La valoración de los activos de renta fija renta fija
Transcript of La valoración de los activos de renta fija renta fija
Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
La valoración de los activos de La valoración de los activos de renta fijarenta fija
© Juan Mascareñas
Universidad Complutense de Madrid
Versión inicial: mayo 1991 - Última versión: marzo 2013
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Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
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Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
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P1 = 12,51,1212 + 12,5
(1,1212)(1,1357) + 12,5 + 100(1,1212) (1.1357) (1.1551) = 97,45 ! !
Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
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P1 = 12,5(1 + 1r3)
+ 12,5(1 + 1r3)2
+ 12,5 + 100(1 + 1r3)3
= 97,45 !" 1r3 = 13,59%!
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r = 12,50 + 97,45100 - 1 = 9,95% !
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Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
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Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
5
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P = Q(1 + k) + Q
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Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
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##
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.%*&-(&.%*&-(& !!!^',! /6.(=$*(+," $)/0'(;$6.%" /" 0%&*$'$6.%" $,'(*(1$-$)%,'%! ($! ,8/A--,! ('! -,! 8/(! $/!()+$#&! *+('(! (-! .(&(<@#! .(! &(<#)%&,&-,?! ,! /'! %&(<+#! %&(H+:,.#?! ,'*($! .(! $/! ;('<+F)+('*#5!4'! -,!H+>/&,!Y!$(!#9$(&;,'! -,$!</&;,$!%&(<+#c&('.+)+('*#!.(!/',!#9-+>,<+0'!'#&),-!J!.(!/',!8/(!$(&=!,)#&*+3,.,!,'*+<+%,.,)('*(!('!</,'*#!$/!%&(<+#!.(!)(&F<,.#!,-<,'<(!-#$!NRQ!(/&#$5!I,!</&;,!%&(<+#c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
,)#&*+3,<+0'QB!NRQ!(/&#$5!M&(<+$,)('*(?!</,'.#!-#$!*+%#$!.(!+'*(&A$!$#'!+'H(&+#&($!,!
/'! &('.+)+('*#!.(*(&)+',.#! &d! D8/(!,/'8/(!%/(.(!$(&!.($<#'#<+.#!$,9()#$!8/(!(1+$*(E!(-!%&(<+#!.(!)(&<,.#!.(!-,!#9-+>,<+0'!,)#&*+3,9-(!$(!$(%,&,!.(!-,!#*&,!</&;,!J!*+('.(!@,<+,!(-!%&(<+#!.(!&(()9#-$#!,'*+<+%,.#]!($*,!%,&*(!.(-!>&=H+<#!*+('(!/',!H#&F),!8/(!$(!.('#)+',"*/,:%D(-$-",%=$'(:$!J!($!+'.+<,*+;,!.(!-,!*/)10%&(+,"-%."10%*(/!.(!($*(!*+%#!.(!#9-+>,<+#'($5!4'!<#'<-/$+0'?!$+!-#$!*+%#$!.(!+'*(&A$!,$<+('.('!(-!<#)F%#&*,)+('*#! .(! ,)9#$! *+%#$! .(! 9#'#$! ($! (-!)+$)#?! .+H+&+('.#! $+! ,8/A--#$! .($<('F.+($('5!!
!O+>5Y!C/&;,$!%&(<+#c&('.+)+('*#!$(>G'!8/(!-,!#9-+>,<+0'!$(,!'#&),-!#!,)#&*+3,9-(!<#'!,'*+<+%,<+0'!('!
</,'*#!$/!%&(<+#!,-<,'<(!-,$!NRQ!(/&#$!
!I#$! +';(&$#&($!('!($*(!*+%#!.(!9#'#$!$,-('!%(&:/.+<,.#$!*,'*#!%#&8/(!(-!%&(<+#!.(-!9#'#!*+('(!/'!e*(<@#f!<#)#!%#&8/(!$(!;('!#9-+>,.#$!,!<#&&(&!/'!&+($>#!.(!&(+';(&F
2 El precio de mercado podría superar el precio de amortización anticipada si aún queda suficiente tiempo para la
fecha en que ésta se pueda producir. Lo mismo que les ocurre a las obligaciones normales cuyo precio de mercado puede superar el precio de reembolso si su rendimiento desciende por debajo del tipo de interés del cupón.
Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
7
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
F<&*2/0B! K/%#'>,)#$!8/(!/',!()%&($,!@,!()+*+.#!/'!()%&A$*+*#! <#)%/($*#!%#&!#9-+>,<+#'($!.(!NRR!(/&#$!8/(!%&#)(*(!%,>,&!/'!NRS!,'/,-?!%#&!,'/,-+.,.($!;('<+F.,$?!J!,-!8/(!-(!&($*,'!<+'<#!,2#$!.(!;+.,5!I,!()+$+0'!--(;,!,%,&(:,.,!-,!%#$+9+-+.,.!.(!$(&!,)#&*+3,.,!,'*+<+%,.,)('*(!.('*&#!.(!.#$!,2#$?!%#&!/'!%&(<+#!.(!&(()9#-$#!.(!NRQ!(/&#$5!K/!%&(<+#!.(!)(&<,.#!($!,<*/,-)('*(!.(!NRX?WR!(/&#$5!!4-!&('.+)+('*#!@,$*,!(-!;('<+)+('*#!.(!.+<@,!#9-+>,<+0'!$(!<,-</-,&=!.($%(:,'.#!&;!
.(!-,!$+>/+('*(!(</,<+0'B!!
!
104,5 = 10(1 + rv)j
j=1
5
" + 100(1 + rv)5
# rv = 8,8476% !
!M#&!#*&#!-,.#?!(-!&('.+)+('*#!@,$*,!-,!%&+)(&,!H(<@,!.(!;('<+)+('*#!D&,E!$(!<,-</-,&=!
.(!-,!$+>/+('*(!H#&),B!!
!
104,5 = 10(1 + ra )
+ 112(1 + ra)2
" ra = 8,4215%!
!C#)#!&,!g!&;!*#),&()#$!<#)#!&('.+)+('*#!.(!-,!#9-+>,<+0'!`?XQNWS5!h*&,!H#&),!.(!
<#)%	,&-#!<#'$+$*(!('! +>/,-,&!,)9,$!(</,<+#'($?!.($%(:,&!&?!J!<,-</-,&!</=-!($!(-!%&(<+#!.(!-,!#9-+>,<+0'!%,&,!.+<@,!&?!<#'!-#!8/(!#9*('.&()#$!(-!.('#)+',.#!10%*(/"-%"*03*%B!!
!
10(1 + r )j
j=1
5
" + 100(1 + r )5 = 10
(1 + r ) + 112(1 + r )2 # r = 9,207% !
!(-!;,-#&!.(!-,!#9-+>,<+0'!%,&,!/'!&('.+)+('*#!.(-!_?QRVS!($!+>/,-!,!NRU?RY`!b!8/(!($!(-!10%*(/" -%" *03*%5! C#)#! 8/+(&,! 8/(! A$*(! G-*+)#! ($! +'H(&+#&! ,-! %&(<+#! .(!)(&<,.#!DNRX?W!(/&#$E!&(%&($('*,!8/(!@,J!>&,'.($!%	,9+-+.,.($!.(!8/(!-,!()%&($,!%&#<(.,!,!,)#&*+3,&!-,!()+$+0'!.('*&#!.(!/'!%,&!.(!,2#$5!
!
Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
8
;"!#F/#&-?0G4&#.&#/%#(&01H%#.&#B%/01%+),-#.+)0-&'U!
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)+('*#!8/(!;(&()#$!,!<#'*+'/,<+0'X5!^',!;(3!8/(!*('>,)#$!,)9#$!;,-#&($!%#.&(F
)#$!<,-</-,&!(-!%&(<+#!*(0&+<#!.(!-,!()+$+0'!.(!&('*,!H+:,!<#'!%#$+9+-+.,.!.(!,)#&*+3,F<+0'!,'*+<+%,.,5!C#'!(--#!%#.&()#$!;(&!$+!($*=!$#9&(;,-#&,.,!#!+'H&,;,-#&,.,5!!
3 6!($*(!('H#8/(!*,)9+A'!$(!-(!<#'#<(!<#)#!(-!0%,-()(%,'/"$F3&'$-/"$".$"/1*(+,!D/1'(/,!$-F3&'%-">(%.-E5!T(9+.#!,!8/(!-#$!+';(&$#&($!<#*+3,'!($*#$!9#'#$!,!*&,;A$!.(!$/$!&('.+)+('*#$!<#)%,&='.#-#$!<#'!-#$!9#'#$!.(-!4$*,.#!.(-!)+$)#!%-,3#!($!'(<($,&+#!.(H+'+&!(-!h6K!#!-(A%0%,*($."$F3&'$-/"$".$"/1*(+,!8/(!($!(-!.+H(&('<+,-!<#'$*,'*(!8/(!,2,.+.#!,!-#$!*+%#$!,!%-,3#!+)%-7<+*#$!%&#%#&<+#',!-,!$(&+(!.(!*+%#$!.(!.($</('*#!8/(!$(!/*+-+3,'!%,&,!.($<#'*,&!-#$!H-/:#$!.(!<,:,!@,<+('.#!8/(!(-!%&(<+#!*(0&+<#!.(-!9#'#!$(,!+.A'*+<#!,-!.(!)(&<,.#]!.+<@#$!H-/:#$!.(!<,:,!@,'!$+F.#!,:/$*,.#$!%,&,!&(H-(:,&!-,!#%<+0'!+)%-7<+*,5!M#&!*,'*#?!(-!h6K!)+.(!(-!.+H(&('<+,-!.(-!&('.+)+('*#!.(!/'!,<*+;#!.(!&('*,!H+:,!8/(!'#!($!,*&+9/+9-(!,!-,!#%<+0'!+)%-7<+*,5!
M#&!(:()%-#?!/'!9#'#!,)#&*+3,9-(!<#'!/'!;('<+)+('*#!,!NR!,2#$!J!/'!</%0'!.(-!YS!$(!;('.(!,!NNY?QQ5!K/!Z[\!($!.(-!XS?!$+! -,!#9-+>,<+0'!.(-!4$*,.#!.(-!)+$)#!%-,3#!*+('(!/',!Z[\!.(-!U?NWS?!(-!.+H(&('<+,-!$(&=!.(!`W!%95!M#&!#*&,!%,&*(?!$+!(-!;,-#&!($*+),.#!.(!-,!#%<+0'!($!U?YX!('*#'<($!(-!;,-#&!+)%-7<+*#!.(-!9#'#!'#!&($<,*,9-(!($!NN_?`Y!J!$/!&('.+)+('*#!($!.(-!U?YS!D&('.+)+('*#!,:/$*,.#!,!-,!#%<+0'E5!6$7!8/(!(-!h6K!($!.(!XW!%9!D#%/($*#!,-!.+H(&('<+,-!.(!`W!%9E?!($!.(<+&?!U?YS!F!U?NWS!a!R?XWS5!X! 4'! (-! ,%A'.+<(! 6! .(-! %&+)(&! <,%7*/-#! .(-! -+9&#! K,*J,:+*! T6KG" H'03*'30%-" I/'%&" $,-" 2%0(:$'(:%" J)6%--%-"H%*30('(%&5! 4/&#)#'(J5! I#'.&($5! N__Y?! $(! <#)('*,'! -#$! %&+'<+%,-($! )A*#.#$! .(! ;,-#&,<+0'! .(! ($*(! *+%#! .(!#%<+#'($B!i(&*#']!j,--FZ#&#/$]!K<@,(H(&FK<@k,&*3]!P,$+<(l]!C#/&*,.#']!C#1F['>(&$#--F\#$$]!j&('','FK<@k,&*3]!m/--Fn@+*(]!m(,*@Fo,&&#kFi#&*#']!m#FI((]!j-,<lFT(&),'FZ#J5
Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
9
I,$!%&+'<+%,-($!.+H(&('<+,$!.(!-,!;,-#&,<+0'!.(!-,!#%<+0'!.(!<#)%&,!.(!-#$!9#'#$!%#&!%,&*(!.(!-,!()%&($,!<#'!&(-,<+0'!,!-,!;,-#&,<+0'!.(!-,$!#%<+#'($!$#9&(!,<<+#'($!#&.+F',&+,$!$#'B!! ! ! ! ! ! ! ! !!
,E!4-!%&(<+#!.(!(:(&<+<+#!.(!-,!#%<+0'!%/(.(!$(&!;,&+,9-(!9E!I,!#%<+0'!%/(.(!*('(&!;,&+,$!H(<@,$!.(!(:(&<+<+#!J!$+!'#!$(!(:(&<(!('!/',!.(!
(--,$!9+('!%#.&7,!@,<(&$(!('!-,!$+>/+('*(!D($?!%/($?!/',!#%<+0'!6%0)3-$E5!<E!I,!;#-,*+-+.,.!.(-!,<*+;#!$/9J,<('*(!($!.(<&(<+('*(!<#'!(-!*+()%#5!4-!%&(<+#!
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/!a!(!!!!!!!!!!!!!.!a!("!!a!Nc.!!P,!,!$(&!G*+-!<#'#<(&!-,!&(-,<+0'!('*&(!,)9#$B!/c.!!!
/c.!a!(!!p!("!!a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i,$<,&(2,$?! o/,'! DQRNNEB! eh%<+#'($! &(,-($B! ;,-#&,<+0'! %#&! (-!)A*#.#! 9+'#)+,-f5! N/,/=0$AB$&" -%" O3$," N$&*$0%P$&" &/60%" Q(,$,;$&" R/01/0$'(:$&! 'q! UQ5! [KK"BN_``FN`V`!T($<,&>,9-(!('B!@**%Bcckkk5/<)5($c+'H#c:),$c)#'#>&,H5@*)
Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
10
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Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
11
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Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
12
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Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
13
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Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
14
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Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
15
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Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
16
!
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Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
17
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!
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ratio de conversión = valor nominal de la obligación convertibleprecio de conversión !
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Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
18
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10 ^'!(:()%-#!.(!$+$*(),!.(!%&#*(<<+0'!<#'*&,!-,!.+-/<+0'!%&#./<+.,!,-!(1+$*+&!/',!,)%-+,<+0'!.(!<,%+*,-!./&,'*(!(-!%(&7#.#!.(!<#';(&$+0'!.(!-,!#9-+>,<+0'!%/(.(!<#'$/-*,&$(!('!-,!#9&,!.(!o#$A!45!C6Cmh"?!8/(!H+>/&,!('!-,!9+9-+#>&,H7,!D%=>+',$B!QYWFQVRE5
Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
19
;#<,!/'!+'<&()('*#!('!(-!&('.+)+('*#!(1+>+.#!%#&!-#$!+';(&$#&($!,!-,!#9-+>,<+0'!'#&F),-! 8/(! H#&),!%,&*(! .(-! *7*/-#! <#';(&*+9-(5! M(&#?! %#&! #*&#! -,.#?! ($*(! ,/)('*#! .(-!&+($>#!9('(H+<+,!,!-,!;#-,*+-+.,.!.(-!%&(<+#!.(!-,!,<<+0'!#&.+',&+,!J?!%#&!*,'*#?!,!-,!#%F<+0'!.(!<#';(&$+0']!</,'*#!),J#&!$(,!(-!&+($>#!J!-,!;#-,*+-+.,.!.(-!%&(<+#!.(!-,!,<<+0'!#&.+',&+,?!),J#&!$(&=!-,!%	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v,! @,! 8/(.,.#! <-,&#! 8/(! -,! #9-+>,<+0'! <#';(&*+9-(! $(! <#)%#'(! .(! /',! #9-+>,<+0'!'#&),-!J!/',!#%<+0'!.(!<#';(&$+0'?!%#&!(--#!$/!;,-#&!*(0&+<#!($!$/%(&+#&!#!+>/,-!,-!.(!/',!#9-+>,<+0'!'#&),-5!4$*#!$(!%/(.(!<#)%	,&!,-!#9$(&;,&!<#)#!*,'*#!-#$!</%#'($!<#)#!(-!&('.+)+('*#!@,$*,!(-!;('<+)+('*#!.(!-,$!#9-+>,<+#'($!<#';(&*+9-($!$/(-('!$(&!
Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
20
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
!O+>5QR!I,!&(-,<+0'!('*&(!-#$!%&(<+#$!.(!)(&<,.#!.(!-,!#9-+>,<+0'!<#';(&*+9-(!J!.(!-,!,<<+0'!#&.+',&+,!
!4-!)#.(-#!.(!;,-#&,<+0'!.(!/',!#9-+>,<+0'!<#';(&*+9-(! <#)9+',!(-! ;,-#&! *(0&+<#!.(!/',!#9-+>,<+0'!'#&),-?!<#'!(-!;,-#&!*(0&+<#!.(!-,$!,<<+#'($!,!('*&(>,&!,!<,)9+#!.(!.+F<@,!#9-+>,<+0'!('!(-!)#)('*#!.(!-,!<#';(&$+0'5!C#)#!$,9()#$?!(-!;,-#&!*(0&+<#!.(!-,!#9-+>,<+0'!#&.+',&+,!;+('(!.,.#!%#&!-,!(1%&($+0'!DC!($!(-!;,-#&!.(-!</%0']!M
'!($!(-!%&(F
<+#!.(!&(()9#-$#]!J!l!($!-,!*,$,!.(!&('.+)+('*#!)7'+),!&(8/(&+.,EB!!
!
P0 = C(1 + k)jj=1
n
" + Pn(1 + k)n !
!)+('*&,$!8/(!(-!:$./0"-%"*/,:%0&(+,!('!-,!H(<@,!.(!-,!)+$),!DPC*E!.(%('.(&=!.(-!%&(F<+#!.(!)(&<,.#!,<*/,-!.(! -,$! ,<<+#'($!.(! -,! <#)%,27,! DKRE?! .(! -,! *,$,!($%(&,.,!.(!<&(<+)+('*#!,'/,-!J!,</)/-,*+;#!.(!-,$!)+$),$!D>E!J!.(-!&,*+#!.(!<#';(&$+0'!D\CEB!!
PC*!a!KR!1!DNr>E*!1!\C!
!6$7!8/(!<#)9+','.#!,)9,$!(1%&($+#'($!J!$/$*+*/J('.#?!('! -,! H(<@,!.(!<#';(&$+0'?!-#$!</%#'($!8/(! &($*,'!%#&!%,>,&!)=$!(-!%&(<+#!.(! &(()9#-$#!%#&!(-!),J#&!.(! -#$!.#$!$+>/+('*($!;,-#&($B!(-!;,-#&!.(!<#';(&$+0'!DPC*E!J!(-!;,-#&!.(-!9#'#!#&.+',&+#!('!-,!H(<@,!.(!<#';(&$+0'! DM*E?!#9*('.&()#$!(-!;,-#&! *(0&+<#!.(! -,!#9-+>,<+0'!<#';(&*+9-(!('!(-!)#)('*#!,<*/,-B!!
Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
21
!
P0 = C(1 + k)jj=1
t" + Máx [VCt ; Pt]
(1 + k)t !
!!
F<&*2/0N!^',!<#)%,27,!@,!()+*+.#!/',$!#9-+>,<+#'($!<#';(&*+9-($!,!-,$!8/(!-($!8/(F.,'!'/(;(!,2#$!@,$*,!$/!;('<+)+('*#?!$/!;,-#&!'#)+',-!($!.(!NRR!(/&#$!J!%,>,!/'!</%0'!.(!NR!(/&#$!,'/,-($5!I,!#9-+>,<+0'!%/(.(!<#';(&*+&$(!%#&!*&($!,<<+#'($!#&.+',F&+,$!/',!;(3!*&,'$</&&+.#$!</,*&#!,2#$!.($.(!,@#&,5!4-!%&(<+#!,<*/,-!.(!-,$!,<<+#'($!.(!-,!<#)%,27,!($!.(!UX!(/&#$!%#&!,<<+0'!J!$(!($%(&,!8/(!<&(3<,!,!/',!*,$,!)(.+,!,'/,-!J!,</)/-,*+;,!.(-!VS5!I,! *,$,!.(!.($</('*#!,%&#%+,.,!($!.(-!_S5!I,! *,$,!.(!&('.+)+('*#!,'/,-!)(.+,!.(! -#$!9#'#$!#&.+',&+#$! $+)+-,&($! ,! A$*(!8/(! &(>+&=! ('!(-!%(&+#.#!8/(!;,!.($.(!(-!H+',-!.(-!,2#!Xq!@,$*,!(-!H+',-!.(!-,!;+.,!.(!-,!()+$+0'!($!.(-!`S! ,'/,-5! C,-</-,&()#$! (-! %&(<+#! *(0&+<#! .(! -,! #9-+>,<+0'! <#';(&*+9-(! $/%#'+('.#!8/(!$/!%&#%+(*,&+#!*#),!-,!.(<+$+0'!.(!<#';(&*+&-,?!#!'#?!('!,<<+#'($!('! -,!%&+)(&,!H(<@,!%#$+9-(5!!4-!%&(<+#!,<*/,-!.(!-,!#9-+>,<+0'!'#&),-!D'#!$(!#-;+.(!8/(!@,!*&,'$</&&+.#!/'!,2#!.($F.(!-,!()+$+0'?!-/(>#!,!-,!#9-+>,<+0'!-(!8/(.,'!'/(;(!,2#$!.(!;+.,E!($!+>/,-!,B!!
!
P0 = 10(1,09)jj=1
9" + 100
(1,09)9 = 106 euros!
!4-!%&(<+#!.(!-,!#9-+>,<+0'!'#&),-!,-!H+',-!.(-!</,&*#!,2#!u<#'*,'.#!.($.(!,@#&,F!$(&=!+>/,-!,!D&(</(&.(!X&W!a!`SEB!!
!
P4 = 10(1,08) + 10
(1,08)2 + 10(1,08)3 + 10
(1,08)4 + 110(1,08)5 = 108 euros !
!6@#&,!%&#<(.(&()#$!,!<,-</-,&!(-!;,-#&!.(!<#';(&$+0'!.(!-,!()+$+0'!.('*&#!.(!</,*&#!,2#$?!8/(!($!-,!%&+)(&,!.(!-,$!H(<@,$!%#$+9-($!%,&,!<#';(&*+&!-,!()+$+0'B!!
VC4 = S0 x (1+g)t x RC = 34 x (1,07)
4 x 3 = 133,7 euros
!I/(>#!(-!%&(<+#!+'*&7'$(<#!.(!-,!#9-+>,<+0'!<#';(&*+9-(!$(&=B!!
!
P0 = 10(1,09)jj=1
4" + Máx(108;133,7)
(1,09)4 = 127,11 euros !
!J?!<#)#!$(!,%&(<+,?!(-!;,-#&!.(!-,!#%<+0'!.(!<#';(&$+0'!($!+>/,-!,!QN?NN!(/&#$!DNQV?NN!F!NRYE5!
!!!
Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
22
VTWT8"#$":$./0$*(+,"$"'0$:M&"-%".$"6(,/)($."6!($*,$!,-*/&,$!@,!8/(.,.#!<-,&#!8/(!(-!;,-#&!*(0&+<#!.(!-,!#9-+>,<+0'!<#';(&*+9-(!($!+>/,-!,!-,!$/),!.(-!;,-#&!*(0&+<#!.(!-,!#9-+>,<+0'!(8/+;,-('*(!)=$!-,!#%<+0'!.(!<#)F%&,!.(!,<<+#'($!8/(!-(!,<#)%,2,5!!51&+)0#.&#/%#07/)C%+),-#+0-B&1()7/&#I##
51&+)0#.&#/%#07/)C%+),-#-01*%/#A#J%/01#-&(0#.&#/%#02+),-#.&#+0*21%!!I,!;,-#&,<+0'!.(! -,!#%<+0'!('! -,!%&=<*+<,!($!.+H7<+-!.(!,%-+<,&!.(9+.#!,! -,$!$+>/+('*($!&,3#'($B!!
,E!4-!%&(<+#!.(!<#';(&$+0'!$/(-(!,/)('*,&!<#'!(-!*+()%#!-#!8/(!8/+(&(!.(<+&!8/(!(-!%&(<+#!.(!(:(&<+<+#!.(!-,!#%<+0'!<,)9+,5!6.()=$?!%/(.(!@,9(&!.+FH(&('*($!H(<@,$!.(!<#';(&$+0'?!($!.(<+&?!;,&+,$!H(<@,$!.(!;('<+)+('*#!.(!-,!#%<+0'5!
9E!I,$!,<<+#'($!%/(.('!%,>,&!.+;(&$#$!.+;+.('.#$!,!-#!-,&>#!.(!-,!;+.,!.(!-,!#9-+>,<+0'!<#';(&*+9-(! -#!8/(!<#)%-+<,!,G'!)=$!(-!,'=-+$+$!.(! -,!;,-#&,F<+0'!.(!-,!#%<+0'5!
<E!i/<@,$! #9-+>,<+#'($! <#';(&*+9-($! $#'! *,)9+A'! ,)#&*+3,9-($! ,'*+<+%,.,F)('*(!,!>/$*#!.(-!()+$#&!.(!-,$!)+$),$5!
!K+'!()9,&>#?!;,)#$!,!,%-+<,&!(-!)#.(-#!9+'#)+,-!.(!;,-#&,<+0'!.(!#%<+#'($?!<#'!-,!)#.+H+<,<+0'!.(!i(&*#'!%,&,!(-! <,$#!.(! &(%,&*#!.(!.+;+.('.#$?!,!/'!(:()%-#!%,&,!;(&! /'!)A*#.#! ,%+),.#! .(! ;,-#&,<+0'! .(! -,! #%<+0'! .(! <#)%&,! +)%-7<+*,! ('! -,$!#9-+>,<+#'($!<#';(&*+9-($5!M,&,!(--#!/*+-+3,&()#$!-#$!.,*#$!.(-!(:()%-#!,'*(&+#&!,!-#$!8/(! ,2,.+&()#$! ,->/'#!)=$! <#)#B! -,! *,$,! .(! &('.+)+('*#! $+'! &+($>#! %,&,! </,*&#!,2#$!.(!%-,3#!($!.(-!VS?!-,!;#-,*+-+.,.!,'/,-!)(.+,!.(!-,!,<<+0'!#&.+',&+,!($!.(-!QWS!J!-,!*,$,!.(!&('.+)+('*#!$#9&(!.+;+.('.#$!('!H#&),!<#'*+'/,!($!.(-!US5!!v,! $,9()#$!8/(!(-! ;,-#&! *(0&+<#!.(! -,!#9-+>,<+0'!'#&),-! D'/(;(!,2#$!.(!;+.,!J!/'!&('.+)+('*#!@,$*,!(-! ;('<+)+('*#!.(-!_SE!($!.(!NRY!(/&#$?!)+('*&,$!8/(!(-!%&(<+#!($%(&,.#!.(-!9#'#!.('*&#!.(!</,*&#!,2#$!$(&=!+>/,-!,B!!!
!
P5 = 10(1,08) + 10
(1,08)2 + 10(1,08)3 + 10
(1,08)4 + 110(1,08)5 = 108 euros!
!C#';(&*+&! -,$!#9-+>,<+#'($!.('*&#!.(!</,*&#!,2#$! +)%-+<,&7,!$,<&+H+<,&!/'#$!H-/:#$!.(!<,:,!;,-#&,.#$!('!NR`!(/&#$!,!<,)9+#!.(!*&($!,<<+#'($?!#!-#!8/(!($!-#!)+$)#?!UY!(/F&#$!%#&!,<<+0'5!4$*(!G-*+)#!($!(-!%&(<+#!.(!(:(&<+<+#!.(!-,!#%<+0'!.(!<#)%&,5!!!4'!-,!H+>/&,!QN!$(!)/($*&,!(-!=&9#-!9+'#)+,-!&(%&($('*,*+;#!.(-!;,-#&!,<*/,-!.(!-,$!,<F<+#'($5!4-!=&9#-!$(!@,!<#'$*&/+.#!)/-*+%-+<,'.#!<,.,!;,-#&!%#&!/'!<#(H+<+('*(!.(!,$F<('$#!F/F!8/(!($!+>/,-!,!(!!1!(>!a!(R?QW!1!(R?RV!a!N?UVVN!J!%#&!/'#!.(!.($<('$#!F.F!8/(!
($!+>/,-!,!(F!!1!(>!a!(FR?QW!1!(R?RV!a!R?`UWU5!h9$A&;($(!8/(!('!(-!<=-</-#!.(!,)9#$!<#(H+F<+('*($!$(!@,!+'<-/+.#!-,!*,$,!.(!<&(<+)+('*#!,'/,-!)(.+#!,</)/-,*+;,!8/(?!&(<#&.(F
Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
23
)#$?!(&,!.(-!VS5!4-!=&9#-!$(!(1*+('.(!./&,'*(!</,*&#!,2#$5!Z,)9+A'!$(!%/(.(!,%&(F<+,&!<#)#!('!<,.,!,2#!$(!.(*&,(!(-!US!.(-!;,-#&!.(!-,!,<<+0'!('!<#'<(%*#!.(!&(%,&*#!.(!.+;+.('.#$5!!
!O+>5!QN!w&9#-!9+'#)+,-!.(!-,!(;#-/<+0'!.(-!%&(<+#!.(!-,!,<<+0'!./&,'*(!-#$!%&01+)#$!</,*&#!,2#$!
!^',!;(3!.+9/:,.#!(-!=&9#-!9+'#)+,-?! J! *('+('.#!('!</('*,!8/(! -,!%&+)(&,! H(<@,!.(!<#';(&$+0'!($!.('*&#!.(!</,*&#!,2#$?!%&#<(.(&()#$!,!<#)%,&,&!(-!;,-#&!8/(?!('!.+F<@,! H(<@,!.(! <#';(&$+0'?! *('.&=! -,! ,<<+0'! <#'! &($%(<*#! ,-! 8/(! *('.&=!(-! %&(<+#!.(!(:(&<+<+#5!K+!,8/A-!($!),J#&!8/(!A$*(!<,-</-,&()#$! -,!.+H(&('<+,?!8/(!($!(-!;,-#&! +'F*&7'$(<#!.(! -,!#%<+0'!.(!<#)%&,?!('!<,$#!<#'*&,&+#?!(-!&($/-*,.#!$(&=!<(!6$7?!%#&!(:()%-#?!(-!;,-#&!.(!NR`?QY!b!$(&=!<#)%,&,.#!<#'!(-!%&(<+#!.(!(:(&<+<+#!UY!b!J!<#)#!,8/A-!($!),J#&!<,-</-,&()#$!(-!;,-#&!+'*&7'$(<#!.(!-,!#%<+0'!VQ?QY!b5!P(,!('!-,!H+>/&,!QQ!D('!;(&.(E!<#)#!.+<@#!;,-#&!,%,&(<(!(-!%&+)(&#!('!-,!<#-/)',!.(!)=$!,!-,!.(&(F<@,5!K+'!()9,&>#?!$+!(-!;,-#&!.(-!$/9J,<('*(!H/($(!QX?_R!b!,-!$(&!+'H(&+#&!,!-#$!UY!b!.(-!%&(<+#!.(!(:(&<+<+#!(-!;,-#&!+'*&7'$(<#!($!'/-#NN5!T(!($*,!),'(&,!#9*('.&()#$!-#$!;,F-#&($!+'*&7'$(<#$!.(!-,!#%<+0'!.(!<#)%&,!.('*&#!.(!</,*&#!,2#$!8/(!H+>/&,'!('!;(&.(!('!-,!%&+)(&,!<#-/)',!.(!-,!.(&(<@,!.(!-,!H+>/&,!QQ5!!!
11 \(</(&.(!8/(!-,!#%<+0'!%&#%#&<+#',!/'!.(&(<@#?!'#!/',!#9-+>,<+0'?!J!(-!;,-#&!.(!/'!.(&(<@#!$0-#!%/(.(!$(&!%#$+*+;#!#!'/-#?!'/'<,!'(>,*+;#!D%#&8/(!-#$!.(&(<@#$!$(!(:(&<('!#!'#!$(!(:(&<('!J!$(!$/%#'(!8/(!$(!(:(&<('!$0-#!</,'.#!$(!#9*+('(!/'!9('(H+<+#!#!$,*+$H,<<+0'E5
Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
24
!O+>5QQ!P,-#&!.(!-,!#%<+0'!.(!<#)%&,!
!6@#&,!<,-</-,&()#$?!.(!H#&),!&(</&$+;,?!(-!;,-#&!.(!-,!#%<+0'!('!<,.,!/'#!.(!-#$!%(F&7#.#$!)#;+A'.#'#$!.(!.(&(<@,!@,<+,!+38/+(&.,5!M,&,!(--#!%&+)(&,)('*(!.(9(&()#$!<,-</-,&!(-!;,-#&!.(!-,$!e%	,9+-+.,.($!'(/*&,-($!,-!&+($>#f!8/(!+'.+<,'!-,$!%#'.(&,F<+#'($!8/(!(-!)#.(-#!,$+>',!,!<,.,!,$<('$#!J!,!<,.,!.($<('$#5!6$7?! -,!%	,9+-+.,.!.(!,$<('$#!$(&=?!$+()%&(!8/(!-,!;#-,*+-+.,.!$(!),'*('>,!<#'$*,'*(?!+>/,-!,B!!
!
p =1 + rf " du - d = 1,07 - 0,8353
1,3771 - 0,8353= 0,4332 = 43,32%
!)+('*&,$!8/(!-,!.(!<,.,!.($<('$#!$(&=!+>/,-!,!NF%!a!WY?Y`S5!M#&!*,'*#?!(-!%&+)(&!;,F-#&!.(!-,!#%<+0'!.(!<#)%&,!('!(-!,2#!*(&<(&#!$(&=!+>/,-!,!#9*('(&!-,!)(.+,!%#'.(&,F.,!.(!-#$!.#$!;,-#&($!8/(!%/(.(!*#),&!('!(-!</,&*#!,2#?!,<*/,-+3,.,!/'!%(&+#.#!,-!*+F%#!.(!+'*(&A$!$+'!&+($>#!<#'*+'/#B!!
!
cuuu = 72,26 " p + 29,66 " (1 -p)(1,07) = 44,97 !
!(-!$+>/+('*(!;,-#&!$(&7,B!!
!
cuud = 29,66 " p + 3,83 " (1 -p)1,07 = 14,04 !
!J!(-!*(&<(&!;,-#&!.(!($(!,2#!$(&7,B!!
!
cudd = 3,83 " p + 0 " (1 -p)1,07 = 1,55 !
!
Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
25
J!(-!G-*+)#!;,-#&!.(!($(!,2#!*#),!/'!;,-#&!'/-#!%#&8/(!$/!;,-#&!,!H+',-($!.(-!</,&*#!,2#!*,)9+A'!-#!($5!4-!)+$)#!%&#<(.+)+('*#!/*+-+3,&7,)#$!%,&,!<,-</-,&!(-!;,-#&!*(0&+F<#!.(!-,!#%<+0'!.(!<#)%&,!,-!H+',-!.(-!$(>/'.#!,2#!DQW?YX!b]!Y?WR!b]!J!R?YU!bE?!,-!H+',-!.(-!%&+)(&#!DNU?`U!b!J!Q?_Y!bE?! --(>,'.#!,$7!,-!)#)('*#!,<*/,-!</J#!;,-#&!$(!<,-</F-,&7,!.(!+>/,-!),'(&,B!!
!
c = 13,83 " p + 2,96 " (1 -p)1,07 a!V?NV!b!
!M#&!*,'*#?!V?NV!b!($!(-!;,-#&!.(!-,!#%<+0'!.(!<#)%&,!.(!/',!G'+<,!,<<+0'!J!<#)#!<,.,!#9-+>,<+0'!<#';(&*+9-(!<#'<(.7,!(-!.(&(<@#!,!,.8/+&+&!*&($!,<<+#'($!$/!;,-#&!$(&7,!(-!*&+%-(?!($!.(<+&?!QN?WN!b5!!!I/(>#!(-!%&(<+#!.(-!*7*/-#!<#';(&*+9-(!$(&=!+>/,-!,B!
!MR!a!NRY!r!QN?WN!a!NQV?WN!b5!
!4$!<#';('+('*(!&($,-*,&?!8/(!('!($*(! *+%#!.(!;,-#&,<+0'!($!)/J! +)%#&*,'*(! -,!(-(<F<+0'! .(! -,! ;#-,*+-+.,.! .(! -,! ,<<+0'! #&.+',&+,?! (-! &('.+)+('*#! <#'! &+($>#! ($%(&,.#! ,!%,&*+&!.(!-,!H(<@,!.(!-,!<#';(&$+0'NQ?!J!(-!&('.+)+('*#!$#9&(!.+;+.('.#$5!!4$!)/J!%#$+9-(!8/(!($*(!;,-#&!$(,!,->#!+'H(&+#&!,-!&(,-!.(9+.#!,!8/(!$0-#!@()#$!*(F'+.#!('!</('*,!-,!%#$+9+-+.,.!.(!<#';(&*+&! -,!#9-+>,<+0'!('!-,!%&+)(&,!H(<@,!.(!<#'F;(&$+0'!J!'#!('!-,$!&($*,'*($5!M,&,!&($#-;(&!($*(!%	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b?! *('>,! /',! %&+),!.(! <#';(&$+0'! .(-!URS!J!/'!/)9&,-!.(!<#';(&$+0'!<#'*+'>('*(!.(-!NQRS?!%/(.(!<#';(&*+&$(!,!NUb!$0-#!$+!-,!,<<+0'!<#*+3,!%#&!('<+),!.(!NW?Yb!Da!NUb!1!N?QE!,!-#!-,&>#!.(!/'!%(&+#.#!.(*(&)+F',.#!D%#&!(:()%-#?!./&,'*(!QR!.(!-#$!UR!.7,$!,'*(&+#&($!,-!H+',-!.(-!*&+)($*&(E5!
12 M,&,!($*#!($!<#';('+('*(!.+$%#'(&!.(!-#$!*+%#$!.(!+'*(&A$!,!%-,3#!+)%-7<+*#$!($%(&,.#$!,!%,&*+&!.(! -,!H(<@,!.(!<#';(&$+0'?!8/(!$(!#9*('.&='!,!*&,;A$!.(!-,!($*&/<*/&,!*()%#&,-!.(!-#$!*+%#$!.(!+'*(&A$5
Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
26
!4-! $(>/'.#!*+%#!.(!<#';(&*+9-($!<#'*+'>('*($!$/(-(!$(&!()+*+.#!%#&!,->/'#$!9,'<#$!.(!<,&,!,!,/)('*,&!$/!*/0%"*$1('$.!DZ+(&!NE!</,'.#!A$*(!<,(!%#&!.(9,:#!.(!/',!<+H&,!.(*(&)+',.,!D(-!/)9&,-!.(!<#';(&$+0'E5!M#&!(:()%-#?!('!(-!<,$#!.(-!I-#J.$!j,'l?!$+!(-!/)9&,-!.(!$/!*/0%"*$1('$.!*+(&!N!$(!$+*G,!%#&!.(9,:#!.(-!WS!$(!<#';(&*+&7,'!-#$!C#C#$!<#'! -#!8/(!.+<@#!;,-#&! $,-*,&7,!@,$*,!(-! Y?WS5!h9$A&;($(!8/(!('!($*,!)#.,-+.,.!(-!8/(!.+$%,&,!-,!<#';(&$+0'!($!/'!.,*#!<#'*,9-(!.(-!()+$#&!.(!-#$!*7*/-#$!J!'#!(-!%&#F%+(*,&+#!.(!-#$!)+$)#$5!!!!Q"#$%#07/)C%+),-#+0-B&1()7/&#R#1&'+%(%7/&#%-()+)2%.%*&-(&#!i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v!($*#!G-*+)#!$(!<#'$+>/(!&($<,*,'.#!-,$!#9-+F>,<+#'($!*,'!%&#'*#!<#)#!-,!#%<+0'!.(!<#';(&$+0'!$(,!.(-!*+%#!e.('*&#!.(!.+'(&#f?!($*#!($?!</,'.#!(-!;,-#&!.(!<#';(&$+0'!$/%(&(!,-!%&(<+#!.(!,)#&*+3,<+0'!,'*+<+%,.,5!4'*#'<($?!%,&(<(!-0>+<#!$/%#'(&?!8/(!-#$!#9-+>,<+#'+$*,$!<#';(&*+&='!$/$!*7*/-#$!%#&F8/(!(-!;,-#&!.(!<#';(&$+0'!($?!,-!)('#$?!*,'!>&,'.(!<#)#!(-!%&(<+#!.(!,)#&*+3,<+0'5!!P(,)#$! /'! (:()%-#5! I,! (;#-/<+0'! .(-! ;,-#&! .(! /',! ()%&($,! ./&,'*(! -#$! %&01+)#$!.#$!,2#$!;+('(!.(H+'+.,!%#&!(-!=&9#-!9+'#)+,-!8/(!,%,&(<(!('!-,!H+>/&,!QU5!!
!O+>5!QU!
!K/%#'>,!8/(!-,!()%&($,!@,!()+*+.#!$0-#!/',!,<<+0'!J!/',!#9-+>,<+0'!<#';(&*+9-(5!x$F*,!*+('(!/'!;,-#&!'#)+',-!.(!UR!J!.(9(!$(&!&(()9#-$,.#!,-! H+',-!.(-!,2#!Q5!I,!#9-+F
Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
27
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Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
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Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878
9 - La Valoración de los Activos Financieros de Renta Fija
29
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