Opción real de diferir un proyecto de inversión

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Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
33 Opción real de diferir un proyecto de inversión
Opción real de diferir un proyecto
de inversión
© Juan Mascareñas
Universidad Complutense de Madrid
Primera versión: ene 1994 - Última versión: feb 2013
- Introducción, 1
- Costes, 2
- Ejemplo I, 4
- Ejemplo II, 9
- La opción de aprendizaje, 11
- Bibliografía, 15
- Ejercicios, 16
Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
33 Opción real de diferir un proyecto de inversión
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Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
33 Opción real de diferir un proyecto de inversión
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Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
33 Opción real de diferir un proyecto de inversión
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Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
33 Opción real de diferir un proyecto de inversión
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Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
33 Opción real de diferir un proyecto de inversión
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5
Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
33 Opción real de diferir un proyecto de inversión
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6
Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
33 Opción real de diferir un proyecto de inversión
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7
Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
33 Opción real de diferir un proyecto de inversión
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8
Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
33 Opción real de diferir un proyecto de inversión
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//$!<8%!)$%:$/!()!?/'&#42'!<(!?8(/&(!#%!-a!&()!G$)'/!$42#$)!&()!98<9'!(%!(<(!$*'.!@<!?#(<!
#%$!'?48B%!&(!4'9?/$!&(!28?'!;(/9#&$!?#(<2'!D#(!<#!?/'?8(2$/8'!?#(&(!&(48&8/!(=(/4(/)$!
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%(<!&(!(#/'<!SI]Z!T!+[ZU!)'!D#(!&(!?'/!<3!N$/3$!$4'%<(=$;)(!)$!8%G(/<8B%!<8%'!H#(/$!?'/!()!$)2'!
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&()!?/'0(42'U!&#/$%2(!)'<!?/BM89'<!&'<!$*'<!&(!$4#(/&'!$)!G$)'/!&(!<#!/8(<A'.!@)!4'(H848(%2(!
$%#$)!&(!$<4(%<'!P!i!(Z>``!i!+>jYYY!98(%2/$<!D#(!R!i!+kP!i!Z>`j,].!@%!)$!H8A#/$!,!?#(&(!G(/I
<(!&84N$!(G')#48B%!(%!)$!D#(!<(!?#(&(!$?/(48$/!4'9'!?'/!4$&$!$*'!D#(!<(!/(2/$<(!<#!(=(4#I
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)8:$!(%!()!?/89(/!$*'!()!4'<2(!$<4(%&(/O!$!]Z!M!+>Z`!i!]\>`!98))'%(<!&(!(#/'<>!98(%2/$<!D#(!
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!
9
Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
33 Opción real de diferir un proyecto de inversión
!
b8A.!,!
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10
Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
33 Opción real de diferir un proyecto de inversión
VAN+1 =
!
&'%&(!?!(<!8A#$)!$J!
!
!
p =
205,905 x p + 2,345 x (1 - p)
= 79,71 !
1,03
(1 + rf ) - D
1,03 - 0,5769
=
= 0,3918 !
U - D
1,7333 - 0,5769
!
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/8'/!$)!G$)'/!&(!?'<2?'%(/)$!Sj]>j+!98))'%(<U!2$)!0!4'9'!<(!$?/(48$!(%!)$!H8A#/$!j.!78%!(9;$/I
!
A'>!)$!&(48<8B%!(<!)$!'?#(<2$!<8!()!G$)'/!&()!?/'0(42'!(%!()!?/89(/!$*'!(<!&(!,Y>jZ!98))'%(<!
?'/D#(! ()! 61X! <(/O! %(A$28G'! S%'! <(! /($)8:$/O! ()! ?/'0(42'U>! 98(%2/$<! D#(! ?'<2?'%(/)$! $)!
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2(<!?/';$;8)8&$&(<!%(#2/$)(<!$)!/8(<A'!0!&(<4'%2$&'<!$)!28?'!&(!8%2(/E<!<8%!/8(<A'!';2(%&/(I
9'<!()!61X!2'2$)!&()!?/'0(42'J!
!
96,85 x p + 0,89 x (1 - p)
VAN total =
= 37,37 !
1,03
!
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48B%>!?'/!(=(9?)'U!0!#28)8:$/!)'!D#(!N$!$?/(%&8&'!4'%!';=(2'!&(!4$)4#)$/!9(='/!)$!&(9$%&$!&(!
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11
Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
33 Opción real de diferir un proyecto de inversión
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12
Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
33 Opción real de diferir un proyecto de inversión
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)$!&(9$%&$!?'2(%48$)!/($)!&()!=#A#(2(!(%!4#(<28B%.!C'/D#(!<#<!H#(%2(<!&(!8%4(/28	/(!<'%!
&'<J!)$!&(9$%&$!(<?(/$&$!SG$/8$;)(!%'!4'%2/')$;)(U!0!()!?/(48'!&()!?/'&#42'!SG$/8$;)(!4'%I
2/')$;)(U.!@<!(G8&(%2(!D#(!()!9OM89'!4'<2(!&()!<'%&('!#!'?48B%!&(!$?/(%&8:$=(!&(;(!<(/!YZa!
13
Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
33 Opción real de diferir un proyecto de inversión
M!`Z.ZZZ!l!i!+`.ZZZ!l!?'/D#(!+`.ZZZ!(#/'<!(<!)'!D#(!&(2/$(!&()!?/'0(42'!?'/!2E/98%'!9(&8'!
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%'!/($)8:$/O!)$!8%G(/<8B%>!$)!9(%'<>!$%2(<!&(!<(8<!9(<(<.!C$/$!';2(%(/!()!G$)'/!&(!)$!G')$28)8I
&$&!4'%!$//(A)'!$!)'<!&$2'<!$%2(/8'/(<!0!<$;8(%&'!$&(9O<!D#(!)$!2$<$!&(!/(%&898(%2'!$=#<2$I
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)8&$&.!p<2$!/(<#)2$-!<(/!8A#$)!$)![Z>Y+a!<(9(<2/$).!1!?$/28/!&(!(<2(!&$2'!?'&(9'<!4$)4#)$/!)'<!
4'(H848(%2(<!P!i!(Z>[ZY+!i!+>[[`[!0!R!i!+kP!i!Z>-+,[!4'%!)'<!D#(!?'&(9'<!4'%<2/#8/!)$!(G')#I
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(<!&(!Y`Z.ZZZ!(#/'<!0!&(%2/'!&(!<(8<!9(<(<!<(!(<?(/$!D#(!$)4$%4(!)'<!Y``.[`Z!(#/'<>!D#(!(<!
()! /(<#)2$&'! &(! 4$?82$)8:$/! )$! 48H/$! $42#$)! $)! +>`a! <(9(<2/$)! S28?'! <8%! /8(<A'! <(9(<2/$)! D#(!
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&8%(/'!'!%'!4'%!()!?/'0(42'>!<8!?(/&(9'<!$?#%2$/(9'<!4#O%2'!0!<8!%'!?'%&/(9'<!#%!4(/'.!
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1,015 - 0,8162
p =
= 48,607% !
1,2252 - 0,8162
!
7
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[
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[
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8
14
Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
33 Opción real de diferir un proyecto de inversión
!
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0 x p + 28.772 x (1 - p)
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1,015
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/8;)(!?(/&(/!)$!?/89$!&(!)$!'?48B%>!)'<!+\.`,-!(#/'<>!D#(!)'<![-.jj[!(#/'<!<8!()!(<4(%$/8'!H8%$)!
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eQ@F>!b.!C(2(/!S[ZZ[UJ!:;)'8),-'9"/$!&2'<!-=/$!&.!t'N%!u8)(0.!X#(G$!d'/h.!
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!
!
15
Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
33 Opción real de diferir un proyecto de inversión
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G$)'/! $42#$)! 9(&8'! &(! )'<! H)#='<! &(! 4$=$! (<?(/$&'<! &(! f(%2/$M$! (%! +`Z! 98))'%(<! &(! (#/'<!
(<289$%&'>! $&(9O<>! D#(! &84N'! G$)'/! ?#(&(! $#9(%2$/! $! /$:B%! &(! #%! +ZZa! $%#$)! '>! ?'/! ()!
4'%2/$/8'>!&(<4(%&(/!$!#%!/829'!&(!#%!`Za!$%#$)_!$9;$<!?'<8;8)8&$&(<!<'%!(D#8?/';$;)(<.!@)!
28?'!&(!/(%&898(%2'!93%89'!(M8A8&'!$!(<2$!8%G(/<8B%!(<!&()![`a>!98(%2/$<!D#(!()!28?'!)8;/(!
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/$&'!&(!8%2/'&#48/)'!(%!()!9(/4$&'!(<!&(!+[Z!98))'%(<!&(!(#/'<!4'%!#%$!G')$28)8&$&!$%#$)!(<28I
9$&$! &()! +`a! 0! #%! 4'<2(! &()! 4$?82$)! 9(&8'! ?'%&(/$&'! &()! +[a.! c$! 8%G(/<8B%! /(D#(/8&$! ?$/$!
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<'!(<!&(!&'<!$*'<>!$!)'!)$/A'!&(!)'<!4#O)(<!)$!4$%28&$&!$!?$A$/!?(/9$%(4(/O!4'%<2$%2(.!@)!(D#8?'!
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&(<G8$48B%!23?84$!&()!\Za!S4$)4#)$&$!(%!H#%48B%!&(!<#<!/(%&898(%2'<!$%#$)(<U.!c$!2$<$!&(!&(<I
4#(%2'! $?/'?8$&$! $)! /8(<A'! &()! ?/'0(42'! (<! &()! +`a.! c$! 2$<$! &(! 8%2(/E<! <8%! /8(<A'! (<! &()! `a!
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?/'&#42'!$)!9(/4$&'.!@)!G$)'/!$42#$)!9(&8'!&(!)'<!H)#='<!&(!4$=$!D#(!<(!(<?(/$!A(%(/(!<(!(<289$!
16
Monografías de Juan Mascareñas sobre Finanzas Corporativas
ISSN: 1988-1878
33 Opción real de diferir un proyecto de inversión
(%![\!98))'%(<!&(!(#/'<!4'%!#%$!&(<G8$48B%!23?84$!&()!,[a!$%#$).!@)!4'<2(!&()!?/'0(42'!$<48(%&(!
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17
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