Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 04 - El valor temporal del dinero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onografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 04 - El valor temporal del dinero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onografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 04 - El valor temporal del dinero )*%*,?&+2)(" '(," *$" ',*6&(" E4*" &=42$2" $2" )*?2+)2" <" $2" (3*,%2" )*" ,*64,.(." 3&+2+6&*,(." @$P)'%*/)*8#=0&)*3C;* * * 4)*)*?2+)2*(%*&%50&','*8#")"5#%&,'*$#%"%*(%1%&-#")()*.,&*/)'*,.,&10"#()(%'*(%*#"$%&9 '#6"*.&,(051#$)*70%*1#%"%"*/)*1,1)/#()(*(%*/)'*%-.&%')'*@P'1)'*"%5%'#1)"*(#"%&,*.)&)*5,-9 .&)&*)51#$,'*5,-,*-)70#")&#)A*5,-.01)(,&%'A*%(#8#5#,'A*.)1%"1%'A*%15P1%&)C;*\I,&)*?#%"A* /)'* %-.&%')'* %/%=#&L"* '6/,* )70%//)'* #"$%&'#,"%'* 50D)* &%"1)?#/#()(* '0.%&%* )/* 5,'1%* (%* 8#9 ")"5#)&/)'*@%'*(%5#&A*%/*1#.,*(%*#"1%&P'*70%*/%*5,?&%"*/,'*.&%'1)-#'1)'*(%*/,'*&%50&','*8#9 ")"5#%&,'C;*4)*'0-)*(%*1,()'*%')'*#"$%&'#,"%'*%/%=#()'*#"(#5)*%/*$)/,&*(%*/)*(%-)"()*(%* 8,"(,'* "%5%')&#,'* .)&)* //%$)&/)'* )* 5)?,;* \'>* 70%* /)'* ,.,&10"#()(%'* (%* #"$%&'#6"* (%* /)'* %-.&%')'*DA*.,&*1)"1,A*/)*(%-)"()*(%*&%50&','*8#")"5#%&,'*',"*0")*80"5#6"*#"$%&')*(%/*1#9 .,* (%* #"1%&P'* @50)"1,* -L'* ?)N,* '%)* P'1%A* -)D,&%'* #"$%&'#,"%'* '%* .,(&L"* )5,-%1%&* D* /,* 5,"1&)&#,C;* 4)'* ,&=)"#:)5#,"%'A* .Q?/#5)'* ,* .&#$)()'A* ,?1#%"%"* 8#")"5#)5#6"* )* 1&)$P'* (%* /)* %-#'#6"*D*$%"1)*(%*1>10/,'*(%*&%"1)*8#N)*@?,",'*D*,?/#=)5#,"%'C*,*$)&#)?/%*@)55#,"%'CA*,*)* 1&)$P'*(%*/)*',/#5#10(*(%*.&P'1)-,';* [#=;*3;*4)*(%1%&-#")5#6"*(%/*1#.,*(%*#"1%&P'*5,-,*5,"1&).,'#5#6"*(%*/)*,8%&1)* D*(%*/)*(%-)"()*(%*&%50&','*8#")"5#%&,';* * 4)*(3*,%2*(%*&%50&','*8#")"5#%&,'*(%.%"(%*(%*/)*5)"1#()(*70%*%'1L"*(#'.0%'1,'*)*)I,&&)&* %*#"$%&1#&*/,'*#"(#$#(0,'*D*/)'*#"'1#105#,"%'A*/,*70%*%'*0")*80"5#6"*(#&%51)*(%/*1#.,*(%*#"1%9 &P'*@/)'*.%&',")'*%'1)&L"*-L'*(#'.0%'1)'*)*)I,&&)&*50)"1,*-L'*'%*/%'*&%-0"%&%*'0*')5&#9 8#5#,A*D*$#5%$%&')J*)'>A*",*%'*/,*-#'-,*70%*/%*,8&%:5)"*0"*]K*)"0)/-%"1%*.,&*%/*(#"%&,*70%* )I,&&%*70%*'#*/%*,8&%5%"*0"*WK*)/*)H,J*%'1)&L*-L'*-,1#$)(,*)*)I,&&)&*%"*%/*.&#-%&*5)',C;* !")* 8,&-)* 70%* 1#%"%"* /)'* .%&',")'* ,* #"'1#105#,"%'* (%* .&,.,&5#,")&* 8#")"5#)5#6"* %'* -%9 (#)"1%*/)*'0'5&#.5#6"*,*)(70#'#5#6"*(%*)51#$,'*(%*&%"1)*8#N)*,*$)&#)?/%A*)'>*70%*/)*5,-.&)* (%* )51#$,'* 8#")"5#%&,'* %'* 0")* 8,&-)* (%* ,8%&1)* (%* 5).#1)/;* V)-?#P"* .0%(%"* (%.,'#1)&* '0* (#"%&,*%"*/)'*%"1#()(%'*8#")"5#%&)'*@?)"5,'*D*5)N)'*(%*)I,&&,C;* E"*"0%'1&,*-0"(,*'#"*#"8/)5#6"*0")*.%&',")*70%*.,'%D%'%*SF;FFF*%0&,'*.,(&>)*5,-.&)&9 '%*0"*5,5I%*(%*'0*-)&5)*8)$,&#1)A*1)"1,*%"*%/*-,-%"1,*)510)/*5,-,*(%"1&,*(%*0"*)H,A* .0%'1,* 70%* ",* I)D* )/:)* (%* .&%5#,';* \I,&)* ?#%"A* .,&* ')5&#8#5)&'%* D* %'.%&)&* 0"* )H,* .)&)* )(70#&#&*%/*$%I>50/,*%/*E'1)(,*/%*.)=)A*.,&*%N%-./,A*W;FFF*Y*@0"*GK*(%*#"1%&P'C;*\'>*70%A* .)&)*"0%'1&,*#"$%&',&A*/)*5,-.&)*)510)/*(%*0"*5,5I%*%70#$)/%*)*5,-.&)&/,*(%"1&,*(%*0"* )H,*.,&*%/*-#'-,*.&%5#,*@&%50%&(%A*",*I)D*#"8/)5#6"C*D*)(%-L'*&%5#?#&*W;FFF*Y;* W* Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 04 - El valor temporal del dinero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`)* =)")(,*\*,*I)*.%&(#(,*^Z*a%)/-%"1%A*^*I)*.%&(#(,*@,*5,-,*(%5#-,'*/,'*%5,",-#'1)'*bI)* (%N)(,*(%*=)")&c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d%*(%?%&L**$*=&,"$2"2$%*,+2%&12"64<("6(.%*")*"('(,%4+&)2)" .*2"?2<(,/"%'*(%5#&A*%"*"0%'1&,*%N%-./,A*'#*^*,.1)*.,&*(%N)&*%/*(#"%&,*%"*5)')*&%5#?#&L*FY* -#%"1&)'* 70%* /)* )/1%&")1#$)* .&,.,&5#,")?)* W;FFFYJ* %/* 5,'1%* (%* ,.,&10"#()(* '%&L_* F* e* W;FFF*f*9WFFF*Y;*d#A*.,&*%/*5,"1&)&#,A*\*/%*.&%'1)*'0*(#"%&,*)/*E'1)(,A*%/*5,'1%*(%*,.,&10"#9 ()(*'%&L*#=0)/*)_*W;FFF*e*F*f*W;FFF*Y;*4)*)/1%&")1#$)*50D,*5,'1%*(%*,.,&10"#()(*%'*-L'*)/9 1,*%'*P'1)*Q/1#-)*D*%//)*'%&L*/)*%/%=#();*+,-,70#%&)*70%*/)*-)D,&>)*(%*/,'*%'.)H,/%'*.0%9 (%"*#"$%&1#&*%"*1>10/,'*(%/*E'1)(,RA*)70P/*70%*.0(#%"(,*I)5%&/,*",*/,*I)=)*D*5,/,70%*'0* (#"%&,* %"* /)* 5)N)* 80%&1%* (%* '0* 5)')* %'1)&L* b(%N)"(,* (%* =)")&c* (#"%&,J* -#%"1&)'* 70%* /,'* 70%*'%*/,*.&%'1%"*)/*E'1)(,A*(%'(%*%/*.0"1,*(%*$#'1)*8#")"5#%&,A*"#*=)")"*"#*.#%&(%";* * * 5=5=#?%#)@-0().2-%#,)#"%#-.A"%2-1.# g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h* '0.,"=)-,'* 70%* ",* %B#'1%"* /,'* /)(&,"%'* )'>* 70%* 1%"%&*%/*(#"%&,*%"*5)')*,*.&%'1L&'%/,*)/*E'1)(,*1#%"%"*%/*-#'-,*&#%'=,_*"#"=0",;* W * E/* 5,'1%* (%* ,.,&10"#()(* %'* 0"* #"(#5)(,&* (%* /)* #-.,&1)"5#)* &%/)1#$)* (%* 0")* (%5#'#6"* (%1%&-#")();* #$" )*6&.(," *$*=&,H" 2E4-$"64,.(")*"266&@+"E4*"%*+=2"4+"?2<(,"6(.%*")*"('(,%4+&)2);** R * a%)/-%"1%* /,'* %'.)H,/%'* .0%(%"* #"$%&1#&* %"* 1>10/,'* (%* ,1&,'* -05I,'* E'1)(,'A* )0"70%* /,'* -L'* .)&%5#(,'* )/* E'1)(,* %'.)H,/*',"*)70%//,'*70%A*'#%"(,*-#%-?&,'*(%*/)*!EA*%-#1%"*%"*%0&,';*E"*50)/70#%&*5)',*%/*/%51,&*(%?%*%'1)&*)$#')(,* (%*70%*%/*&#%'=,*",*%'*5%&,A*I)D*E'1)(,'*(%*/)*!E*70%*1#%"%*-L'*&#%'=,*70%*E'.)H)A*)*/)*I,&)*(%*#"$%&1#&*%"*%//,'A*D*,1&,'* 70%*/,*1#%"%"*#"8%&#,&;* R* Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 04 - El valor temporal del dinero $%=)(,&* iMd* .)&)* '0* $%I>50/,A* 70%* '#"* #"8/)5#6"* $)/(&>)* W;FFF* YA* .%&,* 70%* 5,"* #"8/)5#6"* $)/%*0"*RK*-L'_*W;FjF*YC;*\'>*70%*I)?&>)*70%*.)=)&/%*W;FjF*Y*%"*5,"5%.1,*(%*#"1%&%'%'A* %'*(%5#&A*0"*]A3WK;*E'1)*5#8&)*'%*.0%(%*5)/50/)&*I)5#%"(,*/)*'#=0#%"1%*,.%&)5#6"_* * @3*k*1#.,*",-#")/C*f*@3*k*1#.,*&%)/C*B*@3*k*1)')*(%*#"8/)5#6"C* 1#.,*",-#")/*f*1#.,*&%)/*k*1)')*(%*#"8/)5#6"*k*@1#.,*&%)/*B*1)')*(%*#"8/)5#6"C* * )'>* 70%* %/* %&'(" +(?&+2$* '%&L* #=0)/* )_* FAFG* k* FAFR* k* @FAFG* B* FAFRC* f* FAF]3WA* %'* (%5#&A* %/* ]A3WK;* * g%)-,'*0"*5)',*.&L51#5,;*E"*%/*-,-%"1,*(%*%'5&#?#&*%'1%*1&)?)N,A*/)'*4%1&)'*(%/*V%',&,* @I11._llmmm;1%',&,;%'C* %'1L"* .)=)"(,* 0"* FAnnGK* (%* #"1%&P'* )"0)/J* '#* '0.,"%-,'* 70%* .)&)*%/*.&6B#-,*)H,*'%*%'.%&)*0")*#"8/)5#6"*(%/*FASKA*.,(%-,'*5)/50/)&*%/*1#.,*(%*#"1%&P'* &%)/*70%*%'1L*.)=)"(,*%/*E'1)(,*%'.)H,/G_*FAGnWK;*d#*%/*V%',&,*'#=0%*.%"')"(,*%"*.)=)&* %'1%*#"1%&P'*&%)/*(0&)"1%*/,'*.&6B#-,'*)H,'A*?)'1)&>)*5,"*')?%&*50L/*%'*/)*#"8/)5#6"*70%*P/* %'.%&)A*.)&)*5,",5%&*%/*1#.,*(%*#"1%&P'*",-#")/*(%*/)'*4%1&)'*(%/*V%',&,*%"*/,'*.&6B#-,'* )H,';*+/)&,*70%*1)-?#P"*.0%(%*,50&&#&*70%*/)*1)')*(%*#"8/)5#6"*%'.%&)()*'%)*(%/*3ASK*%"* %'%*5)',*%/*1#.,*(%*#"1%&P'*&%)/*'%&L*"%=)1#$,*%*#=0)/*)S_*9FAGnoSKA*70%*&%8/%N)*/)*.P&(#()* &%)/*)"0)/*(%*/,'*#"$%&',&%'*70%*5,/,70%"*'0*(#"%&,*%"*)51#$,'*8#")"5#%&,'*%-#1#(,'*.,&*%/* E'1)(,;* * a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e(%1%&-#")(,*.,&* %/*U+E9*%B./#70%*)70P//)';*E'*(%5#&A*%/*U+E*01#/#:)*)/*1#.,*(%*#"1%&P'*5,-,*0")*.)/)"5)*.)&)* (#&#=#&*/)*-)&5I)*(%*/)*%5,",->)*(%*1)/*-)"%&)*70%A*'#*P'1)*Q/1#-)*%'1L*%'1)"5)()*,*)-%9 "):)*0")*&%5%'#6"A*'#-./%-%"1%*?)N)*%/*1#.,*(%*#"1%&P'*)/*70%*.&%'1)*)*/)'*%"1#()(%'*8#9 ")"5#%&)'* 5,"* ,?N%1,* (%* 8)$,&%5%&* /)* &%)/#:)5#6"* (%* #"$%&'#,"%'* .&,(051#$)'* @70%* $%&L"* (%'5%"(%&*'0*5,'1%*(%/*5).#1)/C*70%*%-.0N%"*I)5#)*)&&#?)*)*/)*%5,",->);*M,&*%/*5,"1&)&#,A* '#*/)*%5,",->)*%'1L*&%5)/%"1)()*D*/)*#"8/)5#6"*)-%"):)*5,"*(%'?,5)&'%A*'#-./%-%"1%*'09 ?%*%/*1#.,*(%*#"1%&P'*.)&)*(%'#"5%"1#$)&*/)*&%)/#:)5#6"*(%*.&,D%51,'*(%*#"$%&'#6"*8&%")"(,* )'>*/)*)51#$#()(*%5,"6-#5);* * V)-.,5,*I)D*70%*,/$#()&*70%*/)*)01,&#()(*-,"%1)&#)*.0%(%*)0-%"1)&*,*(#'-#"0#&*/)*-)9 ')*-,"%1)&#)*%"*5#&50/)5#6"*/,*70%A*&%'.%51#$)-%"1%A*I)&L*(%'5%"(%&*,*)'5%"(%&*/,'*1#.,'* (%*#"1%&P';* * 4 5 FAFFnnG*f*&*k*FAFFS*k*@&*B*FAFFSC*!*&*f*@FAFFnnG*e*FAFFSC*l*@3*k*FAFFSC*f*FAFFGnW*f*FAGnWK* FAFFnnG*f*&*k*FAF3S*k*@&*B*FAF3SC*!*&*f*@FAFFnnG*e*FAF3SC*l*@3*k*FAF3SC*f*9FAFFGnoS*f*9FAGnoSK* G* Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 04 - El valor temporal del dinero +,-,*I%-,'*-%"5#,")(,A*0")*(%*/)'*.)/)"5)'*70%*01#/#:)*%/*U+E*%'*/)*)/1%&)5#6"*(%/*1#.,* (%*#"1%&P'*.,&*%/*70%*.&%'1)*)*/,'*?)"5,';*M%&,*%'1,'*%"1&%*'>*1)-?#P"*'%*.&%'1)"*(#"%&,*D* %/*1#.,*(%*#"1%&P'*&%'0/1)"1%*(%*(#5I,'*.&P'1)-,'*%'*/)*?)'%*(%*/,'*1#.,'*(%*#"1%&P'*(%*/,'* (%-L'*)51#$,'*8#")"5#%&,'A*)'>*70%*5,"$#%"%*%5I)&/%'*0"*$#'1):,;* * 5=<#!"#*)'2%,&#-.()'4%.2%'-&=# 4)'*#"'1#105#,"%'*8#")"5#%&)'*)50(%"*)/*-%&5)(,*#"1%&?)"5)&#,*%"*5)/#()(*(%*.&%'1)-#'1)'* ,*(%*.&%'1)1)&#,'*D*8#N)"j*%/*#4,&D(,"@#4,('2"&+%*,D2+I"(33*,*)",2%*C/"%'*(%5#&A*/)*1)')*(%*#"9 1%&P'*,8%&1)()*%"*%/*-%&5)(,*#"1%&?)"5)&#,*(%*/)*%0&,:,")]*70%A*'%*%B1#%"(%*(%'(%*0")* '%-)")*I)'1)*0"*)H,*@$P)'%*/)*1)?/)*3C;*M,&*'0*.)&1%A*%/*#(+&2*@#4,("(1*,+&=J%"&+)*K*21*! ,2=*C*%'*5)/50/)(,*.,&*%/*U)"5,*+%"1&)/*E0&,.%,*5,-,*/)*-%(#)*.,"(%&)()*(%*1,()'*/)'* ,.%&)5#,"%'*(%*5&P(#1,*)*0"*(>)*",*=)&)"1#:)()'A*&%)/#:)()'*%"*%/*-%&5)(,*#"1%&?)"5)&#,o;* \-?,'*>"(#5%'*'%*.0?/#5)"*?)N,*%/*.)1&,5#"#,*(%*/)*[%(%&)5#6"*U)"5)&#)*(%*/)*!E*D*/)*\',9 5#)5#6"*(%*+)-?#'1)'*<"1%&")5#,")/%';*4,'*.,&5%"1)N%'*&%.&%'%"1)1#$,'*(%*/,'*(#$%&','*./)9 :,'*(%/*E0&#?,&*D*(%/*E,"#)*'%*%B.&%')"*%"*1P&-#",'*",-#")/%'*)"0)/%'J*)'>A*.,&*%N%-./,A* %/*1#.,*E0&#?,&*)*3*-%'*%"*1P&-#",'*-%"'0)/%'*%'*#=0)/*)*(#$#(#&*FARoWKA*70%*%&)*%/*E0&#9 ?,&93*-%'*%/*3S*(%*N0"#,*(%*WF3W*%"1&%*3W*@fFAFRWK*-%"'0)/C;* * 5#0# FARWK* * E#*# FAnRnK* :#0# FARRoK* * F#*# FAno]K* <#0# FARSoK* * G#*# 3AFR]K* 5#*# FARoWK* * 6#*# 3AFojK* :#*# FAGoRK* * 5;#*# 3A3RGK* <#*# FAjjWK* * 55#*# 3A3oRK* C#*# FA]jK* * 5:#*# 3AWWjK* D#*# FAoGoK* * # * V)?/)*3*E0&#?,&*%/*3S*(%*p0"#,*(%*WF3W*q[0%"1%_*I11._llmmm;%0&#?,&9%?8;%0r* * E/*E0&#?,&*%'*01#/#:)(,*5,-,*0"*1#.,*(%*#"1%&P'*(%*&%8%&%"5#)*.)&)*?)'1)"1%'*,.%&)5#,"%'* 8#")"5#%&)'*5,-,A*.0%(%"*'%&*/,'*.&P'1)-,'A*/)'*.%&-01)'*8#")"5#%&)'*@,*.L2'.CA*%15;A*70%* 1,1)/#:)"* eN0"1,* )/* 4#?,&" 9* 5,-,* ->"#-,* -L'* (%* RSF* ?#//,"%'* (%* (6/)&%'* )* /,* /)&=,* (%/* -0"(,;** * *** [#=;W*E$,/05#6"*(%*Est<\*D*E!a<Usa*)*n*D*3W*-%'%'A*)*/,*/)&=,*(%*/,'*)H,'*WF3F9WF3W* q[0%"1%_*I11._llmmm;%0&#?,&9%?8;%0r* * 6 !")'*GF*%"1#()(%'*8#")"5#%&)'*8#N)"*%/*$)/,&*(%/*E0&#?,&;* [,&-)*5,/,70#)/*(%*&%8%&#&'%*)/*5,"N0"1,*(%*E'1)(,'*%0&,.%,'*70%*1#%"%"*%/*%0&,*5,-,*-,"%();* 8 d%*01#/#:)*5,-,*1#.,*(%*#"1%&P'*'0?D)5%"1%*.)&)*"0-%&,','*.&,(051,'*8#")"5#%&,'*(%&#$)(,';* 7 S* Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 04 - El valor temporal del dinero M,&*,1&,*/)(,A*5,"$#%"%*')?%&*70%*%/*1#.,*(%*#"1%&P'*#"1%&?)"5)&#,*-L'*8)-,',*)*"#$%/*#"9 1%&")5#,")/* %'* %/* (%* 4,"(&%'* -L'* 5,",5#(,* 5,-,* >&D(,* @>(+)(+" &+%*,D2+I" (33*,*)" ,2%*CA* 70%*%'*0")*&%8%&%"5#)*.)&)*(#%:*(#$#')'_*!dOA*iUMA*pMTA*+`[A*+\OA*\!OA*E!aA*OuuA*dEuA*D* t^O*5,"*3S*$%"5#-#%"1,'*9(%*#"1&)(>)*)*3W*-%'%'*@$P)'%*/)*1)?/)*WC*D*70%*'%*1,-)*5,-,* &%8%&%"5#)*#"1%&")5#,")/*(%*/,'*.&P'1)-,'*)*5,&1,*./):,n;** * V)?/)*W*2)1&#:*(%*/,'*3SF*5&05%'*(%/*4#?,&*%/*(>)*3*(%*-)&:,*(%*WF3W*q[0%"1%_*I11._llmmm;??)/#?,&;5,-lr* * d%=0#()-%"1%*$)-,'*)*$%&*/)'*(#$%&')'*8,&-)'*(%*01#/#:)5#6"*(%/*1#.,*(%*#"1%&P'*5,-,*&%9 /)5#6"*(%*#"1%&5)-?#,*(%/*$)/,&*1%-.,&)/*(%/*(#"%&,*%"*(#$%&','*-,-%"1,'*(%/*1#%-.,;* :=#!"#$%"&'#AB(B'& # * M,'%%&*0"*%0&,*I,D*",*$)/%*/,*-#'-,*70%*%'.%&)&*.,'%%&/,*(%"1&,*(%*0"*)H,;*d#*0'1%(* (#'.0'#%&)*)I,&)*-#'-,*(%*P/A*.,(&>)*#"$%&1#&/,A*=)")&*0"*#"1%&P'A*D*1&)"'50&&#(,*0"*)H,* 0'1%(*1%"(&>)*)/=,*-L'*70%*0"*%0&,;* * d#*0'1%(*(#'.,"%*I,D*(%*3;FFF*Y*D*/,'*#"$#%&1%*%"*0")*50%"1)*)*./):,*70%*/%*.)=0%*%/*SK* ",-#")/*)"0)/A*1&)"'50&&#(,*0"*)H,*'0*5).#1)/*I)?&L*)'5%"(#(,*)*3;FSF*Y;*\'>*70%*%/*12$(," 34%4,(*@g[C*(%*3;FFF*Y*#"$%&1#(,'*)510)/-%"1%*)/*SK*(%*#"1%&P'*%'*#=0)/*3;FSF*Y*(%"1&,*(%* 0"* )H,;* g%)-,'* 56-,* '%* I)* 5)/50/)(,A* ')?#%"(,* 70%* )/* 8#")/* (%/* )H,* 0'1%(* &%5#?%* /,'* 3;FFF*Y*70%*(%.,'#16*@'%*/%*(%",-#")*',&+6&'2$C*-L'*/,'*#"1%&%'%'*.,&*I)?%&*.&%'1)(,*%'%* (#"%&,*)/*?)"5,*(0&)"1%*(#5I,*.%&>,(,*@SF*YC_* * g[f*3;FFF*k*3;FFF*B*FAFS*f*3;FFF*k*SF*f*3;FSF*Y* * ,*%B.&%')(,*%"*0")*8,&-)*-L'*-)1%-L1#5)* 9 d%*.&%=0"1)*)*3j*%"1#()(%'*5&%(#1#5#)' ',?&%*%/*1#.,*(%*#"1%&P'*)/*70%*.#%"')"*70%*.,(&>)"*8#")"5#)&'%*%"*0")*(#$#')* (%1%&-#")()*D*)*70P*$%"5#-#%"1,*%"*5,"5&%1,;*O%*/)'*&%'.0%'1)'*'%*%/#-#")"*/,'*50)1&,*()1,'*-L'*)/1,'*D*/,'*50)1&,* -L'*?)N,'*D*'%*,?1#%"%*%/*$)/,&*(%/*4<Usa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j* * Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 04 - El valor temporal del dinero * g[*f*3;FFF*k*3;FFF*B*FAFS*f*3;FFF*B*@3kFAFSCf*3;FFF*B*3AFS*f*3;FSF*Y* * d#*%'1%*5L/50/,*/,*=%"%&)/#:)-,'*.)&)*50)/70#%&*5)"1#()(*D*(%",-#")-,'*)/*12$(,"26%42$* (%/*(#"%&,*g\A*)/*1#.,*(%*#"1%&P'*vA*D*)/*12$(,"34%4,(*g[A*,?1%"(&%-,'*/)*%B.&%'#6"*=%"%&)/* (%*P'1%*Q/1#-,*.)&)*0"*Q"#5,*.%&>,(,_* * g[*f*g\*k*g\*B*v*f*g\*B*@3*k*vC* * * d#*)I,&)*'0.,"%-,'*70%*0'1%(*",*&%1#&)*%/*(#"%&,*)/*5)?,*(%*0"*)H,A*'#",*(%'.0P'*(%*70%* 1&)"'50&&)"*5#"5,*.%&>,(,'*)"0)/%'A*%/*$)/,&*(%*'0*(#"%&,*)/*8#")/*(%*5)()*0",*(%*/,'*5#"5,* )H,'*'%&L3F_* * w*\/*8#")/*(%/*.&#-%&*)H,*,?1%"(&L_*3;FFF*k*3FFF*B*FAFS*f*3;FSF*Y* w*\/*8#")/*(%/*'%=0"(,*)H,*,?1%"(&L_*3;FSF*k*3;FSF*B*FAFS*f*3;3FWASF*Y* w*\/*8#")/*(%/*1%&5%&*)H,*,?1%"(&L_*3;3FWASF*k*3;3FWASF*B*FAFS*f*3;3S]AjR*Y* w*\/*8#")/*(%/*50)&1,*)H,*,?1%"(&L_*3;3S]AjR*k*3;3S]AjR*B*FAFS*f*3;W3SAS3*Y** w*\/*8#")/*(%/*70#"1,*)H,*,?1%"(&L_*3;W3SAS3*k*3;W3SAS3*B*FAFS*f*3;W]jAWn*Y* * a%)/-%"1%A*/,*Q"#5,*70%*I%-,'*I%5I,*%70#$)/%*)*#&*')5)"(,*%/*(#"%&,*70%*0'1%(*.,'%%*)/* 8#")/*(%*5)()*.%&>,(,*DA*)01,-L1#5)-%"1%A*/,*$,/$%-,'*)*(%.,'#1)&*(0&)"1%*,1&,*)H,A*)/* 8#")/*(%/*50)/*$,/$%-,'*)*&%.%1#&*/)*,.%&)5#6"*D*)'>*'05%'#$)-%"1%*I)'1)*5,-./%1)&*/,'*5#"9 5,*)H,';*M%&,*",*'%*.&%,50.%A*%'1%*5L/50/,*",*%'*1)"*%"=,&&,',*5,-,*.)&%5%*)*'#-./%*$#'9 1)A*.0%'1,*70%*",*I%-,'*I%5I,*,1&)*5,')*70%*&%.%1#&*5#"5,*$%5%'*/)*%B.&%'#6"*(%/*12$(," 34%4,(* (%* 0")* 5)"1#()(* @g[C* 70%* $#-,'* )"1%&#,&-%"1%;* \'>A* /,'* $)/,&%'* 8010&,'* %"* 5)()* -,-%"1,*'%*.0%(%"*5)/50/)&*(%*/)*'#=0#%"1%*8,&-)_* * g[3*f*g\*B*@3*k*vC*f*3;FFF*B*3AFS*f*3;FSF*Y* * g[W*f*g[3*B*@3*k*vC*f*g\*B*@3*k*vCW*f*3;FFF*B*@3AFSCW*f*3;3FWASF*Y* g[R*f*g[W*B*@3*k*vC*f*g\*B*@3*k*vCR*f*3;FFF*B*@3AFSCR*f*3;3S]AjR*Y* g[G*f*g[R*B*@3*k*vC*f*g\*B*@3*k*vCG*f*3;FFF*B*@3AFSCG*f*3;W3SAS3*Y* g[S*f*g[G*B*@3*k*vC*f*g\*B*@3*k*vCS*f*3;FFF*B*@3AFSCS*f*3;W]jAWn*Y* * i%"%&)/#:)"(,*.)&)*%/*5L/50/,*(%/*12$(,"34%4,(*(%*50)/70#%&*$)/,&*)510)/*@g\C*#"$%&1#(,*)* 0"*1#.,*(%*#"1%&P'*",-#")/*@vCA*(0&)"1%*"*.%&>,(,'A*,?1%"(&%-,'*/)*'#=0#%"1%*%B.&%'#6"_* * g["*f*g\*B*@3*k*vC"* * :=5=#H.()'>0#0-*+")#)#-.()'>0#2&*+B)0(&# \* /,* /)&=,* (%* %'1%* 1%-)* $)-,'* )* 1&)?)N)&* 5,"* /)* 5).#1)/#:)5#6"* 5,-.0%'1)* D* ",* 5,"* /)* 5).#1)/#:)5#6"*'#-./%*.,&*/,*70%*I)*//%=)(,*%/*-,-%"1,*(%*%B./#5)&*%"*70P*'%*(#8%&%"5#)";* * 10 4)'* 5#8&)'* '%* -0%'1&)"* &%(,"(%)()'* I)'1)* /)* '%=0"()* 5#8&)* (%5#-)/* .%&,* %"* /,'* 5L/50/,'* '%* I)"* #"5/0#(,* 1,(,'* /,'* (%5#-)/%'; ]* Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 04 - El valor temporal del dinero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jAWn*Y*5,-,*,50&&>)*%"*/)*5).#1)/#:)5#6"*5,-.0%'1);*\*%'1)*8,&-)*(%*5)/509 /)&*'%*/)*(%",-#")*62'&%2$&A26&@+".&?'$*00;*E"*%//)*'%*'0.,"%*70%*/,'*#"1%&%'%'*'%*&%#"$#%&9 1%"* )* 0"* 1#.,* (%* #"1%&P'* (%/* FKA* .,&* 1)"1,* /)* %B.&%'#6"* =%"%&)/* (%/* $)/,&* 8010&,* (%* 0")* 5)"1#()(*(%"1&,*(%*"*.%&>,(,'*5)/50/)()*)*1&)$P'*(%*/)*5).#1)/#:)5#6"*'#-./%*'%&L*#=0)/*)_** * g["*f*g\*B*@3*k*"*B*vC;* * [#=;R*g)/,&*8010&,*5)/50/)(,*5,"*#"1%&P'*'#-./%*D*5,"*#"1%&P'*5,-.0%'1,*@g\*f*3;FFF*D*v*f*SKC* * E"*/)*8#=0&)*R*'%*.0%(%*$%&*56-,*5,"8,&-%*)0-%"1)*%/*1#%-.,*/)*(#8%&%"5#)*(%/*$)/,&*809 10&,*%"1&%*)-?,'*-P1,(,'*(%*5L/50/,*%-.#%:)*)*'%&*#-.,&1)"1%;* * * * * * * 11 4)*5).#1)/#:)5#6"*'#-./%*'%*01#/#:)*I)?#10)/-%"1%*.)&)*/,'*5L/50/,'*8#")"5#%&,'*70%*#-./#70%"*I,&#:,"1%'*1%-.,&)/%'* #"8%&#,&%'*)*0"*)H,; o* Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 04 - El valor temporal del dinero Curiosidad: En 1700 AC, cuando en el reino de Babilonia reinaba Hammurabi, se escribió en una tableta de arcilla el que puede ser el problema más antiguo de cálculo financiero. Se trata de calcular cuánto tiempo tarda una mina de plata, que se invierte al 20% de interés anual, en alcanzar el valor de 64 minas. El cálculo de interés compuesto debe hacerse en una forma extraña (20% del principal se acumula –interés simple- hasta que el interés es igual al principal, momento en el que se añade al propio principal –interés compuesto-), la respuesta al problema es 30 años, en lugar de 22,81 años. Su solución requiere conocer el ¡cálculo logarítmico! (y todo esto escrito en sistema cuneiforme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f*g\*B*@3*k*FAFSCR* * (%'.%N)"(,*g\A*,?1%"(&%-,'*'0*$)/,&_* * * * \'>*70%A*8#")"5#%&)-%"1%*I)?/)"(,A*,?1%"%&*3;FFF*%0&,'*(%"1&,*(%*1&%'*)H,'*'%&>)*/,*-#'9 -,*70%*&%5#?#&*)510)/-%"1%*ojRAoG*%0&,'*'#*%/*1#.,*(%*#"1%&P'*).&,.#)(,*80%'%*%/*SK;*i%9 "%&)/#:)"(,*.)&)*50)/70#%&*5)"1#()(A*.%&>,(,*D*1#.,*(%*#"1%&P'*,?1%"(&%-,'*/)*'#=0#%"1%* %B.&%'#6"*(%/*$)/,&*)510)/_* * * * \'>A*.,&*%N%-./,A** * f*3;FFF*Y* * n* Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 04 - El valor temporal del dinero d#*%"*%/*%.>=&)8%*)"1%&#,&*I)5>)-,'*&%8%&%"5#)*)*/)*5).#1)/#:)5#6"*5,-.0%'1)*)/*5)/50/)&*%/* $)/,&* 8010&,* (%* 0")* 5)"1#()(A* )I,&)* I)?/)&%-,'* (%* )*.64*+%(" 6(?'4*.%(* 50)"(,* ",'* &%8%&#-,'*)*/)*,?1%"5#6"*(%/*$)/,&*)510)/*(%*0")*5#8&)*8010&)*@(%*I%5I,*/,'*%5,",-#'1)'* I)?/)-,'* (%* b(%'5,"1)&c* ,* b)510)/#:)&c* )* /)* ,.%&)5#6"* (%* ,?1%"%&* %/* $)/,&* %70#$)/%"1%* I,D*%"*(>)*(%*0")*5)"1#()(*70%*'%*%'.%&)*&%5#?#&*%"*0"*8010&,*(%1%&-#")(,J*-#%"1&)'*70%* (%",-#")-,'* b5).#1)/#:)&c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x* %0&,'*(0&)"1%*5#"5,*.%&>,(,';*d#*70%&%-,'*5)/50/)&*'0*12$(,"34%4,(*)/*1P&-#",*(%/*70#"1,* .%&>,(,A*/,*70%*1%"(&%-,'*70%*I)5%&*%'*,?1%"%&*%/*$)/,&*8010&,*%"*(#5I,*-,-%"1,*(%*5)9 ()*0")*(%*/)'*5)"1#()(%'*D*/0%=,*'0-)&*1,(,'*/,'*$)/,&%'*8010&,';* * * [#=;G*a%"1)'*.,'1.)=)?/%'* * \'>A*.0%'A*%/*$)/,&*8010&,*(%*%'1)*&%"1)*)/*8#")/*(%/*.%&#,(,*70#"1,*@g[SC*'%&L3R_* * g[S*f*x*B*@3kvCG*k*x*B*@3kvCR*k*x*B*@3kvCW*k*x*B*@3kvC*k*x* * d#A*.,&*%N%-./,A*%/*$)/,&*(%*x*80%'%*(%*3;FFF*YA*D*%/*(%*v*(%/*SKA*%/*$)/,&*8010&,*'%&>)_* * g[S*f*3;FFF*B*@3AFSCG*k*3;FFF*B*@3AFSCR*k*3;FFF*B*@3AFSCW*k*3;FFF*B*@3AFSC*k*3;FFF*f* *******f*S;SWSAjR*Y* * g,/$#%"(,*)*"0%'1&)*%B.&%'#6"*1%6&#5)*(%/*$)/,&*8010&,*(%*/)*&%"1)*%B.&%')()*%"*/)*8#=0&)* RA*.,(&>)-,'*,?1%"%&*0")*86&-0/)*70%A*%"*5)',*(%*",*(#'.,"%&*(%*0")*5)/50/)(,&)*8#")"9 3W *V)-?#P"*&%5#?%*%/*",-?&%*(%*2+42$&)2)*'#*%/*.%&#,(,*'%*&%8#%&%*)*0"*)H,;* *E'1)-,'*'0.,"#%"(,A*.)&)*'#-./#8#5)&A*70%*v*%'*5,"'1)"1%*)*/,*/)&=,*(%*1,(,*%/*.%&>,(,*70#"70%")/*.%&,A*,?$#)-%"1%A* %//,*",*%'*)'>*.,&70%*/,'*1#.,'*(%*#"1%&P'*$)&>)"*5,"1#"0)-%"1%; 3R 3F* Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 04 - El valor temporal del dinero 5#%&)A*.,(&>)*)I,&&)&",'*)/=Q"*1#%-.,;*M)&)*%//,*-0/1#./#5)&%-,'*)-?,'*-#%-?&,'*.,&*@3* kvC_* * g[S*B*@3kvC*f*x*B*@3kvCS*k*x*B*@3kvCG*k*x*B*@3kvCR*k*x*B*@3kvCW*k*x*B*@3kvC* * '#*)I,&)*/%*&%'1)-,'*)*%'1)*%B.&%'#6"*%/*$)/,&*(%*g[S_* * g[S*B*@3kvC*9*g[S*f*x*B*@3kvCS*k*x*B*@3kvCG*k*x*B*@3kvCR*k*x*B*@3kvCW*k*x*B*@3kvC*e*qx*B*@3kvCG* k*x*B*@3kvCR*k*x*B*@3kvCW*k*x*B*@3kvC*k*xr** ******************************f*x*B*@3kvCS*e*x* * ,.%&)"(,A*",'*70%()&>)*70%_* * g[S*B*v*f*x*B*q@3kvCS*9*3r* * (%'.%N)"(,*)I,&)*g[S*,?1%"(&%-,'*%/*$)/,&*8010&,*(%*/)*&%"1)_* * A*,*=%"%&)/#:)"(,A* ** * \'>*70%*)I,&)*D)*.,(%-,'*5)/50/)&*%/*12$(,"34%4,(*(%*0")*&%"1)*.,'1.)=)?/%*(%*3;FFF*%09 &,'*(0&)"1%*S*)H,'*)/*1#.,*(%*#"1%&P'*(%/*SK_* * f*S;SWSAjR*Y* * !K)*+"&3*E/*(>)*70%*2)&1)*50-./#6*/,'*3G*)H,'*'0'*.)(&%'*/%*.&,-%1#%&,"*.)=)&/%*3FF*Y* -%"'0)/%'*I)'1)*70%*50-./#%'%*/,'*3o*)H,';*d#*2)&1)*.0(#%&)*#"$%&1#&*(#5I)'*5)"1#()(%'* )/*FA3K*-%"'0)/*I)'1)*/)*8%5I)*(%*'0*3o*50-./%)H,'*50L/*'%&>)*/)*5)"1#()(*(%*(#"%&,*(%*/)* 70%*(#'.,"(&>)*%"*%'%*#"'1)"1%;** t,1)_*d0'*.)(&%'*/%*.)=)"*%/*(#"%&,*)/*8#")/*(%/*-%';* * E/*.%&#,(,*%'*(%*Go*-%'%';*\'>*70%*)./#5)"(,*/)*%B.&%'#6"*-)1%-L1#5)*)"1%&#,&*"*f*GoJ*v*f* FA3K*D*x*f*3FFY;*E/*12$(,"34%4,(*(%*(#5I)*&%"1)*.,'1.)=)?/%*'%&L*#=0)/*)_* * f*G;n3GASS*Y* * C=:=#I).(%0#+')+%J%4")0# E"*/)*8#=0&)*S*'%*-0%'1&)*0"*%'70%-)*(%*/,*70%*.0%(%*'%&*0")*,*+%2"',*'2=2D$**(%*x*%09 &,'* (0&)"1%* 5#"5,* .%&>,(,';* E/* .&,5%(#-#%"1,* (%* 5L/50/,* (%/* 12$(," 34%4,(* (%* 0")* &%"1)* .&%.)=)?/%*%'*#(P"1#5,*)/*(%*/)'*.,'1.)=)?/%';* * 33* Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 04 - El valor temporal del dinero * [#=;S*a%"1)'*.&%.)=)?/%'* * E/*$)/,&*8010&,*(%*%'1)*&%"1)*)/*8#")/*(%/*.%&#,(,*70#"1,*@g[SCA*'%&L*#=0)/*)_* * g[S*f*x*B*@3kvCS*k*x*B*@3kvCG*k*x*B*@3kvCR*k*x*B*@3kvCW*k*x*B*@3kvC* * d#A*.,&*%N%-./,A*%/*$)/,&*(%*x*80%'%*(%*3;FFF*YA*D*%/*(%*v*(%/*SKA*%/*$)/,&*8010&,*'%&>)_* * g[S*f*3;FFF*B*@3AFSCS*k*3;FFF*B*@3AFSCG*k*3;FFF*B*@3AFSCR*k*3;FFF*B*@3AFSCW*k* ***********k*3;FFF*B*@3AFSC*f*S;oF3An3*Y* * E"* &%)/#()(A* /)* %B.&%'#6"* %'* /)* -#'-)A* 70%* %"* %/* 5)',* (%* /)'* &%"1)'* .,'1.)=)?/%'A* .%&,* -0/1#./#5)()* .,&* @3kvC;* E8%51#$)-%"1%A* ,?'%&$%* 70%* S;oF3An3* f* S;SWSAjR* B* @3kFAFSC;* \'>* .0%'A*/)*%B.&%'#6"*-)1%-L1#5)*(%/*$)/,&*8010&,*(%*0")*&%"1)*.&%.)=)?/%*70%*'%*%B1#%"(%* )*/,*/)&=,*(%*"*)H,'*'%&L_* * * # !K)*+"&3*a%1,-%-,'*%/*5)',*(%*/)*.)=)*-%"'0)/*(%*2)&1)A*.%&,*%"*%'1%*5)',*$)*)*&%5#?#&* '0'*3FF*Y*%/*.&#-%&*(>)*(%/*-%'*%"*/0=)&*(%/*Q/1#-,;*d%*1&)1)*(%*5)/50/)&*%/*$)/,&*8010&,*(%* 1,()*/)*'%&#%*(%*.)=,'*%/*(>)*%"*70%*2)&1)*50-./%*'0'*3o*)H,';** * E/*.%&#,(,*%'*(%*Go*-%'%';*\'>*70%*)./#5)"(,*/)*%B.&%'#6"*-)1%-L1#5)*)"1%&#,&*"*f*GoJ*v*f* FA3K*D*x*f*3FFY;*E/*12$(,"34%4,(*(%*(#5I)*&%"1)*.&%.)=)?/%*'%&L*#=0)/*)_* * *B*@3*k*FAFF3C*f*G;n3nAGj*Y* * * * D=#!"#$%"&'#%2(B%"#,)#B.%#').(% # D=5=#I).(%0#+&0(+%J%4")0# d0.,"=)*70%*)*0'1%(*/%*,8&%5%"*/)'*'#=0#%"1%'*)/1%&")1#$)'_** * )C*&%5#?#&*0")*&%"1)*(%*3;FFF*%0&,'*.)=)(%&,'*)*8#"*(%*)H,*(0&)"1%*5#"5,*)H,'* ?C*&%5#?#&*0")*'0-)*(%*(#"%&,*I,D;** * 3W* Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 04 - El valor temporal del dinero !'1%(*",*"%5%'#1)*%/*(#"%&,*(0&)"1%*/,'*.&6B#-,'*5#"5,*)H,'A*)'>*70%*'#*)5%.1)*&%5#?#&*/)* &%"1)A*(%.,'#1)&>)*/,'*.)=,'*%"*0")*50%"1)*(%*)I,&&,*70%*.)=)*%/*SK*(%*#"1%&P'*5,-.0%'9 1,;*O%*8,&-)*'#-#/)&A*/)*'0-)*(%*(#"%&,*)510)/*1)-?#P"*'%&>)*(%.,'#1)()*%"*0")*50%"1)* 70%*.)=)*%/*-#'-,*1#.,*(%*#"1%&P'*(0&)"1%*5#"5,*)H,';*Xx0P*1)-)H,*(%?%&L*1%"%&*(#5I)* '0-)*(%*(#"%&,*)510)/-%"1%*.)&)*70%*/%*'%)*#"(#8%&%"1%*%/%=#&*0")*0*,1&)*)/1%&")1#$)Z* * * [#=;j*a%"1)'*.,'1.)=)?/%'* * E"*/)*8#=0&)*j*1%"%-,'*%/*%'70%-)*(%*.)=,'*(%*0")*&%"1)*.,'1.)=)?/%*(%*x*%0&,'A*(0&)"9 1%*5#"5,*)H,';*M)&)*5)/50/)&*%/*$)/,&*)510)/*@g\C*(%*0")*5,&&#%"1%*(%*.)=,'*#=0)/%'*I)?&L* 70%*'0-)&*%/*$)/,&*)510)/*(%*5)()*0",*(%*%//,'A*%'*(%5#&_* * * * '#*)I,&)*'0'1#10#-,'*x*.,&*'0*$)/,&*3;FFF*YA*D*v*.,&*%/*SKA*,?1%"(&%-,'*%/*$)/,&*)510)/*(%* /)*&%"1)*(%*/)*.&#-%&)*)/1%&")1#$)A*70%*/)*I)&L*#"(#8%&%"1%*)*/)*'%=0"()_* * f*G;RWnAGo*Y* * 4,*-#'-,*70%*%"*%/*5)',*(%/*$)/,&*8010&,*(%*0")*&%"1)*.,'1.)=)?/%*%B#'1>)*0")*%B.&%'#6"* -)1%-L1#5)*70%*.%&-#1>)*,?1%"%&*'0*$)/,&*01#/#:)"(,*0")*5)/50/)(,&)*",*8#")"5#%&)A*1)-9 ?#P"*%B#'1%*0")*%B.&%'#6"*-)1%-L1#5)*.)&)*%/*$)/,&*)510)/*(%*0")*&%"1)*.,'1.)=)?/%;*4)* 8,&-)*(%*,?1%"%&/)*%'*#(P"1#5)*)*/)*70%*$#-,'*%"*%/*%.>=&)8%*G;3A*%'*(%5#&A*-0/1#./#5)&*.,&* @3kvC*)-?,'*-#%-?&,'*D*/0%=,*&%'1)&/%*g\;*M%&,*)70>*$)-,'*)*01#/#:)&*,1&,*.&,5%(#-#%"1,* )*1&)$P'*(%*/)*01#/#:)5#6"*(%*/)*%B.&%'#6"*70%*$#-,'*%"*%/*%.>=&)8%*WA*X&%50%&()Z_*g["*f*g\* B*@3kvC";*d)?%-,'*/)*%B.&%'#6"*70%*5)/50/)*g[SA*.,&*1)"1,A*(%'.%N)"(,*g\A*,?1%"(&%-,'_* * * * ,*=%"%&)/#:)"(,*.)&)*"*.%&#,(,'* * * * !K)*+"&3*O%'.0P'*(%*/)*.&,.0%'1)*70%*'0'*.)(&%'*/%*I)5%"*)*2)&1)A*P'1)*/%'*.#(%*70%*/%* (%"*0")*Q"#5)*5)"1#()(*(%*(#"%&,*)I,&)*-#'-,*%"*/0=)&*(%*Go*.)=,'*-%"'0)/%'*(%*3FF*Y;* 3R* Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 04 - El valor temporal del dinero t,1)'_*d0'*.)(&%'*/%*.)=)"*%/*(#"%&,*)/*8#")/*(%/*-%'*D*%/*1#.,*(%*#"1%&P'*%'*(%/*FAFF3K* -%"'0)/;* E/*.%&#,(,*%'*(%*Go*-%'%';*\'>*70%*)./#5)"(,*/)*%B.&%'#6"*-)1%-L1#5)*)"1%&#,&*"*f*GoJ*v*f* FA3K*D*x*f*3FFY;*E/*12$(,"26%42$*(%*(#5I)*&%"1)*.,'1.)=)?/%*'%&L*#=0)/*)_* * *f*G;joGARG*Y* * s?'%&$%*70%*G;joGARG*B*@3AFF3CGo*f*G;n3GASS*YA*70%*%&)*%/*$)/,&*8#")/*(%*/)*&%"1)*.,'1.)=)9 ?/%;*E'1,*",'*.%&-#1%*,?1%"%&*%/*$)/,&*)510)/*50)"(,*.,'%%-,'*%/*$)/,&*8#")/A*,*P'1%*Q/1#9 -,*50)"(,*(#'.,"%-,'*(%/*.&#-%&,;* * # D=:=#I).(%0#+')+%J%4")0# E"* /)* 8#=0&)* ]* '%* -0%'1&)* 0"* %'70%-)* (%* /,* 70%* .0%(%* '%&* 0")* &%"1)* .&%.)=)?/%* (%* x* %0&,'*(0&)"1%*5#"5,*.%&>,(,';*E/*.&,5%(#-#%"1,*(%*5L/50/,*(%/*12$(,"26%42$")*"4+2",*+%2" ',*'2=2D$*"%'*#(P"1#5,*)/*(%*/)'*.,'1.)=)?/%'_* * * * * [#=;]*a%"1)'*.&%.)=)?/%'* * d#A*.,&*%N%-./,A*%/*$)/,&*(%*x*80%'%*(%*3;FFF*Y*D*%/*(%*v*(%/*SKA*%/*$)/,&*)510)/*'%&>)_* * f*G;SGSAnS*Y* * E"* &%)/#()(A* /)* %B.&%'#6"* %'* /)* -#'-)A* 70%* %"* %/* 5)',* (%* /)'* &%"1)'* .,'1.)=)?/%'A* .%&,* -0/1#./#5)()* .,&* @3kvC;* E8%51#$)-%"1%A* ,?'%&$%* 70%* G;SGSAnS* f* G;RWnAGo* B* @3kFAFSC;* \'>* .0%'A*/)*%B.&%'#6"*-)1%-L1#5)*(%/*$)/,&*)510)/*(%*0")*&%"1)*.&%.)=)?/%*'%&L_* * * * !K)*+"&3* g,/$)-,'* )* 5)/50/)&* %/* $)/,&* )510)/* (%* /)* &%"1)* (%* Go* .)=,'* (%* 3FF* Y* 70%* /,'* .)(&%'*(%*2)&1)*/%*I)5%"*)*%//)*'#*(#5I,'*.)=,'*/,'*I#5#%'%"*)/*5,-#%":,*(%*5)()*.%&#,(,* -%"'0)/;** * 3G* Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 04 - El valor temporal del dinero \./#5)"(,*/)*%B.&%'#6"*-)1%-L1#5)*)"1%&#,&*"*f*GoJ*v*f*FA3K*D*x*f*3FFY;*E/*12$(,"26%42$*(%* (#5I)*&%"1)*.&%.)=)?/%*'%&L*#=0)/*)_* * f*G;jonAFW*Y* * * * * * * * * * E=#!"#$%"&'#%2(B%"#,)#B.%#').(%#+)'+)(B% # * \0"70%* ",* '0%/%* '%&* ",&-)/A* '>* %'* .,'#?/%* %"5,"1&)&'%* 5,"* ,*+%2." '*,'*%42.A* %'* (%5#&A* )70%//)'*50D)*(0&)5#6"*%'*-0D*=&)"(%A*1)"1,*70%*'%*5,"'#(%&)*70%*/)*5,&&#%"1%*(%*.)=,'* 1#%"%*/0=)&*)*/,*/)&=,*(%*#"8#"#1,'*.%&#,(,'*@1)-?#P"*'%*/)'*(%",-#")*b.%&.%10#()(%'cC;* * d0* 12$(," 26%42$* '%* 5)/50/)&>)* ).)&%"1%-%"1%* #=0)/* 70%* '#* 80%'%* 0")* &%"1)* .,'1.)=)?/%* ",&-)/A*.%&,*5,-,*%/*"Q-%&,*(%*.%&>,(,'*1#%"(%*)*#"8#"#1,*/)*%B.&%'#6"*-)1%-L1#5)*%'_* * * * \'>A*.,&*%N%-./,A*'#*/)*&%"1)*80%'%*(%*3;FFF*Y*D*%/*1#.,*(%*#"1%&P'*v*(%/*SKA*%/*$)/,&*)510)/* (%*0")*&%"1)*.%&.%10)*.,'1.)=)?/%*'%&>)_** * f*WF;FFF*Y;* * M,(&>)* ()&'%* %/* 5)',* (%* 70%* 70#'#P&)-,'* 5)/50/)&* %/* $)/,&* )510)/* (%* 0")* &%"1)* .%&.%10)* .&%.)=)?/%;*E"*%'%*5)',*')?%-,'*70%*?)'1)*5,"*-0/1#./#5)&*.,&*@3kvC*%/*$)/,&*)510)/*(%*/)* .,'1.)=)?/%*%70#$)/%"1%A*%'*(%5#&_* * * * t,*5)#=)*%"*/)*1%"1)5#6"*(%*5)/50/)&*%/*$)/,&*8010&,*(%*0")*&%"1)*.%&.%10)A*y",*)5)?)&>)* "0"5)zA*.0%'*'0*$)/,&*1#%"(%*)*#"8#"#1,;* * * * F=#/%"&')0#%2(B%"#9#AB(B'&#,)#B.%#2&''-).()#,)#+%J&0# ,)0-JB%")0 # * `)'1)*)I,&)*I%-,'*5)/50/)(,*%/*$)/,&*)510)/*D*%/*8010&,*(%*0")*5,&&#%"1%*(%*.)=,'*5,"'9 1)"1%'*)*/,'*70%*(%",-#"L?)-,'*&%"1)A*.%&,A*X70P*,50&&%*'#*/,'*.)=,'*",*',"*5,"'1)"1%'* 3S* Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 04 - El valor temporal del dinero '#",* (%'#=0)/%'Z;* M,&* %N%-./,A* $%)-,'* %/* %'70%-)* (%* /)* 8#=0&)* oA* %"* /)* 70%* '%* .0%(%"* ).&%5#)&*5#"5,*8/0N,'*(%*5)N)*5,"*(#8%&%"1%'*5)"1#()(%'*)*/)'*70%*1&)1)&%-,'*(%*5)/50/)&*'0* $)/,&*)510)/;* * * [#=;*o* * O%?%&%-,'*,?1%"%&*%/*$)/,&*)510)/*(%*5)()*0")*(%*/)'*5)"1#()(%'*70%*).)&%5%"*%"*(#5I)* 5,&&#%"1%* (%* 8/0N,'* (%* 5)N)* .)&)A* )* 5,"1#"0)5#6"A* '0-)&/,'* D* ,?1%"%&* )'>* %/* $)/,&* )510)/* 1,1)/*@'0.,"=)-,'*0"*$)/,&*5,"'1)"1%*(%*v*f*SKC_* * f*W;Fj3A3R*Y* * E"*8,&-)*=%"%&)/A*/)*%B.&%'#6"*'%&>)*/)*'#=0#%"1%_* * * * M,&*,1&,*/)(,A*'#*70#'#P&)-,'*,?1%"%&*'0*$)/,&*8010&,*",*I)?&>)*-L'*70%*)./#5)&*/)*%B.&%9 '#6"_*g[S*f*g\*B*@3kvCS;*\'>*,?1%"(&>)-,'*0"*$)/,&*(%*g[S*f*W;jRFASo*Y;* * !K)*+"&3*+)/50/%*%/*$)/,&*)510)/*(%*/)*'#=0#%"1%*5,&&#%"1%*(%*8/0N,'*(%*/#70#(%:*.,'1.)=)9 ?/%'*')?#%"(,*70%*%/*1#.,*(%*#"1%&P'*%'*%/*GK*)"0)/;* * LM&0# 5# :# <# C# D# [/0N,'* S;FFF* RF;FFF* WF;FFF* GF;FFF* WF;FFF* * \510)/#:)&%-,'*5)()*5)"1#()(*D*'0-)&%-,'*%/*$)/,&*)510)/*(%*1,()'*%//)'_* * f*3FF;nSSAFW*Y* * F=5#NO#0-#"&0#(-+&0#,)#-.()'>0#%.B%")0#.&#0&.#2&.0(%.()0P# d0.,"=)-,'*70%*/,'*1#.,'*(%*#"1%&P'*)"0)/%'*(0&)"1%*/,'*.&6B#-,'*5#"5,*)H,'*$)"*)*'%&A* &%'.%51#$)-%"1%A* .)&)* %/* )H,'* 3A* WA* RA* G* D* S* /,'* '#=0#%"1%'_* SKA* SASKA* jKA* jASK* D* SASK;* \I,&)*70%&%-,'*5)/50/)&*%/*$)/,&*)510)/*(%*/)'*5)"1#()(%'*70%*).)&%5>)*%"*%/*%.>=&)8%*)"9 1%&#,&;*M)&)*%//,*(%?%&%-,'*#&*)510)/#:)"(,*)"0)/-%"1%*5)()*0")*(%*/)'*5)"1#()(%'*)"1%9 &#,&%';*+,-%"5%-,'*.,&*%/*8#")/*D*5)/50/%-,'*%/*g\*%"*%/*50)&1,*)H,*@&%50%&(%*70%*%/*1#.,* (%*#"1%&P'*%"*%'1%*.%&#,(,*%'*(%/*SASKC_* * 3j* Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 04 - El valor temporal del dinero g\G*f*F*k* f*G]RAnR*Y* * )I,&)*$)D)-,'*)/*1%&5%&*)H,*D*,?1%"=)-,'*%/*g\;*M)&)*%//,*(%'5,"1)&%-,'*g\G*0"*)H,*D* /%*'0-)&%-,'*/)*5)"1#()(*)*&%5#?#&*%"*%/*1%&5%&*)H,_* * g\R*f*WFF*k* *f*jGSAF3*Y* * E"*%/*'%=0"(,*)H,*D*%"*%/*.&#-%&*)H,*%/*$)/,&*)510)/*'%&LA*.,&*1)"1,_* * g\W*f*jFF*k* f*3;WFoAS*Y* g\3*f*3;FFF*k* f*W;3GSAS*Y* * M,&*Q/1#-,A*%"*/)*)510)/#()(* * g\*f* f*W;FGRARR*Y* * s1&)*8,&-)*(%*-,'1&)&*/,*)"1%&#,&A*(%*I%5I,*%'*/)*I)?#10)/A*%'_* * * * g\*f*W;FGRARR*Y* * E"*50)"1,*)/*$)/,&*8010&,*50)"(,*/,'*1#.,'*(%*#"1%&P'*(%*5)()*.%&#,(,*',"*(#8%&%"1%'*(%9 ?%&%-,'*#&*5).#1)/#:)"(,*5)()*5)"1#()(*-,"%1)&#);*\'>A*.,&*%N%-./,A*%"*%/*5)',*)"1%&#,&* '%&>)_* * g[*f*3;FFF*B*@3AFSSC*B*@3AFjC*B*@3AFjSC*B*@3AFSSC*k** ******k*jFF*B*@3AFjC*B*@3AFjSC*B*@3AFSSC*k** ******k*WFF*B*@3AFjSC*B*@3AFSSC*k** ******k*F*B*@3AFSSC*k** ******k*SFF*f** ******f3;WSjAGn*k*]3GASn*k*WWGA]W*k*F*k*SFF*f* ******f*W;jnSAoF*Y* * * * * * 3]* Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 04 - El valor temporal del dinero G=#?%#,)()'*-.%2-1.#,)#"%0#(%0%0#,)#-.()'>0#9#,)"#+" %Q&= # * M,(%-,'*01#/#:)&*/)'*%50)5#,"%'*?L'#5)'*(%')&&,//)()'*)"1%&#,&-%"1%*.)&)*(%1%&-#")&*/,'* 1#.,'*(%*#"1%&P'*#-./>5#1,'*%"*/,'*5,"1&)1,'*8#")"5#%&,';* * \'>*.,&*%N%-./,A*0"*?)"5,*/%*,8&%5%*.&%'1)&/%*3F;FFF*Y*'#*0'1%(*8#&-)*0"*.)=)&P*)*5#"5,* )H,'*.,&*0"*$)/,&*(%*3j;3FS*Y*X+0L/*%'*%/*1#.,*(%*#"1%&P'*)"0)/*-%(#,*70%*%'1L*5,?&)"(,* %/*?)"5,Z*V%"#%"(,*%"*50%"1)*70%*/)*.&#-%&)*5#8&)*-0%'1&)*%/*$)/,&*)510)/*D*/)*'%=0"()*%/* $)/,&*8#")/*(%"1&,*(%*5#"5,*)H,'A* * 3j;3FS*f*3F;FFF*B*@3*k*vCS* @3kvCS*f*3Aj3FS* * EB1&)D%"(,*/)*&)>:*70#"1)*D*&%'1L"(,/%*/)*0"#()(*,?1%"(&%-,'*%/*$)/,&*(%/*3FK;* * g%)-,'* ,1&,* %N%-./,A* 0"* ?)"5,* /%* ,8&%5%* .&%'1)&/%* RSF;FFF* Y* .)&)* 70%* .0%()* )(70#&#&* 0")*5)');*M)&)*%//,*0'1%(*(%?%&L*8#&-)&*0"*5&P(#1,*I#.,1%5)&#,*.,&*%/*70%*.)=)&L*0")*&%"9 1)*(%*Wn;WnF*YA*)/*8#")/*(%*5)()*)H,*(0&)"1%*$%#"1%*)H,';*X+0L/*%'*%/*1#.,*(%*#"1%&P'*)"0)/* 70%*%'1L*5)&=)"(,*%/*?)"5,Z* * * * !1#/#:)"(,* 0")* 5)/50/)(,&)* 8#")"5#%&)* ,* 0")* I,N)* (%* 5L/50/,* $%&%-,'* 70%* v* %'* #=0)/* )/* SASK*)"0)/;* * M,&* ,1&,* /)(,A* ()(,'* %/* $)/,&* )510)/* (%* 0"* .)=,* @g\CA* '0* $)/,&* 8010&,* @g[C* D* %/* 1#.,* (%* #"1%&P'* @vC* .,(%-,'* ,?1%"%&* %/* "Q-%&,* (%* .%&>,(,'* 70%* &%/)5#,")"* /)'* 1&%'* $)&#)?/%'* )"1%&#,&%';*\'>A*.,&*%N%-./,A*'#*%"*%/*.&#-%&,*(%*/,'*%N%-./,'*(%*%'1%*%.>=&)8%*(%'5,",9 5#P'%-,'*%/*$)/,&*(%/*1#%-.,A*1%"(&>)-,'*/)*'#=0#%"1%*%50)5#6"_* * 3j;3FS*f*3F;FFF*B*@3*k*FA3C"* * "0%$)-%"1%*)*1&)$P'*(%*0")*5)/50/)(,&)*8#")"5#%&)*,*0")*I,N)*(%*5L/50/,*,?1%"(&%-,'* 70%*"*%'*#=0)/*)*S*)H,';* Caso real: El manuscrito en el que Einstein escribió su famosa teoría que relacionaba la masa y la 2 energía (E=mc ) fue adquirido en 1987 por 1,2 millones de euros. Su propietario lo puso a la venta mediante una subasta pública en 1996 pidiendo un mínimo de 4 millones, la mejor oferta sólo llegó a 3,3 millones de euros. ¿Qué rentabilidad anual hubiera obtenido de haberlo vendido por los cuatro millones de euros? Y ¿cuál hubiera obtenido de vendérselo al mejor postor? 1er caso ! 1.200.000 x (1 + k)(1996-1987) = 4.000.000 ! k = 14,31% anual 2º caso ! 1.200.000 x (1 + k)(1996-1987) = 3.300.000 ! k = 11,90% anual 3o* Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 04 - El valor temporal del dinero 9. Cap ital ización semestral, trimestral, etc. * * `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f*3R3AWS*Y*)*/,'*70%*I)D*70%*)H)(#&*/,'*,1&,'*3WS*YA* 70%*5,&&%'.,"(%"*)/*'%=0"(,*'%-%'1&%;*E"*1,1)/A*0'1%(*&%5#?%*)*8#"*(%*)H,*WSjAWS*YA*/,* 70%*5,&&%'.,"(%*)*0"*%&'(")*"&+%*,-."*3*6%&1(*(%/* * WSjAWS*{*S;FFF*f*FAFS3WS*f*SA3WSK* * E'1)*(#'.)&#()(*%"1&%*%/*1#.,*",-#")/*D*%/*1#.,*%8%51#$,*,50&&%*.,&70%*0'1%(*=)")*0"*#"1%9 &P'*',?&%*%/*#"1%&P'*5,"*-)D,&*8&%50%"5#)*(%*/,*",&-)/;*M)&)*5)/50/)&*%/*$)/,&*8010&,*(%* S;FFF*YA*5).#1)/#:)()'*'%-%'1&)/-%"1%*(0&)"1%*0"*)H,*)/*1#.,*(%*#"1%&P'*",-#")/*(%/*SKA* )./#5)&%-,'*/)*'#=0#%"1%*%B.&%'#6"_** * * * d#* 70#'#P&)-,'* =%"%&)/#:)&* %/* 5L/50/,* .)&)* 50)/70#%&* 5).#1)/#:)5#6"* (0&)"1%* "* .%&>,(,'* )"0)/%'A*)./#5)&>)-,'*/)*'#=0#%"1%*%B.&%'#6"*@-*%'*%/*"Q-%&,*(%*.)&1%'*%"*/)'*70%*'%*(#$#9 (%*%/*)H,J*.)&)*/,'*'%-%'1&%'*-*f*WA*.)&)*/,'*1&#-%'1&%'*-*f*GA*.)&)*/,'*-%'%'*-*f*3WA* %15;C_* * * * \'>A*.,&*%N%-./,A*'#*0'1%(*(%.,'#1)*/)'*S;FFF*Y*%"*%/*?)"5,*)*0"*1#.,*(%/*SK*",-#")/*)"0)/* 5).#1)/#:)(,*1&#-%'1&)/-%"1%*@-*f*GC*(0&)"1%*5#"5,*)H,'A*%/*$)/,&*8010&,*'%&L_* * = Caso real: j;G3FA3n*Y* En una operación de compra de una empresa –omitiré su nombre por razones de privaci- dad- el comprador y el vendedor llegaron a un acuerdo por el que las acciones de éste último pasaban a poder de aquél a cambio de un precio global de 130 millones de euros. Ambas partes acuerdan que el pago se realice en varias fechas: - En el momento inicial: 70,3 millones de euros - 6 meses después: 9,5 millones de euros - 18 meses después: 20,4 millones de euros 3n* Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 04 - El valor temporal del dinero - 30 meses después: 29,8 millones de euros Como observará si suma las cuatro cantidades el valor total es de 130 millones de euros, lo que quiere decir que en el contrato no se tuvo en cuenta el valor temporal del dinero. Por tanto, queremos saber cuál es el dinero realmente pagado por el comprador sabiendo que el tipo de interés utilizado fue del 8% nominal anual que equivale a un 4% semestral. En el gráfico que figura a continuación se muestran las cantidades a pagar en millones de euros y en los semestres futuros previstos. Para calcular el valor actual deberemos hacer lo siguiente: = 122,06 millones de euros Lo que quiere decir que el comprador paga una cantidad actual equivalente a 122,06 millones de euros y en modo alguno los 130 millones que figuran en el contrato. M,&*,1&)*.)&1%A*/,*-#'-,*70%*'%*.0%(%*5)/50/)&*%/*$)/,&*8010&,*(%*0")*5)"1#()(*)510)/*5)9 .#1)/#:)()*(0&)"1%*"*)H,'A*.,(%-,'*&%)/#:)&*%/*5L/50/,*#"$%&',A*%'*(%5#&A*5)/50/)&*%/*$)/,&* )510)/*(%*0")*5)"1#()(*70%*'%*&%5#?#&L*%"*%/*8010&,*D*70%*'%&L*(%'5,"1)()*.,&*.%&>,(,'* #"8%&#,&%'*)/*)H,*D*50D)*%B.&%'#6"*=%"%&)/*'%&L*@-*%'*%/*"Q-%&,*(%*.)&1%'*%"*/)'*70%*'%* (#$#(%*%/*)H,J*.)&)*/,'*'%-%'1&%'*-*f*WA*.)&)*/,'*1&#-%'1&%'*-*f*GA*.)&)*/,'*-%'%'*-*f*3WA* %15;C_* 6=5#R%+-(%"-Q%2-1.#2&.(-.B%## \I,&)* $,/$%&%-,'* )* 5%"1&)-,'* %"* /)* (#8%&%"5#)* %"1&%* %/* %&'(" +(?&+2$* D* %/" %&'(" *3*6%&1(;* M)&)*%//,*")()*-%N,&*70%*0"*%N%-./,;*d0.,"=)-,'*70%*(%.,'#1)-,'*%"*0"*?)"5,*0"*%09 &,*)*0"*1#.,*",-#")/*)"0)/*(%/*SK*(0&)"1%*0"*)H,*D*70%*%/*?)"5,*",'*.)=)*/,'*#"1%&%'%'* 5).#1)/#:)(,'* )"0)/-%"1%A* '%-%'1&)/-%"1%A* 1&#-%'1&)/-%"1%A* -%"'0)/-%"1%* D* (#)&#)9 -%"1%;*g%)-,'*'0'*$)/,&%'*8010&,'*D*'0'*1#.,'*%8%51#$,';* * g[*f*3*B*@3*k*FAFSCf*3AFS** * * !*v*%8%51#$,*f*SK* W g[*f*3*B*@3*k*FAFSlWC f*3AFSFjWS** * !*v*%8%51#$,*f*SAFjWSK* G g[*f*3*B*@3*k*FAFSlGC f*3AFSFnGS** * !*v*%8%51#$,*f*SAFnGSK* 3W g[*f*3*B*@3*k*FAFSl3WC f*3AFS33jW** * !*v*%8%51#$,*f*SA33jWK* g[*f*3*B*@3*k*FAFSlRjSCRjSf*3AFS3Wj]** !*v*%8%51#$,*f*SA3Wj]K* * WF* Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 04 - El valor temporal del dinero 5,"*/,*70%*.,(%-,'*,?'%&$)&*70%*%/*1#.,*%8%51#$,*)"0)/*%'*'0.%&#,&*)/*1#.,*",-#")/*)"0)/* '#%-.&%*70%*/)*5).#1)/#:)5#6"*'%*I)=)*%"*.%&>,(,'*#"8%&#,&%'*)/*)H,;*\-?)'*1)')'*5,#"5#(#9 &>)"*'#*/)*5).#1)/#:)5#6"*'%*I#5#%&)*.,&*.%&>,(,'*)"0)/%';* * +,-,*0'1%(*I)*.,(#(,*).&%5#)&*%"*%/*5L/50/,*(%*/)*1)')*%8%51#$)*(%/*%N%-./,A*70%*I%-,'* )")/#:)(,*)"1%&#,&-%"1%A*.,(&>)-,'*I)?%&*'%=0#(,*&%(05#%"(,*%/*1)-)H,*(%*/)'*.)&1#5#,9 "%'*(%/*)H,*%"*1&,:,'*5)()*$%:*-L'*.%70%H,';*\'>*.,&*%N%-./,A*.,(&>)-,'*I)?%&*5)/50/)9 (,*/)*1)')*%8%51#$)*.)&)*0")*5).#1)/#:)5#6"*I,&)&#)*(0&)"1%*0"*)H,;* * g[*f*3*B*@3*k*FAFSlo]jFCo]jFf*3AFS3W]3** !*v*%8%51#$,*f*SA3W]3K* * D*.,(&>)-,'*'%=0#&*&%(05#%"(,*%/*.%&>,(,*(%*/)*5).#1)/#:)5#6"*5)()*$%:*-L'*I)'1)*&%)/#9 :)&/)*5)()*-#/P'#-)*(%*'%=0"(,A*.,&*%N%-./,;*E/*/>-#1%*(%*%'1)*&%(055#6"*'%*(%",-#")*62! '&%2$&A26&@+"6(+%&+42A*'#%"(,*/)*%50)5#6"*(%*'0*$)/,&*8010&,*/)*'#=0#%"1%_* * g[*f*g\*B*%v"* * (,"(%*)*%'*/)*?)'%*(%*/,'*/,=)&#1-,'*")10&)/%'*50D,*$)/,&*%'*WA]3oWo3oJ*v*#"(#5)*%/*1#.,* (%*#"1%&P'*",-#")/*)"0)/J*DA*"*%/*"Q-%&,*(%*.%&>,(,'*)"0)/%'*%"*/,'*70%*'%*&%)/#:)*/)*5).#9 1)/#:)5#6";*\'>*.0%'A*'#*"f3A*vfFAFS*D*g\f3*%0&,A*%"1,"5%'*g[*f*3AFS3W]33;*O%*)70>*,?1%"9 (&%-,'*/)*1)')*)"0)/*%8%51#$)A*v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d#*0"*.&P'1)9 -,*(%?%*'%&*(%$0%/1,*)*1&)$P'*(%*0")*'%&#%*(%*5)"1#()(%'*70%*'%*I)5%"*)/*8#")/*(%*5)()* .%&>,(,*@-%'%'A*1&#-%'1&%'A*%15;C;*'%*(#5%*70%*%'1)-,'*)"1%*/)*)-,&1#:)5#6"*8#")"5#%&)*(%* 0"*.&P'1)-,;* * `)D*$)&#,'*-P1,(,'*(%*)-,&1#:)&*8#")"5#%&)-%"1%*0"*.&P'1)-,*.%&,*)70>*'6/,*I)&%-,'* -%"5#6"*)*/,'*1&%'*-L'*5,",5#(,'_** * )C*%/*-P1,(,*8&)"5P'*,*(%*)"0)/#()(*5,"'1)"1%** ?C*%/*(%*/)'*50,1)'*(%*)-,&1#:)5#6"*5,"'1)"1%'* 5C*%/*-P1,(,*)-%&#5)",;* * * W3* Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 04 - El valor temporal del dinero 5;=5#!"#*>(&,&#A'%.2>0#&#,)#%.B%"-,%,#2&.0(%.()# d0.,"=)-,'*70%*0")*%-.&%')*.#(%*.&%'1)(,'*3FF;FFF*%0&,'*@%/*.&#"5#.)/*(%/*.&P'1)-,C* )*(%$,/$%&*%"*5#"5,*)H,'*D*)*5)-?#,*'%*5,-.&,-%1%*)_** * 3|;*M)=)&*)"0)/-%"1%*/,'*#"1%&%'%'*70%*5,&&%'.,"()"*)*/)*.)&1%*(%/*.&#"5#.)/*)Q"*",* (%$0%/1)** W|*O%$,/$%&*0")*.)&1%*(%/*.&#"5#.)/*5)()*)H,;** * \*/)*'0-)*(%*/,'*#"1%&%'%'*D*(%*/)*.)&1%*(%/*.&#"5#.)/*)-,&1#:)()*5)()*)H,*'%*/%*(%",-#")* 2+42$&)2);*M0%'*?#%"A*%/*?-%()("3,2+6-.*5,"'#'1%*%"*.)=)&*1,(,'*/,'*)H,'*0")*)"0)/#()(* #(P"1#5)*,*5,"'1)"1%;** * E/*.&%'1)-#'1)*5)&=)*0"*oK*(%*#"1%&P'*)"0)/*',?&%*/)*.)&1%*(%/*.&#"5#.)/*",*(%$0%/1);*4,* .&#-%&,*70%*(%?%-,'*I)5%&*%'*5)/50/)&*/)*2+42$&)2)*@.,&*'#-./#5#()(A*",*1%"(&%-,'*%"* 50%"1)*/)'*5,-#'#,"%'C;** * +,-,* /)* )"0)/#()(* %'* 5,"'1)"1%* ",'* %"5,"1&)&%-,'* 5,"* 70%* /)* 5)"1#()(* (%* 3FF;FFF* Y* '%&L*%/*$)/,&*)510)/*@g\C*(%*0")*&%"1)*(%*M*%0&,'*)"0)/%'*(0&)"1%*5#"5,*)H,'*)/*1#.,*(%* #"1%&P'*(%/*oK*@$%)*,1&)*$%:*%/*%.>=&)8%*S;3*'#*(%'%)*&%5,&()&*/)*%B.&%'#6"*-)1%-L1#5)*(%/* g\*(%*0")*&%"1)*.,'1.)=)?/%C_* * * * M*f*3FF;FFF*{*RAnnW]3*f*WS;FGSAjS*Y* * \'>*70%*5)()*)H,*(%?%&L*.)=)&*WS;FGSAj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oK*(%*/,'*3FF;FFF*%0&,'*(%/* .&#"5#.)/_* o;FFF* Y;* +,-,* /)* )"0)/#()(* 1#%"%* 70%* '%&* (%* WS;FGSAjS* Y* /)* (#8%&%"5#)* %"1&%* P'1)*Q/1#-)*D*/,'*#"1%&%'%'*",'*()*%/*$)/,&*(%*/)*.)&1%*)*)-,&1#:)&*(%/*.&#"5#.)/_*3];FGSAjS* Y*/,*70%*#-./#5)*70%*)/*5,-#%":,*(%/*)H,*W*%/*.&#"5#.)/*(%/*.&P'1)-,*%'*(%*oW;nSGARS*Y;* 4,'* #"1%&%'%'* (%/* )H,* W* ',"* %/* oK* (%* %'1)* Q/1#-)* 5#8&)_* j;jRSARS* Y* D* /)* )-,&1#:)5#6"* %'A* WW* Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 04 - El valor temporal del dinero "0%$)-%"1%A* /)* (#8%&%"5#)* %"1&%* /)* )"0)/#()(* D* /,'* #"1%&%'%'* (%/* )H,_* 3o;GFnAR* Y;* T* )'>* '%=0#&%-,'*I)'1)*%/*8#")/;* ** 5;=:=#!"#*>(&,&#,)#"%#2B&(%#,)#%*&'(-Q%2-1.#2&.0(%.()# E'1%*-P1,(,*5,"'#'1%*%"*'0.,"%&*70%*/)*50,1)*(%*)-,&1#:)5#6"*(%/*.&P'1)-,*%'*/)*-#'-)* .)&)*1,(,'*/,'*)H,'A*/,*70%*#-./#5)*70%*/)*)"0)/#()(*",*/,*'%&L;*d#*.,&*%N%-./,A*1,-)-,'* %/*5)',*)"1%&#,&*.%&,*/,*)-,&1#:)-,'*'%=Q"*%'1%*-P1,(,A*/,*.&#-%&,*'%&L*5)/50/)&*(#5I)* 50,1)*5,"'1)"1%_* * \-,&1#:)5#6"*f*3FF;FFF*{*S*f*WF;FFF*Y* * * E"*/)*1)?/)*G*'%*.0%(%*$%&*/)*)-,&1#:)5#6"*%*#"1%&%'%'*(%*%'1%*5)',;*4,'*#"1%&%'%'*'%*5)/509 /)"*-0/1#./#5)"(,*%/*.&#"5#.)/*)/*5,-#%":,*(%/*)H,*.,&*%/*1#.,*(%*#"1%&P'*@%/*o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o;FFF*YA*%"*5,"5%.1,*(%*#"1%&%'%'*(0&)"1%*5)()*)H,*D* %/*Q/1#-,*(>)*(%/*70#"1,*)H,*.)=)&LA*)(%-L'A*%/*.&#"5#.)/*@3FF;FFF*YC;* * E"*/)*8#=0&)*n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onografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 04 - El valor temporal del dinero [#=;*n*M)=,*(%*#"1%&%'%'*%"*5)()*.%&>,(,*'%=Q"*5)()*0",*(%*/,'*1&%'*-P1,(,'*(%*)-,&1#:)5#6"*8#")"5#%&)*)")/#:)(,'* * S-4"-&J'%AT% # * Usdd\EaVdA*M%1%&*D*}OEi\\aOA*U%&"1*@WFF3C_*>*6%4,*."(+"C(,'(,2%*"M&+2+6*;*~,&/(*d5#%"1#8#5;*d#"=).0&;* Ua<i`\2A*E0=%"%J*D*i\MEtdu<A*4,0#'*@3nooC_*M&+2+6&2$"N2+2=*?*+%A*t0%$)*T,&vA*VI%*O&D(%"*M&%''A*3noo;* [!44EaA*a0''%//_*D*[\aaE44A*p)-%'*@3no]C_*N()*,+"O+1*.%?*+%."2+)"P*64,&%<"Q+2$<&.&.A*t0%$)*T,&vA*25i&)m* `#//* 2\d+\aE\dA*p0)"*D*4Ep\aa<\i\A*i0'1)$,*@3nnWC_*Q+H$&.&.")*"R,(<*6%(.")*"O+1*,.&@+;*E0(%-);*2)(&#(* ds4s2stA*E:&):*D*Ma<ti4EA*p,I"*@3noGC_*O+%,()466&@+"2"$2"Q)?&+&.%,26&@+"M&+2+6&*,2/"2PB#5,A*O#)");* * !K)'2-2-&0 # * 3C*d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onografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 04 - El valor temporal del dinero (C*4,*-#'-,*70%*%"*%/*.0"1,*)"1%&#,&A*.%&,*%/*1#.,*(%*#"1%&P'*$)/%*%/*3SK;* * RC*E"50%"1&%*%/*$)/,&*8010&,*(%*/)'*&%"1)'*.,'1.)=)?/%'*'#=0#%"1%'*50D,*.&#-%&*.)=,*1#%"%* /0=)&*)/*8#")/*(%/*.&#-%&*)H,_* )C*WFF;FFF*Y*)"0)/%'*(0&)"1%*3F*)H,'*)/*3FK*(%*#"1%&P'* ?C*3FFFFF*Y*)"0)/%'*(0&)"1%*S*)H,'*)/*SK*(%*#"1%&P'* 5C*WFF;FFF*Y*)"0)/%'*(0&)"1%*S*)H,'*)/*FK*(%*#"1%&P'* (C*SFF;FFF*Y*)"0)/%'*(0&)"1%*#"8#"#1,'*)H,'*)/*3FK*(%*#"1%&P';* %C*a%.#1)*/,'*5L/50/,'*)"1%&#,&%'*.%&,*'0.,"#%"(,*70%*/,'*.)=,'*1#%"%"*/0=)&*)*.&#"9 5#.#,'*(%/*)H,*@&%"1)'*.&%.)=)?/%'C;* * GC*E"50%"1&%*%/*$)/,&*)510)/*(%*/)'*&%"1)'*.,'1.)=)?/%'*'#=0#%"1%'_* )C*WFF;FFF*Y*)"0)/%'*(0&)"1%*3F*)H,'*)/*3FK*(%*#"1%&P'* ?C*3FF;FFF*Y*)"0)/%'*(0&)"1%*S*)H,'*)/*SK*(%*#"1%&P'* 5C*WFF;FFF*Y*)"0)/%'*(0&)"1%*S*)H,'*)/*FK*(%*#"1%&P'* (C*SFF;FFF*Y*)"0)/%'*(0&)"1%*#"8#"#1,'*)H,'*)/*3FK*(%*#"1%&P';* %C* a%.#1)* /,'* 5L/50/,'* )"1%&#,&%'A* .%&,* '0.,"#%"(,* 70%* '%* 1&)1)* (%* &%"1)'* .&%.)9 =)?/%';* * SC*E"50%"1&%*%/*$)/,&*)510)/*D*%/*$)/,&*8010&,*(%*/)'*(,'*'%&#%'*'#=0#%"1%'*(%*8/0N,'*(%*1%',9 &%&>)*'#*%/*1#.,*(%*(%'50%"1,*80%'%*(%/*3FK*)"0)/*D*(%/*FK*)"0)/;* * LM&0# 5# :# <# C# D# d%&#%*\* 3F;FFF* GF;FFF* GF;FFF* GF;FFF* RF;FFF* d%&#%*U* RF;FFF* GF;FFF* GF;FFF* GF;FFF* 3F;FFF* * jC*X+0L/*%'*%/*$)/,&*)510)/*(%*/)*'#=0#%"1%*5,&&#%"1%*(%*8/0N,'*(%*/#70#(%:*(%'5,"1)()*)/*SK* (%*#"1%&P'*)"0)/Z* * * LM&0# 5# :# <# C# DU:;# [/0N,'* 3F;FFF* GF;FFF* RF;FFF* RF;FFF* RF;FFF* * ]C* Xx0P* 5)"1#()(* (%* (#"%&,* $)/%* -L'* I,D* (>)_* 0"* -#//6"* (%* %0&,'* I,DA* ,* (,'* -#//,"%'* (%"1&,*(%*o*)H,'*'#*%/*1#.,*(%*(%'50%"1,*%'*(%/*3FKZ* * oC*4)*%-.&%')*2sas*d\*10$,*%/*)H,*WFFS*0",'*#"=&%','*.,&*$%"1)'*(%*jFF*-#//,"%'*(%* %0&,';*d#*I)5%*5#"5,*)H,'A*%"*WFFFA*/)'*$%"1)'*80%&,"*(%*RFF*-#//,"%';* )C*<"(#70%*)*70P*1)')*)"0)/*I)"*%'1)(,*5&%5#%"(,*/)'*$%"1)';* ?C*<-)=>"%'%*70%*0"*)-#=,*'0D,*&%'.,"(%*(%*/)*'#=0#%"1%*-)"%&)*)*/)*.&%=0"1)*)"9 1%&#,&_*Äd#*/)'*$%"1)'*'%*I)"*(,?/)(,*%"*5#"5,*)H,'A*#-./#5)*70%*I)"*5&%5#(,*0"* 3FFKJ*)'>*70%*'#*(#$#(#-,'*3FF*%"1&%*S*,?1%"(&%-,'*0"*5&%5#-#%"1,*)"0)/*(%/* WFKÅ;*+,-%"1%*%'1)*)8#&-)5#6";* * nC*X+0L/*80%*%/*1#.,*(%*(%'50%"1,*01#/#:)(,*%"*/,'*'#=0#%"1%'*5)','Z_* WS* Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 04 - El valor temporal del dinero )C*!'1%(*.#(#6*.&%'1)(,'*SFF;FFF*Y*D*'%*5,-.&,-%1#6*)*(%$,/$%&*SRF;FFF*Y*0"*)H,* (%'.0P';* ?C* !'1%(* .#(#6* .&%'1)(,'* GFF;FFF* Y* D* '%* 5,-.&,-%1#6* )* (%$,/$%&* jS3;SjF* Y* (#%:* )H,'*(%'.0P';* 5C*!'1%(*.#(#6*.&%'1)(,'*GFF;FFF*Y*D*'%*5,-.&,-%1#6*)*&%)/#:)&*.)=,'*)"0)/%'*#=0)9 /%'*(%*33F;FFF*Y*(0&)"1%*5#"5,*)H,';* * 3FC*!"*?)"5,*/%*5,"5%(%*0"*.&P'1)-,*I#.,1%5)&#,*)*0")*%-.&%')*(%*(#%:*-#//,"%'*(%*%09 &,'A*70%*#-./#5)*.)=)&*3AFnS;G]W*Y*)"0)/%'*(0&)"1%*WF*)H,';*X+0L/*%'*%/*1#.,*(%*#"1%&P'* 5,-.0%'1,*70%*/%*%'1L"*5)&=)"(,*)*/)*%-.&%')Z* * 33C*40#'*'%*(#'.,"%*)*#&*)*/)*!"#$%&'#()(*(%"1&,*(%*0"*)H,;*M)&)*'08&)=)&*'0'*=)'1,'*"%9 5%'#1)&L*3F;FFF*Y*)"0)/%'*(0&)"1%*5)()*0",*(%*/,'*5#"5,*)H,'*70%*%'.%&)*%'1)&*%"*%//);*d0* 1>,*a#=,?%&1,A*1,(,*0"*-)=")1%*8#")"5#%&,A*/%*,8&%5%*()&/%*/)*5)"1#()(*(%*(#"%&,*"%5%')&#)* .)&)*70%*40#'*.0%()*.)=)&'%*'0'*%'10(#,';*O#5I)*5)"1#()(*%'*(%.,'#1)()*I,D*%"*0"*?)"5,* )*0"*1#.,*(%*#"1%&P'*)"0)/*(%/*oK;* )C*X+0L/*%'*%/*-,"1)"1%*(%*%')*5)"1#()(*(%*(#"%&,Z* ?C*+)/50/%*50L/*'%&L*%/*')/(,*%"*%/*?)"5,*(%*/)*'0-)*(%.,'#1)()*.,&*%/*1>,*(%*40#'*)/* 8#")/*(%*5)()*)H,;* * 3WC* d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d#*0'1%(*(%.,'#1)*3SF;FFF*Y*)"0)/-%"1%*%"*0")*50%"1)*70%*/%*.&,.,&5#,")*%/*3FK*(%* #"1%&P'*)"0)/A*X50L"1,*1#%-.,*"%5%'#1)&L*0'1%(*.)&)*)50-0/)&*0"*-#//6"*(%*%0&,'Z* * 3SC*d#*0'1%(*1#%"%*I,D*(>)*WF;FFF*Y*D*/)'*#"$#%&1%*%"*/)'*'#=0#%"1%'*5,"(#5#,"%'*X50L/*'%&L* '0*$)/,&*8010&,*(%"1&,*(%*5#"5,*)H,'Z* )C*\*0"*1#.,*(%*#"1%&P'*)"0)/*5,-.0%'1,*(%/*3WK;* ?C*\*0"*1#.,*(%*#"1%&P'*)"0)/*5,-.0%'1,*(%/*3WK*5).#1)/#:)(,*'%-%'1&)/-%"1%;* 5C*\*0"*1#.,*(%*#"1%&P'*)"0)/*5,-.0%'1,*(%/*3WK*5).#1)/#:)(,*1&#-%'1&)/-%"1%;** (C*\*0"*1#.,*(%*#"1%&P'*)"0)/*5,-.0%'1,*(%/*3WK*5).#1)/#:)(,*-%"'0)/-%"1%;* * 3jC*d#*0'1%(*%'.%&)*1%"%&*0"*-#//6"*(%*%0&,'*(%"1&,*(%*5#"5,*)H,'*5)/50/%*'0*$)/,&*)510)/* %"*/)'*'#=0#%"1%'*5,"(#5#,"%'A*'0.,"#%"(,*70%*%/*1#.,*(%*(%'50%"1,*%'*(%/*3FK_* )C*+)/50/)(,*)/*#"1%&P'*5,-.0%'1,*)"0)/-%"1%;* ?C*+)/50/)(,*)/*#"1%&P'*5,-.0%'1,*'%-%'1&)/-%"1%;* 5C*+)/50/)(,*)/*#"1%&P'*5,-.0%'1,*1&#-%'1&)/-%"1%;* (C*+)/50/)(,*)/*#"1%&P'*5,-.0%'1,*-%"'0)/-%"1%;* * 3]C*+)/50/%_* Wj* Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 04 - El valor temporal del dinero )C*E/*$)/,&*8010&,*(%*WF;FFF*Y*#"$%&1#(,'*5)()*'%#'*-%'%'*)*/,*/)&=,*(%*5#"5,*)H,'*)* 0"*1#.,*",-#")/*(%/*3WK*)"0)/;* ?C*E/*$)/,&*)510)/*(%*WF;FFF*Y*#"$%&1#(,'*5)()*1&%'*-%'%'*(0&)"1%*5#"5,*)H,'*)*0"*1#9 .,*(%*#"1%&P'*",-#")/*(%/*3WK*)"0)/;* * 3oC*4)*+)N)*(%*\I,",'*(%*V&#N0%70%*.)=)*%/*nK*(%*#"1%&P'*)"0)/A*-#%"1&)'*70%*/)*+)N)*(%* E/*V,?,',*.)=)*%/*oK*(%*#"1%&P'*)"0)/*5).#1)/#:)(,*1&#-%'1&)/-%"1%;*XE"*70P*+)N)*.&%8%&#9 &>)*0'1%(*(%.,'#1)&*'0*(#"%&,Z* * 3nC*!")*%-.&%')*"%5%'#1)*8#")"5#)&*0"*.&,D%51,*(%*#"$%&'#6";*V&%'*?)"5,'*/%*I)5%"*/)'*'#9 =0#%"1%'*,8%&1)';*E/*.&#-%&,*/%*.#(%*0"*GASK*(%*#"1%&P'*",-#")/*)"0)/*.)=)(%&,*'%-%'9 1&)/-%"1%;*E/*'%=0"(,*/%*.#(%*0"*GARK*",-#")/*)"0)/*.)=)(%&,*-%"'0)/-%"1%;*E/*1%&5%&,* /%*.#(%*0"*GAWSK*",-#")/*)"0)/*.)=)(%&,*)"0)/-%"1%;*X+0L/*%'*/)*-%N,&*,8%&1)Z* * W]* Monografías de Juan Mascareñas sobre Finanzas Corporativas ISSN: 1988-1878 04 - El valor temporal del dinero Apéndice: Diccionario Español-Inglés Español Inglés Español Inglés Amortización de préstamos Loan rescue Oferta Offer Anualidad Annuity Perpetuidad Perpetuity Coste de oportunidad Opportunity cost Préstamo Loan Demanda Demand Renta Rent Inflación Inflation Rentas perpetuas Perpetual rents Interés compuesto Compound interest Riesgo Risk Interés continuo Continuous interest Tasa de inflación Inflation rate Interés simple Simple interest Tasa de interés Interest rate Letra del Tesoro Treasury Bill Valor futuro Future value Valor actual Present value Wo*