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 !"# $%&'()*++$,% # ! ! "#$%&'!(%!()!$*'!+,-!$.".!()!/(0!1%23'4'!56!&(!78/8$!4'9(%:$;$!$!<828$/!1)(=$%&/3$>!)$!4$?82$)! &()!@A8?2'!2')(9$84'>!<$)8B!$!<#!(%4#(%2/'!()!4B%<#)!/'9$%'!"$0'!C'?8)8'!4'%!D#8E%!)(!#%3$! 48(/2$! $98<2$&! &(<&(! D#(! <(! 4'%'48(/'%! (%! F'9$! <8(%&'! =BG(%(<.! C'?8)8'! %'! 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C'/!'2/'!)$&'>!()!4'<2(!&()!?/'0(42'!$#9(%2$!$!/$:B%!&(!#%!`a!$%#$)>!(<!&(48/>!D#(!<8!<(!/($I )8:$!(%!()!?/89(/!$*'!()!4'<2(!$<4(%&(/O!$!]Z!M!+>Z`!i!]\>`!98))'%(<!&(!(#/'<>!98(%2/$<!D#(! &(!/($)8:$/<(!(%!()!<(A#%&'!$<4(%&(/O!$!]\>`!M!+>Z`!i!]]>[[`!98))'%(<.! ! 9 Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 33 Opción real de diferir un proyecto de inversión ! b8A.!,! ! P%$!G(:!D#(!<$;(9'<!)$!(G')#48B%!&()!G$)'/!&()!$428G'!<#;0$4(%2(!$!2/$GE<!&()!O/;')!;8%'I 98$)!?$<$9'<!$)!$%O)8<8<!&(!)$!&(&848B%!$!2'9$/.!C$/$!())'!4'9(%:$9'<!?'/!()!(M2/(9'!&(/(I 4N'! &()! O/;')! 4'9?$/$%&'! 4$&$! #%'! &(! )'<! G$)'/(<! D#(! ?#(&(! 2'9$/! ()! $428G'! <#;0$4(%2(! 4'%!)'!D#(!4#(<2$!/($)8:$/!()!?/'0(42'!(%!(<(!8%<2$%2(J!]]>[[`!98))'%(<!&(!(#/'<.!"'9'!<(! $?/(48$!(%!)$!H8A#/$!j!<B)'!(%!)'<!&'<!?/89(/'<!(<4(%$/8'<!()!61X!&()!<(A#%&'!$*'!(<!?'<828I G'J![Z`>]Z`!98))'%(<!0![>Y\`!98))'%(<!/(<?(428G$9(%2(.! ! b8A.!j! ! @%! ()! ?/89(/! $*'! ()! &(48<'/! ?#(&(! N$4(/! &'<! 4'<$<>! '! ;8(%! /($)8:$/! ()! ?/'0(42'! (%! (<(! 9'9(%2'>!'!;8(%!?'<2?'%(/!)$!&(48<8B%!$)!<8A#8(%2(!$*'.!7#!&(48<8B%!&(?(%&(/O!&(!4#O)!&(! )$<!&'<!&(48<8'%(<!)(!$?'/2(!9$0'/!G$)'/.!C'/!(=(9?)'>!<8!()!?/'0(42'!G$)(!+]+>Y`!98))'%(<!0! &(48&(!/($)8:$/!()!?/'0(42'!()!61X!<(/O!8A#$)!$!],>-`!98))'%(<!S/(4#(/&(!D#(!$N'/$!()!4'<2(! &(!)$!8%G(/<8B%!(<!&(!]\>`!98))'%(<U_!<8%!(9;$/A'>!<8!&(48&(!(<?(/$/!()!G$)'/!D#(!';28(%(!(<! 8A#$)!$J! ! 10 Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 33 Opción real de diferir un proyecto de inversión VAN+1 = ! &'%&(!?!(<!8A#$)!$J! ! ! p = 205,905 x p + 2,345 x (1 - p) = 79,71 ! 1,03 (1 + rf ) - D 1,03 - 0,5769 = = 0,3918 ! U - D 1,7333 - 0,5769 ! (<!&(48/>!()(A8/O!/($)8:$/!()!?/'0(42'!?'/D#(!()!G$)'/!&(!(<$!&(48<8B%!S],>-`!98))'%(<U!(<!<#?(I /8'/!$)!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?'%(/)$! $)! <8A#8(%2(!$*'!G$)(!Z>-]!98))'%(<!&(!(#/'<.! ! "'%!)'<!&'<!G$)'/(<!&(!],>-`!98))'%(<!0!Z>-]!98))'%(<!9#)28?)84$&'<!?'/!<#<!4'//(<?'%&8(%I 2(<!?/';$;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 ! 7$;8(%&'!D#(!()!61X!;O<84'!&()!?/'0(42'!(<!&(!YZ!98))'%(<!&(!(#/'<!()!G$)'/!&(!)$!'?48B%!&(! &8H(/8/)'>!#%'!'!&'<!$*'<>!(<!8A#$)!$!)$!&8H(/(%48$!(%2/(!()!61X!2'2$)!0!()!61X!;O<84'>!(<!&(48/>! ! j>Yj!98))'%(<!&(!(#/'<.! ! ! ! ? "# 4@#(3+$,%#)/#@3'/%)$ A@1/! A@1/ ! c$!G$)'/$48B%!&(!)$!'?48B%!&(!&8H(/8/!%'<!&84(!4#O%2'!G$)(!()!&(/(4N'!$!/(2/$<$/!)$!/($)8:$48B%! &(!#%!?/'0(42'!&(!8%G(/<8B%.!78%!(9;$/A'>!N$0!'2/$!'?48B%!D#(!%'<!&84(!4#O%2'!G$)(!/($)8:$/! $N'/$!98<9'!#%$!?(D#(*$!?$/2(!&()!?/'0(42'>!$!)$!D#(!4'%'4(9'<!4'9'!<'%&('!#!'?48B%! &(!$?/(%&8:$=(.!Q;G8$9(%2(>!(<2$!V)289$!'?48B%!/(<2$!G$)'/!$!)$!'?48B%!&(!&8H(/8/.! ! c$! !"#$%&' ()' ,"+)&($4,5)! <#/A(! 4#$%&'! #%$! (9?/(<$! <(! (%4#(%2/$! $%2(! )$! ?'<8;8)8&$&! &(! 8%G(/28/!&8%(/'!4'%!';=(2'!&(!$4()(/$/!)$!$&D#8<848B%!&(!4'%'4898(%2'!'!8%H'/9$48B%!S/(&#48/! ()!&(<H$<(!2(4%')BA84'!(%!5TR!'!$G(/8A#$/!)$!4$%28&$&!&(!98%(/$)!&8<?'%8;)(!(%!#%$!(M?)'2$I 48B%>!?'/!(=(9?)'U!0!#28)8:$/!)'!D#(!N$!$?/(%&8&'!4'%!';=(2'!&(!4$)4#)$/!9(='/!)$!&(9$%&$!&(! <#!?/'&#42'!0>!?'/!2$%2'>!/(428H84$/!'!4'%H8/9$/!<#<!(M?(42$28G$<!$4(/4$!&(!)'<!H)#='<!&(!4$=$! ?/(G8<2'<.!c$!(9?/(<$!&(;(!4'%2/$?'%(/!()!G$)'/!&(!)$!'?48B%!?$/$!$42#$/!4'%!)$!8%H'/9$48B%! ';2(%8&$!4'%2/$!()!4'<2(!&(!$&D#8/8/!E<2$!V)289$.! ! C'/! (=(9?)'>! )$<! (9?/(<$<! 98%(/$<! 28(%(%! D#(! &(48&8/! 4#O%&'! &(<$//'))$/! )$<! ?/'?8(&$&(<! D#(! ?'<((%! 0! 4#O%2'! 'H/(4(/! ?'/! ()! &(/(4N'! $! &(<$//'))$/! ?/'?8(&$&(<! $&848'%$)(<.! R84N$<! 11 Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 33 Opción real de diferir un proyecto de inversión &(48<8'%(<!<#()(%!89?)84$/!#%$!4'9;8%$48B%!&(!'?48'%(<.!1<3>!(%!()!4$<'!&(!#%$!(M?)'2$48B%! ?(2/')(/$! (<! 8%2(/(<$%2(! (<?(/$/! $! G(/! <8! ()! ?/(48'! &()! 4/#&'! $<48(%&(! ?$/$! ?/'4(&(/! $! (MI 2/$(/)'!?(/'>!2$9;8E%>!&(;(9'<!4'%'4(/!()!G')#9(%!&(!)$!;')<$!&(!?(2/B)('!D#(!?(%<$9'<! (M?)'2$/>!)'!D#(!<(!4'%<8A#(!4'%!#%$!<(/8(!&(!?/#(;$<!D#(!4#(<2$%!&8%(/'!S?/#(;$!<3<984$!m 9O<!;$/$2$!?(/'!9O<!8%(M$42$I!'!#%$!?(/H'/$48B%!&(!?/#(;$!m9O<!4$/$!0!9O<!(M$42$U.!c$<! H#(%2(<!&(!)$!8%4(/28&#9;/(!<'%!()!?/(48'!&()!;$//8)!&(!?(2/B)('!4/#&'!0!()!2$9$*'!&()!0$I 4898(%2'.!C'/!2$%2'>!N$0!D#(!?'%&(/$/!()!G$)'/!&(!)$!'?48B%!&(!&8H(/8/!4'%!/(<?(42'!$)!&(!)$! 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(%! )$! &8/(448B%! &(<($&$.! c'<! $428G'<! <#;0$4(%2(<! ?#(&(%! 2(%(/! &8H(/(%2(<! 4$/$42(/3<284$<>!2$)(<!4'9'!H(4N$!&(!G(%4898(%2'!0!?/(48'!&(!(=(/4848'>!?(/'!2'&'<!&(;(%!9'G(/<(!(%!)$!98<9$!&8/(448B%!(%! )$!D#(!()!2(%(&'/!&(!)$!'?48B%!N$!$?'<2$&'. 12 Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 33 Opción real de diferir un proyecto de inversión ! 1#%D#(!(%!#%'<!2E/98%'<!9O<!A(%E/84'<>!()!G$)'/!&(!)$!'?48B%!&(!$?/(%&(/!(<!H#%48B%!&()! ?/(48'!&(!(=(/4848'!ID#(!(<!()!4'<2(!&(!$?/(%&(/I!&()!%8G()!&(!4(/28&#9;/(!D#(!<(!4/($!4'%!()! $?/(%&8:$=(>!0!&(!4B9'!(<2'!<(!2/$&#4(!(%!#%$!9(='/$!&(!)$!2'9$!&(!&(48<8'%(<!?$/$!4/($/! 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M!Z>\!T!SI[+>Y\aI\>--aU 8 14 Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 33 Opción real de diferir un proyecto de inversión ! 0!+I?!<(/O!8A#$)!$!`+>Y]Ya.!"'%!())$<!4$)4#)$/(9'<!()!G$)'/!$42#$)!&(!)'<!?/(48'<!8%2/3%<(4'<! &(!)$!'?48B%!&(!G(%2$!(%!)$!H(4N$!&(!(=(/4848'_!Z!0![-.jj[!(#/'<>!/(<?(428G$9(%2(.! ! ! b8A.!]! ! ! VA (pérdida) = ! 0 x p + 28.772 x (1 - p) = 14.568! ! 1,015 ! @<2(!G$)'/!8%&84$/O!()!9OM89'!A$<2'!$!/($)8:$/!(%!#%!<'%&('!&(!'?8%8B%!S<8(9?/(!<(/O!?/(H(I /8;)(!?(/&(/!)$!?/89$!&(!)$!'?48B%>!)'<!+\.`,-!(#/'<>!D#(!)'<![-.jj[!(#/'<!<8!()!(<4(%$/8'!H8%$)! ! /(<#)2$!<(/!()!?('/U.! ! ! # E$E4$(F'@G$@# ! 1^F1X>!^$/2N$!0!rPc1g5c1r1>!X$)89!S+]]]UJ!8),-'9"/$!&2.!s$/G$/&!P%8G(/<820!C/(<<.! eQ@F>!b.!C(2(/!S[ZZ[UJ!:;)'8),-'9"/$!&2'<!-=/$!&.!t'N%!u8)(0.!X#(G$!d'/h.! eF1"s>!^$/8'%!S[ZZYUJ!8),-'9"/$!&2'$&'>+,#/$#).!t'N%!u8)(0.!X#(G$!d'/h.! "QC@c1XR>!g.>!1Xg5r1FQ6>!6.!S[ZZYUJ!8),-'9"/$!&2?'@'>+,#/$/$!&)+A2'B=$()>!"(%A$A(!c($/%8%A>!X#(G$!d'/h.! 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G$)'/! &()! ?/'0(42'!&()!+Za.!{"#O%2'!G$)(!$N'/$!)$!'?48B%!&(!&8H(/8/|!! ! >I"!c'<!&8/(428G'<!&(!#%$!4'9?$*3$!(<2O%!&(48&8(%&'!<';/(!)$!4'%G(%8(%48$!&(!)$%:$/!#%!%#(G'! ?/'&#42'!$)!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(%&(! $!+j!98))'%(<!&(!(#/'<.!@)!A(/(%2(!&(!?/'&#42'!$)!D#(!<(!(%4$/A$!(<2(!?/'0(42'!<')8482$!$?)$:$/! )$!&(48<8B%!<(8<!9(<(<!?$/$!?'&(/!/($)8:$/!#%!<'%&('!D#(!)(!?(/982$!<$;(/!4#O)!(<!)$!&(9$%&$! (<?(/$&$.! 7$;8(%&'! D#(! ()! 28?'! &(! 8%2(/E<! <8%! /8(<A'! $%#$)! (<! &()! Ya! <(! &(<($! 4'%'4(/! )$! 4$%28&$&!9OM89$!D#(!&(;(!A$<2$/<(!(%!()!<'%&('.! 17