.
Solución
Ve "'#+$ E'e).
5. REEMPLAZO REEMPLAZO DE M#$UIN M#$UINAS AS EN EM EMPRESA PRESA TE%TIL TE%TIL Un" empe!" (e) !e'%$ %e%#) (e*e (" (e *"" !! m&;#n"! #)"($"!. /"" ! eemp)">$, (#!p$ne (e ($! ")%en"%#+"! #)"($"! ")em"n"! e #)"($"! '$e"n"!. L"! m&;#n"! ")em"n"! %#enen n '$!%$ (e 250 m#))$ne!, n" +#(" %#) e'$nm#'" (e 12 "$! n +")$ e!#(") e'$nm#'$ (e 5 m#))$ne! ") #n") (e e!e pe<$($. A(em&!, !e e!%#m" ;e )$! '$!%$! "n")e! (e p$(''#n !e e('#<"n en 25 m#))$ne! '$n e)"'#n " )$! "'%")e!. L"! m&;#n"! '$e"n"! %#enen n '$!%$ *"!%"n%e #ne#$, (e n$! 180 m#))$ne!Q n$ $*!%"n%e, ! +#(" %#) e'$nm#'" e! (e !)$ 9 "$! !e e!%#m" ;e ") #n") (e e!e pe<$($ p$(<"n !e +en(#("! en 5 m#))$ne!. E!%"! m&;#n"! pem#%#<"n e('# )$! '$!%$! "n")e! en 20 m#))$ne!. /"" #ne! %#*%"#$! "m*"! m&;#n"! pe(en !e (epe'#"("! en %e! "$!, '$n n +")$ e!#(") (e 'e$. L" %"!" (e #mpe!%$! " )"! %#)#("(e! e! (e n 15 e) '$!%$ (e $p$%n#("( (e) '"p#%") e! 12 )$! #n-e!$! (e )" empe!" !$n !#'#en%emen%e ")%$! p"" %ene %#)#("(e! '$n%"*)e! p$!#%#+"! en %$($! )$! pe<$($!.
-2 / E)"*$e e) )$ (e '"" e)e+"n%e p"" '"(" ")%en"%#+". -2 / B m&;#n"! e'$men("<" '$mp" !%##;e '"n%#%"%#+"men%e. -2 / / S# )e $e'en "en(" )" m&;#n" e'$men("(" en "@ en 27,5 m#))$ne! "n")e! ?p"-"($! "n%#'#p"("men%e ") '$m#en>$ (e '"(" "$. BC$n+#ene m&! '$mp")" $ "en(")"
5.1.
Solución
"!" (e Impe!%$!
15
"@ D)$! (e C"" (e '"(" n" (e )"! ")%en"%#+"! :&;#n"! A)em"n"! C$!%$ 250 V#(" U%#) E'$nm#'" 12 V")$ Re!#(") E'$nm#'$ 5 Re(''#n (e C$!%$! 25
0
A$$ '$!%$! =epe'#"'#n :N G"n"n'#" (e '"p#%") U Imp%$ U=I =epe'#"'#n :N G"n"n'#" (e '"p#%") V")$ e!(") e!( ") In+e!#n D. C"" V/N IR V/S :&;#n"! C$e"n"! C$!%$ V#(" U%#) E'$nm#'" V")$ Re!#(") E'$nm#'$ Re(''#n (e C$!%$!
V/N IR
3
83
1 1 1
1
2
3
4
5
6
7
8
9
25 83
25 83
25 83
25
25
25
25
25
25
0
0
0
0 0
0 0
0 0
0 0
0 0
0 0
0 0 0 0 0 5
58
58
58
9
9
9
50 83
50 83
50 83
25 4 21
25 4 21
25 4 21
25 4 21
25 4 21
25 4 21
2 2 3 2 2 2
0 0 250 0
0 0 0
0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
250
34
34
21
21
21
21
21
21
0 0 0 0 0 0
34
73 2.99 98 180
/e<$($ (e (epe'#"'#n C$%" (e (epe'#"'#n
9 5
3
60
20 0
A$$ '$!%$! =epe'#"'#n :N G"n"n'#" (e '"p#%") U Imp%$ U=I =epe'#"'#n :N G"n"n'#" (e '"p#%") V")$ e!(") e!( ") In+e!#n D. C""
/e<$($ (e (epe'#"'#n C$%" (e (epe'#"'#n
0 0 0 0 0 0
180 180 58 0.50
1
2
3
4
5
6
7
8
9
20 60
20 60
20 60
20
20
20
20
20
20
0
0
0
0 0
0 0
0 0
0 0
0 0
0 5
40
40
40
6
6
6
34 60
34 60
34 60
20 3 17
20 3 17
20 3 17
20 3 17
20 3 17
25 4 21
0 0 0
0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0
0 0 0
0 0 0 0
26
26
26
17
17
17
17
17
5 5 0
21
0 0 0 0
21
0
5 0
V/S
91
A)em"n"! 73 2.99 98
*@ E)e''#n (e me$ m&;#n" C$!%$! IR V/S
C$e"n 58 0.50 91
C$m$ !$n '$!%$! !e e)#-e )" ;e p$('e men$! p(#(" C$e"n"! A(em&! %#ene n" me$ IR ! '$!%$ "(#'#$n") en '"(" '#')$ e! men$. '@ E)e''#n en%e " "#en($ Sp$nem$! e)e-#(" )" '$e"n"
C$!%$! (e "#en($ 0
A$$ '$!%$! C$!%$ "(#'#$n") (e U (e)%" #mpe!%$ U=I D. C""
27.5
1
2
3
4
5
6
7
8
9
20
20
20
20
20 27.5 7.5 1.1 8.6 8.6
20
20
20
20
V/N 50 ES :EOR ARREN=AR IR O$ ;e "$" n$ (e!'en%$ #mpe!%$ p$ )"! '$%"! (e (epe'#"'#n (e!'en%$ #mpe!%$ V/S 78 p$ e) m"$ '$!%$ $pe"'#$n") ="<" )$ m#!m$ %"m*#n (e%em#n" e) V/N (e )$! '$!%$! ne+$! ?"$$ "#en($ #mpe!%$@
6. ER ERRO RORE RESS EN EN FC FC Un #n-en#e$T e!%(# n ne-$'#$, #>$ e) '$e!p$n(#en%e )$ (e '"", '")') e) V/N '$n') ;e n$ )e e! '$n+en#en%e. C$m$ e!%& '$n!'#en%e (e )$! +"'<$! ;e %#ene en e!%e &m*#%$, )e p#(e ;e )$ e+#!e, ;e )$ '$#" )e ( ! e'$men("'#n. E) )$ (e '"" (e ) e! e) !#-#en%e 0
1
2
3
4
In e!$! e!$! $pe $pe"'# "'#$n") $n")e! e! C$!%$! $pe"'#$n")e!
500,0 286,0
800,0 336,0
1.000,0 386,0
1.100,0 386,0
C$mp" (e "'%#+$! C"p#%") (e %"*"$ Ven%"! (e "'%#+$!
1.300,0 600,0
500,0
/!%"m$
1.000,0
1.100,0
/"-$ /!%"m$ U%#)#("( "n%e! (e #mpe!%$! Impe!%$! U%#)#("( (e!p! (e #mpe!%$!
?900,0@
?900,0@
315,5 ?101,5 ?15,2@ ?86,3@
315,5 ?351,5 ?52,7@ ?298,8
315,5 298,5 44,8 253,7
315,5 1.498,5 224,8 1.273,7
V/N?@ M ?165@ M 10 ?L$! "'%#+$! !e (epe'#"n en '#n'$ "$!@. "@ I(en%##'" )$! e$e! (e) )$ (e '"" (e) #n-en#e$T. *@ H"'e e) )$ )$ (e '"" '$e'%$. '$e'%$. '@ H"'e n" e'$men("'#n e'$men("'#n " p"%# (e )$! ne+$! e!)%"($!. e!)%"($!.
6.1.
Solución
"@ Se %#enen )$! !#-#en%e! e$e! L" (epe'#"'#n n$ e!%& (e!'$n%"n($ #mpe!%$. C"n($ " p(#("!, " )" empe!" n$ !e )e (" (#ne$ ?)$! #mpe!%$! n$ !e (e+e)+en@. L"! p(#("! (e) ee'#'#$ "n%e#$ n$ !e e!%&n %$m"n($ en 'en%". L" -"n"n'#" ?p(#("@ (e '"p#%") p"-" #mpe!%$. E) +")$ (e e+en%" (e )$! "'%#+$! n$ p"-" #mpe!%$. L" "m$%#>"'#n (e )$! p!%"m$! n$ p"-" #mpe!%$ ?e! p"%e (e) )$ (e '"p#%")@. L$! #n%ee!e! ?-"!%$! #n"n'#e$!@ p"-"n #mpe!%$!. *@ La depreciación de los activos adquiridos en el período 0 es La depreciación de los activos adquiridos en el período 2 es
1.300 500
= 260.
5
= 100.
5
E) +")$ +")$ )#*$ )#*$ (e )$! "'%#+$ "'%#+$!! ") ") #n" #n")) (e) (e) $#>$n $#>$n%e %e ?") #n") #n") (e) '"%$ '"%$ pe<$($@ pe<$($@ +" " !e !e VL M 1.30 1.3000 4260 4260 500 2100 M 560. /$ )$ %"n%$, )" -"n"n'#" (e '"p#%") +" " !e 1.000 560 M 540. E) p"-$ p$ p!%"m$ '$e!p$n(e " )"! '$%"!. =e) )$ (e '""T !e +e ; e )"! '$%"! !$n #"!. ⋅ ⎛ (1 + i) − 1⎞ 4
⇒
1.000
=
315,5
⎜ ⎟ 4 ⎝ (1 + i) ⋅ i ⎠
⇒ # M 0,1
Le-$, %$m"n($ en 'en%" ;e '$%" M "m$%#>"'#n #n%ee!e!, !e %#ene e) !#-#en%e )$ (e '"".
0
1
2
3
4
500,0 286,0 260,0 100,0
800,0 336,0 260,0 78,5
1.000,0 386,0 360,0 54,8
1.100,0 386,0 360,0 28,7 540
?146,0@
146,0 ?20,5@
?146,0@ 260,0
?20,5@ 260,0
20,5 178,7 26,8 151,9 360,0
146,0 385,5
20,5 532,4
500,0
D)$ $pe"'#$n") In-e!$! $pe"'#$n")e! C$!%$! $pe"'#$n")e! =epe'#"'#n G"!%$! #n"n'#e$! G"n"n'#" (e '"p#%") /(#(" (e) ee'#'#$ "n%e#$ U%#)#("( "n%e! (e #mpe!%$! Impe!%$! U%#)#("( (e!p! (e #mpe!%$! =epe'#"'#n G"n"n'#" (e '"p#%") /(#(" (e) ee'#'#$ "n%e#$
114,0
865,3 129,8 735,5 360,0 540 555,5
D)$ (e '"p#%")e! C$mp" (e "'%#+$! C"p#%") (e %"*"$ Re'pe"'#n '"p#%") (e %"*"$ V")$ (e e+en%" (e "'%#+$! /!%"m$ Am$%#>"'#n
1.300,0 600,0
?900,0@
215,5 ?215,5@
237,0 ?737,0@
260,7 ?260,7@
286,8 1.413,2
?900,0@
?101,5@
?351,5@
271,7
1.968,7
1.000,0
D)$ (e '""
600 1.100,0
'@ Se '")')" e) V/N (e) p$e'%$. V! = −"00 +
−101,5 −351,5 2#1,# 1."6$,# 2 3 4 266 1,1 + 1,1 + 1,1 + 1,1 =
C$m$ e) V/N (e) p$e'%$ e! m"$ ;e 'e$, e) ne-$'#$ e! '$n+en#en%e
. PL PLAN ANTTA AV' AV'CO COLA LA e!%& '$n!#(e"n($ #n+e%# en n" p)"n%" "+<'$)". /"" e))$ e;#ee '$mp" n -")pn (e 1. ! Un empe!"#$ e!%& 5.000 m2. E) '#')$ '#')$ (e) ne-$'#$ ne-$'#$ '$m#en> '$m#en>"" '$mp"n( '$mp"n($$ p$))$! p$))$! (e 1 (<" " 50 'F, 'F, )$! ;e !e '$)$' '$)$'"n "n en n" 2 (en!#("( (e 14 p$))$!Fm . E) pe!$ (e) p$))$ (epen(e& (e) nme$ (e !em"n"! (e +#(" ;e %en-" Sem"n" /e!$ ?-@
4
5
6
7
8
9
1.000
1.300
1.600
2.200
2.600
2.700
10 2.750
11 2.754
12 2.756
L$! '$!%$! "n")e! +"#"*)e! (e $pe"'#n (e) ne-$'#$ en Fp$))$ !$n 120 p$ ")#men%$! "-" 30 en '")e"''#n. A(em&! !e (e*e #n'# en )$! !#-#en%e! -"!%$! "n")e! 30.000.000 en /e!$n") 10.000.000 en In!m$! V"#$!. /$ $%$ )"($, e) p$))$ !e +en(e " )$! m"%"(e$! en 500 e) - L" #n+e!#n e;e#(" en e! )" !#-#en%e een$ 50.000.000 G")pn C$n!%''#$ne! 120.000.000 (epe'#"*)e en 15 "$!
E;#p ;#p$! $! e Im Imp)em p)emen en%$ %$!! 40.0 40.000 00.0 .000 00
(ep (epe' e'#" #"*) *)ee en en 10 "$! "$!
L" #n+e!#n %#ene n +")$ e!#(") ;e ")'"n>" e) 60 (e )" #n+e!#n #n#'#"). /"" #n"n'#" )$! (e!"!e! (e p"-$! (e e-e!$! e #n-e!$! (e) p$e'%$ !e (e*e #n'$p$" n '"p#%") (e %"*"$ (e 15.000.000. E) $#>$n%e (e e+")"'#n e! (e 5 "$!. E) '$!%$ (e $p$%n#("( (e) (#ne$ (e) empe!"#$ ")'"n>" ") 14 e") "n"), e) #mpe!%$ (e p#me" '"%e-$<" ?" )"! %#)#("(e! (e )" empe!"@ e! (e 15, )" %"!" m"-#n") (e #mpe!%$ " )" en%" (e) #n+e!#$n#!%" e! (e 45.
N Un "$ %#ene 52 !em"n"!. $($! )$! pe'#$! e!%&n !#n IVA. "@ C")' C")')e )e e) m$me m$men% n%$$ p% p%#m #m$$ (e !em"n !em"n"! "! (e +#( +#("" (e (e )$! )$! p$) p$))$ )$!! p" p""" ! ! +en% +en%". ". *@ E)"*$e e) )$ (e '"" (e) #n+e!#$n#!%". C")')e e) "p$%e (e) p$e'%$ " ! #;e>". '@ Sp$n-" Sp$n-" ;e e) ne-$'#$ " !e #mp)emen% ;e n$! en'$n%"m$! en'$n%"m$! " #n")e! (e) "$ 2. E) (e$ (e) p$e'%$ p$e'%$ " e'#*#($ n" $e%" (e #n%en'#n (e '$mp". BC&) (e*e<" !e e) pe'#$ m"n "m$%#>"n #n%ee!e!@, " n" %"!" (e #n%e! e") (e) 7 "n")
7.1.
"@
Solución
="($ ="($ ;e n$! en'$ en'$n% n%" "m$ m$!! "n%e "n%e n p$e' p$e'%$ %$ epe% epe%#* #*)e, )e, en e) ;e ;e '$n$'e '$n$'em$ m$!! n" e!% e!%' '% %" " (e '$!% '$!%$! $! ;eem$! +e )$! *ene#'#$!, $'p"m$! e) #n(#'"($ JAUE. /e'#$ (e +en%" 500 p$ -. C$!%$ #n#'#") 50 p$ p$))$ 14 "n") =e*em$! '$n+e%# e) "n") " !em"n"), (e )" !#-#en%e $m"
(1+ r anual ) = (1+
52
)
r semanal semanal
⇒ r semanal = 521+ r anual −1 ⇒ r semanal = 0,0025 ⇒ r semanal = 0,25% Le-$, '")')"m$! e) +")$ (e) V/N p"" '"(" !em"n" VPN
valor (t ) =
t
(1 + r )
⇒
VPN (t
4) =
=
⇒ VPN (t = 4) =
valor (t = 4)
(1 + 4
0,0025)
500 1,0025
4
⇒ VPN (t = 4) = 4"5
N$ p$(em$! '$mp"" )$! V/N (e )$! p$e'%$! (e (#!%#n%" +#(" %#), p$ )$ ;e $'p"m$! e) #n(#'"($ JAUE. BAUE
=
VPN
×
FRC
(1 + r ⇒ BAUE =
VPN
×
4"5
⇒ BAUE =
n
)
×
r
semanal
(1 + r semanal ) )
sema nal n
−
(1 + 0,0025)
4
1
×
0,0025
×
(1 + 0,0025)
4
−
1
125
⇒ BAUE =
R789:; 8 <=8<8, 7<7, >7 ;7? =8@ /? <> 7;. D7 7 ?;, <;/87; 8 9@977 B8
Sem"n" /e!$ /e'#$ V")$ p$))$ ?@ V/N ?@ JAUE ?@
2.700 500 1.350
10 2.750 500 1.375
11 2.754 500 1.377
12 2.756 500 1.378
1.274
1.320
1.341
1.339
1.337
161
148
136
124
113
4
5
6
7
8
9
1.000 500 500
1.300 500 650
1.600 500 800
2.200 500 1.100
2.600 500 1.300
495
642
788
1.081
125
129
132
156
=e )" %"*)" !e $*!e+" ;e e) m"$ JAUE p$!#*)e !e )$-" p"" e) pe<$($ (e 8 !em"n"! ?JAUEM161@. C$m$ !e %en<"n 8 !em"n"! '$m$ '#')$ p%#m$, e!%$ -ene" n p$*)em", en n "$ !e )$-"&n %ene 6,5 '#')$!, p$ )$ ;e !e (e%em#n" ee'%" 6 '#')$! en e) p#me "$ 7 '#')$! en e) !e-n($ "!< !'e!#+"men%e "!%" )$-" e) $#>$n%e (e e+")"'#n 5 !.
Se-n e) enn'#"($ !e %#enen )$! !#-#en%e! ("%$!
B
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P7?>G. D7 C/98 E! )" (#een'#" en%e Ve!#(") V)#*$ Ve!#(") M 60 (e) +")$ (e )" #n+e!#n M 0.6 W 210 M 126 V)#*$M V")$ #n") (e )$! *#ene! (e!p! (e n pe<$($ (e (epe'#"'#n, en e!%e '"!$ !e (epe'#" ::12 'F"$, )e-$ )" (epe'#"'#n %$%") en e) pe<$($ e! (e 12W5"$! M ::60. :#en%"! ;e )$! *#ene! " (epe'#" e"n ::210, en%$n'e! V)#*$ M 21060M ::150. D#n")men%e /e(FG"n. =e C"p#%") M 126150 H ! 24 ?!e %"n!$m" en n" p(#(" (e '"p#%"), " ;e e) +")$ e'$nm#'$ e! men$ (e )$ ;e '$n%"*)emen%e +")e e) *#en@. In-e!$! /"" e) '&)')$ (e )$! #n-e!$! e! ne'e!"#$ !e (e*e '$n!#(e" ?") men$! p"" e!%e '"!$@, ;e )$! "$! #mp"e! !e '$n!#(e"&n 6 '#')$! )$! p"e! 7 '#')$!. A)%en"%#+"! " e!%$ !e<" '$n!#(e" 6.5 '#')$! '")')" #n-e!$! '$n!%"n%e!. E! n" ")%en"%#+". /"" e!%e '"!$ !e %#ene m&#m$M 14 p$))$! F m%!2 W 5000 m2 M 70.000 p$))$!, '$m$ '"p"'#("( (e) -")pn. D#n")men%e e) #n-e!$ / M pe'#$, M '"n%#("( (e p$))$!, M pe!$ (e) p$))$ en e) '#')$, CM nme$ (e '#')$!.
IM/WWWC 1 $($! )$! ("%$!
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=e 12 V 126 VL 150 /. (e 24 C. C. . 15
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2
FLUJO FL UJO DE CAJA CAJ A DE LA EMPRESA EMPR ESA
0
C#')$! In-e!$! /(#(" (e C. C$!%$! V"#"*)e! D#$! =epe'#"'#n U. "n%e! Imp%$ ?15@ U. /(#(" (e C. =epe'#"'#n In+e!#n V")$ C. (e . Re'. C. (e . D)$ (e C"" V/N ?14@M
1 6
2 7
3 6
546
637
5
4 7
5 6
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84 40 12 410 62 349
98 40 12 487 73 414
4 6 3
4 73 4
12
12
1
12
581 24 98 40 12 407 61 346 24 12
210 126 225 1.186
361 ::
426
3
4
15 523
::F"$ mm mm mm mm
N N 8 8 8 8 >7 <
Re'$(em$! e en '"!$ (e e e) en 'e!%#n n$ /AGAR I:/UESOYYY I:/UESOYYY )$ e en e!$! '"!$! !e '$n!#(e" )" 'e)(" #m e!% e!%$$ !e !e n" "(#'#$n") (e) e . An%e#$ An%e#$ /EA /EA e n$ e! m&! ""!%e (e )"! (#("! pe<$ pe<$($ ($ !# #en% #en%ee (e!'$n%"n($ C$n!#(eem$! ;e )"! )$! '$!%$! #mpe!%$ " )" en%" #-") ;e )"! p(#("! (e
utilidades,NOPUEDE E!%" e! n" +"#"'#n " )" ')"!e "#)#" en )" ;e !e %#)#> e) m#!m$ #n-e!$ ;e en )$! "$! 1 3. S$n ")%en"%#+"! (#!%#n%"! ;e !e (e*e e+")", en e!%e '"!$ !e '$n!#(e" 6 '#')$! (e 8 !em"n"! !e )e !m" e) .5 e;#+")en%e " 4 !em"n"! )$ ;e +")(<" e) p$))$ e n e!e #n!%"n%e
2
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/"" /"" %$(" %$(" e+")"' e+")"'#n #n (e '"n%$ '"n%$ 'e! 'e!%" %" n p$e p$e'%$ '%$,, !e (e*en (e*en '$n! '$n!#(e #(e" " )$ ;e e) #n+e #n+e!# !#$n# $n#!%" !%" (e" (e"<" <" (e (e -"n" '$n e) p$e'%$, e!%e +")$ e! e) ") men$! e) #n+e!#$n#!%" ;e ") (e"<" ne%"). En e!%e '"!$ '$n!#(e"n($ ;e e!%"m$! " #n")e! (e) 2 pe<$($ !e (e*e '$n!#(e" )$! #n-e!$! %$! (e )$! 3 !#-#en%e! pe<$($!. 2
D)$ (e C"" V/N ?14@M
997
3
4
5
361
426
523
::
Le-$, e) m
(@
En e!%e e!%e '"!$ '"!$ )" ")%e ")%en"% n"%#+" #+" pe(e pe(e '$n! '$n!#(e #(e"! "!ee '$m$ '$m$ n p$e' p$e'%$ %$ "(#'#$ "(#'#$n") n") ;e, ;e, '$n '$n ")-n"! ")-n"! +"# +"#"'# "'#$ne $ne!! en e) "p$%e en (e!'en%$ (e #mpe!%$! ?'$!%$! #n"n'#e$!@, !e (e*e !m" en #;e>" ") "n%e#$. E!%$ e! )$ ;e '$mnmen%e !e ))"m" )$ (e '"" m"-#n").
Calculo de Cuota
C$%" #" M / W ?1 # @ W ??1 #@Z% W #@ ??1 # @Z% [ 1@ En e!%e '"!$ e) % M 4 "$!, "n '$n!#(e"n($ ;e e! '$n n "$ (e -"'#". E) pp%m$ e! n 50 (e )" #n+e!#n '"p#%") (e %"*"$ M ::112.5 ?/@ L" %"!" (e #n%e! e! #M 0.07 =e!pe"n($..... C M 35,538 :: ") "$ C$n )" '$%" e) !")($ (e) p !%"m$ !e (e%em#n"n )$! #n%ee!e! "!$'#"($! ") pe<$($ S")($ W 0.07, D#n")men%e )" "m$%#>"'#n !e (e%em#n" " p"%# (e A M C$%" [ In%ee!e!.
/e<$($ S")($
Am$%# >"
In%ee!e !
C$%" /!%"m$
C$%" In% In % 1 "$ " $
C$%" $%")
N$%"! ") #n"n'#"m#en%$ /e(e '$n!#(e"!e ;e en e) p#me "$ (e p"-$ !e 1 112,5 p"-en p"-en %$($! %$($! )$! #n%ee! #n%ee!e! e! 112,5 25,338 7,875 33,21 2,324 35,5381 2 (e -"'#". O%" ")%en"%#+" 87,161 27,111 6,10133 33,21 2,324 35,5381 3 e) '"!$ (e 60,05 29,009 4,2035 33,21 2,324 35,5381 4 n#$memen%e )$! #n%ee!e! 31,040 31,040 2,17282 33,21 2,324 35,5381 5 p#me "$ en )$! 112,5 !#-#en%e!, ;e e! )$ ;e !e "'e ";<. W !%$! #n%ee!e! n$ !e p"-"n, -ene"n n" !e-n(" '$%" p"" p"-")$! (e) "$ 2 ") 5 Re'$(" ;e )" !m" (e )"! "m$%#>"'#$ne! %#ene ;e !e #-") ") p!%"m$ D#n")men%e e) D)$ (e '"" (e) #n"n'#"m#en%$ ;e(" '$m$ !#-e
C$n!#(e"n($
p"-$ (e (e) pe<$($ (#!%#*'#n (e )$! #n%ee!e! pe<$($ (e -"'#".
MATERIAL DOCENTE IN42A – MARZO 2006 0
G"!%$ ='%$. =e G"!%$ D#n. Ne%$ /!%"m$ Am$%#>"'#$ne! D)$ /!%"m$
1
2
3
4
5
1,5299
1,263
0,9792
4,49775 0,67466 3,82308
112,5
E) e'$ (e e) -"!%$ 112,5 '$m$ '$!%$, en '");#e )$ (e!'en%$ en e) n#+e) V/N 3M5 80 :: (e #mpe!%$! " ?14 p"-" ? e! n '$!%$ Am$%#>"'#$ne! @M "(#'#$n")@, "(#'#$n")@, p$ )$ ;e '$m$ -"!%$! ;e n$ 8<8 /?9? >78 7?<7? /7 !e '")')" e) 15 (e) (e!'en%"n F98;77 78 8 8 >78 /?7< >7 9<9;97 7 '$!%$ ?> K7'$m$ 7 78"p$%e " < K7 97?7 <;/??. A VPN H !MM"0 n ( e ! 'en en%$ (e $'#$ e! 80 :: men$! Le-$, e) pe'#$ m
31,0403 34,8634
". ME MERC RCAD ADO O DE C COR ORRE REOS OS Un" empe!" e!%& e!%(#"n($ )" p$!#*#)#("( (e en%" ") me'"($ '#)en$ (e !e+#'#$! (e '$e$. Se-n n e!%(#$ e")#>"($ p$ n" '$n!)%$" n"'#$n"), e!%" empe!" p$(<" !"%#!"'e en ! p#me "$ (e $pe"'#n n 10 (e )" (em"n(" %$%") p$ '$e$, '#" '#" ;e !*#<" 2 ") "$, p"" ))e-" " n 18 ") '"*$ (e) ;#n%$ "$ (e $pe"'#n (e) p$e'%$. L" '+" (e (em"n(" p$ '$e$ %#ene )" $m" n'#$n") /?@ M 250 5 × , ($n(e / e! e) pe'#$ n#%"#$ p$ en+<$ ?Fen+<$@ e! e) nme$ (e en+<$! "n")e! ?epe!"($ en m#))$ne! (e n#("(e!@. L" (em"n(" %$%") p$ '$e$ %en(<" n #n'emen%$ (e) 5 "n"). A'%")men%e e) pe'#$ (e e;#)#*#$ e! (e 200. E) e!%(#$ !e")" ;e e!%e pe'#$ !e m"n%en(& ("n%e )$! p#m$! 5 "$!. L" #n+e!#n '$n!#(e"(" p"" e) p$e'%$ !e pe!en%" en )" !#-#en%e %"*)" P%em In!%")"'#$ne! E;#p$! C"p#%") (e "*"$
C$!%$ 300 m#))$ne! 40 m#))$ne! 20 m#))$ne!
V#(" \%#) 20 "$! 5 "$!
L" empe!" "en("& n$! %een$! (e!p$*)"($! *#'"($! en )"! "e"! (e S"n%#"-$ p"" '$n!%# !! #n!%")"'#$ne!. L$! '$!%$! #$! (e $pe"'#n ?"#en($ (e) %een$ e #n!m$!@ !e e!%#m"$n en 500.000 p$ me!Q )$! '$!%$! +"#"*)e! ?!)$ (e m"%e#")e!@ !e e!%#m"n en 40 p$ en+<$. E) pe!$n") "(m#n#!%"%#+$ (e )" empe!" !e e!%#m en 10 pe!$n"! !e& e) n#'$ '$n%"%"($ en $m" #", e) !e)($ p$me(#$ !e # en 250.000 men!")e! p$ emp)e"($. A )$! ep"%#($e! (e '$e!p$n(en'#" !e )e! p"-"& n +")$ (e 75 p$ '"%" en%e-"(".
E) p$e'%$ ("& n pe<$($ (e 5 "$!. C"n($ !e )#;#(e e) ne-$'#$, e) (e$ (e) %een$ p"-"& " )" empe!" e) +")$ )#*$ (e )"! #n!%")"'#$ne!. E) '$!%$ (e '"p#%") (e )" empe!" p"" e!%e p$e'%$ e! (e 16 )" %"!" (e #mpe!%$ " )"! %#)#("(e! e! (e n 15. C$n!%# e) )$ (e '"" (e) p$e'%$ p"" n $#>$n%e (e 5 "$!. C$m$ "n")#!%" (e) p$e'%$, "-" n" e'$men("'#n " )" empe!" "'e'" (e )" '$n+en#en'#" (e ee'%")$.
8.1.
Solución
/"" e")#>" e) )$ (e '"" ee'%"m$! )"! !#-#en%e! $pe"'#$ne!
⎛250 200 ⎞
&n'resos por &n'resos por ventas ao i = 200 ×
i−1
×1,05
⎞ ⎟ × (0,1 + 0,02 × (i − 1))
5
⇒ &n'reso ao1 = 200.000.000
&n'reso ao 2 = 252.000.000 &n'reso ao 3 = 30$.#00.000 &n'reso ao 4 = 3#0.440.000 &n'reso ao 5 = 43#.5$2.250 *epreciación le'al =
300.000.000
+
40.000.000
20
= 23.000.000
5
&nversión = 340.000.000 +apital de traa-o = 20.000.000
+ostos operacionales operacionales ao i × 250.000) +ostos /i-os = 12 × (500.000 + 10250 200 = 36.000.000 − +ostos variales = (40 + #5) × ⎜ ⎟ ×1,05i 1 × (0,1× 0,02 × (i − 1))
⎛ ⎝
⎞ ⎠
5
⇒ +ostos variales ao1 = 115.000.000
+ostos variales ao 2 = 144."00.000 +ostos variales ao 3 = 1##.502.500 +ostos variales ao 4 = 213.003.000 +ostos variales ao 5 = 251.60".#"4
Le-$, '$n e!%" #n$m"'#n, p$'e(em$! " '$mp)e%" e) )$ (e '"" ?en m#))$ne! (e pe!$!@
0
1
2
3
4
5
In-e!$! p$ +en%"! C$!%$! $pe"'#$n")e! =epe'#"'#n )e-") G"!%$! #n"n'#e$! G"n"n'#" (e '"p#%")
200 151 23
252 189,9 23
308,7 213,5 23
370,44 249,0 23
437,58 286, 6 23
U%#)#("( "n%e! (e #mpe!%$ Impe!%$ ?15@
26 3,9
48,1 7,21
72,19 10,83
98,43 14,77
126,97 19,05
U%#)#("( (e!p! (e #mpe!%$ =epe'#"'#n )e-")
22,1 23
40,89 23
61,36 23
83,67 23
107,92 23
D)$ $pe"'#$n")
45,1
63,89
84,37
106,67
130,93
G"n"n'#" (e '"p#%") In+e!#n V")$ e!#(") C"p#%") (e %"*"$ Re'pe"'#n '"p#%") (e %"*"$
340 225 20 20
D)$ n$ $pe"'#$n")
360
D)$ (e C""
360
245 45,1
63,89
84,37
106,67
375,93
="($ ;e e) '$!%$ (e '"p#%") (e )" empe!" e! (e) 16, e) V/N '$e!p$n(e " V! = −360 +
45,1 63,$" $4,3# 106,6# 3#5,"3 2 3 + 1,164 + 1,165 1,16 + 1,16 +1,16
V! = 1$.30 illones de pesos
/$ )$ %"n%$, e) "p$%e " )" #;e>" (e) empe!"#$ e! p$!#%#+$, )$ ;e #mp)#'" )" '$n+en#en'#" (e ee'%" e) p$e'%$.
&. PR PRO( O(EC ECTO TO MINE MINERO RO 4 A) A)OS OS Un empe!"#$ n"'#$n") e!%& e!%(#"n($ )" p$!#*#)#("( (e #n+e%# en n p$e'%$ m#ne$. L" #n$m"'#n ;e (#!p$ne e! ;e )" m#n" en 'e!%#n !e ep)$%"<" %$%")men%e en !$)$ 4 "$!. Un "n")#!%" (e ! '$n#"n>" )e p$p$'#$n )$! !#-#en%e! "n%e'e(en%e! ?)$! +")$e! m$ne%"#$! e!%&n en m#)e! (e ()"e!@ 0
1
2
3
4
/$(''#n ?$nF"$@ /e'#$! ?:USF$n@
100 10
250 10
400 10
50 10
In-e!$! ?:USF$n@
1.000
2.500
4.000
5.0
C$!%$! +"#"*)e! C$!%$! D#$! =epe'#"'#n )e-") ?10 "$!@ In+e!#n #" V")$ e!#(") C"p#%") (e %"*"$
400 500 200
1.000 500 200
1.600 500 200
2.000 50 20
2.000 50 500
E) '$!%$ (e $p$%n#("( (e) (#ne$ p"" e) #n+e!#$n#!%" e! (e 10 e") "n") )" %"!" (e #mpe!%$ " )" en%" e! (e 15. E)"*$" e) )$ (e '"" e)e+"n%e (e%em#n" !# e) p$e'%$ e! '$n+en#en%e. Un e'$n$m#!%" e'$n$m#!%" )e !-## !-## ;e e!%(#"" e!%(#"" )" p$!#*#)#("( p$!#*#)#("( (e ep)$%" ep)$%" )" m#n" en n men$ %#emp$. S "!e!$ )e !e")$ ;e '$n n" #n+e!#n "(#'#$n") (e 1000 ?:US@ p$(<" "-$%" )" m#n" en !)$ 3 "$!, pe$ pe(e<"n 50 $n. E) me$ p$-"m" (e p$(''#n !e<" !"'" 200 $n e) p#me "$, 500 e) !e-n($ "$ 400 e) %e'e$. E) '"p#%") (e %"*"$ )$! '$!%$! +"#"*)e! n#%"#$! !e<"n )$! m#!m$!, )" e'pe"'#n (e )" #n+e!#n ") #n") (e) %e'e "$ !e<" (e 1.200 ?:US@ )" (epe'#"'#n )e-") !e<" " 10 "$!. BSe<" e'$men("*)e )" ep)$%"'#n "'e)e"(" (e )" m#n". A) #n+e!#$n#!%" )e $e'en n p!%"m$ " 1.500 ?:US@ '$n n #n%e! (e) 8 "n") !$*e !")($!, p"-"(e$! en 3 "m$%#>"'#$n "m$%#>"'#$ne! e! #-")e!. BRe'$men("<" BRe'$men("<" !%e( %$m" e) '(#%$ '(#%$ p"" #n"n'#" )" #n+e!#n. #n+e!#n. B/$ ;, "
9.1.
Solución
G"n"n'#" (e '"p#%") M V")$ e!#(") =epe'#"'#n "'m)"(" G"n"n'#" (e '"p#%") M 500 ?2.000 4 × 200@ M 700 Le-$, e) )$ (e '"" ;e(" '$m$ !#-e 0
In-e!$ p$ +en%" C$!%$! $pe"'#$n")e!
1
2
3
4
1.000 900
2.500 1.500
4.000 2.100
5.000 2.500
=epe'#"'#n )e-") G"!%$! #n"n'#e$! G"n"n'#" (e '"p#%") /(#(" (e) ee'#'#$ "n%e#$
200
U%#)#("( "n%e! (e #mpe!%$ Impe!%$ ?15@ U%#)#("( (e!p! (e #mpe!%$ =epe'#"'#n )e-") G"n"n'#" (e '"p#%") /(#(" (e) ee'#'#$ "n%e#$
100
D)$ $pe"'#$n")
100
200
200
700 100
100 200
700 105 595 200
1.700 255 1.445 200
1.600 240 1.360 200 700
1.645
2.260
100
In+e!#n V")$ e!#(") C"p#%") (e %"*"$ Re'pe"'#n '"p#%") (e %"*"$
2.000
D)$ n$ $pe"'#$n")
2.500
D)$ (e '""
2.500
895
500 500 500 1.000 100
895
1.645
E) V/N (e) p$e'%$ '$e!p$n(e " V! = −2.500 +
200
100 $"5 1.645 3.260 2 3 4 1,1 + 1,1 + 1,1 + 1,1 1,1
V! = 1#"3
Le-$, e) p$e'%$ e! '$n+en#en%e In+e!#n M 3.000 G"n"n'#" (e '"p#%") M 1.200 ?3.000 300 × 3@ M 900 3 pe<$($!. Le-$, e) )$ (e '"" e!)%" !e 0
1
2
3
In-e!$ p$ +en%" C$!%$! $pe"'#$n")e! =epe'#"'#n )e-") G"!%$! #n"n'#e$! G"n"n'#" (e '"p#%") /(#(" (e) ee'#'#$ "n%e#$
2.000 1.300 300
5.000 2.500 300
4.000 2.100 300
U%#)#("( "n%e! (e #mpe!%$ Impe!%$ ?15@ U%#)#("( (e!p! (e #mpe!%$
400 60 340
900 2.200 330 1.870
700 105 595
3.260
=epe'#"'#n )e-") G"n"n'#" (e '"p#%") /(#(" (e) ee'#'#$ "n%e#$
300
300
300 900
D)$ $pe"'#$n")
640
2.170
1.795
In+e!#n V")$ e!#(") C"p#%") (e %"*"$ Re'pe"'#n '"p#%") (e %"*"$
3.000
D)$ n$ $pe"'#$n")
3.500
D)$ (e '""
3.500
E) '")')$ (e) V/N e!
1.200 500 500
V! = −3.500 +
640
+
1.700 640
2.1#0
+
2
1,1
2.170
3.495
3.4"5 3
1,1
1,1
V! = 1.501
Le-$, )" ep)$%"'#n "'e)e"(" (e )" m#n" n$ e! '$n+en#en%e, " ;e e!%e V/N e! men$ ;e e) en'$n%"($ en )" p"%e "@. E+")"m$! )" '$n+en#en'#" (e) '(#%$ G"n"n'#" (e '"p#%") M 500 ?2.000 200 × 4@ M 700 Re'$("m$! ;e C$%" M In%e! Am$%#>"'#n, %enem$! )" !#-#en%e %"*)"
A$ 1 2 3 4
=e(" ") #n#'#$ (e) pe<$($ 1.500 1.000 500
In%ee!e! 120 80 40
Am$%#>"'#n 500 500 500
0
0
0
=e(" ") #n") (e) pe<$($ 1.000 500 0 0
Le-$, e) )$ (e '"" ;e(" '$m$ !#-e 0
In-e!$ p$ +en%" C$!%$! $pe"'#$n")e! =epe'#"'#n )e-")
1
2
3
4
1.000 900 200
2.500 1.500 200
4.000 2.100 200
5.000 2.500 200
G"!%$! #n"n'#e$! G"n"n'#" (e '"p#%") /(#(" (e) ee'#'#$ "n%e#$
120
U%#)#("( "n%e! (e #mpe!%$ Impe!%$ ?15@ U%#)#("( (e!p! (e #mpe!%$ =epe'#"'#n )e-") G"n"n'#" (e '"p#%") /(#(" (e) ee'#'#$ "n%e#$
220
D)$ $pe"'#$n")
20
In+e!#n V")$ e!#(") C"p#%") (e %"*"$ Re'pe"'#n '"p#%") (e %"*"$ /!%"m$ Am$%#>"'#n
80
40 700
220
220 200
500 75 425 200
1.660 249 1.411 200
1.600 240 1.360 200 700
1.611
2.260
220 845
2.000 500 500 500 1.500 500
500
500
D)$ n$ $pe"'#$n")
1.000
500
500
500
1.000
D)$ (e '""
1.000
520
345
1.111
3.260
Le-$, e) V/N !e $*%#ene (e )" !#-#en%e m"ne" V! = −1.000 +
− 520 345 1.111 3.260 4 1,1 + 1,1 1,1 + 1,1 + 1,1 2
3
V! = 1.$#4
En%$n'e!, ("($ ;e e!%e V/N e! m"$ ;e )$! "n%e#$men%e en'$n%"($!, '$n')#m$! ;e '$n+#ene %$m" e) '(#%$.
10. LICIT LICITACIÓN ACIÓN LOCOMOCIÓN COLECTIVA Un empe!"#$ e!%& e+")"n($ )" ")%en"%#+" (e #n-e!" ") ne-$'#$ (e )" )$'$m$'#n '$)e'%#+" )#'#%"n($ n" )" "%$#>" (epe'#" (epe'#" '$mp)e%" '$mp)e%"men%e men%e )$! *!e! en )$! )$! m#!m$! m#!m$! 10 "$! ;e ("& e)
p$e'%$ , "(#'#$n")men%e, pem#%e ;e e) empe!"#$ p"-e e) IVA (e ! #n+e!#n ") #n") (e) p#me "$ (e $pe"'#n ?p"-$ (e) IVA (#e#($@. L$! e!%(#$! (e me'"($ #n(#'"n ;e " )" %"#" p$me(#$ "'%") (e 220 ?#n')#($! e!'$)"e!@, e) '$*"($ e-#!%"& 16.000 p"!"e$! p$ m&;#n" ") me!. E) '$!%$ #$ en '$ee! ?2 p$ *!@ e! (e 8.000.000 ") me!, m&! n" '$m#!#n +"#"*)e ;e e;#+")e " 20 p$ p"!"e$ e-#!%"($. A(#'#$n")men%e !e (e*e& p"-" -"#%e$!, n !pe+#!$, "!e"($e!, !e+#'#$ (e '$n%"*#)#("(, e%'., ;e '$!%"&n en %$%") 2.5 2.500 00.0 .000 00 ") me!. me!. E) '$!% '$!%$$ p$me p$me(# (#$$ en '$m* '$m*! !%#%#*) *)ee !e& !e& (e 1.0 1.000 00.00 .0000 p$ p$ m&; m&;#n #n"Fm "Fme! e! en m"n%en#m#en%$ '#("($ (e )$! *!e! !e -"!%"&n 5.000.000 men!")e! en %$%"). A(em&! !e e!%#m" n '$!%$ p$ #mpe+#!%$! (e 2.000.000.
/"" n'#$n" ") #n#'#$ (e '"(" "$ )" empe!" %en(& ;e p"-" 20.000.000 p$ pem#!$ "n") (e '#')"'#n "n%#'#p"("men%e 2.000.000 men!")e! p$ '$n'ep%$ (e !e-$!. Re;e#& %"m*#n 500.000 (#"#$! p$ '$n'ep%$ (e '$m*!%#*)e! +e)%$! ") #n#'#$ (e '"(" (<" (e*e& p"-" //: e;#+")en%e! ") 1 (e !! #n-e!$! *%$! men!")e!. L" empe!" e!%& "e'%" " n #mpe!%$ (e p#me" '"%e-$<" (e) 15 !$*e )"! %#)#("(e! ") #n") (e '"(" "$. L" )$'$m$'#n '$)e'%#+" e!%& een%" (e IVA ?p$ )$ ;e e) IVA e! n '$!%$ p"" )" empe!"@. EL '$!%$ (e $p$%n#("( (e) (#ne$ p"" )" empe!" e! (e n 14 e") "n"). Sp$n-" ;e %$($! )$! +")$e! en%e-"($! !e m"n%en(&n en %m#n$! e")e! p$ )$! 10 "$! ;e (" e) p$e'%$. =e%em#n" Sp$n#en($ ;e, " #-")("( (e '$!%$!, e) p#me me! )$! *!e! ))e+"n )" m#%"( (e p"!"e$! ;e e) e!%$ (e) "$, '")')e e) '"p#%") (e %"*"$ ne'e!"#$ p"" e) n'#$n"m#en%$ (e )" empe!". C")')e e) )$ (e '"" (e) p$e'%$ (e n" e'$men("'#n !$*e )" '$n+en#en'#" p"" )" empe!" (e e")#>")$. S# ") #n#'#$ (e) p$e'%$ )" empe!" pe(e '$n!e-# n p!%"m$ p$ 500.000.000, p"-"(e$ en 4 '$%"! "n")e! #"! " n" %"!" (e) 10 e") "n") n pe<$($ (e -"'#". BLe '$n+#ene e")#>" e) p$e'%$. C"n%##;e e) ee'%$ (e) p!%"m$. BCm$ '"m*#" )" '$n+en#en'#" (e) p$e'%$ !# !e pe(e '$n!#(e" ;e e) p$e'%$ !e epe%#& (e m"ne" #n(e#n#(" en #-")e! '$n(#'#$ne! " )"! (e!'#%"! en )" p"%e ?"@. C"n%##;e e) ee'%$. Sp$n-" ;e e#!%en 2 p$!#*)e! *!e! " !e '$mp"($! p"" e) p$e'%$ m#'$*!e$. L$! ("%$! e)e+"n%e! (e "m*$! !e pe!en%"n "n )" !#-#en%e %"*)" #p$ J!
C"p"'#("( ?/"!"e$!@
100 100
A J
V")$ J! ?:@ 60.000 50.000
C$!%$ %$%") "n") ?:@ 22.000 25.000
V#(" \%#) ?"$!@ 10 8
V")$ Re+en%" ?:@ 18.000 12.000
=e!pe'#"n($ =e!pe'#"n($ e) "n&)#!#! "n&)#!#! #mp$!#%#+$ #mp$!#%#+$ !p$n#en($ !p$n#en($ ;e en '");#e '"!$ e) p$e'%$ (e )$! *!e! !e pe(e epe%# #n(e#n#("men%e. B *! pee#<". BC&n%$ me$ e! ! ")%en"%#+" e)e-#(". !%##;e ! e!pe!%".
10.1. Solución
In+e!#n G"#%"!
20000
IVA 3600
=ep 2360
*! '$*"($ $%")
V")$
1000000 100000 1120000 30 336000
180000 18000 201600
118000 11800 132160
"@ CA/IAL :en!") /em#!$! Se-$!
20000 2000 0
In-e!$! C"p (e %"* Ope"'#n O%$! //:
2
35200
70400
70400
43900 2000 352
43900 2000 704
43900 2000 704
11052 33552
23796 12744
23796 47592
500 22000
$%") A'm)"%#+$!
22500
N*$)e%$! pe'#$ :e!e! C+"
16000 220 12 20
C$!%$! #$! C$ee! $%$! C$m*!%#*)e :"n% Impe+#!%$! C$m#!#$n
p$ m";
320
%$%") me! 8000 2500 20000 5000 2000 6400
%$%") "$ 96000 30000 240000 60000 24000 76800
p$ m"; 42240
43900 %$%") 844800
450000 p$ me! 70400
0
1
1000
$%") In-e!$!
1
*@ D)$ (e C"" In-e!$! G. =e C"p C$!%$! 1 /em#!$! =epe'#"'#n /EA U*%"!
844800
844800
450000 44000 132160
450000 44000 132160
10 844800 336000 450000 44000 132160
218640
218640
554640
Impe!%$ U Ne%"! =ep /EA G. =e '"p D (e '"p In+e!#n Re+en%" C"p (e %"*
1120000
DC
1153552
32796 185844 132160
32796 185844 132160
83196 471444 132160
0 0
0 0
0
318004
318004
336000 267604
201600 336000 33552
33552 116404
318004
637156
V/N?14@
414440,8 14
'@ n
0,1
"! /e!%"m$ C$%" In%ee! Am$%#> S")($ #n!$)%$
2,8816958 500 173,50894
4
173,508942 105 68,5089420 431,491058
500
173,508942 43,1491058 130,359836 301,131221 7
173,508942 30,1131221 143,395819 157,735401 9
L$! #n%ee!e! !$n men$e! ;e )"! %#)#("(e! *%"!, p$ %"n%$ (e!'en%"n #mpe!%$! (e)%" V/N
165,807871 ::
(@ ' V/N *"e V/S me$" en en
0,19171354 414440,811 79453,9153 567527,966 153087,155
e@ ?:@ A J
C"p"'#("( 100 100 JUS A
V")$ 60.000 50.000
C$!%$ "n") 22.000 25.000 *! J
V#(" %#) 10 8
V")$ 18.000 12.000
173,508942 15,7735401 157,735401 0
+pn '#')$ ' CAUE V/C IND
14 169899,155 0,19171354 32571,9687 232656,919
me $ $ " en
22899,4851
14 165968,7929 0,215570024 35777,89663 255556,4045 :
11. 11. CL'NICA ( NUEVO E$UIPO En $'%*e (e 1997, n -p$ (e m(#'$! #n+e!#$n#!%"! #n"- n" ne+" ')"(" e (e US 300.000 en "'%#+$! #$! US 150.000 en '"p#%") (e %"*"$. En )$! ($! "$! e'#n p"!"($!, )" ')
USFA]O 450.000 250.000 30.000 60.000 70.000 40.000 6.000 34.000
/$ )"! p$e''#$ne p$e''#$ne!! (e) me'"($ (e )" !")( )"! '""'%e
p"-"(e$ en )$! %e! p#me$! "$! (e $pe"'#n '$n "m$%#>"'#$ne! (e US 100.000 "n")e! n" %"!" (e #n%e! (e) 10 "n") en ()"e!. "@ C$n!%# C$n!%# e) )$ (e '"" (e) p$e'%$ (e 'e"'#n (e) Se+#'#$ Se+#'#$ (e :e(#'#n" N')e" N')e" en )" ')$n%e (e e+")"'#n e! e) pe#$($ $'%*e 1999 " !ep%#em*e 2003. *@ S# e) '$!%$ (e $p$%n#("( $p$%n#("( (e) (#ne$ (#ne$ p"" )" !$'#e("( !$'#e("( (e m(#'$! (e$! (e )" ')$ne!.
11.1. Solución a) Flujo de Caja del servicio de Medicina Nuclear. 0 + + = = + + = + + + = =
Ingresos Costos !eracionales %ueldo Médicos &astos Financieros &anancias de Ca!ital 'e!reciaciones (egales Pérdidas jercicio +tilidad ,ruta Im!uestos /1$) +tilidad Neta Pérdidas jercicio 'e!reciaciones (egales &anancias de Ca!ital Flujo de Caja Operacional Muina rans5ormaciones 6alor 7esidual Ca!ital de ra8ajo 7ec. Ca!ital de ra8ajo Crédito *morti9aciones Flujo de Capitales Flujo de Caja
1 344000 "#$000 "4#000 "30000 "133333.33
2 344000 "#$000 "4#000 "20000
"133333.33
3 344000 "#$000 "4#000 "10000 300000 "133333.33
4- 4-. ."-1$0.000$ 40$1 40$1. .
$- $-. ."#$0.000$ 401 401. .
3- 3- .." 312$ 312$1 1. .-
133333.33 1 73850
13 133333.33
1 33 33333.33 "300000 14585 0
182 350
"400000 "20000 300000 "30000
30000
300000 -1 50000
"100000 -1 0 00 00
"100000 -1 00000
"100000 23000 0
-1 50000
7 3 8 4 9 .9 9 9
8 2 3 4 9 .9 9 9
37585 0
8) %e de8e calcular el 6PN del Pro:ecto al 12 6PN ; 2410.02 <0 Por lo tanto= conviene invertir !orue el 6PN < 0= es decir= aumenta nuestra riue9a.
12. ERRORES EN FC VERSIÓN 2 Un '$)e-" #n-en#e$ e!%(# n ne-$'#$, #>$ e) '$e!p$n(#en%e )$ (e '"", '")') e) V/N '$n') ;e n$ )e e! '$n+en#en%e. C$m$ e!%& '$n!'#en%e ;e %#ene +"'<$! en e!%e &m*#%$, !e "'e'" " U(., )e p#(e ;e )$ e+#!e, ;e )$ '$#" )e ( ! e'$men("'#n. E) )$ (e '"" (e ! '$)e-" e! e) !#-#en%e In-e!$! Ope"'#$n")e! 588 788 988 Ven%" (e A'%#+$! 1.000 C$!%$! Ope"'#$n")e! 386 386 386 =epe'#"'#n 280 280 280 U%#). An%e! (e Impe!%$! Impe!%$! ?15@ U%#). =e!p. (e Impe!%$! =epe'#"'#n
?78@ ?12@ ?66@ 280
122 18 104 280
1.322 198 1.124 280
/!%"m$
600
/"-$ /!%"m$
260
240
220
In+e!#n C"p#%") (e "*"$
1.240 360
D)$ (e C""
?1.000@
?46@
144
1.184
V/N?@ M M
?131@ 14
Se p#(e I(en%##'" )$! e$e! (e) )$ (e '"" (e) '$)e-". H"'e e) )$ '$e'%$. H"'e n" e'$men("'#n " p"%# (e )$! ne+$! e!)%"($!.
12.1. Solución "@ E$e E$e! ! N$ (#!%#n-e en%e D)$ Ope"'#$n") D)$ C"p#%")e! :e>')" Am$%#>"'#n '$n G"!%$! D#n"n'#e$! N$ %$m" en '$n!#(e"'#n )" e'pe"'#n (e) C"p#%") (e "*"$ C")')" #mpe!%$ " %#)#("(e! ne-"%#+"! N$ '$)$'" G"n"n'#" (e C"p#%") N$ '$)$'" /(#(" (e Ee'#'#$ An%e#$ *@ D)$ D)$ (e C"" C"" 0 + + = = + + =
Ingresos !eracionales Costos !eracionales &astos Financieros &anancias de Ca!ital 'e!reciaciones (egales Pérdidas jercicio +tilidad ,ruta Im!uestos /1$) +tilidad Neta Pérdidas jercicio 'e!reciaciones (egales &anancias de Ca!ital Flujo de Caja Operacional
+ + + =
Inversi>n 6alor 7esidual Ca!ital de ra8ajo 7ec. Ca!ital de ra8ajo Préstamo Pago Préstamo Flujo de Capitales
1 $## "3# "0
2 -## "3# "40
"2#0
"2#0 "13# "$
"13#
"13# 2#0 142
"$ 13# 2#0 32
3 ## "3# "20 00 "2#0 "$ #4 "12. -1.1 $ 2#0 "00 455.1
"1240
1000
"30 30 00 -1000
"200 -200
"2 "200 -200
"2 "200 110
=
Flujo de Caja
-1000 6PN ; 13.2304
-58 <0
12
115.1
'@ Re'$men("'#n C$m$ V/N 0 en%$n'e! '$n+#ene "'e e) p$e'%$.
13. GERENTE ( NUEVO E$UIPAMIENTO E$UIPAMIENTO E) -een -een%e %e (e n" emp empe! e!"" (e(#' (e(#'"(" "(" " )" #n$ #n$m m&% &%#' #'"" e'#* e'#*# # )" $e $e%" %" (e n ne+$ ne+$ e;# e;#p"m p"m#e #en% n%$$ '$mp '$mp% %"' "'#$n #$n") ") ;e ;e )e pem pem#%#%##<" <" "men% "men%" " !! !! +en% +en%"! "! e(' e('## en ")-$ ")-$ !! !! '$!% '$!%$! $! (e $pe" $pe"'# '#n n m"n%en'#n. En e) pe!en%e, !! e;#p$! +")en US 80.000, !! +en%"! ))e-"n " 100.000 USF"$ )$! '$!%$! (e $pe"'#n m"n%en'#n "!'#en(en " 20.000 USF"$. =e '$n%#n" '$n )$! e;#p$! "'%")e!, )"! +en%"! '"e&n " US 95.000 en e) "$ p#m$ " US 90.000 en e) "$ !#-#en%e. L$! '$!%$! 'e'e&n " 26.000 32.000, e!pe'%#+"men%e. E) E) +")$ '$me'#") (e !! e;#p$! "'%")e! *""& " US 50.000 en n "$, " US 20.000 en ($! "$! %en(&n +")$ n)$ ") %e'e "$. En e!e m$men%$, "*& ;e eemp)">" )$! e;#p$! (e %$($! m$($!. L$! ne+$! e;#p$! +")en, en e!%e m$men%$, US 150.000. Se !"*e ;e e!%e pe'#$ #& e('#n($!e en n 15 '"(" "$. L" +#(" %#) (e e!%$! e;#p$! e! (e 5 "$!, ") '"*$ (e )$! '")e! e) +")$ e!#(") !e e!%#m" ;e !e& n 20 (e) +")$ (e "(;#!#'#n. L$! '$!%$! (e $pe"'#n m"n%en'#n (e )$! ne+$! e;#p$! !e e!%#m"n en US 16.000 e)p#me "$ !e e)e+"&n " 18.000, 20.000, 24.000 28.000 en )$! "$! !#-#en%e!. C$n )$! e;#p$! ne+$!, e) Geen%e e!%#m" ;e !! +en%"! "men%"&n " 110.000 USF"$. L" %"!" (e (e!'en%$ p"" )" empe!", )#*e (e #mpe!%$! e! (e 12. BRe'$men("" )$! "'%")e! e;#p$! S# ! e!pe!%" e" p$!#%#+", B'&n($ e'$men("<" "'e)$. !%##;e !! e!pe!%"!.
14. EMPRESA DE SERVICIO DE ALIMENTACION ALIMENTACION Un #n+e!#$n#!%" e!%& e+")"n($ )" '$n+en#en'#" (e $m" n" empe!" (e !e+#'#$ (e ")#men%"'#n m"!#+" " empe!"! en n eme-en%e !e'%$ #n(!%#") (e )" e-#n me%$p$)#%"n". E) !e'%$ en ;e !e e")#>"<" e) !e+#'#$ !e en'en%" +"#$! #)me%$! (#!%"n%e (e )$! "'%")e! 'en%$! (e $e%", p$ )$ ;e e) !e+#'#$ (e ")#men%"'#n (e )$! emp)e"($! !e " %"n!$m"($ en n p$*)em" e)e+"n%e p"" )"! empe!"! ;e !e "n #n!%")"($ )"! nme$!"! ;e !e e!pe" !e #n!%")en en e) me(#"n$ p)">$ en e) )-". L" empe!" " '$n%emp)"($ (" )$! !e+#'#$! (e en%e-" (e ")#men%$! en+"!"($!, %"n!p$%e (e ")#men%$! " -"ne) )" '$n'e!#n (e '"!#n$! en e) '"!$ (e empe!"! m"$e!. A p"%# (e e!%" )$! (e '"(" "$ I%em In-e!$! /e!$n")
A$ 1
A$ 2
A$ 3
A$ 4
A$ 5
"n%#'#p" 0 10
80.000 35.000
233.000 60.000
418.000 85.000
504.000 95.000
523.000 95.000
In!m$! G"!%$! *&!#'$! -ene")e! :"n%en#m#en%$ (e e;#p$!, $%") G"!%$!
10 0 5
41.000 7.000 2.500
120.000 18.000 5.000
210.000 21.000 6.500
250.000 23.000 7.000
260.000 22.000 7.500
85.500
203.000
322.500
375.000
384.500
E) "#en($ (e) )$'") 'e!%" 1.000 : men!")e!, !e (e*e '"n'e)" "n%#'#p"("men%e, n%$ '$n n me! (e -""n%<". E) %een$ en %"n%$, 'e!%" 100.000 :. E) '$!%$ (e $p$%n#("( (e) (#ne$ p"" e) #n+e!#$n#!%" e! (e) 15 e") "n") )" %"!" ( e #mpe!%$ " )"! %#)#("(e! (e )" emp e!" e! 17. /"" e) ne-$'#$ !e e;#een e")#>" )"! !#-#en%e! #n+e!#$ne! ?" #ne! (e '"(" "$@ P%em
V#(" %#) 30 10 10
C$n!%''#n E;#p"m#en%$ C$'#n" E;#p"m#en%$ '$me($e! O%$! e;#p$! Ve<')$! $%") #n+e!#n
A $0
A $1 80.000 20.000 20.000 3.000 5.000 128.000
15.000 5.0 6.0 5.000 31.000
3 5
A $2
A $3
5.0 5.0
V")$ e+en%" e +en%" ?en "$ 5 en 70.000 30.000 5.000 1.000 5.000 110.000
C$n e!%" #n$m"'#n !e p#(e
50C8 50C8<8 <8? ? 78 </ </9 988 >7 ?B ?B 7<7? 7<7?9 9 /? 78 <9 <9; ;97 97 >78 /?7< /?7< 79; 79;? ? 8 8 >7 < >78 /?7< /97> ?9:7 >7 78<9 >7 5 , K7 <> 8 8 >7 < /99, 8 >7 8 ?79? 8 98 >78 . R7<;7>? 8 77<<9 >78 /?7< 8 97?99. P?KQ. B 10 S9 8 98 98 >78 /?9;7? /?9;7? 87 ?7<7 ?7<7 /?Q; /?Q; /? /? 9<9? 9<9? 8 97? 97?9 9 /? 200.00 200.0000 M /@>7? 7 3 < 9@87 < 1 >7 @?<9 >78 12 ?78 8 <7>? ;? 78 /?Q;. C99K7 78 77< >78 /?Q; 7 78 VAN >78 /?7<. < 10 C; C; 77 7 @? @? >7 >7 /? 78 7;/?7 7;/?7?9 ?9,, 87 8 89<9 9<9 K7 87 7/89 7/89K7 K7 <; <; />? />? ?789:? =899 >7 7<7?9 ?7/7< 77 7@<9. > 15 E8 7;/?7?9 7;/?7?9 7 77?> K7 797 78 ?97@ 97;=9<, 97;=9<, 7= 7@? >7 K7 8 >78 15 7 8 <??7< /? >7<? 8 8. P? 8 7 87 /9>7 7> K7 7 B7 8 9@977 /7, ?7<8<87 8 >7 >7<7. S/7 • R: >7> /?9;9 0.6 • T 89B?7 >7 ?97@ ", >7 ;7?<> 10. • *7 >78 /?9;9H0.". /?9;9H0.". • T >7 8 >7> 12 ?78 8. 7 15 S9 78 /?7< /?7< 7? ?7/79B87 ?7/79B87 999 999;7 ;77, 7, 9@7 9@7 97> 97> ?7B87, ?7B87, <8<878 <8<878. . P7I'
0
'atos del ui!o *ctual 6entas Costos 6alor #0 'atos del ui!o Nuevo 6entas Costos 6alor 1$0 Inversi>n 7eem!la9ar *?ora@ 6entas Costos 6alor 1$0 Inversi>n
1
2
3
20 0
$ $ 2 30
0 32
110
110
1
1#
110
1
100
4
$
110
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0
-
#
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1. EMPRESA RU*RO RU*RO VIDRIO ( *OTELLAS Un" empe!" en e) *$ (e) +#(#$ %#ene en '"pe%" n p$e'%$ ;e '$n!#!%e en )" "*#'"'#n (e *$%e))"! (e ")%" '")#("( p"" +#n$ (e ep$%"'#n. /"" e))$, p)"ne" %#)#>" n" %e'n$)$-<" (e "*#'"'#n e$pe", )" ;e !e $*%#ene " %"+! (e )" '$mp" (e n" "n;#'#". L" #n+e!%#-"'#n (e e!%e me'"($ #n(#'" ;e !e p$(<"n +en(e 20.000 *$%e))"! ("n%e )$! p#me$! '"%$ '"%$ "$! (e $pe"'#n, 28.000 en%e e) ;#n%$ $'%"+$ "$ 30.000 n#("(e! p"" e) n$+en$ e) ('#m$. /$ $%" p"%e, !e e!%#m ;e e) pe'#$ (e +en%" !e<" (e 580 )" n#("(. E) p$e'%$ '$n!#(e" '$n%"%" n -p$ (e +en(e($e!, ;e e'#*#&n n" '$m#!#n (e) 1,5 (e )"! +en%"!. E) e!%(#$ %'n#'$ #n(#'" ;e p"" )$! n#+e)e! (e p$(''#n !e")"($!, )$! '$!%$! n#%"#$! !e<"n )$! !#-#en%e! Insu
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17.1. Solución
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:$n%$ UD ?S#n/)">$ IVA@ ?(<"!@ 160 90 30 0 70 30 90 60 50 60 120 60 250 90 90 30 50 30 180 60 90 30 100 60 250 90
C$mp"! p"-$D"'%"! '$*"n>" 250 315 327 374 413 451 490 528 567 605 644
Em#!#n 30Sep 30Sep 30Sep 30O'% 30O'% 30O'% 30N$+ 30N$+ 30N$+ 30=#' 30=#'
:$n%$ UD ?!#n/)">$ (e p"-$ IVA@ ?(< 100 0 50 30 80 30 200 0 50 60 120 60 120 90 90 30 50 30 150 60 80 30
525 526 527 528
30=#' 30=#' 30=#' 30=#'
160 210 50 300
30 60 0
60
NN " !"*#en("! (e )$! '$n$'#m#en%$! ;e U(. " "(;##($ en )"! )%#m"! ')"!e! )e " pe(#($ " !%e( ;e '")')e )$! e;e#m#en%$! (e '"p#%") (e %"*"$ ;e %en(& p"" e) '$m#en>$ (e )" $pe"'#n ;e, !p$n#en($ !p$n#en($ ;e e!%e <?9;7?7 !e ep#%e ("n%e )$! 5 "$! (e $pe"'#n (e )" empe!", empe!", '")')e e) )$ (e '"" "n") p"" %$(" )" $pe"'#n. N$%" NN e!%& "e'%" ") #mpe!%$ (e p#me" '"%e-$<" (e) 15 , p$ !#mp)#'#("(, !p$n-" ;e e) IVA e! (e) 20, !e p"-" e) (<" 1` (e '"(" me!, ;e )" (e')""'#n (e #mpe!%$ " )" en%" !e ee'%" e) (<" 31 (e )#$.
20. EJERCICIO CON *ALANCE C")')" e) )$ (e '"" " p"%# (e )$! !#-#en%e! ("%$! A$
0
=ESE:JOLSO
22.000
1
2
3
4
5
3.000
3.500
3.800
4.000
4.500
1.000
1.500
2.000
2.000
2.500
INGRESOS
30.000
GASOS
20.000
ACIVO CIRCULANE
1.500
/ASIVO CIRCULANE
E) pe'#$ (e +en%" !*#& "n")men%e n 5, m#en%"! ;e )$! '$!%e! !e #n'emen%"&n n 3 )$! ($! p#me$! p#me$! "$! n 2 )$! !#-#en%e!. !#-#en%e!. L" "m$%#>"'# "m$%#>"'#nn !e& )#ne") $*%en#en($ $*%en#en($ n +")$ e!#(") e!#(") #-") ") 10 (e) '$!%e. L" %"!" #mp$!#%#+" "!'#en(e ") 35.
21. EMPRESA INVERSIÓN AF Un" empe!" +" " #n+e%# en n$! e)emen%$! (e "'%#+$ #$ 160.000 .m.. Se e!pe" ;e en "$ 4 %en-"n n +")$ e!#(") (e 40.000 .m. E) !#!%em" (e " m$%#>"'#n ;e !e-#& )" empe!" e! e) )#ne"). L"! +en%"! e!pe"("! (e) p$('%$ ;e +" " "*#'" !$n )"! ;e #-"n en e) !#-#en%e '"($
Ven%"! e!pe"("! A$ 1
100
A$ 2
120
A$ 3
150
A$ 4
160
E) pe'#$ (e +en%" p"" e!%e "$ e! (e 2.100 .m. )" empe!" #n'emen%"& !! pe'#$! n 4 en e) !e-n($ "$ n 3 en )$! "$! %e'e$ '"%$. L" empe!" p"" "*#'" !%e p$('%$ ne'e!#%"& '$mp" 3 %#p$! (e m"%e#" p#m", ! '$n!m$ !e& e) !#-#en%e
:"%e#" p#m" 1 ?(!. :"%e#" p#m" 2 ?(!. :"%e#" p#m" 3 ?(!.
40.000 25.000 15.000
A(em&! ne'e!#%" '$mp" epe!%$! p$ +")$ (e 20.000 .m., em*")"e! p$ 1.000 .m. en+"!e! p$ 2.500 .m.. L$! p$+ee($e! "men%"&n e) pe'#$ (e e!%$! "'%$e! p$('%#+$! n 2,5 e) !e-n($ "$ n 2 en )$! !#-#en%e! "$!. L$! !")"#$! " p"-" e) p#me "$ !e<"n )$! !#-#en%e!
A(m#n#!%"%#+$! =#e'%#+$! Ope"#$!
5.000 15.000 1.000
E!%$! !")"#$! !e #n'emen%"&n n 3 "n"). A )$! (#!%#*#($e! !e )e! p"-"& n"! '$m#!#$ne! (e) 10 !$*e e) +$)men (e +en%"!. A(em&! !e '$n$'en )$! !#-#en%e! -"!%$! -ene")e! L> e)$n$ C$m*!%#*)e! :"%e#") (e $#'#n" "n!p$%e! A-" O%$!
6.000 2.000 2.600 1.000 3.000 1.500 1.000
E!%$! -"!%$! %en(&n n "men%$ pe+#!%$ (e) 1 '"(" "$. "m*#n !e '$n$'en )$! e!%"($! pe+#!#$n")e! (e A'%#+$ /"!#+$ C#')"n%e! !$n )$! !#-#en%e!
ACIVO CIRCULANE EXISENCIAS CLIENES ESORERPA /ASIVO CIRCULANE CIRC ULANE /ROVEE=ORES HACIEN=A
A]O 0
A]O 1
A]O 2
A]O 3
A]O 4
25000 19000
30.000 110.000 19.053
32.130 113.333 19.435
34.411 121.380 19.823
28.000 129.998 20.220
48.000 12.000
50.220 13.107
52.814 19.814
55.572 27.232
C$n e!%$! ("%$!, !e (e!e" '$n$'e )$! )$! (e '"" (e) p$e'%O
22. CALCULE CALCULE PUNTEADO " C$n!#(ee e) !#-#en%e p$e'%$ '$n )"! !#-#en%e! '""'%e
p#m$! ($! "$! " p"%# (e) ;#n%$ "$ !e pe!en%" n e%e #n'emen%$ (e )"! +en%"! p$ )$ ;e !e +en(en 60,000 n#("(e! "n")e!. E) e!%(#$ (e (em"n(" '$n') ;e e) pe'#$ (e +en%" ("n%e )$! ($! p#me$! "$! !e& 500, p$!%e#$men%e !*#& " 600. L"! #n+e!#$ne! e;e#("! !$n een$! 12,000,000Q O*"! D" '"(" 6 "$!, pe'#$ (e +en%" 2,500,000. /"" p$(e p$('# )"! m"$e! n#("(e! " p"%# (e) '"%$ "$ !e e;e#& n" #n+e!#n "(#'#$n") en O*"! D"'#n (e A'%#+$! In%"n-#*)e! e! en 5 "$!. L$! -"!%$! -"!%$! (e pe!%" en m"'" m"'" "!'#en(en " 2,000,000. Se %$m" n )e"!#n- p"" )" m";#n"#" ;e +")e 38,000,000 p"" n p)">$ (e 8 "$! " n" %"!" (e 10 "n"). A!#m#!m$ !e %$m" n p!%"m$ (e 40,000,000 p"" n p)">$ (e 8 "$! " n" %"!" (e 8 "n"). In+e!#n en '"p#%") (e %"*"$, 6 me!e! (e) '$!%$ %$%") (e!em*$)!"*)e ?n$ '$n!#(e" -"!%$! #n"n'#e$! n# e) )$ (e) )e"!#n-@. Se !"*e ;e " p"%# (e) $'%"+$ "$ )"! %#)#("(e! (e )" empe!" !e&n e!%"*)e!. Sp$n-" ;e )" empe!" n$ %em#n" (e $pe" ") %m#n$ (e )$! 8 "$! (e) $#>$n%e (e e+")"'#n. L" "!" "!" (e Impe!%$! " )"! %#)#("(e! e! 17. L" %"!" (e (e!'en%$ e! 10.
Se p#(e ;e '")')e e) )$ (e '"".
23. PROPUESTA PROPUESTA MA$ MINERA MINERA /1@ U(. e! $ n p!pe$ empe!"#$ en e) ne-$'#$ (e Imp$%"'#n +en%" (e :";#n"#"!. E!%e ne-$'#$, ;e !e en'en%" en 'e'#m#en%$, )e -ene" n" en%"*#)#("( (e) 15. S#n em*"-$, en e) )%#m$ %#emp$ !e "n
-ene"($ ne+"! $p$%n#("(e! (e ne-$'#$ ;e U(. pe%en(e e+")", n" (e e))"! e! en%" en e) ne-$'#$ (e "#en($ (e m";#n"#"! p"" empe!"! m#ne"!. L" C$mp"<" :#ne", e!%& (#!pe!%" " en%e-")e n '$n%"%$ '$n )"! !#-#en%e! '""'%e
(@
"@ U(. Le en%een%e-" "<" <" en " "#en #en($ ($ n" m&;# m&;#n" n" p$ 32 UDFm UDFme! e!,, m&! m&! #mpe #mpe!% !%$! $!.. *@ L" m&; m&;#n #n"" (e*e (e*e !e !e " "en en("( ("("" '$n '$n n $pe $pe" "#$ #$,, e) ;e ;e e'# e'#*e *e n n !")" !")"##$$ (e 300 300.0 .000F 00Fme me!. !. '@ L$! L$! '$!% '$!%$! $! (e '$m* '$m*! !%#%#*)e *)e!! (e $pe $pe"' "'# #nn (e )" m&;# m&;#n" n" !e& !e&nn "!m "!m#($ #($!! p$ p$ )" '$m '$mp" p"< <"" m#ne m#ne". ". E! $*)#$*)#-"'# "'#n n (e) '$n% '$n%"%$ "%$ m"n%ene m"n%ene en p%#m$ p%#m$ n' n'#$n #$n"m# "m#en% en%$$ )" m&;#n m&;#n"" "en("( "en("(", ", p"" p"" )$ ;e ;e !e )e e#e#-ee %$m" n aC$n%"%$ (e :"n%en'#na p$ 3 UDFme!. e@ E) '$n% '$n%" "%$ %$ '$n '$n )" )" '$m '$mp" p"< <"" m#n m#ne e"" ;e ;e U(. U(. #m #m" "&, &, e! p$ p$ 5 "$ "$!. !. L" m&;#n" ;e U(. "en("<", %#enen n V")$ Ne%$ pe!%$ en ! *$(e-" (e US35.000 n$m")men%e !%e( )"! +en(e " US50.000 '"(" n". L" V#(" U%#) ;e !e '$n!#(e" p"" e))", e! (e 7 "$!. Se e!%#m" ;e e) V")$ Re!#(") ") ;#n%$ "$ !e& (e) 10 (e) +")$ $#-#n"). L"! m&;#n"! !$n "(;##("! '$n C"p#%") /$p#$. L" %"!" (e #mpe!%$! +#-en%e e! (e) 15 !$*e )"! %#)#("(e!.
In(#'"'#$ne! V")$ UD 16.000 V")$ =)" 700 =epe'#"'#n L#ne") "!" (e In%e! (e ( e =ep!#%$! " /)">$ 7 "n").
2.1. Solución
In-e!$! 32 UD 12 M 384 UDF"$ G"!%$! en Ope"#$ 300.00012F16.000 ?UDF@ M 225 UDF"$ C$!%$ Re)e+"n%e (e) e;#p$ p"" (e#n# )" In+e!#n M US 35.000 0 1531,3 UD. UD. V")$ Re!#(") U3.500 M B153,1 UD ") "$ 7. =epe'#"'#n M ?35.000 3.500@ F 7 M US 4.500B M 196,9BUD E) "'%#+$ !e p$(<" +en(e ") #n") (e) "$ 5 en e) V")$ Re!#(") m&! e) +")$ ;e ;e(" p$ ($! "$! (e $pe"'#n M 2196,9 153,1B M546,9YYD "!" (e (e!'en%$ " "p)#'" M 15 1 5
Re!pe'%$ " )$! #mpe!%$!, ("($ ;e " p(#(" %$($! )$! me!e!, n$ !e p"-". En
Ingresos &asto !erario &astos de Manteci>n 'e!reciaci>n +tilidad antes Im!. Im!uesto +t. des!ues de Im!. 'e!reciaci>n Pérdida de Ca!ital Flujo !erativo Inversi>n 6alor 7esidual Flujo de Ca!itales Flujo de Caja Flujo *ctuali9ado 6*N
/e!$! 0
1
0 0 0 0 0 0 0 0 0 0 " 0 " " " "
.144.0 " " " " 0 " 3.1$0.4 0 1.#.0 0 0 1.#.0 1.-11.30
Im!uesto
0=1$
asa 'cto
0=1$
2
3
4
$
.144.000 " "$-.000 " " 0 " 3.1$0.400 0 1.#.000
.144.0 " " " " 0 " 3.1$0.4 0 1.#.0
.144.0 " " " " 0 " 3.1$0.4 0 1.#.0
.144.000 "3.00.000 " "3.1$0.400 "1.1#2.400 0 "1.1#2.400 3.1$0.400 0 1.#.000
0 0 1.#.000 1.4##.01
0 0 1.#.0 1.23.
0 0 1.#.0 1.12$.2
#.-$0.400 #.-$0.400 10.-1#.400 $.32#.3
3
4
En UD 0 Ingresos &asto !erario &astos de Manteci>n 'e!reciaci>n +tilidad antes Im!. Im!uesto +t. des!ues de Im!. 'e!reciaci>n Pérdida de Ca!ital Flujo !erativo Inversi>n 6alor 7esidual Flujo de Ca!itales Flujo de Caja Flujo *ctuali9ado 6*N
0= 0= 0= 0= 0= 0= 0= 0= 0= 0= "1$31=30 0= "1$31=30 "1$31=30 "1$31=30 "#4-=0#
Im!uesto
0=1$
asa 'cto
0=1$
1
2
$
3#4=00 "22$=00 "3=00 "1=0 "-3=0 0=00 "-3=0 1=0 0=00 123=00
3#4=00 "22$=00 "3=00 "1=0 "-3=0 0= "-3=0 1=0 0= 123=00
3#4=00 "22$=00 "3=00 "1=0 "-3=0 0= "-3=0 1=0 0= 123=00
3#4= " " " " 0=00 " 1= 0=00 123=
3#4=00 "22$=00 "3=00 "1=0 "-3=0 0=00 "-3=0 1=0 0=00 123=00
0=00 0=00 123=00 10=
0= 0= 123=00 3=01
0= 0= 123=00 #0=#-
0=00 0=00 123= -0=3
$4=0 $4=0 =0 333=0
24.GALPÓN /"" "'e e) m"n%en#m#en%$, )" empe!" $'p" n -")pn (e ! p$p#e("(, *#'"($ " 2 #)me%$! (e )" p)"n%". E) -")pn %#ene n +")$ '$me'#"), #n')#($ e) %een$, (e 350 m#))$ne!, n +")$ '$n%"*)e ?$ (e )#*$!@ (e 320 m#))$ne! ?80 m#))$ne! e) %een$ 240 m#))$ne! )" '$n!%''#n@. E) -")pn !e '$n!% "'e (#e> "$!, '"n($ !e (e'#(# "'e e) m"n%en#m#en%$ #n%en$, )e e!%" n" +#(" %#) %#*%"#" (e 5 "$!. A(em&!, en e) m"n%en#m#en%$ !e $'p" m";#n"#" )#+#"n" m$*#)#"#$ "(;##($! en 70 m#))$ne! "'e 10 "$!, )$! ;e !e en'en%"n '$mp)e%"men%e (epe'#"($!, pe$ !e p$(<"n )#;#(" " n +")$ '$me'#") (e 20 m#))$ne!. S# n$ !e e%en")#>" e) m"n%en#m#en%$, %"n%$ e) -")pn '$m$ )" m";#n"#" e) m$*#)#"#$ p$(<"n !e-# !#en($ %#)#>"( %#)#>"($! $! p$ 10 "$! m&!. Se e!%#m" ;e ") #n") #n") (e e!e pe<$($, e) -")pn, '$n %een$ #n')#($, !e p$(<" +en(e en 100 m#))$ne!, )" m";#n"#" e) m$*#)#"#$ en n$! 5 m#))$ne!. S# !e e%en")#>", )" empe!" (e*e& p"-" n (e!"'#$ e;#+")en%e " $'$ me!e! (e !e)($ " )$! %"*""($e! ;e (e"<"n (e !e e;e#($! en e) (e!"$))$ (e) p$'e!$ #n%en$. S# )" %"!" (e #mpe!%$! e! (e) 15 )" (e '$!%$ (e '"p#%") (e) 16, (e%em#ne ; '$n+#ene "'e !# e) !e+#'#$ e%en$ 'e!%" 138 m#))$ne! "n")e! e) p$e'%$ !e e+")" en n $#>$n%e (e (#e> "$!.
24.1. Solución 0
G"n"n'#" ?p(#("@ (e '"p#%") :"$ '$!%$ =e!"'#$ pe!$n") m"n%en'#n :en$ :"$ ?men$@ %#)#("( Impe!%$ :"$ ?men$@ %#)#("( ?G"n"n'#"@ p(#(" (e '"p#%") :en$ (epe'#"'#n V")$ e!#(") DLUO =E CAA VAN N$ '$n+#ene e%en")#>" )" m"n%en'#n
1
2
3
4
5
6
7
82
82
82
82
82
82
42 6,3 35,7 50
48 34 5,1 28,9
48 34 5,1 28,9
48 34 5,1 28,9
48 34 5,1 28,9
48 34 5,1 28,9
82 12,3 69,7
12
0
0
0
0
0
0
48
48
48
48
48
0 0
0 0
370 355,7
76,9
76,9
76,9
76,9
76,9
69,7
69
50 8
27,70
"m*#n !e pe(e pe( e e!$)+e en %e! p"!$! 1. DC S#%"'#n S#%"'#n !#n p$e'%$ p$e'%$ 2. DC S#%"'#n S#%"'#n '$n p$e'%$ p$e'%$ 3. =#een'#" =#een'#" ?2@ ?2@ ?3@ 1. DC S#%"'#n !#n 0
G"n"n'#" ?p(#("@ (e '"p#%") C$!%$ =e!"'#$ pe!$n") m"n%en'#n =epe'#"'#n U%#)#("( *%" Impe!%$ U%#)#("( ne%" ?G"n"n'#"@ p(#(" (e '"p#%") =epe'#"'#n V")$ e!#(") DLUO =E CAA
1
2
3
4
5
6
7
56
56
56
56
56
56
56
48 104 15,6 88,4
48 104 15,6 88,4
48 104 15,6 88,4
48 104 15,6 88,4
48 104 15,6 88,4
56 8,4 47,6
8,
0
0
0
0
0
0
48
48
48
48
48
0 0
0 0
0
40,4
40,4
40,4
40,4
40,4
47,6
47
1
2
3
4
5
6
7
138
138
138
138
138
138
138 20,7
138 20,7
138 20,7
138 20,7
138 20,7
138 20,7
20
0 0
0 0
0 0
0 0
0 0
0 0
0 0
117,3
117,3
117,3
117,3
117,3
117,3
11
50
1 0
2 0
3 0
4 0
5 0
6 0
7 0
0
82
82
82
82
82
82
8
0
0
0
0
0
0
48 34 5,1 28,9
48 34 5,1 28,9
48 34 5,1 28,9
48 34 5,1 28,9
0 0
42 6,3 35,7 50
48 34 5,1 28,9
0 0
82 12,3 69,7
12
0
0
0
0
0
0
48
48
48
48
48
0 0
0 0
0 0 0 0
2. DC S#%"'#n '$n 0
G"n"n'#" ?p(#("@ (e '"p#%") C$!%$ =e!"'#$ pe!$n") m"n%en'#n =epe'#"'#n U%#)#("( *%" Impe!%$ U%#)#("( ne%" ?G"n"n'#"@ p(#(" (e '"p#%") =epe'#"'#n V")$ e!#(") DLUO =E CAA
50 8 6,3 35,7 50 0
370 355,7
3. =#een'#" ?2@ ?3@ 0
G"n"n'#" ?p(#("@ (e '"p#%") :"$ '$!%$ =e!"'#$ pe!$n") m"n%en'#n :en$ (epe'#"'#n :"$ ?men$@ %#)#("( *%" Impe!%$ :"$ ?men$@ %#)#("( ne%" ?G"n"n'#"@ p(#(" (e '"p#%") :en$ (epe'#"'#n
V")$ e!#(") DLUO =E CAA
370 355,7
VAN N$ '$n+#ene e%en")#>" )" m"n%en'#n
27,70
0
0
0
0
0
0
0
76,9
76,9
76,9
76,9
76,9
69,7
69
25. AMIGO E INVERSION INVERSION S/@ K7 ;9@ 87 89<9 K7, /?7<> <<9;97 >K9?9> 7 78 <?, 87 <77 B?7 8 <797<9 >7 >7??88? /?7< >7 97?9 K7 87 ?7<9>. L > B?7 9@?7 < 7 /?77 7 78 9@977 <>? In-e!$!?:@ C$!%$! $%")e! ?:@
1
2
3
4
5
6
28.800 25.300
36.000 31.625
64.800 56.925
158.400 139.150
165.600 145.475
172.800 151.800
A!#m#!m$, )" #n+e!#n e;e#(" !e (e!'$mp$ne '$m$ !#-e ?n$ !e e;#een %een$!@
In+e!#$ne!
: ?!FIVA@
V#(" %#) )e-")
V")$ Re+en%" ?: "$ 6@
C$n!%''#n
12.000
30
8.000
:";#n"#" e;#p$!
9.600
8
1.500
Ve<')$!
6.000
6
1.200
Sp$n-" ;e %$($! )$! +")$e! en%e-"($! !$n e")e! ?e;#+")en%e! en UDb!@ ! "m#-$ p$!ee #n+e!#$ne! #n+e!#$ne! (e #-") n#+e) (e #e!-$ ;e )e ep$%"n n" en%"*#)#("( en%"*#)#("( (e) 14 e") "n") e) #mpe!%$ ") ;e e!%& "e'%$ e ! (e n 15.
C")')e e) )$ (e '"" (e) p$e'%$ (e n" e'$men("'#n " ! "m#-$ !$*e )" '$n+en#en'#" (e e")#>" e) p$e'%$. Sp$n-" ;e n$ e#!%en #mpe!%$!.
Solución =e) m#!m$ m$($ ;e en e) e emp)$ 2, (e*em$! '$ne''#$n" n )$ (e '"". E) e!)%"($ $*%en#($ !e me!%" en )" !#-#en%e %"*)" 25.1.
0
!nresos Costos *epreciacione s Capital
+tilidad ,ntes !puestos !puestos '156) +tilidad *espus !puestos *epreciaciones Capital FCO !nersiones #alor residual FCC FC #" '146) !%
1
2
3
4
5
(28 (25 (2
(3 (31 (2
(4 (5 (2
(158 (139 (20
(15 (145 (20
(90 (13 (7 (2
(17 (2 (15 (2
(52 (79 (44 (2
(1 (249 (141 (20
(175 (22 (148 (20
33
41
70
17
174
(172 (151 (20 (830 (101 (151 (858 (20 (830 194
(0 (33
(0 (41
(0 (70
(0 (17
(0 (174
(107 (107 (301
27 (105 276
L$! pn%$! #mp$%"n%e! (e !%e p$*)em" !$n e) '&)')$ (e )"! (epe'#"'#$ne! (e )" G/ (e C"p#%"). Re")#>"em$! e) '&)')$ p"" '"(" n$ (e )$! <%em! (e) p$*)em" p$ !ep""($
C?<<97 E) +")$ (e )$! "'%#+$! "!$'#"($! " !%e <%em ")'"n>" )$! 12.000 c:d ! +#(" %#) e! (e 30 "$!. E) '&)')$ (e )" (epe'#"'#n ?)#ne")@ e! e) !#-#en%e Valor Activos 12.000 Dt = 400[ M ] Años vida útil = 30 =
/"" $*%ene e) +")$ (e )" G"n"n'#" $ /(#(" (e '"p#%") (e !%$! "'%#+$!, e! ne'e!"#$ '$n$'e e) +")$ (e e+en%" (e e!%"!, e) '") en !%e '"!$ e! (e 8.000 c:d. Le-$ !e %#ene
⎛
i
=
t
⎞
Pérdida Capital Capital t = Vt − VRt = ⎜VA − ∑ Di ⎟ − VRt = (12.000 − 6 400) − $.000 = 1.600 [ M ]
⎝
i
1
=
⎠
O$, e! p(#(" (e '"p#%") ?+")$ p$!#%#+$ en e) e!)%"($@, ("($ ;e e) p#me +")$ VL % n$! #n(#'" e) +")$ ;e ?!e-n e) e-#!%$ '$n%"*)e@ (e*e<" %ene !e "'%#+$ e) !e-n($ +")$ VR % e! )$ ;e !%" (#!pe!%$ " p"-" e) me'"($ p$ !e "'%#+$. Le-$, !# e) +")$ e! p$!#%#+$ ?'$m$ en !%e '"!$@ e!%"m$! (#'#en($ ;e e) "'%#+$ %#ene n +")$ '$n%"*)e m&! ")%$ ;e e) ;e e!%&n '"n'e)"n($ p$ e), )$ '") n$! e!%& -ene"n($ n" p(#(" '$m$ empe!".
MK9?9 EK9/ E) +")$ (e )$! "'%#+$! "!$'#"($! " !%e <%em ")'"n>" )$! 9.600 c:d ! +#(" %#) e! (e 8 "$!. E) '&)')$ (e )" (epe'#"'#n ?)#ne")@ e! e) !#-#en%e
Valor Activos ".600 Dt = = = 1.200[ M ] Años vida útil $
/"" $*%ene e) +")$ (e )" G"n"n'#" $ /(#(" (e '"p#%") (e !%$! "'%#+$!, e! ne'e!"#$ '$n$'e e) +")$ (e e+en%" (e e!%"!, e) '") en !%e '"!$ e! (e 1.500 c:d. Le-$ !e %#ene
⎛ ⎞ Pérdida Capital Capital t = Vt − VRt = ⎜VA − ∑ Di ⎟ − VRt = (".600 − 6 1.200) − 1.500 = "00 [ M ] 1 ⎠ ⎝ i
=
i
=
t
En !%e '"!$ %"m*#n e! p(#(" (e '"p#%") ?m$%#+$! ep)#'"($! "n%e#$men%e@.
V7<8 E) +")$ (e )$! "'%#+$! "!$'#"($! " !%e <%em ")'"n>" )$! 6.000 c:d ! +#(" %#) e! (e 6 "$!. E) '&)')$ (e )" (epe'#"'#n ?)#ne")@ e! e) !#-#en%e Valor Activos 6.000 Dt = = = 1.000[ M ] Años vida útil 6
/"" $*%ene e) +")$ (e )" G"n"n'#" $ /(#(" (e '"p#%") (e !%$! "'%#+$!, e! ne'e!"#$ '$n$'e e) +")$ (e e+en%" (e e!%"!, e) '") en !%e '"!$ e! (e 1.200 c:d. Le-$ !e %#ene
⎛
i
=
t
⎞
!anancia Capital t = Vt − VRt = ⎜VA − ∑ Di ⎟ − VRt = (6.000 − 6 1.000) − 1.200 = −1.200 [ M ]
⎝
i
=
1
⎠
O$, e! -"n"n'#" (e '"p#%") '"p#%") ?+")$ ne-"%#+$ en e) e!)%"($@, e!)%"($@, ("($ ;e e) p#me +")$ VL% n$! #n(#'" e) +")$ ;e ?!e-n e) e-#!%$ '$n%"*)e@ (e*e<" %ene !e "'%#+$ e) !e-n($ +")$ VR % e! )$ ;e !%" (#!pe!%$ " p"-" e) me'"($ p$ !e "'%#+$. Le-$, !# e) +")$ e! ne-"%#+$ ?'$m$ en !%e '"!$@ e!%"m$! (#'#en($ ;e e) "'%#+$ %#ene n +")$ '$n%"*)e m&! *"$ ;e e) ;e e!%&n '"n'e)"n($ p$ e), )$ '") n$! !%" -ene"n($ en%$n'e! n" -"n"n'#" '$m$ empe!".
26. EMPRESARIO EMPRESARIO TRANSPORTE TRANSPORTE Un empe!"#$ (e) %"n!p$%e e!%& e!%(#"n($ )" p$!#*#)#("( (e '$mp" $ ($! +e<')$! ;e )e $e'en, '$n #n"n'#"m#en%$ #n')#($, n %e'e$ en ($! "$! m&!. H"!%" e) m$men%$ !)$ " '")')"($ e) D)$ (e C"" (e e!%e p$e'%$, ;e "p"en%emen%e e!%& '$e'%$. L$! ("%$!, epe!"($! en Un#("(e! (e D$men%$ !#n IVA, IVA, !$n )$! !#-#en%e! D)$ (e C"" Ope"'#$n") 0 O O
In-e!$! $pe"'#$n")e! G"n"n'#"! (e C"p#%") C$!%$! $pe"'#$n")e! In%ee!e! (e '(#%$ =epe'#"'#n Le-") /(#(" (e) Ee'#'#$ "n%e#$
1
2
3
4
500
800
1000
286 100 260
336 78,45 260 146
386 54,75 390 20,45
1200 650 386 28,67 390
M M O O M
U%#)#("( (e+en-"(" Impe!%$ " )" Ren%" ?15@ U%#)#("( Ne%" =epe'#"'#n Le-") /(#(" (e) Ee'#'#$ "n%e#$ G"n"n'#"! (e C"p#%") D)$ (e C"" Ope"'#$n")
0 0 0
146 0,00 146,00 260
20,45 0,00 20,45 260 146
148,8 22,32 126,48 390 20,45
1045,33 156,80 888,53 390
0
114,00
385,55
536,93
650 628,53
0
1
2
3
4
D)$ (e C"p#%")e! O O O M
In+e!#n D#" V")$ Re!#(") (e A'%#+$! C"p#%") (e "*"$ Re'pe"'#n (e C"p#%") (e "*"$ /e!%"m$! Am$%#>"'#$ne! D)$ (e C"p#%")e!
1300
650 1300
600 600 1000 900
215,50 215,50
237,05 887,05
260,76 260,76
286,83 1613,17
0,00 900,00 900
114,00 215,50 101,50
385,55 887,05 501,5
536,93 260,76 276,17
628,53 1613,17 2241,700
D)$ (e C"" O O M
D)$ (e C"" Ope"'#$n") D)$ (e C"p#%")e! D)$ (e C"" /#+"($
L" "!" (e C$!%$ (e Op$%n#("( p"" e) empe!"#$ e! (e 8 e") "n").
E) empe!"#$ )e p#(e " U(. ;e )e e'$m#en(e !# '$n+#ene $ n$ "'e e) p$e'%$, '$men%&n($)e !# e#!%en $%"! $p'#$ne! $p'#$ne! ;e !e"n m&! '$n+en#en%e! '$n+en#en%e! ;e )" ;e ) " '$n!#(e"($. '$n!#(e"($. /"" %") ee'%$, U(. (e*e e")#>" e")#>" )$! !#-#en%e! '&)')$! ?2.0 p%!.@ C")')" e) V")$ /e!en%e Ne%$ (e) /$e'%$ )" IR. Re'$men(" !# *"$ e!%e e!'en"#$ )e '$n+#ene e")#>" e) p$e'%$. ?1.0 p%!.@ S# e) p$e'%$ p(#e" epe%#!e #n(e#n#("men%e #n(e#n#("men%e en e) %#emp$, B!e<" e!%" !#%"'#n !#%"'#n m&! '$n+en#en%e '$n+en#en%e ;e )" "n%e#$ ?3.0 p%!.@ S# e) empe!"#$ %+#e" )" p$!#*#)#("( (e n$ pe(# e) p!%"m$ ;e #n') en e) D)$ (e C"" "n%e#$, B)e e'$men("<" U(. e")#>" e) p$e'%$ !#n e) p!%"m$ B/$ ;
26.1. Solución /"%e "@ 0
#@
1
2
3
4
500
800
1000
286 100 260
336 78,45 260 146 20,45 0,00 20,45 260 146
386 54,75 390 20,45 148,8 22,32 126,48 390 20,45
1200 650 386 28,67 390
O O M M O O M
In-e!$! $pe"'#$n")e! G"n"n'#"! (e C"p#%") C$!%$! $pe"'#$n")e! In%ee!e! (e '(#%$ =epe'#"'#n Le-") /(#(" (e) Ee'#'#$ "n%e#$ U%#)#("( (e+en-"(" Impe!%$ " )" Ren%" ?15@ U%#)#("( Ne%" =epe'#"'#n Le-") /(#(" (e) Ee'#'#$ "n%e#$ G"n"n'#"! (e C"p#%") D)$ (e C"" Ope"'#$n")
O O O M
In+e!#n D#" 1300 V")$ Re!#(") (e A'%#+$! C"p#%") (e "*"$ 600 Re'pe"'#n (e C"p#%") (e "*"$ /e!%"m$! 1000 Am$%#>"'#$ne! D)$ (e C"p#%")e! 900
215,50 215,50
237,05 887,05
260,76 260,76
286,83 1613,17
O O M
D)$ (e C"" Ope"'#$n") D)$ (e C"p#%")e! D)$ (e C"" /#+"($
114,00 215,50 101,50
385,55 887,05 501,5
536,93 260,76 276,17
628,53 1613,17 2241,7005
0 0 0
0
0,00 900,00 900
146 0,00 146,00 260 114,00
385,55
536,93
1045,33 156,80 888,53 390 650 628,53
650 1300 600
C=8<8 >7 I7?77 /"" '")')" '$%"! #-")e! %#)#>"m$! e) D"'%$ (e R e'pe"'#n (e C"p#%") C$%" M 315,5 /!%"m$ M 1000 DRCM F c ?1@n 1d '$n n M 4 ?"$!@ /e<$($! M 4 (e!'$n$'#(" E) +")$ (e '"(" '$%" '$%" C e!%"& ("($ p$ C M V/N W DRC /$ )$ %"n%$, )" %"!" (e #n%e! !e $*%#ene 315,5 M 1000 W F c ?1@ 4 M 10 1d f e!$)+#en($ D#n")men%e, !e $*%#ene /e<$($ 0 1 2 3 4
S")($ 1000 785 547 287 0
Am$%#>"'#n
In%ee!e!
C$%"
0
215,50 237,05 260,76 286,83
100,00 78,45 54,75 28,67
315,5 315,5 315,5 315,5
$%") Am$%#>"($
1000
##@ C=8<8 >7 8 D7/?7<9<9 C$n!#(e"m$! (epe'#"'#n )e-") C"(" "'%#+$ !e (epe'#" en '#n'$ "$!. /$ )$ %"n%$, ! (epe'#"'#n p$ "$ !e& =epe'#"'#n M 650 F 5 M 130
"@ C&)') C&)')$$ (e) V/N )" IR (e) (e) p$e p$e'%$ '%$.. C&)')$ (e) V/N V/N M 443,01 C&)')$ (e )" IR IR M 17,41
*@ C&)')$ (e) V/NS
C&)')$ (e) V/NS V/NS M 1.671,93
'@ C&)') C&)')$$ (e) (e) V/N V/N !#n !#n #n"n #n"n'#" '#"m#e m#en%$ n%$ 0 O O M M O O M
In-e!$! $pe"'#$n")e! G"n"n'#"! (e C"p#%") C$!%$! $pe"'#$n")e! In%ee!e! (e '(#%$ =epe'#"'#n Le-") /(#(" (e) Ee'#'#$ "n%e#$ U%#)#("( (e+en-"(" Impe!%$ " )" Ren%" ?15@ U%#)#("( Ne%" =epe'#"'#n Le-") /(#(" (e) Ee'#'#$ "n%e#$ G"n"n'#"! (e C"p#%") D)$ (e C"" Ope"'#$n")
O O O M
In+e!#n D#" 1300 V")$ Re!#(") (e A'%#+$! C"p#%") (e "*"$ 600 Re'pe"'#n (e C"p#%") (e "*"$ /e!%"m$! Am$%#>"'#$ne! D)$ (e C"p#%")e! 1900
0 0 0
0
1
2
3
4
500
800
1000
286
336
386
1200 650 386
260
260 46 158 23,70 134,30 260 46
390
390
224 33,60 190,40 390
1074 161,10 912,90 390
580,40
650 652,90
46 0,00 46,00 260 214,00
440,30 650
1300 600 0,00
650,00
0,00
1900,00
O D)$ (e C"" Ope"'#$n") O D)$ (e C"p#%")e! M D)$ (e C"" /#+"($
0,00 1900,00 1900
214,00 0,00 214,00
440,30 650,00 209,7
580,40 0,00 580,4
652,90 1900,00 2552,9
C&)')$ (e) V/N V/N M
455,56
2. CALCULAR CALCULAR FC -CORTO C")')" e) )$ (e '"" " p"%# (e )$! !#-#en%e! ("%$!
A$
0
=ESE:JOLSO
22.000
1
2
3
4
5
3.000
3.500
3.800
4.000
4.500
1.000
1.500
2.000
2.000
2.500
INGRESOS
30.000
GASOS
20.000
ACIVO CIRCULANE /ASIVO CIRCULANE
1.500
E) pe'#$ (e +en%" !*#& "n")men%e n 5, m#en%"! ;e )$! '$!%e! !e #n'emen%"&n n 3 )$! ($! p#me$! "$! n 2 )$! !#-#en%e!. L" "m$%#>"'#n !e& )#ne") $*%en#en($ n +")$ e!#(") #-") ") 10 (e) '$!%e. L" %"!" #mp$!#%#+" "!'#en(e ") 35.
2". CAMPERA CAMPERA E) p$p#e%"#$ (e )" empe!" CA:/ERA,S.A. CA:/ERA,S.A. !e p)"n%e" )" p$!#*#)#("( (e "mp)#" e) ne-$'#$ #n'$p$"n($ " ! p$(''#n %"m*#n )" "*#'"'#n (e '")>"($!. /"" e))$ ne'e!#%" e")#>" $*"! (e "'$n(#'#$n"m#en%$ p$ 18.000 e$!. A!< m#!m$ !e ne'e!#%" '$mp" m";#n"#" p$ #mp$%e (e 88.230 e$!, "m$%#>&n($!e (e $m" )#ne") ("n%e )$! (#e> "$! (e ! +#(" %#), m$men%$ en e) ;e " n$ %en(& +")$ e!#(") ")-n$.
"m*#n e! ne'e!"#$ ");#)" )" n"+e '$n%#-" p$ 14.200 e$! "n")e!, p"-"(e$! " p#n'#p#$! (e '"(" "$.
L" ne+" #n+e!#n pem#%e e!%#m" n "men%$ (e )"! +en%"! "n")e! (e) ne-$'#$ (e 169.920 e$!, !#en($ p"" e))$ ne'e!"#$ "men%" )$! -"!%$! (e m"%e#"! p#m"! en 81.000 e$! "n")e! )$! -"!%$! (e pe!$n") en 36.700 e$! ") "$. A(em&! )$! -"!%$! (e )> p"!"&n (e 3.520 " 5.984 e$!, m"n%en#n($!e e) e!%$ (e -"!%$! -ene")e! en 4.820 e$!. L$! -"!%$! (e#+"($! (e )" #n"n'#"'#n (e) ne+$ p$e'%$ !p$nen n p"-$ "n") (e 30.000 e$! (e )$! ;e 3.000 '$e!p$n(en " #n%ee!e! *"n'"#$!.
Se pe+ n" ("'#n (e 10 "$! p"" e!%e ne-$'#$.
S# e) %#p$ #mp$!#%#+$ !$*e *ene#'#$! e! e) 35, e) '$!%e (e '"p#%") p"" )" empe!" !e m"n%#ene en e) 12 "'%"), B!e<" e'$men("*)e "'$me%e (#'$ p$e'%$
2&. AMIGO A(UD A(UDA A Sp$n-" ;e n "m#-$ !$ )e !$)#'#%" ;e, "p$+e'"n($ !! '$n$'#m#en%$! "(;##($! en e) '!$, )e "'$n!ee !$*e )" '$n+en#en'#" (e e")#>" n p$e'%$ (e #n+e!#n ;e )e "n $e'#($. L$! ("%$! !$*e #n-e!$! '$!%$! !e pe!en%"n en e) !#-#en%e '"($
In-e!$! ?:@ C$!%$! $%") ?:@
1
2
3
4
5
6
28.800 25.300
36.000 31.625
64.800 56.925
158.400 139.150
165.600 145.475
172.800 151.800
A!#m#!m$, )" #n+e!#n '"p#%") (e %"*"$ e;e#(" !e (e!'$mp$ne '$m$ !#-e ?n$ !e e;#een %een$!@ In+e!#$ne!
: ?!F#+"@
V#("
C$n!%''#n :";#n"#" e;#p$! Ve<')$!
12000 9600 6000
30 8 6
V")$ e+en%" 8000 1500 1200
Sp$n-" ;e %$($! )$! +")$e! en%e-"($! !$n e")e! ?e;#+")en%e! en UD_!@ ! "m#-$ p$!ee #n+e!#$ne! (e #-") n#+e) (e #e!-$ ;e )e ep$%"n n" en%"*#)#("( (e) 14 e") "n"). C")')e e) )$ (e '"" (e) p$e'%$ (e n" e'$men("'#n " ! "m#-$ !$*e )" '$n+en#en'#" (e e")#>" e) p$e'%$.
29.1. Solución D)$ (e C"" 0
1
2
3
4
5
6
In-e!$! G. =e C"p C$!%$! =epe'#"'#n
28.800
36.000
64.800
158.400
165.600
25.300 2.600
31.625 2.600
56.925 2.600
139.150 2.600
145.475 2.600
172.800 1.300 151.800 2.600
U Ne%"! =ep G. =e '"p D $pe"'#$n")
900 2.600
1.775 2.600
5.275 2.600
16.650 2.600
17.525 2.600
3.500
4.375
7.875
19.250
20.125
In+e!#n
27.600
17.100 2.600 1.300 18.400
Re+en%" D '"p#%")e! DC V/N?14@
27.600
0
0
0
0
0
10.700 10.700
27.600 65.315,27 14
3.500
4.375
7.875
19.250
20.125
29.100
30. PLANTA PLANTA DE CONCENTRADOS Se p)"n%e" )" p$!#*#)#("( p$!#*#)#("( " n -p$ (e #n+e!#$n#!%"! #n+e!#$n#!%"! (e e!%"*)e'e e!%"*)e'e n p$e'%$ p$e'%$ (e ")#men%$! ")#men%$! '$n'en%"($! '$n'en%"($! p"" "n#m")e! "!< "%en(e )" (em"n(" (e) me'"($ n"'#$n") ep$%" e) e'e(en%e (e )" p$(''#n, e!%#m"($ en n 30, " p"" ! %#)#>"'#n p)en". E) pe'#$ (e +en%" p$ %$ne)"(" !e e!%#m" en 140,000. 2. E) $#>$n%e (e) p$e'%$ !e !e " e!%#m"($ en 10 "$!, e) p#me$ p"" )" #n!%")"'#n, )$! 8 !#-#en%e! (e n'#$n"m#en%$ e) )%#m$ (e )#;#("'#n. 3. E) m$n%$ m$n%$ (e )"! #n+e!#$ne! #n+e!#$ne! e! e) !#-#en% !#-#en%ee ".
Se "( "(;#ee n %e %een$ p$ 70 70gg000 000,000 000
*. /"" )" '$n!%''#n (e #n!%")"'#$ne! "*#)e!, $#'#n"! "(m#n#!%"%#+"!, *$(e-"!, +<"! +e#')"e! #n%en"!, >$n"! (e p";e$, e%'. !e '")')" n" #n+e!#n (e 80g000,000. '. L$! e!%(#$! %'n#'$! e'$m#en("n )" '$mp" (e n" m";#n"#" #mp$%"(" p$ 180g000,000 ?e) 10 '$e!p$n(e " '$!%$! (e #mp$%"'#n@, n e;#p$ n"'#$n") p$ 130g000,000. (. =e!p! (e (#!e" )" e!%'%" "(m#n#!%"%#+" !e e!%#m" n" #n+e!#n en m$*#)#"#$ p$ 52g000,000. e. /"" %"n!p$%e #n%en$ (e #n!m$! p"" (#!%#*'#n (e) p$('%$ !e "(;#ee n +e<')$ p$ +")$ (e 71g000,000. . L$! e!%(#$! %'n#'$! e'$nm#'$! !e '$n%"%"$n '$n n '$n!$'#$ '$n!$'#$ m#%$ ?50 n"'#$n") 50 e%"ne"@ p$ )" !m" (e 26g000,000. -. L$! -"!%$! n$%"#")e! (e '$n!%#%'#n, e-#!%$! e!%(#$ (e ($'men%$! "!'#en(en " 12g000,000. . E) m$n%"e (e )" m";#n"#" %"n%$ #mp$%"(" '$m$ n"'#$n") !e "'e p$ n 10 (e ! +")$.
#. L$! '$!%$! '$!%$! (e pe*"! pe*"! pe!%" en m"'" m"'" "!'#en(en "!'#en(en " 10g000,000. 10g000,000. . E!%e p$e'%$ e! #n%en!#+$ en m"n$ (e $*" n$ '")##'"(" p$ )$ %"n%$ !e pe'#!" n p$-"m" (e '"p"'#%"'#n ;e 'e!%" 15g000,000.
. E) ee'%#+$ ee'%#+$ !e e!%#m" e!%#m" en 15 (<"! (<"! (e) '$!%$ (e "*#' "*#'"'# "'#n n (e) p#me p#me "$ (e p$('' p$(''#n, #n, e')en e')en($ ($ (epe'#"'#$ne (epe'#"'#$ne!, !, "m$%#>"'#n "m$%#>"'#n (e (#e#($! (#e#($! pe!%"'#$ne! pe!%"'#$ne!,, "(em&! (e) +")$ (e )" m"%e#" p#m" '$ m$n%$ ;e("& #n')#($ en ! #n+en%"#$ '$e!p$n(#en%e. ). E) #n+en%"#$ #n+en%"#$ (e m"%e#" m"%e#" p#m" !e e!%#m" e!%#m" en n me! (e )"! ne'e!#("(e! ne'e!#("(e! (e) p#me p#me "$. m. /"" '")')" '")')" e) #n+en%"#$ #n+en%"#$ (e p$('%$! p$('%$! en en p$'e!$ p$'e!$ !e !"*e ;e ;e e) '#')$ '#')$ *&!#'$ *&!#'$ (e p$(''#n p$(''#n !e (em$" (em$" 3 (<"! !e %"*""n 288 (<"! ") "$. n. Se e!%#m" ;e )$! p$('%$! %em#n"($! pem"ne'en en *$(e-" 4 (<"!. $. L" p$)<%#'" #n%en" (e )" '$mp"<" (e%em#n" ;e e) 20 (e )"! +en%"! !e "'e " '(#%$, " 45 (<"!. 4. L$! '$!%$! '$!%$! (e n'#$n"m#en%$ n'#$n"m#en%$ !$n )$! !#-#en% !#-#en%e! e! ". Se pe'#!"n pe'#!"n 40,000 %$ne)"("! %$ne)"("! (e m"%e#" p#m" en e) p#me "$ (e $pe"'#n 48,000 en e) !e-n($Q 56,000 p"" e) %e'e$Q 64,000 p"" e) '"%$ "$ 72,000 p"" e) ;#n%$ 80,000 p"" e) !e%$ '"n($ )" '"p"'#("( #n!%")"(" !e "" '$p"($ en ! %$%")#("(. L$! "$! !#-#en%e! (e $pe"'#n e;#een )" m#!m" '"n%#("(. E) pe'#$ p$ %$ne)"(" !e " e!%#m"($ en 72,000. *. L"! ne'e!#("(e! (e m"%e#")e! (#e'%$! %")e! '$m$ emp";e! !e e!%#m"n en 1g600,000 n#("(e! en e) p#me "$ (e $pe"'#n, '$n #n'emen%$ "n") !#m#)" " )" p$(''#n. E) pe'#$ n#%"#$ p$ emp";e e! (e 30. '. L" ne'e!#("( ne'e!#("( (e m"n$ (e $*" %#ene )" m#!m" %"!" (e #n'emen%$ #n'emen%$ (e )" p$(''#n. Se %#)#>" %#)#>" m"n$ (e $*" (e )" e-#n en )" '") e#!%e n" %"!" (e (e!emp)e$ (e) 12. L" nm#n" (e m"n$ (e $*" (#e'%" en e) p#me "$ (e n'#$n"m#en%$ (e) p$e'%$ 'e!%" 110g000,000. E) 60 (e )" m"n$ (e $*" n$ e! '")##'"(". (. O%$! m"%e#")e! (#e'%$! '$m$ '$m$ p#n%"!, m"'"($e! e%'. "!'#en(en "!'#en(en " 15g000,000 ") "$ '$n #n'emen%$ !#m#)" ") (e )" p$(''#n. e. L$! m"%e#")e! #n(#e'%$! !e '")')"n en 10g000,000 "n")e!. . L" nm#n" "n") "n") (e m"n$ (e $*" #n(#e'%" #n(#e'%" !e '")')" '")')" en 13g000,0 13g000,000. 00. -. E) '$!%$ (e )$! !e+#'#$! "n")e! e! (e 36g000,000. . E) '$!%$ (e m"n%en#m#en%$ "n") (e) e;#p$ e! (e 45g000,000. #. L" Empe!" %$m" %$m" n" p)#>" (e !e-$ '" '" p#m" "n") "!'#en(e "!'#en(e " 22g500,000 22g500,000 p"" )" p$%e''#n p$%e''#n (e )"! #n!%")"'#$ne! "*#)e!. . L$! #mpe!%$! (e #n(!%#" '$me'#$ pe(#") !m"n ") "$ 12g000,000. . E) '$!%$ (e )" nm#n" "(m#n#!%"%#+" e! (e 160g000,000 ") "$.
). L$! -"!%$! -"!%$! (e +en%"! !e !e e!%#m"n e!%#m"n en 1O (e )"! +en%"! +en%"! "n")e!. "n")e!.
5. Se e'#*e n '(#%$ " 6 "$!, p$ 255 m#))$ne!, '$n '$n n "$ me%$ n" %"!" %"!" (e #n%e! (e $men%$ (e) 32 "n"). E) '(#%$ !e p"-"& '$n '$%"! #-")e!. 6. E) pe'#$ pe'#$ (e +en%" p$ %$ne)"(" %$ne)"(" !e " '")')"($ '")')"($ en 140,000. 140,000. 7. L" empe!" %#ene %#ene n" '"p"'#("( '"p"'#("( #n!%")"(" #n!%")"(" m&#m" (e 60,000 %$n %$n ") "$. 8. L"! pe!%"'#$n pe!%"'#$ne! e! !e e!%#m"n e!%#m"n en n 45. 45. 9. L$! "'%#+$! (epe'#")e! %#enen %#enen ") )#;#("!e e) p$e'%$ n +")$ '$me'#") e;#+")en%e ") 20 (e ! +")$ (e '$mp".
31. PLANTA PLANTA PROCESADORA DE MANGO Un -p$ (e #n+e!#$n#!%"! e!%& #n%ee!"($ en "(e)"n%" n p$e'%$ en ($n(e !e pe%en(e #n!%")" n" pe;e" p)"n%" p$'e!"($" (e p)p" (e m"n-$, ("(" )" "*n("n'#" (e )" %" en )" e-#n en )" (#!p$n#*#)#("( (e m"n$ (e $*". Un e!%(#$ pe)#m#n" "$ )$! !#-#en%e! e!)%"($! 1. A) !e n" epe#en' epe#en'#" #" ne+", !e " (e'#(#($ (e'#(#($ )#m#%" )#m#%" e) p$e'%$ p$e'%$ " 6 "$! "$! En e) p#me p#me "$ !e !e e)"*$"&n e)"*$"&n )$! e!%(#$! '$mp)emen%"#$! !e ne-$'#"&n )$! e;#p$! ?S$n )"! #n+e!#$ne! ") #n#'#$ (e) p$e'%$@. E) p$e'%$ n'#$n"& ("n%e '#n'$ "$! !e )#;#("& en e) )%#m$. Se e!%#m" ;e e) +")$ (e !")+"men%$ (e )$! e;#p$! !e& (e) 40 (e ! +")$ (e '$mp". 2. L" '"p"'#("( '"p"'#("( #n!%")"(" #n!%")"(" %$%") %$%") !e !e " '")') '")')"($ "($ en 500 %$ne)"("! %$ne)"("! p$ "$. "$.
3. E) pe'# pe'#$$ (e +en%" +en%" en en e) me'" me'"($ ($ e! (e (e 100.000 100.000 p$ p$ %$ne)"( %$ne)"("" 4. E) '$!%$ '$!%$ e!%#m"( e!%#m"($$ p"" p$'e!" p$'e!" n" %$ne)"(" %$ne)"(" (e %" e! (e 50.000 50.000 (e )$! '")e! '")e! n 85 e! '$!%$ '$!%$ +"#"*)e. L$! '$!%$! #$! !$n e) 15 (e) '$!%$ #n!%")"($ p"" p$'e!" )" %". 5. L"! #n+ #n+e e!# !#$ne $ne!! e;e e;e##(" ("!! !$n !$n E;#p$
70g000.000
E!%( !%(#$ #$!! -"! -"!%$! (e m$n% m$n%" "e e
4g00 4g000. 0.00 0000
C"p#%") (e %"*"$
3g000.000
6. L$! #n+e!# #n+e!#$n# $n#!%" !%"!! "p$%"&n "p$%"&n 50 m#))$ne! m#))$ne! )"! ne'e!#("(e ne'e!#("(e!! "(#'#$n") "(#'#$n")e! e! (e '"p#%" '"p#%")) !e '*#& '*#&nn '$n n '(#%$ (e 27 m#))$ne!, p"-"(e$ en %e! "$! '$n '$%"! #-")e!, '$n n "$ (e -"'#" n" %"!" (e #n%e! (e) 15 "n").
7. L" %"!" %"!" (e #mpe #mpe!%$ !%$ p"" p"" e!%" e!%" #n(!% #n(!%#" #" e) e) (e) 30 30 8. L$! p)"ne! p)"ne! (e p$(''#n p$(''#n +en%"! +en%"! e!%&n e!%&n ("($! ("($! p$ )" %#)#>"' %#)#>"'#n #n (e )" '"p"'#(" '"p"'#("(( #n!%")"(" #n!%")"(" en n 80 p"" e) p#me "$ (e n'#$n"m#en%$Q 90 p"" e) !e-n($ 100 (e "))< en "(e)"n%e. 9. L$! "'%#+$! "'%#+$! #$! #$! !e (epe'#" (epe'#"&n &n en '#n'$ '#n'$ "$! )"! )"! #n+e!#$ne! #n+e!#$ne! !e (#e#&n (#e#&n en '#n'$ '#n'$ "$!. "$!. 10. N$ !e '$n!#(e"& '$n!#(e"& )" #n)"' #n)"'#n. #n. Se e;#ee '$n$'e )$! )$! (e ee'%#+$ (e e!%e p$e'%$ ? S#n #n"n'#"'#n '$n #n"n'#"'#n@.
JALANCE /RELI:INAR L" #n+e!#n #n+e!#n (e )$! !$'#$! !$'#$! (e 50g000.000 50g000.000 '$n!%#%e '$n!%#%e e) p"%#m$n# p"%#m$n#$$ (e )" empe!". empe!". Sm"($ " )$! 27g000.000 (e) '(#%$ pem#%#& '*# )"! #n+e!#$ne! #n#'#")e! (e A'%#+$! #$! 70g000.000 =#e#($! 4g000.000 C"p#%") (e %"*"$ 3g000.000 JALANCE INICIAL
?m#)e! @
ACIVOS
/ASIVOS
C""
3g000
O*)#-"'#$ne!
27g000
=#e#($!
4g000
/"%#m$n#$
50g000
A'%#+$! #$!
70g000
C$n *"!e en )" '"p"'#("( (e )" p)"n%", )$! pe'#$! (e#n#($!, e")#>"em$! n e!%#m"($ (e +en%"!. VENAS 0
1
2
3
4
5
6
C"n%#("(e! ?%$n@
400
450
500
500
50
Ven%"!
40g000
45g000
50g000
50g000
50g
En e) p#me "$ n$ " p$(''#n, )" '") !e #n#'#" en e) !e-n($ "$ '$n%#n" "!%" e) !e%$ "$, #n'emen%&n($!e )" p$(''#n (e "'e($ " )" '"p"'#("( #n!%")"(". En e) !e%$ "$! !e e!pe" )#;#(" )" empe!". Ap"e'en )$! +")$e! (e +en%" (e )$! e;#p$! e'pe"'#n (e) '"p#%") (e %"*"$.
/"" e")#>" e) "n&)#!#! e'$nm#'$ (e e!%e '"!$, ne'e!#%"m$! '$n#-" e) )$ (e '"" $ )$ (e ee'%#+$, e) '") #em$! '$n!%en($ " me(#(" ;e e")#'em$! e) "n&)#!#!. /RESU/UESO =E INVERSIONES CON RECURSOS /RO/IOS 0
?m#)e! @
1
2
3
4
5
6
A'%#+$! #$!
70g000
28g000
=#e#($!
4g000
C"p#%") (e %"*"$
3g000
3g000
DLUO =E INVERSION
77g000
31g000
En e) )%#m$ "$ !e +en(en )$! e;#p$! e;# p$! !e e'pe" e) '"p#%") (e %"*" $ S$n #n-e!$!.
COSOS =E O/ERACION
?m#)e! @
0
1
2
3
4
5
6
C$!%$! #$!
3g750
3g750
3g750
3g750
3g750
C$!%$! +"#"*)e!
17g000
19g125
21g250
21g250
21g250
COSOS OALES
20g750
22g875
25g000
25g000
25g000
C$n e!%" "(" #n#'#") !e '$n%#n" '$n$m"n($ )$! )$! (e ee'%#+$, !"n($ )$! '"($! (e) m$(e)$ e!m#($ $ !#mp)##'"($.
32. PRO(ECTO 50 MIL UNIDADES C$n!#(ee e) !#-#en%e p$e'%$ ;e '$n!#(e" p$!#*)e +en(e 50,000 n#("(e! ") "$ (e n p$('%$ " 500 '"(" n" ("n%e )$! p#me$! ($! "$! " 600 " p"%# (e) %e'e "$, '"n($ e) p$('%$ !e "" '$n!$)#("($ en e) me'"($. E) e!%(#$ %'n#'$ (e#n# n" %e'n$)$-<" p%#m" p"" e) p$e'%$ ;e e;##<" )"! !#-#en%e! #n+e!#$ne! een$! 12,000,000Q O*"! D"!e '"(" $'$ "$! p$ $%" !#m#)". L" m&;#n" !"(" p$(<" +en(e!e en 2,500,000. L" )e-#!)"'#n +#-en%e pem#%e (epe'#" )"! $* "!
L" #n+e!#n en '"p#%") (e %"*"$ !e e!%#m" en 4,000. Se $*%en(& n p!%"m$ (e 80,000,000 " n" %"!" (e #n%e! (e 8 ;e (e*e& !e p"-"(" en '$%"! "n")e! #-")e! ("n%e 8 "$!. L" %"!" (e #mpe!%$! " )"! %#)#("(e! e! 15 e) '$!%$ (e $p$%n#("( (e) '"p#%") e! 12.
E) $#>$n%e (e e+")"'#n e! (e 10 "$!, " ;e !e '$n!#(e" ;e (e!p! )"! '$n(#'#$ne! (e me'"($ !e&n m&! e!%"*)e! p$ )$ ;e e) +")$ pe!en%e (e )$! )$! %$! (e )" empe!" e! 139,000. C")')e e) )$ (e '"" e) +")$ pe!en%e ne%$.
2.1. Solución! "#$ %$c&i"o #'c#l.
33.EMPRE 33. EMPRESA SA CA*LE Un" empe!" (e %e)e+#!#n p$ '"*)e !e en'en%" e!%(#"n($ )" '$n+en#en'#" (e #n+e%# en n p$e'%$ (e "mp)#"'#n (e ! &e" (e !e+#'#$. L$! e!%(#$! %'n#'$! #n(#'"n ;e )" #n+e!#n #n#'#") !e<" (e US100.000, )" ;e !e (epe'#" )#ne")men%e en 5 "$! !#n +")$ e!#("). ="("! )"! '""'%e$n%e (e e+")"'#n e! (e !)$ n 5 (e) m$n%$ #n#'#"). E) p$e'%$ p$('#& n #n'emen%$ (e US24.000 "n")e! en )$! '$!%$! #$! (e $pe"'#n. E) '$!%$ +"#"*)e p$ !"#$ e! (e!pe'#"*)e )$! '$!%$! -ene"($! p$ )" '$ne#n ") !e+#'#$ !$n p"-"($! p$ e) !"#$. E) '"p#%") (e %"*"$ "(#'#$n") e;e#($ p$ )" empe!" p"" e!%e p$e'%$ e! e;#+")en%e " n me! (e )$! '$!%$! #$! #mp%"*)e! ") p$e'%$. /$ $%" p"%e, e) e!%(#$ (e me'"($ !e")" ;e e) pe'#$ ;e )"! pe!$n"! e!%&n (#!pe!%"! " p"-" e! (e US 25 men!")e!. S# )"! epe'%"%#+"! epe'%"%#+"! (e !"#$! !"#$! '$ne'%"($! '$ne'%"($! ") !#!%em" !#!%em" e! )" ;e !e (e%"))" en e) '"($ Nh1, )" %"!" (e #mpe!%$ (e )" empe!" e! (e 10, e) $#>$n%e (e e+")"'#n (e) p$e'%$ e! (e 10 "$! )" %"!" (e!'en%$ e)e+"n%e e! (e 12, !e !$)#'#%" ;e
". C$n!% C$n!%" " e) e) )$ )$ (e '"" '"" (e) (e) p$e p$e'%$ '%$ ?50@. ?50@. *. C")') C")')ee e) VAN (e) (e) p$ p$e'% e'%$$ ?20@. ?20@. C"($ Nh1 E!%#m"'#n (em"n(" ?!"#$! '$ne'%"($!@ A$ Nh U!"#$! 1 150 180 2 3 270 300 4 5 " 10 400
.1. .1. Soluci Solución! ón! "#$ "#$ %$c& %$c&i"o i"o #'c#l. #'c#l.
34. RENOVACIÓN RENOVACIÓN DE E$UIPOS U(. (e!e" en$+" ! e;#p$ p$ $%$ m&! m$(en$ ;e pem#%#<" (#!m#n# )$! '$!%$! (e $pe"'#n. L" +#(" %#) e'$nm#'" (e "m*$! e;#p$! e! (e '"%$ "$! ?n$%" n$ '$n!#(ee en n#n-n '"!$ )" (epe'#"'#n (e )$! e;#p$!@. Se pe!en%"n " '$n%#n"'#n )$! +")$e! (e )$! e;#p$! '$n !! #n-e!$! '$!%$! "n")e! e!pe"($!.
EK9/ 9@ V")$ V")$ (e +en%" $ 10.000 C$!%$ (e $pe"'#n "n") 500 In-e!$! "n")e! 5.500. V")$ V")$ (e +en%" (en%$ (e '"%$ "$! 7.000. EK9/ 7 V")$ (e '$mp" ?#n+e!#n@ C$!%$ $pe"'#n "n") In-e!$! "n")e! V")$ V")$ (e +en%" (en%$ (e '"%$
16.000 200 9.000
=e%em#ne )" '$n+en#en'#" (e ee'%" e) '"m*#$ me(#"n%e n )$ #n'emen%") !# )" %"!" (e #mpe!%$ " )"! %#)#("(e! e! (e 15, )" %"!" (e (e!'en%$ pe%#nen%e e! (e 10 "n").
4.1. Solución A87?9 A -;77? 7<8@9 <8 9@?7 < >7 /7?<9 7 7K9/ U. A7 >7 9;/7 9;/7 15 U. D7/7 >7 F8 7 VAN
A)O 0
A)O
A)O
A)O
A)O
55
55
550
50 42 42
50 42 42
500
55 70 120 102 102
425 425
1,535.
ALTERNATIVA * ->K9?9? 7<8@9 7 A A O I@?7 C >7 /7?<9 100 V7 >7 7K9/ 100 U. A7 >7 9;/7 9;/7 15 850 U. D7/7 >7
A O 850
A O
85
830 705
83 70
A O 850
200
830 705
85 90 173 147
I7?9 F8 N7
705
70
705
147
VAN
1",262.23
FLUJO INCREMENTAL -ALTERNATIVA *!A I@?7 < >7 /7?<9 7 7K9/ U. A7 >7 9;/7 I;/715 U. D7/7 >7 I7?9 F8 7 VAN
A)O 0
A)O
10000 10000 1500 8500 16000 7500 2,320.54
A)O
A)O
A)O
30 3
30 3
300 300
33 28
33 28
330
300 300 200 530
280
450
28
28
280
450
9@ C$n'ep%$ (e TIR epe!en%" )" %"!" (e #n%ee! m&! ")%" ;e n #n+e!#$n#!%" p$(<" p"-" !#n pe(e (#ne$. E!%e '#%e#$ e! e;#+")en%e " "'e e) VAN M 0 (e%em#n" )" %"!" ;e pem#%e ") )$ "'%")#>"($ !e 'e$. IR ∑ JN%
=$n(e JN epe!en%" e) *ene#'#$ ne%$ (e '"(" pe#$($. Le-$ )" %"!" "!< '")')"(" !e '$mp"" '$n )" %"!" (e (e!'en%$ (e )" empe!". S# )" IR e! #-") $ m"$ ;e !%", e) p$e'%$ (e*e "'ep%"!e !# e! men$ (e*e e'">"!e.
35. GERENTE DE DE SUPERMERCADO SUPERMERCADO E) -een%e (e n !peme'"($ !peme'"($ e!%& pe$'p"($ pe$'p"($ p$;e (#"#"men%e !e p$('en $*$! $m#-"T, ;e "n e('#($ )"! %#)#("(e! "n")e! (e )" empe!" en $m" '$n!#(e"*)e. /"" !$)'#$n" e!%e p$*)em", e!%& "n")#>"n($ 3 ")%en"%#+"! !e !#!%em"! (e !e-#("( "@ Un (e%e'%$ (e%e'%$ (e !e))$! !e))$! (e p$('%$!, p$('%$!, m"'" m"'" RX, '$ '$ '$!%$ '$!%$ e! (e 3.000.000. 3.000.000. E!%e E!%e !#!%em" !#!%em" pem#%e e('# )$! $*$! en 1.500.000 p$ "$. S +#(" %#) e! (e 5 "$! ! '$!%$ (e $pe"'#n m"n%e'#n e! (e 200.000 "n"). *@ Un (e%e'%$ (e%e'%$ (e !e))$! !e))$! (e p$('% p$('%$!, $!, m"'" m"'" Se- :", '$ '$ '$!%$ e! (e 1.500.00 1.500.000. 0. E!%e (e%e'% (e%e'%$ $ pem#%#<" e('# )"! p(#("! en 800.000 "n")e!. S +#(" %#) e! (e 4 "$! ! '$!%$ (e $pe"'#n m"n%en'#n e! (e 250.000 "n"). '@ L#'#%" L#'#%" e) !#!%em !#!%em"" (e +#-#)" +#-#)"n'# n'#"" " n" empe!" empe!" p#+"(" p#+"(" e!pe'#" e!pe'#")#> )#>"(", "(", '$n )" '") !e e('#< e('#<"n "n )$! $*$! en 600.000 ") "$. E!%" empe!" '$*" 1.250.000 "n"), p"-"($! p$ "(e)"n%"($, ? e) 1 (e ene$ (e '"(" "$ !e (e*e p"-" e) '$*$ "n")@, pe$ e) !peme'"($ " n$ %en(<" ;e p"-" )$! !e)($! (e !! "'%")e! -"(#"!, ;e "!'#en(en " 1.000.000 "n"). E) '$n%"%$ '$n e!%" empe!" e! p$ 3 "$!, p(#en($ en$+"!e. ="%$! A(#'#$n")e!
"!" (e (e!'en%$ e)e+"n%e p"" e) !peme'"($ M 10 "n") Impe!%$! " )"! %#)#("(e! M 15 V")$ e!#(") (e )$! (e%e'%$e! M 20 (e ! +")$ (e '$mp"
L$! (e%e'%$e! !e (epe'#"n en 3 "$! Sp$n-" ;e "'%")men%e )" empe!" n$ pe(e (e!'$n%" !e !! %#)#("(e! )"! p(#("! p$ $*$.
BC&) e! !#!%em" (e +#-#)"n'#" m&! '$n+en#en%e
5.1. Solución 87?9 D77<? >7 788 ;?< RT% /e#$($ U989>>7 :"$e! C$!%$ $p Ven%" (e%e'%$ "men%$ "men%$ #mpe!%$
F8 >7 C In+e!#n :"$e! In-e!$! C$!%$ $p Ven%" (e%e'%$ "men%$ #mpe!%$! D)$ (e C"" V")$ pe!en%e JAE
0
1
2
3
4
5
1.500.0
1.500.00
1.500.000
1.500.00
1.500.000
20 200.000
200.000
200.000
20 200.000
200.000
600.000 300.000 45.000
300.000 45.000
300.000 45.000
1.300.00 195.000
1.900.000 285.000
1.500.0
1.500.00
1.500.000
1.500.00
1.500.000
20 200.000
200.000
200.000
20 200.000
200.000
3.000.000 600.000 3.000.000
45.000 1.255.0
45.000 195 195.0 .000 00 1.255.000 1.105.00
1.878.517
495.548
87?9 B D77<? >7 788 ;?< S7@ M /e#$($ 0 1 U989>>7 :"$e! In-e!$! 800.000 C$!%$ $p 250 250..000 000 Ven%" 500 500..000 000 (e%e'%$ "men%$ 50.000 "men%$ #mpe!%$ 7.500 F8 >7 C In+e!#n :"$e! In-e!$! C$!%$ $p Ven%" (e%e'%$ "men%$ #mpe!%$! D)$ (e C"" V")$ pe!en%e JAE
45.000 1.255.00
3
4
800.000
800.000
25 250.0 0.000
250. 250.00 0000
50 500.0 0.000
500. 500.00 0000
50.000 7.500
50.000 7.500
850.000 127.500
800.000
800.000
800.000
250 250..000 000
25 250.0 0.000
250. 250.00 0000
7.500
7 7.500
7 7.500
542.500
542.500
542.500
800.000 250.000 300.000 127.500 722.500
800.000 250.000 300.000
1.500.000
1.500.000 342.594
2
108.079
285 285.0 .000 00
1.615.000
87?9 < E;/?7 >7 S7@?9>> 7/7<989:> /e#$($ 0 1 2 U989>>7 :"$e! In-e!$! 600.000 600.000 C$!%$ A$$ !e)($! -"(#"! 1.000.0 1.000.00 "men%$ %#)#("( 350.000 350.000 "men%$ #mpe!%$ 52.500 52.500
3
600.000 1.000.000 350.000 52.500
F8 >7 C :"$e! In-e!$! C$!%$
1.250.000
A$$ !e)($! -"(#"!
"men%$ #mpe!%$! D)$ (e C"" V")$ pe!en%e JAE
1.250.000 428.982
172.500
600.000 1.000.0 52.500 297.500
600.000 1.000.00 52.500 297.500
600.000 1.000.000 52.500 1.547.500
